diff --git "a/count_the_number_of_good_subarrays/haskell_tests/Main.hs" "b/count_the_number_of_good_subarrays/haskell_tests/Main.hs"
new file mode 100644--- /dev/null
+++ "b/count_the_number_of_good_subarrays/haskell_tests/Main.hs"
@@ -0,0 +1,45 @@
+
+module Main where
+import Test.HUnit
+
+--Program start
+
+--Program end
+
+-- Test cases
+
+test1 :: Test
+test1 = TestCase (assertEqual "for (countGood [1,1,1,1,1] 10)," 1 (countGood [1,1,1,1,1] 10))
+
+test2 :: Test
+test2 = TestCase (assertEqual "for (countGood [3,1,4,3,2,2,4] 2)," 4 (countGood [3,1,4,3,2,2,4] 2))
+
+test3 :: Test
+test3 = TestCase (assertEqual "for (countGood [713266785, 593714318, 726677122, 228510719, 974275658, 502563836, 608899572, 868339812, 325376701, 924905384, 564553715, 670146791, 316817432, 901886228, 803884455, 742594874, 557194907, 115802587, 720555749, 991762853, 100576487, 835029766, 536266444, 756934742, 457139896, 602722133, 846647262, 947653735, 898187040, 83709337, 634095880, 704971896, 783564368, 995621950, 999473990, 774850340, 717274609, 708708282, 697048895, 901825359, 398459560, 921753372, 169968346, 350592080, 569017390, 85458705, 194179555, 341114764, 139495728, 850334426, 195920607, 664381495, 811566683, 223337520, 587938407, 550635139, 263173158, 297712743, 147399614, 12466771, 133096904, 820083965, 870511951, 615596964, 125366068, 299174943, 549491790, 445914921, 499849664, 886915818, 48553493, 628915904, 685050871, 58650287, 928505239, 473898681, 488293265, 275319368, 886371932, 119413776, 97404427, 828654064, 120560826, 84139043, 451888618, 438907772, 126163600, 889984396, 101698596, 773529319, 36150549, 675637390, 804619723, 291507530, 241487751, 502866904, 809710027, 665848339, 673414535, 153261462, 903671788, 948725136, 4363148, 871540828, 205496145, 830041161, 511344306, 954121074, 105510773, 847900135, 162463543, 698123469, 416891378, 64374342, 546521179, 899188484, 91289106, 131842201, 641957025, 383369872, 741013976, 783861959, 833814601, 236176019, 77197884, 539078342, 524167032, 888706284, 356882385, 640841656, 728102, 149999282, 385292076, 331387133, 886695345, 802775970, 952187247, 512649759, 338954605, 779892957, 344913751, 936249574, 150489108, 189172817, 664999985, 643360409, 342623380, 581920318, 938712592, 896933502, 238497513, 606086180, 484278894, 380584769, 545781304, 148059501, 107836544, 304441409, 994027816, 739286882, 421129552, 315727634, 996894460, 157456665, 714169989, 975479181, 377555496, 723639266, 108766162, 643270537, 9575038, 177116950, 201247945, 719181089, 63781280, 534349716, 727393545, 707558551, 366748167, 928145847, 914560046, 492278036, 805695772, 621324334, 536060485, 303157486, 86470183, 995340789, 866086192, 494746256, 590490737, 203697200, 525248405, 721963445, 635057875, 70148240, 148337993, 584533399, 110076339, 388595759, 313774083, 583092334, 10575004, 563025856, 152210359, 91852544, 361175706, 313635727, 165351998, 735438422, 944989630, 832076562, 630229408, 372076632, 409781304, 745259888, 245940315, 884643948, 627897480, 916644392, 528475600, 335073711, 203672260, 692640174, 629443517, 237640508, 364379702, 275481262, 693741863, 863547125, 859065733, 646442643, 868741958, 786780270, 367695452, 349133598, 81188283, 997221899, 498441857, 185166627, 59439711, 153708693, 165419414, 268349802, 750517042, 733131574, 411846587, 387825088, 757955261, 791795156, 166918257, 229623338, 156009663, 155368827, 867943360, 922907828, 720432325, 128106528, 403007049, 168351514, 442703620, 427476088, 306051055, 773313269, 497568905, 641584067, 712407098, 389021256, 553889860, 64459595, 791018689, 34941194, 855146247, 564550599, 77472476, 500011512, 124727205, 904380418, 538750457, 111671976, 571979630, 367328742, 162887313, 768953948, 196039337, 850816625, 517003452, 495462649, 24306999, 402608414, 983771097, 150660948, 503261188, 816966077, 561888765, 666646615, 502701677, 951943945, 607956420, 271831315, 265091097, 272924653, 80783996, 872280109, 770871754, 866973918, 377829651, 893713043, 482966851, 909669620, 745592912, 554125636, 457391829, 822312080, 492418260, 438501766, 872411930, 11858491, 627980414, 777444877, 421972055, 367875725, 333653109, 882407242, 889473067, 447717835, 322284883, 924368126, 223096426, 598466688, 922025224, 91193075, 771999039, 364061988, 613955181, 944237730, 865645549, 450823835, 410081763, 58259492, 69771112, 275252025, 545052800, 221660139, 453569014, 521168057, 782581906, 774561167, 748751830, 92919730, 181886331, 682838164, 757793702, 62718807, 964961688, 177874602, 874414975, 594832806, 760633244, 748878397, 354312558, 11193964, 322211248, 464413664, 580359512, 726120467, 702860096, 458962526, 43360713, 677191094, 478061939, 110454317, 663248960, 835709966, 388021537, 982472254, 718810515, 749498389, 685104848, 204253444, 398974623, 303513512, 91736960, 442994536, 285730555, 552703821, 83058159, 805559621, 90961548, 923820345, 896213060, 657049177, 880655449, 235519901, 202840411, 30133112, 615849148, 981252887, 763447991, 879070033, 242099610, 487150073, 135078268, 312663415, 379890079, 508578852, 869040143, 695579907, 152958886, 913548191, 482240146, 477458323, 946999142, 966176905, 704478467, 849317879, 468753843, 542461157, 847255702, 778448513, 483281546, 739836822, 327672208, 469311662, 263679941, 468228149, 928219691, 565074368, 511839711, 221696401, 802509194, 445500465, 54167810, 496709013, 540756789, 76676415, 697688313, 258117078, 923161390, 241014272, 594233972, 173953923, 999501802, 983362590, 578822035, 855453835, 403498130, 595515540, 247425949, 296841910, 59883598, 908509414, 927215046, 346781462, 791939272, 326236489, 179674178, 659644443, 530806839, 227269386, 739678393, 460379390, 710475676, 168663128, 596134724, 643405875, 852380220, 168485213, 544207625, 132699914, 613257448, 909382704, 144797760, 478439517, 606654074, 756860589, 851522770, 692348002, 149343144, 127108777, 758926067, 194730154, 207385620, 835473346, 930258497, 186427663, 147464973, 359032725, 332755962, 177152621, 202929852, 101504807, 464963617, 46175766, 701624682, 342137102, 856822657, 706876299, 515681065, 48125867, 392957187, 102164730, 745623895, 481991656, 763734044, 859132387, 389339150, 554626219, 763959001, 743050237, 83878569, 455525132, 814835987, 409506276, 341812906, 276257659, 371943833, 406019352, 565085376, 633051080, 979808309, 567765446, 467895602, 279735227, 702964441, 267121007, 569799086, 267292287, 211272491, 801560914, 310129370, 849585578, 608910568, 31127656, 829454740, 421343689, 331677601, 419027808, 18040912, 269078803, 356006188, 896629331, 604068823, 464824598, 451404857, 989866630, 517707141, 76281290, 58335477, 514396531, 598839555, 396513619, 920909117, 896065636, 591424643, 867291085, 144088876, 622325614, 956838228, 707453512, 687223101, 598118081, 135378221, 43186938, 644183555, 245398363, 197012551, 258339046, 267377075, 88699058, 446165501, 589829630, 661251206, 265421232, 200293861, 625900832, 867163708, 961742794, 242560554, 606358952, 655046067, 265643852, 453544361, 155900102, 720909441, 960907764, 698346722, 136515345, 567769103, 485058002, 174361076, 354453869, 31362312, 745772588, 344688676, 911422899, 768341254, 556577039, 961670809, 373188433, 843233302, 851395355, 337839379, 177083752, 958307166, 375724672, 562134949, 577680178, 8708222, 132861167, 310465958, 514418647, 224967380, 455101849, 468698463, 580868900, 803023653, 270561897, 421751526, 912367997, 267087465, 382702293, 640957677, 657318030, 668112033, 338353781, 959270063, 937600801, 369608349, 176217915, 995266556, 683476402, 923233123, 357944670, 364495500, 608221045, 925911647, 545437886, 832957192, 752245668, 342433682, 248062488, 659903390, 484483094, 654093090, 449049771, 655281777, 818430602, 486823738, 561558207, 707713057, 822621055, 634682132, 969276275, 352030708, 760466462, 490666169, 907667522, 551847006, 346358732, 382462248, 553658088, 919348126, 522837587, 443538292, 115453231, 630182081, 627963661, 581392063, 545369927, 391001502, 652335206, 144425994, 946436936, 539314361, 562923939, 865162509, 67508974, 281712606, 980158716, 594163498, 292870681, 606403876, 288494918, 273053215, 122338929, 415563921, 700398451, 430737461, 996363367, 382229876, 413154432, 633487131, 11330742, 431681116, 496468527, 130905070, 26040603, 451603351, 560257086, 502948333, 757983925, 743142770, 551828836, 599072993, 545773265, 210385193, 571939080, 271880734, 557036563, 756850647, 265487132, 875431786, 857867324, 241536747, 840281808, 991516615, 259707799, 887881197, 646126689, 568089836, 238682962, 825228230, 657339893, 879158468, 252934971, 123363279, 879299327, 937601143, 826615097, 871977762, 176719796, 834432353, 894268616, 886206734, 613811053, 476227420, 34062728, 783361446, 914296155, 190250348, 750992370, 990153442, 106708057, 33115484, 811890729, 608837396, 119713330, 841682146, 540080452, 682820926, 756809462, 254940310, 29865682, 60716980, 519400575, 84314475, 212511985, 739803857, 743417434, 140738609, 772343117, 718924385, 204182482, 311253638, 123698045, 902088498, 37009336, 663227730, 588550675, 262937624, 84151269, 71364842, 272318693, 491547975, 712649954, 248362457, 680086757, 592308619, 302887122, 241417406, 312730632, 301053728, 944039262, 688513116, 322417694, 505343990, 389425708, 691611356, 739779349, 991434408, 208177262, 125463144, 246693104, 249379456, 562194163, 600923961, 555481255, 210410986, 333451230, 579007337, 721826176, 368586175, 719296413, 956695151, 890600264, 659003480, 179543613, 798788684, 970031620, 226335524, 206330802, 584805315, 907977527, 859149175, 498755838, 2586564, 312348722, 309350048, 216917566, 298898150, 547285644, 108651878, 480237611, 290843100, 794797415, 996167608, 429147065, 913323839, 779516622, 550584566, 30796004, 800748575, 908569185, 709531074, 601696687, 122752418, 845629244, 610969025, 53432233, 1541560, 317828461, 874972617, 177207784, 706624484, 152884218, 648142922, 510420698, 859736499, 371178873, 343680253, 624014122, 268907327, 456345065, 700198017, 292949532, 404856482, 7105026, 18063795, 589006601, 953250351, 369630258, 861059144, 759827492, 261345319, 815737704, 777743627, 603797241, 297896816, 992276583, 58141788, 546511735, 584392743, 150480560, 193530907, 941762796, 516998770, 426888033, 867948245, 879186229, 874736817, 564523469, 826793696, 230040046, 940563199, 722153770, 476785512, 470561578, 445233795, 328918864, 114647747, 563189826, 831682360, 164522368, 1508063, 758415321, 328940355, 647426677, 310428746, 503737666, 333312579, 758885162, 636742183, 107261840, 430750844, 642136309, 478566984, 299270373, 506613058, 388927827, 428115891, 563580389, 101718183, 905315926, 62448438, 733182987, 143926318, 735314022, 952470916, 589053730, 252938446, 816731708, 476723656, 65454794, 950937003, 896226282, 604454372, 353459919, 42410741, 463460537, 649669772, 2471673, 434626282, 86614073, 788970309, 283341418, 715587319, 990755909, 586612860, 304129932, 689855760, 804506860, 495499821, 750570295, 348388705, 585770494, 330316523, 525267050, 815062917, 319201403, 268456191, 684906936, 212261073, 393297492, 394964041, 459234822, 739650710, 235392730, 240908437, 421242705, 239588263, 243628491, 119725167, 907340600, 178001537, 794109162, 571077481, 53317984, 925836334, 932060812, 594506150, 903465859, 654049324, 220938413, 832940127, 566182774, 512068621, 927354308, 724912605, 592394167, 970965177, 17302437, 560316806, 684934365, 311394186, 580125950, 504555408, 558435575, 821902692, 326603537, 233957482, 321799999, 570512588, 77926545, 476124291, 663198050, 220846740, 602048933, 770605071, 447139168, 568768444, 12966997, 320921416, 469045102, 20882682, 706159577, 127243208, 520562888, 761072776, 89352386, 866470800, 828538010, 991626537, 950438705, 784366891, 859860896, 547563758, 620523262, 258736485, 513812277, 128213210, 462205107, 199507622, 273981397, 420553520, 712750197, 91207478, 832835290, 56106206, 739763860, 875904911, 5303466, 184395595, 247949642, 609184946, 413495897, 963006396, 262238086, 317362859, 527235905, 77788367, 552482787, 402604540, 877903598, 297558439, 98853020, 841764842, 950770093, 673173992, 309711228, 915316807, 47760048, 947504433, 568786882, 482997035, 771611148, 425650018, 454333485, 812614768, 860181493, 12586825, 494997147, 851747271, 629892350, 435932152, 869600714, 862919520, 182723600, 113090857, 105467485, 535201965, 280284826, 247178941, 34208389, 119673596, 379770283, 365412038, 136876344, 235735207, 92912718, 863710298, 833465180, 8830193, 866089153, 985738147, 535269139, 715245162, 372464775, 255301742, 251902268, 839412673, 601130321, 690419744, 149038907, 831961047, 976797511, 131119434, 100596448, 719226608, 623235036, 178635369, 464199972, 457759503, 136909799, 868521677, 894433125, 766003852, 971372088, 815132647, 337466218, 789627970, 629380133, 267772099, 576526979, 403492882, 750928651, 790976688, 926772080, 187853592, 162745906, 758380515, 224935026, 471231886, 773492693, 591054590, 336506734, 848877039, 415784901, 363458381, 992742551, 562170869, 191720235, 977223777, 688649417, 862357327, 831933978, 414060503, 717486156, 286978698, 546469813, 975232152, 703334032, 644379266, 466263159, 104486553, 829780491, 527566885, 810408257, 756544832, 417843583, 686660512, 230607939, 919515237, 461836809, 123966110, 398920290, 28869641, 422336012, 767010422, 613471806, 490391172, 677840516, 848288409, 151334875, 856441703, 113459777, 996259457, 950515743, 629418149, 295647108, 797663755, 805070696, 452590027, 266773215, 785977793, 300382033, 539879266, 842676789, 120010380, 259911954, 32884422, 573921554, 758710660, 144659938, 653901663, 99901993, 927134724, 851077267, 377485888, 856337009, 665098357, 997405325, 761349459, 710709028, 38040598, 849944398, 532807776, 529524520, 512653335, 213113957, 770917651, 548744441, 980388701, 816319179, 844825090, 148398959, 962148536, 885139400, 342836770, 912989722, 809692364, 89928939, 629045892, 392802955, 379577643, 70294423, 712905665, 755615544, 434193571, 219009080, 124342459, 191448064, 662722024, 824500130, 255385397, 981437412, 882664331, 212174910, 687462067, 591639644, 594902628, 474434949, 163442041, 272446288, 400294600, 274343366, 944304848, 920388609, 838750905, 405916638, 159326289, 163313594, 39531972, 645277940, 496497682, 935990903, 949802230, 102149714, 3614848, 828529720, 115720151, 380239706, 249042653, 252775633, 159589669, 640013748, 465259810, 778164564, 80615675, 999051801, 939406027, 706144333, 995365134, 35756915, 701258731, 23146939, 447906963, 340524756, 624839199, 73037806, 193624520, 731605441, 921328313, 171863731, 814584911, 423126066, 490449903, 500550885, 50472874, 407335367, 201913004, 539501520, 278544837, 893565036, 471754690, 878525275, 30110254, 932723656, 470274561, 443807565, 983849906, 401740288, 339754854, 171439227, 496012591, 173821207, 625715598, 152144968, 372290203, 961081011, 281866224, 35286330, 175282430, 474322518, 838720090, 409918423, 993754462, 697270413, 870316169, 628317716, 301694197, 230247527, 37746288, 798745172, 868544488, 720855513, 734346132, 587710893, 32287141, 841733545, 551542636, 535038029, 221050122, 361550612, 856182256, 713554312, 996967140, 157261144, 963726184, 999917298, 761786271, 463901219, 244290164, 942650509, 357016146, 750259259, 618970140, 604837119, 724362675, 185972094, 403856075, 731194541, 244711781, 416131316, 275901472, 514930480, 961900115, 477427271, 961047406, 485914898, 321775045, 999374390, 66173749, 923429586, 438981207, 647897868, 783235803, 726522107, 266534118, 98018768, 51383377, 383426097, 809688210, 252741129, 378244351, 911105087, 997196886, 889367974, 214138799, 116368207, 374527306, 938838912, 906345014, 46475156, 775142153, 107557222, 352546894, 652633992, 324211311, 187398639, 404125188, 794325463, 539198396, 804277281, 99294435, 987843346, 612385075, 8809598, 481514181, 717037107, 693009661, 885849672, 580986386, 516505106, 628184219, 76415425, 534830226, 110668728, 534208352, 985560993, 400070378, 440624242, 514426241, 371955046, 26556461, 140057271, 141051651, 314917772, 140298923, 541008498, 876653978, 243536401, 166167792, 801441351, 799021024, 414450016, 834430248, 979056141, 545579812, 683917404, 776342862, 332514514, 463511737, 755365279, 935381358, 26073603, 512165351, 706595497, 426728679, 58159300, 222739523, 129048388, 142935975, 96042187, 801071540, 602379855, 718365574, 817667915, 94811070, 452812412, 515111323, 869217500, 143886969, 584092430, 186561460, 915132256, 435008861, 107790108, 208019248, 581622053, 973900851, 466851102, 833959711, 578133486, 303756470, 701635914, 509267281, 86773300, 193875583, 779634989, 63267598, 860348701, 167055137, 71984373, 476711616, 250190289, 955422100, 377385565, 557040291, 903821277, 226627934, 821471906, 505898035, 453243090, 964886664, 763021226, 587125631, 814276161, 285683704, 833734058, 8772491, 182631126, 177345940, 444151346, 691256395, 110278036, 657246467, 497310358, 492263600, 331138107, 546364932, 250962148, 364053538, 410464451, 94992232, 32338290, 389388079, 88221040, 50666542, 821070571, 333512967, 679659176, 523472536, 941572042, 383398216, 780372565, 618572985, 522925079, 242594958, 847807484, 188955075, 617420982, 884766139, 131358494, 251235289, 47966118, 137711154, 861076599, 843345714, 944825547, 200372083, 663296620, 53739298, 493232808, 724365750, 184218851, 797115333, 141769666, 25337296, 529513010, 256187103, 392212241, 369185939, 255352364, 27485794, 38393464, 197655610, 799930963, 744404175, 654960257, 45774569, 212835820, 369539777, 126551413, 499994048, 167747549, 596078634, 25794653, 975690092, 926536833, 807598954, 725635796, 399480827, 625750882, 144557807, 726613024, 678414701, 807815208, 535729001, 578562931, 31045440, 26707196, 843108272, 756057577, 970927884, 797873641, 628344463, 617218583, 578194813, 625587535, 290666539, 568711648, 938889991, 532566432, 49561399, 526523826, 404803675, 584372217, 428725000, 138298205, 866777471, 406766386, 463639599, 499628419, 536075682, 789382091, 571958378, 542342347, 987188775, 717034623, 413423411, 883681565, 463205939, 876457931, 160214846, 754319447, 883239658, 24593904, 322812843, 115373493, 879745007, 764915527, 509505511, 86082962, 284801449, 829315659, 467080692, 224632842, 283816172, 76594296, 163651286, 556024277, 965492361, 837682388, 803933055, 125666272, 972748936, 666667931, 586722241, 479259847, 192547142, 497088834, 707189831, 879489604, 175273504, 370549303, 706029343, 743214105, 344354434, 335804733, 452762773, 994456421, 521407687, 566711774, 925161191, 137562292, 175391340, 918040918, 143285845, 944515729, 261067759, 281182772, 738454311, 83494997, 530634457, 196811375, 265527186, 654640106, 704445804, 316962777, 843592687, 370285529, 779024373, 494582877, 96065596, 585656288, 161834090, 806564955, 216880096, 852181244, 673033448, 899793178, 595313864, 791375306, 217081223, 152798079, 526091859, 311840779, 465110964, 507034436, 486421009, 237051030, 48457641, 787516002, 685939892, 334962885, 565669041, 713801935, 779991357, 775110444, 481569269, 16466650, 697335118, 617917929, 352262757, 987321761, 578563678, 402356097, 955715796, 347661988, 934724985, 151554657, 320567662, 462029822, 210248947, 272402077, 856581003, 907084660, 675788428, 107584443, 463998899, 577771253, 486065752, 679748883, 110243887, 568386161, 569074211, 877376016, 515931774, 240193902, 571928647, 508177335, 201314041, 436517448, 372888666, 858965621, 401246507, 1362878, 534059203, 472698585, 746904344, 586325538, 685188876, 669421313, 139403635, 700311801, 755264715, 730203600, 812754282, 547097733, 537863514, 450587768, 673492065, 894426693, 466165023, 621337659, 428976178, 150012898, 201636689, 856745401, 744676608, 737850914, 328828250, 793789922, 492592263, 229040835, 181671781, 367441251, 120933301, 173781313, 994714799, 853741653, 547125863, 319184618, 435450553, 396228050, 61675533, 301163186, 82099357, 458901431, 763295801, 441953888, 354781562, 900476233, 849604496, 764807247, 759115938, 827148186, 137941776, 999016146, 717381242, 527917445, 705940467, 306439117, 565328791, 539947565, 482676790, 798315895, 244055016, 434736738, 820314688, 898955771, 736017764, 309464568, 739670851, 3661856, 992150555, 434523774, 625733822, 311459611, 895812435, 866313544, 610840323, 115030746, 423462182, 128820483, 272230659, 337538097, 646628277, 734006069, 63831542, 19921017, 986902920, 488847633, 886250231, 545228951, 578779077, 185680150, 210451671, 392748110, 339772987, 124117134, 443093959, 470263939, 701176042, 332450997, 802251279, 629074872, 146665259, 748622543, 831318742, 452205686, 198852829, 918793396, 866651102, 186977867, 538692169, 810679120, 926383410, 239044014, 13402741, 671550517, 105051620, 301789381, 249205436, 136880707, 637608840, 329014138, 71300735, 607071525, 544930419, 936461671, 234597568, 388828175, 49329641, 793197472, 988384229, 81449652, 455679035, 37964247, 478541372, 384694909, 491149997, 765723651, 370964516, 892204641, 397422517, 676275718, 205257169, 69634637, 791543529, 877020405, 103812865, 681628648, 341443113, 60631194, 892620582, 54741432, 852541525, 157361085, 689605485, 114553583, 184443942, 301865832, 481485139, 308574297, 82763919, 443777254, 684566655, 840054860, 67311554, 258000555, 120170886, 574960493, 535741559, 483398025, 451980690, 820451583, 358690258, 607881289, 351855719, 802130601, 41663216, 54974739, 372798962, 155725171, 641649755, 384308850, 215473318, 448533909, 494017417, 544260012, 368274346, 318830451, 771301993, 406439138, 724966476, 908656787, 588664279, 454258357, 809082659, 616960610, 956933015, 158508772, 23706577, 778431409, 687820744, 502743231, 436368147, 492564339, 135414257, 485805516, 587301547, 335559082, 674732719, 372035851, 427844917, 83587401, 356805031, 296735118, 115404286, 210762301, 947531529, 101221568, 138795327, 645566378, 447534087, 41812037, 89448612, 224091034, 198676811, 374457885, 948658932, 763180497, 353412436, 62651963, 274793856, 754816785, 206449765, 207460643, 663297557, 187899369, 942153309, 12605208, 638801703, 581707403, 479986632, 216961002, 432307415, 287207046, 938847285, 231671719, 213953825, 670826218, 179912525, 499005625, 724199583, 975226789, 66287981, 163179425, 962114288, 321930179, 318567340, 465228083, 591918382, 114669637, 325571583, 720289027, 220567450, 183398974, 842638099, 89586889, 622968365, 545982054, 101133403, 400734832, 225872271, 493866395, 899749293, 971175505, 122488020, 50536913, 734379581, 518898140, 35573035, 229261821, 313383381, 981718078, 556001907, 576394518, 797819655, 93377855, 854434117, 722420488, 451004954, 539452964, 778868198, 599645585, 87046906, 34298514, 931526448, 492707339, 469763185, 946553466, 449691714, 300724697, 662115756, 728293954, 409935073, 481008169, 35588935, 104285299, 592293254, 709136652, 29839512, 956276643, 903614272, 639375032, 109878801, 13404445, 334232534, 715217046, 339003742, 846798587, 131035766, 383734008, 599878426, 518220342, 606957069, 799330925, 727458512, 655513145, 209662046, 518829163, 868307517, 169429360, 996821396, 337218919, 394697730, 439297461, 46900835, 735301569, 635379671, 213169993, 329138307, 741531388, 520637530, 640862604, 305577968, 283166380, 291624427, 394395517, 135010868, 220744907, 862113342, 444000363, 497170313, 596341750, 337172824, 496609944, 670715313, 230213536, 324710656, 776260448, 548952672, 929252771, 388095366, 860740437, 888365945, 24991331, 754428175, 445163211, 44873194, 886909290, 108344878, 196148486, 500793356, 227237318, 826681571, 375178053, 316709819, 990267340, 86960419, 150730331, 134725028, 933877431, 589453470, 448868629, 643577127, 581741128, 778364482, 57961321, 486876688, 193957924, 122209021, 339892952, 415460796, 781511402, 916713079, 798612956, 549810274, 884976815, 240396054, 301957601, 162695201, 409386403, 858335327, 908523031, 459479655, 675449927, 796455276, 268826575, 605042015, 830641729, 851413604, 831598677, 631100082, 856806062, 868925878, 223952440, 407350204, 133337612, 976991861, 521871813, 853967324, 12561762, 501740473, 281156383, 994166796, 252302931, 283397212, 150702765, 750302238, 858107033, 479791333, 212168732, 803052498, 978660512, 851477952, 514580559, 758244995, 977625634, 213609401, 293999095, 728625249, 836940312, 512312841, 101057761, 22843450, 94460731, 780857093, 491951802, 14177690, 883336020, 900834720, 96222347, 71117880, 718418971, 683294873, 613235709, 313111577, 490782035, 418025793, 574734413, 191121844, 810482471, 423069507, 551542822, 955672474, 909416251, 183077003, 16067992, 350582009, 191636199, 182739128, 614586990, 378644080, 242012153, 282796972, 498450173, 942040419, 222543061, 218837523, 22460398, 687722652, 242486175, 832807122, 517932131, 894063578, 267181489, 573171714, 401785714, 783392745, 590186679, 695107951, 438310812, 375965824, 463866912, 69533260, 680697002, 508045562, 274060292, 646895228, 143191343, 153556223, 670995963, 413060827, 196009659, 748654030, 287348787, 174697046, 13463371, 183924735, 636111193, 23763069, 768313818, 805208569, 321553755, 207320364, 75095248, 19653427, 790463479, 927288299, 452650915, 696223827, 933138921, 394714707, 58293686, 778774728, 191017726, 871218171, 681594948, 797920188, 850816382, 802359595, 333138888, 254516378, 361270545, 394039420, 628975900, 913683336, 35606451, 543056164, 546453169, 708727099, 523486162, 365856179, 699923010, 282682315, 206981985, 357689906, 902107379, 828618020, 557127142, 255460337, 559985622, 92510647, 68476230, 470879937, 297734821, 473853919, 640678593, 915951738, 771831483, 317570614, 664729511, 786524532, 320120768, 889623553, 644762501, 698143534, 633932342, 864969524, 317074401, 581215693, 808161839, 379334743, 52607210, 586466456, 892174886, 183519952, 123990914, 567407222, 90214590, 19343864, 157659097, 127131603, 209436246, 200371365, 530124031, 383012329, 961014158, 151701351, 289437095, 741903775, 787172173, 76773328, 824520321, 525149780, 722252990, 409832922, 455156874, 320893299, 882971308, 834865638, 14835752, 788800348, 216539218, 377721092, 79380477, 765321458, 601414377, 899081014, 600845676, 883948106, 284332409, 244203953, 522972346, 742115513, 872945075, 264278337, 637584190, 309266183, 205808835, 404167819, 784961757, 696436356, 927918126, 753844785, 292945867, 423642462, 205401225, 130677058, 225246065, 173449814, 72580039, 275991792, 417175039, 883947310, 598878232, 836638527, 416648847, 151204359, 685303785, 597445232, 824819878, 511820002, 454912306, 66761920, 182986456, 602762611, 369550941, 41179411, 985381107, 743488821, 730623082, 704034122, 611298475, 123198709, 944648699, 436135619, 970808007, 751915069, 830506196, 151970527, 835057448, 78332330, 896344248, 815418196, 90922646, 542782280, 55889322, 757726932, 732886627, 183735547, 517941737, 564016220, 102523422, 362729542, 977638156, 428970105, 427275586, 342312125, 413978156, 430249829, 923873865, 408101672, 345389766, 342655458, 334346519, 871137833, 701430651, 770027986, 556466472, 5794813, 971938863, 178202079, 120853907, 694469724, 855387972, 37409781, 92568707, 925846516, 296069817, 823532004, 797726457, 905023224, 728972944, 564531519, 648386592, 957210314, 556249794, 50743989, 565612416, 411226519, 668664717, 477647595, 50961747, 623350869, 563165200, 393762906, 717262774, 88062855, 215470709, 380652131, 939216752, 479097077, 636244497, 729152659, 747249285, 691659226, 929934890, 100726195, 412152960, 256827814, 128883551, 695727122, 76097452, 907649757, 141985970, 55986142, 827124989, 769025842, 98561780, 210539796, 771411862, 69460485, 71424018, 957242200, 251619354, 824226500, 326755742, 393341991, 204803097, 552346180, 981320814, 248656353, 849815577, 169561588, 374249765, 1645124, 558743577, 245402602, 87703629, 861497064, 867824771, 508398879, 599077918, 312111822, 447967259, 906822482, 394552855, 431039114, 523332324, 392511491, 885918602, 80356831, 421586139, 226193562, 250007006, 351235452, 249492416, 690972051, 347953517, 97173272, 861585987, 615315793, 412917492, 393377083, 930259368, 792648101, 234232531, 424383872, 954361053, 362093603, 502707749, 715108298, 576590109, 364687184, 389061863, 872965925, 695076008, 463409290, 55590428, 393691163, 505252597, 357175900, 311257925, 146826316, 666691713, 285636039, 753747267, 437982122, 445332226, 94208419, 276779722, 733569302, 959076210, 358916014, 997441939, 57764010, 932918184, 804136499, 357600477, 616748306, 392903792, 547008850, 480627564, 67124944, 715829122, 529622708, 411820369, 663655751, 675202486, 123808946, 832314851, 396027077, 794155986, 246467003, 850110448, 164407864, 118302496, 928652064, 894037753, 411839085, 515964560, 860829820, 325483595, 670184926, 739988264, 951783604, 689413375, 687186072, 672702671, 366780911, 771105016, 663910018, 697686501, 607844562, 927142078, 21412149, 963240717, 235986448, 603301271, 528933947, 892650279, 151325400, 725615972, 991127481, 869853220, 75138554, 473962372, 811358282, 37241739, 908744950, 579651113, 954863217, 927447128, 421579657, 48535697, 606283819, 435913, 248169966, 16938979, 599584488, 979564200, 176234227, 705902658, 577976348, 771559677, 618316077, 893639142, 810121055, 155060659, 542744665, 388907164, 299781923, 844413182, 125830788, 994134457, 974349563, 861456649, 85926132, 958693503, 99185331, 793946483, 145922022, 977432924, 72104632, 565530979, 55574060, 722964569, 38295701, 748362973, 794209446, 555391097, 642686397, 514527768, 887574255, 616950195, 947175162, 865137182, 225210477, 98503142, 447831586, 659932616, 498210661, 481431045, 221916617, 989570198, 242530356, 723876938, 671027432, 298292312, 246502797, 321824757, 61490957, 920862528, 247924628, 170806078, 828012417, 295034586, 11705410, 433429681, 727892211, 707663335, 515664861, 906991421, 801916819, 627931633, 37179746, 465883382, 81130708, 327276515, 947235609, 131917723, 937765785, 556579714, 1494475, 105641219, 962523177, 633481374, 22555318, 51043155, 369178526, 276966738, 588892906, 602087737, 638619972, 89282396, 631192409, 898399813, 402961215, 332266413, 861914026, 830114264, 486553736, 976106987, 462678366, 468548294, 590067406, 375317769, 991762095, 107750152, 354104316, 966872928, 478638207, 415223404, 22490508, 124275658, 759989226, 491740067, 536839751, 155444096, 519689424, 298579194, 945231679, 251683409, 111882850, 502321135, 728295429, 474600355, 965271886, 534915477, 753505699, 236244488, 18886075, 195192316, 948503689, 866644073, 401714180, 377996680, 839157483, 603512560, 322098380, 267161440, 47217921, 861333262, 112235214, 214061299, 887827815, 149315772, 425702028, 686388712, 757016146, 477967763, 573433607, 974051218, 682921082, 625551741, 805947762, 182149723, 378402, 134942075, 318351191, 165766437, 785795938, 792659462, 311816482, 661432916, 251397856, 566898749, 975524487, 39697722, 735214870, 266541568, 622025239, 967411143, 799432989, 999565049, 281867256, 45080200, 926355924, 24444437, 677331890, 753114433, 804410569, 766381842, 349470244, 278786822, 431650058, 363037029, 123601134, 786616507, 107990291, 386780441, 573149716, 783903562, 133048853, 121662397, 665772100, 556031284, 283643771, 401688749, 272304792, 739782948, 301830717, 12812241, 330024637, 623731682, 918127428, 692427745, 442004299, 476240511, 198554545, 305023762, 25274762, 997686032, 639103968, 44535314, 567541725, 331169605, 205638237, 250997352, 77552225, 26515659, 311705056, 687336548, 467968666, 190433820, 414757651, 398192588, 628900540, 689955275, 936006330, 350269773, 368714024, 72435552, 152702001, 616722353, 462147891, 119686911, 745317444, 184071042, 233547137, 457988141, 648752427, 427632546, 613778898, 450455060, 456229490, 46601244, 566643715, 766202631, 457198631, 83079118, 880858224, 864682165, 696170955, 274808001, 270577037, 148731666, 632791601, 973001471, 586511839, 965992283, 188014201, 114092900, 836162301, 358306407, 17455157, 683484984, 190861426, 551983732, 263975769, 278754623, 66223477, 243583163, 453807694, 687763184, 432361586, 361768936, 594588840, 631295765, 514033881, 408557349, 289642122, 335957207, 280124610, 130900429, 735182278, 631297568, 435918808, 270744050, 514690361, 417434536, 565903699, 872441896, 56754774, 334999892, 375791860, 388014637, 360679545, 789522899, 271440681, 696690335, 993346754, 680437503, 602213476, 742716213, 875326659, 120458572, 878448653, 616715950, 431600983, 525791004, 641843104, 412743094, 486196487, 428016496, 388347014, 215613123, 263997799, 155465304, 335286892, 406482605, 339330130, 131258695, 772975036, 335663747, 339432346, 255623362, 313238497, 547116071, 663276731, 709131779, 845731248, 412516171, 885542470, 172624227, 528340267, 337091868, 714077356, 647453083, 298597643, 874307901, 197982793, 836045273, 222696392, 809408583, 173470067, 369401154, 100173317, 302120985, 765084800, 195671808, 389561563, 803274608, 803492292, 124781692, 978393824, 390614383, 649436238, 438595260, 271845019, 539060443, 11072913, 652508035, 861041215, 833987606, 469522463, 643954377, 209599519, 719588736, 297352977, 132121197, 911425011, 662614382, 867088754, 325993511, 127977039, 164409029, 176739227, 100160573, 34107734, 673971117, 226614164, 599067120, 907721474, 326976764, 31277628, 473774927, 285281317, 864087057, 553799369, 588936487, 692975568, 436590729, 703676372, 787194809, 583942163, 358361282, 658613414, 131594086, 258904707, 234366830, 452810070, 493242370, 370372996, 283600128, 982419018, 304422851, 148756086, 31980023, 635341452, 238550712, 352368290, 599355067, 855651681, 300787972, 49601525, 217575907, 473393449, 261842767, 811546545, 915832836, 87615204, 193898528, 371893376, 817271359, 280381046, 569752132, 893585927, 37275666, 173170317, 916535909, 972494306, 883366909, 720296882, 250306505, 931721318, 205237722, 79987030, 978087563, 2220495, 732466376, 40786862, 966775368, 571872189, 63518195, 938331051, 664562584, 406570233, 575431597, 569411853, 151325854, 681473374, 187463234, 587721562, 148891295, 144181543, 288240973, 773808299, 375833596, 172592961, 593692940, 663356446, 922702071, 944316268, 136466524, 131890377, 736872488, 259190029, 587542254, 50691789, 363124477, 783488661, 585375390, 345820647, 138361126, 172560026, 774782340, 696657313, 735339102, 622804652, 111787013, 378227148, 895465915, 394242722, 809790167, 484673458, 788233154, 43828199, 201332268, 369766540, 983769639, 713017442, 88921506, 902154779, 150873642, 906210494, 588690896, 940064971, 123420797, 168943917, 407821530, 695993083, 109343365, 117553401, 977389816, 600132566, 445435306, 671471166, 399760133, 826429325, 454896440, 669398197, 62166605, 324235873, 906248360, 933054494, 652436628, 848811353, 603605375, 402511825, 832081377, 238604026, 901526456, 877278976, 618821930, 844793814, 621395866, 71342159, 782440939, 441153307, 794317793, 599344953, 599852766, 88636289, 202557075, 135774882, 978520622, 339848269, 428479832, 708686272, 282761090, 522924668, 31740763, 836449420, 35969975, 829652766, 395823937, 133986763, 686291172, 970464108, 661963193, 952550989, 707753128, 643320157, 39005166, 116322517, 428372175, 761018502, 506679493, 655571923, 7801257, 363061367, 519866797, 81883662, 36890664, 280376465, 514836105, 686689777, 738695040, 678104004, 167425851, 520200019, 364504179, 737850332, 174357495, 840683809, 586334996, 185063057, 878798083, 765371116, 69135487, 529917523, 311027251, 771225727, 495737112, 906706956, 985654859, 126461566, 477142019, 790710253, 997831232, 579605315, 25928116, 500842456, 967749176, 834958564, 527605299, 746931345, 470793667, 531332226, 79693170, 308999063, 739239506, 169392674, 613123024, 644406275, 82259634, 549531225, 971177918, 132184897, 259825014, 969100154, 559310328, 403533960, 662423291, 179745276, 351096464, 43205680, 848202121, 341665647, 626626696, 307003873, 885582921, 552531080, 510349255, 97252084, 841851477, 186620431, 593951784, 569599856, 521729001, 550099410, 564945668, 745322679, 371867618, 196907709, 949305498, 372150906, 589694302, 608674266, 617372465, 833750045, 800808660, 525047402, 200854459, 775339245, 42767769, 472463388, 630375579, 874936418, 934700565, 615453961, 118575379, 776087399, 614115466, 184470126, 482774202, 365467146, 461552823, 883016544, 743097566, 736143588, 21096739, 942852271, 24023362, 864142117, 294971532, 130522457, 154003987, 375240313, 648656663, 247180376, 705118007, 14807499, 458658737, 117206931, 193606101, 148883174, 587064505, 183896491, 211440280, 164983362, 843319309, 213068193, 41810763, 924677509, 944799979, 350238241, 85967299, 840985092, 948424309, 431422453, 227330745, 843385622, 710304026, 303662880, 377286703, 905930374, 384882572, 661003353, 107545180, 930596445, 501047745, 251066282, 475766289, 818056477, 88609556, 624447386, 196320646, 290116157, 379878771, 568125235, 290453489, 424844438, 795907959, 965270322, 941773790, 714188103, 292707108, 972707971, 702801057, 979616132, 677257373, 967980961, 985354002, 822528031, 689673529, 295263196, 480490894, 82744095, 173847878, 215908522, 861711042, 952498907, 350719847, 940179028, 658726098, 908143906, 410408631, 129803437, 192504630, 106646802, 68820879, 26320344, 66390661, 403677865, 406856109, 183775644, 898868813, 187126918, 181208894, 342939012, 352463059, 40040404, 244968152, 466669078, 618506392, 786601737, 615305726, 393839371, 725021375, 792845022, 403458260, 909637020, 392981841, 552820870, 205677750, 87714497, 843225235, 109719571, 588410334, 471848153, 354610685, 310364825, 300305419, 844989740, 399236872, 180734467, 450957434, 354865753, 733070384, 23472234, 977091250, 569522709, 591364753, 227899375, 471925259, 740601328, 970197823, 716156807, 319013384, 680650364, 162900488, 528657870, 601507903, 476289932, 109131916, 704014861, 257264743, 873462411, 942392616, 471746876, 55521572, 160419874, 460206908, 73654909, 368882450, 443793309, 548164131, 610169625, 74513662, 769066725, 131466275, 469226827, 311413187, 991776042, 563621585, 796739214, 460275327, 481846153, 87859905, 41175485, 198133863, 890732582, 366069800, 647726356, 861632140, 17578907, 38027179, 369809879, 860276923, 161783225, 828035480, 39384546, 631300981, 732277180, 163732493, 258128478, 444838071, 283953246, 305772891, 699615217, 377248226, 237838954, 286927370, 594579995, 755000224, 437320563, 200640830, 690766786, 126818382, 552333493, 50022928, 849532467, 163746565, 239798934, 287560539, 500604484, 151795405, 802119426, 167034500, 826461269, 619294493, 46367581, 696383685, 367757495, 104122627, 15300525, 420885445, 560445079, 573755880, 11092749, 328412300, 106418167, 35509790, 209357350, 150671793, 844499966, 1513617, 454433764, 915182343, 404538924, 382562618, 846295699, 484717068, 699911216, 234218666, 222612807, 265677393, 813550051, 131413655, 664404960, 282799273, 853654701, 259627174, 203698118, 648040387, 271555831, 54055325, 168272813, 63361028, 738217987, 455204084, 610678120, 460522658, 652808327, 83456213, 49715240, 751136971, 724852039, 494573557, 561479078, 103175356, 889521662, 475607462, 753064844, 229579094, 766274951, 964152258, 496585896, 869317966, 575507636, 932611611, 491496431, 305926260, 937551748, 239626576, 610298955, 688253395, 91169623, 22053501, 842372196, 680157508, 912384265, 579376049, 414207950, 479410866, 934588115, 896770163, 293305916, 954621427, 235990720, 350527733, 827968527, 662398359, 527407942, 716221323, 428253592, 774045389, 173386083, 717898840, 606177659, 977383842, 261133135, 467881534, 862510252, 879775619, 218813500, 626136293, 604898211, 770800093, 490651746, 613758877, 926441383, 946964962, 974570127, 342990126, 441607756, 329583277, 831811094, 160663354, 46491160, 880360045, 218845404, 319682521, 923992342, 471189973, 716523476, 213554049, 857466177, 752370395, 416416203, 316639268, 19359524, 271737509, 947345539, 566973305, 677016569, 616826630, 724930612, 669722279, 285728066, 813496283, 103638096, 396786189, 921947060, 420443887, 456874624, 488232671, 244905530, 264643752, 681759756, 20560260, 914820075, 230469047, 891390734, 840487146, 365166029, 303809719, 774339954, 193581590, 125125649, 797443236, 991295478, 349203148, 955892456, 816115637, 796472773, 939844241, 429046501, 246541495, 29176036, 612643910, 416924757, 925958743, 665755773, 625585290, 881188034, 188008790, 28739169, 192632031, 237564132, 412284931, 611227117, 719906452, 807697303, 28732645, 999349525, 778564968, 685141617, 77963938, 131038605, 448273632, 962949259, 45027751, 433440359, 237472017, 642647617, 293385325, 476671969, 998193089, 621200747, 759090289, 308324973, 325664915, 377990488, 541477423, 758798592, 753462957, 426267318, 115875468, 768820466, 396461011, 551628739, 259126165, 497642847, 641541970, 816832812, 450825192, 49125159, 754677820, 300996493, 870574571, 554238236, 802919191, 464598414, 630952169, 373653883, 280556885, 843801664, 440883645, 839182044, 878864680, 498668544, 680176876, 467780237, 606900868, 875444588, 212517716, 90714494, 189074689, 41121560, 561532505, 437793169, 696910839, 531202653, 479283783, 554688984, 503665402, 362558592, 309821505, 603007542, 300547042, 533397046, 183117242, 233105709, 731068577, 298408506, 399878352, 305777953, 831202544, 592906329, 235091433, 868120376, 402924872, 728113455, 758631348, 872007776, 741941007, 705358125, 958166976, 511753829, 8934915, 698915715, 445557494, 303677119, 512947422, 65406581, 419309193, 221123433, 718412766, 670858105, 752341129, 916582328, 127866159, 881141158, 423065069, 796938836, 593910206, 545673309, 557754385, 541916316, 528814791, 235360613, 665188723, 224242846, 268124915, 167526850, 687087803, 163540023, 224247237, 193386566, 68651900, 762227279, 24460267, 118561530, 451874443, 627795919, 587234543, 903332757, 680769380, 278925720, 560002193, 719333471, 301503380, 66923983, 25769472, 181278306, 317584448, 997113957, 325629017, 876026644, 871150805, 217408306, 650752316, 203719922, 575409127, 639785611, 746225692, 684567148, 614712131, 264936302, 809200463, 330767144, 931447910, 691522954, 52867578, 878371508, 151494749, 100379831, 567185866, 600295638, 116471398, 209430472, 137189074, 755966413, 698510623, 277056147, 748133087, 901170545, 647533470, 971291404, 343454149, 128117989, 582683624, 945157629, 245795787, 240140938, 895591573, 317080374, 834040665, 447853016, 849501217, 83178662, 292440052, 313263559, 326373391, 729802267, 292100423, 28007434, 714725788, 295533197, 106894054, 513974967, 606136485, 385489295, 879400966, 865645488, 858179991, 210054468, 460064925, 29390666, 890552166, 412227633, 635021394, 274481698, 742811499, 859456305, 25140295, 307847543, 644482331, 775629652, 139904582, 232844386, 699528145, 893300730, 839471153, 540974000, 121696807, 421559228, 221169298, 398748987, 427125597, 34792912, 252925773, 734888786, 800867886, 555120798, 767428398, 407276085, 806647875, 234803751, 71334445, 854436995, 571895869, 324873271, 359858878, 351541695, 284891354, 606657478, 222724892, 381602345, 876821997, 257893250, 586141292, 520506937, 469271628, 145316041, 794600022, 290933515, 267778994, 698588983, 216798585, 522821983, 519036819, 753375409, 299248337, 715431539, 282716913, 228043585, 956288725, 447155815, 982848990, 528821777, 457565223, 855728017, 312321988, 115508417, 130027111, 747611734, 102359748, 877213696, 68756477, 414661812, 875618155, 838279264, 149594305, 402267257, 766971530, 51610192, 698562733, 563252024, 242837474, 255877169, 546014884, 101455065, 623443054, 439645072, 614543774, 232896423, 501135389, 316686451, 440947141, 976575821, 956781935, 155837813, 659050358, 329218229, 711589390, 107833663, 844220454, 856364244, 514914645, 242134596, 372739178, 719783820, 661215518, 792000098, 22562514, 788570610, 500073712, 973627001, 850001257, 396553022, 147991873, 741461579, 297911522, 791003177, 697642795, 943692967, 546823249, 785308117, 472444534, 179201990, 686124609, 360302048, 739574983, 565897009, 454135258, 90822836, 433484454, 537280464, 513284328, 297872994, 867883093, 449605986, 838817243, 313403505, 635524704, 687181130, 85457914, 516873242, 408183980, 699985823, 468654880, 496503249, 250894937, 305131155, 743492133, 778507923, 221123528, 837250030, 342503751, 693526682, 969924201, 383570015, 872793716, 703696367, 988570347, 937340555, 423357077, 598134129, 663799752, 817460075, 232846972, 257481168, 90808458, 195702862, 430793288, 592328605, 585825777, 411325278, 26122530, 789478274, 492757022, 986735793, 759164990, 503323613, 981159212, 185007553, 696912302, 432389010, 727270843, 946291488, 112155773, 520205464, 644485812, 69001056, 139277358, 622093172, 706961960, 260646988, 585593792, 413587041, 200805717, 140212412, 681694983, 749698296, 309754973, 789991299, 226070865, 140281332, 986796623, 374834202, 957055355, 183287486, 746401711, 601891689, 519754523, 708053914, 63039135, 830245388, 893225871, 448181424, 600744390, 951218832, 360735399, 102633041, 807197099, 133762828, 512116129, 648113862, 747676937, 437933064, 353526954, 427306111, 593312547, 312641368, 910739543, 510567071, 456449102, 487456726, 126465812, 331826470, 774450620, 527375378, 816056259, 344410642, 615325012, 151795328, 472926683, 383341722, 904372114, 276287491, 348076645, 229033245, 391771317, 868202441, 241989684, 619098124, 842190421, 728161502, 724874151, 716019843, 553097045, 223323711, 445294335, 244203010, 650180495, 987924557, 554330517, 781159876, 694366259, 941992611, 979223499, 160072024, 247047658, 887918461, 447141646, 558157754, 845271322, 329512877, 100383418, 743555743, 476626549, 349601179, 926469857, 513788107, 555090472, 418962238, 751508427, 781894829, 863880234, 5510123, 111366459, 147557905, 564296292, 876205406, 818272158, 816361455, 547411175, 792635715, 397845518, 496592161, 678594500, 460177301, 87876384, 294103286, 132335460, 29273659, 825931804, 952611339, 801807154, 937052505, 939859894, 782607749, 610414389, 727968273, 272707806, 193081234, 513818160, 630413442, 770125648, 92877696, 878292516, 127014609, 220943450, 215656072, 437679790, 601222649, 437253461, 213670828, 893725515, 456496784, 395670675, 715079138, 483901707, 533515869, 191372967, 821326053, 309692252, 814168596, 190309679, 15661856, 739054605, 59374353, 181513706, 458293152, 443675328, 793921561, 3414586, 899249662, 938231177, 16352190, 443705188, 934836390, 490220831, 800401364, 814756611, 52571294, 635224760, 840891442, 528172468, 903317248, 817179135, 80814712, 269517559, 869937261, 531714086, 850268726, 532614002, 601033, 523116136, 871490066, 22158997, 104712984, 80142630, 750743927, 628131133, 862705801, 774881982, 885462963, 341140822, 466874572, 444201370, 271209912, 579758139, 61690626, 537582641, 817871844, 327517030, 479859178, 72459818, 282103528, 200109771, 307338908, 388357328, 11321606, 706305926, 565483763, 115929231, 399642570, 811385355, 93457216, 618371383, 39828062, 507006999, 437526765, 917064805, 387851869, 533431129, 330032566, 981703437, 698746170, 128613856, 342483164, 516863139, 539244812, 735898405, 588366823, 543679610, 404394244, 571432709, 930479717, 835237740, 568317937, 231155382, 978532624, 440707797, 941059486, 754532703, 487997770, 834881239, 49628151, 194302122, 680175173, 654417317, 183821434, 178614901, 330392223, 50389047, 868424619, 799729485, 183653865, 548430183, 266871154, 163670132, 793060369, 354179441, 20522839, 142714764, 115554431, 828257699, 74336747, 86744558, 771295394, 628250428, 922987064, 103535795, 387007995, 947196582, 889869692, 563416817, 718817583, 777018915, 289941235, 115120779, 803339081, 594629439, 391346521, 298550614, 947468664, 899760939, 322359409, 390048862, 358787575, 775652553, 50478671, 275548502, 559590276, 489786367, 674929179, 643219855, 177284570, 456678502, 18997845, 697058558, 191637312, 476199947, 993250216, 384789888, 389190708, 611817852, 6305295, 157879180, 932149128, 409009459, 651693380, 886529792, 626638072, 891255490, 612337347, 576678138, 989126523, 333166746, 22365528, 32358506, 67924742, 143776025, 387150624, 427839579, 976750793, 563077101, 843164345, 762098277, 154419083, 637685271, 618756764, 447918540, 762842968, 186526288, 819806593, 921072591, 717761672, 558273510, 135512909, 410233995, 872679834, 105632238, 372186396, 600429819, 423480612, 163344877, 255933334, 155838139, 148479717, 659061955, 944752378, 503335203, 561080895, 536978458, 741701093, 920271675, 732494921, 746859091, 345682723, 290153257, 380502066, 119048065, 911881833, 217517056, 806286037, 683303361, 758305495, 655521482, 871887806, 592725403, 587121077, 622714456, 81018759, 696827083, 268252873, 619414423, 778233323, 11229717, 287792850, 483193541, 921074771, 183849305, 800929204, 156119612, 723922764, 703723476, 829781450, 597227071, 423177514, 303908653, 889520488, 345743397, 215369457, 286008307, 143696843, 545634607, 127497236, 610262052, 624903881, 956088212, 209681262, 879830518, 855557824, 628853399, 973443479, 48599884, 213803804, 814229726, 896498965, 147220501, 135572169, 41753184, 854457518, 138047619, 798843841, 725382768, 249826956, 154917700, 773391913, 560101927, 510002832, 343937789, 98050283, 51124881, 159157452, 774517127, 761818150, 196865098, 644477050, 435166219, 202941205, 261728069, 905817613, 192692175, 393435001, 136501410, 209247862, 211767835, 350241844, 502622262, 579445728, 572858790, 8560455, 827331510, 19672428, 753470693, 414143815, 842443906, 735013326, 555604161, 889861286, 985079612, 563293391, 21820448, 548370668, 271288174, 983938685, 860098610, 298959355, 480262253, 266173473, 550459379, 604717683, 502746807, 144822, 415094251, 300966331, 646562325, 149358959, 101479941, 776913334, 367253000, 154728419, 934707489, 857315377, 866018665, 509975874, 895155282, 50408483, 739766601, 267983594, 878380018, 843344410, 801959714, 861784180, 868871126, 806139053, 913541879, 255894959, 669971039, 205134505, 260587232, 312068906, 590416399, 293666318, 681094230, 215780528, 755742933, 358553175, 323844765, 924816401, 928323553, 75762310, 491282188, 279835639, 115558495, 575118137, 549373328, 469535886, 16577677, 81758146, 406899385, 726995565, 952316959, 379621431, 625798372, 885905703, 194875983, 893142168, 555298916, 133822511, 686898488, 251603051, 877833641, 625558396, 5639984, 989132367, 899746455, 195058109, 147447034, 21496266, 400483135, 406246253, 381428108, 70649495, 802623563, 631976778, 55504589, 860712072, 916078954, 572646119, 669216640, 995584206, 776735639, 658677299, 652875702, 409100329, 960854042, 618744563, 921191614, 558829155, 376047268, 206539620, 159273577, 877294437, 857995993, 440026371, 347225195, 627177039, 712197314, 817251097, 654525898, 963136866, 723896130, 560629630, 734549371, 697002944, 515121646, 571657363, 21052817, 974106355, 493311238, 877903409, 39416941, 259367508, 208737505, 989162672, 599889530, 575218019, 336548071, 728935887, 181547300, 44188447, 49975748, 716059091, 934642880, 431617747, 415825855, 976712143, 965801219, 17726733, 492094268, 860085948, 726245381, 162480901, 638147464, 321250299, 119935692, 374760318, 146852761, 875759360, 756272790, 911195821, 127674993, 45140596, 84266615, 959771719, 328105663, 353808410, 612910072, 695399882, 427908444, 201521901, 978209055, 401766442, 80937735, 24806364, 357633173, 35643075, 985934594, 540344989, 472490188, 956758150, 313272500, 87350364, 283372671, 916771460, 722289578, 672414003, 169252948, 758536920, 864485055, 361932650, 126539702, 628917119, 645791756, 603211152, 436315660, 211396462, 147753705, 670106657, 393622980, 353893114, 770365054, 876970550, 739733723, 808359789, 304345522, 237502368, 742688808, 138567156, 126738954, 436738293, 333609526, 778008807, 931379646, 115921533, 775880514, 994151267, 239843380, 489765847, 428907331, 948728290, 161555438, 868056678, 615550565, 30666071, 184379613, 518206745, 294602660, 235453784, 839727157, 362113796, 980422874, 595606323, 548670878, 921589400, 39775433, 70935610, 305992899, 668938240, 64875801, 290253458, 953477972, 163024964, 6635488, 666985498, 314279812, 249372191, 484474836, 674996098, 237494254, 617038572, 895433317, 179978085, 686212109, 42951779, 844062411, 557806083, 506402118, 635367273, 587824489, 987607183, 83123696, 114978240, 802852738, 581792832, 485962848, 367689303, 51296687, 113995354, 76109763, 397041510, 650935194, 482356612, 523213106, 99166834, 48328679, 491013492, 304748718, 790367719, 613624035, 886881331, 774911533, 596671695, 784620273, 305711947, 783467480, 567749473, 192663962, 32706872, 455376384, 836781760, 324781066, 123584365, 791723364, 950330100, 410278665, 498391404, 740933254, 241768299, 868067181, 437187846, 7509661, 597369189, 934308515, 60974910, 506869102, 978625505, 533828193, 417742734, 716599272, 173736111, 130818063, 909721201, 410046528, 502202603, 813629232, 17818294, 67368760, 254527872, 221398431, 585563181, 177395962, 112203421, 873465433, 64184523, 574362900, 227555690, 150921697, 140637239, 426843164, 574522796, 103513171, 235822312, 496370477, 625041261, 655541544, 660135344, 641819939, 626660712, 566894973, 820428836, 222405477, 296567915, 243178183, 977980572, 660472249, 140273467, 748885322, 113776463, 929105202, 883521910, 407893429, 121827394, 800077694, 811010923, 172082536, 70002203, 741789607, 133833777, 2419948, 327241004, 245520364, 412552788, 798040626, 770096288, 431345096, 366375895, 112491528, 415991588, 124017658, 903904426, 177388272, 279502935, 188698171, 141580505, 708086481, 28606400, 150896075, 488220056, 301013405, 461951839, 29295494, 256507455, 62806875, 577836463, 634820797, 8527333, 866385813, 762228822, 307677691, 822309267, 421602140, 366408313, 59416710, 190298398, 70872311, 712629710, 260056412, 175376591, 359455327, 289335289, 959948851, 608439348, 515987596, 543376972, 13914984, 476073952, 788058393, 19951791, 24960311, 591007601, 951392378, 346360155, 901409346, 58078536, 677821980, 65008367, 344906500, 379957128, 990654373, 223369352, 831789305, 43984562, 795863302, 56122590, 278458141, 74796791, 677901443, 903866099, 659148859, 758081263, 348104695, 945760641, 940362786, 817424286, 619994315, 874319100, 293367520, 636443941, 807035873, 735217810, 291118348, 182629775, 458297959, 72519839, 205176858, 295751125, 672980124, 993426293, 624316278, 484961729, 604070329, 879774064, 721423280, 255336948, 536894793, 647110946, 107722139, 2854381, 211362739, 959842754, 874515642, 415438079, 59517984, 74152804, 668046457, 522121174, 487596733, 60109533, 212733874, 840891458, 569089932, 122658003, 355375460, 467853222, 271303947, 141262660, 639662035, 745471976, 459790752, 920538460, 634879202, 158895843, 114671215, 344178280, 720308450, 913758170, 704452684, 951038338, 790753325, 447195373, 295562213, 713754886, 947466166, 81465135, 575118577, 401232415, 262283610, 699184781, 541039090, 866034759, 836380954, 95886012, 759732704, 533554824, 48193402, 594788049, 312018398, 520842356, 459816322, 775632843, 222983445, 276850637, 25812647, 882463869, 458893678, 73542262, 635944524, 426471514, 847430257, 422975499, 68803751, 357601853, 844407981, 904740035, 405530114, 391310661, 719483824, 318594077, 707239272, 751600598, 85952735, 561267898, 688047779, 817606634, 392439136, 437615016, 293073288, 619118088, 129330380, 641823778, 612307328, 914098632, 643656188, 186331599, 2519975, 332457394, 481831852, 628576666, 638798605, 714366651, 282860998, 107857728, 8079106, 699754478, 997776379, 831838450, 947717926, 713319657, 787555490, 203973578, 47967761, 498082842, 49920728, 14076276, 557954600, 932234677, 878219207, 809641637, 159726901, 519328231, 962601966, 708162811, 134860465, 647834399, 722214406, 153759302, 31762750, 701356446, 359425081, 60449109, 453012865, 582209966, 775978236, 899664582, 24742215, 526466767, 232938299, 552946310, 826123525, 733566672, 924243275, 197644581, 414151721, 472780562, 137957859, 978875696, 912568553, 306287938, 876085001, 342470143, 330533994, 548418477, 903850354, 234860520, 166780275, 643826855, 59458007, 938873456, 688370274, 775980231, 187316746, 99260216, 770308893, 530129471, 360274735, 84529900, 901503225, 131304153, 835166142, 379205358, 258133360, 841814568, 208881197, 736557126, 319395837, 71537247, 502515684, 95779321, 217079238, 879640901, 185897615, 263898145, 225546634, 196172113, 375969659, 550074863, 303342276, 493758599, 992306241, 266431136, 922478957, 448783044, 945872470, 560763699, 770344593, 330119274, 442630092, 421517515, 899063069, 210185142, 4338948, 571075719, 909669549, 728904289, 746646048, 757121564, 285765908, 596589722, 567013803, 724415001, 542937933, 545281003, 732087500, 489419765, 967187067, 642726246, 410465187, 619612618, 227057382, 776561124, 161903557, 225156524, 494278654, 852318717, 579458505, 23661303, 635846150, 598494344, 318126270, 297918692, 291965902, 476878637, 394289997, 696444910, 802512250, 521655518, 963004788, 38324591, 762610732, 810928634, 908002998, 221556345, 970002773, 51174712, 792485508, 304697086, 361226601, 609900288, 227843877, 490413552, 354408172, 808707522, 419635048, 295881866, 554269493, 159202303, 2544533, 463114592, 487201693, 821194138, 441198082, 424001820, 722459397, 747440602, 353851129, 899572888, 342972797, 583941641, 959827286, 889829003, 330484426, 430064415, 249267518, 94838108, 269518676, 295557157, 839405748, 112801699, 792541297, 161324854, 258449449, 781645291, 229092086, 288822180, 500742756, 586825502, 695728567, 95407469, 719699528, 586515352, 102794149, 878821179, 701915268, 857184902, 988021197, 137063100, 486149035, 305649046, 305130362, 771020668, 34784607, 559847851, 70061313, 763482838, 267438715, 851332253, 851183041, 742290710, 570197984, 134562031, 804468727, 96111828, 296601141, 262104990, 234688897, 311279441, 125926789, 510479419, 340423407, 224892178, 736115503, 50042165, 484147427, 798482206, 722447139, 514668984, 761079723, 933823335, 298689978, 39440928, 316425820, 53389257, 684109859, 98297156, 927744140, 947326092, 895328185, 872101859, 469563330, 958998604, 645740621, 397937998, 685882229, 376316187, 776033069, 319634951, 503731306, 517958223, 567596655, 66864512, 511178274, 559564420, 802203542, 894364966, 474425213, 77031498, 718001796, 589082888, 927585667, 30461890, 845813576, 153757430, 611392997, 444417390, 602666301, 217288682, 864733240, 740132402, 269420350, 817598403, 617375466, 224745798, 690434260, 843851200, 662556191, 498386253, 289877849, 801120728, 885584349, 156183966, 920547184, 812734040, 840686577, 143704363, 209135302, 141701160, 956701506, 160273033, 379277997, 702687495, 712894731, 990070113, 309195545, 928153826, 947279743, 923533304, 135765978, 224504466, 551902753, 59574402, 75763424, 860426697, 59295926, 942605892, 96521009, 894750332, 22968147, 424455882, 628028187, 544083981, 808503826, 675473844, 694135501, 101285299, 807118480, 485989488, 740519065, 614048885, 945841585, 282956990, 55577621, 602942451, 453378914, 142669521, 103180983, 728866810, 367833888, 441520441, 831251394, 398644822, 435005367, 934709324, 331628664, 312977841, 325699700, 593614809, 648624405, 567288334, 207888762, 907637138, 856299572, 3878827, 160328977, 924061639, 949578444, 169786182, 872352007, 84912370, 272859537, 772111092, 612335676, 648160416, 491460497, 706860210, 253169380, 210677891, 274872576, 25557287, 17573693, 759747441, 824011410, 94219021, 963785720, 169244488, 467569118, 461928299, 907681192, 66651743, 65830471, 33263675, 452283896, 741835291, 47039134, 114795757, 390809792, 796727681, 44515231, 356444094, 799202913, 792742517, 801091658, 38034148, 755037404, 857885023, 967568019, 260900131, 460887066, 221729223, 962822619, 507231428, 330592847, 861462628, 216622325, 307059432, 592676567, 285216957, 26481132, 771140283, 613912118, 942968230, 240422522, 811056020, 801766248, 830070396, 667452032, 205190833, 301317676, 823674346, 6784604, 658971741, 209073596, 298019229, 985095357, 579394707, 755960833, 358452727, 643156332, 253164321, 455709199, 927135433, 156044158, 686909274, 330788670, 483505316, 934531469, 343146560, 534703057, 69690806, 116324969, 13848851, 310235933, 201356797, 343422207, 165692579, 819953100, 495999471, 579860399, 908376793, 158341651, 363998274, 278656318, 328998608, 496234504, 120112215, 543281406, 411712818, 209514995, 857074467, 794216038, 429789713, 221142261, 765355668, 307788911, 525968789, 110795209, 619717381, 12570426, 359809506, 833376233, 577670554, 657681977, 999847900, 787112965, 254448789, 575447580, 918056127, 672414421, 623646033, 529838926, 327639122, 759505237, 314697822, 887338058, 555205084, 548215139, 502040026, 268111705, 64840288, 770159801, 381821025, 692447475, 794374457, 39935657, 445135412, 631263438, 843071769, 134944259, 775653879, 680048774, 880845633, 872792064, 729940878, 389907404, 481767655, 957879253, 269556457, 119530620, 234881375, 919211743, 862487869, 703902018, 105320359, 711236432, 476513896, 227837700, 950577956, 5619892, 620874878, 753050612, 545515393, 561249403, 496850792, 415992493, 788028610, 140269805, 735717193, 965438105, 13914614, 354232020, 998731605, 695865200, 489899964, 9433773, 775376419, 188077737, 402445054, 860800329, 981060001, 570829826, 27049499, 208247618, 86421011, 534543637, 967992138, 791703968, 208619614, 972408773, 554042464, 418172287, 552549505, 259949021, 730414338, 39895301, 473443999, 484703705, 503421951, 89093747, 367267136, 120299792, 145871963, 155101997, 228360882, 497828072, 189807636, 949769641, 876510148, 105314062, 954345439, 879949360, 262668794, 659147059, 734555693, 897374012, 776823890, 159588515, 421281624, 61341941, 703046928, 343278543, 953740536, 719310879, 998850677, 734246798, 606830342, 84081903, 551199406, 476583448, 644597027, 750707832, 322997962, 776570800, 591619676, 219940253, 800586665, 410598168, 153898935, 62271718, 684446457, 825998907, 102798990, 139990316, 669748785, 392925865, 345982125, 609549744, 450760198, 590699210, 134677681, 525555258, 737873171, 859513411, 878900216, 278461745, 169833394, 250763404, 613546689, 508284931, 813761644, 993229956, 387814399, 246029618, 782256484, 35084104, 459345739, 126774289, 604753198, 703567765, 16123812, 58718029, 971419338, 971160700, 218246173, 657658631, 47239226, 698612141, 299637196, 369243924, 308934396, 228825613, 883656024, 258644941, 570594926, 779610579, 122212936, 314058187, 179785264, 484759963, 122800630, 710376970, 659497887, 924535503, 19128611, 546381701, 925862047, 284312648, 393649671, 404801549, 725647227, 922525705, 177252945, 41552947, 547986230, 826194751, 671231862, 621739063, 524915160, 776475623, 938271045, 8519424, 328053129, 885456833, 241622865, 798082285, 184436130, 838165645, 394165041, 392205335, 282597329, 622279892, 798345039, 180008696, 548630516, 182086158, 720151047, 734520316, 811349291, 878082665, 746362741, 594850060, 915102558, 385222054, 211127477, 192202523, 28144502, 173956602, 82348921, 706937869, 471853826, 970473440, 946500278, 417837327, 812312467, 684907782, 453855148, 502024788, 790284870, 289645587, 914964942, 513940959, 664342273, 728134715, 684824366, 390323013, 387949185, 862574689, 62260059, 626360185, 201421312, 272748903, 556941630, 829473191, 314534366, 251111749, 30672672, 644309007, 125892130, 772826810, 735580243, 132287039, 530719818, 793311939, 282769777, 695922612, 762321273, 598218719, 171959022, 962205037, 918489093, 382898829, 855828509, 207387520, 253039263, 985142001, 346319450, 105936844, 810245589, 541087907, 722266736, 282407177, 283860590, 942727627, 408381928, 373422696, 708485283, 296087571, 578140344, 898407458, 233698082, 360130451, 176913739, 144467026, 725604749, 513249492, 855792731, 741198899, 78710289, 943189003, 13012886, 243618404, 328915528, 911018550, 685108303, 715973710, 71350163, 948563903, 246518041, 360119994, 706796039, 433641299, 662973806, 809173254, 712119122, 860496498, 256263141, 832708440, 915749114, 672724852, 93825234, 167428316, 826710938, 198950881, 779505376, 738786490, 165116105, 476449570, 264410922, 495671590, 7000587, 897683624, 890092597, 40143674, 472386324, 896872855, 983013517, 543203778, 499750414, 863763492, 666270384, 941246479, 793189493, 579145603, 143805681, 10053185, 885231231, 712481247, 66896803, 315730474, 56606001, 867252755, 669828058, 383832638, 469769867, 911807341, 831654638, 871894202, 766983185, 677932282, 658454369, 801229798, 698831041, 105123417, 625929542, 769190521, 239444665, 48515003, 308464140, 344156902, 595800122, 632391020, 708671240, 801798111, 409633214, 229001504, 923592824, 428600425, 759932668, 340522482, 299251037, 953750072, 398284115, 854163671, 368802860, 234024493, 275454997, 368109179, 690978904, 350285576, 339713965, 159006646, 740046075, 25964492, 546325415, 764465606, 278370318, 384168742, 651873126, 550905746, 984817949, 601039850, 602716244, 768448004, 157162933, 765632023, 667261924, 366000853, 193947979, 821096624, 123988200, 438491527, 87296299, 315834238, 47925563, 700407435, 646382605, 118691401, 638516721, 762875958, 488768406, 952128704, 36456899, 361987455, 604726810, 672206231, 405518099, 364054984, 288635484, 207486039, 593023087, 568668051, 895082882, 148051241, 364457525, 321007137, 185840449, 900634781, 586138731, 651254275, 746587189, 258087018, 54137765, 812562925, 792995392, 171935267, 736020558, 550140491, 130009259, 827551462, 44044568, 899574262, 839695605, 47537462, 830079404, 720267671, 432080180, 896122449, 475424400, 763215391, 23467240, 899066978, 170244228, 529563959, 72911148, 397808701, 910972936, 303635026, 507827008, 910833353, 384951550, 295203987, 541803383, 283144992, 137609511, 791372828, 72960959, 414137553, 739320584, 431478608, 352298533, 879915538, 74335446, 945475068, 89151172, 503860026, 544203984, 77130967, 907455377, 409439581, 714658534, 997845208, 124780716, 181825951, 785667200, 317674446, 742659235, 704807882, 288055735, 642648767, 360766250, 11982691, 429352124, 174477159, 825604284, 484337245, 78383506, 231576073, 407066245, 465926866, 761814268, 614601202, 686171465, 391851222, 869554289, 686578838, 689104944, 339189291, 532563650, 651172607, 989626160, 281164368, 274828908, 202882378, 582496236, 543439865, 818834164, 662860952, 870030869, 939083475, 504128342, 933254055, 157623565, 953609874, 601330183, 898557109, 950266788, 631695687, 115265979, 351039247, 481263384, 637085478, 276254399, 754302544, 920229820, 972375259, 549468925, 223688764, 651554341, 362040882, 442313270, 71429019, 420781490, 897895985, 977599092, 783619174, 398015465, 360772300, 909714636, 151149924, 334223474, 515019353, 495281722, 481520833, 636894311, 235314565, 943043401, 590595082, 962981688, 942193120, 40266422, 241264831, 795548143, 364445374, 596689425, 184254924, 20397488, 520451378, 646368274, 832793545, 931569084, 438784879, 494101227, 712521144, 962832893, 817231989, 828834707, 709967851, 806067476, 995867182, 654602406, 226669144, 675212539, 678897474, 862507146, 567709872, 89649829, 283177256, 563732308, 491717181, 629985305, 217488911, 648073162, 57408341, 141894643, 540565685, 609913280, 551090621, 326511592, 647709046, 861047103, 569854621, 295454240, 167346309, 894629602, 692016084, 384485155, 791307806, 290512868, 965653307, 219837610, 807013708, 459698586, 227034843, 507699655, 606959802, 930652225, 500311094, 924320273, 72016154, 423036369, 752265195, 977761693, 215526059, 33625244, 930367947, 234393739, 772803194, 496217988, 155670518, 425593010, 267064596, 164114273, 434606633, 299701692, 333372607, 198417263, 485048297, 558205766, 383324846, 60511739, 410761899, 977498671, 8942469, 458439391, 282562967, 270030395, 631858351, 958205229, 40838430, 953957184, 158409086, 932440088, 817431179, 443159480, 278855481, 30222174, 937348366, 744980385, 915487208, 903912080, 609114533, 571404147, 576442097, 243578419, 704867355, 99006671, 319071500, 287907711, 258642912, 596311746, 772514030, 969853566, 146562807, 331458200, 854963147, 315072077, 715574925, 966579792, 180641587, 451809362, 721297249, 277874301, 69425637, 486549839, 171310342, 824826506, 578388118, 849197917, 168579831, 942238083, 318363139, 138702743, 825983541, 410308969, 442496867, 593928063, 151055458, 277317968, 427693472, 898554088, 799398037, 794281171, 665197844, 506389487, 441276644, 623141871, 459891464, 748359051, 824140761, 675730571, 780695390, 131548456, 895887405, 366945134, 688872004, 874592209, 118865255, 359713604, 345995407, 603291028, 159880235, 493455210, 128259285, 264825330, 595776550, 744665595, 162351144, 57857186, 462554488, 405259708, 694324362, 117144775, 547311489, 899935283, 241060990, 455815952, 36569808, 717148101, 766084426, 197093004, 927015188, 814594324, 560889369, 465709557, 891431586, 590015545, 781116547, 163367281, 271976119, 911969359, 503046359, 997460938, 289424613, 92817257, 125080875, 713755388, 200486848, 822164774, 455081975, 888506116, 172199104, 448323552, 255154738, 620780036, 86037367, 437695830, 372534324, 995041987, 783014211, 88633459, 980408625, 557390327, 104240485, 145428680, 608215675, 288028587, 739753407, 965465588, 222092286, 348430353, 11933797, 325086590, 239362158, 144111313, 235678842, 59083548, 839006287, 894236970, 885593510, 142536913, 424533616, 588282978, 537390384, 696733125, 905738164, 468480286, 268445993, 55939375, 77331719, 435252631, 309464250, 116651731, 150308765, 479101482, 78590954, 941396355, 614817921, 172295188, 674994502, 684082704, 372354485, 779274102, 956967294, 794963571, 415732121, 551899308, 93635522, 921431355, 764743538, 313897309, 607784734, 404034485, 756266701, 998460435, 84741717, 835483076, 440392567, 225622155, 176934532, 583787022, 364259854, 551935066, 290477590, 248434839, 924749713, 837884499, 941817128, 206907444, 782825377, 517457968, 429432934, 740702747, 278541550, 558549768, 471876758, 702990311, 79756000, 761826837, 391757699, 80398455, 422346792, 639516951, 334475822, 251549014, 66938816, 11187158, 313616052, 469516981, 420501602, 147151604, 699898411, 609046182, 665322328, 242172632, 229245721, 941645898, 622334887, 507931115, 115816294, 790681075, 328357432, 465246030, 927808462, 643031113, 332717933, 660195845, 626738863, 295454690, 975554412, 207893138, 258079266, 24016706, 898883477, 710134509, 500297829, 310466648, 348950479, 129353021, 697003771, 863254037, 73090420, 935062900, 202013481, 512068567, 604210, 277031759, 901036713, 73212886, 671799651, 863170425, 557820128, 705665747, 661135779, 724424534, 281301772, 771725744, 122115330, 416186670, 569302435, 260468188, 345168170, 553499747, 197142048, 218458390, 898263181, 948530389, 704191001, 337791814, 683324824, 655986010, 928678867, 100061775, 5772981, 564272423, 239849799, 994090783, 432332850, 211822745, 61685693, 872848390, 555248622, 751971899, 536271666, 717672986, 37080815, 604181318, 829569464, 492750704, 249677498, 739800034, 853239812, 213702496, 490298086, 380103196, 542960389, 795707164, 842091066, 12585626, 457308493, 957782262, 300233895, 80698673, 12561003, 702963877, 498381437, 121143957, 510591773, 765108975, 195632690, 589293204, 601416134, 622678331, 155881041, 577043042, 311770283, 964942853, 324362584, 682299934, 446632144, 415586035, 659717588, 910071270, 218782120, 122088233, 295034006, 453235340, 900861622, 362054457, 639629866, 648907517, 261420333, 362499675, 641705833, 120316188, 217791636, 541932304, 142495477, 263709227, 987517919, 23334506, 959688473, 620973258, 515714209, 883303229, 88995753, 445101701, 916488025, 96605257, 844581502, 846637017, 810516513, 131602167, 314098052, 889114641, 743027059, 530856698, 914637749, 804864246, 603484608, 597167415, 81984963, 377230119, 552915424, 131540252, 539996529, 554505933, 661599379, 191350669, 483683164, 505907262, 787251102, 461968169, 72071380, 169175606, 760409542, 882207366, 485229628, 347380756, 106503105, 153182094, 593105873, 224213914, 658611858, 290212311, 717548692, 652693916, 85538525, 458689606, 259240789, 985830922, 535347856, 190614239, 563824676, 930077704, 143937895, 692689722, 678163235, 689947730, 64063679, 803403623, 136727211, 824417243, 762803953, 916287907, 126914185, 254612020, 422127023, 270880890, 505662388, 17119020, 908052238, 132404487, 3626023, 239180789, 972428709, 112468194, 320652392, 173573191, 780569648, 882287389, 59447635, 679325696, 95151182, 94919381, 492076569, 144252512, 612815461, 908491602, 396971439, 827251414, 119029066, 966782194, 518982527, 934954052, 605968826, 960527485, 936683372, 720670999, 857894976, 527175666, 963288404, 158671562, 561618090, 299734715, 481562454, 567257501, 779961035, 892729806, 588432106, 973911657, 269806007, 393916548, 813102111, 431016357, 158356351, 274209043, 301940487, 138894673, 717632210, 823625679, 846112742, 922771023, 960557148, 874856829, 272149070, 952000667, 660621214, 564044070, 882780388, 753544792, 418452354, 858648309, 931652580, 920612332, 872433741, 499396987, 228381774, 632237784, 345048058, 921103705, 373108802, 75821717, 601825390, 98985281, 560489760, 564631470, 94099991, 144182748, 822768308, 196265177, 847098130, 937033187, 597451630, 618929776, 970594126, 333059387, 470638718, 549898777, 924495511, 348222790, 367272848, 885931203, 806197457, 398602396, 503289361, 55331957, 910904448, 107368004, 15623745, 50508128, 192014095, 54604780, 329798411, 725030539, 205738152, 664098447, 683031355, 995933080, 344795307, 313666261, 31541000, 648109073, 662032848, 431519254, 108752670, 321014383, 964527093, 764467424, 892979896, 649297975, 308458104, 516295411, 60456700, 276585967, 526952944, 695281719, 161357340, 960572487, 527163985, 123116741, 223281476, 562458331, 220369399, 67600904, 444513741, 566898162, 280880576, 971239077, 847336131, 995340359, 302432164, 330416108, 44130808, 831593365, 826539195, 993591603, 449767188, 562340589, 453142101, 42784706, 844228765, 793506839, 738916275, 288211641, 725671613, 209135371, 554425524, 616858589, 335227410, 859215615, 920019803, 349957260, 998343420, 131486847, 757311505, 429401832, 489978419, 737584940, 390316798, 931821906, 6996689, 793137286, 862613639, 830945276, 836280843, 676242256, 371606094, 43500230, 381169145, 985147726, 575500403, 693039696, 15984702, 358325485, 320778670, 811700409, 658318422, 555373982, 470958711, 477667112, 682282729, 171092703, 278388508, 180259239, 909444982, 309247041, 468390596, 162434975, 692357956, 528646257, 484602602, 587809222, 394815344, 517318468, 635304252, 194279076, 599471050, 679441885, 255520079, 970745239, 727055220, 812704371, 309520845, 371139127, 682986714, 16227520, 489344814, 151368607, 91292936, 562515135, 31348998, 906273, 844868903, 152341169, 796696659, 846961972, 940521018, 595318665, 976084836, 548701481, 259228250, 236133939, 728566304, 814390262, 85813858, 904980707, 212614902, 272891499, 101380164, 712913854, 170790475, 410181758, 475469572, 677542365, 845404272, 659029990, 124551425, 575116689, 570934970, 612700173, 676409267, 510821160, 849975938, 657124607, 265684592, 779147534, 718436154, 358254617, 246793657, 579327789, 115500517, 989976174, 900966063, 691222392, 628855171, 43339127, 604246569, 381406534, 211522993, 428238726, 175826922, 296119083, 562892366, 493306341, 262463457, 499811077, 648435836, 427899314, 236028358, 428732053, 852601467, 276657068, 86376190, 149967031, 707263860, 405333385, 796079769, 597354911, 37234958, 98095999, 206073284, 995891262, 485115516, 780698787, 347658344, 171675563, 227854479, 259242527, 338336843, 192553830, 280283415, 82320891, 795335141, 735378356, 408271350, 706752749, 461559647, 191540030, 538239381, 12192891, 496916769, 312733268, 938920680, 104477802, 687512764, 544433204, 30316024, 401890139, 626295934, 991296426, 987638253, 543568682, 12442626, 207600320, 809559338, 844430303, 426101488, 934996777, 306486307, 85616646, 759123250, 521975757, 933706133, 753777798, 505182501, 906659100, 707503433, 856930581, 939062234, 863029917, 886313752, 727371490, 606438622, 774370640, 710097189, 564299735, 260731013, 356568188, 913354408, 631386034, 209770535, 920684303, 671053655, 440632704, 844422519, 769499328, 554221764, 440885426, 958029548, 358441410, 75527825, 54575928, 78708895, 752681399, 755121085, 748519172, 246137670, 207444774, 176207773, 212867745, 747996258, 842257547, 849683423, 640676843, 11686139, 540411508, 231148781, 338202820, 465695568, 623673834, 242831818, 830881418, 713650478, 479429267, 103613963, 263946072, 541019105, 679287052, 179179671, 721801101, 860841421, 84805950, 720200637, 171994745, 557048419, 578977956, 424512503, 778484366, 946376390, 27500264, 528149238, 314880024, 63352414, 335539868, 548824900, 944713419, 84088561, 383856211, 448529877, 241261798, 615495583, 797127593, 510034808, 503705755, 75162035, 947153626, 95185444, 918210545, 363104803, 454669826, 886577349, 367841669, 297219725, 35356036, 862075362, 731941, 704775895, 243375716, 213067342, 979686959, 558607951, 272382436, 378600652, 988685925, 204008334, 865774743, 418250704, 272392773, 323481712, 996683109, 697812552, 433902692, 903288084, 104558587, 321112168, 303732082, 990314794, 835282132, 552661953, 352735955, 653797660, 574124054, 654723366, 349752076, 240224891, 709805775, 760714753, 166394506, 830363476, 358259771, 916448721, 895003915, 796206482, 356611237, 615133287, 238615450, 565727131, 924413296, 813207178, 481229918, 697357703, 839079351, 525675299, 123146009, 955808302, 476491188, 144219121, 695240904, 207235667, 315236921, 34721922, 788826668, 994542736, 955629958, 771794913, 275668194, 439079363, 709737183, 865252072, 475052956, 918704735, 777286246, 902916202, 64765816, 160967129, 49950874, 276640481, 394441517, 99677126, 351889550, 884448063, 508957408, 860648207, 23601675, 208524720, 829698170, 393358738, 130222454, 470402737, 440328142, 398519478, 675039373, 223821374, 347309428, 422060174, 991522356, 880899727, 638677365, 579518745, 969341328, 148058927, 500958486, 999963918, 410922871, 691982459, 780630041, 945131798, 687263253, 384458554, 120842530, 230888638, 711926495, 303324442, 988631626, 654563708, 114844638, 93969821, 448409819, 761517366, 195464961, 48407620, 776427759, 774266391, 723130197, 950355880, 2982687, 143574408, 815036288, 811386239, 61318472, 506863576, 86151068, 614163506, 850547210, 917267020, 28803393, 189121872, 905953370, 197150099, 555890956, 341929558, 540459975, 81276559, 396777734, 596688947, 742778406, 909740087, 261727069, 338847309, 713022005, 644348341, 294823329, 566753083, 653040782, 898802876, 287285024, 702317575, 776491665, 777194953, 571645261, 845079167, 745713651, 313269057, 192430709, 94760856, 722971750, 242828629, 618745170, 169472574, 660077405, 235640345, 867572042, 301198549, 149116857, 735347503, 763946496, 418294152, 810271557, 872603862, 824493903, 901108906, 577328135, 376020843, 408810909, 599338383, 862682777, 8728889, 727175968, 220531477, 745941868, 65796373, 359767593, 781785518, 360168622, 312171420, 219643783, 798528358, 14812286, 825305745, 725041472, 714761093, 58434648, 601338683, 937035895, 464882962, 869703883, 43707952, 8937056, 592603001, 162497959, 988520173, 542435128, 555194199, 892712223, 56462513, 478885279, 975704690, 993156400, 984275839, 422392213, 685257001, 797843915, 58926598, 819665914, 693092656, 689537060, 278424864, 137941590, 64644028, 5408466, 881771639, 836028750, 814939888, 443884347, 652797066, 554110202, 65157763, 457250622, 831462500, 518296077, 185328462, 352085060, 980684797, 310049493, 886964351, 318742301, 807840456, 570224376, 390363398, 260568398, 559919706, 531739221, 630963382, 328222664, 557804988, 547682183, 71922935, 926652083, 895352362, 445827854, 664172757, 163233192, 433244554, 356763487, 982952696, 702860699, 328824295, 934231705, 890169681, 510710013, 939498314, 358943254, 490449670, 289143132, 83548911, 443492667, 44906453, 447271988, 981764825, 80690636, 854990132, 38106353, 11375929, 284178369, 754921908, 497835118, 138127444, 201799388, 193850466, 183803884, 698180591, 903145574, 178814249, 608234816, 252288486, 994330207, 426541558, 122816716, 453058621, 950460539, 973585550, 580886454, 684971774, 291217029, 528236241, 876575454, 25455362, 534122438, 19355622, 642698024, 825085633, 506003615, 562708885, 236954619, 122466354, 938601453, 218228716, 93293275, 527258642, 928689371, 309115137, 828894006, 468801067, 441514281, 932537282, 310012667, 582143679, 59818370, 617754277, 686251858, 728044223, 269602267, 196329691, 840261936, 21318384, 776750742, 756560819, 757695892, 635773110, 967122697, 508409732, 268141258, 756667312, 3920831, 814985879, 523927750, 831713889, 275374169, 129149043, 222173344, 359788591, 552589470, 444672014, 191201847, 196476404, 219787441, 802856954, 609621459, 789178470, 121693374, 493893616, 691014801, 405190520, 607622402, 62045861, 460079534, 315761116, 725302952, 311195818, 558305049, 181289950, 329771730, 703704786, 771846821, 212537185, 793515846, 604993578, 832992094, 469313579, 712546122, 270720120, 4932316, 763985785, 652450170, 253013054, 291268957, 99562699, 128076152, 525987238, 201878997, 853203585, 279433480, 264004420, 572228472, 19506898, 772597892, 684871925, 631839042, 528584449, 139384521, 488202488, 852883278, 979558729, 963841892, 726641899, 781979454, 961792840, 327073714, 274767041, 594629924, 847124032, 883350573, 862218167, 962188041, 705495839, 849053232, 921884202, 738595896, 366278145, 150695077, 137088372, 202562370, 265265321, 327266745, 713370898, 446534476, 396535732, 465642586, 401925024, 340356168, 896048090, 830504383, 47417508, 16643735, 65729671, 34011328, 223789087, 480559230, 941886255, 108986595, 761643614, 593907640, 979859767, 989649640, 15160314, 519332478, 432133546, 471305254, 430926391, 722568087, 319033459, 448659653, 586828003, 115772386, 707599793, 332030974, 764054410, 435072811, 541760009, 163567128, 613891895, 245907874, 456436930, 934734175, 378902753, 409709994, 960075346, 221120301, 50164028, 366273085, 845049643, 917191172, 926161132, 249180285, 739290219, 173057459, 700414788, 507786825, 148815917, 534177894, 622010533, 320813396, 385489427, 895813885, 747051405, 102499978, 43051776, 584421225, 620526347, 206910142, 712516289, 743779560, 651682078, 341349426, 790638186, 865245107, 2840664, 628119815, 399193198, 141281273, 745857705, 612079866, 511537477, 633184512, 661219418, 481735969, 871151257, 490636301, 396794594, 772790802, 13450920, 386689930, 838081567, 821835135, 987811032, 929639411, 796706008, 435474755, 135251038, 465064400, 621547954, 493565773, 763476291, 401815261, 126011417, 73302427, 816806265, 572962607, 835635581, 287051485, 182648075, 442809843, 719762333, 796228337, 430440004, 225593188, 433720405, 392379047, 568946136, 307391272, 451644729, 266271913, 703559019, 779728561, 736252799, 452470114, 941630711, 327386799, 414069762, 90235672, 669929456, 700481801, 6916393, 889548888, 353944264, 20938327, 117684594, 729436880, 835870713, 205072830, 189545412, 523689325, 651681983, 667675016, 721133526, 86721018, 589544557, 282824253, 330022764, 516520596, 504493904, 719154829, 516955688, 396364598, 110390279, 551685449, 278632593, 84751882, 196167921, 604628413, 57280517, 339530352, 689572382, 173207111, 735409845, 117089959, 976707059, 624307366, 73067694, 846852728, 918196154, 680418340, 937653140, 190258068, 648527222, 219773510, 141015109, 698505606, 216804792, 468425730, 764729109, 829345825, 218453978, 443477190, 665582020, 194955139, 515653292, 978254637, 948414459, 824242871, 142275718, 77968795, 688388829, 2456810, 451986892, 775648997, 312351185, 540977862, 179609441, 407554862, 31065634, 473440546, 894957865, 328585524, 79284787, 147125531, 797206681, 368482167, 932151350, 140966209, 897365678, 122479858, 940352036, 953489863, 793584690, 163961016, 918620001, 892236585, 624122022, 993760348, 782726792, 433948744, 710907547, 332045656, 857931357, 516565629, 654847571, 186143507, 782933563, 85410362, 580652260, 582107919, 813662847, 747279679, 832884859, 857538431, 131672177, 63425778, 440004994, 233800146, 989776273, 236302223, 522138042, 956096534, 354439849, 743775692, 421944266, 470679620, 254833326, 584222188, 162319831, 654284943, 677805259, 820072884, 174976009, 860824140, 230533500, 791825766, 557360775, 40150151, 667949758, 907440038, 45445498, 79229875, 107150741, 554652562, 562785953, 670180429, 980360032, 209214023, 756032207, 279996706, 176505062, 634263732, 94757442, 588426530, 461066261, 433720029, 910886788, 263953150, 33312439, 426844228, 169101354, 868628853, 915559174, 60995544, 168506467, 590404854, 409244369, 436666389, 451474580, 707653892, 275772296, 119435654, 724127065, 206188548, 857983058, 633069555, 629040560, 829150626, 501441386, 793880309, 942004167, 601393498, 3146764, 410927210, 445197891, 430962942, 858781900, 621543734, 919121447, 388792686, 205220284, 653817142, 297190923, 994322579, 230286710, 307664788, 687135549, 654749389, 902681463, 301471753, 126456415, 2453020, 535946189, 330126020, 119436478, 571657176, 652753859, 861265734, 12932263, 13691460, 396987803, 736163506, 953736168, 913680911, 62271399, 325083772, 306445414, 347597264, 777471242, 398964280, 577097972, 416759943, 201346610, 255629521, 441603379, 833778157, 787796312, 823057045, 421626948, 536762612, 545269902, 940183238, 592729066, 395294039, 664415725, 723208300, 487074130, 860933591, 334864662, 342332710, 842240715, 11203273, 628672295, 375902886, 202079247, 765414472, 693233741, 545436729, 868291206, 641710246, 979030983, 912911276, 898336649, 737923326, 565625954, 658753285, 806402483, 231733626, 988483078, 735123532, 847308869, 198624488, 737408051, 740371085, 786314807, 421969029, 461746164, 84258280, 750011733, 527524495, 504986663, 678276182, 687925749, 423234980, 330729597, 291909280, 443342466, 879326114, 792628579, 895152706, 196620524, 194768400, 705638170, 806222930, 366476108, 339187042, 946211698, 462752673, 565752462, 718688888, 835966975, 3240383, 124235426, 350013877, 449692305, 570906683, 502078310, 675662376, 311922441, 654018859, 859673255, 265247960, 870751188, 498170740, 567009605, 288644727, 46929834, 470601829, 554946002, 120101670, 265999385, 319154884, 828002480, 568156544, 522212023, 455618985, 915100601, 182191291, 445867566, 670286574, 459114182, 814970609, 16033654, 411314438, 310138660, 721057593, 767737297, 564238073, 914668013, 82295977, 639672573, 800235241, 184084720, 897369659, 467497414, 488762673, 790032878, 237118469, 727806070, 362738582, 584561681, 496888805, 862284600, 498129068, 274397686, 567450711, 270400062, 955891908, 879143579, 950792749, 469683001, 365844894, 757231162, 671746901, 287844891, 16868526, 375087880, 687045518, 123602737, 153432665, 755034354, 270004322, 261242840, 602196619, 264871651, 504940209, 56718247, 408312123, 76290661, 54433746, 104271876, 857252720, 406744804, 131553839, 721100010, 891330188, 531702917, 959784442, 64814415, 575666486, 184245352, 279799482, 513036509, 301416360, 717698400, 473141891, 468016841, 794043367, 762103960, 53050290, 83313845, 652317300, 844476083, 78354990, 942648140, 443598163, 390236185, 882840369, 110897849, 257872649, 147364581, 257647792, 7326540, 753568972, 407120353, 609033938, 606797359, 992237404, 157115583, 552714277, 82414024, 350525810, 512994332, 747500272, 702956549, 917608755, 418527664, 603790107, 841214909, 237163107, 804285765, 768228252, 811395313, 933670247, 73255559, 347006520, 829446984, 251286419, 523295986, 648768780, 805873091, 874900463, 269662088, 707804781, 444477577, 658425560, 810895990, 511493336, 738202989, 813753998, 390040819, 867555624, 454278971, 341212428, 412980381, 100479028, 437637114, 852004455, 337642974, 679666123, 434427181, 915961089, 5953140, 984920187, 860348496, 668971911, 912103558, 190581027, 21709604, 775265902, 216770800, 254810125, 619678390, 334349514, 130968653, 288163360, 511863043, 845589329, 356879126, 312524222, 332328451, 844530320, 367124078, 783876099, 748872624, 423954894, 170747992, 720815098, 634112066, 252168945, 367578867, 331482196, 546751990, 384724275, 814686802, 451016386, 278672339, 742484856, 166136573, 281613644, 785999441, 818033416, 242811058, 461526221, 147435207, 410837933, 758678365, 391352478, 198848210, 780309569, 94519153, 351122343, 455477973, 967842207, 311465223, 318075362, 966264088, 181833523, 585640999, 599574303, 716546911, 355623877, 201046818, 58897650, 812157604, 945248637, 290763865, 271626522, 582176809, 445231031, 953330595, 938672449, 617786790, 29860300, 873007869, 908247748, 387913342, 646935264, 391689310, 54363467, 295426468, 619799355, 99413327, 145938850, 966964547, 891832743, 98753486, 978706387, 841807149, 409654430, 902638336, 1153071, 856340174, 68507199, 66559684, 188531222, 170716526, 229287690, 114967003, 202840309, 614481200, 624103813, 678953752, 128954081, 215960563, 699616064, 729248500, 54479270, 900242078, 57339131, 701535672, 374991873, 157521105, 763338124, 666411084, 686198389, 989947590, 145191136, 255337672, 109608743, 73845974, 137695291, 664793929, 476547228, 1783258, 787855732, 626231003, 407512729, 747301634, 951105752, 257769292, 62112344, 138807955, 335987272, 342272230, 190591669, 782258573, 82923459, 670143550, 996365753, 320140920, 263619734, 385089510, 722282181, 856728544, 890625413, 551401777, 100146795, 556348906, 13516096, 993667811, 758927322, 930622447, 518095076, 193206838, 418728088, 690485183, 856632870, 697206303, 88489289, 539611771, 121160287, 506094813, 476268254, 336031087, 363718884, 124045401, 140474015, 213121469, 838122195, 859749887, 442355737, 80214061, 808006183, 251841025, 332612411, 190416854, 622498317, 48913982, 124911909, 937567735, 567811252, 277164984, 669068877, 743352563, 342319911, 658188976, 721212429, 196618779, 7884080, 705358934, 276282444, 442769525, 602168022, 93127850, 881126778, 387445345, 993447951, 819142562, 25718028, 256044446, 377177071, 752544515, 658469800, 541123492, 706841569, 382553144, 498510894, 798619806, 737758127, 303524696, 480053139, 568879970, 41186026, 322222344, 83062947, 519729386, 887640655, 416326044, 745799090, 129619728, 948857222, 116785763, 717097244, 499133691, 890691237, 82450265, 614892448, 398704678, 646380487, 773864487, 22076797, 616916245, 398421500, 291707053, 247574743, 376703364, 778060507, 756647642, 473339235, 415140564, 967180969, 166819161, 81680075, 750385857, 7062926, 454500607, 63164336, 828822209, 158225277, 935923014, 977855147, 351211848, 878323803, 555739086, 570137610, 866677692, 135173532, 116370528, 300818722, 262245096, 445584035, 66615060, 563475099, 11905483, 697558009, 916381988, 285287521, 796610537, 76933667, 206837046, 700540628, 189889725, 765446413, 353322915, 446841879, 760735783, 121188667, 809349469, 163712700, 214436961, 364706684, 719644966, 428067693, 692317204, 941492906, 237049342, 376949077, 916156159, 124715817, 463147106, 167568080, 451059316, 317194022, 559112678, 460745356, 512850206, 984593315, 680909307, 703685207, 678878170, 720286052, 797897514, 723888904, 933943432, 858359674, 673735053, 976692728, 344998443, 919554016, 341761370, 497599321, 127355792, 252846472, 216612843, 156365637, 508146926, 490374668, 766792762, 371378521, 613413717, 936823466, 631683508, 644444472, 373811915, 109659029, 163342641, 534292823, 482802152, 394408912, 326349679, 313097078, 525070101, 72969907, 627747731, 359981445, 690720285, 775731920, 615759398, 199042095, 397086507, 106423047, 253808934, 785269700, 662079587, 172345445, 644326993, 278325367, 861587656, 543604858, 234984275, 611449258, 908181930, 177599370, 933596489, 126955793, 121962442, 299925016, 184881421, 100127388, 207157590, 999205893, 801566117, 937705829, 211849035, 262466264, 972129217, 963135630, 706170110, 925976646, 43196190, 322546067, 46635790, 516109981, 190747016, 17308310, 916333110, 763257034, 668198620, 806545658, 362730298, 763059032, 813288869, 393318017, 660171797, 773287065, 490808120, 26518979, 464072101, 294464147, 415360527, 11760449, 852613904, 956098538, 785968704, 252864426, 559607617, 8907736, 386965250, 544079325, 101963024, 665276461, 967453015, 941804315, 517302002, 293480160, 215874832, 588421604, 62655679, 658144039, 862321775, 6947628, 91110779, 57592871, 372388800, 325308606, 570679376, 778046106, 596164658, 415761963, 540839263, 531200856, 922649638, 908559386, 948929522, 54619179, 444880709, 571501352, 378622837, 655684514, 85770634, 550091071, 214085439, 245643709, 303610931, 792257900, 534442610, 475484063, 504870421, 903674421, 184000839, 892491675, 943343368, 399920296, 782162708, 726233804, 474849991, 540433383, 313202405, 964055313, 821342633, 980502905, 29234411, 440860218, 393501379, 347366045, 454719306, 140541386, 127408482, 37798637, 919566294, 807357157, 581141539, 317282273, 441842485, 701690964, 628831613, 63456000, 303044548, 649267816, 455134679, 155488800, 837816721, 620372399, 114897336, 85708371, 595140194, 899079795, 520650273, 450090331, 669657893, 985788477, 487365212, 276185273, 443195010, 783664623, 381228519, 668047198, 100074298, 630768539, 276777080, 687310737, 729978611, 908665928, 809231264, 697352298, 187237226, 466182983, 65180147, 638111204, 752532563, 173203260, 982463095, 530616881, 740920381, 805638744, 155875122, 120179403, 534801129, 379523326, 613108419, 179913324, 152044771, 400923517, 418721357, 950969925, 861932492, 890203515, 346408303, 81122048, 669751467, 862143584, 591374198, 996102927, 859191683, 429835911, 521918275, 652431663, 97777761, 980245810, 508269212, 245470740, 386098970, 16139196, 34525828, 915259063, 386925581, 543705997, 352321975, 813339597, 35445941, 676123787, 793906432, 331577809, 358868621, 526498740, 306933340, 661854998, 360406334, 644318431, 603807489, 282250739, 83122763, 275293198, 679555232, 776524233, 345213436, 968567939, 431843473, 644953085, 849094136, 497492142, 226596528, 791644475, 395449914, 272309147, 289557792, 165405216, 663597906, 595545227, 702900867, 347367591, 462460280, 66814252, 809491373, 571586088, 332942605, 447032037, 958727247, 371679978, 672262086, 972357170, 32199640, 749763841, 775623382, 119740179, 930403942, 440620798, 983970061, 243009298, 226666130, 481647448, 635554036, 103054593, 907077205, 551800072, 124970601, 97869518, 537557186, 356449468, 884004729, 239604997, 935183556, 715123145, 94088555, 583801370, 479118988, 335355627, 892492899, 449548180, 262649305, 169908472, 329389241, 535710096, 74946083, 156857305, 717634052, 431191593, 68077649, 706829295, 297772618, 696966025, 302611013, 30774269, 238417621, 655986707, 215602529, 495472219, 12802072, 249584884, 866427691, 171126526, 291180092, 228246488, 436858292, 284180384, 455464838, 598256019, 931845488, 135945297, 32470679, 537137212, 439608069, 426921484, 521841148, 321833755, 725596330, 188638951, 391897864, 415605795, 739188673, 935515740, 247464691, 513201166, 209671183, 865429977, 883764260, 415240150, 55566219, 547312289, 163072077, 80730443, 775312148, 863410930, 679639486, 769647158, 301742606, 207211225, 905900635, 245246120, 821772307, 6610940, 485689198, 172227516, 391124104, 199939255, 429277091, 371250638, 291772172, 767822454, 540734041, 922545017, 337464612, 796433986, 429425581, 411011973, 377034755, 532009893, 994079877, 797604420, 847678630, 21423635, 736353712, 945328351, 947409851, 600208666, 334177695, 295585987, 181093297, 762516732, 850700984, 639780744, 783552033, 884133745, 405517391, 629530421, 777735679, 619946603, 620614008, 966541222, 117707835, 976679868, 722998505, 882377474, 177038741, 960219145, 638787825, 349553235, 93240072, 872106483, 505633305, 952850099, 110105846, 414748771, 703357395, 288106701, 38215727, 182732392, 977540815, 487877864, 522170107, 682474885, 694614609, 253915741, 803953228, 474315443, 590463550, 909124895, 550228378, 752395962, 211715435, 380135754, 236800608, 871148932, 604406947, 733557743, 275879784, 896969149, 84007655, 386765431, 361817417, 831147251, 312665455, 220529821, 43136302, 252113433, 784494312, 444000451, 559021303, 946758763, 612065340, 130572861, 96308662, 275248623, 48280223, 780850648, 753158718, 714437109, 704727767, 372498375, 902173157, 423729095, 34722725, 337765136, 161641438, 682599920, 127202196, 791388539, 411784474, 208400634, 18069528, 350530374, 781461039, 352668031, 918061109, 926364803, 896287397, 548592703, 326649290, 619565135, 922113, 344615183, 158529343, 168245471, 627020267, 140492447, 990165625, 298363436, 465192683, 782225170, 222394351, 730782046, 134537882, 58976863, 106752158, 674174917, 89579623, 426325076, 205322142, 119851755, 477121728, 107107409, 301107037, 16165064, 513330816, 71459727, 358122268, 567893620, 132332682, 944514208, 135518934, 560627896, 435068558, 730839957, 192713746, 758855800, 220509333, 828208608, 540327895, 504685023, 844258839, 337171893, 980240055, 736579024, 522503556, 532209555, 90966617, 796987155, 92859010, 904679764, 535751438, 245845533, 354605705, 960521754, 557757033, 91274642, 770976576, 684112498, 976035429, 218122130, 73448295, 795359907, 599293817, 856333110, 749210502, 891851348, 286962521, 899894877, 346457617, 748287923, 597114610, 723522463, 731149017, 761611412, 169238799, 398514297, 211664548, 691030655, 91486741, 696985365, 584038917, 776619519, 687678017, 885740174, 125985454, 634942558, 633413228, 707158203, 842800659, 438112658, 892640696, 286760954, 8505067, 205513179, 286490416, 338145998, 6655993, 414947996, 284784062, 861681153, 268008649, 106107968, 635302965, 74130853, 425481365, 429720783, 273851272, 302308433, 174113002, 435619978, 532301892, 594428930, 768711841, 936824935, 253067087, 595697106, 331006723, 824367896, 712035461, 550033034, 888528313, 665474571, 661652612, 961126425, 964060542, 285738237, 963016757, 555531458, 445508186, 529085582, 242813591, 856584154, 621999481, 560795268, 638892856, 27943021, 931060752, 903692888, 562683080, 527776211, 91919541, 906392149, 334050156, 565942356, 63149767, 833103355, 301957303, 306816218, 89272697, 645295297, 19354029, 776777303, 328027236, 968355910, 993315484, 505948951, 884938690, 926255254, 859755266, 439077720, 996071448, 9615739, 612767024, 392700523, 629916658, 237651498, 138107874, 282174809, 389803291, 102820517, 350145131, 890089446, 238570846, 426865287, 172247807, 631844405, 68736494, 850813220, 770436050, 889754281, 672538192, 715821264, 261596592, 375707080, 525145473, 803696416, 530241722, 496735112, 140616805, 526506915, 862181158, 309927710, 309865677, 680976363, 122439580, 417313026, 877248980, 2413514, 515079478, 541083378, 936166559, 982558755, 486392206, 793179952, 762010035, 288599512, 813425228, 188224314, 766285230, 830767849, 926584222, 196431903, 929665016, 292884968, 136539033, 91196680, 454678944, 17166809, 504206140, 555340576, 507907162, 180195184, 152487428, 330201259, 258041225, 584842209, 30721170, 780484279, 53261920, 401685057, 671060529, 351774093, 216321240, 972799512, 842364357, 280681595, 254812598, 999361968, 826963358, 752608966, 360948334, 686902252, 752230499, 921985794, 378887599, 136762058, 335390407, 63737562, 151520154, 226162578, 256377919, 991646195, 916331605, 574736089, 25223521, 982730198, 579692686, 889439254, 594867089, 403630531, 475345, 232765927, 270891484, 610254666, 242431914, 253747350, 656851445, 277296976, 419320973, 204626684, 22622207, 603826526, 367979874, 833788628, 535579749, 896731608, 108011360, 923289058, 174589347, 952029700, 55817456, 61688274, 235236642, 105069217, 712769193, 556892704, 19205846, 866197432, 771382731, 220919016, 679316908, 385167392, 882080631, 591624903, 190580244, 583767819, 349607305, 738763502, 943434737, 200811438, 611435138, 844452020, 552595573, 970323055, 296219206, 535557017, 860981247, 249053486, 497961406, 351537344, 466182424, 349551855, 300562891, 728516471, 731179267, 120475116, 786912483, 183398803, 228465072, 701030238, 464553323, 764689826, 460524792, 496020173, 504709289, 10515697, 836519890, 130593721, 625889954, 184396700, 454264319, 800180028, 351712102, 906314593, 509790295, 878310086, 52199887, 764436337, 51534959, 50040595, 572512475, 356288641, 874359877, 596772613, 545683577, 39086426, 212462269, 881826165, 268191213, 992033150, 959732346, 546492129, 532121453, 588588336, 715724220, 170152294, 710174125, 400356335, 764686294, 705461137, 67611545, 21912932, 45220117, 649050133, 240154848, 974474448, 987072379, 398420942, 479099623, 627446160, 316971663, 506111186, 979809168, 633618956, 845811606, 105389280, 213119388, 248313634, 27234139, 976683346, 335187773, 706869141, 437474862, 110107397, 3644420, 730043910, 67150468, 999820480, 812194053, 28513491, 189179559, 391757941, 87565923, 101911704, 547754451, 111194561, 233851201, 897844537, 896511600, 820489051, 181417696, 533020342, 695796313, 209653137, 522652140, 406745037, 24491327, 886426030, 758718155, 118838029, 83128939, 516206073, 961051416, 659559426, 910820139, 73884938, 591766118, 17294435, 651927917, 913606219, 919993243, 738613463, 584949349, 117530848, 214619357, 751470713, 232890587, 321751509, 361160692, 222054934, 929567774, 307987314, 553986206, 531356571, 854560535, 432057908, 547697156, 950014431, 186331706, 365757881, 828389421, 233884514, 199857442, 957092617, 783601313, 892597525, 233396935, 961410311, 772357670, 50248887, 149505708, 998401848, 630147299, 607718935, 375835806, 716219155, 521439598, 251138999, 671118823, 122812912, 637659255, 639208950, 70683951, 376095042, 858063904, 593837071, 321175753, 727140714, 823666600, 917887174, 448708029, 379874611, 672231010, 81992376, 674064258, 112150331, 228601160, 998958946, 18394413, 654991051, 714074660, 958095989, 943666114, 100563996, 66503823, 316448019, 830437256, 224349484, 940959742, 324931889, 175971039, 4371886, 207337823, 907667704, 499519992, 551274946, 937081703, 391548351, 409242045, 93327366, 114629904, 184324210, 188275180, 982932982, 524240361, 827613841, 385402018, 896360151, 452568063, 463199029, 459381862, 20925520, 277521378, 63458651, 979796526, 507419699, 962005852, 979209197, 43605010, 30119952, 712000640, 101976744, 841546008, 830007386, 978675753, 609477611, 404604556, 891343111, 729466075, 611336132, 686247718, 850638920, 600491953, 909998568, 802857971, 318261567, 444862566, 717253059, 933092225, 859272259, 854652287, 840924310, 528975134, 367938881, 871956205, 997053558, 481212059, 468565982, 810743934, 363234805, 700754287, 135667289, 793530225, 299094016, 397613200, 288264089, 787128168, 857858874, 690270883, 508047980, 931977419, 735579109, 283165592, 46456315, 3132560, 324620371, 747798897, 465818507, 967082277, 202885984, 198516887, 998151446, 470008419, 180236065, 794687816, 157569496, 524038631, 825265907, 716082061, 906279789, 695925568, 753963253, 491557054, 178878155, 208308196, 40957288, 336602182, 218069286, 218704848, 985814422, 16351665, 729399912, 140930044, 571953277, 578486206, 487344635, 522547319, 186903131, 637807769, 246413727, 236483335, 623558477, 572668891, 246232009, 560461531, 773804536, 612413759, 40048946, 683677971, 12944377, 462703140, 301919985, 482101034, 122659492, 741594185, 365220716, 377161399, 70127640, 467705480, 580131866, 639266378, 533364416, 437338376, 334533602, 645622966, 546171136, 708268308, 727550023, 527044385, 240539202, 357779901, 728765910, 708923751, 966495049, 475764101, 958897205, 459827510, 402373957, 220540186, 224944578, 611196734, 991291457, 896417304, 103071403, 344162127, 932778760, 931585373, 847792772, 415125828, 398202436, 782752066, 455963471, 670895926, 515539507, 488580828, 891678741, 361794187, 790712426, 791508393, 796967927, 10175204, 937639302, 794464517, 21853710, 997512745, 315514454, 261617685, 242605997, 243233007, 521288744, 715823418, 401225042, 303350873, 819855980, 345440658, 480386824, 624867266, 35597519, 676925252, 951447840, 680516405, 216803173, 523432812, 364481635, 813270945, 516721205, 530723249, 881480830, 874960074, 170595021, 531226408, 175626880, 884003158, 966817430, 460027226, 99062056, 788539880, 981798345, 376199652, 471205876, 456564853, 850086463, 880547318, 288641470, 92210339, 115567198, 912237741, 375633234, 745054455, 500805399, 589317328, 651825066, 851362669, 843433747, 644660740, 932954960, 987658246, 66931800, 405168042, 832161882, 567037491, 416739010, 210612814, 5488643, 631548861, 871921720, 202056445, 155606033, 792845927, 71428010, 447249568, 616733958, 907759479, 87377293, 125390521, 845329941, 116461410, 930830117, 820026081, 45942551, 683881654, 458269946, 18339583, 460653424, 310434566, 305349189, 632229199, 213619744, 689353448, 831380599, 974269606, 876654958, 849086790, 975427834, 934683097, 924913275, 290296204, 846175338, 564017989, 111454019, 122294000, 795073630, 782033152, 464630100, 164121325, 429393580, 137477693, 988120322, 976926535, 621774836, 87829670, 454886963, 82340185, 124103355, 206469393, 548267995, 500111283, 306738910, 949490943, 94981737, 732930037, 569246147, 778128495, 79294401, 152961881, 449095637, 516203166, 41840362, 126989496, 341716227, 729671851, 685277085, 561706208, 452316610, 279516267, 861337265, 134921073, 249240902, 572366297, 783645886, 76024265, 6338799, 235464204, 723257391, 479121522, 206440779, 43016785, 68368175, 958690097, 9407405, 611260155, 758721698, 236580660, 935195478, 256574840, 432592111, 824373147, 265139216, 32919762, 98855184, 517295113, 408089998, 622233961, 101639192, 397027323, 561994320, 706224985, 696878161, 178940892, 263947122, 554387715, 40526252, 355594371, 249592922, 836677576, 723051034, 703894124, 757646318, 566681877, 188401442, 498767470, 678366862, 554304632, 270608075, 388052374, 365605076, 727759334, 830733921, 822158894, 898169974, 4487718, 418204856, 31923644, 381471865, 868534303, 501502102, 679329833, 907117186, 836583885, 264273186, 482762083, 336936988, 714733726, 352854725, 12691995, 906670067, 529448947, 860883832, 652383909, 490353666, 672636479, 784310555, 200611707, 765259113, 184431056, 971737853, 699010980, 976814227, 828977596, 781570717, 376497701, 630185714, 424941478, 338140830, 260151229, 692227017, 639014088, 831446131, 731596179, 625356295, 475042221, 643649731, 647940811, 245222645, 143335678, 364945250, 419464863, 764867478, 187046712, 832926349, 82522674, 496488464, 5238099, 553521676, 14712954, 73912939, 630481010, 770575884, 995333409, 307218294, 200195189, 812376949, 991350806, 139930358, 233285784, 707142008, 805276253, 458856822, 389568963, 450421817, 514187938, 818016037, 751711689, 137288879, 993417031, 399693497, 404036146, 199573767, 306997620, 345162926, 792856625, 130170064, 104982155, 845383444, 168118351, 536194824, 393369481, 302758014, 154683110, 769828956, 256650450, 414631908, 517102394, 287842204, 119437546, 858079710, 67828374, 686772641, 843238412, 84745511, 161330952, 109004139, 676353564, 520904125, 419366066, 897264761, 15980106, 998054820, 886900596, 315407350, 233760075, 101508753, 630163861, 805355126, 423411200, 440748340, 253832229, 708029489, 784687002, 133357296, 901669567, 947745821, 177496276, 125603064, 197746381, 45213824, 891939579, 732539904, 489992365, 853395291, 95733830, 743240679, 986724674, 443885890, 761395711, 680194964, 998188878, 21009936, 684956502, 650338902, 985632780, 202675882, 531971115, 297171435, 280561811, 505236594, 649712603, 566683160, 25521969, 620099521, 381646330, 586099064, 31849734, 957857745, 552665971, 436781164, 245155417, 773392751, 156609944, 986981415, 625742619, 196820311, 637725508, 427160385, 363146009, 158070463, 823163270, 788222478, 692259443, 303440806, 142208920, 558365091, 992742018, 880652097, 498346015, 345557189, 914965919, 792370070, 508201639, 317044557, 739267790, 542499047, 153060151, 490176017, 438057334, 985703535, 587744415, 497472165, 682953303, 592137514, 115688142, 331890291, 76379579, 142610982, 971182755, 520640354, 274637137, 404454791, 972490529, 324133462, 890824610, 116837943, 149291607, 998797142, 188572371, 87130679, 158957328, 763282128, 580091503, 224919392, 708040362, 550774371, 779269663, 654561889, 854805267, 583881259, 235516641, 270080538, 330957349, 969180359, 8152681, 802535529, 153793254, 785530966, 65385953, 729217324, 600162134, 616044825, 778444145, 647196951, 723131268, 700481567, 488010948, 564695936, 52657683, 876506768, 897700227, 883053546, 897079576, 9408466, 109763170, 472845488, 929329590, 132901163, 953472342, 550134112, 302551777, 19452577, 164555235, 147917700, 749795953, 822435067, 458089631, 852176101, 932665817, 658103345, 442754123, 421152341, 558353395, 631071928, 982194550, 887894312, 623417613, 691071143, 695325394, 831282950, 508006677, 776341478, 314360334, 312449652, 68456795, 98412963, 615954638, 350710263, 797387371, 576589992, 149510361, 941165100, 804036623, 516668613, 778996451, 639421046, 938587407, 515809086, 925219101, 372307490, 859819470, 221690623, 705366373, 33014146, 140336350, 551103604, 838985583, 912290588, 897738408, 276994102, 25405120, 306190921, 642932942, 891402265, 245167442, 726674553, 389020213, 167823740, 267418430, 464595533, 774179364, 626332560, 88401229, 533383307, 415021728, 409804156, 757822276, 615355708, 912323480, 422271545, 972880091, 132238177, 224470154, 15591488, 359790402, 960941536, 204093008, 697466463, 450777254, 348855404, 282260983, 354842017, 715204520, 738485629, 243324091, 438527890, 380266837, 701837012, 35557794, 991308549, 320156007, 86123973, 40271642, 178717464, 506853262, 727951651, 968750911, 253734283, 616030240, 615920270, 983067730, 342509365, 192095048, 80668951, 929920579, 159410443, 814884683, 975711779, 645361989, 246280081, 282385768, 281034920, 36607792, 594629222, 248568339, 302574516, 95389477, 318671910, 617516781, 396754619, 758880290, 484308510, 567168142, 971360350, 355479579, 347419022, 321526069, 779001773, 682253099, 853230275, 369147682, 657862571, 928147302, 579209623, 396952417, 532035625, 752816565, 977187428, 358600877, 316195777, 467777647, 775993359, 774207478, 411122601, 85250061, 903743027, 20331610, 478536641, 560010869, 490690999, 155002322, 858558426, 598672464, 141286205, 843741300, 882637314, 430380354, 392024855, 272202212, 703519489, 485347874, 586634827, 45752588, 914193201, 590188565, 459834903, 960942682, 989355552, 786778429, 305922335, 168415801, 526415462, 971721636, 568212456, 231170266, 309383179, 505912442, 659763964, 486890852, 768545711, 171555552, 416994616, 969711318, 607416721, 882006205, 595179259, 816453922, 615742702, 731274368, 574608857, 338660058, 81100906, 742966939, 34765536, 859509732, 90068119, 501753228, 318488451, 801578805, 174432386, 567917350, 243202020, 231176373, 548413039, 817360560, 279009913, 589831645, 373021596, 517485006, 434627343, 118335877, 590287915, 450223958, 690820349, 873554052, 398989254, 523382893, 576462218, 432646272, 265085103, 185125669, 383980933, 420938698, 580759596, 417158253, 109466298, 592295321, 764705163, 229292657, 932355521, 562523215, 848079301, 36476418, 16233196, 942828160, 865045116, 937307799, 110796275, 693630739, 281526377, 748849164, 394103016, 940862735, 308961309, 712611114, 306618125, 241549342, 696029649, 273629473, 196835451, 271248153, 229657587, 942654211, 593425874, 561386241, 696024304, 963792420, 438288206, 427392649, 150190487, 667103568, 979614435, 109498848, 206355611, 465816810, 874587248, 35491373, 418675725, 886354936, 458868386, 535099477, 170625067, 939477532, 315521682, 71575609, 133113857, 759410295, 473248739, 43594986, 729667075, 168268122, 410133503, 943009589, 662880406, 592176876, 767174269, 76515827, 663054559, 787384173, 867751670, 459249214, 947756152, 851188640, 749377059, 788885957, 77037603, 75522393, 662485904, 339018184, 761551957, 996513242, 786530861, 884508217, 640574612, 132870763, 15528630, 813962264, 583105577, 98350569, 746464267, 223167306, 384633930, 467507935, 597669478, 389148629, 476639696, 847132030, 673779095, 280754272, 503342838, 697871388, 867329756, 132080206, 376249417, 266296464, 324461206, 828523866, 915170012, 182356181, 464444371, 16043229, 322173816, 538746862, 431203308, 43584620, 522190595, 984768231, 715898615, 706781193, 455843844, 597273630, 886430252, 259946315, 253341519, 872625352, 876455962, 979061505, 534738468, 26685589, 609874084, 54559675, 960526090, 290378932, 509405232, 397131465, 875446774, 305140402, 59121901, 248115374, 295838713, 488947652, 568183412, 449543497, 355695396, 990185746, 426610753, 420390561, 13396679, 362055407, 589661973, 536614129, 139921360, 814238372, 375624192, 474551730, 611456899, 24495009, 617569262, 801195633, 842950366, 93970384, 961713012, 21096224, 395086584, 973544796, 584541820, 625296180, 305852411, 71032108, 46575177, 424447385, 322376187, 961093531, 600846844, 378814698, 857000594, 766585452, 611212510, 780110829, 664783219, 226652252, 767806239, 124713593, 739444150, 808972547, 579938416, 595074016, 748148550, 22039283, 295783046, 125382145, 896434060, 51624842, 129792231, 368670464, 180691129, 383084459, 541674021, 60190918, 789092616, 589774624, 42035095, 671894424, 306853632, 11160822, 689737085, 310080062, 191804666, 993933054, 494070971, 785242432, 240518210, 360110215, 775990165, 718729927, 329200431, 495551588, 266593450, 385242600, 621075290, 951114803, 782118196, 818004287, 30347908, 649895892, 47991574, 95933372, 300977946, 532814112, 783790774, 641698254, 64475494, 964441150, 66595053, 564380595, 22509330, 836179315, 139089021, 615769186, 750355930, 92203070, 822753081, 782077332, 657406287, 921568091, 404504268, 408389042, 164371935, 525347354, 880396637, 136945716, 47609002, 24232886, 10789996, 713786817, 624245766, 345317680, 209535393, 39934816, 681628963, 746206747, 234739653, 530944157, 983658446, 664270646, 29413081, 330962861, 620617754, 476466202, 684098654, 452715513, 119212656, 441224360, 332367873, 376738139, 526743735, 235472634, 912942579, 153034268, 940895281, 533087651, 810168434, 34111374, 425257580, 876719764, 805762488, 339466822, 919504597, 38865933, 675804964, 808101540, 595147720, 602431507, 112519037, 756502473, 660223765, 593635689, 312890159, 625128449, 545463184, 315775553, 425048676, 104349983, 354155617, 871769917, 475143102, 206058822, 770774019, 623459799, 278158456, 450478663, 243338233, 924249916, 180183850, 566147924, 788428870, 434595358, 377525756, 16758349, 941407054, 250628852, 94870362, 126700429, 871642917, 570962317, 427117462, 251642545, 374224458, 58663525, 822365380, 927905671, 564511857, 583895463, 428291622, 807869033, 783368818, 176821703, 977828446, 31399121, 758235107, 420764989, 635314685, 150657355, 617126675, 626224714, 200015845, 753737222, 673456215, 46431929, 941358413, 538962773, 207653203, 353785389, 169964063, 151124017, 646707296, 100765457, 374432087, 295517813, 678670649, 848132115, 501879248, 464689018, 935892945, 867220430, 385094591, 152654241, 893228093, 311245164, 162297628, 521677684, 286852934, 971888749, 612135438, 827096251, 848224760, 262790654, 920603911, 27814081, 63786895, 260306966, 846217708, 114096462, 249634253, 862859177, 903414711, 818502125, 290697591, 457969457, 125958722, 611742891, 795993748, 442093614, 343422645, 661562939, 487960291, 252693105, 210281568, 373993167, 500329313, 384713052, 73847940, 48638216, 644914215, 112100355, 543893037, 62256015, 30397948, 944459225, 929132919, 191302462, 945488901, 877367644, 720667470, 481114380, 783735075, 444859232, 404057036, 886469436, 136823720, 992823864, 755679881, 947526747, 884813457, 105092863, 149861214, 387221510, 196200110, 571767243, 467147061, 664350461, 260444916, 849002726, 367558389, 476437687, 406989624, 618303595, 891731791, 482614067, 204414004, 104456875, 90329119, 955029127, 495853632, 819718746, 430196811, 191133139, 794938191, 310260300, 895596307, 723391382, 93903561, 272289168, 84014873, 841110727, 261776490, 375697412, 591791812, 461576998, 561017099, 608358605, 619811335, 973221718, 494005778, 892473334, 296201033, 400158715, 226722574, 759830557, 573915594, 217799658, 246190507, 622167624, 136041597, 108588752, 684327832, 253958236, 247153040, 969623604, 36999162, 409728843, 902042934, 481587060, 45914884, 805676685, 459874571, 868440986, 863429002, 235709534, 199603358, 904832375, 887323739, 513261727, 65971482, 681943620, 698196363, 85985533, 671819884, 140350028, 57528094, 76971855, 232447512, 227625291, 526554693, 884445937, 507533267, 38473356, 95337296, 73651817, 791224999, 548972589, 190678466, 31958368, 444645740, 622146412, 777490550, 272313684, 880000198, 847655583, 455581656, 795904275, 854325357, 8847560, 196258884, 591987879, 801152793, 78843040, 50892102, 771105807, 921233488, 248560847, 744058240, 952430311, 795783822, 978130938, 49580274, 451853086, 604369413, 111091496, 199094376, 605412079, 707910583, 824807382, 843465002, 254510581, 154548214, 777788349, 393940823, 470942223, 61548804, 612166797, 892505239, 905756255, 38194574, 299846229, 801637960, 708872179, 346758497, 900370274, 712910743, 728874054, 208970398, 409678088, 191408559, 328761231, 528279167, 995551943, 174148973, 391263103, 284159262, 763274196, 488048296, 271651526, 460176903, 751161431, 120123428, 860021016, 12118673, 235276701, 831966010, 107436908, 333786814, 852150115, 226826645, 459876747, 602426249, 882681049, 930673547, 376401270, 178326575, 482325166, 41886314, 679508586, 611868016, 306767137, 313276505, 547421455, 304854845, 505602125, 55907299, 118050197, 397159694, 747354415, 736099087, 722643811, 443841501, 60453891, 431406994, 722060532, 867827417, 27170450, 783621131, 510293659, 928834869, 377509817, 225539156, 345923713, 283554971, 47937118, 419928552, 432034267, 948982219, 406781389, 768662783, 313063485, 912413270, 477509931, 354709586, 908458312, 31262238, 51357111, 824015165, 369470753, 627021521, 439138111, 793496484, 300633189, 66334007, 315688032, 827797538, 585610679, 425989406, 620723755, 313198517, 168642736, 302724238, 134891329, 625027837, 136173119, 763713648, 403084512, 450335705, 850835087, 946820825, 800989328, 894146086, 792543039, 640867633, 268548126, 30747053, 967167684, 495890486, 322259389, 208451167, 439441365, 415454062, 592345246, 893848882, 322948412, 192063501, 900608108, 234825308, 339942850, 287624835, 105353874, 71921941, 306502993, 179596835, 127426718, 98340149, 775217264, 504068197, 836091146, 387875510, 453171916, 636955871, 476545528, 904631007, 441455188, 133311931, 539014527, 682446913, 142890148, 702054634, 358991455, 522342760, 172767606, 971073909, 291472064, 250181758, 684686726, 820654018, 171139150, 484927204, 568061157, 439389079, 336488028, 342760243, 132584616, 489765223, 318952057, 177663628, 860129970, 815346591, 169432775, 712915016, 975527670, 796930163, 791310162, 522076563, 260531714, 380418674, 293642600, 388180538, 728609617, 683766829, 317301177, 998554466, 324182880, 262757333, 23336730, 878302522, 426296323, 740507026, 511709168, 159208001, 438484837, 787546589, 978693062, 955520663, 973603273, 22683045, 321816225, 328499013, 757091566, 760792671, 586969859, 860208645, 338681612, 381069664, 5252899, 57906660, 318513535, 427167381, 813320481, 999499233, 306461591, 178592968, 416105577, 320465605, 615146444, 241062900, 955532755, 604271585, 903269180, 744299574, 388401449, 354781413, 242409241, 298236260, 530352939, 845841829, 456509089, 991033078, 143325399, 589027608, 557051433, 293757511, 912137104, 260512250, 759288313, 753295624, 648346966, 817504930, 466166292, 715230888, 328675385, 168245788, 747855523, 385664890, 343774849, 195721672, 853792444, 104769523, 666768265, 895082606, 144134440, 577680983, 477095425, 958128105, 341590384, 405512448, 557992374, 68799498, 959040422, 984758824, 803029122, 845626254, 562071559, 449497343, 204790761, 498696748, 916170250, 915902877, 997406538, 754156186, 607349952, 594704687, 847548906, 623171121, 832621122, 626173075, 227370416, 756990497, 270158769, 151170371, 20162336, 43363479, 231639432, 247158470, 828414282, 425569197, 687114555, 634437853, 480197203, 212937073, 114607695, 318268433, 227695936, 549982482, 318989225, 111547558, 187330537, 723566508, 266670690, 651975814, 431633498, 797154082, 599189065, 942837289, 641316461, 51633178, 129131985, 417697799, 36791900, 650154684, 95060753, 973393407, 114229205, 95133875, 534349051, 260551285, 944379105, 484587507, 457363800, 391010187, 245172794, 920141770, 332094459, 550353992, 584620421, 5837476, 462452049, 477015891, 918902380, 825566574, 810310135, 840693278, 559451697, 911626628, 374869256, 874381684, 476189887, 857737970, 964284088, 285901310, 246705720, 672646101, 392493496, 197290460, 306138093, 281957642, 213196964, 557301744, 85892527, 560810765, 57329470, 495868414, 932079961, 867957701, 945876940, 979685875, 520800610, 349440460, 319432960, 171302720, 570824326, 912074273, 97984210, 835781567, 787620620, 761362995, 46615739, 75102139, 177448014, 317862234, 442921040, 297744643, 763293149, 257321723, 507508918, 396404639, 996023127, 666698241, 495252135, 578966743, 790581947, 712082028, 927777020, 45923074, 148488072, 599469320, 364848880, 406531020, 478483517, 25527778, 871230522, 91152040, 668512159, 152800415, 857428918, 701917753, 475564951, 258218490, 934333485, 557445846, 959878908, 550775181, 341873277, 802793423, 931916116, 308492905, 406368462, 544767945, 224600028, 379982185, 244803164, 457890465, 83381479, 237947297, 450886702, 130143994, 636532840, 314277578, 98560368, 756552944, 154666974, 217972014, 115114833, 312741439, 491743879, 818602943, 425313626, 437319585, 761272488, 731263961, 664278007, 675844536, 441278510, 710783403, 736782184, 872737472, 404386871, 620237917, 159081966, 549745092, 584783132, 1443160, 87166957, 457352770, 298340976, 611288770, 633262831, 691403832, 877747283, 601869323, 328496962, 943366095, 823170415, 231766668, 310923170, 346256001, 411624313, 812847698, 625965246, 583336730, 874357666, 264523097, 252188659, 362554688, 900107986, 759959107, 593982193, 996664218, 202073169, 539721140, 980448183, 465133397, 165345796, 710656349, 227282662, 463408203, 290253728, 413946449, 303455462, 40155430, 411997838, 510843747, 8069817, 698059338, 969223387, 516655684, 676472415, 736288597, 894071111, 807735290, 600618979, 357365437, 293873676, 506628448, 186537163, 935642484, 803529991, 292167535, 5061597, 983864758, 878507855, 324415866, 454145850, 392366963, 420952044, 548688383, 497597967, 807791122, 94709035, 49714687, 580975280, 726131001, 765157213, 630136265, 242176237, 79894468, 735393499, 853830878, 730817405, 875568952, 858688388, 129510764, 195729032, 688397824, 279899596, 151974018, 884755513, 753384840, 865065485, 980200427, 100726608, 722347681, 266775817, 155172328, 429384485, 934007156, 604413928, 373928584, 670869991, 911186892, 252351403, 702014866, 401731655, 837455278, 95645998, 981631927, 715504011, 580372553, 303336241, 37532076, 258010314, 82136960, 475468541, 542837526, 402044985, 514129362, 508702838, 266880981, 358451727, 779474334, 639945877, 274248883, 805037113, 660168583, 432635751, 126470562, 643091025, 956134379, 861801462, 365986429, 879137311, 623421377, 36277783, 797893284, 815618777, 84451694, 953551471, 187827130, 307956974, 211500628, 243115531, 916437335, 680482509, 111067542, 189812709, 449640454, 371212469, 281998557, 815558610, 582234361, 162747496, 762664468, 591589281, 381929412, 978133498, 953211448, 566810743, 452928107, 449831891, 70911323, 260142271, 292086054, 875318513, 296633370, 943378614, 333454493, 123126715, 912094957, 50921704, 828508551, 460010149, 778586303, 148420027, 50541515, 695799059, 175947147, 252194167, 581195156, 141777547, 765716758, 925499170, 748981648, 324082894, 912045071, 717186250, 347235560, 694333790, 39640533, 818457742, 819385712, 444949868, 432371838, 486638877, 376206562, 226342725, 329361940, 595818965, 948488783, 640945396, 254577712, 409276582, 60120779, 611598620, 852963725, 515061986, 771610259, 128208647, 718099346, 915515791, 90348916, 700075765, 46216162, 373802373, 856898905, 36003750, 836294485, 677200908, 125246017, 343368974, 175024215, 136778443, 451633594, 889317324, 895639749, 164584582, 296062597, 213868707, 809302097, 834037897, 868456932, 71672085, 813129535, 858981541, 846357999, 500312004, 321621085, 330896298, 864267517, 556480211, 936514815, 432411502, 614472179, 480645841, 287921008, 627057242, 382932282, 511231452, 328985056, 765181333, 439185512, 235237629, 416478874, 57859426, 481261607, 433959007, 440899174, 775426656, 72881404, 632142928, 130293474, 786969524, 70250706, 148223687, 203799353, 850451721, 771314633, 600191935, 412600864, 381102651, 228787965, 700864335, 870494863, 483365868, 589497800, 280032353, 496033475, 884136598, 490733319, 910045552, 142691571, 70857880, 88195155, 408781611, 700660009, 740491305, 807378522, 18965543, 730931500, 890311599, 367047731, 743633714, 324861412, 193039353, 672031760, 862986473, 128474895, 470884993, 99646588, 727707336, 68553024, 12650663, 863004707, 286062669, 242320387, 734170973, 795331174, 107724248, 479793590, 228889103, 355523655, 785967601, 781867853, 731550664, 973473338, 889031445, 554772371, 863535939, 874409012, 974784889, 333154337, 448759190, 613011019, 365253799, 491296245, 530508880, 583426394, 753166062, 840664473, 482249257, 535596264, 842505944, 138848425, 945794584, 898282321, 22841884, 656493524, 24648094, 981259270, 491692706, 969044808, 813818257, 842245661, 797892688, 749971478, 516390205, 968630318, 821749410, 885697056, 542254303, 348372444, 971692784, 273053560, 403089096, 27188888, 687521038, 399746517, 534923522, 104720691, 418867375, 4600806, 219693902, 799878754, 947614591, 100623592, 456537266, 464481318, 446599320, 302485549, 133891270, 284576148, 666442899, 42836622, 309605641, 215924028, 203602632, 262495473, 246656142, 129520625, 765211649, 93554174, 150729567, 282468415, 832693590, 97436219, 237565198, 95651258, 388718443, 866572164, 532723952, 12136518, 174455160, 405550447, 355379828, 385903154, 635094002, 241052844, 73469041, 300641416, 101986907, 384846652, 471363203, 211237880, 24939828, 292400964, 884042664, 512430087, 808902343, 909538798, 332159662, 976239732, 650845430, 56461156, 899920573, 94462166, 626755528, 804291112, 200410049, 361133110, 175217478, 296116737, 134915341, 949610433, 373511980, 333611318, 736207878, 389494385, 925071522, 425351423, 808428745, 785798074, 742742331, 721906158, 371827649, 154595872, 58297087, 383171931, 184117398, 214068533, 492233161, 346046812, 512588750, 173066648, 18464269, 474809770, 524653367, 533971076, 440508618, 513817936, 657623952, 867656519, 677103090, 3823211, 391907812, 215871195, 561359569, 948276996, 537217493, 495857247, 356744212, 781997393, 857395015, 866519459, 672089959, 84961911, 317861300, 658022744, 837179453, 504580487, 6696181, 384567163, 785598528, 206358981, 389983144, 482161654, 170197295, 638677546, 593331939, 168285602, 698197252, 484324030, 52894369, 581783057, 534359028, 965557315, 57041106, 478982686, 126855944, 829710201, 797569783, 524217698, 492870972, 705015078, 256395953, 117081934, 847981025, 903105025, 783909962, 450195998, 118826575, 908671928, 507757120, 940045559, 131406996, 769790341, 76316198, 292478409, 145087934, 16796482, 898403519, 700320315, 589134496, 317457956, 892946027, 259734586, 421642964, 844481897, 613200179, 35418354, 607375053, 128478975, 320805797, 171961974, 212613049, 637858821, 477090117, 878909836, 135980357, 758093080, 671871146, 603902552, 881538431, 275871737, 280428292, 307886416, 908597640, 676034479, 189670764, 113054762, 350614744, 863979448, 275113313, 180867505, 84609062, 974552088, 229873697, 754530171, 923815080, 81433589, 290418723, 798436595, 752831321, 813931958, 830909527, 229374958, 579704899, 96632576, 544643344, 783698349, 432597908, 447320386, 857239222, 54641427, 429112602, 836481657, 999697604, 2463198, 241881609, 871557254, 454335027, 294195970, 889520041, 636526651, 192904739, 562376084, 959698916, 223485460, 326587449, 510409301, 17346104, 644389799, 478589192, 870458450, 371057239, 581493128, 469420425, 330032923, 327751329, 814975874, 2937955, 690634974, 348962790, 183699057, 504362303, 145723912, 569893019, 464103113, 60238632, 377860630, 918477038, 87248142, 329582109, 439394882, 582582370, 916313548, 14256488, 657461681, 211669176, 515939973, 569599005, 775840883, 955575583, 403847446, 562773611, 35932008, 470474919, 933876541, 528642984, 355453711, 562964323, 47683520, 134543976, 413071239, 305536303, 958332977, 784107788, 631182361, 98057025, 490444449, 460944424, 123294093, 479346329, 196096626, 170079888, 586216543, 247543115, 950346748, 34418373, 140146461, 235975796, 193525511, 841369823, 221109466, 244949403, 51376185, 9579414, 743945926, 400953224, 210532782, 743673517, 430147976, 167165616, 738412961, 385452521, 743636676, 768109099, 325087206, 534603652, 985054057, 983382624, 140809840, 460546858, 880503642, 173626594, 246327469, 396644255, 74882449, 662457616, 840143867, 800005068, 453214507, 17636580, 911958763, 302316273, 488543094, 495299079, 490526609, 738338, 273598117, 768164086, 342033506, 549067785, 775831969, 77007484, 760569174, 956226011, 982311777, 412951309, 489833152, 550571090, 920834592, 334140769, 773416884, 562958400, 659689103, 261859442, 792582867, 18459599, 1206656, 553759561, 368720252, 523950869, 849459061, 880210334, 591237220, 367236594, 42203703, 848364275, 272854593, 1136973, 637535100, 225623395, 655282948, 164997680, 775719090, 151194214, 116237320, 95402966, 901346278, 556131281, 990685218, 803988193, 435132853, 965936967, 840240729, 456907954, 100460867, 73676762, 813636879, 547300378, 435349477, 629065010, 714656387, 403207286, 158302968, 422828309, 676326269, 244836358, 591895639, 561966201, 198658533, 993201111, 194332005, 240966868, 908108174, 60165265, 178571060, 482317452, 463884161, 989881751, 767959933, 464219802, 503229929, 626308194, 517329920, 112482641, 962133898, 780419659, 382244496, 78227064, 412826642, 993976728, 610691920, 764626949, 976378466, 38889209, 959776816, 39728243, 163983686, 210404557, 444135119, 190399860, 365916997, 35393878, 131421803, 931741770, 615838361, 556058434, 662683580, 722034567, 318380540, 370051490, 250327647, 757124344, 22199900, 873783895, 118401521, 202888058, 88736248, 115288384, 300599331, 56690332, 898893193, 875341595, 847480420, 575951635, 592248949, 998268670, 283946093, 713275043, 992752955, 415816064, 497744671, 155380013, 702710486, 46131000, 40402372, 173717446, 834244508, 343682005, 299669252, 788875318, 616639016, 182105251, 460169058, 816361095, 579104040, 765920300, 979856343, 272295846, 970468651, 990890876, 115339880, 274942840, 575416455, 449677761, 118714995, 446500353, 429900214, 336281705, 456484717, 306447489, 85725145, 354950101, 528292768, 274847154, 847886588, 420193506, 582790380, 471622819, 321365400, 230804699, 374512033, 452372330, 911301884, 132475336, 228211060, 388332209, 950950597, 754194425, 240154233, 436940555, 767481832, 514661855, 57447223, 967000107, 507767439, 302229675, 657623153, 795101307, 659992549, 442784491, 744569125, 202541295, 231734069, 410942070, 506056667, 300470406, 281618308, 321287470, 701490047, 5874910, 867310544, 118600154, 294257926, 791743636, 132068053, 796104697, 753537288, 213417833, 569283985, 462928261, 521942458, 47036974, 752148162, 214780347, 24534469, 573636293, 509730029, 387560122, 219767979, 998243035, 355040561, 401607283, 201305074, 744038613, 704518198, 728961628, 229928705, 912836872, 794279424, 396513034, 799006014, 827822304, 653417448, 939276213, 589714619, 543096815, 549551377, 212378095, 370691104, 80349932, 49577513, 205905556, 498541566, 124368654, 977160193, 869636415, 519910021, 503964314, 279412134, 47639629, 50484771, 106650864, 622624654, 390508096, 710385224, 436918654, 694878924, 85465690, 275848851, 888723612, 706359765, 702362924, 576241046, 269943027, 140527535, 249639862, 967822731, 860022014, 855022526, 816691678, 432057378, 516351268, 95672883, 469787781, 991125894, 949996497, 695620083, 956326722, 85294060, 514118183, 395368444, 444564429, 764670716, 674572093, 502870018, 14421806, 560769937, 182175728, 733745508, 2431269, 896747356, 104864148, 58091386, 580261615, 712194007, 726062750, 240592913, 168057551, 209859691, 396201989, 643090320, 268337033, 180407785, 29685001, 579947063, 662870311, 782805009, 836771603, 569239112, 55478778, 145003070, 978157021, 768580345, 435754775, 248319921, 681129609, 711652318, 538672172, 946596050, 749465620, 934767557, 314261323, 975714593, 119541685, 145830430, 678185599, 297471203, 293250036, 930614603, 948083738, 603825960, 369041492, 903471660, 235875996, 744796602, 183168869, 9957904, 882942932, 31501108, 393625703, 462357489, 111002823, 828894717, 767348142, 707307748, 324200151, 903167387, 640149767, 711327208, 825303506, 733268553, 856517477, 737612419, 450291783, 113870693, 540734272, 143050477, 136686631, 87875136, 820043321, 285694048, 504460655, 315839054, 49868016, 652047918, 585043264, 501933476, 223592501, 820997165, 5176639, 868849871, 271887783, 784821594, 255451712, 621762362, 250014406, 38162491, 275019526, 883663696, 852240401, 89423699, 479059171, 274290012, 661835922, 860742359, 800075366, 423486162, 335155815, 202324861, 682379807, 970471310, 145275731, 954120421, 921298954, 220940499, 266040173, 833083771, 753956569, 541010675, 443899232, 332131621, 26126189, 866654248, 31646796, 806052849, 858900375, 741260183, 302154979, 16314075, 559334508, 167353228, 726376448, 77508225, 362344835, 847857123, 330111508, 305374833, 739805029, 23725623, 415312310, 308209665, 784735073, 78064826, 186269435, 155830786, 430639155, 642272666, 335541534, 773808279, 847777155, 439646261, 733435917, 245988137, 865107533, 788225641, 976354828, 628739090, 678947592, 990959094, 478071378, 195796892, 836500894, 14108845, 465657257, 257480014, 416103192, 47865838, 439416981, 532243908, 397866763, 142569779, 373612589, 490540287, 787301049, 438207961, 572171700, 321346477, 305175894, 94770299, 950678230, 514987989, 998580186, 55310052, 163178250, 852932232, 592533540, 809198147, 703283817, 83151573, 532506539, 428947676, 345822837, 288624328, 872280857, 852067177, 101763445, 392761789, 310144298, 386244542, 545368455, 893460400, 820729527, 228882993, 836750648, 870259222, 869508054, 743256436, 306373118, 636984186, 816525353, 217227024, 995083417, 920590743, 76371524, 846373672, 496176638, 194904703, 882438328, 101568401, 32254322, 485352280, 666686949, 793924779, 99156715, 26334580, 955151265, 597689478, 786946240, 963333901, 189963815, 631303739, 194589357, 145826370, 191349912, 135744228, 500731671, 111181619, 181587175, 591122475, 546394865, 954411267, 945521647, 655739724, 238662832, 749996882, 485576331, 214579245, 751796272, 213311778, 384311394, 523248390, 680122605, 744381905, 494337286, 150030546, 753232196, 784960438, 795726473, 162709641, 625924657, 178978720, 74507708, 522662172, 571125954, 288362326, 602854411, 935912786, 73363957, 558503321, 447111222, 16266861, 165646821, 625982298, 855871133, 709746822, 430740455, 889357284, 581096753, 755653841, 969516521, 799027275, 205311816, 143949212, 831537844, 431436392, 448243448, 326957139, 404603065, 852833929, 708518142, 349337614, 687334566, 685262033, 686103217, 387043349, 378696967, 237074732, 601294924, 915696425, 692526885, 788848932, 50623405, 776356418, 266008691, 278281432, 142563510, 888984711, 453630114, 167398903, 258792669, 791229567, 648543175, 526616463, 941175681, 513764711, 125139857, 653421172, 440546167, 318437859, 575238136, 199216926, 996568408, 120524564, 555890572, 905490185, 810096521, 198341323, 809413247, 707190222, 914460536, 168749305, 655719597, 302188561, 614895779, 904259753, 605591258, 924266145, 825038048, 655995592, 413690146, 736216192, 552332573, 857809834, 365251426, 162760871, 390920486, 394976694, 837512165, 657370406, 753771115, 21189361, 576774036, 541404916, 595253188, 925882371, 102516070, 800084923, 640317391, 825542354, 552984701, 114571536, 350035924, 930678892, 415424745, 920469849, 635226069, 519390781, 792900688, 518629740, 920237754, 199337211, 555060327, 879201582, 506253809, 378052697, 376685670, 26830361, 620245641, 558939823, 314699068, 581522135, 867489221, 699462395, 686419989, 622308397, 683127612, 341833047, 81628094, 336515458, 929529381, 181114774, 857718014, 953144129, 379369925, 504062089, 487243988, 102262966, 357271778, 897282068, 736427164, 771205453, 699076120, 126310890, 443756051, 712643822, 345165920, 866136402, 833002101, 296711186, 724307548, 917166882, 957210174, 138549269, 380584071, 478419885, 849656883, 794008426, 542737076, 461011829, 185024716, 363841590, 172841919, 196192525, 899870529, 148727109, 864301703, 557275999, 836783805, 388859294, 949045414, 72182668, 971347661, 78839229, 653601326, 893288268, 152741144, 852874188, 588152512, 840584224, 128678537, 315260994, 127322286, 435554802, 209962811, 959580586, 706809330, 903677337, 277780393, 723755230, 659660082, 2895991, 918992944, 775937905, 989769896, 18893467, 295045129, 346723023, 537942431, 141180558, 321945706, 14070177, 887344068, 325687308, 127670372, 423471517, 959631004, 884628947, 23608250, 187008225, 849921984, 816850398, 462947214, 97697763, 624473922, 157622526, 623461119, 667005415, 611192225, 850346457, 946659911, 200383316, 695125656, 83028955, 931137688, 511782045, 903667538, 489307387, 532741546, 60141944, 34329048, 739800564, 375135378, 740219189, 592752280, 436380428, 814553219, 562008375, 155878974, 605685124, 862066752, 264617709, 915662747, 715270698, 935475145, 24577088, 189163312, 985927841, 375644741, 732897708, 87926909, 407535121, 694507141, 404580816, 50903985, 255948380, 707304774, 530438134, 263145509, 898715354, 814525072, 927358735, 441595376, 431674568, 53949386, 78277572, 623226004, 808949602, 421156296, 182568886, 323677239, 406535334, 35713857, 331004707, 557880082, 673509087, 890326910, 642918639, 82803668, 656880031, 704959979, 120382301, 377565135, 455120940, 627114569, 841805903, 342482183, 153352956, 650191397, 949275492, 438771726, 628062267, 646265338, 68903029, 956489202, 374767524, 595566639, 275297491, 371390181, 797312214, 318771346, 144337792, 129770978, 27392123, 810198981, 351085855, 667443170, 847738543, 357653724, 498789335, 832363959, 929562440, 768793137, 105631271, 984299959, 334337562, 95505817, 559104315, 539554170, 404428621, 172796506, 977937171, 635089683, 292638894, 668168673, 439533774, 783320201, 737561402, 96564778, 446680211, 342530631, 691203309, 178038827, 738147728, 85040938, 661585742, 808574059, 925691454, 336504919, 232983972, 893923766, 670645218, 857100324, 793368675, 112229066, 948262826, 363817095, 192586245, 592551951, 139027185, 877699638, 581339144, 734891806, 22683388, 453921947, 683384537, 973583373, 417792132, 309921781, 737630053, 241235551, 231735689, 298523315, 319516579, 563250493, 55235862, 334019934, 911543089, 180555023, 208153845, 429180514, 181739943, 913827762, 261768316, 90670875, 233709681, 535283782, 236054250, 814807053, 365347403, 317087932, 789296620, 384187692, 283211808, 162218730, 604725107, 463333357, 253180925, 40557055, 201236484, 136073893, 189247787, 790964857, 607115151, 586061514, 695891853, 569637692, 391328684, 908597555, 828348727, 143832164, 74891702, 65149921, 528626193, 334363261, 394231625, 76137253, 873442899, 447471855, 350051461, 512217744, 539013452, 880577735, 816720168, 714946928, 781269966, 593550596, 492713545, 407874786, 197256339, 613956792, 395432429, 52377010, 242737823, 172929837, 706525862, 220367538, 50076778, 805753600, 833308644, 485110337, 184339788, 812655654, 138456305, 654432964, 523060271, 932556009, 1257136, 728143801, 975794790, 987819929, 894218501, 620332398, 583481360, 306388945, 750696046, 193848986, 370509887, 128027377, 890980994, 343294398, 366184222, 948888404, 330065047, 398104816, 237709333, 266303482, 387411079, 370945732, 852315840, 404078761, 909020045, 398279108, 434039631, 500757102, 618667665, 123253112, 501128568, 434188248, 366540730, 166110361, 577237401, 147155005, 141612641, 133837586, 996805733, 842263559, 67705157, 116491253, 151163997, 19058130, 330078075, 965489010, 940006218, 863371436, 533473507, 795226711, 962705140, 967530018, 717947032, 544979369, 436781888, 895542479, 699209507, 118523226, 549572345, 630357309, 909720603, 423292512, 604425635, 553557739, 471971509, 395458637, 931677705, 414193617, 120923678, 995682216, 345730094, 10947293, 479338618, 357492549, 501399606, 730000797, 417493241, 633256020, 434295529, 593750673, 20384449, 480526708, 274265630, 785994700, 878821385, 460211504, 670564944, 692795146, 24610740, 925901895, 378453516, 844118961, 505031644, 926099584, 551136833, 316061098, 339271100, 197015609, 466051002, 195479873, 938008386, 480935770, 699843240, 121980664, 794624869, 372972296, 245300270, 951831050, 396014020, 96406569, 151734762, 903930656, 17095650, 950465421, 916256490, 476810694, 512072955, 569319602, 314203924, 106585571, 273646504, 895811237, 119881185, 72811784, 882548697, 964238213, 712870979, 48556147, 211501013, 988773693, 982025053, 87508293, 469566960, 110353559, 306500046, 884113273, 703812238, 370191078, 473370635, 862058107, 754863439, 503098570, 171842489, 33312466, 106391490, 222011568, 726441066, 266357198, 13164447, 205164474, 814148027, 194719420, 784430968, 274812869, 648059374, 767342341, 265939359, 238497207, 514630619, 617844568, 875248158, 472770333, 479116009, 656507148, 335989396, 283916968, 364625663, 213818762, 941211634, 852939358, 433188377, 540914878, 412475175, 410929296, 506112680, 595542076, 279391748, 440167103, 183850861, 263644753, 155436380, 346197634, 267960535, 591333226, 922697927, 582050637, 69736265, 463569042, 909194740, 122857220, 880558445, 86825094, 817349343, 769659989, 766966827, 882112009, 617741121, 726026817, 757333304, 423500657, 532778051, 445239870, 44687087, 599942031, 163309594, 36297908, 581681446, 918714516, 79875384, 694853226, 150857814, 493533729, 722362804, 58632509, 579102547, 892309726, 476229640, 70754509, 156352814, 117777421, 134719130, 441713221, 413167027, 233968070, 345850161, 574924012, 207232486, 347744932, 769572207, 976326454, 711819333, 522053803, 130449985, 139491517, 689966216, 959944308, 40874294, 998984935, 556466256, 386835859, 424403877, 934782067, 874465705, 584097928, 14583046, 746701599, 313622973, 473446249, 437253656, 709563042, 665267329, 228425898, 582636937, 875903063, 605976884, 53582222, 958648658, 814561310, 608398879, 440433651, 136709183, 312899790, 4230078, 608523956, 914846572, 559124634, 17536639, 316470685, 704831666, 928373246, 850885245, 149454089, 462772667, 391012426, 524502841, 920386434, 480100797, 138637424, 182600127, 734963865, 901233893, 974447880, 786438618, 29410333, 823524123, 608988754, 531613852, 762696634, 32776145, 887343484, 75906930, 611456971, 273387270, 850069433, 499396940, 456661358, 5502091, 993638312, 779840919, 126966020, 213077589, 211626873, 586015904, 464484075, 260161042, 182943949, 91267841, 621323523, 445312809, 267851336, 142701209, 415328608, 421957785, 993056348, 848525829, 90786408, 732437198, 719382780, 333051744, 736188081, 203654659, 744117351, 499326706, 110149455, 401619776, 776416953, 232971211, 757115594, 928295231, 64411890, 270874186, 121189986, 430571073, 686491594, 324709143, 956915569, 132329393, 470663841, 431397705, 769150078, 568987637, 108549400, 420021689, 263563199, 316113115, 699015249, 961242446, 118431961, 497264941, 978981929, 50361174, 472034145, 675057982, 89220089, 421603701, 784075043, 878217840, 511463780, 504660764, 621789199, 376194809, 913993369, 837764406, 424803859, 998643297, 959460417, 501657302, 539679038, 305830893, 658936969, 30265529, 41814188, 868950210, 69806774, 138798105, 289372764, 22260909, 609325602, 967316213, 517347965, 204715260, 231124839, 2036485, 421012289, 693455742, 675606662, 527993750, 422835124, 5187566, 635322793, 222538246, 582411384, 682032891, 374867431, 314964966, 88462578, 132885370, 66982610, 773083500, 716203755, 452294861, 958648898, 402806853, 263128477, 789938008, 601974841, 399626901, 259306836, 271641739, 345135200, 118094142, 369898749, 168892462, 895760546, 726791266, 80813971, 699735854, 714890025, 574152683, 422062490, 449470024, 429819072, 34475200, 95443825, 626179218, 196171282, 502003923, 353114266, 638383310, 819504413, 239880866, 781188143, 658785896, 526498561, 637306718, 768434778, 151215110, 378846334, 566663311, 62329709, 873411730, 199518439, 535152483, 485427937, 980024052, 502436839, 612147623, 365953848, 999392316, 798806689, 40519571, 962617532, 11514690, 712390223, 539923617, 746911821, 86765217, 684184460, 875581868, 31367999, 573730609, 619553309, 726866384, 3844065, 198194342, 61829641, 436791548, 676214136, 692199687, 455723241, 189286245, 13301505, 311775777, 228618519, 660569273, 68905730, 204245330, 264837023, 504241098, 334766535, 915838896, 368411848, 362808075, 649011987, 559016882, 237649837, 648042378, 618567595, 275048924, 239748224, 819400356, 951177874, 936820694, 940072367, 185355162, 487698882, 807751803, 193271332, 860232041, 405031889, 524038058, 266145885, 834507998, 690166949, 674933398, 914981968, 648342120, 221812632, 256477615, 74620699, 689154014, 665740183, 583265356, 840757362, 401527065, 532715561, 847247597, 976599842, 160628009, 713161002, 31020634, 335555848, 475726940, 80703603, 5962721, 154461326, 310584999, 276041321, 145493698, 129574129, 491753826, 720553986, 555907079, 383345046, 658476074, 934695744, 294004470, 220335955, 371556217, 772373585, 293733344, 411301972, 444237268, 254883856, 48207632, 535576366, 51982123, 305538062, 865140565, 217389938, 13161033, 441284174, 446797431, 128796826, 416682283, 526930475, 660443941, 820262822, 613116378, 842404481, 482764987, 143503905, 584266361, 713502907, 418958229, 826962825, 160323495, 490454323, 311073909, 10746792, 884841278, 578891765, 658815694, 839449939, 895240373, 182973784, 747353246, 65467814, 77952023, 842245386, 859632954, 708722610, 777045440, 888006697, 891989148, 49291337, 647984600, 852225482, 155272827, 427219962, 592375905, 904960041, 891891389, 455753626, 717831409, 914477891, 798070303, 379031327, 22680085, 404385166, 818653245, 388486525, 467124282, 463875967, 592019380, 701168655, 513720336, 661657028, 979425454, 718403017, 571318094, 5356534, 958716480, 88934314, 267150099, 550425956, 607025763, 248266821, 107483752, 988160909, 559500951, 163669624, 412689176, 128793040, 163231370, 307072388, 362907701, 708177700, 736743333, 702103698, 612943529, 569057660, 904106940, 15415042, 118674709, 559472356, 533753590, 244210273, 348095444, 50250812, 813210057, 703175433, 136800571, 167462781, 215798444, 681939200, 697818267, 440553228, 339166816, 274889178, 267077698, 733743858, 935364864, 660203668, 441471374, 188248497, 463733939, 629143250, 57994819, 563393340, 855850363, 901457752, 414753711, 876159574, 229281003, 502140456, 972866100, 779164519, 350197262, 676757342, 197628470, 767396210, 465822643, 641975505, 977962128, 421666875, 759099208, 426614687, 72493481, 858421177, 206749512, 515704395, 54066072, 345802935, 312059270, 185921718, 493722422, 790911409, 455467346, 527253230, 828743314, 19737478, 31330297, 981847272, 875988219, 958587525, 397074732, 293098532, 290087849, 952594743, 256962067, 976601155, 971431242, 368701093, 304741907, 227095324, 782095303, 496223216, 766438434, 701055800, 23662897, 713425092, 263271356, 504608951, 102619642, 8677641, 834935435, 653219253, 69042881, 911918034, 600645812, 329111455, 238557589, 727553362, 556703214, 569115899, 791735983, 269409244, 734682342, 720189335, 924054117, 614693689, 165026106, 321778456, 841400545, 713185441, 875264516, 710664706, 751133210, 820807045, 846745283, 740937917, 799895107, 480168417, 508689595, 509822200, 880077958, 816346249, 809090539, 623573416, 56272958, 508091916, 681350514, 901991136, 137829930, 669184238, 814465370, 696278277, 250302654, 745554205, 249253912, 445724867, 706868754, 16966542, 231265431, 349472, 982970377, 626089307, 24914270, 769205712, 364766662, 738676571, 79319805, 431907223, 878822302, 789339398, 481712415, 818638557, 750407820, 419694727, 113821994, 534022729, 702101212, 237962389, 217684276, 845305125, 134946085, 526481334, 471441371, 983435505, 440079509, 610461745, 175985362, 328475000, 204617219, 61232624, 56836264, 845817680, 913665011, 322771150, 991223641, 391958204, 220772767, 170857236, 701636895, 126580622, 856945774, 741654292, 203811229, 270493116, 661340626, 213584416, 813414921, 921396780, 508340454, 300429626, 521018285, 958861811, 379779984, 934726322, 479422945, 306534588, 149008564, 289636771, 47027067, 911711700, 247559102, 364320676, 911011416, 568947485, 500157650, 253690182, 957222905, 570782751, 101114116, 321082667, 14973113, 142999529, 814519560, 117702705, 114705682, 178415532, 262336065, 238392337, 571827267, 973229860, 745285157, 50490327, 988400765, 590344758, 46063367, 814120399, 238379126, 781080287, 392541562, 563418160, 55915953, 268380525, 887322747, 29465244, 652572834, 532152360, 868867855, 94542742, 587442860, 635572482, 948944527, 361355542, 188824498, 740829355, 626670028, 295180767, 18581500, 995750847, 980769364, 925865633, 667010053, 278290367, 733642707, 678907350, 349777508, 578564760, 776787192, 827577234, 997150851, 576452410, 74972737, 738747953, 298543124, 435661528, 334923759, 354602678, 521125105, 511889374, 305646041, 394123748, 330367943, 610458263, 690822243, 732806893, 693784261, 13579696, 342934647, 280463526, 935349518, 310799215, 991892723, 582455793, 1996531, 176887678, 99079211, 189592907, 189740591, 100811852, 470332664, 848690219, 874592458, 508673845, 43786980, 609734295, 955312493, 791771427, 389858014, 260091126, 975283937, 572819709, 81682011, 728092761, 2794359, 980375701, 203708844, 949138936, 586270268, 549946846, 764865872, 328830478, 512425138, 194494583, 890461390, 892215205, 694389298, 534488167, 331481367, 685813145, 745159725, 332559633, 857588288, 592987057, 835585421, 106808292, 909182814, 122929361, 109031413, 374846291, 584457473, 357771619, 148225371, 746788293, 741349221, 405420355, 484979417, 353022648, 660403429, 88628697, 535414399, 934945174, 808574658, 510056615, 173507200, 196157619, 710463578, 608929894, 243547782, 554582125, 536245112, 759488793, 348716610, 43431959, 631356680, 147920746, 392880155, 11811216, 939753556, 594189150, 654039483, 352353911, 562948797, 170600947, 469481932, 500946004, 942175293, 743492014, 158151195, 822332440, 684629598, 14366329, 755398641, 50498096, 152129794, 804549761, 428131128, 570747667, 549626899, 207318486, 697576518, 836687794, 544688360, 628376727, 808180881, 166754077, 337331169, 497777677, 187825327, 584943649, 190555628, 450547528, 420471270, 823590130, 316365538, 848609010, 298458191, 996071276, 193651155, 444373533, 899892149, 575833289, 859305981, 301741512, 906617227, 714864650, 744672329, 561101640, 836173132, 37530972, 755728344, 502150725, 755100635, 821752894, 310267570, 986279571, 938289129, 928103898, 511785887, 311446066, 503547412, 753929921, 10683226, 462065363, 878118499, 443591256, 510909239, 612612670, 65867771, 500347298, 680802269, 838190336, 42602449, 725275662, 690196296, 350473602, 358345025, 191138325, 936716039, 412071964, 352172548, 269573264, 611135926, 575631929, 422431673, 549922506, 491836169, 517883005, 873014159, 207473458, 315437072, 445619030, 636800022, 411109399, 240227844, 9027332, 674523834, 151546099, 672403072, 251907445, 640362251, 363302744, 997483448, 227370422, 13674339, 276189449, 112415941, 957851216, 260354565, 74043436, 934638485, 452885367, 434766258, 627283242, 271620986, 950665274, 711607592, 866238708, 21403500, 727896044, 56966751, 643714526, 558866122, 333697288, 413161547, 30598434, 172451902, 115514126, 146642585, 532527049, 156262455, 407433862, 231301458, 481522844, 291480614, 116821273, 96608406, 82555983, 96589819, 674712940, 826453036, 594267853, 760894310, 455051200, 114688518, 364611619, 383265052, 683454989, 808659152, 961087937, 162227591, 848795145, 602105688, 440077763, 863709189, 256939346, 168122190, 802984604, 534346295, 615828994, 287437930, 986499340, 111806392, 29540386, 299598080, 189147925, 373641393, 445469379, 644313259, 172044062, 839671707, 432197675, 406746136, 777362244, 538428956, 213255751, 943180158, 956782765, 814639193, 924804731, 730265423, 766559299, 153922179, 268723145, 963968370, 871768203, 864493950, 881358511, 862251682, 432018512, 331918642, 546583677, 223494632, 22780477, 494795106, 493994712, 351155003, 787936962, 954036689, 246197491, 667932819, 757380998, 903623559, 610243783, 300291951, 161145601, 521158681, 735378439, 896256707, 961128257, 756449631, 724276643, 626011745, 283801299, 363117875, 549090947, 385928898, 533782512, 448961088, 769148274, 285637989, 873860917, 352131475, 186631686, 379282536, 535709111, 225874458, 530490507, 35895743, 520861048, 93351086, 598548541, 919218859, 876163206, 784444451, 669930495, 806557873, 253745213, 232225111, 428561130, 712886467, 790196386, 390456364, 846749093, 728685112, 525099428, 263404666, 789837757, 35643794, 657037279, 533843805, 582878120, 799780126, 467345198, 84767022, 98963334, 821378610, 475294711, 472058578, 926303956, 688648566, 480015811, 559196567, 76717221, 428214742, 718588218, 283242746, 738021632, 46603088, 772880073, 382589361, 832795564, 877775199, 76438573, 903098978, 748703523, 509749742, 571240205, 575033751, 809758811, 314222703, 848712029, 77113206, 696278692, 55105117, 940829710, 125474639, 712850809, 229904100, 828743699, 158292592, 675351478, 482745686, 322241684, 405023338, 281621692, 309138515, 998898548, 294203463, 869015059, 833897186, 159766377, 399591650, 526212534, 472882680, 142712690, 320152719, 900359551, 847228465, 486369627, 748791431, 608637180, 951214310, 24764745, 737074077, 460530992, 717730422, 726175824, 142744981, 397450583, 134143944, 131997533, 414295757, 387945207, 702226079, 549091674, 462219124, 46154024, 479061943, 208877592, 469052037, 171923241, 116236998, 223699361, 953236363, 518968697, 55665552, 973909517, 129979061, 840694708, 266681093, 162517952, 299953769, 160282958, 873326805, 366907197, 410690879, 938427133, 443518416, 580810614, 32765560, 103912242, 998224099, 406807293, 664174399, 835970806, 691661766, 113026880, 927525183, 903294972, 969936508, 670857929, 130348178, 655020556, 528167941, 326823522, 439782938, 714709781, 663136321, 900531417, 432110257, 114551394, 301994237, 436494358, 633859964, 818748607, 151590336, 860890682, 927881034, 953288157, 152198876, 637760950, 590822690, 12312232, 605129874, 802788009, 406341031, 477684266, 49220318, 277302424, 445193755, 964535905, 957053703, 608567425, 152232935, 100997231, 655644260, 875455235, 954901597, 205392174, 878542878, 134816801, 982618712, 221326603, 94478373, 314306570, 900383264, 198231281, 649819132, 608819575, 980391374, 837764615, 197988036, 204778485, 776307396, 564540816, 128276944, 758128293, 239707143, 350474646, 922516842, 714954326, 156136398, 954795360, 315067680, 420174109, 998023582, 980996112, 136776296, 157960947, 413113290, 907478288, 882478381, 116356076, 888318289, 493076379, 230149641, 890700459, 806813643, 818388566, 77675583, 188802720, 681825044, 417189437, 769676883, 740752757, 107012871, 897737128, 691942031, 900928785, 255523522, 873245939, 557770190, 343817804, 848550195, 965594354, 899199831, 197809201, 207339999, 519425611, 635033324, 144919279, 596935413, 396728239, 25567060, 419627978, 668299798, 129709890, 523398258, 714915339, 200295041, 41467548, 632734708, 720631991, 650195921, 956136882, 748480049, 479852144, 57122587, 844825691, 578360668, 925150682, 838713064, 745282509, 764993752, 336355460, 888546524, 533554393, 624145110, 466975956, 920378557, 444962804, 685180072, 187914865, 808484212, 475010791, 390485374, 536722717, 594326857, 59669671, 658148369, 182255791, 675437078, 624308361, 73548307, 773916829, 873515432, 332165825, 418299995, 747871135, 59434090, 806499392, 538891327, 913530308, 432297664, 23063770, 438048576, 171026026, 709529135, 416456669, 827898973, 870910533, 261096871, 391102890, 762849633, 906734682, 266481882, 631433787, 355645639, 918413388, 397378390, 746016134, 475410013, 538229016, 963785233, 233116653, 256354338, 683910719, 301721407, 2936519, 673418649, 506869400, 370567173, 426735470, 669260502, 978995919, 398149448, 604710308, 103130420, 146912166, 698217608, 290503200, 427300041, 228406261, 753389153, 332642935, 666342636, 715022690, 211783163, 436813350, 481949092, 499994598, 909142008, 209280129, 956749293, 370671273, 636275361, 837146011, 409617745, 877729419, 158379865, 153741815, 304584712, 797949384, 777907745, 423457329, 427921490, 516648836, 313848834, 406155169, 665547535, 561488815, 459683948, 263840494, 79285356, 467943497, 594742798, 827868482, 830966983, 856847913, 579893333, 658136686, 551882609, 354893348, 643105901, 200114805, 488247052, 859553558, 799619479, 470016325, 960431712, 53960499, 626692431, 153596835, 402951107, 424388475, 216388757, 146287776, 506586504, 292639240, 203262779, 627604045, 436386992, 460896946, 460630049, 669914550, 765879924, 972761086, 703527892, 65580563, 233000274, 770319957, 303759515, 785916045, 23613755, 842653220, 203841614, 756921119, 341334855, 74237814, 627333060, 466474433, 309560547, 670004761, 579756941, 818546040, 621311756, 63967494, 56364656, 416323506, 680552485, 82774689, 379994490, 471801728, 349735004, 415671384, 739852222, 142939580, 875399602, 919830387, 283480863, 669516666, 842972661, 487187648, 187399150, 725342505, 590302352, 448314623, 557320795, 731888689, 489117313, 411659339, 206081547, 50668615, 616114298, 700394393, 315918775, 325992699, 957734720, 370631304, 329643683, 611241411, 584414601, 264925738, 487803699, 499415869, 45118522, 170982313, 205300024, 539646532, 901765250, 617460007, 718645763, 620660115, 766097366, 992812633, 240435420, 535195597, 346682278, 705534906, 968570749, 323535817, 707518395, 530456876, 54656702, 938336673, 756436648, 316336413, 715109879, 155922064, 235780641, 73758336, 473412967, 607279089, 625924550, 649123887, 546777124, 141392244, 202594308, 81934320, 338819783, 397658451, 723054788, 930285247, 733775828, 732865202, 559220213, 547599868, 77988007, 287962210, 340376816, 184277348, 467527125, 78547858, 282532905, 192640352, 653162650, 797472383, 906796755, 829359989, 180655969, 100729461, 204858166, 34903686, 64386898, 145023595, 218970726, 142182067, 142625742, 919345669, 592684720, 791310915, 524092244, 57490220, 661664065, 487464513, 501086140, 653795454, 510041728, 561234289, 280274785, 707580117, 881156484, 766664319, 505969681, 684924257, 640462853, 653765939, 336045181, 821723026, 872898240, 401580993, 380737418, 97505267, 184648408, 175872127, 423850385, 910290356, 688763753, 160481575, 171816866, 155021503, 929653822, 256936855, 549420108, 6947510, 662855744, 898731852, 501207670, 727772824, 422514265, 851655087, 892667710, 957165733, 25363354, 489859575, 773548135, 772943973, 143721480, 691957281, 520108541, 784321518, 744726276, 873542624, 406617338, 724723155, 454258977, 951191582, 650873886, 353626022, 429528896, 713041096, 404495789, 681423771, 747366241, 843458903, 538597106, 403229353, 289759640, 323261368, 96385538, 229165847, 511065706, 47894762, 869062293, 608650899, 78284193, 485061878, 33818071, 124670913, 476786276, 545122089, 140230034, 846761531, 390097959, 715112010, 957296220, 362284455, 739487160, 631238597, 759189329, 250599816, 49207406, 463653130, 199377677, 825497854, 58983345, 879256314, 898566773, 838677620, 127477843, 442954492, 765816920, 918581671, 167351885, 801159793, 886528046, 734332096, 29501796, 729874078, 739915130, 738712028, 277965248, 804407935, 262121163, 656484239, 670502570, 547634488, 910211590, 197311062, 832616159, 884135512, 405322363, 763548497, 527264553, 699275369, 514526083, 233201490, 574891275, 87938247, 111576089, 325198144, 57692742, 991858480, 903661646, 136837510, 513931875, 916534679, 805504178, 346593107, 872867803, 753963694, 620358583, 3248542, 580055418, 28744599, 928193077, 268493295, 448381384, 865288328, 33480529, 503148223, 206347249, 174233364, 32448688, 617348943, 844458825, 374687824, 239754306, 690329394, 451510196, 945603909, 315219887, 895308530, 150372780, 533057566, 486072123, 121326303, 326151769, 473855725, 337931674, 811457578, 873908710, 285574005, 163327968, 362983329, 114278061, 917697396, 588277913, 874957703, 310691346, 221453414, 467207645, 587503239, 585846222, 548916687, 877235601, 872900539, 202415760, 297409377, 843383674, 780283063, 507016016, 47722965, 962278265, 446032952, 611967232, 861221423, 993609304, 106467817, 433214893, 753947410, 975652529, 707782932, 325737113, 760620997, 254238448, 215687213, 710880467, 738815036, 837411409, 759833505, 354085276, 513484812, 593535287, 82933625, 804058990, 430959977, 241779776, 563398483, 146945985, 859583555, 217792607, 571754621, 525202015, 680366325, 508292772, 186414385, 716169203, 528646303, 518472515, 185898780, 26223641, 54608521, 442807157, 163367696, 509776799, 282457169, 408864850, 475080495, 913925439, 44201348, 164008329, 239586498, 688126618, 535333792, 764082589, 273702144, 313555715, 903871866, 399360272, 816997270, 281691110, 842247578, 769123923, 844253664, 442959794, 863523798, 603611524, 812425767, 45547919, 581368802, 839707034, 595124266, 533717248, 825819211, 166599065, 1063026, 394415670, 655808778, 180560340, 538941794, 125644536, 989348144, 750553448, 979551173, 780768620, 787052235, 212874275, 619517177, 479597881, 503167226, 816638895, 790254675, 176336340, 644913779, 753808327, 785009477, 188555683, 601442483, 481360895, 285478638, 737706224, 979390231, 86473693, 496526911, 80179055, 218169120, 436318195, 148006521, 181465307, 576668273, 461037412, 788648355, 887788701, 361119705, 805717384, 488750799, 329701341, 746076478, 246633829, 208483151, 942732460, 845682705, 454301781, 367795314, 750624908, 541313067, 456332611, 595983761, 710807909, 354353548, 103302145, 513986271, 360544020, 503136858, 543864756, 249497061, 248231786, 691332259, 69853713, 963332493, 271145797, 4925573, 115964541, 197458382, 571950230, 399353232, 540827583, 53303829, 694246091, 359461225, 561646213, 231764413, 232415396, 51614721, 630212044, 657875945, 496163989, 773390644, 101974781, 689963757, 383424798, 542058927, 111719927, 964021722, 482079373, 39773019, 991854693, 981749574, 347248832, 949042323, 977129210, 113825863, 273940878, 637448664, 261541348, 993815811, 781745731, 392201481, 358552413, 17687945, 220105025, 369004988, 136071965, 351402043, 803390130, 493769218, 256108489, 845142498, 656897390, 416670531, 941403018, 688390683, 897321520, 327225009, 529730595, 226163448, 914550503, 586749315, 114833627, 960940751, 256562548, 7996020, 582011527, 453624493, 476264469, 956112498, 455155933, 655007998, 72360707, 952452879, 83832007, 516099556, 704269743, 631451326, 482230687, 551371913, 831718949, 182881019, 136031173, 165959551, 166577271, 449046493, 84772370, 354363488, 328518299, 506043458, 644124719, 210881298, 359069962, 48463683, 919631345, 846307891, 194902030, 337160825, 695147885, 242895916, 18595093, 340914142, 330583897, 322200375, 11121062, 264455480, 955486628, 511174673, 759064468, 948124652, 387471931, 382953738, 965830010, 501068320, 732758238, 654476736, 103363689, 545175396, 275860286, 698434935, 761360774, 65124022, 176525877, 676856402, 299344922, 517973188, 607394509, 499289422, 753243316, 14962006, 593037093, 210804198, 281281808, 304135286, 799820165, 807351503, 242935010, 753918826, 888203531, 100214192, 301761644, 619510454, 688760812, 257993340, 804472381, 818538317, 233616090, 848192825, 749146358, 342665224, 541132302, 349691133, 667403500, 606478108, 734977381, 131500554, 245016974, 863748946, 915473726, 28855630, 343722383, 184872224, 68011623, 374058072, 345730809, 483339371, 670132604, 851025423, 490300592, 37917688, 781597300, 862469556, 244844540, 106424805, 855751689, 968130344, 720808717, 731141916, 636582080, 975453081, 782783239, 266007638, 679725349, 196976104, 554579391, 433302140, 877460768, 430927002, 214119709, 691939298, 954462824, 610879285, 226477348, 4368013, 974956510, 755089581, 235840670, 103389481, 901456841, 324457331, 569914212, 359847322, 603654299, 286486900, 930649679, 956376086, 650226962, 686781761, 176835140, 135428992, 514690110, 530742915, 358229599, 437247778, 839208542, 930110334, 526021862, 277526107, 481347058, 621787335, 801869165, 448997211, 715802639, 757086902, 769039072, 39532461, 472269735, 319638707, 595834, 698429759, 23536034, 932904884, 978054687, 909884767, 200570729, 887635729, 866167182, 961678150, 657908526, 815892073, 858328300, 918257391, 385665159, 242751686, 441316547, 241598595, 336472944, 559991665, 640949082, 717965451, 912615443, 981818629, 535801185, 979562937, 280805127, 487854116, 266761571, 425094849, 901285554, 374309386, 804057924, 768993352, 646052988, 219613388, 819349699, 498402414, 14702385, 981458963, 747840998, 809715200, 237063105, 140110468, 952605921, 104563340, 902425042, 880987042, 90888234, 129092914, 373916309, 136420675, 67181533, 326339506, 927020336, 782636837, 623707051, 226543448, 728126211, 391332825, 595213, 130052730, 97008725, 351728897, 55133542, 885863734, 284648396, 482905029, 788372593, 918907321, 25105133, 144373248, 650518226, 468532022, 41023309, 278751871, 33511958, 470172538, 302850778, 235194389, 190315762, 491388118, 78558733, 621055230, 416230191, 914702066, 36740351, 135446815, 896208948, 794066717, 200178952, 72583287, 969802323, 50989391, 761540801, 165228651, 381239619, 833058727, 558920013, 998997510, 764476714, 799397436, 990249403, 570289496, 162587627, 294883055, 93075083, 545823366, 380519743, 232902908, 336745393, 420775460, 858391885, 161327642, 909251960, 692442158, 726478163, 470794598, 598773686, 343988150, 872407798, 750092470, 30278713, 358509267, 575490181, 44579381, 852017546, 890623943, 167454430, 208696536, 510219643, 258687175, 639757683, 726383610, 8019691, 715324976, 863827145, 492135963, 617353827, 394930921, 439028418, 571897630, 175155592, 499145978, 759179021, 111565069, 853403340, 271455748, 825961881, 446711290, 98010108, 630710948, 401979259, 493393433, 145803408, 608809903, 445185182, 152114459, 781577009, 944560501, 877347148, 537337744, 117437575, 10842844, 216489864, 868752893, 751259447, 780171636, 700015056, 772438673, 154293672, 759830297, 76938858, 582740552, 41867058, 866863894, 628643300, 128929614, 391825111, 774441669, 896452337, 107702255, 130318898, 525804714, 772264778, 715882842, 684055851, 357977535, 186812587, 195541370, 220361228, 33092786, 951932622, 705297865, 511301810, 541957152, 581812388, 230568491, 712321118, 714184419, 902766224, 303410077, 821520558, 574731813, 668887993, 749297568, 472716278, 907059330, 271069052, 666047596, 210514200, 984574073, 633956563, 324191714, 325816794, 512054867, 730149079, 466615858, 573278880, 679735594, 442608170, 770100343, 285728295, 742426125, 661016589, 630022407, 926772377, 321344858, 158763783, 521698384, 304789982, 265495614, 999628989, 293589970, 245760419, 700278075, 251378973, 590563932, 411175927, 668421885, 308702162, 213223486, 218538413, 171980924, 425542036, 962021703, 28859948, 162217827, 275672495, 907144287, 917293702, 762742119, 274473707, 799291821, 69949868, 331644526, 167926340, 442927871, 362611729, 209298835, 602341202, 373864889, 513569269, 992640916, 108882853, 447301684, 456500927, 139107436, 650001316, 557792029, 15271242, 985840300, 950366897, 570921453, 219148046, 353423387, 859443219, 671521335, 554535360, 373071904, 582236045, 710337483, 184974746, 885278093, 600716318, 215394942, 265871505, 141377576, 272055615, 211930982, 351926705, 389751579, 730756378, 314447026, 517510708, 120741938, 357486632, 311694689, 356440016, 261538824, 22507978, 864781555, 899637591, 772624133, 656239279, 32951775, 668842183, 161991947, 774720871, 554653884, 688371147, 461011602, 785420983, 901893938, 431489437, 80484455, 336921280, 75137890, 674041254, 982607356, 247682947, 746387959, 30425646, 585603332, 388729749, 79669827, 307588824, 396234942, 417506435, 230493242, 384217644, 557623285, 772880044, 33840941, 972092009, 864959585, 735263, 922411384, 97069909, 948776235, 947043026, 496284669, 330609566, 346097539, 164332816, 333157478, 797650547, 298772950, 459633507, 356188259, 996758625, 13888025, 308148454, 691305897, 66846545, 303802886, 818309712, 184927371, 601977840, 857917266, 706421901, 520089303, 20989393, 683599536, 670133608, 737339729, 634980760, 331809535, 405117613, 845066212, 870327734, 404126797, 570352075, 635099804, 64752773, 952487508, 710346637, 296339625, 828527860, 960436830, 617360855, 994866100, 639929608, 673458050, 36884551, 554633429, 647301702, 887039875, 553832566, 389069525, 757490528, 436785902, 473186988, 167061656, 624845687, 589223475, 319106968, 399027177, 370810432, 877203696, 223851029, 31541248, 562675713, 909842183, 978273980, 92090628, 691630581, 517836305, 287901647, 729356055, 745022280, 720190649, 186558518, 688000078, 128986956, 747737280, 823250204, 738095471, 335077999, 45291544, 507035198, 698836983, 745502954, 578453729, 248056668, 698305079, 990935081, 194995947, 914370716, 948321277, 375803393, 329701308, 419247131, 332504458, 57043136, 731509763, 325864923, 581286560, 783622158, 519707114, 591988203, 883536457, 61854700, 579039938, 938651771, 967102718, 139348053, 177411364, 438261919, 814517820, 250366103, 557034992, 611473808, 950429909, 632578776, 261899432, 394896492, 356600348, 290944993, 899254080, 131533115, 587380816, 905011382, 247500933, 70256311, 853309430, 823641750, 731205380, 651322618, 650635664, 235369470, 551544431, 700713841, 7329536, 649879063, 972391428, 264722027, 46276024, 754503663, 976612108, 397651508, 249176660, 572545434, 533857577, 357844771, 847153778, 289561354, 536952962, 197998469, 725051691, 444966349, 477843481, 686916694, 97021959, 767942036, 206088704, 165007669, 748039357, 578473933, 397399706, 685244533, 6768851, 215295946, 162548025, 780660068, 360678673, 9219384, 409107490, 532107150, 145664491, 912176691, 850381365, 35063609, 795623574, 497595607, 919994285, 829068833, 336461873, 814374788, 679747966, 46049487, 674627427, 606025854, 280955947, 572117156, 598066127, 289119203, 218146629, 813282662, 218819826, 134781018, 144306330, 80094312, 754784279, 715578083, 575949711, 837552408, 775468260, 38820816, 749497805, 213571740, 491644419, 334893518, 542083794, 917954962, 808712274, 559222718, 969772759, 155122569, 989498210, 445109833, 839758155, 528207037, 767870071, 184089968, 184785735, 322704298, 87798236, 788299681, 9929936, 502536143, 724779864, 321842472, 613656365, 603171231, 725514923, 85713908, 134445189, 712681074, 787827367, 594870194, 440379611, 12092070, 18346189, 429479349, 3054646, 213853848, 613745554, 950327339, 472915456, 842124827, 227030572, 562381564, 358271607, 736042149, 289731876, 151054022, 389852238, 64311782, 511699594, 647954371, 782041944, 67800681, 225866186, 506608592, 682236888, 107919527, 608934199, 655135089, 740913560, 880919155, 57127664, 106804378, 940049403, 214226332, 335587855, 272054457, 533418423, 229153210, 685756160, 628752839, 952299294, 54406640, 563560910, 273520092, 210547166, 674052591, 691143438, 665559559, 319449288, 663738267, 42031059, 687293268, 52852765, 382951004, 756012197, 790985263, 833437002, 640239598, 497028494, 319509718, 437428245, 758724027, 2657367, 47427458, 965574982, 428120917, 555747906, 35023455, 637140570, 791402909, 758391806, 981442224, 28934264, 970447254, 419000072, 604449871, 445360265, 407362721, 551303143, 891373825, 195984881, 484979976, 840003728, 409625818, 587744912, 616216982, 836798261, 98683008, 583805832, 911883327, 185874546, 851613268, 628861254, 427820235, 983404536, 443305096, 513793426, 614266131, 502504246, 515772037, 484478506, 990222176, 543845162, 318928680, 316855193, 211394378, 49039686, 175430701, 668207678, 927217049, 498277820, 236628520, 290788025, 658672737, 516331025, 849045482, 649723522, 473410973, 222787452, 253014185, 908881163, 620336285, 121147253, 217409935, 868843057, 803204947, 9764089, 518573360, 229830616, 366494981, 914149591, 44102561, 619159418, 522459521, 567017054, 77891270, 579730610, 486618175, 200608190, 220988358, 57375965, 526766775, 176771017, 510298417, 93328612, 901140621, 788709817, 203824884, 654930068, 951569913, 791007333, 758502588, 568305925, 35994235, 306802222, 775103181, 243305767, 76136968, 930272706, 8948764, 682519548, 462245218, 980862440, 7270620, 569812338, 547650407, 650868726, 786439987, 313287093, 639549114, 22035264, 879333954, 429856448, 175873725, 80067248, 535037487, 355138643, 305447609, 901118846, 601444480, 328039250, 703329940, 910798587, 68471739, 366166200, 162148633, 735418140, 442666997, 686360487, 238445656, 846158245, 611166117, 599402714, 248545478, 205639904, 68638776, 852107120, 220443259, 549792466, 860297573, 788465563, 725302464, 327328935, 856240623, 150726498, 447446540, 743543595, 568133808, 787583473, 559370004, 368587978, 472507616, 701192840, 364331583, 332878883, 491998785, 77398123, 567111265, 722508328, 224307096, 867385140, 44596741, 659298514, 365938773, 848344032, 188446501, 612727640, 906761489, 218547003, 619539359, 119998106, 326564342, 33030412, 19752201, 167554792, 690652550, 489232315, 18440920, 589551253, 157079948, 458823118, 220679422, 629279661, 583806183, 317349454, 70416496, 780721223, 689133822, 40220477, 226178330, 706140314, 950155689, 16042521, 100681873, 405804440, 987600653, 748609843, 464842957, 698792856, 345462535, 167822419, 714985666, 941584798, 410398964, 345166620, 900431177, 647908419, 656064010, 27684305, 81923327, 499440723, 701195437, 293905313, 856206626, 485687532, 954982280, 330557021, 530458366, 176036328, 814342157, 770545679, 254086743, 409061983, 883216806, 95866711, 194588473, 293669783, 313957586, 387930843, 410484347, 595271931, 409559, 941227580, 64855197, 313368324, 231320277, 779254399, 887827952, 682817156, 430458177, 486406449, 264202273, 130606796, 881171850, 359799120, 648513148, 974610738, 516709505, 366323203, 17925676, 362893031, 126989389, 456620049, 312161312, 442899377, 211977371, 514983815, 479306705, 72377630, 889691558, 167687836, 833438680, 376494235, 299623703, 872188516, 304906221, 802686133, 106901540, 469674434, 976703280, 925103843, 853132114, 250212729, 94584215, 307481149, 455822732, 91395793, 879054191, 789920106, 724008654, 952094636, 9168995, 722395754, 698091798, 965843440, 113397109, 36382294, 744862570, 691466008, 747417642, 178426572, 812099554, 940383041, 566845657, 811006722, 819861638, 876986016, 524821643, 787523403, 607454111, 885613, 196225231, 832846525, 407334688, 996627702, 713015117, 179911451, 619199599, 687090412, 205532899, 892324812, 829491481, 901491096, 148167278, 704586046, 81436708, 971049416, 48848918, 2376752, 567548736, 147372710, 288938787, 871021344, 729927204, 145226184, 958268384, 936481189, 606299763, 668019891, 136144997, 278605056, 23824309, 493574259, 474186280, 60282966, 780922671, 542121340, 813899872, 914489909, 808625518, 545866936, 181183126, 262239990, 277005782, 109622253, 915825118, 881423661, 857986777, 877157564, 939574465, 56654439, 591328162, 470192709, 821663723, 885509954, 176926081, 272183519, 56426313, 219914390, 943940045, 538453719, 718764109, 228045794, 368350402, 265449908, 302809688, 59767125, 52628009, 701574907, 545430538, 56120191, 938540063, 393582249, 60219497, 691593873, 15977682, 206098566, 60447191, 223046480, 628986509, 919613513, 311469660, 825933001, 421284028, 873753975, 153750469, 912772603, 208485470, 668508955, 113409827, 606007861, 831686180, 202689850, 481545853, 701089099, 87311409, 671789734, 658134896, 357299477, 478387226, 296366078, 574418424, 964168264, 456997414, 917265881, 246304982, 340459504, 748639839, 552665860, 365248410, 778956871, 337153966, 813388783, 149655311, 527358479, 507064701, 859130512, 946126139, 676564169, 790755265, 100270635, 902769193, 359964620, 421962914, 805434960, 580443099, 129575200, 951828228, 667001163, 726670454, 600049389, 943218904, 330588622, 118352733, 719166318, 267172501, 549737950, 976206124, 882325366, 982381339, 98631539, 837185574, 123563108, 974973730, 482203840, 23062594, 391897264, 464303883, 228977585, 707383385, 850150538, 343601256, 648872622, 389467677, 601595343, 720779734, 302484444, 262432069, 952999807, 875170288, 415549014, 631830968, 331582594, 251988254, 422067795, 432937295, 951653033, 158751707, 648793398, 481314004, 939708045, 123096673, 215198909, 130063212, 785024161, 455974181, 945032934, 5435765, 685210915, 701651364, 731772009, 937632860, 608142816, 836129326, 836307429, 929509035, 167867033, 438643031, 176771550, 525438888, 311286944, 911975446, 591826172, 33705666, 297066343, 977603094, 48719062, 512950906, 225543047, 726733785, 155483429, 490030312, 794184381, 938659817, 147863338, 416791562, 1217638, 237981363, 860677753, 708991333, 764201228, 185422875, 708118697, 698854227, 650240075, 648483627, 731274194, 430045789, 23319114, 597189953, 52002124, 628479637, 655395921, 584186824, 659460264, 873831927, 450816702, 420928851, 446149648, 438244573, 461061312, 511990686, 508592843, 827496984, 644948646, 408076990, 809849999, 532905759, 961977061, 488362995, 87508299, 6262759, 779713344, 813795059, 62778249, 532556094, 149599248, 835089747, 43040211, 610236968, 250133656, 539115854, 92941826, 191228593, 915744941, 525407472, 945600000, 39338476, 899140918, 982770728, 971562766, 833882059, 486631314, 377195791, 54816942, 980150819, 262518312, 148531266, 361588819, 659724413, 203218195, 582099661, 800070434, 692048503, 293495284, 815514112, 485476726, 225993561, 938118179, 259958235, 3591646, 2167445, 428506161, 32293227, 667206877, 385086551, 296932566, 425514726, 686126120, 390516599, 470948051, 675715027, 496158234, 942741936, 820699932, 740272207, 410943202, 911856989, 84646271, 662646785, 824420271, 517055488, 939739330, 567791088, 852677202, 388375169, 137380836, 544574312, 753808311, 620499034, 25513004, 838901877, 601511780, 560262691, 27768965, 284920427, 630157474, 299092074, 395601141, 687252455, 573556358, 652267924, 232882619, 932880456, 135186964, 691916649, 835494608, 309113268, 904624732, 661443766, 246142412, 630018548, 181226179, 289713716, 465606241, 31680840, 86418209, 906205205, 141959789, 814622348, 543856712, 551751570, 635551585, 316137611, 387706245, 268218004, 547922532, 759853905, 156095445, 807561116, 59605378, 57465949, 79735363, 679129886, 939351155, 884154653, 957817442, 894818817, 151565324, 728526447, 741462947, 723907984, 468012433, 521668931, 743904692, 440586730, 591953696, 921357064, 926918200, 189190160, 887011742, 264764457, 413672386, 365158408, 297384118, 337499152, 316622405, 740582800, 301554146, 179625080, 740693471, 880132723, 331806573, 789352903, 46470713, 595151962, 448170452, 994135222, 918954161, 736294264, 340531813, 251923841, 113647050, 82752426, 119113076, 636149680, 905172066, 132649007, 317102143, 50938916, 120416712, 962254075, 666797177, 954391864, 665643102, 723579339, 2926687, 431156927, 89565686, 91565734, 588337749, 621057525, 481579214, 538894698, 642500881, 501529058, 557947041, 114396651, 587523522, 18047272, 186474519, 789763401, 365014332, 51174386, 571858261, 287119932, 421247858, 993018236, 376125570, 495486704, 700967878, 16308563, 996136262, 247186047, 459524632, 296663075, 987095768, 920434533, 552711166, 335008363, 15583432, 757783673, 178579880, 743751877, 310847158, 69100142, 892984349, 919393673, 29733084, 860459088, 863863800, 113047149, 477263236, 419861260, 587688561, 843210099, 369318001, 889509115, 623881119, 614277740, 811085709, 636017784, 482320423, 668438947, 978243925, 780708407, 905011501, 385688567, 135630004, 49711462, 736956484, 445795937, 825755738, 781452377, 147416435, 310756317, 228002292, 688902464, 100282922, 316416389, 758376375, 177020123, 26516048, 634933424, 783455672, 301585248, 575224230, 964226874, 756692785, 409465541, 212464643, 348425635, 211487922, 901758195, 29698014, 170612370, 330891627, 408968507, 471038364, 921473432, 310949115, 227284619, 68411109, 290621564, 250825070, 567168065, 166524706, 353148370, 695216230, 905924238, 736157205, 204001352, 760010489, 278466398, 32235847, 872046988, 670489704, 462144077, 840572075, 833013949, 27887915, 3709422, 713227937, 233298278, 117449449, 718849149, 790870095, 361461349, 34785039, 987719909, 223554724, 921424251, 706962800, 297564796, 285729224, 481012260, 784560913, 482475773, 362200478, 272654942, 90278106, 290103657, 65335993, 845807475, 59125540, 250395692, 81614314, 769096700, 194402266, 418459071, 375097907, 892849483, 220914180, 80153984, 898006726, 411970632, 843644175, 304706799, 418371240, 577137207, 149131122, 198363414, 516762177, 67540180, 432226008, 160703025, 666772806, 351445111, 206772295, 38625417, 436410878, 41933420, 606291819, 27050121, 774946615, 459773778, 678343419, 914484653, 276117425, 964889428, 686262240, 802430055, 925877731, 328541551, 139344849, 907190217, 184140256, 286245732, 92422579, 806730815, 126968346, 364423003, 805812620, 147556216, 720221355, 253526599, 193617957, 943126589, 424021578, 369575691, 596575938, 866019566, 886508394, 409466079, 963734997, 698223349, 682223721, 136093700, 233362076, 99664561, 217893966, 114356668, 65596681, 348466452, 729678087, 832018299, 772870399, 117594324, 813198042, 414711675, 780408917, 679991884, 404844692, 627845522, 498185095, 507003554, 374749402, 193759698, 295676867, 556955556, 998915484, 545552732, 758742578, 296160285, 466582501, 16945618, 468271159, 817417439, 48139693, 96625173, 76226279, 702858167, 922735787, 36226251, 296935506, 831638014, 526644373, 41763368, 959457, 102657213, 698703000, 215661258, 990680841, 246480037, 501927070, 238661448, 593898222, 784616316, 879582074, 662714175, 457630494, 255684492, 374962455, 75665683, 820918420, 336820579, 63247322, 891847498, 728701375, 467875131, 162799236, 659503195, 37936845, 581179966, 591517806, 701886346, 328295057, 991170566, 482162887, 597077132, 998962765, 267016270, 241668109, 142907836, 476574851, 995801229, 435346129, 900492843, 308685712, 126777249, 548043660, 397696955, 914715916, 879892755, 943186002, 111549840, 240608138, 544509465, 431481394, 191435602, 540119677, 803929094, 682681347, 692192520, 879061046, 403724321, 446271348, 419301114, 262306367, 243339803, 585205655, 321585795, 48796545, 346941539, 565986863, 207455534, 212590238, 469157204, 153007321, 540906532, 334279246, 873914985, 979916147, 410544839, 624989126, 808827595, 833424588, 802251588, 513039552, 796093264, 628822362, 313640230, 587650556, 900819951, 191652751, 822809077, 194335260, 861451325, 356640403, 506310440, 345927443, 757350650, 975903529, 205731426, 228089268, 454227243, 523827298, 814257451, 917376836, 823615923, 9240561, 899181692, 458352194, 179334925, 376574522, 36325179, 479485379, 177445468, 339230048, 897266732, 662394709, 938853586, 901971544, 197744136, 23194304, 707416496, 637398627, 504960045, 754162127, 296764892, 150680309, 854627110, 870610649, 722214813, 299122632, 826674990, 859260937, 289043177, 187247884, 567922468, 77642446, 614762587, 939721335, 532579631, 200459015, 483960631, 968598535, 645766319, 670885708, 687305896, 85107756, 679564602, 790465681, 506689847, 319124687, 601307156, 757434904, 436022428, 101999936, 178134751, 715482096, 593040270, 59176979, 131445906, 657094936, 547305729, 11166988, 753019542, 8181590, 344979608, 411513199, 515528601, 28224093, 586292440, 556447834, 773305734, 871414971, 621302402, 419065785, 986267383, 464179984, 977140385, 333182168, 685383854, 305519962, 456087715, 619304385, 186646459, 745489107, 542767510, 654998577, 117640326, 86402771, 724242531, 728935634, 865180680, 455581117, 341056175, 326358052, 885721199, 711199965, 574717754, 225788400, 157083977, 705799260, 176244847, 35844985, 449164137, 910188966, 632542038, 537428346, 981423850, 958682541, 537904986, 755515183, 263792122, 673611819, 48195244, 689624974, 193692326, 443779560, 17726441, 310478176, 650850918, 340802795, 331114041, 787436971, 563026479, 617839994, 780439574, 823837472, 681245094, 694927048, 885154445, 896040864, 322783154, 603401741, 790918252, 363232544, 404086351, 12972141, 837918980, 353090751, 325717360, 940743363, 717081518, 27335266, 604492152, 945412355, 226129150, 125790652, 863827864, 144577145, 892920573, 994369071, 371165686, 742434965, 7223656, 865042216, 390477620, 22772605, 978846766, 682455832, 903101206, 370889578, 357021037, 527370870, 840134795, 253621379, 54966452, 677827737, 485715411, 403685301, 649167861, 382720238, 811816518, 15954138, 781015182, 313441582, 305678337, 416462770, 433272622, 165698287, 755371836, 545012992, 774658725, 698402247, 141658808, 253460598, 60598028, 279931269, 891609940, 741768409, 732213606, 205806595, 188040183, 489705369, 818974217, 685499142, 735935669, 455752331, 244187457, 98838453, 905883841, 771906771, 707884604, 295109508, 751211538, 307941931, 273653537, 49657790, 847927965, 103103201, 288026997, 289138612, 825749341, 386404624, 256006134, 979662086, 622427816, 604560039, 391177947, 391602376, 566311647, 727798688, 667506092, 325043990, 150346191, 277580429, 535368263, 357844051, 251661227, 193757723, 140435114, 664764995, 999095337, 21263184, 195925903, 856664404, 156945945, 846376356, 416203961, 247361047, 211301188, 5176075, 133050835, 372595045, 681821797, 58885080, 310782507, 820814616, 884861627, 566195635, 388947384, 672505292, 848939238, 286829068, 15514905, 572748733, 498290230, 741244040, 144398530, 388552198, 396312686, 144806125, 614929052, 560589079, 966406021, 852293323, 424922410, 513606641, 42728000, 848089600, 915621381, 94930046, 264783204, 224167793, 380789048, 364997785, 161883142, 54727510, 626264584, 306913520, 609833924, 912116374, 310688447, 344935411, 524348860, 201690112, 142263080, 564624938, 86047901, 961795129, 103615544, 241587044, 773422302, 151714931, 330033349, 972914599, 692500993, 201148465, 847452691, 412376013, 865400458, 476493195, 245435864, 951799723, 122663485, 244011054, 631306237, 312234162, 123663829, 544130714, 195888396, 643975234, 850948181, 845081169, 311463349, 928196381, 13014816, 873751013, 841971046, 336168649, 55113806, 875618942, 469306776, 581885089, 164778181, 626481934, 931033722, 630562717, 228046446, 719833528, 930948590, 583199081, 683249662, 565470455, 152949674, 498002544, 505572673, 695172278, 235079546, 496753557, 873585160, 834260403, 126932737, 598771592, 635242494, 344347424, 346008343, 580762722, 8799608, 674925920, 731872177, 831816181, 325526250, 242740763, 557138314, 51588925, 662718541, 260279012, 803795845, 720121295, 808438364, 981677965, 683868449, 280049909, 144268717, 684952758, 79586079, 265766989, 20977229, 714609876, 85821647, 750345924, 539110373, 424496278, 92828622, 329279338, 155253553, 427374362, 615242971, 685792250, 254871217, 702862477, 727021308, 249803095, 6755081, 894489004, 511938717, 74843567, 18087893, 899867854, 315640292, 630344701, 275866830, 717485284, 731948916, 390906332, 589461429, 996346466, 800131796, 440370287, 866512857, 454489484, 1138909, 374348359, 315920739, 714589668, 432075543, 206061029, 191289971, 327224589, 301888109, 642593029, 233608827, 328352613, 256683307, 196127307, 214686127, 633838599, 533391989, 349731951, 120091228, 324801824, 876885927, 231098057, 493960921, 485711729, 241223631, 302408037, 595008768, 335550943, 214021691, 258815200, 893996520, 604946047, 91313590, 312057918, 473467789, 901673959, 129826938, 372965272, 646820176, 758432734, 158749866, 330220997, 38616981, 126221718, 127071531, 486102216, 292756059, 248078561, 797640945, 355294242, 812351006, 547212933, 115696738, 349389655, 980074232, 258783480, 472165967, 635491940, 368895025, 215641088, 543362095, 812136131, 567193831, 746210514, 132079149, 486760714, 297755703, 857672904, 260088726, 209663220, 557695640, 934341130, 264187526, 689714443, 630211332, 114697769, 289122476, 820911383, 267923660, 389252105, 506805806, 820320235, 732279933, 381884588, 174939179, 50059783, 7994802, 261801053, 276800367, 406094047, 893895193, 317537371, 361530518, 857549024, 860619859, 591484270, 288443909, 216093183, 251957920, 691123868, 137672690, 981487389, 29526494, 288912688, 832851416, 375884020, 55944692, 471111503, 905446108, 842589791, 419403521, 134686239, 146014501, 965011868, 441820228, 770697239, 866016332, 421514460, 956665101, 377423377, 710631422, 184870049, 52623389, 498369168, 465512751, 957359888, 780035658, 35461448, 867950557, 988895917, 368916876, 950176152, 663096239, 628766161, 540768368, 716636609, 867084981, 726183856, 175515075, 130030299, 82683598, 106246389, 360863678, 210129500, 467343843, 2318388, 856425874, 55529701, 116403957, 702518153, 491423385, 844813040, 19942056, 90318142, 321572695, 507742166, 888473579, 343082511, 280389896, 88835941, 581695546, 84598378, 202118379, 707715476, 756838549, 506609805, 549950854, 742742766, 184316849, 511046619, 244141767, 41768375, 526217850, 852458073, 930137622, 209534726, 423634317, 425470857, 445936903, 748008496, 918187912, 153025384, 471995314, 363618227, 632965112, 804152082, 774661307, 807305321, 982683306, 162586336, 846290934, 470804293, 535477668, 54662840, 448874964, 990451790, 227893794, 493706324, 355881331, 799146813, 842529920, 743154338, 552863863, 232682241, 622066956, 136204551, 382934685, 407859651, 962259736, 119425259, 252390571, 909040082, 902226263, 917362181, 922457746, 599510740, 851408421, 548311240, 30995963, 331127051, 168022150, 911527150, 500390856, 280389797, 657971847, 362279407, 428081231, 520439765, 68580530, 355801, 686155522, 337295776, 221185715, 713424884, 12280284, 617597562, 887213138, 308245939, 672692727, 680488699, 633224510, 515241320, 274749018, 825154160, 376171522, 128766550, 778431237, 572370335, 423559891, 548418830, 306606007, 587546829, 388301133, 547076168, 21248210, 961860821, 202547496, 165516392, 344038976, 952521120, 808280928, 876340438, 923380847, 970923831, 132815264, 56508866, 984231586, 714875291, 966571995, 735452228, 743284770, 486341209, 866594768, 266974709, 623678648, 860622002, 255614012, 587485440, 889026045, 531789315, 252849562, 995395725, 130605159, 619512146, 244031476, 301347553, 467858292, 522756650, 561729337, 346498475, 94244307, 961610747, 20679859, 53708481, 714472922, 673202953, 199287217, 629198856, 531808628, 148709767, 303612048, 359846394, 778511783, 55219169, 496286508, 684810883, 649050284, 815385750, 521532756, 71257786, 309485104, 868808462, 804709790, 540082980, 171944137, 581849314, 163383495, 131849873, 34221148, 549957367, 246742800, 820694402, 723718335, 450582097, 707959421, 676661475, 622799772, 787306691, 734266000, 348778684, 425913247, 625043188, 992747087, 293315236, 23917881, 78857065, 131803311, 797192249, 923062000, 35674380, 240276217, 143199705, 68313186, 700017740, 71335875, 269191606, 719530552, 321790148, 424321912, 781275466, 469541853, 995994694, 810100340, 375309275, 779013989, 735441089, 413014578, 644069270, 345403330, 720256229, 651788483, 799146219, 966843581, 583542007, 972385090, 873694543, 450627945, 373153408, 941458443, 993320752, 948321409, 327641647, 392092151, 695343062, 396527136, 332908455, 820621633, 433173341, 154842661, 879402165, 102882936, 900921324, 85970222, 277368188, 511079849, 408719452, 437216929, 134941439, 125832629, 6505561, 710884233, 36916137, 415427911, 872948777, 56962124, 829900676, 289500345, 171944690, 153088584, 821857249, 605658069, 550814406, 625079551, 326458714, 395875587, 32056224, 57837929, 111324629, 396359887, 981934238, 89976377, 55066562, 657210197, 627038060, 434998175, 394638254, 480619608, 347533477, 7292997, 742517742, 338707521, 314341897, 164228952, 776024837, 980877699, 655162478, 967955650, 563793718, 80994582, 572102819, 31711095, 957252300, 798979490, 362945174, 981125241, 272504073, 621143178, 9462265, 198991530, 291852837, 495732368, 499880289, 68969488, 650295991, 263942364, 326494246, 719069375, 451323953, 370320919, 268483784, 463229443, 967801425, 34502145, 501138741, 841531297, 461853424, 993211713, 729015662, 210124973, 576237851, 768776934, 919683306, 42758242, 636105662, 903712657, 503670968, 963622420, 336880597, 737029487, 484555997, 512449774, 943773030, 660603497, 489925595, 785093058, 329602160, 593653695, 112084744, 116701873, 928621580, 740412980, 538256514, 535475314, 608504786, 665384475, 499709270, 204902890, 921753512, 234450652, 947715833, 134125134, 962173227, 948087700, 552293213, 143737591, 438869440, 566165094, 844016668, 399614683, 775482021, 319762836, 687246378, 274150320, 448374985, 659411660, 931177386, 637775575, 564100716, 747650900, 431424876, 976659110, 58047318, 693348530, 244861339, 610178225, 257635705, 994680710, 670162978, 217056212, 801206184, 634104896, 316602441, 179668043, 707590532, 594871942, 644923389, 29936009, 222948288, 946320649, 252788953, 333116109, 889607623, 881254454, 764962617, 288217113, 300232731, 730783068, 893873697, 22660712, 994155535, 293134370, 830155520, 124049792, 442088081, 105307522, 168737004, 703051199, 789910178, 642440838, 459561794, 626887772, 750824261, 366832648, 310214304, 513664657, 6626312, 721932290, 530392865, 331793315, 661987045, 400027443, 292065583, 959314828, 113229573, 687429650, 426065631, 668314610, 811646207, 930420646, 146916252, 577953035, 816171003, 854071446, 780389219, 647129521, 208752652, 151473367, 873207070, 796729974, 173263214, 370095027, 727617979, 585174769, 215098243, 971912596, 598875928, 721882283, 550649418, 912847526, 55009752, 343288790, 346928340, 460531000, 680694044, 238714263, 884044681, 184009043, 21534691, 831145707, 677730809, 472307949, 710709636, 481184261, 389235267, 628235351, 412532511, 493818200, 830983144, 446530226, 62273591, 778097966, 659106386, 949679916, 863037103, 806339375, 647541377, 562668582, 258350894, 767275019, 51185320, 929547290, 677925382, 657271962, 463144046, 7598987, 131871410, 644584899, 424950380, 597489200, 47575533, 986853735, 766687219, 612938482, 412137279, 50111786, 39055907, 457662910, 590159604, 290568992, 412254998, 848695058, 214559455, 867128832, 978276393, 548420269, 818005475, 424144877, 696481153, 693858371, 417776430, 118970781, 588049837, 428377209, 401368303, 868666565, 741896562, 513463457, 390949740, 745559919, 895521180, 825141662, 95029779, 965521217, 534614447, 466231749, 597247473, 159058428, 15783729, 779355606, 987266220, 754195341, 362278558, 67560779, 54188219, 198630214, 589034590, 824705149, 162516494, 810725801, 674573454, 764116278, 456756928, 173214560, 642546202, 827170383, 424092195, 865818909, 356397340, 325047161, 697551635, 583378174, 11029285, 125090288, 622267723, 617940703, 845814762, 420533074, 887864783, 540499308, 120458400, 786571590, 321377, 971887311, 586723394, 906984339, 37670420, 553185331, 456900044, 284127243, 665438086, 620542533, 644875631, 395785341, 741618055, 46763733, 103146331, 581734066, 647582991, 271376239, 522464577, 417001352, 901266863, 364156478, 128305690, 554177636, 107869956, 898091237, 860624166, 194273438, 835447354, 740542300, 113563114, 706470003, 979043218, 622936956, 526417039, 525757845, 367066642, 493307858, 72754907, 566634746, 779387624, 996694820, 60261497, 834998299, 398781199, 465452537, 759915044, 451861417, 589194100, 203958624, 520632060, 282569133, 252980596, 283375976, 805297980, 943729517, 411706877, 143331370, 108592269, 330496074, 223336525, 814063695, 195360198, 791407228, 267995602, 357301508, 296791470, 874524896, 794982119, 735661473, 540088158, 980883434, 729154386, 890670849, 779873114, 13359235, 568630761, 8221343, 941334671, 945470319, 704275976, 602326976, 633278148, 553929571, 32334953, 57482771, 40824310, 549771390, 458942956, 827320380, 397058471, 322218224, 99497286, 124774180, 573989323, 240458374, 572797234, 77060934, 883644730, 126236418, 528907394, 142633364, 993959306, 323834778, 262853583, 725643515, 607831378, 788125932, 764567302, 18332817, 351588255, 814949145, 515285230, 368522124, 853764797, 28642597, 74411268, 129418418, 40023002, 336622507, 180813987, 5434819, 303432278, 392854973, 288775593, 721612199, 479413911, 243246717, 293858870, 673066411, 454354933, 264802686, 766157661, 512108498, 206708193, 531728087, 1961185, 798074698, 427415692, 211735082, 265695521, 920186845, 641622533, 241745568, 291284695, 292305658, 935398378, 355597712, 939417220, 601943934, 265538032, 667839948, 372650809, 300761874, 580692499, 845446989, 589802248, 481194707, 794430214, 198354287, 192468243, 363605861, 501435035, 348694068, 991993289, 191920655, 20099653, 579058593, 162285112, 518058772, 743721051, 711717853, 776790937, 616905328, 80974608, 876103520, 610414065, 27975247, 26438815, 166737454, 967901999, 743214267, 703515050, 536428737, 978061031, 935264173, 924251998, 337992971, 733463029, 218397794, 878350319, 401780154, 36995050, 941857545, 932966663, 719284937, 569910526, 359510994, 903696247, 515044359, 3989503, 811825063, 577221427, 524675567, 559085441, 872444085, 479396545, 351988832, 246091357, 921402258, 154182947, 349633493, 229428793, 474381495, 828414233, 417358382, 823012525, 767149620, 711466170, 117593017, 252084811, 729317428, 623267683, 164308394, 546533448, 117095506, 865066033, 306471173, 107957898, 986359077, 599141213, 866509403, 730171328, 507033514, 435937348, 640183396, 490796943, 180767400, 917110408, 49102307, 723026434, 37374062, 739431450, 436978473, 498834922, 146719759, 694200478, 563692939, 664566225, 34825771, 910437487, 530775135, 150971335, 938679477, 889900379, 441863979, 265082541, 177939638, 585891637, 319235807, 16721120, 260882229, 956328858, 758505656, 299441462, 624300549, 592629688, 542732495, 875811897, 482146160, 718184444, 892832540, 119841165, 890436302, 641724305, 127487048, 2547731, 710047342, 485372820, 328031116, 932137784, 922695609, 791323347, 928544862, 646831109, 216647239, 223043597, 565822266, 709362433, 358023577, 30814995, 963382680, 966278826, 842050410, 307850411, 18797355, 947811235, 689728487, 375251689, 620052348, 689007619, 370892134, 157176249, 46197685, 951772530, 110240202, 989525723, 386087354, 892991134, 7947869, 469035346, 596752339, 202114148, 729682084, 371908991, 112398537, 277829927, 257411397, 926701566, 503052169, 473964071, 155681867, 565359051, 545000770, 755084478, 19163338, 532334095, 14247541, 660555305, 375646955, 722984329, 209100206, 158670568, 559066793, 389285600, 533832801, 774070416, 184132980, 534817166, 529645805, 541559784, 319560840, 600932808, 812955771, 950609735, 653513710, 960721993, 896188005, 985289357, 202017650, 385566689, 280554431, 78322313, 867982586, 814222196, 656505736, 949017387, 594764588, 56397573, 219808097, 666649776, 164764857, 530314474, 860247611, 632499954, 988980139, 596191408, 33596551, 29987940, 351326109, 466488595, 746534625, 624814682, 625755647, 84131063, 153876250, 706328838, 733971914, 502705171, 259898865, 869116666, 132760273, 800113220, 389648307, 39563575, 125024512, 524120662, 262419493, 985276631, 228356738, 653480521, 728507977, 548815334, 669388929, 651283894, 615218238, 860950164, 764226785, 53388328, 974352754, 537948675, 21098326, 63563385, 573251640, 4990792, 814541506, 592599971, 508286218, 213309392, 585990422, 861287244, 530410610, 937996518, 270505649, 614883021, 924992889, 491206884, 250801231, 140207921, 613343919, 509565297, 384654980, 777000083, 685613357, 690816891, 12568180, 459597813, 852696562, 845014380, 801919037, 489917558, 479058211, 644060221, 610182621, 332514153, 547363341, 309631252, 618432967, 595797047, 139380703, 40597037, 231518728, 371988395, 860038767, 433052152, 504598165, 713445269, 194639675, 592877364, 572670260, 257745164, 494617779, 664515917, 162072879, 780192081, 549165400, 304232620, 910992394, 60845477, 401121076, 820226580, 507960553, 99093727, 114388004, 584406081, 858860735, 340590670, 170742417, 345510076, 414273350, 301646248, 365207107, 749736367, 51285652, 352148061, 112608516, 575839494, 13413833, 405337218, 139927339, 183237450, 7605675, 602378093, 772849971, 577827745, 247839479, 73471241, 543236760, 611936685, 476570150, 913739351, 601044002, 517352209, 504721665, 253951513, 342923240, 52908852, 667691157, 322525120, 626519203, 625372999, 179460258, 584401411, 117668295, 196589866, 538254071, 916390006, 588947190, 167039796, 977980084, 509760877, 382480052, 565103444, 459117307, 654034552, 662256293, 450325783, 159143013, 38590359, 624577468, 81575174, 201090044, 435304335, 601406954, 247095837, 525783156, 223599561, 410390116, 386481786, 669638482, 801927006, 608971246, 424064193, 38390041, 688118830, 487694207, 208470037, 250799807, 877520736, 454315164, 905869492, 996912324, 552272712, 939395596, 846024435, 473130588, 390391558, 511776775, 443456264, 339379968, 772976794, 527567908, 611181482, 726583227, 760076668, 328077256, 987750912, 612640063, 864353081, 648464478, 694474359, 608258084, 573378377, 336569178, 492802046, 207782977, 743094104, 231781774, 731082472, 638166581, 621718742, 371849087, 230709424, 7323962, 430959270, 313228951, 876001330, 839931042, 509304387, 923639909, 556775506, 98517387, 627834569, 311355269, 81996313, 686253763, 800611643, 34179007, 252435792, 245329666, 900127837, 607267349, 540381982, 73840234, 224172364, 243924492, 459785494, 621507996, 324701279, 772334024, 356930258, 760010938, 810320643, 298800241, 166509615, 947461673, 338378519, 295995233, 159803743, 595387154, 37345812, 244577444, 63521197, 550441603, 24638684, 37221413, 658659974, 96052689, 822172044, 934842076, 107560786, 899257841, 459961510, 33980624, 134019494, 472714658, 316847527, 729614888, 571830628, 631374627, 85128057, 558818344, 443459599, 804751380, 773551054, 414356889, 588960756, 18467686, 413004261, 895245133, 317048395, 664489187, 512479021, 471554592, 94276977, 105261595, 433696084, 48309988, 48479733, 727761124, 363190484, 935866134, 585542856, 784984698, 308500231, 863667775, 755786610, 310044115, 299024371, 140506926, 760939634, 89287573, 880016212, 547635407, 646847872, 944545171, 583381352, 476391055, 662033915, 900916689, 124637157, 642420341, 575880834, 220295991, 642323266, 323175146, 801396356, 153020753, 833543937, 774391494, 973169866, 548287564, 670556041, 350675532, 64874626, 147750883, 943858260, 218468977, 136998701, 741710081, 757763266, 394612758, 84699931, 212879053, 455918103, 126157666, 576574014, 204081762, 948922286, 212510838, 358031587, 611408924, 353439799, 618816998, 161331627, 518347808, 654408897, 492076830, 826347058, 148351460, 494174485, 805910868, 182999158, 114566382, 532865295, 650147231, 21045727, 747839694, 344933762, 755066599, 915644830, 283724674, 921568689, 572343349, 28826776, 109642928, 326017282, 288261904, 616971234, 474804103, 47410468, 921558871, 274690799, 940600349, 569879983, 99375586, 177253988, 383004369, 86263554, 892897772, 993383295, 635647816, 611276397, 413548979, 797656644, 457182631, 323336878, 948329663, 816307206, 463702514, 7764597, 533771533, 298778576, 744029934, 731006120, 59924984, 735703923, 409947267, 732900462, 685238808, 585746258, 825358955, 385562306, 471926399, 155149896, 672783873, 271261198, 362230916, 299278299, 63119430, 40029247, 965247374, 931327060, 183847865, 968851074, 864277792, 60745440, 388317802, 528742388, 768647371, 988498940, 776574556, 258808774, 409377615, 654653727, 506032311, 325210677, 21748680, 707432358, 82717115, 102465784, 566421390, 351157539, 531370080, 31814106, 243695939, 873484172, 583982487, 186029921, 180368049, 972608087, 803802169, 314129615, 615160558, 787379451, 427472026, 911673120, 125168716, 39398373, 908924573, 582831826, 137315820, 774460046, 440664294, 355179495, 522298761, 479312770, 91008834, 737161029, 524296448, 349439824, 410784859, 271159281, 534175769, 431981265, 763332873, 930810901, 969273844, 563421876, 84193865, 426991220, 889444865, 866700214, 817763413, 875472158, 305880246, 427631434, 431688630, 328841383, 147893156, 342541079, 29756291, 457107144, 91985340, 669789975, 389204767, 585962960, 654518387, 829134220, 543622880, 182157608, 878809105, 329708105, 815406844, 928884407, 206343963, 781921689, 527461545, 757458755, 118935369, 901148351, 598937838, 818375226, 485714951, 35164081, 742283614, 916843728, 766656773, 521184156, 234974025, 239456823, 169297033, 280478698, 576023258, 842810482, 498642408, 932635013, 85982958, 531915263, 777627152, 260796077, 852830090, 127378125, 936758434, 661676088, 102070441, 779742155, 510607475, 276891360, 46178546, 871545510, 226330205, 417547769, 759170098, 26051044, 196964504, 641774658, 864383507, 438389415, 488030500, 38248196, 130654416, 306930583, 95153180, 442770074, 351939447, 191419631, 514996872, 251400898, 515732148, 822125627, 478659806, 951919548, 129345145, 647941974, 893227688, 892993670, 890708424, 642861352, 589963918, 78874596, 757942531, 553792268, 143293346, 661786467, 413601693, 84550560, 780576751, 95706687, 115234170, 10052162, 166566784, 485173505, 586697459, 932658252, 891021236, 77335201, 993241236, 972496440, 596083236, 282850677, 11947818, 333454539, 19210033, 710069833, 364024685, 879612268, 257289298, 856633024, 488367314, 976854737, 310367617, 772232249, 495260768, 467370790, 728821813, 890755201, 936714283, 686693007, 860207758, 673341894, 707767677, 828045547, 798920876, 955979922, 935763449, 130342599, 558781125, 33448879, 915011681, 106777839, 845448855, 238199847, 477838222, 736908183, 923139337, 427663496, 286406495, 863033972, 451129759, 473731131, 745722358, 307056269, 283473053, 883310935, 304024356, 771212419, 815713177, 65955335, 847549624, 880423290, 582467647, 685522404, 820804018, 535002781, 857111, 207589809, 958144209, 566914200, 741981708, 904097151, 982529342, 464366860, 592861019, 423229553, 542569478, 346226650, 113753782, 286108177, 199775978, 683042635, 854683567, 197184607, 981852, 8664388, 568050018, 876611420, 259390607, 236262712, 10261401, 294761581, 267030174, 896403218, 103947656, 30147920, 871248877, 377254307, 648462458, 790709063, 590129098, 406207023, 585250853, 202622229, 818505241, 117054252, 394794914, 696855351, 749033487, 489496590, 345094375, 679583837, 178173194, 574466561, 41167975, 271240494, 479424005, 975752818, 833337885, 251764267, 295438891, 979596071, 766107207, 556155685, 690346627, 644854826, 99033357, 186961047, 995205302, 639887846, 303810749, 806504794, 641497575, 489110580, 604315628, 229748706, 76742895, 97408008, 755842593, 525745399, 61730974, 999544288, 871636422, 907416890, 119091676, 208590241, 48047630, 415232138, 415971828, 621138470, 94268715, 299921949, 766009358, 291883148, 611834651, 616223149, 437098838, 866331745, 627910257, 929119730, 673220859, 354636353, 905668242, 605829789, 662235383, 883267914, 898478728, 52767748, 115739151, 578914156, 821391526, 451301543, 952712619, 465741352, 179540047, 986343792, 284763612, 249837592, 734427942, 703970399, 105861838, 282164548, 442603476, 131750286, 746279419, 399681064, 887180647, 451109540, 475405289, 777934325, 217772475, 229725819, 486887842, 396447623, 678485463, 959747959, 311148006, 978537181, 788933855, 890828207, 585365295, 979148467, 437061933, 781586707, 686456887, 366187528, 109277747, 960366493, 701243595, 277970318, 94603239, 756050020, 821626446, 901189589, 702299423, 202770401, 712845241, 340108414, 288732063, 870961652, 249523182, 710391599, 969673635, 963119399, 342469704, 912956633, 344066833, 748854241, 870479072, 722799607, 998829866, 274145009, 548183174, 89243200, 398964153, 900829609, 489742572, 413035945, 517839797, 692731634, 110954633, 818694677, 835567979, 543470894, 667768072, 229269574, 270491169, 743937477, 893922580, 460150625, 416291835, 700713341, 20765521, 835913743, 998332867, 596839441, 306107931, 365289660, 507633265, 890521127, 332740616, 278531095, 580376018, 845896961, 779988087, 571506201, 642338044, 877898886, 560041696, 206400480, 645865886, 371929206, 601759004, 48837290, 870336002, 857981206, 976047095, 640285633, 185351714, 212438211, 939681169, 330821192, 86114897, 352951049, 577387632, 948523714, 445408982, 765357390, 83973173, 37785149, 459210029, 940343250, 312983310, 190549130, 41750091, 967156706, 583083992, 279433345, 769259269, 240788305, 502064298, 356212386, 780293562, 283134196, 981292667, 641249721, 98546513, 195770425, 968897701, 865721531, 556402517, 599908514, 319767955, 928703544, 208215054, 459412125, 315145328, 534782437, 641474392, 976608756, 629158859, 330923948, 650715628, 885391179, 453599700, 899023922, 180390635, 800589423, 61964397, 279207185, 739157481, 624788510, 827722199, 314895517, 923954430, 2257847, 993759404, 492991104, 225590319, 157714890, 253023488, 490708026, 23707536, 142973892, 246224099, 607669378, 562950901, 493132909, 66257271, 227794403, 476810447, 349191103, 500977785, 167960628, 205799920, 194015344, 476962796, 403479951, 569094768, 600325967, 804869249, 763945002, 376534838, 69646092, 783696146, 258292664, 608725399, 363804183, 460508326, 876305477, 558624242, 367419550, 564442582, 160696685, 982804585, 978204388, 179406453, 877887388, 665231144, 666117840, 189732025, 465789569, 92887371, 784904848, 248242221, 251435079, 540913722, 760482344, 677683599, 567366009, 141751623, 18225575, 783380287, 55275881, 984332958, 715287428, 249200246, 454234659, 672316234, 810324933, 978061156, 919147992, 135807936, 818919845, 488612346, 126249991, 495454650, 801650687, 106474796, 165406228, 636451057, 947737341, 235391093, 510993798, 352843623, 931245781, 780974043, 247325768, 927363705, 391754928, 449119040, 172799241, 889850245, 689781083, 415628069, 816168114, 743117679, 729943496, 488567164, 822902773, 297250122, 903459937, 357579380, 212455774, 765683557, 490572175, 464633534, 448349988, 601822913, 444834033, 89377675, 709674004, 724627110, 317502820, 619579117, 185722428, 312179356, 638468343, 523126627, 328264659, 977728633, 741876311, 465205294, 234409756, 371036377, 269516102, 596531317, 145690870, 963719434, 424238263, 592305189, 12674139, 690575093, 69967443, 730819162, 509321025, 527096999, 960880832, 307446194, 920563962, 580840440, 605644707, 548668294, 389722448, 937509339, 223062448, 410576667, 209999261, 628349231, 416054777, 440535791, 775871516, 31645637, 508285427, 601060219, 724038098, 968183045, 330967813, 629108484, 922031418, 654207020, 965432353, 228093624, 82057221, 244140668, 371624641, 374667852, 961533171, 741256429, 152792018, 328493753, 900067562, 537971098, 412490563, 413439703, 159513652, 200884971, 95941788, 912302220, 222491912, 34755627, 696044630, 920549813, 130069638, 447906413, 370081435, 697395386, 377447091, 560499327, 977835229, 731975672, 858677072, 411793079, 150477489, 587126173, 38884493, 896777077, 46762150, 973787878, 738291010, 5913864, 293174246, 427248136, 963824567, 301946759, 309408830, 256384362, 705136512, 304027921, 434270894, 9041133, 740102315, 357696065, 980443911, 35594251, 721680917, 225939056, 37849216, 836529804, 207005375, 408726138, 357902586, 365807531, 309659246, 228547226, 169206737, 866360599, 24894611, 319567879, 698216238, 543886957, 179933846, 902737109, 474391668, 797456935, 702284936, 213657310, 452392966, 305525122, 746695983, 17760309, 622503386, 336345237, 989816497, 84148170, 264145816, 643274534, 9198265, 534165934, 986819046, 640042614, 198331619, 848322823, 135473594, 325767229, 709320842, 785014562, 395978076, 730188907, 797215092, 701660513, 367596118, 671046491, 768124030, 848189270, 146608172, 792395148, 807400509, 235756048, 139675401, 149122187, 968222600, 105441364, 80572030, 336196915, 277310241, 698441957, 347015559, 450321779, 415927374, 324950751, 304490733, 847917488, 817060164, 788598376, 28485136, 157046577, 956831484, 548591730, 425299744, 389963381, 436355103, 274306471, 391691454, 973025100, 85449634, 832671099, 824737436, 27881003, 162464261, 3480401, 692275859, 818619429, 381572141, 993825316, 729453749, 116373278, 111261009, 99652910, 800585579, 327991921, 348729161, 504840896, 947715587, 253593330, 385188498, 204545161, 816619908, 674789369, 816717127, 993993457, 164867080, 363821005, 641246221, 491090155, 129367157, 409522754, 823949342, 414125684, 987891851, 371146443, 304879737, 170541443, 541022487, 743450934, 159912681, 482695654, 647779348, 753689424, 2693238, 319319855, 834565107, 145657413, 461225572, 783719917, 740520313, 220089484, 121999077, 265897920, 864685459, 503333411, 541312218, 923265914, 904301436, 443181132, 889569623, 495996244, 979912522, 71874121, 432914416, 158909995, 972687516, 443554980, 661239446, 696440468, 575715731, 433036798, 678218421, 202452294, 274027097, 981117579, 463711252, 354215037, 19312990, 49008098, 470289016, 531405895, 649721317, 813264027, 371624194, 277775472, 96054708, 823273221, 599650864, 528748538, 246083244, 656381409, 828118423, 939584354, 63215315, 587086759, 537194882, 952938738, 753663781, 329211367, 226301294, 244824056, 54919220, 192505517, 903291479, 917633846, 528012927, 83319616, 438588809, 370078780, 183565882, 158944814, 481346400, 112864559, 265974599, 281522129, 662428856, 941070613, 964087745, 377710805, 892127637, 798664228, 45072875, 952900706, 783998352, 790063837, 402446572, 607575848, 656822372, 477052789, 281378975, 935749098, 149737628, 679982744, 60865403, 600776789, 600403497, 627042074, 526807132, 402408586, 909277748, 570437413, 718939138, 361947850, 976028758, 80228267, 717711572, 717864672, 638471455, 700884440, 184871712, 971114074, 374419475, 117177706, 967229485, 278369966, 649146525, 751469851, 569427315, 208321560, 874638448, 196466672, 122928863, 263787883, 610307824, 603026847, 650244300, 211295555, 305236180, 97799444, 273851956, 86796706, 914093261, 372017817, 972302369, 204100362, 569667199, 771555873, 884312329, 558703764, 206502656, 628030187, 701030356, 450655172, 605381419, 706247053, 74520617, 568287074, 439555279, 295067475, 26291789, 324206196, 295591657, 31788332, 175050434, 140599094, 685822171, 256293006, 88083999, 240306629, 862633353, 778765140, 381467615, 900242240, 364415891, 383766286, 353196278, 585488714, 410014171, 565319775, 270020572, 588298360, 710429125, 315992273, 206439882, 518530832, 4360922, 569764779, 62494365, 377348279, 700301108, 948231005, 526972636, 33203992, 67903819, 325772967, 327062962, 252529499, 615539381, 437210207, 439463259, 929774785, 846325792, 712161525, 377726355, 308729513, 608493610, 677246892, 929202142, 873450290, 835979119, 140976385, 267613431, 737388934, 502846962, 383817944, 214534815, 735196856, 419885350, 284275878, 298925611, 22767546, 68435888, 736139133, 63866352, 268872711, 988210784, 771950070, 5785483, 235479247, 401646773, 67658814, 60916195, 589055802, 779137673, 822790623, 225322290, 348174868, 147026335, 570926295, 253837622, 382129048, 632049395, 906715473, 690191510, 326403229, 933301029, 848966468, 440357746, 379008665, 162391163, 372819054, 870000088, 707430315, 434351603, 13007650, 460633467, 19613315, 495747725, 392986385, 895949623, 287992204, 105641445, 210709210, 230761842, 363083335, 654218611, 69476690, 653781027, 393490916, 610303675, 771929660, 68286209, 589704822, 487767744, 524352048, 683607317, 886418557, 414936009, 83515477, 379172090, 804891202, 101612600, 935099665, 132185612, 492087545, 407032630, 429614086, 166414431, 814792368, 97845970, 395611734, 35385813, 804647975, 939948897, 699366287, 185553463, 955723655, 322068913, 11658702, 719134776, 602727600, 371555641, 331842438, 480690233, 408258632, 214315960, 331228091, 694047959, 880302251, 456159822, 315798478, 725357008, 204821811, 750661359, 946765175, 825548719, 522654307, 938294857, 632743202, 571653236, 684448274, 563576180, 882960989, 717358089, 317125894, 195220557, 626255077, 350096526, 996745190, 367552237, 263452893, 614714431, 85481015, 278976343, 159209727, 279828122, 244500167, 571790957, 447887458, 303463135, 428175288, 466868251, 375624243, 723800582, 443174796, 635135551, 823904270, 611363590, 808514579, 865765901, 307953530, 913148932, 273824017, 272446733, 543372249, 122651942, 126271145, 810464746, 17065883, 780057737, 330261422, 369801884, 231751347, 2244294, 748900665, 353155615, 232529935, 540977808, 108815455, 963094142, 397717420, 553586394, 806568779, 780477756, 140463403, 585443928, 315778770, 460793745, 667808364, 421287706, 790789290, 684205260, 46555973, 179965605, 2254774, 282034157, 940230784, 48725213, 435996273, 216683812, 212293139, 367430924, 4664241, 961079291, 291970651, 994695452, 643827618, 467663997, 287021936, 830318372, 681837390, 318022218, 356827478, 4320430, 138685227, 949611979, 909963046, 585316519, 380090206, 818115611, 597173827, 213578413, 6738316, 780348947, 620552900, 861114732, 78738913, 987241446, 383692737, 742385503, 806272481, 542440086, 224706607, 869238074, 577599775, 796429987, 567249428, 457331016, 167351048, 612243841, 362306133, 912813278, 353059803, 244364334, 546486686, 589798056, 329374629, 282649232, 261386320, 408205565, 441106646, 233729971, 116071004, 344324602, 280174908, 457145809, 889939054, 314303717, 547645908, 967256935, 351218731, 435562284, 4991148, 568135865, 385444774, 729000892, 56441059, 443660895, 530427912, 189551454, 791662237, 525838969, 963989383, 358515283, 357453191, 527967313, 224126178, 136824419, 750734487, 401095000, 215491371, 652345928, 189851536, 657214525, 660015827, 423096547, 736086765, 193385499, 434251671, 710435734, 318054982, 111509022, 650162070, 694418021, 81919128, 278431493, 53751359, 658115666, 716821855, 99698994, 309818484, 43261678, 577434085, 926397761, 767276634, 831078040, 868794297, 986880544, 166536660, 359603185, 411060913, 257236989, 637178296, 152309214, 793372209, 525941412, 51173854, 217216112, 987417202, 959911174, 821371623, 18515141, 756148135, 352771736, 86989120, 933592427, 969554811, 639534834, 91766098, 549618396, 667586921, 766987599, 480094789, 357765371, 220514717, 878028579, 113312375, 442703120, 611368824, 968449133, 63954974, 558238620, 63886835, 746182869, 370620370, 878267079, 511768784, 233352158, 710784561, 154626114, 904460265, 625949657, 16072662, 284018649, 446745667, 756458618, 221143074, 644955671, 175838639, 905730308, 873253560, 653525134, 674265571, 981000655, 480899856, 373781324, 745554324, 670738330, 167516478, 408015880, 635544350, 356157594, 24947312, 964343961, 374050732, 730036067, 892351150, 521627842, 788573422, 150936531, 482764725, 748515254, 457784469, 106772481, 626736817, 527469223, 325191257, 263771102, 419452771, 505222820, 151503084, 864416308, 727366447, 377999912, 860220788, 816553392, 934409067, 231830245, 215942264, 808302, 547135960, 69100290, 694095158, 675693291, 817510370, 86715513, 105852811, 910195862, 218349580, 31973184, 537010630, 640712053, 684004973, 375393781, 875761919, 338694871, 604829721, 569933021, 125965009, 262900169, 849652576, 642221122, 104167380, 130184487, 331289064, 173599975, 902595042, 749811230, 847861182, 582884279, 785249982, 404256665, 62654259, 689759529, 126649530, 311993046, 810467943, 665650932, 220139332, 455939567, 994007993, 257629298, 550932202, 993478715, 109844588, 865833567, 272270207, 169036647, 242668410, 651316636, 445220371, 371255199, 411656725, 908016525, 575569532, 847209471, 682373560, 773398357, 760628101, 71151496, 930645990, 63226402, 792741873, 629453285, 941040572, 95831364, 878244335, 965022040, 469407438, 707012766, 811277183, 749024304, 556864653, 906631390, 370091567, 358394873, 383840082, 859893467, 558594016, 748529786, 932870226, 328384819, 173336623, 77297920, 19060326, 953140409, 763806228, 739444102, 164938522, 961379851, 303750817, 857063904, 495218668, 623022859, 973450009, 292976568, 195553674, 978267793, 817627837, 386658578, 582761216, 489702997, 904436057, 756744451, 857884438, 609174963, 149750585, 665575211, 935183396, 117862713, 655339237, 799076438, 460656109, 136338696, 732921434, 726225742, 803226088, 569878333, 225263986, 306927602, 252854889, 53580392, 179859184, 528658898, 361730780, 974997916, 938221206, 809338629, 51574041, 757895731, 957387806, 680978656, 653015471, 676314097, 491695120, 820376527, 296209786, 214968813, 187391972, 867496729, 801794636, 751226934, 259018934, 717570527, 914327844, 767552715, 649591506, 940265488, 411309379, 925302371, 110587269, 527123159, 338150984, 267045625, 669791133, 789810859, 916811378, 716491163, 447865507, 30623796, 457477324, 810277774, 615730733, 273440911, 544697408, 989449631, 190940859, 333541730, 899963663, 651842833, 388515270, 478217258, 811798704, 950057901, 99903603, 76590284, 849327838, 116157099, 139743333, 574758199, 640499756, 201809366, 332030537, 263121975, 86626787, 308269653, 285554321, 657214918, 328146129, 514626269, 739362123, 772911898, 267791411, 718951465, 170415178, 248335947, 774990289, 299716461, 897895290, 832205167, 268218299, 35393940, 224521669, 255659314, 136850092, 132039858, 855614761, 405400329, 514852055, 908398234, 614134782, 386199881, 982442743, 683298939, 353422672, 771231791, 427416725, 590813933, 978592526, 947817061, 1477168, 252802162, 921340748, 726106895, 730029356, 23128889, 237356991, 16232633, 595040286, 768372154, 609767268, 562783612, 656866806, 964578203, 318774460, 933729836, 711860583, 402223020, 680720959, 957347910, 753251404, 262507304, 147842175, 819182754, 654065202, 856568863, 227562345, 294733082, 125940059, 69649084, 693108083, 439477586, 673308986, 970280232, 623379477, 846563577, 921147693, 533937837, 777237615, 654031028, 678860924, 312167241, 620862330, 838508239, 90240679, 604344598, 570297686, 726123270, 116928307, 277563401, 123881404, 812741209, 395870418, 639566916, 101670125, 231896255, 679390421, 73185328, 110859017, 541431209, 885965686, 230683932, 676800740, 468439163, 145827058, 482248179, 71185987, 730093893, 680345208, 687202049, 828000011, 375768326, 638526145, 257522609, 626010111, 194121085, 443343544, 333584607, 269580470, 525945687, 244711037, 852474587, 917049034, 158653734, 566653158, 263266261, 241940726, 571586174, 649675932, 777388606, 583029795, 509443871, 396777226, 989261474, 394309265, 959571579, 838712667, 602989874, 507842254, 322643378, 128449193, 819871064, 986918234, 507648903, 142887899, 709600003, 421470198, 811938048, 18935632, 119726218, 50226468, 151293900, 202737026, 518113843, 849689534, 507826653, 254379763, 978025749, 253287831, 196594898, 962826635, 358477618, 383038412, 834518385, 867730464, 156189664, 468412530, 47778929, 234564547, 210522056, 842043900, 296203518, 949326458, 6534769, 747289785, 94342719, 990729766, 895719266, 194590327, 576682649, 697667317, 592827199, 334933216, 409775127, 232655357, 704043523, 209429718, 322210805, 138181848, 770677898, 638350940, 724868710, 52589463, 795509758, 320783900, 803204363, 9030086, 280182892, 239301730, 943609375, 944562680, 912933157, 10884480, 826535674, 71439597, 506550404, 426022480, 476258171, 419688493, 383667906, 12689601, 623740309, 611866890, 83068450, 377492405, 133297863, 314733511, 343147398, 873350259, 314493851, 885534843, 192106634, 756159942, 996074651, 748381862, 47644119, 993981841, 491709317, 59042432, 428951812, 720237824, 748079748, 291441949, 664730857, 303763264, 722952738, 964212500, 74165547, 368807957, 597674447, 798804024, 58449482, 975420078, 279664405, 646468590, 956864576, 75756830, 707250099, 769516933, 503829729, 746285710, 720797680, 864247854, 304166777, 92560338, 457669813, 952124753, 670843410, 893219387, 752560158, 643448127, 271542498, 763083941, 216985240, 439409276, 650260240, 713733678, 3744459, 496595222, 153131910, 326485347, 871912662, 971111789, 998904778, 894708101, 249622053, 860235534, 999265513, 939581181, 524563860, 904827330, 767835657, 429795312, 558026670, 76658022, 993504850, 171911794, 306538887, 557786969, 44419989, 511586135, 151944322, 139184595, 140060052, 251843222, 212603895, 97370207, 769800300, 489843059, 957918478, 697078068, 433761743, 926513922, 85348080, 79237564, 84614445, 252362446, 903267426, 546241344, 92299612, 800948462, 258808368, 347332394, 394017425, 574448825, 12425041, 831120095, 548220274, 136157680, 784903322, 774776507, 981762762, 444492657, 844914581, 100397887, 820625742, 792834930, 939960356, 44951162, 7933102, 859388376, 304962692, 889574704, 578318188, 255692001, 691994544, 552239612, 482058053, 790056751, 362288841, 931466647, 344075109, 157355631, 603679700, 271258484, 157878371, 104031226, 168743369, 190457714, 174765109, 596556517, 34678184, 223854898, 468066723, 905641864, 823864108, 861967543, 510888983, 911089659, 147127305, 899801968, 175798591, 994578630, 326010976, 398007961, 235754245, 6512656, 456669781, 176225774, 262513379, 342409789, 925406905, 48828846, 534180955, 341532732, 746033549, 760433488, 337053955, 861665214, 949606341, 979651996, 418703215, 411760032, 650713877, 417219560, 427550849, 650953070, 968428194, 465951534, 291056192, 892469589, 496946536, 505340293, 70561657, 509882554, 310631786, 10271477, 994643874, 480788875, 897185761, 235300196, 265511306, 16961527, 736675308, 193430479, 568934129, 501260675, 934775363, 787253662, 521916822, 909620275, 522771838, 654060027, 347418359, 55583857, 816485938, 307000907, 340188300, 642127298, 432582390, 735180560, 190433091, 195592807, 615379477, 436312960, 305304093, 493645503, 103557590, 952675050, 372185881, 39853932, 829050026, 943194763, 865950674, 574475038, 292733043, 657451372, 821396696, 54189582, 917158199, 688484490, 530485959, 726457066, 820418820, 334991599, 416837653, 737963305, 608013231, 689887619, 772224772, 347419770, 816164209, 539051615, 166390932, 831390785, 216176450, 540581149, 556662812, 521461857, 490455265, 516902472, 541226509, 705250964, 207835613, 653743329, 299110419, 681276643, 393844387, 421723814, 418324214, 636493798, 210545507, 558273796, 673660000, 906449055, 648032693, 574059485, 311256395, 501968997, 584258362, 412669276, 555787617, 643203217, 120732948, 48945766, 643128841, 749674698, 178290232, 207139405, 234820836, 569182298, 3807847, 287779326, 478346241, 938268560, 149702740, 440129970, 981553737, 346044036, 672092114, 873074373, 9093143, 162619816, 801089465, 703582948, 455314355, 25971669, 450331381, 234416414, 365129837, 963896542, 25001332, 844067162, 812109954, 381255458, 744772268, 170157643, 143172804, 844074135, 97360880, 621668256, 267713960, 31277343, 420863592, 650393805, 60809852, 667102707, 670334554, 213937154, 370133019, 780663272, 865366189, 653520950, 456651365, 619257801, 730807377, 804625860, 366072101, 306907326, 350130321, 125035829, 948888991, 180083187, 590164987, 594149377, 490444304, 965690354, 23762448, 752369970, 282132503, 192860617, 880265751, 589214264, 108148070, 852915108, 682569486, 643349342, 501419453, 192394686, 796426420, 121279675, 124107520, 471888859, 575333603, 478522907, 608115677, 387306078, 435824736, 335055823, 473491504, 825412232, 764957088, 889834400, 190007616, 554987142, 384968172, 104130897, 764786488, 326365200, 681088577, 845776881, 660981391, 668810927, 54670318, 980413598, 189398196, 872133280, 273284463, 619029535, 569626030, 607715446, 169139966, 226179075, 672269915, 338649045, 415330086, 94297357, 461736963, 947007556, 207629887, 94075233, 982399648, 398660089, 570709673, 669611193, 31239936, 633974783, 629930738, 309271861, 903391978, 687590088, 809167109, 986379256, 40788263, 672248872, 876359599, 891147874, 284795815, 185239851, 200698660, 914389746, 552695579, 239225958, 277140249, 972795480, 724477921, 212828289, 93048489, 197048969, 560423445, 700375577, 999984197, 691675778, 536521267, 425401886, 279295033, 441865876, 121085615, 771210979, 514652109, 741356490, 603873943, 889992543, 844507839, 494112613, 600360119, 823705021, 130107203, 55792892, 846272385, 361758402, 169836447, 378701138, 843921527, 889344122, 434862286, 143616381, 420484232, 482033806, 281713846, 79246954, 1097828, 672572584, 233427679, 300029815, 273176727, 717546128, 999231840, 420717035, 637884674, 47493846, 522039329, 943201849, 448836489, 991281684, 311943349, 140649180, 137882312, 205215925, 207055252, 874389446, 817822963, 69742327, 285636106, 240433605, 381145732, 90032822, 195216947, 492037424, 762377296, 172255259, 470230590, 764456579, 676989263, 694428609, 408209149, 441678073, 19026748, 921756279, 556542339, 415596860, 292863020, 366480289, 613300515, 767807697, 272151325, 311123115, 777554023, 162912556, 664585438, 893840943, 615045606, 973571213, 962799695, 294574456, 466843909, 966143454, 43251095, 226882433, 739783313, 629015963, 793206626, 11545106, 674156161, 276052918, 865389051, 658610312, 799400494, 880496660, 525823110, 220559461, 781978744, 444548857, 18507646, 336627779, 743553420, 496070248, 862975616, 329745198, 684523651, 598472873, 641919517, 300090306, 183952129, 740862474, 593109090, 218581919, 103514280, 185849183, 106944393, 821634641, 877500261, 178196486, 625828740, 115004815, 28739329, 762752571, 847758207, 160979259, 56118498, 737004267, 472528916, 346025555, 66039395, 193039722, 80053871, 897611578, 400255699, 497778814, 207663557, 780513895, 809444038, 361236354, 438039627, 88811343, 566259475, 310850813, 765608091, 967452558, 25704311, 415853848, 562304725, 164519196, 187606372, 916179500, 759654280, 974851092, 291823262, 593956633, 920223761, 701477616, 795900182, 581374977, 254464858, 706691229, 298489974, 518110572, 894919137, 773317896, 172391929, 120877229, 767338776, 94655200, 269068183, 552144396, 842477773, 808618996, 818138560, 290912754, 36110904, 154384729, 811954667, 471254136, 989144174, 600613630, 500950016, 124829473, 465218832, 934369958, 472396481, 300185865, 702287796, 84053138, 351018955, 921800939, 831993605, 869416228, 47160760, 411263993, 933546575, 387963706, 215152823, 460154904, 648716781, 493762736, 939788914, 951996095, 248967258, 36847762, 899274731, 215122196, 988463900, 752975026, 446844345, 194312086, 868786198, 981525324, 897388333, 376404870, 720162321, 200074075, 481307446, 614281237, 6522820, 691325088, 97588340, 134563440, 677209170, 709769826, 599439656, 393892787, 689959020, 58886729, 660630999, 690356590, 531330293, 365629425, 411297146, 323496448, 87233090, 767897590, 369890093, 640851420, 776748245, 756875755, 406952282, 747769690, 377040414, 829496726, 119620741, 889875546, 520391862, 176718319, 506863785, 296610604, 950393606, 754703940, 469751791, 335180856, 203791791, 763827547, 770930604, 893078443, 446440929, 10816432, 624477984, 208996652, 201690092, 950837631, 923166386, 522957238, 78212813, 751793468, 832023868, 158479353, 330582333, 50546716, 515957035, 885512753, 390078468, 89852162, 950458950, 819546984, 186836295, 522121397, 59813720, 431436848, 547029266, 576584697, 950251587, 888106352, 97952637, 948490740, 675882809, 966047516, 585548957, 372061945, 841155110, 148522172, 694774505, 877497495, 406495044, 885131939, 596964300, 699567650, 867789890, 736069646, 355354473, 128294763, 23850028, 670588126, 8207281, 680145612, 560664448, 683313373, 646016454, 242828395, 21461264, 755563345, 934269852, 51504984, 904635604, 770449434, 756492052, 147186936, 674421614, 606844352, 615064665, 336901658, 768144174, 445307183, 214794445, 150489587, 356229491, 945002998, 989862243, 561180543, 164636991, 600710716, 388913692, 551944523, 440480768, 353755005, 247094171, 657840253, 627119458, 65026308, 591595235, 159437638, 851035198, 455207229, 318026076, 45089285, 780702056, 521756403, 338927864, 91125581, 54787537, 906118870, 996405005, 73468262, 416416717, 949937536, 35461569, 926339347, 575017051, 831537424, 192651605, 487078449, 475064832, 946953954, 933945279, 249499047, 199201059, 109806629, 842551396, 994848176, 815354554, 26441255, 512462733, 744101654, 851276259, 412586253, 184593959, 625561819, 150269174, 688375533, 758371840, 428653533, 439950441, 401720415, 856601981, 921704062, 430021115, 288095446, 518961076, 612720489, 510752663, 694127114, 276151406, 373594541, 193369269, 325880880, 771787465, 191701435, 16919214, 971399718, 304390093, 408017171, 942584730, 57428694, 390990454, 321843558, 245834566, 671148530, 488509328, 278127623, 995495545, 392500321, 291436349, 40745202, 863897465, 900443786, 777655812, 515984658, 470328247, 129061802, 244552020, 81827592, 131191468, 864632449, 279096659, 175114640, 390331003, 870134261, 227948226, 874373269, 323227506, 416150009, 395445133, 329888733, 76021654, 212238382, 778288655, 507654501, 894868541, 5258735, 566670229, 380131503, 240489757, 110402690, 691165218, 354380912, 589372635, 28908069, 50866513, 842059669, 7244675, 720235191, 682022589, 985025948, 389968718, 316407545, 816228131, 875826652, 411453524, 351994758, 646602430, 182640194, 128743343, 226782170, 471448343, 244267416, 376552599, 485442119, 739668602, 844249611, 984753539, 108595757, 309277030, 374204828, 551300811, 999483759, 469589663, 543449071, 15984434, 878371379, 645386944, 537159412, 579913786, 890717778, 693768747, 189710547, 73437620, 6129022, 853031666, 516364200, 874154299, 563799942, 170279737, 118396865, 69311174, 504130913, 384029192, 131578776, 476632442, 68008301, 604887401, 626998880, 309743148, 613525193, 445382821, 9660442, 172860565, 555540935, 739556555, 683868148, 42741542, 886761226, 831971337, 274596743, 661341847, 53293569, 118862813, 624112, 331668407, 160192513, 813141465, 342927284, 956833890, 218752776, 20906130, 273502295, 399754339, 810037074, 197896364, 838514384, 177803043, 435935647, 488330645, 492598085, 773301301, 224274487, 726241692, 696571125, 316604069, 54992567, 178501812, 659374497, 604184930, 724588786, 754103901, 710899112, 854967777, 296445384, 914109973, 516912122, 348471452, 480932230, 130193074, 288267888, 85226564, 762613498, 626491714, 670252487, 94101504, 414852347, 278239694, 519766451, 305069034, 455270617, 67465230, 517732183, 605937262, 397437649, 418913159, 202858552, 559269258, 503443180, 344093946, 447048312, 217620062, 47429719, 386195822, 792884751, 380188952, 200815773, 640702094, 355756552, 453290730, 434349584, 961644775, 169779326, 590813081, 308885610, 230108856, 336515391, 521810635, 100596706, 755489319, 58684003, 347524351, 313455606, 470781352, 593941039, 1675087, 517466461, 411076356, 544031592, 415189121, 944105394, 587092588, 788789640, 129049204, 217741621, 269696379, 832152418, 84486534, 492454558, 424808428, 755712181, 439563608, 172083853, 973133112, 394158418, 845764718, 683053931, 345331067, 579388643, 475685911, 763354494, 828990883, 633051585, 346941237, 537896308, 418446856, 352200082, 152084457, 999776458, 155985223, 222955810, 109959494, 420214299, 831680598, 273983646, 38300706, 26450087, 788048085, 424749521, 563532827, 582296974, 842362068, 544162413, 961874660, 452421883, 250053468, 935175136, 780828275, 89459386, 970946547, 714547581, 319519327, 157357034, 351787007, 742842267, 124198337, 984588244, 939661536, 383849405, 861218311, 571654919, 151906168, 410770512, 856370476, 57428939, 865895378, 808086590, 651499349, 611045476, 433637916, 827012054, 332384758, 601527270, 49189873, 222263406, 263513597, 580346977, 676271413, 146775495, 493773592, 859030563, 513638782, 476912500, 914879199, 962011509, 884786261, 175306001, 93432958, 620278972, 947662557, 114653499, 629404305, 410704479, 379985777, 587908477, 987786971, 645852137, 739289897, 872176851, 764252730, 17427682, 545899138, 605823812, 555948623, 283990390, 64902752, 391445707, 202558030, 182244180, 952888759, 154304534, 400936645, 307267549, 654133737, 335885019, 17674792, 978341136, 2669333, 161223747, 177892318, 300385490, 319016386, 615539210, 262493032, 446577160, 950784521, 10491959, 978449745, 808333072, 137373295, 960798279, 504423565, 178326527, 323127243, 625011097, 279857931, 221722740, 344886758, 183505734, 776526713, 970543502, 252857431, 949926527, 317286094, 251827126, 360685357, 142804213, 28164564, 836699955, 288807287, 612134878, 961046435, 272653415, 254551081, 221192599, 580170274, 988622804, 18041874, 543042384, 807469033, 302342606, 113722015, 462114725, 773267374, 794459293, 20604615, 402024226, 38225120, 821224260, 755289404, 31256500, 325295583, 197685348, 840399456, 411520603, 997640602, 541647871, 840726809, 413876194, 845059381, 844411724, 964902688, 937271663, 458944701, 292654712, 967925521, 462844389, 903326247, 534952016, 633018019, 124118212, 345194549, 216228943, 844316152, 339138844, 353392646, 874671232, 788613947, 353755586, 659222129, 124557199, 373161022, 442881820, 142111688, 337865886, 174009148, 994631778, 192955300, 221607504, 339756754, 836609128, 539383772, 740485345, 300057856, 432192614, 569877521, 178216090, 686709279, 39834648, 837084117, 838583509, 603684062, 628109777, 66447071, 419979086, 525181590, 410767700, 751281704, 154378452, 172182168, 675567306, 389989808, 519990797, 146722500, 792817399, 780418054, 200789732, 911331006, 562259906, 919183076, 521143195, 401972115, 419615266, 636357741, 933942955, 402035098, 540557094, 3394990, 742665653, 896584305, 489056218, 273004753, 734773664, 962862592, 924520527, 481224319, 458077155, 817147785, 73437819, 313838438, 157283265, 789200410, 958759180, 942843496, 162421753, 234917953, 602118726, 32378867, 547035256, 598267772, 312351681, 865925194, 794801016, 895513111, 597618865, 665111566, 293489732, 700774355, 921640779, 742004793, 673364557, 219656889, 33035347, 722164539, 836433148, 350090117, 930779766, 438721213, 353139725, 952823345, 413721996, 883650311, 73663439, 320581662, 12579377, 79287286, 164203342, 353917951, 780677539, 531837434, 136882484, 231544565, 142619574, 5041304, 547566001, 706862578, 730275107, 351894393, 364201990, 374425711, 331529513, 556705843, 286748115, 844492432, 429293682, 352912597, 846452394, 214692149, 879544241, 161098617, 150646380, 799089004, 459856342, 947474600, 425862618, 384631680, 390130833, 86449368, 220019151, 424231859, 41655823, 100607187, 576758054, 689359421, 920593883, 963309850, 832395314, 574856753, 601529150, 163121772, 852123971, 143490038, 847914919, 52755318, 771094158, 118503648, 783677737, 885976279, 372759544, 970317528, 135739606, 862569920, 553245802, 442850457, 285125610, 209076617, 411117807, 938791396, 830893702, 695369887, 833520293, 156594044, 993922252, 287744692, 224829094, 40357946, 180178517, 377588598, 42407396, 216962754, 351070603, 905535526, 688668844, 281830419, 902680469, 985997036, 151140504, 937910295, 598448932, 354098635, 35861135, 332291786, 113044356, 20090113, 157313178, 633250728, 283123727, 656821365, 747797151, 48640783, 669426064, 348381406, 814637731, 461033089, 633958809, 852398870, 648332454, 886294518, 154336691, 744911319, 712124449, 789595451, 617015706, 514705551, 901198613, 880179460, 26603149, 236131977, 74840269, 79168212, 792800650, 739280358, 513238932, 706331303, 275815278, 233783354, 858859305, 565298978, 267831319, 462747840, 987321660, 519834235, 780695035, 299303535, 925310511, 617795505, 905126957, 86757297, 524436630, 638590971, 469407572, 362810907, 490010604, 762748205, 697433575, 329305522, 285192265, 679380111, 676800663, 675697423, 599362000, 678855378, 144753632, 471358250, 3473178, 987415476, 851581212, 399165011, 787218153, 831636427, 210003347, 54761561, 458371693, 467130869, 40234154, 131683067, 779485858, 946649814, 381672697, 358637962, 798500679, 855501430, 889389104, 973285935, 621028560, 874113797, 675325398, 274753966, 614203259, 323327328, 320476929, 769512487, 462767691, 760528358, 865656284, 554116969, 30010592, 352163552, 826120628, 404452235, 660486895, 506371934, 761516461, 716701630, 281380262, 408043766, 839934993, 95175920, 881669249, 827869905, 741474310, 702736536, 437290484, 357064182, 157268481, 676012638, 609383006, 17403628, 774197319, 879139224, 749245058, 298227883, 454857508, 701986919, 996182705, 387068149, 997823136, 525575668, 956332751, 445734070, 863225442, 783273637, 130799510, 41556526, 977379234, 610315251, 537906784, 743570895, 555669889, 995610895, 941073458, 775710473, 959584076, 224109238, 659483839, 932715932, 479612651, 340415958, 277271945, 235130439, 225851060, 951696741, 75337, 392842044, 735900158, 666814293, 763807348, 612706583, 830805053, 469615919, 925667305, 586853427, 491985431, 952369426, 336902460, 493404750, 548553518, 940243891, 546496141, 873881052, 823622003, 686324094, 443644710, 683689407, 873588877, 935729015, 465084375, 755881745, 296701003, 680961470, 523599735, 944926791, 10106319, 41109202, 154594173, 578834688, 19732470, 217045961, 174081920, 768861397, 618392309, 427109096, 627740213, 291386213, 534550460, 673110233, 419374108, 717642777, 502770793, 253445470, 421437533, 828222230, 851592566, 427766607, 678414671, 507423098, 274983645, 648631682, 376462845, 420823414, 258043314, 986153660, 580690130, 16939468, 930274549, 30672823, 611797683, 265336784, 709467993, 69682033, 789063114, 41143908, 953430862, 261400082, 311430719, 756338878, 430266008, 968686044, 602062638, 650473507, 793310427, 630686112, 227142172, 480828624, 188512258, 144297655, 853094417, 466795049, 99107093, 604587004, 92603433, 201513490, 117139168, 62761998, 321477321, 598018420, 89960737, 265708992, 931807514, 184396410, 211279188, 642873400, 247190637, 135791942, 470434004, 669488664, 716765466, 643711682, 140322755, 354796178, 604123349, 17918014, 311439296, 228964263, 181457900, 259107642, 802570050, 483663468, 361845151, 383223645, 257332621, 352843417, 907248331, 520362005, 640157191, 435118330, 943656715, 99963776, 479131264, 608800286, 271876447, 180033307, 144445902, 523808627, 659819370, 841635303, 742153640, 376531263, 110649273, 668965042, 984637449, 709540521, 977363753, 571528920, 291290197, 354814151, 44482435, 567149027, 74324627, 696164214, 383701855, 986895450, 606222336, 823678774, 546308518, 103107177, 897278437, 339116865, 364586879, 326194315, 434692693, 626066443, 700121887, 928777629, 85849130, 487064639, 613735618, 817189703, 565371729, 511342105, 450550624, 137758955, 791279534, 375764047, 193888716, 834444341, 258106193, 439375437, 586412273, 350356514, 867788615, 417039114, 220430707, 563117993, 627069058, 241020170, 626641174, 369860349, 970804938, 216424838, 988569707, 688105027, 601385961, 66819626, 962130456, 962277653, 340878040, 61160218, 196027552, 151160844, 265178679, 530283451, 391888537, 948945877, 869826897, 900593012, 115466788, 764476398, 532105360, 367349098, 281499800, 950754394, 242311121, 852713516, 533299593, 178555708, 174282468, 785214989, 219413062, 189538255, 685907641, 462583674, 248787867, 214341696, 943786446, 835201145, 709342362, 90438803, 195280683, 927773880, 101141151, 435052271, 435169655, 55421799, 236412900, 209016483, 571947747, 979662442, 126872832, 401753177, 970295486, 727338608, 279308091, 14841428, 694691116, 814772640, 920562368, 260643846, 652703110, 245011963, 271503464, 982075327, 441146753, 367216301, 279913485, 38164225, 112671034, 734066733, 46937356, 907703499, 631781546, 636293687, 841945477, 631632188, 831040553, 473575467, 923690, 745716857, 503825085, 411942776, 864890779, 23400653, 733097043, 309833623, 825194229, 929238299, 783429183, 542584173, 128097361, 564361923, 756831557, 946265844, 438125233, 905128028, 923508079, 979971861, 963822007, 231012152, 351476156, 203748826, 49249239, 21279872, 330831795, 986987865, 701436793, 408101934, 840788140, 212370638, 345035494, 506490311, 450393199, 624094365, 113691736, 154803603, 491229987, 168741360, 356404124, 744074021, 102817517, 289360854, 813812832, 969856702, 179935665, 347528069, 430305608, 448487177, 111446315, 97818172, 944526202, 295536017, 468686585, 879899962, 712650151, 878598531, 653483047, 351839200, 386991650, 428584440, 239111075, 747269271, 692537563, 268475511, 524060245, 264746095, 29921666, 100527052, 697799315, 345683245, 137486139, 52169335, 915241253, 181434744, 295199558, 679338976, 753000064, 414303171, 647283372, 488118345, 670316852, 448408905, 638669534, 778990881, 484455708, 798515688, 53442431, 922659582, 451858036, 105502031, 888693547, 236819335, 998585947, 820088791, 851213351, 852433057, 646011622, 397891567, 535558330, 659229474, 490139495, 986078461, 359524931, 819826707, 650237965, 282648699, 195907278, 119658349, 704725979, 280312330, 260166687, 382860458, 59040971, 506280147, 400522103, 746766793, 319696435, 993598815, 725117224, 961036156, 937182392, 948628937, 515932129, 818498162, 599656943, 45021419, 788417538, 815384792, 713520399, 644443684, 239868500, 908338351, 899893801, 769224454, 227540683, 891915908, 457033238, 923773519, 26899203, 72861727, 720510145, 122817765, 687213314, 516918467, 907123102, 320168196, 686754367, 171378255, 241472724, 859709281, 795399184, 212098727, 178118998, 192732559, 695758370, 798229526, 150124832, 890656935, 686976345, 37737347, 86411656, 115446178, 490604649, 978432894, 118421588, 679756187, 256170424, 921636442, 677002039, 175505661, 968175989, 299244654, 227762241, 385199744, 219099155, 147236760, 987523058, 729303789, 196073148, 747431358, 161242933, 788579651, 817669142, 45412379, 147182622, 705190350, 631169966, 304778084, 144156945, 617684483, 768114424, 421300476, 851847127, 150849314, 240111944, 359294938, 155826183, 813032863, 630115470, 616921923, 294118099, 33859326, 573799678, 349268806, 827345736, 416043953, 923815917, 684542642, 574834378, 965193974, 591032746, 177556278, 416897715, 602194143, 709408420, 893478405, 717141488, 583881781, 37365934, 647455369, 296834125, 627609112, 582639104, 409211365, 488572190, 598869087, 183160430, 838045500, 21644572, 327552179, 805630158, 385869190, 188625289, 375811943, 955648742, 17060267, 669038185, 230859786, 387676851, 150306079, 45662598, 413728290, 663856775, 590459657, 446691901, 461204926, 877022752, 289961857, 756779032, 690550692, 614915903, 498098677, 894878789, 543398123, 447097356, 932483183, 264990267, 351975173, 955277636, 474755058, 233813917, 444781119, 505840881, 15118304, 489662722, 849955174, 405452268, 579932483, 410287653, 178547899, 532150369, 860438265, 796550457, 336408558, 838746891, 619676012, 804209765, 424929430, 781130852, 624393010, 358832041, 7324187, 745234822, 136170229, 671198387, 258951326, 846719790, 7450815, 959308195, 161105772, 401466064, 61993322, 661369727, 221063795, 500452230, 939412341, 828283904, 880850805, 819490368, 595329146, 941943961, 887573825, 107743716, 513721232, 19010205, 452910453, 373248392, 296582756, 931587432, 53549101, 554348056, 363984990, 401957884, 349695962, 162656557, 208499658, 684625822, 893930042, 196877242, 818125936, 558817346, 489273886, 834652806, 33526279, 575076485, 518645286, 856058721, 876160626, 951499410, 839266770, 92089157, 192207025, 751744085, 201155713, 883488785, 554303197, 881944284, 421985410, 449950443, 664380367, 526647150, 346355969, 421658571, 713528486, 545630697, 287400349, 67282717, 993389725, 242289222, 546519086, 943314728, 776600795, 572778545, 146499104, 83500835, 217328072, 265744084, 760971168, 54087731, 774944605, 865066741, 432413680, 610597869, 256698547, 701084904, 948146663, 697468929, 766318484, 26141921, 201861165, 604380730, 731466111, 560830650, 897079721, 504112887, 361443718, 735972837, 269404845, 125947167, 284444181, 666798276, 933517100, 147194607, 51298577, 544041980, 357458845, 388586429, 133753075, 433764252, 239809883, 784727858, 715099603, 156382487, 503553182, 446693692, 929013992, 120177641, 115740883, 318595548, 982859427, 20516421, 3855217, 472751699, 407938254, 531212347, 642715810, 179813539, 66608143, 711454417, 999226441, 453271486, 389601045, 568132238, 415657100, 427437602, 934132556, 774003765, 807562463, 740378033, 130729297, 950093271, 885905068, 826014049, 387087765, 407034207, 970295341, 105938193, 52427236, 971314369, 330928894, 58831646, 269777014, 591504635, 209963016, 946516373, 739563820, 863307873, 411621519, 424259202, 269769897, 133515260, 181385115, 172993193, 819387979, 754257617, 301988093, 790168721, 752199155, 408891925, 888771097, 241808928, 391534339, 403358027, 410939250, 991438125, 261126717, 876202554, 180109633, 815261004, 422746430, 762308154, 278892761, 257946457, 472875690, 274960064, 861680265, 115210104, 971090369, 309721278, 110185859, 709810080, 830127982, 863750018, 295515938, 145864357, 286402861, 583089900, 872028086, 853134612, 830647046, 803631739, 399612890, 385320229, 491379172, 195825536, 871875888, 832476178, 547273372, 574083150, 17326200, 411445086, 56533589, 312469179, 400311650, 111085463, 67264350, 541341989, 341197344, 583029086, 438897092, 361020243, 554577226, 222018001, 759214301, 177761974, 103672149, 752590054, 89166920, 680374719, 259028064, 68329826, 542469189, 634589249, 250517702, 338446467, 875354049, 389169223, 452202380, 747470378, 632104730, 906158866, 664427226, 818598772, 592261335, 893799222, 727442960, 185336335, 982298404, 202045340, 796473879, 270408867, 248405428, 185779386, 495270972, 457041768, 781381503, 886466489, 789110395, 320670611, 33136004, 716904905, 588939678, 280381943, 138281841, 219970662, 768541257, 404756515, 75279475, 295922869, 520640894, 382056560, 50402892, 403242331, 794066651, 17123668, 120458279, 933407734, 770188272, 11225350, 608072617, 673128885, 869650616, 727466696, 786870298, 89066028, 26907938, 202279212, 29029440, 836466134, 962929507, 509944080, 878362087, 787185589, 366763457, 644079587, 373668255, 753381056, 217877902, 447992745, 739325664, 828324584, 41728806, 704486702, 225182554, 597230116, 388872115, 740115431, 765030877, 313448290, 884099166, 278353103, 722782069, 990503115, 266029023, 81026303, 909065785, 997003272, 471313364, 874915505, 591130688, 982500247, 364668571, 17967554, 541298279, 227379356, 290708113, 347369326, 405297679, 839710007, 33773952, 820317615, 215957384, 736274141, 346257182, 185004022, 217532122, 918017749, 587436182, 426557667, 197146669, 469279605, 808303168, 181734809, 799117918, 950395166, 442201260, 705212122, 31638504, 927366778, 964006814, 783160514, 639143768, 619245826, 89206131, 826675342, 874293974, 433529856, 526049232, 790745651, 888785029, 794170824, 222518582, 606364142, 755923641, 668581885, 241264480, 656361857, 900290019, 228763089, 338020037, 420562217, 195820253, 190901034, 795727098, 871250832, 599200521, 83349365, 412803857, 136610192, 143536172, 459807023, 207612797, 147262862, 58667957, 185366527, 482395312, 39898778, 235691959, 145104926, 168321175, 519986442, 524253937, 696458210, 562337382, 438488606, 943807455, 374095150, 267273102, 958879628, 280389714, 841244062, 295346370, 654091030, 740905662, 700485622, 105523901, 526678723, 113255576, 861198948, 535586435, 867583309, 225455464, 676403559, 198663026, 869639921, 324417505, 232240651, 137779233, 417420738, 677032359, 611252118, 562920166, 287319978, 668457283, 429331597, 263494899, 972034607, 11862715, 28490222, 693720111, 681784316, 572673667, 117377635, 669357651, 708188439, 709273845, 387511834, 522645822, 448814818, 577713885, 994949499, 646804432, 558406978, 402969423, 174822184, 449070493, 957510430, 609732556, 924557335, 22439857, 709729108, 747130335, 289109902, 647524070, 31558936, 676348693, 259067303, 851814019, 388220500, 84683469, 564731100, 409848722, 336168721, 169427159, 933348332, 132372061, 711247917, 190326697, 849631768, 327736923, 750163464, 958557779, 44040145, 451248613, 298024883, 756480543, 845481644, 430548688, 879808216, 515917978, 809959614, 93297093, 982627424, 886406011, 880055853, 194963106, 594586733, 204082680, 305583632, 467311247, 357102036, 919917389, 298754153, 591881378, 369158617, 426161933, 772413527, 446550729, 480644581, 195434042, 644708154, 382329774, 465092906, 131482458, 6314867, 455205167, 97726191, 653444697, 154526682, 322472395, 926913852, 644319463, 13002455, 869653537, 48599117, 210249684, 136737876, 985445318, 859025818, 364463726, 382063006, 574379580, 337380118, 649797105, 640808559, 357159682, 36632779, 725385155, 496361691, 145875835, 28443421, 200915662, 168047515, 617047638, 657908330, 176034789, 99671401, 117837804, 374972889, 190043855, 249703093, 90475613, 40934812, 87728155, 515113371, 721204877, 339445714, 580644493, 87496954, 25831220, 463251213, 568248355, 301164063, 560853873, 683857558, 790770881, 880715170, 463780261, 696773691, 366025734, 89998947, 322769540, 411012219, 889528299, 355094643, 163379887, 13021287, 499775596, 896845688, 704111050, 863209132, 144824948, 689363641, 826924979, 188450904, 343414290, 749102718, 369717407, 762889233, 674311331, 191087213, 193481575, 720811807, 311096367, 707525317, 309920541, 414581153, 506536577, 706840329, 134811782, 860817506, 215032404, 995946141, 319968034, 292737588, 653662064, 451260124, 374614625, 300936501, 872125222, 265690204, 813980997, 199928842, 990171086, 819291553, 743593438, 853130387, 518242582, 525002438, 792603763, 12441038, 932988228, 344366239, 630012746, 178246202, 597346897, 213414744, 972566307, 697972819, 382865170, 28616870, 929856199, 385214983, 767043254, 505163429, 767463613, 251108528, 413074171, 483446176, 126865679, 851129127, 345142818, 779966861, 991874351, 997551924, 5570910, 595504515, 575728181, 487882468, 950068656, 433383084, 592617472, 294940035, 936368891, 373524577, 344551688, 169101187, 302608602, 368963759, 136928318, 391996522, 645654318, 957836632, 79211900, 873585645, 105177616, 412300217, 837376447, 189664645, 870331099, 325538039, 548489837, 352632694, 393540726, 595734748, 798595967, 648584037, 443931742, 672923124, 723356892, 551239510, 364580882, 577048434, 644865628, 429199617, 700898876, 64412124, 430597975, 732860594, 493481704, 220241735, 479078071, 415698654, 164401198, 994321645, 128935031, 713018357, 721798327, 927098457, 213552391, 205223340, 982378761, 267029036, 184379048, 718877251, 408061823, 453087973, 178318890, 142764872, 946578567, 595091627, 131435763, 314508232, 466598678, 23367083, 106923254, 612618120, 431635427, 552736000, 963981312, 880584965, 175812998, 56851339, 406001022, 145409471, 755280817, 538718834, 72197020, 940608618, 57500660, 491673943, 167071230, 206176887, 619356812, 943129450, 95576148, 31027235, 765350501, 392645538, 993300249, 775710748, 917408665, 31932885, 736888127, 105427617, 793940273, 438639224, 170249453, 319992918, 100917108, 455740135, 360289842, 225897488, 36160264, 602821419, 424946340, 796199410, 211225751, 112496361, 313474899, 186706248, 371356847, 572437009, 953195837, 323745429, 252068832, 751165705, 464857717, 190467784, 811134978, 520368517, 817152349, 500067485, 113983743, 905169485, 797011188, 178632008, 413768743, 710723614, 159378137, 175571158, 566673881, 284960713, 261252832, 196531735, 904657374, 47570069, 521155399, 212471912, 342524426, 174762946, 503043608, 520331864, 849074377, 582763971, 292521590, 753118561, 993154732, 969942503, 147234640, 445649864, 774517998, 993615605, 786994672, 842275723, 785798744, 542836367, 67242908, 411637186, 84020335, 232304063, 733825328, 588236377, 331997819, 647998067, 271958361, 535127508, 320121145, 334535709, 17906845, 228500557, 528899486, 9770479, 552983197, 919786450, 925510780, 707587665, 999823103, 845453587, 858176799, 270852827, 802905281, 926678331, 437437770, 900127670, 831573360, 297832158, 278431985, 540890695, 901844146, 871573804, 183532698, 632962103, 999382875, 439748190, 3653825, 948417886, 277672232, 641114424, 629261917, 882564462, 58619986, 413179381, 249332044, 713787601, 372667667, 760083430, 716966425, 175712787, 259919776, 309191941, 423378352, 333355810, 322190453, 456407030, 869422293, 975331602, 321540639, 231949658, 12136166, 643212052, 250458825, 94833860, 412519065, 903621121, 55680348, 362106837, 519278369, 542787736, 63386929, 990938244, 355133580, 347181643, 203137781, 615878343, 913186330, 924511793, 294898550, 963872521, 857877324, 928296451, 975802347, 589971196, 403887477, 966985496, 607483076, 590097727, 954030604, 457476746, 546446734, 483014036, 412406556, 201822034, 812894823, 315227804, 364424635, 806816927, 750812320, 399557425, 799304733, 648692990, 957895183, 439071944, 228778543, 80742306, 769069277, 146616598, 596329549, 588329657, 781390384, 462745321, 144709830, 489445078, 12413982, 271386744, 867094963, 964503111, 992825719, 552264679, 405025407, 23071921, 502577985, 856837895, 93352764, 539812519, 865309806, 246213997, 80577867, 94044670, 34259491, 900214355, 283861340, 143152553, 453573952, 678052406, 196678166, 234151592, 984516832, 159833631, 854172879, 559890426, 116216195, 975014756, 54447424, 647582410, 224494882, 550422547, 44583604, 677596439, 566922880, 151210688, 717807878, 438536318, 779070822, 331908567, 409577997, 663343273, 473936805, 623216215, 626185677, 275484820, 875880498, 192215315, 739364134, 661976839, 296776081, 557467470, 201779627, 375941250, 33375632, 359999608, 918227095, 843101138, 441735271, 675777667, 249384347, 607163241, 830705024, 70511010, 541455456, 805695658, 718643434, 632401717, 101763647, 176342387, 707552675, 675128759, 629081108, 181786333, 521577826, 745788608, 876195896, 766835597, 679139093, 804048018, 356794241, 251030513, 740848795, 814570834, 662785240, 330767278, 44418447, 620149305, 400969524, 548583246, 677630055, 121790490, 303476886, 373870405, 420396182, 358459286, 491826218, 34828716, 994789436, 484029044, 760132543, 786582504, 532209398, 797095850, 732225562, 168913392, 239467469, 926411074, 408341901, 134762475, 975668957, 807162764, 511766112, 31669802, 594425057, 51618979, 226755114, 485643563, 819888706, 233142528, 376969510, 637850422, 853674140, 100055835, 222032176, 543660820, 106642716, 724656558, 575986504, 149379502, 540836323, 629897945, 258052832, 196791976, 187832264, 978240781, 479063334, 299982489, 688269303, 896958041, 687721499, 571257993, 635748947, 562855532, 773190014, 844454868, 936177744, 485618824, 746181728, 994671344, 324749162, 331590571, 110544199, 506472528, 205390263, 807492612, 348447774, 395622943, 100748327, 417533146, 767941167, 428538689, 550506612, 69834539, 557900075, 193423704, 549224416, 82834920, 721236604, 430683312, 27844092, 486329375, 221603882, 403709448, 808182877, 742769817, 650694517, 996607299, 182204080, 427724911, 796947882, 204255252, 248951169, 268592481, 594561978, 390279214, 14247241, 634631864, 21411322, 836389976, 607647759, 868427740, 773730280, 854258916, 893590835, 425728318, 145598965, 709781879, 214889669, 910369190, 655136979, 575784759, 450689284, 829187283, 644043409, 328219003, 578415525, 948262613, 710028145, 765610128, 277903742, 987737975, 279358564, 237032751, 113174972, 210224511, 93941532, 306959045, 940049898, 521388085, 226687173, 112050903, 717821252, 344071582, 985474352, 250766258, 105100576, 661551682, 873790388, 918338889, 293251957, 29531396, 81619563, 248748261, 108684215, 567496235, 320380358, 593981254, 459562454, 22318442, 288708328, 146314257, 320217519, 368011937, 712530690, 310576298, 503994681, 63056866, 821435231, 388929688, 987046503, 371135713, 353886346, 942035211, 476153635, 198466302, 532143254, 352135634, 373693982, 878595979, 646433550, 298581404, 445358813, 279537788, 819777524, 783936909, 475799906, 107030603, 829534351, 822915941, 946371738, 571700067, 570181302, 584353306, 762498724, 50589566, 328905896, 418822509, 533506614, 157534741, 906429409, 824141821, 990465531, 689690516, 676356201, 971493111, 821862416, 145800174, 150048480, 374268541, 841401314, 117491063, 99594416, 572803135, 478058600, 426529624, 286459110, 233447206, 871355469, 400806489, 146370502, 944064645, 771880070, 479298792, 462148428, 251254268, 776981886, 428813488, 179149013, 874747848, 434944151, 699416347, 19392475, 826833308, 202975985, 867777273, 643780650, 857207510, 644566825, 219411030, 538159448, 278034470, 300883962, 398511046, 193533840, 834170745, 605858346, 50137582, 694071780, 478930569, 748150130, 474561880, 154149830, 754655577, 349277979, 519420164, 568016691, 865585194, 358362160, 124053756, 599330893, 435790517, 522710349, 284294313, 932959788, 887398681, 377131721, 937057475, 824901247, 569841837, 9583234, 465549251, 393077469, 643889862, 460946677, 545731719, 661790966, 739416316, 361215636, 410607123, 484351007, 227354926, 40258216, 51069916, 563712441, 848262356, 661697090, 654055548, 110286337, 962824946, 709048668, 918401820, 340884341, 999632645, 384996596, 152886205, 18468877, 768735069, 528191800, 731221884, 28318792, 33660352, 545153441, 202943173, 569820465, 202058795, 615990719, 706582543, 621731490, 129224970, 554914347, 707251924, 702468226, 410667958, 132537788, 117220327, 237174665, 211930193, 460520330, 876077023, 224788650, 130611665, 929393872, 47487092, 138789710, 210598402, 931801412, 865692805, 459725685, 853776083, 458438163, 65274865, 965209016, 445544681, 663629337, 682085080, 114093044, 936366950, 89363, 217430139, 486048642, 217871301, 658534276, 122213183, 546056347, 356207059, 811216927, 96029299, 718763570, 313385225, 853672014, 771278886, 653335542, 738006576, 64060677, 580861309, 808826847, 272503481, 523811510, 100119483, 948070289, 205793974, 709951288, 437669039, 969534088, 524233285, 671801681, 579268847, 397045506, 21497734, 789083943, 896348274, 922524404, 143107094, 180106030, 137701149, 626190807, 878385978, 445296034, 517569237, 208988864, 495134697, 837313210, 469806632, 35529180, 761276905, 473000315, 359747200, 473685057, 968384182, 602652556, 649157550, 180429768, 383857424, 398194683, 222587300, 744809284, 69628311, 351236983, 860024100, 223829553, 910020713, 882947342, 688975046, 86903986, 981165657, 809709505, 222859366, 203255811, 527242678, 696293994, 823485094, 61802878, 344912815, 613306841, 69023475, 867084731, 837567956, 612341749, 578867691, 252226542, 384597804, 470209007, 391201939, 899571598, 837952184, 871611285, 801505376, 730557012, 830762600, 521608161, 456426336, 521565797, 173194348, 730902744, 390620487, 15968335, 523478395, 340305049, 5874986, 652262252, 614114501, 717436120, 695232264, 983393419, 193653650, 105821155, 914220299, 319796848, 329406054, 792639845, 334065980, 374450058, 980750860, 924078228, 201343031, 9561264, 883265873, 565097981, 650373479, 750995213, 154859965, 615869213, 44905596, 216612622, 810824857, 226718620, 223211499, 221649749, 798643976, 134283029, 668011262, 974538732, 925254228, 775955938, 427625015, 443605112, 632091591, 673485255, 272200991, 501935246, 994550162, 680875930, 415886953, 637430306, 68458935, 851572113, 894829958, 424655790, 816025772, 736328611, 28033139, 815086246, 189454368, 592927326, 250163546, 814124644, 528441363, 984635635, 789161116, 215416051, 16758527, 895219758, 548468686, 872413611, 716216350, 511365946, 687398025, 536395305, 445030815, 497902667, 1177655, 595933107, 522234534, 955072856, 329219405, 126060345, 520309534, 283702922, 861346108, 203370225, 133687454, 108453027, 401918396, 928525299, 902641679, 627478841, 528921737, 441963945, 511796080, 15507689, 263763757, 525244869, 626287752, 600707817, 965975424, 317361764, 686395317, 459823709, 594464276, 673314685, 762500088, 72845653, 534337927, 187674068, 780742001, 310265627, 186558412, 133000072, 548795239, 770747532, 908525691, 615221376, 973298150, 944632111, 750029093, 551534617, 658113730, 364681897, 877950739, 693046878, 420475574, 322726044, 551336842, 563269836, 400246572, 895854770, 567168150, 593593849, 328670355, 80749394, 432561913, 950721362, 688512757, 433436843, 312230675, 259241287, 695933257, 960314664, 335630498, 709404917, 878874637, 312093144, 336308109, 265409281, 293805434, 576588532, 313507471, 725403036, 415485037, 649427876, 487409989, 559613082, 550313377, 758272468, 63152961, 834975855, 523129228, 564147822, 44779077, 531385870, 388113133, 221629944, 225340142, 939158887, 374037998, 446324485, 106134864, 267632441, 447847340, 42974145, 906147345, 34214786, 625869996, 956803478, 700727220, 151842856, 655736674, 4624401, 504226019, 272277318, 678693976, 376662844, 904263650, 230766007, 421217960, 411926693, 533671160, 131067384, 551058909, 10876618, 655626010, 193211374, 889366582, 34759107, 350126711, 596677409, 621921342, 17499064, 788996027, 876310672, 361364854, 672402430, 909109818, 156356135, 791933790, 827619231, 422750181, 597425534, 722032661, 335692732, 904376069, 744685996, 109177096, 701394742, 805766703, 764698639, 303220855, 164543496, 627369648, 638254112, 404991042, 457684944, 642153536, 576676224, 832533671, 328837287, 983461619, 782244797, 311720022, 758146781, 330983643, 94000418, 742530503, 8469865, 585677783, 304944771, 619792206, 773539433, 381711074, 998900780, 650503527, 577153382, 490173158, 423502895, 801300980, 433022558, 364314396, 970572310, 591705679, 727392456, 205787746, 912366167, 802843607, 873818331, 645906868, 913320301, 376033160, 646065100, 921125412, 147790276, 381405707, 943672056, 588010805, 450762387, 504538377, 482569206, 260788992, 881855914, 29236663, 217545449, 753198116, 122700669, 690920404, 970316738, 475461957, 700732461, 473569919, 98537509, 593506898, 769506596, 490671124, 634167504, 905085837, 695129447, 959921258, 785222307, 617725503, 535178494, 910855315, 26227769, 590016880, 305002831, 594371625, 897605433, 429024479, 570478378, 724661393, 130521678, 968924295, 766242546, 79552939, 255762211, 31307805, 335504252, 383033106, 786802654, 235676654, 117219966, 8020342, 545796586, 957621445, 168905937, 182679094, 379725780, 573847425, 797273324, 358170846, 42022350, 98467955, 11870691, 845236485, 65435095, 727802086, 500620936, 946821061, 635914927, 389611341, 111027405, 84911723, 796153970, 854563102, 521677418, 378697149, 287750945, 791491627, 586513652, 973675468, 274122223, 237792852, 857243859, 794856200, 571266445, 751083570, 558158066, 921949499, 974597197, 861804875, 727213334, 286318198, 54170509, 799356136, 300527844, 392539226, 585888280, 375717125, 827492841, 3627712, 435796156, 579181031, 84546009, 643662611, 614872004, 670046970, 981847279, 260226473, 849845418, 409310615, 235544480, 18149707, 428950389, 741122482, 375661106, 939406679, 250078698, 154035758, 194838436, 933871139, 794868459, 688201079, 12632821, 614226222, 946954493, 620888848, 13732048, 293310250, 668432133, 860446116, 109975481, 22193594, 705161162, 677005177, 759170689, 288823090, 206457515, 62149203, 432140663, 810585733, 615693176, 745288387, 138605600, 436994113, 84214731, 888000420, 555544016, 730013377, 428524813, 465514749, 353912417, 649731060, 925260156, 710642409, 757017510, 144117879, 397149031, 769696938, 286557394, 814645801, 416172764, 67451152, 1894392, 133524942, 840310671, 250193199, 92309960, 130206474, 899586319, 117282305, 343364854, 806065046, 76894018, 954242050, 831404243, 214929781, 88053016, 432083790, 477435737, 204926044, 653378003, 293340223, 607443676, 45969032, 232454317, 879287277, 354825014, 537089979, 371712947, 640029941, 477070920, 649070188, 852234413, 733409927, 897596611, 805493483, 238593287, 101377551, 111994773, 299533291, 550373993, 278121331, 412181196, 451724169, 275757973, 283434016, 129023214, 580470825, 677945279, 156635794, 185718286, 902918670, 65278197, 264589553, 901837350, 752794744, 618902216, 241833334, 510637884, 37125083, 408460840, 686222533, 449205940, 851267703, 762501494, 471172033, 590275827, 391711585, 37924792, 885472182, 691595856, 394562893, 447542295, 220501614, 701426310, 954834133, 850494673, 486370221, 324464242, 987656738, 760069842, 467603325, 847245207, 859481154, 692820800, 25654109, 391289021, 335315327, 932826936, 664545584, 86408162, 81989762, 819740514, 580937911, 888137919, 918345186, 236903536, 444095022, 782239983, 755367216, 483021501, 171893402, 842851639, 820054763, 995542571, 890314944, 304062765, 982753133, 299781172, 938212367, 323087214, 755904494, 768839365, 572152167, 643627346, 76940079, 349905877, 22602733, 702998003, 320038850, 342848492, 525901436, 476043410, 871562070, 129686392, 27514613, 134537199, 70595755, 429997523, 199026592, 909775465, 824728126, 385988912, 689101958, 882924997, 140966939, 115597754, 652683617, 168669280, 928304130, 137940902, 735495475, 262746991, 482006778, 895023204, 711993735, 534582154, 168764603, 363300019, 789868574, 495493936, 867364459, 373636770, 276123385, 205958110, 622868061, 986088011, 571634399, 875304613, 724804817, 811446558, 916272857, 360072142, 298594435, 640087263, 133444161, 104210175, 185994179, 188452246, 710618780, 58149119, 457951517, 757721293, 9174418, 290520106, 817277368, 410517594, 637013035, 42341729, 496937076, 443340843, 898548855, 643010971, 476132652, 460319427, 887544631, 551914617, 186420878, 964073122, 373733611, 541038716, 31607562, 160339235, 914466745, 363023829, 474228307, 383358251, 58213346, 857677657, 99274665, 487024479, 356387601, 920683512, 169932504, 14409882, 454906605, 335314185, 523421258, 322597424, 663249274, 688041867, 918640240, 402431346, 934846555, 831463482, 159147783, 26580257, 316663652, 192603404, 245461332, 844791115, 865207132, 473300106, 361789962, 656400977, 245668491, 191408477, 321826164, 778639348, 719341041, 915745811, 208528099, 77154621, 277235233, 489136891, 174385330, 747307370, 28920098, 294225766, 578519494, 967189433, 91266145, 996036795, 596104331, 705844886, 163584615, 613593887, 2576051, 526711755, 880711049, 422339272, 419557299, 599199041, 14522705, 893780929, 219071079, 598319534, 271972927, 903795013, 15301565, 317863367, 38169379, 338228557, 179408884, 629383526, 410612719, 831416232, 469616139, 583607663, 190569759, 516568062, 474930273, 309643836, 507981556, 226069188, 904228421, 96685930, 863084734, 923521085, 636733821, 639982389, 718718242, 517526358, 949824077, 857078438, 353818152, 298601087, 259792954, 378491110, 334416457, 32723774, 68707890, 972581571, 693307003, 245047902, 448249765, 496827874, 614305873, 698418114, 890933433, 141305247, 819738067, 303644412, 894206155, 299037045, 274508711, 216545185, 578321887, 20278251, 332991880, 566295424, 318840052, 766303526, 675907587, 610617542, 63196646, 983314076, 527669096, 612508056, 493384818, 101934620, 637734391, 418518460, 503751720, 141860994, 243615824, 806764273, 67045785, 711416216, 223611714, 132626683, 489113190, 265502859, 788244920, 575068657, 341094481, 993197080, 169854595, 779504607, 987260955, 536453695, 130499676, 940978610, 180359419, 973353395, 684211990, 173550136, 276445212, 293753703, 624090845, 284981247, 721751160, 540042771, 497057377, 112234686, 131666525, 677327170, 476222183, 197978395, 924012840, 584705778, 98767466, 154913779, 918105060, 383620514, 506398769, 571555275, 847908703, 100983053, 129884219, 67683247, 569993348, 358311073, 909468076, 275492522, 312803961, 55265591, 466808235, 340836773, 248079423, 65948703, 420735860, 218841610, 689521458, 850545062, 2101501, 69891180, 865061801, 941280578, 68758190, 299537483, 338702138, 514397865, 775772949, 926909520, 894639410, 825508704, 814056287, 84881938, 891143313, 777078431, 596168750, 26473339, 968708216, 25154574, 580399746, 612634838, 534497152, 178423014, 137036105, 631053843, 768050265, 360711496, 38820296, 444518350, 676442758, 346679134, 659589456, 839868048, 284355183, 534060560, 471961234, 54951774, 247615991, 971499772, 913411129, 928811285, 919167339, 28131548, 416919312, 462646952, 180102490, 716436846, 483257480, 801557041, 114771424, 462635178, 772574258, 621168789, 231713116, 551285453, 27880772, 718921775, 706818308, 678003139, 146781575, 73117734, 479741154, 67119098, 93376157, 560079481, 77064198, 385445986, 413568853, 714756175, 868835988, 737742219, 125090207, 40464506, 643885922, 41202652, 292605522, 684968136, 617642233, 374065041, 89895500, 281200289, 765942031, 908190106, 761820326, 948351123, 489932033, 875463697, 527801832, 874469716, 654334866, 71641426, 189720298, 573580245, 489555410, 650082067, 599834514, 5484139, 14222353, 452354926, 314887026, 722157439, 910890085, 386166536, 267360934, 423389455, 663481150, 895439275, 38047623, 42524828, 666241291, 306386862, 334094788, 913998053, 505106174, 206426766, 739722943, 335370374, 305021004, 203690052, 106809444, 289798742, 526702570, 322068448, 840355764, 820143558, 377388284, 152871725, 408395507, 546137556, 195035881, 109845907, 369054789, 472645867, 183339676, 752757746, 634579622, 690350815, 876313779, 622012310, 943834356, 760171311, 765883315, 923809453, 863819357, 761909999, 944775139, 313104158, 218698649, 657563700, 798951774, 94550071, 66886871, 133200376, 189795811, 36950711, 626464264, 99790418, 960461136, 385371212, 445807087, 780363728, 511331829, 241346047, 778718410, 802413168, 751853232, 170600651, 309572803, 99752789, 284321298, 23235627, 873496852, 108305689, 138157747, 269780742, 79684914, 41647684, 931151611, 310201077, 836102510, 909275923, 175000804, 304743713, 779419726, 577588327, 702600981, 191724920, 647337343, 575271606, 439525412, 202836557, 631388112, 517053956, 655041467, 415056267, 111362288, 382353658, 766726887, 370491117, 931814477, 761480454, 146583158, 801598457, 210602949, 426392255, 352933670, 828586655, 582625635, 428380199, 161312077, 458676086, 210753022, 771174268, 965840126, 748293517, 92942587, 41062322, 731634808, 354720081, 34118444, 653457307, 579030932, 336812309, 210286746, 258464669, 939453694, 77168787, 19397039, 779136975, 764639918, 249757849, 419058333, 986454564, 434057736, 733273686, 790981101, 48959148, 489828397, 736795444, 290855696, 414022904, 415679695, 834015762, 938999841, 132394204, 307395310, 158357129, 918242421, 163293750, 299740439, 830982173, 371187224, 377996445, 861989427, 45127532, 784055032, 802534066, 925493738, 469521753, 209555816, 221314737, 289219131, 761571908, 547837642, 345986597, 676223702, 771668910, 513641082, 102432159, 975485393, 463200884, 388047471, 909679141, 905846725, 645519595, 142329258, 419624679, 477578987, 664095759, 647044172, 738521682, 827263187, 288077983, 449508175, 459707544, 577143932, 342147380, 662883287, 89338155, 954628796, 867605434, 226799815, 768708120, 251171224, 631018412, 55528773, 134157107, 119273579, 122477013, 22365147, 323116668, 742694354, 766305129, 29513243, 777254021, 13391101, 514924670, 228866401, 68721710, 414327528, 990768163, 153041571, 862694100, 477767024, 509161734, 842346857, 735802324, 492900178, 367145971, 98263732, 224452598, 124564421, 539577993, 64672172, 560073467, 476897429, 814634331, 903116002, 651152634, 895195961, 121579303, 469136146, 384798029, 318370818, 324028460, 186804508, 340064058, 780039931, 197050081, 232346138, 888059596, 480283873, 528376582, 819766706, 922309708, 535721431, 77750426, 329743480, 810418248, 593421799, 665888131, 749990, 781547087, 381566867, 923025625, 766328123, 889055508, 692315206, 460430263, 526944993, 2098389, 580420130, 306211844, 818688064, 351669168, 210546299, 902194636, 68087605, 235229988, 593479585, 707632202, 803891852, 750380135, 204447647, 909111337, 450392548, 737356003, 772296128, 551565676, 581274679, 885369183, 82352390, 295275308, 451600007, 67418900, 19794254, 796483097, 338580479, 140514874, 280799999, 866388971, 294741876, 205735152, 944773332, 686936633, 771556036, 1534412, 49312668, 721344130, 175876690, 820679718, 797708890, 750341547, 18142227, 239393663, 322771565, 555955968, 169010002, 569074714, 869515184, 158245089, 72913053, 892707900, 967214415, 430704353, 470543745, 322790870, 542589931, 535442240, 54363697, 84557517, 495566403, 630248585, 752881448, 839567500, 779689583, 240162702, 383295733, 668232107, 131390300, 760900203, 312756882, 40798119, 133574170, 981995981, 195225777, 71445527, 356082708, 832650298, 817184141, 700796355, 911719345, 351767840, 503475090, 354617970, 86112138, 371961375, 729022259, 428198073, 582094085, 639136322, 112464722, 646434091, 636459573, 688149574, 284587344, 150819546, 276443905, 6035577, 230337752, 380228659, 481679537, 207665564, 75150291, 580060423, 996850934, 567940948, 346913533, 513855728, 214657181, 870349552, 483448321, 801125208, 190343440, 682813125, 280059865, 68544223, 853476365, 384851668, 310872366, 126104806, 225820029, 932878921, 418820166, 92173362, 462035619, 510606509, 563462253, 294031496, 314799116, 579270796, 185060549, 508285394, 128518217, 722676839, 213356142, 562785359, 236012688, 492412980, 380666940, 940961231, 8425231, 311656023, 381071304, 760351651, 362080591, 132256487, 44056827, 371198215, 751956853, 642885306, 651846033, 633261517, 971930861, 552604591, 638158344, 370245535, 498381627, 3153016, 725499175, 85548529, 844075954, 54905095, 891883428, 906728316, 564559566, 89568645, 432366414, 385820105, 405053772, 492141763, 476799619, 912802574, 453684751, 397743035, 42946978, 328568886, 456373303, 610244020, 984346282, 888176754, 628597232, 20858228, 247482468, 977757160, 621855350, 551038584, 527638418, 875397502, 282035970, 19399997, 386798804, 20104204, 818219049, 454901339, 533614627, 746221997, 65051192, 328370030, 377079756, 922609875, 659963566, 616719332, 47046405, 224949760, 404656552, 794253081, 350267993, 729005964, 802700990, 524907234, 9021734, 526290811, 476232458, 912305934, 667161858, 108029198, 202644394, 621604248, 697035270, 356015194, 63498934, 800311021, 275171079, 341302583, 399584447, 642143140, 314091942, 887803491, 556087158, 221322099, 664107786, 482909368, 830937996, 240324033, 549732381, 674413376, 705983442, 864220638, 829969093, 3893605, 52043863, 956252540, 454209902, 537271026, 987658606, 791441035, 590990027, 330530674, 205584240, 101776232, 841136691, 671115085, 965492865, 356250137, 469151410, 537465055, 316021434, 184168341, 356557960, 496602656, 125534268, 531989395, 482814134, 73360906, 780945473, 113261608, 582865647, 514348730, 561112158, 382665649, 649411486, 707422433, 317471382, 115293429, 318370062, 677486434, 737231737, 627690803, 667706488, 796312086, 765341418, 189897316, 28129338, 684223392, 924922586, 748845563, 698743606, 69134699, 934463937, 234612004, 596642462, 656897682, 482258674, 778739118, 902324320, 106328880, 310864913, 294983701, 788691232, 553981795, 447316025, 483598057, 894834725, 619074810, 294286317, 869173436, 37987364, 911834632, 646746839, 830264924, 849414648, 193866988, 844646840, 117858721, 991682510, 40348022, 253204415, 653018280, 423767445, 175664734, 346216077, 189920127, 557742404, 897296405, 76930158, 17566031, 100408640, 516975020, 418813640, 539118499, 383039123, 500655129, 354485915, 362181173, 378003307, 626107051, 910193867, 345949278, 555386804, 95339431, 565136147, 450797510, 736916848, 2435720, 68700586, 473355872, 108604874, 245832699, 62667594, 986925472, 540153956, 994535836, 342671395, 893596853, 550464502, 79196005, 108136474, 411520899, 795496622, 796720212, 386053925, 271334425, 523198377, 14830368, 215294434, 934936471, 351838049, 839749441, 78916376, 262746991, 345304927, 993683707, 58179424, 786237186, 888839506, 980407247, 332945480, 366863331, 734516266, 892413501, 731412348, 861795686, 255827059, 176483088, 374796843, 403573549, 96124549, 114252329, 566204971, 415169685, 837992282, 517688184, 466758301, 677904524, 454631675, 659650968, 964105623, 219809876, 269287596, 461672685, 809485322, 342901769, 319056999, 759658419, 220244799, 390229643, 755983491, 520031327, 672595471, 222209035, 162963856, 518342698, 731144151, 139215777, 899076148, 617631755, 948249783, 697292064, 600748096, 444781927, 732172617, 719803570, 859117889, 165075103, 273132991, 636191958, 228398484, 465999590, 951623802, 489848918, 724466829, 625383124, 916496473, 938690559, 411220051, 885391124, 597534908, 896344374, 808571321, 752242062, 360304427, 583503057, 41849687, 310088897, 893255803, 916232271, 714072215, 494091785, 571428781, 528032246, 523984445, 967738201, 730564940, 702372550, 435009603, 701557373, 608561388, 140637147, 327022721, 781012152, 63057974, 289179347, 811733278, 51326933, 139414786, 806340905, 407286299, 298043729, 909249712, 944241631, 772132840, 469340244, 610519007, 3929845, 472846245, 98461440, 518261072, 670706028, 617180714, 103363263, 131451462, 479713047, 833502713, 342834153, 388135164, 754482326, 81763704, 433502844, 877688350, 128164567, 36217508, 427548130, 695110251, 323985344, 590144927, 546873591, 673781570, 731876752, 102726394, 687996085, 266486598, 878709215, 209268891, 458668987, 930016128, 424082622, 928341593, 690173533, 395268565, 773017730, 805704566, 220480686, 25016110, 788259879, 457705641, 125894734, 173005901, 354033169, 947482679, 851734997, 884939221, 581225386, 711593742, 9746517, 251381620, 970543376, 809576589, 906716609, 760018168, 28325491, 714126594, 157966998, 165665404, 838548171, 642850206, 119771335, 901991334, 549904193, 181713675, 238003926, 822382940, 211601180, 636601626, 688802091, 160017360, 100374805, 222332575, 966534206, 850329236, 734357890, 439384898, 932307180, 862977265, 78939555, 4453674, 249426049, 459846919, 628839638, 509747853, 94741098, 913028640, 994570594, 634728954, 450105489, 602542009, 594487299, 959968792, 632265514, 288018375, 963971844, 987254727, 366561122, 971069967, 293814556, 558670163, 196968908, 100529559, 277360412, 800352631, 467383433, 776029303, 631230215, 28984219, 174080649, 949873929, 576297143, 537290484, 621084382, 950390182, 240506959, 165980310, 164035411, 671517661, 454265774, 337009434, 587573759, 711777892, 859672575, 746567980, 180070478, 659092104, 853573779, 78019997, 826261474, 580606375, 904741072, 802523309, 351176654, 372324303, 57915953, 229587910, 899706072, 757201998, 179379397, 219563714, 566360771, 295380330, 743797879, 550816298, 350313261, 754450040, 736961393, 215895853, 70612637, 996965131, 265837219, 486083543, 864630779, 467601913, 773697849, 555143778, 635323276, 866048893, 674139190, 232776698, 442702722, 574423553, 74677636, 25310844, 873510254, 236053671, 905229802, 703286448, 302370978, 918833542, 970090802, 947069264, 988815609, 210880451, 583928924, 909039884, 751284943, 29571015, 936828470, 811410688, 836658519, 104268096, 999367623, 736377196, 516553509, 958369053, 624019676, 483746271, 671002004, 622811623, 799188956, 468234487, 109269690, 199441908, 952129290, 555033725, 620718064, 108837250, 603335409, 632755876, 442029989, 902477556, 817306109, 446481716, 626710571, 317481366, 971199975, 51538903, 545861049, 714387215, 630114458, 576608222, 748360497, 315630742, 96793577, 876005790, 901751596, 684588896, 554300853, 510219220, 541562772, 807142244, 623197316, 787551030, 954016928, 481917123, 104452565, 546786279, 985761828, 904435725, 740175488, 771601387, 723613541, 573766298, 566859016, 984932043, 734024046, 634153998, 432299325, 953082075, 877548215, 700267173, 174310867, 810206437, 453103454, 865721227, 39441058, 176547971, 575567395, 353025287, 483442174, 816332150, 319175535, 481153710, 187964216, 911210205, 778351751, 648344180, 537843092, 96877141, 661317758, 538944689, 24249537, 617316633, 84815015, 644212787, 584844516, 633731329, 546327961, 445369203, 775284552, 164588287, 331328054, 773991214, 46865780, 215627802, 397321870, 362205332, 843577493, 536673610, 433635575, 181920407, 292129642, 981257240, 111184092, 929912675, 971881332, 594943464, 426602752, 409745110, 845085775, 785636997, 160781847, 775358254, 31370666, 948444215, 392980051, 723187877, 473533032, 659620523, 708517848, 273719538, 950734294, 800549114, 515437642, 924974921, 924067535, 4759756, 192903496, 972101888, 77387998, 902782068, 534802721, 744126977, 227425387, 314779646, 630282542, 191547934, 615187713, 171541531, 211467804, 640426267, 881713467, 692355130, 107613713, 567875809, 470006453, 838282675, 541705621, 243508899, 558028448, 709069070, 553306780, 408816508, 627101267, 692075887, 270392870, 688600804, 151128475, 131668789, 454334381, 471845589, 586649242, 745062973, 786340124, 914215190, 517662652, 803971997, 546874932, 557584764, 308781995, 187343329, 498074973, 109165856, 590204156, 373768313, 913154822, 991779236, 224029087, 248531518, 612908984, 927181389, 642961733, 611026196, 845161975, 566348890, 197092204, 744095424, 742738556, 827406317, 623231560, 651458371, 894208580, 236092014, 106600007, 925799141, 887361454, 256524843, 675067559, 530481716, 283848199, 562098725, 475190851, 472855889, 206732040, 416787367, 92859522, 239669732, 229175663, 760048726, 113027011, 261217033, 528655458, 532183433, 380685340, 7491376, 121420405, 784237728, 414591949, 125725552, 826269461, 718061133, 314258615, 232355738, 631403064, 133759312, 85932838, 516851702, 182474444, 178520459, 234195859, 999623785, 742811206, 571311252, 541618875, 119306725, 316300531, 611870701, 217626890, 896526528, 502215006, 676957479, 666619975, 211104029, 623662484, 557975726, 536112899, 866195054, 591696760, 408952389, 77623226, 546344153, 626681812, 626245072, 518821807, 17448113, 479659801, 115076492, 979002361, 617963722, 215622436, 864295264, 544069696, 362214835, 669093499, 484065176, 209212516, 520113498, 373835787, 750342674, 223934877, 200353789, 840631857, 585558499, 968254011, 338113996, 136864345, 612336078, 840292901, 978495551, 164715716, 315351229, 880238548, 499937716, 267197584, 124458892, 700291348, 588636181, 222514272, 708053659, 929083656, 593608230, 990685216, 398062478, 150919724, 925169311, 897665517, 270712500, 45442133, 55497759, 856654437, 255076565, 990255684, 97217283, 580747342, 708297038, 575728935, 753235070, 296702553, 715766527, 223484879, 661393784, 434287031, 807613254, 398298662, 351485815, 797088382, 233274516, 148686866, 613545905, 460579019, 582088772, 522182457, 284814438, 831792330, 89649420, 671848830, 984104794, 648259683, 844704473, 426865148, 789308596, 610608792, 614318740, 930453697, 381738082, 942677411, 743044322, 777380033, 229434320, 853754482, 347702681, 482461786, 939346465, 873713917, 44161821, 290169353, 637887491, 257430554, 249714745, 509127171, 486771189, 402101506, 155680454, 717372961, 56209499, 296020297, 701316637, 246330680, 302926191, 552235594, 112610451, 462970829, 411751887, 341306686, 3628202, 304612092, 660067426, 232638923, 58754339, 74126086, 75372549, 498775997, 939538343, 49061727, 528652205, 285658375, 279659666, 519967740, 998416641, 206718632, 413988531, 513513403, 818990373, 399416702, 698104034, 191172053, 145396379, 337577439, 684408924, 778737330, 981555766, 161098639, 664647791, 884861814, 587087467, 461595092, 678851979, 386783540, 954505516, 176302385, 387122964, 601854330, 57833758, 914490428, 6263305, 521945035, 530018613, 858327244, 570105051, 554378922, 960130020, 179969613, 419743510, 478851477, 947885443, 529244432, 294021965, 692830115, 25787575, 168344183, 398452859, 388977715, 376447412, 237319695, 274691480, 591210762, 573505791, 431269508, 466650940, 633563109, 726393070, 291807719, 145011921, 386271360, 844942480, 584997321, 247515966, 489321654, 66100726, 612667122, 396861011, 222811737, 803750376, 772151678, 557704911, 82726290, 725586304, 466462754, 83509364, 745608318, 579186885, 252496136, 549302977, 769546481, 596224686, 237422742, 323173079, 487158714, 317830425, 201889083, 257578175, 320182328, 594150342, 248347186, 183206729, 431619387, 920167252, 916734675, 623778261, 793249938, 267878488, 864487647, 6375561, 321422794, 65000140, 756980048, 550257347, 283130578, 774801993, 459507777, 767982544, 681435773, 238370649, 348419890, 795532951, 511516214, 348734910, 66048431, 282899022, 215753670, 980001844, 716776380, 171018263, 689972809, 817509248, 936630407, 574106654, 232361293, 334717235, 339601535, 446898835, 869857435, 914935792, 963971195, 65519925, 82584814, 976091712, 586590191, 891678667, 322593083, 656125928, 934440927, 88385195, 765133457, 74163827, 968485348, 371901094, 665189307, 641282028, 415231469, 164545403, 425035556, 686904905, 495901021, 929086667, 380137305, 84649657, 724930212, 283171196, 563656198, 112624901, 284477150, 540621020, 844658270, 663970617, 87705278, 430414710, 529563532, 240404517, 107987898, 656696246, 65057439, 686699210, 269531347, 334707314, 516576884, 343522570, 771436467, 546359245, 691148649, 619178334, 729811175, 835612701, 83092900, 798441417, 232717861, 725512130, 100854092, 475510773, 885466183, 980345594, 405978255, 598098030, 498806283, 58673105, 950990279, 617931004, 86049138, 791365954, 78998151, 228422129, 561596910, 676253486, 138725133, 669968431, 301686276, 669087737, 102354411, 713514019, 229057710, 224394870, 605632917, 603760675, 854065047, 46087002, 105778804, 268873810, 340348803, 372644827, 520559605, 240669793, 598176823, 835410138, 783243734, 941468916, 52469929, 655492544, 78214223, 814445757, 882692235, 794452862, 979731952, 842652762, 870332773, 124731267, 401017136, 643393046, 693715570, 667872609, 840964007, 883144971, 895398336, 513553824, 614760739, 13194618, 636595969, 919842581, 618435650, 169878065, 496630297, 142785413, 671376093, 421262244, 716336698, 336006901, 829402074, 455529338, 421101954, 273266595, 278734122, 279649921, 769751229, 282497736, 17913634, 219525327, 344286328, 967397515, 424181909, 743098085, 309691620, 714688281, 610527487, 324738804, 735160402, 626785430, 603092367, 721767119, 171204454, 732048451, 3763751, 963906794, 772879620, 301464364, 784679172, 615010321, 577733270, 259252761, 707155017, 812306325, 422162599, 505329123, 549211455, 145570718, 783277684, 837035361, 187510671, 852457093, 736912470, 826253611, 727631054, 652559878, 266860000, 982133312, 573785311, 355518613, 548351723, 736788881, 476878847, 244649976, 855499544, 721938907, 437110973, 536946887, 759846511, 718683004, 609433184, 558354259, 909499033, 889355305, 716309871, 961646994, 989490574, 384308793, 782681653, 961820222, 918597761, 11674438, 208288941, 633909094, 430776648, 362364269, 542007615, 16527021, 510666880, 839544602, 586237195, 636017127, 957222862, 573908781, 792976214, 252326890, 726412907, 922451046, 208700929, 86632833, 223936032, 182316012, 726433668, 644061742, 993687014, 326434381, 362627737, 928931257, 699892955, 972938234, 525226589, 502056685, 833892097, 874992013, 356832161, 95134482, 202872109, 853620848, 130986062, 94107658, 924158588, 954735507, 611672045, 567390248, 875225990, 855800659, 595977508, 158547916, 481275296, 506915578, 781493317, 133754668, 813568108, 522940504, 415264460, 965050762, 232920042, 551669528, 260648401, 83691900, 562789162, 395538871, 530253686, 607594386, 669398767, 562906716, 81289877, 866237259, 181896863, 59311791, 746191261, 615960672, 895537990, 440108765, 69819166, 181537071, 51199507, 979902408, 241064633, 353013767, 31473696, 681385862, 490444761, 260180250, 642451187, 996515094, 535253532, 484942635, 906633741, 728062661, 645149084, 794345457, 349831650, 634070298, 109363087, 326638250, 999505131, 124348075, 467146505, 725900621, 732532788, 943659069, 248575506, 527169926, 84254906, 521457621, 732643069, 233356957, 151750054, 995921369, 308290688, 708710560, 132945657, 150085363, 365161359, 566859744, 925037055, 341271007, 895864650, 686917901, 285706496, 658411449, 199746388, 888564131, 643871947, 421019140, 623838398, 523366576, 157730145, 207243145, 566666252, 103843927, 999514840, 954000182, 110081835, 610680885, 535175092, 630104717, 434326543, 183270736, 767046431, 152637871, 687556268, 119037123, 338826712, 206611149, 12814591, 47090709, 22554588, 384816318, 604975910, 222156444, 827866031, 666809003, 882838783, 851713795, 513436448, 158512575, 375085834, 822048603, 463000201, 482954017, 707679237, 837038098, 264046456, 946912927, 628975149, 68649343, 806120130, 897697458, 836025111, 36672649, 633348325, 327871233, 21009710, 138036442, 643066569, 786620293, 277804894, 378604574, 607676781, 97460136, 609823463, 767622777, 314325288, 415506328, 696120678, 817937678, 350543830, 300927892, 857966390, 847073721, 753641627, 58052606, 619717523, 515925357, 843331179, 43608015, 707286427, 396249944, 539203930, 594464083, 294694147, 337188265, 352364388, 350013150, 361495263, 149847213, 303662167, 354908965, 562763944, 2459310, 104785333, 320576526, 47148602, 96696134, 51517322, 349095023, 197863226, 630539504, 783114255, 964283165, 187017506, 354102259, 110974184, 906541220, 967721856, 290816006, 878778930, 391405464, 836509638, 299827205, 188612405, 244841390, 595316750, 598160695, 767397604, 691733604, 919652065, 376341062, 130315356, 397792233, 492794954, 465822824, 418124019, 242837244, 954970550, 629214408, 198940238, 785754554, 477895381, 281067561, 209591082, 984620464, 474859885, 29992022, 925742831, 870860040, 712597303, 617940750, 782636049, 455869405, 73619314, 770303559, 63810144, 515442202, 338093063, 464925969, 459652307, 682500949, 60759112, 25847456, 532602463, 46839727, 304464677, 192495835, 719616746, 348967753, 95901392, 385510401, 296550165, 417591764, 930877528, 713022746, 643056957, 834540659, 513381276, 827815959, 380355025, 648093664, 881628054, 176941997, 896541292, 101250469, 466559328, 940901857, 897649744, 133219655, 630312653, 453025266, 748509882, 358864173, 646349297, 476264427, 24047552, 585781628, 69233809, 539835718, 386481475, 171479211, 751259153, 352967285, 400554273, 311064618, 77487743, 300960356, 822342098, 21693856, 598402619, 307134550, 239651558, 468102423, 80872760, 538841755, 81779771, 101482094, 650285123, 347740030, 240251398, 909474599, 894317648, 290686465, 666881836, 274159838, 874479463, 91959278, 585498160, 942472395, 826705444, 50651524, 156971874, 520272236, 601848278, 470009131, 114364269, 986334116, 725712729, 94921599, 815133927, 25641438, 471947738, 774895761, 467361809, 113999943, 740936380, 3683410, 372377755, 56915063, 249726604, 743255242, 647985301, 933023312, 559483753, 533555283, 603750402, 163460471, 820959569, 804184433, 840521834, 136730633, 83880863, 349913373, 578320014, 204042561, 733288465, 348503454, 654936976, 480553423, 988797987, 472280499, 230454367, 289337410, 86475627, 728765923, 435872328, 406007851, 514719826, 867354215, 203062723, 351051563, 699936057, 396338227, 850083665, 634539995, 493594477, 309213980, 707030437, 848415408, 315267670, 703217301, 101025283, 515178958, 594207471, 614665165, 181960944, 232372626, 653823078, 271337155, 5144710, 774399460, 812564568, 936381900, 650750340, 958887294, 303023615, 664205364, 552501504, 731281579, 268681591, 54132495, 778547028, 246091833, 354330977, 438056762, 735248756, 498487908, 68980467, 326464519, 135824448, 12711935, 937974735, 218679130, 230178618, 395271205, 622837380, 568627274, 797403546, 709345495, 976969026, 38262165, 363387465, 31734949, 989917207, 516769567, 657696951, 268099700, 126669456, 685078262, 6345509, 983611259, 672644984, 61961261, 398957024, 635555505, 307968625, 656531671, 908460512, 958203509, 989673147, 918491488, 823636294, 292655188, 110495113, 673731356, 428811030, 720677253, 902010674, 330183436, 650816083, 293762733, 457252631, 725278564, 666514059, 619377070, 843319410, 839022139, 197345219, 467989117, 330803566, 128082258, 694195593, 801840919, 121555697, 423228804, 430418507, 724494330, 120008909, 766556267, 111078275, 938650731, 153044619, 218219787, 690881128, 788965846, 942584852, 318880592, 294772359, 672110996, 362289008, 665920381, 525449181, 18118282, 387079579, 930066408, 132917197, 775275648, 448694284, 894630432, 634297466, 907298035, 191660195, 92839095, 189309382, 134599539, 678016269, 567479027, 791401751, 521994639, 586828899, 781851985, 392023863, 175841347, 694458211, 559633328, 461989451, 569747145, 896734687, 90297731, 793277519, 447044575, 38894082, 772039494, 606685862, 745406281, 506593715, 759787256, 809712244, 371285649, 384893347, 20429005, 855250830, 900107594, 606601215, 601473886, 733407350, 792435055, 303076280, 325825800, 53159855, 634671554, 117601339, 870773043, 813818741, 385051297, 232462244, 511513884, 180762973, 982890473, 668109818, 323496756, 727489049, 624825958, 681747797, 778559567, 123961064, 694504567, 415500270, 973851578, 695801495, 660737820, 838069254, 614823012, 82230797, 704648681, 605958559, 889869024, 565346673, 309166770, 789374520, 866961093, 364520304, 193077150, 71760800, 404141750, 438635835, 737271367, 167219, 438246460, 622368131, 600398665, 735078266, 630945227, 306389378, 775239645, 990612420, 195615407, 251161529, 331504959, 659829971, 601937662, 327595622, 901701856, 231355832, 357919411, 505093044, 742579873, 410512380, 462435206, 249252687, 451835719, 686848669, 558814987, 592888172, 627869501, 312950084, 302310058, 234914791, 22077745, 688864237, 299200784, 680453544, 150150145, 429854411, 287809144, 691936216, 939122091, 235631166, 139529862, 174685997, 433264363, 262944406, 372249807, 850713168, 619994027, 817456956, 420142646, 746817867, 566722794, 109005997, 783221150, 778684778, 413632048, 660926339, 994527566, 897122032, 241170410, 231489897, 27246424, 699222728, 576711319, 409353687, 645614836, 196452579, 366373267, 75085990, 151862855, 185270732, 674910479, 680848770, 358402903, 338555407, 485055526, 522005262, 426837780, 727230706, 765811778, 405473033, 956136411, 346317379, 63337372, 352703383, 836188799, 171454504, 801483841, 741426796, 529584877, 747492693, 801366286, 732458983, 881699574, 671714544, 671640847, 543413422, 960307940, 880309852, 383860226, 505066429, 855869175, 765440945, 798359106, 886375232, 507173319, 565155519, 673569591, 252945579, 208749312, 447386001, 674029877, 230599565, 619829172, 223022267, 675585367, 235994119, 836530443, 885155066, 28021137, 608838559, 521310800, 885073596, 946891098, 669287576, 74898475, 942919744, 184969088, 729556805, 362137171, 406068002, 33508622, 604652471, 670052863, 456635236, 696940651, 915103677, 363274495, 411207494, 827548351, 811724891, 554910360, 549258421, 829302454, 450771317, 333532763, 378999076, 619270557, 111584806, 176546743, 741553509, 333042963, 22517991, 543670360, 693007458, 492507299, 179996891, 190720379, 606148251, 717890176, 522210677, 30286808, 750359928, 184012031, 920218345, 840299531, 138707447, 863325602, 317938262, 781274335, 370902539, 78610741, 616841199, 799277903, 874658757, 533296296, 279412137, 290090116, 882280984, 20799141, 205353525, 282671026, 663210132, 702989456, 543647348, 222995767, 410450518, 918803151, 347277944, 16758267, 681043159, 918918885, 194251797, 916562725, 397633285, 510854553, 638346355, 314160459, 41102830, 967938598, 752763081, 95608317, 28725989, 256568087, 741995597, 505736121, 318787116, 223653358, 277030003, 482743529, 606136685, 743440259, 579217907, 108188346, 144405293, 695516082, 480691685, 451405396, 796801841, 929445734, 310799099, 146352666, 428140421, 397958962, 735795467, 814496865, 478856195, 57276844, 318246687, 37564713, 638506811, 36559325, 364856153, 243480136, 647213889, 141724182, 142896120, 632265634, 935879148, 850753756, 817160056, 479335458, 593127359, 70976848, 693449568, 710683639, 219275512, 45499135, 52108067, 131470287, 676556879, 602326114, 722073053, 408648760, 506835449, 593951911, 862897807, 578394496, 794398791, 179752455, 798780396, 579294321, 534308218, 19714167, 358390515, 698368011, 627691040, 245212069, 726056620, 750260185, 663102308, 568216378, 639290175, 33498253, 210261130, 384933244, 939558394, 649897579, 107383303, 923077700, 6302907, 578820520, 21943136, 870692100, 650802225, 625258811, 127668842, 564992516, 618928077, 317640785, 795256458, 572715329, 582629837, 180015881, 256229516, 53235903, 234703544, 148756378, 496412710, 909900826, 503584334, 193342497, 101769659, 301978065, 409420044, 760911529, 468521824, 117667521, 23073166, 740185817, 247380945, 191509859, 628474390, 596690817, 938503395, 251821785, 701514223, 137674069, 37485821, 544925425, 979904044, 600522042, 971337554, 679194345, 31350596, 587051228, 869680848, 4125675, 464224792, 65444790, 175870458, 453726815, 707736120, 38409222, 383148844, 572146556, 494547547, 817306060, 44363385, 809131657, 922773276, 689404782, 335202253, 96902797, 44046747, 795707723, 173975066, 14471569, 7415, 154539714, 260229121, 157472390, 510737622, 569535295, 124638817, 976724609, 543125325, 640699800, 276860450, 905165685, 46517566, 734589446, 907578122, 296453629, 679465238, 454796234, 957029762, 434163655, 86623860, 445721345, 412675924, 580956419, 224383519, 985236582, 150500563, 765842421, 830826343, 77075114, 676556487, 104687459, 526278507, 30067041, 120201852, 815355763, 452115821, 841601795, 994843307, 331452819, 905060315, 632943835, 923996144, 904888257, 579246988, 66097420, 753270701, 873317272, 81779386, 276449444, 794495649, 974641814, 204575584, 128402257, 444693717, 524416315, 331635982, 937771784, 701354333, 918600441, 685183790, 321680646, 960889152, 43003695, 509304856, 640199580, 451461209, 169711789, 674404734, 216706227, 733674461, 785717476, 827989547, 302898581, 660957272, 175948540, 626211488, 682271495, 857763277, 762972081, 133235163, 434979278, 361886295, 776787038, 608035470, 858521006, 598269094, 781725750, 747224740, 141615870, 610343464, 535986146, 541127654, 693605906, 560266370, 470259701, 499753419, 243423478, 174237266, 469370410, 791320986, 438272190, 128125005, 264610488, 34938133, 691690209, 909489946, 583467794, 799563634, 263115679, 21124801, 399369505, 143132035, 2036861, 583655578, 660229180, 314174494, 593409956, 106288637, 67836657, 336573702, 294985499, 406947918, 305767577, 333790955, 78480863, 891380243, 434267607, 682599792, 140120763, 654932022, 532702053, 719572066, 516385745, 843939086, 385693962, 686127219, 811932572, 277331140, 167535765, 261176968, 964504122, 947734140, 128356187, 896225797, 44140281, 467577797, 909605242, 634447245, 422880799, 738956054, 704297147, 434651674, 734878100, 734260820, 657189735, 284707195, 529377177, 332028067, 933729790, 614333434, 709858722, 721550762, 40221557, 631244550, 310896375, 601811740, 530407783, 421242351, 656930315, 771771558, 856681546, 73896037, 445075125, 538492181, 517760657, 429424031, 328283790, 866711620, 463347682, 803751512, 309067933, 564215239, 208386078, 802383019, 762267940, 797720209, 841740996, 190703296, 867872124, 947238101, 524202743, 75316918, 679627874, 373012170, 239846899, 936644606, 941179963, 230142600, 463002003, 537238229, 971374141, 142539053, 3479305, 117049967, 833208370, 629038648, 477722794, 636299330, 985051245, 237726679, 779467712, 554479484, 183775679, 282981592, 54685357, 379987226, 761509695, 993880116, 32238124, 414024523, 126812169, 446091016, 840171848, 191535344, 367826041, 328315001, 881522473, 840229765, 157924573, 86187665, 593602311, 135746807, 238466615, 338272445, 334448520, 340671393, 978080752, 907774323, 460565218, 970010009, 510456731, 277320079, 125716882, 756207172, 637846007, 552391654, 773239742, 611125386, 525415352, 484483924, 28048564, 761978757, 362512340, 52797880, 730519819, 633931354, 446808165, 788321021, 522550287, 645675522, 270976775, 359618101, 620714808, 259490505, 246160747, 10671229, 952435973, 310111288, 402514431, 310395188, 981027984, 524082829, 508344191, 242834640, 757336126, 489824296, 522469608, 539745528, 907854035, 919367226, 940718498, 436605284, 300483650, 35763885, 698815856, 241403622, 258148181, 951738507, 243750254, 124636782, 225172306, 85031428, 301868968, 725697886, 870827760, 532575754, 757383639, 495448194, 164259639, 947555717, 5618098, 364629334, 530997325, 334953914, 957091826, 552088540, 642888576, 159683968, 799743557, 762858180, 774091754, 4572203, 357965338, 686887481, 462686590, 989349683, 712503147, 275743377, 977255052, 960263739, 204811040, 901359323, 67636874, 737496715, 925939289, 758359009, 679262052, 48746710, 194418964, 126085954, 187917200, 951978149, 266592789, 109928021, 186150730, 550694176, 989461027, 588887430, 975360912, 637631001, 426800927, 662450943, 87283766, 209569692, 930765142, 539826023, 253994921, 276292707, 282936856, 894237062, 521239631, 239012913, 284041939, 981121172, 168514854, 367191614, 178475108, 696040947, 437847775, 905868556, 624198202, 705705004, 571701689, 55320743, 480390187, 742549098, 592483402, 823258212, 87288056, 659870204, 330329387, 295617333, 276890703, 677642159, 724821802, 554878844, 168020617, 918648594, 401990004, 92038636, 428334650, 715314528, 493354656, 778874280, 813800921, 362347042, 418382571, 712888058, 734378239, 800639691, 713272323, 833567724, 528992218, 505121386, 439434750, 532417612, 823174270, 441991031, 171861665, 858151810, 298247708, 234143664, 204588798, 415666216, 761885200, 125394633, 505358924, 290281399, 507261796, 37947797, 988853823, 219796237, 277289437, 92154181, 300661496, 504713252, 308472712, 794057888, 822909135, 970240017, 747823335, 598728477, 511598607, 748607870, 94214517, 227590431, 681946058, 617363162, 625776667, 517933866, 949726305, 928453187, 566900128, 163388271, 964119773, 824017165, 88122449, 547151334, 851714855, 607586184, 791857229, 576128466, 587724113, 836795549, 487570595, 232688896, 820405571, 132144706, 658278720, 804618318, 813227361, 804577123, 841131224, 882447236, 682265064, 561938747, 81422939, 585227539, 597528885, 717772918, 347947265, 336263985, 861343650, 752347724, 4530787, 571060414, 702631332, 244765422, 832924493, 204997280, 206826263, 500396319, 299630330, 616446796, 253293133, 604465793, 277863998, 481352757, 738895508, 353930390, 214723896, 771746091, 55134744, 901701690, 781133754, 525357952, 441123312, 604576368, 858105946, 957012280, 144387490, 984668945, 994804834, 780182368, 509412149, 507375251, 502213415, 690974372, 1797372, 423949162, 636046452, 425239551, 198874544, 10768497, 45154392, 891600653, 466698093, 569346079, 813988466, 592533845, 836537815, 897809074, 792395726, 551029922, 664376518, 750669652, 870921786, 773840688, 578435192, 229483266, 125052207, 256245001, 807009141, 132516650, 471023718, 927900380, 888678394, 531825435, 425389736, 374952539, 182570353, 439178379, 633027751, 495763337, 621248477, 521875271, 535797780, 107810769, 948066060, 629988175, 887763671, 711686336, 226360777, 52446779, 194185297, 588130278, 48079876, 817988789, 570582820, 641353776, 223402141, 253504674, 195829409, 614231727, 631441412, 58952324, 261131377, 357876410, 604289363, 733753060, 760318265, 622618525, 215101876, 132906188, 800730673, 201720573, 861518483, 370032952, 413598513, 543092199, 281350554, 463173754, 288475802, 770760278, 946533055, 994886649, 969433726, 902730109, 181840569, 412401349, 791040213, 976713507, 214938155, 878422642, 236487715, 634348897, 324500500, 857376173, 351563365, 711669717, 870325623, 197284219, 653889654, 272193556, 830424769, 471904128, 960771777, 71023915, 892768411, 471542315, 661286460, 582520408, 276264910, 137212845, 152346020, 60003985, 452503542, 664022623, 168855730, 833189942, 345308712, 566579640, 555224952, 35862346, 976538686, 490701624, 682886677, 400750107, 180430730, 143031029, 837396982, 920694184, 190613565, 901398961, 626493967, 875072384, 34129268, 523851900, 543414355, 411485660, 717789767, 48548457, 258306381, 620634884, 962562730, 108852851, 109967398, 47191107, 737307059, 354288161, 347237537, 182750364, 206604950, 727348405, 647668143, 111944497, 241600738, 940661028, 886749311, 123728789, 119176182, 205398375, 445016234, 538288446, 306825106, 506411067, 388612552, 318781982, 735876945, 590477070, 173971617, 491170183, 867859686, 885722043, 149234374, 859272201, 924440423, 460796473, 372004168, 684787355, 222634272, 616179896, 46995781, 81909115, 595106469, 950628959, 640977857, 394038828, 288440598, 726339603, 434085130, 812750938, 463345987, 231751173, 227224025, 841262327, 160759587, 235497901, 418773608, 630523626, 745008206, 440498929, 846592072, 976351694, 999282374, 706401000, 419324063, 343935647, 972302722, 510551736, 882722934, 466626025, 295456198, 648197447, 958069099, 730892633, 396183378, 429368684, 921051058, 565658205, 540548872, 83804394, 365188820, 275622041, 158798118, 747332772, 892675678, 773023060, 405626132, 586892417, 357056059, 547172690, 762450270, 163431035, 125435032, 78077975, 362358430, 671770379, 719346114, 343334441, 259542325, 864882730, 861163134, 4428235, 666345248, 257636763, 388729071, 775734192, 45979056, 831273812, 268945918, 302387445, 417469767, 730836902, 831305076, 396396241, 839132878, 382389850, 942748813, 756518212, 588548253, 159887355, 204546885, 473343760, 432564320, 808999235, 193700763, 435265373, 362570934, 301888523, 752811089, 509543766, 866431909, 301056684, 18758788, 310813015, 431180239, 714954995, 843606803, 873933330, 489899386, 311506005, 137993608, 941333422, 17942339, 276996827, 285288372, 588270058, 753372505, 688190963, 290195707, 511264279, 94452605, 798847635, 217889437, 908966945, 983336811, 401265592, 268705768, 262159721, 820704298, 915167584, 101474195, 581661298, 349152789, 241201850, 262263601, 534485749, 391339213, 744755738, 448347737, 191677330, 137775460, 288344550, 128013735, 114214890, 500570073, 408309029, 466889955, 409563176, 724698678, 125262246, 337857830, 368684437, 242125996, 54337243, 762832477, 25033148, 726493558, 695502060, 670472556, 149881599, 792962140, 927805602, 335870335, 105614326, 369296639, 64186155, 725833673, 415553973, 224932588, 731771319, 356170199, 799489517, 70315567, 762310593, 433037595, 625670668, 726821587, 203096933, 212506218, 439658840, 135497042, 565894043, 473197810, 35466004, 552881197, 798739396, 774898826, 678969260, 457278552, 905054423, 561299854, 724720843, 749961505, 984597920, 162564265, 570735734, 248816389, 958775282, 995711954, 503835305, 866044040, 282110102, 81968772, 887658529, 612155408, 984625659, 873331429, 602825446, 6506720, 547967261, 565082325, 37071579, 458388891, 601670581, 941893218, 419918641, 264034501, 515671721, 9186795, 156128666, 180653219, 719761674, 10879515, 26880642, 151873922, 543607369, 270470885, 741839259, 72007055, 115475701, 230294699, 5764200, 603959748, 703240027, 992352462, 824975554, 578105811, 634784112, 837422263, 527696075, 24323940, 598671634, 488769185, 932885506, 32143385, 653294714, 838971115, 375523026, 370180072, 387077045, 846292232, 190015239, 363996602, 514661263, 288262666, 3138327, 362741808, 675674344, 270239363, 704712286, 112315309, 873595938, 623679768, 545348644, 825305634, 266961761, 63452304, 435552005, 339033526, 871574705, 446478455, 781148385, 146041619, 733637069, 269534442, 345960466, 281357764, 729285022, 350773179, 696482585, 414353950, 449760748, 245617016, 90001745, 118546892, 673564189, 823077042, 319322586, 62433058, 519180575, 922758712, 73911634, 634993019, 535868719, 502498640, 218906883, 915515250, 657918096, 839793771, 365250803, 258606360, 245769172, 914905034, 964330794, 475984438, 13314871, 246553210, 961877978, 691394006, 598363567, 22314766, 775856948, 655401508, 101850964, 166112090, 210858382, 635381863, 853106439, 460990483, 834297255, 598392829, 296735268, 757978285, 638056403, 824636137, 923051524, 298911627, 12871030, 501324372, 134900737, 830666871, 982631311, 880422712, 848926979, 150086720, 439155348, 949944765, 719692137, 172171675, 39755283, 387248434, 832685653, 899881238, 392633539, 655907438, 827029795, 323222569, 532467940, 646404347, 722137423, 343835249, 665772354, 881744529, 876132524, 188334874, 957239613, 517131299, 439340951, 592720481, 646553652, 951894232, 74827150, 750070270, 650984688, 367874769, 68590735, 114652484, 68428500, 340631361, 979517828, 289563335, 626662893, 514137464, 827654267, 151162058, 292858493, 996591095, 817287684, 978994685, 697895002, 731158619, 406199529, 33986223, 464201268, 200360064, 628516873, 295030881, 152786017, 608055000, 835060884, 495341672, 26216840, 34749951, 115038000, 936519723, 447433250, 475106484, 946826721, 828437230, 398023732, 12596740, 781966677, 832738731, 600331391, 613232972, 193215181, 830256351, 287819825, 880172011, 623905891, 926219371, 302624582, 826430952, 40355245, 703562440, 390556024, 144991358, 364220933, 758783805, 889611994, 410067483, 285917750, 768139045, 305426207, 239459884, 58584949, 408547149, 657734292, 994662537, 448762138, 225101913, 665890667, 322615692, 878647480, 812853736, 721349107, 692490874, 369100400, 770324805, 263838487, 408929745, 464556168, 407202424, 887248317, 341995209, 623009101, 921864870, 617786442, 291666421, 711588146, 153270536, 776845056, 467773192, 908470218, 592958146, 46531879, 442721180, 218839469, 219413798, 513875515, 68782125, 703637158, 602238937, 102975950, 65266490, 873221914, 864811023, 127672821, 906704600, 367148991, 115341754, 718175900, 520094182, 537276964, 955322042, 852085635, 499352227, 6812832, 929883776, 186092830, 13564504, 196904337, 93734079, 908727944, 705168648, 971843292, 450177363, 67337536, 81096465, 387397584, 860012980, 829839024, 118062882, 608844455, 165353765, 285869791, 218319736, 16694419, 679358965, 520165096, 86840782, 634497644, 184535622, 765965017, 820854170, 357245255, 808031932, 60942589, 474826686, 399133004, 273293723, 880328602, 715403518, 925059663, 967170821, 807753404, 928762105, 386897909, 123229420, 113568472, 224253512, 915685838, 391206436, 238589858, 25735716, 117114621, 391495798, 989276205, 387266945, 478720675, 791556486, 234875412, 231656362, 14600228, 441780572, 49769146, 96890317, 793354927, 341005064, 780464458, 795930785, 441757546, 494335238, 728189746, 322012514, 768431207, 72606777, 611401565, 81178581, 661508760, 930682998, 463196385, 893314567, 549977443, 752517586, 844996089, 230029139, 562977552, 788850529, 628252874, 448073245, 466034075, 298294400, 699141507, 950263493, 7278169, 741021457, 360008071, 15448658, 773608793, 889560198, 101167734, 194291399, 135664807, 186640001, 257599895, 538026343, 91624800, 363294830, 176301807, 91041485, 116108655, 504397066, 395688174, 39781835, 253366528, 692358460, 98883092, 128610336, 466412127, 187111285, 164450740, 582980245, 709190826, 175787289, 784858318, 384088655, 467757922, 1870608, 368832386, 733708039, 624445747, 93407510, 357427675, 314849566, 160619456, 472966665, 424471670, 15214661, 7646509, 606901817, 422215328, 751590246, 159858568, 608612969, 658420555, 107845776, 204158244, 215480873, 311577908, 855198898, 79471763, 148974908, 858875874, 68972966, 669423014, 793350598, 888329748, 424732049, 650211175, 256438392, 907016008, 283015761, 801361010, 887746138, 977847808, 309691246, 919396601, 193568811, 858809140, 403055308, 280290088, 38360302, 516448280, 536133974, 701493472, 60489098, 424579573, 437967128, 911055409, 775047091, 457807322, 727249851, 560048969, 244855541, 524607360, 965828197, 689184112, 911477047, 88975493, 519870436, 648294725, 445654757, 791303036, 378418468, 729788058, 81290754, 629918411, 297385061, 607779434, 935130976, 508303727, 557872536, 130273535, 352085018, 862257612, 674890160, 654331446, 738748709, 594328026, 959978800, 377502812, 235493598, 623972353, 69344639, 19909072, 94109180, 349418362, 24316748, 800463089, 391300264, 351652137, 333473324, 664330507, 174982829, 468353555, 543686739, 772575614, 510551907, 945118877, 964358302, 114423335, 422509212, 836666098, 83402492, 550156320, 144947385, 324495192, 716023979, 711806020, 454789754, 628379122, 755661897, 238642349, 58296006, 465714864, 707371212, 695022237, 863930822, 49184878, 684665412, 929793034, 340780677, 279844084, 309375078, 426366944, 134722255, 933748317, 550966082, 214406011, 482325520, 62645035, 751725920, 605089656, 585063097, 451213734, 147024796, 379131541, 70228656, 18727108, 424174519, 895355003, 840577175, 676931966, 93807629, 42208802, 57888254, 879836797, 454302607, 283231212, 820818702, 601228904, 597628580, 933665967, 707869634, 206746153, 623573449, 117176550, 550394455, 94232990, 932641179, 683039154, 825249063, 557693723, 347137906, 382057983, 196812489, 458815056, 721862041, 699079787, 121372404, 387857104, 797250718, 86346337, 365850214, 294879334, 323097577, 310321405, 6283062, 580685920, 241493850, 353888900, 635318585, 716454677, 107324882, 922103334, 382248657, 658380495, 111148935, 717687462, 368289488, 189656886, 533857484, 28313785, 45146723, 489123775, 527019461, 871494127, 832068635, 920120294, 422634108, 858036774, 541700345, 698457509, 274845258, 39692009, 791553916, 406783393, 505970838, 635112822, 607632356, 837584934, 403259253, 215030514, 930149864, 681665985, 294149548, 901406824, 549171123, 67460536, 200737011, 379581569, 228283977, 206492113, 341900211, 240856286, 714096754, 511543545, 362609438, 234806737, 660482668, 994301831, 602467326, 923692189, 624291915, 553380478, 296092165, 883419379, 352964371, 165040760, 527383096, 156221842, 426196266, 345747768, 744907756, 41151811, 492856399, 765556498, 92524167, 139957966, 662218414, 452611750, 84806952, 553029881, 755356728, 956751733, 829733202, 406674142, 623284714, 794326836, 552693981, 731439269, 534556230, 234595589, 358612908, 589572740, 529488290, 687344506, 822127459, 694893315, 250134216, 908323535, 522642892, 354322917, 408710405, 930660967, 789887823, 880224030, 744939049, 393714086, 975556732, 776526615, 928807710, 577548083, 799496006, 433348938, 182363516, 376961379, 918370346, 504007895, 470405212, 694313062, 291446614, 866357055, 821507238, 207066044, 726282440, 532786359, 791868124, 681123095, 857302124, 230655134, 776531342, 5996149, 627590951, 302654790, 388778303, 622649148, 454939058, 476251807, 927381847, 216100125, 705917385, 901544800, 984776302, 231304953, 349279227, 519153975, 172840860, 920278591, 995105485, 220428229, 725073161, 681135986, 667324155, 362261695, 564990693, 194909089, 75996610, 905914035, 782360881, 38942159, 646418707, 267705197, 339757227, 836013726, 275322562, 610334649, 976404286, 711175154, 201862971, 391959256, 230473569, 810817686, 771000175, 784051250, 412441531, 967535708, 370274729, 642476969, 226718057, 757729476, 53755979, 189494610, 657096396, 266281085, 412951975, 398036685, 273605666, 398613423, 51028872, 321678187, 534062863, 846815727, 457454010, 741624115, 678845481, 697607781, 404440308, 461215494, 90808442, 910511153, 340585719, 76218777, 219071482, 207376856, 390521944, 614093927, 494103598, 128790710, 864399966, 235236299, 711927835, 705077552, 479176925, 237198756, 497374925, 37900226, 867749358, 482349564, 709799946, 428121223, 426634226, 898284977, 239964308, 299993123, 197754541, 939655580, 23832867, 39476905, 921722919, 788458735, 181031034, 540082113, 183514235, 350491347, 761538118, 162126514, 943855727, 180612127, 702557614, 815065402, 232985630, 232154583, 365209544, 102047742, 510248480, 66424760, 396467227, 493641, 670497303, 37776867, 25851422, 482574937, 523841348, 312542812, 934573313, 528432699, 31555844, 847220296, 209863108, 16962564, 614692541, 400497262, 823541159, 256842965, 586389911, 763518526, 424893622, 55061918, 231307933, 596143676, 898160574, 806652288, 924440528, 225353085, 249977087, 581805231, 492712095, 600733495, 906343200, 619096773, 743773052, 188936611, 67689318, 365573136, 429362126, 212205644, 163561656, 984409519, 325239100, 982856774, 228648630, 146895795, 581405915, 561846229, 392608157, 669449644, 951532585, 853740577, 162042869, 796010912, 56685315, 656080078, 238817355, 158415694, 266331140, 876806518, 544814078, 357697807, 214080287, 697290668, 259627649, 882480867, 228725185, 671999949, 294687686, 630438058, 177943746, 147662823, 628212993, 967512083, 70614149, 39962861, 129258268, 216887599, 862571389, 407156290, 290448724, 291631194, 144903832, 337861561, 86099321, 872515248, 667784724, 304684750, 676003523, 885917583, 559751964, 97446463, 527437664, 971466624, 998531442, 478508543, 934135718, 574928020, 226015981, 565543704, 943039883, 138072084, 672856105, 784172638, 983073420, 300079751, 683555624, 426527780, 758164902, 621335971, 374018393, 686588749, 701403580, 41212034, 994600494, 345857929, 432637196, 953605470, 879367191, 349164648, 761455335, 637408732, 698458706, 605934339, 703195568, 934890978, 498047382, 375566191, 856992546, 417200753, 793722990, 463854449, 318283369, 48105003, 594330126, 596892884, 217546094, 466314048, 677665348, 148542581, 525550870, 949131451, 562807073, 533745518, 658464846, 460672152, 655673054, 14500482, 988037083, 438333615, 865437848, 50585644, 391105592, 145392011, 505648568, 971639383, 431200906, 221619406, 1795808, 812683758, 327921689, 457813557, 426179804, 614781301, 424617634, 947614046, 236310258, 178427853, 200883222, 54935261, 718224501, 254676364, 688082053, 694823768, 831009574, 934122745, 103471048, 177298943, 546462383, 225422257, 131077329, 480220180, 880419279, 961915205, 393951945, 684902611, 140831391, 896133559, 93729691, 45302573, 22819389, 895982799, 942236361, 85723811, 845544239, 697659143, 364376645, 341378642, 6264125, 476869912, 489228168, 791086989, 406271875, 799580794, 568706161, 365462306, 461329364, 241312403, 948796527, 73438222, 846526631, 594770345, 400295423, 769414795, 572891832, 802857646, 583634605, 374167657, 671506184, 613971306, 952030745, 43813245, 118785931, 721582654, 227447473, 802921813, 666251157, 126866710, 581826615, 900633185, 344132562, 233241896, 812543044, 834330679, 313692451, 398247967, 392725161, 219472142, 300575451, 705283805, 900727752, 16501472, 757617541, 303034463, 358118981, 506969309, 852913039, 350210705, 838107924, 526627494, 628718390, 319647307, 826371522, 177294310, 839825467, 587729228, 62274733, 134530472, 967988919, 278665925, 767713279, 932157909, 717882913, 617425516, 22830521, 370873995, 190002652, 665472682, 23268909, 588940925, 744620791, 686208655, 306208659, 185700753, 353531032, 949636125, 182980122, 872366000, 331348755, 282518083, 353973153, 207210003, 54420089, 400452217, 358325533, 862218322, 329282061, 343237407, 314642145, 590264991, 984320481, 131955896, 610229281, 522671317, 212420741, 788285669, 383429213, 692914451, 984467821, 500761317, 939613889, 763343494, 173160201, 555921912, 711419396, 205193645, 114204173, 427633732, 795110917, 512254500, 416883607, 508609911, 737353352, 186177019, 382019099, 538318543, 423512127, 637262931, 589336139, 824538042, 820305133, 656481624, 525013525, 837712738, 422535315, 595946951, 609540990, 990634748, 945450641, 646779909, 286489766, 459143376, 422165507, 121285087, 37045330, 65192215, 260023993, 1675627, 602260502, 193878775, 589496779, 219919666, 641002621, 622850756, 865229475, 768811804, 247487680, 536083517, 337285022, 783161922, 751675827, 633850957, 126285390, 930964100, 505609003, 998694041, 296534645, 14567884, 675019982, 159503899, 478324931, 451349646, 90655513, 197550184, 585598721, 569115493, 139057994, 460816341, 592386784, 648110878, 350081594, 69580981, 656099633, 973274997, 135270910, 841791915, 500992162, 584023717, 253523461, 221669924, 931649174, 407265680, 155581629, 363076529, 449750640, 911407050, 442528818, 421227095, 744305669, 68467484, 968970475, 120620586, 388849057, 692541222, 927937853, 269020812, 55109632, 585909193, 21803478, 484042259, 653166286, 686227797, 788727194, 821503520, 938351106, 63165443, 48798459, 245792982, 27342599, 156179139, 608746385, 860888473, 108086195, 624442743, 165019618, 734835245, 202169042, 140228919, 39599492, 29530666, 48560437, 123777926, 272823731, 519359819, 554358354, 85805626, 491974, 531256705, 323809651, 616787972, 242415869, 924933796, 657992645, 836578291, 713624567, 358521855, 404889050, 956030633, 121483692, 72523286, 241543612, 624930301, 349711106, 676622826, 659283804, 544354129, 201937365, 447635354, 726174375, 210386754, 892109832, 183322890, 307209259, 249730417, 322998201, 723932571, 413261137, 956474217, 558415398, 515499263, 154288889, 862905050, 376273444, 374202761, 638805102, 311583480, 791880138, 431952796, 613818005, 973729451, 704751237, 557031954, 216468990, 760193027, 990434622, 502442687, 878291741, 436159415, 640127104, 301496085, 736084249, 867071928, 467373780, 293623565, 166279758, 813530240, 448248022, 685599806, 828095192, 625301285, 976336396, 483741116, 184016423, 545460450, 786331917, 86078623, 540584568, 402833368, 245141947, 834964996, 686860337, 548582141, 264459396, 616380173, 959533233, 566666316, 690308520, 534948109, 580355045, 292510250, 866645973, 731521023, 585529509, 266718800, 841362799, 340683354, 309983629, 313545999, 121011212, 462873261, 434380566, 69126070, 133515896, 430949697, 75709034, 331493807, 67416641, 318490175, 682355792, 262769664, 42113770, 949823812, 184844096, 965726007, 669123944, 673967757, 496173720, 639697104, 410289413, 675684763, 457928112, 909473473, 625924509, 918930937, 173337500, 821203232, 551781701, 905803782, 620319858, 987834854, 382570247, 77086494, 730331984, 961689921, 128429524, 967303182, 964628104, 214352719, 452375987, 977428741, 587159966, 706837554, 643913021, 17898480, 518608009, 316463278, 591982549, 533223171, 385635039, 365884547, 400768127, 69771452, 119837796, 269648590, 154130019, 821327134, 807399259, 598859603, 972681767, 599820435, 535447415, 737046605, 748350545, 929429578, 839596262, 127710566, 650641856, 771956719, 38363972, 990264315, 591504439, 923471074, 299445294, 527364866, 812356858, 229021025, 76483319, 344564973, 948567462, 621280601, 253676732, 150292371, 544910682, 745349347, 674486479, 464633863, 308435311, 763644885, 622391850, 231462376, 505964556, 142967699, 780693432, 116823200, 234318930, 577541735, 818431677, 835355380, 66784046, 195399025, 720627207, 221720098, 691218716, 374732360, 679608804, 998299308, 358535210, 6485044, 912167224, 423721117, 237870203, 382513491, 245856286, 646460479, 92852415, 610749338, 451721251, 426552367, 56964080, 255602109, 122876331, 748434666, 77851612, 367752281, 877030606, 567391699, 918410637, 505370587, 465870352, 331395594, 233744030, 322122830, 850188307, 368091991, 360578745, 252103130, 905070391, 480166017, 328588862, 497089962, 809205520, 552791616, 266990350, 743441162, 593229031, 903773077, 942840325, 70289566, 452660240, 534309165, 314970293, 372006313, 683598659, 650875941, 383218003, 53660837, 432384186, 729717867, 296550367, 700363258, 660787433, 796703562, 454147622, 45363971, 115946710, 178739389, 505996041, 874800668, 457799025, 389824654, 946573175, 358146654, 797608335, 598291138, 8888762, 90985589, 686721412, 281463715, 939025125, 73523995, 170788476, 152839147, 131042100, 50939820, 106562741, 432433645, 976256312, 344015902, 901477444, 327929651, 29203316, 249219381, 843921492, 931950605, 581735317, 49575777, 671102179, 477031259, 509796319, 926661364, 86753192, 881510453, 311422133, 162104056, 260307118, 83733754, 605479890, 923223819, 35026407, 814536746, 344359655, 541717174, 379041546, 651882996, 112508590, 974170490, 459361828, 28599342, 558320488, 552650606, 102222724, 256050826, 440067803, 505948563, 838071993, 688950803, 643784040, 294467614, 125608958, 15926561, 53246653, 613775499, 791962860, 220081529, 822506945, 601233122, 877886142, 176395640, 967674707, 572547269, 427451825, 420221556, 699596595, 100892038, 518029089, 48552039, 70511398, 61471090, 850924033, 561388159, 389225371, 843404397, 186747183, 209963805, 653702981, 536838852, 320371866, 841285072, 237419312, 567015018, 616822360, 460362545, 394119310, 258658152, 79221488, 96899023, 865903526, 523949472, 916334399, 995486689, 920415329, 435526422, 475048224, 759135830, 31790083, 546862881, 261583404, 16845413, 136882507, 523035120, 978097224, 361909678, 965427868, 194369705, 346703182, 435506739, 481974328, 146688928, 4986273, 560258276, 371870078, 907146705, 383520751, 573732900, 160582878, 655491502, 350065512, 807873122, 519817692, 878021379, 517313448, 778928217, 597800249, 445901652, 41776517, 707891763, 323719267, 143192924, 859888667, 968742627, 257318635, 736119655, 731390807, 694589343, 425182121, 451828223, 598070422, 246284262, 139886852, 782836774, 773553022, 84997085, 365002409, 382158707, 587495890, 791062768, 976449076, 924412074, 210464573, 97104920, 170977058, 407961229, 784629433] 841315121)," 0 (countGood [713266785, 593714318, 726677122, 228510719, 974275658, 502563836, 608899572, 868339812, 325376701, 924905384, 564553715, 670146791, 316817432, 901886228, 803884455, 742594874, 557194907, 115802587, 720555749, 991762853, 100576487, 835029766, 536266444, 756934742, 457139896, 602722133, 846647262, 947653735, 898187040, 83709337, 634095880, 704971896, 783564368, 995621950, 999473990, 774850340, 717274609, 708708282, 697048895, 901825359, 398459560, 921753372, 169968346, 350592080, 569017390, 85458705, 194179555, 341114764, 139495728, 850334426, 195920607, 664381495, 811566683, 223337520, 587938407, 550635139, 263173158, 297712743, 147399614, 12466771, 133096904, 820083965, 870511951, 615596964, 125366068, 299174943, 549491790, 445914921, 499849664, 886915818, 48553493, 628915904, 685050871, 58650287, 928505239, 473898681, 488293265, 275319368, 886371932, 119413776, 97404427, 828654064, 120560826, 84139043, 451888618, 438907772, 126163600, 889984396, 101698596, 773529319, 36150549, 675637390, 804619723, 291507530, 241487751, 502866904, 809710027, 665848339, 673414535, 153261462, 903671788, 948725136, 4363148, 871540828, 205496145, 830041161, 511344306, 954121074, 105510773, 847900135, 162463543, 698123469, 416891378, 64374342, 546521179, 899188484, 91289106, 131842201, 641957025, 383369872, 741013976, 783861959, 833814601, 236176019, 77197884, 539078342, 524167032, 888706284, 356882385, 640841656, 728102, 149999282, 385292076, 331387133, 886695345, 802775970, 952187247, 512649759, 338954605, 779892957, 344913751, 936249574, 150489108, 189172817, 664999985, 643360409, 342623380, 581920318, 938712592, 896933502, 238497513, 606086180, 484278894, 380584769, 545781304, 148059501, 107836544, 304441409, 994027816, 739286882, 421129552, 315727634, 996894460, 157456665, 714169989, 975479181, 377555496, 723639266, 108766162, 643270537, 9575038, 177116950, 201247945, 719181089, 63781280, 534349716, 727393545, 707558551, 366748167, 928145847, 914560046, 492278036, 805695772, 621324334, 536060485, 303157486, 86470183, 995340789, 866086192, 494746256, 590490737, 203697200, 525248405, 721963445, 635057875, 70148240, 148337993, 584533399, 110076339, 388595759, 313774083, 583092334, 10575004, 563025856, 152210359, 91852544, 361175706, 313635727, 165351998, 735438422, 944989630, 832076562, 630229408, 372076632, 409781304, 745259888, 245940315, 884643948, 627897480, 916644392, 528475600, 335073711, 203672260, 692640174, 629443517, 237640508, 364379702, 275481262, 693741863, 863547125, 859065733, 646442643, 868741958, 786780270, 367695452, 349133598, 81188283, 997221899, 498441857, 185166627, 59439711, 153708693, 165419414, 268349802, 750517042, 733131574, 411846587, 387825088, 757955261, 791795156, 166918257, 229623338, 156009663, 155368827, 867943360, 922907828, 720432325, 128106528, 403007049, 168351514, 442703620, 427476088, 306051055, 773313269, 497568905, 641584067, 712407098, 389021256, 553889860, 64459595, 791018689, 34941194, 855146247, 564550599, 77472476, 500011512, 124727205, 904380418, 538750457, 111671976, 571979630, 367328742, 162887313, 768953948, 196039337, 850816625, 517003452, 495462649, 24306999, 402608414, 983771097, 150660948, 503261188, 816966077, 561888765, 666646615, 502701677, 951943945, 607956420, 271831315, 265091097, 272924653, 80783996, 872280109, 770871754, 866973918, 377829651, 893713043, 482966851, 909669620, 745592912, 554125636, 457391829, 822312080, 492418260, 438501766, 872411930, 11858491, 627980414, 777444877, 421972055, 367875725, 333653109, 882407242, 889473067, 447717835, 322284883, 924368126, 223096426, 598466688, 922025224, 91193075, 771999039, 364061988, 613955181, 944237730, 865645549, 450823835, 410081763, 58259492, 69771112, 275252025, 545052800, 221660139, 453569014, 521168057, 782581906, 774561167, 748751830, 92919730, 181886331, 682838164, 757793702, 62718807, 964961688, 177874602, 874414975, 594832806, 760633244, 748878397, 354312558, 11193964, 322211248, 464413664, 580359512, 726120467, 702860096, 458962526, 43360713, 677191094, 478061939, 110454317, 663248960, 835709966, 388021537, 982472254, 718810515, 749498389, 685104848, 204253444, 398974623, 303513512, 91736960, 442994536, 285730555, 552703821, 83058159, 805559621, 90961548, 923820345, 896213060, 657049177, 880655449, 235519901, 202840411, 30133112, 615849148, 981252887, 763447991, 879070033, 242099610, 487150073, 135078268, 312663415, 379890079, 508578852, 869040143, 695579907, 152958886, 913548191, 482240146, 477458323, 946999142, 966176905, 704478467, 849317879, 468753843, 542461157, 847255702, 778448513, 483281546, 739836822, 327672208, 469311662, 263679941, 468228149, 928219691, 565074368, 511839711, 221696401, 802509194, 445500465, 54167810, 496709013, 540756789, 76676415, 697688313, 258117078, 923161390, 241014272, 594233972, 173953923, 999501802, 983362590, 578822035, 855453835, 403498130, 595515540, 247425949, 296841910, 59883598, 908509414, 927215046, 346781462, 791939272, 326236489, 179674178, 659644443, 530806839, 227269386, 739678393, 460379390, 710475676, 168663128, 596134724, 643405875, 852380220, 168485213, 544207625, 132699914, 613257448, 909382704, 144797760, 478439517, 606654074, 756860589, 851522770, 692348002, 149343144, 127108777, 758926067, 194730154, 207385620, 835473346, 930258497, 186427663, 147464973, 359032725, 332755962, 177152621, 202929852, 101504807, 464963617, 46175766, 701624682, 342137102, 856822657, 706876299, 515681065, 48125867, 392957187, 102164730, 745623895, 481991656, 763734044, 859132387, 389339150, 554626219, 763959001, 743050237, 83878569, 455525132, 814835987, 409506276, 341812906, 276257659, 371943833, 406019352, 565085376, 633051080, 979808309, 567765446, 467895602, 279735227, 702964441, 267121007, 569799086, 267292287, 211272491, 801560914, 310129370, 849585578, 608910568, 31127656, 829454740, 421343689, 331677601, 419027808, 18040912, 269078803, 356006188, 896629331, 604068823, 464824598, 451404857, 989866630, 517707141, 76281290, 58335477, 514396531, 598839555, 396513619, 920909117, 896065636, 591424643, 867291085, 144088876, 622325614, 956838228, 707453512, 687223101, 598118081, 135378221, 43186938, 644183555, 245398363, 197012551, 258339046, 267377075, 88699058, 446165501, 589829630, 661251206, 265421232, 200293861, 625900832, 867163708, 961742794, 242560554, 606358952, 655046067, 265643852, 453544361, 155900102, 720909441, 960907764, 698346722, 136515345, 567769103, 485058002, 174361076, 354453869, 31362312, 745772588, 344688676, 911422899, 768341254, 556577039, 961670809, 373188433, 843233302, 851395355, 337839379, 177083752, 958307166, 375724672, 562134949, 577680178, 8708222, 132861167, 310465958, 514418647, 224967380, 455101849, 468698463, 580868900, 803023653, 270561897, 421751526, 912367997, 267087465, 382702293, 640957677, 657318030, 668112033, 338353781, 959270063, 937600801, 369608349, 176217915, 995266556, 683476402, 923233123, 357944670, 364495500, 608221045, 925911647, 545437886, 832957192, 752245668, 342433682, 248062488, 659903390, 484483094, 654093090, 449049771, 655281777, 818430602, 486823738, 561558207, 707713057, 822621055, 634682132, 969276275, 352030708, 760466462, 490666169, 907667522, 551847006, 346358732, 382462248, 553658088, 919348126, 522837587, 443538292, 115453231, 630182081, 627963661, 581392063, 545369927, 391001502, 652335206, 144425994, 946436936, 539314361, 562923939, 865162509, 67508974, 281712606, 980158716, 594163498, 292870681, 606403876, 288494918, 273053215, 122338929, 415563921, 700398451, 430737461, 996363367, 382229876, 413154432, 633487131, 11330742, 431681116, 496468527, 130905070, 26040603, 451603351, 560257086, 502948333, 757983925, 743142770, 551828836, 599072993, 545773265, 210385193, 571939080, 271880734, 557036563, 756850647, 265487132, 875431786, 857867324, 241536747, 840281808, 991516615, 259707799, 887881197, 646126689, 568089836, 238682962, 825228230, 657339893, 879158468, 252934971, 123363279, 879299327, 937601143, 826615097, 871977762, 176719796, 834432353, 894268616, 886206734, 613811053, 476227420, 34062728, 783361446, 914296155, 190250348, 750992370, 990153442, 106708057, 33115484, 811890729, 608837396, 119713330, 841682146, 540080452, 682820926, 756809462, 254940310, 29865682, 60716980, 519400575, 84314475, 212511985, 739803857, 743417434, 140738609, 772343117, 718924385, 204182482, 311253638, 123698045, 902088498, 37009336, 663227730, 588550675, 262937624, 84151269, 71364842, 272318693, 491547975, 712649954, 248362457, 680086757, 592308619, 302887122, 241417406, 312730632, 301053728, 944039262, 688513116, 322417694, 505343990, 389425708, 691611356, 739779349, 991434408, 208177262, 125463144, 246693104, 249379456, 562194163, 600923961, 555481255, 210410986, 333451230, 579007337, 721826176, 368586175, 719296413, 956695151, 890600264, 659003480, 179543613, 798788684, 970031620, 226335524, 206330802, 584805315, 907977527, 859149175, 498755838, 2586564, 312348722, 309350048, 216917566, 298898150, 547285644, 108651878, 480237611, 290843100, 794797415, 996167608, 429147065, 913323839, 779516622, 550584566, 30796004, 800748575, 908569185, 709531074, 601696687, 122752418, 845629244, 610969025, 53432233, 1541560, 317828461, 874972617, 177207784, 706624484, 152884218, 648142922, 510420698, 859736499, 371178873, 343680253, 624014122, 268907327, 456345065, 700198017, 292949532, 404856482, 7105026, 18063795, 589006601, 953250351, 369630258, 861059144, 759827492, 261345319, 815737704, 777743627, 603797241, 297896816, 992276583, 58141788, 546511735, 584392743, 150480560, 193530907, 941762796, 516998770, 426888033, 867948245, 879186229, 874736817, 564523469, 826793696, 230040046, 940563199, 722153770, 476785512, 470561578, 445233795, 328918864, 114647747, 563189826, 831682360, 164522368, 1508063, 758415321, 328940355, 647426677, 310428746, 503737666, 333312579, 758885162, 636742183, 107261840, 430750844, 642136309, 478566984, 299270373, 506613058, 388927827, 428115891, 563580389, 101718183, 905315926, 62448438, 733182987, 143926318, 735314022, 952470916, 589053730, 252938446, 816731708, 476723656, 65454794, 950937003, 896226282, 604454372, 353459919, 42410741, 463460537, 649669772, 2471673, 434626282, 86614073, 788970309, 283341418, 715587319, 990755909, 586612860, 304129932, 689855760, 804506860, 495499821, 750570295, 348388705, 585770494, 330316523, 525267050, 815062917, 319201403, 268456191, 684906936, 212261073, 393297492, 394964041, 459234822, 739650710, 235392730, 240908437, 421242705, 239588263, 243628491, 119725167, 907340600, 178001537, 794109162, 571077481, 53317984, 925836334, 932060812, 594506150, 903465859, 654049324, 220938413, 832940127, 566182774, 512068621, 927354308, 724912605, 592394167, 970965177, 17302437, 560316806, 684934365, 311394186, 580125950, 504555408, 558435575, 821902692, 326603537, 233957482, 321799999, 570512588, 77926545, 476124291, 663198050, 220846740, 602048933, 770605071, 447139168, 568768444, 12966997, 320921416, 469045102, 20882682, 706159577, 127243208, 520562888, 761072776, 89352386, 866470800, 828538010, 991626537, 950438705, 784366891, 859860896, 547563758, 620523262, 258736485, 513812277, 128213210, 462205107, 199507622, 273981397, 420553520, 712750197, 91207478, 832835290, 56106206, 739763860, 875904911, 5303466, 184395595, 247949642, 609184946, 413495897, 963006396, 262238086, 317362859, 527235905, 77788367, 552482787, 402604540, 877903598, 297558439, 98853020, 841764842, 950770093, 673173992, 309711228, 915316807, 47760048, 947504433, 568786882, 482997035, 771611148, 425650018, 454333485, 812614768, 860181493, 12586825, 494997147, 851747271, 629892350, 435932152, 869600714, 862919520, 182723600, 113090857, 105467485, 535201965, 280284826, 247178941, 34208389, 119673596, 379770283, 365412038, 136876344, 235735207, 92912718, 863710298, 833465180, 8830193, 866089153, 985738147, 535269139, 715245162, 372464775, 255301742, 251902268, 839412673, 601130321, 690419744, 149038907, 831961047, 976797511, 131119434, 100596448, 719226608, 623235036, 178635369, 464199972, 457759503, 136909799, 868521677, 894433125, 766003852, 971372088, 815132647, 337466218, 789627970, 629380133, 267772099, 576526979, 403492882, 750928651, 790976688, 926772080, 187853592, 162745906, 758380515, 224935026, 471231886, 773492693, 591054590, 336506734, 848877039, 415784901, 363458381, 992742551, 562170869, 191720235, 977223777, 688649417, 862357327, 831933978, 414060503, 717486156, 286978698, 546469813, 975232152, 703334032, 644379266, 466263159, 104486553, 829780491, 527566885, 810408257, 756544832, 417843583, 686660512, 230607939, 919515237, 461836809, 123966110, 398920290, 28869641, 422336012, 767010422, 613471806, 490391172, 677840516, 848288409, 151334875, 856441703, 113459777, 996259457, 950515743, 629418149, 295647108, 797663755, 805070696, 452590027, 266773215, 785977793, 300382033, 539879266, 842676789, 120010380, 259911954, 32884422, 573921554, 758710660, 144659938, 653901663, 99901993, 927134724, 851077267, 377485888, 856337009, 665098357, 997405325, 761349459, 710709028, 38040598, 849944398, 532807776, 529524520, 512653335, 213113957, 770917651, 548744441, 980388701, 816319179, 844825090, 148398959, 962148536, 885139400, 342836770, 912989722, 809692364, 89928939, 629045892, 392802955, 379577643, 70294423, 712905665, 755615544, 434193571, 219009080, 124342459, 191448064, 662722024, 824500130, 255385397, 981437412, 882664331, 212174910, 687462067, 591639644, 594902628, 474434949, 163442041, 272446288, 400294600, 274343366, 944304848, 920388609, 838750905, 405916638, 159326289, 163313594, 39531972, 645277940, 496497682, 935990903, 949802230, 102149714, 3614848, 828529720, 115720151, 380239706, 249042653, 252775633, 159589669, 640013748, 465259810, 778164564, 80615675, 999051801, 939406027, 706144333, 995365134, 35756915, 701258731, 23146939, 447906963, 340524756, 624839199, 73037806, 193624520, 731605441, 921328313, 171863731, 814584911, 423126066, 490449903, 500550885, 50472874, 407335367, 201913004, 539501520, 278544837, 893565036, 471754690, 878525275, 30110254, 932723656, 470274561, 443807565, 983849906, 401740288, 339754854, 171439227, 496012591, 173821207, 625715598, 152144968, 372290203, 961081011, 281866224, 35286330, 175282430, 474322518, 838720090, 409918423, 993754462, 697270413, 870316169, 628317716, 301694197, 230247527, 37746288, 798745172, 868544488, 720855513, 734346132, 587710893, 32287141, 841733545, 551542636, 535038029, 221050122, 361550612, 856182256, 713554312, 996967140, 157261144, 963726184, 999917298, 761786271, 463901219, 244290164, 942650509, 357016146, 750259259, 618970140, 604837119, 724362675, 185972094, 403856075, 731194541, 244711781, 416131316, 275901472, 514930480, 961900115, 477427271, 961047406, 485914898, 321775045, 999374390, 66173749, 923429586, 438981207, 647897868, 783235803, 726522107, 266534118, 98018768, 51383377, 383426097, 809688210, 252741129, 378244351, 911105087, 997196886, 889367974, 214138799, 116368207, 374527306, 938838912, 906345014, 46475156, 775142153, 107557222, 352546894, 652633992, 324211311, 187398639, 404125188, 794325463, 539198396, 804277281, 99294435, 987843346, 612385075, 8809598, 481514181, 717037107, 693009661, 885849672, 580986386, 516505106, 628184219, 76415425, 534830226, 110668728, 534208352, 985560993, 400070378, 440624242, 514426241, 371955046, 26556461, 140057271, 141051651, 314917772, 140298923, 541008498, 876653978, 243536401, 166167792, 801441351, 799021024, 414450016, 834430248, 979056141, 545579812, 683917404, 776342862, 332514514, 463511737, 755365279, 935381358, 26073603, 512165351, 706595497, 426728679, 58159300, 222739523, 129048388, 142935975, 96042187, 801071540, 602379855, 718365574, 817667915, 94811070, 452812412, 515111323, 869217500, 143886969, 584092430, 186561460, 915132256, 435008861, 107790108, 208019248, 581622053, 973900851, 466851102, 833959711, 578133486, 303756470, 701635914, 509267281, 86773300, 193875583, 779634989, 63267598, 860348701, 167055137, 71984373, 476711616, 250190289, 955422100, 377385565, 557040291, 903821277, 226627934, 821471906, 505898035, 453243090, 964886664, 763021226, 587125631, 814276161, 285683704, 833734058, 8772491, 182631126, 177345940, 444151346, 691256395, 110278036, 657246467, 497310358, 492263600, 331138107, 546364932, 250962148, 364053538, 410464451, 94992232, 32338290, 389388079, 88221040, 50666542, 821070571, 333512967, 679659176, 523472536, 941572042, 383398216, 780372565, 618572985, 522925079, 242594958, 847807484, 188955075, 617420982, 884766139, 131358494, 251235289, 47966118, 137711154, 861076599, 843345714, 944825547, 200372083, 663296620, 53739298, 493232808, 724365750, 184218851, 797115333, 141769666, 25337296, 529513010, 256187103, 392212241, 369185939, 255352364, 27485794, 38393464, 197655610, 799930963, 744404175, 654960257, 45774569, 212835820, 369539777, 126551413, 499994048, 167747549, 596078634, 25794653, 975690092, 926536833, 807598954, 725635796, 399480827, 625750882, 144557807, 726613024, 678414701, 807815208, 535729001, 578562931, 31045440, 26707196, 843108272, 756057577, 970927884, 797873641, 628344463, 617218583, 578194813, 625587535, 290666539, 568711648, 938889991, 532566432, 49561399, 526523826, 404803675, 584372217, 428725000, 138298205, 866777471, 406766386, 463639599, 499628419, 536075682, 789382091, 571958378, 542342347, 987188775, 717034623, 413423411, 883681565, 463205939, 876457931, 160214846, 754319447, 883239658, 24593904, 322812843, 115373493, 879745007, 764915527, 509505511, 86082962, 284801449, 829315659, 467080692, 224632842, 283816172, 76594296, 163651286, 556024277, 965492361, 837682388, 803933055, 125666272, 972748936, 666667931, 586722241, 479259847, 192547142, 497088834, 707189831, 879489604, 175273504, 370549303, 706029343, 743214105, 344354434, 335804733, 452762773, 994456421, 521407687, 566711774, 925161191, 137562292, 175391340, 918040918, 143285845, 944515729, 261067759, 281182772, 738454311, 83494997, 530634457, 196811375, 265527186, 654640106, 704445804, 316962777, 843592687, 370285529, 779024373, 494582877, 96065596, 585656288, 161834090, 806564955, 216880096, 852181244, 673033448, 899793178, 595313864, 791375306, 217081223, 152798079, 526091859, 311840779, 465110964, 507034436, 486421009, 237051030, 48457641, 787516002, 685939892, 334962885, 565669041, 713801935, 779991357, 775110444, 481569269, 16466650, 697335118, 617917929, 352262757, 987321761, 578563678, 402356097, 955715796, 347661988, 934724985, 151554657, 320567662, 462029822, 210248947, 272402077, 856581003, 907084660, 675788428, 107584443, 463998899, 577771253, 486065752, 679748883, 110243887, 568386161, 569074211, 877376016, 515931774, 240193902, 571928647, 508177335, 201314041, 436517448, 372888666, 858965621, 401246507, 1362878, 534059203, 472698585, 746904344, 586325538, 685188876, 669421313, 139403635, 700311801, 755264715, 730203600, 812754282, 547097733, 537863514, 450587768, 673492065, 894426693, 466165023, 621337659, 428976178, 150012898, 201636689, 856745401, 744676608, 737850914, 328828250, 793789922, 492592263, 229040835, 181671781, 367441251, 120933301, 173781313, 994714799, 853741653, 547125863, 319184618, 435450553, 396228050, 61675533, 301163186, 82099357, 458901431, 763295801, 441953888, 354781562, 900476233, 849604496, 764807247, 759115938, 827148186, 137941776, 999016146, 717381242, 527917445, 705940467, 306439117, 565328791, 539947565, 482676790, 798315895, 244055016, 434736738, 820314688, 898955771, 736017764, 309464568, 739670851, 3661856, 992150555, 434523774, 625733822, 311459611, 895812435, 866313544, 610840323, 115030746, 423462182, 128820483, 272230659, 337538097, 646628277, 734006069, 63831542, 19921017, 986902920, 488847633, 886250231, 545228951, 578779077, 185680150, 210451671, 392748110, 339772987, 124117134, 443093959, 470263939, 701176042, 332450997, 802251279, 629074872, 146665259, 748622543, 831318742, 452205686, 198852829, 918793396, 866651102, 186977867, 538692169, 810679120, 926383410, 239044014, 13402741, 671550517, 105051620, 301789381, 249205436, 136880707, 637608840, 329014138, 71300735, 607071525, 544930419, 936461671, 234597568, 388828175, 49329641, 793197472, 988384229, 81449652, 455679035, 37964247, 478541372, 384694909, 491149997, 765723651, 370964516, 892204641, 397422517, 676275718, 205257169, 69634637, 791543529, 877020405, 103812865, 681628648, 341443113, 60631194, 892620582, 54741432, 852541525, 157361085, 689605485, 114553583, 184443942, 301865832, 481485139, 308574297, 82763919, 443777254, 684566655, 840054860, 67311554, 258000555, 120170886, 574960493, 535741559, 483398025, 451980690, 820451583, 358690258, 607881289, 351855719, 802130601, 41663216, 54974739, 372798962, 155725171, 641649755, 384308850, 215473318, 448533909, 494017417, 544260012, 368274346, 318830451, 771301993, 406439138, 724966476, 908656787, 588664279, 454258357, 809082659, 616960610, 956933015, 158508772, 23706577, 778431409, 687820744, 502743231, 436368147, 492564339, 135414257, 485805516, 587301547, 335559082, 674732719, 372035851, 427844917, 83587401, 356805031, 296735118, 115404286, 210762301, 947531529, 101221568, 138795327, 645566378, 447534087, 41812037, 89448612, 224091034, 198676811, 374457885, 948658932, 763180497, 353412436, 62651963, 274793856, 754816785, 206449765, 207460643, 663297557, 187899369, 942153309, 12605208, 638801703, 581707403, 479986632, 216961002, 432307415, 287207046, 938847285, 231671719, 213953825, 670826218, 179912525, 499005625, 724199583, 975226789, 66287981, 163179425, 962114288, 321930179, 318567340, 465228083, 591918382, 114669637, 325571583, 720289027, 220567450, 183398974, 842638099, 89586889, 622968365, 545982054, 101133403, 400734832, 225872271, 493866395, 899749293, 971175505, 122488020, 50536913, 734379581, 518898140, 35573035, 229261821, 313383381, 981718078, 556001907, 576394518, 797819655, 93377855, 854434117, 722420488, 451004954, 539452964, 778868198, 599645585, 87046906, 34298514, 931526448, 492707339, 469763185, 946553466, 449691714, 300724697, 662115756, 728293954, 409935073, 481008169, 35588935, 104285299, 592293254, 709136652, 29839512, 956276643, 903614272, 639375032, 109878801, 13404445, 334232534, 715217046, 339003742, 846798587, 131035766, 383734008, 599878426, 518220342, 606957069, 799330925, 727458512, 655513145, 209662046, 518829163, 868307517, 169429360, 996821396, 337218919, 394697730, 439297461, 46900835, 735301569, 635379671, 213169993, 329138307, 741531388, 520637530, 640862604, 305577968, 283166380, 291624427, 394395517, 135010868, 220744907, 862113342, 444000363, 497170313, 596341750, 337172824, 496609944, 670715313, 230213536, 324710656, 776260448, 548952672, 929252771, 388095366, 860740437, 888365945, 24991331, 754428175, 445163211, 44873194, 886909290, 108344878, 196148486, 500793356, 227237318, 826681571, 375178053, 316709819, 990267340, 86960419, 150730331, 134725028, 933877431, 589453470, 448868629, 643577127, 581741128, 778364482, 57961321, 486876688, 193957924, 122209021, 339892952, 415460796, 781511402, 916713079, 798612956, 549810274, 884976815, 240396054, 301957601, 162695201, 409386403, 858335327, 908523031, 459479655, 675449927, 796455276, 268826575, 605042015, 830641729, 851413604, 831598677, 631100082, 856806062, 868925878, 223952440, 407350204, 133337612, 976991861, 521871813, 853967324, 12561762, 501740473, 281156383, 994166796, 252302931, 283397212, 150702765, 750302238, 858107033, 479791333, 212168732, 803052498, 978660512, 851477952, 514580559, 758244995, 977625634, 213609401, 293999095, 728625249, 836940312, 512312841, 101057761, 22843450, 94460731, 780857093, 491951802, 14177690, 883336020, 900834720, 96222347, 71117880, 718418971, 683294873, 613235709, 313111577, 490782035, 418025793, 574734413, 191121844, 810482471, 423069507, 551542822, 955672474, 909416251, 183077003, 16067992, 350582009, 191636199, 182739128, 614586990, 378644080, 242012153, 282796972, 498450173, 942040419, 222543061, 218837523, 22460398, 687722652, 242486175, 832807122, 517932131, 894063578, 267181489, 573171714, 401785714, 783392745, 590186679, 695107951, 438310812, 375965824, 463866912, 69533260, 680697002, 508045562, 274060292, 646895228, 143191343, 153556223, 670995963, 413060827, 196009659, 748654030, 287348787, 174697046, 13463371, 183924735, 636111193, 23763069, 768313818, 805208569, 321553755, 207320364, 75095248, 19653427, 790463479, 927288299, 452650915, 696223827, 933138921, 394714707, 58293686, 778774728, 191017726, 871218171, 681594948, 797920188, 850816382, 802359595, 333138888, 254516378, 361270545, 394039420, 628975900, 913683336, 35606451, 543056164, 546453169, 708727099, 523486162, 365856179, 699923010, 282682315, 206981985, 357689906, 902107379, 828618020, 557127142, 255460337, 559985622, 92510647, 68476230, 470879937, 297734821, 473853919, 640678593, 915951738, 771831483, 317570614, 664729511, 786524532, 320120768, 889623553, 644762501, 698143534, 633932342, 864969524, 317074401, 581215693, 808161839, 379334743, 52607210, 586466456, 892174886, 183519952, 123990914, 567407222, 90214590, 19343864, 157659097, 127131603, 209436246, 200371365, 530124031, 383012329, 961014158, 151701351, 289437095, 741903775, 787172173, 76773328, 824520321, 525149780, 722252990, 409832922, 455156874, 320893299, 882971308, 834865638, 14835752, 788800348, 216539218, 377721092, 79380477, 765321458, 601414377, 899081014, 600845676, 883948106, 284332409, 244203953, 522972346, 742115513, 872945075, 264278337, 637584190, 309266183, 205808835, 404167819, 784961757, 696436356, 927918126, 753844785, 292945867, 423642462, 205401225, 130677058, 225246065, 173449814, 72580039, 275991792, 417175039, 883947310, 598878232, 836638527, 416648847, 151204359, 685303785, 597445232, 824819878, 511820002, 454912306, 66761920, 182986456, 602762611, 369550941, 41179411, 985381107, 743488821, 730623082, 704034122, 611298475, 123198709, 944648699, 436135619, 970808007, 751915069, 830506196, 151970527, 835057448, 78332330, 896344248, 815418196, 90922646, 542782280, 55889322, 757726932, 732886627, 183735547, 517941737, 564016220, 102523422, 362729542, 977638156, 428970105, 427275586, 342312125, 413978156, 430249829, 923873865, 408101672, 345389766, 342655458, 334346519, 871137833, 701430651, 770027986, 556466472, 5794813, 971938863, 178202079, 120853907, 694469724, 855387972, 37409781, 92568707, 925846516, 296069817, 823532004, 797726457, 905023224, 728972944, 564531519, 648386592, 957210314, 556249794, 50743989, 565612416, 411226519, 668664717, 477647595, 50961747, 623350869, 563165200, 393762906, 717262774, 88062855, 215470709, 380652131, 939216752, 479097077, 636244497, 729152659, 747249285, 691659226, 929934890, 100726195, 412152960, 256827814, 128883551, 695727122, 76097452, 907649757, 141985970, 55986142, 827124989, 769025842, 98561780, 210539796, 771411862, 69460485, 71424018, 957242200, 251619354, 824226500, 326755742, 393341991, 204803097, 552346180, 981320814, 248656353, 849815577, 169561588, 374249765, 1645124, 558743577, 245402602, 87703629, 861497064, 867824771, 508398879, 599077918, 312111822, 447967259, 906822482, 394552855, 431039114, 523332324, 392511491, 885918602, 80356831, 421586139, 226193562, 250007006, 351235452, 249492416, 690972051, 347953517, 97173272, 861585987, 615315793, 412917492, 393377083, 930259368, 792648101, 234232531, 424383872, 954361053, 362093603, 502707749, 715108298, 576590109, 364687184, 389061863, 872965925, 695076008, 463409290, 55590428, 393691163, 505252597, 357175900, 311257925, 146826316, 666691713, 285636039, 753747267, 437982122, 445332226, 94208419, 276779722, 733569302, 959076210, 358916014, 997441939, 57764010, 932918184, 804136499, 357600477, 616748306, 392903792, 547008850, 480627564, 67124944, 715829122, 529622708, 411820369, 663655751, 675202486, 123808946, 832314851, 396027077, 794155986, 246467003, 850110448, 164407864, 118302496, 928652064, 894037753, 411839085, 515964560, 860829820, 325483595, 670184926, 739988264, 951783604, 689413375, 687186072, 672702671, 366780911, 771105016, 663910018, 697686501, 607844562, 927142078, 21412149, 963240717, 235986448, 603301271, 528933947, 892650279, 151325400, 725615972, 991127481, 869853220, 75138554, 473962372, 811358282, 37241739, 908744950, 579651113, 954863217, 927447128, 421579657, 48535697, 606283819, 435913, 248169966, 16938979, 599584488, 979564200, 176234227, 705902658, 577976348, 771559677, 618316077, 893639142, 810121055, 155060659, 542744665, 388907164, 299781923, 844413182, 125830788, 994134457, 974349563, 861456649, 85926132, 958693503, 99185331, 793946483, 145922022, 977432924, 72104632, 565530979, 55574060, 722964569, 38295701, 748362973, 794209446, 555391097, 642686397, 514527768, 887574255, 616950195, 947175162, 865137182, 225210477, 98503142, 447831586, 659932616, 498210661, 481431045, 221916617, 989570198, 242530356, 723876938, 671027432, 298292312, 246502797, 321824757, 61490957, 920862528, 247924628, 170806078, 828012417, 295034586, 11705410, 433429681, 727892211, 707663335, 515664861, 906991421, 801916819, 627931633, 37179746, 465883382, 81130708, 327276515, 947235609, 131917723, 937765785, 556579714, 1494475, 105641219, 962523177, 633481374, 22555318, 51043155, 369178526, 276966738, 588892906, 602087737, 638619972, 89282396, 631192409, 898399813, 402961215, 332266413, 861914026, 830114264, 486553736, 976106987, 462678366, 468548294, 590067406, 375317769, 991762095, 107750152, 354104316, 966872928, 478638207, 415223404, 22490508, 124275658, 759989226, 491740067, 536839751, 155444096, 519689424, 298579194, 945231679, 251683409, 111882850, 502321135, 728295429, 474600355, 965271886, 534915477, 753505699, 236244488, 18886075, 195192316, 948503689, 866644073, 401714180, 377996680, 839157483, 603512560, 322098380, 267161440, 47217921, 861333262, 112235214, 214061299, 887827815, 149315772, 425702028, 686388712, 757016146, 477967763, 573433607, 974051218, 682921082, 625551741, 805947762, 182149723, 378402, 134942075, 318351191, 165766437, 785795938, 792659462, 311816482, 661432916, 251397856, 566898749, 975524487, 39697722, 735214870, 266541568, 622025239, 967411143, 799432989, 999565049, 281867256, 45080200, 926355924, 24444437, 677331890, 753114433, 804410569, 766381842, 349470244, 278786822, 431650058, 363037029, 123601134, 786616507, 107990291, 386780441, 573149716, 783903562, 133048853, 121662397, 665772100, 556031284, 283643771, 401688749, 272304792, 739782948, 301830717, 12812241, 330024637, 623731682, 918127428, 692427745, 442004299, 476240511, 198554545, 305023762, 25274762, 997686032, 639103968, 44535314, 567541725, 331169605, 205638237, 250997352, 77552225, 26515659, 311705056, 687336548, 467968666, 190433820, 414757651, 398192588, 628900540, 689955275, 936006330, 350269773, 368714024, 72435552, 152702001, 616722353, 462147891, 119686911, 745317444, 184071042, 233547137, 457988141, 648752427, 427632546, 613778898, 450455060, 456229490, 46601244, 566643715, 766202631, 457198631, 83079118, 880858224, 864682165, 696170955, 274808001, 270577037, 148731666, 632791601, 973001471, 586511839, 965992283, 188014201, 114092900, 836162301, 358306407, 17455157, 683484984, 190861426, 551983732, 263975769, 278754623, 66223477, 243583163, 453807694, 687763184, 432361586, 361768936, 594588840, 631295765, 514033881, 408557349, 289642122, 335957207, 280124610, 130900429, 735182278, 631297568, 435918808, 270744050, 514690361, 417434536, 565903699, 872441896, 56754774, 334999892, 375791860, 388014637, 360679545, 789522899, 271440681, 696690335, 993346754, 680437503, 602213476, 742716213, 875326659, 120458572, 878448653, 616715950, 431600983, 525791004, 641843104, 412743094, 486196487, 428016496, 388347014, 215613123, 263997799, 155465304, 335286892, 406482605, 339330130, 131258695, 772975036, 335663747, 339432346, 255623362, 313238497, 547116071, 663276731, 709131779, 845731248, 412516171, 885542470, 172624227, 528340267, 337091868, 714077356, 647453083, 298597643, 874307901, 197982793, 836045273, 222696392, 809408583, 173470067, 369401154, 100173317, 302120985, 765084800, 195671808, 389561563, 803274608, 803492292, 124781692, 978393824, 390614383, 649436238, 438595260, 271845019, 539060443, 11072913, 652508035, 861041215, 833987606, 469522463, 643954377, 209599519, 719588736, 297352977, 132121197, 911425011, 662614382, 867088754, 325993511, 127977039, 164409029, 176739227, 100160573, 34107734, 673971117, 226614164, 599067120, 907721474, 326976764, 31277628, 473774927, 285281317, 864087057, 553799369, 588936487, 692975568, 436590729, 703676372, 787194809, 583942163, 358361282, 658613414, 131594086, 258904707, 234366830, 452810070, 493242370, 370372996, 283600128, 982419018, 304422851, 148756086, 31980023, 635341452, 238550712, 352368290, 599355067, 855651681, 300787972, 49601525, 217575907, 473393449, 261842767, 811546545, 915832836, 87615204, 193898528, 371893376, 817271359, 280381046, 569752132, 893585927, 37275666, 173170317, 916535909, 972494306, 883366909, 720296882, 250306505, 931721318, 205237722, 79987030, 978087563, 2220495, 732466376, 40786862, 966775368, 571872189, 63518195, 938331051, 664562584, 406570233, 575431597, 569411853, 151325854, 681473374, 187463234, 587721562, 148891295, 144181543, 288240973, 773808299, 375833596, 172592961, 593692940, 663356446, 922702071, 944316268, 136466524, 131890377, 736872488, 259190029, 587542254, 50691789, 363124477, 783488661, 585375390, 345820647, 138361126, 172560026, 774782340, 696657313, 735339102, 622804652, 111787013, 378227148, 895465915, 394242722, 809790167, 484673458, 788233154, 43828199, 201332268, 369766540, 983769639, 713017442, 88921506, 902154779, 150873642, 906210494, 588690896, 940064971, 123420797, 168943917, 407821530, 695993083, 109343365, 117553401, 977389816, 600132566, 445435306, 671471166, 399760133, 826429325, 454896440, 669398197, 62166605, 324235873, 906248360, 933054494, 652436628, 848811353, 603605375, 402511825, 832081377, 238604026, 901526456, 877278976, 618821930, 844793814, 621395866, 71342159, 782440939, 441153307, 794317793, 599344953, 599852766, 88636289, 202557075, 135774882, 978520622, 339848269, 428479832, 708686272, 282761090, 522924668, 31740763, 836449420, 35969975, 829652766, 395823937, 133986763, 686291172, 970464108, 661963193, 952550989, 707753128, 643320157, 39005166, 116322517, 428372175, 761018502, 506679493, 655571923, 7801257, 363061367, 519866797, 81883662, 36890664, 280376465, 514836105, 686689777, 738695040, 678104004, 167425851, 520200019, 364504179, 737850332, 174357495, 840683809, 586334996, 185063057, 878798083, 765371116, 69135487, 529917523, 311027251, 771225727, 495737112, 906706956, 985654859, 126461566, 477142019, 790710253, 997831232, 579605315, 25928116, 500842456, 967749176, 834958564, 527605299, 746931345, 470793667, 531332226, 79693170, 308999063, 739239506, 169392674, 613123024, 644406275, 82259634, 549531225, 971177918, 132184897, 259825014, 969100154, 559310328, 403533960, 662423291, 179745276, 351096464, 43205680, 848202121, 341665647, 626626696, 307003873, 885582921, 552531080, 510349255, 97252084, 841851477, 186620431, 593951784, 569599856, 521729001, 550099410, 564945668, 745322679, 371867618, 196907709, 949305498, 372150906, 589694302, 608674266, 617372465, 833750045, 800808660, 525047402, 200854459, 775339245, 42767769, 472463388, 630375579, 874936418, 934700565, 615453961, 118575379, 776087399, 614115466, 184470126, 482774202, 365467146, 461552823, 883016544, 743097566, 736143588, 21096739, 942852271, 24023362, 864142117, 294971532, 130522457, 154003987, 375240313, 648656663, 247180376, 705118007, 14807499, 458658737, 117206931, 193606101, 148883174, 587064505, 183896491, 211440280, 164983362, 843319309, 213068193, 41810763, 924677509, 944799979, 350238241, 85967299, 840985092, 948424309, 431422453, 227330745, 843385622, 710304026, 303662880, 377286703, 905930374, 384882572, 661003353, 107545180, 930596445, 501047745, 251066282, 475766289, 818056477, 88609556, 624447386, 196320646, 290116157, 379878771, 568125235, 290453489, 424844438, 795907959, 965270322, 941773790, 714188103, 292707108, 972707971, 702801057, 979616132, 677257373, 967980961, 985354002, 822528031, 689673529, 295263196, 480490894, 82744095, 173847878, 215908522, 861711042, 952498907, 350719847, 940179028, 658726098, 908143906, 410408631, 129803437, 192504630, 106646802, 68820879, 26320344, 66390661, 403677865, 406856109, 183775644, 898868813, 187126918, 181208894, 342939012, 352463059, 40040404, 244968152, 466669078, 618506392, 786601737, 615305726, 393839371, 725021375, 792845022, 403458260, 909637020, 392981841, 552820870, 205677750, 87714497, 843225235, 109719571, 588410334, 471848153, 354610685, 310364825, 300305419, 844989740, 399236872, 180734467, 450957434, 354865753, 733070384, 23472234, 977091250, 569522709, 591364753, 227899375, 471925259, 740601328, 970197823, 716156807, 319013384, 680650364, 162900488, 528657870, 601507903, 476289932, 109131916, 704014861, 257264743, 873462411, 942392616, 471746876, 55521572, 160419874, 460206908, 73654909, 368882450, 443793309, 548164131, 610169625, 74513662, 769066725, 131466275, 469226827, 311413187, 991776042, 563621585, 796739214, 460275327, 481846153, 87859905, 41175485, 198133863, 890732582, 366069800, 647726356, 861632140, 17578907, 38027179, 369809879, 860276923, 161783225, 828035480, 39384546, 631300981, 732277180, 163732493, 258128478, 444838071, 283953246, 305772891, 699615217, 377248226, 237838954, 286927370, 594579995, 755000224, 437320563, 200640830, 690766786, 126818382, 552333493, 50022928, 849532467, 163746565, 239798934, 287560539, 500604484, 151795405, 802119426, 167034500, 826461269, 619294493, 46367581, 696383685, 367757495, 104122627, 15300525, 420885445, 560445079, 573755880, 11092749, 328412300, 106418167, 35509790, 209357350, 150671793, 844499966, 1513617, 454433764, 915182343, 404538924, 382562618, 846295699, 484717068, 699911216, 234218666, 222612807, 265677393, 813550051, 131413655, 664404960, 282799273, 853654701, 259627174, 203698118, 648040387, 271555831, 54055325, 168272813, 63361028, 738217987, 455204084, 610678120, 460522658, 652808327, 83456213, 49715240, 751136971, 724852039, 494573557, 561479078, 103175356, 889521662, 475607462, 753064844, 229579094, 766274951, 964152258, 496585896, 869317966, 575507636, 932611611, 491496431, 305926260, 937551748, 239626576, 610298955, 688253395, 91169623, 22053501, 842372196, 680157508, 912384265, 579376049, 414207950, 479410866, 934588115, 896770163, 293305916, 954621427, 235990720, 350527733, 827968527, 662398359, 527407942, 716221323, 428253592, 774045389, 173386083, 717898840, 606177659, 977383842, 261133135, 467881534, 862510252, 879775619, 218813500, 626136293, 604898211, 770800093, 490651746, 613758877, 926441383, 946964962, 974570127, 342990126, 441607756, 329583277, 831811094, 160663354, 46491160, 880360045, 218845404, 319682521, 923992342, 471189973, 716523476, 213554049, 857466177, 752370395, 416416203, 316639268, 19359524, 271737509, 947345539, 566973305, 677016569, 616826630, 724930612, 669722279, 285728066, 813496283, 103638096, 396786189, 921947060, 420443887, 456874624, 488232671, 244905530, 264643752, 681759756, 20560260, 914820075, 230469047, 891390734, 840487146, 365166029, 303809719, 774339954, 193581590, 125125649, 797443236, 991295478, 349203148, 955892456, 816115637, 796472773, 939844241, 429046501, 246541495, 29176036, 612643910, 416924757, 925958743, 665755773, 625585290, 881188034, 188008790, 28739169, 192632031, 237564132, 412284931, 611227117, 719906452, 807697303, 28732645, 999349525, 778564968, 685141617, 77963938, 131038605, 448273632, 962949259, 45027751, 433440359, 237472017, 642647617, 293385325, 476671969, 998193089, 621200747, 759090289, 308324973, 325664915, 377990488, 541477423, 758798592, 753462957, 426267318, 115875468, 768820466, 396461011, 551628739, 259126165, 497642847, 641541970, 816832812, 450825192, 49125159, 754677820, 300996493, 870574571, 554238236, 802919191, 464598414, 630952169, 373653883, 280556885, 843801664, 440883645, 839182044, 878864680, 498668544, 680176876, 467780237, 606900868, 875444588, 212517716, 90714494, 189074689, 41121560, 561532505, 437793169, 696910839, 531202653, 479283783, 554688984, 503665402, 362558592, 309821505, 603007542, 300547042, 533397046, 183117242, 233105709, 731068577, 298408506, 399878352, 305777953, 831202544, 592906329, 235091433, 868120376, 402924872, 728113455, 758631348, 872007776, 741941007, 705358125, 958166976, 511753829, 8934915, 698915715, 445557494, 303677119, 512947422, 65406581, 419309193, 221123433, 718412766, 670858105, 752341129, 916582328, 127866159, 881141158, 423065069, 796938836, 593910206, 545673309, 557754385, 541916316, 528814791, 235360613, 665188723, 224242846, 268124915, 167526850, 687087803, 163540023, 224247237, 193386566, 68651900, 762227279, 24460267, 118561530, 451874443, 627795919, 587234543, 903332757, 680769380, 278925720, 560002193, 719333471, 301503380, 66923983, 25769472, 181278306, 317584448, 997113957, 325629017, 876026644, 871150805, 217408306, 650752316, 203719922, 575409127, 639785611, 746225692, 684567148, 614712131, 264936302, 809200463, 330767144, 931447910, 691522954, 52867578, 878371508, 151494749, 100379831, 567185866, 600295638, 116471398, 209430472, 137189074, 755966413, 698510623, 277056147, 748133087, 901170545, 647533470, 971291404, 343454149, 128117989, 582683624, 945157629, 245795787, 240140938, 895591573, 317080374, 834040665, 447853016, 849501217, 83178662, 292440052, 313263559, 326373391, 729802267, 292100423, 28007434, 714725788, 295533197, 106894054, 513974967, 606136485, 385489295, 879400966, 865645488, 858179991, 210054468, 460064925, 29390666, 890552166, 412227633, 635021394, 274481698, 742811499, 859456305, 25140295, 307847543, 644482331, 775629652, 139904582, 232844386, 699528145, 893300730, 839471153, 540974000, 121696807, 421559228, 221169298, 398748987, 427125597, 34792912, 252925773, 734888786, 800867886, 555120798, 767428398, 407276085, 806647875, 234803751, 71334445, 854436995, 571895869, 324873271, 359858878, 351541695, 284891354, 606657478, 222724892, 381602345, 876821997, 257893250, 586141292, 520506937, 469271628, 145316041, 794600022, 290933515, 267778994, 698588983, 216798585, 522821983, 519036819, 753375409, 299248337, 715431539, 282716913, 228043585, 956288725, 447155815, 982848990, 528821777, 457565223, 855728017, 312321988, 115508417, 130027111, 747611734, 102359748, 877213696, 68756477, 414661812, 875618155, 838279264, 149594305, 402267257, 766971530, 51610192, 698562733, 563252024, 242837474, 255877169, 546014884, 101455065, 623443054, 439645072, 614543774, 232896423, 501135389, 316686451, 440947141, 976575821, 956781935, 155837813, 659050358, 329218229, 711589390, 107833663, 844220454, 856364244, 514914645, 242134596, 372739178, 719783820, 661215518, 792000098, 22562514, 788570610, 500073712, 973627001, 850001257, 396553022, 147991873, 741461579, 297911522, 791003177, 697642795, 943692967, 546823249, 785308117, 472444534, 179201990, 686124609, 360302048, 739574983, 565897009, 454135258, 90822836, 433484454, 537280464, 513284328, 297872994, 867883093, 449605986, 838817243, 313403505, 635524704, 687181130, 85457914, 516873242, 408183980, 699985823, 468654880, 496503249, 250894937, 305131155, 743492133, 778507923, 221123528, 837250030, 342503751, 693526682, 969924201, 383570015, 872793716, 703696367, 988570347, 937340555, 423357077, 598134129, 663799752, 817460075, 232846972, 257481168, 90808458, 195702862, 430793288, 592328605, 585825777, 411325278, 26122530, 789478274, 492757022, 986735793, 759164990, 503323613, 981159212, 185007553, 696912302, 432389010, 727270843, 946291488, 112155773, 520205464, 644485812, 69001056, 139277358, 622093172, 706961960, 260646988, 585593792, 413587041, 200805717, 140212412, 681694983, 749698296, 309754973, 789991299, 226070865, 140281332, 986796623, 374834202, 957055355, 183287486, 746401711, 601891689, 519754523, 708053914, 63039135, 830245388, 893225871, 448181424, 600744390, 951218832, 360735399, 102633041, 807197099, 133762828, 512116129, 648113862, 747676937, 437933064, 353526954, 427306111, 593312547, 312641368, 910739543, 510567071, 456449102, 487456726, 126465812, 331826470, 774450620, 527375378, 816056259, 344410642, 615325012, 151795328, 472926683, 383341722, 904372114, 276287491, 348076645, 229033245, 391771317, 868202441, 241989684, 619098124, 842190421, 728161502, 724874151, 716019843, 553097045, 223323711, 445294335, 244203010, 650180495, 987924557, 554330517, 781159876, 694366259, 941992611, 979223499, 160072024, 247047658, 887918461, 447141646, 558157754, 845271322, 329512877, 100383418, 743555743, 476626549, 349601179, 926469857, 513788107, 555090472, 418962238, 751508427, 781894829, 863880234, 5510123, 111366459, 147557905, 564296292, 876205406, 818272158, 816361455, 547411175, 792635715, 397845518, 496592161, 678594500, 460177301, 87876384, 294103286, 132335460, 29273659, 825931804, 952611339, 801807154, 937052505, 939859894, 782607749, 610414389, 727968273, 272707806, 193081234, 513818160, 630413442, 770125648, 92877696, 878292516, 127014609, 220943450, 215656072, 437679790, 601222649, 437253461, 213670828, 893725515, 456496784, 395670675, 715079138, 483901707, 533515869, 191372967, 821326053, 309692252, 814168596, 190309679, 15661856, 739054605, 59374353, 181513706, 458293152, 443675328, 793921561, 3414586, 899249662, 938231177, 16352190, 443705188, 934836390, 490220831, 800401364, 814756611, 52571294, 635224760, 840891442, 528172468, 903317248, 817179135, 80814712, 269517559, 869937261, 531714086, 850268726, 532614002, 601033, 523116136, 871490066, 22158997, 104712984, 80142630, 750743927, 628131133, 862705801, 774881982, 885462963, 341140822, 466874572, 444201370, 271209912, 579758139, 61690626, 537582641, 817871844, 327517030, 479859178, 72459818, 282103528, 200109771, 307338908, 388357328, 11321606, 706305926, 565483763, 115929231, 399642570, 811385355, 93457216, 618371383, 39828062, 507006999, 437526765, 917064805, 387851869, 533431129, 330032566, 981703437, 698746170, 128613856, 342483164, 516863139, 539244812, 735898405, 588366823, 543679610, 404394244, 571432709, 930479717, 835237740, 568317937, 231155382, 978532624, 440707797, 941059486, 754532703, 487997770, 834881239, 49628151, 194302122, 680175173, 654417317, 183821434, 178614901, 330392223, 50389047, 868424619, 799729485, 183653865, 548430183, 266871154, 163670132, 793060369, 354179441, 20522839, 142714764, 115554431, 828257699, 74336747, 86744558, 771295394, 628250428, 922987064, 103535795, 387007995, 947196582, 889869692, 563416817, 718817583, 777018915, 289941235, 115120779, 803339081, 594629439, 391346521, 298550614, 947468664, 899760939, 322359409, 390048862, 358787575, 775652553, 50478671, 275548502, 559590276, 489786367, 674929179, 643219855, 177284570, 456678502, 18997845, 697058558, 191637312, 476199947, 993250216, 384789888, 389190708, 611817852, 6305295, 157879180, 932149128, 409009459, 651693380, 886529792, 626638072, 891255490, 612337347, 576678138, 989126523, 333166746, 22365528, 32358506, 67924742, 143776025, 387150624, 427839579, 976750793, 563077101, 843164345, 762098277, 154419083, 637685271, 618756764, 447918540, 762842968, 186526288, 819806593, 921072591, 717761672, 558273510, 135512909, 410233995, 872679834, 105632238, 372186396, 600429819, 423480612, 163344877, 255933334, 155838139, 148479717, 659061955, 944752378, 503335203, 561080895, 536978458, 741701093, 920271675, 732494921, 746859091, 345682723, 290153257, 380502066, 119048065, 911881833, 217517056, 806286037, 683303361, 758305495, 655521482, 871887806, 592725403, 587121077, 622714456, 81018759, 696827083, 268252873, 619414423, 778233323, 11229717, 287792850, 483193541, 921074771, 183849305, 800929204, 156119612, 723922764, 703723476, 829781450, 597227071, 423177514, 303908653, 889520488, 345743397, 215369457, 286008307, 143696843, 545634607, 127497236, 610262052, 624903881, 956088212, 209681262, 879830518, 855557824, 628853399, 973443479, 48599884, 213803804, 814229726, 896498965, 147220501, 135572169, 41753184, 854457518, 138047619, 798843841, 725382768, 249826956, 154917700, 773391913, 560101927, 510002832, 343937789, 98050283, 51124881, 159157452, 774517127, 761818150, 196865098, 644477050, 435166219, 202941205, 261728069, 905817613, 192692175, 393435001, 136501410, 209247862, 211767835, 350241844, 502622262, 579445728, 572858790, 8560455, 827331510, 19672428, 753470693, 414143815, 842443906, 735013326, 555604161, 889861286, 985079612, 563293391, 21820448, 548370668, 271288174, 983938685, 860098610, 298959355, 480262253, 266173473, 550459379, 604717683, 502746807, 144822, 415094251, 300966331, 646562325, 149358959, 101479941, 776913334, 367253000, 154728419, 934707489, 857315377, 866018665, 509975874, 895155282, 50408483, 739766601, 267983594, 878380018, 843344410, 801959714, 861784180, 868871126, 806139053, 913541879, 255894959, 669971039, 205134505, 260587232, 312068906, 590416399, 293666318, 681094230, 215780528, 755742933, 358553175, 323844765, 924816401, 928323553, 75762310, 491282188, 279835639, 115558495, 575118137, 549373328, 469535886, 16577677, 81758146, 406899385, 726995565, 952316959, 379621431, 625798372, 885905703, 194875983, 893142168, 555298916, 133822511, 686898488, 251603051, 877833641, 625558396, 5639984, 989132367, 899746455, 195058109, 147447034, 21496266, 400483135, 406246253, 381428108, 70649495, 802623563, 631976778, 55504589, 860712072, 916078954, 572646119, 669216640, 995584206, 776735639, 658677299, 652875702, 409100329, 960854042, 618744563, 921191614, 558829155, 376047268, 206539620, 159273577, 877294437, 857995993, 440026371, 347225195, 627177039, 712197314, 817251097, 654525898, 963136866, 723896130, 560629630, 734549371, 697002944, 515121646, 571657363, 21052817, 974106355, 493311238, 877903409, 39416941, 259367508, 208737505, 989162672, 599889530, 575218019, 336548071, 728935887, 181547300, 44188447, 49975748, 716059091, 934642880, 431617747, 415825855, 976712143, 965801219, 17726733, 492094268, 860085948, 726245381, 162480901, 638147464, 321250299, 119935692, 374760318, 146852761, 875759360, 756272790, 911195821, 127674993, 45140596, 84266615, 959771719, 328105663, 353808410, 612910072, 695399882, 427908444, 201521901, 978209055, 401766442, 80937735, 24806364, 357633173, 35643075, 985934594, 540344989, 472490188, 956758150, 313272500, 87350364, 283372671, 916771460, 722289578, 672414003, 169252948, 758536920, 864485055, 361932650, 126539702, 628917119, 645791756, 603211152, 436315660, 211396462, 147753705, 670106657, 393622980, 353893114, 770365054, 876970550, 739733723, 808359789, 304345522, 237502368, 742688808, 138567156, 126738954, 436738293, 333609526, 778008807, 931379646, 115921533, 775880514, 994151267, 239843380, 489765847, 428907331, 948728290, 161555438, 868056678, 615550565, 30666071, 184379613, 518206745, 294602660, 235453784, 839727157, 362113796, 980422874, 595606323, 548670878, 921589400, 39775433, 70935610, 305992899, 668938240, 64875801, 290253458, 953477972, 163024964, 6635488, 666985498, 314279812, 249372191, 484474836, 674996098, 237494254, 617038572, 895433317, 179978085, 686212109, 42951779, 844062411, 557806083, 506402118, 635367273, 587824489, 987607183, 83123696, 114978240, 802852738, 581792832, 485962848, 367689303, 51296687, 113995354, 76109763, 397041510, 650935194, 482356612, 523213106, 99166834, 48328679, 491013492, 304748718, 790367719, 613624035, 886881331, 774911533, 596671695, 784620273, 305711947, 783467480, 567749473, 192663962, 32706872, 455376384, 836781760, 324781066, 123584365, 791723364, 950330100, 410278665, 498391404, 740933254, 241768299, 868067181, 437187846, 7509661, 597369189, 934308515, 60974910, 506869102, 978625505, 533828193, 417742734, 716599272, 173736111, 130818063, 909721201, 410046528, 502202603, 813629232, 17818294, 67368760, 254527872, 221398431, 585563181, 177395962, 112203421, 873465433, 64184523, 574362900, 227555690, 150921697, 140637239, 426843164, 574522796, 103513171, 235822312, 496370477, 625041261, 655541544, 660135344, 641819939, 626660712, 566894973, 820428836, 222405477, 296567915, 243178183, 977980572, 660472249, 140273467, 748885322, 113776463, 929105202, 883521910, 407893429, 121827394, 800077694, 811010923, 172082536, 70002203, 741789607, 133833777, 2419948, 327241004, 245520364, 412552788, 798040626, 770096288, 431345096, 366375895, 112491528, 415991588, 124017658, 903904426, 177388272, 279502935, 188698171, 141580505, 708086481, 28606400, 150896075, 488220056, 301013405, 461951839, 29295494, 256507455, 62806875, 577836463, 634820797, 8527333, 866385813, 762228822, 307677691, 822309267, 421602140, 366408313, 59416710, 190298398, 70872311, 712629710, 260056412, 175376591, 359455327, 289335289, 959948851, 608439348, 515987596, 543376972, 13914984, 476073952, 788058393, 19951791, 24960311, 591007601, 951392378, 346360155, 901409346, 58078536, 677821980, 65008367, 344906500, 379957128, 990654373, 223369352, 831789305, 43984562, 795863302, 56122590, 278458141, 74796791, 677901443, 903866099, 659148859, 758081263, 348104695, 945760641, 940362786, 817424286, 619994315, 874319100, 293367520, 636443941, 807035873, 735217810, 291118348, 182629775, 458297959, 72519839, 205176858, 295751125, 672980124, 993426293, 624316278, 484961729, 604070329, 879774064, 721423280, 255336948, 536894793, 647110946, 107722139, 2854381, 211362739, 959842754, 874515642, 415438079, 59517984, 74152804, 668046457, 522121174, 487596733, 60109533, 212733874, 840891458, 569089932, 122658003, 355375460, 467853222, 271303947, 141262660, 639662035, 745471976, 459790752, 920538460, 634879202, 158895843, 114671215, 344178280, 720308450, 913758170, 704452684, 951038338, 790753325, 447195373, 295562213, 713754886, 947466166, 81465135, 575118577, 401232415, 262283610, 699184781, 541039090, 866034759, 836380954, 95886012, 759732704, 533554824, 48193402, 594788049, 312018398, 520842356, 459816322, 775632843, 222983445, 276850637, 25812647, 882463869, 458893678, 73542262, 635944524, 426471514, 847430257, 422975499, 68803751, 357601853, 844407981, 904740035, 405530114, 391310661, 719483824, 318594077, 707239272, 751600598, 85952735, 561267898, 688047779, 817606634, 392439136, 437615016, 293073288, 619118088, 129330380, 641823778, 612307328, 914098632, 643656188, 186331599, 2519975, 332457394, 481831852, 628576666, 638798605, 714366651, 282860998, 107857728, 8079106, 699754478, 997776379, 831838450, 947717926, 713319657, 787555490, 203973578, 47967761, 498082842, 49920728, 14076276, 557954600, 932234677, 878219207, 809641637, 159726901, 519328231, 962601966, 708162811, 134860465, 647834399, 722214406, 153759302, 31762750, 701356446, 359425081, 60449109, 453012865, 582209966, 775978236, 899664582, 24742215, 526466767, 232938299, 552946310, 826123525, 733566672, 924243275, 197644581, 414151721, 472780562, 137957859, 978875696, 912568553, 306287938, 876085001, 342470143, 330533994, 548418477, 903850354, 234860520, 166780275, 643826855, 59458007, 938873456, 688370274, 775980231, 187316746, 99260216, 770308893, 530129471, 360274735, 84529900, 901503225, 131304153, 835166142, 379205358, 258133360, 841814568, 208881197, 736557126, 319395837, 71537247, 502515684, 95779321, 217079238, 879640901, 185897615, 263898145, 225546634, 196172113, 375969659, 550074863, 303342276, 493758599, 992306241, 266431136, 922478957, 448783044, 945872470, 560763699, 770344593, 330119274, 442630092, 421517515, 899063069, 210185142, 4338948, 571075719, 909669549, 728904289, 746646048, 757121564, 285765908, 596589722, 567013803, 724415001, 542937933, 545281003, 732087500, 489419765, 967187067, 642726246, 410465187, 619612618, 227057382, 776561124, 161903557, 225156524, 494278654, 852318717, 579458505, 23661303, 635846150, 598494344, 318126270, 297918692, 291965902, 476878637, 394289997, 696444910, 802512250, 521655518, 963004788, 38324591, 762610732, 810928634, 908002998, 221556345, 970002773, 51174712, 792485508, 304697086, 361226601, 609900288, 227843877, 490413552, 354408172, 808707522, 419635048, 295881866, 554269493, 159202303, 2544533, 463114592, 487201693, 821194138, 441198082, 424001820, 722459397, 747440602, 353851129, 899572888, 342972797, 583941641, 959827286, 889829003, 330484426, 430064415, 249267518, 94838108, 269518676, 295557157, 839405748, 112801699, 792541297, 161324854, 258449449, 781645291, 229092086, 288822180, 500742756, 586825502, 695728567, 95407469, 719699528, 586515352, 102794149, 878821179, 701915268, 857184902, 988021197, 137063100, 486149035, 305649046, 305130362, 771020668, 34784607, 559847851, 70061313, 763482838, 267438715, 851332253, 851183041, 742290710, 570197984, 134562031, 804468727, 96111828, 296601141, 262104990, 234688897, 311279441, 125926789, 510479419, 340423407, 224892178, 736115503, 50042165, 484147427, 798482206, 722447139, 514668984, 761079723, 933823335, 298689978, 39440928, 316425820, 53389257, 684109859, 98297156, 927744140, 947326092, 895328185, 872101859, 469563330, 958998604, 645740621, 397937998, 685882229, 376316187, 776033069, 319634951, 503731306, 517958223, 567596655, 66864512, 511178274, 559564420, 802203542, 894364966, 474425213, 77031498, 718001796, 589082888, 927585667, 30461890, 845813576, 153757430, 611392997, 444417390, 602666301, 217288682, 864733240, 740132402, 269420350, 817598403, 617375466, 224745798, 690434260, 843851200, 662556191, 498386253, 289877849, 801120728, 885584349, 156183966, 920547184, 812734040, 840686577, 143704363, 209135302, 141701160, 956701506, 160273033, 379277997, 702687495, 712894731, 990070113, 309195545, 928153826, 947279743, 923533304, 135765978, 224504466, 551902753, 59574402, 75763424, 860426697, 59295926, 942605892, 96521009, 894750332, 22968147, 424455882, 628028187, 544083981, 808503826, 675473844, 694135501, 101285299, 807118480, 485989488, 740519065, 614048885, 945841585, 282956990, 55577621, 602942451, 453378914, 142669521, 103180983, 728866810, 367833888, 441520441, 831251394, 398644822, 435005367, 934709324, 331628664, 312977841, 325699700, 593614809, 648624405, 567288334, 207888762, 907637138, 856299572, 3878827, 160328977, 924061639, 949578444, 169786182, 872352007, 84912370, 272859537, 772111092, 612335676, 648160416, 491460497, 706860210, 253169380, 210677891, 274872576, 25557287, 17573693, 759747441, 824011410, 94219021, 963785720, 169244488, 467569118, 461928299, 907681192, 66651743, 65830471, 33263675, 452283896, 741835291, 47039134, 114795757, 390809792, 796727681, 44515231, 356444094, 799202913, 792742517, 801091658, 38034148, 755037404, 857885023, 967568019, 260900131, 460887066, 221729223, 962822619, 507231428, 330592847, 861462628, 216622325, 307059432, 592676567, 285216957, 26481132, 771140283, 613912118, 942968230, 240422522, 811056020, 801766248, 830070396, 667452032, 205190833, 301317676, 823674346, 6784604, 658971741, 209073596, 298019229, 985095357, 579394707, 755960833, 358452727, 643156332, 253164321, 455709199, 927135433, 156044158, 686909274, 330788670, 483505316, 934531469, 343146560, 534703057, 69690806, 116324969, 13848851, 310235933, 201356797, 343422207, 165692579, 819953100, 495999471, 579860399, 908376793, 158341651, 363998274, 278656318, 328998608, 496234504, 120112215, 543281406, 411712818, 209514995, 857074467, 794216038, 429789713, 221142261, 765355668, 307788911, 525968789, 110795209, 619717381, 12570426, 359809506, 833376233, 577670554, 657681977, 999847900, 787112965, 254448789, 575447580, 918056127, 672414421, 623646033, 529838926, 327639122, 759505237, 314697822, 887338058, 555205084, 548215139, 502040026, 268111705, 64840288, 770159801, 381821025, 692447475, 794374457, 39935657, 445135412, 631263438, 843071769, 134944259, 775653879, 680048774, 880845633, 872792064, 729940878, 389907404, 481767655, 957879253, 269556457, 119530620, 234881375, 919211743, 862487869, 703902018, 105320359, 711236432, 476513896, 227837700, 950577956, 5619892, 620874878, 753050612, 545515393, 561249403, 496850792, 415992493, 788028610, 140269805, 735717193, 965438105, 13914614, 354232020, 998731605, 695865200, 489899964, 9433773, 775376419, 188077737, 402445054, 860800329, 981060001, 570829826, 27049499, 208247618, 86421011, 534543637, 967992138, 791703968, 208619614, 972408773, 554042464, 418172287, 552549505, 259949021, 730414338, 39895301, 473443999, 484703705, 503421951, 89093747, 367267136, 120299792, 145871963, 155101997, 228360882, 497828072, 189807636, 949769641, 876510148, 105314062, 954345439, 879949360, 262668794, 659147059, 734555693, 897374012, 776823890, 159588515, 421281624, 61341941, 703046928, 343278543, 953740536, 719310879, 998850677, 734246798, 606830342, 84081903, 551199406, 476583448, 644597027, 750707832, 322997962, 776570800, 591619676, 219940253, 800586665, 410598168, 153898935, 62271718, 684446457, 825998907, 102798990, 139990316, 669748785, 392925865, 345982125, 609549744, 450760198, 590699210, 134677681, 525555258, 737873171, 859513411, 878900216, 278461745, 169833394, 250763404, 613546689, 508284931, 813761644, 993229956, 387814399, 246029618, 782256484, 35084104, 459345739, 126774289, 604753198, 703567765, 16123812, 58718029, 971419338, 971160700, 218246173, 657658631, 47239226, 698612141, 299637196, 369243924, 308934396, 228825613, 883656024, 258644941, 570594926, 779610579, 122212936, 314058187, 179785264, 484759963, 122800630, 710376970, 659497887, 924535503, 19128611, 546381701, 925862047, 284312648, 393649671, 404801549, 725647227, 922525705, 177252945, 41552947, 547986230, 826194751, 671231862, 621739063, 524915160, 776475623, 938271045, 8519424, 328053129, 885456833, 241622865, 798082285, 184436130, 838165645, 394165041, 392205335, 282597329, 622279892, 798345039, 180008696, 548630516, 182086158, 720151047, 734520316, 811349291, 878082665, 746362741, 594850060, 915102558, 385222054, 211127477, 192202523, 28144502, 173956602, 82348921, 706937869, 471853826, 970473440, 946500278, 417837327, 812312467, 684907782, 453855148, 502024788, 790284870, 289645587, 914964942, 513940959, 664342273, 728134715, 684824366, 390323013, 387949185, 862574689, 62260059, 626360185, 201421312, 272748903, 556941630, 829473191, 314534366, 251111749, 30672672, 644309007, 125892130, 772826810, 735580243, 132287039, 530719818, 793311939, 282769777, 695922612, 762321273, 598218719, 171959022, 962205037, 918489093, 382898829, 855828509, 207387520, 253039263, 985142001, 346319450, 105936844, 810245589, 541087907, 722266736, 282407177, 283860590, 942727627, 408381928, 373422696, 708485283, 296087571, 578140344, 898407458, 233698082, 360130451, 176913739, 144467026, 725604749, 513249492, 855792731, 741198899, 78710289, 943189003, 13012886, 243618404, 328915528, 911018550, 685108303, 715973710, 71350163, 948563903, 246518041, 360119994, 706796039, 433641299, 662973806, 809173254, 712119122, 860496498, 256263141, 832708440, 915749114, 672724852, 93825234, 167428316, 826710938, 198950881, 779505376, 738786490, 165116105, 476449570, 264410922, 495671590, 7000587, 897683624, 890092597, 40143674, 472386324, 896872855, 983013517, 543203778, 499750414, 863763492, 666270384, 941246479, 793189493, 579145603, 143805681, 10053185, 885231231, 712481247, 66896803, 315730474, 56606001, 867252755, 669828058, 383832638, 469769867, 911807341, 831654638, 871894202, 766983185, 677932282, 658454369, 801229798, 698831041, 105123417, 625929542, 769190521, 239444665, 48515003, 308464140, 344156902, 595800122, 632391020, 708671240, 801798111, 409633214, 229001504, 923592824, 428600425, 759932668, 340522482, 299251037, 953750072, 398284115, 854163671, 368802860, 234024493, 275454997, 368109179, 690978904, 350285576, 339713965, 159006646, 740046075, 25964492, 546325415, 764465606, 278370318, 384168742, 651873126, 550905746, 984817949, 601039850, 602716244, 768448004, 157162933, 765632023, 667261924, 366000853, 193947979, 821096624, 123988200, 438491527, 87296299, 315834238, 47925563, 700407435, 646382605, 118691401, 638516721, 762875958, 488768406, 952128704, 36456899, 361987455, 604726810, 672206231, 405518099, 364054984, 288635484, 207486039, 593023087, 568668051, 895082882, 148051241, 364457525, 321007137, 185840449, 900634781, 586138731, 651254275, 746587189, 258087018, 54137765, 812562925, 792995392, 171935267, 736020558, 550140491, 130009259, 827551462, 44044568, 899574262, 839695605, 47537462, 830079404, 720267671, 432080180, 896122449, 475424400, 763215391, 23467240, 899066978, 170244228, 529563959, 72911148, 397808701, 910972936, 303635026, 507827008, 910833353, 384951550, 295203987, 541803383, 283144992, 137609511, 791372828, 72960959, 414137553, 739320584, 431478608, 352298533, 879915538, 74335446, 945475068, 89151172, 503860026, 544203984, 77130967, 907455377, 409439581, 714658534, 997845208, 124780716, 181825951, 785667200, 317674446, 742659235, 704807882, 288055735, 642648767, 360766250, 11982691, 429352124, 174477159, 825604284, 484337245, 78383506, 231576073, 407066245, 465926866, 761814268, 614601202, 686171465, 391851222, 869554289, 686578838, 689104944, 339189291, 532563650, 651172607, 989626160, 281164368, 274828908, 202882378, 582496236, 543439865, 818834164, 662860952, 870030869, 939083475, 504128342, 933254055, 157623565, 953609874, 601330183, 898557109, 950266788, 631695687, 115265979, 351039247, 481263384, 637085478, 276254399, 754302544, 920229820, 972375259, 549468925, 223688764, 651554341, 362040882, 442313270, 71429019, 420781490, 897895985, 977599092, 783619174, 398015465, 360772300, 909714636, 151149924, 334223474, 515019353, 495281722, 481520833, 636894311, 235314565, 943043401, 590595082, 962981688, 942193120, 40266422, 241264831, 795548143, 364445374, 596689425, 184254924, 20397488, 520451378, 646368274, 832793545, 931569084, 438784879, 494101227, 712521144, 962832893, 817231989, 828834707, 709967851, 806067476, 995867182, 654602406, 226669144, 675212539, 678897474, 862507146, 567709872, 89649829, 283177256, 563732308, 491717181, 629985305, 217488911, 648073162, 57408341, 141894643, 540565685, 609913280, 551090621, 326511592, 647709046, 861047103, 569854621, 295454240, 167346309, 894629602, 692016084, 384485155, 791307806, 290512868, 965653307, 219837610, 807013708, 459698586, 227034843, 507699655, 606959802, 930652225, 500311094, 924320273, 72016154, 423036369, 752265195, 977761693, 215526059, 33625244, 930367947, 234393739, 772803194, 496217988, 155670518, 425593010, 267064596, 164114273, 434606633, 299701692, 333372607, 198417263, 485048297, 558205766, 383324846, 60511739, 410761899, 977498671, 8942469, 458439391, 282562967, 270030395, 631858351, 958205229, 40838430, 953957184, 158409086, 932440088, 817431179, 443159480, 278855481, 30222174, 937348366, 744980385, 915487208, 903912080, 609114533, 571404147, 576442097, 243578419, 704867355, 99006671, 319071500, 287907711, 258642912, 596311746, 772514030, 969853566, 146562807, 331458200, 854963147, 315072077, 715574925, 966579792, 180641587, 451809362, 721297249, 277874301, 69425637, 486549839, 171310342, 824826506, 578388118, 849197917, 168579831, 942238083, 318363139, 138702743, 825983541, 410308969, 442496867, 593928063, 151055458, 277317968, 427693472, 898554088, 799398037, 794281171, 665197844, 506389487, 441276644, 623141871, 459891464, 748359051, 824140761, 675730571, 780695390, 131548456, 895887405, 366945134, 688872004, 874592209, 118865255, 359713604, 345995407, 603291028, 159880235, 493455210, 128259285, 264825330, 595776550, 744665595, 162351144, 57857186, 462554488, 405259708, 694324362, 117144775, 547311489, 899935283, 241060990, 455815952, 36569808, 717148101, 766084426, 197093004, 927015188, 814594324, 560889369, 465709557, 891431586, 590015545, 781116547, 163367281, 271976119, 911969359, 503046359, 997460938, 289424613, 92817257, 125080875, 713755388, 200486848, 822164774, 455081975, 888506116, 172199104, 448323552, 255154738, 620780036, 86037367, 437695830, 372534324, 995041987, 783014211, 88633459, 980408625, 557390327, 104240485, 145428680, 608215675, 288028587, 739753407, 965465588, 222092286, 348430353, 11933797, 325086590, 239362158, 144111313, 235678842, 59083548, 839006287, 894236970, 885593510, 142536913, 424533616, 588282978, 537390384, 696733125, 905738164, 468480286, 268445993, 55939375, 77331719, 435252631, 309464250, 116651731, 150308765, 479101482, 78590954, 941396355, 614817921, 172295188, 674994502, 684082704, 372354485, 779274102, 956967294, 794963571, 415732121, 551899308, 93635522, 921431355, 764743538, 313897309, 607784734, 404034485, 756266701, 998460435, 84741717, 835483076, 440392567, 225622155, 176934532, 583787022, 364259854, 551935066, 290477590, 248434839, 924749713, 837884499, 941817128, 206907444, 782825377, 517457968, 429432934, 740702747, 278541550, 558549768, 471876758, 702990311, 79756000, 761826837, 391757699, 80398455, 422346792, 639516951, 334475822, 251549014, 66938816, 11187158, 313616052, 469516981, 420501602, 147151604, 699898411, 609046182, 665322328, 242172632, 229245721, 941645898, 622334887, 507931115, 115816294, 790681075, 328357432, 465246030, 927808462, 643031113, 332717933, 660195845, 626738863, 295454690, 975554412, 207893138, 258079266, 24016706, 898883477, 710134509, 500297829, 310466648, 348950479, 129353021, 697003771, 863254037, 73090420, 935062900, 202013481, 512068567, 604210, 277031759, 901036713, 73212886, 671799651, 863170425, 557820128, 705665747, 661135779, 724424534, 281301772, 771725744, 122115330, 416186670, 569302435, 260468188, 345168170, 553499747, 197142048, 218458390, 898263181, 948530389, 704191001, 337791814, 683324824, 655986010, 928678867, 100061775, 5772981, 564272423, 239849799, 994090783, 432332850, 211822745, 61685693, 872848390, 555248622, 751971899, 536271666, 717672986, 37080815, 604181318, 829569464, 492750704, 249677498, 739800034, 853239812, 213702496, 490298086, 380103196, 542960389, 795707164, 842091066, 12585626, 457308493, 957782262, 300233895, 80698673, 12561003, 702963877, 498381437, 121143957, 510591773, 765108975, 195632690, 589293204, 601416134, 622678331, 155881041, 577043042, 311770283, 964942853, 324362584, 682299934, 446632144, 415586035, 659717588, 910071270, 218782120, 122088233, 295034006, 453235340, 900861622, 362054457, 639629866, 648907517, 261420333, 362499675, 641705833, 120316188, 217791636, 541932304, 142495477, 263709227, 987517919, 23334506, 959688473, 620973258, 515714209, 883303229, 88995753, 445101701, 916488025, 96605257, 844581502, 846637017, 810516513, 131602167, 314098052, 889114641, 743027059, 530856698, 914637749, 804864246, 603484608, 597167415, 81984963, 377230119, 552915424, 131540252, 539996529, 554505933, 661599379, 191350669, 483683164, 505907262, 787251102, 461968169, 72071380, 169175606, 760409542, 882207366, 485229628, 347380756, 106503105, 153182094, 593105873, 224213914, 658611858, 290212311, 717548692, 652693916, 85538525, 458689606, 259240789, 985830922, 535347856, 190614239, 563824676, 930077704, 143937895, 692689722, 678163235, 689947730, 64063679, 803403623, 136727211, 824417243, 762803953, 916287907, 126914185, 254612020, 422127023, 270880890, 505662388, 17119020, 908052238, 132404487, 3626023, 239180789, 972428709, 112468194, 320652392, 173573191, 780569648, 882287389, 59447635, 679325696, 95151182, 94919381, 492076569, 144252512, 612815461, 908491602, 396971439, 827251414, 119029066, 966782194, 518982527, 934954052, 605968826, 960527485, 936683372, 720670999, 857894976, 527175666, 963288404, 158671562, 561618090, 299734715, 481562454, 567257501, 779961035, 892729806, 588432106, 973911657, 269806007, 393916548, 813102111, 431016357, 158356351, 274209043, 301940487, 138894673, 717632210, 823625679, 846112742, 922771023, 960557148, 874856829, 272149070, 952000667, 660621214, 564044070, 882780388, 753544792, 418452354, 858648309, 931652580, 920612332, 872433741, 499396987, 228381774, 632237784, 345048058, 921103705, 373108802, 75821717, 601825390, 98985281, 560489760, 564631470, 94099991, 144182748, 822768308, 196265177, 847098130, 937033187, 597451630, 618929776, 970594126, 333059387, 470638718, 549898777, 924495511, 348222790, 367272848, 885931203, 806197457, 398602396, 503289361, 55331957, 910904448, 107368004, 15623745, 50508128, 192014095, 54604780, 329798411, 725030539, 205738152, 664098447, 683031355, 995933080, 344795307, 313666261, 31541000, 648109073, 662032848, 431519254, 108752670, 321014383, 964527093, 764467424, 892979896, 649297975, 308458104, 516295411, 60456700, 276585967, 526952944, 695281719, 161357340, 960572487, 527163985, 123116741, 223281476, 562458331, 220369399, 67600904, 444513741, 566898162, 280880576, 971239077, 847336131, 995340359, 302432164, 330416108, 44130808, 831593365, 826539195, 993591603, 449767188, 562340589, 453142101, 42784706, 844228765, 793506839, 738916275, 288211641, 725671613, 209135371, 554425524, 616858589, 335227410, 859215615, 920019803, 349957260, 998343420, 131486847, 757311505, 429401832, 489978419, 737584940, 390316798, 931821906, 6996689, 793137286, 862613639, 830945276, 836280843, 676242256, 371606094, 43500230, 381169145, 985147726, 575500403, 693039696, 15984702, 358325485, 320778670, 811700409, 658318422, 555373982, 470958711, 477667112, 682282729, 171092703, 278388508, 180259239, 909444982, 309247041, 468390596, 162434975, 692357956, 528646257, 484602602, 587809222, 394815344, 517318468, 635304252, 194279076, 599471050, 679441885, 255520079, 970745239, 727055220, 812704371, 309520845, 371139127, 682986714, 16227520, 489344814, 151368607, 91292936, 562515135, 31348998, 906273, 844868903, 152341169, 796696659, 846961972, 940521018, 595318665, 976084836, 548701481, 259228250, 236133939, 728566304, 814390262, 85813858, 904980707, 212614902, 272891499, 101380164, 712913854, 170790475, 410181758, 475469572, 677542365, 845404272, 659029990, 124551425, 575116689, 570934970, 612700173, 676409267, 510821160, 849975938, 657124607, 265684592, 779147534, 718436154, 358254617, 246793657, 579327789, 115500517, 989976174, 900966063, 691222392, 628855171, 43339127, 604246569, 381406534, 211522993, 428238726, 175826922, 296119083, 562892366, 493306341, 262463457, 499811077, 648435836, 427899314, 236028358, 428732053, 852601467, 276657068, 86376190, 149967031, 707263860, 405333385, 796079769, 597354911, 37234958, 98095999, 206073284, 995891262, 485115516, 780698787, 347658344, 171675563, 227854479, 259242527, 338336843, 192553830, 280283415, 82320891, 795335141, 735378356, 408271350, 706752749, 461559647, 191540030, 538239381, 12192891, 496916769, 312733268, 938920680, 104477802, 687512764, 544433204, 30316024, 401890139, 626295934, 991296426, 987638253, 543568682, 12442626, 207600320, 809559338, 844430303, 426101488, 934996777, 306486307, 85616646, 759123250, 521975757, 933706133, 753777798, 505182501, 906659100, 707503433, 856930581, 939062234, 863029917, 886313752, 727371490, 606438622, 774370640, 710097189, 564299735, 260731013, 356568188, 913354408, 631386034, 209770535, 920684303, 671053655, 440632704, 844422519, 769499328, 554221764, 440885426, 958029548, 358441410, 75527825, 54575928, 78708895, 752681399, 755121085, 748519172, 246137670, 207444774, 176207773, 212867745, 747996258, 842257547, 849683423, 640676843, 11686139, 540411508, 231148781, 338202820, 465695568, 623673834, 242831818, 830881418, 713650478, 479429267, 103613963, 263946072, 541019105, 679287052, 179179671, 721801101, 860841421, 84805950, 720200637, 171994745, 557048419, 578977956, 424512503, 778484366, 946376390, 27500264, 528149238, 314880024, 63352414, 335539868, 548824900, 944713419, 84088561, 383856211, 448529877, 241261798, 615495583, 797127593, 510034808, 503705755, 75162035, 947153626, 95185444, 918210545, 363104803, 454669826, 886577349, 367841669, 297219725, 35356036, 862075362, 731941, 704775895, 243375716, 213067342, 979686959, 558607951, 272382436, 378600652, 988685925, 204008334, 865774743, 418250704, 272392773, 323481712, 996683109, 697812552, 433902692, 903288084, 104558587, 321112168, 303732082, 990314794, 835282132, 552661953, 352735955, 653797660, 574124054, 654723366, 349752076, 240224891, 709805775, 760714753, 166394506, 830363476, 358259771, 916448721, 895003915, 796206482, 356611237, 615133287, 238615450, 565727131, 924413296, 813207178, 481229918, 697357703, 839079351, 525675299, 123146009, 955808302, 476491188, 144219121, 695240904, 207235667, 315236921, 34721922, 788826668, 994542736, 955629958, 771794913, 275668194, 439079363, 709737183, 865252072, 475052956, 918704735, 777286246, 902916202, 64765816, 160967129, 49950874, 276640481, 394441517, 99677126, 351889550, 884448063, 508957408, 860648207, 23601675, 208524720, 829698170, 393358738, 130222454, 470402737, 440328142, 398519478, 675039373, 223821374, 347309428, 422060174, 991522356, 880899727, 638677365, 579518745, 969341328, 148058927, 500958486, 999963918, 410922871, 691982459, 780630041, 945131798, 687263253, 384458554, 120842530, 230888638, 711926495, 303324442, 988631626, 654563708, 114844638, 93969821, 448409819, 761517366, 195464961, 48407620, 776427759, 774266391, 723130197, 950355880, 2982687, 143574408, 815036288, 811386239, 61318472, 506863576, 86151068, 614163506, 850547210, 917267020, 28803393, 189121872, 905953370, 197150099, 555890956, 341929558, 540459975, 81276559, 396777734, 596688947, 742778406, 909740087, 261727069, 338847309, 713022005, 644348341, 294823329, 566753083, 653040782, 898802876, 287285024, 702317575, 776491665, 777194953, 571645261, 845079167, 745713651, 313269057, 192430709, 94760856, 722971750, 242828629, 618745170, 169472574, 660077405, 235640345, 867572042, 301198549, 149116857, 735347503, 763946496, 418294152, 810271557, 872603862, 824493903, 901108906, 577328135, 376020843, 408810909, 599338383, 862682777, 8728889, 727175968, 220531477, 745941868, 65796373, 359767593, 781785518, 360168622, 312171420, 219643783, 798528358, 14812286, 825305745, 725041472, 714761093, 58434648, 601338683, 937035895, 464882962, 869703883, 43707952, 8937056, 592603001, 162497959, 988520173, 542435128, 555194199, 892712223, 56462513, 478885279, 975704690, 993156400, 984275839, 422392213, 685257001, 797843915, 58926598, 819665914, 693092656, 689537060, 278424864, 137941590, 64644028, 5408466, 881771639, 836028750, 814939888, 443884347, 652797066, 554110202, 65157763, 457250622, 831462500, 518296077, 185328462, 352085060, 980684797, 310049493, 886964351, 318742301, 807840456, 570224376, 390363398, 260568398, 559919706, 531739221, 630963382, 328222664, 557804988, 547682183, 71922935, 926652083, 895352362, 445827854, 664172757, 163233192, 433244554, 356763487, 982952696, 702860699, 328824295, 934231705, 890169681, 510710013, 939498314, 358943254, 490449670, 289143132, 83548911, 443492667, 44906453, 447271988, 981764825, 80690636, 854990132, 38106353, 11375929, 284178369, 754921908, 497835118, 138127444, 201799388, 193850466, 183803884, 698180591, 903145574, 178814249, 608234816, 252288486, 994330207, 426541558, 122816716, 453058621, 950460539, 973585550, 580886454, 684971774, 291217029, 528236241, 876575454, 25455362, 534122438, 19355622, 642698024, 825085633, 506003615, 562708885, 236954619, 122466354, 938601453, 218228716, 93293275, 527258642, 928689371, 309115137, 828894006, 468801067, 441514281, 932537282, 310012667, 582143679, 59818370, 617754277, 686251858, 728044223, 269602267, 196329691, 840261936, 21318384, 776750742, 756560819, 757695892, 635773110, 967122697, 508409732, 268141258, 756667312, 3920831, 814985879, 523927750, 831713889, 275374169, 129149043, 222173344, 359788591, 552589470, 444672014, 191201847, 196476404, 219787441, 802856954, 609621459, 789178470, 121693374, 493893616, 691014801, 405190520, 607622402, 62045861, 460079534, 315761116, 725302952, 311195818, 558305049, 181289950, 329771730, 703704786, 771846821, 212537185, 793515846, 604993578, 832992094, 469313579, 712546122, 270720120, 4932316, 763985785, 652450170, 253013054, 291268957, 99562699, 128076152, 525987238, 201878997, 853203585, 279433480, 264004420, 572228472, 19506898, 772597892, 684871925, 631839042, 528584449, 139384521, 488202488, 852883278, 979558729, 963841892, 726641899, 781979454, 961792840, 327073714, 274767041, 594629924, 847124032, 883350573, 862218167, 962188041, 705495839, 849053232, 921884202, 738595896, 366278145, 150695077, 137088372, 202562370, 265265321, 327266745, 713370898, 446534476, 396535732, 465642586, 401925024, 340356168, 896048090, 830504383, 47417508, 16643735, 65729671, 34011328, 223789087, 480559230, 941886255, 108986595, 761643614, 593907640, 979859767, 989649640, 15160314, 519332478, 432133546, 471305254, 430926391, 722568087, 319033459, 448659653, 586828003, 115772386, 707599793, 332030974, 764054410, 435072811, 541760009, 163567128, 613891895, 245907874, 456436930, 934734175, 378902753, 409709994, 960075346, 221120301, 50164028, 366273085, 845049643, 917191172, 926161132, 249180285, 739290219, 173057459, 700414788, 507786825, 148815917, 534177894, 622010533, 320813396, 385489427, 895813885, 747051405, 102499978, 43051776, 584421225, 620526347, 206910142, 712516289, 743779560, 651682078, 341349426, 790638186, 865245107, 2840664, 628119815, 399193198, 141281273, 745857705, 612079866, 511537477, 633184512, 661219418, 481735969, 871151257, 490636301, 396794594, 772790802, 13450920, 386689930, 838081567, 821835135, 987811032, 929639411, 796706008, 435474755, 135251038, 465064400, 621547954, 493565773, 763476291, 401815261, 126011417, 73302427, 816806265, 572962607, 835635581, 287051485, 182648075, 442809843, 719762333, 796228337, 430440004, 225593188, 433720405, 392379047, 568946136, 307391272, 451644729, 266271913, 703559019, 779728561, 736252799, 452470114, 941630711, 327386799, 414069762, 90235672, 669929456, 700481801, 6916393, 889548888, 353944264, 20938327, 117684594, 729436880, 835870713, 205072830, 189545412, 523689325, 651681983, 667675016, 721133526, 86721018, 589544557, 282824253, 330022764, 516520596, 504493904, 719154829, 516955688, 396364598, 110390279, 551685449, 278632593, 84751882, 196167921, 604628413, 57280517, 339530352, 689572382, 173207111, 735409845, 117089959, 976707059, 624307366, 73067694, 846852728, 918196154, 680418340, 937653140, 190258068, 648527222, 219773510, 141015109, 698505606, 216804792, 468425730, 764729109, 829345825, 218453978, 443477190, 665582020, 194955139, 515653292, 978254637, 948414459, 824242871, 142275718, 77968795, 688388829, 2456810, 451986892, 775648997, 312351185, 540977862, 179609441, 407554862, 31065634, 473440546, 894957865, 328585524, 79284787, 147125531, 797206681, 368482167, 932151350, 140966209, 897365678, 122479858, 940352036, 953489863, 793584690, 163961016, 918620001, 892236585, 624122022, 993760348, 782726792, 433948744, 710907547, 332045656, 857931357, 516565629, 654847571, 186143507, 782933563, 85410362, 580652260, 582107919, 813662847, 747279679, 832884859, 857538431, 131672177, 63425778, 440004994, 233800146, 989776273, 236302223, 522138042, 956096534, 354439849, 743775692, 421944266, 470679620, 254833326, 584222188, 162319831, 654284943, 677805259, 820072884, 174976009, 860824140, 230533500, 791825766, 557360775, 40150151, 667949758, 907440038, 45445498, 79229875, 107150741, 554652562, 562785953, 670180429, 980360032, 209214023, 756032207, 279996706, 176505062, 634263732, 94757442, 588426530, 461066261, 433720029, 910886788, 263953150, 33312439, 426844228, 169101354, 868628853, 915559174, 60995544, 168506467, 590404854, 409244369, 436666389, 451474580, 707653892, 275772296, 119435654, 724127065, 206188548, 857983058, 633069555, 629040560, 829150626, 501441386, 793880309, 942004167, 601393498, 3146764, 410927210, 445197891, 430962942, 858781900, 621543734, 919121447, 388792686, 205220284, 653817142, 297190923, 994322579, 230286710, 307664788, 687135549, 654749389, 902681463, 301471753, 126456415, 2453020, 535946189, 330126020, 119436478, 571657176, 652753859, 861265734, 12932263, 13691460, 396987803, 736163506, 953736168, 913680911, 62271399, 325083772, 306445414, 347597264, 777471242, 398964280, 577097972, 416759943, 201346610, 255629521, 441603379, 833778157, 787796312, 823057045, 421626948, 536762612, 545269902, 940183238, 592729066, 395294039, 664415725, 723208300, 487074130, 860933591, 334864662, 342332710, 842240715, 11203273, 628672295, 375902886, 202079247, 765414472, 693233741, 545436729, 868291206, 641710246, 979030983, 912911276, 898336649, 737923326, 565625954, 658753285, 806402483, 231733626, 988483078, 735123532, 847308869, 198624488, 737408051, 740371085, 786314807, 421969029, 461746164, 84258280, 750011733, 527524495, 504986663, 678276182, 687925749, 423234980, 330729597, 291909280, 443342466, 879326114, 792628579, 895152706, 196620524, 194768400, 705638170, 806222930, 366476108, 339187042, 946211698, 462752673, 565752462, 718688888, 835966975, 3240383, 124235426, 350013877, 449692305, 570906683, 502078310, 675662376, 311922441, 654018859, 859673255, 265247960, 870751188, 498170740, 567009605, 288644727, 46929834, 470601829, 554946002, 120101670, 265999385, 319154884, 828002480, 568156544, 522212023, 455618985, 915100601, 182191291, 445867566, 670286574, 459114182, 814970609, 16033654, 411314438, 310138660, 721057593, 767737297, 564238073, 914668013, 82295977, 639672573, 800235241, 184084720, 897369659, 467497414, 488762673, 790032878, 237118469, 727806070, 362738582, 584561681, 496888805, 862284600, 498129068, 274397686, 567450711, 270400062, 955891908, 879143579, 950792749, 469683001, 365844894, 757231162, 671746901, 287844891, 16868526, 375087880, 687045518, 123602737, 153432665, 755034354, 270004322, 261242840, 602196619, 264871651, 504940209, 56718247, 408312123, 76290661, 54433746, 104271876, 857252720, 406744804, 131553839, 721100010, 891330188, 531702917, 959784442, 64814415, 575666486, 184245352, 279799482, 513036509, 301416360, 717698400, 473141891, 468016841, 794043367, 762103960, 53050290, 83313845, 652317300, 844476083, 78354990, 942648140, 443598163, 390236185, 882840369, 110897849, 257872649, 147364581, 257647792, 7326540, 753568972, 407120353, 609033938, 606797359, 992237404, 157115583, 552714277, 82414024, 350525810, 512994332, 747500272, 702956549, 917608755, 418527664, 603790107, 841214909, 237163107, 804285765, 768228252, 811395313, 933670247, 73255559, 347006520, 829446984, 251286419, 523295986, 648768780, 805873091, 874900463, 269662088, 707804781, 444477577, 658425560, 810895990, 511493336, 738202989, 813753998, 390040819, 867555624, 454278971, 341212428, 412980381, 100479028, 437637114, 852004455, 337642974, 679666123, 434427181, 915961089, 5953140, 984920187, 860348496, 668971911, 912103558, 190581027, 21709604, 775265902, 216770800, 254810125, 619678390, 334349514, 130968653, 288163360, 511863043, 845589329, 356879126, 312524222, 332328451, 844530320, 367124078, 783876099, 748872624, 423954894, 170747992, 720815098, 634112066, 252168945, 367578867, 331482196, 546751990, 384724275, 814686802, 451016386, 278672339, 742484856, 166136573, 281613644, 785999441, 818033416, 242811058, 461526221, 147435207, 410837933, 758678365, 391352478, 198848210, 780309569, 94519153, 351122343, 455477973, 967842207, 311465223, 318075362, 966264088, 181833523, 585640999, 599574303, 716546911, 355623877, 201046818, 58897650, 812157604, 945248637, 290763865, 271626522, 582176809, 445231031, 953330595, 938672449, 617786790, 29860300, 873007869, 908247748, 387913342, 646935264, 391689310, 54363467, 295426468, 619799355, 99413327, 145938850, 966964547, 891832743, 98753486, 978706387, 841807149, 409654430, 902638336, 1153071, 856340174, 68507199, 66559684, 188531222, 170716526, 229287690, 114967003, 202840309, 614481200, 624103813, 678953752, 128954081, 215960563, 699616064, 729248500, 54479270, 900242078, 57339131, 701535672, 374991873, 157521105, 763338124, 666411084, 686198389, 989947590, 145191136, 255337672, 109608743, 73845974, 137695291, 664793929, 476547228, 1783258, 787855732, 626231003, 407512729, 747301634, 951105752, 257769292, 62112344, 138807955, 335987272, 342272230, 190591669, 782258573, 82923459, 670143550, 996365753, 320140920, 263619734, 385089510, 722282181, 856728544, 890625413, 551401777, 100146795, 556348906, 13516096, 993667811, 758927322, 930622447, 518095076, 193206838, 418728088, 690485183, 856632870, 697206303, 88489289, 539611771, 121160287, 506094813, 476268254, 336031087, 363718884, 124045401, 140474015, 213121469, 838122195, 859749887, 442355737, 80214061, 808006183, 251841025, 332612411, 190416854, 622498317, 48913982, 124911909, 937567735, 567811252, 277164984, 669068877, 743352563, 342319911, 658188976, 721212429, 196618779, 7884080, 705358934, 276282444, 442769525, 602168022, 93127850, 881126778, 387445345, 993447951, 819142562, 25718028, 256044446, 377177071, 752544515, 658469800, 541123492, 706841569, 382553144, 498510894, 798619806, 737758127, 303524696, 480053139, 568879970, 41186026, 322222344, 83062947, 519729386, 887640655, 416326044, 745799090, 129619728, 948857222, 116785763, 717097244, 499133691, 890691237, 82450265, 614892448, 398704678, 646380487, 773864487, 22076797, 616916245, 398421500, 291707053, 247574743, 376703364, 778060507, 756647642, 473339235, 415140564, 967180969, 166819161, 81680075, 750385857, 7062926, 454500607, 63164336, 828822209, 158225277, 935923014, 977855147, 351211848, 878323803, 555739086, 570137610, 866677692, 135173532, 116370528, 300818722, 262245096, 445584035, 66615060, 563475099, 11905483, 697558009, 916381988, 285287521, 796610537, 76933667, 206837046, 700540628, 189889725, 765446413, 353322915, 446841879, 760735783, 121188667, 809349469, 163712700, 214436961, 364706684, 719644966, 428067693, 692317204, 941492906, 237049342, 376949077, 916156159, 124715817, 463147106, 167568080, 451059316, 317194022, 559112678, 460745356, 512850206, 984593315, 680909307, 703685207, 678878170, 720286052, 797897514, 723888904, 933943432, 858359674, 673735053, 976692728, 344998443, 919554016, 341761370, 497599321, 127355792, 252846472, 216612843, 156365637, 508146926, 490374668, 766792762, 371378521, 613413717, 936823466, 631683508, 644444472, 373811915, 109659029, 163342641, 534292823, 482802152, 394408912, 326349679, 313097078, 525070101, 72969907, 627747731, 359981445, 690720285, 775731920, 615759398, 199042095, 397086507, 106423047, 253808934, 785269700, 662079587, 172345445, 644326993, 278325367, 861587656, 543604858, 234984275, 611449258, 908181930, 177599370, 933596489, 126955793, 121962442, 299925016, 184881421, 100127388, 207157590, 999205893, 801566117, 937705829, 211849035, 262466264, 972129217, 963135630, 706170110, 925976646, 43196190, 322546067, 46635790, 516109981, 190747016, 17308310, 916333110, 763257034, 668198620, 806545658, 362730298, 763059032, 813288869, 393318017, 660171797, 773287065, 490808120, 26518979, 464072101, 294464147, 415360527, 11760449, 852613904, 956098538, 785968704, 252864426, 559607617, 8907736, 386965250, 544079325, 101963024, 665276461, 967453015, 941804315, 517302002, 293480160, 215874832, 588421604, 62655679, 658144039, 862321775, 6947628, 91110779, 57592871, 372388800, 325308606, 570679376, 778046106, 596164658, 415761963, 540839263, 531200856, 922649638, 908559386, 948929522, 54619179, 444880709, 571501352, 378622837, 655684514, 85770634, 550091071, 214085439, 245643709, 303610931, 792257900, 534442610, 475484063, 504870421, 903674421, 184000839, 892491675, 943343368, 399920296, 782162708, 726233804, 474849991, 540433383, 313202405, 964055313, 821342633, 980502905, 29234411, 440860218, 393501379, 347366045, 454719306, 140541386, 127408482, 37798637, 919566294, 807357157, 581141539, 317282273, 441842485, 701690964, 628831613, 63456000, 303044548, 649267816, 455134679, 155488800, 837816721, 620372399, 114897336, 85708371, 595140194, 899079795, 520650273, 450090331, 669657893, 985788477, 487365212, 276185273, 443195010, 783664623, 381228519, 668047198, 100074298, 630768539, 276777080, 687310737, 729978611, 908665928, 809231264, 697352298, 187237226, 466182983, 65180147, 638111204, 752532563, 173203260, 982463095, 530616881, 740920381, 805638744, 155875122, 120179403, 534801129, 379523326, 613108419, 179913324, 152044771, 400923517, 418721357, 950969925, 861932492, 890203515, 346408303, 81122048, 669751467, 862143584, 591374198, 996102927, 859191683, 429835911, 521918275, 652431663, 97777761, 980245810, 508269212, 245470740, 386098970, 16139196, 34525828, 915259063, 386925581, 543705997, 352321975, 813339597, 35445941, 676123787, 793906432, 331577809, 358868621, 526498740, 306933340, 661854998, 360406334, 644318431, 603807489, 282250739, 83122763, 275293198, 679555232, 776524233, 345213436, 968567939, 431843473, 644953085, 849094136, 497492142, 226596528, 791644475, 395449914, 272309147, 289557792, 165405216, 663597906, 595545227, 702900867, 347367591, 462460280, 66814252, 809491373, 571586088, 332942605, 447032037, 958727247, 371679978, 672262086, 972357170, 32199640, 749763841, 775623382, 119740179, 930403942, 440620798, 983970061, 243009298, 226666130, 481647448, 635554036, 103054593, 907077205, 551800072, 124970601, 97869518, 537557186, 356449468, 884004729, 239604997, 935183556, 715123145, 94088555, 583801370, 479118988, 335355627, 892492899, 449548180, 262649305, 169908472, 329389241, 535710096, 74946083, 156857305, 717634052, 431191593, 68077649, 706829295, 297772618, 696966025, 302611013, 30774269, 238417621, 655986707, 215602529, 495472219, 12802072, 249584884, 866427691, 171126526, 291180092, 228246488, 436858292, 284180384, 455464838, 598256019, 931845488, 135945297, 32470679, 537137212, 439608069, 426921484, 521841148, 321833755, 725596330, 188638951, 391897864, 415605795, 739188673, 935515740, 247464691, 513201166, 209671183, 865429977, 883764260, 415240150, 55566219, 547312289, 163072077, 80730443, 775312148, 863410930, 679639486, 769647158, 301742606, 207211225, 905900635, 245246120, 821772307, 6610940, 485689198, 172227516, 391124104, 199939255, 429277091, 371250638, 291772172, 767822454, 540734041, 922545017, 337464612, 796433986, 429425581, 411011973, 377034755, 532009893, 994079877, 797604420, 847678630, 21423635, 736353712, 945328351, 947409851, 600208666, 334177695, 295585987, 181093297, 762516732, 850700984, 639780744, 783552033, 884133745, 405517391, 629530421, 777735679, 619946603, 620614008, 966541222, 117707835, 976679868, 722998505, 882377474, 177038741, 960219145, 638787825, 349553235, 93240072, 872106483, 505633305, 952850099, 110105846, 414748771, 703357395, 288106701, 38215727, 182732392, 977540815, 487877864, 522170107, 682474885, 694614609, 253915741, 803953228, 474315443, 590463550, 909124895, 550228378, 752395962, 211715435, 380135754, 236800608, 871148932, 604406947, 733557743, 275879784, 896969149, 84007655, 386765431, 361817417, 831147251, 312665455, 220529821, 43136302, 252113433, 784494312, 444000451, 559021303, 946758763, 612065340, 130572861, 96308662, 275248623, 48280223, 780850648, 753158718, 714437109, 704727767, 372498375, 902173157, 423729095, 34722725, 337765136, 161641438, 682599920, 127202196, 791388539, 411784474, 208400634, 18069528, 350530374, 781461039, 352668031, 918061109, 926364803, 896287397, 548592703, 326649290, 619565135, 922113, 344615183, 158529343, 168245471, 627020267, 140492447, 990165625, 298363436, 465192683, 782225170, 222394351, 730782046, 134537882, 58976863, 106752158, 674174917, 89579623, 426325076, 205322142, 119851755, 477121728, 107107409, 301107037, 16165064, 513330816, 71459727, 358122268, 567893620, 132332682, 944514208, 135518934, 560627896, 435068558, 730839957, 192713746, 758855800, 220509333, 828208608, 540327895, 504685023, 844258839, 337171893, 980240055, 736579024, 522503556, 532209555, 90966617, 796987155, 92859010, 904679764, 535751438, 245845533, 354605705, 960521754, 557757033, 91274642, 770976576, 684112498, 976035429, 218122130, 73448295, 795359907, 599293817, 856333110, 749210502, 891851348, 286962521, 899894877, 346457617, 748287923, 597114610, 723522463, 731149017, 761611412, 169238799, 398514297, 211664548, 691030655, 91486741, 696985365, 584038917, 776619519, 687678017, 885740174, 125985454, 634942558, 633413228, 707158203, 842800659, 438112658, 892640696, 286760954, 8505067, 205513179, 286490416, 338145998, 6655993, 414947996, 284784062, 861681153, 268008649, 106107968, 635302965, 74130853, 425481365, 429720783, 273851272, 302308433, 174113002, 435619978, 532301892, 594428930, 768711841, 936824935, 253067087, 595697106, 331006723, 824367896, 712035461, 550033034, 888528313, 665474571, 661652612, 961126425, 964060542, 285738237, 963016757, 555531458, 445508186, 529085582, 242813591, 856584154, 621999481, 560795268, 638892856, 27943021, 931060752, 903692888, 562683080, 527776211, 91919541, 906392149, 334050156, 565942356, 63149767, 833103355, 301957303, 306816218, 89272697, 645295297, 19354029, 776777303, 328027236, 968355910, 993315484, 505948951, 884938690, 926255254, 859755266, 439077720, 996071448, 9615739, 612767024, 392700523, 629916658, 237651498, 138107874, 282174809, 389803291, 102820517, 350145131, 890089446, 238570846, 426865287, 172247807, 631844405, 68736494, 850813220, 770436050, 889754281, 672538192, 715821264, 261596592, 375707080, 525145473, 803696416, 530241722, 496735112, 140616805, 526506915, 862181158, 309927710, 309865677, 680976363, 122439580, 417313026, 877248980, 2413514, 515079478, 541083378, 936166559, 982558755, 486392206, 793179952, 762010035, 288599512, 813425228, 188224314, 766285230, 830767849, 926584222, 196431903, 929665016, 292884968, 136539033, 91196680, 454678944, 17166809, 504206140, 555340576, 507907162, 180195184, 152487428, 330201259, 258041225, 584842209, 30721170, 780484279, 53261920, 401685057, 671060529, 351774093, 216321240, 972799512, 842364357, 280681595, 254812598, 999361968, 826963358, 752608966, 360948334, 686902252, 752230499, 921985794, 378887599, 136762058, 335390407, 63737562, 151520154, 226162578, 256377919, 991646195, 916331605, 574736089, 25223521, 982730198, 579692686, 889439254, 594867089, 403630531, 475345, 232765927, 270891484, 610254666, 242431914, 253747350, 656851445, 277296976, 419320973, 204626684, 22622207, 603826526, 367979874, 833788628, 535579749, 896731608, 108011360, 923289058, 174589347, 952029700, 55817456, 61688274, 235236642, 105069217, 712769193, 556892704, 19205846, 866197432, 771382731, 220919016, 679316908, 385167392, 882080631, 591624903, 190580244, 583767819, 349607305, 738763502, 943434737, 200811438, 611435138, 844452020, 552595573, 970323055, 296219206, 535557017, 860981247, 249053486, 497961406, 351537344, 466182424, 349551855, 300562891, 728516471, 731179267, 120475116, 786912483, 183398803, 228465072, 701030238, 464553323, 764689826, 460524792, 496020173, 504709289, 10515697, 836519890, 130593721, 625889954, 184396700, 454264319, 800180028, 351712102, 906314593, 509790295, 878310086, 52199887, 764436337, 51534959, 50040595, 572512475, 356288641, 874359877, 596772613, 545683577, 39086426, 212462269, 881826165, 268191213, 992033150, 959732346, 546492129, 532121453, 588588336, 715724220, 170152294, 710174125, 400356335, 764686294, 705461137, 67611545, 21912932, 45220117, 649050133, 240154848, 974474448, 987072379, 398420942, 479099623, 627446160, 316971663, 506111186, 979809168, 633618956, 845811606, 105389280, 213119388, 248313634, 27234139, 976683346, 335187773, 706869141, 437474862, 110107397, 3644420, 730043910, 67150468, 999820480, 812194053, 28513491, 189179559, 391757941, 87565923, 101911704, 547754451, 111194561, 233851201, 897844537, 896511600, 820489051, 181417696, 533020342, 695796313, 209653137, 522652140, 406745037, 24491327, 886426030, 758718155, 118838029, 83128939, 516206073, 961051416, 659559426, 910820139, 73884938, 591766118, 17294435, 651927917, 913606219, 919993243, 738613463, 584949349, 117530848, 214619357, 751470713, 232890587, 321751509, 361160692, 222054934, 929567774, 307987314, 553986206, 531356571, 854560535, 432057908, 547697156, 950014431, 186331706, 365757881, 828389421, 233884514, 199857442, 957092617, 783601313, 892597525, 233396935, 961410311, 772357670, 50248887, 149505708, 998401848, 630147299, 607718935, 375835806, 716219155, 521439598, 251138999, 671118823, 122812912, 637659255, 639208950, 70683951, 376095042, 858063904, 593837071, 321175753, 727140714, 823666600, 917887174, 448708029, 379874611, 672231010, 81992376, 674064258, 112150331, 228601160, 998958946, 18394413, 654991051, 714074660, 958095989, 943666114, 100563996, 66503823, 316448019, 830437256, 224349484, 940959742, 324931889, 175971039, 4371886, 207337823, 907667704, 499519992, 551274946, 937081703, 391548351, 409242045, 93327366, 114629904, 184324210, 188275180, 982932982, 524240361, 827613841, 385402018, 896360151, 452568063, 463199029, 459381862, 20925520, 277521378, 63458651, 979796526, 507419699, 962005852, 979209197, 43605010, 30119952, 712000640, 101976744, 841546008, 830007386, 978675753, 609477611, 404604556, 891343111, 729466075, 611336132, 686247718, 850638920, 600491953, 909998568, 802857971, 318261567, 444862566, 717253059, 933092225, 859272259, 854652287, 840924310, 528975134, 367938881, 871956205, 997053558, 481212059, 468565982, 810743934, 363234805, 700754287, 135667289, 793530225, 299094016, 397613200, 288264089, 787128168, 857858874, 690270883, 508047980, 931977419, 735579109, 283165592, 46456315, 3132560, 324620371, 747798897, 465818507, 967082277, 202885984, 198516887, 998151446, 470008419, 180236065, 794687816, 157569496, 524038631, 825265907, 716082061, 906279789, 695925568, 753963253, 491557054, 178878155, 208308196, 40957288, 336602182, 218069286, 218704848, 985814422, 16351665, 729399912, 140930044, 571953277, 578486206, 487344635, 522547319, 186903131, 637807769, 246413727, 236483335, 623558477, 572668891, 246232009, 560461531, 773804536, 612413759, 40048946, 683677971, 12944377, 462703140, 301919985, 482101034, 122659492, 741594185, 365220716, 377161399, 70127640, 467705480, 580131866, 639266378, 533364416, 437338376, 334533602, 645622966, 546171136, 708268308, 727550023, 527044385, 240539202, 357779901, 728765910, 708923751, 966495049, 475764101, 958897205, 459827510, 402373957, 220540186, 224944578, 611196734, 991291457, 896417304, 103071403, 344162127, 932778760, 931585373, 847792772, 415125828, 398202436, 782752066, 455963471, 670895926, 515539507, 488580828, 891678741, 361794187, 790712426, 791508393, 796967927, 10175204, 937639302, 794464517, 21853710, 997512745, 315514454, 261617685, 242605997, 243233007, 521288744, 715823418, 401225042, 303350873, 819855980, 345440658, 480386824, 624867266, 35597519, 676925252, 951447840, 680516405, 216803173, 523432812, 364481635, 813270945, 516721205, 530723249, 881480830, 874960074, 170595021, 531226408, 175626880, 884003158, 966817430, 460027226, 99062056, 788539880, 981798345, 376199652, 471205876, 456564853, 850086463, 880547318, 288641470, 92210339, 115567198, 912237741, 375633234, 745054455, 500805399, 589317328, 651825066, 851362669, 843433747, 644660740, 932954960, 987658246, 66931800, 405168042, 832161882, 567037491, 416739010, 210612814, 5488643, 631548861, 871921720, 202056445, 155606033, 792845927, 71428010, 447249568, 616733958, 907759479, 87377293, 125390521, 845329941, 116461410, 930830117, 820026081, 45942551, 683881654, 458269946, 18339583, 460653424, 310434566, 305349189, 632229199, 213619744, 689353448, 831380599, 974269606, 876654958, 849086790, 975427834, 934683097, 924913275, 290296204, 846175338, 564017989, 111454019, 122294000, 795073630, 782033152, 464630100, 164121325, 429393580, 137477693, 988120322, 976926535, 621774836, 87829670, 454886963, 82340185, 124103355, 206469393, 548267995, 500111283, 306738910, 949490943, 94981737, 732930037, 569246147, 778128495, 79294401, 152961881, 449095637, 516203166, 41840362, 126989496, 341716227, 729671851, 685277085, 561706208, 452316610, 279516267, 861337265, 134921073, 249240902, 572366297, 783645886, 76024265, 6338799, 235464204, 723257391, 479121522, 206440779, 43016785, 68368175, 958690097, 9407405, 611260155, 758721698, 236580660, 935195478, 256574840, 432592111, 824373147, 265139216, 32919762, 98855184, 517295113, 408089998, 622233961, 101639192, 397027323, 561994320, 706224985, 696878161, 178940892, 263947122, 554387715, 40526252, 355594371, 249592922, 836677576, 723051034, 703894124, 757646318, 566681877, 188401442, 498767470, 678366862, 554304632, 270608075, 388052374, 365605076, 727759334, 830733921, 822158894, 898169974, 4487718, 418204856, 31923644, 381471865, 868534303, 501502102, 679329833, 907117186, 836583885, 264273186, 482762083, 336936988, 714733726, 352854725, 12691995, 906670067, 529448947, 860883832, 652383909, 490353666, 672636479, 784310555, 200611707, 765259113, 184431056, 971737853, 699010980, 976814227, 828977596, 781570717, 376497701, 630185714, 424941478, 338140830, 260151229, 692227017, 639014088, 831446131, 731596179, 625356295, 475042221, 643649731, 647940811, 245222645, 143335678, 364945250, 419464863, 764867478, 187046712, 832926349, 82522674, 496488464, 5238099, 553521676, 14712954, 73912939, 630481010, 770575884, 995333409, 307218294, 200195189, 812376949, 991350806, 139930358, 233285784, 707142008, 805276253, 458856822, 389568963, 450421817, 514187938, 818016037, 751711689, 137288879, 993417031, 399693497, 404036146, 199573767, 306997620, 345162926, 792856625, 130170064, 104982155, 845383444, 168118351, 536194824, 393369481, 302758014, 154683110, 769828956, 256650450, 414631908, 517102394, 287842204, 119437546, 858079710, 67828374, 686772641, 843238412, 84745511, 161330952, 109004139, 676353564, 520904125, 419366066, 897264761, 15980106, 998054820, 886900596, 315407350, 233760075, 101508753, 630163861, 805355126, 423411200, 440748340, 253832229, 708029489, 784687002, 133357296, 901669567, 947745821, 177496276, 125603064, 197746381, 45213824, 891939579, 732539904, 489992365, 853395291, 95733830, 743240679, 986724674, 443885890, 761395711, 680194964, 998188878, 21009936, 684956502, 650338902, 985632780, 202675882, 531971115, 297171435, 280561811, 505236594, 649712603, 566683160, 25521969, 620099521, 381646330, 586099064, 31849734, 957857745, 552665971, 436781164, 245155417, 773392751, 156609944, 986981415, 625742619, 196820311, 637725508, 427160385, 363146009, 158070463, 823163270, 788222478, 692259443, 303440806, 142208920, 558365091, 992742018, 880652097, 498346015, 345557189, 914965919, 792370070, 508201639, 317044557, 739267790, 542499047, 153060151, 490176017, 438057334, 985703535, 587744415, 497472165, 682953303, 592137514, 115688142, 331890291, 76379579, 142610982, 971182755, 520640354, 274637137, 404454791, 972490529, 324133462, 890824610, 116837943, 149291607, 998797142, 188572371, 87130679, 158957328, 763282128, 580091503, 224919392, 708040362, 550774371, 779269663, 654561889, 854805267, 583881259, 235516641, 270080538, 330957349, 969180359, 8152681, 802535529, 153793254, 785530966, 65385953, 729217324, 600162134, 616044825, 778444145, 647196951, 723131268, 700481567, 488010948, 564695936, 52657683, 876506768, 897700227, 883053546, 897079576, 9408466, 109763170, 472845488, 929329590, 132901163, 953472342, 550134112, 302551777, 19452577, 164555235, 147917700, 749795953, 822435067, 458089631, 852176101, 932665817, 658103345, 442754123, 421152341, 558353395, 631071928, 982194550, 887894312, 623417613, 691071143, 695325394, 831282950, 508006677, 776341478, 314360334, 312449652, 68456795, 98412963, 615954638, 350710263, 797387371, 576589992, 149510361, 941165100, 804036623, 516668613, 778996451, 639421046, 938587407, 515809086, 925219101, 372307490, 859819470, 221690623, 705366373, 33014146, 140336350, 551103604, 838985583, 912290588, 897738408, 276994102, 25405120, 306190921, 642932942, 891402265, 245167442, 726674553, 389020213, 167823740, 267418430, 464595533, 774179364, 626332560, 88401229, 533383307, 415021728, 409804156, 757822276, 615355708, 912323480, 422271545, 972880091, 132238177, 224470154, 15591488, 359790402, 960941536, 204093008, 697466463, 450777254, 348855404, 282260983, 354842017, 715204520, 738485629, 243324091, 438527890, 380266837, 701837012, 35557794, 991308549, 320156007, 86123973, 40271642, 178717464, 506853262, 727951651, 968750911, 253734283, 616030240, 615920270, 983067730, 342509365, 192095048, 80668951, 929920579, 159410443, 814884683, 975711779, 645361989, 246280081, 282385768, 281034920, 36607792, 594629222, 248568339, 302574516, 95389477, 318671910, 617516781, 396754619, 758880290, 484308510, 567168142, 971360350, 355479579, 347419022, 321526069, 779001773, 682253099, 853230275, 369147682, 657862571, 928147302, 579209623, 396952417, 532035625, 752816565, 977187428, 358600877, 316195777, 467777647, 775993359, 774207478, 411122601, 85250061, 903743027, 20331610, 478536641, 560010869, 490690999, 155002322, 858558426, 598672464, 141286205, 843741300, 882637314, 430380354, 392024855, 272202212, 703519489, 485347874, 586634827, 45752588, 914193201, 590188565, 459834903, 960942682, 989355552, 786778429, 305922335, 168415801, 526415462, 971721636, 568212456, 231170266, 309383179, 505912442, 659763964, 486890852, 768545711, 171555552, 416994616, 969711318, 607416721, 882006205, 595179259, 816453922, 615742702, 731274368, 574608857, 338660058, 81100906, 742966939, 34765536, 859509732, 90068119, 501753228, 318488451, 801578805, 174432386, 567917350, 243202020, 231176373, 548413039, 817360560, 279009913, 589831645, 373021596, 517485006, 434627343, 118335877, 590287915, 450223958, 690820349, 873554052, 398989254, 523382893, 576462218, 432646272, 265085103, 185125669, 383980933, 420938698, 580759596, 417158253, 109466298, 592295321, 764705163, 229292657, 932355521, 562523215, 848079301, 36476418, 16233196, 942828160, 865045116, 937307799, 110796275, 693630739, 281526377, 748849164, 394103016, 940862735, 308961309, 712611114, 306618125, 241549342, 696029649, 273629473, 196835451, 271248153, 229657587, 942654211, 593425874, 561386241, 696024304, 963792420, 438288206, 427392649, 150190487, 667103568, 979614435, 109498848, 206355611, 465816810, 874587248, 35491373, 418675725, 886354936, 458868386, 535099477, 170625067, 939477532, 315521682, 71575609, 133113857, 759410295, 473248739, 43594986, 729667075, 168268122, 410133503, 943009589, 662880406, 592176876, 767174269, 76515827, 663054559, 787384173, 867751670, 459249214, 947756152, 851188640, 749377059, 788885957, 77037603, 75522393, 662485904, 339018184, 761551957, 996513242, 786530861, 884508217, 640574612, 132870763, 15528630, 813962264, 583105577, 98350569, 746464267, 223167306, 384633930, 467507935, 597669478, 389148629, 476639696, 847132030, 673779095, 280754272, 503342838, 697871388, 867329756, 132080206, 376249417, 266296464, 324461206, 828523866, 915170012, 182356181, 464444371, 16043229, 322173816, 538746862, 431203308, 43584620, 522190595, 984768231, 715898615, 706781193, 455843844, 597273630, 886430252, 259946315, 253341519, 872625352, 876455962, 979061505, 534738468, 26685589, 609874084, 54559675, 960526090, 290378932, 509405232, 397131465, 875446774, 305140402, 59121901, 248115374, 295838713, 488947652, 568183412, 449543497, 355695396, 990185746, 426610753, 420390561, 13396679, 362055407, 589661973, 536614129, 139921360, 814238372, 375624192, 474551730, 611456899, 24495009, 617569262, 801195633, 842950366, 93970384, 961713012, 21096224, 395086584, 973544796, 584541820, 625296180, 305852411, 71032108, 46575177, 424447385, 322376187, 961093531, 600846844, 378814698, 857000594, 766585452, 611212510, 780110829, 664783219, 226652252, 767806239, 124713593, 739444150, 808972547, 579938416, 595074016, 748148550, 22039283, 295783046, 125382145, 896434060, 51624842, 129792231, 368670464, 180691129, 383084459, 541674021, 60190918, 789092616, 589774624, 42035095, 671894424, 306853632, 11160822, 689737085, 310080062, 191804666, 993933054, 494070971, 785242432, 240518210, 360110215, 775990165, 718729927, 329200431, 495551588, 266593450, 385242600, 621075290, 951114803, 782118196, 818004287, 30347908, 649895892, 47991574, 95933372, 300977946, 532814112, 783790774, 641698254, 64475494, 964441150, 66595053, 564380595, 22509330, 836179315, 139089021, 615769186, 750355930, 92203070, 822753081, 782077332, 657406287, 921568091, 404504268, 408389042, 164371935, 525347354, 880396637, 136945716, 47609002, 24232886, 10789996, 713786817, 624245766, 345317680, 209535393, 39934816, 681628963, 746206747, 234739653, 530944157, 983658446, 664270646, 29413081, 330962861, 620617754, 476466202, 684098654, 452715513, 119212656, 441224360, 332367873, 376738139, 526743735, 235472634, 912942579, 153034268, 940895281, 533087651, 810168434, 34111374, 425257580, 876719764, 805762488, 339466822, 919504597, 38865933, 675804964, 808101540, 595147720, 602431507, 112519037, 756502473, 660223765, 593635689, 312890159, 625128449, 545463184, 315775553, 425048676, 104349983, 354155617, 871769917, 475143102, 206058822, 770774019, 623459799, 278158456, 450478663, 243338233, 924249916, 180183850, 566147924, 788428870, 434595358, 377525756, 16758349, 941407054, 250628852, 94870362, 126700429, 871642917, 570962317, 427117462, 251642545, 374224458, 58663525, 822365380, 927905671, 564511857, 583895463, 428291622, 807869033, 783368818, 176821703, 977828446, 31399121, 758235107, 420764989, 635314685, 150657355, 617126675, 626224714, 200015845, 753737222, 673456215, 46431929, 941358413, 538962773, 207653203, 353785389, 169964063, 151124017, 646707296, 100765457, 374432087, 295517813, 678670649, 848132115, 501879248, 464689018, 935892945, 867220430, 385094591, 152654241, 893228093, 311245164, 162297628, 521677684, 286852934, 971888749, 612135438, 827096251, 848224760, 262790654, 920603911, 27814081, 63786895, 260306966, 846217708, 114096462, 249634253, 862859177, 903414711, 818502125, 290697591, 457969457, 125958722, 611742891, 795993748, 442093614, 343422645, 661562939, 487960291, 252693105, 210281568, 373993167, 500329313, 384713052, 73847940, 48638216, 644914215, 112100355, 543893037, 62256015, 30397948, 944459225, 929132919, 191302462, 945488901, 877367644, 720667470, 481114380, 783735075, 444859232, 404057036, 886469436, 136823720, 992823864, 755679881, 947526747, 884813457, 105092863, 149861214, 387221510, 196200110, 571767243, 467147061, 664350461, 260444916, 849002726, 367558389, 476437687, 406989624, 618303595, 891731791, 482614067, 204414004, 104456875, 90329119, 955029127, 495853632, 819718746, 430196811, 191133139, 794938191, 310260300, 895596307, 723391382, 93903561, 272289168, 84014873, 841110727, 261776490, 375697412, 591791812, 461576998, 561017099, 608358605, 619811335, 973221718, 494005778, 892473334, 296201033, 400158715, 226722574, 759830557, 573915594, 217799658, 246190507, 622167624, 136041597, 108588752, 684327832, 253958236, 247153040, 969623604, 36999162, 409728843, 902042934, 481587060, 45914884, 805676685, 459874571, 868440986, 863429002, 235709534, 199603358, 904832375, 887323739, 513261727, 65971482, 681943620, 698196363, 85985533, 671819884, 140350028, 57528094, 76971855, 232447512, 227625291, 526554693, 884445937, 507533267, 38473356, 95337296, 73651817, 791224999, 548972589, 190678466, 31958368, 444645740, 622146412, 777490550, 272313684, 880000198, 847655583, 455581656, 795904275, 854325357, 8847560, 196258884, 591987879, 801152793, 78843040, 50892102, 771105807, 921233488, 248560847, 744058240, 952430311, 795783822, 978130938, 49580274, 451853086, 604369413, 111091496, 199094376, 605412079, 707910583, 824807382, 843465002, 254510581, 154548214, 777788349, 393940823, 470942223, 61548804, 612166797, 892505239, 905756255, 38194574, 299846229, 801637960, 708872179, 346758497, 900370274, 712910743, 728874054, 208970398, 409678088, 191408559, 328761231, 528279167, 995551943, 174148973, 391263103, 284159262, 763274196, 488048296, 271651526, 460176903, 751161431, 120123428, 860021016, 12118673, 235276701, 831966010, 107436908, 333786814, 852150115, 226826645, 459876747, 602426249, 882681049, 930673547, 376401270, 178326575, 482325166, 41886314, 679508586, 611868016, 306767137, 313276505, 547421455, 304854845, 505602125, 55907299, 118050197, 397159694, 747354415, 736099087, 722643811, 443841501, 60453891, 431406994, 722060532, 867827417, 27170450, 783621131, 510293659, 928834869, 377509817, 225539156, 345923713, 283554971, 47937118, 419928552, 432034267, 948982219, 406781389, 768662783, 313063485, 912413270, 477509931, 354709586, 908458312, 31262238, 51357111, 824015165, 369470753, 627021521, 439138111, 793496484, 300633189, 66334007, 315688032, 827797538, 585610679, 425989406, 620723755, 313198517, 168642736, 302724238, 134891329, 625027837, 136173119, 763713648, 403084512, 450335705, 850835087, 946820825, 800989328, 894146086, 792543039, 640867633, 268548126, 30747053, 967167684, 495890486, 322259389, 208451167, 439441365, 415454062, 592345246, 893848882, 322948412, 192063501, 900608108, 234825308, 339942850, 287624835, 105353874, 71921941, 306502993, 179596835, 127426718, 98340149, 775217264, 504068197, 836091146, 387875510, 453171916, 636955871, 476545528, 904631007, 441455188, 133311931, 539014527, 682446913, 142890148, 702054634, 358991455, 522342760, 172767606, 971073909, 291472064, 250181758, 684686726, 820654018, 171139150, 484927204, 568061157, 439389079, 336488028, 342760243, 132584616, 489765223, 318952057, 177663628, 860129970, 815346591, 169432775, 712915016, 975527670, 796930163, 791310162, 522076563, 260531714, 380418674, 293642600, 388180538, 728609617, 683766829, 317301177, 998554466, 324182880, 262757333, 23336730, 878302522, 426296323, 740507026, 511709168, 159208001, 438484837, 787546589, 978693062, 955520663, 973603273, 22683045, 321816225, 328499013, 757091566, 760792671, 586969859, 860208645, 338681612, 381069664, 5252899, 57906660, 318513535, 427167381, 813320481, 999499233, 306461591, 178592968, 416105577, 320465605, 615146444, 241062900, 955532755, 604271585, 903269180, 744299574, 388401449, 354781413, 242409241, 298236260, 530352939, 845841829, 456509089, 991033078, 143325399, 589027608, 557051433, 293757511, 912137104, 260512250, 759288313, 753295624, 648346966, 817504930, 466166292, 715230888, 328675385, 168245788, 747855523, 385664890, 343774849, 195721672, 853792444, 104769523, 666768265, 895082606, 144134440, 577680983, 477095425, 958128105, 341590384, 405512448, 557992374, 68799498, 959040422, 984758824, 803029122, 845626254, 562071559, 449497343, 204790761, 498696748, 916170250, 915902877, 997406538, 754156186, 607349952, 594704687, 847548906, 623171121, 832621122, 626173075, 227370416, 756990497, 270158769, 151170371, 20162336, 43363479, 231639432, 247158470, 828414282, 425569197, 687114555, 634437853, 480197203, 212937073, 114607695, 318268433, 227695936, 549982482, 318989225, 111547558, 187330537, 723566508, 266670690, 651975814, 431633498, 797154082, 599189065, 942837289, 641316461, 51633178, 129131985, 417697799, 36791900, 650154684, 95060753, 973393407, 114229205, 95133875, 534349051, 260551285, 944379105, 484587507, 457363800, 391010187, 245172794, 920141770, 332094459, 550353992, 584620421, 5837476, 462452049, 477015891, 918902380, 825566574, 810310135, 840693278, 559451697, 911626628, 374869256, 874381684, 476189887, 857737970, 964284088, 285901310, 246705720, 672646101, 392493496, 197290460, 306138093, 281957642, 213196964, 557301744, 85892527, 560810765, 57329470, 495868414, 932079961, 867957701, 945876940, 979685875, 520800610, 349440460, 319432960, 171302720, 570824326, 912074273, 97984210, 835781567, 787620620, 761362995, 46615739, 75102139, 177448014, 317862234, 442921040, 297744643, 763293149, 257321723, 507508918, 396404639, 996023127, 666698241, 495252135, 578966743, 790581947, 712082028, 927777020, 45923074, 148488072, 599469320, 364848880, 406531020, 478483517, 25527778, 871230522, 91152040, 668512159, 152800415, 857428918, 701917753, 475564951, 258218490, 934333485, 557445846, 959878908, 550775181, 341873277, 802793423, 931916116, 308492905, 406368462, 544767945, 224600028, 379982185, 244803164, 457890465, 83381479, 237947297, 450886702, 130143994, 636532840, 314277578, 98560368, 756552944, 154666974, 217972014, 115114833, 312741439, 491743879, 818602943, 425313626, 437319585, 761272488, 731263961, 664278007, 675844536, 441278510, 710783403, 736782184, 872737472, 404386871, 620237917, 159081966, 549745092, 584783132, 1443160, 87166957, 457352770, 298340976, 611288770, 633262831, 691403832, 877747283, 601869323, 328496962, 943366095, 823170415, 231766668, 310923170, 346256001, 411624313, 812847698, 625965246, 583336730, 874357666, 264523097, 252188659, 362554688, 900107986, 759959107, 593982193, 996664218, 202073169, 539721140, 980448183, 465133397, 165345796, 710656349, 227282662, 463408203, 290253728, 413946449, 303455462, 40155430, 411997838, 510843747, 8069817, 698059338, 969223387, 516655684, 676472415, 736288597, 894071111, 807735290, 600618979, 357365437, 293873676, 506628448, 186537163, 935642484, 803529991, 292167535, 5061597, 983864758, 878507855, 324415866, 454145850, 392366963, 420952044, 548688383, 497597967, 807791122, 94709035, 49714687, 580975280, 726131001, 765157213, 630136265, 242176237, 79894468, 735393499, 853830878, 730817405, 875568952, 858688388, 129510764, 195729032, 688397824, 279899596, 151974018, 884755513, 753384840, 865065485, 980200427, 100726608, 722347681, 266775817, 155172328, 429384485, 934007156, 604413928, 373928584, 670869991, 911186892, 252351403, 702014866, 401731655, 837455278, 95645998, 981631927, 715504011, 580372553, 303336241, 37532076, 258010314, 82136960, 475468541, 542837526, 402044985, 514129362, 508702838, 266880981, 358451727, 779474334, 639945877, 274248883, 805037113, 660168583, 432635751, 126470562, 643091025, 956134379, 861801462, 365986429, 879137311, 623421377, 36277783, 797893284, 815618777, 84451694, 953551471, 187827130, 307956974, 211500628, 243115531, 916437335, 680482509, 111067542, 189812709, 449640454, 371212469, 281998557, 815558610, 582234361, 162747496, 762664468, 591589281, 381929412, 978133498, 953211448, 566810743, 452928107, 449831891, 70911323, 260142271, 292086054, 875318513, 296633370, 943378614, 333454493, 123126715, 912094957, 50921704, 828508551, 460010149, 778586303, 148420027, 50541515, 695799059, 175947147, 252194167, 581195156, 141777547, 765716758, 925499170, 748981648, 324082894, 912045071, 717186250, 347235560, 694333790, 39640533, 818457742, 819385712, 444949868, 432371838, 486638877, 376206562, 226342725, 329361940, 595818965, 948488783, 640945396, 254577712, 409276582, 60120779, 611598620, 852963725, 515061986, 771610259, 128208647, 718099346, 915515791, 90348916, 700075765, 46216162, 373802373, 856898905, 36003750, 836294485, 677200908, 125246017, 343368974, 175024215, 136778443, 451633594, 889317324, 895639749, 164584582, 296062597, 213868707, 809302097, 834037897, 868456932, 71672085, 813129535, 858981541, 846357999, 500312004, 321621085, 330896298, 864267517, 556480211, 936514815, 432411502, 614472179, 480645841, 287921008, 627057242, 382932282, 511231452, 328985056, 765181333, 439185512, 235237629, 416478874, 57859426, 481261607, 433959007, 440899174, 775426656, 72881404, 632142928, 130293474, 786969524, 70250706, 148223687, 203799353, 850451721, 771314633, 600191935, 412600864, 381102651, 228787965, 700864335, 870494863, 483365868, 589497800, 280032353, 496033475, 884136598, 490733319, 910045552, 142691571, 70857880, 88195155, 408781611, 700660009, 740491305, 807378522, 18965543, 730931500, 890311599, 367047731, 743633714, 324861412, 193039353, 672031760, 862986473, 128474895, 470884993, 99646588, 727707336, 68553024, 12650663, 863004707, 286062669, 242320387, 734170973, 795331174, 107724248, 479793590, 228889103, 355523655, 785967601, 781867853, 731550664, 973473338, 889031445, 554772371, 863535939, 874409012, 974784889, 333154337, 448759190, 613011019, 365253799, 491296245, 530508880, 583426394, 753166062, 840664473, 482249257, 535596264, 842505944, 138848425, 945794584, 898282321, 22841884, 656493524, 24648094, 981259270, 491692706, 969044808, 813818257, 842245661, 797892688, 749971478, 516390205, 968630318, 821749410, 885697056, 542254303, 348372444, 971692784, 273053560, 403089096, 27188888, 687521038, 399746517, 534923522, 104720691, 418867375, 4600806, 219693902, 799878754, 947614591, 100623592, 456537266, 464481318, 446599320, 302485549, 133891270, 284576148, 666442899, 42836622, 309605641, 215924028, 203602632, 262495473, 246656142, 129520625, 765211649, 93554174, 150729567, 282468415, 832693590, 97436219, 237565198, 95651258, 388718443, 866572164, 532723952, 12136518, 174455160, 405550447, 355379828, 385903154, 635094002, 241052844, 73469041, 300641416, 101986907, 384846652, 471363203, 211237880, 24939828, 292400964, 884042664, 512430087, 808902343, 909538798, 332159662, 976239732, 650845430, 56461156, 899920573, 94462166, 626755528, 804291112, 200410049, 361133110, 175217478, 296116737, 134915341, 949610433, 373511980, 333611318, 736207878, 389494385, 925071522, 425351423, 808428745, 785798074, 742742331, 721906158, 371827649, 154595872, 58297087, 383171931, 184117398, 214068533, 492233161, 346046812, 512588750, 173066648, 18464269, 474809770, 524653367, 533971076, 440508618, 513817936, 657623952, 867656519, 677103090, 3823211, 391907812, 215871195, 561359569, 948276996, 537217493, 495857247, 356744212, 781997393, 857395015, 866519459, 672089959, 84961911, 317861300, 658022744, 837179453, 504580487, 6696181, 384567163, 785598528, 206358981, 389983144, 482161654, 170197295, 638677546, 593331939, 168285602, 698197252, 484324030, 52894369, 581783057, 534359028, 965557315, 57041106, 478982686, 126855944, 829710201, 797569783, 524217698, 492870972, 705015078, 256395953, 117081934, 847981025, 903105025, 783909962, 450195998, 118826575, 908671928, 507757120, 940045559, 131406996, 769790341, 76316198, 292478409, 145087934, 16796482, 898403519, 700320315, 589134496, 317457956, 892946027, 259734586, 421642964, 844481897, 613200179, 35418354, 607375053, 128478975, 320805797, 171961974, 212613049, 637858821, 477090117, 878909836, 135980357, 758093080, 671871146, 603902552, 881538431, 275871737, 280428292, 307886416, 908597640, 676034479, 189670764, 113054762, 350614744, 863979448, 275113313, 180867505, 84609062, 974552088, 229873697, 754530171, 923815080, 81433589, 290418723, 798436595, 752831321, 813931958, 830909527, 229374958, 579704899, 96632576, 544643344, 783698349, 432597908, 447320386, 857239222, 54641427, 429112602, 836481657, 999697604, 2463198, 241881609, 871557254, 454335027, 294195970, 889520041, 636526651, 192904739, 562376084, 959698916, 223485460, 326587449, 510409301, 17346104, 644389799, 478589192, 870458450, 371057239, 581493128, 469420425, 330032923, 327751329, 814975874, 2937955, 690634974, 348962790, 183699057, 504362303, 145723912, 569893019, 464103113, 60238632, 377860630, 918477038, 87248142, 329582109, 439394882, 582582370, 916313548, 14256488, 657461681, 211669176, 515939973, 569599005, 775840883, 955575583, 403847446, 562773611, 35932008, 470474919, 933876541, 528642984, 355453711, 562964323, 47683520, 134543976, 413071239, 305536303, 958332977, 784107788, 631182361, 98057025, 490444449, 460944424, 123294093, 479346329, 196096626, 170079888, 586216543, 247543115, 950346748, 34418373, 140146461, 235975796, 193525511, 841369823, 221109466, 244949403, 51376185, 9579414, 743945926, 400953224, 210532782, 743673517, 430147976, 167165616, 738412961, 385452521, 743636676, 768109099, 325087206, 534603652, 985054057, 983382624, 140809840, 460546858, 880503642, 173626594, 246327469, 396644255, 74882449, 662457616, 840143867, 800005068, 453214507, 17636580, 911958763, 302316273, 488543094, 495299079, 490526609, 738338, 273598117, 768164086, 342033506, 549067785, 775831969, 77007484, 760569174, 956226011, 982311777, 412951309, 489833152, 550571090, 920834592, 334140769, 773416884, 562958400, 659689103, 261859442, 792582867, 18459599, 1206656, 553759561, 368720252, 523950869, 849459061, 880210334, 591237220, 367236594, 42203703, 848364275, 272854593, 1136973, 637535100, 225623395, 655282948, 164997680, 775719090, 151194214, 116237320, 95402966, 901346278, 556131281, 990685218, 803988193, 435132853, 965936967, 840240729, 456907954, 100460867, 73676762, 813636879, 547300378, 435349477, 629065010, 714656387, 403207286, 158302968, 422828309, 676326269, 244836358, 591895639, 561966201, 198658533, 993201111, 194332005, 240966868, 908108174, 60165265, 178571060, 482317452, 463884161, 989881751, 767959933, 464219802, 503229929, 626308194, 517329920, 112482641, 962133898, 780419659, 382244496, 78227064, 412826642, 993976728, 610691920, 764626949, 976378466, 38889209, 959776816, 39728243, 163983686, 210404557, 444135119, 190399860, 365916997, 35393878, 131421803, 931741770, 615838361, 556058434, 662683580, 722034567, 318380540, 370051490, 250327647, 757124344, 22199900, 873783895, 118401521, 202888058, 88736248, 115288384, 300599331, 56690332, 898893193, 875341595, 847480420, 575951635, 592248949, 998268670, 283946093, 713275043, 992752955, 415816064, 497744671, 155380013, 702710486, 46131000, 40402372, 173717446, 834244508, 343682005, 299669252, 788875318, 616639016, 182105251, 460169058, 816361095, 579104040, 765920300, 979856343, 272295846, 970468651, 990890876, 115339880, 274942840, 575416455, 449677761, 118714995, 446500353, 429900214, 336281705, 456484717, 306447489, 85725145, 354950101, 528292768, 274847154, 847886588, 420193506, 582790380, 471622819, 321365400, 230804699, 374512033, 452372330, 911301884, 132475336, 228211060, 388332209, 950950597, 754194425, 240154233, 436940555, 767481832, 514661855, 57447223, 967000107, 507767439, 302229675, 657623153, 795101307, 659992549, 442784491, 744569125, 202541295, 231734069, 410942070, 506056667, 300470406, 281618308, 321287470, 701490047, 5874910, 867310544, 118600154, 294257926, 791743636, 132068053, 796104697, 753537288, 213417833, 569283985, 462928261, 521942458, 47036974, 752148162, 214780347, 24534469, 573636293, 509730029, 387560122, 219767979, 998243035, 355040561, 401607283, 201305074, 744038613, 704518198, 728961628, 229928705, 912836872, 794279424, 396513034, 799006014, 827822304, 653417448, 939276213, 589714619, 543096815, 549551377, 212378095, 370691104, 80349932, 49577513, 205905556, 498541566, 124368654, 977160193, 869636415, 519910021, 503964314, 279412134, 47639629, 50484771, 106650864, 622624654, 390508096, 710385224, 436918654, 694878924, 85465690, 275848851, 888723612, 706359765, 702362924, 576241046, 269943027, 140527535, 249639862, 967822731, 860022014, 855022526, 816691678, 432057378, 516351268, 95672883, 469787781, 991125894, 949996497, 695620083, 956326722, 85294060, 514118183, 395368444, 444564429, 764670716, 674572093, 502870018, 14421806, 560769937, 182175728, 733745508, 2431269, 896747356, 104864148, 58091386, 580261615, 712194007, 726062750, 240592913, 168057551, 209859691, 396201989, 643090320, 268337033, 180407785, 29685001, 579947063, 662870311, 782805009, 836771603, 569239112, 55478778, 145003070, 978157021, 768580345, 435754775, 248319921, 681129609, 711652318, 538672172, 946596050, 749465620, 934767557, 314261323, 975714593, 119541685, 145830430, 678185599, 297471203, 293250036, 930614603, 948083738, 603825960, 369041492, 903471660, 235875996, 744796602, 183168869, 9957904, 882942932, 31501108, 393625703, 462357489, 111002823, 828894717, 767348142, 707307748, 324200151, 903167387, 640149767, 711327208, 825303506, 733268553, 856517477, 737612419, 450291783, 113870693, 540734272, 143050477, 136686631, 87875136, 820043321, 285694048, 504460655, 315839054, 49868016, 652047918, 585043264, 501933476, 223592501, 820997165, 5176639, 868849871, 271887783, 784821594, 255451712, 621762362, 250014406, 38162491, 275019526, 883663696, 852240401, 89423699, 479059171, 274290012, 661835922, 860742359, 800075366, 423486162, 335155815, 202324861, 682379807, 970471310, 145275731, 954120421, 921298954, 220940499, 266040173, 833083771, 753956569, 541010675, 443899232, 332131621, 26126189, 866654248, 31646796, 806052849, 858900375, 741260183, 302154979, 16314075, 559334508, 167353228, 726376448, 77508225, 362344835, 847857123, 330111508, 305374833, 739805029, 23725623, 415312310, 308209665, 784735073, 78064826, 186269435, 155830786, 430639155, 642272666, 335541534, 773808279, 847777155, 439646261, 733435917, 245988137, 865107533, 788225641, 976354828, 628739090, 678947592, 990959094, 478071378, 195796892, 836500894, 14108845, 465657257, 257480014, 416103192, 47865838, 439416981, 532243908, 397866763, 142569779, 373612589, 490540287, 787301049, 438207961, 572171700, 321346477, 305175894, 94770299, 950678230, 514987989, 998580186, 55310052, 163178250, 852932232, 592533540, 809198147, 703283817, 83151573, 532506539, 428947676, 345822837, 288624328, 872280857, 852067177, 101763445, 392761789, 310144298, 386244542, 545368455, 893460400, 820729527, 228882993, 836750648, 870259222, 869508054, 743256436, 306373118, 636984186, 816525353, 217227024, 995083417, 920590743, 76371524, 846373672, 496176638, 194904703, 882438328, 101568401, 32254322, 485352280, 666686949, 793924779, 99156715, 26334580, 955151265, 597689478, 786946240, 963333901, 189963815, 631303739, 194589357, 145826370, 191349912, 135744228, 500731671, 111181619, 181587175, 591122475, 546394865, 954411267, 945521647, 655739724, 238662832, 749996882, 485576331, 214579245, 751796272, 213311778, 384311394, 523248390, 680122605, 744381905, 494337286, 150030546, 753232196, 784960438, 795726473, 162709641, 625924657, 178978720, 74507708, 522662172, 571125954, 288362326, 602854411, 935912786, 73363957, 558503321, 447111222, 16266861, 165646821, 625982298, 855871133, 709746822, 430740455, 889357284, 581096753, 755653841, 969516521, 799027275, 205311816, 143949212, 831537844, 431436392, 448243448, 326957139, 404603065, 852833929, 708518142, 349337614, 687334566, 685262033, 686103217, 387043349, 378696967, 237074732, 601294924, 915696425, 692526885, 788848932, 50623405, 776356418, 266008691, 278281432, 142563510, 888984711, 453630114, 167398903, 258792669, 791229567, 648543175, 526616463, 941175681, 513764711, 125139857, 653421172, 440546167, 318437859, 575238136, 199216926, 996568408, 120524564, 555890572, 905490185, 810096521, 198341323, 809413247, 707190222, 914460536, 168749305, 655719597, 302188561, 614895779, 904259753, 605591258, 924266145, 825038048, 655995592, 413690146, 736216192, 552332573, 857809834, 365251426, 162760871, 390920486, 394976694, 837512165, 657370406, 753771115, 21189361, 576774036, 541404916, 595253188, 925882371, 102516070, 800084923, 640317391, 825542354, 552984701, 114571536, 350035924, 930678892, 415424745, 920469849, 635226069, 519390781, 792900688, 518629740, 920237754, 199337211, 555060327, 879201582, 506253809, 378052697, 376685670, 26830361, 620245641, 558939823, 314699068, 581522135, 867489221, 699462395, 686419989, 622308397, 683127612, 341833047, 81628094, 336515458, 929529381, 181114774, 857718014, 953144129, 379369925, 504062089, 487243988, 102262966, 357271778, 897282068, 736427164, 771205453, 699076120, 126310890, 443756051, 712643822, 345165920, 866136402, 833002101, 296711186, 724307548, 917166882, 957210174, 138549269, 380584071, 478419885, 849656883, 794008426, 542737076, 461011829, 185024716, 363841590, 172841919, 196192525, 899870529, 148727109, 864301703, 557275999, 836783805, 388859294, 949045414, 72182668, 971347661, 78839229, 653601326, 893288268, 152741144, 852874188, 588152512, 840584224, 128678537, 315260994, 127322286, 435554802, 209962811, 959580586, 706809330, 903677337, 277780393, 723755230, 659660082, 2895991, 918992944, 775937905, 989769896, 18893467, 295045129, 346723023, 537942431, 141180558, 321945706, 14070177, 887344068, 325687308, 127670372, 423471517, 959631004, 884628947, 23608250, 187008225, 849921984, 816850398, 462947214, 97697763, 624473922, 157622526, 623461119, 667005415, 611192225, 850346457, 946659911, 200383316, 695125656, 83028955, 931137688, 511782045, 903667538, 489307387, 532741546, 60141944, 34329048, 739800564, 375135378, 740219189, 592752280, 436380428, 814553219, 562008375, 155878974, 605685124, 862066752, 264617709, 915662747, 715270698, 935475145, 24577088, 189163312, 985927841, 375644741, 732897708, 87926909, 407535121, 694507141, 404580816, 50903985, 255948380, 707304774, 530438134, 263145509, 898715354, 814525072, 927358735, 441595376, 431674568, 53949386, 78277572, 623226004, 808949602, 421156296, 182568886, 323677239, 406535334, 35713857, 331004707, 557880082, 673509087, 890326910, 642918639, 82803668, 656880031, 704959979, 120382301, 377565135, 455120940, 627114569, 841805903, 342482183, 153352956, 650191397, 949275492, 438771726, 628062267, 646265338, 68903029, 956489202, 374767524, 595566639, 275297491, 371390181, 797312214, 318771346, 144337792, 129770978, 27392123, 810198981, 351085855, 667443170, 847738543, 357653724, 498789335, 832363959, 929562440, 768793137, 105631271, 984299959, 334337562, 95505817, 559104315, 539554170, 404428621, 172796506, 977937171, 635089683, 292638894, 668168673, 439533774, 783320201, 737561402, 96564778, 446680211, 342530631, 691203309, 178038827, 738147728, 85040938, 661585742, 808574059, 925691454, 336504919, 232983972, 893923766, 670645218, 857100324, 793368675, 112229066, 948262826, 363817095, 192586245, 592551951, 139027185, 877699638, 581339144, 734891806, 22683388, 453921947, 683384537, 973583373, 417792132, 309921781, 737630053, 241235551, 231735689, 298523315, 319516579, 563250493, 55235862, 334019934, 911543089, 180555023, 208153845, 429180514, 181739943, 913827762, 261768316, 90670875, 233709681, 535283782, 236054250, 814807053, 365347403, 317087932, 789296620, 384187692, 283211808, 162218730, 604725107, 463333357, 253180925, 40557055, 201236484, 136073893, 189247787, 790964857, 607115151, 586061514, 695891853, 569637692, 391328684, 908597555, 828348727, 143832164, 74891702, 65149921, 528626193, 334363261, 394231625, 76137253, 873442899, 447471855, 350051461, 512217744, 539013452, 880577735, 816720168, 714946928, 781269966, 593550596, 492713545, 407874786, 197256339, 613956792, 395432429, 52377010, 242737823, 172929837, 706525862, 220367538, 50076778, 805753600, 833308644, 485110337, 184339788, 812655654, 138456305, 654432964, 523060271, 932556009, 1257136, 728143801, 975794790, 987819929, 894218501, 620332398, 583481360, 306388945, 750696046, 193848986, 370509887, 128027377, 890980994, 343294398, 366184222, 948888404, 330065047, 398104816, 237709333, 266303482, 387411079, 370945732, 852315840, 404078761, 909020045, 398279108, 434039631, 500757102, 618667665, 123253112, 501128568, 434188248, 366540730, 166110361, 577237401, 147155005, 141612641, 133837586, 996805733, 842263559, 67705157, 116491253, 151163997, 19058130, 330078075, 965489010, 940006218, 863371436, 533473507, 795226711, 962705140, 967530018, 717947032, 544979369, 436781888, 895542479, 699209507, 118523226, 549572345, 630357309, 909720603, 423292512, 604425635, 553557739, 471971509, 395458637, 931677705, 414193617, 120923678, 995682216, 345730094, 10947293, 479338618, 357492549, 501399606, 730000797, 417493241, 633256020, 434295529, 593750673, 20384449, 480526708, 274265630, 785994700, 878821385, 460211504, 670564944, 692795146, 24610740, 925901895, 378453516, 844118961, 505031644, 926099584, 551136833, 316061098, 339271100, 197015609, 466051002, 195479873, 938008386, 480935770, 699843240, 121980664, 794624869, 372972296, 245300270, 951831050, 396014020, 96406569, 151734762, 903930656, 17095650, 950465421, 916256490, 476810694, 512072955, 569319602, 314203924, 106585571, 273646504, 895811237, 119881185, 72811784, 882548697, 964238213, 712870979, 48556147, 211501013, 988773693, 982025053, 87508293, 469566960, 110353559, 306500046, 884113273, 703812238, 370191078, 473370635, 862058107, 754863439, 503098570, 171842489, 33312466, 106391490, 222011568, 726441066, 266357198, 13164447, 205164474, 814148027, 194719420, 784430968, 274812869, 648059374, 767342341, 265939359, 238497207, 514630619, 617844568, 875248158, 472770333, 479116009, 656507148, 335989396, 283916968, 364625663, 213818762, 941211634, 852939358, 433188377, 540914878, 412475175, 410929296, 506112680, 595542076, 279391748, 440167103, 183850861, 263644753, 155436380, 346197634, 267960535, 591333226, 922697927, 582050637, 69736265, 463569042, 909194740, 122857220, 880558445, 86825094, 817349343, 769659989, 766966827, 882112009, 617741121, 726026817, 757333304, 423500657, 532778051, 445239870, 44687087, 599942031, 163309594, 36297908, 581681446, 918714516, 79875384, 694853226, 150857814, 493533729, 722362804, 58632509, 579102547, 892309726, 476229640, 70754509, 156352814, 117777421, 134719130, 441713221, 413167027, 233968070, 345850161, 574924012, 207232486, 347744932, 769572207, 976326454, 711819333, 522053803, 130449985, 139491517, 689966216, 959944308, 40874294, 998984935, 556466256, 386835859, 424403877, 934782067, 874465705, 584097928, 14583046, 746701599, 313622973, 473446249, 437253656, 709563042, 665267329, 228425898, 582636937, 875903063, 605976884, 53582222, 958648658, 814561310, 608398879, 440433651, 136709183, 312899790, 4230078, 608523956, 914846572, 559124634, 17536639, 316470685, 704831666, 928373246, 850885245, 149454089, 462772667, 391012426, 524502841, 920386434, 480100797, 138637424, 182600127, 734963865, 901233893, 974447880, 786438618, 29410333, 823524123, 608988754, 531613852, 762696634, 32776145, 887343484, 75906930, 611456971, 273387270, 850069433, 499396940, 456661358, 5502091, 993638312, 779840919, 126966020, 213077589, 211626873, 586015904, 464484075, 260161042, 182943949, 91267841, 621323523, 445312809, 267851336, 142701209, 415328608, 421957785, 993056348, 848525829, 90786408, 732437198, 719382780, 333051744, 736188081, 203654659, 744117351, 499326706, 110149455, 401619776, 776416953, 232971211, 757115594, 928295231, 64411890, 270874186, 121189986, 430571073, 686491594, 324709143, 956915569, 132329393, 470663841, 431397705, 769150078, 568987637, 108549400, 420021689, 263563199, 316113115, 699015249, 961242446, 118431961, 497264941, 978981929, 50361174, 472034145, 675057982, 89220089, 421603701, 784075043, 878217840, 511463780, 504660764, 621789199, 376194809, 913993369, 837764406, 424803859, 998643297, 959460417, 501657302, 539679038, 305830893, 658936969, 30265529, 41814188, 868950210, 69806774, 138798105, 289372764, 22260909, 609325602, 967316213, 517347965, 204715260, 231124839, 2036485, 421012289, 693455742, 675606662, 527993750, 422835124, 5187566, 635322793, 222538246, 582411384, 682032891, 374867431, 314964966, 88462578, 132885370, 66982610, 773083500, 716203755, 452294861, 958648898, 402806853, 263128477, 789938008, 601974841, 399626901, 259306836, 271641739, 345135200, 118094142, 369898749, 168892462, 895760546, 726791266, 80813971, 699735854, 714890025, 574152683, 422062490, 449470024, 429819072, 34475200, 95443825, 626179218, 196171282, 502003923, 353114266, 638383310, 819504413, 239880866, 781188143, 658785896, 526498561, 637306718, 768434778, 151215110, 378846334, 566663311, 62329709, 873411730, 199518439, 535152483, 485427937, 980024052, 502436839, 612147623, 365953848, 999392316, 798806689, 40519571, 962617532, 11514690, 712390223, 539923617, 746911821, 86765217, 684184460, 875581868, 31367999, 573730609, 619553309, 726866384, 3844065, 198194342, 61829641, 436791548, 676214136, 692199687, 455723241, 189286245, 13301505, 311775777, 228618519, 660569273, 68905730, 204245330, 264837023, 504241098, 334766535, 915838896, 368411848, 362808075, 649011987, 559016882, 237649837, 648042378, 618567595, 275048924, 239748224, 819400356, 951177874, 936820694, 940072367, 185355162, 487698882, 807751803, 193271332, 860232041, 405031889, 524038058, 266145885, 834507998, 690166949, 674933398, 914981968, 648342120, 221812632, 256477615, 74620699, 689154014, 665740183, 583265356, 840757362, 401527065, 532715561, 847247597, 976599842, 160628009, 713161002, 31020634, 335555848, 475726940, 80703603, 5962721, 154461326, 310584999, 276041321, 145493698, 129574129, 491753826, 720553986, 555907079, 383345046, 658476074, 934695744, 294004470, 220335955, 371556217, 772373585, 293733344, 411301972, 444237268, 254883856, 48207632, 535576366, 51982123, 305538062, 865140565, 217389938, 13161033, 441284174, 446797431, 128796826, 416682283, 526930475, 660443941, 820262822, 613116378, 842404481, 482764987, 143503905, 584266361, 713502907, 418958229, 826962825, 160323495, 490454323, 311073909, 10746792, 884841278, 578891765, 658815694, 839449939, 895240373, 182973784, 747353246, 65467814, 77952023, 842245386, 859632954, 708722610, 777045440, 888006697, 891989148, 49291337, 647984600, 852225482, 155272827, 427219962, 592375905, 904960041, 891891389, 455753626, 717831409, 914477891, 798070303, 379031327, 22680085, 404385166, 818653245, 388486525, 467124282, 463875967, 592019380, 701168655, 513720336, 661657028, 979425454, 718403017, 571318094, 5356534, 958716480, 88934314, 267150099, 550425956, 607025763, 248266821, 107483752, 988160909, 559500951, 163669624, 412689176, 128793040, 163231370, 307072388, 362907701, 708177700, 736743333, 702103698, 612943529, 569057660, 904106940, 15415042, 118674709, 559472356, 533753590, 244210273, 348095444, 50250812, 813210057, 703175433, 136800571, 167462781, 215798444, 681939200, 697818267, 440553228, 339166816, 274889178, 267077698, 733743858, 935364864, 660203668, 441471374, 188248497, 463733939, 629143250, 57994819, 563393340, 855850363, 901457752, 414753711, 876159574, 229281003, 502140456, 972866100, 779164519, 350197262, 676757342, 197628470, 767396210, 465822643, 641975505, 977962128, 421666875, 759099208, 426614687, 72493481, 858421177, 206749512, 515704395, 54066072, 345802935, 312059270, 185921718, 493722422, 790911409, 455467346, 527253230, 828743314, 19737478, 31330297, 981847272, 875988219, 958587525, 397074732, 293098532, 290087849, 952594743, 256962067, 976601155, 971431242, 368701093, 304741907, 227095324, 782095303, 496223216, 766438434, 701055800, 23662897, 713425092, 263271356, 504608951, 102619642, 8677641, 834935435, 653219253, 69042881, 911918034, 600645812, 329111455, 238557589, 727553362, 556703214, 569115899, 791735983, 269409244, 734682342, 720189335, 924054117, 614693689, 165026106, 321778456, 841400545, 713185441, 875264516, 710664706, 751133210, 820807045, 846745283, 740937917, 799895107, 480168417, 508689595, 509822200, 880077958, 816346249, 809090539, 623573416, 56272958, 508091916, 681350514, 901991136, 137829930, 669184238, 814465370, 696278277, 250302654, 745554205, 249253912, 445724867, 706868754, 16966542, 231265431, 349472, 982970377, 626089307, 24914270, 769205712, 364766662, 738676571, 79319805, 431907223, 878822302, 789339398, 481712415, 818638557, 750407820, 419694727, 113821994, 534022729, 702101212, 237962389, 217684276, 845305125, 134946085, 526481334, 471441371, 983435505, 440079509, 610461745, 175985362, 328475000, 204617219, 61232624, 56836264, 845817680, 913665011, 322771150, 991223641, 391958204, 220772767, 170857236, 701636895, 126580622, 856945774, 741654292, 203811229, 270493116, 661340626, 213584416, 813414921, 921396780, 508340454, 300429626, 521018285, 958861811, 379779984, 934726322, 479422945, 306534588, 149008564, 289636771, 47027067, 911711700, 247559102, 364320676, 911011416, 568947485, 500157650, 253690182, 957222905, 570782751, 101114116, 321082667, 14973113, 142999529, 814519560, 117702705, 114705682, 178415532, 262336065, 238392337, 571827267, 973229860, 745285157, 50490327, 988400765, 590344758, 46063367, 814120399, 238379126, 781080287, 392541562, 563418160, 55915953, 268380525, 887322747, 29465244, 652572834, 532152360, 868867855, 94542742, 587442860, 635572482, 948944527, 361355542, 188824498, 740829355, 626670028, 295180767, 18581500, 995750847, 980769364, 925865633, 667010053, 278290367, 733642707, 678907350, 349777508, 578564760, 776787192, 827577234, 997150851, 576452410, 74972737, 738747953, 298543124, 435661528, 334923759, 354602678, 521125105, 511889374, 305646041, 394123748, 330367943, 610458263, 690822243, 732806893, 693784261, 13579696, 342934647, 280463526, 935349518, 310799215, 991892723, 582455793, 1996531, 176887678, 99079211, 189592907, 189740591, 100811852, 470332664, 848690219, 874592458, 508673845, 43786980, 609734295, 955312493, 791771427, 389858014, 260091126, 975283937, 572819709, 81682011, 728092761, 2794359, 980375701, 203708844, 949138936, 586270268, 549946846, 764865872, 328830478, 512425138, 194494583, 890461390, 892215205, 694389298, 534488167, 331481367, 685813145, 745159725, 332559633, 857588288, 592987057, 835585421, 106808292, 909182814, 122929361, 109031413, 374846291, 584457473, 357771619, 148225371, 746788293, 741349221, 405420355, 484979417, 353022648, 660403429, 88628697, 535414399, 934945174, 808574658, 510056615, 173507200, 196157619, 710463578, 608929894, 243547782, 554582125, 536245112, 759488793, 348716610, 43431959, 631356680, 147920746, 392880155, 11811216, 939753556, 594189150, 654039483, 352353911, 562948797, 170600947, 469481932, 500946004, 942175293, 743492014, 158151195, 822332440, 684629598, 14366329, 755398641, 50498096, 152129794, 804549761, 428131128, 570747667, 549626899, 207318486, 697576518, 836687794, 544688360, 628376727, 808180881, 166754077, 337331169, 497777677, 187825327, 584943649, 190555628, 450547528, 420471270, 823590130, 316365538, 848609010, 298458191, 996071276, 193651155, 444373533, 899892149, 575833289, 859305981, 301741512, 906617227, 714864650, 744672329, 561101640, 836173132, 37530972, 755728344, 502150725, 755100635, 821752894, 310267570, 986279571, 938289129, 928103898, 511785887, 311446066, 503547412, 753929921, 10683226, 462065363, 878118499, 443591256, 510909239, 612612670, 65867771, 500347298, 680802269, 838190336, 42602449, 725275662, 690196296, 350473602, 358345025, 191138325, 936716039, 412071964, 352172548, 269573264, 611135926, 575631929, 422431673, 549922506, 491836169, 517883005, 873014159, 207473458, 315437072, 445619030, 636800022, 411109399, 240227844, 9027332, 674523834, 151546099, 672403072, 251907445, 640362251, 363302744, 997483448, 227370422, 13674339, 276189449, 112415941, 957851216, 260354565, 74043436, 934638485, 452885367, 434766258, 627283242, 271620986, 950665274, 711607592, 866238708, 21403500, 727896044, 56966751, 643714526, 558866122, 333697288, 413161547, 30598434, 172451902, 115514126, 146642585, 532527049, 156262455, 407433862, 231301458, 481522844, 291480614, 116821273, 96608406, 82555983, 96589819, 674712940, 826453036, 594267853, 760894310, 455051200, 114688518, 364611619, 383265052, 683454989, 808659152, 961087937, 162227591, 848795145, 602105688, 440077763, 863709189, 256939346, 168122190, 802984604, 534346295, 615828994, 287437930, 986499340, 111806392, 29540386, 299598080, 189147925, 373641393, 445469379, 644313259, 172044062, 839671707, 432197675, 406746136, 777362244, 538428956, 213255751, 943180158, 956782765, 814639193, 924804731, 730265423, 766559299, 153922179, 268723145, 963968370, 871768203, 864493950, 881358511, 862251682, 432018512, 331918642, 546583677, 223494632, 22780477, 494795106, 493994712, 351155003, 787936962, 954036689, 246197491, 667932819, 757380998, 903623559, 610243783, 300291951, 161145601, 521158681, 735378439, 896256707, 961128257, 756449631, 724276643, 626011745, 283801299, 363117875, 549090947, 385928898, 533782512, 448961088, 769148274, 285637989, 873860917, 352131475, 186631686, 379282536, 535709111, 225874458, 530490507, 35895743, 520861048, 93351086, 598548541, 919218859, 876163206, 784444451, 669930495, 806557873, 253745213, 232225111, 428561130, 712886467, 790196386, 390456364, 846749093, 728685112, 525099428, 263404666, 789837757, 35643794, 657037279, 533843805, 582878120, 799780126, 467345198, 84767022, 98963334, 821378610, 475294711, 472058578, 926303956, 688648566, 480015811, 559196567, 76717221, 428214742, 718588218, 283242746, 738021632, 46603088, 772880073, 382589361, 832795564, 877775199, 76438573, 903098978, 748703523, 509749742, 571240205, 575033751, 809758811, 314222703, 848712029, 77113206, 696278692, 55105117, 940829710, 125474639, 712850809, 229904100, 828743699, 158292592, 675351478, 482745686, 322241684, 405023338, 281621692, 309138515, 998898548, 294203463, 869015059, 833897186, 159766377, 399591650, 526212534, 472882680, 142712690, 320152719, 900359551, 847228465, 486369627, 748791431, 608637180, 951214310, 24764745, 737074077, 460530992, 717730422, 726175824, 142744981, 397450583, 134143944, 131997533, 414295757, 387945207, 702226079, 549091674, 462219124, 46154024, 479061943, 208877592, 469052037, 171923241, 116236998, 223699361, 953236363, 518968697, 55665552, 973909517, 129979061, 840694708, 266681093, 162517952, 299953769, 160282958, 873326805, 366907197, 410690879, 938427133, 443518416, 580810614, 32765560, 103912242, 998224099, 406807293, 664174399, 835970806, 691661766, 113026880, 927525183, 903294972, 969936508, 670857929, 130348178, 655020556, 528167941, 326823522, 439782938, 714709781, 663136321, 900531417, 432110257, 114551394, 301994237, 436494358, 633859964, 818748607, 151590336, 860890682, 927881034, 953288157, 152198876, 637760950, 590822690, 12312232, 605129874, 802788009, 406341031, 477684266, 49220318, 277302424, 445193755, 964535905, 957053703, 608567425, 152232935, 100997231, 655644260, 875455235, 954901597, 205392174, 878542878, 134816801, 982618712, 221326603, 94478373, 314306570, 900383264, 198231281, 649819132, 608819575, 980391374, 837764615, 197988036, 204778485, 776307396, 564540816, 128276944, 758128293, 239707143, 350474646, 922516842, 714954326, 156136398, 954795360, 315067680, 420174109, 998023582, 980996112, 136776296, 157960947, 413113290, 907478288, 882478381, 116356076, 888318289, 493076379, 230149641, 890700459, 806813643, 818388566, 77675583, 188802720, 681825044, 417189437, 769676883, 740752757, 107012871, 897737128, 691942031, 900928785, 255523522, 873245939, 557770190, 343817804, 848550195, 965594354, 899199831, 197809201, 207339999, 519425611, 635033324, 144919279, 596935413, 396728239, 25567060, 419627978, 668299798, 129709890, 523398258, 714915339, 200295041, 41467548, 632734708, 720631991, 650195921, 956136882, 748480049, 479852144, 57122587, 844825691, 578360668, 925150682, 838713064, 745282509, 764993752, 336355460, 888546524, 533554393, 624145110, 466975956, 920378557, 444962804, 685180072, 187914865, 808484212, 475010791, 390485374, 536722717, 594326857, 59669671, 658148369, 182255791, 675437078, 624308361, 73548307, 773916829, 873515432, 332165825, 418299995, 747871135, 59434090, 806499392, 538891327, 913530308, 432297664, 23063770, 438048576, 171026026, 709529135, 416456669, 827898973, 870910533, 261096871, 391102890, 762849633, 906734682, 266481882, 631433787, 355645639, 918413388, 397378390, 746016134, 475410013, 538229016, 963785233, 233116653, 256354338, 683910719, 301721407, 2936519, 673418649, 506869400, 370567173, 426735470, 669260502, 978995919, 398149448, 604710308, 103130420, 146912166, 698217608, 290503200, 427300041, 228406261, 753389153, 332642935, 666342636, 715022690, 211783163, 436813350, 481949092, 499994598, 909142008, 209280129, 956749293, 370671273, 636275361, 837146011, 409617745, 877729419, 158379865, 153741815, 304584712, 797949384, 777907745, 423457329, 427921490, 516648836, 313848834, 406155169, 665547535, 561488815, 459683948, 263840494, 79285356, 467943497, 594742798, 827868482, 830966983, 856847913, 579893333, 658136686, 551882609, 354893348, 643105901, 200114805, 488247052, 859553558, 799619479, 470016325, 960431712, 53960499, 626692431, 153596835, 402951107, 424388475, 216388757, 146287776, 506586504, 292639240, 203262779, 627604045, 436386992, 460896946, 460630049, 669914550, 765879924, 972761086, 703527892, 65580563, 233000274, 770319957, 303759515, 785916045, 23613755, 842653220, 203841614, 756921119, 341334855, 74237814, 627333060, 466474433, 309560547, 670004761, 579756941, 818546040, 621311756, 63967494, 56364656, 416323506, 680552485, 82774689, 379994490, 471801728, 349735004, 415671384, 739852222, 142939580, 875399602, 919830387, 283480863, 669516666, 842972661, 487187648, 187399150, 725342505, 590302352, 448314623, 557320795, 731888689, 489117313, 411659339, 206081547, 50668615, 616114298, 700394393, 315918775, 325992699, 957734720, 370631304, 329643683, 611241411, 584414601, 264925738, 487803699, 499415869, 45118522, 170982313, 205300024, 539646532, 901765250, 617460007, 718645763, 620660115, 766097366, 992812633, 240435420, 535195597, 346682278, 705534906, 968570749, 323535817, 707518395, 530456876, 54656702, 938336673, 756436648, 316336413, 715109879, 155922064, 235780641, 73758336, 473412967, 607279089, 625924550, 649123887, 546777124, 141392244, 202594308, 81934320, 338819783, 397658451, 723054788, 930285247, 733775828, 732865202, 559220213, 547599868, 77988007, 287962210, 340376816, 184277348, 467527125, 78547858, 282532905, 192640352, 653162650, 797472383, 906796755, 829359989, 180655969, 100729461, 204858166, 34903686, 64386898, 145023595, 218970726, 142182067, 142625742, 919345669, 592684720, 791310915, 524092244, 57490220, 661664065, 487464513, 501086140, 653795454, 510041728, 561234289, 280274785, 707580117, 881156484, 766664319, 505969681, 684924257, 640462853, 653765939, 336045181, 821723026, 872898240, 401580993, 380737418, 97505267, 184648408, 175872127, 423850385, 910290356, 688763753, 160481575, 171816866, 155021503, 929653822, 256936855, 549420108, 6947510, 662855744, 898731852, 501207670, 727772824, 422514265, 851655087, 892667710, 957165733, 25363354, 489859575, 773548135, 772943973, 143721480, 691957281, 520108541, 784321518, 744726276, 873542624, 406617338, 724723155, 454258977, 951191582, 650873886, 353626022, 429528896, 713041096, 404495789, 681423771, 747366241, 843458903, 538597106, 403229353, 289759640, 323261368, 96385538, 229165847, 511065706, 47894762, 869062293, 608650899, 78284193, 485061878, 33818071, 124670913, 476786276, 545122089, 140230034, 846761531, 390097959, 715112010, 957296220, 362284455, 739487160, 631238597, 759189329, 250599816, 49207406, 463653130, 199377677, 825497854, 58983345, 879256314, 898566773, 838677620, 127477843, 442954492, 765816920, 918581671, 167351885, 801159793, 886528046, 734332096, 29501796, 729874078, 739915130, 738712028, 277965248, 804407935, 262121163, 656484239, 670502570, 547634488, 910211590, 197311062, 832616159, 884135512, 405322363, 763548497, 527264553, 699275369, 514526083, 233201490, 574891275, 87938247, 111576089, 325198144, 57692742, 991858480, 903661646, 136837510, 513931875, 916534679, 805504178, 346593107, 872867803, 753963694, 620358583, 3248542, 580055418, 28744599, 928193077, 268493295, 448381384, 865288328, 33480529, 503148223, 206347249, 174233364, 32448688, 617348943, 844458825, 374687824, 239754306, 690329394, 451510196, 945603909, 315219887, 895308530, 150372780, 533057566, 486072123, 121326303, 326151769, 473855725, 337931674, 811457578, 873908710, 285574005, 163327968, 362983329, 114278061, 917697396, 588277913, 874957703, 310691346, 221453414, 467207645, 587503239, 585846222, 548916687, 877235601, 872900539, 202415760, 297409377, 843383674, 780283063, 507016016, 47722965, 962278265, 446032952, 611967232, 861221423, 993609304, 106467817, 433214893, 753947410, 975652529, 707782932, 325737113, 760620997, 254238448, 215687213, 710880467, 738815036, 837411409, 759833505, 354085276, 513484812, 593535287, 82933625, 804058990, 430959977, 241779776, 563398483, 146945985, 859583555, 217792607, 571754621, 525202015, 680366325, 508292772, 186414385, 716169203, 528646303, 518472515, 185898780, 26223641, 54608521, 442807157, 163367696, 509776799, 282457169, 408864850, 475080495, 913925439, 44201348, 164008329, 239586498, 688126618, 535333792, 764082589, 273702144, 313555715, 903871866, 399360272, 816997270, 281691110, 842247578, 769123923, 844253664, 442959794, 863523798, 603611524, 812425767, 45547919, 581368802, 839707034, 595124266, 533717248, 825819211, 166599065, 1063026, 394415670, 655808778, 180560340, 538941794, 125644536, 989348144, 750553448, 979551173, 780768620, 787052235, 212874275, 619517177, 479597881, 503167226, 816638895, 790254675, 176336340, 644913779, 753808327, 785009477, 188555683, 601442483, 481360895, 285478638, 737706224, 979390231, 86473693, 496526911, 80179055, 218169120, 436318195, 148006521, 181465307, 576668273, 461037412, 788648355, 887788701, 361119705, 805717384, 488750799, 329701341, 746076478, 246633829, 208483151, 942732460, 845682705, 454301781, 367795314, 750624908, 541313067, 456332611, 595983761, 710807909, 354353548, 103302145, 513986271, 360544020, 503136858, 543864756, 249497061, 248231786, 691332259, 69853713, 963332493, 271145797, 4925573, 115964541, 197458382, 571950230, 399353232, 540827583, 53303829, 694246091, 359461225, 561646213, 231764413, 232415396, 51614721, 630212044, 657875945, 496163989, 773390644, 101974781, 689963757, 383424798, 542058927, 111719927, 964021722, 482079373, 39773019, 991854693, 981749574, 347248832, 949042323, 977129210, 113825863, 273940878, 637448664, 261541348, 993815811, 781745731, 392201481, 358552413, 17687945, 220105025, 369004988, 136071965, 351402043, 803390130, 493769218, 256108489, 845142498, 656897390, 416670531, 941403018, 688390683, 897321520, 327225009, 529730595, 226163448, 914550503, 586749315, 114833627, 960940751, 256562548, 7996020, 582011527, 453624493, 476264469, 956112498, 455155933, 655007998, 72360707, 952452879, 83832007, 516099556, 704269743, 631451326, 482230687, 551371913, 831718949, 182881019, 136031173, 165959551, 166577271, 449046493, 84772370, 354363488, 328518299, 506043458, 644124719, 210881298, 359069962, 48463683, 919631345, 846307891, 194902030, 337160825, 695147885, 242895916, 18595093, 340914142, 330583897, 322200375, 11121062, 264455480, 955486628, 511174673, 759064468, 948124652, 387471931, 382953738, 965830010, 501068320, 732758238, 654476736, 103363689, 545175396, 275860286, 698434935, 761360774, 65124022, 176525877, 676856402, 299344922, 517973188, 607394509, 499289422, 753243316, 14962006, 593037093, 210804198, 281281808, 304135286, 799820165, 807351503, 242935010, 753918826, 888203531, 100214192, 301761644, 619510454, 688760812, 257993340, 804472381, 818538317, 233616090, 848192825, 749146358, 342665224, 541132302, 349691133, 667403500, 606478108, 734977381, 131500554, 245016974, 863748946, 915473726, 28855630, 343722383, 184872224, 68011623, 374058072, 345730809, 483339371, 670132604, 851025423, 490300592, 37917688, 781597300, 862469556, 244844540, 106424805, 855751689, 968130344, 720808717, 731141916, 636582080, 975453081, 782783239, 266007638, 679725349, 196976104, 554579391, 433302140, 877460768, 430927002, 214119709, 691939298, 954462824, 610879285, 226477348, 4368013, 974956510, 755089581, 235840670, 103389481, 901456841, 324457331, 569914212, 359847322, 603654299, 286486900, 930649679, 956376086, 650226962, 686781761, 176835140, 135428992, 514690110, 530742915, 358229599, 437247778, 839208542, 930110334, 526021862, 277526107, 481347058, 621787335, 801869165, 448997211, 715802639, 757086902, 769039072, 39532461, 472269735, 319638707, 595834, 698429759, 23536034, 932904884, 978054687, 909884767, 200570729, 887635729, 866167182, 961678150, 657908526, 815892073, 858328300, 918257391, 385665159, 242751686, 441316547, 241598595, 336472944, 559991665, 640949082, 717965451, 912615443, 981818629, 535801185, 979562937, 280805127, 487854116, 266761571, 425094849, 901285554, 374309386, 804057924, 768993352, 646052988, 219613388, 819349699, 498402414, 14702385, 981458963, 747840998, 809715200, 237063105, 140110468, 952605921, 104563340, 902425042, 880987042, 90888234, 129092914, 373916309, 136420675, 67181533, 326339506, 927020336, 782636837, 623707051, 226543448, 728126211, 391332825, 595213, 130052730, 97008725, 351728897, 55133542, 885863734, 284648396, 482905029, 788372593, 918907321, 25105133, 144373248, 650518226, 468532022, 41023309, 278751871, 33511958, 470172538, 302850778, 235194389, 190315762, 491388118, 78558733, 621055230, 416230191, 914702066, 36740351, 135446815, 896208948, 794066717, 200178952, 72583287, 969802323, 50989391, 761540801, 165228651, 381239619, 833058727, 558920013, 998997510, 764476714, 799397436, 990249403, 570289496, 162587627, 294883055, 93075083, 545823366, 380519743, 232902908, 336745393, 420775460, 858391885, 161327642, 909251960, 692442158, 726478163, 470794598, 598773686, 343988150, 872407798, 750092470, 30278713, 358509267, 575490181, 44579381, 852017546, 890623943, 167454430, 208696536, 510219643, 258687175, 639757683, 726383610, 8019691, 715324976, 863827145, 492135963, 617353827, 394930921, 439028418, 571897630, 175155592, 499145978, 759179021, 111565069, 853403340, 271455748, 825961881, 446711290, 98010108, 630710948, 401979259, 493393433, 145803408, 608809903, 445185182, 152114459, 781577009, 944560501, 877347148, 537337744, 117437575, 10842844, 216489864, 868752893, 751259447, 780171636, 700015056, 772438673, 154293672, 759830297, 76938858, 582740552, 41867058, 866863894, 628643300, 128929614, 391825111, 774441669, 896452337, 107702255, 130318898, 525804714, 772264778, 715882842, 684055851, 357977535, 186812587, 195541370, 220361228, 33092786, 951932622, 705297865, 511301810, 541957152, 581812388, 230568491, 712321118, 714184419, 902766224, 303410077, 821520558, 574731813, 668887993, 749297568, 472716278, 907059330, 271069052, 666047596, 210514200, 984574073, 633956563, 324191714, 325816794, 512054867, 730149079, 466615858, 573278880, 679735594, 442608170, 770100343, 285728295, 742426125, 661016589, 630022407, 926772377, 321344858, 158763783, 521698384, 304789982, 265495614, 999628989, 293589970, 245760419, 700278075, 251378973, 590563932, 411175927, 668421885, 308702162, 213223486, 218538413, 171980924, 425542036, 962021703, 28859948, 162217827, 275672495, 907144287, 917293702, 762742119, 274473707, 799291821, 69949868, 331644526, 167926340, 442927871, 362611729, 209298835, 602341202, 373864889, 513569269, 992640916, 108882853, 447301684, 456500927, 139107436, 650001316, 557792029, 15271242, 985840300, 950366897, 570921453, 219148046, 353423387, 859443219, 671521335, 554535360, 373071904, 582236045, 710337483, 184974746, 885278093, 600716318, 215394942, 265871505, 141377576, 272055615, 211930982, 351926705, 389751579, 730756378, 314447026, 517510708, 120741938, 357486632, 311694689, 356440016, 261538824, 22507978, 864781555, 899637591, 772624133, 656239279, 32951775, 668842183, 161991947, 774720871, 554653884, 688371147, 461011602, 785420983, 901893938, 431489437, 80484455, 336921280, 75137890, 674041254, 982607356, 247682947, 746387959, 30425646, 585603332, 388729749, 79669827, 307588824, 396234942, 417506435, 230493242, 384217644, 557623285, 772880044, 33840941, 972092009, 864959585, 735263, 922411384, 97069909, 948776235, 947043026, 496284669, 330609566, 346097539, 164332816, 333157478, 797650547, 298772950, 459633507, 356188259, 996758625, 13888025, 308148454, 691305897, 66846545, 303802886, 818309712, 184927371, 601977840, 857917266, 706421901, 520089303, 20989393, 683599536, 670133608, 737339729, 634980760, 331809535, 405117613, 845066212, 870327734, 404126797, 570352075, 635099804, 64752773, 952487508, 710346637, 296339625, 828527860, 960436830, 617360855, 994866100, 639929608, 673458050, 36884551, 554633429, 647301702, 887039875, 553832566, 389069525, 757490528, 436785902, 473186988, 167061656, 624845687, 589223475, 319106968, 399027177, 370810432, 877203696, 223851029, 31541248, 562675713, 909842183, 978273980, 92090628, 691630581, 517836305, 287901647, 729356055, 745022280, 720190649, 186558518, 688000078, 128986956, 747737280, 823250204, 738095471, 335077999, 45291544, 507035198, 698836983, 745502954, 578453729, 248056668, 698305079, 990935081, 194995947, 914370716, 948321277, 375803393, 329701308, 419247131, 332504458, 57043136, 731509763, 325864923, 581286560, 783622158, 519707114, 591988203, 883536457, 61854700, 579039938, 938651771, 967102718, 139348053, 177411364, 438261919, 814517820, 250366103, 557034992, 611473808, 950429909, 632578776, 261899432, 394896492, 356600348, 290944993, 899254080, 131533115, 587380816, 905011382, 247500933, 70256311, 853309430, 823641750, 731205380, 651322618, 650635664, 235369470, 551544431, 700713841, 7329536, 649879063, 972391428, 264722027, 46276024, 754503663, 976612108, 397651508, 249176660, 572545434, 533857577, 357844771, 847153778, 289561354, 536952962, 197998469, 725051691, 444966349, 477843481, 686916694, 97021959, 767942036, 206088704, 165007669, 748039357, 578473933, 397399706, 685244533, 6768851, 215295946, 162548025, 780660068, 360678673, 9219384, 409107490, 532107150, 145664491, 912176691, 850381365, 35063609, 795623574, 497595607, 919994285, 829068833, 336461873, 814374788, 679747966, 46049487, 674627427, 606025854, 280955947, 572117156, 598066127, 289119203, 218146629, 813282662, 218819826, 134781018, 144306330, 80094312, 754784279, 715578083, 575949711, 837552408, 775468260, 38820816, 749497805, 213571740, 491644419, 334893518, 542083794, 917954962, 808712274, 559222718, 969772759, 155122569, 989498210, 445109833, 839758155, 528207037, 767870071, 184089968, 184785735, 322704298, 87798236, 788299681, 9929936, 502536143, 724779864, 321842472, 613656365, 603171231, 725514923, 85713908, 134445189, 712681074, 787827367, 594870194, 440379611, 12092070, 18346189, 429479349, 3054646, 213853848, 613745554, 950327339, 472915456, 842124827, 227030572, 562381564, 358271607, 736042149, 289731876, 151054022, 389852238, 64311782, 511699594, 647954371, 782041944, 67800681, 225866186, 506608592, 682236888, 107919527, 608934199, 655135089, 740913560, 880919155, 57127664, 106804378, 940049403, 214226332, 335587855, 272054457, 533418423, 229153210, 685756160, 628752839, 952299294, 54406640, 563560910, 273520092, 210547166, 674052591, 691143438, 665559559, 319449288, 663738267, 42031059, 687293268, 52852765, 382951004, 756012197, 790985263, 833437002, 640239598, 497028494, 319509718, 437428245, 758724027, 2657367, 47427458, 965574982, 428120917, 555747906, 35023455, 637140570, 791402909, 758391806, 981442224, 28934264, 970447254, 419000072, 604449871, 445360265, 407362721, 551303143, 891373825, 195984881, 484979976, 840003728, 409625818, 587744912, 616216982, 836798261, 98683008, 583805832, 911883327, 185874546, 851613268, 628861254, 427820235, 983404536, 443305096, 513793426, 614266131, 502504246, 515772037, 484478506, 990222176, 543845162, 318928680, 316855193, 211394378, 49039686, 175430701, 668207678, 927217049, 498277820, 236628520, 290788025, 658672737, 516331025, 849045482, 649723522, 473410973, 222787452, 253014185, 908881163, 620336285, 121147253, 217409935, 868843057, 803204947, 9764089, 518573360, 229830616, 366494981, 914149591, 44102561, 619159418, 522459521, 567017054, 77891270, 579730610, 486618175, 200608190, 220988358, 57375965, 526766775, 176771017, 510298417, 93328612, 901140621, 788709817, 203824884, 654930068, 951569913, 791007333, 758502588, 568305925, 35994235, 306802222, 775103181, 243305767, 76136968, 930272706, 8948764, 682519548, 462245218, 980862440, 7270620, 569812338, 547650407, 650868726, 786439987, 313287093, 639549114, 22035264, 879333954, 429856448, 175873725, 80067248, 535037487, 355138643, 305447609, 901118846, 601444480, 328039250, 703329940, 910798587, 68471739, 366166200, 162148633, 735418140, 442666997, 686360487, 238445656, 846158245, 611166117, 599402714, 248545478, 205639904, 68638776, 852107120, 220443259, 549792466, 860297573, 788465563, 725302464, 327328935, 856240623, 150726498, 447446540, 743543595, 568133808, 787583473, 559370004, 368587978, 472507616, 701192840, 364331583, 332878883, 491998785, 77398123, 567111265, 722508328, 224307096, 867385140, 44596741, 659298514, 365938773, 848344032, 188446501, 612727640, 906761489, 218547003, 619539359, 119998106, 326564342, 33030412, 19752201, 167554792, 690652550, 489232315, 18440920, 589551253, 157079948, 458823118, 220679422, 629279661, 583806183, 317349454, 70416496, 780721223, 689133822, 40220477, 226178330, 706140314, 950155689, 16042521, 100681873, 405804440, 987600653, 748609843, 464842957, 698792856, 345462535, 167822419, 714985666, 941584798, 410398964, 345166620, 900431177, 647908419, 656064010, 27684305, 81923327, 499440723, 701195437, 293905313, 856206626, 485687532, 954982280, 330557021, 530458366, 176036328, 814342157, 770545679, 254086743, 409061983, 883216806, 95866711, 194588473, 293669783, 313957586, 387930843, 410484347, 595271931, 409559, 941227580, 64855197, 313368324, 231320277, 779254399, 887827952, 682817156, 430458177, 486406449, 264202273, 130606796, 881171850, 359799120, 648513148, 974610738, 516709505, 366323203, 17925676, 362893031, 126989389, 456620049, 312161312, 442899377, 211977371, 514983815, 479306705, 72377630, 889691558, 167687836, 833438680, 376494235, 299623703, 872188516, 304906221, 802686133, 106901540, 469674434, 976703280, 925103843, 853132114, 250212729, 94584215, 307481149, 455822732, 91395793, 879054191, 789920106, 724008654, 952094636, 9168995, 722395754, 698091798, 965843440, 113397109, 36382294, 744862570, 691466008, 747417642, 178426572, 812099554, 940383041, 566845657, 811006722, 819861638, 876986016, 524821643, 787523403, 607454111, 885613, 196225231, 832846525, 407334688, 996627702, 713015117, 179911451, 619199599, 687090412, 205532899, 892324812, 829491481, 901491096, 148167278, 704586046, 81436708, 971049416, 48848918, 2376752, 567548736, 147372710, 288938787, 871021344, 729927204, 145226184, 958268384, 936481189, 606299763, 668019891, 136144997, 278605056, 23824309, 493574259, 474186280, 60282966, 780922671, 542121340, 813899872, 914489909, 808625518, 545866936, 181183126, 262239990, 277005782, 109622253, 915825118, 881423661, 857986777, 877157564, 939574465, 56654439, 591328162, 470192709, 821663723, 885509954, 176926081, 272183519, 56426313, 219914390, 943940045, 538453719, 718764109, 228045794, 368350402, 265449908, 302809688, 59767125, 52628009, 701574907, 545430538, 56120191, 938540063, 393582249, 60219497, 691593873, 15977682, 206098566, 60447191, 223046480, 628986509, 919613513, 311469660, 825933001, 421284028, 873753975, 153750469, 912772603, 208485470, 668508955, 113409827, 606007861, 831686180, 202689850, 481545853, 701089099, 87311409, 671789734, 658134896, 357299477, 478387226, 296366078, 574418424, 964168264, 456997414, 917265881, 246304982, 340459504, 748639839, 552665860, 365248410, 778956871, 337153966, 813388783, 149655311, 527358479, 507064701, 859130512, 946126139, 676564169, 790755265, 100270635, 902769193, 359964620, 421962914, 805434960, 580443099, 129575200, 951828228, 667001163, 726670454, 600049389, 943218904, 330588622, 118352733, 719166318, 267172501, 549737950, 976206124, 882325366, 982381339, 98631539, 837185574, 123563108, 974973730, 482203840, 23062594, 391897264, 464303883, 228977585, 707383385, 850150538, 343601256, 648872622, 389467677, 601595343, 720779734, 302484444, 262432069, 952999807, 875170288, 415549014, 631830968, 331582594, 251988254, 422067795, 432937295, 951653033, 158751707, 648793398, 481314004, 939708045, 123096673, 215198909, 130063212, 785024161, 455974181, 945032934, 5435765, 685210915, 701651364, 731772009, 937632860, 608142816, 836129326, 836307429, 929509035, 167867033, 438643031, 176771550, 525438888, 311286944, 911975446, 591826172, 33705666, 297066343, 977603094, 48719062, 512950906, 225543047, 726733785, 155483429, 490030312, 794184381, 938659817, 147863338, 416791562, 1217638, 237981363, 860677753, 708991333, 764201228, 185422875, 708118697, 698854227, 650240075, 648483627, 731274194, 430045789, 23319114, 597189953, 52002124, 628479637, 655395921, 584186824, 659460264, 873831927, 450816702, 420928851, 446149648, 438244573, 461061312, 511990686, 508592843, 827496984, 644948646, 408076990, 809849999, 532905759, 961977061, 488362995, 87508299, 6262759, 779713344, 813795059, 62778249, 532556094, 149599248, 835089747, 43040211, 610236968, 250133656, 539115854, 92941826, 191228593, 915744941, 525407472, 945600000, 39338476, 899140918, 982770728, 971562766, 833882059, 486631314, 377195791, 54816942, 980150819, 262518312, 148531266, 361588819, 659724413, 203218195, 582099661, 800070434, 692048503, 293495284, 815514112, 485476726, 225993561, 938118179, 259958235, 3591646, 2167445, 428506161, 32293227, 667206877, 385086551, 296932566, 425514726, 686126120, 390516599, 470948051, 675715027, 496158234, 942741936, 820699932, 740272207, 410943202, 911856989, 84646271, 662646785, 824420271, 517055488, 939739330, 567791088, 852677202, 388375169, 137380836, 544574312, 753808311, 620499034, 25513004, 838901877, 601511780, 560262691, 27768965, 284920427, 630157474, 299092074, 395601141, 687252455, 573556358, 652267924, 232882619, 932880456, 135186964, 691916649, 835494608, 309113268, 904624732, 661443766, 246142412, 630018548, 181226179, 289713716, 465606241, 31680840, 86418209, 906205205, 141959789, 814622348, 543856712, 551751570, 635551585, 316137611, 387706245, 268218004, 547922532, 759853905, 156095445, 807561116, 59605378, 57465949, 79735363, 679129886, 939351155, 884154653, 957817442, 894818817, 151565324, 728526447, 741462947, 723907984, 468012433, 521668931, 743904692, 440586730, 591953696, 921357064, 926918200, 189190160, 887011742, 264764457, 413672386, 365158408, 297384118, 337499152, 316622405, 740582800, 301554146, 179625080, 740693471, 880132723, 331806573, 789352903, 46470713, 595151962, 448170452, 994135222, 918954161, 736294264, 340531813, 251923841, 113647050, 82752426, 119113076, 636149680, 905172066, 132649007, 317102143, 50938916, 120416712, 962254075, 666797177, 954391864, 665643102, 723579339, 2926687, 431156927, 89565686, 91565734, 588337749, 621057525, 481579214, 538894698, 642500881, 501529058, 557947041, 114396651, 587523522, 18047272, 186474519, 789763401, 365014332, 51174386, 571858261, 287119932, 421247858, 993018236, 376125570, 495486704, 700967878, 16308563, 996136262, 247186047, 459524632, 296663075, 987095768, 920434533, 552711166, 335008363, 15583432, 757783673, 178579880, 743751877, 310847158, 69100142, 892984349, 919393673, 29733084, 860459088, 863863800, 113047149, 477263236, 419861260, 587688561, 843210099, 369318001, 889509115, 623881119, 614277740, 811085709, 636017784, 482320423, 668438947, 978243925, 780708407, 905011501, 385688567, 135630004, 49711462, 736956484, 445795937, 825755738, 781452377, 147416435, 310756317, 228002292, 688902464, 100282922, 316416389, 758376375, 177020123, 26516048, 634933424, 783455672, 301585248, 575224230, 964226874, 756692785, 409465541, 212464643, 348425635, 211487922, 901758195, 29698014, 170612370, 330891627, 408968507, 471038364, 921473432, 310949115, 227284619, 68411109, 290621564, 250825070, 567168065, 166524706, 353148370, 695216230, 905924238, 736157205, 204001352, 760010489, 278466398, 32235847, 872046988, 670489704, 462144077, 840572075, 833013949, 27887915, 3709422, 713227937, 233298278, 117449449, 718849149, 790870095, 361461349, 34785039, 987719909, 223554724, 921424251, 706962800, 297564796, 285729224, 481012260, 784560913, 482475773, 362200478, 272654942, 90278106, 290103657, 65335993, 845807475, 59125540, 250395692, 81614314, 769096700, 194402266, 418459071, 375097907, 892849483, 220914180, 80153984, 898006726, 411970632, 843644175, 304706799, 418371240, 577137207, 149131122, 198363414, 516762177, 67540180, 432226008, 160703025, 666772806, 351445111, 206772295, 38625417, 436410878, 41933420, 606291819, 27050121, 774946615, 459773778, 678343419, 914484653, 276117425, 964889428, 686262240, 802430055, 925877731, 328541551, 139344849, 907190217, 184140256, 286245732, 92422579, 806730815, 126968346, 364423003, 805812620, 147556216, 720221355, 253526599, 193617957, 943126589, 424021578, 369575691, 596575938, 866019566, 886508394, 409466079, 963734997, 698223349, 682223721, 136093700, 233362076, 99664561, 217893966, 114356668, 65596681, 348466452, 729678087, 832018299, 772870399, 117594324, 813198042, 414711675, 780408917, 679991884, 404844692, 627845522, 498185095, 507003554, 374749402, 193759698, 295676867, 556955556, 998915484, 545552732, 758742578, 296160285, 466582501, 16945618, 468271159, 817417439, 48139693, 96625173, 76226279, 702858167, 922735787, 36226251, 296935506, 831638014, 526644373, 41763368, 959457, 102657213, 698703000, 215661258, 990680841, 246480037, 501927070, 238661448, 593898222, 784616316, 879582074, 662714175, 457630494, 255684492, 374962455, 75665683, 820918420, 336820579, 63247322, 891847498, 728701375, 467875131, 162799236, 659503195, 37936845, 581179966, 591517806, 701886346, 328295057, 991170566, 482162887, 597077132, 998962765, 267016270, 241668109, 142907836, 476574851, 995801229, 435346129, 900492843, 308685712, 126777249, 548043660, 397696955, 914715916, 879892755, 943186002, 111549840, 240608138, 544509465, 431481394, 191435602, 540119677, 803929094, 682681347, 692192520, 879061046, 403724321, 446271348, 419301114, 262306367, 243339803, 585205655, 321585795, 48796545, 346941539, 565986863, 207455534, 212590238, 469157204, 153007321, 540906532, 334279246, 873914985, 979916147, 410544839, 624989126, 808827595, 833424588, 802251588, 513039552, 796093264, 628822362, 313640230, 587650556, 900819951, 191652751, 822809077, 194335260, 861451325, 356640403, 506310440, 345927443, 757350650, 975903529, 205731426, 228089268, 454227243, 523827298, 814257451, 917376836, 823615923, 9240561, 899181692, 458352194, 179334925, 376574522, 36325179, 479485379, 177445468, 339230048, 897266732, 662394709, 938853586, 901971544, 197744136, 23194304, 707416496, 637398627, 504960045, 754162127, 296764892, 150680309, 854627110, 870610649, 722214813, 299122632, 826674990, 859260937, 289043177, 187247884, 567922468, 77642446, 614762587, 939721335, 532579631, 200459015, 483960631, 968598535, 645766319, 670885708, 687305896, 85107756, 679564602, 790465681, 506689847, 319124687, 601307156, 757434904, 436022428, 101999936, 178134751, 715482096, 593040270, 59176979, 131445906, 657094936, 547305729, 11166988, 753019542, 8181590, 344979608, 411513199, 515528601, 28224093, 586292440, 556447834, 773305734, 871414971, 621302402, 419065785, 986267383, 464179984, 977140385, 333182168, 685383854, 305519962, 456087715, 619304385, 186646459, 745489107, 542767510, 654998577, 117640326, 86402771, 724242531, 728935634, 865180680, 455581117, 341056175, 326358052, 885721199, 711199965, 574717754, 225788400, 157083977, 705799260, 176244847, 35844985, 449164137, 910188966, 632542038, 537428346, 981423850, 958682541, 537904986, 755515183, 263792122, 673611819, 48195244, 689624974, 193692326, 443779560, 17726441, 310478176, 650850918, 340802795, 331114041, 787436971, 563026479, 617839994, 780439574, 823837472, 681245094, 694927048, 885154445, 896040864, 322783154, 603401741, 790918252, 363232544, 404086351, 12972141, 837918980, 353090751, 325717360, 940743363, 717081518, 27335266, 604492152, 945412355, 226129150, 125790652, 863827864, 144577145, 892920573, 994369071, 371165686, 742434965, 7223656, 865042216, 390477620, 22772605, 978846766, 682455832, 903101206, 370889578, 357021037, 527370870, 840134795, 253621379, 54966452, 677827737, 485715411, 403685301, 649167861, 382720238, 811816518, 15954138, 781015182, 313441582, 305678337, 416462770, 433272622, 165698287, 755371836, 545012992, 774658725, 698402247, 141658808, 253460598, 60598028, 279931269, 891609940, 741768409, 732213606, 205806595, 188040183, 489705369, 818974217, 685499142, 735935669, 455752331, 244187457, 98838453, 905883841, 771906771, 707884604, 295109508, 751211538, 307941931, 273653537, 49657790, 847927965, 103103201, 288026997, 289138612, 825749341, 386404624, 256006134, 979662086, 622427816, 604560039, 391177947, 391602376, 566311647, 727798688, 667506092, 325043990, 150346191, 277580429, 535368263, 357844051, 251661227, 193757723, 140435114, 664764995, 999095337, 21263184, 195925903, 856664404, 156945945, 846376356, 416203961, 247361047, 211301188, 5176075, 133050835, 372595045, 681821797, 58885080, 310782507, 820814616, 884861627, 566195635, 388947384, 672505292, 848939238, 286829068, 15514905, 572748733, 498290230, 741244040, 144398530, 388552198, 396312686, 144806125, 614929052, 560589079, 966406021, 852293323, 424922410, 513606641, 42728000, 848089600, 915621381, 94930046, 264783204, 224167793, 380789048, 364997785, 161883142, 54727510, 626264584, 306913520, 609833924, 912116374, 310688447, 344935411, 524348860, 201690112, 142263080, 564624938, 86047901, 961795129, 103615544, 241587044, 773422302, 151714931, 330033349, 972914599, 692500993, 201148465, 847452691, 412376013, 865400458, 476493195, 245435864, 951799723, 122663485, 244011054, 631306237, 312234162, 123663829, 544130714, 195888396, 643975234, 850948181, 845081169, 311463349, 928196381, 13014816, 873751013, 841971046, 336168649, 55113806, 875618942, 469306776, 581885089, 164778181, 626481934, 931033722, 630562717, 228046446, 719833528, 930948590, 583199081, 683249662, 565470455, 152949674, 498002544, 505572673, 695172278, 235079546, 496753557, 873585160, 834260403, 126932737, 598771592, 635242494, 344347424, 346008343, 580762722, 8799608, 674925920, 731872177, 831816181, 325526250, 242740763, 557138314, 51588925, 662718541, 260279012, 803795845, 720121295, 808438364, 981677965, 683868449, 280049909, 144268717, 684952758, 79586079, 265766989, 20977229, 714609876, 85821647, 750345924, 539110373, 424496278, 92828622, 329279338, 155253553, 427374362, 615242971, 685792250, 254871217, 702862477, 727021308, 249803095, 6755081, 894489004, 511938717, 74843567, 18087893, 899867854, 315640292, 630344701, 275866830, 717485284, 731948916, 390906332, 589461429, 996346466, 800131796, 440370287, 866512857, 454489484, 1138909, 374348359, 315920739, 714589668, 432075543, 206061029, 191289971, 327224589, 301888109, 642593029, 233608827, 328352613, 256683307, 196127307, 214686127, 633838599, 533391989, 349731951, 120091228, 324801824, 876885927, 231098057, 493960921, 485711729, 241223631, 302408037, 595008768, 335550943, 214021691, 258815200, 893996520, 604946047, 91313590, 312057918, 473467789, 901673959, 129826938, 372965272, 646820176, 758432734, 158749866, 330220997, 38616981, 126221718, 127071531, 486102216, 292756059, 248078561, 797640945, 355294242, 812351006, 547212933, 115696738, 349389655, 980074232, 258783480, 472165967, 635491940, 368895025, 215641088, 543362095, 812136131, 567193831, 746210514, 132079149, 486760714, 297755703, 857672904, 260088726, 209663220, 557695640, 934341130, 264187526, 689714443, 630211332, 114697769, 289122476, 820911383, 267923660, 389252105, 506805806, 820320235, 732279933, 381884588, 174939179, 50059783, 7994802, 261801053, 276800367, 406094047, 893895193, 317537371, 361530518, 857549024, 860619859, 591484270, 288443909, 216093183, 251957920, 691123868, 137672690, 981487389, 29526494, 288912688, 832851416, 375884020, 55944692, 471111503, 905446108, 842589791, 419403521, 134686239, 146014501, 965011868, 441820228, 770697239, 866016332, 421514460, 956665101, 377423377, 710631422, 184870049, 52623389, 498369168, 465512751, 957359888, 780035658, 35461448, 867950557, 988895917, 368916876, 950176152, 663096239, 628766161, 540768368, 716636609, 867084981, 726183856, 175515075, 130030299, 82683598, 106246389, 360863678, 210129500, 467343843, 2318388, 856425874, 55529701, 116403957, 702518153, 491423385, 844813040, 19942056, 90318142, 321572695, 507742166, 888473579, 343082511, 280389896, 88835941, 581695546, 84598378, 202118379, 707715476, 756838549, 506609805, 549950854, 742742766, 184316849, 511046619, 244141767, 41768375, 526217850, 852458073, 930137622, 209534726, 423634317, 425470857, 445936903, 748008496, 918187912, 153025384, 471995314, 363618227, 632965112, 804152082, 774661307, 807305321, 982683306, 162586336, 846290934, 470804293, 535477668, 54662840, 448874964, 990451790, 227893794, 493706324, 355881331, 799146813, 842529920, 743154338, 552863863, 232682241, 622066956, 136204551, 382934685, 407859651, 962259736, 119425259, 252390571, 909040082, 902226263, 917362181, 922457746, 599510740, 851408421, 548311240, 30995963, 331127051, 168022150, 911527150, 500390856, 280389797, 657971847, 362279407, 428081231, 520439765, 68580530, 355801, 686155522, 337295776, 221185715, 713424884, 12280284, 617597562, 887213138, 308245939, 672692727, 680488699, 633224510, 515241320, 274749018, 825154160, 376171522, 128766550, 778431237, 572370335, 423559891, 548418830, 306606007, 587546829, 388301133, 547076168, 21248210, 961860821, 202547496, 165516392, 344038976, 952521120, 808280928, 876340438, 923380847, 970923831, 132815264, 56508866, 984231586, 714875291, 966571995, 735452228, 743284770, 486341209, 866594768, 266974709, 623678648, 860622002, 255614012, 587485440, 889026045, 531789315, 252849562, 995395725, 130605159, 619512146, 244031476, 301347553, 467858292, 522756650, 561729337, 346498475, 94244307, 961610747, 20679859, 53708481, 714472922, 673202953, 199287217, 629198856, 531808628, 148709767, 303612048, 359846394, 778511783, 55219169, 496286508, 684810883, 649050284, 815385750, 521532756, 71257786, 309485104, 868808462, 804709790, 540082980, 171944137, 581849314, 163383495, 131849873, 34221148, 549957367, 246742800, 820694402, 723718335, 450582097, 707959421, 676661475, 622799772, 787306691, 734266000, 348778684, 425913247, 625043188, 992747087, 293315236, 23917881, 78857065, 131803311, 797192249, 923062000, 35674380, 240276217, 143199705, 68313186, 700017740, 71335875, 269191606, 719530552, 321790148, 424321912, 781275466, 469541853, 995994694, 810100340, 375309275, 779013989, 735441089, 413014578, 644069270, 345403330, 720256229, 651788483, 799146219, 966843581, 583542007, 972385090, 873694543, 450627945, 373153408, 941458443, 993320752, 948321409, 327641647, 392092151, 695343062, 396527136, 332908455, 820621633, 433173341, 154842661, 879402165, 102882936, 900921324, 85970222, 277368188, 511079849, 408719452, 437216929, 134941439, 125832629, 6505561, 710884233, 36916137, 415427911, 872948777, 56962124, 829900676, 289500345, 171944690, 153088584, 821857249, 605658069, 550814406, 625079551, 326458714, 395875587, 32056224, 57837929, 111324629, 396359887, 981934238, 89976377, 55066562, 657210197, 627038060, 434998175, 394638254, 480619608, 347533477, 7292997, 742517742, 338707521, 314341897, 164228952, 776024837, 980877699, 655162478, 967955650, 563793718, 80994582, 572102819, 31711095, 957252300, 798979490, 362945174, 981125241, 272504073, 621143178, 9462265, 198991530, 291852837, 495732368, 499880289, 68969488, 650295991, 263942364, 326494246, 719069375, 451323953, 370320919, 268483784, 463229443, 967801425, 34502145, 501138741, 841531297, 461853424, 993211713, 729015662, 210124973, 576237851, 768776934, 919683306, 42758242, 636105662, 903712657, 503670968, 963622420, 336880597, 737029487, 484555997, 512449774, 943773030, 660603497, 489925595, 785093058, 329602160, 593653695, 112084744, 116701873, 928621580, 740412980, 538256514, 535475314, 608504786, 665384475, 499709270, 204902890, 921753512, 234450652, 947715833, 134125134, 962173227, 948087700, 552293213, 143737591, 438869440, 566165094, 844016668, 399614683, 775482021, 319762836, 687246378, 274150320, 448374985, 659411660, 931177386, 637775575, 564100716, 747650900, 431424876, 976659110, 58047318, 693348530, 244861339, 610178225, 257635705, 994680710, 670162978, 217056212, 801206184, 634104896, 316602441, 179668043, 707590532, 594871942, 644923389, 29936009, 222948288, 946320649, 252788953, 333116109, 889607623, 881254454, 764962617, 288217113, 300232731, 730783068, 893873697, 22660712, 994155535, 293134370, 830155520, 124049792, 442088081, 105307522, 168737004, 703051199, 789910178, 642440838, 459561794, 626887772, 750824261, 366832648, 310214304, 513664657, 6626312, 721932290, 530392865, 331793315, 661987045, 400027443, 292065583, 959314828, 113229573, 687429650, 426065631, 668314610, 811646207, 930420646, 146916252, 577953035, 816171003, 854071446, 780389219, 647129521, 208752652, 151473367, 873207070, 796729974, 173263214, 370095027, 727617979, 585174769, 215098243, 971912596, 598875928, 721882283, 550649418, 912847526, 55009752, 343288790, 346928340, 460531000, 680694044, 238714263, 884044681, 184009043, 21534691, 831145707, 677730809, 472307949, 710709636, 481184261, 389235267, 628235351, 412532511, 493818200, 830983144, 446530226, 62273591, 778097966, 659106386, 949679916, 863037103, 806339375, 647541377, 562668582, 258350894, 767275019, 51185320, 929547290, 677925382, 657271962, 463144046, 7598987, 131871410, 644584899, 424950380, 597489200, 47575533, 986853735, 766687219, 612938482, 412137279, 50111786, 39055907, 457662910, 590159604, 290568992, 412254998, 848695058, 214559455, 867128832, 978276393, 548420269, 818005475, 424144877, 696481153, 693858371, 417776430, 118970781, 588049837, 428377209, 401368303, 868666565, 741896562, 513463457, 390949740, 745559919, 895521180, 825141662, 95029779, 965521217, 534614447, 466231749, 597247473, 159058428, 15783729, 779355606, 987266220, 754195341, 362278558, 67560779, 54188219, 198630214, 589034590, 824705149, 162516494, 810725801, 674573454, 764116278, 456756928, 173214560, 642546202, 827170383, 424092195, 865818909, 356397340, 325047161, 697551635, 583378174, 11029285, 125090288, 622267723, 617940703, 845814762, 420533074, 887864783, 540499308, 120458400, 786571590, 321377, 971887311, 586723394, 906984339, 37670420, 553185331, 456900044, 284127243, 665438086, 620542533, 644875631, 395785341, 741618055, 46763733, 103146331, 581734066, 647582991, 271376239, 522464577, 417001352, 901266863, 364156478, 128305690, 554177636, 107869956, 898091237, 860624166, 194273438, 835447354, 740542300, 113563114, 706470003, 979043218, 622936956, 526417039, 525757845, 367066642, 493307858, 72754907, 566634746, 779387624, 996694820, 60261497, 834998299, 398781199, 465452537, 759915044, 451861417, 589194100, 203958624, 520632060, 282569133, 252980596, 283375976, 805297980, 943729517, 411706877, 143331370, 108592269, 330496074, 223336525, 814063695, 195360198, 791407228, 267995602, 357301508, 296791470, 874524896, 794982119, 735661473, 540088158, 980883434, 729154386, 890670849, 779873114, 13359235, 568630761, 8221343, 941334671, 945470319, 704275976, 602326976, 633278148, 553929571, 32334953, 57482771, 40824310, 549771390, 458942956, 827320380, 397058471, 322218224, 99497286, 124774180, 573989323, 240458374, 572797234, 77060934, 883644730, 126236418, 528907394, 142633364, 993959306, 323834778, 262853583, 725643515, 607831378, 788125932, 764567302, 18332817, 351588255, 814949145, 515285230, 368522124, 853764797, 28642597, 74411268, 129418418, 40023002, 336622507, 180813987, 5434819, 303432278, 392854973, 288775593, 721612199, 479413911, 243246717, 293858870, 673066411, 454354933, 264802686, 766157661, 512108498, 206708193, 531728087, 1961185, 798074698, 427415692, 211735082, 265695521, 920186845, 641622533, 241745568, 291284695, 292305658, 935398378, 355597712, 939417220, 601943934, 265538032, 667839948, 372650809, 300761874, 580692499, 845446989, 589802248, 481194707, 794430214, 198354287, 192468243, 363605861, 501435035, 348694068, 991993289, 191920655, 20099653, 579058593, 162285112, 518058772, 743721051, 711717853, 776790937, 616905328, 80974608, 876103520, 610414065, 27975247, 26438815, 166737454, 967901999, 743214267, 703515050, 536428737, 978061031, 935264173, 924251998, 337992971, 733463029, 218397794, 878350319, 401780154, 36995050, 941857545, 932966663, 719284937, 569910526, 359510994, 903696247, 515044359, 3989503, 811825063, 577221427, 524675567, 559085441, 872444085, 479396545, 351988832, 246091357, 921402258, 154182947, 349633493, 229428793, 474381495, 828414233, 417358382, 823012525, 767149620, 711466170, 117593017, 252084811, 729317428, 623267683, 164308394, 546533448, 117095506, 865066033, 306471173, 107957898, 986359077, 599141213, 866509403, 730171328, 507033514, 435937348, 640183396, 490796943, 180767400, 917110408, 49102307, 723026434, 37374062, 739431450, 436978473, 498834922, 146719759, 694200478, 563692939, 664566225, 34825771, 910437487, 530775135, 150971335, 938679477, 889900379, 441863979, 265082541, 177939638, 585891637, 319235807, 16721120, 260882229, 956328858, 758505656, 299441462, 624300549, 592629688, 542732495, 875811897, 482146160, 718184444, 892832540, 119841165, 890436302, 641724305, 127487048, 2547731, 710047342, 485372820, 328031116, 932137784, 922695609, 791323347, 928544862, 646831109, 216647239, 223043597, 565822266, 709362433, 358023577, 30814995, 963382680, 966278826, 842050410, 307850411, 18797355, 947811235, 689728487, 375251689, 620052348, 689007619, 370892134, 157176249, 46197685, 951772530, 110240202, 989525723, 386087354, 892991134, 7947869, 469035346, 596752339, 202114148, 729682084, 371908991, 112398537, 277829927, 257411397, 926701566, 503052169, 473964071, 155681867, 565359051, 545000770, 755084478, 19163338, 532334095, 14247541, 660555305, 375646955, 722984329, 209100206, 158670568, 559066793, 389285600, 533832801, 774070416, 184132980, 534817166, 529645805, 541559784, 319560840, 600932808, 812955771, 950609735, 653513710, 960721993, 896188005, 985289357, 202017650, 385566689, 280554431, 78322313, 867982586, 814222196, 656505736, 949017387, 594764588, 56397573, 219808097, 666649776, 164764857, 530314474, 860247611, 632499954, 988980139, 596191408, 33596551, 29987940, 351326109, 466488595, 746534625, 624814682, 625755647, 84131063, 153876250, 706328838, 733971914, 502705171, 259898865, 869116666, 132760273, 800113220, 389648307, 39563575, 125024512, 524120662, 262419493, 985276631, 228356738, 653480521, 728507977, 548815334, 669388929, 651283894, 615218238, 860950164, 764226785, 53388328, 974352754, 537948675, 21098326, 63563385, 573251640, 4990792, 814541506, 592599971, 508286218, 213309392, 585990422, 861287244, 530410610, 937996518, 270505649, 614883021, 924992889, 491206884, 250801231, 140207921, 613343919, 509565297, 384654980, 777000083, 685613357, 690816891, 12568180, 459597813, 852696562, 845014380, 801919037, 489917558, 479058211, 644060221, 610182621, 332514153, 547363341, 309631252, 618432967, 595797047, 139380703, 40597037, 231518728, 371988395, 860038767, 433052152, 504598165, 713445269, 194639675, 592877364, 572670260, 257745164, 494617779, 664515917, 162072879, 780192081, 549165400, 304232620, 910992394, 60845477, 401121076, 820226580, 507960553, 99093727, 114388004, 584406081, 858860735, 340590670, 170742417, 345510076, 414273350, 301646248, 365207107, 749736367, 51285652, 352148061, 112608516, 575839494, 13413833, 405337218, 139927339, 183237450, 7605675, 602378093, 772849971, 577827745, 247839479, 73471241, 543236760, 611936685, 476570150, 913739351, 601044002, 517352209, 504721665, 253951513, 342923240, 52908852, 667691157, 322525120, 626519203, 625372999, 179460258, 584401411, 117668295, 196589866, 538254071, 916390006, 588947190, 167039796, 977980084, 509760877, 382480052, 565103444, 459117307, 654034552, 662256293, 450325783, 159143013, 38590359, 624577468, 81575174, 201090044, 435304335, 601406954, 247095837, 525783156, 223599561, 410390116, 386481786, 669638482, 801927006, 608971246, 424064193, 38390041, 688118830, 487694207, 208470037, 250799807, 877520736, 454315164, 905869492, 996912324, 552272712, 939395596, 846024435, 473130588, 390391558, 511776775, 443456264, 339379968, 772976794, 527567908, 611181482, 726583227, 760076668, 328077256, 987750912, 612640063, 864353081, 648464478, 694474359, 608258084, 573378377, 336569178, 492802046, 207782977, 743094104, 231781774, 731082472, 638166581, 621718742, 371849087, 230709424, 7323962, 430959270, 313228951, 876001330, 839931042, 509304387, 923639909, 556775506, 98517387, 627834569, 311355269, 81996313, 686253763, 800611643, 34179007, 252435792, 245329666, 900127837, 607267349, 540381982, 73840234, 224172364, 243924492, 459785494, 621507996, 324701279, 772334024, 356930258, 760010938, 810320643, 298800241, 166509615, 947461673, 338378519, 295995233, 159803743, 595387154, 37345812, 244577444, 63521197, 550441603, 24638684, 37221413, 658659974, 96052689, 822172044, 934842076, 107560786, 899257841, 459961510, 33980624, 134019494, 472714658, 316847527, 729614888, 571830628, 631374627, 85128057, 558818344, 443459599, 804751380, 773551054, 414356889, 588960756, 18467686, 413004261, 895245133, 317048395, 664489187, 512479021, 471554592, 94276977, 105261595, 433696084, 48309988, 48479733, 727761124, 363190484, 935866134, 585542856, 784984698, 308500231, 863667775, 755786610, 310044115, 299024371, 140506926, 760939634, 89287573, 880016212, 547635407, 646847872, 944545171, 583381352, 476391055, 662033915, 900916689, 124637157, 642420341, 575880834, 220295991, 642323266, 323175146, 801396356, 153020753, 833543937, 774391494, 973169866, 548287564, 670556041, 350675532, 64874626, 147750883, 943858260, 218468977, 136998701, 741710081, 757763266, 394612758, 84699931, 212879053, 455918103, 126157666, 576574014, 204081762, 948922286, 212510838, 358031587, 611408924, 353439799, 618816998, 161331627, 518347808, 654408897, 492076830, 826347058, 148351460, 494174485, 805910868, 182999158, 114566382, 532865295, 650147231, 21045727, 747839694, 344933762, 755066599, 915644830, 283724674, 921568689, 572343349, 28826776, 109642928, 326017282, 288261904, 616971234, 474804103, 47410468, 921558871, 274690799, 940600349, 569879983, 99375586, 177253988, 383004369, 86263554, 892897772, 993383295, 635647816, 611276397, 413548979, 797656644, 457182631, 323336878, 948329663, 816307206, 463702514, 7764597, 533771533, 298778576, 744029934, 731006120, 59924984, 735703923, 409947267, 732900462, 685238808, 585746258, 825358955, 385562306, 471926399, 155149896, 672783873, 271261198, 362230916, 299278299, 63119430, 40029247, 965247374, 931327060, 183847865, 968851074, 864277792, 60745440, 388317802, 528742388, 768647371, 988498940, 776574556, 258808774, 409377615, 654653727, 506032311, 325210677, 21748680, 707432358, 82717115, 102465784, 566421390, 351157539, 531370080, 31814106, 243695939, 873484172, 583982487, 186029921, 180368049, 972608087, 803802169, 314129615, 615160558, 787379451, 427472026, 911673120, 125168716, 39398373, 908924573, 582831826, 137315820, 774460046, 440664294, 355179495, 522298761, 479312770, 91008834, 737161029, 524296448, 349439824, 410784859, 271159281, 534175769, 431981265, 763332873, 930810901, 969273844, 563421876, 84193865, 426991220, 889444865, 866700214, 817763413, 875472158, 305880246, 427631434, 431688630, 328841383, 147893156, 342541079, 29756291, 457107144, 91985340, 669789975, 389204767, 585962960, 654518387, 829134220, 543622880, 182157608, 878809105, 329708105, 815406844, 928884407, 206343963, 781921689, 527461545, 757458755, 118935369, 901148351, 598937838, 818375226, 485714951, 35164081, 742283614, 916843728, 766656773, 521184156, 234974025, 239456823, 169297033, 280478698, 576023258, 842810482, 498642408, 932635013, 85982958, 531915263, 777627152, 260796077, 852830090, 127378125, 936758434, 661676088, 102070441, 779742155, 510607475, 276891360, 46178546, 871545510, 226330205, 417547769, 759170098, 26051044, 196964504, 641774658, 864383507, 438389415, 488030500, 38248196, 130654416, 306930583, 95153180, 442770074, 351939447, 191419631, 514996872, 251400898, 515732148, 822125627, 478659806, 951919548, 129345145, 647941974, 893227688, 892993670, 890708424, 642861352, 589963918, 78874596, 757942531, 553792268, 143293346, 661786467, 413601693, 84550560, 780576751, 95706687, 115234170, 10052162, 166566784, 485173505, 586697459, 932658252, 891021236, 77335201, 993241236, 972496440, 596083236, 282850677, 11947818, 333454539, 19210033, 710069833, 364024685, 879612268, 257289298, 856633024, 488367314, 976854737, 310367617, 772232249, 495260768, 467370790, 728821813, 890755201, 936714283, 686693007, 860207758, 673341894, 707767677, 828045547, 798920876, 955979922, 935763449, 130342599, 558781125, 33448879, 915011681, 106777839, 845448855, 238199847, 477838222, 736908183, 923139337, 427663496, 286406495, 863033972, 451129759, 473731131, 745722358, 307056269, 283473053, 883310935, 304024356, 771212419, 815713177, 65955335, 847549624, 880423290, 582467647, 685522404, 820804018, 535002781, 857111, 207589809, 958144209, 566914200, 741981708, 904097151, 982529342, 464366860, 592861019, 423229553, 542569478, 346226650, 113753782, 286108177, 199775978, 683042635, 854683567, 197184607, 981852, 8664388, 568050018, 876611420, 259390607, 236262712, 10261401, 294761581, 267030174, 896403218, 103947656, 30147920, 871248877, 377254307, 648462458, 790709063, 590129098, 406207023, 585250853, 202622229, 818505241, 117054252, 394794914, 696855351, 749033487, 489496590, 345094375, 679583837, 178173194, 574466561, 41167975, 271240494, 479424005, 975752818, 833337885, 251764267, 295438891, 979596071, 766107207, 556155685, 690346627, 644854826, 99033357, 186961047, 995205302, 639887846, 303810749, 806504794, 641497575, 489110580, 604315628, 229748706, 76742895, 97408008, 755842593, 525745399, 61730974, 999544288, 871636422, 907416890, 119091676, 208590241, 48047630, 415232138, 415971828, 621138470, 94268715, 299921949, 766009358, 291883148, 611834651, 616223149, 437098838, 866331745, 627910257, 929119730, 673220859, 354636353, 905668242, 605829789, 662235383, 883267914, 898478728, 52767748, 115739151, 578914156, 821391526, 451301543, 952712619, 465741352, 179540047, 986343792, 284763612, 249837592, 734427942, 703970399, 105861838, 282164548, 442603476, 131750286, 746279419, 399681064, 887180647, 451109540, 475405289, 777934325, 217772475, 229725819, 486887842, 396447623, 678485463, 959747959, 311148006, 978537181, 788933855, 890828207, 585365295, 979148467, 437061933, 781586707, 686456887, 366187528, 109277747, 960366493, 701243595, 277970318, 94603239, 756050020, 821626446, 901189589, 702299423, 202770401, 712845241, 340108414, 288732063, 870961652, 249523182, 710391599, 969673635, 963119399, 342469704, 912956633, 344066833, 748854241, 870479072, 722799607, 998829866, 274145009, 548183174, 89243200, 398964153, 900829609, 489742572, 413035945, 517839797, 692731634, 110954633, 818694677, 835567979, 543470894, 667768072, 229269574, 270491169, 743937477, 893922580, 460150625, 416291835, 700713341, 20765521, 835913743, 998332867, 596839441, 306107931, 365289660, 507633265, 890521127, 332740616, 278531095, 580376018, 845896961, 779988087, 571506201, 642338044, 877898886, 560041696, 206400480, 645865886, 371929206, 601759004, 48837290, 870336002, 857981206, 976047095, 640285633, 185351714, 212438211, 939681169, 330821192, 86114897, 352951049, 577387632, 948523714, 445408982, 765357390, 83973173, 37785149, 459210029, 940343250, 312983310, 190549130, 41750091, 967156706, 583083992, 279433345, 769259269, 240788305, 502064298, 356212386, 780293562, 283134196, 981292667, 641249721, 98546513, 195770425, 968897701, 865721531, 556402517, 599908514, 319767955, 928703544, 208215054, 459412125, 315145328, 534782437, 641474392, 976608756, 629158859, 330923948, 650715628, 885391179, 453599700, 899023922, 180390635, 800589423, 61964397, 279207185, 739157481, 624788510, 827722199, 314895517, 923954430, 2257847, 993759404, 492991104, 225590319, 157714890, 253023488, 490708026, 23707536, 142973892, 246224099, 607669378, 562950901, 493132909, 66257271, 227794403, 476810447, 349191103, 500977785, 167960628, 205799920, 194015344, 476962796, 403479951, 569094768, 600325967, 804869249, 763945002, 376534838, 69646092, 783696146, 258292664, 608725399, 363804183, 460508326, 876305477, 558624242, 367419550, 564442582, 160696685, 982804585, 978204388, 179406453, 877887388, 665231144, 666117840, 189732025, 465789569, 92887371, 784904848, 248242221, 251435079, 540913722, 760482344, 677683599, 567366009, 141751623, 18225575, 783380287, 55275881, 984332958, 715287428, 249200246, 454234659, 672316234, 810324933, 978061156, 919147992, 135807936, 818919845, 488612346, 126249991, 495454650, 801650687, 106474796, 165406228, 636451057, 947737341, 235391093, 510993798, 352843623, 931245781, 780974043, 247325768, 927363705, 391754928, 449119040, 172799241, 889850245, 689781083, 415628069, 816168114, 743117679, 729943496, 488567164, 822902773, 297250122, 903459937, 357579380, 212455774, 765683557, 490572175, 464633534, 448349988, 601822913, 444834033, 89377675, 709674004, 724627110, 317502820, 619579117, 185722428, 312179356, 638468343, 523126627, 328264659, 977728633, 741876311, 465205294, 234409756, 371036377, 269516102, 596531317, 145690870, 963719434, 424238263, 592305189, 12674139, 690575093, 69967443, 730819162, 509321025, 527096999, 960880832, 307446194, 920563962, 580840440, 605644707, 548668294, 389722448, 937509339, 223062448, 410576667, 209999261, 628349231, 416054777, 440535791, 775871516, 31645637, 508285427, 601060219, 724038098, 968183045, 330967813, 629108484, 922031418, 654207020, 965432353, 228093624, 82057221, 244140668, 371624641, 374667852, 961533171, 741256429, 152792018, 328493753, 900067562, 537971098, 412490563, 413439703, 159513652, 200884971, 95941788, 912302220, 222491912, 34755627, 696044630, 920549813, 130069638, 447906413, 370081435, 697395386, 377447091, 560499327, 977835229, 731975672, 858677072, 411793079, 150477489, 587126173, 38884493, 896777077, 46762150, 973787878, 738291010, 5913864, 293174246, 427248136, 963824567, 301946759, 309408830, 256384362, 705136512, 304027921, 434270894, 9041133, 740102315, 357696065, 980443911, 35594251, 721680917, 225939056, 37849216, 836529804, 207005375, 408726138, 357902586, 365807531, 309659246, 228547226, 169206737, 866360599, 24894611, 319567879, 698216238, 543886957, 179933846, 902737109, 474391668, 797456935, 702284936, 213657310, 452392966, 305525122, 746695983, 17760309, 622503386, 336345237, 989816497, 84148170, 264145816, 643274534, 9198265, 534165934, 986819046, 640042614, 198331619, 848322823, 135473594, 325767229, 709320842, 785014562, 395978076, 730188907, 797215092, 701660513, 367596118, 671046491, 768124030, 848189270, 146608172, 792395148, 807400509, 235756048, 139675401, 149122187, 968222600, 105441364, 80572030, 336196915, 277310241, 698441957, 347015559, 450321779, 415927374, 324950751, 304490733, 847917488, 817060164, 788598376, 28485136, 157046577, 956831484, 548591730, 425299744, 389963381, 436355103, 274306471, 391691454, 973025100, 85449634, 832671099, 824737436, 27881003, 162464261, 3480401, 692275859, 818619429, 381572141, 993825316, 729453749, 116373278, 111261009, 99652910, 800585579, 327991921, 348729161, 504840896, 947715587, 253593330, 385188498, 204545161, 816619908, 674789369, 816717127, 993993457, 164867080, 363821005, 641246221, 491090155, 129367157, 409522754, 823949342, 414125684, 987891851, 371146443, 304879737, 170541443, 541022487, 743450934, 159912681, 482695654, 647779348, 753689424, 2693238, 319319855, 834565107, 145657413, 461225572, 783719917, 740520313, 220089484, 121999077, 265897920, 864685459, 503333411, 541312218, 923265914, 904301436, 443181132, 889569623, 495996244, 979912522, 71874121, 432914416, 158909995, 972687516, 443554980, 661239446, 696440468, 575715731, 433036798, 678218421, 202452294, 274027097, 981117579, 463711252, 354215037, 19312990, 49008098, 470289016, 531405895, 649721317, 813264027, 371624194, 277775472, 96054708, 823273221, 599650864, 528748538, 246083244, 656381409, 828118423, 939584354, 63215315, 587086759, 537194882, 952938738, 753663781, 329211367, 226301294, 244824056, 54919220, 192505517, 903291479, 917633846, 528012927, 83319616, 438588809, 370078780, 183565882, 158944814, 481346400, 112864559, 265974599, 281522129, 662428856, 941070613, 964087745, 377710805, 892127637, 798664228, 45072875, 952900706, 783998352, 790063837, 402446572, 607575848, 656822372, 477052789, 281378975, 935749098, 149737628, 679982744, 60865403, 600776789, 600403497, 627042074, 526807132, 402408586, 909277748, 570437413, 718939138, 361947850, 976028758, 80228267, 717711572, 717864672, 638471455, 700884440, 184871712, 971114074, 374419475, 117177706, 967229485, 278369966, 649146525, 751469851, 569427315, 208321560, 874638448, 196466672, 122928863, 263787883, 610307824, 603026847, 650244300, 211295555, 305236180, 97799444, 273851956, 86796706, 914093261, 372017817, 972302369, 204100362, 569667199, 771555873, 884312329, 558703764, 206502656, 628030187, 701030356, 450655172, 605381419, 706247053, 74520617, 568287074, 439555279, 295067475, 26291789, 324206196, 295591657, 31788332, 175050434, 140599094, 685822171, 256293006, 88083999, 240306629, 862633353, 778765140, 381467615, 900242240, 364415891, 383766286, 353196278, 585488714, 410014171, 565319775, 270020572, 588298360, 710429125, 315992273, 206439882, 518530832, 4360922, 569764779, 62494365, 377348279, 700301108, 948231005, 526972636, 33203992, 67903819, 325772967, 327062962, 252529499, 615539381, 437210207, 439463259, 929774785, 846325792, 712161525, 377726355, 308729513, 608493610, 677246892, 929202142, 873450290, 835979119, 140976385, 267613431, 737388934, 502846962, 383817944, 214534815, 735196856, 419885350, 284275878, 298925611, 22767546, 68435888, 736139133, 63866352, 268872711, 988210784, 771950070, 5785483, 235479247, 401646773, 67658814, 60916195, 589055802, 779137673, 822790623, 225322290, 348174868, 147026335, 570926295, 253837622, 382129048, 632049395, 906715473, 690191510, 326403229, 933301029, 848966468, 440357746, 379008665, 162391163, 372819054, 870000088, 707430315, 434351603, 13007650, 460633467, 19613315, 495747725, 392986385, 895949623, 287992204, 105641445, 210709210, 230761842, 363083335, 654218611, 69476690, 653781027, 393490916, 610303675, 771929660, 68286209, 589704822, 487767744, 524352048, 683607317, 886418557, 414936009, 83515477, 379172090, 804891202, 101612600, 935099665, 132185612, 492087545, 407032630, 429614086, 166414431, 814792368, 97845970, 395611734, 35385813, 804647975, 939948897, 699366287, 185553463, 955723655, 322068913, 11658702, 719134776, 602727600, 371555641, 331842438, 480690233, 408258632, 214315960, 331228091, 694047959, 880302251, 456159822, 315798478, 725357008, 204821811, 750661359, 946765175, 825548719, 522654307, 938294857, 632743202, 571653236, 684448274, 563576180, 882960989, 717358089, 317125894, 195220557, 626255077, 350096526, 996745190, 367552237, 263452893, 614714431, 85481015, 278976343, 159209727, 279828122, 244500167, 571790957, 447887458, 303463135, 428175288, 466868251, 375624243, 723800582, 443174796, 635135551, 823904270, 611363590, 808514579, 865765901, 307953530, 913148932, 273824017, 272446733, 543372249, 122651942, 126271145, 810464746, 17065883, 780057737, 330261422, 369801884, 231751347, 2244294, 748900665, 353155615, 232529935, 540977808, 108815455, 963094142, 397717420, 553586394, 806568779, 780477756, 140463403, 585443928, 315778770, 460793745, 667808364, 421287706, 790789290, 684205260, 46555973, 179965605, 2254774, 282034157, 940230784, 48725213, 435996273, 216683812, 212293139, 367430924, 4664241, 961079291, 291970651, 994695452, 643827618, 467663997, 287021936, 830318372, 681837390, 318022218, 356827478, 4320430, 138685227, 949611979, 909963046, 585316519, 380090206, 818115611, 597173827, 213578413, 6738316, 780348947, 620552900, 861114732, 78738913, 987241446, 383692737, 742385503, 806272481, 542440086, 224706607, 869238074, 577599775, 796429987, 567249428, 457331016, 167351048, 612243841, 362306133, 912813278, 353059803, 244364334, 546486686, 589798056, 329374629, 282649232, 261386320, 408205565, 441106646, 233729971, 116071004, 344324602, 280174908, 457145809, 889939054, 314303717, 547645908, 967256935, 351218731, 435562284, 4991148, 568135865, 385444774, 729000892, 56441059, 443660895, 530427912, 189551454, 791662237, 525838969, 963989383, 358515283, 357453191, 527967313, 224126178, 136824419, 750734487, 401095000, 215491371, 652345928, 189851536, 657214525, 660015827, 423096547, 736086765, 193385499, 434251671, 710435734, 318054982, 111509022, 650162070, 694418021, 81919128, 278431493, 53751359, 658115666, 716821855, 99698994, 309818484, 43261678, 577434085, 926397761, 767276634, 831078040, 868794297, 986880544, 166536660, 359603185, 411060913, 257236989, 637178296, 152309214, 793372209, 525941412, 51173854, 217216112, 987417202, 959911174, 821371623, 18515141, 756148135, 352771736, 86989120, 933592427, 969554811, 639534834, 91766098, 549618396, 667586921, 766987599, 480094789, 357765371, 220514717, 878028579, 113312375, 442703120, 611368824, 968449133, 63954974, 558238620, 63886835, 746182869, 370620370, 878267079, 511768784, 233352158, 710784561, 154626114, 904460265, 625949657, 16072662, 284018649, 446745667, 756458618, 221143074, 644955671, 175838639, 905730308, 873253560, 653525134, 674265571, 981000655, 480899856, 373781324, 745554324, 670738330, 167516478, 408015880, 635544350, 356157594, 24947312, 964343961, 374050732, 730036067, 892351150, 521627842, 788573422, 150936531, 482764725, 748515254, 457784469, 106772481, 626736817, 527469223, 325191257, 263771102, 419452771, 505222820, 151503084, 864416308, 727366447, 377999912, 860220788, 816553392, 934409067, 231830245, 215942264, 808302, 547135960, 69100290, 694095158, 675693291, 817510370, 86715513, 105852811, 910195862, 218349580, 31973184, 537010630, 640712053, 684004973, 375393781, 875761919, 338694871, 604829721, 569933021, 125965009, 262900169, 849652576, 642221122, 104167380, 130184487, 331289064, 173599975, 902595042, 749811230, 847861182, 582884279, 785249982, 404256665, 62654259, 689759529, 126649530, 311993046, 810467943, 665650932, 220139332, 455939567, 994007993, 257629298, 550932202, 993478715, 109844588, 865833567, 272270207, 169036647, 242668410, 651316636, 445220371, 371255199, 411656725, 908016525, 575569532, 847209471, 682373560, 773398357, 760628101, 71151496, 930645990, 63226402, 792741873, 629453285, 941040572, 95831364, 878244335, 965022040, 469407438, 707012766, 811277183, 749024304, 556864653, 906631390, 370091567, 358394873, 383840082, 859893467, 558594016, 748529786, 932870226, 328384819, 173336623, 77297920, 19060326, 953140409, 763806228, 739444102, 164938522, 961379851, 303750817, 857063904, 495218668, 623022859, 973450009, 292976568, 195553674, 978267793, 817627837, 386658578, 582761216, 489702997, 904436057, 756744451, 857884438, 609174963, 149750585, 665575211, 935183396, 117862713, 655339237, 799076438, 460656109, 136338696, 732921434, 726225742, 803226088, 569878333, 225263986, 306927602, 252854889, 53580392, 179859184, 528658898, 361730780, 974997916, 938221206, 809338629, 51574041, 757895731, 957387806, 680978656, 653015471, 676314097, 491695120, 820376527, 296209786, 214968813, 187391972, 867496729, 801794636, 751226934, 259018934, 717570527, 914327844, 767552715, 649591506, 940265488, 411309379, 925302371, 110587269, 527123159, 338150984, 267045625, 669791133, 789810859, 916811378, 716491163, 447865507, 30623796, 457477324, 810277774, 615730733, 273440911, 544697408, 989449631, 190940859, 333541730, 899963663, 651842833, 388515270, 478217258, 811798704, 950057901, 99903603, 76590284, 849327838, 116157099, 139743333, 574758199, 640499756, 201809366, 332030537, 263121975, 86626787, 308269653, 285554321, 657214918, 328146129, 514626269, 739362123, 772911898, 267791411, 718951465, 170415178, 248335947, 774990289, 299716461, 897895290, 832205167, 268218299, 35393940, 224521669, 255659314, 136850092, 132039858, 855614761, 405400329, 514852055, 908398234, 614134782, 386199881, 982442743, 683298939, 353422672, 771231791, 427416725, 590813933, 978592526, 947817061, 1477168, 252802162, 921340748, 726106895, 730029356, 23128889, 237356991, 16232633, 595040286, 768372154, 609767268, 562783612, 656866806, 964578203, 318774460, 933729836, 711860583, 402223020, 680720959, 957347910, 753251404, 262507304, 147842175, 819182754, 654065202, 856568863, 227562345, 294733082, 125940059, 69649084, 693108083, 439477586, 673308986, 970280232, 623379477, 846563577, 921147693, 533937837, 777237615, 654031028, 678860924, 312167241, 620862330, 838508239, 90240679, 604344598, 570297686, 726123270, 116928307, 277563401, 123881404, 812741209, 395870418, 639566916, 101670125, 231896255, 679390421, 73185328, 110859017, 541431209, 885965686, 230683932, 676800740, 468439163, 145827058, 482248179, 71185987, 730093893, 680345208, 687202049, 828000011, 375768326, 638526145, 257522609, 626010111, 194121085, 443343544, 333584607, 269580470, 525945687, 244711037, 852474587, 917049034, 158653734, 566653158, 263266261, 241940726, 571586174, 649675932, 777388606, 583029795, 509443871, 396777226, 989261474, 394309265, 959571579, 838712667, 602989874, 507842254, 322643378, 128449193, 819871064, 986918234, 507648903, 142887899, 709600003, 421470198, 811938048, 18935632, 119726218, 50226468, 151293900, 202737026, 518113843, 849689534, 507826653, 254379763, 978025749, 253287831, 196594898, 962826635, 358477618, 383038412, 834518385, 867730464, 156189664, 468412530, 47778929, 234564547, 210522056, 842043900, 296203518, 949326458, 6534769, 747289785, 94342719, 990729766, 895719266, 194590327, 576682649, 697667317, 592827199, 334933216, 409775127, 232655357, 704043523, 209429718, 322210805, 138181848, 770677898, 638350940, 724868710, 52589463, 795509758, 320783900, 803204363, 9030086, 280182892, 239301730, 943609375, 944562680, 912933157, 10884480, 826535674, 71439597, 506550404, 426022480, 476258171, 419688493, 383667906, 12689601, 623740309, 611866890, 83068450, 377492405, 133297863, 314733511, 343147398, 873350259, 314493851, 885534843, 192106634, 756159942, 996074651, 748381862, 47644119, 993981841, 491709317, 59042432, 428951812, 720237824, 748079748, 291441949, 664730857, 303763264, 722952738, 964212500, 74165547, 368807957, 597674447, 798804024, 58449482, 975420078, 279664405, 646468590, 956864576, 75756830, 707250099, 769516933, 503829729, 746285710, 720797680, 864247854, 304166777, 92560338, 457669813, 952124753, 670843410, 893219387, 752560158, 643448127, 271542498, 763083941, 216985240, 439409276, 650260240, 713733678, 3744459, 496595222, 153131910, 326485347, 871912662, 971111789, 998904778, 894708101, 249622053, 860235534, 999265513, 939581181, 524563860, 904827330, 767835657, 429795312, 558026670, 76658022, 993504850, 171911794, 306538887, 557786969, 44419989, 511586135, 151944322, 139184595, 140060052, 251843222, 212603895, 97370207, 769800300, 489843059, 957918478, 697078068, 433761743, 926513922, 85348080, 79237564, 84614445, 252362446, 903267426, 546241344, 92299612, 800948462, 258808368, 347332394, 394017425, 574448825, 12425041, 831120095, 548220274, 136157680, 784903322, 774776507, 981762762, 444492657, 844914581, 100397887, 820625742, 792834930, 939960356, 44951162, 7933102, 859388376, 304962692, 889574704, 578318188, 255692001, 691994544, 552239612, 482058053, 790056751, 362288841, 931466647, 344075109, 157355631, 603679700, 271258484, 157878371, 104031226, 168743369, 190457714, 174765109, 596556517, 34678184, 223854898, 468066723, 905641864, 823864108, 861967543, 510888983, 911089659, 147127305, 899801968, 175798591, 994578630, 326010976, 398007961, 235754245, 6512656, 456669781, 176225774, 262513379, 342409789, 925406905, 48828846, 534180955, 341532732, 746033549, 760433488, 337053955, 861665214, 949606341, 979651996, 418703215, 411760032, 650713877, 417219560, 427550849, 650953070, 968428194, 465951534, 291056192, 892469589, 496946536, 505340293, 70561657, 509882554, 310631786, 10271477, 994643874, 480788875, 897185761, 235300196, 265511306, 16961527, 736675308, 193430479, 568934129, 501260675, 934775363, 787253662, 521916822, 909620275, 522771838, 654060027, 347418359, 55583857, 816485938, 307000907, 340188300, 642127298, 432582390, 735180560, 190433091, 195592807, 615379477, 436312960, 305304093, 493645503, 103557590, 952675050, 372185881, 39853932, 829050026, 943194763, 865950674, 574475038, 292733043, 657451372, 821396696, 54189582, 917158199, 688484490, 530485959, 726457066, 820418820, 334991599, 416837653, 737963305, 608013231, 689887619, 772224772, 347419770, 816164209, 539051615, 166390932, 831390785, 216176450, 540581149, 556662812, 521461857, 490455265, 516902472, 541226509, 705250964, 207835613, 653743329, 299110419, 681276643, 393844387, 421723814, 418324214, 636493798, 210545507, 558273796, 673660000, 906449055, 648032693, 574059485, 311256395, 501968997, 584258362, 412669276, 555787617, 643203217, 120732948, 48945766, 643128841, 749674698, 178290232, 207139405, 234820836, 569182298, 3807847, 287779326, 478346241, 938268560, 149702740, 440129970, 981553737, 346044036, 672092114, 873074373, 9093143, 162619816, 801089465, 703582948, 455314355, 25971669, 450331381, 234416414, 365129837, 963896542, 25001332, 844067162, 812109954, 381255458, 744772268, 170157643, 143172804, 844074135, 97360880, 621668256, 267713960, 31277343, 420863592, 650393805, 60809852, 667102707, 670334554, 213937154, 370133019, 780663272, 865366189, 653520950, 456651365, 619257801, 730807377, 804625860, 366072101, 306907326, 350130321, 125035829, 948888991, 180083187, 590164987, 594149377, 490444304, 965690354, 23762448, 752369970, 282132503, 192860617, 880265751, 589214264, 108148070, 852915108, 682569486, 643349342, 501419453, 192394686, 796426420, 121279675, 124107520, 471888859, 575333603, 478522907, 608115677, 387306078, 435824736, 335055823, 473491504, 825412232, 764957088, 889834400, 190007616, 554987142, 384968172, 104130897, 764786488, 326365200, 681088577, 845776881, 660981391, 668810927, 54670318, 980413598, 189398196, 872133280, 273284463, 619029535, 569626030, 607715446, 169139966, 226179075, 672269915, 338649045, 415330086, 94297357, 461736963, 947007556, 207629887, 94075233, 982399648, 398660089, 570709673, 669611193, 31239936, 633974783, 629930738, 309271861, 903391978, 687590088, 809167109, 986379256, 40788263, 672248872, 876359599, 891147874, 284795815, 185239851, 200698660, 914389746, 552695579, 239225958, 277140249, 972795480, 724477921, 212828289, 93048489, 197048969, 560423445, 700375577, 999984197, 691675778, 536521267, 425401886, 279295033, 441865876, 121085615, 771210979, 514652109, 741356490, 603873943, 889992543, 844507839, 494112613, 600360119, 823705021, 130107203, 55792892, 846272385, 361758402, 169836447, 378701138, 843921527, 889344122, 434862286, 143616381, 420484232, 482033806, 281713846, 79246954, 1097828, 672572584, 233427679, 300029815, 273176727, 717546128, 999231840, 420717035, 637884674, 47493846, 522039329, 943201849, 448836489, 991281684, 311943349, 140649180, 137882312, 205215925, 207055252, 874389446, 817822963, 69742327, 285636106, 240433605, 381145732, 90032822, 195216947, 492037424, 762377296, 172255259, 470230590, 764456579, 676989263, 694428609, 408209149, 441678073, 19026748, 921756279, 556542339, 415596860, 292863020, 366480289, 613300515, 767807697, 272151325, 311123115, 777554023, 162912556, 664585438, 893840943, 615045606, 973571213, 962799695, 294574456, 466843909, 966143454, 43251095, 226882433, 739783313, 629015963, 793206626, 11545106, 674156161, 276052918, 865389051, 658610312, 799400494, 880496660, 525823110, 220559461, 781978744, 444548857, 18507646, 336627779, 743553420, 496070248, 862975616, 329745198, 684523651, 598472873, 641919517, 300090306, 183952129, 740862474, 593109090, 218581919, 103514280, 185849183, 106944393, 821634641, 877500261, 178196486, 625828740, 115004815, 28739329, 762752571, 847758207, 160979259, 56118498, 737004267, 472528916, 346025555, 66039395, 193039722, 80053871, 897611578, 400255699, 497778814, 207663557, 780513895, 809444038, 361236354, 438039627, 88811343, 566259475, 310850813, 765608091, 967452558, 25704311, 415853848, 562304725, 164519196, 187606372, 916179500, 759654280, 974851092, 291823262, 593956633, 920223761, 701477616, 795900182, 581374977, 254464858, 706691229, 298489974, 518110572, 894919137, 773317896, 172391929, 120877229, 767338776, 94655200, 269068183, 552144396, 842477773, 808618996, 818138560, 290912754, 36110904, 154384729, 811954667, 471254136, 989144174, 600613630, 500950016, 124829473, 465218832, 934369958, 472396481, 300185865, 702287796, 84053138, 351018955, 921800939, 831993605, 869416228, 47160760, 411263993, 933546575, 387963706, 215152823, 460154904, 648716781, 493762736, 939788914, 951996095, 248967258, 36847762, 899274731, 215122196, 988463900, 752975026, 446844345, 194312086, 868786198, 981525324, 897388333, 376404870, 720162321, 200074075, 481307446, 614281237, 6522820, 691325088, 97588340, 134563440, 677209170, 709769826, 599439656, 393892787, 689959020, 58886729, 660630999, 690356590, 531330293, 365629425, 411297146, 323496448, 87233090, 767897590, 369890093, 640851420, 776748245, 756875755, 406952282, 747769690, 377040414, 829496726, 119620741, 889875546, 520391862, 176718319, 506863785, 296610604, 950393606, 754703940, 469751791, 335180856, 203791791, 763827547, 770930604, 893078443, 446440929, 10816432, 624477984, 208996652, 201690092, 950837631, 923166386, 522957238, 78212813, 751793468, 832023868, 158479353, 330582333, 50546716, 515957035, 885512753, 390078468, 89852162, 950458950, 819546984, 186836295, 522121397, 59813720, 431436848, 547029266, 576584697, 950251587, 888106352, 97952637, 948490740, 675882809, 966047516, 585548957, 372061945, 841155110, 148522172, 694774505, 877497495, 406495044, 885131939, 596964300, 699567650, 867789890, 736069646, 355354473, 128294763, 23850028, 670588126, 8207281, 680145612, 560664448, 683313373, 646016454, 242828395, 21461264, 755563345, 934269852, 51504984, 904635604, 770449434, 756492052, 147186936, 674421614, 606844352, 615064665, 336901658, 768144174, 445307183, 214794445, 150489587, 356229491, 945002998, 989862243, 561180543, 164636991, 600710716, 388913692, 551944523, 440480768, 353755005, 247094171, 657840253, 627119458, 65026308, 591595235, 159437638, 851035198, 455207229, 318026076, 45089285, 780702056, 521756403, 338927864, 91125581, 54787537, 906118870, 996405005, 73468262, 416416717, 949937536, 35461569, 926339347, 575017051, 831537424, 192651605, 487078449, 475064832, 946953954, 933945279, 249499047, 199201059, 109806629, 842551396, 994848176, 815354554, 26441255, 512462733, 744101654, 851276259, 412586253, 184593959, 625561819, 150269174, 688375533, 758371840, 428653533, 439950441, 401720415, 856601981, 921704062, 430021115, 288095446, 518961076, 612720489, 510752663, 694127114, 276151406, 373594541, 193369269, 325880880, 771787465, 191701435, 16919214, 971399718, 304390093, 408017171, 942584730, 57428694, 390990454, 321843558, 245834566, 671148530, 488509328, 278127623, 995495545, 392500321, 291436349, 40745202, 863897465, 900443786, 777655812, 515984658, 470328247, 129061802, 244552020, 81827592, 131191468, 864632449, 279096659, 175114640, 390331003, 870134261, 227948226, 874373269, 323227506, 416150009, 395445133, 329888733, 76021654, 212238382, 778288655, 507654501, 894868541, 5258735, 566670229, 380131503, 240489757, 110402690, 691165218, 354380912, 589372635, 28908069, 50866513, 842059669, 7244675, 720235191, 682022589, 985025948, 389968718, 316407545, 816228131, 875826652, 411453524, 351994758, 646602430, 182640194, 128743343, 226782170, 471448343, 244267416, 376552599, 485442119, 739668602, 844249611, 984753539, 108595757, 309277030, 374204828, 551300811, 999483759, 469589663, 543449071, 15984434, 878371379, 645386944, 537159412, 579913786, 890717778, 693768747, 189710547, 73437620, 6129022, 853031666, 516364200, 874154299, 563799942, 170279737, 118396865, 69311174, 504130913, 384029192, 131578776, 476632442, 68008301, 604887401, 626998880, 309743148, 613525193, 445382821, 9660442, 172860565, 555540935, 739556555, 683868148, 42741542, 886761226, 831971337, 274596743, 661341847, 53293569, 118862813, 624112, 331668407, 160192513, 813141465, 342927284, 956833890, 218752776, 20906130, 273502295, 399754339, 810037074, 197896364, 838514384, 177803043, 435935647, 488330645, 492598085, 773301301, 224274487, 726241692, 696571125, 316604069, 54992567, 178501812, 659374497, 604184930, 724588786, 754103901, 710899112, 854967777, 296445384, 914109973, 516912122, 348471452, 480932230, 130193074, 288267888, 85226564, 762613498, 626491714, 670252487, 94101504, 414852347, 278239694, 519766451, 305069034, 455270617, 67465230, 517732183, 605937262, 397437649, 418913159, 202858552, 559269258, 503443180, 344093946, 447048312, 217620062, 47429719, 386195822, 792884751, 380188952, 200815773, 640702094, 355756552, 453290730, 434349584, 961644775, 169779326, 590813081, 308885610, 230108856, 336515391, 521810635, 100596706, 755489319, 58684003, 347524351, 313455606, 470781352, 593941039, 1675087, 517466461, 411076356, 544031592, 415189121, 944105394, 587092588, 788789640, 129049204, 217741621, 269696379, 832152418, 84486534, 492454558, 424808428, 755712181, 439563608, 172083853, 973133112, 394158418, 845764718, 683053931, 345331067, 579388643, 475685911, 763354494, 828990883, 633051585, 346941237, 537896308, 418446856, 352200082, 152084457, 999776458, 155985223, 222955810, 109959494, 420214299, 831680598, 273983646, 38300706, 26450087, 788048085, 424749521, 563532827, 582296974, 842362068, 544162413, 961874660, 452421883, 250053468, 935175136, 780828275, 89459386, 970946547, 714547581, 319519327, 157357034, 351787007, 742842267, 124198337, 984588244, 939661536, 383849405, 861218311, 571654919, 151906168, 410770512, 856370476, 57428939, 865895378, 808086590, 651499349, 611045476, 433637916, 827012054, 332384758, 601527270, 49189873, 222263406, 263513597, 580346977, 676271413, 146775495, 493773592, 859030563, 513638782, 476912500, 914879199, 962011509, 884786261, 175306001, 93432958, 620278972, 947662557, 114653499, 629404305, 410704479, 379985777, 587908477, 987786971, 645852137, 739289897, 872176851, 764252730, 17427682, 545899138, 605823812, 555948623, 283990390, 64902752, 391445707, 202558030, 182244180, 952888759, 154304534, 400936645, 307267549, 654133737, 335885019, 17674792, 978341136, 2669333, 161223747, 177892318, 300385490, 319016386, 615539210, 262493032, 446577160, 950784521, 10491959, 978449745, 808333072, 137373295, 960798279, 504423565, 178326527, 323127243, 625011097, 279857931, 221722740, 344886758, 183505734, 776526713, 970543502, 252857431, 949926527, 317286094, 251827126, 360685357, 142804213, 28164564, 836699955, 288807287, 612134878, 961046435, 272653415, 254551081, 221192599, 580170274, 988622804, 18041874, 543042384, 807469033, 302342606, 113722015, 462114725, 773267374, 794459293, 20604615, 402024226, 38225120, 821224260, 755289404, 31256500, 325295583, 197685348, 840399456, 411520603, 997640602, 541647871, 840726809, 413876194, 845059381, 844411724, 964902688, 937271663, 458944701, 292654712, 967925521, 462844389, 903326247, 534952016, 633018019, 124118212, 345194549, 216228943, 844316152, 339138844, 353392646, 874671232, 788613947, 353755586, 659222129, 124557199, 373161022, 442881820, 142111688, 337865886, 174009148, 994631778, 192955300, 221607504, 339756754, 836609128, 539383772, 740485345, 300057856, 432192614, 569877521, 178216090, 686709279, 39834648, 837084117, 838583509, 603684062, 628109777, 66447071, 419979086, 525181590, 410767700, 751281704, 154378452, 172182168, 675567306, 389989808, 519990797, 146722500, 792817399, 780418054, 200789732, 911331006, 562259906, 919183076, 521143195, 401972115, 419615266, 636357741, 933942955, 402035098, 540557094, 3394990, 742665653, 896584305, 489056218, 273004753, 734773664, 962862592, 924520527, 481224319, 458077155, 817147785, 73437819, 313838438, 157283265, 789200410, 958759180, 942843496, 162421753, 234917953, 602118726, 32378867, 547035256, 598267772, 312351681, 865925194, 794801016, 895513111, 597618865, 665111566, 293489732, 700774355, 921640779, 742004793, 673364557, 219656889, 33035347, 722164539, 836433148, 350090117, 930779766, 438721213, 353139725, 952823345, 413721996, 883650311, 73663439, 320581662, 12579377, 79287286, 164203342, 353917951, 780677539, 531837434, 136882484, 231544565, 142619574, 5041304, 547566001, 706862578, 730275107, 351894393, 364201990, 374425711, 331529513, 556705843, 286748115, 844492432, 429293682, 352912597, 846452394, 214692149, 879544241, 161098617, 150646380, 799089004, 459856342, 947474600, 425862618, 384631680, 390130833, 86449368, 220019151, 424231859, 41655823, 100607187, 576758054, 689359421, 920593883, 963309850, 832395314, 574856753, 601529150, 163121772, 852123971, 143490038, 847914919, 52755318, 771094158, 118503648, 783677737, 885976279, 372759544, 970317528, 135739606, 862569920, 553245802, 442850457, 285125610, 209076617, 411117807, 938791396, 830893702, 695369887, 833520293, 156594044, 993922252, 287744692, 224829094, 40357946, 180178517, 377588598, 42407396, 216962754, 351070603, 905535526, 688668844, 281830419, 902680469, 985997036, 151140504, 937910295, 598448932, 354098635, 35861135, 332291786, 113044356, 20090113, 157313178, 633250728, 283123727, 656821365, 747797151, 48640783, 669426064, 348381406, 814637731, 461033089, 633958809, 852398870, 648332454, 886294518, 154336691, 744911319, 712124449, 789595451, 617015706, 514705551, 901198613, 880179460, 26603149, 236131977, 74840269, 79168212, 792800650, 739280358, 513238932, 706331303, 275815278, 233783354, 858859305, 565298978, 267831319, 462747840, 987321660, 519834235, 780695035, 299303535, 925310511, 617795505, 905126957, 86757297, 524436630, 638590971, 469407572, 362810907, 490010604, 762748205, 697433575, 329305522, 285192265, 679380111, 676800663, 675697423, 599362000, 678855378, 144753632, 471358250, 3473178, 987415476, 851581212, 399165011, 787218153, 831636427, 210003347, 54761561, 458371693, 467130869, 40234154, 131683067, 779485858, 946649814, 381672697, 358637962, 798500679, 855501430, 889389104, 973285935, 621028560, 874113797, 675325398, 274753966, 614203259, 323327328, 320476929, 769512487, 462767691, 760528358, 865656284, 554116969, 30010592, 352163552, 826120628, 404452235, 660486895, 506371934, 761516461, 716701630, 281380262, 408043766, 839934993, 95175920, 881669249, 827869905, 741474310, 702736536, 437290484, 357064182, 157268481, 676012638, 609383006, 17403628, 774197319, 879139224, 749245058, 298227883, 454857508, 701986919, 996182705, 387068149, 997823136, 525575668, 956332751, 445734070, 863225442, 783273637, 130799510, 41556526, 977379234, 610315251, 537906784, 743570895, 555669889, 995610895, 941073458, 775710473, 959584076, 224109238, 659483839, 932715932, 479612651, 340415958, 277271945, 235130439, 225851060, 951696741, 75337, 392842044, 735900158, 666814293, 763807348, 612706583, 830805053, 469615919, 925667305, 586853427, 491985431, 952369426, 336902460, 493404750, 548553518, 940243891, 546496141, 873881052, 823622003, 686324094, 443644710, 683689407, 873588877, 935729015, 465084375, 755881745, 296701003, 680961470, 523599735, 944926791, 10106319, 41109202, 154594173, 578834688, 19732470, 217045961, 174081920, 768861397, 618392309, 427109096, 627740213, 291386213, 534550460, 673110233, 419374108, 717642777, 502770793, 253445470, 421437533, 828222230, 851592566, 427766607, 678414671, 507423098, 274983645, 648631682, 376462845, 420823414, 258043314, 986153660, 580690130, 16939468, 930274549, 30672823, 611797683, 265336784, 709467993, 69682033, 789063114, 41143908, 953430862, 261400082, 311430719, 756338878, 430266008, 968686044, 602062638, 650473507, 793310427, 630686112, 227142172, 480828624, 188512258, 144297655, 853094417, 466795049, 99107093, 604587004, 92603433, 201513490, 117139168, 62761998, 321477321, 598018420, 89960737, 265708992, 931807514, 184396410, 211279188, 642873400, 247190637, 135791942, 470434004, 669488664, 716765466, 643711682, 140322755, 354796178, 604123349, 17918014, 311439296, 228964263, 181457900, 259107642, 802570050, 483663468, 361845151, 383223645, 257332621, 352843417, 907248331, 520362005, 640157191, 435118330, 943656715, 99963776, 479131264, 608800286, 271876447, 180033307, 144445902, 523808627, 659819370, 841635303, 742153640, 376531263, 110649273, 668965042, 984637449, 709540521, 977363753, 571528920, 291290197, 354814151, 44482435, 567149027, 74324627, 696164214, 383701855, 986895450, 606222336, 823678774, 546308518, 103107177, 897278437, 339116865, 364586879, 326194315, 434692693, 626066443, 700121887, 928777629, 85849130, 487064639, 613735618, 817189703, 565371729, 511342105, 450550624, 137758955, 791279534, 375764047, 193888716, 834444341, 258106193, 439375437, 586412273, 350356514, 867788615, 417039114, 220430707, 563117993, 627069058, 241020170, 626641174, 369860349, 970804938, 216424838, 988569707, 688105027, 601385961, 66819626, 962130456, 962277653, 340878040, 61160218, 196027552, 151160844, 265178679, 530283451, 391888537, 948945877, 869826897, 900593012, 115466788, 764476398, 532105360, 367349098, 281499800, 950754394, 242311121, 852713516, 533299593, 178555708, 174282468, 785214989, 219413062, 189538255, 685907641, 462583674, 248787867, 214341696, 943786446, 835201145, 709342362, 90438803, 195280683, 927773880, 101141151, 435052271, 435169655, 55421799, 236412900, 209016483, 571947747, 979662442, 126872832, 401753177, 970295486, 727338608, 279308091, 14841428, 694691116, 814772640, 920562368, 260643846, 652703110, 245011963, 271503464, 982075327, 441146753, 367216301, 279913485, 38164225, 112671034, 734066733, 46937356, 907703499, 631781546, 636293687, 841945477, 631632188, 831040553, 473575467, 923690, 745716857, 503825085, 411942776, 864890779, 23400653, 733097043, 309833623, 825194229, 929238299, 783429183, 542584173, 128097361, 564361923, 756831557, 946265844, 438125233, 905128028, 923508079, 979971861, 963822007, 231012152, 351476156, 203748826, 49249239, 21279872, 330831795, 986987865, 701436793, 408101934, 840788140, 212370638, 345035494, 506490311, 450393199, 624094365, 113691736, 154803603, 491229987, 168741360, 356404124, 744074021, 102817517, 289360854, 813812832, 969856702, 179935665, 347528069, 430305608, 448487177, 111446315, 97818172, 944526202, 295536017, 468686585, 879899962, 712650151, 878598531, 653483047, 351839200, 386991650, 428584440, 239111075, 747269271, 692537563, 268475511, 524060245, 264746095, 29921666, 100527052, 697799315, 345683245, 137486139, 52169335, 915241253, 181434744, 295199558, 679338976, 753000064, 414303171, 647283372, 488118345, 670316852, 448408905, 638669534, 778990881, 484455708, 798515688, 53442431, 922659582, 451858036, 105502031, 888693547, 236819335, 998585947, 820088791, 851213351, 852433057, 646011622, 397891567, 535558330, 659229474, 490139495, 986078461, 359524931, 819826707, 650237965, 282648699, 195907278, 119658349, 704725979, 280312330, 260166687, 382860458, 59040971, 506280147, 400522103, 746766793, 319696435, 993598815, 725117224, 961036156, 937182392, 948628937, 515932129, 818498162, 599656943, 45021419, 788417538, 815384792, 713520399, 644443684, 239868500, 908338351, 899893801, 769224454, 227540683, 891915908, 457033238, 923773519, 26899203, 72861727, 720510145, 122817765, 687213314, 516918467, 907123102, 320168196, 686754367, 171378255, 241472724, 859709281, 795399184, 212098727, 178118998, 192732559, 695758370, 798229526, 150124832, 890656935, 686976345, 37737347, 86411656, 115446178, 490604649, 978432894, 118421588, 679756187, 256170424, 921636442, 677002039, 175505661, 968175989, 299244654, 227762241, 385199744, 219099155, 147236760, 987523058, 729303789, 196073148, 747431358, 161242933, 788579651, 817669142, 45412379, 147182622, 705190350, 631169966, 304778084, 144156945, 617684483, 768114424, 421300476, 851847127, 150849314, 240111944, 359294938, 155826183, 813032863, 630115470, 616921923, 294118099, 33859326, 573799678, 349268806, 827345736, 416043953, 923815917, 684542642, 574834378, 965193974, 591032746, 177556278, 416897715, 602194143, 709408420, 893478405, 717141488, 583881781, 37365934, 647455369, 296834125, 627609112, 582639104, 409211365, 488572190, 598869087, 183160430, 838045500, 21644572, 327552179, 805630158, 385869190, 188625289, 375811943, 955648742, 17060267, 669038185, 230859786, 387676851, 150306079, 45662598, 413728290, 663856775, 590459657, 446691901, 461204926, 877022752, 289961857, 756779032, 690550692, 614915903, 498098677, 894878789, 543398123, 447097356, 932483183, 264990267, 351975173, 955277636, 474755058, 233813917, 444781119, 505840881, 15118304, 489662722, 849955174, 405452268, 579932483, 410287653, 178547899, 532150369, 860438265, 796550457, 336408558, 838746891, 619676012, 804209765, 424929430, 781130852, 624393010, 358832041, 7324187, 745234822, 136170229, 671198387, 258951326, 846719790, 7450815, 959308195, 161105772, 401466064, 61993322, 661369727, 221063795, 500452230, 939412341, 828283904, 880850805, 819490368, 595329146, 941943961, 887573825, 107743716, 513721232, 19010205, 452910453, 373248392, 296582756, 931587432, 53549101, 554348056, 363984990, 401957884, 349695962, 162656557, 208499658, 684625822, 893930042, 196877242, 818125936, 558817346, 489273886, 834652806, 33526279, 575076485, 518645286, 856058721, 876160626, 951499410, 839266770, 92089157, 192207025, 751744085, 201155713, 883488785, 554303197, 881944284, 421985410, 449950443, 664380367, 526647150, 346355969, 421658571, 713528486, 545630697, 287400349, 67282717, 993389725, 242289222, 546519086, 943314728, 776600795, 572778545, 146499104, 83500835, 217328072, 265744084, 760971168, 54087731, 774944605, 865066741, 432413680, 610597869, 256698547, 701084904, 948146663, 697468929, 766318484, 26141921, 201861165, 604380730, 731466111, 560830650, 897079721, 504112887, 361443718, 735972837, 269404845, 125947167, 284444181, 666798276, 933517100, 147194607, 51298577, 544041980, 357458845, 388586429, 133753075, 433764252, 239809883, 784727858, 715099603, 156382487, 503553182, 446693692, 929013992, 120177641, 115740883, 318595548, 982859427, 20516421, 3855217, 472751699, 407938254, 531212347, 642715810, 179813539, 66608143, 711454417, 999226441, 453271486, 389601045, 568132238, 415657100, 427437602, 934132556, 774003765, 807562463, 740378033, 130729297, 950093271, 885905068, 826014049, 387087765, 407034207, 970295341, 105938193, 52427236, 971314369, 330928894, 58831646, 269777014, 591504635, 209963016, 946516373, 739563820, 863307873, 411621519, 424259202, 269769897, 133515260, 181385115, 172993193, 819387979, 754257617, 301988093, 790168721, 752199155, 408891925, 888771097, 241808928, 391534339, 403358027, 410939250, 991438125, 261126717, 876202554, 180109633, 815261004, 422746430, 762308154, 278892761, 257946457, 472875690, 274960064, 861680265, 115210104, 971090369, 309721278, 110185859, 709810080, 830127982, 863750018, 295515938, 145864357, 286402861, 583089900, 872028086, 853134612, 830647046, 803631739, 399612890, 385320229, 491379172, 195825536, 871875888, 832476178, 547273372, 574083150, 17326200, 411445086, 56533589, 312469179, 400311650, 111085463, 67264350, 541341989, 341197344, 583029086, 438897092, 361020243, 554577226, 222018001, 759214301, 177761974, 103672149, 752590054, 89166920, 680374719, 259028064, 68329826, 542469189, 634589249, 250517702, 338446467, 875354049, 389169223, 452202380, 747470378, 632104730, 906158866, 664427226, 818598772, 592261335, 893799222, 727442960, 185336335, 982298404, 202045340, 796473879, 270408867, 248405428, 185779386, 495270972, 457041768, 781381503, 886466489, 789110395, 320670611, 33136004, 716904905, 588939678, 280381943, 138281841, 219970662, 768541257, 404756515, 75279475, 295922869, 520640894, 382056560, 50402892, 403242331, 794066651, 17123668, 120458279, 933407734, 770188272, 11225350, 608072617, 673128885, 869650616, 727466696, 786870298, 89066028, 26907938, 202279212, 29029440, 836466134, 962929507, 509944080, 878362087, 787185589, 366763457, 644079587, 373668255, 753381056, 217877902, 447992745, 739325664, 828324584, 41728806, 704486702, 225182554, 597230116, 388872115, 740115431, 765030877, 313448290, 884099166, 278353103, 722782069, 990503115, 266029023, 81026303, 909065785, 997003272, 471313364, 874915505, 591130688, 982500247, 364668571, 17967554, 541298279, 227379356, 290708113, 347369326, 405297679, 839710007, 33773952, 820317615, 215957384, 736274141, 346257182, 185004022, 217532122, 918017749, 587436182, 426557667, 197146669, 469279605, 808303168, 181734809, 799117918, 950395166, 442201260, 705212122, 31638504, 927366778, 964006814, 783160514, 639143768, 619245826, 89206131, 826675342, 874293974, 433529856, 526049232, 790745651, 888785029, 794170824, 222518582, 606364142, 755923641, 668581885, 241264480, 656361857, 900290019, 228763089, 338020037, 420562217, 195820253, 190901034, 795727098, 871250832, 599200521, 83349365, 412803857, 136610192, 143536172, 459807023, 207612797, 147262862, 58667957, 185366527, 482395312, 39898778, 235691959, 145104926, 168321175, 519986442, 524253937, 696458210, 562337382, 438488606, 943807455, 374095150, 267273102, 958879628, 280389714, 841244062, 295346370, 654091030, 740905662, 700485622, 105523901, 526678723, 113255576, 861198948, 535586435, 867583309, 225455464, 676403559, 198663026, 869639921, 324417505, 232240651, 137779233, 417420738, 677032359, 611252118, 562920166, 287319978, 668457283, 429331597, 263494899, 972034607, 11862715, 28490222, 693720111, 681784316, 572673667, 117377635, 669357651, 708188439, 709273845, 387511834, 522645822, 448814818, 577713885, 994949499, 646804432, 558406978, 402969423, 174822184, 449070493, 957510430, 609732556, 924557335, 22439857, 709729108, 747130335, 289109902, 647524070, 31558936, 676348693, 259067303, 851814019, 388220500, 84683469, 564731100, 409848722, 336168721, 169427159, 933348332, 132372061, 711247917, 190326697, 849631768, 327736923, 750163464, 958557779, 44040145, 451248613, 298024883, 756480543, 845481644, 430548688, 879808216, 515917978, 809959614, 93297093, 982627424, 886406011, 880055853, 194963106, 594586733, 204082680, 305583632, 467311247, 357102036, 919917389, 298754153, 591881378, 369158617, 426161933, 772413527, 446550729, 480644581, 195434042, 644708154, 382329774, 465092906, 131482458, 6314867, 455205167, 97726191, 653444697, 154526682, 322472395, 926913852, 644319463, 13002455, 869653537, 48599117, 210249684, 136737876, 985445318, 859025818, 364463726, 382063006, 574379580, 337380118, 649797105, 640808559, 357159682, 36632779, 725385155, 496361691, 145875835, 28443421, 200915662, 168047515, 617047638, 657908330, 176034789, 99671401, 117837804, 374972889, 190043855, 249703093, 90475613, 40934812, 87728155, 515113371, 721204877, 339445714, 580644493, 87496954, 25831220, 463251213, 568248355, 301164063, 560853873, 683857558, 790770881, 880715170, 463780261, 696773691, 366025734, 89998947, 322769540, 411012219, 889528299, 355094643, 163379887, 13021287, 499775596, 896845688, 704111050, 863209132, 144824948, 689363641, 826924979, 188450904, 343414290, 749102718, 369717407, 762889233, 674311331, 191087213, 193481575, 720811807, 311096367, 707525317, 309920541, 414581153, 506536577, 706840329, 134811782, 860817506, 215032404, 995946141, 319968034, 292737588, 653662064, 451260124, 374614625, 300936501, 872125222, 265690204, 813980997, 199928842, 990171086, 819291553, 743593438, 853130387, 518242582, 525002438, 792603763, 12441038, 932988228, 344366239, 630012746, 178246202, 597346897, 213414744, 972566307, 697972819, 382865170, 28616870, 929856199, 385214983, 767043254, 505163429, 767463613, 251108528, 413074171, 483446176, 126865679, 851129127, 345142818, 779966861, 991874351, 997551924, 5570910, 595504515, 575728181, 487882468, 950068656, 433383084, 592617472, 294940035, 936368891, 373524577, 344551688, 169101187, 302608602, 368963759, 136928318, 391996522, 645654318, 957836632, 79211900, 873585645, 105177616, 412300217, 837376447, 189664645, 870331099, 325538039, 548489837, 352632694, 393540726, 595734748, 798595967, 648584037, 443931742, 672923124, 723356892, 551239510, 364580882, 577048434, 644865628, 429199617, 700898876, 64412124, 430597975, 732860594, 493481704, 220241735, 479078071, 415698654, 164401198, 994321645, 128935031, 713018357, 721798327, 927098457, 213552391, 205223340, 982378761, 267029036, 184379048, 718877251, 408061823, 453087973, 178318890, 142764872, 946578567, 595091627, 131435763, 314508232, 466598678, 23367083, 106923254, 612618120, 431635427, 552736000, 963981312, 880584965, 175812998, 56851339, 406001022, 145409471, 755280817, 538718834, 72197020, 940608618, 57500660, 491673943, 167071230, 206176887, 619356812, 943129450, 95576148, 31027235, 765350501, 392645538, 993300249, 775710748, 917408665, 31932885, 736888127, 105427617, 793940273, 438639224, 170249453, 319992918, 100917108, 455740135, 360289842, 225897488, 36160264, 602821419, 424946340, 796199410, 211225751, 112496361, 313474899, 186706248, 371356847, 572437009, 953195837, 323745429, 252068832, 751165705, 464857717, 190467784, 811134978, 520368517, 817152349, 500067485, 113983743, 905169485, 797011188, 178632008, 413768743, 710723614, 159378137, 175571158, 566673881, 284960713, 261252832, 196531735, 904657374, 47570069, 521155399, 212471912, 342524426, 174762946, 503043608, 520331864, 849074377, 582763971, 292521590, 753118561, 993154732, 969942503, 147234640, 445649864, 774517998, 993615605, 786994672, 842275723, 785798744, 542836367, 67242908, 411637186, 84020335, 232304063, 733825328, 588236377, 331997819, 647998067, 271958361, 535127508, 320121145, 334535709, 17906845, 228500557, 528899486, 9770479, 552983197, 919786450, 925510780, 707587665, 999823103, 845453587, 858176799, 270852827, 802905281, 926678331, 437437770, 900127670, 831573360, 297832158, 278431985, 540890695, 901844146, 871573804, 183532698, 632962103, 999382875, 439748190, 3653825, 948417886, 277672232, 641114424, 629261917, 882564462, 58619986, 413179381, 249332044, 713787601, 372667667, 760083430, 716966425, 175712787, 259919776, 309191941, 423378352, 333355810, 322190453, 456407030, 869422293, 975331602, 321540639, 231949658, 12136166, 643212052, 250458825, 94833860, 412519065, 903621121, 55680348, 362106837, 519278369, 542787736, 63386929, 990938244, 355133580, 347181643, 203137781, 615878343, 913186330, 924511793, 294898550, 963872521, 857877324, 928296451, 975802347, 589971196, 403887477, 966985496, 607483076, 590097727, 954030604, 457476746, 546446734, 483014036, 412406556, 201822034, 812894823, 315227804, 364424635, 806816927, 750812320, 399557425, 799304733, 648692990, 957895183, 439071944, 228778543, 80742306, 769069277, 146616598, 596329549, 588329657, 781390384, 462745321, 144709830, 489445078, 12413982, 271386744, 867094963, 964503111, 992825719, 552264679, 405025407, 23071921, 502577985, 856837895, 93352764, 539812519, 865309806, 246213997, 80577867, 94044670, 34259491, 900214355, 283861340, 143152553, 453573952, 678052406, 196678166, 234151592, 984516832, 159833631, 854172879, 559890426, 116216195, 975014756, 54447424, 647582410, 224494882, 550422547, 44583604, 677596439, 566922880, 151210688, 717807878, 438536318, 779070822, 331908567, 409577997, 663343273, 473936805, 623216215, 626185677, 275484820, 875880498, 192215315, 739364134, 661976839, 296776081, 557467470, 201779627, 375941250, 33375632, 359999608, 918227095, 843101138, 441735271, 675777667, 249384347, 607163241, 830705024, 70511010, 541455456, 805695658, 718643434, 632401717, 101763647, 176342387, 707552675, 675128759, 629081108, 181786333, 521577826, 745788608, 876195896, 766835597, 679139093, 804048018, 356794241, 251030513, 740848795, 814570834, 662785240, 330767278, 44418447, 620149305, 400969524, 548583246, 677630055, 121790490, 303476886, 373870405, 420396182, 358459286, 491826218, 34828716, 994789436, 484029044, 760132543, 786582504, 532209398, 797095850, 732225562, 168913392, 239467469, 926411074, 408341901, 134762475, 975668957, 807162764, 511766112, 31669802, 594425057, 51618979, 226755114, 485643563, 819888706, 233142528, 376969510, 637850422, 853674140, 100055835, 222032176, 543660820, 106642716, 724656558, 575986504, 149379502, 540836323, 629897945, 258052832, 196791976, 187832264, 978240781, 479063334, 299982489, 688269303, 896958041, 687721499, 571257993, 635748947, 562855532, 773190014, 844454868, 936177744, 485618824, 746181728, 994671344, 324749162, 331590571, 110544199, 506472528, 205390263, 807492612, 348447774, 395622943, 100748327, 417533146, 767941167, 428538689, 550506612, 69834539, 557900075, 193423704, 549224416, 82834920, 721236604, 430683312, 27844092, 486329375, 221603882, 403709448, 808182877, 742769817, 650694517, 996607299, 182204080, 427724911, 796947882, 204255252, 248951169, 268592481, 594561978, 390279214, 14247241, 634631864, 21411322, 836389976, 607647759, 868427740, 773730280, 854258916, 893590835, 425728318, 145598965, 709781879, 214889669, 910369190, 655136979, 575784759, 450689284, 829187283, 644043409, 328219003, 578415525, 948262613, 710028145, 765610128, 277903742, 987737975, 279358564, 237032751, 113174972, 210224511, 93941532, 306959045, 940049898, 521388085, 226687173, 112050903, 717821252, 344071582, 985474352, 250766258, 105100576, 661551682, 873790388, 918338889, 293251957, 29531396, 81619563, 248748261, 108684215, 567496235, 320380358, 593981254, 459562454, 22318442, 288708328, 146314257, 320217519, 368011937, 712530690, 310576298, 503994681, 63056866, 821435231, 388929688, 987046503, 371135713, 353886346, 942035211, 476153635, 198466302, 532143254, 352135634, 373693982, 878595979, 646433550, 298581404, 445358813, 279537788, 819777524, 783936909, 475799906, 107030603, 829534351, 822915941, 946371738, 571700067, 570181302, 584353306, 762498724, 50589566, 328905896, 418822509, 533506614, 157534741, 906429409, 824141821, 990465531, 689690516, 676356201, 971493111, 821862416, 145800174, 150048480, 374268541, 841401314, 117491063, 99594416, 572803135, 478058600, 426529624, 286459110, 233447206, 871355469, 400806489, 146370502, 944064645, 771880070, 479298792, 462148428, 251254268, 776981886, 428813488, 179149013, 874747848, 434944151, 699416347, 19392475, 826833308, 202975985, 867777273, 643780650, 857207510, 644566825, 219411030, 538159448, 278034470, 300883962, 398511046, 193533840, 834170745, 605858346, 50137582, 694071780, 478930569, 748150130, 474561880, 154149830, 754655577, 349277979, 519420164, 568016691, 865585194, 358362160, 124053756, 599330893, 435790517, 522710349, 284294313, 932959788, 887398681, 377131721, 937057475, 824901247, 569841837, 9583234, 465549251, 393077469, 643889862, 460946677, 545731719, 661790966, 739416316, 361215636, 410607123, 484351007, 227354926, 40258216, 51069916, 563712441, 848262356, 661697090, 654055548, 110286337, 962824946, 709048668, 918401820, 340884341, 999632645, 384996596, 152886205, 18468877, 768735069, 528191800, 731221884, 28318792, 33660352, 545153441, 202943173, 569820465, 202058795, 615990719, 706582543, 621731490, 129224970, 554914347, 707251924, 702468226, 410667958, 132537788, 117220327, 237174665, 211930193, 460520330, 876077023, 224788650, 130611665, 929393872, 47487092, 138789710, 210598402, 931801412, 865692805, 459725685, 853776083, 458438163, 65274865, 965209016, 445544681, 663629337, 682085080, 114093044, 936366950, 89363, 217430139, 486048642, 217871301, 658534276, 122213183, 546056347, 356207059, 811216927, 96029299, 718763570, 313385225, 853672014, 771278886, 653335542, 738006576, 64060677, 580861309, 808826847, 272503481, 523811510, 100119483, 948070289, 205793974, 709951288, 437669039, 969534088, 524233285, 671801681, 579268847, 397045506, 21497734, 789083943, 896348274, 922524404, 143107094, 180106030, 137701149, 626190807, 878385978, 445296034, 517569237, 208988864, 495134697, 837313210, 469806632, 35529180, 761276905, 473000315, 359747200, 473685057, 968384182, 602652556, 649157550, 180429768, 383857424, 398194683, 222587300, 744809284, 69628311, 351236983, 860024100, 223829553, 910020713, 882947342, 688975046, 86903986, 981165657, 809709505, 222859366, 203255811, 527242678, 696293994, 823485094, 61802878, 344912815, 613306841, 69023475, 867084731, 837567956, 612341749, 578867691, 252226542, 384597804, 470209007, 391201939, 899571598, 837952184, 871611285, 801505376, 730557012, 830762600, 521608161, 456426336, 521565797, 173194348, 730902744, 390620487, 15968335, 523478395, 340305049, 5874986, 652262252, 614114501, 717436120, 695232264, 983393419, 193653650, 105821155, 914220299, 319796848, 329406054, 792639845, 334065980, 374450058, 980750860, 924078228, 201343031, 9561264, 883265873, 565097981, 650373479, 750995213, 154859965, 615869213, 44905596, 216612622, 810824857, 226718620, 223211499, 221649749, 798643976, 134283029, 668011262, 974538732, 925254228, 775955938, 427625015, 443605112, 632091591, 673485255, 272200991, 501935246, 994550162, 680875930, 415886953, 637430306, 68458935, 851572113, 894829958, 424655790, 816025772, 736328611, 28033139, 815086246, 189454368, 592927326, 250163546, 814124644, 528441363, 984635635, 789161116, 215416051, 16758527, 895219758, 548468686, 872413611, 716216350, 511365946, 687398025, 536395305, 445030815, 497902667, 1177655, 595933107, 522234534, 955072856, 329219405, 126060345, 520309534, 283702922, 861346108, 203370225, 133687454, 108453027, 401918396, 928525299, 902641679, 627478841, 528921737, 441963945, 511796080, 15507689, 263763757, 525244869, 626287752, 600707817, 965975424, 317361764, 686395317, 459823709, 594464276, 673314685, 762500088, 72845653, 534337927, 187674068, 780742001, 310265627, 186558412, 133000072, 548795239, 770747532, 908525691, 615221376, 973298150, 944632111, 750029093, 551534617, 658113730, 364681897, 877950739, 693046878, 420475574, 322726044, 551336842, 563269836, 400246572, 895854770, 567168150, 593593849, 328670355, 80749394, 432561913, 950721362, 688512757, 433436843, 312230675, 259241287, 695933257, 960314664, 335630498, 709404917, 878874637, 312093144, 336308109, 265409281, 293805434, 576588532, 313507471, 725403036, 415485037, 649427876, 487409989, 559613082, 550313377, 758272468, 63152961, 834975855, 523129228, 564147822, 44779077, 531385870, 388113133, 221629944, 225340142, 939158887, 374037998, 446324485, 106134864, 267632441, 447847340, 42974145, 906147345, 34214786, 625869996, 956803478, 700727220, 151842856, 655736674, 4624401, 504226019, 272277318, 678693976, 376662844, 904263650, 230766007, 421217960, 411926693, 533671160, 131067384, 551058909, 10876618, 655626010, 193211374, 889366582, 34759107, 350126711, 596677409, 621921342, 17499064, 788996027, 876310672, 361364854, 672402430, 909109818, 156356135, 791933790, 827619231, 422750181, 597425534, 722032661, 335692732, 904376069, 744685996, 109177096, 701394742, 805766703, 764698639, 303220855, 164543496, 627369648, 638254112, 404991042, 457684944, 642153536, 576676224, 832533671, 328837287, 983461619, 782244797, 311720022, 758146781, 330983643, 94000418, 742530503, 8469865, 585677783, 304944771, 619792206, 773539433, 381711074, 998900780, 650503527, 577153382, 490173158, 423502895, 801300980, 433022558, 364314396, 970572310, 591705679, 727392456, 205787746, 912366167, 802843607, 873818331, 645906868, 913320301, 376033160, 646065100, 921125412, 147790276, 381405707, 943672056, 588010805, 450762387, 504538377, 482569206, 260788992, 881855914, 29236663, 217545449, 753198116, 122700669, 690920404, 970316738, 475461957, 700732461, 473569919, 98537509, 593506898, 769506596, 490671124, 634167504, 905085837, 695129447, 959921258, 785222307, 617725503, 535178494, 910855315, 26227769, 590016880, 305002831, 594371625, 897605433, 429024479, 570478378, 724661393, 130521678, 968924295, 766242546, 79552939, 255762211, 31307805, 335504252, 383033106, 786802654, 235676654, 117219966, 8020342, 545796586, 957621445, 168905937, 182679094, 379725780, 573847425, 797273324, 358170846, 42022350, 98467955, 11870691, 845236485, 65435095, 727802086, 500620936, 946821061, 635914927, 389611341, 111027405, 84911723, 796153970, 854563102, 521677418, 378697149, 287750945, 791491627, 586513652, 973675468, 274122223, 237792852, 857243859, 794856200, 571266445, 751083570, 558158066, 921949499, 974597197, 861804875, 727213334, 286318198, 54170509, 799356136, 300527844, 392539226, 585888280, 375717125, 827492841, 3627712, 435796156, 579181031, 84546009, 643662611, 614872004, 670046970, 981847279, 260226473, 849845418, 409310615, 235544480, 18149707, 428950389, 741122482, 375661106, 939406679, 250078698, 154035758, 194838436, 933871139, 794868459, 688201079, 12632821, 614226222, 946954493, 620888848, 13732048, 293310250, 668432133, 860446116, 109975481, 22193594, 705161162, 677005177, 759170689, 288823090, 206457515, 62149203, 432140663, 810585733, 615693176, 745288387, 138605600, 436994113, 84214731, 888000420, 555544016, 730013377, 428524813, 465514749, 353912417, 649731060, 925260156, 710642409, 757017510, 144117879, 397149031, 769696938, 286557394, 814645801, 416172764, 67451152, 1894392, 133524942, 840310671, 250193199, 92309960, 130206474, 899586319, 117282305, 343364854, 806065046, 76894018, 954242050, 831404243, 214929781, 88053016, 432083790, 477435737, 204926044, 653378003, 293340223, 607443676, 45969032, 232454317, 879287277, 354825014, 537089979, 371712947, 640029941, 477070920, 649070188, 852234413, 733409927, 897596611, 805493483, 238593287, 101377551, 111994773, 299533291, 550373993, 278121331, 412181196, 451724169, 275757973, 283434016, 129023214, 580470825, 677945279, 156635794, 185718286, 902918670, 65278197, 264589553, 901837350, 752794744, 618902216, 241833334, 510637884, 37125083, 408460840, 686222533, 449205940, 851267703, 762501494, 471172033, 590275827, 391711585, 37924792, 885472182, 691595856, 394562893, 447542295, 220501614, 701426310, 954834133, 850494673, 486370221, 324464242, 987656738, 760069842, 467603325, 847245207, 859481154, 692820800, 25654109, 391289021, 335315327, 932826936, 664545584, 86408162, 81989762, 819740514, 580937911, 888137919, 918345186, 236903536, 444095022, 782239983, 755367216, 483021501, 171893402, 842851639, 820054763, 995542571, 890314944, 304062765, 982753133, 299781172, 938212367, 323087214, 755904494, 768839365, 572152167, 643627346, 76940079, 349905877, 22602733, 702998003, 320038850, 342848492, 525901436, 476043410, 871562070, 129686392, 27514613, 134537199, 70595755, 429997523, 199026592, 909775465, 824728126, 385988912, 689101958, 882924997, 140966939, 115597754, 652683617, 168669280, 928304130, 137940902, 735495475, 262746991, 482006778, 895023204, 711993735, 534582154, 168764603, 363300019, 789868574, 495493936, 867364459, 373636770, 276123385, 205958110, 622868061, 986088011, 571634399, 875304613, 724804817, 811446558, 916272857, 360072142, 298594435, 640087263, 133444161, 104210175, 185994179, 188452246, 710618780, 58149119, 457951517, 757721293, 9174418, 290520106, 817277368, 410517594, 637013035, 42341729, 496937076, 443340843, 898548855, 643010971, 476132652, 460319427, 887544631, 551914617, 186420878, 964073122, 373733611, 541038716, 31607562, 160339235, 914466745, 363023829, 474228307, 383358251, 58213346, 857677657, 99274665, 487024479, 356387601, 920683512, 169932504, 14409882, 454906605, 335314185, 523421258, 322597424, 663249274, 688041867, 918640240, 402431346, 934846555, 831463482, 159147783, 26580257, 316663652, 192603404, 245461332, 844791115, 865207132, 473300106, 361789962, 656400977, 245668491, 191408477, 321826164, 778639348, 719341041, 915745811, 208528099, 77154621, 277235233, 489136891, 174385330, 747307370, 28920098, 294225766, 578519494, 967189433, 91266145, 996036795, 596104331, 705844886, 163584615, 613593887, 2576051, 526711755, 880711049, 422339272, 419557299, 599199041, 14522705, 893780929, 219071079, 598319534, 271972927, 903795013, 15301565, 317863367, 38169379, 338228557, 179408884, 629383526, 410612719, 831416232, 469616139, 583607663, 190569759, 516568062, 474930273, 309643836, 507981556, 226069188, 904228421, 96685930, 863084734, 923521085, 636733821, 639982389, 718718242, 517526358, 949824077, 857078438, 353818152, 298601087, 259792954, 378491110, 334416457, 32723774, 68707890, 972581571, 693307003, 245047902, 448249765, 496827874, 614305873, 698418114, 890933433, 141305247, 819738067, 303644412, 894206155, 299037045, 274508711, 216545185, 578321887, 20278251, 332991880, 566295424, 318840052, 766303526, 675907587, 610617542, 63196646, 983314076, 527669096, 612508056, 493384818, 101934620, 637734391, 418518460, 503751720, 141860994, 243615824, 806764273, 67045785, 711416216, 223611714, 132626683, 489113190, 265502859, 788244920, 575068657, 341094481, 993197080, 169854595, 779504607, 987260955, 536453695, 130499676, 940978610, 180359419, 973353395, 684211990, 173550136, 276445212, 293753703, 624090845, 284981247, 721751160, 540042771, 497057377, 112234686, 131666525, 677327170, 476222183, 197978395, 924012840, 584705778, 98767466, 154913779, 918105060, 383620514, 506398769, 571555275, 847908703, 100983053, 129884219, 67683247, 569993348, 358311073, 909468076, 275492522, 312803961, 55265591, 466808235, 340836773, 248079423, 65948703, 420735860, 218841610, 689521458, 850545062, 2101501, 69891180, 865061801, 941280578, 68758190, 299537483, 338702138, 514397865, 775772949, 926909520, 894639410, 825508704, 814056287, 84881938, 891143313, 777078431, 596168750, 26473339, 968708216, 25154574, 580399746, 612634838, 534497152, 178423014, 137036105, 631053843, 768050265, 360711496, 38820296, 444518350, 676442758, 346679134, 659589456, 839868048, 284355183, 534060560, 471961234, 54951774, 247615991, 971499772, 913411129, 928811285, 919167339, 28131548, 416919312, 462646952, 180102490, 716436846, 483257480, 801557041, 114771424, 462635178, 772574258, 621168789, 231713116, 551285453, 27880772, 718921775, 706818308, 678003139, 146781575, 73117734, 479741154, 67119098, 93376157, 560079481, 77064198, 385445986, 413568853, 714756175, 868835988, 737742219, 125090207, 40464506, 643885922, 41202652, 292605522, 684968136, 617642233, 374065041, 89895500, 281200289, 765942031, 908190106, 761820326, 948351123, 489932033, 875463697, 527801832, 874469716, 654334866, 71641426, 189720298, 573580245, 489555410, 650082067, 599834514, 5484139, 14222353, 452354926, 314887026, 722157439, 910890085, 386166536, 267360934, 423389455, 663481150, 895439275, 38047623, 42524828, 666241291, 306386862, 334094788, 913998053, 505106174, 206426766, 739722943, 335370374, 305021004, 203690052, 106809444, 289798742, 526702570, 322068448, 840355764, 820143558, 377388284, 152871725, 408395507, 546137556, 195035881, 109845907, 369054789, 472645867, 183339676, 752757746, 634579622, 690350815, 876313779, 622012310, 943834356, 760171311, 765883315, 923809453, 863819357, 761909999, 944775139, 313104158, 218698649, 657563700, 798951774, 94550071, 66886871, 133200376, 189795811, 36950711, 626464264, 99790418, 960461136, 385371212, 445807087, 780363728, 511331829, 241346047, 778718410, 802413168, 751853232, 170600651, 309572803, 99752789, 284321298, 23235627, 873496852, 108305689, 138157747, 269780742, 79684914, 41647684, 931151611, 310201077, 836102510, 909275923, 175000804, 304743713, 779419726, 577588327, 702600981, 191724920, 647337343, 575271606, 439525412, 202836557, 631388112, 517053956, 655041467, 415056267, 111362288, 382353658, 766726887, 370491117, 931814477, 761480454, 146583158, 801598457, 210602949, 426392255, 352933670, 828586655, 582625635, 428380199, 161312077, 458676086, 210753022, 771174268, 965840126, 748293517, 92942587, 41062322, 731634808, 354720081, 34118444, 653457307, 579030932, 336812309, 210286746, 258464669, 939453694, 77168787, 19397039, 779136975, 764639918, 249757849, 419058333, 986454564, 434057736, 733273686, 790981101, 48959148, 489828397, 736795444, 290855696, 414022904, 415679695, 834015762, 938999841, 132394204, 307395310, 158357129, 918242421, 163293750, 299740439, 830982173, 371187224, 377996445, 861989427, 45127532, 784055032, 802534066, 925493738, 469521753, 209555816, 221314737, 289219131, 761571908, 547837642, 345986597, 676223702, 771668910, 513641082, 102432159, 975485393, 463200884, 388047471, 909679141, 905846725, 645519595, 142329258, 419624679, 477578987, 664095759, 647044172, 738521682, 827263187, 288077983, 449508175, 459707544, 577143932, 342147380, 662883287, 89338155, 954628796, 867605434, 226799815, 768708120, 251171224, 631018412, 55528773, 134157107, 119273579, 122477013, 22365147, 323116668, 742694354, 766305129, 29513243, 777254021, 13391101, 514924670, 228866401, 68721710, 414327528, 990768163, 153041571, 862694100, 477767024, 509161734, 842346857, 735802324, 492900178, 367145971, 98263732, 224452598, 124564421, 539577993, 64672172, 560073467, 476897429, 814634331, 903116002, 651152634, 895195961, 121579303, 469136146, 384798029, 318370818, 324028460, 186804508, 340064058, 780039931, 197050081, 232346138, 888059596, 480283873, 528376582, 819766706, 922309708, 535721431, 77750426, 329743480, 810418248, 593421799, 665888131, 749990, 781547087, 381566867, 923025625, 766328123, 889055508, 692315206, 460430263, 526944993, 2098389, 580420130, 306211844, 818688064, 351669168, 210546299, 902194636, 68087605, 235229988, 593479585, 707632202, 803891852, 750380135, 204447647, 909111337, 450392548, 737356003, 772296128, 551565676, 581274679, 885369183, 82352390, 295275308, 451600007, 67418900, 19794254, 796483097, 338580479, 140514874, 280799999, 866388971, 294741876, 205735152, 944773332, 686936633, 771556036, 1534412, 49312668, 721344130, 175876690, 820679718, 797708890, 750341547, 18142227, 239393663, 322771565, 555955968, 169010002, 569074714, 869515184, 158245089, 72913053, 892707900, 967214415, 430704353, 470543745, 322790870, 542589931, 535442240, 54363697, 84557517, 495566403, 630248585, 752881448, 839567500, 779689583, 240162702, 383295733, 668232107, 131390300, 760900203, 312756882, 40798119, 133574170, 981995981, 195225777, 71445527, 356082708, 832650298, 817184141, 700796355, 911719345, 351767840, 503475090, 354617970, 86112138, 371961375, 729022259, 428198073, 582094085, 639136322, 112464722, 646434091, 636459573, 688149574, 284587344, 150819546, 276443905, 6035577, 230337752, 380228659, 481679537, 207665564, 75150291, 580060423, 996850934, 567940948, 346913533, 513855728, 214657181, 870349552, 483448321, 801125208, 190343440, 682813125, 280059865, 68544223, 853476365, 384851668, 310872366, 126104806, 225820029, 932878921, 418820166, 92173362, 462035619, 510606509, 563462253, 294031496, 314799116, 579270796, 185060549, 508285394, 128518217, 722676839, 213356142, 562785359, 236012688, 492412980, 380666940, 940961231, 8425231, 311656023, 381071304, 760351651, 362080591, 132256487, 44056827, 371198215, 751956853, 642885306, 651846033, 633261517, 971930861, 552604591, 638158344, 370245535, 498381627, 3153016, 725499175, 85548529, 844075954, 54905095, 891883428, 906728316, 564559566, 89568645, 432366414, 385820105, 405053772, 492141763, 476799619, 912802574, 453684751, 397743035, 42946978, 328568886, 456373303, 610244020, 984346282, 888176754, 628597232, 20858228, 247482468, 977757160, 621855350, 551038584, 527638418, 875397502, 282035970, 19399997, 386798804, 20104204, 818219049, 454901339, 533614627, 746221997, 65051192, 328370030, 377079756, 922609875, 659963566, 616719332, 47046405, 224949760, 404656552, 794253081, 350267993, 729005964, 802700990, 524907234, 9021734, 526290811, 476232458, 912305934, 667161858, 108029198, 202644394, 621604248, 697035270, 356015194, 63498934, 800311021, 275171079, 341302583, 399584447, 642143140, 314091942, 887803491, 556087158, 221322099, 664107786, 482909368, 830937996, 240324033, 549732381, 674413376, 705983442, 864220638, 829969093, 3893605, 52043863, 956252540, 454209902, 537271026, 987658606, 791441035, 590990027, 330530674, 205584240, 101776232, 841136691, 671115085, 965492865, 356250137, 469151410, 537465055, 316021434, 184168341, 356557960, 496602656, 125534268, 531989395, 482814134, 73360906, 780945473, 113261608, 582865647, 514348730, 561112158, 382665649, 649411486, 707422433, 317471382, 115293429, 318370062, 677486434, 737231737, 627690803, 667706488, 796312086, 765341418, 189897316, 28129338, 684223392, 924922586, 748845563, 698743606, 69134699, 934463937, 234612004, 596642462, 656897682, 482258674, 778739118, 902324320, 106328880, 310864913, 294983701, 788691232, 553981795, 447316025, 483598057, 894834725, 619074810, 294286317, 869173436, 37987364, 911834632, 646746839, 830264924, 849414648, 193866988, 844646840, 117858721, 991682510, 40348022, 253204415, 653018280, 423767445, 175664734, 346216077, 189920127, 557742404, 897296405, 76930158, 17566031, 100408640, 516975020, 418813640, 539118499, 383039123, 500655129, 354485915, 362181173, 378003307, 626107051, 910193867, 345949278, 555386804, 95339431, 565136147, 450797510, 736916848, 2435720, 68700586, 473355872, 108604874, 245832699, 62667594, 986925472, 540153956, 994535836, 342671395, 893596853, 550464502, 79196005, 108136474, 411520899, 795496622, 796720212, 386053925, 271334425, 523198377, 14830368, 215294434, 934936471, 351838049, 839749441, 78916376, 262746991, 345304927, 993683707, 58179424, 786237186, 888839506, 980407247, 332945480, 366863331, 734516266, 892413501, 731412348, 861795686, 255827059, 176483088, 374796843, 403573549, 96124549, 114252329, 566204971, 415169685, 837992282, 517688184, 466758301, 677904524, 454631675, 659650968, 964105623, 219809876, 269287596, 461672685, 809485322, 342901769, 319056999, 759658419, 220244799, 390229643, 755983491, 520031327, 672595471, 222209035, 162963856, 518342698, 731144151, 139215777, 899076148, 617631755, 948249783, 697292064, 600748096, 444781927, 732172617, 719803570, 859117889, 165075103, 273132991, 636191958, 228398484, 465999590, 951623802, 489848918, 724466829, 625383124, 916496473, 938690559, 411220051, 885391124, 597534908, 896344374, 808571321, 752242062, 360304427, 583503057, 41849687, 310088897, 893255803, 916232271, 714072215, 494091785, 571428781, 528032246, 523984445, 967738201, 730564940, 702372550, 435009603, 701557373, 608561388, 140637147, 327022721, 781012152, 63057974, 289179347, 811733278, 51326933, 139414786, 806340905, 407286299, 298043729, 909249712, 944241631, 772132840, 469340244, 610519007, 3929845, 472846245, 98461440, 518261072, 670706028, 617180714, 103363263, 131451462, 479713047, 833502713, 342834153, 388135164, 754482326, 81763704, 433502844, 877688350, 128164567, 36217508, 427548130, 695110251, 323985344, 590144927, 546873591, 673781570, 731876752, 102726394, 687996085, 266486598, 878709215, 209268891, 458668987, 930016128, 424082622, 928341593, 690173533, 395268565, 773017730, 805704566, 220480686, 25016110, 788259879, 457705641, 125894734, 173005901, 354033169, 947482679, 851734997, 884939221, 581225386, 711593742, 9746517, 251381620, 970543376, 809576589, 906716609, 760018168, 28325491, 714126594, 157966998, 165665404, 838548171, 642850206, 119771335, 901991334, 549904193, 181713675, 238003926, 822382940, 211601180, 636601626, 688802091, 160017360, 100374805, 222332575, 966534206, 850329236, 734357890, 439384898, 932307180, 862977265, 78939555, 4453674, 249426049, 459846919, 628839638, 509747853, 94741098, 913028640, 994570594, 634728954, 450105489, 602542009, 594487299, 959968792, 632265514, 288018375, 963971844, 987254727, 366561122, 971069967, 293814556, 558670163, 196968908, 100529559, 277360412, 800352631, 467383433, 776029303, 631230215, 28984219, 174080649, 949873929, 576297143, 537290484, 621084382, 950390182, 240506959, 165980310, 164035411, 671517661, 454265774, 337009434, 587573759, 711777892, 859672575, 746567980, 180070478, 659092104, 853573779, 78019997, 826261474, 580606375, 904741072, 802523309, 351176654, 372324303, 57915953, 229587910, 899706072, 757201998, 179379397, 219563714, 566360771, 295380330, 743797879, 550816298, 350313261, 754450040, 736961393, 215895853, 70612637, 996965131, 265837219, 486083543, 864630779, 467601913, 773697849, 555143778, 635323276, 866048893, 674139190, 232776698, 442702722, 574423553, 74677636, 25310844, 873510254, 236053671, 905229802, 703286448, 302370978, 918833542, 970090802, 947069264, 988815609, 210880451, 583928924, 909039884, 751284943, 29571015, 936828470, 811410688, 836658519, 104268096, 999367623, 736377196, 516553509, 958369053, 624019676, 483746271, 671002004, 622811623, 799188956, 468234487, 109269690, 199441908, 952129290, 555033725, 620718064, 108837250, 603335409, 632755876, 442029989, 902477556, 817306109, 446481716, 626710571, 317481366, 971199975, 51538903, 545861049, 714387215, 630114458, 576608222, 748360497, 315630742, 96793577, 876005790, 901751596, 684588896, 554300853, 510219220, 541562772, 807142244, 623197316, 787551030, 954016928, 481917123, 104452565, 546786279, 985761828, 904435725, 740175488, 771601387, 723613541, 573766298, 566859016, 984932043, 734024046, 634153998, 432299325, 953082075, 877548215, 700267173, 174310867, 810206437, 453103454, 865721227, 39441058, 176547971, 575567395, 353025287, 483442174, 816332150, 319175535, 481153710, 187964216, 911210205, 778351751, 648344180, 537843092, 96877141, 661317758, 538944689, 24249537, 617316633, 84815015, 644212787, 584844516, 633731329, 546327961, 445369203, 775284552, 164588287, 331328054, 773991214, 46865780, 215627802, 397321870, 362205332, 843577493, 536673610, 433635575, 181920407, 292129642, 981257240, 111184092, 929912675, 971881332, 594943464, 426602752, 409745110, 845085775, 785636997, 160781847, 775358254, 31370666, 948444215, 392980051, 723187877, 473533032, 659620523, 708517848, 273719538, 950734294, 800549114, 515437642, 924974921, 924067535, 4759756, 192903496, 972101888, 77387998, 902782068, 534802721, 744126977, 227425387, 314779646, 630282542, 191547934, 615187713, 171541531, 211467804, 640426267, 881713467, 692355130, 107613713, 567875809, 470006453, 838282675, 541705621, 243508899, 558028448, 709069070, 553306780, 408816508, 627101267, 692075887, 270392870, 688600804, 151128475, 131668789, 454334381, 471845589, 586649242, 745062973, 786340124, 914215190, 517662652, 803971997, 546874932, 557584764, 308781995, 187343329, 498074973, 109165856, 590204156, 373768313, 913154822, 991779236, 224029087, 248531518, 612908984, 927181389, 642961733, 611026196, 845161975, 566348890, 197092204, 744095424, 742738556, 827406317, 623231560, 651458371, 894208580, 236092014, 106600007, 925799141, 887361454, 256524843, 675067559, 530481716, 283848199, 562098725, 475190851, 472855889, 206732040, 416787367, 92859522, 239669732, 229175663, 760048726, 113027011, 261217033, 528655458, 532183433, 380685340, 7491376, 121420405, 784237728, 414591949, 125725552, 826269461, 718061133, 314258615, 232355738, 631403064, 133759312, 85932838, 516851702, 182474444, 178520459, 234195859, 999623785, 742811206, 571311252, 541618875, 119306725, 316300531, 611870701, 217626890, 896526528, 502215006, 676957479, 666619975, 211104029, 623662484, 557975726, 536112899, 866195054, 591696760, 408952389, 77623226, 546344153, 626681812, 626245072, 518821807, 17448113, 479659801, 115076492, 979002361, 617963722, 215622436, 864295264, 544069696, 362214835, 669093499, 484065176, 209212516, 520113498, 373835787, 750342674, 223934877, 200353789, 840631857, 585558499, 968254011, 338113996, 136864345, 612336078, 840292901, 978495551, 164715716, 315351229, 880238548, 499937716, 267197584, 124458892, 700291348, 588636181, 222514272, 708053659, 929083656, 593608230, 990685216, 398062478, 150919724, 925169311, 897665517, 270712500, 45442133, 55497759, 856654437, 255076565, 990255684, 97217283, 580747342, 708297038, 575728935, 753235070, 296702553, 715766527, 223484879, 661393784, 434287031, 807613254, 398298662, 351485815, 797088382, 233274516, 148686866, 613545905, 460579019, 582088772, 522182457, 284814438, 831792330, 89649420, 671848830, 984104794, 648259683, 844704473, 426865148, 789308596, 610608792, 614318740, 930453697, 381738082, 942677411, 743044322, 777380033, 229434320, 853754482, 347702681, 482461786, 939346465, 873713917, 44161821, 290169353, 637887491, 257430554, 249714745, 509127171, 486771189, 402101506, 155680454, 717372961, 56209499, 296020297, 701316637, 246330680, 302926191, 552235594, 112610451, 462970829, 411751887, 341306686, 3628202, 304612092, 660067426, 232638923, 58754339, 74126086, 75372549, 498775997, 939538343, 49061727, 528652205, 285658375, 279659666, 519967740, 998416641, 206718632, 413988531, 513513403, 818990373, 399416702, 698104034, 191172053, 145396379, 337577439, 684408924, 778737330, 981555766, 161098639, 664647791, 884861814, 587087467, 461595092, 678851979, 386783540, 954505516, 176302385, 387122964, 601854330, 57833758, 914490428, 6263305, 521945035, 530018613, 858327244, 570105051, 554378922, 960130020, 179969613, 419743510, 478851477, 947885443, 529244432, 294021965, 692830115, 25787575, 168344183, 398452859, 388977715, 376447412, 237319695, 274691480, 591210762, 573505791, 431269508, 466650940, 633563109, 726393070, 291807719, 145011921, 386271360, 844942480, 584997321, 247515966, 489321654, 66100726, 612667122, 396861011, 222811737, 803750376, 772151678, 557704911, 82726290, 725586304, 466462754, 83509364, 745608318, 579186885, 252496136, 549302977, 769546481, 596224686, 237422742, 323173079, 487158714, 317830425, 201889083, 257578175, 320182328, 594150342, 248347186, 183206729, 431619387, 920167252, 916734675, 623778261, 793249938, 267878488, 864487647, 6375561, 321422794, 65000140, 756980048, 550257347, 283130578, 774801993, 459507777, 767982544, 681435773, 238370649, 348419890, 795532951, 511516214, 348734910, 66048431, 282899022, 215753670, 980001844, 716776380, 171018263, 689972809, 817509248, 936630407, 574106654, 232361293, 334717235, 339601535, 446898835, 869857435, 914935792, 963971195, 65519925, 82584814, 976091712, 586590191, 891678667, 322593083, 656125928, 934440927, 88385195, 765133457, 74163827, 968485348, 371901094, 665189307, 641282028, 415231469, 164545403, 425035556, 686904905, 495901021, 929086667, 380137305, 84649657, 724930212, 283171196, 563656198, 112624901, 284477150, 540621020, 844658270, 663970617, 87705278, 430414710, 529563532, 240404517, 107987898, 656696246, 65057439, 686699210, 269531347, 334707314, 516576884, 343522570, 771436467, 546359245, 691148649, 619178334, 729811175, 835612701, 83092900, 798441417, 232717861, 725512130, 100854092, 475510773, 885466183, 980345594, 405978255, 598098030, 498806283, 58673105, 950990279, 617931004, 86049138, 791365954, 78998151, 228422129, 561596910, 676253486, 138725133, 669968431, 301686276, 669087737, 102354411, 713514019, 229057710, 224394870, 605632917, 603760675, 854065047, 46087002, 105778804, 268873810, 340348803, 372644827, 520559605, 240669793, 598176823, 835410138, 783243734, 941468916, 52469929, 655492544, 78214223, 814445757, 882692235, 794452862, 979731952, 842652762, 870332773, 124731267, 401017136, 643393046, 693715570, 667872609, 840964007, 883144971, 895398336, 513553824, 614760739, 13194618, 636595969, 919842581, 618435650, 169878065, 496630297, 142785413, 671376093, 421262244, 716336698, 336006901, 829402074, 455529338, 421101954, 273266595, 278734122, 279649921, 769751229, 282497736, 17913634, 219525327, 344286328, 967397515, 424181909, 743098085, 309691620, 714688281, 610527487, 324738804, 735160402, 626785430, 603092367, 721767119, 171204454, 732048451, 3763751, 963906794, 772879620, 301464364, 784679172, 615010321, 577733270, 259252761, 707155017, 812306325, 422162599, 505329123, 549211455, 145570718, 783277684, 837035361, 187510671, 852457093, 736912470, 826253611, 727631054, 652559878, 266860000, 982133312, 573785311, 355518613, 548351723, 736788881, 476878847, 244649976, 855499544, 721938907, 437110973, 536946887, 759846511, 718683004, 609433184, 558354259, 909499033, 889355305, 716309871, 961646994, 989490574, 384308793, 782681653, 961820222, 918597761, 11674438, 208288941, 633909094, 430776648, 362364269, 542007615, 16527021, 510666880, 839544602, 586237195, 636017127, 957222862, 573908781, 792976214, 252326890, 726412907, 922451046, 208700929, 86632833, 223936032, 182316012, 726433668, 644061742, 993687014, 326434381, 362627737, 928931257, 699892955, 972938234, 525226589, 502056685, 833892097, 874992013, 356832161, 95134482, 202872109, 853620848, 130986062, 94107658, 924158588, 954735507, 611672045, 567390248, 875225990, 855800659, 595977508, 158547916, 481275296, 506915578, 781493317, 133754668, 813568108, 522940504, 415264460, 965050762, 232920042, 551669528, 260648401, 83691900, 562789162, 395538871, 530253686, 607594386, 669398767, 562906716, 81289877, 866237259, 181896863, 59311791, 746191261, 615960672, 895537990, 440108765, 69819166, 181537071, 51199507, 979902408, 241064633, 353013767, 31473696, 681385862, 490444761, 260180250, 642451187, 996515094, 535253532, 484942635, 906633741, 728062661, 645149084, 794345457, 349831650, 634070298, 109363087, 326638250, 999505131, 124348075, 467146505, 725900621, 732532788, 943659069, 248575506, 527169926, 84254906, 521457621, 732643069, 233356957, 151750054, 995921369, 308290688, 708710560, 132945657, 150085363, 365161359, 566859744, 925037055, 341271007, 895864650, 686917901, 285706496, 658411449, 199746388, 888564131, 643871947, 421019140, 623838398, 523366576, 157730145, 207243145, 566666252, 103843927, 999514840, 954000182, 110081835, 610680885, 535175092, 630104717, 434326543, 183270736, 767046431, 152637871, 687556268, 119037123, 338826712, 206611149, 12814591, 47090709, 22554588, 384816318, 604975910, 222156444, 827866031, 666809003, 882838783, 851713795, 513436448, 158512575, 375085834, 822048603, 463000201, 482954017, 707679237, 837038098, 264046456, 946912927, 628975149, 68649343, 806120130, 897697458, 836025111, 36672649, 633348325, 327871233, 21009710, 138036442, 643066569, 786620293, 277804894, 378604574, 607676781, 97460136, 609823463, 767622777, 314325288, 415506328, 696120678, 817937678, 350543830, 300927892, 857966390, 847073721, 753641627, 58052606, 619717523, 515925357, 843331179, 43608015, 707286427, 396249944, 539203930, 594464083, 294694147, 337188265, 352364388, 350013150, 361495263, 149847213, 303662167, 354908965, 562763944, 2459310, 104785333, 320576526, 47148602, 96696134, 51517322, 349095023, 197863226, 630539504, 783114255, 964283165, 187017506, 354102259, 110974184, 906541220, 967721856, 290816006, 878778930, 391405464, 836509638, 299827205, 188612405, 244841390, 595316750, 598160695, 767397604, 691733604, 919652065, 376341062, 130315356, 397792233, 492794954, 465822824, 418124019, 242837244, 954970550, 629214408, 198940238, 785754554, 477895381, 281067561, 209591082, 984620464, 474859885, 29992022, 925742831, 870860040, 712597303, 617940750, 782636049, 455869405, 73619314, 770303559, 63810144, 515442202, 338093063, 464925969, 459652307, 682500949, 60759112, 25847456, 532602463, 46839727, 304464677, 192495835, 719616746, 348967753, 95901392, 385510401, 296550165, 417591764, 930877528, 713022746, 643056957, 834540659, 513381276, 827815959, 380355025, 648093664, 881628054, 176941997, 896541292, 101250469, 466559328, 940901857, 897649744, 133219655, 630312653, 453025266, 748509882, 358864173, 646349297, 476264427, 24047552, 585781628, 69233809, 539835718, 386481475, 171479211, 751259153, 352967285, 400554273, 311064618, 77487743, 300960356, 822342098, 21693856, 598402619, 307134550, 239651558, 468102423, 80872760, 538841755, 81779771, 101482094, 650285123, 347740030, 240251398, 909474599, 894317648, 290686465, 666881836, 274159838, 874479463, 91959278, 585498160, 942472395, 826705444, 50651524, 156971874, 520272236, 601848278, 470009131, 114364269, 986334116, 725712729, 94921599, 815133927, 25641438, 471947738, 774895761, 467361809, 113999943, 740936380, 3683410, 372377755, 56915063, 249726604, 743255242, 647985301, 933023312, 559483753, 533555283, 603750402, 163460471, 820959569, 804184433, 840521834, 136730633, 83880863, 349913373, 578320014, 204042561, 733288465, 348503454, 654936976, 480553423, 988797987, 472280499, 230454367, 289337410, 86475627, 728765923, 435872328, 406007851, 514719826, 867354215, 203062723, 351051563, 699936057, 396338227, 850083665, 634539995, 493594477, 309213980, 707030437, 848415408, 315267670, 703217301, 101025283, 515178958, 594207471, 614665165, 181960944, 232372626, 653823078, 271337155, 5144710, 774399460, 812564568, 936381900, 650750340, 958887294, 303023615, 664205364, 552501504, 731281579, 268681591, 54132495, 778547028, 246091833, 354330977, 438056762, 735248756, 498487908, 68980467, 326464519, 135824448, 12711935, 937974735, 218679130, 230178618, 395271205, 622837380, 568627274, 797403546, 709345495, 976969026, 38262165, 363387465, 31734949, 989917207, 516769567, 657696951, 268099700, 126669456, 685078262, 6345509, 983611259, 672644984, 61961261, 398957024, 635555505, 307968625, 656531671, 908460512, 958203509, 989673147, 918491488, 823636294, 292655188, 110495113, 673731356, 428811030, 720677253, 902010674, 330183436, 650816083, 293762733, 457252631, 725278564, 666514059, 619377070, 843319410, 839022139, 197345219, 467989117, 330803566, 128082258, 694195593, 801840919, 121555697, 423228804, 430418507, 724494330, 120008909, 766556267, 111078275, 938650731, 153044619, 218219787, 690881128, 788965846, 942584852, 318880592, 294772359, 672110996, 362289008, 665920381, 525449181, 18118282, 387079579, 930066408, 132917197, 775275648, 448694284, 894630432, 634297466, 907298035, 191660195, 92839095, 189309382, 134599539, 678016269, 567479027, 791401751, 521994639, 586828899, 781851985, 392023863, 175841347, 694458211, 559633328, 461989451, 569747145, 896734687, 90297731, 793277519, 447044575, 38894082, 772039494, 606685862, 745406281, 506593715, 759787256, 809712244, 371285649, 384893347, 20429005, 855250830, 900107594, 606601215, 601473886, 733407350, 792435055, 303076280, 325825800, 53159855, 634671554, 117601339, 870773043, 813818741, 385051297, 232462244, 511513884, 180762973, 982890473, 668109818, 323496756, 727489049, 624825958, 681747797, 778559567, 123961064, 694504567, 415500270, 973851578, 695801495, 660737820, 838069254, 614823012, 82230797, 704648681, 605958559, 889869024, 565346673, 309166770, 789374520, 866961093, 364520304, 193077150, 71760800, 404141750, 438635835, 737271367, 167219, 438246460, 622368131, 600398665, 735078266, 630945227, 306389378, 775239645, 990612420, 195615407, 251161529, 331504959, 659829971, 601937662, 327595622, 901701856, 231355832, 357919411, 505093044, 742579873, 410512380, 462435206, 249252687, 451835719, 686848669, 558814987, 592888172, 627869501, 312950084, 302310058, 234914791, 22077745, 688864237, 299200784, 680453544, 150150145, 429854411, 287809144, 691936216, 939122091, 235631166, 139529862, 174685997, 433264363, 262944406, 372249807, 850713168, 619994027, 817456956, 420142646, 746817867, 566722794, 109005997, 783221150, 778684778, 413632048, 660926339, 994527566, 897122032, 241170410, 231489897, 27246424, 699222728, 576711319, 409353687, 645614836, 196452579, 366373267, 75085990, 151862855, 185270732, 674910479, 680848770, 358402903, 338555407, 485055526, 522005262, 426837780, 727230706, 765811778, 405473033, 956136411, 346317379, 63337372, 352703383, 836188799, 171454504, 801483841, 741426796, 529584877, 747492693, 801366286, 732458983, 881699574, 671714544, 671640847, 543413422, 960307940, 880309852, 383860226, 505066429, 855869175, 765440945, 798359106, 886375232, 507173319, 565155519, 673569591, 252945579, 208749312, 447386001, 674029877, 230599565, 619829172, 223022267, 675585367, 235994119, 836530443, 885155066, 28021137, 608838559, 521310800, 885073596, 946891098, 669287576, 74898475, 942919744, 184969088, 729556805, 362137171, 406068002, 33508622, 604652471, 670052863, 456635236, 696940651, 915103677, 363274495, 411207494, 827548351, 811724891, 554910360, 549258421, 829302454, 450771317, 333532763, 378999076, 619270557, 111584806, 176546743, 741553509, 333042963, 22517991, 543670360, 693007458, 492507299, 179996891, 190720379, 606148251, 717890176, 522210677, 30286808, 750359928, 184012031, 920218345, 840299531, 138707447, 863325602, 317938262, 781274335, 370902539, 78610741, 616841199, 799277903, 874658757, 533296296, 279412137, 290090116, 882280984, 20799141, 205353525, 282671026, 663210132, 702989456, 543647348, 222995767, 410450518, 918803151, 347277944, 16758267, 681043159, 918918885, 194251797, 916562725, 397633285, 510854553, 638346355, 314160459, 41102830, 967938598, 752763081, 95608317, 28725989, 256568087, 741995597, 505736121, 318787116, 223653358, 277030003, 482743529, 606136685, 743440259, 579217907, 108188346, 144405293, 695516082, 480691685, 451405396, 796801841, 929445734, 310799099, 146352666, 428140421, 397958962, 735795467, 814496865, 478856195, 57276844, 318246687, 37564713, 638506811, 36559325, 364856153, 243480136, 647213889, 141724182, 142896120, 632265634, 935879148, 850753756, 817160056, 479335458, 593127359, 70976848, 693449568, 710683639, 219275512, 45499135, 52108067, 131470287, 676556879, 602326114, 722073053, 408648760, 506835449, 593951911, 862897807, 578394496, 794398791, 179752455, 798780396, 579294321, 534308218, 19714167, 358390515, 698368011, 627691040, 245212069, 726056620, 750260185, 663102308, 568216378, 639290175, 33498253, 210261130, 384933244, 939558394, 649897579, 107383303, 923077700, 6302907, 578820520, 21943136, 870692100, 650802225, 625258811, 127668842, 564992516, 618928077, 317640785, 795256458, 572715329, 582629837, 180015881, 256229516, 53235903, 234703544, 148756378, 496412710, 909900826, 503584334, 193342497, 101769659, 301978065, 409420044, 760911529, 468521824, 117667521, 23073166, 740185817, 247380945, 191509859, 628474390, 596690817, 938503395, 251821785, 701514223, 137674069, 37485821, 544925425, 979904044, 600522042, 971337554, 679194345, 31350596, 587051228, 869680848, 4125675, 464224792, 65444790, 175870458, 453726815, 707736120, 38409222, 383148844, 572146556, 494547547, 817306060, 44363385, 809131657, 922773276, 689404782, 335202253, 96902797, 44046747, 795707723, 173975066, 14471569, 7415, 154539714, 260229121, 157472390, 510737622, 569535295, 124638817, 976724609, 543125325, 640699800, 276860450, 905165685, 46517566, 734589446, 907578122, 296453629, 679465238, 454796234, 957029762, 434163655, 86623860, 445721345, 412675924, 580956419, 224383519, 985236582, 150500563, 765842421, 830826343, 77075114, 676556487, 104687459, 526278507, 30067041, 120201852, 815355763, 452115821, 841601795, 994843307, 331452819, 905060315, 632943835, 923996144, 904888257, 579246988, 66097420, 753270701, 873317272, 81779386, 276449444, 794495649, 974641814, 204575584, 128402257, 444693717, 524416315, 331635982, 937771784, 701354333, 918600441, 685183790, 321680646, 960889152, 43003695, 509304856, 640199580, 451461209, 169711789, 674404734, 216706227, 733674461, 785717476, 827989547, 302898581, 660957272, 175948540, 626211488, 682271495, 857763277, 762972081, 133235163, 434979278, 361886295, 776787038, 608035470, 858521006, 598269094, 781725750, 747224740, 141615870, 610343464, 535986146, 541127654, 693605906, 560266370, 470259701, 499753419, 243423478, 174237266, 469370410, 791320986, 438272190, 128125005, 264610488, 34938133, 691690209, 909489946, 583467794, 799563634, 263115679, 21124801, 399369505, 143132035, 2036861, 583655578, 660229180, 314174494, 593409956, 106288637, 67836657, 336573702, 294985499, 406947918, 305767577, 333790955, 78480863, 891380243, 434267607, 682599792, 140120763, 654932022, 532702053, 719572066, 516385745, 843939086, 385693962, 686127219, 811932572, 277331140, 167535765, 261176968, 964504122, 947734140, 128356187, 896225797, 44140281, 467577797, 909605242, 634447245, 422880799, 738956054, 704297147, 434651674, 734878100, 734260820, 657189735, 284707195, 529377177, 332028067, 933729790, 614333434, 709858722, 721550762, 40221557, 631244550, 310896375, 601811740, 530407783, 421242351, 656930315, 771771558, 856681546, 73896037, 445075125, 538492181, 517760657, 429424031, 328283790, 866711620, 463347682, 803751512, 309067933, 564215239, 208386078, 802383019, 762267940, 797720209, 841740996, 190703296, 867872124, 947238101, 524202743, 75316918, 679627874, 373012170, 239846899, 936644606, 941179963, 230142600, 463002003, 537238229, 971374141, 142539053, 3479305, 117049967, 833208370, 629038648, 477722794, 636299330, 985051245, 237726679, 779467712, 554479484, 183775679, 282981592, 54685357, 379987226, 761509695, 993880116, 32238124, 414024523, 126812169, 446091016, 840171848, 191535344, 367826041, 328315001, 881522473, 840229765, 157924573, 86187665, 593602311, 135746807, 238466615, 338272445, 334448520, 340671393, 978080752, 907774323, 460565218, 970010009, 510456731, 277320079, 125716882, 756207172, 637846007, 552391654, 773239742, 611125386, 525415352, 484483924, 28048564, 761978757, 362512340, 52797880, 730519819, 633931354, 446808165, 788321021, 522550287, 645675522, 270976775, 359618101, 620714808, 259490505, 246160747, 10671229, 952435973, 310111288, 402514431, 310395188, 981027984, 524082829, 508344191, 242834640, 757336126, 489824296, 522469608, 539745528, 907854035, 919367226, 940718498, 436605284, 300483650, 35763885, 698815856, 241403622, 258148181, 951738507, 243750254, 124636782, 225172306, 85031428, 301868968, 725697886, 870827760, 532575754, 757383639, 495448194, 164259639, 947555717, 5618098, 364629334, 530997325, 334953914, 957091826, 552088540, 642888576, 159683968, 799743557, 762858180, 774091754, 4572203, 357965338, 686887481, 462686590, 989349683, 712503147, 275743377, 977255052, 960263739, 204811040, 901359323, 67636874, 737496715, 925939289, 758359009, 679262052, 48746710, 194418964, 126085954, 187917200, 951978149, 266592789, 109928021, 186150730, 550694176, 989461027, 588887430, 975360912, 637631001, 426800927, 662450943, 87283766, 209569692, 930765142, 539826023, 253994921, 276292707, 282936856, 894237062, 521239631, 239012913, 284041939, 981121172, 168514854, 367191614, 178475108, 696040947, 437847775, 905868556, 624198202, 705705004, 571701689, 55320743, 480390187, 742549098, 592483402, 823258212, 87288056, 659870204, 330329387, 295617333, 276890703, 677642159, 724821802, 554878844, 168020617, 918648594, 401990004, 92038636, 428334650, 715314528, 493354656, 778874280, 813800921, 362347042, 418382571, 712888058, 734378239, 800639691, 713272323, 833567724, 528992218, 505121386, 439434750, 532417612, 823174270, 441991031, 171861665, 858151810, 298247708, 234143664, 204588798, 415666216, 761885200, 125394633, 505358924, 290281399, 507261796, 37947797, 988853823, 219796237, 277289437, 92154181, 300661496, 504713252, 308472712, 794057888, 822909135, 970240017, 747823335, 598728477, 511598607, 748607870, 94214517, 227590431, 681946058, 617363162, 625776667, 517933866, 949726305, 928453187, 566900128, 163388271, 964119773, 824017165, 88122449, 547151334, 851714855, 607586184, 791857229, 576128466, 587724113, 836795549, 487570595, 232688896, 820405571, 132144706, 658278720, 804618318, 813227361, 804577123, 841131224, 882447236, 682265064, 561938747, 81422939, 585227539, 597528885, 717772918, 347947265, 336263985, 861343650, 752347724, 4530787, 571060414, 702631332, 244765422, 832924493, 204997280, 206826263, 500396319, 299630330, 616446796, 253293133, 604465793, 277863998, 481352757, 738895508, 353930390, 214723896, 771746091, 55134744, 901701690, 781133754, 525357952, 441123312, 604576368, 858105946, 957012280, 144387490, 984668945, 994804834, 780182368, 509412149, 507375251, 502213415, 690974372, 1797372, 423949162, 636046452, 425239551, 198874544, 10768497, 45154392, 891600653, 466698093, 569346079, 813988466, 592533845, 836537815, 897809074, 792395726, 551029922, 664376518, 750669652, 870921786, 773840688, 578435192, 229483266, 125052207, 256245001, 807009141, 132516650, 471023718, 927900380, 888678394, 531825435, 425389736, 374952539, 182570353, 439178379, 633027751, 495763337, 621248477, 521875271, 535797780, 107810769, 948066060, 629988175, 887763671, 711686336, 226360777, 52446779, 194185297, 588130278, 48079876, 817988789, 570582820, 641353776, 223402141, 253504674, 195829409, 614231727, 631441412, 58952324, 261131377, 357876410, 604289363, 733753060, 760318265, 622618525, 215101876, 132906188, 800730673, 201720573, 861518483, 370032952, 413598513, 543092199, 281350554, 463173754, 288475802, 770760278, 946533055, 994886649, 969433726, 902730109, 181840569, 412401349, 791040213, 976713507, 214938155, 878422642, 236487715, 634348897, 324500500, 857376173, 351563365, 711669717, 870325623, 197284219, 653889654, 272193556, 830424769, 471904128, 960771777, 71023915, 892768411, 471542315, 661286460, 582520408, 276264910, 137212845, 152346020, 60003985, 452503542, 664022623, 168855730, 833189942, 345308712, 566579640, 555224952, 35862346, 976538686, 490701624, 682886677, 400750107, 180430730, 143031029, 837396982, 920694184, 190613565, 901398961, 626493967, 875072384, 34129268, 523851900, 543414355, 411485660, 717789767, 48548457, 258306381, 620634884, 962562730, 108852851, 109967398, 47191107, 737307059, 354288161, 347237537, 182750364, 206604950, 727348405, 647668143, 111944497, 241600738, 940661028, 886749311, 123728789, 119176182, 205398375, 445016234, 538288446, 306825106, 506411067, 388612552, 318781982, 735876945, 590477070, 173971617, 491170183, 867859686, 885722043, 149234374, 859272201, 924440423, 460796473, 372004168, 684787355, 222634272, 616179896, 46995781, 81909115, 595106469, 950628959, 640977857, 394038828, 288440598, 726339603, 434085130, 812750938, 463345987, 231751173, 227224025, 841262327, 160759587, 235497901, 418773608, 630523626, 745008206, 440498929, 846592072, 976351694, 999282374, 706401000, 419324063, 343935647, 972302722, 510551736, 882722934, 466626025, 295456198, 648197447, 958069099, 730892633, 396183378, 429368684, 921051058, 565658205, 540548872, 83804394, 365188820, 275622041, 158798118, 747332772, 892675678, 773023060, 405626132, 586892417, 357056059, 547172690, 762450270, 163431035, 125435032, 78077975, 362358430, 671770379, 719346114, 343334441, 259542325, 864882730, 861163134, 4428235, 666345248, 257636763, 388729071, 775734192, 45979056, 831273812, 268945918, 302387445, 417469767, 730836902, 831305076, 396396241, 839132878, 382389850, 942748813, 756518212, 588548253, 159887355, 204546885, 473343760, 432564320, 808999235, 193700763, 435265373, 362570934, 301888523, 752811089, 509543766, 866431909, 301056684, 18758788, 310813015, 431180239, 714954995, 843606803, 873933330, 489899386, 311506005, 137993608, 941333422, 17942339, 276996827, 285288372, 588270058, 753372505, 688190963, 290195707, 511264279, 94452605, 798847635, 217889437, 908966945, 983336811, 401265592, 268705768, 262159721, 820704298, 915167584, 101474195, 581661298, 349152789, 241201850, 262263601, 534485749, 391339213, 744755738, 448347737, 191677330, 137775460, 288344550, 128013735, 114214890, 500570073, 408309029, 466889955, 409563176, 724698678, 125262246, 337857830, 368684437, 242125996, 54337243, 762832477, 25033148, 726493558, 695502060, 670472556, 149881599, 792962140, 927805602, 335870335, 105614326, 369296639, 64186155, 725833673, 415553973, 224932588, 731771319, 356170199, 799489517, 70315567, 762310593, 433037595, 625670668, 726821587, 203096933, 212506218, 439658840, 135497042, 565894043, 473197810, 35466004, 552881197, 798739396, 774898826, 678969260, 457278552, 905054423, 561299854, 724720843, 749961505, 984597920, 162564265, 570735734, 248816389, 958775282, 995711954, 503835305, 866044040, 282110102, 81968772, 887658529, 612155408, 984625659, 873331429, 602825446, 6506720, 547967261, 565082325, 37071579, 458388891, 601670581, 941893218, 419918641, 264034501, 515671721, 9186795, 156128666, 180653219, 719761674, 10879515, 26880642, 151873922, 543607369, 270470885, 741839259, 72007055, 115475701, 230294699, 5764200, 603959748, 703240027, 992352462, 824975554, 578105811, 634784112, 837422263, 527696075, 24323940, 598671634, 488769185, 932885506, 32143385, 653294714, 838971115, 375523026, 370180072, 387077045, 846292232, 190015239, 363996602, 514661263, 288262666, 3138327, 362741808, 675674344, 270239363, 704712286, 112315309, 873595938, 623679768, 545348644, 825305634, 266961761, 63452304, 435552005, 339033526, 871574705, 446478455, 781148385, 146041619, 733637069, 269534442, 345960466, 281357764, 729285022, 350773179, 696482585, 414353950, 449760748, 245617016, 90001745, 118546892, 673564189, 823077042, 319322586, 62433058, 519180575, 922758712, 73911634, 634993019, 535868719, 502498640, 218906883, 915515250, 657918096, 839793771, 365250803, 258606360, 245769172, 914905034, 964330794, 475984438, 13314871, 246553210, 961877978, 691394006, 598363567, 22314766, 775856948, 655401508, 101850964, 166112090, 210858382, 635381863, 853106439, 460990483, 834297255, 598392829, 296735268, 757978285, 638056403, 824636137, 923051524, 298911627, 12871030, 501324372, 134900737, 830666871, 982631311, 880422712, 848926979, 150086720, 439155348, 949944765, 719692137, 172171675, 39755283, 387248434, 832685653, 899881238, 392633539, 655907438, 827029795, 323222569, 532467940, 646404347, 722137423, 343835249, 665772354, 881744529, 876132524, 188334874, 957239613, 517131299, 439340951, 592720481, 646553652, 951894232, 74827150, 750070270, 650984688, 367874769, 68590735, 114652484, 68428500, 340631361, 979517828, 289563335, 626662893, 514137464, 827654267, 151162058, 292858493, 996591095, 817287684, 978994685, 697895002, 731158619, 406199529, 33986223, 464201268, 200360064, 628516873, 295030881, 152786017, 608055000, 835060884, 495341672, 26216840, 34749951, 115038000, 936519723, 447433250, 475106484, 946826721, 828437230, 398023732, 12596740, 781966677, 832738731, 600331391, 613232972, 193215181, 830256351, 287819825, 880172011, 623905891, 926219371, 302624582, 826430952, 40355245, 703562440, 390556024, 144991358, 364220933, 758783805, 889611994, 410067483, 285917750, 768139045, 305426207, 239459884, 58584949, 408547149, 657734292, 994662537, 448762138, 225101913, 665890667, 322615692, 878647480, 812853736, 721349107, 692490874, 369100400, 770324805, 263838487, 408929745, 464556168, 407202424, 887248317, 341995209, 623009101, 921864870, 617786442, 291666421, 711588146, 153270536, 776845056, 467773192, 908470218, 592958146, 46531879, 442721180, 218839469, 219413798, 513875515, 68782125, 703637158, 602238937, 102975950, 65266490, 873221914, 864811023, 127672821, 906704600, 367148991, 115341754, 718175900, 520094182, 537276964, 955322042, 852085635, 499352227, 6812832, 929883776, 186092830, 13564504, 196904337, 93734079, 908727944, 705168648, 971843292, 450177363, 67337536, 81096465, 387397584, 860012980, 829839024, 118062882, 608844455, 165353765, 285869791, 218319736, 16694419, 679358965, 520165096, 86840782, 634497644, 184535622, 765965017, 820854170, 357245255, 808031932, 60942589, 474826686, 399133004, 273293723, 880328602, 715403518, 925059663, 967170821, 807753404, 928762105, 386897909, 123229420, 113568472, 224253512, 915685838, 391206436, 238589858, 25735716, 117114621, 391495798, 989276205, 387266945, 478720675, 791556486, 234875412, 231656362, 14600228, 441780572, 49769146, 96890317, 793354927, 341005064, 780464458, 795930785, 441757546, 494335238, 728189746, 322012514, 768431207, 72606777, 611401565, 81178581, 661508760, 930682998, 463196385, 893314567, 549977443, 752517586, 844996089, 230029139, 562977552, 788850529, 628252874, 448073245, 466034075, 298294400, 699141507, 950263493, 7278169, 741021457, 360008071, 15448658, 773608793, 889560198, 101167734, 194291399, 135664807, 186640001, 257599895, 538026343, 91624800, 363294830, 176301807, 91041485, 116108655, 504397066, 395688174, 39781835, 253366528, 692358460, 98883092, 128610336, 466412127, 187111285, 164450740, 582980245, 709190826, 175787289, 784858318, 384088655, 467757922, 1870608, 368832386, 733708039, 624445747, 93407510, 357427675, 314849566, 160619456, 472966665, 424471670, 15214661, 7646509, 606901817, 422215328, 751590246, 159858568, 608612969, 658420555, 107845776, 204158244, 215480873, 311577908, 855198898, 79471763, 148974908, 858875874, 68972966, 669423014, 793350598, 888329748, 424732049, 650211175, 256438392, 907016008, 283015761, 801361010, 887746138, 977847808, 309691246, 919396601, 193568811, 858809140, 403055308, 280290088, 38360302, 516448280, 536133974, 701493472, 60489098, 424579573, 437967128, 911055409, 775047091, 457807322, 727249851, 560048969, 244855541, 524607360, 965828197, 689184112, 911477047, 88975493, 519870436, 648294725, 445654757, 791303036, 378418468, 729788058, 81290754, 629918411, 297385061, 607779434, 935130976, 508303727, 557872536, 130273535, 352085018, 862257612, 674890160, 654331446, 738748709, 594328026, 959978800, 377502812, 235493598, 623972353, 69344639, 19909072, 94109180, 349418362, 24316748, 800463089, 391300264, 351652137, 333473324, 664330507, 174982829, 468353555, 543686739, 772575614, 510551907, 945118877, 964358302, 114423335, 422509212, 836666098, 83402492, 550156320, 144947385, 324495192, 716023979, 711806020, 454789754, 628379122, 755661897, 238642349, 58296006, 465714864, 707371212, 695022237, 863930822, 49184878, 684665412, 929793034, 340780677, 279844084, 309375078, 426366944, 134722255, 933748317, 550966082, 214406011, 482325520, 62645035, 751725920, 605089656, 585063097, 451213734, 147024796, 379131541, 70228656, 18727108, 424174519, 895355003, 840577175, 676931966, 93807629, 42208802, 57888254, 879836797, 454302607, 283231212, 820818702, 601228904, 597628580, 933665967, 707869634, 206746153, 623573449, 117176550, 550394455, 94232990, 932641179, 683039154, 825249063, 557693723, 347137906, 382057983, 196812489, 458815056, 721862041, 699079787, 121372404, 387857104, 797250718, 86346337, 365850214, 294879334, 323097577, 310321405, 6283062, 580685920, 241493850, 353888900, 635318585, 716454677, 107324882, 922103334, 382248657, 658380495, 111148935, 717687462, 368289488, 189656886, 533857484, 28313785, 45146723, 489123775, 527019461, 871494127, 832068635, 920120294, 422634108, 858036774, 541700345, 698457509, 274845258, 39692009, 791553916, 406783393, 505970838, 635112822, 607632356, 837584934, 403259253, 215030514, 930149864, 681665985, 294149548, 901406824, 549171123, 67460536, 200737011, 379581569, 228283977, 206492113, 341900211, 240856286, 714096754, 511543545, 362609438, 234806737, 660482668, 994301831, 602467326, 923692189, 624291915, 553380478, 296092165, 883419379, 352964371, 165040760, 527383096, 156221842, 426196266, 345747768, 744907756, 41151811, 492856399, 765556498, 92524167, 139957966, 662218414, 452611750, 84806952, 553029881, 755356728, 956751733, 829733202, 406674142, 623284714, 794326836, 552693981, 731439269, 534556230, 234595589, 358612908, 589572740, 529488290, 687344506, 822127459, 694893315, 250134216, 908323535, 522642892, 354322917, 408710405, 930660967, 789887823, 880224030, 744939049, 393714086, 975556732, 776526615, 928807710, 577548083, 799496006, 433348938, 182363516, 376961379, 918370346, 504007895, 470405212, 694313062, 291446614, 866357055, 821507238, 207066044, 726282440, 532786359, 791868124, 681123095, 857302124, 230655134, 776531342, 5996149, 627590951, 302654790, 388778303, 622649148, 454939058, 476251807, 927381847, 216100125, 705917385, 901544800, 984776302, 231304953, 349279227, 519153975, 172840860, 920278591, 995105485, 220428229, 725073161, 681135986, 667324155, 362261695, 564990693, 194909089, 75996610, 905914035, 782360881, 38942159, 646418707, 267705197, 339757227, 836013726, 275322562, 610334649, 976404286, 711175154, 201862971, 391959256, 230473569, 810817686, 771000175, 784051250, 412441531, 967535708, 370274729, 642476969, 226718057, 757729476, 53755979, 189494610, 657096396, 266281085, 412951975, 398036685, 273605666, 398613423, 51028872, 321678187, 534062863, 846815727, 457454010, 741624115, 678845481, 697607781, 404440308, 461215494, 90808442, 910511153, 340585719, 76218777, 219071482, 207376856, 390521944, 614093927, 494103598, 128790710, 864399966, 235236299, 711927835, 705077552, 479176925, 237198756, 497374925, 37900226, 867749358, 482349564, 709799946, 428121223, 426634226, 898284977, 239964308, 299993123, 197754541, 939655580, 23832867, 39476905, 921722919, 788458735, 181031034, 540082113, 183514235, 350491347, 761538118, 162126514, 943855727, 180612127, 702557614, 815065402, 232985630, 232154583, 365209544, 102047742, 510248480, 66424760, 396467227, 493641, 670497303, 37776867, 25851422, 482574937, 523841348, 312542812, 934573313, 528432699, 31555844, 847220296, 209863108, 16962564, 614692541, 400497262, 823541159, 256842965, 586389911, 763518526, 424893622, 55061918, 231307933, 596143676, 898160574, 806652288, 924440528, 225353085, 249977087, 581805231, 492712095, 600733495, 906343200, 619096773, 743773052, 188936611, 67689318, 365573136, 429362126, 212205644, 163561656, 984409519, 325239100, 982856774, 228648630, 146895795, 581405915, 561846229, 392608157, 669449644, 951532585, 853740577, 162042869, 796010912, 56685315, 656080078, 238817355, 158415694, 266331140, 876806518, 544814078, 357697807, 214080287, 697290668, 259627649, 882480867, 228725185, 671999949, 294687686, 630438058, 177943746, 147662823, 628212993, 967512083, 70614149, 39962861, 129258268, 216887599, 862571389, 407156290, 290448724, 291631194, 144903832, 337861561, 86099321, 872515248, 667784724, 304684750, 676003523, 885917583, 559751964, 97446463, 527437664, 971466624, 998531442, 478508543, 934135718, 574928020, 226015981, 565543704, 943039883, 138072084, 672856105, 784172638, 983073420, 300079751, 683555624, 426527780, 758164902, 621335971, 374018393, 686588749, 701403580, 41212034, 994600494, 345857929, 432637196, 953605470, 879367191, 349164648, 761455335, 637408732, 698458706, 605934339, 703195568, 934890978, 498047382, 375566191, 856992546, 417200753, 793722990, 463854449, 318283369, 48105003, 594330126, 596892884, 217546094, 466314048, 677665348, 148542581, 525550870, 949131451, 562807073, 533745518, 658464846, 460672152, 655673054, 14500482, 988037083, 438333615, 865437848, 50585644, 391105592, 145392011, 505648568, 971639383, 431200906, 221619406, 1795808, 812683758, 327921689, 457813557, 426179804, 614781301, 424617634, 947614046, 236310258, 178427853, 200883222, 54935261, 718224501, 254676364, 688082053, 694823768, 831009574, 934122745, 103471048, 177298943, 546462383, 225422257, 131077329, 480220180, 880419279, 961915205, 393951945, 684902611, 140831391, 896133559, 93729691, 45302573, 22819389, 895982799, 942236361, 85723811, 845544239, 697659143, 364376645, 341378642, 6264125, 476869912, 489228168, 791086989, 406271875, 799580794, 568706161, 365462306, 461329364, 241312403, 948796527, 73438222, 846526631, 594770345, 400295423, 769414795, 572891832, 802857646, 583634605, 374167657, 671506184, 613971306, 952030745, 43813245, 118785931, 721582654, 227447473, 802921813, 666251157, 126866710, 581826615, 900633185, 344132562, 233241896, 812543044, 834330679, 313692451, 398247967, 392725161, 219472142, 300575451, 705283805, 900727752, 16501472, 757617541, 303034463, 358118981, 506969309, 852913039, 350210705, 838107924, 526627494, 628718390, 319647307, 826371522, 177294310, 839825467, 587729228, 62274733, 134530472, 967988919, 278665925, 767713279, 932157909, 717882913, 617425516, 22830521, 370873995, 190002652, 665472682, 23268909, 588940925, 744620791, 686208655, 306208659, 185700753, 353531032, 949636125, 182980122, 872366000, 331348755, 282518083, 353973153, 207210003, 54420089, 400452217, 358325533, 862218322, 329282061, 343237407, 314642145, 590264991, 984320481, 131955896, 610229281, 522671317, 212420741, 788285669, 383429213, 692914451, 984467821, 500761317, 939613889, 763343494, 173160201, 555921912, 711419396, 205193645, 114204173, 427633732, 795110917, 512254500, 416883607, 508609911, 737353352, 186177019, 382019099, 538318543, 423512127, 637262931, 589336139, 824538042, 820305133, 656481624, 525013525, 837712738, 422535315, 595946951, 609540990, 990634748, 945450641, 646779909, 286489766, 459143376, 422165507, 121285087, 37045330, 65192215, 260023993, 1675627, 602260502, 193878775, 589496779, 219919666, 641002621, 622850756, 865229475, 768811804, 247487680, 536083517, 337285022, 783161922, 751675827, 633850957, 126285390, 930964100, 505609003, 998694041, 296534645, 14567884, 675019982, 159503899, 478324931, 451349646, 90655513, 197550184, 585598721, 569115493, 139057994, 460816341, 592386784, 648110878, 350081594, 69580981, 656099633, 973274997, 135270910, 841791915, 500992162, 584023717, 253523461, 221669924, 931649174, 407265680, 155581629, 363076529, 449750640, 911407050, 442528818, 421227095, 744305669, 68467484, 968970475, 120620586, 388849057, 692541222, 927937853, 269020812, 55109632, 585909193, 21803478, 484042259, 653166286, 686227797, 788727194, 821503520, 938351106, 63165443, 48798459, 245792982, 27342599, 156179139, 608746385, 860888473, 108086195, 624442743, 165019618, 734835245, 202169042, 140228919, 39599492, 29530666, 48560437, 123777926, 272823731, 519359819, 554358354, 85805626, 491974, 531256705, 323809651, 616787972, 242415869, 924933796, 657992645, 836578291, 713624567, 358521855, 404889050, 956030633, 121483692, 72523286, 241543612, 624930301, 349711106, 676622826, 659283804, 544354129, 201937365, 447635354, 726174375, 210386754, 892109832, 183322890, 307209259, 249730417, 322998201, 723932571, 413261137, 956474217, 558415398, 515499263, 154288889, 862905050, 376273444, 374202761, 638805102, 311583480, 791880138, 431952796, 613818005, 973729451, 704751237, 557031954, 216468990, 760193027, 990434622, 502442687, 878291741, 436159415, 640127104, 301496085, 736084249, 867071928, 467373780, 293623565, 166279758, 813530240, 448248022, 685599806, 828095192, 625301285, 976336396, 483741116, 184016423, 545460450, 786331917, 86078623, 540584568, 402833368, 245141947, 834964996, 686860337, 548582141, 264459396, 616380173, 959533233, 566666316, 690308520, 534948109, 580355045, 292510250, 866645973, 731521023, 585529509, 266718800, 841362799, 340683354, 309983629, 313545999, 121011212, 462873261, 434380566, 69126070, 133515896, 430949697, 75709034, 331493807, 67416641, 318490175, 682355792, 262769664, 42113770, 949823812, 184844096, 965726007, 669123944, 673967757, 496173720, 639697104, 410289413, 675684763, 457928112, 909473473, 625924509, 918930937, 173337500, 821203232, 551781701, 905803782, 620319858, 987834854, 382570247, 77086494, 730331984, 961689921, 128429524, 967303182, 964628104, 214352719, 452375987, 977428741, 587159966, 706837554, 643913021, 17898480, 518608009, 316463278, 591982549, 533223171, 385635039, 365884547, 400768127, 69771452, 119837796, 269648590, 154130019, 821327134, 807399259, 598859603, 972681767, 599820435, 535447415, 737046605, 748350545, 929429578, 839596262, 127710566, 650641856, 771956719, 38363972, 990264315, 591504439, 923471074, 299445294, 527364866, 812356858, 229021025, 76483319, 344564973, 948567462, 621280601, 253676732, 150292371, 544910682, 745349347, 674486479, 464633863, 308435311, 763644885, 622391850, 231462376, 505964556, 142967699, 780693432, 116823200, 234318930, 577541735, 818431677, 835355380, 66784046, 195399025, 720627207, 221720098, 691218716, 374732360, 679608804, 998299308, 358535210, 6485044, 912167224, 423721117, 237870203, 382513491, 245856286, 646460479, 92852415, 610749338, 451721251, 426552367, 56964080, 255602109, 122876331, 748434666, 77851612, 367752281, 877030606, 567391699, 918410637, 505370587, 465870352, 331395594, 233744030, 322122830, 850188307, 368091991, 360578745, 252103130, 905070391, 480166017, 328588862, 497089962, 809205520, 552791616, 266990350, 743441162, 593229031, 903773077, 942840325, 70289566, 452660240, 534309165, 314970293, 372006313, 683598659, 650875941, 383218003, 53660837, 432384186, 729717867, 296550367, 700363258, 660787433, 796703562, 454147622, 45363971, 115946710, 178739389, 505996041, 874800668, 457799025, 389824654, 946573175, 358146654, 797608335, 598291138, 8888762, 90985589, 686721412, 281463715, 939025125, 73523995, 170788476, 152839147, 131042100, 50939820, 106562741, 432433645, 976256312, 344015902, 901477444, 327929651, 29203316, 249219381, 843921492, 931950605, 581735317, 49575777, 671102179, 477031259, 509796319, 926661364, 86753192, 881510453, 311422133, 162104056, 260307118, 83733754, 605479890, 923223819, 35026407, 814536746, 344359655, 541717174, 379041546, 651882996, 112508590, 974170490, 459361828, 28599342, 558320488, 552650606, 102222724, 256050826, 440067803, 505948563, 838071993, 688950803, 643784040, 294467614, 125608958, 15926561, 53246653, 613775499, 791962860, 220081529, 822506945, 601233122, 877886142, 176395640, 967674707, 572547269, 427451825, 420221556, 699596595, 100892038, 518029089, 48552039, 70511398, 61471090, 850924033, 561388159, 389225371, 843404397, 186747183, 209963805, 653702981, 536838852, 320371866, 841285072, 237419312, 567015018, 616822360, 460362545, 394119310, 258658152, 79221488, 96899023, 865903526, 523949472, 916334399, 995486689, 920415329, 435526422, 475048224, 759135830, 31790083, 546862881, 261583404, 16845413, 136882507, 523035120, 978097224, 361909678, 965427868, 194369705, 346703182, 435506739, 481974328, 146688928, 4986273, 560258276, 371870078, 907146705, 383520751, 573732900, 160582878, 655491502, 350065512, 807873122, 519817692, 878021379, 517313448, 778928217, 597800249, 445901652, 41776517, 707891763, 323719267, 143192924, 859888667, 968742627, 257318635, 736119655, 731390807, 694589343, 425182121, 451828223, 598070422, 246284262, 139886852, 782836774, 773553022, 84997085, 365002409, 382158707, 587495890, 791062768, 976449076, 924412074, 210464573, 97104920, 170977058, 407961229, 784629433] 841315121))
+
+test4 :: Test
+test4 = TestCase (assertEqual "for (countGood [816003760, 105617541, 381582697, 452191656, 291270597, 772269031, 798947817, 507003482, 741396149, 863782215, 307574709, 249561446, 870886608, 463481644, 770713545, 842274976, 349885794, 63750806, 322491262, 893932779, 381864541, 92311276, 613992358, 986298761, 648372061, 498165346, 71101780, 190930000, 339743148, 300637497, 72455589, 299726510, 451680243, 881722313, 906613195, 157676383, 176328908, 628022258, 24126930, 101376418, 485425967, 178995541, 747983475, 488833781, 425258372, 761424968, 993994563, 101118321, 982857177, 260495070, 571049840, 999035629, 140299606, 527275139, 590854643, 316885954, 466666105, 669359699, 232736528, 200285730, 712598384, 391893681, 117822731, 118350410, 555273135, 523242630, 560613728, 354629816, 995504282, 536281979, 558790585, 356409168, 389324678, 98861911, 687959584, 125752269, 179489977, 978043486, 316613292, 190761868, 579993878, 828020830, 461362455, 979982405, 69227367, 167990092, 73475102, 528041232, 706937500, 605379514, 609342595, 628573254, 147407481, 918926476, 206504995, 292799335, 397749211, 932522397, 415290799, 344320191, 285616582, 589783973, 482333309, 893977821, 157411928, 557706598, 776963536, 948875572, 32165988, 918975049, 155462158, 31721938, 156622208, 283361284, 592618339, 544214378, 414678386, 526308370, 675849980, 927276627, 348785046, 56239409, 289762487, 513366216, 956860492, 75976471, 687924987, 868583331, 336073771, 405130608, 468287642, 747863352, 306313703, 894466751, 686906962, 202413488, 541449073, 889805979, 445280208, 138475301, 783518723, 928528633, 150675893, 854152060, 49671387, 545325161, 202503515, 794624349, 122330859, 211449765, 25352155, 799849471, 295425882, 182676306, 248155714, 423165846, 494008014, 640816678, 112148290, 86963247, 431942878, 719351436, 651534360, 189523184, 619038367, 370339257, 597701803, 47291216, 110117788, 930216019, 994755236, 62365285, 834195215, 848238353, 989939945, 74105069, 532477213, 777739249, 721427196, 720876218, 109095062, 993149158, 31089504, 922734947, 34345985, 929948243, 972855983, 443876944, 35923734, 879780320, 585956713, 216415072, 124022053, 434818790, 671343799, 643368957, 803302203, 912459864, 496666770, 954655444, 74026617, 594213031, 328416006, 275969568, 436903562, 458646794, 397914137, 339006984, 872262588, 5568623, 866959845, 461354892, 496730983, 709338388, 293929956, 561739563, 87013544, 541759828, 519043388, 372034476, 189223108, 743125384, 782689791, 965918898, 496681135, 875851810, 178388302, 893905038, 530408461, 746064981, 675734396, 504718027, 979760750, 633892444, 628618440, 488144865, 509323422, 441260241, 139784417, 254876921, 887862325, 920541999, 139703894, 680353547, 730412000, 482536224, 950055096, 384036533, 247117313, 348670650, 516697075, 515099739, 565463981, 598129659, 334355581, 16671940, 784553599, 75517038, 471379938, 673541517, 584184904, 884946697, 959337324, 521984551, 384713506, 166671497, 81564156, 893476417, 406913600, 96687788, 396226244, 938156304, 723324835, 910477005, 806439994, 673643153, 62030498, 751440579, 505594404, 831755882, 641574506, 391786949, 798696024, 932309071, 99475455, 327906913, 303121135, 724855105, 708353622, 700652536, 71144930, 835805933, 797303905, 578443491, 79658818, 458390424, 412991202, 979327215, 108968972, 526334222, 299489184, 247405458, 956336121, 275880937, 98277323, 994366614, 867331830, 969999142, 846321887, 914568362, 695927115, 474535039, 851307805, 531678131, 18418570, 45305049, 12753221, 949438342, 137527488, 77077347, 109908504, 897336417, 208959140, 588615510, 864947008, 989697435, 604876827, 972191949, 353944182, 639626289, 294083029, 54830477, 674725836, 693740472, 253406601, 532692412, 991091529, 174102520, 617224761, 566167446, 289759796, 293957877, 684735615, 964381932, 463367088, 523361906, 56679302, 825215818, 884070354, 836150769, 643099983, 43037052, 411954845, 736040729, 640492534, 36885647, 226774394, 563685133, 283188492, 898275451, 467288719, 954744077, 45135393, 316232998, 156648173, 651564379, 19926440, 473071304, 720436461, 719803245, 643599736, 654953034, 814862487, 685668666, 763378319, 427912631, 584849398, 429825065, 826479288, 764676762, 254944883, 427641332, 83095264, 653215684, 108440844, 888531383, 353681408, 141154047, 820007457, 940041837, 168697259, 543050085, 696418059, 91391283, 273801990, 465186390, 430041080, 811834757, 848949575, 44378095, 345312235, 376201541, 546664621, 994143821, 679655408, 935648650, 252950842, 946362663, 989563613, 557765239, 562199597, 427761244, 86165487, 887818250, 632821972, 49599215, 862905697, 496013029, 785531403, 104197079, 427417728, 127875809, 607471862, 326284373, 477631820, 375263205, 270093068, 197216420, 274219117, 338085705, 605580996, 479030723, 609234963, 825504540, 518293958, 915171876, 917308857, 338991370, 298176599, 388068737, 556249956, 690577888, 816960257, 778166945, 727378607, 249242927, 759959255, 490883544, 66787980, 524382157, 643672041, 17141069, 196314173, 134198429, 619557490, 25792189, 224755735, 181633438, 475801611, 387808896, 798195842, 424023480, 269523046, 737984545, 600253052, 34321165, 138244987, 135986340, 131280979, 608483961, 860464502, 321559656, 661348256, 563577405, 895523556, 264353982, 752581538, 309939057, 447763711, 182200781, 917597315, 385199535, 253554012, 424527273, 71295990, 925823835, 448260748, 988689491, 886866625, 577790037, 82768709, 783291770, 986978624, 653499700, 549986263, 30894301, 595506588, 827929353, 102992704, 971860915, 968709952, 996706521, 369887421, 880117307, 285128036, 270506547, 368050103, 23480181, 577825323, 452160726, 504045782, 812642559, 923096501, 772922675, 450949811, 476961529, 601068893, 14876879, 20074851, 852446841, 397806317, 525313410, 32663510, 118883865, 846884921, 360880997, 652438785, 350015555, 141312941, 60189667, 342026748, 609506437, 413490000, 526136205, 803314956, 578952685, 945793879, 300768454, 566279253, 230685335, 397671248, 60750515, 320046421, 227384545, 54634742, 303757557, 390122990, 149922015, 528957971, 220857648, 560377157, 709668943, 657461611, 580832566, 194131417, 577785277, 996282153, 190062702, 536330884, 370151872, 978444768, 890026225, 162527306, 623302720, 239485674, 814955782, 844376028, 183398240, 591158933, 416210635, 909918213, 625390135, 339878548, 636358361, 138991684, 753496598, 457467971, 860781021, 69339488, 742680768, 115560092, 90516201, 822675011, 546812293, 477937343, 824495151, 348037163, 912528688, 896892775, 791235434, 51007457, 598690869, 737895951, 984937509, 32835749, 507137313, 792717694, 196833390, 575514468, 434798710, 342941400, 28384978, 549110985, 226283797, 81210757, 156229053, 342221981, 464173614, 400784159, 403561363, 173653686, 661121223, 933702764, 406701431, 103362837, 83330449, 636300615, 83570597, 89731708, 438756835, 419346550, 68622498, 508133926, 548902344, 449093120, 810939898, 290142012, 873213256, 581537848, 942765916, 211446611, 460521320, 572188735, 900071815, 531907326, 236212800, 13252663, 629943776, 535827485, 981448913, 492837228, 112960326, 683264438, 607358475, 930091469, 350985280, 448337199, 814895761, 589194115, 178999784, 267942570, 568959536, 451950351, 913651593, 620296641, 788173555, 519497344, 531119498, 299482438, 89259589, 416126381, 37228838, 357183596, 227388653, 951032609, 744842113, 615500660, 724930831, 357681975, 604653494, 650205684, 930713711, 993102190, 72700158, 142564866, 172227453, 867457311, 134186109, 740723130, 862755666, 333663219, 751381879, 162092763, 743427171, 987621838, 588572794, 80181680, 415221332, 290739565, 885080056, 922641739, 453662746, 236503008, 265310005, 215635841, 666612307, 409650042, 393182500, 71020617, 478801496, 74770632, 832182267, 250690157, 72854691, 247871710, 738451787, 935168935, 379554924, 188114187, 415659558, 189800341, 321523921, 56927981, 183353295, 119824598, 524536829, 538746882, 752042405, 216878507, 672144264, 944258471, 640669562, 713089531, 5461245, 723870350, 252525468, 881572946, 478713833, 392764075, 744365118, 324288493, 297255218, 755594979, 811786084, 704888075, 969956919, 583017741, 580722286, 354791269, 717039618, 469597965, 356478461, 376350376, 547188166, 452754295, 673886941, 293433025, 172511523, 982562062, 817636218, 888302105, 588066792, 898848836, 250107847, 220009073, 445727623, 507367481, 544438977, 492361358, 397093723, 873458540, 337128519, 935217743, 775208151, 990190752, 761622899, 7081606, 251897706, 402543488, 958912539, 173789326, 643966468, 746720604, 959675258, 972308316, 727267421, 449738629, 209097667, 938978936, 241480177, 388380605, 423378715, 285740491, 792051408, 656574630, 818187273, 927440732, 2150748, 2468410, 504834582, 337862271, 900321647, 279712986, 868274643, 578999657, 954562687, 821931391, 399003560, 49863770, 946631526, 887068666, 390801364, 281407178, 842199461, 8566044, 689443310, 373279409, 556260193, 826498675, 154239836, 710040590, 667077320, 562186349, 296365885, 896989867, 101201041, 528426346, 227154593, 522924195, 422727131, 450334620, 192216458, 48386488, 992374183, 756825956, 766252029, 314436992, 595636010, 936735385, 60433181, 544952440, 162338270, 895894196, 822617303, 880558314, 330310246, 159813196, 722717181, 822171319, 69130758, 977938591, 442117328, 340215468, 706858390, 434377591, 788717570, 462777784, 915272134, 419047900, 221433392, 827549691, 798952311, 373400583, 169831360, 404609183, 837611654, 867003476, 506789519, 88230646, 464691805, 193308403, 797976553, 743628337, 861373051, 178906848, 365880417, 336841522, 420243323, 205784712, 900657618, 573208147, 88974613, 128625570, 834456685, 907419321, 71637942, 669170391, 646714607, 236169161, 478829653, 927396910, 208827664, 804519325, 498013980, 396490101, 328620857, 936465040, 856523041, 550681625, 216838618, 87501022, 46393530, 314655645, 179523124, 606187469, 949592009, 565004098, 515198295, 827187632, 489830616, 828656057, 982701274, 813822069, 199908200, 482243350, 493932949, 925260757, 271622156, 654171110, 32331073, 502620833, 979083366, 347348977, 82930806, 585109897, 299066766, 546816791, 212330554, 183117480, 91573462, 185831477, 483335628, 627055466, 195326552, 304699274, 452314690, 214616700, 949946869, 49764553, 715623383, 611740519, 281518875, 117871791, 295972531, 19880910, 444923079, 525489716, 303914020, 185480482, 570764374, 173144740, 688290665, 159223619, 605204804, 270425792, 853118160, 982588529, 434944064, 607106349, 879612511, 60059051, 624165170, 757122720, 660281615, 47893853, 289177237, 417194221, 873824647, 116617826, 474337881, 759502121, 813261725, 256879203, 249440718, 736288523, 137315680, 693860659, 108928413, 591369854, 978394523, 652213491, 333793563, 860267825, 794551731, 663449071, 244921126, 576098398, 222856621, 600610502, 516595860, 711249292, 900761769, 182968346, 176164284, 122329860, 665580477, 456486550, 744779587, 458353638, 820977233, 925167155, 753501620, 760623333, 387081840, 874729582, 685676437, 691173058, 31788677, 423456378, 557597791, 436626816, 436439357, 219064655, 754550357, 139930791, 569200776, 975065061, 657074805, 404539013, 25659306, 63170668, 553990130, 983026961, 857113961, 996220313, 667541921, 526241986, 37212399, 506434555, 780571821, 899233265, 794774536, 916850899, 120629121, 3918519, 188569776, 482091831, 727835751, 556619499, 799768522, 106854929, 562289834, 259967643, 477121708, 798075269, 656036929, 936487386, 758293744, 747325322, 62159563, 207988674, 84066929, 312947561, 505669068, 920531879, 617465434, 753621490, 627191065, 363509386, 532796313, 783568361, 680690082, 699292350, 764181770, 249523816, 141038192, 542141216, 674034862, 722407874, 365922428, 857496007, 438998583, 29989051, 874798290, 384085599, 539003807, 411278740, 66137631, 795603081, 248433617, 495412454, 930334215, 205085228, 374771655, 576653242, 792267941, 954297211, 843219508, 14191363, 504729123, 383553860, 899284394, 268441663, 665110442, 985296885, 281049247, 265622572, 662918363, 811751619, 739074938, 482545610, 764042086, 452016815, 579780517, 263248638, 497813570, 823032249, 145694230, 12622784, 583331164, 723607602, 863909995, 118428370, 154884637, 474565849, 970484486, 75394507, 816573197, 489300713, 173770533, 347391197, 597852352, 720552421, 462723176, 943372012, 98509568, 90552689, 408008179, 15363463, 741431093, 266206886, 763829841, 624882327, 458419120, 962589479, 313115258, 419842376, 898550163, 749956728, 304737044, 731623758, 303028863, 977902335, 725819572, 133812473, 804652526, 839420416, 299429451, 950528785, 900389547, 782924137, 616223123, 149926065, 922102802, 419117492, 304976364, 889003497, 868533889, 228950208, 343773034, 635738701, 754544839, 392617707, 148700252, 172881728, 573428990, 965144980, 662513728, 402057846, 741687394, 865346675, 477220042, 269501290, 127115265, 986979644, 667929936, 187133277, 250073873, 666229928, 749266333, 162407569, 961921709, 23662352, 550613003, 985131269, 459069032, 308045078, 120609898, 699527838, 574505241, 305877156, 654134709, 963561326, 151241619, 110035105, 7120634, 836253956, 836255633, 201696756, 386995196, 718888495, 896714865, 667007639, 238333542, 220812952, 165596690, 133996392, 234268193, 154592229, 592339530, 504152382, 73872470, 984770548, 495063688, 503531133, 110409021, 32067179, 493849273, 497498745, 200821285, 16542452, 777425224, 247083076, 682331944, 644736114, 896773064, 101947913, 258056072, 748106973, 211224880, 557454424, 226727579, 183687338, 628166502, 988119393, 512812941, 735327321, 389116040, 747832681, 307809326, 387732865, 731613288, 712548125, 981937672, 630143015, 811133314, 707563325, 284887926, 124725982, 938636946, 344735497, 106125092, 216904408, 489663520, 559947900, 8566686, 587989894, 949446897, 175140, 629717707, 769263692, 942352497, 312692631, 229723048, 718097026, 8376903, 351995801, 43145342, 326799063, 318928282, 124538205, 471547422, 567133660, 789488652, 202239736, 651548949, 632524130, 145293747, 325263787, 896247562, 90574487, 996519077, 765183105, 771791820, 737344916, 786883315, 294196512, 862084993, 844534079, 58478123, 97939360, 358350086, 267765936, 547918622, 401986854, 925493252, 741125634, 600534436, 539652722, 660726632, 197991918, 715337900, 125502853, 803628521, 432558726, 652391625, 102766111, 893298499, 651640120, 633131919, 777024818, 781405772, 599916022, 279556661, 594359094, 581138111, 3269085, 258602085, 11541743, 897591344, 399901042, 335283716, 808668476, 301748708, 577143536, 897745165, 766595836, 926142584, 673885285, 852335314, 997531517, 929292630, 838200323, 566380831, 2243243, 317261279, 896105077, 572967158, 322120005, 687496055, 859033373, 586931074, 935629418, 889889446, 738609336, 495817881, 965178873, 556698860, 397226926, 14469334, 506193044, 356735503, 16984003, 333677565, 944013609, 967782167, 817320142, 136097594, 176299847, 564067534, 258552350, 492807656, 193505206, 524723998, 645720274, 110583328, 378012440, 965289883, 73204797, 929250352, 606381357, 994547522, 456954775, 583758154, 387342530, 933941104, 651801211, 611138353, 734970898, 442304533, 103359560, 36188793, 471773314, 668121012, 388329053, 523582925, 149185953, 532663369, 613568404, 129850708, 197061554, 322037979, 567289078, 102458860, 908696251, 319996987, 395364542, 324881997, 166975884, 492124956, 429130114, 836451819, 266218307, 28654922, 28597480, 418157919, 520944898, 757060140, 386938292, 38454595, 93193327, 125428016, 556995069, 49371939, 673960757, 138386693, 962011400, 404406647, 7444608, 701043419, 200403401, 725709057, 745404031, 150464118, 949560189, 81912724, 43853026, 473562953, 768225243, 182186680, 562988320, 554871387, 94498246, 494861089, 55550661, 277253299, 129305025, 72137424, 202758153, 970452169, 683254009, 692698757, 931100153, 11346702, 244878259, 595929976, 406001067, 546169513, 890821832, 105613970, 619886329, 661021093, 788620863, 640366677, 580304622, 795853385, 808783554, 797658220, 731518457, 247202584, 221687131, 575757716, 834274581, 394783482, 177576669, 205829808, 414053222, 49289094, 936063681, 28134571, 655712761, 472956255, 253540280, 311183781, 852019248, 659770669, 280057757, 521001232, 886557973, 811806837, 810461343, 371236913, 640056033, 117222640, 567970092, 176669409, 827830266, 551972347, 568573570, 573605111, 852988810, 412726228, 21619896, 631520761, 353828511, 148794137, 372381342, 988740092, 575537120, 736634544, 11432270, 593079230, 933675685, 783748502, 737340676, 219594527, 735131385, 418649663, 539016957, 862603331, 382142067, 906594808, 587382771, 570188779, 144408428, 127102218, 24609379, 460615835, 479768376, 999296131, 111250625, 482440622, 197668273, 877257241, 473737445, 381285061, 140338631, 24980115, 102510505, 874576399, 709200525, 759749269, 563196931, 105755757, 953715533, 161370761, 294967358, 682878303, 175916899, 169862253, 372883938, 694769577, 852901601, 321656398, 39127653, 548873884, 959437146, 336772658, 586932984, 702457111, 545178792, 627268329, 543530326, 105906593, 482865953, 28197885, 655026230, 758568168, 462985148, 991926450, 769842931, 515274681, 980171793, 717370994, 442002823, 133228807, 216114565, 755976932, 560938586, 10592835, 329675745, 413959829, 644914172, 775057625, 656020182, 680943633, 496688295, 786196254, 16986549, 952143686, 114553875, 88186603, 997613728, 73422663, 324377248, 292988269, 395950237, 687389738, 675446895, 677998015, 437141462, 659041587, 715581788, 399864712, 854167513, 793210635, 633176702, 901220900, 427175822, 874746553, 166269703, 199508010, 38208694, 131457604, 234167359, 912581385, 252568161, 711932462, 671607202, 7355662, 578056604, 357630350, 514946820, 768489565, 218608784, 619315901, 46051013, 742822326, 793617474, 418867046, 569584778, 72550436, 914288735, 757935749, 344354833, 359727165, 614207972, 924864892, 785303731, 332731099, 746960396, 746849196, 761450596, 662099947, 681415526, 975187759, 244188464, 834390349, 86190143, 331758546, 344151536, 517379628, 421929008, 525237797, 351741140, 29360660, 219674586, 444766678, 729106278, 956081659, 385832014, 649295725, 440661583, 66749125, 733498994, 107850857, 648641849, 863927208, 471404273, 763527056, 639422515, 58487521, 648096257, 342298921, 775097889, 446079442, 569241968, 476540513, 911003787, 952195997, 37274774, 518655652, 478316640, 91090155, 936266937, 375458832, 716285674, 135230885, 219732452, 310586302, 396919133, 504044210, 256428754, 638037115, 14271780, 894130980, 402149569, 106392973, 603860321, 141900632, 898322281, 441655946, 100975696, 261257073, 774976375, 315585925, 364682808, 822789892, 657976541, 83831711, 455054716, 495323642, 260202935, 139884222, 150620012, 317569763, 256402591, 551506757, 180913027, 275828266, 178178997, 677706642, 818071803, 415128272, 822408620, 829546467, 980722664, 370650312, 582405327, 725991136, 703168554, 243128163, 490361694, 485986042, 212673677, 225364576, 970092615, 738360389, 340747604, 724759722, 540832013, 105805871, 65635476, 696839166, 848560210, 63951241, 630515173, 895044365, 358021451, 678511428, 376066869, 430422809, 790694269, 847420376, 917789459, 523683830, 709758581, 917698439, 624552340, 482762473, 960576947, 333204132, 81635582, 94378975, 930971301, 168311553, 187473824, 200437669, 839241235, 119613439, 254313437, 461910137, 229437209, 933292631, 716136338, 345831873, 816310182, 685163908, 35247022, 798831409, 344711088, 617295191, 681947666, 211013412, 297152690, 148675160, 588010922, 90939012, 874980627, 264409952, 608432649, 179781935, 116658637, 552028019, 458766149, 901128080, 850963021, 169466150, 776106695, 154037774, 252923172, 709378700, 548670744, 569159030, 343813443, 40388570, 741022951, 239154205, 313283764, 559145167, 553460865, 655369453, 997073810, 966393053, 171669470, 66801959, 450084780, 593175451, 438982798, 871296910, 262463742, 100529383, 585092450, 440928901, 920874386, 38790584, 392932152, 499238781, 550530443, 924079724, 337912229, 304872187, 393010469, 864051705, 731991552, 622596182, 794479948, 975632718, 123923811, 84150951, 30893606, 975119530, 998795314, 105672836, 616111275, 324147156, 636222433, 265414061, 80818897, 842292436, 38775375, 685015210, 793104594, 720835671, 256117567, 770961096, 83716131, 152040473, 131135822, 761566993, 814475099, 105104274, 541849283, 943591664, 654043357, 913500134, 447986980, 811868646, 713759451, 116085564, 554739223, 558759653, 439740560, 778177939, 829652321, 306417542, 280203088, 481256002, 367568600, 446629111, 949510972, 348496929, 251906777, 505130152, 15560243, 35425136, 240570904, 740080244, 311909427, 538763003, 822244784, 494901339, 95583442, 287112237, 966077591, 654304220, 620118304, 73067545, 625417580, 457872217, 740187195, 514199334, 419195729, 662872071, 897442542, 761824313, 602438906, 125327880, 272549360, 509941609, 590865896, 755849355, 584013490, 548995455, 109133425, 375213858, 602744769, 941748392, 957786259, 145185122, 553416698, 210152886, 164208319, 516143415, 867689174, 208555599, 219493662, 462407809, 437599593, 816824335, 790053536, 535505224, 613744441, 770139022, 328002324, 550823398, 78907118, 974901700, 114198326, 824486198, 711104911, 925860330, 653522158, 978820978, 271791709, 394678034, 442048100, 57041014, 360602449, 341929704, 335982180, 115864621, 830870587, 338625011, 666669391, 341063876, 136592259, 681457719, 330769648, 476552340, 765827748, 119421427, 6388074, 992732545, 769717031, 436703530, 460561993, 414267794, 739492166, 858150454, 203866039, 953219975, 217060136, 265491316, 170908133, 929496115, 54832936, 285374789, 243917794, 816162801, 749910482, 724414495, 581233587, 588135995, 864923438, 218964856, 563577167, 583925642, 28657294, 319647450, 218108920, 782277167, 133220068, 428901450, 670936110, 496297632, 97245768, 353890762, 711225412, 981751294, 980309308, 468752705, 190184392, 759299706, 128912774, 905900129, 978251193, 868047334, 719336220, 103648446, 926378669, 472151655, 262353861, 414806718, 376346423, 651644345, 451487665, 674200600, 79156394, 58192955, 10098118, 437060666, 547506780, 892888644, 486696138, 341494971, 90651670, 536451781, 734286984, 756787227, 919136621, 918448302, 881177347, 813775640, 580605577, 483055217, 793302907, 550556524, 210235610, 743225869, 226012221, 27549473, 115145729, 361947828, 265084709, 160853817, 346841521, 602471260, 788012452, 229641499, 788598907, 411472093, 283900514, 221298895, 813121583, 989603, 137883788, 6709211, 257583962, 719262895, 898693940, 744685537, 825588266, 661749241, 316521839, 980676040, 611020332, 594776538, 40197885, 492614346, 987827478, 815787905, 226123273, 261115622, 308700802, 671108614, 391098262, 665197379, 293375706, 756564149, 882860356, 941628426, 724944070, 340353011, 161697560, 498145631, 115628171, 589071429, 713225461, 134687489, 43912319, 801845497, 28769737, 942188503, 238162247, 218656700, 279958498, 43305779, 202387048, 169779437, 145304880, 928403567, 275221258, 82703947, 159924111, 981414063, 850528820, 73052868, 238690693, 693685636, 274784393, 236932087, 121300053, 874486598, 236844142, 154869040, 544429562, 817028266, 568834891, 373123276, 950574056, 170342598, 947468181, 236866770, 162337983, 409255485, 447655402, 29590740, 575002502, 391027113, 936248057, 714406061, 160412537, 964050575, 861770452, 251056132, 45370220, 123793055, 162955480, 495415694, 757304921, 49065590, 571822835, 868101110, 906101454, 753957927, 529649009, 456885999, 892946230, 408180746, 38830349, 506607047, 713221673, 397652388, 268753813, 786082779, 109754911, 828441618, 648011665, 58606968, 527032985, 731412673, 726249240, 978504632, 27864750, 235166795, 624804113, 221297422, 478202211, 286236931, 302304479, 468418346, 564142646, 103183422, 164397106, 154964239, 431742760, 614558967, 520193277, 776728842, 657172878, 831505423, 418263522, 723315579, 372178380, 851663973, 67515178, 722339274, 309837096, 616367930, 665118134, 185118928, 372004907, 748645287, 488269641, 677265940, 26148260, 250719080, 444201799, 852439864, 713818257, 212167247, 295909973, 178392423, 745297195, 302362375, 833985453, 599720238, 267368353, 347410023, 563571446, 481870668, 30910115, 226738197, 935868695, 189515626, 847217776, 625598451, 908547065, 4416791, 868809945, 700959962, 17905997, 360060055, 525781992, 567535123, 629669083, 471246742, 339207706, 12282117, 789537708, 415711784, 906222641, 866588722, 62562538, 958940564, 750039589, 545611340, 968048587, 37506190, 892988623, 827036892, 611617492, 198996890, 16106355, 305980009, 853129943, 587430322, 411437400, 722667563, 926403424, 525120620, 454330422, 963375896, 278686296, 58359698, 385339337, 96238361, 937500718, 387583833, 47383713, 914797457, 602251815, 636165096, 251792704, 476239741, 977951445, 300455186, 826706102, 755192763, 409544833, 236824422, 162030097, 694259917, 845333620, 332327599, 849395286, 275485724, 218560689, 446174662, 460215276, 377743485, 56957207, 43216789, 65445624, 178209338, 662880368, 250581557, 854053161, 619731888, 517109573, 363203242, 757265852, 202860842, 725155815, 582464635, 6979989, 66770370, 803184057, 386488348, 586854804, 552272269, 513359286, 858253207, 781144399, 510789402, 526664832, 728251197, 485843078, 381434367, 549622457, 829053518, 801058328, 671199019, 739061037, 927720597, 465322312, 28802226, 484503370, 650504283, 734881531, 935190564, 799791116, 161530414, 114161867, 85532429, 97841121, 604737309, 486497061, 506893566, 286891614, 310332064, 815968871, 888565874, 705733613, 430456407, 396111622, 9035090, 621725541, 364474602, 258782719, 47074588, 499746220, 530536215, 131868157, 445188200, 799420348, 351427437, 927442393, 371963264, 969141327, 918766230, 273687264, 962963049, 223856765, 232796118, 599271429, 931294868, 545669291, 24638253, 107399944, 112642947, 362807506, 546830937, 596219881, 739310450, 41451484, 406106390, 631361680, 278286725, 223718840, 759807438, 244429217, 768998789, 557400199, 760687283, 443778306, 342142809, 777031927, 812968420, 563566654, 803997350, 348519397, 745073429, 188259635, 387281002, 766695567, 129202466, 804527315, 92451314, 838735709, 563446027, 934551147, 177274766, 557970582, 703276516, 458460595, 537424309, 937201923, 567015752, 176884275, 595853198, 58434347, 588491264, 740497092, 55943088, 8217371, 661500828, 361354990, 630501247, 266990101, 335357216, 394448719, 825412557, 278107741, 999645716, 1480794, 467508701, 948111993, 292752648, 237048798, 90171599, 925410239, 304826316, 575400960, 251048162, 942455432, 950661591, 902150760, 48696770, 424739996, 764000495, 702045382, 303584960, 730268708, 268186124, 995592141, 932979253, 918394555, 629955481, 330566281, 177291271, 978099264, 856690391, 886706081, 763906651, 444325011, 626018181, 936316153, 284362616, 406826516, 649350185, 512544742, 15052238, 773751981, 671014501, 179039491, 583074412, 169294104, 971228622, 27128642, 531491949, 637185539, 47217541, 792549782, 415061820, 151675921, 347109496, 192592715, 721479741, 509118554, 501652534, 940744672, 721392325, 801702181, 290245597, 455636771, 215001571, 955095429, 224875381, 92455356, 872328693, 856232002, 790334210, 227967176, 891012362, 444240006, 237223501, 370638583, 227678560, 213557077, 600029388, 649083866, 255635686, 634263429, 992072233, 109218428, 77879266, 584529985, 935677380, 224417920, 773585558, 431337432, 32304647, 512747829, 82726355, 729645374, 748234906, 802682254, 914616847, 540554479, 521675597, 708158854, 663483115, 876292573, 485397289, 289094233, 992880596, 591118032, 832512753, 29386565, 941689562, 240574460, 951980397, 600912265, 476741600, 829005669, 856967118, 731432702, 400500264, 774795749, 946905300, 102221851, 948637966, 302485849, 372400492, 477972823, 608399837, 432751532, 448283779, 760134163, 625705422, 408514401, 851842610, 249583322, 225441274, 781641365, 804645745, 413226052, 716315651, 672760073, 632079962, 858800650, 969076563, 876808355, 913068730, 66812929, 325159857, 218422460, 258037910, 494387794, 12801880, 431952741, 423288677, 968692353, 598972604, 421593353, 680951090, 807228148, 61188312, 634399163, 890631469, 565719491, 408834115, 692493011, 355807230, 444340122, 752253443, 345373697, 847947857, 701354579, 442959251, 361940050, 61914982, 825324475, 540090707, 928178354, 677537896, 89787453, 910177086, 890985219, 968812357, 349772345, 434693640, 162594036, 671480453, 376470341, 31480700, 193032395, 48961338, 562461387, 915757862, 616406898, 520718930, 983835894, 463332312, 190795584, 60297314, 777550190, 433032127, 624216152, 715221577, 58051862, 830935225, 969779224, 936908529, 237609092, 360832523, 256452070, 943210036, 449666262, 774304560, 808743112, 349341080, 705244378, 865835367, 891987790, 382722587, 15031852, 690928071, 921511920, 705812419, 95245690, 464384682, 560525982, 150626842, 353224970, 693436272, 504316815, 793999736, 681471052, 939473671, 49498991, 730066656, 595451217, 996281959, 660987285, 896450102, 476284111, 717975711, 812851454, 74371084, 529717015, 101933269, 68177826, 300972820, 467133913, 879169347, 374713229, 483154886, 516723646, 353248707, 513997471, 395093147, 364952099, 482469514, 981067360, 594483948, 362144110, 475442192, 521337847, 737728172, 566750436, 595334633, 78328701, 45866286, 233948550, 426522066, 704040399, 871910803, 43383637, 514072745, 290464967, 924786922, 548157185, 498126991, 758749430, 28253055, 819147359, 15633161, 919021489, 214493130, 373352644, 418773347, 969105533, 20899126, 719987674, 211036055, 460539607, 818063859, 759327702, 534752604, 794170133, 707050975, 756953624, 549516705, 317838442, 3968397, 951834409, 990551404, 452900713, 104652614, 76196276, 951329132, 219073689, 967024312, 833806778, 692732224, 950393979, 911741748, 575044238, 484165621, 4265464, 243929753, 258779201, 711655285, 149746934, 88453871, 51401379, 616989680, 9547002, 956660508, 886834070, 662892187, 301256227, 401173340, 404057828, 573267322, 436239916, 487988692, 907790144, 715817137, 630355344, 755885608, 916955895, 37882715, 445440186, 336854136, 461032578, 954958582, 857630659, 763915841, 529752523, 756421967, 890354521, 547432338, 589771094, 878429854, 729605995, 595311552, 252001076, 652342680, 936000727, 716115563, 962907309, 94148859, 762758430, 191774254, 812981340, 524634944, 677567681, 920541404, 744981119, 148195658, 513181865, 242413379, 621874039, 224768569, 227839426, 318586628, 503623027, 518185584, 284677634, 135568650, 774275980, 713652754, 188256386, 475481350, 421904380, 858686350, 531328121, 936211896, 466020653, 686928859, 287191560, 139651419, 974305841, 177302426, 660054067, 958535168, 968148540, 448240863, 180507488, 643588895, 636785167, 345581932, 974425280, 608440611, 911376727, 240267473, 671702717, 581517263, 686661331, 771470633, 168563971, 442890999, 938352175, 624267566, 211645783, 511126834, 44650880, 196959957, 419219894, 160342454, 111700427, 798066505, 221182871, 769909451, 688363616, 565634122, 627252503, 509287590, 412259553, 400704715, 22575386, 464957921, 534251439, 597448590, 723447228, 200919730, 639016510, 346125094, 695567075, 208276744, 763415862, 42159815, 880906515, 706722921, 429801071, 409519800, 163508984, 334190030, 557466226, 552457059, 504808941, 984841465, 966326511, 376738187, 589663651, 323670585, 485262093, 413731109, 548501560, 484621474, 308353007, 149409670, 19336989, 123228943, 740257823, 679562267, 380417212, 626470058, 975492694, 31061513, 262306512, 190249807, 237461872, 646903426, 360499866, 607349647, 984589742, 620314322, 78512167, 448325199, 930345985, 615214164, 64993740, 633672185, 566648487, 410940567, 232940868, 344443762, 19106219, 270321506, 345258369, 523320277, 970269284, 706128760, 40827931, 478150760, 250267767, 271710875, 333735446, 964568083, 253397703, 143805939, 240715918, 233996423, 525456191, 959114026, 117870527, 890962057, 753989949, 202145466, 237532303, 144698602, 890871058, 712308699, 252913313, 855404445, 770678263, 410344059, 871376285, 543550208, 754764991, 32044699, 116206623, 370646017, 377460953, 803739843, 4682035, 628157619, 732143885, 3381442, 992844973, 847432170, 239613786, 781160520, 819239023, 56690617, 993936901, 352355864, 192396988, 78114613, 181608927, 715651823, 532125336, 344117872, 669732691, 77402466, 952502024, 695016815, 583352105, 912322178, 817667730, 786717951, 407584785, 363288226, 869320167, 172705174, 996667480, 309563102, 232855632, 187647755, 602799721, 127904209, 993306975, 402262110, 987347312, 713468833, 420367556, 370530882, 725074792, 61287878, 349096980, 579949959, 24292385, 25169561, 582707661, 772107980, 933710125, 287673391, 532136496, 67021509, 439636607, 741022459, 675596073, 124167973, 415287220, 263795993, 602664116, 988033288, 243331315, 290283168, 718898864, 476877244, 982543111, 256170010, 848350678, 467341768, 734452974, 841585320, 469325011, 130756031, 19706390, 904291895, 358848105, 321585511, 553368087, 558244186, 413779183, 930789677, 173643799, 415724396, 621852616, 298613817, 278042166, 255824527, 317153099, 602125322, 861934781, 866813016, 826737698, 228687705, 345052583, 302276922, 170231405, 717011147, 598353081, 783236461, 467556091, 127647163, 386670902, 648975995, 335066100, 148311151, 893982919, 909498909, 703196015, 608159784, 580722521, 807058636, 668456521, 481176648, 196639986, 558034839, 265409923, 102181656, 620602848, 142324491, 194081088, 719918148, 24084863, 54860228, 955605948, 415914491, 926096448, 156404858, 723423851, 851487836, 825033296, 351002467, 404735453, 156355185, 954759335, 174496758, 255835923, 117050390, 316662345, 83673529, 231982975, 794029457, 560394172, 532961380, 63430085, 399477641, 395781602, 946666464, 924401477, 100507033, 732763046, 451877245, 668574991, 235773981, 733816168, 1675442, 907352981, 397476349, 904092236, 106863606, 299766114, 799813301, 234371833, 576712404, 926416770, 650308397, 528573227, 482156975, 605906484, 842308690, 690781728, 348517415, 40498914, 508071806, 298374999, 520556953, 301153586, 487989321, 709272225, 230164740, 314655141, 997561623, 311908633, 822970290, 165816439, 455179906, 127828234, 782820112, 455480924, 893390476, 267780873, 88703330, 674797408, 391842828, 315521581, 659824807, 678175837, 464519838, 131624859, 358423912, 689680775, 946454760, 438081974, 439641635, 577386034, 877701560, 223242109, 736525652, 157439, 700800072, 670443720, 514123995, 570458388, 122708032, 797280411, 54271213, 274414218, 176454815, 766191496, 662828740, 447340879, 781936216, 883834661, 990896920, 215397781, 88574472, 300919126, 115938135, 341487334, 146651865, 142791956, 839546766, 87028053, 493566695, 800995065, 312946054, 229785267, 543377757, 684669851, 106435231, 719408867, 261858356, 334986818, 566819683, 709070369, 209652853, 253055881, 949398814, 450034264, 563828634, 517781300, 523539276, 584009346, 974670411, 960875319, 842002822, 926598632, 498708471, 985580768, 79792388, 614090348, 645056441, 387358396, 919011919, 950285922, 946451980, 354571524, 258247690, 462889054, 636602285, 347069200, 470526862, 948418030, 536477397, 839046943, 892540409, 193970535, 228829789, 771361651, 372927120, 530474144, 819617365, 427387879, 293414917, 695441479, 605161847, 902397822, 414325777, 995076347, 335633874, 13348457, 942203143, 964640106, 30271291, 170066127, 38724881, 994802010, 56165384, 376901849, 169971451, 540685410, 59002952, 460049249, 934076431, 85298051, 215014878, 809446847, 835263994, 925493728, 812019729, 543479954, 191039803, 897287170, 125679581, 182054799, 926416132, 763684638, 387688442, 584618412, 288109772, 308959937, 197428243, 717680286, 998848511, 698142230, 124035960, 862351917, 447599166, 921344112, 917927850, 841829885, 212999445, 841877475, 641302095, 141480191, 423021695, 272802696, 588443886, 292549739, 356348433, 72739624, 109149507, 830024012, 74296534, 190281803, 850884296, 822864789, 339219074, 315402147, 187390707, 89575702, 744440446, 954354621, 950659563, 718248431, 821777882, 696082910, 5076053, 371447895, 655240300, 468010536, 188196609, 755849468, 894910722, 311943311, 671090128, 171562424, 540938766, 930627612, 359513687, 63706487, 629356554, 411082514, 772266656, 766778185, 422708691, 418591032, 71793865, 365192089, 773785965, 32739148, 24791128, 23275880, 976752263, 167289511, 339642712, 842885630, 889416748, 125736418, 968764074, 707994075, 321160912, 659001996, 297118170, 260848204, 941463939, 17288686, 918323292, 51045052, 819075501, 322849223, 200101422, 370371893, 178091639, 725525792, 683750347, 651278927, 834700400, 864650844, 197484436, 653208176, 233876457, 133557584, 406636773, 655329052, 372356900, 512129107, 918530707, 816965063, 321881186, 852728932, 696175963, 919443919, 896866131, 210482089, 270816373, 223694819, 883255471, 706567496, 888638314, 752636537, 226740036, 381745339, 750645224, 243788648, 191396963, 455834830, 832881439, 12316396, 418592649, 342084133, 19657330, 102706988, 40895738, 606364767, 371950617, 165283642, 520171751, 234760468, 268221532, 414503178, 819743603, 568689267, 626354639, 818116829, 912484473, 601072011, 984979142, 621452268, 560758771, 66789748, 377624036, 342804822, 25007382, 728429895, 664903069, 833699057, 615287153, 329362403, 771085164, 19700669, 891546143, 813499724, 980358915, 103269452, 967792136, 299846844, 507492807, 410188263, 241696126, 556007458, 283878687, 182976363, 211256638, 320191295, 806546050, 792427314, 597937081, 578616620, 771865277, 851490052, 959740442, 983866758, 748049652, 718895795, 250546122, 785570295, 132782506, 356294352, 456614591, 809691964, 933783721, 146851424, 232028016, 699793958, 442340180, 826066433, 266607032, 703846838, 606131914, 394358999, 677589293, 980693619, 553656205, 606433820, 504508177, 361187855, 747893591, 388169780, 113367586, 397252430, 869499321, 393585056, 347345605, 859270156, 590132186, 379413509, 618360288, 670444159, 586055606, 756979850, 607331331, 94488364, 94989906, 174007718, 987651967, 654085672, 753182524, 87441438, 524737670, 143249211, 65291955, 865253605, 760069152, 549711117, 301841704, 826899460, 397630384, 662230779, 359635035, 512766000, 878089062, 540232103, 763740029, 228708044, 721520885, 935178196, 551161743, 125976668, 472763540, 404934600, 501260861, 797120127, 408515714, 427154219, 480930978, 911134825, 580030450, 643393581, 255807617, 836220724, 886628469, 769365646, 962786390, 423667787, 489311032, 703836040, 255633157, 666585387, 9374831, 632827274, 338514983, 765248077, 235981780, 457234253, 693331216, 194459184, 746325660, 515758523, 122707236, 227288092, 974503643, 750952524, 207250719, 322272446, 486591551, 519524124, 780218842, 69690574, 135761401, 441567910, 351449835, 983837302, 531908582, 325169422, 427738179, 453805391, 553309631, 652079520, 166951243, 662589494, 349685545, 718122103, 728245814, 855477501, 130819594, 557134029, 33933770, 938168459, 829226971, 86584268, 451025167, 456704743, 573875490, 824246095, 916998301, 923251010, 134459946, 521771658, 108925578, 738122961, 407297908, 546315078, 597460276, 468987623, 862503371, 980171453, 256245678, 943264659, 439133864, 158575923, 232369052, 920586651, 632718116, 691208199, 242190136, 196818405, 24944756, 811366433, 654116065, 578731316, 708049144, 510135198, 819299726, 166271852, 193400718, 3374491, 329847504, 179460191, 805048182, 734825361, 606756609, 910516949, 29573288, 226380030, 655787472, 821732267, 633222108, 705272660, 945566783, 403257175, 820373461, 536408346, 668848260, 366611919, 722605207, 167378944, 743967190, 353959819, 391238841, 756260129, 789800017, 279259766, 877150398, 873284823, 610912337, 737126350, 950245335, 286022725, 62035885, 550097046, 743519456, 405352637, 417125918, 110423682, 169906139, 410528305, 965349091, 43666199, 879012966, 553200446, 397771101, 831677560, 996705899, 85775751, 341341132, 368832426, 931885711, 881090857, 102898258, 410597709, 922431177, 551292409, 975784010, 64395778, 318490709, 934319052, 712053489, 311988917, 808863261, 799623294, 518251203, 820129187, 424712489, 966723820, 822759496, 344927041, 713905569, 669114087, 712031914, 463088477, 111725858, 722721946, 130392211, 389573592, 832411001, 865888646, 940808714, 526880664, 9647730, 117805038, 206930284, 145526341, 541175465, 442646239, 590069600, 674238799, 825530768, 149134760, 461038437, 544289659, 95075909, 120424377, 38772396, 838432928, 789190143, 426074974, 61711711, 874015810, 245864862, 286083057, 685407533, 418292143, 736170200, 459568516, 749116646, 666245723, 358492692, 117531243, 485753275, 396663879, 461329475, 699295687, 684193501, 956717615, 1326917, 347941539, 234445377, 538210679, 540282473, 273518140, 160750980, 668031840, 932309243, 575978676, 574428525, 418401460, 433688659, 707358781, 973942062, 331653959, 482903931, 551132453, 882380055, 629414708, 706028763, 592942618, 345057620, 858720518, 895322421, 200535496, 373842069, 118187318, 985207219, 92568462, 830256420, 60077211, 106535437, 12496180, 731047868, 22409132, 777681957, 355071613, 867058146, 758834692, 875224834, 623840079, 305190358, 361501001, 298526032, 822917260, 992289222, 985102526, 202923532, 951444943, 359886984, 612755604, 750806613, 15889401, 759043500, 978553016, 576552668, 877497219, 464168814, 788784338, 582851702, 297485484, 947959474, 18313172, 873438247, 152025804, 212227440, 184144473, 453749980, 752515987, 772224472, 479548937, 948996158, 914344924, 35468813, 735519988, 9292128, 981905689, 843681036, 612622742, 11339262, 568912513, 584874290, 67831520, 938680317, 247613643, 36438936, 579781766, 48901301, 759712020, 417753015, 582455742, 478489248, 669979654, 479755854, 387803991, 976966355, 721786358, 709009066, 309506816, 358697650, 384554837, 646201519, 359166219, 407715832, 564444154, 382924164, 232123169, 5555336, 361819335, 90095281, 812832555, 345170832, 889072690, 790619510, 461422491, 238375892, 749085794, 429400368, 810853598, 590973120, 227362162, 300022541, 85673390, 892282096, 409351026, 401408141, 185398696, 808766753, 824621943, 377063803, 884088913, 99033983, 376372432, 584275556, 482766028, 608337578, 752861896, 327230923, 427558125, 175282379, 550545581, 833074915, 174893393, 341351214, 852773915, 165072045, 543879858, 758382645, 565294480, 361449896, 944984010, 872206677, 139400045, 966432305, 719051274, 989508317, 81445778, 364385133, 198237824, 879568982, 99759754, 508116752, 502902223, 67625983, 307843017, 420625888, 311744118, 817937816, 527967179, 919265370, 377636671, 911737817, 931675642, 521465128, 624274094, 561904195, 218624189, 578635188, 798062593, 982899128, 794145961, 103090215, 500444808, 491316065, 75959320, 936894376, 721413781, 388989268, 452414488, 703851948, 77279640, 285174576, 419294711, 61946296, 329174313, 942625312, 373453568, 200479649, 859078461, 707831826, 964120152, 322964749, 39026139, 568132723, 21920827, 673055553, 418265513, 211748469, 907883837, 510693450, 751585624, 104875594, 40071539, 767807158, 530982435, 196827994, 546336991, 263328755, 544468871, 812977878, 223031657, 138563920, 180602492, 467178674, 196784536, 209081451, 694379058, 980108137, 463254999, 874062064, 962266407, 2128521, 454739501, 49805792, 329412368, 745587844, 377908587, 165554105, 493011586, 927619336, 543138890, 45034094, 712168436, 13544150, 576580750, 790472502, 548443011, 766652153, 292430602, 956162454, 891493132, 705134763, 445647308, 848961799, 130188409, 516792809, 300688368, 453580760, 187607578, 445402223, 210377220, 164005310, 789637386, 861353398, 137506379, 74634312, 373336262, 504434591, 454593666, 798650872, 949401974, 65659144, 154636830, 692863549, 639190105, 386991502, 482050151, 867297778, 878462729, 476559879, 787494944, 453657001, 876003771, 87953959, 247085762, 477966686, 328391587, 702988112, 824585844, 54661627, 583605635, 597871742, 803084174, 567179868, 198349934, 944835726, 50622695, 120131477, 179803770, 170400032, 448663794, 785507629, 848753712, 610925410, 771433092, 685526945, 342929816, 188543874, 730520967, 943026385, 311208689, 534816733, 366574390, 948737745, 745476088, 11123090, 368741016, 389626733, 295207466, 344237580, 974926772, 792503950, 313830796, 600363210, 820729830, 352101119, 259720525, 569769471, 962576766, 28178787, 369653001, 620958044, 617613488, 136752804, 141836797, 637133661, 862624177, 534930346, 122482269, 491414225, 557368412, 688214004, 391882049, 840364758, 29288704, 97532379, 513954984, 955417963, 35091212, 875337420, 429680604, 14617161, 348627098, 372787583, 529088363, 537833513, 965418650, 227711567, 288419072, 471568690, 551097205, 916852087, 817634269, 250259136, 325553770, 161156239, 612429450, 201494558, 943471523, 93995657, 623488180, 932785881, 672656005, 888754532, 480859594, 316730808, 441294508, 242153733, 186757069, 644845664, 206334890, 753294916, 119840254, 869382942, 776364183, 760008796, 312509155, 358417492, 263484315, 15071814, 401264509, 703211705, 155446588, 678797369, 551372283, 692857239, 858084897, 333429603, 199004821, 47797923, 503946551, 80360623, 238938430, 352314646, 956142590, 255799204, 574046343, 797123126, 524969062, 435786882, 563837544, 952450030, 400239916, 946920278, 456663093, 696191222, 760001493, 579456785, 71762501, 597389907, 701863800, 988789726, 546352477, 485861828, 412045218, 350877804, 270416192, 854092046, 308062088, 924531782, 479125326, 207742734, 210516698, 604148141, 695512497, 400238433, 362845319, 582228746, 918316855, 316617201, 357566559, 811927257, 370807608, 902387534, 148155939, 997051705, 688202728, 96634174, 796687756, 412263606, 561060866, 649711925, 618176700, 595380728, 56124252, 153428424, 805668067, 397639421, 263063724, 767157964, 880336539, 264202230, 361362953, 579953546, 638620103, 272126702, 691726619, 848008809, 219524384, 470202674, 488798188, 737806693, 613638790, 932171293, 766917622, 838654523, 422475366, 227518122, 483092598, 604118743, 88636022, 365223155, 311203761, 488520625, 721771668, 936814978, 86512386, 229651549, 459045971, 383139958, 201090866, 551388056, 395636544, 337288371, 372809277, 795868513, 106949045, 952362074, 961580871, 174655401, 120347282, 550729914, 906864003, 208740679, 314946644, 427403651, 394694806, 448103443, 910888129, 806167715, 217000105, 500091577, 223633983, 816652927, 191083163, 308439882, 100648126, 881857912, 487130658, 793345979, 773357455, 516688711, 723366662, 804308774, 920351388, 821775469, 225333230, 71446734, 465264995, 598050552, 998314633, 722247911, 781771436, 428367016, 899561945, 772556990, 292567513, 299858862, 905014162, 831583690, 236040756, 634586571, 328325384, 624942536, 789988405, 61480213, 194308714, 838143579, 736051108, 496922134, 878176915, 980843910, 237261374, 964630813, 954880882, 258232725, 250976209, 780301062, 444930011, 668876544, 680027871, 586289987, 198454698, 108698700, 766982741, 787653584, 407830264, 430077292, 171695572, 230273283, 352221398, 701321424, 347969744, 300957527, 702963098, 65935656, 979334618, 606453445, 124720868, 585691864, 962402592, 919473142, 359840730, 289814195, 616621852, 419387230, 348423996, 981937093, 497745193, 165217360, 721718295, 739669191, 77407168, 942893870, 472902272, 813955517, 355037477, 249544199, 313324758, 863431060, 958837851, 47672120, 715645713, 953643194, 366397540, 885420338, 763422309, 934300538, 801723245, 387423497, 345298041, 972547766, 959938476, 72535190, 233153063, 564113908, 826914896, 702004149, 749666700, 139960858, 90130022, 542881600, 18820210, 441940764, 244755376, 93157454, 855151027, 447679230, 231164320, 804657874, 227989570, 762352434, 298345202, 184590488, 704017379, 826060931, 104889897, 348193581, 430504059, 162469718, 712663058, 266383724, 296095251, 401738224, 150544154, 985735470, 124647337, 762385676, 749721703, 445712181, 779102274, 712239212, 27612147, 259403207, 412993342, 85914848, 541207074, 777573764, 614362788, 171261193, 955218393, 793373361, 86061670, 889610995, 9136531, 328062965, 705443949, 672652921, 710952744, 810259052, 494358169, 981140645, 547024367, 129587477, 625619741, 869430896, 303560859, 473831149, 498153271, 668939561, 300070939, 571371343, 122400599, 119162718, 893429410, 873722400, 54345633, 435242772, 48470669, 490820814, 108990502, 128323483, 467863281, 454278049, 370138483, 735069740, 34745348, 319877195, 870450102, 132633353, 638591675, 579657540, 483000569, 192797534, 647791391, 744743943, 76944854, 292418736, 208696048, 504420533, 435444999, 589089116, 26982715, 180745535, 26016926, 749342429, 178214251, 239936493, 500115803, 586198271, 212989267, 856039326, 41583897, 348566021, 87125265, 715103666, 972109403, 331102865, 775760341, 628569615, 177635189, 13408695, 46437353, 89842229, 986728366, 383662183, 504967916, 645154965, 969668228, 479496502, 206224466, 989739467, 123079257, 114026065, 442726154, 486007093, 514865930, 410804441, 423532992, 674360476, 193238996, 962687936, 725179532, 966638306, 377909767, 604856050, 419453567, 134730948, 578081095, 405577418, 381895681, 608730239, 899442199, 6480577, 415569409, 138221034, 760129118, 69104736, 418190967, 472625216, 433992916, 672197555, 723340757, 368440986, 107623112, 908201714, 192682733, 211908125, 984660782, 886353812, 378531400, 829488374, 448624100, 734172238, 65005368, 655732873, 746675894, 600808582, 972278650, 75678251, 219318919, 224902446, 599111319, 678531611, 343123448, 463575068, 683470934, 52224550, 56818877, 968647401, 784974678, 204631441, 313799244, 382176741, 344556081, 737185437, 393954981, 945625102, 39409426, 222157303, 528678898, 782090332, 528764385, 454008403, 904393133, 704431750, 222362466, 968691142, 311910670, 485940090, 599194468, 115603557, 155996702, 189631665, 789148589, 828816616, 42319993, 8491946, 732475201, 773018200, 763635103, 843601584, 218059669, 682723825, 105754692, 108837743, 201224300, 131405596, 784215754, 963275694, 735139552, 809236263, 565640193, 939846941, 304323500, 693499066, 435244424, 646171764, 140880293, 153302550, 797945436, 954483126, 455983817, 525501758, 363247912, 291358150, 690187423, 696677103, 268098910, 476697820, 662540636, 950721311, 115513536, 758213475, 416879499, 531950635, 395032648, 952482795, 67995085, 238718685, 691081798, 887280203, 27555211, 652302821, 916285321, 444293402, 237871115, 76294540, 784403426, 250184376, 107984448, 528447609, 459470601, 16454975, 139849280, 13202023, 564120208, 805976858, 693058749, 376161408, 226599089, 9291735, 635530479, 747199660, 364469089, 915146737, 202667632, 13893463, 544585118, 251503463, 991533552, 867804833, 65352389, 10312035, 769746989, 870604945, 633911516, 931928086, 627456067, 321293282, 697527932, 386870754, 161677459, 757644498, 248885941, 580733846, 465171109, 721221390, 557705675, 475468086, 99270783, 70080117, 177476719, 376103580, 735546804, 798560639, 655888222, 239428354, 350555767, 573582903, 830874982, 727847227, 939940404, 759776322, 614278631, 807210009, 54760004, 141480810, 285006736, 682720554, 96209452, 641512065, 690328561, 741538019, 338655607, 716861300, 856487635, 307347379, 871288308, 362993093, 912012124, 376750850, 408546578, 71219723, 880369122, 630117210, 943312951, 767393549, 789029240, 392735659, 401648495, 442947834, 286866692, 273985770, 716455686, 894901479, 52924879, 492870421, 686139867, 846895475, 149697524, 267452127, 575135318, 48360941, 24537292, 288528395, 392186073, 295771520, 459904793, 598957257, 712980690, 828980959, 705882769, 439314393, 549391768, 202204410, 492278672, 864540626, 407735958, 256537564, 450130927, 521719842, 670603588, 362239907, 204541323, 21852840, 876100034, 177138547, 99387842, 709156338, 539020872, 773306502, 329743575, 390418554, 348209520, 576188771, 135406022, 741588496, 255165529, 245928938, 754054890, 169703066, 169231639, 70693793, 885701467, 790139722, 690180045, 597210252, 858632087, 184001721, 385626885, 256272909, 757395344, 246159848, 327617502, 933420617, 125561000, 298412432, 319384869, 390993441, 983615861, 68068382, 583431254, 581433494, 658515967, 71014606, 607147677, 661701514, 611255380, 145682128, 381703509, 671663092, 345061433, 707202494, 761060933, 444544390, 927084328, 221784989, 705522480, 242578310, 840473624, 253951509, 880853693, 618194185, 870771522, 883445152, 426668529, 930182421, 406695387, 793751340, 287870069, 320792884, 738511881, 836268413, 257929511, 746668268, 465785100, 714565086, 275033140, 919133130, 629430632, 955488592, 877525342, 19469020, 249700415, 110951661, 906631858, 93290178, 108514709, 78725195, 697249995, 410508075, 214389206, 552844616, 98971203, 325757361, 225923730, 925822730, 410601902, 649877048, 553526413, 597286097, 51573557, 700811747, 80849537, 440435348, 532543181, 228911239, 654397970, 466853932, 468755427, 140298993, 745012524, 803472800, 296387730, 472611276, 888623347, 572152933, 159369194, 718891902, 480738754, 541681487, 166946954, 151172451, 709599397, 773960788, 857488583, 375676857, 514095434, 502856673, 279207737, 403119894, 6892136, 317272575, 823380878, 122151538, 391921186, 700782350, 779686764, 832907996, 369039077, 235289298, 716261677, 431297123, 341160527, 961496408, 746715149, 199882489, 823721752, 620732638, 448347962, 867814690, 233823227, 56488141, 118603640, 52576040, 411757641, 142350644, 492634603, 306003856, 610099868, 739638769, 943195188, 875568739, 639881846, 774993183, 677347946, 406540971, 790409527, 376625205, 340147547, 777755776, 797614553, 90900014, 979292128, 139834203, 980329260, 652136817, 312801699, 896970307, 316691644, 577699661, 331332784, 203347783, 975148065, 824941373, 566374625, 499824312, 449363415, 860416570, 668243216, 811300142, 701097539, 309878219, 196733879, 26088815, 227147411, 438828226, 530429833, 597281900, 590864083, 156802289, 747311280, 929317800, 687573527, 712020806, 690632602, 642324245, 685053684, 503634844, 504761366, 227294474, 845990185, 530352148, 60955138, 36046237, 434120512, 793486823, 359239782, 850117551, 891461396, 127918149, 991023211, 671051894, 427195595, 983234730, 400249628, 866768149, 110389786, 458111270, 211955813, 247765870, 460516794, 969702706, 445318688, 7551179, 601564079, 845466353, 582162388, 629825189, 651947772, 480259280, 745998356, 81647420, 465165902, 353707226, 671384864, 362557094, 725856031, 637040439, 621851389, 981280002, 380576111, 20237400, 335431051, 618285090, 204548248, 492696316, 699892787, 231477684, 222595121, 30616354, 409791079, 626402335, 337736614, 574674972, 378773191, 279399753, 706166243, 821466308, 668110548, 4768985, 290983379, 697115279, 597580848, 98837752, 240566261, 511457106, 427067560, 923786150, 719895969, 237357903, 210578536, 947358304, 210025220, 285297633, 142962368, 870618986, 488137028, 936701422, 967196376, 598777320, 64315817, 14939709, 188406130, 706351575, 621378043, 796477349, 338050066, 893121479, 583355411, 472712064, 75424539, 491090081, 489849009, 550104454, 347643671, 275192707, 28799775, 822415718, 829274925, 866968117, 528035304, 548223247, 275904426, 200537934, 602876469, 869600611, 934080664, 941571732, 334006197, 873070541, 365447600, 359672976, 816561171, 873892611, 249076798, 896776712, 813292394, 121641594, 875195784, 557667652, 72195903, 133926041, 786274998, 897453781, 890591780, 857459149, 989575892, 958984251, 949626393, 696892850, 526951538, 696686561, 412411217, 684183446, 72995161, 754315882, 9018824, 59015872, 619090334, 49814961, 295880720, 803369682, 459082, 989263169, 557814294, 848090648, 547080479, 515430667, 93483564, 932919975, 766099615, 887731810, 753417266, 917823456, 252516003, 519319206, 283488931, 645681322, 256045379, 454493621, 165879428, 799419824, 597814447, 808242134, 86446330, 998182015, 44706590, 382929511, 87059595, 262818977, 492503510, 389734478, 664709603, 605553282, 948850436, 346439513, 172952603, 816474656, 36101927, 612221974, 721450412, 500363694, 632495416, 196718607, 608590268, 352986573, 306149959, 684385643, 821697457, 245087021, 194645472, 346951643, 711692201, 183772271, 810563647, 478294571, 242231708, 378486680, 509295573, 356877520, 403950887, 463241865, 963173878, 860342749, 481710489, 739555242, 556077551, 551762227, 928317394, 384629278, 474920817, 192667464, 850121343, 45929782, 541960773, 934819970, 169315744, 74065812, 822352017, 669142703, 846268544, 844181869, 238722544, 751839236, 730831413, 286784508, 612928974, 326862622, 470072460, 197574618, 218853884, 978605919, 838705070, 25967553, 33636407, 720955150, 506263357, 931949167, 581542420, 524486448, 866401980, 513258512, 124343961, 375818285, 914810060, 839342493, 974371820, 1789613, 190006007, 188049377, 712486689, 369713320, 144286951, 529246296, 991572998, 535794191, 926198586, 698596310, 741888421, 263452541, 325730928, 970321891, 667279986, 835813334, 402491155, 44062787, 204940820, 299808189, 510506166, 718065045, 179036167, 130395, 620857224, 944091857, 669854433, 616226453, 58869596, 513954344, 891672826, 320171725, 354919313, 129688300, 674682190, 121597131, 716273237, 248167058, 214194443, 418982086, 343722916, 135922221, 782505276, 794862817, 356395777, 315629794, 541972940, 168847838, 305763143, 172977471, 912121057, 592228478, 442729566, 110857525, 946851721, 539274016, 635568330, 484130659, 331602504, 208658163, 593025257, 721922677, 989975843, 590418488, 236087018, 27422398, 412408848, 381704462, 159836746, 457803065, 127947802, 269935704, 281749737, 3240213, 847547734, 602942410, 92719398, 185973846, 162635182, 98258929, 107260838, 370826874, 167928828, 379820059, 491761579, 795442385, 732167659, 347878647, 274472175, 259197451, 142761104, 633033256, 474557322, 476110135, 621569719, 746192369, 286867779, 406313476, 671389859, 265752202, 848739833, 383673654, 60067186, 61134538, 86396751, 469089778, 566227287, 1034466, 773367162, 817594396, 148244214, 406664731, 194729462, 525735160, 727907033, 590413665, 958956710, 488195675, 983178384, 907252662, 464995914, 630983276, 879861605, 997660513, 393586376, 902437416, 240215030, 188388577, 170502340, 55092716, 12538036, 455392296, 871800157, 722176727, 22756625, 255602653, 831125958, 939990535, 607786476, 590978389, 707773201, 687432434, 696194715, 814767925, 969151182, 784353271, 497844037, 303214581, 635231992, 37535894, 485430010, 605016317, 574067494, 163667500, 444714651, 839106296, 337095472, 13562138, 436199827, 203335822, 57069380, 246045104, 643882296, 791299007, 218703351, 318796300, 425125597, 658026875, 87592006, 172415814, 460222627, 704186373, 773858180, 763332052, 827064371, 653968780, 988003978, 393263354, 51597279, 711459698, 610912088, 581888352, 451498001, 150425125, 23483553, 265677575, 59616528, 293509206, 338602725, 316867051, 903223902, 593655239, 374582494, 783874751, 566729339, 792152587, 421592074, 923535614, 542718128, 188418989, 540752036, 762297813, 106141314, 398444271, 348063029, 787561769, 381215856, 288362720, 497328241, 71862776, 15283828, 98765329, 39562563, 256210050, 885703977, 7201879, 706041117, 5306199, 965538837, 275828160, 320092171, 894083562, 42424874, 832144536, 684692222, 138615440, 263303097, 445463690, 24254260, 699448784, 426597007, 747625460, 290012393, 950590415, 687465684, 39293608, 380599980, 544416634, 705961295, 426331112, 296187530, 867429081, 858141603, 68943546, 227907927, 795602806, 94778603, 224005450, 927867177, 769147225, 790856490, 357547402, 861878882, 24642122, 83482556, 553139198, 581512319, 682005866, 436553933, 722868934, 766198636, 886285124, 667950911, 947029486, 607950871, 927768407, 932456590, 915501862, 207850702, 818584261, 445984977, 814180356, 678575852, 22189066, 211083013, 67211064, 766633857, 810320839, 271616962, 240275331, 7761574, 763768877, 421366224, 197786339, 773320358, 960274014, 295971020, 417620885, 979907299, 711050185, 365220345, 834467899, 212838946, 161325841, 559887970, 861868957, 88035575, 21439878, 623048580, 693030684, 183372432, 751455597, 109430833, 324498269, 72803052, 237844490, 491281572, 480232774, 17807216, 371791229, 797413021, 346471666, 588623411, 904202960, 561710782, 155090972, 113927131, 130386397, 802703644, 975966805, 353240982, 757287498, 398540335, 497092060, 434461822, 552417030, 170683652, 397701369, 485414431, 557624617, 915928554, 530120977, 262230051, 732050338, 487536491, 242118150, 566234486, 113204674, 755156030, 445536834, 853906644, 927605660, 482989406, 866341407, 877586797, 405737004, 908149588, 546109327, 895635435, 877329176, 661786636, 300047999, 721624256, 968587955, 887103124, 828811721, 506317567, 896103987, 648888739, 414897785, 752592836, 723353182, 998579157, 247994626, 956600525, 537549380, 550031944, 86872376, 367437156, 863047376, 441618388, 619473697, 282876243, 14929814, 826134463, 44046004, 454377539, 125018709, 415579271, 607215660, 347811085, 843052568, 527908292, 851942447, 492791973, 506210884, 310170858, 755092121, 331917494, 762356149, 111221223, 240437264, 470768700, 246808557, 684370917, 550129158, 735558651, 433366236, 917998360, 372579934, 297577979, 380657045, 704289911, 719585027, 551145238, 884378453, 454481603, 968777817, 674692414, 697328465, 208953677, 80578629, 280168588, 819039396, 737098031, 129084513, 610560206, 554272408, 92909630, 563470119, 736967763, 756712209, 801272448, 10315653, 347085365, 539044566, 302014162, 335331603, 345457037, 908460091, 209845130, 311485514, 200710572, 525322047, 708547840, 63521065, 547665994, 534163447, 364888557, 502757889, 960829878, 805740870, 361920285, 354794785, 338337729, 928271098, 295672604, 709112678, 304521804, 463752595, 153395740, 153220767, 206099561, 946175300, 661668288, 344914103, 11414168, 890598317, 955348760, 316799753, 556386099, 418082547, 901459766, 366494594, 222472861, 70154974, 91071834, 130504072, 463461072, 363306671, 485805068, 992141342, 223601361, 217522871, 998945869, 72487481, 762201431, 710020993, 827419080, 836471499, 899650659, 485317290, 246317974, 773674376, 901539505, 980295533, 365069997, 702273279, 934656012, 747577980, 34659196, 819869911, 816051373, 181767339, 253711674, 859980156, 512366737, 295927302, 860035692, 314625636, 611132605, 727278934, 906449566, 589942947, 598213026, 227461901, 975104698, 116840954, 801394032, 215586493, 341822551, 983700887, 206269303, 841812826, 38309536, 630430536, 819753349, 875242049, 680017660, 73607646, 269558393, 6859291, 984676295, 408745712, 101738176, 500114592, 483734078, 315376079, 620856960, 871981365, 241931573, 293079228, 289112202, 184645965, 662809342, 964826533, 611905934, 646736410, 45777197, 430758731, 249765695, 182632473, 230687519, 650967447, 140532148, 268278315, 434848778, 974718937, 520349468, 324564805, 695701420, 83085151, 353176045, 79654396, 50693159, 781685317, 6199128, 332046051, 444359738, 698101819, 939546051, 645725230, 185512967, 582732069, 543153422, 933158628, 302279040, 398306103, 825549104, 220260744, 825793937, 119070795, 278718885, 707398406, 663731460, 678502439, 469075822, 977907072, 980331820, 105014535, 336880013, 349497082, 303660199, 712478788, 449036758, 467780740, 860230731, 334561564, 850544893, 276238058, 890888470, 772817263, 314980420, 155297729, 502711782, 419340213, 809947108, 903896687, 927363475, 481766361, 180745660, 885717198, 72776356, 534066534, 100480496, 120780716, 530302662, 669732985, 288602322, 897123781, 638537103, 894388492, 509497201, 67043153, 596579250, 561530236, 187331790, 480405486, 936614980, 332788086, 791232449, 434600138, 53832392, 93146346, 437675645, 286245058, 611395562, 665891237, 725400896, 743377013, 574479851, 757259003, 39057648, 182270318, 217040574, 295961412, 833875180, 418059261, 23314200, 280986342, 898074629, 867420544, 524036168, 558386304, 183924750, 134483070, 924075452, 124765320, 215427898, 102344351, 172496078, 86622312, 334990312, 521407677, 129937565, 760570208, 400802950, 880672523, 669452077, 477115743, 75338458, 667688656, 432097917, 623390527, 163151758, 324167924, 357067194, 40355367, 503301155, 260921014, 876262020, 964217039, 754547145, 264999569, 295905438, 39706728, 78191246, 149074565, 667267381, 64860521, 953396981, 22343335, 596251999, 348063658, 168085245, 294461110, 753116371, 701555584, 490808296, 940074100, 716198675, 877064303, 689854695, 527856897, 707924903, 894294972, 141714737, 30968589, 321323264, 804941547, 902690448, 34068878, 873342675, 828922349, 342395930, 701363703, 19336904, 435215444, 159569465, 964157849, 132701559, 575723575, 427394968, 597560143, 576719469, 863931091, 344718657, 92807006, 219083619, 357484819, 421246201, 889950460, 669656310, 798463412, 589687149, 70790920, 317389275, 679983952, 519547653, 698962520, 915051003, 451756971, 359737382, 670421660, 973795387, 149968319, 8456768, 230306705, 100589525, 586769068, 439315603, 996793081, 798285433, 731393030, 714875105, 279856430, 485022977, 759947648, 195409090, 631663574, 184382952, 571220558, 637267896, 33849871, 882658292, 288519542, 95087708, 742870298, 983952284, 660280221, 319550543, 673747145, 122648835, 594524317, 561865119, 690994417, 815420623, 675409645, 399190273, 250074074, 959542908, 419026045, 906405911, 295373743, 786739421, 611352197, 115274349, 653968553, 535955567, 110709948, 859721565, 507701924, 40036884, 434247729, 225977470, 95809371, 380507896, 583023647, 995617495, 645018116, 87661681, 366507887, 672424585, 889294609, 453618730, 561083072, 756497756, 133218984, 410582143, 703407487, 376183507, 278503564, 520887697, 281114361, 134140402, 297760628, 936371840, 114971881, 282544677, 120626798, 470503259, 67419993, 269836083, 61098311, 172756669, 364954680, 281855893, 308408048, 92384882, 263367507, 529599980, 381247169, 740545547, 788304677, 757052311, 986742570, 795151172, 37786099, 874704492, 332152562, 990000624, 406435325, 343515191, 717647662, 22103284, 162950375, 977907822, 451006974, 603231657, 4209549, 920100950, 953854006, 598902326, 548789259, 965088046, 153112648, 118687687, 191331255, 248789120, 928633171, 495845217, 637308384, 328826315, 258754347, 267912487, 660177960, 80103105, 235654131, 595892920, 923452539, 451168135, 503056411, 843325938, 328660988, 292858143, 393740021, 466329640, 943434602, 971870629, 989030807, 35595940, 273219292, 930085639, 454020658, 69217174, 931131873, 824193507, 555361823, 727350016, 763776867, 152876181, 638065049, 42356264, 200625537, 927068057, 394391773, 743686658, 571976119, 21769467, 903157721, 438564682, 440853407, 469421798, 518569208, 584015413, 112729830, 893215219, 732603801, 463298546, 914784220, 624759052, 495588641, 283913848, 66928048, 22842852, 460673207, 428961004, 828000665, 644808536, 810885106, 745796311, 585424047, 757326468, 638790695, 202280710, 602670424, 502736736, 242830461, 569218836, 585090248, 737692309, 143720206, 804187725, 159821383, 337482239, 146565748, 779138101, 541119901, 766130601, 577496413, 298703231, 568749861, 944278408, 731244641, 359978965, 45318491, 292896313, 233682594, 850298845, 396478080, 925798177, 163546418, 576898513, 89676376, 560162628, 77017208, 245142845, 626227776, 266092348, 314611460, 454210528, 44448926, 706897538, 483053437, 727765863, 576366690, 675388131, 202938250, 860259015, 679785251, 673106332, 111595085, 175278136, 611598977, 578513018, 224566265, 172673898, 695002538, 547676637, 192950772, 157740230, 980938487, 284348055, 365403758, 583099946, 63998113, 1736509, 580586333, 686708335, 178602271, 905488143, 4888350, 985354132, 233444649, 249053257, 450183500, 971711235, 390684073, 303573576, 896814954, 826388556, 455070287, 991035688, 948862147, 380431772, 711616919, 742546647, 960895564, 65847571, 785459730, 147853542, 461331145, 16291398, 8640098, 422056289, 700516209, 713413580, 998112657, 468720165, 849647465, 839659453, 949802395, 454969983, 4544748, 879083990, 136447059, 64116258, 456303365, 541637479, 448003665, 569713311, 291424292, 973116437, 341634078, 582988359, 146711569, 387815515, 685339058, 609445312, 337058465, 149406298, 978517637, 217322417, 974019624, 471733109, 554800705, 802648790, 979966986, 821925251, 677983143, 76134964, 441187190, 51041325, 821543986, 781018505, 120769490, 717218043, 583527753, 836198688, 212899089, 871992807, 644413892, 551829153, 27531618, 103192103, 621267414, 390592567, 871303597, 80084674, 379804465, 788732736, 12408366, 964631051, 972126213, 213877915, 363464150, 972517430, 767110263, 735704907, 177333749, 340882926, 265382566, 88302548, 626138920, 975052119, 211514005, 749293394, 99965675, 431006533, 809349024, 630852298, 602099752, 664981969, 581387820, 351963544, 783682546, 447377527, 562292759, 634594411, 493432267, 941744525, 824348125, 935566776, 199113028, 928859359, 52842207, 452060742, 234600401, 563823565, 728960718, 489671034, 161835505, 330760464, 921344557, 706858791, 95483438, 448107785, 306927060, 916743451, 166752287, 673527211, 732685231, 648776650, 589369862, 328082522, 232631988, 403833629, 330016573, 510771655, 698741427, 350072010, 611156429, 267046087, 480915618, 752830611, 703567147, 954423343, 755604340, 325363264, 750351492, 868956355, 616715734, 36611746, 467062899, 458500712, 604664849, 965556732, 296105630, 840882451, 248880773, 81941240, 772014343, 486228355, 266282115, 919583053, 699250327, 844055736, 457494118, 923149579, 432381036, 953943163, 136034898, 680940843, 511743241, 292279928, 386250696, 407451823, 282626034, 197389088, 293509731, 941031322, 667032894, 882180005, 888874305, 455354633, 133014515, 721663310, 668341596, 987256277, 869055658, 225523749, 62384457, 707673461, 797105825, 28661502, 537014617, 936546823, 239205941, 109501967, 603051373, 971305634, 306998846, 170413283, 643948768, 143190893, 943744251, 305690898, 55236290, 498915553, 465866724, 711213417, 369087246, 539812202, 613342066, 918616999, 837000003, 248835268, 526391979, 659313867, 858543096, 468000722, 648219540, 945923390, 100384407, 434393395, 989051966, 386219789, 424757440, 657766436, 676514766, 24099038, 377112908, 494340686, 83211419, 40851084, 876574609, 454563306, 755743747, 114592294, 726617402, 86225952, 628166546, 603115288, 916682611, 637971531, 757013954, 476878862, 649165815, 725751219, 949076763, 805002007, 120341436, 454936621, 166173871, 965494938, 721906956, 175145138, 719917714, 218053230, 384192637, 441225973, 724718953, 124758884, 768853822, 41135392, 241255944, 264325778, 606821983, 350129404, 868727131, 937283946, 165744121, 175105005, 187899850, 325459283, 975514325, 396222132, 799560627, 6725923, 206647259, 743638908, 190117010, 366446343, 403469776, 331893932, 543923588, 497221888, 204823874, 581938940, 824980253, 285859948, 859591533, 286446732, 274942313, 569062393, 156256471, 279038571, 602502968, 416822984, 891144106, 56464161, 511513677, 448167505, 831956812, 805485689, 601308169, 459010309, 537043850, 422050679, 487916531, 969266233, 660625314, 715449543, 281512859, 120804909, 214234397, 726193487, 394928368, 934295670, 150537107, 402147187, 53644779, 884400285, 61059312, 376763144, 828375056, 405739049, 458888231, 102180100, 442161518, 481828806, 712139984, 381873137, 927461989, 268881151, 285811471, 585004537, 978284509, 907531708, 507786277, 755230827, 465020102, 389332161, 115800775, 257637267, 262695943, 748803152, 751846622, 397580277, 463695531, 166314092, 829624998, 387607650, 18228479, 600094041, 549588319, 486922445, 468428116, 73370936, 745270368, 427243214, 689654130, 108470527, 918017685, 502256482, 995902355, 198042262, 814832395, 466075647, 421385925, 560132508, 175216519, 230606361, 644862612, 131278366, 448103345, 839376168, 815398530, 888191740, 197614758, 831935092, 803250914, 785172294, 707821557, 404928267, 774357885, 569742538, 65026919, 564937689, 707324527, 349918205, 944218966, 130623285, 83495326, 638589982, 776316174, 657465827, 226432989, 450136727, 358905087, 23912477, 665269297, 952349381, 102344852, 580069534, 414654811, 828157822, 427220099, 426479081, 728921307, 146383425, 72765343, 732550203, 992562961, 386014109, 296519270, 616803172, 685955675, 934653179, 556159779, 558308797, 925427293, 827122790, 885111941, 776180089, 163953281, 934145674, 449160931, 575863311, 487682828, 16272654, 172054128, 822508005, 874891545, 406793385, 655282323, 62603592, 799497538, 379534260, 626695468, 608038640, 235574486, 703901574, 180796185, 53754986, 20744764, 530798792, 128803656, 442073220, 618055145, 226028161, 925077452, 427299406, 67278615, 582824500, 748048367, 631549628, 948406058, 613340409, 570045320, 894886607, 221470495, 877716523, 236840082, 368367515, 109044070, 57556462, 522813052, 639816823, 539271470, 506218450, 291609886, 758548402, 124134935, 335990540, 861721314, 888698021, 406492494, 676483021, 79599377, 679892329, 201155423, 376867032, 188758596, 152283947, 999838549, 401573230, 575633128, 352425805, 128325232, 417565751, 357520300, 856146672, 291228458, 628545566, 549343449, 954950792, 578019052, 82525425, 496245471, 473015155, 446289455, 220781553, 413679404, 948534742, 460832917, 122409761, 281151339, 810777575, 646786180, 314355261, 570315761, 275041316, 3179957, 323699205, 301463397, 360444718, 396729314, 689992560, 358124518, 270759250, 408136194, 302855644, 192414608, 941338909, 177630014, 784944396, 415527843, 94409216, 807351197, 726459109, 901398273, 209018875, 503959635, 111451874, 705042180, 810065297, 423580076, 475811848, 13786312, 595719198, 282287451, 940715273, 76026810, 675759293, 799360260, 256793748, 540984854, 987735026, 646971159, 463230923, 910117452, 816598817, 189372587, 647142955, 172969308, 686307241, 830770918, 708034502, 229864376, 600662634, 408461707, 45177753, 164066850, 328983971, 870204580, 168659704, 870552839, 28902911, 969361410, 925829555, 450943055, 563754569, 419906343, 435369167, 366581877, 816653176, 846750110, 559488129, 369048221, 136090507, 939867071, 340765284, 829153859, 753779136, 451857004, 444607559, 593709522, 92503569, 216752189, 552403286, 678685566, 750217332, 434081275, 23208858, 521582126, 681888108, 580333631, 435435689, 511803982, 209639621, 607581588, 125571877, 487843881, 166117324, 42588721, 787431716, 411182607, 842240221, 284771117, 762778314, 857313535, 295695836, 937976451, 362091758, 755882101, 612911117, 971463146, 971110885, 760167513, 249872932, 568834645, 392712376, 861001821, 616087901, 843777303, 902421415, 438249251, 865014232, 294244025, 280338343, 402246561, 330177952, 797300467, 413455263, 89745720, 238544032, 330244401, 983427252, 795266988, 698607710, 121892610, 500807540, 596821400, 579864820, 959511820, 951977953, 21046157, 127437782, 797826940, 415749582, 868969945, 807220051, 449104888, 32714673, 745262503, 215326131, 8681537, 276657770, 797838422, 487678918, 498573158, 323166770, 833053227, 100946132, 381791690, 855512415, 898439036, 337315731, 948502364, 873739409, 299624738, 954586217, 618033914, 708354508, 67434492, 394586467, 380290846, 433413262, 676242467, 130758275, 999372014, 432138807, 698110170, 717329726, 479605252, 777413004, 166174604, 279849400, 808742214, 238735405, 925478764, 531792239, 359650380, 350202290, 607434715, 540047806, 81447218, 391755333, 948848222, 1797905, 401564789, 693156692, 316489177, 423993280, 554836673, 247558168, 424350871, 153598566, 650471667, 152829748, 590968829, 883381423, 908676519, 816138848, 871528149, 524720183, 897696110, 370046714, 358986522, 385896748, 541878018, 422853149, 328074501, 550025363, 686099954, 985630604, 548880991, 497076722, 948655895, 821643555, 268330120, 893352922, 743333572, 495785009, 910529107, 603030227, 115719338, 912753333, 336627122, 740022103, 752607439, 635136921, 899338967, 645889588, 106169480, 170340102, 804639553, 168169354, 713419380, 82112045, 350181511, 199920659, 538974675, 506669843, 530739740, 823922026, 800634091, 625171951, 809828770, 304832837, 768288780, 701617644, 628451152, 172293838, 355184563, 879877781, 270088698, 995234101, 996068260, 638348600, 890358691, 417020001, 613526543, 990949933, 245936491, 331647157, 794339954, 443940263, 825462677, 827140128, 246268549, 305281149, 734190756, 157035376, 687739579, 870402848, 908748494, 634484367, 829508461, 832824698, 127085746, 316105688, 427822377, 335700617, 227204526, 139310609, 238393549, 147813161, 669005817, 656133739, 741142991, 738916182, 236850124, 40412263, 65962287, 335412376, 907818224, 414506762, 793285997, 302534624, 861569085, 196568721, 771421090, 306041796, 434365415, 222735103, 357589600, 102760387, 388439206, 918841097, 645784118, 939599812, 978333753, 147448838, 666750935, 642744043, 777214023, 713739151, 924139075, 779721871, 503782615, 251189088, 689422474, 923745113, 736262767, 805073344, 528178524, 631286730, 247391125, 568299926, 113745197, 879305996, 103293962, 577580622, 68623341, 134191822, 114225032, 104944831, 471656871, 175046347, 821659432, 868043974, 108624313, 531004270, 742653229, 627133854, 833948359, 972795038, 560423868, 853795849, 371534246, 376761238, 103980278, 56903431, 523701734, 664940778, 886982365, 552684493, 316828602, 533699983, 265528981, 208999921, 712384058, 301240646, 757618960, 476911954, 581571916, 661770983, 694919175, 632822042, 703645715, 8358659, 692522902, 900882499, 930009975, 373107866, 997825683, 978934608, 911063364, 154646877, 740751538, 118707595, 89480798, 656840298, 44109199, 4741059, 6067376, 745689948, 995545654, 181522348, 27778687, 145529675, 395366003, 999015023, 772011745, 592781309, 196216298, 997549245, 999165857, 223513841, 887487341, 804886333, 144826437, 301402162, 881325286, 988058989, 507847204, 543750552, 422203735, 671161552, 859659908, 396561738, 649915945, 531120329, 161194358, 318204724, 263651091, 61721641, 865282686, 214880919, 840582518, 100930523, 225843692, 473806670, 344021294, 121658541, 30303554, 877404557, 979245658, 261915871, 150132486, 483437698, 25878365, 411687090, 662410519, 949915562, 719277940, 744851802, 49055633, 562295657, 116244007, 412127481, 774269066, 381418218, 878588005, 542952297, 288621607, 942043529, 663859084, 6078905, 386340759, 80919665, 994011797, 793918608, 530290601, 500826497, 694448076, 638513323, 139600341, 644845359, 642356176, 721647782, 77765265, 749471541, 76300508, 941184465, 378620225, 582534091, 567472936, 680870599, 39169508, 663788122, 488173103, 716324129, 989027694, 726043418, 775080453, 885839043, 299173201, 17077597, 274015711, 593466749, 504791212, 104875712, 145439352, 409477982, 380354714, 400691060, 196180461, 902333722, 324374984, 338028295, 205913778, 355912849, 228594127, 102855150, 137160292, 615489822, 860867591, 654271563, 254385338, 835691448, 551051744, 573490335, 610004998, 878622681, 279625284, 836389898, 545976553, 900263177, 308715529, 609816100, 186604744, 930280387, 922255546, 276406889, 473586566, 715151957, 829780523, 533665585, 143898281, 809992053, 731652401, 4907252, 772667616, 246528320, 739494310, 280942068, 839787275, 732950556, 749435777, 310064789, 422655853, 876635580, 611856191, 535532814, 511310785, 274355587, 11805688, 844174330, 698846283, 389512238, 504295881, 20640200, 674162862, 213471219, 786231336, 772631274, 230417949, 851996930, 948912891, 933829938, 843090844, 945540219, 477110688, 778482083, 563940558, 779696209, 736224579, 134250231, 480906754, 623214650, 928710201, 212734299, 466330031, 419953804, 33053002, 72627743, 267643548, 892993677, 700819024, 784460121, 623320665, 753435868, 836463178, 952629918, 785723599, 55889789, 167909312, 800740027, 747364326, 407153924, 828909700, 491286559, 905168951, 641157896, 86865938, 147526959, 797387143, 409892020, 244313605, 116070408, 731013996, 382371356, 621234308, 169113373, 396006151, 54097553, 322684512, 955241163, 893444425, 941449769, 508681110, 812350839, 192255106, 932238521, 236571953, 157940648, 910622363, 347217491, 464234186, 706456121, 764124969, 836788994, 987689809, 425423122, 902238250, 614827191, 955534475, 912850779, 18007842, 995508001, 320026511, 345150802, 684896087, 845628139, 764936021, 356995398, 332050453, 927284300, 836627708, 481226954, 910504747, 819492134, 377851140, 535343743, 273335747, 326749605, 313329887, 479774229, 351870186, 250333886, 198571668, 335403095, 692818877, 786924125, 754841676, 199193366, 11933097, 62113033, 266885148, 885458500, 230830009, 965114925, 69944796, 477148102, 649999778, 747567079, 623827081, 595915793, 734652975, 150894523, 675246937, 306506273, 476524125, 489207797, 385152303, 548563859, 61120868, 529422942, 152544180, 245780718, 508934635, 317916786, 174537627, 455959816, 82009091, 800499518, 28598455, 647445010, 385934780, 888352936, 809100582, 450585602, 218239339, 123981272, 882440010, 197781319, 469667782, 212599578, 332793186, 183512244, 379861289, 190816713, 103987453, 152807152, 504544724, 770304414, 573790486, 96769432, 230920789, 357732705, 652474390, 999127942, 503815576, 926119311, 777144690, 584446416, 95066183, 117639897, 741416356, 487662112, 473178929, 898353791, 525597362, 158370878, 235873965, 42446310, 944485390, 209882139, 111839040, 899047767, 265278207, 396245687, 92553531, 193710261, 257754548, 559414493, 686413140, 666901379, 19069842, 843048255, 847832994, 480452728, 798323029, 276071875, 36521831, 362997552, 689974941, 718712762, 78505625, 867449254, 991231847, 781100660, 993877577, 586767293, 50164522, 242693598, 544402067, 512325404, 286808716, 382687020, 985652218, 371670605, 635100505, 728685954, 658590589, 821861455, 165540935, 147538579, 460369188, 816619671, 371454794, 786286766, 94241492, 886389318, 723295235, 484437968, 248761559, 818196283, 711249267, 210313511, 143708080, 322433553, 889425298, 781079235, 3756908, 740305495, 772775509, 845874680, 436777733, 573175895, 159134944, 343602430, 651257518, 629345796, 177099365, 98221041, 62723203, 671641570, 656211400, 911668522, 837285420, 444918910, 669588941, 90354483, 612096821, 994545989, 970557375, 344918465, 784424893, 412501500, 731906150, 295087930, 855332732, 548392294, 690695394, 381853925, 976856791, 741798560, 110084894, 522442813, 841064134, 175343236, 739301720, 781034503, 973772062, 643245229, 17695640, 497301580, 14611697, 406390558, 831884802, 347623001, 604002543, 354182280, 859281807, 457446158, 374651860, 406805908, 465875850, 8837311, 267260473, 309646425, 528879308, 854997525, 872789416, 422980831, 994708172, 375100908, 423536960, 654453744, 674126272, 364153288, 670360707, 528824670, 986131860, 80150879, 237873268, 346912485, 144569440, 924477043, 726387199, 88465124, 813762621, 182705955, 192460554, 831460632, 52925915, 383375005, 984179169, 784193152, 478543656, 344288919, 521583599, 955922507, 694989509, 220793749, 32027685, 891723064, 956671581, 358154600, 924518257, 22466840, 195300810, 613575234, 800436104, 245972859, 699918716, 299567718, 772725772, 126787924, 869165937, 230161752, 637202821, 342258637, 26197636, 556867175, 75606774, 100525479, 167777031, 505783931, 43212374, 346071789, 843317591, 546011334, 640738406, 128686360, 881473589, 785909849, 990105547, 161262733, 551859847, 450124897, 437753077, 234114791, 703753067, 818230239, 973473219, 606720166, 727255967, 83901628, 525385077, 307034266, 194705178, 17321757, 910594939, 274668534, 524238485, 939304097, 635480216, 680848900, 950209807, 783573244, 79786341, 292008032, 711765601, 434758637, 515342481, 76845556, 587806149, 362560519, 387320451, 257535327, 1642509, 422394947, 4670629, 9836553, 876359457, 236748276, 832130333, 459086899, 332198624, 794844494, 624104313, 771049344, 386854686, 271721560, 181019844, 531795157, 157249619, 798955121, 551404544, 737712129, 296306334, 571883200, 980764353, 712551039, 747434852, 7736859, 438092651, 786772498, 326133704, 459095337, 492444016, 641046454, 832702341, 715111177, 203268007, 598091868, 538438742, 57957306, 630157007, 770093342, 267818451, 355867249, 375699939, 432767253, 390565461, 989752749, 143516343, 582202570, 71307628, 799978529, 733794478, 53331850, 351610391, 941640820, 137641485, 624822988, 382803787, 904217527, 294004256, 58580848, 993435238, 743624823, 351888456, 437246907, 567282919, 277493992, 810088556, 620996740, 828984026, 46116577, 583067436, 95870839, 205731386, 28834149, 345603907, 44846079, 111742394, 113125204, 657845799, 336095891, 469604082, 887317564, 743914730, 373912661, 582836664, 929116154, 663090445, 443433091, 493499889, 616063120, 26867444, 730794703, 575674878, 831009222, 112451127, 366640775, 275701312, 837137138, 284871236, 12834850, 542263697, 814391530, 877610853, 961819184, 579099344, 626350927, 565228025, 836925874, 783427744, 922543082, 981819301, 454951416, 307420418, 143121142, 723510185, 58636492, 603850782, 473125593, 110816487, 497537477, 534249674, 451048964, 787033439, 613500021, 805127754, 13867166, 124988111, 916312559, 446732805, 626154057, 58460674, 576903909, 193212683, 56075449, 357199907, 143855334, 448616659, 650559507, 911875956, 619852281, 522749787, 732794172, 490141197, 319537120, 973422018, 661012452, 310187187, 332547468, 332307877, 829413351, 310403305, 823060730, 779633008, 324045717, 754875360, 292366595, 496721944, 370027285, 556168303, 91253378, 62920229, 219627968, 708446861, 974593785, 563405293, 748640326, 527426116, 399260481, 598263586, 91495378, 609303773, 328813934, 454667841, 386605170, 329230973, 137829958, 399680067, 477461705, 105388384, 680290127, 629475600, 958887554, 499575382, 501436008, 671645742, 384740193, 987537421, 633934952, 503786183, 560676236, 525351100, 524414498, 81093117, 608239899, 988176545, 655878355, 195641472, 86034588, 942182600, 376845937, 290106824, 588959296, 402716043, 822144657, 145484814, 340672495, 201281162, 130349332, 276704809, 224147511, 825258113, 532517875, 395114250, 386011094, 107466290, 13338191, 519779969, 874166305, 449917134, 200703983, 947127784, 556236870, 446452404, 383703713, 622774675, 730848579, 107130019, 295699289, 270151132, 856058606, 917051428, 488988445, 74721115, 282025436, 158909230, 878804164, 253088683, 48519890, 954596937, 33528980, 396225802, 890391340, 813235142, 901650449, 179569694, 994363055, 224099611, 294050245, 702365054, 145219425, 11911367, 361413428, 630048423, 18683913, 981741227, 725886838, 508132745, 198586098, 475739473, 902654622, 564905623, 789583448, 296100861, 132825703, 398843388, 40034925, 16799039, 419229737, 827532720, 413938052, 371842996, 137208337, 467872956, 970490152, 566380450, 750037254, 41611988, 443289564, 288270429, 566232557, 157234222, 264727008, 933905618, 103918464, 585251407, 722197988, 102427194, 558994107, 511165011, 333675692, 564810851, 278825741, 59781148, 983226742, 735067033, 518185226, 341212194, 751035199, 243123558, 183433779, 660238954, 476108741, 764745266, 376305765, 301602075, 418508300, 791666202, 776731403, 958070379, 180306467, 500514464, 763818462, 441553664, 638575066, 519904861, 343737826, 184773636, 607252278, 344360291, 418000357, 905980724, 650771154, 459830948, 568896366, 209245464, 135521135, 155283914, 63619182, 431788886, 494662865, 30047924, 874845115, 217551133, 339974622, 691154799, 357471270, 664899252, 536279561, 18706810, 683683605, 592253253, 514294564, 548175462, 777945217, 759929235, 29678391, 927174509, 229390430, 927251628, 320478187, 891102371, 228893057, 542589687, 822730035, 525004241, 279887968, 418287136, 596258242, 556324316, 686243866, 906022853, 13063104, 403659757, 191273048, 572972905, 407001928, 197157450, 788843619, 614406920, 977710809, 597232554, 652183622, 291828872, 406169168, 570783394, 940011608, 941330625, 51260085, 832684056, 105184295, 924963444, 225052982, 841404955, 6539514, 480887670, 993034225, 168744463, 86358057, 131221487, 680437127, 443438669, 641115731, 908053165, 972674179, 895581212, 930459368, 88481086, 308825638, 924688885, 689550932, 916534624, 435005571, 736301976, 788641310, 425308021, 281946477, 156710471, 368798967, 639172875, 884642953, 859000967, 205523858, 514595354, 54527571, 542892604, 249566783, 482808495, 632192514, 83423687, 993985093, 655436058, 2113006, 623402615, 63280487, 210810468, 321385845, 692627260, 959971139, 904886351, 180948180, 751348071, 639258966, 686478431, 723161486, 87409391, 66972121, 707509130, 33062643, 891770759, 913110281, 345148110, 987719363, 918145723, 924970740, 936678676, 607025339, 681142094, 650950729, 980021822, 792447820, 486449148, 549297539, 64964401, 427452997, 457339346, 25802978, 285669031, 672352369, 700748223, 525292781, 602831464, 827125007, 218774644, 872713286, 262045995, 555854084, 965350701, 263818413, 219392545, 252843793, 393619982, 996146196, 615819094, 883192665, 853385762, 259647094, 20394305, 624424755, 562722107, 585167827, 384814727, 14819997, 945830767, 690407151, 316353220, 645005650, 963006385, 307239730, 238519456, 280930792, 912951661, 400785809, 582434938, 208831888, 463285444, 66569148, 205497626, 114360716, 892711772, 984174495, 326755686, 559815711, 212567870, 323261509, 387372907, 676756663, 662792529, 65487723, 866016445, 145907135, 486638923, 506649762, 619306148, 145981288, 370553863, 546609655, 539476717, 14069815, 260720470, 145127351, 484001351, 967703962, 482502623, 893489810, 449868022, 168296579, 812947098, 112578705, 378460925, 120759255, 730759849, 676835487, 489164477, 731498639, 826261938, 214570728, 551758447, 946402470, 768525184, 779872216, 26674916, 807030443, 255531062, 821132856, 670039436, 87418007, 670948383, 529899566, 803166630, 131471166, 480745443, 193054264, 299526262, 716723962, 415090943, 438864812, 106108975, 526480378, 53426299, 978409941, 794341952, 7345663, 246702181, 162563748, 564818337, 722682923, 516301099, 321448487, 404068139, 29813397, 995584727, 737116158, 666954711, 422558553, 359202019, 5654419, 839199772, 663417127, 160619585, 221747437, 322509755, 738075732, 752554754, 266893121, 488424316, 384497324, 820232562, 573069589, 319688795, 715277272, 247054561, 659315919, 380227979, 445405546, 384585816, 551983395, 833716292, 643605459, 859522772, 18616351, 8595366, 863035512, 669675703, 131471774, 537891225, 190164, 822171038, 112637317, 882375255, 976485625, 62786481, 903178642, 983524999, 936015895, 975775765, 194391559, 48515180, 676592006, 117169426, 218185689, 484779738, 922779517, 871708277, 995022637, 756745125, 696095007, 686448478, 761586508, 620126722, 368491505, 309523253, 585097761, 289527047, 853177153, 839993266, 371230556, 749576631, 214861115, 543757746, 448398377, 723900299, 994069230, 11087264, 115417934, 550094515, 400351221, 82173582, 149656983, 715900460, 120191872, 444770669, 570775511, 186238303, 747372709, 443723342, 214548877, 598595256, 390089237, 801337113, 249609902, 430703138, 926128617, 651024042, 833240534, 736813116, 137920043, 579614287, 346682330, 215578846, 783927150, 437316423, 324518074, 442769584, 384638964, 798408685, 8595757, 810783300, 240225516, 894965254, 906457996, 505585129, 803114277, 603034791, 519307242, 424671065, 489674895, 371162328, 846964066, 930846714, 683880646, 497714631, 340109063, 758187280, 900086794, 659764785, 127068498, 29048261, 123668453, 293144221, 831691142, 42847095, 339901657, 509105824, 922181046, 714328367, 161693692, 558453545, 911493430, 440745388, 411127508, 116442247, 965689195, 634095672, 272838064, 113734053, 242570735, 447575238, 602884825, 582995402, 616928758, 774370941, 196263979, 861275793, 106471868, 131250553, 426601757, 810783118, 913248479, 975806202, 835155273, 63631304, 149971990, 839890172, 797185133, 181411790, 400240828, 817864347, 850380853, 884112479, 15262194, 855796250, 936472948, 494965649, 400208310, 997606100, 620542328, 579924933, 450034066, 172807144, 816870514, 206000749, 406884952, 925729753, 577886452, 204116637, 89098958, 607154858, 140783410, 12431763, 351116677, 796660266, 427732712, 416832702, 8480503, 955773735, 21573622, 391763262, 150466996, 560072511, 529712650, 810949581, 911251937, 697470719, 626285078, 172429929, 435636308, 312433604, 94474976, 444603290, 71991336, 845600784, 208349973, 389405398, 845878782, 268186003, 778470953, 953692091, 47857422, 560057272, 474757006, 943155687, 491450273, 327009089, 233127737, 570470836, 210023912, 226769592, 371084801, 592078863, 233745729, 823073619, 391316452, 822597793, 794648857, 650733364, 693162194, 321624917, 106620523, 291111729, 266623559, 317092349, 936286360, 513871412, 293590430, 731659918, 108176131, 205573449, 258165403, 16452027, 757096369, 614731950, 782259303, 670316999, 988467074, 816830001, 269005319, 463075210, 618849573, 762079891, 758752470, 615940656, 746574524, 617773725, 800202903, 683206066, 718772858, 630537168, 47058170, 821132417, 277094556, 699986463, 702136765, 351699200, 144724609, 411095353, 863353239, 27535307, 479110797, 94421211, 200395141, 534148309, 588247518, 674773826, 205818199, 584557931, 644270598, 959565846, 156965633, 80298282, 328307298, 298536105, 472326959, 675026797, 845410539, 684070547, 529577429, 120342193, 781834824, 433655470, 968414480, 682248652, 565949245, 403284893, 857154809, 234637230, 654319720, 236094768, 43729190, 612602156, 300493693, 978179043, 142388197, 894814899, 856306975, 6329349, 200248082, 764702477, 284797928, 746738242, 634357868, 999111748, 300686816, 215784979, 507721916, 125379, 477778795, 587501144, 325348710, 697960753, 262072762, 556809545, 540228432, 174010294, 824378427, 659786989, 690404822, 687951716, 423430603, 47773317, 746933772, 599655246, 444068633, 434576651, 323326640, 502555465, 581011290, 785977700, 71380091, 209909561, 811772724, 698715789, 405495910, 71054422, 754294648, 668896302, 913719269, 370588834, 615789378, 562228701, 627963828, 872099008, 602144782, 542302887, 996637520, 155859997, 569115214, 28628811, 841944136, 55165975, 90420810, 623451294, 416594775, 763590442, 969490131, 810117887, 1015309, 962486057, 994445430, 906206104, 440821040, 107780623, 666292023, 405743039, 690698105, 81594498, 385200428, 520266785, 117610393, 591390689, 426540617, 961067296, 389299234, 548862149, 953223491, 321004239, 483716324, 762957153, 464558468, 916695937, 360556520, 863307515, 744469165, 191228684, 703394069, 599757137, 149935983, 574583746, 272636041, 135363119, 249941589, 634261731, 470775006, 990619669, 615615920, 439789233, 423660535, 171478538, 825922874, 685532619, 867373672, 480493445, 964710640, 286460424, 551773216, 818113898, 229926200, 307423865, 543902789, 56313412, 721363153, 717158556, 723806388, 26236551, 476413378, 166779866, 270135782, 383809148, 754772945, 887277880, 61160141, 331943354, 147613196, 818680320, 916199487, 588819652, 975300893, 945264295, 962115189, 819704362, 353591116, 837915644, 751300329, 151387218, 680961865, 503356352, 719638372, 400774937, 722769831, 921725942, 541180089, 668529566, 479203742, 167727020, 989594628, 217075700, 131379790, 377297628, 519397750, 157646160, 762537523, 451131350, 862738745, 407618141, 684255184, 188968235, 854728202, 205328284, 963039000, 823677321, 598208195, 370904032, 894843032, 191898415, 570756780, 639554426, 884196367, 497469278, 83823810, 794231523, 309366109, 660217259, 825434274, 17717693, 948605453, 838651898, 546265094, 841736992, 180919865, 372855826, 460650129, 662809214, 227275504, 912116826, 677605253, 529033182, 110519982, 579804562, 737123226, 281484617, 719059607, 992744160, 964526429, 210611378, 496272621, 739314491, 657792938, 307157797, 332065288, 373151498, 729954340, 548283442, 923722678, 722826057, 339448651, 522976694, 251041205, 214556220, 913510100, 960720811, 29728035, 219915904, 533415193, 764294410, 545407125, 526173974, 147105542, 154080141, 441447878, 157840448, 167883964, 718024468, 446304386, 382777149, 628113174, 668317509, 681501271, 416019274, 751751839, 743918451, 183359079, 416371149, 477990461, 194050598, 388434325, 818996580, 310834182, 186406580, 149283293, 973766246, 468733041, 205727743, 10999963, 513324383, 368346829, 429214825, 576801708, 274866209, 453708863, 107260349, 314362791, 122393433, 134269498, 643131546, 800847713, 429712720, 412084763, 937046898, 627631612, 801755046, 901074109, 705959093, 943592718, 965040818, 839408959, 136888279, 309834944, 894542593, 556970111, 983242085, 493531221, 618892632, 176548580, 453363647, 254554707, 607482169, 80777801, 223117071, 172613757, 228262426, 390962202, 886698267, 550096909, 993055027, 92193184, 645741985, 12633267, 187982505, 483923747, 291887331, 181528464, 950908929, 124197621, 197117578, 298978803, 44781632, 914458639, 371049460, 716970647, 675144832, 314736349, 140083125, 918225251, 729166063, 752414487, 57302144, 640892849, 206319, 630215619, 426923136, 181671157, 394892348, 95798236, 151563101, 821732106, 116898306, 819777974, 353445482, 147896874, 999636423, 992651647, 28834375, 57347733, 483604618, 170051927, 944084721, 765040695, 138962127, 882142157, 191006124, 219705353, 144217872, 130346796, 445119569, 309545448, 774635594, 999786478, 791856290, 200843732, 855933301, 119502441, 264940146, 954435325, 277688818, 883960503, 345373645, 841281671, 868524909, 895015196, 719813393, 361443490, 717314589, 40281049, 700820940, 96210706, 731323571, 720374465, 629532865, 671354014, 422475216, 861510326, 423880787, 701306108, 91236651, 683889216, 728298868, 571148287, 255575487, 120373746, 629641368, 276100605, 102106149, 100655358, 230862841, 737041460, 130626482, 135911134, 482870833, 970625217, 670885333, 93379387, 275761767, 415886313, 543209646, 745083398, 21074790, 217530670, 361607560, 27895609, 578789474, 888721675, 91616752, 385070244, 192133673, 161322574, 347514643, 966313778, 511561110, 849468424, 747797545, 108626963, 526866508, 379731583, 452069481, 89999225, 200315162, 609366732, 16891103, 889408204, 562017393, 501118168, 867474733, 531417964, 416958532, 252774463, 385095203, 6967480, 808772028, 456572613, 268310075, 161700326, 718092126, 381882253, 958286893, 516997580, 427863836, 941495273, 660246128, 927084082, 87672265, 898694955, 885506550, 102142976, 396176853, 944019601, 263837718, 386174799, 78522530, 570342264, 324768456, 38791486, 993763330, 813634430, 839146193, 838347457, 420124273, 289116840, 939505576, 692109524, 715682468, 536788146, 237139172, 550107707, 458836418, 328592474, 162151577, 757571662, 638842006, 160356912, 579191991, 906417574, 801047410, 206808449, 535305910, 557530642, 514317933, 448208470, 628716735, 641621766, 261137437, 742664724, 872632359, 489980011, 614909671, 23846955, 595031983, 976032802, 74470099, 842572023, 500054437, 495332763, 645410131, 147360968, 983268563, 657583589, 68922879, 800697199, 643488612, 768550914, 451368614, 701755243, 999143697, 735266188, 543965776, 780260992, 958790592, 635472244, 4597298, 43663814, 454321058, 331317031, 932217852, 673556653, 869809620, 797943403, 646677502, 810762797, 762217968, 870329428, 875384197, 879692785, 723999338, 962277663, 109946172, 727253035, 729200242, 595331570, 218525896, 121851632, 158824502, 168040417, 763165828, 830083673, 428865432, 144467273, 907281339, 928112336, 769746888, 565985963, 14155855, 11838305, 350656156, 721001624, 591060459, 791430425, 271430717, 763040126, 338516623, 557626453, 838546221, 922110412, 367595326, 263487641, 790006027, 751715724, 851512496, 983695849, 954343, 863338600, 969854032, 793776127, 130652292, 886530201, 567878197, 741584710, 183844393, 762904502, 744667193, 155614896, 288324534, 468753789, 330727184, 578782492, 210279935, 310427971, 647432005, 832678576, 796744411, 693155817, 582872573, 2576157, 377725932, 615823699, 534391504, 745561902, 504934572, 571810734, 835972431, 131314753, 870432822, 904921059, 27103840, 991868092, 814826668, 293719622, 1813025, 94745225, 250309918, 65813048, 978627382, 898305404, 268031043, 781795180, 982076400, 994597511, 309254109, 86839600, 544246847, 769698724, 373019446, 558539740, 539671787, 68754812, 314787382, 785355371, 957845125, 411658761, 239071164, 975024956, 571967345, 923190689, 837048632, 272810127, 216214032, 43906665, 189744768, 967829062, 890760707, 410119199, 453819507, 321248481, 572072302, 272617592, 882407964, 581277909, 35028223, 305748711, 340289002, 422174316, 922974273, 235369465, 848758827, 378098213, 14778942, 478120245, 207997290, 188051026, 937806471, 116391921, 495258967, 635055175, 203828172, 153118823, 812968080, 826993248, 995798105, 260694644, 307878199, 231233281, 589755311, 938097204, 668891857, 685255971, 126825625, 543397818, 478934145, 989112905, 684844213, 939641293, 863649002, 131292106, 148746195, 120515732, 820103198, 371808021, 426866574, 199074019, 477300815, 236956155, 855609521, 295197389, 87934145, 828940852, 646238697, 987452754, 608890025, 740304836, 131409531, 165058413, 767279941, 401634698, 703259610, 605773656, 858892193, 8120218, 241142660, 803285167, 326629730, 114937507, 646564975, 523481110, 708840684, 630144406, 784320409, 514360908, 729833588, 521944575, 18842214, 873732857, 321037569, 317686834, 294362226, 140341624, 338770147, 563273797, 588929899, 550933525, 723651379, 366303636, 378819436, 857743077, 592062731, 101605689, 605345064, 430647160, 198396885, 151414614, 396341250, 533062634, 568795746, 63460162, 99791208, 338950091, 23883940, 140403656, 113293763, 29893405, 267697220, 636608502, 117679226, 863010173, 977712198, 244453167, 267268564, 332028981, 993854733, 817833974, 790682136, 624121104, 470346636, 929986886, 307570346, 623133785, 415851819, 558840164, 558257329, 285744271, 292021419, 300732048, 890799141, 734265759, 141402670, 544425373, 884423531, 429897991, 351799413, 911303249, 425663729, 937977759, 366575480, 443459351, 473461067, 486405343, 207325852, 506905936, 832150910, 656908213, 675924449, 366727267, 609746947, 326058863, 645690319, 980484481, 901379779, 299044838, 958348640, 924509582, 788375773, 769761651, 581212968, 632437447, 500764279, 132663217, 913635844, 482985065, 933783431, 531649244, 105517909, 342589308, 392505010, 892966991, 271867472, 982790901, 162654595, 611968681, 170266970, 304278219, 483874778, 913790366, 201420594, 955267273, 716260706, 556026613, 403174412, 44573811, 571754177, 40687141, 306883009, 873457990, 538459717, 607500586, 448576861, 73466554, 154859593, 173237393, 93198608, 692254172, 767274876, 84348242, 165197583, 307020940, 19622256, 348131046, 139510182, 363215109, 927629956, 656311086, 67309768, 111598506, 869344991, 574044651, 839073590, 974074620, 984931445, 188285008, 660878791, 877586638, 297570756, 605495937, 805647504, 701913454, 646003504, 709814911, 627931079, 476036517, 691263673, 575479137, 507949077, 263136432, 474619179, 789742480, 873252195, 44874291, 546144405, 294910763, 150148958, 555764280, 629286299, 28699316, 938684609, 197004406, 807054555, 876436630, 185778826, 244943467, 857602761, 994979605, 852347439, 102914376, 413056184, 343919411, 624075188, 872312782, 114069754, 292022811, 182755200, 452452959, 620591131, 282093084, 622377700, 868148443, 613109538, 650774786, 402020023, 422098904, 546547739, 2055577, 89982511, 387198084, 357632389, 839693346, 204389404, 798850028, 988318452, 242020293, 96439509, 179006942, 514223922, 202743865, 991631004, 521343682, 581081310, 460122485, 112476748, 247695479, 611478444, 229211064, 501838278, 785971191, 201601014, 328433140, 493033092, 67201836, 240457252, 970372261, 713444059, 983037859, 702008131, 59270619, 811816881, 534848939, 778563304, 262682156, 531231670, 203146448, 356840873, 585338971, 19454262, 225453596, 491512191, 407786055, 227050683, 532652846, 370147791, 986329760, 764748601, 247889589, 875903449, 279122194, 632681620, 198317344, 260223900, 529508148, 518256643, 108789705, 58180392, 334884107, 823195732, 467207489, 640372156, 248158025, 216761817, 168636200, 447673165, 943564728, 560616603, 248544606, 93287907, 220544816, 971477563, 715046153, 504296697, 325101111, 684648242, 628272504, 407846676, 566690491, 158564806, 999787105, 556419087, 141968168, 174112041, 6398401, 976393389, 289732754, 293799625, 70063147, 999550940, 879967732, 352376979, 714426357, 51291353, 867127266, 700003660, 760211153, 534876683, 568640563, 529845641, 984810881, 772076197, 122105085, 589093499, 239705114, 132152163, 417431943, 64369571, 128580996, 739557356, 936330686, 759489931, 556054814, 350776026, 356676971, 87662174, 886576345, 424047500, 609125281, 40310702, 439985177, 556855382, 102947877, 633819571, 256630390, 693415872, 565493139, 607134732, 650184820, 986104773, 921509324, 610064177, 715217626, 976079916, 998324171, 470990246, 407550407, 571479173, 244255915, 72787987, 63052606, 14357102, 437308825, 414184951, 538672533, 17594499, 612144304, 381700039, 698240783, 70859944, 63899742, 181620059, 829299882, 574280321, 39875926, 167214934, 478573653, 453814504, 610404080, 494220355, 454728746, 797180370, 910545122, 935758077, 390401344, 143365424, 125161511, 21394188, 68879812, 696393525, 215399522, 433191747, 404462831, 555999105, 858819863, 798226, 452099037, 603673054, 943964936, 945126609, 495889127, 500253713, 13637869, 462875541, 373740789, 958537294, 189878024, 308130328, 988616681, 864596628, 544804553, 241653989, 639301820, 941698776, 640596619, 857192310, 673626039, 668041836, 689083836, 807219325, 670010837, 260027322, 573385907, 113561171, 569380793, 652911823, 680059607, 504570756, 302843136, 865087646, 596858445, 98365129, 612110115, 969651289, 303633516, 675463731, 809752848, 607750123, 664999061, 691289325, 71282328, 55611456, 801682103, 926076543, 964530058, 95722041, 876903350, 798349149, 282254745, 301000032, 154471657, 182446948, 201842093, 799198544, 677842493, 603757886, 870943887, 511493317, 490043339, 514910834, 687371425, 417584031, 323962204, 849703192, 780203942, 661606310, 23176094, 911500067, 451684071, 420817955, 458130952, 646234615, 537786750, 116149767, 7676927, 396116083, 961215456, 9702414, 36453179, 918721542, 880204391, 409431306, 570827224, 834781183, 885289581, 381294703, 893282373, 820005531, 176187591, 540347263, 670767435, 256513592, 601378756, 321101627, 553507906, 959060225, 716952610, 125389357, 467957237, 923478903, 840464451, 738566071, 896535691, 74016515, 618662370, 69837081, 834793929, 344132278, 812799540, 449830355, 295253516, 937778930, 728750324, 303342760, 879462575, 163927740, 66313997, 811009904, 169251114, 134728652, 824249573, 3761375, 343297747, 494277669, 232640213, 861983744, 3795357, 921921264, 389781619, 434970687, 197913629, 367837408, 236795668, 354534247, 947184788, 31686230, 871392482, 222003240, 104325320, 682385853, 80378405, 428391431, 391795854, 700670454, 790116298, 150130944, 394665102, 869314223, 637882936, 457528377, 619617915, 689772237, 217838239, 622410412, 393883158, 134707361, 361646148, 283151584, 876366709, 41998663, 358802408, 259180635, 307850374, 534238290, 796553732, 690748651, 976628721, 942316817, 27092533, 498925554, 341424695, 443494342, 888152212, 843119421, 529237113, 856271616, 75262899, 746454854, 601314534, 940936969, 975575992, 378159888, 699149183, 186952120, 468013114, 606522285, 697534366, 179313990, 907210324, 918327338, 517923806, 810550619, 203557582, 567033604, 49490419, 306273249, 171849037, 559448527, 721249782, 894493862, 829164413, 995999198, 50092148, 178185989, 869961302, 661782950, 544113288, 660686667, 54988042, 574050073, 410214048, 79702962, 39992843, 506364883, 923824874, 136613408, 305354662, 864296675, 344228865, 471678613, 225356460, 82612333, 788655350, 622770584, 798357786, 108726461, 62176861, 128768161, 146673652, 42739345, 676735735, 680238386, 508943833, 565927258, 968887451, 979861179, 97572640, 762562876, 177853887, 992949951, 471547101, 184678238, 934852826, 829015439, 21854208, 549417757, 147207389, 657624831, 204858104, 519396492, 400682373, 937809597, 202760407, 795017109, 320184399, 818763199, 857901284, 61483061, 997060038, 190752287, 372764546, 503702771, 981444884, 969018712, 814177264, 813031634, 861172652, 72161604, 609428857, 706923737, 248394951, 589576465, 420309618, 981583296, 50999936, 604817546, 254373331, 969103480, 444896286, 236507832, 813235128, 758702885, 38155411, 754754020, 859990943, 66778307, 397737258, 644339165, 991282287, 8829049, 989886698, 770524924, 35576281, 859028269, 996726849, 476787520, 375778873, 656286093, 46992957, 725236144, 814616687, 789572632, 717233991, 856752506, 440887033, 394164315, 21925285, 710916981, 463380728, 2959097, 194931108, 127103050, 390419672, 499680547, 976146129, 226510250, 523926601, 946946559, 842085319, 949027288, 413652276, 437817241, 592243065, 968891348, 455891081, 897982563, 749166618, 404351686, 710904744, 601423662, 892721933, 939039767, 872481086, 535370369, 467851338, 509002672, 593396830, 79527955, 268671959, 744165517, 652377326, 169425608, 796193059, 962470896, 237207361, 111905279, 783948764, 8397631, 281705450, 13843193, 433748335, 2179731, 204846814, 499465770, 380044208, 807732254, 583899807, 301441248, 187067551, 758496194, 590823156, 628950154, 264107821, 315716956, 761270630, 812455716, 680599504, 531449965, 483455575, 600694977, 449069316, 556596979, 325231029, 129952842, 259885887, 87864961, 570363084, 937823406, 300254172, 681247114, 422886462, 405010927, 527637921, 706526568, 421728175, 769531311, 192490149, 132692520, 155588750, 967318497, 836641126, 91391081, 215643239, 535452208, 61570621, 778767094, 475586630, 905146784, 238976901, 316401945, 257206058, 847019751, 619660381, 633658606, 270398039, 311060142, 67994889, 747896343, 546521303, 587324512, 594146725, 421114765, 339984861, 833160789, 809735121, 506969950, 39475435, 414721515, 745377661, 481214337, 292581129, 923959032, 842716165, 681147491, 504635540, 301174062, 539391745, 358704179, 588976795, 370880066, 635379676, 901226003, 279199735, 507952605, 772690457, 986806732, 764802555, 142726217, 885575924, 434125861, 190518398, 236881375, 482092263, 42879824, 506960438, 675302660, 395989207, 124587710, 440870239, 74557928, 311330697, 25671288, 173805516, 532499004, 456306964, 649977534, 254808895, 199346118, 592600464, 762305038, 920083056, 918914122, 614697642, 77566612, 62291312, 138686950, 407192609, 982023390, 489469495, 760250310, 24015159, 176760380, 8885486, 402323797, 460095176, 433754374, 959922467, 367634160, 396492391, 108867480, 391141004, 415686131, 126207944, 431365638, 558329685, 769898362, 897184470, 336709924, 399319194, 877287282, 3383685, 507074371, 859159149, 263046491, 246569059, 757646972, 744118881, 595809661, 814211586, 914580063, 685547101, 284747458, 124485340, 146272011, 965486697, 57303256, 667328539, 788312021, 911487362, 995552948, 785308243, 84160644, 171639883, 716306628, 833854072, 566737588, 178169131, 948946911, 18240411, 319205570, 25935188, 444388401, 384992609, 589126252, 190123078, 35422589, 114606175, 331750792, 268267648, 626792351, 479195164, 219824583, 625177609, 876703450, 96515287, 280425864, 617596917, 869460733, 205966384, 70546850, 387617952, 87993223, 899231936, 574330888, 157422280, 179153955, 113209974, 32282245, 707949898, 212046476, 231995947, 759606004, 438801168, 831138001, 98239628, 738366929, 578411638, 735371562, 749273159, 942104324, 378419211, 40493914, 458251806, 212101209, 289480550, 748202095, 31748073, 697052585, 501402867, 668749823, 515221906, 428342965, 810164419, 291037735, 304998699, 32605387, 614711239, 889138423, 233188883, 463780407, 93303405, 343611552, 424715802, 422432576, 565044738, 84585497, 891732583, 234950129, 17630493, 937643237, 461138423, 859859736, 122560127, 593915135, 293004988, 569603215, 425714287, 846200317, 910631469, 41410629, 376918003, 110436470, 397981850, 497043387, 549729301, 225668500, 597601343, 62382119, 453598457, 975669612, 842434106, 445440516, 983084250, 666039333, 237516261, 978553918, 626666546, 815060716, 748471496, 60501966, 162304950, 795633004, 168262321, 791274626, 827388989, 476063294, 201533864, 97516348, 72616856, 240715445, 164215555, 189809441, 977268775, 398555709, 573202320, 4485769, 667042229, 666502833, 266256426, 545684314, 691388380, 692671748, 717736630, 472560451, 46389059, 819529868, 681616996, 584941614, 112987452, 718267524, 802855390, 55478393, 700273000, 324077444, 953627824, 828850219, 364218982, 46296191, 379940417, 578267494, 408319902, 358862533, 230481002, 122357405, 623340189, 963153656, 454237513, 793756561, 158196632, 600411826, 734114474, 284604697, 63697770, 813287137, 927041228, 934204875, 80055022, 593335379, 487867797, 400667858, 553634078, 356428065, 135347283, 932092364, 22301733, 504936962, 548944521, 546552576, 673338979, 35952365, 645016773, 463437633, 109258776, 294646352, 427915278, 637203921, 519265012, 227680138, 210939049, 899627051, 898878181, 883381864, 713752218, 361452110, 533629140, 645337518, 461872098, 891376414, 194620991, 488467086, 661134869, 705005783, 939392130, 747178036, 887384331, 838705099, 696828656, 492670448, 179445422, 833099035, 702114352, 917063524, 497589183, 606761215, 124417116, 616885554, 858521867, 407022149, 588534154, 83869930, 77149564, 504433229, 580496266, 495843782, 714968434, 631132794, 724938785, 81790856, 698611281, 887197071, 323942727, 445177987, 97091912, 109672617, 883293974, 299320307, 368508096, 618017423, 221162818, 885935087, 361052810, 966210837, 663255432, 703120983, 83151555, 523072384, 107499104, 207870726, 121668296, 312756870, 463170680, 928924211, 984983796, 749846819, 345633237, 968097333, 606932352, 838446377, 715009767, 619886051, 571998640, 548099781, 228599961, 426423397, 583129292, 374576861, 907006317, 174537770, 251955218, 871126236, 903770394, 933228828, 602240066, 921838210, 957285281, 385141365, 480116205, 109611613, 94866019, 16489980, 630153886, 549894818, 156318548, 961065738, 240062198, 652051089, 724801171, 687226604, 849648570, 185499393, 25195206, 311564096, 564802544, 560459904, 310445512, 333574031, 230914744, 284664766, 933170078, 909225512, 234915724] 168907727)," 0 (countGood [816003760, 105617541, 381582697, 452191656, 291270597, 772269031, 798947817, 507003482, 741396149, 863782215, 307574709, 249561446, 870886608, 463481644, 770713545, 842274976, 349885794, 63750806, 322491262, 893932779, 381864541, 92311276, 613992358, 986298761, 648372061, 498165346, 71101780, 190930000, 339743148, 300637497, 72455589, 299726510, 451680243, 881722313, 906613195, 157676383, 176328908, 628022258, 24126930, 101376418, 485425967, 178995541, 747983475, 488833781, 425258372, 761424968, 993994563, 101118321, 982857177, 260495070, 571049840, 999035629, 140299606, 527275139, 590854643, 316885954, 466666105, 669359699, 232736528, 200285730, 712598384, 391893681, 117822731, 118350410, 555273135, 523242630, 560613728, 354629816, 995504282, 536281979, 558790585, 356409168, 389324678, 98861911, 687959584, 125752269, 179489977, 978043486, 316613292, 190761868, 579993878, 828020830, 461362455, 979982405, 69227367, 167990092, 73475102, 528041232, 706937500, 605379514, 609342595, 628573254, 147407481, 918926476, 206504995, 292799335, 397749211, 932522397, 415290799, 344320191, 285616582, 589783973, 482333309, 893977821, 157411928, 557706598, 776963536, 948875572, 32165988, 918975049, 155462158, 31721938, 156622208, 283361284, 592618339, 544214378, 414678386, 526308370, 675849980, 927276627, 348785046, 56239409, 289762487, 513366216, 956860492, 75976471, 687924987, 868583331, 336073771, 405130608, 468287642, 747863352, 306313703, 894466751, 686906962, 202413488, 541449073, 889805979, 445280208, 138475301, 783518723, 928528633, 150675893, 854152060, 49671387, 545325161, 202503515, 794624349, 122330859, 211449765, 25352155, 799849471, 295425882, 182676306, 248155714, 423165846, 494008014, 640816678, 112148290, 86963247, 431942878, 719351436, 651534360, 189523184, 619038367, 370339257, 597701803, 47291216, 110117788, 930216019, 994755236, 62365285, 834195215, 848238353, 989939945, 74105069, 532477213, 777739249, 721427196, 720876218, 109095062, 993149158, 31089504, 922734947, 34345985, 929948243, 972855983, 443876944, 35923734, 879780320, 585956713, 216415072, 124022053, 434818790, 671343799, 643368957, 803302203, 912459864, 496666770, 954655444, 74026617, 594213031, 328416006, 275969568, 436903562, 458646794, 397914137, 339006984, 872262588, 5568623, 866959845, 461354892, 496730983, 709338388, 293929956, 561739563, 87013544, 541759828, 519043388, 372034476, 189223108, 743125384, 782689791, 965918898, 496681135, 875851810, 178388302, 893905038, 530408461, 746064981, 675734396, 504718027, 979760750, 633892444, 628618440, 488144865, 509323422, 441260241, 139784417, 254876921, 887862325, 920541999, 139703894, 680353547, 730412000, 482536224, 950055096, 384036533, 247117313, 348670650, 516697075, 515099739, 565463981, 598129659, 334355581, 16671940, 784553599, 75517038, 471379938, 673541517, 584184904, 884946697, 959337324, 521984551, 384713506, 166671497, 81564156, 893476417, 406913600, 96687788, 396226244, 938156304, 723324835, 910477005, 806439994, 673643153, 62030498, 751440579, 505594404, 831755882, 641574506, 391786949, 798696024, 932309071, 99475455, 327906913, 303121135, 724855105, 708353622, 700652536, 71144930, 835805933, 797303905, 578443491, 79658818, 458390424, 412991202, 979327215, 108968972, 526334222, 299489184, 247405458, 956336121, 275880937, 98277323, 994366614, 867331830, 969999142, 846321887, 914568362, 695927115, 474535039, 851307805, 531678131, 18418570, 45305049, 12753221, 949438342, 137527488, 77077347, 109908504, 897336417, 208959140, 588615510, 864947008, 989697435, 604876827, 972191949, 353944182, 639626289, 294083029, 54830477, 674725836, 693740472, 253406601, 532692412, 991091529, 174102520, 617224761, 566167446, 289759796, 293957877, 684735615, 964381932, 463367088, 523361906, 56679302, 825215818, 884070354, 836150769, 643099983, 43037052, 411954845, 736040729, 640492534, 36885647, 226774394, 563685133, 283188492, 898275451, 467288719, 954744077, 45135393, 316232998, 156648173, 651564379, 19926440, 473071304, 720436461, 719803245, 643599736, 654953034, 814862487, 685668666, 763378319, 427912631, 584849398, 429825065, 826479288, 764676762, 254944883, 427641332, 83095264, 653215684, 108440844, 888531383, 353681408, 141154047, 820007457, 940041837, 168697259, 543050085, 696418059, 91391283, 273801990, 465186390, 430041080, 811834757, 848949575, 44378095, 345312235, 376201541, 546664621, 994143821, 679655408, 935648650, 252950842, 946362663, 989563613, 557765239, 562199597, 427761244, 86165487, 887818250, 632821972, 49599215, 862905697, 496013029, 785531403, 104197079, 427417728, 127875809, 607471862, 326284373, 477631820, 375263205, 270093068, 197216420, 274219117, 338085705, 605580996, 479030723, 609234963, 825504540, 518293958, 915171876, 917308857, 338991370, 298176599, 388068737, 556249956, 690577888, 816960257, 778166945, 727378607, 249242927, 759959255, 490883544, 66787980, 524382157, 643672041, 17141069, 196314173, 134198429, 619557490, 25792189, 224755735, 181633438, 475801611, 387808896, 798195842, 424023480, 269523046, 737984545, 600253052, 34321165, 138244987, 135986340, 131280979, 608483961, 860464502, 321559656, 661348256, 563577405, 895523556, 264353982, 752581538, 309939057, 447763711, 182200781, 917597315, 385199535, 253554012, 424527273, 71295990, 925823835, 448260748, 988689491, 886866625, 577790037, 82768709, 783291770, 986978624, 653499700, 549986263, 30894301, 595506588, 827929353, 102992704, 971860915, 968709952, 996706521, 369887421, 880117307, 285128036, 270506547, 368050103, 23480181, 577825323, 452160726, 504045782, 812642559, 923096501, 772922675, 450949811, 476961529, 601068893, 14876879, 20074851, 852446841, 397806317, 525313410, 32663510, 118883865, 846884921, 360880997, 652438785, 350015555, 141312941, 60189667, 342026748, 609506437, 413490000, 526136205, 803314956, 578952685, 945793879, 300768454, 566279253, 230685335, 397671248, 60750515, 320046421, 227384545, 54634742, 303757557, 390122990, 149922015, 528957971, 220857648, 560377157, 709668943, 657461611, 580832566, 194131417, 577785277, 996282153, 190062702, 536330884, 370151872, 978444768, 890026225, 162527306, 623302720, 239485674, 814955782, 844376028, 183398240, 591158933, 416210635, 909918213, 625390135, 339878548, 636358361, 138991684, 753496598, 457467971, 860781021, 69339488, 742680768, 115560092, 90516201, 822675011, 546812293, 477937343, 824495151, 348037163, 912528688, 896892775, 791235434, 51007457, 598690869, 737895951, 984937509, 32835749, 507137313, 792717694, 196833390, 575514468, 434798710, 342941400, 28384978, 549110985, 226283797, 81210757, 156229053, 342221981, 464173614, 400784159, 403561363, 173653686, 661121223, 933702764, 406701431, 103362837, 83330449, 636300615, 83570597, 89731708, 438756835, 419346550, 68622498, 508133926, 548902344, 449093120, 810939898, 290142012, 873213256, 581537848, 942765916, 211446611, 460521320, 572188735, 900071815, 531907326, 236212800, 13252663, 629943776, 535827485, 981448913, 492837228, 112960326, 683264438, 607358475, 930091469, 350985280, 448337199, 814895761, 589194115, 178999784, 267942570, 568959536, 451950351, 913651593, 620296641, 788173555, 519497344, 531119498, 299482438, 89259589, 416126381, 37228838, 357183596, 227388653, 951032609, 744842113, 615500660, 724930831, 357681975, 604653494, 650205684, 930713711, 993102190, 72700158, 142564866, 172227453, 867457311, 134186109, 740723130, 862755666, 333663219, 751381879, 162092763, 743427171, 987621838, 588572794, 80181680, 415221332, 290739565, 885080056, 922641739, 453662746, 236503008, 265310005, 215635841, 666612307, 409650042, 393182500, 71020617, 478801496, 74770632, 832182267, 250690157, 72854691, 247871710, 738451787, 935168935, 379554924, 188114187, 415659558, 189800341, 321523921, 56927981, 183353295, 119824598, 524536829, 538746882, 752042405, 216878507, 672144264, 944258471, 640669562, 713089531, 5461245, 723870350, 252525468, 881572946, 478713833, 392764075, 744365118, 324288493, 297255218, 755594979, 811786084, 704888075, 969956919, 583017741, 580722286, 354791269, 717039618, 469597965, 356478461, 376350376, 547188166, 452754295, 673886941, 293433025, 172511523, 982562062, 817636218, 888302105, 588066792, 898848836, 250107847, 220009073, 445727623, 507367481, 544438977, 492361358, 397093723, 873458540, 337128519, 935217743, 775208151, 990190752, 761622899, 7081606, 251897706, 402543488, 958912539, 173789326, 643966468, 746720604, 959675258, 972308316, 727267421, 449738629, 209097667, 938978936, 241480177, 388380605, 423378715, 285740491, 792051408, 656574630, 818187273, 927440732, 2150748, 2468410, 504834582, 337862271, 900321647, 279712986, 868274643, 578999657, 954562687, 821931391, 399003560, 49863770, 946631526, 887068666, 390801364, 281407178, 842199461, 8566044, 689443310, 373279409, 556260193, 826498675, 154239836, 710040590, 667077320, 562186349, 296365885, 896989867, 101201041, 528426346, 227154593, 522924195, 422727131, 450334620, 192216458, 48386488, 992374183, 756825956, 766252029, 314436992, 595636010, 936735385, 60433181, 544952440, 162338270, 895894196, 822617303, 880558314, 330310246, 159813196, 722717181, 822171319, 69130758, 977938591, 442117328, 340215468, 706858390, 434377591, 788717570, 462777784, 915272134, 419047900, 221433392, 827549691, 798952311, 373400583, 169831360, 404609183, 837611654, 867003476, 506789519, 88230646, 464691805, 193308403, 797976553, 743628337, 861373051, 178906848, 365880417, 336841522, 420243323, 205784712, 900657618, 573208147, 88974613, 128625570, 834456685, 907419321, 71637942, 669170391, 646714607, 236169161, 478829653, 927396910, 208827664, 804519325, 498013980, 396490101, 328620857, 936465040, 856523041, 550681625, 216838618, 87501022, 46393530, 314655645, 179523124, 606187469, 949592009, 565004098, 515198295, 827187632, 489830616, 828656057, 982701274, 813822069, 199908200, 482243350, 493932949, 925260757, 271622156, 654171110, 32331073, 502620833, 979083366, 347348977, 82930806, 585109897, 299066766, 546816791, 212330554, 183117480, 91573462, 185831477, 483335628, 627055466, 195326552, 304699274, 452314690, 214616700, 949946869, 49764553, 715623383, 611740519, 281518875, 117871791, 295972531, 19880910, 444923079, 525489716, 303914020, 185480482, 570764374, 173144740, 688290665, 159223619, 605204804, 270425792, 853118160, 982588529, 434944064, 607106349, 879612511, 60059051, 624165170, 757122720, 660281615, 47893853, 289177237, 417194221, 873824647, 116617826, 474337881, 759502121, 813261725, 256879203, 249440718, 736288523, 137315680, 693860659, 108928413, 591369854, 978394523, 652213491, 333793563, 860267825, 794551731, 663449071, 244921126, 576098398, 222856621, 600610502, 516595860, 711249292, 900761769, 182968346, 176164284, 122329860, 665580477, 456486550, 744779587, 458353638, 820977233, 925167155, 753501620, 760623333, 387081840, 874729582, 685676437, 691173058, 31788677, 423456378, 557597791, 436626816, 436439357, 219064655, 754550357, 139930791, 569200776, 975065061, 657074805, 404539013, 25659306, 63170668, 553990130, 983026961, 857113961, 996220313, 667541921, 526241986, 37212399, 506434555, 780571821, 899233265, 794774536, 916850899, 120629121, 3918519, 188569776, 482091831, 727835751, 556619499, 799768522, 106854929, 562289834, 259967643, 477121708, 798075269, 656036929, 936487386, 758293744, 747325322, 62159563, 207988674, 84066929, 312947561, 505669068, 920531879, 617465434, 753621490, 627191065, 363509386, 532796313, 783568361, 680690082, 699292350, 764181770, 249523816, 141038192, 542141216, 674034862, 722407874, 365922428, 857496007, 438998583, 29989051, 874798290, 384085599, 539003807, 411278740, 66137631, 795603081, 248433617, 495412454, 930334215, 205085228, 374771655, 576653242, 792267941, 954297211, 843219508, 14191363, 504729123, 383553860, 899284394, 268441663, 665110442, 985296885, 281049247, 265622572, 662918363, 811751619, 739074938, 482545610, 764042086, 452016815, 579780517, 263248638, 497813570, 823032249, 145694230, 12622784, 583331164, 723607602, 863909995, 118428370, 154884637, 474565849, 970484486, 75394507, 816573197, 489300713, 173770533, 347391197, 597852352, 720552421, 462723176, 943372012, 98509568, 90552689, 408008179, 15363463, 741431093, 266206886, 763829841, 624882327, 458419120, 962589479, 313115258, 419842376, 898550163, 749956728, 304737044, 731623758, 303028863, 977902335, 725819572, 133812473, 804652526, 839420416, 299429451, 950528785, 900389547, 782924137, 616223123, 149926065, 922102802, 419117492, 304976364, 889003497, 868533889, 228950208, 343773034, 635738701, 754544839, 392617707, 148700252, 172881728, 573428990, 965144980, 662513728, 402057846, 741687394, 865346675, 477220042, 269501290, 127115265, 986979644, 667929936, 187133277, 250073873, 666229928, 749266333, 162407569, 961921709, 23662352, 550613003, 985131269, 459069032, 308045078, 120609898, 699527838, 574505241, 305877156, 654134709, 963561326, 151241619, 110035105, 7120634, 836253956, 836255633, 201696756, 386995196, 718888495, 896714865, 667007639, 238333542, 220812952, 165596690, 133996392, 234268193, 154592229, 592339530, 504152382, 73872470, 984770548, 495063688, 503531133, 110409021, 32067179, 493849273, 497498745, 200821285, 16542452, 777425224, 247083076, 682331944, 644736114, 896773064, 101947913, 258056072, 748106973, 211224880, 557454424, 226727579, 183687338, 628166502, 988119393, 512812941, 735327321, 389116040, 747832681, 307809326, 387732865, 731613288, 712548125, 981937672, 630143015, 811133314, 707563325, 284887926, 124725982, 938636946, 344735497, 106125092, 216904408, 489663520, 559947900, 8566686, 587989894, 949446897, 175140, 629717707, 769263692, 942352497, 312692631, 229723048, 718097026, 8376903, 351995801, 43145342, 326799063, 318928282, 124538205, 471547422, 567133660, 789488652, 202239736, 651548949, 632524130, 145293747, 325263787, 896247562, 90574487, 996519077, 765183105, 771791820, 737344916, 786883315, 294196512, 862084993, 844534079, 58478123, 97939360, 358350086, 267765936, 547918622, 401986854, 925493252, 741125634, 600534436, 539652722, 660726632, 197991918, 715337900, 125502853, 803628521, 432558726, 652391625, 102766111, 893298499, 651640120, 633131919, 777024818, 781405772, 599916022, 279556661, 594359094, 581138111, 3269085, 258602085, 11541743, 897591344, 399901042, 335283716, 808668476, 301748708, 577143536, 897745165, 766595836, 926142584, 673885285, 852335314, 997531517, 929292630, 838200323, 566380831, 2243243, 317261279, 896105077, 572967158, 322120005, 687496055, 859033373, 586931074, 935629418, 889889446, 738609336, 495817881, 965178873, 556698860, 397226926, 14469334, 506193044, 356735503, 16984003, 333677565, 944013609, 967782167, 817320142, 136097594, 176299847, 564067534, 258552350, 492807656, 193505206, 524723998, 645720274, 110583328, 378012440, 965289883, 73204797, 929250352, 606381357, 994547522, 456954775, 583758154, 387342530, 933941104, 651801211, 611138353, 734970898, 442304533, 103359560, 36188793, 471773314, 668121012, 388329053, 523582925, 149185953, 532663369, 613568404, 129850708, 197061554, 322037979, 567289078, 102458860, 908696251, 319996987, 395364542, 324881997, 166975884, 492124956, 429130114, 836451819, 266218307, 28654922, 28597480, 418157919, 520944898, 757060140, 386938292, 38454595, 93193327, 125428016, 556995069, 49371939, 673960757, 138386693, 962011400, 404406647, 7444608, 701043419, 200403401, 725709057, 745404031, 150464118, 949560189, 81912724, 43853026, 473562953, 768225243, 182186680, 562988320, 554871387, 94498246, 494861089, 55550661, 277253299, 129305025, 72137424, 202758153, 970452169, 683254009, 692698757, 931100153, 11346702, 244878259, 595929976, 406001067, 546169513, 890821832, 105613970, 619886329, 661021093, 788620863, 640366677, 580304622, 795853385, 808783554, 797658220, 731518457, 247202584, 221687131, 575757716, 834274581, 394783482, 177576669, 205829808, 414053222, 49289094, 936063681, 28134571, 655712761, 472956255, 253540280, 311183781, 852019248, 659770669, 280057757, 521001232, 886557973, 811806837, 810461343, 371236913, 640056033, 117222640, 567970092, 176669409, 827830266, 551972347, 568573570, 573605111, 852988810, 412726228, 21619896, 631520761, 353828511, 148794137, 372381342, 988740092, 575537120, 736634544, 11432270, 593079230, 933675685, 783748502, 737340676, 219594527, 735131385, 418649663, 539016957, 862603331, 382142067, 906594808, 587382771, 570188779, 144408428, 127102218, 24609379, 460615835, 479768376, 999296131, 111250625, 482440622, 197668273, 877257241, 473737445, 381285061, 140338631, 24980115, 102510505, 874576399, 709200525, 759749269, 563196931, 105755757, 953715533, 161370761, 294967358, 682878303, 175916899, 169862253, 372883938, 694769577, 852901601, 321656398, 39127653, 548873884, 959437146, 336772658, 586932984, 702457111, 545178792, 627268329, 543530326, 105906593, 482865953, 28197885, 655026230, 758568168, 462985148, 991926450, 769842931, 515274681, 980171793, 717370994, 442002823, 133228807, 216114565, 755976932, 560938586, 10592835, 329675745, 413959829, 644914172, 775057625, 656020182, 680943633, 496688295, 786196254, 16986549, 952143686, 114553875, 88186603, 997613728, 73422663, 324377248, 292988269, 395950237, 687389738, 675446895, 677998015, 437141462, 659041587, 715581788, 399864712, 854167513, 793210635, 633176702, 901220900, 427175822, 874746553, 166269703, 199508010, 38208694, 131457604, 234167359, 912581385, 252568161, 711932462, 671607202, 7355662, 578056604, 357630350, 514946820, 768489565, 218608784, 619315901, 46051013, 742822326, 793617474, 418867046, 569584778, 72550436, 914288735, 757935749, 344354833, 359727165, 614207972, 924864892, 785303731, 332731099, 746960396, 746849196, 761450596, 662099947, 681415526, 975187759, 244188464, 834390349, 86190143, 331758546, 344151536, 517379628, 421929008, 525237797, 351741140, 29360660, 219674586, 444766678, 729106278, 956081659, 385832014, 649295725, 440661583, 66749125, 733498994, 107850857, 648641849, 863927208, 471404273, 763527056, 639422515, 58487521, 648096257, 342298921, 775097889, 446079442, 569241968, 476540513, 911003787, 952195997, 37274774, 518655652, 478316640, 91090155, 936266937, 375458832, 716285674, 135230885, 219732452, 310586302, 396919133, 504044210, 256428754, 638037115, 14271780, 894130980, 402149569, 106392973, 603860321, 141900632, 898322281, 441655946, 100975696, 261257073, 774976375, 315585925, 364682808, 822789892, 657976541, 83831711, 455054716, 495323642, 260202935, 139884222, 150620012, 317569763, 256402591, 551506757, 180913027, 275828266, 178178997, 677706642, 818071803, 415128272, 822408620, 829546467, 980722664, 370650312, 582405327, 725991136, 703168554, 243128163, 490361694, 485986042, 212673677, 225364576, 970092615, 738360389, 340747604, 724759722, 540832013, 105805871, 65635476, 696839166, 848560210, 63951241, 630515173, 895044365, 358021451, 678511428, 376066869, 430422809, 790694269, 847420376, 917789459, 523683830, 709758581, 917698439, 624552340, 482762473, 960576947, 333204132, 81635582, 94378975, 930971301, 168311553, 187473824, 200437669, 839241235, 119613439, 254313437, 461910137, 229437209, 933292631, 716136338, 345831873, 816310182, 685163908, 35247022, 798831409, 344711088, 617295191, 681947666, 211013412, 297152690, 148675160, 588010922, 90939012, 874980627, 264409952, 608432649, 179781935, 116658637, 552028019, 458766149, 901128080, 850963021, 169466150, 776106695, 154037774, 252923172, 709378700, 548670744, 569159030, 343813443, 40388570, 741022951, 239154205, 313283764, 559145167, 553460865, 655369453, 997073810, 966393053, 171669470, 66801959, 450084780, 593175451, 438982798, 871296910, 262463742, 100529383, 585092450, 440928901, 920874386, 38790584, 392932152, 499238781, 550530443, 924079724, 337912229, 304872187, 393010469, 864051705, 731991552, 622596182, 794479948, 975632718, 123923811, 84150951, 30893606, 975119530, 998795314, 105672836, 616111275, 324147156, 636222433, 265414061, 80818897, 842292436, 38775375, 685015210, 793104594, 720835671, 256117567, 770961096, 83716131, 152040473, 131135822, 761566993, 814475099, 105104274, 541849283, 943591664, 654043357, 913500134, 447986980, 811868646, 713759451, 116085564, 554739223, 558759653, 439740560, 778177939, 829652321, 306417542, 280203088, 481256002, 367568600, 446629111, 949510972, 348496929, 251906777, 505130152, 15560243, 35425136, 240570904, 740080244, 311909427, 538763003, 822244784, 494901339, 95583442, 287112237, 966077591, 654304220, 620118304, 73067545, 625417580, 457872217, 740187195, 514199334, 419195729, 662872071, 897442542, 761824313, 602438906, 125327880, 272549360, 509941609, 590865896, 755849355, 584013490, 548995455, 109133425, 375213858, 602744769, 941748392, 957786259, 145185122, 553416698, 210152886, 164208319, 516143415, 867689174, 208555599, 219493662, 462407809, 437599593, 816824335, 790053536, 535505224, 613744441, 770139022, 328002324, 550823398, 78907118, 974901700, 114198326, 824486198, 711104911, 925860330, 653522158, 978820978, 271791709, 394678034, 442048100, 57041014, 360602449, 341929704, 335982180, 115864621, 830870587, 338625011, 666669391, 341063876, 136592259, 681457719, 330769648, 476552340, 765827748, 119421427, 6388074, 992732545, 769717031, 436703530, 460561993, 414267794, 739492166, 858150454, 203866039, 953219975, 217060136, 265491316, 170908133, 929496115, 54832936, 285374789, 243917794, 816162801, 749910482, 724414495, 581233587, 588135995, 864923438, 218964856, 563577167, 583925642, 28657294, 319647450, 218108920, 782277167, 133220068, 428901450, 670936110, 496297632, 97245768, 353890762, 711225412, 981751294, 980309308, 468752705, 190184392, 759299706, 128912774, 905900129, 978251193, 868047334, 719336220, 103648446, 926378669, 472151655, 262353861, 414806718, 376346423, 651644345, 451487665, 674200600, 79156394, 58192955, 10098118, 437060666, 547506780, 892888644, 486696138, 341494971, 90651670, 536451781, 734286984, 756787227, 919136621, 918448302, 881177347, 813775640, 580605577, 483055217, 793302907, 550556524, 210235610, 743225869, 226012221, 27549473, 115145729, 361947828, 265084709, 160853817, 346841521, 602471260, 788012452, 229641499, 788598907, 411472093, 283900514, 221298895, 813121583, 989603, 137883788, 6709211, 257583962, 719262895, 898693940, 744685537, 825588266, 661749241, 316521839, 980676040, 611020332, 594776538, 40197885, 492614346, 987827478, 815787905, 226123273, 261115622, 308700802, 671108614, 391098262, 665197379, 293375706, 756564149, 882860356, 941628426, 724944070, 340353011, 161697560, 498145631, 115628171, 589071429, 713225461, 134687489, 43912319, 801845497, 28769737, 942188503, 238162247, 218656700, 279958498, 43305779, 202387048, 169779437, 145304880, 928403567, 275221258, 82703947, 159924111, 981414063, 850528820, 73052868, 238690693, 693685636, 274784393, 236932087, 121300053, 874486598, 236844142, 154869040, 544429562, 817028266, 568834891, 373123276, 950574056, 170342598, 947468181, 236866770, 162337983, 409255485, 447655402, 29590740, 575002502, 391027113, 936248057, 714406061, 160412537, 964050575, 861770452, 251056132, 45370220, 123793055, 162955480, 495415694, 757304921, 49065590, 571822835, 868101110, 906101454, 753957927, 529649009, 456885999, 892946230, 408180746, 38830349, 506607047, 713221673, 397652388, 268753813, 786082779, 109754911, 828441618, 648011665, 58606968, 527032985, 731412673, 726249240, 978504632, 27864750, 235166795, 624804113, 221297422, 478202211, 286236931, 302304479, 468418346, 564142646, 103183422, 164397106, 154964239, 431742760, 614558967, 520193277, 776728842, 657172878, 831505423, 418263522, 723315579, 372178380, 851663973, 67515178, 722339274, 309837096, 616367930, 665118134, 185118928, 372004907, 748645287, 488269641, 677265940, 26148260, 250719080, 444201799, 852439864, 713818257, 212167247, 295909973, 178392423, 745297195, 302362375, 833985453, 599720238, 267368353, 347410023, 563571446, 481870668, 30910115, 226738197, 935868695, 189515626, 847217776, 625598451, 908547065, 4416791, 868809945, 700959962, 17905997, 360060055, 525781992, 567535123, 629669083, 471246742, 339207706, 12282117, 789537708, 415711784, 906222641, 866588722, 62562538, 958940564, 750039589, 545611340, 968048587, 37506190, 892988623, 827036892, 611617492, 198996890, 16106355, 305980009, 853129943, 587430322, 411437400, 722667563, 926403424, 525120620, 454330422, 963375896, 278686296, 58359698, 385339337, 96238361, 937500718, 387583833, 47383713, 914797457, 602251815, 636165096, 251792704, 476239741, 977951445, 300455186, 826706102, 755192763, 409544833, 236824422, 162030097, 694259917, 845333620, 332327599, 849395286, 275485724, 218560689, 446174662, 460215276, 377743485, 56957207, 43216789, 65445624, 178209338, 662880368, 250581557, 854053161, 619731888, 517109573, 363203242, 757265852, 202860842, 725155815, 582464635, 6979989, 66770370, 803184057, 386488348, 586854804, 552272269, 513359286, 858253207, 781144399, 510789402, 526664832, 728251197, 485843078, 381434367, 549622457, 829053518, 801058328, 671199019, 739061037, 927720597, 465322312, 28802226, 484503370, 650504283, 734881531, 935190564, 799791116, 161530414, 114161867, 85532429, 97841121, 604737309, 486497061, 506893566, 286891614, 310332064, 815968871, 888565874, 705733613, 430456407, 396111622, 9035090, 621725541, 364474602, 258782719, 47074588, 499746220, 530536215, 131868157, 445188200, 799420348, 351427437, 927442393, 371963264, 969141327, 918766230, 273687264, 962963049, 223856765, 232796118, 599271429, 931294868, 545669291, 24638253, 107399944, 112642947, 362807506, 546830937, 596219881, 739310450, 41451484, 406106390, 631361680, 278286725, 223718840, 759807438, 244429217, 768998789, 557400199, 760687283, 443778306, 342142809, 777031927, 812968420, 563566654, 803997350, 348519397, 745073429, 188259635, 387281002, 766695567, 129202466, 804527315, 92451314, 838735709, 563446027, 934551147, 177274766, 557970582, 703276516, 458460595, 537424309, 937201923, 567015752, 176884275, 595853198, 58434347, 588491264, 740497092, 55943088, 8217371, 661500828, 361354990, 630501247, 266990101, 335357216, 394448719, 825412557, 278107741, 999645716, 1480794, 467508701, 948111993, 292752648, 237048798, 90171599, 925410239, 304826316, 575400960, 251048162, 942455432, 950661591, 902150760, 48696770, 424739996, 764000495, 702045382, 303584960, 730268708, 268186124, 995592141, 932979253, 918394555, 629955481, 330566281, 177291271, 978099264, 856690391, 886706081, 763906651, 444325011, 626018181, 936316153, 284362616, 406826516, 649350185, 512544742, 15052238, 773751981, 671014501, 179039491, 583074412, 169294104, 971228622, 27128642, 531491949, 637185539, 47217541, 792549782, 415061820, 151675921, 347109496, 192592715, 721479741, 509118554, 501652534, 940744672, 721392325, 801702181, 290245597, 455636771, 215001571, 955095429, 224875381, 92455356, 872328693, 856232002, 790334210, 227967176, 891012362, 444240006, 237223501, 370638583, 227678560, 213557077, 600029388, 649083866, 255635686, 634263429, 992072233, 109218428, 77879266, 584529985, 935677380, 224417920, 773585558, 431337432, 32304647, 512747829, 82726355, 729645374, 748234906, 802682254, 914616847, 540554479, 521675597, 708158854, 663483115, 876292573, 485397289, 289094233, 992880596, 591118032, 832512753, 29386565, 941689562, 240574460, 951980397, 600912265, 476741600, 829005669, 856967118, 731432702, 400500264, 774795749, 946905300, 102221851, 948637966, 302485849, 372400492, 477972823, 608399837, 432751532, 448283779, 760134163, 625705422, 408514401, 851842610, 249583322, 225441274, 781641365, 804645745, 413226052, 716315651, 672760073, 632079962, 858800650, 969076563, 876808355, 913068730, 66812929, 325159857, 218422460, 258037910, 494387794, 12801880, 431952741, 423288677, 968692353, 598972604, 421593353, 680951090, 807228148, 61188312, 634399163, 890631469, 565719491, 408834115, 692493011, 355807230, 444340122, 752253443, 345373697, 847947857, 701354579, 442959251, 361940050, 61914982, 825324475, 540090707, 928178354, 677537896, 89787453, 910177086, 890985219, 968812357, 349772345, 434693640, 162594036, 671480453, 376470341, 31480700, 193032395, 48961338, 562461387, 915757862, 616406898, 520718930, 983835894, 463332312, 190795584, 60297314, 777550190, 433032127, 624216152, 715221577, 58051862, 830935225, 969779224, 936908529, 237609092, 360832523, 256452070, 943210036, 449666262, 774304560, 808743112, 349341080, 705244378, 865835367, 891987790, 382722587, 15031852, 690928071, 921511920, 705812419, 95245690, 464384682, 560525982, 150626842, 353224970, 693436272, 504316815, 793999736, 681471052, 939473671, 49498991, 730066656, 595451217, 996281959, 660987285, 896450102, 476284111, 717975711, 812851454, 74371084, 529717015, 101933269, 68177826, 300972820, 467133913, 879169347, 374713229, 483154886, 516723646, 353248707, 513997471, 395093147, 364952099, 482469514, 981067360, 594483948, 362144110, 475442192, 521337847, 737728172, 566750436, 595334633, 78328701, 45866286, 233948550, 426522066, 704040399, 871910803, 43383637, 514072745, 290464967, 924786922, 548157185, 498126991, 758749430, 28253055, 819147359, 15633161, 919021489, 214493130, 373352644, 418773347, 969105533, 20899126, 719987674, 211036055, 460539607, 818063859, 759327702, 534752604, 794170133, 707050975, 756953624, 549516705, 317838442, 3968397, 951834409, 990551404, 452900713, 104652614, 76196276, 951329132, 219073689, 967024312, 833806778, 692732224, 950393979, 911741748, 575044238, 484165621, 4265464, 243929753, 258779201, 711655285, 149746934, 88453871, 51401379, 616989680, 9547002, 956660508, 886834070, 662892187, 301256227, 401173340, 404057828, 573267322, 436239916, 487988692, 907790144, 715817137, 630355344, 755885608, 916955895, 37882715, 445440186, 336854136, 461032578, 954958582, 857630659, 763915841, 529752523, 756421967, 890354521, 547432338, 589771094, 878429854, 729605995, 595311552, 252001076, 652342680, 936000727, 716115563, 962907309, 94148859, 762758430, 191774254, 812981340, 524634944, 677567681, 920541404, 744981119, 148195658, 513181865, 242413379, 621874039, 224768569, 227839426, 318586628, 503623027, 518185584, 284677634, 135568650, 774275980, 713652754, 188256386, 475481350, 421904380, 858686350, 531328121, 936211896, 466020653, 686928859, 287191560, 139651419, 974305841, 177302426, 660054067, 958535168, 968148540, 448240863, 180507488, 643588895, 636785167, 345581932, 974425280, 608440611, 911376727, 240267473, 671702717, 581517263, 686661331, 771470633, 168563971, 442890999, 938352175, 624267566, 211645783, 511126834, 44650880, 196959957, 419219894, 160342454, 111700427, 798066505, 221182871, 769909451, 688363616, 565634122, 627252503, 509287590, 412259553, 400704715, 22575386, 464957921, 534251439, 597448590, 723447228, 200919730, 639016510, 346125094, 695567075, 208276744, 763415862, 42159815, 880906515, 706722921, 429801071, 409519800, 163508984, 334190030, 557466226, 552457059, 504808941, 984841465, 966326511, 376738187, 589663651, 323670585, 485262093, 413731109, 548501560, 484621474, 308353007, 149409670, 19336989, 123228943, 740257823, 679562267, 380417212, 626470058, 975492694, 31061513, 262306512, 190249807, 237461872, 646903426, 360499866, 607349647, 984589742, 620314322, 78512167, 448325199, 930345985, 615214164, 64993740, 633672185, 566648487, 410940567, 232940868, 344443762, 19106219, 270321506, 345258369, 523320277, 970269284, 706128760, 40827931, 478150760, 250267767, 271710875, 333735446, 964568083, 253397703, 143805939, 240715918, 233996423, 525456191, 959114026, 117870527, 890962057, 753989949, 202145466, 237532303, 144698602, 890871058, 712308699, 252913313, 855404445, 770678263, 410344059, 871376285, 543550208, 754764991, 32044699, 116206623, 370646017, 377460953, 803739843, 4682035, 628157619, 732143885, 3381442, 992844973, 847432170, 239613786, 781160520, 819239023, 56690617, 993936901, 352355864, 192396988, 78114613, 181608927, 715651823, 532125336, 344117872, 669732691, 77402466, 952502024, 695016815, 583352105, 912322178, 817667730, 786717951, 407584785, 363288226, 869320167, 172705174, 996667480, 309563102, 232855632, 187647755, 602799721, 127904209, 993306975, 402262110, 987347312, 713468833, 420367556, 370530882, 725074792, 61287878, 349096980, 579949959, 24292385, 25169561, 582707661, 772107980, 933710125, 287673391, 532136496, 67021509, 439636607, 741022459, 675596073, 124167973, 415287220, 263795993, 602664116, 988033288, 243331315, 290283168, 718898864, 476877244, 982543111, 256170010, 848350678, 467341768, 734452974, 841585320, 469325011, 130756031, 19706390, 904291895, 358848105, 321585511, 553368087, 558244186, 413779183, 930789677, 173643799, 415724396, 621852616, 298613817, 278042166, 255824527, 317153099, 602125322, 861934781, 866813016, 826737698, 228687705, 345052583, 302276922, 170231405, 717011147, 598353081, 783236461, 467556091, 127647163, 386670902, 648975995, 335066100, 148311151, 893982919, 909498909, 703196015, 608159784, 580722521, 807058636, 668456521, 481176648, 196639986, 558034839, 265409923, 102181656, 620602848, 142324491, 194081088, 719918148, 24084863, 54860228, 955605948, 415914491, 926096448, 156404858, 723423851, 851487836, 825033296, 351002467, 404735453, 156355185, 954759335, 174496758, 255835923, 117050390, 316662345, 83673529, 231982975, 794029457, 560394172, 532961380, 63430085, 399477641, 395781602, 946666464, 924401477, 100507033, 732763046, 451877245, 668574991, 235773981, 733816168, 1675442, 907352981, 397476349, 904092236, 106863606, 299766114, 799813301, 234371833, 576712404, 926416770, 650308397, 528573227, 482156975, 605906484, 842308690, 690781728, 348517415, 40498914, 508071806, 298374999, 520556953, 301153586, 487989321, 709272225, 230164740, 314655141, 997561623, 311908633, 822970290, 165816439, 455179906, 127828234, 782820112, 455480924, 893390476, 267780873, 88703330, 674797408, 391842828, 315521581, 659824807, 678175837, 464519838, 131624859, 358423912, 689680775, 946454760, 438081974, 439641635, 577386034, 877701560, 223242109, 736525652, 157439, 700800072, 670443720, 514123995, 570458388, 122708032, 797280411, 54271213, 274414218, 176454815, 766191496, 662828740, 447340879, 781936216, 883834661, 990896920, 215397781, 88574472, 300919126, 115938135, 341487334, 146651865, 142791956, 839546766, 87028053, 493566695, 800995065, 312946054, 229785267, 543377757, 684669851, 106435231, 719408867, 261858356, 334986818, 566819683, 709070369, 209652853, 253055881, 949398814, 450034264, 563828634, 517781300, 523539276, 584009346, 974670411, 960875319, 842002822, 926598632, 498708471, 985580768, 79792388, 614090348, 645056441, 387358396, 919011919, 950285922, 946451980, 354571524, 258247690, 462889054, 636602285, 347069200, 470526862, 948418030, 536477397, 839046943, 892540409, 193970535, 228829789, 771361651, 372927120, 530474144, 819617365, 427387879, 293414917, 695441479, 605161847, 902397822, 414325777, 995076347, 335633874, 13348457, 942203143, 964640106, 30271291, 170066127, 38724881, 994802010, 56165384, 376901849, 169971451, 540685410, 59002952, 460049249, 934076431, 85298051, 215014878, 809446847, 835263994, 925493728, 812019729, 543479954, 191039803, 897287170, 125679581, 182054799, 926416132, 763684638, 387688442, 584618412, 288109772, 308959937, 197428243, 717680286, 998848511, 698142230, 124035960, 862351917, 447599166, 921344112, 917927850, 841829885, 212999445, 841877475, 641302095, 141480191, 423021695, 272802696, 588443886, 292549739, 356348433, 72739624, 109149507, 830024012, 74296534, 190281803, 850884296, 822864789, 339219074, 315402147, 187390707, 89575702, 744440446, 954354621, 950659563, 718248431, 821777882, 696082910, 5076053, 371447895, 655240300, 468010536, 188196609, 755849468, 894910722, 311943311, 671090128, 171562424, 540938766, 930627612, 359513687, 63706487, 629356554, 411082514, 772266656, 766778185, 422708691, 418591032, 71793865, 365192089, 773785965, 32739148, 24791128, 23275880, 976752263, 167289511, 339642712, 842885630, 889416748, 125736418, 968764074, 707994075, 321160912, 659001996, 297118170, 260848204, 941463939, 17288686, 918323292, 51045052, 819075501, 322849223, 200101422, 370371893, 178091639, 725525792, 683750347, 651278927, 834700400, 864650844, 197484436, 653208176, 233876457, 133557584, 406636773, 655329052, 372356900, 512129107, 918530707, 816965063, 321881186, 852728932, 696175963, 919443919, 896866131, 210482089, 270816373, 223694819, 883255471, 706567496, 888638314, 752636537, 226740036, 381745339, 750645224, 243788648, 191396963, 455834830, 832881439, 12316396, 418592649, 342084133, 19657330, 102706988, 40895738, 606364767, 371950617, 165283642, 520171751, 234760468, 268221532, 414503178, 819743603, 568689267, 626354639, 818116829, 912484473, 601072011, 984979142, 621452268, 560758771, 66789748, 377624036, 342804822, 25007382, 728429895, 664903069, 833699057, 615287153, 329362403, 771085164, 19700669, 891546143, 813499724, 980358915, 103269452, 967792136, 299846844, 507492807, 410188263, 241696126, 556007458, 283878687, 182976363, 211256638, 320191295, 806546050, 792427314, 597937081, 578616620, 771865277, 851490052, 959740442, 983866758, 748049652, 718895795, 250546122, 785570295, 132782506, 356294352, 456614591, 809691964, 933783721, 146851424, 232028016, 699793958, 442340180, 826066433, 266607032, 703846838, 606131914, 394358999, 677589293, 980693619, 553656205, 606433820, 504508177, 361187855, 747893591, 388169780, 113367586, 397252430, 869499321, 393585056, 347345605, 859270156, 590132186, 379413509, 618360288, 670444159, 586055606, 756979850, 607331331, 94488364, 94989906, 174007718, 987651967, 654085672, 753182524, 87441438, 524737670, 143249211, 65291955, 865253605, 760069152, 549711117, 301841704, 826899460, 397630384, 662230779, 359635035, 512766000, 878089062, 540232103, 763740029, 228708044, 721520885, 935178196, 551161743, 125976668, 472763540, 404934600, 501260861, 797120127, 408515714, 427154219, 480930978, 911134825, 580030450, 643393581, 255807617, 836220724, 886628469, 769365646, 962786390, 423667787, 489311032, 703836040, 255633157, 666585387, 9374831, 632827274, 338514983, 765248077, 235981780, 457234253, 693331216, 194459184, 746325660, 515758523, 122707236, 227288092, 974503643, 750952524, 207250719, 322272446, 486591551, 519524124, 780218842, 69690574, 135761401, 441567910, 351449835, 983837302, 531908582, 325169422, 427738179, 453805391, 553309631, 652079520, 166951243, 662589494, 349685545, 718122103, 728245814, 855477501, 130819594, 557134029, 33933770, 938168459, 829226971, 86584268, 451025167, 456704743, 573875490, 824246095, 916998301, 923251010, 134459946, 521771658, 108925578, 738122961, 407297908, 546315078, 597460276, 468987623, 862503371, 980171453, 256245678, 943264659, 439133864, 158575923, 232369052, 920586651, 632718116, 691208199, 242190136, 196818405, 24944756, 811366433, 654116065, 578731316, 708049144, 510135198, 819299726, 166271852, 193400718, 3374491, 329847504, 179460191, 805048182, 734825361, 606756609, 910516949, 29573288, 226380030, 655787472, 821732267, 633222108, 705272660, 945566783, 403257175, 820373461, 536408346, 668848260, 366611919, 722605207, 167378944, 743967190, 353959819, 391238841, 756260129, 789800017, 279259766, 877150398, 873284823, 610912337, 737126350, 950245335, 286022725, 62035885, 550097046, 743519456, 405352637, 417125918, 110423682, 169906139, 410528305, 965349091, 43666199, 879012966, 553200446, 397771101, 831677560, 996705899, 85775751, 341341132, 368832426, 931885711, 881090857, 102898258, 410597709, 922431177, 551292409, 975784010, 64395778, 318490709, 934319052, 712053489, 311988917, 808863261, 799623294, 518251203, 820129187, 424712489, 966723820, 822759496, 344927041, 713905569, 669114087, 712031914, 463088477, 111725858, 722721946, 130392211, 389573592, 832411001, 865888646, 940808714, 526880664, 9647730, 117805038, 206930284, 145526341, 541175465, 442646239, 590069600, 674238799, 825530768, 149134760, 461038437, 544289659, 95075909, 120424377, 38772396, 838432928, 789190143, 426074974, 61711711, 874015810, 245864862, 286083057, 685407533, 418292143, 736170200, 459568516, 749116646, 666245723, 358492692, 117531243, 485753275, 396663879, 461329475, 699295687, 684193501, 956717615, 1326917, 347941539, 234445377, 538210679, 540282473, 273518140, 160750980, 668031840, 932309243, 575978676, 574428525, 418401460, 433688659, 707358781, 973942062, 331653959, 482903931, 551132453, 882380055, 629414708, 706028763, 592942618, 345057620, 858720518, 895322421, 200535496, 373842069, 118187318, 985207219, 92568462, 830256420, 60077211, 106535437, 12496180, 731047868, 22409132, 777681957, 355071613, 867058146, 758834692, 875224834, 623840079, 305190358, 361501001, 298526032, 822917260, 992289222, 985102526, 202923532, 951444943, 359886984, 612755604, 750806613, 15889401, 759043500, 978553016, 576552668, 877497219, 464168814, 788784338, 582851702, 297485484, 947959474, 18313172, 873438247, 152025804, 212227440, 184144473, 453749980, 752515987, 772224472, 479548937, 948996158, 914344924, 35468813, 735519988, 9292128, 981905689, 843681036, 612622742, 11339262, 568912513, 584874290, 67831520, 938680317, 247613643, 36438936, 579781766, 48901301, 759712020, 417753015, 582455742, 478489248, 669979654, 479755854, 387803991, 976966355, 721786358, 709009066, 309506816, 358697650, 384554837, 646201519, 359166219, 407715832, 564444154, 382924164, 232123169, 5555336, 361819335, 90095281, 812832555, 345170832, 889072690, 790619510, 461422491, 238375892, 749085794, 429400368, 810853598, 590973120, 227362162, 300022541, 85673390, 892282096, 409351026, 401408141, 185398696, 808766753, 824621943, 377063803, 884088913, 99033983, 376372432, 584275556, 482766028, 608337578, 752861896, 327230923, 427558125, 175282379, 550545581, 833074915, 174893393, 341351214, 852773915, 165072045, 543879858, 758382645, 565294480, 361449896, 944984010, 872206677, 139400045, 966432305, 719051274, 989508317, 81445778, 364385133, 198237824, 879568982, 99759754, 508116752, 502902223, 67625983, 307843017, 420625888, 311744118, 817937816, 527967179, 919265370, 377636671, 911737817, 931675642, 521465128, 624274094, 561904195, 218624189, 578635188, 798062593, 982899128, 794145961, 103090215, 500444808, 491316065, 75959320, 936894376, 721413781, 388989268, 452414488, 703851948, 77279640, 285174576, 419294711, 61946296, 329174313, 942625312, 373453568, 200479649, 859078461, 707831826, 964120152, 322964749, 39026139, 568132723, 21920827, 673055553, 418265513, 211748469, 907883837, 510693450, 751585624, 104875594, 40071539, 767807158, 530982435, 196827994, 546336991, 263328755, 544468871, 812977878, 223031657, 138563920, 180602492, 467178674, 196784536, 209081451, 694379058, 980108137, 463254999, 874062064, 962266407, 2128521, 454739501, 49805792, 329412368, 745587844, 377908587, 165554105, 493011586, 927619336, 543138890, 45034094, 712168436, 13544150, 576580750, 790472502, 548443011, 766652153, 292430602, 956162454, 891493132, 705134763, 445647308, 848961799, 130188409, 516792809, 300688368, 453580760, 187607578, 445402223, 210377220, 164005310, 789637386, 861353398, 137506379, 74634312, 373336262, 504434591, 454593666, 798650872, 949401974, 65659144, 154636830, 692863549, 639190105, 386991502, 482050151, 867297778, 878462729, 476559879, 787494944, 453657001, 876003771, 87953959, 247085762, 477966686, 328391587, 702988112, 824585844, 54661627, 583605635, 597871742, 803084174, 567179868, 198349934, 944835726, 50622695, 120131477, 179803770, 170400032, 448663794, 785507629, 848753712, 610925410, 771433092, 685526945, 342929816, 188543874, 730520967, 943026385, 311208689, 534816733, 366574390, 948737745, 745476088, 11123090, 368741016, 389626733, 295207466, 344237580, 974926772, 792503950, 313830796, 600363210, 820729830, 352101119, 259720525, 569769471, 962576766, 28178787, 369653001, 620958044, 617613488, 136752804, 141836797, 637133661, 862624177, 534930346, 122482269, 491414225, 557368412, 688214004, 391882049, 840364758, 29288704, 97532379, 513954984, 955417963, 35091212, 875337420, 429680604, 14617161, 348627098, 372787583, 529088363, 537833513, 965418650, 227711567, 288419072, 471568690, 551097205, 916852087, 817634269, 250259136, 325553770, 161156239, 612429450, 201494558, 943471523, 93995657, 623488180, 932785881, 672656005, 888754532, 480859594, 316730808, 441294508, 242153733, 186757069, 644845664, 206334890, 753294916, 119840254, 869382942, 776364183, 760008796, 312509155, 358417492, 263484315, 15071814, 401264509, 703211705, 155446588, 678797369, 551372283, 692857239, 858084897, 333429603, 199004821, 47797923, 503946551, 80360623, 238938430, 352314646, 956142590, 255799204, 574046343, 797123126, 524969062, 435786882, 563837544, 952450030, 400239916, 946920278, 456663093, 696191222, 760001493, 579456785, 71762501, 597389907, 701863800, 988789726, 546352477, 485861828, 412045218, 350877804, 270416192, 854092046, 308062088, 924531782, 479125326, 207742734, 210516698, 604148141, 695512497, 400238433, 362845319, 582228746, 918316855, 316617201, 357566559, 811927257, 370807608, 902387534, 148155939, 997051705, 688202728, 96634174, 796687756, 412263606, 561060866, 649711925, 618176700, 595380728, 56124252, 153428424, 805668067, 397639421, 263063724, 767157964, 880336539, 264202230, 361362953, 579953546, 638620103, 272126702, 691726619, 848008809, 219524384, 470202674, 488798188, 737806693, 613638790, 932171293, 766917622, 838654523, 422475366, 227518122, 483092598, 604118743, 88636022, 365223155, 311203761, 488520625, 721771668, 936814978, 86512386, 229651549, 459045971, 383139958, 201090866, 551388056, 395636544, 337288371, 372809277, 795868513, 106949045, 952362074, 961580871, 174655401, 120347282, 550729914, 906864003, 208740679, 314946644, 427403651, 394694806, 448103443, 910888129, 806167715, 217000105, 500091577, 223633983, 816652927, 191083163, 308439882, 100648126, 881857912, 487130658, 793345979, 773357455, 516688711, 723366662, 804308774, 920351388, 821775469, 225333230, 71446734, 465264995, 598050552, 998314633, 722247911, 781771436, 428367016, 899561945, 772556990, 292567513, 299858862, 905014162, 831583690, 236040756, 634586571, 328325384, 624942536, 789988405, 61480213, 194308714, 838143579, 736051108, 496922134, 878176915, 980843910, 237261374, 964630813, 954880882, 258232725, 250976209, 780301062, 444930011, 668876544, 680027871, 586289987, 198454698, 108698700, 766982741, 787653584, 407830264, 430077292, 171695572, 230273283, 352221398, 701321424, 347969744, 300957527, 702963098, 65935656, 979334618, 606453445, 124720868, 585691864, 962402592, 919473142, 359840730, 289814195, 616621852, 419387230, 348423996, 981937093, 497745193, 165217360, 721718295, 739669191, 77407168, 942893870, 472902272, 813955517, 355037477, 249544199, 313324758, 863431060, 958837851, 47672120, 715645713, 953643194, 366397540, 885420338, 763422309, 934300538, 801723245, 387423497, 345298041, 972547766, 959938476, 72535190, 233153063, 564113908, 826914896, 702004149, 749666700, 139960858, 90130022, 542881600, 18820210, 441940764, 244755376, 93157454, 855151027, 447679230, 231164320, 804657874, 227989570, 762352434, 298345202, 184590488, 704017379, 826060931, 104889897, 348193581, 430504059, 162469718, 712663058, 266383724, 296095251, 401738224, 150544154, 985735470, 124647337, 762385676, 749721703, 445712181, 779102274, 712239212, 27612147, 259403207, 412993342, 85914848, 541207074, 777573764, 614362788, 171261193, 955218393, 793373361, 86061670, 889610995, 9136531, 328062965, 705443949, 672652921, 710952744, 810259052, 494358169, 981140645, 547024367, 129587477, 625619741, 869430896, 303560859, 473831149, 498153271, 668939561, 300070939, 571371343, 122400599, 119162718, 893429410, 873722400, 54345633, 435242772, 48470669, 490820814, 108990502, 128323483, 467863281, 454278049, 370138483, 735069740, 34745348, 319877195, 870450102, 132633353, 638591675, 579657540, 483000569, 192797534, 647791391, 744743943, 76944854, 292418736, 208696048, 504420533, 435444999, 589089116, 26982715, 180745535, 26016926, 749342429, 178214251, 239936493, 500115803, 586198271, 212989267, 856039326, 41583897, 348566021, 87125265, 715103666, 972109403, 331102865, 775760341, 628569615, 177635189, 13408695, 46437353, 89842229, 986728366, 383662183, 504967916, 645154965, 969668228, 479496502, 206224466, 989739467, 123079257, 114026065, 442726154, 486007093, 514865930, 410804441, 423532992, 674360476, 193238996, 962687936, 725179532, 966638306, 377909767, 604856050, 419453567, 134730948, 578081095, 405577418, 381895681, 608730239, 899442199, 6480577, 415569409, 138221034, 760129118, 69104736, 418190967, 472625216, 433992916, 672197555, 723340757, 368440986, 107623112, 908201714, 192682733, 211908125, 984660782, 886353812, 378531400, 829488374, 448624100, 734172238, 65005368, 655732873, 746675894, 600808582, 972278650, 75678251, 219318919, 224902446, 599111319, 678531611, 343123448, 463575068, 683470934, 52224550, 56818877, 968647401, 784974678, 204631441, 313799244, 382176741, 344556081, 737185437, 393954981, 945625102, 39409426, 222157303, 528678898, 782090332, 528764385, 454008403, 904393133, 704431750, 222362466, 968691142, 311910670, 485940090, 599194468, 115603557, 155996702, 189631665, 789148589, 828816616, 42319993, 8491946, 732475201, 773018200, 763635103, 843601584, 218059669, 682723825, 105754692, 108837743, 201224300, 131405596, 784215754, 963275694, 735139552, 809236263, 565640193, 939846941, 304323500, 693499066, 435244424, 646171764, 140880293, 153302550, 797945436, 954483126, 455983817, 525501758, 363247912, 291358150, 690187423, 696677103, 268098910, 476697820, 662540636, 950721311, 115513536, 758213475, 416879499, 531950635, 395032648, 952482795, 67995085, 238718685, 691081798, 887280203, 27555211, 652302821, 916285321, 444293402, 237871115, 76294540, 784403426, 250184376, 107984448, 528447609, 459470601, 16454975, 139849280, 13202023, 564120208, 805976858, 693058749, 376161408, 226599089, 9291735, 635530479, 747199660, 364469089, 915146737, 202667632, 13893463, 544585118, 251503463, 991533552, 867804833, 65352389, 10312035, 769746989, 870604945, 633911516, 931928086, 627456067, 321293282, 697527932, 386870754, 161677459, 757644498, 248885941, 580733846, 465171109, 721221390, 557705675, 475468086, 99270783, 70080117, 177476719, 376103580, 735546804, 798560639, 655888222, 239428354, 350555767, 573582903, 830874982, 727847227, 939940404, 759776322, 614278631, 807210009, 54760004, 141480810, 285006736, 682720554, 96209452, 641512065, 690328561, 741538019, 338655607, 716861300, 856487635, 307347379, 871288308, 362993093, 912012124, 376750850, 408546578, 71219723, 880369122, 630117210, 943312951, 767393549, 789029240, 392735659, 401648495, 442947834, 286866692, 273985770, 716455686, 894901479, 52924879, 492870421, 686139867, 846895475, 149697524, 267452127, 575135318, 48360941, 24537292, 288528395, 392186073, 295771520, 459904793, 598957257, 712980690, 828980959, 705882769, 439314393, 549391768, 202204410, 492278672, 864540626, 407735958, 256537564, 450130927, 521719842, 670603588, 362239907, 204541323, 21852840, 876100034, 177138547, 99387842, 709156338, 539020872, 773306502, 329743575, 390418554, 348209520, 576188771, 135406022, 741588496, 255165529, 245928938, 754054890, 169703066, 169231639, 70693793, 885701467, 790139722, 690180045, 597210252, 858632087, 184001721, 385626885, 256272909, 757395344, 246159848, 327617502, 933420617, 125561000, 298412432, 319384869, 390993441, 983615861, 68068382, 583431254, 581433494, 658515967, 71014606, 607147677, 661701514, 611255380, 145682128, 381703509, 671663092, 345061433, 707202494, 761060933, 444544390, 927084328, 221784989, 705522480, 242578310, 840473624, 253951509, 880853693, 618194185, 870771522, 883445152, 426668529, 930182421, 406695387, 793751340, 287870069, 320792884, 738511881, 836268413, 257929511, 746668268, 465785100, 714565086, 275033140, 919133130, 629430632, 955488592, 877525342, 19469020, 249700415, 110951661, 906631858, 93290178, 108514709, 78725195, 697249995, 410508075, 214389206, 552844616, 98971203, 325757361, 225923730, 925822730, 410601902, 649877048, 553526413, 597286097, 51573557, 700811747, 80849537, 440435348, 532543181, 228911239, 654397970, 466853932, 468755427, 140298993, 745012524, 803472800, 296387730, 472611276, 888623347, 572152933, 159369194, 718891902, 480738754, 541681487, 166946954, 151172451, 709599397, 773960788, 857488583, 375676857, 514095434, 502856673, 279207737, 403119894, 6892136, 317272575, 823380878, 122151538, 391921186, 700782350, 779686764, 832907996, 369039077, 235289298, 716261677, 431297123, 341160527, 961496408, 746715149, 199882489, 823721752, 620732638, 448347962, 867814690, 233823227, 56488141, 118603640, 52576040, 411757641, 142350644, 492634603, 306003856, 610099868, 739638769, 943195188, 875568739, 639881846, 774993183, 677347946, 406540971, 790409527, 376625205, 340147547, 777755776, 797614553, 90900014, 979292128, 139834203, 980329260, 652136817, 312801699, 896970307, 316691644, 577699661, 331332784, 203347783, 975148065, 824941373, 566374625, 499824312, 449363415, 860416570, 668243216, 811300142, 701097539, 309878219, 196733879, 26088815, 227147411, 438828226, 530429833, 597281900, 590864083, 156802289, 747311280, 929317800, 687573527, 712020806, 690632602, 642324245, 685053684, 503634844, 504761366, 227294474, 845990185, 530352148, 60955138, 36046237, 434120512, 793486823, 359239782, 850117551, 891461396, 127918149, 991023211, 671051894, 427195595, 983234730, 400249628, 866768149, 110389786, 458111270, 211955813, 247765870, 460516794, 969702706, 445318688, 7551179, 601564079, 845466353, 582162388, 629825189, 651947772, 480259280, 745998356, 81647420, 465165902, 353707226, 671384864, 362557094, 725856031, 637040439, 621851389, 981280002, 380576111, 20237400, 335431051, 618285090, 204548248, 492696316, 699892787, 231477684, 222595121, 30616354, 409791079, 626402335, 337736614, 574674972, 378773191, 279399753, 706166243, 821466308, 668110548, 4768985, 290983379, 697115279, 597580848, 98837752, 240566261, 511457106, 427067560, 923786150, 719895969, 237357903, 210578536, 947358304, 210025220, 285297633, 142962368, 870618986, 488137028, 936701422, 967196376, 598777320, 64315817, 14939709, 188406130, 706351575, 621378043, 796477349, 338050066, 893121479, 583355411, 472712064, 75424539, 491090081, 489849009, 550104454, 347643671, 275192707, 28799775, 822415718, 829274925, 866968117, 528035304, 548223247, 275904426, 200537934, 602876469, 869600611, 934080664, 941571732, 334006197, 873070541, 365447600, 359672976, 816561171, 873892611, 249076798, 896776712, 813292394, 121641594, 875195784, 557667652, 72195903, 133926041, 786274998, 897453781, 890591780, 857459149, 989575892, 958984251, 949626393, 696892850, 526951538, 696686561, 412411217, 684183446, 72995161, 754315882, 9018824, 59015872, 619090334, 49814961, 295880720, 803369682, 459082, 989263169, 557814294, 848090648, 547080479, 515430667, 93483564, 932919975, 766099615, 887731810, 753417266, 917823456, 252516003, 519319206, 283488931, 645681322, 256045379, 454493621, 165879428, 799419824, 597814447, 808242134, 86446330, 998182015, 44706590, 382929511, 87059595, 262818977, 492503510, 389734478, 664709603, 605553282, 948850436, 346439513, 172952603, 816474656, 36101927, 612221974, 721450412, 500363694, 632495416, 196718607, 608590268, 352986573, 306149959, 684385643, 821697457, 245087021, 194645472, 346951643, 711692201, 183772271, 810563647, 478294571, 242231708, 378486680, 509295573, 356877520, 403950887, 463241865, 963173878, 860342749, 481710489, 739555242, 556077551, 551762227, 928317394, 384629278, 474920817, 192667464, 850121343, 45929782, 541960773, 934819970, 169315744, 74065812, 822352017, 669142703, 846268544, 844181869, 238722544, 751839236, 730831413, 286784508, 612928974, 326862622, 470072460, 197574618, 218853884, 978605919, 838705070, 25967553, 33636407, 720955150, 506263357, 931949167, 581542420, 524486448, 866401980, 513258512, 124343961, 375818285, 914810060, 839342493, 974371820, 1789613, 190006007, 188049377, 712486689, 369713320, 144286951, 529246296, 991572998, 535794191, 926198586, 698596310, 741888421, 263452541, 325730928, 970321891, 667279986, 835813334, 402491155, 44062787, 204940820, 299808189, 510506166, 718065045, 179036167, 130395, 620857224, 944091857, 669854433, 616226453, 58869596, 513954344, 891672826, 320171725, 354919313, 129688300, 674682190, 121597131, 716273237, 248167058, 214194443, 418982086, 343722916, 135922221, 782505276, 794862817, 356395777, 315629794, 541972940, 168847838, 305763143, 172977471, 912121057, 592228478, 442729566, 110857525, 946851721, 539274016, 635568330, 484130659, 331602504, 208658163, 593025257, 721922677, 989975843, 590418488, 236087018, 27422398, 412408848, 381704462, 159836746, 457803065, 127947802, 269935704, 281749737, 3240213, 847547734, 602942410, 92719398, 185973846, 162635182, 98258929, 107260838, 370826874, 167928828, 379820059, 491761579, 795442385, 732167659, 347878647, 274472175, 259197451, 142761104, 633033256, 474557322, 476110135, 621569719, 746192369, 286867779, 406313476, 671389859, 265752202, 848739833, 383673654, 60067186, 61134538, 86396751, 469089778, 566227287, 1034466, 773367162, 817594396, 148244214, 406664731, 194729462, 525735160, 727907033, 590413665, 958956710, 488195675, 983178384, 907252662, 464995914, 630983276, 879861605, 997660513, 393586376, 902437416, 240215030, 188388577, 170502340, 55092716, 12538036, 455392296, 871800157, 722176727, 22756625, 255602653, 831125958, 939990535, 607786476, 590978389, 707773201, 687432434, 696194715, 814767925, 969151182, 784353271, 497844037, 303214581, 635231992, 37535894, 485430010, 605016317, 574067494, 163667500, 444714651, 839106296, 337095472, 13562138, 436199827, 203335822, 57069380, 246045104, 643882296, 791299007, 218703351, 318796300, 425125597, 658026875, 87592006, 172415814, 460222627, 704186373, 773858180, 763332052, 827064371, 653968780, 988003978, 393263354, 51597279, 711459698, 610912088, 581888352, 451498001, 150425125, 23483553, 265677575, 59616528, 293509206, 338602725, 316867051, 903223902, 593655239, 374582494, 783874751, 566729339, 792152587, 421592074, 923535614, 542718128, 188418989, 540752036, 762297813, 106141314, 398444271, 348063029, 787561769, 381215856, 288362720, 497328241, 71862776, 15283828, 98765329, 39562563, 256210050, 885703977, 7201879, 706041117, 5306199, 965538837, 275828160, 320092171, 894083562, 42424874, 832144536, 684692222, 138615440, 263303097, 445463690, 24254260, 699448784, 426597007, 747625460, 290012393, 950590415, 687465684, 39293608, 380599980, 544416634, 705961295, 426331112, 296187530, 867429081, 858141603, 68943546, 227907927, 795602806, 94778603, 224005450, 927867177, 769147225, 790856490, 357547402, 861878882, 24642122, 83482556, 553139198, 581512319, 682005866, 436553933, 722868934, 766198636, 886285124, 667950911, 947029486, 607950871, 927768407, 932456590, 915501862, 207850702, 818584261, 445984977, 814180356, 678575852, 22189066, 211083013, 67211064, 766633857, 810320839, 271616962, 240275331, 7761574, 763768877, 421366224, 197786339, 773320358, 960274014, 295971020, 417620885, 979907299, 711050185, 365220345, 834467899, 212838946, 161325841, 559887970, 861868957, 88035575, 21439878, 623048580, 693030684, 183372432, 751455597, 109430833, 324498269, 72803052, 237844490, 491281572, 480232774, 17807216, 371791229, 797413021, 346471666, 588623411, 904202960, 561710782, 155090972, 113927131, 130386397, 802703644, 975966805, 353240982, 757287498, 398540335, 497092060, 434461822, 552417030, 170683652, 397701369, 485414431, 557624617, 915928554, 530120977, 262230051, 732050338, 487536491, 242118150, 566234486, 113204674, 755156030, 445536834, 853906644, 927605660, 482989406, 866341407, 877586797, 405737004, 908149588, 546109327, 895635435, 877329176, 661786636, 300047999, 721624256, 968587955, 887103124, 828811721, 506317567, 896103987, 648888739, 414897785, 752592836, 723353182, 998579157, 247994626, 956600525, 537549380, 550031944, 86872376, 367437156, 863047376, 441618388, 619473697, 282876243, 14929814, 826134463, 44046004, 454377539, 125018709, 415579271, 607215660, 347811085, 843052568, 527908292, 851942447, 492791973, 506210884, 310170858, 755092121, 331917494, 762356149, 111221223, 240437264, 470768700, 246808557, 684370917, 550129158, 735558651, 433366236, 917998360, 372579934, 297577979, 380657045, 704289911, 719585027, 551145238, 884378453, 454481603, 968777817, 674692414, 697328465, 208953677, 80578629, 280168588, 819039396, 737098031, 129084513, 610560206, 554272408, 92909630, 563470119, 736967763, 756712209, 801272448, 10315653, 347085365, 539044566, 302014162, 335331603, 345457037, 908460091, 209845130, 311485514, 200710572, 525322047, 708547840, 63521065, 547665994, 534163447, 364888557, 502757889, 960829878, 805740870, 361920285, 354794785, 338337729, 928271098, 295672604, 709112678, 304521804, 463752595, 153395740, 153220767, 206099561, 946175300, 661668288, 344914103, 11414168, 890598317, 955348760, 316799753, 556386099, 418082547, 901459766, 366494594, 222472861, 70154974, 91071834, 130504072, 463461072, 363306671, 485805068, 992141342, 223601361, 217522871, 998945869, 72487481, 762201431, 710020993, 827419080, 836471499, 899650659, 485317290, 246317974, 773674376, 901539505, 980295533, 365069997, 702273279, 934656012, 747577980, 34659196, 819869911, 816051373, 181767339, 253711674, 859980156, 512366737, 295927302, 860035692, 314625636, 611132605, 727278934, 906449566, 589942947, 598213026, 227461901, 975104698, 116840954, 801394032, 215586493, 341822551, 983700887, 206269303, 841812826, 38309536, 630430536, 819753349, 875242049, 680017660, 73607646, 269558393, 6859291, 984676295, 408745712, 101738176, 500114592, 483734078, 315376079, 620856960, 871981365, 241931573, 293079228, 289112202, 184645965, 662809342, 964826533, 611905934, 646736410, 45777197, 430758731, 249765695, 182632473, 230687519, 650967447, 140532148, 268278315, 434848778, 974718937, 520349468, 324564805, 695701420, 83085151, 353176045, 79654396, 50693159, 781685317, 6199128, 332046051, 444359738, 698101819, 939546051, 645725230, 185512967, 582732069, 543153422, 933158628, 302279040, 398306103, 825549104, 220260744, 825793937, 119070795, 278718885, 707398406, 663731460, 678502439, 469075822, 977907072, 980331820, 105014535, 336880013, 349497082, 303660199, 712478788, 449036758, 467780740, 860230731, 334561564, 850544893, 276238058, 890888470, 772817263, 314980420, 155297729, 502711782, 419340213, 809947108, 903896687, 927363475, 481766361, 180745660, 885717198, 72776356, 534066534, 100480496, 120780716, 530302662, 669732985, 288602322, 897123781, 638537103, 894388492, 509497201, 67043153, 596579250, 561530236, 187331790, 480405486, 936614980, 332788086, 791232449, 434600138, 53832392, 93146346, 437675645, 286245058, 611395562, 665891237, 725400896, 743377013, 574479851, 757259003, 39057648, 182270318, 217040574, 295961412, 833875180, 418059261, 23314200, 280986342, 898074629, 867420544, 524036168, 558386304, 183924750, 134483070, 924075452, 124765320, 215427898, 102344351, 172496078, 86622312, 334990312, 521407677, 129937565, 760570208, 400802950, 880672523, 669452077, 477115743, 75338458, 667688656, 432097917, 623390527, 163151758, 324167924, 357067194, 40355367, 503301155, 260921014, 876262020, 964217039, 754547145, 264999569, 295905438, 39706728, 78191246, 149074565, 667267381, 64860521, 953396981, 22343335, 596251999, 348063658, 168085245, 294461110, 753116371, 701555584, 490808296, 940074100, 716198675, 877064303, 689854695, 527856897, 707924903, 894294972, 141714737, 30968589, 321323264, 804941547, 902690448, 34068878, 873342675, 828922349, 342395930, 701363703, 19336904, 435215444, 159569465, 964157849, 132701559, 575723575, 427394968, 597560143, 576719469, 863931091, 344718657, 92807006, 219083619, 357484819, 421246201, 889950460, 669656310, 798463412, 589687149, 70790920, 317389275, 679983952, 519547653, 698962520, 915051003, 451756971, 359737382, 670421660, 973795387, 149968319, 8456768, 230306705, 100589525, 586769068, 439315603, 996793081, 798285433, 731393030, 714875105, 279856430, 485022977, 759947648, 195409090, 631663574, 184382952, 571220558, 637267896, 33849871, 882658292, 288519542, 95087708, 742870298, 983952284, 660280221, 319550543, 673747145, 122648835, 594524317, 561865119, 690994417, 815420623, 675409645, 399190273, 250074074, 959542908, 419026045, 906405911, 295373743, 786739421, 611352197, 115274349, 653968553, 535955567, 110709948, 859721565, 507701924, 40036884, 434247729, 225977470, 95809371, 380507896, 583023647, 995617495, 645018116, 87661681, 366507887, 672424585, 889294609, 453618730, 561083072, 756497756, 133218984, 410582143, 703407487, 376183507, 278503564, 520887697, 281114361, 134140402, 297760628, 936371840, 114971881, 282544677, 120626798, 470503259, 67419993, 269836083, 61098311, 172756669, 364954680, 281855893, 308408048, 92384882, 263367507, 529599980, 381247169, 740545547, 788304677, 757052311, 986742570, 795151172, 37786099, 874704492, 332152562, 990000624, 406435325, 343515191, 717647662, 22103284, 162950375, 977907822, 451006974, 603231657, 4209549, 920100950, 953854006, 598902326, 548789259, 965088046, 153112648, 118687687, 191331255, 248789120, 928633171, 495845217, 637308384, 328826315, 258754347, 267912487, 660177960, 80103105, 235654131, 595892920, 923452539, 451168135, 503056411, 843325938, 328660988, 292858143, 393740021, 466329640, 943434602, 971870629, 989030807, 35595940, 273219292, 930085639, 454020658, 69217174, 931131873, 824193507, 555361823, 727350016, 763776867, 152876181, 638065049, 42356264, 200625537, 927068057, 394391773, 743686658, 571976119, 21769467, 903157721, 438564682, 440853407, 469421798, 518569208, 584015413, 112729830, 893215219, 732603801, 463298546, 914784220, 624759052, 495588641, 283913848, 66928048, 22842852, 460673207, 428961004, 828000665, 644808536, 810885106, 745796311, 585424047, 757326468, 638790695, 202280710, 602670424, 502736736, 242830461, 569218836, 585090248, 737692309, 143720206, 804187725, 159821383, 337482239, 146565748, 779138101, 541119901, 766130601, 577496413, 298703231, 568749861, 944278408, 731244641, 359978965, 45318491, 292896313, 233682594, 850298845, 396478080, 925798177, 163546418, 576898513, 89676376, 560162628, 77017208, 245142845, 626227776, 266092348, 314611460, 454210528, 44448926, 706897538, 483053437, 727765863, 576366690, 675388131, 202938250, 860259015, 679785251, 673106332, 111595085, 175278136, 611598977, 578513018, 224566265, 172673898, 695002538, 547676637, 192950772, 157740230, 980938487, 284348055, 365403758, 583099946, 63998113, 1736509, 580586333, 686708335, 178602271, 905488143, 4888350, 985354132, 233444649, 249053257, 450183500, 971711235, 390684073, 303573576, 896814954, 826388556, 455070287, 991035688, 948862147, 380431772, 711616919, 742546647, 960895564, 65847571, 785459730, 147853542, 461331145, 16291398, 8640098, 422056289, 700516209, 713413580, 998112657, 468720165, 849647465, 839659453, 949802395, 454969983, 4544748, 879083990, 136447059, 64116258, 456303365, 541637479, 448003665, 569713311, 291424292, 973116437, 341634078, 582988359, 146711569, 387815515, 685339058, 609445312, 337058465, 149406298, 978517637, 217322417, 974019624, 471733109, 554800705, 802648790, 979966986, 821925251, 677983143, 76134964, 441187190, 51041325, 821543986, 781018505, 120769490, 717218043, 583527753, 836198688, 212899089, 871992807, 644413892, 551829153, 27531618, 103192103, 621267414, 390592567, 871303597, 80084674, 379804465, 788732736, 12408366, 964631051, 972126213, 213877915, 363464150, 972517430, 767110263, 735704907, 177333749, 340882926, 265382566, 88302548, 626138920, 975052119, 211514005, 749293394, 99965675, 431006533, 809349024, 630852298, 602099752, 664981969, 581387820, 351963544, 783682546, 447377527, 562292759, 634594411, 493432267, 941744525, 824348125, 935566776, 199113028, 928859359, 52842207, 452060742, 234600401, 563823565, 728960718, 489671034, 161835505, 330760464, 921344557, 706858791, 95483438, 448107785, 306927060, 916743451, 166752287, 673527211, 732685231, 648776650, 589369862, 328082522, 232631988, 403833629, 330016573, 510771655, 698741427, 350072010, 611156429, 267046087, 480915618, 752830611, 703567147, 954423343, 755604340, 325363264, 750351492, 868956355, 616715734, 36611746, 467062899, 458500712, 604664849, 965556732, 296105630, 840882451, 248880773, 81941240, 772014343, 486228355, 266282115, 919583053, 699250327, 844055736, 457494118, 923149579, 432381036, 953943163, 136034898, 680940843, 511743241, 292279928, 386250696, 407451823, 282626034, 197389088, 293509731, 941031322, 667032894, 882180005, 888874305, 455354633, 133014515, 721663310, 668341596, 987256277, 869055658, 225523749, 62384457, 707673461, 797105825, 28661502, 537014617, 936546823, 239205941, 109501967, 603051373, 971305634, 306998846, 170413283, 643948768, 143190893, 943744251, 305690898, 55236290, 498915553, 465866724, 711213417, 369087246, 539812202, 613342066, 918616999, 837000003, 248835268, 526391979, 659313867, 858543096, 468000722, 648219540, 945923390, 100384407, 434393395, 989051966, 386219789, 424757440, 657766436, 676514766, 24099038, 377112908, 494340686, 83211419, 40851084, 876574609, 454563306, 755743747, 114592294, 726617402, 86225952, 628166546, 603115288, 916682611, 637971531, 757013954, 476878862, 649165815, 725751219, 949076763, 805002007, 120341436, 454936621, 166173871, 965494938, 721906956, 175145138, 719917714, 218053230, 384192637, 441225973, 724718953, 124758884, 768853822, 41135392, 241255944, 264325778, 606821983, 350129404, 868727131, 937283946, 165744121, 175105005, 187899850, 325459283, 975514325, 396222132, 799560627, 6725923, 206647259, 743638908, 190117010, 366446343, 403469776, 331893932, 543923588, 497221888, 204823874, 581938940, 824980253, 285859948, 859591533, 286446732, 274942313, 569062393, 156256471, 279038571, 602502968, 416822984, 891144106, 56464161, 511513677, 448167505, 831956812, 805485689, 601308169, 459010309, 537043850, 422050679, 487916531, 969266233, 660625314, 715449543, 281512859, 120804909, 214234397, 726193487, 394928368, 934295670, 150537107, 402147187, 53644779, 884400285, 61059312, 376763144, 828375056, 405739049, 458888231, 102180100, 442161518, 481828806, 712139984, 381873137, 927461989, 268881151, 285811471, 585004537, 978284509, 907531708, 507786277, 755230827, 465020102, 389332161, 115800775, 257637267, 262695943, 748803152, 751846622, 397580277, 463695531, 166314092, 829624998, 387607650, 18228479, 600094041, 549588319, 486922445, 468428116, 73370936, 745270368, 427243214, 689654130, 108470527, 918017685, 502256482, 995902355, 198042262, 814832395, 466075647, 421385925, 560132508, 175216519, 230606361, 644862612, 131278366, 448103345, 839376168, 815398530, 888191740, 197614758, 831935092, 803250914, 785172294, 707821557, 404928267, 774357885, 569742538, 65026919, 564937689, 707324527, 349918205, 944218966, 130623285, 83495326, 638589982, 776316174, 657465827, 226432989, 450136727, 358905087, 23912477, 665269297, 952349381, 102344852, 580069534, 414654811, 828157822, 427220099, 426479081, 728921307, 146383425, 72765343, 732550203, 992562961, 386014109, 296519270, 616803172, 685955675, 934653179, 556159779, 558308797, 925427293, 827122790, 885111941, 776180089, 163953281, 934145674, 449160931, 575863311, 487682828, 16272654, 172054128, 822508005, 874891545, 406793385, 655282323, 62603592, 799497538, 379534260, 626695468, 608038640, 235574486, 703901574, 180796185, 53754986, 20744764, 530798792, 128803656, 442073220, 618055145, 226028161, 925077452, 427299406, 67278615, 582824500, 748048367, 631549628, 948406058, 613340409, 570045320, 894886607, 221470495, 877716523, 236840082, 368367515, 109044070, 57556462, 522813052, 639816823, 539271470, 506218450, 291609886, 758548402, 124134935, 335990540, 861721314, 888698021, 406492494, 676483021, 79599377, 679892329, 201155423, 376867032, 188758596, 152283947, 999838549, 401573230, 575633128, 352425805, 128325232, 417565751, 357520300, 856146672, 291228458, 628545566, 549343449, 954950792, 578019052, 82525425, 496245471, 473015155, 446289455, 220781553, 413679404, 948534742, 460832917, 122409761, 281151339, 810777575, 646786180, 314355261, 570315761, 275041316, 3179957, 323699205, 301463397, 360444718, 396729314, 689992560, 358124518, 270759250, 408136194, 302855644, 192414608, 941338909, 177630014, 784944396, 415527843, 94409216, 807351197, 726459109, 901398273, 209018875, 503959635, 111451874, 705042180, 810065297, 423580076, 475811848, 13786312, 595719198, 282287451, 940715273, 76026810, 675759293, 799360260, 256793748, 540984854, 987735026, 646971159, 463230923, 910117452, 816598817, 189372587, 647142955, 172969308, 686307241, 830770918, 708034502, 229864376, 600662634, 408461707, 45177753, 164066850, 328983971, 870204580, 168659704, 870552839, 28902911, 969361410, 925829555, 450943055, 563754569, 419906343, 435369167, 366581877, 816653176, 846750110, 559488129, 369048221, 136090507, 939867071, 340765284, 829153859, 753779136, 451857004, 444607559, 593709522, 92503569, 216752189, 552403286, 678685566, 750217332, 434081275, 23208858, 521582126, 681888108, 580333631, 435435689, 511803982, 209639621, 607581588, 125571877, 487843881, 166117324, 42588721, 787431716, 411182607, 842240221, 284771117, 762778314, 857313535, 295695836, 937976451, 362091758, 755882101, 612911117, 971463146, 971110885, 760167513, 249872932, 568834645, 392712376, 861001821, 616087901, 843777303, 902421415, 438249251, 865014232, 294244025, 280338343, 402246561, 330177952, 797300467, 413455263, 89745720, 238544032, 330244401, 983427252, 795266988, 698607710, 121892610, 500807540, 596821400, 579864820, 959511820, 951977953, 21046157, 127437782, 797826940, 415749582, 868969945, 807220051, 449104888, 32714673, 745262503, 215326131, 8681537, 276657770, 797838422, 487678918, 498573158, 323166770, 833053227, 100946132, 381791690, 855512415, 898439036, 337315731, 948502364, 873739409, 299624738, 954586217, 618033914, 708354508, 67434492, 394586467, 380290846, 433413262, 676242467, 130758275, 999372014, 432138807, 698110170, 717329726, 479605252, 777413004, 166174604, 279849400, 808742214, 238735405, 925478764, 531792239, 359650380, 350202290, 607434715, 540047806, 81447218, 391755333, 948848222, 1797905, 401564789, 693156692, 316489177, 423993280, 554836673, 247558168, 424350871, 153598566, 650471667, 152829748, 590968829, 883381423, 908676519, 816138848, 871528149, 524720183, 897696110, 370046714, 358986522, 385896748, 541878018, 422853149, 328074501, 550025363, 686099954, 985630604, 548880991, 497076722, 948655895, 821643555, 268330120, 893352922, 743333572, 495785009, 910529107, 603030227, 115719338, 912753333, 336627122, 740022103, 752607439, 635136921, 899338967, 645889588, 106169480, 170340102, 804639553, 168169354, 713419380, 82112045, 350181511, 199920659, 538974675, 506669843, 530739740, 823922026, 800634091, 625171951, 809828770, 304832837, 768288780, 701617644, 628451152, 172293838, 355184563, 879877781, 270088698, 995234101, 996068260, 638348600, 890358691, 417020001, 613526543, 990949933, 245936491, 331647157, 794339954, 443940263, 825462677, 827140128, 246268549, 305281149, 734190756, 157035376, 687739579, 870402848, 908748494, 634484367, 829508461, 832824698, 127085746, 316105688, 427822377, 335700617, 227204526, 139310609, 238393549, 147813161, 669005817, 656133739, 741142991, 738916182, 236850124, 40412263, 65962287, 335412376, 907818224, 414506762, 793285997, 302534624, 861569085, 196568721, 771421090, 306041796, 434365415, 222735103, 357589600, 102760387, 388439206, 918841097, 645784118, 939599812, 978333753, 147448838, 666750935, 642744043, 777214023, 713739151, 924139075, 779721871, 503782615, 251189088, 689422474, 923745113, 736262767, 805073344, 528178524, 631286730, 247391125, 568299926, 113745197, 879305996, 103293962, 577580622, 68623341, 134191822, 114225032, 104944831, 471656871, 175046347, 821659432, 868043974, 108624313, 531004270, 742653229, 627133854, 833948359, 972795038, 560423868, 853795849, 371534246, 376761238, 103980278, 56903431, 523701734, 664940778, 886982365, 552684493, 316828602, 533699983, 265528981, 208999921, 712384058, 301240646, 757618960, 476911954, 581571916, 661770983, 694919175, 632822042, 703645715, 8358659, 692522902, 900882499, 930009975, 373107866, 997825683, 978934608, 911063364, 154646877, 740751538, 118707595, 89480798, 656840298, 44109199, 4741059, 6067376, 745689948, 995545654, 181522348, 27778687, 145529675, 395366003, 999015023, 772011745, 592781309, 196216298, 997549245, 999165857, 223513841, 887487341, 804886333, 144826437, 301402162, 881325286, 988058989, 507847204, 543750552, 422203735, 671161552, 859659908, 396561738, 649915945, 531120329, 161194358, 318204724, 263651091, 61721641, 865282686, 214880919, 840582518, 100930523, 225843692, 473806670, 344021294, 121658541, 30303554, 877404557, 979245658, 261915871, 150132486, 483437698, 25878365, 411687090, 662410519, 949915562, 719277940, 744851802, 49055633, 562295657, 116244007, 412127481, 774269066, 381418218, 878588005, 542952297, 288621607, 942043529, 663859084, 6078905, 386340759, 80919665, 994011797, 793918608, 530290601, 500826497, 694448076, 638513323, 139600341, 644845359, 642356176, 721647782, 77765265, 749471541, 76300508, 941184465, 378620225, 582534091, 567472936, 680870599, 39169508, 663788122, 488173103, 716324129, 989027694, 726043418, 775080453, 885839043, 299173201, 17077597, 274015711, 593466749, 504791212, 104875712, 145439352, 409477982, 380354714, 400691060, 196180461, 902333722, 324374984, 338028295, 205913778, 355912849, 228594127, 102855150, 137160292, 615489822, 860867591, 654271563, 254385338, 835691448, 551051744, 573490335, 610004998, 878622681, 279625284, 836389898, 545976553, 900263177, 308715529, 609816100, 186604744, 930280387, 922255546, 276406889, 473586566, 715151957, 829780523, 533665585, 143898281, 809992053, 731652401, 4907252, 772667616, 246528320, 739494310, 280942068, 839787275, 732950556, 749435777, 310064789, 422655853, 876635580, 611856191, 535532814, 511310785, 274355587, 11805688, 844174330, 698846283, 389512238, 504295881, 20640200, 674162862, 213471219, 786231336, 772631274, 230417949, 851996930, 948912891, 933829938, 843090844, 945540219, 477110688, 778482083, 563940558, 779696209, 736224579, 134250231, 480906754, 623214650, 928710201, 212734299, 466330031, 419953804, 33053002, 72627743, 267643548, 892993677, 700819024, 784460121, 623320665, 753435868, 836463178, 952629918, 785723599, 55889789, 167909312, 800740027, 747364326, 407153924, 828909700, 491286559, 905168951, 641157896, 86865938, 147526959, 797387143, 409892020, 244313605, 116070408, 731013996, 382371356, 621234308, 169113373, 396006151, 54097553, 322684512, 955241163, 893444425, 941449769, 508681110, 812350839, 192255106, 932238521, 236571953, 157940648, 910622363, 347217491, 464234186, 706456121, 764124969, 836788994, 987689809, 425423122, 902238250, 614827191, 955534475, 912850779, 18007842, 995508001, 320026511, 345150802, 684896087, 845628139, 764936021, 356995398, 332050453, 927284300, 836627708, 481226954, 910504747, 819492134, 377851140, 535343743, 273335747, 326749605, 313329887, 479774229, 351870186, 250333886, 198571668, 335403095, 692818877, 786924125, 754841676, 199193366, 11933097, 62113033, 266885148, 885458500, 230830009, 965114925, 69944796, 477148102, 649999778, 747567079, 623827081, 595915793, 734652975, 150894523, 675246937, 306506273, 476524125, 489207797, 385152303, 548563859, 61120868, 529422942, 152544180, 245780718, 508934635, 317916786, 174537627, 455959816, 82009091, 800499518, 28598455, 647445010, 385934780, 888352936, 809100582, 450585602, 218239339, 123981272, 882440010, 197781319, 469667782, 212599578, 332793186, 183512244, 379861289, 190816713, 103987453, 152807152, 504544724, 770304414, 573790486, 96769432, 230920789, 357732705, 652474390, 999127942, 503815576, 926119311, 777144690, 584446416, 95066183, 117639897, 741416356, 487662112, 473178929, 898353791, 525597362, 158370878, 235873965, 42446310, 944485390, 209882139, 111839040, 899047767, 265278207, 396245687, 92553531, 193710261, 257754548, 559414493, 686413140, 666901379, 19069842, 843048255, 847832994, 480452728, 798323029, 276071875, 36521831, 362997552, 689974941, 718712762, 78505625, 867449254, 991231847, 781100660, 993877577, 586767293, 50164522, 242693598, 544402067, 512325404, 286808716, 382687020, 985652218, 371670605, 635100505, 728685954, 658590589, 821861455, 165540935, 147538579, 460369188, 816619671, 371454794, 786286766, 94241492, 886389318, 723295235, 484437968, 248761559, 818196283, 711249267, 210313511, 143708080, 322433553, 889425298, 781079235, 3756908, 740305495, 772775509, 845874680, 436777733, 573175895, 159134944, 343602430, 651257518, 629345796, 177099365, 98221041, 62723203, 671641570, 656211400, 911668522, 837285420, 444918910, 669588941, 90354483, 612096821, 994545989, 970557375, 344918465, 784424893, 412501500, 731906150, 295087930, 855332732, 548392294, 690695394, 381853925, 976856791, 741798560, 110084894, 522442813, 841064134, 175343236, 739301720, 781034503, 973772062, 643245229, 17695640, 497301580, 14611697, 406390558, 831884802, 347623001, 604002543, 354182280, 859281807, 457446158, 374651860, 406805908, 465875850, 8837311, 267260473, 309646425, 528879308, 854997525, 872789416, 422980831, 994708172, 375100908, 423536960, 654453744, 674126272, 364153288, 670360707, 528824670, 986131860, 80150879, 237873268, 346912485, 144569440, 924477043, 726387199, 88465124, 813762621, 182705955, 192460554, 831460632, 52925915, 383375005, 984179169, 784193152, 478543656, 344288919, 521583599, 955922507, 694989509, 220793749, 32027685, 891723064, 956671581, 358154600, 924518257, 22466840, 195300810, 613575234, 800436104, 245972859, 699918716, 299567718, 772725772, 126787924, 869165937, 230161752, 637202821, 342258637, 26197636, 556867175, 75606774, 100525479, 167777031, 505783931, 43212374, 346071789, 843317591, 546011334, 640738406, 128686360, 881473589, 785909849, 990105547, 161262733, 551859847, 450124897, 437753077, 234114791, 703753067, 818230239, 973473219, 606720166, 727255967, 83901628, 525385077, 307034266, 194705178, 17321757, 910594939, 274668534, 524238485, 939304097, 635480216, 680848900, 950209807, 783573244, 79786341, 292008032, 711765601, 434758637, 515342481, 76845556, 587806149, 362560519, 387320451, 257535327, 1642509, 422394947, 4670629, 9836553, 876359457, 236748276, 832130333, 459086899, 332198624, 794844494, 624104313, 771049344, 386854686, 271721560, 181019844, 531795157, 157249619, 798955121, 551404544, 737712129, 296306334, 571883200, 980764353, 712551039, 747434852, 7736859, 438092651, 786772498, 326133704, 459095337, 492444016, 641046454, 832702341, 715111177, 203268007, 598091868, 538438742, 57957306, 630157007, 770093342, 267818451, 355867249, 375699939, 432767253, 390565461, 989752749, 143516343, 582202570, 71307628, 799978529, 733794478, 53331850, 351610391, 941640820, 137641485, 624822988, 382803787, 904217527, 294004256, 58580848, 993435238, 743624823, 351888456, 437246907, 567282919, 277493992, 810088556, 620996740, 828984026, 46116577, 583067436, 95870839, 205731386, 28834149, 345603907, 44846079, 111742394, 113125204, 657845799, 336095891, 469604082, 887317564, 743914730, 373912661, 582836664, 929116154, 663090445, 443433091, 493499889, 616063120, 26867444, 730794703, 575674878, 831009222, 112451127, 366640775, 275701312, 837137138, 284871236, 12834850, 542263697, 814391530, 877610853, 961819184, 579099344, 626350927, 565228025, 836925874, 783427744, 922543082, 981819301, 454951416, 307420418, 143121142, 723510185, 58636492, 603850782, 473125593, 110816487, 497537477, 534249674, 451048964, 787033439, 613500021, 805127754, 13867166, 124988111, 916312559, 446732805, 626154057, 58460674, 576903909, 193212683, 56075449, 357199907, 143855334, 448616659, 650559507, 911875956, 619852281, 522749787, 732794172, 490141197, 319537120, 973422018, 661012452, 310187187, 332547468, 332307877, 829413351, 310403305, 823060730, 779633008, 324045717, 754875360, 292366595, 496721944, 370027285, 556168303, 91253378, 62920229, 219627968, 708446861, 974593785, 563405293, 748640326, 527426116, 399260481, 598263586, 91495378, 609303773, 328813934, 454667841, 386605170, 329230973, 137829958, 399680067, 477461705, 105388384, 680290127, 629475600, 958887554, 499575382, 501436008, 671645742, 384740193, 987537421, 633934952, 503786183, 560676236, 525351100, 524414498, 81093117, 608239899, 988176545, 655878355, 195641472, 86034588, 942182600, 376845937, 290106824, 588959296, 402716043, 822144657, 145484814, 340672495, 201281162, 130349332, 276704809, 224147511, 825258113, 532517875, 395114250, 386011094, 107466290, 13338191, 519779969, 874166305, 449917134, 200703983, 947127784, 556236870, 446452404, 383703713, 622774675, 730848579, 107130019, 295699289, 270151132, 856058606, 917051428, 488988445, 74721115, 282025436, 158909230, 878804164, 253088683, 48519890, 954596937, 33528980, 396225802, 890391340, 813235142, 901650449, 179569694, 994363055, 224099611, 294050245, 702365054, 145219425, 11911367, 361413428, 630048423, 18683913, 981741227, 725886838, 508132745, 198586098, 475739473, 902654622, 564905623, 789583448, 296100861, 132825703, 398843388, 40034925, 16799039, 419229737, 827532720, 413938052, 371842996, 137208337, 467872956, 970490152, 566380450, 750037254, 41611988, 443289564, 288270429, 566232557, 157234222, 264727008, 933905618, 103918464, 585251407, 722197988, 102427194, 558994107, 511165011, 333675692, 564810851, 278825741, 59781148, 983226742, 735067033, 518185226, 341212194, 751035199, 243123558, 183433779, 660238954, 476108741, 764745266, 376305765, 301602075, 418508300, 791666202, 776731403, 958070379, 180306467, 500514464, 763818462, 441553664, 638575066, 519904861, 343737826, 184773636, 607252278, 344360291, 418000357, 905980724, 650771154, 459830948, 568896366, 209245464, 135521135, 155283914, 63619182, 431788886, 494662865, 30047924, 874845115, 217551133, 339974622, 691154799, 357471270, 664899252, 536279561, 18706810, 683683605, 592253253, 514294564, 548175462, 777945217, 759929235, 29678391, 927174509, 229390430, 927251628, 320478187, 891102371, 228893057, 542589687, 822730035, 525004241, 279887968, 418287136, 596258242, 556324316, 686243866, 906022853, 13063104, 403659757, 191273048, 572972905, 407001928, 197157450, 788843619, 614406920, 977710809, 597232554, 652183622, 291828872, 406169168, 570783394, 940011608, 941330625, 51260085, 832684056, 105184295, 924963444, 225052982, 841404955, 6539514, 480887670, 993034225, 168744463, 86358057, 131221487, 680437127, 443438669, 641115731, 908053165, 972674179, 895581212, 930459368, 88481086, 308825638, 924688885, 689550932, 916534624, 435005571, 736301976, 788641310, 425308021, 281946477, 156710471, 368798967, 639172875, 884642953, 859000967, 205523858, 514595354, 54527571, 542892604, 249566783, 482808495, 632192514, 83423687, 993985093, 655436058, 2113006, 623402615, 63280487, 210810468, 321385845, 692627260, 959971139, 904886351, 180948180, 751348071, 639258966, 686478431, 723161486, 87409391, 66972121, 707509130, 33062643, 891770759, 913110281, 345148110, 987719363, 918145723, 924970740, 936678676, 607025339, 681142094, 650950729, 980021822, 792447820, 486449148, 549297539, 64964401, 427452997, 457339346, 25802978, 285669031, 672352369, 700748223, 525292781, 602831464, 827125007, 218774644, 872713286, 262045995, 555854084, 965350701, 263818413, 219392545, 252843793, 393619982, 996146196, 615819094, 883192665, 853385762, 259647094, 20394305, 624424755, 562722107, 585167827, 384814727, 14819997, 945830767, 690407151, 316353220, 645005650, 963006385, 307239730, 238519456, 280930792, 912951661, 400785809, 582434938, 208831888, 463285444, 66569148, 205497626, 114360716, 892711772, 984174495, 326755686, 559815711, 212567870, 323261509, 387372907, 676756663, 662792529, 65487723, 866016445, 145907135, 486638923, 506649762, 619306148, 145981288, 370553863, 546609655, 539476717, 14069815, 260720470, 145127351, 484001351, 967703962, 482502623, 893489810, 449868022, 168296579, 812947098, 112578705, 378460925, 120759255, 730759849, 676835487, 489164477, 731498639, 826261938, 214570728, 551758447, 946402470, 768525184, 779872216, 26674916, 807030443, 255531062, 821132856, 670039436, 87418007, 670948383, 529899566, 803166630, 131471166, 480745443, 193054264, 299526262, 716723962, 415090943, 438864812, 106108975, 526480378, 53426299, 978409941, 794341952, 7345663, 246702181, 162563748, 564818337, 722682923, 516301099, 321448487, 404068139, 29813397, 995584727, 737116158, 666954711, 422558553, 359202019, 5654419, 839199772, 663417127, 160619585, 221747437, 322509755, 738075732, 752554754, 266893121, 488424316, 384497324, 820232562, 573069589, 319688795, 715277272, 247054561, 659315919, 380227979, 445405546, 384585816, 551983395, 833716292, 643605459, 859522772, 18616351, 8595366, 863035512, 669675703, 131471774, 537891225, 190164, 822171038, 112637317, 882375255, 976485625, 62786481, 903178642, 983524999, 936015895, 975775765, 194391559, 48515180, 676592006, 117169426, 218185689, 484779738, 922779517, 871708277, 995022637, 756745125, 696095007, 686448478, 761586508, 620126722, 368491505, 309523253, 585097761, 289527047, 853177153, 839993266, 371230556, 749576631, 214861115, 543757746, 448398377, 723900299, 994069230, 11087264, 115417934, 550094515, 400351221, 82173582, 149656983, 715900460, 120191872, 444770669, 570775511, 186238303, 747372709, 443723342, 214548877, 598595256, 390089237, 801337113, 249609902, 430703138, 926128617, 651024042, 833240534, 736813116, 137920043, 579614287, 346682330, 215578846, 783927150, 437316423, 324518074, 442769584, 384638964, 798408685, 8595757, 810783300, 240225516, 894965254, 906457996, 505585129, 803114277, 603034791, 519307242, 424671065, 489674895, 371162328, 846964066, 930846714, 683880646, 497714631, 340109063, 758187280, 900086794, 659764785, 127068498, 29048261, 123668453, 293144221, 831691142, 42847095, 339901657, 509105824, 922181046, 714328367, 161693692, 558453545, 911493430, 440745388, 411127508, 116442247, 965689195, 634095672, 272838064, 113734053, 242570735, 447575238, 602884825, 582995402, 616928758, 774370941, 196263979, 861275793, 106471868, 131250553, 426601757, 810783118, 913248479, 975806202, 835155273, 63631304, 149971990, 839890172, 797185133, 181411790, 400240828, 817864347, 850380853, 884112479, 15262194, 855796250, 936472948, 494965649, 400208310, 997606100, 620542328, 579924933, 450034066, 172807144, 816870514, 206000749, 406884952, 925729753, 577886452, 204116637, 89098958, 607154858, 140783410, 12431763, 351116677, 796660266, 427732712, 416832702, 8480503, 955773735, 21573622, 391763262, 150466996, 560072511, 529712650, 810949581, 911251937, 697470719, 626285078, 172429929, 435636308, 312433604, 94474976, 444603290, 71991336, 845600784, 208349973, 389405398, 845878782, 268186003, 778470953, 953692091, 47857422, 560057272, 474757006, 943155687, 491450273, 327009089, 233127737, 570470836, 210023912, 226769592, 371084801, 592078863, 233745729, 823073619, 391316452, 822597793, 794648857, 650733364, 693162194, 321624917, 106620523, 291111729, 266623559, 317092349, 936286360, 513871412, 293590430, 731659918, 108176131, 205573449, 258165403, 16452027, 757096369, 614731950, 782259303, 670316999, 988467074, 816830001, 269005319, 463075210, 618849573, 762079891, 758752470, 615940656, 746574524, 617773725, 800202903, 683206066, 718772858, 630537168, 47058170, 821132417, 277094556, 699986463, 702136765, 351699200, 144724609, 411095353, 863353239, 27535307, 479110797, 94421211, 200395141, 534148309, 588247518, 674773826, 205818199, 584557931, 644270598, 959565846, 156965633, 80298282, 328307298, 298536105, 472326959, 675026797, 845410539, 684070547, 529577429, 120342193, 781834824, 433655470, 968414480, 682248652, 565949245, 403284893, 857154809, 234637230, 654319720, 236094768, 43729190, 612602156, 300493693, 978179043, 142388197, 894814899, 856306975, 6329349, 200248082, 764702477, 284797928, 746738242, 634357868, 999111748, 300686816, 215784979, 507721916, 125379, 477778795, 587501144, 325348710, 697960753, 262072762, 556809545, 540228432, 174010294, 824378427, 659786989, 690404822, 687951716, 423430603, 47773317, 746933772, 599655246, 444068633, 434576651, 323326640, 502555465, 581011290, 785977700, 71380091, 209909561, 811772724, 698715789, 405495910, 71054422, 754294648, 668896302, 913719269, 370588834, 615789378, 562228701, 627963828, 872099008, 602144782, 542302887, 996637520, 155859997, 569115214, 28628811, 841944136, 55165975, 90420810, 623451294, 416594775, 763590442, 969490131, 810117887, 1015309, 962486057, 994445430, 906206104, 440821040, 107780623, 666292023, 405743039, 690698105, 81594498, 385200428, 520266785, 117610393, 591390689, 426540617, 961067296, 389299234, 548862149, 953223491, 321004239, 483716324, 762957153, 464558468, 916695937, 360556520, 863307515, 744469165, 191228684, 703394069, 599757137, 149935983, 574583746, 272636041, 135363119, 249941589, 634261731, 470775006, 990619669, 615615920, 439789233, 423660535, 171478538, 825922874, 685532619, 867373672, 480493445, 964710640, 286460424, 551773216, 818113898, 229926200, 307423865, 543902789, 56313412, 721363153, 717158556, 723806388, 26236551, 476413378, 166779866, 270135782, 383809148, 754772945, 887277880, 61160141, 331943354, 147613196, 818680320, 916199487, 588819652, 975300893, 945264295, 962115189, 819704362, 353591116, 837915644, 751300329, 151387218, 680961865, 503356352, 719638372, 400774937, 722769831, 921725942, 541180089, 668529566, 479203742, 167727020, 989594628, 217075700, 131379790, 377297628, 519397750, 157646160, 762537523, 451131350, 862738745, 407618141, 684255184, 188968235, 854728202, 205328284, 963039000, 823677321, 598208195, 370904032, 894843032, 191898415, 570756780, 639554426, 884196367, 497469278, 83823810, 794231523, 309366109, 660217259, 825434274, 17717693, 948605453, 838651898, 546265094, 841736992, 180919865, 372855826, 460650129, 662809214, 227275504, 912116826, 677605253, 529033182, 110519982, 579804562, 737123226, 281484617, 719059607, 992744160, 964526429, 210611378, 496272621, 739314491, 657792938, 307157797, 332065288, 373151498, 729954340, 548283442, 923722678, 722826057, 339448651, 522976694, 251041205, 214556220, 913510100, 960720811, 29728035, 219915904, 533415193, 764294410, 545407125, 526173974, 147105542, 154080141, 441447878, 157840448, 167883964, 718024468, 446304386, 382777149, 628113174, 668317509, 681501271, 416019274, 751751839, 743918451, 183359079, 416371149, 477990461, 194050598, 388434325, 818996580, 310834182, 186406580, 149283293, 973766246, 468733041, 205727743, 10999963, 513324383, 368346829, 429214825, 576801708, 274866209, 453708863, 107260349, 314362791, 122393433, 134269498, 643131546, 800847713, 429712720, 412084763, 937046898, 627631612, 801755046, 901074109, 705959093, 943592718, 965040818, 839408959, 136888279, 309834944, 894542593, 556970111, 983242085, 493531221, 618892632, 176548580, 453363647, 254554707, 607482169, 80777801, 223117071, 172613757, 228262426, 390962202, 886698267, 550096909, 993055027, 92193184, 645741985, 12633267, 187982505, 483923747, 291887331, 181528464, 950908929, 124197621, 197117578, 298978803, 44781632, 914458639, 371049460, 716970647, 675144832, 314736349, 140083125, 918225251, 729166063, 752414487, 57302144, 640892849, 206319, 630215619, 426923136, 181671157, 394892348, 95798236, 151563101, 821732106, 116898306, 819777974, 353445482, 147896874, 999636423, 992651647, 28834375, 57347733, 483604618, 170051927, 944084721, 765040695, 138962127, 882142157, 191006124, 219705353, 144217872, 130346796, 445119569, 309545448, 774635594, 999786478, 791856290, 200843732, 855933301, 119502441, 264940146, 954435325, 277688818, 883960503, 345373645, 841281671, 868524909, 895015196, 719813393, 361443490, 717314589, 40281049, 700820940, 96210706, 731323571, 720374465, 629532865, 671354014, 422475216, 861510326, 423880787, 701306108, 91236651, 683889216, 728298868, 571148287, 255575487, 120373746, 629641368, 276100605, 102106149, 100655358, 230862841, 737041460, 130626482, 135911134, 482870833, 970625217, 670885333, 93379387, 275761767, 415886313, 543209646, 745083398, 21074790, 217530670, 361607560, 27895609, 578789474, 888721675, 91616752, 385070244, 192133673, 161322574, 347514643, 966313778, 511561110, 849468424, 747797545, 108626963, 526866508, 379731583, 452069481, 89999225, 200315162, 609366732, 16891103, 889408204, 562017393, 501118168, 867474733, 531417964, 416958532, 252774463, 385095203, 6967480, 808772028, 456572613, 268310075, 161700326, 718092126, 381882253, 958286893, 516997580, 427863836, 941495273, 660246128, 927084082, 87672265, 898694955, 885506550, 102142976, 396176853, 944019601, 263837718, 386174799, 78522530, 570342264, 324768456, 38791486, 993763330, 813634430, 839146193, 838347457, 420124273, 289116840, 939505576, 692109524, 715682468, 536788146, 237139172, 550107707, 458836418, 328592474, 162151577, 757571662, 638842006, 160356912, 579191991, 906417574, 801047410, 206808449, 535305910, 557530642, 514317933, 448208470, 628716735, 641621766, 261137437, 742664724, 872632359, 489980011, 614909671, 23846955, 595031983, 976032802, 74470099, 842572023, 500054437, 495332763, 645410131, 147360968, 983268563, 657583589, 68922879, 800697199, 643488612, 768550914, 451368614, 701755243, 999143697, 735266188, 543965776, 780260992, 958790592, 635472244, 4597298, 43663814, 454321058, 331317031, 932217852, 673556653, 869809620, 797943403, 646677502, 810762797, 762217968, 870329428, 875384197, 879692785, 723999338, 962277663, 109946172, 727253035, 729200242, 595331570, 218525896, 121851632, 158824502, 168040417, 763165828, 830083673, 428865432, 144467273, 907281339, 928112336, 769746888, 565985963, 14155855, 11838305, 350656156, 721001624, 591060459, 791430425, 271430717, 763040126, 338516623, 557626453, 838546221, 922110412, 367595326, 263487641, 790006027, 751715724, 851512496, 983695849, 954343, 863338600, 969854032, 793776127, 130652292, 886530201, 567878197, 741584710, 183844393, 762904502, 744667193, 155614896, 288324534, 468753789, 330727184, 578782492, 210279935, 310427971, 647432005, 832678576, 796744411, 693155817, 582872573, 2576157, 377725932, 615823699, 534391504, 745561902, 504934572, 571810734, 835972431, 131314753, 870432822, 904921059, 27103840, 991868092, 814826668, 293719622, 1813025, 94745225, 250309918, 65813048, 978627382, 898305404, 268031043, 781795180, 982076400, 994597511, 309254109, 86839600, 544246847, 769698724, 373019446, 558539740, 539671787, 68754812, 314787382, 785355371, 957845125, 411658761, 239071164, 975024956, 571967345, 923190689, 837048632, 272810127, 216214032, 43906665, 189744768, 967829062, 890760707, 410119199, 453819507, 321248481, 572072302, 272617592, 882407964, 581277909, 35028223, 305748711, 340289002, 422174316, 922974273, 235369465, 848758827, 378098213, 14778942, 478120245, 207997290, 188051026, 937806471, 116391921, 495258967, 635055175, 203828172, 153118823, 812968080, 826993248, 995798105, 260694644, 307878199, 231233281, 589755311, 938097204, 668891857, 685255971, 126825625, 543397818, 478934145, 989112905, 684844213, 939641293, 863649002, 131292106, 148746195, 120515732, 820103198, 371808021, 426866574, 199074019, 477300815, 236956155, 855609521, 295197389, 87934145, 828940852, 646238697, 987452754, 608890025, 740304836, 131409531, 165058413, 767279941, 401634698, 703259610, 605773656, 858892193, 8120218, 241142660, 803285167, 326629730, 114937507, 646564975, 523481110, 708840684, 630144406, 784320409, 514360908, 729833588, 521944575, 18842214, 873732857, 321037569, 317686834, 294362226, 140341624, 338770147, 563273797, 588929899, 550933525, 723651379, 366303636, 378819436, 857743077, 592062731, 101605689, 605345064, 430647160, 198396885, 151414614, 396341250, 533062634, 568795746, 63460162, 99791208, 338950091, 23883940, 140403656, 113293763, 29893405, 267697220, 636608502, 117679226, 863010173, 977712198, 244453167, 267268564, 332028981, 993854733, 817833974, 790682136, 624121104, 470346636, 929986886, 307570346, 623133785, 415851819, 558840164, 558257329, 285744271, 292021419, 300732048, 890799141, 734265759, 141402670, 544425373, 884423531, 429897991, 351799413, 911303249, 425663729, 937977759, 366575480, 443459351, 473461067, 486405343, 207325852, 506905936, 832150910, 656908213, 675924449, 366727267, 609746947, 326058863, 645690319, 980484481, 901379779, 299044838, 958348640, 924509582, 788375773, 769761651, 581212968, 632437447, 500764279, 132663217, 913635844, 482985065, 933783431, 531649244, 105517909, 342589308, 392505010, 892966991, 271867472, 982790901, 162654595, 611968681, 170266970, 304278219, 483874778, 913790366, 201420594, 955267273, 716260706, 556026613, 403174412, 44573811, 571754177, 40687141, 306883009, 873457990, 538459717, 607500586, 448576861, 73466554, 154859593, 173237393, 93198608, 692254172, 767274876, 84348242, 165197583, 307020940, 19622256, 348131046, 139510182, 363215109, 927629956, 656311086, 67309768, 111598506, 869344991, 574044651, 839073590, 974074620, 984931445, 188285008, 660878791, 877586638, 297570756, 605495937, 805647504, 701913454, 646003504, 709814911, 627931079, 476036517, 691263673, 575479137, 507949077, 263136432, 474619179, 789742480, 873252195, 44874291, 546144405, 294910763, 150148958, 555764280, 629286299, 28699316, 938684609, 197004406, 807054555, 876436630, 185778826, 244943467, 857602761, 994979605, 852347439, 102914376, 413056184, 343919411, 624075188, 872312782, 114069754, 292022811, 182755200, 452452959, 620591131, 282093084, 622377700, 868148443, 613109538, 650774786, 402020023, 422098904, 546547739, 2055577, 89982511, 387198084, 357632389, 839693346, 204389404, 798850028, 988318452, 242020293, 96439509, 179006942, 514223922, 202743865, 991631004, 521343682, 581081310, 460122485, 112476748, 247695479, 611478444, 229211064, 501838278, 785971191, 201601014, 328433140, 493033092, 67201836, 240457252, 970372261, 713444059, 983037859, 702008131, 59270619, 811816881, 534848939, 778563304, 262682156, 531231670, 203146448, 356840873, 585338971, 19454262, 225453596, 491512191, 407786055, 227050683, 532652846, 370147791, 986329760, 764748601, 247889589, 875903449, 279122194, 632681620, 198317344, 260223900, 529508148, 518256643, 108789705, 58180392, 334884107, 823195732, 467207489, 640372156, 248158025, 216761817, 168636200, 447673165, 943564728, 560616603, 248544606, 93287907, 220544816, 971477563, 715046153, 504296697, 325101111, 684648242, 628272504, 407846676, 566690491, 158564806, 999787105, 556419087, 141968168, 174112041, 6398401, 976393389, 289732754, 293799625, 70063147, 999550940, 879967732, 352376979, 714426357, 51291353, 867127266, 700003660, 760211153, 534876683, 568640563, 529845641, 984810881, 772076197, 122105085, 589093499, 239705114, 132152163, 417431943, 64369571, 128580996, 739557356, 936330686, 759489931, 556054814, 350776026, 356676971, 87662174, 886576345, 424047500, 609125281, 40310702, 439985177, 556855382, 102947877, 633819571, 256630390, 693415872, 565493139, 607134732, 650184820, 986104773, 921509324, 610064177, 715217626, 976079916, 998324171, 470990246, 407550407, 571479173, 244255915, 72787987, 63052606, 14357102, 437308825, 414184951, 538672533, 17594499, 612144304, 381700039, 698240783, 70859944, 63899742, 181620059, 829299882, 574280321, 39875926, 167214934, 478573653, 453814504, 610404080, 494220355, 454728746, 797180370, 910545122, 935758077, 390401344, 143365424, 125161511, 21394188, 68879812, 696393525, 215399522, 433191747, 404462831, 555999105, 858819863, 798226, 452099037, 603673054, 943964936, 945126609, 495889127, 500253713, 13637869, 462875541, 373740789, 958537294, 189878024, 308130328, 988616681, 864596628, 544804553, 241653989, 639301820, 941698776, 640596619, 857192310, 673626039, 668041836, 689083836, 807219325, 670010837, 260027322, 573385907, 113561171, 569380793, 652911823, 680059607, 504570756, 302843136, 865087646, 596858445, 98365129, 612110115, 969651289, 303633516, 675463731, 809752848, 607750123, 664999061, 691289325, 71282328, 55611456, 801682103, 926076543, 964530058, 95722041, 876903350, 798349149, 282254745, 301000032, 154471657, 182446948, 201842093, 799198544, 677842493, 603757886, 870943887, 511493317, 490043339, 514910834, 687371425, 417584031, 323962204, 849703192, 780203942, 661606310, 23176094, 911500067, 451684071, 420817955, 458130952, 646234615, 537786750, 116149767, 7676927, 396116083, 961215456, 9702414, 36453179, 918721542, 880204391, 409431306, 570827224, 834781183, 885289581, 381294703, 893282373, 820005531, 176187591, 540347263, 670767435, 256513592, 601378756, 321101627, 553507906, 959060225, 716952610, 125389357, 467957237, 923478903, 840464451, 738566071, 896535691, 74016515, 618662370, 69837081, 834793929, 344132278, 812799540, 449830355, 295253516, 937778930, 728750324, 303342760, 879462575, 163927740, 66313997, 811009904, 169251114, 134728652, 824249573, 3761375, 343297747, 494277669, 232640213, 861983744, 3795357, 921921264, 389781619, 434970687, 197913629, 367837408, 236795668, 354534247, 947184788, 31686230, 871392482, 222003240, 104325320, 682385853, 80378405, 428391431, 391795854, 700670454, 790116298, 150130944, 394665102, 869314223, 637882936, 457528377, 619617915, 689772237, 217838239, 622410412, 393883158, 134707361, 361646148, 283151584, 876366709, 41998663, 358802408, 259180635, 307850374, 534238290, 796553732, 690748651, 976628721, 942316817, 27092533, 498925554, 341424695, 443494342, 888152212, 843119421, 529237113, 856271616, 75262899, 746454854, 601314534, 940936969, 975575992, 378159888, 699149183, 186952120, 468013114, 606522285, 697534366, 179313990, 907210324, 918327338, 517923806, 810550619, 203557582, 567033604, 49490419, 306273249, 171849037, 559448527, 721249782, 894493862, 829164413, 995999198, 50092148, 178185989, 869961302, 661782950, 544113288, 660686667, 54988042, 574050073, 410214048, 79702962, 39992843, 506364883, 923824874, 136613408, 305354662, 864296675, 344228865, 471678613, 225356460, 82612333, 788655350, 622770584, 798357786, 108726461, 62176861, 128768161, 146673652, 42739345, 676735735, 680238386, 508943833, 565927258, 968887451, 979861179, 97572640, 762562876, 177853887, 992949951, 471547101, 184678238, 934852826, 829015439, 21854208, 549417757, 147207389, 657624831, 204858104, 519396492, 400682373, 937809597, 202760407, 795017109, 320184399, 818763199, 857901284, 61483061, 997060038, 190752287, 372764546, 503702771, 981444884, 969018712, 814177264, 813031634, 861172652, 72161604, 609428857, 706923737, 248394951, 589576465, 420309618, 981583296, 50999936, 604817546, 254373331, 969103480, 444896286, 236507832, 813235128, 758702885, 38155411, 754754020, 859990943, 66778307, 397737258, 644339165, 991282287, 8829049, 989886698, 770524924, 35576281, 859028269, 996726849, 476787520, 375778873, 656286093, 46992957, 725236144, 814616687, 789572632, 717233991, 856752506, 440887033, 394164315, 21925285, 710916981, 463380728, 2959097, 194931108, 127103050, 390419672, 499680547, 976146129, 226510250, 523926601, 946946559, 842085319, 949027288, 413652276, 437817241, 592243065, 968891348, 455891081, 897982563, 749166618, 404351686, 710904744, 601423662, 892721933, 939039767, 872481086, 535370369, 467851338, 509002672, 593396830, 79527955, 268671959, 744165517, 652377326, 169425608, 796193059, 962470896, 237207361, 111905279, 783948764, 8397631, 281705450, 13843193, 433748335, 2179731, 204846814, 499465770, 380044208, 807732254, 583899807, 301441248, 187067551, 758496194, 590823156, 628950154, 264107821, 315716956, 761270630, 812455716, 680599504, 531449965, 483455575, 600694977, 449069316, 556596979, 325231029, 129952842, 259885887, 87864961, 570363084, 937823406, 300254172, 681247114, 422886462, 405010927, 527637921, 706526568, 421728175, 769531311, 192490149, 132692520, 155588750, 967318497, 836641126, 91391081, 215643239, 535452208, 61570621, 778767094, 475586630, 905146784, 238976901, 316401945, 257206058, 847019751, 619660381, 633658606, 270398039, 311060142, 67994889, 747896343, 546521303, 587324512, 594146725, 421114765, 339984861, 833160789, 809735121, 506969950, 39475435, 414721515, 745377661, 481214337, 292581129, 923959032, 842716165, 681147491, 504635540, 301174062, 539391745, 358704179, 588976795, 370880066, 635379676, 901226003, 279199735, 507952605, 772690457, 986806732, 764802555, 142726217, 885575924, 434125861, 190518398, 236881375, 482092263, 42879824, 506960438, 675302660, 395989207, 124587710, 440870239, 74557928, 311330697, 25671288, 173805516, 532499004, 456306964, 649977534, 254808895, 199346118, 592600464, 762305038, 920083056, 918914122, 614697642, 77566612, 62291312, 138686950, 407192609, 982023390, 489469495, 760250310, 24015159, 176760380, 8885486, 402323797, 460095176, 433754374, 959922467, 367634160, 396492391, 108867480, 391141004, 415686131, 126207944, 431365638, 558329685, 769898362, 897184470, 336709924, 399319194, 877287282, 3383685, 507074371, 859159149, 263046491, 246569059, 757646972, 744118881, 595809661, 814211586, 914580063, 685547101, 284747458, 124485340, 146272011, 965486697, 57303256, 667328539, 788312021, 911487362, 995552948, 785308243, 84160644, 171639883, 716306628, 833854072, 566737588, 178169131, 948946911, 18240411, 319205570, 25935188, 444388401, 384992609, 589126252, 190123078, 35422589, 114606175, 331750792, 268267648, 626792351, 479195164, 219824583, 625177609, 876703450, 96515287, 280425864, 617596917, 869460733, 205966384, 70546850, 387617952, 87993223, 899231936, 574330888, 157422280, 179153955, 113209974, 32282245, 707949898, 212046476, 231995947, 759606004, 438801168, 831138001, 98239628, 738366929, 578411638, 735371562, 749273159, 942104324, 378419211, 40493914, 458251806, 212101209, 289480550, 748202095, 31748073, 697052585, 501402867, 668749823, 515221906, 428342965, 810164419, 291037735, 304998699, 32605387, 614711239, 889138423, 233188883, 463780407, 93303405, 343611552, 424715802, 422432576, 565044738, 84585497, 891732583, 234950129, 17630493, 937643237, 461138423, 859859736, 122560127, 593915135, 293004988, 569603215, 425714287, 846200317, 910631469, 41410629, 376918003, 110436470, 397981850, 497043387, 549729301, 225668500, 597601343, 62382119, 453598457, 975669612, 842434106, 445440516, 983084250, 666039333, 237516261, 978553918, 626666546, 815060716, 748471496, 60501966, 162304950, 795633004, 168262321, 791274626, 827388989, 476063294, 201533864, 97516348, 72616856, 240715445, 164215555, 189809441, 977268775, 398555709, 573202320, 4485769, 667042229, 666502833, 266256426, 545684314, 691388380, 692671748, 717736630, 472560451, 46389059, 819529868, 681616996, 584941614, 112987452, 718267524, 802855390, 55478393, 700273000, 324077444, 953627824, 828850219, 364218982, 46296191, 379940417, 578267494, 408319902, 358862533, 230481002, 122357405, 623340189, 963153656, 454237513, 793756561, 158196632, 600411826, 734114474, 284604697, 63697770, 813287137, 927041228, 934204875, 80055022, 593335379, 487867797, 400667858, 553634078, 356428065, 135347283, 932092364, 22301733, 504936962, 548944521, 546552576, 673338979, 35952365, 645016773, 463437633, 109258776, 294646352, 427915278, 637203921, 519265012, 227680138, 210939049, 899627051, 898878181, 883381864, 713752218, 361452110, 533629140, 645337518, 461872098, 891376414, 194620991, 488467086, 661134869, 705005783, 939392130, 747178036, 887384331, 838705099, 696828656, 492670448, 179445422, 833099035, 702114352, 917063524, 497589183, 606761215, 124417116, 616885554, 858521867, 407022149, 588534154, 83869930, 77149564, 504433229, 580496266, 495843782, 714968434, 631132794, 724938785, 81790856, 698611281, 887197071, 323942727, 445177987, 97091912, 109672617, 883293974, 299320307, 368508096, 618017423, 221162818, 885935087, 361052810, 966210837, 663255432, 703120983, 83151555, 523072384, 107499104, 207870726, 121668296, 312756870, 463170680, 928924211, 984983796, 749846819, 345633237, 968097333, 606932352, 838446377, 715009767, 619886051, 571998640, 548099781, 228599961, 426423397, 583129292, 374576861, 907006317, 174537770, 251955218, 871126236, 903770394, 933228828, 602240066, 921838210, 957285281, 385141365, 480116205, 109611613, 94866019, 16489980, 630153886, 549894818, 156318548, 961065738, 240062198, 652051089, 724801171, 687226604, 849648570, 185499393, 25195206, 311564096, 564802544, 560459904, 310445512, 333574031, 230914744, 284664766, 933170078, 909225512, 234915724] 168907727))
+
+test5 :: Test
+test5 = TestCase (assertEqual "for (countGood [217706376, 176224481, 414853751, 360784308, 399375492, 941597389, 106851333, 441913586, 947317130, 914922940, 846297059, 757462564, 464491619, 53183692, 750452757, 357678359, 105330506, 93457988, 79483012, 964421862, 527257327, 708964453, 128180685, 1573100, 757724008, 466606556, 232583468, 121995288, 796663596, 488600355, 9188128, 262499378, 968232102, 506785053, 997428, 97831813, 455004004, 389233120, 605066830, 186485673, 883227896, 812459989, 357297053, 971729077, 226837358, 411471539, 244789916, 91594399, 553861492, 618617171, 222420495, 281073509, 556026175, 917966899, 219694458, 398886608, 133483508, 794514401, 937093071, 851613798, 713103967, 834334425, 87667992, 421909706, 511882128, 474169819, 230971531, 121831416, 70235029, 872655488, 660684334, 270932348, 417614935, 324511141, 936339338, 507717871, 89484871, 857860027, 817210708, 181199820, 764517409, 874095904, 456161596, 24945559, 570444117, 139124333, 875157265, 923091481, 979235831, 213908342, 613900157, 717081132, 770041904, 191984888, 586105063, 223446895, 60935557, 6607331, 169951049, 649736495, 537507832, 541445025, 47479214, 185710585, 809829797, 217316587, 486506172, 573761607, 136568425, 270021418, 510394401, 971931726, 529895346, 783659016, 528525824, 635264797, 925276241, 547594048, 327144357, 100473838, 297748496, 215080395, 204959156, 754752536, 14366392, 753243580, 307649139, 348481450, 441707033, 652951094, 225507330, 255319279, 499190834, 649005056, 897221511, 807181363, 933500397, 646505271, 298913266, 393410384, 784576972, 429491598, 673388207, 115247560, 204784413, 175698197, 684048886, 824128491, 72956419, 388310206, 131129913, 43847103, 79004156, 492315328, 391537479, 656163153, 639283306, 290003724, 138338137, 600258186, 327969487, 107741669, 273838978, 875754930, 37249409, 353706684, 905026945, 247106422, 221736619, 23073436, 600142271, 510131771, 413149446, 941791830, 52056917, 519371096, 106216138, 611936555, 910871070, 530149114, 176726859, 991741647, 410175704, 903477370, 58615933, 841691300, 279284216, 635097399, 296723259, 245690715, 952039538, 515514311, 751339763, 15649616, 57193154, 573331418, 85562912, 315568059, 813690098, 294649224, 792709870, 345387153, 365179768, 879892162, 187554500, 713936217, 323716036, 279086548, 426861714, 974042645, 727308362, 627265202, 24140535, 54089777, 326986708, 992796984, 884501098, 580766794, 349608542, 618169190, 618005992, 68587336, 823700952, 491493306, 987960693, 184079002, 362602900, 422850367, 613220782, 850433406, 210874176, 88904294, 542805647, 597678467, 375727022, 971347361, 386206664, 751041120, 467384212, 177054772, 955660126, 875095116, 871662294, 186604549, 436175888, 900747336, 230353173, 740027850, 554643846, 575045772, 131026181, 590226403, 329189160, 386731452, 808748641, 195065161, 913656275, 919620681, 154863607, 376759524, 755684655, 559201604, 671312144, 327359399, 505114710, 453798092, 575618470, 208363970, 39518789, 77151826, 880705180, 324021765, 159496031, 693992095, 812583733, 9253626, 278896204, 928403601, 998138338, 100469387, 800902279, 819639970, 786738086, 945485893, 817844425, 119272434, 4974788, 23615608, 97089319, 501244016, 264778647, 670948064, 228885984, 246998077, 30547844, 797916102, 437897494, 36820317, 363919868, 646144563, 410048779, 544747996, 35817639, 339745977, 340343059, 846684965, 771156896, 799236193, 422367489, 589501820, 250473494, 244672617, 761243770, 598936384, 984336143, 229026114, 427624955, 577333087, 132527074, 64211422, 573409292, 737872451, 19067878, 995601894, 27978068, 727589896, 667677798, 214040047, 843946589, 190333685, 717831738, 853849883, 766848080, 357420453, 480641806, 967501968, 604015451, 197966015, 880087364, 987746799, 617535340, 972198720, 458777237, 291244023, 154664055, 266610801, 486986365, 762161457, 405010295, 389442622, 558617510, 878959207, 34166532, 669043402, 268218540, 805593184, 559862370, 390825717, 854245444, 728459560, 866813828, 570451641, 264709118, 489747448, 267405215, 208796642, 985241994, 228909623, 858134810, 674717596, 625012613, 109292814, 392520947, 331846475, 213530046, 423208974, 815926747, 690257453, 344287189, 562371575, 915849756, 435886049, 592734479, 253272469, 510727610, 241506503, 180759087, 136602966, 895591090, 887506948, 28366570, 194299504, 478962879, 371461351, 184710996, 2471966, 982559196, 437574298, 976058299, 852570548, 462319954, 422099021, 87965626, 546123154, 643938173, 993270830, 111956291, 81045852, 39346096, 584508169, 285247812, 953352480, 194877756, 748033066, 186783454, 13031222, 382293580, 513234231, 512618501, 375604804, 352659319, 100417427, 159931289, 598624520, 371749029, 358929540, 71306534, 512170517, 669243002, 924193039, 805502173, 3455425, 418854972, 236119865, 98651755, 917079543, 214862120, 40358841, 729997555, 337745979, 400626675, 463504489, 457104891, 176588390, 426134079, 46703545, 311481392, 49522983, 989940398, 453881786, 351123033, 260363528, 174136269, 550105115, 602132297, 818803195, 980351864, 96903381, 919762914, 665945213, 709211115, 411109062, 298775403, 768865984, 969255158, 307626756, 512219899, 503172791, 316672438, 245675970, 865729327, 385484114, 100870226, 906988941, 630660706, 220487572, 633257026, 651994573, 459901745, 490336326, 979315877, 701980243, 857827069, 731823475, 12636160, 988161462, 194944050, 498849504, 790196898, 663876868, 27215250, 232384027, 544025545, 960586084, 330444514, 946787214, 678964740, 183564301, 464988183, 982691855, 300878188, 478919702, 512189372, 531547829, 401232835, 741240480, 590276225, 452868629, 541636630, 402381503, 281855431, 986028601, 927503641, 348663166, 805197801, 235633843, 703117851, 157580387, 959143853, 998849401, 600267376, 674384962, 942278829, 95114837, 639733581, 291358432, 670745032, 126637908, 557152028, 711719167, 927754401, 361439347, 198919693, 298728034, 138222217, 172855043, 387437294, 478740019, 715520891, 419863903, 400524277, 420203380, 480089465, 436622053, 262404747, 416005291, 736454824, 257700758, 906381595, 504607397, 888155051, 243866824, 14773920, 698577366, 808121045, 383053625, 117198835, 552524858, 22855130, 598378711, 812194420, 946892186, 294077115, 656084826, 835310248, 72396368, 585842267, 365666616, 695332789, 497050625, 881386148, 84794409, 745976413, 386650559, 537856734, 608699887, 510083498, 662811706, 514519772, 720361766, 146706283, 983728168, 748731706, 785448761, 694990872, 431386963, 928419020, 607472263, 287856616, 193258690, 43147059, 199906049, 206131823, 974009866, 64091919, 841033508, 415490829, 215306772, 987198173, 851059222, 717490393, 667601139, 465727741, 645995594, 113180107, 378870758, 795022306, 452608629, 757512422, 15937112, 732722913, 478752431, 450352046, 442089705, 411449551, 531898028, 424959169, 554767864, 900120139, 806241671, 368609175, 186676329, 905557398, 363862051, 283953086, 344205204, 551741670, 36406590, 996951602, 685211970, 794044596, 113027336, 967554602, 816418239, 735697152, 454655769, 984827409, 86050289, 874307964, 493617366, 202747809, 872987298, 26270731, 251430191, 520993979, 897508892, 100307604, 961696624, 553476579, 776658041, 764687450, 960190593, 279402869, 567235617, 428631974, 814066981, 115341666, 21418216, 349412020, 792321570, 813400187, 991981699, 26055562, 42035330, 442157941, 246005046, 522950975, 105476225, 923273880, 950376002, 13438382, 721181335, 614360442, 528577759, 611649433, 601923364, 745404716, 608955077, 639848098, 496296827, 646168435, 92789522, 305283825, 361877526, 469298822, 926423657, 951168219, 541277856, 466701787, 368479364, 986762951, 695398742, 215738069, 688601945, 321664524, 446641430, 996786526, 49664041, 752855085, 590033632, 756322254, 694583971, 275305905, 806122705, 314365689, 873387456, 28135429, 640302832, 748410501, 240416576, 176598974, 350353729, 259448968, 337929302, 666031505, 748636201, 202717729, 953652672, 446309242, 596514968, 560585271, 936653490, 473596023, 32566738, 144696896, 888243352, 586985825, 100337319, 8219047, 861112587, 344565315, 3204157, 681129432, 724552717, 80494826, 36547220, 945122001, 551776899, 257703178, 874802974, 493399905, 2928898, 238733950, 967217848, 17363469, 552752860, 577971328, 187446848, 436443573, 730882414, 656354306, 103813236, 79481500, 126052999, 667791712, 947628974, 201190273, 454077012, 570968518, 718662114, 456002072, 357958051, 378232614, 608881172, 553695017, 239989085, 852622739, 732317022, 881560691, 26124802, 773469427, 284007720, 514883371, 432306728, 350672134, 943674649, 224549428, 21050835, 652233506, 444147118, 397544274, 73263833, 844758478, 645151923, 929906325, 150961026, 321593901, 925243803, 459606674, 276290890, 291003879, 936520681, 560799846, 308839716, 418897818, 428132084, 758412441, 507205410, 803633364, 762489509, 903488215, 28751068, 935148751, 869415498, 263799909, 446242688, 305699855, 424450148, 388340465, 839823456, 430039677, 218371076, 218743912, 643676207, 737138114, 892573119, 33023718, 668574519, 118070865, 685171299, 582086269, 276713026, 259847223, 883856157, 73728564, 879594718, 14704464, 731627954, 415057986, 860276138, 529891973, 625739041, 597654021, 911398430, 394989933, 253937305, 55984490, 97854406, 151957628, 349915196, 851305767, 794371225, 23486717, 799176045, 317703067, 929237136, 35200698, 687950391, 351562123, 364513082, 777107439, 837706064, 78259818, 560154346, 695399721, 28255771, 420273877, 545667561, 817515171, 853899036, 730119376, 295813260, 569394989, 908694373, 73745477, 963513613, 838138524, 856440569, 203454818, 611554818, 266644447, 531524608, 28909188, 607478116, 754907450, 940107272, 746433471, 460809168, 689983827, 929432705, 45503674, 77519458, 564215390, 805697747, 183302546, 935693442, 619917637, 534817073, 905627987, 40102837, 714040184, 857062837, 646702657, 933760056, 429232866, 455252507, 941319849, 261733610, 410861745, 391959058, 582875981, 701648616, 468703918, 112489271, 479508862, 791300969, 756672848, 221359948, 693687748, 511515709, 989927747, 134654354, 727594146, 717363361, 997861479, 767059468, 704883800, 49876500, 46350342, 443988673, 596301548, 221524035, 796691684, 802094359, 307698969, 97081103, 576146114, 962584514, 714547177, 347074992, 340883105, 740928432, 411262134, 48941995, 793665544, 539896248, 815857516, 54843327, 742603162, 177087073, 465893954, 563449580, 236244593, 97790893, 850444812, 15249137, 380362249, 840521832, 227262654, 565040177, 588682396, 739353733, 162447416, 165046552, 884740507, 910321862, 608192674, 35137453, 894195193, 805579015, 365685426, 797889244, 433386459, 128080568, 497576687, 870363835, 402472806, 306950571, 902859883, 368294756, 890057956, 251903002, 686391302, 588275667, 659719908, 997700425, 214269407, 850611043, 856305655, 766442511, 162669722, 627306806, 546808357, 540532039, 109008225, 106898364, 549917846, 35391222, 217685014, 760199593, 216590560, 345164550, 938538947, 663908410, 739079259, 927574360, 382408284, 127550326, 737170587, 113920704, 56514957, 564765877, 412330838, 514828133, 494113515, 75227310, 58779227, 117982367, 481534022, 949914, 445717250, 289264536, 199783878, 823973435, 197971014, 535375853, 740342294, 838199759, 162106843, 722612974, 106258445, 697668682, 782794247, 519222817, 300171354, 29510997, 673619272, 753273685, 954079371, 454281188, 658532133, 121886281, 816311049, 528859117, 153784652, 820440366, 211958929, 670004794, 161402763, 305176126, 713979999, 818720446, 767670386, 718009457, 571672329, 634770437, 53557938, 347113299, 458508330, 523876664, 789581784, 996962206, 855636802, 465503207, 753825333, 485431783, 605967465, 604435651, 10603916, 437695568, 393788845, 99338155, 297725277, 749498989, 349749511, 775973455, 416681553, 64578807, 8999456, 808097677, 388897438, 719885548, 108990627, 624987915, 535535933, 316680846, 813296706, 198849344, 947946304, 994173457, 677590298, 267932306, 464989141, 904213428, 626902443, 200970003, 412943260, 772137552, 552642468, 1048102, 161348391, 813727282, 198955235, 13405025, 204721581, 812840971, 296968818, 560864439, 380262777, 288128425, 418175662, 689223436, 332620935, 269896605, 484021953, 505419832, 548826848, 592974892, 81873113, 786247531, 164553113, 652981759, 331485347, 732487513, 804784708, 301233518, 985556892, 210525727, 5927474, 769388814, 325892179, 72290371, 741634624, 428963183, 530438771, 3088198, 178131311, 191393275, 458534038, 621239502, 740202220, 279557688, 50079953, 387265840, 868270172, 395617967, 564180935, 917630989, 787607404, 779026154, 810347755, 494231676, 666866362, 589911116, 74233432, 421535328, 39039953, 872099662, 702051717, 743007593, 219178278, 852452505, 616138287, 47863759, 642985785, 970671337, 697366824, 767041437, 130252251, 435428247, 99873188, 531733116, 449484305, 675874174, 579942500, 74848612, 528524197, 318998695, 928069243, 42091661, 933998573, 404317109, 283961432, 675316884, 852304479, 829634065, 773579344, 415800891, 597662360, 302127895, 543135978, 890182335, 464052683, 206328993, 379297634, 61512808, 357468370, 330506158, 91085195, 749377017, 499002442, 685034630, 967023522, 738145785, 165710049, 811895530, 255130945, 774109779, 764633260, 746854239, 773564348, 212527518, 220621816, 674406475, 747782388, 731831444, 371558079, 950458399, 610037602, 207359505, 486272874, 993152074, 552166082, 956006932, 440018570, 414469557, 995401764, 400615100, 255676742, 246633001, 468598847, 529540357, 229520735, 405826888, 53517886, 583835332, 620279927, 246263684, 502319428, 256311363, 758802463, 802076409, 49929265, 67794018, 865181447, 263586956, 750861391, 755738310, 156083623, 361629405, 813443175, 875669209, 317103845, 889439767, 432583828, 464571701, 816581913, 706991995, 604815817, 531024286, 246186654, 365729077, 724465095, 222598092, 449180384, 513936235, 507133585, 725036271, 94124005, 166434801, 467192920, 110511062, 663029207, 807164855, 958583195, 17200980, 194475494, 119179279, 165637979, 990144495, 514779454, 855986748, 760106233, 415935880, 66556780, 911431466, 369823516, 902525286, 906439544, 272980449, 588447716, 529430251, 566357323, 259444183, 459449044, 54028796, 388090348, 648564663, 517054578, 518687905, 935865214, 882375255, 79360793, 998247970, 655372724, 72804967, 985206559, 78813974, 43713894, 556495400, 27348170, 552237879, 485760533, 665777327, 902802600, 998944128, 818741832, 281468082, 319987398, 369844889, 246373607, 539039507, 12878703, 566359132, 241629000, 505205501, 974857565, 494170840, 359637601, 287948172, 13733365, 58273631, 895562134, 161703918, 490294251, 942635744, 134907616, 325339589, 951502027, 262996280, 735688184, 193894912, 780659013, 592088402, 299376110, 563783043, 550196306, 164183953, 35019700, 153817756, 771194998, 930870506, 756292746, 130005854, 561204753, 358682608, 554234270, 231335422, 666704247, 206049776, 521878239, 127535192, 269971236, 74565840, 713726398, 769444042, 846079060, 308917750, 12716331, 794902451, 159632362, 330267520, 334846086, 763723036, 485180805, 801095249, 797231966, 607400178, 843497831, 855842848, 220075921, 81020833, 702023856, 17708106, 980543129, 601914207, 350096903, 632385802, 986384156, 405741229, 786624722, 650306308, 567749650, 447618318, 543778032, 756850620, 204868509, 379960374, 215899945, 642948716, 490733084, 373672794, 187802220, 393439967, 908914985, 503893893, 723579337, 269513317, 900518647, 620506075, 998059242, 742961132, 490830714, 281112303, 683917349, 84515502, 367122570, 783128774, 120336959, 534318320, 394154988, 493358203, 327027937, 619576680, 135423610, 563743369, 729433160, 629822, 644566007, 174562931, 956680322, 412433287, 30659269, 401096833, 123699377, 323135384, 929784976, 550221059, 159304327, 870331871, 1530682, 583756291, 21917369, 607462535, 181757613, 363709110, 312649960, 803248931, 998042756, 199024219, 812762985, 293305766, 182353577, 372868339, 309310593, 500510835, 640500047, 736819150, 142952127, 232070662, 266288200, 218676135, 430993362, 199187823, 695304499, 577985388, 871915140, 844849105, 215806478, 352555080, 857693977, 167377047, 225851158, 584478170, 648141814, 212441499, 555048579, 863837818, 552127555, 595378795, 350770483, 51553556, 143693134, 28372093, 297820980, 95314215, 614364488, 969123149, 288690666, 739493938, 54586024, 404524005, 456304262, 886305603, 381001311, 827188365, 868461864, 980058142, 606502816, 30515367, 155532030, 583051428, 240461459, 723088270, 708474755, 60688789, 287279476, 599632183, 977099230, 14495013, 783998950, 470531331, 436470436, 670402974, 890027958, 432833231, 752209214, 631782786, 698275788, 603941751, 447742269, 672115921, 785211953, 946541678, 528703420, 235984979, 79950486, 868634726, 232002167, 655492144, 841175811, 680144135, 943477392, 887310660, 462309610, 936339820, 352452333, 132878926, 170777437, 729679687, 521748538, 514338796, 61484268, 92767189, 918090404, 934467715, 153216794, 264311915, 898428672, 691007294, 384143532, 338983282, 740711617, 259672783, 598006771, 667050790, 89567627, 475585788, 147293612, 436577422, 700474486, 822645976, 398695173, 488446709, 875698486, 41010204, 958633798, 303719437, 660742867, 410880541, 782372313, 545215403, 424117590, 325681343, 688754946, 298920079, 13805471, 149759102, 13763820, 218615125, 472424830, 398921782, 960811090, 198433036, 502895703, 560583824, 637568823, 596902581, 73376344, 735060527, 777534138, 830828766, 650053437, 626630826, 621053883, 861566328, 284639660, 210575701, 692070433, 143068600, 572610646, 263139511, 191001880, 86507768, 220432507, 492602256, 216728608, 497777754, 777322975, 219518821, 76779408, 999518537, 484613722, 733164049, 618998521, 141749689, 570565400, 452469657, 419954808, 918259331, 357753192, 899188011, 944361272, 19285905, 131926286, 145115598, 750893696, 498290354, 661519067, 740062325, 659244219, 338941020, 772271885, 509548285, 582270288, 95052959, 95982715, 755131186, 240913039, 767006177, 333187506, 17698424, 118406374, 62227012, 10258091, 454685271, 254947675, 704718606, 65732133, 832191909, 159048762, 95150529, 410341424, 857584078, 20368325, 371537252, 838707570, 657477246, 814338293, 970369753, 955114681, 831081186, 90700562, 31517990, 808381330, 387955301, 493263287, 864653394, 69994362, 502558526, 403452019, 438061701, 478398483, 229838158, 333063704, 136143763, 155458568, 703506690, 58638800, 447738544, 21018295, 389743997, 895930824, 749563332, 156409611, 735971146, 332317841, 25427011, 248621588, 279310012, 408958767, 133456212, 151420039, 246208145, 687575809, 30688863, 981846753, 43216340, 330542190, 80794048, 751250669, 603002353, 13056282, 612524073, 732755648, 354012348, 143903730, 601949098, 9589251, 900754501, 259905093, 485902323, 882047469, 272154825, 281607361, 625796190, 70599758, 17966816, 654082273, 487673017, 968297095, 967669886, 906558659, 290065819, 205519208, 804075425, 561537671, 436828350, 864096614, 455123907, 11909159, 702475498, 710541014, 224129070, 392608282, 559521553, 800912727, 982384712, 190090090, 42738691, 530469577, 168638678, 574211873, 616056305, 34270859, 937984677, 474065067, 403623160, 317872645, 779296706, 695206257, 664379453, 71412867, 816235327, 364606426, 266183632, 916193918, 16667583, 639424724, 176399337, 807480044, 970018288, 637647096, 834020708, 14019614, 649280162, 495459629, 692536283, 572570856, 597760516, 382674574, 420184941, 620258451, 430217, 723704620, 229378893, 885381145, 995022013, 77141666, 682912848, 213094044, 972044429, 284506900, 785347351, 365218547, 90893654, 360045633, 469814364, 624609727, 670808120, 386046823, 822628712, 189471237, 475691308, 968161815, 117658394, 713783650, 930454234, 552483669, 726421626, 590396500, 100997414, 614789886, 854263056, 118808675, 448018965, 577377732, 457941142, 880506503, 655779337, 569473220, 469990048, 646228396, 534537451, 9411599, 103132547, 360795552, 489768778, 718414961, 5754723, 900018561, 336321626, 908774205, 763523912, 956662134, 78165680, 723055919, 758442657, 416432360, 633370956, 674558077, 861771380, 173027820, 181759457, 502875614, 487520022, 977405785, 887768141, 449072258, 187657046, 404028364, 837672944, 624495681, 672552165, 97487483, 532823272, 793819269, 297679058, 391713571, 65754591, 681423132, 298154525, 583440630, 271544704, 320977572, 988330205, 758815343, 481023858, 154897272, 162714999, 959576594, 294778246, 319986058, 93748403, 564361348, 743622888, 513844589, 302840274, 173188263, 833069356, 390444918, 57912153, 653174993, 532855762, 807085608, 340703283, 859134400, 106018899, 269692352, 161256973, 484335943, 467990244, 806657625, 146379160, 45318774, 190600729, 764975157, 229177804, 822020396, 958343109, 783094632, 564599770, 93375977, 818534665, 216261843, 335693981, 667083353, 814329026, 933153818, 624206759, 574966007, 663604524, 567399996, 378849821, 112569525, 200580262, 945182607, 701804794, 938499128, 542899252, 931762968, 509739084, 682199178, 205704354, 871772048, 975198950, 225675511, 893112039, 960939302, 450842460, 988287823, 390140151, 995734977, 737690833, 858971816, 288659772, 499404373, 412054342, 313656107, 431678881, 921846496, 545035742, 116561356, 625986208, 985959789, 404115453, 62820313, 704124634, 41011170, 292152678, 187334265, 741842606, 732573805, 970810598, 873792787, 341624501, 316923557, 587633512, 942418888, 837903783, 442813356, 539307550, 7442149, 195408365, 416492766, 527414808, 326851078, 491604422, 21514939, 478344723, 233390764, 198202191, 332324626, 108882273, 921368797, 84100739, 292712818, 449177779, 482199321, 203798854, 370526631, 171462642, 741658757, 830305075, 68042875, 654055121, 675457110, 927560465, 45499810, 339116489, 135304834, 962977469, 321051603, 830583124, 330549269, 958815781, 394867000, 98846837, 741311318, 226988614, 120059101, 749113302, 658568596, 366496856, 889962580, 584951651, 377902437, 364652606, 688447722, 38135301, 350300153, 64348878, 226659404, 310017461, 57664275, 477649366, 903830154, 448845034, 510504877, 413481288, 312227854, 394259628, 865257422, 585762197, 552374156, 166492382, 104141472, 761824193, 732353658, 737325467, 322617224, 590458098, 381081869, 933675474, 84020601, 569222148, 900830757, 769533711, 496699226, 293675013, 24614661, 557436946, 972286557, 346087127, 417430945, 888039922, 94107641, 350937489, 494809982, 257199373, 554200783, 986400721, 313157421, 642537044, 511359785, 995290703, 348555602, 115474962, 976203687, 235260528, 147314152, 97011669, 428213767, 907462278, 348166173, 102815802, 564455070, 180137588, 237376922, 488288178, 171292894, 253596536, 21796264, 885629666, 649294787, 978225955, 821349608, 977596921, 646864926, 306650308, 281338228, 889767335, 574748284, 376872488, 936692912, 186149770, 440859092, 670197153, 164500993, 392351899, 517628584, 62734694, 214767353, 627507541, 704502090, 112421123, 633812390, 423297920, 337993440, 642224929, 107435554, 859501496, 664983713, 754787138, 231816111, 479950394, 966559689, 337833419, 343052312, 927104235, 28605341, 155845612, 863320431, 633795566, 885589084, 10309468, 517790636, 682179659, 198038584, 313578715, 53150565, 462355499, 721686429, 375492255, 963696470, 575750043, 172875552, 553958312, 12642800, 469281867, 754614894, 902566910, 857481109, 536153938, 646550005, 251599650, 550916335, 952570452, 334776772, 864383223, 248217282, 171072868, 809828681, 857812960, 113368414, 542165126, 111444145, 13066278, 788332753, 560964414, 418459666, 41576232, 156948689, 135698144, 488369341, 760406105, 733468163, 362956785, 649681943, 101443337, 875858754, 325737660, 682833665, 95640840, 40791796, 757258681, 66648822, 52300506, 893977666, 384072799, 644420619, 674520602, 265185812, 458604997, 232113300, 309008916, 549767948, 769501405, 611964671, 699284417, 838314591, 773579852, 982684601, 149115914, 65023882, 899133851, 188277779, 579352414, 459498593, 183920814, 525680618, 557273612, 483129336, 519525891, 714977075, 339689908, 666337379, 68327623, 758815284, 823970114, 444300748, 778841355, 835664149, 841097714, 676351828, 730663683, 128967490, 594137937, 630572559, 577400936, 648505887, 569912799, 655313166, 718028618, 132809230, 689255786, 925635120, 242609818, 466645468, 199398771, 301967383, 246206480, 986648155, 415761156, 767152262, 315532574, 952488157, 448505609, 877264347, 199833255, 835656666, 551627184, 684400342, 797860522, 352390055, 688793669, 367635230, 539698224, 835500262, 990066377, 395553876, 687904244, 752462486, 928141955, 98253188, 278228501, 799452353, 783811765, 869612284, 38356855, 913693722, 828380103, 985285568, 398255614, 303218305, 917911776, 425889998, 375850910, 687936362, 781171653, 489700245, 442654257, 555880837, 696839697, 981358021, 354583388, 628776238, 437427713, 265264705, 953861052, 344362229, 696190367, 935275859, 54528679, 563307595, 65099325, 630316498, 12089617, 927082010, 165566799, 740832393, 631163743, 997876158, 812975659, 101443192, 988971890, 463592939, 748009857, 42017961, 246907393, 456721493, 130606982, 253495516, 581934281, 902320601, 125911097, 636544367, 679259436, 349889948, 833525536, 418975494, 791515099, 329918403, 930057348, 966677441, 514270539, 583335570, 300969201, 987680338, 350219144, 567219402, 48672803, 240781658, 601670357, 251752050, 645940371, 550437061, 842821145, 617895233, 879096819, 785438541, 192814342, 116792593, 435564808, 539536288, 92257663, 293822331, 779909699, 687707060, 250592335, 736684773, 468403796, 561266215, 307399076, 183832645, 826876177, 533406082, 14197507, 886902131, 312446969, 706303231, 807448262, 847252530, 416745809, 390324624, 578511369, 826377627, 101146419, 601920874, 315658979, 815014033, 723601750, 838864410, 928684196, 6535703, 75111435, 528739675, 769858587, 668561251, 762749112, 401385206, 270714051, 550299676, 521668580, 268828083, 796644300, 635677428, 416474696, 736786037, 16857499, 823107613, 975836473, 45545457, 398716573, 474122509, 359559845, 493941019, 253666259, 581308384, 660352577, 220365532, 322462645, 643233118, 170112082, 103939724, 504878213, 148536378, 324382342, 297964180, 928071172, 421844040, 850115437, 843838273, 513973681, 328234619, 606036033, 615490908, 998975394, 642936879, 564745255, 149869766, 640673618, 222096928, 280147638, 619315878, 473931313, 874175561, 874916944, 178798023, 567306382, 840953534, 949331171, 842266689, 497931284, 56323067, 650278154, 806363095, 210680321, 552289041, 368016393, 122751186, 565233475, 327041815, 359638844, 89878384, 522758325, 912751684, 319027170, 66479784, 373317223, 3511935, 444852711, 454262336, 823806776, 266159293, 332547233, 633223620, 341201725, 966873560, 807995845, 631670093, 921326636, 263179379, 661618806, 731995330, 690833491, 659714130, 719760204, 803403886, 42023284, 182375867, 868540157, 347333745, 286043873, 110114797, 273386606, 411239735, 87410285, 941948355, 305616683, 326225238, 780947976, 233342879, 667088365, 587927081, 546099361, 169828895, 547475534, 207581899, 600344986, 97483639, 47071803, 591995687, 146724563, 232441652, 579839140, 886364629, 562081697, 601374338, 836633832, 630552700, 270881105, 593167746, 46768143, 323302337, 295770010, 897065470, 664523123, 446770682, 983911377, 63010808, 267042848, 547679912, 971353854, 306989269, 56588406, 46617623, 934178687, 540537333, 498056416, 243102062, 594538910, 782659670, 936078639, 450841167, 396955440, 921271358, 448094176, 797051021, 814480347, 363536269, 616790793, 754829537, 944900746, 369991151, 849141317, 300366909, 633634164, 921068847, 205056354, 604755522, 884872287, 347255334, 779398270, 988382178, 175811394, 168039821, 921092705, 577259359, 923576057, 823618138, 17376623, 112814871, 375711753, 440544628, 37961951, 354701358, 204577065, 837988764, 995361393, 916856574, 88308613, 947072131, 760956775, 875798582, 857459188, 86625146, 414179125, 797025006, 806612231, 651921465, 517210952, 128953148, 588418293, 95898175, 338363133, 116150567, 408061854, 16453948, 67065019, 225804948, 766112676, 699603382, 228769978, 815054486, 578187154, 987395379, 986062570, 9795337, 889445247, 89974477, 169948757, 162928987, 381193602, 719959882, 860370267, 748106312, 417668663, 250872918, 361427859, 992820021, 621426622, 218933896, 87611965, 405823411, 898799603, 620432356, 786501221, 537548440, 439389607, 17356814, 451426571, 117195605, 359239026, 241851759, 151304090, 945012917, 147630085, 97617376, 738374952, 461981938, 315551414, 237168771, 716360211, 358852423, 573662317, 860712098, 699368219, 117383103, 654229852, 216211810, 332213045, 925424936, 65319527, 727825307, 496950096, 103743212, 296500023, 63264726, 443850312, 129005059, 934331257, 877078529, 99515057, 115239396, 607170056, 832923725, 758337500, 471158187, 442356374, 822263554, 251268858, 657629559, 822395472, 352375568, 483859659, 786911081, 385025771, 377675974, 797447678, 719271847, 35510552, 474222959, 110251121, 609040516, 461902216, 177577513, 638469961, 216306733, 322770490, 318127269, 933876548, 138921140, 724379278, 304814376, 457544865, 581178715, 902332271, 274562251, 400389470, 459302846, 872093055, 433107251, 875138776, 428724604, 471644528, 168406985, 395627839, 529023773, 492201484, 3978266, 243595567, 613288453, 822244295, 494735491, 634682148, 533611182, 778103258, 793646726, 749193336, 720501748, 887653824, 37296353, 795733982, 257017482, 296581479, 567683156, 497269281, 283747942, 202046574, 708080645, 218578491, 341683674, 197013814, 300199952, 15233448, 808989733, 483599500, 305466110, 325328679, 198826996, 10783101, 739455963, 113403919, 777313835, 924207958, 525411585, 215220829, 622283724, 373378489, 598185386, 2856734, 235924034, 663204591, 946958286, 288777685, 63149293, 918737078, 45818698, 596610352, 636041206, 36696525, 436199983, 606316949, 648777002, 455869568, 964590844, 121361129, 8906889, 2807218, 258725484, 187090079, 620351666, 331844700, 422181164, 54784472, 462961229, 757335955, 660084246, 842197592, 568443055, 893657913, 697204788, 331336364, 188509034, 320471618, 812265493, 104776062, 280160670, 121501747, 995450759, 23066797, 868740743, 843960387, 762499536, 195239302, 491710849, 850915931, 285401007, 797786880, 382667533, 551000639, 770149674, 842857691, 446403064, 52597344, 692276281, 775340299, 610681705, 446208179, 940864108, 126692668, 156920176, 308791582, 434344174, 501011952, 844456914, 468967409, 201773898, 75839026, 17238289, 227326601, 598534793, 203932394, 906394860, 252927987, 936922683, 344242713, 568825410, 145908274, 580466386, 945598081, 546880513, 610282776, 118102882, 453693822, 82494528, 674001274, 338989315, 936793798, 364950222, 364043234, 122834771, 559131214, 72637243, 456647572, 781548699, 81108051, 773297573, 381258548, 213553316, 696960010, 44453744, 512017743, 47853760, 910158741, 280934499, 671630292, 403019417, 77182487, 412429694, 848523748, 45198482, 970698647, 966259809, 820222293, 696654775, 179224957, 400936974, 811707648, 305593409, 934233728, 418833243, 291169283, 990952554, 505675420, 793021378, 495773998, 773104829, 408441238, 55823649, 194463767, 734203381, 817323465, 365719102, 572087282, 966872864, 702917232, 667476883, 1412191, 690930708, 839442209, 368112020, 194426393, 600304383, 546550990, 979464511, 199023594, 512272561, 139623946, 242091821, 579517753, 88727211, 509254005, 620093702, 677460937, 949712411, 102463128, 45911417, 846001458, 900763551, 740819468, 179375563, 213386601, 620797778, 534471096, 740900412, 261861096, 317893311, 222591154, 774283246, 817145743, 71840589, 530940329, 821091678, 809080281, 221563065, 861803865, 613464391, 449591967, 445541097, 254121683, 605759768, 55388060, 680385190, 702926071, 34766898, 355266127, 437824, 923974372, 279675745, 687568976, 683544618, 936675547, 949212710, 133452768, 730518951, 225136987, 359472241, 501287859, 977837825, 751160691, 296336689, 365246037, 473182624, 584689387, 917963845, 885794891, 817454160, 837976091, 493612367, 903357196, 105661426, 924783496, 336038748, 996391373, 484243702, 691300764, 456980612, 199522853, 605610581, 832438423, 159914398, 942559344, 330106488, 75960325, 859485539, 889447618, 367905320, 266885447, 873355253, 445936835, 99630253, 89181206, 810856301, 795810860, 61271385, 540001526, 888497490, 779179020, 247424142, 987064974, 461146232, 185656468, 943218914, 462020552, 608010418, 499556174, 617604023, 592301225, 586990404, 942901194, 496302981, 439511357, 787536520, 184869300, 544034242, 149068196, 729450147, 596269017, 883289228, 901551219, 846336908, 740399885, 89500961, 103823796, 791549518, 973973177, 612196170, 546931186, 781484391, 992522469, 544341846, 495316214, 767211707, 67853799, 107131554, 884741488, 272050773, 768663719, 644460256, 925253371, 247863029, 122892994, 774054448, 533904953, 84471234, 872657046, 548414192, 508597936, 488182417, 165409362, 159396155, 231707339, 993756396, 175231816, 218792602, 21858962, 8967700, 818690299, 730557163, 446024973, 879852313, 151557792, 106936475, 387270065, 12407302, 566000596, 102609129, 83906378, 926844975, 513809772, 876741009, 886860087, 116071150, 197769444, 763757294, 39606578, 889148359, 633886248, 933076591, 196181647, 160245313, 375818083, 211779770, 816000604, 431405197, 912863564, 879692569, 914362605, 104799451, 166627673, 42349992, 786743081, 402641137, 762450859, 547055886, 581045484, 864251695, 64092826, 83442765, 570996095, 230039741, 39986777, 404207951, 27734644, 895392387, 692079197, 728405760, 791575567, 163418481, 590907358, 63797651, 374243607, 327551165, 739638885, 941595716, 902969366, 602999663, 302720278, 324170533, 796957447, 771425713, 977752055, 35915097, 781283197, 143611899, 426192075, 465107096, 838582709, 82893725, 971844017, 627397798, 55044539, 360962095, 849829765, 504426719, 843754405, 609917895, 512479579, 159666341, 316485897, 863942287, 328512892, 270649683, 428497356, 627117592, 796161214, 544074879, 76573029, 663182678, 974716787, 131568660, 700390475, 933824055, 65716524, 76549628, 735176998, 118208072, 5233419, 11151931, 365135650, 134174234, 311550607, 920690308, 244750774, 770101435, 499404310, 309412934, 79178716, 29870876, 884937711, 150135167, 869011938, 941606186, 466042785, 100735782, 680241632, 75164413, 711289479, 163825289, 282584954, 249098300, 51834444, 716093906, 86653207, 25123122, 197221733, 597054589, 232755036, 44792103, 207785148, 452056016, 666588809, 276539189, 847492245, 239292622, 295863094, 497153525, 922914541, 937410542, 178761551, 290300916, 14455121, 312890025, 712959375, 785636398, 367084183, 56676126, 908179235, 243187235, 134704131, 643880461, 773674654, 451114191, 453319756, 908024425, 105106171, 363993779, 802482170, 953405829, 275057132, 18548986, 324860524, 313396563, 456581555, 953416851, 373222491, 515873165, 296266741, 527181122, 126025571, 351161475, 788341235, 823491477, 968686636, 673769775, 381523837, 333563859, 795635196, 904052399, 736722853, 476710920, 118875545, 22952119, 483080461, 62866873, 466822217, 815795246, 956536033, 235592647, 669105880, 185922502, 438537221, 422674170, 317482454, 660153836, 419103796, 859656855, 980994824, 764467831, 741593774, 16745342, 558529444, 761764772, 34835474, 244945486, 775077993, 801083552, 854691923, 17770102, 681780751, 588830110, 440785810, 333101695, 164628867, 273064174, 935691447, 222794562, 929729336, 634767256, 730879721, 817117269, 322062995, 462247838, 823291168, 588322864, 767507731, 355805552, 587826766, 420778566, 232175031, 475267818, 629264790, 343369476, 476490014, 670277547, 687215719, 396362407, 91548078, 949464667, 227498543, 586921660, 368065209, 296624923, 160683805, 120150037, 507681008, 967307954, 153459764, 882450498, 539107987, 932795660, 609565587, 108383840, 448238224, 95022708, 514639049, 984952176, 118630809, 908643508, 849533922, 715129530, 986747414, 807509917, 697325056, 271680833, 290071687, 822638052, 573583711, 649449210, 650908699, 642216924, 913531970, 757931725, 800292053, 295353214, 983560332, 447472845, 903204686, 360985472, 256918164, 736560427, 921034243, 200235797, 665052742, 151551687, 703139444, 536349269, 28036084, 762861801, 851962386, 208511400, 831135269, 81270830, 659810227, 800854963, 867200975, 113341494, 682062342, 445384924, 696604263, 326108224, 790041624, 911224208, 856438702, 422073175, 937730451, 865138195, 581313415, 821996400, 322329216, 656605500, 967837748, 627303260, 555817231, 80980755, 819269359, 889835367, 624456805, 699720348, 247322051, 207511952, 275833480, 636480277, 848318283, 269797009, 122198719, 505859094, 131628343, 19265504, 733132249, 991249091, 812170061, 895009340, 685881241, 213523368, 415897363, 942599760, 102123268, 851585630, 716926724, 216476439, 759466886, 406517323, 204856328, 961416676, 447300163, 661801649, 323598532, 662808608, 866851265, 580259024, 857057608, 209562171, 742142778, 921589305, 915027317, 507210008, 998149791, 918911911, 737008633, 634285329, 428500361, 325770205, 401096168, 281281441, 479329947, 470355713, 912131021, 722383267, 330263098, 745651148, 859361802, 92529302, 238985913, 889100896, 722513724, 253641468, 299965681, 498662847, 487290079, 540400509, 689309414, 362852798, 961916607, 460115040, 577258542, 635874601, 382256406, 253162915, 867799803, 702859528, 515637664, 388212768, 398975521, 204415356, 762752062, 404190945, 446096666, 789524227, 59099115, 839704299, 499371039, 694344092, 142847931, 66277556, 683785680, 906747195, 17255193, 502743260, 957278577, 895201483, 507037933, 431587031, 49872645, 956404777, 161513998, 527448193, 820099864, 234253767, 454799938, 227526758, 440291255, 528163738, 768264930, 442524774, 858391075, 810062522, 919469443, 770792681, 134853149, 776478711, 504313905, 257879096, 162644015, 712187114, 478839370, 363350381, 412269800, 547820650, 397136853, 936833745, 237623799, 593902769, 802089207, 793882085, 992363773, 157477053, 686852842, 761493005, 958429371, 760575427, 204260503, 302616773, 671256597, 939231258, 640518098, 222416688, 768405362, 812783351, 600202010, 607581618, 257006053, 365726376, 926245388, 204141422, 621767352, 97313547, 402551056, 82130651, 229679603, 764157744, 854089516, 104200677, 756602456, 984922181, 380420308, 505487924, 447826705, 373485587, 110415075, 666867626, 780878441, 477334469, 894715321, 381631171, 137905810, 428018624, 628819919, 985282226, 274780594, 246714696, 664886750, 741799719, 608380182, 218481048, 797644514, 599201585, 615503871, 125009360, 279879491, 779174470, 19977430, 512560393, 702528078, 403648617, 930876297, 624696404, 695694134, 609029316, 137579281, 751844501, 804183481, 799814975, 388185905, 933955100, 990624386, 871864052, 285181531, 268619606, 928402889, 37180253, 809448780, 24947901, 603079991, 398813644, 387752451, 106021087, 888972867, 541335922, 259133330, 373875567, 345085857, 162023902, 140205229, 21239629, 745742508, 130345159, 690129144, 48784709, 761231915, 382384164, 345121570, 964891945, 977855273, 235553846, 251562391, 228887740, 953442437, 287357782, 937238323, 263247656, 85517507, 150143849, 630174830, 133992689, 911705356, 815079398, 255279742, 680501310, 651752652, 853717485, 901357950, 161418464, 95915093, 671231214, 231339710, 742188699, 44834015, 938869515, 304999332, 786062701, 38330751, 321345631, 762516074, 693151421, 425474569, 561309519, 650730690, 726883990, 13045303, 656594207, 220227962, 397286509, 554896382, 346779409, 529566015, 925110138, 786206953, 332394006, 560401946, 168604075, 425168360, 87496738, 641222016, 815741960, 725524170, 497428343, 963460103, 91028633, 910215416, 144551797, 828056934, 36581954, 912895109, 179989928, 828954969, 788509011, 537362847, 719165542, 390258558, 605504355, 541415306, 156226239, 908016911, 55512255, 934457787, 160976749, 773359968, 799577863, 842687823, 156474013, 868668199, 770244393, 412676495, 282392542, 447482263, 556496990, 687346898, 449911535, 653898196, 689535790, 587288523, 699613860, 237984561, 99558943, 329869654, 238632674, 681681313, 396614068, 941674450, 726358160, 765891519, 414694786, 19031705, 858631351, 807393795, 709618981, 683222192, 320805344, 855722640, 483017292, 922841779, 278726616, 882689882, 114064464, 347299784, 298845346, 828458633, 252409491, 309826728, 865641320, 723081113, 327088692, 451376511, 851648179, 39460281, 427331191, 663854921, 371495202, 77613739, 260078649, 87577273, 845090336, 738474731, 993867292, 173509328, 377340241, 69453442, 564998905, 242325693, 524545710, 758853865, 862648493, 41653423, 817788930, 634409881, 535787283, 837411106, 335301150, 484258464, 129650271, 937872544, 105556442, 383236756, 937994611, 940016215, 128562534, 331475176, 826948308, 150942328, 852060920, 10003293, 925828525, 791853070, 184842898, 153873167, 482533201, 732290867, 132527904, 792338956, 78649508, 135772009, 913428310, 198148674, 366985442, 247071999, 243913742, 315237675, 293682083, 29841006, 923119101, 259197694, 894884201, 863128774, 337160262, 405626618, 520735534, 365814699, 516456987, 703653696, 930913965, 231949164, 705611131, 25464482, 632148910, 539790326, 899507911, 45656858, 588079396, 63808055, 711399530, 257744587, 535242426, 272291832, 472400372, 556520313, 893775279, 885827767, 4870049, 39322415, 259369456, 724464884, 402422844, 859809556, 219032413, 354933947, 235893049, 54488951, 728363709, 769913368, 728403709, 459811713, 707222466, 464715763, 370513428, 406821088, 944004244, 538840296, 332049093, 902553817, 658555925, 616437257, 259457310, 27650951, 191057994, 858155505, 486286709, 664240757, 237629889, 423559740, 800753941, 16539190, 137786576, 445752269, 227318743, 949971549, 411503180, 984101305, 631248046, 803212385, 236954125, 826317355, 554438601, 325187317, 394329212, 276636570, 696702275, 106388317, 130165266, 420713372, 162373174, 27248540, 551706134, 774166890, 223199751, 968303930, 499273997, 595319328, 32553464, 983629281, 608270930, 115641316, 544349946, 446677581, 260569555, 674606355, 116212881, 711595691, 818092358, 237288819, 560402765, 776424324, 909169994, 269788184, 117142044, 926295801, 982481773, 223332285, 272885620, 20077238, 260905099, 780289572, 43853296, 723252136, 495407515, 65557156, 539142489, 204062040, 934819968, 130920309, 769431599, 572565532, 527260735, 988505053, 844121970, 432791935, 896076663, 970495913, 323509484, 747933495, 139590954, 675796587, 260849816, 213417719, 99793891, 919704606, 262544960, 71328725, 158958220, 91831833, 146016852, 207621913, 545417549, 237168835, 449597384, 633075469, 480383147, 7295173, 989885934, 869101349, 10500482, 789420944, 565191619, 616094641, 803364148, 71742573, 531192608, 555762263, 798876640, 585568712, 111738034, 253122385, 556869718, 289351834, 568541448, 433440027, 755179651, 408232434, 247629562, 143754546, 153127201, 156901137, 787966300, 690485995, 127990825, 818435796, 669952713, 985122027, 135315229, 124917373, 138840840, 691311343, 377010496, 414608141, 631028542, 207924330, 780674561, 261863200, 612574258, 988888343, 463805325, 743520923, 289937585, 11773984, 634618877, 272014981, 698915189, 863654967, 595928081, 32495010, 138800744, 398587519, 623366663, 834878690, 182471538, 303274060, 379600239, 732452467, 625868248, 972684142, 710406078, 581049653, 633054423, 804574123, 507093944, 712655021, 590589729, 622293920, 477686575, 484930536, 407203001, 860263086, 805825769, 87867543, 144373534, 591872920, 339472771, 190934084, 483243709, 401965556, 401328558, 51940813, 229804257, 427875052, 592301247, 559592111, 141003689, 33665881, 542595633, 890945060, 107598970, 116130486, 961585318, 737702959, 35910831, 864848800, 166628798, 153392950, 126587201, 520738710, 914218326, 98013769, 836930928, 700188347, 548560752, 394263839, 429304939, 339965283, 412605670, 264454927, 334537714, 462357289, 948737569, 314836043, 925967681, 680871278, 283248407, 451243810, 186124525, 649682017, 506352903, 832910630, 820322040, 369779213, 68363675, 406989859, 619913342, 251384832, 163307768, 522744822, 199935868, 559865566, 314936409, 195856370, 809023316, 929580840, 518508437, 664452890, 290683876, 378166473, 887558914, 458264966, 189337908, 751693124, 260414707, 312110725, 213197654, 508728760, 908504482, 248569505, 498930585, 408401834, 453696233, 221278409, 182917150, 97342540, 132697772, 805653410, 638379784, 241368098, 722572732, 110792839, 292415245, 897763521, 256012363, 481218043, 163707907, 980860710, 141013127, 752663799, 325844637, 346318063, 395753841, 866375396, 444447786, 17233007, 2105645, 426092943, 365686263, 992977505, 112648190, 527651470, 226547289, 254856105, 669360424, 811404545, 174223583, 932341269, 686641605, 359485584, 160125661, 300889006, 674698387, 101298933, 749169858, 641741781, 510178618, 793033167, 396161884, 495566705, 934452067, 218054217, 280686926, 800448135, 767367540, 728347385, 120076992, 629089455, 516948674, 349598384, 880828279, 527787500, 160050883, 654900180, 275535090, 569052771, 273593831, 22475410, 45189067, 626587842, 251090890, 102558603, 656815430, 593613234, 191141559, 126845617, 822093634, 872204143, 138688701, 95254528, 747946176, 71289893, 970482137, 17003999, 708491687, 820718268, 509291292, 308942114, 915462377, 265034190, 3325192, 400394725, 326887936, 640343829, 94568797, 386764442, 35974004, 318903272, 452620094, 779070114, 759188303, 860953934, 6773228, 745143312, 17714571, 236711340, 309595481, 24104769, 293023363, 277095026, 733115616, 330379408, 320241810, 704286824, 2929387, 44110033, 100039216, 224464930, 87778587, 684816488, 190498132, 996350296, 170516197, 430198657, 815670922, 659590939, 553978805, 342696091, 45605955, 981763043, 620850670, 354482904, 836438256, 879274366, 418287282, 517776853, 595658614, 714316118, 517395531, 221600075, 682816936, 153760047, 252601515, 643075364, 982058901, 887893382, 873153481, 885598323, 857559909, 838483456, 836767811, 571649592, 829531460, 354876579, 236915556, 202342280, 307463187, 540715639, 264624167, 626992372, 206853929, 564529580, 801957423, 529890120, 103279161, 925908326, 106002422, 563892621, 451546653, 640605427, 195383787, 356497348, 841643901, 244411466, 351269459, 869290103, 659293512, 875561516, 877214069, 598078695, 597788238, 995083991, 772285192, 231042397, 898276978, 718154029, 644585077, 773015846, 559812649, 216058844, 399191978, 507888298, 578065487, 812953185, 609206394, 502679105, 977545397, 868135747, 686225106, 427480133, 920046391, 103756546, 980117183, 765893717, 368029247, 27773694, 568728912, 579189561, 315107033, 927874153, 304764408, 575482672, 15617110, 5980372, 263056240, 530805909, 209830899, 841065257, 673158598, 955228016, 764691518, 846417871, 429745951, 654126969, 86664008, 574548593, 416009408, 27795022, 118272518, 644105994, 931521238, 456275234, 75899384, 193557308, 778420457, 689165766, 942155854, 447859650, 890301054, 577915859, 438089560, 183635620, 574722456, 845325911, 147662777, 603783982, 956134914, 891530022, 295450047, 411350110, 646949110, 463990574, 679885741, 45381683, 20661115, 253282356, 910468648, 114026297, 750161349, 604518899, 236894378, 304154224, 517476559, 442960075, 760661822, 49101356, 453082679, 222637801, 577184442, 942681960, 423093914, 524575798, 66406294, 428128768, 66780223, 852568340, 291700875, 832492448, 123484984, 794743954, 980928289, 375521515, 265258692, 656430813, 15028290, 90000328, 777125224, 271891290, 198278834, 638213831, 366488161, 729560118, 177658583, 560380748, 910412360, 690580998, 296757440, 765756970, 229674062, 993065491, 465104255, 606798582, 185746319, 846162746, 366223540, 730156215, 534782640, 555440918, 642214316, 625404957, 8276999, 245698867, 541430583, 245031958, 657851192, 677117308, 842633501, 59487354, 143688149, 895384769, 661578812, 411515394, 423714587, 77923856, 792951650, 534255440, 172983252, 160039771, 188856879, 64372028, 199638198, 894691198, 736773362, 372648998, 223403667, 485085317, 211944777, 554832273, 753065857, 906462502, 513820711, 537637048, 325609854, 318445437, 50368605, 50711134, 875504429, 571209028, 564557384, 790959589, 324317438, 18641472, 958412919, 564873529, 2252269, 171152602, 332486514, 861974017, 405702002, 56733736, 365788862, 437011405, 241894037, 493375642, 848817427, 351599741, 526684284, 386282502, 816618329, 474519907, 279001795, 85000623, 906626887, 950526466, 674547701, 473955870, 972788282, 755372768, 588853832, 637509877, 861592, 833564774, 596474260, 901748253, 14501539, 216282230, 971154789, 23755635, 242435571, 370634999, 606602193, 142367437, 274224850, 268865017, 643291846, 288516250, 974213917, 65116554, 773970964, 185715986, 717084507, 440744734, 727780059, 316321661, 879976946, 564501068, 731457918, 204227560, 67004761, 69805206, 994574899, 583423702, 317306557, 449386586, 277937831, 509393576, 837953521, 456003231, 367376397, 489369100, 173468485, 556858707, 704166405, 877818318, 651154449, 657833045, 503973455, 923984801, 548817832, 310280910, 621689759, 8137729, 807345069, 525580396, 416445075, 113741183, 597452935, 988577864, 444024866, 565669725, 644384067, 766602784, 651466568, 715862517, 156534750, 797277577, 259910059, 759070212, 936612718, 225509525, 824839051, 52498637, 735501346, 90311656, 246987625, 918692057, 722214920, 674057369, 868044017, 653593686, 919125602, 361960347, 146582545, 97365364, 336428671, 487459788, 760244561, 326601146, 47344543, 815505356, 970717165, 122548633, 93914036, 987311768, 145479951, 608103792, 384053346, 318202972, 27209517, 570600042, 560712363, 135981302, 192013259, 193141954, 147317579, 643271035, 333433867, 620003413, 846647576, 981897351, 837401803, 620494991, 787284302, 505822026, 514560888, 1821806, 271977650, 306684960, 136932422, 342138412, 543840161, 210408656, 992013784, 326711390, 768571227, 82028917, 167940358, 540061548, 209820562, 287902047, 999710296, 978591478, 962694957, 676133936, 264933834, 367470591, 643203411, 132451995, 171365593, 442308854, 270757467, 499294064, 959386524, 341793477, 199875524, 385770149, 199041906, 485059103, 862749994, 60646999, 437359556, 409183834, 366007344, 890579141, 146047815, 682949333, 347506225, 568529501, 787655933, 588008445, 238376677, 635850586, 62181093, 787528671, 371064831, 404877676, 933773876, 243709230, 317605114, 771699493, 497201554, 247651580, 100636089, 233275580, 662409208, 558381314, 898006823, 724868055, 70232050, 686022190, 638197634, 92797840, 814022754, 209097912, 912451203, 118911201, 768261550, 269872186, 616955236, 455019174, 406871355, 237053223, 289956365, 979121202, 440298868, 251220209, 756075944, 362345487, 328284664, 7162003, 177636958, 227646320, 387291673, 365388444, 674120056, 668911512, 207639997, 330962312, 416602802, 530868778, 949994672, 137605808, 547795151, 76839608, 916403776, 312185682, 687742349, 706890446, 802155033, 560064324, 598024044, 619973646, 970671570, 868279140, 912147326, 372987547, 298699453, 173401359, 321689191, 91789768, 212215955, 102356336, 661808690, 795026910, 537367856, 541120037, 405829478, 358667881, 656125462, 206905294, 483352065, 202304636, 454371712, 297359571, 124013855, 261141423, 178310019, 82252212, 434483400, 95270367, 995175028, 771632509, 619279370, 122791256, 196412392, 29834371, 140447596, 350826282, 79197194, 642561261, 648030740, 541177729, 446914918, 660790466, 704953913, 671369634, 515793718, 92419761, 941774852, 749238829, 472069351, 95065896, 759412792, 375574065, 339574676, 357571430, 72689256, 540044409, 626184039, 235660045, 852745653, 901884731, 22974673, 349440312, 536209213, 628910357, 54376137, 337758062, 595500095, 978171002, 339140151, 378212376, 912857047, 519393014, 280114364, 434045987, 751530876, 518243282, 682027000, 907153607, 531704457, 21587993, 849626515, 636314656, 916402213, 317147506, 662103302, 357290312, 65946550, 11233318, 578349888, 163210011, 377300585, 791968094, 168889513, 27726428, 46118124, 274133957, 745292128, 610601860, 297002275, 522933229, 923304623, 519323016, 316049735, 965238173, 202430773, 196661392, 355220140, 476692501, 868034019, 90588917, 785984344, 701431458, 947733453, 972104479, 538440082, 406243331, 523275546, 223116102, 730196050, 905447194, 655660102, 575901298, 871570100, 750455576, 792331297, 740801940, 906200735, 918434381, 170091764, 89215583, 833809127, 117070850, 51648198, 633876522, 445411572, 72136155, 513469653, 499389169, 633242521, 655942606, 365549785, 60487037, 330057305, 174689116, 849145240, 96533623, 749278605, 777582319, 860980524, 517760999, 17026340, 660558324, 325108476, 533839273, 695132353, 78127079, 328939731, 832221669, 723910405, 533058992, 481603640, 96065116, 793448858, 221143400, 496779522, 120334032, 493307184, 826002019, 655748044, 679447518, 304677678, 262342367, 816103460, 413985673, 212608243, 190585225, 894870071, 68898881, 149509937, 737436692, 81978265, 354799200, 627832767, 577022239, 737860482, 812283496, 174088487, 317010943, 345449137, 67336888, 110777919, 370042394, 38972372, 137392663, 543887481, 123896461, 867173825, 938776725, 92311852, 708576229, 231649291, 663573741, 101287292, 567502326, 860011853, 99643152, 44161651, 810660047, 62521305, 169554035, 794998903, 644478440, 585335529, 813985942, 618007946, 575778716, 725673846, 287824162, 677760717, 88527000, 724675733, 613880732, 852439936, 920379078, 139798806, 365285319, 324080123, 527918502, 88999212, 756091346, 881940662, 202350405, 103872479, 7147888, 928015531, 581450968, 447914977, 860286322, 604246213, 67595060, 808422878, 326976051, 277750346, 98903213, 292088139, 349212813, 655623588, 118094686, 767467067, 471928289, 720714047, 566730109, 699499609, 209406319, 51662575, 815765325, 339633468, 936069633, 445338441, 276618888, 945302354, 891772301, 622978520, 769425140, 58940181, 573555954, 981671483, 271743561, 875922640, 399156438, 600925094, 383704080, 563652187, 8249996, 603588985, 265934055, 794684241, 799191856, 717096532, 49892253, 878539250, 699926581, 88855125, 258993959, 6305548, 605650523, 661916677, 503100200, 955296498, 406640849, 747464217, 60505407, 699062378, 495355057, 834258057, 101707327, 925956524, 841444633, 79406896, 769710257, 339760974, 324328020, 932819585, 417277957, 493270931, 564522341, 607101745, 232727928, 76478342, 60438927, 113704695, 335631059, 573470156, 776001642, 835283131, 110627921, 199506612, 902937145, 320967206, 312742001, 432988013, 840446518, 313287911, 613112989, 564891928, 846558835, 649501160, 560925569, 39022690, 932599356, 662491188, 850826567, 624439899, 674965258, 643689409, 789626031, 699152199, 299793502, 866891710, 663158468, 736387700, 272370406, 182930863, 761633044, 941311690, 416151442, 222068288, 738399678, 575615548, 324308648, 14299180, 933774119, 878359557, 124092571, 120509981, 853112841, 405254444, 65246504, 646781691, 854286833, 905022023, 258571851, 773206784, 212683208, 310394939, 880178936, 892380689, 455290582, 476628057, 72045697, 927172906, 476743324, 391333543, 168142430, 776695504, 132276285, 659235631, 1660691, 135192494, 333543041, 864417493, 606763396, 685475429, 423218350, 368209821, 103828860, 321671631, 137979476, 316281973, 372404462, 221832205, 410181624, 804610874, 516785988, 389342175, 654755392, 523995878, 113811307, 574556074, 185091874, 402418757, 346783221, 397316426, 580581435, 550105066, 73756126, 587018875, 258017538, 966704560, 694265026, 679982379, 275466592, 151617780, 538309898, 586747368, 283940653, 89533331, 45885817, 591165142, 305500955, 870161754, 322934498, 239054962, 33513902, 60695302, 519553288, 358130973, 112748068, 740884935, 902953155, 91948747, 707461427, 476979330, 842230230, 321337851, 900640158, 502517278, 996080407, 422060503, 404898112, 365500870, 5535686, 751931467, 948848412, 653978539, 166691995, 497484700, 767224040, 491214105, 384824574, 238565678, 437579108, 967883024, 524514732, 988835501, 868128682, 735830551, 715761606, 286953963, 877379049, 548707652, 710083727, 162608999, 346902960, 417279210, 819391568, 451625698, 483741214, 19170629, 651575336, 715899471, 612274865, 510514369, 839676484, 200835607, 668253641, 841807491, 329295207, 714955169, 973514453, 263686954, 936723861, 134864630, 468250441, 470841290, 956683544, 102342139, 643485964, 535412987, 330812579, 157765249, 259098750, 669443979, 687958966, 708291141, 604412176, 590218838, 12525062, 652025347, 600046341, 329176886, 354953037, 203847451, 784952871, 335192310, 832399847, 408605999, 875678746, 736259856, 140320421, 200244811, 826590541, 670938128, 699200210, 343982539, 196486209, 581192782, 812644140, 875011954, 533700755, 959853373, 686355120, 356074104, 622394669, 165603916, 578265424, 406088363, 270493902, 408333238, 138259384, 776068613, 186541338, 795697167, 495864294, 835048399, 25270480, 16728807, 3542983, 917503867, 589749844, 241593727, 947896329, 29607492, 849438666, 875178093, 444204823, 738146435, 743104750, 147644700, 411039093, 499510609, 521734977, 133120889, 726799633, 571614153, 436293035, 725000654, 863870009, 800010295, 654696624, 803504927, 102508526, 684533506, 381400722, 859894188, 247957929, 489538323, 366927654, 961389106, 731098552, 117945763, 914565853, 284593830, 319095613, 273371762, 124793234, 590183089, 687287757, 998696237, 618878156, 984149146, 67976113, 792766731, 146733858, 814478380, 125807308, 917451246, 618310510, 738697137, 131901073, 164254206, 776107800, 774708417, 652939718, 852689728, 650598172, 757122686, 36665763, 851979581, 785750694, 674531303, 52565541, 565124311, 741232755, 725858393, 687824099, 878601085, 631137259, 546792812, 227714474, 540825143, 341399191, 261342176, 60860319, 223437763, 428270651, 478271050, 720003651, 116140079, 746833466, 504479778, 824883970, 93252012, 782758508, 67472002, 810984473, 904764835, 814297003, 277780577, 532794311, 978784004, 76519236, 792751061, 412606098, 88085456, 225708749, 518023448, 709147244, 48970907, 402696424, 29662307, 714041430, 661309800, 261979299, 560539701, 886901872, 340741900, 260136327, 89740707, 51946123, 803956810, 753581110, 748144783, 525948783, 881918154, 148420125, 239891659, 896814208, 522613695, 32629159, 779167631, 825791865, 580786658, 584652801, 165951626, 184242026, 695883387, 79479869, 916696287, 920248272, 405060823, 218733257, 901533592, 701165441, 988013558, 488214769, 659025294, 955273087, 734035369, 482529496, 708312846, 82590689, 416569634, 532144491, 141709787, 457357157, 259372602, 765336675, 904126400, 139892099, 299791216, 581301488, 321436696, 489508663, 956339656, 243771600, 807978899, 909941990, 438098549, 203076013, 195128450, 677691312, 991946975, 36143080, 204712120, 723331028, 905605967, 141204344, 247599990, 407953977, 498420061, 244012781, 129697233, 420765310, 436833627, 936194687, 486762705, 393699712, 807002269, 627209985, 506943161, 445352646, 457846530, 2736100, 978664343, 792285921, 398018394, 569411309, 776705632, 893776722, 248901464, 891853675, 295586751, 124151353, 562251544, 451577779, 131852516, 912461818, 268057502, 792587385, 622885222, 961026341, 258670710, 755197155, 308816902, 570754213, 224424390, 918703980, 661840725, 651652864, 852407466, 138840618, 956611839, 97540371, 717550681, 78780525, 280709315, 722621730, 517294797, 338453170, 764590527, 508108235, 34249587, 617710952, 784471734, 843744397, 872877562, 929333059, 881890140, 248544883, 156318150, 353173230, 191245764, 916757863, 673494228, 571756461, 515378021, 584010073, 707817062, 601166474, 1561834, 772388198, 832519155, 445694857, 221534863, 666378018, 306855398, 474283765, 475035760, 542875177, 853231185, 690451545, 4458614, 640238276, 411595329, 745678586, 708093763, 819594145, 932053203, 385698748, 300710100, 310253510, 289092200, 612136228, 348678200, 749278433, 308541833, 338020365, 718669511, 46811924, 257801158, 629168951, 69888617, 646990019, 204126598, 871877721, 574904300, 750546803, 253425792, 48176646, 114596757, 913036836, 294511390, 864443525, 680072677, 818081282, 105430523, 329540951, 764366340, 113559013, 597794360, 410162560, 201107054, 879542732, 716232817, 22436955, 941897147, 590815326, 706530461, 281818967, 160317731, 187638948, 687615448, 663030600, 596457904, 110205612, 337111917, 190018659, 785201344, 102230950, 864488265, 229765450, 731915661, 64285948, 781701385, 91133116, 265752236, 450527867, 640908235, 221854303, 669723940, 6483316, 443429555, 60634241, 164364562, 132139249, 360423136, 530081172, 624877738, 737669957, 868416952, 61569597, 761514663, 996511706, 756079110, 950620897, 181849571, 956492415, 274471083, 36545375, 752441733, 511494577, 473712667, 326277127, 732438079, 247894079, 456525970, 800716098, 135593065, 535781951, 120266337, 623439580, 520111970, 477758236, 693024014, 894474188, 168388962, 978024688, 337702873, 262075767, 523634696, 474780829, 752058232, 632911431, 653102949, 294256785, 183969713, 385309445, 743462612, 241430795, 171185087, 431274935, 326719437, 632047571, 113899787, 672500809, 324127290, 677934332, 138145, 511014401, 722048829, 688632372, 804250195, 131664137, 720530631, 536619756, 463726440, 421173166, 102820251, 361633322, 372732383, 436067034, 114066025, 946195539, 70282456, 664858958, 597471141, 608059243, 323356278, 89985184, 933000169, 332668858, 64319580, 870453853, 307345885, 162247309, 340507795, 915922572, 377767791, 858284924, 169746134, 322959139, 503597143, 338316522, 689972756, 363732903, 483040850, 175520171, 77825594, 457260845, 934452967, 242305795, 347660426, 354186087, 70887819, 700271049, 237314403, 402573302, 641218542, 996544578, 467448739, 41705925, 512163137, 884036825, 423849729, 156442430, 730940501, 547360188, 777393233, 295235074, 342140245, 486939880, 990311551, 524123563, 12507612, 473173398, 771285009, 869707132, 775198200, 727986712, 35346947, 833445560, 602869394, 265728613, 701602572, 502120956, 178486159, 511557858, 221245662, 638813492, 571807018, 846522812, 799011176, 244665606, 973718101, 730120647, 453501184, 654592913, 773803275, 992516541, 296345205, 521841892, 281084027, 629433584, 340478675, 259561268, 989579840, 392931953, 454946589, 171434576, 552040070, 665787723, 990037513, 910350674, 949312766, 791845959, 489215192, 888847429, 223037973, 440534778, 444860674, 798605886, 384037204, 337425375, 615092430, 153127370, 600165187, 276789982, 431401848, 897355133, 658741456, 442746334, 293271422, 589220875, 359438729, 820668272, 858749573, 348548530, 593141541, 498205883, 905904784, 365480910, 968864399, 379694539, 880973832, 33827288, 33559329, 876820086, 755812006, 721099564, 26443199, 519532710, 762175970, 295252429, 524254248, 511406147, 913564643, 397611965, 269305284, 875007974, 570603921, 62233689, 275779472, 961758665, 831875724, 51889693, 173048031, 387630133, 422349260, 187763246, 303676060, 466257137, 922581953, 532725408, 263793576, 626659290, 105190847, 256745276, 378980506, 6347156, 324086627, 513250380, 587852461, 907531969, 867365379, 959425269, 737904321, 544343276, 917358002, 988356456, 79275853, 76770294, 532470166, 743521212, 943454472, 125441412, 431076281, 407377714, 492954771, 843102000, 640971420, 325387977, 888604364, 615997657, 34291435, 533236330, 80819995, 753023782, 912189995, 541175269, 151754262, 96427025, 728611375, 895053839, 748582547, 71919374, 372076022, 405114210, 43887428, 242899707, 887024772, 563996213, 158852893, 418349105, 533735719, 59445805, 527373799, 663759584, 763866410, 392538047, 640908369, 147320923, 444792578, 860036222, 106303011, 210898262, 723427807, 347137869, 624182864, 9652775, 329422022, 910491605, 787808461, 570440450, 898659991, 162878952, 268976196, 268090808, 449699096, 869389157, 875327979, 461686957, 997286400, 681360029, 624959963, 350418450, 702442286, 418870013, 876988295, 537512349, 784413145, 957703809, 606054451, 970273117, 731074824, 311960110, 551759776, 709571387, 905665792, 488851330, 106880356, 612384418, 591079437, 10020007, 159692886, 557823756, 341422799, 454223178, 487565143, 364561478, 271583069, 407010306, 133065881, 770317891, 434488259, 782639801, 561467622, 529807007, 914426973, 220051677, 425994194, 885360454, 22811002, 408096257, 831054822, 68200500, 141166928, 10709569, 202562255, 519905026, 688945192, 804184329, 184218580, 233920201, 537652725, 713415214, 494021949, 649777259, 828187740, 530092386, 47901878, 691436995, 213485665, 605558056, 230088945, 118299821, 744594082, 982322959, 759759296, 685523078, 484335543, 263076650, 254395399, 579331518, 705338661, 18459473, 762573986, 477551280, 511503175, 542139582, 648292357, 461007934, 763842583, 347220569, 3564674, 808378463, 912550086, 544428471, 598330098, 773540462, 43582943, 625009750, 473481907, 39769223, 402985304, 515875734, 983148542, 497487484, 82225021, 753915624, 143039101, 870688496, 204178303, 943612831, 998074457, 107077833, 84673658, 451419090, 66213349, 213701760, 442810049, 272848490, 492052934, 905119303, 394676650, 390774656, 483664772, 529424987, 882838538, 367629784, 151536927, 516658476, 977502641, 793047961, 114586086, 98669845, 464828063, 193127734, 851945178, 933198837, 546877076, 26633656, 295754720, 514025900, 89880701, 684523995, 339329253, 295767827, 433367074, 613651563, 580102702, 109424756, 721342651, 290952929, 574041178, 154577334, 129808435, 716090124, 898768967, 674423554, 719497348, 19246208, 421641833, 26772714, 200780604, 758333230, 294351100, 883675087, 976555198, 297658134, 915376239, 765099167, 572595276, 167474036, 858119367, 454401184, 943995546, 808193199, 259475591, 32600443, 590079882, 701276662, 41022351, 579306069, 904787662, 463436225, 140347591, 183125249, 899007093, 395260358, 222183093, 55452492, 813363279, 61081776, 759080201, 763424226, 275285936, 207711574, 818752723, 231277172, 13373331, 56179912, 136319728, 518336843, 590320015, 403437021, 78940624, 191179454, 405033425, 488286155, 139315447, 641232292, 220596045, 220106009, 471430685, 439027307, 249899543, 910260855, 364926186, 994579482, 704243790, 763444443, 9700263, 469789722, 29053198, 413802891, 204546081, 889812217, 728411243, 173794494, 519955572, 704221020, 184340119, 590196841, 947640658, 936025337, 78125058, 291595264, 548647211, 502954398, 306704710, 572904361, 521594859, 447623689, 304602016, 13051706, 391691255, 346154342, 943169948, 596419708, 397015916, 422753555, 395877473, 716677364, 117790402, 516501853, 831320349, 235121973, 58012494, 890328184, 174750143, 682055630, 434930600, 700013125, 424830951, 845428620, 449652421, 415292910, 148626172, 360727851, 703437040, 739711758, 496427560, 738686665, 889237179, 660971676, 760651284, 471341857, 489104276, 290369496, 164933815, 121643440, 765520684, 333964830, 966614157, 811877503, 929366863, 62810929, 368159974, 834492631, 555386714, 351113092, 932811793, 972353919, 720590500, 527538503, 683790128, 214697006, 154430808, 313581461, 386843695, 790292550, 959940200, 511815888, 247410563, 242715925, 182372722, 998927945, 346572902, 480430887, 653287452, 894428463, 85285340, 813209607, 776505487, 650246801, 130714856, 658790537, 663994563, 483197706, 75543058, 994293091, 611388761, 416673040, 104080768, 740771548, 102652064, 940050547, 706177364, 529114811, 408343613, 362960372, 250552917, 556956188, 773555775, 460704506, 6407027, 251214177, 891772438, 519343633, 910581483, 43026318, 894776829, 379751227, 974793501, 884804045, 734054238, 28383983, 939771354, 989132362, 742282999, 308902347, 153503831, 32102025, 596687103, 88404659, 306751740, 212844343, 845325830, 522510191, 800647612, 681007524, 264822147, 484163532, 109199396, 116124926, 625227854, 931551851, 808137053, 641006024, 921899582, 968962168, 427458532, 936914840, 173729271, 634152973, 410408525, 757216825, 984747090, 413625212, 510789629, 603151816, 919971121, 344157624, 335158708, 986673351, 527867743, 700107082, 535596142, 110836417, 267228090, 565229923, 40687025, 538103915, 816035306, 448200968, 163980952, 89193680, 921385082, 595362825, 287187620, 798495843, 489307117, 714494809, 917303450, 558710860, 673012640, 345579877, 654812344, 984551703, 149505044, 615162666, 941703950, 780544321, 201348481, 804506090, 883464479, 314933342, 627936096, 672952267, 789339530, 888781889, 247268791, 499706329, 768041020, 20215919, 253141465, 162882232, 512856810, 527963015, 137033393, 279398135, 538296929, 286728564, 995977216, 188788925, 433815111, 919660176, 197822900, 764272553, 749595701, 148318783, 295493353, 848238545, 38829597, 74150916, 877586986, 414425990, 55519318, 963833045, 402238245, 537853309, 400110852, 769847212, 57223655, 356771224, 495922509, 86172799, 906696167, 24475545, 66567021, 335560142, 127134658, 95205132, 957083481, 582476730, 551360725, 443614460, 805980803, 677735142, 703015294, 100212600, 645038063, 860827467, 215395267, 481128436, 626774278, 802949620, 373195846, 719831573, 755806410, 539157670, 184786276, 673647703, 22281943, 226276161, 814919089, 678933494, 269308281, 949935064, 710319123, 974909383, 934083537, 354650632, 179545293, 339519569, 238776736, 666339713, 89548253, 338520980, 577993804, 632754197, 385944336, 134491381, 811468214, 732123800, 299686331, 451574499, 804871435, 588156519, 373728604, 538717383, 576397829, 304946573, 453295690, 381544407, 125350419, 399571512, 702630901, 318630855, 651602950, 270811948, 839322486, 666045334, 709653830, 509532809, 613641554, 669300751, 236667899, 740644641, 649869769, 548753811, 391306783, 752508496, 928429390, 802537227, 624395075, 974703729, 959998189, 731868494, 49167350, 701936928, 745050719, 891670277, 311977112, 878305922, 980231276, 876744566, 7289449, 327700410, 252237090, 520806456, 215041016, 695629105, 877372835, 902163432, 647338455, 500077322, 927549207, 2359048, 389529886, 410908744, 973982883, 951166245, 245797115, 550849982, 497640690, 266352193, 407495107, 161338469, 882577414, 355637977, 420272005, 221837685, 177564360, 774432181, 695243929, 386377197, 386203719, 636578948, 62948625, 587440028, 687106019, 654706809, 946529019, 78995154, 26203674, 674436383, 819827463, 249748456, 404408914, 327088867, 845708280, 233357690, 784275856, 900015410, 528783923, 210275217, 357350317, 456173713, 414841663, 210158051, 602950508, 685957249, 387924378, 486428542, 277456019, 168526776, 150569855, 923259352, 223848621, 406489191, 963012756, 196027969, 353942164, 58990168, 928709490, 232266708, 191768535, 659535917, 432845083, 172513289, 526541315, 135078467, 904898709, 815541376, 152314230, 973590310, 312192598, 221571827, 631653052, 662805632, 424343372, 864725921, 307026683, 763135946, 749419211, 5345470, 315573570, 712027350, 36210652, 783234809, 742221784, 936980351, 114815016, 468543229, 391489917, 79795198, 948388959, 345907238, 677867861, 335010306, 31105341, 909173706, 904201563, 213806860, 803628678, 655777775, 470576094, 247365135, 727855014, 617835592, 500097249, 136571637, 694687767, 801031800, 60711766, 613802332, 793011519, 925780243, 242304862, 471902508, 110202982, 826238418, 174773870, 897372465, 238708073, 415821866, 155976922, 600354863, 340941852, 761188956, 964151125, 207699658, 285999462, 417793361, 842982771, 466049831, 973425874, 234800447, 873436863, 538144330, 282138918, 921523809, 889219190, 905201854, 516241796, 961938724, 713362339, 836123918, 906569178, 208456058, 677564357, 185994071, 722236035, 698014587, 224147777, 976847473, 385135093, 597886742, 128159082, 613938237, 305888262, 910663643, 151588061, 505408779, 433124830, 848975079, 618956524, 602086044, 344109151, 698307056, 292862150, 213529841, 67050221, 873688399, 224852835, 59334136, 73549060, 115471741, 435592358, 116354669, 700965828, 182307880, 474404006, 727048699, 706574493, 978169876, 578025784, 533778441, 853607546, 427038672, 907121791, 452770648, 559067851, 29556983, 588332803, 439261548, 527672958, 340907675, 878918065, 144775781, 135097511, 833029823, 142180076, 781037482, 423699560, 788988345, 98673751, 511267321, 144412791, 647860213, 993004553, 137736872, 828598136, 211807640, 366116871, 615706166, 204113500, 348167295, 476742520, 87530892, 168469180, 739330126, 125834481, 464512201, 17967555, 41046943, 903973105, 79453975, 402326197, 674054020, 626034261, 809195061, 718407907, 451981733, 336503625, 16182622, 315351635, 754136045, 858615191, 898396563, 742576368, 651157887, 496996903, 529868292, 960099282, 20150981, 421084450, 651588795, 901003273, 955406631, 634468757, 212862670, 237863992, 994749028, 655750146, 263557465, 759646715, 407224295, 413804370, 884236660, 596214627, 91689609, 542168995, 481875314, 372241971, 254209364, 783860766, 222989076, 450914445, 546741198, 304845829, 998909898, 456654815, 188891120, 412280822, 460606113, 269887000, 456574811, 201250006, 216178341, 805304368, 801939211, 38709053, 326601191, 336250346, 365870344, 385388885, 378182001, 222336827, 225244928, 234498907, 641543815, 47190874, 196032154, 596319519, 40080518, 835538851, 130087285, 475332688, 965953160, 203207849, 968866722, 403748097, 454448095, 697531232, 539165676, 536142744, 842826167, 112518948, 343279662, 30371999, 21515555, 963972630, 621716189, 708829695, 192286232, 339765966, 321424627, 888872432, 954078049, 348800342, 16433791, 296434987, 883874904, 633255506, 499147540, 928600918, 899702109, 380787796, 777147949, 237943528, 191601486, 230402122, 40671452, 924429152, 357456162, 677294944, 19326591, 529289879, 198682369, 164036242, 235442, 817715698, 76691110, 508105318, 507018633, 481134189, 691403554, 880333949, 248859452, 309357595, 832775567, 853291835, 607505871, 569619649, 30966555, 378573043, 634481712, 502586920, 630392538, 480101144, 624883348, 128396040, 963346751, 558881465, 688532596, 134213685, 913084148, 963555470, 596870910, 719015940, 803225017, 721779089, 777671759, 180307969, 713361759, 77147478, 404329718, 941434588, 286138650, 692457232, 1967187, 917297380, 689116230, 767429653, 952322991, 171147938, 946619219, 199402444, 378892372, 886916983, 880638662, 348389899, 238275513, 208205095, 881730055, 969823821, 345590629, 321429606, 503701164, 845267367, 550320345, 862896558, 215240293, 736856866, 407036009, 995015329, 869112440, 448455676, 376839468, 74633768, 762607102, 801478745, 331223003, 27636158, 110873694, 475381659, 642691022, 304021394, 62628891, 254604407, 688586897, 776375198, 771612596, 743023092, 833330554, 340636670, 854210974, 995055617, 557703459, 403072596, 411212818, 852583762, 154730709, 363085356, 68542167, 853875311, 606282552, 590448687, 718167838, 628522857, 837400750, 864044387, 213205297, 523997384, 731403199, 658957682, 169047195, 105907197, 479185119, 442522350, 914631903, 51150878, 72114266, 378710915, 193506669, 420251011, 426295333, 422360700, 52827177, 650252150, 623817042, 315928731, 384115413, 864059360, 127461481, 664995421, 393786355, 782232714, 790227505, 470629211, 214978517, 689904522, 970516057, 198090445, 251424336, 279547766, 165185816, 223327429, 611002370, 11121375, 626444801, 714539053, 549561977, 499108071, 495530731, 187419668, 474897948, 821460936, 185246432, 187110460, 432537129, 553524848, 17826500, 372446681, 847982436, 898380956, 616364211, 419834901, 942287161, 709982842, 911271820, 222414855, 949394413, 339980219, 692481903, 731992194, 990558873, 109473720, 471087183, 89235536, 966244168, 889686661, 412096002, 945219183, 702973537, 353677605, 649861337, 130211698, 255060560, 901614768, 564459986, 610913341, 659747726, 666679966, 143492692, 192466853, 770731297, 53203778, 244722923, 836036517, 717469618, 214837887, 588197707, 322770250, 411352330, 266596343, 854466256, 398217550, 413853788, 733080393, 404757517, 55920740, 835951664, 179378407, 981971067, 685479574, 53098284, 202111776, 84049151, 916461403, 51097607, 687882704, 51835517, 820728354, 32394072, 378683971, 496319856, 841223625, 990246739, 442240152, 601220965, 619130783, 925905343, 121685609, 659249226, 404079278, 43134989, 811093856, 594003383, 759059103, 993914116, 420016096, 45199314, 507050473, 29851288, 104981688, 961120367, 679673340, 283992916, 135066968, 693123630, 934273222, 971995252, 372042126, 873256838, 979587268, 935799891, 936235782, 19768028, 363468108, 717087698, 527899639, 188753041, 871865806, 136720173, 587167538, 551584705, 759306625, 71997715, 677815860, 520957723, 73806830, 565528785, 914964940, 555432182, 895578895, 461219584, 726964950, 585875986, 361111497, 168698403, 496330063, 714736579, 218408592, 379979619, 12663334, 98860036, 170423158, 390273836, 872801054, 53327987, 572466017, 55307026, 148170739, 469450600, 285000703, 182141732, 11412673, 301780655, 991824848, 279002390, 606585869, 317696101, 891363685, 612282511, 752942925, 182091088, 263145068, 649361592, 871078866, 801954894, 294229622, 72486627, 309516228, 694245264, 760870062, 809507121, 729597674, 815594947, 640422384, 436483666, 891086585, 724496623, 387562992, 921768986, 166480232, 389459517, 237236927, 727142529, 52084050, 696833911, 441598104, 549072352, 263221197, 955598446, 882213710, 229089097, 576770437, 239977696, 999879523, 805721963, 409004800, 326163162, 38820383, 973840425, 135839154, 854727410, 919040116, 860627645, 603964195, 432161211, 937164618, 275185393, 630841755, 43596847, 480979498, 173642189, 55651013, 743973105, 278846720, 436487064, 886058053, 4229634, 494458796, 991443131, 670359884, 788073234, 240380569, 528380041, 454224517, 161914816, 241808302, 75651050, 819527866, 707942739, 575313819, 37311372, 423346320, 782796355, 921590842, 39402412, 671048455, 373248453, 137968838, 436959094, 460081451, 773957093, 423261960, 290216629, 975448752, 128128952, 45216981, 335635152, 122986230, 520609386, 3790868, 302830096, 212303833, 782536672, 874938551, 578380774, 292089118, 531784165, 4486727, 9720841, 215393659, 925177806, 936104587, 878590412, 392961059, 781417449, 464079545, 312418812, 663436558, 528941619, 644002951, 959154149, 223076702, 542687413, 91546838, 322102555, 623617804, 763502479, 918147494, 56189381, 883713686, 841993526, 369107614, 408141171, 749842894, 485192224, 268079006, 82229533, 145380412, 252463334, 954124908, 367529719, 835715944, 919076631, 644598900, 15734106, 715580069, 396420718, 499338234, 640466244, 514303229, 81818204, 342916705, 139867405, 606955596, 851708998, 694438440, 798331810, 787229798, 983053750, 488658467, 235004543, 618585659, 161862668, 337838886, 608650198, 610826359, 385918935, 520312637, 253428366, 958991519, 979389749, 922732508, 896317019, 169032142, 131395806, 884377726, 359870174, 849119573, 148440990, 882763067, 326557542, 647649439, 267680854, 990663970, 91855737, 174302753, 803592865, 238949226, 523160764, 83169638, 528865223, 383022357, 170225110, 622447692, 740659390, 888724578, 70274843, 38012385, 957137561, 347864165, 782510412, 646797808, 721045808, 5007416, 826713860, 578323628, 749283364, 255341928, 690233578, 883245054, 487102503, 929820213, 435048068, 135227317, 529653065, 137883136, 599125536, 324092985, 347582355, 382561803, 712301569, 597333667, 519863800, 553298193, 989491880, 302766895, 296112753, 637199307, 999587755, 667906613, 274758004, 791877380, 568135864, 717989499, 927420618, 165082599, 507405598, 776570312, 261323518, 368502695, 914641281, 46661104, 325524490, 135236469, 291700790, 828501586, 847108386, 868421591, 420970647, 76456432, 926919090, 774232425, 755906030, 763766354, 261424483, 850972604, 930195658, 382199736, 880571208, 826704942, 168698314, 433768212, 301115569, 200655595, 783914546, 957383014, 382088424, 323657627, 306095593, 469123520, 425624319, 712265753, 598924407, 219007702, 69754837, 917135125, 838550441, 768847692, 540896131, 246138391, 650676193, 769835657, 315374659, 337878402, 849967326, 560587886, 931640167, 799681802, 738518661, 110354791, 847654269, 945773557, 227772725, 892463410, 828304619, 19587805, 302288706, 95060899, 234808172, 60140707, 729141249, 400828038, 554342037, 306534455, 312685364, 581745569, 380568967, 662683973, 870398382, 905227863, 207251144, 537775574, 391614923, 641522307, 715412168, 571540273, 467273019, 939770258, 783069145, 623738449, 156097135, 303859226, 662934071, 600332842, 762530875, 878294820, 164188938, 48017046, 997573630, 812981314, 910889653, 525989597, 90657109, 850324647, 437536451, 574342995, 818751749, 84384810, 222397891, 680846102, 98453285, 524356532, 561432155, 322287320, 32223804, 831118829, 695683194, 742288138, 155735283, 729825309, 116293817, 305352218, 772176630, 390605388, 957377103, 974117653, 697363499, 415256878, 88263952, 748219746, 829091118, 62419002, 306528870, 46773089, 313887498, 379391635, 466405945, 559329409, 615341590, 624584525, 920334301, 983571653, 399794015, 670322568, 502732411, 942601501, 929793102, 218332722, 218609277, 712314629, 269172606, 202633930, 845144494, 308582606, 281268268, 832479473, 555605421, 719781156, 885293923, 50212770, 985951510, 80147900, 730613367, 605506393, 20070901, 973301005, 708806193, 772951220, 612105149, 506241290, 50155095, 15293608, 254567521, 904625520, 911290294, 558130150, 110302460, 652254927, 492741093, 838389115, 370173819, 153911888, 203511612, 191703076, 835317541, 826415736, 601751599, 713641656, 344962467, 120810118, 119682493, 913220351, 126611894, 292304143, 933874072, 943893657, 781844385, 116321313, 226698734, 510647482, 988263802, 342288310, 769364805, 64705132, 986022803, 675001916, 723777286, 616181584, 419550985, 350755356, 881536141, 849290230, 337822105, 395055436, 461700031, 838509585, 895682709, 340268287, 670733266, 469063274, 123918337, 697244364, 690512801, 50057987, 687212925, 570966211, 62871774, 416867120, 964062917, 500017236, 506203205, 408381637, 103929607, 654101024, 732702124, 497264983, 966301474, 391388274, 829372046, 700053401, 419074180, 298552405, 445904651, 442399860, 121092424, 127416440, 592861444, 700919477, 323261488, 803533620, 452925546, 534839233, 365201473, 415578753, 162870732, 162296485, 14345401, 166485911, 395166973, 73941141, 156162073, 522803272, 66312811, 188442137, 301790778, 968761833, 628034707, 853536506, 572862090, 32253085, 285477429, 466117986, 441044847, 621465799, 423669165, 602606113, 715799012, 219359208, 942773851, 130522655, 308443413, 297542955, 617904672, 944193914, 7611057, 384148711, 74925161, 377769226, 398540946, 592863079, 140219060, 989894334, 780655927, 744864086, 631320715, 865496757, 558757249, 644950973, 304713064, 205669696, 696860999, 905457969, 587201405, 927054790, 827796694, 517676457, 631288717, 923487219, 819406228, 617300471, 600455294, 390624066, 75270409, 798295971, 15244260, 942806134, 225778256, 781866688, 29463351, 585976537, 384639108, 228716741, 495253396, 118526399, 853604421, 233767280, 881246065, 168237182, 642057878, 477319228, 266259975, 354415084, 565966165, 157447932, 353041953, 59679971, 397266246, 710118874, 263816664, 659931364, 113219465, 181312211, 295937043, 303283250, 972435213, 128786451, 942151986, 279239428, 829545441, 553434966, 478174259, 606354407, 717267217, 278952454, 18473335, 241161603, 572571143, 84587915, 523822729, 792474828, 648112815, 12800998, 197223728, 95027615, 422748252, 728582506, 449985245, 668634094, 384984432, 924422779, 965638663, 691927963, 546259866, 540129275, 633768997, 182248835, 948590391, 563300637, 506336317, 916553042, 526655007, 552585207, 424977640, 917727897, 502772657, 23391770, 400005691, 189439764, 520980052, 993354156, 974995071, 208544521, 61551377, 457307247, 168276597, 701508935, 288473946, 965050608, 717306768, 842673895, 719047910, 73784046, 354683669, 732928034, 915075208, 707391397, 99652967, 217995247, 825028835, 731495871, 713268247, 769566304, 294836952, 654742451, 345455914, 896455821, 473118896, 166497833, 589205441, 162352433, 464728937, 112953668, 91042068, 836102039, 470104604, 348355647, 149313141, 848890103, 913441224, 766787884, 224851198, 509670189, 766088692, 21304282, 576895809, 723001059, 224232603, 198939741, 362592581, 881896119, 892991083, 857836550, 219935269, 165822143, 889117962, 954676257, 831563418, 137586781, 153479587, 144675133, 737340712, 467363582, 53114142, 853296729, 314031197, 112585815, 854978662, 590242453, 627765137, 232301027, 99078717, 145812710, 812925041, 41418269, 942100043, 314744507, 298319674, 144298652, 265986410, 165621762, 620306875, 168067667, 234474526, 282234823, 316653000, 748442519, 305674244, 932317376, 611621000, 590728210, 447227085, 460475924, 331291512, 621833213, 256596592, 830610145, 354329604, 947012516, 794925626, 924110976, 824084780, 458857674, 197543851, 352253261, 48776393, 319970583, 87817332, 853617922, 306494563, 348746534, 892163888, 300677078, 269241859, 750025218, 630198224, 140124328, 631872043, 23737701, 126288564, 57671046, 417128051, 836606748, 873042637, 356566428, 161702521, 598847091, 436128048, 599411195, 734924244, 93340512, 495243817, 156098501, 43314970, 455846085, 369206408, 772867129, 92178329, 275720890, 986711109, 186646975, 178196114, 973520548, 261957672, 602371251, 814416199, 451309556, 469310925, 823660673, 136957227, 611967874, 248773019, 320098883, 485660871, 894287973, 380005086, 33394479, 36496111, 447993545, 306531261, 823639688, 928305050, 834988042, 56908959, 165282971, 258645802, 992129770, 594947423, 40123475, 385134689, 277668340, 672912171, 283720930, 772562470, 75951286, 346657899, 796353243, 677886566, 91556203, 377494571, 438375606, 763127592, 196191357, 387022557, 754865635, 792858617, 672558691, 635780810, 401052509, 94847794, 90175836, 655154743, 270916468, 186031385, 230581484, 154964275, 538965581, 340715941, 703454190, 282252362, 833687890, 716876785, 328055824, 656155671, 287224489, 300152897, 447591185, 335470064, 526178472, 711350509, 249432578, 594503298, 699148079, 632331648, 564901764, 639024911, 662744849, 348760470, 98697152, 126569495, 467150116, 329206022, 586895445, 543567273, 291230250, 49404278, 896822055, 415282647, 411768411, 856650972, 265630554, 430630475, 448658667, 754763413, 390293330, 877547232, 838984790, 632935565, 662889508, 545545341, 854754934, 724235776, 543121500, 221970271, 406378716, 209207523, 168481160, 996093941, 334549432, 638138147, 146908365, 686972741, 162291213, 153061982, 25032419, 867686604, 431603394, 791975966, 590661893, 932520912, 928643528, 140295045, 328528811, 830224441, 933302134, 891399030, 793639136, 286767829, 527937055, 563349117, 921851934, 140523127, 727370337, 144255913, 381512509, 736001995, 653148681, 983334170, 145997949, 904989824, 594267952, 841993070, 347072927, 471427668, 635387675, 159117113, 487285069, 579003892, 299451015, 232025035, 916528519, 560327587, 367085537, 194837929, 751348232, 394713842, 612814251, 917752901, 543401953, 497094887, 546876191, 127918463, 664298607, 264645835, 816444205, 405960689, 963661783, 731964857, 153525619, 501269422, 496385136, 558337516, 253070126, 364985115, 622761400, 295284503, 423748098, 892234995, 666290279, 34915267, 843879826, 673707033, 28298229, 329869996, 159117548, 276916895, 942917634, 129827938, 317737306, 995188137, 866986899, 53920003, 524390925, 197787197, 261037447, 444935299, 742782672, 567239282, 54952624, 145593264, 993244998, 829074739, 98833006, 236269750, 173576919, 536797437, 744174687, 885339984, 728208875, 232471908, 944874898, 279220402, 72548582, 2029260, 111069132, 756682363, 477840804, 437813184, 836075159, 43098038, 262194304, 770460702, 361581216, 939073237, 58263451, 32253110, 410727911, 272265668, 118859086, 537952267, 424362727, 337835721, 763091514, 971301214, 830291076, 524369422, 757084358, 310682249, 501070581, 809806429, 541151142, 183342332, 9660801, 460682795, 55676423, 317790748, 697652971, 967393116, 186198634, 136295075, 384244488, 426038398, 772147672, 7938128, 385740254, 100725500, 200030418, 114516534, 224129847, 404947819, 27279770, 762221856, 499570881, 800653338, 666707048, 990348923, 366391771, 644391617, 893998924, 200620294, 964850959, 626909046, 823397655, 242419760, 451472655, 463586829, 960842354, 603972341, 402588281, 604494341, 649711581, 768140037, 63315066, 230394743, 866094344, 495500634, 603504175, 835499035, 733911161, 436694822, 995234337, 365563313, 811143533, 648059356, 335355663, 221738784, 183350552, 535026356, 47797370, 947820842, 759656834, 708775028, 732810626, 171106859, 627552214, 753986953, 881249834, 341161838, 115146675, 313828218, 103861254, 231677108, 809131073, 823036973, 148886983, 39653063, 418260929, 892811291, 669543419, 658310911, 150192422, 413029142, 66176261, 919103082, 867081101, 262723582, 604758931, 8757246, 193937417, 337456444, 923329389, 52083974, 263324155, 470706616, 586100211, 513165648, 291987895, 52122684, 391898162, 5324696, 450540572, 844686948, 773148233, 48945159, 629377640, 361069299, 519868123, 277993522, 450910992, 86824495, 152687254, 485014011, 989389035, 432698008, 486710649, 557685337, 572322721, 182014848, 123473672, 166474212, 876353371, 421466534, 651824426, 668345748, 719007414, 886297051, 826913695, 429232766, 730444412, 150284926, 278234920, 952640159, 54103103, 468204912, 849523616, 72086063, 322440457, 999646261, 429590059, 112225640, 101101496, 770111402, 245987143, 985008206, 566019737, 462569817, 176719490, 265766792, 991948948, 959623673, 779850282, 185784215, 437727972, 590770382, 7849316, 594849595, 443013443, 879704323, 540827183, 55255883, 638295425, 397887120, 245500976, 924784076, 207841432, 413479857, 319210948, 137560699, 632603681, 310292742, 851316511, 664081690, 170044352, 987905770, 820395181, 396099291, 355966999, 968012758, 527725721, 514866385, 17481074, 494653329, 930147992, 350681796, 708095719, 983969499, 452037148, 87882185, 339300442, 219663543, 697782541, 420751337, 46748827, 710665612, 754047282, 153489454, 4738975, 729059329, 778218933, 748073230, 771114940, 780298648, 562046751, 511597909, 424488332, 696675929, 11026623, 137079903, 311105990, 936756541, 964725409, 264059453, 508648416, 165747843, 494226406, 64103255, 195146713, 957290194, 443006195, 296423618, 139199097, 273505527, 329021238, 905134359, 298747494, 37125820, 328202753, 245120904, 535566513, 755862755, 757216101, 560727534, 628378075, 258113354, 606535937, 719558934, 652820103, 472452673, 576594433, 277346087, 471001407, 570834154, 75957542, 112973489, 339085195, 443543102, 566024206, 133689851, 516029387, 840386172, 417792758, 844418160, 928667811, 937755967, 373943068, 772545475, 313183510, 841989941, 811682346, 991955990, 553890074, 865600276, 616918886, 434462963, 106552666, 610182022, 938162927, 700495819, 678119751, 490123310, 287156160, 404274203, 662973190, 396683639, 936568388, 735514313, 580836716, 619401218, 853556548, 305739887, 963415274, 284802332, 381681398, 157495764, 891007432, 530605994, 66403873, 843555881, 153716623, 652321269, 573588840, 990373712, 88367769, 525243619, 199271015, 945588008, 655280249, 330130758, 980322699, 571327172, 792077548, 253019265, 449503149, 293251803, 233937467, 504802015, 4330590, 607080174, 582527926, 217456793, 906197723, 699940771, 919125252, 687229386, 397452484, 281441495, 409940372, 783104932, 490200172, 468160484, 864866740, 507686798, 120858611, 377190598, 229032894, 540525741, 202604408, 960919156, 415027931, 650652452, 965653035, 969017156, 423392799, 275821021, 770779679, 401903253, 805886130, 223038188, 894764365, 356479427, 878606662, 723918940, 893265403, 462947978, 676886453, 881893275, 592621718, 63668072, 411526541, 157408598, 253849301, 599201930, 381981275, 35974282, 77394724, 423372912, 566044156, 751512679, 232084288, 576778938, 319702096, 348308620, 546989743, 255990229, 758894635, 367523732, 967446393, 987911983, 619262451, 804636017, 288022862, 780527289, 330315838, 652723938, 691204921, 851114016, 746060026, 45602371, 172405864, 824614643, 174798728, 477940461, 367421525, 988037497, 402700092, 5583166, 686096817, 814046306, 878992529, 836076924, 448915595, 950169413, 603899655, 959093444, 665291174, 723951335, 386297589, 520242327, 107077016, 485354857, 113878980, 472954095, 533366893, 669968015, 959868729, 337071029, 881682649, 291316099, 68902490, 608913038, 436293764, 609709581, 181388967, 789721233, 970552662, 527355848, 83019376, 242970971, 668204630, 562091960, 117308308, 483081408, 299075798, 184323794, 444029282, 125687169, 914330743, 17748265, 738100174, 385938017, 263253288, 621470755, 51087688, 623815871, 603551250, 948413734, 69816826, 872358985, 177686674, 890747610, 420737038, 773248999, 957144732, 348674825, 662645140, 694137346, 370075371, 549288202, 448590732, 910432229, 164158750, 738524635, 586675519, 390700683, 849472535, 976561718, 482547788, 329891384, 714179681, 499528065, 73656548, 711289797, 404418606, 199449814, 947492241, 325603992, 478164065, 710813970, 590532875, 184913528, 49269821, 985798047, 184234947, 277867070, 906732537, 729033708, 172267194, 570508616, 684063204, 93934755, 745474432, 547797281, 678524246, 799869927, 219419653, 705112893, 761820249, 913354294, 180319274, 493139207, 367979398, 145543485, 465510643, 367341925, 948763487, 363029983, 251271086, 115611421, 486129167, 361133297, 582799030, 640432794, 59356317, 483623680, 7003196, 227523962, 346464331, 700165738, 601347522, 537019928, 230333303, 544840659, 140403515, 654507479, 217963288, 637355983, 202171354, 547597735, 621051360, 205092841, 531385151, 629752339, 86838521, 272722310, 270414663, 902157293, 911239505, 492894810, 270435122, 786907119, 476054001, 280911987, 7566941, 89584698, 213503231, 876760443, 219930832, 586211964, 210719565, 694536195, 723721204, 570798676, 881815799, 859945744, 136847538, 959805929, 778867525, 991782565, 597038553, 565866888, 282885628, 941735927, 766529798, 695028610, 885390325, 281596286, 447249272, 242455553, 281384037, 549087973, 367601914, 545716714, 468418956, 512865658, 452614348, 541302845, 497636889, 910606838, 106927921, 641902409, 523536337, 294610872, 46503564, 702960279, 751760139, 826041184, 95766994, 847400985, 553692594, 105846934, 399693832, 834427434, 684589630, 43064800, 7082069, 401576192, 159446671, 289281946, 537968531, 891582440, 516785244, 493512953, 705187941, 857018441, 223400733, 410730192, 127933361, 644653451, 447100768, 136125533, 383177005, 468190358, 859481632, 232435668, 827757361, 257218637, 494205012, 298333119, 642971146, 787492714, 862448267, 245565402, 85227649, 525678475, 13553557, 559176815, 162408213, 521283679, 759799728, 333769521, 237506368, 980402874, 794528546, 960583224, 237932319, 5485017, 391811278, 300557638, 511028530, 643131161, 763516972, 756249259, 228283647, 573534850, 915377496, 291273428, 920269030, 813044004, 610443521, 426956569, 612830303, 774329480, 840579938, 677815585, 811774189, 367355550, 931345937, 12875150, 906499093, 77024420, 12052184, 872913324, 964685552, 193460260, 843747966, 324378191, 308694800, 78390791, 709661949, 789898833, 272736331, 166630141, 516163142, 525625462, 182394987, 912917027, 446637953, 427217164, 167627442, 895310272, 846842006, 247491247, 330691243, 105892710, 981747306, 523578267, 622720585, 681518609, 318356715, 651580259, 349414555, 102033061, 719908093, 172061875, 511389064, 51668312, 727751713, 552879648, 533251161, 116246402, 833153472, 450513154, 777446220, 346652394, 728655773, 939462622, 57875572, 931068412, 75257992, 363206058, 716576239, 460084617, 329940360, 372824540, 891096083, 20263379, 192255510, 208986200, 478759621, 785831959, 41607970, 493795184, 94017542, 822360120, 993329865, 857327300, 439380404, 270603156, 329737171, 573560861, 64878259, 721826538, 841454115, 866295127, 167971208, 668165003, 570420877, 603617944, 143524354, 250063942, 182626976, 699677184, 652342523, 705380451, 370324945, 84109098, 555420739, 487476470, 136176164, 376348311, 264603188, 229215488, 569777366, 531520519, 582840068, 222614771, 205671831, 502922140, 197242275, 404950034, 738417493, 165162555, 137333466, 191315672, 213875214, 912354703, 822564118, 827066348, 11095286, 396213921, 752918427, 329923285, 402216400, 922372051, 837972248, 732710905, 280986462, 422265148, 46337803, 654870680, 65705599, 370059143, 824155357, 494377786, 263498489, 325924795, 595039623, 872667029, 246331185, 860428108, 661877391, 452839054, 79852664, 940268430, 498643939, 654853627, 129584605, 622544907, 100749032, 527334111, 96607103, 663104714, 80278973, 49069733, 421581985, 89245648, 85806741, 911549823, 146767833, 762903682, 558854776, 281748105, 478093545, 861738309, 588423409, 72748006, 113097106, 435817628, 216120391, 23932798, 295920393, 594761077, 124939232, 759994579, 7539346, 872142312, 709174854, 292712317, 745782847, 770795479, 529860054, 190816597, 310390471, 321645390, 817892300, 876717306, 702856657, 773067837, 532936340, 205806892, 659616594, 945419164, 253959528, 664036920, 352643029, 545127339, 523782010, 556671542, 187642737, 973899891, 284333551, 750268022, 8356103, 620131203, 599143072, 633787482, 593225918, 432125746, 590594254, 954916225, 23190899, 549004733, 287035470, 200962900, 444133545, 386014134, 602347209, 920864668, 584265313, 393184066, 47260019, 624851956, 701619735, 994268986, 158178362, 852270222, 152609349, 390093416, 57947328, 855943661, 185564503, 832012874, 513661072, 513894026, 198569256, 7751970, 496089631, 229422242, 656410845, 117229770, 347682912, 409537461, 838864699, 664078965, 631189379, 596961167, 140555845, 930561411, 707608943, 573718349, 631010403, 388300250, 756346023, 850060351, 147316842, 904562893, 235919844, 574858832, 322613775, 993631143, 447807777, 95253246, 221502601, 361866144, 151348067, 811971473, 458654561, 156060102, 461559754, 286972178, 732201551, 774212498, 787901759, 944117817, 560596316, 550238434, 407847170, 242846838, 351563948, 547875759, 834460894, 954091282, 243401069, 75122643, 65107532, 783882272, 761910764, 766741958, 775311449, 786430131, 244401947, 997903544, 408931816, 223162318, 569519251, 842803491, 482845111, 806186691, 350877364, 900633439, 31501102, 47612250, 985484860, 940255781, 325418459, 780793433, 467565424, 990370224, 661708737, 599852670, 585217406, 590954753, 996121923, 577205209, 359618639, 520444103, 340216134, 177622617, 58352946, 625273844, 529814209, 365122523, 619627956, 656366373, 957427246, 832447610, 413989753, 515683533, 650268181, 704102471, 423603877, 41743945, 197537696, 498361096, 63731100, 169184278, 755223590, 398054148, 985991342, 333381931, 169668885, 109216780, 139814075, 931576622, 245762832, 593513568, 384903238, 195136621, 544879632, 658543307, 667217136, 671580313, 451959706, 24482609, 4785670, 485541953, 31909824, 512674016, 143659125, 777539198, 863919853, 402323547, 241713904, 160190381, 817920990, 417637923, 155858274, 886103832, 673703580, 302428141, 669282967, 136445322, 674041303, 357219694, 87484716, 728863898, 147164112, 40035546, 395871254, 560428573, 655265042, 736043335, 758023585, 29156509, 507481967, 547179296, 734230261, 672567361, 392445286, 229882980, 512494616, 126857037, 783460914, 910855381, 943315924, 532914823, 993542346, 251588658, 392135515, 26918851, 109204111, 199984302, 668768764, 980064421, 104705303, 410238665, 182499281, 387071341, 130900657, 334615967, 564345824, 877696552, 672249829, 199241780, 908615167, 546007130, 763518199, 484500533, 738668715, 883070630, 51216212, 440409244, 540058562, 399063431, 404738898, 239987538, 354704023, 395490010, 359624533, 177337565, 733952319, 944608463, 414600162, 315424842, 101590243, 817007106, 130155640, 325675480, 976106700, 293543518, 243927761, 656430659, 319432036, 283447623, 86950044, 277115418, 472558277, 668788560, 154780899, 393293952, 419765284, 77114233, 960976238, 379593892, 928985859, 322656591, 216640440, 744283589, 241988975, 279788189, 349010037, 869328489, 367722336, 71782290, 158960078, 63131613, 280810596, 13337576, 637045909, 793985007, 349379671, 458248735, 445343515, 832407844, 650717323, 449009758, 681340355, 880044538, 513452105, 470809076, 57512871, 772162729, 687866965, 908351263, 877096290, 198534273, 159287470, 227824819, 554999475, 322253982, 139444302, 290044933, 535610304, 581918512, 41433480, 463213297, 152511214, 446580902, 223094168, 782556768, 383238310, 18134065, 796431024, 881522051, 797223519, 421339717, 172620422, 535868088, 540816575, 662891523, 692920804, 525857729, 654699672, 586818742, 416129927, 208909638, 425064313, 44011465, 919605474, 220020006, 915147293, 379587687, 403627455, 733276996, 82199329, 787113151, 819228444, 352913306, 159762977, 181716518, 450949087, 625775427, 953986891, 64686920, 643365757, 53684229, 345949565, 681515035, 923100519, 264533295, 390791823, 189290151, 54992851, 122278194, 295495792, 457428271, 849467864, 808075892, 45310713, 258558154, 449160594, 33876868, 655619261, 596940743, 961236577, 264150260, 467344980, 180996522, 254072607, 858431846, 37000497, 679759235, 597981190, 101384968, 520984581, 642991624, 985476915, 31511610, 716466742, 384981311, 414966943, 672802712, 621014549, 708113165, 454557742, 904110801, 893501686, 32846327, 496674117, 386235440, 845220939, 658604541, 847309960, 253799736, 633408076, 90818060, 338315709, 301614028, 242812373, 863653190, 741937944, 588255493, 862578345, 428165178, 220257943, 715772409, 909062575, 835702333, 757494079, 188839928, 375158651, 312221888, 237217037, 205865512, 493481948, 804839134, 884058332, 25613910, 871861228, 838057261, 649705239, 904191716, 957513518, 160859755, 631371589, 801067206, 167731003, 642685422, 480994438, 277760353, 751757421, 462826245, 531250364, 199425821, 566639949, 551974499, 623439582, 622354456, 752365839, 964251520, 167283824, 291235094, 669486526, 952834782, 641477665, 338589892, 185051150, 813299070, 161634671, 54671277, 594759524, 701326000, 947547307, 700552175, 964824780, 312852173, 613707285, 10758598, 227329416, 838811058, 733240202, 45255162, 162565796, 323927706, 44899625, 619010457, 376706605, 812367974, 638895577, 534000721, 495725075, 241024327, 509154843, 336771322, 914292597, 766263892, 487433225, 36672302, 894224933, 738266890, 107410758, 636573857, 866460761, 876769367, 657938126, 653846233, 328456110, 884435008, 425358379, 563911954, 292361145, 548538069, 996699994, 529079025, 914808766, 444090534, 416249008, 738973453, 400732058, 636587599, 819119748, 538164590, 795399132, 659618808, 194218011, 139985444, 883499661, 14106605, 676521066, 225320529, 452118500, 667761165, 399898595, 143371036, 28856049, 583960461, 682169218, 829859876, 364520488, 732004750, 178388714, 8684511, 813008851, 444087144, 457366163, 509014799, 931421424, 430998517, 764522288, 986412369, 548698493, 543977286, 584136970, 766036857, 912376783, 74538691, 834138311, 266064600, 258923504, 657150540, 804501040, 783709137, 477328808, 241027215, 151965742, 751750448, 881069849, 705521564, 794874189, 947406997, 81524434, 479195293, 157234410, 349924636, 30938509, 71054884, 616841084, 204378044, 511661741, 803261147, 504514116, 826620434, 816321990, 808226478, 462897265, 214555635, 505446830, 696598544, 985292950, 951444105, 534439625, 464586046, 645891437, 652762830, 895486027, 513119001, 71504417, 683821234, 552251352, 583133354, 897386546, 717079374, 354025601, 390330342, 954189711, 669537749, 376448610, 282621712, 318783737, 934602603, 23298648, 619743735, 193035145, 581983816, 208499783, 441728334, 380104557, 363644488, 325819977, 784879548, 608631330, 384526060, 239997607, 696788885, 14669101, 743400897, 893083067, 378262756, 724661128, 411510759, 160150584, 272380198, 131095234, 368251856, 612638200, 426435154, 104436608, 441026002, 53945106, 845803392, 234672343, 327938382, 991652227, 856672075, 357413294, 177383843, 182770981, 752732201, 219158235, 241002422, 506734962, 667355679, 124613236, 599117553, 617195576, 499790772, 745091158, 776687708, 998499751, 685740078, 751167454, 174004123, 780997012, 385802493, 640506268, 994268356, 245742995, 191603166, 370916532, 18541636, 664229116, 414521933, 438684141, 909867694, 918400617, 412149634, 586856482, 635921237, 395584872, 705657545, 621655612, 242087235, 56659528, 807333086, 51213480, 608672173, 590958869, 67213054, 75088066, 568199941, 283016337, 871359879, 572051856, 847604255, 42774886, 100985112, 209491175, 730458630, 737645368, 271156702, 554231560, 950353033, 122638103, 1263200, 135867209, 241495642, 598296934, 396017749, 630310403, 714182774, 768054705, 820888316, 42933946, 571011907, 710594361, 761991264, 836701738, 10037951, 564085174, 128549564, 328339384, 692550063, 250379777, 232864883, 326551484, 3402843, 887198515, 342213761, 911524095, 327275621, 265630525, 142623660, 758311598, 495158176, 20605513, 334902761, 421743261, 282333000, 370251799, 260509031, 845360601, 897337022, 287817684, 851432933, 517864642, 636166031, 168052222, 7952604, 62486489, 699414438, 377280970, 655719585, 445607128, 559495546, 796856748, 271049425, 143780569, 989295781, 756624026, 649345020, 936281754, 30031357, 436089491, 959293285, 943843468, 538876307, 741228188, 165632983, 64505029, 681427210, 202418817, 106412496, 116120952, 639777648, 715281622, 835980478, 843223907, 583239317, 877701289, 879869675, 462516571, 196906850, 284870888, 276719631, 999116902, 968100764, 270156045, 328955743, 863121047, 179136826, 3657835, 348285356, 909414226, 670821053, 554805369, 567190820, 407718294, 757017990, 155322828, 450043042, 190282435, 382579047, 176771366, 27688214, 399519, 476605037, 332539452, 29366646, 258181372, 968143261, 635224649, 411075339, 976718766, 949726799, 744483625, 323477342, 113678247, 705302848, 976044779, 962789053, 832096341, 495130790, 622933379, 328399430, 557360961, 598701824, 615742355, 375443914, 187961103, 385444072, 733234120, 449773634, 928119839, 61775163, 983643955, 104516778, 232340652, 787166737, 893497280, 459091414, 116107979, 500147233, 339894587, 931546135, 154016429, 526165254, 879108555, 668660236, 19474303, 976196875, 865963578, 714169523, 535535318, 889838609, 272003721, 793464957, 397481547, 683684947, 431663959, 415091882, 793895153, 208192301, 505537777, 557412215, 15912750, 395611488, 785662053, 912247577, 699583373, 367307022, 423465656, 384560790, 430205211, 920083647, 224402171, 115608806, 527119002, 638580687, 114091729, 119123877, 947403088, 400643138, 766344687, 543897718, 19644408, 37362733, 578208051, 475867908, 288521670, 311470134, 840513998, 828073096, 559195947, 358896597, 974845973, 835732923, 765143557, 888335644, 62743429, 618226679, 306146739, 235391575, 326354479, 940853394, 387434484, 531064136, 498957639, 772672828, 116793804, 192697751, 149076792, 747181403, 144289228, 638777708, 684054408, 197236008, 695800094, 327522029, 16782654, 321070770, 532428107, 515377652, 828155327, 607864949, 480734658, 186822512, 186876386, 563552735, 953845738, 978382734, 732108420, 914260273, 316614546, 156694610, 228431090, 838554840, 262963832, 590723530, 575921468, 2727057, 882678407, 289597267, 828058831, 487486558, 968319354, 327327047, 850964350, 94427171, 988048929, 449351092, 321478302, 672551249, 676595562, 32316687, 147198424, 715930194, 521311657, 141409499, 155999735, 749482941, 276217922, 498838314, 791611861, 244000596, 743898015, 995987154, 582299048, 937730549, 584906329, 421359353, 65149568, 821032733, 199250665, 305269783, 657755164, 800915542, 745031011, 989948100, 664598017, 923282601, 557668797, 793328505, 794922175, 368778121, 864249852, 379172855, 990041114, 759161502, 559324050, 170031565, 737123931, 934762795, 160470906, 489671375, 652156413, 72536314, 874713933, 427465004, 134609514, 146413147, 72374622, 366041596, 249339340, 308083920, 17221121, 600586082, 51939790, 656346915, 105802789, 471772720, 519697587, 290943751, 147816901, 124522713, 780589054, 893011137, 337428847, 322604823, 814046083, 70866518, 831576254, 881004478, 995577014, 944593566, 254585744, 652189390, 777260855, 73780064, 482901269, 470592039, 869685318, 392874195, 138924631, 914935332, 932688160, 289407031, 17631138, 316587504, 164323441, 98210720, 105645734, 920873928, 161651289, 479883217, 506884752, 37878788, 358626813, 957300808, 942978495, 701520506, 436374181, 437252403, 341666622, 99183517, 526283479, 604786356, 590966041, 947396484, 85989512, 914945787, 6814398, 393616826, 718474519, 378586398, 852966559, 40388076, 629256938, 19928821, 705695995, 283132067, 869937073, 873897007, 751603212, 539665487, 825027570, 491284526, 986166603, 530525751, 252769064, 891794740, 98240089, 710889725, 63437242, 873215738, 325919020, 509657986, 972621075, 149702773, 827744736, 90120026, 849259271, 408146464, 594697513, 820271379, 9802091, 830371988, 553406432, 334094738, 641974612, 33011167, 697763537, 447015338, 249324612, 4713534, 985367361, 499978219, 943082796, 32361042, 114255391, 748301865, 987812342, 449178328, 323637868, 137637376, 23110127, 181482418, 69327619, 519864094, 566021760, 386366479, 549529940, 284363525, 442328272, 813031221, 253838879, 111755694, 172738360, 35447942, 684825780, 992967223, 521082065, 128853602, 555328660, 748689963, 444534545, 949846591, 13872175, 938035850, 825737167, 312202095, 390696408, 322061700, 527375299, 509931912, 411301641, 300632541, 589905534, 385746192, 338424735, 128267797, 189880321, 79037140, 904802371, 23921503, 703453186, 170698794, 850768860, 907253073, 71306765, 56889984, 692242883, 200707476, 604884099, 757236249, 159707061, 957248150, 841924452, 812397195, 121539975, 787422267, 721115921, 230173200, 37293826, 629289809, 600156455, 245720250, 325907863, 692075904, 641726417, 100052959, 678050245, 421628482, 210278715, 609036228, 799497709, 749667568, 338433046, 658376996, 574741919, 490403599, 258468557, 96149127, 835931501, 430970268, 84166859, 86620600, 508406418, 134424922, 406997103, 149599857, 44713623, 116421987, 722195094, 679642323, 24988374, 418526266, 84566743, 691602653, 690343059, 275329179, 29592968, 236299463, 90125090, 788131328, 935206674, 459189913, 53885121, 84060280, 25562792, 969229954, 159500235, 262301158, 63053729, 477776356, 32494893, 303844219, 733034564, 26869915, 486702992, 362019249, 654491669, 697240805, 688509281, 242726945, 828981969, 808657754, 799136934, 385225020, 833610083, 25786311, 493666198, 524799550, 145154479, 474602891, 487820431, 111104201, 297956202, 808296769, 907373010, 77827591, 909716903, 58758849, 781452704, 788910679, 233694727, 598866682, 323307755, 595569756, 91592178, 663137105, 386094460, 739465946, 524245143, 593450710, 398246969, 220377151, 644129526, 679366440, 427142924, 799471724, 218675508, 469631070, 665655201, 679222015, 846309383, 870264394, 941931502, 95706940, 448391390, 201247515, 691973675, 739833989, 68875204, 241256315, 475204190, 177074284, 757151589, 601854985, 257087531, 138201248, 667925903, 277618473, 222304778, 973135708, 166251963, 675175830, 116233780, 83797920, 503860149, 317358146, 358885847, 439211946, 607110153, 179388521, 841230067, 178483097, 772840121, 168808919, 192690301, 42457903, 229510674, 828710165, 834122330, 704517415, 16775559, 77103370, 812248985, 995477296, 234720321, 728222196, 647713503, 504247982, 596630794, 527481397, 888719849, 582142747, 246585470, 999357065, 555906918, 89344728, 71613259, 454652808, 922678481, 276140192, 582723882, 932258860, 50248510, 927817312, 745994117, 732765863, 594611889, 193783648, 814147680, 444553849, 179487305, 581814890, 218595307, 254543094, 386430722, 806244230, 70769247, 53516331, 139588907, 69454632, 396741883, 389426728, 780195815, 66784793, 948494819, 330060938, 477057904, 799600135, 526949520, 94284290, 302320644, 63353900, 165681353, 1523371, 972342075, 721037576, 842021345, 630492509, 197660405, 289225736, 9257973, 650697370, 191597760, 933056381, 956718081, 504493483, 980723645, 840612480, 915357007, 449182876, 633325880, 609644218, 288089613, 107086806, 741238054, 970855996, 169533914, 550781399, 527273939, 472305158, 490459087, 428531884, 482919864, 757598314, 304676503, 616622457, 560585048, 788473317, 803912631, 34396285, 201619690, 570539545, 53650148, 765886690, 479846118, 774701086, 171695238, 86824785, 595336315, 71255124, 745461268, 925620398, 134339855, 647323032, 389887006, 105553824, 767429457, 237347633, 302958908, 500720223, 417867557, 962875482, 312426976, 374199601, 856223788, 298021122, 336560094, 65310009, 299970987, 373490018, 35741178, 926974435, 889887733, 221326394, 736245135, 69847138, 881067910, 222346440, 856878763, 213372778, 293841355, 816251971, 940029956, 639516750, 357502194, 503784814, 688298455, 500609761, 186913039, 650393792, 287921616, 917601494, 274994800, 918149327, 857402039, 737709168, 13660187, 175119897, 41077913, 712901546, 520269592, 560009434, 359546394, 380768595, 401808166, 486497587, 51180245, 755620080, 249009071, 137128824, 317278759, 15452093, 347111896, 588109506, 759638482, 769728417, 471760292, 178632438, 475298843, 26507913, 411887394, 6476397, 43766224, 644017976, 287887980, 108234729, 39916854, 191858680, 634266942, 149990071, 715679975, 28128700, 388578893, 478709528, 486540754, 568053183, 809602857, 264057968, 399756227, 690461956, 885128689, 677574841, 173634543, 873054357, 496037971, 813225195, 519534912, 186411209, 7689353, 644623265, 696269553, 857255432, 132921913, 706818366, 711889635, 599669004, 529967468, 827146507, 215435982, 455060042, 810859824, 890911529, 348850441, 81550994, 541642960, 388773443, 889148690, 564805641, 24810815, 575289562, 303830501, 40465712, 275288235, 167871280, 620452222, 576113657, 347163285, 719839508, 426768320, 496329175, 771398456, 933222958, 171607233, 707384482, 878339015, 878070273, 874151395, 635490245, 966537179, 136622288, 582540012, 875706742, 712416859, 543918162, 914096614, 615971310, 908670546, 183433481, 951237399, 310104811, 440761904, 769726246, 322034803, 424159113, 447510439, 164259583, 507523429, 654519250, 369344194, 405164637, 805897420, 361812922, 220142140, 794516775, 737838097, 223375569, 677226024, 166511044, 874060232, 125713071, 975280400, 515246372, 498074039, 823565935, 999987211, 368618706, 567365706, 51538839, 168792254, 102441250, 240129992, 886870403, 219980980, 404677341, 812207997, 693064624, 201242626, 420541252, 898764540, 25184973, 150595677, 724942901, 153672002, 177759692, 408293616, 92190143, 274728391, 435942908, 439898505, 797002028, 783002652, 304393937, 655317408, 946754776, 38667127, 352393741, 721749307, 420482556, 141609213, 768009813, 81617091, 823518064, 860651057, 788665149, 423974339, 230442806, 853370612, 382598067, 64234706, 914953440, 270895779, 976378558, 931198717, 232888359, 685809379, 876773392, 728561196, 52327325, 179840358, 999218151, 499895566, 473329017, 570421011, 512938950, 870487513, 530214900, 459733715, 423237136, 875843533, 682364770, 233011699, 356983018, 394858157, 670329649, 493302955, 550363414, 186338704, 591150123, 262004150, 445405941, 21891661, 739565938, 854507294, 159519009, 230116647, 782677129, 998637832, 923965787, 715783047, 888012270, 898332037, 286701053, 176820738, 636398494, 138827281, 529753484, 407860856, 471183249, 950388452, 821320807, 356131666, 349063769, 194856178, 375634375, 878750588, 790804270, 33590603, 335661719, 901363413, 154723710, 471654323, 100784315, 889699447, 584548902, 176254703, 565024315, 447784464, 265669677, 46505312, 206764649, 770202312, 729510687, 315700202, 461064873, 258173268, 430893765, 286502243, 688672548, 42525653, 68907050, 257778338, 372624979, 484972, 346160130, 715273996, 703646877, 826706776, 53823671, 93886290, 396951433, 146684539, 949603302, 920756339, 171090964, 25553110, 672286513, 394747455, 258362186, 166143502, 764278989, 739850735, 972591586, 98755055, 42474433, 874924202, 649188185, 916718960, 954449808, 643154088, 582958213, 612922450, 358855761, 136464029, 400523433, 75957193, 587353339, 297647259, 359570744, 270252372, 971320663, 75234456, 977966884, 581027621, 730997435, 455137623, 773688355, 826024693, 416976714, 407056877, 687474869, 280771540, 834945806, 7990597, 56007293, 39929309, 512537894, 188215085, 493795663, 326499998, 408250854, 737882072, 666762708, 849388261, 961531075, 331473181, 630741428, 549531689, 385190620, 704358361, 429392976, 95665335, 69994714, 632226965, 666573031, 103922723, 490438896, 632173929, 670819942, 579296535, 898475233, 897284365, 109413250, 199682100, 428474415, 667616278, 317495743, 166984198, 804209462, 176900770, 381330295, 744552754, 188974380, 559481916, 664901896, 17500599, 861038616, 28128264, 294258062, 121198079, 616699020, 501289060, 349989264, 62040347, 39426847, 294943182, 813125606, 111640841, 513580596, 350373421, 439328395, 843185223, 241232751, 325998949, 862053432, 948762392, 104133063, 53022107, 345707221, 406424849, 491103221, 536019103, 756655825, 56611713, 848161916, 764522632, 995744220, 601280770, 458115152, 812369821, 675169916, 409814855, 492411182, 978044060, 99750622, 965542983, 392725385, 202914020, 4415446, 884299586, 334603648, 981154774, 811962004, 258335215, 513782748, 77106461, 64507789, 917801437, 501629477, 884372344, 821053080, 206984222, 294282699, 416138154, 778602241, 309713093, 828491447, 321336133, 947679952, 808466943, 759618063, 914072670, 861488060, 295215871, 261166578, 362046080, 473461598, 469163724, 96850399, 581417235, 663676526, 231755079, 622677690, 569825915, 502278814, 329144202, 245988867, 700858423, 131206775, 435923218, 202643769, 696681782, 895587484, 691970320, 415721786, 864981249, 584014115, 255099659, 98635228, 836577014, 942282833, 253097858, 79302665, 989287100, 497241075, 587917768, 349328119, 819885188, 583749845, 239962303, 115139363, 293725334, 591773925, 722604595, 286509040, 565435610, 818363754, 594040, 452807620, 557065908, 91304394, 863533932, 826880710, 337619901, 416044890, 506860821, 931628752, 596791797, 645315731, 784509024, 742491720, 551732340, 839458439, 470744103, 967293604, 834065886, 518193826, 527328752, 986529577, 769164221, 75950425, 114253633, 453736205, 698143631, 256013216, 181086056, 983778734, 955085984, 701637229, 569174863, 765757423, 424478412, 334318738, 978492411, 146193904, 575434296, 766070377, 640254122, 210893741, 249904342, 361577552, 242517380, 442154967, 176943930, 712076575, 719811259, 609766295, 672328061, 363900360, 470254555, 324311721, 395516363, 219550606, 753151363, 261494362, 723162070, 467678518, 472738838, 246179846, 977238103, 435885933, 555684596, 655151282, 984644303, 27915639, 545880976, 686354289, 260376350, 771836313, 838575650, 844254215, 748098099, 306877454, 285887120, 608327909, 111333507, 296928589, 912086308, 305745165, 34853323, 566961576, 517652954, 953476956, 955939163, 393231141, 703860758, 411843607, 191907354, 139839831, 761098142, 395271755, 801468981, 656469346, 848230612, 87218954, 795697661, 793985034, 192847944, 545752006, 571121389, 757513316, 167460212, 424515515, 13334769, 220837370, 878089422, 144665305, 942025960, 477519167, 702401923, 430674974, 853935524, 911715648, 939394029, 832324889, 401148874, 708274051, 505542706, 526717156, 405171122, 634345447, 382636162, 651841754, 95933202, 91827591, 146685022, 256491937, 235437593, 880373887, 320887915, 279970114, 6397586, 380887241, 556980239, 849337762, 304851199, 735610349, 93406998, 882232248, 333829505, 163650743, 218372497, 80227852, 738966748, 884249204, 786707555, 234779413, 299103230, 867224194, 373231895, 192282270, 275098648, 152110681, 131369065, 284263953, 600544585, 472890959, 87255408, 913227842, 175133612, 751111137, 114998479, 75724063, 234173939, 881290353, 775650750, 120696543, 549643384, 133481432, 136870582, 823725960, 944831625, 534885821, 190709376, 87592633, 770746631, 994133650, 246694949, 995442158, 947024261, 726018543, 312242865, 371145779, 465038924, 489740017, 888462972, 910280544, 625169101, 661048376, 205696258, 732377071, 912393007, 282038484, 150281847, 517530748, 16377047, 15203115, 691315291, 932000809, 211599455, 451128589, 273855477, 292751403, 202094465, 551367573, 690473532, 495021898, 149058253, 641344148, 467119473, 876929017, 342165855, 560306529, 405688755, 304008150, 794444246, 749908223, 917692556, 412054712, 936160847, 419714204, 255183150, 97836291, 870157725, 161134925, 646401360, 794073269, 667028060, 16877885, 454729830, 305618821, 719622979, 300408003, 518897462, 654636479, 379281010, 426528965, 82055968, 808687223, 462989059, 567784709, 186048551, 477222772, 472983523, 848737934, 598201137, 720053828, 231004581, 906539378, 400660682, 415390865, 983013248, 923448108, 935027540, 576204352, 969547032, 358435812, 282830, 719048728, 338314999, 206159339, 61220474, 138165482, 164506651, 540738336, 653235664, 567279356, 769599842, 901022687, 168292533, 14215859, 57291036, 647595363, 991714812, 436228143, 885894246, 761947051, 63433863, 279626841, 71467384, 617688445, 816620504, 994985034, 601964810, 690681688, 296253661, 147014120, 293347076, 20330155, 767760082, 917170642, 334173639, 108671163, 325405711, 328753855, 540167431, 877112379, 427651131, 152481057, 730540407, 81138992, 575606643, 203185009, 733868241, 987412760, 951334258, 176047254, 100609784, 123165228, 51057039, 57202775, 310923288, 539350121, 422599331, 310385052, 804542369, 162375407, 224862770, 150802326, 642808810, 100948094, 206648259, 786919632, 168698223, 95916430, 973081248, 465501375, 955567815, 827595490, 403463011, 677299323, 45985973, 285966745, 907723988, 498207884, 659447231, 920234178, 210689320, 147630328, 272067129, 329590476, 955091961, 452937200, 873928377, 545236512, 388999448, 579907264, 121541087, 906540644, 247592828, 971258226, 650350534, 242827560, 627987775, 672601537, 1551903, 787774589, 52277062, 81980683, 144736744, 62996777, 458053965, 896950054, 600726798, 313499520, 189096625, 139121049, 379944332, 448939464, 835579787, 142837087, 368310625, 573599459, 466002397, 7106140, 903224960, 530295923, 151910863, 186314359, 104912059, 725409751, 820212090, 416322617, 829388762, 42974691, 147543631, 924372233, 815776648, 528120052, 496963597, 738129475, 600374222, 137352096, 725648064, 545770599, 808128282, 231842675, 70090098, 837218046, 908837671, 904557386, 539697842, 173140493, 339922433, 6373810, 537882418, 401824123, 149102268, 351245796, 822593425, 957794600, 116867105, 652286036, 976140428, 937564693, 393107098, 547631592, 335588192, 680393139, 202530198, 559670832, 116901548, 933161734, 916591510, 518921923, 642837464, 788927025, 893368448, 814163858, 302697070, 749117770, 870537852, 178887783, 288809910, 160596350, 495562256, 701688914, 680257452, 618437786, 354451361, 354768598, 211030120, 909563097, 127831834, 988965254, 75270118, 149588762, 728491117, 566639174, 147583669, 328884209, 6129787, 28951807, 856202099, 989077247, 190418344, 154415722, 827825149, 625039130, 414442972, 59269678, 153761889, 477718204, 330301344, 179254436, 549652154, 817546916, 303248692, 122975452, 306007217, 406977868, 369487347, 279045878, 746979591, 265417449, 226234684, 991889390, 795321745, 442961031, 23776727, 361726666, 457230734, 848820261, 228358765, 990610734, 607656812, 709386519, 459994037, 837713203, 67678855, 521359012, 765651090, 152700119, 291779574, 979563010, 384590769, 333369437, 230130808, 379469544, 789703244, 594057525, 472531111, 555172159, 255138431, 469160669, 770810742, 224014354, 245497359, 845598655, 426550120, 306652233, 837840291, 564737371, 263774315, 921854945, 715648004, 675654517, 337268265, 323600288, 838762189, 482904224, 539646127, 509187407, 671777711, 985253356, 554767320, 324249061, 901098391, 816969038, 881980222, 718547010, 634791164, 177787622, 204620013, 338902975, 600979314, 728934004, 573075446, 36902966, 988205444, 207932819, 70902004, 449751760, 506380837, 573143940, 133895629, 199579084, 116957325, 765805286, 69318133, 256808406, 515872716, 188485921, 127364034, 59272270, 378888197, 254264173, 31243098, 189298133, 946739035, 972579743, 159044628, 777002312, 840111755, 556071961, 3143592, 215024963, 914533460, 449248244, 599772511, 60590829, 382373138, 341774055, 38664669, 66929459, 415742322, 681878288, 193918778, 315581998, 483042518, 132922927, 897135020, 977175563, 86921468, 505610350, 407932142, 811379634, 463791886, 983119924, 876123012, 329250506, 55905597, 356751302, 413226020, 972182562, 739824053, 616157794, 222901597, 438158469, 760850079, 282333090, 971582799, 648264169, 81917122, 221702282, 314402376, 584408671, 813889865, 808198133, 845688740, 168420356, 886653652, 37563227, 461895041, 384530425, 249080945, 849765199, 290374268, 402897768, 302468813, 266958560, 58446738, 314733455, 308845660, 552242621, 878090115, 23468112, 624645667, 621783675, 492555653, 795504089, 657281689, 545192612, 797780431, 470185410, 353316437, 295490240, 73691772, 694025273, 115122878, 301082772, 371131757, 919426439, 3240734, 294754693, 868411098, 173907630, 704929987, 129947602, 290210438, 574762277, 762095203, 648542177, 126783000, 202682113, 154928424, 578228662, 147275428, 43275473, 390620740, 894872741, 637345018, 866932077, 520676190, 168958878, 43454253, 607704045, 138533505, 207807324, 910754127, 456576815, 777442361, 373639278, 663616534, 929287650, 603389087, 863766811, 720713058, 590335061, 239071385, 983146800, 172578449, 344447207, 209549691, 774287982, 302308709, 247895535, 724429676, 7840935, 902764939, 45784116, 374193348, 946068076, 954340135, 577459737, 166764495, 410261835, 74587444, 183730901, 124503264, 247462058, 209874324, 144848881, 984021158, 663988923, 173389682, 96037109, 198303596, 141298307, 517883747, 373378796, 136414946, 563607033, 818910684, 308525442, 413497853, 649009855, 998723940, 896399193, 175635539, 452805025, 699709379, 56419280, 146191137, 823322088, 912155702, 847788337, 723260123, 348021359, 367314584, 45613605, 272553596, 250430508, 602855370, 883677996, 627588039, 297841617, 196639525, 167041862, 951797018, 149264034, 531271233, 766552198, 106281613, 667687391, 631445277, 710908388, 795378204, 76415852, 741286354, 78289421, 926238137, 396886434, 330124594, 50618997, 626513196, 57743595, 356601441, 275577923, 830987406, 560632489, 149110664, 604069966, 226266681, 704750531, 110649251, 206532811, 509506677, 584140809, 66554430, 439514151, 920364982, 990005082, 913859097, 645415144, 779668267, 142466768, 680887681, 673787261, 829144583, 688083113, 940540841, 106678396, 798520813, 797301616, 313251498, 438630559, 763224876, 925301154, 48993259, 580013699, 643320010, 79322618, 672235372, 148973156, 607029039, 766944023, 919528067, 921786995, 268225103, 900653495, 771379990, 827307044, 233420716, 130064681, 319958415, 91817255, 985040932, 838860757, 749784845, 575559864, 492739685, 198327158, 296326344, 666524324, 155406962, 455936722, 313183990, 540673299, 311684766, 396597180, 477572766, 498975842, 252768814, 377209300, 435273615, 361759833, 25087890, 963691601, 671663561, 132091848, 490722147, 336600691, 27136027, 868521659, 883162715, 852219613, 418707568, 475269983, 254887759, 198007359, 609796553, 648452408, 192581633, 194050265, 291927454, 866106948, 169208268, 955283722, 97526587, 445250440, 269700483, 651956097, 609509652, 711997603, 627285294, 483732093, 198304624, 311444904, 859242919, 464105170, 349104552, 40304316, 540874525, 60138399, 2826839, 990583476, 779708043, 266767601, 852992273, 385901809, 792525536, 391133782, 384025019, 510774156, 785841324, 31791074, 96292032, 466328417, 386897051, 314264397, 917169180, 574570217, 587863082, 163863321, 321422150, 888419969, 630291048, 798221899, 449686483, 561599537, 128845079, 16082185, 120184125, 601776822, 620601828, 13924303, 826636677, 720394884, 924808915, 916981397, 513770509, 648166992, 963444423, 26842667, 30016973, 253493178, 722413622, 827410980, 581532351, 372512814, 447983178, 248097099, 883465530, 284158484, 53066250, 661422923, 257850985, 219082808, 161909853, 200589103, 735470281, 600331965, 98700440, 721656227, 264174392, 499324930, 286540756, 180354780, 998774019, 865401081, 351277559, 440089621, 324388621, 783622626, 542586477, 686635088, 335020533, 948735551, 658075462, 466122306, 927771329, 703670250, 132112374, 901871955, 883775650, 600841167, 373172785, 208807221, 365778627, 562524059, 158868587, 293012564, 11396016, 106624104, 969634955, 743985517, 56611997, 513000670, 145488298, 819279180, 788418371, 751072731, 17551705, 616611103, 569006825, 728644900, 991726423, 259258249, 885323138, 367878942, 375039943, 926376741, 181565919, 326286647, 925517711, 515819323, 999990870, 37414613, 712120149, 179263378, 994274648, 655125128, 955606473, 58129861, 517420091, 731499632, 965927781, 64655035, 97055413, 449609237, 632279059, 604679602, 167782450, 814703537, 502610020, 366806641, 348709410, 563981022, 355984561, 481050016, 197732326, 240200039, 158218689, 562030991, 456052999, 821011043, 791522297, 136341249, 107837789, 1683313, 229480859, 571340382, 222387782, 772551439, 793421873, 971789907, 870494293, 650301686, 195408299, 132212135, 399649517, 86852339, 648617469, 480355583, 521510619, 436872647, 329505946, 532948844, 880075055, 709534164, 683716067, 172803689, 174213500, 608773054, 623607797, 403800956, 664121470, 463949926, 115422400, 569640708, 742567134, 671364897, 757779290, 590274956, 838164675, 952039089, 539803039, 895594029, 943732890, 521609599, 108939973, 763953935, 626205620, 424620300, 161866484, 601015177, 888273643, 256214925, 648582338, 302429820, 225223123, 945776412, 88018506, 726655484, 311507029, 220403691, 732875101, 892516013, 39859404, 351413895, 965745354, 991091632, 464084958, 535020153, 574925678, 383707513, 29750896, 761788003, 933117273, 71588115, 908151637, 403483425, 664001611, 575747168, 711670764, 639837485, 439672868, 372163275, 776750900, 985268814, 266834885, 71189094, 688296140, 651942753, 560218527, 936161397, 429207540, 36225769, 984392144, 670253188, 787633483, 818391112, 930412250, 474109508, 824476402, 734827060, 354199243, 353457193, 451950120, 609227759, 450412138, 442288546, 601984962, 685122189, 54867862, 35901814, 260824657, 2559426, 284457664, 25839186, 398926157, 179320527, 767931468, 843528527, 827388443, 283854689, 881056741, 760360889, 30425339, 543172235, 515733258, 41034664, 224680268, 430783803, 9659635, 242913469, 91574354, 512208257, 547375770, 777344558, 57162791, 810240135, 666711834, 993773551, 957496960, 445661662, 414623893, 330702892, 960362183, 181672940, 511646162, 642794219, 286302317, 551857122, 691348248, 409676394, 807699915, 194538104, 366147870, 28083981, 70289325, 870608662, 363774366, 415310994, 409192011, 573882863, 55179712, 52081355, 384869097, 87296276, 236002895, 509573950, 437998673, 571592057, 597145897, 884118934, 403243402, 822145459, 418190790, 461978143, 482352970, 885789699, 270708343, 742227898, 913763487, 571312902, 352621265, 753135174, 971878590, 85500524, 942935326, 971355902, 190105039, 849534389, 160208597, 816135185, 825389906, 385897415, 524434892, 194386751, 917353000, 409437086, 795127401, 613013595, 511067147, 728455236, 120330417, 567344728, 371215115, 899740854, 857465171, 680592388, 372844760, 665032260, 706726898, 489874943, 337746758, 241968129, 271604715, 464149723, 62758011, 746680821, 622854375, 688120678, 41544599, 980874064, 555872842, 613478974, 977710037, 661907844, 19532843, 62954869, 988601009, 460459700, 512011603, 185374272, 981695367, 546319984, 723315135, 302828738, 438618685, 409250100, 576407936, 440840624, 151264941, 625645644, 611073255, 149808386, 945410182, 994431590, 548945364, 102191400, 826800462, 429281436, 879645335, 846618658, 149426894, 22309092, 914636732, 92027541, 398713529, 161159418, 633556401, 229820001, 76845106, 607046593, 148533147, 111608788, 844288133, 158508291, 594410770, 749460902, 52797168, 164256219, 261095380, 610503110, 350997296, 151836925, 56354954, 170909038, 276505946, 739074050, 60641376, 142926033, 504383787, 148538980, 866952564, 231747423, 506681718, 46025908, 682644565, 770457964, 270948637, 621831944, 364447510, 328888841, 862618082, 798011239, 704073061, 966801718, 599954488, 240591383, 160719530, 80413525, 109228493, 714210044, 317612976, 719907648, 869081045, 800210182, 377389259, 816296699, 973226913, 195729934, 539898557, 745257411, 364497065, 578457341, 494052165, 818929179, 35729788, 252824453, 973559240, 607774025, 655235205, 281476985, 831987980, 220722274, 516330888, 900665038, 712122160, 212634831, 587019298, 297871972, 788246276, 884677689, 877195169, 917779084, 685918339, 244926582, 38368269, 793216462, 864229758, 136353119, 158820308, 549975457, 553151012, 21286983, 824938484, 177837882, 14310315, 729278297, 338663473, 786879114, 945497512, 516113471, 152804480, 756864705, 883734354, 506622295, 930521109, 938306154, 658703856, 618007019, 643843811, 630439991, 221926127, 284546728, 859319815, 948518078, 67329734, 281838014, 947664623, 508674420, 513962562, 381164876, 777610799, 926426279, 783308682, 847861709, 550647942, 852305311, 857479213, 275504574, 605292192, 632705511, 313624523, 539525409, 377727840, 391035973, 280786386, 803390305, 508978946, 762481839, 722803754, 200690543, 989844506, 904651981, 730810675, 692296615, 826219388, 765267956, 495474599, 382878339, 55733176, 661649389, 983603599, 5519234, 619532680, 716473985, 982696346, 552931016, 371317741, 537890858, 32159499, 788611646, 403628686, 497307425, 214232262, 37052892, 533962407, 406565773, 463344154, 6870792, 761050513, 949798778, 728510245, 1254412, 992469795, 437485466, 34629152, 423449978, 953835515, 500266389, 945036280, 344292085, 295943402, 745194103, 458540742, 200114666, 158765400, 491105124, 699031805, 147693552, 479293731, 594153036, 535755990, 310629883, 90657964, 664222505, 772617323, 797641940, 836946929, 311986170, 147498916, 511425466, 295386365, 177217037, 233147380, 817025398, 660224472, 519159459, 377285449, 207040538, 575720042, 952276229, 924312938, 422524659, 662988787, 962981497, 145484447, 922374069, 842995249, 186490553, 720698187, 803169976, 933847845, 807717068, 404632521, 413454094, 222049011, 730249610, 50421510, 828153539, 908698576, 584049001, 676114301, 200196379, 787133514, 590439326, 530765977, 417812282, 509941575, 890953017, 558753913, 200383293, 605482277, 379534170, 766064930, 808277177, 293519740, 352311195, 247156839, 806017902, 671115003, 323894121, 248568617, 871102954, 905980134, 240740116, 492387707, 401327940, 638184096, 942022922, 17418809, 436952058, 666952419, 480627422, 575742944, 194779111, 303004455, 697010958, 44845968, 985971102, 745333466, 986767064, 180349330, 853665276, 146268535, 357022512, 984410919, 846493698, 403274489, 680040964, 750366072, 310212136, 738685219, 92425577, 642952401, 50548306, 11591474, 252819889, 663008993, 855679632, 417343926, 108660992, 223015472, 875785006, 260432931, 569165397, 76880127, 28995209, 622067505, 731105289, 307538826, 114293852, 984112287, 412147631, 26504257, 139570360, 666010731, 31343525, 997133033, 316945712, 998429674, 615864848, 881518111, 203419261, 616109234, 572532404, 678541705, 420407952, 491587251, 13518659, 497328985, 81072512, 176346620, 517131650, 202727695, 535853017, 966720398, 815801913, 401321298, 386918798, 778666585, 698760276, 18399591, 130979886, 819504142, 6643898, 395406863, 869805063, 67213253, 844231718, 937552265, 363791047, 924039698, 15800849, 474346633, 186287764, 135557675, 673880800, 293074246, 400101627, 373591127, 160549811, 317538469, 784255631, 896766705, 148110832, 266372883, 394926565, 536076082, 407693144, 657518794, 955973838, 967147587, 172231024, 530860093, 824061797, 578599225, 153462131, 890380333, 43200268, 290853444, 90938947, 806974376, 945843982, 776674058, 919840079, 363330893, 543440260, 241099698, 335223016, 67832337, 79167461, 551597750, 848227028, 248399656, 246338913, 548855223, 670832160, 955796552, 30757417, 283936488, 791736194, 33828014, 776458269, 562703196, 328868231, 366659977, 661380085, 461927387, 975699533, 65565000, 199073384, 716817120, 748917927, 588886534, 264694323, 69546625, 998939022, 765926192, 19971614, 293066568, 70253272, 827240922, 83520528, 871024216, 239781504, 935687011, 410706985, 438586400, 505828807, 557299319, 765520903, 777144319, 723598136, 199619470, 733175162, 241842263, 608346613, 399126221, 592036789, 476238657, 16520202, 655177473, 811737786, 298828877, 935276124, 689517206, 797070416, 756759991, 78850724, 625199220, 290066533, 800609978, 447884216, 12600509, 650086867, 203763634, 486248610, 465268655, 958431398, 812283384, 402409968, 387922335, 231547272, 487714039, 715712478, 211020752, 625024467, 327024143, 252803707, 77103547, 306749924, 205185187, 608844573, 673214046, 88265684, 323320765, 509711413, 53007991, 848242797, 230733361, 830942160, 303276721, 279752514, 387294594, 94110443, 282837377, 535039712, 942457602, 144338425, 77721435, 74080838, 822769144, 655437925, 635332372, 688470584, 494780116, 271674281, 612932177, 350586253, 846154929, 203792337, 125306978, 212752120, 404011661, 172971397, 189412164, 196016176, 962269283, 368329464, 268944885, 171921411, 931340370, 187318815, 579694198, 213749396, 354784935, 922786180, 273590371, 196959061, 447593159, 71629613, 62383907, 85755478, 201918907, 883847057, 500696280, 481874280, 51162438, 217389154, 993564722, 468632869, 515373483, 62936671, 990595054, 955834003, 522667374, 36897701, 21172428, 425960261, 817241710, 717492922, 862530712, 944573870, 522736036, 33978540, 933105951, 6658537, 434319424, 24100880, 507041098, 165369671, 77063521, 987271939, 747561125, 500074634, 527097222, 215288375, 242818407, 49002057, 118564564, 920858303, 442791151, 125052863, 811195703, 322277631, 900137297, 628822161, 344430421, 784413822, 431117666, 169763825, 383528061, 341145409, 538734624, 795971668, 968235171, 301652112, 994421453, 826808227, 14879819, 148914969, 44169026, 250199462, 196473180, 642458812, 57566216, 230804282, 571474432, 620122213, 846217610, 67276511, 825825941, 918367993, 745508909, 827216953, 569394637, 152006273, 696083784, 115672805, 739476119, 943891813, 18564183, 927701646, 470277718, 342031811, 172303478, 868439930, 134499217, 254055794, 745328725, 449925451, 490768473, 587582511, 389987093, 78108430, 421836681, 173673462, 966161497, 912889722, 104093715, 823872976, 835599462, 174008341, 838548951, 161190675, 953709473, 459665111, 97061351, 419672456, 456949344, 741333035, 436584448, 857154621, 332844493, 714758998, 723903079, 387224924, 835493008, 740535050, 728583637, 914288779, 160665668, 920876162, 405963822, 740886806, 185071856, 273632222, 31431427, 643265195, 33463550, 574635125, 375573992, 661256963, 269303307, 820561944, 520257120, 975839931, 685381929, 61326023, 810807735, 212732436, 376219141, 509281750, 102971511, 998479393, 971129081, 315042100, 479419276, 82430763, 341097522, 739037707, 540746859, 758186461, 912584522, 693512386, 853990840, 820136121, 511452497, 147275836, 155084368, 875170476, 854238584, 918340419, 771308578, 354462286, 624832549, 391584269, 453972770, 840766435, 942184610, 44914616, 45821795, 428754317, 122489618, 699199856, 808875612, 757663059, 574638559, 74973444, 16082197, 998831496, 839032945, 839241112, 929237250, 999897699, 897752918, 933682059, 359657171, 485401210, 536087536, 895416199, 755918045, 693899906, 792692512, 180602435, 881818607, 656766438, 995477794, 760470937, 905806719, 858532755, 290575897, 718719232, 172426070, 925066920, 558928967, 393445536, 894900829, 962229349, 755716561, 155793001, 596939405, 184417128, 976896811, 924300418, 10907983, 979542800, 852120476, 982702673, 568812390, 314634231, 726528090, 42326003, 605001809, 85777556, 251423290, 716458553, 553745279, 575814059, 426561983, 198277431, 952123875, 833068656, 671292486, 561671928, 977954188, 86830409, 786573675, 699586992, 70349782, 459941624, 939760849, 918176143, 816765632, 855368570, 35469950, 790428170, 151283720, 609227358, 140136829, 970479868, 17169085, 964421036, 386491098, 84740902, 714500612, 556616883, 242634398, 465167708, 254501868, 923782439, 425781862, 782872377, 79817973, 173145918, 529690694, 464167165, 607121369, 688098947, 952792550, 383525106, 474064540, 844064949, 966331083, 276910089, 123017522, 540943011, 83681407, 970250876, 845311316, 337194076, 697259417, 220789728, 605453986, 611837444, 201681692, 981118571, 464905505, 85026054, 513638849, 867088931, 31317237, 384460459, 389635285, 794965256, 516210937, 624006534, 804794930, 897746940, 815961658, 153762914, 160111694, 473345892, 224154569, 868905195, 710569205, 21512717, 588225078, 108213221, 946445268, 546208997, 393856768, 413171163, 736018692, 886607686, 903213863, 852887374, 287334450, 494388445, 483195480, 113131526, 924410709, 36443018, 41810877, 720336196, 37460097, 193391510, 58636094, 570569139, 805045630, 790046193, 93396966, 403487263, 452675304, 399000086, 930943055, 5339415, 540932015, 931947259, 483739220, 547105270, 749260712, 902502913, 993831405, 776639006, 469378193, 474044889, 664245478, 27505861, 540388337, 981645664, 143976424, 278583267, 193040602, 520222899, 478153633, 288409988, 589935433, 732111399, 305751886, 539539276, 890736742, 496862128, 841630682, 562334924, 371083070, 593264120, 997826622, 854129729, 400744683, 483260273, 995559589, 117139494, 12858661, 826352655, 146017668, 193110536, 547048736, 641764186, 572399691, 685421014, 436635893, 834825320, 645992784, 308749215, 210926529, 641852412, 208284057, 427927798, 740819663, 908657344, 986949205, 210459351, 21084825, 699761283, 187785811, 695725690, 465136388, 247907259, 3572948, 700377011, 838115366, 109873176, 701934011, 668109974, 964880107, 145206717, 69440227, 361910508, 486823337, 754038113, 451924854, 195313646, 70345505, 736030553, 683476916, 934398356, 601079791, 54189601, 967218025, 117977430, 342039708, 524252124, 76639243, 326315965, 315616686, 524960169, 311148819, 811952350, 52384908, 943567978, 63046039, 332455533, 837039057, 836085403, 20194688, 782684335, 598972752, 896191160, 663690593, 188598829, 82713767, 618099194, 731431135, 343772972, 197663144, 87744546, 28814071, 618862540, 447535592, 319557935, 269773477, 860840648, 512731214, 734573098, 921308009, 341999306, 88003726, 894117557, 491790694, 922301003, 717962107, 666241402, 765973129, 843894289, 775521522, 863977129, 580705598, 726622438, 850342190, 239454899, 351058545, 585096113, 458248838, 789579279, 848495717, 516735640, 754786091, 805920623, 959266096, 667046330, 475649189, 676183266, 613543790, 197431434, 679073658, 22295688, 647746221, 306298693, 434957116, 863081601, 981710508, 190840941, 710609927, 310649508, 135682537, 901779149, 281345734, 53070352, 543570014, 551382077, 365225529, 800462689, 506174159, 853862012, 144036419, 294138201, 274360891, 127560190, 749233063, 973034585, 584264689, 941460751, 305879537, 760811305, 969988607, 811536046, 444151882, 366592334, 223483624, 980967292, 919231609, 144247215, 839417834, 707626290, 987965100, 335426514, 390469370, 469398012, 744635147, 663440985, 565553297, 951404307, 869828741, 96955322, 490241038, 63188284, 605262088, 178790409, 509216990, 939624726, 102104911, 587985614, 890532218, 322434281, 989531129, 721102263, 400373188, 15443474, 367623161, 442288287, 455228069, 84840407, 214563229, 820838062, 850583612, 82555182, 297147814, 467196905, 420152254, 97614786, 140130194, 602730924, 545828090, 930948917, 806061481, 755967178, 693053918, 961572102, 634956346, 296440446, 921826888, 823470408, 104290287, 950304906, 927405037, 999633710, 827340244, 225124649, 427087398, 651483054, 234147059, 605188617, 672258067, 452317674, 390141346, 58773508, 208341280, 89349753, 656598701, 995147372, 704022104, 509912591, 645647379, 880689684, 471349936, 530703140, 246458939, 567155859, 106558007, 640083851, 811568262, 275883007, 519127987, 817084301, 710558437, 535888418, 622861835, 99046065, 168571158, 669547601, 988405059, 402654983, 375331146, 471234415, 8957418, 632552708, 998717050, 308735919, 142535750, 532176976, 642421570, 734591784, 832735851, 510154767, 47031943, 305014054, 718513336, 111403366, 441681512, 137016549, 461037330, 923004452, 90882293, 212386131, 976528134, 278355471, 860135502, 845175186, 711384491, 470401607, 118125787, 638518851, 967831959, 354617594, 289261229, 551075069, 315444670, 16358633, 73550926, 384291372, 479513453, 863554746, 392123213, 329309116, 283229437, 155378623, 116587935, 461444563, 639495448, 387605873, 896206253, 320997959, 833639266, 889963211, 2911407, 248079591, 313585422, 54268611, 761022821, 478997502, 867708445, 891010135, 653374024, 51509837, 763195683, 997376989, 815686850, 545080242, 768730682, 314785384, 859937961, 601956464, 922862864, 526266014, 163190087, 127677942, 700747930, 237519942, 505358480, 742980612, 306901455, 441594738, 121317526, 820647299, 107377626, 878830199, 631283110, 338104792, 484150366, 246806787, 760092845, 820129930, 482092746, 553766839, 51142335, 84012844, 766023329, 111395498, 153805139, 719039258, 194584443, 323285326, 387763293, 25579707, 542872165, 850506884, 540765611, 916521774, 146870780, 131645796, 960484796, 133172270, 610742340, 120382089, 303471466, 375058626, 369839462, 535600264, 275329149, 818044413, 778813023, 794614508, 295810446, 106022088, 389758244, 620744241, 820520435, 780945294, 417796571, 811987550, 918431830, 154432207, 214402854, 447352288, 670681780, 181006395, 257303370, 811400223, 882562502, 826891760, 868659309, 727699922, 551785053, 891946772, 497854510, 864319938, 995544408, 248531341, 449302894, 300454045, 618327382, 509254848, 345956961, 152457242, 319157069, 293712094, 141020988, 975068628, 784708000, 318092382, 871486528, 342102430, 185820865, 286188502, 906616756, 417420438, 853835570, 274995982, 432037849, 263745241, 924566058, 995019602, 315099579, 21981033, 791388782, 254351292, 745037028, 868124719, 213313202, 450607338, 659572425, 888392891, 215293451, 887141287, 800476539, 160185343, 55380021, 274768770, 470103995, 423446675, 91134315, 190019793, 720693053, 729294290, 685780846, 176065827, 516249347, 745593193, 255683846, 119931576, 805008689, 259768095, 901461510, 593629804, 164686155, 13388440, 656652871, 826196658, 416128041, 160098347, 597185629, 516825472, 425361655, 266391949, 560267040, 113176879, 875669159, 854808441, 368537512, 456748808, 194524694, 536653635, 606581416, 846847830, 982340970, 111158242, 28405691, 510081541, 516919492, 678371035, 349132307, 390563734, 674177925, 569334459, 853147925, 937944235, 747420716, 476976327, 416895243, 756580437, 497811972, 521792898, 416640757, 826017822, 949263936, 388236922, 60667409, 661121142, 247390196, 495366388, 881038824, 877479637, 233811352, 462090266, 764188500, 90468041, 191373488, 909053838, 251695746, 375682111, 820559203, 886292963, 670628445, 809336539, 787840830, 545038497, 958131444, 235368117, 998548060, 417323192, 619416558, 272280791, 672632758, 148543640, 565728935, 829420504, 922597409, 908193161, 254178799, 967443973, 34747906, 359599529, 121485562, 827311307, 849141771, 409276271, 706865146, 876005451, 297354512, 984363723, 284306274, 514828952, 316522464, 712581844, 487457439, 840747264, 642678143, 313258445, 467537521, 482976792, 403209745, 895371701, 94828175, 348919456, 496811154, 590623205, 950866089, 902769478, 853266044, 100018027, 711790550, 826205828, 219820016, 120612347, 120122924, 472680355, 630717955, 410991938, 904585127, 560572285, 506349100, 574356968, 246519033, 30234486, 649517050, 813802264, 507113538, 857036295, 721219485, 880521062, 789009926, 693355989, 195754008, 780646424, 758225969, 767649473, 16570265, 820351814, 154323000, 7684082, 645898462, 425810234, 845485461, 386138425, 605051857, 923118389, 810943796, 181828321, 960227784, 199770631, 708598513, 547512956, 293819563, 458233261, 86679475, 867405082, 954934231, 42354931, 522349987, 267406275, 236020551, 878543984, 922646198, 81620770, 439188960, 215951202, 319943326, 743088733, 604771097, 914398041, 654940608, 585921106, 991034583, 604698633, 68199971, 245566941, 562290409, 134207660, 293090192, 731155653, 786618368, 119937899, 329551527, 330892409, 198928729, 898737288, 153336124, 881494206, 835673335, 804098184, 176117947, 996296611, 510419330, 21614284, 852011484, 373375790, 260882257, 189516701, 233743194, 182409922, 785378887, 803307026, 816203982, 484094253, 354016914, 222061925, 669358064, 940534431, 999573400, 702412161, 304110639, 34065097, 346983930, 67298328, 558121602, 123328623, 678185157, 189596508, 478997651, 421017347, 62915970, 950667883, 662124291, 843059673, 353476263, 813891908, 115029668, 425272174, 269839419, 970876251, 583680673, 381669881, 555052653, 643020566, 232865122, 947179783, 255160745, 793395269, 284661301, 220990675, 693450996, 910896688, 832331375, 151286818, 441550719, 790213518, 932478410, 436219095, 869280150, 970825201, 622277976, 436466923, 946839047, 891742026, 670134071, 881319295, 3225321, 573596999, 123688780, 528142158, 544772924, 492268738, 86553588, 257490915, 378514743, 352477565, 940036812, 590873088, 68291854, 871460318, 493820513, 737837428, 931519211, 297061216, 978678762, 834576065, 902186436, 743615146, 745083355, 487178628, 33494162, 153944938, 665282160, 952702906, 847615421, 330574411, 143317974, 165719066, 629944985, 81796313, 663387138, 497860251, 505523219, 699526011, 603671496, 441337412, 10174599, 644975644, 312684159, 922406718, 289253084, 358976904, 218758231, 395821148, 123327354, 859891815, 655876193, 484703436, 291366829, 148788362, 891584793, 496538262, 4701558, 629965759, 204565792, 201536724, 242928987, 597760138, 767752324, 649028525, 981962877, 209191221, 513164117, 219185990, 315208756, 868727575, 622557580, 653620417, 81587328, 939736136, 669850975, 355546914, 779263670, 226549278, 817179884, 417261930, 70976956, 174896232, 297821343, 890633896, 326703385, 617687763, 3194787, 192890349, 715202785, 75462950, 254946148, 68042897, 783918921, 806670264, 905719616, 514869540, 169240827, 279797011, 979576806, 829160540, 773713804, 935376784, 744409227, 274390090, 12113249, 215727617, 581459508, 925533272, 675109124, 821381982, 135715074, 318487742, 867896099, 402113218, 336473345, 832732356, 511765323, 399062457, 659146063, 547171031, 20309861, 668222437, 85404819, 733908265, 901786565, 480104867, 771476676, 184380177, 336398113, 616276375, 355600475, 962789548, 398919224, 103561203, 38375890, 732944583, 689271367, 972399585, 691128789, 375732436, 394989988, 864217813, 434252645, 809892459, 938305218, 64898836, 357907728, 844838857, 703036951, 691035106, 640478884, 187119878, 266975836, 79356234, 88909657, 440797888, 384513289, 661108376, 680954959, 974949262, 981080695, 793513465, 759452337, 144855166, 246077953, 568452782, 546317449, 412233065, 296178844, 460410649, 89382193, 861900060, 137176535, 322530992, 22180524, 431745164, 597865216, 492439455, 222886219, 442705431, 70756911, 425719770, 578880501, 941984011, 179313412, 41127944, 836546095, 600538101, 197448911, 611407875, 381766244, 377376210, 801589933, 763249481, 408175798, 442949374, 475809072, 283824135, 250700207, 594635643, 912799566, 315787410, 427663669, 18477673, 952405451, 900879357, 665016353, 913864003, 705683910, 92277662, 32015844, 994684489, 568918847, 446588969, 500279188, 220171163, 994798037, 162985442, 891048962, 273846616, 466484732, 139492966, 604472736, 558434222, 311126350, 140074310, 459669431, 660067820, 173227889, 512373610, 755072850, 845103148, 96161667, 184155983, 812075338, 350408422, 791678491, 766737338, 39878890, 654945917, 254585887, 49168936, 963342108, 96690232, 752516874, 152349790, 861408071, 223025422, 858394544, 820831481, 268804989, 590268284, 628515908, 500748513, 214817527, 984283385, 919663550, 801216536, 321734267, 79629119, 621071655, 251885874, 811390841, 705860515, 683060731, 387763365, 847883805, 650127885, 952025619, 306105755, 790783494, 149441531, 302073800, 109993220, 195973122, 123901475, 485956610, 598603381, 954896570, 106618693, 439825053, 17266374, 579258419, 549251808, 654943123, 356239210, 177269443, 710263927, 879607187, 788233209, 973789797, 28682307, 798200541, 81373454, 793273023, 19125903, 518513618, 311779637, 630979051, 609970754, 235961461, 947625485, 760428097, 67201240, 311158804, 612976032, 48581368, 510149262, 128355094, 504184551, 474880714, 119614327, 709451310, 96725908, 615471230, 470322930, 546761910, 486417133, 941319207, 45471834, 237141308, 287766855, 153411490, 254708576, 949226197, 975459790, 165708921, 611521003, 779065886, 230835031, 580996891, 157337171, 918977619, 972372657, 74863275, 609883312, 989257144, 753726350, 607970786, 527921814, 751336599, 391400270, 59431755, 92128704, 507041939, 740480677, 955629676, 197854554, 442427363, 174782866, 178373647, 701752508, 538422794, 67551083, 859801967, 118348534, 443682734, 863026240, 127527454, 280531781, 359187768, 870419227, 136507191, 43458494, 162945252, 616749104, 270499664, 367685121, 799392695, 211819073, 915815511, 94925312, 789894664, 340128811, 616146629, 954444817, 960128885, 838093932, 924406169, 928635641, 781161577, 937036738, 5516405, 44107035, 572813809, 891799214, 635447392, 944285706, 184711213, 967406822, 39622610, 987301712, 462749015, 354548724, 106147955, 865408439, 401850489, 542372011, 830987056, 99317686, 348157139, 978066421, 453985888, 945116427, 558373227, 246729134, 434256609, 923851015, 101104023, 31804873, 130757588, 748327709, 140835695, 432846331, 336017866, 842200624, 273460204, 148272278, 995918210, 937935909, 938838965, 846339149, 43094403, 492744230, 576999738, 289422522, 359454061, 935865367, 198926517, 97351966, 392947727, 399414749, 211853670, 725976909, 31262433, 618456033, 968113583, 240658708, 798081132, 361052345, 693652657, 619628496, 329311876, 38568090, 623769335, 784818339, 802303256, 121811499, 892769281, 983047945, 724875377, 777505653, 105031576, 968974364, 105798721, 608564026, 484576038, 122380766, 600150971, 434404838, 187260499, 987291024, 666907826, 486808148, 886918355, 231108913, 43055270, 951019523, 49335407, 267019909, 429684002, 137620016, 700078524, 499374745, 763512088, 137151660, 480201203, 785859521, 506445506, 539703395, 249095498, 659315645, 85180129, 294386140, 249548205, 98524117, 582956561, 449752238, 501751038, 684246901, 46054252, 524517719, 505971090, 812245745, 312427369, 509480761, 64335086, 357992194, 421347993, 410650888, 959805926, 768165455, 137676552, 932938915, 48984943, 274750529, 491958719, 709035467, 785650375, 60871287, 46155294, 72233102, 193365982, 397044868, 140165201, 293200970, 723263101, 28985326, 624949833, 51949738, 37707712, 57106650, 149573471, 197217586, 63483112, 963368505, 42772711, 168400130, 90735036, 790895757, 665045475, 975871345, 781195412, 267089449, 25156421, 455309751, 237332733, 904708919, 709293879, 253425235, 404588652, 240574105, 921089685, 699177581, 104301610, 450335447, 120342500, 590669245, 841030438, 230490441, 996597423, 159818237, 159235604, 263118122, 160393160, 455898473, 205205812, 20607460, 499343406, 628061893, 175704564, 420845274, 485679189, 893780125, 977297712, 931965206, 26072844, 353477648, 510012967, 990084124, 266248135, 997452711, 276109761, 107634541, 732180358, 777245385, 844625876, 828656916, 488802068, 123055070, 7845122, 801379827, 813331412, 280696294, 604482252, 551230391, 618027930, 312210896, 185306190, 849669293, 434975470, 557779197, 531786544, 19068960, 427866991, 424547707, 208156104, 304208058, 477799720, 965581532, 800343995, 674349296, 610427080, 482733439, 470644830, 153177449, 181983193, 475390542, 618288660, 975385962, 230439542, 647316207, 812917132, 661768787, 476135682, 449056158, 81677831, 371773145, 580814236, 631262233, 486999335, 876882446, 536518922, 980691374, 2701988, 862375743, 990054925, 977001164, 899007407, 242153842, 292029484, 173180314, 647601209, 645080830, 793785610, 364864340, 606158902, 394336015, 84695934, 696609622, 222838954, 647190088, 874073278, 99517213, 590692700, 254983314, 568231389, 885502202, 101805241, 704563953, 919265603, 912615612, 116639340, 361552810, 352740368, 951717247, 915667562, 801255297, 755260302, 195000949, 963350051, 635373308, 308146711, 550364275, 905158274, 406020626, 294680384, 319100210, 914989720, 201350166, 863290567, 427246264, 332055571, 195674912, 496622633, 212435774, 79645460, 484523559, 747920957, 31673606, 83344681, 816653213, 67778766, 568347, 236311212, 583956683, 489622077, 57523654, 335197898, 768999954, 518071361, 410818403, 126818663, 620348556, 818183189, 218035011, 498090449, 143421592, 45555792, 80683836, 664722177, 689834780, 518549624, 458634878, 61346922, 460185524, 577738056, 335308772, 387549859, 783641462, 724770429, 492111054, 911205052, 575645018, 186872810, 10087502, 242839305, 717157165, 831173483, 1493577, 339049375, 961455917, 290152027, 540579095, 291463088, 754086278, 238197683, 697985736, 364574002, 518170202, 461659422, 780579743, 872175952, 351498593, 184425577, 367698536, 214785180, 558091841, 607715418, 302546392, 714991191, 210936557, 44791723, 706905888, 104709056, 385433208, 869725894, 747933150, 736225036, 811501600, 934666473, 311761263, 405408896, 355050290, 707664939, 198821466, 387698998, 729725926, 914111257, 35366616, 26384962, 71974731, 95170065, 296772449, 459310750, 487965652, 74607303, 109502822, 325312103, 175251526, 303800002, 915344672, 704961931, 107633874, 569914625, 487181475, 129434245, 590980160, 574936769, 911928149, 313407995, 600731114, 589320060, 472921333, 875028495, 522907222, 709479598, 736887764, 79315330, 117410809, 851238049, 989480632, 21903417, 329135731, 98317165, 32978050, 655515589, 52877968, 24679012, 374598901, 286475396, 351560691, 852122307, 613681589, 487409336, 125457220, 213097204, 616717718, 553719103, 629303184, 888586523, 658595139, 459950771, 66438854, 710214118, 938997106, 873068358, 806282124, 439495377, 586500099, 920878484, 832271009, 570139053, 753189782, 694934973, 933358189, 624789722, 645720273, 980601053, 308532076, 582021328, 494993152, 450675760, 415411051, 832369546, 307723042, 499330207, 711009932, 93387549, 695803196, 471438244, 119599602, 572687974, 785783951, 590230477, 695250082, 667138764, 139559471, 754798675, 526247777, 348352765, 907131992, 287948971, 977714074, 247698676, 347783690, 729644965, 86637535, 310141770, 871170260, 927592881, 93027078, 284854762, 180403106, 846259816, 406107512, 65795424, 657322761, 795294112, 865528574, 580406034, 663234513, 560939289, 851733341, 88597447, 700372583, 20280483, 236033841, 41823843, 681246405, 255180085, 37879035, 294057366, 650028385, 832003397, 528533171, 899962238, 488117511, 58240980, 966904304, 524142771, 321957887, 650383033, 256035905, 561799711, 239201270, 929576979, 486682307, 739215915, 55929969, 636192536, 502073791, 600208037, 599112135, 895748711, 247259347, 678501096, 244885292, 480012777, 765866653, 928762842, 310432616, 624775035, 806292931, 306252130, 38711922, 890804730, 182039630, 817966418, 69162297, 411290032, 101765797, 360521513, 416728698, 45064800, 726794059, 917415796, 31518600, 819066292, 620164368, 984057090, 788529184, 430906559, 641384681, 382745563, 75137620, 984301271, 419354803, 983565252, 492830707, 607986007, 784402077, 366905116, 4685611, 671711612, 692189524, 495527749, 178154976, 355970045, 69209478, 903210123, 948557236, 351918039, 734898224, 22855452, 630847319, 961804573, 434700383, 719262, 713272197, 856016233, 567303174, 730578042, 436971483, 214201950, 277814244, 491743076, 417829072, 517238825, 779134149, 602592045, 868370054, 446237783, 540668469, 631860231, 563260491, 656034092, 82410502, 529554692, 925749695, 598278830, 422744599, 321746113, 616218131, 357331194, 782184513, 783061436, 457111145, 228636636, 389512896, 782064358, 825684933, 423044311, 548093025, 537333168, 552931855, 609522061, 440893646, 455344197, 393370929, 236952901, 466665556, 133210352, 186517086, 80051006, 921703240, 600011273, 300581492, 988817531, 693090672, 268680998, 38642623, 860106166, 873723802, 386664984, 383166634, 714372961, 565851064, 127175713, 41419798, 994133409, 404788744, 607173948, 980499437, 755463582, 4641275, 898124750, 722088297, 195891629, 300761072, 593836921, 301030600, 162222696, 965763991, 367933666, 719578579, 627103950, 180905920, 594565332, 967026042, 666011029, 473259453, 37553876, 667773526, 597843344, 151814723, 243059768, 921291999, 26168364, 839484328, 467266858, 438267096, 732749341, 702890041, 159010018, 168636041, 864045145, 710388773, 212746416, 716598766, 593823070, 9153061, 298243144, 659739710, 78143278, 484998322, 600360209, 343722058, 231212025, 900167508, 785302022, 824267975, 689861887, 954130157, 494848007, 729492779, 436501747, 453407808, 513989405, 393133957, 612905518, 755690856, 590001505, 870613457, 401442462, 298511246, 893101796, 665578064, 847165638, 58444502, 144286501, 277051402, 376445366, 970325909, 538233182, 807689490, 839065070, 524581037, 914320494, 430079698, 272508344, 969172308, 342396142, 676112558, 396243871, 42744098, 667703817, 789018660, 674119749, 713930056, 84320590, 51204476, 700737192, 4362936, 17736203, 245837042, 51329826, 923527606, 459859169, 777872637, 931856372, 303835399, 781188676, 11912719, 571418641, 869413248, 586650783, 962228130, 303567067, 553387930, 289294834, 724227468, 309191064, 287519606, 563783234, 450473287, 202581769, 605850151, 926778616, 721271596, 70554857, 278200855, 154756045, 819214215, 779891452, 306660698, 249798719, 117058496, 702475239, 354768540, 200921023, 267088968, 423164818, 830258617, 182446850, 878022946, 281222897, 299219599, 74117752, 345706656, 386840284, 245535508, 274025619, 700118247, 714386605, 673675315, 716581252, 268698002, 542585462, 416572552, 971359299, 652812626, 208854825, 168909769, 286865657, 242982345, 399923227, 34701971, 784506798, 998713295, 393625647, 60590970, 360007300, 687266834, 96440525, 975223438, 235759397, 901715382, 50313579, 542770154, 28893308, 20366502, 929668025, 188405548, 37723749, 531960383, 183523169, 300451394, 189455538, 375441509, 734760467, 920500357, 362395772, 606438013, 684050417, 932477038, 788379879, 739955174, 161031951, 22259211, 948266813, 696983208, 62436271, 236585938, 787193464, 768004646, 972135729, 812073113, 755290054, 611105258, 271905239, 704151428, 20993057, 353306115, 576285039, 653799592, 298970074, 769310045, 164441932, 996851059, 152886971, 940905428, 616782311, 951441871, 790459951, 301871791, 932079078, 568386236, 667874342, 166303676, 990164375, 474765091, 895840805, 142827025, 897644753, 428918858, 278758168, 53866220, 603845864, 951655512, 931558715, 53011976, 869714952, 125579894, 334961987, 476562462, 876990064, 520802909, 117548441, 93505147, 835696361, 720081713, 600859303, 617068882, 690409420, 135283782, 871087585, 923959321, 938986844, 300737678, 410834300, 672726351, 441679636, 843048691, 194251870, 789717073, 158588939, 698969477, 432283858, 192998670, 32865539, 629932119, 490774296, 500932238, 148373023, 842824094, 575834957, 243023123, 393367469, 531168378, 199247395, 375500329, 813803772, 536860540, 677123904, 769235001, 330073071, 456369305, 54490237, 798167202, 585586978, 646621746, 955410991, 940263721, 680712100, 483720327, 542965740, 783637229, 879377919, 648289130, 387405198, 460783423, 718393025, 630706126, 23294287, 239558005, 445051764, 647485334, 871143959, 221148271, 960921283, 797341720, 153271367, 115170400, 867453554, 381825020, 962581450, 895731403, 619996682, 648584961, 264148380, 416694326, 164534671, 884905266, 295729041, 788434909, 428512456, 954009372, 103621808, 746602544, 720422394, 864142672, 660663033, 199649985, 391981166, 629072989, 432402290, 972437869, 352609661, 516799635, 722377986, 898513906, 117042010, 427915962, 201498284, 340798795, 748309040, 344373968, 641845711, 659998630, 582456598, 431090047, 650641043, 768542193, 122249533, 935937343, 541298368, 56492233, 981581652, 288854920, 967936249, 747637863, 355751768, 787806153, 61176864, 237689272, 693375649, 308840931, 211430797, 654936914, 377602918, 927777536, 672575253, 821886396, 140267121, 333510527, 798965944, 129317195, 836060083, 108113522, 245153198, 333642528, 96049620, 384082882, 90873753, 957269401, 2067530, 334956345, 329744552, 726110231, 69142549, 647711090, 728837178, 265639878, 832388582, 290417185, 192309131, 784438655, 554248538, 685001086, 653898363, 663075063, 605332087, 304556157, 850412128, 135378083, 830546704, 233772150, 410071102, 833880245, 817484605, 752443599, 520200385, 793484436, 536935226, 154577917, 516495047, 414723355, 516895002, 349677352, 669020064, 802185212, 414744270, 248500390, 26054071, 810727014, 841520891, 426934654, 26180175, 283905086, 273238163, 795243103, 929850884, 860460999, 506677590, 372059227, 450035690, 42191728, 204725613, 448304114, 781319213, 301025327, 576257569, 672976362, 546790859, 228206371, 400710854, 550659599, 711277380, 922945574, 612444158, 416607645, 293164807, 100497018, 960156457, 536641889, 76721711, 448540111, 366864751, 184223107, 355661612, 489872491, 734843896, 305635316, 117514713, 82529506, 921520194, 572179541, 371425365, 639843817, 679303718, 744381505, 356487154, 7727788, 840018440, 335862930, 271122652, 649630529, 651484859, 505466013, 62557434, 458479821, 988346279, 716509351, 56040440, 797180244, 560112851, 223944322, 75512943, 505534073, 14664320, 50316470, 713138974, 813384859, 54236893, 587336258, 161582019, 546243342, 150369043, 558365841, 942562943, 480482824, 766834600, 886376589, 747880623, 521480552, 39600955, 792237326, 507541869, 912908245, 22577081, 415461580, 745847516, 21715566, 88348904, 563470657, 404119613, 6409731, 779410900, 364753651, 505541177, 223232914, 986049346, 665607485, 617946706, 162589129, 965551415, 524680990, 723493365, 774163313, 809133465, 855347544, 920675169, 771251321, 577269270, 476756289, 764051960, 787813837, 531092888, 284369931, 597352790, 281346884, 634312121, 309743316, 671841838, 119761271, 409243138, 694647667, 53395886, 99888097, 478423975, 120758506, 182734063, 223434952, 789175868, 504707498, 225420053, 602327429, 918800183, 121265368, 412272363, 295760624, 219789330, 443365270, 704788069, 871853032, 892456764, 955201519, 439384420, 632889028, 175531434, 782563978, 558592758, 390155064, 22193597, 76779283, 468986855, 972203160, 119837872, 345651376, 521393816, 149582755, 985549132, 450996166, 934041656, 9924281, 312481789, 837046504, 522417409, 628486956, 48115564, 53463477, 592083492, 409108438, 572056085, 480245006, 54990126, 611439134, 243655290, 44527490, 32132359, 438572888, 471607878, 549846557, 975842141, 276190953, 473067688, 268646764, 712376346, 19253279, 678605096, 540688313, 833660768, 969030180, 983321749, 230161582, 247079476, 853132406, 435425653, 735174104, 520284154, 480177358, 716656035, 938783644, 828974702, 506312979, 644369759, 60640462, 276335450, 174835117, 625881208, 900284702, 445133768, 946041977, 240045860, 879881432, 794070706, 95401274, 585261430, 544151231, 814510571, 206715830, 316606177, 940777792, 24241467, 723556923, 316649918, 856024740, 629003587, 512250004, 142031958, 943586866, 424315530, 276805351, 909138693, 655589730, 260037694, 978453947, 306254686, 717627494, 663136796, 828941386, 232769769, 896814494, 698321462, 295179712, 399926083, 597703974, 244693959, 334714311, 511948264, 222948946, 343575356, 384252886, 352936485, 882118290, 794198700, 355930081, 160326530, 57496231, 732845076, 497705626, 733657093, 588084880, 205181322, 465686379, 189323440, 830893133, 775272530, 618718603, 347960247, 571810509, 629882219, 13006830, 945672996, 431202317, 506636424, 545135913, 496774072, 543104966, 131151020, 869150818, 950611389, 668429129, 74731512, 638393414, 258913856, 68810847, 95729201, 216200383, 397971198, 56896290, 384406360, 354661168, 869326153, 615383644, 766794794, 153727552, 621914753, 363209352, 701827939, 66130479, 406873650, 364708753, 586261838, 307749220, 129932074, 240934063, 810615196, 493518458, 735504846, 683588119, 547725623, 570775041, 566242099, 803473264, 741486430, 746715984, 383260335, 85984860, 484212941, 991181362, 239120248, 874442751, 393468577, 281144165, 581653713, 887791989, 186418636, 172819763, 785514325, 917640534, 892986342, 220654029, 695288742, 801666149, 684212787, 929057947, 314206948, 803253311, 278433148, 469030749, 711661960, 79470611, 926313865, 329602522, 29163926, 141806679, 367469089, 159630680, 180768403, 172082227, 496461723, 164391916, 152425766, 660227988, 773396539, 618907701, 793115758, 10128122, 328419376, 523504780, 57248889, 331353181, 221571626, 694525206, 154302876, 642845820, 372686149, 341312023, 234590262, 928569191, 281814023, 534853289, 434872195, 950151051, 468391993, 412590532, 523159634, 163987518, 734397688, 547342408, 735652394, 956469251, 443266641, 414138742, 784231085, 288160362, 791261213, 182168703, 519329271, 433459554, 714088410, 23657649, 370650384, 397977525, 664722027, 96877394, 386050484, 483553209, 936661301, 825654147, 911962540, 687455023, 170987108, 46075500, 332348578, 580909988, 275700855, 703992090, 315789233, 187283295, 653608037, 161716226, 682894886, 140224336, 685514106, 464140639, 395257890, 999929635, 897967881, 575672027, 54501848, 965506353, 92594223, 857697569, 466023533, 99175980, 217554700, 925635045, 218572452, 729353601, 219787064, 794251517, 434204722, 32524149, 987174240, 935659477, 658219017, 344060053, 267473016, 353654618, 161009765, 275103748, 200597381, 894528778, 536433881, 223993756, 619383649, 418315655, 95938585, 922286105, 498036255, 25582275, 611671056, 665616081, 856372382, 587482243, 61440397, 3859201, 40594191, 56496847, 951589902, 536508764, 682695513, 112815348, 394402549, 445211004, 829121033, 940580945, 864121979, 403999979, 295621953, 95492073, 231821104, 279197522, 775378573, 158427820, 475749165, 145134238, 231296193, 430039664, 933712219, 245658463, 891936338, 762903729, 644766490, 21350642, 261696938, 355015844, 287591324, 458937271, 113118757, 372392640, 935679229, 226106906, 157258859, 91385117, 893227686, 52994303, 499002823, 130604181, 879746719, 334022447, 588681870, 364728650, 912970026, 589171195, 700732288, 747273132, 865083852, 941025113, 495728243, 436264235, 940501413, 791159989, 315199173, 472845918, 638408574, 583531701, 955450219, 684673361, 412524770, 176609789, 94208163, 995448536, 816482102, 132989370, 745629012, 565992907, 863036401, 83186847, 982773072, 567067531, 552186666, 32251103, 972805147, 842405809, 302057178, 740474766, 715991214, 508533636, 422095734, 274548074, 777576196, 444253297, 692521382, 4815953, 595757646, 986773973, 106096367, 164362032, 660147427, 455553943, 918040007, 660206585, 224550564, 64753739, 216662999, 373041205, 897375595, 324663849, 567301070, 281377775, 391324187, 809341049, 235411390, 492459840, 751482180, 133313493, 865257589, 722144826, 882375524, 828002513, 225024271, 294412940, 521149959, 12706054, 720443948, 14445739, 741508852, 834668695, 486536577, 948840375, 72664959, 699369056, 643604480, 288381435, 53110533, 367975450, 630762667, 906243722, 871658920, 975766246, 837890321, 316334606, 385596443, 537292710, 253322224, 696235793, 441208121, 82733867, 708878173, 496199338, 708231925, 572688513, 983230866, 375301384, 923523666, 333169312, 334741017, 283891198, 217614756, 790880488, 726960266, 801463919, 635385083, 30494037, 868035166, 101899227, 241631898, 695225624, 285588265, 280023858, 17567201, 598841737, 785767375, 958445686, 226561271, 964355197, 452314359, 685521637, 453691301, 695867088, 720466652, 181251760, 281011486, 526215318, 711381008, 371637772, 642651783, 34603771, 144062800, 800900029, 120599355, 294267944, 343173440, 972394974, 290773761, 338512758, 930157946, 590780434, 499430658, 252997792, 145743621, 250542668, 958408988, 425482724, 123261526, 199940898, 731464180, 115537021, 987739148, 957053311, 917152447, 579849099, 376464806, 253712421, 491872629, 147938166, 453773964, 256186530, 733528290, 348355521, 556174789, 595479731, 207361583, 268886635, 900433683, 823860726, 920596470, 64579066, 462525914, 777659352, 150407084, 387806281, 972253615, 224093689, 63596215, 619517822, 82369362, 91978506, 950060958, 710789949, 872482556, 398364687, 11702612, 194774064, 507988402, 334640842, 817905932, 318180699, 646999215, 513415787, 697633723, 159082577, 749208359, 198980680, 247952849, 386750706, 989278914, 525648320, 378635197, 552513303, 440550801, 92511721, 770753760, 868513100, 497218419, 363925046, 687981561, 650423926, 777628911, 853342244, 16630455, 230654439, 319873285, 113516998, 474906816, 235003415, 317745875, 559391803, 425480618, 809497163, 125012956, 295956257, 264521918, 22369791, 236373956, 232944116, 236440572, 943483106, 893138099, 49491619, 796058206, 113141507, 107679427, 160522245, 308725121, 379899662, 217323251, 515167382, 232300318, 997497397, 423884918, 280848849, 648393000, 238528493, 185663065, 957316439, 810770571, 216284545, 481294418, 633027381, 588016463, 769751591, 899692349, 254615065, 41353551, 923863325, 443637717, 281653814, 477551658, 208696591, 366175762, 543508778, 668047273, 599715355, 220542737, 515300015, 537498590, 572694650, 565168856, 367747968, 906406232, 407480768, 643760901, 392714587, 285875803, 81564594, 34752602, 861718027, 380532681, 457378790, 387029523, 650261200, 146988677, 22113762, 253395175, 180461386, 182828487, 213316292, 234895715, 432654851, 369985053, 626361352, 201658309, 366635774, 97866100, 932519263, 462254092, 364256696, 799868045, 596086577, 667466138, 248660547, 279674391, 318399261, 114149691, 986860512, 731485717, 743179864, 230544459, 4502369, 788823801, 915812714, 582503877, 324617113, 437219944, 958568476, 654987148, 792221702, 197632019, 351842058, 26519545, 905557765, 447410753, 426006279, 248379205, 985745414, 149269483, 912711708, 897795281, 516698131, 558414952, 764642776, 145133394, 911117034, 839434113, 980646869, 959887903, 589268297, 152606669, 902248696, 547231138, 528324546, 188906915, 254265608, 19697501, 556507801, 554793374, 580024927, 616514917, 304947795, 815092604, 785869908, 666870871, 913816377, 604294760, 292938103, 402237890, 801971297, 961103379, 978018762, 560832979, 812943478, 134695535, 155453895, 449716860, 5427980, 672436276, 226450160, 488897493, 704198630, 344044523, 20223576, 614171596, 51771075, 323570821, 400492099, 995342012, 352912163, 859310997, 554585568, 32658917, 309939169, 162578037, 455336090, 323790849, 617082073, 609458429, 959576853, 361843905, 602477982, 874155541, 565329873, 323652354, 885346544, 564522855, 283228205, 351666672, 47120761, 832247817, 717602153, 277816227, 76500396, 646719887, 827599966, 943670337, 49514691, 988501163, 35783486, 882391576, 886593531, 129724940, 394337001, 180373836, 819723373, 585585342, 368029283, 681303676, 722752496, 252096806, 98047442, 529901360, 317452949, 695436635, 349647306, 604940342, 432344224, 594387176, 368708594, 527951377, 293490683, 111968475, 606836618, 275261541, 853604862, 416513984, 572719207, 627362698, 51001893, 938002668, 215193523, 738115126, 837731172, 463532279, 241550637, 192204714, 942445521, 119959636, 698977966, 483249005, 700166433, 115225591, 86361777, 779059330, 544154484, 969008363, 395729333, 283326396, 464298704, 788090920, 200671484, 584197009, 136902404, 313609911, 130211813, 143117146, 861851111, 285447962, 968188924, 557491375, 911510153, 363820130, 508327426, 412186723, 421008233, 478934067, 216677248, 966789108, 539865986, 217890221, 728218895, 881398694, 882677400, 761054491, 155569249, 344032843, 774170894, 976587616, 536194647, 143475747, 904272640, 816639006, 178162004, 530030724, 44307619, 956383276, 801532169, 24821345, 175985780, 135248018, 610420771, 901447496, 31798212, 248777735, 464577312, 718391349, 416189119, 492146969, 157828927, 94655209, 547393565, 983954065, 750877304, 949914610, 174453757, 503341320, 32709561, 501896759, 430564433, 379386402, 598275056, 389509066, 362903161, 396694588, 764496982, 819964596, 156537729, 429405869, 130855496, 629238951, 238299758, 697659858, 86135891, 980447583, 692269559, 781545210, 675741063, 827514716, 415611775, 113611756, 563538368, 247122132, 529996955, 88693434, 14006646, 238842873, 733362467, 927229583, 462718775, 297888938, 652237173, 206944467, 403322706, 977916728, 497673591, 855407859, 990550013, 461776905, 895994076, 766116711, 41285857, 32630889, 767663631, 282568764, 654367779, 488355263, 717772706, 499762100, 35317858, 853527461, 150862325, 413307832, 24534151, 377364720, 353301531, 399588594, 948404443, 340429366, 104241377, 58715330, 244634784, 218112988, 182969565, 789927097, 172531787, 34226484, 153849264, 899092707, 670485999, 624643720, 937949670, 751063304, 133557576, 152206399, 43078700, 225916445, 350140846, 745845511, 745678592, 681544081, 48888179, 632841261, 463177846, 440221512, 593162781, 794420160, 49161050, 155446006, 531082769, 483388695, 662881638, 185399060, 402565788, 871875122, 917961856, 545644169, 79759552, 596111667, 430706562, 753555503, 978408225, 376660843, 440654074, 248325311, 801651930, 36524819, 628865747, 414427296, 880191330, 239051359, 271208113, 975985427, 281909704, 337597640, 852178244, 968428616, 58983751, 512181640, 435103508, 442832146, 694101451, 259232055, 154758335, 747710375, 887214359, 739736309, 605011718, 192352319, 412515374, 407765964, 926454065, 228446908, 118141811, 961064692, 551092062, 822928360, 287512562, 141865376, 99971601, 347149699, 543097283, 173817195, 67350078, 96436126, 713589538, 875922557, 25026066, 290384353, 830070275, 296724613, 520510224, 893654108, 386364384, 748846323, 36909808, 698052983, 417487595, 670493024, 840184348, 402851943, 295417442, 673825349, 485783293, 674734558, 188660082, 971946239, 156749852, 51311480, 115096254, 71716456, 147304467, 295127919, 477308784, 815101002, 877782883, 951314004, 714704664, 281961408, 958066973, 605712132, 336832299, 291859167, 616268293, 944760482, 890201714, 917659359, 862829524, 380012580, 859465147, 750639857, 792708465, 832781179, 844844550, 599506814, 910522052, 357945758, 729634247, 61540120, 615465109, 914214029, 592016845, 950071813, 668482566, 343314893, 718124078, 375169042, 377706923, 511167294, 277645640, 354553419, 640540464, 43505884, 936631558, 781787103, 591526692, 412034290, 313112396, 418925021, 407862045, 980785201, 884841924, 714118055, 153595806, 681784673, 774245029, 747188189, 642053807, 405824114, 490015022, 352593379, 264572813, 356063440, 425513453, 495205393, 408223024, 736758860, 650098915, 696010632, 957022328, 176023522, 911340395, 783106399, 386741928, 822562334, 737788013, 957994409, 194284800, 91398980, 185055960, 420328742, 386997750, 354273469, 120188002, 82823010, 159682618, 586103774, 114313797, 162719584, 609429628, 710491987, 566450426, 652170835, 231355614, 216019207, 424828995, 821209124, 860270149, 398057000, 740930114, 156894483, 548146453, 603501240, 813753147, 873549197, 820193674, 772593779, 327372085, 370212410, 159829672, 78368611, 159698119, 590268572, 130427277, 726810719, 964080863, 62548518, 50151304, 869515915, 5446858, 362651821, 407285254, 208081515, 70422496, 944434759, 680531293, 245975077, 247753322, 395366495, 592469708, 962393297, 364207772, 775723825, 845145158, 103415283, 686625982, 30024668, 374301611, 314392979, 120081734, 778930338, 923118661, 799041222, 933701904, 985202902, 80325165, 268857524, 156858026, 487621420, 839579848, 320377178, 476303109, 631035591, 127659383, 689972293, 775551453, 621874848, 374701570, 266777116, 972600379, 493787816, 699484624, 937604569, 956634993, 963251574, 97455740, 111186237, 354885622, 603840812, 216457160, 15151241, 116029395, 198069675, 670098738, 522595000, 492443157, 923799269, 250520488, 276909425, 891830888, 759379301, 41652167, 245621607, 384951801, 376990886, 951495267, 865799669, 943165668, 156461909, 534422835, 134453727, 213832846, 923880493, 728620753, 853090717, 655234244, 415373631, 792893294, 88627913, 618048695, 980049737, 487662349, 482436669, 55982910, 210676, 919776770, 602213715, 154589423, 731133549, 516864028, 920928442, 534847974, 393386850, 301968380, 323748009, 208066944, 768722675, 244412863, 184578854, 769651603, 329999648, 152680372, 355425099, 56457266, 538446104, 217134518, 8945554, 854216431, 289943501, 287119311, 45475369, 217050623, 982088122, 530950531, 287208994, 307868799, 48618, 455216419, 704207698, 151705214, 933670534, 816006858, 176393971, 375790348, 561049055, 160241968, 374749080, 55300501, 251172474, 27791853, 752599972, 59287429, 562748691, 482075764, 147531595, 73367338, 832384343, 797418921, 214967787, 642607824, 544340938, 89279509, 608740254, 352636939, 509744005, 68830300, 395305661, 185054131, 97704870, 620279038, 720979832, 635640149, 181393467, 576720349, 571306599, 629727242, 134937394, 197679526, 704539079, 4150282, 807317441, 522567703, 737030573, 377499386, 539379093, 529104908, 408414960, 490128123, 199571380, 586241028, 252169612, 291355102, 535106126, 422922107, 753625318, 901646259, 159403840, 441516985, 829538077, 185598075, 368667653, 120104958, 623427014, 931741075, 423472476, 170608177, 912653975, 698538874, 583962612, 346273994, 521167786, 188751381, 80548016, 893371412, 454051620, 345277765, 663676418, 747374349, 779576698, 755886806, 871074272, 409316208, 461302187, 233949356, 6213489, 862459134, 223294871, 922570728, 758596062, 586167885, 184438429, 339081575, 494919857, 180495699, 630922439, 26692476, 424247421, 31615634, 199322053, 210099609, 936702786, 111158366, 118712252, 686003560, 83019304, 759686777, 270506797, 776181824, 22400442, 810376537, 766683104, 888923748, 510909918, 540472951, 624770153, 540778662, 455934209, 34214274, 324247557, 705123052, 483461615, 91141032, 112674870, 785455846, 216457330, 863790237, 743108650, 164374124, 701433045, 576554903, 507457882, 603388819, 296031419, 353238741, 691876715, 901122270, 163738521, 266949616, 130405573, 483438316, 535597664, 674902794, 16943684, 405057960, 808862510, 139264337, 939037294, 29929021, 881956190, 834069718, 349076295, 971553817, 465070836, 322473672, 481060935, 162617052, 538465165, 365163242, 815441557, 460281958, 494743640, 454480909, 678294934, 146051946, 645287550, 505238202, 77580920, 654049662, 391735698, 136627937, 990359929, 196495684, 622535821, 262554802, 134701415, 607409138, 34189204, 613246204, 4412735, 809500446, 712269254, 757281368, 411841625, 260193597, 275288619, 492622073, 390046649, 883592740, 172577899, 338114303, 469080968, 61487370, 212804940, 831178729, 662388463, 714619515, 486133015, 296260584, 22319474, 927332502, 659255925, 679953637, 65545367, 18484285, 836895559, 59257672, 83643715, 213998779, 314915359, 576206372, 887396552, 630395845, 185539529, 669211042, 48276723, 39392332, 826220798, 308405041, 472727303, 678048004, 848017700, 492004381, 807813410, 106945331, 879873228, 224858472, 237654235, 772469112, 455936580, 190934267, 685908441, 569661616, 163378829, 237679871, 643592877, 878976469, 576852474, 818985036, 602236384, 16841923, 750973994, 987012902, 985826482, 800290138, 825074603, 24613864, 620115313, 964551550, 566162807, 94449635, 625017133, 402341438, 693296197, 945730863, 62918853, 420726065, 717562465, 321762686, 59088560, 675644308, 385677793, 225836417, 786275639, 862168881, 49563399, 43845680, 574411002, 193249659, 96034500, 981458435, 45753146, 710920506, 421149699, 731999408, 630276363, 167419565, 401925306, 455400767, 421071337, 575336435, 776767121, 116984711, 451299792, 234429228, 954645410, 845646500, 382684874, 666316507, 684231164, 762775461, 339131633, 624957814, 198508032, 866634712, 270938589, 107452678, 696998674, 400257249, 99818315, 585077301, 190761605, 150531499, 961667780, 273540298, 361310835, 234492467, 973467829, 742162143, 233721851, 780337051, 804034874, 647442996, 643732854, 55834200, 233021220, 983325175, 155441528, 859557968, 770133448, 347887025, 767006802, 851752771, 665342700, 929159371, 829786942, 713335476, 411216241, 314727638, 893037321, 859979073, 128338657, 114109504, 451623959, 795743326, 824861160, 600765765, 36121324, 427831571, 200963882, 973718026, 149386822, 6581396, 468123825, 222927927, 187341154, 8349168, 954587762, 189865960, 213955236, 537923506, 21335816, 84065583, 213658460, 464348863, 762296043, 929752018, 819756565, 297414873, 363054802, 764983546, 647742994, 582396877, 693324405, 866475438, 470279810, 525210491, 850893280, 559162423, 17548223, 198515778, 571154523, 487807382, 13752551, 257259342, 19968318, 93286066, 574209430, 755332167, 806308421, 956583956, 14258080, 634330889, 93786263, 886654467, 628341350, 390234032, 145331869, 284014832, 977724303, 759867279, 922563400, 685316845, 823321267, 387661129, 518609813, 775761678, 384055786, 626795199, 234707295, 66503953, 953675326, 330615666, 682934710, 123683986, 169191640, 288624681, 576149045, 656591144, 597482321, 404060240, 129642286, 578649823, 875276615, 108392902, 503029188, 470349319, 358954205, 51599442, 893510337, 536857160, 256979465, 924757694, 446085061, 198276757, 785675611, 238865915, 401242010, 474823153, 270812226, 227747689, 598931285, 507902275, 730739755, 551136493, 404854282, 542250180, 156131146, 371173739, 948754706, 700192829, 268420376, 386596074, 610249189, 731548698, 77309236, 241554729, 522622488, 583888127, 928897752, 777818369, 4446266, 944227789, 724092451, 929381341, 422822560, 505474610, 140547134, 146558926, 740936825, 26400557, 790608901, 977546956, 991740715, 814810611, 969727111, 258453673, 81992681, 69567305, 343388729, 226630034, 281600845, 778617343, 957728808, 125389363, 377889496, 88402755, 258985767, 697018238, 232476334, 613997663, 959792023, 934258310, 100492480, 300673931, 259904544, 723099013, 855941143, 163991762, 704506620, 18603588, 380361274, 778030007, 872368720, 981828243, 594780955, 626124696, 744504664, 233623237, 888125121, 573891101, 446563795, 632527521, 237548578, 495583612, 58189736, 175473566, 44603827, 974724389, 817845628, 441933394, 577160948, 607098876, 354797299, 474219375, 511702959, 899960278, 846733598, 203385171, 531202804, 736228056, 507747846, 373094040, 643676624, 119932417, 791561926, 912004223, 731768008, 860577867, 928915870, 833219454, 450070742, 906169214, 689491781, 883832985, 655177089, 439067169, 589119343, 349962834, 335834244, 206747989, 846526033, 737365614, 255269951, 168423876, 674932524, 478461931, 571366619, 454480685, 686955669, 369937396, 175642843, 287401115, 997393736, 137297865, 445744332, 639300159, 708124959, 334337593, 951144910, 420425930, 128790576, 44120860, 297789859, 785810479, 772002357, 223286803, 235348613, 79918069, 910848621, 981436695, 653468656, 657250520, 794710005, 2086121, 118855236, 169676925, 790958830, 325297670, 9871582, 408319234, 67904152, 339155789, 134700805, 320121348, 358184360, 998881327, 974566225, 145821514, 47076992, 65409242, 696810482, 802891925, 856271905, 73230712, 282160951, 297772208, 802562510, 450004297, 96844007, 249736448, 14948744, 240256627, 438235853, 368297161, 132980636, 988621692, 676796057, 137569426, 891212554, 91101035, 324061271, 789314255, 43211515, 122084001, 306342726, 916580738, 301783651, 154866493, 570993343, 587779969, 442305889, 763418904, 804391898, 124551812, 32972518, 645854993, 522580936, 711238360, 761261578, 526477684, 96750957, 58302268, 846757157, 116278086, 784733393, 495362193, 983799870, 953342091, 743597256, 74427827, 659625812, 858951435, 514396405, 63297188, 966233854, 592021497, 508725409, 975098758, 718973297, 959993246, 651146359, 717464645, 509592670, 323118699, 605626684, 374375344, 588824600, 495210972, 193660009, 971813439, 802529343, 525903198, 546298794, 843494747, 256457920, 617899102, 832389398, 170952251, 915470404, 831647093, 705484131, 570637442, 978709861, 239103128, 731395004, 307912865, 447677948, 527060950, 701456733, 809278871, 401181942, 725640418, 517726548, 549401969, 799167245, 715814561, 44982254, 281552860, 963418619, 84054246, 519218201, 665501276, 200076832, 660081564, 448033921, 620484603, 234332752, 297642299, 599397789, 723047269, 411698197, 548584234, 372775460, 147031203, 657992849, 441287621, 433818563, 682780119, 915305888, 54162798, 243030053, 424746277, 102100704, 330327284, 487441170, 498309470, 803675214, 748152437, 137665535, 894861410, 378709336, 680700403, 82998019, 370800518, 900865840, 440576252, 684319034, 345182084, 187978362, 223640671, 817467527, 248590382, 364297589, 701923116, 743554837, 332180778, 707781379, 226397984, 612458675, 160357650, 16948920, 127594751, 405690049, 726820964, 634448019, 891525870, 971443799, 4395097, 382173541, 589224841, 114520217, 966951068, 391037058, 429060775, 199318923, 482146768, 800724989, 537040130, 816162175, 877592494, 533534678, 725773808, 884507553, 819407820, 880468000, 304109992, 84858826, 39484358, 783101423, 543818928, 43404414, 2046914, 324210775, 85834064, 461482467, 56828134, 525820524, 464673240, 491336750, 271354035, 430055051, 594463569, 894872477, 300624522, 611321085, 388536232, 93693106, 991804123, 248605406, 110234755, 383441479, 209061218, 826239295, 543948668, 760599149, 764902709, 266872637, 892263265, 836671211, 691952358, 422092933, 131948569, 837820275, 562051575, 69531510, 714223648, 669574413, 949664323, 12612397, 872266824, 694397473, 100491567, 625047384, 628862300, 898364378, 870010150, 222743866, 881243540, 975753882, 251221709, 67053612, 71353226, 997462937, 850667823, 502839084, 435000858, 428929592, 342943970, 512319441, 778578130, 150577904, 633642828, 999906857, 646041668, 228214653, 188836020, 553186987, 592695176, 26226177, 115532387, 534201115, 373862795, 461507735, 909703370, 403356248, 997857492, 14765257, 845967053, 507818374, 891654972, 932661070, 427034032, 606703804, 510110633, 22046272, 110257613, 773893314, 386459215, 295578734, 585890930, 11484233, 787012716, 98642861, 331519300, 872744490, 940936442, 794503352, 133278950, 400489780, 112458257, 509313094, 187040205, 256023912, 181173640, 776167959, 675740910, 268080785, 748325903, 990662405, 686091215, 77771383, 171869287, 496185340, 532179299, 603883066, 174035913, 691405885, 153591697, 796766491, 826858599, 62027545, 571631474, 623801581, 760816300, 59287112, 82232000, 410683434, 333201398, 731395669, 712269148, 632631941, 328544689, 668511850, 944102722, 344954218, 840225101, 875251088, 270338719, 363426347, 856794010, 93288959, 356935615, 916900190, 651684998, 971344536, 381221698, 230556523, 528246768, 377754593, 5597431, 746851462, 204918129, 397323572, 531186028, 272164619, 524100644, 377904503, 698379080, 996121891, 357183996, 332706128, 218570064, 682825056, 452639618, 54521103, 3966534, 537296561, 37625003, 273097384, 996301102, 904542363, 672724655, 294365484, 310867970, 448407321, 6223007, 711776798, 145919435, 393781822, 165750851, 140122478, 498821347, 807426451, 891839350, 484430212, 593857645, 700384524, 125675039, 431026290, 118604141, 732510079, 773740411, 152138990, 542695656, 673442597, 591072226, 930701205, 169844217, 666318847, 557930777, 864657364, 190061095, 498428660, 970178270, 639808717, 771961245, 474031825, 630540497, 706219196, 915832958, 648599036, 490859276, 495801654, 9731347, 76589518, 237966772, 428859540, 368679260, 67145143, 402869948, 261740734, 791610104, 372186929, 987682676, 447619901, 816274861, 887334668, 347876400, 921861868, 809119553, 733981517, 494998678, 104712965, 389143245, 183458710, 393310665, 789466857, 773862337, 651347351, 241833305, 940162174, 977309828, 428846034, 104163234, 157966584, 893768609, 737721716, 918027169, 659710202, 557250424, 169643259, 837296188, 973863645, 31580454, 240287212, 619685968, 349526211, 704467702, 229428881, 947223659, 997024056, 115384395, 721001078, 124411877, 933750693, 63504886, 228856186, 370331399, 842752937, 917941340, 26945709, 235119965, 921280036, 262730090, 227993490, 891366450, 232434551, 259319724, 65793012, 928239376, 295364301, 352767982, 671250444, 42744321, 453359550, 63180203, 287669994, 356076642, 236590414, 517622048, 783558187, 682093170, 50632074, 993258654, 837117670, 530491614, 197671084, 110206143, 331051144, 133228943, 138396187, 956199720, 934224651, 401884854, 809017149, 637729080, 683531164, 282047536, 654311798, 157906145, 47500836, 669778707, 138729787, 815228461, 55200382, 23946964, 548381551, 942971517, 621860621, 800393651, 541577608, 533330036, 64293155, 124460345, 271325520, 434328143, 64585797, 970336708, 523742822, 722352208, 746821722, 92477526, 440126286, 675190847, 106365610, 987799234, 861620784, 907869679, 913984972, 555806314, 67676916, 236255923, 446795207, 803814238, 258774917, 65285201, 875305325, 743221686, 534511297, 73341959, 363675007, 285724048, 439494579, 642569142, 115787396, 114247314, 559155471, 388010862, 260127367, 130770068, 842502, 175531580, 139762506, 415543916, 163481767, 350552935, 775162622, 353285964, 145631558, 385690811, 430541081, 441266947, 41848710, 478888874, 763310719, 668206823, 694699681, 429930239, 754922845, 377598085, 364402975, 945108890, 788251920, 769967303, 969806740, 715319022, 530563301, 453304989, 461278698, 851469940, 949818162, 546938762, 206008892, 43361235, 643417641, 460154502, 562520083, 633371637, 694247546, 968065160, 613691840, 803985091, 693600738, 251587378, 25849320, 209450811, 256063252, 921291945, 907190886, 976913435, 933048749, 816712861, 661977361, 388187841, 467327766, 243954051, 991438406, 539411433, 963830451, 932722715, 823442333, 433932370, 850809287, 622954765, 773607805, 205373930, 668470175, 503163322, 395776127, 620957241, 124472155, 643254008, 832235226, 179476408, 359544055, 359548713, 264132818, 546719388, 6157802, 500213951, 2208515, 635273158, 795387218, 473955350, 73584802, 547874188, 430518811, 950714620, 754461419, 266498372, 119351437, 377229601, 146151487, 709405015, 348273475, 53861859, 71955578, 327147495, 605955190, 756252996, 943598055, 574315965, 531638517, 339010581, 170274552, 826329053, 209284857, 767327224, 762917404, 599218026, 632046185, 201966660, 121699011, 693474106, 940439178, 861904971, 30818223, 829913488, 543945972, 208026749, 840396714, 441392220, 802802992, 717314012, 479171774, 424284213, 903151616, 112754617, 583296508, 847101379, 701443327, 854732926, 951456349, 61008383, 759599569, 675669925, 20428852, 837686698, 600367229, 272938950, 554487859, 96667296, 912575351, 762049099, 406109155, 245577956, 242080427, 181450036, 428069070, 842929337, 396160092, 358779834, 259633790, 901087149, 291443952, 766013220, 151607958, 624933106, 816344467, 335853237, 948893593, 632409956, 450333583, 78411644, 208569438, 897215788, 483470665, 390042602, 382837185, 908567745, 633443700, 949206804, 344948477, 730336096, 290881726, 565836619, 630647163, 75939278, 639026258, 339001487, 738748018, 511274078, 628633774, 806452506, 489065404, 1651246, 867523521, 248952943, 528033060, 915323406, 255209380, 894247558, 713492383, 260550073, 444795743, 214898348, 221264551, 272791258, 719387604, 948464718, 565873963, 183445340, 563120275, 392603086, 396574618, 646673398, 624797265, 378309577, 858481409, 112410804, 697452182, 40773065, 316525368, 484826772, 506188205, 267753928, 908843085, 446686155, 510891486, 666842263, 168326325, 403227707, 962008480, 389460747, 615324854, 578924833, 797730245, 744434190, 486250409, 82702806, 859209663, 58346728, 55209955, 859314684, 627762343, 713427297, 255323440, 323450784, 77670267, 59418304, 423434053, 697356583, 86291428, 580845560, 433248973, 3867593, 862324993, 551597801, 233846102, 182920148, 877174686, 691365045, 698412259, 336297146, 297183575, 131374004, 480069654, 676954020, 712031782, 697363920, 230479167, 81330369, 202516866, 60189433, 836708705, 239215977, 686004639, 963441444, 861051628, 298576606, 746859673, 479960476, 835232477, 186745901, 468428422, 425560968, 365523246, 175671725, 847966235, 412441549, 858669842, 204368139, 957956035, 691910347, 227899268, 880245210, 883743278, 910047736, 9777351, 113041489, 156175865, 81025947, 699587195, 795565884, 205992577, 4893388, 659289840, 713426101, 685586646, 899769621, 427053208, 539817839, 820611242, 357964091, 986097767, 705690860, 51606843, 577793141, 312533213, 188004202, 427984610, 301745704, 385238921, 947868015, 106082218, 612171678, 358207641, 716699042, 157186895, 973278030, 996026860, 947030941, 281185142, 101298158, 914601078, 185689672, 812884289, 912839991, 289053019, 865715466, 160152118, 19423762, 616512789, 634341712, 657643643, 282351197, 775476332, 111941313, 224698295, 359570922, 101496727, 899734930, 691235267, 485270035, 627191095, 43031289, 106148039, 814751472, 795898468, 515105433, 971769011, 927551150, 418208976, 565079579, 741550109, 887563520, 487909496, 235868834, 138905494, 304456358, 494398517, 622530155, 585989237, 691057363, 116558980, 231096660, 150684938, 429698981, 654886766, 100741769, 429613794, 832590580, 52124496, 322795054, 794636875, 491452075, 95173085, 463231644, 267789513, 806829908, 970084922, 636489011, 60852126, 728750368, 353424492, 207484809, 953273030, 903505884, 480342851, 411668759, 421294347, 923053448, 579231764, 354380124, 57382141, 165662528, 815301297, 397318252, 868560532, 327424686, 794121891, 675346074, 552880426, 578212722, 683715825, 369717532, 186904468, 345576708, 222832351, 753097618, 268655945, 911049276, 415006558, 104505958, 748218179, 534162415, 947213911, 509825956, 536020964, 80233934, 681084910, 219992260, 618111615, 957077882, 947542612, 575913489, 368964814, 249112087, 515104626, 626124728, 602797402, 576142592, 610825126, 301234100, 569940576, 211901568, 842163, 939611165, 514347383, 658971221, 475581335, 94349566, 481514077, 578272485, 350284109, 233743667, 411093153, 703051403, 420801295, 915115815, 699429822, 945726399, 727620533, 893054356, 835070339, 577919659, 533637476, 67705154, 513284437, 927320113, 868937447, 74857835, 640178801, 784236128, 521490190, 806030716, 844840822, 50056513, 526029717, 479733254, 484252818, 738703848, 822110355, 860366603, 608187609, 904262934, 331869428, 475359869, 476507221, 188857487, 693274843, 661481066, 583188929, 755392237, 246204734, 699517534, 183780445, 925322920, 432490358, 321322882, 461968161, 335747578, 407479258, 433796304, 838311859, 58909367, 391678764, 771389446, 749528083, 974202628, 303612154, 195360889, 908290995, 71946165, 577472873, 465602646, 487444005, 77006747, 180044241, 739757470, 262016419, 344168661, 133882270, 163890151, 669496469, 226929011, 159043576, 157013513, 812111973, 484750172, 75902573, 531928856, 496698687, 673389163, 463577890, 941934067, 264929948, 615934852, 21062570, 389250425, 418591951, 590267297, 43666318, 182392161, 672445071, 214340813, 908231084, 792399476, 217404100, 194621620, 99744679, 419676644, 114093072, 679032944, 430012263, 195490501, 169949189, 959095080, 134248137, 739969221, 70953554, 672353070, 553966936, 738212154, 686701565, 506359548, 990428264, 528434040, 968675370, 576669089, 973965603, 944420514, 790843249, 312023004, 339671338, 158357023, 562008294, 337595451, 538636446, 185872528, 334226428, 196927335, 633870286, 611409009, 146492662, 304548230, 243376886, 63947950, 143960048, 396408155, 761582858, 2627732, 402079624, 709482044, 525259226, 304835051, 686479125, 906443337, 637968331, 657712352, 625588548, 520328620, 366364065, 438292958, 651427125, 115216290, 485424674, 828112564, 645120493, 430432256, 437667227, 342380540, 619205627, 789087602, 277616231, 637683699, 216571997, 62652029, 271259401, 601173725, 803501532, 580710630, 154746852, 383746285, 885403924, 316790032, 158608501, 535239613, 498235199, 658995464, 321172420, 799683406, 880349320, 486858300, 786394233, 76388207, 807487344, 671655565, 821502484, 187247908, 51272329, 610190122, 322918908, 166922264, 628103859, 890331771, 907517878, 207259920, 644180428, 376095418, 385707086, 448823071, 874357559, 999449460, 923286647, 943654015, 284208308, 377217899, 936543106, 983313436, 132393895, 440352278, 651189331, 620822910, 697351747, 572624363, 184975674, 37725079, 636769964, 755065637, 231490266, 619033536, 679138744, 412903244, 658480322, 800270651, 804638541, 407581812, 772547581, 872823791, 971761226, 375441051, 145705341, 463707313, 826772255, 726501439, 302482077, 217859930, 730172070, 780202130, 312012448, 84441333, 159272031, 278306064, 636131924, 571207395, 186369584, 539636195, 174174562, 383252849, 549641602, 765610364, 653504969, 90778664, 36395333, 18149766, 776630494, 299753075, 951060656, 853493390, 753311714, 214712625, 519333324, 491595391, 134432099, 60426506, 714736528, 158180147, 28833136, 270877371, 990212384, 367408355, 389436290, 358668618, 242346432, 781185230, 563815352, 510560493, 996648797, 990985234, 317045332, 292308215, 950620354, 730144337, 91592314, 548335621, 890069903, 714040731, 409300582, 247885785, 573318239, 972961390, 948130459, 543369847, 840711267, 408297414, 726533687, 335013960, 912262679, 212519744, 530515067, 9534714, 845944053, 754644634, 981061936, 945806864, 831416814, 622714655, 252322191, 65847614, 307317166, 981712506, 917370993, 666329782, 490584960, 315351144, 740989337, 225052731, 993422358, 334561291, 331937243, 137313975, 223274315, 136234391, 542837460, 140881804, 388738255, 794943348, 519749544, 322301807, 583495889, 789420913, 421862339, 8083273, 439701068, 863617024, 477243629, 978582479, 9946487, 432135903, 914779821, 811902513, 172350093, 780252980, 43737072, 787433600, 593032659, 894173108, 579377304, 971292612, 916804739, 847139827, 236083855, 190274726, 396010783, 674546980, 547535890, 271524423, 16505778, 590321397, 238711272, 405548005, 218101848, 172524200, 859395071, 153706292, 840070636, 551738063, 489619459, 23751683, 724371425, 742900867, 866803551, 877342608, 647515, 42717040, 547922136, 949363130, 248415272, 776114788, 893598950, 189344707, 89977644, 288474042, 409353080, 459189692, 250073140, 620840426, 300406294, 441809969, 327015395, 504278678, 774306267, 203503126, 563473546, 117776951, 156336165, 230705439, 800547620, 366256900, 586101386, 247569885, 790949579, 35432961, 862815694, 176524138, 247537523, 443659898, 803214485, 676511999, 871695364, 419319156, 331955150, 609242254, 85684972, 6317986, 692709298, 293753956, 53658431, 893218037, 506832575, 238811838, 25350313, 394521947, 176177683, 35667000, 292325266, 779762006, 588365857, 400215746, 524215576, 606186624, 54797831, 980767363, 58487519, 343225487, 134110520, 934462894, 21105126, 335430735, 902703325, 506902746, 637220693, 364838334, 423897210, 361837180, 119726265, 18505385, 611829135, 977829572, 991091171, 604849955, 619955990, 761647679, 975899777, 899239686, 482563029, 391295023, 728365707, 671440469, 671562447, 849569115, 87311837, 170267064, 866876371, 693281978, 146210496, 663325287, 82705030, 725874220, 598091851, 614834544, 857449690, 972304046, 555178785, 841889116, 352520967, 115803339, 954199430, 530516253, 805290283, 659055027, 503564786, 238473049, 791813547, 665987213, 957931823, 553754961, 103622388, 397396133, 365257872, 976539070, 855089007, 447152131, 173374812, 818311646, 975672270, 850728568, 497396952, 231787082, 111610553, 479835766, 813075875, 202205263, 354725199, 51284925, 446898711, 395279504, 592027551, 21487739, 844868400, 992007498, 114161950, 871394399, 508857629, 395521089, 768521640, 205439689, 266850470, 288687359, 335533947, 983910236, 177197539, 775524008, 434961411, 225272287, 687711896, 195833410, 356972600, 601046892, 764168496, 673771143, 181500439, 8804954, 53217906, 798732350, 947873935, 757096185, 212854922, 497552626, 154279325, 81194307, 186490094, 772206912, 235300825, 673680776, 350335769, 786920393, 512305469, 375935022, 503448482, 804176532, 549028136, 680715212, 523724038, 457965143, 723372212, 249574372, 350903972, 98699786, 150215826, 609865124, 37664884, 320182619, 299671998, 248414727, 162465204, 727436356, 656025360, 422866557, 414317187, 292381830, 740426807, 706336119, 218649294, 7074830, 153759618, 112232768, 721506706, 275210930, 445464953, 970984561, 863839820, 744742129, 588925298, 205333427, 16521046, 56395008, 603352884, 588181456, 219554338, 527106517, 223103717, 117926464, 945689924, 419269745, 56229632, 175058158, 321283534, 662705964, 662297974, 853441213, 75337337, 109805547, 245532006, 705499869, 208120205, 842959789, 211401476, 552573831, 9657094, 871000811, 795839313, 873201784, 128671418, 860319099, 66046563, 272599545, 772949044, 209703491, 743009703, 410464447, 887821274, 410882538, 540120895, 601132763, 510082156, 917164193, 662785654, 79734576, 792542435, 583856497, 929439752, 459150542, 23880254, 355201827, 2469516, 121988314, 924796260, 905479593, 724222764, 232929785, 667524824, 387688652, 922562315, 536044006, 699517630, 687680279, 915827257, 615824798, 60204951, 598727854, 789051963, 633038699, 278779076, 271191194, 601592956, 176645597, 915227301, 252981251, 90141924, 112867586, 239463998, 374601105, 101697171, 142006364, 185777805, 178805687, 380537522, 16027179, 730599674, 482607643, 809175745, 36937374, 29707037, 434801045, 536581934, 330224514, 718448316, 808326216, 987110670, 573828729, 529847586, 652315433, 826858504, 765658202, 260600501, 67755106, 952974140, 741034357, 159938771, 860195462, 124941707, 574657338, 110087425, 270061754, 138683467, 220187067, 323461591, 665518392, 907686790, 435049581, 679555046, 108347870, 498465870, 463701725, 988903774, 646622346, 259172527, 342286795, 177338615, 568437089, 630655106, 615841897, 618408941, 149143163, 934978574, 554919052, 561183712, 884523401, 450924615, 258306464, 623220132, 710407638, 312300566, 692216822, 710699823, 353813942, 776683355, 338088425, 658363837, 644150234, 222592712, 927382069, 322588799, 843762132, 562032277, 671628784, 296416119, 208249512, 419034502, 85166959, 848314438, 88764987, 393209154, 793158291, 855001914, 953725629, 378223684, 829813705, 388096376, 729300559, 52077904, 497719661, 274882154, 339473132, 627379400, 738927573, 980196049, 986007333, 604179280, 438244120, 113154514, 785400875, 257967422, 913433670, 140689246, 404709641, 590223889, 33815227, 998611845, 594134120, 60248526, 8758257, 88108053, 181500391, 681746621, 34467654, 114878354, 982704435, 826113974, 572474912, 838311425, 707310892, 683611379, 508390368, 492893070, 722437034, 563754051, 868513111, 820815794, 423490362, 983344575, 637524889, 343834753, 761381782, 695609157, 270913092, 928498000, 326451246, 601694363, 921374720, 945482170, 598876739, 766160436, 988628196, 359857655, 140318096, 661479287, 976468286, 603091248, 618515855, 704278572, 979286756, 873029419, 365879038, 596891769, 738221394, 602669328, 851325020, 565694207, 483196863, 843125480, 660118625, 992958928, 38915438, 318551734, 335305005, 573308576, 784152992, 135516162, 97728223, 699514361, 297660910, 595576916, 149981470, 948752742, 360770901, 267773287, 589360553, 488772290, 952649402, 54332318, 145375438, 696877745, 53786615, 990329861, 400903064, 344632746, 138497393, 576025937, 939466461, 685539101, 31153488, 795684247, 85715231, 440420132, 927785918, 270333853, 981969722, 363716046, 843436575, 476941586, 156592809, 587716782, 913438009, 773284158, 755831786, 520500002, 700488281, 765589536, 84860703, 706149793, 764830953, 698999546, 543813218, 824873123, 740469533, 123796162, 388152674, 963029959, 348387639, 72889819, 860613438, 930759116, 868935096, 123979317, 752096715, 964135129, 620857060, 458280065, 425374405, 757585319, 966819307, 585531476, 335943883, 134916308, 642786026, 627193873, 913733463, 726700701, 698456832, 802642310, 992955028, 598827431, 764955282, 469042869, 407629041, 9886906, 606989428, 959883211, 466198011, 523643283, 892087173, 245043877, 383154190, 389265597, 749480315, 654453655, 155977597, 626384718, 648943906, 474079200, 800154895, 133272222, 656748490, 51031185, 606251876, 583668337, 487042790, 512968449, 698637743, 563852698, 497734154, 688226516, 421415273, 84542240, 108480298, 714548904, 302451357, 110871581, 39526359, 167521907, 256132408, 741082385, 441918200, 14314174, 773285523, 789815126, 905437616, 370907310, 962159405, 963020638, 69279814, 567981541, 681636380, 152144880, 369808047, 352540613, 565527815, 257739476, 429572632, 624070183, 515036985, 323146608, 923135942, 744716680, 440770784, 310204731, 752156206, 938208456, 602581018, 218636762, 891463534, 601924480, 93720726, 393698185, 819245009, 61542970, 18602879, 247802616, 478987037, 737504903, 100526187, 793924576, 37182339, 811611287, 944711828, 585507605, 84251650, 757600466, 943502687, 973038272, 950521908, 434103059, 424347679, 796509624, 298736030, 797574150, 422389961, 975082458, 557439642, 806999057, 478423201, 720788782, 338426938, 451685247, 478532330, 321770983, 786029931, 797320569, 946791816, 671280852, 815540840, 91575603, 827516866, 506095344, 149797922, 400253185, 938125627, 924499641, 588050339, 943339663, 904763345, 899577795, 545902426, 614586064, 752676838, 230324287, 9302940, 818242344, 31731342, 706163726, 301317970, 957627607, 348356992, 698223168, 964979471, 647250025, 387088284, 540538714, 416860359, 707620883, 800030424, 488522561, 727110812, 53244655, 868932744, 298249546, 772119465, 206783352, 443576273, 699730453, 337896255, 13304574, 89446544, 887134773, 396727835, 676589011, 748818620, 790797160, 270764442, 672012996, 20606631, 16273290, 354591060, 617872116, 160544971, 954304071, 703131677, 315212145, 935910664, 555988490, 481723955, 997365402, 555122234, 685692631, 978975012, 116615045, 84832441, 875293513, 545339196, 311010103, 727227628, 875213700, 812216246, 362716451, 262701048, 532554421, 441717568, 560909158, 169579480, 861893050, 721603368, 966427682, 878229106, 444781774, 816250683, 316296083, 508718963, 822098825, 972296829, 786506400, 731229497, 731474057, 868905925, 578746666, 188771416, 310698783, 197885515, 462307147, 501327280, 5626411, 264951203, 68705156, 412472741, 413566782, 48438443, 9684532, 447035450, 960597404, 363156623, 386790753, 896325235, 512699610, 657100841, 979264888, 791116790, 376418881, 76589923, 801697656, 449902248, 241588742, 194893759, 346091548, 313495160, 275470684, 530904193, 72371843, 334579381, 112567456, 897172310, 573005636, 850766379, 802172865, 964150306, 506121640, 573601266, 207721222, 449562678, 767685211, 374876945, 860901058, 176687936, 150389518, 660763921, 261340067, 991983324, 406747989, 435738950, 376190613, 535912553, 724851556, 70528634, 990742747, 931732817, 464575337, 627975964, 352011812, 110588671, 367786187, 876020049, 514650198, 815035537, 707695561, 186003671, 452163189, 933965269, 785035456, 418457145, 229079467, 687886023, 901428759, 502821040, 543119146, 795139434, 540499142, 278992795, 927878539, 611762204, 354725460, 700664555, 297343561, 778653387, 309922085, 430762701, 524736531, 111769400, 503373812, 904111761, 812773077, 841240745, 151023631, 373795019, 901193535, 738750951, 403497272, 860399090, 844399978, 649652423, 497401463, 300250297, 334157300, 724402628, 569227395, 374254558, 801760166, 995738358, 858429730, 218491684, 221438036, 338405260, 465378109, 972628576, 305020444, 205052333, 699599006, 879516637, 63540567, 983833070, 638691279, 663214309, 804122824, 891710992, 526842808, 68928398, 802616558, 115795431, 294892789, 577140681, 163636227, 482086440, 770677762, 796880694, 435667942, 348258656, 477474519, 383789253, 456730902, 513512887, 184103088, 659752607, 998015374, 810941655, 635391029, 748465789, 852665809, 444091680, 203999384, 398476445, 584955052, 310989044, 590555720, 827119976, 897010148, 460441399, 870693842, 585695936, 208778750, 560905935, 800823053, 722363302, 72760767, 507040674, 446272197, 839651999, 292683615, 968124073, 434095543, 191520357, 50009956, 769098742, 11422397, 103155204, 165437866, 619297167, 557522214, 655871800, 316015074, 662150443, 712216625, 195842390, 230552666, 141798015, 366411838, 224081916, 282613195, 638193716, 905252496, 187023191, 593693404, 147095093, 94789982, 234755421, 855120811, 507066203, 796178434, 167822055, 574021949, 983212168, 591640972, 823349640, 548046733, 252982165, 363522555, 421757780, 104110823, 317190716, 290662425, 776540515, 53255559, 77883304, 511742157, 158596025, 668793503, 533319136, 46066144, 651293427, 477119694, 688306733, 536335294, 806055967, 258167609, 550566568, 457950032, 751754177, 763512490, 844500048, 71625303, 310674518, 569607902, 357391990, 270363383, 675536033, 298575747, 168120953, 907925869, 426139719, 696020272, 144627341, 457960642, 210452419, 343899449, 72959457, 150248417, 719505134, 473663095, 262530767, 408646703, 605094636, 151323296, 151695593, 935713200, 610755584, 107604606, 565951111, 391887726, 930113875, 93586073, 815553597, 132594417, 891909954, 980585781, 660298933, 526773972, 677709624, 789769177, 389825856, 525415965, 752494771, 421930093, 281324798, 680914483, 95135658, 393902699, 422499111, 590450557, 359123440, 867316026, 95396292, 714008580, 668656234, 282568497, 962830377, 459255543, 649728879, 916717629, 285942324, 119350320, 682076699, 541780343, 393047497, 851704129, 28684839, 904132617, 5684572, 359238945, 75032169, 797333611, 218094619, 194582236, 67604951, 350631319, 212856907, 350182504, 710366673, 569063629, 356472623, 55855991, 145783420, 374694721, 201402055, 379237974, 224904037, 958751383, 371302666, 522094618, 308306054, 97280072, 981850834, 576670415, 343626469, 500746659, 842051786, 92013695, 971760591, 434179576, 281983879, 339152114, 405951212, 792068957, 555750540, 250260166, 467885185, 116200724, 699847309, 437341618, 691959667, 797386641, 924881704, 626875944, 816601993, 406235322, 571318080, 984607385, 968555347, 646859565, 274008966, 187425425, 459045455, 83428528, 582221981, 763419644, 736597849, 85016126, 428236627, 914667205, 948784946, 90566462, 693760937, 1280364, 220610323, 424039803, 482864442, 569299202, 457578835, 162045457, 724689128, 415319812, 870015403, 798724593, 470536350, 330935190, 737965805, 668267794, 310568443, 206968807, 549098160, 635950589, 868796363, 243997247, 907244225, 988036876, 619189411, 40094302, 303404082, 643033789, 450002523, 488044025, 417355164, 882188530, 667076920, 864889446, 500980537, 227694838, 437701491, 258744220, 316658910, 121336591, 720269402, 844151419, 735337368, 408427414, 621204849, 520871302, 72164144, 158622267, 408732103, 627539679, 368355396, 410948853, 318553478, 558350494, 96203793, 587761682, 18915235, 563928255, 11990722, 855345666, 868624228, 337914099, 283217433, 634235463, 513257615, 50000521, 602625442, 216238180, 25182513, 930327708, 968102554, 691158274, 598240406, 733104099, 736952711, 39722396, 473746301, 131482433, 65318379, 203744924, 408195074, 145714384, 327332040, 140290554, 446804436, 967648259, 588858690, 50826711, 74993313, 361183161, 292635032, 150827290, 384306066, 617165664, 494187736, 953698543, 809091377, 350670807, 843162105, 475261164, 965790413, 881412356, 266956245, 680998031, 180174775, 809525258, 143624525, 532333014, 582165027, 152326583, 718629791, 542098262, 26494516, 944825552, 616680158, 366862847, 972032058, 332309286, 264435104, 691173640, 737370359, 123141517, 70787133, 508389191, 480283640, 877170742, 352084861, 709277717, 576983428, 910937460, 721805037, 129327489, 998835589, 169784035, 196873200, 158897923, 804772602, 761274920, 187894026, 915355401, 98868620, 717239038, 638471597, 978922610, 308023229, 249233680, 927402826, 243810232, 561070243, 95234581, 737508993, 892279408, 585997081, 933403551, 150706638, 317267498, 98710757, 539021097, 140216723, 451967720, 488589803, 573373888, 152976154, 640921966, 134181556, 674863159, 569058313, 300588737, 960390324, 155173687, 901484242, 872205507, 945513709, 399772745, 173401909, 846816213, 898109747, 859126053, 924000313, 374868330, 991921098, 426817079, 330111078, 944573369, 358824922, 439952616, 27419002, 455443507, 571440350, 828905878, 349047075, 578335228, 351411207, 346244875, 492229883, 110501519, 617374489, 766837186, 72439974, 157537328, 408572276, 583260490, 370348093, 828409099, 387891073, 499687251, 163204356, 262511155, 234518303, 139917334, 881211047, 228131701, 545327336, 306008710, 357731253, 503849299, 980032130, 11049102, 779594867, 165297643, 254600668, 842373780, 726438040, 820086607, 293075555, 557450039, 358164234, 351996543, 111408013, 869701513, 39988440, 774292593, 69968024, 239983364, 373736157, 747719262, 455972013, 106114575, 43836947, 679627664, 726037149, 92955945, 795276792, 578778216, 327716799, 199337866, 595958689, 447497596, 705045958, 366448081, 918921705, 851008486, 104680089, 573365857, 896205531, 363483234, 498436872, 837315281, 339866959, 543891940, 193136460, 980848049, 543873538, 507390762, 509430822, 729553879, 919498136, 231758222, 938695695, 724116921, 38274230, 863431343, 808625660, 556258485, 780553397, 975204568, 581160772, 716829576, 510052628, 243199373, 375227672, 645477771, 17700864, 182992798, 129798795, 14119282, 703275900, 709050034, 71139757, 903049073, 209604249, 833275634, 274110774, 780227412, 847180572, 971135462, 182206421, 567394162, 874662334, 983358366, 125809044, 593960974, 871870805, 152651654, 776205917, 192243525, 335431980, 871854230, 77454784, 597993573, 512797088, 107492087, 95942542, 246913248, 14119820, 714924901, 93178366, 776100136, 944094997, 522956468, 814976513, 761193747, 817790080, 165854116, 53673356, 452567172, 957043537, 230751640, 893596872, 424443878, 747778357, 786534320, 547536083, 627991983, 119760098, 981753657, 552034492, 893684853, 440291026, 261839116, 355164669, 148834870, 598431051, 1841832, 583568456, 413549138, 103312634, 243604550, 264588124, 134751446, 49895115, 488822394, 32547721, 870915037, 907124117, 15058547, 39594567, 93374935, 970216570, 188625255, 610826124, 149244516, 742935795, 78131974, 396440440, 78920282, 277650937, 365763587, 885377956, 926423245, 520141868, 496884301, 598799711, 944607007, 731967930, 943375649, 319984638, 487693307, 242439392, 334343288, 646648159, 587320142, 489762695, 605078487, 570191180, 654059732, 390115579, 200654674, 951373361, 4479251, 481891977, 45273171, 688908244, 670351018, 298746070, 796936922, 831919368, 583466276, 457347191, 745179599, 660228994, 186048542, 757919670, 464111394, 208200135, 11241366, 679562336, 718288871, 483070164, 452499554, 150487187, 761249380, 415737755, 856554196, 870089627, 831038050, 42189128, 886303960, 272613026, 393042272, 548242217, 70844946, 850828288, 522095054, 10920115, 982205401, 105977046, 132665754, 905321169, 272901940, 450845613, 305631693, 191947959, 197358735, 265459045, 487177321, 616812086, 356718233, 904952198, 386141275, 313761335, 9790401, 470783125, 450334563, 211892982, 932745098, 811994380, 457886842, 734665058, 273589892, 306604542, 960760895, 926322627, 754273221, 558458903, 191502653, 194815193, 631450141, 890417868, 896706029, 339701102, 532209350, 362825327, 153604529, 906677259, 361371862, 402583930, 257178717, 74622425, 597775188, 5850083, 9776058, 294684453, 536853121, 482081159, 17060575, 890840377, 553403352, 390871384, 35128961, 792892485, 969321269, 521912358, 571034185, 539422254, 311350202, 596391700, 185992101, 573829920, 862489190, 32066117, 649076597, 803166160, 314222757, 172441122, 593609408, 778348240, 283377052, 724378405, 802003453, 907713152, 461648976, 311973474, 611357257, 439941511, 56305646, 549576233, 836290806, 893817592, 330371324, 65834883, 616221598, 963650531, 932886911, 40943100, 7521793, 975083971, 57824254, 818889911, 296120006, 927733397, 513934247, 604290841, 283741329, 802286264, 546992860, 317880452, 490674637, 432294912, 434409617, 369564370, 325554887, 162428818, 896783176, 713441757, 129821415, 707936987, 979967679, 884274514, 211259221, 362677769, 903142437, 234382210, 838663569, 930231098, 175911418, 698398574, 675578031, 520486285, 355050990, 262665307, 407030872, 3611581, 105498768, 466218448, 354245734, 259238165, 357857394, 662281485, 211646798, 233245489, 36013722, 966920783, 418907914, 478961826, 195387617, 389879953, 410869747, 318460121, 854917365, 889458736, 626983301, 767267974, 901180371, 776593183, 722570692, 919004844, 139906718, 588049323, 111059193, 507433680, 351580504, 708316291, 115333523, 980771980, 138034699, 680521212, 796649765, 53059385, 95084153, 610644249, 830252948, 113892168, 627345696, 784904014, 29078348, 852520222, 769924624, 760838235, 727340097, 140850268, 404809880, 835826941, 880470295, 161803942, 402533654, 172768034, 500652487, 670889705, 463919013, 515773357, 491198990, 402306602, 829466907, 546857676, 880999701, 15599370, 285429842, 925395256, 326585846, 527625869, 939710101, 874460810, 332690301, 905939195, 103409329, 252912383, 589870069, 453659550, 291328386, 369972201, 639771448, 622012059, 87726421, 562770160, 452821650, 334085309, 830428461, 190405846, 586248297, 252321908, 583745173, 551244035, 888929509, 489857452, 94190090, 193038475, 671569325, 847853453, 941810958, 499399235, 607459909, 541358223, 779791790, 980492103, 254613410, 710607846, 809068583, 829994089, 695787356, 895082134, 735054767, 993389110, 279090673, 389528466, 802287547, 109623337, 73840992, 497603897, 743178819, 710578844, 110688821, 248224441, 522173856, 727861238, 111778062, 603708329, 138348808, 295058948, 464223625, 536477617, 224510723, 454597141, 281729500, 452092686, 557715154, 201092278, 387752790, 438868766, 579342481, 345641132, 407084156, 457790427, 793337664, 523631119, 678258929, 585419116, 779342207, 382636023, 742457897, 845812582, 51441736, 808315957, 388949766, 155500763, 110584337, 660099784, 542698576, 127550430, 185435591, 762785626, 361649543, 280614614, 608202826, 872646251, 290478628, 728613938, 302245721, 163210907, 586612590, 726702806, 66073902, 907853468, 640824562, 841915509, 42962589, 117963659, 407227762, 693487195, 880154658, 570292040, 624851936, 603057260, 263980657, 880700734, 409638714, 475290158, 197499009, 951936227, 814787368, 575133697, 197201246, 713398042, 791780941, 788660094, 915928215, 391928033, 150724806, 587170709, 10076519, 620147424, 346132439, 301913389, 235408605, 431935565, 730053886, 285482754, 60806380, 461899172, 54877922, 825400351, 787463710, 923880133, 666513305, 340878940, 283398403, 167236342, 268636004, 121267192, 398508400, 166470071, 941865292, 302742019, 932383584, 780922707, 206525890, 401101568, 820407336, 224257325, 833505405, 601459213, 52014659, 971685056, 661024042, 899503422, 45674085, 114120303, 779015828, 533128986, 580402383, 483783717, 729475542, 90671608, 804541093, 580292783, 500421920, 257000873, 749117719, 982597508, 382067439, 354141558, 174017512, 92581781, 696140224, 825592805, 387610827, 772555515, 294896238, 137881205, 80127413, 252964638, 702580193, 120797064, 279307012, 966373291, 979503184, 60227740, 927853126, 500825034, 246204399, 962822625, 743388680, 960059095, 517423481, 171017388, 419022374, 231324145, 764218970, 797080861, 582869776, 682761864, 643243705, 719441571, 46896365, 152609592, 852514770, 828746529, 80025630, 847913532, 541942812, 35524967, 570601925, 98964489, 541910690, 164736845, 276084993, 933007928, 120953489, 53240839, 626070228, 607086123, 393509736, 635069309, 679485614, 925540870, 807071979, 887177198, 751748374, 842023066, 765668700, 881844148, 945412039, 180706880, 906170079, 422517034, 746397254, 730344971, 492339239, 144150409, 968476904, 33217993, 250317424, 308544411, 515235000, 688350889, 31677665, 694953687, 680638486, 429652317, 614052908, 952885185, 945626779, 283433702, 105767140, 232914971, 606853104, 797407385, 838002932, 548959178, 806643518, 300320201, 429835953, 742678744, 201536386, 540461450, 819156607, 921924706, 644837653, 282530190, 439813321, 729153897, 646755675, 746970370, 750928041, 10116742, 95217106, 295763778, 431120847, 260583366, 808836176, 114371495, 826344772, 18789731, 882207166, 500644309, 298829387, 733648031, 221056286, 309700302, 122894928, 241833810, 539976973, 70561097, 23325085, 739380316, 111460587, 541308894, 315356166, 760151970, 365996239, 741514774, 51564244, 263921870, 700834379, 423228681, 251772888, 120043135, 745658801, 776552196, 224407314, 842715101, 405397922, 207374727, 511039911, 58889179, 187292839, 421338574, 159533671, 436716818, 28103297, 652592006, 947640700, 212864176, 735862917, 812087879, 653613558, 313495362, 974901368, 787527134, 66752561, 6271450, 791587603, 982109858, 238837304, 711344261, 972938, 924428531, 79382139, 49095746, 660024078, 935209180, 948164760, 378112431, 434440073, 876231036, 100715710, 501493414, 217716071, 699382800, 100802131, 539301082, 718802011, 883880637, 976138466, 375087385, 541562504, 90090049, 822523086, 779332933, 997921440, 776737332, 695263386, 698478080, 143651748, 698642231, 9833267, 873520901, 773754090, 302264656, 498439845, 218843932, 851549150, 117117447, 272288368, 574124829, 195649477, 787009501, 244069715, 660500793, 630172220, 999557671, 71336605, 972435092, 975623434, 941507032, 114060877, 900351404, 903731885, 656322089, 986206662, 326476330, 217705719, 919241194, 775388653, 685529222, 67883237, 940661166, 248737008, 857543323, 971088049, 57343045, 731477365, 943133476, 564824119, 31154575, 337314119, 358562641, 95689454, 396596962, 166584521, 795602113, 268864526, 16686206, 754044434, 19826672, 948305368, 534550323, 218726457, 168588752, 786389297, 372090148, 632010983, 32562310, 890106176, 901615518, 919248171, 781833060, 627873218, 549969945, 343085098, 215044732, 930188517, 377044806, 269995203, 992264453, 504857637, 359198308, 641752160, 778861867, 504338834, 705213949, 852379133, 51756007, 678377824, 214926458, 461315311, 48199256, 915773227, 863258001, 393178196, 614297688, 638376107, 358424554, 829057823, 412193081, 819141430, 221719034, 209470528, 648564212, 255648817, 67073829, 282882238, 380241196, 719525600, 896634757, 466772584, 931689316, 398608264, 211865549, 609115628, 789419981, 42347760, 356936371, 844010807, 669795520, 576194902, 542076881, 26062627, 592829099, 583233510, 628523986, 354568213, 756715364, 707115783, 140474419, 737810749, 653308111, 928824972, 997424309, 455344991, 237683492, 840182782, 555372362, 951713422, 324916779, 84338765, 842389968, 871482062, 66194655, 667769866, 615132550, 164819134, 431019351, 294954924, 25590565, 234392322, 73849526, 95907267, 239918184, 147135954, 338334481, 670624411, 263819381, 146713768, 224889676, 20689198, 224807129, 313449551, 640980337, 382079031, 828381641, 844888263, 991547410, 550591377, 781035605, 798807840, 394039323, 117788348, 450775948, 87049878, 221819503, 957833690, 411808123, 892468664, 968139965, 859788952, 407018048, 650103130, 588802658, 747515758, 462865907, 917004286, 727856738, 188781105, 797240766, 120201518, 586397035, 49594432, 525352070, 777383562, 864453567, 829151741, 438579899, 760619411, 873118754, 667573452, 743386267, 637878768, 374307043, 997982833, 970315524, 10200038, 422353194, 612137508, 5769358, 603420440, 959573489, 322248804, 559981535, 442942832, 27177619, 65571969, 6420809, 260634277, 421336521, 98858996, 277694623, 286829782, 962836284, 773336501, 301383732, 719633066, 68151691, 378071960, 852984042, 891464189, 701063978, 699597610, 448381095, 780657006, 849343432, 91497797, 440756813, 750946917, 617793804, 295122165, 636917064, 19393280, 868728733, 894060178, 140646694, 606562509, 334628228, 953567100, 975761315, 819410201, 606256554, 258114473, 266998022, 473941038, 395327564, 629826378, 922161917, 494376084, 552842909, 176982605, 815879822, 111316943, 719395140, 412468709, 397990779, 70051636, 563862684, 933613258, 538384741, 108771385, 495909890, 607715391, 112320521, 453812265, 249271246, 63939674, 502270160, 930250965, 760533533, 993373498, 990148382, 664461234, 716800224, 202623630, 69837321, 952059768, 475999586, 162622451, 179010783, 496824521, 198549046, 33920408, 92865271, 703995260, 31979664, 599615834, 136062910, 453062229, 444108770, 370681060, 746886233, 897646, 343842895, 592885528, 135730618, 649508957, 363352159, 548801320, 584116731, 871025121, 857921705, 493578748, 837088575, 607238138, 95865292, 885946622, 866805445, 620799420, 340193548, 41289316, 232192902, 668431986, 220680343, 721914547, 703511372, 921728921, 772413086, 426260722, 823521578, 750488150, 430475, 744841910, 681838332, 103645779, 263717168, 363800237, 614311149, 53619642, 899771110, 193785615, 664706981, 553861091, 611846650, 207362476, 982082915, 457734963, 399699591, 604237585, 891457208, 66966923, 916111755, 520659607, 876903531, 743679240, 258696938, 658002912, 815152377, 230557816, 775515365, 607182542, 415592524, 861229844, 245601191, 221200895, 717010520, 105588519, 740783163, 940353563, 26485027, 964287373, 489280606, 275709046, 383557973, 655050137, 651015823, 844522970, 376580439, 907640685, 928553060, 611136170, 221520984, 92498420, 904954541, 350750338, 807963797, 574802765, 630037961, 974946971, 422617754, 457324127, 665355581, 237679413, 908124578, 669006789, 810167152, 53063359, 888241132, 521819158, 317066647, 140626765, 49137572, 929332257, 780818453, 412315291, 987167769, 85110046, 531820839, 298326563, 746774793, 118535229, 326252103, 858002862, 52958210, 883420115, 412177846, 984459228, 100311263, 491113229, 636497682, 775387866, 138221374, 363938479, 250261399, 569631728, 205555745, 963487202, 229134912, 787252461, 936773736, 398393368, 875530493, 788739514, 160658412, 95351119, 222070928, 560561365, 35384959, 832380824, 570703401, 636840350, 101351135, 308705037, 789552867, 879065841, 998546398, 546544441, 855327512, 493488794, 907981862, 649681994, 514728682, 777974353, 813377900, 618470830, 724863435, 829136232, 823631998, 933472124, 148446098, 682066655, 664980932, 534223263, 922090810, 430426353, 109730842, 657938603, 741124818, 139163359, 429362382, 349574138, 194142963, 702717920, 412624175, 102177302, 864624307, 620235242, 36253281, 668595717, 71807264, 12191871, 787765776, 858839513, 118598052, 609632732, 365163915, 195699480, 665912277, 738607963, 400672929, 801979206, 365980643, 912119484, 438688964, 615374328, 283685764, 645122106, 745551469, 185517973, 928169900, 252512731, 381568501, 668772460, 517742945, 436340808, 409342629, 79584531, 43109263, 413429668, 43374299, 156789871, 162425614, 622742352, 877902952, 475524834, 679826869, 35713459, 414595986, 734543732, 701169578, 865673555, 160050315, 622798488, 150131361, 25783676, 914408902, 767298328, 179812761, 117796765, 563038925, 528180326, 128411895, 293847196, 609004075, 619432505, 950396608, 246151671, 157177604, 474786888, 55057769, 961540103, 549433046, 852544322, 849354048, 700578743, 794100876, 622490003, 754100557, 476915376, 307636739, 837147039, 102702330, 139862412, 240651102, 40773354, 383398854, 749708747, 237790833, 263069656, 838059450, 29604026, 506335598, 715667927, 589448777, 773809759, 795630704, 632182084, 810641115, 255271191, 141099411, 401296886, 837937448, 281176822, 156363669, 160570229, 434804638, 390752733, 139040758, 703656410, 512233141, 3172674, 954177274, 489918341, 564544537, 513394844, 669123809, 908592092, 729523636, 995747300, 686367976, 379036929, 741063321, 89815316, 107802610, 25889846, 592264974, 600191486, 805565247, 347498177, 429763773, 552613429, 238479651, 450157865, 315506137, 985254916, 845549830, 453154953, 256713761, 57422938, 87459522, 979397684, 137611918, 368915181, 963626348, 973370995, 13343232, 645007501, 992607362, 430239215, 613714602, 50342328, 499683557, 887773451, 139694803, 705179866, 263676034, 49742883, 531103016, 756075927, 176451070, 611230391, 834961138, 480148760, 640775032, 873472504, 887119056, 123255506, 577959192, 614337767, 69581295, 819992787, 65284082, 671529561, 395882239, 912764499, 472240521, 962367965, 911989192, 275261341, 760024304, 754222553, 12350814, 974259603, 457218340, 285882729, 691418057, 949539659, 894500471, 378544381, 790201238, 587331317, 776633517, 736815475, 639724732, 625258713, 370056257, 617603404, 986041129, 289214904, 725658803, 215411360, 359455844, 437516725, 365060986, 943426981, 561644811, 159737872, 269151636, 459177169, 352561822, 559414830, 534365945, 610877965, 959988893, 431121639, 703759335, 106671051, 876980676, 846208034, 634225722, 19822232, 383511638, 86546934, 382755924, 704094026, 910985174, 273423282, 242650463, 689250763, 861928085, 466404521, 552141901, 788444783, 293311150, 586693668, 260974954, 318315139, 531097424, 160554573, 867504115, 735411146, 301464111, 979595276, 647820687, 662950461, 350673096, 896544856, 8542170, 956735510, 691177752, 566838997, 580484234, 720989425, 812294511, 534077949, 388474412, 453331771, 312942698, 133480128, 364859511, 288552861, 269788026, 225520656, 238810313, 687072888, 582599432, 156289643, 901898168, 957141320, 259094806, 767606656, 590273903, 160714225, 152202262, 553952822, 228770071, 186551501, 886004015, 522375726, 895031439, 37327005, 958256672, 334310149, 189583438, 897310916, 330965447, 53991849, 876468965, 63221478, 755157388, 737302403, 137971943, 903556211, 116995607, 514390226, 315325536, 916014311, 762370764, 739896962, 431787060, 193060383, 211532599, 782627366, 584472607, 239192541, 397250554, 91057250, 612628969, 140040163, 557071383, 371652749, 719297217, 444632068, 978159338, 235354362, 570756414, 742971100, 585448937, 145469912, 404439761, 65476962, 116308208, 328969931, 63549086, 383105464, 150149373, 22285542, 989669866, 227997321, 272178220, 451031834, 139521739, 307846414, 193157917, 708398386, 12631829, 424129873, 665582311, 536651204, 766034341, 698729197, 369369549, 100882927, 1788778, 149950911, 807086726, 446506092, 215613952, 91342322, 378229803, 86199034, 294437811, 4034989, 457042750, 383136084, 486660406, 337160173, 765313138, 732335543, 781757396, 309931422, 936994235, 734133880, 447021332, 141551987, 645603867, 397349059, 817738625, 704274414, 216353776, 834915954, 539730800, 110048200, 49782084, 659278013, 201300169, 439031330, 426269145, 108572914, 611649616, 566119280, 104305112, 179739489, 615500847, 298167427, 545445939, 519284617, 495195091, 323873228, 323398381, 272835125, 63929231, 135619144, 736452325, 559978724, 256177916, 87537851, 527442297, 114929236, 458957722, 701876759, 702777379, 72154694, 412808463, 126860122, 330804838, 19371041, 924649878, 518356966, 103122426, 825700202, 45374632, 198821899, 168842332, 517877046, 935749431, 460553389, 118546041, 483323641, 203915031, 418048745, 280441408, 776567433, 912831365, 862349837, 430226388, 135532029, 275470598, 129558728, 68573337, 246247228, 22864945, 516180605, 572619890, 738021857, 825353847, 852233679, 38952567, 579285712, 129105751, 874913501, 113073418, 361628561, 825031455, 38435147, 190327256, 715197537, 265463834, 761698825, 390509331, 376561256, 539289004, 790876427, 442273203, 242878673, 868548592, 525313039, 500326346, 22979524, 520480739, 543607644, 53360985, 512547499, 551186257, 979279409, 313292457, 995366764, 909852348, 753602176, 62650735, 205426282, 494810927, 333604996, 306887322, 374846096, 172705697, 68727808, 984245536, 920419558, 973366072, 990661448, 320199354, 477119701, 973398858, 518751685, 588609438, 258874033, 930996960, 754215298, 508867705, 507036907, 74300267, 60786900, 322679140, 193918253, 661056750, 118494686, 409454447, 420139802, 925334461, 445399922, 320127941, 207382517, 727362275, 826850714, 697903195, 346285348, 773544282, 640159936, 243802870, 210764178, 862192864, 322259170, 673846231, 139413893, 818308068, 295879982, 687029806, 571500186, 340367124, 120246166, 820517678, 329899859, 533158473, 18667880, 373300701, 425076035, 395082976, 549210472, 11339794, 638688941, 797507608, 200459526, 558554162, 16931319, 290451407, 264781736, 650688265, 582172904, 117536742, 558211698, 462472165, 529913810, 124155418, 150277411, 334038114, 45049496, 200794258, 53316716, 270056518, 298009079, 518676644, 592229154, 29503276, 63264160, 266887304, 95253803, 746666703, 936184013, 712616140, 348832305, 962677274, 949078354, 633284858, 693931279, 778506102, 627701531, 530786143, 395468364, 514111450, 16706978, 115424980, 822441508, 272764882, 152696681, 993935379, 975998791, 14540047, 40112244, 809921106, 598028082, 114842585, 830925356, 32427134, 457589525, 739303981, 61137809, 158834515, 317330935, 60538735, 936717707, 448377134, 952062831, 205650383, 112744027, 806789429, 11774216, 558728099, 47644927, 784933837, 424133001, 328262507, 759627384, 783626435, 193202385, 741639196, 745776738, 8117508, 672137423, 55374245, 592362714, 93440479, 945524710, 530022929, 143632373, 152670593, 795359183, 251304913, 334947911, 431863003, 243408076, 972627515, 80036205, 774342072, 403935107, 919194102, 39710346, 222269638, 149963353, 238720201, 388058841, 195958901, 668132117, 601409279, 860918924, 836578258, 965407096, 763752709, 592565408, 401063707, 561152325, 82866280, 198059306, 637819924, 971615504, 386833251, 577343242, 567361320, 586049918, 890149448, 119707575, 323472025, 298253290, 753249754, 794204380, 569337005, 512849969, 275753009, 785937825, 26070810, 977794116, 866784033, 599332386, 827059888, 549966951, 512892891, 869713400, 492687183, 157040932, 391508752, 922607495, 965610921, 227842797, 708165456, 40465942, 395267371, 278745969, 142086947, 108058435, 740759421, 76630809, 983168897, 871870484, 444919478, 228584105, 128588008, 517888447, 21009984, 234198767, 492544646, 323410067, 379716045, 590555770, 57093352, 40486760, 10854722, 26819044, 605873836, 815220868, 259738040, 496241034, 656738021, 390217685, 322326545, 70003895, 405791124, 114224184, 920463210, 527879457, 283574162, 956737814, 495009327, 5499718, 743903345, 621517050, 700762205, 765373717, 737819550, 402287409, 417865423, 881771972, 354570036, 17450552, 154837560, 15011088, 195965525, 120515566, 845175904, 634944417, 931930478, 601850910, 119662328, 917096995, 815341389, 397679271, 909592303, 489859049, 332467563, 35764782, 264798306, 824659558, 583932733, 837982795, 24796587, 85560170, 233443746, 531954924, 408133714, 815446245, 603491377, 158475150, 565576516, 918468034, 627926675, 698559225, 239843209, 585890210, 309552278, 110621102, 175850271, 389525829, 142226674, 642386022, 482226723, 205060080, 526434455, 897169511, 586417410, 470301604, 530460123, 601975880, 462823049, 350217274, 826721027, 402751492, 619813496, 593141876, 109706507, 174977039, 734871899, 102126787, 695265262, 15978382, 835327015, 570097265, 668940507, 423070365, 106359475, 423973759, 544313032, 902826688, 858513130, 305421737, 503362377, 597115030, 323098570, 608051808, 576253200, 102272254, 155091774, 118547477, 88632462, 74121290, 241465516, 669196175, 220339123, 210764280, 111922080, 604202662, 166365124, 772017100, 625460094, 154463305, 48818953, 331509332, 159851459, 993365156, 965833561, 72500755, 821306439, 679753673, 239870391, 8384798, 488741969, 631702022, 467727418, 200160114, 207765723, 641152706, 316582460, 238498485, 132332374, 161053518, 947107194, 96132532, 193038581, 607541732, 499209401, 520956396, 147923848, 249186335, 444937864, 967726623, 341028217, 362494225, 722429841, 824775211, 325710612, 929977779, 923966199, 397689807, 755183560, 993441330, 248879971, 139588908, 787789174, 78496869, 905868168, 181152778, 258706705, 758971672, 278246158, 194485665, 16329407, 696432906, 763503629, 519806194, 534322481, 943990222, 310551278, 128048981, 419518585, 675400711, 248246442, 317580683, 448848585, 476915291, 754172980, 860114513, 273376935, 419566254, 395439000, 33026531, 199001435, 802505401, 769382117, 987878623, 954518793, 114436501, 184326949, 35818355, 339030756, 329401339, 420368685, 916165576, 390309910, 363990372, 713471042, 202720981, 750985322, 707065125, 125370272, 748872293, 677429776, 432084128, 495420715, 852068242, 757425184, 433299600, 85533992, 889205842, 464783953, 917987671, 279010456, 173391696, 44197070, 234986980, 590582065, 521143145, 574323935, 560293220, 248163796, 686781873, 282484139, 3084546, 324915522, 613896552, 65207940, 625255643, 735539883, 366586924, 393920446, 528297357, 883680362, 374662062, 907486183, 720775296, 272358706, 42262306, 584500925, 97466126, 882390010, 544796835, 978520757, 429623999, 365088467, 968309347, 270212872, 354299244, 850533757, 484333831, 787324573, 372121231, 652303415, 59242939, 233294800, 631952536, 592593463, 637307600, 340651392, 576726386, 744368012, 16606114, 555109227, 698394968, 672868802, 643336978, 4076763, 281321831, 820197818, 87069297, 574293928, 812189651, 181111526, 719521377, 401566762, 400956408, 789227280, 178319536, 500536135, 998829215, 692182653, 74819033, 479526165, 922482457, 119033832, 943143180, 959158995, 753868064, 366276921, 618634002, 604817798, 51553192, 193010759, 339843828, 291748338, 973568669, 191764006, 352102600, 467468715, 803323418, 652285385, 100179704, 987807059, 336953767, 65049263, 901395538, 816037270, 883615304, 115056174, 393623564, 380045311, 792114993, 439390265, 265692195, 797829382, 421879001, 47544492, 629627788, 910702356, 98457661, 70458552, 155600247, 438265609, 498040006, 222352821, 147546550, 396609224, 892132725, 776938992, 527913152, 39253931, 686231206, 546057126, 859816699, 714061531, 128656387, 690150484, 328403836, 555245389, 311171566, 992940777, 12632846, 541408934, 40616179, 295813209, 706925100, 398814583, 646783407, 684729042, 354095601, 148910526, 783649490, 333214232, 951752866, 106428109, 413737291, 37370113, 993740549, 410528662, 241251044, 878349280, 305523602, 452922907, 362330216, 719615813, 466554486, 652363346, 497710195, 903640789, 703794448, 561689325, 297821119, 651748204, 557063649, 569571447, 603035576, 468814169, 857847997, 667834680, 470827841, 673035913, 196674780, 854186148, 292401456, 52982970, 268688900, 854674224, 29579753, 820171017, 145935795, 948666136, 57048397, 197417919, 569167245, 476085103, 132924498, 799291095, 503142059, 884427117, 208544444, 266509444, 958461633, 286110462, 443714250, 345434736, 783408679, 934503256, 978561634, 849290096, 327566667, 715863371, 455536872, 997035018, 219087314, 764359443, 496087632, 290832679, 542206781, 894585460, 905569670, 737830120, 333236306, 695790667, 254756063, 486203940, 961172806, 769311148, 190879537, 912395175, 424524568, 439657266, 298017299, 172774067, 125811925, 461937741, 298614348, 92453669, 173104962, 80545515, 160356568, 222793884, 948015331, 824953200, 521016249, 952483933, 211434161, 511467447, 844534611, 562339510, 126352241, 332267613, 44773054, 302660262, 569912743, 507339983, 1244482, 598677167, 150349270, 235849214, 46881015, 986854128, 817265375, 659544355, 977397028, 666452054, 784869002, 373382491, 257382953, 201983180, 118619822, 22260822, 154787075, 91305753, 758188902, 859679515, 192710392, 41721976, 274578221, 744476422, 673261983, 660574196, 95312688, 245445449, 545683318, 998582089, 516448590, 320716189, 851397253, 746343856, 978716192, 286229704, 135179463, 420411974, 546182235, 30167201, 39594940, 978432668, 432046407, 234160223, 396484562, 775030522, 250932992, 794060125, 44618925, 764841983, 884843410, 920656216, 177981381, 140095478, 560853296, 981630773, 216817489, 580436894, 294876269, 11580577, 807906777, 795603645, 934166691, 748773528, 468882633, 918710973, 120168750, 603723971, 588324253, 312001437, 183065416, 737254053, 705589146, 894372519, 124146733, 249910643, 837516441, 309560857, 334120351, 230135861, 971834588, 818967857, 641162606, 511985829, 444803519, 474981067, 89064335, 585854230, 12573990, 360895881, 485722281, 687117807, 445776917, 298729013, 284019548, 828192420, 706294350, 38144439, 256867545, 452808667, 67424965, 191752694, 990633012, 74855332, 84995502, 366786300, 963594833, 830797546, 567947599, 481706705, 733035947, 455323410, 778290380, 954838313, 638974974, 327323916, 252593560, 240097850, 991006556, 644638498, 530245925, 78148948, 498751962, 172309053, 683404657, 550715234, 621517316, 954647836, 130050996, 797845364, 272532424, 81173522, 498154183, 421676489, 503407805, 577650203, 578514113, 144431290, 511164679, 201597031, 323855612, 197920146, 623244439, 985282487, 602820200, 253004174, 122743202, 456088765, 301216437, 892626901, 951348254, 676177878, 250750347, 696996546, 646003377, 781982475, 725861031, 568450030, 96714031, 858880467, 229658411, 70462843, 220296659, 549994245, 397136763, 810912449, 645112153, 704236124, 493358147, 834112157, 28361561, 386354327, 646205256, 7647459, 204874087, 359453778, 249009733, 576692764, 477087402, 155492476, 508677238, 384556938, 833090179, 911299165, 759390821, 985134685, 487336541, 486647980, 229780704, 802914215, 832399698, 585584794, 649078700, 651831199, 259404662, 137278406, 927612377, 855618257, 386347068, 406326203, 45907843, 60445599, 108755167, 588022534, 940897715, 273757346, 526564122, 415386597, 60194596, 76588448, 787621908, 704573555, 646392589, 378793327, 325261193, 584180756, 654302244, 805201922, 297075994, 591184430, 943202888, 217343555, 794094344, 476871705, 538168306, 343952575, 858904696, 880404099, 936659520, 844204906, 67704593, 37830763, 764913447, 196441918, 711472722, 279132661, 669071436, 55699687, 703339296, 37489844, 712339795, 619896229, 139400238, 733281625, 627380233, 85083499, 603869194, 428562455, 535104377, 316217886, 38432526, 947232784, 572465179, 131304924, 870255126, 323688497, 723232788, 114138544, 574930814, 937267390, 796000776, 665168979, 824021924, 882653640, 186023834, 172932146, 352528211, 305027326, 180268658, 515518501, 35885971, 194569604, 280271432, 291987615, 91827575, 135918610, 190145440, 273228810, 106256457, 185766385, 428129442, 445845410, 956222227, 656154205, 973603572, 278613040, 734188425, 621256326, 552089577, 729866350, 761732927, 994612952, 38330029, 800771262, 166350107, 160121269, 78198699, 821633672, 602167948, 531197481, 113292661, 863810183, 288073276, 892065408, 943250810, 517862574, 96690819, 662761249, 18136830, 637209490, 501304458, 209244001, 233086021, 537360137, 251737625, 301479038, 154088800, 856799120, 850061081, 179959220, 96151351, 323959791, 666726879, 564456125, 249820890, 808931720, 650857813, 181591692, 955193966, 849867398, 154440237, 984205322, 869609561, 379456851, 196246373, 595033330, 317572218, 582890159, 623511822, 87439271, 805599218, 362470204, 540832770, 205459969, 485286802, 915241621, 794826959, 121064252, 340181046, 383550396, 459861461, 345462606, 752098612, 80064622, 673854453, 730078969, 865053405, 979245744, 936957842, 628081722, 633271077, 169301756, 879824585, 386743141, 91171972, 366460760, 352502960, 811383652, 400194503, 797747774, 893580912, 874681274, 144031010, 497957168, 934321576, 950548181, 363484699, 945540091, 699624157, 154158076, 609019444, 135516277, 256409378, 196580712, 515042816, 726644109, 874546752, 137393106, 197250028, 445688896, 320234027, 686767918, 166764899, 593313949, 260725936, 783357000, 164383154, 75177031, 13892414, 342227145, 894450994, 634655578, 809666483, 132212803, 565163321, 510396602, 250828155, 231116646, 23516477, 621030011, 464534424, 43370380, 855639111, 98676820, 313220518, 986915278, 593086735, 893415536, 259558547, 15329984, 289242650, 157927903, 285954673, 204746528, 124485169, 459849487, 857316088, 623008458, 680632874, 329157480, 318347883, 967892061, 759911680, 833469359, 17477548, 389656001, 765102586, 836672968, 864359051, 28492311, 947358051, 885521869, 112279591, 36580710, 895043903, 939788215, 148420287, 531436489, 355000285, 580206731, 994367690, 404865092, 340197144, 36300713, 578133001, 581161730, 490581678, 785569555, 226266753, 227832255, 707607419, 40703532, 473325898, 241029902, 942616058, 788116669, 298605622, 737801393, 768846507, 358095618, 82134036, 239261994, 149514270, 445894950, 456191758, 721846131, 136500007, 284412394, 953532048, 120220767, 445676706, 981780296, 149339871, 203468507, 892290364, 919025749, 478973957, 921563195, 387475414, 409313432, 261152881, 95038238, 912357441, 677675514, 527079900, 813305572, 665846057, 286153818, 71915578, 43983920, 897337919, 606230501, 843509176, 929280661, 354265913, 345640090, 350245688, 271086410, 831031313, 427238395, 311765377, 400972685, 351227411, 696093543, 670755539, 636188773, 280621701, 206321353, 438224298, 271329062, 51666548, 246701649, 59747412, 289456354, 330583093, 808241711, 162666618, 298119973, 184333119, 7086568, 45944432, 171639748, 466065973, 784719243, 309144425, 987277387, 682725524, 449840203, 309833216, 993642870, 629534392, 4200536, 232848237, 400885003, 473674708, 710992814, 212237033, 11616474, 965651879, 237689513, 548097049, 191323476, 607419564, 122152909, 529124425, 934041905, 572597211, 883636663, 403996829, 44240380, 827797435, 307477985, 620334859, 143860070, 873132852, 273271905, 367619701, 647914176, 548269496, 319034724, 322379788, 811027418, 513543052, 679559321, 758149125, 956498455, 598781964, 482697906, 456154027, 611127292, 202208604, 415139560, 511121361, 334320123, 812425498, 149382533, 260225700, 382987491, 838924411, 438647217, 327864815, 127566875, 270210860, 257499661, 813069364, 700445329, 725059697, 878654180, 291714976, 692217258, 491188085, 197380687, 977880654, 347221759, 309958355, 591935431, 83513344, 723000736, 949528284, 187018629, 627243578, 431955168, 163594466, 645230761, 628188787, 40490177, 753120263, 536718322, 32076008, 393622143, 931388383, 944940430, 574944393, 852408526, 709611020, 90746099, 619854173, 269047770, 430751669, 58304788, 539772654, 377173618, 94563894, 568083531, 370863108, 697906375, 356006016, 314235364, 230960373, 147317475, 295092309, 155298657, 968545681, 880711256, 145203480, 188305914, 749729612, 33364171, 104390930, 946539009, 819001186, 744257317, 47344188, 471220867, 870533006, 804864950, 600114888, 274072290, 123160038, 562975973, 999162265, 130179909, 945827511, 95827808, 201762334, 951531288, 188054709, 875268900, 279498671, 846531858, 160406439, 400627330, 310255406, 23237945, 368403017, 962197538, 639233714, 481471955, 483624539, 784977051, 964914968, 596800633, 971679727, 734974642, 312411247, 547117610, 793287720, 896690800, 927098821, 742083494, 603857528, 72307338, 560698613, 766229561, 916821994, 438158680, 219786526, 131411164, 387693144, 37533639, 870031401, 150315558, 939085496, 46292287, 771887729, 231668021, 958326, 669635525, 523116342, 273915359, 173977735, 228423721, 700140138, 261622382, 631683896, 513413510, 589145945, 232865879, 502587849, 286229385, 190435174, 116517978, 193033174, 337898450, 473593642, 198042822, 232106052, 102856890, 758144864, 628005218, 770519030, 69513060, 177378632, 208351881, 521472080, 703627138, 991463172, 166863862, 300157389, 260109639, 134828126, 543737327, 296214178, 120966161, 961996880, 410797125, 860840254, 885680379, 69995075, 889610931, 312486793, 485279669, 167452680, 720500859, 407996988, 481785907, 608836207, 733071214, 378135920, 715363684, 16159639, 220289654, 705583278, 264674787, 628004245, 349693813, 525760337, 957191088, 278022517, 584913786, 371268475, 294784474, 653332422, 396350640, 214858434, 835248639, 89139065, 400455546, 979173490, 405921974, 384775632, 317074777, 765706135, 955528351, 204033963, 223193994, 684175545, 433695658, 882476908, 403080891, 70993168, 868611368, 301933327, 454112630, 435597038, 827060094, 967611843, 976883024, 392725305, 946365951, 527478191, 616998878, 508745465, 615238079, 443990321, 554172083, 231436859, 855592382, 879983922, 891045039, 394980001, 573089382, 118359095, 424656998, 391630368, 734042930, 533230711, 605334908, 361834190, 14363565, 365008482, 457244253, 334339572, 914883496, 558885660, 561935057, 385367782, 961328348, 78486783, 636514157, 582962961, 311108259, 182444695, 941918154, 349801536, 694617264, 165948739, 52230621, 827538549, 942896427, 184938805, 386038352, 392236795, 831188991, 657831408, 208022308, 660466043, 488248054, 896823160, 801810893, 78870217, 574435846, 330952914, 444144422, 739962903, 747326511, 717596496, 249754731, 836184250, 167557258, 308693656, 815762893, 288827380, 548101257, 933793814, 420497391, 508568584, 364294888, 213526798, 697859175, 182560316, 72035530, 580862572, 484010586, 394605225, 768517142, 177469087, 356318961, 404565036, 939133228, 79308952, 871872963, 349878957, 933318511, 232791364, 474087904, 171607860, 466168835, 192239892, 512221831, 443627616, 592488377, 94689852, 761010058, 322432186, 451054255, 735449158, 186834805, 503448754, 902793503, 568343371, 930337882, 336197738, 498526497, 872607311, 542892765, 733101972, 613634563, 575206972, 829311407, 636852135, 233765990, 827238181, 817925283, 26562445, 396551130, 40762344, 232782553, 357088047, 945459523, 529610756, 181506577, 734993831, 118835425, 952238361, 476989152, 109096639, 530973935, 845708023, 708483050, 626807200, 889752412, 802733102, 10950649, 815236959, 459809721, 616170467, 217924886, 157521509, 273761611, 874151232, 62369997, 737537823, 354641977, 827129698, 146577915, 278565255, 339036763, 781608217, 942310396, 757796644, 799026227, 531220083, 691229131, 690670610, 60664673, 13671599, 656476823, 713588913, 306466933, 730449101, 958193169, 606110804, 373061642, 419487598, 844268770, 212588678, 860733200, 503637558, 650409053, 519006704, 728911927, 849782146, 406993043, 109670293, 580704578, 622804184, 176569984, 682829679, 977637180, 121601062, 53894054, 949260511, 671396744, 197739674, 661673918, 712872895, 615788689, 535855487, 894257916, 130550597, 304124010, 881199109, 66421163, 932041018, 29193010, 720902334, 386175905, 426540038, 305780172, 133884219, 221725158, 463417822, 619221491, 258445569, 240008830, 185142377, 875374544, 211150117, 457186635, 518505468, 714395316, 365656481, 55518952, 970079295, 660106587, 404966891, 961725069, 525134878, 458449257, 281161366, 616143724, 664242014, 480168850, 929128353, 986922001, 108812136, 521208125, 593364814, 29110261, 222628463, 491275843, 44943070, 255822063, 407234362, 855217119, 361725582, 176905171, 853531021, 41649296, 192683760, 892270174, 179944503, 88159099, 960883197, 405453517, 146043906, 35340790, 814020032, 93420799, 428826728, 909496276, 619306044, 282877743, 349164399, 626098922, 355025950, 488757797, 809646610, 272135928, 835748588, 293342061, 807881762, 173257788, 936842157, 598049112, 146056220, 904546650, 972319912, 809785171, 158585428, 529888036, 893541613, 525544476, 951520081, 375274643, 242318163, 21102091, 856583360, 580801583, 460702582, 941734729, 9628653, 258598399, 148079651, 460236534, 403653265, 412615121, 589671649, 676003594, 350339506, 170386684, 963802792, 279231265, 290721325, 204382171, 688516801, 175774923, 642224347, 213687900, 830020958, 245012480, 376709290, 548278569, 514137227, 391725681, 976940368, 933349760, 956543262, 78507137, 269840172, 539294400, 238157984, 748261959, 224325627, 741453312, 659622508, 613683400, 244710960, 862642772, 378913186, 685845647, 377865261, 652314660, 80909761, 339644701, 851667799, 254191351, 395958711, 960869636, 288392763, 664066306, 2898794, 433694921, 928800433, 5533100, 30827249, 761254802, 244296355, 789409779, 527066742, 562809466, 887220676, 799730337, 720308992, 586512992, 745790700, 897475297, 912632138, 883005360, 569426699, 718310717, 931472054, 388102165, 13516337, 152747789, 485302542, 686004581, 497686477, 883075151, 122011379, 508183124, 342763375, 395997127, 337394481, 813877420, 586387264, 182480526, 931188972, 177441824, 279560901, 30134395, 266674697, 808461432, 171626253, 578605673, 444250789, 690149104, 240220710, 23150474, 962793942, 903793973, 15652537, 263773501, 164588042, 863609245, 508953157, 213548320, 810514140, 722398792, 894819211, 30495166, 189716864, 583067617, 672041613, 453677660, 427663192, 285455448, 156061893, 289291455, 591709543, 669490946, 486886482, 135315832, 787884688, 444809149, 767939428, 736987617, 958400820, 151328033, 331056482, 429187314, 868463521, 906159791, 465947834, 227479893, 743883246, 817238339, 289769453, 501302102, 2260817, 861372105, 432266555, 52176552, 630759305, 397757642, 937620831, 386503554, 229591456, 165910803, 136328256, 547799330, 686109467, 310461167, 103514286, 866272075, 642516857, 125119211, 350708246, 629288418, 911343658, 119773348, 624975410, 713949324, 122992573, 5197840, 517481104, 838106933, 312492566, 513293681, 334122734, 118639575, 971121286, 304450085, 588343293, 803394849, 30493340, 603288275, 693166447, 448005163, 478848219, 129523603, 619166741, 858894823, 361031340, 881476404, 36115612, 126081601, 474898610, 282611117, 59822895, 821710746, 866987773, 175993230, 194864538, 990384715, 616135824, 363824767, 306715295, 335129289, 569507969, 713198461, 73064765, 143248416, 260307471, 281415339, 94841836, 970495645, 307026813, 922877163, 92485190, 815313479, 834397275, 314068865, 280256969, 934629275, 944979003, 473218125, 883253774, 257661289, 805780366, 102883491, 636060519, 956093233, 210783709, 633579255, 235328569, 667617672, 461871987, 548552967, 188048062, 471592261, 886090685, 87219345, 367294980, 283094108, 540466893, 118370104, 292922890, 240510040, 282705551, 801407941, 574389780, 12822579, 37788482, 589002254, 728261066, 413688219, 826071415, 548437192, 201040515, 170391405, 244489990, 990644370, 569830215, 560358012, 888535868, 362434321, 741092258, 329370005, 136205057, 391366218, 124643442, 169443729, 587436165, 326811638, 839636065, 396067767, 358139333, 260855901, 445952033, 601846242, 119192684, 507098280, 847918528, 736481548, 258465849, 826240501, 730229739, 62768991, 712614297, 836636767, 284170978, 619492970, 48413282, 397094283, 120621483, 192308676, 547766009, 865944251, 225752508, 622695215, 196958139, 834289011, 805517332, 216100662, 400108334, 566333269, 17814353, 642738760, 747364862, 582089051, 254473148, 949551183, 701197059, 977790990, 684689182, 85021496, 88673627, 211822430, 194124333, 868792796, 378966038, 772025973, 514369517, 941918659, 323507850, 937565683, 219442918, 35795862, 881750529, 109961272, 532116136, 669513061, 443383439, 814213119, 929913432, 402683974, 796381085, 589090322, 279183956, 857387017, 304534548, 327257562, 844346444, 869936859, 671061216, 752868557, 453734960, 785972207, 593318054, 687005302, 782771435, 979742321, 339470294, 640405108, 666232101, 159260311, 225767774, 759025287, 354682878, 437963484, 481711726, 700188294, 30161239, 452404525, 807565556, 822152559, 787105838, 627999297, 817524926, 321210059, 955191161, 779441098, 637935291, 122165825, 435838740, 102081840, 737002786, 370324768, 302057675, 203937650, 743655470, 832540232, 260879052, 490593862, 894656648, 262532565, 732850488, 611978872, 427364218, 268548619, 950795960, 205570376, 205167494, 432589619, 660202631, 556286830, 347171661, 148918341, 52635419, 353064519, 150579321, 279248774, 996540817, 265233568, 617171961, 872019186, 662518598, 778949201, 257834568, 948914534, 691504179, 86094394, 143516841, 234241268, 187216552, 985145868, 370371591, 44991617, 678683126, 172350349, 953432798, 713208148, 245873183, 195960651, 856356583, 808824405, 868798578, 388977347, 621132370, 226907867, 242612009, 65939666, 393253977, 529060295, 215160762, 871150434, 347173614, 971719812, 254586085, 821205895, 41290503, 309740952, 263171803, 273729346, 444792511, 46805938, 13838447, 620126829, 748795807, 616134087, 929945318, 481114238, 822597991, 493107104, 491885382, 289888367, 124605346, 299568255, 999580698, 588778767, 548103481, 701996517, 614383158, 312031859, 318670414, 906221360, 167365081, 128671186, 539663374, 78213808, 918271849, 572130675, 62967452, 874972062, 914402612, 172546931, 93213264, 964823166, 356421358, 789500525, 1528701, 562547666, 279853145, 225627549, 653318277, 77532103, 170830244, 421767643, 977778019, 991369150, 570295507, 50110640, 672828440, 947808746, 586836744, 146991052, 635870551, 824271888, 527839777, 138045899, 620182558, 894478375, 43713760, 643252557, 642550817, 565140343, 852404499, 573629647, 702414157, 597656469, 39884686, 647245058, 446905937, 67690333, 497578074, 790921798, 137123531, 943677154, 806264279, 799313454, 73030282, 404285518, 208569975, 143186288, 415429475, 9092231, 88261845, 310836423, 248184411, 565836844, 406255847, 294513609, 667202038, 878065587, 385600710, 662035052, 823943019, 57915158, 581482735, 773491752, 509416616, 677716212, 406855993, 116703521, 31568441, 540332506, 914721951, 568016013, 913084930, 316019195, 72511077, 723641029, 829147681, 961138856, 628298482, 11311728, 642991948, 890402386, 635304934, 22691796, 183245190, 658855669, 888268024, 193225542, 736347764, 813067249, 718925160, 426087241, 677353657, 7743391, 241391837, 697667258, 431192581, 605662080, 646452229, 475177954, 118656334, 771027644, 826944910, 659620947, 76958764, 355697282, 558861171, 348702125, 926624449, 385777573, 741400707, 269965102, 7927919, 289740636, 409672024, 495568132, 480706932, 620136967, 142040365, 258647224, 212703352, 525936292, 647064814, 758127192, 950563276, 334497148, 56831160, 698809037, 596052232, 654631768, 726890851, 835107246, 196445946, 51332061, 790813441, 294354893, 847844354, 437651840, 947175740, 364549475, 889521783, 614418297, 534590406, 95057907, 834223734, 427558088, 381858517, 978937021, 436435924, 141397928, 478915742, 717997568, 608362210, 564334622, 818204266, 393105153, 711456453, 438334273, 322620803, 67216434, 617610139, 425204, 375084368, 460179249, 430516398, 835910300, 918688862, 418566149, 457472571, 222087028, 94515968, 41456835, 776133561, 847349969, 388302198, 3934367, 229837638, 745547638, 480615636, 857246935, 433556838, 822230705, 878909534, 829012176, 114795040, 606135974, 723463456, 989512534, 475907025, 719576331, 823478156, 22683821, 169360279, 59367231, 580921930, 152719218, 441204618, 546105169, 927960589, 867872311, 209199805, 521110924, 925605896, 879047874, 460533674, 780779134, 723489970, 485153744, 903631511, 647224767, 924311572, 479443182, 573029243, 189364301, 259894256, 918655344, 689898952, 603743686, 442028421, 322421089, 832665068, 460427772, 879715412, 686407867, 739988996, 42594883, 604505737, 165654124, 166051775, 919795466, 792523056, 327048287, 271561648, 963261250, 524412632, 431695106, 810165676, 41927458, 804133610, 542461746, 350563897, 130854747, 677009583, 843067665, 117288002, 277384357, 39104115, 384751350, 163960218, 748774920, 339093680, 941778208, 50276496, 481939652, 891279199, 401861228, 511092573, 224392571, 774858178, 436768927, 86139189, 654542105, 7396952, 474619985, 211281699, 840158453, 123044029, 12953320, 447600664, 759515476, 117668913, 932013413, 847147321, 812366860, 424424453, 302504089, 572312425, 469361879, 41081826, 281674149, 938134319, 270685706, 817355146, 116003572, 818189516, 109801962, 919423245, 416670247, 249764560, 465620550, 884224182, 410523448, 633558962, 936904219, 451161315, 67720129, 672198178, 189388336, 486117898, 680381845, 730583529, 216938140, 591194020, 672786785, 774687511, 479327783, 796608669, 250090830, 274243286, 548247135, 260284502, 385748209, 32612351, 417517789, 955329299, 952288907, 807683900, 567718564, 575148360, 486510072, 728714889, 822298282, 660856040, 156676919, 852609139, 48069725, 917576742, 663720926, 783667597, 343012060, 907737578, 30211233, 4632903, 418289143, 560355504, 839523476, 250113730, 110049818, 825063591, 586166180, 811132510, 168135088, 363459334, 382964979, 563226392, 969427197, 545825776, 468867405, 728682202, 921097555, 9931821, 167679190, 830079209, 976858950, 884775238, 669096095, 427117671, 927373232, 222190472, 605274855, 66895264, 694458818, 658572240, 733627842, 171629011, 570642525, 604585246, 859849753, 577283843, 156270688, 477837255, 430131743, 928356123, 413189001, 274710742, 645144793, 983661054, 49005015, 386823515, 190161338, 990960707, 892185773, 454587219, 886726376, 634733904, 620837235, 964878315, 948332790, 382308522, 22222996, 989071976, 940078288, 582777591, 39333808, 818392538, 212113015, 219824275, 190056036, 413840322, 202093295, 785737619, 421326818, 942778477, 464984944, 425981375, 935576871, 539576701, 883803918, 179706039, 389033815, 305116012, 247336886, 134470787, 775612284, 228988811, 780751079, 607353453, 224523688, 239442241, 723028836, 786922247, 670216016, 245194586, 176759846, 23293547, 164428274, 988828916, 821363829, 660675978, 927513307, 97032982, 442377955, 411697214, 157261655, 587904122, 597388062, 156646720, 367592841, 447131686, 592577367, 936539670, 426862096, 992538472, 172015427, 929113954, 624921666, 244806062, 76783752, 242963579, 82881991, 886581239, 683962521, 153992154, 646101472, 560029900, 705008765, 174138067, 580040449, 979131519, 5139979, 979005933, 155811053, 174560919, 612232787, 47518204, 634590028, 875312678, 170085824, 187042499, 797479395, 14256116, 135271656, 10814347, 101141466, 967834089, 472645574, 524483075, 219164455, 372309512, 282542027, 527592466, 455870252, 260145772, 451619878, 288061214, 181827915, 294902909, 207358855, 537389859, 515943673, 740236344, 252943383, 560887177, 759342904, 637893240, 120345231, 265030452, 294176600, 738645559, 623311102, 566937426, 157142703, 33023966, 525322312, 241443447, 768440616, 854777904, 570157015, 411949314, 123610224, 727395727, 136260251, 457836698, 396279939, 370815188, 356394921, 39394568, 565194976, 864670469, 344808370, 374658589, 832845830, 948623539, 464609082, 17148947, 117376014, 613661347, 172745034, 854566995, 182049396, 168353970, 327073102, 934082257, 645253575, 941555101, 947315817, 104654843, 667215387, 198453096, 264895232, 247780180, 925586411, 468478179, 549900248, 9776199, 941741978, 505497406, 348168205, 824466442, 535497818, 224416542, 118927005, 487388315, 597632272, 124532550, 15551517, 38956918, 712549407, 334135697, 78909920, 662114663, 861248004, 281811807, 797229192, 444305197, 153811705, 814455253, 532157978, 935596923, 883387197, 241300708, 890957589, 300531029, 754426068, 858855540, 478750920, 228521723, 391994712, 534342839, 56708289, 197127216, 700669122, 278201413, 623239725, 399552032, 864021297, 66620412, 23493315, 2373820, 699952136, 754647002, 668622485, 377942252, 187223050, 921875433, 366334966, 774520812, 36478757, 492348744, 882277671, 691887292, 818162256, 598680937, 435100688, 852387800, 435485968, 690723481, 11048466, 400852474, 654246737, 550909418, 961674261, 289527781, 982650555, 199756452, 112045175, 303753723, 449628698, 143377101, 532285066, 199677633, 338187132, 444962049, 280891743, 749901989, 595635678, 861700588, 960244368, 127713728, 55137631, 872517430, 100649318, 493683912, 412697412, 217365775, 464284880, 38140333, 593014171, 592049458, 479179571, 621479064, 774635590, 838735483, 719854370, 268003898, 787742246, 996086767, 560347804, 236784641, 600975309, 950851574, 706228344, 166762877, 176997967, 493131053, 391872185, 552981466, 115309020, 583586861, 896985605, 802056274, 240097944, 660842340, 660062281, 742671269, 508751661, 130464973, 504145271, 573166045, 717490139, 76202415, 942289426, 665566165, 60149166, 269847800, 783010672, 697406915, 872488217, 532550147, 571699970, 857919391, 454618184, 282102835, 859695189, 92802774, 363321249, 734116573, 668193595, 647373216, 686483311, 129554719, 255172362, 10540563, 353605093, 454947297, 203772997, 156546481, 744061941, 659807168, 578415095, 952703903, 558132384, 810955224, 696150268, 879149174, 178540483, 770028201, 380148373, 879795411, 814439799, 974197843, 266154771, 612168489, 260026986, 369822830, 784291452, 732166907, 429412715, 574879101, 220482682, 684326753, 702861342, 733161798, 740050409, 939275175, 142025861, 872702627, 699445213, 496329302, 865172734, 581672945, 568414354, 566876018, 203803461, 339909229, 844576962, 778082291, 322929745, 757245286, 877589405, 350499685, 460595393, 295221034, 961535861, 187404562, 716770456, 195615576, 393836289, 271992008, 229261593, 425935594, 503956832, 289656015, 395210122, 179639615, 823131611, 334728776, 828454752, 695884511, 120454049, 904418182, 344649966, 274034558, 867954073, 693195275, 584586444, 794813703, 552371161, 610926353, 431337466, 223863254, 439845147, 960980093, 56258434, 14892642, 470584683, 371155055, 903479972, 317832965, 953070580, 870015742, 108998420, 990277232, 307936921, 691402524, 497245044, 111809379, 756698979, 530892292, 168371073, 667800759, 342927223, 458183688, 523540742, 59287784, 228132446, 757485661, 712249190, 191440547, 514558236, 346717131, 813138137, 282871346, 807216735, 6082505, 305401036, 816622793, 938171957, 852185668, 84727579, 442802351, 269161536, 926998719, 601231595, 226401821, 766625003, 130254911, 872868870, 840265128, 37791074, 787165779, 187866962, 398025976, 237521522, 90823011, 244536508, 863149771, 338566134, 825347563, 487124957, 420703516, 170093791, 907325692, 945437504, 670504556, 133704989, 439367080, 410430747, 186072313, 218324738, 245650375, 526864322, 635764877, 746262361, 239694097, 241324482, 810714122, 978749081, 981463210, 278969154, 509282853, 669729791, 268713042, 438185752, 910824300, 422041410, 72648210, 240544082, 744499205, 145639103, 410984510, 487488669, 691687676, 734150650, 505411163, 236047821, 68041520, 71165995, 5524466, 398029964, 290894243, 53360799, 261816778, 540270870, 193199989, 790953037, 644491469, 330230496, 936654217, 849940043, 838890821, 175100242, 658306239, 105456797, 531828036, 935500365, 731744708, 541380954, 885477770, 596418036, 754398949, 711635914, 868620848, 87621260, 585103256, 240782050, 396960153, 571970098, 151637509, 693404706, 929569524, 505629323, 224183468, 666206189, 731835824, 158740187, 285823853, 427050695, 5383512, 175662378, 812630871, 932332959, 48269272, 95576393, 344369623, 754309953, 550649400, 109517287, 241240195, 715655684, 961469918, 129941256, 831529443, 4282207, 921271171, 741520240, 923663347, 678190715, 323610883, 696769672, 403015997, 348871113, 629463588, 212313490, 307152763, 354958189, 389661852, 830922111, 631266615, 148034072, 819618427, 573110193, 425986712, 465072482, 783001005, 584042359, 100212392, 247274999, 580587642, 497631908, 357749917, 431645629, 798196959, 192796459, 65230773, 751087409, 311022729, 540635390, 859068493, 70854997, 864831551, 880886847, 172581670, 677576474, 964953789, 411196628, 894550127, 313151810, 338443193, 653687543, 799159454, 219586213, 118158754, 497256285, 110321256, 262342079, 198962403, 457460269, 448915376, 779663886, 98968955, 894870746, 96272533, 294512888, 623843918, 736947344, 29342985, 245757875, 115267057, 665819866, 797822805, 138220466, 535363392, 338910119, 830310976, 791777308, 195300116, 562547962, 860019048, 687600655, 289563207, 179287573, 185447478, 846598609, 821216729, 479170555, 626574052, 146385521, 86258804, 134265248, 228121711, 404624175, 713477981, 888349324, 393189096, 15994262, 82336043, 326836785, 178705371, 853367919, 50460023, 565298, 388116192, 964989985, 833614474, 458781955, 568176826, 851953041, 418698570, 821186061, 136179736, 65855056, 892662001, 709228261, 192096614, 347132551, 967609529, 702929036, 203282135, 88103767, 279787852, 88801913, 272421328, 597683359, 909725188, 728954736, 411345716, 587388435, 784959931, 261815612, 471939703, 576113012, 754456741, 122384052, 713608538, 863207934, 676116094, 510941057, 399439030, 38510639, 256959133, 228808321, 846120804, 383184606, 811760723, 257999147, 824449678, 426529467, 711725428, 351554399, 222840205, 146634599, 841324209, 336903251, 387153748, 16883230, 925562294, 101334281, 764801959, 761120495, 336576391, 809673259, 26595009, 215965780, 256702831, 794649397, 434460381, 584850356, 783127152, 497499315, 949329706, 830305942, 785000328, 788617304, 947663248, 455444152, 955078256, 337338639, 232154052, 393587257, 970477362, 444554050, 432739012, 359763402, 373733965, 696547210, 28870375, 26477076, 760575995, 837591706, 46303218, 643272104, 210446887, 773019963, 7506384, 258987160, 332691042, 754017741, 37628850, 585927224, 776117969, 524338220, 298542640, 167533508, 521756811, 653889548, 764943476, 187995252, 448119753, 770931277, 772479866, 868934883, 194978787, 936721703, 672220489, 952815112, 641242315, 676322172, 922940438, 707911316, 494041030, 643265018, 697874467, 170533181, 118848741, 522501194, 740976439, 660112879, 767423941, 794115635, 855324864, 180128934, 926211905, 832051408, 244617317, 976870275, 966058022, 969865477, 349109381, 145068279, 383865023, 497466000, 64658057, 916990469, 684758870, 264847057, 388978794, 798164364, 875703834, 8407558, 977049033, 699700702, 875171164, 310243638, 818664654, 376621856, 472606438, 431383426, 168027283, 413979566, 872929395, 523678531, 1302727, 939902668, 934193018, 764794072, 331957398, 545701726, 232732661, 520337045, 677666971, 58775894, 273847675, 458912846, 213014131, 783342071, 163653705, 448792445, 499008954, 881983420, 70229320, 851273099, 790351572, 671075479, 302678399, 977301454, 1879281, 738844431, 457171413, 893227114, 23193, 944553954, 263517177, 651310674, 307454246, 111517366, 336837468, 211296288, 279504331, 337918564, 343589022, 123374171, 991095542, 760161428, 138552186, 183580606, 185661428, 340019690, 632285878, 511207623, 547780604, 626473607, 311707592, 636454817, 706854729, 842947213, 496657508, 895222054, 68285852, 998154681, 521993783, 137781650, 852339145, 583909701, 350529564, 306978793, 744484252, 54848283, 210632567, 868918722, 687798064, 86791525, 538488513, 308111495, 493802435, 830232304, 864921517, 344865914, 867063080, 755994758, 511276410, 774058560, 409899833, 646101659, 705493991, 769681837, 216409414, 384845127, 31552895, 703089215, 256708847, 310668230, 517557679, 576802810, 494237423, 93615800, 1746612, 114092400, 497407515, 480675645, 931032422, 11733763, 857147031, 536477294, 182504344, 736667424, 768118097, 652922072, 22215552, 413496159, 92423772, 831712243, 798334619, 935321096, 848279203, 990359969, 329123274, 988954764, 977605589, 603794624, 385049459, 340941904, 268200916, 780478248, 185834792, 458626737, 697885115, 702734388, 247026776, 645128755, 393649661, 580040678, 607461041, 235163029, 946017274, 816502588, 90224609, 629595368, 865044633, 652891413, 558615110, 177015927, 287757341, 850579324, 580317750, 798425866, 29461034, 1438802, 753893782, 899772498, 491100820, 897236605, 654842545, 269531859, 91618273, 599991873, 838803447, 709238848, 176248746, 544526129, 475395259, 285452388, 166284229, 837254824, 660658035, 299816467, 130699671, 790560681, 624460094, 268657282, 965872215, 904895970, 759103123, 555714937, 648890048, 397666568, 199462215, 953229164, 541360273, 486714300, 766311690, 769402025, 73446915, 458847052, 990187779, 603071426, 627687530, 859932850, 478280577, 314918354, 994540851, 944392780, 347749498, 580222378, 528438476, 271413948, 481000353, 471069412, 146168432, 77682561, 325657345, 329566549, 218233981, 571307441, 54714641, 830005589, 968457369, 132575127, 779484979, 774004950, 598281451, 696060621, 596786510, 507208362, 506458769, 907518218, 382250859, 618362637, 311752420, 322862643, 987962081, 440629580, 614116095, 511469653, 893389365, 277858322, 2880268, 379361910, 654772779, 301434741, 168143740, 618929855, 697713555, 748800739, 624833681, 442724271, 182190141, 483162033, 799538085, 118202660, 173001472, 712728959, 844076761, 69110074, 160970839, 758558322, 240730235, 973987940, 517101861, 714427707, 325261206, 834873583, 211333455, 136475340, 81148535, 721303602, 192308654, 136668420, 689640940, 191081279, 599016597, 843259187, 972045188, 712515738, 31813758, 165745112, 633411046, 436334852, 89760348, 806099612, 213437730, 748126787, 199361812, 900993305, 379310116, 530993077, 444534922, 858437189, 890282626, 361927101, 153544422, 131576779, 570629177, 88790538, 763514685, 40312476, 859009917, 821452257, 170487818, 375246640, 731144754, 961646131, 395019632, 235460538, 420300479, 634198424, 822432197, 999146195, 105320123, 852527653, 400973156, 452354557, 342799909, 299901414, 249755854, 524912365, 852973737, 441068663, 171206754, 110461532, 544952201, 898896241, 207896430, 359327995, 419398997, 120776050, 958910731, 410776566, 801860753, 233944961, 871669790, 416230257, 761934058, 346271284, 311793025, 683055891, 648090231, 134748868, 169406476, 169043562, 6283939, 65081871, 924904118, 127124666, 179704668, 963180494, 97390591, 911687580, 229631350, 173041952, 901745461, 436330490, 637311076, 465150664, 904106333, 530422922, 674003994, 496163165, 306436475, 917646686, 261640072, 806869069, 907393447, 964943192, 204716516, 438049109, 659352289, 284257964, 857403054, 761717189, 657313768, 66735458, 61164437, 879414632, 161710773, 177544536, 153438410, 466441433, 823626326, 437463661, 861355425, 951104672, 34104158, 693091752, 243245749, 309933475, 674223400, 237340393, 637277247, 881219302, 481118509, 186710334, 400131195, 741124614, 645832678, 982465905, 770495542, 510065156, 789109003, 296014384, 217569406, 515438679, 627371332, 623142016, 230617860, 567527174, 563352512, 587921292, 112018193, 168043405, 95565013, 80866778, 921454879, 362865257, 407681981, 332306839, 538257679, 119203048, 248209589, 97350544, 453668692, 605781864, 241561682, 912427561, 491816771, 576596221, 208135502, 974947259, 791743625, 620307819, 479394090, 538864503, 549411093, 960887984, 10535408, 527390716, 882793781, 780543816, 955563006, 450906397, 544255091, 698367597, 66809509, 219384358, 98241493, 158734142, 904805314, 935363605, 912575039, 112958850, 540850624, 632157721, 937694278, 776210771, 747111581, 882358275, 46905853, 261874974, 953065003, 689256986, 359824322, 375985439, 645179056, 844166038, 993705642, 834343847, 127370002, 681423301, 222249432, 881170859, 758310296, 631257289, 515848753, 244460826, 811492150, 523085846, 822247734, 601869707, 649906073, 235135386, 336884306, 81315991, 246068746, 257223582, 345095227, 192929393, 402650854, 849280798, 77711816, 232146633, 54200746, 857148175, 757861007, 380027308, 113817735, 413129157, 100400063, 491920484, 631080617, 560583807, 129726757, 484661029, 441657945, 458352719, 101457648, 139408574, 389914761, 608365826, 225325952, 463365434, 232150783, 294749216, 687523201, 534453309, 433570969, 827725764, 646727480, 454313821, 147549313, 403705434, 355521854, 790333152, 700393005, 306974861, 401970994, 284244446, 879886783, 310923074, 253221743, 49110114, 450965118, 801239007, 910694863, 167882868, 686877313, 542309179, 909914870, 998817757, 172739491, 934197212, 51916192, 405659064, 226897571, 139972488, 280644215, 905865184, 877593773, 450863275, 253846032, 159408474, 255259474, 323853919, 793363965, 6544860, 935146255, 371381276, 508962120, 653862298, 11978819, 367985956, 5880775, 454902311, 489677320, 153349492, 198584986, 878227602, 5263893, 826106186, 696817819, 184051874, 80481946, 299358131, 746501917, 424416757, 685850515, 372459208, 506038715, 52041921, 545935476, 546945713, 731595134, 82046909, 513420125, 788745899, 743654860, 616115366, 948410123, 885537111, 854219367, 209584111, 538912097, 672726608, 339559988, 497183018, 50341680, 960292420, 607593782, 701916588, 752780576, 908821459, 60161140, 235086238, 239644538, 530429012, 7249599, 536998974, 131815518, 308980932, 569515278, 414633641, 733636750, 454970812, 107291430, 29208398, 196646289, 110789167, 629098676, 677512122, 958725656, 256072460, 269038590, 872505614, 409447497, 684342596, 974226110, 784869734, 492540202, 476989355, 947198993, 654692594, 59318480, 476963498, 526257262, 324282163, 825087976, 482449029, 503199560, 18564678, 383796259, 157139412, 508227326, 791030388, 11828958, 715349016, 367903878, 337648498, 170453637, 855572347, 881349050, 992339471, 285307033, 946067708, 119697732, 585461748, 18074668, 949751115, 860947290, 688713147, 838799972, 655306552, 804432437, 359858422, 28001385, 76276130, 458425137, 762671349, 883298956, 888718652, 473318665, 202836922, 521657566, 916478873, 241394726, 220369575, 20008578, 22662259, 987515439, 354982253, 48697177, 159175141, 472575738, 255315407, 287707027, 404572736, 688840923, 308517976, 278084973, 742353694, 895765580, 435117204, 368073614, 382779527, 206820738, 387230169, 589192413, 341563691, 436474420, 80143531, 971853661, 177535684, 395768546, 112393070, 511553055, 891234084, 556766157, 359632134, 367994247, 867158639, 348539708, 516549791, 247539452, 438183718, 711737639, 589532875, 789507715, 307475348, 472541708, 530871449, 273349687, 596169564, 121776461, 336400483, 865624329, 577343449, 830096196, 496812181, 779642657, 82660092, 670235785, 665313906, 807840441, 22203324, 900996762, 785152572, 29582729, 323192638, 955705565, 528438280, 551111075, 362228829, 51319437, 314591767, 346814220, 326052349, 713216092, 172735782, 672971049, 520290731, 591753449, 595441028, 519317977, 550970984, 5723357, 269070139, 851904337, 456743586, 445538138, 982148981, 484542352, 588795549, 929138890, 337638394, 970925713, 892009297, 235294756, 782312289, 785976991, 365133039, 507306693, 832828110, 808297898, 334360396, 216050791, 173009835, 435979932, 293666713, 473062195, 385679816, 322617140, 359375499, 419028672, 205207977, 705833525, 907732913, 266042971, 397658116, 686646023, 14991156, 95859484, 897071220, 99200581, 381779151, 731473160, 991841006, 90200154, 248265036, 547582926, 570205519, 254971165, 923397788, 942685145, 586450030, 446178471, 254609219, 722092564, 31554288, 564877549, 848597238, 140894701, 624543827, 772450811, 642481898, 934682131, 766604082, 275765001, 279598965, 453033639, 607046833, 827800330, 201220787, 869863040, 820679099, 341665299, 754826114, 952007855, 80423839, 503665715, 374696003, 858967338, 605017370, 404712393, 769351356, 95356475, 702187426, 109116101, 871546142, 415371779, 777257486, 575211910, 648920827, 795643303, 615478596, 19789480, 830837107, 626490392, 581667877, 52424559, 560179339, 259832310, 180123320, 909838678, 954206463, 621967650, 252440774, 190429394, 110159616, 835646733, 485777721, 990486006, 129126688, 273359765, 772019067, 529444244, 957697270, 503617679, 51388337, 837706836, 458843403, 6504053, 429766244, 51542209, 968023275, 607846351, 3436315, 830106208, 985171844, 331208313, 475847768, 395945199, 533234467, 571631202, 886149961, 134242957, 520900744, 583741890, 309678533, 462435149, 17760876, 84007578, 431985145, 888017432, 854192208, 574021080, 651758734, 352240347, 342782375, 599240632, 180578768, 124601778, 744932152, 766090199, 37975808, 539533051, 958709549, 680044303, 591584115, 842485489, 350346757, 504586345, 5094160, 655362185, 187141833, 633949781, 884021879, 746543660, 635445684, 509480188, 352844761, 17892203, 859198676, 387783440, 69435631, 780192926, 667927453, 563317178, 494313569, 84719651, 966000168, 517308129, 571191996, 712107716, 401437341, 451711962, 252642170, 627089536, 929248320, 550144794, 969486053, 704531289, 567073311, 140798201, 365486613, 531634221, 747189479, 75274323, 840331770, 494562564, 603326906, 943982046, 565416493, 944454861, 117501161, 938364142, 735963035, 963913725, 495496892, 878253067, 509969471, 413120215, 893463490, 101007004, 624367520, 186337196, 443865583, 332108319, 884621417, 560416554, 887525856, 153761119, 340377371, 939958428, 518442212, 110561344, 615596892, 43989525, 288338468, 483041017, 596856601, 880627959, 206908546, 970391867, 961468387, 748289067, 130631741, 681889914, 986923002, 753091988, 594732678, 761561690, 699119949, 811378520, 727587706, 793661500, 484941571, 891763736, 160196128, 729722417, 120211242, 636032022, 237649915, 13964299, 919902232, 141973490, 94859259, 323723141, 867719919, 270056045, 852845487, 643057482, 127149839, 49385112, 438453389, 228922372, 200319022, 273145224, 156059351, 27582328, 226176610, 910378905, 674782740, 28481096, 143293514, 75663150, 693211042, 531536307, 281910515, 39685185, 707514924, 861329141, 73759813, 626862334, 500854855, 686142410, 590577679, 747157591, 429237509, 70918669, 362872067, 920229988, 865832931, 459197099, 985068604, 240741831, 146668343, 693908549, 307735588, 733196828, 893612140, 326430678, 946325345, 283017623, 858042156, 331914813, 459264123, 849720476, 513380722, 406522713, 808573146, 63943093, 846804005, 454376597, 975748402, 433968949, 350272599, 348122305, 667976320, 139205776, 188872580, 6963379, 87487626, 953701950, 25028426, 586487275, 200306294, 880641492, 723891544, 391858952, 818795085, 340539246, 153287477, 469867941, 195857775, 619766075, 856954505, 689432611, 223247877, 163430972, 51128033, 779790654, 457134465, 322229339, 317699525, 946536730, 856249424, 576950247, 887436825, 673660377, 28288870, 427839157, 831052622, 895434106, 528959147, 96830227, 984494919, 761999797, 321489615, 500747096, 421835795, 806112174, 223668545, 151925627, 241597474, 195049974, 183725970, 65065091, 585882438, 782204897, 734746330, 669239157, 330080426, 446536653, 418826703, 413358284, 609982718, 958484943, 559037343, 409692273, 239329798, 506180958, 675200066, 187327152, 210123713, 761154341, 27622081, 311177964, 973670755, 751547474, 227781595, 599275423, 706230699, 66631085, 351992627, 682409532, 238954125, 279953150, 129314414, 60098552, 389091498, 49259092, 225936758, 679662671, 310713783, 882624795, 819192581, 486602053, 757228202, 890788287, 31770605, 717970383, 802623202, 813352779, 771029995, 433679896, 830335086, 532823380, 329950246, 842514647, 480064256, 638168775, 787196226, 41790942, 95101142, 398786135, 28435643, 549124525, 826417478, 834156086, 163136802, 456732910, 809337934, 314970846, 605382297, 219004271, 292419084, 596359369, 393262345, 273066196, 275716586, 135613344, 797448648, 623479461, 754063886, 442534025, 693755032, 820414004, 746035194, 946371544, 566219946, 930538732, 782353944, 785625271, 616672009, 36282205, 513963191, 135537363, 797723749, 184222672, 659493442, 779304535, 902921443, 5933822, 247378822, 190618710, 832703994, 174747764, 620407829, 832130999, 544736749, 184139558, 849689164, 527393589, 302415192, 628691337, 295454388, 926839852, 947559783, 604268578, 22376802, 374286620, 397652428, 953909287, 646179565, 538342798, 878987993, 900155781, 111229766, 30660264, 773487392, 755852835, 973659288, 931902692, 184449056, 789093505, 554823372, 896750419, 991953772, 356291054, 937072661, 368033812, 696991726, 93619602, 100938482, 227734631, 103604103, 818715290, 151248466, 140597748, 172921614, 832734328, 994611557, 443899226, 815247988, 36671405, 954984959, 807872864, 56305154, 581958288, 358124049, 639408411, 548236229, 185337215, 485011236, 876861056, 601744861, 966929409, 717912596, 63443753, 862644421, 855004367, 378217721, 990446151, 815771102, 500747822, 426778952, 488881298, 590073970, 767899452, 673285149, 21475971, 696721615, 156963253, 754375305, 142105770, 459263026, 465700447, 464219920, 124609559, 219956052, 52594040, 659978553, 289405232, 882776748, 188092483, 661645056, 881373988, 305594143, 74273105, 861065223, 401068566, 194536271, 535516797, 225278165, 608686813, 806475326, 894050977, 660861369, 344073983, 149350823, 628287825, 549592208, 403709988, 681120159, 857718883, 360386551, 789462991, 312421685, 667466764, 5334816, 198365042, 975127734, 520943646, 744672228, 356565655, 212494117, 267800256, 966058035, 665707329, 135444263, 738396422, 431565545, 498449894, 245830679, 800189308, 981044365, 719793234, 289794344, 948798721, 538991363, 366397995, 590346279, 146994173, 780452536, 630793461, 924542186, 618162983, 482752944, 790293100, 540051776, 781960509, 968489336, 674125787, 51060670, 562069557, 564783333, 813431464, 527028935, 733388584, 113423904, 819374333, 769521749, 384468022, 737238252, 719070678, 984284557, 170437997, 302846863, 226706732, 481539575, 901491292, 899262911, 13592404, 334288425, 704064071, 813270243, 334440930, 333459080, 71830107, 433666249, 699876006, 726471526, 104506784, 189656172, 424330734, 437297322, 816026767, 343789637, 404706987, 274074202, 110232275, 810691959, 745413114, 216852458, 307670556, 473250156, 700445650, 361742112, 190053353, 426796508, 116729547, 931407218, 198998251, 281646414, 441788290, 157017450, 599536367, 881211190, 930376207, 543583574, 945429557, 974882364, 118483521, 225419039, 77229344, 79730284, 437537591, 483673369, 188739477, 559239839, 296409823, 274955536, 978135667, 826383795, 342975035, 787017930, 383832804, 620091716, 841615424, 503111751, 909008801, 844721549, 459891490, 254762823, 118396743, 102795888, 75660320, 911845071, 111744909, 942652146, 230810739, 892502476, 386033604, 878458600, 451007582, 842902789, 782193653, 938882988, 844866486, 558792059, 335372542, 298913872, 526022132, 779811774, 420114593, 660192227, 11244331, 54776702, 80093256, 190873177, 198230110, 71707585, 671386752, 573252302, 149067566, 41328216, 271155197, 593892314, 349636794, 728678449, 234798568, 980245470, 665234644, 315202187, 615148724, 626379605, 677707970, 465000207, 483237308, 431326287, 179481292, 957840847, 868614188, 455103215, 449326713, 962900576, 591661628, 604362547, 364177671, 793309937, 98602503, 749305006, 171761817, 699111707, 511534256, 110852790, 876683430, 851985050, 615564150, 491535416, 799255352, 756581242, 390755140, 975837860, 522460648, 914037681, 651951895, 612295069, 176760272, 242195170, 933333702, 391515831, 647273414, 110756113, 693210558, 659850112, 432372999, 661905012, 172045868, 639496346, 903137055, 42583524, 847080224, 847172818, 553251928, 312930905, 994954245, 250513110, 677551006, 37474838, 795510933, 134999783, 478577509, 130487803, 965514919, 834617973, 298862326, 50366053, 358390421, 213461016, 108494587, 343390879, 199747643, 371807465, 914167178, 372950395, 463989910, 864687180, 753633856, 382099167, 213048954, 951686376, 230622566, 883623722, 511379739, 617978000, 703581817, 840430784, 570830368, 949127700, 631354798, 304815677, 730889984, 412871634, 723629424, 493458927, 310921850, 574224527, 308960908, 797958238, 286257422, 848719470, 99163902, 869020884, 651622188, 394843088, 170953269, 738591943, 616296481, 845847394, 36612118, 900954834, 142073981, 212012830, 432233847, 414962492, 562504238, 646440726, 893834606, 225918963, 131159010, 670897695, 311370878, 574315016, 254737091, 309904659, 365321016, 171720089, 281380001, 150512242, 935903942, 482370883, 522413565, 981971044, 62474589, 572176005, 279862779, 530955454, 966491379, 449830589, 618114569, 35595793, 286375254, 625729577, 796389499, 648767517, 577383354, 23674707, 276947039, 476262230, 341228337, 22465325, 49482011, 596240111, 765238757, 634640258, 495033004, 514884559, 899834961, 959679663, 169885526, 857156842, 50908880, 663200996, 770640101, 569714228, 787454520, 36595490, 978545712, 476270969, 414475922, 650763208, 155569539, 821540545, 985451667, 907214903, 777259964, 39473937, 901634564, 475083527, 115677439, 349006940, 973885210, 104195474, 130657519, 166422928, 188731573, 723136423, 355197275, 782337225, 975441996, 415538954, 174076049, 148365618, 336818339, 40981350, 612971770, 516479812, 747780016, 193494796, 105782964, 785042921, 98264619, 555160543, 828975860, 756396598, 771394758, 432590145, 789849118, 655556446, 795636289, 522152526, 962059375, 456067879, 775674015, 495632758, 61109045, 660548756, 37245402, 381804854, 764035773, 342249006, 30368480, 497261191, 957309144, 789489312, 906972415, 741803171, 452890151, 453003847, 435603884, 14039024, 384661373, 117547948, 148637185, 41193060, 992120870, 542547719, 156958055, 173946277, 932421963, 524010420, 296505127, 57007376, 471162186, 366455640, 458423278, 175344660, 445884274, 298455833, 891528673, 35056237, 433748939, 458350550, 871603218, 536263438, 449400177, 552678324, 522451556, 688814146, 621275720, 256149864, 806144793, 623597002, 425371881, 821656267, 299940574, 803584180, 961148268, 820971158, 424046416, 240780317, 552039731, 229922805, 411174554, 575515497, 791568722, 277641676, 881104944, 220145688, 39634166, 667944547, 586029457, 463939432, 790899309, 562476661, 513926704, 982480106, 178821072, 114514775, 950751390, 558511654, 490799137, 655043380, 4701465, 432777696, 283208984, 357121558, 995337148, 465159109, 754808663, 140755704, 426078629, 238232123, 567784284, 519618650, 897961201, 111536807, 23195437, 672094945, 295272838, 833550820, 167027231, 717927112, 989100965, 709413326, 363543700, 667323097, 519791721, 19341301, 123076327, 615462128, 519748121, 549224867, 548796455, 215923745, 77289035, 488863157, 311490211, 729133309, 771225476, 716878234, 778892538, 366408729, 135418553, 775380149, 633553065, 222544523, 970082584, 729554312, 868710555, 871719819, 389062715, 855982003, 656880141, 862426016, 763252503, 92702196, 712323474, 828517090, 422446570, 429890661, 912884672, 424702851, 82836687, 962511857, 315249452, 209060176, 847709424, 767343952, 964988189, 804220047, 932022967, 422967345, 23350896, 757770705, 395768848, 947176972, 511626467, 713499950, 36425901, 676068620, 742000872, 181808519, 319794657, 169818213, 832945073, 155958589, 860266189, 782036573, 328651999, 203035355, 604723301, 695271520, 599020246, 485800088, 816459867, 897271842, 343590482, 744239557, 167412758, 681911228, 592145296, 28993647, 256630211, 877087155, 69450532, 18565594, 639154860, 79545406, 484333109, 596942694, 826929943, 913065212, 976820255, 976176769, 797163262, 987109444, 964840570, 641000213, 291004350, 801884848, 463597232, 445704124, 139915205, 25160827, 276477204, 145073705, 257366349, 269684227, 450089346, 552623220, 402867939, 53477792, 224054958, 645343281, 630443154, 623682075, 878424310, 498352342, 990830825, 519943652, 175747170, 58765314, 31820364, 16975999, 323043341, 331314905, 380015991, 905184659, 959828858, 263591095, 588092328, 564339857, 449859601, 887411630, 454743293, 236718242, 248502028, 767273490, 359665852, 722246329, 985924250, 45627433, 769759211, 579002773, 60514021, 904834842, 257506050, 893180977, 733903787, 601480207, 268373790, 514733710, 945173808, 750054771, 102864464, 829423574, 154578946, 599257007, 729299092, 402693633, 658772335, 566086666, 740472244, 484036543, 390141372, 752612573, 443371133, 696869252, 858739476, 471911374, 278753551, 435870174, 123970126, 997506544, 937443236, 419096370, 715936094, 535367684, 667966442, 781100007, 991375673, 783757703, 453686425, 415568256, 720621777, 588014113, 654712554, 429841191, 898130807, 15223587, 520834873, 700959184, 583858840, 987489175, 705472976, 718617697, 288016256, 136917372, 274105196, 413768758, 901667660, 190529408, 393392497, 241328020, 534390101, 118866205, 347825989, 412406284, 273100116, 429508720, 194857584, 481011318, 684963572, 730078262, 747568911, 832900305, 796154932, 264454418, 695576772, 978158695, 60522644, 418102056, 215240939, 294057728, 816056297, 999624635, 849813210, 91546277, 701620951, 108085573, 961665920, 409785169, 793228229, 31979989, 425923348, 717705174, 368644505, 904747741, 933837451, 380545792, 796862562, 619217044, 412333348, 439171060, 934054864, 620570894, 965297179, 598377823, 119721037, 58233675, 423743653, 641671047, 332388694, 782566989, 712576503, 984265656, 878588933, 851558304, 596126337, 708708555, 788309744, 755705806, 430042758, 957300911, 665562033, 648243766, 69732417, 158879461, 648717197, 857132295, 993426381, 672847612, 284574550, 412566467, 887862070, 476616789, 217735171, 849726688, 669667054, 521050897, 193990562, 728145554, 280673249, 447241612, 45049690, 320854189, 807700354, 158954358, 933285387, 259561932, 945967169, 78023190, 101198162, 449079053, 570949024, 451217342, 263212831, 900459984, 332633191, 5081452, 972099318, 635290893, 157070811, 907490046, 567244763, 812137823, 640806992, 870162688, 800295433, 271662137, 643381695, 770618508, 624844405, 17897094, 475190064, 494831373, 460228825, 745480271, 975366515, 735234783, 418735876, 953211770, 653845351, 362777028, 554479521, 935038956, 611482532, 652085213, 947036322, 433881511, 508358467, 409903244, 515714449, 357143975, 683259841, 384611830, 473671236, 3512143, 578550213, 365664973, 846669466, 620571324, 356637952, 16136386, 126236448, 823480670, 858400340, 484316339, 829401024, 252816814, 780255516, 847583117, 34824192, 164187865, 819230450, 206398662, 871515237, 558710027, 647184365, 328807960, 90540709, 308121063, 591244903, 921984276, 877412243, 652480409, 126826116, 227329656, 929622688, 752508890, 230967934, 777279105, 211032595, 714958403, 202107441, 676699857, 704750092, 948925801, 59665373, 341869414, 520921627, 954416750, 390783679, 641104267, 382599622, 59010358, 113981612, 523604301, 986908542, 471706521, 786434848, 666704487, 253042587, 703889574, 352241203, 409891130, 161368514, 340622495, 572281467, 435696736, 545140410, 639468171, 5964300, 474637927, 784164190, 492618156, 350018100, 421491467, 630529512, 174848490, 894380788, 249584631, 357191455, 949261484, 451888482, 658882606, 735256715, 691302883, 349270568, 992649463, 14012227, 3476653, 716183853, 820569867, 211873674, 861952525, 511982578, 937080013, 776377225, 621101611, 812551574, 843701471, 322536427, 471721388, 385162826, 770157034, 565848913, 528291626, 422935045, 96698915, 371236144, 171537349, 308072170, 574778164, 300760824, 187687771, 650147820, 248364031, 868442649, 193851093, 153184471, 130164223, 65600973, 682128510, 501017456, 145285426, 971864715, 615871640, 147373905, 699013112, 229574284, 523926713, 550947529, 568295342, 133125532, 830147851, 158195792, 618336295, 757841622, 739022231, 181764216, 372442636, 549952204, 364746481, 377115346, 882557656, 489491661, 213371324, 120300995, 971566730, 483198903, 943982761, 393848084, 676325111, 114412230, 13482916, 522249008, 117825085, 851843307, 965092798, 211449131, 516337423, 82266469, 765129286, 413174956, 439936968, 958772330, 53681833, 429166318, 462280188, 342252392, 437044034, 414122761, 841429156, 618035206, 293715957, 881319488, 515689403, 184904267, 334486787, 470338223, 840315221, 927596904, 733302988, 811327994, 897480261, 810583774, 816778160, 897775009, 258996942, 973447353, 240969413, 952540084, 389337548, 343591748, 882859927, 72706569, 577927390, 175455265, 770756470, 196247535, 541572392, 10551262, 677646402, 642596700, 452596390, 522135045, 156674722, 627233610, 888349494, 978195006, 672348436, 249439576, 802627801, 413303381, 828630624, 694242248, 818555735, 983004484, 963195621, 703216758, 583003342, 463672510, 697248222, 768660505, 410001384, 705667754, 129386802, 639486728, 24440595, 136329006, 553043084, 407270673, 870283929, 309044764, 883637794, 317435099, 688716123, 7371903, 527280185, 925357306, 189763246, 734280479, 17874129, 498787986, 670215720, 606575438, 832674144, 626530186, 942627977, 46618258, 761265530, 743946639, 871652438, 990079212, 652574364, 984345983, 431470819, 880139002, 901143093, 954899171, 153476466, 458934531, 343252288, 339317068, 870036815, 861610502, 65737503, 311671961, 724000243, 670350964, 64877180, 341672020, 652975873, 49614244, 490164466, 726846406, 396166331, 747449221, 279499975, 800685507, 157787655, 798775869, 944109400, 463662460, 843353004, 177923856, 878838519, 709594530, 206624464, 787088750, 328861841, 515387367, 309611160, 666723874, 435141079, 611284132, 883823030, 93685285, 456237310, 887822662, 324075449, 50851809, 282508828, 356740534, 16105050, 412703380, 352891556, 671448208, 295801158, 414022309, 996627513, 335483162, 374858687, 634053736, 809179996, 858426714, 870194454, 542775513, 515923558, 601545133, 464742630, 37608837, 910853551, 405101314, 291960372, 426580178, 732142687, 743330682, 201361798, 44999672, 964948206, 857143505, 908229816, 584778444, 665160319, 839106283, 164193438, 109564877, 488929333, 366874588, 247577455, 322142588, 930224348, 488911492, 282640067, 751928303, 433497719, 784507561, 999494648, 157181025, 168038402, 636339899, 419256674, 808803113, 971029300, 821893513, 242369974, 690128767, 931528564, 781490590, 487202336, 35279642, 690354562, 279055026, 48753006, 760571040, 362969944, 838088421, 510453563, 260552722, 559401329, 244959761, 598308741, 562691587, 653331298, 893868597, 965272879, 245567118, 184470051, 258332899, 99077133, 280863544, 511433012, 922353528, 327060757, 296490817, 848671877, 782659847, 274915546, 500783092, 92380568, 790383696, 319475918, 613044765, 822630907, 97929665, 45376248, 47905350, 447859552, 433115270, 54547643, 492620470, 806700456, 727125423, 418964265, 671934754, 778506023, 246299098, 109278402, 939555767, 980423962, 424371503, 655485304, 13890072, 392170418, 918323322, 998642807, 809430881, 491339234, 226758583, 768203261, 64000493, 34275465, 618478921, 411905385, 358853659, 957112850, 762440322, 751242250, 827520513, 171492006, 983049123, 458464139, 724949656, 341276325, 468082218, 495709809, 453580614, 441783040, 582457836, 406539854, 195695195, 364288287, 254460694, 190702407, 567240914, 117498855, 229696579, 82598146, 685082403, 552895353, 566073922, 600567826, 186807598, 731676898, 822278836, 70309537, 359211138, 704277386, 252848488, 719120017, 109791539, 951338165, 687226256, 961452134, 387792501, 610214499, 540564300, 449473413, 350334859, 919063769, 509091548, 821892413, 707019876, 115226973, 117118458, 292171864, 381951759, 412504252, 969069719, 69094792, 349368941, 79477936, 945192803, 29867006, 173844828, 89029736, 933489068, 26444677, 484215571, 224314492, 49034845, 632884738, 206617826, 766463023, 65084671, 661533177, 220347425, 843007796, 942044467, 91482559, 761988198, 682745328, 328856473, 414220500, 62169633, 10079662, 108002342, 872044622, 538081349, 699437180, 487180949, 836405376, 219124884, 806333833, 369691595, 410801514, 135722933, 765878533, 201022056, 646187359, 11142719, 786471012, 370953961, 903476590, 611864613, 770437253, 457157282, 181749229, 966020750, 674250777, 299976502, 671864467, 63333986, 37916515, 213972739, 910564724, 943591586, 445618816, 616771019, 262340349, 432466534, 427541481, 478192834, 121581068, 456946150, 549246900, 395821330, 856798386, 763084313, 28583423, 780747266, 929102478, 37290886, 554226564, 534051226, 921768404, 840083558, 68706624, 716934804, 611931043, 953182980, 526975388, 922976390, 90963315, 382725334, 730705404, 435935489, 209204822, 284889575, 758878164, 390106252, 83888072, 651822629, 187199230, 979255246, 887168495, 880766682, 727203401, 319730770, 874437686, 28174265, 629353495, 412022485, 44518011, 644340687, 102589719, 185971803, 123923014, 219396514, 799453793, 30346542, 415396393, 573857933, 707454503, 250539329, 309691675, 599152596, 768081634, 566763918, 110507003, 252014683, 603663223, 868566099, 521241849, 256582979, 333670701, 501358492, 509564334, 409199563, 367700532, 491192466, 326561547, 455284015, 135264385, 979201264, 127520693, 82980629, 428649451, 745366105, 564547076, 355851031, 640068964, 620772859, 906729223, 685236538, 336786795, 816413373, 225274864, 842201115, 845356337, 255335894, 25738307, 510128225, 887428123, 244031584, 914262957, 180363601, 49737231, 380708328, 435129552, 867170727, 121756627, 793163686, 31308559, 766199801, 194047731, 580056813, 81608336, 387081776, 43243479, 959337568, 567941995, 330419244, 468287700, 379228711, 287635239, 70240596, 345589599, 560473024, 171029392, 843449251, 622561331, 452697004, 265697345, 351058836, 164738615, 819929136, 302370664, 219237213, 451183156, 864748925, 673759028, 321389678, 239775213, 309796173, 802188852, 982105995, 139886253, 978295737, 286185838, 190893602, 197294905, 211724141, 958783945, 204860025, 823201627, 706341102, 792867139, 203485699, 373338720, 799930885, 714383027, 344623411, 922891112, 236076311, 329967794, 473955701, 227807574, 348313331, 509850490, 811115274, 13390041, 541628398, 903286327, 660356278, 34113928, 965803935, 968025415, 309476737, 440491725, 136406547, 522681686, 779357237, 195844670, 321477878, 760919979, 141663346, 152463356, 76272181, 377875489, 605754403, 352504906, 61780443, 262923752, 823508074, 802418449, 818668731, 128322626, 138628348, 752284285, 11533078, 271543268, 913120201, 74887220, 470231704, 41619021, 220459110, 899310081, 97371401, 565534986, 724204067, 775323775, 594273417, 108246864, 749966849, 763566605, 74660802, 374079648, 90419247, 997908357, 323295808, 112383634, 905649332, 262231695, 695272745, 765885930, 424099695, 750426217, 173023966, 517603966, 659745260, 850635072, 139162526, 799216407, 977375500, 293078319, 682079279, 283226412, 568898877, 99889458, 17303861, 72688695, 622294953, 292247658, 948297738, 553674662, 883399243, 630816169, 491774504, 29244051, 60484896, 498157156, 612856135, 203979771, 520795053, 961186376, 615470979, 85337764, 212556205, 392762986, 39931799, 857958864, 888634847, 269319201, 428908077, 945796575, 130124961, 960958116, 709943791, 156783426, 595016331, 409855403, 230479010, 890481997, 486778372, 734818398, 897427655, 74956965, 126158092, 28693937, 235388675, 349178915, 556299049, 167779257, 827933876, 142516884, 486178930, 918691570, 540286217, 940647463, 704311984, 735770184, 249822998, 535045676, 421913503, 841410800, 237032807, 384445510, 657102051, 298452454, 728686494, 324877735, 709477140, 279838526, 557854922, 735764543, 980423038, 258730942, 21360403, 577282363, 193719874, 831572804, 732465883, 847396020, 792636393, 666990986, 407658671, 19374907, 454828539, 527975843, 739895838, 84940925, 462561059, 523247742, 581341571, 420173735, 207973215, 339857726, 952449761, 233863729, 711513220, 57683478, 156122498, 565111893, 794972688, 274566175, 42377831, 650146767, 272717817, 658361970, 528095277, 130401375, 710322016, 171770287, 817901136, 257990019, 69945332, 211098497, 861200459, 738416644, 92763838, 303191390, 177106464, 592491528, 527975160, 519790030, 565870154, 900836109, 137143262, 152706523, 705684800, 8479113, 538969236, 819609472, 842426113, 171456602, 722046681, 35923094, 896978392, 969451920, 118543167, 600231870, 899079749, 904335128, 23822058, 145267654, 243377415, 760027976, 247918465, 284541948, 558873518, 85943984, 872237512, 361034565, 694088227, 306764687, 669252317, 59189075, 796311756, 252868036, 832877976, 758957773, 995707387, 359316924, 75381670, 226694152, 671359681, 486518126, 399839253, 384726830, 265162888, 716940271, 105990264, 846037773, 419370129, 507024181, 250884518, 576422801, 835952608, 796919130, 27195249, 717161833, 28137637, 48087402, 255044400, 922913802, 234202355, 674409045, 763586305, 941301936, 172328064, 369020772, 601256773, 761342703, 474464176, 596696035, 586732616, 597960686, 429947999, 807089550, 374009374, 172504605, 282625805, 267843057, 184309731, 955152781, 48154206, 44684040, 452944090, 930342948, 712107126, 740256268, 181371257, 86271601, 533717715, 608673362, 305992484, 459446099, 101865683, 697206346, 569625609, 499915051, 830200436, 183627467, 805358321, 72080724, 927897373, 849486943, 232078882, 528651624, 862931937, 31946934, 902519452, 793599682, 19949445, 568914665, 714083290, 246009859, 584967519, 768235476, 319934347, 433187203, 484885701, 639954599, 184779029, 266877982, 401554635, 29176959, 815657647, 214278844, 924917416, 46907957, 552698434, 104906562, 31807019, 173363474, 850034797, 872477906, 687406718, 144973400, 815193586, 749261712, 739406166, 335211725, 961259917, 336237218, 905776805, 987780767, 255119869, 556989817, 667099663, 247362810, 785138658, 479635702, 956204016, 298188744, 747817228, 496203412, 635369238, 527339352, 6735108, 97958281, 659875238, 474149315, 228173147, 125380362, 683114253, 75421926, 296859043, 174828852, 716266479, 19227510, 765671869, 404659329, 72377795, 769508988, 74523061, 466187987, 151355769, 335775044, 316205566, 556319423, 268841855, 324062000, 885048430, 362727061, 832955361, 608631561, 27796998, 356928986, 948576812, 474615766, 79089507, 272234992, 604520633, 86889015, 78430233, 665456353, 871887484, 622857185, 375818718, 708591309, 165022869, 86871068, 653959158, 312972870, 371438585, 869470345, 39054041, 513140464, 307393393, 438405370, 552269710, 346400572, 919955838, 737665495, 167127188, 558412408, 806536686, 740341462, 303477234, 842052101, 238604879, 982032165, 601714935, 510572024, 443857020, 431443478, 545105100, 994006296, 541214476, 837701464, 66946282, 976243091, 414796732, 901603534, 23650734, 822255945, 363176079, 757436634, 313135395, 245464161, 29266999, 320564800, 840844554, 300721469, 965221721, 40796784, 104008714, 30687654, 596762479, 847806205, 572658155, 410162100, 32337824, 987688178, 104952469, 364902388, 459478112, 359781313, 400524707, 497818173, 429674715, 777374041, 798344918, 552690868, 227275091, 428877096, 322860893, 376517113, 29734789, 847121385, 299465364, 780242687, 585035086, 647573809, 131128019, 572045876, 385177250, 760539830, 355499843, 647410391, 970162647, 397469628, 560402623, 780466076, 904985732, 996225598, 292757060, 949735814, 901987964, 73350398, 432105039, 569651027, 514620812, 548864144, 426706036, 751994976, 245236390, 369781736, 870317649, 140456659, 447027059, 905616232, 475430747, 376357087, 294616067, 267863351, 264844786, 457981523, 225145882, 102487301, 919356795, 488385479, 731521796, 563273295, 427166239, 996961511, 280582107, 463982125, 97616409, 536734503, 210207571, 257199424, 526058656, 590677672, 36910195, 273835870, 54908500, 185241388, 67079015, 941823182, 252595529, 155810672, 350027739, 995276579, 280074130, 995638796, 646775124, 255292071, 72194732, 869394037, 366534808, 605841865, 542439796, 501568653, 396315225, 644826329, 480113769, 751063771, 342983316, 8018962, 654126174, 691201100, 481550251, 103605976, 160273042, 886745958, 282957598, 137192972, 480477175, 759159732, 24511414, 835809486, 205485071, 825703298, 296749070, 312169773, 814780015, 996540804, 66904690, 338130342, 59275674, 801405716, 666842376, 937922713, 260735545, 918575964, 999100006, 540492083, 137987021, 8683885, 268459288, 60824883, 276378523, 769376848, 708922897, 108655634, 790871106, 491346480, 998844424, 26179908, 836055901, 83257145, 97482578, 17296121, 752806504, 494254317, 33634349, 316362054, 473069675, 869847903, 666085573, 41559500, 823168207, 496496754, 413151432, 481321331, 451000488, 979929542, 833666924, 956154568, 485701971, 282479705, 828238298, 783533987, 745505079, 198856872, 498477285, 720085607, 663184416, 692957877, 356690195, 937517604, 681652396, 677149492, 393901863, 552080758, 571399148, 872691540, 742515758, 859258574, 438723404, 695541455, 659650274, 715388328, 402487304, 42515088, 666501990, 38763362, 339584721, 267640143, 936399284, 178817430, 614692579, 381146015, 236659755, 74325033, 388339721, 794592273, 943540748, 53367256, 169838891, 231002668, 806267494, 577051311, 438252305, 329753565, 781667413, 577704415, 476844717, 599411540, 589332754, 869102493, 598554611, 386701049, 937365100, 440105931, 906357071, 974028720, 737842146, 329087719, 552666337, 613644299, 972077109, 401354112, 619821337, 790923733, 246604398, 852856450, 325619908, 565261679, 834399733, 96051215, 450551109, 47174383, 161138919, 832015954, 435660446, 752374516, 504041736, 246533884, 12817524, 314668916, 778650268, 702013525, 723900698, 919169029, 155721817, 101482088, 58561336, 533793128, 724881377, 411517258, 946623672, 401093840, 869688746, 618927589, 226832023, 266694653, 838580871, 696518472, 315687627, 361246962, 751907198, 376771607, 308909107, 736600935, 125273931, 517434102, 487824598, 27785521, 301563068, 643991377, 815824642, 311137073, 123712280, 343614670, 563663706, 802178105, 367318691, 78572087, 333952960, 193322041, 592483511, 700043314, 727752245, 230678439, 85088048, 947852561, 390345305, 252943910, 744151391, 1298358, 934169448, 167138726, 791612697, 794224453, 197038742, 357966055, 895057429, 27200044, 906925178, 408898665, 124949666, 369841857, 399702037, 291647668, 492553563, 1471559, 860937712, 640279990, 49834614, 304519271, 769527554, 937190552, 61383138, 17274549, 15962674, 474990749, 717447798, 296285072, 731837711, 878389550, 667871664, 379218425, 370395156, 172076821, 816055829, 520423550, 843367566, 65624877, 400327028, 581622603, 477590953, 847896688, 744948403, 438007423, 581791658, 592525165, 943660304, 43187845, 82821355, 151780223, 353646317, 562980308, 223585218, 835606502, 592181102, 439503305, 737818491, 909542252, 543407370, 89411046, 759104436, 502384441, 315844422, 469293373, 428346255, 473535848, 753751664, 272000723, 314097752, 795035351, 945970706, 323231333, 113571939, 716187291, 142981638, 797827381, 758249540, 696756643, 553403693, 503308186, 574118691, 811124720, 65374267, 817785588, 327591771, 535630616, 373010352, 334413733, 617613719, 599679815, 964487083, 69406101, 928893006, 223387712, 832031352, 249052010, 428760914, 128601519, 592082436, 241506916, 503841277, 870292527, 974496990, 595385388, 450100191, 793272840, 466679582, 244995662, 453566861, 680501750, 91038156, 984676472, 925666095, 953987167, 271879129, 345173798, 690161429, 795264215, 691676994, 363464218, 792422576, 534437775, 479946998, 733275463, 467964980, 431091162, 110632839, 496525488, 887737911, 634626631, 188484491, 588264216, 976849118, 698717878, 739103240, 309765013, 802058815, 455052906, 497550441, 957659419, 959220420, 859823926, 125219622, 329351530, 403689035, 474329890, 737742437, 946050683, 577462685, 385738309, 287819136, 702543164, 963389263, 96199104, 901501687, 513515782, 230079726, 135633538, 759891377, 563085473, 891620430, 957654778, 65680545, 702906121, 974819880, 713756068, 963981419, 160889217, 38653391, 164426630, 645119816, 130028724, 216710757, 173864646, 762071484, 883379237, 866889165, 92623230, 834951512, 934728794, 930723537, 701019791, 927090255, 732630966, 593577613, 852844033, 468614696, 411684893, 83763367, 634014499, 284604290, 435436603, 248983670, 969582055, 523356133, 456911590, 528610375, 597304299, 921128475, 58961954, 224605009, 472545789, 273824401, 497703654, 954374790, 125668944, 766360340, 992028485, 70108650, 657441160, 736979918, 191587527, 618896549, 626913967, 168592796, 316927759, 880549036, 969524666, 949273739, 92502500, 543453919, 326264090, 759669411, 388065037, 402108464, 133026545, 959370641, 174416698, 441419828, 670051629, 357066239, 380063169, 193727421, 665944575, 492288834, 88083278, 954512963, 663500332, 898847425, 17845226, 363229183, 982008317, 288021262, 199749304, 900773110, 887279550, 63916038, 607986119, 294522803, 470122009, 376454037, 160527786, 5292493, 815111517, 55580864, 957059583, 300167003, 748560169, 519101954, 976193630, 201082800, 861051709, 294741248, 675169348, 665950723, 636055897, 839876370, 873266478, 207818694, 936870820, 33526764, 340518041, 503853928, 268996073, 727703183, 706621144, 917141377, 8131907, 731321570, 705202518, 29461271, 567835516, 244961336, 261991222, 652194815, 969400053, 559930136, 688621791, 428374061, 709560221, 602440239, 264251550, 859728712, 715895738, 380759681, 143866626, 634103308, 270146672, 951493922, 878128547, 638410077, 148363635, 374431486, 682462637, 463735529, 464292740, 840297122, 252429838, 931538673, 804581709, 884831836, 557596711, 826682164, 601538411, 270549825, 500418662, 641768591, 547336212, 26003175, 773370732, 288876775, 968096660, 285620603, 759082821, 930230212, 402301924, 731006653, 56779667, 117634617, 800602931, 248824268, 102270151, 839585325, 704862759, 327476054, 462066936, 957458846, 394454554, 782833226, 417041396, 503539961, 247244147, 268517729, 151506534, 935824210, 686600249, 633386596, 983934852, 825387970, 456923222, 104482721, 262794377, 606489323, 976808577, 741813992, 970112608, 608917916, 754189819, 514616497, 220989324, 289215635, 876426847, 411603291, 2940699, 423005980, 35564910, 362986068, 159954894, 206719206, 857308929, 565713225, 860063598, 458231991, 784635047, 763906585, 696565974, 183837695, 505116211, 796456754, 601712037, 899218055, 757365422, 940182553, 298120629, 393051571, 700491962, 287018287, 272889967, 81053723, 240285025, 343262037, 314494297, 218093759, 509522121, 517118896, 101153404, 497699226, 11089865, 465135252, 640102402, 741582307, 240485001, 185781076, 197627474, 616199565, 454428223, 704029460, 502063469, 913468895, 240633525, 571846819, 830906236, 907111755, 645093678, 197548171, 920411966, 590620471, 13506605, 302750876, 389851192, 973187553, 876310222, 949460487, 925821589, 752858015, 40415382, 328143263, 382462818, 527955079, 223283238, 283744368, 906282166, 753835275, 84646218, 713107879, 398069947, 624565479, 543272935, 579660476, 843959946, 699140292, 910605634, 95509459, 915576113, 786984251, 183519068, 725288323, 184042461, 983557689, 89193216, 103458619, 208940250, 218878148, 407716280, 827778342, 994002452, 924233751, 604420700, 378481120, 777064465, 211776617, 139182419, 238247080, 214827398, 283560398, 585130131, 148036490, 576211465, 878646657, 77371450, 943198959, 872974067, 465761232, 436335259, 796178201, 605705885, 466463475, 995355543, 69359002, 203318522, 654253188, 450786481, 702199111, 158339052, 592758048, 957465196, 599090847, 274527687, 631708816, 465071360, 637947028, 964030720, 298815925, 818030450, 139046880, 587906352, 503555536, 951933593, 446490674, 554305661, 794108919, 162356695, 20055215, 983978844, 942969274, 248343966, 550631913, 156073634, 193818043, 976931647, 327655623, 989645961, 778518410, 523420394, 477258357, 899562098, 468471115, 624277495, 361533210, 214900874, 538193145, 140541237, 255868980, 481559297, 181178288, 80609392, 593583577, 974618169, 41510086, 248987627, 110649778, 191595579, 293288501, 473826649, 188836715, 514468452, 371835845, 876174117, 839087075, 225212719, 895461759, 300866220, 12231719, 244903276, 151007553, 888560639, 221046636, 802229382, 48548095, 811485403, 839533261, 889808923, 658906915, 327828994, 897329173, 605617218, 572291788, 911957310, 258248397, 767800856, 556643548, 185288874, 932528936, 279132595, 286615867, 595089090, 762494721, 883765073, 641481909, 712854992, 329741885, 862572926, 59008271, 302985253, 82667163, 409540807, 553351553, 520367458, 590631102, 96126617, 389483595, 63158959, 638983644, 829785449, 781531808, 555156964, 253505934, 145633970, 646000218, 525641269, 858051758, 377657006, 716960427, 889189945, 325193787, 480248533, 356182025, 195260871, 968009118, 355284855, 868086196, 643494629, 986223886, 546986447, 273882983, 781915693, 790659310, 498525982, 861689118, 588621136, 999939858, 174075051, 581948462, 549111407, 721208760, 416206283, 964362893, 771357028, 151696028, 656671904, 756927334, 726952640, 733800101, 509846755, 616277950, 862171618, 91294425, 731616792, 774278373, 68982917, 823333948, 184284126, 102255144, 594557768, 245460426, 297512932, 530470480, 824127337, 517153809, 586134924, 233175257, 799064690, 885241193, 990126054, 599018509, 308342482, 573356692, 261031934, 382697826, 832509347, 355764642, 263193016, 553912276, 109291323, 979213980, 563470673, 603744734, 363251182, 471218956, 168144257, 953961227, 501162374, 755951106, 774089783, 794700361, 988881500, 565624184, 407893398, 163706817, 980403595, 766288837, 953623866, 830840530, 520164295, 491832880, 809445945, 810976615, 239244408, 944127536, 768255311, 712378376, 873980251, 495728383, 366038534, 612665954, 230644512, 345294424, 606370559, 778527501, 18463809, 556017517, 145915451, 303638223, 656157379, 330983058, 266828628, 997371456, 120701769, 346361561, 617692731, 617834878, 388441516, 546369553, 981560966, 110639980, 746932427, 760203313, 966111611, 94544327, 405027088, 51954415, 277381842, 970211074, 696228701, 950510505, 655816811, 796457956, 161140794, 41568162, 600590405, 688031797, 586552209, 952299555, 38722014, 714953144, 368910018, 32535053, 220695437, 213575821, 561993886, 689164682, 740639560, 220667237, 596491732, 290911563, 7717467, 820919370, 369980991, 5013732, 875198609, 174106567, 644847037, 395006726, 39823091, 864343073, 433572078, 875180665, 632787856, 93043695, 231719296, 36987362, 66617597, 600739114, 430023389, 514164353, 175697037, 595553853, 303933096, 385909372, 206804956, 890876275, 286097301, 864598528, 59908218, 209760163, 512583210, 21587440, 552117213, 731054489, 413415449, 111520438, 569647873, 565747471, 546033937, 344385298, 203805569, 724160912, 831392651, 707197647, 807265790, 596430039, 655352352, 382689609, 147110684, 993230769, 779531290, 531091809, 817356382, 717932458, 263121535, 874228637, 471616087, 457176071, 875624126, 639969562, 880326841, 266778511, 773198112, 748994770, 798027173, 429251527, 794716192, 80485719, 805028287, 213450181, 862945569, 326993592, 740363167, 469114383, 719403299, 355708590, 37044483, 113525734, 26048903, 154099793, 38870919, 331088370, 80201952, 597187275, 171596980, 139758970, 350788794, 914025235, 730351467, 759884772, 335272066, 257700193, 697431910, 784571292, 925264149, 476489657, 255835214, 247740670, 550958168, 812637408, 883602545, 316328275, 598939452, 732264860, 63627068, 463757186, 120514084, 155224825, 972864856, 614483389, 465463243, 311276282, 94866679, 701632235, 63851340, 329075738, 626449826, 580827503, 645915261, 765603495, 672828608, 948417200, 251747169, 135280192, 379676987, 358498670, 559121855, 469643576, 297089015, 860874862, 137819112, 832990984, 68236158, 762185670, 488984413, 894809079, 679231023, 802930468, 120348310, 914710766, 161192193, 737054237, 912069941, 62103540, 647997535, 199300618, 844253818, 257585413, 439401859, 72984363, 144892592, 448993970, 320503251, 690164592, 108947315, 549541576, 428985183, 769348168, 487915056, 874964306, 82175536, 187552544, 822245811, 180978962, 227639795, 640900929, 412720659, 525771173, 725849839, 990051308, 566642248, 821971871, 439672354, 194291760, 373930807, 353411132, 547462974, 368591412, 585955431, 426359989, 675971847, 558128937, 694411825, 345163684, 605341912, 620040532, 984810283, 396128396, 104396019, 690650659, 146187750, 340962621, 137986882, 984061982, 399146108, 770834962, 854904821, 16884416, 558751424, 421233043, 96534170, 833070657, 892474244, 917856654, 55253753, 781029089, 44509110, 181807819, 243853908, 850993824, 50688806, 426373777, 550752317, 13256221, 957365071, 745888689, 923812420, 919020362, 427471772, 926624087, 101748292, 743817459, 617303231, 409475743, 990937164, 976053907, 714120097, 999138218, 315145484, 838580883, 583630053, 716638028, 887350104, 932033952, 260343692, 960808554, 596663183, 894494792, 541131785, 870163381, 333282445, 470196428, 614251396, 153994378, 251062253, 971720224, 836953883, 164249799, 660494988, 419317076, 344249891, 72970831, 332649434, 95359088, 2780483, 680440505, 650674666, 175982300, 956740609, 157355510, 480093515, 808140563, 566307076, 519461133, 94152281, 336967077, 357283862, 627287498, 84054768, 236574236, 873469096, 246606327, 275417563, 163304891, 797169351, 67896601, 603963127, 979863165, 840937834, 169846960, 296947427, 445110610, 500653315, 316585317, 401808648, 178074724, 913518706, 670247793, 864522993, 662038198, 331053216, 53094878, 675221096, 215975178, 609589034, 922813501, 359029011, 200225028, 675154233, 539025986, 367760943, 366264042, 810353298, 314736993, 136124570, 710715078, 715706539, 810764168, 139945072, 728887296, 198434635, 32717972, 904060148, 943304807, 827418750, 481267357, 723686156, 159141597, 934867018, 713131786, 246723264, 802104393, 267844017, 718531111, 481827844, 498985370, 197403384, 656614642, 169589521, 336983929, 644954743, 211717670, 235924414, 383190699, 271036706, 166547629, 771106112, 828862403, 34751410, 765418372, 727623215, 18000497, 918673689, 67974463, 803392923, 800369143, 28518570, 558804645, 257875805, 712301255, 985617568, 784328276, 390186151, 145966259, 633792466, 54816143, 956127037, 73369382, 552956666, 466619897, 416222657, 700173323, 25969405, 247101454, 832498646, 4650809, 1461191, 952270875, 698352209, 648893276, 894447321, 246114467, 83994647, 755639876, 335830933, 244931927, 107828507, 776099656, 966438485, 853962326, 202139728, 604244519, 612077768, 850114974, 333066616, 911639250, 514221379, 576835339, 698478147, 786220397, 66219467, 917963874, 226189992, 782944876, 898794637, 732178481, 215051158, 455288112, 325328766, 407271703, 223826196, 307262432, 579974864, 359217760, 341656769, 128161195, 371578404, 369993074, 938017882, 114018136, 197426111, 604696402, 122015817, 110126187, 923955643, 347580633, 435872528, 830793256, 942540071, 97249629, 449699434, 540691260, 359904138, 372913660, 103559966, 952675718, 526637191, 957532903, 350107011, 624881975, 28781638, 193858885, 871843277, 223235760, 801756888, 341732508, 989229899, 804320620, 781161567, 944819016, 652153960, 50107736, 463413227, 881639283, 90294010, 857774696, 997430080, 748242924, 65920836, 260863883, 764202189, 879460013, 790182725, 228605852, 877702002, 265235027, 298522372, 626285047, 508078607, 650128416, 56053142, 228050198, 931572207, 946992485, 473561154, 678297536, 492487725, 497531665, 341728700, 229905345, 973164150, 850893042, 789404158, 215565532, 588113015, 72085182, 948028068, 877216234, 543254288, 597957164, 363480188, 620838984, 897060914, 845297592, 431826458, 762679104, 586341308, 121189065, 976375841, 976812529, 419027966, 729898698, 583791355, 383558807, 798165101, 7296926, 706814547, 5193072, 869597785, 240392518, 324956448, 116303663, 308899376, 124177273, 793735933, 594717312, 42468071, 994585102, 600710499, 735618504, 619491316, 899450737, 523337712, 444816970, 229008131, 405041991, 631945752, 673712149, 578339937, 242338970, 191936760, 213613661, 229815082, 828897569, 270636457, 585735442, 75130829, 545205067, 153726566, 11957187, 539698058, 966455616, 498735981, 523524411, 167055682, 982810674, 389048635, 501422830, 672210365, 961861580, 876412239, 608660856, 552011527, 153516360, 231921525, 380572217, 333677295, 338695519, 127322035, 455756056, 652754072, 749919638, 967950912, 531844675, 568023189, 328630707, 668537509, 566467066, 528980072, 401722379, 71256457, 120812666, 749672040, 279212340, 269889054, 996352014, 455055522, 658452332, 372636, 283478385, 449666518, 356359071, 223621329, 145879235, 815155489, 618445385, 228027245, 59816242, 181061516, 743792136, 817181550, 392785188, 224433813, 693677981, 252826200, 735236389, 936137543, 568289576, 84737954, 527387387, 798539914, 813193552, 346445608, 208974163, 639759503, 969764672, 54961566, 337437993, 760529549, 6194973, 675506346, 682463985, 473254061, 736861949, 55804018, 142294271, 978084596, 857185209, 814906320, 473261275, 547459248, 414555893, 660033878, 279556069, 553439882, 621905242, 94144376, 966857217, 886033293, 405984584, 523097419, 652741031, 814221755, 156347913, 134834660, 486109380, 63082336, 450033086, 538681549, 371430463, 767759034, 790011569, 335079678, 779663715, 65961668, 429779124, 367367351, 686144791, 237776277, 584639553, 188959134, 599774647, 50536144, 54649394, 21661274, 175366762, 636301336, 285719442, 464774661, 39335320, 39297764, 830233428, 35964195, 4449787, 319546741, 787758747, 372430071, 594491926, 336254979, 728320341, 346859752, 282468364, 330439961, 779357307, 772427377, 689044334, 244146705, 61882505, 46670715, 858850295, 55580069, 408428902, 128601233, 980712344, 658924602, 400152237, 669456164, 733259690, 362648445, 180082953, 945200714, 421797627, 185709787, 896154159, 662991063, 229936241, 296976334, 789553672, 535526807, 598370060, 389757900, 554416094, 556830790, 19200231, 843295788, 972347380, 52521105, 975784663, 484877892, 117420321, 167840092, 520904493, 569344278, 639066030, 578343749, 61206212, 920658446, 808777731, 416503605, 939892641, 241242470, 630514491, 287533110, 976001044, 673522115, 498113569, 778895907, 4028436, 358453560, 574994599, 758064354, 820841235, 859007131, 480659066, 440227498, 93188021, 370847458, 98189838, 447239328, 67039205, 69952693, 357307925, 119714556, 109412229, 911356950, 346211996, 369002940, 581233405, 833391648, 911051706, 823609766, 78852718, 548996475, 727243968, 458217284, 220206332, 520953184, 318451653, 572737319, 382479468, 797126218, 583944307, 291716679, 504205461, 927181312, 962164872, 890249981, 831712018, 52122813, 854940345, 327189278, 778259708, 490460232, 763068583, 634370554, 224600196, 363079451, 996824922, 712406098, 159752546, 23030520, 313993920, 914014996, 57792371, 344759520, 612772300, 838918833, 195071941, 657784450, 789617114, 725847474, 247019327, 687249265, 600461674, 825300871, 71907924, 982751108, 994190253, 682903459, 422443887, 600234567, 196834372, 32076598, 823025048, 974642309, 663965257, 609500258, 867017851, 372791947, 721270175, 437433519, 229024885, 536668418, 356093671, 786689075, 61133986, 182091083, 424731611, 335366363, 744351188, 888585652, 11008767, 111386124, 72844882, 486923261, 752987822, 186626235, 484445091, 879771796, 840917347, 139887256, 348048623, 255714786, 337452144, 338420174, 97571323, 311382142, 450154362, 416695347, 554807280, 632356682, 29389469, 11739034, 302827670, 204244934, 93506956, 11078390, 910970703, 701980060, 126712492, 407177651, 778635777, 590449054, 442645416, 781458136, 715482827, 805976148, 436471934, 989609680, 567128678, 446352964, 962642401, 234136670, 221066500, 684176528, 452409751, 668867769, 330548088, 154592797, 974656729, 644812132, 489511430, 687732577, 657587809, 787147093, 417311703, 707303740, 693073825, 18700288, 956685, 493023621, 479731591, 415124670, 409247435, 368054358, 526170268, 790052360, 718420274, 119506215, 431852640, 431412122, 638709480, 722041722, 760393988, 61095931, 465662827, 455259196, 689844625, 537649878, 200050782, 71507842, 919713614, 96446907, 116900343, 8337323, 816765597, 709746904, 782782055, 717632395, 758457902, 791199989, 344877059, 209567164, 406016228, 126458631, 953762541, 286584934, 101169155, 297112382, 497766552, 157745462, 699921050, 201842788, 380348707, 757213532, 892906712, 653878604, 185808090, 951319506, 328992151, 187145018, 315604440, 6640207, 782287900, 794499737, 600478622, 822497389, 178120551, 332002927, 326805968, 957338513, 5215308, 951639797, 968177220, 368704902, 209279966, 980031894, 498281102, 896735135, 696112907, 636522820, 17832361, 155254262, 650084170, 305925466, 442055276, 585401705, 173424696, 332906007, 613030435, 997252488, 903398921, 480918340, 565945078, 767212967, 733723141, 673628224, 819662925, 360064529, 64738740, 981419209, 111092720, 388468742, 198525793, 46380517, 881313528, 119044721, 508467495, 522004044, 943077604, 279790033, 852903595, 540404985, 52763901, 402034520, 605811008, 430660610, 834610606, 188194320, 82930520, 50115704, 338227449, 367301187, 601948554, 283505225, 149220509, 963793698, 637398726, 655127895, 634846813, 887606475, 616867752, 348715407, 218610796, 277629653, 816167298, 341454185, 738094640, 975844069, 701855673, 367385422, 213519356, 856922361, 112636644, 919140067, 739119646, 64223577, 185143294, 992946226, 118290949, 177750768, 321361730, 795220763, 934445073, 740216738, 110667826, 458595780, 580660407, 656978489, 24861390, 885437756, 315595048, 905013994, 180850977, 376906627, 932181825, 253520766, 666895222, 373507152, 310397566, 444680781, 492180908, 156643915, 57025922, 950987583, 100600972, 695739985, 589140098, 790280689, 736144641, 117541633, 932206337, 110541151, 440968435, 627746684, 367038005, 569574844, 915708509, 247130319, 558641898, 167429882, 42196834, 489856749, 696504395, 325766297, 633842996, 151410338, 921043277, 575468314, 934322595, 381775883, 68515272, 449616504, 839142537, 829985084, 725816853, 321196811, 857341512, 636366781, 891944540, 272933390, 473534133, 592639456, 485402549, 559118694, 267516977, 168163584, 392726310, 895840876, 256081395, 899263407, 542474872, 878053357, 409623326, 831899112, 325137790, 550602483, 148354982, 574439577, 668925288, 314733770, 958526476, 149190996, 802991035, 867482651, 158594406, 245358433, 822875429, 563616697, 53227066, 193116974, 861997632, 205534719, 916909567, 480677850, 76814097, 756078089, 529076074, 993072909, 838095440, 432649790, 814615846, 122835179, 301581210, 687896869, 723085365, 127965115, 879077435, 514875171, 974416133, 92390281, 748044674, 849450517, 904057607, 161916125, 109729662, 169010650, 737888990, 915150562, 771566002, 190521555, 81478305, 686755511, 108477674, 862591123, 555343977, 853961982, 322872817, 618958254, 984369968, 236612804, 341462076, 529313356, 202716102, 82614818, 669452503, 821057964, 620448489, 479950099, 138041749, 566542259, 79147678, 46902178, 616426816, 911805533, 12318908, 151021860, 154071431, 134346439, 68907117, 143357939, 636288118, 640150747, 907258790, 391917248, 656652681, 884168132, 781009254, 598905667, 6320096, 548916621, 706101765, 473489469, 511366699, 946579182, 45779615, 449395649, 757710947, 770504235, 656112296, 557319239, 597029527, 282073022, 778525209, 849269663, 9735352, 828711856, 743596882, 500007610, 918410167, 279756781, 718354322, 626461791, 212146436, 668580518, 505519397, 708756615, 13256597, 693325640, 126516942, 595319826, 827142217, 166054397, 746729779, 932115397, 95678828, 145534, 226714825, 813260913, 770496736, 373475313, 319944651, 980150450, 208754534, 443573935, 291546898, 41169970, 487312517, 457858177, 914558963, 658477270, 91913894, 971053634, 321072331, 841236745, 915109330, 61337693, 888658627, 674528027, 724872706, 46051359, 164890361, 6864002, 472908389, 729106265, 610329539, 966121467, 227069042, 270420562, 199672868, 691602695, 59164363, 4579345, 36845551, 543013376, 397420449, 699871845, 682328020, 692728342, 315428159, 466540965, 780594213, 58141264, 526270825, 515573435, 508583134, 102191749, 234251989, 979865654, 102975284, 214968856, 895481756, 146113674, 878553574, 928499521, 74142749, 890865050, 526199581, 942995995, 196897729, 722523519, 990979024, 461141927, 581989349, 710697788, 202681804, 70739742, 852282902, 199964461, 261994745, 205413392, 609256446, 52268434, 995319386, 117991270, 83714390, 369058162, 478345858, 374541900, 470691248, 618298848, 953910475, 138903753, 624044457, 758739814, 748045633, 546976156, 378666687, 204145097, 427645625, 153616481, 491772692, 934403368, 872725466, 386662376, 395481974, 875576113, 242559951, 886183544, 244170300, 545066079, 259349504, 619650071, 121259257, 170081102, 571646646, 862274298, 38739789, 665088937, 623946798, 550911172, 719348522, 220676557, 240946721, 627221444, 295481854, 137032785, 914486523, 274317249, 36103446, 844344748, 567329365, 518616291, 181188897, 609922969, 123701485, 274531003, 376423840, 808741744, 83302084, 470425888, 842410315, 659472008, 649671509, 42038712, 288609700, 454379024, 855284302, 53889196, 488736087, 952899716, 308199026, 651312096, 944348951, 271978843, 175838783, 964133853, 520481311, 570452267, 263707975, 654560191, 281261369, 454346488, 941878099, 865631416, 192896800, 740164609, 247486631, 697815643, 472053961, 251082534, 892298119, 390757224, 54420718, 100407071, 31974825, 990167972, 798784283, 395829561, 94292722, 387869712, 977987468, 449370906, 982603171, 214779317, 862316959, 388975313, 898923136, 73860419, 211864925, 731940371, 325504403, 727096809, 744393956, 193878944, 528238994, 228698747, 25306766, 696221569, 958798697, 360612533, 171983439, 308245806, 202650846, 914448130, 209437884, 201832401, 193247049, 98778129, 101422173, 836633742, 102038152, 466264271, 602950545, 448735968, 72227426, 733146103, 713596513, 791469392, 477637802, 19088398, 174558477, 189266737, 529414891, 341502886, 551578886, 500299527, 225321174, 781092109, 381227576, 445573756, 918601682, 585588648, 965734557, 20114374, 753890369, 230739842, 943620713, 518969060, 143319803, 793424850, 618327326, 65995909, 471566920, 43985244, 941560748, 388789133, 945375076, 343217428, 749393550, 817917902, 265981538, 449558020, 322472761, 500951296, 214547727, 222960432, 724352787, 658074712, 528603660, 115187092, 809509308, 668870883, 32469459, 312022275, 194994215, 360108829, 753181563, 980062344, 937817186, 60018998, 324831606, 608661336, 189852018, 577347033, 966616780, 578713419, 337988391, 60191087, 465567052, 234481667, 570273199, 684243219, 866502159, 362431584, 79380882, 691328651, 699469843, 668799042, 395217261, 529249157, 720396585, 786024623, 736296169, 355088383, 535612376, 181913337, 511766071, 325093155, 355998102, 856003534, 722471279, 710566805, 768581619, 329676900, 296756380, 524555629, 898710493] 209422566)," 0 (countGood [217706376, 176224481, 414853751, 360784308, 399375492, 941597389, 106851333, 441913586, 947317130, 914922940, 846297059, 757462564, 464491619, 53183692, 750452757, 357678359, 105330506, 93457988, 79483012, 964421862, 527257327, 708964453, 128180685, 1573100, 757724008, 466606556, 232583468, 121995288, 796663596, 488600355, 9188128, 262499378, 968232102, 506785053, 997428, 97831813, 455004004, 389233120, 605066830, 186485673, 883227896, 812459989, 357297053, 971729077, 226837358, 411471539, 244789916, 91594399, 553861492, 618617171, 222420495, 281073509, 556026175, 917966899, 219694458, 398886608, 133483508, 794514401, 937093071, 851613798, 713103967, 834334425, 87667992, 421909706, 511882128, 474169819, 230971531, 121831416, 70235029, 872655488, 660684334, 270932348, 417614935, 324511141, 936339338, 507717871, 89484871, 857860027, 817210708, 181199820, 764517409, 874095904, 456161596, 24945559, 570444117, 139124333, 875157265, 923091481, 979235831, 213908342, 613900157, 717081132, 770041904, 191984888, 586105063, 223446895, 60935557, 6607331, 169951049, 649736495, 537507832, 541445025, 47479214, 185710585, 809829797, 217316587, 486506172, 573761607, 136568425, 270021418, 510394401, 971931726, 529895346, 783659016, 528525824, 635264797, 925276241, 547594048, 327144357, 100473838, 297748496, 215080395, 204959156, 754752536, 14366392, 753243580, 307649139, 348481450, 441707033, 652951094, 225507330, 255319279, 499190834, 649005056, 897221511, 807181363, 933500397, 646505271, 298913266, 393410384, 784576972, 429491598, 673388207, 115247560, 204784413, 175698197, 684048886, 824128491, 72956419, 388310206, 131129913, 43847103, 79004156, 492315328, 391537479, 656163153, 639283306, 290003724, 138338137, 600258186, 327969487, 107741669, 273838978, 875754930, 37249409, 353706684, 905026945, 247106422, 221736619, 23073436, 600142271, 510131771, 413149446, 941791830, 52056917, 519371096, 106216138, 611936555, 910871070, 530149114, 176726859, 991741647, 410175704, 903477370, 58615933, 841691300, 279284216, 635097399, 296723259, 245690715, 952039538, 515514311, 751339763, 15649616, 57193154, 573331418, 85562912, 315568059, 813690098, 294649224, 792709870, 345387153, 365179768, 879892162, 187554500, 713936217, 323716036, 279086548, 426861714, 974042645, 727308362, 627265202, 24140535, 54089777, 326986708, 992796984, 884501098, 580766794, 349608542, 618169190, 618005992, 68587336, 823700952, 491493306, 987960693, 184079002, 362602900, 422850367, 613220782, 850433406, 210874176, 88904294, 542805647, 597678467, 375727022, 971347361, 386206664, 751041120, 467384212, 177054772, 955660126, 875095116, 871662294, 186604549, 436175888, 900747336, 230353173, 740027850, 554643846, 575045772, 131026181, 590226403, 329189160, 386731452, 808748641, 195065161, 913656275, 919620681, 154863607, 376759524, 755684655, 559201604, 671312144, 327359399, 505114710, 453798092, 575618470, 208363970, 39518789, 77151826, 880705180, 324021765, 159496031, 693992095, 812583733, 9253626, 278896204, 928403601, 998138338, 100469387, 800902279, 819639970, 786738086, 945485893, 817844425, 119272434, 4974788, 23615608, 97089319, 501244016, 264778647, 670948064, 228885984, 246998077, 30547844, 797916102, 437897494, 36820317, 363919868, 646144563, 410048779, 544747996, 35817639, 339745977, 340343059, 846684965, 771156896, 799236193, 422367489, 589501820, 250473494, 244672617, 761243770, 598936384, 984336143, 229026114, 427624955, 577333087, 132527074, 64211422, 573409292, 737872451, 19067878, 995601894, 27978068, 727589896, 667677798, 214040047, 843946589, 190333685, 717831738, 853849883, 766848080, 357420453, 480641806, 967501968, 604015451, 197966015, 880087364, 987746799, 617535340, 972198720, 458777237, 291244023, 154664055, 266610801, 486986365, 762161457, 405010295, 389442622, 558617510, 878959207, 34166532, 669043402, 268218540, 805593184, 559862370, 390825717, 854245444, 728459560, 866813828, 570451641, 264709118, 489747448, 267405215, 208796642, 985241994, 228909623, 858134810, 674717596, 625012613, 109292814, 392520947, 331846475, 213530046, 423208974, 815926747, 690257453, 344287189, 562371575, 915849756, 435886049, 592734479, 253272469, 510727610, 241506503, 180759087, 136602966, 895591090, 887506948, 28366570, 194299504, 478962879, 371461351, 184710996, 2471966, 982559196, 437574298, 976058299, 852570548, 462319954, 422099021, 87965626, 546123154, 643938173, 993270830, 111956291, 81045852, 39346096, 584508169, 285247812, 953352480, 194877756, 748033066, 186783454, 13031222, 382293580, 513234231, 512618501, 375604804, 352659319, 100417427, 159931289, 598624520, 371749029, 358929540, 71306534, 512170517, 669243002, 924193039, 805502173, 3455425, 418854972, 236119865, 98651755, 917079543, 214862120, 40358841, 729997555, 337745979, 400626675, 463504489, 457104891, 176588390, 426134079, 46703545, 311481392, 49522983, 989940398, 453881786, 351123033, 260363528, 174136269, 550105115, 602132297, 818803195, 980351864, 96903381, 919762914, 665945213, 709211115, 411109062, 298775403, 768865984, 969255158, 307626756, 512219899, 503172791, 316672438, 245675970, 865729327, 385484114, 100870226, 906988941, 630660706, 220487572, 633257026, 651994573, 459901745, 490336326, 979315877, 701980243, 857827069, 731823475, 12636160, 988161462, 194944050, 498849504, 790196898, 663876868, 27215250, 232384027, 544025545, 960586084, 330444514, 946787214, 678964740, 183564301, 464988183, 982691855, 300878188, 478919702, 512189372, 531547829, 401232835, 741240480, 590276225, 452868629, 541636630, 402381503, 281855431, 986028601, 927503641, 348663166, 805197801, 235633843, 703117851, 157580387, 959143853, 998849401, 600267376, 674384962, 942278829, 95114837, 639733581, 291358432, 670745032, 126637908, 557152028, 711719167, 927754401, 361439347, 198919693, 298728034, 138222217, 172855043, 387437294, 478740019, 715520891, 419863903, 400524277, 420203380, 480089465, 436622053, 262404747, 416005291, 736454824, 257700758, 906381595, 504607397, 888155051, 243866824, 14773920, 698577366, 808121045, 383053625, 117198835, 552524858, 22855130, 598378711, 812194420, 946892186, 294077115, 656084826, 835310248, 72396368, 585842267, 365666616, 695332789, 497050625, 881386148, 84794409, 745976413, 386650559, 537856734, 608699887, 510083498, 662811706, 514519772, 720361766, 146706283, 983728168, 748731706, 785448761, 694990872, 431386963, 928419020, 607472263, 287856616, 193258690, 43147059, 199906049, 206131823, 974009866, 64091919, 841033508, 415490829, 215306772, 987198173, 851059222, 717490393, 667601139, 465727741, 645995594, 113180107, 378870758, 795022306, 452608629, 757512422, 15937112, 732722913, 478752431, 450352046, 442089705, 411449551, 531898028, 424959169, 554767864, 900120139, 806241671, 368609175, 186676329, 905557398, 363862051, 283953086, 344205204, 551741670, 36406590, 996951602, 685211970, 794044596, 113027336, 967554602, 816418239, 735697152, 454655769, 984827409, 86050289, 874307964, 493617366, 202747809, 872987298, 26270731, 251430191, 520993979, 897508892, 100307604, 961696624, 553476579, 776658041, 764687450, 960190593, 279402869, 567235617, 428631974, 814066981, 115341666, 21418216, 349412020, 792321570, 813400187, 991981699, 26055562, 42035330, 442157941, 246005046, 522950975, 105476225, 923273880, 950376002, 13438382, 721181335, 614360442, 528577759, 611649433, 601923364, 745404716, 608955077, 639848098, 496296827, 646168435, 92789522, 305283825, 361877526, 469298822, 926423657, 951168219, 541277856, 466701787, 368479364, 986762951, 695398742, 215738069, 688601945, 321664524, 446641430, 996786526, 49664041, 752855085, 590033632, 756322254, 694583971, 275305905, 806122705, 314365689, 873387456, 28135429, 640302832, 748410501, 240416576, 176598974, 350353729, 259448968, 337929302, 666031505, 748636201, 202717729, 953652672, 446309242, 596514968, 560585271, 936653490, 473596023, 32566738, 144696896, 888243352, 586985825, 100337319, 8219047, 861112587, 344565315, 3204157, 681129432, 724552717, 80494826, 36547220, 945122001, 551776899, 257703178, 874802974, 493399905, 2928898, 238733950, 967217848, 17363469, 552752860, 577971328, 187446848, 436443573, 730882414, 656354306, 103813236, 79481500, 126052999, 667791712, 947628974, 201190273, 454077012, 570968518, 718662114, 456002072, 357958051, 378232614, 608881172, 553695017, 239989085, 852622739, 732317022, 881560691, 26124802, 773469427, 284007720, 514883371, 432306728, 350672134, 943674649, 224549428, 21050835, 652233506, 444147118, 397544274, 73263833, 844758478, 645151923, 929906325, 150961026, 321593901, 925243803, 459606674, 276290890, 291003879, 936520681, 560799846, 308839716, 418897818, 428132084, 758412441, 507205410, 803633364, 762489509, 903488215, 28751068, 935148751, 869415498, 263799909, 446242688, 305699855, 424450148, 388340465, 839823456, 430039677, 218371076, 218743912, 643676207, 737138114, 892573119, 33023718, 668574519, 118070865, 685171299, 582086269, 276713026, 259847223, 883856157, 73728564, 879594718, 14704464, 731627954, 415057986, 860276138, 529891973, 625739041, 597654021, 911398430, 394989933, 253937305, 55984490, 97854406, 151957628, 349915196, 851305767, 794371225, 23486717, 799176045, 317703067, 929237136, 35200698, 687950391, 351562123, 364513082, 777107439, 837706064, 78259818, 560154346, 695399721, 28255771, 420273877, 545667561, 817515171, 853899036, 730119376, 295813260, 569394989, 908694373, 73745477, 963513613, 838138524, 856440569, 203454818, 611554818, 266644447, 531524608, 28909188, 607478116, 754907450, 940107272, 746433471, 460809168, 689983827, 929432705, 45503674, 77519458, 564215390, 805697747, 183302546, 935693442, 619917637, 534817073, 905627987, 40102837, 714040184, 857062837, 646702657, 933760056, 429232866, 455252507, 941319849, 261733610, 410861745, 391959058, 582875981, 701648616, 468703918, 112489271, 479508862, 791300969, 756672848, 221359948, 693687748, 511515709, 989927747, 134654354, 727594146, 717363361, 997861479, 767059468, 704883800, 49876500, 46350342, 443988673, 596301548, 221524035, 796691684, 802094359, 307698969, 97081103, 576146114, 962584514, 714547177, 347074992, 340883105, 740928432, 411262134, 48941995, 793665544, 539896248, 815857516, 54843327, 742603162, 177087073, 465893954, 563449580, 236244593, 97790893, 850444812, 15249137, 380362249, 840521832, 227262654, 565040177, 588682396, 739353733, 162447416, 165046552, 884740507, 910321862, 608192674, 35137453, 894195193, 805579015, 365685426, 797889244, 433386459, 128080568, 497576687, 870363835, 402472806, 306950571, 902859883, 368294756, 890057956, 251903002, 686391302, 588275667, 659719908, 997700425, 214269407, 850611043, 856305655, 766442511, 162669722, 627306806, 546808357, 540532039, 109008225, 106898364, 549917846, 35391222, 217685014, 760199593, 216590560, 345164550, 938538947, 663908410, 739079259, 927574360, 382408284, 127550326, 737170587, 113920704, 56514957, 564765877, 412330838, 514828133, 494113515, 75227310, 58779227, 117982367, 481534022, 949914, 445717250, 289264536, 199783878, 823973435, 197971014, 535375853, 740342294, 838199759, 162106843, 722612974, 106258445, 697668682, 782794247, 519222817, 300171354, 29510997, 673619272, 753273685, 954079371, 454281188, 658532133, 121886281, 816311049, 528859117, 153784652, 820440366, 211958929, 670004794, 161402763, 305176126, 713979999, 818720446, 767670386, 718009457, 571672329, 634770437, 53557938, 347113299, 458508330, 523876664, 789581784, 996962206, 855636802, 465503207, 753825333, 485431783, 605967465, 604435651, 10603916, 437695568, 393788845, 99338155, 297725277, 749498989, 349749511, 775973455, 416681553, 64578807, 8999456, 808097677, 388897438, 719885548, 108990627, 624987915, 535535933, 316680846, 813296706, 198849344, 947946304, 994173457, 677590298, 267932306, 464989141, 904213428, 626902443, 200970003, 412943260, 772137552, 552642468, 1048102, 161348391, 813727282, 198955235, 13405025, 204721581, 812840971, 296968818, 560864439, 380262777, 288128425, 418175662, 689223436, 332620935, 269896605, 484021953, 505419832, 548826848, 592974892, 81873113, 786247531, 164553113, 652981759, 331485347, 732487513, 804784708, 301233518, 985556892, 210525727, 5927474, 769388814, 325892179, 72290371, 741634624, 428963183, 530438771, 3088198, 178131311, 191393275, 458534038, 621239502, 740202220, 279557688, 50079953, 387265840, 868270172, 395617967, 564180935, 917630989, 787607404, 779026154, 810347755, 494231676, 666866362, 589911116, 74233432, 421535328, 39039953, 872099662, 702051717, 743007593, 219178278, 852452505, 616138287, 47863759, 642985785, 970671337, 697366824, 767041437, 130252251, 435428247, 99873188, 531733116, 449484305, 675874174, 579942500, 74848612, 528524197, 318998695, 928069243, 42091661, 933998573, 404317109, 283961432, 675316884, 852304479, 829634065, 773579344, 415800891, 597662360, 302127895, 543135978, 890182335, 464052683, 206328993, 379297634, 61512808, 357468370, 330506158, 91085195, 749377017, 499002442, 685034630, 967023522, 738145785, 165710049, 811895530, 255130945, 774109779, 764633260, 746854239, 773564348, 212527518, 220621816, 674406475, 747782388, 731831444, 371558079, 950458399, 610037602, 207359505, 486272874, 993152074, 552166082, 956006932, 440018570, 414469557, 995401764, 400615100, 255676742, 246633001, 468598847, 529540357, 229520735, 405826888, 53517886, 583835332, 620279927, 246263684, 502319428, 256311363, 758802463, 802076409, 49929265, 67794018, 865181447, 263586956, 750861391, 755738310, 156083623, 361629405, 813443175, 875669209, 317103845, 889439767, 432583828, 464571701, 816581913, 706991995, 604815817, 531024286, 246186654, 365729077, 724465095, 222598092, 449180384, 513936235, 507133585, 725036271, 94124005, 166434801, 467192920, 110511062, 663029207, 807164855, 958583195, 17200980, 194475494, 119179279, 165637979, 990144495, 514779454, 855986748, 760106233, 415935880, 66556780, 911431466, 369823516, 902525286, 906439544, 272980449, 588447716, 529430251, 566357323, 259444183, 459449044, 54028796, 388090348, 648564663, 517054578, 518687905, 935865214, 882375255, 79360793, 998247970, 655372724, 72804967, 985206559, 78813974, 43713894, 556495400, 27348170, 552237879, 485760533, 665777327, 902802600, 998944128, 818741832, 281468082, 319987398, 369844889, 246373607, 539039507, 12878703, 566359132, 241629000, 505205501, 974857565, 494170840, 359637601, 287948172, 13733365, 58273631, 895562134, 161703918, 490294251, 942635744, 134907616, 325339589, 951502027, 262996280, 735688184, 193894912, 780659013, 592088402, 299376110, 563783043, 550196306, 164183953, 35019700, 153817756, 771194998, 930870506, 756292746, 130005854, 561204753, 358682608, 554234270, 231335422, 666704247, 206049776, 521878239, 127535192, 269971236, 74565840, 713726398, 769444042, 846079060, 308917750, 12716331, 794902451, 159632362, 330267520, 334846086, 763723036, 485180805, 801095249, 797231966, 607400178, 843497831, 855842848, 220075921, 81020833, 702023856, 17708106, 980543129, 601914207, 350096903, 632385802, 986384156, 405741229, 786624722, 650306308, 567749650, 447618318, 543778032, 756850620, 204868509, 379960374, 215899945, 642948716, 490733084, 373672794, 187802220, 393439967, 908914985, 503893893, 723579337, 269513317, 900518647, 620506075, 998059242, 742961132, 490830714, 281112303, 683917349, 84515502, 367122570, 783128774, 120336959, 534318320, 394154988, 493358203, 327027937, 619576680, 135423610, 563743369, 729433160, 629822, 644566007, 174562931, 956680322, 412433287, 30659269, 401096833, 123699377, 323135384, 929784976, 550221059, 159304327, 870331871, 1530682, 583756291, 21917369, 607462535, 181757613, 363709110, 312649960, 803248931, 998042756, 199024219, 812762985, 293305766, 182353577, 372868339, 309310593, 500510835, 640500047, 736819150, 142952127, 232070662, 266288200, 218676135, 430993362, 199187823, 695304499, 577985388, 871915140, 844849105, 215806478, 352555080, 857693977, 167377047, 225851158, 584478170, 648141814, 212441499, 555048579, 863837818, 552127555, 595378795, 350770483, 51553556, 143693134, 28372093, 297820980, 95314215, 614364488, 969123149, 288690666, 739493938, 54586024, 404524005, 456304262, 886305603, 381001311, 827188365, 868461864, 980058142, 606502816, 30515367, 155532030, 583051428, 240461459, 723088270, 708474755, 60688789, 287279476, 599632183, 977099230, 14495013, 783998950, 470531331, 436470436, 670402974, 890027958, 432833231, 752209214, 631782786, 698275788, 603941751, 447742269, 672115921, 785211953, 946541678, 528703420, 235984979, 79950486, 868634726, 232002167, 655492144, 841175811, 680144135, 943477392, 887310660, 462309610, 936339820, 352452333, 132878926, 170777437, 729679687, 521748538, 514338796, 61484268, 92767189, 918090404, 934467715, 153216794, 264311915, 898428672, 691007294, 384143532, 338983282, 740711617, 259672783, 598006771, 667050790, 89567627, 475585788, 147293612, 436577422, 700474486, 822645976, 398695173, 488446709, 875698486, 41010204, 958633798, 303719437, 660742867, 410880541, 782372313, 545215403, 424117590, 325681343, 688754946, 298920079, 13805471, 149759102, 13763820, 218615125, 472424830, 398921782, 960811090, 198433036, 502895703, 560583824, 637568823, 596902581, 73376344, 735060527, 777534138, 830828766, 650053437, 626630826, 621053883, 861566328, 284639660, 210575701, 692070433, 143068600, 572610646, 263139511, 191001880, 86507768, 220432507, 492602256, 216728608, 497777754, 777322975, 219518821, 76779408, 999518537, 484613722, 733164049, 618998521, 141749689, 570565400, 452469657, 419954808, 918259331, 357753192, 899188011, 944361272, 19285905, 131926286, 145115598, 750893696, 498290354, 661519067, 740062325, 659244219, 338941020, 772271885, 509548285, 582270288, 95052959, 95982715, 755131186, 240913039, 767006177, 333187506, 17698424, 118406374, 62227012, 10258091, 454685271, 254947675, 704718606, 65732133, 832191909, 159048762, 95150529, 410341424, 857584078, 20368325, 371537252, 838707570, 657477246, 814338293, 970369753, 955114681, 831081186, 90700562, 31517990, 808381330, 387955301, 493263287, 864653394, 69994362, 502558526, 403452019, 438061701, 478398483, 229838158, 333063704, 136143763, 155458568, 703506690, 58638800, 447738544, 21018295, 389743997, 895930824, 749563332, 156409611, 735971146, 332317841, 25427011, 248621588, 279310012, 408958767, 133456212, 151420039, 246208145, 687575809, 30688863, 981846753, 43216340, 330542190, 80794048, 751250669, 603002353, 13056282, 612524073, 732755648, 354012348, 143903730, 601949098, 9589251, 900754501, 259905093, 485902323, 882047469, 272154825, 281607361, 625796190, 70599758, 17966816, 654082273, 487673017, 968297095, 967669886, 906558659, 290065819, 205519208, 804075425, 561537671, 436828350, 864096614, 455123907, 11909159, 702475498, 710541014, 224129070, 392608282, 559521553, 800912727, 982384712, 190090090, 42738691, 530469577, 168638678, 574211873, 616056305, 34270859, 937984677, 474065067, 403623160, 317872645, 779296706, 695206257, 664379453, 71412867, 816235327, 364606426, 266183632, 916193918, 16667583, 639424724, 176399337, 807480044, 970018288, 637647096, 834020708, 14019614, 649280162, 495459629, 692536283, 572570856, 597760516, 382674574, 420184941, 620258451, 430217, 723704620, 229378893, 885381145, 995022013, 77141666, 682912848, 213094044, 972044429, 284506900, 785347351, 365218547, 90893654, 360045633, 469814364, 624609727, 670808120, 386046823, 822628712, 189471237, 475691308, 968161815, 117658394, 713783650, 930454234, 552483669, 726421626, 590396500, 100997414, 614789886, 854263056, 118808675, 448018965, 577377732, 457941142, 880506503, 655779337, 569473220, 469990048, 646228396, 534537451, 9411599, 103132547, 360795552, 489768778, 718414961, 5754723, 900018561, 336321626, 908774205, 763523912, 956662134, 78165680, 723055919, 758442657, 416432360, 633370956, 674558077, 861771380, 173027820, 181759457, 502875614, 487520022, 977405785, 887768141, 449072258, 187657046, 404028364, 837672944, 624495681, 672552165, 97487483, 532823272, 793819269, 297679058, 391713571, 65754591, 681423132, 298154525, 583440630, 271544704, 320977572, 988330205, 758815343, 481023858, 154897272, 162714999, 959576594, 294778246, 319986058, 93748403, 564361348, 743622888, 513844589, 302840274, 173188263, 833069356, 390444918, 57912153, 653174993, 532855762, 807085608, 340703283, 859134400, 106018899, 269692352, 161256973, 484335943, 467990244, 806657625, 146379160, 45318774, 190600729, 764975157, 229177804, 822020396, 958343109, 783094632, 564599770, 93375977, 818534665, 216261843, 335693981, 667083353, 814329026, 933153818, 624206759, 574966007, 663604524, 567399996, 378849821, 112569525, 200580262, 945182607, 701804794, 938499128, 542899252, 931762968, 509739084, 682199178, 205704354, 871772048, 975198950, 225675511, 893112039, 960939302, 450842460, 988287823, 390140151, 995734977, 737690833, 858971816, 288659772, 499404373, 412054342, 313656107, 431678881, 921846496, 545035742, 116561356, 625986208, 985959789, 404115453, 62820313, 704124634, 41011170, 292152678, 187334265, 741842606, 732573805, 970810598, 873792787, 341624501, 316923557, 587633512, 942418888, 837903783, 442813356, 539307550, 7442149, 195408365, 416492766, 527414808, 326851078, 491604422, 21514939, 478344723, 233390764, 198202191, 332324626, 108882273, 921368797, 84100739, 292712818, 449177779, 482199321, 203798854, 370526631, 171462642, 741658757, 830305075, 68042875, 654055121, 675457110, 927560465, 45499810, 339116489, 135304834, 962977469, 321051603, 830583124, 330549269, 958815781, 394867000, 98846837, 741311318, 226988614, 120059101, 749113302, 658568596, 366496856, 889962580, 584951651, 377902437, 364652606, 688447722, 38135301, 350300153, 64348878, 226659404, 310017461, 57664275, 477649366, 903830154, 448845034, 510504877, 413481288, 312227854, 394259628, 865257422, 585762197, 552374156, 166492382, 104141472, 761824193, 732353658, 737325467, 322617224, 590458098, 381081869, 933675474, 84020601, 569222148, 900830757, 769533711, 496699226, 293675013, 24614661, 557436946, 972286557, 346087127, 417430945, 888039922, 94107641, 350937489, 494809982, 257199373, 554200783, 986400721, 313157421, 642537044, 511359785, 995290703, 348555602, 115474962, 976203687, 235260528, 147314152, 97011669, 428213767, 907462278, 348166173, 102815802, 564455070, 180137588, 237376922, 488288178, 171292894, 253596536, 21796264, 885629666, 649294787, 978225955, 821349608, 977596921, 646864926, 306650308, 281338228, 889767335, 574748284, 376872488, 936692912, 186149770, 440859092, 670197153, 164500993, 392351899, 517628584, 62734694, 214767353, 627507541, 704502090, 112421123, 633812390, 423297920, 337993440, 642224929, 107435554, 859501496, 664983713, 754787138, 231816111, 479950394, 966559689, 337833419, 343052312, 927104235, 28605341, 155845612, 863320431, 633795566, 885589084, 10309468, 517790636, 682179659, 198038584, 313578715, 53150565, 462355499, 721686429, 375492255, 963696470, 575750043, 172875552, 553958312, 12642800, 469281867, 754614894, 902566910, 857481109, 536153938, 646550005, 251599650, 550916335, 952570452, 334776772, 864383223, 248217282, 171072868, 809828681, 857812960, 113368414, 542165126, 111444145, 13066278, 788332753, 560964414, 418459666, 41576232, 156948689, 135698144, 488369341, 760406105, 733468163, 362956785, 649681943, 101443337, 875858754, 325737660, 682833665, 95640840, 40791796, 757258681, 66648822, 52300506, 893977666, 384072799, 644420619, 674520602, 265185812, 458604997, 232113300, 309008916, 549767948, 769501405, 611964671, 699284417, 838314591, 773579852, 982684601, 149115914, 65023882, 899133851, 188277779, 579352414, 459498593, 183920814, 525680618, 557273612, 483129336, 519525891, 714977075, 339689908, 666337379, 68327623, 758815284, 823970114, 444300748, 778841355, 835664149, 841097714, 676351828, 730663683, 128967490, 594137937, 630572559, 577400936, 648505887, 569912799, 655313166, 718028618, 132809230, 689255786, 925635120, 242609818, 466645468, 199398771, 301967383, 246206480, 986648155, 415761156, 767152262, 315532574, 952488157, 448505609, 877264347, 199833255, 835656666, 551627184, 684400342, 797860522, 352390055, 688793669, 367635230, 539698224, 835500262, 990066377, 395553876, 687904244, 752462486, 928141955, 98253188, 278228501, 799452353, 783811765, 869612284, 38356855, 913693722, 828380103, 985285568, 398255614, 303218305, 917911776, 425889998, 375850910, 687936362, 781171653, 489700245, 442654257, 555880837, 696839697, 981358021, 354583388, 628776238, 437427713, 265264705, 953861052, 344362229, 696190367, 935275859, 54528679, 563307595, 65099325, 630316498, 12089617, 927082010, 165566799, 740832393, 631163743, 997876158, 812975659, 101443192, 988971890, 463592939, 748009857, 42017961, 246907393, 456721493, 130606982, 253495516, 581934281, 902320601, 125911097, 636544367, 679259436, 349889948, 833525536, 418975494, 791515099, 329918403, 930057348, 966677441, 514270539, 583335570, 300969201, 987680338, 350219144, 567219402, 48672803, 240781658, 601670357, 251752050, 645940371, 550437061, 842821145, 617895233, 879096819, 785438541, 192814342, 116792593, 435564808, 539536288, 92257663, 293822331, 779909699, 687707060, 250592335, 736684773, 468403796, 561266215, 307399076, 183832645, 826876177, 533406082, 14197507, 886902131, 312446969, 706303231, 807448262, 847252530, 416745809, 390324624, 578511369, 826377627, 101146419, 601920874, 315658979, 815014033, 723601750, 838864410, 928684196, 6535703, 75111435, 528739675, 769858587, 668561251, 762749112, 401385206, 270714051, 550299676, 521668580, 268828083, 796644300, 635677428, 416474696, 736786037, 16857499, 823107613, 975836473, 45545457, 398716573, 474122509, 359559845, 493941019, 253666259, 581308384, 660352577, 220365532, 322462645, 643233118, 170112082, 103939724, 504878213, 148536378, 324382342, 297964180, 928071172, 421844040, 850115437, 843838273, 513973681, 328234619, 606036033, 615490908, 998975394, 642936879, 564745255, 149869766, 640673618, 222096928, 280147638, 619315878, 473931313, 874175561, 874916944, 178798023, 567306382, 840953534, 949331171, 842266689, 497931284, 56323067, 650278154, 806363095, 210680321, 552289041, 368016393, 122751186, 565233475, 327041815, 359638844, 89878384, 522758325, 912751684, 319027170, 66479784, 373317223, 3511935, 444852711, 454262336, 823806776, 266159293, 332547233, 633223620, 341201725, 966873560, 807995845, 631670093, 921326636, 263179379, 661618806, 731995330, 690833491, 659714130, 719760204, 803403886, 42023284, 182375867, 868540157, 347333745, 286043873, 110114797, 273386606, 411239735, 87410285, 941948355, 305616683, 326225238, 780947976, 233342879, 667088365, 587927081, 546099361, 169828895, 547475534, 207581899, 600344986, 97483639, 47071803, 591995687, 146724563, 232441652, 579839140, 886364629, 562081697, 601374338, 836633832, 630552700, 270881105, 593167746, 46768143, 323302337, 295770010, 897065470, 664523123, 446770682, 983911377, 63010808, 267042848, 547679912, 971353854, 306989269, 56588406, 46617623, 934178687, 540537333, 498056416, 243102062, 594538910, 782659670, 936078639, 450841167, 396955440, 921271358, 448094176, 797051021, 814480347, 363536269, 616790793, 754829537, 944900746, 369991151, 849141317, 300366909, 633634164, 921068847, 205056354, 604755522, 884872287, 347255334, 779398270, 988382178, 175811394, 168039821, 921092705, 577259359, 923576057, 823618138, 17376623, 112814871, 375711753, 440544628, 37961951, 354701358, 204577065, 837988764, 995361393, 916856574, 88308613, 947072131, 760956775, 875798582, 857459188, 86625146, 414179125, 797025006, 806612231, 651921465, 517210952, 128953148, 588418293, 95898175, 338363133, 116150567, 408061854, 16453948, 67065019, 225804948, 766112676, 699603382, 228769978, 815054486, 578187154, 987395379, 986062570, 9795337, 889445247, 89974477, 169948757, 162928987, 381193602, 719959882, 860370267, 748106312, 417668663, 250872918, 361427859, 992820021, 621426622, 218933896, 87611965, 405823411, 898799603, 620432356, 786501221, 537548440, 439389607, 17356814, 451426571, 117195605, 359239026, 241851759, 151304090, 945012917, 147630085, 97617376, 738374952, 461981938, 315551414, 237168771, 716360211, 358852423, 573662317, 860712098, 699368219, 117383103, 654229852, 216211810, 332213045, 925424936, 65319527, 727825307, 496950096, 103743212, 296500023, 63264726, 443850312, 129005059, 934331257, 877078529, 99515057, 115239396, 607170056, 832923725, 758337500, 471158187, 442356374, 822263554, 251268858, 657629559, 822395472, 352375568, 483859659, 786911081, 385025771, 377675974, 797447678, 719271847, 35510552, 474222959, 110251121, 609040516, 461902216, 177577513, 638469961, 216306733, 322770490, 318127269, 933876548, 138921140, 724379278, 304814376, 457544865, 581178715, 902332271, 274562251, 400389470, 459302846, 872093055, 433107251, 875138776, 428724604, 471644528, 168406985, 395627839, 529023773, 492201484, 3978266, 243595567, 613288453, 822244295, 494735491, 634682148, 533611182, 778103258, 793646726, 749193336, 720501748, 887653824, 37296353, 795733982, 257017482, 296581479, 567683156, 497269281, 283747942, 202046574, 708080645, 218578491, 341683674, 197013814, 300199952, 15233448, 808989733, 483599500, 305466110, 325328679, 198826996, 10783101, 739455963, 113403919, 777313835, 924207958, 525411585, 215220829, 622283724, 373378489, 598185386, 2856734, 235924034, 663204591, 946958286, 288777685, 63149293, 918737078, 45818698, 596610352, 636041206, 36696525, 436199983, 606316949, 648777002, 455869568, 964590844, 121361129, 8906889, 2807218, 258725484, 187090079, 620351666, 331844700, 422181164, 54784472, 462961229, 757335955, 660084246, 842197592, 568443055, 893657913, 697204788, 331336364, 188509034, 320471618, 812265493, 104776062, 280160670, 121501747, 995450759, 23066797, 868740743, 843960387, 762499536, 195239302, 491710849, 850915931, 285401007, 797786880, 382667533, 551000639, 770149674, 842857691, 446403064, 52597344, 692276281, 775340299, 610681705, 446208179, 940864108, 126692668, 156920176, 308791582, 434344174, 501011952, 844456914, 468967409, 201773898, 75839026, 17238289, 227326601, 598534793, 203932394, 906394860, 252927987, 936922683, 344242713, 568825410, 145908274, 580466386, 945598081, 546880513, 610282776, 118102882, 453693822, 82494528, 674001274, 338989315, 936793798, 364950222, 364043234, 122834771, 559131214, 72637243, 456647572, 781548699, 81108051, 773297573, 381258548, 213553316, 696960010, 44453744, 512017743, 47853760, 910158741, 280934499, 671630292, 403019417, 77182487, 412429694, 848523748, 45198482, 970698647, 966259809, 820222293, 696654775, 179224957, 400936974, 811707648, 305593409, 934233728, 418833243, 291169283, 990952554, 505675420, 793021378, 495773998, 773104829, 408441238, 55823649, 194463767, 734203381, 817323465, 365719102, 572087282, 966872864, 702917232, 667476883, 1412191, 690930708, 839442209, 368112020, 194426393, 600304383, 546550990, 979464511, 199023594, 512272561, 139623946, 242091821, 579517753, 88727211, 509254005, 620093702, 677460937, 949712411, 102463128, 45911417, 846001458, 900763551, 740819468, 179375563, 213386601, 620797778, 534471096, 740900412, 261861096, 317893311, 222591154, 774283246, 817145743, 71840589, 530940329, 821091678, 809080281, 221563065, 861803865, 613464391, 449591967, 445541097, 254121683, 605759768, 55388060, 680385190, 702926071, 34766898, 355266127, 437824, 923974372, 279675745, 687568976, 683544618, 936675547, 949212710, 133452768, 730518951, 225136987, 359472241, 501287859, 977837825, 751160691, 296336689, 365246037, 473182624, 584689387, 917963845, 885794891, 817454160, 837976091, 493612367, 903357196, 105661426, 924783496, 336038748, 996391373, 484243702, 691300764, 456980612, 199522853, 605610581, 832438423, 159914398, 942559344, 330106488, 75960325, 859485539, 889447618, 367905320, 266885447, 873355253, 445936835, 99630253, 89181206, 810856301, 795810860, 61271385, 540001526, 888497490, 779179020, 247424142, 987064974, 461146232, 185656468, 943218914, 462020552, 608010418, 499556174, 617604023, 592301225, 586990404, 942901194, 496302981, 439511357, 787536520, 184869300, 544034242, 149068196, 729450147, 596269017, 883289228, 901551219, 846336908, 740399885, 89500961, 103823796, 791549518, 973973177, 612196170, 546931186, 781484391, 992522469, 544341846, 495316214, 767211707, 67853799, 107131554, 884741488, 272050773, 768663719, 644460256, 925253371, 247863029, 122892994, 774054448, 533904953, 84471234, 872657046, 548414192, 508597936, 488182417, 165409362, 159396155, 231707339, 993756396, 175231816, 218792602, 21858962, 8967700, 818690299, 730557163, 446024973, 879852313, 151557792, 106936475, 387270065, 12407302, 566000596, 102609129, 83906378, 926844975, 513809772, 876741009, 886860087, 116071150, 197769444, 763757294, 39606578, 889148359, 633886248, 933076591, 196181647, 160245313, 375818083, 211779770, 816000604, 431405197, 912863564, 879692569, 914362605, 104799451, 166627673, 42349992, 786743081, 402641137, 762450859, 547055886, 581045484, 864251695, 64092826, 83442765, 570996095, 230039741, 39986777, 404207951, 27734644, 895392387, 692079197, 728405760, 791575567, 163418481, 590907358, 63797651, 374243607, 327551165, 739638885, 941595716, 902969366, 602999663, 302720278, 324170533, 796957447, 771425713, 977752055, 35915097, 781283197, 143611899, 426192075, 465107096, 838582709, 82893725, 971844017, 627397798, 55044539, 360962095, 849829765, 504426719, 843754405, 609917895, 512479579, 159666341, 316485897, 863942287, 328512892, 270649683, 428497356, 627117592, 796161214, 544074879, 76573029, 663182678, 974716787, 131568660, 700390475, 933824055, 65716524, 76549628, 735176998, 118208072, 5233419, 11151931, 365135650, 134174234, 311550607, 920690308, 244750774, 770101435, 499404310, 309412934, 79178716, 29870876, 884937711, 150135167, 869011938, 941606186, 466042785, 100735782, 680241632, 75164413, 711289479, 163825289, 282584954, 249098300, 51834444, 716093906, 86653207, 25123122, 197221733, 597054589, 232755036, 44792103, 207785148, 452056016, 666588809, 276539189, 847492245, 239292622, 295863094, 497153525, 922914541, 937410542, 178761551, 290300916, 14455121, 312890025, 712959375, 785636398, 367084183, 56676126, 908179235, 243187235, 134704131, 643880461, 773674654, 451114191, 453319756, 908024425, 105106171, 363993779, 802482170, 953405829, 275057132, 18548986, 324860524, 313396563, 456581555, 953416851, 373222491, 515873165, 296266741, 527181122, 126025571, 351161475, 788341235, 823491477, 968686636, 673769775, 381523837, 333563859, 795635196, 904052399, 736722853, 476710920, 118875545, 22952119, 483080461, 62866873, 466822217, 815795246, 956536033, 235592647, 669105880, 185922502, 438537221, 422674170, 317482454, 660153836, 419103796, 859656855, 980994824, 764467831, 741593774, 16745342, 558529444, 761764772, 34835474, 244945486, 775077993, 801083552, 854691923, 17770102, 681780751, 588830110, 440785810, 333101695, 164628867, 273064174, 935691447, 222794562, 929729336, 634767256, 730879721, 817117269, 322062995, 462247838, 823291168, 588322864, 767507731, 355805552, 587826766, 420778566, 232175031, 475267818, 629264790, 343369476, 476490014, 670277547, 687215719, 396362407, 91548078, 949464667, 227498543, 586921660, 368065209, 296624923, 160683805, 120150037, 507681008, 967307954, 153459764, 882450498, 539107987, 932795660, 609565587, 108383840, 448238224, 95022708, 514639049, 984952176, 118630809, 908643508, 849533922, 715129530, 986747414, 807509917, 697325056, 271680833, 290071687, 822638052, 573583711, 649449210, 650908699, 642216924, 913531970, 757931725, 800292053, 295353214, 983560332, 447472845, 903204686, 360985472, 256918164, 736560427, 921034243, 200235797, 665052742, 151551687, 703139444, 536349269, 28036084, 762861801, 851962386, 208511400, 831135269, 81270830, 659810227, 800854963, 867200975, 113341494, 682062342, 445384924, 696604263, 326108224, 790041624, 911224208, 856438702, 422073175, 937730451, 865138195, 581313415, 821996400, 322329216, 656605500, 967837748, 627303260, 555817231, 80980755, 819269359, 889835367, 624456805, 699720348, 247322051, 207511952, 275833480, 636480277, 848318283, 269797009, 122198719, 505859094, 131628343, 19265504, 733132249, 991249091, 812170061, 895009340, 685881241, 213523368, 415897363, 942599760, 102123268, 851585630, 716926724, 216476439, 759466886, 406517323, 204856328, 961416676, 447300163, 661801649, 323598532, 662808608, 866851265, 580259024, 857057608, 209562171, 742142778, 921589305, 915027317, 507210008, 998149791, 918911911, 737008633, 634285329, 428500361, 325770205, 401096168, 281281441, 479329947, 470355713, 912131021, 722383267, 330263098, 745651148, 859361802, 92529302, 238985913, 889100896, 722513724, 253641468, 299965681, 498662847, 487290079, 540400509, 689309414, 362852798, 961916607, 460115040, 577258542, 635874601, 382256406, 253162915, 867799803, 702859528, 515637664, 388212768, 398975521, 204415356, 762752062, 404190945, 446096666, 789524227, 59099115, 839704299, 499371039, 694344092, 142847931, 66277556, 683785680, 906747195, 17255193, 502743260, 957278577, 895201483, 507037933, 431587031, 49872645, 956404777, 161513998, 527448193, 820099864, 234253767, 454799938, 227526758, 440291255, 528163738, 768264930, 442524774, 858391075, 810062522, 919469443, 770792681, 134853149, 776478711, 504313905, 257879096, 162644015, 712187114, 478839370, 363350381, 412269800, 547820650, 397136853, 936833745, 237623799, 593902769, 802089207, 793882085, 992363773, 157477053, 686852842, 761493005, 958429371, 760575427, 204260503, 302616773, 671256597, 939231258, 640518098, 222416688, 768405362, 812783351, 600202010, 607581618, 257006053, 365726376, 926245388, 204141422, 621767352, 97313547, 402551056, 82130651, 229679603, 764157744, 854089516, 104200677, 756602456, 984922181, 380420308, 505487924, 447826705, 373485587, 110415075, 666867626, 780878441, 477334469, 894715321, 381631171, 137905810, 428018624, 628819919, 985282226, 274780594, 246714696, 664886750, 741799719, 608380182, 218481048, 797644514, 599201585, 615503871, 125009360, 279879491, 779174470, 19977430, 512560393, 702528078, 403648617, 930876297, 624696404, 695694134, 609029316, 137579281, 751844501, 804183481, 799814975, 388185905, 933955100, 990624386, 871864052, 285181531, 268619606, 928402889, 37180253, 809448780, 24947901, 603079991, 398813644, 387752451, 106021087, 888972867, 541335922, 259133330, 373875567, 345085857, 162023902, 140205229, 21239629, 745742508, 130345159, 690129144, 48784709, 761231915, 382384164, 345121570, 964891945, 977855273, 235553846, 251562391, 228887740, 953442437, 287357782, 937238323, 263247656, 85517507, 150143849, 630174830, 133992689, 911705356, 815079398, 255279742, 680501310, 651752652, 853717485, 901357950, 161418464, 95915093, 671231214, 231339710, 742188699, 44834015, 938869515, 304999332, 786062701, 38330751, 321345631, 762516074, 693151421, 425474569, 561309519, 650730690, 726883990, 13045303, 656594207, 220227962, 397286509, 554896382, 346779409, 529566015, 925110138, 786206953, 332394006, 560401946, 168604075, 425168360, 87496738, 641222016, 815741960, 725524170, 497428343, 963460103, 91028633, 910215416, 144551797, 828056934, 36581954, 912895109, 179989928, 828954969, 788509011, 537362847, 719165542, 390258558, 605504355, 541415306, 156226239, 908016911, 55512255, 934457787, 160976749, 773359968, 799577863, 842687823, 156474013, 868668199, 770244393, 412676495, 282392542, 447482263, 556496990, 687346898, 449911535, 653898196, 689535790, 587288523, 699613860, 237984561, 99558943, 329869654, 238632674, 681681313, 396614068, 941674450, 726358160, 765891519, 414694786, 19031705, 858631351, 807393795, 709618981, 683222192, 320805344, 855722640, 483017292, 922841779, 278726616, 882689882, 114064464, 347299784, 298845346, 828458633, 252409491, 309826728, 865641320, 723081113, 327088692, 451376511, 851648179, 39460281, 427331191, 663854921, 371495202, 77613739, 260078649, 87577273, 845090336, 738474731, 993867292, 173509328, 377340241, 69453442, 564998905, 242325693, 524545710, 758853865, 862648493, 41653423, 817788930, 634409881, 535787283, 837411106, 335301150, 484258464, 129650271, 937872544, 105556442, 383236756, 937994611, 940016215, 128562534, 331475176, 826948308, 150942328, 852060920, 10003293, 925828525, 791853070, 184842898, 153873167, 482533201, 732290867, 132527904, 792338956, 78649508, 135772009, 913428310, 198148674, 366985442, 247071999, 243913742, 315237675, 293682083, 29841006, 923119101, 259197694, 894884201, 863128774, 337160262, 405626618, 520735534, 365814699, 516456987, 703653696, 930913965, 231949164, 705611131, 25464482, 632148910, 539790326, 899507911, 45656858, 588079396, 63808055, 711399530, 257744587, 535242426, 272291832, 472400372, 556520313, 893775279, 885827767, 4870049, 39322415, 259369456, 724464884, 402422844, 859809556, 219032413, 354933947, 235893049, 54488951, 728363709, 769913368, 728403709, 459811713, 707222466, 464715763, 370513428, 406821088, 944004244, 538840296, 332049093, 902553817, 658555925, 616437257, 259457310, 27650951, 191057994, 858155505, 486286709, 664240757, 237629889, 423559740, 800753941, 16539190, 137786576, 445752269, 227318743, 949971549, 411503180, 984101305, 631248046, 803212385, 236954125, 826317355, 554438601, 325187317, 394329212, 276636570, 696702275, 106388317, 130165266, 420713372, 162373174, 27248540, 551706134, 774166890, 223199751, 968303930, 499273997, 595319328, 32553464, 983629281, 608270930, 115641316, 544349946, 446677581, 260569555, 674606355, 116212881, 711595691, 818092358, 237288819, 560402765, 776424324, 909169994, 269788184, 117142044, 926295801, 982481773, 223332285, 272885620, 20077238, 260905099, 780289572, 43853296, 723252136, 495407515, 65557156, 539142489, 204062040, 934819968, 130920309, 769431599, 572565532, 527260735, 988505053, 844121970, 432791935, 896076663, 970495913, 323509484, 747933495, 139590954, 675796587, 260849816, 213417719, 99793891, 919704606, 262544960, 71328725, 158958220, 91831833, 146016852, 207621913, 545417549, 237168835, 449597384, 633075469, 480383147, 7295173, 989885934, 869101349, 10500482, 789420944, 565191619, 616094641, 803364148, 71742573, 531192608, 555762263, 798876640, 585568712, 111738034, 253122385, 556869718, 289351834, 568541448, 433440027, 755179651, 408232434, 247629562, 143754546, 153127201, 156901137, 787966300, 690485995, 127990825, 818435796, 669952713, 985122027, 135315229, 124917373, 138840840, 691311343, 377010496, 414608141, 631028542, 207924330, 780674561, 261863200, 612574258, 988888343, 463805325, 743520923, 289937585, 11773984, 634618877, 272014981, 698915189, 863654967, 595928081, 32495010, 138800744, 398587519, 623366663, 834878690, 182471538, 303274060, 379600239, 732452467, 625868248, 972684142, 710406078, 581049653, 633054423, 804574123, 507093944, 712655021, 590589729, 622293920, 477686575, 484930536, 407203001, 860263086, 805825769, 87867543, 144373534, 591872920, 339472771, 190934084, 483243709, 401965556, 401328558, 51940813, 229804257, 427875052, 592301247, 559592111, 141003689, 33665881, 542595633, 890945060, 107598970, 116130486, 961585318, 737702959, 35910831, 864848800, 166628798, 153392950, 126587201, 520738710, 914218326, 98013769, 836930928, 700188347, 548560752, 394263839, 429304939, 339965283, 412605670, 264454927, 334537714, 462357289, 948737569, 314836043, 925967681, 680871278, 283248407, 451243810, 186124525, 649682017, 506352903, 832910630, 820322040, 369779213, 68363675, 406989859, 619913342, 251384832, 163307768, 522744822, 199935868, 559865566, 314936409, 195856370, 809023316, 929580840, 518508437, 664452890, 290683876, 378166473, 887558914, 458264966, 189337908, 751693124, 260414707, 312110725, 213197654, 508728760, 908504482, 248569505, 498930585, 408401834, 453696233, 221278409, 182917150, 97342540, 132697772, 805653410, 638379784, 241368098, 722572732, 110792839, 292415245, 897763521, 256012363, 481218043, 163707907, 980860710, 141013127, 752663799, 325844637, 346318063, 395753841, 866375396, 444447786, 17233007, 2105645, 426092943, 365686263, 992977505, 112648190, 527651470, 226547289, 254856105, 669360424, 811404545, 174223583, 932341269, 686641605, 359485584, 160125661, 300889006, 674698387, 101298933, 749169858, 641741781, 510178618, 793033167, 396161884, 495566705, 934452067, 218054217, 280686926, 800448135, 767367540, 728347385, 120076992, 629089455, 516948674, 349598384, 880828279, 527787500, 160050883, 654900180, 275535090, 569052771, 273593831, 22475410, 45189067, 626587842, 251090890, 102558603, 656815430, 593613234, 191141559, 126845617, 822093634, 872204143, 138688701, 95254528, 747946176, 71289893, 970482137, 17003999, 708491687, 820718268, 509291292, 308942114, 915462377, 265034190, 3325192, 400394725, 326887936, 640343829, 94568797, 386764442, 35974004, 318903272, 452620094, 779070114, 759188303, 860953934, 6773228, 745143312, 17714571, 236711340, 309595481, 24104769, 293023363, 277095026, 733115616, 330379408, 320241810, 704286824, 2929387, 44110033, 100039216, 224464930, 87778587, 684816488, 190498132, 996350296, 170516197, 430198657, 815670922, 659590939, 553978805, 342696091, 45605955, 981763043, 620850670, 354482904, 836438256, 879274366, 418287282, 517776853, 595658614, 714316118, 517395531, 221600075, 682816936, 153760047, 252601515, 643075364, 982058901, 887893382, 873153481, 885598323, 857559909, 838483456, 836767811, 571649592, 829531460, 354876579, 236915556, 202342280, 307463187, 540715639, 264624167, 626992372, 206853929, 564529580, 801957423, 529890120, 103279161, 925908326, 106002422, 563892621, 451546653, 640605427, 195383787, 356497348, 841643901, 244411466, 351269459, 869290103, 659293512, 875561516, 877214069, 598078695, 597788238, 995083991, 772285192, 231042397, 898276978, 718154029, 644585077, 773015846, 559812649, 216058844, 399191978, 507888298, 578065487, 812953185, 609206394, 502679105, 977545397, 868135747, 686225106, 427480133, 920046391, 103756546, 980117183, 765893717, 368029247, 27773694, 568728912, 579189561, 315107033, 927874153, 304764408, 575482672, 15617110, 5980372, 263056240, 530805909, 209830899, 841065257, 673158598, 955228016, 764691518, 846417871, 429745951, 654126969, 86664008, 574548593, 416009408, 27795022, 118272518, 644105994, 931521238, 456275234, 75899384, 193557308, 778420457, 689165766, 942155854, 447859650, 890301054, 577915859, 438089560, 183635620, 574722456, 845325911, 147662777, 603783982, 956134914, 891530022, 295450047, 411350110, 646949110, 463990574, 679885741, 45381683, 20661115, 253282356, 910468648, 114026297, 750161349, 604518899, 236894378, 304154224, 517476559, 442960075, 760661822, 49101356, 453082679, 222637801, 577184442, 942681960, 423093914, 524575798, 66406294, 428128768, 66780223, 852568340, 291700875, 832492448, 123484984, 794743954, 980928289, 375521515, 265258692, 656430813, 15028290, 90000328, 777125224, 271891290, 198278834, 638213831, 366488161, 729560118, 177658583, 560380748, 910412360, 690580998, 296757440, 765756970, 229674062, 993065491, 465104255, 606798582, 185746319, 846162746, 366223540, 730156215, 534782640, 555440918, 642214316, 625404957, 8276999, 245698867, 541430583, 245031958, 657851192, 677117308, 842633501, 59487354, 143688149, 895384769, 661578812, 411515394, 423714587, 77923856, 792951650, 534255440, 172983252, 160039771, 188856879, 64372028, 199638198, 894691198, 736773362, 372648998, 223403667, 485085317, 211944777, 554832273, 753065857, 906462502, 513820711, 537637048, 325609854, 318445437, 50368605, 50711134, 875504429, 571209028, 564557384, 790959589, 324317438, 18641472, 958412919, 564873529, 2252269, 171152602, 332486514, 861974017, 405702002, 56733736, 365788862, 437011405, 241894037, 493375642, 848817427, 351599741, 526684284, 386282502, 816618329, 474519907, 279001795, 85000623, 906626887, 950526466, 674547701, 473955870, 972788282, 755372768, 588853832, 637509877, 861592, 833564774, 596474260, 901748253, 14501539, 216282230, 971154789, 23755635, 242435571, 370634999, 606602193, 142367437, 274224850, 268865017, 643291846, 288516250, 974213917, 65116554, 773970964, 185715986, 717084507, 440744734, 727780059, 316321661, 879976946, 564501068, 731457918, 204227560, 67004761, 69805206, 994574899, 583423702, 317306557, 449386586, 277937831, 509393576, 837953521, 456003231, 367376397, 489369100, 173468485, 556858707, 704166405, 877818318, 651154449, 657833045, 503973455, 923984801, 548817832, 310280910, 621689759, 8137729, 807345069, 525580396, 416445075, 113741183, 597452935, 988577864, 444024866, 565669725, 644384067, 766602784, 651466568, 715862517, 156534750, 797277577, 259910059, 759070212, 936612718, 225509525, 824839051, 52498637, 735501346, 90311656, 246987625, 918692057, 722214920, 674057369, 868044017, 653593686, 919125602, 361960347, 146582545, 97365364, 336428671, 487459788, 760244561, 326601146, 47344543, 815505356, 970717165, 122548633, 93914036, 987311768, 145479951, 608103792, 384053346, 318202972, 27209517, 570600042, 560712363, 135981302, 192013259, 193141954, 147317579, 643271035, 333433867, 620003413, 846647576, 981897351, 837401803, 620494991, 787284302, 505822026, 514560888, 1821806, 271977650, 306684960, 136932422, 342138412, 543840161, 210408656, 992013784, 326711390, 768571227, 82028917, 167940358, 540061548, 209820562, 287902047, 999710296, 978591478, 962694957, 676133936, 264933834, 367470591, 643203411, 132451995, 171365593, 442308854, 270757467, 499294064, 959386524, 341793477, 199875524, 385770149, 199041906, 485059103, 862749994, 60646999, 437359556, 409183834, 366007344, 890579141, 146047815, 682949333, 347506225, 568529501, 787655933, 588008445, 238376677, 635850586, 62181093, 787528671, 371064831, 404877676, 933773876, 243709230, 317605114, 771699493, 497201554, 247651580, 100636089, 233275580, 662409208, 558381314, 898006823, 724868055, 70232050, 686022190, 638197634, 92797840, 814022754, 209097912, 912451203, 118911201, 768261550, 269872186, 616955236, 455019174, 406871355, 237053223, 289956365, 979121202, 440298868, 251220209, 756075944, 362345487, 328284664, 7162003, 177636958, 227646320, 387291673, 365388444, 674120056, 668911512, 207639997, 330962312, 416602802, 530868778, 949994672, 137605808, 547795151, 76839608, 916403776, 312185682, 687742349, 706890446, 802155033, 560064324, 598024044, 619973646, 970671570, 868279140, 912147326, 372987547, 298699453, 173401359, 321689191, 91789768, 212215955, 102356336, 661808690, 795026910, 537367856, 541120037, 405829478, 358667881, 656125462, 206905294, 483352065, 202304636, 454371712, 297359571, 124013855, 261141423, 178310019, 82252212, 434483400, 95270367, 995175028, 771632509, 619279370, 122791256, 196412392, 29834371, 140447596, 350826282, 79197194, 642561261, 648030740, 541177729, 446914918, 660790466, 704953913, 671369634, 515793718, 92419761, 941774852, 749238829, 472069351, 95065896, 759412792, 375574065, 339574676, 357571430, 72689256, 540044409, 626184039, 235660045, 852745653, 901884731, 22974673, 349440312, 536209213, 628910357, 54376137, 337758062, 595500095, 978171002, 339140151, 378212376, 912857047, 519393014, 280114364, 434045987, 751530876, 518243282, 682027000, 907153607, 531704457, 21587993, 849626515, 636314656, 916402213, 317147506, 662103302, 357290312, 65946550, 11233318, 578349888, 163210011, 377300585, 791968094, 168889513, 27726428, 46118124, 274133957, 745292128, 610601860, 297002275, 522933229, 923304623, 519323016, 316049735, 965238173, 202430773, 196661392, 355220140, 476692501, 868034019, 90588917, 785984344, 701431458, 947733453, 972104479, 538440082, 406243331, 523275546, 223116102, 730196050, 905447194, 655660102, 575901298, 871570100, 750455576, 792331297, 740801940, 906200735, 918434381, 170091764, 89215583, 833809127, 117070850, 51648198, 633876522, 445411572, 72136155, 513469653, 499389169, 633242521, 655942606, 365549785, 60487037, 330057305, 174689116, 849145240, 96533623, 749278605, 777582319, 860980524, 517760999, 17026340, 660558324, 325108476, 533839273, 695132353, 78127079, 328939731, 832221669, 723910405, 533058992, 481603640, 96065116, 793448858, 221143400, 496779522, 120334032, 493307184, 826002019, 655748044, 679447518, 304677678, 262342367, 816103460, 413985673, 212608243, 190585225, 894870071, 68898881, 149509937, 737436692, 81978265, 354799200, 627832767, 577022239, 737860482, 812283496, 174088487, 317010943, 345449137, 67336888, 110777919, 370042394, 38972372, 137392663, 543887481, 123896461, 867173825, 938776725, 92311852, 708576229, 231649291, 663573741, 101287292, 567502326, 860011853, 99643152, 44161651, 810660047, 62521305, 169554035, 794998903, 644478440, 585335529, 813985942, 618007946, 575778716, 725673846, 287824162, 677760717, 88527000, 724675733, 613880732, 852439936, 920379078, 139798806, 365285319, 324080123, 527918502, 88999212, 756091346, 881940662, 202350405, 103872479, 7147888, 928015531, 581450968, 447914977, 860286322, 604246213, 67595060, 808422878, 326976051, 277750346, 98903213, 292088139, 349212813, 655623588, 118094686, 767467067, 471928289, 720714047, 566730109, 699499609, 209406319, 51662575, 815765325, 339633468, 936069633, 445338441, 276618888, 945302354, 891772301, 622978520, 769425140, 58940181, 573555954, 981671483, 271743561, 875922640, 399156438, 600925094, 383704080, 563652187, 8249996, 603588985, 265934055, 794684241, 799191856, 717096532, 49892253, 878539250, 699926581, 88855125, 258993959, 6305548, 605650523, 661916677, 503100200, 955296498, 406640849, 747464217, 60505407, 699062378, 495355057, 834258057, 101707327, 925956524, 841444633, 79406896, 769710257, 339760974, 324328020, 932819585, 417277957, 493270931, 564522341, 607101745, 232727928, 76478342, 60438927, 113704695, 335631059, 573470156, 776001642, 835283131, 110627921, 199506612, 902937145, 320967206, 312742001, 432988013, 840446518, 313287911, 613112989, 564891928, 846558835, 649501160, 560925569, 39022690, 932599356, 662491188, 850826567, 624439899, 674965258, 643689409, 789626031, 699152199, 299793502, 866891710, 663158468, 736387700, 272370406, 182930863, 761633044, 941311690, 416151442, 222068288, 738399678, 575615548, 324308648, 14299180, 933774119, 878359557, 124092571, 120509981, 853112841, 405254444, 65246504, 646781691, 854286833, 905022023, 258571851, 773206784, 212683208, 310394939, 880178936, 892380689, 455290582, 476628057, 72045697, 927172906, 476743324, 391333543, 168142430, 776695504, 132276285, 659235631, 1660691, 135192494, 333543041, 864417493, 606763396, 685475429, 423218350, 368209821, 103828860, 321671631, 137979476, 316281973, 372404462, 221832205, 410181624, 804610874, 516785988, 389342175, 654755392, 523995878, 113811307, 574556074, 185091874, 402418757, 346783221, 397316426, 580581435, 550105066, 73756126, 587018875, 258017538, 966704560, 694265026, 679982379, 275466592, 151617780, 538309898, 586747368, 283940653, 89533331, 45885817, 591165142, 305500955, 870161754, 322934498, 239054962, 33513902, 60695302, 519553288, 358130973, 112748068, 740884935, 902953155, 91948747, 707461427, 476979330, 842230230, 321337851, 900640158, 502517278, 996080407, 422060503, 404898112, 365500870, 5535686, 751931467, 948848412, 653978539, 166691995, 497484700, 767224040, 491214105, 384824574, 238565678, 437579108, 967883024, 524514732, 988835501, 868128682, 735830551, 715761606, 286953963, 877379049, 548707652, 710083727, 162608999, 346902960, 417279210, 819391568, 451625698, 483741214, 19170629, 651575336, 715899471, 612274865, 510514369, 839676484, 200835607, 668253641, 841807491, 329295207, 714955169, 973514453, 263686954, 936723861, 134864630, 468250441, 470841290, 956683544, 102342139, 643485964, 535412987, 330812579, 157765249, 259098750, 669443979, 687958966, 708291141, 604412176, 590218838, 12525062, 652025347, 600046341, 329176886, 354953037, 203847451, 784952871, 335192310, 832399847, 408605999, 875678746, 736259856, 140320421, 200244811, 826590541, 670938128, 699200210, 343982539, 196486209, 581192782, 812644140, 875011954, 533700755, 959853373, 686355120, 356074104, 622394669, 165603916, 578265424, 406088363, 270493902, 408333238, 138259384, 776068613, 186541338, 795697167, 495864294, 835048399, 25270480, 16728807, 3542983, 917503867, 589749844, 241593727, 947896329, 29607492, 849438666, 875178093, 444204823, 738146435, 743104750, 147644700, 411039093, 499510609, 521734977, 133120889, 726799633, 571614153, 436293035, 725000654, 863870009, 800010295, 654696624, 803504927, 102508526, 684533506, 381400722, 859894188, 247957929, 489538323, 366927654, 961389106, 731098552, 117945763, 914565853, 284593830, 319095613, 273371762, 124793234, 590183089, 687287757, 998696237, 618878156, 984149146, 67976113, 792766731, 146733858, 814478380, 125807308, 917451246, 618310510, 738697137, 131901073, 164254206, 776107800, 774708417, 652939718, 852689728, 650598172, 757122686, 36665763, 851979581, 785750694, 674531303, 52565541, 565124311, 741232755, 725858393, 687824099, 878601085, 631137259, 546792812, 227714474, 540825143, 341399191, 261342176, 60860319, 223437763, 428270651, 478271050, 720003651, 116140079, 746833466, 504479778, 824883970, 93252012, 782758508, 67472002, 810984473, 904764835, 814297003, 277780577, 532794311, 978784004, 76519236, 792751061, 412606098, 88085456, 225708749, 518023448, 709147244, 48970907, 402696424, 29662307, 714041430, 661309800, 261979299, 560539701, 886901872, 340741900, 260136327, 89740707, 51946123, 803956810, 753581110, 748144783, 525948783, 881918154, 148420125, 239891659, 896814208, 522613695, 32629159, 779167631, 825791865, 580786658, 584652801, 165951626, 184242026, 695883387, 79479869, 916696287, 920248272, 405060823, 218733257, 901533592, 701165441, 988013558, 488214769, 659025294, 955273087, 734035369, 482529496, 708312846, 82590689, 416569634, 532144491, 141709787, 457357157, 259372602, 765336675, 904126400, 139892099, 299791216, 581301488, 321436696, 489508663, 956339656, 243771600, 807978899, 909941990, 438098549, 203076013, 195128450, 677691312, 991946975, 36143080, 204712120, 723331028, 905605967, 141204344, 247599990, 407953977, 498420061, 244012781, 129697233, 420765310, 436833627, 936194687, 486762705, 393699712, 807002269, 627209985, 506943161, 445352646, 457846530, 2736100, 978664343, 792285921, 398018394, 569411309, 776705632, 893776722, 248901464, 891853675, 295586751, 124151353, 562251544, 451577779, 131852516, 912461818, 268057502, 792587385, 622885222, 961026341, 258670710, 755197155, 308816902, 570754213, 224424390, 918703980, 661840725, 651652864, 852407466, 138840618, 956611839, 97540371, 717550681, 78780525, 280709315, 722621730, 517294797, 338453170, 764590527, 508108235, 34249587, 617710952, 784471734, 843744397, 872877562, 929333059, 881890140, 248544883, 156318150, 353173230, 191245764, 916757863, 673494228, 571756461, 515378021, 584010073, 707817062, 601166474, 1561834, 772388198, 832519155, 445694857, 221534863, 666378018, 306855398, 474283765, 475035760, 542875177, 853231185, 690451545, 4458614, 640238276, 411595329, 745678586, 708093763, 819594145, 932053203, 385698748, 300710100, 310253510, 289092200, 612136228, 348678200, 749278433, 308541833, 338020365, 718669511, 46811924, 257801158, 629168951, 69888617, 646990019, 204126598, 871877721, 574904300, 750546803, 253425792, 48176646, 114596757, 913036836, 294511390, 864443525, 680072677, 818081282, 105430523, 329540951, 764366340, 113559013, 597794360, 410162560, 201107054, 879542732, 716232817, 22436955, 941897147, 590815326, 706530461, 281818967, 160317731, 187638948, 687615448, 663030600, 596457904, 110205612, 337111917, 190018659, 785201344, 102230950, 864488265, 229765450, 731915661, 64285948, 781701385, 91133116, 265752236, 450527867, 640908235, 221854303, 669723940, 6483316, 443429555, 60634241, 164364562, 132139249, 360423136, 530081172, 624877738, 737669957, 868416952, 61569597, 761514663, 996511706, 756079110, 950620897, 181849571, 956492415, 274471083, 36545375, 752441733, 511494577, 473712667, 326277127, 732438079, 247894079, 456525970, 800716098, 135593065, 535781951, 120266337, 623439580, 520111970, 477758236, 693024014, 894474188, 168388962, 978024688, 337702873, 262075767, 523634696, 474780829, 752058232, 632911431, 653102949, 294256785, 183969713, 385309445, 743462612, 241430795, 171185087, 431274935, 326719437, 632047571, 113899787, 672500809, 324127290, 677934332, 138145, 511014401, 722048829, 688632372, 804250195, 131664137, 720530631, 536619756, 463726440, 421173166, 102820251, 361633322, 372732383, 436067034, 114066025, 946195539, 70282456, 664858958, 597471141, 608059243, 323356278, 89985184, 933000169, 332668858, 64319580, 870453853, 307345885, 162247309, 340507795, 915922572, 377767791, 858284924, 169746134, 322959139, 503597143, 338316522, 689972756, 363732903, 483040850, 175520171, 77825594, 457260845, 934452967, 242305795, 347660426, 354186087, 70887819, 700271049, 237314403, 402573302, 641218542, 996544578, 467448739, 41705925, 512163137, 884036825, 423849729, 156442430, 730940501, 547360188, 777393233, 295235074, 342140245, 486939880, 990311551, 524123563, 12507612, 473173398, 771285009, 869707132, 775198200, 727986712, 35346947, 833445560, 602869394, 265728613, 701602572, 502120956, 178486159, 511557858, 221245662, 638813492, 571807018, 846522812, 799011176, 244665606, 973718101, 730120647, 453501184, 654592913, 773803275, 992516541, 296345205, 521841892, 281084027, 629433584, 340478675, 259561268, 989579840, 392931953, 454946589, 171434576, 552040070, 665787723, 990037513, 910350674, 949312766, 791845959, 489215192, 888847429, 223037973, 440534778, 444860674, 798605886, 384037204, 337425375, 615092430, 153127370, 600165187, 276789982, 431401848, 897355133, 658741456, 442746334, 293271422, 589220875, 359438729, 820668272, 858749573, 348548530, 593141541, 498205883, 905904784, 365480910, 968864399, 379694539, 880973832, 33827288, 33559329, 876820086, 755812006, 721099564, 26443199, 519532710, 762175970, 295252429, 524254248, 511406147, 913564643, 397611965, 269305284, 875007974, 570603921, 62233689, 275779472, 961758665, 831875724, 51889693, 173048031, 387630133, 422349260, 187763246, 303676060, 466257137, 922581953, 532725408, 263793576, 626659290, 105190847, 256745276, 378980506, 6347156, 324086627, 513250380, 587852461, 907531969, 867365379, 959425269, 737904321, 544343276, 917358002, 988356456, 79275853, 76770294, 532470166, 743521212, 943454472, 125441412, 431076281, 407377714, 492954771, 843102000, 640971420, 325387977, 888604364, 615997657, 34291435, 533236330, 80819995, 753023782, 912189995, 541175269, 151754262, 96427025, 728611375, 895053839, 748582547, 71919374, 372076022, 405114210, 43887428, 242899707, 887024772, 563996213, 158852893, 418349105, 533735719, 59445805, 527373799, 663759584, 763866410, 392538047, 640908369, 147320923, 444792578, 860036222, 106303011, 210898262, 723427807, 347137869, 624182864, 9652775, 329422022, 910491605, 787808461, 570440450, 898659991, 162878952, 268976196, 268090808, 449699096, 869389157, 875327979, 461686957, 997286400, 681360029, 624959963, 350418450, 702442286, 418870013, 876988295, 537512349, 784413145, 957703809, 606054451, 970273117, 731074824, 311960110, 551759776, 709571387, 905665792, 488851330, 106880356, 612384418, 591079437, 10020007, 159692886, 557823756, 341422799, 454223178, 487565143, 364561478, 271583069, 407010306, 133065881, 770317891, 434488259, 782639801, 561467622, 529807007, 914426973, 220051677, 425994194, 885360454, 22811002, 408096257, 831054822, 68200500, 141166928, 10709569, 202562255, 519905026, 688945192, 804184329, 184218580, 233920201, 537652725, 713415214, 494021949, 649777259, 828187740, 530092386, 47901878, 691436995, 213485665, 605558056, 230088945, 118299821, 744594082, 982322959, 759759296, 685523078, 484335543, 263076650, 254395399, 579331518, 705338661, 18459473, 762573986, 477551280, 511503175, 542139582, 648292357, 461007934, 763842583, 347220569, 3564674, 808378463, 912550086, 544428471, 598330098, 773540462, 43582943, 625009750, 473481907, 39769223, 402985304, 515875734, 983148542, 497487484, 82225021, 753915624, 143039101, 870688496, 204178303, 943612831, 998074457, 107077833, 84673658, 451419090, 66213349, 213701760, 442810049, 272848490, 492052934, 905119303, 394676650, 390774656, 483664772, 529424987, 882838538, 367629784, 151536927, 516658476, 977502641, 793047961, 114586086, 98669845, 464828063, 193127734, 851945178, 933198837, 546877076, 26633656, 295754720, 514025900, 89880701, 684523995, 339329253, 295767827, 433367074, 613651563, 580102702, 109424756, 721342651, 290952929, 574041178, 154577334, 129808435, 716090124, 898768967, 674423554, 719497348, 19246208, 421641833, 26772714, 200780604, 758333230, 294351100, 883675087, 976555198, 297658134, 915376239, 765099167, 572595276, 167474036, 858119367, 454401184, 943995546, 808193199, 259475591, 32600443, 590079882, 701276662, 41022351, 579306069, 904787662, 463436225, 140347591, 183125249, 899007093, 395260358, 222183093, 55452492, 813363279, 61081776, 759080201, 763424226, 275285936, 207711574, 818752723, 231277172, 13373331, 56179912, 136319728, 518336843, 590320015, 403437021, 78940624, 191179454, 405033425, 488286155, 139315447, 641232292, 220596045, 220106009, 471430685, 439027307, 249899543, 910260855, 364926186, 994579482, 704243790, 763444443, 9700263, 469789722, 29053198, 413802891, 204546081, 889812217, 728411243, 173794494, 519955572, 704221020, 184340119, 590196841, 947640658, 936025337, 78125058, 291595264, 548647211, 502954398, 306704710, 572904361, 521594859, 447623689, 304602016, 13051706, 391691255, 346154342, 943169948, 596419708, 397015916, 422753555, 395877473, 716677364, 117790402, 516501853, 831320349, 235121973, 58012494, 890328184, 174750143, 682055630, 434930600, 700013125, 424830951, 845428620, 449652421, 415292910, 148626172, 360727851, 703437040, 739711758, 496427560, 738686665, 889237179, 660971676, 760651284, 471341857, 489104276, 290369496, 164933815, 121643440, 765520684, 333964830, 966614157, 811877503, 929366863, 62810929, 368159974, 834492631, 555386714, 351113092, 932811793, 972353919, 720590500, 527538503, 683790128, 214697006, 154430808, 313581461, 386843695, 790292550, 959940200, 511815888, 247410563, 242715925, 182372722, 998927945, 346572902, 480430887, 653287452, 894428463, 85285340, 813209607, 776505487, 650246801, 130714856, 658790537, 663994563, 483197706, 75543058, 994293091, 611388761, 416673040, 104080768, 740771548, 102652064, 940050547, 706177364, 529114811, 408343613, 362960372, 250552917, 556956188, 773555775, 460704506, 6407027, 251214177, 891772438, 519343633, 910581483, 43026318, 894776829, 379751227, 974793501, 884804045, 734054238, 28383983, 939771354, 989132362, 742282999, 308902347, 153503831, 32102025, 596687103, 88404659, 306751740, 212844343, 845325830, 522510191, 800647612, 681007524, 264822147, 484163532, 109199396, 116124926, 625227854, 931551851, 808137053, 641006024, 921899582, 968962168, 427458532, 936914840, 173729271, 634152973, 410408525, 757216825, 984747090, 413625212, 510789629, 603151816, 919971121, 344157624, 335158708, 986673351, 527867743, 700107082, 535596142, 110836417, 267228090, 565229923, 40687025, 538103915, 816035306, 448200968, 163980952, 89193680, 921385082, 595362825, 287187620, 798495843, 489307117, 714494809, 917303450, 558710860, 673012640, 345579877, 654812344, 984551703, 149505044, 615162666, 941703950, 780544321, 201348481, 804506090, 883464479, 314933342, 627936096, 672952267, 789339530, 888781889, 247268791, 499706329, 768041020, 20215919, 253141465, 162882232, 512856810, 527963015, 137033393, 279398135, 538296929, 286728564, 995977216, 188788925, 433815111, 919660176, 197822900, 764272553, 749595701, 148318783, 295493353, 848238545, 38829597, 74150916, 877586986, 414425990, 55519318, 963833045, 402238245, 537853309, 400110852, 769847212, 57223655, 356771224, 495922509, 86172799, 906696167, 24475545, 66567021, 335560142, 127134658, 95205132, 957083481, 582476730, 551360725, 443614460, 805980803, 677735142, 703015294, 100212600, 645038063, 860827467, 215395267, 481128436, 626774278, 802949620, 373195846, 719831573, 755806410, 539157670, 184786276, 673647703, 22281943, 226276161, 814919089, 678933494, 269308281, 949935064, 710319123, 974909383, 934083537, 354650632, 179545293, 339519569, 238776736, 666339713, 89548253, 338520980, 577993804, 632754197, 385944336, 134491381, 811468214, 732123800, 299686331, 451574499, 804871435, 588156519, 373728604, 538717383, 576397829, 304946573, 453295690, 381544407, 125350419, 399571512, 702630901, 318630855, 651602950, 270811948, 839322486, 666045334, 709653830, 509532809, 613641554, 669300751, 236667899, 740644641, 649869769, 548753811, 391306783, 752508496, 928429390, 802537227, 624395075, 974703729, 959998189, 731868494, 49167350, 701936928, 745050719, 891670277, 311977112, 878305922, 980231276, 876744566, 7289449, 327700410, 252237090, 520806456, 215041016, 695629105, 877372835, 902163432, 647338455, 500077322, 927549207, 2359048, 389529886, 410908744, 973982883, 951166245, 245797115, 550849982, 497640690, 266352193, 407495107, 161338469, 882577414, 355637977, 420272005, 221837685, 177564360, 774432181, 695243929, 386377197, 386203719, 636578948, 62948625, 587440028, 687106019, 654706809, 946529019, 78995154, 26203674, 674436383, 819827463, 249748456, 404408914, 327088867, 845708280, 233357690, 784275856, 900015410, 528783923, 210275217, 357350317, 456173713, 414841663, 210158051, 602950508, 685957249, 387924378, 486428542, 277456019, 168526776, 150569855, 923259352, 223848621, 406489191, 963012756, 196027969, 353942164, 58990168, 928709490, 232266708, 191768535, 659535917, 432845083, 172513289, 526541315, 135078467, 904898709, 815541376, 152314230, 973590310, 312192598, 221571827, 631653052, 662805632, 424343372, 864725921, 307026683, 763135946, 749419211, 5345470, 315573570, 712027350, 36210652, 783234809, 742221784, 936980351, 114815016, 468543229, 391489917, 79795198, 948388959, 345907238, 677867861, 335010306, 31105341, 909173706, 904201563, 213806860, 803628678, 655777775, 470576094, 247365135, 727855014, 617835592, 500097249, 136571637, 694687767, 801031800, 60711766, 613802332, 793011519, 925780243, 242304862, 471902508, 110202982, 826238418, 174773870, 897372465, 238708073, 415821866, 155976922, 600354863, 340941852, 761188956, 964151125, 207699658, 285999462, 417793361, 842982771, 466049831, 973425874, 234800447, 873436863, 538144330, 282138918, 921523809, 889219190, 905201854, 516241796, 961938724, 713362339, 836123918, 906569178, 208456058, 677564357, 185994071, 722236035, 698014587, 224147777, 976847473, 385135093, 597886742, 128159082, 613938237, 305888262, 910663643, 151588061, 505408779, 433124830, 848975079, 618956524, 602086044, 344109151, 698307056, 292862150, 213529841, 67050221, 873688399, 224852835, 59334136, 73549060, 115471741, 435592358, 116354669, 700965828, 182307880, 474404006, 727048699, 706574493, 978169876, 578025784, 533778441, 853607546, 427038672, 907121791, 452770648, 559067851, 29556983, 588332803, 439261548, 527672958, 340907675, 878918065, 144775781, 135097511, 833029823, 142180076, 781037482, 423699560, 788988345, 98673751, 511267321, 144412791, 647860213, 993004553, 137736872, 828598136, 211807640, 366116871, 615706166, 204113500, 348167295, 476742520, 87530892, 168469180, 739330126, 125834481, 464512201, 17967555, 41046943, 903973105, 79453975, 402326197, 674054020, 626034261, 809195061, 718407907, 451981733, 336503625, 16182622, 315351635, 754136045, 858615191, 898396563, 742576368, 651157887, 496996903, 529868292, 960099282, 20150981, 421084450, 651588795, 901003273, 955406631, 634468757, 212862670, 237863992, 994749028, 655750146, 263557465, 759646715, 407224295, 413804370, 884236660, 596214627, 91689609, 542168995, 481875314, 372241971, 254209364, 783860766, 222989076, 450914445, 546741198, 304845829, 998909898, 456654815, 188891120, 412280822, 460606113, 269887000, 456574811, 201250006, 216178341, 805304368, 801939211, 38709053, 326601191, 336250346, 365870344, 385388885, 378182001, 222336827, 225244928, 234498907, 641543815, 47190874, 196032154, 596319519, 40080518, 835538851, 130087285, 475332688, 965953160, 203207849, 968866722, 403748097, 454448095, 697531232, 539165676, 536142744, 842826167, 112518948, 343279662, 30371999, 21515555, 963972630, 621716189, 708829695, 192286232, 339765966, 321424627, 888872432, 954078049, 348800342, 16433791, 296434987, 883874904, 633255506, 499147540, 928600918, 899702109, 380787796, 777147949, 237943528, 191601486, 230402122, 40671452, 924429152, 357456162, 677294944, 19326591, 529289879, 198682369, 164036242, 235442, 817715698, 76691110, 508105318, 507018633, 481134189, 691403554, 880333949, 248859452, 309357595, 832775567, 853291835, 607505871, 569619649, 30966555, 378573043, 634481712, 502586920, 630392538, 480101144, 624883348, 128396040, 963346751, 558881465, 688532596, 134213685, 913084148, 963555470, 596870910, 719015940, 803225017, 721779089, 777671759, 180307969, 713361759, 77147478, 404329718, 941434588, 286138650, 692457232, 1967187, 917297380, 689116230, 767429653, 952322991, 171147938, 946619219, 199402444, 378892372, 886916983, 880638662, 348389899, 238275513, 208205095, 881730055, 969823821, 345590629, 321429606, 503701164, 845267367, 550320345, 862896558, 215240293, 736856866, 407036009, 995015329, 869112440, 448455676, 376839468, 74633768, 762607102, 801478745, 331223003, 27636158, 110873694, 475381659, 642691022, 304021394, 62628891, 254604407, 688586897, 776375198, 771612596, 743023092, 833330554, 340636670, 854210974, 995055617, 557703459, 403072596, 411212818, 852583762, 154730709, 363085356, 68542167, 853875311, 606282552, 590448687, 718167838, 628522857, 837400750, 864044387, 213205297, 523997384, 731403199, 658957682, 169047195, 105907197, 479185119, 442522350, 914631903, 51150878, 72114266, 378710915, 193506669, 420251011, 426295333, 422360700, 52827177, 650252150, 623817042, 315928731, 384115413, 864059360, 127461481, 664995421, 393786355, 782232714, 790227505, 470629211, 214978517, 689904522, 970516057, 198090445, 251424336, 279547766, 165185816, 223327429, 611002370, 11121375, 626444801, 714539053, 549561977, 499108071, 495530731, 187419668, 474897948, 821460936, 185246432, 187110460, 432537129, 553524848, 17826500, 372446681, 847982436, 898380956, 616364211, 419834901, 942287161, 709982842, 911271820, 222414855, 949394413, 339980219, 692481903, 731992194, 990558873, 109473720, 471087183, 89235536, 966244168, 889686661, 412096002, 945219183, 702973537, 353677605, 649861337, 130211698, 255060560, 901614768, 564459986, 610913341, 659747726, 666679966, 143492692, 192466853, 770731297, 53203778, 244722923, 836036517, 717469618, 214837887, 588197707, 322770250, 411352330, 266596343, 854466256, 398217550, 413853788, 733080393, 404757517, 55920740, 835951664, 179378407, 981971067, 685479574, 53098284, 202111776, 84049151, 916461403, 51097607, 687882704, 51835517, 820728354, 32394072, 378683971, 496319856, 841223625, 990246739, 442240152, 601220965, 619130783, 925905343, 121685609, 659249226, 404079278, 43134989, 811093856, 594003383, 759059103, 993914116, 420016096, 45199314, 507050473, 29851288, 104981688, 961120367, 679673340, 283992916, 135066968, 693123630, 934273222, 971995252, 372042126, 873256838, 979587268, 935799891, 936235782, 19768028, 363468108, 717087698, 527899639, 188753041, 871865806, 136720173, 587167538, 551584705, 759306625, 71997715, 677815860, 520957723, 73806830, 565528785, 914964940, 555432182, 895578895, 461219584, 726964950, 585875986, 361111497, 168698403, 496330063, 714736579, 218408592, 379979619, 12663334, 98860036, 170423158, 390273836, 872801054, 53327987, 572466017, 55307026, 148170739, 469450600, 285000703, 182141732, 11412673, 301780655, 991824848, 279002390, 606585869, 317696101, 891363685, 612282511, 752942925, 182091088, 263145068, 649361592, 871078866, 801954894, 294229622, 72486627, 309516228, 694245264, 760870062, 809507121, 729597674, 815594947, 640422384, 436483666, 891086585, 724496623, 387562992, 921768986, 166480232, 389459517, 237236927, 727142529, 52084050, 696833911, 441598104, 549072352, 263221197, 955598446, 882213710, 229089097, 576770437, 239977696, 999879523, 805721963, 409004800, 326163162, 38820383, 973840425, 135839154, 854727410, 919040116, 860627645, 603964195, 432161211, 937164618, 275185393, 630841755, 43596847, 480979498, 173642189, 55651013, 743973105, 278846720, 436487064, 886058053, 4229634, 494458796, 991443131, 670359884, 788073234, 240380569, 528380041, 454224517, 161914816, 241808302, 75651050, 819527866, 707942739, 575313819, 37311372, 423346320, 782796355, 921590842, 39402412, 671048455, 373248453, 137968838, 436959094, 460081451, 773957093, 423261960, 290216629, 975448752, 128128952, 45216981, 335635152, 122986230, 520609386, 3790868, 302830096, 212303833, 782536672, 874938551, 578380774, 292089118, 531784165, 4486727, 9720841, 215393659, 925177806, 936104587, 878590412, 392961059, 781417449, 464079545, 312418812, 663436558, 528941619, 644002951, 959154149, 223076702, 542687413, 91546838, 322102555, 623617804, 763502479, 918147494, 56189381, 883713686, 841993526, 369107614, 408141171, 749842894, 485192224, 268079006, 82229533, 145380412, 252463334, 954124908, 367529719, 835715944, 919076631, 644598900, 15734106, 715580069, 396420718, 499338234, 640466244, 514303229, 81818204, 342916705, 139867405, 606955596, 851708998, 694438440, 798331810, 787229798, 983053750, 488658467, 235004543, 618585659, 161862668, 337838886, 608650198, 610826359, 385918935, 520312637, 253428366, 958991519, 979389749, 922732508, 896317019, 169032142, 131395806, 884377726, 359870174, 849119573, 148440990, 882763067, 326557542, 647649439, 267680854, 990663970, 91855737, 174302753, 803592865, 238949226, 523160764, 83169638, 528865223, 383022357, 170225110, 622447692, 740659390, 888724578, 70274843, 38012385, 957137561, 347864165, 782510412, 646797808, 721045808, 5007416, 826713860, 578323628, 749283364, 255341928, 690233578, 883245054, 487102503, 929820213, 435048068, 135227317, 529653065, 137883136, 599125536, 324092985, 347582355, 382561803, 712301569, 597333667, 519863800, 553298193, 989491880, 302766895, 296112753, 637199307, 999587755, 667906613, 274758004, 791877380, 568135864, 717989499, 927420618, 165082599, 507405598, 776570312, 261323518, 368502695, 914641281, 46661104, 325524490, 135236469, 291700790, 828501586, 847108386, 868421591, 420970647, 76456432, 926919090, 774232425, 755906030, 763766354, 261424483, 850972604, 930195658, 382199736, 880571208, 826704942, 168698314, 433768212, 301115569, 200655595, 783914546, 957383014, 382088424, 323657627, 306095593, 469123520, 425624319, 712265753, 598924407, 219007702, 69754837, 917135125, 838550441, 768847692, 540896131, 246138391, 650676193, 769835657, 315374659, 337878402, 849967326, 560587886, 931640167, 799681802, 738518661, 110354791, 847654269, 945773557, 227772725, 892463410, 828304619, 19587805, 302288706, 95060899, 234808172, 60140707, 729141249, 400828038, 554342037, 306534455, 312685364, 581745569, 380568967, 662683973, 870398382, 905227863, 207251144, 537775574, 391614923, 641522307, 715412168, 571540273, 467273019, 939770258, 783069145, 623738449, 156097135, 303859226, 662934071, 600332842, 762530875, 878294820, 164188938, 48017046, 997573630, 812981314, 910889653, 525989597, 90657109, 850324647, 437536451, 574342995, 818751749, 84384810, 222397891, 680846102, 98453285, 524356532, 561432155, 322287320, 32223804, 831118829, 695683194, 742288138, 155735283, 729825309, 116293817, 305352218, 772176630, 390605388, 957377103, 974117653, 697363499, 415256878, 88263952, 748219746, 829091118, 62419002, 306528870, 46773089, 313887498, 379391635, 466405945, 559329409, 615341590, 624584525, 920334301, 983571653, 399794015, 670322568, 502732411, 942601501, 929793102, 218332722, 218609277, 712314629, 269172606, 202633930, 845144494, 308582606, 281268268, 832479473, 555605421, 719781156, 885293923, 50212770, 985951510, 80147900, 730613367, 605506393, 20070901, 973301005, 708806193, 772951220, 612105149, 506241290, 50155095, 15293608, 254567521, 904625520, 911290294, 558130150, 110302460, 652254927, 492741093, 838389115, 370173819, 153911888, 203511612, 191703076, 835317541, 826415736, 601751599, 713641656, 344962467, 120810118, 119682493, 913220351, 126611894, 292304143, 933874072, 943893657, 781844385, 116321313, 226698734, 510647482, 988263802, 342288310, 769364805, 64705132, 986022803, 675001916, 723777286, 616181584, 419550985, 350755356, 881536141, 849290230, 337822105, 395055436, 461700031, 838509585, 895682709, 340268287, 670733266, 469063274, 123918337, 697244364, 690512801, 50057987, 687212925, 570966211, 62871774, 416867120, 964062917, 500017236, 506203205, 408381637, 103929607, 654101024, 732702124, 497264983, 966301474, 391388274, 829372046, 700053401, 419074180, 298552405, 445904651, 442399860, 121092424, 127416440, 592861444, 700919477, 323261488, 803533620, 452925546, 534839233, 365201473, 415578753, 162870732, 162296485, 14345401, 166485911, 395166973, 73941141, 156162073, 522803272, 66312811, 188442137, 301790778, 968761833, 628034707, 853536506, 572862090, 32253085, 285477429, 466117986, 441044847, 621465799, 423669165, 602606113, 715799012, 219359208, 942773851, 130522655, 308443413, 297542955, 617904672, 944193914, 7611057, 384148711, 74925161, 377769226, 398540946, 592863079, 140219060, 989894334, 780655927, 744864086, 631320715, 865496757, 558757249, 644950973, 304713064, 205669696, 696860999, 905457969, 587201405, 927054790, 827796694, 517676457, 631288717, 923487219, 819406228, 617300471, 600455294, 390624066, 75270409, 798295971, 15244260, 942806134, 225778256, 781866688, 29463351, 585976537, 384639108, 228716741, 495253396, 118526399, 853604421, 233767280, 881246065, 168237182, 642057878, 477319228, 266259975, 354415084, 565966165, 157447932, 353041953, 59679971, 397266246, 710118874, 263816664, 659931364, 113219465, 181312211, 295937043, 303283250, 972435213, 128786451, 942151986, 279239428, 829545441, 553434966, 478174259, 606354407, 717267217, 278952454, 18473335, 241161603, 572571143, 84587915, 523822729, 792474828, 648112815, 12800998, 197223728, 95027615, 422748252, 728582506, 449985245, 668634094, 384984432, 924422779, 965638663, 691927963, 546259866, 540129275, 633768997, 182248835, 948590391, 563300637, 506336317, 916553042, 526655007, 552585207, 424977640, 917727897, 502772657, 23391770, 400005691, 189439764, 520980052, 993354156, 974995071, 208544521, 61551377, 457307247, 168276597, 701508935, 288473946, 965050608, 717306768, 842673895, 719047910, 73784046, 354683669, 732928034, 915075208, 707391397, 99652967, 217995247, 825028835, 731495871, 713268247, 769566304, 294836952, 654742451, 345455914, 896455821, 473118896, 166497833, 589205441, 162352433, 464728937, 112953668, 91042068, 836102039, 470104604, 348355647, 149313141, 848890103, 913441224, 766787884, 224851198, 509670189, 766088692, 21304282, 576895809, 723001059, 224232603, 198939741, 362592581, 881896119, 892991083, 857836550, 219935269, 165822143, 889117962, 954676257, 831563418, 137586781, 153479587, 144675133, 737340712, 467363582, 53114142, 853296729, 314031197, 112585815, 854978662, 590242453, 627765137, 232301027, 99078717, 145812710, 812925041, 41418269, 942100043, 314744507, 298319674, 144298652, 265986410, 165621762, 620306875, 168067667, 234474526, 282234823, 316653000, 748442519, 305674244, 932317376, 611621000, 590728210, 447227085, 460475924, 331291512, 621833213, 256596592, 830610145, 354329604, 947012516, 794925626, 924110976, 824084780, 458857674, 197543851, 352253261, 48776393, 319970583, 87817332, 853617922, 306494563, 348746534, 892163888, 300677078, 269241859, 750025218, 630198224, 140124328, 631872043, 23737701, 126288564, 57671046, 417128051, 836606748, 873042637, 356566428, 161702521, 598847091, 436128048, 599411195, 734924244, 93340512, 495243817, 156098501, 43314970, 455846085, 369206408, 772867129, 92178329, 275720890, 986711109, 186646975, 178196114, 973520548, 261957672, 602371251, 814416199, 451309556, 469310925, 823660673, 136957227, 611967874, 248773019, 320098883, 485660871, 894287973, 380005086, 33394479, 36496111, 447993545, 306531261, 823639688, 928305050, 834988042, 56908959, 165282971, 258645802, 992129770, 594947423, 40123475, 385134689, 277668340, 672912171, 283720930, 772562470, 75951286, 346657899, 796353243, 677886566, 91556203, 377494571, 438375606, 763127592, 196191357, 387022557, 754865635, 792858617, 672558691, 635780810, 401052509, 94847794, 90175836, 655154743, 270916468, 186031385, 230581484, 154964275, 538965581, 340715941, 703454190, 282252362, 833687890, 716876785, 328055824, 656155671, 287224489, 300152897, 447591185, 335470064, 526178472, 711350509, 249432578, 594503298, 699148079, 632331648, 564901764, 639024911, 662744849, 348760470, 98697152, 126569495, 467150116, 329206022, 586895445, 543567273, 291230250, 49404278, 896822055, 415282647, 411768411, 856650972, 265630554, 430630475, 448658667, 754763413, 390293330, 877547232, 838984790, 632935565, 662889508, 545545341, 854754934, 724235776, 543121500, 221970271, 406378716, 209207523, 168481160, 996093941, 334549432, 638138147, 146908365, 686972741, 162291213, 153061982, 25032419, 867686604, 431603394, 791975966, 590661893, 932520912, 928643528, 140295045, 328528811, 830224441, 933302134, 891399030, 793639136, 286767829, 527937055, 563349117, 921851934, 140523127, 727370337, 144255913, 381512509, 736001995, 653148681, 983334170, 145997949, 904989824, 594267952, 841993070, 347072927, 471427668, 635387675, 159117113, 487285069, 579003892, 299451015, 232025035, 916528519, 560327587, 367085537, 194837929, 751348232, 394713842, 612814251, 917752901, 543401953, 497094887, 546876191, 127918463, 664298607, 264645835, 816444205, 405960689, 963661783, 731964857, 153525619, 501269422, 496385136, 558337516, 253070126, 364985115, 622761400, 295284503, 423748098, 892234995, 666290279, 34915267, 843879826, 673707033, 28298229, 329869996, 159117548, 276916895, 942917634, 129827938, 317737306, 995188137, 866986899, 53920003, 524390925, 197787197, 261037447, 444935299, 742782672, 567239282, 54952624, 145593264, 993244998, 829074739, 98833006, 236269750, 173576919, 536797437, 744174687, 885339984, 728208875, 232471908, 944874898, 279220402, 72548582, 2029260, 111069132, 756682363, 477840804, 437813184, 836075159, 43098038, 262194304, 770460702, 361581216, 939073237, 58263451, 32253110, 410727911, 272265668, 118859086, 537952267, 424362727, 337835721, 763091514, 971301214, 830291076, 524369422, 757084358, 310682249, 501070581, 809806429, 541151142, 183342332, 9660801, 460682795, 55676423, 317790748, 697652971, 967393116, 186198634, 136295075, 384244488, 426038398, 772147672, 7938128, 385740254, 100725500, 200030418, 114516534, 224129847, 404947819, 27279770, 762221856, 499570881, 800653338, 666707048, 990348923, 366391771, 644391617, 893998924, 200620294, 964850959, 626909046, 823397655, 242419760, 451472655, 463586829, 960842354, 603972341, 402588281, 604494341, 649711581, 768140037, 63315066, 230394743, 866094344, 495500634, 603504175, 835499035, 733911161, 436694822, 995234337, 365563313, 811143533, 648059356, 335355663, 221738784, 183350552, 535026356, 47797370, 947820842, 759656834, 708775028, 732810626, 171106859, 627552214, 753986953, 881249834, 341161838, 115146675, 313828218, 103861254, 231677108, 809131073, 823036973, 148886983, 39653063, 418260929, 892811291, 669543419, 658310911, 150192422, 413029142, 66176261, 919103082, 867081101, 262723582, 604758931, 8757246, 193937417, 337456444, 923329389, 52083974, 263324155, 470706616, 586100211, 513165648, 291987895, 52122684, 391898162, 5324696, 450540572, 844686948, 773148233, 48945159, 629377640, 361069299, 519868123, 277993522, 450910992, 86824495, 152687254, 485014011, 989389035, 432698008, 486710649, 557685337, 572322721, 182014848, 123473672, 166474212, 876353371, 421466534, 651824426, 668345748, 719007414, 886297051, 826913695, 429232766, 730444412, 150284926, 278234920, 952640159, 54103103, 468204912, 849523616, 72086063, 322440457, 999646261, 429590059, 112225640, 101101496, 770111402, 245987143, 985008206, 566019737, 462569817, 176719490, 265766792, 991948948, 959623673, 779850282, 185784215, 437727972, 590770382, 7849316, 594849595, 443013443, 879704323, 540827183, 55255883, 638295425, 397887120, 245500976, 924784076, 207841432, 413479857, 319210948, 137560699, 632603681, 310292742, 851316511, 664081690, 170044352, 987905770, 820395181, 396099291, 355966999, 968012758, 527725721, 514866385, 17481074, 494653329, 930147992, 350681796, 708095719, 983969499, 452037148, 87882185, 339300442, 219663543, 697782541, 420751337, 46748827, 710665612, 754047282, 153489454, 4738975, 729059329, 778218933, 748073230, 771114940, 780298648, 562046751, 511597909, 424488332, 696675929, 11026623, 137079903, 311105990, 936756541, 964725409, 264059453, 508648416, 165747843, 494226406, 64103255, 195146713, 957290194, 443006195, 296423618, 139199097, 273505527, 329021238, 905134359, 298747494, 37125820, 328202753, 245120904, 535566513, 755862755, 757216101, 560727534, 628378075, 258113354, 606535937, 719558934, 652820103, 472452673, 576594433, 277346087, 471001407, 570834154, 75957542, 112973489, 339085195, 443543102, 566024206, 133689851, 516029387, 840386172, 417792758, 844418160, 928667811, 937755967, 373943068, 772545475, 313183510, 841989941, 811682346, 991955990, 553890074, 865600276, 616918886, 434462963, 106552666, 610182022, 938162927, 700495819, 678119751, 490123310, 287156160, 404274203, 662973190, 396683639, 936568388, 735514313, 580836716, 619401218, 853556548, 305739887, 963415274, 284802332, 381681398, 157495764, 891007432, 530605994, 66403873, 843555881, 153716623, 652321269, 573588840, 990373712, 88367769, 525243619, 199271015, 945588008, 655280249, 330130758, 980322699, 571327172, 792077548, 253019265, 449503149, 293251803, 233937467, 504802015, 4330590, 607080174, 582527926, 217456793, 906197723, 699940771, 919125252, 687229386, 397452484, 281441495, 409940372, 783104932, 490200172, 468160484, 864866740, 507686798, 120858611, 377190598, 229032894, 540525741, 202604408, 960919156, 415027931, 650652452, 965653035, 969017156, 423392799, 275821021, 770779679, 401903253, 805886130, 223038188, 894764365, 356479427, 878606662, 723918940, 893265403, 462947978, 676886453, 881893275, 592621718, 63668072, 411526541, 157408598, 253849301, 599201930, 381981275, 35974282, 77394724, 423372912, 566044156, 751512679, 232084288, 576778938, 319702096, 348308620, 546989743, 255990229, 758894635, 367523732, 967446393, 987911983, 619262451, 804636017, 288022862, 780527289, 330315838, 652723938, 691204921, 851114016, 746060026, 45602371, 172405864, 824614643, 174798728, 477940461, 367421525, 988037497, 402700092, 5583166, 686096817, 814046306, 878992529, 836076924, 448915595, 950169413, 603899655, 959093444, 665291174, 723951335, 386297589, 520242327, 107077016, 485354857, 113878980, 472954095, 533366893, 669968015, 959868729, 337071029, 881682649, 291316099, 68902490, 608913038, 436293764, 609709581, 181388967, 789721233, 970552662, 527355848, 83019376, 242970971, 668204630, 562091960, 117308308, 483081408, 299075798, 184323794, 444029282, 125687169, 914330743, 17748265, 738100174, 385938017, 263253288, 621470755, 51087688, 623815871, 603551250, 948413734, 69816826, 872358985, 177686674, 890747610, 420737038, 773248999, 957144732, 348674825, 662645140, 694137346, 370075371, 549288202, 448590732, 910432229, 164158750, 738524635, 586675519, 390700683, 849472535, 976561718, 482547788, 329891384, 714179681, 499528065, 73656548, 711289797, 404418606, 199449814, 947492241, 325603992, 478164065, 710813970, 590532875, 184913528, 49269821, 985798047, 184234947, 277867070, 906732537, 729033708, 172267194, 570508616, 684063204, 93934755, 745474432, 547797281, 678524246, 799869927, 219419653, 705112893, 761820249, 913354294, 180319274, 493139207, 367979398, 145543485, 465510643, 367341925, 948763487, 363029983, 251271086, 115611421, 486129167, 361133297, 582799030, 640432794, 59356317, 483623680, 7003196, 227523962, 346464331, 700165738, 601347522, 537019928, 230333303, 544840659, 140403515, 654507479, 217963288, 637355983, 202171354, 547597735, 621051360, 205092841, 531385151, 629752339, 86838521, 272722310, 270414663, 902157293, 911239505, 492894810, 270435122, 786907119, 476054001, 280911987, 7566941, 89584698, 213503231, 876760443, 219930832, 586211964, 210719565, 694536195, 723721204, 570798676, 881815799, 859945744, 136847538, 959805929, 778867525, 991782565, 597038553, 565866888, 282885628, 941735927, 766529798, 695028610, 885390325, 281596286, 447249272, 242455553, 281384037, 549087973, 367601914, 545716714, 468418956, 512865658, 452614348, 541302845, 497636889, 910606838, 106927921, 641902409, 523536337, 294610872, 46503564, 702960279, 751760139, 826041184, 95766994, 847400985, 553692594, 105846934, 399693832, 834427434, 684589630, 43064800, 7082069, 401576192, 159446671, 289281946, 537968531, 891582440, 516785244, 493512953, 705187941, 857018441, 223400733, 410730192, 127933361, 644653451, 447100768, 136125533, 383177005, 468190358, 859481632, 232435668, 827757361, 257218637, 494205012, 298333119, 642971146, 787492714, 862448267, 245565402, 85227649, 525678475, 13553557, 559176815, 162408213, 521283679, 759799728, 333769521, 237506368, 980402874, 794528546, 960583224, 237932319, 5485017, 391811278, 300557638, 511028530, 643131161, 763516972, 756249259, 228283647, 573534850, 915377496, 291273428, 920269030, 813044004, 610443521, 426956569, 612830303, 774329480, 840579938, 677815585, 811774189, 367355550, 931345937, 12875150, 906499093, 77024420, 12052184, 872913324, 964685552, 193460260, 843747966, 324378191, 308694800, 78390791, 709661949, 789898833, 272736331, 166630141, 516163142, 525625462, 182394987, 912917027, 446637953, 427217164, 167627442, 895310272, 846842006, 247491247, 330691243, 105892710, 981747306, 523578267, 622720585, 681518609, 318356715, 651580259, 349414555, 102033061, 719908093, 172061875, 511389064, 51668312, 727751713, 552879648, 533251161, 116246402, 833153472, 450513154, 777446220, 346652394, 728655773, 939462622, 57875572, 931068412, 75257992, 363206058, 716576239, 460084617, 329940360, 372824540, 891096083, 20263379, 192255510, 208986200, 478759621, 785831959, 41607970, 493795184, 94017542, 822360120, 993329865, 857327300, 439380404, 270603156, 329737171, 573560861, 64878259, 721826538, 841454115, 866295127, 167971208, 668165003, 570420877, 603617944, 143524354, 250063942, 182626976, 699677184, 652342523, 705380451, 370324945, 84109098, 555420739, 487476470, 136176164, 376348311, 264603188, 229215488, 569777366, 531520519, 582840068, 222614771, 205671831, 502922140, 197242275, 404950034, 738417493, 165162555, 137333466, 191315672, 213875214, 912354703, 822564118, 827066348, 11095286, 396213921, 752918427, 329923285, 402216400, 922372051, 837972248, 732710905, 280986462, 422265148, 46337803, 654870680, 65705599, 370059143, 824155357, 494377786, 263498489, 325924795, 595039623, 872667029, 246331185, 860428108, 661877391, 452839054, 79852664, 940268430, 498643939, 654853627, 129584605, 622544907, 100749032, 527334111, 96607103, 663104714, 80278973, 49069733, 421581985, 89245648, 85806741, 911549823, 146767833, 762903682, 558854776, 281748105, 478093545, 861738309, 588423409, 72748006, 113097106, 435817628, 216120391, 23932798, 295920393, 594761077, 124939232, 759994579, 7539346, 872142312, 709174854, 292712317, 745782847, 770795479, 529860054, 190816597, 310390471, 321645390, 817892300, 876717306, 702856657, 773067837, 532936340, 205806892, 659616594, 945419164, 253959528, 664036920, 352643029, 545127339, 523782010, 556671542, 187642737, 973899891, 284333551, 750268022, 8356103, 620131203, 599143072, 633787482, 593225918, 432125746, 590594254, 954916225, 23190899, 549004733, 287035470, 200962900, 444133545, 386014134, 602347209, 920864668, 584265313, 393184066, 47260019, 624851956, 701619735, 994268986, 158178362, 852270222, 152609349, 390093416, 57947328, 855943661, 185564503, 832012874, 513661072, 513894026, 198569256, 7751970, 496089631, 229422242, 656410845, 117229770, 347682912, 409537461, 838864699, 664078965, 631189379, 596961167, 140555845, 930561411, 707608943, 573718349, 631010403, 388300250, 756346023, 850060351, 147316842, 904562893, 235919844, 574858832, 322613775, 993631143, 447807777, 95253246, 221502601, 361866144, 151348067, 811971473, 458654561, 156060102, 461559754, 286972178, 732201551, 774212498, 787901759, 944117817, 560596316, 550238434, 407847170, 242846838, 351563948, 547875759, 834460894, 954091282, 243401069, 75122643, 65107532, 783882272, 761910764, 766741958, 775311449, 786430131, 244401947, 997903544, 408931816, 223162318, 569519251, 842803491, 482845111, 806186691, 350877364, 900633439, 31501102, 47612250, 985484860, 940255781, 325418459, 780793433, 467565424, 990370224, 661708737, 599852670, 585217406, 590954753, 996121923, 577205209, 359618639, 520444103, 340216134, 177622617, 58352946, 625273844, 529814209, 365122523, 619627956, 656366373, 957427246, 832447610, 413989753, 515683533, 650268181, 704102471, 423603877, 41743945, 197537696, 498361096, 63731100, 169184278, 755223590, 398054148, 985991342, 333381931, 169668885, 109216780, 139814075, 931576622, 245762832, 593513568, 384903238, 195136621, 544879632, 658543307, 667217136, 671580313, 451959706, 24482609, 4785670, 485541953, 31909824, 512674016, 143659125, 777539198, 863919853, 402323547, 241713904, 160190381, 817920990, 417637923, 155858274, 886103832, 673703580, 302428141, 669282967, 136445322, 674041303, 357219694, 87484716, 728863898, 147164112, 40035546, 395871254, 560428573, 655265042, 736043335, 758023585, 29156509, 507481967, 547179296, 734230261, 672567361, 392445286, 229882980, 512494616, 126857037, 783460914, 910855381, 943315924, 532914823, 993542346, 251588658, 392135515, 26918851, 109204111, 199984302, 668768764, 980064421, 104705303, 410238665, 182499281, 387071341, 130900657, 334615967, 564345824, 877696552, 672249829, 199241780, 908615167, 546007130, 763518199, 484500533, 738668715, 883070630, 51216212, 440409244, 540058562, 399063431, 404738898, 239987538, 354704023, 395490010, 359624533, 177337565, 733952319, 944608463, 414600162, 315424842, 101590243, 817007106, 130155640, 325675480, 976106700, 293543518, 243927761, 656430659, 319432036, 283447623, 86950044, 277115418, 472558277, 668788560, 154780899, 393293952, 419765284, 77114233, 960976238, 379593892, 928985859, 322656591, 216640440, 744283589, 241988975, 279788189, 349010037, 869328489, 367722336, 71782290, 158960078, 63131613, 280810596, 13337576, 637045909, 793985007, 349379671, 458248735, 445343515, 832407844, 650717323, 449009758, 681340355, 880044538, 513452105, 470809076, 57512871, 772162729, 687866965, 908351263, 877096290, 198534273, 159287470, 227824819, 554999475, 322253982, 139444302, 290044933, 535610304, 581918512, 41433480, 463213297, 152511214, 446580902, 223094168, 782556768, 383238310, 18134065, 796431024, 881522051, 797223519, 421339717, 172620422, 535868088, 540816575, 662891523, 692920804, 525857729, 654699672, 586818742, 416129927, 208909638, 425064313, 44011465, 919605474, 220020006, 915147293, 379587687, 403627455, 733276996, 82199329, 787113151, 819228444, 352913306, 159762977, 181716518, 450949087, 625775427, 953986891, 64686920, 643365757, 53684229, 345949565, 681515035, 923100519, 264533295, 390791823, 189290151, 54992851, 122278194, 295495792, 457428271, 849467864, 808075892, 45310713, 258558154, 449160594, 33876868, 655619261, 596940743, 961236577, 264150260, 467344980, 180996522, 254072607, 858431846, 37000497, 679759235, 597981190, 101384968, 520984581, 642991624, 985476915, 31511610, 716466742, 384981311, 414966943, 672802712, 621014549, 708113165, 454557742, 904110801, 893501686, 32846327, 496674117, 386235440, 845220939, 658604541, 847309960, 253799736, 633408076, 90818060, 338315709, 301614028, 242812373, 863653190, 741937944, 588255493, 862578345, 428165178, 220257943, 715772409, 909062575, 835702333, 757494079, 188839928, 375158651, 312221888, 237217037, 205865512, 493481948, 804839134, 884058332, 25613910, 871861228, 838057261, 649705239, 904191716, 957513518, 160859755, 631371589, 801067206, 167731003, 642685422, 480994438, 277760353, 751757421, 462826245, 531250364, 199425821, 566639949, 551974499, 623439582, 622354456, 752365839, 964251520, 167283824, 291235094, 669486526, 952834782, 641477665, 338589892, 185051150, 813299070, 161634671, 54671277, 594759524, 701326000, 947547307, 700552175, 964824780, 312852173, 613707285, 10758598, 227329416, 838811058, 733240202, 45255162, 162565796, 323927706, 44899625, 619010457, 376706605, 812367974, 638895577, 534000721, 495725075, 241024327, 509154843, 336771322, 914292597, 766263892, 487433225, 36672302, 894224933, 738266890, 107410758, 636573857, 866460761, 876769367, 657938126, 653846233, 328456110, 884435008, 425358379, 563911954, 292361145, 548538069, 996699994, 529079025, 914808766, 444090534, 416249008, 738973453, 400732058, 636587599, 819119748, 538164590, 795399132, 659618808, 194218011, 139985444, 883499661, 14106605, 676521066, 225320529, 452118500, 667761165, 399898595, 143371036, 28856049, 583960461, 682169218, 829859876, 364520488, 732004750, 178388714, 8684511, 813008851, 444087144, 457366163, 509014799, 931421424, 430998517, 764522288, 986412369, 548698493, 543977286, 584136970, 766036857, 912376783, 74538691, 834138311, 266064600, 258923504, 657150540, 804501040, 783709137, 477328808, 241027215, 151965742, 751750448, 881069849, 705521564, 794874189, 947406997, 81524434, 479195293, 157234410, 349924636, 30938509, 71054884, 616841084, 204378044, 511661741, 803261147, 504514116, 826620434, 816321990, 808226478, 462897265, 214555635, 505446830, 696598544, 985292950, 951444105, 534439625, 464586046, 645891437, 652762830, 895486027, 513119001, 71504417, 683821234, 552251352, 583133354, 897386546, 717079374, 354025601, 390330342, 954189711, 669537749, 376448610, 282621712, 318783737, 934602603, 23298648, 619743735, 193035145, 581983816, 208499783, 441728334, 380104557, 363644488, 325819977, 784879548, 608631330, 384526060, 239997607, 696788885, 14669101, 743400897, 893083067, 378262756, 724661128, 411510759, 160150584, 272380198, 131095234, 368251856, 612638200, 426435154, 104436608, 441026002, 53945106, 845803392, 234672343, 327938382, 991652227, 856672075, 357413294, 177383843, 182770981, 752732201, 219158235, 241002422, 506734962, 667355679, 124613236, 599117553, 617195576, 499790772, 745091158, 776687708, 998499751, 685740078, 751167454, 174004123, 780997012, 385802493, 640506268, 994268356, 245742995, 191603166, 370916532, 18541636, 664229116, 414521933, 438684141, 909867694, 918400617, 412149634, 586856482, 635921237, 395584872, 705657545, 621655612, 242087235, 56659528, 807333086, 51213480, 608672173, 590958869, 67213054, 75088066, 568199941, 283016337, 871359879, 572051856, 847604255, 42774886, 100985112, 209491175, 730458630, 737645368, 271156702, 554231560, 950353033, 122638103, 1263200, 135867209, 241495642, 598296934, 396017749, 630310403, 714182774, 768054705, 820888316, 42933946, 571011907, 710594361, 761991264, 836701738, 10037951, 564085174, 128549564, 328339384, 692550063, 250379777, 232864883, 326551484, 3402843, 887198515, 342213761, 911524095, 327275621, 265630525, 142623660, 758311598, 495158176, 20605513, 334902761, 421743261, 282333000, 370251799, 260509031, 845360601, 897337022, 287817684, 851432933, 517864642, 636166031, 168052222, 7952604, 62486489, 699414438, 377280970, 655719585, 445607128, 559495546, 796856748, 271049425, 143780569, 989295781, 756624026, 649345020, 936281754, 30031357, 436089491, 959293285, 943843468, 538876307, 741228188, 165632983, 64505029, 681427210, 202418817, 106412496, 116120952, 639777648, 715281622, 835980478, 843223907, 583239317, 877701289, 879869675, 462516571, 196906850, 284870888, 276719631, 999116902, 968100764, 270156045, 328955743, 863121047, 179136826, 3657835, 348285356, 909414226, 670821053, 554805369, 567190820, 407718294, 757017990, 155322828, 450043042, 190282435, 382579047, 176771366, 27688214, 399519, 476605037, 332539452, 29366646, 258181372, 968143261, 635224649, 411075339, 976718766, 949726799, 744483625, 323477342, 113678247, 705302848, 976044779, 962789053, 832096341, 495130790, 622933379, 328399430, 557360961, 598701824, 615742355, 375443914, 187961103, 385444072, 733234120, 449773634, 928119839, 61775163, 983643955, 104516778, 232340652, 787166737, 893497280, 459091414, 116107979, 500147233, 339894587, 931546135, 154016429, 526165254, 879108555, 668660236, 19474303, 976196875, 865963578, 714169523, 535535318, 889838609, 272003721, 793464957, 397481547, 683684947, 431663959, 415091882, 793895153, 208192301, 505537777, 557412215, 15912750, 395611488, 785662053, 912247577, 699583373, 367307022, 423465656, 384560790, 430205211, 920083647, 224402171, 115608806, 527119002, 638580687, 114091729, 119123877, 947403088, 400643138, 766344687, 543897718, 19644408, 37362733, 578208051, 475867908, 288521670, 311470134, 840513998, 828073096, 559195947, 358896597, 974845973, 835732923, 765143557, 888335644, 62743429, 618226679, 306146739, 235391575, 326354479, 940853394, 387434484, 531064136, 498957639, 772672828, 116793804, 192697751, 149076792, 747181403, 144289228, 638777708, 684054408, 197236008, 695800094, 327522029, 16782654, 321070770, 532428107, 515377652, 828155327, 607864949, 480734658, 186822512, 186876386, 563552735, 953845738, 978382734, 732108420, 914260273, 316614546, 156694610, 228431090, 838554840, 262963832, 590723530, 575921468, 2727057, 882678407, 289597267, 828058831, 487486558, 968319354, 327327047, 850964350, 94427171, 988048929, 449351092, 321478302, 672551249, 676595562, 32316687, 147198424, 715930194, 521311657, 141409499, 155999735, 749482941, 276217922, 498838314, 791611861, 244000596, 743898015, 995987154, 582299048, 937730549, 584906329, 421359353, 65149568, 821032733, 199250665, 305269783, 657755164, 800915542, 745031011, 989948100, 664598017, 923282601, 557668797, 793328505, 794922175, 368778121, 864249852, 379172855, 990041114, 759161502, 559324050, 170031565, 737123931, 934762795, 160470906, 489671375, 652156413, 72536314, 874713933, 427465004, 134609514, 146413147, 72374622, 366041596, 249339340, 308083920, 17221121, 600586082, 51939790, 656346915, 105802789, 471772720, 519697587, 290943751, 147816901, 124522713, 780589054, 893011137, 337428847, 322604823, 814046083, 70866518, 831576254, 881004478, 995577014, 944593566, 254585744, 652189390, 777260855, 73780064, 482901269, 470592039, 869685318, 392874195, 138924631, 914935332, 932688160, 289407031, 17631138, 316587504, 164323441, 98210720, 105645734, 920873928, 161651289, 479883217, 506884752, 37878788, 358626813, 957300808, 942978495, 701520506, 436374181, 437252403, 341666622, 99183517, 526283479, 604786356, 590966041, 947396484, 85989512, 914945787, 6814398, 393616826, 718474519, 378586398, 852966559, 40388076, 629256938, 19928821, 705695995, 283132067, 869937073, 873897007, 751603212, 539665487, 825027570, 491284526, 986166603, 530525751, 252769064, 891794740, 98240089, 710889725, 63437242, 873215738, 325919020, 509657986, 972621075, 149702773, 827744736, 90120026, 849259271, 408146464, 594697513, 820271379, 9802091, 830371988, 553406432, 334094738, 641974612, 33011167, 697763537, 447015338, 249324612, 4713534, 985367361, 499978219, 943082796, 32361042, 114255391, 748301865, 987812342, 449178328, 323637868, 137637376, 23110127, 181482418, 69327619, 519864094, 566021760, 386366479, 549529940, 284363525, 442328272, 813031221, 253838879, 111755694, 172738360, 35447942, 684825780, 992967223, 521082065, 128853602, 555328660, 748689963, 444534545, 949846591, 13872175, 938035850, 825737167, 312202095, 390696408, 322061700, 527375299, 509931912, 411301641, 300632541, 589905534, 385746192, 338424735, 128267797, 189880321, 79037140, 904802371, 23921503, 703453186, 170698794, 850768860, 907253073, 71306765, 56889984, 692242883, 200707476, 604884099, 757236249, 159707061, 957248150, 841924452, 812397195, 121539975, 787422267, 721115921, 230173200, 37293826, 629289809, 600156455, 245720250, 325907863, 692075904, 641726417, 100052959, 678050245, 421628482, 210278715, 609036228, 799497709, 749667568, 338433046, 658376996, 574741919, 490403599, 258468557, 96149127, 835931501, 430970268, 84166859, 86620600, 508406418, 134424922, 406997103, 149599857, 44713623, 116421987, 722195094, 679642323, 24988374, 418526266, 84566743, 691602653, 690343059, 275329179, 29592968, 236299463, 90125090, 788131328, 935206674, 459189913, 53885121, 84060280, 25562792, 969229954, 159500235, 262301158, 63053729, 477776356, 32494893, 303844219, 733034564, 26869915, 486702992, 362019249, 654491669, 697240805, 688509281, 242726945, 828981969, 808657754, 799136934, 385225020, 833610083, 25786311, 493666198, 524799550, 145154479, 474602891, 487820431, 111104201, 297956202, 808296769, 907373010, 77827591, 909716903, 58758849, 781452704, 788910679, 233694727, 598866682, 323307755, 595569756, 91592178, 663137105, 386094460, 739465946, 524245143, 593450710, 398246969, 220377151, 644129526, 679366440, 427142924, 799471724, 218675508, 469631070, 665655201, 679222015, 846309383, 870264394, 941931502, 95706940, 448391390, 201247515, 691973675, 739833989, 68875204, 241256315, 475204190, 177074284, 757151589, 601854985, 257087531, 138201248, 667925903, 277618473, 222304778, 973135708, 166251963, 675175830, 116233780, 83797920, 503860149, 317358146, 358885847, 439211946, 607110153, 179388521, 841230067, 178483097, 772840121, 168808919, 192690301, 42457903, 229510674, 828710165, 834122330, 704517415, 16775559, 77103370, 812248985, 995477296, 234720321, 728222196, 647713503, 504247982, 596630794, 527481397, 888719849, 582142747, 246585470, 999357065, 555906918, 89344728, 71613259, 454652808, 922678481, 276140192, 582723882, 932258860, 50248510, 927817312, 745994117, 732765863, 594611889, 193783648, 814147680, 444553849, 179487305, 581814890, 218595307, 254543094, 386430722, 806244230, 70769247, 53516331, 139588907, 69454632, 396741883, 389426728, 780195815, 66784793, 948494819, 330060938, 477057904, 799600135, 526949520, 94284290, 302320644, 63353900, 165681353, 1523371, 972342075, 721037576, 842021345, 630492509, 197660405, 289225736, 9257973, 650697370, 191597760, 933056381, 956718081, 504493483, 980723645, 840612480, 915357007, 449182876, 633325880, 609644218, 288089613, 107086806, 741238054, 970855996, 169533914, 550781399, 527273939, 472305158, 490459087, 428531884, 482919864, 757598314, 304676503, 616622457, 560585048, 788473317, 803912631, 34396285, 201619690, 570539545, 53650148, 765886690, 479846118, 774701086, 171695238, 86824785, 595336315, 71255124, 745461268, 925620398, 134339855, 647323032, 389887006, 105553824, 767429457, 237347633, 302958908, 500720223, 417867557, 962875482, 312426976, 374199601, 856223788, 298021122, 336560094, 65310009, 299970987, 373490018, 35741178, 926974435, 889887733, 221326394, 736245135, 69847138, 881067910, 222346440, 856878763, 213372778, 293841355, 816251971, 940029956, 639516750, 357502194, 503784814, 688298455, 500609761, 186913039, 650393792, 287921616, 917601494, 274994800, 918149327, 857402039, 737709168, 13660187, 175119897, 41077913, 712901546, 520269592, 560009434, 359546394, 380768595, 401808166, 486497587, 51180245, 755620080, 249009071, 137128824, 317278759, 15452093, 347111896, 588109506, 759638482, 769728417, 471760292, 178632438, 475298843, 26507913, 411887394, 6476397, 43766224, 644017976, 287887980, 108234729, 39916854, 191858680, 634266942, 149990071, 715679975, 28128700, 388578893, 478709528, 486540754, 568053183, 809602857, 264057968, 399756227, 690461956, 885128689, 677574841, 173634543, 873054357, 496037971, 813225195, 519534912, 186411209, 7689353, 644623265, 696269553, 857255432, 132921913, 706818366, 711889635, 599669004, 529967468, 827146507, 215435982, 455060042, 810859824, 890911529, 348850441, 81550994, 541642960, 388773443, 889148690, 564805641, 24810815, 575289562, 303830501, 40465712, 275288235, 167871280, 620452222, 576113657, 347163285, 719839508, 426768320, 496329175, 771398456, 933222958, 171607233, 707384482, 878339015, 878070273, 874151395, 635490245, 966537179, 136622288, 582540012, 875706742, 712416859, 543918162, 914096614, 615971310, 908670546, 183433481, 951237399, 310104811, 440761904, 769726246, 322034803, 424159113, 447510439, 164259583, 507523429, 654519250, 369344194, 405164637, 805897420, 361812922, 220142140, 794516775, 737838097, 223375569, 677226024, 166511044, 874060232, 125713071, 975280400, 515246372, 498074039, 823565935, 999987211, 368618706, 567365706, 51538839, 168792254, 102441250, 240129992, 886870403, 219980980, 404677341, 812207997, 693064624, 201242626, 420541252, 898764540, 25184973, 150595677, 724942901, 153672002, 177759692, 408293616, 92190143, 274728391, 435942908, 439898505, 797002028, 783002652, 304393937, 655317408, 946754776, 38667127, 352393741, 721749307, 420482556, 141609213, 768009813, 81617091, 823518064, 860651057, 788665149, 423974339, 230442806, 853370612, 382598067, 64234706, 914953440, 270895779, 976378558, 931198717, 232888359, 685809379, 876773392, 728561196, 52327325, 179840358, 999218151, 499895566, 473329017, 570421011, 512938950, 870487513, 530214900, 459733715, 423237136, 875843533, 682364770, 233011699, 356983018, 394858157, 670329649, 493302955, 550363414, 186338704, 591150123, 262004150, 445405941, 21891661, 739565938, 854507294, 159519009, 230116647, 782677129, 998637832, 923965787, 715783047, 888012270, 898332037, 286701053, 176820738, 636398494, 138827281, 529753484, 407860856, 471183249, 950388452, 821320807, 356131666, 349063769, 194856178, 375634375, 878750588, 790804270, 33590603, 335661719, 901363413, 154723710, 471654323, 100784315, 889699447, 584548902, 176254703, 565024315, 447784464, 265669677, 46505312, 206764649, 770202312, 729510687, 315700202, 461064873, 258173268, 430893765, 286502243, 688672548, 42525653, 68907050, 257778338, 372624979, 484972, 346160130, 715273996, 703646877, 826706776, 53823671, 93886290, 396951433, 146684539, 949603302, 920756339, 171090964, 25553110, 672286513, 394747455, 258362186, 166143502, 764278989, 739850735, 972591586, 98755055, 42474433, 874924202, 649188185, 916718960, 954449808, 643154088, 582958213, 612922450, 358855761, 136464029, 400523433, 75957193, 587353339, 297647259, 359570744, 270252372, 971320663, 75234456, 977966884, 581027621, 730997435, 455137623, 773688355, 826024693, 416976714, 407056877, 687474869, 280771540, 834945806, 7990597, 56007293, 39929309, 512537894, 188215085, 493795663, 326499998, 408250854, 737882072, 666762708, 849388261, 961531075, 331473181, 630741428, 549531689, 385190620, 704358361, 429392976, 95665335, 69994714, 632226965, 666573031, 103922723, 490438896, 632173929, 670819942, 579296535, 898475233, 897284365, 109413250, 199682100, 428474415, 667616278, 317495743, 166984198, 804209462, 176900770, 381330295, 744552754, 188974380, 559481916, 664901896, 17500599, 861038616, 28128264, 294258062, 121198079, 616699020, 501289060, 349989264, 62040347, 39426847, 294943182, 813125606, 111640841, 513580596, 350373421, 439328395, 843185223, 241232751, 325998949, 862053432, 948762392, 104133063, 53022107, 345707221, 406424849, 491103221, 536019103, 756655825, 56611713, 848161916, 764522632, 995744220, 601280770, 458115152, 812369821, 675169916, 409814855, 492411182, 978044060, 99750622, 965542983, 392725385, 202914020, 4415446, 884299586, 334603648, 981154774, 811962004, 258335215, 513782748, 77106461, 64507789, 917801437, 501629477, 884372344, 821053080, 206984222, 294282699, 416138154, 778602241, 309713093, 828491447, 321336133, 947679952, 808466943, 759618063, 914072670, 861488060, 295215871, 261166578, 362046080, 473461598, 469163724, 96850399, 581417235, 663676526, 231755079, 622677690, 569825915, 502278814, 329144202, 245988867, 700858423, 131206775, 435923218, 202643769, 696681782, 895587484, 691970320, 415721786, 864981249, 584014115, 255099659, 98635228, 836577014, 942282833, 253097858, 79302665, 989287100, 497241075, 587917768, 349328119, 819885188, 583749845, 239962303, 115139363, 293725334, 591773925, 722604595, 286509040, 565435610, 818363754, 594040, 452807620, 557065908, 91304394, 863533932, 826880710, 337619901, 416044890, 506860821, 931628752, 596791797, 645315731, 784509024, 742491720, 551732340, 839458439, 470744103, 967293604, 834065886, 518193826, 527328752, 986529577, 769164221, 75950425, 114253633, 453736205, 698143631, 256013216, 181086056, 983778734, 955085984, 701637229, 569174863, 765757423, 424478412, 334318738, 978492411, 146193904, 575434296, 766070377, 640254122, 210893741, 249904342, 361577552, 242517380, 442154967, 176943930, 712076575, 719811259, 609766295, 672328061, 363900360, 470254555, 324311721, 395516363, 219550606, 753151363, 261494362, 723162070, 467678518, 472738838, 246179846, 977238103, 435885933, 555684596, 655151282, 984644303, 27915639, 545880976, 686354289, 260376350, 771836313, 838575650, 844254215, 748098099, 306877454, 285887120, 608327909, 111333507, 296928589, 912086308, 305745165, 34853323, 566961576, 517652954, 953476956, 955939163, 393231141, 703860758, 411843607, 191907354, 139839831, 761098142, 395271755, 801468981, 656469346, 848230612, 87218954, 795697661, 793985034, 192847944, 545752006, 571121389, 757513316, 167460212, 424515515, 13334769, 220837370, 878089422, 144665305, 942025960, 477519167, 702401923, 430674974, 853935524, 911715648, 939394029, 832324889, 401148874, 708274051, 505542706, 526717156, 405171122, 634345447, 382636162, 651841754, 95933202, 91827591, 146685022, 256491937, 235437593, 880373887, 320887915, 279970114, 6397586, 380887241, 556980239, 849337762, 304851199, 735610349, 93406998, 882232248, 333829505, 163650743, 218372497, 80227852, 738966748, 884249204, 786707555, 234779413, 299103230, 867224194, 373231895, 192282270, 275098648, 152110681, 131369065, 284263953, 600544585, 472890959, 87255408, 913227842, 175133612, 751111137, 114998479, 75724063, 234173939, 881290353, 775650750, 120696543, 549643384, 133481432, 136870582, 823725960, 944831625, 534885821, 190709376, 87592633, 770746631, 994133650, 246694949, 995442158, 947024261, 726018543, 312242865, 371145779, 465038924, 489740017, 888462972, 910280544, 625169101, 661048376, 205696258, 732377071, 912393007, 282038484, 150281847, 517530748, 16377047, 15203115, 691315291, 932000809, 211599455, 451128589, 273855477, 292751403, 202094465, 551367573, 690473532, 495021898, 149058253, 641344148, 467119473, 876929017, 342165855, 560306529, 405688755, 304008150, 794444246, 749908223, 917692556, 412054712, 936160847, 419714204, 255183150, 97836291, 870157725, 161134925, 646401360, 794073269, 667028060, 16877885, 454729830, 305618821, 719622979, 300408003, 518897462, 654636479, 379281010, 426528965, 82055968, 808687223, 462989059, 567784709, 186048551, 477222772, 472983523, 848737934, 598201137, 720053828, 231004581, 906539378, 400660682, 415390865, 983013248, 923448108, 935027540, 576204352, 969547032, 358435812, 282830, 719048728, 338314999, 206159339, 61220474, 138165482, 164506651, 540738336, 653235664, 567279356, 769599842, 901022687, 168292533, 14215859, 57291036, 647595363, 991714812, 436228143, 885894246, 761947051, 63433863, 279626841, 71467384, 617688445, 816620504, 994985034, 601964810, 690681688, 296253661, 147014120, 293347076, 20330155, 767760082, 917170642, 334173639, 108671163, 325405711, 328753855, 540167431, 877112379, 427651131, 152481057, 730540407, 81138992, 575606643, 203185009, 733868241, 987412760, 951334258, 176047254, 100609784, 123165228, 51057039, 57202775, 310923288, 539350121, 422599331, 310385052, 804542369, 162375407, 224862770, 150802326, 642808810, 100948094, 206648259, 786919632, 168698223, 95916430, 973081248, 465501375, 955567815, 827595490, 403463011, 677299323, 45985973, 285966745, 907723988, 498207884, 659447231, 920234178, 210689320, 147630328, 272067129, 329590476, 955091961, 452937200, 873928377, 545236512, 388999448, 579907264, 121541087, 906540644, 247592828, 971258226, 650350534, 242827560, 627987775, 672601537, 1551903, 787774589, 52277062, 81980683, 144736744, 62996777, 458053965, 896950054, 600726798, 313499520, 189096625, 139121049, 379944332, 448939464, 835579787, 142837087, 368310625, 573599459, 466002397, 7106140, 903224960, 530295923, 151910863, 186314359, 104912059, 725409751, 820212090, 416322617, 829388762, 42974691, 147543631, 924372233, 815776648, 528120052, 496963597, 738129475, 600374222, 137352096, 725648064, 545770599, 808128282, 231842675, 70090098, 837218046, 908837671, 904557386, 539697842, 173140493, 339922433, 6373810, 537882418, 401824123, 149102268, 351245796, 822593425, 957794600, 116867105, 652286036, 976140428, 937564693, 393107098, 547631592, 335588192, 680393139, 202530198, 559670832, 116901548, 933161734, 916591510, 518921923, 642837464, 788927025, 893368448, 814163858, 302697070, 749117770, 870537852, 178887783, 288809910, 160596350, 495562256, 701688914, 680257452, 618437786, 354451361, 354768598, 211030120, 909563097, 127831834, 988965254, 75270118, 149588762, 728491117, 566639174, 147583669, 328884209, 6129787, 28951807, 856202099, 989077247, 190418344, 154415722, 827825149, 625039130, 414442972, 59269678, 153761889, 477718204, 330301344, 179254436, 549652154, 817546916, 303248692, 122975452, 306007217, 406977868, 369487347, 279045878, 746979591, 265417449, 226234684, 991889390, 795321745, 442961031, 23776727, 361726666, 457230734, 848820261, 228358765, 990610734, 607656812, 709386519, 459994037, 837713203, 67678855, 521359012, 765651090, 152700119, 291779574, 979563010, 384590769, 333369437, 230130808, 379469544, 789703244, 594057525, 472531111, 555172159, 255138431, 469160669, 770810742, 224014354, 245497359, 845598655, 426550120, 306652233, 837840291, 564737371, 263774315, 921854945, 715648004, 675654517, 337268265, 323600288, 838762189, 482904224, 539646127, 509187407, 671777711, 985253356, 554767320, 324249061, 901098391, 816969038, 881980222, 718547010, 634791164, 177787622, 204620013, 338902975, 600979314, 728934004, 573075446, 36902966, 988205444, 207932819, 70902004, 449751760, 506380837, 573143940, 133895629, 199579084, 116957325, 765805286, 69318133, 256808406, 515872716, 188485921, 127364034, 59272270, 378888197, 254264173, 31243098, 189298133, 946739035, 972579743, 159044628, 777002312, 840111755, 556071961, 3143592, 215024963, 914533460, 449248244, 599772511, 60590829, 382373138, 341774055, 38664669, 66929459, 415742322, 681878288, 193918778, 315581998, 483042518, 132922927, 897135020, 977175563, 86921468, 505610350, 407932142, 811379634, 463791886, 983119924, 876123012, 329250506, 55905597, 356751302, 413226020, 972182562, 739824053, 616157794, 222901597, 438158469, 760850079, 282333090, 971582799, 648264169, 81917122, 221702282, 314402376, 584408671, 813889865, 808198133, 845688740, 168420356, 886653652, 37563227, 461895041, 384530425, 249080945, 849765199, 290374268, 402897768, 302468813, 266958560, 58446738, 314733455, 308845660, 552242621, 878090115, 23468112, 624645667, 621783675, 492555653, 795504089, 657281689, 545192612, 797780431, 470185410, 353316437, 295490240, 73691772, 694025273, 115122878, 301082772, 371131757, 919426439, 3240734, 294754693, 868411098, 173907630, 704929987, 129947602, 290210438, 574762277, 762095203, 648542177, 126783000, 202682113, 154928424, 578228662, 147275428, 43275473, 390620740, 894872741, 637345018, 866932077, 520676190, 168958878, 43454253, 607704045, 138533505, 207807324, 910754127, 456576815, 777442361, 373639278, 663616534, 929287650, 603389087, 863766811, 720713058, 590335061, 239071385, 983146800, 172578449, 344447207, 209549691, 774287982, 302308709, 247895535, 724429676, 7840935, 902764939, 45784116, 374193348, 946068076, 954340135, 577459737, 166764495, 410261835, 74587444, 183730901, 124503264, 247462058, 209874324, 144848881, 984021158, 663988923, 173389682, 96037109, 198303596, 141298307, 517883747, 373378796, 136414946, 563607033, 818910684, 308525442, 413497853, 649009855, 998723940, 896399193, 175635539, 452805025, 699709379, 56419280, 146191137, 823322088, 912155702, 847788337, 723260123, 348021359, 367314584, 45613605, 272553596, 250430508, 602855370, 883677996, 627588039, 297841617, 196639525, 167041862, 951797018, 149264034, 531271233, 766552198, 106281613, 667687391, 631445277, 710908388, 795378204, 76415852, 741286354, 78289421, 926238137, 396886434, 330124594, 50618997, 626513196, 57743595, 356601441, 275577923, 830987406, 560632489, 149110664, 604069966, 226266681, 704750531, 110649251, 206532811, 509506677, 584140809, 66554430, 439514151, 920364982, 990005082, 913859097, 645415144, 779668267, 142466768, 680887681, 673787261, 829144583, 688083113, 940540841, 106678396, 798520813, 797301616, 313251498, 438630559, 763224876, 925301154, 48993259, 580013699, 643320010, 79322618, 672235372, 148973156, 607029039, 766944023, 919528067, 921786995, 268225103, 900653495, 771379990, 827307044, 233420716, 130064681, 319958415, 91817255, 985040932, 838860757, 749784845, 575559864, 492739685, 198327158, 296326344, 666524324, 155406962, 455936722, 313183990, 540673299, 311684766, 396597180, 477572766, 498975842, 252768814, 377209300, 435273615, 361759833, 25087890, 963691601, 671663561, 132091848, 490722147, 336600691, 27136027, 868521659, 883162715, 852219613, 418707568, 475269983, 254887759, 198007359, 609796553, 648452408, 192581633, 194050265, 291927454, 866106948, 169208268, 955283722, 97526587, 445250440, 269700483, 651956097, 609509652, 711997603, 627285294, 483732093, 198304624, 311444904, 859242919, 464105170, 349104552, 40304316, 540874525, 60138399, 2826839, 990583476, 779708043, 266767601, 852992273, 385901809, 792525536, 391133782, 384025019, 510774156, 785841324, 31791074, 96292032, 466328417, 386897051, 314264397, 917169180, 574570217, 587863082, 163863321, 321422150, 888419969, 630291048, 798221899, 449686483, 561599537, 128845079, 16082185, 120184125, 601776822, 620601828, 13924303, 826636677, 720394884, 924808915, 916981397, 513770509, 648166992, 963444423, 26842667, 30016973, 253493178, 722413622, 827410980, 581532351, 372512814, 447983178, 248097099, 883465530, 284158484, 53066250, 661422923, 257850985, 219082808, 161909853, 200589103, 735470281, 600331965, 98700440, 721656227, 264174392, 499324930, 286540756, 180354780, 998774019, 865401081, 351277559, 440089621, 324388621, 783622626, 542586477, 686635088, 335020533, 948735551, 658075462, 466122306, 927771329, 703670250, 132112374, 901871955, 883775650, 600841167, 373172785, 208807221, 365778627, 562524059, 158868587, 293012564, 11396016, 106624104, 969634955, 743985517, 56611997, 513000670, 145488298, 819279180, 788418371, 751072731, 17551705, 616611103, 569006825, 728644900, 991726423, 259258249, 885323138, 367878942, 375039943, 926376741, 181565919, 326286647, 925517711, 515819323, 999990870, 37414613, 712120149, 179263378, 994274648, 655125128, 955606473, 58129861, 517420091, 731499632, 965927781, 64655035, 97055413, 449609237, 632279059, 604679602, 167782450, 814703537, 502610020, 366806641, 348709410, 563981022, 355984561, 481050016, 197732326, 240200039, 158218689, 562030991, 456052999, 821011043, 791522297, 136341249, 107837789, 1683313, 229480859, 571340382, 222387782, 772551439, 793421873, 971789907, 870494293, 650301686, 195408299, 132212135, 399649517, 86852339, 648617469, 480355583, 521510619, 436872647, 329505946, 532948844, 880075055, 709534164, 683716067, 172803689, 174213500, 608773054, 623607797, 403800956, 664121470, 463949926, 115422400, 569640708, 742567134, 671364897, 757779290, 590274956, 838164675, 952039089, 539803039, 895594029, 943732890, 521609599, 108939973, 763953935, 626205620, 424620300, 161866484, 601015177, 888273643, 256214925, 648582338, 302429820, 225223123, 945776412, 88018506, 726655484, 311507029, 220403691, 732875101, 892516013, 39859404, 351413895, 965745354, 991091632, 464084958, 535020153, 574925678, 383707513, 29750896, 761788003, 933117273, 71588115, 908151637, 403483425, 664001611, 575747168, 711670764, 639837485, 439672868, 372163275, 776750900, 985268814, 266834885, 71189094, 688296140, 651942753, 560218527, 936161397, 429207540, 36225769, 984392144, 670253188, 787633483, 818391112, 930412250, 474109508, 824476402, 734827060, 354199243, 353457193, 451950120, 609227759, 450412138, 442288546, 601984962, 685122189, 54867862, 35901814, 260824657, 2559426, 284457664, 25839186, 398926157, 179320527, 767931468, 843528527, 827388443, 283854689, 881056741, 760360889, 30425339, 543172235, 515733258, 41034664, 224680268, 430783803, 9659635, 242913469, 91574354, 512208257, 547375770, 777344558, 57162791, 810240135, 666711834, 993773551, 957496960, 445661662, 414623893, 330702892, 960362183, 181672940, 511646162, 642794219, 286302317, 551857122, 691348248, 409676394, 807699915, 194538104, 366147870, 28083981, 70289325, 870608662, 363774366, 415310994, 409192011, 573882863, 55179712, 52081355, 384869097, 87296276, 236002895, 509573950, 437998673, 571592057, 597145897, 884118934, 403243402, 822145459, 418190790, 461978143, 482352970, 885789699, 270708343, 742227898, 913763487, 571312902, 352621265, 753135174, 971878590, 85500524, 942935326, 971355902, 190105039, 849534389, 160208597, 816135185, 825389906, 385897415, 524434892, 194386751, 917353000, 409437086, 795127401, 613013595, 511067147, 728455236, 120330417, 567344728, 371215115, 899740854, 857465171, 680592388, 372844760, 665032260, 706726898, 489874943, 337746758, 241968129, 271604715, 464149723, 62758011, 746680821, 622854375, 688120678, 41544599, 980874064, 555872842, 613478974, 977710037, 661907844, 19532843, 62954869, 988601009, 460459700, 512011603, 185374272, 981695367, 546319984, 723315135, 302828738, 438618685, 409250100, 576407936, 440840624, 151264941, 625645644, 611073255, 149808386, 945410182, 994431590, 548945364, 102191400, 826800462, 429281436, 879645335, 846618658, 149426894, 22309092, 914636732, 92027541, 398713529, 161159418, 633556401, 229820001, 76845106, 607046593, 148533147, 111608788, 844288133, 158508291, 594410770, 749460902, 52797168, 164256219, 261095380, 610503110, 350997296, 151836925, 56354954, 170909038, 276505946, 739074050, 60641376, 142926033, 504383787, 148538980, 866952564, 231747423, 506681718, 46025908, 682644565, 770457964, 270948637, 621831944, 364447510, 328888841, 862618082, 798011239, 704073061, 966801718, 599954488, 240591383, 160719530, 80413525, 109228493, 714210044, 317612976, 719907648, 869081045, 800210182, 377389259, 816296699, 973226913, 195729934, 539898557, 745257411, 364497065, 578457341, 494052165, 818929179, 35729788, 252824453, 973559240, 607774025, 655235205, 281476985, 831987980, 220722274, 516330888, 900665038, 712122160, 212634831, 587019298, 297871972, 788246276, 884677689, 877195169, 917779084, 685918339, 244926582, 38368269, 793216462, 864229758, 136353119, 158820308, 549975457, 553151012, 21286983, 824938484, 177837882, 14310315, 729278297, 338663473, 786879114, 945497512, 516113471, 152804480, 756864705, 883734354, 506622295, 930521109, 938306154, 658703856, 618007019, 643843811, 630439991, 221926127, 284546728, 859319815, 948518078, 67329734, 281838014, 947664623, 508674420, 513962562, 381164876, 777610799, 926426279, 783308682, 847861709, 550647942, 852305311, 857479213, 275504574, 605292192, 632705511, 313624523, 539525409, 377727840, 391035973, 280786386, 803390305, 508978946, 762481839, 722803754, 200690543, 989844506, 904651981, 730810675, 692296615, 826219388, 765267956, 495474599, 382878339, 55733176, 661649389, 983603599, 5519234, 619532680, 716473985, 982696346, 552931016, 371317741, 537890858, 32159499, 788611646, 403628686, 497307425, 214232262, 37052892, 533962407, 406565773, 463344154, 6870792, 761050513, 949798778, 728510245, 1254412, 992469795, 437485466, 34629152, 423449978, 953835515, 500266389, 945036280, 344292085, 295943402, 745194103, 458540742, 200114666, 158765400, 491105124, 699031805, 147693552, 479293731, 594153036, 535755990, 310629883, 90657964, 664222505, 772617323, 797641940, 836946929, 311986170, 147498916, 511425466, 295386365, 177217037, 233147380, 817025398, 660224472, 519159459, 377285449, 207040538, 575720042, 952276229, 924312938, 422524659, 662988787, 962981497, 145484447, 922374069, 842995249, 186490553, 720698187, 803169976, 933847845, 807717068, 404632521, 413454094, 222049011, 730249610, 50421510, 828153539, 908698576, 584049001, 676114301, 200196379, 787133514, 590439326, 530765977, 417812282, 509941575, 890953017, 558753913, 200383293, 605482277, 379534170, 766064930, 808277177, 293519740, 352311195, 247156839, 806017902, 671115003, 323894121, 248568617, 871102954, 905980134, 240740116, 492387707, 401327940, 638184096, 942022922, 17418809, 436952058, 666952419, 480627422, 575742944, 194779111, 303004455, 697010958, 44845968, 985971102, 745333466, 986767064, 180349330, 853665276, 146268535, 357022512, 984410919, 846493698, 403274489, 680040964, 750366072, 310212136, 738685219, 92425577, 642952401, 50548306, 11591474, 252819889, 663008993, 855679632, 417343926, 108660992, 223015472, 875785006, 260432931, 569165397, 76880127, 28995209, 622067505, 731105289, 307538826, 114293852, 984112287, 412147631, 26504257, 139570360, 666010731, 31343525, 997133033, 316945712, 998429674, 615864848, 881518111, 203419261, 616109234, 572532404, 678541705, 420407952, 491587251, 13518659, 497328985, 81072512, 176346620, 517131650, 202727695, 535853017, 966720398, 815801913, 401321298, 386918798, 778666585, 698760276, 18399591, 130979886, 819504142, 6643898, 395406863, 869805063, 67213253, 844231718, 937552265, 363791047, 924039698, 15800849, 474346633, 186287764, 135557675, 673880800, 293074246, 400101627, 373591127, 160549811, 317538469, 784255631, 896766705, 148110832, 266372883, 394926565, 536076082, 407693144, 657518794, 955973838, 967147587, 172231024, 530860093, 824061797, 578599225, 153462131, 890380333, 43200268, 290853444, 90938947, 806974376, 945843982, 776674058, 919840079, 363330893, 543440260, 241099698, 335223016, 67832337, 79167461, 551597750, 848227028, 248399656, 246338913, 548855223, 670832160, 955796552, 30757417, 283936488, 791736194, 33828014, 776458269, 562703196, 328868231, 366659977, 661380085, 461927387, 975699533, 65565000, 199073384, 716817120, 748917927, 588886534, 264694323, 69546625, 998939022, 765926192, 19971614, 293066568, 70253272, 827240922, 83520528, 871024216, 239781504, 935687011, 410706985, 438586400, 505828807, 557299319, 765520903, 777144319, 723598136, 199619470, 733175162, 241842263, 608346613, 399126221, 592036789, 476238657, 16520202, 655177473, 811737786, 298828877, 935276124, 689517206, 797070416, 756759991, 78850724, 625199220, 290066533, 800609978, 447884216, 12600509, 650086867, 203763634, 486248610, 465268655, 958431398, 812283384, 402409968, 387922335, 231547272, 487714039, 715712478, 211020752, 625024467, 327024143, 252803707, 77103547, 306749924, 205185187, 608844573, 673214046, 88265684, 323320765, 509711413, 53007991, 848242797, 230733361, 830942160, 303276721, 279752514, 387294594, 94110443, 282837377, 535039712, 942457602, 144338425, 77721435, 74080838, 822769144, 655437925, 635332372, 688470584, 494780116, 271674281, 612932177, 350586253, 846154929, 203792337, 125306978, 212752120, 404011661, 172971397, 189412164, 196016176, 962269283, 368329464, 268944885, 171921411, 931340370, 187318815, 579694198, 213749396, 354784935, 922786180, 273590371, 196959061, 447593159, 71629613, 62383907, 85755478, 201918907, 883847057, 500696280, 481874280, 51162438, 217389154, 993564722, 468632869, 515373483, 62936671, 990595054, 955834003, 522667374, 36897701, 21172428, 425960261, 817241710, 717492922, 862530712, 944573870, 522736036, 33978540, 933105951, 6658537, 434319424, 24100880, 507041098, 165369671, 77063521, 987271939, 747561125, 500074634, 527097222, 215288375, 242818407, 49002057, 118564564, 920858303, 442791151, 125052863, 811195703, 322277631, 900137297, 628822161, 344430421, 784413822, 431117666, 169763825, 383528061, 341145409, 538734624, 795971668, 968235171, 301652112, 994421453, 826808227, 14879819, 148914969, 44169026, 250199462, 196473180, 642458812, 57566216, 230804282, 571474432, 620122213, 846217610, 67276511, 825825941, 918367993, 745508909, 827216953, 569394637, 152006273, 696083784, 115672805, 739476119, 943891813, 18564183, 927701646, 470277718, 342031811, 172303478, 868439930, 134499217, 254055794, 745328725, 449925451, 490768473, 587582511, 389987093, 78108430, 421836681, 173673462, 966161497, 912889722, 104093715, 823872976, 835599462, 174008341, 838548951, 161190675, 953709473, 459665111, 97061351, 419672456, 456949344, 741333035, 436584448, 857154621, 332844493, 714758998, 723903079, 387224924, 835493008, 740535050, 728583637, 914288779, 160665668, 920876162, 405963822, 740886806, 185071856, 273632222, 31431427, 643265195, 33463550, 574635125, 375573992, 661256963, 269303307, 820561944, 520257120, 975839931, 685381929, 61326023, 810807735, 212732436, 376219141, 509281750, 102971511, 998479393, 971129081, 315042100, 479419276, 82430763, 341097522, 739037707, 540746859, 758186461, 912584522, 693512386, 853990840, 820136121, 511452497, 147275836, 155084368, 875170476, 854238584, 918340419, 771308578, 354462286, 624832549, 391584269, 453972770, 840766435, 942184610, 44914616, 45821795, 428754317, 122489618, 699199856, 808875612, 757663059, 574638559, 74973444, 16082197, 998831496, 839032945, 839241112, 929237250, 999897699, 897752918, 933682059, 359657171, 485401210, 536087536, 895416199, 755918045, 693899906, 792692512, 180602435, 881818607, 656766438, 995477794, 760470937, 905806719, 858532755, 290575897, 718719232, 172426070, 925066920, 558928967, 393445536, 894900829, 962229349, 755716561, 155793001, 596939405, 184417128, 976896811, 924300418, 10907983, 979542800, 852120476, 982702673, 568812390, 314634231, 726528090, 42326003, 605001809, 85777556, 251423290, 716458553, 553745279, 575814059, 426561983, 198277431, 952123875, 833068656, 671292486, 561671928, 977954188, 86830409, 786573675, 699586992, 70349782, 459941624, 939760849, 918176143, 816765632, 855368570, 35469950, 790428170, 151283720, 609227358, 140136829, 970479868, 17169085, 964421036, 386491098, 84740902, 714500612, 556616883, 242634398, 465167708, 254501868, 923782439, 425781862, 782872377, 79817973, 173145918, 529690694, 464167165, 607121369, 688098947, 952792550, 383525106, 474064540, 844064949, 966331083, 276910089, 123017522, 540943011, 83681407, 970250876, 845311316, 337194076, 697259417, 220789728, 605453986, 611837444, 201681692, 981118571, 464905505, 85026054, 513638849, 867088931, 31317237, 384460459, 389635285, 794965256, 516210937, 624006534, 804794930, 897746940, 815961658, 153762914, 160111694, 473345892, 224154569, 868905195, 710569205, 21512717, 588225078, 108213221, 946445268, 546208997, 393856768, 413171163, 736018692, 886607686, 903213863, 852887374, 287334450, 494388445, 483195480, 113131526, 924410709, 36443018, 41810877, 720336196, 37460097, 193391510, 58636094, 570569139, 805045630, 790046193, 93396966, 403487263, 452675304, 399000086, 930943055, 5339415, 540932015, 931947259, 483739220, 547105270, 749260712, 902502913, 993831405, 776639006, 469378193, 474044889, 664245478, 27505861, 540388337, 981645664, 143976424, 278583267, 193040602, 520222899, 478153633, 288409988, 589935433, 732111399, 305751886, 539539276, 890736742, 496862128, 841630682, 562334924, 371083070, 593264120, 997826622, 854129729, 400744683, 483260273, 995559589, 117139494, 12858661, 826352655, 146017668, 193110536, 547048736, 641764186, 572399691, 685421014, 436635893, 834825320, 645992784, 308749215, 210926529, 641852412, 208284057, 427927798, 740819663, 908657344, 986949205, 210459351, 21084825, 699761283, 187785811, 695725690, 465136388, 247907259, 3572948, 700377011, 838115366, 109873176, 701934011, 668109974, 964880107, 145206717, 69440227, 361910508, 486823337, 754038113, 451924854, 195313646, 70345505, 736030553, 683476916, 934398356, 601079791, 54189601, 967218025, 117977430, 342039708, 524252124, 76639243, 326315965, 315616686, 524960169, 311148819, 811952350, 52384908, 943567978, 63046039, 332455533, 837039057, 836085403, 20194688, 782684335, 598972752, 896191160, 663690593, 188598829, 82713767, 618099194, 731431135, 343772972, 197663144, 87744546, 28814071, 618862540, 447535592, 319557935, 269773477, 860840648, 512731214, 734573098, 921308009, 341999306, 88003726, 894117557, 491790694, 922301003, 717962107, 666241402, 765973129, 843894289, 775521522, 863977129, 580705598, 726622438, 850342190, 239454899, 351058545, 585096113, 458248838, 789579279, 848495717, 516735640, 754786091, 805920623, 959266096, 667046330, 475649189, 676183266, 613543790, 197431434, 679073658, 22295688, 647746221, 306298693, 434957116, 863081601, 981710508, 190840941, 710609927, 310649508, 135682537, 901779149, 281345734, 53070352, 543570014, 551382077, 365225529, 800462689, 506174159, 853862012, 144036419, 294138201, 274360891, 127560190, 749233063, 973034585, 584264689, 941460751, 305879537, 760811305, 969988607, 811536046, 444151882, 366592334, 223483624, 980967292, 919231609, 144247215, 839417834, 707626290, 987965100, 335426514, 390469370, 469398012, 744635147, 663440985, 565553297, 951404307, 869828741, 96955322, 490241038, 63188284, 605262088, 178790409, 509216990, 939624726, 102104911, 587985614, 890532218, 322434281, 989531129, 721102263, 400373188, 15443474, 367623161, 442288287, 455228069, 84840407, 214563229, 820838062, 850583612, 82555182, 297147814, 467196905, 420152254, 97614786, 140130194, 602730924, 545828090, 930948917, 806061481, 755967178, 693053918, 961572102, 634956346, 296440446, 921826888, 823470408, 104290287, 950304906, 927405037, 999633710, 827340244, 225124649, 427087398, 651483054, 234147059, 605188617, 672258067, 452317674, 390141346, 58773508, 208341280, 89349753, 656598701, 995147372, 704022104, 509912591, 645647379, 880689684, 471349936, 530703140, 246458939, 567155859, 106558007, 640083851, 811568262, 275883007, 519127987, 817084301, 710558437, 535888418, 622861835, 99046065, 168571158, 669547601, 988405059, 402654983, 375331146, 471234415, 8957418, 632552708, 998717050, 308735919, 142535750, 532176976, 642421570, 734591784, 832735851, 510154767, 47031943, 305014054, 718513336, 111403366, 441681512, 137016549, 461037330, 923004452, 90882293, 212386131, 976528134, 278355471, 860135502, 845175186, 711384491, 470401607, 118125787, 638518851, 967831959, 354617594, 289261229, 551075069, 315444670, 16358633, 73550926, 384291372, 479513453, 863554746, 392123213, 329309116, 283229437, 155378623, 116587935, 461444563, 639495448, 387605873, 896206253, 320997959, 833639266, 889963211, 2911407, 248079591, 313585422, 54268611, 761022821, 478997502, 867708445, 891010135, 653374024, 51509837, 763195683, 997376989, 815686850, 545080242, 768730682, 314785384, 859937961, 601956464, 922862864, 526266014, 163190087, 127677942, 700747930, 237519942, 505358480, 742980612, 306901455, 441594738, 121317526, 820647299, 107377626, 878830199, 631283110, 338104792, 484150366, 246806787, 760092845, 820129930, 482092746, 553766839, 51142335, 84012844, 766023329, 111395498, 153805139, 719039258, 194584443, 323285326, 387763293, 25579707, 542872165, 850506884, 540765611, 916521774, 146870780, 131645796, 960484796, 133172270, 610742340, 120382089, 303471466, 375058626, 369839462, 535600264, 275329149, 818044413, 778813023, 794614508, 295810446, 106022088, 389758244, 620744241, 820520435, 780945294, 417796571, 811987550, 918431830, 154432207, 214402854, 447352288, 670681780, 181006395, 257303370, 811400223, 882562502, 826891760, 868659309, 727699922, 551785053, 891946772, 497854510, 864319938, 995544408, 248531341, 449302894, 300454045, 618327382, 509254848, 345956961, 152457242, 319157069, 293712094, 141020988, 975068628, 784708000, 318092382, 871486528, 342102430, 185820865, 286188502, 906616756, 417420438, 853835570, 274995982, 432037849, 263745241, 924566058, 995019602, 315099579, 21981033, 791388782, 254351292, 745037028, 868124719, 213313202, 450607338, 659572425, 888392891, 215293451, 887141287, 800476539, 160185343, 55380021, 274768770, 470103995, 423446675, 91134315, 190019793, 720693053, 729294290, 685780846, 176065827, 516249347, 745593193, 255683846, 119931576, 805008689, 259768095, 901461510, 593629804, 164686155, 13388440, 656652871, 826196658, 416128041, 160098347, 597185629, 516825472, 425361655, 266391949, 560267040, 113176879, 875669159, 854808441, 368537512, 456748808, 194524694, 536653635, 606581416, 846847830, 982340970, 111158242, 28405691, 510081541, 516919492, 678371035, 349132307, 390563734, 674177925, 569334459, 853147925, 937944235, 747420716, 476976327, 416895243, 756580437, 497811972, 521792898, 416640757, 826017822, 949263936, 388236922, 60667409, 661121142, 247390196, 495366388, 881038824, 877479637, 233811352, 462090266, 764188500, 90468041, 191373488, 909053838, 251695746, 375682111, 820559203, 886292963, 670628445, 809336539, 787840830, 545038497, 958131444, 235368117, 998548060, 417323192, 619416558, 272280791, 672632758, 148543640, 565728935, 829420504, 922597409, 908193161, 254178799, 967443973, 34747906, 359599529, 121485562, 827311307, 849141771, 409276271, 706865146, 876005451, 297354512, 984363723, 284306274, 514828952, 316522464, 712581844, 487457439, 840747264, 642678143, 313258445, 467537521, 482976792, 403209745, 895371701, 94828175, 348919456, 496811154, 590623205, 950866089, 902769478, 853266044, 100018027, 711790550, 826205828, 219820016, 120612347, 120122924, 472680355, 630717955, 410991938, 904585127, 560572285, 506349100, 574356968, 246519033, 30234486, 649517050, 813802264, 507113538, 857036295, 721219485, 880521062, 789009926, 693355989, 195754008, 780646424, 758225969, 767649473, 16570265, 820351814, 154323000, 7684082, 645898462, 425810234, 845485461, 386138425, 605051857, 923118389, 810943796, 181828321, 960227784, 199770631, 708598513, 547512956, 293819563, 458233261, 86679475, 867405082, 954934231, 42354931, 522349987, 267406275, 236020551, 878543984, 922646198, 81620770, 439188960, 215951202, 319943326, 743088733, 604771097, 914398041, 654940608, 585921106, 991034583, 604698633, 68199971, 245566941, 562290409, 134207660, 293090192, 731155653, 786618368, 119937899, 329551527, 330892409, 198928729, 898737288, 153336124, 881494206, 835673335, 804098184, 176117947, 996296611, 510419330, 21614284, 852011484, 373375790, 260882257, 189516701, 233743194, 182409922, 785378887, 803307026, 816203982, 484094253, 354016914, 222061925, 669358064, 940534431, 999573400, 702412161, 304110639, 34065097, 346983930, 67298328, 558121602, 123328623, 678185157, 189596508, 478997651, 421017347, 62915970, 950667883, 662124291, 843059673, 353476263, 813891908, 115029668, 425272174, 269839419, 970876251, 583680673, 381669881, 555052653, 643020566, 232865122, 947179783, 255160745, 793395269, 284661301, 220990675, 693450996, 910896688, 832331375, 151286818, 441550719, 790213518, 932478410, 436219095, 869280150, 970825201, 622277976, 436466923, 946839047, 891742026, 670134071, 881319295, 3225321, 573596999, 123688780, 528142158, 544772924, 492268738, 86553588, 257490915, 378514743, 352477565, 940036812, 590873088, 68291854, 871460318, 493820513, 737837428, 931519211, 297061216, 978678762, 834576065, 902186436, 743615146, 745083355, 487178628, 33494162, 153944938, 665282160, 952702906, 847615421, 330574411, 143317974, 165719066, 629944985, 81796313, 663387138, 497860251, 505523219, 699526011, 603671496, 441337412, 10174599, 644975644, 312684159, 922406718, 289253084, 358976904, 218758231, 395821148, 123327354, 859891815, 655876193, 484703436, 291366829, 148788362, 891584793, 496538262, 4701558, 629965759, 204565792, 201536724, 242928987, 597760138, 767752324, 649028525, 981962877, 209191221, 513164117, 219185990, 315208756, 868727575, 622557580, 653620417, 81587328, 939736136, 669850975, 355546914, 779263670, 226549278, 817179884, 417261930, 70976956, 174896232, 297821343, 890633896, 326703385, 617687763, 3194787, 192890349, 715202785, 75462950, 254946148, 68042897, 783918921, 806670264, 905719616, 514869540, 169240827, 279797011, 979576806, 829160540, 773713804, 935376784, 744409227, 274390090, 12113249, 215727617, 581459508, 925533272, 675109124, 821381982, 135715074, 318487742, 867896099, 402113218, 336473345, 832732356, 511765323, 399062457, 659146063, 547171031, 20309861, 668222437, 85404819, 733908265, 901786565, 480104867, 771476676, 184380177, 336398113, 616276375, 355600475, 962789548, 398919224, 103561203, 38375890, 732944583, 689271367, 972399585, 691128789, 375732436, 394989988, 864217813, 434252645, 809892459, 938305218, 64898836, 357907728, 844838857, 703036951, 691035106, 640478884, 187119878, 266975836, 79356234, 88909657, 440797888, 384513289, 661108376, 680954959, 974949262, 981080695, 793513465, 759452337, 144855166, 246077953, 568452782, 546317449, 412233065, 296178844, 460410649, 89382193, 861900060, 137176535, 322530992, 22180524, 431745164, 597865216, 492439455, 222886219, 442705431, 70756911, 425719770, 578880501, 941984011, 179313412, 41127944, 836546095, 600538101, 197448911, 611407875, 381766244, 377376210, 801589933, 763249481, 408175798, 442949374, 475809072, 283824135, 250700207, 594635643, 912799566, 315787410, 427663669, 18477673, 952405451, 900879357, 665016353, 913864003, 705683910, 92277662, 32015844, 994684489, 568918847, 446588969, 500279188, 220171163, 994798037, 162985442, 891048962, 273846616, 466484732, 139492966, 604472736, 558434222, 311126350, 140074310, 459669431, 660067820, 173227889, 512373610, 755072850, 845103148, 96161667, 184155983, 812075338, 350408422, 791678491, 766737338, 39878890, 654945917, 254585887, 49168936, 963342108, 96690232, 752516874, 152349790, 861408071, 223025422, 858394544, 820831481, 268804989, 590268284, 628515908, 500748513, 214817527, 984283385, 919663550, 801216536, 321734267, 79629119, 621071655, 251885874, 811390841, 705860515, 683060731, 387763365, 847883805, 650127885, 952025619, 306105755, 790783494, 149441531, 302073800, 109993220, 195973122, 123901475, 485956610, 598603381, 954896570, 106618693, 439825053, 17266374, 579258419, 549251808, 654943123, 356239210, 177269443, 710263927, 879607187, 788233209, 973789797, 28682307, 798200541, 81373454, 793273023, 19125903, 518513618, 311779637, 630979051, 609970754, 235961461, 947625485, 760428097, 67201240, 311158804, 612976032, 48581368, 510149262, 128355094, 504184551, 474880714, 119614327, 709451310, 96725908, 615471230, 470322930, 546761910, 486417133, 941319207, 45471834, 237141308, 287766855, 153411490, 254708576, 949226197, 975459790, 165708921, 611521003, 779065886, 230835031, 580996891, 157337171, 918977619, 972372657, 74863275, 609883312, 989257144, 753726350, 607970786, 527921814, 751336599, 391400270, 59431755, 92128704, 507041939, 740480677, 955629676, 197854554, 442427363, 174782866, 178373647, 701752508, 538422794, 67551083, 859801967, 118348534, 443682734, 863026240, 127527454, 280531781, 359187768, 870419227, 136507191, 43458494, 162945252, 616749104, 270499664, 367685121, 799392695, 211819073, 915815511, 94925312, 789894664, 340128811, 616146629, 954444817, 960128885, 838093932, 924406169, 928635641, 781161577, 937036738, 5516405, 44107035, 572813809, 891799214, 635447392, 944285706, 184711213, 967406822, 39622610, 987301712, 462749015, 354548724, 106147955, 865408439, 401850489, 542372011, 830987056, 99317686, 348157139, 978066421, 453985888, 945116427, 558373227, 246729134, 434256609, 923851015, 101104023, 31804873, 130757588, 748327709, 140835695, 432846331, 336017866, 842200624, 273460204, 148272278, 995918210, 937935909, 938838965, 846339149, 43094403, 492744230, 576999738, 289422522, 359454061, 935865367, 198926517, 97351966, 392947727, 399414749, 211853670, 725976909, 31262433, 618456033, 968113583, 240658708, 798081132, 361052345, 693652657, 619628496, 329311876, 38568090, 623769335, 784818339, 802303256, 121811499, 892769281, 983047945, 724875377, 777505653, 105031576, 968974364, 105798721, 608564026, 484576038, 122380766, 600150971, 434404838, 187260499, 987291024, 666907826, 486808148, 886918355, 231108913, 43055270, 951019523, 49335407, 267019909, 429684002, 137620016, 700078524, 499374745, 763512088, 137151660, 480201203, 785859521, 506445506, 539703395, 249095498, 659315645, 85180129, 294386140, 249548205, 98524117, 582956561, 449752238, 501751038, 684246901, 46054252, 524517719, 505971090, 812245745, 312427369, 509480761, 64335086, 357992194, 421347993, 410650888, 959805926, 768165455, 137676552, 932938915, 48984943, 274750529, 491958719, 709035467, 785650375, 60871287, 46155294, 72233102, 193365982, 397044868, 140165201, 293200970, 723263101, 28985326, 624949833, 51949738, 37707712, 57106650, 149573471, 197217586, 63483112, 963368505, 42772711, 168400130, 90735036, 790895757, 665045475, 975871345, 781195412, 267089449, 25156421, 455309751, 237332733, 904708919, 709293879, 253425235, 404588652, 240574105, 921089685, 699177581, 104301610, 450335447, 120342500, 590669245, 841030438, 230490441, 996597423, 159818237, 159235604, 263118122, 160393160, 455898473, 205205812, 20607460, 499343406, 628061893, 175704564, 420845274, 485679189, 893780125, 977297712, 931965206, 26072844, 353477648, 510012967, 990084124, 266248135, 997452711, 276109761, 107634541, 732180358, 777245385, 844625876, 828656916, 488802068, 123055070, 7845122, 801379827, 813331412, 280696294, 604482252, 551230391, 618027930, 312210896, 185306190, 849669293, 434975470, 557779197, 531786544, 19068960, 427866991, 424547707, 208156104, 304208058, 477799720, 965581532, 800343995, 674349296, 610427080, 482733439, 470644830, 153177449, 181983193, 475390542, 618288660, 975385962, 230439542, 647316207, 812917132, 661768787, 476135682, 449056158, 81677831, 371773145, 580814236, 631262233, 486999335, 876882446, 536518922, 980691374, 2701988, 862375743, 990054925, 977001164, 899007407, 242153842, 292029484, 173180314, 647601209, 645080830, 793785610, 364864340, 606158902, 394336015, 84695934, 696609622, 222838954, 647190088, 874073278, 99517213, 590692700, 254983314, 568231389, 885502202, 101805241, 704563953, 919265603, 912615612, 116639340, 361552810, 352740368, 951717247, 915667562, 801255297, 755260302, 195000949, 963350051, 635373308, 308146711, 550364275, 905158274, 406020626, 294680384, 319100210, 914989720, 201350166, 863290567, 427246264, 332055571, 195674912, 496622633, 212435774, 79645460, 484523559, 747920957, 31673606, 83344681, 816653213, 67778766, 568347, 236311212, 583956683, 489622077, 57523654, 335197898, 768999954, 518071361, 410818403, 126818663, 620348556, 818183189, 218035011, 498090449, 143421592, 45555792, 80683836, 664722177, 689834780, 518549624, 458634878, 61346922, 460185524, 577738056, 335308772, 387549859, 783641462, 724770429, 492111054, 911205052, 575645018, 186872810, 10087502, 242839305, 717157165, 831173483, 1493577, 339049375, 961455917, 290152027, 540579095, 291463088, 754086278, 238197683, 697985736, 364574002, 518170202, 461659422, 780579743, 872175952, 351498593, 184425577, 367698536, 214785180, 558091841, 607715418, 302546392, 714991191, 210936557, 44791723, 706905888, 104709056, 385433208, 869725894, 747933150, 736225036, 811501600, 934666473, 311761263, 405408896, 355050290, 707664939, 198821466, 387698998, 729725926, 914111257, 35366616, 26384962, 71974731, 95170065, 296772449, 459310750, 487965652, 74607303, 109502822, 325312103, 175251526, 303800002, 915344672, 704961931, 107633874, 569914625, 487181475, 129434245, 590980160, 574936769, 911928149, 313407995, 600731114, 589320060, 472921333, 875028495, 522907222, 709479598, 736887764, 79315330, 117410809, 851238049, 989480632, 21903417, 329135731, 98317165, 32978050, 655515589, 52877968, 24679012, 374598901, 286475396, 351560691, 852122307, 613681589, 487409336, 125457220, 213097204, 616717718, 553719103, 629303184, 888586523, 658595139, 459950771, 66438854, 710214118, 938997106, 873068358, 806282124, 439495377, 586500099, 920878484, 832271009, 570139053, 753189782, 694934973, 933358189, 624789722, 645720273, 980601053, 308532076, 582021328, 494993152, 450675760, 415411051, 832369546, 307723042, 499330207, 711009932, 93387549, 695803196, 471438244, 119599602, 572687974, 785783951, 590230477, 695250082, 667138764, 139559471, 754798675, 526247777, 348352765, 907131992, 287948971, 977714074, 247698676, 347783690, 729644965, 86637535, 310141770, 871170260, 927592881, 93027078, 284854762, 180403106, 846259816, 406107512, 65795424, 657322761, 795294112, 865528574, 580406034, 663234513, 560939289, 851733341, 88597447, 700372583, 20280483, 236033841, 41823843, 681246405, 255180085, 37879035, 294057366, 650028385, 832003397, 528533171, 899962238, 488117511, 58240980, 966904304, 524142771, 321957887, 650383033, 256035905, 561799711, 239201270, 929576979, 486682307, 739215915, 55929969, 636192536, 502073791, 600208037, 599112135, 895748711, 247259347, 678501096, 244885292, 480012777, 765866653, 928762842, 310432616, 624775035, 806292931, 306252130, 38711922, 890804730, 182039630, 817966418, 69162297, 411290032, 101765797, 360521513, 416728698, 45064800, 726794059, 917415796, 31518600, 819066292, 620164368, 984057090, 788529184, 430906559, 641384681, 382745563, 75137620, 984301271, 419354803, 983565252, 492830707, 607986007, 784402077, 366905116, 4685611, 671711612, 692189524, 495527749, 178154976, 355970045, 69209478, 903210123, 948557236, 351918039, 734898224, 22855452, 630847319, 961804573, 434700383, 719262, 713272197, 856016233, 567303174, 730578042, 436971483, 214201950, 277814244, 491743076, 417829072, 517238825, 779134149, 602592045, 868370054, 446237783, 540668469, 631860231, 563260491, 656034092, 82410502, 529554692, 925749695, 598278830, 422744599, 321746113, 616218131, 357331194, 782184513, 783061436, 457111145, 228636636, 389512896, 782064358, 825684933, 423044311, 548093025, 537333168, 552931855, 609522061, 440893646, 455344197, 393370929, 236952901, 466665556, 133210352, 186517086, 80051006, 921703240, 600011273, 300581492, 988817531, 693090672, 268680998, 38642623, 860106166, 873723802, 386664984, 383166634, 714372961, 565851064, 127175713, 41419798, 994133409, 404788744, 607173948, 980499437, 755463582, 4641275, 898124750, 722088297, 195891629, 300761072, 593836921, 301030600, 162222696, 965763991, 367933666, 719578579, 627103950, 180905920, 594565332, 967026042, 666011029, 473259453, 37553876, 667773526, 597843344, 151814723, 243059768, 921291999, 26168364, 839484328, 467266858, 438267096, 732749341, 702890041, 159010018, 168636041, 864045145, 710388773, 212746416, 716598766, 593823070, 9153061, 298243144, 659739710, 78143278, 484998322, 600360209, 343722058, 231212025, 900167508, 785302022, 824267975, 689861887, 954130157, 494848007, 729492779, 436501747, 453407808, 513989405, 393133957, 612905518, 755690856, 590001505, 870613457, 401442462, 298511246, 893101796, 665578064, 847165638, 58444502, 144286501, 277051402, 376445366, 970325909, 538233182, 807689490, 839065070, 524581037, 914320494, 430079698, 272508344, 969172308, 342396142, 676112558, 396243871, 42744098, 667703817, 789018660, 674119749, 713930056, 84320590, 51204476, 700737192, 4362936, 17736203, 245837042, 51329826, 923527606, 459859169, 777872637, 931856372, 303835399, 781188676, 11912719, 571418641, 869413248, 586650783, 962228130, 303567067, 553387930, 289294834, 724227468, 309191064, 287519606, 563783234, 450473287, 202581769, 605850151, 926778616, 721271596, 70554857, 278200855, 154756045, 819214215, 779891452, 306660698, 249798719, 117058496, 702475239, 354768540, 200921023, 267088968, 423164818, 830258617, 182446850, 878022946, 281222897, 299219599, 74117752, 345706656, 386840284, 245535508, 274025619, 700118247, 714386605, 673675315, 716581252, 268698002, 542585462, 416572552, 971359299, 652812626, 208854825, 168909769, 286865657, 242982345, 399923227, 34701971, 784506798, 998713295, 393625647, 60590970, 360007300, 687266834, 96440525, 975223438, 235759397, 901715382, 50313579, 542770154, 28893308, 20366502, 929668025, 188405548, 37723749, 531960383, 183523169, 300451394, 189455538, 375441509, 734760467, 920500357, 362395772, 606438013, 684050417, 932477038, 788379879, 739955174, 161031951, 22259211, 948266813, 696983208, 62436271, 236585938, 787193464, 768004646, 972135729, 812073113, 755290054, 611105258, 271905239, 704151428, 20993057, 353306115, 576285039, 653799592, 298970074, 769310045, 164441932, 996851059, 152886971, 940905428, 616782311, 951441871, 790459951, 301871791, 932079078, 568386236, 667874342, 166303676, 990164375, 474765091, 895840805, 142827025, 897644753, 428918858, 278758168, 53866220, 603845864, 951655512, 931558715, 53011976, 869714952, 125579894, 334961987, 476562462, 876990064, 520802909, 117548441, 93505147, 835696361, 720081713, 600859303, 617068882, 690409420, 135283782, 871087585, 923959321, 938986844, 300737678, 410834300, 672726351, 441679636, 843048691, 194251870, 789717073, 158588939, 698969477, 432283858, 192998670, 32865539, 629932119, 490774296, 500932238, 148373023, 842824094, 575834957, 243023123, 393367469, 531168378, 199247395, 375500329, 813803772, 536860540, 677123904, 769235001, 330073071, 456369305, 54490237, 798167202, 585586978, 646621746, 955410991, 940263721, 680712100, 483720327, 542965740, 783637229, 879377919, 648289130, 387405198, 460783423, 718393025, 630706126, 23294287, 239558005, 445051764, 647485334, 871143959, 221148271, 960921283, 797341720, 153271367, 115170400, 867453554, 381825020, 962581450, 895731403, 619996682, 648584961, 264148380, 416694326, 164534671, 884905266, 295729041, 788434909, 428512456, 954009372, 103621808, 746602544, 720422394, 864142672, 660663033, 199649985, 391981166, 629072989, 432402290, 972437869, 352609661, 516799635, 722377986, 898513906, 117042010, 427915962, 201498284, 340798795, 748309040, 344373968, 641845711, 659998630, 582456598, 431090047, 650641043, 768542193, 122249533, 935937343, 541298368, 56492233, 981581652, 288854920, 967936249, 747637863, 355751768, 787806153, 61176864, 237689272, 693375649, 308840931, 211430797, 654936914, 377602918, 927777536, 672575253, 821886396, 140267121, 333510527, 798965944, 129317195, 836060083, 108113522, 245153198, 333642528, 96049620, 384082882, 90873753, 957269401, 2067530, 334956345, 329744552, 726110231, 69142549, 647711090, 728837178, 265639878, 832388582, 290417185, 192309131, 784438655, 554248538, 685001086, 653898363, 663075063, 605332087, 304556157, 850412128, 135378083, 830546704, 233772150, 410071102, 833880245, 817484605, 752443599, 520200385, 793484436, 536935226, 154577917, 516495047, 414723355, 516895002, 349677352, 669020064, 802185212, 414744270, 248500390, 26054071, 810727014, 841520891, 426934654, 26180175, 283905086, 273238163, 795243103, 929850884, 860460999, 506677590, 372059227, 450035690, 42191728, 204725613, 448304114, 781319213, 301025327, 576257569, 672976362, 546790859, 228206371, 400710854, 550659599, 711277380, 922945574, 612444158, 416607645, 293164807, 100497018, 960156457, 536641889, 76721711, 448540111, 366864751, 184223107, 355661612, 489872491, 734843896, 305635316, 117514713, 82529506, 921520194, 572179541, 371425365, 639843817, 679303718, 744381505, 356487154, 7727788, 840018440, 335862930, 271122652, 649630529, 651484859, 505466013, 62557434, 458479821, 988346279, 716509351, 56040440, 797180244, 560112851, 223944322, 75512943, 505534073, 14664320, 50316470, 713138974, 813384859, 54236893, 587336258, 161582019, 546243342, 150369043, 558365841, 942562943, 480482824, 766834600, 886376589, 747880623, 521480552, 39600955, 792237326, 507541869, 912908245, 22577081, 415461580, 745847516, 21715566, 88348904, 563470657, 404119613, 6409731, 779410900, 364753651, 505541177, 223232914, 986049346, 665607485, 617946706, 162589129, 965551415, 524680990, 723493365, 774163313, 809133465, 855347544, 920675169, 771251321, 577269270, 476756289, 764051960, 787813837, 531092888, 284369931, 597352790, 281346884, 634312121, 309743316, 671841838, 119761271, 409243138, 694647667, 53395886, 99888097, 478423975, 120758506, 182734063, 223434952, 789175868, 504707498, 225420053, 602327429, 918800183, 121265368, 412272363, 295760624, 219789330, 443365270, 704788069, 871853032, 892456764, 955201519, 439384420, 632889028, 175531434, 782563978, 558592758, 390155064, 22193597, 76779283, 468986855, 972203160, 119837872, 345651376, 521393816, 149582755, 985549132, 450996166, 934041656, 9924281, 312481789, 837046504, 522417409, 628486956, 48115564, 53463477, 592083492, 409108438, 572056085, 480245006, 54990126, 611439134, 243655290, 44527490, 32132359, 438572888, 471607878, 549846557, 975842141, 276190953, 473067688, 268646764, 712376346, 19253279, 678605096, 540688313, 833660768, 969030180, 983321749, 230161582, 247079476, 853132406, 435425653, 735174104, 520284154, 480177358, 716656035, 938783644, 828974702, 506312979, 644369759, 60640462, 276335450, 174835117, 625881208, 900284702, 445133768, 946041977, 240045860, 879881432, 794070706, 95401274, 585261430, 544151231, 814510571, 206715830, 316606177, 940777792, 24241467, 723556923, 316649918, 856024740, 629003587, 512250004, 142031958, 943586866, 424315530, 276805351, 909138693, 655589730, 260037694, 978453947, 306254686, 717627494, 663136796, 828941386, 232769769, 896814494, 698321462, 295179712, 399926083, 597703974, 244693959, 334714311, 511948264, 222948946, 343575356, 384252886, 352936485, 882118290, 794198700, 355930081, 160326530, 57496231, 732845076, 497705626, 733657093, 588084880, 205181322, 465686379, 189323440, 830893133, 775272530, 618718603, 347960247, 571810509, 629882219, 13006830, 945672996, 431202317, 506636424, 545135913, 496774072, 543104966, 131151020, 869150818, 950611389, 668429129, 74731512, 638393414, 258913856, 68810847, 95729201, 216200383, 397971198, 56896290, 384406360, 354661168, 869326153, 615383644, 766794794, 153727552, 621914753, 363209352, 701827939, 66130479, 406873650, 364708753, 586261838, 307749220, 129932074, 240934063, 810615196, 493518458, 735504846, 683588119, 547725623, 570775041, 566242099, 803473264, 741486430, 746715984, 383260335, 85984860, 484212941, 991181362, 239120248, 874442751, 393468577, 281144165, 581653713, 887791989, 186418636, 172819763, 785514325, 917640534, 892986342, 220654029, 695288742, 801666149, 684212787, 929057947, 314206948, 803253311, 278433148, 469030749, 711661960, 79470611, 926313865, 329602522, 29163926, 141806679, 367469089, 159630680, 180768403, 172082227, 496461723, 164391916, 152425766, 660227988, 773396539, 618907701, 793115758, 10128122, 328419376, 523504780, 57248889, 331353181, 221571626, 694525206, 154302876, 642845820, 372686149, 341312023, 234590262, 928569191, 281814023, 534853289, 434872195, 950151051, 468391993, 412590532, 523159634, 163987518, 734397688, 547342408, 735652394, 956469251, 443266641, 414138742, 784231085, 288160362, 791261213, 182168703, 519329271, 433459554, 714088410, 23657649, 370650384, 397977525, 664722027, 96877394, 386050484, 483553209, 936661301, 825654147, 911962540, 687455023, 170987108, 46075500, 332348578, 580909988, 275700855, 703992090, 315789233, 187283295, 653608037, 161716226, 682894886, 140224336, 685514106, 464140639, 395257890, 999929635, 897967881, 575672027, 54501848, 965506353, 92594223, 857697569, 466023533, 99175980, 217554700, 925635045, 218572452, 729353601, 219787064, 794251517, 434204722, 32524149, 987174240, 935659477, 658219017, 344060053, 267473016, 353654618, 161009765, 275103748, 200597381, 894528778, 536433881, 223993756, 619383649, 418315655, 95938585, 922286105, 498036255, 25582275, 611671056, 665616081, 856372382, 587482243, 61440397, 3859201, 40594191, 56496847, 951589902, 536508764, 682695513, 112815348, 394402549, 445211004, 829121033, 940580945, 864121979, 403999979, 295621953, 95492073, 231821104, 279197522, 775378573, 158427820, 475749165, 145134238, 231296193, 430039664, 933712219, 245658463, 891936338, 762903729, 644766490, 21350642, 261696938, 355015844, 287591324, 458937271, 113118757, 372392640, 935679229, 226106906, 157258859, 91385117, 893227686, 52994303, 499002823, 130604181, 879746719, 334022447, 588681870, 364728650, 912970026, 589171195, 700732288, 747273132, 865083852, 941025113, 495728243, 436264235, 940501413, 791159989, 315199173, 472845918, 638408574, 583531701, 955450219, 684673361, 412524770, 176609789, 94208163, 995448536, 816482102, 132989370, 745629012, 565992907, 863036401, 83186847, 982773072, 567067531, 552186666, 32251103, 972805147, 842405809, 302057178, 740474766, 715991214, 508533636, 422095734, 274548074, 777576196, 444253297, 692521382, 4815953, 595757646, 986773973, 106096367, 164362032, 660147427, 455553943, 918040007, 660206585, 224550564, 64753739, 216662999, 373041205, 897375595, 324663849, 567301070, 281377775, 391324187, 809341049, 235411390, 492459840, 751482180, 133313493, 865257589, 722144826, 882375524, 828002513, 225024271, 294412940, 521149959, 12706054, 720443948, 14445739, 741508852, 834668695, 486536577, 948840375, 72664959, 699369056, 643604480, 288381435, 53110533, 367975450, 630762667, 906243722, 871658920, 975766246, 837890321, 316334606, 385596443, 537292710, 253322224, 696235793, 441208121, 82733867, 708878173, 496199338, 708231925, 572688513, 983230866, 375301384, 923523666, 333169312, 334741017, 283891198, 217614756, 790880488, 726960266, 801463919, 635385083, 30494037, 868035166, 101899227, 241631898, 695225624, 285588265, 280023858, 17567201, 598841737, 785767375, 958445686, 226561271, 964355197, 452314359, 685521637, 453691301, 695867088, 720466652, 181251760, 281011486, 526215318, 711381008, 371637772, 642651783, 34603771, 144062800, 800900029, 120599355, 294267944, 343173440, 972394974, 290773761, 338512758, 930157946, 590780434, 499430658, 252997792, 145743621, 250542668, 958408988, 425482724, 123261526, 199940898, 731464180, 115537021, 987739148, 957053311, 917152447, 579849099, 376464806, 253712421, 491872629, 147938166, 453773964, 256186530, 733528290, 348355521, 556174789, 595479731, 207361583, 268886635, 900433683, 823860726, 920596470, 64579066, 462525914, 777659352, 150407084, 387806281, 972253615, 224093689, 63596215, 619517822, 82369362, 91978506, 950060958, 710789949, 872482556, 398364687, 11702612, 194774064, 507988402, 334640842, 817905932, 318180699, 646999215, 513415787, 697633723, 159082577, 749208359, 198980680, 247952849, 386750706, 989278914, 525648320, 378635197, 552513303, 440550801, 92511721, 770753760, 868513100, 497218419, 363925046, 687981561, 650423926, 777628911, 853342244, 16630455, 230654439, 319873285, 113516998, 474906816, 235003415, 317745875, 559391803, 425480618, 809497163, 125012956, 295956257, 264521918, 22369791, 236373956, 232944116, 236440572, 943483106, 893138099, 49491619, 796058206, 113141507, 107679427, 160522245, 308725121, 379899662, 217323251, 515167382, 232300318, 997497397, 423884918, 280848849, 648393000, 238528493, 185663065, 957316439, 810770571, 216284545, 481294418, 633027381, 588016463, 769751591, 899692349, 254615065, 41353551, 923863325, 443637717, 281653814, 477551658, 208696591, 366175762, 543508778, 668047273, 599715355, 220542737, 515300015, 537498590, 572694650, 565168856, 367747968, 906406232, 407480768, 643760901, 392714587, 285875803, 81564594, 34752602, 861718027, 380532681, 457378790, 387029523, 650261200, 146988677, 22113762, 253395175, 180461386, 182828487, 213316292, 234895715, 432654851, 369985053, 626361352, 201658309, 366635774, 97866100, 932519263, 462254092, 364256696, 799868045, 596086577, 667466138, 248660547, 279674391, 318399261, 114149691, 986860512, 731485717, 743179864, 230544459, 4502369, 788823801, 915812714, 582503877, 324617113, 437219944, 958568476, 654987148, 792221702, 197632019, 351842058, 26519545, 905557765, 447410753, 426006279, 248379205, 985745414, 149269483, 912711708, 897795281, 516698131, 558414952, 764642776, 145133394, 911117034, 839434113, 980646869, 959887903, 589268297, 152606669, 902248696, 547231138, 528324546, 188906915, 254265608, 19697501, 556507801, 554793374, 580024927, 616514917, 304947795, 815092604, 785869908, 666870871, 913816377, 604294760, 292938103, 402237890, 801971297, 961103379, 978018762, 560832979, 812943478, 134695535, 155453895, 449716860, 5427980, 672436276, 226450160, 488897493, 704198630, 344044523, 20223576, 614171596, 51771075, 323570821, 400492099, 995342012, 352912163, 859310997, 554585568, 32658917, 309939169, 162578037, 455336090, 323790849, 617082073, 609458429, 959576853, 361843905, 602477982, 874155541, 565329873, 323652354, 885346544, 564522855, 283228205, 351666672, 47120761, 832247817, 717602153, 277816227, 76500396, 646719887, 827599966, 943670337, 49514691, 988501163, 35783486, 882391576, 886593531, 129724940, 394337001, 180373836, 819723373, 585585342, 368029283, 681303676, 722752496, 252096806, 98047442, 529901360, 317452949, 695436635, 349647306, 604940342, 432344224, 594387176, 368708594, 527951377, 293490683, 111968475, 606836618, 275261541, 853604862, 416513984, 572719207, 627362698, 51001893, 938002668, 215193523, 738115126, 837731172, 463532279, 241550637, 192204714, 942445521, 119959636, 698977966, 483249005, 700166433, 115225591, 86361777, 779059330, 544154484, 969008363, 395729333, 283326396, 464298704, 788090920, 200671484, 584197009, 136902404, 313609911, 130211813, 143117146, 861851111, 285447962, 968188924, 557491375, 911510153, 363820130, 508327426, 412186723, 421008233, 478934067, 216677248, 966789108, 539865986, 217890221, 728218895, 881398694, 882677400, 761054491, 155569249, 344032843, 774170894, 976587616, 536194647, 143475747, 904272640, 816639006, 178162004, 530030724, 44307619, 956383276, 801532169, 24821345, 175985780, 135248018, 610420771, 901447496, 31798212, 248777735, 464577312, 718391349, 416189119, 492146969, 157828927, 94655209, 547393565, 983954065, 750877304, 949914610, 174453757, 503341320, 32709561, 501896759, 430564433, 379386402, 598275056, 389509066, 362903161, 396694588, 764496982, 819964596, 156537729, 429405869, 130855496, 629238951, 238299758, 697659858, 86135891, 980447583, 692269559, 781545210, 675741063, 827514716, 415611775, 113611756, 563538368, 247122132, 529996955, 88693434, 14006646, 238842873, 733362467, 927229583, 462718775, 297888938, 652237173, 206944467, 403322706, 977916728, 497673591, 855407859, 990550013, 461776905, 895994076, 766116711, 41285857, 32630889, 767663631, 282568764, 654367779, 488355263, 717772706, 499762100, 35317858, 853527461, 150862325, 413307832, 24534151, 377364720, 353301531, 399588594, 948404443, 340429366, 104241377, 58715330, 244634784, 218112988, 182969565, 789927097, 172531787, 34226484, 153849264, 899092707, 670485999, 624643720, 937949670, 751063304, 133557576, 152206399, 43078700, 225916445, 350140846, 745845511, 745678592, 681544081, 48888179, 632841261, 463177846, 440221512, 593162781, 794420160, 49161050, 155446006, 531082769, 483388695, 662881638, 185399060, 402565788, 871875122, 917961856, 545644169, 79759552, 596111667, 430706562, 753555503, 978408225, 376660843, 440654074, 248325311, 801651930, 36524819, 628865747, 414427296, 880191330, 239051359, 271208113, 975985427, 281909704, 337597640, 852178244, 968428616, 58983751, 512181640, 435103508, 442832146, 694101451, 259232055, 154758335, 747710375, 887214359, 739736309, 605011718, 192352319, 412515374, 407765964, 926454065, 228446908, 118141811, 961064692, 551092062, 822928360, 287512562, 141865376, 99971601, 347149699, 543097283, 173817195, 67350078, 96436126, 713589538, 875922557, 25026066, 290384353, 830070275, 296724613, 520510224, 893654108, 386364384, 748846323, 36909808, 698052983, 417487595, 670493024, 840184348, 402851943, 295417442, 673825349, 485783293, 674734558, 188660082, 971946239, 156749852, 51311480, 115096254, 71716456, 147304467, 295127919, 477308784, 815101002, 877782883, 951314004, 714704664, 281961408, 958066973, 605712132, 336832299, 291859167, 616268293, 944760482, 890201714, 917659359, 862829524, 380012580, 859465147, 750639857, 792708465, 832781179, 844844550, 599506814, 910522052, 357945758, 729634247, 61540120, 615465109, 914214029, 592016845, 950071813, 668482566, 343314893, 718124078, 375169042, 377706923, 511167294, 277645640, 354553419, 640540464, 43505884, 936631558, 781787103, 591526692, 412034290, 313112396, 418925021, 407862045, 980785201, 884841924, 714118055, 153595806, 681784673, 774245029, 747188189, 642053807, 405824114, 490015022, 352593379, 264572813, 356063440, 425513453, 495205393, 408223024, 736758860, 650098915, 696010632, 957022328, 176023522, 911340395, 783106399, 386741928, 822562334, 737788013, 957994409, 194284800, 91398980, 185055960, 420328742, 386997750, 354273469, 120188002, 82823010, 159682618, 586103774, 114313797, 162719584, 609429628, 710491987, 566450426, 652170835, 231355614, 216019207, 424828995, 821209124, 860270149, 398057000, 740930114, 156894483, 548146453, 603501240, 813753147, 873549197, 820193674, 772593779, 327372085, 370212410, 159829672, 78368611, 159698119, 590268572, 130427277, 726810719, 964080863, 62548518, 50151304, 869515915, 5446858, 362651821, 407285254, 208081515, 70422496, 944434759, 680531293, 245975077, 247753322, 395366495, 592469708, 962393297, 364207772, 775723825, 845145158, 103415283, 686625982, 30024668, 374301611, 314392979, 120081734, 778930338, 923118661, 799041222, 933701904, 985202902, 80325165, 268857524, 156858026, 487621420, 839579848, 320377178, 476303109, 631035591, 127659383, 689972293, 775551453, 621874848, 374701570, 266777116, 972600379, 493787816, 699484624, 937604569, 956634993, 963251574, 97455740, 111186237, 354885622, 603840812, 216457160, 15151241, 116029395, 198069675, 670098738, 522595000, 492443157, 923799269, 250520488, 276909425, 891830888, 759379301, 41652167, 245621607, 384951801, 376990886, 951495267, 865799669, 943165668, 156461909, 534422835, 134453727, 213832846, 923880493, 728620753, 853090717, 655234244, 415373631, 792893294, 88627913, 618048695, 980049737, 487662349, 482436669, 55982910, 210676, 919776770, 602213715, 154589423, 731133549, 516864028, 920928442, 534847974, 393386850, 301968380, 323748009, 208066944, 768722675, 244412863, 184578854, 769651603, 329999648, 152680372, 355425099, 56457266, 538446104, 217134518, 8945554, 854216431, 289943501, 287119311, 45475369, 217050623, 982088122, 530950531, 287208994, 307868799, 48618, 455216419, 704207698, 151705214, 933670534, 816006858, 176393971, 375790348, 561049055, 160241968, 374749080, 55300501, 251172474, 27791853, 752599972, 59287429, 562748691, 482075764, 147531595, 73367338, 832384343, 797418921, 214967787, 642607824, 544340938, 89279509, 608740254, 352636939, 509744005, 68830300, 395305661, 185054131, 97704870, 620279038, 720979832, 635640149, 181393467, 576720349, 571306599, 629727242, 134937394, 197679526, 704539079, 4150282, 807317441, 522567703, 737030573, 377499386, 539379093, 529104908, 408414960, 490128123, 199571380, 586241028, 252169612, 291355102, 535106126, 422922107, 753625318, 901646259, 159403840, 441516985, 829538077, 185598075, 368667653, 120104958, 623427014, 931741075, 423472476, 170608177, 912653975, 698538874, 583962612, 346273994, 521167786, 188751381, 80548016, 893371412, 454051620, 345277765, 663676418, 747374349, 779576698, 755886806, 871074272, 409316208, 461302187, 233949356, 6213489, 862459134, 223294871, 922570728, 758596062, 586167885, 184438429, 339081575, 494919857, 180495699, 630922439, 26692476, 424247421, 31615634, 199322053, 210099609, 936702786, 111158366, 118712252, 686003560, 83019304, 759686777, 270506797, 776181824, 22400442, 810376537, 766683104, 888923748, 510909918, 540472951, 624770153, 540778662, 455934209, 34214274, 324247557, 705123052, 483461615, 91141032, 112674870, 785455846, 216457330, 863790237, 743108650, 164374124, 701433045, 576554903, 507457882, 603388819, 296031419, 353238741, 691876715, 901122270, 163738521, 266949616, 130405573, 483438316, 535597664, 674902794, 16943684, 405057960, 808862510, 139264337, 939037294, 29929021, 881956190, 834069718, 349076295, 971553817, 465070836, 322473672, 481060935, 162617052, 538465165, 365163242, 815441557, 460281958, 494743640, 454480909, 678294934, 146051946, 645287550, 505238202, 77580920, 654049662, 391735698, 136627937, 990359929, 196495684, 622535821, 262554802, 134701415, 607409138, 34189204, 613246204, 4412735, 809500446, 712269254, 757281368, 411841625, 260193597, 275288619, 492622073, 390046649, 883592740, 172577899, 338114303, 469080968, 61487370, 212804940, 831178729, 662388463, 714619515, 486133015, 296260584, 22319474, 927332502, 659255925, 679953637, 65545367, 18484285, 836895559, 59257672, 83643715, 213998779, 314915359, 576206372, 887396552, 630395845, 185539529, 669211042, 48276723, 39392332, 826220798, 308405041, 472727303, 678048004, 848017700, 492004381, 807813410, 106945331, 879873228, 224858472, 237654235, 772469112, 455936580, 190934267, 685908441, 569661616, 163378829, 237679871, 643592877, 878976469, 576852474, 818985036, 602236384, 16841923, 750973994, 987012902, 985826482, 800290138, 825074603, 24613864, 620115313, 964551550, 566162807, 94449635, 625017133, 402341438, 693296197, 945730863, 62918853, 420726065, 717562465, 321762686, 59088560, 675644308, 385677793, 225836417, 786275639, 862168881, 49563399, 43845680, 574411002, 193249659, 96034500, 981458435, 45753146, 710920506, 421149699, 731999408, 630276363, 167419565, 401925306, 455400767, 421071337, 575336435, 776767121, 116984711, 451299792, 234429228, 954645410, 845646500, 382684874, 666316507, 684231164, 762775461, 339131633, 624957814, 198508032, 866634712, 270938589, 107452678, 696998674, 400257249, 99818315, 585077301, 190761605, 150531499, 961667780, 273540298, 361310835, 234492467, 973467829, 742162143, 233721851, 780337051, 804034874, 647442996, 643732854, 55834200, 233021220, 983325175, 155441528, 859557968, 770133448, 347887025, 767006802, 851752771, 665342700, 929159371, 829786942, 713335476, 411216241, 314727638, 893037321, 859979073, 128338657, 114109504, 451623959, 795743326, 824861160, 600765765, 36121324, 427831571, 200963882, 973718026, 149386822, 6581396, 468123825, 222927927, 187341154, 8349168, 954587762, 189865960, 213955236, 537923506, 21335816, 84065583, 213658460, 464348863, 762296043, 929752018, 819756565, 297414873, 363054802, 764983546, 647742994, 582396877, 693324405, 866475438, 470279810, 525210491, 850893280, 559162423, 17548223, 198515778, 571154523, 487807382, 13752551, 257259342, 19968318, 93286066, 574209430, 755332167, 806308421, 956583956, 14258080, 634330889, 93786263, 886654467, 628341350, 390234032, 145331869, 284014832, 977724303, 759867279, 922563400, 685316845, 823321267, 387661129, 518609813, 775761678, 384055786, 626795199, 234707295, 66503953, 953675326, 330615666, 682934710, 123683986, 169191640, 288624681, 576149045, 656591144, 597482321, 404060240, 129642286, 578649823, 875276615, 108392902, 503029188, 470349319, 358954205, 51599442, 893510337, 536857160, 256979465, 924757694, 446085061, 198276757, 785675611, 238865915, 401242010, 474823153, 270812226, 227747689, 598931285, 507902275, 730739755, 551136493, 404854282, 542250180, 156131146, 371173739, 948754706, 700192829, 268420376, 386596074, 610249189, 731548698, 77309236, 241554729, 522622488, 583888127, 928897752, 777818369, 4446266, 944227789, 724092451, 929381341, 422822560, 505474610, 140547134, 146558926, 740936825, 26400557, 790608901, 977546956, 991740715, 814810611, 969727111, 258453673, 81992681, 69567305, 343388729, 226630034, 281600845, 778617343, 957728808, 125389363, 377889496, 88402755, 258985767, 697018238, 232476334, 613997663, 959792023, 934258310, 100492480, 300673931, 259904544, 723099013, 855941143, 163991762, 704506620, 18603588, 380361274, 778030007, 872368720, 981828243, 594780955, 626124696, 744504664, 233623237, 888125121, 573891101, 446563795, 632527521, 237548578, 495583612, 58189736, 175473566, 44603827, 974724389, 817845628, 441933394, 577160948, 607098876, 354797299, 474219375, 511702959, 899960278, 846733598, 203385171, 531202804, 736228056, 507747846, 373094040, 643676624, 119932417, 791561926, 912004223, 731768008, 860577867, 928915870, 833219454, 450070742, 906169214, 689491781, 883832985, 655177089, 439067169, 589119343, 349962834, 335834244, 206747989, 846526033, 737365614, 255269951, 168423876, 674932524, 478461931, 571366619, 454480685, 686955669, 369937396, 175642843, 287401115, 997393736, 137297865, 445744332, 639300159, 708124959, 334337593, 951144910, 420425930, 128790576, 44120860, 297789859, 785810479, 772002357, 223286803, 235348613, 79918069, 910848621, 981436695, 653468656, 657250520, 794710005, 2086121, 118855236, 169676925, 790958830, 325297670, 9871582, 408319234, 67904152, 339155789, 134700805, 320121348, 358184360, 998881327, 974566225, 145821514, 47076992, 65409242, 696810482, 802891925, 856271905, 73230712, 282160951, 297772208, 802562510, 450004297, 96844007, 249736448, 14948744, 240256627, 438235853, 368297161, 132980636, 988621692, 676796057, 137569426, 891212554, 91101035, 324061271, 789314255, 43211515, 122084001, 306342726, 916580738, 301783651, 154866493, 570993343, 587779969, 442305889, 763418904, 804391898, 124551812, 32972518, 645854993, 522580936, 711238360, 761261578, 526477684, 96750957, 58302268, 846757157, 116278086, 784733393, 495362193, 983799870, 953342091, 743597256, 74427827, 659625812, 858951435, 514396405, 63297188, 966233854, 592021497, 508725409, 975098758, 718973297, 959993246, 651146359, 717464645, 509592670, 323118699, 605626684, 374375344, 588824600, 495210972, 193660009, 971813439, 802529343, 525903198, 546298794, 843494747, 256457920, 617899102, 832389398, 170952251, 915470404, 831647093, 705484131, 570637442, 978709861, 239103128, 731395004, 307912865, 447677948, 527060950, 701456733, 809278871, 401181942, 725640418, 517726548, 549401969, 799167245, 715814561, 44982254, 281552860, 963418619, 84054246, 519218201, 665501276, 200076832, 660081564, 448033921, 620484603, 234332752, 297642299, 599397789, 723047269, 411698197, 548584234, 372775460, 147031203, 657992849, 441287621, 433818563, 682780119, 915305888, 54162798, 243030053, 424746277, 102100704, 330327284, 487441170, 498309470, 803675214, 748152437, 137665535, 894861410, 378709336, 680700403, 82998019, 370800518, 900865840, 440576252, 684319034, 345182084, 187978362, 223640671, 817467527, 248590382, 364297589, 701923116, 743554837, 332180778, 707781379, 226397984, 612458675, 160357650, 16948920, 127594751, 405690049, 726820964, 634448019, 891525870, 971443799, 4395097, 382173541, 589224841, 114520217, 966951068, 391037058, 429060775, 199318923, 482146768, 800724989, 537040130, 816162175, 877592494, 533534678, 725773808, 884507553, 819407820, 880468000, 304109992, 84858826, 39484358, 783101423, 543818928, 43404414, 2046914, 324210775, 85834064, 461482467, 56828134, 525820524, 464673240, 491336750, 271354035, 430055051, 594463569, 894872477, 300624522, 611321085, 388536232, 93693106, 991804123, 248605406, 110234755, 383441479, 209061218, 826239295, 543948668, 760599149, 764902709, 266872637, 892263265, 836671211, 691952358, 422092933, 131948569, 837820275, 562051575, 69531510, 714223648, 669574413, 949664323, 12612397, 872266824, 694397473, 100491567, 625047384, 628862300, 898364378, 870010150, 222743866, 881243540, 975753882, 251221709, 67053612, 71353226, 997462937, 850667823, 502839084, 435000858, 428929592, 342943970, 512319441, 778578130, 150577904, 633642828, 999906857, 646041668, 228214653, 188836020, 553186987, 592695176, 26226177, 115532387, 534201115, 373862795, 461507735, 909703370, 403356248, 997857492, 14765257, 845967053, 507818374, 891654972, 932661070, 427034032, 606703804, 510110633, 22046272, 110257613, 773893314, 386459215, 295578734, 585890930, 11484233, 787012716, 98642861, 331519300, 872744490, 940936442, 794503352, 133278950, 400489780, 112458257, 509313094, 187040205, 256023912, 181173640, 776167959, 675740910, 268080785, 748325903, 990662405, 686091215, 77771383, 171869287, 496185340, 532179299, 603883066, 174035913, 691405885, 153591697, 796766491, 826858599, 62027545, 571631474, 623801581, 760816300, 59287112, 82232000, 410683434, 333201398, 731395669, 712269148, 632631941, 328544689, 668511850, 944102722, 344954218, 840225101, 875251088, 270338719, 363426347, 856794010, 93288959, 356935615, 916900190, 651684998, 971344536, 381221698, 230556523, 528246768, 377754593, 5597431, 746851462, 204918129, 397323572, 531186028, 272164619, 524100644, 377904503, 698379080, 996121891, 357183996, 332706128, 218570064, 682825056, 452639618, 54521103, 3966534, 537296561, 37625003, 273097384, 996301102, 904542363, 672724655, 294365484, 310867970, 448407321, 6223007, 711776798, 145919435, 393781822, 165750851, 140122478, 498821347, 807426451, 891839350, 484430212, 593857645, 700384524, 125675039, 431026290, 118604141, 732510079, 773740411, 152138990, 542695656, 673442597, 591072226, 930701205, 169844217, 666318847, 557930777, 864657364, 190061095, 498428660, 970178270, 639808717, 771961245, 474031825, 630540497, 706219196, 915832958, 648599036, 490859276, 495801654, 9731347, 76589518, 237966772, 428859540, 368679260, 67145143, 402869948, 261740734, 791610104, 372186929, 987682676, 447619901, 816274861, 887334668, 347876400, 921861868, 809119553, 733981517, 494998678, 104712965, 389143245, 183458710, 393310665, 789466857, 773862337, 651347351, 241833305, 940162174, 977309828, 428846034, 104163234, 157966584, 893768609, 737721716, 918027169, 659710202, 557250424, 169643259, 837296188, 973863645, 31580454, 240287212, 619685968, 349526211, 704467702, 229428881, 947223659, 997024056, 115384395, 721001078, 124411877, 933750693, 63504886, 228856186, 370331399, 842752937, 917941340, 26945709, 235119965, 921280036, 262730090, 227993490, 891366450, 232434551, 259319724, 65793012, 928239376, 295364301, 352767982, 671250444, 42744321, 453359550, 63180203, 287669994, 356076642, 236590414, 517622048, 783558187, 682093170, 50632074, 993258654, 837117670, 530491614, 197671084, 110206143, 331051144, 133228943, 138396187, 956199720, 934224651, 401884854, 809017149, 637729080, 683531164, 282047536, 654311798, 157906145, 47500836, 669778707, 138729787, 815228461, 55200382, 23946964, 548381551, 942971517, 621860621, 800393651, 541577608, 533330036, 64293155, 124460345, 271325520, 434328143, 64585797, 970336708, 523742822, 722352208, 746821722, 92477526, 440126286, 675190847, 106365610, 987799234, 861620784, 907869679, 913984972, 555806314, 67676916, 236255923, 446795207, 803814238, 258774917, 65285201, 875305325, 743221686, 534511297, 73341959, 363675007, 285724048, 439494579, 642569142, 115787396, 114247314, 559155471, 388010862, 260127367, 130770068, 842502, 175531580, 139762506, 415543916, 163481767, 350552935, 775162622, 353285964, 145631558, 385690811, 430541081, 441266947, 41848710, 478888874, 763310719, 668206823, 694699681, 429930239, 754922845, 377598085, 364402975, 945108890, 788251920, 769967303, 969806740, 715319022, 530563301, 453304989, 461278698, 851469940, 949818162, 546938762, 206008892, 43361235, 643417641, 460154502, 562520083, 633371637, 694247546, 968065160, 613691840, 803985091, 693600738, 251587378, 25849320, 209450811, 256063252, 921291945, 907190886, 976913435, 933048749, 816712861, 661977361, 388187841, 467327766, 243954051, 991438406, 539411433, 963830451, 932722715, 823442333, 433932370, 850809287, 622954765, 773607805, 205373930, 668470175, 503163322, 395776127, 620957241, 124472155, 643254008, 832235226, 179476408, 359544055, 359548713, 264132818, 546719388, 6157802, 500213951, 2208515, 635273158, 795387218, 473955350, 73584802, 547874188, 430518811, 950714620, 754461419, 266498372, 119351437, 377229601, 146151487, 709405015, 348273475, 53861859, 71955578, 327147495, 605955190, 756252996, 943598055, 574315965, 531638517, 339010581, 170274552, 826329053, 209284857, 767327224, 762917404, 599218026, 632046185, 201966660, 121699011, 693474106, 940439178, 861904971, 30818223, 829913488, 543945972, 208026749, 840396714, 441392220, 802802992, 717314012, 479171774, 424284213, 903151616, 112754617, 583296508, 847101379, 701443327, 854732926, 951456349, 61008383, 759599569, 675669925, 20428852, 837686698, 600367229, 272938950, 554487859, 96667296, 912575351, 762049099, 406109155, 245577956, 242080427, 181450036, 428069070, 842929337, 396160092, 358779834, 259633790, 901087149, 291443952, 766013220, 151607958, 624933106, 816344467, 335853237, 948893593, 632409956, 450333583, 78411644, 208569438, 897215788, 483470665, 390042602, 382837185, 908567745, 633443700, 949206804, 344948477, 730336096, 290881726, 565836619, 630647163, 75939278, 639026258, 339001487, 738748018, 511274078, 628633774, 806452506, 489065404, 1651246, 867523521, 248952943, 528033060, 915323406, 255209380, 894247558, 713492383, 260550073, 444795743, 214898348, 221264551, 272791258, 719387604, 948464718, 565873963, 183445340, 563120275, 392603086, 396574618, 646673398, 624797265, 378309577, 858481409, 112410804, 697452182, 40773065, 316525368, 484826772, 506188205, 267753928, 908843085, 446686155, 510891486, 666842263, 168326325, 403227707, 962008480, 389460747, 615324854, 578924833, 797730245, 744434190, 486250409, 82702806, 859209663, 58346728, 55209955, 859314684, 627762343, 713427297, 255323440, 323450784, 77670267, 59418304, 423434053, 697356583, 86291428, 580845560, 433248973, 3867593, 862324993, 551597801, 233846102, 182920148, 877174686, 691365045, 698412259, 336297146, 297183575, 131374004, 480069654, 676954020, 712031782, 697363920, 230479167, 81330369, 202516866, 60189433, 836708705, 239215977, 686004639, 963441444, 861051628, 298576606, 746859673, 479960476, 835232477, 186745901, 468428422, 425560968, 365523246, 175671725, 847966235, 412441549, 858669842, 204368139, 957956035, 691910347, 227899268, 880245210, 883743278, 910047736, 9777351, 113041489, 156175865, 81025947, 699587195, 795565884, 205992577, 4893388, 659289840, 713426101, 685586646, 899769621, 427053208, 539817839, 820611242, 357964091, 986097767, 705690860, 51606843, 577793141, 312533213, 188004202, 427984610, 301745704, 385238921, 947868015, 106082218, 612171678, 358207641, 716699042, 157186895, 973278030, 996026860, 947030941, 281185142, 101298158, 914601078, 185689672, 812884289, 912839991, 289053019, 865715466, 160152118, 19423762, 616512789, 634341712, 657643643, 282351197, 775476332, 111941313, 224698295, 359570922, 101496727, 899734930, 691235267, 485270035, 627191095, 43031289, 106148039, 814751472, 795898468, 515105433, 971769011, 927551150, 418208976, 565079579, 741550109, 887563520, 487909496, 235868834, 138905494, 304456358, 494398517, 622530155, 585989237, 691057363, 116558980, 231096660, 150684938, 429698981, 654886766, 100741769, 429613794, 832590580, 52124496, 322795054, 794636875, 491452075, 95173085, 463231644, 267789513, 806829908, 970084922, 636489011, 60852126, 728750368, 353424492, 207484809, 953273030, 903505884, 480342851, 411668759, 421294347, 923053448, 579231764, 354380124, 57382141, 165662528, 815301297, 397318252, 868560532, 327424686, 794121891, 675346074, 552880426, 578212722, 683715825, 369717532, 186904468, 345576708, 222832351, 753097618, 268655945, 911049276, 415006558, 104505958, 748218179, 534162415, 947213911, 509825956, 536020964, 80233934, 681084910, 219992260, 618111615, 957077882, 947542612, 575913489, 368964814, 249112087, 515104626, 626124728, 602797402, 576142592, 610825126, 301234100, 569940576, 211901568, 842163, 939611165, 514347383, 658971221, 475581335, 94349566, 481514077, 578272485, 350284109, 233743667, 411093153, 703051403, 420801295, 915115815, 699429822, 945726399, 727620533, 893054356, 835070339, 577919659, 533637476, 67705154, 513284437, 927320113, 868937447, 74857835, 640178801, 784236128, 521490190, 806030716, 844840822, 50056513, 526029717, 479733254, 484252818, 738703848, 822110355, 860366603, 608187609, 904262934, 331869428, 475359869, 476507221, 188857487, 693274843, 661481066, 583188929, 755392237, 246204734, 699517534, 183780445, 925322920, 432490358, 321322882, 461968161, 335747578, 407479258, 433796304, 838311859, 58909367, 391678764, 771389446, 749528083, 974202628, 303612154, 195360889, 908290995, 71946165, 577472873, 465602646, 487444005, 77006747, 180044241, 739757470, 262016419, 344168661, 133882270, 163890151, 669496469, 226929011, 159043576, 157013513, 812111973, 484750172, 75902573, 531928856, 496698687, 673389163, 463577890, 941934067, 264929948, 615934852, 21062570, 389250425, 418591951, 590267297, 43666318, 182392161, 672445071, 214340813, 908231084, 792399476, 217404100, 194621620, 99744679, 419676644, 114093072, 679032944, 430012263, 195490501, 169949189, 959095080, 134248137, 739969221, 70953554, 672353070, 553966936, 738212154, 686701565, 506359548, 990428264, 528434040, 968675370, 576669089, 973965603, 944420514, 790843249, 312023004, 339671338, 158357023, 562008294, 337595451, 538636446, 185872528, 334226428, 196927335, 633870286, 611409009, 146492662, 304548230, 243376886, 63947950, 143960048, 396408155, 761582858, 2627732, 402079624, 709482044, 525259226, 304835051, 686479125, 906443337, 637968331, 657712352, 625588548, 520328620, 366364065, 438292958, 651427125, 115216290, 485424674, 828112564, 645120493, 430432256, 437667227, 342380540, 619205627, 789087602, 277616231, 637683699, 216571997, 62652029, 271259401, 601173725, 803501532, 580710630, 154746852, 383746285, 885403924, 316790032, 158608501, 535239613, 498235199, 658995464, 321172420, 799683406, 880349320, 486858300, 786394233, 76388207, 807487344, 671655565, 821502484, 187247908, 51272329, 610190122, 322918908, 166922264, 628103859, 890331771, 907517878, 207259920, 644180428, 376095418, 385707086, 448823071, 874357559, 999449460, 923286647, 943654015, 284208308, 377217899, 936543106, 983313436, 132393895, 440352278, 651189331, 620822910, 697351747, 572624363, 184975674, 37725079, 636769964, 755065637, 231490266, 619033536, 679138744, 412903244, 658480322, 800270651, 804638541, 407581812, 772547581, 872823791, 971761226, 375441051, 145705341, 463707313, 826772255, 726501439, 302482077, 217859930, 730172070, 780202130, 312012448, 84441333, 159272031, 278306064, 636131924, 571207395, 186369584, 539636195, 174174562, 383252849, 549641602, 765610364, 653504969, 90778664, 36395333, 18149766, 776630494, 299753075, 951060656, 853493390, 753311714, 214712625, 519333324, 491595391, 134432099, 60426506, 714736528, 158180147, 28833136, 270877371, 990212384, 367408355, 389436290, 358668618, 242346432, 781185230, 563815352, 510560493, 996648797, 990985234, 317045332, 292308215, 950620354, 730144337, 91592314, 548335621, 890069903, 714040731, 409300582, 247885785, 573318239, 972961390, 948130459, 543369847, 840711267, 408297414, 726533687, 335013960, 912262679, 212519744, 530515067, 9534714, 845944053, 754644634, 981061936, 945806864, 831416814, 622714655, 252322191, 65847614, 307317166, 981712506, 917370993, 666329782, 490584960, 315351144, 740989337, 225052731, 993422358, 334561291, 331937243, 137313975, 223274315, 136234391, 542837460, 140881804, 388738255, 794943348, 519749544, 322301807, 583495889, 789420913, 421862339, 8083273, 439701068, 863617024, 477243629, 978582479, 9946487, 432135903, 914779821, 811902513, 172350093, 780252980, 43737072, 787433600, 593032659, 894173108, 579377304, 971292612, 916804739, 847139827, 236083855, 190274726, 396010783, 674546980, 547535890, 271524423, 16505778, 590321397, 238711272, 405548005, 218101848, 172524200, 859395071, 153706292, 840070636, 551738063, 489619459, 23751683, 724371425, 742900867, 866803551, 877342608, 647515, 42717040, 547922136, 949363130, 248415272, 776114788, 893598950, 189344707, 89977644, 288474042, 409353080, 459189692, 250073140, 620840426, 300406294, 441809969, 327015395, 504278678, 774306267, 203503126, 563473546, 117776951, 156336165, 230705439, 800547620, 366256900, 586101386, 247569885, 790949579, 35432961, 862815694, 176524138, 247537523, 443659898, 803214485, 676511999, 871695364, 419319156, 331955150, 609242254, 85684972, 6317986, 692709298, 293753956, 53658431, 893218037, 506832575, 238811838, 25350313, 394521947, 176177683, 35667000, 292325266, 779762006, 588365857, 400215746, 524215576, 606186624, 54797831, 980767363, 58487519, 343225487, 134110520, 934462894, 21105126, 335430735, 902703325, 506902746, 637220693, 364838334, 423897210, 361837180, 119726265, 18505385, 611829135, 977829572, 991091171, 604849955, 619955990, 761647679, 975899777, 899239686, 482563029, 391295023, 728365707, 671440469, 671562447, 849569115, 87311837, 170267064, 866876371, 693281978, 146210496, 663325287, 82705030, 725874220, 598091851, 614834544, 857449690, 972304046, 555178785, 841889116, 352520967, 115803339, 954199430, 530516253, 805290283, 659055027, 503564786, 238473049, 791813547, 665987213, 957931823, 553754961, 103622388, 397396133, 365257872, 976539070, 855089007, 447152131, 173374812, 818311646, 975672270, 850728568, 497396952, 231787082, 111610553, 479835766, 813075875, 202205263, 354725199, 51284925, 446898711, 395279504, 592027551, 21487739, 844868400, 992007498, 114161950, 871394399, 508857629, 395521089, 768521640, 205439689, 266850470, 288687359, 335533947, 983910236, 177197539, 775524008, 434961411, 225272287, 687711896, 195833410, 356972600, 601046892, 764168496, 673771143, 181500439, 8804954, 53217906, 798732350, 947873935, 757096185, 212854922, 497552626, 154279325, 81194307, 186490094, 772206912, 235300825, 673680776, 350335769, 786920393, 512305469, 375935022, 503448482, 804176532, 549028136, 680715212, 523724038, 457965143, 723372212, 249574372, 350903972, 98699786, 150215826, 609865124, 37664884, 320182619, 299671998, 248414727, 162465204, 727436356, 656025360, 422866557, 414317187, 292381830, 740426807, 706336119, 218649294, 7074830, 153759618, 112232768, 721506706, 275210930, 445464953, 970984561, 863839820, 744742129, 588925298, 205333427, 16521046, 56395008, 603352884, 588181456, 219554338, 527106517, 223103717, 117926464, 945689924, 419269745, 56229632, 175058158, 321283534, 662705964, 662297974, 853441213, 75337337, 109805547, 245532006, 705499869, 208120205, 842959789, 211401476, 552573831, 9657094, 871000811, 795839313, 873201784, 128671418, 860319099, 66046563, 272599545, 772949044, 209703491, 743009703, 410464447, 887821274, 410882538, 540120895, 601132763, 510082156, 917164193, 662785654, 79734576, 792542435, 583856497, 929439752, 459150542, 23880254, 355201827, 2469516, 121988314, 924796260, 905479593, 724222764, 232929785, 667524824, 387688652, 922562315, 536044006, 699517630, 687680279, 915827257, 615824798, 60204951, 598727854, 789051963, 633038699, 278779076, 271191194, 601592956, 176645597, 915227301, 252981251, 90141924, 112867586, 239463998, 374601105, 101697171, 142006364, 185777805, 178805687, 380537522, 16027179, 730599674, 482607643, 809175745, 36937374, 29707037, 434801045, 536581934, 330224514, 718448316, 808326216, 987110670, 573828729, 529847586, 652315433, 826858504, 765658202, 260600501, 67755106, 952974140, 741034357, 159938771, 860195462, 124941707, 574657338, 110087425, 270061754, 138683467, 220187067, 323461591, 665518392, 907686790, 435049581, 679555046, 108347870, 498465870, 463701725, 988903774, 646622346, 259172527, 342286795, 177338615, 568437089, 630655106, 615841897, 618408941, 149143163, 934978574, 554919052, 561183712, 884523401, 450924615, 258306464, 623220132, 710407638, 312300566, 692216822, 710699823, 353813942, 776683355, 338088425, 658363837, 644150234, 222592712, 927382069, 322588799, 843762132, 562032277, 671628784, 296416119, 208249512, 419034502, 85166959, 848314438, 88764987, 393209154, 793158291, 855001914, 953725629, 378223684, 829813705, 388096376, 729300559, 52077904, 497719661, 274882154, 339473132, 627379400, 738927573, 980196049, 986007333, 604179280, 438244120, 113154514, 785400875, 257967422, 913433670, 140689246, 404709641, 590223889, 33815227, 998611845, 594134120, 60248526, 8758257, 88108053, 181500391, 681746621, 34467654, 114878354, 982704435, 826113974, 572474912, 838311425, 707310892, 683611379, 508390368, 492893070, 722437034, 563754051, 868513111, 820815794, 423490362, 983344575, 637524889, 343834753, 761381782, 695609157, 270913092, 928498000, 326451246, 601694363, 921374720, 945482170, 598876739, 766160436, 988628196, 359857655, 140318096, 661479287, 976468286, 603091248, 618515855, 704278572, 979286756, 873029419, 365879038, 596891769, 738221394, 602669328, 851325020, 565694207, 483196863, 843125480, 660118625, 992958928, 38915438, 318551734, 335305005, 573308576, 784152992, 135516162, 97728223, 699514361, 297660910, 595576916, 149981470, 948752742, 360770901, 267773287, 589360553, 488772290, 952649402, 54332318, 145375438, 696877745, 53786615, 990329861, 400903064, 344632746, 138497393, 576025937, 939466461, 685539101, 31153488, 795684247, 85715231, 440420132, 927785918, 270333853, 981969722, 363716046, 843436575, 476941586, 156592809, 587716782, 913438009, 773284158, 755831786, 520500002, 700488281, 765589536, 84860703, 706149793, 764830953, 698999546, 543813218, 824873123, 740469533, 123796162, 388152674, 963029959, 348387639, 72889819, 860613438, 930759116, 868935096, 123979317, 752096715, 964135129, 620857060, 458280065, 425374405, 757585319, 966819307, 585531476, 335943883, 134916308, 642786026, 627193873, 913733463, 726700701, 698456832, 802642310, 992955028, 598827431, 764955282, 469042869, 407629041, 9886906, 606989428, 959883211, 466198011, 523643283, 892087173, 245043877, 383154190, 389265597, 749480315, 654453655, 155977597, 626384718, 648943906, 474079200, 800154895, 133272222, 656748490, 51031185, 606251876, 583668337, 487042790, 512968449, 698637743, 563852698, 497734154, 688226516, 421415273, 84542240, 108480298, 714548904, 302451357, 110871581, 39526359, 167521907, 256132408, 741082385, 441918200, 14314174, 773285523, 789815126, 905437616, 370907310, 962159405, 963020638, 69279814, 567981541, 681636380, 152144880, 369808047, 352540613, 565527815, 257739476, 429572632, 624070183, 515036985, 323146608, 923135942, 744716680, 440770784, 310204731, 752156206, 938208456, 602581018, 218636762, 891463534, 601924480, 93720726, 393698185, 819245009, 61542970, 18602879, 247802616, 478987037, 737504903, 100526187, 793924576, 37182339, 811611287, 944711828, 585507605, 84251650, 757600466, 943502687, 973038272, 950521908, 434103059, 424347679, 796509624, 298736030, 797574150, 422389961, 975082458, 557439642, 806999057, 478423201, 720788782, 338426938, 451685247, 478532330, 321770983, 786029931, 797320569, 946791816, 671280852, 815540840, 91575603, 827516866, 506095344, 149797922, 400253185, 938125627, 924499641, 588050339, 943339663, 904763345, 899577795, 545902426, 614586064, 752676838, 230324287, 9302940, 818242344, 31731342, 706163726, 301317970, 957627607, 348356992, 698223168, 964979471, 647250025, 387088284, 540538714, 416860359, 707620883, 800030424, 488522561, 727110812, 53244655, 868932744, 298249546, 772119465, 206783352, 443576273, 699730453, 337896255, 13304574, 89446544, 887134773, 396727835, 676589011, 748818620, 790797160, 270764442, 672012996, 20606631, 16273290, 354591060, 617872116, 160544971, 954304071, 703131677, 315212145, 935910664, 555988490, 481723955, 997365402, 555122234, 685692631, 978975012, 116615045, 84832441, 875293513, 545339196, 311010103, 727227628, 875213700, 812216246, 362716451, 262701048, 532554421, 441717568, 560909158, 169579480, 861893050, 721603368, 966427682, 878229106, 444781774, 816250683, 316296083, 508718963, 822098825, 972296829, 786506400, 731229497, 731474057, 868905925, 578746666, 188771416, 310698783, 197885515, 462307147, 501327280, 5626411, 264951203, 68705156, 412472741, 413566782, 48438443, 9684532, 447035450, 960597404, 363156623, 386790753, 896325235, 512699610, 657100841, 979264888, 791116790, 376418881, 76589923, 801697656, 449902248, 241588742, 194893759, 346091548, 313495160, 275470684, 530904193, 72371843, 334579381, 112567456, 897172310, 573005636, 850766379, 802172865, 964150306, 506121640, 573601266, 207721222, 449562678, 767685211, 374876945, 860901058, 176687936, 150389518, 660763921, 261340067, 991983324, 406747989, 435738950, 376190613, 535912553, 724851556, 70528634, 990742747, 931732817, 464575337, 627975964, 352011812, 110588671, 367786187, 876020049, 514650198, 815035537, 707695561, 186003671, 452163189, 933965269, 785035456, 418457145, 229079467, 687886023, 901428759, 502821040, 543119146, 795139434, 540499142, 278992795, 927878539, 611762204, 354725460, 700664555, 297343561, 778653387, 309922085, 430762701, 524736531, 111769400, 503373812, 904111761, 812773077, 841240745, 151023631, 373795019, 901193535, 738750951, 403497272, 860399090, 844399978, 649652423, 497401463, 300250297, 334157300, 724402628, 569227395, 374254558, 801760166, 995738358, 858429730, 218491684, 221438036, 338405260, 465378109, 972628576, 305020444, 205052333, 699599006, 879516637, 63540567, 983833070, 638691279, 663214309, 804122824, 891710992, 526842808, 68928398, 802616558, 115795431, 294892789, 577140681, 163636227, 482086440, 770677762, 796880694, 435667942, 348258656, 477474519, 383789253, 456730902, 513512887, 184103088, 659752607, 998015374, 810941655, 635391029, 748465789, 852665809, 444091680, 203999384, 398476445, 584955052, 310989044, 590555720, 827119976, 897010148, 460441399, 870693842, 585695936, 208778750, 560905935, 800823053, 722363302, 72760767, 507040674, 446272197, 839651999, 292683615, 968124073, 434095543, 191520357, 50009956, 769098742, 11422397, 103155204, 165437866, 619297167, 557522214, 655871800, 316015074, 662150443, 712216625, 195842390, 230552666, 141798015, 366411838, 224081916, 282613195, 638193716, 905252496, 187023191, 593693404, 147095093, 94789982, 234755421, 855120811, 507066203, 796178434, 167822055, 574021949, 983212168, 591640972, 823349640, 548046733, 252982165, 363522555, 421757780, 104110823, 317190716, 290662425, 776540515, 53255559, 77883304, 511742157, 158596025, 668793503, 533319136, 46066144, 651293427, 477119694, 688306733, 536335294, 806055967, 258167609, 550566568, 457950032, 751754177, 763512490, 844500048, 71625303, 310674518, 569607902, 357391990, 270363383, 675536033, 298575747, 168120953, 907925869, 426139719, 696020272, 144627341, 457960642, 210452419, 343899449, 72959457, 150248417, 719505134, 473663095, 262530767, 408646703, 605094636, 151323296, 151695593, 935713200, 610755584, 107604606, 565951111, 391887726, 930113875, 93586073, 815553597, 132594417, 891909954, 980585781, 660298933, 526773972, 677709624, 789769177, 389825856, 525415965, 752494771, 421930093, 281324798, 680914483, 95135658, 393902699, 422499111, 590450557, 359123440, 867316026, 95396292, 714008580, 668656234, 282568497, 962830377, 459255543, 649728879, 916717629, 285942324, 119350320, 682076699, 541780343, 393047497, 851704129, 28684839, 904132617, 5684572, 359238945, 75032169, 797333611, 218094619, 194582236, 67604951, 350631319, 212856907, 350182504, 710366673, 569063629, 356472623, 55855991, 145783420, 374694721, 201402055, 379237974, 224904037, 958751383, 371302666, 522094618, 308306054, 97280072, 981850834, 576670415, 343626469, 500746659, 842051786, 92013695, 971760591, 434179576, 281983879, 339152114, 405951212, 792068957, 555750540, 250260166, 467885185, 116200724, 699847309, 437341618, 691959667, 797386641, 924881704, 626875944, 816601993, 406235322, 571318080, 984607385, 968555347, 646859565, 274008966, 187425425, 459045455, 83428528, 582221981, 763419644, 736597849, 85016126, 428236627, 914667205, 948784946, 90566462, 693760937, 1280364, 220610323, 424039803, 482864442, 569299202, 457578835, 162045457, 724689128, 415319812, 870015403, 798724593, 470536350, 330935190, 737965805, 668267794, 310568443, 206968807, 549098160, 635950589, 868796363, 243997247, 907244225, 988036876, 619189411, 40094302, 303404082, 643033789, 450002523, 488044025, 417355164, 882188530, 667076920, 864889446, 500980537, 227694838, 437701491, 258744220, 316658910, 121336591, 720269402, 844151419, 735337368, 408427414, 621204849, 520871302, 72164144, 158622267, 408732103, 627539679, 368355396, 410948853, 318553478, 558350494, 96203793, 587761682, 18915235, 563928255, 11990722, 855345666, 868624228, 337914099, 283217433, 634235463, 513257615, 50000521, 602625442, 216238180, 25182513, 930327708, 968102554, 691158274, 598240406, 733104099, 736952711, 39722396, 473746301, 131482433, 65318379, 203744924, 408195074, 145714384, 327332040, 140290554, 446804436, 967648259, 588858690, 50826711, 74993313, 361183161, 292635032, 150827290, 384306066, 617165664, 494187736, 953698543, 809091377, 350670807, 843162105, 475261164, 965790413, 881412356, 266956245, 680998031, 180174775, 809525258, 143624525, 532333014, 582165027, 152326583, 718629791, 542098262, 26494516, 944825552, 616680158, 366862847, 972032058, 332309286, 264435104, 691173640, 737370359, 123141517, 70787133, 508389191, 480283640, 877170742, 352084861, 709277717, 576983428, 910937460, 721805037, 129327489, 998835589, 169784035, 196873200, 158897923, 804772602, 761274920, 187894026, 915355401, 98868620, 717239038, 638471597, 978922610, 308023229, 249233680, 927402826, 243810232, 561070243, 95234581, 737508993, 892279408, 585997081, 933403551, 150706638, 317267498, 98710757, 539021097, 140216723, 451967720, 488589803, 573373888, 152976154, 640921966, 134181556, 674863159, 569058313, 300588737, 960390324, 155173687, 901484242, 872205507, 945513709, 399772745, 173401909, 846816213, 898109747, 859126053, 924000313, 374868330, 991921098, 426817079, 330111078, 944573369, 358824922, 439952616, 27419002, 455443507, 571440350, 828905878, 349047075, 578335228, 351411207, 346244875, 492229883, 110501519, 617374489, 766837186, 72439974, 157537328, 408572276, 583260490, 370348093, 828409099, 387891073, 499687251, 163204356, 262511155, 234518303, 139917334, 881211047, 228131701, 545327336, 306008710, 357731253, 503849299, 980032130, 11049102, 779594867, 165297643, 254600668, 842373780, 726438040, 820086607, 293075555, 557450039, 358164234, 351996543, 111408013, 869701513, 39988440, 774292593, 69968024, 239983364, 373736157, 747719262, 455972013, 106114575, 43836947, 679627664, 726037149, 92955945, 795276792, 578778216, 327716799, 199337866, 595958689, 447497596, 705045958, 366448081, 918921705, 851008486, 104680089, 573365857, 896205531, 363483234, 498436872, 837315281, 339866959, 543891940, 193136460, 980848049, 543873538, 507390762, 509430822, 729553879, 919498136, 231758222, 938695695, 724116921, 38274230, 863431343, 808625660, 556258485, 780553397, 975204568, 581160772, 716829576, 510052628, 243199373, 375227672, 645477771, 17700864, 182992798, 129798795, 14119282, 703275900, 709050034, 71139757, 903049073, 209604249, 833275634, 274110774, 780227412, 847180572, 971135462, 182206421, 567394162, 874662334, 983358366, 125809044, 593960974, 871870805, 152651654, 776205917, 192243525, 335431980, 871854230, 77454784, 597993573, 512797088, 107492087, 95942542, 246913248, 14119820, 714924901, 93178366, 776100136, 944094997, 522956468, 814976513, 761193747, 817790080, 165854116, 53673356, 452567172, 957043537, 230751640, 893596872, 424443878, 747778357, 786534320, 547536083, 627991983, 119760098, 981753657, 552034492, 893684853, 440291026, 261839116, 355164669, 148834870, 598431051, 1841832, 583568456, 413549138, 103312634, 243604550, 264588124, 134751446, 49895115, 488822394, 32547721, 870915037, 907124117, 15058547, 39594567, 93374935, 970216570, 188625255, 610826124, 149244516, 742935795, 78131974, 396440440, 78920282, 277650937, 365763587, 885377956, 926423245, 520141868, 496884301, 598799711, 944607007, 731967930, 943375649, 319984638, 487693307, 242439392, 334343288, 646648159, 587320142, 489762695, 605078487, 570191180, 654059732, 390115579, 200654674, 951373361, 4479251, 481891977, 45273171, 688908244, 670351018, 298746070, 796936922, 831919368, 583466276, 457347191, 745179599, 660228994, 186048542, 757919670, 464111394, 208200135, 11241366, 679562336, 718288871, 483070164, 452499554, 150487187, 761249380, 415737755, 856554196, 870089627, 831038050, 42189128, 886303960, 272613026, 393042272, 548242217, 70844946, 850828288, 522095054, 10920115, 982205401, 105977046, 132665754, 905321169, 272901940, 450845613, 305631693, 191947959, 197358735, 265459045, 487177321, 616812086, 356718233, 904952198, 386141275, 313761335, 9790401, 470783125, 450334563, 211892982, 932745098, 811994380, 457886842, 734665058, 273589892, 306604542, 960760895, 926322627, 754273221, 558458903, 191502653, 194815193, 631450141, 890417868, 896706029, 339701102, 532209350, 362825327, 153604529, 906677259, 361371862, 402583930, 257178717, 74622425, 597775188, 5850083, 9776058, 294684453, 536853121, 482081159, 17060575, 890840377, 553403352, 390871384, 35128961, 792892485, 969321269, 521912358, 571034185, 539422254, 311350202, 596391700, 185992101, 573829920, 862489190, 32066117, 649076597, 803166160, 314222757, 172441122, 593609408, 778348240, 283377052, 724378405, 802003453, 907713152, 461648976, 311973474, 611357257, 439941511, 56305646, 549576233, 836290806, 893817592, 330371324, 65834883, 616221598, 963650531, 932886911, 40943100, 7521793, 975083971, 57824254, 818889911, 296120006, 927733397, 513934247, 604290841, 283741329, 802286264, 546992860, 317880452, 490674637, 432294912, 434409617, 369564370, 325554887, 162428818, 896783176, 713441757, 129821415, 707936987, 979967679, 884274514, 211259221, 362677769, 903142437, 234382210, 838663569, 930231098, 175911418, 698398574, 675578031, 520486285, 355050990, 262665307, 407030872, 3611581, 105498768, 466218448, 354245734, 259238165, 357857394, 662281485, 211646798, 233245489, 36013722, 966920783, 418907914, 478961826, 195387617, 389879953, 410869747, 318460121, 854917365, 889458736, 626983301, 767267974, 901180371, 776593183, 722570692, 919004844, 139906718, 588049323, 111059193, 507433680, 351580504, 708316291, 115333523, 980771980, 138034699, 680521212, 796649765, 53059385, 95084153, 610644249, 830252948, 113892168, 627345696, 784904014, 29078348, 852520222, 769924624, 760838235, 727340097, 140850268, 404809880, 835826941, 880470295, 161803942, 402533654, 172768034, 500652487, 670889705, 463919013, 515773357, 491198990, 402306602, 829466907, 546857676, 880999701, 15599370, 285429842, 925395256, 326585846, 527625869, 939710101, 874460810, 332690301, 905939195, 103409329, 252912383, 589870069, 453659550, 291328386, 369972201, 639771448, 622012059, 87726421, 562770160, 452821650, 334085309, 830428461, 190405846, 586248297, 252321908, 583745173, 551244035, 888929509, 489857452, 94190090, 193038475, 671569325, 847853453, 941810958, 499399235, 607459909, 541358223, 779791790, 980492103, 254613410, 710607846, 809068583, 829994089, 695787356, 895082134, 735054767, 993389110, 279090673, 389528466, 802287547, 109623337, 73840992, 497603897, 743178819, 710578844, 110688821, 248224441, 522173856, 727861238, 111778062, 603708329, 138348808, 295058948, 464223625, 536477617, 224510723, 454597141, 281729500, 452092686, 557715154, 201092278, 387752790, 438868766, 579342481, 345641132, 407084156, 457790427, 793337664, 523631119, 678258929, 585419116, 779342207, 382636023, 742457897, 845812582, 51441736, 808315957, 388949766, 155500763, 110584337, 660099784, 542698576, 127550430, 185435591, 762785626, 361649543, 280614614, 608202826, 872646251, 290478628, 728613938, 302245721, 163210907, 586612590, 726702806, 66073902, 907853468, 640824562, 841915509, 42962589, 117963659, 407227762, 693487195, 880154658, 570292040, 624851936, 603057260, 263980657, 880700734, 409638714, 475290158, 197499009, 951936227, 814787368, 575133697, 197201246, 713398042, 791780941, 788660094, 915928215, 391928033, 150724806, 587170709, 10076519, 620147424, 346132439, 301913389, 235408605, 431935565, 730053886, 285482754, 60806380, 461899172, 54877922, 825400351, 787463710, 923880133, 666513305, 340878940, 283398403, 167236342, 268636004, 121267192, 398508400, 166470071, 941865292, 302742019, 932383584, 780922707, 206525890, 401101568, 820407336, 224257325, 833505405, 601459213, 52014659, 971685056, 661024042, 899503422, 45674085, 114120303, 779015828, 533128986, 580402383, 483783717, 729475542, 90671608, 804541093, 580292783, 500421920, 257000873, 749117719, 982597508, 382067439, 354141558, 174017512, 92581781, 696140224, 825592805, 387610827, 772555515, 294896238, 137881205, 80127413, 252964638, 702580193, 120797064, 279307012, 966373291, 979503184, 60227740, 927853126, 500825034, 246204399, 962822625, 743388680, 960059095, 517423481, 171017388, 419022374, 231324145, 764218970, 797080861, 582869776, 682761864, 643243705, 719441571, 46896365, 152609592, 852514770, 828746529, 80025630, 847913532, 541942812, 35524967, 570601925, 98964489, 541910690, 164736845, 276084993, 933007928, 120953489, 53240839, 626070228, 607086123, 393509736, 635069309, 679485614, 925540870, 807071979, 887177198, 751748374, 842023066, 765668700, 881844148, 945412039, 180706880, 906170079, 422517034, 746397254, 730344971, 492339239, 144150409, 968476904, 33217993, 250317424, 308544411, 515235000, 688350889, 31677665, 694953687, 680638486, 429652317, 614052908, 952885185, 945626779, 283433702, 105767140, 232914971, 606853104, 797407385, 838002932, 548959178, 806643518, 300320201, 429835953, 742678744, 201536386, 540461450, 819156607, 921924706, 644837653, 282530190, 439813321, 729153897, 646755675, 746970370, 750928041, 10116742, 95217106, 295763778, 431120847, 260583366, 808836176, 114371495, 826344772, 18789731, 882207166, 500644309, 298829387, 733648031, 221056286, 309700302, 122894928, 241833810, 539976973, 70561097, 23325085, 739380316, 111460587, 541308894, 315356166, 760151970, 365996239, 741514774, 51564244, 263921870, 700834379, 423228681, 251772888, 120043135, 745658801, 776552196, 224407314, 842715101, 405397922, 207374727, 511039911, 58889179, 187292839, 421338574, 159533671, 436716818, 28103297, 652592006, 947640700, 212864176, 735862917, 812087879, 653613558, 313495362, 974901368, 787527134, 66752561, 6271450, 791587603, 982109858, 238837304, 711344261, 972938, 924428531, 79382139, 49095746, 660024078, 935209180, 948164760, 378112431, 434440073, 876231036, 100715710, 501493414, 217716071, 699382800, 100802131, 539301082, 718802011, 883880637, 976138466, 375087385, 541562504, 90090049, 822523086, 779332933, 997921440, 776737332, 695263386, 698478080, 143651748, 698642231, 9833267, 873520901, 773754090, 302264656, 498439845, 218843932, 851549150, 117117447, 272288368, 574124829, 195649477, 787009501, 244069715, 660500793, 630172220, 999557671, 71336605, 972435092, 975623434, 941507032, 114060877, 900351404, 903731885, 656322089, 986206662, 326476330, 217705719, 919241194, 775388653, 685529222, 67883237, 940661166, 248737008, 857543323, 971088049, 57343045, 731477365, 943133476, 564824119, 31154575, 337314119, 358562641, 95689454, 396596962, 166584521, 795602113, 268864526, 16686206, 754044434, 19826672, 948305368, 534550323, 218726457, 168588752, 786389297, 372090148, 632010983, 32562310, 890106176, 901615518, 919248171, 781833060, 627873218, 549969945, 343085098, 215044732, 930188517, 377044806, 269995203, 992264453, 504857637, 359198308, 641752160, 778861867, 504338834, 705213949, 852379133, 51756007, 678377824, 214926458, 461315311, 48199256, 915773227, 863258001, 393178196, 614297688, 638376107, 358424554, 829057823, 412193081, 819141430, 221719034, 209470528, 648564212, 255648817, 67073829, 282882238, 380241196, 719525600, 896634757, 466772584, 931689316, 398608264, 211865549, 609115628, 789419981, 42347760, 356936371, 844010807, 669795520, 576194902, 542076881, 26062627, 592829099, 583233510, 628523986, 354568213, 756715364, 707115783, 140474419, 737810749, 653308111, 928824972, 997424309, 455344991, 237683492, 840182782, 555372362, 951713422, 324916779, 84338765, 842389968, 871482062, 66194655, 667769866, 615132550, 164819134, 431019351, 294954924, 25590565, 234392322, 73849526, 95907267, 239918184, 147135954, 338334481, 670624411, 263819381, 146713768, 224889676, 20689198, 224807129, 313449551, 640980337, 382079031, 828381641, 844888263, 991547410, 550591377, 781035605, 798807840, 394039323, 117788348, 450775948, 87049878, 221819503, 957833690, 411808123, 892468664, 968139965, 859788952, 407018048, 650103130, 588802658, 747515758, 462865907, 917004286, 727856738, 188781105, 797240766, 120201518, 586397035, 49594432, 525352070, 777383562, 864453567, 829151741, 438579899, 760619411, 873118754, 667573452, 743386267, 637878768, 374307043, 997982833, 970315524, 10200038, 422353194, 612137508, 5769358, 603420440, 959573489, 322248804, 559981535, 442942832, 27177619, 65571969, 6420809, 260634277, 421336521, 98858996, 277694623, 286829782, 962836284, 773336501, 301383732, 719633066, 68151691, 378071960, 852984042, 891464189, 701063978, 699597610, 448381095, 780657006, 849343432, 91497797, 440756813, 750946917, 617793804, 295122165, 636917064, 19393280, 868728733, 894060178, 140646694, 606562509, 334628228, 953567100, 975761315, 819410201, 606256554, 258114473, 266998022, 473941038, 395327564, 629826378, 922161917, 494376084, 552842909, 176982605, 815879822, 111316943, 719395140, 412468709, 397990779, 70051636, 563862684, 933613258, 538384741, 108771385, 495909890, 607715391, 112320521, 453812265, 249271246, 63939674, 502270160, 930250965, 760533533, 993373498, 990148382, 664461234, 716800224, 202623630, 69837321, 952059768, 475999586, 162622451, 179010783, 496824521, 198549046, 33920408, 92865271, 703995260, 31979664, 599615834, 136062910, 453062229, 444108770, 370681060, 746886233, 897646, 343842895, 592885528, 135730618, 649508957, 363352159, 548801320, 584116731, 871025121, 857921705, 493578748, 837088575, 607238138, 95865292, 885946622, 866805445, 620799420, 340193548, 41289316, 232192902, 668431986, 220680343, 721914547, 703511372, 921728921, 772413086, 426260722, 823521578, 750488150, 430475, 744841910, 681838332, 103645779, 263717168, 363800237, 614311149, 53619642, 899771110, 193785615, 664706981, 553861091, 611846650, 207362476, 982082915, 457734963, 399699591, 604237585, 891457208, 66966923, 916111755, 520659607, 876903531, 743679240, 258696938, 658002912, 815152377, 230557816, 775515365, 607182542, 415592524, 861229844, 245601191, 221200895, 717010520, 105588519, 740783163, 940353563, 26485027, 964287373, 489280606, 275709046, 383557973, 655050137, 651015823, 844522970, 376580439, 907640685, 928553060, 611136170, 221520984, 92498420, 904954541, 350750338, 807963797, 574802765, 630037961, 974946971, 422617754, 457324127, 665355581, 237679413, 908124578, 669006789, 810167152, 53063359, 888241132, 521819158, 317066647, 140626765, 49137572, 929332257, 780818453, 412315291, 987167769, 85110046, 531820839, 298326563, 746774793, 118535229, 326252103, 858002862, 52958210, 883420115, 412177846, 984459228, 100311263, 491113229, 636497682, 775387866, 138221374, 363938479, 250261399, 569631728, 205555745, 963487202, 229134912, 787252461, 936773736, 398393368, 875530493, 788739514, 160658412, 95351119, 222070928, 560561365, 35384959, 832380824, 570703401, 636840350, 101351135, 308705037, 789552867, 879065841, 998546398, 546544441, 855327512, 493488794, 907981862, 649681994, 514728682, 777974353, 813377900, 618470830, 724863435, 829136232, 823631998, 933472124, 148446098, 682066655, 664980932, 534223263, 922090810, 430426353, 109730842, 657938603, 741124818, 139163359, 429362382, 349574138, 194142963, 702717920, 412624175, 102177302, 864624307, 620235242, 36253281, 668595717, 71807264, 12191871, 787765776, 858839513, 118598052, 609632732, 365163915, 195699480, 665912277, 738607963, 400672929, 801979206, 365980643, 912119484, 438688964, 615374328, 283685764, 645122106, 745551469, 185517973, 928169900, 252512731, 381568501, 668772460, 517742945, 436340808, 409342629, 79584531, 43109263, 413429668, 43374299, 156789871, 162425614, 622742352, 877902952, 475524834, 679826869, 35713459, 414595986, 734543732, 701169578, 865673555, 160050315, 622798488, 150131361, 25783676, 914408902, 767298328, 179812761, 117796765, 563038925, 528180326, 128411895, 293847196, 609004075, 619432505, 950396608, 246151671, 157177604, 474786888, 55057769, 961540103, 549433046, 852544322, 849354048, 700578743, 794100876, 622490003, 754100557, 476915376, 307636739, 837147039, 102702330, 139862412, 240651102, 40773354, 383398854, 749708747, 237790833, 263069656, 838059450, 29604026, 506335598, 715667927, 589448777, 773809759, 795630704, 632182084, 810641115, 255271191, 141099411, 401296886, 837937448, 281176822, 156363669, 160570229, 434804638, 390752733, 139040758, 703656410, 512233141, 3172674, 954177274, 489918341, 564544537, 513394844, 669123809, 908592092, 729523636, 995747300, 686367976, 379036929, 741063321, 89815316, 107802610, 25889846, 592264974, 600191486, 805565247, 347498177, 429763773, 552613429, 238479651, 450157865, 315506137, 985254916, 845549830, 453154953, 256713761, 57422938, 87459522, 979397684, 137611918, 368915181, 963626348, 973370995, 13343232, 645007501, 992607362, 430239215, 613714602, 50342328, 499683557, 887773451, 139694803, 705179866, 263676034, 49742883, 531103016, 756075927, 176451070, 611230391, 834961138, 480148760, 640775032, 873472504, 887119056, 123255506, 577959192, 614337767, 69581295, 819992787, 65284082, 671529561, 395882239, 912764499, 472240521, 962367965, 911989192, 275261341, 760024304, 754222553, 12350814, 974259603, 457218340, 285882729, 691418057, 949539659, 894500471, 378544381, 790201238, 587331317, 776633517, 736815475, 639724732, 625258713, 370056257, 617603404, 986041129, 289214904, 725658803, 215411360, 359455844, 437516725, 365060986, 943426981, 561644811, 159737872, 269151636, 459177169, 352561822, 559414830, 534365945, 610877965, 959988893, 431121639, 703759335, 106671051, 876980676, 846208034, 634225722, 19822232, 383511638, 86546934, 382755924, 704094026, 910985174, 273423282, 242650463, 689250763, 861928085, 466404521, 552141901, 788444783, 293311150, 586693668, 260974954, 318315139, 531097424, 160554573, 867504115, 735411146, 301464111, 979595276, 647820687, 662950461, 350673096, 896544856, 8542170, 956735510, 691177752, 566838997, 580484234, 720989425, 812294511, 534077949, 388474412, 453331771, 312942698, 133480128, 364859511, 288552861, 269788026, 225520656, 238810313, 687072888, 582599432, 156289643, 901898168, 957141320, 259094806, 767606656, 590273903, 160714225, 152202262, 553952822, 228770071, 186551501, 886004015, 522375726, 895031439, 37327005, 958256672, 334310149, 189583438, 897310916, 330965447, 53991849, 876468965, 63221478, 755157388, 737302403, 137971943, 903556211, 116995607, 514390226, 315325536, 916014311, 762370764, 739896962, 431787060, 193060383, 211532599, 782627366, 584472607, 239192541, 397250554, 91057250, 612628969, 140040163, 557071383, 371652749, 719297217, 444632068, 978159338, 235354362, 570756414, 742971100, 585448937, 145469912, 404439761, 65476962, 116308208, 328969931, 63549086, 383105464, 150149373, 22285542, 989669866, 227997321, 272178220, 451031834, 139521739, 307846414, 193157917, 708398386, 12631829, 424129873, 665582311, 536651204, 766034341, 698729197, 369369549, 100882927, 1788778, 149950911, 807086726, 446506092, 215613952, 91342322, 378229803, 86199034, 294437811, 4034989, 457042750, 383136084, 486660406, 337160173, 765313138, 732335543, 781757396, 309931422, 936994235, 734133880, 447021332, 141551987, 645603867, 397349059, 817738625, 704274414, 216353776, 834915954, 539730800, 110048200, 49782084, 659278013, 201300169, 439031330, 426269145, 108572914, 611649616, 566119280, 104305112, 179739489, 615500847, 298167427, 545445939, 519284617, 495195091, 323873228, 323398381, 272835125, 63929231, 135619144, 736452325, 559978724, 256177916, 87537851, 527442297, 114929236, 458957722, 701876759, 702777379, 72154694, 412808463, 126860122, 330804838, 19371041, 924649878, 518356966, 103122426, 825700202, 45374632, 198821899, 168842332, 517877046, 935749431, 460553389, 118546041, 483323641, 203915031, 418048745, 280441408, 776567433, 912831365, 862349837, 430226388, 135532029, 275470598, 129558728, 68573337, 246247228, 22864945, 516180605, 572619890, 738021857, 825353847, 852233679, 38952567, 579285712, 129105751, 874913501, 113073418, 361628561, 825031455, 38435147, 190327256, 715197537, 265463834, 761698825, 390509331, 376561256, 539289004, 790876427, 442273203, 242878673, 868548592, 525313039, 500326346, 22979524, 520480739, 543607644, 53360985, 512547499, 551186257, 979279409, 313292457, 995366764, 909852348, 753602176, 62650735, 205426282, 494810927, 333604996, 306887322, 374846096, 172705697, 68727808, 984245536, 920419558, 973366072, 990661448, 320199354, 477119701, 973398858, 518751685, 588609438, 258874033, 930996960, 754215298, 508867705, 507036907, 74300267, 60786900, 322679140, 193918253, 661056750, 118494686, 409454447, 420139802, 925334461, 445399922, 320127941, 207382517, 727362275, 826850714, 697903195, 346285348, 773544282, 640159936, 243802870, 210764178, 862192864, 322259170, 673846231, 139413893, 818308068, 295879982, 687029806, 571500186, 340367124, 120246166, 820517678, 329899859, 533158473, 18667880, 373300701, 425076035, 395082976, 549210472, 11339794, 638688941, 797507608, 200459526, 558554162, 16931319, 290451407, 264781736, 650688265, 582172904, 117536742, 558211698, 462472165, 529913810, 124155418, 150277411, 334038114, 45049496, 200794258, 53316716, 270056518, 298009079, 518676644, 592229154, 29503276, 63264160, 266887304, 95253803, 746666703, 936184013, 712616140, 348832305, 962677274, 949078354, 633284858, 693931279, 778506102, 627701531, 530786143, 395468364, 514111450, 16706978, 115424980, 822441508, 272764882, 152696681, 993935379, 975998791, 14540047, 40112244, 809921106, 598028082, 114842585, 830925356, 32427134, 457589525, 739303981, 61137809, 158834515, 317330935, 60538735, 936717707, 448377134, 952062831, 205650383, 112744027, 806789429, 11774216, 558728099, 47644927, 784933837, 424133001, 328262507, 759627384, 783626435, 193202385, 741639196, 745776738, 8117508, 672137423, 55374245, 592362714, 93440479, 945524710, 530022929, 143632373, 152670593, 795359183, 251304913, 334947911, 431863003, 243408076, 972627515, 80036205, 774342072, 403935107, 919194102, 39710346, 222269638, 149963353, 238720201, 388058841, 195958901, 668132117, 601409279, 860918924, 836578258, 965407096, 763752709, 592565408, 401063707, 561152325, 82866280, 198059306, 637819924, 971615504, 386833251, 577343242, 567361320, 586049918, 890149448, 119707575, 323472025, 298253290, 753249754, 794204380, 569337005, 512849969, 275753009, 785937825, 26070810, 977794116, 866784033, 599332386, 827059888, 549966951, 512892891, 869713400, 492687183, 157040932, 391508752, 922607495, 965610921, 227842797, 708165456, 40465942, 395267371, 278745969, 142086947, 108058435, 740759421, 76630809, 983168897, 871870484, 444919478, 228584105, 128588008, 517888447, 21009984, 234198767, 492544646, 323410067, 379716045, 590555770, 57093352, 40486760, 10854722, 26819044, 605873836, 815220868, 259738040, 496241034, 656738021, 390217685, 322326545, 70003895, 405791124, 114224184, 920463210, 527879457, 283574162, 956737814, 495009327, 5499718, 743903345, 621517050, 700762205, 765373717, 737819550, 402287409, 417865423, 881771972, 354570036, 17450552, 154837560, 15011088, 195965525, 120515566, 845175904, 634944417, 931930478, 601850910, 119662328, 917096995, 815341389, 397679271, 909592303, 489859049, 332467563, 35764782, 264798306, 824659558, 583932733, 837982795, 24796587, 85560170, 233443746, 531954924, 408133714, 815446245, 603491377, 158475150, 565576516, 918468034, 627926675, 698559225, 239843209, 585890210, 309552278, 110621102, 175850271, 389525829, 142226674, 642386022, 482226723, 205060080, 526434455, 897169511, 586417410, 470301604, 530460123, 601975880, 462823049, 350217274, 826721027, 402751492, 619813496, 593141876, 109706507, 174977039, 734871899, 102126787, 695265262, 15978382, 835327015, 570097265, 668940507, 423070365, 106359475, 423973759, 544313032, 902826688, 858513130, 305421737, 503362377, 597115030, 323098570, 608051808, 576253200, 102272254, 155091774, 118547477, 88632462, 74121290, 241465516, 669196175, 220339123, 210764280, 111922080, 604202662, 166365124, 772017100, 625460094, 154463305, 48818953, 331509332, 159851459, 993365156, 965833561, 72500755, 821306439, 679753673, 239870391, 8384798, 488741969, 631702022, 467727418, 200160114, 207765723, 641152706, 316582460, 238498485, 132332374, 161053518, 947107194, 96132532, 193038581, 607541732, 499209401, 520956396, 147923848, 249186335, 444937864, 967726623, 341028217, 362494225, 722429841, 824775211, 325710612, 929977779, 923966199, 397689807, 755183560, 993441330, 248879971, 139588908, 787789174, 78496869, 905868168, 181152778, 258706705, 758971672, 278246158, 194485665, 16329407, 696432906, 763503629, 519806194, 534322481, 943990222, 310551278, 128048981, 419518585, 675400711, 248246442, 317580683, 448848585, 476915291, 754172980, 860114513, 273376935, 419566254, 395439000, 33026531, 199001435, 802505401, 769382117, 987878623, 954518793, 114436501, 184326949, 35818355, 339030756, 329401339, 420368685, 916165576, 390309910, 363990372, 713471042, 202720981, 750985322, 707065125, 125370272, 748872293, 677429776, 432084128, 495420715, 852068242, 757425184, 433299600, 85533992, 889205842, 464783953, 917987671, 279010456, 173391696, 44197070, 234986980, 590582065, 521143145, 574323935, 560293220, 248163796, 686781873, 282484139, 3084546, 324915522, 613896552, 65207940, 625255643, 735539883, 366586924, 393920446, 528297357, 883680362, 374662062, 907486183, 720775296, 272358706, 42262306, 584500925, 97466126, 882390010, 544796835, 978520757, 429623999, 365088467, 968309347, 270212872, 354299244, 850533757, 484333831, 787324573, 372121231, 652303415, 59242939, 233294800, 631952536, 592593463, 637307600, 340651392, 576726386, 744368012, 16606114, 555109227, 698394968, 672868802, 643336978, 4076763, 281321831, 820197818, 87069297, 574293928, 812189651, 181111526, 719521377, 401566762, 400956408, 789227280, 178319536, 500536135, 998829215, 692182653, 74819033, 479526165, 922482457, 119033832, 943143180, 959158995, 753868064, 366276921, 618634002, 604817798, 51553192, 193010759, 339843828, 291748338, 973568669, 191764006, 352102600, 467468715, 803323418, 652285385, 100179704, 987807059, 336953767, 65049263, 901395538, 816037270, 883615304, 115056174, 393623564, 380045311, 792114993, 439390265, 265692195, 797829382, 421879001, 47544492, 629627788, 910702356, 98457661, 70458552, 155600247, 438265609, 498040006, 222352821, 147546550, 396609224, 892132725, 776938992, 527913152, 39253931, 686231206, 546057126, 859816699, 714061531, 128656387, 690150484, 328403836, 555245389, 311171566, 992940777, 12632846, 541408934, 40616179, 295813209, 706925100, 398814583, 646783407, 684729042, 354095601, 148910526, 783649490, 333214232, 951752866, 106428109, 413737291, 37370113, 993740549, 410528662, 241251044, 878349280, 305523602, 452922907, 362330216, 719615813, 466554486, 652363346, 497710195, 903640789, 703794448, 561689325, 297821119, 651748204, 557063649, 569571447, 603035576, 468814169, 857847997, 667834680, 470827841, 673035913, 196674780, 854186148, 292401456, 52982970, 268688900, 854674224, 29579753, 820171017, 145935795, 948666136, 57048397, 197417919, 569167245, 476085103, 132924498, 799291095, 503142059, 884427117, 208544444, 266509444, 958461633, 286110462, 443714250, 345434736, 783408679, 934503256, 978561634, 849290096, 327566667, 715863371, 455536872, 997035018, 219087314, 764359443, 496087632, 290832679, 542206781, 894585460, 905569670, 737830120, 333236306, 695790667, 254756063, 486203940, 961172806, 769311148, 190879537, 912395175, 424524568, 439657266, 298017299, 172774067, 125811925, 461937741, 298614348, 92453669, 173104962, 80545515, 160356568, 222793884, 948015331, 824953200, 521016249, 952483933, 211434161, 511467447, 844534611, 562339510, 126352241, 332267613, 44773054, 302660262, 569912743, 507339983, 1244482, 598677167, 150349270, 235849214, 46881015, 986854128, 817265375, 659544355, 977397028, 666452054, 784869002, 373382491, 257382953, 201983180, 118619822, 22260822, 154787075, 91305753, 758188902, 859679515, 192710392, 41721976, 274578221, 744476422, 673261983, 660574196, 95312688, 245445449, 545683318, 998582089, 516448590, 320716189, 851397253, 746343856, 978716192, 286229704, 135179463, 420411974, 546182235, 30167201, 39594940, 978432668, 432046407, 234160223, 396484562, 775030522, 250932992, 794060125, 44618925, 764841983, 884843410, 920656216, 177981381, 140095478, 560853296, 981630773, 216817489, 580436894, 294876269, 11580577, 807906777, 795603645, 934166691, 748773528, 468882633, 918710973, 120168750, 603723971, 588324253, 312001437, 183065416, 737254053, 705589146, 894372519, 124146733, 249910643, 837516441, 309560857, 334120351, 230135861, 971834588, 818967857, 641162606, 511985829, 444803519, 474981067, 89064335, 585854230, 12573990, 360895881, 485722281, 687117807, 445776917, 298729013, 284019548, 828192420, 706294350, 38144439, 256867545, 452808667, 67424965, 191752694, 990633012, 74855332, 84995502, 366786300, 963594833, 830797546, 567947599, 481706705, 733035947, 455323410, 778290380, 954838313, 638974974, 327323916, 252593560, 240097850, 991006556, 644638498, 530245925, 78148948, 498751962, 172309053, 683404657, 550715234, 621517316, 954647836, 130050996, 797845364, 272532424, 81173522, 498154183, 421676489, 503407805, 577650203, 578514113, 144431290, 511164679, 201597031, 323855612, 197920146, 623244439, 985282487, 602820200, 253004174, 122743202, 456088765, 301216437, 892626901, 951348254, 676177878, 250750347, 696996546, 646003377, 781982475, 725861031, 568450030, 96714031, 858880467, 229658411, 70462843, 220296659, 549994245, 397136763, 810912449, 645112153, 704236124, 493358147, 834112157, 28361561, 386354327, 646205256, 7647459, 204874087, 359453778, 249009733, 576692764, 477087402, 155492476, 508677238, 384556938, 833090179, 911299165, 759390821, 985134685, 487336541, 486647980, 229780704, 802914215, 832399698, 585584794, 649078700, 651831199, 259404662, 137278406, 927612377, 855618257, 386347068, 406326203, 45907843, 60445599, 108755167, 588022534, 940897715, 273757346, 526564122, 415386597, 60194596, 76588448, 787621908, 704573555, 646392589, 378793327, 325261193, 584180756, 654302244, 805201922, 297075994, 591184430, 943202888, 217343555, 794094344, 476871705, 538168306, 343952575, 858904696, 880404099, 936659520, 844204906, 67704593, 37830763, 764913447, 196441918, 711472722, 279132661, 669071436, 55699687, 703339296, 37489844, 712339795, 619896229, 139400238, 733281625, 627380233, 85083499, 603869194, 428562455, 535104377, 316217886, 38432526, 947232784, 572465179, 131304924, 870255126, 323688497, 723232788, 114138544, 574930814, 937267390, 796000776, 665168979, 824021924, 882653640, 186023834, 172932146, 352528211, 305027326, 180268658, 515518501, 35885971, 194569604, 280271432, 291987615, 91827575, 135918610, 190145440, 273228810, 106256457, 185766385, 428129442, 445845410, 956222227, 656154205, 973603572, 278613040, 734188425, 621256326, 552089577, 729866350, 761732927, 994612952, 38330029, 800771262, 166350107, 160121269, 78198699, 821633672, 602167948, 531197481, 113292661, 863810183, 288073276, 892065408, 943250810, 517862574, 96690819, 662761249, 18136830, 637209490, 501304458, 209244001, 233086021, 537360137, 251737625, 301479038, 154088800, 856799120, 850061081, 179959220, 96151351, 323959791, 666726879, 564456125, 249820890, 808931720, 650857813, 181591692, 955193966, 849867398, 154440237, 984205322, 869609561, 379456851, 196246373, 595033330, 317572218, 582890159, 623511822, 87439271, 805599218, 362470204, 540832770, 205459969, 485286802, 915241621, 794826959, 121064252, 340181046, 383550396, 459861461, 345462606, 752098612, 80064622, 673854453, 730078969, 865053405, 979245744, 936957842, 628081722, 633271077, 169301756, 879824585, 386743141, 91171972, 366460760, 352502960, 811383652, 400194503, 797747774, 893580912, 874681274, 144031010, 497957168, 934321576, 950548181, 363484699, 945540091, 699624157, 154158076, 609019444, 135516277, 256409378, 196580712, 515042816, 726644109, 874546752, 137393106, 197250028, 445688896, 320234027, 686767918, 166764899, 593313949, 260725936, 783357000, 164383154, 75177031, 13892414, 342227145, 894450994, 634655578, 809666483, 132212803, 565163321, 510396602, 250828155, 231116646, 23516477, 621030011, 464534424, 43370380, 855639111, 98676820, 313220518, 986915278, 593086735, 893415536, 259558547, 15329984, 289242650, 157927903, 285954673, 204746528, 124485169, 459849487, 857316088, 623008458, 680632874, 329157480, 318347883, 967892061, 759911680, 833469359, 17477548, 389656001, 765102586, 836672968, 864359051, 28492311, 947358051, 885521869, 112279591, 36580710, 895043903, 939788215, 148420287, 531436489, 355000285, 580206731, 994367690, 404865092, 340197144, 36300713, 578133001, 581161730, 490581678, 785569555, 226266753, 227832255, 707607419, 40703532, 473325898, 241029902, 942616058, 788116669, 298605622, 737801393, 768846507, 358095618, 82134036, 239261994, 149514270, 445894950, 456191758, 721846131, 136500007, 284412394, 953532048, 120220767, 445676706, 981780296, 149339871, 203468507, 892290364, 919025749, 478973957, 921563195, 387475414, 409313432, 261152881, 95038238, 912357441, 677675514, 527079900, 813305572, 665846057, 286153818, 71915578, 43983920, 897337919, 606230501, 843509176, 929280661, 354265913, 345640090, 350245688, 271086410, 831031313, 427238395, 311765377, 400972685, 351227411, 696093543, 670755539, 636188773, 280621701, 206321353, 438224298, 271329062, 51666548, 246701649, 59747412, 289456354, 330583093, 808241711, 162666618, 298119973, 184333119, 7086568, 45944432, 171639748, 466065973, 784719243, 309144425, 987277387, 682725524, 449840203, 309833216, 993642870, 629534392, 4200536, 232848237, 400885003, 473674708, 710992814, 212237033, 11616474, 965651879, 237689513, 548097049, 191323476, 607419564, 122152909, 529124425, 934041905, 572597211, 883636663, 403996829, 44240380, 827797435, 307477985, 620334859, 143860070, 873132852, 273271905, 367619701, 647914176, 548269496, 319034724, 322379788, 811027418, 513543052, 679559321, 758149125, 956498455, 598781964, 482697906, 456154027, 611127292, 202208604, 415139560, 511121361, 334320123, 812425498, 149382533, 260225700, 382987491, 838924411, 438647217, 327864815, 127566875, 270210860, 257499661, 813069364, 700445329, 725059697, 878654180, 291714976, 692217258, 491188085, 197380687, 977880654, 347221759, 309958355, 591935431, 83513344, 723000736, 949528284, 187018629, 627243578, 431955168, 163594466, 645230761, 628188787, 40490177, 753120263, 536718322, 32076008, 393622143, 931388383, 944940430, 574944393, 852408526, 709611020, 90746099, 619854173, 269047770, 430751669, 58304788, 539772654, 377173618, 94563894, 568083531, 370863108, 697906375, 356006016, 314235364, 230960373, 147317475, 295092309, 155298657, 968545681, 880711256, 145203480, 188305914, 749729612, 33364171, 104390930, 946539009, 819001186, 744257317, 47344188, 471220867, 870533006, 804864950, 600114888, 274072290, 123160038, 562975973, 999162265, 130179909, 945827511, 95827808, 201762334, 951531288, 188054709, 875268900, 279498671, 846531858, 160406439, 400627330, 310255406, 23237945, 368403017, 962197538, 639233714, 481471955, 483624539, 784977051, 964914968, 596800633, 971679727, 734974642, 312411247, 547117610, 793287720, 896690800, 927098821, 742083494, 603857528, 72307338, 560698613, 766229561, 916821994, 438158680, 219786526, 131411164, 387693144, 37533639, 870031401, 150315558, 939085496, 46292287, 771887729, 231668021, 958326, 669635525, 523116342, 273915359, 173977735, 228423721, 700140138, 261622382, 631683896, 513413510, 589145945, 232865879, 502587849, 286229385, 190435174, 116517978, 193033174, 337898450, 473593642, 198042822, 232106052, 102856890, 758144864, 628005218, 770519030, 69513060, 177378632, 208351881, 521472080, 703627138, 991463172, 166863862, 300157389, 260109639, 134828126, 543737327, 296214178, 120966161, 961996880, 410797125, 860840254, 885680379, 69995075, 889610931, 312486793, 485279669, 167452680, 720500859, 407996988, 481785907, 608836207, 733071214, 378135920, 715363684, 16159639, 220289654, 705583278, 264674787, 628004245, 349693813, 525760337, 957191088, 278022517, 584913786, 371268475, 294784474, 653332422, 396350640, 214858434, 835248639, 89139065, 400455546, 979173490, 405921974, 384775632, 317074777, 765706135, 955528351, 204033963, 223193994, 684175545, 433695658, 882476908, 403080891, 70993168, 868611368, 301933327, 454112630, 435597038, 827060094, 967611843, 976883024, 392725305, 946365951, 527478191, 616998878, 508745465, 615238079, 443990321, 554172083, 231436859, 855592382, 879983922, 891045039, 394980001, 573089382, 118359095, 424656998, 391630368, 734042930, 533230711, 605334908, 361834190, 14363565, 365008482, 457244253, 334339572, 914883496, 558885660, 561935057, 385367782, 961328348, 78486783, 636514157, 582962961, 311108259, 182444695, 941918154, 349801536, 694617264, 165948739, 52230621, 827538549, 942896427, 184938805, 386038352, 392236795, 831188991, 657831408, 208022308, 660466043, 488248054, 896823160, 801810893, 78870217, 574435846, 330952914, 444144422, 739962903, 747326511, 717596496, 249754731, 836184250, 167557258, 308693656, 815762893, 288827380, 548101257, 933793814, 420497391, 508568584, 364294888, 213526798, 697859175, 182560316, 72035530, 580862572, 484010586, 394605225, 768517142, 177469087, 356318961, 404565036, 939133228, 79308952, 871872963, 349878957, 933318511, 232791364, 474087904, 171607860, 466168835, 192239892, 512221831, 443627616, 592488377, 94689852, 761010058, 322432186, 451054255, 735449158, 186834805, 503448754, 902793503, 568343371, 930337882, 336197738, 498526497, 872607311, 542892765, 733101972, 613634563, 575206972, 829311407, 636852135, 233765990, 827238181, 817925283, 26562445, 396551130, 40762344, 232782553, 357088047, 945459523, 529610756, 181506577, 734993831, 118835425, 952238361, 476989152, 109096639, 530973935, 845708023, 708483050, 626807200, 889752412, 802733102, 10950649, 815236959, 459809721, 616170467, 217924886, 157521509, 273761611, 874151232, 62369997, 737537823, 354641977, 827129698, 146577915, 278565255, 339036763, 781608217, 942310396, 757796644, 799026227, 531220083, 691229131, 690670610, 60664673, 13671599, 656476823, 713588913, 306466933, 730449101, 958193169, 606110804, 373061642, 419487598, 844268770, 212588678, 860733200, 503637558, 650409053, 519006704, 728911927, 849782146, 406993043, 109670293, 580704578, 622804184, 176569984, 682829679, 977637180, 121601062, 53894054, 949260511, 671396744, 197739674, 661673918, 712872895, 615788689, 535855487, 894257916, 130550597, 304124010, 881199109, 66421163, 932041018, 29193010, 720902334, 386175905, 426540038, 305780172, 133884219, 221725158, 463417822, 619221491, 258445569, 240008830, 185142377, 875374544, 211150117, 457186635, 518505468, 714395316, 365656481, 55518952, 970079295, 660106587, 404966891, 961725069, 525134878, 458449257, 281161366, 616143724, 664242014, 480168850, 929128353, 986922001, 108812136, 521208125, 593364814, 29110261, 222628463, 491275843, 44943070, 255822063, 407234362, 855217119, 361725582, 176905171, 853531021, 41649296, 192683760, 892270174, 179944503, 88159099, 960883197, 405453517, 146043906, 35340790, 814020032, 93420799, 428826728, 909496276, 619306044, 282877743, 349164399, 626098922, 355025950, 488757797, 809646610, 272135928, 835748588, 293342061, 807881762, 173257788, 936842157, 598049112, 146056220, 904546650, 972319912, 809785171, 158585428, 529888036, 893541613, 525544476, 951520081, 375274643, 242318163, 21102091, 856583360, 580801583, 460702582, 941734729, 9628653, 258598399, 148079651, 460236534, 403653265, 412615121, 589671649, 676003594, 350339506, 170386684, 963802792, 279231265, 290721325, 204382171, 688516801, 175774923, 642224347, 213687900, 830020958, 245012480, 376709290, 548278569, 514137227, 391725681, 976940368, 933349760, 956543262, 78507137, 269840172, 539294400, 238157984, 748261959, 224325627, 741453312, 659622508, 613683400, 244710960, 862642772, 378913186, 685845647, 377865261, 652314660, 80909761, 339644701, 851667799, 254191351, 395958711, 960869636, 288392763, 664066306, 2898794, 433694921, 928800433, 5533100, 30827249, 761254802, 244296355, 789409779, 527066742, 562809466, 887220676, 799730337, 720308992, 586512992, 745790700, 897475297, 912632138, 883005360, 569426699, 718310717, 931472054, 388102165, 13516337, 152747789, 485302542, 686004581, 497686477, 883075151, 122011379, 508183124, 342763375, 395997127, 337394481, 813877420, 586387264, 182480526, 931188972, 177441824, 279560901, 30134395, 266674697, 808461432, 171626253, 578605673, 444250789, 690149104, 240220710, 23150474, 962793942, 903793973, 15652537, 263773501, 164588042, 863609245, 508953157, 213548320, 810514140, 722398792, 894819211, 30495166, 189716864, 583067617, 672041613, 453677660, 427663192, 285455448, 156061893, 289291455, 591709543, 669490946, 486886482, 135315832, 787884688, 444809149, 767939428, 736987617, 958400820, 151328033, 331056482, 429187314, 868463521, 906159791, 465947834, 227479893, 743883246, 817238339, 289769453, 501302102, 2260817, 861372105, 432266555, 52176552, 630759305, 397757642, 937620831, 386503554, 229591456, 165910803, 136328256, 547799330, 686109467, 310461167, 103514286, 866272075, 642516857, 125119211, 350708246, 629288418, 911343658, 119773348, 624975410, 713949324, 122992573, 5197840, 517481104, 838106933, 312492566, 513293681, 334122734, 118639575, 971121286, 304450085, 588343293, 803394849, 30493340, 603288275, 693166447, 448005163, 478848219, 129523603, 619166741, 858894823, 361031340, 881476404, 36115612, 126081601, 474898610, 282611117, 59822895, 821710746, 866987773, 175993230, 194864538, 990384715, 616135824, 363824767, 306715295, 335129289, 569507969, 713198461, 73064765, 143248416, 260307471, 281415339, 94841836, 970495645, 307026813, 922877163, 92485190, 815313479, 834397275, 314068865, 280256969, 934629275, 944979003, 473218125, 883253774, 257661289, 805780366, 102883491, 636060519, 956093233, 210783709, 633579255, 235328569, 667617672, 461871987, 548552967, 188048062, 471592261, 886090685, 87219345, 367294980, 283094108, 540466893, 118370104, 292922890, 240510040, 282705551, 801407941, 574389780, 12822579, 37788482, 589002254, 728261066, 413688219, 826071415, 548437192, 201040515, 170391405, 244489990, 990644370, 569830215, 560358012, 888535868, 362434321, 741092258, 329370005, 136205057, 391366218, 124643442, 169443729, 587436165, 326811638, 839636065, 396067767, 358139333, 260855901, 445952033, 601846242, 119192684, 507098280, 847918528, 736481548, 258465849, 826240501, 730229739, 62768991, 712614297, 836636767, 284170978, 619492970, 48413282, 397094283, 120621483, 192308676, 547766009, 865944251, 225752508, 622695215, 196958139, 834289011, 805517332, 216100662, 400108334, 566333269, 17814353, 642738760, 747364862, 582089051, 254473148, 949551183, 701197059, 977790990, 684689182, 85021496, 88673627, 211822430, 194124333, 868792796, 378966038, 772025973, 514369517, 941918659, 323507850, 937565683, 219442918, 35795862, 881750529, 109961272, 532116136, 669513061, 443383439, 814213119, 929913432, 402683974, 796381085, 589090322, 279183956, 857387017, 304534548, 327257562, 844346444, 869936859, 671061216, 752868557, 453734960, 785972207, 593318054, 687005302, 782771435, 979742321, 339470294, 640405108, 666232101, 159260311, 225767774, 759025287, 354682878, 437963484, 481711726, 700188294, 30161239, 452404525, 807565556, 822152559, 787105838, 627999297, 817524926, 321210059, 955191161, 779441098, 637935291, 122165825, 435838740, 102081840, 737002786, 370324768, 302057675, 203937650, 743655470, 832540232, 260879052, 490593862, 894656648, 262532565, 732850488, 611978872, 427364218, 268548619, 950795960, 205570376, 205167494, 432589619, 660202631, 556286830, 347171661, 148918341, 52635419, 353064519, 150579321, 279248774, 996540817, 265233568, 617171961, 872019186, 662518598, 778949201, 257834568, 948914534, 691504179, 86094394, 143516841, 234241268, 187216552, 985145868, 370371591, 44991617, 678683126, 172350349, 953432798, 713208148, 245873183, 195960651, 856356583, 808824405, 868798578, 388977347, 621132370, 226907867, 242612009, 65939666, 393253977, 529060295, 215160762, 871150434, 347173614, 971719812, 254586085, 821205895, 41290503, 309740952, 263171803, 273729346, 444792511, 46805938, 13838447, 620126829, 748795807, 616134087, 929945318, 481114238, 822597991, 493107104, 491885382, 289888367, 124605346, 299568255, 999580698, 588778767, 548103481, 701996517, 614383158, 312031859, 318670414, 906221360, 167365081, 128671186, 539663374, 78213808, 918271849, 572130675, 62967452, 874972062, 914402612, 172546931, 93213264, 964823166, 356421358, 789500525, 1528701, 562547666, 279853145, 225627549, 653318277, 77532103, 170830244, 421767643, 977778019, 991369150, 570295507, 50110640, 672828440, 947808746, 586836744, 146991052, 635870551, 824271888, 527839777, 138045899, 620182558, 894478375, 43713760, 643252557, 642550817, 565140343, 852404499, 573629647, 702414157, 597656469, 39884686, 647245058, 446905937, 67690333, 497578074, 790921798, 137123531, 943677154, 806264279, 799313454, 73030282, 404285518, 208569975, 143186288, 415429475, 9092231, 88261845, 310836423, 248184411, 565836844, 406255847, 294513609, 667202038, 878065587, 385600710, 662035052, 823943019, 57915158, 581482735, 773491752, 509416616, 677716212, 406855993, 116703521, 31568441, 540332506, 914721951, 568016013, 913084930, 316019195, 72511077, 723641029, 829147681, 961138856, 628298482, 11311728, 642991948, 890402386, 635304934, 22691796, 183245190, 658855669, 888268024, 193225542, 736347764, 813067249, 718925160, 426087241, 677353657, 7743391, 241391837, 697667258, 431192581, 605662080, 646452229, 475177954, 118656334, 771027644, 826944910, 659620947, 76958764, 355697282, 558861171, 348702125, 926624449, 385777573, 741400707, 269965102, 7927919, 289740636, 409672024, 495568132, 480706932, 620136967, 142040365, 258647224, 212703352, 525936292, 647064814, 758127192, 950563276, 334497148, 56831160, 698809037, 596052232, 654631768, 726890851, 835107246, 196445946, 51332061, 790813441, 294354893, 847844354, 437651840, 947175740, 364549475, 889521783, 614418297, 534590406, 95057907, 834223734, 427558088, 381858517, 978937021, 436435924, 141397928, 478915742, 717997568, 608362210, 564334622, 818204266, 393105153, 711456453, 438334273, 322620803, 67216434, 617610139, 425204, 375084368, 460179249, 430516398, 835910300, 918688862, 418566149, 457472571, 222087028, 94515968, 41456835, 776133561, 847349969, 388302198, 3934367, 229837638, 745547638, 480615636, 857246935, 433556838, 822230705, 878909534, 829012176, 114795040, 606135974, 723463456, 989512534, 475907025, 719576331, 823478156, 22683821, 169360279, 59367231, 580921930, 152719218, 441204618, 546105169, 927960589, 867872311, 209199805, 521110924, 925605896, 879047874, 460533674, 780779134, 723489970, 485153744, 903631511, 647224767, 924311572, 479443182, 573029243, 189364301, 259894256, 918655344, 689898952, 603743686, 442028421, 322421089, 832665068, 460427772, 879715412, 686407867, 739988996, 42594883, 604505737, 165654124, 166051775, 919795466, 792523056, 327048287, 271561648, 963261250, 524412632, 431695106, 810165676, 41927458, 804133610, 542461746, 350563897, 130854747, 677009583, 843067665, 117288002, 277384357, 39104115, 384751350, 163960218, 748774920, 339093680, 941778208, 50276496, 481939652, 891279199, 401861228, 511092573, 224392571, 774858178, 436768927, 86139189, 654542105, 7396952, 474619985, 211281699, 840158453, 123044029, 12953320, 447600664, 759515476, 117668913, 932013413, 847147321, 812366860, 424424453, 302504089, 572312425, 469361879, 41081826, 281674149, 938134319, 270685706, 817355146, 116003572, 818189516, 109801962, 919423245, 416670247, 249764560, 465620550, 884224182, 410523448, 633558962, 936904219, 451161315, 67720129, 672198178, 189388336, 486117898, 680381845, 730583529, 216938140, 591194020, 672786785, 774687511, 479327783, 796608669, 250090830, 274243286, 548247135, 260284502, 385748209, 32612351, 417517789, 955329299, 952288907, 807683900, 567718564, 575148360, 486510072, 728714889, 822298282, 660856040, 156676919, 852609139, 48069725, 917576742, 663720926, 783667597, 343012060, 907737578, 30211233, 4632903, 418289143, 560355504, 839523476, 250113730, 110049818, 825063591, 586166180, 811132510, 168135088, 363459334, 382964979, 563226392, 969427197, 545825776, 468867405, 728682202, 921097555, 9931821, 167679190, 830079209, 976858950, 884775238, 669096095, 427117671, 927373232, 222190472, 605274855, 66895264, 694458818, 658572240, 733627842, 171629011, 570642525, 604585246, 859849753, 577283843, 156270688, 477837255, 430131743, 928356123, 413189001, 274710742, 645144793, 983661054, 49005015, 386823515, 190161338, 990960707, 892185773, 454587219, 886726376, 634733904, 620837235, 964878315, 948332790, 382308522, 22222996, 989071976, 940078288, 582777591, 39333808, 818392538, 212113015, 219824275, 190056036, 413840322, 202093295, 785737619, 421326818, 942778477, 464984944, 425981375, 935576871, 539576701, 883803918, 179706039, 389033815, 305116012, 247336886, 134470787, 775612284, 228988811, 780751079, 607353453, 224523688, 239442241, 723028836, 786922247, 670216016, 245194586, 176759846, 23293547, 164428274, 988828916, 821363829, 660675978, 927513307, 97032982, 442377955, 411697214, 157261655, 587904122, 597388062, 156646720, 367592841, 447131686, 592577367, 936539670, 426862096, 992538472, 172015427, 929113954, 624921666, 244806062, 76783752, 242963579, 82881991, 886581239, 683962521, 153992154, 646101472, 560029900, 705008765, 174138067, 580040449, 979131519, 5139979, 979005933, 155811053, 174560919, 612232787, 47518204, 634590028, 875312678, 170085824, 187042499, 797479395, 14256116, 135271656, 10814347, 101141466, 967834089, 472645574, 524483075, 219164455, 372309512, 282542027, 527592466, 455870252, 260145772, 451619878, 288061214, 181827915, 294902909, 207358855, 537389859, 515943673, 740236344, 252943383, 560887177, 759342904, 637893240, 120345231, 265030452, 294176600, 738645559, 623311102, 566937426, 157142703, 33023966, 525322312, 241443447, 768440616, 854777904, 570157015, 411949314, 123610224, 727395727, 136260251, 457836698, 396279939, 370815188, 356394921, 39394568, 565194976, 864670469, 344808370, 374658589, 832845830, 948623539, 464609082, 17148947, 117376014, 613661347, 172745034, 854566995, 182049396, 168353970, 327073102, 934082257, 645253575, 941555101, 947315817, 104654843, 667215387, 198453096, 264895232, 247780180, 925586411, 468478179, 549900248, 9776199, 941741978, 505497406, 348168205, 824466442, 535497818, 224416542, 118927005, 487388315, 597632272, 124532550, 15551517, 38956918, 712549407, 334135697, 78909920, 662114663, 861248004, 281811807, 797229192, 444305197, 153811705, 814455253, 532157978, 935596923, 883387197, 241300708, 890957589, 300531029, 754426068, 858855540, 478750920, 228521723, 391994712, 534342839, 56708289, 197127216, 700669122, 278201413, 623239725, 399552032, 864021297, 66620412, 23493315, 2373820, 699952136, 754647002, 668622485, 377942252, 187223050, 921875433, 366334966, 774520812, 36478757, 492348744, 882277671, 691887292, 818162256, 598680937, 435100688, 852387800, 435485968, 690723481, 11048466, 400852474, 654246737, 550909418, 961674261, 289527781, 982650555, 199756452, 112045175, 303753723, 449628698, 143377101, 532285066, 199677633, 338187132, 444962049, 280891743, 749901989, 595635678, 861700588, 960244368, 127713728, 55137631, 872517430, 100649318, 493683912, 412697412, 217365775, 464284880, 38140333, 593014171, 592049458, 479179571, 621479064, 774635590, 838735483, 719854370, 268003898, 787742246, 996086767, 560347804, 236784641, 600975309, 950851574, 706228344, 166762877, 176997967, 493131053, 391872185, 552981466, 115309020, 583586861, 896985605, 802056274, 240097944, 660842340, 660062281, 742671269, 508751661, 130464973, 504145271, 573166045, 717490139, 76202415, 942289426, 665566165, 60149166, 269847800, 783010672, 697406915, 872488217, 532550147, 571699970, 857919391, 454618184, 282102835, 859695189, 92802774, 363321249, 734116573, 668193595, 647373216, 686483311, 129554719, 255172362, 10540563, 353605093, 454947297, 203772997, 156546481, 744061941, 659807168, 578415095, 952703903, 558132384, 810955224, 696150268, 879149174, 178540483, 770028201, 380148373, 879795411, 814439799, 974197843, 266154771, 612168489, 260026986, 369822830, 784291452, 732166907, 429412715, 574879101, 220482682, 684326753, 702861342, 733161798, 740050409, 939275175, 142025861, 872702627, 699445213, 496329302, 865172734, 581672945, 568414354, 566876018, 203803461, 339909229, 844576962, 778082291, 322929745, 757245286, 877589405, 350499685, 460595393, 295221034, 961535861, 187404562, 716770456, 195615576, 393836289, 271992008, 229261593, 425935594, 503956832, 289656015, 395210122, 179639615, 823131611, 334728776, 828454752, 695884511, 120454049, 904418182, 344649966, 274034558, 867954073, 693195275, 584586444, 794813703, 552371161, 610926353, 431337466, 223863254, 439845147, 960980093, 56258434, 14892642, 470584683, 371155055, 903479972, 317832965, 953070580, 870015742, 108998420, 990277232, 307936921, 691402524, 497245044, 111809379, 756698979, 530892292, 168371073, 667800759, 342927223, 458183688, 523540742, 59287784, 228132446, 757485661, 712249190, 191440547, 514558236, 346717131, 813138137, 282871346, 807216735, 6082505, 305401036, 816622793, 938171957, 852185668, 84727579, 442802351, 269161536, 926998719, 601231595, 226401821, 766625003, 130254911, 872868870, 840265128, 37791074, 787165779, 187866962, 398025976, 237521522, 90823011, 244536508, 863149771, 338566134, 825347563, 487124957, 420703516, 170093791, 907325692, 945437504, 670504556, 133704989, 439367080, 410430747, 186072313, 218324738, 245650375, 526864322, 635764877, 746262361, 239694097, 241324482, 810714122, 978749081, 981463210, 278969154, 509282853, 669729791, 268713042, 438185752, 910824300, 422041410, 72648210, 240544082, 744499205, 145639103, 410984510, 487488669, 691687676, 734150650, 505411163, 236047821, 68041520, 71165995, 5524466, 398029964, 290894243, 53360799, 261816778, 540270870, 193199989, 790953037, 644491469, 330230496, 936654217, 849940043, 838890821, 175100242, 658306239, 105456797, 531828036, 935500365, 731744708, 541380954, 885477770, 596418036, 754398949, 711635914, 868620848, 87621260, 585103256, 240782050, 396960153, 571970098, 151637509, 693404706, 929569524, 505629323, 224183468, 666206189, 731835824, 158740187, 285823853, 427050695, 5383512, 175662378, 812630871, 932332959, 48269272, 95576393, 344369623, 754309953, 550649400, 109517287, 241240195, 715655684, 961469918, 129941256, 831529443, 4282207, 921271171, 741520240, 923663347, 678190715, 323610883, 696769672, 403015997, 348871113, 629463588, 212313490, 307152763, 354958189, 389661852, 830922111, 631266615, 148034072, 819618427, 573110193, 425986712, 465072482, 783001005, 584042359, 100212392, 247274999, 580587642, 497631908, 357749917, 431645629, 798196959, 192796459, 65230773, 751087409, 311022729, 540635390, 859068493, 70854997, 864831551, 880886847, 172581670, 677576474, 964953789, 411196628, 894550127, 313151810, 338443193, 653687543, 799159454, 219586213, 118158754, 497256285, 110321256, 262342079, 198962403, 457460269, 448915376, 779663886, 98968955, 894870746, 96272533, 294512888, 623843918, 736947344, 29342985, 245757875, 115267057, 665819866, 797822805, 138220466, 535363392, 338910119, 830310976, 791777308, 195300116, 562547962, 860019048, 687600655, 289563207, 179287573, 185447478, 846598609, 821216729, 479170555, 626574052, 146385521, 86258804, 134265248, 228121711, 404624175, 713477981, 888349324, 393189096, 15994262, 82336043, 326836785, 178705371, 853367919, 50460023, 565298, 388116192, 964989985, 833614474, 458781955, 568176826, 851953041, 418698570, 821186061, 136179736, 65855056, 892662001, 709228261, 192096614, 347132551, 967609529, 702929036, 203282135, 88103767, 279787852, 88801913, 272421328, 597683359, 909725188, 728954736, 411345716, 587388435, 784959931, 261815612, 471939703, 576113012, 754456741, 122384052, 713608538, 863207934, 676116094, 510941057, 399439030, 38510639, 256959133, 228808321, 846120804, 383184606, 811760723, 257999147, 824449678, 426529467, 711725428, 351554399, 222840205, 146634599, 841324209, 336903251, 387153748, 16883230, 925562294, 101334281, 764801959, 761120495, 336576391, 809673259, 26595009, 215965780, 256702831, 794649397, 434460381, 584850356, 783127152, 497499315, 949329706, 830305942, 785000328, 788617304, 947663248, 455444152, 955078256, 337338639, 232154052, 393587257, 970477362, 444554050, 432739012, 359763402, 373733965, 696547210, 28870375, 26477076, 760575995, 837591706, 46303218, 643272104, 210446887, 773019963, 7506384, 258987160, 332691042, 754017741, 37628850, 585927224, 776117969, 524338220, 298542640, 167533508, 521756811, 653889548, 764943476, 187995252, 448119753, 770931277, 772479866, 868934883, 194978787, 936721703, 672220489, 952815112, 641242315, 676322172, 922940438, 707911316, 494041030, 643265018, 697874467, 170533181, 118848741, 522501194, 740976439, 660112879, 767423941, 794115635, 855324864, 180128934, 926211905, 832051408, 244617317, 976870275, 966058022, 969865477, 349109381, 145068279, 383865023, 497466000, 64658057, 916990469, 684758870, 264847057, 388978794, 798164364, 875703834, 8407558, 977049033, 699700702, 875171164, 310243638, 818664654, 376621856, 472606438, 431383426, 168027283, 413979566, 872929395, 523678531, 1302727, 939902668, 934193018, 764794072, 331957398, 545701726, 232732661, 520337045, 677666971, 58775894, 273847675, 458912846, 213014131, 783342071, 163653705, 448792445, 499008954, 881983420, 70229320, 851273099, 790351572, 671075479, 302678399, 977301454, 1879281, 738844431, 457171413, 893227114, 23193, 944553954, 263517177, 651310674, 307454246, 111517366, 336837468, 211296288, 279504331, 337918564, 343589022, 123374171, 991095542, 760161428, 138552186, 183580606, 185661428, 340019690, 632285878, 511207623, 547780604, 626473607, 311707592, 636454817, 706854729, 842947213, 496657508, 895222054, 68285852, 998154681, 521993783, 137781650, 852339145, 583909701, 350529564, 306978793, 744484252, 54848283, 210632567, 868918722, 687798064, 86791525, 538488513, 308111495, 493802435, 830232304, 864921517, 344865914, 867063080, 755994758, 511276410, 774058560, 409899833, 646101659, 705493991, 769681837, 216409414, 384845127, 31552895, 703089215, 256708847, 310668230, 517557679, 576802810, 494237423, 93615800, 1746612, 114092400, 497407515, 480675645, 931032422, 11733763, 857147031, 536477294, 182504344, 736667424, 768118097, 652922072, 22215552, 413496159, 92423772, 831712243, 798334619, 935321096, 848279203, 990359969, 329123274, 988954764, 977605589, 603794624, 385049459, 340941904, 268200916, 780478248, 185834792, 458626737, 697885115, 702734388, 247026776, 645128755, 393649661, 580040678, 607461041, 235163029, 946017274, 816502588, 90224609, 629595368, 865044633, 652891413, 558615110, 177015927, 287757341, 850579324, 580317750, 798425866, 29461034, 1438802, 753893782, 899772498, 491100820, 897236605, 654842545, 269531859, 91618273, 599991873, 838803447, 709238848, 176248746, 544526129, 475395259, 285452388, 166284229, 837254824, 660658035, 299816467, 130699671, 790560681, 624460094, 268657282, 965872215, 904895970, 759103123, 555714937, 648890048, 397666568, 199462215, 953229164, 541360273, 486714300, 766311690, 769402025, 73446915, 458847052, 990187779, 603071426, 627687530, 859932850, 478280577, 314918354, 994540851, 944392780, 347749498, 580222378, 528438476, 271413948, 481000353, 471069412, 146168432, 77682561, 325657345, 329566549, 218233981, 571307441, 54714641, 830005589, 968457369, 132575127, 779484979, 774004950, 598281451, 696060621, 596786510, 507208362, 506458769, 907518218, 382250859, 618362637, 311752420, 322862643, 987962081, 440629580, 614116095, 511469653, 893389365, 277858322, 2880268, 379361910, 654772779, 301434741, 168143740, 618929855, 697713555, 748800739, 624833681, 442724271, 182190141, 483162033, 799538085, 118202660, 173001472, 712728959, 844076761, 69110074, 160970839, 758558322, 240730235, 973987940, 517101861, 714427707, 325261206, 834873583, 211333455, 136475340, 81148535, 721303602, 192308654, 136668420, 689640940, 191081279, 599016597, 843259187, 972045188, 712515738, 31813758, 165745112, 633411046, 436334852, 89760348, 806099612, 213437730, 748126787, 199361812, 900993305, 379310116, 530993077, 444534922, 858437189, 890282626, 361927101, 153544422, 131576779, 570629177, 88790538, 763514685, 40312476, 859009917, 821452257, 170487818, 375246640, 731144754, 961646131, 395019632, 235460538, 420300479, 634198424, 822432197, 999146195, 105320123, 852527653, 400973156, 452354557, 342799909, 299901414, 249755854, 524912365, 852973737, 441068663, 171206754, 110461532, 544952201, 898896241, 207896430, 359327995, 419398997, 120776050, 958910731, 410776566, 801860753, 233944961, 871669790, 416230257, 761934058, 346271284, 311793025, 683055891, 648090231, 134748868, 169406476, 169043562, 6283939, 65081871, 924904118, 127124666, 179704668, 963180494, 97390591, 911687580, 229631350, 173041952, 901745461, 436330490, 637311076, 465150664, 904106333, 530422922, 674003994, 496163165, 306436475, 917646686, 261640072, 806869069, 907393447, 964943192, 204716516, 438049109, 659352289, 284257964, 857403054, 761717189, 657313768, 66735458, 61164437, 879414632, 161710773, 177544536, 153438410, 466441433, 823626326, 437463661, 861355425, 951104672, 34104158, 693091752, 243245749, 309933475, 674223400, 237340393, 637277247, 881219302, 481118509, 186710334, 400131195, 741124614, 645832678, 982465905, 770495542, 510065156, 789109003, 296014384, 217569406, 515438679, 627371332, 623142016, 230617860, 567527174, 563352512, 587921292, 112018193, 168043405, 95565013, 80866778, 921454879, 362865257, 407681981, 332306839, 538257679, 119203048, 248209589, 97350544, 453668692, 605781864, 241561682, 912427561, 491816771, 576596221, 208135502, 974947259, 791743625, 620307819, 479394090, 538864503, 549411093, 960887984, 10535408, 527390716, 882793781, 780543816, 955563006, 450906397, 544255091, 698367597, 66809509, 219384358, 98241493, 158734142, 904805314, 935363605, 912575039, 112958850, 540850624, 632157721, 937694278, 776210771, 747111581, 882358275, 46905853, 261874974, 953065003, 689256986, 359824322, 375985439, 645179056, 844166038, 993705642, 834343847, 127370002, 681423301, 222249432, 881170859, 758310296, 631257289, 515848753, 244460826, 811492150, 523085846, 822247734, 601869707, 649906073, 235135386, 336884306, 81315991, 246068746, 257223582, 345095227, 192929393, 402650854, 849280798, 77711816, 232146633, 54200746, 857148175, 757861007, 380027308, 113817735, 413129157, 100400063, 491920484, 631080617, 560583807, 129726757, 484661029, 441657945, 458352719, 101457648, 139408574, 389914761, 608365826, 225325952, 463365434, 232150783, 294749216, 687523201, 534453309, 433570969, 827725764, 646727480, 454313821, 147549313, 403705434, 355521854, 790333152, 700393005, 306974861, 401970994, 284244446, 879886783, 310923074, 253221743, 49110114, 450965118, 801239007, 910694863, 167882868, 686877313, 542309179, 909914870, 998817757, 172739491, 934197212, 51916192, 405659064, 226897571, 139972488, 280644215, 905865184, 877593773, 450863275, 253846032, 159408474, 255259474, 323853919, 793363965, 6544860, 935146255, 371381276, 508962120, 653862298, 11978819, 367985956, 5880775, 454902311, 489677320, 153349492, 198584986, 878227602, 5263893, 826106186, 696817819, 184051874, 80481946, 299358131, 746501917, 424416757, 685850515, 372459208, 506038715, 52041921, 545935476, 546945713, 731595134, 82046909, 513420125, 788745899, 743654860, 616115366, 948410123, 885537111, 854219367, 209584111, 538912097, 672726608, 339559988, 497183018, 50341680, 960292420, 607593782, 701916588, 752780576, 908821459, 60161140, 235086238, 239644538, 530429012, 7249599, 536998974, 131815518, 308980932, 569515278, 414633641, 733636750, 454970812, 107291430, 29208398, 196646289, 110789167, 629098676, 677512122, 958725656, 256072460, 269038590, 872505614, 409447497, 684342596, 974226110, 784869734, 492540202, 476989355, 947198993, 654692594, 59318480, 476963498, 526257262, 324282163, 825087976, 482449029, 503199560, 18564678, 383796259, 157139412, 508227326, 791030388, 11828958, 715349016, 367903878, 337648498, 170453637, 855572347, 881349050, 992339471, 285307033, 946067708, 119697732, 585461748, 18074668, 949751115, 860947290, 688713147, 838799972, 655306552, 804432437, 359858422, 28001385, 76276130, 458425137, 762671349, 883298956, 888718652, 473318665, 202836922, 521657566, 916478873, 241394726, 220369575, 20008578, 22662259, 987515439, 354982253, 48697177, 159175141, 472575738, 255315407, 287707027, 404572736, 688840923, 308517976, 278084973, 742353694, 895765580, 435117204, 368073614, 382779527, 206820738, 387230169, 589192413, 341563691, 436474420, 80143531, 971853661, 177535684, 395768546, 112393070, 511553055, 891234084, 556766157, 359632134, 367994247, 867158639, 348539708, 516549791, 247539452, 438183718, 711737639, 589532875, 789507715, 307475348, 472541708, 530871449, 273349687, 596169564, 121776461, 336400483, 865624329, 577343449, 830096196, 496812181, 779642657, 82660092, 670235785, 665313906, 807840441, 22203324, 900996762, 785152572, 29582729, 323192638, 955705565, 528438280, 551111075, 362228829, 51319437, 314591767, 346814220, 326052349, 713216092, 172735782, 672971049, 520290731, 591753449, 595441028, 519317977, 550970984, 5723357, 269070139, 851904337, 456743586, 445538138, 982148981, 484542352, 588795549, 929138890, 337638394, 970925713, 892009297, 235294756, 782312289, 785976991, 365133039, 507306693, 832828110, 808297898, 334360396, 216050791, 173009835, 435979932, 293666713, 473062195, 385679816, 322617140, 359375499, 419028672, 205207977, 705833525, 907732913, 266042971, 397658116, 686646023, 14991156, 95859484, 897071220, 99200581, 381779151, 731473160, 991841006, 90200154, 248265036, 547582926, 570205519, 254971165, 923397788, 942685145, 586450030, 446178471, 254609219, 722092564, 31554288, 564877549, 848597238, 140894701, 624543827, 772450811, 642481898, 934682131, 766604082, 275765001, 279598965, 453033639, 607046833, 827800330, 201220787, 869863040, 820679099, 341665299, 754826114, 952007855, 80423839, 503665715, 374696003, 858967338, 605017370, 404712393, 769351356, 95356475, 702187426, 109116101, 871546142, 415371779, 777257486, 575211910, 648920827, 795643303, 615478596, 19789480, 830837107, 626490392, 581667877, 52424559, 560179339, 259832310, 180123320, 909838678, 954206463, 621967650, 252440774, 190429394, 110159616, 835646733, 485777721, 990486006, 129126688, 273359765, 772019067, 529444244, 957697270, 503617679, 51388337, 837706836, 458843403, 6504053, 429766244, 51542209, 968023275, 607846351, 3436315, 830106208, 985171844, 331208313, 475847768, 395945199, 533234467, 571631202, 886149961, 134242957, 520900744, 583741890, 309678533, 462435149, 17760876, 84007578, 431985145, 888017432, 854192208, 574021080, 651758734, 352240347, 342782375, 599240632, 180578768, 124601778, 744932152, 766090199, 37975808, 539533051, 958709549, 680044303, 591584115, 842485489, 350346757, 504586345, 5094160, 655362185, 187141833, 633949781, 884021879, 746543660, 635445684, 509480188, 352844761, 17892203, 859198676, 387783440, 69435631, 780192926, 667927453, 563317178, 494313569, 84719651, 966000168, 517308129, 571191996, 712107716, 401437341, 451711962, 252642170, 627089536, 929248320, 550144794, 969486053, 704531289, 567073311, 140798201, 365486613, 531634221, 747189479, 75274323, 840331770, 494562564, 603326906, 943982046, 565416493, 944454861, 117501161, 938364142, 735963035, 963913725, 495496892, 878253067, 509969471, 413120215, 893463490, 101007004, 624367520, 186337196, 443865583, 332108319, 884621417, 560416554, 887525856, 153761119, 340377371, 939958428, 518442212, 110561344, 615596892, 43989525, 288338468, 483041017, 596856601, 880627959, 206908546, 970391867, 961468387, 748289067, 130631741, 681889914, 986923002, 753091988, 594732678, 761561690, 699119949, 811378520, 727587706, 793661500, 484941571, 891763736, 160196128, 729722417, 120211242, 636032022, 237649915, 13964299, 919902232, 141973490, 94859259, 323723141, 867719919, 270056045, 852845487, 643057482, 127149839, 49385112, 438453389, 228922372, 200319022, 273145224, 156059351, 27582328, 226176610, 910378905, 674782740, 28481096, 143293514, 75663150, 693211042, 531536307, 281910515, 39685185, 707514924, 861329141, 73759813, 626862334, 500854855, 686142410, 590577679, 747157591, 429237509, 70918669, 362872067, 920229988, 865832931, 459197099, 985068604, 240741831, 146668343, 693908549, 307735588, 733196828, 893612140, 326430678, 946325345, 283017623, 858042156, 331914813, 459264123, 849720476, 513380722, 406522713, 808573146, 63943093, 846804005, 454376597, 975748402, 433968949, 350272599, 348122305, 667976320, 139205776, 188872580, 6963379, 87487626, 953701950, 25028426, 586487275, 200306294, 880641492, 723891544, 391858952, 818795085, 340539246, 153287477, 469867941, 195857775, 619766075, 856954505, 689432611, 223247877, 163430972, 51128033, 779790654, 457134465, 322229339, 317699525, 946536730, 856249424, 576950247, 887436825, 673660377, 28288870, 427839157, 831052622, 895434106, 528959147, 96830227, 984494919, 761999797, 321489615, 500747096, 421835795, 806112174, 223668545, 151925627, 241597474, 195049974, 183725970, 65065091, 585882438, 782204897, 734746330, 669239157, 330080426, 446536653, 418826703, 413358284, 609982718, 958484943, 559037343, 409692273, 239329798, 506180958, 675200066, 187327152, 210123713, 761154341, 27622081, 311177964, 973670755, 751547474, 227781595, 599275423, 706230699, 66631085, 351992627, 682409532, 238954125, 279953150, 129314414, 60098552, 389091498, 49259092, 225936758, 679662671, 310713783, 882624795, 819192581, 486602053, 757228202, 890788287, 31770605, 717970383, 802623202, 813352779, 771029995, 433679896, 830335086, 532823380, 329950246, 842514647, 480064256, 638168775, 787196226, 41790942, 95101142, 398786135, 28435643, 549124525, 826417478, 834156086, 163136802, 456732910, 809337934, 314970846, 605382297, 219004271, 292419084, 596359369, 393262345, 273066196, 275716586, 135613344, 797448648, 623479461, 754063886, 442534025, 693755032, 820414004, 746035194, 946371544, 566219946, 930538732, 782353944, 785625271, 616672009, 36282205, 513963191, 135537363, 797723749, 184222672, 659493442, 779304535, 902921443, 5933822, 247378822, 190618710, 832703994, 174747764, 620407829, 832130999, 544736749, 184139558, 849689164, 527393589, 302415192, 628691337, 295454388, 926839852, 947559783, 604268578, 22376802, 374286620, 397652428, 953909287, 646179565, 538342798, 878987993, 900155781, 111229766, 30660264, 773487392, 755852835, 973659288, 931902692, 184449056, 789093505, 554823372, 896750419, 991953772, 356291054, 937072661, 368033812, 696991726, 93619602, 100938482, 227734631, 103604103, 818715290, 151248466, 140597748, 172921614, 832734328, 994611557, 443899226, 815247988, 36671405, 954984959, 807872864, 56305154, 581958288, 358124049, 639408411, 548236229, 185337215, 485011236, 876861056, 601744861, 966929409, 717912596, 63443753, 862644421, 855004367, 378217721, 990446151, 815771102, 500747822, 426778952, 488881298, 590073970, 767899452, 673285149, 21475971, 696721615, 156963253, 754375305, 142105770, 459263026, 465700447, 464219920, 124609559, 219956052, 52594040, 659978553, 289405232, 882776748, 188092483, 661645056, 881373988, 305594143, 74273105, 861065223, 401068566, 194536271, 535516797, 225278165, 608686813, 806475326, 894050977, 660861369, 344073983, 149350823, 628287825, 549592208, 403709988, 681120159, 857718883, 360386551, 789462991, 312421685, 667466764, 5334816, 198365042, 975127734, 520943646, 744672228, 356565655, 212494117, 267800256, 966058035, 665707329, 135444263, 738396422, 431565545, 498449894, 245830679, 800189308, 981044365, 719793234, 289794344, 948798721, 538991363, 366397995, 590346279, 146994173, 780452536, 630793461, 924542186, 618162983, 482752944, 790293100, 540051776, 781960509, 968489336, 674125787, 51060670, 562069557, 564783333, 813431464, 527028935, 733388584, 113423904, 819374333, 769521749, 384468022, 737238252, 719070678, 984284557, 170437997, 302846863, 226706732, 481539575, 901491292, 899262911, 13592404, 334288425, 704064071, 813270243, 334440930, 333459080, 71830107, 433666249, 699876006, 726471526, 104506784, 189656172, 424330734, 437297322, 816026767, 343789637, 404706987, 274074202, 110232275, 810691959, 745413114, 216852458, 307670556, 473250156, 700445650, 361742112, 190053353, 426796508, 116729547, 931407218, 198998251, 281646414, 441788290, 157017450, 599536367, 881211190, 930376207, 543583574, 945429557, 974882364, 118483521, 225419039, 77229344, 79730284, 437537591, 483673369, 188739477, 559239839, 296409823, 274955536, 978135667, 826383795, 342975035, 787017930, 383832804, 620091716, 841615424, 503111751, 909008801, 844721549, 459891490, 254762823, 118396743, 102795888, 75660320, 911845071, 111744909, 942652146, 230810739, 892502476, 386033604, 878458600, 451007582, 842902789, 782193653, 938882988, 844866486, 558792059, 335372542, 298913872, 526022132, 779811774, 420114593, 660192227, 11244331, 54776702, 80093256, 190873177, 198230110, 71707585, 671386752, 573252302, 149067566, 41328216, 271155197, 593892314, 349636794, 728678449, 234798568, 980245470, 665234644, 315202187, 615148724, 626379605, 677707970, 465000207, 483237308, 431326287, 179481292, 957840847, 868614188, 455103215, 449326713, 962900576, 591661628, 604362547, 364177671, 793309937, 98602503, 749305006, 171761817, 699111707, 511534256, 110852790, 876683430, 851985050, 615564150, 491535416, 799255352, 756581242, 390755140, 975837860, 522460648, 914037681, 651951895, 612295069, 176760272, 242195170, 933333702, 391515831, 647273414, 110756113, 693210558, 659850112, 432372999, 661905012, 172045868, 639496346, 903137055, 42583524, 847080224, 847172818, 553251928, 312930905, 994954245, 250513110, 677551006, 37474838, 795510933, 134999783, 478577509, 130487803, 965514919, 834617973, 298862326, 50366053, 358390421, 213461016, 108494587, 343390879, 199747643, 371807465, 914167178, 372950395, 463989910, 864687180, 753633856, 382099167, 213048954, 951686376, 230622566, 883623722, 511379739, 617978000, 703581817, 840430784, 570830368, 949127700, 631354798, 304815677, 730889984, 412871634, 723629424, 493458927, 310921850, 574224527, 308960908, 797958238, 286257422, 848719470, 99163902, 869020884, 651622188, 394843088, 170953269, 738591943, 616296481, 845847394, 36612118, 900954834, 142073981, 212012830, 432233847, 414962492, 562504238, 646440726, 893834606, 225918963, 131159010, 670897695, 311370878, 574315016, 254737091, 309904659, 365321016, 171720089, 281380001, 150512242, 935903942, 482370883, 522413565, 981971044, 62474589, 572176005, 279862779, 530955454, 966491379, 449830589, 618114569, 35595793, 286375254, 625729577, 796389499, 648767517, 577383354, 23674707, 276947039, 476262230, 341228337, 22465325, 49482011, 596240111, 765238757, 634640258, 495033004, 514884559, 899834961, 959679663, 169885526, 857156842, 50908880, 663200996, 770640101, 569714228, 787454520, 36595490, 978545712, 476270969, 414475922, 650763208, 155569539, 821540545, 985451667, 907214903, 777259964, 39473937, 901634564, 475083527, 115677439, 349006940, 973885210, 104195474, 130657519, 166422928, 188731573, 723136423, 355197275, 782337225, 975441996, 415538954, 174076049, 148365618, 336818339, 40981350, 612971770, 516479812, 747780016, 193494796, 105782964, 785042921, 98264619, 555160543, 828975860, 756396598, 771394758, 432590145, 789849118, 655556446, 795636289, 522152526, 962059375, 456067879, 775674015, 495632758, 61109045, 660548756, 37245402, 381804854, 764035773, 342249006, 30368480, 497261191, 957309144, 789489312, 906972415, 741803171, 452890151, 453003847, 435603884, 14039024, 384661373, 117547948, 148637185, 41193060, 992120870, 542547719, 156958055, 173946277, 932421963, 524010420, 296505127, 57007376, 471162186, 366455640, 458423278, 175344660, 445884274, 298455833, 891528673, 35056237, 433748939, 458350550, 871603218, 536263438, 449400177, 552678324, 522451556, 688814146, 621275720, 256149864, 806144793, 623597002, 425371881, 821656267, 299940574, 803584180, 961148268, 820971158, 424046416, 240780317, 552039731, 229922805, 411174554, 575515497, 791568722, 277641676, 881104944, 220145688, 39634166, 667944547, 586029457, 463939432, 790899309, 562476661, 513926704, 982480106, 178821072, 114514775, 950751390, 558511654, 490799137, 655043380, 4701465, 432777696, 283208984, 357121558, 995337148, 465159109, 754808663, 140755704, 426078629, 238232123, 567784284, 519618650, 897961201, 111536807, 23195437, 672094945, 295272838, 833550820, 167027231, 717927112, 989100965, 709413326, 363543700, 667323097, 519791721, 19341301, 123076327, 615462128, 519748121, 549224867, 548796455, 215923745, 77289035, 488863157, 311490211, 729133309, 771225476, 716878234, 778892538, 366408729, 135418553, 775380149, 633553065, 222544523, 970082584, 729554312, 868710555, 871719819, 389062715, 855982003, 656880141, 862426016, 763252503, 92702196, 712323474, 828517090, 422446570, 429890661, 912884672, 424702851, 82836687, 962511857, 315249452, 209060176, 847709424, 767343952, 964988189, 804220047, 932022967, 422967345, 23350896, 757770705, 395768848, 947176972, 511626467, 713499950, 36425901, 676068620, 742000872, 181808519, 319794657, 169818213, 832945073, 155958589, 860266189, 782036573, 328651999, 203035355, 604723301, 695271520, 599020246, 485800088, 816459867, 897271842, 343590482, 744239557, 167412758, 681911228, 592145296, 28993647, 256630211, 877087155, 69450532, 18565594, 639154860, 79545406, 484333109, 596942694, 826929943, 913065212, 976820255, 976176769, 797163262, 987109444, 964840570, 641000213, 291004350, 801884848, 463597232, 445704124, 139915205, 25160827, 276477204, 145073705, 257366349, 269684227, 450089346, 552623220, 402867939, 53477792, 224054958, 645343281, 630443154, 623682075, 878424310, 498352342, 990830825, 519943652, 175747170, 58765314, 31820364, 16975999, 323043341, 331314905, 380015991, 905184659, 959828858, 263591095, 588092328, 564339857, 449859601, 887411630, 454743293, 236718242, 248502028, 767273490, 359665852, 722246329, 985924250, 45627433, 769759211, 579002773, 60514021, 904834842, 257506050, 893180977, 733903787, 601480207, 268373790, 514733710, 945173808, 750054771, 102864464, 829423574, 154578946, 599257007, 729299092, 402693633, 658772335, 566086666, 740472244, 484036543, 390141372, 752612573, 443371133, 696869252, 858739476, 471911374, 278753551, 435870174, 123970126, 997506544, 937443236, 419096370, 715936094, 535367684, 667966442, 781100007, 991375673, 783757703, 453686425, 415568256, 720621777, 588014113, 654712554, 429841191, 898130807, 15223587, 520834873, 700959184, 583858840, 987489175, 705472976, 718617697, 288016256, 136917372, 274105196, 413768758, 901667660, 190529408, 393392497, 241328020, 534390101, 118866205, 347825989, 412406284, 273100116, 429508720, 194857584, 481011318, 684963572, 730078262, 747568911, 832900305, 796154932, 264454418, 695576772, 978158695, 60522644, 418102056, 215240939, 294057728, 816056297, 999624635, 849813210, 91546277, 701620951, 108085573, 961665920, 409785169, 793228229, 31979989, 425923348, 717705174, 368644505, 904747741, 933837451, 380545792, 796862562, 619217044, 412333348, 439171060, 934054864, 620570894, 965297179, 598377823, 119721037, 58233675, 423743653, 641671047, 332388694, 782566989, 712576503, 984265656, 878588933, 851558304, 596126337, 708708555, 788309744, 755705806, 430042758, 957300911, 665562033, 648243766, 69732417, 158879461, 648717197, 857132295, 993426381, 672847612, 284574550, 412566467, 887862070, 476616789, 217735171, 849726688, 669667054, 521050897, 193990562, 728145554, 280673249, 447241612, 45049690, 320854189, 807700354, 158954358, 933285387, 259561932, 945967169, 78023190, 101198162, 449079053, 570949024, 451217342, 263212831, 900459984, 332633191, 5081452, 972099318, 635290893, 157070811, 907490046, 567244763, 812137823, 640806992, 870162688, 800295433, 271662137, 643381695, 770618508, 624844405, 17897094, 475190064, 494831373, 460228825, 745480271, 975366515, 735234783, 418735876, 953211770, 653845351, 362777028, 554479521, 935038956, 611482532, 652085213, 947036322, 433881511, 508358467, 409903244, 515714449, 357143975, 683259841, 384611830, 473671236, 3512143, 578550213, 365664973, 846669466, 620571324, 356637952, 16136386, 126236448, 823480670, 858400340, 484316339, 829401024, 252816814, 780255516, 847583117, 34824192, 164187865, 819230450, 206398662, 871515237, 558710027, 647184365, 328807960, 90540709, 308121063, 591244903, 921984276, 877412243, 652480409, 126826116, 227329656, 929622688, 752508890, 230967934, 777279105, 211032595, 714958403, 202107441, 676699857, 704750092, 948925801, 59665373, 341869414, 520921627, 954416750, 390783679, 641104267, 382599622, 59010358, 113981612, 523604301, 986908542, 471706521, 786434848, 666704487, 253042587, 703889574, 352241203, 409891130, 161368514, 340622495, 572281467, 435696736, 545140410, 639468171, 5964300, 474637927, 784164190, 492618156, 350018100, 421491467, 630529512, 174848490, 894380788, 249584631, 357191455, 949261484, 451888482, 658882606, 735256715, 691302883, 349270568, 992649463, 14012227, 3476653, 716183853, 820569867, 211873674, 861952525, 511982578, 937080013, 776377225, 621101611, 812551574, 843701471, 322536427, 471721388, 385162826, 770157034, 565848913, 528291626, 422935045, 96698915, 371236144, 171537349, 308072170, 574778164, 300760824, 187687771, 650147820, 248364031, 868442649, 193851093, 153184471, 130164223, 65600973, 682128510, 501017456, 145285426, 971864715, 615871640, 147373905, 699013112, 229574284, 523926713, 550947529, 568295342, 133125532, 830147851, 158195792, 618336295, 757841622, 739022231, 181764216, 372442636, 549952204, 364746481, 377115346, 882557656, 489491661, 213371324, 120300995, 971566730, 483198903, 943982761, 393848084, 676325111, 114412230, 13482916, 522249008, 117825085, 851843307, 965092798, 211449131, 516337423, 82266469, 765129286, 413174956, 439936968, 958772330, 53681833, 429166318, 462280188, 342252392, 437044034, 414122761, 841429156, 618035206, 293715957, 881319488, 515689403, 184904267, 334486787, 470338223, 840315221, 927596904, 733302988, 811327994, 897480261, 810583774, 816778160, 897775009, 258996942, 973447353, 240969413, 952540084, 389337548, 343591748, 882859927, 72706569, 577927390, 175455265, 770756470, 196247535, 541572392, 10551262, 677646402, 642596700, 452596390, 522135045, 156674722, 627233610, 888349494, 978195006, 672348436, 249439576, 802627801, 413303381, 828630624, 694242248, 818555735, 983004484, 963195621, 703216758, 583003342, 463672510, 697248222, 768660505, 410001384, 705667754, 129386802, 639486728, 24440595, 136329006, 553043084, 407270673, 870283929, 309044764, 883637794, 317435099, 688716123, 7371903, 527280185, 925357306, 189763246, 734280479, 17874129, 498787986, 670215720, 606575438, 832674144, 626530186, 942627977, 46618258, 761265530, 743946639, 871652438, 990079212, 652574364, 984345983, 431470819, 880139002, 901143093, 954899171, 153476466, 458934531, 343252288, 339317068, 870036815, 861610502, 65737503, 311671961, 724000243, 670350964, 64877180, 341672020, 652975873, 49614244, 490164466, 726846406, 396166331, 747449221, 279499975, 800685507, 157787655, 798775869, 944109400, 463662460, 843353004, 177923856, 878838519, 709594530, 206624464, 787088750, 328861841, 515387367, 309611160, 666723874, 435141079, 611284132, 883823030, 93685285, 456237310, 887822662, 324075449, 50851809, 282508828, 356740534, 16105050, 412703380, 352891556, 671448208, 295801158, 414022309, 996627513, 335483162, 374858687, 634053736, 809179996, 858426714, 870194454, 542775513, 515923558, 601545133, 464742630, 37608837, 910853551, 405101314, 291960372, 426580178, 732142687, 743330682, 201361798, 44999672, 964948206, 857143505, 908229816, 584778444, 665160319, 839106283, 164193438, 109564877, 488929333, 366874588, 247577455, 322142588, 930224348, 488911492, 282640067, 751928303, 433497719, 784507561, 999494648, 157181025, 168038402, 636339899, 419256674, 808803113, 971029300, 821893513, 242369974, 690128767, 931528564, 781490590, 487202336, 35279642, 690354562, 279055026, 48753006, 760571040, 362969944, 838088421, 510453563, 260552722, 559401329, 244959761, 598308741, 562691587, 653331298, 893868597, 965272879, 245567118, 184470051, 258332899, 99077133, 280863544, 511433012, 922353528, 327060757, 296490817, 848671877, 782659847, 274915546, 500783092, 92380568, 790383696, 319475918, 613044765, 822630907, 97929665, 45376248, 47905350, 447859552, 433115270, 54547643, 492620470, 806700456, 727125423, 418964265, 671934754, 778506023, 246299098, 109278402, 939555767, 980423962, 424371503, 655485304, 13890072, 392170418, 918323322, 998642807, 809430881, 491339234, 226758583, 768203261, 64000493, 34275465, 618478921, 411905385, 358853659, 957112850, 762440322, 751242250, 827520513, 171492006, 983049123, 458464139, 724949656, 341276325, 468082218, 495709809, 453580614, 441783040, 582457836, 406539854, 195695195, 364288287, 254460694, 190702407, 567240914, 117498855, 229696579, 82598146, 685082403, 552895353, 566073922, 600567826, 186807598, 731676898, 822278836, 70309537, 359211138, 704277386, 252848488, 719120017, 109791539, 951338165, 687226256, 961452134, 387792501, 610214499, 540564300, 449473413, 350334859, 919063769, 509091548, 821892413, 707019876, 115226973, 117118458, 292171864, 381951759, 412504252, 969069719, 69094792, 349368941, 79477936, 945192803, 29867006, 173844828, 89029736, 933489068, 26444677, 484215571, 224314492, 49034845, 632884738, 206617826, 766463023, 65084671, 661533177, 220347425, 843007796, 942044467, 91482559, 761988198, 682745328, 328856473, 414220500, 62169633, 10079662, 108002342, 872044622, 538081349, 699437180, 487180949, 836405376, 219124884, 806333833, 369691595, 410801514, 135722933, 765878533, 201022056, 646187359, 11142719, 786471012, 370953961, 903476590, 611864613, 770437253, 457157282, 181749229, 966020750, 674250777, 299976502, 671864467, 63333986, 37916515, 213972739, 910564724, 943591586, 445618816, 616771019, 262340349, 432466534, 427541481, 478192834, 121581068, 456946150, 549246900, 395821330, 856798386, 763084313, 28583423, 780747266, 929102478, 37290886, 554226564, 534051226, 921768404, 840083558, 68706624, 716934804, 611931043, 953182980, 526975388, 922976390, 90963315, 382725334, 730705404, 435935489, 209204822, 284889575, 758878164, 390106252, 83888072, 651822629, 187199230, 979255246, 887168495, 880766682, 727203401, 319730770, 874437686, 28174265, 629353495, 412022485, 44518011, 644340687, 102589719, 185971803, 123923014, 219396514, 799453793, 30346542, 415396393, 573857933, 707454503, 250539329, 309691675, 599152596, 768081634, 566763918, 110507003, 252014683, 603663223, 868566099, 521241849, 256582979, 333670701, 501358492, 509564334, 409199563, 367700532, 491192466, 326561547, 455284015, 135264385, 979201264, 127520693, 82980629, 428649451, 745366105, 564547076, 355851031, 640068964, 620772859, 906729223, 685236538, 336786795, 816413373, 225274864, 842201115, 845356337, 255335894, 25738307, 510128225, 887428123, 244031584, 914262957, 180363601, 49737231, 380708328, 435129552, 867170727, 121756627, 793163686, 31308559, 766199801, 194047731, 580056813, 81608336, 387081776, 43243479, 959337568, 567941995, 330419244, 468287700, 379228711, 287635239, 70240596, 345589599, 560473024, 171029392, 843449251, 622561331, 452697004, 265697345, 351058836, 164738615, 819929136, 302370664, 219237213, 451183156, 864748925, 673759028, 321389678, 239775213, 309796173, 802188852, 982105995, 139886253, 978295737, 286185838, 190893602, 197294905, 211724141, 958783945, 204860025, 823201627, 706341102, 792867139, 203485699, 373338720, 799930885, 714383027, 344623411, 922891112, 236076311, 329967794, 473955701, 227807574, 348313331, 509850490, 811115274, 13390041, 541628398, 903286327, 660356278, 34113928, 965803935, 968025415, 309476737, 440491725, 136406547, 522681686, 779357237, 195844670, 321477878, 760919979, 141663346, 152463356, 76272181, 377875489, 605754403, 352504906, 61780443, 262923752, 823508074, 802418449, 818668731, 128322626, 138628348, 752284285, 11533078, 271543268, 913120201, 74887220, 470231704, 41619021, 220459110, 899310081, 97371401, 565534986, 724204067, 775323775, 594273417, 108246864, 749966849, 763566605, 74660802, 374079648, 90419247, 997908357, 323295808, 112383634, 905649332, 262231695, 695272745, 765885930, 424099695, 750426217, 173023966, 517603966, 659745260, 850635072, 139162526, 799216407, 977375500, 293078319, 682079279, 283226412, 568898877, 99889458, 17303861, 72688695, 622294953, 292247658, 948297738, 553674662, 883399243, 630816169, 491774504, 29244051, 60484896, 498157156, 612856135, 203979771, 520795053, 961186376, 615470979, 85337764, 212556205, 392762986, 39931799, 857958864, 888634847, 269319201, 428908077, 945796575, 130124961, 960958116, 709943791, 156783426, 595016331, 409855403, 230479010, 890481997, 486778372, 734818398, 897427655, 74956965, 126158092, 28693937, 235388675, 349178915, 556299049, 167779257, 827933876, 142516884, 486178930, 918691570, 540286217, 940647463, 704311984, 735770184, 249822998, 535045676, 421913503, 841410800, 237032807, 384445510, 657102051, 298452454, 728686494, 324877735, 709477140, 279838526, 557854922, 735764543, 980423038, 258730942, 21360403, 577282363, 193719874, 831572804, 732465883, 847396020, 792636393, 666990986, 407658671, 19374907, 454828539, 527975843, 739895838, 84940925, 462561059, 523247742, 581341571, 420173735, 207973215, 339857726, 952449761, 233863729, 711513220, 57683478, 156122498, 565111893, 794972688, 274566175, 42377831, 650146767, 272717817, 658361970, 528095277, 130401375, 710322016, 171770287, 817901136, 257990019, 69945332, 211098497, 861200459, 738416644, 92763838, 303191390, 177106464, 592491528, 527975160, 519790030, 565870154, 900836109, 137143262, 152706523, 705684800, 8479113, 538969236, 819609472, 842426113, 171456602, 722046681, 35923094, 896978392, 969451920, 118543167, 600231870, 899079749, 904335128, 23822058, 145267654, 243377415, 760027976, 247918465, 284541948, 558873518, 85943984, 872237512, 361034565, 694088227, 306764687, 669252317, 59189075, 796311756, 252868036, 832877976, 758957773, 995707387, 359316924, 75381670, 226694152, 671359681, 486518126, 399839253, 384726830, 265162888, 716940271, 105990264, 846037773, 419370129, 507024181, 250884518, 576422801, 835952608, 796919130, 27195249, 717161833, 28137637, 48087402, 255044400, 922913802, 234202355, 674409045, 763586305, 941301936, 172328064, 369020772, 601256773, 761342703, 474464176, 596696035, 586732616, 597960686, 429947999, 807089550, 374009374, 172504605, 282625805, 267843057, 184309731, 955152781, 48154206, 44684040, 452944090, 930342948, 712107126, 740256268, 181371257, 86271601, 533717715, 608673362, 305992484, 459446099, 101865683, 697206346, 569625609, 499915051, 830200436, 183627467, 805358321, 72080724, 927897373, 849486943, 232078882, 528651624, 862931937, 31946934, 902519452, 793599682, 19949445, 568914665, 714083290, 246009859, 584967519, 768235476, 319934347, 433187203, 484885701, 639954599, 184779029, 266877982, 401554635, 29176959, 815657647, 214278844, 924917416, 46907957, 552698434, 104906562, 31807019, 173363474, 850034797, 872477906, 687406718, 144973400, 815193586, 749261712, 739406166, 335211725, 961259917, 336237218, 905776805, 987780767, 255119869, 556989817, 667099663, 247362810, 785138658, 479635702, 956204016, 298188744, 747817228, 496203412, 635369238, 527339352, 6735108, 97958281, 659875238, 474149315, 228173147, 125380362, 683114253, 75421926, 296859043, 174828852, 716266479, 19227510, 765671869, 404659329, 72377795, 769508988, 74523061, 466187987, 151355769, 335775044, 316205566, 556319423, 268841855, 324062000, 885048430, 362727061, 832955361, 608631561, 27796998, 356928986, 948576812, 474615766, 79089507, 272234992, 604520633, 86889015, 78430233, 665456353, 871887484, 622857185, 375818718, 708591309, 165022869, 86871068, 653959158, 312972870, 371438585, 869470345, 39054041, 513140464, 307393393, 438405370, 552269710, 346400572, 919955838, 737665495, 167127188, 558412408, 806536686, 740341462, 303477234, 842052101, 238604879, 982032165, 601714935, 510572024, 443857020, 431443478, 545105100, 994006296, 541214476, 837701464, 66946282, 976243091, 414796732, 901603534, 23650734, 822255945, 363176079, 757436634, 313135395, 245464161, 29266999, 320564800, 840844554, 300721469, 965221721, 40796784, 104008714, 30687654, 596762479, 847806205, 572658155, 410162100, 32337824, 987688178, 104952469, 364902388, 459478112, 359781313, 400524707, 497818173, 429674715, 777374041, 798344918, 552690868, 227275091, 428877096, 322860893, 376517113, 29734789, 847121385, 299465364, 780242687, 585035086, 647573809, 131128019, 572045876, 385177250, 760539830, 355499843, 647410391, 970162647, 397469628, 560402623, 780466076, 904985732, 996225598, 292757060, 949735814, 901987964, 73350398, 432105039, 569651027, 514620812, 548864144, 426706036, 751994976, 245236390, 369781736, 870317649, 140456659, 447027059, 905616232, 475430747, 376357087, 294616067, 267863351, 264844786, 457981523, 225145882, 102487301, 919356795, 488385479, 731521796, 563273295, 427166239, 996961511, 280582107, 463982125, 97616409, 536734503, 210207571, 257199424, 526058656, 590677672, 36910195, 273835870, 54908500, 185241388, 67079015, 941823182, 252595529, 155810672, 350027739, 995276579, 280074130, 995638796, 646775124, 255292071, 72194732, 869394037, 366534808, 605841865, 542439796, 501568653, 396315225, 644826329, 480113769, 751063771, 342983316, 8018962, 654126174, 691201100, 481550251, 103605976, 160273042, 886745958, 282957598, 137192972, 480477175, 759159732, 24511414, 835809486, 205485071, 825703298, 296749070, 312169773, 814780015, 996540804, 66904690, 338130342, 59275674, 801405716, 666842376, 937922713, 260735545, 918575964, 999100006, 540492083, 137987021, 8683885, 268459288, 60824883, 276378523, 769376848, 708922897, 108655634, 790871106, 491346480, 998844424, 26179908, 836055901, 83257145, 97482578, 17296121, 752806504, 494254317, 33634349, 316362054, 473069675, 869847903, 666085573, 41559500, 823168207, 496496754, 413151432, 481321331, 451000488, 979929542, 833666924, 956154568, 485701971, 282479705, 828238298, 783533987, 745505079, 198856872, 498477285, 720085607, 663184416, 692957877, 356690195, 937517604, 681652396, 677149492, 393901863, 552080758, 571399148, 872691540, 742515758, 859258574, 438723404, 695541455, 659650274, 715388328, 402487304, 42515088, 666501990, 38763362, 339584721, 267640143, 936399284, 178817430, 614692579, 381146015, 236659755, 74325033, 388339721, 794592273, 943540748, 53367256, 169838891, 231002668, 806267494, 577051311, 438252305, 329753565, 781667413, 577704415, 476844717, 599411540, 589332754, 869102493, 598554611, 386701049, 937365100, 440105931, 906357071, 974028720, 737842146, 329087719, 552666337, 613644299, 972077109, 401354112, 619821337, 790923733, 246604398, 852856450, 325619908, 565261679, 834399733, 96051215, 450551109, 47174383, 161138919, 832015954, 435660446, 752374516, 504041736, 246533884, 12817524, 314668916, 778650268, 702013525, 723900698, 919169029, 155721817, 101482088, 58561336, 533793128, 724881377, 411517258, 946623672, 401093840, 869688746, 618927589, 226832023, 266694653, 838580871, 696518472, 315687627, 361246962, 751907198, 376771607, 308909107, 736600935, 125273931, 517434102, 487824598, 27785521, 301563068, 643991377, 815824642, 311137073, 123712280, 343614670, 563663706, 802178105, 367318691, 78572087, 333952960, 193322041, 592483511, 700043314, 727752245, 230678439, 85088048, 947852561, 390345305, 252943910, 744151391, 1298358, 934169448, 167138726, 791612697, 794224453, 197038742, 357966055, 895057429, 27200044, 906925178, 408898665, 124949666, 369841857, 399702037, 291647668, 492553563, 1471559, 860937712, 640279990, 49834614, 304519271, 769527554, 937190552, 61383138, 17274549, 15962674, 474990749, 717447798, 296285072, 731837711, 878389550, 667871664, 379218425, 370395156, 172076821, 816055829, 520423550, 843367566, 65624877, 400327028, 581622603, 477590953, 847896688, 744948403, 438007423, 581791658, 592525165, 943660304, 43187845, 82821355, 151780223, 353646317, 562980308, 223585218, 835606502, 592181102, 439503305, 737818491, 909542252, 543407370, 89411046, 759104436, 502384441, 315844422, 469293373, 428346255, 473535848, 753751664, 272000723, 314097752, 795035351, 945970706, 323231333, 113571939, 716187291, 142981638, 797827381, 758249540, 696756643, 553403693, 503308186, 574118691, 811124720, 65374267, 817785588, 327591771, 535630616, 373010352, 334413733, 617613719, 599679815, 964487083, 69406101, 928893006, 223387712, 832031352, 249052010, 428760914, 128601519, 592082436, 241506916, 503841277, 870292527, 974496990, 595385388, 450100191, 793272840, 466679582, 244995662, 453566861, 680501750, 91038156, 984676472, 925666095, 953987167, 271879129, 345173798, 690161429, 795264215, 691676994, 363464218, 792422576, 534437775, 479946998, 733275463, 467964980, 431091162, 110632839, 496525488, 887737911, 634626631, 188484491, 588264216, 976849118, 698717878, 739103240, 309765013, 802058815, 455052906, 497550441, 957659419, 959220420, 859823926, 125219622, 329351530, 403689035, 474329890, 737742437, 946050683, 577462685, 385738309, 287819136, 702543164, 963389263, 96199104, 901501687, 513515782, 230079726, 135633538, 759891377, 563085473, 891620430, 957654778, 65680545, 702906121, 974819880, 713756068, 963981419, 160889217, 38653391, 164426630, 645119816, 130028724, 216710757, 173864646, 762071484, 883379237, 866889165, 92623230, 834951512, 934728794, 930723537, 701019791, 927090255, 732630966, 593577613, 852844033, 468614696, 411684893, 83763367, 634014499, 284604290, 435436603, 248983670, 969582055, 523356133, 456911590, 528610375, 597304299, 921128475, 58961954, 224605009, 472545789, 273824401, 497703654, 954374790, 125668944, 766360340, 992028485, 70108650, 657441160, 736979918, 191587527, 618896549, 626913967, 168592796, 316927759, 880549036, 969524666, 949273739, 92502500, 543453919, 326264090, 759669411, 388065037, 402108464, 133026545, 959370641, 174416698, 441419828, 670051629, 357066239, 380063169, 193727421, 665944575, 492288834, 88083278, 954512963, 663500332, 898847425, 17845226, 363229183, 982008317, 288021262, 199749304, 900773110, 887279550, 63916038, 607986119, 294522803, 470122009, 376454037, 160527786, 5292493, 815111517, 55580864, 957059583, 300167003, 748560169, 519101954, 976193630, 201082800, 861051709, 294741248, 675169348, 665950723, 636055897, 839876370, 873266478, 207818694, 936870820, 33526764, 340518041, 503853928, 268996073, 727703183, 706621144, 917141377, 8131907, 731321570, 705202518, 29461271, 567835516, 244961336, 261991222, 652194815, 969400053, 559930136, 688621791, 428374061, 709560221, 602440239, 264251550, 859728712, 715895738, 380759681, 143866626, 634103308, 270146672, 951493922, 878128547, 638410077, 148363635, 374431486, 682462637, 463735529, 464292740, 840297122, 252429838, 931538673, 804581709, 884831836, 557596711, 826682164, 601538411, 270549825, 500418662, 641768591, 547336212, 26003175, 773370732, 288876775, 968096660, 285620603, 759082821, 930230212, 402301924, 731006653, 56779667, 117634617, 800602931, 248824268, 102270151, 839585325, 704862759, 327476054, 462066936, 957458846, 394454554, 782833226, 417041396, 503539961, 247244147, 268517729, 151506534, 935824210, 686600249, 633386596, 983934852, 825387970, 456923222, 104482721, 262794377, 606489323, 976808577, 741813992, 970112608, 608917916, 754189819, 514616497, 220989324, 289215635, 876426847, 411603291, 2940699, 423005980, 35564910, 362986068, 159954894, 206719206, 857308929, 565713225, 860063598, 458231991, 784635047, 763906585, 696565974, 183837695, 505116211, 796456754, 601712037, 899218055, 757365422, 940182553, 298120629, 393051571, 700491962, 287018287, 272889967, 81053723, 240285025, 343262037, 314494297, 218093759, 509522121, 517118896, 101153404, 497699226, 11089865, 465135252, 640102402, 741582307, 240485001, 185781076, 197627474, 616199565, 454428223, 704029460, 502063469, 913468895, 240633525, 571846819, 830906236, 907111755, 645093678, 197548171, 920411966, 590620471, 13506605, 302750876, 389851192, 973187553, 876310222, 949460487, 925821589, 752858015, 40415382, 328143263, 382462818, 527955079, 223283238, 283744368, 906282166, 753835275, 84646218, 713107879, 398069947, 624565479, 543272935, 579660476, 843959946, 699140292, 910605634, 95509459, 915576113, 786984251, 183519068, 725288323, 184042461, 983557689, 89193216, 103458619, 208940250, 218878148, 407716280, 827778342, 994002452, 924233751, 604420700, 378481120, 777064465, 211776617, 139182419, 238247080, 214827398, 283560398, 585130131, 148036490, 576211465, 878646657, 77371450, 943198959, 872974067, 465761232, 436335259, 796178201, 605705885, 466463475, 995355543, 69359002, 203318522, 654253188, 450786481, 702199111, 158339052, 592758048, 957465196, 599090847, 274527687, 631708816, 465071360, 637947028, 964030720, 298815925, 818030450, 139046880, 587906352, 503555536, 951933593, 446490674, 554305661, 794108919, 162356695, 20055215, 983978844, 942969274, 248343966, 550631913, 156073634, 193818043, 976931647, 327655623, 989645961, 778518410, 523420394, 477258357, 899562098, 468471115, 624277495, 361533210, 214900874, 538193145, 140541237, 255868980, 481559297, 181178288, 80609392, 593583577, 974618169, 41510086, 248987627, 110649778, 191595579, 293288501, 473826649, 188836715, 514468452, 371835845, 876174117, 839087075, 225212719, 895461759, 300866220, 12231719, 244903276, 151007553, 888560639, 221046636, 802229382, 48548095, 811485403, 839533261, 889808923, 658906915, 327828994, 897329173, 605617218, 572291788, 911957310, 258248397, 767800856, 556643548, 185288874, 932528936, 279132595, 286615867, 595089090, 762494721, 883765073, 641481909, 712854992, 329741885, 862572926, 59008271, 302985253, 82667163, 409540807, 553351553, 520367458, 590631102, 96126617, 389483595, 63158959, 638983644, 829785449, 781531808, 555156964, 253505934, 145633970, 646000218, 525641269, 858051758, 377657006, 716960427, 889189945, 325193787, 480248533, 356182025, 195260871, 968009118, 355284855, 868086196, 643494629, 986223886, 546986447, 273882983, 781915693, 790659310, 498525982, 861689118, 588621136, 999939858, 174075051, 581948462, 549111407, 721208760, 416206283, 964362893, 771357028, 151696028, 656671904, 756927334, 726952640, 733800101, 509846755, 616277950, 862171618, 91294425, 731616792, 774278373, 68982917, 823333948, 184284126, 102255144, 594557768, 245460426, 297512932, 530470480, 824127337, 517153809, 586134924, 233175257, 799064690, 885241193, 990126054, 599018509, 308342482, 573356692, 261031934, 382697826, 832509347, 355764642, 263193016, 553912276, 109291323, 979213980, 563470673, 603744734, 363251182, 471218956, 168144257, 953961227, 501162374, 755951106, 774089783, 794700361, 988881500, 565624184, 407893398, 163706817, 980403595, 766288837, 953623866, 830840530, 520164295, 491832880, 809445945, 810976615, 239244408, 944127536, 768255311, 712378376, 873980251, 495728383, 366038534, 612665954, 230644512, 345294424, 606370559, 778527501, 18463809, 556017517, 145915451, 303638223, 656157379, 330983058, 266828628, 997371456, 120701769, 346361561, 617692731, 617834878, 388441516, 546369553, 981560966, 110639980, 746932427, 760203313, 966111611, 94544327, 405027088, 51954415, 277381842, 970211074, 696228701, 950510505, 655816811, 796457956, 161140794, 41568162, 600590405, 688031797, 586552209, 952299555, 38722014, 714953144, 368910018, 32535053, 220695437, 213575821, 561993886, 689164682, 740639560, 220667237, 596491732, 290911563, 7717467, 820919370, 369980991, 5013732, 875198609, 174106567, 644847037, 395006726, 39823091, 864343073, 433572078, 875180665, 632787856, 93043695, 231719296, 36987362, 66617597, 600739114, 430023389, 514164353, 175697037, 595553853, 303933096, 385909372, 206804956, 890876275, 286097301, 864598528, 59908218, 209760163, 512583210, 21587440, 552117213, 731054489, 413415449, 111520438, 569647873, 565747471, 546033937, 344385298, 203805569, 724160912, 831392651, 707197647, 807265790, 596430039, 655352352, 382689609, 147110684, 993230769, 779531290, 531091809, 817356382, 717932458, 263121535, 874228637, 471616087, 457176071, 875624126, 639969562, 880326841, 266778511, 773198112, 748994770, 798027173, 429251527, 794716192, 80485719, 805028287, 213450181, 862945569, 326993592, 740363167, 469114383, 719403299, 355708590, 37044483, 113525734, 26048903, 154099793, 38870919, 331088370, 80201952, 597187275, 171596980, 139758970, 350788794, 914025235, 730351467, 759884772, 335272066, 257700193, 697431910, 784571292, 925264149, 476489657, 255835214, 247740670, 550958168, 812637408, 883602545, 316328275, 598939452, 732264860, 63627068, 463757186, 120514084, 155224825, 972864856, 614483389, 465463243, 311276282, 94866679, 701632235, 63851340, 329075738, 626449826, 580827503, 645915261, 765603495, 672828608, 948417200, 251747169, 135280192, 379676987, 358498670, 559121855, 469643576, 297089015, 860874862, 137819112, 832990984, 68236158, 762185670, 488984413, 894809079, 679231023, 802930468, 120348310, 914710766, 161192193, 737054237, 912069941, 62103540, 647997535, 199300618, 844253818, 257585413, 439401859, 72984363, 144892592, 448993970, 320503251, 690164592, 108947315, 549541576, 428985183, 769348168, 487915056, 874964306, 82175536, 187552544, 822245811, 180978962, 227639795, 640900929, 412720659, 525771173, 725849839, 990051308, 566642248, 821971871, 439672354, 194291760, 373930807, 353411132, 547462974, 368591412, 585955431, 426359989, 675971847, 558128937, 694411825, 345163684, 605341912, 620040532, 984810283, 396128396, 104396019, 690650659, 146187750, 340962621, 137986882, 984061982, 399146108, 770834962, 854904821, 16884416, 558751424, 421233043, 96534170, 833070657, 892474244, 917856654, 55253753, 781029089, 44509110, 181807819, 243853908, 850993824, 50688806, 426373777, 550752317, 13256221, 957365071, 745888689, 923812420, 919020362, 427471772, 926624087, 101748292, 743817459, 617303231, 409475743, 990937164, 976053907, 714120097, 999138218, 315145484, 838580883, 583630053, 716638028, 887350104, 932033952, 260343692, 960808554, 596663183, 894494792, 541131785, 870163381, 333282445, 470196428, 614251396, 153994378, 251062253, 971720224, 836953883, 164249799, 660494988, 419317076, 344249891, 72970831, 332649434, 95359088, 2780483, 680440505, 650674666, 175982300, 956740609, 157355510, 480093515, 808140563, 566307076, 519461133, 94152281, 336967077, 357283862, 627287498, 84054768, 236574236, 873469096, 246606327, 275417563, 163304891, 797169351, 67896601, 603963127, 979863165, 840937834, 169846960, 296947427, 445110610, 500653315, 316585317, 401808648, 178074724, 913518706, 670247793, 864522993, 662038198, 331053216, 53094878, 675221096, 215975178, 609589034, 922813501, 359029011, 200225028, 675154233, 539025986, 367760943, 366264042, 810353298, 314736993, 136124570, 710715078, 715706539, 810764168, 139945072, 728887296, 198434635, 32717972, 904060148, 943304807, 827418750, 481267357, 723686156, 159141597, 934867018, 713131786, 246723264, 802104393, 267844017, 718531111, 481827844, 498985370, 197403384, 656614642, 169589521, 336983929, 644954743, 211717670, 235924414, 383190699, 271036706, 166547629, 771106112, 828862403, 34751410, 765418372, 727623215, 18000497, 918673689, 67974463, 803392923, 800369143, 28518570, 558804645, 257875805, 712301255, 985617568, 784328276, 390186151, 145966259, 633792466, 54816143, 956127037, 73369382, 552956666, 466619897, 416222657, 700173323, 25969405, 247101454, 832498646, 4650809, 1461191, 952270875, 698352209, 648893276, 894447321, 246114467, 83994647, 755639876, 335830933, 244931927, 107828507, 776099656, 966438485, 853962326, 202139728, 604244519, 612077768, 850114974, 333066616, 911639250, 514221379, 576835339, 698478147, 786220397, 66219467, 917963874, 226189992, 782944876, 898794637, 732178481, 215051158, 455288112, 325328766, 407271703, 223826196, 307262432, 579974864, 359217760, 341656769, 128161195, 371578404, 369993074, 938017882, 114018136, 197426111, 604696402, 122015817, 110126187, 923955643, 347580633, 435872528, 830793256, 942540071, 97249629, 449699434, 540691260, 359904138, 372913660, 103559966, 952675718, 526637191, 957532903, 350107011, 624881975, 28781638, 193858885, 871843277, 223235760, 801756888, 341732508, 989229899, 804320620, 781161567, 944819016, 652153960, 50107736, 463413227, 881639283, 90294010, 857774696, 997430080, 748242924, 65920836, 260863883, 764202189, 879460013, 790182725, 228605852, 877702002, 265235027, 298522372, 626285047, 508078607, 650128416, 56053142, 228050198, 931572207, 946992485, 473561154, 678297536, 492487725, 497531665, 341728700, 229905345, 973164150, 850893042, 789404158, 215565532, 588113015, 72085182, 948028068, 877216234, 543254288, 597957164, 363480188, 620838984, 897060914, 845297592, 431826458, 762679104, 586341308, 121189065, 976375841, 976812529, 419027966, 729898698, 583791355, 383558807, 798165101, 7296926, 706814547, 5193072, 869597785, 240392518, 324956448, 116303663, 308899376, 124177273, 793735933, 594717312, 42468071, 994585102, 600710499, 735618504, 619491316, 899450737, 523337712, 444816970, 229008131, 405041991, 631945752, 673712149, 578339937, 242338970, 191936760, 213613661, 229815082, 828897569, 270636457, 585735442, 75130829, 545205067, 153726566, 11957187, 539698058, 966455616, 498735981, 523524411, 167055682, 982810674, 389048635, 501422830, 672210365, 961861580, 876412239, 608660856, 552011527, 153516360, 231921525, 380572217, 333677295, 338695519, 127322035, 455756056, 652754072, 749919638, 967950912, 531844675, 568023189, 328630707, 668537509, 566467066, 528980072, 401722379, 71256457, 120812666, 749672040, 279212340, 269889054, 996352014, 455055522, 658452332, 372636, 283478385, 449666518, 356359071, 223621329, 145879235, 815155489, 618445385, 228027245, 59816242, 181061516, 743792136, 817181550, 392785188, 224433813, 693677981, 252826200, 735236389, 936137543, 568289576, 84737954, 527387387, 798539914, 813193552, 346445608, 208974163, 639759503, 969764672, 54961566, 337437993, 760529549, 6194973, 675506346, 682463985, 473254061, 736861949, 55804018, 142294271, 978084596, 857185209, 814906320, 473261275, 547459248, 414555893, 660033878, 279556069, 553439882, 621905242, 94144376, 966857217, 886033293, 405984584, 523097419, 652741031, 814221755, 156347913, 134834660, 486109380, 63082336, 450033086, 538681549, 371430463, 767759034, 790011569, 335079678, 779663715, 65961668, 429779124, 367367351, 686144791, 237776277, 584639553, 188959134, 599774647, 50536144, 54649394, 21661274, 175366762, 636301336, 285719442, 464774661, 39335320, 39297764, 830233428, 35964195, 4449787, 319546741, 787758747, 372430071, 594491926, 336254979, 728320341, 346859752, 282468364, 330439961, 779357307, 772427377, 689044334, 244146705, 61882505, 46670715, 858850295, 55580069, 408428902, 128601233, 980712344, 658924602, 400152237, 669456164, 733259690, 362648445, 180082953, 945200714, 421797627, 185709787, 896154159, 662991063, 229936241, 296976334, 789553672, 535526807, 598370060, 389757900, 554416094, 556830790, 19200231, 843295788, 972347380, 52521105, 975784663, 484877892, 117420321, 167840092, 520904493, 569344278, 639066030, 578343749, 61206212, 920658446, 808777731, 416503605, 939892641, 241242470, 630514491, 287533110, 976001044, 673522115, 498113569, 778895907, 4028436, 358453560, 574994599, 758064354, 820841235, 859007131, 480659066, 440227498, 93188021, 370847458, 98189838, 447239328, 67039205, 69952693, 357307925, 119714556, 109412229, 911356950, 346211996, 369002940, 581233405, 833391648, 911051706, 823609766, 78852718, 548996475, 727243968, 458217284, 220206332, 520953184, 318451653, 572737319, 382479468, 797126218, 583944307, 291716679, 504205461, 927181312, 962164872, 890249981, 831712018, 52122813, 854940345, 327189278, 778259708, 490460232, 763068583, 634370554, 224600196, 363079451, 996824922, 712406098, 159752546, 23030520, 313993920, 914014996, 57792371, 344759520, 612772300, 838918833, 195071941, 657784450, 789617114, 725847474, 247019327, 687249265, 600461674, 825300871, 71907924, 982751108, 994190253, 682903459, 422443887, 600234567, 196834372, 32076598, 823025048, 974642309, 663965257, 609500258, 867017851, 372791947, 721270175, 437433519, 229024885, 536668418, 356093671, 786689075, 61133986, 182091083, 424731611, 335366363, 744351188, 888585652, 11008767, 111386124, 72844882, 486923261, 752987822, 186626235, 484445091, 879771796, 840917347, 139887256, 348048623, 255714786, 337452144, 338420174, 97571323, 311382142, 450154362, 416695347, 554807280, 632356682, 29389469, 11739034, 302827670, 204244934, 93506956, 11078390, 910970703, 701980060, 126712492, 407177651, 778635777, 590449054, 442645416, 781458136, 715482827, 805976148, 436471934, 989609680, 567128678, 446352964, 962642401, 234136670, 221066500, 684176528, 452409751, 668867769, 330548088, 154592797, 974656729, 644812132, 489511430, 687732577, 657587809, 787147093, 417311703, 707303740, 693073825, 18700288, 956685, 493023621, 479731591, 415124670, 409247435, 368054358, 526170268, 790052360, 718420274, 119506215, 431852640, 431412122, 638709480, 722041722, 760393988, 61095931, 465662827, 455259196, 689844625, 537649878, 200050782, 71507842, 919713614, 96446907, 116900343, 8337323, 816765597, 709746904, 782782055, 717632395, 758457902, 791199989, 344877059, 209567164, 406016228, 126458631, 953762541, 286584934, 101169155, 297112382, 497766552, 157745462, 699921050, 201842788, 380348707, 757213532, 892906712, 653878604, 185808090, 951319506, 328992151, 187145018, 315604440, 6640207, 782287900, 794499737, 600478622, 822497389, 178120551, 332002927, 326805968, 957338513, 5215308, 951639797, 968177220, 368704902, 209279966, 980031894, 498281102, 896735135, 696112907, 636522820, 17832361, 155254262, 650084170, 305925466, 442055276, 585401705, 173424696, 332906007, 613030435, 997252488, 903398921, 480918340, 565945078, 767212967, 733723141, 673628224, 819662925, 360064529, 64738740, 981419209, 111092720, 388468742, 198525793, 46380517, 881313528, 119044721, 508467495, 522004044, 943077604, 279790033, 852903595, 540404985, 52763901, 402034520, 605811008, 430660610, 834610606, 188194320, 82930520, 50115704, 338227449, 367301187, 601948554, 283505225, 149220509, 963793698, 637398726, 655127895, 634846813, 887606475, 616867752, 348715407, 218610796, 277629653, 816167298, 341454185, 738094640, 975844069, 701855673, 367385422, 213519356, 856922361, 112636644, 919140067, 739119646, 64223577, 185143294, 992946226, 118290949, 177750768, 321361730, 795220763, 934445073, 740216738, 110667826, 458595780, 580660407, 656978489, 24861390, 885437756, 315595048, 905013994, 180850977, 376906627, 932181825, 253520766, 666895222, 373507152, 310397566, 444680781, 492180908, 156643915, 57025922, 950987583, 100600972, 695739985, 589140098, 790280689, 736144641, 117541633, 932206337, 110541151, 440968435, 627746684, 367038005, 569574844, 915708509, 247130319, 558641898, 167429882, 42196834, 489856749, 696504395, 325766297, 633842996, 151410338, 921043277, 575468314, 934322595, 381775883, 68515272, 449616504, 839142537, 829985084, 725816853, 321196811, 857341512, 636366781, 891944540, 272933390, 473534133, 592639456, 485402549, 559118694, 267516977, 168163584, 392726310, 895840876, 256081395, 899263407, 542474872, 878053357, 409623326, 831899112, 325137790, 550602483, 148354982, 574439577, 668925288, 314733770, 958526476, 149190996, 802991035, 867482651, 158594406, 245358433, 822875429, 563616697, 53227066, 193116974, 861997632, 205534719, 916909567, 480677850, 76814097, 756078089, 529076074, 993072909, 838095440, 432649790, 814615846, 122835179, 301581210, 687896869, 723085365, 127965115, 879077435, 514875171, 974416133, 92390281, 748044674, 849450517, 904057607, 161916125, 109729662, 169010650, 737888990, 915150562, 771566002, 190521555, 81478305, 686755511, 108477674, 862591123, 555343977, 853961982, 322872817, 618958254, 984369968, 236612804, 341462076, 529313356, 202716102, 82614818, 669452503, 821057964, 620448489, 479950099, 138041749, 566542259, 79147678, 46902178, 616426816, 911805533, 12318908, 151021860, 154071431, 134346439, 68907117, 143357939, 636288118, 640150747, 907258790, 391917248, 656652681, 884168132, 781009254, 598905667, 6320096, 548916621, 706101765, 473489469, 511366699, 946579182, 45779615, 449395649, 757710947, 770504235, 656112296, 557319239, 597029527, 282073022, 778525209, 849269663, 9735352, 828711856, 743596882, 500007610, 918410167, 279756781, 718354322, 626461791, 212146436, 668580518, 505519397, 708756615, 13256597, 693325640, 126516942, 595319826, 827142217, 166054397, 746729779, 932115397, 95678828, 145534, 226714825, 813260913, 770496736, 373475313, 319944651, 980150450, 208754534, 443573935, 291546898, 41169970, 487312517, 457858177, 914558963, 658477270, 91913894, 971053634, 321072331, 841236745, 915109330, 61337693, 888658627, 674528027, 724872706, 46051359, 164890361, 6864002, 472908389, 729106265, 610329539, 966121467, 227069042, 270420562, 199672868, 691602695, 59164363, 4579345, 36845551, 543013376, 397420449, 699871845, 682328020, 692728342, 315428159, 466540965, 780594213, 58141264, 526270825, 515573435, 508583134, 102191749, 234251989, 979865654, 102975284, 214968856, 895481756, 146113674, 878553574, 928499521, 74142749, 890865050, 526199581, 942995995, 196897729, 722523519, 990979024, 461141927, 581989349, 710697788, 202681804, 70739742, 852282902, 199964461, 261994745, 205413392, 609256446, 52268434, 995319386, 117991270, 83714390, 369058162, 478345858, 374541900, 470691248, 618298848, 953910475, 138903753, 624044457, 758739814, 748045633, 546976156, 378666687, 204145097, 427645625, 153616481, 491772692, 934403368, 872725466, 386662376, 395481974, 875576113, 242559951, 886183544, 244170300, 545066079, 259349504, 619650071, 121259257, 170081102, 571646646, 862274298, 38739789, 665088937, 623946798, 550911172, 719348522, 220676557, 240946721, 627221444, 295481854, 137032785, 914486523, 274317249, 36103446, 844344748, 567329365, 518616291, 181188897, 609922969, 123701485, 274531003, 376423840, 808741744, 83302084, 470425888, 842410315, 659472008, 649671509, 42038712, 288609700, 454379024, 855284302, 53889196, 488736087, 952899716, 308199026, 651312096, 944348951, 271978843, 175838783, 964133853, 520481311, 570452267, 263707975, 654560191, 281261369, 454346488, 941878099, 865631416, 192896800, 740164609, 247486631, 697815643, 472053961, 251082534, 892298119, 390757224, 54420718, 100407071, 31974825, 990167972, 798784283, 395829561, 94292722, 387869712, 977987468, 449370906, 982603171, 214779317, 862316959, 388975313, 898923136, 73860419, 211864925, 731940371, 325504403, 727096809, 744393956, 193878944, 528238994, 228698747, 25306766, 696221569, 958798697, 360612533, 171983439, 308245806, 202650846, 914448130, 209437884, 201832401, 193247049, 98778129, 101422173, 836633742, 102038152, 466264271, 602950545, 448735968, 72227426, 733146103, 713596513, 791469392, 477637802, 19088398, 174558477, 189266737, 529414891, 341502886, 551578886, 500299527, 225321174, 781092109, 381227576, 445573756, 918601682, 585588648, 965734557, 20114374, 753890369, 230739842, 943620713, 518969060, 143319803, 793424850, 618327326, 65995909, 471566920, 43985244, 941560748, 388789133, 945375076, 343217428, 749393550, 817917902, 265981538, 449558020, 322472761, 500951296, 214547727, 222960432, 724352787, 658074712, 528603660, 115187092, 809509308, 668870883, 32469459, 312022275, 194994215, 360108829, 753181563, 980062344, 937817186, 60018998, 324831606, 608661336, 189852018, 577347033, 966616780, 578713419, 337988391, 60191087, 465567052, 234481667, 570273199, 684243219, 866502159, 362431584, 79380882, 691328651, 699469843, 668799042, 395217261, 529249157, 720396585, 786024623, 736296169, 355088383, 535612376, 181913337, 511766071, 325093155, 355998102, 856003534, 722471279, 710566805, 768581619, 329676900, 296756380, 524555629, 898710493] 209422566))
+
+test6 :: Test
+test6 = TestCase (assertEqual "for (countGood [161967799, 681623006, 221232871, 51765712, 913800325, 990085770, 723548992, 364584681, 855417049, 899823462, 422694314, 889676630, 673968150, 912396775, 833451209, 107256951, 960272301, 229223754, 287528208, 497084249, 177383682, 195145824, 102073314, 986427427, 122660816, 453049766, 140289286, 227103866, 400441266, 462135794, 277239698, 620859141, 710699715, 227253198, 304184655, 202106727, 390054309, 258175023, 716185207, 626854895, 17418304, 146963151, 344803075, 899334299, 519001199, 258287016, 491250824, 896184722, 833604719, 971890238, 916466993, 178224933, 548374589, 371695688, 762480124, 512767796, 536184012, 74127376, 230486095, 293572286, 570531537, 672363525, 949197441, 51643770, 769928596, 372811891, 661395020, 743335814, 568250511, 354699456, 251512198, 318996559, 974697025, 698870358, 722911597, 12424549, 586117951, 560424888, 105861160, 772789600, 508811625, 573069625, 231769117, 539287572, 704831785, 318633108, 930461457, 667393925, 139777810, 881241914, 307656562, 805421920, 206308408, 365464262, 325663140, 841779490, 726550949, 711365713, 128943033, 639769914, 711478802, 190713683, 26888024, 428891657, 576703055, 556372457, 848354169, 754379244, 292274429, 166174798, 72314706, 986060263, 820477751, 38313942, 809233827, 306823123, 531061426, 721445246, 216233128, 738149164, 283927216, 648556427, 239145386, 156885846, 532195739, 876791985, 781277450, 367178203, 467092047, 232389113, 869475343, 387175261, 824765730, 896118162, 319507049, 408179026, 662689014, 807559898, 796346207, 662616804, 12454472, 445635713, 254494995, 620546339, 312064433, 150331859, 990043127, 139099385, 412475325, 305580590, 649698988, 864939411, 420161935, 671147660, 421013301, 137923332, 196893655, 293397640, 358265828, 377653304, 127273103, 953645380, 654225135, 622623027, 323904272, 167382740, 690947130, 856949556, 789079020, 283048085, 249791243, 285594657, 797897547, 121790733, 940020966, 851690350, 768603378, 448696490, 270956474, 803845944, 677493444, 751229815, 898398279, 343890697, 53030657, 468857313, 589083834, 870779588, 126342271, 892291374, 156281747, 50029538, 617614232, 788047622, 675817016, 217629227, 518553323, 313295545, 19521599, 906792771, 24160025, 78921933, 773650229, 375952221, 708703218, 886121422, 302999117, 548546193, 72886793, 853508024, 390203406, 785082560, 198247709, 784799071, 610334880, 484188751, 362048230, 539666687, 732825768, 872194948, 865312885, 993693986, 961312552, 37722647, 77646013, 806874201, 948436643, 872154573, 221226974, 380229658, 834673673, 810865551, 127462311, 780803782, 941633183, 871797703, 357303872, 352124489, 770531984, 605702472, 875831770, 929234176, 781621698, 786762802, 583261854, 125534117, 371933387, 517256524, 347773103, 718876971, 610755637, 887100112, 947577443, 51859185, 422896345, 624877583, 667673609, 553778805, 125364668, 890472249, 598421302, 539343010, 334124287, 197503883, 779736994, 220449104, 682623488, 642350435, 682740241, 209664798, 690441083, 669494634, 314597548, 315057719, 255734171, 731429710, 987814613, 546194067, 345943013, 711577633, 596240880, 943461261, 685911249, 886993066, 207501333, 811914577, 841674967, 525526026, 149394825, 882318873, 108716340, 244891748, 282724347, 24655664, 322397298, 677962802, 124977024, 267957179, 577998559, 805760912, 265446117, 53033497, 221632906, 402921737, 853318581, 25612971, 430074016, 420879312, 739524150, 52637873, 694674358, 276848019, 882761419, 271645028, 940173541, 890309869, 326568584, 87193068, 869427559, 68804000, 332093558, 455449070, 175069380, 173225039, 173776907, 697108511, 71168839, 977731154, 932276411, 634401554, 688635719, 613524510, 376625061, 3182195, 49442464, 378220883, 200378122, 721912932, 994085770, 483670849, 573898627, 571772691, 624064529, 838180703, 231674900, 891145744, 511595311, 173300256, 310547908, 925225889, 178895054, 498906072, 994156436, 546610397, 263335818, 22366107, 500935139, 846055889, 53150662, 740741334, 665710168, 362336887, 531224637, 554568873, 922569754, 987286250, 659651140, 442450092, 230535526, 284781184, 587205344, 825363165, 260320333, 35374734, 317314702, 472037358, 43506453, 240199480, 602299040, 809890764, 174312178, 129757275, 925612063, 783783152, 536272974, 698179085, 81975114, 780959593, 891436144, 827730399, 623128536, 145756503, 292221939, 120927865, 331293725, 870316131, 836599684, 403462696, 431786038, 875040548, 439183572, 166493864, 198943791, 894405730, 169830296, 633683933, 539717525, 314754521, 719179684, 726814352, 13197389, 908940581, 237309086, 260765552, 912761153, 56887265, 406218444, 749858460, 397076246, 522077453, 769889465, 363807372, 976857579, 538870112, 167558432, 134616844, 89644504, 565334827, 371871213, 534563643, 45357839, 260650373, 600829906, 715412390, 397639709, 138205189, 323385785, 245408515, 26184713, 66126406, 478464322, 767461852, 848399102, 850946648, 103302222, 859720626, 651493756, 497223947, 826957000, 619174803, 716159560, 846350796, 227071059, 990674103, 149016756, 954671295, 956047913, 247672232, 172592214, 410799478, 137559933, 452535031, 320392121, 619457874, 497265891, 79277916, 103381359, 950588608, 814723465, 93297033, 704421426, 703679636, 397645767, 661144912, 86915219, 733327629, 898816857, 962305466, 389465395, 117433764, 814022549, 743299290, 963640314, 265544365, 378432952, 680286926, 151467104, 790860243, 683483009, 626547454, 558769426, 501107451, 587046271, 764214898, 495245436, 105660974, 571390786, 633554371, 180191519, 89451255, 470207970, 478100176, 400067798, 796879311, 976227286, 979799061, 932864036, 192419691, 681186695, 46298564, 276658498, 972626387, 111071028, 884397453, 433464652, 765225532, 913749310, 419612536, 196765603, 914852868, 303177278, 618131884, 803078583, 976903057, 733215844, 533894655, 714395035, 147475732, 299980843, 869726220, 680831703, 224313071, 269935587, 925734575, 151585847, 896642505, 107908029, 478066386, 247716843, 488456998, 705803612, 904426796, 552294325, 939471348, 407002080, 342428389, 312276297, 367201846, 548579965, 600591612, 812537662, 183999343, 224892564, 806630522, 588553941, 421652947, 181071256, 356038030, 901545678, 782383286, 433957318, 177986556, 401797677, 471136631, 588631479, 317503336, 306757719, 626380128, 137663185, 9239034, 834176322, 54126424, 437342530, 945889079, 113806234, 595053160, 239670517, 14492975, 430169691, 130222496, 143215262, 143301312, 465595850, 13932141, 968740932, 806405469, 541258004, 363887722, 411821994, 538895258, 506048930, 714410367, 488583116, 451813117, 386510696, 92445316, 117871226, 799394593, 208813109, 715051821, 763324673, 779980617, 34488188, 24136343, 152087919, 651368170, 322796666, 281515391, 421729427, 219740211, 572517288, 273713435, 50413082, 192182939, 529317756, 645804249, 408861343, 545293986, 870615710, 159484281, 115633838, 261163755, 981389997, 14845685, 147240331, 173447876, 841919576, 359751270, 935618903, 74052322, 509406876, 315178609, 398334342, 294898580, 354393980, 459145311, 835005908, 385835230, 333908703, 388622295, 913965842, 883370171, 37733974, 663263960, 113044512, 836045438, 265480885, 287487584, 946445692, 345762881, 978570603, 88110338, 288197812, 342893762, 807883683, 508875432, 987873303, 136521266, 768321755, 444343893, 793346865, 163302093, 856296023, 200671878, 15047286, 368846051, 677522074, 466242424, 309613927, 936339012, 121147162, 726367505, 982605110, 744223207, 696282864, 682270746, 258619548, 27891862, 413635221, 351000757, 381145845, 902464407, 456161046, 414098190, 617646433, 554161149, 601827336, 957000611, 150304122, 511919645, 150335356, 367423217, 556830825, 614932758, 593865840, 686450163, 638963895, 280988620, 185327483, 42380117, 762920584, 350514984, 317656198, 113804000, 754252861, 786142339, 698511954, 154774990, 137114317, 71223265, 489755892, 511914917, 504909636, 748152547, 470206947, 81492689, 902700625, 180973071, 477186358, 248413282, 372588413, 854769650, 164003363, 689611908, 190040766, 166896484, 953316670, 556190634, 201678050, 174836048, 219071176, 801012698, 718920009, 749470319, 479834371, 540777970, 220739625, 670785916, 931651389, 244791892, 268365642, 325023247, 802388163, 362397936, 499077074, 448591393, 931007588, 941619948, 940408372, 460099711, 396839848, 102577379, 842266721, 707980531, 713331920, 473558180, 185450351, 292826147, 705035407, 196904019, 782938541, 998601257, 662325292, 175233807, 914742913, 889562865, 737342148, 805886200, 562741314, 139707593, 254762835, 999086288, 652131093, 163195247, 736817707, 367217918, 707471537, 862610881, 425036318, 492840706, 607603105, 289036699, 633660730, 372637256, 861988022, 113072852, 818428255, 304918770, 705256065, 923856377, 752788642, 425282691, 804329261, 717270580, 424126270, 74012738, 78826919, 51273232, 907649661, 594962256, 330401591, 819285279, 698542428, 679881509, 765010411, 293970415, 959319886, 896983893, 172700832, 58078305, 370511254, 961472049, 248876502, 235110356, 393291911, 531160371, 290056218, 865518798, 988075293, 3835366, 350672229, 182596158, 421106063, 632161320, 416931062, 902145344, 74790417, 724325115, 794060579, 339316426, 134312135, 126331836, 440430494, 932609608, 737825630, 207616128, 18912879, 550103836, 57825187, 931355319, 391517916, 976716580, 166917674, 475934480, 898573565, 851364994, 607800388, 66912998, 753518146, 377022115, 503132972, 716847572, 811230189, 870238621, 970407998, 148732030, 548695873, 622540482, 629751397, 692275439, 856782538, 235675797, 722695856, 347959889, 277677555, 134621844, 311400948, 813039165, 403328381, 105247030, 984532301, 27627160, 767083097, 635790223, 281252986, 356835864, 946009105, 442945658, 555398024, 750468970, 90842168, 874156236, 999849989, 134791833, 179270583, 705781838, 721811573, 806075925, 502801005, 297291180, 952402086, 401845051, 634380995, 28334245, 247069759, 465291588, 475221100, 14974347, 974264802, 173233118, 649345105, 524472580, 972274340, 233693916, 673641775, 459090893, 514639226, 763367489, 254100469, 15987429, 227725233, 51646449, 825289673, 837648703, 807048948, 694748635, 13282835, 797903780, 534386347, 926280271, 343349390, 2087247, 971404943, 764846142, 968408258, 992229875, 276874019, 187067072, 718822101, 485824518, 199612299, 646294885, 637022942, 217994706, 651148791, 958159252, 45980859, 400015690, 305935901, 882784637, 318655131, 955318005, 365724450, 587169455, 452819222, 555440645, 723849543, 583016334, 312402820, 264672757, 756730417, 267536002, 14338191, 719248906, 377810102, 430960864, 325503792, 85512222, 489741048, 757147326, 539642470, 246966932, 274103330, 930846928, 560683073, 507145275, 920704190, 142810447, 323888679, 851512011, 581384557, 884006704, 249617361, 706548712, 274848656, 814414138, 683228681, 883921799, 937552178, 474086621, 798328093, 276002792, 88480778, 869570379, 526579957, 833597912, 167546708, 919170131, 514507749, 348014811, 110669370, 104771257, 350673395, 446778832, 294514157, 342222799, 776963938, 452368774, 856930693, 97548499, 100566349, 578770713, 907931981, 263769836, 546837795, 110877669, 273424209, 915502693, 921826106, 782895233, 583622396, 959560358, 101265394, 133019395, 278689851, 542497766, 950194269, 138037338, 261195218, 798270887, 928223034, 434725395, 740010975, 672825445, 119302026, 850159799, 221666709, 59610103, 60264124, 34330524, 89569243, 496131321, 424025419, 867024632, 758479646, 744103747, 728697462, 736394433, 467365833, 498006372, 106547833, 618357121, 55372062, 555816344, 41618220, 688196758, 360599826, 483918106, 322842751, 889655649, 621809211, 238482626, 840203853, 763225495, 352166014, 786345707, 725248085, 783832553, 798912499, 868595974, 655739167, 181276066, 750593501, 342881308, 452684089, 964525999, 838938910, 136416250, 239537469, 143789670, 998987844, 300039529, 293084061, 740531399, 284395681, 695559739, 633812658, 631438315, 273647772, 721633998, 758378190, 468334512, 491220736, 130124455, 847351158, 84448966, 154540076, 407083657, 895590263, 97475302, 671329173, 89838886, 817873617, 952654302, 832307714, 348315957, 682584879, 991034759, 961658352, 199138224, 124477745, 812744063, 367236117, 806660904, 398038700, 145549192, 174574714, 412978064, 569889363, 773717006, 59539642, 699805300, 153877216, 277221892, 245213800, 545182422, 890547945, 290523147, 411851688, 80987584, 87547270, 29738540, 188731042, 459236863, 190221783, 155449193, 142844664, 866743363, 653327106, 724942946, 30251718, 309158765, 411061662, 67231670, 693758663, 955271724, 627518628, 240781210, 746269241, 250397977, 202150924, 286518827, 675983970, 493795749, 906438248, 378513587, 306160215, 98500505, 193721839, 384266375, 745124381, 105134868, 716371474, 680077551, 818548337, 842747264, 498810270, 627093321, 158865611, 131403817, 117277980, 890512806, 682321729, 119052687, 268205813, 253393427, 613149163, 667087674, 59282137, 30889587, 86166428, 416749902, 237564833, 678975653, 835210350, 657413039, 878698818, 702282709, 48631058, 616394656, 563321960, 591542031, 127546313, 867813212, 986827652, 283676390, 44557697, 843072941, 323528884, 220990144, 421872941, 497384561, 965663885, 244314842, 190422723, 411163645, 316106878, 951067099, 211059050, 807476700, 458071523, 13501033, 462116398, 525262193, 513826966, 717614402, 25872574, 401575246, 120566241, 413874606, 33912109, 860416090, 382297028, 635384038, 165333409, 225524222, 948836173, 136261959, 790496396, 183898360, 173929896, 196836085, 965002806, 959085870, 579782357, 413349831, 320554019, 946221430, 26885005, 83485189, 915706056, 16070041, 151783227, 704404517, 419940589, 597002870, 863603696, 678442414, 391704067, 600881374, 709562601, 70706440, 925175503, 54208799, 131530048, 368459070, 917704621, 267887758, 818446592, 615970232, 622757563, 237499620, 597192613, 148242814, 893148120, 950328045, 778056359, 476589192, 960471588, 227074092, 596387256, 798786580, 714351330, 704158785, 289850390, 660767635, 226382806, 316350502, 843607426, 247039119, 569731602, 53554828, 108871453, 742246261, 845483974, 246826279, 149830584, 135363966, 940234449, 875922481, 277473268, 843357316, 526267157, 723671354, 49521021, 16884633, 301770535, 427755037, 77320411, 872244934, 818241380, 731790405, 76279371, 589578668, 596496098, 292932447, 551815036, 573796603, 969943744, 832910547, 648867391, 170923356, 426518003, 402146898, 91910, 144970484, 677952302, 73634173, 828895229, 245987945, 225283383, 209328476, 598356520, 111546487, 945330425, 189307181, 614821202, 216614281, 703833003, 916638569, 925215640, 101147898, 897301777, 649793946, 852536905, 84735642, 408898834, 224353265, 254902275, 572879240, 562192458, 292916034, 172231268, 315082427, 236825760, 453959261, 617911480, 203048783, 984219380, 774661631, 913906826, 685343669, 244731276, 26439520, 466257698, 288796301, 893972108, 927821600, 691848637, 837521745, 121722833, 812501273, 713151006, 237349804, 160379183, 754137668, 774724953, 577928419, 447761292, 636761766, 383479546, 331520949, 15101415, 278617984, 782959494, 409740979, 228681705, 37057191, 74670028, 187119199, 810208419, 597604201, 639585008, 302627393, 700814335, 682217282, 18225746, 959813116, 454372102, 418934416, 906005948, 295145925, 461518591, 583632606, 722737555, 717882375, 229180874, 648828354, 491590979, 344610362, 83742705, 877552913, 148971676, 107170400, 472811056, 287149160, 776972294, 574267811, 94375855, 867345554, 279901708, 699108935, 975469301, 477370278, 217765969, 613105942, 740980992, 650393292, 904095699, 843740054, 708445692, 982089516, 896913698, 505720653, 858852025, 691126128, 855326129, 803108528, 544341164, 359071449, 202044193, 494304306, 305124894, 479347617, 244006012, 437636824, 7269656, 256267559, 917431778, 916241414, 817202438, 700478667, 136568143, 738508278, 679576619, 164207860, 278595386, 404827509, 405189743, 131934679, 753986950, 540074629, 731017953, 488852194, 163553639, 650352535, 860398287, 895365676, 942566395, 384921406, 643115696, 996223450, 128825428, 570349806, 705542073, 165241450, 29544252, 198790469, 11626195, 405839361, 612239714, 695362317, 581273186, 853162224, 87681875, 641414560, 671409247, 70103450, 447173900, 934132442, 968734082, 367687942, 527135296, 146555548, 96779300, 159257751, 445028301, 604590474, 90509062, 621715482, 175155826, 833662649, 792509154, 841631547, 202385369, 333295753, 185893302, 159435265, 812362902, 397507634, 641293453, 988038775, 188664662, 1649414, 591023713, 635779248, 176216740, 297965377, 724370697, 102647738, 932184020, 590508740, 856672499, 374597672, 751792406, 220322315, 937548869, 608074200, 669858332, 47558712, 883362685, 820284618, 457859663, 507668377, 563658879, 255484267, 377794520, 745664265, 428209374, 284813851, 362625860, 191381022, 871696851, 68311274, 327531863, 563153288, 754695612, 896413595, 914936839, 950237416, 443564631, 331244087, 820882721, 917044084, 202681948, 235399445, 795989553, 911047345, 747067720, 253287422, 259058255, 824250394, 885582292, 236059363, 240841120, 716832377, 620594843, 796847529, 896589094, 254886034, 574717558, 406362064, 944774140, 528172455, 110442702, 306407293, 540708545, 42709002, 431574225, 653647493, 596786732, 887143664, 180292374, 827904303, 683391138, 113441719, 868611553, 555389900, 910926215, 990354825, 38382202, 890181265, 188131845, 110119346, 632843222, 365149849, 916794817, 941492477, 121537926, 336569203, 458683131, 235111774, 151236877, 653142944, 281708323, 563602671, 640719145, 243960135, 743016995, 664485783, 50230281, 61863549, 124733694, 921426571, 804315951, 260418410, 29603858, 868680398, 563219871, 210253323, 720148953, 68830444, 952305285, 734888013, 616183966, 498553984, 200285637, 827816904, 248163234, 322875428, 324638052, 350801214, 545449216, 911165469, 220768782, 502324025, 536475950, 686151260, 358354944, 769470015, 27854171, 163195121, 992940769, 624613342, 365286965, 133697716, 545680623, 408504170, 232940013, 773902097, 857208453, 494927188, 950965871, 994589875, 9773725, 941095821, 762192912, 58831310, 270912924, 89674126, 459720186, 180621329, 491470147, 742696082, 386866975, 137159418, 593499137, 451367153, 650954604, 887934397, 490886032, 848886140, 642416441, 309715739, 83817454, 973822066, 594370327, 980400708, 660411076, 805282717, 87474376, 319829848, 777415896, 626009146, 175414783, 775646525, 210953307, 489932588, 626526847, 749038356, 305073784, 870069332, 36961950, 432322284, 274716583, 677684364, 475537520, 583673912, 12272119, 794997610, 50070762, 526770193, 352235278, 584881611, 540232029, 58580834, 961674091, 217164708, 904670724, 82979115, 85157685, 852467491, 901185061, 294999476, 100542515, 281774205, 171861794, 64453438, 919656102, 465116336, 843672583, 999700876, 496350632, 865811428, 177352846, 329049094, 761950651, 205251573, 502712306, 875472472, 858343954, 133807759, 957960613, 379021882, 719617300, 739046266, 758233649, 707980200, 228686401, 798193039, 348296585, 834210389, 998432327, 176778266, 135263799, 345472947, 459068069, 107982080, 596789665, 109313626, 310471874, 639385985, 712926409, 498679793, 342169956, 877482889, 822579924, 754567414, 467920797, 668965258, 182163240, 275729049, 23107755, 10205050, 929392146, 552380508, 603019539, 286958872, 919764815, 618772097, 517101502, 763320612, 624488997, 715363529, 315714706, 799867900, 209067068, 257851399, 94722404, 876605539, 702777628, 502946331, 822910971, 477363436, 927858174, 71246248, 661369602, 741128133, 683743617, 994797217, 673305176, 518004315, 582433273, 276502736, 389678498, 897737841, 240267152, 429859171, 172766933, 837252640, 87322115, 980135899, 588067296, 129971735, 480498870, 825117989, 340620146, 48282590, 282017248, 634759130, 875306350, 864972741, 790093814, 511775975, 919652901, 724494727, 891485572, 131970832, 501341005, 187321718, 957775263, 2863490, 789264868, 51102663, 344264888, 604061913, 640274209, 868248714, 232704503, 796507746, 336017064, 856013712, 961770107, 886117529, 253357529, 501931133, 836820203, 774270711, 323988141, 273430302, 935280438, 192761927, 744593727, 69103705, 922715191, 80412602, 92383889, 91106668, 689333169, 201951340, 569815115, 875496340, 302260425, 728708420, 965501494, 829406981, 187084826, 524364034, 812676024, 277111850, 293857364, 305438842, 652487629, 47177007, 730152412, 421906619, 579156332, 63109228, 587450576, 387182114, 45576708, 68623389, 68978134, 974028360, 685528714, 920921394, 107823883, 316890496, 952125160, 179621939, 795586461, 306401466, 302044533, 659458707, 445751509, 741076834, 629320951, 179635688, 378313601, 629800472, 449326066, 538502275, 700789847, 324623180, 313199472, 354550595, 3948815, 906014780, 533803615, 14766636, 588478954, 231217559, 270362109, 235814881, 742044838, 130772964, 711407652, 823556420, 935315506, 224830541, 361670549, 654332377, 682678137, 475145486, 229901727, 717720507, 492542533, 869328927, 997480751, 315721999, 911133533, 642610086, 893913630, 57037329, 570056864, 366590497, 742719052, 922413029, 644795512, 600527174, 711734360, 258392186, 823705595, 118607606, 228297648, 888485114, 271683302, 65675931, 338310112, 301847154, 988297262, 285502060, 791813690, 996364597, 56276335, 255502762, 430750993, 425613835, 847851890, 758644432, 180551321, 813179019, 969427455, 210745009, 856341548, 832264851, 817421752, 516861503, 640991512, 312644078, 8142963, 349722603, 248003725, 178631812, 203270441, 560095405, 283851847, 951499632, 710956479, 353985197, 413183060, 501104001, 147063697, 741940472, 452343750, 841670668, 66224024, 476983966, 49823081, 214254160, 52426799, 470145200, 620882906, 636779038, 734157633, 427864766, 562425493, 584415422, 335349183, 17480198, 447014804, 499952334, 297016751, 620193230, 183780545, 355753401, 834697197, 77265042, 358901771, 101617197, 722410458, 652676610, 888780137, 787264314, 526285612, 184754090, 845580838, 150366701, 405987866, 17157846, 169191612, 716751523, 809129658, 166641044, 766665000, 262560791, 448773855, 409114594, 730000470, 675207674, 700508201, 232406183, 119409123, 823694104, 325425896, 414879851, 452619666, 164627738, 519375976, 827790201, 292508162, 684057192, 236859782, 906965502, 900776096, 587140836, 929565136, 155786437, 899403339, 964098978, 445645214, 453344736, 327026112, 79958564, 187395240, 474087495, 83387553, 644179649, 455893221, 135648656, 419158595, 199562836, 339365655, 222627779, 457774258, 431525350, 628864260, 920749883, 630540095, 548739680, 712496934, 141495967, 640153285, 320294141, 524743609, 331786559, 645140469, 364239569, 925275093, 829651665, 83392087, 424999620, 906894153, 920404572, 872584754, 496744947, 132969537, 711006896, 113139106, 786341918, 777711660, 892896516, 238788419, 525388000, 650336825, 242618942, 361763939, 775617426, 558190073, 55224913, 814317005, 431695432, 623883995, 981242659, 128907337, 79261473, 449459356, 484660628, 700041545, 105350766, 972951390, 614653271, 664234100, 324009826, 612208289, 926217601, 248636670, 203228166, 921984590, 623733483, 636741098, 135808418, 710527560, 47813135, 369050863, 88216980, 668250057, 452852580, 629020230, 248548171, 874553189, 192455282, 971055167, 586130414, 562639962, 660422696, 755089151, 795352093, 716535757, 605134493, 87494323, 898485531, 855808784, 310261346, 255176252, 333340334, 914910742, 63197080, 440703615, 413093464, 546850076, 249367879, 501050325, 96843418, 702372087, 36772713, 160066841, 706375361, 190829434, 789259789, 139947948, 131026065, 412032712, 681607310, 822001186, 739775052, 463444877, 354695303, 324636480, 805575896, 491153655, 642242519, 624691256, 515732839, 666061975, 344495069, 933154195, 339429854, 457301561, 754181916, 341590796, 947800177, 819945391, 884583814, 485548176, 689525568, 403634928, 409466000, 38887573, 204295343, 651951097, 150943665, 269366518, 514781455, 64910138, 381831714, 705266450, 183010173, 727476922, 879585002, 662247694, 486145576, 486301845, 741087862, 661222870, 943789666, 346475047, 955810592, 296876428, 446477246, 247010289, 873959475, 595335208, 980239066, 504952457, 40807405, 730695579, 546543587, 515069889, 906195681, 208576015, 694513335, 360224806, 63122818, 561749832, 358918381, 949577397, 786929035, 336920072, 581622111, 184309981, 40300648, 596900219, 54715844, 180976690, 123680843, 381434712, 858633768, 57659419, 823227392, 763205619, 730683986, 463534579, 422361228, 996519059, 844684818, 739188648, 666827056, 64523057, 565082396, 112780229, 467412361, 888256285, 45795915, 671085194, 212164651, 853191140, 381103441, 571244460, 160525992, 193614632, 584857379, 355477581, 646333104, 995732027, 27053799, 849612721, 64480452, 189427443, 433918848, 364684891, 940925057, 625758889, 236369165, 785530870, 296358066, 342510720, 528250656, 591677778, 151083667, 519489807, 676477578, 293052419, 804113470, 922883096, 43254441, 778684162, 422078569, 440022828, 756746986, 114050149, 738275832, 49006232, 773407086, 717008139, 931960344, 664357353, 503219258, 309609389, 687142738, 226739855, 988016051, 551085207, 586694530, 651734371, 745212757, 408469902, 852277307, 723188795, 987319197, 615516872, 985202286, 43393697, 657273157, 256541788, 461479800, 897232080, 949128824, 791130069, 548040030, 459913410, 689817108, 180239469, 737209965, 871750815, 767400657, 55165515, 627355095, 447861194, 202092950, 225465730, 696451203, 189950495, 250280824, 541962474, 10331367, 405504058, 413018999, 234822340, 772048043, 645292841, 625276161, 408174264, 691320949, 565124391, 722928988, 400534918, 251042911, 963092232, 795206892, 711777713, 180019144, 953781872, 200196512, 82443972, 815531906, 374536470, 183923702, 816934875, 999045215, 110209325, 975552199, 961118380, 761915771, 37347245, 495713255, 642758530, 25654987, 981228876, 539057691, 474415701, 477588711, 975643869, 104864362, 267024667, 136661166, 759149100, 330965707, 799791015, 945504294, 785921051, 280481216, 756999593, 947563130, 938028498, 543947618, 412830122, 999107186, 284461167, 798509217, 576869634, 128382748, 507484701, 612575583, 927829610, 876335535, 838048108, 676333356, 610668981, 744832156, 104196194, 795051530, 253122251, 873638111, 461886272, 115415884, 40155985, 223452081, 992046983, 804673188, 830726677, 56503588, 989595204, 817185478, 74005720, 570972128, 70413347, 176948037, 440985196, 124049623, 323871846, 169387349, 45784413, 371984936, 185158163, 905795779, 328897391, 393406693, 448328422, 189325244, 703292378, 688870410, 380770915, 252730932, 688392139, 114945196, 24450013, 213570293, 356330639, 753268155, 58675197, 598772808, 449277117, 890025478, 718306317, 734216528, 670685708, 996934905, 673786434, 754269863, 936391823, 13103536, 534646643, 250831174, 33902083, 383569367, 45004999, 629092415, 368193914, 287604506, 947133398, 852214426, 933125729, 845325277, 713145590, 74654635, 102851907, 403432060, 312665871, 123264000, 625966133, 760954490, 509620101, 934087657, 291322874, 439707946, 169989498, 131252766, 794935049, 543949886, 241171069, 548835688, 733747284, 707488206, 331304470, 30584544, 473835051, 1557906, 744831085, 309662149, 443958956, 974229454, 28159170, 708122587, 198695791, 223979635, 600527380, 987418775, 740745496, 551923481, 823417845, 313297411, 802214285, 941282753, 265921318, 291583297, 937848783, 227489742, 722803231, 3360986, 701196984, 425692090, 208594793, 381123193, 207677452, 290634989, 789824312, 244547166, 672454965, 871970986, 817378632, 541835190, 626994109, 236922642, 767610432, 183508428, 995148763, 243744704, 1549748, 367666494, 428528970, 76300401, 931967167, 485005240, 420604834, 834257659, 314716261, 491564122, 290242899, 27075944, 40495388, 823396742, 228682072, 927755553, 915496475, 648156172, 157059296, 994690042, 850514952, 110284220, 3676784, 867711481, 834591536, 626038521, 967362766, 336619041, 492024852, 785901532, 584827752, 85392787, 751217860, 954405261, 234210752, 243930359, 83237078, 908446173, 725590130, 580869321, 890340564, 788537183, 983390195, 548297436, 214791383, 744003326, 25553673, 381052978, 984140820, 496127763, 297817217, 890792019, 197807239, 38987652, 459234868, 728984012, 643483674, 497330288, 662900275, 321223743, 485347205, 730869153, 553241487, 329975402, 432755758, 64397121, 473324643, 184134586, 432295179, 459222683, 648462649, 557424872, 995417926, 355301122, 24354516, 50980879, 395967329, 144082917, 145092221, 661382764, 53309471, 456673319, 456926674, 307418535, 661221677, 339395757, 462873456, 626186282, 256708673, 373334824, 633718808, 849667309, 813657811, 723590947, 736969934, 947884727, 598697673, 118665293, 318748527, 983231246, 429134577, 285187985, 760828665, 515583167, 967156925, 172091964, 759660727, 802395570, 45671012, 266288098, 396178150, 599814848, 997179029, 945414470, 251257609, 494205505, 287089243, 235319113, 592801883, 412370965, 893660806, 898322355, 963093829, 810047984, 225603925, 847217490, 47755231, 593587376, 328357034, 88828934, 385374161, 153525135, 237910531, 761997598, 716255073, 127264059, 102165780, 798850655, 106257163, 489545805, 364659480, 445289145, 617120918, 838193158, 942560747, 486148315, 768572483, 533620324, 151545625, 449235677, 708332750, 780668734, 961382023, 417583079, 177479143, 484711677, 576121451, 460636831, 396888176, 265039553, 116831476, 536791579, 90911221, 187993607, 520881192, 262215117, 485728551, 96565536, 461617423, 219279345, 610571036, 541173918, 483546494, 518087628, 611985097, 365814953, 803026773, 433958196, 657973633, 472759331, 516508069, 858704818, 753934915, 509898239, 977028045, 156642797, 840691469, 394852559, 112870469, 488558356, 140065675, 313726185, 670565406, 569474199, 791514837, 339814471, 489316920, 687362973, 161695789, 840699801, 280103047, 658451198, 301112922, 898934562, 579794834, 828539917, 284535968, 536080739, 656485085, 217803908, 136029114, 364592255, 298041991, 565126409, 382986756, 137643822, 836004327, 296499619, 891943245, 870060751, 78908171, 260805666, 483183050, 297932747, 961249878, 989824821, 267582850, 722687313, 822136253, 217932606, 681510420, 495694433, 677170372, 698206915, 190850406, 797870059, 131916928, 477597394, 246946451, 291887805, 140120876, 465247370, 612530074, 518623097, 224240047, 578407786, 891828839, 297564095, 763465029, 541046622, 776903408, 784897426, 551650668, 768326366, 577147637, 562655433, 42855284, 145209377, 838561613, 727839852, 132314521, 219810208, 168193454, 990216315, 498488259, 132990457, 73541773, 752934563, 425384649, 23649230, 869993463, 470323569, 61414262, 618922620, 917468172, 400656147, 887092487, 345621515, 338587717, 641005139, 507203655, 177704044, 541349606, 137375360, 857531933, 912595422, 408030270, 932799040, 753643114, 870932420, 445438362, 438550427, 359547224, 640051100, 600379750, 796857665, 232069155, 963698675, 481887894, 232962489, 870476955, 934453371, 645632162, 142034901, 312665184, 30674452, 619107333, 426451601, 77110672, 94807317, 907241587, 101967460, 221955660, 757526006, 954755790, 942162034, 854779538, 762238615, 784233947, 347875443, 417366959, 658555232, 59099005, 244781466, 543710733, 842886704, 432508333, 393155854, 858906094, 80599492, 73147169, 861138707, 787569104, 917991970, 522206755, 714043738, 895844013, 749987192, 799054013, 376853619, 607603741, 324732491, 58378468, 10734232, 846717427, 133543943, 25794416, 728836054, 185544573, 713086903, 254964345, 159104288, 831271977, 801834024, 653701047, 948359217, 647814639, 29534846, 998846316, 607070540, 645077441, 250950202, 969946497, 928268137, 273474070, 524975746, 941119453, 496316064, 602921351, 141022093, 694932747, 632349293, 131208014, 418977347, 45115832, 704107886, 537116735, 192297645, 314607717, 953615882, 497634179, 571907405, 734933090, 849253627, 834978741, 831078031, 118952545, 559901055, 177692889, 955729680, 470325619, 628378844, 805980295, 232695773, 194091150, 765316558, 264667766, 347724967, 645024954, 509020153, 18654811, 279432131, 438275488, 726409903, 603613257, 555216038, 800125134, 80004240, 824950429, 961162482, 191203985, 589450524, 639600393, 460828096, 298330040, 836247191, 991078787, 453576447, 424595779, 723107714, 925530103, 931071910, 119512693, 431848950, 485738496, 945551756, 653331590, 472211758, 712829345, 376476081, 237111438, 260102306, 478064803, 367731145, 160211268, 296397341, 620532678, 720256517, 344907399, 957555624, 42703193, 343431014, 683717440, 886407758, 924306473, 634782376, 53062846, 325599059, 759169470, 649709056, 931761784, 476281993, 534038740, 700843252, 570603394, 601364427, 194392050, 842775318, 469249749, 701853074, 873100606, 260145804, 783376672, 974173400, 455187182, 730708821, 526697410, 358899363, 549555776, 963849339, 949065796, 455894723, 655683586, 600403109, 340520225, 529868543, 750526407, 3426174, 941128382, 356346524, 713774498, 295778664, 924007909, 986512005, 554515651, 339482173, 168148414, 886281483, 271361685, 360314311, 371421811, 308864803, 112048678, 594422957, 617398656, 318488539, 73615751, 455433302, 77783618, 258330439, 402344120, 979471355, 4175400, 350769851, 951796972, 448117163, 122615603, 676989872, 913433765, 254703514, 925537937, 426328774, 63096041, 444655398, 992301706, 610533703, 447973676, 531032294, 427458416, 957013864, 848494138, 450267574, 718921505, 19177184, 148487823, 811377367, 854858268, 597531161, 514789359, 189870802, 769864862, 875041114, 484699551, 796492567, 155155807, 8735801, 203172456, 692891235, 248263748, 222504507, 647491988, 631444069, 34765159, 152749936, 56620853, 615127346, 536275104, 157288524, 400392040, 935873692, 541464270, 727442015, 910629926, 10586094, 524876467, 312556732, 609655846, 562349411, 167015044, 846481201, 1443027, 564643169, 236789474, 598347943, 129482182, 371989832, 968326796, 511162082, 969034366, 618514097, 207188946, 623874379, 507527653, 388491810, 447252894, 250082802, 24792015, 67362584, 92213120, 293468656, 564296153, 899591039, 306508672, 781641092, 486784090, 738651633, 98077413, 506311002, 770202338, 860612112, 69778877, 708644928, 689669537, 293548091, 635238270, 874979777, 65181445, 169368514, 10853367, 670859233, 2532985, 161814056, 552392806, 555009002, 241595677, 708099808, 517698307, 607663936, 813707841, 999864652, 874480711, 297939463, 524761197, 14653400, 655293068, 829418114, 696892996, 756866238, 632884198, 275640976, 436968294, 909176543, 321541093, 118503604, 385711179, 60694275, 692663369, 732603906, 848837444, 360585900, 282966591, 356117635, 706605430, 137987924, 17632013, 881379500, 733205184, 837552426, 189102165, 288273235, 593490584, 199017395, 365808814, 841338826, 436534186, 925603845, 448098654, 311130140, 410104357, 145371804, 368739866, 494939101, 713582116, 174333373, 184939763, 846351723, 762191864, 260023917, 750390531, 356576356, 501984764, 212098112, 913393707, 108447691, 468229078, 664046440, 239682788, 857239942, 449684641, 343066460, 864044819, 26729404, 450330861, 616186890, 696256023, 603818058, 678451372, 103000522, 62245522, 986813211, 663276948, 948638499, 720914815, 791762142, 613731388, 277877070, 523627115, 600541302, 503884373, 900955636, 137193387, 654947722, 259870537, 390203561, 963845624, 202880841, 761945648, 871897704, 516774410, 798838292, 981495853, 850290169, 178955864, 318398418, 776241989, 211054370, 289271639, 848641857, 568613800, 876354267, 44653433, 672300479, 469186228, 623840781, 845690516, 815054461, 294848310, 324890351, 690968965, 360381367, 726115652, 917859776, 151416661, 970644150, 955848730, 800068228, 354443263, 880631162, 280412882, 317905827, 676651330, 618938725, 972215222, 14390328, 718755540, 320173901, 217276618, 68374163, 28282400, 719808279, 389961864, 795474300, 890691048, 206732238, 687023500, 236095474, 512398992, 234671191, 56965893, 396622391, 554898632, 789998126, 989026781, 934739064, 999832038, 740514002, 563269011, 494074657, 732695522, 597648407, 471456954, 448401404, 262881030, 91675191, 642934117, 321947271, 504949812, 912961132, 794399665, 331303528, 918808035, 535008711, 7587228, 18609891, 456780448, 318048633, 110152877, 912356230, 787868620, 472867382, 693877183, 742811469, 962861992, 546273365, 660241544, 801081023, 692437152, 535247731, 103808460, 338058762, 605629637, 775337911, 921653884, 488225311, 253219099, 352930452, 975787692, 268652965, 950166313, 91480474, 176710196, 502397806, 987992756, 298897589, 133575368, 105223530, 643831167, 256933201, 731403125, 182023127, 316529595, 770870482, 442798077, 540149669, 844219527, 503138249, 120786691, 603643212, 64510649, 533532898, 321765574, 508042822, 217130401, 857310220, 924789997, 355947722, 973247050, 518708241, 726550159, 495760113, 862189768, 934580745, 369848982, 755809518, 424244120, 327477720, 659416301, 729166886, 267287833, 71002540, 122489439, 646192860, 127800598, 308319179, 926640906, 678939701, 833420900, 74008312, 906820409, 894676034, 451971812, 5234458, 449728887, 504540994, 788617865, 792515867, 244128384, 930280077, 901640975, 211718300, 60758147, 222434795, 603977905, 869363044, 954827651, 136193038, 856901867, 604493733, 536137673, 270556835, 650865452, 990112879, 579407712, 285466468, 84276426, 317807844, 44409355, 830410998, 992808214, 52582992, 485694771, 410246126, 250086791, 717356747, 752015676, 43675827, 859728280, 503391041, 592527063, 374801011, 109198477, 765484365, 901494838, 102203092, 549733369, 457513279, 337300608, 531107990, 197371915, 636206344, 947798329, 407563423, 508312460, 311750899, 907336130, 277541288, 373364228, 29586628, 996092865, 213545907, 981998265, 334273761, 421375664, 575775645, 213322676, 677091236, 941371781, 610748748, 883535885, 722606944, 313226247, 498883307, 390620458, 979733316, 93475218, 831318687, 514038045, 565600440, 869749559, 958377771, 998508172, 276231531, 243675311, 625245251, 739065227, 811477956, 653236344, 209665994, 774551807, 789514996, 787277727, 664742260, 472705056, 394730302, 551414688, 249700602, 91623729, 235029717, 715896465, 645074512, 851061532, 464822213, 880358816, 737432343, 807362256, 419983330, 912715826, 422883087, 607729665, 709972920, 852956621, 199129854, 939845782, 729542328, 350908165, 419132844, 873351836, 63681800, 430186801, 945898468, 11843500, 341250834, 161862762, 401399508, 476633053, 351362183, 661478506, 711523692, 664635452, 127521554, 343637772, 691408170, 871516736, 952249244, 119495027, 503000567, 161377767, 436700838, 61432277, 740215913, 760911115, 806826017, 17393464, 456114535, 660043819, 398891011, 2392221, 400135915, 386826890, 689466999, 713688134, 31222215, 430040637, 15397269, 696679662, 344539490, 159593547, 606162511, 675511966, 543908561, 30956064, 521781742, 965036053, 355927463, 507278445, 808832341, 599361838, 962656565, 838691170, 464392432, 575140447, 239206885, 407102078, 773437260, 277867256, 634929674, 938643995, 885547306, 229981804, 643391925, 406272276, 661620704, 12773303, 626677877, 807719602, 694808463, 533772553, 928477316, 447118798, 818351744, 736135306, 278714246, 617771535, 228596556, 733345746, 172041772, 586286108, 582744252, 34820417, 934418430, 915879810, 576201884, 37335739, 948446115, 164486926, 692415739, 440441071, 285978496, 602728283, 835647083, 29387659, 194719988, 125446520, 32358713, 699534017, 773938813, 403940033, 55091871, 85287162, 990138223, 560056961, 829072285, 696810207, 681136031, 170849262, 710908807, 556076114, 439807349, 193397743, 132995189, 120624212, 543881837, 170423549, 715228885, 239794744, 678325706, 264857848, 889393789, 881234867, 590511748, 170437308, 616938436, 125765940, 172907783, 791695899, 926493659, 464197865, 353293499, 475348940, 213925835, 303923102, 722407112, 929943426, 967208753, 616732604, 278345723, 130642812, 890375981, 756153304, 39597564, 797272049, 215716467, 256696200, 19727823, 577630247, 59695919, 469209783, 736165615, 59124112, 643400447, 33082423, 43270446, 311392766, 261784400, 414466271, 479231249, 230225301, 557091894, 744896922, 415333048, 813204167, 460532690, 254638499, 661486630, 439245741, 495042326, 616479721, 101139847, 113508295, 803267316, 758147576, 448782773, 672402615, 94295304, 40111309, 767446526, 222513502, 853201236, 351848265, 794866899, 945061240, 206127461, 640665689, 569823615, 136896704, 586452580, 675143196, 408099955, 642832419, 554533527, 662333450, 45611494, 215551343, 611828506, 822572184, 997932087, 4518992, 232092804, 171948497, 403176431, 917632277, 505829522, 554701015, 613164500, 720420009, 134048619, 962925731, 621568595, 84889183, 974075413, 797681044, 709812217, 394464771, 128711765, 105792990, 482697341, 247939104, 964903511, 421536940, 970787708, 697981718, 382966431, 459490321, 535435982, 505872483, 173931060, 400512519, 412938560, 361236570, 628800345, 646887585, 807438378, 664969845, 618506705, 951677045, 172305409, 158534881, 819353191, 304469732, 215909484, 188785346, 68280068, 354981002, 438376075, 977561801, 91027625, 15391133, 859770543, 100922335, 465518089, 830480080, 425497532, 241398364, 226479409, 355563100, 645492448, 126217610, 744128704, 425046853, 642121650, 30391372, 985991285, 34171875, 228051268, 226775854, 433184018, 234874876, 365547966, 442497745, 804330535, 459366168, 667183087, 946447518, 831972543, 648630464, 605226207, 15936626, 266104203, 928401065, 57732762, 429838323, 935634802, 58913975, 415377031, 694697069, 360531323, 883398389, 403556155, 48384638, 752255980, 373407384, 194285634, 618180992, 693949784, 360141927, 516281978, 241989021, 510209490, 997603785, 515556538, 101223502, 770807684, 544254391, 746058750, 147040516, 941835909, 482109204, 369311636, 948142370, 346984274, 683779079, 934868637, 437714673, 32345929, 824166278, 78121923, 903492092, 126907110, 236319361, 279781275, 395278401, 12740161, 282930929, 857491836, 995383234, 59877594, 218614278, 109587189, 819678733, 862981918, 497110289, 423772751, 743988813, 216017327, 196127784, 135557291, 80102992, 14082792, 500507035, 95839312, 610754726, 997087623, 370214764, 968498327, 898666611, 228795535, 937716255, 875498128, 24088134, 28628960, 723015622, 801550803, 444954866, 383625904, 91217850, 266927696, 750263464, 607437404, 387643906, 211961695, 733636513, 158999402, 24960510, 236388705, 625265172, 726117970, 31982353, 510734366, 463757324, 566973950, 786406013, 477980525, 930438964, 901706294, 860707095, 879321874, 743621624, 934986064, 6452982, 600972706, 75782238, 531359397, 705365214, 711587378, 844320094, 865376022, 151888007, 237539923, 103611569, 257092365, 961751961, 166378975, 104528363, 609420674, 522658952, 673098145, 605683296, 496376898, 408465694, 705058138, 772174868, 471996499, 839421991, 284014352, 616403670, 117997973, 494157714, 553139973, 139431309, 217946473, 645434059, 947849679, 561748685, 282029981, 265538002, 598490839, 596566869, 126613727, 664032027, 930041323, 310723274, 161269590, 442177812, 167310830, 173111709, 510405568, 365030832, 701709530, 8873850, 587301703, 329828177, 645245460, 599126544, 488803472, 251881035, 267734662, 699514202, 728391431, 271423411, 550365434, 592407075, 416588279, 6106566, 949405354, 673861085, 910193563, 626365489, 287940460, 854638037, 78054619, 69933368, 533825186, 916381143, 607264060, 972066406, 846389241, 119249038, 516307467, 887778031, 419888112, 607830426, 628579381, 939973766, 735255996, 807130276, 518563472, 131836026, 917686741, 385734650, 354299322, 909133063, 569951185, 647744383, 216158633, 330516927, 477174019, 700383285, 146450008, 724881768, 329705851, 405092927, 305604775, 795471501, 818192319, 319930039, 289705598, 980834144, 778349753, 782840933, 974746145, 797660294, 294159891, 26796381, 539284343, 246404618, 742725893, 439514298, 942417340, 935921148, 633476721, 209196527, 385306031, 985649863, 895650980, 6863620, 780117140, 879904647, 554641374, 88502107, 505743468, 841918307, 146116068, 586991844, 865706897, 914774851, 885218806, 802554939, 18389092, 794878140, 650489913, 638802213, 598526939, 962278799, 280695272, 562803989, 410543260, 613146685, 923603693, 651922183, 318346254, 650757548, 848484349, 212965983, 490998855, 512256312, 584397912, 341075315, 532594945, 697664204, 116250480, 279601465, 812556712, 257661483, 40205666, 915982557, 38613794, 940014974, 416861751, 757605925, 744666510, 376174996, 979992629, 274024660, 553881654, 804670385, 380618461, 300975532, 225642312, 751578573, 217336348, 727465124, 500438568, 892613006, 872942304, 824004352, 37917579, 738308904, 624667272, 774412247, 838241541, 231217687, 909784506, 382007631, 541671890, 501417076, 712762937, 236614192, 460215540, 388642706, 467650651, 439515344, 905312632, 547398140, 175229729, 164083787, 851253606, 42844686, 392034769, 902539475, 559251213, 408572951, 392344946, 199777530, 94078123, 460407565, 979117543, 696060460, 926045814, 312274761, 778534766, 683742792, 435268549, 561401955, 674892463, 160536561, 413896853, 591974804, 86000933, 665385914, 610098366, 617126639, 313366570, 461330973, 41523775, 607219843, 517747207, 337981062, 997163439, 946153441, 448596743, 942766262, 958744106, 133791885, 153803197, 235110133, 765584384, 833934322, 986949310, 174285622, 225723511, 380568936, 354434129, 390391541, 763655613, 266568166, 666069320, 521499489, 77270692, 250583850, 312694997, 279961443, 551970387, 203125741, 129718452, 348315492, 183080260, 281839220, 575369447, 892396673, 745208405, 522744583, 189890407, 564035126, 538634507, 728929838, 415186718, 843974413, 982386247, 987052200, 598530335, 438719681, 254088391, 105571618, 847792586, 679008098, 692243650, 667425033, 239291041, 42380017, 221493115, 870591389, 475734545, 629753745, 385719192, 850855311, 146640576, 498490786, 358602373, 582424179, 908947287, 567999355, 657613909, 845462147, 203830528, 853543398, 916135926, 927896909, 877858363, 544395664, 68118184, 349074983, 309394988, 836102491, 167050540, 117425494, 959563389, 437047162, 158452583, 997547443, 59369516, 623771574, 33315108, 782684884, 389009987, 707618406, 664343513, 642378231, 275515292, 511569180, 587922370, 194719000, 575658345, 486798891, 386541088, 834323081, 736199022, 992187288, 983662261, 590661068, 137072877, 589232649, 44771480, 122600349, 761354369, 214648451, 504494473, 809581843, 756279604, 364247377, 770446529, 543405904, 36197690, 10746926, 991502904, 705310650, 737396277, 156374889, 369353897, 206176914, 803976760, 648637382, 983737377, 466021404, 997498758, 312392661, 412059754, 634944997, 558488144, 220331065, 16663917, 659662798, 131361018, 623094907, 114281053, 521619555, 152610435, 966473759, 27462334, 712899894, 78728007, 659503235, 762712121, 723445028, 764824883, 471106539, 439908675, 293581246, 130111214, 739706556, 801654729, 657085408, 997731561, 730862507, 340793654, 809387852, 668444232, 954104648, 521891632, 454096704, 560192174, 184401775, 300136081, 194465941, 999382866, 710593045, 529496994, 589042668, 808315447, 99912725, 203248008, 203574866, 774031918, 972786183, 431051661, 547180888, 829497923, 123829015, 13385061, 53304548, 191468087, 469086269, 572064538, 567771303, 829235265, 482360781, 844929154, 384500667, 915863378, 910589232, 772944893, 986653997, 477050993, 430841152, 890051735, 484944879, 671712210, 299506736, 340503275, 852991232, 605824330, 205138596, 311310158, 202085843, 202694224, 853916510, 329214280, 556985976, 606237378, 763985278, 178984458, 756136700, 968604744, 949544714, 685590437, 951272555, 817817570, 195714710, 221208594, 619803964, 531429971, 379502002, 756182903, 294720222, 420712945, 810006584, 669134724, 192068446, 363773798, 331898381, 724573765, 759656758, 685814402, 49956639, 716610814, 434566405, 218598583, 225003675, 224148492, 981862637, 486654405, 592681241, 510037773, 141707123, 248909498, 761951562, 299950984, 316427512, 364835216, 790104135, 15454901, 739811949, 672309511, 9925441, 21137867, 504015020, 966233413, 32498157, 328654124, 653362152, 269658752, 78204251, 714341093, 487356201, 29285221, 81267284, 769112194, 252356259, 850322082, 967678746, 98878329, 340551754, 528563460, 905047227, 871240021, 852095466, 746863747, 840960943, 106838351, 209833779, 660129878, 329400418, 619583635, 918828915, 137344802, 280261916, 181067141, 880467829, 132583675, 177515781, 177903879, 248942253, 291928777, 455926319, 649536428, 266353817, 234345160, 485775408, 269111266, 863225699, 487064245, 209962751, 792606983, 527745092, 162485910, 62781153, 618097462, 282645244, 769179877, 101538608, 602027593, 834811273, 711641692, 397513513, 207139755, 892815717, 927679121, 6310730, 144832737, 145664187, 423653719, 449717461, 314198714, 415157770, 626611522, 953234682, 867177724, 454176279, 879923766, 884485530, 19540780, 946593613, 688122487, 821889154, 705760589, 20976396, 515851448, 519316316, 121361413, 977087503, 671664347, 327051579, 617914432, 548707444, 853631591, 854206912, 437842297, 994634750, 746133515, 182249385, 39165952, 558112973, 770791927, 63878687, 299807914, 760880782, 828186369, 218976010, 558205834, 137368030, 92211752, 415799361, 738015441, 183092287, 908572263, 50645592, 39325517, 588553482, 133396827, 659426826, 81665373, 867285546, 759614466, 460310507, 900900699, 665285494, 508476725, 379267780, 784814464, 337267961, 136768356, 855890505, 22369809, 260938570, 808887591, 834369491, 661717373, 850643942, 657356733, 617527452, 364995861, 483484468, 7904705, 828175387, 885267003, 674198968, 456693761, 56526650, 942545862, 223784335, 78338344, 498834117, 849926572, 621662099, 921082811, 747868162, 290309161, 253197924, 959462170, 936185687, 856821773, 209010577, 970523685, 263701348, 381589662, 178032691, 1088701, 793620432, 648387210, 702453162, 806195245, 249976854, 262047077, 14110629, 156840723, 568791719, 133477763, 286531738, 681461448, 30422814, 161140593, 868790496, 522240312, 355868955, 107604426, 302672409, 173776478, 54028288, 998519616, 801047858, 416402295, 500827539, 787457419, 849903330, 813688780, 756236473, 948074422, 5226952, 536894621, 937728589, 824422918, 655091717, 787591886, 381541707, 547966634, 3837172, 312569655, 440697112, 200102488, 6538186, 848530684, 107191436, 918232081, 566932724, 261474713, 347966910, 911883112, 252885988, 514535175, 104292308, 296807486, 251479486, 414122830, 239658368, 683862440, 146187693, 894457887, 867064483, 9741683, 11604689, 596985169, 30033296, 340698719, 520360990, 441384873, 360638076, 873926482, 816497718, 622291111, 868504535, 735187792, 501696107, 767870749, 951086003, 125257219, 228512018, 110501953, 439308314, 102913476, 443666503, 250888797, 523940583, 96687260, 560204626, 724735541, 826148648, 204007851, 542174534, 384361098, 15863489, 458137295, 454518200, 413930109, 70036134, 87143234, 459653150, 242502135, 235679189, 132606056, 176663868, 224469667, 937037758, 650980817, 887553224, 159163364, 128139103, 814701716, 434680363, 11769828, 538744938, 484830589, 45002843, 229404450, 423606727, 168417424, 233589304, 831218929, 133543932, 19867968, 2923998, 250817978, 348089072, 45177445, 261014359, 271961651, 950706772, 982984501, 815801354, 778748614, 210490024, 36896189, 837668615, 394451856, 601180554, 428996903, 295859504, 791419764, 691800114, 315870807, 118728514, 388586345, 211240770, 771942025, 864677397, 74405962, 254962201, 241941500, 460361167, 879359871, 137814380, 202242196, 286741381, 731103936, 720807142, 386871611, 863233703, 704646216, 870613277, 578920202, 857621830, 397239726, 538938703, 948694484, 712691743, 114490443, 568737163, 287235959, 781448780, 373805395, 379739626, 925328378, 852977412, 574831712, 831427570, 704239091, 734883900, 472327871, 460421949, 630378348, 294788402, 736137074, 569468321, 915590345, 989713209, 759700648, 324826153, 370446228, 548585538, 3483480, 585074191, 290397465, 392679798, 35956585, 329552010, 514510663, 217793144, 403007688, 762018495, 458783533, 376985002, 565158565, 930297642, 177563218, 133456298, 714069419, 895002449, 358339454, 434654277, 117498218, 533910944, 51296917, 777598610, 808386509, 490307965, 996188675, 662765488, 473617430, 353030794, 861960846, 361595033, 612307170, 566510960, 493269925, 843322204, 448703916, 720567881, 782821985, 157641290, 674377988, 412744456, 506759462, 69880212, 223550555, 523045247, 836619286, 322687732, 735159838, 899780520, 242102906, 497873235, 279263998, 747861478, 432940208, 645286845, 305129691, 896641871, 801833820, 156317417, 309342501, 626064826, 4658211, 60203147, 201718825, 898529684, 51929842, 162727778, 493111582, 451815086, 153106620, 984570357, 402796434, 634477666, 393759029, 346694909, 697285963, 612367006, 565894980, 783051789, 603505452, 499055525, 152828487, 754994279, 109366342, 968532721, 279300713, 111785572, 790296007, 52088168, 365259637, 875762315, 217672258, 742907160, 872095688, 996639763, 7278969, 642035053, 2456826, 990473738, 788825239, 719340185, 835531628, 146449995, 7328219, 456312625, 271758112, 748961495, 569652990, 312572441, 95944264, 185734586, 647471618, 900141524, 220506717, 541310388, 638780770, 381875974, 493116061, 315010988, 50698114, 877164747, 366785181, 239083156, 960201210, 352729476, 373583508, 385207052, 155629056, 9562201, 546169022, 404706205, 854620821, 43165603, 600422817, 647896412, 764942737, 472296985, 925577247, 967793409, 46594537, 122154268, 56456646, 961378838, 15572830, 515661368, 230113916, 435352678, 363714652, 515239390, 640142164, 871705520, 626230107, 176519061, 478766313, 33659066, 267646046, 165087496, 882937051, 736054402, 633890050, 800093905, 736947250, 279122783, 898893195, 203073472, 714280634, 73468937, 201578463, 726874711, 676971470, 40789946, 906154187, 505441757, 546403774, 718777162, 1320505, 501622386, 380663328, 381966696, 674607664, 36626952, 158978260, 988402846, 763071482, 48962842, 910064687, 333883331, 884300105, 677024987, 605131675, 380891314, 128125766, 12054545, 455642305, 352140172, 639790342, 589816577, 515093184, 782413156, 737400802, 37860472, 916954425, 26543553, 285646576, 454467177, 264226227, 178222529, 630261915, 977118949, 134034207, 64550944, 901206823, 419728734, 578225190, 22751899, 23231929, 119059507, 246158966, 711471722, 560602619, 881810171, 622284641, 781512642, 461978102, 797558306, 751738941, 169635996, 590152176, 891124479, 105898123, 353593446, 123254435, 856404141, 883037618, 649872557, 929368945, 341905128, 619607741, 986120260, 367042722, 167118840, 351065050, 431525957, 575485580, 148519397, 13970692, 314429121, 484032700, 417467836, 168100353, 761694445, 201353907, 594566865, 202223139, 69498746, 420017557, 127305995, 422014980, 75967405, 641101275, 195361447, 465532064, 309069308, 509868414, 994364225, 854459928, 730662777, 944962349, 16995892, 582822653, 136315691, 177161732, 59909641, 905263521, 228107381, 793788378, 941674456, 932113413, 438223489, 167059745, 693530433, 804694598, 563196, 185895216, 977092607, 377345577, 625346979, 894697558, 172194807, 483144620, 729083381, 209835128, 876290962, 23863170, 430868818, 962415750, 745440670, 176263707, 193372469, 926019522, 16408841, 671460411, 893448944, 200712874, 647217674, 801659167, 454724292, 32927863, 969419201, 721065554, 302249436, 817952175, 263743221, 701427363, 772657812, 722985135, 737068468, 2245480, 200515700, 353025108, 772437538, 578840943, 814817069, 60628124, 450604027, 457588802, 124781510, 590054171, 369327119, 562343553, 735320636, 899843932, 645561853, 444608380, 729346066, 544041530, 319683421, 950172554, 972706280, 294023316, 108855092, 690187058, 298066644, 237991949, 56300104, 557383312, 903650946, 431462802, 996574024, 90517425, 696667221, 322072160, 840324208, 257611327, 139227874, 474343986, 408779906, 680804728, 49398872, 361467534, 427251304, 904378778, 965565784, 891832629, 970380402, 965156085, 1113530, 33313838, 857626916, 232892871, 583991768, 705467003, 778497392, 205078735, 738347240, 186271717, 236503821, 377503963, 236145198, 643050534, 395204324, 449826253, 515166755, 389739614, 519562782, 451414252, 272603606, 80303885, 478140079, 747443672, 835808730, 330516652, 395206263, 550984081, 367793575, 742226480, 176208582, 477967070, 13120154, 645111006, 240288845, 109987970, 491175910, 890937457, 267498712, 36260988, 17309905, 302614077, 845067055, 783262864, 832390674, 581407792, 341566439, 352517925, 873768775, 652457552, 419769791, 598323106, 61569741, 764913497, 853680857, 929269900, 191354, 909447363, 368504218, 938991757, 224900203, 469951729, 461951975, 421537669, 109349759, 60349943, 483888951, 47077559, 7722520, 83097203, 894563038, 758428978, 472456979, 695286616, 777693494, 619957029, 366869462, 478877761, 199556943, 170030324, 391040570, 94320476, 802622525, 896584595, 67520469, 381687491, 643099154, 128471461, 764812447, 158414994, 929178398, 267900532, 800792253, 378495174, 318952110, 504477026, 451240893, 806402794, 351306310, 631630553, 751356496, 99856087, 275389729, 834700934, 480625338, 82619718, 766927405, 490485748, 446327061, 258245237, 791592607, 46112091, 826339847, 434735331, 602098783, 482564644, 321288696, 555577203, 7491220, 260812504, 804784331, 20232355, 842951152, 554668588, 501289019, 699536915, 929167969, 130810584, 871237691, 941004693, 676591906, 694646017, 568475179, 840830264, 406018108, 98701967, 554564370, 883671924, 56310139, 720916321, 1110688, 434432524, 133691844, 919845340, 348079066, 761950056, 78568351, 740586577, 393530941, 375230404, 323136665, 59924376, 223918873, 97958456, 680263865, 586381517, 363212632, 439584683, 695185523, 966894152, 62883090, 775893117, 641408229, 151224402, 459226600, 835871519, 873496096, 700494584, 494397061, 494798699, 576641521, 87420749, 977312338, 162421353, 737643411, 160487964, 623889051, 166968274, 216128735, 367886578, 971935818, 387382014, 393758807, 848005892, 207953193, 28983112, 960686228, 449115289, 211889984, 967104382, 220170298, 780269493, 401019659, 304257593, 376627392, 611365098, 236179488, 12053280, 893575539, 669197512, 3935537, 339730486, 318548558, 112988526, 169911067, 142166619, 860674743, 162091302, 350435268, 485200078, 137049145, 989818538, 263316535, 446339972, 130874336, 16173163, 634776342, 827803356, 156001706, 654670034, 643988070, 143348069, 614388416, 815052221, 331442377, 635938899, 760789911, 372012642, 830081517, 494914957, 931871507, 975343018, 451549961, 763091585, 835894299, 804831414, 570727701, 54681813, 101358947, 586294264, 194671390, 617893459, 447357677, 94177334, 432137109, 502323713, 99017528, 409743315, 906729780, 447590537, 534076984, 436174818, 552402649, 245359583, 159430885, 956757139, 580312761, 823946327, 837249576, 223840045, 287283063, 638910466, 664291040, 243670778, 839832630, 418465351, 923285747, 640442145, 504818079, 190348513, 921460843, 520553154, 654052027, 365900589, 393410801, 228913945, 726665093, 587146114, 964336847, 627314690, 853201636, 188510560, 37345937, 956152993, 348411773, 143165678, 42919137, 934938324, 475319569, 136508229, 348736518, 56573626, 565967934, 819190238, 682413073, 311547202, 760672332, 910452402, 283284224, 315278403, 40906025, 179819815, 650485866, 854109793, 674557107, 621699703, 165497860, 350604555, 856699391, 590311266, 225566870, 582141884, 622874181, 6999760, 704920155, 387909720, 355193720, 978973375, 458854928, 868730343, 883852883, 7430669, 49602235, 621120353, 93795620, 521921076, 679144714, 205659664, 335575452, 394490388, 13825563, 509108318, 616602938, 903849861, 218267704, 871443380, 809507145, 489819553, 646673551, 74402603, 479701728, 507182422, 257562393, 811781733, 271008214, 488202777, 902569656, 334700577, 855890879, 426598339, 147648853, 772321113, 977629670, 949566923, 372985868, 670433213, 288773458, 973212598, 58218581, 722891318, 210596776, 811104649, 332592997, 269215244, 258193978, 933889649, 501183569, 894642494, 986133909, 881742, 936326107, 163157460, 703131493, 329861532, 280054925, 500541264, 950678997, 857377278, 171474115, 364124966, 298678673, 462874729, 209593693, 912373954, 207147124, 1452349, 399043385, 493201652, 87388190, 633245493, 866649042, 179365167, 340112226, 443633770, 423079941, 449657035, 641366853, 414045311, 881359314, 841862877, 600276408, 248753644, 261668826, 94922562, 127277029, 846503306, 589854907, 743977554, 837876056, 949969426, 837293138, 698724276, 313630453, 492460335, 711250028, 862591729, 884996677, 647259037, 293962531, 66404017, 811743084, 750163049, 669482115, 709867632, 18767119, 416200830, 461020653, 872727612, 103144311, 241034325, 52919798, 706988249, 442874395, 979110672, 679088157, 535635678, 99476637, 810830171, 410320073, 456987192, 696243929, 488046922, 826440745, 107970566, 538646709, 451391358, 721846689, 549170359, 16755497, 9646754, 30805451, 258709597, 196127726, 719045149, 184096664, 52250356, 438537343, 290135383, 609324285, 981588878, 858686708, 872446351, 29134495, 874937668, 511528196, 407944612, 413425283, 808625370, 233468219, 819047201, 425871484, 150686465, 198492124, 44235352, 933759601, 343429649, 648469448, 932393450, 99819980, 120868998, 573063082, 940473979, 970302750, 978834148, 549918917, 254198744, 942352357, 602828787, 283548197, 73808806, 323474753, 346355751, 149133817, 699692935, 714068423, 733959129, 266653609, 396658254, 905040827, 782426492, 926766612, 177154441, 593070713, 582783076, 654960885, 725678467, 906039863, 336317748, 122231563, 524395378, 14876020, 1323245, 548826938, 755232643, 587762847, 942319522, 775188427, 832990730, 356957976, 694200476, 647530106, 352171354, 264091448, 631272154, 268833215, 752892445, 442428492, 381618410, 145174212, 635968024, 896696654, 422923450, 302272862, 639409490, 5419632, 118967923, 459447783, 712058886, 535446616, 511662118, 126290697, 93034661, 780448538, 787030109, 727453220, 410172539, 556786426, 867475064, 415301882, 447910413, 669674915, 401582342, 83434794, 842957585, 540851937, 589168692, 717765007, 840396952, 7498736, 175827826, 896789764, 205503830, 156990395, 278198695, 499609095, 217664193, 977202705, 27106147, 104650519, 853521258, 842802888, 400115188, 824639233, 77855956, 749915211, 407944809, 384932229, 506717761, 80140407, 244090664, 825154208, 604914803, 380072545, 636724662, 145968889, 835609034, 605686167, 516611010, 633151584, 315949890, 816148620, 208066031, 973406595, 644203341, 453111953, 98279199, 581994532, 172298172, 194508992, 265726326, 237834834, 499576343, 965836942, 914132854, 29011337, 198137944, 936878097, 705473066, 888109704, 246225853, 560056491, 68685539, 538678873, 838101093, 321090545, 596285736, 937214514, 470747953, 431002558, 206679029, 891248927, 886721999, 59306747, 238849224, 417474742, 165863325, 663648824, 532869357, 132031483, 623043712, 969347202, 697036321, 790920758, 135450937, 910475546, 963757114, 648971723, 666662710, 904810738, 203148983, 153383247, 190363158, 762958622, 613972262, 329675825, 548287301, 424437588, 317454018, 950850211, 352044068, 375233591, 880992840, 10242192, 674823419, 408395784, 675661455, 279878670, 87030322, 583052306, 38201326, 611854129, 979014928, 260727280, 323523218, 495225085, 473357317, 981036006, 523401909, 422281511, 357761924, 874834064, 446394755, 783055505, 732221483, 797576113, 187729732, 584148218, 805521531, 617638428, 174151442, 377228719, 847502719, 614209989, 57867265, 355456132, 531313678, 670451603, 488393079, 786986470, 601171598, 44056874, 370838956, 125392417, 54420223, 940321339, 78399054, 426383548, 565996552, 466545566, 955943100, 395766620, 94910794, 98268530, 118904939, 55250188, 205122008, 962398923, 509793703, 376734982, 356680821, 40353642, 567895790, 518541448, 997457029, 34677008, 954483303, 909657209, 984111569, 17951108, 397073791, 811910938, 234994534, 312132489, 150534723, 245758505, 173828294, 156339558, 201057850, 458191558, 959117628, 670593160, 517163643, 312913843, 376973042, 3676733, 584495385, 504940821, 60124368, 744486185, 747753038, 825988545, 82427004, 791436757, 404306110, 603313578, 770004440, 93764501, 107893997, 983385745, 10575859, 308002420, 655005378, 526545828, 917317572, 505282538, 618297613, 265792243, 75913987, 657564125, 116444190, 301235505, 110425139, 983967452, 283533687, 894345739, 672598109, 716131466, 167634025, 313525863, 147028986, 651325891, 905699185, 315613488, 263166856, 402625378, 432845308, 677144628, 979783131, 223549208, 751262534, 660385368, 568964562, 64915618, 258356241, 57641561, 409399501, 640477379, 402838797, 520673859, 152073807, 209524183, 982221837, 456647597, 444385017, 949602730, 766055114, 822009864, 960847984, 819227375, 41377818, 757966152, 350448697, 256050748, 943152175, 309822315, 582650965, 398390621, 331897230, 647454938, 433892360, 835663232, 461175346, 422336838, 634822578, 227559275, 305527400, 208030402, 567072674, 200058037, 796522202, 976645779, 598907927, 778704516, 195250272, 31136688, 507920739, 568709362, 101650407, 710695871, 855977430, 879364744, 415857392, 77782707, 542278513, 221053626, 395232460, 953710484, 886863146, 799313568, 768562622, 980541115, 454082700, 787203205, 264135614, 582379110, 301733339, 213021848, 265423271, 937819263, 307531255, 108290276, 957352946, 15835600, 657708410, 923115946, 40768815, 932550245, 754406830, 254597857, 995653373, 782064929, 106834181, 390819122, 828934154, 753989680, 935775448, 479434745, 580694192, 481225841, 262114193, 275436118, 202046806, 439080246, 72117728, 568474230, 373666282, 303425749, 29137840, 842358567, 6961476, 157144559, 203604004, 400388469, 972168184, 778262242, 653827245, 958637715, 453206335, 540592587, 958722935, 262975969, 528200183, 821145521, 70008705, 182376982, 30595275, 651580173, 170252101, 702169378, 792295064, 84691347, 759824493, 838989029, 253307487, 366581219, 88195962, 954955619, 618698104, 417860338, 531532043, 188223516, 62347608, 450974978, 924326226, 25944580, 967251747, 888170942, 90693152, 795780204, 792671717, 564688589, 638598479, 846470899, 140443965, 185821326, 218243267, 856757297, 561476712, 361368913, 320434059, 720590593, 466554023, 55381574, 460253798, 344717838, 32956711, 32626809, 519074369, 183579521, 116047525, 344278038, 292204576, 136288003, 294452105, 723797671, 503505919, 842273838, 181664988, 85536392, 640116277, 679066682, 605973478, 829047568, 697923207, 133351497, 879177053, 587025764, 581534264, 163716166, 906502819, 986233365, 92922224, 81028580, 994421684, 936833721, 86565462, 443878644, 582661385, 106944575, 271337024, 677312870, 182493916, 15866692, 463864433, 801628664, 718683708, 426473674, 357932312, 813931591, 579755664, 713737116, 824446930, 58706625, 525680877, 910445152, 622447541, 323735460, 168891464, 36814397, 232661528, 737504571, 4634259, 894846671, 517595322, 310907399, 536446703, 550757347, 430055471, 273936303, 409139312, 455750697, 134501015, 125271932, 326755822, 443352569, 376780156, 427983481, 715063412, 827637999, 684639849, 855399060, 595505888, 195193414, 747818289, 571668996, 91866858, 648521636, 105137854, 462003688, 767578010, 49365157, 177012579, 235260819, 387201065, 244796392, 232307182, 546924809, 149559752, 926058489, 627072610, 588461787, 518219883, 448873667, 834032756, 366405865, 627715375, 503113388, 203827189, 942129848, 987273034, 667530420, 657495279, 154698347, 455694302, 808815834, 614400215, 184379051, 913070741, 898079199, 3857333, 336406739, 160846815, 474021635, 627044194, 704879387, 101642976, 709877406, 796738236, 43219303, 99407396, 835846865, 167667640, 716403238, 303249162, 427193953, 205692093, 211008707, 119323841, 582879994, 204117003, 716946831, 86687981, 947121790, 114693942, 556193858, 835205326, 979791145, 165234077, 758810454, 368237150, 721343514, 958523621, 828431677, 603994311, 487923998, 841691517, 328671316, 454434439, 594053742, 659938428, 304735801, 484948867, 183213041, 728110843, 652095971, 578638609, 322960406, 195432047, 995298355, 641686344, 32809286, 537744581, 980354260, 116042778, 345253770, 50533794, 28777538, 260377784, 105655242, 809682322, 789600751, 892456547, 775598840, 413047579, 732451604, 760613028, 235689221, 968651072, 724236808, 817600920, 780149089, 352304715, 567563119, 227492815, 738388044, 51625537, 329387788, 270652635, 877758950, 780976879, 766717567, 364496710, 862504668, 611572346, 778771345, 834598578, 353505782, 251679522, 928958643, 389936633, 609857669, 883240496, 757801711, 245029751, 356549090, 464301710, 170059868, 743033849, 780011224, 220869253, 421914923, 268443715, 567474947, 947138772, 40791097, 139329121, 817672465, 78703717, 396438314, 725550970, 778991958, 494731097, 257938089, 709331015, 512944356, 464719380, 232690199, 165936520, 458205456, 394138309, 834834697, 82745711, 141278242, 877216501, 797860310, 282880393, 886273495, 413267218, 514119578, 238925224, 646462133, 75188065, 697116342, 579885403, 233940756, 201761125, 315448169, 921545551, 590889968, 608598965, 716592354, 298201153, 384299460, 477693766, 30314450, 714064800, 193354619, 696137373, 914985960, 365522878, 831886505, 562030337, 94445073, 703535374, 940714876, 588250171, 197405707, 432855584, 246925853, 420391270, 414314094, 266929328, 135256401, 383292463, 840231524, 376882264, 633214, 22278984, 907536412, 709730988, 660979948, 482864982, 436836361, 877751622, 569098076, 559604578, 269762000, 511333517, 40115101, 947642737, 889105208, 663479377, 179912654, 820048971, 34437348, 333487341, 345457601, 868132567, 203102779, 320202440, 499892055, 899728936, 183723968, 934705952, 943054829, 243237205, 206879320, 944667846, 860795791, 497244536, 863099310, 40717474, 115635529, 344766787, 404606909, 401014512, 446269976, 491526181, 57895853, 814709451, 837913237, 748636041, 527936675, 718713365, 340228036, 612562353, 787937774, 633094308, 159168816, 5355612, 402708851, 679594181, 780910518, 505720002, 508233968, 111832650, 597693966, 768857503, 839229980, 552440107, 853306172, 808391652, 749329208, 82644199, 572091281, 776109742, 846539989, 209663481, 191678032, 277179621, 846576817, 778702730, 746626244, 593398957, 14781691, 65359852, 115092628, 549674183, 231802611, 422527792, 209674472, 415928927, 646698828, 979562057, 274359287, 324501194, 344521046, 760320339, 627787113, 632525354, 777175714, 34112392, 978836423, 410431535, 297921906, 606476480, 678292891, 847535223, 194763070, 320832882, 435828026, 135959211, 379167767, 583548, 335924716, 649272762, 501472265, 522588167, 17272402, 261059840, 349109480, 441459553, 492518300, 526481363, 263272551, 205825774, 876989217, 325499873, 551735627, 327366809, 252915326, 718934723, 918344174, 541677983, 385147060, 873493290, 570421807, 295437105, 825785781, 757272210, 381853255, 742351943, 721686516, 903125222, 300251418, 271848197, 645930221, 477511215, 288925028, 222669377, 106164719, 690105050, 753983278, 840587755, 421533113, 123843326, 297605803, 388836183, 680230376, 237288715, 875571313, 638334390, 474699777, 367647743, 752453304, 705191583, 244390231, 562619279, 591741917, 694756227, 265636646, 548200306, 211293429, 898798937, 409238983, 514266225, 619917952, 810530298, 394881374, 323505400, 876224402, 35984576, 164991071, 810594534, 228679803, 503623030, 811410950, 927655419, 473685669, 884196656, 349494960, 940906662, 563311310, 684223282, 439590970, 568555748, 163576037, 392930992, 482348288, 230401344, 530549575, 396233542, 536071175, 291603432, 401556001, 940946380, 931870535, 863860112, 533271212, 143120322, 136650057, 450400900, 715885173, 991249974, 560507468, 197748050, 923099605, 159348113, 405503556, 575651102, 395256846, 102848239, 245553740, 246715592, 713421380, 155766988, 956675297, 680933177, 449834239, 732271245, 75329594, 556352096, 796570806, 444465159, 536840054, 567897318, 940858490, 285526594, 50130312, 224145430, 420458249, 924365054, 226779321, 314447845, 533442728, 960711149, 752054446, 902124123, 277010152, 896873832, 31363719, 154088439, 569991417, 590561625, 433834333, 557282882, 74062141, 889090714, 670874786, 9662789, 695875595, 501097305, 351098567, 174443162, 37793376, 249631322, 318845655, 600701387, 824319717, 814336165, 995376955, 850680257, 367246741, 255719700, 389310445, 791155647, 23048400, 403765610, 803380118, 954318290, 929149377, 748310323, 628825534, 210547523, 158172122, 312206425, 615799222, 298635575, 889223177, 390135807, 404386597, 240016674, 137039453, 429251185, 978434715, 742154632, 875873077, 500162453, 84006393, 954691097, 54799275, 171352828, 858240910, 894628837, 298256936, 407551499, 935999761, 11788166, 26202461, 950606858, 716412314, 738005744, 833566093, 743679738, 405777020, 172772084, 452399284, 751876008, 803327896, 516209192, 703756712, 399008259, 756192749, 752382976, 934765351, 336372337, 241502929, 831857770, 43567931, 548288709, 435054433, 482432086, 328242196, 350787738, 403882126, 815821596, 873011178, 490077305, 897493023, 917708964, 653154076, 173199058, 919603414, 803604258, 785234969, 690316422, 698356138, 38421013, 383355595, 999472037, 791216844, 925675065, 638216071, 976092708, 934102837, 835652307, 822046641, 604165037, 616662429, 450510998, 699557882, 809879020, 857568943, 812212039, 947026007, 163326737, 34442694, 75914880, 374829818, 963292983, 425314558, 914006872, 539824917, 6941044, 257493377, 648546831, 780923174, 352406037, 805589907, 22924593, 855251623, 529958540, 77745419, 100096866, 345457034, 779795715, 838281866, 874358283, 473727102, 101655397, 963716119, 790935639, 412534309, 124004488, 405631485, 237328918, 893368551, 748990765, 239257736, 50192524, 697681261, 697405600, 779215278, 31073372, 480951699, 524786104, 522212147, 214810410, 748537868, 972246178, 940161243, 945971140, 314454008, 593609019, 516186362, 327528353, 358683998, 548647893, 317295165, 494426070, 383291807, 436165768, 453792523, 408573211, 293228393, 134948210, 40187200, 905678638, 960420340, 409810392, 518786690, 19964223, 104235721, 188555162, 8307018, 121968029, 682479458, 390671225, 988016694, 698409086, 467584275, 327357446, 440736151, 492254079, 293246370, 97311959, 76375403, 167877756, 708379721, 774247343, 13212849, 199050752, 546189325, 495525178, 9373389, 375568971, 854589869, 540554525, 667651909, 630826899, 131407680, 948771359, 435075070, 547292623, 157324650, 9796653, 977482183, 100890370, 736782948, 837746215, 483455847, 78805828, 420542056, 18601884, 871704204, 123189660, 620268218, 897391820, 721322963, 992166260, 796189681, 520160459, 251713932, 179505135, 257056812, 326264325, 753872745, 79094034, 356631544, 566988958, 375898240, 139991147, 449101339, 689135660, 307283515, 876617619, 125964059, 914556277, 941987678, 718058774, 808989032, 481219931, 771131227, 341150170, 11410917, 625224968, 827232941, 70144210, 515343477, 210114420, 736344577, 929612625, 310063809, 676917935, 620231672, 885919083, 927872267, 222610903, 111755254, 342106788, 627886572, 365112909, 342849190, 318467500, 679065787, 258144575, 724650530, 428466133, 465133553, 912377747, 894397292, 664341241, 425980276, 404198568, 696989236, 944130951, 663577083, 975519998, 687682554, 299398359, 180936291, 921161501, 629282056, 176078605, 534893175, 759295853, 754543047, 301183442, 946174171, 520276857, 23389244, 897723882, 720374853, 161320530, 880970123, 452575369, 852857090, 879958958, 760542710, 473880124, 368484723, 539107863, 284649536, 957841070, 447257744, 140119801, 364516766, 267907848, 941276927, 403155555, 153504, 655126766, 924420580, 514646126, 722007475, 545699703, 249911233, 915317557, 427329898, 879875617, 506060050, 185167826, 260938996, 659597686, 534901169, 339353685, 500134825, 351091543, 851250136, 886542414, 155140120, 274672723, 161370411, 341022017, 74931952, 198841700, 660032397, 162995498, 591644539, 313086685, 552261653, 330164305, 774950971, 46427313, 613454899, 877458821, 153695737, 132855790, 290901874, 809646940, 538214568, 848959076, 871076313, 528282972, 853312842, 572630569, 333743248, 946222176, 81133325, 82128087, 730660898, 698575178, 538256593, 419020455, 96664119, 332735061, 561166021, 158054378, 949688345, 38980290, 346113130, 905141140, 168981424, 286309790, 942420506, 866618891, 476129434, 980176382, 228685737, 779098118, 935674467, 267554645, 509760821, 119951373, 717769957, 756504283, 763083470, 404046766, 60740451, 483313005, 504054512, 790985791, 803306910, 468982300, 701137972, 263191449, 349521983, 138484440, 934127808, 301507638, 561620580, 257567309, 857577514, 495978673, 800721552, 420888977, 657592090, 888021208, 374641119, 220916907, 198606989, 445118087, 728033998, 358334739, 751257131, 538152087, 951556815, 381471773, 473937774, 578227686, 176398857, 538237438, 928079233, 480213735, 199232808, 790187293, 614841600, 947753130, 654949448, 274906128, 492541612, 911589206, 179583492, 532906121, 247507180, 160964823, 248744290, 789313734, 544821722, 463136997, 811815547, 887521415, 514086555, 244077294, 421019035, 749524034, 776729695, 329681922, 419709048, 560928976, 867201777, 297701247, 690321396, 787644081, 980600588, 340497310, 632632750, 441424046, 341904642, 314579068, 849673462, 942717819, 483626322, 246632389, 298304688, 413754922, 923386814, 723745391, 98413070, 749416485, 706417498, 749036298, 619566155, 560178896, 130825527, 751067884, 247133065, 828984915, 177210156, 460891273, 587747685, 19404986, 794556494, 232179100, 920342702, 80898739, 192538506, 582722855, 576764292, 183346651, 107952095, 605965361, 271668018, 293927001, 978868615, 393506676, 438293161, 362718538, 72590096, 458709466, 995449419, 246826768, 391779960, 127233500, 219103441, 559998848, 554183412, 778842363, 996821687, 955685823, 434064136, 357663576, 322074495, 263192248, 633535665, 876633667, 567991481, 781727667, 386570190, 743405160, 326760873, 550356568, 907082295, 723044717, 567419767, 663956887, 938509584, 121305207, 403645491, 332197842, 801237374, 8203421, 739177029, 573407431, 355791997, 610047639, 416544384, 17570177, 496718990, 319920684, 661766851, 432384878, 329890145, 642105625, 946515908, 576426828, 562573605, 167807705, 101005034, 465914932, 289128264, 774806215, 325025763, 296441856, 306357057, 731959644, 185014212, 157688984, 676343740, 9556524, 519337404, 984052673, 931902450, 826588324, 18556670, 492625793, 273635157, 601232587, 423999406, 688489323, 442952339, 373365508, 595453943, 701780090, 845320821, 576668229, 583941931, 816035867, 635334796, 991626690, 507486158, 935725973, 978577142, 416833857, 233345113, 444582947, 203205574, 65104018, 177026926, 699601821, 315452682, 259101362, 495401780, 712335485, 781933449, 34881249, 558216926, 258131577, 770616287, 460367075, 560037626, 825617531, 660297529, 122474979, 497147994, 7378698, 510712732, 344168797, 841608055, 705326698, 948514970, 847024650, 432370685, 659139739, 654775019, 875575996, 530093195, 540779649, 747251255, 326427237, 318291785, 352503009, 277740416, 695245306, 41382533, 380845655, 85503082, 66158635, 749420604, 271030913, 11456229, 134802964, 455332727, 418056542, 986027737, 600474300, 259546735, 674416753, 306696158, 727810117, 233985193, 170245932, 652256183, 922889563, 434078100, 833187632, 807822589, 876737778, 123605858, 363425323, 997860771, 393887001, 301494157, 341621148, 314916684, 247126291, 398776592, 815373081, 178243799, 935591070, 905894386, 526733141, 279004042, 429736082, 640649323, 91463986, 183830835, 896288518, 657811433, 361463524, 201511736, 719537555, 303606973, 960546572, 204842593, 876877228, 109261848, 886339840, 879050847, 157539402, 35606926, 630766887, 667431493, 963237800, 206823021, 271656408, 819103606, 95004578, 172532651, 509979003, 199318973, 884910415, 217057996, 822120881, 334041250, 638859761, 794672075, 571265213, 790945747, 884952765, 3024790, 958377816, 600300065, 166919497, 109674000, 498316233, 722815280, 792734863, 622943730, 215921403, 946991134, 287961169, 530744576, 942626670, 803440847, 845525597, 138443373, 138919760, 411464416, 39815657, 18066354, 628106273, 583651112, 946440258, 299389441, 701802066, 860168063, 501848067, 824214001, 565176100, 234043939, 120765848, 622630584, 470041130, 87864194, 399263159, 885368224, 112864352, 258859007, 255358815, 608361364, 608489464, 771966231, 503006032, 762266905, 364285177, 145110799, 532982388, 904832516, 766427972, 145585392, 53664383, 123425663, 666258345, 50887057, 100806812, 264637336, 23181768, 180661966, 97532924, 966042769, 348157806, 436285368, 130796102, 19237631, 421783372, 742590862, 655162830, 575458681, 843592387, 991467458, 542819711, 811301989, 816356701, 552173299, 920235256, 526153171, 172260420, 67306225, 389109198, 802927070, 39366231, 361649028, 432967733, 344372545, 218152549, 999655649, 218135416, 416475227, 795432612, 202372387, 222954046, 60160522, 648453606, 494506591, 579730011, 298672195, 352523331, 280201880, 314831258, 228326777, 79008568, 49530895, 946145249, 389896927, 835078780, 210962007, 45042946, 242770390, 119900247, 456725021, 175967914, 659737471, 28613904, 540586607, 170395442, 624487637, 114730580, 169645404, 918450510, 4378089, 210734371, 361029176, 714888217, 138801780, 607000060, 768073179, 960753982, 776281604, 802454332, 217235306, 278015978, 443071600, 774928920, 221592097, 455144197, 299474166, 689510999, 96244911, 461269288, 925303883, 436369718, 899501236, 576367837, 639135451, 802497739, 672499438, 255475860, 117055364, 815084669, 723720015, 853766322, 576431941, 415311749, 414085943, 19472072, 706193086, 655003084, 160415575, 45459022, 791983721, 436553492, 838139636, 534414412, 711815807, 819605409, 109184452, 135459271, 318627237, 559492295, 201646765, 377502383, 781037387, 887959404, 868526576, 170015053, 692157411, 118857295, 360022799, 46835710, 396809324, 625665672, 453178807, 638290086, 51587327, 357257480, 476878327, 503563619, 779915420, 50505563, 650143311, 612012147, 958286424, 958812152, 402120230, 13563305, 856959605, 985129284, 396403282, 900439659, 386798786, 8035226, 165076401, 887957049, 678709025, 496200834, 179759126, 823698296, 372016644, 600210188, 770386817, 987263576, 201880677, 821608952, 53575385, 171517939, 415284375, 366672984, 861881497, 243338569, 609641697, 747780363, 81724049, 105860199, 622434241, 355334374, 147978551, 229616306, 728977542, 704877176, 941926190, 754302480, 82590834, 657052026, 472289553, 985599678, 341868967, 30498857, 736760217, 534803625, 656118839, 991341076, 302908016, 921696519, 375241338, 446399356, 398170726, 805839809, 354079777, 622837077, 831700269, 86204273, 423776515, 665526958, 380400990, 886704853, 823290033, 674845918, 486161839, 232422323, 930929592, 930483426, 975399688, 480534474, 473127645, 281744688, 12054349, 675101733, 469120978, 880861294, 101827203, 693657266, 201257548, 94186177, 592392327, 51314329, 233843612, 789238286, 562871666, 374637134, 869461613, 826947767, 867392190, 201358881, 194082224, 353090031, 219570486, 44536236, 87124147, 791536193, 243915756, 412174142, 615204616, 850498614, 682561150, 262576946, 287081489, 847272850, 123771243, 11736334, 397142074, 587427196, 189386100, 628666300, 463152336, 986028681, 589334737, 451181896, 867552055, 241769607, 885582264, 199139920, 460362845, 711702788, 107410379, 257052751, 202593887, 405638716, 800839028, 3682172, 1014714, 170800533, 162200543, 140645215, 607504952, 594246986, 204299936, 895145499, 887798284, 258978798, 398400719, 36020430, 113254193, 599210692, 943189560, 502303201, 18705430, 471067692, 763661537, 790608562, 898197529, 580941665, 85406976, 143295873, 605886239, 222775374, 513873334, 220353779, 368216711, 110567808, 965551374, 154012878, 766468524, 323349293, 984371359, 573437718, 299749527, 646519451, 902506645, 666969953, 978026711, 790574271, 874132864, 638729964, 283735405, 455162749, 541935893, 433514923, 17712278, 663552514, 763500264, 718185227, 891970777, 980592542, 34216800, 102374809, 861070953, 637205013, 277550161, 585296426, 937852048, 805801469, 669814089, 696905187, 862492867, 697880178, 112463146, 430606812, 381409935, 801989647, 45363297, 652295236, 562779606, 303954025, 69496873, 642309726, 477953446, 321382423, 977827444, 91304808, 834539723, 401376431, 967158718, 692538173, 261693291, 236486440, 95746542, 746337361, 890965137, 991600040, 985853811, 860733349, 247121033, 832194219, 537933477, 859063618, 92118509, 214452561, 442911238, 386378845, 285696038, 290027141, 985547929, 173658300, 388013433, 941666013, 161816888, 959890903, 917890140, 251984684, 564870185, 588049865, 708489483, 242835406, 621246973, 653899866, 575564035, 530501087, 912796146, 368678845, 841780733, 705459409, 973348501, 998979326, 166188574, 410076484, 474466800, 708074135, 946319416, 818473992, 917626738, 509662230, 294787067, 576050850, 828854852, 306181122, 745051694, 977231065, 385400916, 595802947, 78963859, 583748962, 449970442, 893489873, 314884979, 970417031, 720462971, 569569051, 722022635, 149804297, 185668700, 674763512, 433182446, 442547834, 371825125, 904467566, 348485019, 122991256, 859544672, 909675127, 458552524, 93387740, 104786381, 23094017, 746807450, 619009128, 995216506, 406182914, 991606153, 677986133, 32195225, 613623851, 373881407, 602935677, 413658586, 959638571, 21051533, 695167868, 40380240, 313615428, 47036659, 633036445, 746069529, 248313062, 19401129, 929587759, 641696459, 288834351, 756196819, 164475749, 284027009, 957640677, 332575567, 578639505, 383881378, 293703405, 433505502, 77482275, 243019629, 691624765, 605768533, 548848729, 126940869, 514782681, 897977678, 909015813, 52909812, 270519889, 920194018, 873439764, 163980878, 555019013, 733503794, 447040838, 865020358, 214829339, 909533903, 797241448, 971537976, 74396207, 458059457, 583280389, 481099012, 200500452, 751124406, 776044450, 34901414, 75810511, 970339246, 124953790, 334677427, 24974265, 610300380, 406487508, 663246670, 969222758, 955440310, 578688324, 709299784, 749323572, 974695675, 175037451, 777868716, 184676652, 285506604, 620740453, 407049388, 880733951, 887684378, 387893251, 261094242, 782021, 488469894, 457742545, 259216965, 676004423, 840314435, 73684110, 124721649, 209328029, 932601153, 854849989, 481180792, 889577176, 803779364, 950034425, 835710590, 780276169, 156606452, 90707638, 659308705, 559638489, 536583096, 671234800, 459109518, 20931593, 757274132, 963944231, 458683468, 993524964, 823500034, 127676639, 113183650, 674038665, 646123967, 626303531, 749836449, 353156411, 825014645, 448660785, 537366260, 41079368, 527182735, 659130936, 190145869, 838159167, 239461928, 110817375, 265736800, 157097638, 950031280, 64796417, 55753429, 935094779, 682589037, 156297091, 429405631, 260426205, 510800848, 823310430, 750864, 500706356, 354385470, 415700358, 716225657, 877064874, 216467423, 652373900, 994693976, 219753121, 357755193, 824040908, 871425938, 828940482, 78526986, 755390809, 601932834, 245473064, 699717034, 30208023, 452993435, 657660649, 72158303, 476742717, 269697017, 796984410, 395156638, 524864587, 294137636, 956748782, 943424478, 608119605, 593718099, 857524439, 198340434, 314383165, 302267434, 67277149, 903591147, 754206983, 586411796, 309890129, 111376705, 723105421, 989495857, 752706921, 363482337, 578635688, 741281238, 231808047, 292710113, 545174430, 821084805, 185172140, 891298846, 388562628, 337310442, 426383189, 592556174, 333416615, 444145872, 841073339, 233377999, 927175804, 757423087, 338809581, 622934854, 437899734, 214159733, 921726572, 765654003, 669939871, 871418698, 148248574, 806606215, 993479530, 35580537, 178512556, 759037733, 111198395, 206127279, 983867288, 722670177, 625320320, 779722988, 738030369, 109196224, 770049040, 12913194, 786885218, 798571274, 811244410, 708937767, 475817511, 540666495, 938449349, 593968383, 325538716, 269904583, 892755025, 832562274, 471873116, 313681991, 687162989, 338629270, 915219112, 617531272, 562046359, 787229903, 682465432, 346490139, 257530407, 644248737, 491955454, 948205132, 847225936, 431596365, 748948505, 489635240, 729778410, 853246827, 983788351, 155174866, 82080743, 476621528, 84533194, 364145911, 637790000, 716745279, 855978770, 289354553, 555593849, 721758439, 927967438, 964484160, 722207739, 934068348, 862711916, 663211697, 909742071, 92343991, 126918300, 489865720, 665849894, 239203030, 4958733, 381323141, 328443274, 72414384, 533378555, 259552388, 18912458, 748079311, 138449945, 608883043, 945759851, 868160641, 211628176, 105818997, 878580549, 351365795, 951360441, 815600354, 28225434, 733209026, 180218532, 369251687, 113854500, 577703300, 167730536, 270968901, 402791630, 786558434, 845965046, 430149079, 576053526, 762639230, 582184386, 981838435, 470249444, 287853691, 563420259, 832533185, 361781365, 371495177, 140172001, 457916459, 224951921, 206837061, 944738690, 20509503, 221755058, 871072693, 564271300, 847355120, 852819135, 83506499, 584000474, 847480758, 993471758, 571384321, 408911568, 88373669, 605833205, 348474862, 335900114, 145175676, 519357443, 653271973, 48436353, 248775873, 962341567, 556459166, 424292267, 972818530, 233483889, 398658513, 125549452, 971738279, 131768914, 281562567, 243292725, 215883436, 27325764, 91416147, 851485269, 685187739, 486457954, 761064724, 811596551, 698807124, 606879324, 591109358, 696140927, 831440358, 214597891, 38040227, 868096227, 876974532, 375122487, 782853946, 755463656, 747014353, 438833786, 775582417, 624617353, 786086607, 700533828, 682543529, 302017086, 807694990, 292632320, 862028010, 568506272, 571130767, 673559014, 23733999, 953315621, 948418222, 515931764, 422832832, 677582736, 900583994, 137999839, 126911983, 789973987, 934585882, 651669043, 853917998, 694905789, 739442433, 976860235, 839600734, 466230652, 615370042, 397612758, 569302848, 388970747, 350131379, 546396309, 4007942, 892740644, 678028659, 987809655, 613991202, 903233873, 23646218, 634877019, 463346646, 924152808, 237354639, 831842250, 985396751, 515846989, 156420926, 419569684, 359327576, 165881265, 845748667, 723098562, 624719571, 350959678, 730828746, 898175699, 734040065, 360942088, 725917063, 141302966, 145282040, 77292959, 661015669, 741542569, 495310834, 598832087, 431426595, 395928898, 882626879, 198123501, 343490236, 612059453, 693696025, 162567313, 291673183, 78635068, 292480937, 394374468, 993447154, 33840873, 913280057, 218925250, 147107709, 616839620, 710938333, 695467273, 234705694, 498415237, 874277992, 867744545, 329547606, 940827198, 412506142, 288382898, 268755190, 26711582, 842172120, 579124197, 160131667, 979046982, 18287168, 666398729, 804208461, 746975598, 606040290, 952178782, 8587901, 764113459, 774005550, 634569644, 860577461, 559835359, 439282915, 741186707, 535062342, 668926418, 961161187, 235215975, 842533161, 537424721, 85245207, 617624865, 335985651, 437799979, 184339433, 522180377, 580336554, 932662733, 592531166, 695497304, 742064573, 73934528, 412385812, 465445496, 641836274, 265530838, 694971464, 761174439, 595082399, 802668591, 22550552, 729279076, 512280301, 852181241, 171603064, 732762002, 376321970, 747867778, 59368657, 221675496, 509413386, 145453962, 171936864, 313834220, 430198765, 480439096, 624922678, 786784795, 363016596, 990082856, 401238299, 809543114, 494279622, 357895319, 655960424, 798213890, 340942888, 961721101, 232759471, 588796194, 754489722, 234478276, 539192391, 224908253, 192218559, 307907537, 415239526, 417726456, 374288955, 658106878, 212402772, 108815637, 588218266, 101543483, 685607815, 513205072, 864719878, 619642676, 3709773, 525814610, 834276737, 99513650, 887254396, 25076088, 510920401, 982020946, 103546672, 727643966, 997764405, 127104453, 171063938, 671267817, 35232131, 856123855, 952413483, 512038609, 693468448, 331968150, 175582103, 163053375, 727281843, 968609698, 52482330, 76936988, 624079488, 332338705, 171956567, 30866891, 79039999, 797992810, 324325213, 468416030, 640961333, 773790965, 589778246, 21843061, 621861700, 377717052, 981095148, 349947961, 489162680, 276388676, 875201697, 32658841, 542535741, 516903802, 686382508, 127458700, 173854577, 149239450, 982911269, 547818564, 17953713, 903681292, 383993180, 846682531, 929042254, 555806559, 93927869, 535632406, 210270193, 532961205, 306635030, 575369822, 913743090, 541271431, 407414036, 464418527, 728187816, 576677969, 213595454, 543466489, 732243110, 996031721, 667059587, 491572404, 127750562, 659212438, 965130933, 755140971, 982393772, 733066723, 867886451, 548492071, 146556578, 114912866, 635702731, 383251364, 383441521, 80976466, 865709155, 280819678, 97857390, 765841376, 235723675, 153838197, 168709700, 670793029, 120808035, 218989676, 113443367, 169617114, 618128065, 540850493, 744000431, 362526752, 574080365, 208560188, 809047884, 627370752, 135170065, 118395811, 257397719, 100996056, 15086025, 401463620, 617335223, 940408606, 629309061, 173444748, 856745532, 298146091, 661145959, 170626147, 94251040, 687393728, 885249742, 853321208, 160282168, 305390792, 776556527, 575188288, 595653624, 102659162, 465108589, 440595662, 671386797, 438170136, 762680995, 841807207, 653354576, 247713849, 584235853, 87943639, 703031980, 20869636, 897335030, 620027239, 418532671, 408617019, 512946979, 592613082, 531706573, 572782378, 583674689, 150079799, 631470192, 821141179, 163063003, 277842420, 463864108, 150539807, 321832359, 439645173, 335423688, 820163504, 901020969, 617596326, 833433969, 369856165, 322092941, 597873405, 376810913, 502551272, 977046235, 303859071, 85197479, 806080399, 625870430, 462990396, 546577272, 645469837, 692188655, 685858038, 582747795, 732185379, 3801359, 212517933, 804709796, 483958169, 146221135, 951924648, 181291892, 31036114, 30401226, 103094694, 623028370, 242501747, 542557242, 885820557, 552343741, 205920505, 740337803, 258404360, 236981305, 369421605, 944417686, 430801192, 215275628, 881795420, 998632200, 127204122, 258909690, 153242677, 580478230, 913743459, 920923123, 593032254, 145046361, 37159180, 927890773, 565728913, 355863064, 150684221, 190568022, 877663193, 630692194, 654065199, 282742346, 509096608, 288368537, 512948400, 826711849, 530728028, 941522648, 613605013, 618262414, 192820065, 647627478, 571851614, 250394249, 913834991, 842255081, 69878685, 313045297, 270232296, 408593611, 56360513, 172442643, 513196690, 873365445, 587663769, 323430906, 310784525, 677618039, 78602492, 92507201, 161868959, 239781892, 481423853, 994617109, 576284479, 45817510, 102040229, 862734783, 667039871, 361239577, 919046364, 452403423, 384393529, 736564464, 197146858, 902312747, 571716980, 342251292, 672636716, 536778184, 479017865, 847280679, 50018166, 120466692, 11587137, 915703525, 303456303, 218965716, 53963857, 328006596, 683160878, 652821072, 554825337, 158575839, 406788338, 802349916, 123697424, 17747855, 336773383, 416354659, 788761936, 522175707, 621665668, 491086893, 44448658, 635085490, 476347712, 174814325, 342843383, 25860737, 564122375, 738974843, 915788288, 117783587, 494050100, 365483712, 303435330, 879836206, 769924202, 914752081, 775788395, 412035154, 444773610, 556770938, 404580979, 606516534, 570821604, 242652324, 711966784, 787019422, 918112023, 782678835, 536752745, 640805485, 964731733, 64048099, 622376363, 191406061, 626956464, 957923620, 515800269, 22911434, 850468369, 155195290, 76501271, 327286328, 95938979, 265247022, 829789963, 758219691, 395296640, 294569111, 664144500, 114474099, 113099423, 872208764, 407000952, 98119729, 261837715, 403593259, 303078739, 666583928, 245372629, 461869167, 885929278, 506877193, 661438536, 221526380, 736223133, 510721074, 201802039, 923615347, 100771786, 82547595, 548876296, 759987711, 803228942, 807405155, 195572945, 905390668, 178012857, 694079227, 399541500, 255766499, 170774060, 880551171, 52928136, 72993077, 501538054, 315557579, 204285637, 866170905, 414630826, 180634929, 890181422, 654852111, 732756038, 22376771, 551864162, 740980633, 949255682, 749339502, 411128618, 566236908, 64540175, 612114175, 442384709, 537791397, 970336646, 907325136, 602155658, 296160967, 204685600, 409145687, 400866024, 61762644, 669242758, 751193755, 201474673, 479528806, 482817405, 587640021, 783231168, 635941233, 502770211, 859136911, 9982312, 664127396, 387632279, 675513704, 393321913, 733483909, 404063814, 120281627, 966719784, 752979920, 491153117, 716258051, 281376297, 133718767, 236809662, 902503200, 391864645, 817187935, 888522386, 599406604, 40567248, 22856348, 78212298, 305698406, 58823586, 815837186, 594831890, 269421075, 387166956, 168580512, 968503952, 803006928, 871622154, 788731232, 922761319, 464816145, 370775000, 249733549, 928456198, 258105018, 9065450, 811776289, 475603957, 629641814, 707840130, 719162730, 292061517, 412718355, 608825873, 837318936, 455475459, 415908277, 66911392, 944611370, 621791447, 23489933, 957352560, 471573667, 724056061, 500266330, 748644426, 230980110, 721850551, 507664328, 771530390, 420619107, 343062624, 358361842, 509667415, 652255254, 444618622, 723682292, 719874499, 239112912, 934034571, 61779228, 63709988, 299593373, 910133404, 718904034, 383601631, 418434927, 103866208, 822739541, 865710843, 297765383, 6075986, 192859980, 474204202, 679522426, 673531516, 154878073, 996395791, 539061240, 478248668, 932192747, 7391904, 900185145, 571441735, 749565495, 538714269, 611136357, 281761195, 308072334, 8290787, 982577826, 233755303, 926861797, 561942621, 626596956, 295794751, 578411805, 843501552, 6039284, 991441890, 262923310, 217298028, 553977494, 547247663, 614134211, 243669618, 750876073, 236891889, 918168164, 411469003, 866366336, 894401939, 486438795, 773472637, 142790602, 9796411, 82003000, 242693478, 118100872, 609054816, 279227515, 683387455, 686666790, 845607405, 961948843, 272456669, 398825710, 622008834, 158496362, 497803716, 333906955, 986873546, 413433332, 334382579, 816398096, 654536039, 489224625, 969397791, 906515282, 334884227, 72495814, 519711061, 555734868, 153610255, 247989994, 823198301, 161672563, 89094434, 111917521, 961449782, 396955442, 984682388, 524973883, 776193283, 294709583, 429524959, 684712327, 435431431, 524980468, 474454346, 581402004, 849889348, 770299155, 555507618, 908531061, 959855118, 712947542, 4876306, 410358510, 108065261, 18250662, 401152509, 401754812, 680741751, 229216535, 426895821, 167609846, 425874131, 904773317, 326857089, 269599415, 842648338, 85741773, 607484068, 959075188, 187098472, 336748861, 830722866, 543521824, 207995273, 381833440, 884905945, 751125859, 137941245, 618436214, 515552017, 20880542, 796724918, 72191390, 740757809, 713557540, 747749734, 175176639, 262351867, 969106022, 980670942, 308087732, 693657451, 565508733, 479100233, 567951699, 380506572, 251154396, 829351131, 60947534, 78679954, 796743680, 558142897, 539775072, 13522397, 339819356, 332172383, 77437358, 70681093, 110977006, 736538313, 729259556, 570331016, 576129737, 360715479, 40869582, 568954632, 817542196, 620048546, 869735386, 245196333, 771825062, 658496336, 781201149, 89814802, 604666986, 53866263, 986433730, 470384694, 487326488, 531414874, 986119242, 840578497, 729027380, 846174689, 436348246, 938026232, 159760807, 654672612, 799335110, 129075132, 878437103, 615159550, 587409752, 923432874, 830884336, 284364021, 192564519, 310926066, 897157458, 954774976, 212479203, 726313446, 888344416, 943387850, 880830109, 626946620, 843463039, 758006658, 141113379, 456813027, 131028759, 811534652, 926539536, 205479843, 341257625, 395073218, 843975751, 704585511, 293334127, 72965894, 915056451, 815495788, 808235938, 793517860, 775520622, 588056206, 175593219, 795190039, 585789075, 230507917, 319095482, 602796160, 342989955, 280057454, 274288382, 507343890, 413272333, 972428668, 250567004, 691483798, 409162983, 843675462, 831956284, 500158795, 323480362, 742715833, 556273845, 729445651, 516595862, 579094511, 67645524, 705945574, 726535112, 49942376, 200616173, 98253397, 728104060, 849593588, 284036826, 812076101, 595792406, 756835803, 902150256, 525047016, 912586439, 324112952, 403762522, 765384789, 74798069, 270571778, 196710847, 669274080, 103826579, 329943872, 751468706, 75861117, 868989627, 542290929, 448365003, 729332205, 883283809, 819933864, 349491263, 524737421, 371686941, 243307910, 834132009, 232415845, 617551696, 292023149, 423618535, 706821796, 495175437, 432191954, 655297347, 724583136, 409282808, 397921307, 367329569, 57846012, 270559584, 190621114, 66171963, 300474554, 656324594, 217208112, 233994572, 305130997, 891005575, 770433402, 996113589, 23714180, 323510275, 627936913, 694791048, 571473390, 325649974, 85384459, 405878109, 212548910, 323507712, 987819571, 352807656, 363711648, 431875427, 770155122, 69674630, 812545567, 189196252, 540706050, 497010584, 339352832, 912502472, 984900997, 593033570, 87685021, 226609055, 21073057, 614164311, 532682259, 429173021, 780498109, 146069475, 802503001, 694705985, 447350801, 319479998, 768504654, 498618790, 660653309, 995170307, 449758876, 465138326, 328951339, 462342224, 107393436, 470804326, 896739740, 637559895, 936248470, 416612045, 499129441, 340373123, 943174000, 560256470, 440456756, 646078603, 563195898, 533800578, 689599970, 269884579, 916043578, 528738858, 450488067, 81937635, 824740886, 531508331, 172447188, 650696163, 247423933, 317849104, 256960047, 435488135, 433290817, 627476741, 49252669, 188813702, 826134056, 594074841, 712877260, 191172655, 307630779, 22185435, 61915836, 715231298, 193466482, 16898178, 900458352, 827907150, 242007841, 305019698, 614455702, 68016144, 128034761, 569416270, 503395655, 897572871, 100427064, 444811351, 199048714, 124646739, 468151742, 954001026, 804983106, 216987199, 712342907, 721060137, 276868657, 29878203, 910436502, 437231843, 773726071, 69212373, 20437155, 3176104, 716596797, 507303984, 549448344, 785094988, 247585125, 423765909, 471921461, 943225273, 537322507, 875278488, 769704026, 871757527, 260129764, 710455913, 44143736, 187529726, 623685405, 774371705, 382016889, 7602766, 268049313, 426886026, 557866712, 804827850, 542252221, 463829956, 306239871, 961282464, 514464612, 503923715, 707517492, 621655059, 750819424, 449818518, 630988162, 691553587, 705982127, 283130076, 975494911, 66240921, 928397274, 409059290, 420345263, 793206534, 471630636, 777709474, 96686639, 367298109, 501361945, 178904472, 176655337, 52390472, 245454924, 360383427, 809798035, 696697416, 588723270, 598874997, 457598554, 858888026, 306257178, 788315320, 793115856, 387890988, 407243786, 668484814, 588082091, 336554461, 612073188, 982104546, 817699233, 59581485, 472810485, 943297004, 975529058, 738740114, 894293957, 52467514, 980953343, 824595184, 671874269, 966981224, 542435277, 972041927, 855321182, 801638417, 364172640, 123142332, 956769998, 188944883, 21227579, 453175156, 266578838, 796752342, 798355171, 960129007, 366561163, 806061153, 252287086, 612895418, 731516621, 56310153, 778807081, 666466, 374008747, 756195600, 507243487, 105685945, 532903797, 96301442, 788587341, 103875116, 535375217, 695393862, 736832596, 486303845, 295374618, 922786304, 519002562, 572594720, 4842441, 205049267, 419353440, 415980052, 127936840, 74304194, 385513463, 200349843, 521721212, 745915770, 607666662, 407211247, 90121316, 538018147, 856421590, 560793923, 217489133, 387778691, 70138545, 571927102, 356966217, 695960183, 970702677, 916307817, 689879264, 221657190, 349184003, 440093953, 751797073, 796735371, 145843751, 676060522, 805479657, 979281550, 328149891, 876472981, 954265996, 18462147, 849830537, 925590400, 323180366, 704760393, 66237134, 13505458, 695913299, 911230946, 941177001, 387012789, 56311255, 657566051, 193222695, 381986983, 358588143, 541551249, 622740013, 54121524, 861015915, 941001839, 737232474, 860364249, 438932200, 893133393, 478736327, 411463490, 766443201, 328872260, 353977302, 758562341, 991582200, 810943188, 191355313, 555292141, 920531075, 165474643, 684503182, 365667877, 253055786, 731266813, 102638045, 361787707, 440059321, 891401855, 705999064, 560000973, 837736453, 358342605, 192848516, 420058944, 383226489, 153985413, 622356106, 456374174, 146510315, 726985487, 82389300, 327041286, 577195302, 247906231, 496039106, 925152762, 546666804, 170018296, 529436969, 956014641, 313477648, 42769696, 260849876, 684030681, 530922099, 742000698, 96556566, 210732809, 319922937, 442310515, 465043522, 365671718, 765589971, 954961514, 294982068, 217297356, 172051720, 978453629, 504062744, 195534840, 796638177, 455114943, 288983681, 429282774, 379169511, 873474003, 387923998, 849328179, 940874228, 244311212, 601174250, 598298181, 338507210, 734998343, 75656292, 531045056, 18170259, 378741948, 815692162, 697065977, 971471385, 168762316, 295494404, 471738879, 701733225, 897686940, 658812795, 855557835, 666498706, 730587107, 526022292, 776619086, 426323995, 318737836, 853164272, 601778421, 483135142, 92205210, 124534822, 951048110, 619074152, 554156796, 762957454, 44749997, 365566627, 892066248, 670015360, 98729558, 811243859, 234821638, 165552663, 216868168, 907043039, 743621838, 654494259, 213584935, 476264610, 269341073, 501255508, 846806261, 848663759, 133116682, 275031336, 160570639, 989262036, 917626777, 950826994, 853225886, 102071811, 238175473, 569400063, 480565493, 894802984, 132446732, 353408286, 35463852, 629397647, 239622662, 662500191, 579963803, 355349461, 535386210, 563467231, 602783411, 225311197, 280087520, 144322862, 739995290, 131693080, 408164371, 981068383, 380405906, 497664005, 186494232, 588999338, 505897777, 20475567, 243026886, 931850227, 839773118, 730499949, 673407454, 766472219, 918697414, 881144398, 1399477, 683836198, 471457932, 477743298, 34968183, 644143447, 881650718, 437600308, 344988057, 434330412, 587111409, 710593542, 574694646, 55351076, 895558391, 182566926, 333283029, 39467079, 555274559, 718022916, 661660566, 637676468, 590212017, 899330877, 524234703, 147225242, 532201406, 102751336, 232057397, 619191521, 142246082, 356305074, 259939654, 815844380, 220852978, 447495120, 805754138, 103718059, 601231798, 427265571, 319937402, 793781826, 126836123, 14283186, 457987480, 99153070, 86337599, 564277239, 44084361, 706833066, 78197617, 298520512, 91318863, 981991903, 899530057, 248792286, 416180552, 214439776, 702037519, 139675721, 848088059, 208851866, 859993270, 545869374, 382323556, 396771278, 916182350, 899650319, 175641350, 212551907, 528875286, 39641048, 184890279, 735369855, 417313959, 399084643, 82977449, 638283287, 81616331, 294170885, 413624409, 269000913, 294008812, 518976769, 798983439, 343979265, 155216648, 789944068, 403134515, 961720392, 479436653, 625687892, 268075796, 503625986, 431353922, 689807324, 920285370, 775084154, 390021951, 434785224, 103517530, 520261610, 517881675, 689309206, 671285659, 625820626, 607846012, 470789541, 290944863, 539260924, 523541098, 805249673, 733173174, 46747036, 143013018, 154643006, 578450327, 964054669, 557552448, 130735779, 163119956, 487887429, 250212083, 558733288, 64446347, 762086935, 929495991, 395412501, 199342427, 206096683, 90888439, 303449604, 602235517, 727228552, 87212068, 833897887, 742591741, 593120074, 453947608, 554909708, 832705724, 389365820, 130677203, 555465614, 494124573, 137597712, 954692905, 184551410, 26296834, 813839172, 350256119, 557379868, 939011698, 299868037, 100010166, 367332932, 922709846, 674698239, 574922490, 52162138, 731895370, 80623225, 994214906, 61096024, 728046655, 742254980, 353861503, 478904123, 692770425, 305061769, 834385609, 748031701, 649105298, 331504251, 324063550, 565352173, 362228056, 844393484, 352546399, 78763424, 52918799, 385568076, 503338289, 332697042, 353728327, 572406538, 743146130, 188897889, 523013033, 751945715, 989707546, 591110749, 352343532, 384131798, 567080775, 367728299, 468801762, 75056091, 376075128, 408560372, 231665785, 416150474, 771543522, 537138175, 195610543, 636517024, 442831330, 831220873, 198270302, 623005964, 83607392, 666673887, 147816264, 860653455, 700422136, 735199396, 591783896, 668584820, 583371878, 3530155, 997361181, 667126487, 35471984, 105630313, 682712785, 899599697, 326282232, 127263581, 932066294, 461729130, 899464425, 818032110, 673351547, 600366839, 495652796, 529808136, 90877130, 457228000, 433441391, 604247831, 753046218, 612509532, 315318833, 580876214, 242939496, 500469599, 577017572, 748510038, 508377695, 782850892, 610038692, 771106549, 830419154, 533375621, 485177838, 23442940, 361748745, 747417697, 261942755, 675171155, 214004535, 162775509, 752992265, 624250104, 139381674, 288747900, 472746309, 873012159, 473769121, 653150843, 753462435, 369735408, 580559760, 912288179, 564122037, 627785748, 580675635, 792641438, 908676676, 164371935, 551727652, 406667580, 854652557, 658643676, 547723923, 503265574, 78052040, 851001067, 220933294, 332831457, 25325595, 97845101, 232616529, 153910804, 472155502, 875593994, 667502676, 414606696, 156823749, 833993549, 351282083, 197862736, 579584458, 956402731, 948074660, 424985882, 617104151, 623826658, 852417210, 409017742, 996771683, 250355714, 874749405, 751028578, 206425816, 502871661, 518657743, 776881225, 30493129, 389591306, 167914817, 634545395, 157923877, 815839536, 75728476, 859771148, 922189982, 266887608, 566799622, 342430558, 950553284, 152687432, 540296755, 367455628, 22450766, 675938704, 431248469, 857060848, 573787240, 737534865, 338018943, 584441893, 192215331, 378469786, 497896821, 449071149, 841448551, 500951668, 931361234, 784997964, 816555066, 391192280, 228814266, 289850065, 959779121, 447647055, 85955198, 904308725, 666656839, 813312960, 741828504, 49924274, 880815601, 944292882, 805569150, 586062160, 410793849, 177760649, 595321118, 489898818, 366968323, 962668948, 325526234, 589131600, 857879380, 292785198, 420765306, 458377075, 709058076, 134254374, 431904856, 272246133, 276231049, 497650769, 217381268, 358004164, 540124877, 623393159, 197074103, 771030576, 404079852, 777669950, 568551960, 531153075, 417843903, 888311488, 371788953, 761892331, 124325527, 566247144, 412837208, 295944716, 27645932, 329221081, 995411583, 337921734, 654298640, 369408130, 650064060, 15974255, 550298437, 249737503, 574999631, 16419956, 974020394, 275612507, 251466885, 986303625, 935868741, 308264931, 717254663, 347423912, 824778739, 694851494, 198355582, 351582309, 428205682, 62771818, 864691258, 554434531, 186698491, 835422488, 973468624, 334265597, 432844404, 895775565, 511874295, 138365361, 17860020, 952563987, 720871646, 764594574, 121701936, 288038017, 503842862, 148620971, 216106471, 798758009, 468393944, 25061640, 520761470, 724059829, 703997426, 138425592, 832918976, 22586215, 384373830, 839029729, 461078461, 145886128, 737988074, 864142888, 509452026, 737237558, 509342725, 950246276, 98370026, 129926651, 385101909, 562325752, 611034729, 758849612, 809852863, 301679377, 554265135, 642455448, 858767633, 980029611, 690919869, 551084177, 722788835, 279123061, 45398226, 944702412, 566772706, 148584380, 114263868, 104995152, 53806891, 759367819, 683288426, 389936749, 116733696, 803251746, 540595083, 56885046, 148893519, 482302991, 916829934, 775189841, 917573417, 703859182, 136078210, 399428405, 124392866, 864666397, 845751833, 565183901, 397041279, 693921829, 329670694, 997973430, 839358041, 108970477, 226530093, 70093336, 204031281, 876057696, 219763742, 434474875, 813881213, 86195555, 604064690, 937837469, 112819150, 702201239, 243408276, 268241103, 692336946, 612671515, 751736835, 409267529, 218548523, 134765528, 991666249, 546165720, 942255300, 424078298, 447244054, 631542736, 8778825, 321320116, 421517657, 907320586, 526637019, 976575169, 907316318, 821743059, 242443421, 495597138, 735043967, 535847629, 811237584, 859121850, 98081895, 745623947, 292098431, 222414564, 963435324, 795512311, 616534920, 327863536, 671809030, 17559758, 710136878, 583276693, 919438940, 966542862, 118467097, 593645519, 379932724, 415183871, 781977986, 909895048, 423071621, 413380785, 430358986, 871687366, 284403922, 761023125, 307128476, 744764170, 145428669, 900206398, 892570505, 822972209, 180776482, 517859532, 250711712, 528636924, 930219892, 544707114, 690257340, 347502261, 457841092, 930949098, 95889488, 418267370, 377417240, 830890472, 40458771, 301771662, 817542054, 344827619, 350345128, 401789884, 351309095, 533359394, 227848107, 832492838, 658990909, 14921391, 956392707, 625513817, 866956486, 147421144, 522712396, 49690916, 507028173, 101374928, 501449535, 958506430, 229386207, 688729330, 994071637, 15256098, 122255747, 50270577, 446224405, 15251695, 216165943, 259084656, 434115374, 67017877, 76575029, 289323671, 273160178, 640194395, 32801561, 990604162, 323502692, 121513237, 224762577, 268124853, 59071061, 310808682, 802394892, 306328444, 6603762, 582552032, 911672887, 254389730, 526344961, 362183379, 63678577, 647759247, 395412778, 735942699, 659760226, 341835241, 622550233, 626896357, 231684907, 761344466, 219336478, 223381251, 220352537, 778864477, 249091969, 620627463, 929685828, 740694569, 274722867, 266899790, 503809521, 354055058, 956921069, 808152159, 881561346, 778203958, 959922642, 403454601, 908603774, 21603560, 499450738, 371548790, 816940670, 686459555, 685298764, 567748341, 222138986, 20339900, 399047571, 374964700, 939732482, 390364364, 82772003, 755741470, 283475725, 346897803, 379304374, 360026697, 260653308, 277742464, 636724033, 722799777, 481768427, 336520007, 483417327, 971512706, 705596465, 860540605, 742790624, 857765273, 301083669, 62210031, 479672205, 645823285, 120235615, 4440687, 727016861, 9038524, 380510084, 261805379, 853478060, 778734162, 154315887, 487768013, 475889578, 501520340, 213839127, 931123780, 855414457, 948802198, 748074987, 563699679, 294675121, 885513808, 582491019, 287017653, 56571732, 766408830, 726897604, 853261745, 228597236, 586364790, 506100112, 646182667, 446712027, 383649380, 353704878, 876149319, 32395757, 633977337, 404653328, 196088468, 846920522, 17100573, 333849401, 238069364, 205757739, 624301373, 796516483, 687953880, 16233830, 62828923, 932518609, 902336547, 581464546, 372108048, 389961240, 892871997, 116251759, 557617533, 419839815, 578623527, 659549240, 390043106, 362215822, 537291143, 522477695, 518744084, 513225490, 692827722, 287627623, 888688704, 941137548, 90314872, 441921839, 637387200, 259668493, 770493213, 552526451, 848296534, 139197183, 4449006, 432310264, 657891952, 29735820, 687620849, 770628137, 112060514, 543651617, 625335130, 924446, 976365234, 647122124, 893970119, 885514797, 79166772, 904907630, 66783589, 161497217, 500344560, 573683160, 81157308, 66254339, 918225986, 239266543, 455972474, 17802734, 901749490, 831385225, 517492200, 38165777, 18463290, 868080063, 233212852, 114527346, 165562528, 473079653, 189252812, 328015721, 94804288, 233135583, 408424871, 364946485, 924409941, 258726851, 481724760, 236708185, 422679948, 107301874, 266201789, 212667625, 779834325, 469831171, 902981636, 305317330, 567286089, 358093384, 53502913, 225607566, 126291493, 580485969, 821191965, 93351434, 405289595, 324780891, 286598469, 884563281, 607911887, 759634449, 869911381, 448477513, 83824034, 381378539, 152993030, 469142539, 426270147, 735389726, 219750723, 889664737, 655464329, 292224130, 420600812, 959730850, 859662962, 183747933, 235073244, 292681457, 514900205, 800359663, 50725260, 402777470, 925650363, 211293719, 972562706, 122372432, 367586417, 600724054, 486431284, 970750871, 473241212, 334408592, 689713684, 933206767, 755847592, 579502931, 318856432, 489834003, 442785953, 879218362, 624580313, 262124872, 939395351, 808245814, 384739581, 581620065, 628025390, 705221269, 146999163, 929233526, 325677688, 241400770, 28415425, 398067654, 98433504, 259668833, 950108888, 763447211, 147425203, 54604118, 451675677, 624531865, 351897057, 459829162, 951553302, 738820071, 368662359, 75201655, 966989820, 166861640, 388889234, 40459895, 605013839, 269712761, 543963719, 132580574, 535381242, 154348753, 695902229, 908136555, 403519010, 871390805, 529765310, 593281796, 54621457, 618471505, 180806143, 145050163, 104735600, 381755610, 837228323, 39327419, 923079360, 111653198, 768585491, 451973210, 655976736, 349762850, 517278224, 770982677, 720050008, 502834542, 82003895, 719596960, 649101131, 101418003, 664864689, 207554451, 658953101, 59585212, 579023290, 737783073, 820041413, 545483163, 818959699, 2113802, 682464267, 181545868, 777717846, 957117384, 936914950, 610918453, 987544688, 457278854, 228193966, 531793921, 1000740, 806304149, 588239009, 812723163, 578635214, 778665956, 799502993, 208809337, 559966930, 602585043, 849439150, 506614683, 975728295, 249679013, 598878386, 562572116, 488444081, 42401566, 409114264, 282895560, 410252395, 204814497, 591016079, 310006500, 410308340, 134197844, 651315485, 1035155, 545372296, 97564933, 206416861, 442144490, 914491018, 377769929, 592738734, 489568227, 424071260, 818783381, 5797652, 491492430, 539058862, 138578722, 464372027, 873041964, 230872448, 526921380, 315716787, 728088491, 804562011, 212967118, 247990241, 473369730, 678800686, 351583682, 792728340, 112873266, 913742186, 550280992, 713888913, 98754274, 443960207, 692726906, 559839696, 80735743, 246272467, 78690526, 583074955, 273260727, 794917474, 12963009, 261650328, 742926277, 412671323, 687307086, 663920810, 918945394, 763403785, 218243154, 268123167, 832946949, 490814111, 885993151, 684425806, 788468512, 89131611, 784266797, 140108067, 697393213, 60792028, 861016579, 141191221, 589134011, 808570994, 354297806, 346114487, 665695651, 114337324, 512343049, 534477655, 220143957, 925411819, 711554781, 717525194, 24719650, 547537250, 874652695, 913817288, 166811697, 880892322, 913596658, 379898319, 546451664, 606100395, 143246943, 267117837, 870042198, 173990917, 846326056, 916987885, 826618663, 25555958, 835082242, 468393463, 469197791, 461395284, 266985500, 2845299, 438567056, 303620089, 897183674, 504460184, 171254470, 911616373, 430811151, 889661509, 54423710, 178974082, 546823735, 814486660, 220769951, 70986423, 52303760, 514323254, 465854612, 651166720, 806587917, 444277430, 941739350, 564166819, 119934510, 674505159, 300503628, 978521265, 905050590, 24315829, 156527765, 76229966, 38580398, 673149838, 608336729, 635829368, 87802678, 666528284, 392178161, 520359297, 510301126, 373876373, 353744445, 358193594, 368546126, 115861634, 294423714, 505352626, 214628048, 32191070, 549826604, 578269071, 585098425, 868945794, 559815169, 434583583, 563997410, 613699040, 608296772, 60558319, 853533344, 543976740, 155595951, 720853383, 268260889, 207354783, 375123150, 598175998, 507039202, 653124557, 29536626, 880675974, 991109982, 411501499, 607459137, 605327441, 362856308, 474649179, 500267054, 578745342, 412233563, 494750794, 705506289, 868714210, 705291891, 417832148, 62243923, 566037489, 14867531, 236576942, 634124240, 773627963, 120413530, 508323876, 925391395, 412225444, 287300215, 306487284, 385978327, 788742007, 61991567, 619463404, 399555244, 653467899, 897059464, 307644898, 230423951, 584500018, 152247272, 15757694, 406116962, 338079303, 648532777, 193362801, 421185037, 60426138, 910505721, 805256454, 180688689, 780148944, 485256770, 691510437, 572727868, 527763478, 470259311, 330114620, 638067972, 367330219, 867708616, 126808177, 916036250, 164699680, 579286712, 335514190, 259175581, 142260341, 174055665, 174614564, 181353740, 931904553, 23549081, 869762179, 599334899, 768214541, 409710535, 633670111, 747300496, 560169485, 462419708, 898898378, 647568638, 115420867, 978976107, 318125565, 888636258, 423627209, 889624178, 183787515, 632149203, 434058347, 729309957, 259755939, 734181396, 358703661, 651238757, 994640589, 258477514, 237435783, 790888204, 684212690, 596616919, 835278894, 93883296, 673292928, 531865213, 767322707, 900743477, 353385855, 90005113, 520834565, 173028423, 960132093, 697588405, 549043880, 798958586, 575440805, 63260686, 752822391, 682035021, 1138466, 835221651, 85964968, 1985769, 181097994, 787023022, 597580720, 129095026, 466859771, 200102517, 422803878, 537858886, 473131444, 674658679, 675700108, 960733246, 814049010, 892069754, 405203441, 431468274, 550069983, 704789739, 561002084, 189720028, 345904517, 884205232, 230893992, 539974155, 668961687, 624402707, 109747835, 227621324, 237029036, 756713959, 409925424, 954324253, 398065478, 419986964, 996258127, 573127119, 997827341, 440205660, 963325998, 683575937, 940794468, 992470158, 397533604, 62386107, 319637321, 959954914, 313633446, 274239610, 534571527, 626170584, 415185262, 279344793, 853477617, 106921155, 692512079, 443377839, 34667822, 117402492, 37542383, 987887481, 272187548, 789283851, 587234903, 550546600, 175824459, 5376410, 611941670, 158206525, 534409409, 203026228, 7979318, 441812052, 331757528, 454978207, 586178673, 146110004, 987552855, 142639582, 83353273, 123652711, 285737006, 869230360, 814273035, 446646398, 319286063, 187317924, 61882611, 332240433, 4807189, 506086408, 766512061, 220469986, 724133957, 740659021, 61889889, 386752621, 429596212, 661286506, 44395830, 693392915, 378987872, 561054037, 240045412, 847493576, 208767244, 757369523, 617463209, 524286567, 516672384, 519820026, 949879013, 490301691, 683327535, 860263267, 743713423, 175349701, 121837866, 725976829, 276911988, 443451121, 434658835, 259782848, 30147916, 718865327, 534780390, 925453858, 771188152, 69612829, 266569676, 347466916, 823339241, 117968022, 360227732, 495588395, 780314943, 347161892, 673728211, 236509845, 380534399, 744466011, 316323869, 763473488, 521062539, 830004272, 806697567, 582599563, 145136041, 19411103, 321358573, 430795439, 213983925, 177725587, 454348106, 852157342, 169252952, 774885132, 139754244, 11845445, 447806970, 893835642, 596872826, 684410800, 71617695, 137147012, 880383548, 937883139, 106001329, 112874383, 46333933, 517490933, 367257439, 866763692, 440859610, 407050615, 913959157, 943312729, 614614477, 558234820, 515275782, 206860096, 405349603, 631902402, 754824295, 337747981, 433740141, 834582116, 394145435, 453457284, 476710908, 168620123, 546052626, 545600657, 773354319, 172070437, 778650478, 472764305, 589764118, 720985646, 385183604, 334748802, 604146908, 948657116, 936984248, 390526216, 125824607, 217657491, 610086986, 144797072, 606677004, 936431975, 825396755, 462754014, 343079363, 493501772, 752521517, 308707498, 846452287, 368722001, 868662115, 171682341, 363141000, 579928905, 979541529, 537827920, 650578318, 288807887, 418730985, 576634921, 463432379, 498244201, 929032113, 794079853, 538579076, 697829082, 499078133, 709415890, 388348189, 702962354, 158317763, 280339080, 282328643, 177791049, 628165045, 493151203, 680104979, 950500601, 15935445, 689075114, 468194240, 648090109, 46223536, 939462422, 343036916, 703636789, 266640064, 118912687, 569452315, 463174350, 942888330, 661935682, 483174672, 450161214, 912388819, 726129325, 316372585, 638285377, 250888543, 581808022, 168396791, 314145349, 57536266, 931622131, 528058141, 907847210, 788040791, 350216742, 52530620, 129503842, 782933634, 993093389, 289665660, 495226695, 737649525, 862036089, 921921914, 917069625, 544452906, 23269850, 218052363, 404978277, 943383544, 872552406, 43050973, 734820646, 569003128, 726004157, 716271383, 179331275, 367281127, 734583707, 902809740, 465394807, 513528103, 766765082, 764395944, 831883086, 593816219, 142030698, 945815572, 203753871, 667658331, 159854212, 366639658, 664943328, 907467819, 17471133, 93981007, 583273758, 392647488, 15483047, 128694940, 250302578, 280492330, 742761091, 496804228, 603144630, 908301195, 854236907, 184086793, 727664363, 179113394, 986210820, 891136463, 871176152, 370441299, 797794251, 753032442, 43805438, 309602783, 805882539, 756904207, 957313668, 434700583, 320388654, 47237841, 3001872, 313958972, 694165034, 257674738, 176067036, 594782636, 444029196, 236953463, 807084536, 248421229, 46722331, 918540780, 981748763, 972139169, 339222759, 664995883, 788228722, 457858917, 253415461, 105556081, 631079246, 973753985, 150964741, 180001531, 86119661, 291400428, 702582205, 589432062, 756022552, 655864038, 540675825, 567554082, 594387248, 792530499, 361554351, 724110710, 946464972, 390452102, 501999070, 366287203, 646139488, 154296410, 968838342, 40633963, 959890894, 400946007, 575861768, 161303022, 545509055, 389267437, 145456957, 692982583, 541150198, 649405218, 330677176, 397412260, 462017806, 924649346, 905544237, 373402228, 50612215, 747996876, 222162966, 520322513, 766821634, 138611104, 774192142, 806369022, 273740382, 21571579, 294248557, 186503125, 879309141, 985628256, 512918700, 418462939, 712622596, 14496527, 463768787, 839998234, 413822603, 577826653, 249917759, 475398001, 711082306, 854211714, 621132325, 838158899, 83996321, 552690069, 781120582, 926286379, 803336132, 731292494, 150809704, 869279715, 608968552, 483393017, 732755118, 534013885, 970361733, 266933450, 368753429, 766050242, 763284592, 605106212, 888780260, 52596483, 963515062, 886130254, 663330223, 510007652, 483147725, 912679982, 52906285, 273285486, 321965528, 562772359, 151430803, 119348581, 117354697, 509529757, 812972521, 640556144, 940069759, 852247337, 645926825, 818522311, 799141333, 870303309, 626207167, 956812415, 798542377, 300741215, 521758120, 846968866, 292307522, 897867629, 21379550, 911315965, 131998325, 99750334, 622555104, 578153451, 441038474, 194670293, 807305861, 599909285, 248015387, 119511542, 422998416, 315045822, 98053192, 56088803, 159447678, 331122174, 541647379, 636735945, 782932919, 204859652, 486068822, 951229896, 816145282, 256032932, 744132008, 90869860, 897586374, 820891406, 583844874, 180446503, 77539746, 199334939, 637887412, 955634913, 690547745, 480679950, 550443669, 975157533, 523529409, 34525763, 776576027, 309798155, 307361224, 718262266, 264044225, 839898773, 450771500, 423837924, 849731007, 536484698, 675531357, 891897990, 463196429, 402606650, 251158810, 498492270, 408688332, 305097564, 571682032, 572007955, 99068130, 640924022, 986039901, 682161021, 895900724, 238093821, 644215117, 533938953, 688054852, 125556723, 434472093, 149002849, 487730876, 280830600, 722370692, 299707513, 202756569, 895327237, 893665869, 350193278, 963511582, 921275378, 332647698, 642170371, 775598537, 517129030, 386568036, 542690706, 736506846, 610822370, 356529534, 672736660, 28669941, 405949208, 761894131, 415148212, 173961385, 214774109, 693364651, 688838628, 965808775, 479101602, 488603326, 521324037, 795014644, 670871328, 894768067, 626600283, 156903012, 826437912, 483807627, 117762220, 40800904, 887394321, 709669657, 609990226, 926202856, 126709437, 566834855, 111599402, 693673492, 72994807, 414953922, 188943744, 339149972, 655736233, 539813144, 60047995, 293119824, 124277026, 503563255, 644859060, 952018766, 735948194, 474777298, 984076133, 744687854, 74009819, 887680145, 463737723, 459564269, 118055669, 327417861, 136256044, 595029926, 707441609, 151595773, 166423154, 954562106, 758161231, 512566085, 504766612, 680892121, 75004551, 918134921, 857405877, 629375490, 92739826, 289149540, 485701744, 283759755, 266428132, 564739933, 821984569, 856426840, 950551701, 371413863, 761190852, 99124232, 596587293, 254978699, 524919272, 214331143, 646779260, 999943622, 848713059, 657230054, 486665071, 932733802, 948726761, 893992849, 426623262, 140257072, 21052658, 302654235, 640057923, 677984346, 517750995, 466461260, 582362584, 924938328, 985772802, 524377254, 994542733, 490830370, 892202596, 921819060, 824118212, 368951141, 428388982, 788533987, 54158599, 984643926, 398889834, 862476892, 481931344, 669588783, 233693351, 330985403, 597407353, 133807588, 730873015, 424569077, 185767139, 894819995, 899048984, 224262508, 48318198, 684223462, 248709333, 250267085, 983190347, 737019456, 58128438, 81621141, 41614376, 870987509, 121148436, 958292781, 894906002, 37751707, 501432764, 232945122, 37794064, 85847027, 660745709, 180789900, 241618426, 95626106, 838315368, 621496156, 261241690, 578298382, 742122637, 880457556, 799222038, 391258358, 458698105, 443379870, 202898008, 586785674, 972896950, 493705674, 375183051, 928176191, 49178726, 184048082, 844720641, 360843199, 420991565, 762432006, 726945989, 586312387, 248360340, 266521062, 194014752, 722243949, 929308537, 91595698, 50058862, 889157142, 219796536, 344301766, 88790177, 364751190, 725773673, 754329565, 427895968, 99299038, 51199912, 202743663, 474169883, 731824517, 527142361, 8766083, 263629182, 470504293, 256859069, 9194713, 744014690, 368260473, 469487350, 991235541, 893855519, 367266635, 986735506, 192759016, 417546672, 925285587, 820617997, 505675315, 348291784, 349295667, 118902582, 518480393, 878131459, 840455081, 602000530, 410431815, 823735188, 105803440, 154564272, 54927648, 810106951, 325243759, 640416707, 308263681, 207011029, 711763012, 62043828, 811714588, 962276112, 15601134, 381002646, 476483059, 801182440, 154928896, 128699991, 543345945, 787763253, 728212020, 271028723, 575979621, 368035108, 176107177, 700835498, 735711105, 617689298, 646513308, 254256120, 532404460, 248726147, 513300164, 22897286, 948360220, 909071291, 651693281, 563563667, 719751090, 702134060, 794053789, 492640278, 130965636, 686968893, 30886243, 784536855, 281234479, 952642256, 793263975, 847946505, 171490250, 131419884, 435038407, 616345794, 300542081, 781480005, 203171762, 657918024, 967804211, 870699091, 971569706, 859795600, 161778117, 667439531, 573481226, 823088711, 633006025, 363621037, 595316715, 394846901, 341071667, 902536076, 714705789, 381324996, 408777455, 37962226, 648561788, 707246175, 219511925, 517064454, 803172368, 359925101, 879879286, 210866724, 111191301, 699751178, 95813792, 497108924, 115055817, 757220308, 241275355, 620454100, 573655226, 969052764, 297052951, 782486843, 194337892, 580998735, 193672630, 389206488, 985446377, 65000898, 215719647, 556486380, 471612904, 704715091, 461442756, 314330231, 383291545, 564847769, 440296695, 86174072, 958289826, 167345463, 406473840, 548158301, 895525695, 739417720, 694948961, 228097285, 549836045, 782201381, 814437652, 337055162, 704741186, 851533973, 865245585, 306880643, 370503494, 534512244, 541433580, 188720392, 759474561, 135258893, 902020430, 311616533, 163121986, 647261686, 230199094, 913334283, 196557525, 704834118, 320811661, 913481115, 518216882, 174734254, 250786153, 169166857, 926979905, 991048411, 65592336, 699371528, 876697811, 899515423, 385538228, 328319629, 238148943, 132376966, 13718213, 917994190, 585741003, 545399187, 263957211, 905994812, 271860670, 52897987, 303573345, 304569305, 562772081, 796366014, 112745930, 225455266, 643606991, 448215520, 200356633, 86933982, 800403615, 162076751, 729112643, 703005965, 958935886, 125778792, 741121122, 120157912, 156652897, 166712892, 536404630, 693230066, 907763225, 665691521, 496017295, 337542615, 46453358, 663269580, 315148735, 471433213, 216801358, 911340796, 661860509, 203261340, 918413583, 774510508, 705908914, 527463214, 302035872, 393745907, 473876082, 615153935, 34447396, 254281467, 914280667, 390979646, 958215195, 597314255, 388287244, 421983809, 77878675, 202486177, 292539327, 456888911, 749132997, 951526115, 954114781, 466555465, 307064232, 746979502, 479328009, 90655593, 330411271, 244665733, 255906930, 491276122, 565253522, 247168322, 826862393, 204764715, 623444304, 669488952, 783434959, 722319274, 249175580, 858046684, 234379476, 915113563, 357636310, 539005549, 917838815, 237506568, 403175135, 290496692, 388182742, 979043124, 466741010, 108504296, 762262911, 764103279, 543387582, 81681853, 684076286, 17659373, 452384170, 694253896, 368604, 961832295, 232149152, 446030125, 931276032, 850331583, 811147881, 693193909, 297659903, 258477431, 414867978, 380207451, 804333238, 477569335, 675503862, 74072804, 594567907, 688238971, 378210575, 540200992, 317591930, 938590754, 878630262, 579446653, 117337419, 633405939, 411956159, 541802417, 442809390, 687918517, 77886883, 365143404, 928648970, 457622050, 565230283, 616604009, 187842314, 478040976, 163976287, 925476747, 300554429, 707749859, 146743954, 895176702, 842535781, 913168768, 867130432, 394035173, 314413093, 4094957, 770791434, 323267730, 15143598, 160396513, 420876262, 656402748, 501526343, 499551647, 802941968, 970256796, 517840368, 224126565, 519886243, 224926863, 916087579, 873569535, 816283169, 475957765, 154196776, 75072641, 992915120, 328889846, 280122849, 479644033, 915652733, 140103022, 915631950, 314391780, 965073674, 713189300, 506918954, 781260339, 375567405, 207744848, 85504724, 929490267, 196112322, 314962167, 391828399, 758518768, 756387342, 320442905, 856919537, 824124250, 417973785, 493216227, 225673418, 707468555, 568910486, 945520071, 521059772, 319342057, 182843572, 703202254, 563495128, 699298966, 951385540, 877337377, 558228917, 362440380, 451096395, 507318585, 975978128, 34291683, 949317178, 934616586, 124512707, 645571259, 157270638, 281425814, 733426782, 518234665, 652515243, 376778766, 289031074, 866156084, 110651716, 751231797, 454481363, 330786403, 365379324, 191440755, 512987560, 790663864, 391994015, 818985382, 426328026, 887811070, 632719000, 699974005, 672906005, 879856802, 155042141, 341653535, 822453744, 600932915, 714223073, 256465300, 28208816, 268898494, 448033637, 927041109, 542880573, 529771117, 418703933, 30153895, 156938527, 789833006, 747663388, 725743532, 343083230, 816081580, 312753263, 21034107, 689314356, 232059213, 819578380, 783462316, 613363151, 637123698, 282459335, 356988139, 549656084, 832903069, 743649527, 127357576, 920447466, 866850399, 679519842, 918499840, 683581687, 704945311, 406356003, 668266550, 857633381, 200632174, 860435119, 931442314, 635021277, 360548291, 535726014, 667849447, 845570138, 111408124, 366008010, 730412026, 296047012, 321210398, 55045813, 592479393, 255706800, 604258449, 855747569, 754447921, 376019678, 365211122, 25058568, 577043986, 567826783, 254149200, 865650641, 701689987, 586937175, 458075552, 589158729, 572319036, 189820212, 95152019, 574229338, 642806392, 121696313, 165424531, 473227803, 37176710, 870697704, 286660182, 808657738, 437884337, 963924340, 712826168, 401797601, 92398849, 786759038, 464188925, 65077088, 375706928, 725555249, 471640816, 584530519, 462137704, 925783954, 596233296, 152756954, 965000210, 467216760, 659429251, 785728281, 789541249, 890078867, 831641952, 599214101, 425308309, 163186712, 280771976, 998628007, 608611591, 46851065, 453437129, 910819905, 813479280, 31605961, 940972639, 645986712, 469541690, 673283085, 53397897, 949524779, 785984086, 884894129, 100728581, 312440943, 492644466, 416055423, 888939612, 858596267, 643045749, 858838878, 946912832, 976952581, 380068226, 773720006, 514061753, 14283246, 777656215, 669390059, 452095529, 424597523, 530690644, 195117550, 323243670, 370955218, 195047971, 228606671, 974755280, 261451915, 297152742, 982462697, 9475296, 576280999, 917259622, 190452947, 755877506, 513623338, 719691690, 149893307, 962522751, 854829066, 790335608, 80871924, 59075248, 636247353, 595445098, 575288506, 248791800, 671144378, 761573223, 306442746, 781779900, 206343050, 627173676, 153279932, 544138619, 371089046, 331461710, 164715545, 396743045, 132296905, 851140675, 711909524, 614358667, 299693452, 14905507, 549230034, 19257492, 779374064, 791384118, 171737685, 437630771, 172466382, 394615882, 930786042, 58662256, 235299759, 607893097, 197639669, 289624857, 174261228, 305179064, 75913685, 617802957, 746395543, 939852589, 383378381, 647310068, 436093282, 645864804, 917058934, 354394142, 645735392, 866346217, 764043782, 813012730, 402002936, 998197901, 760144162, 690795922, 890111560, 336660966, 767709433, 364183014, 939962558, 272139901, 92542215, 800787323, 926686704, 955626424, 709997904, 255953689, 55408392, 223786790, 302144068, 675891294, 822138126, 575162247, 117155008, 118950665, 834498642, 427377797, 56221863, 945019451, 770146880, 726034658, 76477794, 433719902, 519356268, 874774331, 187909485, 853414696, 632366374, 934605083, 556778041, 366224710, 262597988, 286270449, 729554714, 458741071, 397821948, 469263645, 754459429, 436814679, 854141512, 108228267, 735738219, 620684973, 331436199, 292099940, 916883951, 175115430, 431274949, 407864304, 716005406, 225687625, 740366694, 395495184, 540288064, 590046641, 46036295, 745153488, 681598064, 831981806, 589030393, 101767107, 99069931, 106497750, 961327939, 834570981, 16627674, 235512343, 524032372, 657937874, 816294200, 693186034, 574500490, 7686048, 339470627, 280643256, 25485666, 254330591, 114770979, 23646801, 356555033, 264423759, 406397829, 285172653, 250547798, 552453728, 239454580, 434287768, 142009934, 358580192, 732128952, 298648034, 167000648, 95560783, 540235518, 303276815, 197749407, 110190689, 783532891, 82471425, 159404314, 614109577, 298689718, 192580262, 314080810, 936380656, 106924101, 440062734, 567573328, 95899393, 123249316, 136754024, 360179331, 228339262, 827932072, 449663091, 339814742, 704576638, 825921467, 371606388, 60735350, 603620933, 700578023, 874328353, 416656347, 611730492, 775391309, 220755423, 943563093, 149244917, 494932148, 161413399, 282472058, 273178592, 35403266, 938373210, 467122024, 438883083, 681769963, 205608519, 649426798, 781787491, 897450806, 643215340, 921300614, 161621025, 729142351, 565500139, 579429445, 358770378, 611853648, 605439534, 763259155, 566223251, 332083619, 570205557, 640860738, 251835497, 995712532, 633857752, 401073326, 741628142, 681015433, 671835394, 995257108, 697472415, 490832929, 401775749, 68982716, 917102241, 264830058, 645800939, 337152559, 668338080, 99846380, 113768379, 896998935, 107714427, 677676992, 223075902, 348629457, 160166805, 765997516, 376996342, 16779261, 647442156, 952633389, 458470481, 946201342, 844111739, 4400404, 742299841, 320406043, 501796102, 430238106, 15851525, 247963057, 955839647, 964967662, 530530571, 898909015, 274352534, 492911134, 131598738, 606504150, 210254281, 979266533, 857962256, 847301353, 289502511, 722016543, 219057644, 254184322, 486474081, 415479405, 340247065, 257427329, 415936166, 724408472, 227487538, 783174074, 994515414, 948553882, 910273805, 646263613, 798470076, 268304575, 49717201, 753193246, 212199849, 606770398, 804895681, 293179875, 41788896, 120452761, 486393566, 871773071, 734068221, 427508696, 176972151, 370781205, 742868336, 637513772, 64693021, 46191592, 933719618, 176661610, 927691272, 44896222, 953637061, 168996811, 923957298, 480844560, 300085113, 478113007, 451146298, 288266964, 568265632, 4758006, 168701259, 238207161, 341579833, 101923170, 108724949, 203736048, 636169290, 199101607, 142204918, 328802144, 894690022, 50171496, 679773415, 212951128, 325895519, 166965285, 861904015, 852790384, 637804728, 327917691, 706551859, 549310825, 880257217, 935521019, 612612902, 836358758, 913188345, 964146848, 204017821, 876290569, 199578093, 260295984, 331872752, 847656830, 84656439, 205249990, 968415696, 797276530, 243683061, 903312216, 319365000, 511442079, 908565381, 199056756, 501488646, 317506990, 96785909, 932594809, 456555091, 441137599, 444251541, 462098033, 755898581, 808499839, 209877603, 512528477, 421695699, 205474836, 726166912, 426495177, 511194170, 590872876, 462199848, 750906430, 874036457, 330181650, 349814288, 996552538, 286648345, 702801055, 231705994, 327281372, 536071385, 886148518, 386388818, 126927278, 190530738, 30054493, 841087675, 586002777, 771646322, 32194809, 602743400, 569011943, 952110472, 941611605, 524544478, 797483669, 359949065, 70353104, 529631719, 635906400, 229626842, 616935068, 289172146, 750770517, 810191006, 306185976, 459335696, 795491351, 162638458, 115406256, 123319346, 32033531, 355244203, 918594143, 989170573, 780870607, 54600517, 281014698, 51147369, 700580840, 926994657, 502402000, 491898959, 491012474, 805080619, 644496281, 437220689, 417703617, 527946894, 540078552, 498580275, 359378200, 329184642, 611812137, 939935633, 790075679, 609032252, 738123654, 961643501, 669457079, 707682602, 300679403, 763942877, 631109171, 233300788, 908143642, 824507243, 699684324, 317047880, 684094473, 575562221, 315396437, 840412130, 387071080, 70350013, 539010761, 296420987, 717733129, 510126260, 355363453, 353551489, 287183338, 875189556, 308263793, 868077478, 42230943, 71622879, 748197475, 290607651, 239969895, 428213599, 101246415, 545867465, 882390147, 61728066, 525511875, 85428252, 509143524, 567203493, 420183030, 788308074, 864513756, 935012694, 742935005, 868892567, 49803027, 411211113, 699118387, 696067205, 558603096, 47051937, 598550050, 628614440, 319532610, 997102530, 318265616, 587733625, 989961208, 125937687, 43881211, 717837988, 359449172, 858760744, 917829073, 947414023, 470233664, 496276020, 148671415, 870072747, 521419480, 876952956, 505342546, 431799630, 755771950, 828615820, 583379985, 522533580, 305442802, 245876945, 492495791, 85358578, 100321627, 383384750, 13976965, 87550407, 968316638, 872424866, 862957625, 346631196, 767115496, 840873949, 605448943, 80577554, 857792440, 171302170, 18401063, 371772941, 425229791, 88891892, 702191540, 317373491, 271632676, 614945298, 187429799, 95354914, 506458578, 275363518, 254947738, 327365667, 543699433, 409150946, 587586147, 679113863, 826013094, 517764239, 261113364, 469680521, 122713174, 689320808, 56543294, 427375618, 105276514, 433684307, 528232996, 245860870, 793375073, 950418902, 743798022, 163051139, 857605315, 802615563, 322037017, 879488422, 578440848, 228229897, 367379253, 258725011, 859121804, 429149022, 404168147, 282066065, 498928826, 760578485, 326062519, 388353818, 193600220, 51009931, 896410438, 633446376, 383586836, 374529658, 587640568, 690883441, 104304971, 674918799, 534675376, 752690531, 62568960, 499431587, 104385005, 847325008, 264904273, 115247553, 435570681, 372547729, 950230431, 136775786, 856634883, 208138223, 239962292, 839623008, 530105629, 155522797, 165300092, 259330597, 775431007, 534647902, 518355939, 947289105, 456689912, 613874158, 821686305, 560009143, 410324335, 248568434, 144037217, 385488782, 429570739, 612860581, 622037911, 929079427, 873758251, 209342611, 563740819, 992474034, 884210459, 778899989, 611009458, 350339186, 243712701, 669666988, 699035569, 788970844, 558354203, 573205190, 234827948, 164540279, 33413593, 227682832, 997325430, 530514528, 349152525, 802669196, 6500762, 252077496, 434554372, 869368827, 412106121, 479547325, 478624490, 74760604, 569379421, 925793100, 199110806, 635085597, 701007636, 757781683, 284063610, 911006734, 730607193, 701842085, 869582447, 347935090, 857415094, 537297815, 345898650, 108051302, 882111644, 959168045, 612564494, 521139812, 845403596, 271597021, 61275069, 786696972, 299888202, 463067025, 974480062, 240435859, 554055333, 512820310, 789515863, 314468988, 859267998, 523381689, 447859899, 95584819, 953476162, 863343080, 413196516, 105823391, 471205455, 222403050, 17159053, 590711935, 163165805, 792261998, 415019772, 811282507, 11974596, 185239694, 339011508, 810339681, 482667359, 328541606, 808208661, 137021183, 883066464, 123974192, 35617455, 882299873, 541286365, 5909643, 333801487, 249730293, 963359042, 688483606, 303354424, 175511676, 847931745, 435638563, 230324649, 603433653, 714073231, 949478577, 11880124, 990515708, 233152405, 924716097, 602823155, 752741906, 407725222, 928685459, 680311270, 585805770, 714736087, 853610840, 82699440, 712690590, 366877212, 483770849, 518210285, 984240678, 986834731, 273979053, 402474344, 357659136, 237182503, 717439171, 33032844, 796061233, 889809195, 134008933, 801353264, 103632727, 480621196, 528005862, 550230115, 392961059, 428791352, 477790849, 299055413, 811725385, 172448159, 442960844, 898756340, 4150771, 835306039, 695491383, 142141534, 9791908, 884652583, 599942888, 888690651, 812792565, 79026742, 388063102, 941532854, 232807438, 268666534, 894796817, 327162065, 429996888, 777132170, 436486913, 633930407, 277735028, 634782006, 733106584, 502477906, 409624679, 811124874, 289737481, 693453657, 773881401, 950527049, 244317076, 834235875, 817522501, 343565311, 109943134, 851535208, 268360888, 697630145, 908104393, 472357540, 584834037, 273305230, 733827827, 667890382, 432088217, 141166510, 217158068, 788067277, 583563160, 901798007, 997951416, 288224386, 140536945, 151292108, 304475284, 141171390, 533285011, 412286698, 804497433, 277883515, 179710115, 846008686, 605143898, 816643532, 535367180, 773004641, 366624277, 199680352, 684522775, 178263844, 278962433, 346452473, 95543753, 261768869, 921038920, 884576402, 935662361, 254051521, 92530535, 665378833, 649982213, 278212823, 26974489, 289685597, 465302177, 288412453, 828915794, 957544099, 280018161, 619451759, 74730520, 534788627, 832112426, 16511625, 777491842, 182853892, 202853178, 95134758, 882233625, 254788723, 696901641, 163615486, 678428716, 490314425, 983578994, 699567425, 923892494, 313441565, 210518173, 988644068, 746057717, 618063127, 51112296, 988884613, 837963677, 61785452, 17892542, 247684840, 194107396, 488326485, 199330313, 603422967, 465292246, 575757422, 309856572, 246352663, 656868416, 952952436, 32196882, 363235833, 633290484, 59657057, 838924573, 132345936, 639527564, 645909025, 391010996, 694237129, 828246862, 466311656, 322460777, 756187294, 919895638, 29253680, 856802816, 179800142, 776439445, 653835905, 44759219, 471082467, 894516834, 472743285, 862977277, 939182221, 343716203, 986439306, 395592906, 785720336, 72045567, 97064731, 188776644, 877658981, 764129542, 800304347, 919626547, 94718405, 980058195, 46892027, 86474689, 152321523, 226780955, 442461802, 385118582, 142559210, 175813755, 563454200, 479916581, 565115957, 312147944, 108464524, 790586299, 534279882, 947743990, 843411609, 684314462, 114123798, 103843363, 126155340, 472602020, 798018510, 622424689, 528121321, 817280227, 978423265, 625370261, 86927376, 799215119, 201196334, 355087185, 693144349, 731520604, 358502078, 410427339, 751242228, 844919284, 499621490, 763427448, 19807120, 722667617, 987943872, 155841556, 961028585, 451543466, 504270312, 24083333, 333781333, 493673146, 79894553, 454218636, 578884511, 588303103, 363755110, 245680950, 19797474, 426554240, 292038400, 122453662, 147399179, 390694923, 844185061, 550075867, 38828403, 346049081, 663164314, 727012028, 230976673, 632971087, 846925513, 56176667, 513357054, 39184705, 452167246, 70938608, 5428243, 564334187, 912672509, 215229241, 686389120, 986626804, 878350568, 967054676, 754230384, 231683156, 86327375, 405812851, 843806941, 793948421, 797122645, 117227318, 514930750, 986788111, 209886515, 247831720, 625041854, 246107686, 532965029, 499037371, 865705544, 646470024, 633099445, 221731854, 137641085, 427596721, 423212264, 153055615, 371979263, 490209455, 270582025, 556764063, 760881296, 972381411, 757811426, 203570750, 898585252, 19873758, 70739866, 185803516, 395063005, 396166875, 679465581, 174177030, 332444594, 67708510, 175482540, 214571944, 150073934, 933858886, 108579786, 250498265, 810105813, 713090649, 798440586, 232406932, 350065432, 492769557, 142689203, 714513032, 90315489, 737858370, 232288604, 957789082, 82907306, 986258377, 746323153, 382223073, 748390690, 200062697, 880988223, 69710494, 638244504, 391467547, 345027949, 976682929, 246011377, 722816332, 140575350, 136475022, 825965856, 904353122, 61599590, 982009941, 401166277, 884392458, 62342126, 213490001, 218133979, 534576679, 288886660, 837023142, 229308885, 577874384, 335172197, 329623020, 469023504, 96392213, 590886986, 429809355, 165584726, 496553015, 781638898, 726293150, 25573703, 584019654, 289817889, 138514214, 137595026, 571309456, 63107663, 549194203, 774601793, 15649584, 557037647, 969817668, 256824605, 57052508, 199380530, 634577868, 518113968, 945137522, 334327072, 310398622, 617137780, 834491763, 589633777, 29198722, 876012534, 405778582, 455930706, 391908781, 928163492, 603689633, 167126886, 938707084, 174351186, 144031254, 702465484, 184491300, 785594436, 103836850, 70120272, 860487732, 867416669, 423342121, 598131290, 844496749, 723990115, 255780029, 840685097, 305339608, 74974474, 22510221, 76537984, 76034729, 816485126, 915807778, 597708988, 626765530, 24677866, 479254067, 444751120, 796930759, 730892953, 6078785, 507464650, 559740661, 207174774, 257835110, 311760568, 514359433, 287382565, 155348082, 660094544, 125574061, 796952367, 596940556, 87477711, 632023994, 512508875, 566981575, 739517844, 19881324, 767742232, 631605662, 45284765, 3925053, 652540428, 799848411, 992759585, 90987441, 859661128, 970707756, 653438814, 121833976, 803974441, 653421410, 538017899, 334388266, 10856141, 312542232, 387588729, 264083191, 306683025, 957815660, 395286692, 31367088, 619236717, 522581967, 879742564, 261059656, 296429181, 331700415, 159723799, 62209453, 305439516, 585631073, 431640119, 313574001, 779818603, 986754120, 527227611, 953564834, 655186993, 837924749, 871075911, 616521417, 193415179, 290516668, 459937017, 785789013, 19714690, 398295676, 521722100, 122180726, 3925277, 42246748, 93102057, 402088250, 798242306, 348749523, 204658177, 496507005, 235493552, 382446233, 343148472, 973656672, 661322986, 186768395, 535367939, 806663120, 212728833, 555866319, 828097496, 296273138, 80965855, 25493601, 711793981, 886557901, 283524454, 25163026, 190781889, 464476453, 908493221, 449269210, 140138039, 157697560, 699855905, 900872594, 980677233, 183741822, 661013079, 113788717, 439584789, 266517428, 479193190, 885827754, 294378984, 292108762, 405378829, 320235920, 976136176, 327549031, 866162174, 964601445, 152887618, 608330401, 10682923, 473445688, 197816741, 330267283, 624255701, 770870079, 579740312, 967387521, 956873471, 309518496, 124832543, 773222375, 261505083, 41387705, 907752708, 941838501, 268132412, 51875860, 41591704, 903714115, 828584352, 183546250, 396923508, 612740816, 221174526, 782042362, 183480895, 520331839, 892795314, 33989160, 676363621, 977696868, 586107250, 938471122, 782405689, 473720742, 127956862, 556214218, 391623838, 361067210, 56577364, 511681692, 474371130, 589120958, 910627483, 947030845, 355854127, 579621278, 714530292, 898692984, 876857531, 661187893, 805075077, 843835121, 890124496, 258513157, 543385818, 969052231, 759522097, 195817957, 222325749, 366618749, 589980427, 617639148, 125664452, 185717900, 88605048, 400627407, 178255276, 164490758, 905636421, 338027570, 69245214, 483594130, 109962694, 834943323, 746064452, 500483675, 113395562, 676751294, 735137429, 109048753, 198899841, 921938678, 30881601, 141558939, 388993666, 699971468, 305295088, 366159710, 218717628, 806783376, 960579558, 160133194, 211688795, 18853063, 424770959, 47937969, 311255885, 542694705, 389577486, 941306340, 502234042, 633590804, 382704559, 235092215, 164080873, 485181079, 338512596, 225537007, 489082514, 717568802, 673401080, 437869053, 697884857, 36382600, 705198618, 488387309, 92205099, 170291544, 848281341, 940043588, 553244005, 890821697, 757607167, 748120440, 177472176, 331750702, 997128955, 647953913, 397507803, 323097881, 745140800, 858060355, 438992065, 804740563, 799021416, 187267500, 908360057, 981259226, 789279424, 794907655, 139153566, 445472038, 313564781, 508573661, 552650235, 269102920, 494401443, 186218893, 318470867, 954773347, 224462868, 672213484, 650315671, 555915886, 335405160, 544683113, 62478199, 298152817, 167154922, 652171560, 741881833, 363670049, 654446533, 357753997, 775785381, 639099051, 80165635, 673348656, 889671217, 874248116, 973404216, 557554434, 887372581, 776092861, 20416962, 654739036, 251218610, 166527547, 837926965, 564545663, 176583555, 150097370, 448477063, 983270830, 237723005, 994796200, 180576585, 477808490, 131225033, 244131366, 550832312, 193369086, 8541329, 477179894, 455168519, 790832108, 60898395, 52015936, 91844902, 744232911, 247028177, 342114241, 913322744, 644919811, 330776871, 405418236, 139233843, 290184275, 625837088, 166096315, 188263174, 558599177, 524391329, 612280851, 181056512, 973219861, 691316784, 751319934, 530233604, 319022658, 263273210, 701661038, 400468951, 617836529, 274123531, 647872242, 126448130, 492489076, 731573834, 740442976, 584129053, 898569186, 187543769, 819386154, 602021078, 245592223, 329070109, 70040346, 807324398, 307288637, 938655185, 407585276, 504848215, 292739781, 232779590, 901944443, 766868389, 312780899, 967085945, 180216104, 690585471, 795868181, 975308733, 874564934, 162833201, 239062441, 81430735, 437946237, 432790001, 672003732, 28828237, 940079328, 665217508, 54469871, 591571430, 117586205, 473164715, 425992606, 267761107, 14651412, 543090291, 489334924, 372960496, 34527889, 739948577, 870784186, 161726374, 270377411, 443158761, 644280921, 209943296, 828394185, 879157191, 267877612, 919493932, 271192229, 348097505, 710060306, 916910864, 899649357, 945193176, 722986375, 516027937, 758994286, 420899388, 82709791, 222078359, 844883411, 684141082, 538860057, 818616463, 789834341, 609204537, 54072571, 218004713, 746318765, 936294065, 256378198, 663038388, 200761911, 15639758, 306942736, 343433658, 603729920, 948180746, 829513110, 708681139, 482891015, 592041687, 462844260, 433824092, 989495403, 538854258, 453747663, 282719431, 206825397, 336380162, 829392936, 194594668, 12217360, 693764372, 466852271, 149756497, 889971960, 56830249, 722745383, 37964763, 387575675, 193576912, 200549739, 722556407, 207272461, 678598832, 388429374, 176906134, 442769544, 809811857, 243343601, 520070758, 808431312, 861046853, 856469962, 439276281, 168732858, 797238047, 89985522, 632265654, 82853686, 541230380, 49056568, 225562653, 638809547, 954911947, 138503923, 632972267, 911427261, 639744024, 524681283, 820028577, 691074157, 429010654, 678563893, 883959068, 293308367, 28632507, 604751934, 704095315, 928846923, 674302342, 691284773, 152994020, 104875391, 364763591, 656965958, 834608115, 896622688, 28130459, 241259001, 664103727, 485731540, 663042039, 450751470, 862760282, 106689001, 674099869, 879700546, 987679286, 148646132, 946707532, 526894183, 286381662, 314212746, 818339819, 229500576, 819583853, 232466866, 22614141, 696041670, 695998233, 480813324, 207604422, 346788924, 936943897, 583657808, 614775479, 982220453, 109241528, 734625770, 549348991, 89219852, 929732457, 214986151, 668830395, 131439377, 891005866, 749239831, 816907805, 287492585, 158367382, 891277965, 633365297, 860640233, 229172698, 115039222, 233550072, 236490991, 963284431, 195244323, 110620471, 89416723, 449069077, 602666989, 654242416, 740975933, 494500748, 202537295, 800762534, 424117940, 906088871, 725596913, 748437501, 420951321, 158072524, 768368720, 939672075, 643028892, 198648261, 967033936, 399814746, 851987048, 866689183, 209162064, 8634124, 148315338, 707668570, 105831886, 296141412, 176741467, 643975224, 114297765, 633894941, 66180418, 676724594, 562269168, 353268070, 479131678, 591769822, 999714683, 789797405, 851406539, 519768566, 55748707, 713536497, 251311305, 865926583, 347463339, 785569958, 692512983, 799653935, 325277957, 240324189, 148472020, 864057797, 696622551, 654799955, 596257645, 762298740, 737968909, 945913087, 866972214, 844538294, 302920205, 678916581, 145823792, 488576166, 738838712, 404046246, 366449778, 206089870, 745934984, 105838753, 248043567, 492289619, 954173914, 67569310, 415148055, 954272597, 612577581, 789570304, 895817522, 617623446, 297809355, 155576296, 619847391, 989927936, 227284065, 796773227, 562220182, 182050666, 831813632, 12652482, 494957349, 829055741, 579875197, 521371322, 408716386, 696564259, 503111351, 3917543, 783983588, 925549829, 922580824, 472814964, 294780465, 416635263, 696698750, 817731344, 361725986, 999526807, 664145679, 963977811, 332987565, 52280392, 825204701, 64145347, 313074333, 494967087, 537561303, 782286368, 38545302, 142018412, 946093885, 273656234, 633124247, 471258264, 763181844, 977866841, 706023539, 603968404, 39390584, 515893707, 633787732, 320458756, 92782274, 989504893, 304834160, 698463268, 802445119, 32121111, 325880058, 942110046, 598758264, 634728375, 884240609, 604760876, 188233543, 131396245, 78372773, 363590531, 393825991, 559184991, 398607229, 753599138, 395531392, 458846666, 517717967, 620406284, 247934410, 564897027, 510406847, 992064868, 44689077, 473269181, 703708018, 165844551, 388810226, 376594415, 129935980, 206129426, 614032658, 388001929, 896321500, 838097266, 280878402, 424729258, 224915938, 233437566, 985466498, 850272281, 717357892, 703229545, 343001852, 820634892, 277568841, 118490506, 131116498, 943209973, 714374264, 190502351, 612071111, 450044215, 488961535, 822386084, 806812626, 623921960, 948720643, 407432195, 853147248, 523461160, 86223893, 188784785, 299809468, 568778385, 653476608, 349163438, 102456289, 762259886, 605401815, 53317378, 822942474, 539235817, 872807161, 497861677, 559035061, 714960348, 805062523, 40344017, 118421614, 8314628, 212665473, 286644286, 590575974, 789280844, 976094854, 441175556, 828752803, 634473846, 156400775, 352895658, 603931464, 711576759, 3043423, 121617141, 214925222, 792135150, 142509618, 926929615, 108352930, 700700170, 766590590, 675979092, 869251099, 350331042, 87674326, 189395102, 640265724, 313931329, 369487999, 998205743, 272662311, 964800507, 21463426, 328933443, 387177363, 875562930, 231051731, 698145999, 610694312, 968795701, 803699144, 528190669, 771555575, 746435110, 934559029, 395063695, 430835293, 738661654, 43475020, 783762514, 942179535, 408929046, 837745716, 47754299, 641256180, 102491549, 943121294, 472286900, 711513687, 883196464, 561849545, 580759267, 371380547, 750366782, 117910181, 813307840, 578431005, 191568985, 511271898, 363429992, 372442925, 430182256, 688053708, 65737969, 912285547, 379632984, 389717131, 628897495, 146761676, 728949059, 693773138, 838323185, 765740399, 931923837, 365265301, 969634460, 541805111, 766086440, 419896570, 159063024, 53380837, 571727331, 768506711, 304755828, 332850487, 773471030, 963723669, 713102865, 26208830, 618899957, 64108001, 556663722, 864344984, 256614574, 564085649, 227409995, 822800834, 981506611, 271215928, 234477047, 486853985, 231383547, 367608916, 959514980, 643369631, 611121621, 342101405, 482802953, 553845007, 321532619, 113407121, 828143021, 294867584, 977917281, 573494422, 969280421, 338382818, 660542967, 899793846, 713847468, 230307813, 791335488, 468707397, 109689411, 346637001, 887047959, 972006116, 77878104, 988806139, 411281769, 535948911, 711613128, 78267602, 404667084, 774939363, 973255947, 811219750, 488371537, 868781767, 823633775, 359341660, 98059879, 755317580, 700196465, 349206810, 890842747, 93509947, 472689971, 495068477, 421901924, 21496593, 293452859, 137940532, 2249227, 422055727, 118871030, 986887343, 215254639, 15437668, 927626390, 864539051, 525472594, 102192095, 353744182, 143009268, 313855274, 814552023, 556076645, 45989821, 277048410, 406539425, 706491421, 939062268, 151544422, 452448634, 666808411, 338883879, 318336685, 614155434, 304676180, 497707516, 100367481, 965519630, 305750752, 59133076, 102923490, 582234732, 171671137, 249888929, 996195700, 2411388, 259081445, 232337377, 99830258, 931131103, 104896696, 98190375, 900114072, 178090368, 589415835, 567272825, 380226384, 531723416, 515693481, 624500915, 267127847, 719050480, 1519022, 357893007, 630094177, 786442890, 262507547, 102807102, 522570537, 251826305, 876304578, 784749349, 289492787, 106006834, 70000726, 884673505, 779489909, 39093633, 482451619, 527918257, 894475903, 90812483, 566195996, 66719295, 736603135, 242180725, 391533123, 745485825, 817309795, 217580254, 767266346, 174384259, 841507039, 790062393, 970904909, 897222376, 543218052, 555870902, 549685256, 529485384, 320861676, 723953756, 418403353, 596995995, 139494216, 341593297, 243480565, 124919902, 110882373, 104279798, 627615864, 129634856, 151543254, 23011827, 410770684, 494073296, 932936794, 543954994, 909565146, 709146121, 289890485, 597892504, 867304855, 492879211, 986745839, 925302194, 450575929, 183393801, 123685163, 241023669, 448168891, 186758412, 891339071, 680101863, 531859507, 801185761, 23137674, 841351189, 273916979, 276453209, 410443609, 237208962, 42678320, 828971074, 190478864, 526047849, 158713407, 274699467, 198282792, 34095288, 787678827, 163792834, 580492901, 242467856, 159190919, 865870082, 44864525, 966149771, 856352048, 753099261, 592179637, 906943603, 146993941, 525022308, 701933368, 118387311, 277074999, 45164284, 985420734, 165468672, 922556847, 786358118, 315938228, 57607846, 52936690, 448980482, 51999750, 446592165, 743899459, 677772959, 563985682, 454391687, 428622094, 637703557, 180778703, 729935935, 961197566, 818566225, 745879413, 582088368, 214967853, 116919402, 729339762, 286621629, 949881358, 639809527, 703677441, 956562215, 223515027, 151000985, 616644494, 706358090, 678792053, 109970910, 867980953, 54494339, 63484096, 727840142, 766035365, 989167155, 889726972, 205735926, 882373445, 910772831, 486379777, 1528195, 11586809, 577120997, 504537028, 877313838, 525469610, 826531700, 52800066, 514251254, 302825983, 71191671, 279059837, 896613292, 347981457, 137378818, 66383930, 48694454, 236862278, 266336551, 269116772, 667910136, 294974428, 503953527, 174177022, 387030413, 321943873, 250522650, 442679593, 923498379, 23955786, 131802959, 519512302, 588806629, 424167368, 490410558, 459349172, 591368620, 514539920, 402281008, 904311823, 679623118, 602559071, 607641061, 295215943, 457828438, 778590425, 589731436, 359925097, 292348223, 223520005, 993258266, 809431186, 872072855, 434739427, 88410820, 416616648, 20198402, 536473171, 791001307, 369805702, 169815338, 168325531, 402140785, 33613390, 385149207, 480460793, 790407311, 732995258, 168751795, 684558589, 302307972, 612465598, 864190284, 199726561, 371149929, 242357932, 485627826, 829176486, 517928285, 780008178, 119358322, 238327472, 550746079, 308459930, 18414153, 135074156, 814354347, 189232839, 80766940, 459195680, 154878608, 618509325, 566941087, 539482280, 823973249, 411144966, 115803146, 925637142, 631226341, 161204197, 341575216, 173201250, 739800679, 945374008, 322488089, 155905853, 267804580, 827084824, 483030077, 116694568, 110981644, 145667882, 980087401, 409845476, 280354221, 650936790, 306115087, 136695111, 708141572, 348310014, 136705440, 740976002, 601238909, 433465232, 716384826, 744137373, 195142406, 626217251, 279461440, 645096637, 854909814, 442676329, 577330159, 863535061, 613336628, 600553310, 535359179, 864315687, 611856971, 476915306, 535772401, 255283672, 83076158, 280350589, 955675710, 506400675, 592527890, 664688903, 544189454, 575067158, 570228714, 519970499, 121536770, 137004955, 191408531, 5090882, 831118834, 538387445, 780006290, 146600534, 114884568, 648081210, 843300445, 825780675, 8535715, 753777921, 46065788, 333051615, 60651944, 746923145, 902362837, 336466768, 905801364, 50653862, 893301553, 148274975, 410699467, 249444855, 100672203, 513076481, 297643619, 713377886, 664224756, 94435617, 829878316, 498738262, 271283685, 839157457, 10608724, 406089270, 615364891, 668921673, 363092126, 452663069, 951249632, 865029157, 99692881, 825137787, 344444187, 30554267, 256928701, 239668286, 497452768, 835703330, 956492339, 803346767, 325378264, 512003833, 113472920, 62411410, 778979857, 615633922, 555194109, 262849830, 245112313, 726017202, 962905299, 379796326, 526653867, 244159504, 297732870, 708076204, 451916457, 302130017, 20360700, 242510149, 155354527, 731134665, 368578272, 209283578, 65158575, 792579632, 72189196, 230826851, 369817583, 650570062, 275876506, 104465578, 273616412, 215255175, 837441275, 985971062, 170066183, 923466621, 964726621, 269784313, 774594168, 639911286, 907700335, 330289460, 513406145, 111029166, 480808214, 911805182, 370584889, 254362231, 806399718, 812483989, 728869142, 499929066, 695502175, 886598871, 747219912, 127346650, 936895980, 401737410, 340599111, 299603208, 482960177, 900083729, 798817134, 512977608, 964793836, 270719859, 939716076, 58302966, 222687074, 479506367, 260083985, 997241282, 930178599, 420648461, 607955892, 287805086, 988178187, 701556444, 299813449, 290237008, 437026793, 949355657, 755078478, 794656456, 808545859, 251139406, 268963012, 451889153, 66313905, 511745477, 564156923, 935210642, 226438324, 219376536, 604852493, 65151755, 266464941, 615798942, 69429151, 18316440, 713862708, 831165041, 945201039, 920927078, 801920111, 176285854, 208695354, 291164187, 165711750, 46028553, 152850653, 184417401, 467447804, 678840113, 749407524, 830213218, 765632255, 948826517, 166750431, 242071006, 287847876, 897470167, 47215674, 641092968, 104528003, 889383769, 24952630, 642108791, 536729548, 20132118, 280943413, 80555, 112038231, 272010704, 789822345, 42590152, 793006476, 189498691, 663528740, 448636380, 53257150, 291566919, 90421306, 558195929, 125428531, 294036732, 705019583, 73994168, 671696734, 792596126, 319192728, 31950565, 805654989, 804728946, 430272297, 768973951, 717109166, 525601590, 37827784, 562725007, 56599347, 400616281, 893962032, 476416549, 660072456, 523768352, 867126817, 99985017, 382713444, 384788413, 966703809, 253031005, 645895872, 248029664, 899366419, 330963959, 794266905, 410890320, 294159957, 600978597, 311378131, 103108229, 290698216, 912096328, 354966268, 800868170, 943809090, 520346568, 418726954, 440725760, 904435346, 315587711, 269983385, 133620025, 727784926, 576898573, 885661133, 433182910, 824673375, 695317000, 371203419, 514229532, 481794027, 104114018, 860696775, 71414199, 750428155, 926522925, 812326635, 147712899, 572073129, 179556640, 854557215, 111442554, 976171820, 410031924, 510798331, 413072506, 466490293, 752293556, 589659771, 49315702, 555585129, 14569376, 467573839, 10991601, 362907998, 550408644, 536232746, 658551063, 426470208, 262398980, 532445901, 211297101, 864376714, 871696519, 820328744, 97017571, 809042540, 799452192, 294260475, 968190818, 482184019, 622633797, 590156554, 157411036, 243224770, 632199869, 253545890, 621892220, 761423414, 17544086, 471736687, 413936378, 293091130, 399093445, 944755705, 663285909, 341047043, 802531677, 902409020, 379937839, 637992481, 886381880, 289258368, 406270725, 16252952, 855586288, 94815854, 61725242, 272826313, 981022003, 20007088, 561687869, 100826259, 526999741, 698999932, 3065726, 494012342, 369394696, 215020986, 587493700, 501334244, 278267324, 75770188, 575146338, 483627265, 70399842, 875197800, 312241830, 815427265, 274260106, 585430635, 992541098, 838259801, 353491528, 635358790, 916343737, 23155531, 637547668, 603697748, 987296447, 261335184, 202715276, 761809372, 292131272, 248380543, 223592771, 199145774, 985433411, 951993430, 859360348, 542004041, 214270592, 588355846, 668888590, 257144670, 925953726, 319173657, 514696639, 897174004, 52172124, 229020933, 318362342, 400076458, 894786692, 760411531, 290196879, 597809974, 851232477, 261428151, 21802154, 57852100, 118664381, 730092888, 760271656, 843481362, 791548119, 869810959, 511226318, 6358130, 924578809, 176108123, 786136859, 464219026, 545563303, 251982148, 470068489, 701137673, 540928044, 790777103, 198255518, 996702960, 823278047, 18765383, 709901238, 957515532, 627150451, 972371187, 363021405, 88546355, 230377045, 728506387, 52433046, 123044841, 599714375, 501109245, 970844772, 365203560, 816080950, 368894818, 185532516, 161342515, 747259515, 736011646, 677115976, 250346374, 195954377, 935094468, 292720276, 991708265, 706749694, 51346294, 440409975, 80712491, 238256838, 93816865, 496532623, 532732367, 893176251, 159537388, 798826920, 452078714, 207455601, 209917561, 682218490, 811168042, 543701777, 469619757, 533110084, 723935982, 666060591, 358364809, 868979889, 976874893, 899256614, 454468667, 583706707, 324578019, 661636148, 134363000, 252216312, 332084719, 167765545, 893587728, 628025361, 930109561, 422292027, 326937100, 899382188, 920288593, 937982510, 361749742, 62828752, 413848563, 985352358, 903785829, 405021343, 92943354, 894599038, 412689616, 784492268, 491269025, 947315131, 765051905, 624622926, 514944541, 530395889, 406053267, 492919991, 841495324, 275183243, 523733320, 88646358, 491037905, 911453986, 713871126, 504063025, 860033926, 546142166, 941992359, 593957963, 601012630, 405934044, 992273180, 22052492, 751550042, 496057279, 184661508, 26011047, 459148419, 125753686, 394422653, 977722803, 131581317, 391456512, 651579963, 940624274, 498531580, 893898984, 47556309, 921756844, 564116830, 204415695, 808132698, 707261564, 951302294, 743483129, 792869575, 626790182, 256407106, 552803108, 682243703, 475170061, 181525853, 346712613, 847849539, 239948166, 387504545, 391042838, 37451952, 734920909, 401142561, 952291941, 637484412, 310433829, 729055489, 736856208, 309404564, 655102647, 719597863, 882672354, 955929795, 72625235, 181684196, 649652280, 186751381, 377867798, 833177235, 699847316, 729993593, 949308126, 802215045, 636448864, 437301243, 688945454, 7198181, 154257032, 578338475, 93047465, 647079969, 523903735, 301677057, 330828876, 582996631, 445983951, 371544198, 406455549, 392410947, 193950611, 67873123, 291920780, 116359590, 556675399, 576152055, 502469400, 156658294, 139072501, 413558248, 900663362, 982151357, 762223983, 181930717, 842436871, 793072219, 39924315, 18745265, 221471455, 712346945, 611372716, 39862141, 483033924, 984235477, 551793513, 325239895, 200246437, 611868806, 373238373, 485329673, 401420716, 84238295, 283453126, 606178829, 434881534, 825017859, 194807754, 735033431, 826746556, 68720258, 603403355, 231329099, 825642633, 337191823, 438991012, 497680912, 214385654, 475507628, 635683705, 339598511, 918409531, 23696734, 123574333, 79773008, 596695273, 598537942, 551096256, 712169704, 305487288, 707409474, 563734574, 288827954, 30264577, 984655390, 109994506, 279846027, 821860070, 96777593, 269899891, 580003963, 913570793, 463403682, 505533572, 29665186, 164426970, 162613759, 743139178, 625384358, 960788990, 264689990, 271416960, 503844704, 622914633, 928766567, 2600387, 171564678, 763297820, 970325006, 767833330, 421498704, 942831807, 266268831, 940175316, 491547635, 133679203, 290696509, 999344664, 926495776, 519109391, 901524589, 760506301, 200376831, 64369142, 219982939, 45827362, 452625633, 724478398, 401743800, 535295187, 132303486, 814127718, 897116003, 665377862, 713969950, 895858234, 38132880, 163267885, 906366683, 749737574, 215656806, 533697240, 21841036, 536419759, 720993652, 963292737, 745622340, 676968982, 777215855, 908201792, 466905840, 614698513, 437655468, 249179966, 306543333, 811813284, 656558622, 645130756, 847822152, 481469345, 275910002, 234173011, 950130783, 960026388, 643115962, 188226658, 440664746, 985843732, 721756400, 812073693, 949267359, 520139108, 804118709, 392953481, 422560229, 195576811, 607334364, 535339305, 455101026, 461622701, 193554140, 341207125, 902761513, 800988597, 387325905, 318007179, 440831732, 483826865, 263900391, 375162076, 812305731, 494980697, 866902186, 880752098, 871263157, 161538972, 289688460, 958800516, 856088940, 788860365, 889887828, 615812942, 56896209, 16853026, 17073198, 684000938, 568879469, 884021776, 149537808, 674669824, 524199285, 835840629, 296483706, 285480710, 175597111, 79049738, 463711846, 736385570, 928917516, 345843136, 874701134, 444606527, 589547889, 924303453, 648941846, 213028766, 648848378, 320131079, 20199950, 452443775, 284261605, 910995971, 645195755, 808120909, 796600777, 962484898, 246958861, 382476645, 818515471, 653170875, 167587643, 167321787, 155170803, 192868093, 873219814, 590360578, 360697076, 206564245, 343353803, 774170980, 138289434, 299847738, 957823879, 208024569, 81338983, 173053566, 462245974, 920670364, 76007778, 708241934, 104021162, 609920299, 981401321, 790640155, 168916783, 70844558, 718846088, 310851932, 771541245, 47690694, 985832135, 144670664, 817658844, 393615039, 147950800, 559779076, 745895457, 955832864, 290391561, 107352144, 855322563, 832785710, 216884198, 329187359, 180518489, 781202417, 549121325, 400546591, 538853886, 270325097, 570222708, 311594781, 133151431, 199774902, 109452324, 336185459, 292623258, 774067051, 966391597, 838257506, 49619487, 489910458, 834262385, 742221322, 899275508, 687677761, 80622547, 702690189, 780226454, 167030520, 664352583, 101215556, 522685131, 160284707, 714926128, 408951295, 505963832, 989944720, 772676144, 972699309, 529599861, 813158859, 700474521, 315360720, 202996561, 218649369, 917802261, 66466555, 539988213, 824737484, 548768446, 912532150, 807464782, 121197413, 373792611, 767628010, 457489422, 887060656, 286963989, 210880590, 1615754, 767359679, 622522354, 259878103, 726982272, 415899684, 309350485, 453588401, 86955437, 877737171, 646017466, 309146455, 897021264, 978933196, 588061718, 547223087, 672242328, 186721970, 82781793, 712432623, 570459955, 661771353, 806392240, 708274452, 116893122, 992938300, 463517146, 183964916, 615478342, 334943334, 244497616, 623251719, 914550238, 14805660, 447542072, 757947984, 74456232, 297711351, 748775276, 715310176, 375648862, 361828417, 396956545, 290056828, 158508832, 981526921, 40791555, 682970836, 446410792, 267332268, 663539869, 974780405, 171350608, 445686822, 872721341, 705185747, 593939164, 358851139, 364529959, 293323937, 420429630, 144739307, 705199657, 733590559, 551319716, 420626454, 812699002, 194462229, 825841522, 713972231, 553887576, 467383824, 107487264, 954597501, 864560462, 473835863, 236294552, 684033154, 179926854, 75169150, 929195648, 619267422, 150137139, 795259871, 203512242, 145477520, 506777500, 75302510, 875887343, 277899708, 189522223, 958907057, 834612912, 654595918, 519758189, 320358091, 501279916, 399167651, 290889828, 110001116, 885285566, 27883628, 773814193, 676993420, 930654507, 813880688, 142884341, 628198972, 35769995, 947353677, 271686478, 460263573, 670951139, 899364342, 256527918, 669899961, 710628148, 67524611, 202338823, 15866181, 573740758, 194540442, 244750003, 998575649, 820972444, 359327878, 727172783, 569210089, 760795428, 242540008, 550163263, 669088923, 460115739, 982445397, 708968334, 531323125, 559010470, 489431750, 836674929, 117040100, 55566467, 589461905, 817276788, 173872978, 942777802, 473436085, 437295867, 874698829, 807792795, 813021530, 744363318, 395099741, 925301129, 837765945, 915460925, 311795188, 144997545, 270043890, 488608999, 730405657, 10554441, 369426410, 642976642, 497383362, 372672091, 136161949, 314798568, 215576867, 237114283, 600350201, 137885897, 114651629, 714580714, 921514353, 159950190, 413160490, 185062445, 992057585, 672619390, 965007213, 728693549, 242946625, 968553519, 886162069, 683504541, 619862768, 122181947, 795775623, 385620248, 7177874, 887690256, 277559123, 62507181, 877401868, 175277289, 459361416, 395330021, 899410941, 778130150, 847572749, 772388410, 185945745, 612108821, 178658774, 439415334, 509676099, 51944117, 105580772, 227901428, 383812229, 249010927, 352133655, 172339862, 775787035, 556514875, 553801404, 285028160, 633317848, 501120419, 356916202, 238953047, 167181357, 811313354, 346287899, 43043192, 433524442, 332224384, 189812371, 935965373, 777976110, 610243619, 431121839, 959430211, 220339475, 386021272, 98175539, 599627728, 213682915, 346204296, 823818211, 875021549, 237109602, 826892195, 348893021, 303188270, 886537082, 768829755, 430608452, 297432242, 236635487, 864242518, 508675231, 90700963, 115295002, 400644221, 305217723, 416461534, 393553654, 651154676, 962694570, 495185448, 736309788, 620560438, 740609612, 314792405, 536360428, 728552862, 227455438, 54853023, 411680537, 91374866, 776029006, 90519927, 44457921, 632044667, 846318624, 782115305, 492028219, 232921600, 244560077, 473550155, 275864899, 302471728, 847081905, 357125863, 963792472, 695375377, 28244228, 898834520, 392953539, 683390044, 770888751, 289363995, 548802837, 491730392, 441158425, 634540208, 73253954, 175838377, 467731536, 209698817, 627661765, 966452899, 820659179, 459341029, 459587156, 877022760, 296693169, 59365655, 848227807, 11388716, 361119078, 883004060, 661718057, 192102256, 860725284, 959103792, 850496061, 889591599, 593328936, 916643289, 508059660, 715692450, 107095341, 227189924, 310729471, 199367749, 371699057, 36677300, 80697290, 832191312, 613081687, 77711048, 663594273, 256672730, 774648926, 177244829, 323997801, 228373554, 49417498, 985719538, 384313864, 30627300, 460544374, 510536655, 977742010, 136488166, 68520001, 834156488, 706156433, 718830500, 709004215, 659106744, 772194050, 774101040, 352602657, 593519423, 380892825, 523738626, 713742174, 200424011, 38956266, 86990233, 3224932, 473853964, 935929591, 281906632, 431327494, 120933034, 862683254, 52668345, 432224047, 991517325, 607448131, 199609007, 951113436, 883467914, 164695768, 672223507, 654797561, 241352895, 697053562, 924308896, 583233557, 470139943, 531234579, 47308989, 842404029, 626132167, 530539928, 476327714, 982566058, 571133064, 665762847, 452345149, 219935562, 985344480, 769574194, 602144560, 225107710, 151557382, 422989347, 41630584, 373497005, 254374967, 387108647, 127943812, 414515444, 28448416, 703471879, 22708783, 211754764, 736537997, 681471982, 811420120, 488728935, 872143985, 858118680, 567397067, 423709073, 946222064, 373313692, 325096656, 52319893, 830797292, 475228676, 67345068, 215333552, 877956686, 183085227, 573994925, 370332925, 233147809, 198837385, 931433197, 625114352, 881866294, 418232075, 70142888, 942665297, 158168415, 563262288, 809470577, 39376374, 187732101, 580873103, 284112984, 123931310, 122726133, 378346224, 243384295, 345316874, 822834537, 595610992, 681071823, 56652082, 754215701, 178231725, 534096077, 729393544, 468707250, 780999591, 477975065, 873099268, 205104841, 228237044, 205366553, 42736565, 187667579, 388959634, 564872980, 220195191, 134484019, 201650355, 98799981, 619867874, 455187579, 412916813, 880653897, 253634042, 668189501, 828077282, 910613680, 655690423, 440077534, 948981306, 720169779, 756036362, 536555596, 595002270, 168487278, 83717461, 92459896, 69296935, 736561069, 643233896, 567979840, 14483243, 430444224, 293070914, 834841141, 666329856, 206264467, 117270512, 798887085, 380858184, 758305376, 427653206, 744710848, 519602675, 308379063, 625731521, 317094827, 603107494, 964376464, 976993912, 161986015, 193966271, 183606921, 298257758, 780357007, 427715885, 913499822, 346907164, 917356388, 679018902, 829983480, 541657575, 38912315, 463811182, 644860966, 198258303, 882253043, 210677482, 487305367, 384876041, 602330410, 103432622, 231888209, 731514631, 582975659, 571072719, 325529261, 174479345, 321519640, 970740201, 249606327, 512323084, 995474594, 833776229, 455573110, 761147176, 959438970, 688281988, 749767512, 798408624, 805841970, 858038712, 785884968, 243855524, 779371041, 627464407, 132400702, 50649304, 998369172, 68186535, 965854026, 815000619, 285373502, 879346406, 593394341, 383409147, 835192367, 892345973, 706764612, 959539152, 686087181, 379520869, 703060981, 210403037, 1314189, 175311872, 700508441, 470022632, 873477914, 872107943, 946750254, 808521463, 848216758, 247567141, 744925889, 139366308, 604527207, 188858212, 667110449, 338857110, 660260964, 561425329, 274907024, 280180761, 598249479, 390279184, 423411623, 798724376, 235938699, 666843650, 231307164, 201087362, 977641908, 648353097, 278919346, 599862024, 434026296, 691406628, 732351131, 646040684, 577655558, 749599598, 336634423, 672156862, 31922908, 879893045, 915083526, 518446839, 633471843, 191012603, 587632916, 853082439, 651340127, 319593310, 511775804, 900957426, 622028866, 590628102, 888564195, 612293960, 762305020, 520386561, 607149549, 660321417, 576363281, 846023834, 567040235, 197133190, 489673389, 104093165, 40086866, 17918755, 2392152, 213099706, 601346766, 513292702, 291452273, 956740583, 105500108, 695894686, 187282527, 172848486, 221584747, 623582025, 766298911, 922468368, 777286167, 496257920, 471348137, 478873409, 839731968, 144114794, 121853381, 142517167, 433601292, 767528663, 290212830, 440971006, 330197090, 443286959, 154353382, 461979011, 42841172, 48281394, 393166339, 466630300, 114120792, 662228320, 868987087, 199378501, 383791376, 300000700, 74068172, 994710139, 907560076, 624950271, 930967217, 839427570, 85535181, 814437581, 187826791, 654830950, 218291052, 44898062, 495996484, 948247443, 668460286, 927458726, 337068832, 43404391, 919469709, 679074986, 139489927, 857250048, 232363388, 798385348, 987171634, 580463922, 851252738, 302809929, 336800554, 931287308, 213835030, 94043937, 260469503, 927235684, 663912265, 200761339, 573300512, 253573702, 276576081, 550744942, 230664914, 652815769, 970941827, 317200230, 890409398, 788616540, 204489089, 398353634, 109165455, 767093439, 94434508, 943375896, 536539925, 336554795, 83684050, 347584283, 65065289, 344655218, 906947397, 588827206, 658028475, 906745274, 853391878, 351059477, 741390877, 262163043, 212545900, 103906668, 304825163, 157861840, 155824824, 915164111, 990588911, 878941007, 672303729, 9549711, 691462713, 65506143, 822525684, 806009968, 825570243, 426057116, 892505625, 826987225, 708916423, 573132393, 587711437, 420170878, 88791440, 867949530, 10720807, 368430117, 281259372, 732541822, 403648775, 50688962, 311598594, 277835810, 450937771, 533014630, 377308685, 459430115, 927009216, 885155372, 969537698, 863910684, 192646219, 69980122, 305311325, 553283342, 646157439, 116437022, 565376935, 25821708, 370865564, 371240057, 568652499, 561594818, 458529517, 155246844, 426094845, 161818190, 667943326, 328691420, 631905466, 417745632, 68321365, 742716588, 760350602, 683948656, 736603883, 226701209, 156582424, 667390562, 108088853, 898143375, 578124333, 291185514, 227759994, 92006381, 869859984, 85540243, 114172740, 663694219, 616915724, 671399430, 720383342, 523837257, 551510745, 687697430, 926760702, 147258923, 897889912, 681860242, 386217541, 395319894, 70084033, 820459176, 551221558, 960397073, 402908754, 589166475, 257950011, 323777891, 803471710, 636023689, 130581783, 288525931, 313893663, 794989489, 931387137, 425601468, 90414314, 917237090, 172451578, 504345670, 621692869, 565541179, 553102586, 202487636, 131104731, 196977274, 54114596, 478209591, 198546817, 479532144, 500536064, 765232523, 675423616, 511954422, 40009353, 554742961, 12064736, 648120371, 710422533, 579356311, 674444214, 293453477, 433978854, 476558639, 915647996, 385804196, 622379708, 159899705, 667738581, 640679858, 377069782, 60692217, 873039705, 449073823, 168931321, 812357652, 650557512, 972003363, 926356102, 76098206, 414044008, 502113113, 832608634, 283816098, 29814688, 741804533, 678194308, 942190355, 334327026, 752169570, 193261181, 526565787, 43000969, 390675456, 962509585, 443815046, 339618886, 993664626, 8565467, 679642011, 240048055, 508244650, 209253906, 915436692, 802435669, 321831126, 705751902, 793364073, 792028278, 58840530, 534007219, 515120330, 79098297, 680999397, 844372459, 644454537, 183513866, 171035779, 810315571, 270988866, 543045170, 331788810, 605583334, 580978018, 688571697, 40056198, 92022967, 479588442, 243899678, 872450357, 36423962, 389126991, 876887275, 204772962, 220896272, 370995842, 496076656, 762388998, 880675886, 603741332, 390253157, 288860959, 405032962, 340900527, 346619398, 843151499, 747008354, 53676125, 249291035, 420042128, 278659962, 984132844, 364293920, 546378986, 799466212, 607431356, 164598509, 187065858, 230438521, 704187982, 62787612, 333618215, 996039670, 808134851, 790317330, 461916693, 137672880, 562851629, 223692538, 950907128, 539433528, 23091097, 583678106, 66287124, 314161682, 933733599, 223094614, 830806470, 732869651, 643374096, 571341217, 426203681, 782107730, 107441263, 332969853, 557806595, 440336158, 893293614, 660318100, 874843403, 875438093, 176222054, 851087926, 208901932, 152064160, 434260786, 39222633, 767746468, 514771889, 676800378, 395359759, 642726340, 774480914, 948027005, 559224445, 607883849, 126413239, 183516529, 603464992, 919619577, 649097132, 423030354, 480951000, 161551763, 182155458, 913851330, 204428668, 288382185, 564536774, 348029884, 89219135, 499732980, 946987152, 326485, 751050559, 208621953, 266391091, 638721687, 787647764, 75669673, 343449138, 226202112, 667419173, 148313615, 431673743, 610153791, 85759127, 457857721, 16605208, 766574950, 678630081, 841838924, 921172755, 833952357, 659630938, 232327375, 462294168, 845145332, 294075334, 824474928, 82408522, 867745777, 423059460, 286669077, 654015790, 685056108, 247980762, 938939875, 990284274, 605069027, 87722251, 757452688, 656521622, 919260990, 214757789, 894721540, 135523629, 805490357, 301836874, 456590751, 214995679, 198734006, 740871847, 425620890, 369051545, 704404350, 582088001, 494171761, 856779655, 362646832, 828541744, 88464561, 824354620, 886291596, 514794469, 891186411, 844743676, 236931861, 946804501, 88134637, 145401595, 794636762, 692869925, 21124414, 276363102, 29521620, 158451416, 337178797, 656457226, 901845805, 197064410, 272071147, 530508805, 839915198, 332166106, 781426349, 884765967, 172246157, 596074977, 59532603, 959446476, 537003918, 114744423, 899573168, 488564742, 508969803, 817176229, 785893008, 855643312, 761692424, 619609684, 887355114, 309555557, 910002908, 407899543, 177298956, 94317704, 423787052, 987398950, 337882203, 598415654, 425757846, 631895307, 390569390, 89908912, 890165287, 69282820, 648878601, 80093915, 775944472, 935469283, 651648485, 592269839, 283761381, 812811720, 758663968, 157234433, 473551019, 653600363, 212571080, 102773572, 56369971, 726522650, 195351588, 668700942, 741291204, 185547444, 537466269, 208400692, 137391903, 291674190, 848884660, 292228851, 442130010, 479561223, 491937406, 555197810, 199338819, 183680158, 603368460, 272945277, 671784395, 228660027, 454476217, 900755615, 560314949, 722086695, 954459636, 289178654, 531825489, 66518857, 855199607, 592849604, 272106945, 708465382, 853829349, 172651813, 215875175, 987673753, 423334798, 141183748, 648648017, 480499874, 414189896, 747489361, 669956571, 201068885, 436005245, 542483566, 416930340, 559903155, 630135367, 550224213, 165268451, 590509844, 863422537, 755720709, 542857595, 62322078, 995725252, 482331409, 231114576, 374631879, 849162991, 805977444, 121936641, 596775457, 177640800, 263696567, 603196573, 111039241, 896736388, 529161641, 209008467, 1837538, 40108505, 210933827, 820566715, 463385246, 656436190, 450597609, 751400309, 827481621, 644887500, 953562363, 689459182, 47098506, 348449353, 166389121, 271791955, 202023140, 428864907, 721016534, 645014394, 324049458, 734228209, 106822960, 211020269, 665016103, 561552743, 838415140, 589813671, 114687116, 236185627, 426879164, 408489773, 480279763, 644070858, 857197045, 20450253, 454206002, 435561874, 308063647, 199494076, 948604089, 832130221, 510596799, 530327040, 971524203, 969578891, 11978666, 68520051, 85987132, 741913550, 190949099, 286905737, 56848635, 216458647, 3975716, 685494804, 167278513, 783522863, 591441568, 888270350, 537995850, 529104992, 179376187, 270002552, 787549108, 399912924, 594595325, 518007707, 749189649, 588683576, 770216090, 213010199, 14876346, 205751387, 511169692, 41081254, 74731332, 16544675, 911434607, 181890997, 651560876, 916730738, 989549576, 364926263, 111341172, 239966440, 712233587, 59256349, 224720829, 933683999, 172264207, 447733465, 297127008, 294659457, 385379034, 464166427, 386680834, 389939276, 528647032, 572683423, 969772553, 642240316, 534928145, 817558086, 403518561, 801777869, 239118105, 570812661, 356661486, 602975918, 230570319, 126684590, 666402244, 452510651, 201554963, 57258100, 978186849, 131723208, 204174445, 126849525, 125199735, 886950165, 577781251, 550689775, 295957462, 909969310, 115185911, 903376088, 452932221, 763370105, 722162713, 204046393, 956448109, 883201110, 565416778, 900228965, 935020454, 289988297, 758656857, 466363755, 710500458, 696529884, 122161708, 626747595, 587662015, 478692406, 582748493, 795301899, 227033955, 375547985, 931485353, 100006297, 639858340, 267003452, 356072541, 94561532, 338660860, 52286865, 705424230, 996747879, 179995181, 760709300, 663224749, 342509677, 877928844, 68406530, 671767517, 909159700, 663401102, 290405021, 601467970, 425296407, 256197703, 390839426, 893564044, 400572443, 309024395, 462576812, 91530291, 618128265, 909988805, 846636450, 453085254, 856562087, 329845259, 990251419, 131899369, 215850961, 38703929, 164807117, 951417881, 468564766, 25491888, 602235610, 162578057, 266184964, 92815666, 264560672, 746915115, 646060333, 471587702, 544242067, 183391487, 642027506, 165468646, 764342609, 192225112, 402498365, 166021337, 542784732, 837714164, 206262136, 603914886, 250831938, 266559220, 170444732, 447988470, 927652079, 585129985, 605840118, 962811875, 266931918, 423995538, 320951665, 447324806, 450905351, 897983478, 894391513, 411688486, 670297546, 572349940, 688889058, 114915841, 485053349, 884534149, 565235125, 164622967, 446837647, 273704633, 246747305, 793236587, 635776424, 259348799, 109568220, 842346508, 965539028, 496672212, 637971558, 520525277, 121681679, 722404857, 473657222, 486354829, 847875857, 155556318, 727731669, 365905515, 774006980, 734996063, 757069579, 598300784, 523141089, 159502559, 877927843, 313642421, 999030337, 738180639, 125084194, 835319635, 419782884, 340168351, 925921572, 321034174, 283887960, 571653707, 732571533, 743014792, 381939415, 627836702, 889269302, 7123991, 532740815, 863555582, 128410709, 776240688, 877751663, 467443492, 930693290, 749658320, 107687906, 206471886, 313260280, 892535679, 420928337, 6700207, 530751237, 763875131, 295163018, 531930456, 82736444, 74850995, 243456168, 467175709, 305834375, 23110939, 941737948, 976263057, 943612686, 366849260, 781708231, 882645508, 856981522, 843756623, 968468335, 493154696, 921444347, 302197286, 748803368, 36280401, 968549130, 830913972, 161629201, 169313862, 492944670, 366904203, 96733821, 295590775, 991975063, 579576006, 696605037, 534869666, 341760947, 686213558, 113398007, 812179402, 9682776, 956110820, 268531891, 357163118, 901032017, 342652028, 642653574, 175911885, 740857586, 272690426, 550603133, 743891146, 725459734, 119509194, 570982347, 639990195, 234028427, 859285082, 343545305, 109627190, 540768020, 399571093, 492348465, 591358870, 593721840, 477242622, 340095927, 853720549, 728554939, 596634012, 621721927, 692871895, 205612706, 516784907, 446169777, 677876223, 523391022, 580711196, 725059750, 940577720, 491790954, 334092300, 420412799, 413831109, 239160204, 724858857, 365063241, 968739273, 25933612, 219093357, 994902918, 355982220, 348375382, 232072079, 308487059, 775226915, 381468119, 440194596, 561358914, 291508775, 739696705, 430285216, 10854964, 17485309, 245760861, 666011431, 575928858, 829110060, 960694545, 988307277, 992890768, 618488008, 908460207, 684140504, 165924786, 858484516, 554012631, 3761159, 511149043, 820243364, 126687605, 286120599, 850499766, 962814809, 485519076, 569281267, 137208391, 951507912, 801958484, 210875314, 618602805, 7764585, 549008768, 529284805, 186797906, 223768485, 315948529, 278209983, 816084470, 895068959, 792680078, 783060164, 587396018, 391620234, 67226256, 959664525, 490215446, 614471780, 889611739, 2947612, 733525153, 99301596, 960222034, 423498077, 352704900, 491101194, 513499960, 515227671, 784323046, 507092787, 748053281, 695010299, 850772848, 382414274, 516811645, 529685607, 125863075, 872447867, 657684893, 324793847, 365873687, 804016356, 910048980, 859349930, 848979536, 462648860, 569218153, 338120604, 419264317, 136722199, 635205130, 602795399, 914430789, 381911346, 98543266, 561885704, 471651639, 588063367, 149008577, 398192185, 54143125, 86688791, 830256183, 893554013, 785066146, 713243202, 201879057, 740410494, 857891820, 409871308, 273743062, 323227406, 955175571, 453683650, 307771022, 655749257, 552676702, 50261171, 147583924, 156703224, 498824453, 107385416, 620012043, 563204644, 296545009, 677948769, 216829407, 211079648, 23535241, 162275835, 379126373, 933832974, 192227117, 277152709, 876958679, 606629699, 575530664, 513611251, 143544636, 721147031, 685209776, 59103633, 977436404, 934187352, 43981485, 897562900, 970454572, 263743344, 719718238, 596872647, 902784482, 638111933, 384562012, 13152662, 734108488, 162836899, 875245927, 847231272, 168294608, 358691204, 507540168, 156561868, 447761177, 446551560, 902452432, 572077424, 743802544, 586529095, 123132388, 390830716, 258704962, 825241377, 339136231, 597526157, 364104315, 709412666, 867960763, 54281090, 860686841, 429322217, 587476766, 723928128, 866240823, 935796244, 581971335, 861640571, 572724823, 564196433, 736990587, 335448542, 244330468, 16149090, 381279080, 475719944, 134000870, 786950990, 42538795, 922621619, 856153674, 784676804, 779432083, 944966004, 809872771, 179658492, 363844980, 35262315, 684494368, 662603272, 798108285, 772875761, 964731099, 717235340, 307885561, 574888992, 648165303, 444227459, 189274604, 449613683, 891789033, 722313951, 241636368, 691856650, 157336380, 871728038, 813401304, 826444067, 134899693, 262184707, 45394198, 636583592, 767841726, 788973636, 190805492, 701668067, 947829066, 942797307, 357513394, 569399509, 913383168, 812693982, 830652684, 453298101, 918027534, 701383017, 805962701, 54229813, 486928130, 412243391, 949052400, 574205052, 6134759, 963149418, 854764125, 394556274, 109293809, 858107157, 732802705, 343726030, 321362519, 969898802, 295784178, 767772528, 459959213, 391236665, 749852323, 738511374, 38488849, 132085840, 790802989, 640107690, 182327311, 604415298, 597363272, 944364779, 464415271, 298294470, 208684769, 322158822, 645181083, 941692873, 905383509, 837534139, 225719956, 864383054, 787565228, 464738172, 86418804, 5757535, 638122766, 557154114, 431704110, 930166643, 306662678, 652426042, 266633308, 170558694, 594308738, 283866500, 68295465, 4890907, 541415934, 53859063, 956847885, 408056590, 836360340, 881849086, 734652677, 499101525, 498535723, 236443961, 14981818, 711149905, 415239608, 540944963, 550642226, 573892021, 719644042, 955838024, 509522168, 149079883, 181123854, 78445414, 431372592, 246505149, 568475682, 240331110, 948831052, 910293618, 683023922, 758601660, 170564832, 992497351, 441415740, 486819129, 204281388, 195908236, 791263179, 275772860, 373456247, 546563279, 412274196, 235914991, 768513853, 91529635, 191417063, 482641716, 642221744, 758155498, 76759945, 101554244, 221595977, 146992875, 960980880, 978511382, 831214547, 958947521, 326554942, 310046767, 304371412, 102636651, 374906526, 507235420, 773368081, 139704538, 683179428, 281913017, 514213950, 212914419, 624607148, 475257409, 305311786, 95469178, 221236165, 465966867, 135170356, 481820710, 947548581, 734504757, 625355264, 712858897, 105631926, 318648230, 78491553, 804451190, 195160141, 908861220, 701240532, 876168561, 806605633, 732798511, 242135240, 899067199, 978604476, 736739838, 660926632, 44284076, 269523425, 432261980, 773982252, 360041446, 458447406, 341741996, 503169714, 495462843, 893781159, 697705764, 787885704, 700588347, 502046199, 436724369, 32136976, 311394522, 206374205, 720620060, 772511765, 660559884, 446107591, 987248564, 351185042, 330983095, 302705351, 676724720, 651449829, 332536483, 710839550, 479080962, 120924585, 478014165, 763043215, 67739746, 673902562, 424559762, 720431843, 114032938, 48815098, 497446326, 943601701, 505890474, 807901343, 80471019, 770080596, 470488997, 799222179, 611703738, 150647195, 53406361, 386349175, 713447647, 420450500, 123140955, 335626563, 644925086, 52277148, 274481705, 443956667, 763632631, 613625166, 667268834, 446034317, 298243192, 844806946, 3435530, 6557721, 807394702, 541762360, 167629595, 665474089, 283966112, 956838104, 8326734, 879306897, 607853878, 43740315, 819668006, 973432135, 877889420, 410205647, 134403723, 371421504, 536048589, 115821753, 982814601, 925353002, 403672333, 393335386, 634264624, 613859327, 854522609, 894702891, 393017666, 882739217, 2439369, 185899385, 535403711, 476472698, 857273480, 987979352, 511052417, 713886735, 990839054, 825074241, 20703582, 449967089, 849619252, 461766256, 420322986, 748270659, 602568745, 435349261, 703771232, 179315996, 692443688, 978953152, 889844498, 970949454, 561052353, 848755434, 705393860, 835300315, 692416320, 528631075, 789386891, 633502492, 588250037, 358074329, 561120979, 197562352, 535304952, 256436211, 822566470, 65507127, 180880207, 875053906, 75080139, 963973103, 142865288, 573069685, 119924401, 592840738, 965723151, 605016490, 866382851, 666917142, 38618313, 480952156, 957704608, 294623270, 982874980, 504615188, 424807139, 554481517, 613609390, 88200351, 871231843, 702770293, 504347137, 143980795, 768251469, 168693873, 259030550, 504214656, 104984583, 485291900, 351457871, 596812878, 689306583, 290349258, 117728214, 770546325, 623092898, 700681516, 789765351, 746241764, 145643518, 717046855, 529063505, 34903695, 827837316, 89002300, 521703943, 754262823, 273119498, 285603101, 116673519, 940414241, 422894594, 887016546, 683111905, 672868539, 820223678, 932985370, 807767182, 759380130, 311556885, 116735856, 278432898, 710280303, 145301305, 373705529, 666779925, 131685480, 43090602, 744560205, 46921682, 361387748, 820642813, 175356006, 809678317, 334015236, 259799561, 926254189, 171456403, 336302027, 633376049, 443972770, 560054872, 540282956, 878357710, 826595680, 449438050, 569586578, 45919126, 877047943, 48032877, 788900517, 858009017, 480055019, 507662862, 89895924, 882002417, 587449180, 383476081, 284019006, 62191056, 942856234, 379884123, 786557872, 776359483, 322773854, 412906892, 251741720, 253356322, 199702240, 743225957, 7417361, 475403239, 681343361, 198262283, 366041460, 222230274, 650914962, 262421130, 539869209, 869580308, 888383416, 708601960, 27872675, 732130704, 675604531, 296383434, 991358435, 380452892, 394633068, 208013373, 88106817, 948311198, 379733000, 815932824, 753948518, 662291835, 276631254, 298953333, 407960719, 420912838, 821835223, 835863770, 39109486, 189475832, 458779675, 515510593, 657434470, 50557480, 822917168, 332349875, 106685171, 457121662, 935797655, 269954277, 99021484, 292364059, 46117793, 23497657, 242988342, 372596179, 963747873, 683209104, 903117467, 832018610, 168776511, 593176380, 809422276, 447202941, 216255355, 104746102, 58412390, 264106309, 915813574, 379243319, 155011886, 524169630, 34902394, 377006491, 36390884, 759767951, 875182962, 870435384, 970106213, 644157742, 919515729, 698405807, 323117785, 946058120, 812907422, 161972835, 95131406, 354764122, 853500818, 765939155, 579408028, 714781013, 524174213, 432912677, 768371166, 755469585, 845269289, 888473495, 714362686, 426919235, 104769678, 37170452, 636772483, 637953094, 314534441, 535045562, 472538170, 260151658, 792163578, 84201055, 563621787, 790030161, 397809898, 744458177, 45693357, 272169949, 735532259, 342072554, 517821159, 642304357, 646390941, 180220329, 287532236, 824948823, 590095955, 323133307, 26162689, 124623825, 284345347, 595939708, 200396516, 792442377, 245984092, 931591074, 528245412, 18742622, 900862408, 201886575, 129421616, 649074423, 554743461, 419908815, 983879348, 496479151, 913580314, 923942829, 127879309, 263677376, 119286907, 266185999, 123980053, 510359964, 959426947, 15038875, 843131500, 844456644, 99654054, 388697792, 659702556, 876057447, 863837862, 677538602, 430168989, 379892532, 670754654, 194616504, 101041782, 461018132, 727259067, 350637667, 313779126, 578950147, 330946858, 687847806, 601837224, 727431195, 907721789, 706846398, 54724089, 414984239, 964433314, 790566310, 352270890, 418281209, 538077301, 77853653, 311675672, 501330162, 616227996, 55857905, 181268782, 842855574, 591472293, 332008150, 201676908, 173901715, 687199808, 609005845, 746161539, 276438053, 903935118, 844251266, 67777197, 171604057, 503937858, 96818302, 588530286, 401705426, 549666512, 175188421, 703515244, 767922343, 656001598, 682012366, 501939714, 938114243, 989507263, 647593350, 671355895, 720439608, 500655292, 129781503, 371081327, 223053039, 707259117, 352549649, 531741355, 389608901, 841548806, 179065648, 688177513, 13443360, 479150442, 712216911, 324230034, 249848996, 97257424, 772247552, 491205813, 965265249, 310366393, 576287822, 363369942, 620669846, 611547140, 95088994, 974452371, 156733641, 174653864, 679649192, 496399354, 544811897, 664280931, 748847425, 592855732, 292381455, 744751371, 453542326, 432288419, 42542599, 850039497, 729577357, 350036166, 885708852, 883039308, 680922053, 527766822, 197392345, 665271541, 283540663, 97255770, 605739361, 887705105, 368959320, 535327606, 618447539, 501971561, 680359983, 85142424, 93294231, 276229978, 429489865, 589806127, 694645363, 901738830, 653400333, 301905406, 256514244, 927501626, 726437805, 401870353, 711639652, 38061240, 650306178, 512404172, 443612477, 562253771, 141220840, 982455176, 813906345, 245530537, 722617915, 573436742, 423203782, 362268912, 145682782, 81521656, 255571254, 84836064, 339925969, 195146805, 753119393, 268782453, 497254445, 428577139, 115153684, 986083055, 262128159, 622119306, 884725754, 367854589, 79445943, 914386644, 515740123, 12848723, 681897594, 521300552, 491744013, 625915668, 832742318, 856283268, 620644859, 612802308, 420580322, 371393356, 105156178, 126427399, 971454805, 110893848, 856358917, 146580275, 437777808, 789290619, 302353813, 606797976, 945093900, 467346552, 314065321, 401334439, 895171844, 557732338, 826950276, 708981492, 212489497, 894124798, 195286392, 555589775, 569060167, 509353105, 895880262, 89273208, 124414109, 648089744, 503705343, 562832305, 79358499, 432088478, 279563492, 659227423, 227207098, 564731818, 928488620, 82291769, 430065927, 745276353, 479054723, 552474782, 135652713, 81923506, 185524498, 22223432, 524889167, 542014017, 200389257, 980856565, 752263783, 615874229, 23358047, 630578913, 293738029, 370132593, 863565752, 896938097, 957699142, 133239064, 909739725, 619179758, 299359696, 94717937, 617279732, 344421537, 861337658, 640308799, 422514413, 587277228, 516680994, 396614772, 12688038, 970909784, 169976438, 115076529, 685553149, 940766753, 785974964, 894853405, 909674855, 771179387, 292719563, 252560928, 603430962, 41185144, 395545394, 424201732, 213796037, 411515261, 662791869, 402566722, 19028872, 893469204, 946365569, 422334720, 586319968, 944104564, 276704567, 19365386, 777767339, 476192455, 984275562, 100505944, 477296312, 526289876, 919566104, 41704611, 384256858, 420115383, 55299519, 609393829, 492177706, 571503332, 638105297, 359016441, 551415066, 891264501, 957955975, 262280336, 95774379, 354589369, 354436349, 329370363, 604462517, 152181597, 585948006, 768001877, 197591462, 113772770, 200824092, 801512450, 666826574, 129887448, 539354842, 692898978, 898777957, 746171888, 114228911, 749909865, 58131628, 559901739, 481927146, 957714501, 621160595, 367070008, 364366094, 740802269, 443075082, 860073672, 524025861, 83828494, 117050121, 956761809, 326331114, 98263133, 528241711, 270041853, 900880268, 582403589, 268018804, 645142698, 629759811, 969505068, 81102163, 911150390, 341950494, 531806854, 293366898, 101540694, 618431679, 55610735, 97612724, 622600115, 337692547, 154702319, 979848185, 991415053, 904980093, 837821750, 836535750, 292152286, 392416643, 757656954, 193887434, 747356951, 54447187, 446667107, 989629246, 503789600, 770178893, 61200367, 92018006, 317952405, 250462514, 796275460, 907287339, 990615055, 453129463, 999666344, 441494239, 210121435, 952043707, 777274530, 549476196, 303229886, 883125657, 553432430, 630996399, 223297923, 697869339, 822824987, 250678837, 377823153, 722986677, 557178568, 945910492, 34509712, 268161810, 237553991, 652619727, 309611085, 354428228, 16922611, 174145594, 867755824, 113222976, 933526479, 815264017, 196929794, 774831350, 875996236, 666105455, 634379579, 929786415, 475435853, 494295281, 31617341, 326050439, 108822816, 788465425, 736801084, 783133446, 224555035, 73442225, 434368328, 102550564, 425042865, 466897291, 322096428, 332432889, 110296485, 230683836, 825245799, 20000306, 137752834, 767140108, 345162843, 728805647, 695300422, 289459775, 528213371, 54338145, 975100530, 5469376, 945183470, 558730691, 938387375, 870878923, 909439268, 454545045, 995769646, 948660498, 196271911, 649421454, 555912655, 279158504, 660750130, 698251990, 138235502, 214907563, 392061271, 970920005, 116783655, 536787280, 883781401, 175091412, 28513104, 590487326, 73164255, 897988861, 844442202, 838714901, 590224351, 541933756, 380983323, 296824596, 612073210, 290126365, 26231149, 454874165, 83922878, 345267629, 117162324, 165263054, 54957177, 434728416, 622396021, 515336875, 804656450, 725634642, 44005539, 581810065, 770589338, 617446647, 500266513, 868605848, 181545878, 913732011, 740501170, 884609069, 912173953, 294756199, 92820653, 151784373, 649318244, 704190866, 73865561, 879593312, 866794675, 537209498, 952017655, 945499395, 303539162, 224672906, 877972112, 793564784, 725949969, 83331019, 964893890, 619303089, 99308785, 886828259, 784862603, 754209456, 401610828, 146957020, 183635295, 176177384, 914482595, 313044074, 444393738, 527376204, 135793039, 564258849, 113563887, 945694927, 850119962, 480583306, 852582524, 369817799, 386276316, 391971242, 413467370, 341925236, 41160271, 77995631, 457742749, 242082479, 460557811, 402892902, 508445698, 784877670, 716706384, 542400334, 608691160, 807521658, 899175682, 276534494, 117009205, 524920298, 185145801, 404848824, 805816488, 828127560, 559502355, 876598318, 554021502, 537682866, 722275770, 515769229, 586285265, 988398906, 69081042, 908408497, 729903917, 643154286, 366642708, 237710428, 214806057, 587747798, 920084104, 193782339, 715119912, 815546963, 679516554, 250031307, 753248343, 150067871, 101398258, 442902548, 540675418, 840676832, 538073202, 382932860, 131368505, 114596601, 772637470, 394346313, 513864427, 67757792, 519335150, 35976463, 685299275, 491610245, 237159932, 791001839, 503421217, 655326503, 56940744, 717687557, 466713437, 967318126, 759053485, 25982249, 267794135, 90036824, 946748006, 904882662, 792154194, 721516254, 5033496, 148316973, 549751264, 872170377, 263534470, 350495396, 858835521, 520337972, 549993702, 594865007, 551451460, 835444212, 35411503, 100588918, 836301737, 951865456, 898033482, 258191820, 237379674, 518949246, 543521364, 645830600, 726649864, 816589295, 144261314, 540942463, 388934186, 756130000, 430815642, 444133628, 51110565, 556960080, 977601497, 475402651, 318640115, 919833557, 999540048, 666911823, 578788552, 712646789, 606155045, 315957919, 611558242, 830779486, 899785113, 141520882, 229256430, 189351926, 253988084, 639150349, 338755549, 780170557, 900067992, 869974927, 356362707, 763181642, 772337851, 64407878, 461755398, 148160648, 136717618, 774406083, 123743001, 13053951, 530123642, 321409307, 601134394, 11509506, 623512605, 755311945, 8729651, 786266519, 616966802, 562940719, 43068689, 348456894, 613255038, 227637574, 77191866, 141422486, 852836081, 422270152, 183862940, 508024542, 523108016, 24065295, 81763761, 936507643, 604782835, 325619579, 555536147, 389468916, 852850022, 463619686, 350013386, 266799925, 402486639, 658333060, 242272308, 977346101, 512067029, 940316969, 458342389, 625723590, 532896036, 563216081, 782293872, 412604477, 460669008, 576360939, 77225258, 104397243, 338860579, 518691162, 478420792, 615598955, 807336748, 66938803, 269861663, 262584050, 29537080, 539723624, 923906654, 114249914, 527538521, 75616194, 78861878, 729282509, 201902083, 47898480, 306823748, 758710666, 534610947, 253428178, 729860495, 193562801, 571824854, 865636939, 400546178, 883760632, 59459461, 739549850, 654714567, 598481808, 645480036, 118321956, 590823532, 126971334, 895090892, 852109438, 756983145, 927818933, 681510015, 100675898, 950889755, 732553576, 29009683, 198743990, 988409598, 847548298, 470791501, 466383616, 645918273, 283786744, 332122336, 573818652, 264969545, 172930749, 359034479, 755122621, 714068949, 327884302, 28110713, 666094913, 942176122, 456090212, 948505452, 220827823, 303297991, 267157564, 657668093, 937231292, 242794416, 785313774, 130675842, 964390123, 845983663, 363035361, 486814993, 803635992, 143123662, 599438463, 159881363, 163879424, 540116727, 16069181, 28109593, 536254894, 176015775, 516103568, 268878721, 974348846, 370693263, 103148815, 906339959, 502476208, 879295795, 884630682, 962002513, 95105564, 878029778, 933135067, 881768812, 15597735, 195395927, 750569982, 718281710, 20907704, 259175761, 268606201, 518870844, 308350951, 279113496, 182548221, 465944337, 7007321, 166659063, 108637788, 997153104, 70163367, 450431724, 776834689, 553715196, 529386862, 118539429, 63495736, 743161509, 60824796, 324099, 219756489, 251114490, 698257333, 243151823, 961601192, 647576310, 997405603, 266498000, 960178066, 173923187, 688880038, 781223640, 511911795, 233864008, 885449907, 888475972, 229450166, 675554390, 720489235, 468416730, 654051063, 771203786, 236123276, 769579020, 5021025, 58958551, 728041207, 829008071, 367139711, 912224069, 322809747, 509959190, 120403771, 815510752, 478692317, 209568663, 632260948, 599161742, 912499515, 383490696, 751484382, 421317805, 153907930, 625083242, 78116478, 895379416, 278948973, 123303206, 880005261, 158551740, 569703075, 235609430, 430089458, 716340133, 921523824, 427856280, 825557827, 805383400, 935317023, 263532298, 364497945, 148752087, 456597032, 512053844, 316712498, 307888456, 76270406, 808320337, 201608328, 22512929, 170575250, 714560253, 362999615, 366857303, 821386857, 185137144, 246984606, 283920924, 586614519, 461481232, 589429867, 94954045, 884335890, 68556860, 295219831, 433270533, 678114049, 949135737, 982173592, 678293121, 475073872, 109555184, 13940307, 16025120, 771270168, 697508327, 696683054, 259986157, 867675701, 509198862, 714899802, 471839044, 727796914, 216910277, 137281512, 810979184, 648609473, 866112417, 927393678, 702082569, 676374485, 369345718, 231277901, 526055793, 384320473, 268499302, 222169959, 20579137, 666898212, 898263660, 138146246, 791470432, 167010139, 488062056, 632253834, 640569347, 297287614, 728967195, 828904869, 201332615, 875003566, 919538028, 408106446, 303641675, 635290944, 38652343, 839738901, 685977388, 718612869, 322384854, 686092873, 129866682, 631895717, 5040402, 620928642, 305227758, 210265664, 558847767, 327144377, 386634268, 123069666, 416414428, 161478804, 980873341, 453002043, 521915880, 465253352, 275860548, 547377694, 890572115, 791874871, 90246937, 28042740, 847592754, 384380973, 975364734, 964161474, 610192132, 465948459, 491236702, 378058058, 335047674, 513543487, 675933871, 107473098, 707777764, 849814982, 208248959, 874694785, 175756681, 249881996, 955867618, 958283628, 128413486, 778006843, 35047508, 774435542, 250098922, 849119845, 686148950, 72082738, 162322078, 20151846, 750065604, 569606461, 542617283, 218201692, 395726788, 934080478, 193086411, 183769031, 896991250, 48633266, 346052590, 598849631, 300963565, 830034537, 384408876, 512042507, 96891523, 724870593, 311576620, 309936612, 476100044, 614453031, 98881689, 115169634, 968044884, 920094881, 403965297, 920527191, 561732568, 813717974, 325588651, 677478414, 638674684, 642194995, 488466945, 459322815, 569286872, 17986993, 689387042, 206408798, 914726623, 286243114, 891679801, 620512332, 314727961, 220586595, 255151454, 409744474, 978278653, 269408700, 39912468, 684049246, 371119786, 494916321, 940011002, 954781895, 15974389, 41678315, 289385602, 106948325, 949484624, 595523305, 970038712, 655781385, 865668416, 381640700, 289550339, 770494593, 123537352, 918483016, 263932016, 580455826, 243352379, 54350207, 773577000, 28442445, 131385663, 873275154, 137547346, 265881398, 282531649, 273066219, 13820321, 656395, 545024779, 725625603, 410098453, 349111104, 737347513, 464867784, 523462897, 843252954, 646563639, 973754569, 649076731, 614380429, 883951965, 807678110, 837891054, 667044471, 288547609, 434892646, 622484740, 819988081, 615891169, 664919282, 646942271, 38700582, 45073358, 705051936, 613649322, 294817105, 649303935, 869893767, 644060631, 168698439, 301166645, 961683626, 890858953, 796212510, 509623664, 282101875, 48103672, 10336771, 76349320, 822222146, 198781276, 99767622, 134518288, 67542251, 171372917, 466071656, 588655195, 504709485, 516339643, 646159464, 125124643, 567269363, 320422802, 165485631, 889021727, 367576612, 775084146, 296271075, 454351539, 628898974, 193263298, 267364928, 675710094, 600636858, 288875742, 299893679, 967007827, 465850831, 698796892, 24331031, 256331694, 187913781, 242518349, 838295206, 905863526, 548244155, 142453671, 179187806, 230783743, 180223948, 36817385, 169485222, 797863081, 806766106, 286368698, 47925533, 890123777, 480185491, 501602788, 359957959, 352255526, 328122050, 108695279, 565907445, 245539089, 651931456, 240651908, 927242392, 172756153, 963288144, 400241836, 229374718, 518396332, 946975210, 935644105, 595061511, 805835206, 208812574, 694999253, 181419255, 715652893, 513623928, 25852624, 215511311, 673413088, 456973799, 111485473, 689354243, 482221091, 633547668, 613197235, 135356431, 530389303, 925061254, 969671857, 286172811, 615521, 765377626, 103695229, 406684403, 330627136, 147714347, 110842368, 984239830, 687239009, 419025842, 891880186, 267974244, 848902871, 924809676, 987922211, 475098888, 598483876, 730157576, 987236544, 103277657, 839908070, 337831129, 981649524, 36752824, 964064420, 759003020, 699097080, 303724992, 660659397, 930873106, 423245234, 991108189, 408909645, 259284262, 570110059, 550860345, 66003953, 754403164, 14738462, 338450262, 324112592, 897143161, 429105036, 542050599, 543745328, 336165930, 662250626, 798384633, 837154862, 696765949, 815323812, 527548364, 233841674, 596370624, 467124750, 842772370, 758772580, 653841675, 315487963, 969940458, 478888013, 773627446, 159466718, 468617473, 602216315, 40209143, 828752178, 548780757, 81959231, 237452773, 439385413, 681327725, 560286344, 893308832, 139845846, 159248001, 541802282, 644658103, 513740592, 521078919, 622736910, 928314395, 860483068, 59944630, 744671243, 147813142, 570473797, 73121330, 969310929, 667719626, 460671344, 342799387, 520864912, 614825621, 71279945, 968647574, 209611783, 499416591, 816656824, 312072098, 731736440, 444501678, 316465557, 506538744, 653100052, 698987239, 187264610, 754450927, 771977219, 118398515, 866830902, 558400947, 391693299, 329047013, 142137976, 853883260, 633699402, 553631058, 413581862, 602344323, 859488518, 454654908, 167715713, 633311504, 4329993, 177052375, 159422956, 676509149, 358947519, 361771238, 484553006, 376285616, 488426956, 769879446, 898700521, 523187278, 309688802, 402987526, 937935199, 446164612, 927992190, 531929113, 953593698, 210419892, 345425675, 706545325, 293800908, 434933715, 705685011, 831422969, 768503464, 268685125, 350073408, 444688095, 119098901, 995564002, 159079423, 527159012, 288943291, 339762209, 39219530, 879102660, 25261766, 318423475, 784468347, 488662015, 848855073, 114119605, 829927670, 906963459, 722056754, 256455323, 11042442, 418133051, 238486818, 272523758, 677532529, 339791580, 328397968, 38813366, 917412679, 788763945, 744534793, 602882455, 438655669, 592202514, 432018939, 99304301, 481899783, 892577485, 346528272, 399713367, 381575710, 210997757, 978910805, 826061502, 642333104, 903378642, 735748562, 250634230, 35082895, 995534104, 521519862, 858532205, 283033654, 287713090, 540869345, 912120408, 307756789, 707401398, 235960352, 310670757, 381361438, 446111130, 597850076, 351727071, 209732050, 823829591, 440096645, 929803050, 100581656, 784390633, 897718757, 745878161, 571513732, 595173825, 22024999, 613443156, 565943085, 214198612, 410747770, 4393678, 343383081, 637194211, 746094872, 617188103, 403896159, 129020889, 280033211, 367494305, 544836797, 107087833, 310726593, 492554415, 866599152, 834053287, 174712165, 510929023, 799210071, 970005057, 703619560, 349230571, 386548850, 173466383, 861464558, 398507958, 198261312, 663103918, 277962564, 384245494, 515917238, 387130592, 15185473, 826225432, 519111742, 907070747, 928041609, 989835477, 993143335, 386452438, 480997763, 924198499, 581015371, 96999753, 195285324, 292511370, 13691222, 198251211, 641548716, 902742446, 899661024, 295627347, 7774100, 36843177, 680695286, 656621483, 815860735, 56787327, 295083700, 581002716, 508191077, 214378644, 29919182, 612197568, 190453386, 579126342, 687022603, 676175556, 107893505, 585775862, 340479641, 934331638, 673189115, 267699008, 815947697, 500654268, 924215795, 481735477, 750301105, 575381485, 51314432, 507056344, 76312154, 741304764, 492424428, 949743060, 455799063, 854210119, 756688716, 287321123, 801191462, 743616887, 606317427, 716673506, 99175298, 388130399, 852760801, 67548037, 533871791, 138065046, 603806942, 270009553, 24788609, 769979831, 963765754, 854933229, 123938033, 151880986, 196119572, 393718097, 600228588, 626784440, 613892731, 852276551, 168695150, 569144118, 440188887, 339267731, 801954227, 87980362, 307669209, 324265743, 313207816, 812952533, 190732393, 389108348, 683014099, 434162812, 510989949, 10455035, 712071639, 41927045, 236941969, 667282114, 738759152, 136811646, 182134900, 597654320, 283547868, 183331754, 604449275, 196287865, 952377661, 235877585, 69793059, 936417638, 578010408, 505941605, 118724218, 841856174, 559961526, 262507201, 28183342, 915802242, 272231425, 352605406, 988579327, 567031587, 644752941, 982697519, 455117002, 709904728, 732888224, 564318682, 92415899, 365758329, 555613081, 469036365, 515853951, 881731910, 355689967, 35400622, 772208877, 462721377, 950872658, 326520626, 129527421, 102043028, 275584012, 117938554, 454577421, 35761433, 402703189, 995838467, 877685901, 989001364, 989822918, 341788438, 805270224, 776348687, 305321272, 224490971, 82824493, 477525898, 828720382, 674248060, 254605666, 140115463, 234910688, 352723771, 162106112, 173277426, 873785964, 302875472, 530884254, 856496823, 170009947, 418519828, 214773855, 66694933, 655892651, 937803111, 824247039, 60469550, 670403104, 243697872, 833374314, 804939906, 646691348, 706106620, 562737363, 266420966, 326348426, 785752188, 319938131, 220856434, 583421765, 629536635, 464221398, 965928688, 80941561, 880256508, 59533190, 541121174, 961874722, 681240506, 135876716, 847720387, 331533551, 500358370, 631465290, 162550014, 179333816, 124729814, 490569317, 169621751, 389027200, 584818494, 925898118, 726563203, 207533882, 939184580, 414998546, 757044447, 482966789, 775885618, 825759326, 667059478, 335161402, 121303013, 468694260, 436684728, 440112046, 912489767, 991945258, 878977827, 297592448, 229873184, 934582653, 276886106, 404595585, 798724689, 432831878, 204957007, 512477105, 968310334, 161893816, 305660243, 76031398, 218560218, 166289683, 492471418, 508511565, 534632747, 978772490, 217888523, 516166747, 327602573, 667439717, 400308550, 564323373, 462430951, 695087145, 870610682, 696209747, 535661901, 288195888, 271696529, 365831959, 128449397, 754673813, 824157284, 122047530, 609425976, 282155586, 779247181, 139682422, 886074465, 614049244, 532513474, 632385098, 433557506, 539088976, 964094385, 859547485, 775511738, 998520140, 906271855, 160822229, 228630425, 266336695, 990006161, 670760543, 377920834, 312337057, 117342590, 758406254, 118678446, 472626395, 854157876, 768150937, 372284334, 411622286, 380079304, 519853658, 266868294, 678770419, 127194068, 226208481, 926283176, 518982101, 763444392, 970315492, 279100192, 106531472, 246867794, 312178030, 181137109, 626056839, 897438637, 337231267, 595236193, 169781112, 709727238, 2404335, 587646906, 241312744, 475121074, 126638233, 43750901, 190961470, 197683801, 898639298, 520645750, 548377737, 504509840, 883277913, 325725253, 536102691, 133204372, 528150152, 669118207, 560010641, 549567897, 451461555, 64445877, 365916347, 52187043, 37348806, 619405376, 554415420, 491152337, 169530643, 557011421, 102976844, 671178427, 300033763, 860857043, 346056362, 913657182, 575320401, 295537929, 44638954, 623402325, 151189121, 150812084, 580583140, 636908315, 564757183, 535047453, 534480583, 910744572, 120443999, 103825461, 172039910, 622058361, 116342755, 608857071, 663842303, 797875569, 905066407, 153038357, 51501796, 642750442, 890782999, 574721189, 869902447, 262705491, 555165352, 611685749, 543988678, 511858900, 313668316, 119231085, 139068771, 744797695, 115730419, 894842788, 385080437, 874336296, 759541995, 766888242, 104394052, 470029250, 130950218, 100763077, 194670875, 51732648, 660781126, 414911004, 312933626, 638097883, 83752013, 961359349, 332292311, 228530385, 770842018, 450205126, 745606528, 203176101, 173215007, 44192482, 346038041, 580620201, 843768484, 993737295, 983047267, 472661947, 313988640, 726127305, 503896081, 287038365, 743616697, 116493365, 893586988, 975871154, 389090078, 44282382, 711163133, 332964603, 953078839, 379336225, 871608406, 292257799, 558513896, 462237549, 187544547, 931102744, 611878299, 935842645, 218003379, 221249410, 87716058, 704124117, 450238796, 239592040, 6163906, 134060671, 222683998, 80932817, 987756859, 905518721, 97715598, 881024781, 93815653, 262315285, 21237407, 740409165, 879777476, 288443276, 362681196, 310351286, 457328852, 321065470, 969966833, 629113386, 857821506, 194132604, 917205250, 206561862, 132669230, 753248289, 531153744, 551710360, 745556047, 388411963, 990704251, 525024121, 595542071, 259016055, 846934952, 628104300, 170786860, 569753134, 251932198, 474934561, 822220293, 58893916, 139413385, 59550435, 577989527, 426503501, 218697235, 496987686, 553320441, 937410535, 318841122, 662189738, 594214724, 219692569, 166920022, 533738538, 543599514, 112170287, 467980155, 788872031, 674047323, 61679361, 889485302, 902029918, 631430944, 461652843, 99179295, 353932859, 639109227, 907409184, 277158876, 745498322, 208135414, 165293010, 943077192, 102330773, 402838678, 473628925, 225624155, 112952074, 122456005, 643247878, 254625231, 938109435, 174038348, 725962347, 574176002, 897490630, 712032194, 624190311, 418315254, 877183639, 653561457, 188415438, 434825812, 580674239, 643157768, 745088238, 49099591, 623461665, 517371837, 836187721, 658299959, 868761786, 621579482, 752270142, 749484537, 925920870, 606358978, 715138076, 221635759, 598806895, 121252274, 355945380, 663704656, 808985193, 963774738, 928493669, 23359480, 128009523, 907463167, 720348205, 202561132, 547922269, 64116699, 978651089, 103280651, 103958256, 139446405, 545510975, 894434165, 340813008, 849766974, 236899403, 739209322, 308744873, 292860871, 246553646, 292260452, 937593074, 627988473, 710609029, 127277716, 521061486, 202648890, 279714275, 397747257, 336042605, 445814743, 542846330, 203875924, 641805726, 764964368, 756047465, 930893685, 976156315, 738551559, 674104950, 458071693, 226327759, 691174058, 650708951, 804577595, 700953692, 324358742, 851561241, 525876722, 259767412, 194108780, 175087487, 652414855, 369190471, 206589816, 650528581, 982420218, 820847557, 893493960, 418250958, 326066571, 310342544, 926989870, 198861450, 973807903, 867899122, 349909807, 369804296, 783177320, 790650074, 483582415, 559758821, 330783704, 726027070, 335418815, 184087206, 710152291, 84308349, 16163753, 447073488, 964422222, 853918992, 742182668, 237382263, 443793083, 168979468, 87955493, 763123531, 43755888, 660412469, 109840759, 613135949, 258764161, 295632924, 71497477, 782910665, 881768499, 258602668, 760642902, 697020525, 984007170, 580343776, 644459076, 936380808, 265476670, 141637629, 719537675, 336075806, 669682752, 607634683, 882306680, 786576224, 648976290, 159625908, 339277403, 512019142, 57475561, 675283678, 932440832, 393996992, 223266560, 672070105, 992444184, 776142276, 525802188, 92402451, 316917589, 439435182, 159485455, 355403676, 455854719, 719342853, 901250443, 107189806, 540578959, 156383325, 806430119, 156804070, 205692686, 458047306, 892953007, 251679769, 911745260, 770758457, 601251591, 14889869, 335407135, 852943874, 184979448, 606429595, 445703829, 770578772, 623273301, 314782547, 604668397, 889211095, 816929832, 971181444, 396581892, 602303848, 479840663, 892872289, 652693674, 335983401, 140433192, 358206507, 65904764, 778741199, 139341771, 873758590, 937104830, 731330318, 254544322, 576334298, 564725120, 600597258, 534325421, 163587478, 256069389, 751839124, 736870120, 515181795, 776624404, 260547800, 152513471, 25610298, 204051730, 591753307, 133415965, 75447196, 951487734, 307848605, 246950977, 543554146, 925278241, 992576349, 43908370, 695384579, 665702226, 806021446, 986512936, 19933213, 618418406, 113428919, 252157143, 60633841, 434878266, 599668465, 346807626, 657418683, 43939091, 883185126, 112447671, 933198195, 61723675, 469468211, 283437798, 531230066, 785419230, 598330176, 619917124, 554750708, 120164442, 778851181, 948197743, 842489566, 630341398, 879579555, 88211305, 913650670, 294358057, 293726974, 146788258, 224543923, 566326195, 629507782, 326229909, 743555763, 429469133, 526463105, 489007886, 657016982, 346068060, 431295410, 964949737, 604151304, 767750586, 154214684, 27639054, 509786119, 567234980, 694550447, 473769702, 667620843, 185920251, 458837782, 57112603, 567531941, 113176773, 285924593, 31615065, 864432567, 464491816, 628378314, 835224770, 8738197, 47903183, 176268964, 545697477, 960331761, 680123426, 515920725, 671658564, 524655903, 863751568, 870777397, 369275220, 40365702, 552629140, 33796004, 758519573, 652358616, 737152009, 15698048, 360243099, 557647558, 988239341, 609568987, 161427786, 375213264, 530496919, 158540713, 100097263, 615844828, 690476824, 836602979, 216096791, 863438947, 769820119, 366035072, 290023973, 582026359, 68795206, 584474215, 324434176, 812702462, 927239676, 4919858, 845073590, 723882592, 713238615, 786517068, 570622564, 854461, 937475754, 543256639, 528166399, 412919053, 335715549, 750458611, 579624219, 961187760, 38098786, 595982655, 645333651, 798154662, 977782093, 415939910, 695685728, 634737944, 577323942, 466809330, 46478881, 241182860, 878537445, 805187349, 939983174, 780085122, 506265025, 76910412, 641351026, 446704939, 31008044, 676759035, 436028265, 640008735, 718897626, 8264660, 901359633, 88061292, 229851235, 501341398, 198784535, 939765554, 40920736, 851514772, 447178450, 615511582, 852462315, 90881265, 994842553, 255334399, 712928339, 558162561, 19441615, 85303014, 919463369, 160440758, 920380895, 537391721, 723677260, 248182994, 553240109, 16232147, 241140104, 162867027, 892143828, 16686876, 877522003, 418068565, 748372358, 453187061, 502410111, 377244383, 755654713, 758194635, 45442616, 788515691, 473279668, 151928084, 429210130, 691893422, 184224216, 826204367, 409793548, 329993902, 416826532, 221954512, 916348470, 135310146, 620927892, 935792951, 41617692, 272766527, 557682345, 41851285, 531805280, 782427514, 99947353, 39154456, 42879693, 254393795, 45527693, 1648754, 508233266, 405328315, 23721562, 161393862, 914515868, 674666908, 39631238, 456076371, 550668159, 741944340, 858876977, 224097450, 766820507, 842476559, 872046857, 173540395, 614045316, 481824967, 298258460, 961915477, 777335341, 274907482, 300560889, 975546304, 283178400, 765659699, 413081105, 5046767, 329111660, 856934335, 507515207, 77527692, 103103681, 437326910, 727332165, 272793625, 542875060, 911566384, 259257642, 576529630, 495497369, 585843950, 983860567, 247149055, 732382989, 555171587, 304992319, 128094643, 88065359, 186844460, 897389955, 304169776, 894332593, 36705433, 597481738, 662061220, 653126585, 41250676, 736008510, 609132758, 73097924, 284626891, 871047993, 437135457, 891993697, 373046526, 93100654, 211845738, 344182629, 937775148, 829471177, 527109230, 297037980, 947667875, 694863940, 220544084, 63484848, 251523329, 645469717, 507181603, 449771022, 123724983, 815871999, 585072929, 291619428, 203097431, 430851739, 103010805, 204684993, 498146390, 177160878, 78557884, 3873724, 204707100, 341408443, 305242510, 337226225, 329858970, 484963749, 227628041, 671752547, 759347351, 295096215, 352210496, 453265333, 633145845, 215675520, 899409702, 749930504, 766988222, 906072540, 621595342, 339141355, 10171152, 75514235, 290921383, 624851610, 748750634, 831651963, 575463865, 636289817, 348451452, 415384645, 618690884, 548481371, 636727243, 415142053, 584824694, 6245164, 904956257, 675796619, 390117876, 823370966, 206013047, 20442158, 621551433, 481688576, 836522490, 603272947, 800190719, 192991743, 549546780, 219679336, 703051820, 999183858, 204053462, 518360276, 767290548, 281770257, 664028390, 942387951, 280525398, 326558547, 828187412, 765485088, 130759621, 135907725, 829161063, 93255685, 740245593, 685188703, 557096229, 994366533, 793741869, 757278752, 924203870, 905664285, 496215124, 549832224, 984144368, 483752566, 245424159, 10469651, 383501844, 543660364, 634007704, 611617795, 570060141, 865796960, 288231236, 266844235, 549192862, 259000703, 163211192, 947063938, 950669940, 149116626, 706323695, 649665643, 544244683, 616567506, 35010848, 516713494, 729863332, 343277138, 927578676, 382098808, 543437556, 961201484, 321406841, 869862924, 278348871, 416104271, 527329348, 853625392, 940917014, 244842020, 24807004, 670448207, 963747580, 170225807, 93566286, 468362741, 277395227, 427392118, 521227269, 738386738, 259978301, 100753816, 74120057, 97818983, 921546327, 387803397, 804340537, 609169641, 804865502, 674680805, 392233991, 378223270, 916006375, 805609174, 929941126, 323822997, 410552593, 112776259, 799178271, 612493680, 771874974, 93770868, 463726470, 514967811, 585883049, 85201774, 310157110, 392550449, 758851786, 143834434, 597848986, 122076979, 879806992, 655503763, 608009757, 759731894, 103715629, 915566414, 301710351, 415245913, 689199984, 455555291, 643395948, 288697795, 87347540, 101869116, 11005647, 634981411, 126255497, 779268417, 367546879, 234977564, 37671128, 98117563, 341743656, 988463914, 389310430, 34610372, 506286968, 529403731, 226370247, 431542340, 937735376, 6142745, 960354654, 158305861, 374426371, 19324668, 468485098, 418767813, 515594579, 105179188, 324183271, 795915056, 522421914, 326930809, 143360709, 218575601, 734716932, 853317753, 128899577, 262449512, 776399476, 232480804, 439250374, 611669656, 648908388, 742872967, 111852405, 957452093, 584764852, 359895712, 676446469, 535352778, 358460235, 13316028, 291284409, 996990352, 784661895, 884026120, 842974066, 909722954, 432390526, 188170346, 920692519, 465186095, 37560455, 452352385, 505174834, 477805900, 169367121, 989376089, 767130159, 948922561, 566240317, 653099508, 837367581, 511729582, 356066386, 64603735, 552662867, 759390706, 342253670, 81673282, 517883036, 123436315, 77842745, 46890617, 902310976, 269023861, 268671286, 263212118, 964940503, 989166850, 816338170, 349947197, 86376620, 872496959, 585678046, 549108635, 463195410, 783272680, 398025944, 307252278, 930604186, 272286546, 573319383, 147299639, 174129546, 250801196, 728831330, 900281736, 900294602, 555905718, 341582912, 576127690, 635623573, 207843866, 590043272, 169524256, 207144669, 296827053, 829429109, 484308551, 536599789, 107358501, 587157187, 544535040, 451738421, 809662105, 467780324, 275427671, 875302014, 3773932, 822492881, 497271561, 170699863, 714139537, 342111437, 76277894, 786235939, 979354828, 546202837, 667072270, 226799441, 275339104, 1590809, 636121678, 882820226, 802323030, 133280674, 922019594, 93322380, 200294892, 891176025, 586618506, 791228182, 309379974, 124588499, 444131102, 217576869, 874659629, 435308853, 206126560, 425826881, 535371177, 801995240, 652454726, 799364305, 576882284, 288255359, 397294411, 589112092, 543942390, 805393033, 402219175, 638266742, 654389716, 146462131, 621388242, 552902379, 877990285, 568101893, 75980010, 316945816, 378885596, 392915370, 294145308, 957959649, 184901496, 349837596, 939990124, 39506150, 359819658, 9188635, 575973604, 716046183, 432246447, 814705527, 832789478, 645806881, 708718169, 454862848, 485741669, 1391775, 613748271, 321496593, 149770696, 749592527, 926729555, 754282541, 148396315, 141563338, 60127860, 509483534, 300969827, 385604935, 827892673, 598448334, 402698817, 342143903, 318231235, 835595226, 372315740, 5350145, 133898734, 409215977, 879296942, 220323528, 615608705, 552749768, 677351931, 56896767, 752043570, 341000952, 367700963, 340161669, 866345497, 308570127, 663009167, 493129236, 74604406, 577033465, 882204398, 465711828, 457201073, 706412783, 117284344, 829298658, 871640078, 594432617, 713106852, 954759669, 593640291, 566131002, 206115266, 823685238, 207180032, 876409543, 826229117, 89697798, 861030021, 317971911, 409488094, 974644721, 377204987, 630908097, 410495805, 450504509, 706897799, 652116366, 868316479, 124795532, 847224709, 535882909, 163824453, 844344887, 10485476, 619840845, 967351490, 311493815, 631148666, 868263412, 780698979, 910337318, 812570763, 330366021, 181938910, 476890651, 99310072, 392818719, 212666957, 698766964, 280772658, 742508811, 156623627, 386819553, 22426615, 77408307, 301241649, 250132346, 35162351, 228732750, 487957905, 254837731, 189378727, 818222189, 640740139, 789213221, 842541103, 836228408, 391882037, 325674608, 654069065, 321576742, 558817766, 685180652, 213400035, 200853577, 781381860, 863358328, 82854315, 408538988, 487869463, 615246017, 471620712, 17080781, 596727391, 86918774, 446742617, 655962348, 588189295, 670265760, 316494534, 473200000, 599744767, 538458570, 871060488, 204764994, 245122966, 36506400, 502474416, 449106150, 918025036, 386684113, 336182989, 119743723, 994487716, 148143701, 622865375, 417148196, 849070537, 936028356, 477694372, 293584183, 974333653, 712088213, 816280961, 884162604, 16463246, 174592661, 2373450, 864989607, 306542029, 775342857, 518290764, 88656911, 262821443, 136707472, 556406347, 436567486, 513212791, 255510089, 772141897, 388142128, 349619969, 649282797, 635152589, 204513831, 985450178, 372723304, 265844574, 863630745, 953089469, 751308301, 1512105, 891501091, 846820498, 537187801, 93240445, 964860859, 614476808, 163064751, 783052942, 941188363, 279109127, 515301269, 301849884, 971488499, 409297102, 601681265, 257144223, 571099378, 70525449, 484680383, 914802906, 348101589, 454158927, 808020887, 846946017, 737615649, 82207667, 651143487, 289834310, 682382027, 948076126, 491772309, 519184887, 64019246, 928786746, 402940888, 460481539, 780739636, 97391564, 677665771, 99618016, 800399021, 879469078, 829374804, 402514505, 504093452, 147865605, 574441724, 344071917, 224467828, 512288000, 185320297, 798854720, 587268394, 99156914, 315508740, 418454416, 29844313, 239255053, 919137235, 15344499, 158496395, 51068389, 341276828, 116553628, 954155212, 210724413, 929029234, 350849664, 250293846, 25242881, 688583634, 360189277, 826057834, 798381965, 81128187, 386866078, 356342377, 823685902, 329939467, 418166537, 924861482, 850796442, 280718556, 385674929, 579413428, 737108354, 317431351, 971843176, 833404755, 344322154, 220138894, 114437546, 484211867, 9332843, 249015044, 53975866, 596554222, 316464862, 785806083, 359177564, 261021867, 316126367, 734901292, 731737643, 372115659, 809517829, 147610830, 845113867, 611768142, 627534182, 789467839, 298534137, 957738163, 416735537, 461343133, 592907399, 149587884, 680072932, 505908920, 61532296, 219612701, 453914910, 299964911, 711966994, 725670260, 700834168, 314368462, 77898613, 797327235, 753187517, 327627984, 957238519, 294549086, 654990461, 363550850, 959752932, 870425678, 350478650, 216736942, 17511530, 936843706, 299862423, 237563664, 843527876, 869502917, 951659428, 942064915, 541664415, 867482289, 694787201, 137668651, 74616998, 75773816, 759984234, 154635116, 300269921, 93916949, 900334640, 428256078, 125340919, 477418225, 185755878, 287796258, 573127466, 660157072, 234083150, 690262037, 59170918, 990033927, 655491868, 16194789, 471884782, 732521326, 438032358, 337546133, 143163218, 916091721, 948295629, 910839155, 286138161, 657085225, 571536305, 368561245, 519316494, 345011185, 650313216, 385127070, 205797489, 819464995, 352670858, 760320470, 395561762, 74849685, 896992852, 173358698, 562556985, 102903350, 589635601, 188620366, 624285558, 89556272, 407924138, 899311127, 401508961, 903933337, 687463684, 190884496, 596019193, 907369042, 125674772, 515851273, 210424103, 436504084, 944013426, 281275290, 992377660, 795758942, 58037583, 97230954, 499413939, 887305751, 119130421, 965966861, 631474395, 582799117, 595685575, 210471819, 233956584, 749194438, 274443368, 471728638, 305695512, 476531683, 778574444, 72020551, 537765037, 473579251, 11648528, 552468173, 818650130, 808223170, 316430304, 126795718, 906383106, 626555929, 389156040, 863252736, 107443503, 247731006, 44747951, 909056906, 2001293, 162990140, 463946153, 292761089, 461877356, 701301055, 825867142, 585375008, 721622159, 54746562, 809111717, 442737758, 514160323, 826004690, 989506241, 756533488, 958797929, 887525, 860988360, 514729334, 284773480, 497585145, 738899521, 499231963, 988300534, 13037710, 667657227, 822919087, 32455903, 405766793, 826810879, 20141716, 540210916, 489769462, 722405880, 354517625, 849317981, 262390868, 8062244, 180638859, 49189790, 57883323, 705006713, 874216696, 32383781, 690460889, 270647788, 218760045, 801691956, 407629006, 357204106, 122216650, 126558267, 33039434, 901315001, 776982057, 65638943, 854201206, 995796148, 730159349, 159812065, 332500754, 218909174, 614247616, 649918015, 775728427, 970331516, 288250755, 951941172, 778485651, 269221680, 61644044, 41138315, 653304330, 552019307, 956519146, 685382373, 416964377, 799720293, 700724220, 421175450, 213554067, 101951853, 495886819, 520765840, 264317981, 129387680, 903717097, 999879017, 352276682, 763826120, 628203596, 879768857, 851940356, 971581189, 550232348, 634044930, 499329779, 121537311, 445152268, 590815592, 581724760, 362892317, 120479894, 585100629, 577131441, 576754065, 614991396, 772581432, 713077183, 872275778, 887689079, 295203171, 274600336, 860598161, 135232956, 398182725, 16874077, 340555704, 715372736, 724841308, 246413092, 778311148, 73973928, 830227577, 797673006, 274672891, 584662840, 929575117, 53103878, 28014485, 126774341, 579494133, 751550847, 289249513, 211426670, 608198800, 443382971, 453003151, 281495346, 296672864, 798155120, 581309768, 993221422, 757846386, 82809821, 440086456, 142524496, 26475092, 859380773, 782653468, 727539526, 444243574, 100012255, 109951040, 274686900, 357773065, 884970840, 200256928, 430005223, 191088580, 989182792, 939112975, 615257173, 179018331, 583446521, 280011933, 384817965, 936502041, 982311145, 701820497, 681302254, 373472948, 327148980, 809744026, 938700669, 246044093, 642016245, 34630890, 134666308, 339999164, 799691557, 798011854, 686138374, 618721980, 612526829, 955621237, 319794325, 673435601, 300331045, 587517769, 698349325, 820500960, 929482813, 324307231, 742545062, 908979290, 246524143, 751432111, 67893810, 341914662, 355130785, 530834491, 851660314, 51168605, 354818587, 635417169, 159799467, 240266087, 807729778, 652778813, 399336942, 42229046, 657004050, 411368119, 294739373, 975073672, 923724491, 540675747, 511328872, 148983796, 26332388, 442601642, 602320434, 705159045, 237732768, 220069062, 213735065, 742634794, 773782036, 808505188, 302815522, 515253534, 372974288, 311449676, 381214132, 564945861, 653489178, 365615491, 980983269, 416878487, 879098165, 135491652, 239604682, 665537907, 11492652, 90427659, 762826393, 75159251, 235240771, 992379049, 493948737, 910229337, 442798032, 825934490, 135154828, 439880518, 645834938, 169551521, 100119926, 880186477, 763013820, 470683064, 137112372, 508300414, 478672577, 436757546, 411172478, 84332420, 305105385, 61383302, 893405650, 422136894, 833490820, 47799171, 474700614, 911855206, 23441087, 747597041, 933257041, 344762013, 591282782, 142286401, 32448264, 144681072, 200579280, 506136864, 208187170, 24137329, 503267276, 820671276, 183726964, 98732640, 734133956, 742602462, 497355663, 266648508, 564192770, 235862179, 128800146, 375505139, 295634254, 378684132, 609953388, 890285941, 907627345, 186411254, 538801876, 420871649, 256798741, 519897904, 535812370, 775880171, 611059830, 835131519, 344894370, 224873714, 264097368, 713833872, 391385984, 119277082, 137296584, 763755361, 229025491, 398004222, 822947391, 569891595, 454597838, 241532293, 12353437, 241944187, 561377331, 387056895, 404089699, 870495014, 224030319, 985418329, 727462796, 727192766, 109194613, 202054761, 445531069, 941648580, 926465321, 615862018, 402327876, 843409044, 398726781, 624512593, 20444067, 319857126, 980529642, 975693892, 381889623, 488558360, 676111592, 246893233, 550380061, 74667046, 554260511, 30919794, 29921726, 648602037, 110600195, 42091203, 694501592, 826797654, 839115754, 255006946, 627404181, 890682032, 486820241, 601289216, 50131760, 213247890, 14572849, 237702541, 692821565, 94048041, 839154888, 147714937, 113111430, 616968671, 853849002, 978781013, 782266931, 464573588, 23181531, 90915249, 388789911, 7935049, 13267328, 341110996, 93529501, 811323734, 261370435, 451193785, 245736754, 950451912, 478558502, 69409063, 161262504, 267757500, 753495700, 145080833, 295966726, 328680067, 635838842, 835790576, 485735171, 104747145, 943285079, 822784889, 506443443, 629640891, 571024751, 890668909, 764425, 548387456, 103741376, 87927778, 735669078, 740289267, 19079274, 265846855, 316961954, 915761277, 779304448, 807907038, 719803723, 464557391, 545982333, 105245925, 291594096, 942268849, 510465155, 522657243, 333284686, 877129519, 923315521, 29794073, 620254458, 895975848, 633537932, 861935600, 808381568, 719729589, 640530252, 132971679, 879652971, 607540720, 65543677, 235007155, 827355414, 208006353, 695429486, 585863052, 679345384, 282943022, 610685988, 105528024, 1622317, 388199987, 615707440, 285178652, 972563467, 532898725, 17459243, 491323198, 438401568, 303426005, 725212993, 366359910, 925583935, 281577273, 832541744, 949491466, 659980677, 834534594, 231366180, 566989208, 396236385, 576169398, 926844465, 804466569, 58128354, 809268906, 77552450, 685720107, 53277725, 481005952, 284550735, 505303523, 300524419, 38733097, 231466292, 307843877, 553431836, 7092270, 900668282, 789825283, 845312653, 662203053, 617168970, 214673822, 785905550, 416473169, 252434881, 753680559, 720111383, 587933855, 116067498, 871181267, 79055311, 951624862, 891695514, 432377908, 27966405, 790348109, 451052592, 366432705, 39196738, 204780954, 282436968, 449709780, 941643549, 370442348, 502501017, 677913826, 847721090, 431745395, 616738393, 325716776, 781307680, 761776398, 948148389, 582249209, 795840808, 877536372, 259985400, 495135496, 916863345, 820976211, 827343555, 406748183, 514244800, 482564818, 28112928, 112383755, 19980672, 872975010, 139493702, 478674165, 965746867, 587081557, 300474953, 643632712, 381756274, 460906561, 633613820, 161909162, 194415655, 37128613, 668137148, 733649136, 353279674, 597428998, 987932603, 434772198, 415824129, 7650525, 541148360, 184651941, 135766092, 967111416, 616162039, 169818681, 231590619, 636033867, 592028100, 415478678, 746659617, 507802265, 312533702, 92511199, 40876485, 614356958, 322421317, 641302991, 926160446, 418399634, 774703195, 382166911, 552136482, 937662327, 698941975, 303093391, 717756062, 744442826, 676401260, 930815186, 245016376, 110800872, 223675190, 96726875, 542099062, 473939049, 764899401, 185896053, 643185448, 154325028, 785146444, 128152043, 951071811, 364588688, 819117493, 119871600, 943365955, 846336017, 262867478, 53943115, 713379174, 863985695, 489275307, 709601813, 432251222, 299010205, 729514279, 110414872, 568026856, 728854058, 579649488, 847661077, 968907452, 805053999, 953665024, 829700338, 3491891, 461107211, 445628772, 581437196, 326483627, 63468648, 957890182, 732266117, 652574796, 773613966, 204211377, 222212392, 934138030, 937907311, 560282362, 823910603, 701888889, 450253787, 178565754, 655105374, 913693983, 172276774, 877992002, 454415822, 369158564, 466710493, 780300534, 679447837, 864944215, 492110714, 478392216, 502725139, 695704312, 923774864, 329295975, 483198704, 525950820, 132346760, 827736462, 599258251, 536851569, 684820017, 930500767, 588156514, 864369649, 475943872, 157400182, 431727479, 968736432, 591861039, 826263324, 20075948, 817454771, 105228013, 537022440, 643817207, 664721301, 488082430, 852919468, 146794304, 495991047, 621818025, 176258299, 79958727, 870942810, 636284060, 646009002, 437408934, 579588796, 869515096, 162392938, 566487832, 217302936, 350460307, 722427783, 961121768, 844689957, 925010036, 607790912, 300848286, 953013024, 963259948, 984705981, 244738104, 139404939, 248753414, 701461009, 680387568, 853708970, 537150121, 996571215, 46893880, 275467557, 955574219, 257780786, 411994187, 681175035, 388724344, 97727092, 734947465, 96908083, 244595641, 360294967, 222607954, 439945805, 825760831, 854948330, 126598608, 174560936, 617059019, 449402092, 133966947, 83280431, 971374418, 133202977, 677283691, 932308581, 253070505, 477577139, 300363384, 348783669, 239835157, 942629807, 85898295, 64739196, 971532126, 761063875, 743528155, 359122910, 410076290, 350808956, 23258269, 726037292, 873558417, 217988463, 783930074, 381558355, 12329469, 941819308, 851930781, 173657499, 702786896, 188633135, 399037082, 81758938, 534532748, 590470922, 189321955, 207290337, 973023549, 433505165, 130557136, 740736230, 277166951, 68643918, 722652478, 198077242, 141759333, 618620563, 806309953, 849156415, 735607665, 214785500, 955270226, 835679478, 319627931, 564948759, 592637671, 382466380, 183478515, 590029019, 208939781, 497675351, 758486105, 572089929, 293386808, 270252828, 409170819, 888295922, 228498324, 113636408, 18804227, 469879378, 526695743, 485231433, 136287593, 857443159, 17382363, 993192752, 177972632, 706151012, 365070840, 795556250, 814753899, 198331803, 470749112, 678144560, 835564402, 872741780, 248783910, 236311904, 84007940, 31900905, 4677848, 596720353, 691615497, 161993557, 237267531, 551596394, 580864824, 538762960, 846049166, 482133657, 542641923, 397148546, 723939052, 954865840, 406933161, 775873559, 212295444, 572353701, 746207533, 196522035, 250477905, 196588107, 189439395, 298972065, 936038470, 435657925, 135310590, 159731314, 833179193, 6524180, 999722428, 408904070, 768831189, 765657273, 348829647, 982006347, 602638861, 924914159, 574642316, 357955851, 996810330, 449181673, 323498514, 238091079, 111066781, 371868770, 430218637, 224072287, 346969250, 656146232, 133215720, 551237700, 840376715, 502718654, 864681945, 632009085, 123826552, 165377438, 111324852, 851987302, 943348025, 805966966, 427745544, 346203419, 498150820, 87000237, 61984171, 619830115, 326169177, 704012930, 39428631, 274572535, 259288160, 560525254, 384583984, 410599980, 853190817, 61724664, 709720027, 435692970, 116120071, 201298642, 440159602, 615971311, 513973208, 464193214, 823238763, 266613802, 979084632, 921496501, 714899642, 721462631, 28439377, 334336545, 352003811, 27594336, 820182918, 942312783, 174588084, 163558367, 583966565, 643455845, 423636689, 954408813, 797717706, 398128127, 936568541, 770169892, 71461031, 613201510, 636618057, 443238218, 567234407, 702867667, 678728045, 836066865, 167171614, 435904509, 757462099, 728389122, 727936737, 502216891, 382672924, 176801817, 669159828, 943774895, 595964054, 335720203, 670761665, 139798932, 869766272, 644054071, 28915271, 372679899, 266285141, 922178862, 862985177, 806945601, 817183743, 180705169, 791109050, 191621179, 900991753, 325960851, 939973676, 984893969, 630051972, 540724306, 858176580, 479330641, 394391518, 781121124, 363331156, 658196275, 91086897, 389588844, 287655637, 184714667, 861601537, 824346012, 829973855, 257715021, 124283834, 38152516, 882024944, 659794511, 434518918, 568599817, 426926, 433173865, 607495352, 802885696, 903198390, 702289112, 341137818, 816670912, 291303291, 932738495, 112230213, 893146967, 898099551, 669411071, 549558883, 274379096, 315899251, 13843045, 81284739, 344996416, 96527332, 223728475, 29309550, 531406600, 241042141, 321608099, 949828371, 228643218, 317718216, 801827386, 130095295, 672103678, 844010481, 414876135, 19530282, 721207984, 720088321, 76320178, 562981399, 105562987, 436351485, 648993401, 319690343, 155671878, 593323923, 348167111, 763515049, 598483199, 468560636, 687289514, 645136554, 497427344, 455898195, 917702244, 756631871, 792125911, 383316302, 36623122, 866928334, 39302912, 859821542, 240150501, 947144353, 675264793, 715743769, 467492963, 169430878, 167929522, 189651038, 241867571, 351803902, 529011514, 82714321, 436509673, 897017746, 944343473, 231108017, 594104989, 157774616, 386202972, 989146385, 805435566, 577861009, 38201113, 628512344, 808381504, 24011447, 702167415, 901338878, 792558643, 660115602, 722327379, 190656701, 132572937, 779458093, 496866216, 673318840, 633743245, 432726617, 713983357, 188511054, 740974202, 767545498, 345451335, 77330882, 135810105, 816167747, 41557541, 298920019, 234090193, 300993976, 771713584, 692615784, 294712527, 335577960, 913723838, 137153473, 719756693, 764958750, 517106587, 111255463, 833652929, 483372807, 11581633, 111861093, 83111948, 664940437, 825996256, 968823724, 505723749, 249653645, 37134936, 588608171, 222099756, 941840332, 583415543, 278486778, 901424873, 943578699, 438767280, 925756900, 18575370, 928079856, 267128080, 719447041, 638436832, 826553877, 108857187, 391925606, 566480673, 163944908, 995524224, 242310887, 835575876, 2692891, 141275412, 139474283, 235863548, 618515097, 985642125, 369217070, 886520820, 368771429, 740704962, 970209466, 959043472, 16742826, 31673245, 7873388, 240939226, 4743850, 724372929, 64359923, 40252723, 959724500, 267525143, 869341982, 483783405, 779305864, 912171012, 473309656, 651133919, 109857217, 903613246, 962297063, 903186958, 852175240, 850584420, 598389467, 364613353, 947019938, 917374036, 832327085, 560003958, 602308646, 282227503, 80876563, 499178576, 875814126, 484566737, 880549784, 417903774, 439301014, 711181904, 619667788, 183448060, 290002890, 511699961, 178249191, 895684831, 582262866, 502282420, 59949670, 265893276, 790923008, 849218231, 952963505, 357273270, 545995095, 32763384, 600635997, 875469665, 82530814, 357536835, 700481975, 721251531, 412848717, 400653093, 508074544, 704930316, 455304344, 888268047, 914875933, 235623179, 659017860, 904150682, 931341425, 41512454, 290480700, 207411018, 49259686, 768879037, 240721929, 637229607, 139746194, 312023253, 915967678, 622146555, 707106985, 619295784, 942715119, 561323226, 449364614, 128149899, 11999014, 236730689, 81267095, 941171090, 283738754, 156426458, 412150626, 963282623, 522920738, 375608108, 384172270, 143110237, 852746287, 379730991, 360902712, 853949571, 46001475, 275852441, 987040181, 827406642, 739368879, 671662223, 647464086, 867342928, 461459733, 855010765, 106647537, 310189108, 333294724, 141694722, 249899248, 601910042, 141038305, 870390927, 420493222, 187600743, 373304117, 225363716, 225634773, 504041808, 271277067, 559801318, 455423080, 255594661, 815236612, 156789720, 132115752, 925261426, 227557600, 368266795, 714400261, 951268746, 378444673, 32445153, 414942045, 772746232, 281051840, 799009382, 197969230, 119518367, 626686732, 458390672, 935208630, 496684916, 195105810, 512506462, 107974177, 30993077, 182316376, 54496374, 837941295, 329467266, 30307814, 715973655, 238322762, 411165618, 65683092, 105484360, 27362515, 252200779, 690117526, 385232794, 203108958, 434649984, 70787727, 909147699, 245909141, 232691212, 587114018, 18315201, 353820299, 614887774, 850839322, 960513256, 830530588, 732837807, 834677965, 685287914, 190116014, 673423293, 434749354, 532394242, 268331847, 399874668, 19762569, 128487032, 162724344, 856317906, 647855746, 70004781, 7151633, 377739679, 531698297, 13711236, 83459537, 681037711, 777110156, 195151183, 526059753, 113348296, 797035338, 171936011, 87714789, 341001087, 889162702, 371863698, 577013287, 845344593, 547493421, 855520345, 281966983, 466156670, 211882725, 268368742, 650120885, 920607730, 498042757, 897913889, 16864824, 553116475, 985963172, 226357316, 69212963, 482220419, 139840048, 14390419, 679999688, 460063679, 750660685, 767351234, 54198306, 362777187, 251781941, 383457932, 476204016, 156217088, 958667210, 408595072, 976984610, 303403225, 456577593, 443083130, 230793183, 470904895, 378566182, 850146534, 433858169, 456867112, 921333475, 155781615, 733077947, 689842118, 993917346, 420170150, 334707355, 627155919, 82054402, 189010586, 93972765, 756928919, 66815452, 638314094, 43339393, 15724729, 822000889, 488957048, 89036417, 364513933, 80078203, 684998739, 994708656, 957110066, 521631859, 113189080, 852887955, 182631954, 897825927, 491292052, 739495778, 807869837, 504512, 756528686, 763006109, 855551950, 851453248, 912900222, 691626269, 729291119, 616149767, 260505079, 798034204, 467587969, 177917682, 342755712, 293317515, 258488213, 198144305, 637682895, 345819722, 456392769, 587535384, 311013748, 83352856, 153330487, 500599852, 764507403, 20785691, 476676983, 143969571, 292420496, 867134054, 937363704, 335681624, 284023254, 872154835, 789019203, 344834706, 733247690, 866639785, 313817794, 95684602, 278331371, 149087798, 72903751, 987819728, 807544214, 427878942, 700671894, 698378290, 213675105, 484646066, 319233158, 165714290, 890998117, 700020344, 660972776, 440215014, 210603869, 699426333, 741062389, 715646194, 657200962, 861355216, 305809177, 428623850, 511481667, 538695638, 804826418, 89543164, 919120261, 370209406, 666397823, 991148184, 574038061, 100599947, 203537941, 592317995, 566890595, 274385002, 746587803, 261005083, 10890387, 735570858, 359503394, 485583400, 980447524, 901757005, 460548190, 701702668, 429949196, 591013451, 339331955, 373599055, 318800640, 23781742, 454584002, 428862101, 74280172, 162899082, 73557168, 510107877, 394779570, 27570346, 284186884, 731723907, 98487943, 332060234, 536835597, 672473365, 878646804, 870342219, 791225549, 845606501, 495218599, 725057612, 447504389, 183295576, 8184263, 171989490, 481297068, 59839701, 62095786, 220252919, 700143502, 259036056, 621736658, 733202292, 998048897, 636148818, 118797203, 369877295, 730479763, 179914136, 730669323, 177782671, 731868399, 176007806, 12065526, 751885286, 505670442, 542223544, 375630568, 114971905, 296696950, 224531250, 53933137, 604030633, 436744074, 199512723, 427883562, 407324635, 865215685, 741069685, 643087309, 46774446, 228020232, 541672764, 140655192, 529083284, 404874143, 783039132, 316145008, 689995824, 201059388, 648344148, 395725406, 107113068, 200601437, 947032627, 392365846, 465479474, 741433005, 589789159, 711480835, 994017622, 159609638, 339208389, 749571932, 818880128, 368636132, 32447538, 496270433, 203707025, 372096235, 330601046, 118400318, 908006231, 619847380, 945540357, 967740688, 617493100, 582827492, 323969141, 606880498, 585928305, 639369885, 474994131, 943563638, 368100511, 998875216, 327927935, 316708175, 869658383, 328042134, 192009320, 61509710, 592594363, 288519154, 230194181, 931914734, 761529274, 338579285, 556406610, 52545707, 17460663, 919549794, 944863868, 359316762, 546778452, 653931815, 766619388, 664658326, 66552113, 119286795, 606560436, 339476839, 208240508, 867747528, 985532977, 378800272, 228603630, 708214721, 910732813, 931180858, 289820983, 494912593, 117148245, 999116345, 917468677, 82511199, 348043390, 105014328, 271432184, 422131184, 969328866, 333519617, 904128153, 682605035, 714689022, 715265828, 182747742, 497540421, 255024308, 347381164, 967153550, 231882180, 650193649, 69664605, 367393303, 169516518, 486813472, 684449151, 392818515, 719798594, 921710308, 675965435, 331486163, 509051530, 158330133, 34662088, 908188107, 818470487, 989087377, 286735420, 405727231, 23105977, 53894587, 85982795, 71201111, 831471776, 29523516, 464934290, 373389210, 476298832, 992860037, 68972277, 107625429, 815263491, 819498406, 300153253, 590004169, 791949104, 196414041, 756175164, 942566896, 74736756, 217820594, 725171316, 580939885, 228990066, 788142716, 818035568, 184467646, 212833646, 757429209, 218650090, 373434617, 888744675, 189786252, 618801158, 75090424, 428523550, 428896697, 393075150, 497986939, 186594769, 529667440, 852454841, 507213299, 343462935, 781657548, 542600919, 694947578, 957929393, 317635471, 409762122, 343945103, 707357882, 995605790, 339435952, 523727084, 468474294, 919879800, 689660633, 476311552, 211407047, 363906261, 17271408, 538370988, 290038162, 141535715, 690466157, 98287437, 964514845, 174890531, 188874738, 503700083, 179040774, 564849990, 932945665, 147637918, 541051152, 590698753, 837350329, 237091238, 595786167, 402765115, 1161704, 2350093, 158696313, 400382266, 504924841, 569157639, 843271054, 419003686, 307477628, 117673512, 786109964, 351028786, 711890307, 435678312, 622504596, 61568704, 400257137, 402053436, 166627250, 976470367, 455729904, 710059996, 145813972, 317454288, 765111994, 863355349, 672102762, 146004213, 338118924, 760119684, 744331470, 239015838, 138219472, 592507936, 430461605, 699595003, 574087449, 586350133, 274144842, 384870746, 730597638, 327286138, 618659328, 340462936, 213316590, 290610625, 179916811, 710526523, 474264995, 513127427, 759245897, 707310339, 883634152, 659932946, 318998765, 122699587, 24765956, 810151285, 148200897, 595291966, 249812998, 224660955, 351863845, 148319347, 612989527, 109852525, 567981950, 659704914, 643901048, 111303896, 313837278, 639790052, 278652456, 189193999, 526018484, 254117816, 182861514, 205581911, 318575611, 107834326, 43802174, 46693059, 63953378, 768317098, 765818860, 385327464, 688990765, 50329232, 346777850, 253014523, 506904204, 989446793, 873400400, 597312226, 825555548, 749666457, 336027196, 732441662, 351549667, 786931672, 137198288, 291194400, 766646857, 834300045, 523394349, 514620764, 331429035, 945664637, 386931649, 308115910, 590675942, 45605745, 751311943, 774551205, 166566054, 104382893, 205287177, 531437117, 965928230, 812127040, 621679735, 244618999, 688891120, 201671107, 586895941, 27266699, 816917706, 562441814, 44157100, 204173691, 550560629, 146142607, 940826898, 317188061, 999564634, 967440106, 504616903, 387353122, 58499924, 648318881, 924870330, 115838099, 483862646, 819976942, 473474592, 933704405, 282605123, 147595653, 892546116, 771763576, 53863276, 143124444, 808231249, 446099839, 244553231, 475147507, 164044559, 975651580, 379460902, 332486419, 465591164, 38741742, 801455508, 285020037, 347775747, 937409003, 838644076, 684203450, 641051231, 743432761, 891122757, 85926207, 973772645, 476928607, 797798900, 198720725, 446164138, 746920630, 638618780, 699227474, 892605554, 379551941, 55379147, 878645074, 942721295, 346463109, 58795197, 305158398, 852793451, 404553809, 34173172, 108320871, 564681743, 153557355, 548843265, 770404518, 29353109, 291456332, 651810191, 474511678, 38939220, 124467494, 965120011, 337729305, 585014703, 810933404, 165303142, 960607308, 483040718, 441982810, 385463968, 226698502, 492069302, 121950835, 678605309, 975677683, 79580822, 975229494, 435630793, 472788599, 639376627, 588731209, 325729570, 131557290, 379518963, 754067774, 491295094, 243882660, 550113356, 786144065, 693328907, 157418587, 890582020, 710132411, 110579259, 660833852, 232227963, 524239333, 744846013, 588942292, 68571898, 243761386, 421585877, 42505188, 608818250, 612970995, 267760960, 490287447, 94047041, 771975869, 363346375, 979792098, 403917073, 633429818, 203971132, 211390839, 676496292, 478694437, 283725052, 407037423, 974481673, 841413566, 457038728, 868987951, 923843049, 220115429, 500779566, 426325143, 351164439, 899296531, 492057587, 338977864, 777771455, 907675772, 237315661, 611426600, 35678373, 338031544, 732892908, 416889474, 847119098, 326381959, 90576202, 738656027, 620950794, 306203229, 617266428, 109266949, 966416212, 715764775, 251778316, 619515573, 45456016, 729994862, 450689776, 133092148, 122992009, 812475193, 977649600, 732692356, 146078415, 217141528, 632794967, 689443626, 720960380, 778905844, 474726979, 263845908, 361081057, 509786077, 769556867, 156044722, 322229090, 595593070, 576539121, 824735913, 300981866, 574215928, 483545813, 525248109, 126459008, 815743158, 253684226, 895973466, 815596000, 418441899, 998986208, 754891298, 269877146, 622740891, 421356245, 759627207, 685528680, 446566146, 347827920, 693490807, 226145852, 219849417, 269215697, 866824411, 547527752, 526089538, 382513283, 769521672, 291096130, 271153688, 757201946, 704127835, 876170939, 517080789, 469771365, 820748475, 80689325, 485848981, 487038148, 143347922, 898243935, 919138377, 14428908, 777364782, 236177837, 218441183, 701994753, 971375333, 795128350, 617929751, 793356917, 424822804, 536817245, 954922182, 970926031, 370231105, 85060526, 989877188, 442766145, 310782932, 174101856, 932205621, 52844550, 461412922, 500688088, 543124925, 609012664, 824642045, 952052926, 952474519, 75471091, 439455617, 734928939, 215603083, 399987063, 337959457, 445455943, 253102058, 938762295, 535872371, 359798214, 815668526, 826310860, 610788794, 316684719, 533950442, 143223546, 267632411, 212844087, 713201173, 992099237, 976113281, 516978719, 143122742, 562284527, 244475108, 662385687, 184364421, 583191875, 94457817, 792989090, 364009302, 273345019, 438749746, 276739139, 897390574, 532855459, 476136141, 730622350, 60478147, 933385888, 143142192, 565714444, 328179408, 850766358, 237146623, 711443540, 220189940, 589028431, 589060618, 282977093, 516529654, 159704098, 700130351, 127277146, 64992489, 826117038, 194021226, 200159826, 91441865, 652240033, 366238185, 205990807, 114281380, 103369493, 823776036, 488475237, 626298369, 985774172, 139238509, 392513854, 223119822, 600688143, 147865348, 847751580, 135247839, 685840520, 736625371, 164811229, 943149828, 876169916, 108856158, 662905352, 746391560, 297729711, 154278896, 176896617, 869603304, 686853608, 741699189, 338296711, 272592354, 526413649, 669216508, 36958094, 650896108, 685938286, 321346252, 862953852, 626934405, 206133669, 188225066, 510241204, 964646250, 38385964, 925279573, 203160872, 652687455, 329947289, 377271292, 149016289, 439965496, 383874921, 820484755, 402325415, 651097618, 325446492, 660297830, 102106033, 60932310, 353618109, 44999402, 956254998, 422281186, 144549344, 742734569, 149216361, 601380198, 901820899, 889959998, 287294839, 218234031, 319947648, 820739829, 135139180, 911367486, 27397699, 838448625, 527716593, 207525644, 976200020, 996479437, 234910078, 406202440, 912590555, 828758881, 81273371, 662950020, 29450839, 25299659, 139136836, 956987637, 263509512, 783377846, 496292301, 793955626, 546248273, 363891006, 415443193, 739112089, 159198628, 918722081, 328367851, 542820029, 76633690, 92573590, 789377331, 533547951, 412085354, 726668055, 418676879, 600123402, 893826134, 115085306, 769613061, 76040120, 117238845, 637291868, 350431162, 339067929, 617216387, 464704375, 299872806, 316040200, 705496908, 420451822, 445606459, 72377098, 144805956, 841594385, 59738181, 260964779, 923478055, 977641764, 444251671, 816445970, 416887171, 128596490, 572425961, 431135395, 183635440, 787714010, 295153049, 576316677, 610120503, 263415773, 6436725, 45326257, 124643904, 638300879, 299539196, 583637460, 953150664, 678085395, 576494833, 85239096, 731877500, 746803829, 257520209, 165232234, 957872789, 137020182, 307925615, 583156587, 48608061, 200209692, 806126386, 646049218, 292792389, 567042434, 70580500, 864794074, 76511996, 192886914, 862311458, 49202622, 765719883, 284630770, 291701616, 265363431, 361758553, 353578433, 654323500, 637081518, 514700653, 59942715, 136201664, 287673457, 667453740, 13080878, 150251115, 742977429, 616842743, 551680202, 708652698, 836167047, 381032501, 693518844, 616040436, 837663593, 176439514, 718509065, 948344037, 389595674, 338305825, 948042986, 278625340, 643320474, 327751040, 208935899, 940986266, 821828982, 378090105, 229470658, 61766756, 845852302, 367771601, 508975928, 441479288, 831735661, 58342278, 715252642, 271464392, 279089534, 231845541, 78801321, 24621887, 710618830, 791674168, 23066237, 83519086, 326007401, 339833309, 826034112, 662843208, 711953501, 404182302, 446722672, 608431204, 363063986, 864070291, 541447153, 189524391, 965119451, 642847547, 291844907, 229531791, 231983868, 357008881, 746638035, 604108832, 783037305, 716096362, 162106454, 81278233, 206178524, 839029093, 294049645, 809655827, 361034155, 575508388, 198576256, 961580129, 22458358, 117049637, 443830646, 536310999, 954544803, 568146046, 965882967, 343096100, 38749158, 447466469, 342040099, 125530459, 897072195, 559703367, 474227757, 60148703, 191865320, 625718620, 521202569, 756138356, 602674546, 749130355, 991283014, 237108456, 475796465, 121524652, 972443801, 750358328, 82784152, 142330334, 973813260, 126600985, 520734519, 390918006, 582148936, 577802809, 27534894, 989343396, 255170852, 451785916, 551391257, 665245662, 147880231, 517449786, 257371576, 551847268, 398070319, 745228568, 263811302, 333314509, 685825016, 984570210, 325019995, 819122190, 984805617, 183760307, 424767381, 163387130, 313891744, 892660814, 210327368, 527886899, 727066067, 214917515, 969187849, 420319212, 796414921, 825945589, 466689202, 128283100, 362618917, 76964202, 226496276, 966918261, 676269212, 34261505, 859340074, 122972894, 931355561, 933921086, 189260354, 59647891, 460839560, 39603283, 686944123, 10901697, 13069414, 65459814, 210284338, 670021808, 429897999, 755401306, 753008203, 596038270, 477587372, 789448508, 110928111, 199990681, 475647156, 265928342, 641886520, 141174739, 708166791, 491943518, 181426502, 943119433, 15272302, 300689938, 236820442, 173285754, 751359414, 926268310, 152432934, 293663818, 202407644, 241948445, 370764140, 853855284, 545072227, 992771742, 666669690, 340313646, 61173664, 353247330, 385066977, 946681470, 529625480, 644513795, 417702187, 429005818, 324414342, 379275941, 495534502, 797367350, 454152605, 793592756, 382433568, 600982372, 788448150, 199049122, 419392723, 697123612, 301555201, 401610615, 54872322, 17753259, 743261626, 824283154, 129721400, 256775229, 349013194, 41112645, 784603210, 487505879, 205911585, 361143530, 308885627, 602752509, 326379822, 291188982, 970480208, 54993884, 343838356, 308575896, 129423496, 910976358, 197050627, 117763870, 364144891, 105038503, 135592303, 506326197, 290746371, 538588669, 431199848, 906380257, 871754265, 275973207, 36200530, 812969820, 563004838, 246111372, 611038307, 745211700, 591730839, 655120054, 386909509, 880051495, 786037695, 787825930, 770957674, 65671806, 392515938, 509515092, 602209157, 561816617, 187048364, 769130297, 770807729, 4424292, 85830940, 296677680, 957635254, 969691654, 993520072, 188919500, 724415834, 531870405, 728232163, 473522574, 859319931, 303072358, 56096480, 134614559, 868085632, 530947097, 166931250, 683914604, 481503196, 339138226, 995564211, 374182806, 211997413, 417025998, 196163906, 266583316, 24147233, 706341309, 448885813, 369021707, 419931917, 229081899, 978602815, 213698830, 588838783, 615063274, 917413740, 296548354, 498437957, 270262286, 220074577, 467003219, 544915975, 956681113, 331089238, 314632622, 700336872, 317142069, 882515633, 823573889, 632930247, 298947775, 286445385, 268304197, 950148128, 890329722, 776094292, 675865185, 438084010, 108642787, 662918842, 539521024, 558313751, 558437440, 220769491, 265991957, 119340002, 62555568, 459730288, 25851256, 371808833, 514949988, 107605697, 220582178, 610517378, 300973391, 205760886, 728931388, 909284042, 481395259, 546088015, 209749975, 969558389, 216587924, 721189495, 901092037, 742265351, 729760938, 101065132, 117367069, 795773866, 23457525, 381815373, 182663181, 859916557, 71749851, 801231072, 162534146, 227208289, 901043924, 882323486, 373701392, 802528022, 68969517, 645449393, 154820403, 46927925, 788784877, 599047324, 154552753, 84969445, 349139809, 291841261, 605860709, 262381012, 984399421, 978555743, 222264273, 13679843, 262074697, 43261508, 795802901, 798621503, 463887513, 748844497, 551281412, 348663236, 874843386, 146573446, 676139348, 375868914, 497329865, 157240653, 26325912, 707780225, 155311633, 415740620, 124099593, 127144237, 581225606, 396080021, 890657900, 474731149, 454760839, 533333381, 80697475, 61857307, 447096327, 606364731, 251477599, 869635659, 385158800, 99740963, 537758682, 605259205, 295039208, 496396709, 543737682, 215171414, 936292850, 106826541, 59528433, 218859943, 487601235, 620497354, 203916509, 160482229, 356501231, 607190991, 924007371, 194178654, 29673592, 176849822, 406455250, 741395390, 119450972, 312909129, 73602873, 207595410, 872455106, 126288912, 535843918, 588468094, 658209327, 372116092, 579763626, 735296265, 641187571, 487613434, 647647635, 981021390, 168025059, 237618174, 923730669, 262957413, 924772649, 687383046, 582426152, 246317527, 406153225, 215865605, 761577673, 764787874, 678444360, 372452266, 677395509, 940626021, 374600767, 851529351, 711660005, 800319053, 356963173, 433921542, 430153814, 527059283, 563258373, 155833574, 52668982, 459314778, 275318160, 60141003, 129009434, 311736413, 309295734, 730105357, 166205055, 832344624, 585368251, 532997740, 425874460, 201203013, 543079624, 496479153, 709161165, 332246085, 571574697, 375360844, 874834217, 872429448, 511385835, 316751566, 112043831, 721322020, 672057107, 103928647, 190799708, 623680937, 20607010, 545539751, 262612989, 249868125, 324376118, 674055104, 407602393, 341956297, 12537619, 412737295, 773654953, 154996167, 227717049, 85218729, 67814037, 908556963, 990460613, 331371118, 184903564, 187020472, 816031713, 625878914, 677527971, 2247040, 882996174, 102690127, 981022266, 557873347, 921516942, 7120612, 360035350, 156511162, 892304963, 709734229, 991891629, 464479095, 794602124, 609135518, 766983576, 198497953, 553455979, 993545895, 61013761, 251907899, 684394803, 775999715, 515213463, 935771104, 987897761, 356522668, 785613830, 32673446, 641157542, 763278710, 777981040, 954888888, 502509005, 219664171, 765663264, 439909248, 300567870, 441299768, 879690485, 380791278, 497124956, 203459150, 581521898, 524811763, 958147308, 513921902, 763082856, 511135233, 143627903, 996331347, 101579700, 415636677, 603133245, 173885878, 506447852, 958778614, 552202234, 736442742, 921694171, 460942723, 339532572, 228179406, 746484755, 470764913, 758899340, 604034130, 310933093, 126491354, 499334184, 646331977, 460441168, 897803748, 917647138, 316111030, 203200255, 11612640, 477881347, 579846072, 744489797, 47349575, 954241772, 463715665, 75596749, 943342394, 599462026, 632314496, 801269017, 293322226, 40924505, 684998921, 216335466, 631734345, 870033482, 957580044, 81465567, 549330193, 336639865, 151088091, 976535333, 518182584, 995754519, 369916043, 387590539, 711101915, 576994842, 693388107, 433267114, 613163343, 797179220, 295802448, 38807624, 180341443, 981157900, 442578033, 328700685, 2767962, 89631083, 721167447, 639362256, 736893394, 247882246, 770535112, 947166779, 460429273, 297528466, 263919131, 213353075, 739674450, 379029707, 227580499, 876290129, 751068616, 756608537, 563459072, 389503934, 47663380, 127408483, 130381539, 28307727, 893123652, 19209209, 747924446, 419221170, 962106682, 551431768, 907895220, 457211223, 15711571, 255564463, 802454424, 513777114, 611400432, 246908947, 552314935, 280910779, 116504795, 924721586, 528265827, 170540920, 107599911, 674439372, 361063180, 629630298, 183870410, 529267682, 421255712, 996255826, 379736448, 914033656, 158474850, 515573908, 122886376, 525354591, 292724055, 258885748, 709235499, 706834094, 822512438, 587060560, 330093377, 64061877, 578993115, 576310701, 419724664, 572886742, 820994136, 982078059, 840209374, 68593332, 558735850, 960400032, 91558050, 350551099, 972430205, 308495925, 605974448, 111970280, 65245038, 979018325, 401666218, 242207811, 200508310, 546808967, 588915854, 582277459, 622743173, 694301627, 734061476, 140539034, 376755886, 79015803, 830390516, 183437625, 457007093, 98732076, 696365337, 945680241, 941553733, 294470487, 950822757, 675720268, 487296484, 744045045, 49026418, 742556178, 423044614, 998789863, 998472839, 4936812, 473420680, 74791380, 12627318, 173664982, 530133379, 372762836, 832474742, 119193784, 498745397, 771304313, 983589948, 756701872, 356432380, 33164435, 828256453, 252742984, 496957068, 652228088, 179844388, 687039868, 223316942, 19097490, 186515065, 349059159, 339237930, 733941864, 62830389, 307647436, 731242459, 125565680, 42816436, 287198857, 22984686, 726846824, 849034292, 823665259, 841883768, 571898814, 860546498, 514532172, 514686266, 367300007, 30503459, 838364323, 755828171, 835371516, 529243949, 289882143, 863331759, 440851277, 760838997, 438781942, 210035450, 369369799, 232638853, 65272354, 152075047, 723358930, 907727974, 279776395, 307397196, 639482245, 857641479, 80438731, 12458231, 760732974, 428540901, 528753458, 624753974, 42113204, 637684139, 825271370, 710043017, 645577814, 27317513, 128864844, 798454975, 203148743, 325984687, 383860033, 592440226, 32132289, 252111317, 666502778, 937776488, 97168613, 883034449, 438067679, 581175894, 204218807, 180556598, 3478380, 407993441, 463323069, 978022843, 322732006, 255321687, 335969361, 3057290, 330402614, 534560708, 262543356, 524289636, 778644005, 955028273, 698458832, 455181668, 367180398, 804167992, 974464992, 658764650, 935757947, 877190908, 562271332, 185731589, 221360633, 341142149, 341419252, 881310705, 842525880, 404500742, 375025682, 620817285, 80287095, 509669948, 783500205, 728424050, 294123007, 174700803, 506740985, 305604476, 763466932, 770799911, 766559335, 625756038, 116566291, 548188000, 21480095, 953149127, 677179426, 4825517, 703984079, 398028542, 114767368, 749866669, 359726331, 635388264, 634410771, 56687578, 673887926, 487957614, 241791784, 374880086, 192845016, 769229544, 546559922, 982580635, 178913642, 963988079, 658173711, 76120606, 906522733, 534443821, 547291430, 236945690, 253158648, 180719524, 70767895, 329735986, 959936751, 424707431, 991879121, 765316537, 22216795, 659644037, 468784337, 452545832, 764802527, 433863208, 12140839, 359037892, 209911829, 600743622, 831665728, 68130629, 325834617, 935236033, 772437339, 549696287, 305153306, 497952648, 221451158, 288190107, 976768922, 83292588, 256227725, 72833733, 802652227, 314354240, 377335339, 154252606, 103691751, 606499340, 649351110, 393789162, 25575578, 569483388, 84461721, 492544245, 417219424, 696842785, 657956856, 830928085, 664654200, 988059404, 10395017, 472887105, 358636183, 299052624, 465211725, 326333354, 167863031, 482812295, 216323061, 989973559, 375302751, 48853060, 879366, 990142535, 625482646, 932597347, 922873691, 329834121, 819560852, 303361347, 490304894, 223424946, 474769746, 766650935, 920102401, 616707377, 478782415, 650988624, 63683686, 320899464, 614247615, 798115476, 894077449, 906065172, 218699802, 65300544, 47616316, 614852720, 103296676, 192816184, 552853846, 920999190, 637078199, 803665396, 828637194, 911813351, 295752856, 816880651, 75973862, 352009946, 541408433, 828452307, 559095621, 616892129, 555598159, 769410039, 285726819, 447407824, 473264842, 649571793, 699884155, 303209474, 884082445, 781725366, 36879616, 552149437, 869905100, 869961157, 560693338, 116768020, 688537981, 34527236, 495407444, 92183398, 54170172, 163968837, 152772297, 694292609, 469073151, 340718981, 122640091, 997560177, 39240087, 55743026, 919221106, 672353176, 610904367, 260988845, 941244418, 584941472, 662325789, 474513279, 369747521, 545157459, 392913480, 27151924, 582827260, 970941766, 234457443, 552281496, 926721036, 756357369, 129430559, 571140268, 738774408, 980479057, 947304919, 432079243, 339713959, 609402061, 326719255, 980049416, 543984407, 818429157, 729461361, 721820722, 928317731, 13747003, 427952516, 898031972, 196573069, 616997852, 819609365, 282189550, 696373027, 198631234, 778910790, 435649868, 459094296, 962836304, 365833905, 416178176, 140374943, 711306601, 26941606, 445297382, 219210543, 424372096, 821590134, 981625975, 963537504, 243239115, 362594832, 217354252, 596133770, 105169351, 368304257, 795344010, 744584331, 63990357, 497174155, 942856121, 802930635, 659563821, 310881031, 856312633, 458944155, 179633091, 468487638, 799924227, 82152903, 811005276, 930194891, 71195476, 235111195, 951497589, 533244604, 328913875, 974893185, 390984478, 270511720, 920759827, 497995459, 136685394, 418994622, 916059617, 115032647, 386759429, 312137384, 588345195, 333841622, 201891866, 121817731, 638682164, 217975596, 403584557, 30155008, 727702329, 437273717, 934848064, 614864906, 380778497, 826568984, 930698524, 617480481, 663428866, 569271314, 822747808, 140597577, 98876776, 321443221, 55155161, 855609846, 756280928, 509890542, 438351410, 394901868, 161535814, 299866895, 839884642, 762411825, 991440194, 597426580, 559008804, 173727748, 252632960, 87459409, 513249165, 59345498, 425742872, 144341181, 211182424, 691588125, 732630681, 584762562, 846377641, 508346986, 458355412, 685539056, 781706338, 325493993, 995763532, 767453206, 417327428, 613612416, 510508731, 411852344, 387943149, 735523822, 88956128, 870731885, 696309958, 745410762, 108978345, 207942763, 326697670, 875697669, 796928800, 332912496, 252282031, 186927515, 812635334, 630651305, 179179599, 156526465, 819476249, 226993094, 842508361, 255122248, 206849923, 637734584, 289381330, 964147246, 101610543, 856566395, 561601697, 250415746, 637885502, 836585034, 72751471, 160510399, 708203587, 936815111, 868299584, 196235303, 177215254, 177182932, 217055740, 313807155, 571888537, 860824169, 772790701, 815745633, 901306461, 506930862, 956508231, 770019275, 276614146, 47725184, 156574330, 154189683, 358132384, 705029100, 1886784, 979339725, 986216960, 100226626, 815273332, 671645561, 505018766, 222476739, 540149966, 422039130, 892603098, 637144889, 256781569, 518308377, 786040077, 881654159, 45171020, 389073254, 285247002, 501356884, 491186095, 282734464, 556656633, 635727434, 676187406, 357113451, 366453602, 674935242, 942547994, 542514322, 451808536, 667490378, 245605452, 812837410, 299864919, 551385965, 675706494, 351848555, 757631637, 356393211, 167289435, 286566707, 882027861, 327776658, 369293663, 685944891, 486715024, 134596641, 152424206, 435385751, 441704151, 134916686, 979772060, 193943075, 500167225, 631881575, 931299549, 788145923, 972986570, 830701184, 985650294, 72867570, 790403725, 77778465, 993319684, 969605913, 846797105, 152358854, 162040284, 519075290, 959531855, 106213240, 337157689, 761395954, 400403295, 480354472, 57241570, 301736705, 868552825, 761303931, 257070907, 630908323, 508310149, 197469884, 490041310, 73260747, 745124065, 947438717, 318695585, 685016729, 214972385, 709813375, 396159371, 221658549, 21914110, 944046493, 939343099, 838616784, 580211710, 678486080, 259736128, 567997393, 810155689, 267671185, 737342672, 817110190, 418282621, 519634442, 22009478, 487542975, 318351923, 787416831, 592689075, 869570572, 123673324, 497958308, 371148436, 362309264, 92693017, 386188265, 85132104, 766314122, 282298509, 589690148, 894633588, 468404346, 46159131, 791801109, 517257068, 940222398, 188682739, 267195630, 465424974, 206730671, 220876712, 678227781, 572531950, 611790041, 543629691, 980224673, 970745966, 996626933, 549452151, 882107223, 575846511, 455622376, 841974317, 74590583, 774992104, 995744168, 316642723, 817436763, 127697707, 790504628, 428934976, 275997634, 122280181, 525846319, 996337712, 815023494, 252921824, 942587827, 222152324, 435803018, 832693145, 289840185, 387809570, 874962680, 854746012, 483567805, 213590198, 804648241, 534715381, 284248036, 393384803, 283784294, 735974329, 465760033, 759645913, 445363427, 128477542, 203772642, 659605596, 93276115, 129948338, 61335428, 688426298, 45855745, 15865449, 452357455, 585684413, 770326457, 782915131, 904383594, 394573056, 242107458, 631474140, 625715588, 745383373, 961318540, 851669496, 710815315, 761705656, 288964488, 570492558, 419022270, 435668440, 299930418, 39324040, 782298322, 673584702, 265638715, 325024978, 730585634, 87282878, 939688844, 422771089, 225640762, 477077582, 248562463, 460055007, 988810258, 991236053, 8244912, 645039939, 262145970, 58526170, 78115133, 939449762, 52843062, 392484691, 339315113, 327338607, 660632089, 387031581, 794845031, 268332581, 841806943, 99663386, 269783502, 283493632, 151982235, 531117718, 493012378, 463415860, 654257513, 691705674, 153162400, 626635094, 524105186, 387044301, 437752398, 413575864, 323514271, 609706505, 583965426, 407739074, 68486607, 495772000, 287376979, 126396026, 99758641, 445210167, 343427335, 64210273, 80192779, 1332891, 654829057, 822116856, 233636302, 308511397, 604932503, 38534169, 794271096, 892785910, 97809424, 354070472, 710677624, 539845969, 398237679, 399088532, 855130842, 675250829, 522901388, 165139802, 32064608, 916933744, 774609930, 504315989, 779431024, 946473059, 96706667, 133474692, 903464506, 677970143, 426572896, 296399080, 961255453, 522446279, 16509336, 545804924, 157854447, 196342814, 62975903, 960540589, 857397394, 305304861, 73537605, 104313063, 666453460, 88926657, 325731190, 234250252, 267528475, 990927618, 337859652, 721818118, 207474090, 269286029, 436121825, 226537039, 160221125, 715155509, 479017329, 667729873, 754835017, 5189034, 855553683, 964741444, 744895815, 311787737, 54877989, 30064208, 553126861, 539637990, 192746265, 305980936, 830441296, 277399240, 972178537, 23723324, 670568696, 516242250, 156228875, 195405023, 568017140, 119817546, 172472836, 887268111, 757488786, 366614316, 20998226, 586472836, 659904757, 530265971, 922732607, 162374238, 591555659, 164295791, 687151265, 827799759, 557979721, 305602710, 225491509, 44719353, 845933989, 597489851, 926721650, 17827807, 921547188, 697600798, 473521625, 471970088, 771614620, 919002597, 987521662, 173790832, 138543310, 886425882, 342245316, 661983666, 320903952, 810346090, 269932541, 410041184, 245941748, 101533167, 349012342, 375743749, 770701999, 745872058, 594998378, 957568294, 623177702, 542134645, 696476668, 328031785, 620171174, 117514794, 205021870, 227060956, 285867734, 446329756, 630785143, 241816425, 266861127, 756589013, 904972728, 502664635, 157099026, 308962618, 296282207, 690456684, 174532366, 299198046, 809314281, 26941891, 623111108, 248161988, 877525636, 289931098, 24523094, 964559070, 590597229, 760271852, 232828377, 200450282, 934501530, 898771879, 586470345, 126161278, 281914103, 661896801, 332777658, 916172036, 851388723, 86572595, 868497580, 239132061, 49007193, 836087860, 128762176, 275597534, 232446370, 194875603, 170560700, 985917189, 579433936, 347840264, 379340777, 860264522, 697380853, 28357086, 455965700, 60631314, 458962774, 424257703, 354663218, 163132540, 147703887, 963194941, 116849823, 521835360, 251458324, 736012274, 924765913, 302229272, 951191360, 837040620, 819514227, 317388997, 209962533, 536333577, 683464961, 145996365, 28337150, 193677534, 939715337, 267822135, 118731403, 852330917, 773251496, 882812057, 985695862, 794774135, 885704834, 632424852, 873377896, 60516030, 317767218, 159247850, 772776550, 873875410, 315618858, 69682659, 278710891, 181187834, 76836039, 602296532, 780580986, 809625461, 440237866, 217766336, 593986563, 515225194, 15567214, 725464098, 6647314, 452185022, 359537986, 96081184, 507472420, 996676237, 189037343, 563022268, 129795563, 796093498, 829816675, 125345432, 86928635, 604501596, 417295991, 51213297, 584754708, 344110329, 306022885, 248395005, 683964888, 946979736, 177943712, 428848485, 206382897, 105053243, 82358200, 244957449, 429479055, 126126650, 276788914, 576241295, 469956705, 779927163, 190219976, 957933047, 142476669, 224150676, 343604644, 189272332, 574075377, 299530764, 869201423, 277755850, 187236267, 159704206, 574347694, 531982582, 573857632, 681345875, 718445254, 163044861, 530092672, 151253920, 906545920, 731706494, 992118366, 733563599, 593832228, 38872838, 803351115, 406662598, 682786320, 171080777, 711846966, 270322888, 747819098, 40794010, 831246872, 472993322, 996734456, 418172177, 288343011, 213285508, 784523743, 125185099, 334009662, 743405632, 63629311, 223479870, 830075375, 105303897, 166655321, 221119172, 440043849, 389364124, 122560187, 436900065, 405091049, 837899165, 38222771, 747340012, 890458160, 577980432, 677502071, 980828611, 498025815, 453539419, 943184878, 179505036, 253135315, 642805861, 758880092, 747646765, 538401561, 425630280, 526402459, 431331601, 281607554, 386001381, 177402277, 366173009, 271502972, 411982403, 18451874, 20250955, 676011152, 684391473, 874583858, 206420201, 262021918, 832540068, 244946744, 818965484, 818544480, 429574608, 165403445, 598771151, 19394687, 752492557, 875118037, 701574964, 990495538, 866964244, 326327530, 905639151, 223250630, 331637177, 94159725, 483776995, 247978796, 74861336, 856414569, 50907340, 290687708, 253386332, 602363651, 41187914, 769701217, 231320085, 286495556, 954697119, 573225126, 339580991, 484474220, 993289514, 236017981, 936661780, 663321292, 690696114, 494988692, 712174171, 375197710, 182875301, 152194721, 758046854, 799575358, 394096664, 23773797, 91817576, 639142227, 70518295, 89799162, 773886689, 907271991, 855973507, 310893665, 669212737, 396690532, 359439236, 478741453, 83543452, 874754177, 382598105, 122265426, 658791168, 205269727, 547543481, 328188724, 738908788, 330447117, 342957891, 768726767, 142428465, 988197149, 145499775, 681814443, 538564437, 29665379, 690008521, 408350355, 431467069, 445866720, 213028796, 613144265, 54325863, 897905362, 226070228, 119854942, 894476656, 583623356, 268081042, 224490619, 399726146, 241609463, 355597230, 374006751, 178067244, 729765288, 887959483, 295480587, 22468687, 520304193, 294951978, 591058774, 598979425, 942921529, 716126333, 988676051, 788762871, 878898349, 31101244, 808305996, 463069654, 265313280, 394851503, 881648440, 977577620, 445832479, 581564627, 838499109, 581248146, 440842500, 505095879, 988860318, 180020891, 526799560, 783495072, 6798914, 400209609, 49421808, 552590013, 396241951, 112579590, 716126268, 449138242, 241140676, 768445816, 911751218, 240659903, 582690908, 104870402, 599674444, 601834813, 888300075, 177563534, 480402857, 792584243, 821252312, 734509547, 704260015, 748748915, 825017098, 84880080, 422590488, 577837162, 424889021, 852221429, 880421969, 148744716, 90987264, 315274414, 718141454, 306023555, 294702303, 141374615, 737625232, 685504328, 130467656, 610254502, 147587665, 501382307, 237810124, 265071298, 426426983, 125289549, 739967428, 16057855, 517005166, 822128567, 770387465, 870689009, 548028870, 317138787, 108726176, 134603889, 354891654, 960212146, 793265610, 800579470, 526496124, 919567826, 453438803, 847397054, 626075052, 360407811, 87691506, 14723456, 804818058, 52905620, 789690124, 328655826, 724093272, 372191187, 502875523, 434699757, 753745392, 401447659, 21757199, 156249546, 349440250, 64210834, 660610282, 61726710, 689577863, 936840323, 87199027, 175373751, 311512898, 789426588, 22056026, 462560842, 989971361, 435804113, 256723596, 602284988, 974429876, 437663160, 225996022, 827337895, 224151643, 662795934, 480855566, 783415964, 243097271, 890429930, 101104882, 619456227, 496605057, 797262779, 818009126, 52473776, 422700366, 423012451, 394209582, 781677160, 274066441, 592130581, 700219207, 312852958, 34074336, 53737038, 336917756, 992094435, 645676877, 8824858, 574520581, 416014323, 337909118, 93132688, 881576505, 686409529, 249790416, 287556157, 285810688, 276503993, 192814375, 836537696, 900210132, 318232802, 624888327, 258923069, 492966295, 113155722, 661177055, 425233306, 76704714, 841916003, 510307930, 895445982, 654681293, 989432455, 169642383, 575112130, 156442800, 783589409, 137834994, 980239393, 940895538, 766400301, 91830347, 106361996, 661102311, 281004305, 982801447, 561357904, 329528051, 805458681, 870607965, 408059754, 818979861, 150828162, 788628951, 64206476, 970050357, 959803266, 861915987, 366666493, 107890695, 767575570, 782986713, 317802972, 541189095, 291834346, 902756594, 318769610, 314295576, 875192416, 639226885, 935471888, 837654524, 897261059, 270938614, 132718943, 875683079, 183022099, 747608939, 759753566, 744592177, 943907329, 114650929, 98341900, 62228656, 811934735, 842176168, 328713934, 933446187, 457486071, 520943156, 445898853, 214920425, 758585089, 712510727, 24108992, 842372024, 532493328, 7128788, 34006079, 396066951, 759973030, 923536854, 354428048, 169650182, 202033342, 188009206, 418450933, 133715150, 425710700, 971680560, 665185934, 425813003, 819324083, 759944204, 166824728, 576314460, 365382572, 111016253, 355550145, 850518949, 883105014, 744171523, 287805284, 274951617, 886668946, 582961808, 133447877, 636856570, 846624398, 656483599, 933009739, 912863180, 850488068, 945979417, 106876373, 388307627, 726567784, 205632686, 525337380, 950936763, 190744289, 430876138, 398571921, 485850795, 710845125, 409181095, 478625199, 640344633, 675245134, 693437129, 165693315, 991828860, 600732601, 313606952, 933558004, 130649219, 237303999, 827503184, 856609404, 80598594, 948927527, 951799476, 754363167, 191679867, 842293460, 481580834, 956943492, 777880263, 899839435, 522189411, 208402685, 49588606, 869599448, 168648265, 158838081, 295399939, 540525813, 599653416, 92367814, 641073829, 316208996, 253315016, 459509982, 176314278, 644775564, 19998375, 271308952, 572574979, 417447402, 333856038, 950510831, 248718440, 627763284, 286015251, 398619109, 674284191, 898519965, 715019124, 722397626, 275266687, 520451435, 316394254, 752541997, 611374291, 522831247, 239610755, 614273543, 8200748, 547932309, 174325038, 688736544, 678523890, 133684973, 695427289, 834529612, 604245416, 358860752, 402211451, 816492103, 174117854, 84450476, 310242356, 601712248, 531857749, 499640238, 716287765, 948371599, 909765662, 672613308, 557944595, 315289925, 163211343, 472083455, 973224999, 673807141, 400771702, 833981825, 506570865, 862500940, 782136911, 998241697, 465155788, 135153793, 952311786, 330632264, 768434109, 201297315, 699881089, 719620091, 3776197, 536969404, 278577488, 705438931, 489849411, 869961193, 905147610, 576732209, 290905069, 13881679, 658530001, 411299753, 512730173, 420841932, 506721791, 985109268, 942311385, 753093691, 154629809, 707962933, 363624619, 452854065, 62207984, 72387374, 835733092, 870358251, 698617867, 619682071, 82571898, 169587133, 309905133, 533607042, 478269267, 970482835, 466727307, 594425769, 241971185, 878586839, 326274026, 893976412, 544580683, 302777483, 702650750, 334118366, 365015053, 813583251, 557873849, 630019161, 699670933, 560339952, 343522649, 106764273, 197680997, 780716342, 952023672, 641925529, 509905626, 654575990, 768481398, 824435488, 727877947, 978385348, 405125012, 675130234, 813641838, 616170550, 280781052, 682733493, 360789167, 71833873, 688896009, 931390811, 459997029, 797618091, 619848841, 32584510, 267544806, 615263286, 207577059, 323754672, 255336413, 460616170, 116779638, 74854699, 839134078, 289563667, 722795556, 563844889, 118319348, 323154339, 756943526, 547609541, 792630919, 961334824, 247071144, 295294675, 553395957, 461485860, 968781155, 697537112, 529312370, 837842924, 764676352, 795865634, 937390673, 865194872, 368932236, 598088498, 305558620, 79137752, 600476237, 518673184, 812691086, 882286962, 811470166, 186627256, 803162160, 269535547, 562841435, 806360332, 211787370, 285039560, 714664161, 839983518, 78053746, 4763007, 533206030, 460053991, 15542742, 711709447, 407125455, 26001049, 727296879, 571006054, 313168440, 806897934, 549498541, 676305757, 112939676, 316102114, 98169072, 459470914, 214999685, 109028391, 841275917, 255084363, 428373875, 954047339, 387973064, 400787086, 69228479, 167824872, 245106478, 416758221, 726143893, 149189502, 836974358, 58959274, 146923474, 678742783, 990682523, 811325724, 854275235, 180301964, 893495649, 874452770, 657700708, 798845222, 3217992, 423570437, 366432996, 165948481, 306567929, 864132951, 733376192, 623495023, 345606728, 502047326, 851275040, 353215783, 49642351, 383767331, 642882779, 51394807, 315976754, 251281163, 462739518, 575791230, 566309356, 293921564, 230011635, 399037976, 207278745, 104613908, 182538994, 857276772, 633545975, 70431810, 723118159, 92241536, 947308572, 655707907, 331951403, 704585079, 85611681, 203482009, 117020571, 835655969, 662300981, 511391997, 560367716, 46896402, 956978318, 285006507, 765679303, 90456523, 228117218, 56878685, 53967974, 691318641, 780969388, 103297716, 357617961, 597410344, 309788093, 969479257, 728460159, 650606357, 517259818, 6070775, 7009731, 479444623, 103444051, 673307832, 72048448, 458148282, 558975502, 708090112, 534492172, 836671917, 195206062, 93122976, 755929527, 618405004, 137055874, 483469011, 367592456, 576853489, 800972160, 3322772, 413185743, 644345333, 895994294, 717491898, 708016084, 132135569, 598956276, 71344413, 608464781, 963182592, 295366388, 943725021, 380388371, 645330780, 316337760, 334514148, 786945778, 472072886, 209188812, 308681888, 510951930, 812042475, 941815940, 809460158, 306208786, 113678142, 424528429, 936583887, 508895993, 814629550, 359867314, 145933588, 303620289, 168662120, 920894258, 661688340, 732734133, 337776347, 785613409, 558315729, 976129742, 503812329, 902416019, 747899830, 5825912, 293526942, 75222563, 616544718, 43035305, 800592094, 314232706, 317840859, 865593550, 2207941, 609206571, 821996176, 325893954, 136930168, 865022142, 813412847, 45783526, 869568028, 233527311, 465726248, 496810963, 491773483, 71996132, 928727956, 808794229, 425227552, 77381095, 514305598, 151797882, 5473606, 535422234, 333157095, 289739576, 134570333, 252961467, 555109921, 43609255, 349877151, 825586594, 302738252, 620186671, 52861408, 522831393, 907270186, 305466789, 488244582, 587927815, 25342486, 627669495, 433103345, 403013764, 182379148, 14986575, 975269840, 100658601, 714922923, 791338640, 764706193, 440751053, 918567924, 808093351, 669928680, 905519665, 207007763, 183862454, 974294011, 1689062, 633694243, 702414239, 724970065, 375823545, 908286255, 344475287, 83719162, 161504601, 365900345, 657926085, 934474880, 276599646, 524243669, 436034262, 672603076, 153048931, 622614019, 980184892, 183995127, 611466155, 511906665, 813311183, 517434560, 136406817, 727232808, 361047881, 943465706, 898009014, 690475699, 407598628, 173234313, 597090782, 8383952, 780168014, 56563963, 857766704, 100313184, 173313535, 803524062, 350260565, 838613847, 556088662, 903858697, 784987983, 245030735, 994493830, 896018387, 460898162, 127623102, 911164384, 992976950, 804070765, 337298069, 425647840, 85019214, 637448678, 753140584, 298453969, 144868767, 75247218, 655372273, 313993828, 285715687, 185224067, 864035879, 864335890, 28543977, 249254471, 609367967, 367098427, 695741401, 962623863, 943603662, 451366191, 570382228, 804227256, 279901419, 775427475, 44607812, 897544761, 134850249, 322023608, 897632296, 602526974, 517787333, 655698954, 718721880, 20380722, 926172345, 664958057, 183897097, 332079893, 516498387, 394123170, 717186878, 667824628, 62321435, 586715506, 545941178, 666946739, 742575538, 238395327, 999851424, 197108748, 992736885, 411361580, 315046515, 860190000, 508595217, 6035159, 409623695, 8834174, 915587345, 511824665, 738976431, 966942540, 389108580, 251642530, 154569587, 220143206, 109429833, 249470911, 462514749, 897298272, 532753490, 100796365, 785544007, 265884119, 210189475, 754256015, 997617568, 199874007, 917084859, 704744758, 578925450, 158855047, 647701786, 62060340, 373940906, 14866853, 901441742, 839009906, 347731444, 93524013, 531526492, 953826499, 941985393, 946298843, 251440196, 51800114, 199453922, 992166434, 241956933, 111862373, 450387289, 584968379, 584905518, 492432207, 551582468, 74939588, 758987738, 801100193, 781092535, 339408443, 923877914, 199802928, 319685322, 500204695, 742240597, 270955474, 484879, 850057077, 288882490, 581387247, 325772974, 603742873, 861962266, 895740421, 46415249, 84576349, 711689905, 901696745, 732666319, 907257495, 204129014, 113443489, 56465771, 777983648, 594640545, 244950882, 86229943, 813645436, 67340344, 969184602, 758680528, 783554573, 501801240, 385137675, 820461441, 256881121, 300871365, 344407769, 896469437, 802976293, 336784819, 398856561, 850313624, 392432028, 594393592, 331368700, 678491594, 254405345, 623094167, 311685013, 955939810, 306274284, 279234322, 93660763, 77325652, 341616940, 580250742, 959361230, 835187476, 967713742, 714036216, 161266711, 289243661, 546001782, 593570009, 250835155, 450180980, 222592939, 683027278, 691838501, 860655856, 370664928, 692969394, 515116409, 631491522, 335868078, 417968572, 414617027, 889145118, 367966172, 926284969, 260274723, 560104022, 882617722, 769084025, 6019952, 695911787, 81464834, 951416488, 653947688, 313176027, 745442320, 797539277, 752802370, 520120130, 918338597, 818583263, 339889868, 838669381, 201169503, 258882710, 349069860, 203329310, 712718630, 800056970, 598549688, 982483697, 591562552, 478438745, 467917830, 664789322, 462439209, 801169265, 744697845, 999750009, 228182840, 244455158, 826098944, 994283506, 519418889, 724731255, 907191848, 887851914, 435389432, 581106697, 477868022, 181319070, 810980020, 701674749, 764712807, 579938160, 559061275, 427240532, 279571930, 482524512, 228583181, 446404654, 731850842, 673485638, 572082947, 213285227, 869863641, 267760655, 48092002, 620136404, 220738943, 285634956, 797418474, 829720736, 645970865, 406227898, 463151785, 587704075, 757315508, 65841838, 150439454, 262039614, 434500455, 972241580, 426487874, 16924214, 183782613, 495842075, 144753532, 571216293, 189256077, 651975199, 25954659, 209134848, 773934171, 350170390, 697166701, 607994861, 925179013, 82970499, 695177038, 341399390, 439651644, 494556385, 475373026, 7642763, 543454191, 689726303, 436001374, 635859391, 556051281, 467400186, 591102113, 761633549, 927292160, 521204562, 101778916, 892286046, 599950897, 355797789, 18022358, 396886524, 510479066, 939369403, 222773510, 347094845, 17010890, 674244575, 165419473, 702752277, 285574424, 30998072, 478446178, 442909028, 851551149, 319287191, 582339684, 898922218, 487055316, 278183895, 821615836, 964352113, 43975143, 742471087, 804540726, 852887169, 928733847, 703514990, 662946209, 49034351, 767758960, 387103119, 522971253, 565381145, 407259010, 648911864, 595216981, 338173430, 685409270, 465133209, 335573073, 353091555, 999584106, 42148255, 773621439, 230279953, 139876378, 653462243, 421099445, 367594592, 908680677, 33961769, 669501625, 221364946, 186303558, 873446243, 73956944, 769924655, 42647259, 142714443, 274667285, 588723881, 744437907, 201962772, 545247975, 799547935, 79732739, 549084763, 132664727, 582850803, 189781776, 217144359, 68626361, 842512095, 463357982, 797339113, 696584789, 607311689, 534056433, 144794872, 900827920, 581435222, 340000291, 168557319, 354648471, 499876319, 424842967, 107945601, 622855657, 157632054, 142484318, 550084102, 969399719, 447705298, 450182140, 147587227, 228486713, 999725323, 332084898, 227028792, 995958757, 667694736, 19184621, 516366891, 675886465, 309259804, 119399381, 859712190, 554471538, 423724857, 431937310, 782122425, 221479870, 642322768, 17884258, 424630835, 208236829, 875428590, 550560387, 66051364, 838974341, 853883721, 749307584, 990405772, 822380900, 708059186, 779078742, 231436440, 929785968, 75145004, 322732371, 891877424, 826037556, 78095735, 79483080, 760084673, 743579714, 768620199, 645210175, 909678898, 443147694, 550937490, 945365186, 905688929, 839685994, 928202135, 70926130, 345696665, 396025587, 394279842, 826163092, 530285348, 74735560, 35457406, 770845870, 30116416, 391305589, 337308860, 946584736, 530708623, 618029104, 168534049, 489193982, 75669327, 403409889, 869104700, 303669224, 620298838, 666381277, 671331149, 775697732, 418514205, 325745382, 554173868, 850963508, 106415283, 419227468, 599810674, 724624047, 953636923, 476000917, 88784114, 987804303, 954004853, 340025730, 834179801, 208927419, 721847931, 22062159, 869487667, 964626279, 119481704, 442441320, 748782661, 607208444, 598394519, 920982296, 976874463, 864406641, 10468349, 465136864, 227539449, 826901839, 288543893, 719696162, 52771720, 228166397, 461452502, 557784897, 650825035, 876232864, 359544863, 114829654, 649455309, 882044846, 738233218, 105293672, 416923452, 881164976, 810621780, 920299020, 611879305, 352669975, 980659752, 352861366, 686855610, 18603320, 258137090, 531542985, 13785110, 691217484, 119447821, 74005212, 5476934, 603477991, 527175179, 398556437, 964643924, 497707244, 979145708, 722834360, 844923658, 836378529, 423418007, 860461583, 687021983, 775529437, 242841704, 824164241, 170440784, 357133555, 347789066, 481925256, 351674945, 513862481, 11025131, 740866480, 412042015, 461039286, 982182865, 609400748, 590426392, 988327218, 818404646, 772064398, 357189170, 581282020, 337764684, 706720839, 24217674, 906843147, 802843151, 479813467, 780426922, 223667323, 333372449, 247611053, 837305426, 61667544, 469310177, 21604170, 108226890, 97517539, 760710482, 353352090, 927459670, 916627002, 340948069, 46504958, 113327776, 824208974, 195282205, 625715777, 819634377, 437389351, 939877734, 639168343, 251239616, 747691754, 813445453, 472367727, 845719887, 193954130, 6559350, 888730259, 541475215, 767817862, 450592230, 139547052, 774266477, 138275184, 923391527, 434869578, 715928369, 934780629, 650250726, 75832363, 516061105, 488497263, 477435322, 979591371, 742472185, 883505033, 133083850, 558709695, 882091043, 65710629, 387146527, 403288193, 792678568, 228605470, 70142192, 102171406, 552605788, 184469437, 436849332, 317656206, 384839120, 564498985, 849879404, 76290149, 178121343, 49284114, 535449093, 85717292, 806226899, 491355063, 911444142, 369099923, 308670641, 422469511, 486413757, 536328299, 946474457, 559714056, 204595882, 217856293, 759009, 335680338, 101096530, 556240378, 377414836, 478463943, 312947219, 575281509, 986607177, 963789769, 240170628, 553307405, 523296663, 952858654, 403672792, 820732039, 561668009, 687603766, 607250492, 676391508, 392938943, 361298633, 91295726, 549078208, 732558985, 553105742, 963025157, 59874379, 843627599, 161033279, 683265395, 99547484, 16722402, 47875879, 316066911, 358908623, 835853969, 731441892, 581235284, 834082597, 876690799, 162860927, 782324683, 592631314, 500005420, 485243294, 52600313, 516187734, 319493408, 73387198, 548758228, 525500019, 397168762, 393415980, 10086953, 116281170, 511707149, 272357505, 336078477, 172769793, 579852547, 427487729, 658339607, 409727557, 319268892, 960670482, 660567987, 681002929, 935039496, 486849197, 653022340, 205669610, 38656015, 205899286, 368201559, 796527519, 149539153, 708285698, 999328396, 461274600, 1596030, 737969326, 890354097, 888777765, 488141328, 277336801, 1517734, 49684310, 855819225, 980537513, 304283040, 902437994, 575541056, 931239981, 223508274, 173392902, 726534747, 70526262, 567430787, 566086588, 440347226, 672571151, 939337904, 579704648, 256817924, 224562640, 977780924, 55068073, 806659080, 54393476, 3770728, 214541478, 969714932, 144348495, 445648495, 515061786, 256600514, 604313264, 288082298, 473563657, 446944090, 715890410, 833331263, 445340117, 470637029, 296625478, 120246358, 74275213, 244608558, 498689536, 918445672, 67143025, 780961269, 116885013, 814203055, 38995394, 123328365, 740781772, 939794719, 22623261, 4010202, 236033268, 777253246, 586829739, 321209908, 904618058, 487219460, 717198225, 32936795, 529326755, 698044863, 338356463, 849545101, 896497100, 782601803, 29863675, 766551928, 77046784, 683104626, 27918381, 411762827, 791457386, 8388718, 315968039, 838360109, 772968432, 598884063, 865934968, 797106163, 4229922, 156416516, 635064849, 960738057, 618741705, 16401943, 220712897, 857754198, 517222531, 929614760, 671412728, 75715508, 301462485, 654631859, 292791710, 771184097, 393059562, 221436032, 169786888, 471094436, 784346943, 662993988, 394548841, 105824794, 558943140, 750790900, 230763889, 944384141, 845445234, 101562058, 665728277, 292456422, 442351097, 131139679, 173639044, 248919896, 554499938, 249496482, 716618118, 989594086, 518505171, 150996447, 885416945, 764669579, 19127051, 651095200, 228299180, 475368495, 47071415, 304434018, 733912388, 860540909, 71266243, 216232778, 364752788, 511234501, 587644534, 318147985, 183262850, 759101253, 511342834, 741955156, 805326010, 308054940, 654327165, 54546392, 255487081, 143047957, 34581455, 22438976, 434503183, 945815951, 754092363, 350437735, 643212330, 197679626, 447810887, 15411804, 684739953, 148761508, 517097159, 178772892, 854884969, 486433531, 635545176, 778291184, 29646638, 137882875, 770999252, 731132672, 233961842, 938503518, 543804966, 357398535, 844934258, 527571357, 639748933, 5621110, 266403506, 836362278, 285402285, 764014340, 488014449, 943188034, 670306060, 576456835, 946020894, 165041419, 28286583, 583646193, 460811471, 830343180, 647374697, 939900233, 572088146, 73177666, 951367037, 434927406, 224691478, 373065698, 72848908, 54081131, 44583914, 623584330, 606635546, 452858092, 863217165, 856572228, 670068141, 620003959, 928866871, 513295130, 818282681, 667115381, 565225410, 788132362, 986265509, 679757276, 197711728, 447034130, 837693930, 541266879, 491754062, 136531024, 755184558, 52927302, 87383488, 7864404, 879499081, 662193323, 595177536, 795103567, 926539958, 217102875, 408529210, 616562107, 269208166, 86472517, 946113161, 268045063, 539450181, 465525142, 932877666, 526417825, 493015259, 680831854, 295971077, 904494434, 809055032, 636128547, 840143956, 150347794, 997462548, 699125101, 525179441, 252404990, 998707100, 408107167, 682297304, 153081020, 463455184, 885937107, 581077065, 760029554, 456075260, 988143890, 965661057, 491513273, 168426665, 661330883, 280464401, 280417106, 222857588, 54027351, 86030757, 849504211, 609079466, 194219519, 878551801, 951279368, 668182194, 667909912, 423308873, 775897568, 319712654, 871006835, 84959677, 605033932, 129066559, 976138276, 949313217, 583582675, 364427932, 715926668, 853926708, 629163684, 700860064, 101719489, 332410092, 540631362, 142417773, 190911479, 364128615, 462690206, 842126626, 672638004, 222939713, 938683980, 603292599, 263330241, 828114033, 758495149, 619396060, 84301107, 40250594, 537615319, 19810517, 337241474, 655390143, 138289767, 316956936, 714114215, 987425693, 453515126, 862752193, 969229429, 260530268, 573357196, 908579285, 681012918, 599184239, 873810413, 912656857, 384279916, 290369314, 947338682, 981304588, 125525027, 931844392, 417603318, 987127976, 66075792, 849117452, 565478038, 601353766, 997642647, 573282178, 467247, 155858638, 377670823, 373333980, 341666050, 326419383, 578791880, 290718026, 842622804, 667892332, 66451970, 715053233, 406206777, 328716051, 206557738, 601543610, 336601292, 241437738, 603997072, 763512873, 770862634, 51519723, 352779967, 355577306, 589945761, 503850967, 888016848, 770769603, 510193509, 582122613, 744674766, 712093758, 919314544, 21455067, 427198873, 990633369, 773726147, 796822218, 737453199, 845240643, 91378062, 935296050, 118544499, 203773164, 139552924, 647380004, 223687726, 487093824, 790392412, 980318921, 430545908, 753846019, 711104422, 182675393, 460948270, 616283839, 651342658, 340293530, 619725744, 403521165, 334750887, 88368195, 874741767, 350566419, 459105793, 799871585, 951664831, 807336660, 694307382, 521836581, 403759632, 346483002, 301289125, 828398279, 888026209, 333953267, 936604995, 982808107, 572089047, 945225959, 65293185, 818486812, 275078216, 513583474, 896344399, 16865549, 358647924, 421802929, 677376793, 659675941, 176672146, 799678963, 839525896, 713684775, 12419691, 531442941, 847068474, 770963416, 898397376, 353079791, 679028309, 755187545, 471900504, 380923925, 578697226, 391556868, 449767535, 454080925, 616375728, 613646970, 379213877, 718432351, 596218850, 583292245, 568082924, 964046048, 29501752, 709458430, 155002888, 79515887, 464832066, 386057406, 551748962, 438222378, 669466008, 136809004, 94714199, 834086040, 121542069, 191269772, 979250208, 796941740, 916625796, 716574008, 903965018, 567981920, 470462039, 646730382, 312065877, 543916403, 520835676, 980945926, 90051666, 331433432, 720689540, 911190960, 931153079, 177041806, 150693751, 969259968, 646865958, 125173364, 913376061, 352237373, 610443444, 541310897, 93764097, 951605883, 335812884, 115428397, 907117395, 529435069, 413135975, 666312740, 502460834, 259176505, 702737481, 357132375, 280246540, 388195792, 631547643, 299719424, 414848484, 724506601, 272619195, 168000575, 873819931, 861232694, 634454640, 140984311, 290949222, 147548660, 412548279, 41819255, 576650530, 142564951, 236383685, 859748424, 662581123, 580753292, 694939234, 638027669, 411731358, 334218695, 481870180, 685302257, 80468356, 122263826, 404494081, 794849238, 157987314, 352617586, 102528380, 704042253, 780231600, 70979137, 98647534, 55764356, 364050773, 176844046, 662669467, 487767047, 847395628, 192458462, 86422569, 81864171, 662393817, 258314318, 777822879, 232581624, 566814421, 910851052, 756408891, 918616779, 687272071, 281659036, 962958275, 168570940, 188448421, 904810852, 288990039, 669628399, 270882802, 274766337, 888996699, 508479061, 685866033, 437143648, 712710619, 143679971, 234318406, 950858252, 889646802, 269411134, 677446423, 44115364, 147015200, 861855841, 640827645, 179918064, 779130551, 293870682, 335935, 854839838, 254324397, 596637574, 315520662, 144564432, 552867276, 474701730, 202964370, 296509950, 665392786, 130720277, 775756907, 498107471, 544480597, 47268878, 947746099, 503588283, 762525912, 699943183, 374614166, 547075141, 254838252, 70354518, 343450408, 443028037, 6885259, 202961993, 214524462, 957279455, 109543515, 114092890, 437999946, 672051260, 781507336, 219532096, 413057979, 697635658, 379346858, 552067226, 486592498, 618192667, 188926365, 710843846, 396607008, 959607549, 600015440, 106784679, 731346184, 274475005, 369656337, 203859065, 844635173, 577837385, 917258477, 174460654, 812108631, 340245640, 785504838, 257419012, 369935985, 896817694, 981061297, 256309104, 266675463, 294022855, 183421765, 694210717, 977556703, 751912416, 509313412, 966574271, 512552114, 16410405, 775351020, 253919131, 26617280, 475933795, 346261580, 270310263, 542309528, 301394403, 162973110, 237479453, 636226785, 300178716, 822693891, 641532603, 989998860, 864182928, 880898172, 546671898, 935412514, 736966278, 746698431, 212018089, 80400186, 792497565, 490636928, 702550244, 933757558, 578533587, 286498563, 137432689, 339386078, 243251473, 796665811, 416984826, 962279290, 925238383, 722341833, 10084704, 696982556, 396592060, 488192386, 901333890, 528724878, 82893596, 658937120, 419994321, 356892033, 911889408, 169338966, 748328020, 901857310, 756818631, 864599469, 119994563, 710449504, 289299743, 659383625, 881801727, 547450693, 414124169, 966458807, 875784539, 246673385, 388518425, 316388319, 118553200, 927297876, 730209864, 244631513, 181874827, 990737184, 979368186, 35538212, 786765873, 797252699, 647725464, 757217503, 958922254, 177966384, 587242019, 544834815, 760065987, 510144629, 472734957, 488538369, 613160223, 823291635, 744266928, 918892575, 313178554, 693230042, 928358219, 915622406, 865919445, 907166379, 613029377, 648833503, 392160405, 618734610, 983075094, 760448020, 279322967, 158609523, 886369217, 111607452, 969418376, 901748359, 921762849, 995671210, 481291649, 53113946, 578759312, 709803185, 978108036, 452596083, 673096811, 632429020, 705907389, 839430662, 279609652, 410552418, 667552225, 618262034, 92625266, 963979815, 978680434, 68227038, 387197178, 812461868, 161253428, 63002230, 507210346, 451910222, 891525548, 318343592, 983260480, 116567145, 920673598, 792882620, 333452964, 634491172, 781838844, 823612696, 904441350, 590270874, 830614985, 228930401, 120736549, 688373089, 824857080, 620448046, 116155557, 223429062, 943559229, 43274345, 762446171, 286540343, 6424373, 974803222, 651609383, 500381866, 403856977, 392317163, 137255320, 277446304, 387030511, 447771333, 490639170, 848106490, 699228445, 432197427, 922462948, 960098849, 420892436, 901718119, 118166205, 191170744, 322058983, 873565295, 434589311, 495229855, 697412222, 473490762, 749161121, 791085414, 725909923, 941889547, 115088929, 931222, 666957919, 527630562, 306861292, 952154771, 478549219, 740805285, 804608481, 705037409, 980716091, 842007318, 965444584, 469563075, 483660838, 664774735, 65470928, 191838743, 702271585, 490984108, 877131474, 282604895, 624219929, 165769841, 579973790, 780297576, 405860624, 971091595, 915808722, 546481748, 604812984, 506601694, 153882168, 736368808, 836950845, 356022308, 678678637, 326742970, 63790930, 26252134, 623164843, 131271509, 891752715, 371330179, 329644560, 834364052, 929597992, 137660839, 438552536, 855409455, 884591689, 568606762, 658451525, 219288683, 220780372, 307569893, 175663602, 711681626, 573950132, 36838726, 403089331, 34884669, 861460720, 634687553, 450590267, 372307065, 878769316, 499125820, 389284618, 597865933, 351763398, 825673753, 526566787, 501297047, 389891706, 52099058, 933512488, 621368376, 731565180, 714214482, 695187422, 665635490, 305325204, 530955996, 32448031, 243712596, 907483194, 393297801, 743673099, 249093341, 972529406, 880339417, 841189716, 691058561, 880574383, 947032697, 980359304, 383849075, 855068356, 143102121, 823009040, 582732416, 329750323, 744489402, 513834494, 543674552, 369426863, 916121163, 44682672, 832983070, 47411989, 439526151, 192315092, 564051753, 195408506, 473094799, 707450165, 486356783, 772596571, 186859142, 301801625, 529062336, 173216587, 448740197, 269046806, 668649677, 471727514, 51174837, 772787564, 175379200, 292670758, 764254364, 798755928, 500776995, 889254235, 162421283, 458870524, 265906317, 786000170, 312009533, 915522129, 429189438, 915620240, 849785391, 342583369, 412319549, 581272218, 124489411, 576501849, 322147072, 857271742, 499295021, 739697159, 475042645, 209441605, 452214461, 561725111, 839613784, 225155828, 12517205, 880488689, 747079150, 787422143, 478311156, 645260524, 872945874, 8706536, 624796825, 256686629, 340023971, 513241296, 714277446, 807241145, 862910389, 62476434, 842052199, 342357933, 981022544, 993582943, 859554365, 707732003, 930707425, 73874331, 476466480, 209933679, 228473337, 893715312, 20561547, 613241282, 157502038, 56353415, 529358110, 356541965, 721169855, 375929844, 108643721, 905688044, 34642319, 435341604, 824014859, 171888454, 62156371, 781858428, 614815655, 306781903, 900510573, 448308796, 264504381, 125841844, 437381059, 762830633, 76881413, 230860082, 274425317, 768970081, 339066491, 225970997, 14325931, 10093861, 982517342, 784330040, 231162770, 344118538, 809745723, 647986189, 973783301, 73106857, 891777702, 353416611, 27710154, 843009907, 132157367, 745920316, 995063817, 312764437, 528398877, 140068918, 850341087, 443057546, 278290744, 431747039, 386803094, 1564519, 302517015, 383316951, 752347174, 893516251, 485070112, 132556163, 466608033, 399877636, 854157091, 795150408, 886063706, 773149404, 284345335, 106439662, 629095152, 462456598, 592551338, 387216614, 187936352, 95718639, 294817644, 16094680, 897473609, 805172006, 410178358, 270081029, 463839433, 713863759, 972966084, 253019004, 578374274, 188522747, 648398013, 347763148, 287378647, 375220164, 975233663, 527133548, 128278849, 892485276, 931809778, 642849121, 946117871, 766002630, 103176084, 170678269, 340372509, 903664597, 74289596, 448980441, 850931510, 363172860, 505957486, 83129983, 197624120, 258305926, 570080982, 425301439, 725538286, 544197871, 269697831, 806254666, 554718246, 352374931, 930164826, 68723785, 320613336, 802106636, 631071100, 540876672, 767931825, 268823662, 273991581, 477288905, 175842280, 674275696, 833125772, 534788377, 664282663, 805625698, 307131906, 30298495, 697147862, 432204312, 507451212, 101955542, 618634545, 136114690, 287998770, 151876479, 994698462, 133065545, 284962152, 303654976, 316394574, 78750136, 477508829, 870946807, 211673745, 885862396, 78470720, 36341157, 849242566, 744068805, 41463662, 114616259, 549363895, 690671729, 657515348, 447657737, 744052852, 303948899, 770435377, 454520332, 517662107, 244414734, 759918371, 747286353, 176528854, 663651600, 49713818, 69349226, 701277233, 839479212, 679234813, 499455151, 615913635, 387611248, 344078681, 624121661, 750776412, 728923422, 508116317, 366353427, 613757810, 676857867, 698925569, 716742939, 304532283, 777659981, 108655703, 622942123, 369836360, 13696136, 747604362, 794723774, 439701689, 328993570, 791084187, 59918301, 604330340, 821557157, 741132581, 856875068, 522607585, 864455045, 269839317, 419705969, 11508160, 832435727, 908159468, 31184725, 352934163, 470293783, 278603264, 327889655, 243738728, 191755826, 406732513, 12774744, 79620862, 126150125, 720333317, 875104671, 88427894, 371583741, 37345744, 518877444, 501062071, 579579535, 458600377, 967341702, 117716722, 436713909, 443003037, 207498790, 910954022, 664583179, 443560189, 17006668, 560244038, 613737416, 406495660, 348271093, 536118998, 590748131, 251477086, 816346577, 226762214, 263334369, 630140454, 202170637, 844876128, 429581478, 126348447, 747825147, 259247816, 460484493, 800204535, 730540251, 380612143, 623828491, 798625727, 637584532, 655143311, 229655019, 659073062, 400339551, 972527420, 95577356, 935491503, 870188866, 915261011, 58409141, 841396706, 788134925, 571942082, 516532706, 934594197, 136431967, 573069355, 715632275, 160647498, 439089705, 242170145, 839057909, 73268876, 331940700, 917968373, 880230797, 932440132, 123549969, 379500880, 520197548, 808666304, 452352194, 82871481, 210761972, 670581595, 201667499, 233074350, 810337943, 565300509, 27126656, 804224434, 394082828, 295306651, 384618249, 936297581, 561530923, 105977477, 812432299, 756733335, 434547672, 49107565, 330851534, 605896629, 280101328, 194111594, 779032957, 973665377, 468004767, 421323699, 375783491, 550228957, 458993423, 539249411, 851540622, 230592656, 864317756, 13627852, 74516257, 61309880, 97664563, 196048752, 380846005, 690411163, 992801911, 976087852, 266159907, 123971710, 953825180, 527187425, 799318378, 857618225, 163969807, 129245031, 101354404, 429137227, 597858067, 400682571, 586364814, 980160828, 322329075, 14468719, 559484140, 818410095, 471196434, 213930914, 849793834, 338511325, 575739804, 279162455, 819471955, 867203522, 633574139, 965822227, 745274790, 55232367, 195891270, 557261741, 883602479, 20689552, 20160115, 810107966, 510964208, 225453889, 300432069, 860582532, 354810195, 294446032, 291391473, 862473676, 35224512, 346691483, 647003561, 70131997, 4208555, 624579701, 66674625, 784126684, 768473174, 171899812, 153123551, 369632703, 243818486, 905991827, 318791915, 797606282, 248178423, 891225193, 173274673, 170775520, 993852246, 521815518, 37898941, 8482916, 693807696, 331510386, 988374881, 513291327, 457258040, 555599553, 106958027, 460895910, 219087678, 60483599, 295337353, 781395855, 299688883, 796152754, 886962012, 40943000, 938739047, 655457341, 460221070, 728057168, 306175158, 953360068, 330760934, 37076858, 995152498, 219489880, 401524023, 609696276, 146597514, 647654210, 92876105, 215977407, 899240835, 132922831, 5315966, 8019842, 202663715, 270162239, 171130970, 889480027, 221144646, 89805237, 594658288, 735714078, 238083112, 514200317, 272723987, 868739050, 630988181, 94374736, 28832615, 987158905, 442398905, 625282619, 530587621, 971416462, 178791285, 93595959, 360621439, 895208339, 111814989, 854452077, 206047442, 310284489, 338187208, 807597849, 246812240, 722895810, 569367022, 560870237, 161129508, 928507150, 64164746, 890845994, 436740780, 710428792, 146792295, 769692315, 359285303, 76374503, 982494366, 224003819, 508315604, 600462641, 109237433, 419019161, 960677395, 684668264, 989553392, 404374506, 859380372, 11668166, 563668329, 918756716, 759352767, 415020224, 365670182, 436713895, 430110920, 40994229, 960969102, 650343445, 766976181, 375151740, 301373821, 494227525, 306858859, 177341768, 827982390, 470524167, 274064769, 833156876, 789309270, 433872700, 163426720, 924879670, 770204991, 129850158, 854562262, 170591643, 692593168, 54875769, 624999053, 443645244, 509413971, 252527409, 607572067, 896773975, 504824729, 688978547, 720061167, 972136707, 205251361, 797295784, 346144233, 970177719, 893612156, 456472291, 107390883, 325811149, 643962073, 497332197, 964944032, 703904916, 112788580, 648569944, 753321221, 703483218, 382054595, 356406750, 847943647, 617554471, 178704581, 62910877, 139690435, 763511610, 870822730, 981362631, 63351048, 634769912, 224776996, 792734144, 59224894, 789793032, 362420100, 21155378, 710091170, 721149177, 816726000, 20928867, 793138619, 725134156, 224927550, 417637888, 962132478, 502255579, 244752159, 193226595, 116790429, 745121851, 775871591, 649897455, 28632797, 23173289, 61152452, 636737754, 917017748, 131054462, 786801049, 555461272, 102809871, 721181074, 997303759, 471112822, 952350805, 453870448, 510989515, 772488038, 882723196, 22760441, 935198250, 884048330, 15771460, 793552201, 549556046, 31798287, 68734728, 530970934, 261598590, 492820115, 986287717, 606337876, 690973220, 639983118, 825663876, 869362117, 626675890, 327911989, 808723451, 977635344, 747543086, 45030053, 847520435, 820668575, 625833485, 643218877, 131605370, 290006662, 199062883, 868643330, 467662485, 141332395, 604592822, 80994430, 324820228, 872325454, 105769218, 316407695, 26691231, 990079661, 222067363, 138836854, 302969116, 759816492, 511879230, 51652611, 754083165, 758505515, 704026909, 501004394, 47321235, 771785528, 21205566, 571608025, 999792687, 341557509, 424982716, 80871906, 633161363, 200468796, 511012646, 717360604, 541186238, 513887186, 631509557, 723090132, 491944592, 689987272, 700999434, 485797598, 559591186, 338059562, 608690998, 290957032, 631052625, 866172817, 925812211, 599808528, 69768736, 321620242, 988164032, 294634072, 147939836, 272045194, 811783800, 909558769, 249025491, 876159147, 874312626, 942426110, 405369137, 605643918, 639123309, 630520975, 838660792, 690600846, 365676845, 500142014, 572185455, 889888959, 530617517, 929672661, 65865696, 522266797, 337091062, 490180951, 701660166, 597714455, 517052576, 78277461, 73689953, 60541659, 681767044, 817483168, 361177056, 84092367, 70063442, 517063267, 69074897, 652324369, 248789703, 964989389, 972156661, 689549889, 583595886, 286896153, 375308493, 111290782, 818826407, 720526225, 992238802, 263062430, 544713851, 579411336, 332472210, 70588874, 170012458, 409403904, 359279929, 478808822, 591058179, 77458333, 68247465, 579167170, 393298486, 705006365, 122332597, 578959348, 123607959, 432973418, 860122778, 147154963, 917669092, 125507271, 623898320, 559398269, 294151931, 976316360, 327158214, 246654275, 136362569, 443479011, 893585532, 734827105, 230689544, 310651650, 456153120, 696990128, 817484404, 415846994, 639792029, 731717920, 543809874, 295658948, 926005645, 782313713, 879484975, 279772323, 320246564, 380842347, 753168990, 703292355, 115438180, 569861659, 374010041, 303364064, 987690142, 734429804, 533105329, 590169518, 41511392, 478996377, 264571380, 928593942, 400397685, 420795147, 775783750, 807068094, 140721113, 359979860, 653027733, 285364137, 81147581, 453446302, 27527464, 854028308, 148623573, 347440662, 828032149, 528341574, 968528592, 681203175, 711861310, 323657925, 181945738, 757831166, 153633487, 759616596, 346769743, 532588734, 961329353, 252755426, 119932705, 47184267, 124332807, 578231503, 948874253, 387595636, 174820563, 807952501, 489349881, 77453602, 47169849, 155528172, 852146077, 315061776, 987628365, 685973721, 684747720, 80558882, 472500100, 756325665, 473156109, 220533365, 597751599, 115962053, 157871190, 263587609, 537419130, 645170666, 179360070, 176762667, 208389450, 348716085, 814723518, 605862889, 804039943, 297347449, 594629228, 617189706, 297181573, 889317019, 845637254, 260078282, 139521094, 734439411, 837602425, 694766565, 185534684, 400152448, 628314588, 658547836, 9223807, 428357881, 641117678, 360752692, 871877209, 135193411, 916717575, 240039150, 51350218, 355005310, 789614941, 2202017, 366705556, 389947187, 239293013, 668439960, 393710032, 520859086, 579308275, 970191027, 716057992, 79458207, 970319076, 906926101, 363495437, 119641349, 60103623, 457669447, 53091118, 458066663, 287547787, 637022329, 226902877, 183943401, 265022382, 584764688, 4843727, 359084953, 141531516, 51005640, 663583223, 762062853, 532164457, 490650702, 632015110, 744844034, 485714221, 77359111, 201384180, 939510262, 257209026, 777868328, 257712645, 679361970, 183743264, 14756100, 634743211, 519456465, 544255268, 420292124, 110766920, 510418602, 844771620, 999551668, 621737157, 23975982, 696199413, 143008350, 573637887, 543141895, 490525407, 370693975, 942100918, 291580036, 485148230, 823265782, 395398548, 745105189, 391532431, 848537163, 684905498, 117267540, 193678455, 952912426, 451389846, 853636514, 123738544, 511155492, 755427015, 334587945, 856789851, 334553702, 844848953, 617400434, 565350581, 856078251, 622951020, 851953004, 46823451, 407800269, 69361075, 29695753, 909550629, 461571273, 427909281, 292595909, 527809059, 677084723, 430855616, 181051606, 418646044, 952122593, 729634559, 213462533, 523547991, 490627115, 644341357, 273553143, 386297389, 519955308, 965039427, 480353399, 337170860, 520315360, 793846221, 685133057, 416798744, 556365279, 969867965, 120821059, 889454300, 44834740, 736655461, 11011113, 894425369, 480329291, 339227366, 678800741, 639689889, 362315243, 998949692, 88074518, 384852362, 6024266, 610440276, 322600257, 972499822, 240596641, 267772944, 336558720, 952521595, 314019704, 486495388, 391879130, 350324880, 173417107, 245165080, 199158844, 765584218, 25283944, 33876158, 325701185, 40211172, 654056682, 416350349, 292474539, 362427783, 8820435, 62827781, 512149496, 616807130, 670565911, 266124731, 306994871, 140455712, 993866581, 816079023, 931609354, 20766264, 339925146, 607662499, 445020934, 825136970, 906935651, 686769802, 918550003, 883002655, 985437393, 924155053, 70419116, 821356924, 345906117, 29146975, 952801520, 834396892, 674611573, 811677635, 286579141, 770796006, 982214149, 514036954, 469930183, 209269629, 526680221, 946622158, 62874143, 236981414, 928579446, 116085095, 30260119, 413278133, 991966381, 422830253, 677578282, 761663915, 990539394, 891157122, 670317100, 382393703, 212160241, 20463255, 990694813, 344635952, 411034865, 557360027, 37501976, 460730605, 524168111, 291096530, 918882393, 850357635, 717839913, 396816747, 409159041, 483323741, 853116201, 275371369, 171909374, 695034568, 941670264, 244379787, 157518950, 985704033, 73416631, 502321207, 700465667, 586326783, 119472260, 994313148, 882787743, 826443210, 144497897, 48544757, 482453111, 579416776, 153659375, 50062487, 3812374, 101794863, 147908389, 372773302, 743149696, 230076294, 3983738, 288700237, 655491650, 154945772, 271966249, 106090277, 215177578, 149943770, 83606424, 569801146, 972781647, 704145425, 639194431, 326384526, 70214813, 727148888, 515168780, 926500525, 349963753, 186457006, 878736867, 995381767, 221955323, 437790825, 736486513, 409998711, 713238464, 633725846, 502688964, 185780956, 208080264, 957971860, 752728182, 773950567, 821395160, 536185658, 923813643, 215206736, 170046873, 529428616, 807178072, 550205673, 81299194, 550381532, 483723245, 643025955, 361451833, 638795230, 569542712, 850029278, 122584046, 462906679, 177805338, 77191437, 299047793, 470642704, 94185501, 555194546, 493648297, 391726285, 126194292, 745746807, 723778875, 911704124, 289788992, 392355625, 666161390, 427533566, 558598185, 541433902, 885277698, 640254596, 387383449, 622788364, 26697104, 791226469, 855443049, 423823416, 677316417, 705057775, 847454787, 326315164, 866449571, 934764361, 672381738, 709583166, 257638012, 151438028, 897643587, 255399946, 615548075, 387371394, 916998497, 457041538, 306917566, 577032697, 750851630, 105719537, 825064760, 657224595, 63719685, 197891039, 249288023, 918040197, 842713409, 633127879, 851178845, 828552589, 432281810, 35666536, 142067491, 574401299, 986623107, 658233157, 609969122, 946980807, 880327646, 365123289, 506433695, 311397778, 787031387, 891088703, 985976697, 451323995, 908394220, 45508739, 57251330, 789604127, 869422825, 453934191, 15837910, 424313615, 754957113, 950501170, 363354284, 960264565, 831457772, 384202514, 862389001, 796475161, 163400441, 900292692, 146690103, 614854561, 183298631, 994976899, 584423933, 486194625, 332176112, 957254576, 245196505, 952334835, 398388999, 744194748, 256143091, 215744371, 90457506, 881555644, 482930135, 176015137, 419938155, 575641335, 734027512, 755697361, 281141974, 169179855, 780305223, 619776794, 518839741, 657339889, 365556985, 732046172, 334019001, 26614405, 909021903, 11496915, 549339015, 170347713, 761398937, 274131269, 108043270, 809696173, 418340482, 814484900, 413095378, 817831520, 392492934, 476760752, 531343862, 184418561, 717054552, 543514465, 48212593, 761942487, 70744764, 608233559, 655011727, 825769848, 641163561, 246822133, 377032626, 994083675, 748876169, 950576008, 432190228, 268010166, 624221792, 434102127, 831302630, 918626790, 101752299, 877653156, 411658699, 869974362, 573528234, 217372747, 368371813, 801022829, 121308583, 77756616, 616604216, 613941512, 839441322, 384575580, 446774702, 157047621, 541976644, 390231198, 994890003, 867698114, 799989943, 630368142, 362900481, 333475335, 904625711, 232206531, 799811637, 969089609, 202337563, 137883520, 439076116, 492309143, 931827645, 736676608, 642763980, 472246956, 742547057, 583193457, 122871337, 818349893, 950992237, 660418666, 110103856, 190211560, 171518839, 173188116, 802490501, 301257964, 916361176, 391771281, 573278573, 504175083, 773301817, 827798551, 521620211, 233000995, 361535221, 336421580, 927311228, 783012040, 112737861, 800125100, 790348762, 966167411, 394677773, 220105266, 200914172, 368506333, 523322253, 933500700, 557521931, 340372505, 174245169, 642040976, 909166774, 135993297, 809414360, 44833010, 7638152, 914924651, 144813434, 28316688, 790572591, 413773727, 851594431, 880678011, 337152866, 641244760, 962664518, 593736856, 129683677, 919945676, 423726532, 199560425, 947999944, 873706322, 608495127, 403152127, 515399095, 561243749, 257595847, 897708197, 369279930, 671882311, 236222986, 430845667, 474525409, 244587003, 107566266, 553915162, 668626777, 997810692, 325002522, 235864374, 422937385, 716767526, 865305955, 608774118, 501887858, 558129783, 212562515, 718689259, 667658620, 26508847, 36681883, 438943813, 160834431, 73227715, 791763089, 932174115, 928036652, 325671949, 375189156, 783475208, 953362211, 593371620, 800692745, 349063667, 820407632, 976954204, 564172828, 715418382, 571936286, 382546160, 354458719, 160225381, 138049179, 595913262, 20588604, 281446748, 41017255, 483012272, 542791474, 381027352, 513812412, 598841692, 522677407, 97606149, 782168863, 322586598, 238825466, 568904256, 556500294, 986863058, 722045743, 548754950, 436387421, 959087334, 799909770, 378441913, 701085487, 155734900, 594495825, 820187108, 801542156, 796872981, 897929113, 823501202, 538970191, 425980924, 424982640, 766697989, 728029966, 385548624, 904195815, 741038991, 338354955, 726585244, 383856300, 411920995, 587553843, 505454623, 24847050, 421660563, 933597326, 147715046, 474494028, 896640085, 302997809, 488427915, 970026770, 344386130, 868726588, 909702477, 647120649, 413164600, 349601176, 261823004, 410346657, 233430877, 304221060, 582552119, 98217117, 388251597, 631331787, 454942166, 607760785, 602874809, 222136324, 780285576, 362817157, 168794599, 492477164, 978660293, 912012331, 883836490, 873669690, 157795322, 752829595, 643081389, 126919259, 237757644, 649984347, 830136061, 828396629, 589147797, 282987446, 323424404, 752199314, 21177717, 682878336, 688821368, 819904078, 636563580, 411074995, 730275030, 210439061, 848694075, 875374354, 784496912, 714459549, 892390573, 306929399, 213976241, 465483272, 143831384, 242966876, 116855440, 477132937, 174881955, 308237128, 812025195, 177374088, 630276288, 66422999, 861346660, 464259522, 168871874, 522290305, 801454885, 31146534, 334725647, 883780102, 993964650, 898235025, 725334011, 207911129, 253812194, 247397374, 531998969, 639067569, 700013129, 656901049, 198435663, 573430501, 678354286, 263770208, 526546071, 693488969, 713630646, 678878435, 260978886, 798090026, 999288935, 784257787, 812678910, 591583776, 576626492, 914492510, 548647775, 332117648, 917725451, 282826307, 801115102, 653040523, 993953280, 529879300, 79345802, 731935648, 217771180, 146331629, 910848924, 828136879, 121648673, 947120984, 274473315, 960662123, 721063142, 463140842, 212672096, 354377188, 263982264, 16190485, 851002521, 814022866, 296983520, 604520720, 527861623, 553015783, 576683055, 628074101, 492251154, 465507008, 478703577, 813830369, 396849026, 692247449, 488436629, 180332757, 891493596, 294590677, 748380761, 587052541, 426208795, 278158641, 83080540, 408957298, 654279133, 960914166, 75159886, 335902811, 119665579, 340731517, 895261715, 274979473, 334111701, 500140355, 77268605, 899720232, 761681363, 535155220, 470452194, 924706722, 165576216, 621801195, 469167626, 649031565, 132631239, 411287086, 173278326, 838978588, 16276133, 406625624, 712064417, 271508554, 943510663, 475024471, 791921845, 401996245, 807050767, 833360302, 900909904, 868624123, 313032307, 102313370, 125170462, 39495752, 825570697, 356678987, 651326878, 159221774, 606502575, 378471920, 828019979, 889468185, 824238720, 606572076, 143375703, 206980229, 840795524, 923431763, 716714190, 901903224, 111726211, 458979618, 663105344, 413620797, 313804082, 570821386, 598282423, 614123066, 285522262, 789156242, 728371294, 596430561, 266750477, 801121027, 263621606, 654710078, 209625196, 162847860, 372864414, 507803231, 56661177, 470809592, 721397656, 896085583, 733232971, 71577284, 693908044, 669523576, 429824709, 675055551, 142824201, 625266349, 855566639, 818313485, 738868790, 191690655, 427086373, 496725220, 628184780, 423891813, 471711762, 157878543, 270804358, 654528113, 936354486, 835028291, 730562865, 795058864, 672841513, 369450154, 428078397, 345059284, 395095282, 401907260, 988743873, 995168810, 244612991, 718825520, 131680423, 289210679, 427934262, 180162410, 853890195, 606557097, 834484677, 195677250, 702956646, 729837420, 884085533, 531520092, 984034546, 5579978, 436506924, 259416558, 222163560, 327408923, 699747928, 852300308, 150800512, 544800038, 852840997, 525459835, 289305966, 989154897, 993337757, 374499227, 269995459, 168000226, 966513253, 80961882, 109790327, 703482010, 522433523, 823662749, 351833022, 249673988, 296263178, 952206200, 19511360, 801638949, 732494274, 386322075, 34360183, 884343183, 389503770, 790272240, 500861706, 829260667, 162447946, 45318758, 4775565, 374419586, 536740698, 558159125, 754716321, 411526439, 607330371, 426273124, 114163158, 114692484, 678923474, 82084812, 852401916, 995091436, 45911596, 971651389, 982364243, 127163359, 765966913, 803262373, 125352190, 761635463, 24441660, 235090425, 303039017, 291723764, 67159594, 812344654, 794132541, 224504875, 270635257, 17417097, 717284015, 91175965, 628074095, 81858906, 986572617, 298169719, 532493815, 294059500, 885940097, 242553987, 323950925, 326138936, 219050670, 873510894, 245700312, 892741677, 964738808, 32852251, 624726920, 509517537, 462736876, 377301105, 127341858, 77982203, 959383001, 993949686, 215881112, 525872993, 74179287, 875536894, 175981131, 396205225, 203452669, 123175173, 729092109, 133276690, 947665667, 166790648, 100058781, 270846104, 988264970, 924623534, 128735256, 168997984, 446290778, 797228282, 590919308, 668370267, 166604735, 49612857, 937141182, 152349581, 583731701, 89025154, 324220077, 631680049, 152363420, 825903918, 914161101, 342215245, 769816823, 607966546, 648449150, 600160945, 308552436, 343237360, 769629134, 330598385, 752927591, 279754954, 647379666, 285314971, 639422499, 470822087, 235865903, 967184534, 622387463, 227635731, 850883287, 11469402, 770009564, 370653713, 366108786, 299332536, 631505171, 895923967, 319617226, 122825417, 966149808, 931662890, 418542358, 546845275, 542693715, 934046829, 305727810, 936747367, 727727450, 99105866, 331066724, 711080365, 531261026, 861459792, 788358245, 771954838, 531139329, 699029948, 32623795, 75192380, 243264136, 555180926, 242061275, 636605886, 85975445, 119223582, 908600488, 148760287, 712261855, 384097206, 760812639, 57883035, 452116021, 783877485, 537845717, 180424998, 523467479, 630383616, 207167969, 200256806, 270952831, 30514874, 928808696, 274892621, 438068898, 394885067, 3522651, 390900613, 785366814, 260549199, 882285317, 103361736, 814261218, 234702127, 655062304, 685130076, 83420142, 63753933, 63612456, 551475228, 609839124, 248927412, 666203696, 847420315, 561808165, 84337646, 231941244, 799357265, 752742591, 352207280, 176608685, 841869042, 793356532, 74364906, 968291627, 369727613, 783620526, 694422947, 361057241, 247365601, 156243244, 852412076, 637357881, 376675754, 530019328, 876141411, 717046015, 700411125, 408874099, 401615655, 837049776, 249881862, 378320514, 90500318, 364291371, 820768508, 161421643, 291781352, 150206540, 284846773, 219267321, 458971189, 653625592, 146179369, 208296999, 616791577, 485634768, 282102268, 701352813, 57157866, 747121037, 171793729, 932484880, 507899649, 386839933, 39145642, 897915118, 71354965, 228753553, 161282387, 272306750, 426467912, 989587041, 915416224, 713559298, 971211313, 372423675, 456126684, 601862047, 992549987, 216184107, 250448838, 990331522, 80027014, 86573189, 520745121, 253940637, 338443174, 268526377, 641726161, 316147622, 951872710, 293340048, 599314089, 860983233, 618091361, 571601985, 652462854, 125057473, 497557036, 827588946, 238079046, 950280735, 788067079, 392972711, 186275773, 499579911, 628645988, 994869919, 825844481, 748376471, 58379059, 184794787, 720071311, 454233514, 993640238, 449143648, 971567580, 496175241, 387305742, 93651017, 62557112, 128553775, 209668901, 143527204, 603939500, 113691391, 829258116, 271905349, 192349425, 247394635, 634907879, 47145753, 411352894, 92842535, 803450705, 356552126, 331248520, 635487538, 132631851, 496157948, 13093956, 73787456, 543240689, 224511622, 647466305, 233408413, 602506494, 161353747, 294223208, 911952445, 983266197, 651656164, 913498998, 335027016, 381576126, 429695221, 955306449, 168922103, 958074873, 645524474, 84629164, 446609372, 871748455, 978367075, 438801551, 775196221, 649420459, 724033832, 811832697, 965508243, 183239616, 27114022, 441531280, 775654125, 659681895, 711675148, 360396081, 539312252, 52146786, 331807579, 870723858, 980329768, 775325961, 210728900, 283398809, 573169954, 353140245, 838931777, 759318261, 800302114, 939860351, 319143643, 549385992, 695798461, 249533420, 659805436, 400944553, 254736180, 525652279, 914677536, 73115983, 903572885, 241553920, 753072776, 892356870, 926111642, 162777670, 130427051, 351059974, 197181270, 637504747, 470401801, 971234865, 964745011, 136079963, 91973370, 420736668, 385366499, 337860744, 728006338, 723145708, 152248065, 357849279, 358673563, 15792377, 435785288, 746449532, 771181209, 614280440, 216313033, 292619547, 778158022, 986176838, 10853252, 263551543, 300354237, 634530722, 504176886, 293721731, 36280321, 873087865, 659544854, 325478715, 79822553, 390671600, 796148317, 379184830, 359900800, 465072684, 32013168, 963323982, 222392584, 133448977, 811344350, 994377534, 118434757, 586131793, 681421610, 149670665, 794632843, 540009958, 144085373, 526016247, 587535529, 289629526, 99739895, 114140774, 819785882, 814704068, 392217031, 129491260, 951254425, 56604931, 583432883, 122076042, 200905841, 667717482, 155026825, 590854241, 451268041, 274592209, 718592985, 545788052, 977337265, 798084513, 558860627, 961291445, 538043487, 308912329, 306081763, 670848501, 856237125, 834336030, 946921150, 848266309, 356383916, 385917696, 297166052, 683120705, 701655377, 750952904, 487306358, 767832870, 222647333, 360442999, 41815005, 308821441, 125108962, 52850357, 29485904, 726609169, 116248941, 977324413, 882667896, 179214478, 394016097, 17845245, 21313444, 150948015, 493366241, 6278203, 564449039, 621273471, 993399580, 21356932, 404020012, 732027195, 633282262, 451182380, 486153932, 6634355, 234780160, 417834128, 875462150, 454709121, 78655842, 139257624, 407058089, 39525928, 781341078, 555715919, 259228245, 800513179, 723577598, 658790526, 523645791, 836666848, 429565223, 523006271, 339619809, 904569929, 776053316, 687788901, 394021120, 44539708, 66912864, 37767244, 119640553, 499545472, 942862629, 115696545, 100258561, 110340918, 96507383, 398501101, 563447543, 525235348, 19257076, 216481753, 175390437, 822681099, 898900425, 813972408, 277474999, 725741597, 272598557, 842044716, 971377995, 148315714, 55863433, 875465979, 451205235, 142987490, 747196878, 675728170, 254583976, 380651987, 825149855, 500834202, 328810860, 796718300, 415741102, 489939256, 87235099, 551288721, 913726725, 650277256, 389489122, 746753754, 269989523, 359103817, 117425359, 198660174, 876178674, 554037874, 95227339, 419266009, 701886277, 851290426, 223828120, 834183674, 152498403, 482694488, 830917873, 219680605, 763352968, 945792228, 658692400, 695356840, 329120887, 372518147, 808224982, 951858839, 622753471, 564058396, 72272615, 825996966, 808154279, 13564519, 412315017, 788728927, 526942802, 973453485, 229466701, 95147552, 64003926, 448356113, 828400968, 21390896, 625823032, 917438860, 341381561, 205164645, 159191, 811519628, 449519958, 686360477, 830309647, 535932706, 424010819, 399312417, 799757324, 632001709, 111901367, 883582290, 631852657, 642691534, 208908919, 666404484, 951591031, 210602516, 162173693, 761201284, 893747531, 162168212, 753276470, 737972890, 113002910, 260460961, 826633655, 969681365, 518318994, 432441722, 976059464, 861845822, 973406093, 412311445, 500448109, 177684247, 758450960, 456732345, 643575568, 297744428, 311596775, 333355489, 906593511, 500199107, 106106206, 798643927, 650886028, 109639155, 274978174, 715474393, 28681862, 371725427, 287019953, 852174510, 791663494, 772255662, 567192286, 862323849, 643903835, 847788996, 329774390, 525323624, 317649841, 324776729, 386365203, 241173182, 670254116, 78540468, 46735409, 868457126, 786930711, 752621936, 649162814, 526747549, 424375093, 279271753, 123423797, 920422100, 260247092, 203769017, 109794919, 292199539, 483825485, 946742879, 347816013, 6374387, 867080835, 130812495, 505515579, 723801062, 583656295, 571547699, 190828849, 259656917, 413500680, 62969836, 856841358, 620153262, 996539669, 473673758, 805457792, 637834057, 877936646, 232274926, 544804828, 438980896, 677989161, 634588528, 239370225, 739049782, 658576262, 326535575, 534593251, 418036817, 685717763, 744522949, 967076986, 126566279, 554975284, 790161144, 67762594, 873759861, 390222869, 222477452, 778581113, 275860828, 480567969, 7090628, 123934148, 580379232, 717935345, 588060240, 940066353, 14075204, 857397936, 429737925, 707613196, 647015218, 835387519, 408490223, 576219749, 863537905, 389275898, 727852498, 38103441, 642478584, 948638387, 901660516, 57067635, 796859474, 677825795, 562044410, 729808084, 358408419, 986470378, 509591436, 626831294, 804300566, 795708162, 655191492, 930945480, 970535884, 325280762, 381769626, 120196683, 10214582, 460781222, 902952099, 964787295, 99648820, 322628973, 905827688, 758029958, 778905082, 407812407, 64366458, 387995069, 146619446, 245655339, 818382418, 415135339, 733739031, 593885661, 41989954, 780797626, 794029356, 963061265, 164255721, 895860642, 97219176, 661081544, 249257577, 293050476, 472699890, 167502538, 9243660, 421200002, 539802716, 513290279, 710456504, 853441454, 26636464, 587881683, 229281521, 963596302, 341502259, 312720491, 868894641, 6834330, 60334697, 508186060, 649922819, 161046026, 594498103, 533685089, 477738972, 882085175, 908667473, 587311191, 415747609, 961831345, 430062079, 7728495, 560682353, 888945939, 82831900, 766764743, 665220213, 992815571, 271614695, 752421634, 474919190, 344278421, 630411575, 13697369, 11099487, 159192447, 66487959, 95447856, 684203767, 765982937, 892469876, 581901447, 179419508, 602061005, 9384237, 957413410, 254373159, 736989118, 275761375, 957169910, 299191168, 632936397, 32712181, 229950368, 871579732, 129897376, 996011391, 760823705, 787981380, 401204592, 68613339, 856672231, 731395609, 723613563, 409172162, 961290012, 345347150, 432863635, 910128591, 586204670, 920602993, 636180733, 421601793, 507497057, 155353844, 99671060, 150647332, 880105229, 942411597, 355327174, 382975505, 127858912, 416884706, 224704499, 196951491, 718520573, 460147358, 340503470, 830574189, 385507949, 841471932, 473245178, 358136963, 646225886, 577286378, 633816100, 28572871, 857445583, 575512804, 318850455, 128703681, 947497164, 8389930, 995096776, 638026273, 444202572, 995117846, 463415548, 375228493, 702281139, 578242311, 325344200, 763796656, 822299036, 511355452, 41989126, 544998123, 493690586, 688057026, 596039768, 268625810, 313770265, 329592450, 777079931, 880780924, 838620350, 864368229, 987149473, 311225534, 305759732, 119489126, 46961408, 666990373, 856914180, 470913208, 286900305, 663957153, 921846801, 458004417, 866105607, 852264904, 655861959, 992271895, 369352533, 162768638, 135945955, 680865116, 432562433, 898929789, 214906781, 791441818, 438636092, 377351129, 419686808, 359839882, 400589036, 669470749, 430882364, 857657501, 281799183, 173520405, 722769125, 179479084, 264405685, 480390783, 397816906, 675747437, 280119897, 45622021, 125342189, 718264994, 658229131, 561091633, 279032470, 573858615, 943319989, 992355570, 378463856, 922043262, 382861494, 809023237, 917542395, 269841469, 260449790, 195792965, 631513649, 330776416, 326722332, 799809691, 83489791, 611048728, 756672393, 666929326, 902048250, 503605301, 376752115, 330035400, 271622261, 287393862, 309576721, 391891454, 932243317, 448362133, 564825555, 225174058, 226755631, 166213521, 735266002, 810678441, 284299065, 482295851, 679176280, 913492635, 484881276, 142278620, 470407409, 15584444, 952002704, 146428482, 225238136, 64650239, 623385785, 265910181, 457555033, 868430441, 727778891, 937910408, 322066861, 289781417, 913197280, 440512293, 71456163, 250075948, 81616071, 457036799, 152708785, 781379983, 262890969, 298613273, 568113961, 516237862, 253673246, 38245192, 962475200, 746560340, 936246198, 423813930, 850362, 662650081, 354077982, 92816155, 117358978, 144225551, 397564728, 154044365, 432232828, 493165877, 443676806, 443996460, 470742404, 990935460, 264052317, 343818594, 61849331, 911902520, 399477484, 453076158, 973436212, 374663172, 690137776, 909389526, 907573791, 357114957, 160332987, 528893013, 255450306, 519287703, 971815230, 800470686, 366795832, 641381153, 873440476, 686156073, 17992730, 683232910, 120007347, 106005333, 596949700, 468453333, 640396652, 747833685, 515986658, 549557895, 381503889, 210185022, 628309338, 866105254, 952202519, 358111887, 87447949, 580485515, 319330597, 657721059, 954864283, 179436866, 771890867, 622816240, 290369172, 10595717, 362159459, 983487759, 407536323, 639699605, 561254100, 320106474, 942708768, 676031035, 330996712, 691750799, 857880666, 674475878, 89582083, 889073224, 889009831, 1746775, 542138529, 51461472, 487238416, 448353706, 138993898, 448058456, 648087714, 479763781, 874268400, 763849978, 409819834, 441202776, 623202957, 631482119, 971892802, 986536730, 479159144, 949400635, 901128781, 557270163, 818793536, 869358475, 812426858, 857288234, 925733549, 529289147, 558347662, 858950279, 303687152, 483988901, 136326482, 553983209, 610208453, 654050071, 251169727, 395545371, 199289984, 490108475, 970291971, 80917068, 540593534, 68632888, 440505302, 991124385, 12619451, 622484126, 925744459, 330089382, 883048215, 720299133, 612018546, 51606429, 715898127, 921735351, 758374866, 640158920, 285297404, 732086775, 690648032, 280401343, 347799963, 842412303, 545364410, 42219140, 350525236, 704053989, 803284937, 239325824, 703717251, 510223387, 651896718, 900678310, 956449241, 985472302, 395898392, 358137, 948170816, 632443207, 738737326, 724437200, 779913890, 474199047, 712203931, 812336420, 983985455, 709501997, 918757519, 115262018, 744752674, 105312205, 380828969, 263180958, 37408877, 301673721, 741488839, 101228253, 575686920, 285614667, 270390819, 974305049, 693105839, 537485429, 453259790, 266272446, 487398808, 487957966, 927150033, 264623397, 361011978, 502374395, 233551138, 969989436, 863324532, 461898969, 402774933, 849722241, 211874659, 215690688, 351351132, 717709558, 215958826, 612219384, 666048683, 451910478, 743525084, 267804979, 324518755, 103073574, 933711079, 172804324, 707660710, 761179089, 342877153, 119323631, 692786862, 734728225, 732289644, 137949379, 587461101, 138590166, 886515597, 887017284, 876571122, 835636892, 342698155, 4800195, 754711343, 442726110, 761981350, 523272997, 750680051, 865089401, 259376076, 799857773, 714742416, 141308026, 88325727, 521873188, 341514489, 356971414, 555342305, 44634526, 369048779, 58649887, 321946294, 34755477, 118870175, 648551965, 695453174, 971290708, 197204666, 435353082, 954151376, 895697967, 285317754, 124102286, 320156678, 529683788, 600621318, 244098525, 595869710, 591741657, 225525738, 555012584, 613188730, 887573909, 996197231, 576175839, 87749984, 910205824, 621835551, 822613647, 309244728, 606928013, 334651568, 237329070, 451415077, 365970736, 165161409, 668235890, 56806846, 780291502, 624991903, 246211511, 83261697, 840051850, 58599761, 877532391, 187427438, 339058299, 842896750, 838201171, 771105029, 561462041, 100903083, 744057196, 760946373, 717233700, 565179566, 733910698, 128852887, 873962942, 196916727, 221734117, 176092491, 260895437, 686939060, 567882251, 882364733, 527632313, 947043598, 423961409, 442860581, 232259618, 620880626, 342886854, 954675286, 143870700, 629975272, 293212194, 572797166, 341787033, 748914746, 837540920, 642567153, 156488331, 692979530, 520998832, 156945637, 457120466, 824408658, 177592664, 144246788, 525537920, 400577606, 847999314, 799737541, 597276841, 62054153, 162194135, 544677733, 156689525, 587679661, 635692540, 194654720, 96487607, 820326993, 302254851, 474701993, 310280506, 23727267, 13212791, 549448551, 134889868, 667775686, 467173294, 35279630, 297973580, 265172422, 502846914, 419606638, 430123315, 535850960, 674566868, 152442922, 86323311, 734387988, 500766137, 518715426, 743834806, 243647757, 463816936, 845537130, 688506563, 776960826, 606206570, 310141046, 505132207, 243634578, 745760632, 875538845, 515371022, 774954354, 966992216, 190479633, 720343035, 414470796, 208744593, 748383720, 572517057, 821913208, 402917418, 708622358, 172975625, 105836644, 650659460, 306666428, 43593035, 504724866, 113617610, 913065430, 313471761, 456068189, 757963325, 704412265, 596578761, 500853623, 786377719, 329889863, 556441206, 378637656, 947495106, 73888741, 624352613, 893971934, 649169577, 700386693, 55305372, 236322789, 545744061, 280561925, 639176007, 497003202, 7572022, 30511874, 932769953, 635699205, 762246653, 37566449, 275590959, 151308703, 270602992, 739243516, 268060230, 78340233, 298589637, 778096533, 957610434, 373109636, 605132107, 781231796, 753792639, 416450916, 94514631, 608417083, 964211472, 514929, 482074472, 790824270, 171564412, 982070090, 998245465, 681088117, 96058751, 602169238, 123053633, 562312639, 117802765, 896445651, 99433422, 154506470, 157668198, 462704095, 215089074, 809987780, 239167310, 949914410, 34984951, 164995602, 208086517, 13542639, 365010729, 908375564, 433895539, 976155378, 329978210, 907047431, 603146323, 284306512, 823079491, 98208394, 86672606, 231426886, 404009814, 218092254, 163481109, 608768075, 174226944, 56932078, 565076652, 343658609, 275222039, 719207025, 323698896, 274501382, 957407669, 451769527, 959513716, 844371148, 98826286, 693717072, 755949002, 784954274, 982668529, 26491736, 586854588, 910076015, 35174382, 689698473, 557721567, 825688839, 882273695, 835209330, 381517794, 794200973, 575284684, 865489332, 869186561, 635793747, 529207304, 325852535, 57945101, 137501311, 838158137, 674864476, 216186030, 66067473, 261609222, 577458226, 292069895, 50365467, 685287216, 782860945, 29318341, 802070231, 373916873, 976200242, 692115109, 311476132, 399602711, 535597283, 182139678, 763459005, 377208621, 878584764, 689076610, 881818187, 291818467, 756257845, 766790755, 50278171, 628607723, 898496254, 494576456, 29398311, 928556590, 641882776, 599926017, 117773181, 89969993, 919082276, 724554625, 653865975, 761818465, 767174376, 412950210, 182299000, 427397105, 564975593, 525219935, 73638327, 810778679, 205181038, 949530421, 371925102, 314083139, 675450100, 201974902, 402378295, 261847994, 908335171, 75912013, 920008647, 420594563, 22982860, 832985274, 838983897, 618499384, 274904312, 652690143, 446171754, 657687620, 843662677, 371223889, 540519557, 804471670, 701728151, 359897662, 882356487, 146387316, 454624575, 803578687, 369118435, 997861522, 604209579, 972064009, 832237301, 239574477, 775242306, 662911620, 44085316, 847980345, 909377032, 853100829, 10196615, 717249409, 970862240, 726251227, 305513659, 187717665, 313518732, 225982313, 807655533, 206594713, 542165128, 414472897, 723166580, 124497141, 957397460, 172342455, 351496200, 483248400, 998081089, 639158690, 855027580, 193897581, 631149724, 195441034, 397263335, 466562483, 873890412, 637366445, 529916639, 870703854, 219297278, 293660070, 77878107, 258848253, 946228153, 219461806, 533210445, 287176569, 286290422, 149016807, 48115421, 301174301, 724857200, 125073557, 648292837, 755732583, 280720615, 946851006, 934492371, 374979496, 466415718, 649814847, 912062754, 872134516, 614794805, 125374755, 510607377, 182378329, 717131317, 738779964, 243570698, 164411202, 870158614, 507026629, 355658385, 40146055, 243420397, 629966390, 829605267, 733052998, 503786239, 501237062, 187330594, 800031418, 513612435, 753033361, 91114913, 819521805, 293139072, 220706641, 995454294, 996718538, 111996964, 388460647, 567602260, 100562953, 513010476, 176980471, 784236422, 416772747, 922385007, 713982010, 776104691, 771529811, 163941482, 164836743, 805808039, 786624631, 294460806, 894313607, 972013649, 440609408, 482556926, 36068532, 86623290, 843753198, 137977426, 283482180, 82141142, 264532109, 898622758, 282607561, 917121135, 289794228, 557384790, 93740506, 556330024, 972914582, 864307183, 382567521, 351134936, 34653058, 929207851, 39510708, 654312617, 448417498, 614237111, 296174445, 327657293, 544120293, 123455955, 242804298, 955885183, 216438449, 201665062, 576704896, 974770844, 778551536, 395318328, 256434765, 92203084, 358410865, 281385653, 541653705, 883119760, 675098265, 60376793, 255214018, 243407079, 65152540, 158508383, 329265873, 264088342, 704006711, 957459721, 424773082, 95971961, 629070993, 746157815, 355833008, 270273087, 861783113, 334932467, 764229726, 986833007, 424857539, 509469675, 446861919, 738389600, 343146870, 342081827, 400025280, 76714564, 164301561, 515366546, 258290443, 954887698, 622781068, 450946486, 656785799, 492398107, 205964934, 776813561, 460121512, 244656729, 28989588, 845434702, 264695150, 94435945, 799333574, 922741672, 548537046, 107389917, 273986506, 377558353, 435124900, 673513664, 442961477, 501533298, 661969819, 432956555, 691391198, 634451716, 889180886, 948859305, 993915584, 836275207, 508343308, 771267781, 308581213, 323038090, 256553336, 27551510, 879864596, 265216979, 446798800, 432901730, 666874643, 932757219, 638618018, 585823767, 158268340, 63752457, 455810934, 257240723, 901128052, 525716647, 455125049, 387932764, 210821849, 364237500, 168350439, 759879163, 950047841, 629615809, 699164535, 749797253, 699503733, 41233832, 849798142, 8139808, 484470757, 520695163, 793687603, 869291137, 559473104, 60135130, 575151929, 449590951, 586442746, 667654556, 667833060, 49533068, 548726420, 281105542, 749116757, 352644564, 692352883, 322426729, 808614920, 300184473, 231825438, 849499329, 935119016, 743186225, 606971706, 871773206, 157989574, 124942670, 114384724, 433508117, 796425101, 140915767, 621574663, 330057430, 696031584, 612158563, 462832796, 141836196, 416154700, 356813320, 868201307, 152344020, 653234717, 305705569, 105680994, 577928034, 996811217, 798955577, 232375091, 424270432, 732686272, 46825998, 8995106, 559971002, 675462789, 873030855, 267344290, 897679510, 378402867, 41549123, 938825843, 790410598, 122755665, 697603188, 144117009, 338446059, 933605309, 331902270, 179436539, 376729508, 902698389, 248347082, 267735385, 762052609, 242025746, 153316340, 972292164, 91528665, 485198267, 779596175, 104497908, 841174645, 646962761, 776549601, 567020450, 334303167, 759017749, 72022857, 808643475, 569785951, 738166252, 797780293, 796315813, 824597825, 300084234, 481082488, 348713182, 918523119, 463744801, 139808194, 304583776, 903546541, 669396373, 58965258, 410824021, 972214607, 797431878, 585347335, 816754070, 86720195, 771718926, 692484963, 302107106, 506515048, 525841734, 2533911, 64589637, 391617863, 248390645, 528048646, 79487661, 823582891, 758546346, 71367107, 777500274, 166025058, 761953954, 548508194, 593438352, 571840415, 56378547, 181648469, 690073432, 514595744, 496579934, 858419852, 698978732, 681595308, 198880234, 426284925, 946557994, 725626078, 516279178, 255990413, 360276588, 139850762, 666762249, 162938894, 407246519, 478587216, 48737272, 155471260, 299602240, 94619253, 207370158, 448677652, 721784464, 587071122, 62611320, 328246969, 297824286, 977905245, 715287480, 262999010, 726447122, 488093444, 429787988, 803331449, 580941030, 254463988, 38114345, 527633717, 813022196, 722522512, 768170728, 461682307, 313464883, 824055827, 6249571, 726186899, 736252377, 150658766, 434543185, 416969596, 653566533, 853335207, 53754854, 429213979, 300301566, 747592247, 461896811, 60188085, 426109522, 977921794, 500923020, 233239913, 498480294, 588845967, 409514119, 853856397, 923397701, 539791482, 683093194, 700316192, 388888213, 138518166, 725852432, 88108746, 745648734, 13859950, 231522750, 340770053, 831081323, 825144661, 139153490, 376563088, 319255491, 229281389, 74242014, 270908760, 593610916, 551199378, 646326916, 663367009, 457313537, 232755820, 953973635, 209295835, 707053704, 950457793, 971966759, 10446042, 484151744, 22870321, 845496437, 286826297, 882006727, 165625589, 351982853, 259464527, 135603699, 938028296, 213739577, 780721045, 544200068, 651107842, 685108564, 155488542, 30111410, 764976827, 45379849, 501933565, 685653538, 609306702, 277452365, 752139146, 677433175, 365909950, 13377030, 164923193, 675253900, 124943636, 424789852, 499439761, 657038788, 403423956, 922017576, 724340996, 382816086, 569682962, 701790994, 335380172, 849814783, 491926276, 684206295, 944744498, 615816694, 976466850, 578300555, 359418369, 842123571, 987685222, 667950232, 376800068, 873167904, 605979279, 567706486, 905492305, 767685288, 165130244, 562889169, 667793494, 607169136, 900146311, 434883454, 958678589, 691652941, 56630929, 341460911, 174047709, 875279995, 870266152, 350807475, 588766060, 128070962, 609225829, 348093234, 391372909, 783447298, 419263840, 191654463, 245660865, 391682731, 485520977, 728346152, 895941969, 350254604, 626297557, 129480649, 698767433, 672076728, 842382869, 227728938, 129000308, 155319222, 452051533, 458573170, 212527278, 621928099, 436555403, 490719254, 962299316, 250513760, 90015247, 125077838, 281287539, 170942853, 957969336, 185437095, 116418946, 408008075, 346181520, 327754386, 173192009, 172499584, 117373290, 482627255, 809022189, 443210826, 727346555, 927676628, 727597334, 474125990, 444236090, 38619312, 581758175, 874599478, 478187584, 823983939, 171205625, 348206489, 525476713, 459616656, 327908238, 403733998, 742538966, 817277143, 975463198, 363333358, 941928400, 374822379, 940492173, 643026459, 744814748, 231863978, 483994618, 245227307, 789293276, 471845273, 74625270, 658416982, 65905083, 525593200, 424980498, 993097061, 687447861, 614141092, 656792859, 709366389, 600911834, 295158394, 669199687, 860704167, 224403375, 482946533, 997609721, 45195034, 491315178, 377368517, 532464742, 773082668, 481175404, 324582899, 411234959, 250663762, 706841757, 615155981, 963427188, 235930113, 464427346, 84624548, 10329385, 999161678, 178766609, 567207579, 940852033, 615617407, 5272306, 543030349, 887270673, 586042651, 700811006, 767008744, 360007581, 233406017, 723698387, 194608063, 899102086, 733093550, 387873209, 353681125, 611359956, 865378536, 620934396, 586986488, 526699654, 810774340, 394805465, 701313431, 380985775, 703451175, 918266230, 30794491, 353807145, 170027456, 851412662, 119923484, 529345456, 45537914, 824740800, 97786986, 263861585, 462973595, 499667123, 825398789, 276164933, 411365360, 174912472, 673777776, 579660867, 35091877, 607750130, 657371188, 707447123, 904599563, 893382340, 351241409, 52550080, 527901046, 512035056, 314952543, 658096516, 740834267, 741340917, 520030011, 555197369, 789656530, 599948341, 39900186, 537135203, 959338900, 68436801, 915638837, 564211297, 704338579, 803066960, 341405211, 743482529, 630949762, 748302331, 148411393, 813394823, 489652553, 724030620, 944219661, 557453582, 711347054, 947519308, 878310815, 71891524, 511837534, 887146591, 117630441, 806413333, 489916861, 502394880, 341861121, 917657615, 52373529, 56786942, 495332387, 513042833, 204872277, 246882195, 383581452, 825214635, 511749535, 992383867, 421022613, 297690254, 422901704, 975726191, 684729670, 698629894, 453562219, 140645535, 762150077, 369865380, 175716618, 146014753, 939576378, 781891744, 487366867, 522649292, 350084992, 4696145, 806371542, 766412703, 153487992, 368584689, 763578540, 885969551, 257840492, 844382004, 206530252, 134386756, 950611186, 183803226, 526281737, 918974267, 432919343, 564087493, 680752216, 837932138, 321350471, 226894480, 736918475, 664542229, 797143592, 927411409, 381558614, 982752837, 477817534, 374913605, 568692985, 726146772, 493040050, 525698151, 723067233, 478007342, 977447015, 276446276, 151235226, 683562330, 6072099, 141537582, 668373999, 178302582, 879892284, 367775824, 134209918, 803716113, 649842104, 588983008, 960541054, 526774041, 65020233, 301332864, 682806988, 628898380, 99010710, 910778484, 522659078, 116822633, 635495282, 480588280, 365561260, 112243759, 488782535, 718831986, 844395670, 922902906, 845960516, 758017389, 510068791, 376786103, 962737205, 146926134, 572028853, 100884554, 647346361, 869166418, 789048703, 505915429, 384266513, 434510031, 82106992, 732008063, 591834623, 900861945, 906370303, 920104857, 278549592, 639720531, 792044221, 628833337, 228351074, 593099577, 264729188, 430205180, 646049761, 320277989, 17465007, 454976869, 235611465, 934928033, 782307678, 197869424, 811068026, 476942312, 670445618, 139191098, 723646958, 459681283, 231368281, 253475330, 197787933, 897724022, 459859452, 812013482, 178176078, 984222106, 367566118, 129182543, 187334667, 420569438, 641844214, 306752187, 864971063, 256945118, 817554172, 918275173, 30977933, 800731029, 228993331, 103824642, 216680277, 211026477, 435778973, 350090109, 102130165, 255013441, 383329979, 884915941, 433457908, 133942010, 765079168, 188288346, 476603845, 285195309, 209026418, 882351526, 380483071, 801575753, 991339646, 429736123, 246853663, 92797668, 787812504, 813849758, 459436173, 715471103, 684447709, 666546687, 838038832, 105120948, 838098714, 912268049, 829802038, 617779359, 797011394, 59544232, 157188711, 289396009, 897787405, 435252707, 994443969, 206892905, 597978487, 298391009, 514727965, 579158575, 680808983, 74168098, 831480717, 222120931, 161796691, 884412253, 696185852, 173781750, 586304459, 602693362, 948473536, 484016047, 367768213, 868191624, 729875366, 167329586, 824219357, 478558142, 819557399, 735628960, 482615202, 883433768, 697052150, 480372374, 692459891, 59859031, 938593540, 27665947, 700933528, 950643635, 917369395, 202286681, 976775337, 559134375, 106730869, 783355804, 805294497, 704735863, 387806793, 563827724, 351967085, 672234149, 256735743, 459566488, 613858224, 799828045, 49207114, 320532142, 200098596, 118884132, 412232476, 909911050, 908803994, 31550112, 333424389, 348664004, 606809902, 128382601, 269034148, 435612786, 745171186, 685918753, 248843371, 862175250, 662442719, 38162816, 133430055, 194215887, 936499011, 372124100, 524249931, 954554356, 293351019, 275762611, 764193570, 422045293, 290110721, 732423915, 266339079, 283209733, 170384720, 537387839, 883779601, 964350762, 803141065, 245697794, 723228677, 609694865, 257533216, 569464590, 295966432, 860572012, 423088860, 997797013, 841528206, 911312228, 729945297, 974351308, 703818747, 511630204, 313361465, 663002428, 293021775, 800924673, 807330683, 687556835, 208607289, 826733706, 151621203, 654265575, 505868063, 322606078, 413735530, 475356629, 239692320, 210212338, 898357026, 972177139, 746799091, 555366375, 113203604, 4267081, 830856866, 11212022, 423016173, 455933669, 616466322, 864469700, 172884664, 183425625, 352335160, 344698974, 811193042, 912050490, 81882046, 624112155, 828895407, 38894274, 954395495, 955288765, 843487964, 451717638, 893186230, 545359845, 775354538, 249879051, 454449951, 93793658, 953248516, 403751075, 886763337, 433444248, 225208259, 640658071, 560499655, 249686477, 809960001, 188927019, 435111341, 265356367, 80923251, 168220574, 144827379, 801899214, 853304532, 107219421, 692767731, 899177455, 932061772, 311236722, 979630260, 640446471, 973353315, 647731652, 420042866, 458127845, 499500642, 561960572, 796511864, 957021993, 524288246, 625018956, 124979198, 538872325, 596604466, 147077529, 514344992, 367908730, 943610816, 318110276, 158365486, 136009701, 596398084, 394558200, 640841829, 814647426, 126372037, 482872713, 70206090, 298155926, 215526788, 122512825, 413718236, 671668320, 906230637, 590881442, 579603923, 97970946, 522820123, 402922622, 84755917, 742854512, 690120072, 359110696, 652681037, 87512559, 451083446, 507524196, 693139907, 123212503, 728367142, 946387791, 390453919, 553436885, 546421403, 586103897, 263518632, 49653336, 635779485, 587591093, 440057572, 396525905, 264133766, 237293933, 69705031, 214669310, 906183117, 144999571, 637142820, 524603529, 537201765, 624764437, 631871994, 175661382, 990078449, 217399302, 445505865, 513447680, 249762814, 750517993, 587102047, 334655758, 961498506, 69531731, 250639217, 500083391, 535134723, 44683139, 27515731, 925569051, 672587659, 831439160, 704996566, 376884283, 972263884, 253299984, 908933944, 312853683, 718551034, 554563418, 349974679, 495183847, 590364939, 544503339, 168301531, 706024186, 789638536, 854128005, 465929549, 851347935, 380230264, 23651826, 502035915, 39338572, 816994527, 608708811, 243615828, 961046407, 856946654, 47895047, 891715516, 213478018, 798046199, 105081058, 721444184, 201015131, 409281710, 843379827, 154166513, 105459652, 972511493, 111814207, 354513731, 834885417, 107774508, 935670343, 959398237, 557934101, 369446234, 842205167, 819485372, 144459721, 186242778, 956728263, 161758773, 724800828, 748657070, 723888358, 615071379, 83300597, 347696021, 39863362, 65654199, 297969568, 492145430, 57150751, 872004830, 790486146, 748053999, 580133644, 937373990, 634534846, 731110514, 562263989, 178763650, 241270494, 466124052, 503831811, 424229713, 806958152, 163365191, 962707404, 601506629, 903701746, 937502211, 195451472, 751785237, 887070863, 651408829, 723244412, 377300816, 485250612, 146048305, 130888421, 800851611, 766833166, 533039973, 156145645, 664923875, 925913308, 665908352, 434867460, 849050762, 926054768, 655023477, 824995519, 825027742, 968559719, 494980829, 961095020, 525579736, 61417031, 891004821, 446542944, 776130338, 604443668, 606646067, 886593686, 789821731, 332281770, 281310636, 165969168, 936036998, 999031372, 272940236, 328487495, 669903595, 46677491, 376107739, 75798362, 805504539, 430559708, 603086921, 639287253, 325395301, 929904486, 96589773, 956442089, 521367429, 205536308, 18810024, 369176438, 492889162, 225787333, 384903597, 643272829, 481122002, 103897346, 866326301, 828948615, 437942620, 390273266, 895785559, 270129591, 299088555, 634518799, 508209157, 658682738, 239554916, 267183719, 792967563, 185808365, 812123395, 556350645, 995198723, 932303855, 719874277, 348039842, 504704448, 783193041, 765296969, 750799544, 764696883, 313131186, 348354884, 391164736, 676678204, 152087827, 763223279, 989511935, 24525902, 956722101, 134250979, 929423087, 428825236, 333540092, 811441477, 384767902, 61426960, 242809684, 438940368, 692525056, 675869704, 837531115, 579068380, 67581214, 282074096, 659525164, 980665018, 273204192, 842909314, 753758078, 211842978, 541521253, 868830719, 897693726, 556681298, 515199766, 628505226, 563075908, 128836088, 535579156, 608074871, 552563613, 99082630, 82813797, 772220549, 851736905, 406873266, 28174616, 417210675, 30480045, 671577018, 204752892, 150469941, 505808563, 50380084, 63057962, 397251641, 525022445, 261936263, 237138322, 942136085, 509429752, 664096040, 298993461, 107859043, 204289019, 411723303, 545809561, 885721792, 81795185, 946687114, 269168560, 289432859, 436168586, 215377087, 592538990, 682078693, 583412505, 423267469, 672218967, 1951526, 959699821, 352400593, 955513071, 538943806, 273317688, 366438816, 370312809, 743793131, 141387651, 132534063, 128151418, 646965501, 326908726, 278305459, 888693872, 356018145, 7003575, 912599512, 46689707, 509091550, 969189896, 153210644, 53517835, 268705837, 692324551, 644324730, 837646980, 317248953, 152992501, 992332844, 900800630, 172351671, 594538559, 108528712, 494793160, 184720082, 244114256, 4256611, 113464506, 434975965, 343191313, 627413257, 854260083, 495104278, 404341499, 846032101, 782819220, 261219297, 219029843, 514006212, 779951538, 882231934, 909902337, 7220916, 132848740, 574848090, 243139144, 18332526, 290103738, 280556685, 363501520, 969990059, 241311889, 877598016, 596187317, 425106122, 25737316, 100633757, 370330400, 783751878, 708148600, 69028075, 602382953, 87099333, 418282721, 886922666, 463010561, 808650466, 542305108, 884291776, 190800153, 639131934, 696015542, 171390208, 22755519, 301545693, 847412127, 960086178, 582857610, 359496785, 811901532, 337730113, 839749341, 430915187, 806570478, 506321278, 65384854, 678695283, 522152863, 79099935, 1806769, 119198764, 9705923, 101191782, 723729026, 958576303, 824705215, 130741775, 864789218, 376549394, 827231989, 461617455, 538883255, 18411001, 367836360, 906394176, 267702577, 652146789, 790697561, 727123606, 232734873, 893471021, 682154077, 606179356, 939537395, 929766929, 545927556, 223124957, 504892117, 344112022, 795010923, 986176193, 713871477, 150795510, 832961798, 602411624, 623220220, 769797910, 986943371, 602151904, 324485259, 680662955, 83237089, 210714373, 287952491, 41568646, 700330682, 155012783, 230653225, 828390503, 412811879, 970189433, 522993693, 856657418, 394307784, 452618048, 418026872, 69503422, 510478919, 670612124, 268093112, 245780508, 854083595, 330818864, 243105933, 633539740, 708457563, 782305047, 203828470, 660874669, 267140281, 407851082, 96536568, 775545239, 211613217, 629271639, 519463188, 554689676, 661028710, 793284554, 481790426, 306639132, 31387471, 796313828, 801475376, 780551542, 156400823, 242561410, 764149766, 507574375, 142780813, 997123558, 439210719, 432653281, 95926245, 952800643, 881350074, 583414261, 394267862, 57817940, 560054310, 552082376, 385175278, 93635520, 445751281, 880525183, 654843111, 562092018, 587868659, 465081134, 394144737, 619020807, 906255395, 549408180, 859466351, 252839733, 429269940, 88642289, 24044572, 241572484, 303132665, 874729900, 293941835, 299729264, 660038412, 667108941, 953779961, 416006143, 693161513, 55280750, 487995771, 99679603, 966398533, 377939518, 700540120, 187430260, 769363830, 31180959, 777821447, 844405666, 337805852, 285154999, 174532212, 778915165, 63276106, 820042234, 439808442, 248943063, 752122085, 601075583, 256823079, 207759801, 555699391, 417952110, 399537044, 477382039, 221669464, 177129221, 937862326, 331467561, 908664579, 414575088, 591355467, 275976324, 458243082, 338401309, 445472130, 54165454, 368142305, 666860142, 508149250, 301779905, 140656378, 365084287, 784823613, 362935902, 30230538, 244616376, 872180054, 553446661, 532924654, 471545275, 223604936, 66664218, 333847668, 385571583, 671773458, 802905210, 643447718, 342077383, 105804718, 665416166, 548501983, 356847208, 382370586, 12662284, 896686460, 295968728, 947552789, 50219502, 352737864, 658173569, 992695256, 254625288, 881768630, 56445098, 795013581, 127009506, 231232932, 248611984, 265692653, 700178149, 418664699, 381363375, 771348773, 257411330, 448607028, 734489270, 761782928, 560764528, 642934641, 836873016, 633506611, 164198650, 300424374, 819074099, 858856884, 795732630, 842455539, 245466136, 826516125, 95739418, 709180847, 50925401, 600368667, 834758583, 605366385, 146988604, 726719312, 134870403, 373808056, 784026517, 719644763, 760375075, 223627337, 162350306, 913250566, 660731039, 101954215, 522116444, 766946270, 148723543, 988420718, 510983955, 431279633, 34033012, 403807423, 906746012, 450851581, 886055942, 554916224, 270803813, 160038876, 85665179, 988027041, 851775534, 797484946, 438177604, 602862208, 602843216, 357055526, 988374286, 718967143, 521154843, 163935864, 375125145, 76878463, 68172169, 647024079, 536896633, 440559835, 854976980, 495126058, 251943403, 343721437, 105914047, 782762499, 522687092, 404020573, 305000401, 144592256, 985133623, 284485528, 490594528, 880565298, 674159608, 997817067, 264843369, 754175434, 13426004, 474387626, 742650724, 947744663, 921868094, 756850428, 905621858, 12796062, 480974322, 832310819, 616193546, 52457523, 822282182, 260870985, 210503577, 659424771, 321585587, 818933528, 896660015, 625193221, 52265153, 308101819, 969626156, 279313334, 44755688, 989511733, 668390373, 849631831, 818503289, 556506323, 203960185, 508176867, 126787951, 581970405, 893175994, 250507977, 388153985, 237017056, 570574426, 188508806, 372754926, 389302937, 569548833, 478081587, 930272567, 990140370, 60016781, 704820546, 414856602, 98367716, 908755228, 172972317, 982819379, 393551442, 303958464, 283212188, 836285481, 418720997, 110186833, 853343922, 558453282, 403897883, 969992992, 192829234, 890048524, 183873006, 28462017, 479841180, 327383978, 529040339, 628257629, 173361486, 210694157, 296980063, 251381689, 201862726, 643137658, 419977586, 543140962, 994284984, 203849227, 897206945, 186982527, 819532549, 345216123, 341610530, 516690262, 973515867, 591025475, 4070990, 489557197, 107067896, 499087388, 159003731, 705021178, 250014987, 999844820, 807927076, 881121253, 655696184, 199547686, 97874175, 912408118, 428393518, 296312328, 724766920, 415500394, 190604363, 330654097, 137874378, 397031739, 548584003, 863844677, 619001838, 440548940, 277655856, 87697378, 773456601, 193927415, 269158101, 884114523, 102823966, 930780265, 743524144, 203141623, 228122707, 482556337, 471351934, 508611853, 404041121, 974917688, 936738099, 1453103, 913757041, 760715939, 202925272, 465115599, 281189264, 470387425, 457190048, 855927025, 435518036, 688151237, 836987361, 655360385, 349976426, 714187394, 923177453, 478725926, 838316418, 186070324, 40596804, 634352161, 693242505, 630484009, 998121034, 750723179, 936249901, 156371249, 882780372, 631126082, 481589505, 450718208, 519259339, 941394782, 897075008, 279782244, 240936498, 551990351, 878614132, 324020794, 692980546, 801781802, 525781038, 631328555, 753447072, 808281018, 714148264, 506533926, 329823236, 465866873, 629278537, 948589710, 127222667, 213135896, 868476808, 525727400, 243794158, 825988505, 549016657, 683385351, 606817352, 813584588, 515653425, 828681789, 261115651, 169376653, 955096991, 829808493, 100127414, 751942643, 605469438, 845191131, 677526578, 297910853, 860565108, 799864808, 448100016, 401149059, 827312836, 136796921, 181156459, 89294667, 812950654, 445451311, 690227361, 662047208, 909447602, 876771459, 316628968, 884695504, 808393345, 349559337, 280036575, 795905636, 987401726, 546584671, 651098415, 732808957, 196339002, 705827073, 584886338, 192100024, 947766811, 100728024, 902052996, 806827659, 139424394, 324570835, 219337103, 790056774, 330174044, 886327555, 91869883, 279367204, 800544615, 585091811, 206791102, 136876253, 76782574, 400557911, 96849998, 255983046, 600487373, 773662128, 838889469, 311661972, 210084396, 82115959, 587732707, 992034553, 255521344, 410665432, 397402657, 268611520, 892949272, 216784343, 786488211, 406443506, 202599354, 645103932, 264498387, 943026000, 602690093, 714082645, 819936878, 562388268, 518209853, 227146453, 536693437, 96478729, 782283365, 540750737, 618757791, 427903897, 550218897, 384126879, 282654684, 993137955, 653883752, 147468793, 775720296, 434689412, 916906341, 131850982, 173815759, 553607877, 993012500, 444490715, 499902416, 722999018, 502380115, 754593790, 474921140, 847806065, 436885783, 285931076, 208231023, 912739531, 703158946, 310235538, 64415225, 999342790, 219223243, 685382052, 505755493, 638302877, 295028280, 825408164, 328787577, 228565956, 529317406, 62715361, 587159237, 362661263, 535841667, 30320330, 788539964, 99245780, 151539289, 297524315, 559458112, 680524472, 374047415, 875828910, 832287930, 506368722, 593022000, 645840209, 432017754, 232078188, 386346707, 851283997, 499281869, 328352823, 91182836, 273322589, 141832593, 947447269, 629269137, 787533913, 783163255, 573561115, 194156467, 846410042, 826262597, 474425885, 488734476, 804522259, 758912563, 80281626, 348358275, 20099973, 572420827, 994581616, 523251221, 630398317, 970011155, 283253630, 103987736, 483332217, 804777541, 705358140, 886032304, 722224411, 877759635, 603928345, 927613280, 322499831, 571503470, 863248795, 701366855, 946234270, 393382058, 166574349, 64220694, 343205514, 669659552, 22991863, 88205898, 104931329, 596486036, 261391139, 546200561, 299731068, 922331013, 220032848, 894345236, 406821773, 632936054, 994292979, 65992369, 805356500, 283788002, 166103996, 340889354, 956463530, 566809851, 662784275, 609979999, 244529782, 254706099, 272853868, 868393459, 493952107, 235419958, 151645003, 926283087, 941530478, 604732753, 721070203, 298680941, 204453734, 765380094, 845992428, 333030030, 531127057, 382047078, 987105875, 9648548, 953258382, 596904354, 985368844, 868193087, 131482819, 965291085, 813906217, 170813299, 247760862, 362281959, 279730025, 296864290, 360485412, 196453625, 563686029, 558113946, 542617400, 768642580, 911424349, 76480361, 84133367, 813520903, 401695391, 913847077, 789600088, 271067184, 91481965, 58324596, 826590569, 230753818, 427810801, 361728879, 330101277, 543390830, 368321573, 672552230, 32136314, 932155729, 710496926, 966297956, 484197359, 937836422, 577635259, 73739573, 825505319, 603627856, 76450108, 539509624, 88166932, 943751293, 470872507, 992709833, 588801667, 932841583, 639774797, 212639446, 484909857, 933933578, 499796698, 238494899, 270970597, 203079733, 972671773, 612850087, 812868279, 659942773, 194164133, 172080473, 623655291, 328252726, 528023603, 370466212, 851506291, 667705182, 530893661, 209404881, 408257370, 907274215, 894940393, 389816675, 556059337, 591207540, 836505339, 863769372, 272436826, 185350650, 330148116, 601168278, 428103193, 333656052, 464514453, 725173581, 305650272, 82462457, 17396138, 635406476, 606468795, 982077351, 362760149, 459835942, 841501761, 660836389, 528169500, 441690663, 889579079, 62113327, 548730995, 885066104, 837050314, 399748228, 904420500, 949906568, 45317094, 606835951, 738992104, 172498695, 455536985, 299525552, 90660017, 895384927, 446573394, 798638690, 449078677, 155370822, 464440649, 177248040, 884460954, 301010246, 40882891, 326284825, 852643349, 639935507, 28763497, 685732733, 398086441, 942884405, 461204238, 32514529, 985985369, 943427897, 118343264, 420124315, 353698475, 659405775, 176027642, 457008753, 731103510, 396994411, 938006504, 50765380, 688384243, 509241150, 483199923, 843116869, 322426751, 941866245, 927017398, 978873412, 492785497, 847248764, 225018882, 58657667, 315242560, 118931005, 134834064, 231769197, 505210226, 858804006, 485934811, 313503729, 458891121, 75015816, 330963538, 413318248, 111308642, 799980721, 635088738, 542654972, 883414954, 679011925, 158969163, 838209676, 536085708, 767672614, 282575626, 408819038, 990318438, 663454550, 304254788, 371197070, 886936763, 432129052, 419098048, 936754991, 492534940, 422999646, 884253810, 102970508, 298728855, 676115830, 90022754, 580402322, 846075079, 858565972, 268214862, 85458313, 644309341, 850571317, 127482601, 563929031, 725526912, 70381936, 334699265, 674118987, 272667414, 425916830, 976144946, 575657071, 726006461, 541774400, 936162497, 936123158, 441100812, 46150279, 628934297, 694388670, 970965680, 196604069, 399655659, 691691695, 538972715, 91797462, 832931927, 588008164, 281316903, 201605450, 873451745, 278796330, 213860648, 68231033, 203033736, 746946064, 780554996, 711730656, 180659778, 251245299, 951915852, 746215481, 462060565, 626014005, 78556266, 485305622, 73486838, 915221567, 544980541, 534382758, 230127543, 222483929, 419001738, 336284275, 456119445, 938243959, 252182798, 554857684, 212023092, 561804790, 574961845, 949945374, 351270046, 810606466, 996645232, 650781, 44930744, 218149364, 33132591, 768473113, 19263039, 304208502, 182644520, 573799006, 341948419, 976621021, 302701807, 423573476, 651313969, 495507117, 621419411, 468104882, 152067205, 695019256, 656822632, 457212747, 611481532, 180192169, 111745518, 378398886, 651591231, 196275992, 903275979, 578065144, 872409490, 603212501, 410283193, 671285520, 211290981, 590817120, 893002649, 710896695, 897826134, 260279512, 343926595, 78914033, 536914096, 875554819, 767971009, 462525252, 925857005, 983662214, 626297747, 310103463, 411638413, 473009275, 915538129, 935946097, 66679332, 770920490, 982357755, 385822876, 127018293, 691556291, 334629511, 377318389, 126587384, 12753803, 819718286, 167766323, 529534883, 877277478, 470667119, 497004723, 289202587, 97180340, 191003047, 132553703, 217667686, 667190240, 285749437, 121053457, 844977366, 965571874, 360201140, 974543370, 955397061, 267364985, 461785312, 933015800, 6914388, 373132164, 967952805, 205501986, 509746494, 383615936, 959822443, 9714390, 130900773, 213462775, 894594620, 416519321, 550236435, 64741565, 652728863, 34342587, 629333747, 590183664, 857570279, 385844207, 403869114, 555077225, 892813822, 124080048, 840475591, 490072652, 797977933, 832374934, 929810574, 540370835, 892860238, 234054975, 69343478, 467204030, 125770815, 851312061, 225205379, 504905201, 325434647, 299484526, 462536703, 44005098, 35883778, 287251658, 865206928, 854859760, 523601720, 54583975, 745281209, 868456211, 176659243, 426246496, 70862813, 315483628, 324472651, 165471423, 290567015, 980314481, 366245449, 483554948, 122386992, 101845004, 624716814, 375705396, 202768500, 942393928, 403337808, 537829068, 18063427, 590455143, 270532031, 725107560, 904964323, 59561880, 377476135, 352263381, 942532470, 134967607, 467319505, 209273812, 654464018, 78292060, 833267365, 755688207, 431231882, 477228719, 705909683, 520938140, 149003748, 601594811, 331600662, 679627464, 247872188, 151569760, 943287542, 192335328, 670896062, 199777514, 128155994, 296432782, 396759356, 602013892, 875136511, 421455835, 426024527, 242859064, 96006193, 982083245, 926359538, 663704613, 233159053, 738530773, 296465890, 244387560, 442487262, 632862015, 459345432, 277228076, 844019419, 561375808, 822063429, 938794270, 910088879, 994949329, 357626219, 566525366, 956947749, 857800392, 106866669, 662299754, 302694820, 941965044, 585824270, 641274045, 768263852, 635010917, 81444486, 31897139, 59367546, 506952170, 280927189, 618789155, 198554601, 592677629, 562008939, 194385339, 228164578, 558542938, 829312502, 436086352, 721145270, 712985686, 790381676, 313944514, 326188968, 811481280, 515293045, 73472045, 473819435, 903710271, 321289313, 662072213, 927836702, 956532096, 683379177, 550691091, 260975321, 250449082, 660683564, 780460825, 531183439, 698688087, 326546016, 630581014, 768467092, 5449314, 939887400, 85867594, 215250957, 365961478, 961875092, 629552716, 176994967, 127456767, 605908677, 819604484, 455133617, 761669981, 388400943, 223460841, 511124154, 735210255, 750121781, 699536343, 284974591, 720792255, 183370295, 698860904, 503644398, 700565158, 335269182, 723097172, 405546169, 906933334, 283963008, 951092393, 440073957, 969018963, 950388149, 819123862, 201844913, 974030690, 521774228, 549087777, 173228351, 114339585, 962440889, 624694082, 909183613, 309172050, 865855546, 143424868, 155970135, 476326384, 121880766, 943408509, 843285509, 535767316, 768005488, 29593765, 803962458, 32367862, 650895385, 506620773, 54108966, 421713060, 6392878, 105799459, 727503768, 73401949, 309204516, 567685926, 894844829, 813576194, 715189116, 240413876, 376325202, 313655412, 506734686, 39110146, 944789116, 64033596, 250693838, 529041151, 270970346, 948524368, 347621206, 886174284, 633431777, 641115400, 230628769, 153621410, 796291961, 71384031, 224303476, 279758770, 815192671, 437492115, 3657045, 436360260, 708615241, 263663703, 168854408, 149060199, 384023789, 6867902, 265598193, 670854065, 702712740, 982727593, 46026794, 859374058, 498346681, 360592934, 988268881, 816381308, 734637779, 746177133, 548399986, 299563370, 668804343, 273778697, 615297472, 39379314, 407086652, 205278171, 870989414, 389090664, 242699175, 576536154, 113988472, 91192506, 272922923, 134804230, 660815553, 317260875, 993501493, 446462245, 741190852, 483905540, 473822826, 276035217, 709860418, 481699699, 755815432, 82714492, 674744675, 714205100, 970218499, 947098825, 750048650, 953722489, 877178344, 481864949, 41079151, 894868083, 182831177, 658506980, 214401939, 131758681, 674371164, 743705375, 106423111, 598303572, 327664447, 461072255, 584731922, 218404803, 234397979, 275683328, 664480809, 738023986, 749148875, 980244406, 189289486, 518600327, 425559189, 16558427, 111244586, 186074856, 209620448, 473819941, 624881624, 949096781, 682779761, 966286178, 997641152, 347242802, 200286613, 50826106, 558094752, 603877006, 837749400, 750879888, 78220039, 628660687, 54109369, 957146236, 193151301, 60227928, 509845486, 212638279, 439986186, 476904893, 850795960, 811420723, 277228411, 318907222, 779375560, 463036756, 377025685, 448577068, 443316534, 569052393, 123067458, 25358834, 224464844, 153100538, 753648344, 782672087, 118112287, 486821094, 26170073, 41519453, 171247438, 971722861, 266223280, 129371630, 847383066, 605439888, 332343387, 62461367, 953829178, 887865900, 256443625, 129422425, 428933037, 675701632, 377795540, 902711242, 931522922, 615068126, 705659661, 591241479, 897183898, 285821270, 877776077, 932049794, 279103275, 103477907, 656360821, 29314470, 164891995, 53762197, 801367370, 97606714, 60862122, 771351946, 79686605, 592317969, 10727849, 62610408, 624870098, 199295750, 275721000, 662372928, 156534532, 798876161, 162665486, 403073818, 672209503, 472435727, 431315950, 991841324, 576536428, 638209987, 585912215, 78627789, 578949263, 735175399, 986189001, 19449077, 742167761, 706452752, 499467069, 941782783, 540926535, 312929396, 372743127, 493140115, 29125725, 133906240, 169703885, 586546719, 824147445, 939444231, 115249280, 589064996, 638745271, 383403585, 934539567, 531017154, 84435116, 985165904, 761062968, 956813157, 574691556, 325503966, 943747187, 982433650, 314216632, 677030543, 897799797, 117569480, 373055639, 646379252, 277911330, 451504089, 44202129, 5151158, 30196365, 64140907, 743399162, 311129031, 776427874, 344448299, 175929385, 524097957, 515320204, 79875489, 855355894, 553558477, 319367417, 257122392, 263114101, 672458387, 902262209, 353661968, 488867553, 411429765, 951655369, 554449600, 937766620, 101879604, 166068713, 735980798, 703354330, 277075954, 782315314, 350106087, 98125954, 48182334, 44024294, 973595876, 273708271, 43774361, 471156380, 29681037, 411675559, 8140060, 271965493, 568233709, 922218782, 418832450, 205146423, 749150142, 56965068, 727055521, 763225790, 260674257, 675833441, 527746773, 279230034, 802643764, 289658934, 207790732, 943400360, 871030964, 744108831, 265290627, 442379554, 183794566, 483690492, 632342630, 4925126, 865481276, 604601284, 665739354, 553064277, 412748117, 585215640, 250418924, 523450175, 901240450, 722010169, 682894811, 490994769, 608850328, 679195348, 228795019, 51315833, 856307827, 21939872, 948329727, 16866551, 814904391, 686285022, 545071737, 977905440, 604357613, 466350106, 421859723, 52917993, 255540770, 847672789, 813408036, 621428967, 768157475, 329256775, 601459811, 657960685, 756794317, 565649969, 902179910, 601943583, 819518837, 299439866, 151530615, 453131485, 368485306, 885016772, 900060558, 495783504, 645187779, 155792490, 180698859, 893890749, 481990267, 202267891, 602378721, 557496273, 913209218, 739638706, 265814763, 227858521, 454050905, 484443572, 295387683, 196055819, 894904872, 239958248, 493605531, 480229607, 283951063, 617357877, 881070207, 943526157, 263762377, 989261973, 359572200, 227662414, 420310120, 808207591, 830578745, 681112318, 609239357, 275518530, 77575494, 313374376, 714155063, 11097193, 254758306, 775753219, 608571624, 626399401, 989419040, 951742762, 888385905, 481676901, 755659834, 809989514, 766871926, 89684194, 951643264, 641938869, 458221104, 394892379, 93986863, 848429497, 170464304, 638612445, 526757875, 977350969, 867953050, 434072181, 532516310, 997967247, 219385388, 40237970, 423321837, 744887626, 715390806, 250162375, 484891575, 141809359, 809979697, 22366670, 944798748, 487566472, 322676539, 2647541, 165113725, 826248271, 951679386, 747050185, 185461383, 206982869, 278414682, 465182632, 135257731, 467955990, 310936036, 894729530, 383536103, 56226421, 518215857, 872182905, 854185690, 742954097, 540472411, 83885652, 949286563, 68240135, 715337989, 36634242, 610570351, 767414755, 426440116, 547553103, 311863482, 388673186, 643530398, 247766043, 165402763, 209659544, 132453678, 693627248, 32243274, 646391646, 698426844, 429844388, 165361780, 230534374, 225736534, 422338092, 952472406, 204568596, 641390289, 430418257, 9747617, 959217128, 4928186, 294517854, 489882329, 814670131, 515370772, 13888737, 282745084, 485320630, 189467795, 788185995, 844636780, 379179941, 981586211, 732081622, 237987445, 185420791, 740743006, 550157998, 791034947, 813807420, 138840049, 45462466, 556673736, 814220403, 948678976, 938547093, 450680776, 950454910, 719950006, 436156482, 823714066, 883838571, 28745054, 864621907, 997633142, 187791714, 15595013, 735777049, 202773686, 721471103, 521765662, 680842985, 719381418, 818931421, 761220918, 604023486, 290238670, 70484969, 89549697, 678868813, 351801050, 608921892, 400720474, 649665862, 949320801, 975155307, 605777073, 743368711, 711848789, 379647710, 647321294, 689051982, 155335445, 977801369, 563979129, 635441491, 186791946, 585813601, 701869933, 86583490, 303757654, 197476186, 221339145, 876569280, 389534339, 640410849, 833098642, 450414782, 821281068, 706388072, 25539416, 973482426, 483122260, 592583399, 493783156, 201373266, 387655656, 480133101, 563204730, 130488314, 998909434, 21054, 401561145, 401974797, 932163767, 52219485, 867062983, 488380613, 25394274, 936553979, 954001538, 338302368, 439701560, 218743547, 897147197, 717407144, 798734885, 233897463, 148673211, 139057624, 577484431, 322104046, 352137142, 406256405, 849015478, 741975830, 91516207, 283934933, 190923134, 243090986, 682363049, 36722025, 448773823, 243542959, 900694327, 566580451, 914450630, 153341552, 333427091, 225473826, 180176140, 159946379, 687024103, 646560043, 310523555, 917372253, 992261001, 784385290, 642115510, 737079261, 302057448, 219026421, 380687969, 156573837, 508221891, 960025984, 740941908, 715816377, 861280717, 326959547, 92642066, 623314789, 686612938, 712263535, 477525840, 772807964, 377237967, 793725802, 342771639, 416006284, 754690704, 554942322, 354296216, 728709213, 155394087, 970619078, 992809743, 642490691, 506574375, 881202229, 876480359, 900686752, 652798263, 387941773, 262778186, 418493017, 520966190, 478708090, 256125785, 195183448, 346081348, 19945999, 738091280, 293652570, 47888053, 153933871, 500466767, 688294303, 695825505, 472870865, 906141431, 850531876, 664262589, 778638578, 955743736, 935536703, 440569927, 994686691, 497234914, 866117764, 292216867, 75257118, 561712257, 612997861, 189703507, 437056614, 256567660, 950181715, 200387201, 173990166, 429799077, 614437021, 593100999, 181361411, 715354524, 713132928, 537113671, 932759402, 435032183, 511297523, 42360973, 941962989, 19798057, 578778265, 676536917, 637526627, 838628857, 299193272, 459392038, 423843316, 276924253, 893163031, 349735635, 102686979, 56546720, 514126449, 869984873, 15427773, 131400070, 457422866, 528506477, 695353283, 592543257, 98034195, 992051350, 999214069, 303903826, 131428268, 789453201, 995596062, 814365717, 281088631, 519355781, 17878739, 557655482, 17542906, 446528275, 203750153, 344398851, 659615317, 209709876, 254042183, 383182086, 784559399, 298037316, 394955374, 212246956, 404673864, 67269542, 405456602, 780733730, 587736473, 674023020, 627877170, 814422906, 205766668, 797960643, 796942237, 781383042, 277552174, 742497915, 945811883, 400898713, 263327716, 873672065, 774931051, 69442757, 45341772, 575616345, 195294108, 728823535, 79506138, 378037748, 401211167, 484789569, 798798226, 400547792, 846884278, 769307413, 235507112, 982532179, 453550138, 739409149, 110651094, 764828402, 534821851, 53831578, 295371327, 8524365, 145716763, 565453818, 70951726, 586877177, 563465138, 60647731, 935263580, 484480268, 760838133, 40213400, 814879942, 54811196, 732773203, 773903560, 36659551, 285260346, 427558045, 671493933, 558864288, 983062753, 297753792, 831198544, 518080184, 763723059, 248165819, 297043207, 543842093, 998392698, 766795186, 349174701, 611849082, 125588090, 84581434, 751018072, 878535153, 60454756, 644602848, 138180437, 312960086, 116266933, 171752142, 781917891, 552372103, 343364101, 14559864, 433645926, 900613752, 474667072, 572597931, 594736567, 552535093, 426132447, 8204725, 226271822, 360719907, 671088975, 565577540, 729629128, 426281817, 621533931, 375056701, 383016921, 95119362, 605645344, 987271453, 698660939, 998276481, 914063369, 126814897, 27615015, 413132049, 717698571, 884092358, 724273871, 186138775, 535953401, 44062844, 280560285, 916734732, 466559877, 23157498, 768236917, 547231301, 847856980, 504799485, 427223150, 376923178, 193732507, 866925700, 83476706, 838966134, 763611486, 736903308, 647431487, 873542437, 55504522, 989472260, 833422162, 834196644, 601679014, 744863744, 841118911, 125687151, 69793199, 875469405, 1870743, 894142291, 441918830, 951124619, 367613580, 65723703, 778863932, 971588814, 24110148, 737557411, 22955919, 325158814, 116558655, 814488367, 613715211, 58198552, 889719698, 455255544, 275664874, 335285129, 528226123, 254694738, 618402183, 74472794, 290991359, 722320268, 813264262, 590677411, 261723054, 815107708, 969834625, 934188351, 654350805, 199597463, 259353663, 502677653, 354651307, 945445297, 484215981, 185445029, 554586576, 525224106, 504123057, 209733753, 216840266, 866475779, 476595977, 202950017, 519183158, 291629599, 260773498, 851682689, 241014522, 490805128, 182151791, 801893650, 407447150, 596755390, 245541479, 325977650, 344179196, 170975887, 917313350, 489939574, 144491271, 669371331, 549064351, 709927003, 429581539, 981335140, 509667283, 649695948, 455721242, 985049492, 372765860, 644446864, 55776748, 415822375, 764278540, 871414988, 547467872, 53214494, 427440173, 38850830, 373131567, 612344093, 231856134, 515967039, 447749757, 798768342, 881167443, 786197917, 479494305, 577598770, 424959792, 88847751, 461339779, 322192417, 583056249, 476144241, 386740903, 459920832, 260728146, 123411898, 16472245, 542840061, 740232568, 345965282, 96328206, 764311907, 922027188, 822893304, 633401025, 504013783, 823012589, 656686937, 690249138, 840157270, 504765503, 856076456, 552412033, 757968709, 267622725, 324561158, 677326455, 952604543, 559772251, 185605506, 571590947, 17869074, 729121233, 880685606, 365935800, 950503598, 159782247, 565103382, 408750374, 372872723, 874644531, 668827570, 909084674, 621049959, 653450737, 765080155, 993407470, 337268749, 356151883, 473727069, 891785178, 212256936, 58107619, 930270869, 296684982, 703141445, 456825984, 230426742, 272619140, 640525512, 976976234, 665329919, 679733110, 326899178, 869586892, 825747691, 566848541, 628057376, 460650345, 3918371, 397137223, 758659770, 38827322, 47003558, 891942611, 77731026, 886978410, 324755843, 327554194, 918554887, 910836943, 907318720, 448004944, 972207721, 504776667, 560889653, 899222674, 279687841, 791155038, 146726018, 402069623, 346981874, 912589850, 594197733, 349389235, 233002942, 583129912, 588478069, 108631358, 183482524, 139278554, 771011188, 730475955, 259485071, 159143071, 818879418, 902930298, 577939690, 494328612, 495213673, 21616736, 418666847, 40236904, 431312594, 92432890, 611735071, 89569837, 331980998, 977758779, 900522648, 693741310, 786106406, 665676446, 456780797, 612086770, 235443311, 671554661, 711553373, 17213592, 626613043, 593874296, 993929631, 677621623, 632007524, 701852045, 363038047, 943721702, 193545912, 350229389, 791384768, 176936824, 104386937, 247876078, 307374915, 153947877, 854443030, 332642768, 720459725, 732397177, 975913081, 461910311, 934666092, 835336586, 459446247, 668612328, 390431063, 606883004, 653517743, 665984019, 305566644, 348667843, 478821653, 496628253, 118331532, 213406453, 140975294, 120232249, 101416500, 677400612, 115729497, 686722066, 768489026, 202447491, 153628110, 994890119, 169495702, 867121103, 575024506, 207109971, 440852651, 599851836, 713401162, 565908929, 445451809, 114213780, 907105960, 455669937, 827695616, 831145786, 119183451, 306763901, 682634081, 886819537, 921430763, 319107065, 123672106, 30023809, 6977217, 219301642, 909445469, 748200367, 770991667, 533938090, 574444441, 302511004, 331666206, 289503035, 978910961, 268383324, 886749643, 363697395, 425588468, 777961468, 417519935, 201014210, 848918028, 260158414, 732388446, 880012297, 758704934, 307045460, 526733576, 244476403, 350002896, 78680058, 189566269, 5188525, 286202638, 503348257, 417258161, 433778620, 892237611, 983257449, 199219799, 577765827, 68523911, 637560377, 999224609, 892553836, 205884254, 536118447, 597054705, 159560543, 656829759, 412996115, 676332800, 855886201, 697014710, 586631743, 378152976, 633012269, 41426914, 608797249, 156815506, 723444605, 871648964, 304768024, 590211773, 146434615, 599527306, 341969581, 898057355, 521123480, 239503693, 598674493, 469726108, 539273195, 931188679, 807893011, 790742446, 48216981, 993586024, 978291911, 718107629, 666689176, 317347553, 857075894, 104603843, 378439944, 981730548, 133578452, 260217507, 732800827, 39081889, 778812910, 299187672, 17412617, 207951112, 101972662, 183296968, 937244870, 963520035, 579576736, 677957907, 6457120, 644093329, 853146814, 356755493, 152576079, 618783662, 435043581, 345246685, 638489614, 388036554, 838576813, 14435148, 217904844, 696611310, 635027725, 905577099, 71584182, 552021272, 843444449, 881034065, 126881598, 207076416, 611370487, 304456549, 854209713, 559624572, 508339140, 368302067, 458503201, 835582611, 290899685, 98037875, 982289498, 41262334, 498471145, 319242005, 134009323, 856218047, 29287873, 435429917, 219510035, 138396516, 141350265, 797219463, 478679929, 783979961, 93603766, 59649080, 565522725, 474523448, 920053103, 320725755, 479389622, 371315075, 451409562, 219284718, 350021747, 888266976, 158329913, 944576852, 7972446, 856747662, 375621302, 530950897, 978664326, 613220664, 915232449, 96206486, 958435191, 785999038, 455857638, 82916799, 684425840, 255425418, 450103234, 548008296, 317897141, 438249272, 693144456, 253431402, 934377923, 194362404, 371475408, 197182828, 262984053, 783964957, 553824606, 618374207, 630211641, 760542894, 730046492, 322842499, 283021219, 743290267, 880381819, 283736242, 507240562, 926891496, 655453994, 656172434, 533794773, 22052128, 108596406, 846498549, 312143763, 499093120, 892807326, 196804742, 674005708, 399847772, 749159024, 213316568, 594612737, 547676893, 863741621, 908592956, 621610189, 832107312, 862292386, 670158973, 643257236, 371730684, 308714123, 693634391, 219545635, 577866851, 797577992, 765772631, 171883117, 985478317, 969798774, 452520581, 329231328, 244498981, 192134544, 53461881, 860677659, 434871007, 297586992, 815733060, 945159703, 820448236, 580044429, 196464568, 707349593, 455095577, 512032507, 637772932, 572144772, 684812866, 754840140, 818161649, 706745975, 498608497, 977097304, 821601497, 27893987, 452802396, 163564141, 231757400, 409009235, 347560683, 411162015, 111879180, 643260338, 591808019, 606514981, 566646039, 9692417, 47743687, 49801976, 677177353, 865112359, 291963415, 610523964, 218150472, 913907815, 145716644, 54241400, 852980847, 418995766, 497540586, 232227524, 407180623, 806753785, 432797709, 107316235, 250471688, 797280882, 291166622, 219104541, 840682941, 225645702, 15115743, 211725459, 324258858, 158953300, 464706212, 844155369, 933870860, 953609378, 701376400, 281361465, 309919718, 683914018, 186030537, 29665263, 693426536, 851395599, 599259025, 572867015, 271688109, 93772153, 878196300, 89073156, 890188337, 614918694, 994934070, 180145347, 878589447, 53673130, 24780365, 677953631, 451844884, 150019679, 162558999, 355888412, 786371316, 914293652, 12649710, 945945507, 303447275, 753800174, 368925852, 875972648, 878250688, 578323114, 510153090, 392500957, 747334354, 967117099, 218668264, 870837984, 722629012, 708093360, 285559910, 232158131, 989472094, 503643971, 798540943, 86960193, 434410906, 329526503, 575913451, 527953758, 9744594, 27998982, 265378287, 258240393, 399784885, 410773389, 280623510, 662996298, 327580171, 951362666, 127442032, 893465241, 292841116, 387973054, 154126653, 193952621, 905040293, 743188171, 9772731, 730020890, 719235840, 492207324, 114497513, 909633028, 152228517, 875496272, 349613761, 627237533, 834696515, 893835035, 105844556, 856459299, 722136723, 232660199, 78832557, 586560723, 928451558, 378892199, 116023602, 483266435, 489790022, 886990465, 58689741, 50535612, 656891183, 43756458, 73128561, 270676890, 271676741, 638599206, 673187247, 433564224, 931978065, 47724331, 692326198, 148556091, 265773949, 581577576, 630437095, 110491023, 228556960, 882922727, 914265282, 785740408, 105417362, 512425014, 524923925, 325575821, 343226855, 533608971, 120392529, 549577209, 488565298, 796976489, 188320929, 418046621, 225469216, 762788228, 945587212, 923055358, 383746477, 83840393, 854546450, 218346256, 444707046, 973805578, 427655656, 332402105, 343863896, 769704519, 583105000, 814753518, 155904249, 88977599, 949217995, 122712397, 896880722, 271379579, 924590034, 239166228, 591302111, 91874412, 411707909, 863629658, 196109594, 153328075, 597630262, 671469803, 688132016, 834052225, 25063663, 303736982, 625740353, 57556195, 813052956, 212772173, 440686986, 259987938, 940017176, 166454603, 806289021, 400764080, 447112250, 642223503, 543699540, 149372227, 643888637, 633699534, 619962046, 566243597, 314140358, 697404450, 74788080, 62310602, 82904540, 179145024, 782483617, 51368738, 976797584, 697835949, 835196154, 972673782, 533366374, 96009362, 20705698, 770634876, 471754732, 547710134, 385654745, 389278712, 895109332, 954365135, 888092100, 683782137, 209497129, 208208759, 221716306, 882386123, 958260781, 590529184, 153066705, 376981688, 185519905, 124734213, 685277317, 884119730, 672076795, 248600219, 864833222, 125817428, 202781648, 844010458, 965716351, 722629618, 812032315, 816415041, 33344803, 761666379, 569398084, 699021030, 973394182, 918973943, 41191371, 82966253, 737481568, 162323599, 208185512, 188880616, 414132168, 740470461, 648696044, 445815832, 609662532, 52214712, 602067040, 399731053, 247925222, 263213035, 847858430, 490976640, 851972974, 997257216, 591854712, 320527905, 768623979, 47534573, 284458852, 548760446, 499588418, 189393592, 856222908, 914146828, 949919308, 503821590, 928895503, 931356864, 69279094, 521730418, 734271244, 98641501, 984528435, 584220746, 683738474, 523451816, 488700271, 516843275, 220638967, 479625496, 262397187, 128817144, 660002309, 733189901, 900033638, 803028150, 505498514, 117861445, 934649621, 22105786, 815580173, 519917963, 888074618, 879088398, 666324862, 529211443, 185266834, 818143184, 976631510, 499019236, 942512412, 220926475, 640567417, 61283604, 38502324, 268636009, 446784509, 111689894, 722967087, 295722344, 995713604, 694920984, 580129689, 853490847, 301463962, 2989940, 604868855, 717939732, 993446592, 811196675, 427602639, 139036657, 252692816, 150264398, 761774101, 160567745, 453806469, 111167234, 717001473, 3522910, 169530991, 810667425, 808568232, 643497408, 374445027, 764092445, 489264511, 523433448, 258040694, 899773898, 864524712, 689436816, 898642816, 549051809, 637780366, 712628729, 470225064, 428109601, 253258421, 817364601, 445015321, 858945925, 348640137, 787863808, 789241250, 614054150, 907831965, 493357522, 365042193, 81720249, 174656091, 801628546, 386583704, 766336044, 201288952, 177914314, 182777449, 595071776, 787602199, 474674313, 904797974, 192224950, 824652011, 975968436, 993088784, 582813312, 613403285, 799363983, 872053065, 51335382, 496726482, 527016592, 246702747, 492037364, 759265948, 524362685, 825891202, 760040542, 669146190, 128497789, 974522231, 73282835, 167298334, 708918567, 942408167, 47571908, 358495825, 255183044, 542972680, 270838342, 86078621, 771123944, 220165512, 465231026, 485869594, 194373370, 244847399, 364236069, 544874218, 309969018, 150695401, 677483148, 536172311, 276035017, 188247204, 843965659, 295886965, 494539381, 693432689, 740688238, 601673678, 60086535, 81370337, 749410310, 455163040, 661925517, 949743439, 679797717, 916626659, 263173932, 519253854, 383188319, 928623520, 829955684, 29101429, 732480476, 698641262, 419587184, 42612616, 18997159, 725586727, 303297153, 671874027, 879795125, 527880398, 866343300, 144692088, 846215403, 692435697, 758234996, 401113187, 31322861, 757921332, 500065852, 590846276, 481395711, 503463003, 475871175, 625358316, 49621429, 167324950, 314101033, 678795885, 800657538, 418953262, 279375380, 640313139, 816021735, 828386438, 114126611, 71984290, 957036301, 561916861, 522036325, 282411252, 278761045, 679788103, 768062180, 724509516, 351594431, 130017777, 621434132, 921312082, 508498396, 896159159, 921293450, 798414914, 804915789, 102264897, 885275470, 99483110, 559714727, 522300616, 800595666, 851788783, 642520071, 457899718, 794219568, 52934800, 384163852, 856950919, 72863576, 716725065, 573824431, 327783268, 423487974, 846215752, 332973108, 877978304, 807848679, 386257652, 210809071, 591882185, 356455136, 121394250, 174545626, 5243089, 995039939, 684731379, 676820253, 591106594, 743215242, 866016627, 571340075, 126320386, 173445784, 336570255, 106839588, 265854310, 666516670, 169462362, 529680355, 384877468, 500905866, 371140360, 799648968, 430122949, 222060008, 958221708, 304116664, 251214508, 89092239, 473635466, 64934560, 86146462, 691884176, 331565297, 492337024, 381407724, 10454752, 39968780, 122771818, 81221699, 245601136, 624934143, 378751777, 85676829, 951573860, 321082866, 227438993, 742994065, 176055441, 66915306, 396387168, 166365520, 233206237, 847960387, 590817893, 167453466, 504100096, 886404630, 499465676, 911181232, 868651972, 203046458, 877222845, 719341463, 902470698, 983918285, 303019477, 248257953, 779089350, 533109437, 275181463, 685370438, 938984954, 756577334, 830095736, 697486856, 197163621, 207471336, 436113282, 312563054, 812900099, 793740719, 517920551, 890713859, 151161493, 959197136, 429198131, 313883027, 561072981, 759270348, 923645435, 862961470, 30396512, 231567843, 213495846, 331952107, 285511582, 411627964, 874707094, 550304630, 517202784, 774531268, 850525201, 62810826, 998536877, 695721821, 879479039, 538194644, 275564603, 688280403, 592100564, 421233805, 526674884, 134435834, 513323785, 984720561, 557588726, 358729245, 797478327, 223140154, 869600042, 251216902, 640060120, 29703304, 684437125, 317124161, 289064592, 484867402, 550600500, 499505739, 821647566, 306623125, 547795487, 72223109, 382082615, 257205414, 827242775, 872124380, 44206758, 623170978, 89642813, 214149690, 243420480, 724602041, 121246551, 417066359, 958122183, 77894026, 850368493, 898273996, 474305423, 397303447, 384179020, 173426426, 953020587, 855946479, 91186972, 512865851, 823848942, 402049674, 709659652, 520375943, 505990076, 706185712, 390605499, 256850528, 810107990, 926829063, 551177360, 553130850, 333652728, 569851071, 587208897, 645580676, 877757716, 944663799, 560881375, 671311318, 914842805, 528967829, 922171292, 341960340, 108231340, 971207784, 411451508, 404659852, 795272980, 185903552, 482616284, 933423183, 281221919, 642150396, 587841328, 984344136, 24255010, 534458813, 355029138, 393941519, 618121804, 852367332, 875134234, 38452172, 915634639, 319147363, 577280782, 309133963, 305231514, 892213602, 192754954, 805013658, 67465319, 841755354, 719974458, 508317810, 528966606, 626665199, 104325316, 935194112, 455920741, 782942481, 563489963, 334254585, 425260329, 624254917, 744570561, 498105098, 9184011, 133184467, 55981868, 836632210, 139612398, 265336123, 639299853, 993697406, 367153262, 633051150, 719118171, 758812683, 712004777, 260635414, 625374773, 556765081, 439494762, 986759730, 596143433, 758259313, 102810051, 797688643, 790444413, 494783161, 83295961, 157847341, 761034212, 782909782, 13119231, 585500687, 776496401, 577769187, 266322780, 836284106, 772229705, 400224449, 595295610, 899731315, 242814212, 925808546, 886449592, 46823654, 447808857, 57779601, 398682268, 735733225, 335369720, 321858733, 776266670, 805368316, 754397723, 832426608, 393941249, 881955754, 280571395, 576632571, 149336672, 860111815, 622682980, 408191311, 228045183, 693023818, 893624824, 119027395, 136567564, 822502787, 200597990, 484463753, 425196989, 817209007, 551900177, 905305242, 461386395, 507703954, 80491931, 514207115, 161769502, 170138326, 958159700, 317044215, 476388866, 693271232, 837469923, 323759295, 255545099, 912836878, 666730707, 456350170, 220171490, 411408034, 185554532, 793326311, 512998884, 990917560, 369346716, 367325103, 580210189, 815607604, 591559743, 528780050, 944633787, 125267143, 349768099, 875712351, 986058243, 14676040, 974834939, 634202694, 617154679, 756739185, 504173359, 816653934, 899273778, 635595041, 512750072, 357884825, 703477571, 763323574, 187745638, 909360658, 998417372, 499180732, 187742333, 997712714, 679618111, 331128870, 271170885, 244972767, 548843964, 431876525, 461530094, 867830813, 229876307, 401204540, 954783157, 347005450, 946501396, 822614672, 669348660, 813614187, 743212707, 199678414, 866461787, 427576555, 834124583, 471564328, 195567168, 525024185, 183774745, 66566246, 591926102, 558184590, 424974452, 754966014, 525151406, 995895813, 561971559, 116249227, 724454232, 495014136, 955499626, 823848409, 742368817, 638939209, 11028125, 67566945, 18265914, 503733435, 96778739, 383126027, 293872003, 251687513, 455769622, 662853712, 44751065, 600621992, 695493928, 746815633, 923724250, 177519538, 366688644, 381020463, 577198415, 948290332, 710471111, 787373386, 586686667, 725532043, 904600496, 878169317, 672731547, 352221637, 110760246, 321847822, 764488090, 266457306, 3856244, 35962689, 170989072, 169815971, 874949973, 853115242, 146357814, 737986668, 298884144, 260242788, 830966623, 914251763, 443873301, 338877784, 190431990, 588318903, 625610677, 60868134, 182753077, 484771568, 636459310, 39260390, 127908569, 691694242, 390567060, 619899691, 500816396, 99910435, 503215309, 973277675, 693820610, 985337835, 386234253, 14838081, 402428931, 149479950, 241262250, 351628404, 986501272, 247018394, 929606845, 749732885, 159213156, 905493280, 847866972, 307508468, 747018475, 64548566, 107858545, 39428884, 574120114, 873155191, 311962741, 669437947, 622056636, 752085034, 527779934, 186681267, 345155360, 805186800, 62255210, 985802994, 62578064, 575893753, 495019697, 558328588, 854891092, 95673938, 724721416, 754217148, 837896418, 786091547, 578787351, 283472331, 209147796, 169267078, 212074061, 858776731, 717142076, 477291873, 228746229, 325995182, 266882292, 884891781, 217131152, 78060228, 714634771, 655514054, 494265049, 653306509, 384430671, 653285680, 48871440, 453777601, 321327425, 526558590, 730359396, 988615838, 397154617, 578783341, 51305724, 924754899, 450989122, 870402932, 357860969, 398777774, 202117074, 824665545, 713191328, 522412346, 576384234, 996535092, 283026298, 715652348, 498411408, 233805629, 665055847, 683654754, 382332908, 393634246, 243826869, 964665313, 62154374, 697360772, 460705292, 26073929, 268967550, 946987955, 446817113, 898829101, 198281535, 272829651, 352440852, 832488412, 144026018, 48767755, 840827713, 246002369, 336244918, 224550902, 459513502, 563158542, 826664864, 906262581, 240590225, 303504647, 419259236, 6843741, 851783579, 483162774, 822422222, 881097793, 354457453, 286785270, 153434378, 277656430, 86370673, 374590492, 265983813, 875442025, 857547208, 795363409, 930992010, 70795674, 923428641, 858832963, 900524126, 592256539, 108364743, 892221376, 491401429, 669845922, 894598548, 489196847, 68356047, 628409323, 691866113, 597471964, 70869540, 199493348, 973835389, 921759234, 370206683, 468243266, 683578373, 154742500, 197099386, 531412651, 714020254, 305706782, 67929464, 747345366, 30139128, 500261441, 132362212, 152025008, 103888297, 681855368, 384079007, 483602032, 666536650, 689057421, 668400379, 885555599, 330765526, 558566894, 937481130, 827564490, 471602825, 142221837, 133914946, 217816509, 271349675, 829486047, 118714318, 456113896, 597307041, 58478276, 492615318, 928443229, 572153143, 146604374, 653038773, 613159460, 395149532, 466176341, 275507455, 22447753, 840902159, 708750676, 657105347, 370402857, 538548437, 945564393, 254471963, 393637393, 115221222, 657288798, 699967235, 79405028, 513558599, 975662764, 57884206, 617623403, 243658884, 284550067, 358993210, 820294773, 527661721, 347204788, 297960802, 501170195, 919172395, 789141734, 296023964, 235117853, 202394454, 266570964, 284612642, 158848814, 166884637, 557465008, 53848092, 845138411, 237118690, 793245319, 719182985, 902521351, 235939707, 404400086, 850491620, 48416645, 249953830, 20103047, 492409626, 614435624, 522469436, 473264412, 68284906, 859152156, 611097290, 655370318, 435498997, 65262552, 500162546, 575786704, 293169993, 661325608, 514055206, 300589903, 930367594, 104615493, 698946774, 183281711, 463479911, 781312469, 114079444, 642806494, 588226377, 69715898, 614339029, 997089280, 355532969, 316647855, 926945099, 427481133, 475727011, 700883379, 283046579, 262217305, 104891554, 87132608, 853085153, 293427977, 845199273, 819141086, 777646722, 285021476, 758783745, 18618359, 71385069, 153597316, 28073681, 541884013, 770577505, 287883293, 749008943, 135232431, 667061643, 465402609, 516867022, 476728202, 42335168, 45078161, 501193293, 35293684, 52808025, 291288738, 675985669, 766904189, 984982861, 126351316, 923741, 311184609, 23529137, 654789579, 957606987, 192211197, 113208307, 936732000, 396529140, 441869027, 59118362, 354322042, 594858459, 51508543, 271655987, 354647793, 931861091, 935606395, 875407760, 460181749, 302267607, 502208430, 205039013, 57705752, 69940669, 800971480, 617866410, 622207087, 145492908, 629797924, 816393772, 679574385, 73451041, 773522706, 887574688, 970646021, 914217074, 670070828, 137266224, 931140262, 778367584, 706939001, 751357699, 138966057, 390612662, 961479349, 868339347, 182316539, 9711469, 252699221, 107301326, 174588745, 819885295, 477874537, 598856801, 821059257, 898331045, 453975108, 969592773, 354641277, 506643061, 134882151, 855031257, 68958137, 716956574, 744798633, 729065293, 474284602, 896545300, 224728658, 828704453, 717071551, 492567209, 34446913, 554195061, 794637344, 790446292, 91966215, 646099160, 44710208, 952526251, 97992004, 152783303, 768768699, 148290004, 351704449, 678576479, 762522974, 884191465, 598213928, 333652045, 79383384, 187748525, 897916341, 6214986, 902627035, 558456755, 513795947, 228862835, 166674182, 345965039, 358122076, 319382429, 880053275, 749193310, 301702097, 367184495, 798843074, 506373867, 593355377, 603108752, 702483944, 499616022, 674438979, 298531078, 271075246, 185610246, 916067032, 580122374, 645255115, 444328308, 76177741, 181079191, 587542797, 711017196, 966043100, 644486890, 388099628, 175189922, 931948297, 232925624, 40225132, 37432380, 130289664, 742368273, 353201625, 586981143, 244863297, 210966527, 112970923, 493823072, 671154611, 733107456, 677245625, 833714408, 552437456, 125583562, 199145262, 456199751, 827428348, 322275563, 797768970, 379486692, 893659335, 408451534, 674636027, 960811877, 458313102, 493221851, 342819640, 256093911, 767018653, 974440452, 89220677, 124864969, 403348977, 335640388, 877531956, 542451702, 662061661, 940256404, 64853173, 98304326, 499639965, 826077138, 373447381, 274205714, 107104035, 417379249, 285343927, 684285629, 502869783, 122198583, 245908964, 26175367, 711966958, 810916619, 202367636, 567200191, 485792034, 611934669, 367264201, 23041073, 531736842, 452607596, 968469636, 860828381, 108857294, 33037788, 760180121, 679960613, 988582155, 584761957, 228865680, 960728907, 382316843, 908428986, 558924911, 649276632, 822711991, 481241506, 81373696, 76327903, 853630272, 89309305, 241051491, 760735143, 278714450, 404991867, 658137947, 554466567, 583375425, 658103009, 507245417, 389344371, 893263889, 778574536, 778997484, 415514941, 786881370, 955076674, 762235229, 471940820, 625042981, 770036800, 2512626, 894662477, 252708898, 695665848, 180884740, 243027530, 916987662, 258921382, 202848269, 429614444, 456690566, 548866662, 320316166, 646731990, 890694391, 593678719, 370769363, 121847809, 357954402, 394963292, 93891192, 924461052, 778378674, 824727678, 231355583, 348446324, 198910743, 359857367, 419458208, 639005112, 615218062, 257635715, 303176213, 969788222, 666262675, 147729668, 869039939, 864611051, 615523524, 711210738, 75501393, 124964334, 614958037, 181526929, 832123419, 682979827, 684091096, 701294384, 272492630, 804314584, 896987502, 883733285, 420289033, 154143397, 729945238, 254147365, 573454238, 924658862, 501970893, 454140074, 646505975, 686393588, 241078767, 164375228, 984022962, 911329851, 732742109, 354368026, 745836413, 268522315, 696904193, 146803174, 58582517, 808105924, 182988037, 99788286, 326655930, 157318731, 271495747, 965703437, 468355523, 47730296, 146094243, 121091930, 559440452, 997847576, 16506142, 327066226, 140800430, 548000424, 555154902, 736091427, 692547043, 824949822, 903276204, 484282200, 482956064, 371547424, 888918052, 937571373, 671609645, 781683156, 201545106, 251195162, 747097798, 137128818, 247874255, 471841257, 227287059, 749552850, 518542021, 953548422, 133637641, 919700014, 595833652, 800593056, 627758295, 932540363, 856671638, 890635060, 142028238, 836096724, 661893522, 434148440, 362750673, 255104097, 661918578, 746903713, 424954562, 757744457, 749025401, 181894273, 29736447, 578709544, 473219178, 954569183, 432857349, 688548975, 740557354, 229656355, 526177224, 860454198, 196687011, 778985052, 435831724, 745806655, 14331556, 189745315, 101034131, 373326217, 149822213, 298017950, 121094573, 631751162, 196180664, 825489099, 37574285, 116256303, 712567720, 689573651, 371922293, 885006047, 537219599, 182961590, 482571926, 477868377, 557893465, 370181978, 102925668, 349372099, 282375158, 222122198, 904541127, 52749013, 431231323, 49003797, 437263311, 801064928, 32815265, 836219970, 704920395, 873082662, 532809159, 602979992, 74672906, 109638935, 719780102, 895436153, 14293265, 822826246, 897496068, 784944906, 406732837, 693216657, 749978068, 75032213, 121623068, 802982969, 627281617, 173467466, 598391334, 439533891, 558949113, 838359633, 49051695, 879958327, 367583986, 913816149, 306302449, 12886155, 589379288, 861070923, 460938170, 873666793, 191168591, 21962247, 90713798, 688276525, 156779328, 432927866, 633908021, 727847052, 702409254, 39269341, 966321407, 320862468, 518971261, 267367747, 172113296, 535161731, 802273211, 727620111, 258910816, 838334949, 473583354, 403502039, 593794638, 249605297, 986824587, 244548901, 981077001, 602457943, 171809253, 883617344, 194794651, 995094962, 279457736, 472593445, 837985727, 587308899, 203541458, 843747282, 505512857, 527999674, 609736912, 331518421, 287368648, 420039734, 1374192, 45279298, 345136096, 890752247, 868966396, 251013503, 607738409, 735061730, 251826150, 489330348, 984016466, 477082966, 938537905, 506556005, 874102438, 722793281, 633823601, 684954852, 247574379, 683080338, 313342590, 165292917, 614333712, 795903321, 415032921, 657192448, 750782570, 775138379, 115636997, 399969036, 60776209, 358208760, 773980310, 33373959, 666682987, 416171751, 434254541, 879507958, 242617035, 219410508, 604838554, 134762022, 903279163, 381601768, 720693033, 239835876, 820862173, 427479898, 476667942, 553433892, 497023139, 874583880, 396155305, 165017722, 785337908, 979738451, 355202845, 688018382, 862016054, 586859241, 270845524, 871749173, 733997, 216835224, 84802158, 119348631, 734257847, 569668089, 477432752, 342785735, 53727832, 914342142, 154406698, 565599558, 224615006, 342954605, 552990250, 493122673, 9920991, 14386302, 839813717, 292930972, 209512957, 821465143, 89266097, 173031830, 879557921, 988121309, 101968545, 325329658, 412193060, 642484059, 48538861, 189021616, 13402954, 815580342, 76925887, 726948156, 470429999, 309480987, 834273975, 435272357, 984530213, 174777005, 24674694, 99621167, 699325675, 787563819, 37518006, 89752135, 154984872, 797859778, 180138743, 418555314, 946772662, 344665592, 969337342, 180346234, 634308998, 266086624, 122767300, 605830919, 984680257, 934623523, 410298060, 182221302, 121243042, 679393140, 49901482, 3782039, 786369879, 834718627, 955117754, 528669920, 374151341, 311390479, 865169458, 165106287, 131485172, 458867254, 541272550, 497552314, 133116268, 513391982, 330979259, 153621659, 729990360, 20476669, 909886691, 537094124, 579317271, 826042648, 222068774, 701777184, 435660528, 287195394, 202009767, 925381836, 132847320, 734617812, 844041150, 183544781, 327185955, 118141655, 575596589, 651106977, 44854374, 574763782, 441977567, 38306333, 170506688, 499498425, 393868505, 611396096, 742081433, 43166696, 419448422, 137479807, 720047711, 22652227, 363898933, 99288152, 232780539, 760695865, 376051420, 917378270, 357515726, 512807813, 331275722, 474397304, 517043098, 591865825, 615926975, 311787432, 774892810, 565703651, 129407072, 150346627, 627309686, 687118763, 567863377, 501429765, 553513490, 383874995, 896312698, 737497179, 304199242, 768311665, 528887338, 926963935, 923661237, 928822857, 175453154, 575104603, 737537889, 830461928, 122328072, 397330932, 302091444, 798076209, 687649973, 733080473, 276689209, 18060339, 476635649, 104039102, 756327527, 878383446, 144857872, 173979279, 944794252, 133240136, 137886377, 946284882, 729732371, 288587624, 935018794, 681393939, 499406090, 154674692, 842004532, 486985257, 282642245, 889659064, 199443939, 286364643, 230118573, 831897025, 375727554, 329055467, 262269448, 586944657, 35935511, 102469570, 648674662, 561315400, 153153078, 859413683, 431830397, 552768944, 855165708, 748185748, 847390413, 894636854, 617852438, 577308095, 147753562, 770539332, 461541504, 510412302, 119929521, 48059862, 647799715, 716108668, 537460533, 769096166, 224622175, 793494096, 821489970, 309025266, 546119458, 235548273, 490260036, 335102483, 261246871, 347638771, 332946934, 742761622, 876683664, 55369706, 56244840, 557333999, 115954175, 568777833, 261593192, 770000044, 503225057, 486765257, 971476586, 139195212, 67514194, 785448651, 129116738, 346198883, 733678410, 487693461, 391718042, 724808234, 150830641, 229021213, 844827121, 834523830, 498939306, 344341189, 550691294, 674394927, 176043378, 391778269, 562714639, 857465196, 215016755, 70365825, 135943605, 955123189, 663971645, 509899130, 54485874, 337964713, 27162455, 293638443, 676710679, 160944568, 617389210, 644044959, 409182361, 517876405, 627088526, 398145201, 887870407, 884696673, 792683307, 36728751, 997367230, 878807856, 992199146, 459771370, 104967259, 583073713, 341065858, 619564624, 895537171, 876982880, 582846626, 558806513, 825914723, 678386770, 893338141, 453160097, 816273263, 185941397, 799466052, 404067864, 490192829, 225165300, 977724970, 947357018, 96674998, 636587682, 985427083, 109804378, 996107218, 678457130, 119996320, 30399289, 367440510, 838422389, 614700293, 18526878, 37847353, 364964468, 273200435, 972765211, 770726, 548621854, 129554478, 715776153, 59982378, 769964266, 105785631, 332473399, 938187794, 154865190, 813583898, 569545874, 851317954, 828908878, 214957196, 246704667, 167542421, 864703053, 923850854, 761468214, 639158487, 389178181, 637473425, 990428242, 970708461, 867379589, 636084977, 146841802, 299973404, 558322717, 860804316, 235349197, 525713126, 87419750, 486373004, 162221771, 423111832, 333084432, 856967632, 948084116, 863006649, 783316590, 761069448, 525470988, 296353812, 122119335, 323226883, 827272096, 449261260, 681745511, 475364610, 296429044, 885322029, 946461895, 633042597, 102135151, 550205880, 37301199, 878425575, 368119435, 24373870, 397447947, 659502718, 723341979, 308448767, 651448995, 97305907, 536278070, 26546035, 930798952, 894206435, 3586358, 726722078, 329178343, 594864522, 217600664, 315637226, 477620427, 542837397, 354783550, 47834268, 243270637, 538895725, 957833531, 880016578, 979912551, 726766471, 823892324, 236751323, 151918933, 686914341, 348765535, 155985109, 833734217, 687994461, 562310722, 738365448, 623134428, 885308088, 507212746, 826617803, 736992824, 629217337, 423282393, 906732392, 208580809, 208659708, 387783740, 741053260, 933679582, 291648149, 160599425, 171541971, 860119584, 83700014, 796530485, 615603062, 129112805, 47738935, 507678634, 188357262, 190051897, 732060106, 700035815, 943316067, 428803594, 941056890, 980833147, 628845585, 607157254, 342667842, 905724635, 715774226, 724025378, 562046347, 715834465, 558845623, 318847960, 267476602, 830219294, 626770416, 397475144, 562459251, 522638519, 972528032, 558484956, 751373083, 98547373, 226537728, 749514626, 200337076, 977338044, 533404004, 180050450, 82313317, 298974043, 129025622, 28888297, 699188280, 368276346, 480307351, 558610533, 746581437, 502219657, 303187162, 933406755, 803544032, 132702102, 924221379, 564981404, 367781510, 279200114, 820036472, 909335515, 627951029, 698471386, 292961266, 286380086, 237271302, 506137952, 429852428, 389217516, 649473374, 622679620, 689098643, 845981376, 492557047, 61905273, 20674414, 460379769, 905991610, 411031005, 332860937, 323738825, 490419734, 92752942, 409709946, 53120229, 867670070, 100945873, 884335891, 201159534, 751491699, 683398443, 39904840, 470689790, 742412862, 651793359, 485308383, 362410742, 701709139, 657511372, 678972628, 158837337, 741693573, 422189839, 394774960, 440659619, 158440086, 614932298, 774146499, 482021888, 379658174, 592133461, 876675071, 31216353, 837478847, 605552155, 914575631, 996825842, 270361125, 937354279, 430482583, 980964078, 493322882, 228384626, 446238962, 988768825, 640884940, 489340969, 861396926, 87810470, 861133884, 673807428, 71686065, 167674946, 351765953, 574715393, 703265892, 865834626, 901743937, 333458924, 348663786, 571751302, 577451071, 153855683, 427118499, 387640637, 555865209, 646441391, 68486576, 796657118, 576070758, 124912381, 171306870, 474418259, 121284339, 116458433, 892621779, 216124796, 121162893, 905343409, 691994531, 989612599, 166673927, 93865642, 947935921, 143739284, 828954516, 25559166, 361930077, 473250058, 925164624, 757584169, 825330703, 436200287, 364238040, 800583296, 247299251, 599628858, 638801053, 904272443, 982981672, 178990315, 641738806, 485080390, 906878756, 838230429, 270805528, 331368663, 221587895, 990535023, 268162888, 45739148, 238795459, 252643903, 519768275, 39294743, 399248490, 84644819, 330332785, 878740682, 195334245, 257144244, 511076309, 606247166, 129430347, 7361645, 188395308, 977426965, 865069324, 806724605, 943448280, 213865119, 359794663, 745556292, 644202990, 997585968, 425511657, 70559426, 659904624, 872991144, 409133358, 472113610, 547353068, 948338760, 747614394, 22366729, 410720983, 356479491, 808697534, 243779181, 497642313, 820925866, 976777619, 564156186, 571544, 50189854, 540204092, 799187583, 795316290, 462480224, 571234737, 219790749, 938744709, 796719255, 16721064, 664462655, 387890517, 705934661, 239439765, 54277823, 180700453, 328080256, 997453699, 714397934, 636663087, 396625904, 1292071, 165275685, 650216787, 383965394, 402420924, 961293862, 532211372, 165594752, 856663969, 148979919, 957416937, 32588472, 242710874, 662166682, 531007062, 894432641, 291742502, 365272708, 635690439, 461449141, 636386563, 325780370, 758827746, 250248335, 881858420, 748677529, 907114160, 297277325, 193223627, 44818446, 84801999, 583686996, 146303235, 169375783, 103947930, 275689507, 134427244, 774239895, 211988144, 761245407, 250693726, 763879360, 985152783, 508068537, 150523411, 267928625, 346670501, 404062423, 780490325, 615716428, 774435254, 868274576, 119912652, 288146505, 613371017, 673327238, 435575783, 669410344, 299515091, 336707476, 225353283, 58132623, 423189359, 771905798, 799795549, 793626717, 56912334, 21291534, 376365881, 704993856, 21091185, 971174317, 277347129, 249454642, 258378852, 570149907, 721166307, 973394961, 27741646, 459380388, 270161908, 802325813, 632058941, 898675620, 644219508, 856262729, 891059010, 476377335, 28879885, 81142116, 844787872, 474786531, 593540810, 643932929, 305857176, 417762569, 126040316, 90944985, 694575321, 597017862, 89927941, 882904967, 839054042, 435400808, 879389241, 180176536, 737411589, 284240335, 299518453, 249428552, 34638349, 422336884, 667302242, 64893471, 247344957, 42458779, 623411432, 644354015, 746873283, 495850023, 628293369, 749808585, 189539974, 546079436, 473267530, 421040583, 516609044, 487827428, 841809419, 685866090, 542748631, 388924871, 464834016, 140422176, 701278837, 834603168, 97877677, 60237011, 22129447, 816306428, 672972407, 536866322, 143972635, 210849774, 144662678, 6284064, 320921508, 357707542, 987444753, 868989664, 489182290, 754625436, 437695188, 389861468, 48836987, 257799911, 135542341, 43946113, 737535040, 169733820, 168772996, 910618723, 657445874, 105844328, 196917751, 495105844, 378017943, 519251540, 777507563, 772364718, 351107823, 881038193, 672102278, 141142926, 593202143, 293218223, 118024658, 570631157, 712902402, 962185578, 94244750, 219337916, 653201267, 670982196, 332486261, 392657696, 139113495, 786344582, 694147701, 596005622, 462098236, 825846341, 309410866, 381439786, 421634068, 34275541, 358571342, 114946180, 270686236, 714248780, 369940549, 594893942, 675513988, 6700025, 128853925, 111515371, 908956111, 567850040, 161463100, 505250551, 628315252, 215107497, 184343286, 238774926, 83321972, 924742455, 434738482, 354944717, 814887163, 927762365, 480969598, 983020663, 549139775, 98592116, 862736365, 29665491, 516923543, 657865435, 122290128, 768195076, 611986646, 443538649, 752482366, 659297244, 352427481, 917598816, 777186005, 273913329, 803212090, 834102341, 822891600, 166036501, 278430851, 992600662, 410072580, 193228811, 81140301, 724944770, 726578016, 814480572, 319907083, 116044873, 508451343, 544391980, 804926798, 986353185, 137046820, 805905604, 116602917, 447805165, 8516411, 43878812, 56636107, 254557373, 669843307, 105610397, 227035262, 924834231, 260239851, 926756962, 64918668, 275760222, 226460915, 257789478, 751685483, 560820827, 266618284, 57020690, 112487108, 254312280, 101460904, 659712626, 139219272, 870688914, 662863715, 838737974, 752592511, 454284746, 184596597, 23323257, 766398674, 893298351, 913770726, 372740599, 826842877, 88855870, 791702377, 569681086, 518726897, 957701972, 52869006, 103111253, 536902718, 33722202, 531215859, 870101030, 610135865, 862027248, 63467642, 669619876, 966360186, 864399083, 895040808, 191021985, 46320328, 335621012, 237136999, 212477225, 527143817, 573753646, 837250929, 925283302, 915939623, 973103417, 385486689, 923698202, 746155809, 376261716, 451988723, 754253309, 938837054, 485645744, 663144111, 584141185, 213390845, 414893883, 989062689, 134980573, 808212929, 333825958, 203990841, 784129672, 504616920, 428985371, 787965485, 451278215, 774066555, 262818543, 946690453, 143565364, 859213646, 404630278, 657377903, 940594214, 483755162, 49723608, 596359566, 44427972, 961268805, 603154929, 439603307, 970295572, 745400201, 296514882, 114233777, 741099698, 52667186, 941860668, 56333467, 417651804, 982794169, 927668982, 1185338, 213688237, 223403082, 451983254, 261322834, 871564211, 413643644, 639174281, 893452099, 209021625, 317366108, 389727981, 878554477, 889374146, 578090177, 335125240, 760801232, 102274063, 893183385, 591959505, 190054857, 820539006, 240852185, 553909652, 392643256, 163393301, 967093406, 262529794, 37180942, 445070792, 537357205, 368204536, 33647140, 977251845, 212100016, 876234141, 406695559, 260459154, 5530499, 557379128, 918232892, 336902951, 810960089, 203962455, 670798581, 635820767, 106947560, 145641081, 334535449, 514735050, 616021431, 548745232, 680421683, 267488524, 882703997, 739614278, 757192055, 404587566, 462098431, 618604017, 876863091, 458684844, 428271389, 252046105, 340182198, 999695048, 998367669, 348068023, 713404875, 96082561, 362109738, 170356965, 768598187, 507620794, 307418825, 564521973, 113729829, 401513316, 934034314, 63068064, 368135907, 35748766, 799972561, 528795198, 57247638, 700441652, 36405356, 286092229, 958046611, 887426488, 374192432, 887980933, 691750601, 941770152, 963493619, 602652506, 221059030, 708588788, 384328422, 526312328, 516210857, 24427067, 520273815, 802420542, 893055425, 32809887, 585662747, 835573654, 820894458, 700544516, 324535972, 800329620, 531623728, 90432664, 380037855, 754415940, 745557563, 733681369, 542676359, 755245899, 722362010, 982869542, 388407555, 821204005, 143501522, 270375873, 502816655, 453744111, 454419777, 918710035, 865771592, 878644196, 861417901, 967085083, 500682781, 374234038, 77064132, 529638149, 170661863, 838724887, 948427077, 893231857, 183813010, 472462641, 944621621, 447925186, 784168192, 951974345, 272373498, 128376601, 608971778, 411474066, 966929330, 800734533, 275377981, 963560890, 332402058, 833180303, 24548607, 453091875, 123992567, 408847054, 566859617, 114846035, 96916198, 877100190, 830312083, 479875582, 391685105, 797991888, 307876483, 747138252, 634176206, 601692148, 724115897, 193507552, 285808942, 772275311, 51750788, 150881849, 430277410, 332856545, 950910926, 237877524, 775491151, 982285081, 938383782, 617454784, 506869713, 750471174, 407236349, 727694861, 468652569, 676730585, 42364946, 793538611, 961591914, 202451814, 539426498, 753886717, 818276938, 229604039, 610964844, 434657690, 114046986, 507953209, 830268816, 608420272, 411644282, 769154665, 98984470, 913455069, 979848656, 965317705, 576196922, 98150254, 485776667, 830735909, 896888000, 659713743, 35782508, 427405027, 745248318, 900939786, 679183912, 168737041, 98580345, 880742427, 187776000, 887097505, 182642515, 305621981, 254330139, 156189147, 150974412, 600581452, 477793054, 90395591, 315998947, 456311232, 91270646, 399436886, 496578771, 655940822, 671815084, 566015113, 832677516, 395703449, 573852390, 299369692, 637757979, 394364700, 56012680, 678846306, 511248763, 76699597, 561240396, 911577208, 918715799, 276321298, 637698431, 106709715, 703195964, 41571457, 991227916, 357149259, 442687666, 669025428, 505467227, 606229340, 550479776, 959201277, 441603312, 763748009, 387852403, 814089369, 781919261, 555744302, 629169414, 755057909, 364651255, 632352857, 410806672, 920662613, 7593819, 694330406, 685066385, 19448532, 283393348, 251877038, 975394832, 224960389, 509288111, 786894407, 412220128, 927583709, 547339183, 402770161, 311073629, 755903906, 375457727, 750180748, 376688768, 957741806, 592426351, 828137560, 267675926, 92687347, 815898085, 286835915, 806576676, 898537029, 796110039, 825429900, 913350700, 676113570, 49306288, 610455365, 369562632, 716057127, 429319451, 856671162, 229421463, 885574049, 571203668, 405213960, 449640368, 805365720, 149636559, 638873336, 312190432, 441624712, 581710252, 198260826, 304720433, 699661421, 87558408, 771176413, 239384624, 284291177, 673208080, 805211929, 272634760, 298559345, 530255829, 261495883, 316677176, 402206024, 25170806, 346491832, 686847927, 315100598, 933081404, 589140014, 784565705, 23131448, 80866104, 915998192, 525155667, 740267085, 840497982, 79435648, 643778549, 747209371, 609084263, 483219155, 117430117, 737366117, 895988299, 961970239, 188572863, 478025770, 32805671, 227762187, 574099630, 560346985, 389080407, 780796895, 470470859, 667176559, 688336429, 622376517, 279092933, 969217355, 154092943, 561061101, 21156721, 99733022, 535364145, 753347112, 262591499, 4430007, 189111835, 542515846, 632337532, 982244169, 751682102, 4867891, 65143201, 64132330, 881476013, 748925583, 793409369, 207241349, 387694733, 319493451, 333621203, 113371921, 192260356, 374281248, 362142704, 683951754, 987398455, 496748520, 36291075, 273656605, 715543545, 618530065, 339599567, 698660454, 318263316, 622935794, 979459612, 60297760, 771354349, 20985885, 647199115, 981659791, 879820359, 457960656, 201855003, 649825916, 446065258, 868924170, 979239156, 697627735, 492625110, 569789209, 606550944, 907278120, 175773085, 115253492, 700189402, 115486519, 760763666, 759054760, 882343779, 102725596, 994276647, 178128917, 470750778, 63362327, 989941424, 21488471, 69932603, 430105155, 587623761, 321185387, 295564233, 872864380, 696659379, 711304133, 245994939, 995608918, 134985336, 15742661, 383492925, 393630626, 560655686, 811361154, 232194294, 507120689, 396224386, 377623682, 387542784, 608046668, 348647258, 291801493, 271714312, 154463315, 123853573, 156546985, 191859928, 890591711, 469004085, 184173167, 531721968, 180944472, 596583248, 220280553, 876628071, 895789840, 784270864, 862057401, 136502290, 93018023, 964293972, 344713513, 505710572, 902059424, 492676284, 650241664, 727239166, 962116839, 52088322, 524791264, 182897276, 44669300, 990757345, 421581928, 141695531, 41762320, 157447470, 78205657, 816762231, 485305997, 73885679, 101224052, 987359752, 154812022, 789785417, 113738903, 375064025, 278117670, 489060554, 509245758, 385387197, 596552642, 760846257, 915619602, 842969661, 35271739, 70457626, 686054682, 441249022, 628952103, 972145344, 261177805, 569170016, 652629235, 419402625, 401567810, 182831913, 494400756, 657547797, 574443571, 69358680, 638184947, 113197585, 855741281, 112331137, 695446237, 633404352, 303211440, 764305931, 556441609, 768830979, 562232878, 864366688, 738749983, 582684613, 552089441, 619818705, 427547467, 544786455, 276065284, 314217594, 890935127, 46348981, 246695326, 746137627, 294801825, 339240388, 844356735, 230617402, 52187203, 101258781, 533323872, 870239296, 879229899, 489203707, 962357695, 262336243, 899403718, 347041794, 549510641, 789614054, 982122537, 793079057, 745332561, 663260893, 312401600, 783694254, 510463712, 848879321, 772459956, 526414759, 847320526, 39489282, 677045571, 748247934, 425875146, 798119096, 981921836, 342636013, 771083686, 86774005, 171382468, 302657404, 438865488, 814962936, 672869091, 474149587, 943875711, 339956402, 489506984, 572432191, 138101702, 568051355, 61043375, 683851800, 664871665, 38523480, 540992464, 138881569, 899861973, 10173960, 730068367, 851653020, 606171592, 51873519, 998767970, 164875788, 648645474, 181731368, 818660743, 813896338, 950134816, 873037824, 606741174, 921995161, 173930053, 192388972, 61872651, 869781637, 189361832, 350159291, 908384600, 116807156, 421149391, 901030099, 973167955, 580214947, 806227615, 57865086, 409162875, 779974339, 610140379, 170047330, 425536347, 194944852, 341692654, 584151002, 644237317, 750641556, 741781140, 627742019, 587907495, 428132443, 523010667, 710164603, 282212464, 538563106, 150550479, 633540531, 298094704, 60958326, 280912576, 874609632, 384864132, 819178163, 630025394, 329194640, 693823356, 134463809, 62942561, 361688075, 487437754, 307583319, 736304355, 175647120, 422154008, 790137466, 301037080, 567036103, 838084597, 735805449, 762447732, 508234694, 394433519, 214263384, 530715698, 947709355, 107960927, 13700941, 529568205, 3692670, 17875892, 455421345, 669250254, 821079413, 795243322, 243504258, 508364618, 817826686, 375746990, 240690980, 977745602, 223930253, 289093164, 67830373, 939634624, 706842300, 641553594, 167208369, 612989277, 496035240, 407100572, 502743199, 979479527, 258187910, 997165936, 249919556, 630603642, 989022415, 61292619, 285178098, 896903282, 273021775, 654191491, 362884132, 319017616, 846329004, 110569248, 33219911, 309035450, 256939984, 241461451, 333652400, 891138806, 788134900, 716022500, 942070368, 603260191, 142901214, 985474290, 390404889, 15131759, 169098548, 46178956, 774044972, 803914870, 46332327, 118277012, 914476816, 260194153, 859969133, 47550912, 786626264, 865722771, 190877146, 742966833, 769932351, 281157757, 161648489, 809908842, 295828216, 581288538, 928885340, 41076673, 369504825, 761627881, 693004429, 534066290, 105075533, 137160469, 835098603, 347043153, 633159287, 867455240, 74134198, 579986039, 996146200, 993731174, 415355348, 797311873, 209703292, 452145494, 423763886, 513146895, 778427594, 74510852, 252060113, 519631047, 636859237, 51644965, 141019544, 939418719, 406342395, 769249150, 466688319, 549070844, 689924191, 263200652, 704216155, 14326703, 934097964, 117607050, 498542961, 841617898, 51827022, 623573576, 510290201, 734987988, 564341521, 196057046, 689003190, 537776445, 405709837, 598712833, 569344658, 856531975, 389128540, 78063444, 424377894, 228860239, 319009443, 188288993, 259894459, 899623746, 185689466, 217561158, 723679261, 304451226, 846487210, 958620415, 77364386, 24361579, 358640181, 278728384, 137662694, 786914149, 343647714, 157867592, 62853538, 351621490, 594825339, 825256902, 742134343, 13875739, 852998218, 75823732, 431763563, 97232970, 930464216, 794066, 397838739, 514489606, 521656998, 517729661, 188853438, 391163620, 987907028, 517888317, 742286418, 620929215, 447635111, 81679614, 79168665, 311103125, 168662719, 493448163, 527537910, 455036004, 573786944, 42893297, 392852421, 340821374, 940595945, 122910696, 236761387, 232495771, 36334660, 35996641, 258565750, 128521672, 394827736, 708322144, 919281888, 708959957, 280653211, 480709166, 822745179, 491878063, 454033734, 414771611, 111767362, 704931958, 589004106, 380360202, 948271375, 592534264, 966308667, 197571913, 66037590, 575965646, 307309485, 109247777, 935360348, 880193102, 120010364, 6558485, 895266732, 949116416, 451474270, 154061967, 916318021, 637528074, 963704659, 863780465, 878025487, 334353177, 867329393, 375893458, 581405644, 558447280, 425749444, 867718049, 510312284, 455330601, 417161638, 475494946, 929844013, 8068463, 731619888, 79090892, 804327547, 299761338, 71731624, 34684983, 621346797, 452356578, 865216300, 356688118, 349708895, 681942053, 212166375, 295861991, 345119864, 177119219, 759377260, 958797983, 874816462, 171209813, 148741756, 206365680, 772831467, 985497654, 368019837, 567043852, 168138054, 706303074, 275902162, 491176103, 71985993, 951124541, 262957790, 945105760, 133116237, 901268297, 576101661, 719308134, 879057837, 446804163, 410172013, 44227112, 95050654, 680947880, 383580266, 329147949, 483910609, 302414474, 907036361, 383981624, 275625687, 850119192, 939254226, 446601537, 796607026, 317596280, 826057376, 458294897, 592472619, 940626067, 278994567, 275115012, 75910199, 233471724, 471989551, 981993357, 206677145, 935301624, 361301011, 602711543, 865873521, 938933006, 996442703, 658619161, 630284061, 957927851, 919604889, 212474957, 892259340, 46986089, 977072, 469656932, 817671360, 708193390, 478764333, 498645589, 587980499, 632290459, 916555822, 63756097, 156617617, 246097966, 180462966, 340448782, 526017716, 772028165, 247661591, 762637959, 913907244, 321511956, 128520688, 812569279, 52873479, 151285613, 436411464, 20097253, 460066439, 907224203, 207241055, 99565531, 749063189, 574936474, 760694038, 270958932, 406982003, 324760262, 247214503, 875205469, 226381998, 965893931, 362510330, 562771948, 458780731, 255696235, 909887844, 790388504, 126774073, 331471215, 573971726, 343093599, 658309421, 220618360, 565799343, 399177408, 110190257, 563762669, 571530633, 78807756, 446745673, 343874930, 78449002, 448971481, 751776343, 972403633, 968426952, 245958296, 96359839, 732686679, 843586877, 51618049, 826190428, 187154218, 792645532, 905436258, 857214000, 434921150, 476671903, 311953165, 656229434, 776608757, 705483165, 889332605, 87059939, 274365885, 705345213, 791595158, 9841471, 929331235, 720420057, 317602020, 490820349, 665606686, 320601802, 77835311, 945600392, 713393921, 757871814, 528872031, 988456276, 401784670, 999422061, 396767000, 553191824, 248910981, 906112396, 586504044, 662032839, 817144729, 512150752, 498646047, 968197779, 337870345, 123693361, 684558588, 842675669, 942123288, 630482935, 561612465, 275960037, 257299997, 477959512, 110816099, 941922605, 717936345, 439962973, 104720634, 59634788, 994997844, 929064701, 940745464, 16816075, 348884833, 773540914, 709106836, 751583988, 227275322, 462868287, 265432976, 632302205, 716666710, 17805293, 353692894, 239462874, 924121674, 555804683, 128819458, 7661619, 214243050, 798890618, 532686535, 181088968, 537033398, 206932964, 146157882, 664287608, 203403152, 522390522, 220818920, 556987265, 649447902, 380450570, 599089899, 841084637, 400145164, 62322925, 62329690, 22685124, 920892808, 297788887, 948087604, 804356724, 732463191, 226740794, 467709114, 497133323, 484570303, 854496860, 338578801, 518727844, 609114564, 608623087, 539730502, 306844264, 713261506, 729691068, 394522158, 65912771, 125102311, 578860054, 456263470, 630908683, 980915255, 94436754, 861921701, 965386944, 704694604, 385800104, 757372754, 62467614, 885141247, 690696268, 992489732, 480982629, 563527037, 741551919, 252909151, 469745181, 44355375, 532373634, 923649628, 754913709, 223003140, 112181549, 451062519, 565487523, 473083059, 942726443, 961246409, 162323909, 491164231, 414194022, 974280252, 915432669, 101293932, 92263193, 611608793, 753692360, 662822728, 160923744, 963775925, 678188162, 297090731, 968796451, 70760852, 678904222, 345389676, 56605914, 152355228, 307612797, 67480798, 471992745, 1710180, 415336049, 960639433, 274481573, 840404163, 833032837, 892794384, 560535258, 778894146, 372155525, 766259521, 743825859, 537402734, 390996337, 342371243, 552508637, 860764394, 340073333, 683577032, 95977566, 989314894, 990750248, 982420920, 490596436, 510861097, 247936929, 378004226, 320216956, 578692637, 615157606, 56450883, 945065365, 929653915, 528868913, 726666426, 427393120, 680063728, 224666494, 376401601, 950436727, 693710251, 33347163, 542857344, 947152060, 147113554, 119444135, 545093910, 849092052, 267923586, 435499719, 883183704, 828403164, 781328053, 836559274, 204848100, 661327590, 500486915, 446814144, 131334055, 194987545, 170294515, 441331130, 54107191, 918496304, 764702550, 642045656, 917579134, 737715002, 625883402, 369999684, 729822986, 541352732, 181796086, 144209069, 913718268, 489057101, 911959152, 207223401, 154555774, 902406782, 740304011, 185100171, 972804034, 836525430, 799045955, 422603095, 498571161, 518510765, 715024326, 625534768, 461141778, 91471361, 541968796, 545519385, 342135719, 379882254, 436298096, 425613649, 152701866, 300634339, 876067714, 996045795, 568219386, 397847904, 875452664, 771800211, 723342921, 92773760, 223329932, 183790998, 220353822, 496719367, 518071936, 507498718, 828463801, 681099911, 807865722, 305644470, 692216009, 515514266, 141026074, 967461277, 922043220, 981243359, 260428792, 562783809, 51742427, 346701013, 576345812, 271135787, 841957404, 378474775, 793290373, 383173279, 544781484, 148655997, 185671444, 900232998, 792525925, 841461540, 899470103, 513244405, 162855624, 679200079, 855679928, 325625866, 831722375, 219161574, 386579943, 941224565, 300858817, 906036493, 298511629, 452616351, 102534149, 785505682, 775645616, 100862072, 642084734, 693637786, 498578167, 365738584, 232052728, 78105092, 673202739, 216859505, 888776668, 723704765, 365969929, 633087441, 469325646, 943201602, 862363784, 788564889, 400938484, 552721851, 599790455, 990902649, 567512739, 982261594, 77165627, 142998478, 242733980, 348922400, 384126443, 63022187, 483482171, 313680302, 859165598, 37808834, 526749149, 719635794, 642923565, 695315385, 835730350, 327983117, 370709685, 963105830, 82578294, 980764396, 501741346, 128192079, 441901319, 70246715, 250486590, 599423829, 992523220, 974617136, 842777862, 962352734, 977888587, 472538547, 533312752, 697412478, 545796775, 127164569, 795885159, 851774350, 941338776, 709735183, 42362029, 992344488, 4307055, 908476116, 347253676, 505392604, 663899978, 563014812, 860025985, 390637304, 466126168, 975709842, 894282998, 836061896, 597190917, 260619610, 322005298, 389519627, 228696373, 787740361, 885133755, 167651564, 268564016, 447148111, 927477021, 468328332, 733561377, 313354585, 723866854, 355748354, 663223800, 466793908, 694819717, 82692518, 355448981, 820178354, 86482966, 650211243, 875883418, 358402542, 392418119, 750048907, 358391734, 513183346, 842824534, 866607540, 471524501, 915173250, 268025361, 862702049, 159829051, 697030633, 321208547, 598011372, 583454565, 725801906, 671618552, 443943256, 371119720, 36516170, 486489049, 842656015, 963843277, 64129481, 125499085, 262556791, 301270814, 332499106, 300467356, 428961620, 947206086, 830901283, 513365803, 375950696, 638117571, 315702067, 443844762, 898799294, 100476646, 750844314, 584961021, 409126676, 660657746, 767283683, 823854439, 908468492, 805213907, 476892271, 19260270, 652531515, 170515814, 102585774, 448603429, 872232158, 930457526, 223567430, 913320014, 109057294, 667361791, 929861466, 284611302, 376318199, 289968871, 846672638, 235209732, 967342144, 417808597, 484271985, 286379193, 795877397, 337147859, 208624921, 981229529, 991532705, 723045291, 688563377, 346982168, 633842696, 965985806, 60052794, 344307079, 987179971, 844226959, 222915797, 153356017, 410298705, 830415515, 518492197, 361447093, 587749340, 902265735, 146053503, 59818580, 818505551, 252621772, 616111959, 44706096, 891255119, 534445736, 544249502, 356442096, 994574761, 39789999, 367360592, 651650214, 323587192, 796217536, 157835609, 192410532, 448524801, 716299203, 402486535, 40784744, 733664312, 911926067, 625922244, 853506469, 893370723, 731356326, 71540363, 968704401, 491429400, 342877850, 686123229, 623780227, 655128258, 499813266, 478544975, 753004974, 504882640, 65744743, 259474695, 857671904, 16806777, 708091636, 307108368, 937908457, 244707789, 631570785, 585108576, 484746985, 158953647, 109120519, 709598039, 112315426, 775777949, 422622026, 79135264, 247396783, 695596342, 827571323, 697700712, 552216464, 181080093, 799876883, 666580785, 283509659, 171014521, 635405846, 269291865, 995406707, 431957632, 468514677, 474858638, 800537595, 334506263, 919079430, 882769602, 600216189, 503676684, 592448897, 34159068, 224677004, 798380755, 342439271, 860047152, 87036216, 879239311, 251017207, 816538616, 724593007, 386543078, 11781062, 490639682, 256861860, 196925615, 918230128, 735812091, 463213073, 85239599, 590604649, 901451644, 224081835, 198631572, 119202745, 392472651, 699192699, 253629593, 174386059, 995913040, 7473752, 487899416, 682536586, 209234782, 468520454, 949372010, 621229562, 512642917, 854167777, 378046665, 34528293, 379970746, 679359623, 189984140, 205458055, 274899169, 81874024, 142780414, 29816259, 155758467, 18837217, 567948298, 470890964, 778402053, 272872107, 637390148, 613241782, 592601606, 129897116, 512719353, 511184780, 563884879, 30968404, 746457041, 6885793, 966198150, 742742903, 275672964, 819063506, 554096470, 112833234, 256524872, 557016234, 228600085, 370377918, 89083982, 762221272, 515400176, 248360270, 312246224, 944790784, 764075377, 987800460, 649637065, 63536966, 677102455, 47556813, 295218119, 647884668, 542975959, 339983992, 745854299, 696470399, 449376292, 459304540, 535026942, 199722477, 793644986, 782999246, 129716905, 94171789, 585038985, 494480100, 414406523, 288408425, 892345085, 808419766, 929196809, 381281835, 602763660, 840131142, 742834576, 441201188, 316052681, 469998297, 23653176, 214166557, 105311843, 666132660, 359109502, 107218979, 404179662, 798906816, 137113193, 426495919, 698515853, 998014529, 392757633, 261967448, 699302524, 853273562, 763444703, 740329628, 331883055, 981314216, 784243502, 881121880, 126198915, 555852403, 494356689, 737029302, 906663917, 851359891, 469944501, 253872564, 228816435, 173020177, 818406130, 890199403, 501120519, 517677978, 623682043, 386229711, 390723022, 819760277, 420740478, 146775407, 947650556, 677808582, 140152142, 248359296, 851435816, 941287882, 138955640, 336640539, 539916371, 752480385, 155681741, 412641736, 353317844, 452957952, 682368540, 458437612, 646708056, 112074424, 575382506, 558964087, 466646729, 322416820, 783069073, 314492318, 433286985, 149438771, 659114906, 544008562, 933999839, 126751239, 810029682, 624178824, 648503406, 949560071, 51865595, 838391515, 13539986, 521317426, 608338446, 665373475, 134271196, 406420406, 71095529, 665034333, 403120093, 87885308, 60782552, 14001864, 989115956, 975454838, 299281795, 484795653, 515827905, 224804433, 378517074, 591115434, 85690866, 685885628, 398778015, 671901954, 294877384, 761498271, 724306457, 986754197, 956461534, 148391993, 989943209, 380447098, 86719979, 303689111, 926060782, 17935490, 718332028, 981427115, 469623998, 955505917, 249740613, 754817909, 444380684, 819740690, 847491331, 221366774, 999798060, 586173366, 428032573, 188188785, 666748214, 111840052, 83109715, 427170094, 612986031, 239774098, 750459787, 647386959, 464864726, 331985123, 657259355, 160407088, 896618096, 146321028, 669852572, 145235569, 62913900, 243218049, 435321878, 144930043, 412945942, 123271150, 694144335, 396539979, 155945917, 752184643, 411758105, 674748268, 150802453, 100688000, 708662283, 339162229, 645547051, 77783091, 843552244, 925301650, 564528040, 673453903, 13809413, 846969767, 198938738, 978403755, 837145163, 578186220, 597938896, 359252735, 197181237, 967051733, 460880589, 561911885, 295481954, 67247588, 537907460, 818447193, 889244914, 61004062, 269466125, 487824623, 587152691, 929080327, 107921359, 602807498, 149059966, 726233087, 142401979, 652745628, 867122211, 698567300, 104135460, 9428344, 814344144, 339134346, 532733306, 78777892, 791559934, 905385597, 948957750, 363520928, 213543444, 331343006, 22765494, 248034722, 319943405, 581810963, 185346219, 83338185, 121874206, 264745595, 887029075, 521816770, 130400137, 610676686, 777186370, 520814541, 960140507, 710996391, 227758127, 284265093, 16839378, 915672075, 743054339, 615163349, 813235560, 757509378, 929808292, 524760388, 553620835, 705667076, 674906711, 24546129, 724284080, 442568856, 181643278, 881898274, 379604745, 618306193, 96479937, 707743772, 14606326, 272765346, 945241828, 925390951, 945965615, 499375434, 144236517, 25532869, 575193537, 86145203, 12945441, 369337691, 201175424, 330076921, 841191891, 935198807, 233376813, 314246260, 340690689, 374771655, 621353906, 432635139, 390383235, 251825681, 386421297, 579965020, 725578976, 604787719, 910441854, 317795345, 777517488, 70133258, 499210913, 877510240, 778799065, 276394528, 484395940, 867635658, 291332950, 584000355, 491636955, 67912235, 94596971, 95446246, 181805476, 545481137, 636430557, 285975125, 801356174, 206836093, 943610309, 180817989, 22843901, 119022003, 314332205, 878016135, 925569501, 915739127, 792526840, 987980815, 257927404, 463078235, 639738774, 526123726, 661286281, 735761779, 992021185, 406067087, 579761246, 156549196, 310426688, 422480820, 231867508, 804490658, 19087164, 302656839, 998982527, 858911257, 905240810, 965681243, 603970753, 45942517, 444360473, 943513690, 466364285, 904760654, 887245837, 21839104, 369775823, 157905329, 729861436, 432221545, 182167104, 983760221, 790368218, 399809759, 371385110, 861461391, 544607793, 970947707, 908956447, 854627901, 103564930, 6013580, 251944984, 547616773, 199764114, 224529679, 511109815, 580396817, 136181105, 164788639, 493741131, 456648700, 126597505, 437323908, 813466677, 299271189, 436267209, 119836613, 985538758, 910510926, 825819717, 312947671, 375158719, 326849834, 734711243, 463674530, 758080470, 909905803, 630816316, 570906608, 562335365, 430048778, 749926496, 577558094, 843775919, 279459829, 55322933, 229815727, 912905043, 419527049, 471877207, 134700141, 118547818, 768943703, 376626889, 596637855, 600894289, 32903593, 642445419, 213253638, 651221000, 840584431, 316958315, 939743860, 191459502, 378328126, 106212407, 652533430, 9341458, 223348462, 486843327, 540376235, 2462288, 341439537, 426735226, 47664411, 760640847, 73815646, 622992262, 7194431, 27238358, 517697233, 67219384, 235253672, 741700626, 829634266, 580020094, 52045971, 744102019, 449232902, 404155951, 50531921, 61026622, 920186490, 457678289, 399998409, 384732463, 549862897, 172162583, 112863096, 241903791, 415814300, 145970551, 533366535, 496653886, 58397782, 648563685, 299479207, 143071498, 38019631, 217849817, 916594005, 489324289, 496670085, 443249315, 548237379, 568399417, 308809290, 575572673, 582360140, 520324054, 705007137, 138798677, 598904545, 899044413, 353079280, 349784719, 798642227, 135996871, 233166226, 928727971, 290507519, 897829986, 623757480, 398649693, 258197728, 842067870, 770292028, 603021504, 886920778, 696835379, 505790079, 555782729, 929152656, 235523665, 779162766, 932548264, 382326764, 968501062, 268903716, 665370869, 506293102, 762079457, 505620986, 88070594, 655645331, 850616558, 962043516, 136749399, 473056403, 593776215, 958720052, 412779266, 725065346, 898208842, 992265284, 310651847, 785189935, 375886361, 771737672, 55127103, 920754065, 746357978, 754542994, 466697913, 98700848, 731295439, 296003319, 262782740, 141372831, 907952306, 285253434, 271035068, 648859645, 977266267, 985934749, 591290403, 169373841, 602229768, 579836260, 23207808, 316426565, 833738012, 873602276, 432584046, 927639850, 495403283, 366054598, 404997498, 901016906, 887809200, 31757757, 44365461, 673770851, 529928050, 265816060, 810264452, 496503213, 93238128, 49953548, 313102744, 130428047, 898610066, 572713366, 999603243, 433197191, 150018098, 627550496, 457889568, 587314742, 147507966, 394108826, 987069233, 508423463, 578657501, 424019398, 790940870, 60331348, 709829210, 323059106, 380217311, 456478824, 315885346, 735001978, 373279336, 253942234, 277875174, 738308227, 557179201, 864630198, 391421988, 384376047, 697292477, 480171781, 81751447, 730187382, 949279212, 242728568, 417804403, 556602700, 173195793, 409925553, 728035241, 38110462, 853034574, 200910457, 728532080, 770965279, 101736028, 308107207, 76091351, 215573303, 531110391, 415951175, 866493196, 855936137, 975673939, 814455540, 518750057, 116665939, 476582447, 328188649, 946107661, 605567547, 333260709, 406199083, 48678434, 591664832, 423523004, 464348843, 388538321, 100833599, 299482753, 873767372, 909885352, 521580173, 812203983, 607050642, 239279902, 512623707, 48595575, 199297114, 272408131, 467278205, 287639766, 65137720, 843130282, 965297637, 816473167, 636412879, 88760452, 414251944, 731758604, 231753055, 397890824, 972699601, 756121407, 785502247, 728860049, 319902484, 947088545, 616869132, 338231673, 606431533, 610956505, 581478263, 358953127, 198813387, 162889415, 527841638, 506382337, 912450025, 699167378, 25974292, 334361695, 466497053, 359727327, 285204802, 6000475, 990757272, 106697225, 37012485, 230764891, 6494512, 689705846, 671646211, 254688578, 391558856, 842644429, 330962331, 306372310, 785832126, 82186822, 831319853, 966153141, 553036461, 771527033, 25786611, 989084001, 937545174, 503735758, 47938777, 821129054, 705613556, 756523174, 612008328, 126221453, 770624063, 798903375, 906666640, 751256747, 18054264, 979950132, 660451279, 995527153, 316117898, 39452495, 627024645, 613215378, 644429307, 745627505, 398639237, 498497092, 417621509, 451255897, 503492382, 43096870, 571790502, 504914402, 885932005, 832940083, 874826452, 931135978, 407833104, 12885276, 595201928, 528091499, 261972272, 992013387, 608773392, 169114909, 106682535, 781465911, 894283800, 128155615, 497066859, 864558923, 680660406, 370889159, 690313792, 934729806, 129280886, 619834946, 389201546, 206273119, 199965989, 704848965, 615666607, 76273043, 786447396, 434013945, 147873086, 688570271, 10128030, 164940324, 440306485, 658742393, 577613873, 966515067, 4413842, 922223866, 230328401, 171037310, 357282337, 585457537, 615918770, 395742449, 369598785, 195173807, 692260250, 985740719, 47836249, 831523669, 913208344, 329706671, 745382330, 928728615, 822186974, 936217406, 385071889, 653558895, 110251733, 199980373, 788898407, 606830397, 899665003, 914858114, 991223462, 94754434, 97116871, 443804085, 734855636, 376236800, 423431986, 231208448, 557017799, 322504549, 929869478, 65125089, 695279610, 695456085, 746057446, 144590470, 769312874, 474185176, 46079004, 798451968, 622525971, 437971672, 864278338, 958772694, 391380556, 658411768, 884925009, 410898635, 292446366, 693066027, 731414203, 225004040, 983735600, 104955739, 402123986, 543128233, 734058651, 902122909, 664207251, 501969938, 315553787, 734220843, 256422093, 13582695, 488374016, 128957066, 759786510, 625410126, 640557087, 596864618, 369003294, 554821039, 461546124, 601842843, 382367459, 110318789, 720601206, 554128450, 283144864, 123090360, 419588038, 658135284, 656457395, 22034000, 863640885, 815308167, 752904592, 932550454, 428873270, 203736634, 543806721, 851325551, 44189734, 21055831, 968084284, 368415206, 536427667, 610693735, 103741984, 928959198, 168170154, 399711081, 595187587, 481045945, 6732084, 216728179, 529244715, 356405250, 954552032, 577816361, 62631384, 101945486, 276058540, 135176591, 276272499, 990780163, 385607611, 397359304, 876025488, 537205802, 263526079, 88753746, 937805987, 524459914, 498573160, 980872324, 685411249, 881192642, 597946842, 24924436, 689671903, 894928083, 586681734, 483475254, 65412716, 734777747, 761391386, 803630265, 550386623, 935851521, 97500926, 766230539, 188352292, 560490706, 815455368, 164484741, 882121667, 919065822, 186410981, 611748058, 800904262, 901813565, 825860892, 830483313, 143509589, 749676670, 186457427, 579199313, 899428078, 740680212, 276135321, 464294678, 200222053, 819735996, 29973266, 520984106, 751293741, 991021829, 53427425, 727691103, 123255507, 259500160, 878024602, 524000801, 535942986, 729660666, 755293126, 190574469, 42142234, 449472167, 661943300, 665614117, 710975482, 148068352, 233961435, 149926762, 240762613, 936596515, 544941956, 452272381, 436123680, 33079440, 446709617, 749064311, 380351125, 123372051, 374176806, 654526734, 813907944, 37782012, 741677957, 925788352, 668320541, 510283115, 233627548, 101506782, 372028430, 770487911, 936615763, 380003616, 179065698, 973751268, 863598319, 149743096, 41134108, 182110539, 942913401, 998466333, 540067395, 483370853, 62378687, 159614530, 664787727, 800390765, 991015106, 117676448, 532784265, 481214084, 608316925, 256719074, 29839804, 612164993, 357926119, 158110566, 855799531, 919719170, 221368460, 14670426, 339397071, 259801879, 50741783, 509089012, 55041055, 129260490, 103719778, 201277454, 835863093, 867854532, 474926884, 783023068, 692096454, 65811935, 494685553, 726354340, 976590086, 245241045, 526184874, 912632649, 167870803, 181542100, 903299340, 993254463, 755898504, 809609444, 390023850, 455231490, 496454366, 510930533, 428346723, 815157408, 950207780, 344261795, 45475293, 490380888, 558959280, 939433646, 972077208, 310692201, 588002207, 149315367, 106248408, 823314522, 569360706, 61760955, 930443500, 711444128, 733604622, 611032054, 403833889, 721850602, 6516661, 992408074, 552975762, 864285252, 848303158, 644013558, 234246929, 125282197, 684915651, 654250672, 121444837, 453026120, 762144819, 692385470, 757187028, 141977998, 913732173, 292286188, 713138709, 434179118, 543123835, 877038036, 892976547, 376579554, 795149944, 443226866, 571518185, 971903423, 59553141, 925740597, 336565492, 706235384, 747456848, 541349836, 439673576, 414997361, 632356784, 181956468, 545411187, 823204554, 362156403, 42245174, 460441616, 356119819, 17048640, 155668231, 159106198, 147082435, 615351724, 79682513, 233201347, 207662706, 864640769, 777593739, 509468935, 880522287, 201945903, 794283400, 122872102, 482451401, 69479122, 406690132, 331060387, 775638352, 328682911, 29134107, 762751853, 611720653, 741479220, 133362140, 986160866, 41716777, 531271509, 697459996, 688323036, 608072116, 84610578, 70257967, 110074111, 456942763, 271799054, 870269597, 15393442, 553072957, 210791166, 458548827, 510171678, 941449398, 307490191, 190487318, 171931814, 81310947, 994533388, 751371216, 836573508, 925223081, 53038101, 859396624, 179111730, 749169285, 255537121, 285322650, 672657441, 726503016, 141959699, 825468113, 253881180, 780472548, 981538229, 439906101, 837605108, 294623675, 575834180, 968034305, 673300069, 760911515, 598903198, 780701627, 529238067, 448001030, 864716892, 192896303, 215478037, 40364511, 262060571, 472711321, 157739584, 217403531, 912345131, 62793185, 159943327, 898946532, 548133343, 876304312, 417264576, 298201308, 319694182, 896262406, 598226029, 887915578, 904778417, 620309866, 9845904, 744332814, 327213440, 244962519, 353221191, 174014864, 205227258, 672110819, 905282375, 875696530, 98831329, 458454226, 291663103, 389519547, 448978616, 131604224, 624345246, 35887095, 105992979, 245413590, 120569933, 694021544, 854917572, 552630043, 253748342, 331489931, 289506248, 317647763, 733897723, 667530901, 927676715, 660854345, 367455052, 586604392, 540985090, 854759463, 300336202, 232000716, 365115292, 404409315, 601846038, 364242771, 973455452, 775446420, 346015195, 17611227, 539764038, 657485161, 932837223, 147222409, 195841741, 805906220, 183231535, 177821604, 699885797, 849389149, 775452824, 225658233, 543379589, 62391533, 7595106, 955998028, 688329718, 531527699, 74084818, 682186572, 23762633, 494837926, 725631461, 279110784, 509415933, 372873920, 514736932, 105019539, 867806282, 878624689, 151941914, 37735521, 189418407, 239464416, 253277708, 365335349, 174620792, 2908210, 891638542, 308174877, 797424191, 365932517, 709625901, 130231175, 250603791, 834198736, 334828722, 81612273, 493202576, 183197818, 170345332, 9606792, 380333844, 221025955, 198211500, 865425183, 467817926, 868219696, 866538138, 390233798, 437264180, 803205039, 376934163, 124247548, 804095590, 281308597, 275893806, 9017478, 966529531, 139509434, 988884525, 824270022, 596438596, 471697015, 940461563, 446140028, 350804822, 281711506, 259333998, 558144871, 565087275, 234525793, 349327863, 531844477, 17412728, 343907609, 196749157, 702560358, 741574731, 551577127, 983387340, 932212054, 920576105, 716202035, 608135180, 991163999, 697848531, 32379594, 267590319, 76776987, 847954797, 509621934, 177573006, 620443196, 930178900, 24514946, 241840158, 82188869, 487983601, 71671944, 630258667, 737524853, 507967175, 407708697, 750957557, 921617179, 493534215, 947758645, 69907141, 655127384, 115076118, 907755291, 860167862, 987670572, 203426781, 212543286, 466702097, 886752246, 204223539, 79832739, 655785619, 12055918, 831421009, 342937947, 549098057, 577376476, 987167558, 236094256, 161618854, 445518349, 702256235, 918635481, 753622603, 393318241, 91491960, 13537533, 193572012, 264579823, 74083043, 683536527, 894408782, 863423050, 453312813, 247304235, 391522295, 282050220, 649289877, 511180274, 281182673, 222682809, 579726864, 549845639, 86495599, 974659162, 966456675, 161789553, 242616175, 583460379, 613473905, 786613260, 502562876, 640714063, 307118898, 9392812, 384945681, 729240848, 834007233, 775504194, 521341699, 464337392, 465896878, 378865681, 909918393, 2521751, 461808582, 181176033, 924225752, 6960492, 768887943, 992310666, 130645195, 655683840, 525218920, 666168365, 237155204, 921790269, 960672972, 319472480, 909457667, 311705217, 303765429, 943865422, 245372405, 920870889, 845233062, 675599970, 539277526, 524276173, 652210330, 580842718, 526505965, 336558604, 386345345, 666925623, 15341354, 498027646, 532772791, 678127905, 255535348, 682760933, 710779623, 376458848, 657882109, 444977787, 767647696, 898288654, 595854558, 589559965, 561777509, 725625905, 574720422, 729088831, 42382178, 42520421, 100353689, 375674275, 847811702, 639779381, 517154200, 723043533, 97914828, 689822119, 501767179, 584160077, 464005189, 598995640, 861348993, 342975402, 665031523, 404808980, 772536956, 275113209, 640587862, 757799540, 631827723, 422337013, 289809923, 594709660, 868259838, 92026676, 610273056, 621615964, 50754962, 84923145, 910720805, 332762380, 24094487, 509620178, 698619514, 516293368, 104469, 114254313, 770384843, 671119999, 292361520, 648666986, 8036815, 256836953, 444523993, 214711088, 640949143, 679999428, 336011325, 393928576, 273095128, 121356594, 937866534, 349449625, 576766610, 467525637, 592520733, 644655382, 608415487, 924557273, 688989375, 632215923, 684349877, 844380432, 148686216, 354423531, 490373855, 987463868, 78746600, 871325568, 887105456, 778979252, 311043201, 901189398, 584801631, 325643597, 320319248, 45705149, 630686631, 489238418, 628759749, 729775514, 174284125, 434384193, 601272561, 155983879, 307553784, 632383401, 953376109, 636107343, 97839953, 838666512, 739486789, 944535261, 126653133, 119183475, 642679358, 375355576, 505694986, 189618252, 73786647, 582190390, 474760554, 878086370, 508663604, 710068832, 511958478, 279835006, 811312641, 524426250, 921932428, 591441404, 372547912, 2770374, 385503480, 149190937, 903942763, 531231745, 803824889, 332186935, 335534415, 9801659, 954041225, 489127283, 988927079, 897902975, 991880486, 546466300, 465307693, 531357836, 318000805, 746670164, 219416207, 662914300, 325537044, 910522640, 92908850, 459022476, 534577640, 128130350, 912899736, 49782501, 664929156, 794195698, 933644815, 754142787, 340721141, 918035340, 448516218, 851952793, 586449037, 277126251, 490488217, 360393597, 591980523, 843241998, 510381549, 875502485, 335518446, 340643315, 464921004, 255277439, 501005060, 837635510, 590977545, 442433361, 999258861, 35841085, 417349798, 957524995, 460310175, 931328401, 800490061, 231974304, 253134238, 237275047, 758214908, 811962713, 232957295, 253513843, 825095777, 866823615, 996415862, 42172344, 854634691, 419993632, 859292378, 259157067, 363294585, 930886800, 174044960, 489492410, 11072012, 531407142, 690642948, 958660769, 819782395, 284287327, 895438426, 418554146, 920874781, 575327971, 979093721, 10731492, 316572767, 569321136, 889828074, 189178114, 73684362, 802995027, 44002730, 812717105, 473276843, 309851046, 387979963, 824717671, 977642050, 987106754, 997120072, 192581549, 726142624, 478090858, 228178132, 26664937, 980065660, 384528026, 443281724, 504759040, 823592387, 220569384, 726352517, 249870815, 356464665, 776881916, 468366799, 277619138, 550914526, 917971689, 789209085, 497548958, 655658524, 339221865, 403502584, 726393519, 536961744, 655512617, 395075806, 431631406, 518577883, 498374133, 462556241, 782278713, 897523810, 796085415, 784988849, 475336347, 518036965, 266374310, 803275372, 634149631, 624183178, 962403075, 410667172, 100934564, 417095930, 348409926, 928417051, 299255482, 451824674, 13704954, 100129813, 784216520, 955786050, 803872124, 469600528, 877202018, 20368225, 991430339, 896104065, 231356943, 856137800, 428489541, 927890462, 678446698, 667442405, 551083488, 568597212, 593825566, 523269277, 15355000, 204724839, 770428080, 601677349, 594814647, 919079879, 270690525, 859277071, 337069983, 433416557, 919533241, 700968193, 84271745, 58437863, 225677914, 905698646, 757309881, 141801166, 21699373, 894594379, 610292629, 207856722, 693222559, 804646592, 726979890, 830950117, 239715561, 84233397, 678627681, 289729018, 552058115, 466069305, 867602105, 88424422, 525232593, 306933149, 131284130, 390594238, 320153158, 832037007, 20467313, 545973145, 710643137, 59658527, 950476589, 906525477, 139032743, 40682373, 773827526, 609715936, 155196963, 648984896, 840523424, 89404607, 587132702, 169659490, 48575712, 653796651, 384159258, 564379320, 523295062, 603048157, 256074326, 943272174, 785059819, 674258836, 948833630, 45851836, 318679236, 402093468, 792719783, 237751024, 821857477, 679359846, 497216795, 628867370, 790149324, 235297036, 738130234, 473545655, 508743233, 44749133, 960604398, 892497176, 966659179, 258509966, 2037845, 509562258, 575620948, 930093458, 858221598, 838218152, 273964696, 916564298, 878085787, 772760846, 653536512, 907414818, 637923121, 725207922, 644039824, 196587761, 778302809, 941300937, 415974782, 757569220, 529135091, 793473023, 673300695, 842588336, 508023064, 2972269, 180889228, 259071919, 111066762, 905289842, 856449487, 632193256, 522697404, 912978258, 146653183, 775165339, 467622142, 647240743, 207547494, 982078203, 970817425, 354222841, 101181352, 502799643, 593115711, 801588151, 862336796, 547280535, 405844889, 786913596, 873454653, 778396746, 254557691, 308013861, 630947982, 736193201, 742835381, 329300601, 833437395, 138798845, 512907005, 696064617, 182532915, 869267475, 562141386, 625834816, 177678684, 203401057, 135671489, 5684222, 711274310, 676941184, 641905055, 539481593, 718994734, 589274350, 226567457, 402548026, 270801700, 441737208, 713274371, 530132610, 497963596, 624848290, 418368136, 717371144, 586586134, 46548058, 935347494, 199331469, 688349954, 548222371, 1457838, 336237028, 514692015, 479291139, 774435394, 927720095, 493756103, 350636844, 7446060, 85729498, 491394160, 917774732, 738014308, 778796766, 321029693, 865025309, 976184657, 778062134, 649900607, 953892428, 254158859, 724718692, 3297163, 130106698, 111340643, 265388036, 709096067, 741432956, 202009825, 292525566, 67695020, 404001154, 964500125, 512796531, 452002325, 766200469, 544781639, 783161054, 884151202, 570387890, 672839078, 291497632, 258570673, 945951419, 28520227, 266405466, 339457189, 667826354, 271980327, 542651075, 296679221, 358664527, 898531932, 12669755, 598664081, 611110117, 380417105, 286609780, 710138127, 245779157, 336572858, 925604147, 981685565, 221888490, 617895736, 55173331, 918874551, 793634087, 712938360, 101734025, 83948568, 534671271, 954695688, 716296422, 296470946, 4898504, 331880347, 147626901, 498581493, 607647970, 433442542, 733062151, 257390005, 25786400, 352287057, 877833673, 539333351, 188484615, 746933329, 332984492, 494345121, 75990199, 456593331, 136059733, 595313684, 285782393, 634937361, 208978071, 840845713, 16895388, 113343343, 134500882, 128606693, 61390861, 686732653, 103220377, 409671828, 805906305, 548127693, 623675558, 425316308, 525331743, 736435360, 886140135, 219382724, 183320836, 131129825, 147078399, 325630472, 891214647, 845612775, 560253500, 398568543, 416108004, 367335599, 421338492, 664195461, 709739550, 95913635, 583911132, 963873486, 639903914, 358515994, 962222683, 552628235, 163800539, 392000906, 126903825, 805753018, 592189702, 667349083, 87991416, 508337922, 409740554, 897913155, 338679385, 660798316, 845773471, 20708620, 736734298, 229100681, 67199042, 655984391, 251964525, 766254165, 109098177, 293866880, 883188575, 129539817, 654059149, 888519514, 709791541, 996836110, 371915714, 78158013, 575175032, 266643806, 954429731, 555822960, 417696582, 540023698, 823078948, 815906639, 58954453, 953197658, 697836150, 485399910, 949546181, 53679294, 536795155, 114274412, 456996549, 119189051, 570520994, 393659223, 233900129, 821303910, 434491263, 139269512, 547616708, 916580337, 400680803, 330788340, 356392033, 136354642, 240619880, 312828408, 868586924, 181662634, 875358198, 302971867, 860883143, 852491290, 905108242, 618525235, 653238239, 187213773, 693428482, 538455326, 170206038, 715144629, 170285910, 979476117, 575398787, 434478585, 778219555, 36594363, 43274451, 866125922, 461587922, 38630533, 625566766, 516646471, 685552241, 820266112, 415042955, 598398257, 617231295, 392191901, 165620749, 637711319, 417415481, 237334741, 895110227, 668357504, 966286239, 778703014, 1908671, 294948770, 808300257, 777058999, 553961225, 430822883, 16357235, 326215595, 111305000, 298762026, 757035783, 180030409, 484595872, 621277507, 65066398, 945775660, 501174235, 376376272, 399363732, 305978972, 604081945, 955679244, 758942725, 776939694, 885192199, 7014423, 742987092, 64543565, 411090067, 167395434, 271766345, 794237909, 643286293, 903618771, 498723514, 409407167, 882168229, 531973031, 11588510, 412265607, 949437938, 455279542, 810974891, 777828075, 166627416, 486635584, 292126742, 408373289, 13014617, 339588939, 759017119, 83900999, 613706888, 810103107, 496570822, 71417363, 982561523, 578106699, 103219315, 282777138, 632083100, 457807942, 280961365, 257669155, 372793356, 656641224, 518184500, 445681599, 108100818, 453083347, 344581172, 226578754, 225143454, 371105981, 320127004, 701256208, 115375646, 913012909, 382869129, 163693517, 577331620, 681964343, 469353084, 656143313, 848416994, 325190474, 92557563, 157261808, 226973240, 583347161, 402884600, 841764465, 906108612, 34891037, 989263446, 772264847, 443708339, 192282988, 446271236, 244472987, 396690102, 812190849, 212245286, 370873432, 677599090, 190651059, 489814826, 466068097, 112676770, 37694683, 833766639, 859895707, 855273009, 70066714, 857079739, 134481342, 850914094, 439183672, 349089117, 979672524, 377067244, 374776246, 842673200, 940281016, 705707919, 420162535, 235861068, 986424346, 991372342, 57377868, 116304705, 879695891, 550123217, 840791976, 288374410, 375438782, 596656719, 4463449, 299139862, 640239135, 449836924, 730102182, 482352940, 668809864, 886248334, 9676596, 384052091, 294966053, 764811303, 675368840, 229354284, 956989042, 654134457, 649542091, 919196110, 274067597, 272505742, 198939483, 873520453, 988271702, 162045124, 704674157, 820689086, 54979791, 180763856, 303540462, 704630825, 401865869, 134088384, 635971152, 753142021, 300310896, 621904345, 9700595, 365764182, 33566106, 20256763, 619515465, 326346449, 16408192, 576273366, 410383229, 240647200, 298897216, 112711909, 101660961, 949754870, 279049660, 143210856, 860250121, 60275551, 327256560, 344786855, 792272471, 510858534, 947125123, 806808043, 233088040, 604437974, 134637661, 267975337, 970182629, 736938147, 290076505, 70063997, 254988447, 289128088, 161368103, 228337220, 197940958, 991681640, 847587771, 608149176, 597273634, 746118751, 214404563, 712110749, 858395244, 670931634, 21671978, 342423161, 40497125, 817643097, 890113054, 581929377, 377125585, 897993005, 901205017, 712660467, 99991063, 651759922, 925915464, 119486894, 450240750, 921043396, 212749792, 832873288, 953192342, 26151546, 669619834, 778120173, 149546841, 754070716, 355190040, 894023690, 233199424, 113045607, 33790777, 322561868, 243605588, 126680906, 793606161, 941120014, 205334969, 14434518, 63055774, 336725274, 38993727, 598640612, 567503343, 939089454, 9014624, 194775178, 129030434, 48397141, 937536187, 697860720, 379229361, 718636081, 846120438, 237138492, 708997429, 885070886, 692540950, 238551593, 366192927, 848174714, 598278677, 323706203, 475463243, 792463954, 841692914, 299152306, 561602348, 230646315, 580264960, 202998081, 804462731, 403914903, 228950778, 655379818, 453345491, 822479352, 686497357, 898261081, 840643890, 804933556, 971583754, 932619041, 675999687, 514937462, 222164179, 892656005, 231285025, 12321571, 816708474, 51088698, 713598320, 946346974, 7360284, 106779315, 929090858, 38452027, 340797273, 367751595, 3976093, 767273982, 934050951, 99280094, 428026909, 407164933, 379116834, 125528160, 316209710, 280494651, 673974556, 23393273, 638117347, 543143656, 978395632, 928061358, 927799921, 891595080, 147441515, 963567110, 114045447, 763525361, 830013339, 338778976, 830375480, 338753802, 802559013, 943268133, 589999629, 242266150, 304185511, 983517410, 921190344, 304674827, 824841001, 352920704, 778286663, 511800919, 135665669, 445469467, 874843695, 460221017, 147111643, 428570085, 721628901, 653364910, 396877814, 229925598, 481542409, 221391243, 959379749, 985074818, 199470727, 319999633, 641105110, 263625852, 760625291, 601891035, 804603969, 901091415, 381900585, 300297504, 857096086, 282285659, 631854098, 103192097, 260951401, 477675054, 194370689, 171972997, 183406056, 421061214, 260663446, 999392000, 481854162, 515625357, 451286335, 833886196, 645360387, 595831117, 101793250, 140046211, 992324888, 864601800, 801190741, 394626642, 4347775, 753373256, 112447761, 703786326, 70627945, 748280557, 215800924, 893517782, 249133723, 896019585, 223420851, 973323676, 25883385, 151946110, 561540984, 587587165, 85153263, 854623995, 17297742, 686511499, 66867608, 174594489, 637742360, 437726755, 774833550, 982860864, 498516691, 42769856, 808521111, 723010928, 940981779, 944885674, 554231414, 435604985, 506587963, 498888457, 154918225, 757767934, 453579273, 692214776, 315016687, 479732966, 373155680, 437373810, 976380352, 551181663, 135886067, 984147883, 125561316, 75137350, 717306846, 838165916, 987175263, 645011375, 524126495, 486781683, 687479696, 697489419, 557650382, 838413386, 71753477, 955717118, 898356977, 359457439, 761301167, 69152975, 434754916, 362064000, 570225936, 991791776, 892858764, 320926522, 342746693, 951263436, 887616319, 53471080, 837324705, 570273768, 754671654, 387729754, 388969411, 861676729, 198419447, 534943459, 734351313, 888684728, 765911591, 262365846, 859607975, 952816756, 471549348, 819305198, 132182054, 88778559, 406556251, 993114458, 505597136, 760365531, 943999113, 85287060, 626237438, 693796123, 686383041, 659113575, 422908313, 14450343, 151348162, 408619953, 519810062, 290705902, 677196690, 386556295, 660298235, 346882125, 261549882, 310217139, 18790311, 479276720, 123449643, 305247945, 637723244, 676062867, 703442143, 466644362, 463541515, 449410142, 462694543, 395873952, 873344251, 614747267, 646658211, 256771825, 901305262, 718430873, 142249699, 83864451, 45745388, 945964246, 539606915, 140443381, 218357777, 220858810, 620916174, 992387476, 542758666, 851531205, 625424980, 681022519, 58365887, 788325865, 725173949, 248197457, 467337616, 557399098, 749243329, 286516549, 80661464, 484736323, 992193328, 615756131, 656627330, 7608871, 985649936, 39239413, 825298232, 157420824, 857129113, 417472314, 430804445, 413144848, 421971419, 212513315, 165009368, 295600943, 498667730, 443229960, 581725306, 199785045, 947398978, 758680943, 649701766, 350397547, 192931299, 638724756, 51170958, 836817366, 806649932, 943685584, 811563981, 56172960, 291936928, 79728556, 778872258, 522429739, 532178379, 742184636, 373340355, 713817294, 848986282, 569902232, 48267376, 781029566, 849952773, 757095374, 499774473, 308525996, 66203969, 317430894, 606052088, 60028011, 695850709, 598991154, 74147522, 893364996, 17545434, 383130956, 939714444, 461701888, 915212148, 659300406, 999553632, 471536907, 685468868, 775161657, 221282031, 499208974, 878099288, 85247145, 533786109, 948727388, 604386178, 805089176, 572169501, 160108597, 610693366, 411276990, 112496404, 971454903, 178503020, 573146265, 874376094, 605416329, 270650807, 965202831, 966481801, 530191255, 320749193, 776859116, 418458895, 342606640, 140648664, 764186429, 39449528, 63262073, 525570240, 231053071, 354626362, 677410815, 893466574, 921052823, 500255088, 969728739, 995625577, 198934220, 209587555, 274841276, 174106846, 50638354, 79631331, 519129671, 369304575, 696952404, 525865388, 473314460, 566884313, 41996551, 599102410, 84596544, 854473897, 187927733, 237222051, 372985471, 791438953, 840279056, 446843596, 743556451, 772240544, 891912899, 456012128, 220787805, 967311171, 906192889, 240927647, 751675816, 934088552, 233633678, 116241260, 185947259, 265015254, 937778878, 595000904, 703169742, 917123115, 581075035, 19721711, 382550342, 981000547, 483373299, 536251389, 91696833, 270372377, 753442306, 55814437, 456995378, 148202432, 832325457, 215161000, 911293875, 52271669, 432459403, 900624075, 910771041, 954757333, 421385401, 781127100, 886562281, 890834345, 867841478, 752326385, 55202556, 777010292, 640440705, 386281633, 526998409, 217288651, 647798310, 439088495, 38549610, 660848273, 947284970, 803666511, 590564176, 15416206, 673274266, 331081687, 6681780, 683541093, 26468929, 353423255, 762678660, 618057118, 363461601, 758411101, 939348815, 194794871, 264201853, 957736775, 757619604, 979002000, 504979525, 750858751, 109599805, 958455938, 868838455, 14874658, 132677903, 515983539, 130810271, 972596698, 574917092, 744992100, 92207355, 861923855, 542994945, 771935630, 423050732, 767459581, 439453182, 400746759, 124935871, 619566212, 630760896, 63107595, 850385977, 600322473, 538217520, 496340418, 288514166, 190411093, 931512338, 16957936, 493758424, 757300999, 215059271, 807878618, 486708442, 795649255, 666396628, 819754118, 623068354, 970094011, 889610409, 114585248, 581946991, 150629560, 147975812, 132807602, 303854931, 875249672, 550336612, 30515996, 141635240, 565042908, 29985639, 633906765, 964330937, 384329657, 855700340, 762171457, 81891470, 199855352, 626595925, 913768413, 992841044, 203438403, 943301754, 420597659, 666424702, 812489010, 916209499, 344261538, 435903201, 195148378, 533095993, 416874283, 795465088, 722317449, 217107449, 862908933, 987990443, 305901615, 393885572, 737776664, 2700878, 890225101, 225299232, 922680613, 309155572, 302996950, 778130968, 406928160, 750118772, 543277001, 716289120, 544977579, 903615688, 243722791, 117937357, 904790445, 852208094, 853591974, 527367532, 118841222, 583842036, 985351119, 383166529, 656821935, 655784795, 454769585, 666845354, 175227637, 251888459, 787428480, 945587785, 810429465, 299476942, 656776120, 698799571, 575228018, 482156246, 460522845, 706005884, 14785236, 474443557, 920655090, 87275529, 657434312, 973009589, 631225203, 798632919, 94820009, 418983094, 593294289, 195060900, 719736037, 872440077, 397959108, 542800655, 606189751, 366576315, 426067651, 604305436, 861341621, 369367995, 25909635, 674316298, 305601049, 94839962, 693445606, 795743079, 938273640, 589764274, 650604198, 717730107, 104713789, 222872754, 345567873, 233449111, 576742642, 236676961, 66984052, 509800266, 600806145, 633013901, 417260704, 50584647, 285657149, 761131711, 695844869, 605387595, 372637423, 118819115, 493935092, 40162, 610412675, 304400855, 207180926, 129787521, 921457212, 203961118, 983434681, 124636849, 884572434, 201550837, 849957599, 355682486, 326525814, 488189277, 105578295, 285598796, 869413837, 75585187, 179020530, 935452317, 7026973, 695469591, 469336862, 444867521, 971502189, 408596531, 148351487, 261806008, 33373686, 482861979, 894334495, 292450232, 633209864, 284779873, 948519781, 265877901, 912894668, 874429703, 215602662, 850513090, 244491315, 730471176, 962070555, 423364531, 374625481, 577553181, 515427109, 720298293, 321381705, 167225347, 541165480, 300822660, 504708552, 888763462, 35701232, 978291472, 925375510, 738804638, 481415340, 922150636, 439291717, 634097790, 116658410, 466191421, 911956361, 854959955, 314839009, 102570845, 11395542, 430713045, 974824680, 7710161, 366247692, 596383112, 691645080, 419284893, 612355063, 17306668, 384664879, 806161594, 748679649, 114804988, 157873303, 77717571, 355783962, 356375788, 143387614, 805240875, 56983075, 865428093, 58327568, 533833157, 371345834, 989770750, 818425740, 739659890, 368814127, 964587905, 531341628, 688701687, 42866405, 978945381, 810963671, 199400169, 159733509, 853630018, 992631125, 769138296, 93495836, 185909634, 385522770, 803638628, 336176869, 802405716, 213518926, 856173962, 746977130, 534316036, 141392241, 145840836, 904784920, 609044612, 167856213, 790916347, 944205996, 43773202, 510376333, 484854484, 298241234, 501907569, 534782076, 189231980, 991178103, 227940864, 397594257, 266723083, 542575743, 92591277, 869091957, 113538688, 525753091, 962706725, 813231304, 44774392, 180809073, 382547588, 748690597, 512879915, 768045966, 503379356, 516019360, 101657953, 116110435, 315982893, 557922617, 542701837, 682435511, 432893726, 663257571, 350396136, 377928862, 823763758, 164972644, 439683722, 884601078, 502175127, 761508464, 552128347, 555564361, 224475171, 432693793, 868962975, 108210512, 806692486, 833631973, 650240521, 689881217, 358157258, 859288600, 610734301, 383444643, 783735263, 147740808, 45934109, 410664635, 143149675, 56553599, 324002443, 413871246, 371083901, 729286880, 826593876, 399914046, 139144725, 135035111, 298921831, 565079517, 440055469, 257872192, 702300641, 694273007, 685571398, 996666722, 368130696, 512079134, 453952864, 197738527, 890126040, 522228568, 667648148, 716317149, 762836072, 722293279, 243625692, 616444330, 818156186, 680116437, 776167716, 611261880, 37903904, 497600475, 647400699, 204573905, 387616629, 537861045, 824979920, 603320076, 547269765, 989722668, 255566529, 322897768, 663121361, 587225402, 666574051, 132574829, 559210354, 364889877, 667773702, 38559986, 4419803, 535855246, 847265093, 317436516, 177603227, 168378345, 749317670, 770552767, 906359542, 386522306, 124669400, 200462697, 643384509, 248023901, 197699125, 644678740, 836417887, 776629132, 373531816, 172144395, 630433988, 968668930, 855622032, 676490175, 798427577, 558151485, 671651684, 300301760, 797427491, 698487218, 870785613, 335897823, 673131235, 682756415, 395917931, 811553229, 541397796, 957196962, 221462337, 42737211, 3755939, 64792000, 361237990, 531233746, 279716197, 740791242, 880687095, 698683549, 641504830, 775647762, 486345363, 865207809, 21086849, 139477612, 276345965, 161554557, 711602738, 302019989, 854816172, 656345772, 382176726, 606415586, 762964135, 661606113, 19237493, 529326518, 490718547, 872838708, 960982452, 719591560, 749125936, 996297773, 21522703, 624514052, 968917202, 510430279, 593418100, 205756678, 37175304, 589813063, 713077001, 272084245, 749057243, 265609172, 697252949, 241066820, 608158644, 47346193, 236203541, 810407649, 396036719, 294568363, 502115796, 577863787, 908985548, 88642625, 49041762, 611349721, 536618676, 780900907, 437338042, 345818029, 767811379, 915333458, 990235672, 331114005, 373784312, 520131630, 458785319, 608624252, 900021081, 14625694, 61859587, 915174758, 734758550, 219692674, 606619762, 361580782, 414705797, 354117270, 498901458, 812585590, 511769705, 18771959, 527914887, 975399934, 135543589, 763509797, 405267846, 375108765, 982403106, 381063347, 867943388, 852350321, 115614380, 604576374, 980272050, 454830186, 215785957, 127620583, 898167236, 493455218, 292034413, 486409120, 708402864, 157838142, 671674939, 606473739, 204043346, 137009239, 703241280, 912998287, 359785693, 499366418, 796208109, 362522057, 14112395, 989183042, 890151122, 87440465, 593004040, 597588213, 484409928, 963172933, 308836536, 910579342, 604117770, 544350798, 260919498, 949777764, 796230036, 51480423, 627600765, 406806974, 405837984, 606977563, 741767660, 428416804, 780205455, 215770328, 100616833, 156516029, 867460110, 853976192, 790263126, 204295711, 403114549, 421101890, 700986875, 446187116, 788738073, 962007157, 850589196, 57636157, 260897020, 495713890, 953399338, 243369625, 359085418, 27513801, 131641926, 292128163, 476509302, 694292110, 780359505, 248472968, 187329496, 237920812, 922287127, 276841811, 876986034, 980845602, 547138978, 661129250, 946633127, 564503720, 916493648, 879015740, 54208424, 343259975, 412942292, 302183146, 243033909, 252830546, 570182477, 311333463, 6557929, 867531128, 312623111, 372057246, 349759579, 325876598, 818604718, 712640649, 552291497, 324194370, 601494314, 153942896, 915461412, 105528433, 498712484, 256598597, 735856358, 935274658, 36798271, 971819105, 887133106, 347466399, 768336292, 704106667, 997996213, 802892808, 98627216, 254388838, 754366243, 439994043, 474670905, 692051309, 463875367, 400163410, 969323819, 766210325, 630993205, 371867934, 336983509, 446344068, 311627016, 43087057, 53351020, 478135587, 640461840, 559037618, 363559370, 407084030, 878404082, 249530689, 73001547, 311073675, 245331639, 830890370, 882015624, 703363746, 719068195, 273046540, 834329763, 116774315, 672965375, 852675737, 609141249, 317572039, 85574165, 58520244, 751425603, 111211855, 773599325, 494135695, 195079433, 455775271, 21883771, 827079258, 66488600, 800405388, 433814819, 814735990, 1002903, 248118578, 433506108, 193994935, 859298817, 806122038, 223441430, 723657274, 610732534, 737935851, 745718979, 50255562, 767306851, 297202738, 342515318, 282145731, 593612797, 336515468, 948876956, 147233783, 187008096, 960538340, 942414137, 412843607, 41460610, 201820472, 229378821, 390348080, 729658357, 289221503, 44902053, 542350902, 790708673, 336567156, 677629436, 932001821, 83370919, 824031401, 809615962, 786035672, 641728732, 970197534, 550011055, 901013489, 740735289, 54389574, 693220970, 958129322, 468690089, 364022138, 287444598, 397960708, 448352773, 642192769, 613552310, 290696132, 288113917, 909170463, 263545149, 37152268, 958235387, 838121765, 910191417, 399551517, 640207421, 670080794, 353162120, 530067983, 313477593, 725215870, 734474449, 481597005, 431736445, 533784713, 62903044, 751821270, 491438505, 918020260, 85118503, 45360812, 737986223, 524505972, 377996324, 526884629, 236044195, 993345129, 156343000, 984201716, 743487751, 752385680, 499406028, 591538550, 513333382, 936564822, 949346907, 979100076, 401484396, 939633990, 808652523, 150302169, 468198830, 346238870, 434114024, 19216059, 303952268, 338338060, 599331770, 887218133, 68644228, 125354067, 998940933, 567500027, 672517758, 74107318, 122988363, 870427564, 682000186, 648236623, 937882141, 682852875, 979592867, 681885960, 759494929, 924720087, 2135401, 678111233, 911413188, 547436290, 465108344, 196912097, 729223106, 105675570, 761928365, 201060796, 9223303, 542345404, 523129919, 495412895, 224836650, 297897356, 471443392, 880043865, 290170713, 523356845, 647912384, 185380393, 757927819, 362887686, 326056365, 509858022, 619740185, 423225067, 818137092, 263165271, 653986224, 8267094, 243814516, 337269067, 620229258, 717444007, 212523000, 955318253, 750689836, 436049360, 444004239, 957168125, 678753444, 766649289, 351244697, 171073853, 208328634, 625240267, 105103960, 626792501, 911414189, 353674316, 448189855, 427366158, 401537388, 365869092, 125903069, 439496410, 25450376, 479440070, 648562856, 700516853, 364185104, 375067694, 889216980, 263754580, 513947763, 461576412, 932220409, 17600237, 817654528, 144351255, 570105149, 178748575, 894082084, 424883767, 45089457, 65059946, 253155234, 853403784, 954885875, 179567419, 236404844, 383187941, 385284718, 926181399, 465726293, 982724011, 269238026, 554448321, 447950917, 282247288, 282729431, 914550923, 665744118, 755438271, 542783787, 81346603, 764658469, 461155227, 799691304, 924661157, 539703900, 529019735, 552891888, 933148862, 127273568, 860068650, 642525203, 67649532, 795650217, 136631338, 59016093, 324027006, 879483769, 66060121, 471413221, 702615784, 280115394, 751804002, 905853589, 613860829, 106515143, 580828382, 721717202, 716081030, 411125885, 959898266, 945222549, 806921193, 428129542, 40271310, 977772742, 465913347, 278533051, 537597999, 166272990, 849847623, 197539862, 598011903, 724643410, 438450324, 169845986, 213506886, 943914871, 907627317, 500538968, 723930177, 200212823, 210348575, 926388939, 207629699, 665685567, 80466179, 46160602, 353843287, 672696336, 969172436, 582173098, 294049276, 787499094, 604074218, 250828636, 445622752, 878398927, 530334604, 285690607, 958504693, 857488534, 891980640, 432507207, 81623687, 863988245, 571479282, 353479902, 73352069, 272353175, 468089758, 595212013, 217725015, 584195750, 622549327, 550959245, 34184380, 880811751, 919265348, 751910248, 876072696, 79935314, 143365252, 588618266, 430000345, 817527611, 357159293, 541156118, 786579670, 591466966, 776979651, 681088277, 324256825, 310492545, 975026552, 262872079, 705514665, 829741579, 829572900, 591599826, 684234285, 297940205, 185339980, 12318860, 313014457, 119464160, 278120730, 733163062, 243055176, 832656656, 478417960, 576687045, 570937495, 333533186, 292130423, 823127168, 993587675, 643303372, 92346289, 547017660, 103482011, 345263725, 245422951, 239872692, 22212253, 186512422, 333823653, 206323510, 346983788, 873989511, 457218819, 533855124, 457008365, 470247572, 396618707, 869949338, 796127491, 646887629, 447475792, 844096318, 381912512, 979827697, 25427096, 348721892, 498344481, 639145915, 85977817, 583156804, 189072708, 788383352, 793703960, 828337329, 350753060, 241237963, 544518654, 812579049, 12423968, 104590267, 235169154, 447029967, 587494257, 157906716, 644559837, 254578953, 430236819, 216331447, 371089214, 362377387, 346424620, 177133560, 780937175, 35548798, 706830112, 444637007, 451152597, 808825872, 279793504, 408371589, 380454083, 105565485, 656747801, 914204686, 138609820, 341077873, 815462027, 423567620, 429113653, 232201820, 909519294, 353719920, 510252346, 564528509, 501666196, 144715511, 469429398, 932444039, 971230261, 47888662, 765805641, 307458545, 720594391, 915576817, 227300393, 332230507, 58925939, 592372641, 685251871, 893959275, 708438285, 466619873, 916283819, 369459868, 255814221, 719481171, 659647304, 254263481, 534281422, 393921744, 22995430, 317862630, 235312444, 575638083, 248849827, 220865496, 964049532, 516003303, 528623954, 833782416, 566432933, 960900149, 983868916, 201405961, 935540937, 995372308, 493237624, 278760172, 939524001, 245889437, 903609898, 382790618, 667070171, 593277232, 496093307, 68017475, 435437056, 238812320, 841223983, 174751573, 699729079, 174074729, 178384459, 484661965, 450462315, 954518761, 431523976, 607135893, 777390407, 701653454, 387575356, 386965299, 49535356, 978813661, 62133646, 263470435, 355572418, 784762398, 159922591, 83834514, 824514775, 679035052, 692462034, 632426761, 610536970, 731530848, 445883230, 98822876, 870463289, 781700108, 267525215, 275103270, 817528816, 43410908, 967527731, 834417635, 895544092, 881539212, 108499099, 349900985, 303144875, 153437352, 258573843, 157368452, 540565404, 577240850, 47591925, 370633570, 25409411, 244719410, 334924416, 168426143, 297674277, 315615653, 850585506, 191662127, 275476810, 527473638, 715822045, 972768088, 262345166, 750322910, 52383849, 276328155, 441685325, 338098852, 814738206, 87274423, 767133026, 230892779, 125950205, 578947982, 66788418, 798487861, 944545663, 897347980, 426589638, 884179498, 584308199, 45799509, 391607732, 444471280, 379078577, 225491216, 215271690, 252300343, 237250796, 105971983, 295607015, 97539884, 714503124, 632467620, 327984247, 297401034, 35593075, 160138438, 24669690, 643455828, 75775384, 324112622, 739315203, 685327566, 991474417, 973100806, 721576181, 106660377, 61691423, 97073993, 441894609, 523106631, 55226612, 866216679, 258584976, 417333603, 355531983, 534219472, 565642762, 130318299, 129211037, 781070490, 799744422, 278941971, 674842862, 987852761, 466872600, 201597355, 954267672, 680675750, 662861438, 757383335, 244757856, 108700586, 733646525, 624896746, 993189089, 706952586, 312687879, 250092858, 241112124, 851367942, 640216951, 299691251, 773065179, 922648823, 919029442, 810422279, 92138603, 156904733, 961124135, 55954835, 148942681, 70312141, 97161335, 420152257, 147758427, 332345303, 436918794, 604654995, 242694337, 294745565, 188098994, 678372314, 154647006, 627366074, 831711172, 570358862, 996264645, 549839897, 226145396, 509461385, 985949242, 720859718, 576353969, 882042932, 121089776, 705443334, 149885961, 933341619, 167597056, 217082829, 194328946, 476887169, 425715043, 406566921, 935025197, 852264877, 712390179, 663462490, 142603259, 941686359, 231905965, 471168577, 739567322, 449961030, 45882115, 609236680, 733845057, 276103089, 942869857, 638203241, 998540961, 306680210, 391769675, 17025653, 456089000, 662764347, 113403887, 369607783, 878981204, 356216972, 191164230, 647794199, 813293968, 878067735, 707633880, 258590393, 701548384, 233949968, 424668772, 76879314, 483902484, 526909808, 987720715, 771251132, 876708366, 185790559, 542298552, 546663393, 199888514, 373606565, 955082372, 876789586, 393368751, 702577186, 645987586, 499600101, 350800749, 783348642, 262568526, 131921445, 182461119, 341827289, 50872407, 569230147, 165527871, 189915955, 630741055, 693041263, 748153749, 639215223, 250054280, 666059509, 447299650, 834666703, 691537051, 685640269, 340106755, 679954556, 841735243, 900397859, 949429365, 31099831, 84683801, 98602638, 274351171, 153405931, 882957530, 901107677, 410432348, 981402089, 115508299, 191306493, 949138308, 455730112, 778681430, 446086484, 485306306, 103058427, 714517587, 672568811, 445885938, 346525973, 407428646, 479476028, 692526033, 152513160, 111558043, 543833195, 997626489, 561692470, 546103567, 79387492, 321275079, 504319043, 318933610, 746230273, 923284524, 326993801, 637469889, 12056163, 973756104, 756471428, 649228582, 651910676, 109876231, 303135772, 161920233, 304785301, 351663631, 535152075, 547691398, 837904354, 276769271, 532780278, 204703454, 952441355, 994507752, 843327267, 526908113, 601139731, 647531407, 215655578, 984515194, 440408924, 30276378, 420482391, 915930906, 69978944, 692662562, 727748291, 411951747, 261909814, 326357516, 629252958, 394053982, 254070901, 630629944, 203036218, 429663835, 550726608, 527023909, 302026917, 603932711, 383509951, 753977977, 209649169, 855304790, 281283341, 887006546, 791897988, 157934771, 951025360, 276571977, 320356157, 13584873, 443115105, 348148512, 941943416, 389081821, 168819974, 548659114, 337747417, 372582995, 100476066, 809845254, 294686721, 206410896, 559686981, 380705209, 400706996, 151478582, 94475285, 998706396, 860374096, 130025904, 812979240, 242929045, 978595910, 478557033, 363560069, 214467657, 987882992, 861633591, 65533481, 483875589, 514967893, 298220490, 410898035, 906007375, 523660037, 742671262, 74495101, 318711551, 196740695, 588899368, 808102111, 101003413, 235527622, 977986989, 254328296, 292206321, 305861922, 489706799, 56312724, 577978651, 132352060, 855166535, 810056194, 687391089, 439453801, 79290240, 129732686, 596749695, 569718598, 661113703, 672460859, 975504649, 628066249, 518114279, 891733297, 757592107, 605245500, 919207643, 226711693, 820561622, 839316617, 601060555, 657587859, 96573169, 71993957, 222552719, 299754773, 902624329, 300268091, 362198308, 995421572, 750411661, 516858500, 995738254, 684184062, 171329507, 445754749, 387950033, 627120068, 601625231, 611044085, 614071182, 378733416, 182562087, 698161361, 848840674, 523707167, 684239080, 822645628, 348506633, 184924655, 549476994, 286091722, 35918588, 4952547, 670392471, 794888858, 454223854, 293094705, 243557713, 205257600, 865719246, 883300272, 771110659, 381484428, 483285585, 583043132, 848154262, 223091525, 221594454, 207827270, 230305388, 852636604, 353316578, 435734397, 421802086, 534968280, 957717307, 699299427, 9144813, 440683744, 92783452, 636058201, 540164075, 174207563, 271790237, 360711513, 128070692, 225060367, 123187289, 677415439, 835370143, 631452516, 522754397, 580086195, 10122644, 365029855, 465451988, 291530416, 411907313, 999677903, 631010603, 630525047, 673333422, 730394099, 931841921, 85387417, 235867051, 608021679, 542007072, 642839691, 377177821, 585935992, 954530643, 91312952, 130879214, 126458327, 881357744, 900144323, 676449839, 996804870, 597574157, 459156231, 544799656, 615581169, 464314289, 612865777, 380916649, 486025494, 220015740, 630691886, 911575832, 361886497, 786543802, 86652879, 540973194, 540214398, 832754962, 635870279, 936041239, 711521847, 731847720, 789035404, 597341905, 52529850, 386435177, 558438870, 640072696, 599260314, 965753079, 773294249, 417437066, 588217701, 526765905, 573699213, 486998747, 382349400, 545175012, 786299726, 847352605, 663263661, 953602386, 803945819, 634803020, 636734500, 645236271, 71195417, 376235969, 699440833, 688686813, 408120720, 999895759, 256314305, 433410362, 330021374, 815726836, 284519983, 525740676, 707634947, 571779002, 146264880, 416542331, 37193896, 621304466, 365947718, 851615119, 95900414, 404363533, 372817690, 574881347, 412739156, 676560650, 324744295, 419822620, 320383335, 581656077, 740946698, 723944355, 604638180, 30094281, 745799047, 452323762, 414716953, 858391764, 728153956, 61209227, 263107200, 563084336, 983640941, 730643412, 493958155, 714084310, 789240241, 88844211, 102643735, 326156517, 222971483, 75285513, 396906927, 572337688, 134480989, 406521531, 3130887, 469978459, 909281074, 858872367, 130391801, 567696234, 746405394, 233537018, 499148660, 757245255, 368179201, 97166061, 479240623, 491422650, 543808761, 693018607, 824934995, 821110468, 97715329, 477801933, 392800449, 15183862, 132485246, 813569997, 494049508, 966595863, 223811199, 908985887, 146433171, 171464326, 344742699, 282995540, 169209476, 14663021, 130310790, 135613973, 184948517, 362249470, 139220348, 671221847, 699616942, 809649998, 852289716, 165740362, 711365700, 541737629, 607878470, 461567451, 961012569, 485130325, 892578559, 116012953, 489251584, 869738225, 230037275, 358544173, 716030988, 691787448, 371041677, 301449510, 836852364, 682718097, 971222777, 8092838, 445835265, 745777114, 122732996, 93185867, 657737791, 103473, 767218070, 177672474, 833198410, 650926495, 518682419, 157617187, 939799364, 677815457, 579730943, 439430433, 924840363, 583589769, 23802206, 753425229, 711138467, 688751531, 109287845, 986166864, 392760981, 147453251, 61784636, 896001255, 224616996, 592439768, 94062467, 709901295, 869460650, 304527203, 636931717, 807357116, 705564791, 347345719, 189091753, 218306078, 365746599, 583772286, 923181759, 265778318, 238529532, 499127797, 474932662, 617917542, 217920624, 740610920, 976022926, 598322836, 273482823, 44198195, 154653067, 763705580, 826901131, 157235242, 310516911, 240414571, 355582096, 24746605, 920628044, 110028590, 696693506, 822656677, 437154431, 408902417, 461843613, 621078153, 225111897, 658163876, 460287949, 80781412, 308658578, 706003353, 476903768, 34289770, 278022777, 117542139, 33055032, 506776714, 868151536, 82891919, 57628017, 63563644, 148436820, 897833379, 210807853, 101168725, 212145664, 211882165, 989231492, 329647323, 435546735, 123438919, 238064220, 95959284, 776816728, 907329394, 146333550, 9449261, 429925973, 372129657, 867646993, 828248944, 372087788, 207288879, 314550290, 666772003, 380466814, 529695407, 227016864, 414369711, 986220234, 792776022, 680736014, 621067071, 905310303, 912889709, 931096252, 95595473, 578039424, 897520342, 979619741, 361831683, 880673030, 830346039, 143791115, 31728852, 629061433, 265882229, 403423114, 341101000, 814055801, 943445992, 843132907, 322988508, 349176221, 252420129, 397599204, 678203265, 63761482, 691532491, 608218112, 26241339, 279023402, 426392720, 670732079, 394009497, 912455956, 224732750, 832172304, 824925730, 729566801, 556492781, 505358747, 655190360, 491545015, 161775675, 182859903, 214687474, 913184216, 255250368, 395144695, 666171386, 740952223, 105111398, 203345049, 683643608, 200286562, 726744156, 351071619, 684814332, 93754322, 439493730, 272993409, 820513218, 555408576, 182702502, 950116242, 745604270, 281933805, 892821223, 177689869, 807495807, 396726317, 418187377, 666818002, 518025069, 91861856, 408010359, 323495773, 209779338, 334018394, 513847955, 661385822, 936038175, 570877275, 613880052, 367825895, 146688935, 270383116, 193631268, 442396546, 115881190, 628447810, 299283786, 305854157, 452278236, 287964256, 447489320, 366233381, 591186128, 333665044, 96935829, 62234322, 678571869, 794995992, 743174484, 423721526, 467086243, 838851748, 111604633, 903027314, 19494411, 652040499, 322828005, 240102608, 38521129, 302346943, 325517379, 609363587, 397818966, 773160695, 769927058, 499669053, 527184993, 420983323, 582086365, 560214574, 386398673, 432658684, 819525214, 585342107, 557619394, 316317152, 311565078, 919473057, 661495538, 842190288, 530848163, 478434979, 660854640, 757563676, 732505028, 200451197, 924481599, 660542575, 398229969, 133148723, 383115163, 46215080, 107065309, 374494101, 602472773, 957731726, 372196555, 222851270, 324800614, 996696667, 255674622, 464760607, 844021439, 40925706, 461530248, 516754680, 223182732, 934761618, 597932967, 190712852, 50103645, 322303995, 690710398, 819674646, 906645908, 273251754, 782905465, 547948554, 334924702, 267584868, 677268330, 519586004, 806795631, 151985295, 239213100, 768565269, 831139872, 928053778, 857153542, 468580433, 941740746, 537690294, 58132707, 409907360, 770207699, 495496188, 395740321, 359003238, 552545031, 77291302, 654411435, 433037625, 212241242, 23006389, 690230317, 896045934, 778353257, 544108857, 319689704, 742847463, 116864781, 704197834, 929355201, 912815, 253641900, 722297085, 746957883, 903698467, 153779094, 783878210, 497370490, 141655770, 240587000, 48690172, 250279567, 93092854, 779114254, 517325491, 541063757, 264672379, 313585606, 182848933, 303787505, 333340688, 93444577, 675217140, 465106393, 729455250, 778313928, 829774628, 262494801, 955906105, 276214516, 521063537, 119504776, 591508829, 119635058, 872701012, 489185479, 659387152, 868643091, 440711038, 873202129, 109827009, 533202333, 942304046, 496786801, 344783832, 49572867, 910519196, 934438263, 763021604, 717850681, 51051164, 491148553, 575160996, 886581383, 599398595, 423628071, 827677558, 35842512, 73751348, 342267459, 162116828, 178434698, 343700202, 955112838, 835356153, 15135982, 549381945, 913741613, 760202595, 432119737, 222805714, 963147863, 756367437, 233659420, 507503629, 425129841, 810328746, 614561056, 292464234, 610076227, 748266972, 467555861, 621478425, 596020034, 277806376, 701671652, 513930911, 306005380, 230044272, 298592899, 453495496, 958212834, 563778749, 934081465, 920063510, 604309151, 886940591, 641389068, 31147083, 587829754, 176561424, 674906440, 892305229, 63738565, 460731010, 757802508, 323126660, 352810417, 731501486, 240805364, 333425961, 897152796, 438934734, 244158628, 882182131, 185133484, 109883138, 697023038, 207440112, 169118495, 865923239, 789172327, 956336083, 877970078, 840220028, 252077196, 956376773, 509414997, 44253342, 743518881, 240193944, 44415616, 781345102, 39250189, 677059029, 363427955, 738387845, 74940029, 488215579, 544647747, 927113247, 661520665, 861846295, 458509552, 23587989, 752608289, 727901420, 892274048, 187319803, 504018028, 848970356, 76986387, 299680733, 757157146, 605569181, 286951935, 207515071, 834770889, 875047262, 655328533, 433317067, 886769673, 947169284, 187665358, 953860883, 762979920, 7622666, 230906243, 767342972, 749987801, 432112466, 465016422, 62359586, 656538598, 444828156, 329107891, 913246395, 166729401, 868038484, 17545554, 440014518, 58796282, 485133920, 726960096, 20647693, 961966351, 472087176, 534551328, 299683110, 430914445, 612398985, 600680046, 471281754, 914045388, 710838507, 960564289, 418220295, 200389010, 621705965, 47438067, 564695946, 760878090, 383511811, 207451844, 234493115, 535877846, 965604840, 444545624, 870491860, 310875360, 616455897, 233578291, 934333279, 422340413, 25263740, 335390872, 464036925, 172017011, 524364654, 773519776, 822211676, 502661808, 712847463, 377084698, 653034120, 676535616, 297135034, 838440854, 222714633, 251748176, 675064002, 463895775, 595228675, 528703607, 202106345, 829816908, 25185361, 962677418, 324616319, 889117025, 16994791, 404161635, 963852538, 226127406, 649542360, 27043124, 739119173, 953707703, 837801202, 2643495, 530172153, 639894418, 125079674, 622864522, 702936615, 28283982, 792903317, 343132427, 504442270, 401063926, 710990155, 998019554, 487530863, 129331098, 894920170, 663461313, 2413854, 618548267, 427591809, 165402930, 279360730, 1280712, 303334287, 288582021, 867174723, 805701779, 865612578, 547544775, 494487382, 257785407, 781416630, 969420478, 164204561, 199830071, 951574944, 512282273, 798132908, 55514154, 743789675, 562719428, 809696438, 907956430, 434186075, 875421773, 990127868, 36591451, 885161012, 89047198, 135852346, 41355988, 30517238, 169913642, 270168715, 775021, 898250405, 811589535, 461628062, 829171355, 375657920, 988202902, 949257394, 389159353, 800895520, 699175950, 169575090, 172071757, 835609906, 758303661, 54902822, 856736156, 367927825, 886784912, 667019149, 105520851, 450939517, 808987678, 787702571, 680128465, 786166797, 414106013, 867640963, 629509385, 326047692, 90582191, 219782093, 928397786, 801317138, 615175197, 721916817, 457118865, 759145567, 884488712, 171464561, 297332337, 64328846, 871982111, 364504797, 676979602, 831079323, 399635838, 649942543, 866300828, 752427409, 261038523, 853033447, 480143350, 526035627, 37654302, 987054657, 826816106, 607708970, 761414414, 758948730, 332491092, 61716152, 148064327, 494567815, 922465755, 228020196, 377723675, 834124164, 681947058, 377205040, 263805990, 261186887, 850988258, 3513654, 903415976, 712709838, 706909002, 700511087, 157072204, 207520743, 519296312, 717557230, 161358358, 979863036, 135961108, 429171549, 212520517, 754344320, 62109754, 3981981, 588478258, 449019160, 693158368, 915867420, 533421840, 646628478, 473516677, 857917268, 775023150, 313442413, 873706018, 444542630, 961830668, 714964142, 75464110, 292023536, 847284139, 815389282, 967130675, 219333595, 772535893, 823545398, 870789999, 305956583, 642825370, 315823026, 1203196, 525066674, 49433333, 61100965, 599774812, 466254055, 381193397, 562501361, 133110390, 614808953, 111098674, 496779477, 250901750, 953921815, 337693120, 564696177, 928765334, 619350687, 30685056, 642269115, 481679922, 634380814, 161560748, 605844401, 417931185, 602283440, 847807652, 94331342, 356722254, 514396180, 930492585, 177250605, 498009438, 634479412, 838853355, 627556501, 891485215, 168431391, 104610290, 139069942, 892123103, 141049971, 460877986, 408163180, 63380667, 270192052, 403207007, 34254926, 98517697, 845012620, 189505686, 840353162, 920362712, 987360798, 279267386, 425902445, 346590189, 191920990, 677929990, 718991525, 676063068, 817583480, 757955316, 7062452, 789333999, 405153378, 443655182, 167344923, 184441672, 915542333, 654392308, 5469360, 839458827, 952259862, 739109119, 959580797, 630620113, 440177232, 218831640, 905820073, 394811939, 743535473, 944827756, 263599132, 932828748, 215226677, 793895123, 798801752, 76289465, 571380510, 479843998, 311132473, 468978984, 230514246, 295115648, 412739698, 867231183, 894581696, 852030839, 928728844, 335119329, 474536933, 952177333, 779689565, 290854492, 651858346, 714359217, 973230682, 635722736, 849491063, 494264116, 286080923, 9575348, 527607645, 711087952, 774745200, 102483527, 786796773, 875606432, 743174123, 645598378, 326189715, 140121435, 101995085, 426538434, 254595980, 932168064, 808153772, 108087215, 628661543, 415380932, 592144800, 313106095, 808047541, 603230066, 860804746, 758746939, 568175137, 771099776, 254666881, 970646035, 382245467, 368245291, 935050057, 908097287, 893317384, 849504969, 370272046, 217014190, 30274337, 740964368, 790370552, 541440319, 58388419, 227245147, 176629731, 63503179, 671234574, 139761937, 686274758, 366944895, 680969785, 584084769, 946188754, 776332666, 365484146, 393162305, 142682818, 662126823, 931826055, 969127368, 548775025, 644457598, 345402632, 869569557, 192825417, 296550301, 97661522, 340395248, 663162849, 22176929, 353886182, 508881591, 404655064, 363238146, 998268438, 841963433, 283413435, 201651204, 434969901, 237051586, 943186317, 288348675, 411335455, 833456042, 456092474, 249864204, 713373619, 712227257, 345241428, 607791485, 357154560, 595766107, 655542716, 315985101, 408338707, 383504691, 670165715, 989049529, 64530427, 29054150, 220894117, 763938353, 463615913, 692058933, 528374620, 927155966, 691505009, 192210773, 741197045, 570030322, 32887549, 320580996, 366167408, 288055424, 563633325, 832963424, 356036126, 751214780, 212658922, 476099951, 752149859, 891142181, 471202403, 720417545, 150848945, 893061065, 228195380, 382327093, 501412604, 435949469, 170959607, 485298284, 342467035, 650838445, 179179565, 525491178, 544013552, 374188624, 153406798, 753771639, 367621564, 923670313, 737665449, 360388427, 978383399, 236753455, 925440776, 23414014, 726137815, 346599676, 403866484, 801058905, 346928647, 743205723, 8160922, 797663447, 523754238, 446027235, 920437442, 575200347, 513203350, 627057165, 43598547, 143867820, 987817046, 71193666, 339650394, 543213649, 79929348, 368586732, 372782795, 470188605, 44614405, 861174347, 112796782, 596417309, 970263408, 997548010, 806484195, 880996346, 267084249, 222812819, 216977487, 939748642, 694970169, 847153242, 975561912, 437032024, 493167715, 905742534, 843711145, 382119239, 685117276, 482183369, 16950276, 342628045, 763126616, 691695200, 991726038, 575608132, 685015620, 634468668, 538293541, 40725026, 916206965, 665848924, 747019097, 990083476, 81787583, 441392386, 784386574, 766133756, 336941301, 999088406, 680995156, 252916117, 700648800, 764709276, 958593234, 699221666, 961029942, 355446753, 626093901, 73612090, 22900253, 970406702, 721720861, 958102713, 673619293, 101953759, 853004168, 995547272, 733024743, 311949737, 895634253, 144450615, 831988126, 315978835, 681250487, 669548382, 306520569, 496183775, 399943479, 634044392, 779936223, 55354093, 361373638, 646832128, 917371248, 620168754, 291277182, 144437692, 390818756, 233665636, 879032915, 820959640, 58438677, 14603961, 468468772, 138933434, 207790608, 755986319, 738125310, 630484204, 554166010, 212845420, 985769799, 149678994, 88903630, 71736633, 935925996, 302813269, 647900384, 933217982, 812577615, 801350072, 812351570, 249633603, 59012967, 666900000, 348676033, 680211347, 151044415, 836753335, 86688979, 67170788, 85909400, 763957273, 760652942, 141532986, 213976788, 747673659, 248240305, 385179583, 550717794, 298349539, 606660903, 276654223, 161036485, 979202147, 814281445, 402303416, 693353564, 235647318, 851867887, 982680393, 948889148, 910023562, 676843809, 232444846, 875590397, 490966682, 945484109, 366186136, 955635952, 778112204, 226844044, 603220251, 509856564, 701070781, 735103874, 992740098, 783595766, 689941343, 910240645, 133895153, 637568793, 869077001, 722568357, 678869604, 985694477, 26732562, 542831246, 498242699, 542755242, 301108907, 94679937, 551235056, 749291817, 513476979, 361612053, 296507552, 270441798, 723455359, 364838931, 613394234, 158626467, 300442907, 315104035, 20258781, 342993099, 453962891, 648448513, 288878688, 832880709, 669301409, 428305505, 654951683, 81893779, 591561978, 147752670, 558535107, 45655622, 895288519, 988842130, 888378721, 100339359, 622441154, 38904500, 543957090, 788193543, 773779559, 951958476, 854480941, 308131429, 662067438, 187725250, 297350383, 72644772, 385845846, 934748527, 534121241, 578326194, 711670734, 681884683, 689913020, 392569625, 483952436, 124301617, 203110356, 721146962, 902602401, 106670912, 966132279, 833187301, 503249467, 272753605, 332681772, 188375265, 55422284, 160384014, 469966208, 557102092, 669730967, 229980505, 673680543, 671256965, 577249000, 295054635, 216876907, 799024744, 912845681, 777235966, 459111866, 555104621, 464898063, 852637367, 685591455, 20422974, 619533927, 297876172, 78661776, 612075999, 155356439, 591366611, 410157745, 172352489, 220901886, 264845213, 376217937, 771806738, 208860388, 957511319, 542478288, 172867200, 997838410, 182834876, 336311035, 653158364, 965503054, 81587709, 670813079, 185152815, 758028453, 349544572, 215008283, 263225557, 321437435, 770117422, 928244321, 977347313, 953493812, 872949237, 861102843, 231872821, 678999713, 422509665, 603237067, 965219968, 615521865, 124742025, 658144620, 877443357, 937189068, 291952690, 544181865, 682705377, 72207420, 866129674, 857069393, 174473182, 907937558, 628075849, 211038551, 809469047, 33727841, 112288720, 477446071, 848591810, 105011889, 496731272, 738122828, 65209204, 81507138, 120230891, 705749429, 361616979, 473440243, 553061343, 612575146, 26753944, 949711941, 741881243, 282776332, 730674391, 152624613, 248492782, 262177634, 221836997, 250368943, 581897307, 949180671, 716582395, 99441223, 14472854, 926967883, 658997303, 939048403, 844816904, 409785374, 691917145, 407132337, 851748603, 838503944, 276169895, 482506731, 909913019, 456766031, 635787473, 79100550, 884989246, 745455468, 237703765, 244899937, 744362027, 781839645, 481057497, 356477321, 400793732, 947405613, 848671506, 164739664, 600013316, 978344665, 263930475, 871165549, 323488115, 670465718, 161510327, 125629807, 245355800, 246447181, 536233875, 676526545, 402391646, 510862066, 700689977, 521609772, 90535665, 124361395, 322699092, 294221286, 138804184, 455368977, 920774484, 408801899, 175973733, 918148684, 978968218, 393140373, 164871033, 704279248, 336149306, 879345317, 650995613, 153681910, 9563715, 207277279, 269048421, 779179997, 585097748, 474861462, 19137167, 176100462, 745769099, 563580928, 954099831, 180424953, 321730055, 601150207, 887077385, 82977322, 511253042, 973125374, 417561464, 417925854, 465293207, 946246540, 547790372, 893906479, 295277219, 431364184, 448608838, 832827268, 520368241, 7621616, 818606058, 913896860, 499930840, 907824739, 990639909, 652948280, 887161214, 254102183, 930301374, 149075755, 248106534, 415007013, 141453634, 270371816, 664292292, 559508715, 432875622, 961963952, 272771533, 923783480, 604579058, 55407291, 897683232, 702840943, 603157371, 236756936, 194365856, 824367820, 351869142, 885181592, 484636776, 807930252, 164212776, 549188121, 251755302, 343334969, 716594802, 563496348, 528891467, 230041612, 860061918, 2792573, 70414080, 265233859, 178382428, 779644214, 884954289, 186882020, 574749559, 150717492, 743770834, 883251963, 915129178, 546393003, 6470494, 893289592, 798420498, 18611914, 128608024, 217685737, 227103087, 360170088, 143236806, 322214283, 390735714, 659653452, 425877495, 183971242, 82822251, 982296922, 432849816, 467213236, 135286269, 412473185, 801205975, 788878533, 374485513, 942254823, 510037577, 444247209, 629755139, 388546672, 955204057, 121577774, 276328620, 415487063, 837034534, 43461263, 694132215, 409691407, 285976887, 191772462, 114095823, 592834952, 519691, 478497504, 178676893, 835326881, 922683603, 564056915, 578610954, 410596745, 954182182, 909948856, 499557095, 285630005, 626596465, 795830984, 450826435, 942896734, 28777900, 547116396, 283440625, 286097085, 788455470, 481138227, 598183502, 989928417, 798701471, 977097784, 347279333, 153063195, 167415218, 231621502, 530823164, 370609442, 115271949, 726391634, 864251797, 743569354, 71787506, 623397634, 535176194, 461942122, 749814394, 727451302, 2458872, 101737335, 676242221, 867415630, 325356651, 795065254, 190988262, 24468473, 751137197, 32882106, 633651280, 153867512, 622383442, 367123463, 424773731, 43071681, 984161330, 429127363, 80353820, 622890861, 24641396, 721995129, 509875589, 905325124, 244054167, 44679995, 161605605, 564582099, 711379567, 572773361, 31108572, 199732262, 268862924, 265200138, 924710129, 504923413, 535826256, 450890359, 856241107, 116283121, 602566743, 281279471, 981846335, 225112711, 221896243, 201090165, 824017226, 628372880, 53902766, 105247669, 14040793, 799227564, 973114320, 917079386, 310118903, 455335227, 456616767, 767573568, 195684830, 452154395, 677023377, 83755217, 78937537, 503789423, 258257449, 396504128, 224407028, 683079240, 730354761, 672612688, 469410356, 663907988, 389098356, 305029431, 171472816, 610885276, 591947837, 709075998, 822100001, 825966687, 289303963, 433463323, 547042520, 579379665, 720056817, 596625926, 231490749, 432439589, 167645774, 178447921, 293412473, 142280128, 440562687, 998877577, 356133909, 796846934, 346900941, 254343918, 380192580, 603452629, 940848017, 585083436, 914810422, 168970795, 759269610, 131232414, 358749491, 413444121, 751827911, 355987238, 344455643, 895542560, 885286245, 207750434, 321259648, 597348999, 266552122, 571122881, 386150221, 330133240, 178571001, 136533957, 923136494, 856594475, 277574923, 411891029, 73143731, 130672473, 588930774, 993833983, 305889868, 621405367, 618710222, 88209878, 414479182, 689679167, 874605800, 19720371, 597815327, 510019660, 937330641, 576867187, 32954264, 655744234, 536439785, 934758965, 501977293, 554751666, 593994245, 764821116, 152870457, 395889391, 824600068, 182790428, 179051548, 981372004, 934642387, 239571135, 375974193, 491605112, 100375655, 660681566, 645421228, 527659567, 96838534, 541459095, 639761820, 411815078, 344189080, 748759728, 30748214, 757632552, 316674382, 992493466, 812912390, 224312290, 219187856, 781211815, 215293328, 871534187, 373864716, 353782129, 912356776, 303300546, 379351515, 228138408, 169327460, 813965724, 984977262, 250293486, 755391470, 565712011, 679872933, 283743376, 576346122, 845412989, 429344626, 655855472, 106296607, 19563387, 35947009, 206012241, 578629672, 304948073, 861905383, 83428582, 872071708, 807995018, 915976060, 73556492, 2148636, 376776628, 667346097, 536306403, 115045128, 29089651, 283394552, 75070178, 959180502, 996012057, 828818870, 86805438, 174417544, 522373971, 548228839, 916075884, 700764579, 552932139, 301774513, 134509281, 249615707, 177405139, 620299, 596262141, 779104279, 968105040, 469970790, 266606817, 888053493, 906953290, 513441287, 219712821, 660993396, 702560948, 850861424, 268115750, 13259061, 434463479, 14134142, 890323685, 981421238, 518364546, 285891891, 523978451, 361747362, 226593545, 31197124, 109278234, 290417592, 968791927, 525571886, 675079481, 957144214, 247741400, 343956399, 453237016, 533640039, 671026353, 449600232, 75778849, 619494585, 600236814, 750874618, 407298212, 60433037, 987102080, 855294263, 40986248, 978977049, 611093312, 323233185, 174191774, 130320382, 776011525, 149385742, 943167501, 772653359, 578405801, 667586309, 389999432, 122990479, 815607731, 384598077, 407663140, 306649137, 650909977, 538561309, 257079095, 248429112, 100619284, 548434801, 302391445, 916288576, 503427515, 696076234, 672918308, 844816531, 264890027, 27669529, 918643563, 245466828, 152887311, 328498341, 910273891, 968803457, 289764222, 532399313, 833506152, 870190632, 122545396, 596584611, 912573623, 257772705, 237996163, 59561840, 829247167, 982400549, 883222515, 876473258, 522833571, 564352260, 244272938, 310304699, 457394453, 430166376, 830605358, 142171717, 824683595, 497133092, 561945633, 620579863, 673155447, 672946424, 339915033, 588559846, 990078574, 129737351, 243703701, 826299959, 869500628, 959887173, 619198532, 855430895, 688116594, 295045606, 947075526, 40828285, 553747303, 359386583, 31456752, 886333632, 531970194, 614172916, 15918931, 745128812, 897937739, 303596617, 448766798, 848390754, 195478527, 157742076, 36499841, 247300710, 794474169, 882049370, 377909423, 490428196, 392913813, 936476847, 172051242, 798697990, 775652316, 983473373, 35029769, 165002789, 833032950, 611859519, 205378802, 94119789, 10821879, 387436755, 696650551, 271872355, 420317811, 15725044, 754018554, 319248750, 555996868, 168483728, 149798717, 990629532, 762930947, 350156824, 568414564, 669667315, 716921852, 301337336, 506448698, 358687787, 149566263, 475123940, 504538609, 707397808, 918542273, 665718788, 362319076, 825230024, 544629901, 262285306, 383719534, 469569546, 995760957, 32850928, 714723389, 639206777, 686896689, 237305341, 365682458, 170140192, 570570290, 886348850, 231521564, 756867223, 663938991, 481879204, 523012836, 346194326, 707396854, 105640181, 101853566, 47060642, 942641083, 906060505, 850541111, 839953043, 755103609, 202486266, 38983682, 270566107, 670500614, 141477018, 517398355, 407302380, 263273336, 274496678, 280242613, 825250638, 237850600, 261011869, 59152612, 325845566, 877884604, 112024129, 162027506, 512782196, 8283820, 500389901, 279939007, 126708407, 882606826, 355814456, 725425466, 586927711, 907476721, 495886299, 582478306, 558814207, 469027428, 815874426, 932953265, 790133270, 604337311, 367209018, 787991700, 725587357, 922310609, 385955454, 819862133, 571185779, 102776057, 224722387, 822317210, 148395713, 313692795, 664448941, 95251470, 535324342, 571872352, 637863764, 660661770, 427820101, 228435796, 975884044, 595531598, 887069133, 430070978, 237224062, 271486032, 509762434, 34102994, 491560589, 322196399, 233834026, 746193101, 416059492, 386139444, 168657609, 55941183, 327654184, 678836376, 594073587, 854705983, 143492761, 719515160, 688363192, 254663053, 274074928, 794414843, 532093492, 685080757, 399731341, 915758584, 971682314, 870836650, 320279186, 195591912, 82722424, 328382372, 766315861, 846661059, 226778419, 885731076, 535689323, 518119607, 840291332, 834726293, 248346781, 772423681, 773296835, 43797774, 146930733, 90054927, 501069280, 833344244, 145021008, 141125853, 627572362, 612260767, 697820639, 893132156, 245302017, 333046658, 129486073, 777565756, 636054816, 820307334, 39612101, 936241151, 652288105, 909672455, 383603233, 754334967, 240886559, 921754135, 208298987, 501263020, 845860873, 84577777, 707980784, 589619697, 81682326, 603521191, 570367536, 369406300, 31309872, 911349140, 598517027, 469505955, 459174866, 293591933, 746375646, 569698694, 664522532, 716902878, 145811959, 311644068, 802706531, 79281075, 868724005, 199471819, 128684298, 851781260, 254351748, 835015656, 432916348, 15302793, 295475414, 927078964, 680279446, 448400519, 465622661, 324122504, 278057390, 372630742, 827586855, 199352411, 655712976, 741284431, 932911404, 7881230, 922944572, 611622197, 267139831, 821387165, 921423292, 941308754, 496165168, 368445227, 253846303, 10217857, 441124646, 26023149, 349386319, 453438752, 593998725, 849599522, 132747973, 675967472, 508384989, 406728518, 810035604, 860780291, 999895063, 373858476, 162088723, 318106788, 478655994, 129762105, 633452958, 420941516, 158822523, 518071133, 603696482, 308427573, 905687234, 703159088, 320193431, 943134222, 704653120, 819145667, 432990357, 992784204, 438523818, 345420190, 221824026, 333038000, 446377131, 748301397, 250563107, 925619214, 234906362, 707036482, 880919951, 127620177, 601586331, 689444425, 228776354, 666723783, 772943498, 333129441, 105234023, 586046990, 233966310, 859632066, 508661945, 56146989, 969721154, 876471481, 698944482, 859013042, 251332022, 417875696, 408394468, 17312280, 31500683, 670962987, 873393983, 582864107, 604793681, 125523699, 63932462, 465916032, 897039578, 489108169, 653578689, 235820818, 56281452, 701442095, 629435599, 344908985, 508361403, 205263626, 611449656, 909291293, 872790859, 955803466, 647222453, 851139461, 401217462, 176010664, 348838519, 736287225, 241975418, 780928215, 264074250, 38028827, 777770375, 527442449, 339508046, 904561402, 155923880, 714526809, 193109662, 963593698, 360872230, 733172724, 662886069, 610979066, 695014771, 275821959, 284992045, 885826264, 330170540, 743428763, 585876554, 539087472, 503629286, 239332816, 861911364, 706555706, 151564438, 129399927, 848708256, 246062667, 779779842, 146733407, 640689729, 849326859, 510568406, 210130600, 225733498, 13117031, 804885941, 835298391, 851988201, 998426181, 301910847, 695093304, 906676108, 193222703, 411250146, 920461907, 570896210, 586858802, 785743162, 930296664, 975132846, 458383988, 535870095, 897886454, 641091430, 497926112, 414854512, 193513644, 504367020, 414171610, 370371252, 358721060, 999557779, 533566922, 691746794, 849963398, 770126685, 190653006, 354884321, 255945725, 725607467, 139422032, 654436925, 61953011, 141587690, 636733232, 513190965, 734923324, 94694472, 710734447, 147580309, 264323563, 31713633, 395988282, 767818733, 912363558, 624560666, 808808366, 661587534, 371798333, 581285641, 713604253, 518009511, 810231033, 567726957, 348448437, 56726800, 591579529, 849949125, 507896111, 277413112, 31369349, 869745247, 858524582, 272006685, 553818814, 84068482, 556919616, 831951271, 466617710, 688997441, 494332936, 194549070, 168909187, 425016343, 274892698, 141996279, 303402308, 609762296, 672219342, 136921822, 837307688, 537380489, 603798243, 791492353, 233769515, 404026285, 843895488, 511544680, 536818678, 801950576, 544654225, 267916617, 508401529, 578635866, 315556871, 459645359, 321711535, 48054634, 181287339, 392682755, 300048258, 654947248, 512252100, 75591178, 555841657, 982929716, 518230696, 577998703, 775715047, 613957430, 521258931, 926969122, 427885904, 672283897, 379217595, 808202863, 46915506, 849345942, 662848598, 562096562, 530434116, 686999501, 89803360, 259934570, 348681277, 100183236, 302954721, 261396263, 880119009, 693580157, 437427413, 672340316, 876292240, 827061728, 444213789, 21346534, 401755389, 913393401, 197356390, 613926580, 102992082, 171384812, 164576208, 723968766, 908494003, 747705034, 179444800, 702780500, 859647344, 625753785, 707395322, 733984717, 850609327, 722454629, 234510984, 868328453, 535491126, 833065783, 900359274, 931832810, 115931204, 204212126, 175348211, 245332048, 28527999, 127581822, 181315509, 713620985, 951181808, 526264604, 39065997, 700482015, 108261064, 823253783, 550003368, 38166698, 201593805, 820624047, 540559866, 599897479, 226172469, 327786089, 630751770, 722761220, 942796324, 191906572, 361435404, 289971878, 484815374, 325397993, 861739975, 697252994, 581273839, 829927610, 832450194, 39046568, 837140320, 672564598, 915080659, 526921167, 420377995, 504926098, 926207120, 508497781, 425538087, 984160677, 337312719, 437715784, 454597836, 422633743, 288886061, 745236494, 668542346, 658059271, 979334405, 746668968, 601708321, 661970810, 442889405, 647703692, 637246654, 774548264, 799702731, 19176347, 192437672, 727665070, 496404375, 569403712, 845046024, 991745887, 530858029, 790150235, 281660421, 394987855, 847536259, 29241392, 162924736, 198283219, 587538111, 238526408, 907029116, 186005028, 659292724, 784313560, 24685357, 248074363, 4250243, 440015458, 229344444, 33068187, 408082258, 571372105, 552639502, 923213014, 822523859, 326641723, 97993650, 239669674, 713391891, 685559281, 816373218, 620192898, 506709839, 145683762, 310698321, 572618320, 809106698, 138898299, 449083051, 637578942, 314416369, 693294387, 803656862, 816538240, 761870916, 60379716, 712152316, 972492904, 885750746, 185169605, 700887894, 77280187, 404098775, 860945979, 19428486, 616583278, 268095981, 428981862, 954174332, 329112674, 137087055, 902105954, 63318004, 621276185, 735946843, 650959386, 165775661, 457735105, 818180205, 618662061, 486985629, 271078853, 1776130, 198417637, 45004706, 417920039, 102897325, 583252924, 763359741, 383824957, 726647184, 884701266, 382157748, 34022836, 271660023, 231118934, 27434006, 721220628, 962649994, 255173656, 210048080, 205097717, 998531818, 431184872, 236702508, 195582633, 549267441, 827529427, 429534739, 761238506, 98310125, 204438642, 163233544, 328965215, 36846831, 147357325, 40725563, 145579801, 666663870, 18902324, 463008562, 628937657, 233052573, 136401869, 852151763, 950350505, 148633712, 836518752, 555231632, 599953299, 205541826, 659704064, 27069729, 5729833, 781673442, 207630563, 833897853, 436199460, 288509047, 691621156, 569896475, 543530054, 458607876, 766673797, 881763314, 699229779, 567963471, 853393926, 530654614, 602719502, 28414801, 832921436, 662327185, 38914489, 597387246, 365727620, 103236515, 445763306, 551865325, 678249671, 358508487, 266634272, 118814009, 581965785, 676362477, 128536228, 286325169, 259233708, 819708384, 641275806, 229374605, 241505141, 135672399, 506625098, 766774686, 938481391, 46225551, 763869690, 438624008, 909553639, 528892405, 368599688, 124016951, 214747390, 484480842, 584989087, 263969298, 738876589, 880923525, 135515819, 75200311, 956353280, 69576193, 96241090, 870943089, 685546964, 298566533, 390183887, 940579998, 328802077, 213066503, 968991990, 717103462, 351518595, 240057081, 208007497, 27323665, 335597318, 754925393, 71292016, 566109302, 486449086, 423421009, 936354858, 562494580, 311990327, 694329956, 285010404, 462114443, 915602810, 978768191, 714147063, 262391280, 808549108, 356707613, 166884542, 786951698, 109825865, 578801369, 994980222, 173677979, 167014188, 586831098, 286386251, 717708038, 19305426, 760607944, 208333279, 528501563, 427747395, 294517904, 595925374, 953122572, 411912213, 901592794, 556512957, 127700958, 176974712, 756451919, 674795347, 746152643, 245415740, 716156645, 927373395, 281113270, 923163305, 323359271, 382173723, 244643307, 133774971, 338227307, 117974772, 666578382, 55718108, 278859605, 81038170, 61086825, 949232600, 703870184, 597935228, 549293944, 174831447, 446307794, 123628905, 937206970, 119806921, 148825966, 421503328, 500666257, 566917162, 695322143, 789549997, 769945446, 519095344, 149864314, 987677933, 579565889, 251654243, 763407493, 576559201, 973842560, 995858523, 454087804, 459835070, 627164658, 247123830, 346674533, 453917965, 976364877, 464341394, 487150302, 356038673, 722562569, 58996619, 782494319, 620670342, 261361491, 703861395, 813512694, 194483529, 894365486, 177177314, 682609349, 61775207, 140133790, 783826222, 742312565, 630915912, 947826290, 281455472, 244280476, 279152089, 125228196, 775130936, 964137721, 647513718, 56973187, 76314774, 749329452, 50988617, 108749261, 265305450, 999487031, 154233507, 386870134, 75453836, 321196181, 565842696, 390584071, 772909364, 106889133, 776022525, 387544920, 170466626, 190482413, 887993193, 220547255, 38071348, 34091007, 684457287, 192532290, 85947472, 34785748, 47990424, 29604973, 100960265, 660268157, 375816248, 449338634, 38730840, 231695424, 369569578, 934413598, 803106569, 531213684, 411994085, 221181785, 817687047, 444786346, 519508902, 534764053, 728741006, 878279530, 996987679, 234893940, 445542630, 276349361, 579340466, 603932748, 829802289, 642203648, 56915792, 624279790, 561905791, 627063190, 456567004, 388709276, 701380420, 779843903, 825413643, 906627042, 492391224, 538934652, 838338382, 70432486, 391005945, 427592313, 331420433, 693889313, 8640018, 363975840, 171761160, 852248980, 642012689, 1635706, 150229678, 481107151, 555457117, 294173436, 667234027, 966637363, 147938723, 144425516, 479675847, 425291187, 94493481, 578363212, 822779895, 435554894, 391549602, 900429958, 353686798, 257376396, 428678906, 637973739, 462811724, 485845324, 499001374, 103013749, 925093048, 745344531, 508002013, 217623251, 311241313, 510326272, 196805430, 717559799, 347404641, 342398367, 731292027, 914689684, 918794255, 465594884, 735838960, 464596738, 722548264, 978323233, 194993108, 304782696, 420139198, 80041568, 530659855, 804514266, 541827499, 692520668, 992156609, 152959967, 656766032, 53047145, 160068794, 583994714, 378754837, 477366151, 163639735, 280224035, 411359781, 925049500, 43305276, 603091533, 976657643, 30771301, 835160126, 445552413, 351070059, 736419910, 779285623, 579658086, 670026897, 358698569, 973256609, 642523845, 655961846, 432080026, 70214646, 643125161, 163740334, 616713933, 324110247, 781820270, 121205259, 466451888, 855788757, 312339333, 944736212, 566742723, 196890810, 150528305, 499406778, 682870586, 662504167, 890775540, 981690276, 570625450, 815053322, 40552775, 416395102, 548332691, 214844240, 566665196, 125583789, 180427962, 233930449, 7090876, 295918765, 801106018, 990117850, 217174888, 938449978, 478660641, 463193894, 272878875, 756532992, 377866009, 418127861, 41955023, 701657701, 895062047, 747014311, 106218852, 957117059, 830825986, 394441245, 744588641, 533669969, 598141432, 239962060, 98779125, 604621476, 642534526, 863686726, 830547159, 487987853, 845813506, 356421861, 623296046, 452982978, 239540462, 782244997, 378355223, 350045366, 532475657, 214902224, 928602421, 790243813, 390777266, 308735210, 338157091, 861624832, 656150877, 351556337, 643225249, 939853255, 858358808, 859099777, 591373196, 818686687, 642577183, 930743286, 324913082, 381272039, 372671891, 956783921, 509266323, 535071229, 210559800, 443042049, 51898027, 15242974, 29344815, 312753015, 788300870, 222364751, 935270383, 294078659, 597512030, 766853578, 199230591, 720076620, 695943721, 209777994, 664821043, 938423016, 156771306, 277960922, 233524594, 376879313, 976320811, 208559059, 398180957, 814388691, 153912619, 939723197, 464275725, 338077130, 400548636, 863922264, 958303377, 985556937, 331242188, 164735494, 876273686, 309135629, 808064103, 333881857, 389789927, 908469042, 847611042, 738979485, 142603436, 279701050, 935252462, 590684970, 590827046, 983114083, 673573273, 114745076, 811917917, 755617993, 499104027, 49616149, 250984514, 291964083, 709782358, 466805796, 319689729, 804540150, 712125124, 882908320, 185607161, 632142757, 360762359, 332384430, 241555936, 202229979, 663475822, 667487696, 571218122, 579721858, 964112598, 262415874, 621386986, 182306407, 534322921, 750863069, 3532509, 65053792, 53176561, 559764204, 750737910, 957251942, 690530219, 584784851, 21866685, 963468022, 461265410, 337162214, 335156389, 405594213, 192705554, 168702260, 350726142, 606894706, 10222490, 423936714, 874255198, 307744696, 992608238, 378660274, 81160806, 271517507, 623454455, 829081874, 616094268, 509249428, 903314533, 331912088, 170243922, 260989723, 550489049, 779933168, 701521190, 911896880, 687151012, 995816833, 692223554, 340364414, 159975593, 927382661, 691794901, 814634899, 580984608, 825365170, 347927711, 848829039, 899897309, 840617529, 963560366, 648201674, 732910854, 79732550, 380378474, 176473981, 185031284, 355282593, 456890977, 450098163, 486956686, 763921224, 411180319, 801785332, 447625817, 484012772, 985176462, 751037549, 796289518, 179780809, 839646376, 859348313, 411023998, 872664780, 694825019, 225780587, 191093717, 353610029, 888111045, 40847129, 625178407, 581702378, 745120192, 204250467, 731225444, 323939455, 207544400, 95397591, 515396976, 897594262, 138243651, 221647124, 89571012, 111957249, 759692431, 268600023, 990042295, 234970778, 239771360, 307980138, 552007700, 202752953, 399257424, 533832049, 671047882, 94999488, 516930449, 375679345, 554294086, 226978020, 960774750, 308009028, 926480855, 536441700, 126753336, 285391917, 574407763, 274871899, 17813475, 385045773, 17352668, 537717265, 666440325, 241116121, 44527291, 947354458, 596155599, 672489013, 465932164, 476055133, 227262275, 302662083, 431351669, 794186919, 145284321, 372229059, 952821380, 171289458, 638776656, 126761163, 238482658, 222553941, 767609655, 73566241, 698879180, 79105304, 448964305, 826448719, 592440857, 64471673, 438053430, 52128243, 976620028, 902641805, 621335155, 503174748, 566835304, 684726768, 28522162, 304168264, 341679312, 557196984, 650376604, 893746572, 196722488, 490212647, 151650759, 10271143, 91203231, 624608182, 600127051, 357815172, 965638202, 669325742, 406139873, 341534689, 956423080, 987257013, 247551851, 826785459, 835702722, 784942266, 786525898, 296568632, 918079563, 215989698, 834856436, 230688876, 206938593, 260843527, 197301006, 765694651, 948887778, 49213132, 400347374, 151960797, 574645173, 92488953, 983627119, 258131067, 317948614, 163217037, 920433550, 956032057, 232072513, 594540572, 628028225, 175988310, 328033266, 50166691, 309305419, 368384438, 737561632, 388149655, 489038970, 598505537, 934479242, 387901371, 134215526, 286377575, 803528621, 415933590, 437413073, 123403587, 55779488, 463360666, 63123082, 563922315, 12074245, 36548478, 395401623, 975579884, 593776102, 237811, 921520930, 213843514, 775655615, 219684609, 100971944, 77060198, 859889197, 187956769, 32376106, 47943023, 329831557, 683069062, 715705052, 578449664, 28326181, 294318741, 10569413, 907529079, 278762992, 755479295, 222665720, 814277081, 663938852, 53645905, 16951823, 470645652, 304000775, 7325953, 589515890, 69969630, 928513872, 50972286, 466330106, 767612731, 643748707, 29220585, 264422113, 255452326, 739770566, 215094070, 103152685, 436151818, 384979103, 759103117, 970274128, 105182658, 945099254, 851062203, 153875690, 747806665, 464639108, 694112984, 273978855, 842703910, 892778288, 407235498, 947804126, 100739043, 124682889, 919047558, 199760633, 573218853, 660609980, 129461937, 825368333, 52663894, 606919562, 954410383, 740063563, 219903424, 677310412, 912501094, 852980885, 448651320, 706869693, 955751408, 288789560, 278956494, 592560791, 488879013, 659746365, 887435702, 351275498, 352497098, 573433100, 82782475, 957250349, 416487608, 366195670, 585349580, 243127249, 890843884, 333647141, 666351403, 572397104, 288873504, 774996667, 169251953, 108362056, 787432644, 844156518, 589775712, 785162144, 872921469, 11591187, 499571107, 133500628, 779683331, 520413602, 70939678, 793275090, 412935696, 149583284, 384111037, 972836244, 138997060, 637943502, 908576926, 699406083, 72152470, 671088731, 78073630, 615493212, 77956878, 300013798, 624696824, 106138917, 568014008, 414827294, 127402875, 374040819, 547522409, 735581242, 207239826, 269650283, 642543963, 598413760, 491771420, 112147536, 997780468, 554245404, 297103734, 975499906, 816693924, 628223940, 186793941, 259556685, 74788206, 29325616, 470554625, 581261839, 367176982, 893716081, 889887508, 252137235, 396389749, 491275259, 116193472, 416191882, 750380125, 606604120, 251425982, 23681373, 14849311, 43038145, 922777678, 223924721, 822300439, 731117032, 563099338, 983710183, 51706887, 878961273, 35562561, 765177805, 331575402, 278775684, 83621201, 489048963, 688614605, 305252421, 30095524, 673218260, 94311469, 732022176, 643405683, 262456442, 465218315, 971551680, 552520211, 267180346, 907002647, 321201854, 242007277, 15045529, 464585509, 115964469, 62428679, 70047490, 960374523, 169081908, 98806062, 699695660, 299724818, 624412630, 466252632, 685577023, 11636489, 223702218, 591527041, 333452027, 557821376, 134129247, 552727116, 291372408, 223138734, 496168614, 226970312, 642706821, 40409702, 94901043, 93452649, 913798801, 357224689, 207385710, 429954663, 586435491, 474627456, 624528948, 723847807, 882392742, 731958539, 77790803, 396370266, 759335795, 975183079, 488515590, 565458549, 756876967, 78937271, 134919836, 332424758, 177876476, 133448043, 440807064, 960723985, 918331296, 883927573, 92699705, 269211931, 74483293, 20313392, 98696554, 265656872, 781899865, 779753839, 951745058, 193094383, 364912090, 357344339, 628243532, 472873612, 855023757, 117215495, 96781597, 617132101, 246323017, 949882075, 884076371, 100727401, 731717842, 296621375, 79898562, 38917064, 958894157, 55765463, 990489071, 223360556, 532210412, 959393222, 627634378, 99155426, 412944077, 1171106, 947978357, 838927198, 85214018, 30857589, 757004598, 641477805, 181744481, 380424554, 299096491, 194251201, 595077925, 478074768, 473485732, 35979965, 93195103, 441183078, 500925258, 860872428, 661363133, 735917134, 883380398, 869180941, 49733904, 255779038, 777263435, 624703521, 407529370, 98921851, 451569793, 265023009, 995164046, 82740520, 109647027, 910087708, 492721258, 371951897, 171379854, 125034084, 394131403, 76369075, 322480025, 620921628, 540652947, 631545112, 20886589, 287322178, 719520042, 421866909, 494486910, 357466673, 996814378, 136153021, 885077110, 894219085, 22467214, 772854784, 366880924, 342657431, 252812031, 774607348, 785568791, 557483066, 740170353, 240412543, 479096905, 433479089, 492352409, 778621379, 251872573, 240760658, 570836523, 387883857, 903517318, 639012494, 934600631, 52328322, 745576617, 483737880, 961644397, 221712681, 673779188, 690260767, 719448702, 30063428, 359003780, 628920756, 389497429, 261986259, 513060093, 216892536, 909724021, 340190099, 142605452, 482189259, 807026303, 699943143, 56896219, 252966072, 395814926, 198852549, 392267430, 728627070, 485658741, 629744624, 897399305, 982586080, 437726822, 514580584, 232610089, 671892428, 597868181, 728118547, 638336470, 136193925, 63010525, 540732492, 62552399, 583192537, 618285005, 150333524, 932625024, 34533461, 72203433, 576586266, 622925488, 641518061, 218743272, 544781885, 331468967, 237529746, 276044119, 304236983, 663128844, 778002921, 284608725, 590726425, 278362746, 661063395, 384505755, 811987063, 795677494, 257882631, 348089715, 284578608, 274272054, 50713837, 689150784, 261660101, 619775828, 130426571, 396288572, 243614832, 849803935, 633616086, 366972110, 506952108, 534024076, 883331006, 295278913, 755829861, 102068280, 588208873, 185134946, 244527548, 771608279, 126497051, 822734494, 402649509, 55325010, 442832355, 620046921, 226018685, 186361966, 632983365, 946450055, 784376035, 632054858, 617472011, 493845348, 154229559, 645963326, 432610723, 729656841, 179633339, 822730220, 741587995, 29222288, 970430837, 946882743, 447616353, 658951412, 828842551, 420166379, 597385776, 245697320, 857942086, 391429636, 659021117, 909166722, 946868062, 287132857, 700068600, 808533539, 48172271, 522941842, 63222634, 207772326, 961178373, 169572623, 760044481, 654365160, 536923896, 780160747, 852131446, 848371550, 599195704, 382015629, 575857390, 324739753, 512904025, 933448479, 168740788, 482158917, 158400452, 828154491, 898368807, 95518823, 995494320, 503306996, 864458895, 783708330, 323178971, 488791509, 375484297, 651831543, 400421181, 465507675, 271230366, 32700990, 708655620, 572462851, 360106172, 203068634, 383732248, 255569932, 929473692, 10832047, 962620430, 873819019, 720259017, 898314321, 365651762, 380298876, 515415847, 324399780, 568675778, 616214098, 636614542, 359245900, 30836914, 102050091, 615028446, 686076569, 980263985, 367678630, 510474480, 791342303, 697518470, 435139943, 358386740, 470206433, 757918651, 46993567, 825499106, 768080308, 339381376, 195798455, 635312250, 176417837, 612995825, 260504808, 168557342, 802410985, 799778714, 455398611, 456990041, 609420786, 64906455, 811006586, 49323540, 349081071, 814480539, 335186542, 807599182, 711416375, 530278130, 626493628, 70766728, 953360981, 999886221, 507786141, 571767309, 418492849, 63628297, 63751309, 728588187, 488280076, 782463409, 414092816, 680795385, 192568758, 716929483, 869455233, 498749301, 963935194, 869266799, 738265179, 989386119, 150802112, 285973534, 522542219, 148903852, 269546535, 339358547, 787393855, 467865378, 324017264, 456092289, 795477852, 186309493, 817554234, 717641238, 330165950, 74459127, 284342224, 959973673, 174482541, 966482368, 431672366, 705015452, 914693445, 618623225, 676496368, 973014172, 845019191, 791033696, 643899524, 105646509, 146107897, 134575332, 651555269, 939002116, 970658335, 291827502, 113029661, 105826000, 90361395, 648301881, 48425392, 433232124, 994637006, 481449308, 797861352, 970760001, 736515986, 768739956, 490171149, 364119221, 107105179, 610252895, 951969276, 917171995, 945239404, 185069217, 995783879, 438008232, 543781149, 790465436, 305322534, 925914549, 137427048, 788945482, 608656559, 768431230, 217113383, 573875901, 48286690, 442567594, 572344087, 221036736, 894529659, 461924719, 407839580, 733623887, 873842010, 408408578, 122764345, 357769681, 167255338, 641194471, 536011644, 450989687, 652585170, 835305809, 805312629, 147350127, 510867213, 332520562, 991633111, 904306181, 782510370, 366330864, 32750326, 790624820, 399038981, 838048268, 271185359, 905022942, 486882131, 439733653, 179866722, 911776759, 991774694, 649765720, 890019977, 230649073, 547746146, 367136267, 916172773, 867700366, 448458829, 873528531, 417728731, 955478194, 156746723, 910887170, 914577151, 75417596, 34021286, 757855466, 472140146, 311493440, 770762882, 734348069, 351891534, 484300241, 669930425, 874010183, 916071727, 499935089, 953092011, 513407161, 3100482, 765244786, 287144416, 265113460, 972521474, 313630702, 415686391, 24073822, 915906341, 322890367, 44397209, 722718898, 171021961, 594327074, 443566722, 869248066, 445089270, 206203269, 113181083, 942554441, 942295717, 119575550, 806249374, 8749192, 920273644, 722893833, 278688777, 512553169, 967093057, 820115092, 380358544, 300288783, 755697116, 839470879, 559765100, 899824850, 616229888, 55805966, 178968724, 264557878, 481137166, 639760367, 915787471, 618406099, 816901079, 454228338, 816146025, 951029826, 930844644, 919399450, 500755848, 939912405, 181537354, 137465305, 646209083, 494575569, 632522820, 602110574, 60662469, 552230333, 85629889, 959905800, 138613955, 362030074, 949368220, 478971854, 76374000, 614411074, 274135231, 454228404, 640289668, 772889059, 726815792, 165924677, 16444723, 815379153, 408608281, 277454200, 907160268, 927072920, 234544878, 519186229, 435727868, 620094708, 705203904, 738785322, 507850671, 339580951, 441460172, 784829445, 131319078, 527434649, 181533554, 221780514, 980679149, 83249520, 671004651, 631462231, 354094616, 957367129, 835425917, 124917375, 573739281, 12878935, 791298643, 423934990, 841299653, 18846661, 579402009, 850867241, 79131697, 654034887, 779823342, 513307602, 154931843, 774313005, 48567408, 253313637, 593505340, 197918298, 330367804, 239127177, 507691731, 466728790, 789196241, 564906376, 552222875, 424956121, 821385318, 8878655, 71619447, 945977412, 981641894, 654613625, 823022731, 631644339, 986939499, 969625333, 714141816, 935857, 854802565, 851112879, 887616664, 47847764, 987077574, 315079267, 536093844, 696100411, 256518819, 755278080, 112521147, 158913184, 126214991, 983258486, 697973930, 50552860, 160826010, 260378109, 391199470, 179687278, 482661780, 716255045, 915622462, 603957995, 494547183, 605419824, 856301721, 7340017, 203473673, 635819504, 21617979, 267747621, 12414276, 51794952, 421032688, 442651011, 579612799, 766808373, 347260379, 804237972, 100022059, 732688685, 548359315, 317712698, 760524665, 647524177, 255106230, 5947458, 269238760, 372844225, 24109998, 843123561, 849571326, 464917628, 269540440, 597563701, 71700280, 60650965, 303247194, 897959808, 617443672, 908696356, 178944716, 91168302, 660222392, 600268021, 552264400, 319100876, 321443431, 357900049, 501866991, 619635404, 570692795, 442916275, 286128018, 276482083, 53072953, 152923103, 481500526, 66824422, 725433776, 297953276, 249936009, 186682772, 867580340, 967041447, 54227165, 213342590, 110213023, 5037732, 428407447, 100096656, 373553648, 643246867, 414065712, 549730621, 849936340, 467651638, 518257481, 592974332, 289172070, 688001196, 343167976, 663154663, 939750080, 585702151, 225245678, 28113797, 564097127, 50398454, 61244158, 986763552, 915023720, 681329190, 816315610, 169167513, 523317713, 653930559, 624714718, 989248894, 885529714, 60771590, 468897696, 584892518, 404649347, 1576803, 65156988, 364790292, 989950290, 248643097, 811235426, 222396494, 232860369, 172757655, 166046390, 298245050, 329179681, 215972464, 710022092, 406384534, 424828315, 993732896, 115637263, 868988875, 369936362, 162908826, 562192963, 340356130, 674611934, 110222060, 798937526, 355050392, 931539891, 25118887, 924515813, 807654051, 496510517, 641443670, 590919106, 724365478, 321722845, 378637524, 923965950, 134649013, 710264958, 419222432, 916479813, 630447912, 948198983, 982107045, 637755239, 950320000, 134040079, 612263517, 787537225, 543347155, 272641642, 483035472, 726723740, 212222124, 581095404, 416425240, 92694998, 725194564, 600151393, 721634496, 422309741, 147094364, 618042914, 548871509, 566499330, 124014858, 622989069, 499803979, 643759855, 145691438, 573277714, 72275077, 817558042, 157015619, 371155627, 170757934, 635112911, 601339552, 529068475, 410684256, 920262026, 254596495, 665240134, 766398890, 271981000, 496085867, 650742075, 578334779, 314708211, 705237582, 927674923, 417253074, 237274450, 887371823, 641331815, 957284472, 225012362, 405626857, 969341792, 65033107, 764508408, 567005242, 936473143, 786873608, 195622548, 581555533, 249648582, 762371255, 857462141, 227299705, 584610134, 3270463, 919141763, 885852085, 19873241, 368457633, 749679131, 982237009, 870360893, 231739522, 115869996, 176070428, 557945710, 173878233, 487706738, 829155498, 613231787, 624598557, 633844595, 1925448, 925174765, 874732543, 377536241, 427728152, 117500393, 324868534, 384409202, 16939470, 201171382, 190026260, 980439396, 34392947, 319112263, 994889501, 735458429, 544732315, 542110268, 820791667, 989953579, 187795932, 805543078, 928642779, 904877041, 914425068, 114825551, 153184914, 909654232, 802864091, 970915935, 617472923, 286274148, 25238188, 430247854, 132582855, 608843797, 44353159, 177096150, 717538576, 624741034, 199810569, 938788240, 747204671, 177377944, 249273615, 899588686, 588373550, 676749846, 172705124, 176242619, 245315438, 40681447, 931816949, 168803761, 831756315, 803017874, 809202102, 550997060, 469017288, 520920890, 123622508, 581463944, 872003737, 139534558, 817241144, 931689937, 91950820, 551991412, 600781167, 543473878, 201840386, 942593973, 926507444, 157560465, 604821341, 332954151, 160169681, 136705380, 322728866, 462400668, 366892420, 28529203, 757111960, 916053743, 776379547, 464217808, 941131472, 221334765, 294060282, 629314915, 802810888, 276834212, 646336853, 114851126, 893200533, 355817544, 949337020, 509968117, 391370099, 658361698, 653896511, 490138691, 402143976, 79704113, 647701760, 573358012, 825780899, 376897778, 199100719, 562306095, 466870601, 707538192, 246205901, 482149099, 403581832, 852501204, 488225687, 449304911, 51243549, 778789722, 446486760, 626816874, 419167528, 361774071, 190395280, 99472619, 190622178, 184061620, 421985289, 88697674, 297703642, 626874835, 595447328, 780856550, 291063564, 334218081, 218869662, 32326991, 666761589, 150896791, 94012528, 417118868, 9308685, 489658340, 507646101, 622476085, 919454574, 37370172, 760425299, 861454432, 869303748, 693313496, 789317814, 341543312, 235148051, 523518529, 536602482, 62977755, 571697072, 267591366, 428470009, 968649335, 370901819, 540080332, 114645533, 111423229, 658986942, 89229167, 675051609, 294562110, 715303593, 717394887, 41891108, 914470111, 701954596, 710804527, 261523821, 358356248, 761589642, 605721162, 952401619, 110268986, 979543841, 404713137, 77011704, 433385453, 296740015, 193296048, 547508532, 417650340, 343008272, 832176382, 640035764, 653392483, 951951232, 258316952, 714658889, 419076726, 941895602, 83164827, 584423425, 472569335, 174806227, 319933751, 65114353, 572950225, 686009667, 910458944, 681180690, 235737408, 423804241, 280585431, 430822230, 488910771, 963043305, 233179940, 574189147, 459851257, 666061025, 450720900, 643872679, 600415242, 778811829, 489635697, 27060295, 598398400, 917064443, 997359496, 307391789, 476299934, 542276373, 114383509, 166893166, 407294088, 767111154, 71398441, 453360283, 953673631, 887590790, 103581010, 579343929, 817990974, 69592904, 45113224, 653161726, 623619756, 976369382, 821543035, 226357574, 528322315, 107770076, 896121521, 273285814, 852306285, 377367620, 879425267, 515497463, 555086315, 529452098, 447802849, 677559500, 214197882, 838216500, 993612773, 18526095, 624387126, 319354215, 392455376, 626974872, 307044473, 821526301, 854313879, 139050267, 791595970, 512296426, 548864169, 853900709, 350241018, 255121270, 762719615, 289607504, 360232707, 510489068, 807193413, 514456826, 943938866, 795697477, 90560136, 266075818, 394590776, 450947228, 544393210, 461425636, 132185977, 86578567, 323292230, 53925352, 324740501, 825372493, 678423390, 902942008, 152934000, 515439064, 585456879, 929892921, 608715940, 189871882, 236366148, 263122611, 882745511, 222204931, 68372996, 378654087, 495361903, 67397961, 791400293, 776697888, 156405272, 211097881, 847066739, 364008556, 232122166, 915557558, 819991557, 836409220, 791664791, 330618675, 891920779, 821220172, 280507407, 19742833, 432408921, 321898687, 734411931, 842336265, 884463113, 801129249, 155131866, 509917153, 169831607, 818037614, 626313185, 347183625, 363088352, 838945092, 537220656, 435756900, 107182392, 669104273, 651067642, 651111591, 793259459, 237726313, 836864184, 563389390, 437625117, 367437729, 436526537, 572897166, 585080503, 362365999, 767362031, 860742603, 694641314, 328059154, 49436461, 392223489, 614082681, 130475392, 417082784, 89985906, 425631646, 785631361, 556205256, 98460398, 485050318, 653283130, 338675215, 545280303, 668448538, 434673897, 400751589, 300194143, 773587549, 30403157, 606325326, 229770719, 516747504, 23551246, 829424594, 273015545, 26476542, 804935229, 530549417, 996617059, 358705203, 60640010, 689979070, 546263738, 991231184, 680176599, 243532946, 226169546, 161493582, 209572015, 355540676, 451193345, 317046015, 536608673, 803445856, 915830898, 388776665, 618360225, 174481441, 502884685, 792020789, 867784722, 448685180, 569835099, 226415800, 698420297, 329403963, 341243491, 287758821, 993173388, 366063981, 452205122, 61085009, 246037725, 445737386, 855271435, 846058485, 415113461, 956593969, 447069835, 431125159, 942423144, 940609022, 545995020, 911549183, 807148873, 997897144, 485555097, 90898451, 828758231, 269458558, 896907026, 152535717, 560173798, 422374197, 483579792, 298190556, 274803713, 686682367, 851666323, 970079806, 251054941, 864838776, 815069506, 201181166, 178966254, 562958403, 289702261, 65418630, 963539803, 213593392, 368962892, 570663067, 439163370, 541237004, 670021020, 53435483, 146843684, 127388689, 451518591, 893731545, 337649684, 785570868, 306684356, 405247751, 710844103, 35781939, 128561030, 482284788, 740450291, 438178004, 846972716, 957304069, 206296816, 809298036, 43466378, 530649677, 644003144, 682741314, 598126358, 404301802, 696607631, 644024755, 902971462, 630306629, 835588260, 205168447, 475013665, 87656807, 446461747, 532466063, 807596247, 705062694, 345375165, 103393718, 810594194, 170963434, 307319695, 172432276, 177560340, 177559152, 380223240, 43501845, 476350355, 572714498, 122522985, 782522629, 653366647, 231128711, 443342812, 847015854, 834889949, 997817496, 684355880, 817490372, 330824387, 835260130, 687748636, 847908546, 291774533, 605275460, 750932302, 365884346, 985621438, 167375191, 313982272, 424989365, 183567085, 580860284, 382853095, 845514626, 16313462, 117139487, 548337577, 936922909, 959581714, 919583754, 647699985, 386597961, 779175395, 711994334, 706843806, 910400557, 536311232, 204544145, 607778974, 331657503, 833672293, 932733906, 659731731, 749886134, 740848222, 258244532, 376909696, 756358542, 292518956, 570521995, 720222513, 862617948, 537997590, 679849039, 529159570, 22729279, 587515886, 147036792, 291899658, 481066271, 443273171, 519437705, 465554136, 804224992, 553796100, 335827169, 343046450, 809211152, 565589227, 347220487, 32581666, 368922971, 267707082, 787920389, 80116488, 595890218, 802939965, 939035234, 899934970, 79182008, 954430251, 602976323, 592484618, 256143855, 989657369, 804685402, 856399996, 844358171, 532293942, 658577027, 241781629, 955114336, 966585200, 231364437, 767533823, 762446926, 508818213, 187780727, 502742567, 85948496, 103947540, 437139796, 729573637, 234158838, 68586829, 22254095, 15930440, 51431783, 553021021, 958359755, 573028291, 179371396, 195477680, 286749352, 511544145, 784970705, 350688300, 756301700, 812130766, 650186705, 805423433, 583028705, 995849410, 272881281, 752553877, 646458607, 57417688, 739662354, 440880481, 307234954, 28360882, 462434769, 483725400, 850943312, 552773837, 836868094, 424833269, 639558384, 227540036, 844397974, 896274034, 128987507, 290665890, 578740940, 789792681, 197885744, 129846645, 372595190, 375728623, 911683, 688918083, 139974964, 459267049, 18421380, 876506113, 81906205, 555476977, 780358259, 675717209, 647195908, 202655153, 530662701, 473672139, 766359210, 989023737, 584784054, 826566519, 324942189, 290659120, 295794307, 141046612, 405277678, 86888992, 464318948, 578252688, 920141533, 499405333, 24252540, 378622210, 545384189, 122169335, 396168053, 704366728, 629058788, 772485360, 899486389, 340270898, 47313459, 292804477, 67598255, 253816355, 442513282, 803445407, 563639617, 435292236, 941343147, 750855268, 504715441, 369761127, 432080061, 425602687, 703584956, 992854500, 190795622, 360732446, 234643298, 877608507, 370934643, 400656500, 677724443, 7146938, 521299025, 324131318, 329331221, 131746923, 80852281, 561311471, 443939093, 790292311, 630114882, 209120477, 199451857, 106346960, 823787489, 707085129, 28033782, 218682643, 529694794, 414309712, 72594970, 865871453, 524879205, 398310744, 21088111, 821057707, 758587029, 390688255, 565945693, 243493880, 504149326, 268584120, 495031132, 667482124, 618225210, 18184419, 627465124, 354968448, 818208303, 488408467, 129470154, 146924481, 685453103, 128411855, 327119337, 379800919, 764260830, 494165994, 158474301, 76892675, 193777678, 351931560, 118764068, 999089210, 945333957, 559087732, 938927955, 138646392, 987245249, 928957023, 812459651, 710606704, 99470869, 511929754, 255764838, 341581148, 719543497, 217525126, 857520435, 785499899, 527878380, 631231893, 763191095, 460708361, 213857575, 549229479, 84327408, 618049041, 100830291, 421096502, 284748381, 577827071, 792052678, 110186470, 291988398, 429899108, 804563168, 514333579, 869675837, 371448633, 50659808, 657765777, 680492645, 785245998, 269789661, 326964427, 223254739, 15175768, 714038160, 535982761, 25803084, 500851492, 80467667, 373343287, 557750469, 671421301, 395011836, 501598417, 654587582, 837595032, 16629153, 959968397, 852417948, 131255401, 324575710, 213856186, 437336507, 251821848, 725483378, 600381997, 388422732, 632096243, 799300321, 345686178, 298863794, 499256113, 882144525, 409532154, 258849226, 791845531, 439847736, 187204258, 86505035, 872052576, 217140260, 290566746, 315919082, 68387717, 948364335, 797025066, 861249584, 756133520, 537013180, 200361662, 260412364, 791375534, 435726570, 672554377, 246953364, 641506968, 304983972, 405189433, 427959261, 493103394, 735018566, 221483004, 196588842, 374552873, 920101634, 98082926, 427465045, 795745031, 374930104, 440032534, 513910605, 752521230, 34856177, 869350135, 971495289, 595961749, 704092592, 457404568, 15748882, 193725386, 14844470, 580936893, 507068107, 912365129, 436890271, 922172689, 402120263, 74378002, 33368260, 668422306, 323727531, 722740559, 767669700, 86439921, 568566978, 932850643, 3130590, 599001710, 71613077, 361731633, 826789447, 877466240, 280920568, 880958592, 360612946, 55184619, 807689472, 96680836, 799741815, 383124797, 233381046, 527081265, 52992328, 88106571, 118980503, 302920953, 124249397, 329247453, 416152039, 606472381, 373710466, 32019917, 989500522, 53082631, 109687776, 372685873, 773523175, 741820534, 16048196, 937093116, 910942063, 165217426, 39445185, 636071792, 824812096, 192361150, 424552476, 308826518, 430834691, 654170605, 616562829, 35587297, 967088551, 471605155, 232023195, 997456212, 689004129, 461992381, 901892783, 46107977, 890223219, 336817136, 353457368, 447910073, 925278320, 261992814, 681484574, 229954959, 769990957, 956143984, 486781049, 325514384, 45140201, 415931166, 579243714, 456563969, 752904756, 566998776, 40629278, 284250912, 523294036, 51565467, 923675628, 157351641, 822616966, 62848332, 922445500, 342763524, 92230194, 179563667, 178711937, 954829386, 922839282, 899296442, 945154174, 987709017, 263396138, 722643401, 913067893, 457482755, 158888262, 162700551, 328524288, 661651434, 636077934, 690907851, 728776899, 265430876, 265765800, 418773213, 1576338, 937885892, 338473171, 393384990, 438726943, 598725339, 687867258, 888725866, 248541921, 98421310, 236121651, 935260880, 18071954, 704795112, 646501090, 381621054, 88470089, 888014774, 485491381, 201231522, 601118138, 436975284, 849119367, 864783019, 232470481, 576815039, 728969692, 941638046, 612828139, 549624246, 704619324, 752641414, 738814480, 921438304, 770021664, 763000945, 880052891, 275217941, 626652611, 990591917, 44074744, 729169832, 697648860, 810943519, 432129784, 646747071, 990221317, 870479050, 313475740, 39318157, 270028082, 698884231, 162710607, 695201969, 99694736, 231231931, 18586540, 87193212, 541257121, 168808613, 35994164, 444884687, 767855667, 532348636, 6276832, 949961802, 813670722, 414841018, 920193252, 843177119, 140310757, 406104975, 86846736, 34491085, 645710672, 521005178, 939963767, 677659350, 864045104, 692749218, 494889614, 269591793, 659453723, 357920051, 672412503, 433677695, 200858896, 317018077, 619968075, 694164545, 948703925, 735698358, 29306475, 602306771, 611015226, 991652393, 404511579, 434942240, 401449181, 410292284, 677847674, 813737078, 498252362, 810709403, 411197831, 508189671, 443043530, 411300739, 154284836, 648407090, 242020223, 77134714, 980512749, 206228205, 768145523, 375089101, 853811020, 161879068, 921876877, 592307194, 984812817, 150432220, 884188886, 594534946, 541714735, 960434818, 469889152, 146560467, 401505683, 868805992, 309931691, 774680962, 111510627, 719669249, 398924134, 701507886, 855583850, 259199961, 546247819, 67014355, 588658249, 567934815, 745073520, 613394278, 911784469, 198550698, 681040891, 874489152, 26589394, 382089746, 497737824, 485223760, 248843181, 783735898, 872785099, 131396133, 43845028, 264905164, 745670309, 25837015, 13560437, 359138625, 458801315, 853847614, 16848475, 396329231, 975171999, 475950760, 339177646, 629860870, 625668488, 516865914, 215782369, 131544546, 459005375, 784203485, 824424945, 253700703, 352727156, 605390822, 823016972, 593661088, 110176602, 475904356, 177675330, 258808057, 998581805, 942742728, 971433271, 567816541, 946870105, 994158529, 383538564, 663022811, 984645065, 536803657, 997219701, 41484460, 933548402, 938023834, 784408236, 155838159, 784041033, 14805942, 119727540, 131007124, 262071573, 458351509, 469731003, 42712195, 207086130, 482412970, 522154403, 6356318, 463465575, 388530503, 717884665, 379507680, 580295164, 649757329, 419533676, 565699490, 378181794, 121860154, 471965477, 646057596, 243228846, 359747953, 361299305, 151755022, 684267930, 880366261, 715063885, 119222329, 460833800, 402179189, 308670696, 942135885, 833454175, 505600678, 466060385, 657980793, 843855324, 564832622, 398081140, 41964322, 480208796, 70428952, 964740588, 476731202, 40710331, 969160580, 205524360, 576125176, 225051038, 721156647, 478890395, 600242271, 301208103, 289189015, 534706843, 621531279, 204950545, 746909102, 247576448, 567012412, 690259472, 314732892, 185515214, 719371438, 507274436, 570331683, 480735521, 110538204, 920733063, 436363805, 932421879, 442036396, 682846526, 352066367, 804688738, 564050506, 91634934, 45722019, 166923286, 311085240, 13641403, 766511226, 897120017, 897400536, 262756778, 966879028, 29757389, 680991068, 282281094, 799058886, 267173664, 408438108, 139849065, 550249876, 832096495, 714075207, 951322454, 949651860, 160505247, 196882536, 740087359, 236825861, 62256663, 219438305, 176572754, 836944089, 225865249, 463763283, 361833541, 925696593, 802833129, 501351062, 586731665, 212660937, 12732731, 770916336, 315770007, 798733436, 904118862, 418660827, 565349826, 173622058, 785544047, 811246615, 403177698, 142055357, 356296147, 251742190, 57829589, 613520154, 716926590, 874369888, 637863943, 446420796, 183156385, 631424855, 510954926, 261441493, 701290317, 819062678, 879479885, 497657991, 360426932, 951985540, 535805695, 719442103, 935125085, 755709815, 166907046, 890390903, 159702722, 393765900, 157234890, 603229132, 307845924, 120563513, 325447835, 271817018, 971057308, 273059656, 454964846, 991753015, 520696321, 304382721, 704289277, 229262356, 900287034, 157971473, 101915309, 542900370, 556075880, 755028247, 931020193, 281944531, 551354882, 988080386, 828662157, 87188793, 522304824, 84254, 59110942, 352088307, 974359689, 248167349, 854398398, 131095107, 823225781, 877772435, 629190588, 818641374, 216214522, 370877911, 394658166, 882084523, 233637664, 629639076, 189431060, 147454561, 327894421, 774008834, 453909255, 90868988, 712843287, 478722785, 99364123, 426141337, 923325887, 396943732, 638791518, 491766254, 830194803, 46595973, 545091360, 65813342, 185205105, 970379728, 782267730, 56267570, 603387080, 697465082, 550431813, 872320049, 530435336, 945005530, 150023234, 480607408, 333573040, 574234595, 212866314, 756909333, 897572083, 649300858, 61571, 288157472, 648218770, 216294288, 360941129, 656591287, 623785636, 589186449, 492917177, 639989795, 235138069, 385510773, 66999905, 386309368, 854211913, 164013103, 662783294, 389886372, 810965728, 870954670, 428674236, 371618767, 451238498, 276183029, 604144454, 764439433, 821945682, 506906985, 90459567, 704242429, 806644704, 445051701, 246416000, 98202932, 797568237, 947162270, 238625066, 632980122, 976926857, 329882392, 517737048, 41367405, 513617925, 523199324, 183332737, 7059263, 613555738, 461460182, 381798812, 719592369, 208981074, 570891313, 410004597, 132930502, 596729864, 593668844, 586432253, 891296859, 463673602, 687030174, 502053488, 501058563, 695619949, 220685654, 303103398, 622580924, 608489921, 453004239, 731226483, 109662466, 663325575, 463351348, 435519727, 979837516, 699260201, 684186049, 729648211, 31798812, 360742993, 721362173, 502091590, 141563376, 581306402, 210815728, 720030494, 878233417, 12195681, 251470542, 686659850, 130327138, 865706003, 442147374, 261525265, 389177465, 813035006, 81745688, 262013980, 565000396, 109114889, 87642642, 925225810, 853721359, 226125458, 587839961, 67044421, 867231641, 692003073, 473710794, 749717904, 679839986, 198484309, 4181501, 288692074, 748237176, 368372628, 590166673, 588540613, 516216396, 868850074, 346582545, 740369477, 151180229, 44868232, 624192266, 771093599, 73931506, 180578663, 859026089, 545075189, 842589590, 205585564, 246890632, 567836089, 573759104, 960378672, 775777336, 473521723, 690472187, 360166747, 581013874, 992032647, 541040439, 214145900, 309633023, 879199127, 31105030, 813143336, 750724628, 490435558, 720284471, 449300815, 287242279, 8480058, 153201988, 426599656, 583503764, 362444072, 686017875, 188946130, 434894963, 472949455, 560512961, 271130693, 358673017, 596527314, 632078767, 599254921, 734647387, 321742557, 994411624, 313995466, 326971417, 605225925, 222913297, 356592259, 472542666, 917466068, 217418703, 798924710, 19721464, 684662447, 981560469, 177618438, 976880456, 12952547, 57584096, 570100975, 734225310, 629514656, 728132348, 625810792, 386784581, 728683327, 373168813, 92589293, 652741452, 400781166, 754735602, 807336750, 223223194, 779790286, 488531507, 611079715, 723601258, 675467675, 817552428, 389689684, 745894810, 474454870, 433025524, 732700617, 418248267, 968223333, 503511314, 689044829, 177123631, 173236075, 6357348, 711674634, 863766112, 920094733, 555606884, 835935141, 720011457, 775672100, 934074112, 350073960, 116711743, 21003429, 265903981, 117177046, 584078080, 299060729, 922740268, 129709368, 954115308, 342503111, 793947025, 63994691, 588801093, 301818576, 161834852, 398988276, 17415347, 149725861, 802075258, 877903698, 502080128, 55784887, 461522475, 874465435, 168712303, 622563888, 736146391, 766746189, 512249269, 458983155, 400164828, 294893563, 607395531, 753868247, 269832945, 454766371, 976175081, 634820121, 459263186, 699852178, 514058805, 618890712, 581699745, 738253813, 529728538, 157338104, 415795735, 971376035, 793731245, 457003129, 242621569, 331561448, 715221838, 717025744, 384502795, 602931525, 806851926, 592904390, 512702563, 549221521, 805000435, 784780425, 729622612, 289582458, 832434867, 323763135, 368069000, 124011973, 953843631, 675665969, 676087422, 516968891, 477777251, 340672975, 756182469, 63517784, 939780590, 480991811, 387177035, 645741571, 631334645, 388731452, 926881518, 498825225, 521967148, 742505112, 571668444, 740395525, 336440459, 890150579, 704277527, 5413998, 578223197, 368069564, 919007413, 647428299, 139221942, 911924430, 938093099, 653189670, 968113506, 968656185, 177879129, 97124479, 301497899, 831937261, 26434759, 598067420, 796099969, 19444400, 38544742, 706674787, 571678062, 580338654, 777255211, 570866208, 365140762, 631140643, 584861298, 415060463, 105148343, 459185151, 469142478, 37223895, 226314661, 689021992, 569588472, 758854153, 616852744, 968133037, 121776281, 631742545, 473822640, 633699215, 314062158, 837058256, 35118068, 144706637, 291417762, 614062828, 326336300, 494155545, 871391200, 729321260, 799693718, 609778354, 325855633, 260686146, 361551572, 954476119, 217024298, 374513421, 661642413, 926565651, 899648059, 881094693, 48949623, 867129458, 857301624, 901057813, 529338948, 948496801, 360644438, 416885133, 963621155, 823510972, 660143098, 332253135, 728803053, 188125051, 333237727, 634850283, 611515642, 115589532, 448247091, 405503338, 774147781, 509590351, 150420226, 924995925, 956943391, 474455540, 541644996, 395814722, 570960988, 78950201, 496363073, 300576415, 225168421, 674953472, 156984208, 123714188, 657923149, 402481435, 25956005, 276398367, 234685884, 336580175, 220600221, 698369233, 497043794, 17431535, 229639753, 442278849, 425330417, 43565665, 767252037, 72236097, 398173459, 603479298, 223839729, 593908978, 254756977, 693623860, 857192461, 690328391, 506890925, 655869306, 611825278, 21290649, 408872242, 685387530, 331827711, 100452498, 281900294, 523998112, 612266600, 345937911, 844589956, 616483272, 598665746, 905658710, 597573880, 455655423, 473516320, 23737791, 822332610, 128032233, 909573221, 649916796, 424924731, 941842145, 700250800, 291702053, 725654059, 379342645, 140445589, 620804550, 134942996, 129631672, 697372557, 929925431, 656716679, 297016679, 721434612, 117211969, 796110239, 435612452, 480830605, 887675925, 343695646, 914094735, 416653054, 422161621, 311102968, 586655023, 406705881, 358483488, 313873128, 833206671, 754520459, 526975926, 531321251, 435574110, 619490490, 271237585, 338323336, 448941171, 626799220, 624807643, 668873463, 695492003, 43110996, 303265351, 261408320, 234826573, 960096294, 650087222, 530970032, 468477221, 188744435, 502149524, 510577261, 675939640, 30914605, 825292446, 52724938, 733718130, 49304659, 565239000, 104348019, 725739777, 227318152, 301215804, 958740668, 942399656, 764318607, 255321426, 659950244, 641109609, 194199599, 972954165, 586956570, 744741575, 437669795, 567317050, 586572683, 645612860, 371748932, 782223028, 940324340, 261485688, 316550019, 603316646, 640636186, 590444256, 113696077, 290150330, 909175054, 529369604, 606644765, 637617888, 207857937, 110343582, 425450912, 230574, 860372622, 534914788, 796619977, 111005301, 169936825, 534422266, 281201572, 799270815, 762178325, 309365718, 777411932, 767124802, 964557047, 38889181, 723794379, 64104357, 599655391, 254170490, 905969970, 370683060, 301575082, 684499061, 481088537, 887018666, 150259359, 853274758, 754231031, 380653902, 686457494, 747377772, 783001159, 720531500, 526352710, 85077371, 775470312, 898080974, 458524268, 28045816, 187298295, 191797578, 563911646, 496708363, 924539616, 490353612, 746121379, 316534656, 59006864, 522365872, 599052900, 958340468, 59873562, 288236664, 100790711, 118286805, 456738706, 510574490, 264232590, 78789365, 459618817, 553653248, 454157030, 55051265, 995871522, 525969524, 49938355, 657512793, 768925442, 24604121, 174130856, 924094580, 969255202, 153907277, 774096117, 502746790, 721119876, 431676942, 756687946, 629444931, 930718809, 658613861, 919467070, 367237060, 777357557, 677043287, 882132928, 358472433, 479858272, 191418807, 318827160, 355907658, 419096163, 156418258, 534106342, 445633324, 908440989, 514922020, 378808592, 709972343, 981772905, 304972515, 896084971, 196141005, 800018803, 757829892, 773511033, 716712923, 149089169, 725862253, 7055809, 227254281, 125444225, 193943374, 263180782, 19976697, 127343036, 51746413, 150451988, 604157538, 50948557, 606389388, 33872819, 812561186, 916867277, 105470956, 692197165, 947827177, 156889180, 760220727, 408803808, 457311500, 459504917, 996376722, 275134204, 232076318, 744011217, 307340894, 643720863, 108463403, 574628529, 843796150, 192442336, 222622643, 725212509, 359756923, 101346941, 210722557, 520726651, 706115568, 965691408, 528754872, 87672406, 123808734, 664388081, 796783392, 308752089, 523553826, 987756300, 391220151, 374326499, 302993119, 915936079, 273950121, 208456563, 21077792, 984956920, 787686355, 135750264, 941586591, 61473025, 70498800, 114225153, 332790999, 623487300, 987946391, 743132592, 641304289, 914144369, 745623452, 803471928, 449662086, 427881346, 631435942, 858928161, 317199550, 762189919, 901138727, 760281598, 497723638, 601656121, 294699376, 75165641, 818326057, 572491131, 879980198, 472582559, 998599046, 345636622, 289570536, 73295416, 219134008, 308495495, 940842940, 721503075, 538294344, 396006516, 643982146, 754565063, 873109826, 14271423, 485519319, 728739314, 346107499, 71364255, 708893150, 427550191, 846902023, 967630987, 120043650, 489872219, 958449938, 485648099, 135961179, 637587501, 819899285, 267288227, 718646572, 212953034, 414522369, 682283095, 11521432, 832887741, 267049060, 552737158, 139913361, 772431914, 64960637, 625041865, 564562561, 832952794, 506776163, 876961689, 192883421, 806091355, 597958058, 269323367, 376251114, 242431827, 997571306, 208391800, 553690299, 468179077, 551053318, 618751040, 33724323, 20006027, 477399618, 281382955, 639067311, 41435464, 600561961, 991821654, 890686240, 227151899, 805274617, 167465688, 287147871, 184228114, 990114884, 628072440, 331463490, 695951730, 808574383, 249338788, 870532020, 634106244, 65104780, 294693784, 975749354, 580446421, 752460429, 200432158, 656813595, 192281656, 27489142, 970041248, 537886947, 701768476, 646996378, 134745139, 68698918, 344585018, 916873532, 514376046, 11924269, 470131589, 467650526, 322044222, 601140844, 941343857, 438632667, 208907282, 337594500, 133395032, 195637782, 494477012, 975110177, 314830646, 587987846, 420179697, 631304745, 245068202, 385998416, 653572485, 82577556, 622732660, 625946166, 42686876, 226594442, 350189472, 671139374, 647721840, 272506906, 777334064, 736824056, 103537791, 406657099, 596809381, 681957336, 168164259, 613761085, 365527704, 166820819, 554223040, 662863241, 659654980, 260636256, 980137623, 187666908, 908793859, 313196685, 754226272, 182888474, 906408347, 278914234, 661360311, 661667676, 370174101, 890070922, 485711520, 140114035, 472008099, 141946575, 92567460, 777171321, 584192173, 400619000, 710696546, 538718544, 507146054, 17533872, 581884106, 750741274, 218214494, 518834477, 108600445, 856231017, 787795017, 95345115, 481452197, 434586076, 130249803, 75749207, 53665629, 579164229, 572061415, 561105561, 859229549, 821785402, 552450267, 35597691, 49748551, 691131691, 1376032, 361866012, 264263656, 391735381, 629656325, 523467733, 255571079, 599312478, 427677472, 17076935, 111310188, 182971072, 390863150, 333960559, 738448158, 63685451, 56159336, 753581295, 119180776, 439610009, 833605285, 740218373, 457232902, 895364601, 244027996, 106796056, 687403342, 110900108, 930836863, 454339755, 666950724, 943427166, 236196867, 742599799, 87900417, 621073581, 196176216, 334647359, 523505096, 863203609, 896362437, 100744166, 860180281, 845522480, 388141905, 268978876, 604014381, 750849200, 61313177, 285788189, 744492783, 692642477, 394808274, 572930954, 767249767, 644077056, 767287085, 544693393, 103784904, 775073626, 232821921, 221794530, 214777981, 929086005, 194456891, 701017527, 656621118, 244389941, 586770854, 617847973, 147504104, 995335751, 200297442, 862236020, 654288459, 445910413, 446349326, 849938081, 784562654, 698613764, 238450924, 72249165, 453749583, 377683043, 925672916, 15717760, 924089846, 131039767, 791217666, 787014816, 775045947, 326221990, 419552967, 601048147, 328673485, 386398010, 23724706, 302798724, 306920836, 853847371, 563299544, 850904809, 643065971, 634746882, 811606998, 256630949, 214139753, 365050765, 564573603, 528932898, 747743103, 948001159, 906327986, 573109875, 385495456, 582535272, 765646406, 904840917, 792851117, 833826440, 156253257, 601063816, 903846691, 64659310, 924578097, 392689315, 16614200, 659060067, 828844849, 377920254, 262041256, 778437227, 891575230, 701602004, 750142742, 724619567, 596103844, 139693575, 714659598, 587441516, 227868953, 392658342, 145541296, 693626285, 559601543, 644969301, 919489427, 668029785, 646236006, 727770301, 235409156, 884010067, 676560579, 992458187, 774447479, 607721461, 200521544, 956897985, 966621554, 685631321, 312946023, 467320266, 477074259, 738927293, 784404657, 218348297, 736492627, 554971208, 244288734, 94541894, 98859813, 788493117, 379036596, 37621436, 329404188, 837837791, 3888221, 43159758, 236058606, 384593342, 560400320, 186264922, 903999613, 446800232, 772060555, 114971722, 413283595, 698887468, 677772075, 749759115, 29458671, 156959709, 939884638, 358851866, 686326644, 604764689, 815808204, 192247509, 374754074, 304522445, 388715243, 726488012, 399798611, 507448151, 58575830, 406037377, 207415667, 712945600, 79173660, 340461792, 359987541, 103882048, 642170987, 324918583, 454438673, 949950952, 662946492, 334158183, 537365782, 220698976, 617747150, 894612502, 339024119, 995942891, 973376113, 293925360, 942787967, 84649416, 618965587, 931491969, 985376020, 457643006, 95609026, 553061684, 992453696, 966422393, 729268957, 569944510, 1487475, 482463415, 566617560, 18822181, 783107919, 101102225, 937583078, 485770450, 287313452, 768628082, 257522832, 480522648, 965560947, 867516455, 62491436, 474976889, 442378880, 506390858, 413731435, 910059588, 521174238, 596442601, 913984409, 379143386, 248103724, 665559760, 511179637, 53199802, 153534910, 635334637, 704717213, 754161315, 321440950, 923417378, 663856586, 226658085, 81718204, 252352160, 900946431, 600791645, 187256327, 894271970, 84510726, 802266016, 592888758, 933489022, 370014906, 484596612, 321438025, 638949510, 864689087, 257885664, 381882271, 720986536, 455601818, 742790888, 691731024, 740248766, 38237551, 106322294, 487545250, 650942574, 561099799, 345523065, 312009789, 340465922, 14132352, 238206673, 980522808, 645352512, 478021572, 346305292, 170506936, 574028405, 199158396, 715073013, 360293868, 580821241, 322782210, 494313919, 199614477, 416917886, 927845467, 291004347, 47653694, 555037952, 360377115, 293627514, 586188649, 43790661, 790615301, 795558887, 668908681, 506866611, 141079163, 929661526, 500246265, 261975070, 667628248, 845359546, 421277801, 120588416, 738701087, 420100143, 643199117, 61009228, 126556743, 451982993, 116671490, 61614328, 195897545, 554207255, 632902650, 117518608, 128474154, 542686029, 424420707, 587703653, 971823275, 669962133, 368029809, 976176223, 387850508, 260781035, 396084578, 961095478, 65259700, 732071279, 302441886, 568713775, 464558794, 363357300, 521419246, 863084537, 134986988, 260206987, 970527233, 11727144, 672218238, 638274038, 740961936, 693097785, 185393186, 227611651, 456886286, 766175030, 273415726, 377151699, 515463559, 38255211, 851036035, 16606529, 319338661, 239409486, 12093599, 554897406, 883647303, 960171361, 388266996, 921543222, 319047489, 293258269, 652080792, 896377745, 648654072, 689539500, 83647882, 773508444, 722766880, 131209114, 945280269, 890925069, 50282148, 551543532, 284959248, 41522369, 366071497, 556274191, 402219274, 939961832, 733150128, 323159432, 826009353, 917969861, 247861969, 744930537, 79085091, 515541721, 624858643, 801021562, 987737462, 647118155, 269291403, 500092266, 545786145, 558694433, 713389167, 159330580, 856297550, 863182513, 276803406, 508187085, 491564297, 760670317, 135703079, 669439718, 974294085, 601715105, 889040201, 100687470, 653818605, 500433515, 776091019, 475804261, 779065506, 23934904, 531120789, 841960120, 728625531, 43856763, 9824339, 19664813, 829781193, 10847603, 222793492, 20516084, 894068846, 187818337, 107924899, 641882891, 49950630, 716894198, 976249589, 640584171, 466364685, 990571001, 262226137, 446885791, 172156541, 769933792, 760455767, 435660153, 697173979, 610318234, 826717192, 946746935, 395547703, 560196448, 128431131, 534863883, 538998446, 322843215, 343782809, 834277128, 781125649, 242248487, 983570662, 145121669, 415109266, 243862922, 629520199, 683955231, 12987802, 815483950, 573358966, 967227618, 776933048, 285832039, 794662841, 423401647, 565489912, 638414765, 293229273, 471913939, 692309576, 412405068, 11039151, 844335697, 394591960, 582836464, 277111613, 47472643, 336612157, 333708235, 48613435, 942793741, 263297566, 947545845, 427371943, 211081343, 856784042, 610962732, 781965487, 789293898, 122171194, 304072705, 34979789, 492680955, 226414052, 503772679, 572125477, 301954812, 423059718, 935839072, 206578229, 47700270, 550880447, 816055337, 302523328, 405861895, 602327892, 109159180, 971615675, 387388106, 53022366, 831623844, 659380882, 924430613, 755239249, 523138266, 399537996, 479233584, 565478206, 529331479, 283529524, 281639901, 338406608, 118765589, 877020799, 58286088, 775865052, 734698148, 136857409, 466957914, 622686096, 203401602, 619080375, 981891243, 859826589, 827492713, 402521449, 948621803, 256506091, 327277211, 371913448, 740447580, 344028185, 655119772, 519196555, 15778229, 137006473, 167267315, 515531554, 55647370, 701839025, 97525772, 798758290, 781807514, 656971233, 539950126, 86295108, 563271629, 573189573, 927191500, 700148372, 692376142, 3373064, 104354078, 184011785, 85559397, 710473596, 290505220, 990652767, 729115430, 1236767, 104354743, 932116136, 725633873, 791982823, 793991628, 64511258, 164439907, 781119716, 7811670, 320157356, 914642378, 265648533, 168264846, 422571762, 471513862, 333177471, 982805694, 768569801, 747191144, 888800685, 904576263, 629829875, 586171186, 26592980, 190851836, 468706432, 587850600, 836731794, 760590872, 636940484, 991450356, 462217254, 932010093, 32664985, 535486665, 68461269, 39790584, 971754888, 84374011, 258834164, 585911115, 421136181, 764435357, 688528199, 138110279, 955212257, 148185724, 237156407, 175219956, 613817944, 807292124, 670418533, 222767135, 219234231, 160607945, 57883132, 164863512, 443421120, 104647620, 933367097, 675463861, 48369117, 133973301, 426266505, 529497674, 470881152, 342685051, 953776485, 935839226, 414133842, 891693909, 827356027, 99934021, 649267377, 316494311, 344164362, 450158890, 137214177, 272927230, 297748603, 978157941, 616349274, 234479186, 727122966, 617452149, 159081591, 294358993, 88761297, 3767739, 252142227, 47294701, 571130276, 564199324, 518293801, 152502654, 366078133, 871723386, 907169390, 631500894, 173541138, 885404135, 533533648, 673275601, 791645241, 377825695, 360564861, 767364006, 874696419, 301530637, 255574356, 287367235, 543865936, 201236576, 349667522, 742596149, 949673253, 520811011, 224838838, 30058202, 927139327, 230150788, 98140810, 939581651, 425241974, 940799306, 16769442, 99096251, 933826976, 471812033, 779726502, 799402791, 933228630, 415502914, 300576024, 331687988, 468910955, 675382922, 948528514, 432564692, 958699401, 69111995, 665504139, 65020497, 845291454, 95396129, 491659398, 961723124, 948859161, 44082104, 228976690, 838571737, 190159464, 184237137, 238386159, 24393826, 270794893, 232051895, 543880244, 175343057, 875266705, 669186362, 388775289, 829987300, 686019560, 436059276, 447233144, 958448980, 958195448, 232980344, 342455883, 127548266, 99132916, 540301464, 551434647, 520624692, 246495068, 452366614, 113033049, 677990314, 665902840, 676532963, 637440654, 45217252, 24438588, 674857309, 251173552, 475278871, 301534732, 269791244, 671958301, 827890166, 557744083, 91583164, 231898869, 603778274, 658810153, 672424744, 598300585, 990608047, 587367737, 648357940, 909387516, 853176920, 382155278, 425670403, 518501885, 406715373, 154008931, 60144800, 396323374, 691151570, 512992646, 680371210, 840218795, 959838554, 878497807, 613526859, 9535882, 515750215, 941668820, 49856001, 643647764, 282560414, 432420781, 238814035, 159952894, 265729097, 291867846, 264176448, 541352168, 811020051, 217973048, 628341219, 837935502, 570426533, 738850604, 845192616, 289983539, 42369064, 752659257, 550957475, 336358131, 311291195, 154752180, 643080806, 493950247, 582240376, 628809266, 188023484, 781166639, 150888696, 49511103, 682656639, 233968451, 89547333, 127197094, 175147124, 877092870, 667412140, 393048165, 826162790, 151165384, 246739648, 116644930, 525167361, 604596640, 492868794, 328247885, 657465162, 440021035, 153863500, 340298868, 107939784, 113508918, 842208765, 874044924, 567505296, 129089573, 790903639, 591108496, 664386230, 512587223, 874800425, 50016386, 556446247, 134565766, 651304429, 551869909, 488013400, 374686550, 841836090, 332200238, 252160415, 437243282, 492349443, 163399194, 800331343, 640832963, 107889919, 647233122, 612861352, 41081854, 210274071, 283699592, 878107135, 69659331, 910453816, 458996387, 187260032, 43323936, 129571733, 382487412, 161230915, 274982761, 83187454, 401255816, 590765056, 537131329, 722783683, 819327452, 735254151, 882948429, 512222314, 596403741, 50291672, 478329164, 735253994, 834667876, 18859759, 599368896, 23006711, 136543923, 911126452, 672011075, 225385932, 539870058, 2568050, 842023185, 837400299, 18260416, 980929295, 271853743, 830976680, 220822858, 19463998, 238795882, 543658726, 871423010, 825526243, 661832809, 229746004, 129819657, 958268840, 715473356, 839828102, 992735523, 358680465, 727882305, 790424421, 904489755, 72154003, 926446056, 248658836, 392026790, 924591230, 258518170, 521161626, 136619616, 128439710, 167763841, 51186291, 308103745, 576874324, 516596452, 912609937, 972491223, 863487300, 408573368, 70970987, 383430893, 765201353, 813365543, 841893841, 819949636, 672228713, 554567430, 203622247, 419168846, 162059303, 476228889, 992837125, 756286410, 949764606, 91487355, 265674035, 792415421, 347713673, 727712318, 943322383, 617611245, 657782062, 521092748, 629970385, 157425917, 253972171, 148891215, 97605603, 845927808, 613299271, 604944773, 158044856, 932656314, 786576595, 938603621, 777939087, 268972340, 683043584, 259238125, 599758661, 787256684, 217268783, 839022753, 165569860, 804309533, 737002986, 18557565, 533496022, 7763359, 456481679, 344960179, 268479114, 937463775, 929608604, 663839961, 954727451, 422538700, 985016458, 370828619, 814230797, 422034506, 123998601, 454829643, 631883998, 807359410, 768709819, 289338290, 43108126, 819318302, 97134204, 955715090, 259843354, 499005203, 360931953, 250926911, 613981250, 595186253, 912190259, 308411860, 610250139, 580635406, 684662131, 599019936, 674103703, 636354250, 198499612, 602932185, 726886774, 172153379, 311693767, 274644045, 159153632, 697417668, 251805453, 684133797, 551636598, 874882427, 988143269, 500286952, 398371548, 322940445, 47270528, 201898878, 365599505, 500011448, 77078069, 475789885, 751675791, 281098140, 192774159, 819635835, 121265719, 825929081, 377676931, 185106450, 713938121, 335639206, 893377823, 635795413, 546982930, 523381751, 291412483, 533243073, 322342020, 96213643, 692653081, 274697030, 757761443, 451857819, 634913379, 277234523, 201716471, 313054246, 548041065, 352483609, 443952108, 178448339, 735138890, 781154992, 210048368, 818617830, 201659279, 980718070, 52063132, 846543403, 703693834, 406181521, 102100814, 169799763, 717610697, 357465158, 775026389, 928478295, 412060672, 45724248, 864631786, 780029796, 587785899, 684740765, 193563126, 150740822, 474677798, 545716806, 139930731, 618220996, 417142429, 85140854, 413243357, 69587310, 119893987, 680452199, 174351548, 70215934, 502621392, 8881304, 456510036, 737898371, 893629067, 774774801, 824868113, 835991326, 966956386, 832388375, 61214396, 162924693, 926584931, 430357375, 38840972, 559556855, 97767182, 16758066, 104114696, 983610455, 54170089, 785551426, 647470082, 614556482, 223397335, 739245852, 295911581, 981347470, 162672368, 506001525, 827339804, 440010524, 941733787, 756000751, 104122781, 804455289, 772985932, 69149667, 18457965, 4296520, 362318743, 340837389, 495404100, 506382740, 158810882, 417647862, 706275439, 451328123, 883572848, 780334530, 652673285, 455422712, 248406656, 180319367, 798826353, 394024358, 969497641, 787720492, 999297765, 485764782, 219023910, 457605050, 428982767, 410474835, 971494097, 653623400, 246042227, 35822849, 219881352, 28825944, 263054708, 529928453, 478725454, 336043603, 376808633, 399642954, 444323322, 75180120, 454694725, 128007981, 887645370, 433316870, 874571951, 42940262, 150689540, 542783077, 752150898, 529294787, 725406428, 560697603, 500373273, 401757064, 198797718, 808668826, 433036244, 280791436, 467903218, 823422095, 1109515, 117648088, 956320564, 892164946] 479617725)," 0 (countGood [161967799, 681623006, 221232871, 51765712, 913800325, 990085770, 723548992, 364584681, 855417049, 899823462, 422694314, 889676630, 673968150, 912396775, 833451209, 107256951, 960272301, 229223754, 287528208, 497084249, 177383682, 195145824, 102073314, 986427427, 122660816, 453049766, 140289286, 227103866, 400441266, 462135794, 277239698, 620859141, 710699715, 227253198, 304184655, 202106727, 390054309, 258175023, 716185207, 626854895, 17418304, 146963151, 344803075, 899334299, 519001199, 258287016, 491250824, 896184722, 833604719, 971890238, 916466993, 178224933, 548374589, 371695688, 762480124, 512767796, 536184012, 74127376, 230486095, 293572286, 570531537, 672363525, 949197441, 51643770, 769928596, 372811891, 661395020, 743335814, 568250511, 354699456, 251512198, 318996559, 974697025, 698870358, 722911597, 12424549, 586117951, 560424888, 105861160, 772789600, 508811625, 573069625, 231769117, 539287572, 704831785, 318633108, 930461457, 667393925, 139777810, 881241914, 307656562, 805421920, 206308408, 365464262, 325663140, 841779490, 726550949, 711365713, 128943033, 639769914, 711478802, 190713683, 26888024, 428891657, 576703055, 556372457, 848354169, 754379244, 292274429, 166174798, 72314706, 986060263, 820477751, 38313942, 809233827, 306823123, 531061426, 721445246, 216233128, 738149164, 283927216, 648556427, 239145386, 156885846, 532195739, 876791985, 781277450, 367178203, 467092047, 232389113, 869475343, 387175261, 824765730, 896118162, 319507049, 408179026, 662689014, 807559898, 796346207, 662616804, 12454472, 445635713, 254494995, 620546339, 312064433, 150331859, 990043127, 139099385, 412475325, 305580590, 649698988, 864939411, 420161935, 671147660, 421013301, 137923332, 196893655, 293397640, 358265828, 377653304, 127273103, 953645380, 654225135, 622623027, 323904272, 167382740, 690947130, 856949556, 789079020, 283048085, 249791243, 285594657, 797897547, 121790733, 940020966, 851690350, 768603378, 448696490, 270956474, 803845944, 677493444, 751229815, 898398279, 343890697, 53030657, 468857313, 589083834, 870779588, 126342271, 892291374, 156281747, 50029538, 617614232, 788047622, 675817016, 217629227, 518553323, 313295545, 19521599, 906792771, 24160025, 78921933, 773650229, 375952221, 708703218, 886121422, 302999117, 548546193, 72886793, 853508024, 390203406, 785082560, 198247709, 784799071, 610334880, 484188751, 362048230, 539666687, 732825768, 872194948, 865312885, 993693986, 961312552, 37722647, 77646013, 806874201, 948436643, 872154573, 221226974, 380229658, 834673673, 810865551, 127462311, 780803782, 941633183, 871797703, 357303872, 352124489, 770531984, 605702472, 875831770, 929234176, 781621698, 786762802, 583261854, 125534117, 371933387, 517256524, 347773103, 718876971, 610755637, 887100112, 947577443, 51859185, 422896345, 624877583, 667673609, 553778805, 125364668, 890472249, 598421302, 539343010, 334124287, 197503883, 779736994, 220449104, 682623488, 642350435, 682740241, 209664798, 690441083, 669494634, 314597548, 315057719, 255734171, 731429710, 987814613, 546194067, 345943013, 711577633, 596240880, 943461261, 685911249, 886993066, 207501333, 811914577, 841674967, 525526026, 149394825, 882318873, 108716340, 244891748, 282724347, 24655664, 322397298, 677962802, 124977024, 267957179, 577998559, 805760912, 265446117, 53033497, 221632906, 402921737, 853318581, 25612971, 430074016, 420879312, 739524150, 52637873, 694674358, 276848019, 882761419, 271645028, 940173541, 890309869, 326568584, 87193068, 869427559, 68804000, 332093558, 455449070, 175069380, 173225039, 173776907, 697108511, 71168839, 977731154, 932276411, 634401554, 688635719, 613524510, 376625061, 3182195, 49442464, 378220883, 200378122, 721912932, 994085770, 483670849, 573898627, 571772691, 624064529, 838180703, 231674900, 891145744, 511595311, 173300256, 310547908, 925225889, 178895054, 498906072, 994156436, 546610397, 263335818, 22366107, 500935139, 846055889, 53150662, 740741334, 665710168, 362336887, 531224637, 554568873, 922569754, 987286250, 659651140, 442450092, 230535526, 284781184, 587205344, 825363165, 260320333, 35374734, 317314702, 472037358, 43506453, 240199480, 602299040, 809890764, 174312178, 129757275, 925612063, 783783152, 536272974, 698179085, 81975114, 780959593, 891436144, 827730399, 623128536, 145756503, 292221939, 120927865, 331293725, 870316131, 836599684, 403462696, 431786038, 875040548, 439183572, 166493864, 198943791, 894405730, 169830296, 633683933, 539717525, 314754521, 719179684, 726814352, 13197389, 908940581, 237309086, 260765552, 912761153, 56887265, 406218444, 749858460, 397076246, 522077453, 769889465, 363807372, 976857579, 538870112, 167558432, 134616844, 89644504, 565334827, 371871213, 534563643, 45357839, 260650373, 600829906, 715412390, 397639709, 138205189, 323385785, 245408515, 26184713, 66126406, 478464322, 767461852, 848399102, 850946648, 103302222, 859720626, 651493756, 497223947, 826957000, 619174803, 716159560, 846350796, 227071059, 990674103, 149016756, 954671295, 956047913, 247672232, 172592214, 410799478, 137559933, 452535031, 320392121, 619457874, 497265891, 79277916, 103381359, 950588608, 814723465, 93297033, 704421426, 703679636, 397645767, 661144912, 86915219, 733327629, 898816857, 962305466, 389465395, 117433764, 814022549, 743299290, 963640314, 265544365, 378432952, 680286926, 151467104, 790860243, 683483009, 626547454, 558769426, 501107451, 587046271, 764214898, 495245436, 105660974, 571390786, 633554371, 180191519, 89451255, 470207970, 478100176, 400067798, 796879311, 976227286, 979799061, 932864036, 192419691, 681186695, 46298564, 276658498, 972626387, 111071028, 884397453, 433464652, 765225532, 913749310, 419612536, 196765603, 914852868, 303177278, 618131884, 803078583, 976903057, 733215844, 533894655, 714395035, 147475732, 299980843, 869726220, 680831703, 224313071, 269935587, 925734575, 151585847, 896642505, 107908029, 478066386, 247716843, 488456998, 705803612, 904426796, 552294325, 939471348, 407002080, 342428389, 312276297, 367201846, 548579965, 600591612, 812537662, 183999343, 224892564, 806630522, 588553941, 421652947, 181071256, 356038030, 901545678, 782383286, 433957318, 177986556, 401797677, 471136631, 588631479, 317503336, 306757719, 626380128, 137663185, 9239034, 834176322, 54126424, 437342530, 945889079, 113806234, 595053160, 239670517, 14492975, 430169691, 130222496, 143215262, 143301312, 465595850, 13932141, 968740932, 806405469, 541258004, 363887722, 411821994, 538895258, 506048930, 714410367, 488583116, 451813117, 386510696, 92445316, 117871226, 799394593, 208813109, 715051821, 763324673, 779980617, 34488188, 24136343, 152087919, 651368170, 322796666, 281515391, 421729427, 219740211, 572517288, 273713435, 50413082, 192182939, 529317756, 645804249, 408861343, 545293986, 870615710, 159484281, 115633838, 261163755, 981389997, 14845685, 147240331, 173447876, 841919576, 359751270, 935618903, 74052322, 509406876, 315178609, 398334342, 294898580, 354393980, 459145311, 835005908, 385835230, 333908703, 388622295, 913965842, 883370171, 37733974, 663263960, 113044512, 836045438, 265480885, 287487584, 946445692, 345762881, 978570603, 88110338, 288197812, 342893762, 807883683, 508875432, 987873303, 136521266, 768321755, 444343893, 793346865, 163302093, 856296023, 200671878, 15047286, 368846051, 677522074, 466242424, 309613927, 936339012, 121147162, 726367505, 982605110, 744223207, 696282864, 682270746, 258619548, 27891862, 413635221, 351000757, 381145845, 902464407, 456161046, 414098190, 617646433, 554161149, 601827336, 957000611, 150304122, 511919645, 150335356, 367423217, 556830825, 614932758, 593865840, 686450163, 638963895, 280988620, 185327483, 42380117, 762920584, 350514984, 317656198, 113804000, 754252861, 786142339, 698511954, 154774990, 137114317, 71223265, 489755892, 511914917, 504909636, 748152547, 470206947, 81492689, 902700625, 180973071, 477186358, 248413282, 372588413, 854769650, 164003363, 689611908, 190040766, 166896484, 953316670, 556190634, 201678050, 174836048, 219071176, 801012698, 718920009, 749470319, 479834371, 540777970, 220739625, 670785916, 931651389, 244791892, 268365642, 325023247, 802388163, 362397936, 499077074, 448591393, 931007588, 941619948, 940408372, 460099711, 396839848, 102577379, 842266721, 707980531, 713331920, 473558180, 185450351, 292826147, 705035407, 196904019, 782938541, 998601257, 662325292, 175233807, 914742913, 889562865, 737342148, 805886200, 562741314, 139707593, 254762835, 999086288, 652131093, 163195247, 736817707, 367217918, 707471537, 862610881, 425036318, 492840706, 607603105, 289036699, 633660730, 372637256, 861988022, 113072852, 818428255, 304918770, 705256065, 923856377, 752788642, 425282691, 804329261, 717270580, 424126270, 74012738, 78826919, 51273232, 907649661, 594962256, 330401591, 819285279, 698542428, 679881509, 765010411, 293970415, 959319886, 896983893, 172700832, 58078305, 370511254, 961472049, 248876502, 235110356, 393291911, 531160371, 290056218, 865518798, 988075293, 3835366, 350672229, 182596158, 421106063, 632161320, 416931062, 902145344, 74790417, 724325115, 794060579, 339316426, 134312135, 126331836, 440430494, 932609608, 737825630, 207616128, 18912879, 550103836, 57825187, 931355319, 391517916, 976716580, 166917674, 475934480, 898573565, 851364994, 607800388, 66912998, 753518146, 377022115, 503132972, 716847572, 811230189, 870238621, 970407998, 148732030, 548695873, 622540482, 629751397, 692275439, 856782538, 235675797, 722695856, 347959889, 277677555, 134621844, 311400948, 813039165, 403328381, 105247030, 984532301, 27627160, 767083097, 635790223, 281252986, 356835864, 946009105, 442945658, 555398024, 750468970, 90842168, 874156236, 999849989, 134791833, 179270583, 705781838, 721811573, 806075925, 502801005, 297291180, 952402086, 401845051, 634380995, 28334245, 247069759, 465291588, 475221100, 14974347, 974264802, 173233118, 649345105, 524472580, 972274340, 233693916, 673641775, 459090893, 514639226, 763367489, 254100469, 15987429, 227725233, 51646449, 825289673, 837648703, 807048948, 694748635, 13282835, 797903780, 534386347, 926280271, 343349390, 2087247, 971404943, 764846142, 968408258, 992229875, 276874019, 187067072, 718822101, 485824518, 199612299, 646294885, 637022942, 217994706, 651148791, 958159252, 45980859, 400015690, 305935901, 882784637, 318655131, 955318005, 365724450, 587169455, 452819222, 555440645, 723849543, 583016334, 312402820, 264672757, 756730417, 267536002, 14338191, 719248906, 377810102, 430960864, 325503792, 85512222, 489741048, 757147326, 539642470, 246966932, 274103330, 930846928, 560683073, 507145275, 920704190, 142810447, 323888679, 851512011, 581384557, 884006704, 249617361, 706548712, 274848656, 814414138, 683228681, 883921799, 937552178, 474086621, 798328093, 276002792, 88480778, 869570379, 526579957, 833597912, 167546708, 919170131, 514507749, 348014811, 110669370, 104771257, 350673395, 446778832, 294514157, 342222799, 776963938, 452368774, 856930693, 97548499, 100566349, 578770713, 907931981, 263769836, 546837795, 110877669, 273424209, 915502693, 921826106, 782895233, 583622396, 959560358, 101265394, 133019395, 278689851, 542497766, 950194269, 138037338, 261195218, 798270887, 928223034, 434725395, 740010975, 672825445, 119302026, 850159799, 221666709, 59610103, 60264124, 34330524, 89569243, 496131321, 424025419, 867024632, 758479646, 744103747, 728697462, 736394433, 467365833, 498006372, 106547833, 618357121, 55372062, 555816344, 41618220, 688196758, 360599826, 483918106, 322842751, 889655649, 621809211, 238482626, 840203853, 763225495, 352166014, 786345707, 725248085, 783832553, 798912499, 868595974, 655739167, 181276066, 750593501, 342881308, 452684089, 964525999, 838938910, 136416250, 239537469, 143789670, 998987844, 300039529, 293084061, 740531399, 284395681, 695559739, 633812658, 631438315, 273647772, 721633998, 758378190, 468334512, 491220736, 130124455, 847351158, 84448966, 154540076, 407083657, 895590263, 97475302, 671329173, 89838886, 817873617, 952654302, 832307714, 348315957, 682584879, 991034759, 961658352, 199138224, 124477745, 812744063, 367236117, 806660904, 398038700, 145549192, 174574714, 412978064, 569889363, 773717006, 59539642, 699805300, 153877216, 277221892, 245213800, 545182422, 890547945, 290523147, 411851688, 80987584, 87547270, 29738540, 188731042, 459236863, 190221783, 155449193, 142844664, 866743363, 653327106, 724942946, 30251718, 309158765, 411061662, 67231670, 693758663, 955271724, 627518628, 240781210, 746269241, 250397977, 202150924, 286518827, 675983970, 493795749, 906438248, 378513587, 306160215, 98500505, 193721839, 384266375, 745124381, 105134868, 716371474, 680077551, 818548337, 842747264, 498810270, 627093321, 158865611, 131403817, 117277980, 890512806, 682321729, 119052687, 268205813, 253393427, 613149163, 667087674, 59282137, 30889587, 86166428, 416749902, 237564833, 678975653, 835210350, 657413039, 878698818, 702282709, 48631058, 616394656, 563321960, 591542031, 127546313, 867813212, 986827652, 283676390, 44557697, 843072941, 323528884, 220990144, 421872941, 497384561, 965663885, 244314842, 190422723, 411163645, 316106878, 951067099, 211059050, 807476700, 458071523, 13501033, 462116398, 525262193, 513826966, 717614402, 25872574, 401575246, 120566241, 413874606, 33912109, 860416090, 382297028, 635384038, 165333409, 225524222, 948836173, 136261959, 790496396, 183898360, 173929896, 196836085, 965002806, 959085870, 579782357, 413349831, 320554019, 946221430, 26885005, 83485189, 915706056, 16070041, 151783227, 704404517, 419940589, 597002870, 863603696, 678442414, 391704067, 600881374, 709562601, 70706440, 925175503, 54208799, 131530048, 368459070, 917704621, 267887758, 818446592, 615970232, 622757563, 237499620, 597192613, 148242814, 893148120, 950328045, 778056359, 476589192, 960471588, 227074092, 596387256, 798786580, 714351330, 704158785, 289850390, 660767635, 226382806, 316350502, 843607426, 247039119, 569731602, 53554828, 108871453, 742246261, 845483974, 246826279, 149830584, 135363966, 940234449, 875922481, 277473268, 843357316, 526267157, 723671354, 49521021, 16884633, 301770535, 427755037, 77320411, 872244934, 818241380, 731790405, 76279371, 589578668, 596496098, 292932447, 551815036, 573796603, 969943744, 832910547, 648867391, 170923356, 426518003, 402146898, 91910, 144970484, 677952302, 73634173, 828895229, 245987945, 225283383, 209328476, 598356520, 111546487, 945330425, 189307181, 614821202, 216614281, 703833003, 916638569, 925215640, 101147898, 897301777, 649793946, 852536905, 84735642, 408898834, 224353265, 254902275, 572879240, 562192458, 292916034, 172231268, 315082427, 236825760, 453959261, 617911480, 203048783, 984219380, 774661631, 913906826, 685343669, 244731276, 26439520, 466257698, 288796301, 893972108, 927821600, 691848637, 837521745, 121722833, 812501273, 713151006, 237349804, 160379183, 754137668, 774724953, 577928419, 447761292, 636761766, 383479546, 331520949, 15101415, 278617984, 782959494, 409740979, 228681705, 37057191, 74670028, 187119199, 810208419, 597604201, 639585008, 302627393, 700814335, 682217282, 18225746, 959813116, 454372102, 418934416, 906005948, 295145925, 461518591, 583632606, 722737555, 717882375, 229180874, 648828354, 491590979, 344610362, 83742705, 877552913, 148971676, 107170400, 472811056, 287149160, 776972294, 574267811, 94375855, 867345554, 279901708, 699108935, 975469301, 477370278, 217765969, 613105942, 740980992, 650393292, 904095699, 843740054, 708445692, 982089516, 896913698, 505720653, 858852025, 691126128, 855326129, 803108528, 544341164, 359071449, 202044193, 494304306, 305124894, 479347617, 244006012, 437636824, 7269656, 256267559, 917431778, 916241414, 817202438, 700478667, 136568143, 738508278, 679576619, 164207860, 278595386, 404827509, 405189743, 131934679, 753986950, 540074629, 731017953, 488852194, 163553639, 650352535, 860398287, 895365676, 942566395, 384921406, 643115696, 996223450, 128825428, 570349806, 705542073, 165241450, 29544252, 198790469, 11626195, 405839361, 612239714, 695362317, 581273186, 853162224, 87681875, 641414560, 671409247, 70103450, 447173900, 934132442, 968734082, 367687942, 527135296, 146555548, 96779300, 159257751, 445028301, 604590474, 90509062, 621715482, 175155826, 833662649, 792509154, 841631547, 202385369, 333295753, 185893302, 159435265, 812362902, 397507634, 641293453, 988038775, 188664662, 1649414, 591023713, 635779248, 176216740, 297965377, 724370697, 102647738, 932184020, 590508740, 856672499, 374597672, 751792406, 220322315, 937548869, 608074200, 669858332, 47558712, 883362685, 820284618, 457859663, 507668377, 563658879, 255484267, 377794520, 745664265, 428209374, 284813851, 362625860, 191381022, 871696851, 68311274, 327531863, 563153288, 754695612, 896413595, 914936839, 950237416, 443564631, 331244087, 820882721, 917044084, 202681948, 235399445, 795989553, 911047345, 747067720, 253287422, 259058255, 824250394, 885582292, 236059363, 240841120, 716832377, 620594843, 796847529, 896589094, 254886034, 574717558, 406362064, 944774140, 528172455, 110442702, 306407293, 540708545, 42709002, 431574225, 653647493, 596786732, 887143664, 180292374, 827904303, 683391138, 113441719, 868611553, 555389900, 910926215, 990354825, 38382202, 890181265, 188131845, 110119346, 632843222, 365149849, 916794817, 941492477, 121537926, 336569203, 458683131, 235111774, 151236877, 653142944, 281708323, 563602671, 640719145, 243960135, 743016995, 664485783, 50230281, 61863549, 124733694, 921426571, 804315951, 260418410, 29603858, 868680398, 563219871, 210253323, 720148953, 68830444, 952305285, 734888013, 616183966, 498553984, 200285637, 827816904, 248163234, 322875428, 324638052, 350801214, 545449216, 911165469, 220768782, 502324025, 536475950, 686151260, 358354944, 769470015, 27854171, 163195121, 992940769, 624613342, 365286965, 133697716, 545680623, 408504170, 232940013, 773902097, 857208453, 494927188, 950965871, 994589875, 9773725, 941095821, 762192912, 58831310, 270912924, 89674126, 459720186, 180621329, 491470147, 742696082, 386866975, 137159418, 593499137, 451367153, 650954604, 887934397, 490886032, 848886140, 642416441, 309715739, 83817454, 973822066, 594370327, 980400708, 660411076, 805282717, 87474376, 319829848, 777415896, 626009146, 175414783, 775646525, 210953307, 489932588, 626526847, 749038356, 305073784, 870069332, 36961950, 432322284, 274716583, 677684364, 475537520, 583673912, 12272119, 794997610, 50070762, 526770193, 352235278, 584881611, 540232029, 58580834, 961674091, 217164708, 904670724, 82979115, 85157685, 852467491, 901185061, 294999476, 100542515, 281774205, 171861794, 64453438, 919656102, 465116336, 843672583, 999700876, 496350632, 865811428, 177352846, 329049094, 761950651, 205251573, 502712306, 875472472, 858343954, 133807759, 957960613, 379021882, 719617300, 739046266, 758233649, 707980200, 228686401, 798193039, 348296585, 834210389, 998432327, 176778266, 135263799, 345472947, 459068069, 107982080, 596789665, 109313626, 310471874, 639385985, 712926409, 498679793, 342169956, 877482889, 822579924, 754567414, 467920797, 668965258, 182163240, 275729049, 23107755, 10205050, 929392146, 552380508, 603019539, 286958872, 919764815, 618772097, 517101502, 763320612, 624488997, 715363529, 315714706, 799867900, 209067068, 257851399, 94722404, 876605539, 702777628, 502946331, 822910971, 477363436, 927858174, 71246248, 661369602, 741128133, 683743617, 994797217, 673305176, 518004315, 582433273, 276502736, 389678498, 897737841, 240267152, 429859171, 172766933, 837252640, 87322115, 980135899, 588067296, 129971735, 480498870, 825117989, 340620146, 48282590, 282017248, 634759130, 875306350, 864972741, 790093814, 511775975, 919652901, 724494727, 891485572, 131970832, 501341005, 187321718, 957775263, 2863490, 789264868, 51102663, 344264888, 604061913, 640274209, 868248714, 232704503, 796507746, 336017064, 856013712, 961770107, 886117529, 253357529, 501931133, 836820203, 774270711, 323988141, 273430302, 935280438, 192761927, 744593727, 69103705, 922715191, 80412602, 92383889, 91106668, 689333169, 201951340, 569815115, 875496340, 302260425, 728708420, 965501494, 829406981, 187084826, 524364034, 812676024, 277111850, 293857364, 305438842, 652487629, 47177007, 730152412, 421906619, 579156332, 63109228, 587450576, 387182114, 45576708, 68623389, 68978134, 974028360, 685528714, 920921394, 107823883, 316890496, 952125160, 179621939, 795586461, 306401466, 302044533, 659458707, 445751509, 741076834, 629320951, 179635688, 378313601, 629800472, 449326066, 538502275, 700789847, 324623180, 313199472, 354550595, 3948815, 906014780, 533803615, 14766636, 588478954, 231217559, 270362109, 235814881, 742044838, 130772964, 711407652, 823556420, 935315506, 224830541, 361670549, 654332377, 682678137, 475145486, 229901727, 717720507, 492542533, 869328927, 997480751, 315721999, 911133533, 642610086, 893913630, 57037329, 570056864, 366590497, 742719052, 922413029, 644795512, 600527174, 711734360, 258392186, 823705595, 118607606, 228297648, 888485114, 271683302, 65675931, 338310112, 301847154, 988297262, 285502060, 791813690, 996364597, 56276335, 255502762, 430750993, 425613835, 847851890, 758644432, 180551321, 813179019, 969427455, 210745009, 856341548, 832264851, 817421752, 516861503, 640991512, 312644078, 8142963, 349722603, 248003725, 178631812, 203270441, 560095405, 283851847, 951499632, 710956479, 353985197, 413183060, 501104001, 147063697, 741940472, 452343750, 841670668, 66224024, 476983966, 49823081, 214254160, 52426799, 470145200, 620882906, 636779038, 734157633, 427864766, 562425493, 584415422, 335349183, 17480198, 447014804, 499952334, 297016751, 620193230, 183780545, 355753401, 834697197, 77265042, 358901771, 101617197, 722410458, 652676610, 888780137, 787264314, 526285612, 184754090, 845580838, 150366701, 405987866, 17157846, 169191612, 716751523, 809129658, 166641044, 766665000, 262560791, 448773855, 409114594, 730000470, 675207674, 700508201, 232406183, 119409123, 823694104, 325425896, 414879851, 452619666, 164627738, 519375976, 827790201, 292508162, 684057192, 236859782, 906965502, 900776096, 587140836, 929565136, 155786437, 899403339, 964098978, 445645214, 453344736, 327026112, 79958564, 187395240, 474087495, 83387553, 644179649, 455893221, 135648656, 419158595, 199562836, 339365655, 222627779, 457774258, 431525350, 628864260, 920749883, 630540095, 548739680, 712496934, 141495967, 640153285, 320294141, 524743609, 331786559, 645140469, 364239569, 925275093, 829651665, 83392087, 424999620, 906894153, 920404572, 872584754, 496744947, 132969537, 711006896, 113139106, 786341918, 777711660, 892896516, 238788419, 525388000, 650336825, 242618942, 361763939, 775617426, 558190073, 55224913, 814317005, 431695432, 623883995, 981242659, 128907337, 79261473, 449459356, 484660628, 700041545, 105350766, 972951390, 614653271, 664234100, 324009826, 612208289, 926217601, 248636670, 203228166, 921984590, 623733483, 636741098, 135808418, 710527560, 47813135, 369050863, 88216980, 668250057, 452852580, 629020230, 248548171, 874553189, 192455282, 971055167, 586130414, 562639962, 660422696, 755089151, 795352093, 716535757, 605134493, 87494323, 898485531, 855808784, 310261346, 255176252, 333340334, 914910742, 63197080, 440703615, 413093464, 546850076, 249367879, 501050325, 96843418, 702372087, 36772713, 160066841, 706375361, 190829434, 789259789, 139947948, 131026065, 412032712, 681607310, 822001186, 739775052, 463444877, 354695303, 324636480, 805575896, 491153655, 642242519, 624691256, 515732839, 666061975, 344495069, 933154195, 339429854, 457301561, 754181916, 341590796, 947800177, 819945391, 884583814, 485548176, 689525568, 403634928, 409466000, 38887573, 204295343, 651951097, 150943665, 269366518, 514781455, 64910138, 381831714, 705266450, 183010173, 727476922, 879585002, 662247694, 486145576, 486301845, 741087862, 661222870, 943789666, 346475047, 955810592, 296876428, 446477246, 247010289, 873959475, 595335208, 980239066, 504952457, 40807405, 730695579, 546543587, 515069889, 906195681, 208576015, 694513335, 360224806, 63122818, 561749832, 358918381, 949577397, 786929035, 336920072, 581622111, 184309981, 40300648, 596900219, 54715844, 180976690, 123680843, 381434712, 858633768, 57659419, 823227392, 763205619, 730683986, 463534579, 422361228, 996519059, 844684818, 739188648, 666827056, 64523057, 565082396, 112780229, 467412361, 888256285, 45795915, 671085194, 212164651, 853191140, 381103441, 571244460, 160525992, 193614632, 584857379, 355477581, 646333104, 995732027, 27053799, 849612721, 64480452, 189427443, 433918848, 364684891, 940925057, 625758889, 236369165, 785530870, 296358066, 342510720, 528250656, 591677778, 151083667, 519489807, 676477578, 293052419, 804113470, 922883096, 43254441, 778684162, 422078569, 440022828, 756746986, 114050149, 738275832, 49006232, 773407086, 717008139, 931960344, 664357353, 503219258, 309609389, 687142738, 226739855, 988016051, 551085207, 586694530, 651734371, 745212757, 408469902, 852277307, 723188795, 987319197, 615516872, 985202286, 43393697, 657273157, 256541788, 461479800, 897232080, 949128824, 791130069, 548040030, 459913410, 689817108, 180239469, 737209965, 871750815, 767400657, 55165515, 627355095, 447861194, 202092950, 225465730, 696451203, 189950495, 250280824, 541962474, 10331367, 405504058, 413018999, 234822340, 772048043, 645292841, 625276161, 408174264, 691320949, 565124391, 722928988, 400534918, 251042911, 963092232, 795206892, 711777713, 180019144, 953781872, 200196512, 82443972, 815531906, 374536470, 183923702, 816934875, 999045215, 110209325, 975552199, 961118380, 761915771, 37347245, 495713255, 642758530, 25654987, 981228876, 539057691, 474415701, 477588711, 975643869, 104864362, 267024667, 136661166, 759149100, 330965707, 799791015, 945504294, 785921051, 280481216, 756999593, 947563130, 938028498, 543947618, 412830122, 999107186, 284461167, 798509217, 576869634, 128382748, 507484701, 612575583, 927829610, 876335535, 838048108, 676333356, 610668981, 744832156, 104196194, 795051530, 253122251, 873638111, 461886272, 115415884, 40155985, 223452081, 992046983, 804673188, 830726677, 56503588, 989595204, 817185478, 74005720, 570972128, 70413347, 176948037, 440985196, 124049623, 323871846, 169387349, 45784413, 371984936, 185158163, 905795779, 328897391, 393406693, 448328422, 189325244, 703292378, 688870410, 380770915, 252730932, 688392139, 114945196, 24450013, 213570293, 356330639, 753268155, 58675197, 598772808, 449277117, 890025478, 718306317, 734216528, 670685708, 996934905, 673786434, 754269863, 936391823, 13103536, 534646643, 250831174, 33902083, 383569367, 45004999, 629092415, 368193914, 287604506, 947133398, 852214426, 933125729, 845325277, 713145590, 74654635, 102851907, 403432060, 312665871, 123264000, 625966133, 760954490, 509620101, 934087657, 291322874, 439707946, 169989498, 131252766, 794935049, 543949886, 241171069, 548835688, 733747284, 707488206, 331304470, 30584544, 473835051, 1557906, 744831085, 309662149, 443958956, 974229454, 28159170, 708122587, 198695791, 223979635, 600527380, 987418775, 740745496, 551923481, 823417845, 313297411, 802214285, 941282753, 265921318, 291583297, 937848783, 227489742, 722803231, 3360986, 701196984, 425692090, 208594793, 381123193, 207677452, 290634989, 789824312, 244547166, 672454965, 871970986, 817378632, 541835190, 626994109, 236922642, 767610432, 183508428, 995148763, 243744704, 1549748, 367666494, 428528970, 76300401, 931967167, 485005240, 420604834, 834257659, 314716261, 491564122, 290242899, 27075944, 40495388, 823396742, 228682072, 927755553, 915496475, 648156172, 157059296, 994690042, 850514952, 110284220, 3676784, 867711481, 834591536, 626038521, 967362766, 336619041, 492024852, 785901532, 584827752, 85392787, 751217860, 954405261, 234210752, 243930359, 83237078, 908446173, 725590130, 580869321, 890340564, 788537183, 983390195, 548297436, 214791383, 744003326, 25553673, 381052978, 984140820, 496127763, 297817217, 890792019, 197807239, 38987652, 459234868, 728984012, 643483674, 497330288, 662900275, 321223743, 485347205, 730869153, 553241487, 329975402, 432755758, 64397121, 473324643, 184134586, 432295179, 459222683, 648462649, 557424872, 995417926, 355301122, 24354516, 50980879, 395967329, 144082917, 145092221, 661382764, 53309471, 456673319, 456926674, 307418535, 661221677, 339395757, 462873456, 626186282, 256708673, 373334824, 633718808, 849667309, 813657811, 723590947, 736969934, 947884727, 598697673, 118665293, 318748527, 983231246, 429134577, 285187985, 760828665, 515583167, 967156925, 172091964, 759660727, 802395570, 45671012, 266288098, 396178150, 599814848, 997179029, 945414470, 251257609, 494205505, 287089243, 235319113, 592801883, 412370965, 893660806, 898322355, 963093829, 810047984, 225603925, 847217490, 47755231, 593587376, 328357034, 88828934, 385374161, 153525135, 237910531, 761997598, 716255073, 127264059, 102165780, 798850655, 106257163, 489545805, 364659480, 445289145, 617120918, 838193158, 942560747, 486148315, 768572483, 533620324, 151545625, 449235677, 708332750, 780668734, 961382023, 417583079, 177479143, 484711677, 576121451, 460636831, 396888176, 265039553, 116831476, 536791579, 90911221, 187993607, 520881192, 262215117, 485728551, 96565536, 461617423, 219279345, 610571036, 541173918, 483546494, 518087628, 611985097, 365814953, 803026773, 433958196, 657973633, 472759331, 516508069, 858704818, 753934915, 509898239, 977028045, 156642797, 840691469, 394852559, 112870469, 488558356, 140065675, 313726185, 670565406, 569474199, 791514837, 339814471, 489316920, 687362973, 161695789, 840699801, 280103047, 658451198, 301112922, 898934562, 579794834, 828539917, 284535968, 536080739, 656485085, 217803908, 136029114, 364592255, 298041991, 565126409, 382986756, 137643822, 836004327, 296499619, 891943245, 870060751, 78908171, 260805666, 483183050, 297932747, 961249878, 989824821, 267582850, 722687313, 822136253, 217932606, 681510420, 495694433, 677170372, 698206915, 190850406, 797870059, 131916928, 477597394, 246946451, 291887805, 140120876, 465247370, 612530074, 518623097, 224240047, 578407786, 891828839, 297564095, 763465029, 541046622, 776903408, 784897426, 551650668, 768326366, 577147637, 562655433, 42855284, 145209377, 838561613, 727839852, 132314521, 219810208, 168193454, 990216315, 498488259, 132990457, 73541773, 752934563, 425384649, 23649230, 869993463, 470323569, 61414262, 618922620, 917468172, 400656147, 887092487, 345621515, 338587717, 641005139, 507203655, 177704044, 541349606, 137375360, 857531933, 912595422, 408030270, 932799040, 753643114, 870932420, 445438362, 438550427, 359547224, 640051100, 600379750, 796857665, 232069155, 963698675, 481887894, 232962489, 870476955, 934453371, 645632162, 142034901, 312665184, 30674452, 619107333, 426451601, 77110672, 94807317, 907241587, 101967460, 221955660, 757526006, 954755790, 942162034, 854779538, 762238615, 784233947, 347875443, 417366959, 658555232, 59099005, 244781466, 543710733, 842886704, 432508333, 393155854, 858906094, 80599492, 73147169, 861138707, 787569104, 917991970, 522206755, 714043738, 895844013, 749987192, 799054013, 376853619, 607603741, 324732491, 58378468, 10734232, 846717427, 133543943, 25794416, 728836054, 185544573, 713086903, 254964345, 159104288, 831271977, 801834024, 653701047, 948359217, 647814639, 29534846, 998846316, 607070540, 645077441, 250950202, 969946497, 928268137, 273474070, 524975746, 941119453, 496316064, 602921351, 141022093, 694932747, 632349293, 131208014, 418977347, 45115832, 704107886, 537116735, 192297645, 314607717, 953615882, 497634179, 571907405, 734933090, 849253627, 834978741, 831078031, 118952545, 559901055, 177692889, 955729680, 470325619, 628378844, 805980295, 232695773, 194091150, 765316558, 264667766, 347724967, 645024954, 509020153, 18654811, 279432131, 438275488, 726409903, 603613257, 555216038, 800125134, 80004240, 824950429, 961162482, 191203985, 589450524, 639600393, 460828096, 298330040, 836247191, 991078787, 453576447, 424595779, 723107714, 925530103, 931071910, 119512693, 431848950, 485738496, 945551756, 653331590, 472211758, 712829345, 376476081, 237111438, 260102306, 478064803, 367731145, 160211268, 296397341, 620532678, 720256517, 344907399, 957555624, 42703193, 343431014, 683717440, 886407758, 924306473, 634782376, 53062846, 325599059, 759169470, 649709056, 931761784, 476281993, 534038740, 700843252, 570603394, 601364427, 194392050, 842775318, 469249749, 701853074, 873100606, 260145804, 783376672, 974173400, 455187182, 730708821, 526697410, 358899363, 549555776, 963849339, 949065796, 455894723, 655683586, 600403109, 340520225, 529868543, 750526407, 3426174, 941128382, 356346524, 713774498, 295778664, 924007909, 986512005, 554515651, 339482173, 168148414, 886281483, 271361685, 360314311, 371421811, 308864803, 112048678, 594422957, 617398656, 318488539, 73615751, 455433302, 77783618, 258330439, 402344120, 979471355, 4175400, 350769851, 951796972, 448117163, 122615603, 676989872, 913433765, 254703514, 925537937, 426328774, 63096041, 444655398, 992301706, 610533703, 447973676, 531032294, 427458416, 957013864, 848494138, 450267574, 718921505, 19177184, 148487823, 811377367, 854858268, 597531161, 514789359, 189870802, 769864862, 875041114, 484699551, 796492567, 155155807, 8735801, 203172456, 692891235, 248263748, 222504507, 647491988, 631444069, 34765159, 152749936, 56620853, 615127346, 536275104, 157288524, 400392040, 935873692, 541464270, 727442015, 910629926, 10586094, 524876467, 312556732, 609655846, 562349411, 167015044, 846481201, 1443027, 564643169, 236789474, 598347943, 129482182, 371989832, 968326796, 511162082, 969034366, 618514097, 207188946, 623874379, 507527653, 388491810, 447252894, 250082802, 24792015, 67362584, 92213120, 293468656, 564296153, 899591039, 306508672, 781641092, 486784090, 738651633, 98077413, 506311002, 770202338, 860612112, 69778877, 708644928, 689669537, 293548091, 635238270, 874979777, 65181445, 169368514, 10853367, 670859233, 2532985, 161814056, 552392806, 555009002, 241595677, 708099808, 517698307, 607663936, 813707841, 999864652, 874480711, 297939463, 524761197, 14653400, 655293068, 829418114, 696892996, 756866238, 632884198, 275640976, 436968294, 909176543, 321541093, 118503604, 385711179, 60694275, 692663369, 732603906, 848837444, 360585900, 282966591, 356117635, 706605430, 137987924, 17632013, 881379500, 733205184, 837552426, 189102165, 288273235, 593490584, 199017395, 365808814, 841338826, 436534186, 925603845, 448098654, 311130140, 410104357, 145371804, 368739866, 494939101, 713582116, 174333373, 184939763, 846351723, 762191864, 260023917, 750390531, 356576356, 501984764, 212098112, 913393707, 108447691, 468229078, 664046440, 239682788, 857239942, 449684641, 343066460, 864044819, 26729404, 450330861, 616186890, 696256023, 603818058, 678451372, 103000522, 62245522, 986813211, 663276948, 948638499, 720914815, 791762142, 613731388, 277877070, 523627115, 600541302, 503884373, 900955636, 137193387, 654947722, 259870537, 390203561, 963845624, 202880841, 761945648, 871897704, 516774410, 798838292, 981495853, 850290169, 178955864, 318398418, 776241989, 211054370, 289271639, 848641857, 568613800, 876354267, 44653433, 672300479, 469186228, 623840781, 845690516, 815054461, 294848310, 324890351, 690968965, 360381367, 726115652, 917859776, 151416661, 970644150, 955848730, 800068228, 354443263, 880631162, 280412882, 317905827, 676651330, 618938725, 972215222, 14390328, 718755540, 320173901, 217276618, 68374163, 28282400, 719808279, 389961864, 795474300, 890691048, 206732238, 687023500, 236095474, 512398992, 234671191, 56965893, 396622391, 554898632, 789998126, 989026781, 934739064, 999832038, 740514002, 563269011, 494074657, 732695522, 597648407, 471456954, 448401404, 262881030, 91675191, 642934117, 321947271, 504949812, 912961132, 794399665, 331303528, 918808035, 535008711, 7587228, 18609891, 456780448, 318048633, 110152877, 912356230, 787868620, 472867382, 693877183, 742811469, 962861992, 546273365, 660241544, 801081023, 692437152, 535247731, 103808460, 338058762, 605629637, 775337911, 921653884, 488225311, 253219099, 352930452, 975787692, 268652965, 950166313, 91480474, 176710196, 502397806, 987992756, 298897589, 133575368, 105223530, 643831167, 256933201, 731403125, 182023127, 316529595, 770870482, 442798077, 540149669, 844219527, 503138249, 120786691, 603643212, 64510649, 533532898, 321765574, 508042822, 217130401, 857310220, 924789997, 355947722, 973247050, 518708241, 726550159, 495760113, 862189768, 934580745, 369848982, 755809518, 424244120, 327477720, 659416301, 729166886, 267287833, 71002540, 122489439, 646192860, 127800598, 308319179, 926640906, 678939701, 833420900, 74008312, 906820409, 894676034, 451971812, 5234458, 449728887, 504540994, 788617865, 792515867, 244128384, 930280077, 901640975, 211718300, 60758147, 222434795, 603977905, 869363044, 954827651, 136193038, 856901867, 604493733, 536137673, 270556835, 650865452, 990112879, 579407712, 285466468, 84276426, 317807844, 44409355, 830410998, 992808214, 52582992, 485694771, 410246126, 250086791, 717356747, 752015676, 43675827, 859728280, 503391041, 592527063, 374801011, 109198477, 765484365, 901494838, 102203092, 549733369, 457513279, 337300608, 531107990, 197371915, 636206344, 947798329, 407563423, 508312460, 311750899, 907336130, 277541288, 373364228, 29586628, 996092865, 213545907, 981998265, 334273761, 421375664, 575775645, 213322676, 677091236, 941371781, 610748748, 883535885, 722606944, 313226247, 498883307, 390620458, 979733316, 93475218, 831318687, 514038045, 565600440, 869749559, 958377771, 998508172, 276231531, 243675311, 625245251, 739065227, 811477956, 653236344, 209665994, 774551807, 789514996, 787277727, 664742260, 472705056, 394730302, 551414688, 249700602, 91623729, 235029717, 715896465, 645074512, 851061532, 464822213, 880358816, 737432343, 807362256, 419983330, 912715826, 422883087, 607729665, 709972920, 852956621, 199129854, 939845782, 729542328, 350908165, 419132844, 873351836, 63681800, 430186801, 945898468, 11843500, 341250834, 161862762, 401399508, 476633053, 351362183, 661478506, 711523692, 664635452, 127521554, 343637772, 691408170, 871516736, 952249244, 119495027, 503000567, 161377767, 436700838, 61432277, 740215913, 760911115, 806826017, 17393464, 456114535, 660043819, 398891011, 2392221, 400135915, 386826890, 689466999, 713688134, 31222215, 430040637, 15397269, 696679662, 344539490, 159593547, 606162511, 675511966, 543908561, 30956064, 521781742, 965036053, 355927463, 507278445, 808832341, 599361838, 962656565, 838691170, 464392432, 575140447, 239206885, 407102078, 773437260, 277867256, 634929674, 938643995, 885547306, 229981804, 643391925, 406272276, 661620704, 12773303, 626677877, 807719602, 694808463, 533772553, 928477316, 447118798, 818351744, 736135306, 278714246, 617771535, 228596556, 733345746, 172041772, 586286108, 582744252, 34820417, 934418430, 915879810, 576201884, 37335739, 948446115, 164486926, 692415739, 440441071, 285978496, 602728283, 835647083, 29387659, 194719988, 125446520, 32358713, 699534017, 773938813, 403940033, 55091871, 85287162, 990138223, 560056961, 829072285, 696810207, 681136031, 170849262, 710908807, 556076114, 439807349, 193397743, 132995189, 120624212, 543881837, 170423549, 715228885, 239794744, 678325706, 264857848, 889393789, 881234867, 590511748, 170437308, 616938436, 125765940, 172907783, 791695899, 926493659, 464197865, 353293499, 475348940, 213925835, 303923102, 722407112, 929943426, 967208753, 616732604, 278345723, 130642812, 890375981, 756153304, 39597564, 797272049, 215716467, 256696200, 19727823, 577630247, 59695919, 469209783, 736165615, 59124112, 643400447, 33082423, 43270446, 311392766, 261784400, 414466271, 479231249, 230225301, 557091894, 744896922, 415333048, 813204167, 460532690, 254638499, 661486630, 439245741, 495042326, 616479721, 101139847, 113508295, 803267316, 758147576, 448782773, 672402615, 94295304, 40111309, 767446526, 222513502, 853201236, 351848265, 794866899, 945061240, 206127461, 640665689, 569823615, 136896704, 586452580, 675143196, 408099955, 642832419, 554533527, 662333450, 45611494, 215551343, 611828506, 822572184, 997932087, 4518992, 232092804, 171948497, 403176431, 917632277, 505829522, 554701015, 613164500, 720420009, 134048619, 962925731, 621568595, 84889183, 974075413, 797681044, 709812217, 394464771, 128711765, 105792990, 482697341, 247939104, 964903511, 421536940, 970787708, 697981718, 382966431, 459490321, 535435982, 505872483, 173931060, 400512519, 412938560, 361236570, 628800345, 646887585, 807438378, 664969845, 618506705, 951677045, 172305409, 158534881, 819353191, 304469732, 215909484, 188785346, 68280068, 354981002, 438376075, 977561801, 91027625, 15391133, 859770543, 100922335, 465518089, 830480080, 425497532, 241398364, 226479409, 355563100, 645492448, 126217610, 744128704, 425046853, 642121650, 30391372, 985991285, 34171875, 228051268, 226775854, 433184018, 234874876, 365547966, 442497745, 804330535, 459366168, 667183087, 946447518, 831972543, 648630464, 605226207, 15936626, 266104203, 928401065, 57732762, 429838323, 935634802, 58913975, 415377031, 694697069, 360531323, 883398389, 403556155, 48384638, 752255980, 373407384, 194285634, 618180992, 693949784, 360141927, 516281978, 241989021, 510209490, 997603785, 515556538, 101223502, 770807684, 544254391, 746058750, 147040516, 941835909, 482109204, 369311636, 948142370, 346984274, 683779079, 934868637, 437714673, 32345929, 824166278, 78121923, 903492092, 126907110, 236319361, 279781275, 395278401, 12740161, 282930929, 857491836, 995383234, 59877594, 218614278, 109587189, 819678733, 862981918, 497110289, 423772751, 743988813, 216017327, 196127784, 135557291, 80102992, 14082792, 500507035, 95839312, 610754726, 997087623, 370214764, 968498327, 898666611, 228795535, 937716255, 875498128, 24088134, 28628960, 723015622, 801550803, 444954866, 383625904, 91217850, 266927696, 750263464, 607437404, 387643906, 211961695, 733636513, 158999402, 24960510, 236388705, 625265172, 726117970, 31982353, 510734366, 463757324, 566973950, 786406013, 477980525, 930438964, 901706294, 860707095, 879321874, 743621624, 934986064, 6452982, 600972706, 75782238, 531359397, 705365214, 711587378, 844320094, 865376022, 151888007, 237539923, 103611569, 257092365, 961751961, 166378975, 104528363, 609420674, 522658952, 673098145, 605683296, 496376898, 408465694, 705058138, 772174868, 471996499, 839421991, 284014352, 616403670, 117997973, 494157714, 553139973, 139431309, 217946473, 645434059, 947849679, 561748685, 282029981, 265538002, 598490839, 596566869, 126613727, 664032027, 930041323, 310723274, 161269590, 442177812, 167310830, 173111709, 510405568, 365030832, 701709530, 8873850, 587301703, 329828177, 645245460, 599126544, 488803472, 251881035, 267734662, 699514202, 728391431, 271423411, 550365434, 592407075, 416588279, 6106566, 949405354, 673861085, 910193563, 626365489, 287940460, 854638037, 78054619, 69933368, 533825186, 916381143, 607264060, 972066406, 846389241, 119249038, 516307467, 887778031, 419888112, 607830426, 628579381, 939973766, 735255996, 807130276, 518563472, 131836026, 917686741, 385734650, 354299322, 909133063, 569951185, 647744383, 216158633, 330516927, 477174019, 700383285, 146450008, 724881768, 329705851, 405092927, 305604775, 795471501, 818192319, 319930039, 289705598, 980834144, 778349753, 782840933, 974746145, 797660294, 294159891, 26796381, 539284343, 246404618, 742725893, 439514298, 942417340, 935921148, 633476721, 209196527, 385306031, 985649863, 895650980, 6863620, 780117140, 879904647, 554641374, 88502107, 505743468, 841918307, 146116068, 586991844, 865706897, 914774851, 885218806, 802554939, 18389092, 794878140, 650489913, 638802213, 598526939, 962278799, 280695272, 562803989, 410543260, 613146685, 923603693, 651922183, 318346254, 650757548, 848484349, 212965983, 490998855, 512256312, 584397912, 341075315, 532594945, 697664204, 116250480, 279601465, 812556712, 257661483, 40205666, 915982557, 38613794, 940014974, 416861751, 757605925, 744666510, 376174996, 979992629, 274024660, 553881654, 804670385, 380618461, 300975532, 225642312, 751578573, 217336348, 727465124, 500438568, 892613006, 872942304, 824004352, 37917579, 738308904, 624667272, 774412247, 838241541, 231217687, 909784506, 382007631, 541671890, 501417076, 712762937, 236614192, 460215540, 388642706, 467650651, 439515344, 905312632, 547398140, 175229729, 164083787, 851253606, 42844686, 392034769, 902539475, 559251213, 408572951, 392344946, 199777530, 94078123, 460407565, 979117543, 696060460, 926045814, 312274761, 778534766, 683742792, 435268549, 561401955, 674892463, 160536561, 413896853, 591974804, 86000933, 665385914, 610098366, 617126639, 313366570, 461330973, 41523775, 607219843, 517747207, 337981062, 997163439, 946153441, 448596743, 942766262, 958744106, 133791885, 153803197, 235110133, 765584384, 833934322, 986949310, 174285622, 225723511, 380568936, 354434129, 390391541, 763655613, 266568166, 666069320, 521499489, 77270692, 250583850, 312694997, 279961443, 551970387, 203125741, 129718452, 348315492, 183080260, 281839220, 575369447, 892396673, 745208405, 522744583, 189890407, 564035126, 538634507, 728929838, 415186718, 843974413, 982386247, 987052200, 598530335, 438719681, 254088391, 105571618, 847792586, 679008098, 692243650, 667425033, 239291041, 42380017, 221493115, 870591389, 475734545, 629753745, 385719192, 850855311, 146640576, 498490786, 358602373, 582424179, 908947287, 567999355, 657613909, 845462147, 203830528, 853543398, 916135926, 927896909, 877858363, 544395664, 68118184, 349074983, 309394988, 836102491, 167050540, 117425494, 959563389, 437047162, 158452583, 997547443, 59369516, 623771574, 33315108, 782684884, 389009987, 707618406, 664343513, 642378231, 275515292, 511569180, 587922370, 194719000, 575658345, 486798891, 386541088, 834323081, 736199022, 992187288, 983662261, 590661068, 137072877, 589232649, 44771480, 122600349, 761354369, 214648451, 504494473, 809581843, 756279604, 364247377, 770446529, 543405904, 36197690, 10746926, 991502904, 705310650, 737396277, 156374889, 369353897, 206176914, 803976760, 648637382, 983737377, 466021404, 997498758, 312392661, 412059754, 634944997, 558488144, 220331065, 16663917, 659662798, 131361018, 623094907, 114281053, 521619555, 152610435, 966473759, 27462334, 712899894, 78728007, 659503235, 762712121, 723445028, 764824883, 471106539, 439908675, 293581246, 130111214, 739706556, 801654729, 657085408, 997731561, 730862507, 340793654, 809387852, 668444232, 954104648, 521891632, 454096704, 560192174, 184401775, 300136081, 194465941, 999382866, 710593045, 529496994, 589042668, 808315447, 99912725, 203248008, 203574866, 774031918, 972786183, 431051661, 547180888, 829497923, 123829015, 13385061, 53304548, 191468087, 469086269, 572064538, 567771303, 829235265, 482360781, 844929154, 384500667, 915863378, 910589232, 772944893, 986653997, 477050993, 430841152, 890051735, 484944879, 671712210, 299506736, 340503275, 852991232, 605824330, 205138596, 311310158, 202085843, 202694224, 853916510, 329214280, 556985976, 606237378, 763985278, 178984458, 756136700, 968604744, 949544714, 685590437, 951272555, 817817570, 195714710, 221208594, 619803964, 531429971, 379502002, 756182903, 294720222, 420712945, 810006584, 669134724, 192068446, 363773798, 331898381, 724573765, 759656758, 685814402, 49956639, 716610814, 434566405, 218598583, 225003675, 224148492, 981862637, 486654405, 592681241, 510037773, 141707123, 248909498, 761951562, 299950984, 316427512, 364835216, 790104135, 15454901, 739811949, 672309511, 9925441, 21137867, 504015020, 966233413, 32498157, 328654124, 653362152, 269658752, 78204251, 714341093, 487356201, 29285221, 81267284, 769112194, 252356259, 850322082, 967678746, 98878329, 340551754, 528563460, 905047227, 871240021, 852095466, 746863747, 840960943, 106838351, 209833779, 660129878, 329400418, 619583635, 918828915, 137344802, 280261916, 181067141, 880467829, 132583675, 177515781, 177903879, 248942253, 291928777, 455926319, 649536428, 266353817, 234345160, 485775408, 269111266, 863225699, 487064245, 209962751, 792606983, 527745092, 162485910, 62781153, 618097462, 282645244, 769179877, 101538608, 602027593, 834811273, 711641692, 397513513, 207139755, 892815717, 927679121, 6310730, 144832737, 145664187, 423653719, 449717461, 314198714, 415157770, 626611522, 953234682, 867177724, 454176279, 879923766, 884485530, 19540780, 946593613, 688122487, 821889154, 705760589, 20976396, 515851448, 519316316, 121361413, 977087503, 671664347, 327051579, 617914432, 548707444, 853631591, 854206912, 437842297, 994634750, 746133515, 182249385, 39165952, 558112973, 770791927, 63878687, 299807914, 760880782, 828186369, 218976010, 558205834, 137368030, 92211752, 415799361, 738015441, 183092287, 908572263, 50645592, 39325517, 588553482, 133396827, 659426826, 81665373, 867285546, 759614466, 460310507, 900900699, 665285494, 508476725, 379267780, 784814464, 337267961, 136768356, 855890505, 22369809, 260938570, 808887591, 834369491, 661717373, 850643942, 657356733, 617527452, 364995861, 483484468, 7904705, 828175387, 885267003, 674198968, 456693761, 56526650, 942545862, 223784335, 78338344, 498834117, 849926572, 621662099, 921082811, 747868162, 290309161, 253197924, 959462170, 936185687, 856821773, 209010577, 970523685, 263701348, 381589662, 178032691, 1088701, 793620432, 648387210, 702453162, 806195245, 249976854, 262047077, 14110629, 156840723, 568791719, 133477763, 286531738, 681461448, 30422814, 161140593, 868790496, 522240312, 355868955, 107604426, 302672409, 173776478, 54028288, 998519616, 801047858, 416402295, 500827539, 787457419, 849903330, 813688780, 756236473, 948074422, 5226952, 536894621, 937728589, 824422918, 655091717, 787591886, 381541707, 547966634, 3837172, 312569655, 440697112, 200102488, 6538186, 848530684, 107191436, 918232081, 566932724, 261474713, 347966910, 911883112, 252885988, 514535175, 104292308, 296807486, 251479486, 414122830, 239658368, 683862440, 146187693, 894457887, 867064483, 9741683, 11604689, 596985169, 30033296, 340698719, 520360990, 441384873, 360638076, 873926482, 816497718, 622291111, 868504535, 735187792, 501696107, 767870749, 951086003, 125257219, 228512018, 110501953, 439308314, 102913476, 443666503, 250888797, 523940583, 96687260, 560204626, 724735541, 826148648, 204007851, 542174534, 384361098, 15863489, 458137295, 454518200, 413930109, 70036134, 87143234, 459653150, 242502135, 235679189, 132606056, 176663868, 224469667, 937037758, 650980817, 887553224, 159163364, 128139103, 814701716, 434680363, 11769828, 538744938, 484830589, 45002843, 229404450, 423606727, 168417424, 233589304, 831218929, 133543932, 19867968, 2923998, 250817978, 348089072, 45177445, 261014359, 271961651, 950706772, 982984501, 815801354, 778748614, 210490024, 36896189, 837668615, 394451856, 601180554, 428996903, 295859504, 791419764, 691800114, 315870807, 118728514, 388586345, 211240770, 771942025, 864677397, 74405962, 254962201, 241941500, 460361167, 879359871, 137814380, 202242196, 286741381, 731103936, 720807142, 386871611, 863233703, 704646216, 870613277, 578920202, 857621830, 397239726, 538938703, 948694484, 712691743, 114490443, 568737163, 287235959, 781448780, 373805395, 379739626, 925328378, 852977412, 574831712, 831427570, 704239091, 734883900, 472327871, 460421949, 630378348, 294788402, 736137074, 569468321, 915590345, 989713209, 759700648, 324826153, 370446228, 548585538, 3483480, 585074191, 290397465, 392679798, 35956585, 329552010, 514510663, 217793144, 403007688, 762018495, 458783533, 376985002, 565158565, 930297642, 177563218, 133456298, 714069419, 895002449, 358339454, 434654277, 117498218, 533910944, 51296917, 777598610, 808386509, 490307965, 996188675, 662765488, 473617430, 353030794, 861960846, 361595033, 612307170, 566510960, 493269925, 843322204, 448703916, 720567881, 782821985, 157641290, 674377988, 412744456, 506759462, 69880212, 223550555, 523045247, 836619286, 322687732, 735159838, 899780520, 242102906, 497873235, 279263998, 747861478, 432940208, 645286845, 305129691, 896641871, 801833820, 156317417, 309342501, 626064826, 4658211, 60203147, 201718825, 898529684, 51929842, 162727778, 493111582, 451815086, 153106620, 984570357, 402796434, 634477666, 393759029, 346694909, 697285963, 612367006, 565894980, 783051789, 603505452, 499055525, 152828487, 754994279, 109366342, 968532721, 279300713, 111785572, 790296007, 52088168, 365259637, 875762315, 217672258, 742907160, 872095688, 996639763, 7278969, 642035053, 2456826, 990473738, 788825239, 719340185, 835531628, 146449995, 7328219, 456312625, 271758112, 748961495, 569652990, 312572441, 95944264, 185734586, 647471618, 900141524, 220506717, 541310388, 638780770, 381875974, 493116061, 315010988, 50698114, 877164747, 366785181, 239083156, 960201210, 352729476, 373583508, 385207052, 155629056, 9562201, 546169022, 404706205, 854620821, 43165603, 600422817, 647896412, 764942737, 472296985, 925577247, 967793409, 46594537, 122154268, 56456646, 961378838, 15572830, 515661368, 230113916, 435352678, 363714652, 515239390, 640142164, 871705520, 626230107, 176519061, 478766313, 33659066, 267646046, 165087496, 882937051, 736054402, 633890050, 800093905, 736947250, 279122783, 898893195, 203073472, 714280634, 73468937, 201578463, 726874711, 676971470, 40789946, 906154187, 505441757, 546403774, 718777162, 1320505, 501622386, 380663328, 381966696, 674607664, 36626952, 158978260, 988402846, 763071482, 48962842, 910064687, 333883331, 884300105, 677024987, 605131675, 380891314, 128125766, 12054545, 455642305, 352140172, 639790342, 589816577, 515093184, 782413156, 737400802, 37860472, 916954425, 26543553, 285646576, 454467177, 264226227, 178222529, 630261915, 977118949, 134034207, 64550944, 901206823, 419728734, 578225190, 22751899, 23231929, 119059507, 246158966, 711471722, 560602619, 881810171, 622284641, 781512642, 461978102, 797558306, 751738941, 169635996, 590152176, 891124479, 105898123, 353593446, 123254435, 856404141, 883037618, 649872557, 929368945, 341905128, 619607741, 986120260, 367042722, 167118840, 351065050, 431525957, 575485580, 148519397, 13970692, 314429121, 484032700, 417467836, 168100353, 761694445, 201353907, 594566865, 202223139, 69498746, 420017557, 127305995, 422014980, 75967405, 641101275, 195361447, 465532064, 309069308, 509868414, 994364225, 854459928, 730662777, 944962349, 16995892, 582822653, 136315691, 177161732, 59909641, 905263521, 228107381, 793788378, 941674456, 932113413, 438223489, 167059745, 693530433, 804694598, 563196, 185895216, 977092607, 377345577, 625346979, 894697558, 172194807, 483144620, 729083381, 209835128, 876290962, 23863170, 430868818, 962415750, 745440670, 176263707, 193372469, 926019522, 16408841, 671460411, 893448944, 200712874, 647217674, 801659167, 454724292, 32927863, 969419201, 721065554, 302249436, 817952175, 263743221, 701427363, 772657812, 722985135, 737068468, 2245480, 200515700, 353025108, 772437538, 578840943, 814817069, 60628124, 450604027, 457588802, 124781510, 590054171, 369327119, 562343553, 735320636, 899843932, 645561853, 444608380, 729346066, 544041530, 319683421, 950172554, 972706280, 294023316, 108855092, 690187058, 298066644, 237991949, 56300104, 557383312, 903650946, 431462802, 996574024, 90517425, 696667221, 322072160, 840324208, 257611327, 139227874, 474343986, 408779906, 680804728, 49398872, 361467534, 427251304, 904378778, 965565784, 891832629, 970380402, 965156085, 1113530, 33313838, 857626916, 232892871, 583991768, 705467003, 778497392, 205078735, 738347240, 186271717, 236503821, 377503963, 236145198, 643050534, 395204324, 449826253, 515166755, 389739614, 519562782, 451414252, 272603606, 80303885, 478140079, 747443672, 835808730, 330516652, 395206263, 550984081, 367793575, 742226480, 176208582, 477967070, 13120154, 645111006, 240288845, 109987970, 491175910, 890937457, 267498712, 36260988, 17309905, 302614077, 845067055, 783262864, 832390674, 581407792, 341566439, 352517925, 873768775, 652457552, 419769791, 598323106, 61569741, 764913497, 853680857, 929269900, 191354, 909447363, 368504218, 938991757, 224900203, 469951729, 461951975, 421537669, 109349759, 60349943, 483888951, 47077559, 7722520, 83097203, 894563038, 758428978, 472456979, 695286616, 777693494, 619957029, 366869462, 478877761, 199556943, 170030324, 391040570, 94320476, 802622525, 896584595, 67520469, 381687491, 643099154, 128471461, 764812447, 158414994, 929178398, 267900532, 800792253, 378495174, 318952110, 504477026, 451240893, 806402794, 351306310, 631630553, 751356496, 99856087, 275389729, 834700934, 480625338, 82619718, 766927405, 490485748, 446327061, 258245237, 791592607, 46112091, 826339847, 434735331, 602098783, 482564644, 321288696, 555577203, 7491220, 260812504, 804784331, 20232355, 842951152, 554668588, 501289019, 699536915, 929167969, 130810584, 871237691, 941004693, 676591906, 694646017, 568475179, 840830264, 406018108, 98701967, 554564370, 883671924, 56310139, 720916321, 1110688, 434432524, 133691844, 919845340, 348079066, 761950056, 78568351, 740586577, 393530941, 375230404, 323136665, 59924376, 223918873, 97958456, 680263865, 586381517, 363212632, 439584683, 695185523, 966894152, 62883090, 775893117, 641408229, 151224402, 459226600, 835871519, 873496096, 700494584, 494397061, 494798699, 576641521, 87420749, 977312338, 162421353, 737643411, 160487964, 623889051, 166968274, 216128735, 367886578, 971935818, 387382014, 393758807, 848005892, 207953193, 28983112, 960686228, 449115289, 211889984, 967104382, 220170298, 780269493, 401019659, 304257593, 376627392, 611365098, 236179488, 12053280, 893575539, 669197512, 3935537, 339730486, 318548558, 112988526, 169911067, 142166619, 860674743, 162091302, 350435268, 485200078, 137049145, 989818538, 263316535, 446339972, 130874336, 16173163, 634776342, 827803356, 156001706, 654670034, 643988070, 143348069, 614388416, 815052221, 331442377, 635938899, 760789911, 372012642, 830081517, 494914957, 931871507, 975343018, 451549961, 763091585, 835894299, 804831414, 570727701, 54681813, 101358947, 586294264, 194671390, 617893459, 447357677, 94177334, 432137109, 502323713, 99017528, 409743315, 906729780, 447590537, 534076984, 436174818, 552402649, 245359583, 159430885, 956757139, 580312761, 823946327, 837249576, 223840045, 287283063, 638910466, 664291040, 243670778, 839832630, 418465351, 923285747, 640442145, 504818079, 190348513, 921460843, 520553154, 654052027, 365900589, 393410801, 228913945, 726665093, 587146114, 964336847, 627314690, 853201636, 188510560, 37345937, 956152993, 348411773, 143165678, 42919137, 934938324, 475319569, 136508229, 348736518, 56573626, 565967934, 819190238, 682413073, 311547202, 760672332, 910452402, 283284224, 315278403, 40906025, 179819815, 650485866, 854109793, 674557107, 621699703, 165497860, 350604555, 856699391, 590311266, 225566870, 582141884, 622874181, 6999760, 704920155, 387909720, 355193720, 978973375, 458854928, 868730343, 883852883, 7430669, 49602235, 621120353, 93795620, 521921076, 679144714, 205659664, 335575452, 394490388, 13825563, 509108318, 616602938, 903849861, 218267704, 871443380, 809507145, 489819553, 646673551, 74402603, 479701728, 507182422, 257562393, 811781733, 271008214, 488202777, 902569656, 334700577, 855890879, 426598339, 147648853, 772321113, 977629670, 949566923, 372985868, 670433213, 288773458, 973212598, 58218581, 722891318, 210596776, 811104649, 332592997, 269215244, 258193978, 933889649, 501183569, 894642494, 986133909, 881742, 936326107, 163157460, 703131493, 329861532, 280054925, 500541264, 950678997, 857377278, 171474115, 364124966, 298678673, 462874729, 209593693, 912373954, 207147124, 1452349, 399043385, 493201652, 87388190, 633245493, 866649042, 179365167, 340112226, 443633770, 423079941, 449657035, 641366853, 414045311, 881359314, 841862877, 600276408, 248753644, 261668826, 94922562, 127277029, 846503306, 589854907, 743977554, 837876056, 949969426, 837293138, 698724276, 313630453, 492460335, 711250028, 862591729, 884996677, 647259037, 293962531, 66404017, 811743084, 750163049, 669482115, 709867632, 18767119, 416200830, 461020653, 872727612, 103144311, 241034325, 52919798, 706988249, 442874395, 979110672, 679088157, 535635678, 99476637, 810830171, 410320073, 456987192, 696243929, 488046922, 826440745, 107970566, 538646709, 451391358, 721846689, 549170359, 16755497, 9646754, 30805451, 258709597, 196127726, 719045149, 184096664, 52250356, 438537343, 290135383, 609324285, 981588878, 858686708, 872446351, 29134495, 874937668, 511528196, 407944612, 413425283, 808625370, 233468219, 819047201, 425871484, 150686465, 198492124, 44235352, 933759601, 343429649, 648469448, 932393450, 99819980, 120868998, 573063082, 940473979, 970302750, 978834148, 549918917, 254198744, 942352357, 602828787, 283548197, 73808806, 323474753, 346355751, 149133817, 699692935, 714068423, 733959129, 266653609, 396658254, 905040827, 782426492, 926766612, 177154441, 593070713, 582783076, 654960885, 725678467, 906039863, 336317748, 122231563, 524395378, 14876020, 1323245, 548826938, 755232643, 587762847, 942319522, 775188427, 832990730, 356957976, 694200476, 647530106, 352171354, 264091448, 631272154, 268833215, 752892445, 442428492, 381618410, 145174212, 635968024, 896696654, 422923450, 302272862, 639409490, 5419632, 118967923, 459447783, 712058886, 535446616, 511662118, 126290697, 93034661, 780448538, 787030109, 727453220, 410172539, 556786426, 867475064, 415301882, 447910413, 669674915, 401582342, 83434794, 842957585, 540851937, 589168692, 717765007, 840396952, 7498736, 175827826, 896789764, 205503830, 156990395, 278198695, 499609095, 217664193, 977202705, 27106147, 104650519, 853521258, 842802888, 400115188, 824639233, 77855956, 749915211, 407944809, 384932229, 506717761, 80140407, 244090664, 825154208, 604914803, 380072545, 636724662, 145968889, 835609034, 605686167, 516611010, 633151584, 315949890, 816148620, 208066031, 973406595, 644203341, 453111953, 98279199, 581994532, 172298172, 194508992, 265726326, 237834834, 499576343, 965836942, 914132854, 29011337, 198137944, 936878097, 705473066, 888109704, 246225853, 560056491, 68685539, 538678873, 838101093, 321090545, 596285736, 937214514, 470747953, 431002558, 206679029, 891248927, 886721999, 59306747, 238849224, 417474742, 165863325, 663648824, 532869357, 132031483, 623043712, 969347202, 697036321, 790920758, 135450937, 910475546, 963757114, 648971723, 666662710, 904810738, 203148983, 153383247, 190363158, 762958622, 613972262, 329675825, 548287301, 424437588, 317454018, 950850211, 352044068, 375233591, 880992840, 10242192, 674823419, 408395784, 675661455, 279878670, 87030322, 583052306, 38201326, 611854129, 979014928, 260727280, 323523218, 495225085, 473357317, 981036006, 523401909, 422281511, 357761924, 874834064, 446394755, 783055505, 732221483, 797576113, 187729732, 584148218, 805521531, 617638428, 174151442, 377228719, 847502719, 614209989, 57867265, 355456132, 531313678, 670451603, 488393079, 786986470, 601171598, 44056874, 370838956, 125392417, 54420223, 940321339, 78399054, 426383548, 565996552, 466545566, 955943100, 395766620, 94910794, 98268530, 118904939, 55250188, 205122008, 962398923, 509793703, 376734982, 356680821, 40353642, 567895790, 518541448, 997457029, 34677008, 954483303, 909657209, 984111569, 17951108, 397073791, 811910938, 234994534, 312132489, 150534723, 245758505, 173828294, 156339558, 201057850, 458191558, 959117628, 670593160, 517163643, 312913843, 376973042, 3676733, 584495385, 504940821, 60124368, 744486185, 747753038, 825988545, 82427004, 791436757, 404306110, 603313578, 770004440, 93764501, 107893997, 983385745, 10575859, 308002420, 655005378, 526545828, 917317572, 505282538, 618297613, 265792243, 75913987, 657564125, 116444190, 301235505, 110425139, 983967452, 283533687, 894345739, 672598109, 716131466, 167634025, 313525863, 147028986, 651325891, 905699185, 315613488, 263166856, 402625378, 432845308, 677144628, 979783131, 223549208, 751262534, 660385368, 568964562, 64915618, 258356241, 57641561, 409399501, 640477379, 402838797, 520673859, 152073807, 209524183, 982221837, 456647597, 444385017, 949602730, 766055114, 822009864, 960847984, 819227375, 41377818, 757966152, 350448697, 256050748, 943152175, 309822315, 582650965, 398390621, 331897230, 647454938, 433892360, 835663232, 461175346, 422336838, 634822578, 227559275, 305527400, 208030402, 567072674, 200058037, 796522202, 976645779, 598907927, 778704516, 195250272, 31136688, 507920739, 568709362, 101650407, 710695871, 855977430, 879364744, 415857392, 77782707, 542278513, 221053626, 395232460, 953710484, 886863146, 799313568, 768562622, 980541115, 454082700, 787203205, 264135614, 582379110, 301733339, 213021848, 265423271, 937819263, 307531255, 108290276, 957352946, 15835600, 657708410, 923115946, 40768815, 932550245, 754406830, 254597857, 995653373, 782064929, 106834181, 390819122, 828934154, 753989680, 935775448, 479434745, 580694192, 481225841, 262114193, 275436118, 202046806, 439080246, 72117728, 568474230, 373666282, 303425749, 29137840, 842358567, 6961476, 157144559, 203604004, 400388469, 972168184, 778262242, 653827245, 958637715, 453206335, 540592587, 958722935, 262975969, 528200183, 821145521, 70008705, 182376982, 30595275, 651580173, 170252101, 702169378, 792295064, 84691347, 759824493, 838989029, 253307487, 366581219, 88195962, 954955619, 618698104, 417860338, 531532043, 188223516, 62347608, 450974978, 924326226, 25944580, 967251747, 888170942, 90693152, 795780204, 792671717, 564688589, 638598479, 846470899, 140443965, 185821326, 218243267, 856757297, 561476712, 361368913, 320434059, 720590593, 466554023, 55381574, 460253798, 344717838, 32956711, 32626809, 519074369, 183579521, 116047525, 344278038, 292204576, 136288003, 294452105, 723797671, 503505919, 842273838, 181664988, 85536392, 640116277, 679066682, 605973478, 829047568, 697923207, 133351497, 879177053, 587025764, 581534264, 163716166, 906502819, 986233365, 92922224, 81028580, 994421684, 936833721, 86565462, 443878644, 582661385, 106944575, 271337024, 677312870, 182493916, 15866692, 463864433, 801628664, 718683708, 426473674, 357932312, 813931591, 579755664, 713737116, 824446930, 58706625, 525680877, 910445152, 622447541, 323735460, 168891464, 36814397, 232661528, 737504571, 4634259, 894846671, 517595322, 310907399, 536446703, 550757347, 430055471, 273936303, 409139312, 455750697, 134501015, 125271932, 326755822, 443352569, 376780156, 427983481, 715063412, 827637999, 684639849, 855399060, 595505888, 195193414, 747818289, 571668996, 91866858, 648521636, 105137854, 462003688, 767578010, 49365157, 177012579, 235260819, 387201065, 244796392, 232307182, 546924809, 149559752, 926058489, 627072610, 588461787, 518219883, 448873667, 834032756, 366405865, 627715375, 503113388, 203827189, 942129848, 987273034, 667530420, 657495279, 154698347, 455694302, 808815834, 614400215, 184379051, 913070741, 898079199, 3857333, 336406739, 160846815, 474021635, 627044194, 704879387, 101642976, 709877406, 796738236, 43219303, 99407396, 835846865, 167667640, 716403238, 303249162, 427193953, 205692093, 211008707, 119323841, 582879994, 204117003, 716946831, 86687981, 947121790, 114693942, 556193858, 835205326, 979791145, 165234077, 758810454, 368237150, 721343514, 958523621, 828431677, 603994311, 487923998, 841691517, 328671316, 454434439, 594053742, 659938428, 304735801, 484948867, 183213041, 728110843, 652095971, 578638609, 322960406, 195432047, 995298355, 641686344, 32809286, 537744581, 980354260, 116042778, 345253770, 50533794, 28777538, 260377784, 105655242, 809682322, 789600751, 892456547, 775598840, 413047579, 732451604, 760613028, 235689221, 968651072, 724236808, 817600920, 780149089, 352304715, 567563119, 227492815, 738388044, 51625537, 329387788, 270652635, 877758950, 780976879, 766717567, 364496710, 862504668, 611572346, 778771345, 834598578, 353505782, 251679522, 928958643, 389936633, 609857669, 883240496, 757801711, 245029751, 356549090, 464301710, 170059868, 743033849, 780011224, 220869253, 421914923, 268443715, 567474947, 947138772, 40791097, 139329121, 817672465, 78703717, 396438314, 725550970, 778991958, 494731097, 257938089, 709331015, 512944356, 464719380, 232690199, 165936520, 458205456, 394138309, 834834697, 82745711, 141278242, 877216501, 797860310, 282880393, 886273495, 413267218, 514119578, 238925224, 646462133, 75188065, 697116342, 579885403, 233940756, 201761125, 315448169, 921545551, 590889968, 608598965, 716592354, 298201153, 384299460, 477693766, 30314450, 714064800, 193354619, 696137373, 914985960, 365522878, 831886505, 562030337, 94445073, 703535374, 940714876, 588250171, 197405707, 432855584, 246925853, 420391270, 414314094, 266929328, 135256401, 383292463, 840231524, 376882264, 633214, 22278984, 907536412, 709730988, 660979948, 482864982, 436836361, 877751622, 569098076, 559604578, 269762000, 511333517, 40115101, 947642737, 889105208, 663479377, 179912654, 820048971, 34437348, 333487341, 345457601, 868132567, 203102779, 320202440, 499892055, 899728936, 183723968, 934705952, 943054829, 243237205, 206879320, 944667846, 860795791, 497244536, 863099310, 40717474, 115635529, 344766787, 404606909, 401014512, 446269976, 491526181, 57895853, 814709451, 837913237, 748636041, 527936675, 718713365, 340228036, 612562353, 787937774, 633094308, 159168816, 5355612, 402708851, 679594181, 780910518, 505720002, 508233968, 111832650, 597693966, 768857503, 839229980, 552440107, 853306172, 808391652, 749329208, 82644199, 572091281, 776109742, 846539989, 209663481, 191678032, 277179621, 846576817, 778702730, 746626244, 593398957, 14781691, 65359852, 115092628, 549674183, 231802611, 422527792, 209674472, 415928927, 646698828, 979562057, 274359287, 324501194, 344521046, 760320339, 627787113, 632525354, 777175714, 34112392, 978836423, 410431535, 297921906, 606476480, 678292891, 847535223, 194763070, 320832882, 435828026, 135959211, 379167767, 583548, 335924716, 649272762, 501472265, 522588167, 17272402, 261059840, 349109480, 441459553, 492518300, 526481363, 263272551, 205825774, 876989217, 325499873, 551735627, 327366809, 252915326, 718934723, 918344174, 541677983, 385147060, 873493290, 570421807, 295437105, 825785781, 757272210, 381853255, 742351943, 721686516, 903125222, 300251418, 271848197, 645930221, 477511215, 288925028, 222669377, 106164719, 690105050, 753983278, 840587755, 421533113, 123843326, 297605803, 388836183, 680230376, 237288715, 875571313, 638334390, 474699777, 367647743, 752453304, 705191583, 244390231, 562619279, 591741917, 694756227, 265636646, 548200306, 211293429, 898798937, 409238983, 514266225, 619917952, 810530298, 394881374, 323505400, 876224402, 35984576, 164991071, 810594534, 228679803, 503623030, 811410950, 927655419, 473685669, 884196656, 349494960, 940906662, 563311310, 684223282, 439590970, 568555748, 163576037, 392930992, 482348288, 230401344, 530549575, 396233542, 536071175, 291603432, 401556001, 940946380, 931870535, 863860112, 533271212, 143120322, 136650057, 450400900, 715885173, 991249974, 560507468, 197748050, 923099605, 159348113, 405503556, 575651102, 395256846, 102848239, 245553740, 246715592, 713421380, 155766988, 956675297, 680933177, 449834239, 732271245, 75329594, 556352096, 796570806, 444465159, 536840054, 567897318, 940858490, 285526594, 50130312, 224145430, 420458249, 924365054, 226779321, 314447845, 533442728, 960711149, 752054446, 902124123, 277010152, 896873832, 31363719, 154088439, 569991417, 590561625, 433834333, 557282882, 74062141, 889090714, 670874786, 9662789, 695875595, 501097305, 351098567, 174443162, 37793376, 249631322, 318845655, 600701387, 824319717, 814336165, 995376955, 850680257, 367246741, 255719700, 389310445, 791155647, 23048400, 403765610, 803380118, 954318290, 929149377, 748310323, 628825534, 210547523, 158172122, 312206425, 615799222, 298635575, 889223177, 390135807, 404386597, 240016674, 137039453, 429251185, 978434715, 742154632, 875873077, 500162453, 84006393, 954691097, 54799275, 171352828, 858240910, 894628837, 298256936, 407551499, 935999761, 11788166, 26202461, 950606858, 716412314, 738005744, 833566093, 743679738, 405777020, 172772084, 452399284, 751876008, 803327896, 516209192, 703756712, 399008259, 756192749, 752382976, 934765351, 336372337, 241502929, 831857770, 43567931, 548288709, 435054433, 482432086, 328242196, 350787738, 403882126, 815821596, 873011178, 490077305, 897493023, 917708964, 653154076, 173199058, 919603414, 803604258, 785234969, 690316422, 698356138, 38421013, 383355595, 999472037, 791216844, 925675065, 638216071, 976092708, 934102837, 835652307, 822046641, 604165037, 616662429, 450510998, 699557882, 809879020, 857568943, 812212039, 947026007, 163326737, 34442694, 75914880, 374829818, 963292983, 425314558, 914006872, 539824917, 6941044, 257493377, 648546831, 780923174, 352406037, 805589907, 22924593, 855251623, 529958540, 77745419, 100096866, 345457034, 779795715, 838281866, 874358283, 473727102, 101655397, 963716119, 790935639, 412534309, 124004488, 405631485, 237328918, 893368551, 748990765, 239257736, 50192524, 697681261, 697405600, 779215278, 31073372, 480951699, 524786104, 522212147, 214810410, 748537868, 972246178, 940161243, 945971140, 314454008, 593609019, 516186362, 327528353, 358683998, 548647893, 317295165, 494426070, 383291807, 436165768, 453792523, 408573211, 293228393, 134948210, 40187200, 905678638, 960420340, 409810392, 518786690, 19964223, 104235721, 188555162, 8307018, 121968029, 682479458, 390671225, 988016694, 698409086, 467584275, 327357446, 440736151, 492254079, 293246370, 97311959, 76375403, 167877756, 708379721, 774247343, 13212849, 199050752, 546189325, 495525178, 9373389, 375568971, 854589869, 540554525, 667651909, 630826899, 131407680, 948771359, 435075070, 547292623, 157324650, 9796653, 977482183, 100890370, 736782948, 837746215, 483455847, 78805828, 420542056, 18601884, 871704204, 123189660, 620268218, 897391820, 721322963, 992166260, 796189681, 520160459, 251713932, 179505135, 257056812, 326264325, 753872745, 79094034, 356631544, 566988958, 375898240, 139991147, 449101339, 689135660, 307283515, 876617619, 125964059, 914556277, 941987678, 718058774, 808989032, 481219931, 771131227, 341150170, 11410917, 625224968, 827232941, 70144210, 515343477, 210114420, 736344577, 929612625, 310063809, 676917935, 620231672, 885919083, 927872267, 222610903, 111755254, 342106788, 627886572, 365112909, 342849190, 318467500, 679065787, 258144575, 724650530, 428466133, 465133553, 912377747, 894397292, 664341241, 425980276, 404198568, 696989236, 944130951, 663577083, 975519998, 687682554, 299398359, 180936291, 921161501, 629282056, 176078605, 534893175, 759295853, 754543047, 301183442, 946174171, 520276857, 23389244, 897723882, 720374853, 161320530, 880970123, 452575369, 852857090, 879958958, 760542710, 473880124, 368484723, 539107863, 284649536, 957841070, 447257744, 140119801, 364516766, 267907848, 941276927, 403155555, 153504, 655126766, 924420580, 514646126, 722007475, 545699703, 249911233, 915317557, 427329898, 879875617, 506060050, 185167826, 260938996, 659597686, 534901169, 339353685, 500134825, 351091543, 851250136, 886542414, 155140120, 274672723, 161370411, 341022017, 74931952, 198841700, 660032397, 162995498, 591644539, 313086685, 552261653, 330164305, 774950971, 46427313, 613454899, 877458821, 153695737, 132855790, 290901874, 809646940, 538214568, 848959076, 871076313, 528282972, 853312842, 572630569, 333743248, 946222176, 81133325, 82128087, 730660898, 698575178, 538256593, 419020455, 96664119, 332735061, 561166021, 158054378, 949688345, 38980290, 346113130, 905141140, 168981424, 286309790, 942420506, 866618891, 476129434, 980176382, 228685737, 779098118, 935674467, 267554645, 509760821, 119951373, 717769957, 756504283, 763083470, 404046766, 60740451, 483313005, 504054512, 790985791, 803306910, 468982300, 701137972, 263191449, 349521983, 138484440, 934127808, 301507638, 561620580, 257567309, 857577514, 495978673, 800721552, 420888977, 657592090, 888021208, 374641119, 220916907, 198606989, 445118087, 728033998, 358334739, 751257131, 538152087, 951556815, 381471773, 473937774, 578227686, 176398857, 538237438, 928079233, 480213735, 199232808, 790187293, 614841600, 947753130, 654949448, 274906128, 492541612, 911589206, 179583492, 532906121, 247507180, 160964823, 248744290, 789313734, 544821722, 463136997, 811815547, 887521415, 514086555, 244077294, 421019035, 749524034, 776729695, 329681922, 419709048, 560928976, 867201777, 297701247, 690321396, 787644081, 980600588, 340497310, 632632750, 441424046, 341904642, 314579068, 849673462, 942717819, 483626322, 246632389, 298304688, 413754922, 923386814, 723745391, 98413070, 749416485, 706417498, 749036298, 619566155, 560178896, 130825527, 751067884, 247133065, 828984915, 177210156, 460891273, 587747685, 19404986, 794556494, 232179100, 920342702, 80898739, 192538506, 582722855, 576764292, 183346651, 107952095, 605965361, 271668018, 293927001, 978868615, 393506676, 438293161, 362718538, 72590096, 458709466, 995449419, 246826768, 391779960, 127233500, 219103441, 559998848, 554183412, 778842363, 996821687, 955685823, 434064136, 357663576, 322074495, 263192248, 633535665, 876633667, 567991481, 781727667, 386570190, 743405160, 326760873, 550356568, 907082295, 723044717, 567419767, 663956887, 938509584, 121305207, 403645491, 332197842, 801237374, 8203421, 739177029, 573407431, 355791997, 610047639, 416544384, 17570177, 496718990, 319920684, 661766851, 432384878, 329890145, 642105625, 946515908, 576426828, 562573605, 167807705, 101005034, 465914932, 289128264, 774806215, 325025763, 296441856, 306357057, 731959644, 185014212, 157688984, 676343740, 9556524, 519337404, 984052673, 931902450, 826588324, 18556670, 492625793, 273635157, 601232587, 423999406, 688489323, 442952339, 373365508, 595453943, 701780090, 845320821, 576668229, 583941931, 816035867, 635334796, 991626690, 507486158, 935725973, 978577142, 416833857, 233345113, 444582947, 203205574, 65104018, 177026926, 699601821, 315452682, 259101362, 495401780, 712335485, 781933449, 34881249, 558216926, 258131577, 770616287, 460367075, 560037626, 825617531, 660297529, 122474979, 497147994, 7378698, 510712732, 344168797, 841608055, 705326698, 948514970, 847024650, 432370685, 659139739, 654775019, 875575996, 530093195, 540779649, 747251255, 326427237, 318291785, 352503009, 277740416, 695245306, 41382533, 380845655, 85503082, 66158635, 749420604, 271030913, 11456229, 134802964, 455332727, 418056542, 986027737, 600474300, 259546735, 674416753, 306696158, 727810117, 233985193, 170245932, 652256183, 922889563, 434078100, 833187632, 807822589, 876737778, 123605858, 363425323, 997860771, 393887001, 301494157, 341621148, 314916684, 247126291, 398776592, 815373081, 178243799, 935591070, 905894386, 526733141, 279004042, 429736082, 640649323, 91463986, 183830835, 896288518, 657811433, 361463524, 201511736, 719537555, 303606973, 960546572, 204842593, 876877228, 109261848, 886339840, 879050847, 157539402, 35606926, 630766887, 667431493, 963237800, 206823021, 271656408, 819103606, 95004578, 172532651, 509979003, 199318973, 884910415, 217057996, 822120881, 334041250, 638859761, 794672075, 571265213, 790945747, 884952765, 3024790, 958377816, 600300065, 166919497, 109674000, 498316233, 722815280, 792734863, 622943730, 215921403, 946991134, 287961169, 530744576, 942626670, 803440847, 845525597, 138443373, 138919760, 411464416, 39815657, 18066354, 628106273, 583651112, 946440258, 299389441, 701802066, 860168063, 501848067, 824214001, 565176100, 234043939, 120765848, 622630584, 470041130, 87864194, 399263159, 885368224, 112864352, 258859007, 255358815, 608361364, 608489464, 771966231, 503006032, 762266905, 364285177, 145110799, 532982388, 904832516, 766427972, 145585392, 53664383, 123425663, 666258345, 50887057, 100806812, 264637336, 23181768, 180661966, 97532924, 966042769, 348157806, 436285368, 130796102, 19237631, 421783372, 742590862, 655162830, 575458681, 843592387, 991467458, 542819711, 811301989, 816356701, 552173299, 920235256, 526153171, 172260420, 67306225, 389109198, 802927070, 39366231, 361649028, 432967733, 344372545, 218152549, 999655649, 218135416, 416475227, 795432612, 202372387, 222954046, 60160522, 648453606, 494506591, 579730011, 298672195, 352523331, 280201880, 314831258, 228326777, 79008568, 49530895, 946145249, 389896927, 835078780, 210962007, 45042946, 242770390, 119900247, 456725021, 175967914, 659737471, 28613904, 540586607, 170395442, 624487637, 114730580, 169645404, 918450510, 4378089, 210734371, 361029176, 714888217, 138801780, 607000060, 768073179, 960753982, 776281604, 802454332, 217235306, 278015978, 443071600, 774928920, 221592097, 455144197, 299474166, 689510999, 96244911, 461269288, 925303883, 436369718, 899501236, 576367837, 639135451, 802497739, 672499438, 255475860, 117055364, 815084669, 723720015, 853766322, 576431941, 415311749, 414085943, 19472072, 706193086, 655003084, 160415575, 45459022, 791983721, 436553492, 838139636, 534414412, 711815807, 819605409, 109184452, 135459271, 318627237, 559492295, 201646765, 377502383, 781037387, 887959404, 868526576, 170015053, 692157411, 118857295, 360022799, 46835710, 396809324, 625665672, 453178807, 638290086, 51587327, 357257480, 476878327, 503563619, 779915420, 50505563, 650143311, 612012147, 958286424, 958812152, 402120230, 13563305, 856959605, 985129284, 396403282, 900439659, 386798786, 8035226, 165076401, 887957049, 678709025, 496200834, 179759126, 823698296, 372016644, 600210188, 770386817, 987263576, 201880677, 821608952, 53575385, 171517939, 415284375, 366672984, 861881497, 243338569, 609641697, 747780363, 81724049, 105860199, 622434241, 355334374, 147978551, 229616306, 728977542, 704877176, 941926190, 754302480, 82590834, 657052026, 472289553, 985599678, 341868967, 30498857, 736760217, 534803625, 656118839, 991341076, 302908016, 921696519, 375241338, 446399356, 398170726, 805839809, 354079777, 622837077, 831700269, 86204273, 423776515, 665526958, 380400990, 886704853, 823290033, 674845918, 486161839, 232422323, 930929592, 930483426, 975399688, 480534474, 473127645, 281744688, 12054349, 675101733, 469120978, 880861294, 101827203, 693657266, 201257548, 94186177, 592392327, 51314329, 233843612, 789238286, 562871666, 374637134, 869461613, 826947767, 867392190, 201358881, 194082224, 353090031, 219570486, 44536236, 87124147, 791536193, 243915756, 412174142, 615204616, 850498614, 682561150, 262576946, 287081489, 847272850, 123771243, 11736334, 397142074, 587427196, 189386100, 628666300, 463152336, 986028681, 589334737, 451181896, 867552055, 241769607, 885582264, 199139920, 460362845, 711702788, 107410379, 257052751, 202593887, 405638716, 800839028, 3682172, 1014714, 170800533, 162200543, 140645215, 607504952, 594246986, 204299936, 895145499, 887798284, 258978798, 398400719, 36020430, 113254193, 599210692, 943189560, 502303201, 18705430, 471067692, 763661537, 790608562, 898197529, 580941665, 85406976, 143295873, 605886239, 222775374, 513873334, 220353779, 368216711, 110567808, 965551374, 154012878, 766468524, 323349293, 984371359, 573437718, 299749527, 646519451, 902506645, 666969953, 978026711, 790574271, 874132864, 638729964, 283735405, 455162749, 541935893, 433514923, 17712278, 663552514, 763500264, 718185227, 891970777, 980592542, 34216800, 102374809, 861070953, 637205013, 277550161, 585296426, 937852048, 805801469, 669814089, 696905187, 862492867, 697880178, 112463146, 430606812, 381409935, 801989647, 45363297, 652295236, 562779606, 303954025, 69496873, 642309726, 477953446, 321382423, 977827444, 91304808, 834539723, 401376431, 967158718, 692538173, 261693291, 236486440, 95746542, 746337361, 890965137, 991600040, 985853811, 860733349, 247121033, 832194219, 537933477, 859063618, 92118509, 214452561, 442911238, 386378845, 285696038, 290027141, 985547929, 173658300, 388013433, 941666013, 161816888, 959890903, 917890140, 251984684, 564870185, 588049865, 708489483, 242835406, 621246973, 653899866, 575564035, 530501087, 912796146, 368678845, 841780733, 705459409, 973348501, 998979326, 166188574, 410076484, 474466800, 708074135, 946319416, 818473992, 917626738, 509662230, 294787067, 576050850, 828854852, 306181122, 745051694, 977231065, 385400916, 595802947, 78963859, 583748962, 449970442, 893489873, 314884979, 970417031, 720462971, 569569051, 722022635, 149804297, 185668700, 674763512, 433182446, 442547834, 371825125, 904467566, 348485019, 122991256, 859544672, 909675127, 458552524, 93387740, 104786381, 23094017, 746807450, 619009128, 995216506, 406182914, 991606153, 677986133, 32195225, 613623851, 373881407, 602935677, 413658586, 959638571, 21051533, 695167868, 40380240, 313615428, 47036659, 633036445, 746069529, 248313062, 19401129, 929587759, 641696459, 288834351, 756196819, 164475749, 284027009, 957640677, 332575567, 578639505, 383881378, 293703405, 433505502, 77482275, 243019629, 691624765, 605768533, 548848729, 126940869, 514782681, 897977678, 909015813, 52909812, 270519889, 920194018, 873439764, 163980878, 555019013, 733503794, 447040838, 865020358, 214829339, 909533903, 797241448, 971537976, 74396207, 458059457, 583280389, 481099012, 200500452, 751124406, 776044450, 34901414, 75810511, 970339246, 124953790, 334677427, 24974265, 610300380, 406487508, 663246670, 969222758, 955440310, 578688324, 709299784, 749323572, 974695675, 175037451, 777868716, 184676652, 285506604, 620740453, 407049388, 880733951, 887684378, 387893251, 261094242, 782021, 488469894, 457742545, 259216965, 676004423, 840314435, 73684110, 124721649, 209328029, 932601153, 854849989, 481180792, 889577176, 803779364, 950034425, 835710590, 780276169, 156606452, 90707638, 659308705, 559638489, 536583096, 671234800, 459109518, 20931593, 757274132, 963944231, 458683468, 993524964, 823500034, 127676639, 113183650, 674038665, 646123967, 626303531, 749836449, 353156411, 825014645, 448660785, 537366260, 41079368, 527182735, 659130936, 190145869, 838159167, 239461928, 110817375, 265736800, 157097638, 950031280, 64796417, 55753429, 935094779, 682589037, 156297091, 429405631, 260426205, 510800848, 823310430, 750864, 500706356, 354385470, 415700358, 716225657, 877064874, 216467423, 652373900, 994693976, 219753121, 357755193, 824040908, 871425938, 828940482, 78526986, 755390809, 601932834, 245473064, 699717034, 30208023, 452993435, 657660649, 72158303, 476742717, 269697017, 796984410, 395156638, 524864587, 294137636, 956748782, 943424478, 608119605, 593718099, 857524439, 198340434, 314383165, 302267434, 67277149, 903591147, 754206983, 586411796, 309890129, 111376705, 723105421, 989495857, 752706921, 363482337, 578635688, 741281238, 231808047, 292710113, 545174430, 821084805, 185172140, 891298846, 388562628, 337310442, 426383189, 592556174, 333416615, 444145872, 841073339, 233377999, 927175804, 757423087, 338809581, 622934854, 437899734, 214159733, 921726572, 765654003, 669939871, 871418698, 148248574, 806606215, 993479530, 35580537, 178512556, 759037733, 111198395, 206127279, 983867288, 722670177, 625320320, 779722988, 738030369, 109196224, 770049040, 12913194, 786885218, 798571274, 811244410, 708937767, 475817511, 540666495, 938449349, 593968383, 325538716, 269904583, 892755025, 832562274, 471873116, 313681991, 687162989, 338629270, 915219112, 617531272, 562046359, 787229903, 682465432, 346490139, 257530407, 644248737, 491955454, 948205132, 847225936, 431596365, 748948505, 489635240, 729778410, 853246827, 983788351, 155174866, 82080743, 476621528, 84533194, 364145911, 637790000, 716745279, 855978770, 289354553, 555593849, 721758439, 927967438, 964484160, 722207739, 934068348, 862711916, 663211697, 909742071, 92343991, 126918300, 489865720, 665849894, 239203030, 4958733, 381323141, 328443274, 72414384, 533378555, 259552388, 18912458, 748079311, 138449945, 608883043, 945759851, 868160641, 211628176, 105818997, 878580549, 351365795, 951360441, 815600354, 28225434, 733209026, 180218532, 369251687, 113854500, 577703300, 167730536, 270968901, 402791630, 786558434, 845965046, 430149079, 576053526, 762639230, 582184386, 981838435, 470249444, 287853691, 563420259, 832533185, 361781365, 371495177, 140172001, 457916459, 224951921, 206837061, 944738690, 20509503, 221755058, 871072693, 564271300, 847355120, 852819135, 83506499, 584000474, 847480758, 993471758, 571384321, 408911568, 88373669, 605833205, 348474862, 335900114, 145175676, 519357443, 653271973, 48436353, 248775873, 962341567, 556459166, 424292267, 972818530, 233483889, 398658513, 125549452, 971738279, 131768914, 281562567, 243292725, 215883436, 27325764, 91416147, 851485269, 685187739, 486457954, 761064724, 811596551, 698807124, 606879324, 591109358, 696140927, 831440358, 214597891, 38040227, 868096227, 876974532, 375122487, 782853946, 755463656, 747014353, 438833786, 775582417, 624617353, 786086607, 700533828, 682543529, 302017086, 807694990, 292632320, 862028010, 568506272, 571130767, 673559014, 23733999, 953315621, 948418222, 515931764, 422832832, 677582736, 900583994, 137999839, 126911983, 789973987, 934585882, 651669043, 853917998, 694905789, 739442433, 976860235, 839600734, 466230652, 615370042, 397612758, 569302848, 388970747, 350131379, 546396309, 4007942, 892740644, 678028659, 987809655, 613991202, 903233873, 23646218, 634877019, 463346646, 924152808, 237354639, 831842250, 985396751, 515846989, 156420926, 419569684, 359327576, 165881265, 845748667, 723098562, 624719571, 350959678, 730828746, 898175699, 734040065, 360942088, 725917063, 141302966, 145282040, 77292959, 661015669, 741542569, 495310834, 598832087, 431426595, 395928898, 882626879, 198123501, 343490236, 612059453, 693696025, 162567313, 291673183, 78635068, 292480937, 394374468, 993447154, 33840873, 913280057, 218925250, 147107709, 616839620, 710938333, 695467273, 234705694, 498415237, 874277992, 867744545, 329547606, 940827198, 412506142, 288382898, 268755190, 26711582, 842172120, 579124197, 160131667, 979046982, 18287168, 666398729, 804208461, 746975598, 606040290, 952178782, 8587901, 764113459, 774005550, 634569644, 860577461, 559835359, 439282915, 741186707, 535062342, 668926418, 961161187, 235215975, 842533161, 537424721, 85245207, 617624865, 335985651, 437799979, 184339433, 522180377, 580336554, 932662733, 592531166, 695497304, 742064573, 73934528, 412385812, 465445496, 641836274, 265530838, 694971464, 761174439, 595082399, 802668591, 22550552, 729279076, 512280301, 852181241, 171603064, 732762002, 376321970, 747867778, 59368657, 221675496, 509413386, 145453962, 171936864, 313834220, 430198765, 480439096, 624922678, 786784795, 363016596, 990082856, 401238299, 809543114, 494279622, 357895319, 655960424, 798213890, 340942888, 961721101, 232759471, 588796194, 754489722, 234478276, 539192391, 224908253, 192218559, 307907537, 415239526, 417726456, 374288955, 658106878, 212402772, 108815637, 588218266, 101543483, 685607815, 513205072, 864719878, 619642676, 3709773, 525814610, 834276737, 99513650, 887254396, 25076088, 510920401, 982020946, 103546672, 727643966, 997764405, 127104453, 171063938, 671267817, 35232131, 856123855, 952413483, 512038609, 693468448, 331968150, 175582103, 163053375, 727281843, 968609698, 52482330, 76936988, 624079488, 332338705, 171956567, 30866891, 79039999, 797992810, 324325213, 468416030, 640961333, 773790965, 589778246, 21843061, 621861700, 377717052, 981095148, 349947961, 489162680, 276388676, 875201697, 32658841, 542535741, 516903802, 686382508, 127458700, 173854577, 149239450, 982911269, 547818564, 17953713, 903681292, 383993180, 846682531, 929042254, 555806559, 93927869, 535632406, 210270193, 532961205, 306635030, 575369822, 913743090, 541271431, 407414036, 464418527, 728187816, 576677969, 213595454, 543466489, 732243110, 996031721, 667059587, 491572404, 127750562, 659212438, 965130933, 755140971, 982393772, 733066723, 867886451, 548492071, 146556578, 114912866, 635702731, 383251364, 383441521, 80976466, 865709155, 280819678, 97857390, 765841376, 235723675, 153838197, 168709700, 670793029, 120808035, 218989676, 113443367, 169617114, 618128065, 540850493, 744000431, 362526752, 574080365, 208560188, 809047884, 627370752, 135170065, 118395811, 257397719, 100996056, 15086025, 401463620, 617335223, 940408606, 629309061, 173444748, 856745532, 298146091, 661145959, 170626147, 94251040, 687393728, 885249742, 853321208, 160282168, 305390792, 776556527, 575188288, 595653624, 102659162, 465108589, 440595662, 671386797, 438170136, 762680995, 841807207, 653354576, 247713849, 584235853, 87943639, 703031980, 20869636, 897335030, 620027239, 418532671, 408617019, 512946979, 592613082, 531706573, 572782378, 583674689, 150079799, 631470192, 821141179, 163063003, 277842420, 463864108, 150539807, 321832359, 439645173, 335423688, 820163504, 901020969, 617596326, 833433969, 369856165, 322092941, 597873405, 376810913, 502551272, 977046235, 303859071, 85197479, 806080399, 625870430, 462990396, 546577272, 645469837, 692188655, 685858038, 582747795, 732185379, 3801359, 212517933, 804709796, 483958169, 146221135, 951924648, 181291892, 31036114, 30401226, 103094694, 623028370, 242501747, 542557242, 885820557, 552343741, 205920505, 740337803, 258404360, 236981305, 369421605, 944417686, 430801192, 215275628, 881795420, 998632200, 127204122, 258909690, 153242677, 580478230, 913743459, 920923123, 593032254, 145046361, 37159180, 927890773, 565728913, 355863064, 150684221, 190568022, 877663193, 630692194, 654065199, 282742346, 509096608, 288368537, 512948400, 826711849, 530728028, 941522648, 613605013, 618262414, 192820065, 647627478, 571851614, 250394249, 913834991, 842255081, 69878685, 313045297, 270232296, 408593611, 56360513, 172442643, 513196690, 873365445, 587663769, 323430906, 310784525, 677618039, 78602492, 92507201, 161868959, 239781892, 481423853, 994617109, 576284479, 45817510, 102040229, 862734783, 667039871, 361239577, 919046364, 452403423, 384393529, 736564464, 197146858, 902312747, 571716980, 342251292, 672636716, 536778184, 479017865, 847280679, 50018166, 120466692, 11587137, 915703525, 303456303, 218965716, 53963857, 328006596, 683160878, 652821072, 554825337, 158575839, 406788338, 802349916, 123697424, 17747855, 336773383, 416354659, 788761936, 522175707, 621665668, 491086893, 44448658, 635085490, 476347712, 174814325, 342843383, 25860737, 564122375, 738974843, 915788288, 117783587, 494050100, 365483712, 303435330, 879836206, 769924202, 914752081, 775788395, 412035154, 444773610, 556770938, 404580979, 606516534, 570821604, 242652324, 711966784, 787019422, 918112023, 782678835, 536752745, 640805485, 964731733, 64048099, 622376363, 191406061, 626956464, 957923620, 515800269, 22911434, 850468369, 155195290, 76501271, 327286328, 95938979, 265247022, 829789963, 758219691, 395296640, 294569111, 664144500, 114474099, 113099423, 872208764, 407000952, 98119729, 261837715, 403593259, 303078739, 666583928, 245372629, 461869167, 885929278, 506877193, 661438536, 221526380, 736223133, 510721074, 201802039, 923615347, 100771786, 82547595, 548876296, 759987711, 803228942, 807405155, 195572945, 905390668, 178012857, 694079227, 399541500, 255766499, 170774060, 880551171, 52928136, 72993077, 501538054, 315557579, 204285637, 866170905, 414630826, 180634929, 890181422, 654852111, 732756038, 22376771, 551864162, 740980633, 949255682, 749339502, 411128618, 566236908, 64540175, 612114175, 442384709, 537791397, 970336646, 907325136, 602155658, 296160967, 204685600, 409145687, 400866024, 61762644, 669242758, 751193755, 201474673, 479528806, 482817405, 587640021, 783231168, 635941233, 502770211, 859136911, 9982312, 664127396, 387632279, 675513704, 393321913, 733483909, 404063814, 120281627, 966719784, 752979920, 491153117, 716258051, 281376297, 133718767, 236809662, 902503200, 391864645, 817187935, 888522386, 599406604, 40567248, 22856348, 78212298, 305698406, 58823586, 815837186, 594831890, 269421075, 387166956, 168580512, 968503952, 803006928, 871622154, 788731232, 922761319, 464816145, 370775000, 249733549, 928456198, 258105018, 9065450, 811776289, 475603957, 629641814, 707840130, 719162730, 292061517, 412718355, 608825873, 837318936, 455475459, 415908277, 66911392, 944611370, 621791447, 23489933, 957352560, 471573667, 724056061, 500266330, 748644426, 230980110, 721850551, 507664328, 771530390, 420619107, 343062624, 358361842, 509667415, 652255254, 444618622, 723682292, 719874499, 239112912, 934034571, 61779228, 63709988, 299593373, 910133404, 718904034, 383601631, 418434927, 103866208, 822739541, 865710843, 297765383, 6075986, 192859980, 474204202, 679522426, 673531516, 154878073, 996395791, 539061240, 478248668, 932192747, 7391904, 900185145, 571441735, 749565495, 538714269, 611136357, 281761195, 308072334, 8290787, 982577826, 233755303, 926861797, 561942621, 626596956, 295794751, 578411805, 843501552, 6039284, 991441890, 262923310, 217298028, 553977494, 547247663, 614134211, 243669618, 750876073, 236891889, 918168164, 411469003, 866366336, 894401939, 486438795, 773472637, 142790602, 9796411, 82003000, 242693478, 118100872, 609054816, 279227515, 683387455, 686666790, 845607405, 961948843, 272456669, 398825710, 622008834, 158496362, 497803716, 333906955, 986873546, 413433332, 334382579, 816398096, 654536039, 489224625, 969397791, 906515282, 334884227, 72495814, 519711061, 555734868, 153610255, 247989994, 823198301, 161672563, 89094434, 111917521, 961449782, 396955442, 984682388, 524973883, 776193283, 294709583, 429524959, 684712327, 435431431, 524980468, 474454346, 581402004, 849889348, 770299155, 555507618, 908531061, 959855118, 712947542, 4876306, 410358510, 108065261, 18250662, 401152509, 401754812, 680741751, 229216535, 426895821, 167609846, 425874131, 904773317, 326857089, 269599415, 842648338, 85741773, 607484068, 959075188, 187098472, 336748861, 830722866, 543521824, 207995273, 381833440, 884905945, 751125859, 137941245, 618436214, 515552017, 20880542, 796724918, 72191390, 740757809, 713557540, 747749734, 175176639, 262351867, 969106022, 980670942, 308087732, 693657451, 565508733, 479100233, 567951699, 380506572, 251154396, 829351131, 60947534, 78679954, 796743680, 558142897, 539775072, 13522397, 339819356, 332172383, 77437358, 70681093, 110977006, 736538313, 729259556, 570331016, 576129737, 360715479, 40869582, 568954632, 817542196, 620048546, 869735386, 245196333, 771825062, 658496336, 781201149, 89814802, 604666986, 53866263, 986433730, 470384694, 487326488, 531414874, 986119242, 840578497, 729027380, 846174689, 436348246, 938026232, 159760807, 654672612, 799335110, 129075132, 878437103, 615159550, 587409752, 923432874, 830884336, 284364021, 192564519, 310926066, 897157458, 954774976, 212479203, 726313446, 888344416, 943387850, 880830109, 626946620, 843463039, 758006658, 141113379, 456813027, 131028759, 811534652, 926539536, 205479843, 341257625, 395073218, 843975751, 704585511, 293334127, 72965894, 915056451, 815495788, 808235938, 793517860, 775520622, 588056206, 175593219, 795190039, 585789075, 230507917, 319095482, 602796160, 342989955, 280057454, 274288382, 507343890, 413272333, 972428668, 250567004, 691483798, 409162983, 843675462, 831956284, 500158795, 323480362, 742715833, 556273845, 729445651, 516595862, 579094511, 67645524, 705945574, 726535112, 49942376, 200616173, 98253397, 728104060, 849593588, 284036826, 812076101, 595792406, 756835803, 902150256, 525047016, 912586439, 324112952, 403762522, 765384789, 74798069, 270571778, 196710847, 669274080, 103826579, 329943872, 751468706, 75861117, 868989627, 542290929, 448365003, 729332205, 883283809, 819933864, 349491263, 524737421, 371686941, 243307910, 834132009, 232415845, 617551696, 292023149, 423618535, 706821796, 495175437, 432191954, 655297347, 724583136, 409282808, 397921307, 367329569, 57846012, 270559584, 190621114, 66171963, 300474554, 656324594, 217208112, 233994572, 305130997, 891005575, 770433402, 996113589, 23714180, 323510275, 627936913, 694791048, 571473390, 325649974, 85384459, 405878109, 212548910, 323507712, 987819571, 352807656, 363711648, 431875427, 770155122, 69674630, 812545567, 189196252, 540706050, 497010584, 339352832, 912502472, 984900997, 593033570, 87685021, 226609055, 21073057, 614164311, 532682259, 429173021, 780498109, 146069475, 802503001, 694705985, 447350801, 319479998, 768504654, 498618790, 660653309, 995170307, 449758876, 465138326, 328951339, 462342224, 107393436, 470804326, 896739740, 637559895, 936248470, 416612045, 499129441, 340373123, 943174000, 560256470, 440456756, 646078603, 563195898, 533800578, 689599970, 269884579, 916043578, 528738858, 450488067, 81937635, 824740886, 531508331, 172447188, 650696163, 247423933, 317849104, 256960047, 435488135, 433290817, 627476741, 49252669, 188813702, 826134056, 594074841, 712877260, 191172655, 307630779, 22185435, 61915836, 715231298, 193466482, 16898178, 900458352, 827907150, 242007841, 305019698, 614455702, 68016144, 128034761, 569416270, 503395655, 897572871, 100427064, 444811351, 199048714, 124646739, 468151742, 954001026, 804983106, 216987199, 712342907, 721060137, 276868657, 29878203, 910436502, 437231843, 773726071, 69212373, 20437155, 3176104, 716596797, 507303984, 549448344, 785094988, 247585125, 423765909, 471921461, 943225273, 537322507, 875278488, 769704026, 871757527, 260129764, 710455913, 44143736, 187529726, 623685405, 774371705, 382016889, 7602766, 268049313, 426886026, 557866712, 804827850, 542252221, 463829956, 306239871, 961282464, 514464612, 503923715, 707517492, 621655059, 750819424, 449818518, 630988162, 691553587, 705982127, 283130076, 975494911, 66240921, 928397274, 409059290, 420345263, 793206534, 471630636, 777709474, 96686639, 367298109, 501361945, 178904472, 176655337, 52390472, 245454924, 360383427, 809798035, 696697416, 588723270, 598874997, 457598554, 858888026, 306257178, 788315320, 793115856, 387890988, 407243786, 668484814, 588082091, 336554461, 612073188, 982104546, 817699233, 59581485, 472810485, 943297004, 975529058, 738740114, 894293957, 52467514, 980953343, 824595184, 671874269, 966981224, 542435277, 972041927, 855321182, 801638417, 364172640, 123142332, 956769998, 188944883, 21227579, 453175156, 266578838, 796752342, 798355171, 960129007, 366561163, 806061153, 252287086, 612895418, 731516621, 56310153, 778807081, 666466, 374008747, 756195600, 507243487, 105685945, 532903797, 96301442, 788587341, 103875116, 535375217, 695393862, 736832596, 486303845, 295374618, 922786304, 519002562, 572594720, 4842441, 205049267, 419353440, 415980052, 127936840, 74304194, 385513463, 200349843, 521721212, 745915770, 607666662, 407211247, 90121316, 538018147, 856421590, 560793923, 217489133, 387778691, 70138545, 571927102, 356966217, 695960183, 970702677, 916307817, 689879264, 221657190, 349184003, 440093953, 751797073, 796735371, 145843751, 676060522, 805479657, 979281550, 328149891, 876472981, 954265996, 18462147, 849830537, 925590400, 323180366, 704760393, 66237134, 13505458, 695913299, 911230946, 941177001, 387012789, 56311255, 657566051, 193222695, 381986983, 358588143, 541551249, 622740013, 54121524, 861015915, 941001839, 737232474, 860364249, 438932200, 893133393, 478736327, 411463490, 766443201, 328872260, 353977302, 758562341, 991582200, 810943188, 191355313, 555292141, 920531075, 165474643, 684503182, 365667877, 253055786, 731266813, 102638045, 361787707, 440059321, 891401855, 705999064, 560000973, 837736453, 358342605, 192848516, 420058944, 383226489, 153985413, 622356106, 456374174, 146510315, 726985487, 82389300, 327041286, 577195302, 247906231, 496039106, 925152762, 546666804, 170018296, 529436969, 956014641, 313477648, 42769696, 260849876, 684030681, 530922099, 742000698, 96556566, 210732809, 319922937, 442310515, 465043522, 365671718, 765589971, 954961514, 294982068, 217297356, 172051720, 978453629, 504062744, 195534840, 796638177, 455114943, 288983681, 429282774, 379169511, 873474003, 387923998, 849328179, 940874228, 244311212, 601174250, 598298181, 338507210, 734998343, 75656292, 531045056, 18170259, 378741948, 815692162, 697065977, 971471385, 168762316, 295494404, 471738879, 701733225, 897686940, 658812795, 855557835, 666498706, 730587107, 526022292, 776619086, 426323995, 318737836, 853164272, 601778421, 483135142, 92205210, 124534822, 951048110, 619074152, 554156796, 762957454, 44749997, 365566627, 892066248, 670015360, 98729558, 811243859, 234821638, 165552663, 216868168, 907043039, 743621838, 654494259, 213584935, 476264610, 269341073, 501255508, 846806261, 848663759, 133116682, 275031336, 160570639, 989262036, 917626777, 950826994, 853225886, 102071811, 238175473, 569400063, 480565493, 894802984, 132446732, 353408286, 35463852, 629397647, 239622662, 662500191, 579963803, 355349461, 535386210, 563467231, 602783411, 225311197, 280087520, 144322862, 739995290, 131693080, 408164371, 981068383, 380405906, 497664005, 186494232, 588999338, 505897777, 20475567, 243026886, 931850227, 839773118, 730499949, 673407454, 766472219, 918697414, 881144398, 1399477, 683836198, 471457932, 477743298, 34968183, 644143447, 881650718, 437600308, 344988057, 434330412, 587111409, 710593542, 574694646, 55351076, 895558391, 182566926, 333283029, 39467079, 555274559, 718022916, 661660566, 637676468, 590212017, 899330877, 524234703, 147225242, 532201406, 102751336, 232057397, 619191521, 142246082, 356305074, 259939654, 815844380, 220852978, 447495120, 805754138, 103718059, 601231798, 427265571, 319937402, 793781826, 126836123, 14283186, 457987480, 99153070, 86337599, 564277239, 44084361, 706833066, 78197617, 298520512, 91318863, 981991903, 899530057, 248792286, 416180552, 214439776, 702037519, 139675721, 848088059, 208851866, 859993270, 545869374, 382323556, 396771278, 916182350, 899650319, 175641350, 212551907, 528875286, 39641048, 184890279, 735369855, 417313959, 399084643, 82977449, 638283287, 81616331, 294170885, 413624409, 269000913, 294008812, 518976769, 798983439, 343979265, 155216648, 789944068, 403134515, 961720392, 479436653, 625687892, 268075796, 503625986, 431353922, 689807324, 920285370, 775084154, 390021951, 434785224, 103517530, 520261610, 517881675, 689309206, 671285659, 625820626, 607846012, 470789541, 290944863, 539260924, 523541098, 805249673, 733173174, 46747036, 143013018, 154643006, 578450327, 964054669, 557552448, 130735779, 163119956, 487887429, 250212083, 558733288, 64446347, 762086935, 929495991, 395412501, 199342427, 206096683, 90888439, 303449604, 602235517, 727228552, 87212068, 833897887, 742591741, 593120074, 453947608, 554909708, 832705724, 389365820, 130677203, 555465614, 494124573, 137597712, 954692905, 184551410, 26296834, 813839172, 350256119, 557379868, 939011698, 299868037, 100010166, 367332932, 922709846, 674698239, 574922490, 52162138, 731895370, 80623225, 994214906, 61096024, 728046655, 742254980, 353861503, 478904123, 692770425, 305061769, 834385609, 748031701, 649105298, 331504251, 324063550, 565352173, 362228056, 844393484, 352546399, 78763424, 52918799, 385568076, 503338289, 332697042, 353728327, 572406538, 743146130, 188897889, 523013033, 751945715, 989707546, 591110749, 352343532, 384131798, 567080775, 367728299, 468801762, 75056091, 376075128, 408560372, 231665785, 416150474, 771543522, 537138175, 195610543, 636517024, 442831330, 831220873, 198270302, 623005964, 83607392, 666673887, 147816264, 860653455, 700422136, 735199396, 591783896, 668584820, 583371878, 3530155, 997361181, 667126487, 35471984, 105630313, 682712785, 899599697, 326282232, 127263581, 932066294, 461729130, 899464425, 818032110, 673351547, 600366839, 495652796, 529808136, 90877130, 457228000, 433441391, 604247831, 753046218, 612509532, 315318833, 580876214, 242939496, 500469599, 577017572, 748510038, 508377695, 782850892, 610038692, 771106549, 830419154, 533375621, 485177838, 23442940, 361748745, 747417697, 261942755, 675171155, 214004535, 162775509, 752992265, 624250104, 139381674, 288747900, 472746309, 873012159, 473769121, 653150843, 753462435, 369735408, 580559760, 912288179, 564122037, 627785748, 580675635, 792641438, 908676676, 164371935, 551727652, 406667580, 854652557, 658643676, 547723923, 503265574, 78052040, 851001067, 220933294, 332831457, 25325595, 97845101, 232616529, 153910804, 472155502, 875593994, 667502676, 414606696, 156823749, 833993549, 351282083, 197862736, 579584458, 956402731, 948074660, 424985882, 617104151, 623826658, 852417210, 409017742, 996771683, 250355714, 874749405, 751028578, 206425816, 502871661, 518657743, 776881225, 30493129, 389591306, 167914817, 634545395, 157923877, 815839536, 75728476, 859771148, 922189982, 266887608, 566799622, 342430558, 950553284, 152687432, 540296755, 367455628, 22450766, 675938704, 431248469, 857060848, 573787240, 737534865, 338018943, 584441893, 192215331, 378469786, 497896821, 449071149, 841448551, 500951668, 931361234, 784997964, 816555066, 391192280, 228814266, 289850065, 959779121, 447647055, 85955198, 904308725, 666656839, 813312960, 741828504, 49924274, 880815601, 944292882, 805569150, 586062160, 410793849, 177760649, 595321118, 489898818, 366968323, 962668948, 325526234, 589131600, 857879380, 292785198, 420765306, 458377075, 709058076, 134254374, 431904856, 272246133, 276231049, 497650769, 217381268, 358004164, 540124877, 623393159, 197074103, 771030576, 404079852, 777669950, 568551960, 531153075, 417843903, 888311488, 371788953, 761892331, 124325527, 566247144, 412837208, 295944716, 27645932, 329221081, 995411583, 337921734, 654298640, 369408130, 650064060, 15974255, 550298437, 249737503, 574999631, 16419956, 974020394, 275612507, 251466885, 986303625, 935868741, 308264931, 717254663, 347423912, 824778739, 694851494, 198355582, 351582309, 428205682, 62771818, 864691258, 554434531, 186698491, 835422488, 973468624, 334265597, 432844404, 895775565, 511874295, 138365361, 17860020, 952563987, 720871646, 764594574, 121701936, 288038017, 503842862, 148620971, 216106471, 798758009, 468393944, 25061640, 520761470, 724059829, 703997426, 138425592, 832918976, 22586215, 384373830, 839029729, 461078461, 145886128, 737988074, 864142888, 509452026, 737237558, 509342725, 950246276, 98370026, 129926651, 385101909, 562325752, 611034729, 758849612, 809852863, 301679377, 554265135, 642455448, 858767633, 980029611, 690919869, 551084177, 722788835, 279123061, 45398226, 944702412, 566772706, 148584380, 114263868, 104995152, 53806891, 759367819, 683288426, 389936749, 116733696, 803251746, 540595083, 56885046, 148893519, 482302991, 916829934, 775189841, 917573417, 703859182, 136078210, 399428405, 124392866, 864666397, 845751833, 565183901, 397041279, 693921829, 329670694, 997973430, 839358041, 108970477, 226530093, 70093336, 204031281, 876057696, 219763742, 434474875, 813881213, 86195555, 604064690, 937837469, 112819150, 702201239, 243408276, 268241103, 692336946, 612671515, 751736835, 409267529, 218548523, 134765528, 991666249, 546165720, 942255300, 424078298, 447244054, 631542736, 8778825, 321320116, 421517657, 907320586, 526637019, 976575169, 907316318, 821743059, 242443421, 495597138, 735043967, 535847629, 811237584, 859121850, 98081895, 745623947, 292098431, 222414564, 963435324, 795512311, 616534920, 327863536, 671809030, 17559758, 710136878, 583276693, 919438940, 966542862, 118467097, 593645519, 379932724, 415183871, 781977986, 909895048, 423071621, 413380785, 430358986, 871687366, 284403922, 761023125, 307128476, 744764170, 145428669, 900206398, 892570505, 822972209, 180776482, 517859532, 250711712, 528636924, 930219892, 544707114, 690257340, 347502261, 457841092, 930949098, 95889488, 418267370, 377417240, 830890472, 40458771, 301771662, 817542054, 344827619, 350345128, 401789884, 351309095, 533359394, 227848107, 832492838, 658990909, 14921391, 956392707, 625513817, 866956486, 147421144, 522712396, 49690916, 507028173, 101374928, 501449535, 958506430, 229386207, 688729330, 994071637, 15256098, 122255747, 50270577, 446224405, 15251695, 216165943, 259084656, 434115374, 67017877, 76575029, 289323671, 273160178, 640194395, 32801561, 990604162, 323502692, 121513237, 224762577, 268124853, 59071061, 310808682, 802394892, 306328444, 6603762, 582552032, 911672887, 254389730, 526344961, 362183379, 63678577, 647759247, 395412778, 735942699, 659760226, 341835241, 622550233, 626896357, 231684907, 761344466, 219336478, 223381251, 220352537, 778864477, 249091969, 620627463, 929685828, 740694569, 274722867, 266899790, 503809521, 354055058, 956921069, 808152159, 881561346, 778203958, 959922642, 403454601, 908603774, 21603560, 499450738, 371548790, 816940670, 686459555, 685298764, 567748341, 222138986, 20339900, 399047571, 374964700, 939732482, 390364364, 82772003, 755741470, 283475725, 346897803, 379304374, 360026697, 260653308, 277742464, 636724033, 722799777, 481768427, 336520007, 483417327, 971512706, 705596465, 860540605, 742790624, 857765273, 301083669, 62210031, 479672205, 645823285, 120235615, 4440687, 727016861, 9038524, 380510084, 261805379, 853478060, 778734162, 154315887, 487768013, 475889578, 501520340, 213839127, 931123780, 855414457, 948802198, 748074987, 563699679, 294675121, 885513808, 582491019, 287017653, 56571732, 766408830, 726897604, 853261745, 228597236, 586364790, 506100112, 646182667, 446712027, 383649380, 353704878, 876149319, 32395757, 633977337, 404653328, 196088468, 846920522, 17100573, 333849401, 238069364, 205757739, 624301373, 796516483, 687953880, 16233830, 62828923, 932518609, 902336547, 581464546, 372108048, 389961240, 892871997, 116251759, 557617533, 419839815, 578623527, 659549240, 390043106, 362215822, 537291143, 522477695, 518744084, 513225490, 692827722, 287627623, 888688704, 941137548, 90314872, 441921839, 637387200, 259668493, 770493213, 552526451, 848296534, 139197183, 4449006, 432310264, 657891952, 29735820, 687620849, 770628137, 112060514, 543651617, 625335130, 924446, 976365234, 647122124, 893970119, 885514797, 79166772, 904907630, 66783589, 161497217, 500344560, 573683160, 81157308, 66254339, 918225986, 239266543, 455972474, 17802734, 901749490, 831385225, 517492200, 38165777, 18463290, 868080063, 233212852, 114527346, 165562528, 473079653, 189252812, 328015721, 94804288, 233135583, 408424871, 364946485, 924409941, 258726851, 481724760, 236708185, 422679948, 107301874, 266201789, 212667625, 779834325, 469831171, 902981636, 305317330, 567286089, 358093384, 53502913, 225607566, 126291493, 580485969, 821191965, 93351434, 405289595, 324780891, 286598469, 884563281, 607911887, 759634449, 869911381, 448477513, 83824034, 381378539, 152993030, 469142539, 426270147, 735389726, 219750723, 889664737, 655464329, 292224130, 420600812, 959730850, 859662962, 183747933, 235073244, 292681457, 514900205, 800359663, 50725260, 402777470, 925650363, 211293719, 972562706, 122372432, 367586417, 600724054, 486431284, 970750871, 473241212, 334408592, 689713684, 933206767, 755847592, 579502931, 318856432, 489834003, 442785953, 879218362, 624580313, 262124872, 939395351, 808245814, 384739581, 581620065, 628025390, 705221269, 146999163, 929233526, 325677688, 241400770, 28415425, 398067654, 98433504, 259668833, 950108888, 763447211, 147425203, 54604118, 451675677, 624531865, 351897057, 459829162, 951553302, 738820071, 368662359, 75201655, 966989820, 166861640, 388889234, 40459895, 605013839, 269712761, 543963719, 132580574, 535381242, 154348753, 695902229, 908136555, 403519010, 871390805, 529765310, 593281796, 54621457, 618471505, 180806143, 145050163, 104735600, 381755610, 837228323, 39327419, 923079360, 111653198, 768585491, 451973210, 655976736, 349762850, 517278224, 770982677, 720050008, 502834542, 82003895, 719596960, 649101131, 101418003, 664864689, 207554451, 658953101, 59585212, 579023290, 737783073, 820041413, 545483163, 818959699, 2113802, 682464267, 181545868, 777717846, 957117384, 936914950, 610918453, 987544688, 457278854, 228193966, 531793921, 1000740, 806304149, 588239009, 812723163, 578635214, 778665956, 799502993, 208809337, 559966930, 602585043, 849439150, 506614683, 975728295, 249679013, 598878386, 562572116, 488444081, 42401566, 409114264, 282895560, 410252395, 204814497, 591016079, 310006500, 410308340, 134197844, 651315485, 1035155, 545372296, 97564933, 206416861, 442144490, 914491018, 377769929, 592738734, 489568227, 424071260, 818783381, 5797652, 491492430, 539058862, 138578722, 464372027, 873041964, 230872448, 526921380, 315716787, 728088491, 804562011, 212967118, 247990241, 473369730, 678800686, 351583682, 792728340, 112873266, 913742186, 550280992, 713888913, 98754274, 443960207, 692726906, 559839696, 80735743, 246272467, 78690526, 583074955, 273260727, 794917474, 12963009, 261650328, 742926277, 412671323, 687307086, 663920810, 918945394, 763403785, 218243154, 268123167, 832946949, 490814111, 885993151, 684425806, 788468512, 89131611, 784266797, 140108067, 697393213, 60792028, 861016579, 141191221, 589134011, 808570994, 354297806, 346114487, 665695651, 114337324, 512343049, 534477655, 220143957, 925411819, 711554781, 717525194, 24719650, 547537250, 874652695, 913817288, 166811697, 880892322, 913596658, 379898319, 546451664, 606100395, 143246943, 267117837, 870042198, 173990917, 846326056, 916987885, 826618663, 25555958, 835082242, 468393463, 469197791, 461395284, 266985500, 2845299, 438567056, 303620089, 897183674, 504460184, 171254470, 911616373, 430811151, 889661509, 54423710, 178974082, 546823735, 814486660, 220769951, 70986423, 52303760, 514323254, 465854612, 651166720, 806587917, 444277430, 941739350, 564166819, 119934510, 674505159, 300503628, 978521265, 905050590, 24315829, 156527765, 76229966, 38580398, 673149838, 608336729, 635829368, 87802678, 666528284, 392178161, 520359297, 510301126, 373876373, 353744445, 358193594, 368546126, 115861634, 294423714, 505352626, 214628048, 32191070, 549826604, 578269071, 585098425, 868945794, 559815169, 434583583, 563997410, 613699040, 608296772, 60558319, 853533344, 543976740, 155595951, 720853383, 268260889, 207354783, 375123150, 598175998, 507039202, 653124557, 29536626, 880675974, 991109982, 411501499, 607459137, 605327441, 362856308, 474649179, 500267054, 578745342, 412233563, 494750794, 705506289, 868714210, 705291891, 417832148, 62243923, 566037489, 14867531, 236576942, 634124240, 773627963, 120413530, 508323876, 925391395, 412225444, 287300215, 306487284, 385978327, 788742007, 61991567, 619463404, 399555244, 653467899, 897059464, 307644898, 230423951, 584500018, 152247272, 15757694, 406116962, 338079303, 648532777, 193362801, 421185037, 60426138, 910505721, 805256454, 180688689, 780148944, 485256770, 691510437, 572727868, 527763478, 470259311, 330114620, 638067972, 367330219, 867708616, 126808177, 916036250, 164699680, 579286712, 335514190, 259175581, 142260341, 174055665, 174614564, 181353740, 931904553, 23549081, 869762179, 599334899, 768214541, 409710535, 633670111, 747300496, 560169485, 462419708, 898898378, 647568638, 115420867, 978976107, 318125565, 888636258, 423627209, 889624178, 183787515, 632149203, 434058347, 729309957, 259755939, 734181396, 358703661, 651238757, 994640589, 258477514, 237435783, 790888204, 684212690, 596616919, 835278894, 93883296, 673292928, 531865213, 767322707, 900743477, 353385855, 90005113, 520834565, 173028423, 960132093, 697588405, 549043880, 798958586, 575440805, 63260686, 752822391, 682035021, 1138466, 835221651, 85964968, 1985769, 181097994, 787023022, 597580720, 129095026, 466859771, 200102517, 422803878, 537858886, 473131444, 674658679, 675700108, 960733246, 814049010, 892069754, 405203441, 431468274, 550069983, 704789739, 561002084, 189720028, 345904517, 884205232, 230893992, 539974155, 668961687, 624402707, 109747835, 227621324, 237029036, 756713959, 409925424, 954324253, 398065478, 419986964, 996258127, 573127119, 997827341, 440205660, 963325998, 683575937, 940794468, 992470158, 397533604, 62386107, 319637321, 959954914, 313633446, 274239610, 534571527, 626170584, 415185262, 279344793, 853477617, 106921155, 692512079, 443377839, 34667822, 117402492, 37542383, 987887481, 272187548, 789283851, 587234903, 550546600, 175824459, 5376410, 611941670, 158206525, 534409409, 203026228, 7979318, 441812052, 331757528, 454978207, 586178673, 146110004, 987552855, 142639582, 83353273, 123652711, 285737006, 869230360, 814273035, 446646398, 319286063, 187317924, 61882611, 332240433, 4807189, 506086408, 766512061, 220469986, 724133957, 740659021, 61889889, 386752621, 429596212, 661286506, 44395830, 693392915, 378987872, 561054037, 240045412, 847493576, 208767244, 757369523, 617463209, 524286567, 516672384, 519820026, 949879013, 490301691, 683327535, 860263267, 743713423, 175349701, 121837866, 725976829, 276911988, 443451121, 434658835, 259782848, 30147916, 718865327, 534780390, 925453858, 771188152, 69612829, 266569676, 347466916, 823339241, 117968022, 360227732, 495588395, 780314943, 347161892, 673728211, 236509845, 380534399, 744466011, 316323869, 763473488, 521062539, 830004272, 806697567, 582599563, 145136041, 19411103, 321358573, 430795439, 213983925, 177725587, 454348106, 852157342, 169252952, 774885132, 139754244, 11845445, 447806970, 893835642, 596872826, 684410800, 71617695, 137147012, 880383548, 937883139, 106001329, 112874383, 46333933, 517490933, 367257439, 866763692, 440859610, 407050615, 913959157, 943312729, 614614477, 558234820, 515275782, 206860096, 405349603, 631902402, 754824295, 337747981, 433740141, 834582116, 394145435, 453457284, 476710908, 168620123, 546052626, 545600657, 773354319, 172070437, 778650478, 472764305, 589764118, 720985646, 385183604, 334748802, 604146908, 948657116, 936984248, 390526216, 125824607, 217657491, 610086986, 144797072, 606677004, 936431975, 825396755, 462754014, 343079363, 493501772, 752521517, 308707498, 846452287, 368722001, 868662115, 171682341, 363141000, 579928905, 979541529, 537827920, 650578318, 288807887, 418730985, 576634921, 463432379, 498244201, 929032113, 794079853, 538579076, 697829082, 499078133, 709415890, 388348189, 702962354, 158317763, 280339080, 282328643, 177791049, 628165045, 493151203, 680104979, 950500601, 15935445, 689075114, 468194240, 648090109, 46223536, 939462422, 343036916, 703636789, 266640064, 118912687, 569452315, 463174350, 942888330, 661935682, 483174672, 450161214, 912388819, 726129325, 316372585, 638285377, 250888543, 581808022, 168396791, 314145349, 57536266, 931622131, 528058141, 907847210, 788040791, 350216742, 52530620, 129503842, 782933634, 993093389, 289665660, 495226695, 737649525, 862036089, 921921914, 917069625, 544452906, 23269850, 218052363, 404978277, 943383544, 872552406, 43050973, 734820646, 569003128, 726004157, 716271383, 179331275, 367281127, 734583707, 902809740, 465394807, 513528103, 766765082, 764395944, 831883086, 593816219, 142030698, 945815572, 203753871, 667658331, 159854212, 366639658, 664943328, 907467819, 17471133, 93981007, 583273758, 392647488, 15483047, 128694940, 250302578, 280492330, 742761091, 496804228, 603144630, 908301195, 854236907, 184086793, 727664363, 179113394, 986210820, 891136463, 871176152, 370441299, 797794251, 753032442, 43805438, 309602783, 805882539, 756904207, 957313668, 434700583, 320388654, 47237841, 3001872, 313958972, 694165034, 257674738, 176067036, 594782636, 444029196, 236953463, 807084536, 248421229, 46722331, 918540780, 981748763, 972139169, 339222759, 664995883, 788228722, 457858917, 253415461, 105556081, 631079246, 973753985, 150964741, 180001531, 86119661, 291400428, 702582205, 589432062, 756022552, 655864038, 540675825, 567554082, 594387248, 792530499, 361554351, 724110710, 946464972, 390452102, 501999070, 366287203, 646139488, 154296410, 968838342, 40633963, 959890894, 400946007, 575861768, 161303022, 545509055, 389267437, 145456957, 692982583, 541150198, 649405218, 330677176, 397412260, 462017806, 924649346, 905544237, 373402228, 50612215, 747996876, 222162966, 520322513, 766821634, 138611104, 774192142, 806369022, 273740382, 21571579, 294248557, 186503125, 879309141, 985628256, 512918700, 418462939, 712622596, 14496527, 463768787, 839998234, 413822603, 577826653, 249917759, 475398001, 711082306, 854211714, 621132325, 838158899, 83996321, 552690069, 781120582, 926286379, 803336132, 731292494, 150809704, 869279715, 608968552, 483393017, 732755118, 534013885, 970361733, 266933450, 368753429, 766050242, 763284592, 605106212, 888780260, 52596483, 963515062, 886130254, 663330223, 510007652, 483147725, 912679982, 52906285, 273285486, 321965528, 562772359, 151430803, 119348581, 117354697, 509529757, 812972521, 640556144, 940069759, 852247337, 645926825, 818522311, 799141333, 870303309, 626207167, 956812415, 798542377, 300741215, 521758120, 846968866, 292307522, 897867629, 21379550, 911315965, 131998325, 99750334, 622555104, 578153451, 441038474, 194670293, 807305861, 599909285, 248015387, 119511542, 422998416, 315045822, 98053192, 56088803, 159447678, 331122174, 541647379, 636735945, 782932919, 204859652, 486068822, 951229896, 816145282, 256032932, 744132008, 90869860, 897586374, 820891406, 583844874, 180446503, 77539746, 199334939, 637887412, 955634913, 690547745, 480679950, 550443669, 975157533, 523529409, 34525763, 776576027, 309798155, 307361224, 718262266, 264044225, 839898773, 450771500, 423837924, 849731007, 536484698, 675531357, 891897990, 463196429, 402606650, 251158810, 498492270, 408688332, 305097564, 571682032, 572007955, 99068130, 640924022, 986039901, 682161021, 895900724, 238093821, 644215117, 533938953, 688054852, 125556723, 434472093, 149002849, 487730876, 280830600, 722370692, 299707513, 202756569, 895327237, 893665869, 350193278, 963511582, 921275378, 332647698, 642170371, 775598537, 517129030, 386568036, 542690706, 736506846, 610822370, 356529534, 672736660, 28669941, 405949208, 761894131, 415148212, 173961385, 214774109, 693364651, 688838628, 965808775, 479101602, 488603326, 521324037, 795014644, 670871328, 894768067, 626600283, 156903012, 826437912, 483807627, 117762220, 40800904, 887394321, 709669657, 609990226, 926202856, 126709437, 566834855, 111599402, 693673492, 72994807, 414953922, 188943744, 339149972, 655736233, 539813144, 60047995, 293119824, 124277026, 503563255, 644859060, 952018766, 735948194, 474777298, 984076133, 744687854, 74009819, 887680145, 463737723, 459564269, 118055669, 327417861, 136256044, 595029926, 707441609, 151595773, 166423154, 954562106, 758161231, 512566085, 504766612, 680892121, 75004551, 918134921, 857405877, 629375490, 92739826, 289149540, 485701744, 283759755, 266428132, 564739933, 821984569, 856426840, 950551701, 371413863, 761190852, 99124232, 596587293, 254978699, 524919272, 214331143, 646779260, 999943622, 848713059, 657230054, 486665071, 932733802, 948726761, 893992849, 426623262, 140257072, 21052658, 302654235, 640057923, 677984346, 517750995, 466461260, 582362584, 924938328, 985772802, 524377254, 994542733, 490830370, 892202596, 921819060, 824118212, 368951141, 428388982, 788533987, 54158599, 984643926, 398889834, 862476892, 481931344, 669588783, 233693351, 330985403, 597407353, 133807588, 730873015, 424569077, 185767139, 894819995, 899048984, 224262508, 48318198, 684223462, 248709333, 250267085, 983190347, 737019456, 58128438, 81621141, 41614376, 870987509, 121148436, 958292781, 894906002, 37751707, 501432764, 232945122, 37794064, 85847027, 660745709, 180789900, 241618426, 95626106, 838315368, 621496156, 261241690, 578298382, 742122637, 880457556, 799222038, 391258358, 458698105, 443379870, 202898008, 586785674, 972896950, 493705674, 375183051, 928176191, 49178726, 184048082, 844720641, 360843199, 420991565, 762432006, 726945989, 586312387, 248360340, 266521062, 194014752, 722243949, 929308537, 91595698, 50058862, 889157142, 219796536, 344301766, 88790177, 364751190, 725773673, 754329565, 427895968, 99299038, 51199912, 202743663, 474169883, 731824517, 527142361, 8766083, 263629182, 470504293, 256859069, 9194713, 744014690, 368260473, 469487350, 991235541, 893855519, 367266635, 986735506, 192759016, 417546672, 925285587, 820617997, 505675315, 348291784, 349295667, 118902582, 518480393, 878131459, 840455081, 602000530, 410431815, 823735188, 105803440, 154564272, 54927648, 810106951, 325243759, 640416707, 308263681, 207011029, 711763012, 62043828, 811714588, 962276112, 15601134, 381002646, 476483059, 801182440, 154928896, 128699991, 543345945, 787763253, 728212020, 271028723, 575979621, 368035108, 176107177, 700835498, 735711105, 617689298, 646513308, 254256120, 532404460, 248726147, 513300164, 22897286, 948360220, 909071291, 651693281, 563563667, 719751090, 702134060, 794053789, 492640278, 130965636, 686968893, 30886243, 784536855, 281234479, 952642256, 793263975, 847946505, 171490250, 131419884, 435038407, 616345794, 300542081, 781480005, 203171762, 657918024, 967804211, 870699091, 971569706, 859795600, 161778117, 667439531, 573481226, 823088711, 633006025, 363621037, 595316715, 394846901, 341071667, 902536076, 714705789, 381324996, 408777455, 37962226, 648561788, 707246175, 219511925, 517064454, 803172368, 359925101, 879879286, 210866724, 111191301, 699751178, 95813792, 497108924, 115055817, 757220308, 241275355, 620454100, 573655226, 969052764, 297052951, 782486843, 194337892, 580998735, 193672630, 389206488, 985446377, 65000898, 215719647, 556486380, 471612904, 704715091, 461442756, 314330231, 383291545, 564847769, 440296695, 86174072, 958289826, 167345463, 406473840, 548158301, 895525695, 739417720, 694948961, 228097285, 549836045, 782201381, 814437652, 337055162, 704741186, 851533973, 865245585, 306880643, 370503494, 534512244, 541433580, 188720392, 759474561, 135258893, 902020430, 311616533, 163121986, 647261686, 230199094, 913334283, 196557525, 704834118, 320811661, 913481115, 518216882, 174734254, 250786153, 169166857, 926979905, 991048411, 65592336, 699371528, 876697811, 899515423, 385538228, 328319629, 238148943, 132376966, 13718213, 917994190, 585741003, 545399187, 263957211, 905994812, 271860670, 52897987, 303573345, 304569305, 562772081, 796366014, 112745930, 225455266, 643606991, 448215520, 200356633, 86933982, 800403615, 162076751, 729112643, 703005965, 958935886, 125778792, 741121122, 120157912, 156652897, 166712892, 536404630, 693230066, 907763225, 665691521, 496017295, 337542615, 46453358, 663269580, 315148735, 471433213, 216801358, 911340796, 661860509, 203261340, 918413583, 774510508, 705908914, 527463214, 302035872, 393745907, 473876082, 615153935, 34447396, 254281467, 914280667, 390979646, 958215195, 597314255, 388287244, 421983809, 77878675, 202486177, 292539327, 456888911, 749132997, 951526115, 954114781, 466555465, 307064232, 746979502, 479328009, 90655593, 330411271, 244665733, 255906930, 491276122, 565253522, 247168322, 826862393, 204764715, 623444304, 669488952, 783434959, 722319274, 249175580, 858046684, 234379476, 915113563, 357636310, 539005549, 917838815, 237506568, 403175135, 290496692, 388182742, 979043124, 466741010, 108504296, 762262911, 764103279, 543387582, 81681853, 684076286, 17659373, 452384170, 694253896, 368604, 961832295, 232149152, 446030125, 931276032, 850331583, 811147881, 693193909, 297659903, 258477431, 414867978, 380207451, 804333238, 477569335, 675503862, 74072804, 594567907, 688238971, 378210575, 540200992, 317591930, 938590754, 878630262, 579446653, 117337419, 633405939, 411956159, 541802417, 442809390, 687918517, 77886883, 365143404, 928648970, 457622050, 565230283, 616604009, 187842314, 478040976, 163976287, 925476747, 300554429, 707749859, 146743954, 895176702, 842535781, 913168768, 867130432, 394035173, 314413093, 4094957, 770791434, 323267730, 15143598, 160396513, 420876262, 656402748, 501526343, 499551647, 802941968, 970256796, 517840368, 224126565, 519886243, 224926863, 916087579, 873569535, 816283169, 475957765, 154196776, 75072641, 992915120, 328889846, 280122849, 479644033, 915652733, 140103022, 915631950, 314391780, 965073674, 713189300, 506918954, 781260339, 375567405, 207744848, 85504724, 929490267, 196112322, 314962167, 391828399, 758518768, 756387342, 320442905, 856919537, 824124250, 417973785, 493216227, 225673418, 707468555, 568910486, 945520071, 521059772, 319342057, 182843572, 703202254, 563495128, 699298966, 951385540, 877337377, 558228917, 362440380, 451096395, 507318585, 975978128, 34291683, 949317178, 934616586, 124512707, 645571259, 157270638, 281425814, 733426782, 518234665, 652515243, 376778766, 289031074, 866156084, 110651716, 751231797, 454481363, 330786403, 365379324, 191440755, 512987560, 790663864, 391994015, 818985382, 426328026, 887811070, 632719000, 699974005, 672906005, 879856802, 155042141, 341653535, 822453744, 600932915, 714223073, 256465300, 28208816, 268898494, 448033637, 927041109, 542880573, 529771117, 418703933, 30153895, 156938527, 789833006, 747663388, 725743532, 343083230, 816081580, 312753263, 21034107, 689314356, 232059213, 819578380, 783462316, 613363151, 637123698, 282459335, 356988139, 549656084, 832903069, 743649527, 127357576, 920447466, 866850399, 679519842, 918499840, 683581687, 704945311, 406356003, 668266550, 857633381, 200632174, 860435119, 931442314, 635021277, 360548291, 535726014, 667849447, 845570138, 111408124, 366008010, 730412026, 296047012, 321210398, 55045813, 592479393, 255706800, 604258449, 855747569, 754447921, 376019678, 365211122, 25058568, 577043986, 567826783, 254149200, 865650641, 701689987, 586937175, 458075552, 589158729, 572319036, 189820212, 95152019, 574229338, 642806392, 121696313, 165424531, 473227803, 37176710, 870697704, 286660182, 808657738, 437884337, 963924340, 712826168, 401797601, 92398849, 786759038, 464188925, 65077088, 375706928, 725555249, 471640816, 584530519, 462137704, 925783954, 596233296, 152756954, 965000210, 467216760, 659429251, 785728281, 789541249, 890078867, 831641952, 599214101, 425308309, 163186712, 280771976, 998628007, 608611591, 46851065, 453437129, 910819905, 813479280, 31605961, 940972639, 645986712, 469541690, 673283085, 53397897, 949524779, 785984086, 884894129, 100728581, 312440943, 492644466, 416055423, 888939612, 858596267, 643045749, 858838878, 946912832, 976952581, 380068226, 773720006, 514061753, 14283246, 777656215, 669390059, 452095529, 424597523, 530690644, 195117550, 323243670, 370955218, 195047971, 228606671, 974755280, 261451915, 297152742, 982462697, 9475296, 576280999, 917259622, 190452947, 755877506, 513623338, 719691690, 149893307, 962522751, 854829066, 790335608, 80871924, 59075248, 636247353, 595445098, 575288506, 248791800, 671144378, 761573223, 306442746, 781779900, 206343050, 627173676, 153279932, 544138619, 371089046, 331461710, 164715545, 396743045, 132296905, 851140675, 711909524, 614358667, 299693452, 14905507, 549230034, 19257492, 779374064, 791384118, 171737685, 437630771, 172466382, 394615882, 930786042, 58662256, 235299759, 607893097, 197639669, 289624857, 174261228, 305179064, 75913685, 617802957, 746395543, 939852589, 383378381, 647310068, 436093282, 645864804, 917058934, 354394142, 645735392, 866346217, 764043782, 813012730, 402002936, 998197901, 760144162, 690795922, 890111560, 336660966, 767709433, 364183014, 939962558, 272139901, 92542215, 800787323, 926686704, 955626424, 709997904, 255953689, 55408392, 223786790, 302144068, 675891294, 822138126, 575162247, 117155008, 118950665, 834498642, 427377797, 56221863, 945019451, 770146880, 726034658, 76477794, 433719902, 519356268, 874774331, 187909485, 853414696, 632366374, 934605083, 556778041, 366224710, 262597988, 286270449, 729554714, 458741071, 397821948, 469263645, 754459429, 436814679, 854141512, 108228267, 735738219, 620684973, 331436199, 292099940, 916883951, 175115430, 431274949, 407864304, 716005406, 225687625, 740366694, 395495184, 540288064, 590046641, 46036295, 745153488, 681598064, 831981806, 589030393, 101767107, 99069931, 106497750, 961327939, 834570981, 16627674, 235512343, 524032372, 657937874, 816294200, 693186034, 574500490, 7686048, 339470627, 280643256, 25485666, 254330591, 114770979, 23646801, 356555033, 264423759, 406397829, 285172653, 250547798, 552453728, 239454580, 434287768, 142009934, 358580192, 732128952, 298648034, 167000648, 95560783, 540235518, 303276815, 197749407, 110190689, 783532891, 82471425, 159404314, 614109577, 298689718, 192580262, 314080810, 936380656, 106924101, 440062734, 567573328, 95899393, 123249316, 136754024, 360179331, 228339262, 827932072, 449663091, 339814742, 704576638, 825921467, 371606388, 60735350, 603620933, 700578023, 874328353, 416656347, 611730492, 775391309, 220755423, 943563093, 149244917, 494932148, 161413399, 282472058, 273178592, 35403266, 938373210, 467122024, 438883083, 681769963, 205608519, 649426798, 781787491, 897450806, 643215340, 921300614, 161621025, 729142351, 565500139, 579429445, 358770378, 611853648, 605439534, 763259155, 566223251, 332083619, 570205557, 640860738, 251835497, 995712532, 633857752, 401073326, 741628142, 681015433, 671835394, 995257108, 697472415, 490832929, 401775749, 68982716, 917102241, 264830058, 645800939, 337152559, 668338080, 99846380, 113768379, 896998935, 107714427, 677676992, 223075902, 348629457, 160166805, 765997516, 376996342, 16779261, 647442156, 952633389, 458470481, 946201342, 844111739, 4400404, 742299841, 320406043, 501796102, 430238106, 15851525, 247963057, 955839647, 964967662, 530530571, 898909015, 274352534, 492911134, 131598738, 606504150, 210254281, 979266533, 857962256, 847301353, 289502511, 722016543, 219057644, 254184322, 486474081, 415479405, 340247065, 257427329, 415936166, 724408472, 227487538, 783174074, 994515414, 948553882, 910273805, 646263613, 798470076, 268304575, 49717201, 753193246, 212199849, 606770398, 804895681, 293179875, 41788896, 120452761, 486393566, 871773071, 734068221, 427508696, 176972151, 370781205, 742868336, 637513772, 64693021, 46191592, 933719618, 176661610, 927691272, 44896222, 953637061, 168996811, 923957298, 480844560, 300085113, 478113007, 451146298, 288266964, 568265632, 4758006, 168701259, 238207161, 341579833, 101923170, 108724949, 203736048, 636169290, 199101607, 142204918, 328802144, 894690022, 50171496, 679773415, 212951128, 325895519, 166965285, 861904015, 852790384, 637804728, 327917691, 706551859, 549310825, 880257217, 935521019, 612612902, 836358758, 913188345, 964146848, 204017821, 876290569, 199578093, 260295984, 331872752, 847656830, 84656439, 205249990, 968415696, 797276530, 243683061, 903312216, 319365000, 511442079, 908565381, 199056756, 501488646, 317506990, 96785909, 932594809, 456555091, 441137599, 444251541, 462098033, 755898581, 808499839, 209877603, 512528477, 421695699, 205474836, 726166912, 426495177, 511194170, 590872876, 462199848, 750906430, 874036457, 330181650, 349814288, 996552538, 286648345, 702801055, 231705994, 327281372, 536071385, 886148518, 386388818, 126927278, 190530738, 30054493, 841087675, 586002777, 771646322, 32194809, 602743400, 569011943, 952110472, 941611605, 524544478, 797483669, 359949065, 70353104, 529631719, 635906400, 229626842, 616935068, 289172146, 750770517, 810191006, 306185976, 459335696, 795491351, 162638458, 115406256, 123319346, 32033531, 355244203, 918594143, 989170573, 780870607, 54600517, 281014698, 51147369, 700580840, 926994657, 502402000, 491898959, 491012474, 805080619, 644496281, 437220689, 417703617, 527946894, 540078552, 498580275, 359378200, 329184642, 611812137, 939935633, 790075679, 609032252, 738123654, 961643501, 669457079, 707682602, 300679403, 763942877, 631109171, 233300788, 908143642, 824507243, 699684324, 317047880, 684094473, 575562221, 315396437, 840412130, 387071080, 70350013, 539010761, 296420987, 717733129, 510126260, 355363453, 353551489, 287183338, 875189556, 308263793, 868077478, 42230943, 71622879, 748197475, 290607651, 239969895, 428213599, 101246415, 545867465, 882390147, 61728066, 525511875, 85428252, 509143524, 567203493, 420183030, 788308074, 864513756, 935012694, 742935005, 868892567, 49803027, 411211113, 699118387, 696067205, 558603096, 47051937, 598550050, 628614440, 319532610, 997102530, 318265616, 587733625, 989961208, 125937687, 43881211, 717837988, 359449172, 858760744, 917829073, 947414023, 470233664, 496276020, 148671415, 870072747, 521419480, 876952956, 505342546, 431799630, 755771950, 828615820, 583379985, 522533580, 305442802, 245876945, 492495791, 85358578, 100321627, 383384750, 13976965, 87550407, 968316638, 872424866, 862957625, 346631196, 767115496, 840873949, 605448943, 80577554, 857792440, 171302170, 18401063, 371772941, 425229791, 88891892, 702191540, 317373491, 271632676, 614945298, 187429799, 95354914, 506458578, 275363518, 254947738, 327365667, 543699433, 409150946, 587586147, 679113863, 826013094, 517764239, 261113364, 469680521, 122713174, 689320808, 56543294, 427375618, 105276514, 433684307, 528232996, 245860870, 793375073, 950418902, 743798022, 163051139, 857605315, 802615563, 322037017, 879488422, 578440848, 228229897, 367379253, 258725011, 859121804, 429149022, 404168147, 282066065, 498928826, 760578485, 326062519, 388353818, 193600220, 51009931, 896410438, 633446376, 383586836, 374529658, 587640568, 690883441, 104304971, 674918799, 534675376, 752690531, 62568960, 499431587, 104385005, 847325008, 264904273, 115247553, 435570681, 372547729, 950230431, 136775786, 856634883, 208138223, 239962292, 839623008, 530105629, 155522797, 165300092, 259330597, 775431007, 534647902, 518355939, 947289105, 456689912, 613874158, 821686305, 560009143, 410324335, 248568434, 144037217, 385488782, 429570739, 612860581, 622037911, 929079427, 873758251, 209342611, 563740819, 992474034, 884210459, 778899989, 611009458, 350339186, 243712701, 669666988, 699035569, 788970844, 558354203, 573205190, 234827948, 164540279, 33413593, 227682832, 997325430, 530514528, 349152525, 802669196, 6500762, 252077496, 434554372, 869368827, 412106121, 479547325, 478624490, 74760604, 569379421, 925793100, 199110806, 635085597, 701007636, 757781683, 284063610, 911006734, 730607193, 701842085, 869582447, 347935090, 857415094, 537297815, 345898650, 108051302, 882111644, 959168045, 612564494, 521139812, 845403596, 271597021, 61275069, 786696972, 299888202, 463067025, 974480062, 240435859, 554055333, 512820310, 789515863, 314468988, 859267998, 523381689, 447859899, 95584819, 953476162, 863343080, 413196516, 105823391, 471205455, 222403050, 17159053, 590711935, 163165805, 792261998, 415019772, 811282507, 11974596, 185239694, 339011508, 810339681, 482667359, 328541606, 808208661, 137021183, 883066464, 123974192, 35617455, 882299873, 541286365, 5909643, 333801487, 249730293, 963359042, 688483606, 303354424, 175511676, 847931745, 435638563, 230324649, 603433653, 714073231, 949478577, 11880124, 990515708, 233152405, 924716097, 602823155, 752741906, 407725222, 928685459, 680311270, 585805770, 714736087, 853610840, 82699440, 712690590, 366877212, 483770849, 518210285, 984240678, 986834731, 273979053, 402474344, 357659136, 237182503, 717439171, 33032844, 796061233, 889809195, 134008933, 801353264, 103632727, 480621196, 528005862, 550230115, 392961059, 428791352, 477790849, 299055413, 811725385, 172448159, 442960844, 898756340, 4150771, 835306039, 695491383, 142141534, 9791908, 884652583, 599942888, 888690651, 812792565, 79026742, 388063102, 941532854, 232807438, 268666534, 894796817, 327162065, 429996888, 777132170, 436486913, 633930407, 277735028, 634782006, 733106584, 502477906, 409624679, 811124874, 289737481, 693453657, 773881401, 950527049, 244317076, 834235875, 817522501, 343565311, 109943134, 851535208, 268360888, 697630145, 908104393, 472357540, 584834037, 273305230, 733827827, 667890382, 432088217, 141166510, 217158068, 788067277, 583563160, 901798007, 997951416, 288224386, 140536945, 151292108, 304475284, 141171390, 533285011, 412286698, 804497433, 277883515, 179710115, 846008686, 605143898, 816643532, 535367180, 773004641, 366624277, 199680352, 684522775, 178263844, 278962433, 346452473, 95543753, 261768869, 921038920, 884576402, 935662361, 254051521, 92530535, 665378833, 649982213, 278212823, 26974489, 289685597, 465302177, 288412453, 828915794, 957544099, 280018161, 619451759, 74730520, 534788627, 832112426, 16511625, 777491842, 182853892, 202853178, 95134758, 882233625, 254788723, 696901641, 163615486, 678428716, 490314425, 983578994, 699567425, 923892494, 313441565, 210518173, 988644068, 746057717, 618063127, 51112296, 988884613, 837963677, 61785452, 17892542, 247684840, 194107396, 488326485, 199330313, 603422967, 465292246, 575757422, 309856572, 246352663, 656868416, 952952436, 32196882, 363235833, 633290484, 59657057, 838924573, 132345936, 639527564, 645909025, 391010996, 694237129, 828246862, 466311656, 322460777, 756187294, 919895638, 29253680, 856802816, 179800142, 776439445, 653835905, 44759219, 471082467, 894516834, 472743285, 862977277, 939182221, 343716203, 986439306, 395592906, 785720336, 72045567, 97064731, 188776644, 877658981, 764129542, 800304347, 919626547, 94718405, 980058195, 46892027, 86474689, 152321523, 226780955, 442461802, 385118582, 142559210, 175813755, 563454200, 479916581, 565115957, 312147944, 108464524, 790586299, 534279882, 947743990, 843411609, 684314462, 114123798, 103843363, 126155340, 472602020, 798018510, 622424689, 528121321, 817280227, 978423265, 625370261, 86927376, 799215119, 201196334, 355087185, 693144349, 731520604, 358502078, 410427339, 751242228, 844919284, 499621490, 763427448, 19807120, 722667617, 987943872, 155841556, 961028585, 451543466, 504270312, 24083333, 333781333, 493673146, 79894553, 454218636, 578884511, 588303103, 363755110, 245680950, 19797474, 426554240, 292038400, 122453662, 147399179, 390694923, 844185061, 550075867, 38828403, 346049081, 663164314, 727012028, 230976673, 632971087, 846925513, 56176667, 513357054, 39184705, 452167246, 70938608, 5428243, 564334187, 912672509, 215229241, 686389120, 986626804, 878350568, 967054676, 754230384, 231683156, 86327375, 405812851, 843806941, 793948421, 797122645, 117227318, 514930750, 986788111, 209886515, 247831720, 625041854, 246107686, 532965029, 499037371, 865705544, 646470024, 633099445, 221731854, 137641085, 427596721, 423212264, 153055615, 371979263, 490209455, 270582025, 556764063, 760881296, 972381411, 757811426, 203570750, 898585252, 19873758, 70739866, 185803516, 395063005, 396166875, 679465581, 174177030, 332444594, 67708510, 175482540, 214571944, 150073934, 933858886, 108579786, 250498265, 810105813, 713090649, 798440586, 232406932, 350065432, 492769557, 142689203, 714513032, 90315489, 737858370, 232288604, 957789082, 82907306, 986258377, 746323153, 382223073, 748390690, 200062697, 880988223, 69710494, 638244504, 391467547, 345027949, 976682929, 246011377, 722816332, 140575350, 136475022, 825965856, 904353122, 61599590, 982009941, 401166277, 884392458, 62342126, 213490001, 218133979, 534576679, 288886660, 837023142, 229308885, 577874384, 335172197, 329623020, 469023504, 96392213, 590886986, 429809355, 165584726, 496553015, 781638898, 726293150, 25573703, 584019654, 289817889, 138514214, 137595026, 571309456, 63107663, 549194203, 774601793, 15649584, 557037647, 969817668, 256824605, 57052508, 199380530, 634577868, 518113968, 945137522, 334327072, 310398622, 617137780, 834491763, 589633777, 29198722, 876012534, 405778582, 455930706, 391908781, 928163492, 603689633, 167126886, 938707084, 174351186, 144031254, 702465484, 184491300, 785594436, 103836850, 70120272, 860487732, 867416669, 423342121, 598131290, 844496749, 723990115, 255780029, 840685097, 305339608, 74974474, 22510221, 76537984, 76034729, 816485126, 915807778, 597708988, 626765530, 24677866, 479254067, 444751120, 796930759, 730892953, 6078785, 507464650, 559740661, 207174774, 257835110, 311760568, 514359433, 287382565, 155348082, 660094544, 125574061, 796952367, 596940556, 87477711, 632023994, 512508875, 566981575, 739517844, 19881324, 767742232, 631605662, 45284765, 3925053, 652540428, 799848411, 992759585, 90987441, 859661128, 970707756, 653438814, 121833976, 803974441, 653421410, 538017899, 334388266, 10856141, 312542232, 387588729, 264083191, 306683025, 957815660, 395286692, 31367088, 619236717, 522581967, 879742564, 261059656, 296429181, 331700415, 159723799, 62209453, 305439516, 585631073, 431640119, 313574001, 779818603, 986754120, 527227611, 953564834, 655186993, 837924749, 871075911, 616521417, 193415179, 290516668, 459937017, 785789013, 19714690, 398295676, 521722100, 122180726, 3925277, 42246748, 93102057, 402088250, 798242306, 348749523, 204658177, 496507005, 235493552, 382446233, 343148472, 973656672, 661322986, 186768395, 535367939, 806663120, 212728833, 555866319, 828097496, 296273138, 80965855, 25493601, 711793981, 886557901, 283524454, 25163026, 190781889, 464476453, 908493221, 449269210, 140138039, 157697560, 699855905, 900872594, 980677233, 183741822, 661013079, 113788717, 439584789, 266517428, 479193190, 885827754, 294378984, 292108762, 405378829, 320235920, 976136176, 327549031, 866162174, 964601445, 152887618, 608330401, 10682923, 473445688, 197816741, 330267283, 624255701, 770870079, 579740312, 967387521, 956873471, 309518496, 124832543, 773222375, 261505083, 41387705, 907752708, 941838501, 268132412, 51875860, 41591704, 903714115, 828584352, 183546250, 396923508, 612740816, 221174526, 782042362, 183480895, 520331839, 892795314, 33989160, 676363621, 977696868, 586107250, 938471122, 782405689, 473720742, 127956862, 556214218, 391623838, 361067210, 56577364, 511681692, 474371130, 589120958, 910627483, 947030845, 355854127, 579621278, 714530292, 898692984, 876857531, 661187893, 805075077, 843835121, 890124496, 258513157, 543385818, 969052231, 759522097, 195817957, 222325749, 366618749, 589980427, 617639148, 125664452, 185717900, 88605048, 400627407, 178255276, 164490758, 905636421, 338027570, 69245214, 483594130, 109962694, 834943323, 746064452, 500483675, 113395562, 676751294, 735137429, 109048753, 198899841, 921938678, 30881601, 141558939, 388993666, 699971468, 305295088, 366159710, 218717628, 806783376, 960579558, 160133194, 211688795, 18853063, 424770959, 47937969, 311255885, 542694705, 389577486, 941306340, 502234042, 633590804, 382704559, 235092215, 164080873, 485181079, 338512596, 225537007, 489082514, 717568802, 673401080, 437869053, 697884857, 36382600, 705198618, 488387309, 92205099, 170291544, 848281341, 940043588, 553244005, 890821697, 757607167, 748120440, 177472176, 331750702, 997128955, 647953913, 397507803, 323097881, 745140800, 858060355, 438992065, 804740563, 799021416, 187267500, 908360057, 981259226, 789279424, 794907655, 139153566, 445472038, 313564781, 508573661, 552650235, 269102920, 494401443, 186218893, 318470867, 954773347, 224462868, 672213484, 650315671, 555915886, 335405160, 544683113, 62478199, 298152817, 167154922, 652171560, 741881833, 363670049, 654446533, 357753997, 775785381, 639099051, 80165635, 673348656, 889671217, 874248116, 973404216, 557554434, 887372581, 776092861, 20416962, 654739036, 251218610, 166527547, 837926965, 564545663, 176583555, 150097370, 448477063, 983270830, 237723005, 994796200, 180576585, 477808490, 131225033, 244131366, 550832312, 193369086, 8541329, 477179894, 455168519, 790832108, 60898395, 52015936, 91844902, 744232911, 247028177, 342114241, 913322744, 644919811, 330776871, 405418236, 139233843, 290184275, 625837088, 166096315, 188263174, 558599177, 524391329, 612280851, 181056512, 973219861, 691316784, 751319934, 530233604, 319022658, 263273210, 701661038, 400468951, 617836529, 274123531, 647872242, 126448130, 492489076, 731573834, 740442976, 584129053, 898569186, 187543769, 819386154, 602021078, 245592223, 329070109, 70040346, 807324398, 307288637, 938655185, 407585276, 504848215, 292739781, 232779590, 901944443, 766868389, 312780899, 967085945, 180216104, 690585471, 795868181, 975308733, 874564934, 162833201, 239062441, 81430735, 437946237, 432790001, 672003732, 28828237, 940079328, 665217508, 54469871, 591571430, 117586205, 473164715, 425992606, 267761107, 14651412, 543090291, 489334924, 372960496, 34527889, 739948577, 870784186, 161726374, 270377411, 443158761, 644280921, 209943296, 828394185, 879157191, 267877612, 919493932, 271192229, 348097505, 710060306, 916910864, 899649357, 945193176, 722986375, 516027937, 758994286, 420899388, 82709791, 222078359, 844883411, 684141082, 538860057, 818616463, 789834341, 609204537, 54072571, 218004713, 746318765, 936294065, 256378198, 663038388, 200761911, 15639758, 306942736, 343433658, 603729920, 948180746, 829513110, 708681139, 482891015, 592041687, 462844260, 433824092, 989495403, 538854258, 453747663, 282719431, 206825397, 336380162, 829392936, 194594668, 12217360, 693764372, 466852271, 149756497, 889971960, 56830249, 722745383, 37964763, 387575675, 193576912, 200549739, 722556407, 207272461, 678598832, 388429374, 176906134, 442769544, 809811857, 243343601, 520070758, 808431312, 861046853, 856469962, 439276281, 168732858, 797238047, 89985522, 632265654, 82853686, 541230380, 49056568, 225562653, 638809547, 954911947, 138503923, 632972267, 911427261, 639744024, 524681283, 820028577, 691074157, 429010654, 678563893, 883959068, 293308367, 28632507, 604751934, 704095315, 928846923, 674302342, 691284773, 152994020, 104875391, 364763591, 656965958, 834608115, 896622688, 28130459, 241259001, 664103727, 485731540, 663042039, 450751470, 862760282, 106689001, 674099869, 879700546, 987679286, 148646132, 946707532, 526894183, 286381662, 314212746, 818339819, 229500576, 819583853, 232466866, 22614141, 696041670, 695998233, 480813324, 207604422, 346788924, 936943897, 583657808, 614775479, 982220453, 109241528, 734625770, 549348991, 89219852, 929732457, 214986151, 668830395, 131439377, 891005866, 749239831, 816907805, 287492585, 158367382, 891277965, 633365297, 860640233, 229172698, 115039222, 233550072, 236490991, 963284431, 195244323, 110620471, 89416723, 449069077, 602666989, 654242416, 740975933, 494500748, 202537295, 800762534, 424117940, 906088871, 725596913, 748437501, 420951321, 158072524, 768368720, 939672075, 643028892, 198648261, 967033936, 399814746, 851987048, 866689183, 209162064, 8634124, 148315338, 707668570, 105831886, 296141412, 176741467, 643975224, 114297765, 633894941, 66180418, 676724594, 562269168, 353268070, 479131678, 591769822, 999714683, 789797405, 851406539, 519768566, 55748707, 713536497, 251311305, 865926583, 347463339, 785569958, 692512983, 799653935, 325277957, 240324189, 148472020, 864057797, 696622551, 654799955, 596257645, 762298740, 737968909, 945913087, 866972214, 844538294, 302920205, 678916581, 145823792, 488576166, 738838712, 404046246, 366449778, 206089870, 745934984, 105838753, 248043567, 492289619, 954173914, 67569310, 415148055, 954272597, 612577581, 789570304, 895817522, 617623446, 297809355, 155576296, 619847391, 989927936, 227284065, 796773227, 562220182, 182050666, 831813632, 12652482, 494957349, 829055741, 579875197, 521371322, 408716386, 696564259, 503111351, 3917543, 783983588, 925549829, 922580824, 472814964, 294780465, 416635263, 696698750, 817731344, 361725986, 999526807, 664145679, 963977811, 332987565, 52280392, 825204701, 64145347, 313074333, 494967087, 537561303, 782286368, 38545302, 142018412, 946093885, 273656234, 633124247, 471258264, 763181844, 977866841, 706023539, 603968404, 39390584, 515893707, 633787732, 320458756, 92782274, 989504893, 304834160, 698463268, 802445119, 32121111, 325880058, 942110046, 598758264, 634728375, 884240609, 604760876, 188233543, 131396245, 78372773, 363590531, 393825991, 559184991, 398607229, 753599138, 395531392, 458846666, 517717967, 620406284, 247934410, 564897027, 510406847, 992064868, 44689077, 473269181, 703708018, 165844551, 388810226, 376594415, 129935980, 206129426, 614032658, 388001929, 896321500, 838097266, 280878402, 424729258, 224915938, 233437566, 985466498, 850272281, 717357892, 703229545, 343001852, 820634892, 277568841, 118490506, 131116498, 943209973, 714374264, 190502351, 612071111, 450044215, 488961535, 822386084, 806812626, 623921960, 948720643, 407432195, 853147248, 523461160, 86223893, 188784785, 299809468, 568778385, 653476608, 349163438, 102456289, 762259886, 605401815, 53317378, 822942474, 539235817, 872807161, 497861677, 559035061, 714960348, 805062523, 40344017, 118421614, 8314628, 212665473, 286644286, 590575974, 789280844, 976094854, 441175556, 828752803, 634473846, 156400775, 352895658, 603931464, 711576759, 3043423, 121617141, 214925222, 792135150, 142509618, 926929615, 108352930, 700700170, 766590590, 675979092, 869251099, 350331042, 87674326, 189395102, 640265724, 313931329, 369487999, 998205743, 272662311, 964800507, 21463426, 328933443, 387177363, 875562930, 231051731, 698145999, 610694312, 968795701, 803699144, 528190669, 771555575, 746435110, 934559029, 395063695, 430835293, 738661654, 43475020, 783762514, 942179535, 408929046, 837745716, 47754299, 641256180, 102491549, 943121294, 472286900, 711513687, 883196464, 561849545, 580759267, 371380547, 750366782, 117910181, 813307840, 578431005, 191568985, 511271898, 363429992, 372442925, 430182256, 688053708, 65737969, 912285547, 379632984, 389717131, 628897495, 146761676, 728949059, 693773138, 838323185, 765740399, 931923837, 365265301, 969634460, 541805111, 766086440, 419896570, 159063024, 53380837, 571727331, 768506711, 304755828, 332850487, 773471030, 963723669, 713102865, 26208830, 618899957, 64108001, 556663722, 864344984, 256614574, 564085649, 227409995, 822800834, 981506611, 271215928, 234477047, 486853985, 231383547, 367608916, 959514980, 643369631, 611121621, 342101405, 482802953, 553845007, 321532619, 113407121, 828143021, 294867584, 977917281, 573494422, 969280421, 338382818, 660542967, 899793846, 713847468, 230307813, 791335488, 468707397, 109689411, 346637001, 887047959, 972006116, 77878104, 988806139, 411281769, 535948911, 711613128, 78267602, 404667084, 774939363, 973255947, 811219750, 488371537, 868781767, 823633775, 359341660, 98059879, 755317580, 700196465, 349206810, 890842747, 93509947, 472689971, 495068477, 421901924, 21496593, 293452859, 137940532, 2249227, 422055727, 118871030, 986887343, 215254639, 15437668, 927626390, 864539051, 525472594, 102192095, 353744182, 143009268, 313855274, 814552023, 556076645, 45989821, 277048410, 406539425, 706491421, 939062268, 151544422, 452448634, 666808411, 338883879, 318336685, 614155434, 304676180, 497707516, 100367481, 965519630, 305750752, 59133076, 102923490, 582234732, 171671137, 249888929, 996195700, 2411388, 259081445, 232337377, 99830258, 931131103, 104896696, 98190375, 900114072, 178090368, 589415835, 567272825, 380226384, 531723416, 515693481, 624500915, 267127847, 719050480, 1519022, 357893007, 630094177, 786442890, 262507547, 102807102, 522570537, 251826305, 876304578, 784749349, 289492787, 106006834, 70000726, 884673505, 779489909, 39093633, 482451619, 527918257, 894475903, 90812483, 566195996, 66719295, 736603135, 242180725, 391533123, 745485825, 817309795, 217580254, 767266346, 174384259, 841507039, 790062393, 970904909, 897222376, 543218052, 555870902, 549685256, 529485384, 320861676, 723953756, 418403353, 596995995, 139494216, 341593297, 243480565, 124919902, 110882373, 104279798, 627615864, 129634856, 151543254, 23011827, 410770684, 494073296, 932936794, 543954994, 909565146, 709146121, 289890485, 597892504, 867304855, 492879211, 986745839, 925302194, 450575929, 183393801, 123685163, 241023669, 448168891, 186758412, 891339071, 680101863, 531859507, 801185761, 23137674, 841351189, 273916979, 276453209, 410443609, 237208962, 42678320, 828971074, 190478864, 526047849, 158713407, 274699467, 198282792, 34095288, 787678827, 163792834, 580492901, 242467856, 159190919, 865870082, 44864525, 966149771, 856352048, 753099261, 592179637, 906943603, 146993941, 525022308, 701933368, 118387311, 277074999, 45164284, 985420734, 165468672, 922556847, 786358118, 315938228, 57607846, 52936690, 448980482, 51999750, 446592165, 743899459, 677772959, 563985682, 454391687, 428622094, 637703557, 180778703, 729935935, 961197566, 818566225, 745879413, 582088368, 214967853, 116919402, 729339762, 286621629, 949881358, 639809527, 703677441, 956562215, 223515027, 151000985, 616644494, 706358090, 678792053, 109970910, 867980953, 54494339, 63484096, 727840142, 766035365, 989167155, 889726972, 205735926, 882373445, 910772831, 486379777, 1528195, 11586809, 577120997, 504537028, 877313838, 525469610, 826531700, 52800066, 514251254, 302825983, 71191671, 279059837, 896613292, 347981457, 137378818, 66383930, 48694454, 236862278, 266336551, 269116772, 667910136, 294974428, 503953527, 174177022, 387030413, 321943873, 250522650, 442679593, 923498379, 23955786, 131802959, 519512302, 588806629, 424167368, 490410558, 459349172, 591368620, 514539920, 402281008, 904311823, 679623118, 602559071, 607641061, 295215943, 457828438, 778590425, 589731436, 359925097, 292348223, 223520005, 993258266, 809431186, 872072855, 434739427, 88410820, 416616648, 20198402, 536473171, 791001307, 369805702, 169815338, 168325531, 402140785, 33613390, 385149207, 480460793, 790407311, 732995258, 168751795, 684558589, 302307972, 612465598, 864190284, 199726561, 371149929, 242357932, 485627826, 829176486, 517928285, 780008178, 119358322, 238327472, 550746079, 308459930, 18414153, 135074156, 814354347, 189232839, 80766940, 459195680, 154878608, 618509325, 566941087, 539482280, 823973249, 411144966, 115803146, 925637142, 631226341, 161204197, 341575216, 173201250, 739800679, 945374008, 322488089, 155905853, 267804580, 827084824, 483030077, 116694568, 110981644, 145667882, 980087401, 409845476, 280354221, 650936790, 306115087, 136695111, 708141572, 348310014, 136705440, 740976002, 601238909, 433465232, 716384826, 744137373, 195142406, 626217251, 279461440, 645096637, 854909814, 442676329, 577330159, 863535061, 613336628, 600553310, 535359179, 864315687, 611856971, 476915306, 535772401, 255283672, 83076158, 280350589, 955675710, 506400675, 592527890, 664688903, 544189454, 575067158, 570228714, 519970499, 121536770, 137004955, 191408531, 5090882, 831118834, 538387445, 780006290, 146600534, 114884568, 648081210, 843300445, 825780675, 8535715, 753777921, 46065788, 333051615, 60651944, 746923145, 902362837, 336466768, 905801364, 50653862, 893301553, 148274975, 410699467, 249444855, 100672203, 513076481, 297643619, 713377886, 664224756, 94435617, 829878316, 498738262, 271283685, 839157457, 10608724, 406089270, 615364891, 668921673, 363092126, 452663069, 951249632, 865029157, 99692881, 825137787, 344444187, 30554267, 256928701, 239668286, 497452768, 835703330, 956492339, 803346767, 325378264, 512003833, 113472920, 62411410, 778979857, 615633922, 555194109, 262849830, 245112313, 726017202, 962905299, 379796326, 526653867, 244159504, 297732870, 708076204, 451916457, 302130017, 20360700, 242510149, 155354527, 731134665, 368578272, 209283578, 65158575, 792579632, 72189196, 230826851, 369817583, 650570062, 275876506, 104465578, 273616412, 215255175, 837441275, 985971062, 170066183, 923466621, 964726621, 269784313, 774594168, 639911286, 907700335, 330289460, 513406145, 111029166, 480808214, 911805182, 370584889, 254362231, 806399718, 812483989, 728869142, 499929066, 695502175, 886598871, 747219912, 127346650, 936895980, 401737410, 340599111, 299603208, 482960177, 900083729, 798817134, 512977608, 964793836, 270719859, 939716076, 58302966, 222687074, 479506367, 260083985, 997241282, 930178599, 420648461, 607955892, 287805086, 988178187, 701556444, 299813449, 290237008, 437026793, 949355657, 755078478, 794656456, 808545859, 251139406, 268963012, 451889153, 66313905, 511745477, 564156923, 935210642, 226438324, 219376536, 604852493, 65151755, 266464941, 615798942, 69429151, 18316440, 713862708, 831165041, 945201039, 920927078, 801920111, 176285854, 208695354, 291164187, 165711750, 46028553, 152850653, 184417401, 467447804, 678840113, 749407524, 830213218, 765632255, 948826517, 166750431, 242071006, 287847876, 897470167, 47215674, 641092968, 104528003, 889383769, 24952630, 642108791, 536729548, 20132118, 280943413, 80555, 112038231, 272010704, 789822345, 42590152, 793006476, 189498691, 663528740, 448636380, 53257150, 291566919, 90421306, 558195929, 125428531, 294036732, 705019583, 73994168, 671696734, 792596126, 319192728, 31950565, 805654989, 804728946, 430272297, 768973951, 717109166, 525601590, 37827784, 562725007, 56599347, 400616281, 893962032, 476416549, 660072456, 523768352, 867126817, 99985017, 382713444, 384788413, 966703809, 253031005, 645895872, 248029664, 899366419, 330963959, 794266905, 410890320, 294159957, 600978597, 311378131, 103108229, 290698216, 912096328, 354966268, 800868170, 943809090, 520346568, 418726954, 440725760, 904435346, 315587711, 269983385, 133620025, 727784926, 576898573, 885661133, 433182910, 824673375, 695317000, 371203419, 514229532, 481794027, 104114018, 860696775, 71414199, 750428155, 926522925, 812326635, 147712899, 572073129, 179556640, 854557215, 111442554, 976171820, 410031924, 510798331, 413072506, 466490293, 752293556, 589659771, 49315702, 555585129, 14569376, 467573839, 10991601, 362907998, 550408644, 536232746, 658551063, 426470208, 262398980, 532445901, 211297101, 864376714, 871696519, 820328744, 97017571, 809042540, 799452192, 294260475, 968190818, 482184019, 622633797, 590156554, 157411036, 243224770, 632199869, 253545890, 621892220, 761423414, 17544086, 471736687, 413936378, 293091130, 399093445, 944755705, 663285909, 341047043, 802531677, 902409020, 379937839, 637992481, 886381880, 289258368, 406270725, 16252952, 855586288, 94815854, 61725242, 272826313, 981022003, 20007088, 561687869, 100826259, 526999741, 698999932, 3065726, 494012342, 369394696, 215020986, 587493700, 501334244, 278267324, 75770188, 575146338, 483627265, 70399842, 875197800, 312241830, 815427265, 274260106, 585430635, 992541098, 838259801, 353491528, 635358790, 916343737, 23155531, 637547668, 603697748, 987296447, 261335184, 202715276, 761809372, 292131272, 248380543, 223592771, 199145774, 985433411, 951993430, 859360348, 542004041, 214270592, 588355846, 668888590, 257144670, 925953726, 319173657, 514696639, 897174004, 52172124, 229020933, 318362342, 400076458, 894786692, 760411531, 290196879, 597809974, 851232477, 261428151, 21802154, 57852100, 118664381, 730092888, 760271656, 843481362, 791548119, 869810959, 511226318, 6358130, 924578809, 176108123, 786136859, 464219026, 545563303, 251982148, 470068489, 701137673, 540928044, 790777103, 198255518, 996702960, 823278047, 18765383, 709901238, 957515532, 627150451, 972371187, 363021405, 88546355, 230377045, 728506387, 52433046, 123044841, 599714375, 501109245, 970844772, 365203560, 816080950, 368894818, 185532516, 161342515, 747259515, 736011646, 677115976, 250346374, 195954377, 935094468, 292720276, 991708265, 706749694, 51346294, 440409975, 80712491, 238256838, 93816865, 496532623, 532732367, 893176251, 159537388, 798826920, 452078714, 207455601, 209917561, 682218490, 811168042, 543701777, 469619757, 533110084, 723935982, 666060591, 358364809, 868979889, 976874893, 899256614, 454468667, 583706707, 324578019, 661636148, 134363000, 252216312, 332084719, 167765545, 893587728, 628025361, 930109561, 422292027, 326937100, 899382188, 920288593, 937982510, 361749742, 62828752, 413848563, 985352358, 903785829, 405021343, 92943354, 894599038, 412689616, 784492268, 491269025, 947315131, 765051905, 624622926, 514944541, 530395889, 406053267, 492919991, 841495324, 275183243, 523733320, 88646358, 491037905, 911453986, 713871126, 504063025, 860033926, 546142166, 941992359, 593957963, 601012630, 405934044, 992273180, 22052492, 751550042, 496057279, 184661508, 26011047, 459148419, 125753686, 394422653, 977722803, 131581317, 391456512, 651579963, 940624274, 498531580, 893898984, 47556309, 921756844, 564116830, 204415695, 808132698, 707261564, 951302294, 743483129, 792869575, 626790182, 256407106, 552803108, 682243703, 475170061, 181525853, 346712613, 847849539, 239948166, 387504545, 391042838, 37451952, 734920909, 401142561, 952291941, 637484412, 310433829, 729055489, 736856208, 309404564, 655102647, 719597863, 882672354, 955929795, 72625235, 181684196, 649652280, 186751381, 377867798, 833177235, 699847316, 729993593, 949308126, 802215045, 636448864, 437301243, 688945454, 7198181, 154257032, 578338475, 93047465, 647079969, 523903735, 301677057, 330828876, 582996631, 445983951, 371544198, 406455549, 392410947, 193950611, 67873123, 291920780, 116359590, 556675399, 576152055, 502469400, 156658294, 139072501, 413558248, 900663362, 982151357, 762223983, 181930717, 842436871, 793072219, 39924315, 18745265, 221471455, 712346945, 611372716, 39862141, 483033924, 984235477, 551793513, 325239895, 200246437, 611868806, 373238373, 485329673, 401420716, 84238295, 283453126, 606178829, 434881534, 825017859, 194807754, 735033431, 826746556, 68720258, 603403355, 231329099, 825642633, 337191823, 438991012, 497680912, 214385654, 475507628, 635683705, 339598511, 918409531, 23696734, 123574333, 79773008, 596695273, 598537942, 551096256, 712169704, 305487288, 707409474, 563734574, 288827954, 30264577, 984655390, 109994506, 279846027, 821860070, 96777593, 269899891, 580003963, 913570793, 463403682, 505533572, 29665186, 164426970, 162613759, 743139178, 625384358, 960788990, 264689990, 271416960, 503844704, 622914633, 928766567, 2600387, 171564678, 763297820, 970325006, 767833330, 421498704, 942831807, 266268831, 940175316, 491547635, 133679203, 290696509, 999344664, 926495776, 519109391, 901524589, 760506301, 200376831, 64369142, 219982939, 45827362, 452625633, 724478398, 401743800, 535295187, 132303486, 814127718, 897116003, 665377862, 713969950, 895858234, 38132880, 163267885, 906366683, 749737574, 215656806, 533697240, 21841036, 536419759, 720993652, 963292737, 745622340, 676968982, 777215855, 908201792, 466905840, 614698513, 437655468, 249179966, 306543333, 811813284, 656558622, 645130756, 847822152, 481469345, 275910002, 234173011, 950130783, 960026388, 643115962, 188226658, 440664746, 985843732, 721756400, 812073693, 949267359, 520139108, 804118709, 392953481, 422560229, 195576811, 607334364, 535339305, 455101026, 461622701, 193554140, 341207125, 902761513, 800988597, 387325905, 318007179, 440831732, 483826865, 263900391, 375162076, 812305731, 494980697, 866902186, 880752098, 871263157, 161538972, 289688460, 958800516, 856088940, 788860365, 889887828, 615812942, 56896209, 16853026, 17073198, 684000938, 568879469, 884021776, 149537808, 674669824, 524199285, 835840629, 296483706, 285480710, 175597111, 79049738, 463711846, 736385570, 928917516, 345843136, 874701134, 444606527, 589547889, 924303453, 648941846, 213028766, 648848378, 320131079, 20199950, 452443775, 284261605, 910995971, 645195755, 808120909, 796600777, 962484898, 246958861, 382476645, 818515471, 653170875, 167587643, 167321787, 155170803, 192868093, 873219814, 590360578, 360697076, 206564245, 343353803, 774170980, 138289434, 299847738, 957823879, 208024569, 81338983, 173053566, 462245974, 920670364, 76007778, 708241934, 104021162, 609920299, 981401321, 790640155, 168916783, 70844558, 718846088, 310851932, 771541245, 47690694, 985832135, 144670664, 817658844, 393615039, 147950800, 559779076, 745895457, 955832864, 290391561, 107352144, 855322563, 832785710, 216884198, 329187359, 180518489, 781202417, 549121325, 400546591, 538853886, 270325097, 570222708, 311594781, 133151431, 199774902, 109452324, 336185459, 292623258, 774067051, 966391597, 838257506, 49619487, 489910458, 834262385, 742221322, 899275508, 687677761, 80622547, 702690189, 780226454, 167030520, 664352583, 101215556, 522685131, 160284707, 714926128, 408951295, 505963832, 989944720, 772676144, 972699309, 529599861, 813158859, 700474521, 315360720, 202996561, 218649369, 917802261, 66466555, 539988213, 824737484, 548768446, 912532150, 807464782, 121197413, 373792611, 767628010, 457489422, 887060656, 286963989, 210880590, 1615754, 767359679, 622522354, 259878103, 726982272, 415899684, 309350485, 453588401, 86955437, 877737171, 646017466, 309146455, 897021264, 978933196, 588061718, 547223087, 672242328, 186721970, 82781793, 712432623, 570459955, 661771353, 806392240, 708274452, 116893122, 992938300, 463517146, 183964916, 615478342, 334943334, 244497616, 623251719, 914550238, 14805660, 447542072, 757947984, 74456232, 297711351, 748775276, 715310176, 375648862, 361828417, 396956545, 290056828, 158508832, 981526921, 40791555, 682970836, 446410792, 267332268, 663539869, 974780405, 171350608, 445686822, 872721341, 705185747, 593939164, 358851139, 364529959, 293323937, 420429630, 144739307, 705199657, 733590559, 551319716, 420626454, 812699002, 194462229, 825841522, 713972231, 553887576, 467383824, 107487264, 954597501, 864560462, 473835863, 236294552, 684033154, 179926854, 75169150, 929195648, 619267422, 150137139, 795259871, 203512242, 145477520, 506777500, 75302510, 875887343, 277899708, 189522223, 958907057, 834612912, 654595918, 519758189, 320358091, 501279916, 399167651, 290889828, 110001116, 885285566, 27883628, 773814193, 676993420, 930654507, 813880688, 142884341, 628198972, 35769995, 947353677, 271686478, 460263573, 670951139, 899364342, 256527918, 669899961, 710628148, 67524611, 202338823, 15866181, 573740758, 194540442, 244750003, 998575649, 820972444, 359327878, 727172783, 569210089, 760795428, 242540008, 550163263, 669088923, 460115739, 982445397, 708968334, 531323125, 559010470, 489431750, 836674929, 117040100, 55566467, 589461905, 817276788, 173872978, 942777802, 473436085, 437295867, 874698829, 807792795, 813021530, 744363318, 395099741, 925301129, 837765945, 915460925, 311795188, 144997545, 270043890, 488608999, 730405657, 10554441, 369426410, 642976642, 497383362, 372672091, 136161949, 314798568, 215576867, 237114283, 600350201, 137885897, 114651629, 714580714, 921514353, 159950190, 413160490, 185062445, 992057585, 672619390, 965007213, 728693549, 242946625, 968553519, 886162069, 683504541, 619862768, 122181947, 795775623, 385620248, 7177874, 887690256, 277559123, 62507181, 877401868, 175277289, 459361416, 395330021, 899410941, 778130150, 847572749, 772388410, 185945745, 612108821, 178658774, 439415334, 509676099, 51944117, 105580772, 227901428, 383812229, 249010927, 352133655, 172339862, 775787035, 556514875, 553801404, 285028160, 633317848, 501120419, 356916202, 238953047, 167181357, 811313354, 346287899, 43043192, 433524442, 332224384, 189812371, 935965373, 777976110, 610243619, 431121839, 959430211, 220339475, 386021272, 98175539, 599627728, 213682915, 346204296, 823818211, 875021549, 237109602, 826892195, 348893021, 303188270, 886537082, 768829755, 430608452, 297432242, 236635487, 864242518, 508675231, 90700963, 115295002, 400644221, 305217723, 416461534, 393553654, 651154676, 962694570, 495185448, 736309788, 620560438, 740609612, 314792405, 536360428, 728552862, 227455438, 54853023, 411680537, 91374866, 776029006, 90519927, 44457921, 632044667, 846318624, 782115305, 492028219, 232921600, 244560077, 473550155, 275864899, 302471728, 847081905, 357125863, 963792472, 695375377, 28244228, 898834520, 392953539, 683390044, 770888751, 289363995, 548802837, 491730392, 441158425, 634540208, 73253954, 175838377, 467731536, 209698817, 627661765, 966452899, 820659179, 459341029, 459587156, 877022760, 296693169, 59365655, 848227807, 11388716, 361119078, 883004060, 661718057, 192102256, 860725284, 959103792, 850496061, 889591599, 593328936, 916643289, 508059660, 715692450, 107095341, 227189924, 310729471, 199367749, 371699057, 36677300, 80697290, 832191312, 613081687, 77711048, 663594273, 256672730, 774648926, 177244829, 323997801, 228373554, 49417498, 985719538, 384313864, 30627300, 460544374, 510536655, 977742010, 136488166, 68520001, 834156488, 706156433, 718830500, 709004215, 659106744, 772194050, 774101040, 352602657, 593519423, 380892825, 523738626, 713742174, 200424011, 38956266, 86990233, 3224932, 473853964, 935929591, 281906632, 431327494, 120933034, 862683254, 52668345, 432224047, 991517325, 607448131, 199609007, 951113436, 883467914, 164695768, 672223507, 654797561, 241352895, 697053562, 924308896, 583233557, 470139943, 531234579, 47308989, 842404029, 626132167, 530539928, 476327714, 982566058, 571133064, 665762847, 452345149, 219935562, 985344480, 769574194, 602144560, 225107710, 151557382, 422989347, 41630584, 373497005, 254374967, 387108647, 127943812, 414515444, 28448416, 703471879, 22708783, 211754764, 736537997, 681471982, 811420120, 488728935, 872143985, 858118680, 567397067, 423709073, 946222064, 373313692, 325096656, 52319893, 830797292, 475228676, 67345068, 215333552, 877956686, 183085227, 573994925, 370332925, 233147809, 198837385, 931433197, 625114352, 881866294, 418232075, 70142888, 942665297, 158168415, 563262288, 809470577, 39376374, 187732101, 580873103, 284112984, 123931310, 122726133, 378346224, 243384295, 345316874, 822834537, 595610992, 681071823, 56652082, 754215701, 178231725, 534096077, 729393544, 468707250, 780999591, 477975065, 873099268, 205104841, 228237044, 205366553, 42736565, 187667579, 388959634, 564872980, 220195191, 134484019, 201650355, 98799981, 619867874, 455187579, 412916813, 880653897, 253634042, 668189501, 828077282, 910613680, 655690423, 440077534, 948981306, 720169779, 756036362, 536555596, 595002270, 168487278, 83717461, 92459896, 69296935, 736561069, 643233896, 567979840, 14483243, 430444224, 293070914, 834841141, 666329856, 206264467, 117270512, 798887085, 380858184, 758305376, 427653206, 744710848, 519602675, 308379063, 625731521, 317094827, 603107494, 964376464, 976993912, 161986015, 193966271, 183606921, 298257758, 780357007, 427715885, 913499822, 346907164, 917356388, 679018902, 829983480, 541657575, 38912315, 463811182, 644860966, 198258303, 882253043, 210677482, 487305367, 384876041, 602330410, 103432622, 231888209, 731514631, 582975659, 571072719, 325529261, 174479345, 321519640, 970740201, 249606327, 512323084, 995474594, 833776229, 455573110, 761147176, 959438970, 688281988, 749767512, 798408624, 805841970, 858038712, 785884968, 243855524, 779371041, 627464407, 132400702, 50649304, 998369172, 68186535, 965854026, 815000619, 285373502, 879346406, 593394341, 383409147, 835192367, 892345973, 706764612, 959539152, 686087181, 379520869, 703060981, 210403037, 1314189, 175311872, 700508441, 470022632, 873477914, 872107943, 946750254, 808521463, 848216758, 247567141, 744925889, 139366308, 604527207, 188858212, 667110449, 338857110, 660260964, 561425329, 274907024, 280180761, 598249479, 390279184, 423411623, 798724376, 235938699, 666843650, 231307164, 201087362, 977641908, 648353097, 278919346, 599862024, 434026296, 691406628, 732351131, 646040684, 577655558, 749599598, 336634423, 672156862, 31922908, 879893045, 915083526, 518446839, 633471843, 191012603, 587632916, 853082439, 651340127, 319593310, 511775804, 900957426, 622028866, 590628102, 888564195, 612293960, 762305020, 520386561, 607149549, 660321417, 576363281, 846023834, 567040235, 197133190, 489673389, 104093165, 40086866, 17918755, 2392152, 213099706, 601346766, 513292702, 291452273, 956740583, 105500108, 695894686, 187282527, 172848486, 221584747, 623582025, 766298911, 922468368, 777286167, 496257920, 471348137, 478873409, 839731968, 144114794, 121853381, 142517167, 433601292, 767528663, 290212830, 440971006, 330197090, 443286959, 154353382, 461979011, 42841172, 48281394, 393166339, 466630300, 114120792, 662228320, 868987087, 199378501, 383791376, 300000700, 74068172, 994710139, 907560076, 624950271, 930967217, 839427570, 85535181, 814437581, 187826791, 654830950, 218291052, 44898062, 495996484, 948247443, 668460286, 927458726, 337068832, 43404391, 919469709, 679074986, 139489927, 857250048, 232363388, 798385348, 987171634, 580463922, 851252738, 302809929, 336800554, 931287308, 213835030, 94043937, 260469503, 927235684, 663912265, 200761339, 573300512, 253573702, 276576081, 550744942, 230664914, 652815769, 970941827, 317200230, 890409398, 788616540, 204489089, 398353634, 109165455, 767093439, 94434508, 943375896, 536539925, 336554795, 83684050, 347584283, 65065289, 344655218, 906947397, 588827206, 658028475, 906745274, 853391878, 351059477, 741390877, 262163043, 212545900, 103906668, 304825163, 157861840, 155824824, 915164111, 990588911, 878941007, 672303729, 9549711, 691462713, 65506143, 822525684, 806009968, 825570243, 426057116, 892505625, 826987225, 708916423, 573132393, 587711437, 420170878, 88791440, 867949530, 10720807, 368430117, 281259372, 732541822, 403648775, 50688962, 311598594, 277835810, 450937771, 533014630, 377308685, 459430115, 927009216, 885155372, 969537698, 863910684, 192646219, 69980122, 305311325, 553283342, 646157439, 116437022, 565376935, 25821708, 370865564, 371240057, 568652499, 561594818, 458529517, 155246844, 426094845, 161818190, 667943326, 328691420, 631905466, 417745632, 68321365, 742716588, 760350602, 683948656, 736603883, 226701209, 156582424, 667390562, 108088853, 898143375, 578124333, 291185514, 227759994, 92006381, 869859984, 85540243, 114172740, 663694219, 616915724, 671399430, 720383342, 523837257, 551510745, 687697430, 926760702, 147258923, 897889912, 681860242, 386217541, 395319894, 70084033, 820459176, 551221558, 960397073, 402908754, 589166475, 257950011, 323777891, 803471710, 636023689, 130581783, 288525931, 313893663, 794989489, 931387137, 425601468, 90414314, 917237090, 172451578, 504345670, 621692869, 565541179, 553102586, 202487636, 131104731, 196977274, 54114596, 478209591, 198546817, 479532144, 500536064, 765232523, 675423616, 511954422, 40009353, 554742961, 12064736, 648120371, 710422533, 579356311, 674444214, 293453477, 433978854, 476558639, 915647996, 385804196, 622379708, 159899705, 667738581, 640679858, 377069782, 60692217, 873039705, 449073823, 168931321, 812357652, 650557512, 972003363, 926356102, 76098206, 414044008, 502113113, 832608634, 283816098, 29814688, 741804533, 678194308, 942190355, 334327026, 752169570, 193261181, 526565787, 43000969, 390675456, 962509585, 443815046, 339618886, 993664626, 8565467, 679642011, 240048055, 508244650, 209253906, 915436692, 802435669, 321831126, 705751902, 793364073, 792028278, 58840530, 534007219, 515120330, 79098297, 680999397, 844372459, 644454537, 183513866, 171035779, 810315571, 270988866, 543045170, 331788810, 605583334, 580978018, 688571697, 40056198, 92022967, 479588442, 243899678, 872450357, 36423962, 389126991, 876887275, 204772962, 220896272, 370995842, 496076656, 762388998, 880675886, 603741332, 390253157, 288860959, 405032962, 340900527, 346619398, 843151499, 747008354, 53676125, 249291035, 420042128, 278659962, 984132844, 364293920, 546378986, 799466212, 607431356, 164598509, 187065858, 230438521, 704187982, 62787612, 333618215, 996039670, 808134851, 790317330, 461916693, 137672880, 562851629, 223692538, 950907128, 539433528, 23091097, 583678106, 66287124, 314161682, 933733599, 223094614, 830806470, 732869651, 643374096, 571341217, 426203681, 782107730, 107441263, 332969853, 557806595, 440336158, 893293614, 660318100, 874843403, 875438093, 176222054, 851087926, 208901932, 152064160, 434260786, 39222633, 767746468, 514771889, 676800378, 395359759, 642726340, 774480914, 948027005, 559224445, 607883849, 126413239, 183516529, 603464992, 919619577, 649097132, 423030354, 480951000, 161551763, 182155458, 913851330, 204428668, 288382185, 564536774, 348029884, 89219135, 499732980, 946987152, 326485, 751050559, 208621953, 266391091, 638721687, 787647764, 75669673, 343449138, 226202112, 667419173, 148313615, 431673743, 610153791, 85759127, 457857721, 16605208, 766574950, 678630081, 841838924, 921172755, 833952357, 659630938, 232327375, 462294168, 845145332, 294075334, 824474928, 82408522, 867745777, 423059460, 286669077, 654015790, 685056108, 247980762, 938939875, 990284274, 605069027, 87722251, 757452688, 656521622, 919260990, 214757789, 894721540, 135523629, 805490357, 301836874, 456590751, 214995679, 198734006, 740871847, 425620890, 369051545, 704404350, 582088001, 494171761, 856779655, 362646832, 828541744, 88464561, 824354620, 886291596, 514794469, 891186411, 844743676, 236931861, 946804501, 88134637, 145401595, 794636762, 692869925, 21124414, 276363102, 29521620, 158451416, 337178797, 656457226, 901845805, 197064410, 272071147, 530508805, 839915198, 332166106, 781426349, 884765967, 172246157, 596074977, 59532603, 959446476, 537003918, 114744423, 899573168, 488564742, 508969803, 817176229, 785893008, 855643312, 761692424, 619609684, 887355114, 309555557, 910002908, 407899543, 177298956, 94317704, 423787052, 987398950, 337882203, 598415654, 425757846, 631895307, 390569390, 89908912, 890165287, 69282820, 648878601, 80093915, 775944472, 935469283, 651648485, 592269839, 283761381, 812811720, 758663968, 157234433, 473551019, 653600363, 212571080, 102773572, 56369971, 726522650, 195351588, 668700942, 741291204, 185547444, 537466269, 208400692, 137391903, 291674190, 848884660, 292228851, 442130010, 479561223, 491937406, 555197810, 199338819, 183680158, 603368460, 272945277, 671784395, 228660027, 454476217, 900755615, 560314949, 722086695, 954459636, 289178654, 531825489, 66518857, 855199607, 592849604, 272106945, 708465382, 853829349, 172651813, 215875175, 987673753, 423334798, 141183748, 648648017, 480499874, 414189896, 747489361, 669956571, 201068885, 436005245, 542483566, 416930340, 559903155, 630135367, 550224213, 165268451, 590509844, 863422537, 755720709, 542857595, 62322078, 995725252, 482331409, 231114576, 374631879, 849162991, 805977444, 121936641, 596775457, 177640800, 263696567, 603196573, 111039241, 896736388, 529161641, 209008467, 1837538, 40108505, 210933827, 820566715, 463385246, 656436190, 450597609, 751400309, 827481621, 644887500, 953562363, 689459182, 47098506, 348449353, 166389121, 271791955, 202023140, 428864907, 721016534, 645014394, 324049458, 734228209, 106822960, 211020269, 665016103, 561552743, 838415140, 589813671, 114687116, 236185627, 426879164, 408489773, 480279763, 644070858, 857197045, 20450253, 454206002, 435561874, 308063647, 199494076, 948604089, 832130221, 510596799, 530327040, 971524203, 969578891, 11978666, 68520051, 85987132, 741913550, 190949099, 286905737, 56848635, 216458647, 3975716, 685494804, 167278513, 783522863, 591441568, 888270350, 537995850, 529104992, 179376187, 270002552, 787549108, 399912924, 594595325, 518007707, 749189649, 588683576, 770216090, 213010199, 14876346, 205751387, 511169692, 41081254, 74731332, 16544675, 911434607, 181890997, 651560876, 916730738, 989549576, 364926263, 111341172, 239966440, 712233587, 59256349, 224720829, 933683999, 172264207, 447733465, 297127008, 294659457, 385379034, 464166427, 386680834, 389939276, 528647032, 572683423, 969772553, 642240316, 534928145, 817558086, 403518561, 801777869, 239118105, 570812661, 356661486, 602975918, 230570319, 126684590, 666402244, 452510651, 201554963, 57258100, 978186849, 131723208, 204174445, 126849525, 125199735, 886950165, 577781251, 550689775, 295957462, 909969310, 115185911, 903376088, 452932221, 763370105, 722162713, 204046393, 956448109, 883201110, 565416778, 900228965, 935020454, 289988297, 758656857, 466363755, 710500458, 696529884, 122161708, 626747595, 587662015, 478692406, 582748493, 795301899, 227033955, 375547985, 931485353, 100006297, 639858340, 267003452, 356072541, 94561532, 338660860, 52286865, 705424230, 996747879, 179995181, 760709300, 663224749, 342509677, 877928844, 68406530, 671767517, 909159700, 663401102, 290405021, 601467970, 425296407, 256197703, 390839426, 893564044, 400572443, 309024395, 462576812, 91530291, 618128265, 909988805, 846636450, 453085254, 856562087, 329845259, 990251419, 131899369, 215850961, 38703929, 164807117, 951417881, 468564766, 25491888, 602235610, 162578057, 266184964, 92815666, 264560672, 746915115, 646060333, 471587702, 544242067, 183391487, 642027506, 165468646, 764342609, 192225112, 402498365, 166021337, 542784732, 837714164, 206262136, 603914886, 250831938, 266559220, 170444732, 447988470, 927652079, 585129985, 605840118, 962811875, 266931918, 423995538, 320951665, 447324806, 450905351, 897983478, 894391513, 411688486, 670297546, 572349940, 688889058, 114915841, 485053349, 884534149, 565235125, 164622967, 446837647, 273704633, 246747305, 793236587, 635776424, 259348799, 109568220, 842346508, 965539028, 496672212, 637971558, 520525277, 121681679, 722404857, 473657222, 486354829, 847875857, 155556318, 727731669, 365905515, 774006980, 734996063, 757069579, 598300784, 523141089, 159502559, 877927843, 313642421, 999030337, 738180639, 125084194, 835319635, 419782884, 340168351, 925921572, 321034174, 283887960, 571653707, 732571533, 743014792, 381939415, 627836702, 889269302, 7123991, 532740815, 863555582, 128410709, 776240688, 877751663, 467443492, 930693290, 749658320, 107687906, 206471886, 313260280, 892535679, 420928337, 6700207, 530751237, 763875131, 295163018, 531930456, 82736444, 74850995, 243456168, 467175709, 305834375, 23110939, 941737948, 976263057, 943612686, 366849260, 781708231, 882645508, 856981522, 843756623, 968468335, 493154696, 921444347, 302197286, 748803368, 36280401, 968549130, 830913972, 161629201, 169313862, 492944670, 366904203, 96733821, 295590775, 991975063, 579576006, 696605037, 534869666, 341760947, 686213558, 113398007, 812179402, 9682776, 956110820, 268531891, 357163118, 901032017, 342652028, 642653574, 175911885, 740857586, 272690426, 550603133, 743891146, 725459734, 119509194, 570982347, 639990195, 234028427, 859285082, 343545305, 109627190, 540768020, 399571093, 492348465, 591358870, 593721840, 477242622, 340095927, 853720549, 728554939, 596634012, 621721927, 692871895, 205612706, 516784907, 446169777, 677876223, 523391022, 580711196, 725059750, 940577720, 491790954, 334092300, 420412799, 413831109, 239160204, 724858857, 365063241, 968739273, 25933612, 219093357, 994902918, 355982220, 348375382, 232072079, 308487059, 775226915, 381468119, 440194596, 561358914, 291508775, 739696705, 430285216, 10854964, 17485309, 245760861, 666011431, 575928858, 829110060, 960694545, 988307277, 992890768, 618488008, 908460207, 684140504, 165924786, 858484516, 554012631, 3761159, 511149043, 820243364, 126687605, 286120599, 850499766, 962814809, 485519076, 569281267, 137208391, 951507912, 801958484, 210875314, 618602805, 7764585, 549008768, 529284805, 186797906, 223768485, 315948529, 278209983, 816084470, 895068959, 792680078, 783060164, 587396018, 391620234, 67226256, 959664525, 490215446, 614471780, 889611739, 2947612, 733525153, 99301596, 960222034, 423498077, 352704900, 491101194, 513499960, 515227671, 784323046, 507092787, 748053281, 695010299, 850772848, 382414274, 516811645, 529685607, 125863075, 872447867, 657684893, 324793847, 365873687, 804016356, 910048980, 859349930, 848979536, 462648860, 569218153, 338120604, 419264317, 136722199, 635205130, 602795399, 914430789, 381911346, 98543266, 561885704, 471651639, 588063367, 149008577, 398192185, 54143125, 86688791, 830256183, 893554013, 785066146, 713243202, 201879057, 740410494, 857891820, 409871308, 273743062, 323227406, 955175571, 453683650, 307771022, 655749257, 552676702, 50261171, 147583924, 156703224, 498824453, 107385416, 620012043, 563204644, 296545009, 677948769, 216829407, 211079648, 23535241, 162275835, 379126373, 933832974, 192227117, 277152709, 876958679, 606629699, 575530664, 513611251, 143544636, 721147031, 685209776, 59103633, 977436404, 934187352, 43981485, 897562900, 970454572, 263743344, 719718238, 596872647, 902784482, 638111933, 384562012, 13152662, 734108488, 162836899, 875245927, 847231272, 168294608, 358691204, 507540168, 156561868, 447761177, 446551560, 902452432, 572077424, 743802544, 586529095, 123132388, 390830716, 258704962, 825241377, 339136231, 597526157, 364104315, 709412666, 867960763, 54281090, 860686841, 429322217, 587476766, 723928128, 866240823, 935796244, 581971335, 861640571, 572724823, 564196433, 736990587, 335448542, 244330468, 16149090, 381279080, 475719944, 134000870, 786950990, 42538795, 922621619, 856153674, 784676804, 779432083, 944966004, 809872771, 179658492, 363844980, 35262315, 684494368, 662603272, 798108285, 772875761, 964731099, 717235340, 307885561, 574888992, 648165303, 444227459, 189274604, 449613683, 891789033, 722313951, 241636368, 691856650, 157336380, 871728038, 813401304, 826444067, 134899693, 262184707, 45394198, 636583592, 767841726, 788973636, 190805492, 701668067, 947829066, 942797307, 357513394, 569399509, 913383168, 812693982, 830652684, 453298101, 918027534, 701383017, 805962701, 54229813, 486928130, 412243391, 949052400, 574205052, 6134759, 963149418, 854764125, 394556274, 109293809, 858107157, 732802705, 343726030, 321362519, 969898802, 295784178, 767772528, 459959213, 391236665, 749852323, 738511374, 38488849, 132085840, 790802989, 640107690, 182327311, 604415298, 597363272, 944364779, 464415271, 298294470, 208684769, 322158822, 645181083, 941692873, 905383509, 837534139, 225719956, 864383054, 787565228, 464738172, 86418804, 5757535, 638122766, 557154114, 431704110, 930166643, 306662678, 652426042, 266633308, 170558694, 594308738, 283866500, 68295465, 4890907, 541415934, 53859063, 956847885, 408056590, 836360340, 881849086, 734652677, 499101525, 498535723, 236443961, 14981818, 711149905, 415239608, 540944963, 550642226, 573892021, 719644042, 955838024, 509522168, 149079883, 181123854, 78445414, 431372592, 246505149, 568475682, 240331110, 948831052, 910293618, 683023922, 758601660, 170564832, 992497351, 441415740, 486819129, 204281388, 195908236, 791263179, 275772860, 373456247, 546563279, 412274196, 235914991, 768513853, 91529635, 191417063, 482641716, 642221744, 758155498, 76759945, 101554244, 221595977, 146992875, 960980880, 978511382, 831214547, 958947521, 326554942, 310046767, 304371412, 102636651, 374906526, 507235420, 773368081, 139704538, 683179428, 281913017, 514213950, 212914419, 624607148, 475257409, 305311786, 95469178, 221236165, 465966867, 135170356, 481820710, 947548581, 734504757, 625355264, 712858897, 105631926, 318648230, 78491553, 804451190, 195160141, 908861220, 701240532, 876168561, 806605633, 732798511, 242135240, 899067199, 978604476, 736739838, 660926632, 44284076, 269523425, 432261980, 773982252, 360041446, 458447406, 341741996, 503169714, 495462843, 893781159, 697705764, 787885704, 700588347, 502046199, 436724369, 32136976, 311394522, 206374205, 720620060, 772511765, 660559884, 446107591, 987248564, 351185042, 330983095, 302705351, 676724720, 651449829, 332536483, 710839550, 479080962, 120924585, 478014165, 763043215, 67739746, 673902562, 424559762, 720431843, 114032938, 48815098, 497446326, 943601701, 505890474, 807901343, 80471019, 770080596, 470488997, 799222179, 611703738, 150647195, 53406361, 386349175, 713447647, 420450500, 123140955, 335626563, 644925086, 52277148, 274481705, 443956667, 763632631, 613625166, 667268834, 446034317, 298243192, 844806946, 3435530, 6557721, 807394702, 541762360, 167629595, 665474089, 283966112, 956838104, 8326734, 879306897, 607853878, 43740315, 819668006, 973432135, 877889420, 410205647, 134403723, 371421504, 536048589, 115821753, 982814601, 925353002, 403672333, 393335386, 634264624, 613859327, 854522609, 894702891, 393017666, 882739217, 2439369, 185899385, 535403711, 476472698, 857273480, 987979352, 511052417, 713886735, 990839054, 825074241, 20703582, 449967089, 849619252, 461766256, 420322986, 748270659, 602568745, 435349261, 703771232, 179315996, 692443688, 978953152, 889844498, 970949454, 561052353, 848755434, 705393860, 835300315, 692416320, 528631075, 789386891, 633502492, 588250037, 358074329, 561120979, 197562352, 535304952, 256436211, 822566470, 65507127, 180880207, 875053906, 75080139, 963973103, 142865288, 573069685, 119924401, 592840738, 965723151, 605016490, 866382851, 666917142, 38618313, 480952156, 957704608, 294623270, 982874980, 504615188, 424807139, 554481517, 613609390, 88200351, 871231843, 702770293, 504347137, 143980795, 768251469, 168693873, 259030550, 504214656, 104984583, 485291900, 351457871, 596812878, 689306583, 290349258, 117728214, 770546325, 623092898, 700681516, 789765351, 746241764, 145643518, 717046855, 529063505, 34903695, 827837316, 89002300, 521703943, 754262823, 273119498, 285603101, 116673519, 940414241, 422894594, 887016546, 683111905, 672868539, 820223678, 932985370, 807767182, 759380130, 311556885, 116735856, 278432898, 710280303, 145301305, 373705529, 666779925, 131685480, 43090602, 744560205, 46921682, 361387748, 820642813, 175356006, 809678317, 334015236, 259799561, 926254189, 171456403, 336302027, 633376049, 443972770, 560054872, 540282956, 878357710, 826595680, 449438050, 569586578, 45919126, 877047943, 48032877, 788900517, 858009017, 480055019, 507662862, 89895924, 882002417, 587449180, 383476081, 284019006, 62191056, 942856234, 379884123, 786557872, 776359483, 322773854, 412906892, 251741720, 253356322, 199702240, 743225957, 7417361, 475403239, 681343361, 198262283, 366041460, 222230274, 650914962, 262421130, 539869209, 869580308, 888383416, 708601960, 27872675, 732130704, 675604531, 296383434, 991358435, 380452892, 394633068, 208013373, 88106817, 948311198, 379733000, 815932824, 753948518, 662291835, 276631254, 298953333, 407960719, 420912838, 821835223, 835863770, 39109486, 189475832, 458779675, 515510593, 657434470, 50557480, 822917168, 332349875, 106685171, 457121662, 935797655, 269954277, 99021484, 292364059, 46117793, 23497657, 242988342, 372596179, 963747873, 683209104, 903117467, 832018610, 168776511, 593176380, 809422276, 447202941, 216255355, 104746102, 58412390, 264106309, 915813574, 379243319, 155011886, 524169630, 34902394, 377006491, 36390884, 759767951, 875182962, 870435384, 970106213, 644157742, 919515729, 698405807, 323117785, 946058120, 812907422, 161972835, 95131406, 354764122, 853500818, 765939155, 579408028, 714781013, 524174213, 432912677, 768371166, 755469585, 845269289, 888473495, 714362686, 426919235, 104769678, 37170452, 636772483, 637953094, 314534441, 535045562, 472538170, 260151658, 792163578, 84201055, 563621787, 790030161, 397809898, 744458177, 45693357, 272169949, 735532259, 342072554, 517821159, 642304357, 646390941, 180220329, 287532236, 824948823, 590095955, 323133307, 26162689, 124623825, 284345347, 595939708, 200396516, 792442377, 245984092, 931591074, 528245412, 18742622, 900862408, 201886575, 129421616, 649074423, 554743461, 419908815, 983879348, 496479151, 913580314, 923942829, 127879309, 263677376, 119286907, 266185999, 123980053, 510359964, 959426947, 15038875, 843131500, 844456644, 99654054, 388697792, 659702556, 876057447, 863837862, 677538602, 430168989, 379892532, 670754654, 194616504, 101041782, 461018132, 727259067, 350637667, 313779126, 578950147, 330946858, 687847806, 601837224, 727431195, 907721789, 706846398, 54724089, 414984239, 964433314, 790566310, 352270890, 418281209, 538077301, 77853653, 311675672, 501330162, 616227996, 55857905, 181268782, 842855574, 591472293, 332008150, 201676908, 173901715, 687199808, 609005845, 746161539, 276438053, 903935118, 844251266, 67777197, 171604057, 503937858, 96818302, 588530286, 401705426, 549666512, 175188421, 703515244, 767922343, 656001598, 682012366, 501939714, 938114243, 989507263, 647593350, 671355895, 720439608, 500655292, 129781503, 371081327, 223053039, 707259117, 352549649, 531741355, 389608901, 841548806, 179065648, 688177513, 13443360, 479150442, 712216911, 324230034, 249848996, 97257424, 772247552, 491205813, 965265249, 310366393, 576287822, 363369942, 620669846, 611547140, 95088994, 974452371, 156733641, 174653864, 679649192, 496399354, 544811897, 664280931, 748847425, 592855732, 292381455, 744751371, 453542326, 432288419, 42542599, 850039497, 729577357, 350036166, 885708852, 883039308, 680922053, 527766822, 197392345, 665271541, 283540663, 97255770, 605739361, 887705105, 368959320, 535327606, 618447539, 501971561, 680359983, 85142424, 93294231, 276229978, 429489865, 589806127, 694645363, 901738830, 653400333, 301905406, 256514244, 927501626, 726437805, 401870353, 711639652, 38061240, 650306178, 512404172, 443612477, 562253771, 141220840, 982455176, 813906345, 245530537, 722617915, 573436742, 423203782, 362268912, 145682782, 81521656, 255571254, 84836064, 339925969, 195146805, 753119393, 268782453, 497254445, 428577139, 115153684, 986083055, 262128159, 622119306, 884725754, 367854589, 79445943, 914386644, 515740123, 12848723, 681897594, 521300552, 491744013, 625915668, 832742318, 856283268, 620644859, 612802308, 420580322, 371393356, 105156178, 126427399, 971454805, 110893848, 856358917, 146580275, 437777808, 789290619, 302353813, 606797976, 945093900, 467346552, 314065321, 401334439, 895171844, 557732338, 826950276, 708981492, 212489497, 894124798, 195286392, 555589775, 569060167, 509353105, 895880262, 89273208, 124414109, 648089744, 503705343, 562832305, 79358499, 432088478, 279563492, 659227423, 227207098, 564731818, 928488620, 82291769, 430065927, 745276353, 479054723, 552474782, 135652713, 81923506, 185524498, 22223432, 524889167, 542014017, 200389257, 980856565, 752263783, 615874229, 23358047, 630578913, 293738029, 370132593, 863565752, 896938097, 957699142, 133239064, 909739725, 619179758, 299359696, 94717937, 617279732, 344421537, 861337658, 640308799, 422514413, 587277228, 516680994, 396614772, 12688038, 970909784, 169976438, 115076529, 685553149, 940766753, 785974964, 894853405, 909674855, 771179387, 292719563, 252560928, 603430962, 41185144, 395545394, 424201732, 213796037, 411515261, 662791869, 402566722, 19028872, 893469204, 946365569, 422334720, 586319968, 944104564, 276704567, 19365386, 777767339, 476192455, 984275562, 100505944, 477296312, 526289876, 919566104, 41704611, 384256858, 420115383, 55299519, 609393829, 492177706, 571503332, 638105297, 359016441, 551415066, 891264501, 957955975, 262280336, 95774379, 354589369, 354436349, 329370363, 604462517, 152181597, 585948006, 768001877, 197591462, 113772770, 200824092, 801512450, 666826574, 129887448, 539354842, 692898978, 898777957, 746171888, 114228911, 749909865, 58131628, 559901739, 481927146, 957714501, 621160595, 367070008, 364366094, 740802269, 443075082, 860073672, 524025861, 83828494, 117050121, 956761809, 326331114, 98263133, 528241711, 270041853, 900880268, 582403589, 268018804, 645142698, 629759811, 969505068, 81102163, 911150390, 341950494, 531806854, 293366898, 101540694, 618431679, 55610735, 97612724, 622600115, 337692547, 154702319, 979848185, 991415053, 904980093, 837821750, 836535750, 292152286, 392416643, 757656954, 193887434, 747356951, 54447187, 446667107, 989629246, 503789600, 770178893, 61200367, 92018006, 317952405, 250462514, 796275460, 907287339, 990615055, 453129463, 999666344, 441494239, 210121435, 952043707, 777274530, 549476196, 303229886, 883125657, 553432430, 630996399, 223297923, 697869339, 822824987, 250678837, 377823153, 722986677, 557178568, 945910492, 34509712, 268161810, 237553991, 652619727, 309611085, 354428228, 16922611, 174145594, 867755824, 113222976, 933526479, 815264017, 196929794, 774831350, 875996236, 666105455, 634379579, 929786415, 475435853, 494295281, 31617341, 326050439, 108822816, 788465425, 736801084, 783133446, 224555035, 73442225, 434368328, 102550564, 425042865, 466897291, 322096428, 332432889, 110296485, 230683836, 825245799, 20000306, 137752834, 767140108, 345162843, 728805647, 695300422, 289459775, 528213371, 54338145, 975100530, 5469376, 945183470, 558730691, 938387375, 870878923, 909439268, 454545045, 995769646, 948660498, 196271911, 649421454, 555912655, 279158504, 660750130, 698251990, 138235502, 214907563, 392061271, 970920005, 116783655, 536787280, 883781401, 175091412, 28513104, 590487326, 73164255, 897988861, 844442202, 838714901, 590224351, 541933756, 380983323, 296824596, 612073210, 290126365, 26231149, 454874165, 83922878, 345267629, 117162324, 165263054, 54957177, 434728416, 622396021, 515336875, 804656450, 725634642, 44005539, 581810065, 770589338, 617446647, 500266513, 868605848, 181545878, 913732011, 740501170, 884609069, 912173953, 294756199, 92820653, 151784373, 649318244, 704190866, 73865561, 879593312, 866794675, 537209498, 952017655, 945499395, 303539162, 224672906, 877972112, 793564784, 725949969, 83331019, 964893890, 619303089, 99308785, 886828259, 784862603, 754209456, 401610828, 146957020, 183635295, 176177384, 914482595, 313044074, 444393738, 527376204, 135793039, 564258849, 113563887, 945694927, 850119962, 480583306, 852582524, 369817799, 386276316, 391971242, 413467370, 341925236, 41160271, 77995631, 457742749, 242082479, 460557811, 402892902, 508445698, 784877670, 716706384, 542400334, 608691160, 807521658, 899175682, 276534494, 117009205, 524920298, 185145801, 404848824, 805816488, 828127560, 559502355, 876598318, 554021502, 537682866, 722275770, 515769229, 586285265, 988398906, 69081042, 908408497, 729903917, 643154286, 366642708, 237710428, 214806057, 587747798, 920084104, 193782339, 715119912, 815546963, 679516554, 250031307, 753248343, 150067871, 101398258, 442902548, 540675418, 840676832, 538073202, 382932860, 131368505, 114596601, 772637470, 394346313, 513864427, 67757792, 519335150, 35976463, 685299275, 491610245, 237159932, 791001839, 503421217, 655326503, 56940744, 717687557, 466713437, 967318126, 759053485, 25982249, 267794135, 90036824, 946748006, 904882662, 792154194, 721516254, 5033496, 148316973, 549751264, 872170377, 263534470, 350495396, 858835521, 520337972, 549993702, 594865007, 551451460, 835444212, 35411503, 100588918, 836301737, 951865456, 898033482, 258191820, 237379674, 518949246, 543521364, 645830600, 726649864, 816589295, 144261314, 540942463, 388934186, 756130000, 430815642, 444133628, 51110565, 556960080, 977601497, 475402651, 318640115, 919833557, 999540048, 666911823, 578788552, 712646789, 606155045, 315957919, 611558242, 830779486, 899785113, 141520882, 229256430, 189351926, 253988084, 639150349, 338755549, 780170557, 900067992, 869974927, 356362707, 763181642, 772337851, 64407878, 461755398, 148160648, 136717618, 774406083, 123743001, 13053951, 530123642, 321409307, 601134394, 11509506, 623512605, 755311945, 8729651, 786266519, 616966802, 562940719, 43068689, 348456894, 613255038, 227637574, 77191866, 141422486, 852836081, 422270152, 183862940, 508024542, 523108016, 24065295, 81763761, 936507643, 604782835, 325619579, 555536147, 389468916, 852850022, 463619686, 350013386, 266799925, 402486639, 658333060, 242272308, 977346101, 512067029, 940316969, 458342389, 625723590, 532896036, 563216081, 782293872, 412604477, 460669008, 576360939, 77225258, 104397243, 338860579, 518691162, 478420792, 615598955, 807336748, 66938803, 269861663, 262584050, 29537080, 539723624, 923906654, 114249914, 527538521, 75616194, 78861878, 729282509, 201902083, 47898480, 306823748, 758710666, 534610947, 253428178, 729860495, 193562801, 571824854, 865636939, 400546178, 883760632, 59459461, 739549850, 654714567, 598481808, 645480036, 118321956, 590823532, 126971334, 895090892, 852109438, 756983145, 927818933, 681510015, 100675898, 950889755, 732553576, 29009683, 198743990, 988409598, 847548298, 470791501, 466383616, 645918273, 283786744, 332122336, 573818652, 264969545, 172930749, 359034479, 755122621, 714068949, 327884302, 28110713, 666094913, 942176122, 456090212, 948505452, 220827823, 303297991, 267157564, 657668093, 937231292, 242794416, 785313774, 130675842, 964390123, 845983663, 363035361, 486814993, 803635992, 143123662, 599438463, 159881363, 163879424, 540116727, 16069181, 28109593, 536254894, 176015775, 516103568, 268878721, 974348846, 370693263, 103148815, 906339959, 502476208, 879295795, 884630682, 962002513, 95105564, 878029778, 933135067, 881768812, 15597735, 195395927, 750569982, 718281710, 20907704, 259175761, 268606201, 518870844, 308350951, 279113496, 182548221, 465944337, 7007321, 166659063, 108637788, 997153104, 70163367, 450431724, 776834689, 553715196, 529386862, 118539429, 63495736, 743161509, 60824796, 324099, 219756489, 251114490, 698257333, 243151823, 961601192, 647576310, 997405603, 266498000, 960178066, 173923187, 688880038, 781223640, 511911795, 233864008, 885449907, 888475972, 229450166, 675554390, 720489235, 468416730, 654051063, 771203786, 236123276, 769579020, 5021025, 58958551, 728041207, 829008071, 367139711, 912224069, 322809747, 509959190, 120403771, 815510752, 478692317, 209568663, 632260948, 599161742, 912499515, 383490696, 751484382, 421317805, 153907930, 625083242, 78116478, 895379416, 278948973, 123303206, 880005261, 158551740, 569703075, 235609430, 430089458, 716340133, 921523824, 427856280, 825557827, 805383400, 935317023, 263532298, 364497945, 148752087, 456597032, 512053844, 316712498, 307888456, 76270406, 808320337, 201608328, 22512929, 170575250, 714560253, 362999615, 366857303, 821386857, 185137144, 246984606, 283920924, 586614519, 461481232, 589429867, 94954045, 884335890, 68556860, 295219831, 433270533, 678114049, 949135737, 982173592, 678293121, 475073872, 109555184, 13940307, 16025120, 771270168, 697508327, 696683054, 259986157, 867675701, 509198862, 714899802, 471839044, 727796914, 216910277, 137281512, 810979184, 648609473, 866112417, 927393678, 702082569, 676374485, 369345718, 231277901, 526055793, 384320473, 268499302, 222169959, 20579137, 666898212, 898263660, 138146246, 791470432, 167010139, 488062056, 632253834, 640569347, 297287614, 728967195, 828904869, 201332615, 875003566, 919538028, 408106446, 303641675, 635290944, 38652343, 839738901, 685977388, 718612869, 322384854, 686092873, 129866682, 631895717, 5040402, 620928642, 305227758, 210265664, 558847767, 327144377, 386634268, 123069666, 416414428, 161478804, 980873341, 453002043, 521915880, 465253352, 275860548, 547377694, 890572115, 791874871, 90246937, 28042740, 847592754, 384380973, 975364734, 964161474, 610192132, 465948459, 491236702, 378058058, 335047674, 513543487, 675933871, 107473098, 707777764, 849814982, 208248959, 874694785, 175756681, 249881996, 955867618, 958283628, 128413486, 778006843, 35047508, 774435542, 250098922, 849119845, 686148950, 72082738, 162322078, 20151846, 750065604, 569606461, 542617283, 218201692, 395726788, 934080478, 193086411, 183769031, 896991250, 48633266, 346052590, 598849631, 300963565, 830034537, 384408876, 512042507, 96891523, 724870593, 311576620, 309936612, 476100044, 614453031, 98881689, 115169634, 968044884, 920094881, 403965297, 920527191, 561732568, 813717974, 325588651, 677478414, 638674684, 642194995, 488466945, 459322815, 569286872, 17986993, 689387042, 206408798, 914726623, 286243114, 891679801, 620512332, 314727961, 220586595, 255151454, 409744474, 978278653, 269408700, 39912468, 684049246, 371119786, 494916321, 940011002, 954781895, 15974389, 41678315, 289385602, 106948325, 949484624, 595523305, 970038712, 655781385, 865668416, 381640700, 289550339, 770494593, 123537352, 918483016, 263932016, 580455826, 243352379, 54350207, 773577000, 28442445, 131385663, 873275154, 137547346, 265881398, 282531649, 273066219, 13820321, 656395, 545024779, 725625603, 410098453, 349111104, 737347513, 464867784, 523462897, 843252954, 646563639, 973754569, 649076731, 614380429, 883951965, 807678110, 837891054, 667044471, 288547609, 434892646, 622484740, 819988081, 615891169, 664919282, 646942271, 38700582, 45073358, 705051936, 613649322, 294817105, 649303935, 869893767, 644060631, 168698439, 301166645, 961683626, 890858953, 796212510, 509623664, 282101875, 48103672, 10336771, 76349320, 822222146, 198781276, 99767622, 134518288, 67542251, 171372917, 466071656, 588655195, 504709485, 516339643, 646159464, 125124643, 567269363, 320422802, 165485631, 889021727, 367576612, 775084146, 296271075, 454351539, 628898974, 193263298, 267364928, 675710094, 600636858, 288875742, 299893679, 967007827, 465850831, 698796892, 24331031, 256331694, 187913781, 242518349, 838295206, 905863526, 548244155, 142453671, 179187806, 230783743, 180223948, 36817385, 169485222, 797863081, 806766106, 286368698, 47925533, 890123777, 480185491, 501602788, 359957959, 352255526, 328122050, 108695279, 565907445, 245539089, 651931456, 240651908, 927242392, 172756153, 963288144, 400241836, 229374718, 518396332, 946975210, 935644105, 595061511, 805835206, 208812574, 694999253, 181419255, 715652893, 513623928, 25852624, 215511311, 673413088, 456973799, 111485473, 689354243, 482221091, 633547668, 613197235, 135356431, 530389303, 925061254, 969671857, 286172811, 615521, 765377626, 103695229, 406684403, 330627136, 147714347, 110842368, 984239830, 687239009, 419025842, 891880186, 267974244, 848902871, 924809676, 987922211, 475098888, 598483876, 730157576, 987236544, 103277657, 839908070, 337831129, 981649524, 36752824, 964064420, 759003020, 699097080, 303724992, 660659397, 930873106, 423245234, 991108189, 408909645, 259284262, 570110059, 550860345, 66003953, 754403164, 14738462, 338450262, 324112592, 897143161, 429105036, 542050599, 543745328, 336165930, 662250626, 798384633, 837154862, 696765949, 815323812, 527548364, 233841674, 596370624, 467124750, 842772370, 758772580, 653841675, 315487963, 969940458, 478888013, 773627446, 159466718, 468617473, 602216315, 40209143, 828752178, 548780757, 81959231, 237452773, 439385413, 681327725, 560286344, 893308832, 139845846, 159248001, 541802282, 644658103, 513740592, 521078919, 622736910, 928314395, 860483068, 59944630, 744671243, 147813142, 570473797, 73121330, 969310929, 667719626, 460671344, 342799387, 520864912, 614825621, 71279945, 968647574, 209611783, 499416591, 816656824, 312072098, 731736440, 444501678, 316465557, 506538744, 653100052, 698987239, 187264610, 754450927, 771977219, 118398515, 866830902, 558400947, 391693299, 329047013, 142137976, 853883260, 633699402, 553631058, 413581862, 602344323, 859488518, 454654908, 167715713, 633311504, 4329993, 177052375, 159422956, 676509149, 358947519, 361771238, 484553006, 376285616, 488426956, 769879446, 898700521, 523187278, 309688802, 402987526, 937935199, 446164612, 927992190, 531929113, 953593698, 210419892, 345425675, 706545325, 293800908, 434933715, 705685011, 831422969, 768503464, 268685125, 350073408, 444688095, 119098901, 995564002, 159079423, 527159012, 288943291, 339762209, 39219530, 879102660, 25261766, 318423475, 784468347, 488662015, 848855073, 114119605, 829927670, 906963459, 722056754, 256455323, 11042442, 418133051, 238486818, 272523758, 677532529, 339791580, 328397968, 38813366, 917412679, 788763945, 744534793, 602882455, 438655669, 592202514, 432018939, 99304301, 481899783, 892577485, 346528272, 399713367, 381575710, 210997757, 978910805, 826061502, 642333104, 903378642, 735748562, 250634230, 35082895, 995534104, 521519862, 858532205, 283033654, 287713090, 540869345, 912120408, 307756789, 707401398, 235960352, 310670757, 381361438, 446111130, 597850076, 351727071, 209732050, 823829591, 440096645, 929803050, 100581656, 784390633, 897718757, 745878161, 571513732, 595173825, 22024999, 613443156, 565943085, 214198612, 410747770, 4393678, 343383081, 637194211, 746094872, 617188103, 403896159, 129020889, 280033211, 367494305, 544836797, 107087833, 310726593, 492554415, 866599152, 834053287, 174712165, 510929023, 799210071, 970005057, 703619560, 349230571, 386548850, 173466383, 861464558, 398507958, 198261312, 663103918, 277962564, 384245494, 515917238, 387130592, 15185473, 826225432, 519111742, 907070747, 928041609, 989835477, 993143335, 386452438, 480997763, 924198499, 581015371, 96999753, 195285324, 292511370, 13691222, 198251211, 641548716, 902742446, 899661024, 295627347, 7774100, 36843177, 680695286, 656621483, 815860735, 56787327, 295083700, 581002716, 508191077, 214378644, 29919182, 612197568, 190453386, 579126342, 687022603, 676175556, 107893505, 585775862, 340479641, 934331638, 673189115, 267699008, 815947697, 500654268, 924215795, 481735477, 750301105, 575381485, 51314432, 507056344, 76312154, 741304764, 492424428, 949743060, 455799063, 854210119, 756688716, 287321123, 801191462, 743616887, 606317427, 716673506, 99175298, 388130399, 852760801, 67548037, 533871791, 138065046, 603806942, 270009553, 24788609, 769979831, 963765754, 854933229, 123938033, 151880986, 196119572, 393718097, 600228588, 626784440, 613892731, 852276551, 168695150, 569144118, 440188887, 339267731, 801954227, 87980362, 307669209, 324265743, 313207816, 812952533, 190732393, 389108348, 683014099, 434162812, 510989949, 10455035, 712071639, 41927045, 236941969, 667282114, 738759152, 136811646, 182134900, 597654320, 283547868, 183331754, 604449275, 196287865, 952377661, 235877585, 69793059, 936417638, 578010408, 505941605, 118724218, 841856174, 559961526, 262507201, 28183342, 915802242, 272231425, 352605406, 988579327, 567031587, 644752941, 982697519, 455117002, 709904728, 732888224, 564318682, 92415899, 365758329, 555613081, 469036365, 515853951, 881731910, 355689967, 35400622, 772208877, 462721377, 950872658, 326520626, 129527421, 102043028, 275584012, 117938554, 454577421, 35761433, 402703189, 995838467, 877685901, 989001364, 989822918, 341788438, 805270224, 776348687, 305321272, 224490971, 82824493, 477525898, 828720382, 674248060, 254605666, 140115463, 234910688, 352723771, 162106112, 173277426, 873785964, 302875472, 530884254, 856496823, 170009947, 418519828, 214773855, 66694933, 655892651, 937803111, 824247039, 60469550, 670403104, 243697872, 833374314, 804939906, 646691348, 706106620, 562737363, 266420966, 326348426, 785752188, 319938131, 220856434, 583421765, 629536635, 464221398, 965928688, 80941561, 880256508, 59533190, 541121174, 961874722, 681240506, 135876716, 847720387, 331533551, 500358370, 631465290, 162550014, 179333816, 124729814, 490569317, 169621751, 389027200, 584818494, 925898118, 726563203, 207533882, 939184580, 414998546, 757044447, 482966789, 775885618, 825759326, 667059478, 335161402, 121303013, 468694260, 436684728, 440112046, 912489767, 991945258, 878977827, 297592448, 229873184, 934582653, 276886106, 404595585, 798724689, 432831878, 204957007, 512477105, 968310334, 161893816, 305660243, 76031398, 218560218, 166289683, 492471418, 508511565, 534632747, 978772490, 217888523, 516166747, 327602573, 667439717, 400308550, 564323373, 462430951, 695087145, 870610682, 696209747, 535661901, 288195888, 271696529, 365831959, 128449397, 754673813, 824157284, 122047530, 609425976, 282155586, 779247181, 139682422, 886074465, 614049244, 532513474, 632385098, 433557506, 539088976, 964094385, 859547485, 775511738, 998520140, 906271855, 160822229, 228630425, 266336695, 990006161, 670760543, 377920834, 312337057, 117342590, 758406254, 118678446, 472626395, 854157876, 768150937, 372284334, 411622286, 380079304, 519853658, 266868294, 678770419, 127194068, 226208481, 926283176, 518982101, 763444392, 970315492, 279100192, 106531472, 246867794, 312178030, 181137109, 626056839, 897438637, 337231267, 595236193, 169781112, 709727238, 2404335, 587646906, 241312744, 475121074, 126638233, 43750901, 190961470, 197683801, 898639298, 520645750, 548377737, 504509840, 883277913, 325725253, 536102691, 133204372, 528150152, 669118207, 560010641, 549567897, 451461555, 64445877, 365916347, 52187043, 37348806, 619405376, 554415420, 491152337, 169530643, 557011421, 102976844, 671178427, 300033763, 860857043, 346056362, 913657182, 575320401, 295537929, 44638954, 623402325, 151189121, 150812084, 580583140, 636908315, 564757183, 535047453, 534480583, 910744572, 120443999, 103825461, 172039910, 622058361, 116342755, 608857071, 663842303, 797875569, 905066407, 153038357, 51501796, 642750442, 890782999, 574721189, 869902447, 262705491, 555165352, 611685749, 543988678, 511858900, 313668316, 119231085, 139068771, 744797695, 115730419, 894842788, 385080437, 874336296, 759541995, 766888242, 104394052, 470029250, 130950218, 100763077, 194670875, 51732648, 660781126, 414911004, 312933626, 638097883, 83752013, 961359349, 332292311, 228530385, 770842018, 450205126, 745606528, 203176101, 173215007, 44192482, 346038041, 580620201, 843768484, 993737295, 983047267, 472661947, 313988640, 726127305, 503896081, 287038365, 743616697, 116493365, 893586988, 975871154, 389090078, 44282382, 711163133, 332964603, 953078839, 379336225, 871608406, 292257799, 558513896, 462237549, 187544547, 931102744, 611878299, 935842645, 218003379, 221249410, 87716058, 704124117, 450238796, 239592040, 6163906, 134060671, 222683998, 80932817, 987756859, 905518721, 97715598, 881024781, 93815653, 262315285, 21237407, 740409165, 879777476, 288443276, 362681196, 310351286, 457328852, 321065470, 969966833, 629113386, 857821506, 194132604, 917205250, 206561862, 132669230, 753248289, 531153744, 551710360, 745556047, 388411963, 990704251, 525024121, 595542071, 259016055, 846934952, 628104300, 170786860, 569753134, 251932198, 474934561, 822220293, 58893916, 139413385, 59550435, 577989527, 426503501, 218697235, 496987686, 553320441, 937410535, 318841122, 662189738, 594214724, 219692569, 166920022, 533738538, 543599514, 112170287, 467980155, 788872031, 674047323, 61679361, 889485302, 902029918, 631430944, 461652843, 99179295, 353932859, 639109227, 907409184, 277158876, 745498322, 208135414, 165293010, 943077192, 102330773, 402838678, 473628925, 225624155, 112952074, 122456005, 643247878, 254625231, 938109435, 174038348, 725962347, 574176002, 897490630, 712032194, 624190311, 418315254, 877183639, 653561457, 188415438, 434825812, 580674239, 643157768, 745088238, 49099591, 623461665, 517371837, 836187721, 658299959, 868761786, 621579482, 752270142, 749484537, 925920870, 606358978, 715138076, 221635759, 598806895, 121252274, 355945380, 663704656, 808985193, 963774738, 928493669, 23359480, 128009523, 907463167, 720348205, 202561132, 547922269, 64116699, 978651089, 103280651, 103958256, 139446405, 545510975, 894434165, 340813008, 849766974, 236899403, 739209322, 308744873, 292860871, 246553646, 292260452, 937593074, 627988473, 710609029, 127277716, 521061486, 202648890, 279714275, 397747257, 336042605, 445814743, 542846330, 203875924, 641805726, 764964368, 756047465, 930893685, 976156315, 738551559, 674104950, 458071693, 226327759, 691174058, 650708951, 804577595, 700953692, 324358742, 851561241, 525876722, 259767412, 194108780, 175087487, 652414855, 369190471, 206589816, 650528581, 982420218, 820847557, 893493960, 418250958, 326066571, 310342544, 926989870, 198861450, 973807903, 867899122, 349909807, 369804296, 783177320, 790650074, 483582415, 559758821, 330783704, 726027070, 335418815, 184087206, 710152291, 84308349, 16163753, 447073488, 964422222, 853918992, 742182668, 237382263, 443793083, 168979468, 87955493, 763123531, 43755888, 660412469, 109840759, 613135949, 258764161, 295632924, 71497477, 782910665, 881768499, 258602668, 760642902, 697020525, 984007170, 580343776, 644459076, 936380808, 265476670, 141637629, 719537675, 336075806, 669682752, 607634683, 882306680, 786576224, 648976290, 159625908, 339277403, 512019142, 57475561, 675283678, 932440832, 393996992, 223266560, 672070105, 992444184, 776142276, 525802188, 92402451, 316917589, 439435182, 159485455, 355403676, 455854719, 719342853, 901250443, 107189806, 540578959, 156383325, 806430119, 156804070, 205692686, 458047306, 892953007, 251679769, 911745260, 770758457, 601251591, 14889869, 335407135, 852943874, 184979448, 606429595, 445703829, 770578772, 623273301, 314782547, 604668397, 889211095, 816929832, 971181444, 396581892, 602303848, 479840663, 892872289, 652693674, 335983401, 140433192, 358206507, 65904764, 778741199, 139341771, 873758590, 937104830, 731330318, 254544322, 576334298, 564725120, 600597258, 534325421, 163587478, 256069389, 751839124, 736870120, 515181795, 776624404, 260547800, 152513471, 25610298, 204051730, 591753307, 133415965, 75447196, 951487734, 307848605, 246950977, 543554146, 925278241, 992576349, 43908370, 695384579, 665702226, 806021446, 986512936, 19933213, 618418406, 113428919, 252157143, 60633841, 434878266, 599668465, 346807626, 657418683, 43939091, 883185126, 112447671, 933198195, 61723675, 469468211, 283437798, 531230066, 785419230, 598330176, 619917124, 554750708, 120164442, 778851181, 948197743, 842489566, 630341398, 879579555, 88211305, 913650670, 294358057, 293726974, 146788258, 224543923, 566326195, 629507782, 326229909, 743555763, 429469133, 526463105, 489007886, 657016982, 346068060, 431295410, 964949737, 604151304, 767750586, 154214684, 27639054, 509786119, 567234980, 694550447, 473769702, 667620843, 185920251, 458837782, 57112603, 567531941, 113176773, 285924593, 31615065, 864432567, 464491816, 628378314, 835224770, 8738197, 47903183, 176268964, 545697477, 960331761, 680123426, 515920725, 671658564, 524655903, 863751568, 870777397, 369275220, 40365702, 552629140, 33796004, 758519573, 652358616, 737152009, 15698048, 360243099, 557647558, 988239341, 609568987, 161427786, 375213264, 530496919, 158540713, 100097263, 615844828, 690476824, 836602979, 216096791, 863438947, 769820119, 366035072, 290023973, 582026359, 68795206, 584474215, 324434176, 812702462, 927239676, 4919858, 845073590, 723882592, 713238615, 786517068, 570622564, 854461, 937475754, 543256639, 528166399, 412919053, 335715549, 750458611, 579624219, 961187760, 38098786, 595982655, 645333651, 798154662, 977782093, 415939910, 695685728, 634737944, 577323942, 466809330, 46478881, 241182860, 878537445, 805187349, 939983174, 780085122, 506265025, 76910412, 641351026, 446704939, 31008044, 676759035, 436028265, 640008735, 718897626, 8264660, 901359633, 88061292, 229851235, 501341398, 198784535, 939765554, 40920736, 851514772, 447178450, 615511582, 852462315, 90881265, 994842553, 255334399, 712928339, 558162561, 19441615, 85303014, 919463369, 160440758, 920380895, 537391721, 723677260, 248182994, 553240109, 16232147, 241140104, 162867027, 892143828, 16686876, 877522003, 418068565, 748372358, 453187061, 502410111, 377244383, 755654713, 758194635, 45442616, 788515691, 473279668, 151928084, 429210130, 691893422, 184224216, 826204367, 409793548, 329993902, 416826532, 221954512, 916348470, 135310146, 620927892, 935792951, 41617692, 272766527, 557682345, 41851285, 531805280, 782427514, 99947353, 39154456, 42879693, 254393795, 45527693, 1648754, 508233266, 405328315, 23721562, 161393862, 914515868, 674666908, 39631238, 456076371, 550668159, 741944340, 858876977, 224097450, 766820507, 842476559, 872046857, 173540395, 614045316, 481824967, 298258460, 961915477, 777335341, 274907482, 300560889, 975546304, 283178400, 765659699, 413081105, 5046767, 329111660, 856934335, 507515207, 77527692, 103103681, 437326910, 727332165, 272793625, 542875060, 911566384, 259257642, 576529630, 495497369, 585843950, 983860567, 247149055, 732382989, 555171587, 304992319, 128094643, 88065359, 186844460, 897389955, 304169776, 894332593, 36705433, 597481738, 662061220, 653126585, 41250676, 736008510, 609132758, 73097924, 284626891, 871047993, 437135457, 891993697, 373046526, 93100654, 211845738, 344182629, 937775148, 829471177, 527109230, 297037980, 947667875, 694863940, 220544084, 63484848, 251523329, 645469717, 507181603, 449771022, 123724983, 815871999, 585072929, 291619428, 203097431, 430851739, 103010805, 204684993, 498146390, 177160878, 78557884, 3873724, 204707100, 341408443, 305242510, 337226225, 329858970, 484963749, 227628041, 671752547, 759347351, 295096215, 352210496, 453265333, 633145845, 215675520, 899409702, 749930504, 766988222, 906072540, 621595342, 339141355, 10171152, 75514235, 290921383, 624851610, 748750634, 831651963, 575463865, 636289817, 348451452, 415384645, 618690884, 548481371, 636727243, 415142053, 584824694, 6245164, 904956257, 675796619, 390117876, 823370966, 206013047, 20442158, 621551433, 481688576, 836522490, 603272947, 800190719, 192991743, 549546780, 219679336, 703051820, 999183858, 204053462, 518360276, 767290548, 281770257, 664028390, 942387951, 280525398, 326558547, 828187412, 765485088, 130759621, 135907725, 829161063, 93255685, 740245593, 685188703, 557096229, 994366533, 793741869, 757278752, 924203870, 905664285, 496215124, 549832224, 984144368, 483752566, 245424159, 10469651, 383501844, 543660364, 634007704, 611617795, 570060141, 865796960, 288231236, 266844235, 549192862, 259000703, 163211192, 947063938, 950669940, 149116626, 706323695, 649665643, 544244683, 616567506, 35010848, 516713494, 729863332, 343277138, 927578676, 382098808, 543437556, 961201484, 321406841, 869862924, 278348871, 416104271, 527329348, 853625392, 940917014, 244842020, 24807004, 670448207, 963747580, 170225807, 93566286, 468362741, 277395227, 427392118, 521227269, 738386738, 259978301, 100753816, 74120057, 97818983, 921546327, 387803397, 804340537, 609169641, 804865502, 674680805, 392233991, 378223270, 916006375, 805609174, 929941126, 323822997, 410552593, 112776259, 799178271, 612493680, 771874974, 93770868, 463726470, 514967811, 585883049, 85201774, 310157110, 392550449, 758851786, 143834434, 597848986, 122076979, 879806992, 655503763, 608009757, 759731894, 103715629, 915566414, 301710351, 415245913, 689199984, 455555291, 643395948, 288697795, 87347540, 101869116, 11005647, 634981411, 126255497, 779268417, 367546879, 234977564, 37671128, 98117563, 341743656, 988463914, 389310430, 34610372, 506286968, 529403731, 226370247, 431542340, 937735376, 6142745, 960354654, 158305861, 374426371, 19324668, 468485098, 418767813, 515594579, 105179188, 324183271, 795915056, 522421914, 326930809, 143360709, 218575601, 734716932, 853317753, 128899577, 262449512, 776399476, 232480804, 439250374, 611669656, 648908388, 742872967, 111852405, 957452093, 584764852, 359895712, 676446469, 535352778, 358460235, 13316028, 291284409, 996990352, 784661895, 884026120, 842974066, 909722954, 432390526, 188170346, 920692519, 465186095, 37560455, 452352385, 505174834, 477805900, 169367121, 989376089, 767130159, 948922561, 566240317, 653099508, 837367581, 511729582, 356066386, 64603735, 552662867, 759390706, 342253670, 81673282, 517883036, 123436315, 77842745, 46890617, 902310976, 269023861, 268671286, 263212118, 964940503, 989166850, 816338170, 349947197, 86376620, 872496959, 585678046, 549108635, 463195410, 783272680, 398025944, 307252278, 930604186, 272286546, 573319383, 147299639, 174129546, 250801196, 728831330, 900281736, 900294602, 555905718, 341582912, 576127690, 635623573, 207843866, 590043272, 169524256, 207144669, 296827053, 829429109, 484308551, 536599789, 107358501, 587157187, 544535040, 451738421, 809662105, 467780324, 275427671, 875302014, 3773932, 822492881, 497271561, 170699863, 714139537, 342111437, 76277894, 786235939, 979354828, 546202837, 667072270, 226799441, 275339104, 1590809, 636121678, 882820226, 802323030, 133280674, 922019594, 93322380, 200294892, 891176025, 586618506, 791228182, 309379974, 124588499, 444131102, 217576869, 874659629, 435308853, 206126560, 425826881, 535371177, 801995240, 652454726, 799364305, 576882284, 288255359, 397294411, 589112092, 543942390, 805393033, 402219175, 638266742, 654389716, 146462131, 621388242, 552902379, 877990285, 568101893, 75980010, 316945816, 378885596, 392915370, 294145308, 957959649, 184901496, 349837596, 939990124, 39506150, 359819658, 9188635, 575973604, 716046183, 432246447, 814705527, 832789478, 645806881, 708718169, 454862848, 485741669, 1391775, 613748271, 321496593, 149770696, 749592527, 926729555, 754282541, 148396315, 141563338, 60127860, 509483534, 300969827, 385604935, 827892673, 598448334, 402698817, 342143903, 318231235, 835595226, 372315740, 5350145, 133898734, 409215977, 879296942, 220323528, 615608705, 552749768, 677351931, 56896767, 752043570, 341000952, 367700963, 340161669, 866345497, 308570127, 663009167, 493129236, 74604406, 577033465, 882204398, 465711828, 457201073, 706412783, 117284344, 829298658, 871640078, 594432617, 713106852, 954759669, 593640291, 566131002, 206115266, 823685238, 207180032, 876409543, 826229117, 89697798, 861030021, 317971911, 409488094, 974644721, 377204987, 630908097, 410495805, 450504509, 706897799, 652116366, 868316479, 124795532, 847224709, 535882909, 163824453, 844344887, 10485476, 619840845, 967351490, 311493815, 631148666, 868263412, 780698979, 910337318, 812570763, 330366021, 181938910, 476890651, 99310072, 392818719, 212666957, 698766964, 280772658, 742508811, 156623627, 386819553, 22426615, 77408307, 301241649, 250132346, 35162351, 228732750, 487957905, 254837731, 189378727, 818222189, 640740139, 789213221, 842541103, 836228408, 391882037, 325674608, 654069065, 321576742, 558817766, 685180652, 213400035, 200853577, 781381860, 863358328, 82854315, 408538988, 487869463, 615246017, 471620712, 17080781, 596727391, 86918774, 446742617, 655962348, 588189295, 670265760, 316494534, 473200000, 599744767, 538458570, 871060488, 204764994, 245122966, 36506400, 502474416, 449106150, 918025036, 386684113, 336182989, 119743723, 994487716, 148143701, 622865375, 417148196, 849070537, 936028356, 477694372, 293584183, 974333653, 712088213, 816280961, 884162604, 16463246, 174592661, 2373450, 864989607, 306542029, 775342857, 518290764, 88656911, 262821443, 136707472, 556406347, 436567486, 513212791, 255510089, 772141897, 388142128, 349619969, 649282797, 635152589, 204513831, 985450178, 372723304, 265844574, 863630745, 953089469, 751308301, 1512105, 891501091, 846820498, 537187801, 93240445, 964860859, 614476808, 163064751, 783052942, 941188363, 279109127, 515301269, 301849884, 971488499, 409297102, 601681265, 257144223, 571099378, 70525449, 484680383, 914802906, 348101589, 454158927, 808020887, 846946017, 737615649, 82207667, 651143487, 289834310, 682382027, 948076126, 491772309, 519184887, 64019246, 928786746, 402940888, 460481539, 780739636, 97391564, 677665771, 99618016, 800399021, 879469078, 829374804, 402514505, 504093452, 147865605, 574441724, 344071917, 224467828, 512288000, 185320297, 798854720, 587268394, 99156914, 315508740, 418454416, 29844313, 239255053, 919137235, 15344499, 158496395, 51068389, 341276828, 116553628, 954155212, 210724413, 929029234, 350849664, 250293846, 25242881, 688583634, 360189277, 826057834, 798381965, 81128187, 386866078, 356342377, 823685902, 329939467, 418166537, 924861482, 850796442, 280718556, 385674929, 579413428, 737108354, 317431351, 971843176, 833404755, 344322154, 220138894, 114437546, 484211867, 9332843, 249015044, 53975866, 596554222, 316464862, 785806083, 359177564, 261021867, 316126367, 734901292, 731737643, 372115659, 809517829, 147610830, 845113867, 611768142, 627534182, 789467839, 298534137, 957738163, 416735537, 461343133, 592907399, 149587884, 680072932, 505908920, 61532296, 219612701, 453914910, 299964911, 711966994, 725670260, 700834168, 314368462, 77898613, 797327235, 753187517, 327627984, 957238519, 294549086, 654990461, 363550850, 959752932, 870425678, 350478650, 216736942, 17511530, 936843706, 299862423, 237563664, 843527876, 869502917, 951659428, 942064915, 541664415, 867482289, 694787201, 137668651, 74616998, 75773816, 759984234, 154635116, 300269921, 93916949, 900334640, 428256078, 125340919, 477418225, 185755878, 287796258, 573127466, 660157072, 234083150, 690262037, 59170918, 990033927, 655491868, 16194789, 471884782, 732521326, 438032358, 337546133, 143163218, 916091721, 948295629, 910839155, 286138161, 657085225, 571536305, 368561245, 519316494, 345011185, 650313216, 385127070, 205797489, 819464995, 352670858, 760320470, 395561762, 74849685, 896992852, 173358698, 562556985, 102903350, 589635601, 188620366, 624285558, 89556272, 407924138, 899311127, 401508961, 903933337, 687463684, 190884496, 596019193, 907369042, 125674772, 515851273, 210424103, 436504084, 944013426, 281275290, 992377660, 795758942, 58037583, 97230954, 499413939, 887305751, 119130421, 965966861, 631474395, 582799117, 595685575, 210471819, 233956584, 749194438, 274443368, 471728638, 305695512, 476531683, 778574444, 72020551, 537765037, 473579251, 11648528, 552468173, 818650130, 808223170, 316430304, 126795718, 906383106, 626555929, 389156040, 863252736, 107443503, 247731006, 44747951, 909056906, 2001293, 162990140, 463946153, 292761089, 461877356, 701301055, 825867142, 585375008, 721622159, 54746562, 809111717, 442737758, 514160323, 826004690, 989506241, 756533488, 958797929, 887525, 860988360, 514729334, 284773480, 497585145, 738899521, 499231963, 988300534, 13037710, 667657227, 822919087, 32455903, 405766793, 826810879, 20141716, 540210916, 489769462, 722405880, 354517625, 849317981, 262390868, 8062244, 180638859, 49189790, 57883323, 705006713, 874216696, 32383781, 690460889, 270647788, 218760045, 801691956, 407629006, 357204106, 122216650, 126558267, 33039434, 901315001, 776982057, 65638943, 854201206, 995796148, 730159349, 159812065, 332500754, 218909174, 614247616, 649918015, 775728427, 970331516, 288250755, 951941172, 778485651, 269221680, 61644044, 41138315, 653304330, 552019307, 956519146, 685382373, 416964377, 799720293, 700724220, 421175450, 213554067, 101951853, 495886819, 520765840, 264317981, 129387680, 903717097, 999879017, 352276682, 763826120, 628203596, 879768857, 851940356, 971581189, 550232348, 634044930, 499329779, 121537311, 445152268, 590815592, 581724760, 362892317, 120479894, 585100629, 577131441, 576754065, 614991396, 772581432, 713077183, 872275778, 887689079, 295203171, 274600336, 860598161, 135232956, 398182725, 16874077, 340555704, 715372736, 724841308, 246413092, 778311148, 73973928, 830227577, 797673006, 274672891, 584662840, 929575117, 53103878, 28014485, 126774341, 579494133, 751550847, 289249513, 211426670, 608198800, 443382971, 453003151, 281495346, 296672864, 798155120, 581309768, 993221422, 757846386, 82809821, 440086456, 142524496, 26475092, 859380773, 782653468, 727539526, 444243574, 100012255, 109951040, 274686900, 357773065, 884970840, 200256928, 430005223, 191088580, 989182792, 939112975, 615257173, 179018331, 583446521, 280011933, 384817965, 936502041, 982311145, 701820497, 681302254, 373472948, 327148980, 809744026, 938700669, 246044093, 642016245, 34630890, 134666308, 339999164, 799691557, 798011854, 686138374, 618721980, 612526829, 955621237, 319794325, 673435601, 300331045, 587517769, 698349325, 820500960, 929482813, 324307231, 742545062, 908979290, 246524143, 751432111, 67893810, 341914662, 355130785, 530834491, 851660314, 51168605, 354818587, 635417169, 159799467, 240266087, 807729778, 652778813, 399336942, 42229046, 657004050, 411368119, 294739373, 975073672, 923724491, 540675747, 511328872, 148983796, 26332388, 442601642, 602320434, 705159045, 237732768, 220069062, 213735065, 742634794, 773782036, 808505188, 302815522, 515253534, 372974288, 311449676, 381214132, 564945861, 653489178, 365615491, 980983269, 416878487, 879098165, 135491652, 239604682, 665537907, 11492652, 90427659, 762826393, 75159251, 235240771, 992379049, 493948737, 910229337, 442798032, 825934490, 135154828, 439880518, 645834938, 169551521, 100119926, 880186477, 763013820, 470683064, 137112372, 508300414, 478672577, 436757546, 411172478, 84332420, 305105385, 61383302, 893405650, 422136894, 833490820, 47799171, 474700614, 911855206, 23441087, 747597041, 933257041, 344762013, 591282782, 142286401, 32448264, 144681072, 200579280, 506136864, 208187170, 24137329, 503267276, 820671276, 183726964, 98732640, 734133956, 742602462, 497355663, 266648508, 564192770, 235862179, 128800146, 375505139, 295634254, 378684132, 609953388, 890285941, 907627345, 186411254, 538801876, 420871649, 256798741, 519897904, 535812370, 775880171, 611059830, 835131519, 344894370, 224873714, 264097368, 713833872, 391385984, 119277082, 137296584, 763755361, 229025491, 398004222, 822947391, 569891595, 454597838, 241532293, 12353437, 241944187, 561377331, 387056895, 404089699, 870495014, 224030319, 985418329, 727462796, 727192766, 109194613, 202054761, 445531069, 941648580, 926465321, 615862018, 402327876, 843409044, 398726781, 624512593, 20444067, 319857126, 980529642, 975693892, 381889623, 488558360, 676111592, 246893233, 550380061, 74667046, 554260511, 30919794, 29921726, 648602037, 110600195, 42091203, 694501592, 826797654, 839115754, 255006946, 627404181, 890682032, 486820241, 601289216, 50131760, 213247890, 14572849, 237702541, 692821565, 94048041, 839154888, 147714937, 113111430, 616968671, 853849002, 978781013, 782266931, 464573588, 23181531, 90915249, 388789911, 7935049, 13267328, 341110996, 93529501, 811323734, 261370435, 451193785, 245736754, 950451912, 478558502, 69409063, 161262504, 267757500, 753495700, 145080833, 295966726, 328680067, 635838842, 835790576, 485735171, 104747145, 943285079, 822784889, 506443443, 629640891, 571024751, 890668909, 764425, 548387456, 103741376, 87927778, 735669078, 740289267, 19079274, 265846855, 316961954, 915761277, 779304448, 807907038, 719803723, 464557391, 545982333, 105245925, 291594096, 942268849, 510465155, 522657243, 333284686, 877129519, 923315521, 29794073, 620254458, 895975848, 633537932, 861935600, 808381568, 719729589, 640530252, 132971679, 879652971, 607540720, 65543677, 235007155, 827355414, 208006353, 695429486, 585863052, 679345384, 282943022, 610685988, 105528024, 1622317, 388199987, 615707440, 285178652, 972563467, 532898725, 17459243, 491323198, 438401568, 303426005, 725212993, 366359910, 925583935, 281577273, 832541744, 949491466, 659980677, 834534594, 231366180, 566989208, 396236385, 576169398, 926844465, 804466569, 58128354, 809268906, 77552450, 685720107, 53277725, 481005952, 284550735, 505303523, 300524419, 38733097, 231466292, 307843877, 553431836, 7092270, 900668282, 789825283, 845312653, 662203053, 617168970, 214673822, 785905550, 416473169, 252434881, 753680559, 720111383, 587933855, 116067498, 871181267, 79055311, 951624862, 891695514, 432377908, 27966405, 790348109, 451052592, 366432705, 39196738, 204780954, 282436968, 449709780, 941643549, 370442348, 502501017, 677913826, 847721090, 431745395, 616738393, 325716776, 781307680, 761776398, 948148389, 582249209, 795840808, 877536372, 259985400, 495135496, 916863345, 820976211, 827343555, 406748183, 514244800, 482564818, 28112928, 112383755, 19980672, 872975010, 139493702, 478674165, 965746867, 587081557, 300474953, 643632712, 381756274, 460906561, 633613820, 161909162, 194415655, 37128613, 668137148, 733649136, 353279674, 597428998, 987932603, 434772198, 415824129, 7650525, 541148360, 184651941, 135766092, 967111416, 616162039, 169818681, 231590619, 636033867, 592028100, 415478678, 746659617, 507802265, 312533702, 92511199, 40876485, 614356958, 322421317, 641302991, 926160446, 418399634, 774703195, 382166911, 552136482, 937662327, 698941975, 303093391, 717756062, 744442826, 676401260, 930815186, 245016376, 110800872, 223675190, 96726875, 542099062, 473939049, 764899401, 185896053, 643185448, 154325028, 785146444, 128152043, 951071811, 364588688, 819117493, 119871600, 943365955, 846336017, 262867478, 53943115, 713379174, 863985695, 489275307, 709601813, 432251222, 299010205, 729514279, 110414872, 568026856, 728854058, 579649488, 847661077, 968907452, 805053999, 953665024, 829700338, 3491891, 461107211, 445628772, 581437196, 326483627, 63468648, 957890182, 732266117, 652574796, 773613966, 204211377, 222212392, 934138030, 937907311, 560282362, 823910603, 701888889, 450253787, 178565754, 655105374, 913693983, 172276774, 877992002, 454415822, 369158564, 466710493, 780300534, 679447837, 864944215, 492110714, 478392216, 502725139, 695704312, 923774864, 329295975, 483198704, 525950820, 132346760, 827736462, 599258251, 536851569, 684820017, 930500767, 588156514, 864369649, 475943872, 157400182, 431727479, 968736432, 591861039, 826263324, 20075948, 817454771, 105228013, 537022440, 643817207, 664721301, 488082430, 852919468, 146794304, 495991047, 621818025, 176258299, 79958727, 870942810, 636284060, 646009002, 437408934, 579588796, 869515096, 162392938, 566487832, 217302936, 350460307, 722427783, 961121768, 844689957, 925010036, 607790912, 300848286, 953013024, 963259948, 984705981, 244738104, 139404939, 248753414, 701461009, 680387568, 853708970, 537150121, 996571215, 46893880, 275467557, 955574219, 257780786, 411994187, 681175035, 388724344, 97727092, 734947465, 96908083, 244595641, 360294967, 222607954, 439945805, 825760831, 854948330, 126598608, 174560936, 617059019, 449402092, 133966947, 83280431, 971374418, 133202977, 677283691, 932308581, 253070505, 477577139, 300363384, 348783669, 239835157, 942629807, 85898295, 64739196, 971532126, 761063875, 743528155, 359122910, 410076290, 350808956, 23258269, 726037292, 873558417, 217988463, 783930074, 381558355, 12329469, 941819308, 851930781, 173657499, 702786896, 188633135, 399037082, 81758938, 534532748, 590470922, 189321955, 207290337, 973023549, 433505165, 130557136, 740736230, 277166951, 68643918, 722652478, 198077242, 141759333, 618620563, 806309953, 849156415, 735607665, 214785500, 955270226, 835679478, 319627931, 564948759, 592637671, 382466380, 183478515, 590029019, 208939781, 497675351, 758486105, 572089929, 293386808, 270252828, 409170819, 888295922, 228498324, 113636408, 18804227, 469879378, 526695743, 485231433, 136287593, 857443159, 17382363, 993192752, 177972632, 706151012, 365070840, 795556250, 814753899, 198331803, 470749112, 678144560, 835564402, 872741780, 248783910, 236311904, 84007940, 31900905, 4677848, 596720353, 691615497, 161993557, 237267531, 551596394, 580864824, 538762960, 846049166, 482133657, 542641923, 397148546, 723939052, 954865840, 406933161, 775873559, 212295444, 572353701, 746207533, 196522035, 250477905, 196588107, 189439395, 298972065, 936038470, 435657925, 135310590, 159731314, 833179193, 6524180, 999722428, 408904070, 768831189, 765657273, 348829647, 982006347, 602638861, 924914159, 574642316, 357955851, 996810330, 449181673, 323498514, 238091079, 111066781, 371868770, 430218637, 224072287, 346969250, 656146232, 133215720, 551237700, 840376715, 502718654, 864681945, 632009085, 123826552, 165377438, 111324852, 851987302, 943348025, 805966966, 427745544, 346203419, 498150820, 87000237, 61984171, 619830115, 326169177, 704012930, 39428631, 274572535, 259288160, 560525254, 384583984, 410599980, 853190817, 61724664, 709720027, 435692970, 116120071, 201298642, 440159602, 615971311, 513973208, 464193214, 823238763, 266613802, 979084632, 921496501, 714899642, 721462631, 28439377, 334336545, 352003811, 27594336, 820182918, 942312783, 174588084, 163558367, 583966565, 643455845, 423636689, 954408813, 797717706, 398128127, 936568541, 770169892, 71461031, 613201510, 636618057, 443238218, 567234407, 702867667, 678728045, 836066865, 167171614, 435904509, 757462099, 728389122, 727936737, 502216891, 382672924, 176801817, 669159828, 943774895, 595964054, 335720203, 670761665, 139798932, 869766272, 644054071, 28915271, 372679899, 266285141, 922178862, 862985177, 806945601, 817183743, 180705169, 791109050, 191621179, 900991753, 325960851, 939973676, 984893969, 630051972, 540724306, 858176580, 479330641, 394391518, 781121124, 363331156, 658196275, 91086897, 389588844, 287655637, 184714667, 861601537, 824346012, 829973855, 257715021, 124283834, 38152516, 882024944, 659794511, 434518918, 568599817, 426926, 433173865, 607495352, 802885696, 903198390, 702289112, 341137818, 816670912, 291303291, 932738495, 112230213, 893146967, 898099551, 669411071, 549558883, 274379096, 315899251, 13843045, 81284739, 344996416, 96527332, 223728475, 29309550, 531406600, 241042141, 321608099, 949828371, 228643218, 317718216, 801827386, 130095295, 672103678, 844010481, 414876135, 19530282, 721207984, 720088321, 76320178, 562981399, 105562987, 436351485, 648993401, 319690343, 155671878, 593323923, 348167111, 763515049, 598483199, 468560636, 687289514, 645136554, 497427344, 455898195, 917702244, 756631871, 792125911, 383316302, 36623122, 866928334, 39302912, 859821542, 240150501, 947144353, 675264793, 715743769, 467492963, 169430878, 167929522, 189651038, 241867571, 351803902, 529011514, 82714321, 436509673, 897017746, 944343473, 231108017, 594104989, 157774616, 386202972, 989146385, 805435566, 577861009, 38201113, 628512344, 808381504, 24011447, 702167415, 901338878, 792558643, 660115602, 722327379, 190656701, 132572937, 779458093, 496866216, 673318840, 633743245, 432726617, 713983357, 188511054, 740974202, 767545498, 345451335, 77330882, 135810105, 816167747, 41557541, 298920019, 234090193, 300993976, 771713584, 692615784, 294712527, 335577960, 913723838, 137153473, 719756693, 764958750, 517106587, 111255463, 833652929, 483372807, 11581633, 111861093, 83111948, 664940437, 825996256, 968823724, 505723749, 249653645, 37134936, 588608171, 222099756, 941840332, 583415543, 278486778, 901424873, 943578699, 438767280, 925756900, 18575370, 928079856, 267128080, 719447041, 638436832, 826553877, 108857187, 391925606, 566480673, 163944908, 995524224, 242310887, 835575876, 2692891, 141275412, 139474283, 235863548, 618515097, 985642125, 369217070, 886520820, 368771429, 740704962, 970209466, 959043472, 16742826, 31673245, 7873388, 240939226, 4743850, 724372929, 64359923, 40252723, 959724500, 267525143, 869341982, 483783405, 779305864, 912171012, 473309656, 651133919, 109857217, 903613246, 962297063, 903186958, 852175240, 850584420, 598389467, 364613353, 947019938, 917374036, 832327085, 560003958, 602308646, 282227503, 80876563, 499178576, 875814126, 484566737, 880549784, 417903774, 439301014, 711181904, 619667788, 183448060, 290002890, 511699961, 178249191, 895684831, 582262866, 502282420, 59949670, 265893276, 790923008, 849218231, 952963505, 357273270, 545995095, 32763384, 600635997, 875469665, 82530814, 357536835, 700481975, 721251531, 412848717, 400653093, 508074544, 704930316, 455304344, 888268047, 914875933, 235623179, 659017860, 904150682, 931341425, 41512454, 290480700, 207411018, 49259686, 768879037, 240721929, 637229607, 139746194, 312023253, 915967678, 622146555, 707106985, 619295784, 942715119, 561323226, 449364614, 128149899, 11999014, 236730689, 81267095, 941171090, 283738754, 156426458, 412150626, 963282623, 522920738, 375608108, 384172270, 143110237, 852746287, 379730991, 360902712, 853949571, 46001475, 275852441, 987040181, 827406642, 739368879, 671662223, 647464086, 867342928, 461459733, 855010765, 106647537, 310189108, 333294724, 141694722, 249899248, 601910042, 141038305, 870390927, 420493222, 187600743, 373304117, 225363716, 225634773, 504041808, 271277067, 559801318, 455423080, 255594661, 815236612, 156789720, 132115752, 925261426, 227557600, 368266795, 714400261, 951268746, 378444673, 32445153, 414942045, 772746232, 281051840, 799009382, 197969230, 119518367, 626686732, 458390672, 935208630, 496684916, 195105810, 512506462, 107974177, 30993077, 182316376, 54496374, 837941295, 329467266, 30307814, 715973655, 238322762, 411165618, 65683092, 105484360, 27362515, 252200779, 690117526, 385232794, 203108958, 434649984, 70787727, 909147699, 245909141, 232691212, 587114018, 18315201, 353820299, 614887774, 850839322, 960513256, 830530588, 732837807, 834677965, 685287914, 190116014, 673423293, 434749354, 532394242, 268331847, 399874668, 19762569, 128487032, 162724344, 856317906, 647855746, 70004781, 7151633, 377739679, 531698297, 13711236, 83459537, 681037711, 777110156, 195151183, 526059753, 113348296, 797035338, 171936011, 87714789, 341001087, 889162702, 371863698, 577013287, 845344593, 547493421, 855520345, 281966983, 466156670, 211882725, 268368742, 650120885, 920607730, 498042757, 897913889, 16864824, 553116475, 985963172, 226357316, 69212963, 482220419, 139840048, 14390419, 679999688, 460063679, 750660685, 767351234, 54198306, 362777187, 251781941, 383457932, 476204016, 156217088, 958667210, 408595072, 976984610, 303403225, 456577593, 443083130, 230793183, 470904895, 378566182, 850146534, 433858169, 456867112, 921333475, 155781615, 733077947, 689842118, 993917346, 420170150, 334707355, 627155919, 82054402, 189010586, 93972765, 756928919, 66815452, 638314094, 43339393, 15724729, 822000889, 488957048, 89036417, 364513933, 80078203, 684998739, 994708656, 957110066, 521631859, 113189080, 852887955, 182631954, 897825927, 491292052, 739495778, 807869837, 504512, 756528686, 763006109, 855551950, 851453248, 912900222, 691626269, 729291119, 616149767, 260505079, 798034204, 467587969, 177917682, 342755712, 293317515, 258488213, 198144305, 637682895, 345819722, 456392769, 587535384, 311013748, 83352856, 153330487, 500599852, 764507403, 20785691, 476676983, 143969571, 292420496, 867134054, 937363704, 335681624, 284023254, 872154835, 789019203, 344834706, 733247690, 866639785, 313817794, 95684602, 278331371, 149087798, 72903751, 987819728, 807544214, 427878942, 700671894, 698378290, 213675105, 484646066, 319233158, 165714290, 890998117, 700020344, 660972776, 440215014, 210603869, 699426333, 741062389, 715646194, 657200962, 861355216, 305809177, 428623850, 511481667, 538695638, 804826418, 89543164, 919120261, 370209406, 666397823, 991148184, 574038061, 100599947, 203537941, 592317995, 566890595, 274385002, 746587803, 261005083, 10890387, 735570858, 359503394, 485583400, 980447524, 901757005, 460548190, 701702668, 429949196, 591013451, 339331955, 373599055, 318800640, 23781742, 454584002, 428862101, 74280172, 162899082, 73557168, 510107877, 394779570, 27570346, 284186884, 731723907, 98487943, 332060234, 536835597, 672473365, 878646804, 870342219, 791225549, 845606501, 495218599, 725057612, 447504389, 183295576, 8184263, 171989490, 481297068, 59839701, 62095786, 220252919, 700143502, 259036056, 621736658, 733202292, 998048897, 636148818, 118797203, 369877295, 730479763, 179914136, 730669323, 177782671, 731868399, 176007806, 12065526, 751885286, 505670442, 542223544, 375630568, 114971905, 296696950, 224531250, 53933137, 604030633, 436744074, 199512723, 427883562, 407324635, 865215685, 741069685, 643087309, 46774446, 228020232, 541672764, 140655192, 529083284, 404874143, 783039132, 316145008, 689995824, 201059388, 648344148, 395725406, 107113068, 200601437, 947032627, 392365846, 465479474, 741433005, 589789159, 711480835, 994017622, 159609638, 339208389, 749571932, 818880128, 368636132, 32447538, 496270433, 203707025, 372096235, 330601046, 118400318, 908006231, 619847380, 945540357, 967740688, 617493100, 582827492, 323969141, 606880498, 585928305, 639369885, 474994131, 943563638, 368100511, 998875216, 327927935, 316708175, 869658383, 328042134, 192009320, 61509710, 592594363, 288519154, 230194181, 931914734, 761529274, 338579285, 556406610, 52545707, 17460663, 919549794, 944863868, 359316762, 546778452, 653931815, 766619388, 664658326, 66552113, 119286795, 606560436, 339476839, 208240508, 867747528, 985532977, 378800272, 228603630, 708214721, 910732813, 931180858, 289820983, 494912593, 117148245, 999116345, 917468677, 82511199, 348043390, 105014328, 271432184, 422131184, 969328866, 333519617, 904128153, 682605035, 714689022, 715265828, 182747742, 497540421, 255024308, 347381164, 967153550, 231882180, 650193649, 69664605, 367393303, 169516518, 486813472, 684449151, 392818515, 719798594, 921710308, 675965435, 331486163, 509051530, 158330133, 34662088, 908188107, 818470487, 989087377, 286735420, 405727231, 23105977, 53894587, 85982795, 71201111, 831471776, 29523516, 464934290, 373389210, 476298832, 992860037, 68972277, 107625429, 815263491, 819498406, 300153253, 590004169, 791949104, 196414041, 756175164, 942566896, 74736756, 217820594, 725171316, 580939885, 228990066, 788142716, 818035568, 184467646, 212833646, 757429209, 218650090, 373434617, 888744675, 189786252, 618801158, 75090424, 428523550, 428896697, 393075150, 497986939, 186594769, 529667440, 852454841, 507213299, 343462935, 781657548, 542600919, 694947578, 957929393, 317635471, 409762122, 343945103, 707357882, 995605790, 339435952, 523727084, 468474294, 919879800, 689660633, 476311552, 211407047, 363906261, 17271408, 538370988, 290038162, 141535715, 690466157, 98287437, 964514845, 174890531, 188874738, 503700083, 179040774, 564849990, 932945665, 147637918, 541051152, 590698753, 837350329, 237091238, 595786167, 402765115, 1161704, 2350093, 158696313, 400382266, 504924841, 569157639, 843271054, 419003686, 307477628, 117673512, 786109964, 351028786, 711890307, 435678312, 622504596, 61568704, 400257137, 402053436, 166627250, 976470367, 455729904, 710059996, 145813972, 317454288, 765111994, 863355349, 672102762, 146004213, 338118924, 760119684, 744331470, 239015838, 138219472, 592507936, 430461605, 699595003, 574087449, 586350133, 274144842, 384870746, 730597638, 327286138, 618659328, 340462936, 213316590, 290610625, 179916811, 710526523, 474264995, 513127427, 759245897, 707310339, 883634152, 659932946, 318998765, 122699587, 24765956, 810151285, 148200897, 595291966, 249812998, 224660955, 351863845, 148319347, 612989527, 109852525, 567981950, 659704914, 643901048, 111303896, 313837278, 639790052, 278652456, 189193999, 526018484, 254117816, 182861514, 205581911, 318575611, 107834326, 43802174, 46693059, 63953378, 768317098, 765818860, 385327464, 688990765, 50329232, 346777850, 253014523, 506904204, 989446793, 873400400, 597312226, 825555548, 749666457, 336027196, 732441662, 351549667, 786931672, 137198288, 291194400, 766646857, 834300045, 523394349, 514620764, 331429035, 945664637, 386931649, 308115910, 590675942, 45605745, 751311943, 774551205, 166566054, 104382893, 205287177, 531437117, 965928230, 812127040, 621679735, 244618999, 688891120, 201671107, 586895941, 27266699, 816917706, 562441814, 44157100, 204173691, 550560629, 146142607, 940826898, 317188061, 999564634, 967440106, 504616903, 387353122, 58499924, 648318881, 924870330, 115838099, 483862646, 819976942, 473474592, 933704405, 282605123, 147595653, 892546116, 771763576, 53863276, 143124444, 808231249, 446099839, 244553231, 475147507, 164044559, 975651580, 379460902, 332486419, 465591164, 38741742, 801455508, 285020037, 347775747, 937409003, 838644076, 684203450, 641051231, 743432761, 891122757, 85926207, 973772645, 476928607, 797798900, 198720725, 446164138, 746920630, 638618780, 699227474, 892605554, 379551941, 55379147, 878645074, 942721295, 346463109, 58795197, 305158398, 852793451, 404553809, 34173172, 108320871, 564681743, 153557355, 548843265, 770404518, 29353109, 291456332, 651810191, 474511678, 38939220, 124467494, 965120011, 337729305, 585014703, 810933404, 165303142, 960607308, 483040718, 441982810, 385463968, 226698502, 492069302, 121950835, 678605309, 975677683, 79580822, 975229494, 435630793, 472788599, 639376627, 588731209, 325729570, 131557290, 379518963, 754067774, 491295094, 243882660, 550113356, 786144065, 693328907, 157418587, 890582020, 710132411, 110579259, 660833852, 232227963, 524239333, 744846013, 588942292, 68571898, 243761386, 421585877, 42505188, 608818250, 612970995, 267760960, 490287447, 94047041, 771975869, 363346375, 979792098, 403917073, 633429818, 203971132, 211390839, 676496292, 478694437, 283725052, 407037423, 974481673, 841413566, 457038728, 868987951, 923843049, 220115429, 500779566, 426325143, 351164439, 899296531, 492057587, 338977864, 777771455, 907675772, 237315661, 611426600, 35678373, 338031544, 732892908, 416889474, 847119098, 326381959, 90576202, 738656027, 620950794, 306203229, 617266428, 109266949, 966416212, 715764775, 251778316, 619515573, 45456016, 729994862, 450689776, 133092148, 122992009, 812475193, 977649600, 732692356, 146078415, 217141528, 632794967, 689443626, 720960380, 778905844, 474726979, 263845908, 361081057, 509786077, 769556867, 156044722, 322229090, 595593070, 576539121, 824735913, 300981866, 574215928, 483545813, 525248109, 126459008, 815743158, 253684226, 895973466, 815596000, 418441899, 998986208, 754891298, 269877146, 622740891, 421356245, 759627207, 685528680, 446566146, 347827920, 693490807, 226145852, 219849417, 269215697, 866824411, 547527752, 526089538, 382513283, 769521672, 291096130, 271153688, 757201946, 704127835, 876170939, 517080789, 469771365, 820748475, 80689325, 485848981, 487038148, 143347922, 898243935, 919138377, 14428908, 777364782, 236177837, 218441183, 701994753, 971375333, 795128350, 617929751, 793356917, 424822804, 536817245, 954922182, 970926031, 370231105, 85060526, 989877188, 442766145, 310782932, 174101856, 932205621, 52844550, 461412922, 500688088, 543124925, 609012664, 824642045, 952052926, 952474519, 75471091, 439455617, 734928939, 215603083, 399987063, 337959457, 445455943, 253102058, 938762295, 535872371, 359798214, 815668526, 826310860, 610788794, 316684719, 533950442, 143223546, 267632411, 212844087, 713201173, 992099237, 976113281, 516978719, 143122742, 562284527, 244475108, 662385687, 184364421, 583191875, 94457817, 792989090, 364009302, 273345019, 438749746, 276739139, 897390574, 532855459, 476136141, 730622350, 60478147, 933385888, 143142192, 565714444, 328179408, 850766358, 237146623, 711443540, 220189940, 589028431, 589060618, 282977093, 516529654, 159704098, 700130351, 127277146, 64992489, 826117038, 194021226, 200159826, 91441865, 652240033, 366238185, 205990807, 114281380, 103369493, 823776036, 488475237, 626298369, 985774172, 139238509, 392513854, 223119822, 600688143, 147865348, 847751580, 135247839, 685840520, 736625371, 164811229, 943149828, 876169916, 108856158, 662905352, 746391560, 297729711, 154278896, 176896617, 869603304, 686853608, 741699189, 338296711, 272592354, 526413649, 669216508, 36958094, 650896108, 685938286, 321346252, 862953852, 626934405, 206133669, 188225066, 510241204, 964646250, 38385964, 925279573, 203160872, 652687455, 329947289, 377271292, 149016289, 439965496, 383874921, 820484755, 402325415, 651097618, 325446492, 660297830, 102106033, 60932310, 353618109, 44999402, 956254998, 422281186, 144549344, 742734569, 149216361, 601380198, 901820899, 889959998, 287294839, 218234031, 319947648, 820739829, 135139180, 911367486, 27397699, 838448625, 527716593, 207525644, 976200020, 996479437, 234910078, 406202440, 912590555, 828758881, 81273371, 662950020, 29450839, 25299659, 139136836, 956987637, 263509512, 783377846, 496292301, 793955626, 546248273, 363891006, 415443193, 739112089, 159198628, 918722081, 328367851, 542820029, 76633690, 92573590, 789377331, 533547951, 412085354, 726668055, 418676879, 600123402, 893826134, 115085306, 769613061, 76040120, 117238845, 637291868, 350431162, 339067929, 617216387, 464704375, 299872806, 316040200, 705496908, 420451822, 445606459, 72377098, 144805956, 841594385, 59738181, 260964779, 923478055, 977641764, 444251671, 816445970, 416887171, 128596490, 572425961, 431135395, 183635440, 787714010, 295153049, 576316677, 610120503, 263415773, 6436725, 45326257, 124643904, 638300879, 299539196, 583637460, 953150664, 678085395, 576494833, 85239096, 731877500, 746803829, 257520209, 165232234, 957872789, 137020182, 307925615, 583156587, 48608061, 200209692, 806126386, 646049218, 292792389, 567042434, 70580500, 864794074, 76511996, 192886914, 862311458, 49202622, 765719883, 284630770, 291701616, 265363431, 361758553, 353578433, 654323500, 637081518, 514700653, 59942715, 136201664, 287673457, 667453740, 13080878, 150251115, 742977429, 616842743, 551680202, 708652698, 836167047, 381032501, 693518844, 616040436, 837663593, 176439514, 718509065, 948344037, 389595674, 338305825, 948042986, 278625340, 643320474, 327751040, 208935899, 940986266, 821828982, 378090105, 229470658, 61766756, 845852302, 367771601, 508975928, 441479288, 831735661, 58342278, 715252642, 271464392, 279089534, 231845541, 78801321, 24621887, 710618830, 791674168, 23066237, 83519086, 326007401, 339833309, 826034112, 662843208, 711953501, 404182302, 446722672, 608431204, 363063986, 864070291, 541447153, 189524391, 965119451, 642847547, 291844907, 229531791, 231983868, 357008881, 746638035, 604108832, 783037305, 716096362, 162106454, 81278233, 206178524, 839029093, 294049645, 809655827, 361034155, 575508388, 198576256, 961580129, 22458358, 117049637, 443830646, 536310999, 954544803, 568146046, 965882967, 343096100, 38749158, 447466469, 342040099, 125530459, 897072195, 559703367, 474227757, 60148703, 191865320, 625718620, 521202569, 756138356, 602674546, 749130355, 991283014, 237108456, 475796465, 121524652, 972443801, 750358328, 82784152, 142330334, 973813260, 126600985, 520734519, 390918006, 582148936, 577802809, 27534894, 989343396, 255170852, 451785916, 551391257, 665245662, 147880231, 517449786, 257371576, 551847268, 398070319, 745228568, 263811302, 333314509, 685825016, 984570210, 325019995, 819122190, 984805617, 183760307, 424767381, 163387130, 313891744, 892660814, 210327368, 527886899, 727066067, 214917515, 969187849, 420319212, 796414921, 825945589, 466689202, 128283100, 362618917, 76964202, 226496276, 966918261, 676269212, 34261505, 859340074, 122972894, 931355561, 933921086, 189260354, 59647891, 460839560, 39603283, 686944123, 10901697, 13069414, 65459814, 210284338, 670021808, 429897999, 755401306, 753008203, 596038270, 477587372, 789448508, 110928111, 199990681, 475647156, 265928342, 641886520, 141174739, 708166791, 491943518, 181426502, 943119433, 15272302, 300689938, 236820442, 173285754, 751359414, 926268310, 152432934, 293663818, 202407644, 241948445, 370764140, 853855284, 545072227, 992771742, 666669690, 340313646, 61173664, 353247330, 385066977, 946681470, 529625480, 644513795, 417702187, 429005818, 324414342, 379275941, 495534502, 797367350, 454152605, 793592756, 382433568, 600982372, 788448150, 199049122, 419392723, 697123612, 301555201, 401610615, 54872322, 17753259, 743261626, 824283154, 129721400, 256775229, 349013194, 41112645, 784603210, 487505879, 205911585, 361143530, 308885627, 602752509, 326379822, 291188982, 970480208, 54993884, 343838356, 308575896, 129423496, 910976358, 197050627, 117763870, 364144891, 105038503, 135592303, 506326197, 290746371, 538588669, 431199848, 906380257, 871754265, 275973207, 36200530, 812969820, 563004838, 246111372, 611038307, 745211700, 591730839, 655120054, 386909509, 880051495, 786037695, 787825930, 770957674, 65671806, 392515938, 509515092, 602209157, 561816617, 187048364, 769130297, 770807729, 4424292, 85830940, 296677680, 957635254, 969691654, 993520072, 188919500, 724415834, 531870405, 728232163, 473522574, 859319931, 303072358, 56096480, 134614559, 868085632, 530947097, 166931250, 683914604, 481503196, 339138226, 995564211, 374182806, 211997413, 417025998, 196163906, 266583316, 24147233, 706341309, 448885813, 369021707, 419931917, 229081899, 978602815, 213698830, 588838783, 615063274, 917413740, 296548354, 498437957, 270262286, 220074577, 467003219, 544915975, 956681113, 331089238, 314632622, 700336872, 317142069, 882515633, 823573889, 632930247, 298947775, 286445385, 268304197, 950148128, 890329722, 776094292, 675865185, 438084010, 108642787, 662918842, 539521024, 558313751, 558437440, 220769491, 265991957, 119340002, 62555568, 459730288, 25851256, 371808833, 514949988, 107605697, 220582178, 610517378, 300973391, 205760886, 728931388, 909284042, 481395259, 546088015, 209749975, 969558389, 216587924, 721189495, 901092037, 742265351, 729760938, 101065132, 117367069, 795773866, 23457525, 381815373, 182663181, 859916557, 71749851, 801231072, 162534146, 227208289, 901043924, 882323486, 373701392, 802528022, 68969517, 645449393, 154820403, 46927925, 788784877, 599047324, 154552753, 84969445, 349139809, 291841261, 605860709, 262381012, 984399421, 978555743, 222264273, 13679843, 262074697, 43261508, 795802901, 798621503, 463887513, 748844497, 551281412, 348663236, 874843386, 146573446, 676139348, 375868914, 497329865, 157240653, 26325912, 707780225, 155311633, 415740620, 124099593, 127144237, 581225606, 396080021, 890657900, 474731149, 454760839, 533333381, 80697475, 61857307, 447096327, 606364731, 251477599, 869635659, 385158800, 99740963, 537758682, 605259205, 295039208, 496396709, 543737682, 215171414, 936292850, 106826541, 59528433, 218859943, 487601235, 620497354, 203916509, 160482229, 356501231, 607190991, 924007371, 194178654, 29673592, 176849822, 406455250, 741395390, 119450972, 312909129, 73602873, 207595410, 872455106, 126288912, 535843918, 588468094, 658209327, 372116092, 579763626, 735296265, 641187571, 487613434, 647647635, 981021390, 168025059, 237618174, 923730669, 262957413, 924772649, 687383046, 582426152, 246317527, 406153225, 215865605, 761577673, 764787874, 678444360, 372452266, 677395509, 940626021, 374600767, 851529351, 711660005, 800319053, 356963173, 433921542, 430153814, 527059283, 563258373, 155833574, 52668982, 459314778, 275318160, 60141003, 129009434, 311736413, 309295734, 730105357, 166205055, 832344624, 585368251, 532997740, 425874460, 201203013, 543079624, 496479153, 709161165, 332246085, 571574697, 375360844, 874834217, 872429448, 511385835, 316751566, 112043831, 721322020, 672057107, 103928647, 190799708, 623680937, 20607010, 545539751, 262612989, 249868125, 324376118, 674055104, 407602393, 341956297, 12537619, 412737295, 773654953, 154996167, 227717049, 85218729, 67814037, 908556963, 990460613, 331371118, 184903564, 187020472, 816031713, 625878914, 677527971, 2247040, 882996174, 102690127, 981022266, 557873347, 921516942, 7120612, 360035350, 156511162, 892304963, 709734229, 991891629, 464479095, 794602124, 609135518, 766983576, 198497953, 553455979, 993545895, 61013761, 251907899, 684394803, 775999715, 515213463, 935771104, 987897761, 356522668, 785613830, 32673446, 641157542, 763278710, 777981040, 954888888, 502509005, 219664171, 765663264, 439909248, 300567870, 441299768, 879690485, 380791278, 497124956, 203459150, 581521898, 524811763, 958147308, 513921902, 763082856, 511135233, 143627903, 996331347, 101579700, 415636677, 603133245, 173885878, 506447852, 958778614, 552202234, 736442742, 921694171, 460942723, 339532572, 228179406, 746484755, 470764913, 758899340, 604034130, 310933093, 126491354, 499334184, 646331977, 460441168, 897803748, 917647138, 316111030, 203200255, 11612640, 477881347, 579846072, 744489797, 47349575, 954241772, 463715665, 75596749, 943342394, 599462026, 632314496, 801269017, 293322226, 40924505, 684998921, 216335466, 631734345, 870033482, 957580044, 81465567, 549330193, 336639865, 151088091, 976535333, 518182584, 995754519, 369916043, 387590539, 711101915, 576994842, 693388107, 433267114, 613163343, 797179220, 295802448, 38807624, 180341443, 981157900, 442578033, 328700685, 2767962, 89631083, 721167447, 639362256, 736893394, 247882246, 770535112, 947166779, 460429273, 297528466, 263919131, 213353075, 739674450, 379029707, 227580499, 876290129, 751068616, 756608537, 563459072, 389503934, 47663380, 127408483, 130381539, 28307727, 893123652, 19209209, 747924446, 419221170, 962106682, 551431768, 907895220, 457211223, 15711571, 255564463, 802454424, 513777114, 611400432, 246908947, 552314935, 280910779, 116504795, 924721586, 528265827, 170540920, 107599911, 674439372, 361063180, 629630298, 183870410, 529267682, 421255712, 996255826, 379736448, 914033656, 158474850, 515573908, 122886376, 525354591, 292724055, 258885748, 709235499, 706834094, 822512438, 587060560, 330093377, 64061877, 578993115, 576310701, 419724664, 572886742, 820994136, 982078059, 840209374, 68593332, 558735850, 960400032, 91558050, 350551099, 972430205, 308495925, 605974448, 111970280, 65245038, 979018325, 401666218, 242207811, 200508310, 546808967, 588915854, 582277459, 622743173, 694301627, 734061476, 140539034, 376755886, 79015803, 830390516, 183437625, 457007093, 98732076, 696365337, 945680241, 941553733, 294470487, 950822757, 675720268, 487296484, 744045045, 49026418, 742556178, 423044614, 998789863, 998472839, 4936812, 473420680, 74791380, 12627318, 173664982, 530133379, 372762836, 832474742, 119193784, 498745397, 771304313, 983589948, 756701872, 356432380, 33164435, 828256453, 252742984, 496957068, 652228088, 179844388, 687039868, 223316942, 19097490, 186515065, 349059159, 339237930, 733941864, 62830389, 307647436, 731242459, 125565680, 42816436, 287198857, 22984686, 726846824, 849034292, 823665259, 841883768, 571898814, 860546498, 514532172, 514686266, 367300007, 30503459, 838364323, 755828171, 835371516, 529243949, 289882143, 863331759, 440851277, 760838997, 438781942, 210035450, 369369799, 232638853, 65272354, 152075047, 723358930, 907727974, 279776395, 307397196, 639482245, 857641479, 80438731, 12458231, 760732974, 428540901, 528753458, 624753974, 42113204, 637684139, 825271370, 710043017, 645577814, 27317513, 128864844, 798454975, 203148743, 325984687, 383860033, 592440226, 32132289, 252111317, 666502778, 937776488, 97168613, 883034449, 438067679, 581175894, 204218807, 180556598, 3478380, 407993441, 463323069, 978022843, 322732006, 255321687, 335969361, 3057290, 330402614, 534560708, 262543356, 524289636, 778644005, 955028273, 698458832, 455181668, 367180398, 804167992, 974464992, 658764650, 935757947, 877190908, 562271332, 185731589, 221360633, 341142149, 341419252, 881310705, 842525880, 404500742, 375025682, 620817285, 80287095, 509669948, 783500205, 728424050, 294123007, 174700803, 506740985, 305604476, 763466932, 770799911, 766559335, 625756038, 116566291, 548188000, 21480095, 953149127, 677179426, 4825517, 703984079, 398028542, 114767368, 749866669, 359726331, 635388264, 634410771, 56687578, 673887926, 487957614, 241791784, 374880086, 192845016, 769229544, 546559922, 982580635, 178913642, 963988079, 658173711, 76120606, 906522733, 534443821, 547291430, 236945690, 253158648, 180719524, 70767895, 329735986, 959936751, 424707431, 991879121, 765316537, 22216795, 659644037, 468784337, 452545832, 764802527, 433863208, 12140839, 359037892, 209911829, 600743622, 831665728, 68130629, 325834617, 935236033, 772437339, 549696287, 305153306, 497952648, 221451158, 288190107, 976768922, 83292588, 256227725, 72833733, 802652227, 314354240, 377335339, 154252606, 103691751, 606499340, 649351110, 393789162, 25575578, 569483388, 84461721, 492544245, 417219424, 696842785, 657956856, 830928085, 664654200, 988059404, 10395017, 472887105, 358636183, 299052624, 465211725, 326333354, 167863031, 482812295, 216323061, 989973559, 375302751, 48853060, 879366, 990142535, 625482646, 932597347, 922873691, 329834121, 819560852, 303361347, 490304894, 223424946, 474769746, 766650935, 920102401, 616707377, 478782415, 650988624, 63683686, 320899464, 614247615, 798115476, 894077449, 906065172, 218699802, 65300544, 47616316, 614852720, 103296676, 192816184, 552853846, 920999190, 637078199, 803665396, 828637194, 911813351, 295752856, 816880651, 75973862, 352009946, 541408433, 828452307, 559095621, 616892129, 555598159, 769410039, 285726819, 447407824, 473264842, 649571793, 699884155, 303209474, 884082445, 781725366, 36879616, 552149437, 869905100, 869961157, 560693338, 116768020, 688537981, 34527236, 495407444, 92183398, 54170172, 163968837, 152772297, 694292609, 469073151, 340718981, 122640091, 997560177, 39240087, 55743026, 919221106, 672353176, 610904367, 260988845, 941244418, 584941472, 662325789, 474513279, 369747521, 545157459, 392913480, 27151924, 582827260, 970941766, 234457443, 552281496, 926721036, 756357369, 129430559, 571140268, 738774408, 980479057, 947304919, 432079243, 339713959, 609402061, 326719255, 980049416, 543984407, 818429157, 729461361, 721820722, 928317731, 13747003, 427952516, 898031972, 196573069, 616997852, 819609365, 282189550, 696373027, 198631234, 778910790, 435649868, 459094296, 962836304, 365833905, 416178176, 140374943, 711306601, 26941606, 445297382, 219210543, 424372096, 821590134, 981625975, 963537504, 243239115, 362594832, 217354252, 596133770, 105169351, 368304257, 795344010, 744584331, 63990357, 497174155, 942856121, 802930635, 659563821, 310881031, 856312633, 458944155, 179633091, 468487638, 799924227, 82152903, 811005276, 930194891, 71195476, 235111195, 951497589, 533244604, 328913875, 974893185, 390984478, 270511720, 920759827, 497995459, 136685394, 418994622, 916059617, 115032647, 386759429, 312137384, 588345195, 333841622, 201891866, 121817731, 638682164, 217975596, 403584557, 30155008, 727702329, 437273717, 934848064, 614864906, 380778497, 826568984, 930698524, 617480481, 663428866, 569271314, 822747808, 140597577, 98876776, 321443221, 55155161, 855609846, 756280928, 509890542, 438351410, 394901868, 161535814, 299866895, 839884642, 762411825, 991440194, 597426580, 559008804, 173727748, 252632960, 87459409, 513249165, 59345498, 425742872, 144341181, 211182424, 691588125, 732630681, 584762562, 846377641, 508346986, 458355412, 685539056, 781706338, 325493993, 995763532, 767453206, 417327428, 613612416, 510508731, 411852344, 387943149, 735523822, 88956128, 870731885, 696309958, 745410762, 108978345, 207942763, 326697670, 875697669, 796928800, 332912496, 252282031, 186927515, 812635334, 630651305, 179179599, 156526465, 819476249, 226993094, 842508361, 255122248, 206849923, 637734584, 289381330, 964147246, 101610543, 856566395, 561601697, 250415746, 637885502, 836585034, 72751471, 160510399, 708203587, 936815111, 868299584, 196235303, 177215254, 177182932, 217055740, 313807155, 571888537, 860824169, 772790701, 815745633, 901306461, 506930862, 956508231, 770019275, 276614146, 47725184, 156574330, 154189683, 358132384, 705029100, 1886784, 979339725, 986216960, 100226626, 815273332, 671645561, 505018766, 222476739, 540149966, 422039130, 892603098, 637144889, 256781569, 518308377, 786040077, 881654159, 45171020, 389073254, 285247002, 501356884, 491186095, 282734464, 556656633, 635727434, 676187406, 357113451, 366453602, 674935242, 942547994, 542514322, 451808536, 667490378, 245605452, 812837410, 299864919, 551385965, 675706494, 351848555, 757631637, 356393211, 167289435, 286566707, 882027861, 327776658, 369293663, 685944891, 486715024, 134596641, 152424206, 435385751, 441704151, 134916686, 979772060, 193943075, 500167225, 631881575, 931299549, 788145923, 972986570, 830701184, 985650294, 72867570, 790403725, 77778465, 993319684, 969605913, 846797105, 152358854, 162040284, 519075290, 959531855, 106213240, 337157689, 761395954, 400403295, 480354472, 57241570, 301736705, 868552825, 761303931, 257070907, 630908323, 508310149, 197469884, 490041310, 73260747, 745124065, 947438717, 318695585, 685016729, 214972385, 709813375, 396159371, 221658549, 21914110, 944046493, 939343099, 838616784, 580211710, 678486080, 259736128, 567997393, 810155689, 267671185, 737342672, 817110190, 418282621, 519634442, 22009478, 487542975, 318351923, 787416831, 592689075, 869570572, 123673324, 497958308, 371148436, 362309264, 92693017, 386188265, 85132104, 766314122, 282298509, 589690148, 894633588, 468404346, 46159131, 791801109, 517257068, 940222398, 188682739, 267195630, 465424974, 206730671, 220876712, 678227781, 572531950, 611790041, 543629691, 980224673, 970745966, 996626933, 549452151, 882107223, 575846511, 455622376, 841974317, 74590583, 774992104, 995744168, 316642723, 817436763, 127697707, 790504628, 428934976, 275997634, 122280181, 525846319, 996337712, 815023494, 252921824, 942587827, 222152324, 435803018, 832693145, 289840185, 387809570, 874962680, 854746012, 483567805, 213590198, 804648241, 534715381, 284248036, 393384803, 283784294, 735974329, 465760033, 759645913, 445363427, 128477542, 203772642, 659605596, 93276115, 129948338, 61335428, 688426298, 45855745, 15865449, 452357455, 585684413, 770326457, 782915131, 904383594, 394573056, 242107458, 631474140, 625715588, 745383373, 961318540, 851669496, 710815315, 761705656, 288964488, 570492558, 419022270, 435668440, 299930418, 39324040, 782298322, 673584702, 265638715, 325024978, 730585634, 87282878, 939688844, 422771089, 225640762, 477077582, 248562463, 460055007, 988810258, 991236053, 8244912, 645039939, 262145970, 58526170, 78115133, 939449762, 52843062, 392484691, 339315113, 327338607, 660632089, 387031581, 794845031, 268332581, 841806943, 99663386, 269783502, 283493632, 151982235, 531117718, 493012378, 463415860, 654257513, 691705674, 153162400, 626635094, 524105186, 387044301, 437752398, 413575864, 323514271, 609706505, 583965426, 407739074, 68486607, 495772000, 287376979, 126396026, 99758641, 445210167, 343427335, 64210273, 80192779, 1332891, 654829057, 822116856, 233636302, 308511397, 604932503, 38534169, 794271096, 892785910, 97809424, 354070472, 710677624, 539845969, 398237679, 399088532, 855130842, 675250829, 522901388, 165139802, 32064608, 916933744, 774609930, 504315989, 779431024, 946473059, 96706667, 133474692, 903464506, 677970143, 426572896, 296399080, 961255453, 522446279, 16509336, 545804924, 157854447, 196342814, 62975903, 960540589, 857397394, 305304861, 73537605, 104313063, 666453460, 88926657, 325731190, 234250252, 267528475, 990927618, 337859652, 721818118, 207474090, 269286029, 436121825, 226537039, 160221125, 715155509, 479017329, 667729873, 754835017, 5189034, 855553683, 964741444, 744895815, 311787737, 54877989, 30064208, 553126861, 539637990, 192746265, 305980936, 830441296, 277399240, 972178537, 23723324, 670568696, 516242250, 156228875, 195405023, 568017140, 119817546, 172472836, 887268111, 757488786, 366614316, 20998226, 586472836, 659904757, 530265971, 922732607, 162374238, 591555659, 164295791, 687151265, 827799759, 557979721, 305602710, 225491509, 44719353, 845933989, 597489851, 926721650, 17827807, 921547188, 697600798, 473521625, 471970088, 771614620, 919002597, 987521662, 173790832, 138543310, 886425882, 342245316, 661983666, 320903952, 810346090, 269932541, 410041184, 245941748, 101533167, 349012342, 375743749, 770701999, 745872058, 594998378, 957568294, 623177702, 542134645, 696476668, 328031785, 620171174, 117514794, 205021870, 227060956, 285867734, 446329756, 630785143, 241816425, 266861127, 756589013, 904972728, 502664635, 157099026, 308962618, 296282207, 690456684, 174532366, 299198046, 809314281, 26941891, 623111108, 248161988, 877525636, 289931098, 24523094, 964559070, 590597229, 760271852, 232828377, 200450282, 934501530, 898771879, 586470345, 126161278, 281914103, 661896801, 332777658, 916172036, 851388723, 86572595, 868497580, 239132061, 49007193, 836087860, 128762176, 275597534, 232446370, 194875603, 170560700, 985917189, 579433936, 347840264, 379340777, 860264522, 697380853, 28357086, 455965700, 60631314, 458962774, 424257703, 354663218, 163132540, 147703887, 963194941, 116849823, 521835360, 251458324, 736012274, 924765913, 302229272, 951191360, 837040620, 819514227, 317388997, 209962533, 536333577, 683464961, 145996365, 28337150, 193677534, 939715337, 267822135, 118731403, 852330917, 773251496, 882812057, 985695862, 794774135, 885704834, 632424852, 873377896, 60516030, 317767218, 159247850, 772776550, 873875410, 315618858, 69682659, 278710891, 181187834, 76836039, 602296532, 780580986, 809625461, 440237866, 217766336, 593986563, 515225194, 15567214, 725464098, 6647314, 452185022, 359537986, 96081184, 507472420, 996676237, 189037343, 563022268, 129795563, 796093498, 829816675, 125345432, 86928635, 604501596, 417295991, 51213297, 584754708, 344110329, 306022885, 248395005, 683964888, 946979736, 177943712, 428848485, 206382897, 105053243, 82358200, 244957449, 429479055, 126126650, 276788914, 576241295, 469956705, 779927163, 190219976, 957933047, 142476669, 224150676, 343604644, 189272332, 574075377, 299530764, 869201423, 277755850, 187236267, 159704206, 574347694, 531982582, 573857632, 681345875, 718445254, 163044861, 530092672, 151253920, 906545920, 731706494, 992118366, 733563599, 593832228, 38872838, 803351115, 406662598, 682786320, 171080777, 711846966, 270322888, 747819098, 40794010, 831246872, 472993322, 996734456, 418172177, 288343011, 213285508, 784523743, 125185099, 334009662, 743405632, 63629311, 223479870, 830075375, 105303897, 166655321, 221119172, 440043849, 389364124, 122560187, 436900065, 405091049, 837899165, 38222771, 747340012, 890458160, 577980432, 677502071, 980828611, 498025815, 453539419, 943184878, 179505036, 253135315, 642805861, 758880092, 747646765, 538401561, 425630280, 526402459, 431331601, 281607554, 386001381, 177402277, 366173009, 271502972, 411982403, 18451874, 20250955, 676011152, 684391473, 874583858, 206420201, 262021918, 832540068, 244946744, 818965484, 818544480, 429574608, 165403445, 598771151, 19394687, 752492557, 875118037, 701574964, 990495538, 866964244, 326327530, 905639151, 223250630, 331637177, 94159725, 483776995, 247978796, 74861336, 856414569, 50907340, 290687708, 253386332, 602363651, 41187914, 769701217, 231320085, 286495556, 954697119, 573225126, 339580991, 484474220, 993289514, 236017981, 936661780, 663321292, 690696114, 494988692, 712174171, 375197710, 182875301, 152194721, 758046854, 799575358, 394096664, 23773797, 91817576, 639142227, 70518295, 89799162, 773886689, 907271991, 855973507, 310893665, 669212737, 396690532, 359439236, 478741453, 83543452, 874754177, 382598105, 122265426, 658791168, 205269727, 547543481, 328188724, 738908788, 330447117, 342957891, 768726767, 142428465, 988197149, 145499775, 681814443, 538564437, 29665379, 690008521, 408350355, 431467069, 445866720, 213028796, 613144265, 54325863, 897905362, 226070228, 119854942, 894476656, 583623356, 268081042, 224490619, 399726146, 241609463, 355597230, 374006751, 178067244, 729765288, 887959483, 295480587, 22468687, 520304193, 294951978, 591058774, 598979425, 942921529, 716126333, 988676051, 788762871, 878898349, 31101244, 808305996, 463069654, 265313280, 394851503, 881648440, 977577620, 445832479, 581564627, 838499109, 581248146, 440842500, 505095879, 988860318, 180020891, 526799560, 783495072, 6798914, 400209609, 49421808, 552590013, 396241951, 112579590, 716126268, 449138242, 241140676, 768445816, 911751218, 240659903, 582690908, 104870402, 599674444, 601834813, 888300075, 177563534, 480402857, 792584243, 821252312, 734509547, 704260015, 748748915, 825017098, 84880080, 422590488, 577837162, 424889021, 852221429, 880421969, 148744716, 90987264, 315274414, 718141454, 306023555, 294702303, 141374615, 737625232, 685504328, 130467656, 610254502, 147587665, 501382307, 237810124, 265071298, 426426983, 125289549, 739967428, 16057855, 517005166, 822128567, 770387465, 870689009, 548028870, 317138787, 108726176, 134603889, 354891654, 960212146, 793265610, 800579470, 526496124, 919567826, 453438803, 847397054, 626075052, 360407811, 87691506, 14723456, 804818058, 52905620, 789690124, 328655826, 724093272, 372191187, 502875523, 434699757, 753745392, 401447659, 21757199, 156249546, 349440250, 64210834, 660610282, 61726710, 689577863, 936840323, 87199027, 175373751, 311512898, 789426588, 22056026, 462560842, 989971361, 435804113, 256723596, 602284988, 974429876, 437663160, 225996022, 827337895, 224151643, 662795934, 480855566, 783415964, 243097271, 890429930, 101104882, 619456227, 496605057, 797262779, 818009126, 52473776, 422700366, 423012451, 394209582, 781677160, 274066441, 592130581, 700219207, 312852958, 34074336, 53737038, 336917756, 992094435, 645676877, 8824858, 574520581, 416014323, 337909118, 93132688, 881576505, 686409529, 249790416, 287556157, 285810688, 276503993, 192814375, 836537696, 900210132, 318232802, 624888327, 258923069, 492966295, 113155722, 661177055, 425233306, 76704714, 841916003, 510307930, 895445982, 654681293, 989432455, 169642383, 575112130, 156442800, 783589409, 137834994, 980239393, 940895538, 766400301, 91830347, 106361996, 661102311, 281004305, 982801447, 561357904, 329528051, 805458681, 870607965, 408059754, 818979861, 150828162, 788628951, 64206476, 970050357, 959803266, 861915987, 366666493, 107890695, 767575570, 782986713, 317802972, 541189095, 291834346, 902756594, 318769610, 314295576, 875192416, 639226885, 935471888, 837654524, 897261059, 270938614, 132718943, 875683079, 183022099, 747608939, 759753566, 744592177, 943907329, 114650929, 98341900, 62228656, 811934735, 842176168, 328713934, 933446187, 457486071, 520943156, 445898853, 214920425, 758585089, 712510727, 24108992, 842372024, 532493328, 7128788, 34006079, 396066951, 759973030, 923536854, 354428048, 169650182, 202033342, 188009206, 418450933, 133715150, 425710700, 971680560, 665185934, 425813003, 819324083, 759944204, 166824728, 576314460, 365382572, 111016253, 355550145, 850518949, 883105014, 744171523, 287805284, 274951617, 886668946, 582961808, 133447877, 636856570, 846624398, 656483599, 933009739, 912863180, 850488068, 945979417, 106876373, 388307627, 726567784, 205632686, 525337380, 950936763, 190744289, 430876138, 398571921, 485850795, 710845125, 409181095, 478625199, 640344633, 675245134, 693437129, 165693315, 991828860, 600732601, 313606952, 933558004, 130649219, 237303999, 827503184, 856609404, 80598594, 948927527, 951799476, 754363167, 191679867, 842293460, 481580834, 956943492, 777880263, 899839435, 522189411, 208402685, 49588606, 869599448, 168648265, 158838081, 295399939, 540525813, 599653416, 92367814, 641073829, 316208996, 253315016, 459509982, 176314278, 644775564, 19998375, 271308952, 572574979, 417447402, 333856038, 950510831, 248718440, 627763284, 286015251, 398619109, 674284191, 898519965, 715019124, 722397626, 275266687, 520451435, 316394254, 752541997, 611374291, 522831247, 239610755, 614273543, 8200748, 547932309, 174325038, 688736544, 678523890, 133684973, 695427289, 834529612, 604245416, 358860752, 402211451, 816492103, 174117854, 84450476, 310242356, 601712248, 531857749, 499640238, 716287765, 948371599, 909765662, 672613308, 557944595, 315289925, 163211343, 472083455, 973224999, 673807141, 400771702, 833981825, 506570865, 862500940, 782136911, 998241697, 465155788, 135153793, 952311786, 330632264, 768434109, 201297315, 699881089, 719620091, 3776197, 536969404, 278577488, 705438931, 489849411, 869961193, 905147610, 576732209, 290905069, 13881679, 658530001, 411299753, 512730173, 420841932, 506721791, 985109268, 942311385, 753093691, 154629809, 707962933, 363624619, 452854065, 62207984, 72387374, 835733092, 870358251, 698617867, 619682071, 82571898, 169587133, 309905133, 533607042, 478269267, 970482835, 466727307, 594425769, 241971185, 878586839, 326274026, 893976412, 544580683, 302777483, 702650750, 334118366, 365015053, 813583251, 557873849, 630019161, 699670933, 560339952, 343522649, 106764273, 197680997, 780716342, 952023672, 641925529, 509905626, 654575990, 768481398, 824435488, 727877947, 978385348, 405125012, 675130234, 813641838, 616170550, 280781052, 682733493, 360789167, 71833873, 688896009, 931390811, 459997029, 797618091, 619848841, 32584510, 267544806, 615263286, 207577059, 323754672, 255336413, 460616170, 116779638, 74854699, 839134078, 289563667, 722795556, 563844889, 118319348, 323154339, 756943526, 547609541, 792630919, 961334824, 247071144, 295294675, 553395957, 461485860, 968781155, 697537112, 529312370, 837842924, 764676352, 795865634, 937390673, 865194872, 368932236, 598088498, 305558620, 79137752, 600476237, 518673184, 812691086, 882286962, 811470166, 186627256, 803162160, 269535547, 562841435, 806360332, 211787370, 285039560, 714664161, 839983518, 78053746, 4763007, 533206030, 460053991, 15542742, 711709447, 407125455, 26001049, 727296879, 571006054, 313168440, 806897934, 549498541, 676305757, 112939676, 316102114, 98169072, 459470914, 214999685, 109028391, 841275917, 255084363, 428373875, 954047339, 387973064, 400787086, 69228479, 167824872, 245106478, 416758221, 726143893, 149189502, 836974358, 58959274, 146923474, 678742783, 990682523, 811325724, 854275235, 180301964, 893495649, 874452770, 657700708, 798845222, 3217992, 423570437, 366432996, 165948481, 306567929, 864132951, 733376192, 623495023, 345606728, 502047326, 851275040, 353215783, 49642351, 383767331, 642882779, 51394807, 315976754, 251281163, 462739518, 575791230, 566309356, 293921564, 230011635, 399037976, 207278745, 104613908, 182538994, 857276772, 633545975, 70431810, 723118159, 92241536, 947308572, 655707907, 331951403, 704585079, 85611681, 203482009, 117020571, 835655969, 662300981, 511391997, 560367716, 46896402, 956978318, 285006507, 765679303, 90456523, 228117218, 56878685, 53967974, 691318641, 780969388, 103297716, 357617961, 597410344, 309788093, 969479257, 728460159, 650606357, 517259818, 6070775, 7009731, 479444623, 103444051, 673307832, 72048448, 458148282, 558975502, 708090112, 534492172, 836671917, 195206062, 93122976, 755929527, 618405004, 137055874, 483469011, 367592456, 576853489, 800972160, 3322772, 413185743, 644345333, 895994294, 717491898, 708016084, 132135569, 598956276, 71344413, 608464781, 963182592, 295366388, 943725021, 380388371, 645330780, 316337760, 334514148, 786945778, 472072886, 209188812, 308681888, 510951930, 812042475, 941815940, 809460158, 306208786, 113678142, 424528429, 936583887, 508895993, 814629550, 359867314, 145933588, 303620289, 168662120, 920894258, 661688340, 732734133, 337776347, 785613409, 558315729, 976129742, 503812329, 902416019, 747899830, 5825912, 293526942, 75222563, 616544718, 43035305, 800592094, 314232706, 317840859, 865593550, 2207941, 609206571, 821996176, 325893954, 136930168, 865022142, 813412847, 45783526, 869568028, 233527311, 465726248, 496810963, 491773483, 71996132, 928727956, 808794229, 425227552, 77381095, 514305598, 151797882, 5473606, 535422234, 333157095, 289739576, 134570333, 252961467, 555109921, 43609255, 349877151, 825586594, 302738252, 620186671, 52861408, 522831393, 907270186, 305466789, 488244582, 587927815, 25342486, 627669495, 433103345, 403013764, 182379148, 14986575, 975269840, 100658601, 714922923, 791338640, 764706193, 440751053, 918567924, 808093351, 669928680, 905519665, 207007763, 183862454, 974294011, 1689062, 633694243, 702414239, 724970065, 375823545, 908286255, 344475287, 83719162, 161504601, 365900345, 657926085, 934474880, 276599646, 524243669, 436034262, 672603076, 153048931, 622614019, 980184892, 183995127, 611466155, 511906665, 813311183, 517434560, 136406817, 727232808, 361047881, 943465706, 898009014, 690475699, 407598628, 173234313, 597090782, 8383952, 780168014, 56563963, 857766704, 100313184, 173313535, 803524062, 350260565, 838613847, 556088662, 903858697, 784987983, 245030735, 994493830, 896018387, 460898162, 127623102, 911164384, 992976950, 804070765, 337298069, 425647840, 85019214, 637448678, 753140584, 298453969, 144868767, 75247218, 655372273, 313993828, 285715687, 185224067, 864035879, 864335890, 28543977, 249254471, 609367967, 367098427, 695741401, 962623863, 943603662, 451366191, 570382228, 804227256, 279901419, 775427475, 44607812, 897544761, 134850249, 322023608, 897632296, 602526974, 517787333, 655698954, 718721880, 20380722, 926172345, 664958057, 183897097, 332079893, 516498387, 394123170, 717186878, 667824628, 62321435, 586715506, 545941178, 666946739, 742575538, 238395327, 999851424, 197108748, 992736885, 411361580, 315046515, 860190000, 508595217, 6035159, 409623695, 8834174, 915587345, 511824665, 738976431, 966942540, 389108580, 251642530, 154569587, 220143206, 109429833, 249470911, 462514749, 897298272, 532753490, 100796365, 785544007, 265884119, 210189475, 754256015, 997617568, 199874007, 917084859, 704744758, 578925450, 158855047, 647701786, 62060340, 373940906, 14866853, 901441742, 839009906, 347731444, 93524013, 531526492, 953826499, 941985393, 946298843, 251440196, 51800114, 199453922, 992166434, 241956933, 111862373, 450387289, 584968379, 584905518, 492432207, 551582468, 74939588, 758987738, 801100193, 781092535, 339408443, 923877914, 199802928, 319685322, 500204695, 742240597, 270955474, 484879, 850057077, 288882490, 581387247, 325772974, 603742873, 861962266, 895740421, 46415249, 84576349, 711689905, 901696745, 732666319, 907257495, 204129014, 113443489, 56465771, 777983648, 594640545, 244950882, 86229943, 813645436, 67340344, 969184602, 758680528, 783554573, 501801240, 385137675, 820461441, 256881121, 300871365, 344407769, 896469437, 802976293, 336784819, 398856561, 850313624, 392432028, 594393592, 331368700, 678491594, 254405345, 623094167, 311685013, 955939810, 306274284, 279234322, 93660763, 77325652, 341616940, 580250742, 959361230, 835187476, 967713742, 714036216, 161266711, 289243661, 546001782, 593570009, 250835155, 450180980, 222592939, 683027278, 691838501, 860655856, 370664928, 692969394, 515116409, 631491522, 335868078, 417968572, 414617027, 889145118, 367966172, 926284969, 260274723, 560104022, 882617722, 769084025, 6019952, 695911787, 81464834, 951416488, 653947688, 313176027, 745442320, 797539277, 752802370, 520120130, 918338597, 818583263, 339889868, 838669381, 201169503, 258882710, 349069860, 203329310, 712718630, 800056970, 598549688, 982483697, 591562552, 478438745, 467917830, 664789322, 462439209, 801169265, 744697845, 999750009, 228182840, 244455158, 826098944, 994283506, 519418889, 724731255, 907191848, 887851914, 435389432, 581106697, 477868022, 181319070, 810980020, 701674749, 764712807, 579938160, 559061275, 427240532, 279571930, 482524512, 228583181, 446404654, 731850842, 673485638, 572082947, 213285227, 869863641, 267760655, 48092002, 620136404, 220738943, 285634956, 797418474, 829720736, 645970865, 406227898, 463151785, 587704075, 757315508, 65841838, 150439454, 262039614, 434500455, 972241580, 426487874, 16924214, 183782613, 495842075, 144753532, 571216293, 189256077, 651975199, 25954659, 209134848, 773934171, 350170390, 697166701, 607994861, 925179013, 82970499, 695177038, 341399390, 439651644, 494556385, 475373026, 7642763, 543454191, 689726303, 436001374, 635859391, 556051281, 467400186, 591102113, 761633549, 927292160, 521204562, 101778916, 892286046, 599950897, 355797789, 18022358, 396886524, 510479066, 939369403, 222773510, 347094845, 17010890, 674244575, 165419473, 702752277, 285574424, 30998072, 478446178, 442909028, 851551149, 319287191, 582339684, 898922218, 487055316, 278183895, 821615836, 964352113, 43975143, 742471087, 804540726, 852887169, 928733847, 703514990, 662946209, 49034351, 767758960, 387103119, 522971253, 565381145, 407259010, 648911864, 595216981, 338173430, 685409270, 465133209, 335573073, 353091555, 999584106, 42148255, 773621439, 230279953, 139876378, 653462243, 421099445, 367594592, 908680677, 33961769, 669501625, 221364946, 186303558, 873446243, 73956944, 769924655, 42647259, 142714443, 274667285, 588723881, 744437907, 201962772, 545247975, 799547935, 79732739, 549084763, 132664727, 582850803, 189781776, 217144359, 68626361, 842512095, 463357982, 797339113, 696584789, 607311689, 534056433, 144794872, 900827920, 581435222, 340000291, 168557319, 354648471, 499876319, 424842967, 107945601, 622855657, 157632054, 142484318, 550084102, 969399719, 447705298, 450182140, 147587227, 228486713, 999725323, 332084898, 227028792, 995958757, 667694736, 19184621, 516366891, 675886465, 309259804, 119399381, 859712190, 554471538, 423724857, 431937310, 782122425, 221479870, 642322768, 17884258, 424630835, 208236829, 875428590, 550560387, 66051364, 838974341, 853883721, 749307584, 990405772, 822380900, 708059186, 779078742, 231436440, 929785968, 75145004, 322732371, 891877424, 826037556, 78095735, 79483080, 760084673, 743579714, 768620199, 645210175, 909678898, 443147694, 550937490, 945365186, 905688929, 839685994, 928202135, 70926130, 345696665, 396025587, 394279842, 826163092, 530285348, 74735560, 35457406, 770845870, 30116416, 391305589, 337308860, 946584736, 530708623, 618029104, 168534049, 489193982, 75669327, 403409889, 869104700, 303669224, 620298838, 666381277, 671331149, 775697732, 418514205, 325745382, 554173868, 850963508, 106415283, 419227468, 599810674, 724624047, 953636923, 476000917, 88784114, 987804303, 954004853, 340025730, 834179801, 208927419, 721847931, 22062159, 869487667, 964626279, 119481704, 442441320, 748782661, 607208444, 598394519, 920982296, 976874463, 864406641, 10468349, 465136864, 227539449, 826901839, 288543893, 719696162, 52771720, 228166397, 461452502, 557784897, 650825035, 876232864, 359544863, 114829654, 649455309, 882044846, 738233218, 105293672, 416923452, 881164976, 810621780, 920299020, 611879305, 352669975, 980659752, 352861366, 686855610, 18603320, 258137090, 531542985, 13785110, 691217484, 119447821, 74005212, 5476934, 603477991, 527175179, 398556437, 964643924, 497707244, 979145708, 722834360, 844923658, 836378529, 423418007, 860461583, 687021983, 775529437, 242841704, 824164241, 170440784, 357133555, 347789066, 481925256, 351674945, 513862481, 11025131, 740866480, 412042015, 461039286, 982182865, 609400748, 590426392, 988327218, 818404646, 772064398, 357189170, 581282020, 337764684, 706720839, 24217674, 906843147, 802843151, 479813467, 780426922, 223667323, 333372449, 247611053, 837305426, 61667544, 469310177, 21604170, 108226890, 97517539, 760710482, 353352090, 927459670, 916627002, 340948069, 46504958, 113327776, 824208974, 195282205, 625715777, 819634377, 437389351, 939877734, 639168343, 251239616, 747691754, 813445453, 472367727, 845719887, 193954130, 6559350, 888730259, 541475215, 767817862, 450592230, 139547052, 774266477, 138275184, 923391527, 434869578, 715928369, 934780629, 650250726, 75832363, 516061105, 488497263, 477435322, 979591371, 742472185, 883505033, 133083850, 558709695, 882091043, 65710629, 387146527, 403288193, 792678568, 228605470, 70142192, 102171406, 552605788, 184469437, 436849332, 317656206, 384839120, 564498985, 849879404, 76290149, 178121343, 49284114, 535449093, 85717292, 806226899, 491355063, 911444142, 369099923, 308670641, 422469511, 486413757, 536328299, 946474457, 559714056, 204595882, 217856293, 759009, 335680338, 101096530, 556240378, 377414836, 478463943, 312947219, 575281509, 986607177, 963789769, 240170628, 553307405, 523296663, 952858654, 403672792, 820732039, 561668009, 687603766, 607250492, 676391508, 392938943, 361298633, 91295726, 549078208, 732558985, 553105742, 963025157, 59874379, 843627599, 161033279, 683265395, 99547484, 16722402, 47875879, 316066911, 358908623, 835853969, 731441892, 581235284, 834082597, 876690799, 162860927, 782324683, 592631314, 500005420, 485243294, 52600313, 516187734, 319493408, 73387198, 548758228, 525500019, 397168762, 393415980, 10086953, 116281170, 511707149, 272357505, 336078477, 172769793, 579852547, 427487729, 658339607, 409727557, 319268892, 960670482, 660567987, 681002929, 935039496, 486849197, 653022340, 205669610, 38656015, 205899286, 368201559, 796527519, 149539153, 708285698, 999328396, 461274600, 1596030, 737969326, 890354097, 888777765, 488141328, 277336801, 1517734, 49684310, 855819225, 980537513, 304283040, 902437994, 575541056, 931239981, 223508274, 173392902, 726534747, 70526262, 567430787, 566086588, 440347226, 672571151, 939337904, 579704648, 256817924, 224562640, 977780924, 55068073, 806659080, 54393476, 3770728, 214541478, 969714932, 144348495, 445648495, 515061786, 256600514, 604313264, 288082298, 473563657, 446944090, 715890410, 833331263, 445340117, 470637029, 296625478, 120246358, 74275213, 244608558, 498689536, 918445672, 67143025, 780961269, 116885013, 814203055, 38995394, 123328365, 740781772, 939794719, 22623261, 4010202, 236033268, 777253246, 586829739, 321209908, 904618058, 487219460, 717198225, 32936795, 529326755, 698044863, 338356463, 849545101, 896497100, 782601803, 29863675, 766551928, 77046784, 683104626, 27918381, 411762827, 791457386, 8388718, 315968039, 838360109, 772968432, 598884063, 865934968, 797106163, 4229922, 156416516, 635064849, 960738057, 618741705, 16401943, 220712897, 857754198, 517222531, 929614760, 671412728, 75715508, 301462485, 654631859, 292791710, 771184097, 393059562, 221436032, 169786888, 471094436, 784346943, 662993988, 394548841, 105824794, 558943140, 750790900, 230763889, 944384141, 845445234, 101562058, 665728277, 292456422, 442351097, 131139679, 173639044, 248919896, 554499938, 249496482, 716618118, 989594086, 518505171, 150996447, 885416945, 764669579, 19127051, 651095200, 228299180, 475368495, 47071415, 304434018, 733912388, 860540909, 71266243, 216232778, 364752788, 511234501, 587644534, 318147985, 183262850, 759101253, 511342834, 741955156, 805326010, 308054940, 654327165, 54546392, 255487081, 143047957, 34581455, 22438976, 434503183, 945815951, 754092363, 350437735, 643212330, 197679626, 447810887, 15411804, 684739953, 148761508, 517097159, 178772892, 854884969, 486433531, 635545176, 778291184, 29646638, 137882875, 770999252, 731132672, 233961842, 938503518, 543804966, 357398535, 844934258, 527571357, 639748933, 5621110, 266403506, 836362278, 285402285, 764014340, 488014449, 943188034, 670306060, 576456835, 946020894, 165041419, 28286583, 583646193, 460811471, 830343180, 647374697, 939900233, 572088146, 73177666, 951367037, 434927406, 224691478, 373065698, 72848908, 54081131, 44583914, 623584330, 606635546, 452858092, 863217165, 856572228, 670068141, 620003959, 928866871, 513295130, 818282681, 667115381, 565225410, 788132362, 986265509, 679757276, 197711728, 447034130, 837693930, 541266879, 491754062, 136531024, 755184558, 52927302, 87383488, 7864404, 879499081, 662193323, 595177536, 795103567, 926539958, 217102875, 408529210, 616562107, 269208166, 86472517, 946113161, 268045063, 539450181, 465525142, 932877666, 526417825, 493015259, 680831854, 295971077, 904494434, 809055032, 636128547, 840143956, 150347794, 997462548, 699125101, 525179441, 252404990, 998707100, 408107167, 682297304, 153081020, 463455184, 885937107, 581077065, 760029554, 456075260, 988143890, 965661057, 491513273, 168426665, 661330883, 280464401, 280417106, 222857588, 54027351, 86030757, 849504211, 609079466, 194219519, 878551801, 951279368, 668182194, 667909912, 423308873, 775897568, 319712654, 871006835, 84959677, 605033932, 129066559, 976138276, 949313217, 583582675, 364427932, 715926668, 853926708, 629163684, 700860064, 101719489, 332410092, 540631362, 142417773, 190911479, 364128615, 462690206, 842126626, 672638004, 222939713, 938683980, 603292599, 263330241, 828114033, 758495149, 619396060, 84301107, 40250594, 537615319, 19810517, 337241474, 655390143, 138289767, 316956936, 714114215, 987425693, 453515126, 862752193, 969229429, 260530268, 573357196, 908579285, 681012918, 599184239, 873810413, 912656857, 384279916, 290369314, 947338682, 981304588, 125525027, 931844392, 417603318, 987127976, 66075792, 849117452, 565478038, 601353766, 997642647, 573282178, 467247, 155858638, 377670823, 373333980, 341666050, 326419383, 578791880, 290718026, 842622804, 667892332, 66451970, 715053233, 406206777, 328716051, 206557738, 601543610, 336601292, 241437738, 603997072, 763512873, 770862634, 51519723, 352779967, 355577306, 589945761, 503850967, 888016848, 770769603, 510193509, 582122613, 744674766, 712093758, 919314544, 21455067, 427198873, 990633369, 773726147, 796822218, 737453199, 845240643, 91378062, 935296050, 118544499, 203773164, 139552924, 647380004, 223687726, 487093824, 790392412, 980318921, 430545908, 753846019, 711104422, 182675393, 460948270, 616283839, 651342658, 340293530, 619725744, 403521165, 334750887, 88368195, 874741767, 350566419, 459105793, 799871585, 951664831, 807336660, 694307382, 521836581, 403759632, 346483002, 301289125, 828398279, 888026209, 333953267, 936604995, 982808107, 572089047, 945225959, 65293185, 818486812, 275078216, 513583474, 896344399, 16865549, 358647924, 421802929, 677376793, 659675941, 176672146, 799678963, 839525896, 713684775, 12419691, 531442941, 847068474, 770963416, 898397376, 353079791, 679028309, 755187545, 471900504, 380923925, 578697226, 391556868, 449767535, 454080925, 616375728, 613646970, 379213877, 718432351, 596218850, 583292245, 568082924, 964046048, 29501752, 709458430, 155002888, 79515887, 464832066, 386057406, 551748962, 438222378, 669466008, 136809004, 94714199, 834086040, 121542069, 191269772, 979250208, 796941740, 916625796, 716574008, 903965018, 567981920, 470462039, 646730382, 312065877, 543916403, 520835676, 980945926, 90051666, 331433432, 720689540, 911190960, 931153079, 177041806, 150693751, 969259968, 646865958, 125173364, 913376061, 352237373, 610443444, 541310897, 93764097, 951605883, 335812884, 115428397, 907117395, 529435069, 413135975, 666312740, 502460834, 259176505, 702737481, 357132375, 280246540, 388195792, 631547643, 299719424, 414848484, 724506601, 272619195, 168000575, 873819931, 861232694, 634454640, 140984311, 290949222, 147548660, 412548279, 41819255, 576650530, 142564951, 236383685, 859748424, 662581123, 580753292, 694939234, 638027669, 411731358, 334218695, 481870180, 685302257, 80468356, 122263826, 404494081, 794849238, 157987314, 352617586, 102528380, 704042253, 780231600, 70979137, 98647534, 55764356, 364050773, 176844046, 662669467, 487767047, 847395628, 192458462, 86422569, 81864171, 662393817, 258314318, 777822879, 232581624, 566814421, 910851052, 756408891, 918616779, 687272071, 281659036, 962958275, 168570940, 188448421, 904810852, 288990039, 669628399, 270882802, 274766337, 888996699, 508479061, 685866033, 437143648, 712710619, 143679971, 234318406, 950858252, 889646802, 269411134, 677446423, 44115364, 147015200, 861855841, 640827645, 179918064, 779130551, 293870682, 335935, 854839838, 254324397, 596637574, 315520662, 144564432, 552867276, 474701730, 202964370, 296509950, 665392786, 130720277, 775756907, 498107471, 544480597, 47268878, 947746099, 503588283, 762525912, 699943183, 374614166, 547075141, 254838252, 70354518, 343450408, 443028037, 6885259, 202961993, 214524462, 957279455, 109543515, 114092890, 437999946, 672051260, 781507336, 219532096, 413057979, 697635658, 379346858, 552067226, 486592498, 618192667, 188926365, 710843846, 396607008, 959607549, 600015440, 106784679, 731346184, 274475005, 369656337, 203859065, 844635173, 577837385, 917258477, 174460654, 812108631, 340245640, 785504838, 257419012, 369935985, 896817694, 981061297, 256309104, 266675463, 294022855, 183421765, 694210717, 977556703, 751912416, 509313412, 966574271, 512552114, 16410405, 775351020, 253919131, 26617280, 475933795, 346261580, 270310263, 542309528, 301394403, 162973110, 237479453, 636226785, 300178716, 822693891, 641532603, 989998860, 864182928, 880898172, 546671898, 935412514, 736966278, 746698431, 212018089, 80400186, 792497565, 490636928, 702550244, 933757558, 578533587, 286498563, 137432689, 339386078, 243251473, 796665811, 416984826, 962279290, 925238383, 722341833, 10084704, 696982556, 396592060, 488192386, 901333890, 528724878, 82893596, 658937120, 419994321, 356892033, 911889408, 169338966, 748328020, 901857310, 756818631, 864599469, 119994563, 710449504, 289299743, 659383625, 881801727, 547450693, 414124169, 966458807, 875784539, 246673385, 388518425, 316388319, 118553200, 927297876, 730209864, 244631513, 181874827, 990737184, 979368186, 35538212, 786765873, 797252699, 647725464, 757217503, 958922254, 177966384, 587242019, 544834815, 760065987, 510144629, 472734957, 488538369, 613160223, 823291635, 744266928, 918892575, 313178554, 693230042, 928358219, 915622406, 865919445, 907166379, 613029377, 648833503, 392160405, 618734610, 983075094, 760448020, 279322967, 158609523, 886369217, 111607452, 969418376, 901748359, 921762849, 995671210, 481291649, 53113946, 578759312, 709803185, 978108036, 452596083, 673096811, 632429020, 705907389, 839430662, 279609652, 410552418, 667552225, 618262034, 92625266, 963979815, 978680434, 68227038, 387197178, 812461868, 161253428, 63002230, 507210346, 451910222, 891525548, 318343592, 983260480, 116567145, 920673598, 792882620, 333452964, 634491172, 781838844, 823612696, 904441350, 590270874, 830614985, 228930401, 120736549, 688373089, 824857080, 620448046, 116155557, 223429062, 943559229, 43274345, 762446171, 286540343, 6424373, 974803222, 651609383, 500381866, 403856977, 392317163, 137255320, 277446304, 387030511, 447771333, 490639170, 848106490, 699228445, 432197427, 922462948, 960098849, 420892436, 901718119, 118166205, 191170744, 322058983, 873565295, 434589311, 495229855, 697412222, 473490762, 749161121, 791085414, 725909923, 941889547, 115088929, 931222, 666957919, 527630562, 306861292, 952154771, 478549219, 740805285, 804608481, 705037409, 980716091, 842007318, 965444584, 469563075, 483660838, 664774735, 65470928, 191838743, 702271585, 490984108, 877131474, 282604895, 624219929, 165769841, 579973790, 780297576, 405860624, 971091595, 915808722, 546481748, 604812984, 506601694, 153882168, 736368808, 836950845, 356022308, 678678637, 326742970, 63790930, 26252134, 623164843, 131271509, 891752715, 371330179, 329644560, 834364052, 929597992, 137660839, 438552536, 855409455, 884591689, 568606762, 658451525, 219288683, 220780372, 307569893, 175663602, 711681626, 573950132, 36838726, 403089331, 34884669, 861460720, 634687553, 450590267, 372307065, 878769316, 499125820, 389284618, 597865933, 351763398, 825673753, 526566787, 501297047, 389891706, 52099058, 933512488, 621368376, 731565180, 714214482, 695187422, 665635490, 305325204, 530955996, 32448031, 243712596, 907483194, 393297801, 743673099, 249093341, 972529406, 880339417, 841189716, 691058561, 880574383, 947032697, 980359304, 383849075, 855068356, 143102121, 823009040, 582732416, 329750323, 744489402, 513834494, 543674552, 369426863, 916121163, 44682672, 832983070, 47411989, 439526151, 192315092, 564051753, 195408506, 473094799, 707450165, 486356783, 772596571, 186859142, 301801625, 529062336, 173216587, 448740197, 269046806, 668649677, 471727514, 51174837, 772787564, 175379200, 292670758, 764254364, 798755928, 500776995, 889254235, 162421283, 458870524, 265906317, 786000170, 312009533, 915522129, 429189438, 915620240, 849785391, 342583369, 412319549, 581272218, 124489411, 576501849, 322147072, 857271742, 499295021, 739697159, 475042645, 209441605, 452214461, 561725111, 839613784, 225155828, 12517205, 880488689, 747079150, 787422143, 478311156, 645260524, 872945874, 8706536, 624796825, 256686629, 340023971, 513241296, 714277446, 807241145, 862910389, 62476434, 842052199, 342357933, 981022544, 993582943, 859554365, 707732003, 930707425, 73874331, 476466480, 209933679, 228473337, 893715312, 20561547, 613241282, 157502038, 56353415, 529358110, 356541965, 721169855, 375929844, 108643721, 905688044, 34642319, 435341604, 824014859, 171888454, 62156371, 781858428, 614815655, 306781903, 900510573, 448308796, 264504381, 125841844, 437381059, 762830633, 76881413, 230860082, 274425317, 768970081, 339066491, 225970997, 14325931, 10093861, 982517342, 784330040, 231162770, 344118538, 809745723, 647986189, 973783301, 73106857, 891777702, 353416611, 27710154, 843009907, 132157367, 745920316, 995063817, 312764437, 528398877, 140068918, 850341087, 443057546, 278290744, 431747039, 386803094, 1564519, 302517015, 383316951, 752347174, 893516251, 485070112, 132556163, 466608033, 399877636, 854157091, 795150408, 886063706, 773149404, 284345335, 106439662, 629095152, 462456598, 592551338, 387216614, 187936352, 95718639, 294817644, 16094680, 897473609, 805172006, 410178358, 270081029, 463839433, 713863759, 972966084, 253019004, 578374274, 188522747, 648398013, 347763148, 287378647, 375220164, 975233663, 527133548, 128278849, 892485276, 931809778, 642849121, 946117871, 766002630, 103176084, 170678269, 340372509, 903664597, 74289596, 448980441, 850931510, 363172860, 505957486, 83129983, 197624120, 258305926, 570080982, 425301439, 725538286, 544197871, 269697831, 806254666, 554718246, 352374931, 930164826, 68723785, 320613336, 802106636, 631071100, 540876672, 767931825, 268823662, 273991581, 477288905, 175842280, 674275696, 833125772, 534788377, 664282663, 805625698, 307131906, 30298495, 697147862, 432204312, 507451212, 101955542, 618634545, 136114690, 287998770, 151876479, 994698462, 133065545, 284962152, 303654976, 316394574, 78750136, 477508829, 870946807, 211673745, 885862396, 78470720, 36341157, 849242566, 744068805, 41463662, 114616259, 549363895, 690671729, 657515348, 447657737, 744052852, 303948899, 770435377, 454520332, 517662107, 244414734, 759918371, 747286353, 176528854, 663651600, 49713818, 69349226, 701277233, 839479212, 679234813, 499455151, 615913635, 387611248, 344078681, 624121661, 750776412, 728923422, 508116317, 366353427, 613757810, 676857867, 698925569, 716742939, 304532283, 777659981, 108655703, 622942123, 369836360, 13696136, 747604362, 794723774, 439701689, 328993570, 791084187, 59918301, 604330340, 821557157, 741132581, 856875068, 522607585, 864455045, 269839317, 419705969, 11508160, 832435727, 908159468, 31184725, 352934163, 470293783, 278603264, 327889655, 243738728, 191755826, 406732513, 12774744, 79620862, 126150125, 720333317, 875104671, 88427894, 371583741, 37345744, 518877444, 501062071, 579579535, 458600377, 967341702, 117716722, 436713909, 443003037, 207498790, 910954022, 664583179, 443560189, 17006668, 560244038, 613737416, 406495660, 348271093, 536118998, 590748131, 251477086, 816346577, 226762214, 263334369, 630140454, 202170637, 844876128, 429581478, 126348447, 747825147, 259247816, 460484493, 800204535, 730540251, 380612143, 623828491, 798625727, 637584532, 655143311, 229655019, 659073062, 400339551, 972527420, 95577356, 935491503, 870188866, 915261011, 58409141, 841396706, 788134925, 571942082, 516532706, 934594197, 136431967, 573069355, 715632275, 160647498, 439089705, 242170145, 839057909, 73268876, 331940700, 917968373, 880230797, 932440132, 123549969, 379500880, 520197548, 808666304, 452352194, 82871481, 210761972, 670581595, 201667499, 233074350, 810337943, 565300509, 27126656, 804224434, 394082828, 295306651, 384618249, 936297581, 561530923, 105977477, 812432299, 756733335, 434547672, 49107565, 330851534, 605896629, 280101328, 194111594, 779032957, 973665377, 468004767, 421323699, 375783491, 550228957, 458993423, 539249411, 851540622, 230592656, 864317756, 13627852, 74516257, 61309880, 97664563, 196048752, 380846005, 690411163, 992801911, 976087852, 266159907, 123971710, 953825180, 527187425, 799318378, 857618225, 163969807, 129245031, 101354404, 429137227, 597858067, 400682571, 586364814, 980160828, 322329075, 14468719, 559484140, 818410095, 471196434, 213930914, 849793834, 338511325, 575739804, 279162455, 819471955, 867203522, 633574139, 965822227, 745274790, 55232367, 195891270, 557261741, 883602479, 20689552, 20160115, 810107966, 510964208, 225453889, 300432069, 860582532, 354810195, 294446032, 291391473, 862473676, 35224512, 346691483, 647003561, 70131997, 4208555, 624579701, 66674625, 784126684, 768473174, 171899812, 153123551, 369632703, 243818486, 905991827, 318791915, 797606282, 248178423, 891225193, 173274673, 170775520, 993852246, 521815518, 37898941, 8482916, 693807696, 331510386, 988374881, 513291327, 457258040, 555599553, 106958027, 460895910, 219087678, 60483599, 295337353, 781395855, 299688883, 796152754, 886962012, 40943000, 938739047, 655457341, 460221070, 728057168, 306175158, 953360068, 330760934, 37076858, 995152498, 219489880, 401524023, 609696276, 146597514, 647654210, 92876105, 215977407, 899240835, 132922831, 5315966, 8019842, 202663715, 270162239, 171130970, 889480027, 221144646, 89805237, 594658288, 735714078, 238083112, 514200317, 272723987, 868739050, 630988181, 94374736, 28832615, 987158905, 442398905, 625282619, 530587621, 971416462, 178791285, 93595959, 360621439, 895208339, 111814989, 854452077, 206047442, 310284489, 338187208, 807597849, 246812240, 722895810, 569367022, 560870237, 161129508, 928507150, 64164746, 890845994, 436740780, 710428792, 146792295, 769692315, 359285303, 76374503, 982494366, 224003819, 508315604, 600462641, 109237433, 419019161, 960677395, 684668264, 989553392, 404374506, 859380372, 11668166, 563668329, 918756716, 759352767, 415020224, 365670182, 436713895, 430110920, 40994229, 960969102, 650343445, 766976181, 375151740, 301373821, 494227525, 306858859, 177341768, 827982390, 470524167, 274064769, 833156876, 789309270, 433872700, 163426720, 924879670, 770204991, 129850158, 854562262, 170591643, 692593168, 54875769, 624999053, 443645244, 509413971, 252527409, 607572067, 896773975, 504824729, 688978547, 720061167, 972136707, 205251361, 797295784, 346144233, 970177719, 893612156, 456472291, 107390883, 325811149, 643962073, 497332197, 964944032, 703904916, 112788580, 648569944, 753321221, 703483218, 382054595, 356406750, 847943647, 617554471, 178704581, 62910877, 139690435, 763511610, 870822730, 981362631, 63351048, 634769912, 224776996, 792734144, 59224894, 789793032, 362420100, 21155378, 710091170, 721149177, 816726000, 20928867, 793138619, 725134156, 224927550, 417637888, 962132478, 502255579, 244752159, 193226595, 116790429, 745121851, 775871591, 649897455, 28632797, 23173289, 61152452, 636737754, 917017748, 131054462, 786801049, 555461272, 102809871, 721181074, 997303759, 471112822, 952350805, 453870448, 510989515, 772488038, 882723196, 22760441, 935198250, 884048330, 15771460, 793552201, 549556046, 31798287, 68734728, 530970934, 261598590, 492820115, 986287717, 606337876, 690973220, 639983118, 825663876, 869362117, 626675890, 327911989, 808723451, 977635344, 747543086, 45030053, 847520435, 820668575, 625833485, 643218877, 131605370, 290006662, 199062883, 868643330, 467662485, 141332395, 604592822, 80994430, 324820228, 872325454, 105769218, 316407695, 26691231, 990079661, 222067363, 138836854, 302969116, 759816492, 511879230, 51652611, 754083165, 758505515, 704026909, 501004394, 47321235, 771785528, 21205566, 571608025, 999792687, 341557509, 424982716, 80871906, 633161363, 200468796, 511012646, 717360604, 541186238, 513887186, 631509557, 723090132, 491944592, 689987272, 700999434, 485797598, 559591186, 338059562, 608690998, 290957032, 631052625, 866172817, 925812211, 599808528, 69768736, 321620242, 988164032, 294634072, 147939836, 272045194, 811783800, 909558769, 249025491, 876159147, 874312626, 942426110, 405369137, 605643918, 639123309, 630520975, 838660792, 690600846, 365676845, 500142014, 572185455, 889888959, 530617517, 929672661, 65865696, 522266797, 337091062, 490180951, 701660166, 597714455, 517052576, 78277461, 73689953, 60541659, 681767044, 817483168, 361177056, 84092367, 70063442, 517063267, 69074897, 652324369, 248789703, 964989389, 972156661, 689549889, 583595886, 286896153, 375308493, 111290782, 818826407, 720526225, 992238802, 263062430, 544713851, 579411336, 332472210, 70588874, 170012458, 409403904, 359279929, 478808822, 591058179, 77458333, 68247465, 579167170, 393298486, 705006365, 122332597, 578959348, 123607959, 432973418, 860122778, 147154963, 917669092, 125507271, 623898320, 559398269, 294151931, 976316360, 327158214, 246654275, 136362569, 443479011, 893585532, 734827105, 230689544, 310651650, 456153120, 696990128, 817484404, 415846994, 639792029, 731717920, 543809874, 295658948, 926005645, 782313713, 879484975, 279772323, 320246564, 380842347, 753168990, 703292355, 115438180, 569861659, 374010041, 303364064, 987690142, 734429804, 533105329, 590169518, 41511392, 478996377, 264571380, 928593942, 400397685, 420795147, 775783750, 807068094, 140721113, 359979860, 653027733, 285364137, 81147581, 453446302, 27527464, 854028308, 148623573, 347440662, 828032149, 528341574, 968528592, 681203175, 711861310, 323657925, 181945738, 757831166, 153633487, 759616596, 346769743, 532588734, 961329353, 252755426, 119932705, 47184267, 124332807, 578231503, 948874253, 387595636, 174820563, 807952501, 489349881, 77453602, 47169849, 155528172, 852146077, 315061776, 987628365, 685973721, 684747720, 80558882, 472500100, 756325665, 473156109, 220533365, 597751599, 115962053, 157871190, 263587609, 537419130, 645170666, 179360070, 176762667, 208389450, 348716085, 814723518, 605862889, 804039943, 297347449, 594629228, 617189706, 297181573, 889317019, 845637254, 260078282, 139521094, 734439411, 837602425, 694766565, 185534684, 400152448, 628314588, 658547836, 9223807, 428357881, 641117678, 360752692, 871877209, 135193411, 916717575, 240039150, 51350218, 355005310, 789614941, 2202017, 366705556, 389947187, 239293013, 668439960, 393710032, 520859086, 579308275, 970191027, 716057992, 79458207, 970319076, 906926101, 363495437, 119641349, 60103623, 457669447, 53091118, 458066663, 287547787, 637022329, 226902877, 183943401, 265022382, 584764688, 4843727, 359084953, 141531516, 51005640, 663583223, 762062853, 532164457, 490650702, 632015110, 744844034, 485714221, 77359111, 201384180, 939510262, 257209026, 777868328, 257712645, 679361970, 183743264, 14756100, 634743211, 519456465, 544255268, 420292124, 110766920, 510418602, 844771620, 999551668, 621737157, 23975982, 696199413, 143008350, 573637887, 543141895, 490525407, 370693975, 942100918, 291580036, 485148230, 823265782, 395398548, 745105189, 391532431, 848537163, 684905498, 117267540, 193678455, 952912426, 451389846, 853636514, 123738544, 511155492, 755427015, 334587945, 856789851, 334553702, 844848953, 617400434, 565350581, 856078251, 622951020, 851953004, 46823451, 407800269, 69361075, 29695753, 909550629, 461571273, 427909281, 292595909, 527809059, 677084723, 430855616, 181051606, 418646044, 952122593, 729634559, 213462533, 523547991, 490627115, 644341357, 273553143, 386297389, 519955308, 965039427, 480353399, 337170860, 520315360, 793846221, 685133057, 416798744, 556365279, 969867965, 120821059, 889454300, 44834740, 736655461, 11011113, 894425369, 480329291, 339227366, 678800741, 639689889, 362315243, 998949692, 88074518, 384852362, 6024266, 610440276, 322600257, 972499822, 240596641, 267772944, 336558720, 952521595, 314019704, 486495388, 391879130, 350324880, 173417107, 245165080, 199158844, 765584218, 25283944, 33876158, 325701185, 40211172, 654056682, 416350349, 292474539, 362427783, 8820435, 62827781, 512149496, 616807130, 670565911, 266124731, 306994871, 140455712, 993866581, 816079023, 931609354, 20766264, 339925146, 607662499, 445020934, 825136970, 906935651, 686769802, 918550003, 883002655, 985437393, 924155053, 70419116, 821356924, 345906117, 29146975, 952801520, 834396892, 674611573, 811677635, 286579141, 770796006, 982214149, 514036954, 469930183, 209269629, 526680221, 946622158, 62874143, 236981414, 928579446, 116085095, 30260119, 413278133, 991966381, 422830253, 677578282, 761663915, 990539394, 891157122, 670317100, 382393703, 212160241, 20463255, 990694813, 344635952, 411034865, 557360027, 37501976, 460730605, 524168111, 291096530, 918882393, 850357635, 717839913, 396816747, 409159041, 483323741, 853116201, 275371369, 171909374, 695034568, 941670264, 244379787, 157518950, 985704033, 73416631, 502321207, 700465667, 586326783, 119472260, 994313148, 882787743, 826443210, 144497897, 48544757, 482453111, 579416776, 153659375, 50062487, 3812374, 101794863, 147908389, 372773302, 743149696, 230076294, 3983738, 288700237, 655491650, 154945772, 271966249, 106090277, 215177578, 149943770, 83606424, 569801146, 972781647, 704145425, 639194431, 326384526, 70214813, 727148888, 515168780, 926500525, 349963753, 186457006, 878736867, 995381767, 221955323, 437790825, 736486513, 409998711, 713238464, 633725846, 502688964, 185780956, 208080264, 957971860, 752728182, 773950567, 821395160, 536185658, 923813643, 215206736, 170046873, 529428616, 807178072, 550205673, 81299194, 550381532, 483723245, 643025955, 361451833, 638795230, 569542712, 850029278, 122584046, 462906679, 177805338, 77191437, 299047793, 470642704, 94185501, 555194546, 493648297, 391726285, 126194292, 745746807, 723778875, 911704124, 289788992, 392355625, 666161390, 427533566, 558598185, 541433902, 885277698, 640254596, 387383449, 622788364, 26697104, 791226469, 855443049, 423823416, 677316417, 705057775, 847454787, 326315164, 866449571, 934764361, 672381738, 709583166, 257638012, 151438028, 897643587, 255399946, 615548075, 387371394, 916998497, 457041538, 306917566, 577032697, 750851630, 105719537, 825064760, 657224595, 63719685, 197891039, 249288023, 918040197, 842713409, 633127879, 851178845, 828552589, 432281810, 35666536, 142067491, 574401299, 986623107, 658233157, 609969122, 946980807, 880327646, 365123289, 506433695, 311397778, 787031387, 891088703, 985976697, 451323995, 908394220, 45508739, 57251330, 789604127, 869422825, 453934191, 15837910, 424313615, 754957113, 950501170, 363354284, 960264565, 831457772, 384202514, 862389001, 796475161, 163400441, 900292692, 146690103, 614854561, 183298631, 994976899, 584423933, 486194625, 332176112, 957254576, 245196505, 952334835, 398388999, 744194748, 256143091, 215744371, 90457506, 881555644, 482930135, 176015137, 419938155, 575641335, 734027512, 755697361, 281141974, 169179855, 780305223, 619776794, 518839741, 657339889, 365556985, 732046172, 334019001, 26614405, 909021903, 11496915, 549339015, 170347713, 761398937, 274131269, 108043270, 809696173, 418340482, 814484900, 413095378, 817831520, 392492934, 476760752, 531343862, 184418561, 717054552, 543514465, 48212593, 761942487, 70744764, 608233559, 655011727, 825769848, 641163561, 246822133, 377032626, 994083675, 748876169, 950576008, 432190228, 268010166, 624221792, 434102127, 831302630, 918626790, 101752299, 877653156, 411658699, 869974362, 573528234, 217372747, 368371813, 801022829, 121308583, 77756616, 616604216, 613941512, 839441322, 384575580, 446774702, 157047621, 541976644, 390231198, 994890003, 867698114, 799989943, 630368142, 362900481, 333475335, 904625711, 232206531, 799811637, 969089609, 202337563, 137883520, 439076116, 492309143, 931827645, 736676608, 642763980, 472246956, 742547057, 583193457, 122871337, 818349893, 950992237, 660418666, 110103856, 190211560, 171518839, 173188116, 802490501, 301257964, 916361176, 391771281, 573278573, 504175083, 773301817, 827798551, 521620211, 233000995, 361535221, 336421580, 927311228, 783012040, 112737861, 800125100, 790348762, 966167411, 394677773, 220105266, 200914172, 368506333, 523322253, 933500700, 557521931, 340372505, 174245169, 642040976, 909166774, 135993297, 809414360, 44833010, 7638152, 914924651, 144813434, 28316688, 790572591, 413773727, 851594431, 880678011, 337152866, 641244760, 962664518, 593736856, 129683677, 919945676, 423726532, 199560425, 947999944, 873706322, 608495127, 403152127, 515399095, 561243749, 257595847, 897708197, 369279930, 671882311, 236222986, 430845667, 474525409, 244587003, 107566266, 553915162, 668626777, 997810692, 325002522, 235864374, 422937385, 716767526, 865305955, 608774118, 501887858, 558129783, 212562515, 718689259, 667658620, 26508847, 36681883, 438943813, 160834431, 73227715, 791763089, 932174115, 928036652, 325671949, 375189156, 783475208, 953362211, 593371620, 800692745, 349063667, 820407632, 976954204, 564172828, 715418382, 571936286, 382546160, 354458719, 160225381, 138049179, 595913262, 20588604, 281446748, 41017255, 483012272, 542791474, 381027352, 513812412, 598841692, 522677407, 97606149, 782168863, 322586598, 238825466, 568904256, 556500294, 986863058, 722045743, 548754950, 436387421, 959087334, 799909770, 378441913, 701085487, 155734900, 594495825, 820187108, 801542156, 796872981, 897929113, 823501202, 538970191, 425980924, 424982640, 766697989, 728029966, 385548624, 904195815, 741038991, 338354955, 726585244, 383856300, 411920995, 587553843, 505454623, 24847050, 421660563, 933597326, 147715046, 474494028, 896640085, 302997809, 488427915, 970026770, 344386130, 868726588, 909702477, 647120649, 413164600, 349601176, 261823004, 410346657, 233430877, 304221060, 582552119, 98217117, 388251597, 631331787, 454942166, 607760785, 602874809, 222136324, 780285576, 362817157, 168794599, 492477164, 978660293, 912012331, 883836490, 873669690, 157795322, 752829595, 643081389, 126919259, 237757644, 649984347, 830136061, 828396629, 589147797, 282987446, 323424404, 752199314, 21177717, 682878336, 688821368, 819904078, 636563580, 411074995, 730275030, 210439061, 848694075, 875374354, 784496912, 714459549, 892390573, 306929399, 213976241, 465483272, 143831384, 242966876, 116855440, 477132937, 174881955, 308237128, 812025195, 177374088, 630276288, 66422999, 861346660, 464259522, 168871874, 522290305, 801454885, 31146534, 334725647, 883780102, 993964650, 898235025, 725334011, 207911129, 253812194, 247397374, 531998969, 639067569, 700013129, 656901049, 198435663, 573430501, 678354286, 263770208, 526546071, 693488969, 713630646, 678878435, 260978886, 798090026, 999288935, 784257787, 812678910, 591583776, 576626492, 914492510, 548647775, 332117648, 917725451, 282826307, 801115102, 653040523, 993953280, 529879300, 79345802, 731935648, 217771180, 146331629, 910848924, 828136879, 121648673, 947120984, 274473315, 960662123, 721063142, 463140842, 212672096, 354377188, 263982264, 16190485, 851002521, 814022866, 296983520, 604520720, 527861623, 553015783, 576683055, 628074101, 492251154, 465507008, 478703577, 813830369, 396849026, 692247449, 488436629, 180332757, 891493596, 294590677, 748380761, 587052541, 426208795, 278158641, 83080540, 408957298, 654279133, 960914166, 75159886, 335902811, 119665579, 340731517, 895261715, 274979473, 334111701, 500140355, 77268605, 899720232, 761681363, 535155220, 470452194, 924706722, 165576216, 621801195, 469167626, 649031565, 132631239, 411287086, 173278326, 838978588, 16276133, 406625624, 712064417, 271508554, 943510663, 475024471, 791921845, 401996245, 807050767, 833360302, 900909904, 868624123, 313032307, 102313370, 125170462, 39495752, 825570697, 356678987, 651326878, 159221774, 606502575, 378471920, 828019979, 889468185, 824238720, 606572076, 143375703, 206980229, 840795524, 923431763, 716714190, 901903224, 111726211, 458979618, 663105344, 413620797, 313804082, 570821386, 598282423, 614123066, 285522262, 789156242, 728371294, 596430561, 266750477, 801121027, 263621606, 654710078, 209625196, 162847860, 372864414, 507803231, 56661177, 470809592, 721397656, 896085583, 733232971, 71577284, 693908044, 669523576, 429824709, 675055551, 142824201, 625266349, 855566639, 818313485, 738868790, 191690655, 427086373, 496725220, 628184780, 423891813, 471711762, 157878543, 270804358, 654528113, 936354486, 835028291, 730562865, 795058864, 672841513, 369450154, 428078397, 345059284, 395095282, 401907260, 988743873, 995168810, 244612991, 718825520, 131680423, 289210679, 427934262, 180162410, 853890195, 606557097, 834484677, 195677250, 702956646, 729837420, 884085533, 531520092, 984034546, 5579978, 436506924, 259416558, 222163560, 327408923, 699747928, 852300308, 150800512, 544800038, 852840997, 525459835, 289305966, 989154897, 993337757, 374499227, 269995459, 168000226, 966513253, 80961882, 109790327, 703482010, 522433523, 823662749, 351833022, 249673988, 296263178, 952206200, 19511360, 801638949, 732494274, 386322075, 34360183, 884343183, 389503770, 790272240, 500861706, 829260667, 162447946, 45318758, 4775565, 374419586, 536740698, 558159125, 754716321, 411526439, 607330371, 426273124, 114163158, 114692484, 678923474, 82084812, 852401916, 995091436, 45911596, 971651389, 982364243, 127163359, 765966913, 803262373, 125352190, 761635463, 24441660, 235090425, 303039017, 291723764, 67159594, 812344654, 794132541, 224504875, 270635257, 17417097, 717284015, 91175965, 628074095, 81858906, 986572617, 298169719, 532493815, 294059500, 885940097, 242553987, 323950925, 326138936, 219050670, 873510894, 245700312, 892741677, 964738808, 32852251, 624726920, 509517537, 462736876, 377301105, 127341858, 77982203, 959383001, 993949686, 215881112, 525872993, 74179287, 875536894, 175981131, 396205225, 203452669, 123175173, 729092109, 133276690, 947665667, 166790648, 100058781, 270846104, 988264970, 924623534, 128735256, 168997984, 446290778, 797228282, 590919308, 668370267, 166604735, 49612857, 937141182, 152349581, 583731701, 89025154, 324220077, 631680049, 152363420, 825903918, 914161101, 342215245, 769816823, 607966546, 648449150, 600160945, 308552436, 343237360, 769629134, 330598385, 752927591, 279754954, 647379666, 285314971, 639422499, 470822087, 235865903, 967184534, 622387463, 227635731, 850883287, 11469402, 770009564, 370653713, 366108786, 299332536, 631505171, 895923967, 319617226, 122825417, 966149808, 931662890, 418542358, 546845275, 542693715, 934046829, 305727810, 936747367, 727727450, 99105866, 331066724, 711080365, 531261026, 861459792, 788358245, 771954838, 531139329, 699029948, 32623795, 75192380, 243264136, 555180926, 242061275, 636605886, 85975445, 119223582, 908600488, 148760287, 712261855, 384097206, 760812639, 57883035, 452116021, 783877485, 537845717, 180424998, 523467479, 630383616, 207167969, 200256806, 270952831, 30514874, 928808696, 274892621, 438068898, 394885067, 3522651, 390900613, 785366814, 260549199, 882285317, 103361736, 814261218, 234702127, 655062304, 685130076, 83420142, 63753933, 63612456, 551475228, 609839124, 248927412, 666203696, 847420315, 561808165, 84337646, 231941244, 799357265, 752742591, 352207280, 176608685, 841869042, 793356532, 74364906, 968291627, 369727613, 783620526, 694422947, 361057241, 247365601, 156243244, 852412076, 637357881, 376675754, 530019328, 876141411, 717046015, 700411125, 408874099, 401615655, 837049776, 249881862, 378320514, 90500318, 364291371, 820768508, 161421643, 291781352, 150206540, 284846773, 219267321, 458971189, 653625592, 146179369, 208296999, 616791577, 485634768, 282102268, 701352813, 57157866, 747121037, 171793729, 932484880, 507899649, 386839933, 39145642, 897915118, 71354965, 228753553, 161282387, 272306750, 426467912, 989587041, 915416224, 713559298, 971211313, 372423675, 456126684, 601862047, 992549987, 216184107, 250448838, 990331522, 80027014, 86573189, 520745121, 253940637, 338443174, 268526377, 641726161, 316147622, 951872710, 293340048, 599314089, 860983233, 618091361, 571601985, 652462854, 125057473, 497557036, 827588946, 238079046, 950280735, 788067079, 392972711, 186275773, 499579911, 628645988, 994869919, 825844481, 748376471, 58379059, 184794787, 720071311, 454233514, 993640238, 449143648, 971567580, 496175241, 387305742, 93651017, 62557112, 128553775, 209668901, 143527204, 603939500, 113691391, 829258116, 271905349, 192349425, 247394635, 634907879, 47145753, 411352894, 92842535, 803450705, 356552126, 331248520, 635487538, 132631851, 496157948, 13093956, 73787456, 543240689, 224511622, 647466305, 233408413, 602506494, 161353747, 294223208, 911952445, 983266197, 651656164, 913498998, 335027016, 381576126, 429695221, 955306449, 168922103, 958074873, 645524474, 84629164, 446609372, 871748455, 978367075, 438801551, 775196221, 649420459, 724033832, 811832697, 965508243, 183239616, 27114022, 441531280, 775654125, 659681895, 711675148, 360396081, 539312252, 52146786, 331807579, 870723858, 980329768, 775325961, 210728900, 283398809, 573169954, 353140245, 838931777, 759318261, 800302114, 939860351, 319143643, 549385992, 695798461, 249533420, 659805436, 400944553, 254736180, 525652279, 914677536, 73115983, 903572885, 241553920, 753072776, 892356870, 926111642, 162777670, 130427051, 351059974, 197181270, 637504747, 470401801, 971234865, 964745011, 136079963, 91973370, 420736668, 385366499, 337860744, 728006338, 723145708, 152248065, 357849279, 358673563, 15792377, 435785288, 746449532, 771181209, 614280440, 216313033, 292619547, 778158022, 986176838, 10853252, 263551543, 300354237, 634530722, 504176886, 293721731, 36280321, 873087865, 659544854, 325478715, 79822553, 390671600, 796148317, 379184830, 359900800, 465072684, 32013168, 963323982, 222392584, 133448977, 811344350, 994377534, 118434757, 586131793, 681421610, 149670665, 794632843, 540009958, 144085373, 526016247, 587535529, 289629526, 99739895, 114140774, 819785882, 814704068, 392217031, 129491260, 951254425, 56604931, 583432883, 122076042, 200905841, 667717482, 155026825, 590854241, 451268041, 274592209, 718592985, 545788052, 977337265, 798084513, 558860627, 961291445, 538043487, 308912329, 306081763, 670848501, 856237125, 834336030, 946921150, 848266309, 356383916, 385917696, 297166052, 683120705, 701655377, 750952904, 487306358, 767832870, 222647333, 360442999, 41815005, 308821441, 125108962, 52850357, 29485904, 726609169, 116248941, 977324413, 882667896, 179214478, 394016097, 17845245, 21313444, 150948015, 493366241, 6278203, 564449039, 621273471, 993399580, 21356932, 404020012, 732027195, 633282262, 451182380, 486153932, 6634355, 234780160, 417834128, 875462150, 454709121, 78655842, 139257624, 407058089, 39525928, 781341078, 555715919, 259228245, 800513179, 723577598, 658790526, 523645791, 836666848, 429565223, 523006271, 339619809, 904569929, 776053316, 687788901, 394021120, 44539708, 66912864, 37767244, 119640553, 499545472, 942862629, 115696545, 100258561, 110340918, 96507383, 398501101, 563447543, 525235348, 19257076, 216481753, 175390437, 822681099, 898900425, 813972408, 277474999, 725741597, 272598557, 842044716, 971377995, 148315714, 55863433, 875465979, 451205235, 142987490, 747196878, 675728170, 254583976, 380651987, 825149855, 500834202, 328810860, 796718300, 415741102, 489939256, 87235099, 551288721, 913726725, 650277256, 389489122, 746753754, 269989523, 359103817, 117425359, 198660174, 876178674, 554037874, 95227339, 419266009, 701886277, 851290426, 223828120, 834183674, 152498403, 482694488, 830917873, 219680605, 763352968, 945792228, 658692400, 695356840, 329120887, 372518147, 808224982, 951858839, 622753471, 564058396, 72272615, 825996966, 808154279, 13564519, 412315017, 788728927, 526942802, 973453485, 229466701, 95147552, 64003926, 448356113, 828400968, 21390896, 625823032, 917438860, 341381561, 205164645, 159191, 811519628, 449519958, 686360477, 830309647, 535932706, 424010819, 399312417, 799757324, 632001709, 111901367, 883582290, 631852657, 642691534, 208908919, 666404484, 951591031, 210602516, 162173693, 761201284, 893747531, 162168212, 753276470, 737972890, 113002910, 260460961, 826633655, 969681365, 518318994, 432441722, 976059464, 861845822, 973406093, 412311445, 500448109, 177684247, 758450960, 456732345, 643575568, 297744428, 311596775, 333355489, 906593511, 500199107, 106106206, 798643927, 650886028, 109639155, 274978174, 715474393, 28681862, 371725427, 287019953, 852174510, 791663494, 772255662, 567192286, 862323849, 643903835, 847788996, 329774390, 525323624, 317649841, 324776729, 386365203, 241173182, 670254116, 78540468, 46735409, 868457126, 786930711, 752621936, 649162814, 526747549, 424375093, 279271753, 123423797, 920422100, 260247092, 203769017, 109794919, 292199539, 483825485, 946742879, 347816013, 6374387, 867080835, 130812495, 505515579, 723801062, 583656295, 571547699, 190828849, 259656917, 413500680, 62969836, 856841358, 620153262, 996539669, 473673758, 805457792, 637834057, 877936646, 232274926, 544804828, 438980896, 677989161, 634588528, 239370225, 739049782, 658576262, 326535575, 534593251, 418036817, 685717763, 744522949, 967076986, 126566279, 554975284, 790161144, 67762594, 873759861, 390222869, 222477452, 778581113, 275860828, 480567969, 7090628, 123934148, 580379232, 717935345, 588060240, 940066353, 14075204, 857397936, 429737925, 707613196, 647015218, 835387519, 408490223, 576219749, 863537905, 389275898, 727852498, 38103441, 642478584, 948638387, 901660516, 57067635, 796859474, 677825795, 562044410, 729808084, 358408419, 986470378, 509591436, 626831294, 804300566, 795708162, 655191492, 930945480, 970535884, 325280762, 381769626, 120196683, 10214582, 460781222, 902952099, 964787295, 99648820, 322628973, 905827688, 758029958, 778905082, 407812407, 64366458, 387995069, 146619446, 245655339, 818382418, 415135339, 733739031, 593885661, 41989954, 780797626, 794029356, 963061265, 164255721, 895860642, 97219176, 661081544, 249257577, 293050476, 472699890, 167502538, 9243660, 421200002, 539802716, 513290279, 710456504, 853441454, 26636464, 587881683, 229281521, 963596302, 341502259, 312720491, 868894641, 6834330, 60334697, 508186060, 649922819, 161046026, 594498103, 533685089, 477738972, 882085175, 908667473, 587311191, 415747609, 961831345, 430062079, 7728495, 560682353, 888945939, 82831900, 766764743, 665220213, 992815571, 271614695, 752421634, 474919190, 344278421, 630411575, 13697369, 11099487, 159192447, 66487959, 95447856, 684203767, 765982937, 892469876, 581901447, 179419508, 602061005, 9384237, 957413410, 254373159, 736989118, 275761375, 957169910, 299191168, 632936397, 32712181, 229950368, 871579732, 129897376, 996011391, 760823705, 787981380, 401204592, 68613339, 856672231, 731395609, 723613563, 409172162, 961290012, 345347150, 432863635, 910128591, 586204670, 920602993, 636180733, 421601793, 507497057, 155353844, 99671060, 150647332, 880105229, 942411597, 355327174, 382975505, 127858912, 416884706, 224704499, 196951491, 718520573, 460147358, 340503470, 830574189, 385507949, 841471932, 473245178, 358136963, 646225886, 577286378, 633816100, 28572871, 857445583, 575512804, 318850455, 128703681, 947497164, 8389930, 995096776, 638026273, 444202572, 995117846, 463415548, 375228493, 702281139, 578242311, 325344200, 763796656, 822299036, 511355452, 41989126, 544998123, 493690586, 688057026, 596039768, 268625810, 313770265, 329592450, 777079931, 880780924, 838620350, 864368229, 987149473, 311225534, 305759732, 119489126, 46961408, 666990373, 856914180, 470913208, 286900305, 663957153, 921846801, 458004417, 866105607, 852264904, 655861959, 992271895, 369352533, 162768638, 135945955, 680865116, 432562433, 898929789, 214906781, 791441818, 438636092, 377351129, 419686808, 359839882, 400589036, 669470749, 430882364, 857657501, 281799183, 173520405, 722769125, 179479084, 264405685, 480390783, 397816906, 675747437, 280119897, 45622021, 125342189, 718264994, 658229131, 561091633, 279032470, 573858615, 943319989, 992355570, 378463856, 922043262, 382861494, 809023237, 917542395, 269841469, 260449790, 195792965, 631513649, 330776416, 326722332, 799809691, 83489791, 611048728, 756672393, 666929326, 902048250, 503605301, 376752115, 330035400, 271622261, 287393862, 309576721, 391891454, 932243317, 448362133, 564825555, 225174058, 226755631, 166213521, 735266002, 810678441, 284299065, 482295851, 679176280, 913492635, 484881276, 142278620, 470407409, 15584444, 952002704, 146428482, 225238136, 64650239, 623385785, 265910181, 457555033, 868430441, 727778891, 937910408, 322066861, 289781417, 913197280, 440512293, 71456163, 250075948, 81616071, 457036799, 152708785, 781379983, 262890969, 298613273, 568113961, 516237862, 253673246, 38245192, 962475200, 746560340, 936246198, 423813930, 850362, 662650081, 354077982, 92816155, 117358978, 144225551, 397564728, 154044365, 432232828, 493165877, 443676806, 443996460, 470742404, 990935460, 264052317, 343818594, 61849331, 911902520, 399477484, 453076158, 973436212, 374663172, 690137776, 909389526, 907573791, 357114957, 160332987, 528893013, 255450306, 519287703, 971815230, 800470686, 366795832, 641381153, 873440476, 686156073, 17992730, 683232910, 120007347, 106005333, 596949700, 468453333, 640396652, 747833685, 515986658, 549557895, 381503889, 210185022, 628309338, 866105254, 952202519, 358111887, 87447949, 580485515, 319330597, 657721059, 954864283, 179436866, 771890867, 622816240, 290369172, 10595717, 362159459, 983487759, 407536323, 639699605, 561254100, 320106474, 942708768, 676031035, 330996712, 691750799, 857880666, 674475878, 89582083, 889073224, 889009831, 1746775, 542138529, 51461472, 487238416, 448353706, 138993898, 448058456, 648087714, 479763781, 874268400, 763849978, 409819834, 441202776, 623202957, 631482119, 971892802, 986536730, 479159144, 949400635, 901128781, 557270163, 818793536, 869358475, 812426858, 857288234, 925733549, 529289147, 558347662, 858950279, 303687152, 483988901, 136326482, 553983209, 610208453, 654050071, 251169727, 395545371, 199289984, 490108475, 970291971, 80917068, 540593534, 68632888, 440505302, 991124385, 12619451, 622484126, 925744459, 330089382, 883048215, 720299133, 612018546, 51606429, 715898127, 921735351, 758374866, 640158920, 285297404, 732086775, 690648032, 280401343, 347799963, 842412303, 545364410, 42219140, 350525236, 704053989, 803284937, 239325824, 703717251, 510223387, 651896718, 900678310, 956449241, 985472302, 395898392, 358137, 948170816, 632443207, 738737326, 724437200, 779913890, 474199047, 712203931, 812336420, 983985455, 709501997, 918757519, 115262018, 744752674, 105312205, 380828969, 263180958, 37408877, 301673721, 741488839, 101228253, 575686920, 285614667, 270390819, 974305049, 693105839, 537485429, 453259790, 266272446, 487398808, 487957966, 927150033, 264623397, 361011978, 502374395, 233551138, 969989436, 863324532, 461898969, 402774933, 849722241, 211874659, 215690688, 351351132, 717709558, 215958826, 612219384, 666048683, 451910478, 743525084, 267804979, 324518755, 103073574, 933711079, 172804324, 707660710, 761179089, 342877153, 119323631, 692786862, 734728225, 732289644, 137949379, 587461101, 138590166, 886515597, 887017284, 876571122, 835636892, 342698155, 4800195, 754711343, 442726110, 761981350, 523272997, 750680051, 865089401, 259376076, 799857773, 714742416, 141308026, 88325727, 521873188, 341514489, 356971414, 555342305, 44634526, 369048779, 58649887, 321946294, 34755477, 118870175, 648551965, 695453174, 971290708, 197204666, 435353082, 954151376, 895697967, 285317754, 124102286, 320156678, 529683788, 600621318, 244098525, 595869710, 591741657, 225525738, 555012584, 613188730, 887573909, 996197231, 576175839, 87749984, 910205824, 621835551, 822613647, 309244728, 606928013, 334651568, 237329070, 451415077, 365970736, 165161409, 668235890, 56806846, 780291502, 624991903, 246211511, 83261697, 840051850, 58599761, 877532391, 187427438, 339058299, 842896750, 838201171, 771105029, 561462041, 100903083, 744057196, 760946373, 717233700, 565179566, 733910698, 128852887, 873962942, 196916727, 221734117, 176092491, 260895437, 686939060, 567882251, 882364733, 527632313, 947043598, 423961409, 442860581, 232259618, 620880626, 342886854, 954675286, 143870700, 629975272, 293212194, 572797166, 341787033, 748914746, 837540920, 642567153, 156488331, 692979530, 520998832, 156945637, 457120466, 824408658, 177592664, 144246788, 525537920, 400577606, 847999314, 799737541, 597276841, 62054153, 162194135, 544677733, 156689525, 587679661, 635692540, 194654720, 96487607, 820326993, 302254851, 474701993, 310280506, 23727267, 13212791, 549448551, 134889868, 667775686, 467173294, 35279630, 297973580, 265172422, 502846914, 419606638, 430123315, 535850960, 674566868, 152442922, 86323311, 734387988, 500766137, 518715426, 743834806, 243647757, 463816936, 845537130, 688506563, 776960826, 606206570, 310141046, 505132207, 243634578, 745760632, 875538845, 515371022, 774954354, 966992216, 190479633, 720343035, 414470796, 208744593, 748383720, 572517057, 821913208, 402917418, 708622358, 172975625, 105836644, 650659460, 306666428, 43593035, 504724866, 113617610, 913065430, 313471761, 456068189, 757963325, 704412265, 596578761, 500853623, 786377719, 329889863, 556441206, 378637656, 947495106, 73888741, 624352613, 893971934, 649169577, 700386693, 55305372, 236322789, 545744061, 280561925, 639176007, 497003202, 7572022, 30511874, 932769953, 635699205, 762246653, 37566449, 275590959, 151308703, 270602992, 739243516, 268060230, 78340233, 298589637, 778096533, 957610434, 373109636, 605132107, 781231796, 753792639, 416450916, 94514631, 608417083, 964211472, 514929, 482074472, 790824270, 171564412, 982070090, 998245465, 681088117, 96058751, 602169238, 123053633, 562312639, 117802765, 896445651, 99433422, 154506470, 157668198, 462704095, 215089074, 809987780, 239167310, 949914410, 34984951, 164995602, 208086517, 13542639, 365010729, 908375564, 433895539, 976155378, 329978210, 907047431, 603146323, 284306512, 823079491, 98208394, 86672606, 231426886, 404009814, 218092254, 163481109, 608768075, 174226944, 56932078, 565076652, 343658609, 275222039, 719207025, 323698896, 274501382, 957407669, 451769527, 959513716, 844371148, 98826286, 693717072, 755949002, 784954274, 982668529, 26491736, 586854588, 910076015, 35174382, 689698473, 557721567, 825688839, 882273695, 835209330, 381517794, 794200973, 575284684, 865489332, 869186561, 635793747, 529207304, 325852535, 57945101, 137501311, 838158137, 674864476, 216186030, 66067473, 261609222, 577458226, 292069895, 50365467, 685287216, 782860945, 29318341, 802070231, 373916873, 976200242, 692115109, 311476132, 399602711, 535597283, 182139678, 763459005, 377208621, 878584764, 689076610, 881818187, 291818467, 756257845, 766790755, 50278171, 628607723, 898496254, 494576456, 29398311, 928556590, 641882776, 599926017, 117773181, 89969993, 919082276, 724554625, 653865975, 761818465, 767174376, 412950210, 182299000, 427397105, 564975593, 525219935, 73638327, 810778679, 205181038, 949530421, 371925102, 314083139, 675450100, 201974902, 402378295, 261847994, 908335171, 75912013, 920008647, 420594563, 22982860, 832985274, 838983897, 618499384, 274904312, 652690143, 446171754, 657687620, 843662677, 371223889, 540519557, 804471670, 701728151, 359897662, 882356487, 146387316, 454624575, 803578687, 369118435, 997861522, 604209579, 972064009, 832237301, 239574477, 775242306, 662911620, 44085316, 847980345, 909377032, 853100829, 10196615, 717249409, 970862240, 726251227, 305513659, 187717665, 313518732, 225982313, 807655533, 206594713, 542165128, 414472897, 723166580, 124497141, 957397460, 172342455, 351496200, 483248400, 998081089, 639158690, 855027580, 193897581, 631149724, 195441034, 397263335, 466562483, 873890412, 637366445, 529916639, 870703854, 219297278, 293660070, 77878107, 258848253, 946228153, 219461806, 533210445, 287176569, 286290422, 149016807, 48115421, 301174301, 724857200, 125073557, 648292837, 755732583, 280720615, 946851006, 934492371, 374979496, 466415718, 649814847, 912062754, 872134516, 614794805, 125374755, 510607377, 182378329, 717131317, 738779964, 243570698, 164411202, 870158614, 507026629, 355658385, 40146055, 243420397, 629966390, 829605267, 733052998, 503786239, 501237062, 187330594, 800031418, 513612435, 753033361, 91114913, 819521805, 293139072, 220706641, 995454294, 996718538, 111996964, 388460647, 567602260, 100562953, 513010476, 176980471, 784236422, 416772747, 922385007, 713982010, 776104691, 771529811, 163941482, 164836743, 805808039, 786624631, 294460806, 894313607, 972013649, 440609408, 482556926, 36068532, 86623290, 843753198, 137977426, 283482180, 82141142, 264532109, 898622758, 282607561, 917121135, 289794228, 557384790, 93740506, 556330024, 972914582, 864307183, 382567521, 351134936, 34653058, 929207851, 39510708, 654312617, 448417498, 614237111, 296174445, 327657293, 544120293, 123455955, 242804298, 955885183, 216438449, 201665062, 576704896, 974770844, 778551536, 395318328, 256434765, 92203084, 358410865, 281385653, 541653705, 883119760, 675098265, 60376793, 255214018, 243407079, 65152540, 158508383, 329265873, 264088342, 704006711, 957459721, 424773082, 95971961, 629070993, 746157815, 355833008, 270273087, 861783113, 334932467, 764229726, 986833007, 424857539, 509469675, 446861919, 738389600, 343146870, 342081827, 400025280, 76714564, 164301561, 515366546, 258290443, 954887698, 622781068, 450946486, 656785799, 492398107, 205964934, 776813561, 460121512, 244656729, 28989588, 845434702, 264695150, 94435945, 799333574, 922741672, 548537046, 107389917, 273986506, 377558353, 435124900, 673513664, 442961477, 501533298, 661969819, 432956555, 691391198, 634451716, 889180886, 948859305, 993915584, 836275207, 508343308, 771267781, 308581213, 323038090, 256553336, 27551510, 879864596, 265216979, 446798800, 432901730, 666874643, 932757219, 638618018, 585823767, 158268340, 63752457, 455810934, 257240723, 901128052, 525716647, 455125049, 387932764, 210821849, 364237500, 168350439, 759879163, 950047841, 629615809, 699164535, 749797253, 699503733, 41233832, 849798142, 8139808, 484470757, 520695163, 793687603, 869291137, 559473104, 60135130, 575151929, 449590951, 586442746, 667654556, 667833060, 49533068, 548726420, 281105542, 749116757, 352644564, 692352883, 322426729, 808614920, 300184473, 231825438, 849499329, 935119016, 743186225, 606971706, 871773206, 157989574, 124942670, 114384724, 433508117, 796425101, 140915767, 621574663, 330057430, 696031584, 612158563, 462832796, 141836196, 416154700, 356813320, 868201307, 152344020, 653234717, 305705569, 105680994, 577928034, 996811217, 798955577, 232375091, 424270432, 732686272, 46825998, 8995106, 559971002, 675462789, 873030855, 267344290, 897679510, 378402867, 41549123, 938825843, 790410598, 122755665, 697603188, 144117009, 338446059, 933605309, 331902270, 179436539, 376729508, 902698389, 248347082, 267735385, 762052609, 242025746, 153316340, 972292164, 91528665, 485198267, 779596175, 104497908, 841174645, 646962761, 776549601, 567020450, 334303167, 759017749, 72022857, 808643475, 569785951, 738166252, 797780293, 796315813, 824597825, 300084234, 481082488, 348713182, 918523119, 463744801, 139808194, 304583776, 903546541, 669396373, 58965258, 410824021, 972214607, 797431878, 585347335, 816754070, 86720195, 771718926, 692484963, 302107106, 506515048, 525841734, 2533911, 64589637, 391617863, 248390645, 528048646, 79487661, 823582891, 758546346, 71367107, 777500274, 166025058, 761953954, 548508194, 593438352, 571840415, 56378547, 181648469, 690073432, 514595744, 496579934, 858419852, 698978732, 681595308, 198880234, 426284925, 946557994, 725626078, 516279178, 255990413, 360276588, 139850762, 666762249, 162938894, 407246519, 478587216, 48737272, 155471260, 299602240, 94619253, 207370158, 448677652, 721784464, 587071122, 62611320, 328246969, 297824286, 977905245, 715287480, 262999010, 726447122, 488093444, 429787988, 803331449, 580941030, 254463988, 38114345, 527633717, 813022196, 722522512, 768170728, 461682307, 313464883, 824055827, 6249571, 726186899, 736252377, 150658766, 434543185, 416969596, 653566533, 853335207, 53754854, 429213979, 300301566, 747592247, 461896811, 60188085, 426109522, 977921794, 500923020, 233239913, 498480294, 588845967, 409514119, 853856397, 923397701, 539791482, 683093194, 700316192, 388888213, 138518166, 725852432, 88108746, 745648734, 13859950, 231522750, 340770053, 831081323, 825144661, 139153490, 376563088, 319255491, 229281389, 74242014, 270908760, 593610916, 551199378, 646326916, 663367009, 457313537, 232755820, 953973635, 209295835, 707053704, 950457793, 971966759, 10446042, 484151744, 22870321, 845496437, 286826297, 882006727, 165625589, 351982853, 259464527, 135603699, 938028296, 213739577, 780721045, 544200068, 651107842, 685108564, 155488542, 30111410, 764976827, 45379849, 501933565, 685653538, 609306702, 277452365, 752139146, 677433175, 365909950, 13377030, 164923193, 675253900, 124943636, 424789852, 499439761, 657038788, 403423956, 922017576, 724340996, 382816086, 569682962, 701790994, 335380172, 849814783, 491926276, 684206295, 944744498, 615816694, 976466850, 578300555, 359418369, 842123571, 987685222, 667950232, 376800068, 873167904, 605979279, 567706486, 905492305, 767685288, 165130244, 562889169, 667793494, 607169136, 900146311, 434883454, 958678589, 691652941, 56630929, 341460911, 174047709, 875279995, 870266152, 350807475, 588766060, 128070962, 609225829, 348093234, 391372909, 783447298, 419263840, 191654463, 245660865, 391682731, 485520977, 728346152, 895941969, 350254604, 626297557, 129480649, 698767433, 672076728, 842382869, 227728938, 129000308, 155319222, 452051533, 458573170, 212527278, 621928099, 436555403, 490719254, 962299316, 250513760, 90015247, 125077838, 281287539, 170942853, 957969336, 185437095, 116418946, 408008075, 346181520, 327754386, 173192009, 172499584, 117373290, 482627255, 809022189, 443210826, 727346555, 927676628, 727597334, 474125990, 444236090, 38619312, 581758175, 874599478, 478187584, 823983939, 171205625, 348206489, 525476713, 459616656, 327908238, 403733998, 742538966, 817277143, 975463198, 363333358, 941928400, 374822379, 940492173, 643026459, 744814748, 231863978, 483994618, 245227307, 789293276, 471845273, 74625270, 658416982, 65905083, 525593200, 424980498, 993097061, 687447861, 614141092, 656792859, 709366389, 600911834, 295158394, 669199687, 860704167, 224403375, 482946533, 997609721, 45195034, 491315178, 377368517, 532464742, 773082668, 481175404, 324582899, 411234959, 250663762, 706841757, 615155981, 963427188, 235930113, 464427346, 84624548, 10329385, 999161678, 178766609, 567207579, 940852033, 615617407, 5272306, 543030349, 887270673, 586042651, 700811006, 767008744, 360007581, 233406017, 723698387, 194608063, 899102086, 733093550, 387873209, 353681125, 611359956, 865378536, 620934396, 586986488, 526699654, 810774340, 394805465, 701313431, 380985775, 703451175, 918266230, 30794491, 353807145, 170027456, 851412662, 119923484, 529345456, 45537914, 824740800, 97786986, 263861585, 462973595, 499667123, 825398789, 276164933, 411365360, 174912472, 673777776, 579660867, 35091877, 607750130, 657371188, 707447123, 904599563, 893382340, 351241409, 52550080, 527901046, 512035056, 314952543, 658096516, 740834267, 741340917, 520030011, 555197369, 789656530, 599948341, 39900186, 537135203, 959338900, 68436801, 915638837, 564211297, 704338579, 803066960, 341405211, 743482529, 630949762, 748302331, 148411393, 813394823, 489652553, 724030620, 944219661, 557453582, 711347054, 947519308, 878310815, 71891524, 511837534, 887146591, 117630441, 806413333, 489916861, 502394880, 341861121, 917657615, 52373529, 56786942, 495332387, 513042833, 204872277, 246882195, 383581452, 825214635, 511749535, 992383867, 421022613, 297690254, 422901704, 975726191, 684729670, 698629894, 453562219, 140645535, 762150077, 369865380, 175716618, 146014753, 939576378, 781891744, 487366867, 522649292, 350084992, 4696145, 806371542, 766412703, 153487992, 368584689, 763578540, 885969551, 257840492, 844382004, 206530252, 134386756, 950611186, 183803226, 526281737, 918974267, 432919343, 564087493, 680752216, 837932138, 321350471, 226894480, 736918475, 664542229, 797143592, 927411409, 381558614, 982752837, 477817534, 374913605, 568692985, 726146772, 493040050, 525698151, 723067233, 478007342, 977447015, 276446276, 151235226, 683562330, 6072099, 141537582, 668373999, 178302582, 879892284, 367775824, 134209918, 803716113, 649842104, 588983008, 960541054, 526774041, 65020233, 301332864, 682806988, 628898380, 99010710, 910778484, 522659078, 116822633, 635495282, 480588280, 365561260, 112243759, 488782535, 718831986, 844395670, 922902906, 845960516, 758017389, 510068791, 376786103, 962737205, 146926134, 572028853, 100884554, 647346361, 869166418, 789048703, 505915429, 384266513, 434510031, 82106992, 732008063, 591834623, 900861945, 906370303, 920104857, 278549592, 639720531, 792044221, 628833337, 228351074, 593099577, 264729188, 430205180, 646049761, 320277989, 17465007, 454976869, 235611465, 934928033, 782307678, 197869424, 811068026, 476942312, 670445618, 139191098, 723646958, 459681283, 231368281, 253475330, 197787933, 897724022, 459859452, 812013482, 178176078, 984222106, 367566118, 129182543, 187334667, 420569438, 641844214, 306752187, 864971063, 256945118, 817554172, 918275173, 30977933, 800731029, 228993331, 103824642, 216680277, 211026477, 435778973, 350090109, 102130165, 255013441, 383329979, 884915941, 433457908, 133942010, 765079168, 188288346, 476603845, 285195309, 209026418, 882351526, 380483071, 801575753, 991339646, 429736123, 246853663, 92797668, 787812504, 813849758, 459436173, 715471103, 684447709, 666546687, 838038832, 105120948, 838098714, 912268049, 829802038, 617779359, 797011394, 59544232, 157188711, 289396009, 897787405, 435252707, 994443969, 206892905, 597978487, 298391009, 514727965, 579158575, 680808983, 74168098, 831480717, 222120931, 161796691, 884412253, 696185852, 173781750, 586304459, 602693362, 948473536, 484016047, 367768213, 868191624, 729875366, 167329586, 824219357, 478558142, 819557399, 735628960, 482615202, 883433768, 697052150, 480372374, 692459891, 59859031, 938593540, 27665947, 700933528, 950643635, 917369395, 202286681, 976775337, 559134375, 106730869, 783355804, 805294497, 704735863, 387806793, 563827724, 351967085, 672234149, 256735743, 459566488, 613858224, 799828045, 49207114, 320532142, 200098596, 118884132, 412232476, 909911050, 908803994, 31550112, 333424389, 348664004, 606809902, 128382601, 269034148, 435612786, 745171186, 685918753, 248843371, 862175250, 662442719, 38162816, 133430055, 194215887, 936499011, 372124100, 524249931, 954554356, 293351019, 275762611, 764193570, 422045293, 290110721, 732423915, 266339079, 283209733, 170384720, 537387839, 883779601, 964350762, 803141065, 245697794, 723228677, 609694865, 257533216, 569464590, 295966432, 860572012, 423088860, 997797013, 841528206, 911312228, 729945297, 974351308, 703818747, 511630204, 313361465, 663002428, 293021775, 800924673, 807330683, 687556835, 208607289, 826733706, 151621203, 654265575, 505868063, 322606078, 413735530, 475356629, 239692320, 210212338, 898357026, 972177139, 746799091, 555366375, 113203604, 4267081, 830856866, 11212022, 423016173, 455933669, 616466322, 864469700, 172884664, 183425625, 352335160, 344698974, 811193042, 912050490, 81882046, 624112155, 828895407, 38894274, 954395495, 955288765, 843487964, 451717638, 893186230, 545359845, 775354538, 249879051, 454449951, 93793658, 953248516, 403751075, 886763337, 433444248, 225208259, 640658071, 560499655, 249686477, 809960001, 188927019, 435111341, 265356367, 80923251, 168220574, 144827379, 801899214, 853304532, 107219421, 692767731, 899177455, 932061772, 311236722, 979630260, 640446471, 973353315, 647731652, 420042866, 458127845, 499500642, 561960572, 796511864, 957021993, 524288246, 625018956, 124979198, 538872325, 596604466, 147077529, 514344992, 367908730, 943610816, 318110276, 158365486, 136009701, 596398084, 394558200, 640841829, 814647426, 126372037, 482872713, 70206090, 298155926, 215526788, 122512825, 413718236, 671668320, 906230637, 590881442, 579603923, 97970946, 522820123, 402922622, 84755917, 742854512, 690120072, 359110696, 652681037, 87512559, 451083446, 507524196, 693139907, 123212503, 728367142, 946387791, 390453919, 553436885, 546421403, 586103897, 263518632, 49653336, 635779485, 587591093, 440057572, 396525905, 264133766, 237293933, 69705031, 214669310, 906183117, 144999571, 637142820, 524603529, 537201765, 624764437, 631871994, 175661382, 990078449, 217399302, 445505865, 513447680, 249762814, 750517993, 587102047, 334655758, 961498506, 69531731, 250639217, 500083391, 535134723, 44683139, 27515731, 925569051, 672587659, 831439160, 704996566, 376884283, 972263884, 253299984, 908933944, 312853683, 718551034, 554563418, 349974679, 495183847, 590364939, 544503339, 168301531, 706024186, 789638536, 854128005, 465929549, 851347935, 380230264, 23651826, 502035915, 39338572, 816994527, 608708811, 243615828, 961046407, 856946654, 47895047, 891715516, 213478018, 798046199, 105081058, 721444184, 201015131, 409281710, 843379827, 154166513, 105459652, 972511493, 111814207, 354513731, 834885417, 107774508, 935670343, 959398237, 557934101, 369446234, 842205167, 819485372, 144459721, 186242778, 956728263, 161758773, 724800828, 748657070, 723888358, 615071379, 83300597, 347696021, 39863362, 65654199, 297969568, 492145430, 57150751, 872004830, 790486146, 748053999, 580133644, 937373990, 634534846, 731110514, 562263989, 178763650, 241270494, 466124052, 503831811, 424229713, 806958152, 163365191, 962707404, 601506629, 903701746, 937502211, 195451472, 751785237, 887070863, 651408829, 723244412, 377300816, 485250612, 146048305, 130888421, 800851611, 766833166, 533039973, 156145645, 664923875, 925913308, 665908352, 434867460, 849050762, 926054768, 655023477, 824995519, 825027742, 968559719, 494980829, 961095020, 525579736, 61417031, 891004821, 446542944, 776130338, 604443668, 606646067, 886593686, 789821731, 332281770, 281310636, 165969168, 936036998, 999031372, 272940236, 328487495, 669903595, 46677491, 376107739, 75798362, 805504539, 430559708, 603086921, 639287253, 325395301, 929904486, 96589773, 956442089, 521367429, 205536308, 18810024, 369176438, 492889162, 225787333, 384903597, 643272829, 481122002, 103897346, 866326301, 828948615, 437942620, 390273266, 895785559, 270129591, 299088555, 634518799, 508209157, 658682738, 239554916, 267183719, 792967563, 185808365, 812123395, 556350645, 995198723, 932303855, 719874277, 348039842, 504704448, 783193041, 765296969, 750799544, 764696883, 313131186, 348354884, 391164736, 676678204, 152087827, 763223279, 989511935, 24525902, 956722101, 134250979, 929423087, 428825236, 333540092, 811441477, 384767902, 61426960, 242809684, 438940368, 692525056, 675869704, 837531115, 579068380, 67581214, 282074096, 659525164, 980665018, 273204192, 842909314, 753758078, 211842978, 541521253, 868830719, 897693726, 556681298, 515199766, 628505226, 563075908, 128836088, 535579156, 608074871, 552563613, 99082630, 82813797, 772220549, 851736905, 406873266, 28174616, 417210675, 30480045, 671577018, 204752892, 150469941, 505808563, 50380084, 63057962, 397251641, 525022445, 261936263, 237138322, 942136085, 509429752, 664096040, 298993461, 107859043, 204289019, 411723303, 545809561, 885721792, 81795185, 946687114, 269168560, 289432859, 436168586, 215377087, 592538990, 682078693, 583412505, 423267469, 672218967, 1951526, 959699821, 352400593, 955513071, 538943806, 273317688, 366438816, 370312809, 743793131, 141387651, 132534063, 128151418, 646965501, 326908726, 278305459, 888693872, 356018145, 7003575, 912599512, 46689707, 509091550, 969189896, 153210644, 53517835, 268705837, 692324551, 644324730, 837646980, 317248953, 152992501, 992332844, 900800630, 172351671, 594538559, 108528712, 494793160, 184720082, 244114256, 4256611, 113464506, 434975965, 343191313, 627413257, 854260083, 495104278, 404341499, 846032101, 782819220, 261219297, 219029843, 514006212, 779951538, 882231934, 909902337, 7220916, 132848740, 574848090, 243139144, 18332526, 290103738, 280556685, 363501520, 969990059, 241311889, 877598016, 596187317, 425106122, 25737316, 100633757, 370330400, 783751878, 708148600, 69028075, 602382953, 87099333, 418282721, 886922666, 463010561, 808650466, 542305108, 884291776, 190800153, 639131934, 696015542, 171390208, 22755519, 301545693, 847412127, 960086178, 582857610, 359496785, 811901532, 337730113, 839749341, 430915187, 806570478, 506321278, 65384854, 678695283, 522152863, 79099935, 1806769, 119198764, 9705923, 101191782, 723729026, 958576303, 824705215, 130741775, 864789218, 376549394, 827231989, 461617455, 538883255, 18411001, 367836360, 906394176, 267702577, 652146789, 790697561, 727123606, 232734873, 893471021, 682154077, 606179356, 939537395, 929766929, 545927556, 223124957, 504892117, 344112022, 795010923, 986176193, 713871477, 150795510, 832961798, 602411624, 623220220, 769797910, 986943371, 602151904, 324485259, 680662955, 83237089, 210714373, 287952491, 41568646, 700330682, 155012783, 230653225, 828390503, 412811879, 970189433, 522993693, 856657418, 394307784, 452618048, 418026872, 69503422, 510478919, 670612124, 268093112, 245780508, 854083595, 330818864, 243105933, 633539740, 708457563, 782305047, 203828470, 660874669, 267140281, 407851082, 96536568, 775545239, 211613217, 629271639, 519463188, 554689676, 661028710, 793284554, 481790426, 306639132, 31387471, 796313828, 801475376, 780551542, 156400823, 242561410, 764149766, 507574375, 142780813, 997123558, 439210719, 432653281, 95926245, 952800643, 881350074, 583414261, 394267862, 57817940, 560054310, 552082376, 385175278, 93635520, 445751281, 880525183, 654843111, 562092018, 587868659, 465081134, 394144737, 619020807, 906255395, 549408180, 859466351, 252839733, 429269940, 88642289, 24044572, 241572484, 303132665, 874729900, 293941835, 299729264, 660038412, 667108941, 953779961, 416006143, 693161513, 55280750, 487995771, 99679603, 966398533, 377939518, 700540120, 187430260, 769363830, 31180959, 777821447, 844405666, 337805852, 285154999, 174532212, 778915165, 63276106, 820042234, 439808442, 248943063, 752122085, 601075583, 256823079, 207759801, 555699391, 417952110, 399537044, 477382039, 221669464, 177129221, 937862326, 331467561, 908664579, 414575088, 591355467, 275976324, 458243082, 338401309, 445472130, 54165454, 368142305, 666860142, 508149250, 301779905, 140656378, 365084287, 784823613, 362935902, 30230538, 244616376, 872180054, 553446661, 532924654, 471545275, 223604936, 66664218, 333847668, 385571583, 671773458, 802905210, 643447718, 342077383, 105804718, 665416166, 548501983, 356847208, 382370586, 12662284, 896686460, 295968728, 947552789, 50219502, 352737864, 658173569, 992695256, 254625288, 881768630, 56445098, 795013581, 127009506, 231232932, 248611984, 265692653, 700178149, 418664699, 381363375, 771348773, 257411330, 448607028, 734489270, 761782928, 560764528, 642934641, 836873016, 633506611, 164198650, 300424374, 819074099, 858856884, 795732630, 842455539, 245466136, 826516125, 95739418, 709180847, 50925401, 600368667, 834758583, 605366385, 146988604, 726719312, 134870403, 373808056, 784026517, 719644763, 760375075, 223627337, 162350306, 913250566, 660731039, 101954215, 522116444, 766946270, 148723543, 988420718, 510983955, 431279633, 34033012, 403807423, 906746012, 450851581, 886055942, 554916224, 270803813, 160038876, 85665179, 988027041, 851775534, 797484946, 438177604, 602862208, 602843216, 357055526, 988374286, 718967143, 521154843, 163935864, 375125145, 76878463, 68172169, 647024079, 536896633, 440559835, 854976980, 495126058, 251943403, 343721437, 105914047, 782762499, 522687092, 404020573, 305000401, 144592256, 985133623, 284485528, 490594528, 880565298, 674159608, 997817067, 264843369, 754175434, 13426004, 474387626, 742650724, 947744663, 921868094, 756850428, 905621858, 12796062, 480974322, 832310819, 616193546, 52457523, 822282182, 260870985, 210503577, 659424771, 321585587, 818933528, 896660015, 625193221, 52265153, 308101819, 969626156, 279313334, 44755688, 989511733, 668390373, 849631831, 818503289, 556506323, 203960185, 508176867, 126787951, 581970405, 893175994, 250507977, 388153985, 237017056, 570574426, 188508806, 372754926, 389302937, 569548833, 478081587, 930272567, 990140370, 60016781, 704820546, 414856602, 98367716, 908755228, 172972317, 982819379, 393551442, 303958464, 283212188, 836285481, 418720997, 110186833, 853343922, 558453282, 403897883, 969992992, 192829234, 890048524, 183873006, 28462017, 479841180, 327383978, 529040339, 628257629, 173361486, 210694157, 296980063, 251381689, 201862726, 643137658, 419977586, 543140962, 994284984, 203849227, 897206945, 186982527, 819532549, 345216123, 341610530, 516690262, 973515867, 591025475, 4070990, 489557197, 107067896, 499087388, 159003731, 705021178, 250014987, 999844820, 807927076, 881121253, 655696184, 199547686, 97874175, 912408118, 428393518, 296312328, 724766920, 415500394, 190604363, 330654097, 137874378, 397031739, 548584003, 863844677, 619001838, 440548940, 277655856, 87697378, 773456601, 193927415, 269158101, 884114523, 102823966, 930780265, 743524144, 203141623, 228122707, 482556337, 471351934, 508611853, 404041121, 974917688, 936738099, 1453103, 913757041, 760715939, 202925272, 465115599, 281189264, 470387425, 457190048, 855927025, 435518036, 688151237, 836987361, 655360385, 349976426, 714187394, 923177453, 478725926, 838316418, 186070324, 40596804, 634352161, 693242505, 630484009, 998121034, 750723179, 936249901, 156371249, 882780372, 631126082, 481589505, 450718208, 519259339, 941394782, 897075008, 279782244, 240936498, 551990351, 878614132, 324020794, 692980546, 801781802, 525781038, 631328555, 753447072, 808281018, 714148264, 506533926, 329823236, 465866873, 629278537, 948589710, 127222667, 213135896, 868476808, 525727400, 243794158, 825988505, 549016657, 683385351, 606817352, 813584588, 515653425, 828681789, 261115651, 169376653, 955096991, 829808493, 100127414, 751942643, 605469438, 845191131, 677526578, 297910853, 860565108, 799864808, 448100016, 401149059, 827312836, 136796921, 181156459, 89294667, 812950654, 445451311, 690227361, 662047208, 909447602, 876771459, 316628968, 884695504, 808393345, 349559337, 280036575, 795905636, 987401726, 546584671, 651098415, 732808957, 196339002, 705827073, 584886338, 192100024, 947766811, 100728024, 902052996, 806827659, 139424394, 324570835, 219337103, 790056774, 330174044, 886327555, 91869883, 279367204, 800544615, 585091811, 206791102, 136876253, 76782574, 400557911, 96849998, 255983046, 600487373, 773662128, 838889469, 311661972, 210084396, 82115959, 587732707, 992034553, 255521344, 410665432, 397402657, 268611520, 892949272, 216784343, 786488211, 406443506, 202599354, 645103932, 264498387, 943026000, 602690093, 714082645, 819936878, 562388268, 518209853, 227146453, 536693437, 96478729, 782283365, 540750737, 618757791, 427903897, 550218897, 384126879, 282654684, 993137955, 653883752, 147468793, 775720296, 434689412, 916906341, 131850982, 173815759, 553607877, 993012500, 444490715, 499902416, 722999018, 502380115, 754593790, 474921140, 847806065, 436885783, 285931076, 208231023, 912739531, 703158946, 310235538, 64415225, 999342790, 219223243, 685382052, 505755493, 638302877, 295028280, 825408164, 328787577, 228565956, 529317406, 62715361, 587159237, 362661263, 535841667, 30320330, 788539964, 99245780, 151539289, 297524315, 559458112, 680524472, 374047415, 875828910, 832287930, 506368722, 593022000, 645840209, 432017754, 232078188, 386346707, 851283997, 499281869, 328352823, 91182836, 273322589, 141832593, 947447269, 629269137, 787533913, 783163255, 573561115, 194156467, 846410042, 826262597, 474425885, 488734476, 804522259, 758912563, 80281626, 348358275, 20099973, 572420827, 994581616, 523251221, 630398317, 970011155, 283253630, 103987736, 483332217, 804777541, 705358140, 886032304, 722224411, 877759635, 603928345, 927613280, 322499831, 571503470, 863248795, 701366855, 946234270, 393382058, 166574349, 64220694, 343205514, 669659552, 22991863, 88205898, 104931329, 596486036, 261391139, 546200561, 299731068, 922331013, 220032848, 894345236, 406821773, 632936054, 994292979, 65992369, 805356500, 283788002, 166103996, 340889354, 956463530, 566809851, 662784275, 609979999, 244529782, 254706099, 272853868, 868393459, 493952107, 235419958, 151645003, 926283087, 941530478, 604732753, 721070203, 298680941, 204453734, 765380094, 845992428, 333030030, 531127057, 382047078, 987105875, 9648548, 953258382, 596904354, 985368844, 868193087, 131482819, 965291085, 813906217, 170813299, 247760862, 362281959, 279730025, 296864290, 360485412, 196453625, 563686029, 558113946, 542617400, 768642580, 911424349, 76480361, 84133367, 813520903, 401695391, 913847077, 789600088, 271067184, 91481965, 58324596, 826590569, 230753818, 427810801, 361728879, 330101277, 543390830, 368321573, 672552230, 32136314, 932155729, 710496926, 966297956, 484197359, 937836422, 577635259, 73739573, 825505319, 603627856, 76450108, 539509624, 88166932, 943751293, 470872507, 992709833, 588801667, 932841583, 639774797, 212639446, 484909857, 933933578, 499796698, 238494899, 270970597, 203079733, 972671773, 612850087, 812868279, 659942773, 194164133, 172080473, 623655291, 328252726, 528023603, 370466212, 851506291, 667705182, 530893661, 209404881, 408257370, 907274215, 894940393, 389816675, 556059337, 591207540, 836505339, 863769372, 272436826, 185350650, 330148116, 601168278, 428103193, 333656052, 464514453, 725173581, 305650272, 82462457, 17396138, 635406476, 606468795, 982077351, 362760149, 459835942, 841501761, 660836389, 528169500, 441690663, 889579079, 62113327, 548730995, 885066104, 837050314, 399748228, 904420500, 949906568, 45317094, 606835951, 738992104, 172498695, 455536985, 299525552, 90660017, 895384927, 446573394, 798638690, 449078677, 155370822, 464440649, 177248040, 884460954, 301010246, 40882891, 326284825, 852643349, 639935507, 28763497, 685732733, 398086441, 942884405, 461204238, 32514529, 985985369, 943427897, 118343264, 420124315, 353698475, 659405775, 176027642, 457008753, 731103510, 396994411, 938006504, 50765380, 688384243, 509241150, 483199923, 843116869, 322426751, 941866245, 927017398, 978873412, 492785497, 847248764, 225018882, 58657667, 315242560, 118931005, 134834064, 231769197, 505210226, 858804006, 485934811, 313503729, 458891121, 75015816, 330963538, 413318248, 111308642, 799980721, 635088738, 542654972, 883414954, 679011925, 158969163, 838209676, 536085708, 767672614, 282575626, 408819038, 990318438, 663454550, 304254788, 371197070, 886936763, 432129052, 419098048, 936754991, 492534940, 422999646, 884253810, 102970508, 298728855, 676115830, 90022754, 580402322, 846075079, 858565972, 268214862, 85458313, 644309341, 850571317, 127482601, 563929031, 725526912, 70381936, 334699265, 674118987, 272667414, 425916830, 976144946, 575657071, 726006461, 541774400, 936162497, 936123158, 441100812, 46150279, 628934297, 694388670, 970965680, 196604069, 399655659, 691691695, 538972715, 91797462, 832931927, 588008164, 281316903, 201605450, 873451745, 278796330, 213860648, 68231033, 203033736, 746946064, 780554996, 711730656, 180659778, 251245299, 951915852, 746215481, 462060565, 626014005, 78556266, 485305622, 73486838, 915221567, 544980541, 534382758, 230127543, 222483929, 419001738, 336284275, 456119445, 938243959, 252182798, 554857684, 212023092, 561804790, 574961845, 949945374, 351270046, 810606466, 996645232, 650781, 44930744, 218149364, 33132591, 768473113, 19263039, 304208502, 182644520, 573799006, 341948419, 976621021, 302701807, 423573476, 651313969, 495507117, 621419411, 468104882, 152067205, 695019256, 656822632, 457212747, 611481532, 180192169, 111745518, 378398886, 651591231, 196275992, 903275979, 578065144, 872409490, 603212501, 410283193, 671285520, 211290981, 590817120, 893002649, 710896695, 897826134, 260279512, 343926595, 78914033, 536914096, 875554819, 767971009, 462525252, 925857005, 983662214, 626297747, 310103463, 411638413, 473009275, 915538129, 935946097, 66679332, 770920490, 982357755, 385822876, 127018293, 691556291, 334629511, 377318389, 126587384, 12753803, 819718286, 167766323, 529534883, 877277478, 470667119, 497004723, 289202587, 97180340, 191003047, 132553703, 217667686, 667190240, 285749437, 121053457, 844977366, 965571874, 360201140, 974543370, 955397061, 267364985, 461785312, 933015800, 6914388, 373132164, 967952805, 205501986, 509746494, 383615936, 959822443, 9714390, 130900773, 213462775, 894594620, 416519321, 550236435, 64741565, 652728863, 34342587, 629333747, 590183664, 857570279, 385844207, 403869114, 555077225, 892813822, 124080048, 840475591, 490072652, 797977933, 832374934, 929810574, 540370835, 892860238, 234054975, 69343478, 467204030, 125770815, 851312061, 225205379, 504905201, 325434647, 299484526, 462536703, 44005098, 35883778, 287251658, 865206928, 854859760, 523601720, 54583975, 745281209, 868456211, 176659243, 426246496, 70862813, 315483628, 324472651, 165471423, 290567015, 980314481, 366245449, 483554948, 122386992, 101845004, 624716814, 375705396, 202768500, 942393928, 403337808, 537829068, 18063427, 590455143, 270532031, 725107560, 904964323, 59561880, 377476135, 352263381, 942532470, 134967607, 467319505, 209273812, 654464018, 78292060, 833267365, 755688207, 431231882, 477228719, 705909683, 520938140, 149003748, 601594811, 331600662, 679627464, 247872188, 151569760, 943287542, 192335328, 670896062, 199777514, 128155994, 296432782, 396759356, 602013892, 875136511, 421455835, 426024527, 242859064, 96006193, 982083245, 926359538, 663704613, 233159053, 738530773, 296465890, 244387560, 442487262, 632862015, 459345432, 277228076, 844019419, 561375808, 822063429, 938794270, 910088879, 994949329, 357626219, 566525366, 956947749, 857800392, 106866669, 662299754, 302694820, 941965044, 585824270, 641274045, 768263852, 635010917, 81444486, 31897139, 59367546, 506952170, 280927189, 618789155, 198554601, 592677629, 562008939, 194385339, 228164578, 558542938, 829312502, 436086352, 721145270, 712985686, 790381676, 313944514, 326188968, 811481280, 515293045, 73472045, 473819435, 903710271, 321289313, 662072213, 927836702, 956532096, 683379177, 550691091, 260975321, 250449082, 660683564, 780460825, 531183439, 698688087, 326546016, 630581014, 768467092, 5449314, 939887400, 85867594, 215250957, 365961478, 961875092, 629552716, 176994967, 127456767, 605908677, 819604484, 455133617, 761669981, 388400943, 223460841, 511124154, 735210255, 750121781, 699536343, 284974591, 720792255, 183370295, 698860904, 503644398, 700565158, 335269182, 723097172, 405546169, 906933334, 283963008, 951092393, 440073957, 969018963, 950388149, 819123862, 201844913, 974030690, 521774228, 549087777, 173228351, 114339585, 962440889, 624694082, 909183613, 309172050, 865855546, 143424868, 155970135, 476326384, 121880766, 943408509, 843285509, 535767316, 768005488, 29593765, 803962458, 32367862, 650895385, 506620773, 54108966, 421713060, 6392878, 105799459, 727503768, 73401949, 309204516, 567685926, 894844829, 813576194, 715189116, 240413876, 376325202, 313655412, 506734686, 39110146, 944789116, 64033596, 250693838, 529041151, 270970346, 948524368, 347621206, 886174284, 633431777, 641115400, 230628769, 153621410, 796291961, 71384031, 224303476, 279758770, 815192671, 437492115, 3657045, 436360260, 708615241, 263663703, 168854408, 149060199, 384023789, 6867902, 265598193, 670854065, 702712740, 982727593, 46026794, 859374058, 498346681, 360592934, 988268881, 816381308, 734637779, 746177133, 548399986, 299563370, 668804343, 273778697, 615297472, 39379314, 407086652, 205278171, 870989414, 389090664, 242699175, 576536154, 113988472, 91192506, 272922923, 134804230, 660815553, 317260875, 993501493, 446462245, 741190852, 483905540, 473822826, 276035217, 709860418, 481699699, 755815432, 82714492, 674744675, 714205100, 970218499, 947098825, 750048650, 953722489, 877178344, 481864949, 41079151, 894868083, 182831177, 658506980, 214401939, 131758681, 674371164, 743705375, 106423111, 598303572, 327664447, 461072255, 584731922, 218404803, 234397979, 275683328, 664480809, 738023986, 749148875, 980244406, 189289486, 518600327, 425559189, 16558427, 111244586, 186074856, 209620448, 473819941, 624881624, 949096781, 682779761, 966286178, 997641152, 347242802, 200286613, 50826106, 558094752, 603877006, 837749400, 750879888, 78220039, 628660687, 54109369, 957146236, 193151301, 60227928, 509845486, 212638279, 439986186, 476904893, 850795960, 811420723, 277228411, 318907222, 779375560, 463036756, 377025685, 448577068, 443316534, 569052393, 123067458, 25358834, 224464844, 153100538, 753648344, 782672087, 118112287, 486821094, 26170073, 41519453, 171247438, 971722861, 266223280, 129371630, 847383066, 605439888, 332343387, 62461367, 953829178, 887865900, 256443625, 129422425, 428933037, 675701632, 377795540, 902711242, 931522922, 615068126, 705659661, 591241479, 897183898, 285821270, 877776077, 932049794, 279103275, 103477907, 656360821, 29314470, 164891995, 53762197, 801367370, 97606714, 60862122, 771351946, 79686605, 592317969, 10727849, 62610408, 624870098, 199295750, 275721000, 662372928, 156534532, 798876161, 162665486, 403073818, 672209503, 472435727, 431315950, 991841324, 576536428, 638209987, 585912215, 78627789, 578949263, 735175399, 986189001, 19449077, 742167761, 706452752, 499467069, 941782783, 540926535, 312929396, 372743127, 493140115, 29125725, 133906240, 169703885, 586546719, 824147445, 939444231, 115249280, 589064996, 638745271, 383403585, 934539567, 531017154, 84435116, 985165904, 761062968, 956813157, 574691556, 325503966, 943747187, 982433650, 314216632, 677030543, 897799797, 117569480, 373055639, 646379252, 277911330, 451504089, 44202129, 5151158, 30196365, 64140907, 743399162, 311129031, 776427874, 344448299, 175929385, 524097957, 515320204, 79875489, 855355894, 553558477, 319367417, 257122392, 263114101, 672458387, 902262209, 353661968, 488867553, 411429765, 951655369, 554449600, 937766620, 101879604, 166068713, 735980798, 703354330, 277075954, 782315314, 350106087, 98125954, 48182334, 44024294, 973595876, 273708271, 43774361, 471156380, 29681037, 411675559, 8140060, 271965493, 568233709, 922218782, 418832450, 205146423, 749150142, 56965068, 727055521, 763225790, 260674257, 675833441, 527746773, 279230034, 802643764, 289658934, 207790732, 943400360, 871030964, 744108831, 265290627, 442379554, 183794566, 483690492, 632342630, 4925126, 865481276, 604601284, 665739354, 553064277, 412748117, 585215640, 250418924, 523450175, 901240450, 722010169, 682894811, 490994769, 608850328, 679195348, 228795019, 51315833, 856307827, 21939872, 948329727, 16866551, 814904391, 686285022, 545071737, 977905440, 604357613, 466350106, 421859723, 52917993, 255540770, 847672789, 813408036, 621428967, 768157475, 329256775, 601459811, 657960685, 756794317, 565649969, 902179910, 601943583, 819518837, 299439866, 151530615, 453131485, 368485306, 885016772, 900060558, 495783504, 645187779, 155792490, 180698859, 893890749, 481990267, 202267891, 602378721, 557496273, 913209218, 739638706, 265814763, 227858521, 454050905, 484443572, 295387683, 196055819, 894904872, 239958248, 493605531, 480229607, 283951063, 617357877, 881070207, 943526157, 263762377, 989261973, 359572200, 227662414, 420310120, 808207591, 830578745, 681112318, 609239357, 275518530, 77575494, 313374376, 714155063, 11097193, 254758306, 775753219, 608571624, 626399401, 989419040, 951742762, 888385905, 481676901, 755659834, 809989514, 766871926, 89684194, 951643264, 641938869, 458221104, 394892379, 93986863, 848429497, 170464304, 638612445, 526757875, 977350969, 867953050, 434072181, 532516310, 997967247, 219385388, 40237970, 423321837, 744887626, 715390806, 250162375, 484891575, 141809359, 809979697, 22366670, 944798748, 487566472, 322676539, 2647541, 165113725, 826248271, 951679386, 747050185, 185461383, 206982869, 278414682, 465182632, 135257731, 467955990, 310936036, 894729530, 383536103, 56226421, 518215857, 872182905, 854185690, 742954097, 540472411, 83885652, 949286563, 68240135, 715337989, 36634242, 610570351, 767414755, 426440116, 547553103, 311863482, 388673186, 643530398, 247766043, 165402763, 209659544, 132453678, 693627248, 32243274, 646391646, 698426844, 429844388, 165361780, 230534374, 225736534, 422338092, 952472406, 204568596, 641390289, 430418257, 9747617, 959217128, 4928186, 294517854, 489882329, 814670131, 515370772, 13888737, 282745084, 485320630, 189467795, 788185995, 844636780, 379179941, 981586211, 732081622, 237987445, 185420791, 740743006, 550157998, 791034947, 813807420, 138840049, 45462466, 556673736, 814220403, 948678976, 938547093, 450680776, 950454910, 719950006, 436156482, 823714066, 883838571, 28745054, 864621907, 997633142, 187791714, 15595013, 735777049, 202773686, 721471103, 521765662, 680842985, 719381418, 818931421, 761220918, 604023486, 290238670, 70484969, 89549697, 678868813, 351801050, 608921892, 400720474, 649665862, 949320801, 975155307, 605777073, 743368711, 711848789, 379647710, 647321294, 689051982, 155335445, 977801369, 563979129, 635441491, 186791946, 585813601, 701869933, 86583490, 303757654, 197476186, 221339145, 876569280, 389534339, 640410849, 833098642, 450414782, 821281068, 706388072, 25539416, 973482426, 483122260, 592583399, 493783156, 201373266, 387655656, 480133101, 563204730, 130488314, 998909434, 21054, 401561145, 401974797, 932163767, 52219485, 867062983, 488380613, 25394274, 936553979, 954001538, 338302368, 439701560, 218743547, 897147197, 717407144, 798734885, 233897463, 148673211, 139057624, 577484431, 322104046, 352137142, 406256405, 849015478, 741975830, 91516207, 283934933, 190923134, 243090986, 682363049, 36722025, 448773823, 243542959, 900694327, 566580451, 914450630, 153341552, 333427091, 225473826, 180176140, 159946379, 687024103, 646560043, 310523555, 917372253, 992261001, 784385290, 642115510, 737079261, 302057448, 219026421, 380687969, 156573837, 508221891, 960025984, 740941908, 715816377, 861280717, 326959547, 92642066, 623314789, 686612938, 712263535, 477525840, 772807964, 377237967, 793725802, 342771639, 416006284, 754690704, 554942322, 354296216, 728709213, 155394087, 970619078, 992809743, 642490691, 506574375, 881202229, 876480359, 900686752, 652798263, 387941773, 262778186, 418493017, 520966190, 478708090, 256125785, 195183448, 346081348, 19945999, 738091280, 293652570, 47888053, 153933871, 500466767, 688294303, 695825505, 472870865, 906141431, 850531876, 664262589, 778638578, 955743736, 935536703, 440569927, 994686691, 497234914, 866117764, 292216867, 75257118, 561712257, 612997861, 189703507, 437056614, 256567660, 950181715, 200387201, 173990166, 429799077, 614437021, 593100999, 181361411, 715354524, 713132928, 537113671, 932759402, 435032183, 511297523, 42360973, 941962989, 19798057, 578778265, 676536917, 637526627, 838628857, 299193272, 459392038, 423843316, 276924253, 893163031, 349735635, 102686979, 56546720, 514126449, 869984873, 15427773, 131400070, 457422866, 528506477, 695353283, 592543257, 98034195, 992051350, 999214069, 303903826, 131428268, 789453201, 995596062, 814365717, 281088631, 519355781, 17878739, 557655482, 17542906, 446528275, 203750153, 344398851, 659615317, 209709876, 254042183, 383182086, 784559399, 298037316, 394955374, 212246956, 404673864, 67269542, 405456602, 780733730, 587736473, 674023020, 627877170, 814422906, 205766668, 797960643, 796942237, 781383042, 277552174, 742497915, 945811883, 400898713, 263327716, 873672065, 774931051, 69442757, 45341772, 575616345, 195294108, 728823535, 79506138, 378037748, 401211167, 484789569, 798798226, 400547792, 846884278, 769307413, 235507112, 982532179, 453550138, 739409149, 110651094, 764828402, 534821851, 53831578, 295371327, 8524365, 145716763, 565453818, 70951726, 586877177, 563465138, 60647731, 935263580, 484480268, 760838133, 40213400, 814879942, 54811196, 732773203, 773903560, 36659551, 285260346, 427558045, 671493933, 558864288, 983062753, 297753792, 831198544, 518080184, 763723059, 248165819, 297043207, 543842093, 998392698, 766795186, 349174701, 611849082, 125588090, 84581434, 751018072, 878535153, 60454756, 644602848, 138180437, 312960086, 116266933, 171752142, 781917891, 552372103, 343364101, 14559864, 433645926, 900613752, 474667072, 572597931, 594736567, 552535093, 426132447, 8204725, 226271822, 360719907, 671088975, 565577540, 729629128, 426281817, 621533931, 375056701, 383016921, 95119362, 605645344, 987271453, 698660939, 998276481, 914063369, 126814897, 27615015, 413132049, 717698571, 884092358, 724273871, 186138775, 535953401, 44062844, 280560285, 916734732, 466559877, 23157498, 768236917, 547231301, 847856980, 504799485, 427223150, 376923178, 193732507, 866925700, 83476706, 838966134, 763611486, 736903308, 647431487, 873542437, 55504522, 989472260, 833422162, 834196644, 601679014, 744863744, 841118911, 125687151, 69793199, 875469405, 1870743, 894142291, 441918830, 951124619, 367613580, 65723703, 778863932, 971588814, 24110148, 737557411, 22955919, 325158814, 116558655, 814488367, 613715211, 58198552, 889719698, 455255544, 275664874, 335285129, 528226123, 254694738, 618402183, 74472794, 290991359, 722320268, 813264262, 590677411, 261723054, 815107708, 969834625, 934188351, 654350805, 199597463, 259353663, 502677653, 354651307, 945445297, 484215981, 185445029, 554586576, 525224106, 504123057, 209733753, 216840266, 866475779, 476595977, 202950017, 519183158, 291629599, 260773498, 851682689, 241014522, 490805128, 182151791, 801893650, 407447150, 596755390, 245541479, 325977650, 344179196, 170975887, 917313350, 489939574, 144491271, 669371331, 549064351, 709927003, 429581539, 981335140, 509667283, 649695948, 455721242, 985049492, 372765860, 644446864, 55776748, 415822375, 764278540, 871414988, 547467872, 53214494, 427440173, 38850830, 373131567, 612344093, 231856134, 515967039, 447749757, 798768342, 881167443, 786197917, 479494305, 577598770, 424959792, 88847751, 461339779, 322192417, 583056249, 476144241, 386740903, 459920832, 260728146, 123411898, 16472245, 542840061, 740232568, 345965282, 96328206, 764311907, 922027188, 822893304, 633401025, 504013783, 823012589, 656686937, 690249138, 840157270, 504765503, 856076456, 552412033, 757968709, 267622725, 324561158, 677326455, 952604543, 559772251, 185605506, 571590947, 17869074, 729121233, 880685606, 365935800, 950503598, 159782247, 565103382, 408750374, 372872723, 874644531, 668827570, 909084674, 621049959, 653450737, 765080155, 993407470, 337268749, 356151883, 473727069, 891785178, 212256936, 58107619, 930270869, 296684982, 703141445, 456825984, 230426742, 272619140, 640525512, 976976234, 665329919, 679733110, 326899178, 869586892, 825747691, 566848541, 628057376, 460650345, 3918371, 397137223, 758659770, 38827322, 47003558, 891942611, 77731026, 886978410, 324755843, 327554194, 918554887, 910836943, 907318720, 448004944, 972207721, 504776667, 560889653, 899222674, 279687841, 791155038, 146726018, 402069623, 346981874, 912589850, 594197733, 349389235, 233002942, 583129912, 588478069, 108631358, 183482524, 139278554, 771011188, 730475955, 259485071, 159143071, 818879418, 902930298, 577939690, 494328612, 495213673, 21616736, 418666847, 40236904, 431312594, 92432890, 611735071, 89569837, 331980998, 977758779, 900522648, 693741310, 786106406, 665676446, 456780797, 612086770, 235443311, 671554661, 711553373, 17213592, 626613043, 593874296, 993929631, 677621623, 632007524, 701852045, 363038047, 943721702, 193545912, 350229389, 791384768, 176936824, 104386937, 247876078, 307374915, 153947877, 854443030, 332642768, 720459725, 732397177, 975913081, 461910311, 934666092, 835336586, 459446247, 668612328, 390431063, 606883004, 653517743, 665984019, 305566644, 348667843, 478821653, 496628253, 118331532, 213406453, 140975294, 120232249, 101416500, 677400612, 115729497, 686722066, 768489026, 202447491, 153628110, 994890119, 169495702, 867121103, 575024506, 207109971, 440852651, 599851836, 713401162, 565908929, 445451809, 114213780, 907105960, 455669937, 827695616, 831145786, 119183451, 306763901, 682634081, 886819537, 921430763, 319107065, 123672106, 30023809, 6977217, 219301642, 909445469, 748200367, 770991667, 533938090, 574444441, 302511004, 331666206, 289503035, 978910961, 268383324, 886749643, 363697395, 425588468, 777961468, 417519935, 201014210, 848918028, 260158414, 732388446, 880012297, 758704934, 307045460, 526733576, 244476403, 350002896, 78680058, 189566269, 5188525, 286202638, 503348257, 417258161, 433778620, 892237611, 983257449, 199219799, 577765827, 68523911, 637560377, 999224609, 892553836, 205884254, 536118447, 597054705, 159560543, 656829759, 412996115, 676332800, 855886201, 697014710, 586631743, 378152976, 633012269, 41426914, 608797249, 156815506, 723444605, 871648964, 304768024, 590211773, 146434615, 599527306, 341969581, 898057355, 521123480, 239503693, 598674493, 469726108, 539273195, 931188679, 807893011, 790742446, 48216981, 993586024, 978291911, 718107629, 666689176, 317347553, 857075894, 104603843, 378439944, 981730548, 133578452, 260217507, 732800827, 39081889, 778812910, 299187672, 17412617, 207951112, 101972662, 183296968, 937244870, 963520035, 579576736, 677957907, 6457120, 644093329, 853146814, 356755493, 152576079, 618783662, 435043581, 345246685, 638489614, 388036554, 838576813, 14435148, 217904844, 696611310, 635027725, 905577099, 71584182, 552021272, 843444449, 881034065, 126881598, 207076416, 611370487, 304456549, 854209713, 559624572, 508339140, 368302067, 458503201, 835582611, 290899685, 98037875, 982289498, 41262334, 498471145, 319242005, 134009323, 856218047, 29287873, 435429917, 219510035, 138396516, 141350265, 797219463, 478679929, 783979961, 93603766, 59649080, 565522725, 474523448, 920053103, 320725755, 479389622, 371315075, 451409562, 219284718, 350021747, 888266976, 158329913, 944576852, 7972446, 856747662, 375621302, 530950897, 978664326, 613220664, 915232449, 96206486, 958435191, 785999038, 455857638, 82916799, 684425840, 255425418, 450103234, 548008296, 317897141, 438249272, 693144456, 253431402, 934377923, 194362404, 371475408, 197182828, 262984053, 783964957, 553824606, 618374207, 630211641, 760542894, 730046492, 322842499, 283021219, 743290267, 880381819, 283736242, 507240562, 926891496, 655453994, 656172434, 533794773, 22052128, 108596406, 846498549, 312143763, 499093120, 892807326, 196804742, 674005708, 399847772, 749159024, 213316568, 594612737, 547676893, 863741621, 908592956, 621610189, 832107312, 862292386, 670158973, 643257236, 371730684, 308714123, 693634391, 219545635, 577866851, 797577992, 765772631, 171883117, 985478317, 969798774, 452520581, 329231328, 244498981, 192134544, 53461881, 860677659, 434871007, 297586992, 815733060, 945159703, 820448236, 580044429, 196464568, 707349593, 455095577, 512032507, 637772932, 572144772, 684812866, 754840140, 818161649, 706745975, 498608497, 977097304, 821601497, 27893987, 452802396, 163564141, 231757400, 409009235, 347560683, 411162015, 111879180, 643260338, 591808019, 606514981, 566646039, 9692417, 47743687, 49801976, 677177353, 865112359, 291963415, 610523964, 218150472, 913907815, 145716644, 54241400, 852980847, 418995766, 497540586, 232227524, 407180623, 806753785, 432797709, 107316235, 250471688, 797280882, 291166622, 219104541, 840682941, 225645702, 15115743, 211725459, 324258858, 158953300, 464706212, 844155369, 933870860, 953609378, 701376400, 281361465, 309919718, 683914018, 186030537, 29665263, 693426536, 851395599, 599259025, 572867015, 271688109, 93772153, 878196300, 89073156, 890188337, 614918694, 994934070, 180145347, 878589447, 53673130, 24780365, 677953631, 451844884, 150019679, 162558999, 355888412, 786371316, 914293652, 12649710, 945945507, 303447275, 753800174, 368925852, 875972648, 878250688, 578323114, 510153090, 392500957, 747334354, 967117099, 218668264, 870837984, 722629012, 708093360, 285559910, 232158131, 989472094, 503643971, 798540943, 86960193, 434410906, 329526503, 575913451, 527953758, 9744594, 27998982, 265378287, 258240393, 399784885, 410773389, 280623510, 662996298, 327580171, 951362666, 127442032, 893465241, 292841116, 387973054, 154126653, 193952621, 905040293, 743188171, 9772731, 730020890, 719235840, 492207324, 114497513, 909633028, 152228517, 875496272, 349613761, 627237533, 834696515, 893835035, 105844556, 856459299, 722136723, 232660199, 78832557, 586560723, 928451558, 378892199, 116023602, 483266435, 489790022, 886990465, 58689741, 50535612, 656891183, 43756458, 73128561, 270676890, 271676741, 638599206, 673187247, 433564224, 931978065, 47724331, 692326198, 148556091, 265773949, 581577576, 630437095, 110491023, 228556960, 882922727, 914265282, 785740408, 105417362, 512425014, 524923925, 325575821, 343226855, 533608971, 120392529, 549577209, 488565298, 796976489, 188320929, 418046621, 225469216, 762788228, 945587212, 923055358, 383746477, 83840393, 854546450, 218346256, 444707046, 973805578, 427655656, 332402105, 343863896, 769704519, 583105000, 814753518, 155904249, 88977599, 949217995, 122712397, 896880722, 271379579, 924590034, 239166228, 591302111, 91874412, 411707909, 863629658, 196109594, 153328075, 597630262, 671469803, 688132016, 834052225, 25063663, 303736982, 625740353, 57556195, 813052956, 212772173, 440686986, 259987938, 940017176, 166454603, 806289021, 400764080, 447112250, 642223503, 543699540, 149372227, 643888637, 633699534, 619962046, 566243597, 314140358, 697404450, 74788080, 62310602, 82904540, 179145024, 782483617, 51368738, 976797584, 697835949, 835196154, 972673782, 533366374, 96009362, 20705698, 770634876, 471754732, 547710134, 385654745, 389278712, 895109332, 954365135, 888092100, 683782137, 209497129, 208208759, 221716306, 882386123, 958260781, 590529184, 153066705, 376981688, 185519905, 124734213, 685277317, 884119730, 672076795, 248600219, 864833222, 125817428, 202781648, 844010458, 965716351, 722629618, 812032315, 816415041, 33344803, 761666379, 569398084, 699021030, 973394182, 918973943, 41191371, 82966253, 737481568, 162323599, 208185512, 188880616, 414132168, 740470461, 648696044, 445815832, 609662532, 52214712, 602067040, 399731053, 247925222, 263213035, 847858430, 490976640, 851972974, 997257216, 591854712, 320527905, 768623979, 47534573, 284458852, 548760446, 499588418, 189393592, 856222908, 914146828, 949919308, 503821590, 928895503, 931356864, 69279094, 521730418, 734271244, 98641501, 984528435, 584220746, 683738474, 523451816, 488700271, 516843275, 220638967, 479625496, 262397187, 128817144, 660002309, 733189901, 900033638, 803028150, 505498514, 117861445, 934649621, 22105786, 815580173, 519917963, 888074618, 879088398, 666324862, 529211443, 185266834, 818143184, 976631510, 499019236, 942512412, 220926475, 640567417, 61283604, 38502324, 268636009, 446784509, 111689894, 722967087, 295722344, 995713604, 694920984, 580129689, 853490847, 301463962, 2989940, 604868855, 717939732, 993446592, 811196675, 427602639, 139036657, 252692816, 150264398, 761774101, 160567745, 453806469, 111167234, 717001473, 3522910, 169530991, 810667425, 808568232, 643497408, 374445027, 764092445, 489264511, 523433448, 258040694, 899773898, 864524712, 689436816, 898642816, 549051809, 637780366, 712628729, 470225064, 428109601, 253258421, 817364601, 445015321, 858945925, 348640137, 787863808, 789241250, 614054150, 907831965, 493357522, 365042193, 81720249, 174656091, 801628546, 386583704, 766336044, 201288952, 177914314, 182777449, 595071776, 787602199, 474674313, 904797974, 192224950, 824652011, 975968436, 993088784, 582813312, 613403285, 799363983, 872053065, 51335382, 496726482, 527016592, 246702747, 492037364, 759265948, 524362685, 825891202, 760040542, 669146190, 128497789, 974522231, 73282835, 167298334, 708918567, 942408167, 47571908, 358495825, 255183044, 542972680, 270838342, 86078621, 771123944, 220165512, 465231026, 485869594, 194373370, 244847399, 364236069, 544874218, 309969018, 150695401, 677483148, 536172311, 276035017, 188247204, 843965659, 295886965, 494539381, 693432689, 740688238, 601673678, 60086535, 81370337, 749410310, 455163040, 661925517, 949743439, 679797717, 916626659, 263173932, 519253854, 383188319, 928623520, 829955684, 29101429, 732480476, 698641262, 419587184, 42612616, 18997159, 725586727, 303297153, 671874027, 879795125, 527880398, 866343300, 144692088, 846215403, 692435697, 758234996, 401113187, 31322861, 757921332, 500065852, 590846276, 481395711, 503463003, 475871175, 625358316, 49621429, 167324950, 314101033, 678795885, 800657538, 418953262, 279375380, 640313139, 816021735, 828386438, 114126611, 71984290, 957036301, 561916861, 522036325, 282411252, 278761045, 679788103, 768062180, 724509516, 351594431, 130017777, 621434132, 921312082, 508498396, 896159159, 921293450, 798414914, 804915789, 102264897, 885275470, 99483110, 559714727, 522300616, 800595666, 851788783, 642520071, 457899718, 794219568, 52934800, 384163852, 856950919, 72863576, 716725065, 573824431, 327783268, 423487974, 846215752, 332973108, 877978304, 807848679, 386257652, 210809071, 591882185, 356455136, 121394250, 174545626, 5243089, 995039939, 684731379, 676820253, 591106594, 743215242, 866016627, 571340075, 126320386, 173445784, 336570255, 106839588, 265854310, 666516670, 169462362, 529680355, 384877468, 500905866, 371140360, 799648968, 430122949, 222060008, 958221708, 304116664, 251214508, 89092239, 473635466, 64934560, 86146462, 691884176, 331565297, 492337024, 381407724, 10454752, 39968780, 122771818, 81221699, 245601136, 624934143, 378751777, 85676829, 951573860, 321082866, 227438993, 742994065, 176055441, 66915306, 396387168, 166365520, 233206237, 847960387, 590817893, 167453466, 504100096, 886404630, 499465676, 911181232, 868651972, 203046458, 877222845, 719341463, 902470698, 983918285, 303019477, 248257953, 779089350, 533109437, 275181463, 685370438, 938984954, 756577334, 830095736, 697486856, 197163621, 207471336, 436113282, 312563054, 812900099, 793740719, 517920551, 890713859, 151161493, 959197136, 429198131, 313883027, 561072981, 759270348, 923645435, 862961470, 30396512, 231567843, 213495846, 331952107, 285511582, 411627964, 874707094, 550304630, 517202784, 774531268, 850525201, 62810826, 998536877, 695721821, 879479039, 538194644, 275564603, 688280403, 592100564, 421233805, 526674884, 134435834, 513323785, 984720561, 557588726, 358729245, 797478327, 223140154, 869600042, 251216902, 640060120, 29703304, 684437125, 317124161, 289064592, 484867402, 550600500, 499505739, 821647566, 306623125, 547795487, 72223109, 382082615, 257205414, 827242775, 872124380, 44206758, 623170978, 89642813, 214149690, 243420480, 724602041, 121246551, 417066359, 958122183, 77894026, 850368493, 898273996, 474305423, 397303447, 384179020, 173426426, 953020587, 855946479, 91186972, 512865851, 823848942, 402049674, 709659652, 520375943, 505990076, 706185712, 390605499, 256850528, 810107990, 926829063, 551177360, 553130850, 333652728, 569851071, 587208897, 645580676, 877757716, 944663799, 560881375, 671311318, 914842805, 528967829, 922171292, 341960340, 108231340, 971207784, 411451508, 404659852, 795272980, 185903552, 482616284, 933423183, 281221919, 642150396, 587841328, 984344136, 24255010, 534458813, 355029138, 393941519, 618121804, 852367332, 875134234, 38452172, 915634639, 319147363, 577280782, 309133963, 305231514, 892213602, 192754954, 805013658, 67465319, 841755354, 719974458, 508317810, 528966606, 626665199, 104325316, 935194112, 455920741, 782942481, 563489963, 334254585, 425260329, 624254917, 744570561, 498105098, 9184011, 133184467, 55981868, 836632210, 139612398, 265336123, 639299853, 993697406, 367153262, 633051150, 719118171, 758812683, 712004777, 260635414, 625374773, 556765081, 439494762, 986759730, 596143433, 758259313, 102810051, 797688643, 790444413, 494783161, 83295961, 157847341, 761034212, 782909782, 13119231, 585500687, 776496401, 577769187, 266322780, 836284106, 772229705, 400224449, 595295610, 899731315, 242814212, 925808546, 886449592, 46823654, 447808857, 57779601, 398682268, 735733225, 335369720, 321858733, 776266670, 805368316, 754397723, 832426608, 393941249, 881955754, 280571395, 576632571, 149336672, 860111815, 622682980, 408191311, 228045183, 693023818, 893624824, 119027395, 136567564, 822502787, 200597990, 484463753, 425196989, 817209007, 551900177, 905305242, 461386395, 507703954, 80491931, 514207115, 161769502, 170138326, 958159700, 317044215, 476388866, 693271232, 837469923, 323759295, 255545099, 912836878, 666730707, 456350170, 220171490, 411408034, 185554532, 793326311, 512998884, 990917560, 369346716, 367325103, 580210189, 815607604, 591559743, 528780050, 944633787, 125267143, 349768099, 875712351, 986058243, 14676040, 974834939, 634202694, 617154679, 756739185, 504173359, 816653934, 899273778, 635595041, 512750072, 357884825, 703477571, 763323574, 187745638, 909360658, 998417372, 499180732, 187742333, 997712714, 679618111, 331128870, 271170885, 244972767, 548843964, 431876525, 461530094, 867830813, 229876307, 401204540, 954783157, 347005450, 946501396, 822614672, 669348660, 813614187, 743212707, 199678414, 866461787, 427576555, 834124583, 471564328, 195567168, 525024185, 183774745, 66566246, 591926102, 558184590, 424974452, 754966014, 525151406, 995895813, 561971559, 116249227, 724454232, 495014136, 955499626, 823848409, 742368817, 638939209, 11028125, 67566945, 18265914, 503733435, 96778739, 383126027, 293872003, 251687513, 455769622, 662853712, 44751065, 600621992, 695493928, 746815633, 923724250, 177519538, 366688644, 381020463, 577198415, 948290332, 710471111, 787373386, 586686667, 725532043, 904600496, 878169317, 672731547, 352221637, 110760246, 321847822, 764488090, 266457306, 3856244, 35962689, 170989072, 169815971, 874949973, 853115242, 146357814, 737986668, 298884144, 260242788, 830966623, 914251763, 443873301, 338877784, 190431990, 588318903, 625610677, 60868134, 182753077, 484771568, 636459310, 39260390, 127908569, 691694242, 390567060, 619899691, 500816396, 99910435, 503215309, 973277675, 693820610, 985337835, 386234253, 14838081, 402428931, 149479950, 241262250, 351628404, 986501272, 247018394, 929606845, 749732885, 159213156, 905493280, 847866972, 307508468, 747018475, 64548566, 107858545, 39428884, 574120114, 873155191, 311962741, 669437947, 622056636, 752085034, 527779934, 186681267, 345155360, 805186800, 62255210, 985802994, 62578064, 575893753, 495019697, 558328588, 854891092, 95673938, 724721416, 754217148, 837896418, 786091547, 578787351, 283472331, 209147796, 169267078, 212074061, 858776731, 717142076, 477291873, 228746229, 325995182, 266882292, 884891781, 217131152, 78060228, 714634771, 655514054, 494265049, 653306509, 384430671, 653285680, 48871440, 453777601, 321327425, 526558590, 730359396, 988615838, 397154617, 578783341, 51305724, 924754899, 450989122, 870402932, 357860969, 398777774, 202117074, 824665545, 713191328, 522412346, 576384234, 996535092, 283026298, 715652348, 498411408, 233805629, 665055847, 683654754, 382332908, 393634246, 243826869, 964665313, 62154374, 697360772, 460705292, 26073929, 268967550, 946987955, 446817113, 898829101, 198281535, 272829651, 352440852, 832488412, 144026018, 48767755, 840827713, 246002369, 336244918, 224550902, 459513502, 563158542, 826664864, 906262581, 240590225, 303504647, 419259236, 6843741, 851783579, 483162774, 822422222, 881097793, 354457453, 286785270, 153434378, 277656430, 86370673, 374590492, 265983813, 875442025, 857547208, 795363409, 930992010, 70795674, 923428641, 858832963, 900524126, 592256539, 108364743, 892221376, 491401429, 669845922, 894598548, 489196847, 68356047, 628409323, 691866113, 597471964, 70869540, 199493348, 973835389, 921759234, 370206683, 468243266, 683578373, 154742500, 197099386, 531412651, 714020254, 305706782, 67929464, 747345366, 30139128, 500261441, 132362212, 152025008, 103888297, 681855368, 384079007, 483602032, 666536650, 689057421, 668400379, 885555599, 330765526, 558566894, 937481130, 827564490, 471602825, 142221837, 133914946, 217816509, 271349675, 829486047, 118714318, 456113896, 597307041, 58478276, 492615318, 928443229, 572153143, 146604374, 653038773, 613159460, 395149532, 466176341, 275507455, 22447753, 840902159, 708750676, 657105347, 370402857, 538548437, 945564393, 254471963, 393637393, 115221222, 657288798, 699967235, 79405028, 513558599, 975662764, 57884206, 617623403, 243658884, 284550067, 358993210, 820294773, 527661721, 347204788, 297960802, 501170195, 919172395, 789141734, 296023964, 235117853, 202394454, 266570964, 284612642, 158848814, 166884637, 557465008, 53848092, 845138411, 237118690, 793245319, 719182985, 902521351, 235939707, 404400086, 850491620, 48416645, 249953830, 20103047, 492409626, 614435624, 522469436, 473264412, 68284906, 859152156, 611097290, 655370318, 435498997, 65262552, 500162546, 575786704, 293169993, 661325608, 514055206, 300589903, 930367594, 104615493, 698946774, 183281711, 463479911, 781312469, 114079444, 642806494, 588226377, 69715898, 614339029, 997089280, 355532969, 316647855, 926945099, 427481133, 475727011, 700883379, 283046579, 262217305, 104891554, 87132608, 853085153, 293427977, 845199273, 819141086, 777646722, 285021476, 758783745, 18618359, 71385069, 153597316, 28073681, 541884013, 770577505, 287883293, 749008943, 135232431, 667061643, 465402609, 516867022, 476728202, 42335168, 45078161, 501193293, 35293684, 52808025, 291288738, 675985669, 766904189, 984982861, 126351316, 923741, 311184609, 23529137, 654789579, 957606987, 192211197, 113208307, 936732000, 396529140, 441869027, 59118362, 354322042, 594858459, 51508543, 271655987, 354647793, 931861091, 935606395, 875407760, 460181749, 302267607, 502208430, 205039013, 57705752, 69940669, 800971480, 617866410, 622207087, 145492908, 629797924, 816393772, 679574385, 73451041, 773522706, 887574688, 970646021, 914217074, 670070828, 137266224, 931140262, 778367584, 706939001, 751357699, 138966057, 390612662, 961479349, 868339347, 182316539, 9711469, 252699221, 107301326, 174588745, 819885295, 477874537, 598856801, 821059257, 898331045, 453975108, 969592773, 354641277, 506643061, 134882151, 855031257, 68958137, 716956574, 744798633, 729065293, 474284602, 896545300, 224728658, 828704453, 717071551, 492567209, 34446913, 554195061, 794637344, 790446292, 91966215, 646099160, 44710208, 952526251, 97992004, 152783303, 768768699, 148290004, 351704449, 678576479, 762522974, 884191465, 598213928, 333652045, 79383384, 187748525, 897916341, 6214986, 902627035, 558456755, 513795947, 228862835, 166674182, 345965039, 358122076, 319382429, 880053275, 749193310, 301702097, 367184495, 798843074, 506373867, 593355377, 603108752, 702483944, 499616022, 674438979, 298531078, 271075246, 185610246, 916067032, 580122374, 645255115, 444328308, 76177741, 181079191, 587542797, 711017196, 966043100, 644486890, 388099628, 175189922, 931948297, 232925624, 40225132, 37432380, 130289664, 742368273, 353201625, 586981143, 244863297, 210966527, 112970923, 493823072, 671154611, 733107456, 677245625, 833714408, 552437456, 125583562, 199145262, 456199751, 827428348, 322275563, 797768970, 379486692, 893659335, 408451534, 674636027, 960811877, 458313102, 493221851, 342819640, 256093911, 767018653, 974440452, 89220677, 124864969, 403348977, 335640388, 877531956, 542451702, 662061661, 940256404, 64853173, 98304326, 499639965, 826077138, 373447381, 274205714, 107104035, 417379249, 285343927, 684285629, 502869783, 122198583, 245908964, 26175367, 711966958, 810916619, 202367636, 567200191, 485792034, 611934669, 367264201, 23041073, 531736842, 452607596, 968469636, 860828381, 108857294, 33037788, 760180121, 679960613, 988582155, 584761957, 228865680, 960728907, 382316843, 908428986, 558924911, 649276632, 822711991, 481241506, 81373696, 76327903, 853630272, 89309305, 241051491, 760735143, 278714450, 404991867, 658137947, 554466567, 583375425, 658103009, 507245417, 389344371, 893263889, 778574536, 778997484, 415514941, 786881370, 955076674, 762235229, 471940820, 625042981, 770036800, 2512626, 894662477, 252708898, 695665848, 180884740, 243027530, 916987662, 258921382, 202848269, 429614444, 456690566, 548866662, 320316166, 646731990, 890694391, 593678719, 370769363, 121847809, 357954402, 394963292, 93891192, 924461052, 778378674, 824727678, 231355583, 348446324, 198910743, 359857367, 419458208, 639005112, 615218062, 257635715, 303176213, 969788222, 666262675, 147729668, 869039939, 864611051, 615523524, 711210738, 75501393, 124964334, 614958037, 181526929, 832123419, 682979827, 684091096, 701294384, 272492630, 804314584, 896987502, 883733285, 420289033, 154143397, 729945238, 254147365, 573454238, 924658862, 501970893, 454140074, 646505975, 686393588, 241078767, 164375228, 984022962, 911329851, 732742109, 354368026, 745836413, 268522315, 696904193, 146803174, 58582517, 808105924, 182988037, 99788286, 326655930, 157318731, 271495747, 965703437, 468355523, 47730296, 146094243, 121091930, 559440452, 997847576, 16506142, 327066226, 140800430, 548000424, 555154902, 736091427, 692547043, 824949822, 903276204, 484282200, 482956064, 371547424, 888918052, 937571373, 671609645, 781683156, 201545106, 251195162, 747097798, 137128818, 247874255, 471841257, 227287059, 749552850, 518542021, 953548422, 133637641, 919700014, 595833652, 800593056, 627758295, 932540363, 856671638, 890635060, 142028238, 836096724, 661893522, 434148440, 362750673, 255104097, 661918578, 746903713, 424954562, 757744457, 749025401, 181894273, 29736447, 578709544, 473219178, 954569183, 432857349, 688548975, 740557354, 229656355, 526177224, 860454198, 196687011, 778985052, 435831724, 745806655, 14331556, 189745315, 101034131, 373326217, 149822213, 298017950, 121094573, 631751162, 196180664, 825489099, 37574285, 116256303, 712567720, 689573651, 371922293, 885006047, 537219599, 182961590, 482571926, 477868377, 557893465, 370181978, 102925668, 349372099, 282375158, 222122198, 904541127, 52749013, 431231323, 49003797, 437263311, 801064928, 32815265, 836219970, 704920395, 873082662, 532809159, 602979992, 74672906, 109638935, 719780102, 895436153, 14293265, 822826246, 897496068, 784944906, 406732837, 693216657, 749978068, 75032213, 121623068, 802982969, 627281617, 173467466, 598391334, 439533891, 558949113, 838359633, 49051695, 879958327, 367583986, 913816149, 306302449, 12886155, 589379288, 861070923, 460938170, 873666793, 191168591, 21962247, 90713798, 688276525, 156779328, 432927866, 633908021, 727847052, 702409254, 39269341, 966321407, 320862468, 518971261, 267367747, 172113296, 535161731, 802273211, 727620111, 258910816, 838334949, 473583354, 403502039, 593794638, 249605297, 986824587, 244548901, 981077001, 602457943, 171809253, 883617344, 194794651, 995094962, 279457736, 472593445, 837985727, 587308899, 203541458, 843747282, 505512857, 527999674, 609736912, 331518421, 287368648, 420039734, 1374192, 45279298, 345136096, 890752247, 868966396, 251013503, 607738409, 735061730, 251826150, 489330348, 984016466, 477082966, 938537905, 506556005, 874102438, 722793281, 633823601, 684954852, 247574379, 683080338, 313342590, 165292917, 614333712, 795903321, 415032921, 657192448, 750782570, 775138379, 115636997, 399969036, 60776209, 358208760, 773980310, 33373959, 666682987, 416171751, 434254541, 879507958, 242617035, 219410508, 604838554, 134762022, 903279163, 381601768, 720693033, 239835876, 820862173, 427479898, 476667942, 553433892, 497023139, 874583880, 396155305, 165017722, 785337908, 979738451, 355202845, 688018382, 862016054, 586859241, 270845524, 871749173, 733997, 216835224, 84802158, 119348631, 734257847, 569668089, 477432752, 342785735, 53727832, 914342142, 154406698, 565599558, 224615006, 342954605, 552990250, 493122673, 9920991, 14386302, 839813717, 292930972, 209512957, 821465143, 89266097, 173031830, 879557921, 988121309, 101968545, 325329658, 412193060, 642484059, 48538861, 189021616, 13402954, 815580342, 76925887, 726948156, 470429999, 309480987, 834273975, 435272357, 984530213, 174777005, 24674694, 99621167, 699325675, 787563819, 37518006, 89752135, 154984872, 797859778, 180138743, 418555314, 946772662, 344665592, 969337342, 180346234, 634308998, 266086624, 122767300, 605830919, 984680257, 934623523, 410298060, 182221302, 121243042, 679393140, 49901482, 3782039, 786369879, 834718627, 955117754, 528669920, 374151341, 311390479, 865169458, 165106287, 131485172, 458867254, 541272550, 497552314, 133116268, 513391982, 330979259, 153621659, 729990360, 20476669, 909886691, 537094124, 579317271, 826042648, 222068774, 701777184, 435660528, 287195394, 202009767, 925381836, 132847320, 734617812, 844041150, 183544781, 327185955, 118141655, 575596589, 651106977, 44854374, 574763782, 441977567, 38306333, 170506688, 499498425, 393868505, 611396096, 742081433, 43166696, 419448422, 137479807, 720047711, 22652227, 363898933, 99288152, 232780539, 760695865, 376051420, 917378270, 357515726, 512807813, 331275722, 474397304, 517043098, 591865825, 615926975, 311787432, 774892810, 565703651, 129407072, 150346627, 627309686, 687118763, 567863377, 501429765, 553513490, 383874995, 896312698, 737497179, 304199242, 768311665, 528887338, 926963935, 923661237, 928822857, 175453154, 575104603, 737537889, 830461928, 122328072, 397330932, 302091444, 798076209, 687649973, 733080473, 276689209, 18060339, 476635649, 104039102, 756327527, 878383446, 144857872, 173979279, 944794252, 133240136, 137886377, 946284882, 729732371, 288587624, 935018794, 681393939, 499406090, 154674692, 842004532, 486985257, 282642245, 889659064, 199443939, 286364643, 230118573, 831897025, 375727554, 329055467, 262269448, 586944657, 35935511, 102469570, 648674662, 561315400, 153153078, 859413683, 431830397, 552768944, 855165708, 748185748, 847390413, 894636854, 617852438, 577308095, 147753562, 770539332, 461541504, 510412302, 119929521, 48059862, 647799715, 716108668, 537460533, 769096166, 224622175, 793494096, 821489970, 309025266, 546119458, 235548273, 490260036, 335102483, 261246871, 347638771, 332946934, 742761622, 876683664, 55369706, 56244840, 557333999, 115954175, 568777833, 261593192, 770000044, 503225057, 486765257, 971476586, 139195212, 67514194, 785448651, 129116738, 346198883, 733678410, 487693461, 391718042, 724808234, 150830641, 229021213, 844827121, 834523830, 498939306, 344341189, 550691294, 674394927, 176043378, 391778269, 562714639, 857465196, 215016755, 70365825, 135943605, 955123189, 663971645, 509899130, 54485874, 337964713, 27162455, 293638443, 676710679, 160944568, 617389210, 644044959, 409182361, 517876405, 627088526, 398145201, 887870407, 884696673, 792683307, 36728751, 997367230, 878807856, 992199146, 459771370, 104967259, 583073713, 341065858, 619564624, 895537171, 876982880, 582846626, 558806513, 825914723, 678386770, 893338141, 453160097, 816273263, 185941397, 799466052, 404067864, 490192829, 225165300, 977724970, 947357018, 96674998, 636587682, 985427083, 109804378, 996107218, 678457130, 119996320, 30399289, 367440510, 838422389, 614700293, 18526878, 37847353, 364964468, 273200435, 972765211, 770726, 548621854, 129554478, 715776153, 59982378, 769964266, 105785631, 332473399, 938187794, 154865190, 813583898, 569545874, 851317954, 828908878, 214957196, 246704667, 167542421, 864703053, 923850854, 761468214, 639158487, 389178181, 637473425, 990428242, 970708461, 867379589, 636084977, 146841802, 299973404, 558322717, 860804316, 235349197, 525713126, 87419750, 486373004, 162221771, 423111832, 333084432, 856967632, 948084116, 863006649, 783316590, 761069448, 525470988, 296353812, 122119335, 323226883, 827272096, 449261260, 681745511, 475364610, 296429044, 885322029, 946461895, 633042597, 102135151, 550205880, 37301199, 878425575, 368119435, 24373870, 397447947, 659502718, 723341979, 308448767, 651448995, 97305907, 536278070, 26546035, 930798952, 894206435, 3586358, 726722078, 329178343, 594864522, 217600664, 315637226, 477620427, 542837397, 354783550, 47834268, 243270637, 538895725, 957833531, 880016578, 979912551, 726766471, 823892324, 236751323, 151918933, 686914341, 348765535, 155985109, 833734217, 687994461, 562310722, 738365448, 623134428, 885308088, 507212746, 826617803, 736992824, 629217337, 423282393, 906732392, 208580809, 208659708, 387783740, 741053260, 933679582, 291648149, 160599425, 171541971, 860119584, 83700014, 796530485, 615603062, 129112805, 47738935, 507678634, 188357262, 190051897, 732060106, 700035815, 943316067, 428803594, 941056890, 980833147, 628845585, 607157254, 342667842, 905724635, 715774226, 724025378, 562046347, 715834465, 558845623, 318847960, 267476602, 830219294, 626770416, 397475144, 562459251, 522638519, 972528032, 558484956, 751373083, 98547373, 226537728, 749514626, 200337076, 977338044, 533404004, 180050450, 82313317, 298974043, 129025622, 28888297, 699188280, 368276346, 480307351, 558610533, 746581437, 502219657, 303187162, 933406755, 803544032, 132702102, 924221379, 564981404, 367781510, 279200114, 820036472, 909335515, 627951029, 698471386, 292961266, 286380086, 237271302, 506137952, 429852428, 389217516, 649473374, 622679620, 689098643, 845981376, 492557047, 61905273, 20674414, 460379769, 905991610, 411031005, 332860937, 323738825, 490419734, 92752942, 409709946, 53120229, 867670070, 100945873, 884335891, 201159534, 751491699, 683398443, 39904840, 470689790, 742412862, 651793359, 485308383, 362410742, 701709139, 657511372, 678972628, 158837337, 741693573, 422189839, 394774960, 440659619, 158440086, 614932298, 774146499, 482021888, 379658174, 592133461, 876675071, 31216353, 837478847, 605552155, 914575631, 996825842, 270361125, 937354279, 430482583, 980964078, 493322882, 228384626, 446238962, 988768825, 640884940, 489340969, 861396926, 87810470, 861133884, 673807428, 71686065, 167674946, 351765953, 574715393, 703265892, 865834626, 901743937, 333458924, 348663786, 571751302, 577451071, 153855683, 427118499, 387640637, 555865209, 646441391, 68486576, 796657118, 576070758, 124912381, 171306870, 474418259, 121284339, 116458433, 892621779, 216124796, 121162893, 905343409, 691994531, 989612599, 166673927, 93865642, 947935921, 143739284, 828954516, 25559166, 361930077, 473250058, 925164624, 757584169, 825330703, 436200287, 364238040, 800583296, 247299251, 599628858, 638801053, 904272443, 982981672, 178990315, 641738806, 485080390, 906878756, 838230429, 270805528, 331368663, 221587895, 990535023, 268162888, 45739148, 238795459, 252643903, 519768275, 39294743, 399248490, 84644819, 330332785, 878740682, 195334245, 257144244, 511076309, 606247166, 129430347, 7361645, 188395308, 977426965, 865069324, 806724605, 943448280, 213865119, 359794663, 745556292, 644202990, 997585968, 425511657, 70559426, 659904624, 872991144, 409133358, 472113610, 547353068, 948338760, 747614394, 22366729, 410720983, 356479491, 808697534, 243779181, 497642313, 820925866, 976777619, 564156186, 571544, 50189854, 540204092, 799187583, 795316290, 462480224, 571234737, 219790749, 938744709, 796719255, 16721064, 664462655, 387890517, 705934661, 239439765, 54277823, 180700453, 328080256, 997453699, 714397934, 636663087, 396625904, 1292071, 165275685, 650216787, 383965394, 402420924, 961293862, 532211372, 165594752, 856663969, 148979919, 957416937, 32588472, 242710874, 662166682, 531007062, 894432641, 291742502, 365272708, 635690439, 461449141, 636386563, 325780370, 758827746, 250248335, 881858420, 748677529, 907114160, 297277325, 193223627, 44818446, 84801999, 583686996, 146303235, 169375783, 103947930, 275689507, 134427244, 774239895, 211988144, 761245407, 250693726, 763879360, 985152783, 508068537, 150523411, 267928625, 346670501, 404062423, 780490325, 615716428, 774435254, 868274576, 119912652, 288146505, 613371017, 673327238, 435575783, 669410344, 299515091, 336707476, 225353283, 58132623, 423189359, 771905798, 799795549, 793626717, 56912334, 21291534, 376365881, 704993856, 21091185, 971174317, 277347129, 249454642, 258378852, 570149907, 721166307, 973394961, 27741646, 459380388, 270161908, 802325813, 632058941, 898675620, 644219508, 856262729, 891059010, 476377335, 28879885, 81142116, 844787872, 474786531, 593540810, 643932929, 305857176, 417762569, 126040316, 90944985, 694575321, 597017862, 89927941, 882904967, 839054042, 435400808, 879389241, 180176536, 737411589, 284240335, 299518453, 249428552, 34638349, 422336884, 667302242, 64893471, 247344957, 42458779, 623411432, 644354015, 746873283, 495850023, 628293369, 749808585, 189539974, 546079436, 473267530, 421040583, 516609044, 487827428, 841809419, 685866090, 542748631, 388924871, 464834016, 140422176, 701278837, 834603168, 97877677, 60237011, 22129447, 816306428, 672972407, 536866322, 143972635, 210849774, 144662678, 6284064, 320921508, 357707542, 987444753, 868989664, 489182290, 754625436, 437695188, 389861468, 48836987, 257799911, 135542341, 43946113, 737535040, 169733820, 168772996, 910618723, 657445874, 105844328, 196917751, 495105844, 378017943, 519251540, 777507563, 772364718, 351107823, 881038193, 672102278, 141142926, 593202143, 293218223, 118024658, 570631157, 712902402, 962185578, 94244750, 219337916, 653201267, 670982196, 332486261, 392657696, 139113495, 786344582, 694147701, 596005622, 462098236, 825846341, 309410866, 381439786, 421634068, 34275541, 358571342, 114946180, 270686236, 714248780, 369940549, 594893942, 675513988, 6700025, 128853925, 111515371, 908956111, 567850040, 161463100, 505250551, 628315252, 215107497, 184343286, 238774926, 83321972, 924742455, 434738482, 354944717, 814887163, 927762365, 480969598, 983020663, 549139775, 98592116, 862736365, 29665491, 516923543, 657865435, 122290128, 768195076, 611986646, 443538649, 752482366, 659297244, 352427481, 917598816, 777186005, 273913329, 803212090, 834102341, 822891600, 166036501, 278430851, 992600662, 410072580, 193228811, 81140301, 724944770, 726578016, 814480572, 319907083, 116044873, 508451343, 544391980, 804926798, 986353185, 137046820, 805905604, 116602917, 447805165, 8516411, 43878812, 56636107, 254557373, 669843307, 105610397, 227035262, 924834231, 260239851, 926756962, 64918668, 275760222, 226460915, 257789478, 751685483, 560820827, 266618284, 57020690, 112487108, 254312280, 101460904, 659712626, 139219272, 870688914, 662863715, 838737974, 752592511, 454284746, 184596597, 23323257, 766398674, 893298351, 913770726, 372740599, 826842877, 88855870, 791702377, 569681086, 518726897, 957701972, 52869006, 103111253, 536902718, 33722202, 531215859, 870101030, 610135865, 862027248, 63467642, 669619876, 966360186, 864399083, 895040808, 191021985, 46320328, 335621012, 237136999, 212477225, 527143817, 573753646, 837250929, 925283302, 915939623, 973103417, 385486689, 923698202, 746155809, 376261716, 451988723, 754253309, 938837054, 485645744, 663144111, 584141185, 213390845, 414893883, 989062689, 134980573, 808212929, 333825958, 203990841, 784129672, 504616920, 428985371, 787965485, 451278215, 774066555, 262818543, 946690453, 143565364, 859213646, 404630278, 657377903, 940594214, 483755162, 49723608, 596359566, 44427972, 961268805, 603154929, 439603307, 970295572, 745400201, 296514882, 114233777, 741099698, 52667186, 941860668, 56333467, 417651804, 982794169, 927668982, 1185338, 213688237, 223403082, 451983254, 261322834, 871564211, 413643644, 639174281, 893452099, 209021625, 317366108, 389727981, 878554477, 889374146, 578090177, 335125240, 760801232, 102274063, 893183385, 591959505, 190054857, 820539006, 240852185, 553909652, 392643256, 163393301, 967093406, 262529794, 37180942, 445070792, 537357205, 368204536, 33647140, 977251845, 212100016, 876234141, 406695559, 260459154, 5530499, 557379128, 918232892, 336902951, 810960089, 203962455, 670798581, 635820767, 106947560, 145641081, 334535449, 514735050, 616021431, 548745232, 680421683, 267488524, 882703997, 739614278, 757192055, 404587566, 462098431, 618604017, 876863091, 458684844, 428271389, 252046105, 340182198, 999695048, 998367669, 348068023, 713404875, 96082561, 362109738, 170356965, 768598187, 507620794, 307418825, 564521973, 113729829, 401513316, 934034314, 63068064, 368135907, 35748766, 799972561, 528795198, 57247638, 700441652, 36405356, 286092229, 958046611, 887426488, 374192432, 887980933, 691750601, 941770152, 963493619, 602652506, 221059030, 708588788, 384328422, 526312328, 516210857, 24427067, 520273815, 802420542, 893055425, 32809887, 585662747, 835573654, 820894458, 700544516, 324535972, 800329620, 531623728, 90432664, 380037855, 754415940, 745557563, 733681369, 542676359, 755245899, 722362010, 982869542, 388407555, 821204005, 143501522, 270375873, 502816655, 453744111, 454419777, 918710035, 865771592, 878644196, 861417901, 967085083, 500682781, 374234038, 77064132, 529638149, 170661863, 838724887, 948427077, 893231857, 183813010, 472462641, 944621621, 447925186, 784168192, 951974345, 272373498, 128376601, 608971778, 411474066, 966929330, 800734533, 275377981, 963560890, 332402058, 833180303, 24548607, 453091875, 123992567, 408847054, 566859617, 114846035, 96916198, 877100190, 830312083, 479875582, 391685105, 797991888, 307876483, 747138252, 634176206, 601692148, 724115897, 193507552, 285808942, 772275311, 51750788, 150881849, 430277410, 332856545, 950910926, 237877524, 775491151, 982285081, 938383782, 617454784, 506869713, 750471174, 407236349, 727694861, 468652569, 676730585, 42364946, 793538611, 961591914, 202451814, 539426498, 753886717, 818276938, 229604039, 610964844, 434657690, 114046986, 507953209, 830268816, 608420272, 411644282, 769154665, 98984470, 913455069, 979848656, 965317705, 576196922, 98150254, 485776667, 830735909, 896888000, 659713743, 35782508, 427405027, 745248318, 900939786, 679183912, 168737041, 98580345, 880742427, 187776000, 887097505, 182642515, 305621981, 254330139, 156189147, 150974412, 600581452, 477793054, 90395591, 315998947, 456311232, 91270646, 399436886, 496578771, 655940822, 671815084, 566015113, 832677516, 395703449, 573852390, 299369692, 637757979, 394364700, 56012680, 678846306, 511248763, 76699597, 561240396, 911577208, 918715799, 276321298, 637698431, 106709715, 703195964, 41571457, 991227916, 357149259, 442687666, 669025428, 505467227, 606229340, 550479776, 959201277, 441603312, 763748009, 387852403, 814089369, 781919261, 555744302, 629169414, 755057909, 364651255, 632352857, 410806672, 920662613, 7593819, 694330406, 685066385, 19448532, 283393348, 251877038, 975394832, 224960389, 509288111, 786894407, 412220128, 927583709, 547339183, 402770161, 311073629, 755903906, 375457727, 750180748, 376688768, 957741806, 592426351, 828137560, 267675926, 92687347, 815898085, 286835915, 806576676, 898537029, 796110039, 825429900, 913350700, 676113570, 49306288, 610455365, 369562632, 716057127, 429319451, 856671162, 229421463, 885574049, 571203668, 405213960, 449640368, 805365720, 149636559, 638873336, 312190432, 441624712, 581710252, 198260826, 304720433, 699661421, 87558408, 771176413, 239384624, 284291177, 673208080, 805211929, 272634760, 298559345, 530255829, 261495883, 316677176, 402206024, 25170806, 346491832, 686847927, 315100598, 933081404, 589140014, 784565705, 23131448, 80866104, 915998192, 525155667, 740267085, 840497982, 79435648, 643778549, 747209371, 609084263, 483219155, 117430117, 737366117, 895988299, 961970239, 188572863, 478025770, 32805671, 227762187, 574099630, 560346985, 389080407, 780796895, 470470859, 667176559, 688336429, 622376517, 279092933, 969217355, 154092943, 561061101, 21156721, 99733022, 535364145, 753347112, 262591499, 4430007, 189111835, 542515846, 632337532, 982244169, 751682102, 4867891, 65143201, 64132330, 881476013, 748925583, 793409369, 207241349, 387694733, 319493451, 333621203, 113371921, 192260356, 374281248, 362142704, 683951754, 987398455, 496748520, 36291075, 273656605, 715543545, 618530065, 339599567, 698660454, 318263316, 622935794, 979459612, 60297760, 771354349, 20985885, 647199115, 981659791, 879820359, 457960656, 201855003, 649825916, 446065258, 868924170, 979239156, 697627735, 492625110, 569789209, 606550944, 907278120, 175773085, 115253492, 700189402, 115486519, 760763666, 759054760, 882343779, 102725596, 994276647, 178128917, 470750778, 63362327, 989941424, 21488471, 69932603, 430105155, 587623761, 321185387, 295564233, 872864380, 696659379, 711304133, 245994939, 995608918, 134985336, 15742661, 383492925, 393630626, 560655686, 811361154, 232194294, 507120689, 396224386, 377623682, 387542784, 608046668, 348647258, 291801493, 271714312, 154463315, 123853573, 156546985, 191859928, 890591711, 469004085, 184173167, 531721968, 180944472, 596583248, 220280553, 876628071, 895789840, 784270864, 862057401, 136502290, 93018023, 964293972, 344713513, 505710572, 902059424, 492676284, 650241664, 727239166, 962116839, 52088322, 524791264, 182897276, 44669300, 990757345, 421581928, 141695531, 41762320, 157447470, 78205657, 816762231, 485305997, 73885679, 101224052, 987359752, 154812022, 789785417, 113738903, 375064025, 278117670, 489060554, 509245758, 385387197, 596552642, 760846257, 915619602, 842969661, 35271739, 70457626, 686054682, 441249022, 628952103, 972145344, 261177805, 569170016, 652629235, 419402625, 401567810, 182831913, 494400756, 657547797, 574443571, 69358680, 638184947, 113197585, 855741281, 112331137, 695446237, 633404352, 303211440, 764305931, 556441609, 768830979, 562232878, 864366688, 738749983, 582684613, 552089441, 619818705, 427547467, 544786455, 276065284, 314217594, 890935127, 46348981, 246695326, 746137627, 294801825, 339240388, 844356735, 230617402, 52187203, 101258781, 533323872, 870239296, 879229899, 489203707, 962357695, 262336243, 899403718, 347041794, 549510641, 789614054, 982122537, 793079057, 745332561, 663260893, 312401600, 783694254, 510463712, 848879321, 772459956, 526414759, 847320526, 39489282, 677045571, 748247934, 425875146, 798119096, 981921836, 342636013, 771083686, 86774005, 171382468, 302657404, 438865488, 814962936, 672869091, 474149587, 943875711, 339956402, 489506984, 572432191, 138101702, 568051355, 61043375, 683851800, 664871665, 38523480, 540992464, 138881569, 899861973, 10173960, 730068367, 851653020, 606171592, 51873519, 998767970, 164875788, 648645474, 181731368, 818660743, 813896338, 950134816, 873037824, 606741174, 921995161, 173930053, 192388972, 61872651, 869781637, 189361832, 350159291, 908384600, 116807156, 421149391, 901030099, 973167955, 580214947, 806227615, 57865086, 409162875, 779974339, 610140379, 170047330, 425536347, 194944852, 341692654, 584151002, 644237317, 750641556, 741781140, 627742019, 587907495, 428132443, 523010667, 710164603, 282212464, 538563106, 150550479, 633540531, 298094704, 60958326, 280912576, 874609632, 384864132, 819178163, 630025394, 329194640, 693823356, 134463809, 62942561, 361688075, 487437754, 307583319, 736304355, 175647120, 422154008, 790137466, 301037080, 567036103, 838084597, 735805449, 762447732, 508234694, 394433519, 214263384, 530715698, 947709355, 107960927, 13700941, 529568205, 3692670, 17875892, 455421345, 669250254, 821079413, 795243322, 243504258, 508364618, 817826686, 375746990, 240690980, 977745602, 223930253, 289093164, 67830373, 939634624, 706842300, 641553594, 167208369, 612989277, 496035240, 407100572, 502743199, 979479527, 258187910, 997165936, 249919556, 630603642, 989022415, 61292619, 285178098, 896903282, 273021775, 654191491, 362884132, 319017616, 846329004, 110569248, 33219911, 309035450, 256939984, 241461451, 333652400, 891138806, 788134900, 716022500, 942070368, 603260191, 142901214, 985474290, 390404889, 15131759, 169098548, 46178956, 774044972, 803914870, 46332327, 118277012, 914476816, 260194153, 859969133, 47550912, 786626264, 865722771, 190877146, 742966833, 769932351, 281157757, 161648489, 809908842, 295828216, 581288538, 928885340, 41076673, 369504825, 761627881, 693004429, 534066290, 105075533, 137160469, 835098603, 347043153, 633159287, 867455240, 74134198, 579986039, 996146200, 993731174, 415355348, 797311873, 209703292, 452145494, 423763886, 513146895, 778427594, 74510852, 252060113, 519631047, 636859237, 51644965, 141019544, 939418719, 406342395, 769249150, 466688319, 549070844, 689924191, 263200652, 704216155, 14326703, 934097964, 117607050, 498542961, 841617898, 51827022, 623573576, 510290201, 734987988, 564341521, 196057046, 689003190, 537776445, 405709837, 598712833, 569344658, 856531975, 389128540, 78063444, 424377894, 228860239, 319009443, 188288993, 259894459, 899623746, 185689466, 217561158, 723679261, 304451226, 846487210, 958620415, 77364386, 24361579, 358640181, 278728384, 137662694, 786914149, 343647714, 157867592, 62853538, 351621490, 594825339, 825256902, 742134343, 13875739, 852998218, 75823732, 431763563, 97232970, 930464216, 794066, 397838739, 514489606, 521656998, 517729661, 188853438, 391163620, 987907028, 517888317, 742286418, 620929215, 447635111, 81679614, 79168665, 311103125, 168662719, 493448163, 527537910, 455036004, 573786944, 42893297, 392852421, 340821374, 940595945, 122910696, 236761387, 232495771, 36334660, 35996641, 258565750, 128521672, 394827736, 708322144, 919281888, 708959957, 280653211, 480709166, 822745179, 491878063, 454033734, 414771611, 111767362, 704931958, 589004106, 380360202, 948271375, 592534264, 966308667, 197571913, 66037590, 575965646, 307309485, 109247777, 935360348, 880193102, 120010364, 6558485, 895266732, 949116416, 451474270, 154061967, 916318021, 637528074, 963704659, 863780465, 878025487, 334353177, 867329393, 375893458, 581405644, 558447280, 425749444, 867718049, 510312284, 455330601, 417161638, 475494946, 929844013, 8068463, 731619888, 79090892, 804327547, 299761338, 71731624, 34684983, 621346797, 452356578, 865216300, 356688118, 349708895, 681942053, 212166375, 295861991, 345119864, 177119219, 759377260, 958797983, 874816462, 171209813, 148741756, 206365680, 772831467, 985497654, 368019837, 567043852, 168138054, 706303074, 275902162, 491176103, 71985993, 951124541, 262957790, 945105760, 133116237, 901268297, 576101661, 719308134, 879057837, 446804163, 410172013, 44227112, 95050654, 680947880, 383580266, 329147949, 483910609, 302414474, 907036361, 383981624, 275625687, 850119192, 939254226, 446601537, 796607026, 317596280, 826057376, 458294897, 592472619, 940626067, 278994567, 275115012, 75910199, 233471724, 471989551, 981993357, 206677145, 935301624, 361301011, 602711543, 865873521, 938933006, 996442703, 658619161, 630284061, 957927851, 919604889, 212474957, 892259340, 46986089, 977072, 469656932, 817671360, 708193390, 478764333, 498645589, 587980499, 632290459, 916555822, 63756097, 156617617, 246097966, 180462966, 340448782, 526017716, 772028165, 247661591, 762637959, 913907244, 321511956, 128520688, 812569279, 52873479, 151285613, 436411464, 20097253, 460066439, 907224203, 207241055, 99565531, 749063189, 574936474, 760694038, 270958932, 406982003, 324760262, 247214503, 875205469, 226381998, 965893931, 362510330, 562771948, 458780731, 255696235, 909887844, 790388504, 126774073, 331471215, 573971726, 343093599, 658309421, 220618360, 565799343, 399177408, 110190257, 563762669, 571530633, 78807756, 446745673, 343874930, 78449002, 448971481, 751776343, 972403633, 968426952, 245958296, 96359839, 732686679, 843586877, 51618049, 826190428, 187154218, 792645532, 905436258, 857214000, 434921150, 476671903, 311953165, 656229434, 776608757, 705483165, 889332605, 87059939, 274365885, 705345213, 791595158, 9841471, 929331235, 720420057, 317602020, 490820349, 665606686, 320601802, 77835311, 945600392, 713393921, 757871814, 528872031, 988456276, 401784670, 999422061, 396767000, 553191824, 248910981, 906112396, 586504044, 662032839, 817144729, 512150752, 498646047, 968197779, 337870345, 123693361, 684558588, 842675669, 942123288, 630482935, 561612465, 275960037, 257299997, 477959512, 110816099, 941922605, 717936345, 439962973, 104720634, 59634788, 994997844, 929064701, 940745464, 16816075, 348884833, 773540914, 709106836, 751583988, 227275322, 462868287, 265432976, 632302205, 716666710, 17805293, 353692894, 239462874, 924121674, 555804683, 128819458, 7661619, 214243050, 798890618, 532686535, 181088968, 537033398, 206932964, 146157882, 664287608, 203403152, 522390522, 220818920, 556987265, 649447902, 380450570, 599089899, 841084637, 400145164, 62322925, 62329690, 22685124, 920892808, 297788887, 948087604, 804356724, 732463191, 226740794, 467709114, 497133323, 484570303, 854496860, 338578801, 518727844, 609114564, 608623087, 539730502, 306844264, 713261506, 729691068, 394522158, 65912771, 125102311, 578860054, 456263470, 630908683, 980915255, 94436754, 861921701, 965386944, 704694604, 385800104, 757372754, 62467614, 885141247, 690696268, 992489732, 480982629, 563527037, 741551919, 252909151, 469745181, 44355375, 532373634, 923649628, 754913709, 223003140, 112181549, 451062519, 565487523, 473083059, 942726443, 961246409, 162323909, 491164231, 414194022, 974280252, 915432669, 101293932, 92263193, 611608793, 753692360, 662822728, 160923744, 963775925, 678188162, 297090731, 968796451, 70760852, 678904222, 345389676, 56605914, 152355228, 307612797, 67480798, 471992745, 1710180, 415336049, 960639433, 274481573, 840404163, 833032837, 892794384, 560535258, 778894146, 372155525, 766259521, 743825859, 537402734, 390996337, 342371243, 552508637, 860764394, 340073333, 683577032, 95977566, 989314894, 990750248, 982420920, 490596436, 510861097, 247936929, 378004226, 320216956, 578692637, 615157606, 56450883, 945065365, 929653915, 528868913, 726666426, 427393120, 680063728, 224666494, 376401601, 950436727, 693710251, 33347163, 542857344, 947152060, 147113554, 119444135, 545093910, 849092052, 267923586, 435499719, 883183704, 828403164, 781328053, 836559274, 204848100, 661327590, 500486915, 446814144, 131334055, 194987545, 170294515, 441331130, 54107191, 918496304, 764702550, 642045656, 917579134, 737715002, 625883402, 369999684, 729822986, 541352732, 181796086, 144209069, 913718268, 489057101, 911959152, 207223401, 154555774, 902406782, 740304011, 185100171, 972804034, 836525430, 799045955, 422603095, 498571161, 518510765, 715024326, 625534768, 461141778, 91471361, 541968796, 545519385, 342135719, 379882254, 436298096, 425613649, 152701866, 300634339, 876067714, 996045795, 568219386, 397847904, 875452664, 771800211, 723342921, 92773760, 223329932, 183790998, 220353822, 496719367, 518071936, 507498718, 828463801, 681099911, 807865722, 305644470, 692216009, 515514266, 141026074, 967461277, 922043220, 981243359, 260428792, 562783809, 51742427, 346701013, 576345812, 271135787, 841957404, 378474775, 793290373, 383173279, 544781484, 148655997, 185671444, 900232998, 792525925, 841461540, 899470103, 513244405, 162855624, 679200079, 855679928, 325625866, 831722375, 219161574, 386579943, 941224565, 300858817, 906036493, 298511629, 452616351, 102534149, 785505682, 775645616, 100862072, 642084734, 693637786, 498578167, 365738584, 232052728, 78105092, 673202739, 216859505, 888776668, 723704765, 365969929, 633087441, 469325646, 943201602, 862363784, 788564889, 400938484, 552721851, 599790455, 990902649, 567512739, 982261594, 77165627, 142998478, 242733980, 348922400, 384126443, 63022187, 483482171, 313680302, 859165598, 37808834, 526749149, 719635794, 642923565, 695315385, 835730350, 327983117, 370709685, 963105830, 82578294, 980764396, 501741346, 128192079, 441901319, 70246715, 250486590, 599423829, 992523220, 974617136, 842777862, 962352734, 977888587, 472538547, 533312752, 697412478, 545796775, 127164569, 795885159, 851774350, 941338776, 709735183, 42362029, 992344488, 4307055, 908476116, 347253676, 505392604, 663899978, 563014812, 860025985, 390637304, 466126168, 975709842, 894282998, 836061896, 597190917, 260619610, 322005298, 389519627, 228696373, 787740361, 885133755, 167651564, 268564016, 447148111, 927477021, 468328332, 733561377, 313354585, 723866854, 355748354, 663223800, 466793908, 694819717, 82692518, 355448981, 820178354, 86482966, 650211243, 875883418, 358402542, 392418119, 750048907, 358391734, 513183346, 842824534, 866607540, 471524501, 915173250, 268025361, 862702049, 159829051, 697030633, 321208547, 598011372, 583454565, 725801906, 671618552, 443943256, 371119720, 36516170, 486489049, 842656015, 963843277, 64129481, 125499085, 262556791, 301270814, 332499106, 300467356, 428961620, 947206086, 830901283, 513365803, 375950696, 638117571, 315702067, 443844762, 898799294, 100476646, 750844314, 584961021, 409126676, 660657746, 767283683, 823854439, 908468492, 805213907, 476892271, 19260270, 652531515, 170515814, 102585774, 448603429, 872232158, 930457526, 223567430, 913320014, 109057294, 667361791, 929861466, 284611302, 376318199, 289968871, 846672638, 235209732, 967342144, 417808597, 484271985, 286379193, 795877397, 337147859, 208624921, 981229529, 991532705, 723045291, 688563377, 346982168, 633842696, 965985806, 60052794, 344307079, 987179971, 844226959, 222915797, 153356017, 410298705, 830415515, 518492197, 361447093, 587749340, 902265735, 146053503, 59818580, 818505551, 252621772, 616111959, 44706096, 891255119, 534445736, 544249502, 356442096, 994574761, 39789999, 367360592, 651650214, 323587192, 796217536, 157835609, 192410532, 448524801, 716299203, 402486535, 40784744, 733664312, 911926067, 625922244, 853506469, 893370723, 731356326, 71540363, 968704401, 491429400, 342877850, 686123229, 623780227, 655128258, 499813266, 478544975, 753004974, 504882640, 65744743, 259474695, 857671904, 16806777, 708091636, 307108368, 937908457, 244707789, 631570785, 585108576, 484746985, 158953647, 109120519, 709598039, 112315426, 775777949, 422622026, 79135264, 247396783, 695596342, 827571323, 697700712, 552216464, 181080093, 799876883, 666580785, 283509659, 171014521, 635405846, 269291865, 995406707, 431957632, 468514677, 474858638, 800537595, 334506263, 919079430, 882769602, 600216189, 503676684, 592448897, 34159068, 224677004, 798380755, 342439271, 860047152, 87036216, 879239311, 251017207, 816538616, 724593007, 386543078, 11781062, 490639682, 256861860, 196925615, 918230128, 735812091, 463213073, 85239599, 590604649, 901451644, 224081835, 198631572, 119202745, 392472651, 699192699, 253629593, 174386059, 995913040, 7473752, 487899416, 682536586, 209234782, 468520454, 949372010, 621229562, 512642917, 854167777, 378046665, 34528293, 379970746, 679359623, 189984140, 205458055, 274899169, 81874024, 142780414, 29816259, 155758467, 18837217, 567948298, 470890964, 778402053, 272872107, 637390148, 613241782, 592601606, 129897116, 512719353, 511184780, 563884879, 30968404, 746457041, 6885793, 966198150, 742742903, 275672964, 819063506, 554096470, 112833234, 256524872, 557016234, 228600085, 370377918, 89083982, 762221272, 515400176, 248360270, 312246224, 944790784, 764075377, 987800460, 649637065, 63536966, 677102455, 47556813, 295218119, 647884668, 542975959, 339983992, 745854299, 696470399, 449376292, 459304540, 535026942, 199722477, 793644986, 782999246, 129716905, 94171789, 585038985, 494480100, 414406523, 288408425, 892345085, 808419766, 929196809, 381281835, 602763660, 840131142, 742834576, 441201188, 316052681, 469998297, 23653176, 214166557, 105311843, 666132660, 359109502, 107218979, 404179662, 798906816, 137113193, 426495919, 698515853, 998014529, 392757633, 261967448, 699302524, 853273562, 763444703, 740329628, 331883055, 981314216, 784243502, 881121880, 126198915, 555852403, 494356689, 737029302, 906663917, 851359891, 469944501, 253872564, 228816435, 173020177, 818406130, 890199403, 501120519, 517677978, 623682043, 386229711, 390723022, 819760277, 420740478, 146775407, 947650556, 677808582, 140152142, 248359296, 851435816, 941287882, 138955640, 336640539, 539916371, 752480385, 155681741, 412641736, 353317844, 452957952, 682368540, 458437612, 646708056, 112074424, 575382506, 558964087, 466646729, 322416820, 783069073, 314492318, 433286985, 149438771, 659114906, 544008562, 933999839, 126751239, 810029682, 624178824, 648503406, 949560071, 51865595, 838391515, 13539986, 521317426, 608338446, 665373475, 134271196, 406420406, 71095529, 665034333, 403120093, 87885308, 60782552, 14001864, 989115956, 975454838, 299281795, 484795653, 515827905, 224804433, 378517074, 591115434, 85690866, 685885628, 398778015, 671901954, 294877384, 761498271, 724306457, 986754197, 956461534, 148391993, 989943209, 380447098, 86719979, 303689111, 926060782, 17935490, 718332028, 981427115, 469623998, 955505917, 249740613, 754817909, 444380684, 819740690, 847491331, 221366774, 999798060, 586173366, 428032573, 188188785, 666748214, 111840052, 83109715, 427170094, 612986031, 239774098, 750459787, 647386959, 464864726, 331985123, 657259355, 160407088, 896618096, 146321028, 669852572, 145235569, 62913900, 243218049, 435321878, 144930043, 412945942, 123271150, 694144335, 396539979, 155945917, 752184643, 411758105, 674748268, 150802453, 100688000, 708662283, 339162229, 645547051, 77783091, 843552244, 925301650, 564528040, 673453903, 13809413, 846969767, 198938738, 978403755, 837145163, 578186220, 597938896, 359252735, 197181237, 967051733, 460880589, 561911885, 295481954, 67247588, 537907460, 818447193, 889244914, 61004062, 269466125, 487824623, 587152691, 929080327, 107921359, 602807498, 149059966, 726233087, 142401979, 652745628, 867122211, 698567300, 104135460, 9428344, 814344144, 339134346, 532733306, 78777892, 791559934, 905385597, 948957750, 363520928, 213543444, 331343006, 22765494, 248034722, 319943405, 581810963, 185346219, 83338185, 121874206, 264745595, 887029075, 521816770, 130400137, 610676686, 777186370, 520814541, 960140507, 710996391, 227758127, 284265093, 16839378, 915672075, 743054339, 615163349, 813235560, 757509378, 929808292, 524760388, 553620835, 705667076, 674906711, 24546129, 724284080, 442568856, 181643278, 881898274, 379604745, 618306193, 96479937, 707743772, 14606326, 272765346, 945241828, 925390951, 945965615, 499375434, 144236517, 25532869, 575193537, 86145203, 12945441, 369337691, 201175424, 330076921, 841191891, 935198807, 233376813, 314246260, 340690689, 374771655, 621353906, 432635139, 390383235, 251825681, 386421297, 579965020, 725578976, 604787719, 910441854, 317795345, 777517488, 70133258, 499210913, 877510240, 778799065, 276394528, 484395940, 867635658, 291332950, 584000355, 491636955, 67912235, 94596971, 95446246, 181805476, 545481137, 636430557, 285975125, 801356174, 206836093, 943610309, 180817989, 22843901, 119022003, 314332205, 878016135, 925569501, 915739127, 792526840, 987980815, 257927404, 463078235, 639738774, 526123726, 661286281, 735761779, 992021185, 406067087, 579761246, 156549196, 310426688, 422480820, 231867508, 804490658, 19087164, 302656839, 998982527, 858911257, 905240810, 965681243, 603970753, 45942517, 444360473, 943513690, 466364285, 904760654, 887245837, 21839104, 369775823, 157905329, 729861436, 432221545, 182167104, 983760221, 790368218, 399809759, 371385110, 861461391, 544607793, 970947707, 908956447, 854627901, 103564930, 6013580, 251944984, 547616773, 199764114, 224529679, 511109815, 580396817, 136181105, 164788639, 493741131, 456648700, 126597505, 437323908, 813466677, 299271189, 436267209, 119836613, 985538758, 910510926, 825819717, 312947671, 375158719, 326849834, 734711243, 463674530, 758080470, 909905803, 630816316, 570906608, 562335365, 430048778, 749926496, 577558094, 843775919, 279459829, 55322933, 229815727, 912905043, 419527049, 471877207, 134700141, 118547818, 768943703, 376626889, 596637855, 600894289, 32903593, 642445419, 213253638, 651221000, 840584431, 316958315, 939743860, 191459502, 378328126, 106212407, 652533430, 9341458, 223348462, 486843327, 540376235, 2462288, 341439537, 426735226, 47664411, 760640847, 73815646, 622992262, 7194431, 27238358, 517697233, 67219384, 235253672, 741700626, 829634266, 580020094, 52045971, 744102019, 449232902, 404155951, 50531921, 61026622, 920186490, 457678289, 399998409, 384732463, 549862897, 172162583, 112863096, 241903791, 415814300, 145970551, 533366535, 496653886, 58397782, 648563685, 299479207, 143071498, 38019631, 217849817, 916594005, 489324289, 496670085, 443249315, 548237379, 568399417, 308809290, 575572673, 582360140, 520324054, 705007137, 138798677, 598904545, 899044413, 353079280, 349784719, 798642227, 135996871, 233166226, 928727971, 290507519, 897829986, 623757480, 398649693, 258197728, 842067870, 770292028, 603021504, 886920778, 696835379, 505790079, 555782729, 929152656, 235523665, 779162766, 932548264, 382326764, 968501062, 268903716, 665370869, 506293102, 762079457, 505620986, 88070594, 655645331, 850616558, 962043516, 136749399, 473056403, 593776215, 958720052, 412779266, 725065346, 898208842, 992265284, 310651847, 785189935, 375886361, 771737672, 55127103, 920754065, 746357978, 754542994, 466697913, 98700848, 731295439, 296003319, 262782740, 141372831, 907952306, 285253434, 271035068, 648859645, 977266267, 985934749, 591290403, 169373841, 602229768, 579836260, 23207808, 316426565, 833738012, 873602276, 432584046, 927639850, 495403283, 366054598, 404997498, 901016906, 887809200, 31757757, 44365461, 673770851, 529928050, 265816060, 810264452, 496503213, 93238128, 49953548, 313102744, 130428047, 898610066, 572713366, 999603243, 433197191, 150018098, 627550496, 457889568, 587314742, 147507966, 394108826, 987069233, 508423463, 578657501, 424019398, 790940870, 60331348, 709829210, 323059106, 380217311, 456478824, 315885346, 735001978, 373279336, 253942234, 277875174, 738308227, 557179201, 864630198, 391421988, 384376047, 697292477, 480171781, 81751447, 730187382, 949279212, 242728568, 417804403, 556602700, 173195793, 409925553, 728035241, 38110462, 853034574, 200910457, 728532080, 770965279, 101736028, 308107207, 76091351, 215573303, 531110391, 415951175, 866493196, 855936137, 975673939, 814455540, 518750057, 116665939, 476582447, 328188649, 946107661, 605567547, 333260709, 406199083, 48678434, 591664832, 423523004, 464348843, 388538321, 100833599, 299482753, 873767372, 909885352, 521580173, 812203983, 607050642, 239279902, 512623707, 48595575, 199297114, 272408131, 467278205, 287639766, 65137720, 843130282, 965297637, 816473167, 636412879, 88760452, 414251944, 731758604, 231753055, 397890824, 972699601, 756121407, 785502247, 728860049, 319902484, 947088545, 616869132, 338231673, 606431533, 610956505, 581478263, 358953127, 198813387, 162889415, 527841638, 506382337, 912450025, 699167378, 25974292, 334361695, 466497053, 359727327, 285204802, 6000475, 990757272, 106697225, 37012485, 230764891, 6494512, 689705846, 671646211, 254688578, 391558856, 842644429, 330962331, 306372310, 785832126, 82186822, 831319853, 966153141, 553036461, 771527033, 25786611, 989084001, 937545174, 503735758, 47938777, 821129054, 705613556, 756523174, 612008328, 126221453, 770624063, 798903375, 906666640, 751256747, 18054264, 979950132, 660451279, 995527153, 316117898, 39452495, 627024645, 613215378, 644429307, 745627505, 398639237, 498497092, 417621509, 451255897, 503492382, 43096870, 571790502, 504914402, 885932005, 832940083, 874826452, 931135978, 407833104, 12885276, 595201928, 528091499, 261972272, 992013387, 608773392, 169114909, 106682535, 781465911, 894283800, 128155615, 497066859, 864558923, 680660406, 370889159, 690313792, 934729806, 129280886, 619834946, 389201546, 206273119, 199965989, 704848965, 615666607, 76273043, 786447396, 434013945, 147873086, 688570271, 10128030, 164940324, 440306485, 658742393, 577613873, 966515067, 4413842, 922223866, 230328401, 171037310, 357282337, 585457537, 615918770, 395742449, 369598785, 195173807, 692260250, 985740719, 47836249, 831523669, 913208344, 329706671, 745382330, 928728615, 822186974, 936217406, 385071889, 653558895, 110251733, 199980373, 788898407, 606830397, 899665003, 914858114, 991223462, 94754434, 97116871, 443804085, 734855636, 376236800, 423431986, 231208448, 557017799, 322504549, 929869478, 65125089, 695279610, 695456085, 746057446, 144590470, 769312874, 474185176, 46079004, 798451968, 622525971, 437971672, 864278338, 958772694, 391380556, 658411768, 884925009, 410898635, 292446366, 693066027, 731414203, 225004040, 983735600, 104955739, 402123986, 543128233, 734058651, 902122909, 664207251, 501969938, 315553787, 734220843, 256422093, 13582695, 488374016, 128957066, 759786510, 625410126, 640557087, 596864618, 369003294, 554821039, 461546124, 601842843, 382367459, 110318789, 720601206, 554128450, 283144864, 123090360, 419588038, 658135284, 656457395, 22034000, 863640885, 815308167, 752904592, 932550454, 428873270, 203736634, 543806721, 851325551, 44189734, 21055831, 968084284, 368415206, 536427667, 610693735, 103741984, 928959198, 168170154, 399711081, 595187587, 481045945, 6732084, 216728179, 529244715, 356405250, 954552032, 577816361, 62631384, 101945486, 276058540, 135176591, 276272499, 990780163, 385607611, 397359304, 876025488, 537205802, 263526079, 88753746, 937805987, 524459914, 498573160, 980872324, 685411249, 881192642, 597946842, 24924436, 689671903, 894928083, 586681734, 483475254, 65412716, 734777747, 761391386, 803630265, 550386623, 935851521, 97500926, 766230539, 188352292, 560490706, 815455368, 164484741, 882121667, 919065822, 186410981, 611748058, 800904262, 901813565, 825860892, 830483313, 143509589, 749676670, 186457427, 579199313, 899428078, 740680212, 276135321, 464294678, 200222053, 819735996, 29973266, 520984106, 751293741, 991021829, 53427425, 727691103, 123255507, 259500160, 878024602, 524000801, 535942986, 729660666, 755293126, 190574469, 42142234, 449472167, 661943300, 665614117, 710975482, 148068352, 233961435, 149926762, 240762613, 936596515, 544941956, 452272381, 436123680, 33079440, 446709617, 749064311, 380351125, 123372051, 374176806, 654526734, 813907944, 37782012, 741677957, 925788352, 668320541, 510283115, 233627548, 101506782, 372028430, 770487911, 936615763, 380003616, 179065698, 973751268, 863598319, 149743096, 41134108, 182110539, 942913401, 998466333, 540067395, 483370853, 62378687, 159614530, 664787727, 800390765, 991015106, 117676448, 532784265, 481214084, 608316925, 256719074, 29839804, 612164993, 357926119, 158110566, 855799531, 919719170, 221368460, 14670426, 339397071, 259801879, 50741783, 509089012, 55041055, 129260490, 103719778, 201277454, 835863093, 867854532, 474926884, 783023068, 692096454, 65811935, 494685553, 726354340, 976590086, 245241045, 526184874, 912632649, 167870803, 181542100, 903299340, 993254463, 755898504, 809609444, 390023850, 455231490, 496454366, 510930533, 428346723, 815157408, 950207780, 344261795, 45475293, 490380888, 558959280, 939433646, 972077208, 310692201, 588002207, 149315367, 106248408, 823314522, 569360706, 61760955, 930443500, 711444128, 733604622, 611032054, 403833889, 721850602, 6516661, 992408074, 552975762, 864285252, 848303158, 644013558, 234246929, 125282197, 684915651, 654250672, 121444837, 453026120, 762144819, 692385470, 757187028, 141977998, 913732173, 292286188, 713138709, 434179118, 543123835, 877038036, 892976547, 376579554, 795149944, 443226866, 571518185, 971903423, 59553141, 925740597, 336565492, 706235384, 747456848, 541349836, 439673576, 414997361, 632356784, 181956468, 545411187, 823204554, 362156403, 42245174, 460441616, 356119819, 17048640, 155668231, 159106198, 147082435, 615351724, 79682513, 233201347, 207662706, 864640769, 777593739, 509468935, 880522287, 201945903, 794283400, 122872102, 482451401, 69479122, 406690132, 331060387, 775638352, 328682911, 29134107, 762751853, 611720653, 741479220, 133362140, 986160866, 41716777, 531271509, 697459996, 688323036, 608072116, 84610578, 70257967, 110074111, 456942763, 271799054, 870269597, 15393442, 553072957, 210791166, 458548827, 510171678, 941449398, 307490191, 190487318, 171931814, 81310947, 994533388, 751371216, 836573508, 925223081, 53038101, 859396624, 179111730, 749169285, 255537121, 285322650, 672657441, 726503016, 141959699, 825468113, 253881180, 780472548, 981538229, 439906101, 837605108, 294623675, 575834180, 968034305, 673300069, 760911515, 598903198, 780701627, 529238067, 448001030, 864716892, 192896303, 215478037, 40364511, 262060571, 472711321, 157739584, 217403531, 912345131, 62793185, 159943327, 898946532, 548133343, 876304312, 417264576, 298201308, 319694182, 896262406, 598226029, 887915578, 904778417, 620309866, 9845904, 744332814, 327213440, 244962519, 353221191, 174014864, 205227258, 672110819, 905282375, 875696530, 98831329, 458454226, 291663103, 389519547, 448978616, 131604224, 624345246, 35887095, 105992979, 245413590, 120569933, 694021544, 854917572, 552630043, 253748342, 331489931, 289506248, 317647763, 733897723, 667530901, 927676715, 660854345, 367455052, 586604392, 540985090, 854759463, 300336202, 232000716, 365115292, 404409315, 601846038, 364242771, 973455452, 775446420, 346015195, 17611227, 539764038, 657485161, 932837223, 147222409, 195841741, 805906220, 183231535, 177821604, 699885797, 849389149, 775452824, 225658233, 543379589, 62391533, 7595106, 955998028, 688329718, 531527699, 74084818, 682186572, 23762633, 494837926, 725631461, 279110784, 509415933, 372873920, 514736932, 105019539, 867806282, 878624689, 151941914, 37735521, 189418407, 239464416, 253277708, 365335349, 174620792, 2908210, 891638542, 308174877, 797424191, 365932517, 709625901, 130231175, 250603791, 834198736, 334828722, 81612273, 493202576, 183197818, 170345332, 9606792, 380333844, 221025955, 198211500, 865425183, 467817926, 868219696, 866538138, 390233798, 437264180, 803205039, 376934163, 124247548, 804095590, 281308597, 275893806, 9017478, 966529531, 139509434, 988884525, 824270022, 596438596, 471697015, 940461563, 446140028, 350804822, 281711506, 259333998, 558144871, 565087275, 234525793, 349327863, 531844477, 17412728, 343907609, 196749157, 702560358, 741574731, 551577127, 983387340, 932212054, 920576105, 716202035, 608135180, 991163999, 697848531, 32379594, 267590319, 76776987, 847954797, 509621934, 177573006, 620443196, 930178900, 24514946, 241840158, 82188869, 487983601, 71671944, 630258667, 737524853, 507967175, 407708697, 750957557, 921617179, 493534215, 947758645, 69907141, 655127384, 115076118, 907755291, 860167862, 987670572, 203426781, 212543286, 466702097, 886752246, 204223539, 79832739, 655785619, 12055918, 831421009, 342937947, 549098057, 577376476, 987167558, 236094256, 161618854, 445518349, 702256235, 918635481, 753622603, 393318241, 91491960, 13537533, 193572012, 264579823, 74083043, 683536527, 894408782, 863423050, 453312813, 247304235, 391522295, 282050220, 649289877, 511180274, 281182673, 222682809, 579726864, 549845639, 86495599, 974659162, 966456675, 161789553, 242616175, 583460379, 613473905, 786613260, 502562876, 640714063, 307118898, 9392812, 384945681, 729240848, 834007233, 775504194, 521341699, 464337392, 465896878, 378865681, 909918393, 2521751, 461808582, 181176033, 924225752, 6960492, 768887943, 992310666, 130645195, 655683840, 525218920, 666168365, 237155204, 921790269, 960672972, 319472480, 909457667, 311705217, 303765429, 943865422, 245372405, 920870889, 845233062, 675599970, 539277526, 524276173, 652210330, 580842718, 526505965, 336558604, 386345345, 666925623, 15341354, 498027646, 532772791, 678127905, 255535348, 682760933, 710779623, 376458848, 657882109, 444977787, 767647696, 898288654, 595854558, 589559965, 561777509, 725625905, 574720422, 729088831, 42382178, 42520421, 100353689, 375674275, 847811702, 639779381, 517154200, 723043533, 97914828, 689822119, 501767179, 584160077, 464005189, 598995640, 861348993, 342975402, 665031523, 404808980, 772536956, 275113209, 640587862, 757799540, 631827723, 422337013, 289809923, 594709660, 868259838, 92026676, 610273056, 621615964, 50754962, 84923145, 910720805, 332762380, 24094487, 509620178, 698619514, 516293368, 104469, 114254313, 770384843, 671119999, 292361520, 648666986, 8036815, 256836953, 444523993, 214711088, 640949143, 679999428, 336011325, 393928576, 273095128, 121356594, 937866534, 349449625, 576766610, 467525637, 592520733, 644655382, 608415487, 924557273, 688989375, 632215923, 684349877, 844380432, 148686216, 354423531, 490373855, 987463868, 78746600, 871325568, 887105456, 778979252, 311043201, 901189398, 584801631, 325643597, 320319248, 45705149, 630686631, 489238418, 628759749, 729775514, 174284125, 434384193, 601272561, 155983879, 307553784, 632383401, 953376109, 636107343, 97839953, 838666512, 739486789, 944535261, 126653133, 119183475, 642679358, 375355576, 505694986, 189618252, 73786647, 582190390, 474760554, 878086370, 508663604, 710068832, 511958478, 279835006, 811312641, 524426250, 921932428, 591441404, 372547912, 2770374, 385503480, 149190937, 903942763, 531231745, 803824889, 332186935, 335534415, 9801659, 954041225, 489127283, 988927079, 897902975, 991880486, 546466300, 465307693, 531357836, 318000805, 746670164, 219416207, 662914300, 325537044, 910522640, 92908850, 459022476, 534577640, 128130350, 912899736, 49782501, 664929156, 794195698, 933644815, 754142787, 340721141, 918035340, 448516218, 851952793, 586449037, 277126251, 490488217, 360393597, 591980523, 843241998, 510381549, 875502485, 335518446, 340643315, 464921004, 255277439, 501005060, 837635510, 590977545, 442433361, 999258861, 35841085, 417349798, 957524995, 460310175, 931328401, 800490061, 231974304, 253134238, 237275047, 758214908, 811962713, 232957295, 253513843, 825095777, 866823615, 996415862, 42172344, 854634691, 419993632, 859292378, 259157067, 363294585, 930886800, 174044960, 489492410, 11072012, 531407142, 690642948, 958660769, 819782395, 284287327, 895438426, 418554146, 920874781, 575327971, 979093721, 10731492, 316572767, 569321136, 889828074, 189178114, 73684362, 802995027, 44002730, 812717105, 473276843, 309851046, 387979963, 824717671, 977642050, 987106754, 997120072, 192581549, 726142624, 478090858, 228178132, 26664937, 980065660, 384528026, 443281724, 504759040, 823592387, 220569384, 726352517, 249870815, 356464665, 776881916, 468366799, 277619138, 550914526, 917971689, 789209085, 497548958, 655658524, 339221865, 403502584, 726393519, 536961744, 655512617, 395075806, 431631406, 518577883, 498374133, 462556241, 782278713, 897523810, 796085415, 784988849, 475336347, 518036965, 266374310, 803275372, 634149631, 624183178, 962403075, 410667172, 100934564, 417095930, 348409926, 928417051, 299255482, 451824674, 13704954, 100129813, 784216520, 955786050, 803872124, 469600528, 877202018, 20368225, 991430339, 896104065, 231356943, 856137800, 428489541, 927890462, 678446698, 667442405, 551083488, 568597212, 593825566, 523269277, 15355000, 204724839, 770428080, 601677349, 594814647, 919079879, 270690525, 859277071, 337069983, 433416557, 919533241, 700968193, 84271745, 58437863, 225677914, 905698646, 757309881, 141801166, 21699373, 894594379, 610292629, 207856722, 693222559, 804646592, 726979890, 830950117, 239715561, 84233397, 678627681, 289729018, 552058115, 466069305, 867602105, 88424422, 525232593, 306933149, 131284130, 390594238, 320153158, 832037007, 20467313, 545973145, 710643137, 59658527, 950476589, 906525477, 139032743, 40682373, 773827526, 609715936, 155196963, 648984896, 840523424, 89404607, 587132702, 169659490, 48575712, 653796651, 384159258, 564379320, 523295062, 603048157, 256074326, 943272174, 785059819, 674258836, 948833630, 45851836, 318679236, 402093468, 792719783, 237751024, 821857477, 679359846, 497216795, 628867370, 790149324, 235297036, 738130234, 473545655, 508743233, 44749133, 960604398, 892497176, 966659179, 258509966, 2037845, 509562258, 575620948, 930093458, 858221598, 838218152, 273964696, 916564298, 878085787, 772760846, 653536512, 907414818, 637923121, 725207922, 644039824, 196587761, 778302809, 941300937, 415974782, 757569220, 529135091, 793473023, 673300695, 842588336, 508023064, 2972269, 180889228, 259071919, 111066762, 905289842, 856449487, 632193256, 522697404, 912978258, 146653183, 775165339, 467622142, 647240743, 207547494, 982078203, 970817425, 354222841, 101181352, 502799643, 593115711, 801588151, 862336796, 547280535, 405844889, 786913596, 873454653, 778396746, 254557691, 308013861, 630947982, 736193201, 742835381, 329300601, 833437395, 138798845, 512907005, 696064617, 182532915, 869267475, 562141386, 625834816, 177678684, 203401057, 135671489, 5684222, 711274310, 676941184, 641905055, 539481593, 718994734, 589274350, 226567457, 402548026, 270801700, 441737208, 713274371, 530132610, 497963596, 624848290, 418368136, 717371144, 586586134, 46548058, 935347494, 199331469, 688349954, 548222371, 1457838, 336237028, 514692015, 479291139, 774435394, 927720095, 493756103, 350636844, 7446060, 85729498, 491394160, 917774732, 738014308, 778796766, 321029693, 865025309, 976184657, 778062134, 649900607, 953892428, 254158859, 724718692, 3297163, 130106698, 111340643, 265388036, 709096067, 741432956, 202009825, 292525566, 67695020, 404001154, 964500125, 512796531, 452002325, 766200469, 544781639, 783161054, 884151202, 570387890, 672839078, 291497632, 258570673, 945951419, 28520227, 266405466, 339457189, 667826354, 271980327, 542651075, 296679221, 358664527, 898531932, 12669755, 598664081, 611110117, 380417105, 286609780, 710138127, 245779157, 336572858, 925604147, 981685565, 221888490, 617895736, 55173331, 918874551, 793634087, 712938360, 101734025, 83948568, 534671271, 954695688, 716296422, 296470946, 4898504, 331880347, 147626901, 498581493, 607647970, 433442542, 733062151, 257390005, 25786400, 352287057, 877833673, 539333351, 188484615, 746933329, 332984492, 494345121, 75990199, 456593331, 136059733, 595313684, 285782393, 634937361, 208978071, 840845713, 16895388, 113343343, 134500882, 128606693, 61390861, 686732653, 103220377, 409671828, 805906305, 548127693, 623675558, 425316308, 525331743, 736435360, 886140135, 219382724, 183320836, 131129825, 147078399, 325630472, 891214647, 845612775, 560253500, 398568543, 416108004, 367335599, 421338492, 664195461, 709739550, 95913635, 583911132, 963873486, 639903914, 358515994, 962222683, 552628235, 163800539, 392000906, 126903825, 805753018, 592189702, 667349083, 87991416, 508337922, 409740554, 897913155, 338679385, 660798316, 845773471, 20708620, 736734298, 229100681, 67199042, 655984391, 251964525, 766254165, 109098177, 293866880, 883188575, 129539817, 654059149, 888519514, 709791541, 996836110, 371915714, 78158013, 575175032, 266643806, 954429731, 555822960, 417696582, 540023698, 823078948, 815906639, 58954453, 953197658, 697836150, 485399910, 949546181, 53679294, 536795155, 114274412, 456996549, 119189051, 570520994, 393659223, 233900129, 821303910, 434491263, 139269512, 547616708, 916580337, 400680803, 330788340, 356392033, 136354642, 240619880, 312828408, 868586924, 181662634, 875358198, 302971867, 860883143, 852491290, 905108242, 618525235, 653238239, 187213773, 693428482, 538455326, 170206038, 715144629, 170285910, 979476117, 575398787, 434478585, 778219555, 36594363, 43274451, 866125922, 461587922, 38630533, 625566766, 516646471, 685552241, 820266112, 415042955, 598398257, 617231295, 392191901, 165620749, 637711319, 417415481, 237334741, 895110227, 668357504, 966286239, 778703014, 1908671, 294948770, 808300257, 777058999, 553961225, 430822883, 16357235, 326215595, 111305000, 298762026, 757035783, 180030409, 484595872, 621277507, 65066398, 945775660, 501174235, 376376272, 399363732, 305978972, 604081945, 955679244, 758942725, 776939694, 885192199, 7014423, 742987092, 64543565, 411090067, 167395434, 271766345, 794237909, 643286293, 903618771, 498723514, 409407167, 882168229, 531973031, 11588510, 412265607, 949437938, 455279542, 810974891, 777828075, 166627416, 486635584, 292126742, 408373289, 13014617, 339588939, 759017119, 83900999, 613706888, 810103107, 496570822, 71417363, 982561523, 578106699, 103219315, 282777138, 632083100, 457807942, 280961365, 257669155, 372793356, 656641224, 518184500, 445681599, 108100818, 453083347, 344581172, 226578754, 225143454, 371105981, 320127004, 701256208, 115375646, 913012909, 382869129, 163693517, 577331620, 681964343, 469353084, 656143313, 848416994, 325190474, 92557563, 157261808, 226973240, 583347161, 402884600, 841764465, 906108612, 34891037, 989263446, 772264847, 443708339, 192282988, 446271236, 244472987, 396690102, 812190849, 212245286, 370873432, 677599090, 190651059, 489814826, 466068097, 112676770, 37694683, 833766639, 859895707, 855273009, 70066714, 857079739, 134481342, 850914094, 439183672, 349089117, 979672524, 377067244, 374776246, 842673200, 940281016, 705707919, 420162535, 235861068, 986424346, 991372342, 57377868, 116304705, 879695891, 550123217, 840791976, 288374410, 375438782, 596656719, 4463449, 299139862, 640239135, 449836924, 730102182, 482352940, 668809864, 886248334, 9676596, 384052091, 294966053, 764811303, 675368840, 229354284, 956989042, 654134457, 649542091, 919196110, 274067597, 272505742, 198939483, 873520453, 988271702, 162045124, 704674157, 820689086, 54979791, 180763856, 303540462, 704630825, 401865869, 134088384, 635971152, 753142021, 300310896, 621904345, 9700595, 365764182, 33566106, 20256763, 619515465, 326346449, 16408192, 576273366, 410383229, 240647200, 298897216, 112711909, 101660961, 949754870, 279049660, 143210856, 860250121, 60275551, 327256560, 344786855, 792272471, 510858534, 947125123, 806808043, 233088040, 604437974, 134637661, 267975337, 970182629, 736938147, 290076505, 70063997, 254988447, 289128088, 161368103, 228337220, 197940958, 991681640, 847587771, 608149176, 597273634, 746118751, 214404563, 712110749, 858395244, 670931634, 21671978, 342423161, 40497125, 817643097, 890113054, 581929377, 377125585, 897993005, 901205017, 712660467, 99991063, 651759922, 925915464, 119486894, 450240750, 921043396, 212749792, 832873288, 953192342, 26151546, 669619834, 778120173, 149546841, 754070716, 355190040, 894023690, 233199424, 113045607, 33790777, 322561868, 243605588, 126680906, 793606161, 941120014, 205334969, 14434518, 63055774, 336725274, 38993727, 598640612, 567503343, 939089454, 9014624, 194775178, 129030434, 48397141, 937536187, 697860720, 379229361, 718636081, 846120438, 237138492, 708997429, 885070886, 692540950, 238551593, 366192927, 848174714, 598278677, 323706203, 475463243, 792463954, 841692914, 299152306, 561602348, 230646315, 580264960, 202998081, 804462731, 403914903, 228950778, 655379818, 453345491, 822479352, 686497357, 898261081, 840643890, 804933556, 971583754, 932619041, 675999687, 514937462, 222164179, 892656005, 231285025, 12321571, 816708474, 51088698, 713598320, 946346974, 7360284, 106779315, 929090858, 38452027, 340797273, 367751595, 3976093, 767273982, 934050951, 99280094, 428026909, 407164933, 379116834, 125528160, 316209710, 280494651, 673974556, 23393273, 638117347, 543143656, 978395632, 928061358, 927799921, 891595080, 147441515, 963567110, 114045447, 763525361, 830013339, 338778976, 830375480, 338753802, 802559013, 943268133, 589999629, 242266150, 304185511, 983517410, 921190344, 304674827, 824841001, 352920704, 778286663, 511800919, 135665669, 445469467, 874843695, 460221017, 147111643, 428570085, 721628901, 653364910, 396877814, 229925598, 481542409, 221391243, 959379749, 985074818, 199470727, 319999633, 641105110, 263625852, 760625291, 601891035, 804603969, 901091415, 381900585, 300297504, 857096086, 282285659, 631854098, 103192097, 260951401, 477675054, 194370689, 171972997, 183406056, 421061214, 260663446, 999392000, 481854162, 515625357, 451286335, 833886196, 645360387, 595831117, 101793250, 140046211, 992324888, 864601800, 801190741, 394626642, 4347775, 753373256, 112447761, 703786326, 70627945, 748280557, 215800924, 893517782, 249133723, 896019585, 223420851, 973323676, 25883385, 151946110, 561540984, 587587165, 85153263, 854623995, 17297742, 686511499, 66867608, 174594489, 637742360, 437726755, 774833550, 982860864, 498516691, 42769856, 808521111, 723010928, 940981779, 944885674, 554231414, 435604985, 506587963, 498888457, 154918225, 757767934, 453579273, 692214776, 315016687, 479732966, 373155680, 437373810, 976380352, 551181663, 135886067, 984147883, 125561316, 75137350, 717306846, 838165916, 987175263, 645011375, 524126495, 486781683, 687479696, 697489419, 557650382, 838413386, 71753477, 955717118, 898356977, 359457439, 761301167, 69152975, 434754916, 362064000, 570225936, 991791776, 892858764, 320926522, 342746693, 951263436, 887616319, 53471080, 837324705, 570273768, 754671654, 387729754, 388969411, 861676729, 198419447, 534943459, 734351313, 888684728, 765911591, 262365846, 859607975, 952816756, 471549348, 819305198, 132182054, 88778559, 406556251, 993114458, 505597136, 760365531, 943999113, 85287060, 626237438, 693796123, 686383041, 659113575, 422908313, 14450343, 151348162, 408619953, 519810062, 290705902, 677196690, 386556295, 660298235, 346882125, 261549882, 310217139, 18790311, 479276720, 123449643, 305247945, 637723244, 676062867, 703442143, 466644362, 463541515, 449410142, 462694543, 395873952, 873344251, 614747267, 646658211, 256771825, 901305262, 718430873, 142249699, 83864451, 45745388, 945964246, 539606915, 140443381, 218357777, 220858810, 620916174, 992387476, 542758666, 851531205, 625424980, 681022519, 58365887, 788325865, 725173949, 248197457, 467337616, 557399098, 749243329, 286516549, 80661464, 484736323, 992193328, 615756131, 656627330, 7608871, 985649936, 39239413, 825298232, 157420824, 857129113, 417472314, 430804445, 413144848, 421971419, 212513315, 165009368, 295600943, 498667730, 443229960, 581725306, 199785045, 947398978, 758680943, 649701766, 350397547, 192931299, 638724756, 51170958, 836817366, 806649932, 943685584, 811563981, 56172960, 291936928, 79728556, 778872258, 522429739, 532178379, 742184636, 373340355, 713817294, 848986282, 569902232, 48267376, 781029566, 849952773, 757095374, 499774473, 308525996, 66203969, 317430894, 606052088, 60028011, 695850709, 598991154, 74147522, 893364996, 17545434, 383130956, 939714444, 461701888, 915212148, 659300406, 999553632, 471536907, 685468868, 775161657, 221282031, 499208974, 878099288, 85247145, 533786109, 948727388, 604386178, 805089176, 572169501, 160108597, 610693366, 411276990, 112496404, 971454903, 178503020, 573146265, 874376094, 605416329, 270650807, 965202831, 966481801, 530191255, 320749193, 776859116, 418458895, 342606640, 140648664, 764186429, 39449528, 63262073, 525570240, 231053071, 354626362, 677410815, 893466574, 921052823, 500255088, 969728739, 995625577, 198934220, 209587555, 274841276, 174106846, 50638354, 79631331, 519129671, 369304575, 696952404, 525865388, 473314460, 566884313, 41996551, 599102410, 84596544, 854473897, 187927733, 237222051, 372985471, 791438953, 840279056, 446843596, 743556451, 772240544, 891912899, 456012128, 220787805, 967311171, 906192889, 240927647, 751675816, 934088552, 233633678, 116241260, 185947259, 265015254, 937778878, 595000904, 703169742, 917123115, 581075035, 19721711, 382550342, 981000547, 483373299, 536251389, 91696833, 270372377, 753442306, 55814437, 456995378, 148202432, 832325457, 215161000, 911293875, 52271669, 432459403, 900624075, 910771041, 954757333, 421385401, 781127100, 886562281, 890834345, 867841478, 752326385, 55202556, 777010292, 640440705, 386281633, 526998409, 217288651, 647798310, 439088495, 38549610, 660848273, 947284970, 803666511, 590564176, 15416206, 673274266, 331081687, 6681780, 683541093, 26468929, 353423255, 762678660, 618057118, 363461601, 758411101, 939348815, 194794871, 264201853, 957736775, 757619604, 979002000, 504979525, 750858751, 109599805, 958455938, 868838455, 14874658, 132677903, 515983539, 130810271, 972596698, 574917092, 744992100, 92207355, 861923855, 542994945, 771935630, 423050732, 767459581, 439453182, 400746759, 124935871, 619566212, 630760896, 63107595, 850385977, 600322473, 538217520, 496340418, 288514166, 190411093, 931512338, 16957936, 493758424, 757300999, 215059271, 807878618, 486708442, 795649255, 666396628, 819754118, 623068354, 970094011, 889610409, 114585248, 581946991, 150629560, 147975812, 132807602, 303854931, 875249672, 550336612, 30515996, 141635240, 565042908, 29985639, 633906765, 964330937, 384329657, 855700340, 762171457, 81891470, 199855352, 626595925, 913768413, 992841044, 203438403, 943301754, 420597659, 666424702, 812489010, 916209499, 344261538, 435903201, 195148378, 533095993, 416874283, 795465088, 722317449, 217107449, 862908933, 987990443, 305901615, 393885572, 737776664, 2700878, 890225101, 225299232, 922680613, 309155572, 302996950, 778130968, 406928160, 750118772, 543277001, 716289120, 544977579, 903615688, 243722791, 117937357, 904790445, 852208094, 853591974, 527367532, 118841222, 583842036, 985351119, 383166529, 656821935, 655784795, 454769585, 666845354, 175227637, 251888459, 787428480, 945587785, 810429465, 299476942, 656776120, 698799571, 575228018, 482156246, 460522845, 706005884, 14785236, 474443557, 920655090, 87275529, 657434312, 973009589, 631225203, 798632919, 94820009, 418983094, 593294289, 195060900, 719736037, 872440077, 397959108, 542800655, 606189751, 366576315, 426067651, 604305436, 861341621, 369367995, 25909635, 674316298, 305601049, 94839962, 693445606, 795743079, 938273640, 589764274, 650604198, 717730107, 104713789, 222872754, 345567873, 233449111, 576742642, 236676961, 66984052, 509800266, 600806145, 633013901, 417260704, 50584647, 285657149, 761131711, 695844869, 605387595, 372637423, 118819115, 493935092, 40162, 610412675, 304400855, 207180926, 129787521, 921457212, 203961118, 983434681, 124636849, 884572434, 201550837, 849957599, 355682486, 326525814, 488189277, 105578295, 285598796, 869413837, 75585187, 179020530, 935452317, 7026973, 695469591, 469336862, 444867521, 971502189, 408596531, 148351487, 261806008, 33373686, 482861979, 894334495, 292450232, 633209864, 284779873, 948519781, 265877901, 912894668, 874429703, 215602662, 850513090, 244491315, 730471176, 962070555, 423364531, 374625481, 577553181, 515427109, 720298293, 321381705, 167225347, 541165480, 300822660, 504708552, 888763462, 35701232, 978291472, 925375510, 738804638, 481415340, 922150636, 439291717, 634097790, 116658410, 466191421, 911956361, 854959955, 314839009, 102570845, 11395542, 430713045, 974824680, 7710161, 366247692, 596383112, 691645080, 419284893, 612355063, 17306668, 384664879, 806161594, 748679649, 114804988, 157873303, 77717571, 355783962, 356375788, 143387614, 805240875, 56983075, 865428093, 58327568, 533833157, 371345834, 989770750, 818425740, 739659890, 368814127, 964587905, 531341628, 688701687, 42866405, 978945381, 810963671, 199400169, 159733509, 853630018, 992631125, 769138296, 93495836, 185909634, 385522770, 803638628, 336176869, 802405716, 213518926, 856173962, 746977130, 534316036, 141392241, 145840836, 904784920, 609044612, 167856213, 790916347, 944205996, 43773202, 510376333, 484854484, 298241234, 501907569, 534782076, 189231980, 991178103, 227940864, 397594257, 266723083, 542575743, 92591277, 869091957, 113538688, 525753091, 962706725, 813231304, 44774392, 180809073, 382547588, 748690597, 512879915, 768045966, 503379356, 516019360, 101657953, 116110435, 315982893, 557922617, 542701837, 682435511, 432893726, 663257571, 350396136, 377928862, 823763758, 164972644, 439683722, 884601078, 502175127, 761508464, 552128347, 555564361, 224475171, 432693793, 868962975, 108210512, 806692486, 833631973, 650240521, 689881217, 358157258, 859288600, 610734301, 383444643, 783735263, 147740808, 45934109, 410664635, 143149675, 56553599, 324002443, 413871246, 371083901, 729286880, 826593876, 399914046, 139144725, 135035111, 298921831, 565079517, 440055469, 257872192, 702300641, 694273007, 685571398, 996666722, 368130696, 512079134, 453952864, 197738527, 890126040, 522228568, 667648148, 716317149, 762836072, 722293279, 243625692, 616444330, 818156186, 680116437, 776167716, 611261880, 37903904, 497600475, 647400699, 204573905, 387616629, 537861045, 824979920, 603320076, 547269765, 989722668, 255566529, 322897768, 663121361, 587225402, 666574051, 132574829, 559210354, 364889877, 667773702, 38559986, 4419803, 535855246, 847265093, 317436516, 177603227, 168378345, 749317670, 770552767, 906359542, 386522306, 124669400, 200462697, 643384509, 248023901, 197699125, 644678740, 836417887, 776629132, 373531816, 172144395, 630433988, 968668930, 855622032, 676490175, 798427577, 558151485, 671651684, 300301760, 797427491, 698487218, 870785613, 335897823, 673131235, 682756415, 395917931, 811553229, 541397796, 957196962, 221462337, 42737211, 3755939, 64792000, 361237990, 531233746, 279716197, 740791242, 880687095, 698683549, 641504830, 775647762, 486345363, 865207809, 21086849, 139477612, 276345965, 161554557, 711602738, 302019989, 854816172, 656345772, 382176726, 606415586, 762964135, 661606113, 19237493, 529326518, 490718547, 872838708, 960982452, 719591560, 749125936, 996297773, 21522703, 624514052, 968917202, 510430279, 593418100, 205756678, 37175304, 589813063, 713077001, 272084245, 749057243, 265609172, 697252949, 241066820, 608158644, 47346193, 236203541, 810407649, 396036719, 294568363, 502115796, 577863787, 908985548, 88642625, 49041762, 611349721, 536618676, 780900907, 437338042, 345818029, 767811379, 915333458, 990235672, 331114005, 373784312, 520131630, 458785319, 608624252, 900021081, 14625694, 61859587, 915174758, 734758550, 219692674, 606619762, 361580782, 414705797, 354117270, 498901458, 812585590, 511769705, 18771959, 527914887, 975399934, 135543589, 763509797, 405267846, 375108765, 982403106, 381063347, 867943388, 852350321, 115614380, 604576374, 980272050, 454830186, 215785957, 127620583, 898167236, 493455218, 292034413, 486409120, 708402864, 157838142, 671674939, 606473739, 204043346, 137009239, 703241280, 912998287, 359785693, 499366418, 796208109, 362522057, 14112395, 989183042, 890151122, 87440465, 593004040, 597588213, 484409928, 963172933, 308836536, 910579342, 604117770, 544350798, 260919498, 949777764, 796230036, 51480423, 627600765, 406806974, 405837984, 606977563, 741767660, 428416804, 780205455, 215770328, 100616833, 156516029, 867460110, 853976192, 790263126, 204295711, 403114549, 421101890, 700986875, 446187116, 788738073, 962007157, 850589196, 57636157, 260897020, 495713890, 953399338, 243369625, 359085418, 27513801, 131641926, 292128163, 476509302, 694292110, 780359505, 248472968, 187329496, 237920812, 922287127, 276841811, 876986034, 980845602, 547138978, 661129250, 946633127, 564503720, 916493648, 879015740, 54208424, 343259975, 412942292, 302183146, 243033909, 252830546, 570182477, 311333463, 6557929, 867531128, 312623111, 372057246, 349759579, 325876598, 818604718, 712640649, 552291497, 324194370, 601494314, 153942896, 915461412, 105528433, 498712484, 256598597, 735856358, 935274658, 36798271, 971819105, 887133106, 347466399, 768336292, 704106667, 997996213, 802892808, 98627216, 254388838, 754366243, 439994043, 474670905, 692051309, 463875367, 400163410, 969323819, 766210325, 630993205, 371867934, 336983509, 446344068, 311627016, 43087057, 53351020, 478135587, 640461840, 559037618, 363559370, 407084030, 878404082, 249530689, 73001547, 311073675, 245331639, 830890370, 882015624, 703363746, 719068195, 273046540, 834329763, 116774315, 672965375, 852675737, 609141249, 317572039, 85574165, 58520244, 751425603, 111211855, 773599325, 494135695, 195079433, 455775271, 21883771, 827079258, 66488600, 800405388, 433814819, 814735990, 1002903, 248118578, 433506108, 193994935, 859298817, 806122038, 223441430, 723657274, 610732534, 737935851, 745718979, 50255562, 767306851, 297202738, 342515318, 282145731, 593612797, 336515468, 948876956, 147233783, 187008096, 960538340, 942414137, 412843607, 41460610, 201820472, 229378821, 390348080, 729658357, 289221503, 44902053, 542350902, 790708673, 336567156, 677629436, 932001821, 83370919, 824031401, 809615962, 786035672, 641728732, 970197534, 550011055, 901013489, 740735289, 54389574, 693220970, 958129322, 468690089, 364022138, 287444598, 397960708, 448352773, 642192769, 613552310, 290696132, 288113917, 909170463, 263545149, 37152268, 958235387, 838121765, 910191417, 399551517, 640207421, 670080794, 353162120, 530067983, 313477593, 725215870, 734474449, 481597005, 431736445, 533784713, 62903044, 751821270, 491438505, 918020260, 85118503, 45360812, 737986223, 524505972, 377996324, 526884629, 236044195, 993345129, 156343000, 984201716, 743487751, 752385680, 499406028, 591538550, 513333382, 936564822, 949346907, 979100076, 401484396, 939633990, 808652523, 150302169, 468198830, 346238870, 434114024, 19216059, 303952268, 338338060, 599331770, 887218133, 68644228, 125354067, 998940933, 567500027, 672517758, 74107318, 122988363, 870427564, 682000186, 648236623, 937882141, 682852875, 979592867, 681885960, 759494929, 924720087, 2135401, 678111233, 911413188, 547436290, 465108344, 196912097, 729223106, 105675570, 761928365, 201060796, 9223303, 542345404, 523129919, 495412895, 224836650, 297897356, 471443392, 880043865, 290170713, 523356845, 647912384, 185380393, 757927819, 362887686, 326056365, 509858022, 619740185, 423225067, 818137092, 263165271, 653986224, 8267094, 243814516, 337269067, 620229258, 717444007, 212523000, 955318253, 750689836, 436049360, 444004239, 957168125, 678753444, 766649289, 351244697, 171073853, 208328634, 625240267, 105103960, 626792501, 911414189, 353674316, 448189855, 427366158, 401537388, 365869092, 125903069, 439496410, 25450376, 479440070, 648562856, 700516853, 364185104, 375067694, 889216980, 263754580, 513947763, 461576412, 932220409, 17600237, 817654528, 144351255, 570105149, 178748575, 894082084, 424883767, 45089457, 65059946, 253155234, 853403784, 954885875, 179567419, 236404844, 383187941, 385284718, 926181399, 465726293, 982724011, 269238026, 554448321, 447950917, 282247288, 282729431, 914550923, 665744118, 755438271, 542783787, 81346603, 764658469, 461155227, 799691304, 924661157, 539703900, 529019735, 552891888, 933148862, 127273568, 860068650, 642525203, 67649532, 795650217, 136631338, 59016093, 324027006, 879483769, 66060121, 471413221, 702615784, 280115394, 751804002, 905853589, 613860829, 106515143, 580828382, 721717202, 716081030, 411125885, 959898266, 945222549, 806921193, 428129542, 40271310, 977772742, 465913347, 278533051, 537597999, 166272990, 849847623, 197539862, 598011903, 724643410, 438450324, 169845986, 213506886, 943914871, 907627317, 500538968, 723930177, 200212823, 210348575, 926388939, 207629699, 665685567, 80466179, 46160602, 353843287, 672696336, 969172436, 582173098, 294049276, 787499094, 604074218, 250828636, 445622752, 878398927, 530334604, 285690607, 958504693, 857488534, 891980640, 432507207, 81623687, 863988245, 571479282, 353479902, 73352069, 272353175, 468089758, 595212013, 217725015, 584195750, 622549327, 550959245, 34184380, 880811751, 919265348, 751910248, 876072696, 79935314, 143365252, 588618266, 430000345, 817527611, 357159293, 541156118, 786579670, 591466966, 776979651, 681088277, 324256825, 310492545, 975026552, 262872079, 705514665, 829741579, 829572900, 591599826, 684234285, 297940205, 185339980, 12318860, 313014457, 119464160, 278120730, 733163062, 243055176, 832656656, 478417960, 576687045, 570937495, 333533186, 292130423, 823127168, 993587675, 643303372, 92346289, 547017660, 103482011, 345263725, 245422951, 239872692, 22212253, 186512422, 333823653, 206323510, 346983788, 873989511, 457218819, 533855124, 457008365, 470247572, 396618707, 869949338, 796127491, 646887629, 447475792, 844096318, 381912512, 979827697, 25427096, 348721892, 498344481, 639145915, 85977817, 583156804, 189072708, 788383352, 793703960, 828337329, 350753060, 241237963, 544518654, 812579049, 12423968, 104590267, 235169154, 447029967, 587494257, 157906716, 644559837, 254578953, 430236819, 216331447, 371089214, 362377387, 346424620, 177133560, 780937175, 35548798, 706830112, 444637007, 451152597, 808825872, 279793504, 408371589, 380454083, 105565485, 656747801, 914204686, 138609820, 341077873, 815462027, 423567620, 429113653, 232201820, 909519294, 353719920, 510252346, 564528509, 501666196, 144715511, 469429398, 932444039, 971230261, 47888662, 765805641, 307458545, 720594391, 915576817, 227300393, 332230507, 58925939, 592372641, 685251871, 893959275, 708438285, 466619873, 916283819, 369459868, 255814221, 719481171, 659647304, 254263481, 534281422, 393921744, 22995430, 317862630, 235312444, 575638083, 248849827, 220865496, 964049532, 516003303, 528623954, 833782416, 566432933, 960900149, 983868916, 201405961, 935540937, 995372308, 493237624, 278760172, 939524001, 245889437, 903609898, 382790618, 667070171, 593277232, 496093307, 68017475, 435437056, 238812320, 841223983, 174751573, 699729079, 174074729, 178384459, 484661965, 450462315, 954518761, 431523976, 607135893, 777390407, 701653454, 387575356, 386965299, 49535356, 978813661, 62133646, 263470435, 355572418, 784762398, 159922591, 83834514, 824514775, 679035052, 692462034, 632426761, 610536970, 731530848, 445883230, 98822876, 870463289, 781700108, 267525215, 275103270, 817528816, 43410908, 967527731, 834417635, 895544092, 881539212, 108499099, 349900985, 303144875, 153437352, 258573843, 157368452, 540565404, 577240850, 47591925, 370633570, 25409411, 244719410, 334924416, 168426143, 297674277, 315615653, 850585506, 191662127, 275476810, 527473638, 715822045, 972768088, 262345166, 750322910, 52383849, 276328155, 441685325, 338098852, 814738206, 87274423, 767133026, 230892779, 125950205, 578947982, 66788418, 798487861, 944545663, 897347980, 426589638, 884179498, 584308199, 45799509, 391607732, 444471280, 379078577, 225491216, 215271690, 252300343, 237250796, 105971983, 295607015, 97539884, 714503124, 632467620, 327984247, 297401034, 35593075, 160138438, 24669690, 643455828, 75775384, 324112622, 739315203, 685327566, 991474417, 973100806, 721576181, 106660377, 61691423, 97073993, 441894609, 523106631, 55226612, 866216679, 258584976, 417333603, 355531983, 534219472, 565642762, 130318299, 129211037, 781070490, 799744422, 278941971, 674842862, 987852761, 466872600, 201597355, 954267672, 680675750, 662861438, 757383335, 244757856, 108700586, 733646525, 624896746, 993189089, 706952586, 312687879, 250092858, 241112124, 851367942, 640216951, 299691251, 773065179, 922648823, 919029442, 810422279, 92138603, 156904733, 961124135, 55954835, 148942681, 70312141, 97161335, 420152257, 147758427, 332345303, 436918794, 604654995, 242694337, 294745565, 188098994, 678372314, 154647006, 627366074, 831711172, 570358862, 996264645, 549839897, 226145396, 509461385, 985949242, 720859718, 576353969, 882042932, 121089776, 705443334, 149885961, 933341619, 167597056, 217082829, 194328946, 476887169, 425715043, 406566921, 935025197, 852264877, 712390179, 663462490, 142603259, 941686359, 231905965, 471168577, 739567322, 449961030, 45882115, 609236680, 733845057, 276103089, 942869857, 638203241, 998540961, 306680210, 391769675, 17025653, 456089000, 662764347, 113403887, 369607783, 878981204, 356216972, 191164230, 647794199, 813293968, 878067735, 707633880, 258590393, 701548384, 233949968, 424668772, 76879314, 483902484, 526909808, 987720715, 771251132, 876708366, 185790559, 542298552, 546663393, 199888514, 373606565, 955082372, 876789586, 393368751, 702577186, 645987586, 499600101, 350800749, 783348642, 262568526, 131921445, 182461119, 341827289, 50872407, 569230147, 165527871, 189915955, 630741055, 693041263, 748153749, 639215223, 250054280, 666059509, 447299650, 834666703, 691537051, 685640269, 340106755, 679954556, 841735243, 900397859, 949429365, 31099831, 84683801, 98602638, 274351171, 153405931, 882957530, 901107677, 410432348, 981402089, 115508299, 191306493, 949138308, 455730112, 778681430, 446086484, 485306306, 103058427, 714517587, 672568811, 445885938, 346525973, 407428646, 479476028, 692526033, 152513160, 111558043, 543833195, 997626489, 561692470, 546103567, 79387492, 321275079, 504319043, 318933610, 746230273, 923284524, 326993801, 637469889, 12056163, 973756104, 756471428, 649228582, 651910676, 109876231, 303135772, 161920233, 304785301, 351663631, 535152075, 547691398, 837904354, 276769271, 532780278, 204703454, 952441355, 994507752, 843327267, 526908113, 601139731, 647531407, 215655578, 984515194, 440408924, 30276378, 420482391, 915930906, 69978944, 692662562, 727748291, 411951747, 261909814, 326357516, 629252958, 394053982, 254070901, 630629944, 203036218, 429663835, 550726608, 527023909, 302026917, 603932711, 383509951, 753977977, 209649169, 855304790, 281283341, 887006546, 791897988, 157934771, 951025360, 276571977, 320356157, 13584873, 443115105, 348148512, 941943416, 389081821, 168819974, 548659114, 337747417, 372582995, 100476066, 809845254, 294686721, 206410896, 559686981, 380705209, 400706996, 151478582, 94475285, 998706396, 860374096, 130025904, 812979240, 242929045, 978595910, 478557033, 363560069, 214467657, 987882992, 861633591, 65533481, 483875589, 514967893, 298220490, 410898035, 906007375, 523660037, 742671262, 74495101, 318711551, 196740695, 588899368, 808102111, 101003413, 235527622, 977986989, 254328296, 292206321, 305861922, 489706799, 56312724, 577978651, 132352060, 855166535, 810056194, 687391089, 439453801, 79290240, 129732686, 596749695, 569718598, 661113703, 672460859, 975504649, 628066249, 518114279, 891733297, 757592107, 605245500, 919207643, 226711693, 820561622, 839316617, 601060555, 657587859, 96573169, 71993957, 222552719, 299754773, 902624329, 300268091, 362198308, 995421572, 750411661, 516858500, 995738254, 684184062, 171329507, 445754749, 387950033, 627120068, 601625231, 611044085, 614071182, 378733416, 182562087, 698161361, 848840674, 523707167, 684239080, 822645628, 348506633, 184924655, 549476994, 286091722, 35918588, 4952547, 670392471, 794888858, 454223854, 293094705, 243557713, 205257600, 865719246, 883300272, 771110659, 381484428, 483285585, 583043132, 848154262, 223091525, 221594454, 207827270, 230305388, 852636604, 353316578, 435734397, 421802086, 534968280, 957717307, 699299427, 9144813, 440683744, 92783452, 636058201, 540164075, 174207563, 271790237, 360711513, 128070692, 225060367, 123187289, 677415439, 835370143, 631452516, 522754397, 580086195, 10122644, 365029855, 465451988, 291530416, 411907313, 999677903, 631010603, 630525047, 673333422, 730394099, 931841921, 85387417, 235867051, 608021679, 542007072, 642839691, 377177821, 585935992, 954530643, 91312952, 130879214, 126458327, 881357744, 900144323, 676449839, 996804870, 597574157, 459156231, 544799656, 615581169, 464314289, 612865777, 380916649, 486025494, 220015740, 630691886, 911575832, 361886497, 786543802, 86652879, 540973194, 540214398, 832754962, 635870279, 936041239, 711521847, 731847720, 789035404, 597341905, 52529850, 386435177, 558438870, 640072696, 599260314, 965753079, 773294249, 417437066, 588217701, 526765905, 573699213, 486998747, 382349400, 545175012, 786299726, 847352605, 663263661, 953602386, 803945819, 634803020, 636734500, 645236271, 71195417, 376235969, 699440833, 688686813, 408120720, 999895759, 256314305, 433410362, 330021374, 815726836, 284519983, 525740676, 707634947, 571779002, 146264880, 416542331, 37193896, 621304466, 365947718, 851615119, 95900414, 404363533, 372817690, 574881347, 412739156, 676560650, 324744295, 419822620, 320383335, 581656077, 740946698, 723944355, 604638180, 30094281, 745799047, 452323762, 414716953, 858391764, 728153956, 61209227, 263107200, 563084336, 983640941, 730643412, 493958155, 714084310, 789240241, 88844211, 102643735, 326156517, 222971483, 75285513, 396906927, 572337688, 134480989, 406521531, 3130887, 469978459, 909281074, 858872367, 130391801, 567696234, 746405394, 233537018, 499148660, 757245255, 368179201, 97166061, 479240623, 491422650, 543808761, 693018607, 824934995, 821110468, 97715329, 477801933, 392800449, 15183862, 132485246, 813569997, 494049508, 966595863, 223811199, 908985887, 146433171, 171464326, 344742699, 282995540, 169209476, 14663021, 130310790, 135613973, 184948517, 362249470, 139220348, 671221847, 699616942, 809649998, 852289716, 165740362, 711365700, 541737629, 607878470, 461567451, 961012569, 485130325, 892578559, 116012953, 489251584, 869738225, 230037275, 358544173, 716030988, 691787448, 371041677, 301449510, 836852364, 682718097, 971222777, 8092838, 445835265, 745777114, 122732996, 93185867, 657737791, 103473, 767218070, 177672474, 833198410, 650926495, 518682419, 157617187, 939799364, 677815457, 579730943, 439430433, 924840363, 583589769, 23802206, 753425229, 711138467, 688751531, 109287845, 986166864, 392760981, 147453251, 61784636, 896001255, 224616996, 592439768, 94062467, 709901295, 869460650, 304527203, 636931717, 807357116, 705564791, 347345719, 189091753, 218306078, 365746599, 583772286, 923181759, 265778318, 238529532, 499127797, 474932662, 617917542, 217920624, 740610920, 976022926, 598322836, 273482823, 44198195, 154653067, 763705580, 826901131, 157235242, 310516911, 240414571, 355582096, 24746605, 920628044, 110028590, 696693506, 822656677, 437154431, 408902417, 461843613, 621078153, 225111897, 658163876, 460287949, 80781412, 308658578, 706003353, 476903768, 34289770, 278022777, 117542139, 33055032, 506776714, 868151536, 82891919, 57628017, 63563644, 148436820, 897833379, 210807853, 101168725, 212145664, 211882165, 989231492, 329647323, 435546735, 123438919, 238064220, 95959284, 776816728, 907329394, 146333550, 9449261, 429925973, 372129657, 867646993, 828248944, 372087788, 207288879, 314550290, 666772003, 380466814, 529695407, 227016864, 414369711, 986220234, 792776022, 680736014, 621067071, 905310303, 912889709, 931096252, 95595473, 578039424, 897520342, 979619741, 361831683, 880673030, 830346039, 143791115, 31728852, 629061433, 265882229, 403423114, 341101000, 814055801, 943445992, 843132907, 322988508, 349176221, 252420129, 397599204, 678203265, 63761482, 691532491, 608218112, 26241339, 279023402, 426392720, 670732079, 394009497, 912455956, 224732750, 832172304, 824925730, 729566801, 556492781, 505358747, 655190360, 491545015, 161775675, 182859903, 214687474, 913184216, 255250368, 395144695, 666171386, 740952223, 105111398, 203345049, 683643608, 200286562, 726744156, 351071619, 684814332, 93754322, 439493730, 272993409, 820513218, 555408576, 182702502, 950116242, 745604270, 281933805, 892821223, 177689869, 807495807, 396726317, 418187377, 666818002, 518025069, 91861856, 408010359, 323495773, 209779338, 334018394, 513847955, 661385822, 936038175, 570877275, 613880052, 367825895, 146688935, 270383116, 193631268, 442396546, 115881190, 628447810, 299283786, 305854157, 452278236, 287964256, 447489320, 366233381, 591186128, 333665044, 96935829, 62234322, 678571869, 794995992, 743174484, 423721526, 467086243, 838851748, 111604633, 903027314, 19494411, 652040499, 322828005, 240102608, 38521129, 302346943, 325517379, 609363587, 397818966, 773160695, 769927058, 499669053, 527184993, 420983323, 582086365, 560214574, 386398673, 432658684, 819525214, 585342107, 557619394, 316317152, 311565078, 919473057, 661495538, 842190288, 530848163, 478434979, 660854640, 757563676, 732505028, 200451197, 924481599, 660542575, 398229969, 133148723, 383115163, 46215080, 107065309, 374494101, 602472773, 957731726, 372196555, 222851270, 324800614, 996696667, 255674622, 464760607, 844021439, 40925706, 461530248, 516754680, 223182732, 934761618, 597932967, 190712852, 50103645, 322303995, 690710398, 819674646, 906645908, 273251754, 782905465, 547948554, 334924702, 267584868, 677268330, 519586004, 806795631, 151985295, 239213100, 768565269, 831139872, 928053778, 857153542, 468580433, 941740746, 537690294, 58132707, 409907360, 770207699, 495496188, 395740321, 359003238, 552545031, 77291302, 654411435, 433037625, 212241242, 23006389, 690230317, 896045934, 778353257, 544108857, 319689704, 742847463, 116864781, 704197834, 929355201, 912815, 253641900, 722297085, 746957883, 903698467, 153779094, 783878210, 497370490, 141655770, 240587000, 48690172, 250279567, 93092854, 779114254, 517325491, 541063757, 264672379, 313585606, 182848933, 303787505, 333340688, 93444577, 675217140, 465106393, 729455250, 778313928, 829774628, 262494801, 955906105, 276214516, 521063537, 119504776, 591508829, 119635058, 872701012, 489185479, 659387152, 868643091, 440711038, 873202129, 109827009, 533202333, 942304046, 496786801, 344783832, 49572867, 910519196, 934438263, 763021604, 717850681, 51051164, 491148553, 575160996, 886581383, 599398595, 423628071, 827677558, 35842512, 73751348, 342267459, 162116828, 178434698, 343700202, 955112838, 835356153, 15135982, 549381945, 913741613, 760202595, 432119737, 222805714, 963147863, 756367437, 233659420, 507503629, 425129841, 810328746, 614561056, 292464234, 610076227, 748266972, 467555861, 621478425, 596020034, 277806376, 701671652, 513930911, 306005380, 230044272, 298592899, 453495496, 958212834, 563778749, 934081465, 920063510, 604309151, 886940591, 641389068, 31147083, 587829754, 176561424, 674906440, 892305229, 63738565, 460731010, 757802508, 323126660, 352810417, 731501486, 240805364, 333425961, 897152796, 438934734, 244158628, 882182131, 185133484, 109883138, 697023038, 207440112, 169118495, 865923239, 789172327, 956336083, 877970078, 840220028, 252077196, 956376773, 509414997, 44253342, 743518881, 240193944, 44415616, 781345102, 39250189, 677059029, 363427955, 738387845, 74940029, 488215579, 544647747, 927113247, 661520665, 861846295, 458509552, 23587989, 752608289, 727901420, 892274048, 187319803, 504018028, 848970356, 76986387, 299680733, 757157146, 605569181, 286951935, 207515071, 834770889, 875047262, 655328533, 433317067, 886769673, 947169284, 187665358, 953860883, 762979920, 7622666, 230906243, 767342972, 749987801, 432112466, 465016422, 62359586, 656538598, 444828156, 329107891, 913246395, 166729401, 868038484, 17545554, 440014518, 58796282, 485133920, 726960096, 20647693, 961966351, 472087176, 534551328, 299683110, 430914445, 612398985, 600680046, 471281754, 914045388, 710838507, 960564289, 418220295, 200389010, 621705965, 47438067, 564695946, 760878090, 383511811, 207451844, 234493115, 535877846, 965604840, 444545624, 870491860, 310875360, 616455897, 233578291, 934333279, 422340413, 25263740, 335390872, 464036925, 172017011, 524364654, 773519776, 822211676, 502661808, 712847463, 377084698, 653034120, 676535616, 297135034, 838440854, 222714633, 251748176, 675064002, 463895775, 595228675, 528703607, 202106345, 829816908, 25185361, 962677418, 324616319, 889117025, 16994791, 404161635, 963852538, 226127406, 649542360, 27043124, 739119173, 953707703, 837801202, 2643495, 530172153, 639894418, 125079674, 622864522, 702936615, 28283982, 792903317, 343132427, 504442270, 401063926, 710990155, 998019554, 487530863, 129331098, 894920170, 663461313, 2413854, 618548267, 427591809, 165402930, 279360730, 1280712, 303334287, 288582021, 867174723, 805701779, 865612578, 547544775, 494487382, 257785407, 781416630, 969420478, 164204561, 199830071, 951574944, 512282273, 798132908, 55514154, 743789675, 562719428, 809696438, 907956430, 434186075, 875421773, 990127868, 36591451, 885161012, 89047198, 135852346, 41355988, 30517238, 169913642, 270168715, 775021, 898250405, 811589535, 461628062, 829171355, 375657920, 988202902, 949257394, 389159353, 800895520, 699175950, 169575090, 172071757, 835609906, 758303661, 54902822, 856736156, 367927825, 886784912, 667019149, 105520851, 450939517, 808987678, 787702571, 680128465, 786166797, 414106013, 867640963, 629509385, 326047692, 90582191, 219782093, 928397786, 801317138, 615175197, 721916817, 457118865, 759145567, 884488712, 171464561, 297332337, 64328846, 871982111, 364504797, 676979602, 831079323, 399635838, 649942543, 866300828, 752427409, 261038523, 853033447, 480143350, 526035627, 37654302, 987054657, 826816106, 607708970, 761414414, 758948730, 332491092, 61716152, 148064327, 494567815, 922465755, 228020196, 377723675, 834124164, 681947058, 377205040, 263805990, 261186887, 850988258, 3513654, 903415976, 712709838, 706909002, 700511087, 157072204, 207520743, 519296312, 717557230, 161358358, 979863036, 135961108, 429171549, 212520517, 754344320, 62109754, 3981981, 588478258, 449019160, 693158368, 915867420, 533421840, 646628478, 473516677, 857917268, 775023150, 313442413, 873706018, 444542630, 961830668, 714964142, 75464110, 292023536, 847284139, 815389282, 967130675, 219333595, 772535893, 823545398, 870789999, 305956583, 642825370, 315823026, 1203196, 525066674, 49433333, 61100965, 599774812, 466254055, 381193397, 562501361, 133110390, 614808953, 111098674, 496779477, 250901750, 953921815, 337693120, 564696177, 928765334, 619350687, 30685056, 642269115, 481679922, 634380814, 161560748, 605844401, 417931185, 602283440, 847807652, 94331342, 356722254, 514396180, 930492585, 177250605, 498009438, 634479412, 838853355, 627556501, 891485215, 168431391, 104610290, 139069942, 892123103, 141049971, 460877986, 408163180, 63380667, 270192052, 403207007, 34254926, 98517697, 845012620, 189505686, 840353162, 920362712, 987360798, 279267386, 425902445, 346590189, 191920990, 677929990, 718991525, 676063068, 817583480, 757955316, 7062452, 789333999, 405153378, 443655182, 167344923, 184441672, 915542333, 654392308, 5469360, 839458827, 952259862, 739109119, 959580797, 630620113, 440177232, 218831640, 905820073, 394811939, 743535473, 944827756, 263599132, 932828748, 215226677, 793895123, 798801752, 76289465, 571380510, 479843998, 311132473, 468978984, 230514246, 295115648, 412739698, 867231183, 894581696, 852030839, 928728844, 335119329, 474536933, 952177333, 779689565, 290854492, 651858346, 714359217, 973230682, 635722736, 849491063, 494264116, 286080923, 9575348, 527607645, 711087952, 774745200, 102483527, 786796773, 875606432, 743174123, 645598378, 326189715, 140121435, 101995085, 426538434, 254595980, 932168064, 808153772, 108087215, 628661543, 415380932, 592144800, 313106095, 808047541, 603230066, 860804746, 758746939, 568175137, 771099776, 254666881, 970646035, 382245467, 368245291, 935050057, 908097287, 893317384, 849504969, 370272046, 217014190, 30274337, 740964368, 790370552, 541440319, 58388419, 227245147, 176629731, 63503179, 671234574, 139761937, 686274758, 366944895, 680969785, 584084769, 946188754, 776332666, 365484146, 393162305, 142682818, 662126823, 931826055, 969127368, 548775025, 644457598, 345402632, 869569557, 192825417, 296550301, 97661522, 340395248, 663162849, 22176929, 353886182, 508881591, 404655064, 363238146, 998268438, 841963433, 283413435, 201651204, 434969901, 237051586, 943186317, 288348675, 411335455, 833456042, 456092474, 249864204, 713373619, 712227257, 345241428, 607791485, 357154560, 595766107, 655542716, 315985101, 408338707, 383504691, 670165715, 989049529, 64530427, 29054150, 220894117, 763938353, 463615913, 692058933, 528374620, 927155966, 691505009, 192210773, 741197045, 570030322, 32887549, 320580996, 366167408, 288055424, 563633325, 832963424, 356036126, 751214780, 212658922, 476099951, 752149859, 891142181, 471202403, 720417545, 150848945, 893061065, 228195380, 382327093, 501412604, 435949469, 170959607, 485298284, 342467035, 650838445, 179179565, 525491178, 544013552, 374188624, 153406798, 753771639, 367621564, 923670313, 737665449, 360388427, 978383399, 236753455, 925440776, 23414014, 726137815, 346599676, 403866484, 801058905, 346928647, 743205723, 8160922, 797663447, 523754238, 446027235, 920437442, 575200347, 513203350, 627057165, 43598547, 143867820, 987817046, 71193666, 339650394, 543213649, 79929348, 368586732, 372782795, 470188605, 44614405, 861174347, 112796782, 596417309, 970263408, 997548010, 806484195, 880996346, 267084249, 222812819, 216977487, 939748642, 694970169, 847153242, 975561912, 437032024, 493167715, 905742534, 843711145, 382119239, 685117276, 482183369, 16950276, 342628045, 763126616, 691695200, 991726038, 575608132, 685015620, 634468668, 538293541, 40725026, 916206965, 665848924, 747019097, 990083476, 81787583, 441392386, 784386574, 766133756, 336941301, 999088406, 680995156, 252916117, 700648800, 764709276, 958593234, 699221666, 961029942, 355446753, 626093901, 73612090, 22900253, 970406702, 721720861, 958102713, 673619293, 101953759, 853004168, 995547272, 733024743, 311949737, 895634253, 144450615, 831988126, 315978835, 681250487, 669548382, 306520569, 496183775, 399943479, 634044392, 779936223, 55354093, 361373638, 646832128, 917371248, 620168754, 291277182, 144437692, 390818756, 233665636, 879032915, 820959640, 58438677, 14603961, 468468772, 138933434, 207790608, 755986319, 738125310, 630484204, 554166010, 212845420, 985769799, 149678994, 88903630, 71736633, 935925996, 302813269, 647900384, 933217982, 812577615, 801350072, 812351570, 249633603, 59012967, 666900000, 348676033, 680211347, 151044415, 836753335, 86688979, 67170788, 85909400, 763957273, 760652942, 141532986, 213976788, 747673659, 248240305, 385179583, 550717794, 298349539, 606660903, 276654223, 161036485, 979202147, 814281445, 402303416, 693353564, 235647318, 851867887, 982680393, 948889148, 910023562, 676843809, 232444846, 875590397, 490966682, 945484109, 366186136, 955635952, 778112204, 226844044, 603220251, 509856564, 701070781, 735103874, 992740098, 783595766, 689941343, 910240645, 133895153, 637568793, 869077001, 722568357, 678869604, 985694477, 26732562, 542831246, 498242699, 542755242, 301108907, 94679937, 551235056, 749291817, 513476979, 361612053, 296507552, 270441798, 723455359, 364838931, 613394234, 158626467, 300442907, 315104035, 20258781, 342993099, 453962891, 648448513, 288878688, 832880709, 669301409, 428305505, 654951683, 81893779, 591561978, 147752670, 558535107, 45655622, 895288519, 988842130, 888378721, 100339359, 622441154, 38904500, 543957090, 788193543, 773779559, 951958476, 854480941, 308131429, 662067438, 187725250, 297350383, 72644772, 385845846, 934748527, 534121241, 578326194, 711670734, 681884683, 689913020, 392569625, 483952436, 124301617, 203110356, 721146962, 902602401, 106670912, 966132279, 833187301, 503249467, 272753605, 332681772, 188375265, 55422284, 160384014, 469966208, 557102092, 669730967, 229980505, 673680543, 671256965, 577249000, 295054635, 216876907, 799024744, 912845681, 777235966, 459111866, 555104621, 464898063, 852637367, 685591455, 20422974, 619533927, 297876172, 78661776, 612075999, 155356439, 591366611, 410157745, 172352489, 220901886, 264845213, 376217937, 771806738, 208860388, 957511319, 542478288, 172867200, 997838410, 182834876, 336311035, 653158364, 965503054, 81587709, 670813079, 185152815, 758028453, 349544572, 215008283, 263225557, 321437435, 770117422, 928244321, 977347313, 953493812, 872949237, 861102843, 231872821, 678999713, 422509665, 603237067, 965219968, 615521865, 124742025, 658144620, 877443357, 937189068, 291952690, 544181865, 682705377, 72207420, 866129674, 857069393, 174473182, 907937558, 628075849, 211038551, 809469047, 33727841, 112288720, 477446071, 848591810, 105011889, 496731272, 738122828, 65209204, 81507138, 120230891, 705749429, 361616979, 473440243, 553061343, 612575146, 26753944, 949711941, 741881243, 282776332, 730674391, 152624613, 248492782, 262177634, 221836997, 250368943, 581897307, 949180671, 716582395, 99441223, 14472854, 926967883, 658997303, 939048403, 844816904, 409785374, 691917145, 407132337, 851748603, 838503944, 276169895, 482506731, 909913019, 456766031, 635787473, 79100550, 884989246, 745455468, 237703765, 244899937, 744362027, 781839645, 481057497, 356477321, 400793732, 947405613, 848671506, 164739664, 600013316, 978344665, 263930475, 871165549, 323488115, 670465718, 161510327, 125629807, 245355800, 246447181, 536233875, 676526545, 402391646, 510862066, 700689977, 521609772, 90535665, 124361395, 322699092, 294221286, 138804184, 455368977, 920774484, 408801899, 175973733, 918148684, 978968218, 393140373, 164871033, 704279248, 336149306, 879345317, 650995613, 153681910, 9563715, 207277279, 269048421, 779179997, 585097748, 474861462, 19137167, 176100462, 745769099, 563580928, 954099831, 180424953, 321730055, 601150207, 887077385, 82977322, 511253042, 973125374, 417561464, 417925854, 465293207, 946246540, 547790372, 893906479, 295277219, 431364184, 448608838, 832827268, 520368241, 7621616, 818606058, 913896860, 499930840, 907824739, 990639909, 652948280, 887161214, 254102183, 930301374, 149075755, 248106534, 415007013, 141453634, 270371816, 664292292, 559508715, 432875622, 961963952, 272771533, 923783480, 604579058, 55407291, 897683232, 702840943, 603157371, 236756936, 194365856, 824367820, 351869142, 885181592, 484636776, 807930252, 164212776, 549188121, 251755302, 343334969, 716594802, 563496348, 528891467, 230041612, 860061918, 2792573, 70414080, 265233859, 178382428, 779644214, 884954289, 186882020, 574749559, 150717492, 743770834, 883251963, 915129178, 546393003, 6470494, 893289592, 798420498, 18611914, 128608024, 217685737, 227103087, 360170088, 143236806, 322214283, 390735714, 659653452, 425877495, 183971242, 82822251, 982296922, 432849816, 467213236, 135286269, 412473185, 801205975, 788878533, 374485513, 942254823, 510037577, 444247209, 629755139, 388546672, 955204057, 121577774, 276328620, 415487063, 837034534, 43461263, 694132215, 409691407, 285976887, 191772462, 114095823, 592834952, 519691, 478497504, 178676893, 835326881, 922683603, 564056915, 578610954, 410596745, 954182182, 909948856, 499557095, 285630005, 626596465, 795830984, 450826435, 942896734, 28777900, 547116396, 283440625, 286097085, 788455470, 481138227, 598183502, 989928417, 798701471, 977097784, 347279333, 153063195, 167415218, 231621502, 530823164, 370609442, 115271949, 726391634, 864251797, 743569354, 71787506, 623397634, 535176194, 461942122, 749814394, 727451302, 2458872, 101737335, 676242221, 867415630, 325356651, 795065254, 190988262, 24468473, 751137197, 32882106, 633651280, 153867512, 622383442, 367123463, 424773731, 43071681, 984161330, 429127363, 80353820, 622890861, 24641396, 721995129, 509875589, 905325124, 244054167, 44679995, 161605605, 564582099, 711379567, 572773361, 31108572, 199732262, 268862924, 265200138, 924710129, 504923413, 535826256, 450890359, 856241107, 116283121, 602566743, 281279471, 981846335, 225112711, 221896243, 201090165, 824017226, 628372880, 53902766, 105247669, 14040793, 799227564, 973114320, 917079386, 310118903, 455335227, 456616767, 767573568, 195684830, 452154395, 677023377, 83755217, 78937537, 503789423, 258257449, 396504128, 224407028, 683079240, 730354761, 672612688, 469410356, 663907988, 389098356, 305029431, 171472816, 610885276, 591947837, 709075998, 822100001, 825966687, 289303963, 433463323, 547042520, 579379665, 720056817, 596625926, 231490749, 432439589, 167645774, 178447921, 293412473, 142280128, 440562687, 998877577, 356133909, 796846934, 346900941, 254343918, 380192580, 603452629, 940848017, 585083436, 914810422, 168970795, 759269610, 131232414, 358749491, 413444121, 751827911, 355987238, 344455643, 895542560, 885286245, 207750434, 321259648, 597348999, 266552122, 571122881, 386150221, 330133240, 178571001, 136533957, 923136494, 856594475, 277574923, 411891029, 73143731, 130672473, 588930774, 993833983, 305889868, 621405367, 618710222, 88209878, 414479182, 689679167, 874605800, 19720371, 597815327, 510019660, 937330641, 576867187, 32954264, 655744234, 536439785, 934758965, 501977293, 554751666, 593994245, 764821116, 152870457, 395889391, 824600068, 182790428, 179051548, 981372004, 934642387, 239571135, 375974193, 491605112, 100375655, 660681566, 645421228, 527659567, 96838534, 541459095, 639761820, 411815078, 344189080, 748759728, 30748214, 757632552, 316674382, 992493466, 812912390, 224312290, 219187856, 781211815, 215293328, 871534187, 373864716, 353782129, 912356776, 303300546, 379351515, 228138408, 169327460, 813965724, 984977262, 250293486, 755391470, 565712011, 679872933, 283743376, 576346122, 845412989, 429344626, 655855472, 106296607, 19563387, 35947009, 206012241, 578629672, 304948073, 861905383, 83428582, 872071708, 807995018, 915976060, 73556492, 2148636, 376776628, 667346097, 536306403, 115045128, 29089651, 283394552, 75070178, 959180502, 996012057, 828818870, 86805438, 174417544, 522373971, 548228839, 916075884, 700764579, 552932139, 301774513, 134509281, 249615707, 177405139, 620299, 596262141, 779104279, 968105040, 469970790, 266606817, 888053493, 906953290, 513441287, 219712821, 660993396, 702560948, 850861424, 268115750, 13259061, 434463479, 14134142, 890323685, 981421238, 518364546, 285891891, 523978451, 361747362, 226593545, 31197124, 109278234, 290417592, 968791927, 525571886, 675079481, 957144214, 247741400, 343956399, 453237016, 533640039, 671026353, 449600232, 75778849, 619494585, 600236814, 750874618, 407298212, 60433037, 987102080, 855294263, 40986248, 978977049, 611093312, 323233185, 174191774, 130320382, 776011525, 149385742, 943167501, 772653359, 578405801, 667586309, 389999432, 122990479, 815607731, 384598077, 407663140, 306649137, 650909977, 538561309, 257079095, 248429112, 100619284, 548434801, 302391445, 916288576, 503427515, 696076234, 672918308, 844816531, 264890027, 27669529, 918643563, 245466828, 152887311, 328498341, 910273891, 968803457, 289764222, 532399313, 833506152, 870190632, 122545396, 596584611, 912573623, 257772705, 237996163, 59561840, 829247167, 982400549, 883222515, 876473258, 522833571, 564352260, 244272938, 310304699, 457394453, 430166376, 830605358, 142171717, 824683595, 497133092, 561945633, 620579863, 673155447, 672946424, 339915033, 588559846, 990078574, 129737351, 243703701, 826299959, 869500628, 959887173, 619198532, 855430895, 688116594, 295045606, 947075526, 40828285, 553747303, 359386583, 31456752, 886333632, 531970194, 614172916, 15918931, 745128812, 897937739, 303596617, 448766798, 848390754, 195478527, 157742076, 36499841, 247300710, 794474169, 882049370, 377909423, 490428196, 392913813, 936476847, 172051242, 798697990, 775652316, 983473373, 35029769, 165002789, 833032950, 611859519, 205378802, 94119789, 10821879, 387436755, 696650551, 271872355, 420317811, 15725044, 754018554, 319248750, 555996868, 168483728, 149798717, 990629532, 762930947, 350156824, 568414564, 669667315, 716921852, 301337336, 506448698, 358687787, 149566263, 475123940, 504538609, 707397808, 918542273, 665718788, 362319076, 825230024, 544629901, 262285306, 383719534, 469569546, 995760957, 32850928, 714723389, 639206777, 686896689, 237305341, 365682458, 170140192, 570570290, 886348850, 231521564, 756867223, 663938991, 481879204, 523012836, 346194326, 707396854, 105640181, 101853566, 47060642, 942641083, 906060505, 850541111, 839953043, 755103609, 202486266, 38983682, 270566107, 670500614, 141477018, 517398355, 407302380, 263273336, 274496678, 280242613, 825250638, 237850600, 261011869, 59152612, 325845566, 877884604, 112024129, 162027506, 512782196, 8283820, 500389901, 279939007, 126708407, 882606826, 355814456, 725425466, 586927711, 907476721, 495886299, 582478306, 558814207, 469027428, 815874426, 932953265, 790133270, 604337311, 367209018, 787991700, 725587357, 922310609, 385955454, 819862133, 571185779, 102776057, 224722387, 822317210, 148395713, 313692795, 664448941, 95251470, 535324342, 571872352, 637863764, 660661770, 427820101, 228435796, 975884044, 595531598, 887069133, 430070978, 237224062, 271486032, 509762434, 34102994, 491560589, 322196399, 233834026, 746193101, 416059492, 386139444, 168657609, 55941183, 327654184, 678836376, 594073587, 854705983, 143492761, 719515160, 688363192, 254663053, 274074928, 794414843, 532093492, 685080757, 399731341, 915758584, 971682314, 870836650, 320279186, 195591912, 82722424, 328382372, 766315861, 846661059, 226778419, 885731076, 535689323, 518119607, 840291332, 834726293, 248346781, 772423681, 773296835, 43797774, 146930733, 90054927, 501069280, 833344244, 145021008, 141125853, 627572362, 612260767, 697820639, 893132156, 245302017, 333046658, 129486073, 777565756, 636054816, 820307334, 39612101, 936241151, 652288105, 909672455, 383603233, 754334967, 240886559, 921754135, 208298987, 501263020, 845860873, 84577777, 707980784, 589619697, 81682326, 603521191, 570367536, 369406300, 31309872, 911349140, 598517027, 469505955, 459174866, 293591933, 746375646, 569698694, 664522532, 716902878, 145811959, 311644068, 802706531, 79281075, 868724005, 199471819, 128684298, 851781260, 254351748, 835015656, 432916348, 15302793, 295475414, 927078964, 680279446, 448400519, 465622661, 324122504, 278057390, 372630742, 827586855, 199352411, 655712976, 741284431, 932911404, 7881230, 922944572, 611622197, 267139831, 821387165, 921423292, 941308754, 496165168, 368445227, 253846303, 10217857, 441124646, 26023149, 349386319, 453438752, 593998725, 849599522, 132747973, 675967472, 508384989, 406728518, 810035604, 860780291, 999895063, 373858476, 162088723, 318106788, 478655994, 129762105, 633452958, 420941516, 158822523, 518071133, 603696482, 308427573, 905687234, 703159088, 320193431, 943134222, 704653120, 819145667, 432990357, 992784204, 438523818, 345420190, 221824026, 333038000, 446377131, 748301397, 250563107, 925619214, 234906362, 707036482, 880919951, 127620177, 601586331, 689444425, 228776354, 666723783, 772943498, 333129441, 105234023, 586046990, 233966310, 859632066, 508661945, 56146989, 969721154, 876471481, 698944482, 859013042, 251332022, 417875696, 408394468, 17312280, 31500683, 670962987, 873393983, 582864107, 604793681, 125523699, 63932462, 465916032, 897039578, 489108169, 653578689, 235820818, 56281452, 701442095, 629435599, 344908985, 508361403, 205263626, 611449656, 909291293, 872790859, 955803466, 647222453, 851139461, 401217462, 176010664, 348838519, 736287225, 241975418, 780928215, 264074250, 38028827, 777770375, 527442449, 339508046, 904561402, 155923880, 714526809, 193109662, 963593698, 360872230, 733172724, 662886069, 610979066, 695014771, 275821959, 284992045, 885826264, 330170540, 743428763, 585876554, 539087472, 503629286, 239332816, 861911364, 706555706, 151564438, 129399927, 848708256, 246062667, 779779842, 146733407, 640689729, 849326859, 510568406, 210130600, 225733498, 13117031, 804885941, 835298391, 851988201, 998426181, 301910847, 695093304, 906676108, 193222703, 411250146, 920461907, 570896210, 586858802, 785743162, 930296664, 975132846, 458383988, 535870095, 897886454, 641091430, 497926112, 414854512, 193513644, 504367020, 414171610, 370371252, 358721060, 999557779, 533566922, 691746794, 849963398, 770126685, 190653006, 354884321, 255945725, 725607467, 139422032, 654436925, 61953011, 141587690, 636733232, 513190965, 734923324, 94694472, 710734447, 147580309, 264323563, 31713633, 395988282, 767818733, 912363558, 624560666, 808808366, 661587534, 371798333, 581285641, 713604253, 518009511, 810231033, 567726957, 348448437, 56726800, 591579529, 849949125, 507896111, 277413112, 31369349, 869745247, 858524582, 272006685, 553818814, 84068482, 556919616, 831951271, 466617710, 688997441, 494332936, 194549070, 168909187, 425016343, 274892698, 141996279, 303402308, 609762296, 672219342, 136921822, 837307688, 537380489, 603798243, 791492353, 233769515, 404026285, 843895488, 511544680, 536818678, 801950576, 544654225, 267916617, 508401529, 578635866, 315556871, 459645359, 321711535, 48054634, 181287339, 392682755, 300048258, 654947248, 512252100, 75591178, 555841657, 982929716, 518230696, 577998703, 775715047, 613957430, 521258931, 926969122, 427885904, 672283897, 379217595, 808202863, 46915506, 849345942, 662848598, 562096562, 530434116, 686999501, 89803360, 259934570, 348681277, 100183236, 302954721, 261396263, 880119009, 693580157, 437427413, 672340316, 876292240, 827061728, 444213789, 21346534, 401755389, 913393401, 197356390, 613926580, 102992082, 171384812, 164576208, 723968766, 908494003, 747705034, 179444800, 702780500, 859647344, 625753785, 707395322, 733984717, 850609327, 722454629, 234510984, 868328453, 535491126, 833065783, 900359274, 931832810, 115931204, 204212126, 175348211, 245332048, 28527999, 127581822, 181315509, 713620985, 951181808, 526264604, 39065997, 700482015, 108261064, 823253783, 550003368, 38166698, 201593805, 820624047, 540559866, 599897479, 226172469, 327786089, 630751770, 722761220, 942796324, 191906572, 361435404, 289971878, 484815374, 325397993, 861739975, 697252994, 581273839, 829927610, 832450194, 39046568, 837140320, 672564598, 915080659, 526921167, 420377995, 504926098, 926207120, 508497781, 425538087, 984160677, 337312719, 437715784, 454597836, 422633743, 288886061, 745236494, 668542346, 658059271, 979334405, 746668968, 601708321, 661970810, 442889405, 647703692, 637246654, 774548264, 799702731, 19176347, 192437672, 727665070, 496404375, 569403712, 845046024, 991745887, 530858029, 790150235, 281660421, 394987855, 847536259, 29241392, 162924736, 198283219, 587538111, 238526408, 907029116, 186005028, 659292724, 784313560, 24685357, 248074363, 4250243, 440015458, 229344444, 33068187, 408082258, 571372105, 552639502, 923213014, 822523859, 326641723, 97993650, 239669674, 713391891, 685559281, 816373218, 620192898, 506709839, 145683762, 310698321, 572618320, 809106698, 138898299, 449083051, 637578942, 314416369, 693294387, 803656862, 816538240, 761870916, 60379716, 712152316, 972492904, 885750746, 185169605, 700887894, 77280187, 404098775, 860945979, 19428486, 616583278, 268095981, 428981862, 954174332, 329112674, 137087055, 902105954, 63318004, 621276185, 735946843, 650959386, 165775661, 457735105, 818180205, 618662061, 486985629, 271078853, 1776130, 198417637, 45004706, 417920039, 102897325, 583252924, 763359741, 383824957, 726647184, 884701266, 382157748, 34022836, 271660023, 231118934, 27434006, 721220628, 962649994, 255173656, 210048080, 205097717, 998531818, 431184872, 236702508, 195582633, 549267441, 827529427, 429534739, 761238506, 98310125, 204438642, 163233544, 328965215, 36846831, 147357325, 40725563, 145579801, 666663870, 18902324, 463008562, 628937657, 233052573, 136401869, 852151763, 950350505, 148633712, 836518752, 555231632, 599953299, 205541826, 659704064, 27069729, 5729833, 781673442, 207630563, 833897853, 436199460, 288509047, 691621156, 569896475, 543530054, 458607876, 766673797, 881763314, 699229779, 567963471, 853393926, 530654614, 602719502, 28414801, 832921436, 662327185, 38914489, 597387246, 365727620, 103236515, 445763306, 551865325, 678249671, 358508487, 266634272, 118814009, 581965785, 676362477, 128536228, 286325169, 259233708, 819708384, 641275806, 229374605, 241505141, 135672399, 506625098, 766774686, 938481391, 46225551, 763869690, 438624008, 909553639, 528892405, 368599688, 124016951, 214747390, 484480842, 584989087, 263969298, 738876589, 880923525, 135515819, 75200311, 956353280, 69576193, 96241090, 870943089, 685546964, 298566533, 390183887, 940579998, 328802077, 213066503, 968991990, 717103462, 351518595, 240057081, 208007497, 27323665, 335597318, 754925393, 71292016, 566109302, 486449086, 423421009, 936354858, 562494580, 311990327, 694329956, 285010404, 462114443, 915602810, 978768191, 714147063, 262391280, 808549108, 356707613, 166884542, 786951698, 109825865, 578801369, 994980222, 173677979, 167014188, 586831098, 286386251, 717708038, 19305426, 760607944, 208333279, 528501563, 427747395, 294517904, 595925374, 953122572, 411912213, 901592794, 556512957, 127700958, 176974712, 756451919, 674795347, 746152643, 245415740, 716156645, 927373395, 281113270, 923163305, 323359271, 382173723, 244643307, 133774971, 338227307, 117974772, 666578382, 55718108, 278859605, 81038170, 61086825, 949232600, 703870184, 597935228, 549293944, 174831447, 446307794, 123628905, 937206970, 119806921, 148825966, 421503328, 500666257, 566917162, 695322143, 789549997, 769945446, 519095344, 149864314, 987677933, 579565889, 251654243, 763407493, 576559201, 973842560, 995858523, 454087804, 459835070, 627164658, 247123830, 346674533, 453917965, 976364877, 464341394, 487150302, 356038673, 722562569, 58996619, 782494319, 620670342, 261361491, 703861395, 813512694, 194483529, 894365486, 177177314, 682609349, 61775207, 140133790, 783826222, 742312565, 630915912, 947826290, 281455472, 244280476, 279152089, 125228196, 775130936, 964137721, 647513718, 56973187, 76314774, 749329452, 50988617, 108749261, 265305450, 999487031, 154233507, 386870134, 75453836, 321196181, 565842696, 390584071, 772909364, 106889133, 776022525, 387544920, 170466626, 190482413, 887993193, 220547255, 38071348, 34091007, 684457287, 192532290, 85947472, 34785748, 47990424, 29604973, 100960265, 660268157, 375816248, 449338634, 38730840, 231695424, 369569578, 934413598, 803106569, 531213684, 411994085, 221181785, 817687047, 444786346, 519508902, 534764053, 728741006, 878279530, 996987679, 234893940, 445542630, 276349361, 579340466, 603932748, 829802289, 642203648, 56915792, 624279790, 561905791, 627063190, 456567004, 388709276, 701380420, 779843903, 825413643, 906627042, 492391224, 538934652, 838338382, 70432486, 391005945, 427592313, 331420433, 693889313, 8640018, 363975840, 171761160, 852248980, 642012689, 1635706, 150229678, 481107151, 555457117, 294173436, 667234027, 966637363, 147938723, 144425516, 479675847, 425291187, 94493481, 578363212, 822779895, 435554894, 391549602, 900429958, 353686798, 257376396, 428678906, 637973739, 462811724, 485845324, 499001374, 103013749, 925093048, 745344531, 508002013, 217623251, 311241313, 510326272, 196805430, 717559799, 347404641, 342398367, 731292027, 914689684, 918794255, 465594884, 735838960, 464596738, 722548264, 978323233, 194993108, 304782696, 420139198, 80041568, 530659855, 804514266, 541827499, 692520668, 992156609, 152959967, 656766032, 53047145, 160068794, 583994714, 378754837, 477366151, 163639735, 280224035, 411359781, 925049500, 43305276, 603091533, 976657643, 30771301, 835160126, 445552413, 351070059, 736419910, 779285623, 579658086, 670026897, 358698569, 973256609, 642523845, 655961846, 432080026, 70214646, 643125161, 163740334, 616713933, 324110247, 781820270, 121205259, 466451888, 855788757, 312339333, 944736212, 566742723, 196890810, 150528305, 499406778, 682870586, 662504167, 890775540, 981690276, 570625450, 815053322, 40552775, 416395102, 548332691, 214844240, 566665196, 125583789, 180427962, 233930449, 7090876, 295918765, 801106018, 990117850, 217174888, 938449978, 478660641, 463193894, 272878875, 756532992, 377866009, 418127861, 41955023, 701657701, 895062047, 747014311, 106218852, 957117059, 830825986, 394441245, 744588641, 533669969, 598141432, 239962060, 98779125, 604621476, 642534526, 863686726, 830547159, 487987853, 845813506, 356421861, 623296046, 452982978, 239540462, 782244997, 378355223, 350045366, 532475657, 214902224, 928602421, 790243813, 390777266, 308735210, 338157091, 861624832, 656150877, 351556337, 643225249, 939853255, 858358808, 859099777, 591373196, 818686687, 642577183, 930743286, 324913082, 381272039, 372671891, 956783921, 509266323, 535071229, 210559800, 443042049, 51898027, 15242974, 29344815, 312753015, 788300870, 222364751, 935270383, 294078659, 597512030, 766853578, 199230591, 720076620, 695943721, 209777994, 664821043, 938423016, 156771306, 277960922, 233524594, 376879313, 976320811, 208559059, 398180957, 814388691, 153912619, 939723197, 464275725, 338077130, 400548636, 863922264, 958303377, 985556937, 331242188, 164735494, 876273686, 309135629, 808064103, 333881857, 389789927, 908469042, 847611042, 738979485, 142603436, 279701050, 935252462, 590684970, 590827046, 983114083, 673573273, 114745076, 811917917, 755617993, 499104027, 49616149, 250984514, 291964083, 709782358, 466805796, 319689729, 804540150, 712125124, 882908320, 185607161, 632142757, 360762359, 332384430, 241555936, 202229979, 663475822, 667487696, 571218122, 579721858, 964112598, 262415874, 621386986, 182306407, 534322921, 750863069, 3532509, 65053792, 53176561, 559764204, 750737910, 957251942, 690530219, 584784851, 21866685, 963468022, 461265410, 337162214, 335156389, 405594213, 192705554, 168702260, 350726142, 606894706, 10222490, 423936714, 874255198, 307744696, 992608238, 378660274, 81160806, 271517507, 623454455, 829081874, 616094268, 509249428, 903314533, 331912088, 170243922, 260989723, 550489049, 779933168, 701521190, 911896880, 687151012, 995816833, 692223554, 340364414, 159975593, 927382661, 691794901, 814634899, 580984608, 825365170, 347927711, 848829039, 899897309, 840617529, 963560366, 648201674, 732910854, 79732550, 380378474, 176473981, 185031284, 355282593, 456890977, 450098163, 486956686, 763921224, 411180319, 801785332, 447625817, 484012772, 985176462, 751037549, 796289518, 179780809, 839646376, 859348313, 411023998, 872664780, 694825019, 225780587, 191093717, 353610029, 888111045, 40847129, 625178407, 581702378, 745120192, 204250467, 731225444, 323939455, 207544400, 95397591, 515396976, 897594262, 138243651, 221647124, 89571012, 111957249, 759692431, 268600023, 990042295, 234970778, 239771360, 307980138, 552007700, 202752953, 399257424, 533832049, 671047882, 94999488, 516930449, 375679345, 554294086, 226978020, 960774750, 308009028, 926480855, 536441700, 126753336, 285391917, 574407763, 274871899, 17813475, 385045773, 17352668, 537717265, 666440325, 241116121, 44527291, 947354458, 596155599, 672489013, 465932164, 476055133, 227262275, 302662083, 431351669, 794186919, 145284321, 372229059, 952821380, 171289458, 638776656, 126761163, 238482658, 222553941, 767609655, 73566241, 698879180, 79105304, 448964305, 826448719, 592440857, 64471673, 438053430, 52128243, 976620028, 902641805, 621335155, 503174748, 566835304, 684726768, 28522162, 304168264, 341679312, 557196984, 650376604, 893746572, 196722488, 490212647, 151650759, 10271143, 91203231, 624608182, 600127051, 357815172, 965638202, 669325742, 406139873, 341534689, 956423080, 987257013, 247551851, 826785459, 835702722, 784942266, 786525898, 296568632, 918079563, 215989698, 834856436, 230688876, 206938593, 260843527, 197301006, 765694651, 948887778, 49213132, 400347374, 151960797, 574645173, 92488953, 983627119, 258131067, 317948614, 163217037, 920433550, 956032057, 232072513, 594540572, 628028225, 175988310, 328033266, 50166691, 309305419, 368384438, 737561632, 388149655, 489038970, 598505537, 934479242, 387901371, 134215526, 286377575, 803528621, 415933590, 437413073, 123403587, 55779488, 463360666, 63123082, 563922315, 12074245, 36548478, 395401623, 975579884, 593776102, 237811, 921520930, 213843514, 775655615, 219684609, 100971944, 77060198, 859889197, 187956769, 32376106, 47943023, 329831557, 683069062, 715705052, 578449664, 28326181, 294318741, 10569413, 907529079, 278762992, 755479295, 222665720, 814277081, 663938852, 53645905, 16951823, 470645652, 304000775, 7325953, 589515890, 69969630, 928513872, 50972286, 466330106, 767612731, 643748707, 29220585, 264422113, 255452326, 739770566, 215094070, 103152685, 436151818, 384979103, 759103117, 970274128, 105182658, 945099254, 851062203, 153875690, 747806665, 464639108, 694112984, 273978855, 842703910, 892778288, 407235498, 947804126, 100739043, 124682889, 919047558, 199760633, 573218853, 660609980, 129461937, 825368333, 52663894, 606919562, 954410383, 740063563, 219903424, 677310412, 912501094, 852980885, 448651320, 706869693, 955751408, 288789560, 278956494, 592560791, 488879013, 659746365, 887435702, 351275498, 352497098, 573433100, 82782475, 957250349, 416487608, 366195670, 585349580, 243127249, 890843884, 333647141, 666351403, 572397104, 288873504, 774996667, 169251953, 108362056, 787432644, 844156518, 589775712, 785162144, 872921469, 11591187, 499571107, 133500628, 779683331, 520413602, 70939678, 793275090, 412935696, 149583284, 384111037, 972836244, 138997060, 637943502, 908576926, 699406083, 72152470, 671088731, 78073630, 615493212, 77956878, 300013798, 624696824, 106138917, 568014008, 414827294, 127402875, 374040819, 547522409, 735581242, 207239826, 269650283, 642543963, 598413760, 491771420, 112147536, 997780468, 554245404, 297103734, 975499906, 816693924, 628223940, 186793941, 259556685, 74788206, 29325616, 470554625, 581261839, 367176982, 893716081, 889887508, 252137235, 396389749, 491275259, 116193472, 416191882, 750380125, 606604120, 251425982, 23681373, 14849311, 43038145, 922777678, 223924721, 822300439, 731117032, 563099338, 983710183, 51706887, 878961273, 35562561, 765177805, 331575402, 278775684, 83621201, 489048963, 688614605, 305252421, 30095524, 673218260, 94311469, 732022176, 643405683, 262456442, 465218315, 971551680, 552520211, 267180346, 907002647, 321201854, 242007277, 15045529, 464585509, 115964469, 62428679, 70047490, 960374523, 169081908, 98806062, 699695660, 299724818, 624412630, 466252632, 685577023, 11636489, 223702218, 591527041, 333452027, 557821376, 134129247, 552727116, 291372408, 223138734, 496168614, 226970312, 642706821, 40409702, 94901043, 93452649, 913798801, 357224689, 207385710, 429954663, 586435491, 474627456, 624528948, 723847807, 882392742, 731958539, 77790803, 396370266, 759335795, 975183079, 488515590, 565458549, 756876967, 78937271, 134919836, 332424758, 177876476, 133448043, 440807064, 960723985, 918331296, 883927573, 92699705, 269211931, 74483293, 20313392, 98696554, 265656872, 781899865, 779753839, 951745058, 193094383, 364912090, 357344339, 628243532, 472873612, 855023757, 117215495, 96781597, 617132101, 246323017, 949882075, 884076371, 100727401, 731717842, 296621375, 79898562, 38917064, 958894157, 55765463, 990489071, 223360556, 532210412, 959393222, 627634378, 99155426, 412944077, 1171106, 947978357, 838927198, 85214018, 30857589, 757004598, 641477805, 181744481, 380424554, 299096491, 194251201, 595077925, 478074768, 473485732, 35979965, 93195103, 441183078, 500925258, 860872428, 661363133, 735917134, 883380398, 869180941, 49733904, 255779038, 777263435, 624703521, 407529370, 98921851, 451569793, 265023009, 995164046, 82740520, 109647027, 910087708, 492721258, 371951897, 171379854, 125034084, 394131403, 76369075, 322480025, 620921628, 540652947, 631545112, 20886589, 287322178, 719520042, 421866909, 494486910, 357466673, 996814378, 136153021, 885077110, 894219085, 22467214, 772854784, 366880924, 342657431, 252812031, 774607348, 785568791, 557483066, 740170353, 240412543, 479096905, 433479089, 492352409, 778621379, 251872573, 240760658, 570836523, 387883857, 903517318, 639012494, 934600631, 52328322, 745576617, 483737880, 961644397, 221712681, 673779188, 690260767, 719448702, 30063428, 359003780, 628920756, 389497429, 261986259, 513060093, 216892536, 909724021, 340190099, 142605452, 482189259, 807026303, 699943143, 56896219, 252966072, 395814926, 198852549, 392267430, 728627070, 485658741, 629744624, 897399305, 982586080, 437726822, 514580584, 232610089, 671892428, 597868181, 728118547, 638336470, 136193925, 63010525, 540732492, 62552399, 583192537, 618285005, 150333524, 932625024, 34533461, 72203433, 576586266, 622925488, 641518061, 218743272, 544781885, 331468967, 237529746, 276044119, 304236983, 663128844, 778002921, 284608725, 590726425, 278362746, 661063395, 384505755, 811987063, 795677494, 257882631, 348089715, 284578608, 274272054, 50713837, 689150784, 261660101, 619775828, 130426571, 396288572, 243614832, 849803935, 633616086, 366972110, 506952108, 534024076, 883331006, 295278913, 755829861, 102068280, 588208873, 185134946, 244527548, 771608279, 126497051, 822734494, 402649509, 55325010, 442832355, 620046921, 226018685, 186361966, 632983365, 946450055, 784376035, 632054858, 617472011, 493845348, 154229559, 645963326, 432610723, 729656841, 179633339, 822730220, 741587995, 29222288, 970430837, 946882743, 447616353, 658951412, 828842551, 420166379, 597385776, 245697320, 857942086, 391429636, 659021117, 909166722, 946868062, 287132857, 700068600, 808533539, 48172271, 522941842, 63222634, 207772326, 961178373, 169572623, 760044481, 654365160, 536923896, 780160747, 852131446, 848371550, 599195704, 382015629, 575857390, 324739753, 512904025, 933448479, 168740788, 482158917, 158400452, 828154491, 898368807, 95518823, 995494320, 503306996, 864458895, 783708330, 323178971, 488791509, 375484297, 651831543, 400421181, 465507675, 271230366, 32700990, 708655620, 572462851, 360106172, 203068634, 383732248, 255569932, 929473692, 10832047, 962620430, 873819019, 720259017, 898314321, 365651762, 380298876, 515415847, 324399780, 568675778, 616214098, 636614542, 359245900, 30836914, 102050091, 615028446, 686076569, 980263985, 367678630, 510474480, 791342303, 697518470, 435139943, 358386740, 470206433, 757918651, 46993567, 825499106, 768080308, 339381376, 195798455, 635312250, 176417837, 612995825, 260504808, 168557342, 802410985, 799778714, 455398611, 456990041, 609420786, 64906455, 811006586, 49323540, 349081071, 814480539, 335186542, 807599182, 711416375, 530278130, 626493628, 70766728, 953360981, 999886221, 507786141, 571767309, 418492849, 63628297, 63751309, 728588187, 488280076, 782463409, 414092816, 680795385, 192568758, 716929483, 869455233, 498749301, 963935194, 869266799, 738265179, 989386119, 150802112, 285973534, 522542219, 148903852, 269546535, 339358547, 787393855, 467865378, 324017264, 456092289, 795477852, 186309493, 817554234, 717641238, 330165950, 74459127, 284342224, 959973673, 174482541, 966482368, 431672366, 705015452, 914693445, 618623225, 676496368, 973014172, 845019191, 791033696, 643899524, 105646509, 146107897, 134575332, 651555269, 939002116, 970658335, 291827502, 113029661, 105826000, 90361395, 648301881, 48425392, 433232124, 994637006, 481449308, 797861352, 970760001, 736515986, 768739956, 490171149, 364119221, 107105179, 610252895, 951969276, 917171995, 945239404, 185069217, 995783879, 438008232, 543781149, 790465436, 305322534, 925914549, 137427048, 788945482, 608656559, 768431230, 217113383, 573875901, 48286690, 442567594, 572344087, 221036736, 894529659, 461924719, 407839580, 733623887, 873842010, 408408578, 122764345, 357769681, 167255338, 641194471, 536011644, 450989687, 652585170, 835305809, 805312629, 147350127, 510867213, 332520562, 991633111, 904306181, 782510370, 366330864, 32750326, 790624820, 399038981, 838048268, 271185359, 905022942, 486882131, 439733653, 179866722, 911776759, 991774694, 649765720, 890019977, 230649073, 547746146, 367136267, 916172773, 867700366, 448458829, 873528531, 417728731, 955478194, 156746723, 910887170, 914577151, 75417596, 34021286, 757855466, 472140146, 311493440, 770762882, 734348069, 351891534, 484300241, 669930425, 874010183, 916071727, 499935089, 953092011, 513407161, 3100482, 765244786, 287144416, 265113460, 972521474, 313630702, 415686391, 24073822, 915906341, 322890367, 44397209, 722718898, 171021961, 594327074, 443566722, 869248066, 445089270, 206203269, 113181083, 942554441, 942295717, 119575550, 806249374, 8749192, 920273644, 722893833, 278688777, 512553169, 967093057, 820115092, 380358544, 300288783, 755697116, 839470879, 559765100, 899824850, 616229888, 55805966, 178968724, 264557878, 481137166, 639760367, 915787471, 618406099, 816901079, 454228338, 816146025, 951029826, 930844644, 919399450, 500755848, 939912405, 181537354, 137465305, 646209083, 494575569, 632522820, 602110574, 60662469, 552230333, 85629889, 959905800, 138613955, 362030074, 949368220, 478971854, 76374000, 614411074, 274135231, 454228404, 640289668, 772889059, 726815792, 165924677, 16444723, 815379153, 408608281, 277454200, 907160268, 927072920, 234544878, 519186229, 435727868, 620094708, 705203904, 738785322, 507850671, 339580951, 441460172, 784829445, 131319078, 527434649, 181533554, 221780514, 980679149, 83249520, 671004651, 631462231, 354094616, 957367129, 835425917, 124917375, 573739281, 12878935, 791298643, 423934990, 841299653, 18846661, 579402009, 850867241, 79131697, 654034887, 779823342, 513307602, 154931843, 774313005, 48567408, 253313637, 593505340, 197918298, 330367804, 239127177, 507691731, 466728790, 789196241, 564906376, 552222875, 424956121, 821385318, 8878655, 71619447, 945977412, 981641894, 654613625, 823022731, 631644339, 986939499, 969625333, 714141816, 935857, 854802565, 851112879, 887616664, 47847764, 987077574, 315079267, 536093844, 696100411, 256518819, 755278080, 112521147, 158913184, 126214991, 983258486, 697973930, 50552860, 160826010, 260378109, 391199470, 179687278, 482661780, 716255045, 915622462, 603957995, 494547183, 605419824, 856301721, 7340017, 203473673, 635819504, 21617979, 267747621, 12414276, 51794952, 421032688, 442651011, 579612799, 766808373, 347260379, 804237972, 100022059, 732688685, 548359315, 317712698, 760524665, 647524177, 255106230, 5947458, 269238760, 372844225, 24109998, 843123561, 849571326, 464917628, 269540440, 597563701, 71700280, 60650965, 303247194, 897959808, 617443672, 908696356, 178944716, 91168302, 660222392, 600268021, 552264400, 319100876, 321443431, 357900049, 501866991, 619635404, 570692795, 442916275, 286128018, 276482083, 53072953, 152923103, 481500526, 66824422, 725433776, 297953276, 249936009, 186682772, 867580340, 967041447, 54227165, 213342590, 110213023, 5037732, 428407447, 100096656, 373553648, 643246867, 414065712, 549730621, 849936340, 467651638, 518257481, 592974332, 289172070, 688001196, 343167976, 663154663, 939750080, 585702151, 225245678, 28113797, 564097127, 50398454, 61244158, 986763552, 915023720, 681329190, 816315610, 169167513, 523317713, 653930559, 624714718, 989248894, 885529714, 60771590, 468897696, 584892518, 404649347, 1576803, 65156988, 364790292, 989950290, 248643097, 811235426, 222396494, 232860369, 172757655, 166046390, 298245050, 329179681, 215972464, 710022092, 406384534, 424828315, 993732896, 115637263, 868988875, 369936362, 162908826, 562192963, 340356130, 674611934, 110222060, 798937526, 355050392, 931539891, 25118887, 924515813, 807654051, 496510517, 641443670, 590919106, 724365478, 321722845, 378637524, 923965950, 134649013, 710264958, 419222432, 916479813, 630447912, 948198983, 982107045, 637755239, 950320000, 134040079, 612263517, 787537225, 543347155, 272641642, 483035472, 726723740, 212222124, 581095404, 416425240, 92694998, 725194564, 600151393, 721634496, 422309741, 147094364, 618042914, 548871509, 566499330, 124014858, 622989069, 499803979, 643759855, 145691438, 573277714, 72275077, 817558042, 157015619, 371155627, 170757934, 635112911, 601339552, 529068475, 410684256, 920262026, 254596495, 665240134, 766398890, 271981000, 496085867, 650742075, 578334779, 314708211, 705237582, 927674923, 417253074, 237274450, 887371823, 641331815, 957284472, 225012362, 405626857, 969341792, 65033107, 764508408, 567005242, 936473143, 786873608, 195622548, 581555533, 249648582, 762371255, 857462141, 227299705, 584610134, 3270463, 919141763, 885852085, 19873241, 368457633, 749679131, 982237009, 870360893, 231739522, 115869996, 176070428, 557945710, 173878233, 487706738, 829155498, 613231787, 624598557, 633844595, 1925448, 925174765, 874732543, 377536241, 427728152, 117500393, 324868534, 384409202, 16939470, 201171382, 190026260, 980439396, 34392947, 319112263, 994889501, 735458429, 544732315, 542110268, 820791667, 989953579, 187795932, 805543078, 928642779, 904877041, 914425068, 114825551, 153184914, 909654232, 802864091, 970915935, 617472923, 286274148, 25238188, 430247854, 132582855, 608843797, 44353159, 177096150, 717538576, 624741034, 199810569, 938788240, 747204671, 177377944, 249273615, 899588686, 588373550, 676749846, 172705124, 176242619, 245315438, 40681447, 931816949, 168803761, 831756315, 803017874, 809202102, 550997060, 469017288, 520920890, 123622508, 581463944, 872003737, 139534558, 817241144, 931689937, 91950820, 551991412, 600781167, 543473878, 201840386, 942593973, 926507444, 157560465, 604821341, 332954151, 160169681, 136705380, 322728866, 462400668, 366892420, 28529203, 757111960, 916053743, 776379547, 464217808, 941131472, 221334765, 294060282, 629314915, 802810888, 276834212, 646336853, 114851126, 893200533, 355817544, 949337020, 509968117, 391370099, 658361698, 653896511, 490138691, 402143976, 79704113, 647701760, 573358012, 825780899, 376897778, 199100719, 562306095, 466870601, 707538192, 246205901, 482149099, 403581832, 852501204, 488225687, 449304911, 51243549, 778789722, 446486760, 626816874, 419167528, 361774071, 190395280, 99472619, 190622178, 184061620, 421985289, 88697674, 297703642, 626874835, 595447328, 780856550, 291063564, 334218081, 218869662, 32326991, 666761589, 150896791, 94012528, 417118868, 9308685, 489658340, 507646101, 622476085, 919454574, 37370172, 760425299, 861454432, 869303748, 693313496, 789317814, 341543312, 235148051, 523518529, 536602482, 62977755, 571697072, 267591366, 428470009, 968649335, 370901819, 540080332, 114645533, 111423229, 658986942, 89229167, 675051609, 294562110, 715303593, 717394887, 41891108, 914470111, 701954596, 710804527, 261523821, 358356248, 761589642, 605721162, 952401619, 110268986, 979543841, 404713137, 77011704, 433385453, 296740015, 193296048, 547508532, 417650340, 343008272, 832176382, 640035764, 653392483, 951951232, 258316952, 714658889, 419076726, 941895602, 83164827, 584423425, 472569335, 174806227, 319933751, 65114353, 572950225, 686009667, 910458944, 681180690, 235737408, 423804241, 280585431, 430822230, 488910771, 963043305, 233179940, 574189147, 459851257, 666061025, 450720900, 643872679, 600415242, 778811829, 489635697, 27060295, 598398400, 917064443, 997359496, 307391789, 476299934, 542276373, 114383509, 166893166, 407294088, 767111154, 71398441, 453360283, 953673631, 887590790, 103581010, 579343929, 817990974, 69592904, 45113224, 653161726, 623619756, 976369382, 821543035, 226357574, 528322315, 107770076, 896121521, 273285814, 852306285, 377367620, 879425267, 515497463, 555086315, 529452098, 447802849, 677559500, 214197882, 838216500, 993612773, 18526095, 624387126, 319354215, 392455376, 626974872, 307044473, 821526301, 854313879, 139050267, 791595970, 512296426, 548864169, 853900709, 350241018, 255121270, 762719615, 289607504, 360232707, 510489068, 807193413, 514456826, 943938866, 795697477, 90560136, 266075818, 394590776, 450947228, 544393210, 461425636, 132185977, 86578567, 323292230, 53925352, 324740501, 825372493, 678423390, 902942008, 152934000, 515439064, 585456879, 929892921, 608715940, 189871882, 236366148, 263122611, 882745511, 222204931, 68372996, 378654087, 495361903, 67397961, 791400293, 776697888, 156405272, 211097881, 847066739, 364008556, 232122166, 915557558, 819991557, 836409220, 791664791, 330618675, 891920779, 821220172, 280507407, 19742833, 432408921, 321898687, 734411931, 842336265, 884463113, 801129249, 155131866, 509917153, 169831607, 818037614, 626313185, 347183625, 363088352, 838945092, 537220656, 435756900, 107182392, 669104273, 651067642, 651111591, 793259459, 237726313, 836864184, 563389390, 437625117, 367437729, 436526537, 572897166, 585080503, 362365999, 767362031, 860742603, 694641314, 328059154, 49436461, 392223489, 614082681, 130475392, 417082784, 89985906, 425631646, 785631361, 556205256, 98460398, 485050318, 653283130, 338675215, 545280303, 668448538, 434673897, 400751589, 300194143, 773587549, 30403157, 606325326, 229770719, 516747504, 23551246, 829424594, 273015545, 26476542, 804935229, 530549417, 996617059, 358705203, 60640010, 689979070, 546263738, 991231184, 680176599, 243532946, 226169546, 161493582, 209572015, 355540676, 451193345, 317046015, 536608673, 803445856, 915830898, 388776665, 618360225, 174481441, 502884685, 792020789, 867784722, 448685180, 569835099, 226415800, 698420297, 329403963, 341243491, 287758821, 993173388, 366063981, 452205122, 61085009, 246037725, 445737386, 855271435, 846058485, 415113461, 956593969, 447069835, 431125159, 942423144, 940609022, 545995020, 911549183, 807148873, 997897144, 485555097, 90898451, 828758231, 269458558, 896907026, 152535717, 560173798, 422374197, 483579792, 298190556, 274803713, 686682367, 851666323, 970079806, 251054941, 864838776, 815069506, 201181166, 178966254, 562958403, 289702261, 65418630, 963539803, 213593392, 368962892, 570663067, 439163370, 541237004, 670021020, 53435483, 146843684, 127388689, 451518591, 893731545, 337649684, 785570868, 306684356, 405247751, 710844103, 35781939, 128561030, 482284788, 740450291, 438178004, 846972716, 957304069, 206296816, 809298036, 43466378, 530649677, 644003144, 682741314, 598126358, 404301802, 696607631, 644024755, 902971462, 630306629, 835588260, 205168447, 475013665, 87656807, 446461747, 532466063, 807596247, 705062694, 345375165, 103393718, 810594194, 170963434, 307319695, 172432276, 177560340, 177559152, 380223240, 43501845, 476350355, 572714498, 122522985, 782522629, 653366647, 231128711, 443342812, 847015854, 834889949, 997817496, 684355880, 817490372, 330824387, 835260130, 687748636, 847908546, 291774533, 605275460, 750932302, 365884346, 985621438, 167375191, 313982272, 424989365, 183567085, 580860284, 382853095, 845514626, 16313462, 117139487, 548337577, 936922909, 959581714, 919583754, 647699985, 386597961, 779175395, 711994334, 706843806, 910400557, 536311232, 204544145, 607778974, 331657503, 833672293, 932733906, 659731731, 749886134, 740848222, 258244532, 376909696, 756358542, 292518956, 570521995, 720222513, 862617948, 537997590, 679849039, 529159570, 22729279, 587515886, 147036792, 291899658, 481066271, 443273171, 519437705, 465554136, 804224992, 553796100, 335827169, 343046450, 809211152, 565589227, 347220487, 32581666, 368922971, 267707082, 787920389, 80116488, 595890218, 802939965, 939035234, 899934970, 79182008, 954430251, 602976323, 592484618, 256143855, 989657369, 804685402, 856399996, 844358171, 532293942, 658577027, 241781629, 955114336, 966585200, 231364437, 767533823, 762446926, 508818213, 187780727, 502742567, 85948496, 103947540, 437139796, 729573637, 234158838, 68586829, 22254095, 15930440, 51431783, 553021021, 958359755, 573028291, 179371396, 195477680, 286749352, 511544145, 784970705, 350688300, 756301700, 812130766, 650186705, 805423433, 583028705, 995849410, 272881281, 752553877, 646458607, 57417688, 739662354, 440880481, 307234954, 28360882, 462434769, 483725400, 850943312, 552773837, 836868094, 424833269, 639558384, 227540036, 844397974, 896274034, 128987507, 290665890, 578740940, 789792681, 197885744, 129846645, 372595190, 375728623, 911683, 688918083, 139974964, 459267049, 18421380, 876506113, 81906205, 555476977, 780358259, 675717209, 647195908, 202655153, 530662701, 473672139, 766359210, 989023737, 584784054, 826566519, 324942189, 290659120, 295794307, 141046612, 405277678, 86888992, 464318948, 578252688, 920141533, 499405333, 24252540, 378622210, 545384189, 122169335, 396168053, 704366728, 629058788, 772485360, 899486389, 340270898, 47313459, 292804477, 67598255, 253816355, 442513282, 803445407, 563639617, 435292236, 941343147, 750855268, 504715441, 369761127, 432080061, 425602687, 703584956, 992854500, 190795622, 360732446, 234643298, 877608507, 370934643, 400656500, 677724443, 7146938, 521299025, 324131318, 329331221, 131746923, 80852281, 561311471, 443939093, 790292311, 630114882, 209120477, 199451857, 106346960, 823787489, 707085129, 28033782, 218682643, 529694794, 414309712, 72594970, 865871453, 524879205, 398310744, 21088111, 821057707, 758587029, 390688255, 565945693, 243493880, 504149326, 268584120, 495031132, 667482124, 618225210, 18184419, 627465124, 354968448, 818208303, 488408467, 129470154, 146924481, 685453103, 128411855, 327119337, 379800919, 764260830, 494165994, 158474301, 76892675, 193777678, 351931560, 118764068, 999089210, 945333957, 559087732, 938927955, 138646392, 987245249, 928957023, 812459651, 710606704, 99470869, 511929754, 255764838, 341581148, 719543497, 217525126, 857520435, 785499899, 527878380, 631231893, 763191095, 460708361, 213857575, 549229479, 84327408, 618049041, 100830291, 421096502, 284748381, 577827071, 792052678, 110186470, 291988398, 429899108, 804563168, 514333579, 869675837, 371448633, 50659808, 657765777, 680492645, 785245998, 269789661, 326964427, 223254739, 15175768, 714038160, 535982761, 25803084, 500851492, 80467667, 373343287, 557750469, 671421301, 395011836, 501598417, 654587582, 837595032, 16629153, 959968397, 852417948, 131255401, 324575710, 213856186, 437336507, 251821848, 725483378, 600381997, 388422732, 632096243, 799300321, 345686178, 298863794, 499256113, 882144525, 409532154, 258849226, 791845531, 439847736, 187204258, 86505035, 872052576, 217140260, 290566746, 315919082, 68387717, 948364335, 797025066, 861249584, 756133520, 537013180, 200361662, 260412364, 791375534, 435726570, 672554377, 246953364, 641506968, 304983972, 405189433, 427959261, 493103394, 735018566, 221483004, 196588842, 374552873, 920101634, 98082926, 427465045, 795745031, 374930104, 440032534, 513910605, 752521230, 34856177, 869350135, 971495289, 595961749, 704092592, 457404568, 15748882, 193725386, 14844470, 580936893, 507068107, 912365129, 436890271, 922172689, 402120263, 74378002, 33368260, 668422306, 323727531, 722740559, 767669700, 86439921, 568566978, 932850643, 3130590, 599001710, 71613077, 361731633, 826789447, 877466240, 280920568, 880958592, 360612946, 55184619, 807689472, 96680836, 799741815, 383124797, 233381046, 527081265, 52992328, 88106571, 118980503, 302920953, 124249397, 329247453, 416152039, 606472381, 373710466, 32019917, 989500522, 53082631, 109687776, 372685873, 773523175, 741820534, 16048196, 937093116, 910942063, 165217426, 39445185, 636071792, 824812096, 192361150, 424552476, 308826518, 430834691, 654170605, 616562829, 35587297, 967088551, 471605155, 232023195, 997456212, 689004129, 461992381, 901892783, 46107977, 890223219, 336817136, 353457368, 447910073, 925278320, 261992814, 681484574, 229954959, 769990957, 956143984, 486781049, 325514384, 45140201, 415931166, 579243714, 456563969, 752904756, 566998776, 40629278, 284250912, 523294036, 51565467, 923675628, 157351641, 822616966, 62848332, 922445500, 342763524, 92230194, 179563667, 178711937, 954829386, 922839282, 899296442, 945154174, 987709017, 263396138, 722643401, 913067893, 457482755, 158888262, 162700551, 328524288, 661651434, 636077934, 690907851, 728776899, 265430876, 265765800, 418773213, 1576338, 937885892, 338473171, 393384990, 438726943, 598725339, 687867258, 888725866, 248541921, 98421310, 236121651, 935260880, 18071954, 704795112, 646501090, 381621054, 88470089, 888014774, 485491381, 201231522, 601118138, 436975284, 849119367, 864783019, 232470481, 576815039, 728969692, 941638046, 612828139, 549624246, 704619324, 752641414, 738814480, 921438304, 770021664, 763000945, 880052891, 275217941, 626652611, 990591917, 44074744, 729169832, 697648860, 810943519, 432129784, 646747071, 990221317, 870479050, 313475740, 39318157, 270028082, 698884231, 162710607, 695201969, 99694736, 231231931, 18586540, 87193212, 541257121, 168808613, 35994164, 444884687, 767855667, 532348636, 6276832, 949961802, 813670722, 414841018, 920193252, 843177119, 140310757, 406104975, 86846736, 34491085, 645710672, 521005178, 939963767, 677659350, 864045104, 692749218, 494889614, 269591793, 659453723, 357920051, 672412503, 433677695, 200858896, 317018077, 619968075, 694164545, 948703925, 735698358, 29306475, 602306771, 611015226, 991652393, 404511579, 434942240, 401449181, 410292284, 677847674, 813737078, 498252362, 810709403, 411197831, 508189671, 443043530, 411300739, 154284836, 648407090, 242020223, 77134714, 980512749, 206228205, 768145523, 375089101, 853811020, 161879068, 921876877, 592307194, 984812817, 150432220, 884188886, 594534946, 541714735, 960434818, 469889152, 146560467, 401505683, 868805992, 309931691, 774680962, 111510627, 719669249, 398924134, 701507886, 855583850, 259199961, 546247819, 67014355, 588658249, 567934815, 745073520, 613394278, 911784469, 198550698, 681040891, 874489152, 26589394, 382089746, 497737824, 485223760, 248843181, 783735898, 872785099, 131396133, 43845028, 264905164, 745670309, 25837015, 13560437, 359138625, 458801315, 853847614, 16848475, 396329231, 975171999, 475950760, 339177646, 629860870, 625668488, 516865914, 215782369, 131544546, 459005375, 784203485, 824424945, 253700703, 352727156, 605390822, 823016972, 593661088, 110176602, 475904356, 177675330, 258808057, 998581805, 942742728, 971433271, 567816541, 946870105, 994158529, 383538564, 663022811, 984645065, 536803657, 997219701, 41484460, 933548402, 938023834, 784408236, 155838159, 784041033, 14805942, 119727540, 131007124, 262071573, 458351509, 469731003, 42712195, 207086130, 482412970, 522154403, 6356318, 463465575, 388530503, 717884665, 379507680, 580295164, 649757329, 419533676, 565699490, 378181794, 121860154, 471965477, 646057596, 243228846, 359747953, 361299305, 151755022, 684267930, 880366261, 715063885, 119222329, 460833800, 402179189, 308670696, 942135885, 833454175, 505600678, 466060385, 657980793, 843855324, 564832622, 398081140, 41964322, 480208796, 70428952, 964740588, 476731202, 40710331, 969160580, 205524360, 576125176, 225051038, 721156647, 478890395, 600242271, 301208103, 289189015, 534706843, 621531279, 204950545, 746909102, 247576448, 567012412, 690259472, 314732892, 185515214, 719371438, 507274436, 570331683, 480735521, 110538204, 920733063, 436363805, 932421879, 442036396, 682846526, 352066367, 804688738, 564050506, 91634934, 45722019, 166923286, 311085240, 13641403, 766511226, 897120017, 897400536, 262756778, 966879028, 29757389, 680991068, 282281094, 799058886, 267173664, 408438108, 139849065, 550249876, 832096495, 714075207, 951322454, 949651860, 160505247, 196882536, 740087359, 236825861, 62256663, 219438305, 176572754, 836944089, 225865249, 463763283, 361833541, 925696593, 802833129, 501351062, 586731665, 212660937, 12732731, 770916336, 315770007, 798733436, 904118862, 418660827, 565349826, 173622058, 785544047, 811246615, 403177698, 142055357, 356296147, 251742190, 57829589, 613520154, 716926590, 874369888, 637863943, 446420796, 183156385, 631424855, 510954926, 261441493, 701290317, 819062678, 879479885, 497657991, 360426932, 951985540, 535805695, 719442103, 935125085, 755709815, 166907046, 890390903, 159702722, 393765900, 157234890, 603229132, 307845924, 120563513, 325447835, 271817018, 971057308, 273059656, 454964846, 991753015, 520696321, 304382721, 704289277, 229262356, 900287034, 157971473, 101915309, 542900370, 556075880, 755028247, 931020193, 281944531, 551354882, 988080386, 828662157, 87188793, 522304824, 84254, 59110942, 352088307, 974359689, 248167349, 854398398, 131095107, 823225781, 877772435, 629190588, 818641374, 216214522, 370877911, 394658166, 882084523, 233637664, 629639076, 189431060, 147454561, 327894421, 774008834, 453909255, 90868988, 712843287, 478722785, 99364123, 426141337, 923325887, 396943732, 638791518, 491766254, 830194803, 46595973, 545091360, 65813342, 185205105, 970379728, 782267730, 56267570, 603387080, 697465082, 550431813, 872320049, 530435336, 945005530, 150023234, 480607408, 333573040, 574234595, 212866314, 756909333, 897572083, 649300858, 61571, 288157472, 648218770, 216294288, 360941129, 656591287, 623785636, 589186449, 492917177, 639989795, 235138069, 385510773, 66999905, 386309368, 854211913, 164013103, 662783294, 389886372, 810965728, 870954670, 428674236, 371618767, 451238498, 276183029, 604144454, 764439433, 821945682, 506906985, 90459567, 704242429, 806644704, 445051701, 246416000, 98202932, 797568237, 947162270, 238625066, 632980122, 976926857, 329882392, 517737048, 41367405, 513617925, 523199324, 183332737, 7059263, 613555738, 461460182, 381798812, 719592369, 208981074, 570891313, 410004597, 132930502, 596729864, 593668844, 586432253, 891296859, 463673602, 687030174, 502053488, 501058563, 695619949, 220685654, 303103398, 622580924, 608489921, 453004239, 731226483, 109662466, 663325575, 463351348, 435519727, 979837516, 699260201, 684186049, 729648211, 31798812, 360742993, 721362173, 502091590, 141563376, 581306402, 210815728, 720030494, 878233417, 12195681, 251470542, 686659850, 130327138, 865706003, 442147374, 261525265, 389177465, 813035006, 81745688, 262013980, 565000396, 109114889, 87642642, 925225810, 853721359, 226125458, 587839961, 67044421, 867231641, 692003073, 473710794, 749717904, 679839986, 198484309, 4181501, 288692074, 748237176, 368372628, 590166673, 588540613, 516216396, 868850074, 346582545, 740369477, 151180229, 44868232, 624192266, 771093599, 73931506, 180578663, 859026089, 545075189, 842589590, 205585564, 246890632, 567836089, 573759104, 960378672, 775777336, 473521723, 690472187, 360166747, 581013874, 992032647, 541040439, 214145900, 309633023, 879199127, 31105030, 813143336, 750724628, 490435558, 720284471, 449300815, 287242279, 8480058, 153201988, 426599656, 583503764, 362444072, 686017875, 188946130, 434894963, 472949455, 560512961, 271130693, 358673017, 596527314, 632078767, 599254921, 734647387, 321742557, 994411624, 313995466, 326971417, 605225925, 222913297, 356592259, 472542666, 917466068, 217418703, 798924710, 19721464, 684662447, 981560469, 177618438, 976880456, 12952547, 57584096, 570100975, 734225310, 629514656, 728132348, 625810792, 386784581, 728683327, 373168813, 92589293, 652741452, 400781166, 754735602, 807336750, 223223194, 779790286, 488531507, 611079715, 723601258, 675467675, 817552428, 389689684, 745894810, 474454870, 433025524, 732700617, 418248267, 968223333, 503511314, 689044829, 177123631, 173236075, 6357348, 711674634, 863766112, 920094733, 555606884, 835935141, 720011457, 775672100, 934074112, 350073960, 116711743, 21003429, 265903981, 117177046, 584078080, 299060729, 922740268, 129709368, 954115308, 342503111, 793947025, 63994691, 588801093, 301818576, 161834852, 398988276, 17415347, 149725861, 802075258, 877903698, 502080128, 55784887, 461522475, 874465435, 168712303, 622563888, 736146391, 766746189, 512249269, 458983155, 400164828, 294893563, 607395531, 753868247, 269832945, 454766371, 976175081, 634820121, 459263186, 699852178, 514058805, 618890712, 581699745, 738253813, 529728538, 157338104, 415795735, 971376035, 793731245, 457003129, 242621569, 331561448, 715221838, 717025744, 384502795, 602931525, 806851926, 592904390, 512702563, 549221521, 805000435, 784780425, 729622612, 289582458, 832434867, 323763135, 368069000, 124011973, 953843631, 675665969, 676087422, 516968891, 477777251, 340672975, 756182469, 63517784, 939780590, 480991811, 387177035, 645741571, 631334645, 388731452, 926881518, 498825225, 521967148, 742505112, 571668444, 740395525, 336440459, 890150579, 704277527, 5413998, 578223197, 368069564, 919007413, 647428299, 139221942, 911924430, 938093099, 653189670, 968113506, 968656185, 177879129, 97124479, 301497899, 831937261, 26434759, 598067420, 796099969, 19444400, 38544742, 706674787, 571678062, 580338654, 777255211, 570866208, 365140762, 631140643, 584861298, 415060463, 105148343, 459185151, 469142478, 37223895, 226314661, 689021992, 569588472, 758854153, 616852744, 968133037, 121776281, 631742545, 473822640, 633699215, 314062158, 837058256, 35118068, 144706637, 291417762, 614062828, 326336300, 494155545, 871391200, 729321260, 799693718, 609778354, 325855633, 260686146, 361551572, 954476119, 217024298, 374513421, 661642413, 926565651, 899648059, 881094693, 48949623, 867129458, 857301624, 901057813, 529338948, 948496801, 360644438, 416885133, 963621155, 823510972, 660143098, 332253135, 728803053, 188125051, 333237727, 634850283, 611515642, 115589532, 448247091, 405503338, 774147781, 509590351, 150420226, 924995925, 956943391, 474455540, 541644996, 395814722, 570960988, 78950201, 496363073, 300576415, 225168421, 674953472, 156984208, 123714188, 657923149, 402481435, 25956005, 276398367, 234685884, 336580175, 220600221, 698369233, 497043794, 17431535, 229639753, 442278849, 425330417, 43565665, 767252037, 72236097, 398173459, 603479298, 223839729, 593908978, 254756977, 693623860, 857192461, 690328391, 506890925, 655869306, 611825278, 21290649, 408872242, 685387530, 331827711, 100452498, 281900294, 523998112, 612266600, 345937911, 844589956, 616483272, 598665746, 905658710, 597573880, 455655423, 473516320, 23737791, 822332610, 128032233, 909573221, 649916796, 424924731, 941842145, 700250800, 291702053, 725654059, 379342645, 140445589, 620804550, 134942996, 129631672, 697372557, 929925431, 656716679, 297016679, 721434612, 117211969, 796110239, 435612452, 480830605, 887675925, 343695646, 914094735, 416653054, 422161621, 311102968, 586655023, 406705881, 358483488, 313873128, 833206671, 754520459, 526975926, 531321251, 435574110, 619490490, 271237585, 338323336, 448941171, 626799220, 624807643, 668873463, 695492003, 43110996, 303265351, 261408320, 234826573, 960096294, 650087222, 530970032, 468477221, 188744435, 502149524, 510577261, 675939640, 30914605, 825292446, 52724938, 733718130, 49304659, 565239000, 104348019, 725739777, 227318152, 301215804, 958740668, 942399656, 764318607, 255321426, 659950244, 641109609, 194199599, 972954165, 586956570, 744741575, 437669795, 567317050, 586572683, 645612860, 371748932, 782223028, 940324340, 261485688, 316550019, 603316646, 640636186, 590444256, 113696077, 290150330, 909175054, 529369604, 606644765, 637617888, 207857937, 110343582, 425450912, 230574, 860372622, 534914788, 796619977, 111005301, 169936825, 534422266, 281201572, 799270815, 762178325, 309365718, 777411932, 767124802, 964557047, 38889181, 723794379, 64104357, 599655391, 254170490, 905969970, 370683060, 301575082, 684499061, 481088537, 887018666, 150259359, 853274758, 754231031, 380653902, 686457494, 747377772, 783001159, 720531500, 526352710, 85077371, 775470312, 898080974, 458524268, 28045816, 187298295, 191797578, 563911646, 496708363, 924539616, 490353612, 746121379, 316534656, 59006864, 522365872, 599052900, 958340468, 59873562, 288236664, 100790711, 118286805, 456738706, 510574490, 264232590, 78789365, 459618817, 553653248, 454157030, 55051265, 995871522, 525969524, 49938355, 657512793, 768925442, 24604121, 174130856, 924094580, 969255202, 153907277, 774096117, 502746790, 721119876, 431676942, 756687946, 629444931, 930718809, 658613861, 919467070, 367237060, 777357557, 677043287, 882132928, 358472433, 479858272, 191418807, 318827160, 355907658, 419096163, 156418258, 534106342, 445633324, 908440989, 514922020, 378808592, 709972343, 981772905, 304972515, 896084971, 196141005, 800018803, 757829892, 773511033, 716712923, 149089169, 725862253, 7055809, 227254281, 125444225, 193943374, 263180782, 19976697, 127343036, 51746413, 150451988, 604157538, 50948557, 606389388, 33872819, 812561186, 916867277, 105470956, 692197165, 947827177, 156889180, 760220727, 408803808, 457311500, 459504917, 996376722, 275134204, 232076318, 744011217, 307340894, 643720863, 108463403, 574628529, 843796150, 192442336, 222622643, 725212509, 359756923, 101346941, 210722557, 520726651, 706115568, 965691408, 528754872, 87672406, 123808734, 664388081, 796783392, 308752089, 523553826, 987756300, 391220151, 374326499, 302993119, 915936079, 273950121, 208456563, 21077792, 984956920, 787686355, 135750264, 941586591, 61473025, 70498800, 114225153, 332790999, 623487300, 987946391, 743132592, 641304289, 914144369, 745623452, 803471928, 449662086, 427881346, 631435942, 858928161, 317199550, 762189919, 901138727, 760281598, 497723638, 601656121, 294699376, 75165641, 818326057, 572491131, 879980198, 472582559, 998599046, 345636622, 289570536, 73295416, 219134008, 308495495, 940842940, 721503075, 538294344, 396006516, 643982146, 754565063, 873109826, 14271423, 485519319, 728739314, 346107499, 71364255, 708893150, 427550191, 846902023, 967630987, 120043650, 489872219, 958449938, 485648099, 135961179, 637587501, 819899285, 267288227, 718646572, 212953034, 414522369, 682283095, 11521432, 832887741, 267049060, 552737158, 139913361, 772431914, 64960637, 625041865, 564562561, 832952794, 506776163, 876961689, 192883421, 806091355, 597958058, 269323367, 376251114, 242431827, 997571306, 208391800, 553690299, 468179077, 551053318, 618751040, 33724323, 20006027, 477399618, 281382955, 639067311, 41435464, 600561961, 991821654, 890686240, 227151899, 805274617, 167465688, 287147871, 184228114, 990114884, 628072440, 331463490, 695951730, 808574383, 249338788, 870532020, 634106244, 65104780, 294693784, 975749354, 580446421, 752460429, 200432158, 656813595, 192281656, 27489142, 970041248, 537886947, 701768476, 646996378, 134745139, 68698918, 344585018, 916873532, 514376046, 11924269, 470131589, 467650526, 322044222, 601140844, 941343857, 438632667, 208907282, 337594500, 133395032, 195637782, 494477012, 975110177, 314830646, 587987846, 420179697, 631304745, 245068202, 385998416, 653572485, 82577556, 622732660, 625946166, 42686876, 226594442, 350189472, 671139374, 647721840, 272506906, 777334064, 736824056, 103537791, 406657099, 596809381, 681957336, 168164259, 613761085, 365527704, 166820819, 554223040, 662863241, 659654980, 260636256, 980137623, 187666908, 908793859, 313196685, 754226272, 182888474, 906408347, 278914234, 661360311, 661667676, 370174101, 890070922, 485711520, 140114035, 472008099, 141946575, 92567460, 777171321, 584192173, 400619000, 710696546, 538718544, 507146054, 17533872, 581884106, 750741274, 218214494, 518834477, 108600445, 856231017, 787795017, 95345115, 481452197, 434586076, 130249803, 75749207, 53665629, 579164229, 572061415, 561105561, 859229549, 821785402, 552450267, 35597691, 49748551, 691131691, 1376032, 361866012, 264263656, 391735381, 629656325, 523467733, 255571079, 599312478, 427677472, 17076935, 111310188, 182971072, 390863150, 333960559, 738448158, 63685451, 56159336, 753581295, 119180776, 439610009, 833605285, 740218373, 457232902, 895364601, 244027996, 106796056, 687403342, 110900108, 930836863, 454339755, 666950724, 943427166, 236196867, 742599799, 87900417, 621073581, 196176216, 334647359, 523505096, 863203609, 896362437, 100744166, 860180281, 845522480, 388141905, 268978876, 604014381, 750849200, 61313177, 285788189, 744492783, 692642477, 394808274, 572930954, 767249767, 644077056, 767287085, 544693393, 103784904, 775073626, 232821921, 221794530, 214777981, 929086005, 194456891, 701017527, 656621118, 244389941, 586770854, 617847973, 147504104, 995335751, 200297442, 862236020, 654288459, 445910413, 446349326, 849938081, 784562654, 698613764, 238450924, 72249165, 453749583, 377683043, 925672916, 15717760, 924089846, 131039767, 791217666, 787014816, 775045947, 326221990, 419552967, 601048147, 328673485, 386398010, 23724706, 302798724, 306920836, 853847371, 563299544, 850904809, 643065971, 634746882, 811606998, 256630949, 214139753, 365050765, 564573603, 528932898, 747743103, 948001159, 906327986, 573109875, 385495456, 582535272, 765646406, 904840917, 792851117, 833826440, 156253257, 601063816, 903846691, 64659310, 924578097, 392689315, 16614200, 659060067, 828844849, 377920254, 262041256, 778437227, 891575230, 701602004, 750142742, 724619567, 596103844, 139693575, 714659598, 587441516, 227868953, 392658342, 145541296, 693626285, 559601543, 644969301, 919489427, 668029785, 646236006, 727770301, 235409156, 884010067, 676560579, 992458187, 774447479, 607721461, 200521544, 956897985, 966621554, 685631321, 312946023, 467320266, 477074259, 738927293, 784404657, 218348297, 736492627, 554971208, 244288734, 94541894, 98859813, 788493117, 379036596, 37621436, 329404188, 837837791, 3888221, 43159758, 236058606, 384593342, 560400320, 186264922, 903999613, 446800232, 772060555, 114971722, 413283595, 698887468, 677772075, 749759115, 29458671, 156959709, 939884638, 358851866, 686326644, 604764689, 815808204, 192247509, 374754074, 304522445, 388715243, 726488012, 399798611, 507448151, 58575830, 406037377, 207415667, 712945600, 79173660, 340461792, 359987541, 103882048, 642170987, 324918583, 454438673, 949950952, 662946492, 334158183, 537365782, 220698976, 617747150, 894612502, 339024119, 995942891, 973376113, 293925360, 942787967, 84649416, 618965587, 931491969, 985376020, 457643006, 95609026, 553061684, 992453696, 966422393, 729268957, 569944510, 1487475, 482463415, 566617560, 18822181, 783107919, 101102225, 937583078, 485770450, 287313452, 768628082, 257522832, 480522648, 965560947, 867516455, 62491436, 474976889, 442378880, 506390858, 413731435, 910059588, 521174238, 596442601, 913984409, 379143386, 248103724, 665559760, 511179637, 53199802, 153534910, 635334637, 704717213, 754161315, 321440950, 923417378, 663856586, 226658085, 81718204, 252352160, 900946431, 600791645, 187256327, 894271970, 84510726, 802266016, 592888758, 933489022, 370014906, 484596612, 321438025, 638949510, 864689087, 257885664, 381882271, 720986536, 455601818, 742790888, 691731024, 740248766, 38237551, 106322294, 487545250, 650942574, 561099799, 345523065, 312009789, 340465922, 14132352, 238206673, 980522808, 645352512, 478021572, 346305292, 170506936, 574028405, 199158396, 715073013, 360293868, 580821241, 322782210, 494313919, 199614477, 416917886, 927845467, 291004347, 47653694, 555037952, 360377115, 293627514, 586188649, 43790661, 790615301, 795558887, 668908681, 506866611, 141079163, 929661526, 500246265, 261975070, 667628248, 845359546, 421277801, 120588416, 738701087, 420100143, 643199117, 61009228, 126556743, 451982993, 116671490, 61614328, 195897545, 554207255, 632902650, 117518608, 128474154, 542686029, 424420707, 587703653, 971823275, 669962133, 368029809, 976176223, 387850508, 260781035, 396084578, 961095478, 65259700, 732071279, 302441886, 568713775, 464558794, 363357300, 521419246, 863084537, 134986988, 260206987, 970527233, 11727144, 672218238, 638274038, 740961936, 693097785, 185393186, 227611651, 456886286, 766175030, 273415726, 377151699, 515463559, 38255211, 851036035, 16606529, 319338661, 239409486, 12093599, 554897406, 883647303, 960171361, 388266996, 921543222, 319047489, 293258269, 652080792, 896377745, 648654072, 689539500, 83647882, 773508444, 722766880, 131209114, 945280269, 890925069, 50282148, 551543532, 284959248, 41522369, 366071497, 556274191, 402219274, 939961832, 733150128, 323159432, 826009353, 917969861, 247861969, 744930537, 79085091, 515541721, 624858643, 801021562, 987737462, 647118155, 269291403, 500092266, 545786145, 558694433, 713389167, 159330580, 856297550, 863182513, 276803406, 508187085, 491564297, 760670317, 135703079, 669439718, 974294085, 601715105, 889040201, 100687470, 653818605, 500433515, 776091019, 475804261, 779065506, 23934904, 531120789, 841960120, 728625531, 43856763, 9824339, 19664813, 829781193, 10847603, 222793492, 20516084, 894068846, 187818337, 107924899, 641882891, 49950630, 716894198, 976249589, 640584171, 466364685, 990571001, 262226137, 446885791, 172156541, 769933792, 760455767, 435660153, 697173979, 610318234, 826717192, 946746935, 395547703, 560196448, 128431131, 534863883, 538998446, 322843215, 343782809, 834277128, 781125649, 242248487, 983570662, 145121669, 415109266, 243862922, 629520199, 683955231, 12987802, 815483950, 573358966, 967227618, 776933048, 285832039, 794662841, 423401647, 565489912, 638414765, 293229273, 471913939, 692309576, 412405068, 11039151, 844335697, 394591960, 582836464, 277111613, 47472643, 336612157, 333708235, 48613435, 942793741, 263297566, 947545845, 427371943, 211081343, 856784042, 610962732, 781965487, 789293898, 122171194, 304072705, 34979789, 492680955, 226414052, 503772679, 572125477, 301954812, 423059718, 935839072, 206578229, 47700270, 550880447, 816055337, 302523328, 405861895, 602327892, 109159180, 971615675, 387388106, 53022366, 831623844, 659380882, 924430613, 755239249, 523138266, 399537996, 479233584, 565478206, 529331479, 283529524, 281639901, 338406608, 118765589, 877020799, 58286088, 775865052, 734698148, 136857409, 466957914, 622686096, 203401602, 619080375, 981891243, 859826589, 827492713, 402521449, 948621803, 256506091, 327277211, 371913448, 740447580, 344028185, 655119772, 519196555, 15778229, 137006473, 167267315, 515531554, 55647370, 701839025, 97525772, 798758290, 781807514, 656971233, 539950126, 86295108, 563271629, 573189573, 927191500, 700148372, 692376142, 3373064, 104354078, 184011785, 85559397, 710473596, 290505220, 990652767, 729115430, 1236767, 104354743, 932116136, 725633873, 791982823, 793991628, 64511258, 164439907, 781119716, 7811670, 320157356, 914642378, 265648533, 168264846, 422571762, 471513862, 333177471, 982805694, 768569801, 747191144, 888800685, 904576263, 629829875, 586171186, 26592980, 190851836, 468706432, 587850600, 836731794, 760590872, 636940484, 991450356, 462217254, 932010093, 32664985, 535486665, 68461269, 39790584, 971754888, 84374011, 258834164, 585911115, 421136181, 764435357, 688528199, 138110279, 955212257, 148185724, 237156407, 175219956, 613817944, 807292124, 670418533, 222767135, 219234231, 160607945, 57883132, 164863512, 443421120, 104647620, 933367097, 675463861, 48369117, 133973301, 426266505, 529497674, 470881152, 342685051, 953776485, 935839226, 414133842, 891693909, 827356027, 99934021, 649267377, 316494311, 344164362, 450158890, 137214177, 272927230, 297748603, 978157941, 616349274, 234479186, 727122966, 617452149, 159081591, 294358993, 88761297, 3767739, 252142227, 47294701, 571130276, 564199324, 518293801, 152502654, 366078133, 871723386, 907169390, 631500894, 173541138, 885404135, 533533648, 673275601, 791645241, 377825695, 360564861, 767364006, 874696419, 301530637, 255574356, 287367235, 543865936, 201236576, 349667522, 742596149, 949673253, 520811011, 224838838, 30058202, 927139327, 230150788, 98140810, 939581651, 425241974, 940799306, 16769442, 99096251, 933826976, 471812033, 779726502, 799402791, 933228630, 415502914, 300576024, 331687988, 468910955, 675382922, 948528514, 432564692, 958699401, 69111995, 665504139, 65020497, 845291454, 95396129, 491659398, 961723124, 948859161, 44082104, 228976690, 838571737, 190159464, 184237137, 238386159, 24393826, 270794893, 232051895, 543880244, 175343057, 875266705, 669186362, 388775289, 829987300, 686019560, 436059276, 447233144, 958448980, 958195448, 232980344, 342455883, 127548266, 99132916, 540301464, 551434647, 520624692, 246495068, 452366614, 113033049, 677990314, 665902840, 676532963, 637440654, 45217252, 24438588, 674857309, 251173552, 475278871, 301534732, 269791244, 671958301, 827890166, 557744083, 91583164, 231898869, 603778274, 658810153, 672424744, 598300585, 990608047, 587367737, 648357940, 909387516, 853176920, 382155278, 425670403, 518501885, 406715373, 154008931, 60144800, 396323374, 691151570, 512992646, 680371210, 840218795, 959838554, 878497807, 613526859, 9535882, 515750215, 941668820, 49856001, 643647764, 282560414, 432420781, 238814035, 159952894, 265729097, 291867846, 264176448, 541352168, 811020051, 217973048, 628341219, 837935502, 570426533, 738850604, 845192616, 289983539, 42369064, 752659257, 550957475, 336358131, 311291195, 154752180, 643080806, 493950247, 582240376, 628809266, 188023484, 781166639, 150888696, 49511103, 682656639, 233968451, 89547333, 127197094, 175147124, 877092870, 667412140, 393048165, 826162790, 151165384, 246739648, 116644930, 525167361, 604596640, 492868794, 328247885, 657465162, 440021035, 153863500, 340298868, 107939784, 113508918, 842208765, 874044924, 567505296, 129089573, 790903639, 591108496, 664386230, 512587223, 874800425, 50016386, 556446247, 134565766, 651304429, 551869909, 488013400, 374686550, 841836090, 332200238, 252160415, 437243282, 492349443, 163399194, 800331343, 640832963, 107889919, 647233122, 612861352, 41081854, 210274071, 283699592, 878107135, 69659331, 910453816, 458996387, 187260032, 43323936, 129571733, 382487412, 161230915, 274982761, 83187454, 401255816, 590765056, 537131329, 722783683, 819327452, 735254151, 882948429, 512222314, 596403741, 50291672, 478329164, 735253994, 834667876, 18859759, 599368896, 23006711, 136543923, 911126452, 672011075, 225385932, 539870058, 2568050, 842023185, 837400299, 18260416, 980929295, 271853743, 830976680, 220822858, 19463998, 238795882, 543658726, 871423010, 825526243, 661832809, 229746004, 129819657, 958268840, 715473356, 839828102, 992735523, 358680465, 727882305, 790424421, 904489755, 72154003, 926446056, 248658836, 392026790, 924591230, 258518170, 521161626, 136619616, 128439710, 167763841, 51186291, 308103745, 576874324, 516596452, 912609937, 972491223, 863487300, 408573368, 70970987, 383430893, 765201353, 813365543, 841893841, 819949636, 672228713, 554567430, 203622247, 419168846, 162059303, 476228889, 992837125, 756286410, 949764606, 91487355, 265674035, 792415421, 347713673, 727712318, 943322383, 617611245, 657782062, 521092748, 629970385, 157425917, 253972171, 148891215, 97605603, 845927808, 613299271, 604944773, 158044856, 932656314, 786576595, 938603621, 777939087, 268972340, 683043584, 259238125, 599758661, 787256684, 217268783, 839022753, 165569860, 804309533, 737002986, 18557565, 533496022, 7763359, 456481679, 344960179, 268479114, 937463775, 929608604, 663839961, 954727451, 422538700, 985016458, 370828619, 814230797, 422034506, 123998601, 454829643, 631883998, 807359410, 768709819, 289338290, 43108126, 819318302, 97134204, 955715090, 259843354, 499005203, 360931953, 250926911, 613981250, 595186253, 912190259, 308411860, 610250139, 580635406, 684662131, 599019936, 674103703, 636354250, 198499612, 602932185, 726886774, 172153379, 311693767, 274644045, 159153632, 697417668, 251805453, 684133797, 551636598, 874882427, 988143269, 500286952, 398371548, 322940445, 47270528, 201898878, 365599505, 500011448, 77078069, 475789885, 751675791, 281098140, 192774159, 819635835, 121265719, 825929081, 377676931, 185106450, 713938121, 335639206, 893377823, 635795413, 546982930, 523381751, 291412483, 533243073, 322342020, 96213643, 692653081, 274697030, 757761443, 451857819, 634913379, 277234523, 201716471, 313054246, 548041065, 352483609, 443952108, 178448339, 735138890, 781154992, 210048368, 818617830, 201659279, 980718070, 52063132, 846543403, 703693834, 406181521, 102100814, 169799763, 717610697, 357465158, 775026389, 928478295, 412060672, 45724248, 864631786, 780029796, 587785899, 684740765, 193563126, 150740822, 474677798, 545716806, 139930731, 618220996, 417142429, 85140854, 413243357, 69587310, 119893987, 680452199, 174351548, 70215934, 502621392, 8881304, 456510036, 737898371, 893629067, 774774801, 824868113, 835991326, 966956386, 832388375, 61214396, 162924693, 926584931, 430357375, 38840972, 559556855, 97767182, 16758066, 104114696, 983610455, 54170089, 785551426, 647470082, 614556482, 223397335, 739245852, 295911581, 981347470, 162672368, 506001525, 827339804, 440010524, 941733787, 756000751, 104122781, 804455289, 772985932, 69149667, 18457965, 4296520, 362318743, 340837389, 495404100, 506382740, 158810882, 417647862, 706275439, 451328123, 883572848, 780334530, 652673285, 455422712, 248406656, 180319367, 798826353, 394024358, 969497641, 787720492, 999297765, 485764782, 219023910, 457605050, 428982767, 410474835, 971494097, 653623400, 246042227, 35822849, 219881352, 28825944, 263054708, 529928453, 478725454, 336043603, 376808633, 399642954, 444323322, 75180120, 454694725, 128007981, 887645370, 433316870, 874571951, 42940262, 150689540, 542783077, 752150898, 529294787, 725406428, 560697603, 500373273, 401757064, 198797718, 808668826, 433036244, 280791436, 467903218, 823422095, 1109515, 117648088, 956320564, 892164946] 479617725))
+
+test7 :: Test
+test7 = TestCase (assertEqual "for (countGood [517941044, 229380073, 103836370, 344819678, 233695574, 318502540, 142803802, 102355502, 501181094, 29697741, 552840508, 804199286, 32621082, 152263863, 627628942, 985216972, 594021418, 128193036, 311837886, 86593152, 630633829, 601579890, 249136541, 918722655, 330987735, 976288276, 998683988, 990129392, 507610086, 238819662, 781091154, 779698874, 807957786, 245765103, 850045560, 529256851, 337101010, 434328670, 404826293, 2244465, 269194486, 424415744, 382895468, 346387097, 611084214, 901557584, 559174989, 149314435, 842059658, 828568332, 130871115, 688967881, 477349760, 215412277, 955557200, 780794613, 754277039, 608488880, 973506471, 313665972, 635099126, 379948822, 414841866, 234685068, 545458705, 407539502, 276408618, 302199301, 711708581, 674198792, 609433579, 853440843, 108913433, 4845978, 350512141, 360832258, 993467473, 316259931, 361077266, 170240680, 271995674, 808967557, 620615086, 184695100, 437202875, 229849511, 912979240, 309612351, 605683310, 570517367, 733267668, 902832713, 607648938, 859276116, 939844049, 294478843, 685456484, 438193164, 653285813, 45133845, 457267536, 376360359, 566423500, 605108921, 633340433, 82675912, 773912134, 48344290, 615326359, 857719619, 508114993, 291705768, 318914100, 72890507, 259051840, 113584467, 519349245, 398418435, 932400817, 290653997, 902384377, 62267883, 800189947, 28232789, 458869112, 380647621, 474730235, 724441715, 741984959, 607932830, 417905815, 546586515, 927035547, 797988599, 945398883, 138928471, 866803343, 283749581, 961442165, 924535969, 786779517, 825634053, 494897817, 250639984, 682669290, 227206204, 578320582, 343605245, 692645021, 979669420, 386540353, 161313172, 457172882, 566259113, 855351600, 920233623, 475846895, 115904727, 475223253, 712604774, 277748257, 561069675, 857178285, 736993801, 239412716, 656602110, 216275731, 450683978, 759774709, 473121227, 36544013, 965856737, 936003352, 512430080, 562654618, 81298953, 986611089, 799943212, 696880098, 271456495, 608442203, 39326121, 848991672, 409350428, 741911610, 829732488, 602481023, 673349070, 890484532, 282597677, 963813618, 303956777, 868404281, 429829273, 959667437, 434097206, 400453780, 165875823, 950209811, 113493839, 475904207, 335246212, 951870441, 885777667, 197976750, 561473033, 765372459, 546926460, 818920755, 998703583, 554882009, 41213175, 659436981, 255324023, 788038556, 457970021, 388988912, 451208005, 542025643, 342837823, 173530108, 538590729, 763913205, 140893166, 523378129, 559850251, 924321783, 397355260, 780989399, 709489813, 229489241, 963291121, 524383815, 66617311, 588965393, 596225477, 272022624, 39843684, 624720443, 981539921, 187958832, 346948102, 660938103, 152475754, 131851577, 144385374, 864464199, 790637915, 130812162, 904578269, 502176266, 595240703, 347127575, 634499930, 905434469, 570318651, 693524173, 949351405, 915254686, 824775720, 261457901, 752153357, 23548031, 760919491, 843319069, 98581374, 495272919, 279811345, 120168983, 445963177, 343802585, 825846692, 42807990, 871257782, 478116680, 284065095, 528634620, 253739677, 55064061, 206238153, 429513200, 242290772, 241887607, 936209280, 21530402, 57534981, 913384166, 57270443, 492256985, 690288856, 789043079, 934924693, 1966657, 433344792, 538325769, 414928743, 956456456, 583693652, 33028777, 890440251, 277068404, 394008611, 262725412, 711013143, 955401461, 151303777, 295214406, 239532163, 158565224, 139358428, 591328279, 400481282, 739425572, 123080749, 181435293, 215644925, 49225799, 845827013, 444718858, 493621306, 548698881, 360310067, 19855834, 681509939, 555551064, 771651263, 29678001, 68337557, 180037547, 237728565, 401688672, 55753122, 249723875, 608002994, 902852266, 415164495, 67002245, 367141034, 243873968, 969790293, 429738792, 722887611, 500586055, 965280505, 29973186, 485885059, 166498446, 281096416, 983387044, 750312628, 278637709, 626794448, 850202304, 435717501, 482268193, 384073717, 42223020, 284767768, 728244264, 359638938, 998423105, 834578864, 681117118, 468268563, 241168975, 509278113, 672494443, 814545202, 89403837, 184270258, 688609558, 627191891, 118663605, 909514607, 929399229, 791028233, 901957962, 805293683, 729690342, 83488820, 737806256, 324720188, 148975294, 817798189, 238759200, 555736830, 643810047, 939214620, 745457784, 348984080, 910034584, 81271895, 416702911, 904723959, 419435444, 923338087, 529547778, 976774537, 969533989, 54413981, 412985574, 545775355, 714960900, 423192073, 205061086, 296448996, 586354773, 971675148, 141686572, 102502505, 205560506, 349511226, 333964575, 983560392, 416758774, 144918800, 638429401, 540016005, 249474130, 515091634, 863482062, 140512011, 731212175, 798308249, 188703087, 706667163, 974655013, 690088741, 69719111, 847579255, 953522799, 791298717, 92651937, 728445850, 706232361, 416338082, 721980026, 756819320, 191048990, 463509496, 571451715, 353141261, 677056956, 604562763, 224211742, 330172192, 377298719, 641150233, 141745019, 643502389, 934001197, 442790814, 413156857, 900288342, 798846076, 673594225, 355193139, 729718367, 391936538, 83577163, 41001236, 971213100, 901170435, 56293592, 745889632, 850650609, 276995736, 671740510, 207501876, 905382527, 657483421, 572953896, 99342142, 596570445, 330918431, 82941032, 871223891, 881038975, 712682643, 747723041, 360050721, 180466050, 762718170, 956746628, 412715169, 701818276, 961185343, 903941998, 811354248, 64925646, 432071575, 852293745, 785410550, 379396983, 389544708, 946390222, 405208572, 872499694, 1777583, 845782252, 92227647, 794702229, 1049413, 218381166, 535615850, 703851829, 115360146, 891814882, 508609153, 525225501, 542971332, 951727966, 183190730, 165239769, 262706844, 262918458, 888227605, 430728384, 270406079, 60380100, 578056866, 49758563, 512256137, 785288255, 885164353, 344342952, 517796029, 297018139, 448348039, 800908183, 312770393, 622015776, 752787461, 154201686, 277689704, 317516937, 530536451, 989484237, 529923339, 564680590, 144104688, 531774947, 459358378, 751734679, 196502942, 865107156, 217131725, 138924819, 37065792, 888852305, 764825896, 27904870, 192514179, 286674618, 823244331, 906054232, 261894533, 228729036, 691007760, 768076138, 23923193, 633659403, 960514902, 272228640, 5417814, 994187184, 772597428, 690541517, 731968834, 578719860, 743100414, 879593205, 226798509, 710739218, 786697532, 550280518, 837898567, 50785969, 678818353, 234826760, 305846, 607718464, 723879374, 135130156, 949853925, 329165301, 27093896, 809129349, 564270256, 679059829, 305045026, 154378029, 324302900, 678226482, 591063102, 812767185, 676421149, 469556819, 843736807, 902375758, 119004728, 728889009, 828917068, 815081078, 57964391, 461881484, 141884691, 11766180, 72745349, 923790066, 240326540, 533494463, 816871560, 981958408, 809309521, 632304477, 313824604, 686140140, 265574632, 159342404, 689421137, 578265235, 83292225, 942873614, 708552091, 559170677, 73507266, 897453546, 494367766, 835059128, 533946906, 771232436, 941720249, 753753520, 917033904, 724730524, 413424435, 598495794, 755289232, 303289810, 988362528, 64557717, 404009513, 593505960, 313308051, 476554790, 943122476, 972029151, 927225727, 437691588, 454457578, 567695386, 469579292, 697436689, 820868985, 891276059, 74131304, 21862428, 670266270, 320896055, 288906931, 43918576, 746175292, 330473929, 549346021, 251067121, 916518994, 647824273, 764939468, 726043893, 142892103, 539919136, 451429625, 927992479, 153363515, 454787712, 793505662, 731838472, 205081935, 759492753, 461668099, 457822207, 343690117, 817379381, 993241546, 157136774, 162927659, 933544408, 957855493, 262688713, 976918437, 482819153, 552659814, 954986622, 273491818, 524969187, 381207034, 758165457, 33052375, 935204341, 934575668, 718940484, 557418241, 947969767, 177172230, 279964772, 966970940, 675620617, 395483445, 561217360, 96846683, 36884052, 91665045, 885042858, 411384859, 505200283, 33138620, 587081674, 309893963, 324819962, 915159045, 73587732, 617658606, 763470059, 731102725, 876576039, 877117735, 260622944, 614194137, 652820248, 40446815, 106255388, 426883090, 554376318, 181633348, 359608309, 571121312, 399597513, 198422498, 746373705, 827162019, 804601109, 549419538, 86028663, 894119531, 385495786, 998737425, 882267057, 746357252, 250798269, 895558244, 248346459, 620187377, 971577098, 15487468, 365857023, 885700436, 842224500, 920083002, 469582702, 972304508, 306679409, 829239268, 671445193, 409194218, 987807445, 95882127, 41123398, 792974119, 241558971, 634515977, 393964985, 568441236, 409105062, 591514659, 633724935, 238056690, 562328879, 230424429, 835932284, 484557833, 592164756, 196920447, 338336327, 85919822, 882310072, 297839328, 947218198, 30788523, 571839607, 22495712, 177495943, 892964985, 221953314, 980673565, 607921929, 831287435, 812781713, 585051794, 729192243, 223856598, 769636504, 835676457, 811791604, 921993325, 96447671, 360498714, 357173012, 115290824, 293773206, 427344383, 111490543, 68189737, 966602794, 654222265, 156120889, 319718357, 307940227, 949363887, 852070823, 763568685, 870143728, 365049187, 772553172, 631795577, 360673203, 1889278, 648288087, 294346351, 362033192, 897612478, 740265812, 735174589, 820372142, 906537111, 355956489, 824364738, 61422588, 870466760, 214494518, 679294126, 662383292, 545124407, 174526320, 257374547, 363531937, 971720436, 514595088, 746370337, 985322368, 4717234, 446885836, 856144199, 241542273, 464883480, 969244959, 863842875, 257831597, 734378393, 657541642, 125203470, 968853053, 122885018, 201966556, 707602431, 831114369, 158001060, 701722624, 563734894, 858907984, 524924132, 135714935, 727640941, 978491317, 60018121, 327071637, 976315827, 128388484, 715476006, 186616728, 574172672, 11632248, 111737670, 425123445, 467121806, 76902859, 659703484, 590805840, 299519180, 18770163, 870461496, 968149810, 725913660, 860934623, 364366738, 484446505, 412348861, 778998117, 619732721, 141720256, 782904784, 437268023, 868815668, 744956434, 33690006, 88766863, 255106457, 715589169, 123166535, 806926616, 463632317, 338400831, 962786628, 948732595, 91636068, 123383989, 505896934, 590365747, 607904285, 331809578, 226433797, 533394824, 559268167, 975873366, 456189980, 858899646, 945772650, 323910489, 599515410, 658076356, 865241698, 828969924, 912712474, 887807051, 982565443, 226267453, 231187637, 770759175, 325233880, 115272528, 819090397, 735013432, 14917614, 674151510, 51039645, 947460810, 336548326, 332162767, 537321779, 697627856, 748795234, 822842717, 959643316, 615387161, 138685336, 26996525, 534766, 427920342, 447398636, 448721935, 671984215, 34102124, 740500847, 73387652, 539478692, 995481563, 603133586, 221290998, 995638492, 283363769, 813557753, 197936249, 409102331, 898932017, 106530692, 305255310, 77398575, 679066588, 422329787, 75480657, 743426265, 724484288, 532066940, 855173538, 747162461, 741074933, 464945473, 351920279, 556600729, 119165196, 483323641, 535389534, 380932609, 797785136, 97377917, 108441226, 211140780, 989229513, 778171382, 644251380, 854360960, 13720213, 724826524, 68439120, 913684311, 215124761, 306995068, 255574340, 355522791, 289460956, 735444434, 521865912, 422432264, 695171834, 315072407, 434747168, 102237834, 534867995, 896131746, 526736046, 208582053, 217632811, 992195198, 693335212, 828395602, 73690645, 597467422, 204970480, 206967670, 926963161, 173171460, 86804994, 334131695, 824762568, 899885000, 238283698, 243474463, 234550425, 461886649, 183484994, 837770317, 407371919, 704170143, 505739092, 791343647, 330198941, 207071303, 655803095, 652518824, 194902917, 965476419, 939729738, 152382747, 976152434, 62638053, 134914300, 416155455, 372078387, 655851121, 663962205, 715862228, 774405407, 724885717, 872305876, 676189623, 177763574, 438557095, 486605309, 761553459, 403302902, 814411626, 355022102, 131485099, 687486509, 878388655, 345633038, 464323973, 399831630, 44380634, 146002778, 899422754, 574850706, 649812330, 722676342, 874372003, 232854753, 255838073, 149433502, 31639204, 964969732, 339800533, 241559255, 841873899, 215617324, 925566337, 669389115, 635485474, 306997894, 662120709, 877954927, 9973152, 774938215, 302867856, 800540205, 725828071, 231884521, 94501514, 277474105, 807948409, 830267030, 596943406, 473977423, 457485673, 173709075, 199822917, 855754755, 95567003, 862580711, 339334131, 239946147, 185014574, 911516462, 523128100, 688080156, 990315171, 211187103, 447551612, 896226311, 194623100, 597398341, 715377919, 236634940, 945601098, 814138221, 541877435, 882835960, 927955297, 518855667, 602448544, 434829496, 407709212, 853369223, 179731629, 485203645, 85367542, 439972347, 377910328, 261054019, 513658911, 596276969, 949299199, 299121467, 870068505, 850904419, 349632896, 477613040, 841956709, 32842655, 738978837, 526247325, 73955353, 461643761, 164390041, 888623029, 560351822, 484886589, 670537866, 756418866, 188581168, 53860682, 567893971, 97471062, 347285214, 953223340, 962067048, 19752902, 48491040, 883994571, 923470812, 361154321, 564905518, 687785841, 542284487, 65538005, 367897273, 863507261, 853984917, 235039223, 414902579, 905339795, 611567853, 986280387, 735157031, 878881466, 495950029, 300709253, 622085588, 427059134, 598013651, 57637413, 54976415, 339141091, 584666806, 768411525, 528225919, 644690733, 594082898, 210417848, 725295351, 386477314, 126434280, 951231071, 973117472, 392612599, 700757786, 897598912, 230861725, 22003673, 674440342, 94825983, 903197537, 571942928, 487720277, 190318539, 281318021, 475308404, 322242959, 349949006, 276631502, 448787535, 944453304, 643921420, 511272343, 287485397, 434973389, 103131484, 453123526, 683109685, 519094903, 468204233, 338790321, 986497196, 340435669, 321567013, 905820366, 517315593, 736810535, 836948382, 726822040, 254993327, 344869318, 846851471, 812972542, 139438652, 431788859, 650147844, 500740171, 849424101, 285125345, 218895777, 663404859, 469503128, 246691785, 12932861, 613497758, 441343568, 59685213, 146790267, 92885157, 801157784, 199122588, 549248680, 825602675, 678498382, 449899090, 620506338, 465362954, 310269573, 39906771, 879536238, 470220557, 588778737, 973299915, 650010367, 597153692, 943079440, 899309289, 354649921, 180028983, 288847277, 158962449, 424898844, 800687146, 614436424, 408008558, 737862317, 191719064, 529298356, 487092697, 286294604, 628728756, 841561866, 271348296, 832482575, 590475575, 341818404, 855094403, 526866883, 265596632, 884248194, 572524174, 281870055, 774112666, 953439939, 760588861, 252640436, 978875686, 451370806, 543768458, 331285835, 779707462, 804566110, 112835631, 570092541, 124036739, 521002529, 336547905, 58773829, 919346964, 324088080, 690665664, 730895449, 95229480, 191377598, 214735341, 517888080, 214963951, 578942467, 458965079, 554949614, 843196187, 683172561, 15457609, 236598657, 489270737, 887199269, 423895732, 380343143, 231658553, 406975479, 700282607, 991072060, 143761665, 205982259, 30642776, 275375479, 245605564, 766737406, 407851470, 191062190, 525544453, 153780530, 10421766, 140799051, 392928928, 280843058, 821236007, 631333434, 635215453, 248402321, 937788815, 72044985, 890611621, 10147858, 676754560, 345534656, 32559440, 844262575, 471094814, 668380883, 152923508, 864887442, 899147803, 146522142, 619893269, 904063993, 980959299, 17150378, 528214395, 444716040, 990071608, 927389943, 378599249, 446621607, 841972469, 32795226, 722282104, 720261168, 467172106, 246005510, 455378815, 825125912, 457469651, 233738488, 636262416, 988515068, 610880712, 240708682, 464614072, 508121064, 273734715, 724018460, 406248114, 819573316, 389480123, 754423666, 269632111, 484351060, 377506662, 836846918, 334200284, 996755336, 83810651, 508330135, 405635337, 526617590, 47372767, 848216741, 258066641, 158948863, 974101866, 368918931, 118097675, 813438795, 619022760, 486371176, 803576005, 842550323, 743163740, 750240714, 476470279, 11364309, 357570110, 660183537, 541629835, 932447001, 531834079, 960099610, 293174493, 403373460, 899679282, 395704691, 129158990, 425619118, 322278534, 69162083, 854374699, 160790968, 568505992, 375937160, 292226864, 489602891, 592318467, 665874541, 32410786, 541200510, 735175232, 645616187, 950214884, 541284883, 401592703, 231399784, 937313666, 90216720, 228580602, 485555374, 166538342, 265462323, 23756766, 525417941, 701955833, 844324218, 713044453, 445574502, 635154860, 178156544, 247923951, 317993182, 408997205, 430323575, 190753544, 501682675, 507576536, 231724313, 216129339, 276572210, 787047829, 448877830, 350399397, 740251685, 2029556, 125827364, 9720103, 613413502, 662423514, 923025333, 41438773, 732985370, 348679909, 61953944, 964351693, 410153055, 57866157, 966134364, 711537040, 101211651, 257982247, 143578616, 398988814, 552709927, 451018242, 584710128, 924583727, 131558786, 153012350, 137005425, 135912238, 61862659, 8316760, 789510064, 531319985, 151758476, 934330954, 261081578, 456775597, 757866027, 980445506, 767581562, 506218578, 529221351, 83488313, 170479781, 515864736, 566517428, 853956136, 640562823, 837595294, 740226930, 819097646, 188901923, 305840696, 872888504, 261108027, 909240493, 372742861, 905000897, 244161418, 927668965, 916721776, 719840232, 932571658, 210953855, 596632606, 549127667, 361573946, 456148879, 28103745, 644080117, 853679358, 735666210, 617399189, 616553771, 386903702, 309078903, 996612425, 730238287, 250237548, 219650787, 684363436, 899662855, 974059561, 538105865, 396537964, 756632688, 529105993, 196851213, 746691323, 791603510, 961211942, 61143769, 186115353, 648618053, 513560917, 882096103, 88234541, 205840694, 406674654, 311719722, 849857064, 299504283, 749639404, 257264649, 182199771, 396099271, 208873983, 405175777, 875934703, 341655925, 962753860, 822114661, 578819847, 381209260, 266925405, 912737611, 416707475, 612658208, 31803521, 739120346, 578539318, 504071236, 806260420, 285253180, 538009871, 730383202, 332274253, 996086978, 725669422, 439470908, 688128076, 850264051, 605845975, 76867300, 205272873, 724324932, 943070788, 725363719, 676780928, 97266156, 428404864, 943520247, 441515836, 201106961, 36098041, 4739314, 493912644, 832735567, 163481532, 582041783, 170764592, 650221198, 946018612, 322314229, 748571077, 379816572, 586661292, 428006558, 370132161, 802282623, 444248675, 181759840, 351265130, 749121583, 852052034, 725417673, 164285684, 770047162, 334483899, 430362845, 390123182, 870135413, 803584225, 793437067, 824312937, 970146068, 788311136, 543506023, 804301167, 752622039, 540301731, 640017965, 499767210, 843048397, 854089291, 712137856, 88531335, 476199734, 152335167, 956907969, 538971803, 770665917, 190208944, 868352979, 192498771, 443251189, 590147482, 549023396, 248740373, 153209675, 631651963, 773747506, 340955872, 350965671, 92697539, 258451474, 869579626, 326258365, 983455425, 183976154, 648924781, 244890518, 774592863, 31192952, 547129396, 494322110, 456923182, 263883266, 435220227, 420002985, 290307697, 986299954, 87249600, 294350773, 434451708, 508543693, 779211925, 818313330, 707932192, 290469089, 668197130, 900043361, 73035275, 506878982, 252985310, 345295428, 789562656, 287394615, 797451620, 925785767, 792558285, 159977711, 78925352, 993487453, 334177970, 342921094, 511448829, 15850479, 776429566, 433027852, 520831252, 727224928, 691273211, 264928031, 169300263, 83417090, 53288926, 305562350, 885439117, 491111409, 964145974, 639261782, 345535362, 20613281, 614466950, 328868180, 766003555, 255544456, 756740863, 386727787, 748172967, 65815221, 555817059, 95220081, 15853131, 919942678, 863602419, 45544613, 926697787, 860789673, 446891794, 941664860, 744698469, 45025348, 441219268, 140509801, 45336732, 656410701, 242395616, 921269896, 846672053, 429427950, 669496324, 835883336, 278021621, 248465988, 581092471, 775167250, 251539924, 915093262, 542097875, 417291982, 817104046, 478433663, 674094814, 869122582, 446417409, 433630711, 928868810, 448614954, 505643948, 282447173, 695869564, 529581387, 47988822, 639371426, 24777752, 514961251, 93649069, 497893770, 22316839, 137350887, 444335474, 488663110, 986766162, 333978433, 905809792, 187054730, 930825084, 873574930, 176134506, 512099051, 246838058, 656184581, 23252154, 439178962, 15755469, 969389312, 391412123, 152620629, 303968963, 363219254, 287298276, 743640890, 274396361, 713703030, 383468542, 203082923, 595418052, 667770669, 748193089, 92017290, 19659217, 113184924, 208004857, 716355491, 116107415, 337616305, 871079396, 897634781, 100558424, 674189619, 591295890, 306773205, 651004782, 952699771, 142735597, 91390389, 471245802, 820774578, 296208289, 291575718, 294639800, 245714237, 386135540, 5294268, 796335947, 720693962, 957583684, 189972791, 208698220, 171684462, 74297060, 7469724, 859129268, 251397320, 601173843, 390711530, 817822477, 379734590, 243180935, 347927862, 741668655, 559320876, 909820770, 511447022, 796338637, 774371799, 293354888, 522226980, 738335346, 346275787, 737868918, 227879827, 891281094, 74251130, 24927070, 550970274, 63423825, 489209221, 178570911, 612641408, 7422008, 200856837, 189608648, 794916968, 449390510, 878934609, 955832656, 471630374, 91144625, 308824664, 479970041, 210700549, 622641693, 124916219, 553879896, 956028250, 802617161, 236645684, 808178082, 777969925, 733591597, 182245557, 233888318, 939181044, 134595223, 355279242, 999944373, 387919187, 744953800, 821063828, 275084509, 709818802, 333682414, 615537007, 419706286, 818903042, 982048258, 262090312, 177257137, 621449714, 33701540, 602683951, 16452984, 982145135, 394688684, 316606461, 936675536, 708799782, 524603168, 396693413, 986516729, 660723780, 79286277, 572727270, 2726978, 240725203, 162789439, 315240206, 56726029, 116512732, 586698407, 962959964, 140263454, 638553615, 774049295, 672290686, 971317601, 313594448, 449511041, 505142517, 34251915, 75063920, 241481976, 962308364, 443754540, 134385064, 11195150, 163984102, 4740512, 491365924, 203896091, 882164216, 395923652, 495885679, 87821624, 770745437, 391137795, 533274034, 901137904, 996697947, 992062520, 432535533, 12599682, 500649994, 412300859, 735178663, 218888479, 415938128, 571357170, 285727230, 515340697, 164038464, 43533991, 776869848, 249863371, 312161875, 402999224, 895312893, 763569504, 733952035, 846793158, 771129590, 268090959, 787051341, 148336928, 473088661, 197069026, 38229997, 730148584, 297718281, 958736504, 748458521, 594161184, 671721124, 533534159, 950038524, 74756281, 79135860, 319825991, 645331207, 371068393, 695822088, 302270652, 767638409, 688358464, 837868861, 849780734, 962237991, 522558006, 395484758, 682766097, 16361089, 816937412, 611939951, 771498203, 53621569, 291977802, 413357154, 635002443, 195239440, 888726287, 639019404, 495608347, 708070220, 808840523, 724732485, 113975238, 74843776, 124503920, 214391321, 610896627, 692497913, 474725934, 559371529, 97275277, 230836638, 347402227, 245694742, 765378777, 618414039, 753746797, 132968405, 267081447, 779649269, 800771578, 921938820, 409362623, 969828205, 890654565, 395576007, 803703956, 242756250, 270789849, 603119367, 116825181, 343561710, 912692738, 618158550, 608251798, 456437572, 231751207, 31005240, 295249523, 988314356, 462559127, 184808831, 852136864, 694443621, 819461345, 939776453, 315110599, 480273991, 999783923, 253575699, 711589164, 259392032, 859096024, 344587124, 338845850, 643174941, 526973938, 881429444, 647523630, 136080655, 345792269, 670669505, 261953461, 806988588, 243885670, 89074968, 251508045, 123990352, 355717592, 373224070, 350011399, 45148301, 17813173, 164960026, 177159562, 473271673, 303880953, 734332434, 372784867, 16400546, 190003751, 125437115, 188150537, 703131213, 326726922, 452036396, 713697149, 493496752, 681882033, 984853838, 27323121, 157303719, 557053130, 774742937, 463003592, 532121852, 39080311, 525733950, 967257685, 567953936, 358737195, 73273666, 463690716, 193975314, 888463742, 468880215, 706607046, 935760140, 785475617, 776411565, 70836758, 437325962, 772126328, 894284762, 650183427, 270758350, 435376331, 366629299, 957134091, 79119975, 811363375, 75298555, 219172023, 521819137, 776693441, 115826538, 417083191, 816404524, 768678807, 468158489, 611540046, 837202708, 124146330, 638173974, 959833994, 825204655, 225522033, 67138757, 573628640, 818177130, 24416892, 646103445, 282525871, 786904601, 985675157, 410944775, 896948863, 153565371, 109080698, 203284910, 941002385, 148295523, 18528309, 581733580, 923449471, 15437561, 596873007, 547799823, 761818431, 936184776, 563609848, 1308902, 998617150, 94095691, 48982007, 804373653, 352191837, 371809712, 575068048, 886492383, 267247708, 563456277, 734135647, 833266225, 936698277, 91933289, 771727185, 200339196, 306169634, 332934076, 357294183, 822442030, 964102641, 407529302, 371396372, 220226037, 343755268, 954890262, 88747962, 874475836, 194094536, 910803884, 56537510, 102384885, 663183802, 120827874, 578897199, 279997250, 733267979, 174469010, 414424500, 525908301, 725061590, 605172742, 809544525, 139333497, 224771982, 717294498, 512276004, 193885389, 775554451, 105763857, 468754783, 414557985, 882471326, 827221775, 500836905, 638381517, 60475790, 103151579, 469143485, 936544308, 146524581, 81866401, 740101186, 969633949, 325798399, 578522458, 202469898, 235885151, 939507516, 376009849, 767439757, 291384868, 478001368, 615616258, 365282993, 669890695, 467478772, 734273660, 557774538, 170584927, 881747930, 467743870, 442909211, 824224610, 632567989, 657039792, 268578583, 931835391, 403476323, 570772594, 443933013, 272847372, 645732218, 210044015, 742193848, 436340814, 118186002, 582174359, 544720065, 801115746, 777671852, 623558757, 869994653, 428643606, 875194441, 572054508, 183439514, 523025886, 769222341, 190609087, 22739637, 979781033, 485595592, 865280597, 778266911, 9342579, 171241817, 573798180, 238125379, 953304220, 450124162, 98163058, 797252025, 461616112, 667235662, 372042198, 819016394, 385146022, 320767184, 531139172, 735202589, 628464069, 512675241, 771942912, 764277019, 904796809, 711230592, 374357834, 163713171, 145793072, 914399036, 498387216, 691938080, 747795292, 720558281, 101872978, 683289749, 157987221, 660215200, 700944821, 106973117, 304066205, 116254904, 193486252, 459057911, 637392529, 247926939, 225046692, 441379297, 572856727, 341291842, 500520246, 677726802, 780755629, 27326501, 312569409, 674292442, 957432785, 706762126, 307559752, 963344965, 578196513, 38165466, 795634680, 124713744, 77348197, 597564905, 11248521, 19966129, 12904531, 936251698, 477237950, 569752229, 386342691, 239402359, 811201508, 286743747, 810712440, 746477220, 943370251, 28773731, 531432119, 971239789, 856111477, 47535991, 228913436, 985197257, 261769297, 66491843, 783730602, 874641795, 363011645, 690040530, 161776039, 481282672, 993731245, 347330386, 999419656, 761374725, 374898652, 525020419, 689278608, 693498760, 103280479, 495359812, 254281105, 415478985, 286154429, 198788705, 672669508, 18907284, 827300254, 444788721, 946892535, 702506291, 856979387, 616270732, 277808218, 516086014, 293331019, 700120643, 340366773, 768237747, 345892779, 886896310, 94156298, 460091118, 67635884, 111489831, 961638285, 633342594, 487818631, 401882813, 361022353, 4741423, 512093324, 172006304, 264470615, 778821705, 584035285, 218790850, 291807706, 918774413, 284877859, 365149299, 359198909, 61502194, 217102765, 199268424, 132904604, 578176025, 823317120, 31698291, 273871716, 184107416, 628405196, 404809581, 807696550, 900404616, 207273508, 621269746, 82459999, 227083480, 303386118, 804292328, 669513551, 132529845, 351125898, 476009963, 568227391, 125548270, 37450086, 585492516, 549598410, 383935354, 306007563, 736118080, 63358795, 475388118, 432827859, 578163832, 227400522, 545673970, 920560168, 680712023, 904908656, 497855397, 158298627, 153056903, 651279858, 716909531, 150745270, 980106004, 866009884, 541981208, 554582634, 838940931, 168308186, 906877991, 582777507, 610986307, 404051157, 452808940, 947904766, 547076732, 56365405, 416857196, 704678172, 98406193, 923382135, 525205003, 421352948, 33182597, 341931115, 736047393, 875828447, 707611339, 781310867, 671543651, 621336815, 763850320, 379647931, 87953949, 239208326, 425240153, 762601614, 977071013, 274243585, 188688423, 753192009, 95254331, 565184248, 533998256, 664776200, 259327873, 15315868, 509194929, 708020909, 903480374, 577885984, 325795035, 280684933, 537823941, 598961854, 338755630, 37637137, 672650863, 471780445, 812757869, 681240043, 665725229, 102174080, 42292607, 377499880, 540012138, 129226408, 40154655, 774054050, 381466278, 350898260, 366733710, 344226188, 499687266, 482230356, 912063005, 277557616, 61656313, 859915225, 992495038, 413870396, 612231986, 722729598, 50638139, 675562891, 986316500, 251241396, 876878276, 218404821, 525302962, 125367725, 329163963, 741403165, 992040021, 365660473, 125739701, 997968259, 782440029, 774526571, 435664423, 314157187, 290117539, 13952527, 830435777, 950001601, 660036508, 467212272, 860958686, 452520275, 691386949, 456654675, 261332633, 919161872, 809609105, 680062353, 367029625, 49542602, 401103159, 673264224, 504636814, 843417052, 734449567, 990865679, 207367628, 538261839, 456077462, 198919878, 739090900, 869918371, 656163239, 952244540, 911418500, 642080723, 350498977, 244782485, 910241605, 799239451, 501632167, 409555123, 144400747, 844753750, 283785929, 4173308, 323357722, 823479867, 324965153, 793243293, 276691601, 808438059, 3281846, 875349389, 730308192, 150810011, 387226065, 506658274, 288715654, 323110351, 146950497, 648779082, 180159557, 296087035, 296271878, 506948932, 567197614, 452463299, 174597069, 33292814, 585649597, 91474573, 138020769, 482819081, 432865626, 321197628, 2886362, 908035030, 483823609, 462850633, 101153297, 639894833, 425596445, 295327255, 505262432, 944309212, 48681306, 48718169, 335237280, 931923963, 962351135, 214482413, 812411434, 838847499, 992776077, 219282560, 454265805, 168485632, 896727156, 441156067, 273904320, 126808874, 281599382, 155104785, 200127013, 284684230, 139724142, 513540990, 839065980, 782174405, 44228578, 613209503, 379522442, 219560983, 211186397, 647134044, 847868491, 684301397, 296202598, 871065193, 733731867, 438701577, 678411429, 475023110, 119364071, 764919230, 347210024, 87019795, 744052329, 392976664, 271883482, 306165651, 805909638, 534299423, 874841274, 6828585, 634589078, 667308915, 279813852, 704241054, 652227408, 1614326, 739079039, 636522289, 556286652, 738283406, 265181198, 160984179, 698859532, 403698731, 715669230, 970996642, 188534277, 408897714, 812666454, 847574147, 457814403, 275443128, 38185239, 827757202, 927311241, 982636682, 167001997, 874099600, 210040637, 613235210, 269283093, 167699395, 607459984, 298775704, 365541270, 72434761, 351029812, 806803507, 181625451, 625650379, 188156669, 858954681, 471249059, 13466540, 428284661, 763089680, 325386220, 614604084, 721509160, 722822172, 973161288, 545012456, 190730320, 383852758, 398207300, 542539145, 928760372, 319268649, 915628894, 997865339, 182679674, 718448037, 136147762, 47145648, 302092280, 93367414, 949792306, 563942879, 781410385, 120752464, 992840124, 145718807, 726623406, 177506726, 731579636, 565252491, 264693739, 503673858, 109310659, 777072993, 319112990, 333880705, 996119154, 778022976, 970385538, 230947093, 909431712, 379002431, 643416566, 359451875, 486968759, 123825809, 206635333, 271883387, 950440731, 346347980, 262377791, 593295679, 710940709, 882391157, 711428011, 250356985, 736631543, 10356909, 103899879, 15813471, 618002643, 69414573, 800005026, 328139084, 794229752, 422311852, 131027644, 929371485, 797038235, 46322499, 801433840, 6558369, 667293686, 659137526, 588985971, 180848056, 609460268, 142573644, 813458828, 214596344, 144550552, 631266129, 424363514, 407743670, 952172089, 834626903, 423688998, 895534681, 491845087, 709808919, 12459090, 992377737, 343258527, 391634415, 278311470, 300081844, 51270685, 629104085, 54482902, 78551068, 584964749, 699084490, 576068982, 19058576, 409656022, 197127468, 473481684, 731955272, 471765979, 801762552, 952737855, 979816431, 633605975, 581445995, 505851196, 395823780, 246785367, 503652083, 508637724, 725383239, 993435550, 538731525, 956957156, 552708661, 924850014, 462853336, 444439742, 87446781, 727458445, 38320020, 36671746, 115204844, 202238406, 347292502, 171180421, 386642362, 500456810, 934113742, 854435605, 777705164, 576520296, 260112655, 905629567, 812491290, 753331074, 903022037, 652836948, 31104681, 629940819, 166897397, 886636029, 493110497, 304664285, 105779413, 219044877, 631119367, 191383959, 828445065, 857831740, 689421535, 447225042, 227805061, 587504462, 805211232, 148768865, 372462264, 219677492, 960950965, 829993546, 528964310, 320154993, 947011351, 369774587, 66812485, 732518214, 57593619, 911587584, 742997392, 386921474, 573370516, 728697045, 854186016, 638574540, 236661121, 476089652, 266026356, 397796153, 332537293, 678377484, 284386469, 340915401, 941373972, 40025987, 639009437, 603909736, 38933994, 586168782, 113257000, 203508612, 860880800, 500534748, 424614870, 968467236, 770195745, 95234854, 91442004, 157629335, 739885045, 119326123, 288360126, 901452812, 972195734, 981475532, 851036124, 121955998, 778696465, 61453922, 914464927, 714216008, 73604002, 885147651, 300904332, 21661649, 722704185, 235467674, 54560071, 804973502, 10450977, 846797643, 686915502, 561480489, 494846242, 303774905, 130965248, 532715038, 732648768, 901436768, 43150797, 935639404, 478782774, 257836868, 764434247, 761544994, 433477780, 849978003, 457922964, 810813028, 658240779, 584956513, 65790954, 219854634, 904617536, 708107373, 667840074, 31614874, 615187792, 316076381, 976010563, 511733268, 117010101, 1292606, 560813703, 942276056, 698079328, 594511896, 119300251, 154950650, 945850289, 504263788, 205008557, 377489257, 667256472, 175034649, 152879964, 251736818, 112656014, 391202766, 415723578, 905649447, 118948527, 550562270, 480965627, 375678388, 131080362, 250901869, 935100903, 51846293, 619945275, 250809867, 480017684, 828634136, 529520506, 475677776, 398375741, 864889281, 494606168, 442834514, 466647942, 472862711, 456188664, 281911103, 951213216, 318087863, 233359795, 610673749, 420165678, 758714910, 346488071, 752674169, 162943617, 154565109, 370746914, 173633915, 909033317, 28450764, 55670036, 668516678, 612769868, 583213979, 449473498, 931259482, 693641491, 231755199, 939188441, 653921879, 65011084, 52895272, 803729326, 9586877, 206603123, 678832142, 700552707, 569213252, 381267935, 861455641, 618832427, 116287121, 751153593, 237366289, 43873260, 951589064, 681358945, 579904839, 609022318, 436152159, 251445660, 974016264, 429581017, 247505609, 851031698, 817388570, 196024231, 952477523, 351280234, 388425801, 956067601, 754162608, 943382672, 453923534, 116867739, 910948578, 941367448, 215110481, 673853563, 189392957, 581141292, 958153298, 46127430, 622768555, 433398900, 117171927, 212151445, 528075919, 934233203, 770159452, 657635015, 804088552, 176197443, 302962126, 36186348, 440354211, 289620259, 721043532, 115315345, 246019686, 249473643, 487739654, 55559175, 215558696, 510826942, 470747763, 90398917, 232449158, 429543925, 959052625, 203775240, 468141788, 730490332, 602765164, 11773026, 323725289, 595754818, 582476176, 358365956, 995629554, 680395094, 105845147, 348263099, 431300280, 879600419, 302610514, 29732262, 553681565, 932427827, 237957927, 865148877, 232523551, 682475954, 979390965, 229368229, 26360570, 116242371, 828888227, 320209203, 734772277, 852803970, 302014516, 512335057, 221480844, 248099226, 799735578, 954085926, 553536015, 761036762, 107990690, 651105288, 587246802, 204952894, 361105638, 790354143, 180278959, 60381180, 212451925, 902007238, 921870770, 279126332, 814839603, 92177996, 637631802, 610074326, 937379062, 137032331, 304972664, 512393775, 324160089, 836867040, 786163813, 453203323, 110393808, 193497763, 241882349, 727311755, 28221252, 508403456, 334746295, 177487303, 91462779, 805513814, 29431800, 527185960, 563343885, 978438645, 538323264, 549260650, 14874566, 639459964, 239697967, 873507965, 733486447, 20085977, 92307584, 114340161, 13138609, 719497218, 868316651, 290988561, 256770239, 363649440, 847210765, 480414596, 539462598, 499116711, 409254856, 286017419, 650058223, 287238789, 699834521, 270926940, 182820975, 313710972, 970859785, 856814551, 656338026, 602818868, 96775278, 127445212, 636341906, 722917462, 965145553, 897364420, 504396218, 777285133, 432599706, 181141054, 733206405, 607366814, 75907181, 895747552, 810792325, 515632398, 225327567, 949128705, 99222460, 407408100, 483146402, 678340923, 695573852, 919956035, 559588634, 104511822, 65680753, 576297824, 261712887, 144868617, 662026610, 998510501, 777907990, 517333863, 572675298, 891712907, 972574561, 743510749, 943354271, 345466485, 615886785, 291199249, 498809707, 848652126, 214131802, 814217990, 967373931, 706100198, 446080420, 267741250, 316967629, 167220605, 3178762, 36415014, 252113733, 250154199, 348883691, 13708362, 675436544, 782753160, 518384150, 991621216, 282763668, 654180469, 926216919, 121641279, 279960576, 705942658, 918479310, 54624889, 604563073, 977470982, 273012623, 310161307, 773398779, 104524466, 962054305, 347991844, 277969641, 112623080, 162724401, 839576431, 405592221, 434512985, 530765168, 427801523, 328710612, 757505195, 123515440, 87678820, 316612436, 97763919, 121123138, 898150743, 414576112, 414149919, 722575463, 421896490, 413314194, 202425277, 250622499, 417426446, 411582548, 419860211, 194003021, 158924727, 981926763, 941780406, 389458974, 787873981, 845188776, 13566419, 582638586, 746396024, 325660982, 923621322, 467527458, 17818849, 852593631, 263086441, 45753567, 490726169, 237520541, 380011844, 774317335, 336547522, 269586792, 151008625, 740255617, 931428257, 609880130, 288096361, 746637595, 612018192, 641271337, 227249234, 756120102, 748958187, 302049196, 32007000, 809386542, 158615615, 754400011, 607022563, 377599773, 372702169, 263783945, 840440052, 852129992, 565938786, 382330964, 286007911, 785319183, 593950854, 770413809, 793635746, 310936922, 304828871, 31957641, 516755351, 903577238, 92467336, 314103951, 764323686, 792163727, 94081814, 514942048, 475285747, 283490258, 262758507, 329771430, 363219535, 847365448, 356798728, 848163611, 893807770, 85954412, 744126810, 171110327, 121359554, 972825547, 8445835, 687563728, 48635913, 656423681, 355884515, 187107455, 387546295, 299658347, 511290540, 263346770, 887759033, 422290240, 361089437, 8163312, 221030083, 627019253, 653314071, 900130846, 634367720, 831311405, 222655595, 744042066, 173440680, 625260596, 946327937, 776942952, 610786018, 755989691, 62069772, 443132903, 843153893, 587579624, 45371046, 719465587, 124024647, 223032255, 137314976, 300667916, 893211863, 395724731, 334410165, 176441014, 95923563, 376878521, 261738472, 205290095, 501620150, 945626942, 547251130, 419489936, 926610688, 321236092, 4236328, 377980392, 626925884, 289968609, 627029437, 599533113, 288561448, 518505559, 9147511, 487492857, 765394963, 864152528, 411982317, 109668007, 768500566, 44825601, 99231078, 926210818, 44993340, 908515, 624500352, 168913121, 997667177, 863378081, 526522814, 165702724, 342319667, 586688983, 408340652, 757505783, 615584855, 805797154, 809978326, 952937658, 288222693, 965117803, 582485662, 561822755, 45558329, 251172642, 22432428, 870554529, 326162129, 747000026, 237414523, 58847311, 453195873, 48380823, 260586145, 852676687, 594346504, 244648051, 264899687, 799324535, 593619599, 84395101, 884591462, 845568986, 998095839, 595915468, 868654614, 664182998, 480796496, 647153516, 719862953, 661984358, 170354532, 793742913, 357299700, 188435057, 235756830, 194405279, 236770536, 257133360, 293037042, 863977236, 651346447, 991430794, 286100808, 926643536, 756084206, 345935782, 982899412, 977923230, 196345232, 630335142, 807278270, 268830178, 93889089, 484093842, 666079102, 516298948, 406568144, 409605619, 796462949, 237664246, 111154420, 960506509, 991437812, 559423848, 465931725, 250017006, 746803006, 563384317, 358420260, 580727756, 408980340, 241609705, 580191923, 188519983, 228118097, 177007167, 523052855, 808598981, 431832022, 423673902, 248528135, 327671949, 426891675, 611981642, 892566593, 7307647, 533773911, 686774148, 249569766, 163867373, 283744701, 82721918, 654080737, 909270194, 903140968, 385455295, 671477071, 491542334, 920637261, 236986646, 766080349, 585165756, 838314528, 816476133, 388175881, 514335999, 437588520, 417414189, 631682722, 675205970, 457411379, 959453668, 961209223, 769384693, 819523313, 873141058, 116447198, 728417923, 753371459, 154949945, 542735613, 487060943, 882812110, 142565477, 800205371, 358590264, 321280648, 102450646, 300882588, 614492721, 456309200, 817692202, 854605164, 101124969, 740781265, 116100176, 957743873, 680075775, 758721253, 54489248, 524149223, 239717428, 252172685, 340525691, 125510251, 918553289, 488042626, 108801582, 780799243, 352111897, 181622311, 811024627, 535749964, 324736157, 248258340, 351073554, 389106812, 927510314, 437770620, 854529822, 754131203, 7757931, 604161376, 468277743, 655604627, 569434724, 522567835, 541616188, 982456857, 504098449, 106509763, 847769641, 67891405, 651104871, 735935946, 532257383, 848953301, 994007369, 610245690, 734533700, 857391902, 538665366, 982098535, 79343308, 294349734, 641058829, 937035649, 859296659, 314677301, 239054246, 939107102, 930400261, 728356721, 933926359, 98100127, 137447457, 61815460, 335141963, 596183239, 1187022, 710953056, 25592530, 44612064, 953909775, 529971536, 792046137, 110481442, 175578895, 818948302, 246925447, 398000332, 851655331, 404666359, 917464499, 96982756, 711193540, 89260413, 47067766, 327384333, 383607991, 186061891, 942912815, 523051586, 214222380, 742640466, 874934640, 243398170, 231737669, 184886801, 739514818, 218425261, 279510148, 959787098, 877874132, 881987745, 679400311, 901969281, 585212232, 948232720, 961710174, 403921139, 492296035, 194071736, 597079811, 374134034, 878384932, 874006747, 581848941, 900936814, 880393453, 25667541, 278261704, 222085322, 720550001, 953055197, 914358473, 435626095, 630020120, 769701290, 633845749, 98269108, 713365129, 103979240, 367164642, 557876963, 944102529, 753606546, 289332769, 70465398, 603272370, 459386114, 673094460, 43838395, 297341867, 964786667, 232772909, 622263677, 144829348, 501684068, 896388393, 924969257, 936915746, 516481408, 405569183, 29558662, 495646991, 289431512, 557699616, 7501238, 727012277, 948147501, 34145683, 137401428, 974160178, 318165600, 107313564, 107406030, 393021878, 340286212, 666424799, 296444505, 566368293, 266873575, 446355346, 924304095, 964072263, 968874652, 959618286, 232282141, 452028839, 826400427, 532283986, 818818791, 382176056, 478098245, 67882647, 308092028, 260856876, 3457481, 985368990, 261441690, 581712704, 546436609, 809705213, 545994031, 276093631, 747095232, 382513057, 230886434, 438457193, 436102064, 374225527, 439731591, 60647842, 905925665, 785270879, 965331315, 159180134, 587963709, 953436598, 926204028, 370392469, 966283173, 37003108, 747142544, 158861735, 475047295, 83663503, 739324351, 433906572, 521638365, 278404615, 251119225, 364091501, 338536656, 139441639, 42735594, 809566988, 21093943, 924022478, 180869269, 270352803, 256027856, 566078048, 977909478, 623709839, 300363026, 948237158, 658481210, 981378974, 511775637, 122486036, 763784148, 124151564, 723847934, 13268154, 90383777, 323758762, 773793386, 565154912, 836470905, 725190378, 569415589, 677126853, 536556818, 104684668, 858329008, 419739683, 688645326, 41860298, 48032538, 45904702, 395185842, 1640228, 345937286, 674020041, 16511659, 844621541, 174002318, 936536402, 676546453, 407745788, 953891355, 78878659, 562728643, 77135100, 368034838, 479284688, 404162490, 311175989, 718162204, 104689624, 713096437, 204784851, 34372940, 198425513, 499722287, 670299088, 945120283, 635655700, 27302165, 359473227, 803185010, 588911438, 55575673, 398644645, 777110027, 422533784, 924844046, 790377972, 654566452, 702052308, 848372942, 294034546, 666728692, 235768147, 696379602, 81489489, 326639784, 284373271, 695243422, 316951219, 479521523, 640677205, 863065325, 90930448, 168711740, 16843037, 915943279, 148376702, 109753840, 527291303, 367409286, 34822599, 702644237, 874755643, 217631356, 965211867, 449739939, 64548407, 267981586, 366172901, 40822324, 767966957, 884729004, 145385261, 697343929, 733231933, 926913228, 955280859, 470528608, 710845132, 982414687, 479798064, 246943271, 507795372, 17241474, 64518151, 798854512, 330055312, 808017883, 426193365, 68162668, 291852792, 260435993, 306446533, 714876174, 70388460, 552029744, 281480685, 94417272, 430110919, 917084240, 12938678, 181059049, 973154529, 845349582, 265236303, 557347214, 511271848, 507504978, 401702677, 246018341, 152516763, 622880501, 199564864, 176245725, 839872241, 618732496, 497385206, 639982398, 436871079, 861447484, 875257226, 565783044, 71065747, 839515178, 967951118, 812508925, 901430311, 590520787, 821781088, 851340042, 554256785, 701087946, 968011512, 865229319, 182229331, 116866204, 886748327, 770519673, 930679327, 842887427, 569863667, 612256079, 656683931, 130210047, 981761661, 780347359, 251629071, 439898275, 939274651, 611681530, 250930355, 544357562, 694224198, 932519560, 997166517, 646808064, 655465947, 630457442, 455456943, 346628156, 874007566, 99320080, 696522974, 979023826, 376705062, 438076113, 265524720, 275821890, 376292867, 515070372, 736311621, 510575944, 946676288, 429560765, 615919007, 833670957, 382311166, 844582364, 536117514, 413878435, 853188460, 370867564, 66110392, 318599706, 75975578, 692105133, 525208823, 42497257, 503845430, 189481251, 905562611, 519580585, 41242770, 502129013, 924307135, 167575824, 138759470, 372501640, 942829308, 186116292, 304670391, 501952292, 115171217, 153077942, 612710653, 922289003, 197269705, 621545443, 656243097, 970264032, 844948212, 818700517, 174476272, 207771132, 759667224, 504383985, 361080600, 521980256, 356992871, 855088290, 862723238, 657427431, 179980347, 928468188, 412759140, 922548902, 755184409, 487738407, 695984106, 112272952, 296257549, 650844035, 449918874, 486925342, 688446394, 642391750, 795224552, 147770469, 508901234, 837072549, 559603851, 577605399, 396266032, 52001228, 254139571, 699675475, 169404752, 144599070, 309352598, 51618838, 876154176, 538509454, 864381232, 421154320, 246712725, 453756946, 345405532, 822474994, 316938768, 633470870, 445802341, 539113621, 886293781, 628205606, 992315558, 769866220, 738683230, 612005824, 56540630, 717704787, 21482208, 907250819, 357130, 502687581, 79502010, 230288558, 138634138, 169593090, 255265523, 748235270, 752937271, 51596506, 541946888, 102292915, 532098777, 182759947, 605221563, 326256103, 817936537, 973086478, 784184016, 82259282, 235728721, 981784189, 337786545, 361536570, 190380152, 685203910, 781579318, 183296984, 582232104, 360395579, 798133757, 691016473, 543722916, 484454691, 108653181, 571522355, 992980307, 309485069, 525326817, 632672603, 264566648, 719653176, 309433444, 151728885, 231957623, 107857136, 514824071, 431842894, 68518660, 916242510, 701204075, 85973906, 213832517, 103640321, 369877194, 85729101, 346303850, 315015703, 672978270, 287377814, 202134729, 611393636, 403562409, 165842018, 584995614, 295452305, 309519274, 170870911, 683872506, 886883806, 235053826, 227293911, 943628195, 600224401, 7122259, 972929122, 645599351, 454004453, 233332719, 889730525, 248198610, 458417832, 682186820, 869013205, 54365894, 709009404, 799798115, 410846442, 4417835, 711182514, 378837885, 650522744, 918371365, 647590678, 579026969, 943728025, 66011418, 10169057, 818346426, 333834745, 472990778, 685565933, 232464859, 246584808, 743949618, 453971377, 276498849, 209746466, 680827135, 428463270, 838870436, 435986140, 368730351, 822843823, 218470313, 884795899, 669993875, 678701200, 941669540, 688715247, 833113471, 838660794, 305437209, 656915902, 743556817, 687695305, 299689091, 930034036, 210111369, 141028115, 341423089, 472783949, 497221735, 230407912, 26077260, 505828066, 729417310, 143576420, 282689481, 469725505, 701287021, 128110628, 433695197, 394061857, 194998492, 45993487, 912571898, 440634275, 665013495, 972337863, 211764963, 928077407, 245008083, 575628889, 322899592, 760233415, 405831724, 804687759, 501107951, 502389022, 971665126, 442221281, 298853439, 101360727, 584569469, 498411739, 344377724, 875156790, 993802358, 752775020, 106859738, 452738907, 193298189, 361331455, 235836124, 399510995, 654818230, 714476965, 300681220, 473584257, 890448435, 383918534, 656254603, 138328291, 178210209, 592213984, 975289560, 685445819, 757205261, 948915729, 608094660, 380966425, 95448214, 520009842, 476053742, 709055571, 616303535, 868276977, 363667008, 841300276, 684213122, 415125470, 949854475, 943266552, 488814093, 101704105, 761723612, 145856845, 774918522, 710210703, 477033366, 458019695, 938515386, 34086585, 750193004, 995077123, 728322838, 381814060, 223336442, 415384026, 163567863, 132922109, 899747478, 686984986, 913637605, 941862777, 321293554, 869307310, 984163877, 691320939, 218640365, 938987215, 652240258, 542426412, 351882474, 573598337, 856440352, 39955291, 554049881, 817332453, 171056717, 72608332, 375190576, 361283705, 205884792, 745829892, 579994310, 41996303, 313747054, 880542480, 75853112, 369057838, 329509298, 74171897, 657955769, 571855200, 452836329, 422928031, 604220068, 555300283, 991751282, 580325719, 978018366, 259049723, 247988103, 249334673, 663807970, 309493521, 237539417, 712837801, 963843781, 1504769, 4900461, 329554218, 224874884, 76840670, 679038935, 439421484, 76460929, 251576189, 92535668, 440252831, 441710748, 132091696, 605816222, 723533063, 442798172, 431365449, 51800673, 284312277, 174083327, 211393229, 518024919, 363059959, 871685585, 266814661, 380647651, 315508757, 130789700, 457657857, 773116230, 796561670, 789966640, 261094257, 836404133, 729119724, 62213247, 347303472, 11458673, 25978952, 281169068, 608047470, 135767236, 982294323, 585233951, 416915313, 411717239, 598394785, 571780076, 672411729, 279578568, 833597794, 471998112, 123008043, 799039724, 802808834, 830270224, 184529328, 456569999, 954821984, 486293206, 278463011, 7685246, 84819281, 140556017, 692203678, 133567598, 564999305, 78419778, 236996598, 274247841, 887553557, 498140852, 481399598, 374757549, 485270835, 488789957, 509747260, 774783243, 123158113, 99190323, 787298970, 170058738, 997104959, 491498789, 544272001, 621450454, 354564728, 166132663, 692982589, 396437731, 913858217, 31223235, 419375383, 778317334, 99897709, 204956801, 952452182, 286639708, 487114935, 669399968, 873978064, 85292815, 554069006, 266760061, 340731430, 629540703, 217419010, 951570643, 65703842, 497860903, 270203872, 77957575, 201039482, 588673246, 126236701, 412613576, 214928523, 886776058, 514615244, 938371254, 508860954, 440148133, 181545473, 124266116, 294398110, 33886736, 820610484, 952955050, 513862081, 134177093, 64805392, 551142458, 556259701, 155161075, 791685422, 139847128, 395047866, 845478392, 983347673, 591919447, 224379994, 123106172, 281648961, 296006183, 241355467, 805850064, 179872237, 172751918, 830072528, 290415939, 179674743, 360678056, 932905737, 836323716, 860234088, 625267055, 735604296, 304746452, 450608117, 285156403, 477632951, 776423577, 463404671, 77003067, 231309941, 360929576, 315377904, 41300306, 377299964, 740772103, 670120582, 693307824, 32653860, 316794472, 487490095, 976499140, 58837768, 765813670, 844906676, 997295699, 679869129, 809587171, 690036902, 923119201, 695479987, 545173200, 486814701, 992916215, 824220257, 936457743, 72587498, 333059137, 924119848, 847948637, 832769483, 308702941, 62934569, 477855923, 955735990, 773841647, 988950488, 158221971, 636466098, 766102571, 741292900, 797670999, 715145201, 78801434, 374350861, 423381810, 919242655, 447709583, 828525243, 752928203, 291906123, 63985669, 700009979, 782112731, 494579385, 594020573, 333038724, 660867508, 191135361, 177869284, 555658350, 456809464, 660836584, 614908071, 465766100, 706835585, 111726452, 30201436, 608702093, 587348492, 196104151, 187062608, 181601722, 107434541, 250289434, 120171008, 498746495, 423065753, 285060756, 970242052, 207306741, 124769435, 834013136, 978213059, 741787666, 673445827, 33453939, 743489333, 614947698, 54220667, 806714326, 563894678, 444610396, 501043815, 215568915, 836417968, 695684892, 968287713, 184721167, 763328087, 991697667, 463423572, 176687400, 943213498, 96959835, 817309843, 390815770, 588313737, 702412558, 540838815, 326271915, 619630438, 666853220, 628283115, 737875853, 929370336, 345172996, 377185283, 241929081, 549711706, 235951918, 374295076, 154799994, 906109924, 633235263, 506036687, 213334009, 443131661, 313786402, 743592066, 93965869, 54011101, 663388583, 832946726, 580291197, 230019171, 177105228, 967122909, 564507974, 695682604, 170852800, 50441463, 434353679, 898206137, 907926027, 968737417, 140016772, 439093860, 752239060, 896481239, 43126702, 801993311, 308823126, 927029225, 481558953, 226101813, 127572935, 310221865, 635430167, 209969622, 639560312, 853972884, 641901144, 828608676, 106484630, 97043790, 860100845, 840952004, 957368580, 791915887, 483150727, 37982188, 991128064, 826842565, 432647175, 82628819, 655302287, 855184692, 429580845, 695554729, 316129324, 190915055, 409066245, 156059220, 23328261, 693862253, 939324802, 818392641, 216866080, 258569309, 936066410, 274063781, 390792172, 311504975, 263245672, 146924578, 50414399, 804937945, 115034625, 292717504, 3581614, 563259115, 180522000, 713513417, 589439067, 336517437, 387238760, 548603835, 892050661, 183227171, 954607149, 16641428, 908179944, 776724800, 718683860, 404185342, 116349323, 71282275, 279080700, 720620948, 956295173, 106145807, 423577804, 507790392, 321171137, 134408365, 403785983, 111066392, 283115458, 342501550, 839511071, 377677430, 82262042, 961566703, 507155105, 243782003, 248632711, 982094863, 268915551, 191222223, 736093402, 919200039, 596971678, 898165772, 799546243, 388848709, 56947441, 114238162, 666727135, 181786516, 615180255, 46390363, 311474212, 888937163, 101663317, 252768093, 116374437, 367908512, 92602292, 538048559, 596587862, 232418297, 560426833, 30948006, 982367176, 632192425, 894250933, 184947115, 302641906, 224338523, 943937001, 923218516, 86553936, 57059441, 194528482, 489213864, 568560835, 299370158, 987627967, 412507449, 227981404, 127645081, 133648539, 448934653, 125525298, 161726646, 3988256, 433682136, 164787142, 493261597, 598549991, 624288291, 322971763, 670821070, 193920533, 121808120, 383098824, 113921537, 231440112, 276361555, 625864405, 162707929, 537353202, 29330952, 475901080, 316318333, 165729942, 355266475, 183468202, 237509723, 259312159, 379654805, 233599855, 588667992, 817673823, 378056676, 591882471, 669866551, 832121830, 966815975, 907758575, 725607848, 794183776, 766898010, 785067573, 281129553, 70121071, 542014830, 923092187, 475549552, 612687591, 456587960, 692467844, 560973748, 768028082, 868314381, 423380178, 343952479, 788488968, 107513307, 745255644, 889911229, 475571736, 68154597, 990800257, 879207008, 870048315, 381077525, 685759209, 807055398, 122896350, 895019248, 768559884, 243257168, 410219062, 687988805, 537606088, 673530160, 92602796, 315659416, 980366244, 587952697, 643961042, 277975869, 662672302, 355201721, 396566413, 915777372, 673888402, 615882245, 86903733, 696973208, 519000491, 473073639, 686696314, 772683107, 347825758, 35035802, 838880883, 909700181, 934097731, 840377560, 860793273, 875991807, 744972257, 105903817, 181118811, 90715197, 917631616, 366163849, 124153419, 17181545, 368545551, 305480864, 154959180, 277344400, 75530929, 364138054, 970151396, 301377274, 563404168, 177720993, 199708042, 744037695, 887510871, 105202447, 368386697, 456176036, 329632864, 236215712, 457295169, 661086960, 204999369, 832901009, 49901591, 175952914, 441636434, 824281056, 666709597, 530432608, 485095725, 257494862, 198811896, 357634048, 989352127, 213344348, 329353362, 514014083, 438136199, 783672780, 705975089, 651391872, 599493257, 426485491, 257794239, 698569089, 764217065, 281645846, 717899771, 165507135, 718785377, 653014819, 868034494, 223126461, 354776977, 595519402, 270268827, 643280707, 865405545, 235171385, 907684801, 911005116, 549310160, 823269151, 327061029, 660953071, 180257620, 301915010, 387045850, 874024549, 664283964, 596087201, 533252782, 857211409, 387256061, 541723442, 288172969, 695856962, 73163050, 150856689, 775420213, 6399321, 764752821, 577439727, 41233976, 139028658, 248458157, 334689368, 967580678, 478965901, 556646358, 711453128, 150214723, 83256808, 864044670, 31529309, 300114102, 819472474, 755005071, 693460060, 470639469, 280488666, 43316501, 571562252, 872194005, 789221166, 400965956, 386988589, 833874181, 732711192, 948155093, 770154090, 72414715, 925821956, 377938614, 712140488, 278041873, 436104253, 727682386, 827311343, 749132740, 83816967, 266754221, 380450663, 276492790, 406742501, 417780151, 81807465, 249728346, 360591487, 66584004, 594991338, 526768106, 208120945, 230234926, 349867847, 325685030, 651836317, 63923340, 208599078, 772457394, 622250236, 664309561, 30224394, 591807390, 946814373, 309976935, 199033009, 700296798, 47106422, 616529883, 773601528, 991707896, 350842887, 657392307, 217472867, 766434094, 888241934, 952374932, 382963957, 114419531, 805597296, 928857925, 755668264, 376778899, 877429008, 180817329, 467024723, 335329636, 715378643, 605809971, 128402276, 294596546, 462860890, 123006903, 783044006, 861449681, 798370176, 580041097, 772611254, 342374849, 377437460, 621879392, 63811658, 846776522, 866542965, 950205336, 838690464, 488825816, 46258136, 915723913, 867361137, 638024501, 439414102, 890418843, 54389783, 909842410, 811335228, 361373785, 116530036, 954982642, 404035481, 345901676, 638014007, 409021867, 103424335, 99775255, 414733344, 301943495, 231503677, 921592442, 45289403, 427221103, 500107044, 575442664, 269057969, 668087969, 567564553, 732920419, 752196222, 420925183, 117445683, 143276270, 24951741, 253544186, 580929615, 788722128, 73161046, 728888491, 622375375, 422940093, 242284330, 649259282, 207442697, 56265562, 84291079, 931283816, 523110996, 843945080, 227113398, 614132939, 834648060, 601414843, 112483676, 940830443, 232679362, 886653642, 429473053, 910602608, 22925988, 714829594, 689647441, 844840803, 546608275, 89553005, 531162346, 208247302, 611735134, 378016817, 714123144, 520245192, 378442327, 483258550, 153010045, 109647497, 18180217, 75658583, 633084730, 398323174, 834230711, 458833859, 635981016, 918081667, 738733347, 9029765, 63799980, 920805390, 619997875, 526265164, 814140331, 29004181, 227984904, 952267722, 208501377, 962126097, 431938534, 287577970, 77074224, 235730990, 837710194, 372948777, 32932408, 522310968, 266155717, 655595386, 666026855, 356876889, 735004114, 410253849, 173353379, 241468445, 166309658, 187901233, 191131312, 311604481, 746122397, 82451490, 823973168, 79272055, 337757020, 973785260, 26996081, 598910387, 555736520, 428578873, 437582857, 542010620, 524344664, 525981304, 376452806, 912466848, 350486742, 238976516, 844222542, 29648121, 376659410, 399402529, 839696841, 822971024, 460109829, 196490902, 298024993, 601192451, 930688368, 436739701, 578264996, 875436687, 896085633, 588740042, 567781195, 133511727, 56006255, 70669361, 627417697, 929704188, 375393258, 513702455, 67779882, 965640108, 669739700, 945164892, 301112393, 220138841, 423670368, 520630270, 761828386, 349792517, 93727052, 936692853, 521245377, 706829200, 286718537, 774865643, 455683228, 881441550, 45917580, 848216276, 508770648, 200757500, 651890829, 912597952, 892355278, 507231245, 658631135, 501142569, 181933197, 586889422, 155858310, 326607338, 464035008, 102760334, 886465109, 731272167, 425810136, 632086583, 593972870, 156384795, 636999764, 247593416, 41280168, 39685660, 610480927, 463255413, 705238870, 913481465, 218042010, 287642540, 221578694, 597437781, 407727767, 864469128, 142780226, 263131335, 408122810, 80733475, 196754669, 318206976, 223054869, 145637898, 862644778, 95593115, 403782770, 263256034, 189468801, 288025846, 283692079, 800887542, 113710583, 673107204, 20884890, 543298526, 415169140, 627473783, 464069727, 218537778, 479761172, 422803247, 282370492, 869726455, 842498837, 637733739, 307610144, 351032490, 94168978, 987771622, 839218065, 851461806, 932019750, 97757128, 136005579, 155288645, 63738586, 58192551, 924962965, 794856567, 722455802, 752286193, 737818683, 688077946, 478059040, 692195459, 382515199, 17499821, 121054059, 597848960, 449282859, 517011620, 261723480, 968129631, 886312943, 315334745, 335732002, 177967100, 839654040, 212621673, 310426012, 618753075, 696564769, 739088099, 34467422, 643659074, 214090080, 623681404, 550178012, 386086133, 759835072, 118811166, 949713657, 518976761, 782662650, 527562355, 74885339, 195923018, 341532352, 767883986, 104804072, 247520895, 238089180, 314266941, 425393517, 667967987, 270772933, 239984777, 217774000, 251271604, 642492079, 310491484, 275923745, 842677095, 291561877, 400052493, 575613245, 893246953, 663769687, 157295288, 590749144, 568305081, 999778852, 814175118, 388183541, 1745540, 333202274, 342538261, 550784548, 414454185, 472111439, 1337653, 331566682, 553185243, 354946543, 721145697, 109029997, 923764748, 598835238, 896091175, 647497993, 721814969, 545746592, 420291436, 239986537, 268112198, 743028947, 466910308, 889969806, 407561164, 928837227, 195080395, 407656766, 203261371, 647966709, 451052589, 673226199, 354300410, 589683798, 499391653, 55346036, 718276209, 558685475, 430996407, 438923054, 448958267, 21188383, 244473616, 895454747, 853172687, 677484598, 83546095, 378858155, 292337492, 617473822, 232548937, 738980596, 755996078, 510885980, 755986268, 550642647, 818378971, 440981613, 292507116, 521574620, 697967796, 245555360, 663860425, 503862679, 927975251, 771630348, 96434873, 621803170, 506504024, 651635011, 860148284, 293985186, 183818494, 459883119, 202424346, 681015639, 138603747, 345024727, 744836816, 713040223, 360384872, 715063369, 821676688, 203256246, 482869646, 41685255, 707434779, 631487182, 693002645, 155533188, 997161942, 258921631, 706141346, 587136554, 974274834, 979941718, 962040768, 696288331, 1490680, 417206025, 353524582, 797246402, 662227128, 643660255, 883237807, 31393715, 183138060, 284252036, 972588955, 796978149, 432197315, 303924041, 908973529, 668966439, 343854243, 181953994, 225348931, 537931148, 654026997, 33677357, 82165060, 415760337, 205366201, 456985050, 967763077, 529488574, 575762331, 30338482, 291138165, 744623232, 915248918, 131760614, 934989941, 634759657, 178368789, 929027458, 785095091, 736050307, 974714550, 154712934, 463290235, 290121421, 524532997, 397924718, 784264208, 640269118, 273554472, 43572965, 370210770, 959715691, 248998885, 836962803, 521621552, 324168562, 575440709, 253981792, 83534396, 283859919, 235590717, 551556713, 53593677, 318433832, 624138949, 170322397, 517091659, 160907601, 554642215, 346920712, 685996606, 589303427, 752273726, 667286967, 705343321, 234907167, 96228032, 351590763, 4357880, 676906513, 479924485, 458872149, 701775282, 247365814, 50731359, 420206456, 909125527, 879676947, 123883801, 644519395, 837380565, 533590214, 512555936, 70708940, 366700960, 8984802, 930028067, 86280039, 919459587, 760504324, 692116038, 146309510, 704641706, 885644835, 140578709, 156748667, 68154756, 669347757, 716419300, 621340506, 513026593, 279242306, 266076138, 252601245, 968986543, 14194966, 817354996, 751200032, 314212629, 507387874, 650168153, 305619780, 973474405, 417337719, 559364748, 460018552, 172218225, 736402438, 817353348, 605283287, 489266735, 127621040, 633425017, 733812148, 244084955, 368257930, 75379410, 945811580, 273212271, 91214516, 589429354, 380755596, 641791042, 240622080, 124310494, 195826036, 196613657, 768007497, 380183031, 450929936, 492851621, 205063241, 550799287, 553145514, 751542229, 742832784, 788514818, 345501399, 904443793, 645285151, 551998578, 938158396, 156870597, 238312008, 457326990, 106628962, 4017689, 552976136, 930122556, 990712309, 409735187, 294343310, 140949609, 979707902, 523503591, 669283153, 428669071, 632363838, 621977933, 178672246, 200457293, 490335142, 610291799, 531434163, 240937043, 50186441, 21150580, 702560035, 732411506, 388237868, 901912042, 55422331, 158203689, 20723312, 897014930, 10245374, 508750581, 6026008, 211445082, 543809460, 221404863, 247089396, 926248944, 60694982, 741022062, 262738517, 472670807, 821628541, 55954420, 151310766, 983399396, 671086751, 584945898, 41125030, 443788155, 115963382, 674863351, 698058312, 554566724, 262286234, 534455470, 64018329, 639110075, 809019468, 833535871, 843522667, 483199489, 962088668, 381418100, 900432599, 483879275, 918415790, 275442544, 850401357, 546767860, 648250829, 35452498, 474981715, 754616729, 455464415, 308525250, 323762362, 467362316, 276611299, 188429050, 706508104, 41692251, 646330356, 298790824, 282361661, 448448165, 739962753, 713759734, 379680505, 745983851, 257101460, 48874705, 407553997, 951328244, 440175036, 618067978, 482246485, 35743102, 152444988, 677705533, 264119852, 297968137, 962070402, 227036385, 279392617, 468344301, 213130068, 832058768, 389651045, 561124408, 718024464, 477697006, 208542404, 753113134, 386118340, 935168114, 698365608, 299436661, 85070560, 270703619, 297178649, 174196061, 894433141, 309847554, 889344933, 406636190, 784819507, 248763309, 109802916, 658482123, 702784885, 758734771, 457880001, 270629344, 411488366, 289845921, 569257801, 967240464, 424134827, 395921808, 325943841, 105773944, 21725420, 510282807, 796204430, 133208628, 853746529, 431100546, 459333875, 459423590, 897534735, 400355977, 768617285, 523067921, 95303270, 238765710, 113806094, 846955206, 560625540, 475087165, 531363400, 310741838, 735771129, 809352401, 484769123, 798859210, 504766497, 551705663, 159073520, 918573476, 382143539, 175638839, 391689210, 307169190, 169797676, 507704006, 571681107, 249465332, 832932132, 894843262, 356160287, 57754255, 35398651, 610355748, 231665003, 341709721, 307826326, 307622648, 449882280, 745401579, 134758606, 43848569, 107391188, 135101301, 109635574, 851399555, 47464238, 405556740, 632732648, 267240762, 104079944, 790007953, 925977388, 961944976, 374750781, 323206204, 386931723, 935734024, 958337548, 135098835, 598370732, 783303040, 616518035, 148427597, 626010215, 284405227, 201221825, 716506726, 196477562, 171991942, 217879721, 840341301, 657567018, 595058837, 732495634, 143717966, 576816218, 522393582, 454862134, 299897429, 840304134, 545001924, 163405576, 112101630, 429798470, 564138135, 477020724, 851883538, 659006467, 694584752, 334633771, 9290287, 388894565, 528853322, 319864401, 496439288, 498678068, 19281688, 722566624, 530034257, 960066540, 190694752, 36786926, 916403771, 946250811, 550154613, 625905278, 41452310, 421603386, 909460223, 55466161, 246836783, 240540603, 822151015, 667812841, 401146346, 146885143, 319953520, 587359837, 72067181, 467835461, 912407745, 70839299, 908747845, 888511893, 13541127, 517685789, 300500264, 756463748, 885967034, 95355945, 182944591, 833274331, 322513579, 155247267, 360022656, 469980339, 824272905, 639790170, 184157715, 956789249, 561493251, 144369050, 546479732, 717492802, 398730823, 896383135, 107495827, 836987306, 940171735, 432076379, 451401818, 578654373, 530345937, 21319849, 398881563, 571953305, 57603384, 385170773, 676365082, 590139705, 385400661, 347353976, 96310171, 218065914, 746845758, 833216151, 790848606, 912719942, 410908855, 157474757, 909239457, 817510513, 333384151, 509607545, 78548931, 570289517, 667761551, 914869445, 292307568, 154681347, 182888161, 312442576, 240158923, 360990610, 533564959, 37646497, 76222765, 408197122, 915967366, 958746951, 928292173, 68483730, 992840873, 999352124, 371648070, 629018258, 590551082, 418739042, 48008492, 74642880, 767953851, 267392669, 280144906, 175197031, 830138695, 436414889, 286131566, 203647955, 308962350, 897686646, 143855619, 621210782, 374738109, 429416182, 516590157, 540266334, 216341425, 667268740, 366785605, 532625840, 830142312, 70375510, 172108135, 600430285, 564185056, 662084398, 644545126, 549576427, 322157295, 373121489, 988921209, 279982064, 645529728, 178182954, 346051885, 41297434, 401755959, 821118420, 160211559, 699697318, 158395383, 634541685, 447607465, 577810322, 299827354, 83380848, 136673673, 563940271, 200603842, 728205844, 738018619, 255189583, 636562118, 955033335, 247351376, 372441359, 344668033, 147471599, 798557226, 873565766, 135723857, 210491363, 420437228, 984044107, 483763111, 266908530, 708338566, 177289606, 394563555, 775196108, 795109048, 106393684, 388172337, 331857543, 747974408, 248514873, 482339437, 362997907, 350536517, 801634308, 799498164, 618319684, 648875778, 543118108, 735423224, 148396539, 173035347, 109100519, 186485090, 442419785, 699089042, 717546071, 488753088, 495643753, 290233838, 304934223, 160606268, 554955733, 554350574, 814482721, 333888971, 848293511, 42273044, 622373089, 67831571, 602791936, 135019608, 568950881, 258999812, 520965608, 747787589, 618815785, 457233525, 365561643, 482191085, 147399120, 464980507, 734913785, 644802675, 840541995, 86897355, 583131540, 582764622, 179478606, 692164442, 386677961, 634417942, 270655269, 830937708, 627937736, 964754699, 149405845, 576620114, 782193540, 407119085, 751992262, 111581004, 471061545, 950422413, 527448093, 104720794, 61782780, 592896285, 731607503, 151761465, 877061245, 927004055, 480852728, 254094719, 913276813, 156629625, 56927784, 144902532, 784351719, 358266201, 284930015, 831546844, 206026441, 770533131, 682091035, 135283743, 977268241, 680054243, 160257433, 547024374, 228807955, 30821605, 1153598, 368733683, 353838467, 214179815, 480366387, 740220254, 90767168, 273056210, 349833469, 42738608, 375092811, 410092262, 441306542, 49356807, 824379116, 540056931, 890546833, 23622733, 423515516, 118399549, 330660146, 221601240, 453860882, 909055643, 396232715, 49879685, 561922165, 145949144, 730388127, 367245232, 402959531, 784463577, 534825585, 118521261, 556448172, 404266407, 782995712, 928557422, 598372118, 984086999, 840750864, 238962977, 445068554, 914069648, 260955341, 779897511, 544770135, 261007674, 334735884, 915620425, 452517648, 501276593, 280162812, 543950468, 69473247, 966683098, 714615404, 452449967, 497062330, 768838318, 150230809, 760681337, 818872811, 216420467, 361042484, 915360108, 966641336, 33638839, 806014028, 841867816, 889682103, 589153067, 899871469, 269023252, 28501038, 517431538, 941007689, 267184104, 178591121, 299689297, 7799827, 281986243, 72924986, 991281167, 309221343, 996132513, 623035295, 535401303, 893733146, 152065197, 26754324, 522327689, 40000156, 446028337, 805610003, 946821867, 787565460, 328071811, 94869003, 797729986, 441817924, 24127051, 410905412, 16974420, 46662866, 424820675, 483803204, 407155053, 550332179, 349452088, 934776838, 349336307, 792074370, 142931999, 488793256, 209063030, 776716422, 143582227, 185367492, 513963435, 982172380, 683526146, 666560278, 938786508, 483311923, 461808049, 755563125, 270640893, 891903142, 956739464, 70452951, 306261607, 889103842, 617936068, 407516322, 975364665, 13428180, 238568688, 204683457, 263271695, 829153624, 263013883, 320783280, 594928163, 125962965, 194476897, 402185996, 283779716, 934805330, 997978804, 970283453, 765395968, 645581112, 735955545, 388256306, 963023647, 50218743, 382836807, 749746234, 254679889, 265867842, 846397068, 716992038, 529646536, 707085074, 906797853, 325000641, 90452421, 609190080, 873520755, 598469675, 96973809, 107023179, 656332956, 255279349, 898635848, 432791245, 684970708, 732382640, 719530126, 458547032, 255964957, 393567162, 375729843, 645635911, 270754911, 815905617, 820048184, 10396920, 927065231, 966203716, 630796601, 166624537, 194412017, 954303268, 707632081, 406033284, 896065272, 773284891, 806394320, 998372191, 652010596, 735707032, 281778000, 837346487, 430048414, 536257497, 935440022, 267995770, 193220845, 575791850, 438113973, 699253950, 41752913, 552154310, 425262637, 735375653, 320270851, 457244681, 668937667, 812858331, 888876862, 242630108, 842489266, 920441885, 359461305, 732507503, 664534702, 220983635, 259154190, 362199849, 755119840, 560982855, 241985869, 962358604, 456800524, 588189755, 794770599, 611802485, 281274728, 923807684, 771595455, 905611889, 943317156, 175309257, 615019447, 323578008, 708810811, 686391023, 757645062, 709307668, 567935136, 121353508, 189488255, 414400349, 224350160, 661490379, 174552907, 544091763, 195143821, 687716619, 600568315, 543961684, 811201242, 264490115, 824234141, 798959269, 958723359, 834971615, 249175253, 716928816, 334005020, 203553901, 63258845, 280962358, 170162023, 390460054, 958023675, 934420825, 164925362, 443404118, 393074529, 149480785, 244830150, 325435329, 803523400, 71743241, 770329475, 67544378, 902044555, 297898167, 802438823, 682612450, 157096040, 652026299, 667156019, 719895095, 960402242, 960615919, 517331263, 562435035, 121908608, 431754438, 92319423, 470201314, 19612659, 939424483, 32771010, 686812965, 880645159, 354490118, 604852522, 667081263, 409089586, 623689463, 644564174, 830982938, 625364821, 930458915, 379178755, 928418356, 132615766, 548913617, 859686900, 514769289, 713765908, 452439371, 213168771, 501068089, 647184063, 218028207, 759380726, 472283187, 34608476, 514786078, 795762207, 381675140, 103629234, 925262281, 956634499, 378579034, 203409329, 268337394, 592329887, 124623244, 299772068, 192834854, 831471031, 780580311, 456322245, 366720677, 645167000, 203850804, 961625327, 910728195, 415364271, 122791318, 505017618, 988141847, 737087305, 485505648, 849253602, 417103134, 380269102, 962836363, 789760006, 989218067, 837007199, 257362487, 122978697, 617390904, 341446283, 467980584, 547494744, 832250026, 937518249, 397936859, 440410900, 615758374, 769375284, 121444750, 12129087, 670026525, 958839505, 408964293, 377516908, 849269387, 868394763, 19701388, 605370039, 621446478, 59468615, 237719113, 824999212, 852297846, 760536504, 790561110, 74433813, 388002753, 752051695, 583144702, 852918117, 186352976, 634229334, 944154806, 684945818, 663555212, 923398720, 682016777, 366729572, 41497204, 131875653, 503979282, 337016425, 206328067, 672172336, 895595722, 624841936, 284356599, 189913233, 796290155, 722146003, 263607736, 172512682, 350704079, 83873063, 738315906, 534822876, 994131485, 77609423, 931359086, 629966298, 169073476, 426918571, 9526877, 401407800, 522147348, 747139334, 815608280, 262581658, 148338505, 121448308, 131020725, 249694036, 172943639, 140408303, 448169626, 951146641, 632223103, 733078489, 611429281, 778215991, 1142517, 88793786, 332686363, 394665863, 364323390, 303347591, 54854382, 790210469, 434247772, 312844354, 697640527, 381940115, 257137205, 670257802, 487392451, 560224239, 267115273, 710789792, 23536801, 657442299, 435569809, 228013060, 357924246, 43710186, 908894105, 26259431, 356145739, 883584578, 972418948, 419546085, 507156410, 931282809, 395621600, 907334611, 205623480, 190348584, 410225460, 357758278, 659373403, 157116331, 187504662, 515583623, 861874769, 968065021, 699601757, 152379723, 300263948, 474142194, 285741797, 387140350, 240396311, 609159790, 134652808, 235969686, 347694674, 271913585, 732978056, 760967325, 202705300, 647651700, 731166218, 449801713, 553023715, 742445313, 406317725, 1011126, 328491561, 363321519, 360871968, 275779407, 288644138, 925156190, 201649505, 13417121, 686991157, 338388820, 248612360, 111348602, 702303139, 59311619, 419418507, 278391984, 725602486, 398833911, 720748233, 650713868, 360455999, 246447232, 674316100, 143137353, 720524770, 824768674, 403606058, 221561911, 886417953, 688713994, 998900237, 726547176, 55724445, 33095517, 430265912, 523040820, 883386875, 872047743, 99596000, 804509406, 71256015, 800547898, 653044023, 718059417, 101048474, 468605466, 646538896, 366054637, 837466569, 892320917, 387678859, 395064259, 763662038, 471388063, 348210963, 775897266, 192322186, 486181158, 178807154, 49449902, 46835849, 395037803, 331474784, 883624604, 96450196, 986102423, 579172051, 939204518, 652857621, 315092105, 752545428, 741733113, 10652047, 205617073, 834228918, 544069150, 731831911, 329223669, 175318497, 701280151, 624664000, 989609206, 664159660, 103251197, 312998941, 851880404, 303814508, 29232246, 777902628, 685570239, 652375517, 233596861, 728668506, 905510715, 653827646, 678725990, 543386128, 22108915, 690115736, 426560003, 275229246, 487607404, 306768995, 802285621, 953538026, 840537399, 489990715, 731706996, 139813549, 873716174, 43932186, 819059578, 162792954, 253305714, 710660826, 502055570, 810801481, 660177941, 44443762, 383219772, 629312725, 200372522, 243851963, 442736973, 490578230, 401605284, 352079604, 85325165, 481447246, 509597883, 50130411, 748350103, 310606782, 68459903, 808480123, 913704087, 389795034, 64617846, 476776514, 402052113, 615208100, 408331396, 446127600, 568426820, 918766702, 487140040, 23030685, 938348254, 72927646, 49896300, 2888499, 855133131, 50635742, 28451366, 487554311, 409923200, 286395045, 737479807, 464894487, 974093521, 140927033, 253359247, 137654427, 707038191, 111415802, 808774668, 199231986, 56470455, 11980139, 360350743, 89657819, 560279237, 28823047, 469403918, 317109122, 645061071, 77641560, 659511026, 561263349, 489586124, 901928751, 819369429, 339174403, 516330035, 406444539, 353679259, 205974586, 631446537, 643614523, 69397340, 570397257, 689729334, 527902624, 735837002, 501230637, 809811077, 611544513, 296914004, 370631400, 433365725, 412706713, 399660947, 488991741, 83628381, 734301847, 74865809, 898782370, 875197029, 270047554, 859239786, 987710891, 764020212, 848620400, 561282734, 625525234, 952130016, 214022646, 714683735, 41540965, 149500430, 497814168, 122975237, 524278238, 785626739, 375806044, 218947675, 405969108, 290656827, 450716915, 374821889, 857439919, 216639598, 8520586, 503973019, 395054511, 765483500, 647516990, 134826867, 215402755, 217040737, 305200485, 152175722, 667326059, 795095828, 273217383, 805824479, 695314483, 890111317, 760131896, 361472277, 532624383, 516977114, 860507320, 337926968, 718973863, 196188147, 733883056, 23864254, 77372651, 824308253, 191422523, 186148522, 842841489, 886909553, 503783966, 777775429, 260446020, 982341620, 131710841, 96242123, 869834234, 329336158, 105231292, 259641760, 480516407, 187705421, 83322002, 153689151, 737154265, 462461066, 936624374, 699147589, 869484751, 830367738, 65363603, 473344031, 548449264, 450084832, 978123121, 439592242, 358585359, 343298886, 721483435, 103918468, 341303109, 494140829, 802571617, 80600809, 348918524, 56352302, 785733895, 663019721, 647972871, 336739688, 459299903, 248571259, 194733821, 234000420, 996735767, 593059695, 448351802, 132191428, 498495148, 383663972, 693915924, 293754071, 968536275, 953992886, 321005636, 409678684, 196369302, 9219353, 633790369, 897865296, 810504821, 676752120, 768962149, 454174159, 332391118, 967961963, 569992624, 282688436, 941047093, 621228268, 988947006, 783309595, 292246244, 604260806, 118749653, 337509510, 548214668, 77593140, 637271381, 512309446, 864719322, 321989747, 430756436, 360017676, 301553873, 643129162, 246843314, 242805109, 213599143, 585204506, 246623697, 345414079, 400891158, 210855471, 720302472, 481216283, 963208634, 664101325, 713449241, 128234078, 644783700, 955205719, 713192382, 87302266, 176515902, 859742692, 692317274, 130391512, 486728924, 696621048, 748649907, 530103192, 590090404, 390645662, 79391590, 934446428, 754850593, 966595087, 874796964, 347630962, 345092657, 110732367, 274486131, 837888857, 605431632, 496335324, 283545928, 519975696, 907681615, 749359679, 22625646, 432689016, 379855606, 930303278, 516775539, 947785873, 609172512, 305384583, 776114152, 353971442, 103931073, 226169383, 318352841, 300151647, 38235574, 124130812, 414046865, 107847265, 971538625, 395609254, 594907789, 259787910, 169923926, 113285405, 386967424, 816634974, 31145852, 601685106, 782651404, 611633663, 196951189, 585752738, 791245465, 616444734, 874110561, 300179982, 906374448, 760346623, 161762771, 273547379, 58171396, 441774875, 672365302, 712837816, 399371601, 728316903, 36048164, 976132943, 231061517, 57792232, 644048427, 572702610, 946291745, 351780075, 783849430, 39817714, 433874230, 186159993, 460048930, 406941597, 417596788, 514283939, 767719482, 550163399, 274889893, 57104887, 417395237, 33154592, 172038099, 891164732, 295972675, 794581881, 520268702, 625366184, 67972589, 309001897, 204579599, 632551752, 319216172, 393656112, 246888923, 520617209, 876203841, 898689474, 329174783, 524222534, 975608303, 658805136, 475829558, 845421783, 378254013, 387334088, 478647568, 445185377, 825912544, 733506828, 598952203, 639011722, 412073255, 288040487, 944356111, 141677750, 309072386, 888234039, 843541277, 526145771, 261243358, 266753080, 12653490, 517053173, 2759071, 372161483, 903505943, 382250840, 926876299, 237253119, 622440151, 680458391, 907974941, 151901720, 739829496, 378802795, 179310478, 704328347, 12940060, 898105135, 847886061, 285739845, 903757389, 95029268, 422608297, 581650511, 318570032, 287407676, 638265420, 416180315, 524849405, 372815303, 498098776, 163632523, 100507727, 809913151, 195498037, 215615251, 449599377, 575169268, 59129059, 692393120, 482176376, 332598654, 355905716, 518000460, 965177614, 663840994, 869793838, 702172394, 323282948, 139023896, 567996662, 224858452, 245993982, 915035420, 499439876, 87156123, 456206224, 978158072, 831080203, 885689098, 902246078, 931531227, 464570858, 638758685, 731329917, 374411932, 243398782, 400521874, 741261159, 350099128, 588019279, 302145341, 535572567, 261429530, 969312624, 396297848, 864292859, 220927911, 915702808, 432356160, 317773625, 941354404, 44245774, 781484530, 857537979, 356498315, 897538901, 662444470, 437502593, 212184382, 434097611, 398057990, 691705033, 234601294, 820827754, 703625556, 568487077, 693509691, 546856021, 649177288, 108678486, 24869244, 358541842, 564364967, 317377299, 768558253, 578488625, 166832191, 714790165, 662790453, 623908009, 366784054, 112189232, 935124755, 822347426, 703632162, 336064353, 828976792, 783066621, 336416138, 280630562, 739272678, 128242938, 133052657, 675678954, 593843762, 289049914, 410916225, 628872558, 812362488, 208805940, 805563369, 977825623, 960989243, 381285321, 82281963, 921858714, 479299, 769388170, 428966937, 680495123, 473717548, 132469309, 805414272, 594201455, 10424836, 421347909, 976525438, 223255905, 124040760, 723702932, 792048652, 324491233, 161474019, 199781441, 237251386, 487273493, 237121411, 538612674, 852695063, 805103146, 441842643, 531103925, 136664035, 560322816, 77895879, 148601187, 263110792, 188955691, 998471886, 686579815, 669059579, 936678185, 242679579, 204615641, 935751854, 231124633, 294197442, 56580534, 295846542, 788817633, 376784886, 841729207, 170839371, 39926650, 544579555, 611335450, 230995184, 542492768, 344783934, 903812068, 400996259, 306798313, 753253550, 170636592, 265249892, 395452664, 667981420, 601414341, 181990229, 846585012, 760939157, 565182674, 460627167, 221405888, 603952595, 708268322, 828412979, 904313713, 80396978, 867970016, 263258161, 739032057, 223695893, 964958684, 153955545, 3797783, 534693479, 352593617, 834175736, 288502847, 502787146, 85777376, 241484937, 158429751, 830060523, 510141583, 17973291, 152288228, 543583434, 858275275, 340808286, 867939355, 707138640, 265890065, 309848332, 856061549, 854463410, 117233959, 685633689, 685596947, 801352284, 568619371, 874881985, 853107316, 449332350, 84618317, 441538597, 650159752, 100988294, 36794538, 910078572, 706377495, 811329257, 35456793, 802622885, 685748706, 973545501, 446526053, 538640869, 357111786, 576840448, 55467608, 820743764, 482384662, 259812413, 457437640, 374030689, 82198986, 265258237, 264463906, 156168508, 90892016, 44329729, 816545932, 88068929, 365294550, 605568425, 845016959, 144097949, 467274393, 279714276, 59364221, 236551463, 164027390, 515733734, 918356578, 897128983, 173140918, 741113315, 903314296, 822431436, 420126144, 442587895, 869856245, 346559929, 484281339, 99308110, 133627960, 324485985, 997912170, 592702714, 827018955, 301967739, 400651353, 83384396, 103643676, 707236422, 58660542, 196576117, 386960524, 316819344, 427988306, 833837184, 368203646, 627446695, 705540764, 739775392, 503847552, 614118700, 746035526, 12830896, 417836977, 41209100, 863965758, 509389238, 383384690, 344229285, 904646053, 856789357, 359328327, 107638881, 997139870, 237388915, 85539857, 525859039, 583298248, 606513196, 353148437, 399014392, 627020316, 305475659, 728838986, 615564116, 872120068, 289239637, 817968635, 720595221, 913555346, 326844453, 373389245, 246513449, 20409391, 273544769, 409824415, 985819057, 252291157, 61975359, 992060852, 429072055, 796461484, 608759151, 650180191, 340924112, 123214659, 763651284, 258606028, 569589950, 352810937, 805403660, 51151550, 280013237, 436234881, 896065826, 269625450, 310755739, 297801770, 359671842, 643060790, 911009453, 631339327, 523440083, 135306394, 221588802, 946102457, 741534538, 755283620, 292468321, 937367886, 711232189, 312236293, 461813401, 536703126, 3259805, 893765492, 854689089, 504436845, 992412558, 886038955, 711848214, 522807243, 230522386, 112594490, 921524598, 239015780, 520410763, 805999592, 96253297, 11955579, 873722199, 256970703, 65622966, 491289458, 568774574, 966493285, 724524959, 89192657, 971295961, 326941834, 719430577, 395789269, 455837405, 386187699, 488323861, 39880365, 994135583, 384952653, 505341331, 296923553, 247569573, 162522066, 727813183, 940948723, 273578368, 813367408, 906329422, 931740162, 908688847, 610488276, 802666376, 324336687, 405716258, 256861055, 490074991, 211104020, 205309321, 757701159, 619824655, 553822099, 599498423, 760520001, 577089441, 56864716, 475644345, 712217341, 923344174, 968249083, 736949865, 291194083, 625155089, 599893161, 766703220, 959235188, 616063679, 221324524, 167476894, 348889414, 726415637, 34585814, 475907659, 699336432, 900055463, 167161900, 186580729, 17286562, 581542762, 426658468, 254407818, 897551285, 641511750, 616871266, 268811615, 681907361, 837584800, 566505034, 571540793, 146780222, 675312424, 768102338, 621557373, 252778319, 458068774, 238543677, 651632739, 628458068, 690393284, 578306240, 183448590, 139575263, 316701088, 928736447, 560848695, 452198064, 191699171, 308193116, 744153944, 320227755, 50998103, 225147552, 636543188, 231125176, 876864657, 21667691, 993152732, 276972560, 48230708, 383854966, 881624272, 332233966, 403794316, 471942850, 568675176, 113536636, 230177234, 222917330, 677196725, 708749189, 824547550, 778808199, 121606452, 53530232, 910944597, 314475454, 422084192, 399494789, 762319216, 764967738, 825064997, 555116310, 277195738, 746080156, 978185233, 34693595, 897345640, 570126294, 949571703, 284980322, 684373038, 191854860, 407554771, 296682366, 390513414, 2996399, 671988877, 629138781, 107995589, 192288809, 58920229, 304080401, 759279742, 735325495, 44746037, 140143973, 695525294, 430738075, 537583533, 26063954, 822967837, 21340529, 412206680, 293931406, 599850249, 556284798, 106705448, 218174670, 319731816, 903553460, 337860710, 790979391, 736217637, 148716732, 461996201, 554132331, 66651684, 144945842, 395941440, 6482307, 268441185, 524454061, 545991333, 74234436, 494963918, 514861022, 691900955, 302348213, 168779855, 686818131, 587034581, 960277702, 759366688, 125493256, 602132209, 523418517, 48680626, 357488704, 949415478, 343004273, 913983847, 201777855, 230979217, 121541284, 858255504, 377284388, 842970406, 566986662, 52685495, 467107798, 677783590, 838782706, 385946449, 526396403, 411375618, 809337502, 20377672, 413124842, 346808007, 869571432, 827347118, 462570639, 882016005, 433751414, 800316389, 954311941, 713786094, 401910345, 125117949, 849759597, 677084461, 481945606, 197388733, 615710483, 873397146, 184015124, 77256732, 37759441, 331843224, 334736229, 828072991, 507924424, 149779233, 778257573, 932564919, 839919634, 166844263, 872023783, 629239827, 101660188, 440821407, 315684585, 97158945, 278825745, 981110060, 525045866, 944728408, 189412553, 401609593, 483178638, 908792680, 746512304, 439031119, 387339042, 495826268, 288651258, 773642014, 503579611, 385351253, 935732782, 129465004, 791907030, 305689476, 396578369, 575222192, 843293960, 790189805, 781067192, 598353621, 701418877, 721962435, 472194698, 653549406, 191923009, 720290324, 163267653, 802821525, 487102465, 418067740, 765104701, 322765166, 281482320, 980907200, 713995480, 753808545, 786413038, 163873057, 751865275, 209229810, 585121799, 73051895, 491780782, 727777558, 604837128, 474249004, 618306066, 67731307, 286870154, 45564152, 583446731, 977833579, 349108793, 728785739, 438476699, 420443487, 61799658, 196831415, 52996781, 232218993, 339900398, 216198947, 35439957, 546030526, 397870761, 586450581, 799280329, 366246648, 64471988, 908301677, 971824196, 622136169, 141034998, 58592445, 331673386, 555450594, 264348446, 470979640, 987139094, 826484195, 531744824, 672365968, 808384199, 753862915, 759008834, 652140295, 557529513, 656293583, 3942622, 657890956, 203535101, 968387938, 225603152, 802803482, 40221143, 175050636, 608897941, 334634407, 110396804, 900467997, 572034145, 292207886, 392084135, 926169454, 407575473, 114562091, 428489235, 362409179, 491809107, 324895830, 747626796, 461908361, 234135871, 955165251, 934339105, 834162925, 65897761, 315926138, 779829403, 20366405, 542173846, 878923212, 408049388, 55000310, 257862082, 799399626, 953711412, 539760130, 403744419, 453233142, 811683388, 455933460, 323682858, 103541770, 275487635, 586542227, 774514064, 844869726, 544844669, 474373599, 950401400, 601434065, 242711639, 978343419, 956153867, 575242875, 248299993, 117949598, 862428332, 422642815, 623651391, 580693258, 168307102, 369713559, 860457318, 788136883, 167115119, 488738848, 830028009, 611002956, 621713472, 773751766, 322770260, 727189443, 919566669, 145582735, 276581752, 849229725, 741909275, 585685288, 791301336, 605758668, 20352422, 592908720, 881295681, 472698337, 62496042, 17154854, 79587217, 581011510, 176666354, 995189253, 270707901, 36047140, 880967897, 413136879, 821713428, 567458197, 732652698, 595428580, 965588310, 105359795, 538745019, 148253687, 146539135, 592579850, 433382889, 966300659, 826378009, 621840512, 383005099, 211594753, 441575008, 40289098, 604594489, 720149717, 73422711, 643726313, 755594022, 589289381, 98774920, 113831457, 681536034, 562501958, 437886911, 820214202, 821675568, 595657017, 635802717, 36565581, 911306996, 743870692, 144231543, 540828550, 677698117, 142178743, 810579569, 673413749, 87453008, 885893672, 956513359, 123616466, 563879747, 85040029, 375396914, 651106121, 713615521, 475819835, 102364756, 142161001, 100382442, 633798753, 922426688, 32700902, 30061846, 722366175, 78549844, 149564604, 714869719, 174663633, 405955179, 8970480, 708155870, 585210458, 422528406, 300904537, 503121867, 573306421, 64814428, 524746422, 249187387, 891433958, 300083297, 456793741, 132531813, 365404585, 431542462, 575449385, 966589468, 695676107, 543523118, 236448470, 981432531, 833763741, 607303464, 29000102, 593218243, 396425777, 273327670, 122097111, 650161668, 692176638, 78130469, 528178195, 595403040, 29033583, 928463817, 971621669, 81989211, 520327079, 88923124, 976256863, 397636282, 490221264, 364699802, 366576093, 153521367, 267897655, 690055174, 205911538, 663567875, 796812920, 893136838, 657890105, 870698590, 405889677, 49059663, 926336102, 656669692, 63465648, 264477881, 987384728, 513037888, 315533718, 938466947, 784134940, 845846856, 270239222, 683263838, 524955053, 737812787, 610493944, 391166265, 713364227, 632507671, 710541675, 815790971, 815447527, 946456414, 920950862, 103615431, 415968830, 928639919, 331890675, 202574389, 666588019, 391322087, 133263666, 475158782, 772144148, 179978218, 246135609, 979747280, 149565880, 462403245, 729587886, 371426841, 607225940, 56855971, 466682509, 121659878, 6004373, 400425465, 923015251, 796532734, 953219781, 644673111, 73897011, 611480232, 861765102, 53100100, 38911684, 124778699, 428365766, 599926458, 40474259, 740927093, 356147681, 462208787, 936765681, 470768323, 700814462, 356230459, 52601374, 327248717, 315233855, 937457986, 562365716, 869328477, 82597829, 525989357, 795429392, 270340832, 452026970, 616084772, 148969025, 794786392, 104888804, 443689484, 692059232, 930349532, 206222129, 667588690, 256172026, 975611721, 829945935, 905996067, 587042382, 205337080, 367049327, 905249045, 296197623, 819570803, 203254884, 991807972, 593768411, 82055872, 677761044, 314566361, 296362391, 868106305, 94664814, 386995934, 539285319, 183889214, 410971825, 553681987, 163953328, 958863759, 896022770, 147266946, 221829458, 471626159, 779709960, 241905249, 549977171, 63499127, 32455577, 496580315, 791231564, 275230868, 747635397, 730227636, 881725615, 675335248, 85784152, 627078932, 231559397, 198209118, 74473271, 891992456, 907575471, 369126370, 944337119, 175186364, 559031707, 329849403, 987374663, 415006257, 308024691, 667851858, 436956735, 524158183, 352215869, 938142986, 229295043, 438442008, 757210850, 639292075, 345394515, 9891682, 893066843, 616733049, 229473504, 62093981, 718224804, 734023785, 897373834, 416181342, 288540932, 350789891, 602998931, 493188077, 800201193, 2780849, 138128122, 368656721, 628751559, 93570689, 224289260, 816999297, 148759432, 286869903, 582076486, 547626703, 219319137, 817041416, 976862518, 228901338, 748754428, 813212694, 833887245, 482542837, 193324730, 58544933, 272675805, 779283827, 516152717, 990613008, 525016709, 125961215, 629775746, 409973491, 898831067, 140797921, 913343603, 553190669, 884926887, 580130570, 142104147, 295939712, 185342911, 294190493, 767333564, 632518318, 430514029, 134998512, 264684718, 59175710, 382844969, 11748803, 576151542, 725700131, 713118185, 120682787, 917434245, 521074690, 882099462, 727669147, 922362155, 681226715, 953854367, 988005782, 796095185, 872779082, 896714891, 998978173, 588877767, 322804341, 8710233, 507349085, 163541873, 155429883, 796776608, 385429153, 631777526, 896447762, 752537967, 422487470, 45613634, 126856994, 670986194, 22006694, 600284686, 158277307, 748621666, 272742060, 694716555, 559787444, 385271793, 662926336, 366116630, 768783983, 894890473, 339378874, 611909854, 571850742, 747041394, 487322355, 939104540, 793837041, 149847554, 746425379, 500107842, 579618894, 752822458, 401140504, 658091364, 711145221, 210094401, 291933066, 286141545, 632600353, 496395896, 514710954, 401018160, 790613660, 254421535, 46493917, 828118134, 166918381, 294782461, 517729839, 286278351, 788374080, 279383545, 885430983, 716223299, 273932864, 832972654, 48214034, 135576687, 77824539, 209757924, 648283533, 223532828, 462177161, 639510943, 27905089, 914335028, 504156579, 321155345, 440049937, 834661132, 253821274, 475987539, 468853612, 680082292, 45674454, 16250396, 608491880, 644111894, 760233123, 9462255, 257896937, 259214350, 465258342, 311474548, 518654206, 100784778, 980181328, 369100248, 107079491, 136311188, 535052170, 554554783, 184566642, 30476653, 13082149, 458907637, 656742590, 395367354, 244811610, 389513021, 336504331, 702571983, 980252781, 407037727, 36737461, 216780900, 430800565, 89788396, 524376756, 166175327, 507172927, 326651432, 113502128, 224985825, 77772540, 916838264, 932401550, 362566661, 130227011, 169395924, 458243054, 836789330, 586540262, 801465506, 155803754, 998885747, 243403343, 318170027, 629147850, 138683401, 687753621, 444587835, 930709094, 486980538, 903366079, 620142953, 168133035, 562659475, 512251121, 424213955, 349489060, 88281343, 608882995, 397210656, 236051941, 794507316, 447498071, 847295705, 611200317, 665848676, 26882564, 137208444, 905027672, 876328959, 794214011, 291928267, 50231488, 127466280, 236293874, 841126056, 7158204, 399336872, 274221317, 874541219, 455487654, 780118624, 244400035, 452830531, 951059347, 199353141, 295514443, 101155256, 809043234, 725405253, 226619822, 882133773, 725764188, 763728294, 603737554, 970649404, 299788191, 395128001, 540903388, 36931035, 251311141, 157454772, 873570896, 623822201, 540655739, 683946187, 949441324, 550200649, 9622680, 868208461, 664455262, 899249485, 724732908, 669083310, 959600879, 567764196, 394391779, 505256624, 805954782, 194150546, 4085572, 728887263, 993262116, 420436935, 475943802, 594874538, 443379775, 508357942, 894656344, 62524601, 92238422, 755400776, 995554129, 111094043, 772383294, 348267467, 184216556, 623076386, 361964804, 690957803, 820133302, 780929026, 434198548, 625901594, 428692387, 44150416, 679477014, 373453260, 612888818, 888752910, 23764295, 178627974, 292318758, 858537497, 328855926, 235396087, 403418303, 649405571, 220463372, 520735298, 934234735, 445172336, 7946528, 876072351, 574760432, 135317811, 152863911, 71112630, 516863353, 134368099, 119821432, 63106649, 693834311, 134497525, 700388778, 95584553, 522286277, 998093721, 953081988, 650188106, 601862864, 696972807, 453144812, 769591674, 474009045, 118389027, 50339212, 785975363, 780118225, 948088144, 901403338, 364248085, 610988637, 479289542, 798111132, 160485427, 864881267, 665281841, 43266608, 968878426, 33877545, 2379943, 247596063, 507898695, 111393572, 608491009, 606343463, 726819638, 397507240, 584298123, 42108456, 648471873, 415996295, 29798799, 941629686, 309170030, 830107944, 502046658, 456290370, 282707985, 569122776, 322785272, 747595817, 235462684, 599149081, 173082644, 904806798, 590711609, 761580840, 746933561, 984255720, 718986694, 541324410, 984329126, 568631412, 930692803, 750252008, 854630295, 385069449, 488508053, 164334170, 298322003, 357320094, 942868507, 137352248, 819558267, 588065097, 554896963, 520125694, 108827943, 603053518, 46839748, 296482433, 209160893, 328520194, 498596493, 929358883, 822872211, 926170340, 371963463, 463027328, 139686498, 699033748, 44610201, 227177553, 589509520, 458256456, 306279599, 449250005, 527237708, 457610897, 66723446, 376117337, 751300284, 166094101, 549068554, 130342519, 598956778, 145055911, 978773825, 211086730, 486223605, 478053502, 790382132, 443281836, 168005246, 610644711, 99782006, 913929734, 308607295, 324446402, 33773329, 585358931, 565253191, 715754414, 426216884, 305774389, 236140563, 953218863, 696921746, 971882860, 545126360, 617854904, 675651748, 857079527, 429617125, 464607236, 392442566, 8982934, 729058674, 21432408, 459946853, 417495636, 953593244, 865740203, 813307320, 676545966, 393086421, 756152729, 745475902, 148630779, 770413420, 243162209, 411899289, 167177215, 752459479, 588512600, 6342649, 729259487, 11744815, 850764862, 22518996, 552144517, 988620254, 3926540, 51237670, 474473783, 465902758, 930042139, 292756837, 824000515, 541774132, 439320452, 76492350, 965216234, 862793420, 228489748, 979255372, 425080033, 389412677, 990644280, 52582001, 481304806, 830777991, 786231275, 681011996, 330556287, 605976240, 143149391, 402110989, 59207904, 287886278, 803604787, 74308750, 642201755, 86007445, 452778671, 410734655, 580999209, 879863072, 44158140, 699276289, 775085048, 160734521, 382870678, 609390501, 109656861, 988551916, 483765706, 126144859, 779870039, 292787921, 74114741, 561601755, 95537055, 836072111, 238792082, 762278306, 276377628, 758097566, 698037933, 890878983, 328535526, 919108465, 413581866, 479966998, 872665485, 498637047, 738936766, 523890541, 529996160, 916820520, 428068855, 631701009, 955398370, 265344893, 29960413, 31996570, 770224400, 22108613, 223221584, 609295753, 314107465, 947012160, 61338176, 350713915, 100875899, 731803446, 850934286, 783397838, 770812418, 945696980, 460668398, 376603710, 708194020, 488978099, 926150332, 720088391, 234654771, 107445568, 531892525, 110488844, 724624253, 826020042, 450912478, 561128717, 857126167, 863122310, 997442731, 287860608, 114256485, 438419687, 711482704, 574660392, 412618542, 746703475, 867570416, 103573749, 909977362, 781938782, 732787218, 799310106, 361947759, 390786252, 781611489, 919935273, 249561362, 197202747, 407109048, 999889619, 568880166, 742260408, 708883397, 887104034, 925439375, 342870845, 732929203, 392753444, 188145574, 568775805, 171042802, 594771476, 483104313, 492521066, 785295946, 991935682, 699811881, 379872474, 800296770, 373972699, 50406896, 993456903, 273630656, 290483271, 885955911, 61996272, 761689373, 699909899, 241642927, 799969005, 306061722, 62571331, 818624735, 699386224, 814295352, 427992028, 682519744, 909462471, 751010297, 361358649, 759417779, 221327406, 836634785, 369513340, 112302054, 910869943, 616897201, 274876699, 524079589, 614751572, 908005981, 964602547, 595644950, 891823313, 250839295, 932928913, 329865578, 317791838, 194635676, 430586891, 609738860, 521025745, 394665022, 776701916, 621201189, 469277324, 725316938, 195205638, 773568682, 655563670, 210661297, 146142101, 247450292, 489394222, 329609386, 510113526, 512780996, 928066519, 926072827, 917029789, 32216908, 314578377, 266016880, 451408125, 2299165, 716243810, 523078604, 299308218, 463862672, 325246685, 56745963, 891885611, 580965293, 175138507, 905517687, 926318248, 914781684, 893360675, 135379671, 738791488, 401448864, 452050075, 838860962, 68051099, 137109208, 664663860, 390258089, 23395436, 814550887, 742842509, 559676785, 94270816, 243582399, 169923457, 762969408, 998136953, 302730516, 587980898, 915893210, 682059576, 74398694, 605819814, 859999435, 649869448, 393441213, 404665557, 481027586, 763057967, 379558846, 314096455, 166132200, 91565852, 989443596, 867858555, 231825369, 826654362, 535154933, 285849526, 538463539, 872510674, 368276168, 530664836, 338814436, 728866837, 28080080, 846556091, 66611780, 239374258, 685934600, 66893091, 244246531, 356283698, 227558923, 612238949, 193632357, 587863429, 991882445, 547735494, 110560638, 174784917, 932014570, 751664085, 446582777, 615841214, 69043812, 561062070, 988032391, 206014486, 673728149, 943143107, 845383416, 878511018, 732635616, 277702616, 354424529, 568212922, 315614856, 349925108, 661924128, 926892332, 344439039, 78503039, 287943002, 509403175, 773894097, 308523127, 266421633, 503997894, 951251947, 516360213, 554090733, 511839478, 335966971, 630263663, 513260149, 168082117, 75157026, 707422166, 873922403, 187131051, 604344286, 418246475, 498464982, 543219269, 891341367, 535015316, 687749001, 203478090, 556831128, 936004669, 323557748, 328263819, 307129297, 875284365, 343834081, 45252967, 755156997, 994466208, 476756110, 315999572, 823655280, 170437252, 340244507, 490333036, 863045761, 377053966, 426031875, 683937557, 726599804, 803753382, 937021720, 152788583, 829529096, 804322026, 798476180, 569965588, 781705506, 401781994, 285286806, 52957060, 313194112, 260641126, 453671016, 176814010, 744570189, 358982453, 214682291, 245619405, 535690698, 558716693, 358217065, 100343527, 551728458, 434762376, 890096335, 560119803, 381169845, 244472330, 789767423, 510343549, 430139506, 350057532, 171977710, 285708559, 644751300, 214933658, 947402891, 725889660, 389850783, 650165038, 904585990, 40341174, 655183343, 266196993, 687261492, 927544219, 235109351, 595536081, 233890051, 849120632, 928470472, 704173609, 89689630, 375493940, 653648801, 390689515, 786416257, 710890673, 293646445, 764681568, 998326176, 587434969, 493424885, 969538097, 190125778, 756257772, 203556623, 544339870, 327439379, 294701208, 480398807, 269338327, 35387955, 293873253, 692815156, 58182390, 700787143, 277554003, 353184033, 516914696, 302368308, 61273667, 22895964, 413953143, 553149919, 782801001, 285034192, 280984347, 383690954, 234584794, 798304289, 484545104, 336835841, 782696950, 696770159, 755083663, 635595329, 920971067, 104403205, 746263149, 689555619, 898245410, 137956046, 464003333, 271686476, 962404770, 48733236, 831873161, 181420393, 647307512, 520345620, 879906591, 353608380, 226681483, 226715566, 113480883, 667560603, 143593152, 54657257, 602377400, 251258235, 224251298, 746368896, 726726705, 633174575, 942796754, 159420356, 133869600, 707323549, 832046755, 203760915, 296322946, 523200304, 486556117, 224314322, 397681446, 881942485, 882908562, 540225265, 524210503, 569680985, 295101100, 970629482, 436561044, 463314026, 863205618, 230428061, 966650827, 547682797, 878189513, 108075759, 615314463, 475535658, 936979885, 655171861, 1625425, 420066177, 840972924, 443074695, 168299312, 728639181, 662356653, 697001031, 39023331, 277636330, 958932063, 166783950, 760219984, 730335540, 341134200, 903297444, 672147142, 757192697, 612159987, 693449650, 542166225, 397907208, 936524647, 306376221, 403107774, 271792540, 168721673, 129471378, 275238213, 73834303, 551746181, 95426039, 73055717, 5957567, 450011852, 426249418, 486162880, 270503882, 489643211, 682008626, 98733861, 210140052, 274124726, 656340248, 281106139, 202934862, 786381499, 166054489, 950595555, 593409621, 92167038, 490968506, 633751440, 646050009, 409779392, 595285683, 600741589, 223604801, 605660408, 435445511, 647989314, 459411360, 886564084, 363907976, 935909206, 565390278, 955466350, 495127929, 180340718, 796925570, 135194800, 336270082, 412544718, 92791586, 596087276, 983657221, 369250531, 654038947, 68499048, 540594606, 868316387, 399448711, 671828178, 351935510, 927612337, 108796016, 311326729, 204684481, 630939198, 475121059, 697022635, 932075048, 823365047, 541660551, 552822165, 899272453, 371201405, 370591694, 631721051, 361833670, 296646509, 766010327, 293183950, 6959723, 885509808, 702185772, 371665324, 66402451, 275999841, 163165764, 623941269, 156097206, 447184941, 88656699, 313701651, 241538249, 946404394, 741166041, 480078239, 76335252, 997747465, 625922032, 495498664, 168216382, 429813184, 290669700, 26998844, 269308593, 749024654, 757427644, 96038885, 190213410, 112281474, 12369583, 443613488, 461366431, 364467254, 791138982, 308246339, 11582820, 935922143, 47541687, 143739658, 998141976, 586970747, 271820427, 689852561, 8264343, 333527743, 683336889, 748759766, 541959115, 239555431, 950877474, 745101167, 611615914, 957553569, 326156780, 825645783, 904760241, 403629235, 430757472, 827364267, 942204945, 363725711, 719645502, 724584617, 572306477, 804170816, 297029048, 639248611, 162091032, 507669175, 46131183, 680348293, 963374572, 115906414, 553966337, 720685156, 590231449, 500811058, 780023542, 558080361, 826597551, 272190612, 71597029, 218073263, 901314846, 134307396, 607589068, 836789539, 362613370, 164750925, 49789816, 116031580, 543486143, 548602589, 733762993, 689140802, 13284929, 781136346, 536302089, 171686953, 31614697, 185120703, 700078172, 603282522, 308354919, 52641555, 749437548, 395202827, 567188715, 498008890, 433591032, 888609562, 7730070, 121992063, 367258878, 650079916, 674418617, 113215565, 176109281, 300779081, 136235734, 123837550, 162687174, 792076981, 510025047, 323849824, 239754807, 829722554, 178372875, 771702713, 987530164, 659130910, 126816106, 622364121, 890694670, 745288961, 880185416, 333142975, 479744342, 351739326, 13809105, 388295323, 95881579, 250219303, 320685582, 581607595, 373699037, 257245952, 33879807, 537057867, 510550649, 968382568, 968041313, 90870925, 213774232, 326919053, 681526666, 422063152, 172030368, 619714454, 62920980, 904728794, 662630846, 338237389, 895758564, 335890847, 677626750, 623299770, 897561139, 127290272, 186867494, 84664895, 754390481, 428477547, 486178588, 681643936, 124235259, 335451961, 552059906, 86420000, 409337084, 158331272, 719356481, 359631442, 572788348, 703642702, 826892379, 546174661, 293007977, 486856072, 488119965, 885929984, 690207854, 473293984, 80847646, 658984768, 535627622, 668787285, 1030274, 97463330, 763400453, 569834826, 596811924, 89044126, 990855755, 558174078, 506612857, 472399039, 331439114, 312906026, 257403295, 564913727, 999352219, 883208281, 349421392, 498608935, 373446320, 295085391, 925989381, 623193680, 319879653, 766092309, 129291927, 686127102, 196649658, 93248646, 624011592, 652911518, 922660071, 165650225, 4953971, 664793070, 310867134, 409189642, 356530858, 186300432, 179552868, 81853386, 784186435, 158737966, 574570549, 743177125, 929557773, 16869899, 386989690, 390469317, 246162216, 342548173, 235701046, 307636713, 469419631, 16530661, 441753318, 179306913, 381167083, 684808057, 626389281, 839779359, 615973964, 752050870, 722194069, 960922056, 434597764, 137382625, 77615505, 937204582, 84642959, 931658444, 614738857, 911303787, 162881211, 6529969, 884814999, 258107591, 675060884, 315892516, 695384850, 399417468, 899119877, 773298344, 681799091, 420305545, 789164056, 559355035, 650886865, 901329622, 381640152, 249815309, 130461849, 657938453, 268054785, 272145299, 692232058, 411354185, 696998443, 267629226, 359057739, 355890885, 415265055, 538451951, 91976553, 967770516, 327005250, 899885729, 771036927, 469094691, 926844360, 980819754, 845093858, 912430714, 603048447, 87958944, 547208070, 238913891, 611044981, 73251585, 496965715, 588601024, 87412670, 314381884, 985625902, 24557005, 868511808, 669327059, 247750975, 816215276, 621445797, 680976479, 643248511, 485506754, 103173661, 184815355, 164327563, 656547010, 423596455, 466946446, 211895114, 272447487, 741565031, 528701056, 781500551, 684764393, 930186863, 790899884, 795885532, 608892176, 258521817, 610762892, 709357750, 317620112, 50678952, 955180533, 742878238, 64189522, 498778867, 731711215, 64940539, 730285109, 902456864, 511753234, 113855169, 152708138, 776812176, 200708104, 781527464, 735125421, 726114322, 81006507, 568003427, 823955520, 226921140, 129816061, 828507805, 741425559, 983397508, 690614989, 884623382, 23412897, 719552994, 117734305, 788184066, 592868869, 29752457, 839596869, 227469496, 585260980, 968470078, 703591379, 885875523, 456185807, 457130876, 204899998, 955900297, 64885800, 379874113, 357711221, 608336808, 197439537, 648101118, 815216334, 577321860, 384257186, 454354931, 492071687, 516570805, 775769807, 891972333, 29443248, 958606236, 200349984, 137963930, 347163418, 716678420, 545584866, 133581417, 837362566, 658961825, 200391655, 185877868, 902702127, 435753403, 24129578, 211030010, 66593388, 893642182, 910468023, 129996711, 252784141, 797489066, 105199339, 127638921, 656216899, 204056820, 611755757, 544074713, 139898785, 292626243, 720017993, 277025466, 628859236, 946954477, 961611123, 117875736, 501155224, 265516435, 299378942, 596053516, 63227885, 745119159, 92566714, 540787741, 638160104, 150807365, 255745224, 626913060, 525233418, 595427402, 48991782, 387075145, 260536329, 612724545, 825389610, 690004908, 416106191, 752728918, 211953411, 918223303, 127461090, 425661392, 848255004, 185693624, 974097698, 228254421, 97440032, 997102296, 716716828, 924549024, 970540339, 595970759, 12889230, 602889549, 80488064, 373291824, 470841671, 75509081, 917141880, 138877057, 595019802, 629969658, 357212795, 529118854, 442172501, 500392744, 506559285, 517457603, 658082222, 348765651, 327741385, 373223474, 449020112, 206362393, 474395648, 130632732, 677525242, 3584395, 262831452, 601731446, 152080506, 905235771, 425391916, 596175189, 189958622, 132140154, 676674094, 181217790, 894099661, 418833818, 60855971, 293967011, 614549658, 281282339, 142599524, 823725515, 700021960, 352086547, 534684354, 190215926, 627509434, 78744705, 421433750, 658602401, 126687235, 878535374, 404334963, 180451282, 835870119, 336154529, 449342139, 869353622, 828524842, 992374832, 950196984, 523968726, 395945064, 826532949, 969878720, 579511274, 333179474, 783368008, 66347660, 652780213, 29921682, 630434989, 914700321, 676938529, 605901873, 384503135, 120238842, 689936494, 878798288, 352343687, 563658995, 44299351, 814583659, 687607320, 324730946, 262524028, 930977559, 136853781, 722085372, 735675193, 645053150, 625434108, 383603034, 954324442, 357111464, 112390557, 80051073, 907566309, 79943859, 61290820, 746725986, 136927692, 612871234, 180525326, 579722790, 651699908, 670176421, 912018884, 10871275, 40627998, 187246592, 580992848, 561703321, 262712278, 100922893, 986305979, 180389734, 909884468, 308867111, 512067840, 517798464, 924251468, 613017594, 711224376, 760183198, 205647854, 869180414, 97791472, 303075330, 554734440, 3221789, 557762295, 488201735, 227531043, 718940826, 937304988, 378528231, 587749449, 304030949, 547602089, 76165051, 779272162, 822130981, 438621250, 664308606, 47509413, 154277496, 933016163, 396747665, 777132612, 9749052, 612876884, 979380114, 427758530, 24723631, 913694109, 599233438, 235551587, 145120227, 966291317, 53841101, 94175992, 947512734, 95174355, 450609401, 913071412, 107593911, 563221527, 594629414, 481707592, 392929753, 335333447, 313349518, 749830865, 908151886, 839712427, 502996470, 108267099, 286086896, 277554047, 465392174, 421245032, 859357521, 148294323, 583556956, 769640359, 885821047, 648411522, 883787724, 565215571, 551900903, 227381717, 179337799, 215579061, 277768082, 278693776, 1026239, 584583087, 528371462, 27881546, 465620689, 200347228, 564039971, 35181096, 751134920, 755914020, 687547183, 162545303, 738876029, 122568150, 545180164, 180560379, 636716987, 629069532, 510607579, 931638610, 372950545, 161638197, 129598635, 289600872, 582577175, 265271503, 519271160, 337978431, 513825134, 182797289, 553890911, 219382974, 279910065, 146311603, 673743133, 159595467, 124724360, 720233782, 321393619, 906884864, 90926297, 755159125, 849308334, 149686146, 136123939, 793812586, 66218686, 640522610, 630339840, 217702532, 603654024, 362542712, 886598550, 565187380, 45018716, 212390860, 134883046, 758521100, 191210934, 451932049, 215850361, 892572290, 818611148, 209620804, 502275128, 726487412, 291028230, 740682259, 877053525, 219571800, 171330483, 253962049, 727432708, 573056403, 777403197, 914105575, 750305226, 559679635, 561091119, 547577751, 796039775, 971738079, 29905273, 701265228, 759589061, 646642961, 32414453, 555224262, 730056879, 521295703, 202883014, 755998276, 434296667, 816869801, 522006294, 169420067, 895512846, 55939321, 413255446, 1932990, 566791972, 779464792, 909375144, 136244709, 56983629, 968422601, 167817775, 205758987, 262367428, 982289837, 335033228, 727349034, 617541588, 218160552, 879535082, 137183478, 449664955, 649648520, 326003018, 307092994, 981178957, 232457573, 205756936, 531339011, 367310368, 614050915, 374043031, 824751732, 243501226, 963979284, 885413760, 162593816, 266583069, 262007442, 929768126, 524240241, 704521420, 672731936, 63069349, 691358339, 498107543, 732140003, 996339573, 853864280, 8199845, 841400995, 113284341, 696294438, 946021267, 842405338, 155602539, 389287475, 882406311, 299552752, 694176621, 76375646, 375446300, 99700770, 301371350, 680178774, 947986291, 216343896, 923926103, 197498381, 880089955, 682832351, 931299132, 2291854, 411495653, 471131894, 338299517, 467822996, 372298362, 95431939, 524637902, 484706733, 79319468, 728352801, 182406658, 438291293, 240323456, 32807331, 813448324, 388081943, 951627688, 472253822, 226928870, 964921536, 449339131, 652420411, 207889655, 793872474, 649228648, 309651489, 89946019, 945686697, 316091287, 299468881, 759378650, 840185565, 650402416, 199844845, 660382763, 46230231, 190167695, 682845053, 527648497, 895369336, 928605055, 78160345, 277749080, 739220543, 160658503, 255953763, 485874857, 724057010, 206669927, 567042081, 605305394, 989064566, 375561671, 324269624, 820663966, 565569459, 353942730, 332711124, 730876310, 211438830, 560825978, 10880540, 123036380, 717360380, 162993261, 154636101, 798053149, 641884840, 463856691, 245548445, 786403917, 993549722, 856462645, 15295526, 617172314, 245775578, 705873606, 271770260, 94311296, 779699197, 378971812, 696922473, 176139531, 497457604, 584690066, 549640892, 900414950, 929986963, 33196076, 271676298, 210162793, 539367568, 202745220, 65010558, 562426437, 728679498, 172186506, 171334862, 584946673, 359619231, 303977426, 65230784, 252085497, 253876013, 701227005, 128986136, 885427572, 191682412, 377308475, 420902788, 179712760, 725658526, 947535762, 228900794, 256797037, 100213668, 50699736, 563265711, 523101136, 309323731, 62344563, 708267488, 57372597, 553288769, 335681761, 515715235, 113764173, 202754125, 215928382, 413925734, 948301104, 752049806, 69682961, 371955952, 149258948, 824024679, 7000754, 855356995, 955499409, 157586384, 824087867, 70916440, 889068377, 869052279, 26942440, 579303134, 150288214, 480127660, 14786410, 132250984, 768418743, 795316757, 207277247, 963222774, 963198716, 576082704, 857329948, 565389667, 168700653, 402999095, 472246007, 240535579, 136542961, 447368047, 993494432, 396920176, 191884789, 351868965, 64155272, 48322549, 526104909, 132762905, 548651585, 811303194, 950096165, 855550479, 573288513, 277084447, 950144194, 693392938, 624036629, 622616386, 669630360, 704193554, 591939030, 519582001, 695525486, 325628746, 961468805, 533654550, 237560440, 990116913, 658961637, 780379989, 343470601, 219657886, 68943320, 51240894, 624426920, 608347460, 325190579, 293955618, 958857590, 34673312, 225345699, 67923645, 748255536, 827632207, 618633790, 682814202, 38653109, 51003159, 416790156, 927001870, 4843472, 758635726, 103460839, 465828046, 581174801, 284309944, 485987846, 405045476, 320370416, 73143641, 915632623, 1673401, 506078222, 600369427, 770578218, 691367179, 573936140, 345920038, 620755520, 685002275, 454229858, 360814251, 49117107, 143996143, 264254144, 571929996, 47940988, 891888199, 288531746, 427118187, 256712101, 981515345, 85841278, 731450737, 615920333, 844862758, 10209715, 96180445, 757098004, 770866239, 785278617, 825461973, 281286875, 407570741, 139428614, 553487410, 87228230, 590877565, 784880470, 90598589, 40452052, 534711315, 176434382, 955927041, 586106303, 579785638, 155358895, 766181225, 984922029, 438517676, 940004131, 466658744, 847732488, 369593137, 587165877, 877175551, 252324441, 726397362, 373195963, 808957444, 486781397, 740638266, 209862744, 469448217, 494755214, 925120007, 814590019, 245796270, 467509929, 383793345, 624905027, 243894364, 564474821, 113275478, 211436728, 346218392, 462551377, 274340743, 776167844, 530390944, 214240677, 648676161, 651063523, 671774825, 851074799, 478902472, 219901936, 186189885, 640083671, 119484219, 452697116, 144000194, 863037539, 445781175, 994577626, 195777681, 55396941, 677437414, 594069728, 544191844, 34895253, 453281206, 181642393, 867663397, 405877745, 879678106, 445565606, 219437394, 294435913, 871725860, 225336336, 633114662, 174670895, 787559160, 306656437, 960710660, 717208976, 991188529, 97719311, 471220471, 920459882, 97069384, 792130292, 830644206, 429378405, 737218732, 853878125, 523325221, 632668188, 306138379, 54869548, 904830680, 221558975, 8737038, 273895230, 124096195, 717663339, 20861037, 325552626, 37375914, 917466766, 581096325, 525493738, 663286074, 857587858, 353070081, 25944121, 317758961, 946136076, 490370774, 380437284, 259950475, 758261283, 515550247, 327645520, 457795934, 876330508, 713924717, 337006884, 196362031, 255745980, 939323594, 416243846, 80074232, 131037661, 423128491, 238184174, 529798744, 221872770, 535172836, 45193096, 404674896, 73134628, 598416294, 304799985, 964112805, 727084234, 30793647, 929171366, 600464365, 985669253, 117500676, 911895709, 58563335, 974646084, 277598344, 308724974, 557980030, 40880428, 166798507, 781618107, 794235797, 458552605, 20657536, 993278967, 886606311, 562047912, 561860663, 232593431, 747922664, 5459379, 83227078, 395855316, 702583528, 169560403, 749130927, 998815653, 98854320, 72219236, 807416602, 263239594, 965966779, 263470458, 296662703, 111554269, 974552937, 79122957, 303792318, 350165235, 742037021, 4154518, 49750932, 20285562, 53826164, 562467279, 55167286, 469856687, 240991096, 459638691, 111603934, 502479863, 903226983, 574949596, 557380014, 472890615, 86518745, 504447914, 511601832, 8157476, 603468449, 300626425, 891794264, 587847533, 359684525, 555085963, 694983770, 587130367, 141220582, 348638767, 67042578, 686234010, 303374670, 749585339, 10050164, 105301447, 729663263, 476689006, 607135697, 262234419, 789119231, 294478241, 162331272, 659077420, 31525393, 720465659, 735332751, 197115272, 882900851, 667622672, 906600566, 976017673, 814403651, 150041678, 365124610, 654762938, 43528208, 885607303, 489738162, 344743049, 91568512, 16811990, 290006168, 81716164, 485254443, 871675164, 651347275, 481496455, 394434154, 202047619, 722067184, 516743775, 921318432, 539658266, 533446956, 636187761, 580332916, 775251200, 565721407, 411544427, 631108925, 231764000, 383716529, 427994889, 36564662, 108560820, 277685687, 519260415, 351827180, 983368499, 367012544, 425462701, 478347925, 588240383, 216373993, 789258245, 168840447, 124875822, 124938974, 471500893, 687997184, 494435127, 452801396, 348196158, 637460526, 613852951, 67035626, 435694858, 422675205, 202202193, 788519297, 597157693, 738363900, 42136931, 115986582, 901015240, 241072582, 930837940, 874175665, 65482394, 904388329, 747643519, 320084523, 601973098, 379766443, 708905846, 363568140, 720807446, 905246551, 509463445, 660147362, 587693417, 559240353, 263777273, 548889016, 421730945, 599058604, 176003984, 924529862, 502076401, 271942684, 162806317, 568978338, 166958299, 9649071, 115594430, 128957728, 690109308, 551721028, 9383013, 580209654, 769389398, 455186677, 911846438, 454807537, 302797519, 114631389, 702546060, 524577890, 319649914, 375656128, 852945955, 83571093, 695209890, 196506812, 721218516, 606235773, 129836886, 548663025, 265791324, 666708673, 922293786, 623513696, 860710529, 777564418, 845337611, 934654564, 471378674, 432384043, 132538616, 114046268, 809946190, 818723517, 283258802, 693486023, 317243928, 850297010, 81645797, 283411480, 550679287, 767235459, 799046412, 759079842, 583415547, 660527451, 810698860, 484845285, 681816372, 325904739, 955906233, 809202058, 158128549, 913758330, 112712956, 369329559, 433729542, 670495786, 240803513, 860140250, 156272641, 962935905, 419523092, 110029817, 364879333, 162575530, 324782531, 331277335, 141738528, 423534154, 46764790, 481479332, 354120825, 906396208, 964555240, 357000976, 59641766, 486314276, 693520945, 288796553, 749099015, 10759251, 176956905, 857756218, 80827183, 59953503, 682255473, 2381243, 469626649, 277863697, 55102999, 721540690, 855814989, 846988285, 103895767, 505770420, 766059469, 925582402, 701557364, 332424845, 251619142, 828904420, 137444072, 842054878, 28910580, 519120080, 94576497, 562213048, 284726613, 122503535, 105639278, 21120304, 368831421, 989783399, 797513707, 25583415, 145717787, 443124094, 762967548, 731058666, 311308253, 367982965, 377679071, 386484466, 259109615, 799968491, 526443037, 771009350, 971395738, 492454579, 789118017, 363171636, 185904455, 150918733, 232535022, 720363421, 519317708, 197394439, 925825548, 316766281, 526809071, 303334665, 343960510, 168630397, 8187195, 548658771, 791548993, 629387249, 998987026, 19895419, 911344183, 396562254, 381705957, 308235776, 167426455, 908186431, 456340900, 75634104, 400135809, 470930996, 805229484, 469838530, 814364909, 924006687, 797073968, 871300292, 521131620, 152603967, 718046425, 384642287, 794208640, 945079675, 968812255, 34019163, 357037151, 962066701, 328722876, 887283575, 508548692, 232417650, 923974071, 39956870, 409801919, 861671326, 454397471, 462547923, 765375913, 172717550, 418419039, 776352497, 875387370, 37488753, 431439348, 646465863, 406219328, 384667450, 75154559, 303151089, 309899991, 522120916, 785996288, 849611270, 506018677, 629971951, 686968087, 388278502, 597144410, 960327621, 716135765, 601136701, 387509946, 634931410, 949204194, 267750588, 564044294, 233502301, 588908365, 622997794, 777299645, 311135199, 422815915, 30825977, 470131465, 768023135, 721914038, 924217613, 479876121, 677840336, 952336424, 530077473, 524062659, 365924988, 745675734, 849451267, 440047101, 942706320, 620069563, 510047993, 820297875, 155905928, 630955180, 46184373, 74147552, 726922237, 845197600, 726116551, 923878260, 832289345, 652538682, 851352802, 750259860, 706876680, 438874876, 985650633, 349716865, 744038045, 703021210, 223289203, 933229321, 137053780, 41248733, 312319683, 162171586, 158570139, 106818310, 733236410, 5747707, 489014755, 4893366, 643313816, 634875442, 55387775, 481460389, 299654462, 338629995, 596023014, 822526526, 424661120, 731341946, 489599793, 232488623, 835554891, 282047536, 866932499, 492177253, 101036573, 834389950, 533037000, 199042797, 264525425, 523653486, 803024792, 54411242, 116935533, 514300633, 916235762, 838586778, 794076949, 653480771, 320662258, 897021798, 300555967, 869647716, 943693616, 967613960, 22238268, 552753628, 791315247, 136182305, 495348529, 410578192, 599826490, 130990930, 885581284, 4192866, 438779561, 904919864, 809882416, 45368934, 71504288, 563291873, 937644328, 774557337, 743846937, 893293387, 571716078, 473866281, 641506400, 757131486, 939762335, 669357284, 55732135, 167440853, 459865908, 844342581, 918358878, 342821635, 452813176, 318155332, 602939002, 432226818, 737178750, 712425326, 957351279, 910199344, 933499241, 782123607, 875800129, 967176737, 329638625, 825757024, 177727030, 93061971, 828682632, 483736049, 905905831, 191135426, 322153359, 190141672, 874822487, 251923092, 452554399, 55211557, 479929701, 262079971, 13007838, 102178687, 608283311, 925874121, 731095059, 242036093, 777330736, 902949360, 511519284, 727633577, 551800283, 223340363, 389094355, 224381125, 276892740, 449016450, 902796978, 230647426, 421782694, 720544968, 610712440, 579599929, 59353277, 854839522, 787016179, 256068249, 389871162, 940260068, 468816457, 64043553, 537093376, 382331039, 826159478, 659761268, 11510807, 635809656, 945449068, 948686399, 467360451, 835989858, 483678503, 875199295, 393101186, 657977076, 444446494, 581795599, 129068786, 684936930, 646372987, 933126129, 713153971, 846082920, 489920051, 333796721, 620046410, 210020014, 363579120, 380312255, 194386610, 6674001, 571682292, 326325670, 193694927, 490085523, 648295977, 834602537, 149494496, 119406553, 51495365, 347144130, 442977305, 807760759, 165604812, 235972306, 243891366, 105326436, 280404575, 109111680, 747169513, 404461710, 573118577, 109656609, 528516718, 976887712, 693358216, 38683504, 517194821, 521523192, 48579624, 544227584, 826843812, 855435298, 629171361, 807760259, 12522258, 668096641, 329160873, 194237271, 336836258, 589336826, 227806051, 95339346, 414960141, 158689409, 316339601, 643069643, 943657841, 512124231, 708634729, 416076414, 558722946, 666636428, 162614186, 77983086, 543049004, 648150219, 567652605, 9308141, 807023363, 221083517, 731096984, 283346105, 155784880, 717877749, 310201989, 625180319, 983343597, 663510519, 712074694, 912942730, 596871642, 271441999, 953379652, 286318111, 552500531, 604711387, 730219747, 124478436, 584931382, 734796132, 336109819, 333864493, 585071234, 37214523, 92413667, 105917865, 53086192, 769639147, 556015600, 520619778, 720815059, 353193066, 776829977, 867757918, 266242034, 919602474, 880067065, 993626165, 320142211, 877620869, 748665395, 445104305, 900806716, 261447860, 799209058, 69435706, 161785093, 925325580, 151123589, 518645847, 73667068, 388940881, 653258811, 610779229, 152211567, 830856552, 912760117, 341963036, 654685363, 341088237, 827302873, 983040367, 532590096, 865745570, 595253263, 62843680, 954778478, 273719603, 156244788, 327007765, 534113031, 356751392, 557021749, 627493073, 58732674, 259836396, 812286398, 175256776, 2404527, 845286443, 11894875, 920692034, 358312178, 781605285, 849588917, 769039719, 202750077, 107944877, 890636136, 18756295, 759938150, 24766797, 876994388, 882612794, 667392551, 634964409, 851619216, 988482237, 127817297, 695581257, 804744417, 835706955, 246211560, 721479678, 228768960, 374663135, 944755896, 173834511, 531791147, 119916540, 603069208, 726731416, 162815533, 836494221, 143849481, 216532660, 596562365, 644496777, 52751261, 975944600, 640084125, 116270272, 896622134, 71830572, 243351138, 545929565, 160426811, 419584043, 70655846, 682568513, 714968448, 234835602, 655340058, 617526345, 526526396, 300499564, 506643095, 2301160, 822469588, 465856238, 796017271, 750513192, 855197909, 353204643, 896828952, 373145353, 785408877, 283598939, 143813937, 222248637, 32115506, 611697187, 244400252, 456206623, 964897201, 10383796, 348508420, 244679767, 57536453, 534799239, 790986674, 320686837, 896048053, 373545254, 692295585, 457662575, 324900372, 651694674, 579155749, 800650169, 177436433, 994221136, 207416340, 11113481, 179825081, 195281417, 818975565, 470783820, 209019262, 641033620, 729026333, 681742599, 694456317, 694460189, 252036545, 913993842, 218067239, 145382415, 262541207, 214461157, 775315565, 30737723, 63974719, 861998028, 534490378, 786424286, 268991687, 147420657, 13495270, 895425419, 578897008, 578262061, 800229305, 491411603, 892777318, 851833195, 57884514, 854488120, 909928912, 788846125, 213230468, 758263248, 377022205, 850705167, 220644944, 279942837, 951210679, 438039789, 423755433, 494885430, 957637736, 995408914, 270212793, 176096511, 430075380, 722369810, 108016341, 83203569, 146318918, 540276724, 645191838, 898574807, 65249177, 226743149, 641376641, 953705151, 779198562, 541572677, 98403603, 754212686, 897696360, 9415448, 61787708, 9111044, 189540852, 168510667, 17888601, 287786267, 565969451, 506562578, 750030166, 139789830, 166539297, 995089729, 675802827, 102397057, 741910931, 154741923, 226609397, 634230311, 686164807, 163491855, 391985846, 352895145, 226088473, 244249976, 934558825, 417751153, 91133541, 287836938, 37908240, 558723062, 429579339, 330901542, 101048894, 774488319, 189716155, 749212489, 822116455, 629702608, 805896320, 388364797, 471701529, 272650279, 650982539, 337532921, 287759581, 827463140, 7009381, 910735664, 68270091, 969492081, 614016261, 562420273, 369134699, 28283293, 137644096, 870155705, 691606302, 737082800, 147585893, 435312736, 456846962, 90098348, 970558829, 829255120, 35360610, 388531310, 922114877, 463489575, 54367471, 952238556, 682428857, 149675315, 95185812, 4675630, 933183077, 448270727, 707812609, 767728469, 963849845, 101052092, 71806393, 489297868, 390920736, 977587250, 556915450, 264733932, 394562182, 378411767, 518928347, 240021253, 749569497, 349338911, 442042927, 487907342, 182663935, 498684248, 816660544, 294697324, 804702729, 48606227, 727520775, 580489500, 759952738, 498140751, 639167170, 846032802, 720029958, 760671377, 241453602, 945123293, 913948523, 14541462, 63062868, 414949696, 72594923, 865867278, 878454626, 218972035, 35908768, 350878395, 24505844, 697787707, 319808562, 183574629, 408919603, 625132797, 709668629, 605007297, 657843279, 857857988, 361544282, 278607656, 589245199, 76079823, 397580017, 772222653, 279978788, 756142077, 503943651, 521032184, 987076262, 97873147, 868973279, 527978697, 42718736, 607833781, 731820234, 483300806, 786769936, 342367670, 901597049, 24434773, 479753980, 201493212, 423089125, 732457425, 476095062, 539585406, 530583558, 593585194, 352155627, 813779254, 321796043, 201771318, 637270081, 893463084, 168290807, 142437417, 881775902, 695892180, 399407650, 205183788, 570896049, 648429091, 145192383, 330510351, 192081506, 771118283, 50060645, 364994558, 170039893, 717742189, 138314026, 318753208, 857705099, 57561320, 978460897, 769666785, 306055182, 980510368, 520397168, 976676144, 902020734, 492085571, 748872621, 192926066, 917031008, 845244083, 716150466, 63156343, 899918957, 466516598, 445521126, 167495407, 682836445, 742906315, 850072358, 328161145, 530116499, 706044649, 779589576, 421075763, 845540729, 35577712, 657394905, 821789288, 288457336, 824723219, 32261797, 238326731, 18260, 293243174, 103660449, 55359406, 445112581, 567977565, 459593660, 550214428, 709800843, 321689932, 555614772, 359477539, 693691528, 511296426, 563094366, 487125841, 15656349, 179429638, 55710080, 38546366, 998878664, 400515304, 555408954, 645647415, 673389898, 752333791, 841422625, 213640792, 732409374, 811192808, 237205923, 81018473, 767235662, 591449873, 833721899, 212088935, 467233986, 131429950, 612247660, 697019708, 332018073, 603769052, 660367592, 200545046, 578770432, 662677236, 857505470, 695520183, 166617305, 141108696, 809121892, 858255626, 875545738, 196839209, 20542613, 678996575, 858117661, 443146810, 18473261, 748334621, 95262507, 31991300, 645679183, 145093179, 985981275, 368700163, 237020812, 672487816, 449086535, 857160737, 823882041, 99432543, 906871546, 103191920, 644156619, 576936275, 98676457, 837991959, 350785453, 17857977, 663838787, 741919093, 740679896, 378972250, 374203455, 347079826, 110000263, 250555949, 55072078, 293859791, 186450418, 269384489, 428286561, 350876115, 293091469, 948728132, 911375053, 388654737, 922305267, 761841227, 235220125, 171345822, 139831396, 784473113, 333384232, 603176339, 439376964, 170752592, 937667456, 957032239, 678955736, 461976797, 759001081, 562627940, 336103574, 257766346, 713197720, 986127164, 472008409, 633249772, 998233952, 269464063, 61982664, 284787763, 842227964, 586852187, 932190154, 768208775, 881131507, 586169798, 274463646, 101900596, 988485979, 80981980, 469016392, 208688842, 307335214, 454974902, 489003403, 342983769, 286011657, 585838603, 55913500, 245764011, 218206758, 710448113, 634414123, 836663737, 220860548, 866499868, 343106156, 980271187, 908903195, 906575985, 900919181, 13865154, 996292455, 637583375, 596513463, 467538040, 292401674, 478274926, 58058278, 984688075, 94079979, 877201666, 705663465, 543746541, 474060890, 515587786, 973220043, 315551241, 917616820, 946444067, 729592736, 879055742, 214085984, 638436943, 86762697, 454797896, 541379768, 648654200, 383094656, 513094877, 632576349, 386409273, 737107187, 969722542, 480135116, 534333596, 720588362, 342059801, 994330150, 638175231, 783692184, 640138787, 649190807, 32309320, 857348071, 743882549, 992574858, 508445864, 47831666, 249070053, 181261489, 640437593, 119303700, 378383281, 202563138, 492031829, 391201829, 105536271, 685318430, 708117200, 77563126, 8371422, 413669006, 615998721, 452217236, 551738880, 991796856, 362336921, 403778382, 904434001, 263024609, 917921353, 866026249, 847189600, 256958217, 934102126, 931690713, 427141032, 468686391, 420549357, 122254659, 536855618, 27256515, 970535536, 198008661, 299042106, 191462360, 59151141, 159209885, 693023030, 922701726, 421775869, 269231581, 351563964, 175246361, 768501197, 972570681, 449123207, 67751497, 637158532, 690328380, 352896161, 274119093, 793619754, 707240821, 74644290, 806672285, 846142467, 781107702, 317510678, 576317692, 442270613, 725681775, 631900226, 228092108, 578152366, 978736085, 241577821, 442663181, 195987837, 679979578, 453918890, 304230998, 805061131, 275830798, 461669807, 121519172, 769884928, 421987798, 145150763, 138716563, 467456002, 100487028, 383695827, 204255416, 366381417, 263670193, 606508238, 978081882, 51225567, 652080579, 894843137, 786413845, 790569701, 569320768, 571207253, 934564782, 526791901, 842969607, 785718890, 607694149, 217173423, 137481138, 737049957, 837357984, 221697624, 938295588, 155672047, 318598521, 248631263, 401905818, 623741818, 135060185, 921731824, 526648608, 563058618, 849604279, 187873481, 135423967, 169029216, 361676923, 784403392, 549144223, 251248336, 536634986, 837956182, 23231509, 729946810, 309806198, 469716158, 882701964, 824537885, 586586606, 205795448, 444484602, 730450441, 561865152, 263061096, 172483978, 522578876, 778357825, 409099190, 151766587, 780468546, 337927191, 265499442, 856661299, 1394251, 80856485, 114134706, 525887312, 515004071, 561414751, 563891065, 420115388, 457670972, 577223776, 521114001, 2934913, 502398141, 106069733, 205695730, 116437247, 195216110, 304232414, 264693950, 496130715, 311508175, 958158390, 942853486, 623543842, 927839469, 87872275, 178348232, 101681328, 195203363, 152377918, 828230062, 865667823, 242647486, 272624894, 836418407, 50187086, 197062546, 273248035, 81254136, 543908051, 66122985, 356404909, 386699509, 95536886, 732423842, 717831803, 116419965, 982452167, 42710267, 643058368, 163683946, 239103742, 921857091, 720078174, 725983367, 932318794, 280649074, 63997382, 61243793, 706160985, 964200691, 649259340, 972223941, 580081552, 600552643, 968280514, 49216421, 757589056, 37567752, 357043348, 262171963, 661553279, 577726223, 955859685, 463230354, 959653079, 827428782, 719401255, 2569414, 425796434, 367538634, 637206285, 934183696, 626105769, 474044195, 813002006, 552695983, 291185765, 35600352, 258758900, 151947678, 190115898, 364623319, 901495084, 664684679, 999505452, 187267445, 279958029, 201253394, 730486242, 364151641, 769275977, 465633843, 874981252, 131293218, 532211890, 833796744, 977913361, 497996372, 85373383, 623598939, 446253783, 776873912, 494219750, 115309506, 408687535, 584559464, 31534370, 450594357, 47881375, 280170495, 788303847, 134351948, 681249752, 560715547, 977312997, 923838854, 519676119, 804720456, 127468553, 473330005, 399540912, 150383864, 601413927, 887892687, 343515321, 708944670, 720212067, 61506451, 980754004, 231708426, 517714796, 705832419, 937933344, 684758571, 928784375, 623452470, 276578194, 909081914, 268085240, 288316398, 297229204, 86339447, 756285908, 635027767, 938615973, 359537975, 142646694, 990124506, 163617464, 556306732, 311153717, 652539412, 733035681, 270088860, 447372457, 173482233, 776349433, 118239219, 51767685, 125460914, 262963442, 365393763, 600757462, 937186203, 970369111, 477586324, 879529388, 248804310, 625747773, 38425585, 96400573, 281673158, 221138419, 242895088, 726576738, 432468123, 267529500, 335322381, 335536083, 786546225, 825167725, 466799827, 77715718, 13512773, 97285259, 990544091, 737087268, 708100916, 461516001, 216384852, 601136054, 549944420, 297691060, 180815673, 16471110, 99215510, 923275643, 705350332, 239251993, 245800258, 279414447, 322243512, 75262836, 812001412, 124061121, 430087336, 497334782, 861308011, 771034249, 802033890, 901342146, 231562618, 220847247, 607480965, 923959366, 324921077, 129856701, 80596265, 759576405, 454959281, 490579027, 868933938, 381655335, 217000136, 883853925, 94935510, 386375444, 479089002, 299627084, 288237422, 755779728, 744263712, 905043099, 159283522, 994681169, 640962338, 767252120, 450362016, 870390593, 972318359, 284741460, 64409448, 263505887, 319001453, 257453880, 2842780, 426938950, 715844736, 469602321, 668381605, 911492587, 81275691, 268510678, 648831681, 225887400, 827261525, 558307113, 878343341, 634399575, 194165756, 677946449, 53873210, 885766479, 622660773, 406166107, 992875611, 244123267, 623248537, 417003766, 728645744, 941253213, 531436981, 223613202, 444243460, 615226458, 960558780, 224674462, 595756816, 223532756, 307280868, 247927813, 747162801, 892122877, 194570928, 296218542, 546313150, 616199646, 86743386, 140903998, 234682501, 382613809, 491870386, 80247005, 873154494, 280791653, 489030447, 167512790, 341681456, 363193383, 468897832, 854748510, 524171180, 818991988, 664159015, 263535988, 695635016, 543530251, 45953529, 778416548, 149058238, 138530868, 672099484, 750873430, 722114814, 753322639, 720039177, 140835118, 451767621, 910257828, 219427606, 92898961, 480616062, 609647102, 966547907, 758277768, 500263551, 521870031, 888898943, 479613082, 515501522, 418223962, 69022553, 74539409, 99535524, 277251822, 704768987, 355622893, 597499174, 383227198, 41751671, 888441088, 63100576, 16049150, 791332458, 631268038, 323422766, 529110229, 739827710, 116362195, 975088560, 342849749, 921770383, 8807833, 608960070, 903494462, 614577131, 211970090, 494617023, 758509954, 138095561, 935922175, 747881914, 111553058, 296760731, 927308292, 114633751, 292052257, 680492314, 670867667, 369727012, 810575133, 896192078, 754060832, 153454033, 902425184, 162614261, 924044845, 761625092, 982759078, 441057256, 152934166, 621425310, 675857261, 850576022, 755760170, 240353016, 344859623, 828884485, 854470112, 935262031, 418822573, 708859028, 728492088, 520137151, 798008279, 29053262, 332989505, 577454263, 513439417, 266216497, 150807358, 357061697, 241155022, 296149738, 949653667, 857360649, 277547505, 12032924, 720943718, 770263207, 513595359, 742127048, 194927951, 150558129, 486725130, 262374809, 751637620, 464213654, 172666197, 755221094, 722710384, 667007078, 783677716, 816090331, 428860085, 968762054, 655128853, 959563035, 938418542, 669516577, 939723552, 836411102, 367090141, 325151765, 167505141, 951219890, 940500400, 81392320, 407489667, 389212184, 470605770, 614339196, 815358857, 466347618, 883600245, 262189151, 554665415, 383633882, 363622149, 855353892, 205304093, 2228393, 118835755, 124127203, 769118506, 39036799, 944926340, 917413434, 983104951, 136938911, 652575896, 26848935, 518214023, 338871681, 78860205, 624509720, 240392995, 909419244, 473081505, 803595723, 277217768, 66468200, 716785354, 329619216, 48500986, 798676038, 939674053, 182118174, 437093817, 267619280, 946208494, 667855732, 173906004, 618410046, 886231519, 834274728, 235552632, 856110240, 363550144, 161828154, 868656721, 631531070, 329174444, 898342453, 40113463, 368917185, 2159290, 788510769, 420083323, 924508669, 671965247, 476441002, 644050601, 999882306, 590847880, 915155032, 800441775, 453551568, 799666338, 128057424, 310878492, 822306417, 307061928, 760223596, 66598814, 629058950, 179244616, 805932346, 71050953, 11690073, 352660312, 594396308, 137047895, 855286925, 725375122, 769488055, 467816820, 803267451, 410183668, 313505319, 80788621, 841465607, 645562386, 666315060, 464563103, 772196078, 468291000, 121702433, 813539703, 91445342, 825475795, 402351863, 276147520, 727571620, 347235558, 416370894, 223259575, 650399170, 669803702, 995334884, 695701717, 695768976, 819243162, 41840769, 983435405, 673902811, 919962580, 861778884, 140331373, 937791460, 145038861, 882611250, 733707374, 97237429, 843823528, 68903956, 605559301, 732343015, 362114632, 668304517, 190172603, 230799483, 786403818, 543647274, 768960072, 630878559, 6704828, 199247172, 724063703, 379251356, 632224326, 402895556, 622596908, 975741201, 311533734, 10888135, 854395126, 923889141, 768843235, 384416426, 5048158, 932891365, 724910038, 588376725, 886222816, 231710898, 996277666, 194822623, 491273793, 244188839, 102328628, 408443586, 980976385, 511750824, 737247791, 808228662, 322264436, 7728119, 368999099, 224808744, 503002027, 266441822, 614403159, 460615009, 439279448, 70791993, 539746372, 682537993, 838883729, 727432255, 917091822, 937005626, 224821415, 882714531, 455964492, 438705287, 744279680, 939016959, 969897386, 811975434, 707056299, 28465969, 518532113, 44047520, 939939890, 124045652, 727743750, 278906559, 979103363, 395964261, 938291839, 669976982, 638329124, 261864431, 225080144, 999420454, 73220070, 418732478, 615348496, 200386077, 389497151, 549381022, 995376014, 693816665, 86201648, 957840968, 678633649, 36245086, 685677613, 87234598, 760960473, 135830255, 118424122, 636959491, 175009784, 548653284, 477510266, 283239142, 935723245, 535324332, 457270853, 760084543, 713872793, 361225423, 684337215, 643322847, 874923765, 45356532, 334320478, 708659982, 281920044, 447891415, 47612293, 412220162, 96382760, 906235796, 354504989, 362952289, 469680996, 455975947, 514728806, 821732591, 780357278, 359653887, 322278494, 159142543, 957016970, 309628585, 403363932, 277194224, 411374783, 962696191, 160212831, 978775735, 732599887, 264539850, 310948548, 977354408, 468703903, 959717298, 149039326, 734188114, 106092476, 75118842, 498226026, 571231955, 618710812, 574956485, 267877218, 93077414, 256280396, 791663481, 765041991, 347762599, 208158788, 537777192, 235663120, 463575828, 889010930, 551722394, 383901419, 610099252, 224360025, 821238571, 489614484, 623661233, 196543733, 92832440, 175411028, 340365701, 788802318, 793818953, 519841618, 66047330, 448487961, 550143313, 786266031, 111771000, 691099510, 748007987, 177515117, 66492459, 598395640, 850304745, 6962070, 38443827, 958434102, 792886226, 364901519, 110982537, 443301355, 843570004, 792397810, 481782430, 223078306, 948212900, 752483398, 181625857, 429071989, 836839597, 312812875, 998138774, 645716124, 507754267, 533162443, 510544201, 654786600, 859258635, 646793912, 827356245, 86385354, 614240885, 898560407, 857669069, 612593454, 668654087, 51630048, 760137102, 624791077, 815687819, 603587397, 168641939, 57923252, 567610426, 507086402, 98812766, 806717338, 15189597, 448727840, 904549008, 658492091, 229744719, 779462075, 436770824, 799750424, 856561144, 782841688, 310168376, 964332996, 712589072, 958984907, 485381651, 565408232, 75018694, 751693269, 228119549, 653046765, 200292909, 206846983, 268295380, 293943808, 284727240, 881220393, 711293188, 248391510, 911033595, 644065935, 530131948, 118592035, 371428265, 192632173, 74028667, 637846574, 303399615, 183614596, 953058622, 400502275, 292777945, 775476421, 684702920, 365358483, 374629044, 18803402, 245309491, 581964923, 502635872, 847391007, 801414257, 339292262, 699222997, 372465482, 96665443, 795327921, 164598911, 234536908, 466394088, 878933287, 250825448, 314499320, 567557167, 742875575, 37914577, 896208621, 643280003, 118394754, 629474438, 919623053, 904381764, 76965615, 182161054, 27094505, 124032383, 574672686, 65904289, 920186408, 244292897, 918312544, 697995914, 224682779, 304685705, 779626008, 555093546, 228312083, 422438796, 553605561, 210607249, 49682526, 939820469, 461250950, 573387469, 358873831, 25124526, 679911407, 139799481, 647087095, 761401146, 944312869, 353666513, 121956755, 877361664, 700304939, 457481319, 306694161, 347824482, 494620438, 465127796, 59078100, 290172919, 716228270, 848898308, 780307803, 121632222, 651011063, 446155522, 250535087, 400312680, 133770102, 708840583, 972169962, 722661409, 498198567, 872399623, 945581904, 254206460, 126016050, 724148, 144004242, 916568305, 344218361, 479896580, 385741373, 751646651, 889443650, 93280610, 941427402, 416888287, 72338567, 325497786, 762431488, 195821797, 491112487, 884133717, 908003429, 999596047, 627684523, 808060107, 923854765, 177890794, 589799948, 202127206, 41123245, 93864266, 251061958, 285077278, 871146132, 73572174, 448334603, 68887983, 508579959, 638995078, 883043858, 294844466, 742485649, 313346740, 275666655, 203228711, 651860568, 65043222, 526190592, 892572163, 927094728, 25435767, 884650303, 862032627, 968082494, 887765711, 31445820, 77573713, 686163979, 625446972, 160609564, 932632521, 401418014, 867048969, 532042577, 908807752, 729150109, 267425465, 757892613, 384006691, 19260393, 77377432, 190361460, 647172321, 902349140, 442929934, 625346358, 183864679, 987377692, 65489853, 119296855, 744733610, 115393055, 217257204, 928393168, 767250633, 939709481, 605449047, 2835499, 989638599, 846590279, 692250728, 35414405, 43091658, 424464770, 989708021, 702589679, 146344082, 432806932, 66873231, 891398940, 434371896, 697745588, 953076616, 346030533, 475606862, 349325914, 990428749, 397406234, 494878378, 209574212, 836422021, 76892306, 91352656, 829994637, 647112443, 558095873, 394441604, 569299222, 561909741, 16608083, 77089726, 388767200, 293833169, 97785916, 368413163, 36585492, 298189056, 929226017, 444132177, 916341793, 637514096, 875138642, 723678671, 710644722, 429449064, 639474809, 728128093, 151222412, 965811998, 120986673, 958709628, 787643578, 415035123, 149824095, 149173636, 553489732, 943148428, 838260791, 422660239, 925363587, 91251133, 428329787, 314428009, 904112932, 444918765, 992032036, 696023602, 558727401, 354791309, 977617336, 788535124, 940785601, 301489321, 468121703, 655870387, 285454623, 558047715, 499646055, 781350786, 833824867, 597146700, 237902994, 238970447, 58148847, 240185956, 880713891, 199345690, 857806263, 502521120, 119913934, 600545629, 968981449, 909159257, 716466420, 870771471, 396388533, 672970049, 61807624, 768006038, 775807163, 817020325, 686594106, 579661656, 153090518, 842039059, 152158232, 635325747, 473047790, 955370870, 318543198, 33699338, 200540187, 120849820, 715132731, 829985497, 453651690, 303287299, 59505733, 113507107, 847198743, 23471575, 375263546, 513707815, 418810791, 185609318, 133090275, 688279484, 903305260, 404571564, 557411547, 326028571, 800510584, 290613779, 329159149, 941477237, 698918569, 235189671, 815086955, 95356252, 191269666, 61357574, 762209090, 814216514, 264389097, 492411810, 234351775, 745870083, 123161348, 296145865, 595610598, 538121809, 430088091, 233931031, 749390088, 497952039, 515195971, 892782431, 666060474, 910839922, 39892766, 927160025, 66125941, 508901323, 626525800, 588530710, 980889567, 632754637, 48618518, 725111970, 266515964, 778451409, 67840918, 222244768, 841328855, 32798158, 163901121, 17716581, 303548899, 267265543, 5177680, 283515191, 834002525, 470885761, 263954602, 389479099, 634152850, 344438551, 860110796, 725895096, 581009708, 693277357, 735517368, 309387443, 131803534, 980751310, 616748176, 801212515, 880740097, 452397611, 962362361, 62566458, 951566097, 158416935, 376436928, 553085495, 591316173, 101971536, 471558619, 334958569, 940065912, 495452424, 134885967, 414798004, 592032434, 725137748, 711141355, 500851549, 350114478, 129750782, 47332964, 922895488, 450967718, 114003203, 213400653, 935947177, 323476837, 920216117, 565497293, 324366891, 825688902, 301347755, 841478191, 372911427, 315821692, 178059158, 861938274, 281784524, 32959292, 837895822, 875240109, 596464620, 748322926, 146102027, 159065092, 701075258, 287999161, 945141166, 743230045, 51643347, 125534601, 758056202, 804768722, 566698921, 293020982, 485707394, 582325315, 296649382, 743461430, 303000815, 381148646, 827024380, 385506882, 839313565, 167492799, 723733108, 568773558, 263232410, 693667700, 60120020, 567895342, 967569809, 298508124, 379545296, 234791281, 928680916, 929629095, 810263713, 858724685, 645377032, 461712163, 654338866, 772248099, 589687023, 722299501, 499595359, 174908919, 123706878, 307232486, 99639616, 455075587, 491541322, 858381904, 540298657, 556178360, 370624315, 245199457, 158105323, 837886875, 684278229, 81387810, 646528203, 830888771, 247173658, 448591847, 501878956, 350487153, 607089696, 145391196, 16634868, 236263061, 688920529, 247962341, 315163564, 919030137, 579653887, 238498179, 978822111, 722261250, 217237026, 296856509, 396978015, 982001969, 107303011, 476082046, 486973814, 673396206, 809286858, 363092320, 270274531, 146409534, 355947284, 568251815, 23145419, 46239062, 259450382, 250507276, 147773270, 359244144, 537783640, 312099277, 979221141, 638195895, 507396070, 713289412, 544410587, 267772779, 651061714, 938512413, 784328413, 566762936, 557878796, 362373002, 212618029, 858770376, 266968968, 698139722, 65396922, 643783235, 447862548, 868026222, 527426022, 564219689, 886381065, 295003335, 969780662, 166261276, 335625680, 735402223, 718571995, 283709076, 398070534, 338735938, 958154601, 446448638, 569935888, 244333122, 266968534, 554532679, 752649185, 903398710, 270490763, 426452795, 82521048, 932675308, 703175021, 59895821, 329747556, 259011717, 268224285, 821798357, 426556459, 561976630, 213898432, 632431997, 149804668, 809766544, 814011235, 577507070, 761696214, 966570511, 816320720, 408726954, 556154979, 53252392, 691249506, 664446029, 877667753, 437297389, 297926127, 872106419, 820333000, 750907841, 151528264, 716286241, 807661621, 124868202, 342850480, 139091375, 163476709, 449878898, 860355571, 416042001, 785653451, 673107214, 757038407, 851878098, 615046998, 226343856, 241211350, 211390221, 755631369, 210679434, 997740238, 245601575, 124430374, 960209091, 151553470, 438677036, 295212660, 863617629, 945508547, 64084797, 25211918, 163369201, 94257858, 687282118, 72032696, 771168317, 861044474, 665505912, 322004067, 605922103, 736362927, 176203636, 769157424, 3644038, 254103661, 525249496, 589106585, 959122628, 455441739, 415659514, 624512788, 180021290, 371844947, 290235362, 343903094, 271149214, 903686292, 477992342, 977801604, 548871482, 860196860, 923372349, 435314325, 637038768, 180159207, 167830444, 52096347, 666585610, 236236448, 590390724, 933335460, 951903078, 36522136, 337233045, 864322711, 484256598, 558794805, 943586728, 146930646, 399885803, 197140160, 705805228, 238184247, 62368785, 257073492, 270657584, 300012252, 251433836, 459809076, 148882369, 366655794, 125324380, 672133657, 597705499, 567035419, 316683469, 113672383, 623520735, 212710894, 305009079, 954905297, 399130485, 291746838, 864908407, 734272701, 884800058, 81758819, 325893217, 209291218, 407327313, 866804972, 375731169, 249872115, 305295393, 480119789, 102302105, 910889123, 788217879, 542974710, 689881751, 768072212, 125738976, 260985695, 801532127, 886614442, 594692091, 877554214, 605265573, 798376453, 674978587, 427788658, 59713099, 384515824, 731973878, 888829503, 479579025, 355758154, 393115892, 286800827, 456059899, 661698073, 234410898, 461975103, 97991428, 222900398, 4846883, 49400720, 308091877, 91698575, 928396363, 991275566, 112519110, 891284937, 138813720, 679578379, 296413306, 293781351, 272333428, 984854877, 760676774, 593959214, 872157065, 637332544, 481092521, 562415744, 368764802, 839481713, 970173335, 833875989, 692168913, 577266083, 287830028, 554903834, 235101297, 831816526, 211295253, 682662155, 448861824, 615804415, 953807179, 803535442, 132655423, 61049857, 375691391, 636937939, 824638011, 217554368, 968816998, 801674804, 373047154, 251423214, 285191581, 554411704, 172626300, 697297943, 894060950, 436412074, 214201302, 355957741, 128120825, 662907206, 210800642, 715037229, 413979499, 469384130, 744893798, 361067317, 906675802, 316026164, 759956829, 675608472, 572439634, 184318114, 842504301, 141869513, 386243, 977831891, 259226095, 123218933, 314941173, 36101301, 789315042, 369588322, 77141939, 88430484, 332241095, 669051079, 544731115, 366917963, 954181348, 353845807, 201785367, 616850496, 757730541, 123516015, 768073154, 380066390, 689895836, 978240358, 125252855, 618273490, 38076265, 402621810, 822079377, 986637751, 169007939, 719831856, 714240810, 788531057, 567371723, 383967336, 468207053, 988302224, 521516107, 974074080, 862760610, 460963383, 16388311, 953102405, 310026297, 207869441, 875471376, 616119507, 808614862, 633629066, 207872922, 599963217, 698980873, 609042288, 151972129, 274572746, 367974501, 136735769, 828171118, 892487514, 1748445, 258686566, 80191664, 159689139, 162226471, 595703485, 395445758, 757155554, 456644543, 595888199, 26967093, 796330280, 804194274, 37303972, 657583838, 880500042, 591890609, 943955984, 854912703, 693631101, 224035517, 14729531, 598507878, 937818976, 48466110, 194021367, 661503880, 820781755, 31333271, 388863985, 711119051, 442455806, 232549264, 742774054, 435044692, 990201962, 607923978, 44345710, 145730187, 886599346, 452865855, 434117449, 828591270, 988672141, 167992726, 812009704, 745147741, 575965118, 843226653, 56989598, 180915782, 479728463, 856182996, 996211073, 700123759, 108521902, 995131633, 882876926, 599655892, 822253290, 797696446, 152694252, 752738852, 4205870, 547638430, 477032185, 397628763, 419937200, 867028744, 415408202, 722612776, 696801827, 445327677, 25750929, 788521971, 466439533, 387214721, 627781375, 282988857, 983747644, 790673721, 74428791, 672968422, 244925199, 553412267, 486379150, 638697605, 767714736, 107987679, 139863326, 660356645, 339641132, 514380487, 589640981, 142380880, 839239569, 643417233, 847506641, 129195708, 62950777, 779745638, 546795605, 127536123, 137048551, 118329545, 936798010, 136356349, 825912204, 382523957, 718028297, 941339338, 736890248, 260264321, 373869361, 505454798, 230186970, 385032337, 754887530, 704277825, 585929662, 198720376, 466475348, 46019848, 830369468, 971246752, 8853383, 390569444, 91831864, 694829044, 442500977, 204866242, 289965411, 776415064, 274681398, 308316461, 20632716, 717861461, 441157217, 341949929, 553715537, 776797999, 265832055, 709423020, 27899473, 49495807, 608737427, 482739944, 794085924, 365630881, 102130068, 683682661, 861214311, 444063054, 177224876, 432420050, 413338612, 48255471, 700221217, 24374929, 879805025, 111126566, 233359956, 244900634, 524953442, 674433032, 862226750, 24620539, 22021774, 621174877, 53138058, 487984179, 983815836, 684112362, 661158516, 586039970, 773264983, 277551123, 447852322, 462940796, 267429599, 941837724, 896808403, 461188224, 818978815, 140913404, 311075077, 524108700, 259283463, 795964038, 179185555, 877226045, 269801860, 51257855, 142996974, 993692465, 691804966, 116051442, 104265312, 176776616, 413893393, 472945813, 175716083, 547262182, 448732617, 228292989, 807110090, 748908427, 530659407, 786562824, 48917625, 263344489, 677655658, 895928710, 433713174, 550483302, 661997720, 342058031, 452597413, 576369695, 938851926, 289451896, 252777992, 252931744, 355191133, 799310337, 527376151, 292985855, 415631442, 171296411, 121305382, 375861864, 779085123, 552256691, 854819592, 824550861, 753241329, 471191386, 607628351, 747378414, 798330782, 311343491, 481888329, 21125480, 534262528, 342623606, 308167630, 556422696, 221141154, 897826798, 876553476, 502770322, 286801213, 332364316, 954198917, 85481458, 127174635, 369670012, 91163991, 46057904, 918829459, 197861366, 248221014, 731363783, 916255861, 823291081, 484120116, 7209360, 833045739, 949338667, 629115267, 543137707, 501111150, 264941182, 208194644, 995593253, 237607592, 951149708, 352291687, 164281733, 424987100, 567976512, 552517378, 767042451, 448750883, 381462354, 384226358, 426634175, 905601360, 143755233, 231982261, 493593517, 153622079, 501636273, 405274143, 920963862, 679821976, 896385783, 947444088, 387335094, 860973798, 469643136, 937304470, 663902900, 531768995, 756164299, 800378346, 587873474, 460000347, 163078808, 383427251, 512320309, 555317531, 527069719, 804400777, 471379347, 312851996, 736964451, 756934072, 937403482, 823858447, 125717025, 701255033, 510962449, 56452978, 89455975, 915525037, 975901637, 57365727, 755183894, 789859730, 418732596, 831932929, 849926765, 893753079, 470366280, 251030758, 920898334, 379140407, 396770725, 29090572, 334478949, 817488361, 741167841, 241095835, 667441631, 828231336, 388215200, 382200406, 864860235, 919127669, 538458150, 529225285, 767359693, 609451540, 531328522, 226858309, 961896558, 885653456, 782399360, 278826677, 865870480, 725422114, 882796487, 121390852, 966058978, 533177349, 943927567, 971234227, 33928945, 846805338, 293166209, 248332291, 752040509, 582739597, 127666707, 587876709, 418020136, 982764092, 786921126, 680567159, 462966051, 990466236, 24656569, 904589009, 40763553, 704997988, 869811328, 351473931, 338695076, 189384803, 689632185, 698911517, 712384524, 764831976, 452210105, 716435946, 75240747, 104974831, 417417745, 806871630, 109625506, 816064861, 754486570, 107822030, 161799881, 492255458, 747891308, 491850504, 706659468, 734132339, 731862237, 193030648, 8473453, 238234421, 387650330, 376988986, 975932928, 379408034, 81549011, 170319262, 134709727, 260195864, 594264695, 228380770, 924292613, 308641934, 970504400, 250085770, 510722743, 44444285, 116149409, 14100938, 292065625, 930822544, 638296692, 148316215, 139483661, 236259683, 773443530, 227492146, 131784168, 943656038, 141868722, 95038338, 771258879, 64921072, 271867103, 393143060, 179910292, 438307873, 93651291, 524609212, 208600951, 353682332, 866087266, 180747791, 105789780, 248810566, 234777824, 52525202, 914329572, 392500261, 682003186, 272385061, 606315275, 512728361, 774138255, 280440506, 361306200, 995481923, 506693124, 747693493, 220182279, 236540147, 721560645, 44224180, 18471638, 58907449, 156149459, 304873108, 663971418, 742685742, 484520180, 565439527, 160176458, 954608562, 881272368, 711156985, 230527895, 543342820, 209948870, 721632281, 326976702, 549974874, 836714881, 634050704, 682169827, 138099692, 650569667, 204108247, 188814387, 830332170, 756489477, 201744905, 562798987, 3389405, 279571194, 604309321, 727439497, 949573335, 615887825, 357252290, 145171268, 219955320, 603591266, 370837226, 721843152, 768210048, 598125036, 750392829, 257904768, 664731652, 282770266, 424805809, 174149732, 425948966, 90050775, 221911930, 251908718, 197476000, 854827594, 873216949, 1529726, 438703221, 435046651, 756205280, 756778946, 736128084, 827228497, 275344020, 272434171, 694015948, 962187481, 691409540, 172505918, 129109428, 958263016, 879869825, 680712050, 552403481, 820061802, 299539304, 50529349, 582904010, 353437079, 909835133, 815882720, 511452755, 969964547, 830338065, 39380984, 422663976, 935405938, 521422481, 168577497, 53986147, 655716621, 336387844, 456006207, 632240715, 968981488, 578008361, 532276902, 531544375, 498968391, 892464446, 283178272, 853550748, 519649367, 257948619, 789610046, 588768006, 45623361, 278552286, 867501596, 629020579, 843429186, 471462963, 881089346, 455755325, 950107619, 814868771, 702817977, 233213399, 538671670, 189958914, 422881864, 14334166, 742741452, 195561215, 654020852, 295248891, 331488719, 209584742, 700943737, 646672375, 682457884, 538090962, 379188454, 397652054, 369346166, 635086625, 659629527, 648440462, 514289706, 714115582, 975828472, 951717660, 351299591, 403049879, 830480510, 224521797, 360197270, 480591271, 649779306, 2336072, 663244308, 159861376, 198010033, 509131968, 743421661, 481823649, 634187627, 409364741, 144441608, 133340475, 133025078, 808968035, 56564771, 138408412, 833469929, 605578607, 504274136, 59614549, 359017824, 184529196, 131857818, 8870573, 340608650, 790518714, 443952621, 374621246, 166665642, 651337126, 28921394, 308634737, 213675650, 910390269, 789775508, 514184057, 150999742, 451553404, 677730023, 751770196, 384644782, 302711587, 691010590, 110631893, 803590974, 300990780, 111125925, 832446925, 408925824, 848116526, 579180443, 677519932, 689111311, 655473777, 133855590, 636241392, 150239049, 361928531, 79274238, 198920871, 907589539, 923113585, 195198054, 355239382, 774873337, 11234384, 54718318, 573886240, 602144754, 437134287, 853459571, 175025169, 585435753, 198848952, 64290181, 553353544, 135335721, 486987793, 961062058, 8451488, 10892235, 461954772, 63286428, 150404877, 488479165, 587148805, 733147744, 785048771, 719550649, 111251386, 117402930, 864035468, 698339593, 916432447, 500901676, 905842346, 566497365, 104611580, 22960013, 717436593, 143298030, 448699932, 631262844, 258965792, 751364196, 618741638, 890335702, 429551996, 733069516, 902189082, 452769732, 240020544, 285160826, 452388103, 52372594, 386115181, 258907570, 33514894, 322383961, 301573386, 573077054, 805882295, 722966041, 868842879, 804626732, 845958532, 566421954, 65511078, 650548534, 794640643, 922744398, 706479302, 333255928, 530149328, 513862149, 494002469, 984924153, 648491921, 137805429, 277993168, 137095409, 343681914, 18136808, 328882838, 904628387, 693334914, 180895788, 997893495, 415071631, 519974721, 819469181, 781318452, 97058755, 405896487, 740212311, 470840604, 40918994, 580205332, 254581110, 472602240, 742989671, 179119233, 3169967, 186664946, 346885867, 743399539, 650585280, 429845307, 141792759, 709328566, 616416857, 607066292, 867059383, 604570583, 763658514, 20162082, 641079679, 28814795, 68210952, 498122049, 700970332, 130418278, 917228212, 844749278, 414384627, 935913322, 330462538, 697311452, 525832165, 815871480, 449734417, 95926970, 125459252, 627091674, 273049522, 320678521, 366035717, 776945609, 521366167, 222328939, 117275381, 727721604, 867327933, 805268729, 992245910, 10543030, 937754216, 892283384, 421933870, 50824504, 767110628, 992116931, 665422283, 863339231, 19919950, 473577511, 996503430, 256995039, 301222597, 470169754, 436878601, 831461374, 79970133, 86172770, 124810919, 8034865, 528337727, 450481925, 621682866, 304662773, 453098294, 438443457, 828292855, 521040822, 234781885, 281820791, 859653222, 191032603, 31295632, 448448392, 715693488, 56753842, 756854064, 650899361, 925305069, 947868891, 361632935, 237225628, 56174516, 920110558, 907893175, 687347943, 480528953, 650734457, 812741052, 653380700, 611972506, 897386896, 234251908, 829151451, 157935910, 645152507, 16628449, 240002073, 129291996, 533595299, 100736969, 787471686, 79030789, 425778200, 210095028, 406191670, 216326054, 493908522, 490286990, 520051685, 394835958, 397824277, 179232987, 728054364, 459386853, 920277232, 861738003, 534962189, 262558868, 161496499, 531963803, 768371036, 396456739, 879385675, 781937421, 677202055, 89650600, 151746352, 891676427, 382240822, 971290702, 403801308, 324573688, 576640231, 750799545, 547361496, 270944220, 921531277, 695656513, 500715739, 10061638, 699637513, 284346524, 716654315, 907822156, 991721408, 706725654, 578606646, 762703509, 200818843, 462482212, 865900211, 694387666, 715058632, 907956837, 317773229, 649808968, 247475877, 486244957, 125141541, 213304020, 33743451, 508010517, 825046827, 552918218, 231475510, 1638944, 986836137, 186496439, 281009808, 817824771, 300761265, 981967992, 500821860, 351430865, 866526715, 776440609, 259893790, 114617205, 855772327, 725135015, 241302173, 12374883, 885806078, 968272083, 88286924, 413930728, 987979453, 667468331, 421951006, 525052235, 969113820, 407050553, 705538121, 53432089, 844194164, 321239130, 591807413, 876393553, 690421378, 995276547, 852883460, 569305467, 713963020, 273324010, 605471914, 212058356, 528026739, 711938054, 680811416, 726108688, 605984562, 831864802, 510597606, 278246221, 476020321, 577964907, 841938043, 661711753, 721422765, 207124703, 153663489, 513072510, 877081333, 159186063, 132520316, 487976402, 50522396, 289828064, 287875162, 489482838, 28645572, 861707894, 37617819, 293402064, 20366932, 499098620, 429796193, 754776093, 114844069, 587889584, 55652930, 853461378, 608435814, 847819378, 485449381, 239394978, 185932556, 299227483, 906419660, 435792189, 322495497, 448004553, 792622563, 685647051, 400743983, 492316549, 833895223, 32971866, 204712752, 799419097, 29543583, 883727561, 984532367, 485215678, 160978620, 273132593, 276617958, 65024874, 102885398, 871517665, 849375240, 593570908, 706142844, 29884818, 397148139, 685367227, 619886139, 464265623, 46074283, 572880457, 456605045, 324869425, 49520690, 381052934, 926584525, 749069817, 962554845, 669465572, 517680539, 788884757, 971648210, 547963147, 294348840, 194343209, 462458069, 569350718, 933456990, 566229432, 18521256, 271306385, 842030456, 943107572, 510189824, 812387604, 879508431, 6726839, 356718445, 581424168, 126957179, 244489629, 280060111, 655018435, 842732989, 540470592, 442003923, 97629778, 703932053, 335447151, 666379298, 420867847, 342322039, 822318517, 665745283, 865030659, 428836801, 723634903, 699796085, 755944607, 341246771, 36939714, 359027867, 370469210, 648717963, 465869917, 911264704, 626084, 380615085, 879281184, 71434042, 392066495, 220526750, 404535432, 668418529, 54657708, 780412658, 607983000, 830185683, 410507233, 395830852, 72003168, 197249628, 660187513, 742345295, 973528937, 783755461, 708503225, 337769458, 488382265, 869291778, 721449611, 333218570, 600729119, 698142860, 162603160, 899905740, 232845390, 459879839, 581243134, 862039226, 89826026, 667880105, 680593799, 747524470, 732865738, 413067239, 757745853, 631545043, 366977838, 59825607, 581131042, 350383395, 908187649, 412575025, 60809600, 356175771, 883406059, 301561935, 401010333, 511514778, 256063879, 408183785, 288515001, 260014598, 170517128, 510206533, 40709665, 764859660, 967982535, 505401415, 463262311, 848676128, 279838101, 627699891, 1634573, 887778748, 489132529, 115607016, 212739808, 811320845, 931647455, 237994864, 377530503, 871957828, 382525047, 690833632, 751689894, 105369807, 169650544, 345427119, 935802057, 483708854, 849812509, 312509531, 139507713, 297937520, 450289669, 666717491, 571457449, 318942527, 322850649, 684609776, 43349308, 218632056, 837052522, 400662165, 817447705, 334544545, 422657297, 405838156, 313899326, 175121282, 961961122, 119297443, 753288995, 265167250, 870631475, 689001523, 920803725, 720328350, 524954737, 826580380, 892176802, 567615043, 685007393, 105748967, 276223162, 527980861, 443429246, 726412644, 303395805, 797613843, 44052454, 222499371, 680301136, 146616288, 723376726, 663493957, 154703230, 954901156, 396297987, 9162244, 137485018, 597648870, 317897777, 992421786, 455181926, 616713892, 529074986, 175493893, 294729568, 719852758, 677747696, 658575624, 826451341, 727129273, 811273836, 686175438, 859965311, 141370684, 210153473, 395749172, 852892541, 771931223, 760189515, 302625134, 58536459, 517210294, 641578990, 146591582, 522917561, 572667000, 618124165, 509838035, 511666488, 149750707, 410887789, 317895419, 592072568, 519605393, 575068378, 164424515, 225606467, 284926595, 315867299, 797283310, 93818771, 700016876, 639476882, 201907207, 330987976, 161431034, 416557774, 378020569, 95767340, 6240859, 910931610, 528368384, 936634119, 565663985, 732749983, 764809421, 344717787, 944042959, 467509423, 612312739, 489241163, 597937847, 719215446, 280912734, 594137501, 401627609, 878938136, 199495616, 555239515, 259752987, 547286795, 553157899, 416257896, 114631736, 14677274, 902952767, 703003211, 305378819, 245498823, 195739464, 513869536, 998042894, 931667856, 264511426, 426217202, 233546494, 653809820, 950537847, 882778519, 97499232, 871348521, 778484513, 372977467, 312201664, 974294193, 140352916, 382947076, 539284100, 449940757, 409866570, 261673123, 990355011, 843522603, 571112356, 694174901, 999889292, 131522719, 393534062, 222638272, 847234834, 283859471, 695508918, 517057052, 147425227, 628594792, 510249443, 206448834, 387978931, 935969408, 300252572, 489071969, 224167082, 728899011, 57262865, 450635732, 139585925, 645606536, 581697807, 62987776, 958795189, 638772008, 349492950, 931517333, 612830142, 203816430, 123768853, 50579408, 630590809, 690576928, 55209500, 868528598, 334246237, 522511, 129846414, 992874081, 342606497, 43935059, 986470845, 43576314, 689132225, 273687474, 495438259, 747848918, 798315762, 163396077, 251337325, 113869871, 437431892, 84121873, 477832670, 321102193, 614565865, 552506427, 972805745, 145000228, 315247979, 964476790, 838801239, 414932609, 127087313, 462493785, 756193010, 45105929, 152385603, 116313124, 394251793, 703565912, 793125699, 967012657, 956753701, 205206529, 659650574, 864800033, 817183051, 502049103, 337667520, 140139907, 33517416, 546977482, 593056568, 577117097, 263834326, 467133050, 564565863, 221716097, 812865108, 344830523, 830225573, 878276864, 656540740, 75821225, 240780125, 7402149, 41779674, 365608784, 595754318, 841087436, 880974689, 165174267, 944528269, 365341753, 46184935, 330257552, 913003940, 810435059, 317857988, 386602572, 919110582, 500360049, 891738716, 608973889, 908262076, 975193961, 404189930, 566167946, 285521224, 542810968, 726294716, 188015112, 566295784, 977307274, 914293140, 960295359, 169012682, 551682265, 706645501, 98020714, 702753102, 922073686, 636506720, 909058041, 600650752, 239075626, 374770093, 83886745, 40220904, 382746116, 711854958, 773094887, 275875922, 904001885, 834554808, 639973873, 311926365, 186349705, 942975214, 357057370, 227078923, 884849711, 650910018, 199603540, 395411253, 992317699, 100394605, 369732403, 3913935, 395913358, 600243810, 614900413, 361993887, 345043658, 947849120, 986154371, 560096329, 120430702, 788771570, 827532582, 817179447, 775455672, 913167600, 852321820, 829359719, 704381627, 812271812, 375488112, 926196402, 4484747, 420210288, 530939329, 168189771, 485113510, 647580813, 976794478, 526544140, 937177349, 630011555, 664329972, 469634538, 285266379, 553621782, 785879298, 815525018, 449629001, 48066527, 372966316, 739030323, 857356184, 504391086, 433010986, 476761399, 347639705, 693422161, 920131963, 614891877, 956866005, 551084591, 376742469, 898073788, 114541402, 156023224, 956461786, 655419481, 229342602, 28105804, 773458218, 434593315, 945917211, 130703065, 412861526, 523963898, 5959044, 89577991, 152301292, 564513557, 821156474, 631166266, 703166261, 583109788, 992974978, 757485580, 567466768, 377622083, 923487373, 417721441, 152849382, 358965073, 551580064, 806741965, 263618050, 927052782, 790896725, 911235270, 526690623, 809871932, 466254656, 599618069, 29776827, 477940545, 451402132, 228198995, 759169255, 316325756, 843241218, 193438873, 790095359, 764584217, 576215588, 855443815, 992637981, 973077873, 242519230, 819106733, 631476462, 272526138, 798602279, 877257889, 898490, 240129105, 142160327, 311179866, 525207604, 347920947, 700259043, 779353378, 875711360, 51237020, 346235893, 147659986, 419825830, 800968760, 721945798, 240100186, 988003914, 789420563, 489146298, 249537867, 798461359, 134170716, 680267367, 660095397, 441476857, 431894707, 897491219, 729460394, 936705118, 885255878, 924170990, 707484703, 600568102, 573145174, 970976989, 622098710, 116100747, 362304077, 718694509, 95591145, 828443405, 493551138, 428072376, 729612195, 579456041, 87585230, 895790106, 291513101, 958926982, 297083320, 385855314, 341464900, 867972580, 924887984, 419877270, 227195891, 234984913, 572409737, 255231038, 169218791, 689298119, 671154761, 219167535, 205707672, 978367482, 167020308, 964678573, 497942877, 163173583, 77814031, 883711742, 68968237, 647405178, 389081458, 495281618, 623264754, 739946395, 443329688, 561516085, 642419529, 696873522, 556240839, 295152217, 219619638, 282462364, 88315344, 573198815, 680908363, 405037751, 67320932, 302385466, 153627234, 230649536, 358144274, 26335244, 294020906, 2009709, 367555836, 796485357, 771987985, 863696580, 101055395, 740637520, 566425631, 800837167, 430578285, 9830397, 382965593, 567499193, 683129158, 747437417, 617057459, 483274412, 901940563, 259082869, 8768580, 846407564, 985207227, 997293133, 210653948, 965654174, 274386382, 148810351, 570360496, 113557560, 306624415, 470567946, 46647514, 414335922, 165847810, 693505490, 865983308, 15674759, 135436126, 312410641, 875606055, 916184038, 240876288, 998224015, 252936313, 53300312, 231283623, 354722614, 514080790, 830242886, 516523048, 577683014, 377997957, 400353381, 949910212, 656857810, 472710913, 629970258, 805806722, 698034298, 326069541, 842444843, 204247099, 162060287, 533559923, 665713909, 984354355, 433358946, 323481625, 881279763, 861107172, 258385615, 843034813, 474568242, 365457691, 966496125, 782474652, 233629075, 33081089, 375457648, 150680263, 531547273, 844228900, 539319458, 77792118, 713086472, 608579981, 741213895, 233323518, 557670270, 703660044, 83992515, 793659462, 908771981, 599507726, 838707244, 559433247, 437415772, 475406302, 459686647, 661315149, 983686940, 758717517, 788440429, 238507583, 248065598, 774717541, 93304944, 288490785, 502118064, 866774847, 813602061, 953886303, 983325936, 448580869, 195230004, 515255450, 481327966, 361876145, 942576218, 267940917, 535420142, 194424421, 437751707, 889567091, 38553500, 696812449, 64200163, 219372180, 680593489, 415575222, 741627258, 366593973, 458175654, 177492482, 390565646, 334521936, 984763899, 92051309, 485942463, 171273273, 50299693, 61436072, 179201549, 233803893, 125867424, 563503355, 220494152, 779693132, 399332106, 490608623, 819095877, 606783650, 771533595, 35523498, 959081416, 364613026, 219536416, 454699806, 310997495, 461967583, 592353046, 524313656, 958485933, 620100092, 646590678, 254183944, 143309677, 671094766, 816563839, 726094121, 632617223, 274099183, 962381739, 207009432, 223707730, 941898295, 594321043, 930672787, 382991262, 119913511, 412252903, 576871580, 581565144, 38459178, 173797798, 808624900, 468698038, 992039579, 703179365, 407892568, 976307168, 699974967, 634018915, 992042590, 622927583, 486819400, 798263312, 710111768, 818333642, 281277218, 476940948, 559561884, 977198683, 878548077, 835139552, 622884021, 891120205, 241961391, 446094979, 750629220, 632777184, 314348597, 974447340, 865610560, 579833415, 694686064, 755242930, 431825563, 192816481, 142661153, 965362125, 970412697, 953142037, 415609223, 916074244, 67670717, 932886734, 668891570, 837946435, 925317549, 767025515, 157622050, 456597657, 767020678, 414397591, 281291823, 43585611, 495065758, 516268377, 421980783, 757337830, 659934736, 362383932, 832684723, 892580925, 46268010, 92828435, 99698561, 187885918, 311056901, 769120101, 955471827, 631187281, 613056136, 205231377, 48860237, 942937137, 253818944, 311296303, 777801197, 857256708, 391245756, 624535005, 188808243, 384237328, 712593576, 763257968, 284733676, 229335537, 749317500, 348722755, 208413325, 595360285, 631280930, 827919462, 910029807, 11088480, 745906773, 745661455, 792062293, 976788799, 449970676, 905161003, 303730965, 291016182, 847798382, 524852503, 828741578, 370597342, 366650673, 983595381, 329278393, 466220094, 61395993, 798433998, 390644344, 324243437, 877647443, 486884970, 821351495, 768156367, 333626229, 244273130, 358049554, 964691807, 818346420, 700636103, 103897781, 751017164, 805762977, 510465175, 375081694, 491229263, 238423728, 250823395, 55700593, 767693163, 136109388, 341222583, 756103563, 740814956, 532104470, 884880009, 686789374, 870496914, 780589180, 283679628, 925210148, 625319663, 332101222, 482608067, 796011389, 22738546, 399945847, 326884774, 134094921, 971036189, 718071371, 396303212, 683830001, 46527785, 462784045, 191323256, 798582919, 196584261, 844823290, 322228378, 83886441, 799059571, 773004933, 720872194, 340762351, 147453875, 575342100, 919177314, 363118825, 248318265, 194683592, 586647503, 275103684, 970897178, 980958557, 639551548, 874793020, 605291982, 907923292, 302401722, 964372227, 409719287, 51359192, 746346401, 197311401, 178137766, 40493606, 788798318, 454061416, 204783032, 924115858, 131034062, 680027119, 224517920, 415305634, 693312371, 659850498, 698466091, 923520491, 698132533, 620051265, 451998929, 785418353, 829354888, 373217690, 891465786, 562953906, 972420975, 784685562, 551746516, 365956803, 102028354, 419671955, 369364290, 951891324, 482574408, 291897068, 515299963, 807772631, 755514804, 398917003, 323122360, 634809577, 290271523, 514151006, 199282855, 344690374, 821675612, 112780780, 126372866, 289801274, 330768727, 778589723, 893634035, 676283032, 710563702, 272222954, 849063054, 941149077, 127138566, 299301583, 573823912, 846057776, 672511110, 446902066, 645623041, 804001791, 596600075, 775223573, 640183194, 909184908, 325698131, 38826741, 250866982, 677122924, 545140875, 792048671, 491344773, 245455401, 522317427, 460845029, 612457679, 845371685, 446221485, 737791928, 729235721, 518598948, 306154170, 651182206, 501584055, 798602141, 809213778, 639757752, 95505768, 419157233, 755052628, 166601543, 26258771, 957568491, 924513510, 838351865, 680430506, 776806596, 670172, 611180701, 426024095, 595859296, 441701917, 837511017, 493800760, 307262369, 333966412, 270279896, 518931336, 540691260, 684796194, 353857974, 478008359, 357238508, 341004428, 598881724, 494295390, 50401759, 819601332, 315715021, 627841358, 151831814, 159037677, 495299020, 684530944, 159712602, 661595628, 389504232, 775458902, 766590125, 110927915, 652810292, 352975423, 201764533, 727756941, 835705445, 771537007, 806181839, 680464166, 817369931, 23370160, 493942296, 664742605, 675039576, 145852286, 201506613, 583970537, 756159262, 250410841, 506044271, 844387924, 892020119, 808734805, 254173759, 16361415, 205676828, 78313236, 59780507, 37521733, 70882559, 7226348, 298504450, 237092442, 267740828, 243650420, 593066895, 540033199, 78372495, 667897940, 815839885, 648217817, 113643522, 525542940, 822648635, 99975343, 636004953, 516413287, 387183367, 580603965, 524432355, 795195443, 957631626, 10131634, 892156703, 100367959, 194093809, 283869079, 403079015, 49706621, 841384544, 251037939, 511713069, 776994846, 576486770, 271600803, 870268887, 264956871, 664211196, 140670756, 34119966, 294845472, 874787100, 123867792, 271998816, 650312768, 323355357, 955550934, 38031385, 636817978, 630620568, 50976557, 170550888, 319161446, 138197800, 581375165, 555398839, 794703966, 988453962, 833506943, 304985337, 464844283, 142563572, 974293646, 844889460, 348011570, 691099018, 205158179, 7946185, 819729296, 823196283, 305162287, 430783534, 73628155, 591271695, 149984524, 338542459, 187890154, 252807919, 483149770, 320404498, 62222332, 532423930, 532427655, 67245975, 543320669, 909785280, 828983133, 981454277, 624224022, 246076889, 975733441, 81669023, 450516410, 493671011, 833884179, 154873683, 299799732, 549207653, 700312640, 241353074, 924883837, 782873046, 433190647, 564257387, 322412048, 707025734, 99753033, 310001093, 370367977, 220767221, 249075681, 371120760, 163979581, 157498072, 530080613, 709104202, 309924211, 239359841, 404340633, 512677517, 644151301, 42733619, 81555578, 114536314, 444730231, 676148731, 718061331, 559441716, 155783984, 410840089, 180642048, 227304727, 870946127, 456142519, 360178769, 554932980, 232704444, 929589100, 324118427, 111133708, 900847853, 682792259, 921559826, 937205612, 64009478, 765959320, 671399285, 985607408, 721506287, 791452334, 415341192, 618775148, 984960347, 730088281, 914007341, 813106564, 531349967, 5665922, 421894549, 995513305, 916473107, 197109460, 212399369, 320558202, 752654935, 356439272, 231978242, 792244623, 662027549, 127602625, 252949056, 153288750, 671750405, 842135272, 657727993, 370012929, 431898198, 392805825, 425162462, 268489933, 537730482, 174662135, 278990498, 507229586, 489068696, 390972618, 92215890, 226915406, 428138959, 502101452, 315855447, 242675746, 47534996, 847991991, 117836237, 792147285, 547935377, 951364359, 88532390, 474263886, 713592740, 174203671, 755051773, 314184928, 456180578, 82427839, 708474137, 889128420, 80178622, 259692286, 937613054, 995340085, 134202279, 462190805, 57135942, 541210761, 933452979, 911641347, 515419590, 747880585, 867113429, 517982593, 914546758, 727968195, 247510770, 342701056, 873276797, 944970872, 437313327, 212124482, 400952934, 735830330, 793205347, 912743879, 916534149, 69836997, 558995326, 9411885, 548345661, 945752401, 421306476, 980921114, 682607252, 254424896, 641998857, 274757745, 655709063, 560478876, 130221125, 104064683, 257900065, 442593067, 224881157, 692286232, 227564152, 79357724, 970896318, 122637199, 550202521, 80094440, 699927768, 291515686, 337894578, 574837041, 708049405, 636780999, 925204679, 361849241, 636710186, 756416573, 966950776, 981818536, 874438593, 590317357, 597968761, 257305815, 617335516, 187104233, 829860798, 380434125, 335254112, 146850267, 219931732, 586121410, 202828316, 639984123, 969793240, 549427464, 940541145, 513803260, 568127439, 912311043, 834386969, 40490645, 490357783, 555705613, 666471365, 595314526, 27354433, 314525872, 206201528, 126165667, 910873994, 3343967, 166974574, 162099856, 104410511, 590034575, 595926941, 113720549, 693244645, 421558158, 173585905, 695439795, 704622264, 532768587, 531458395, 398060225, 33958980, 50072953, 613040286, 40411581, 880301330, 312800314, 33646488, 236210365, 855369432, 81122212, 916990157, 586056541, 81893071, 856099984, 269709715, 613002303, 618666864, 386565995, 292327364, 962010891, 502610627, 376818614, 753230358, 509213549, 502544121, 711512227, 935744196, 812287685, 256257508, 849612273, 176780095, 910380694, 780042733, 350324341, 236373415, 604190957, 923623393, 469009129, 238335824, 729084395, 489496680, 658768821, 133897864, 779568470, 250097516, 872281711, 591567783, 76801005, 450525182, 877572707, 967814303, 304453093, 980090867, 306009083, 649201219, 109437547, 974680113, 869847620, 937038522, 89480373, 34559559, 497361902, 314916508, 148442625, 616276480, 742649967, 657676882, 939473989, 828845585, 533388762, 809015480, 639853888, 552069399, 639003998, 98322815, 587083027, 218651095, 655695444, 274894556, 669549028, 335843715, 764143815, 457448062, 285524288, 423786327, 690792218, 683683494, 975037804, 879079573, 910235226, 873087673, 436711930, 476249356, 900248598, 249064527, 30381604, 451414054, 527324804, 763363146, 250515352, 587040703, 512556375, 330990710, 711456741, 156781270, 965310796, 635244169, 700446381, 224911513, 719259751, 227953942, 873539690, 723194876, 538716154, 853812681, 344469658, 555005291, 699001927, 357148398, 424767601, 968787156, 368659724, 749990903, 66025044, 227634319, 704205640, 828924791, 401873442, 510141696, 785990879, 531965676, 329857225, 328308370, 16260761, 769216866, 924360353, 55256579, 381064068, 350865361, 810153433, 97677174, 235477522, 360483625, 673434302, 375096380, 735268231, 813596964, 244123968, 608503843, 561931674, 85620686, 774167426, 724631712, 967378589, 710297700, 196541720, 868860900, 993185973, 841244124, 659336871, 588593302, 359804611, 182747753, 955431530, 656111811, 73274195, 210679985, 802457643, 930165090, 994992451, 608369593, 549785755, 380131886, 48378304, 550786525, 942686130, 661146891, 57307887, 535204556, 379984234, 544462812, 417709316, 847472848, 607458279, 219766502, 135730711, 616354060, 846684867, 920893533, 58405904, 835262397, 307676106, 750978741, 629545194, 927172660, 178633565, 142090486, 990104012, 152397477, 513495188, 476933628, 982438307, 812330292, 131691336, 606535878, 875718284, 291393958, 918374428, 216762722, 451493949, 132090734, 998124789, 248769839, 65224715, 67587849, 97201404, 760746510, 342778078, 324854658, 639010432, 92043013, 32279662, 938637862, 766455567, 145042123, 869090524, 909906533, 794748470, 323933373, 962492872, 739295290, 286577148, 620124120, 225353536, 746777665, 432045850, 637148777, 448878645, 146898345, 590027415, 772673870, 217069613, 598845782, 473775225, 110912431, 214165152, 289939136, 372315911, 789348588, 850819550, 644207808, 212024434, 229027063, 354488056, 39221194, 710606330, 669494317, 702827356, 811775728, 976404319, 296119766, 256296966, 745103962, 984269960, 740785680, 691595113, 795179445, 317624914, 881978317, 398629743, 199711619, 282380703, 183270393, 76566853, 688131324, 546744943, 60706000, 802603092, 553916346, 409742792, 172209889, 683840678, 409166121, 623035365, 461683413, 521084796, 848465478, 504123577, 893614132, 587406123, 606952447, 846958236, 991465202, 107636255, 553627934, 833907562, 970369827, 1927265, 583201807, 998699862, 165041163, 379102915, 527096322, 734540207, 274931653, 674260929, 702209295, 871481999, 466089662, 363008159, 140247883, 451156143, 313410987, 137678491, 548246096, 985299031, 541976217, 531023345, 711234368, 520805852, 950086051, 688619460, 521937380, 67513178, 328814833, 718407711, 770100972, 215173820, 139834162, 411783922, 405188386, 532997841, 750673262, 615780789, 626960591, 915486680, 286103411, 187044165, 877484249, 274585143, 343449060, 632683369, 522675276, 869813858, 731890322, 190340728, 769744965, 656916857, 697195247, 378240007, 488689526, 802957726, 910207450, 50566988, 235621195, 914079715, 973661335, 79737017, 497860643, 552114882, 148407533, 654287856, 60144876, 74449210, 923497958, 198544355, 394598931, 710015739, 895928002, 693037852, 685266401, 317754041, 783114468, 236485976, 244398974, 215288656, 813474824, 769520935, 62774805, 13904969, 858189063, 304629991, 579520934, 964941990, 724152802, 937026470, 952404028, 175576763, 588924036, 846474855, 492891355, 336965313, 156635709, 144524921, 829396729, 423873023, 961796214, 480873082, 674370008, 835812518, 62792268, 941329790, 430708228, 906734004, 181716127, 398409164, 299895535, 261300078, 506141713, 384454681, 931208702, 810393829, 411887228, 612748164, 448563460, 432657246, 90941953, 163117217, 633753261, 57773587, 409548191, 68530919, 991012851, 513751807, 872249169, 741499009, 799809950, 333968498, 182030253, 676790431, 259927125, 498836409, 256443509, 282072391, 376689701, 962727142, 48625594, 545278574, 820082034, 875668437, 394188285, 468479308, 455317138, 533922714, 443592459, 55512107, 732519114, 257150203, 351228595, 335162217, 435512845, 500999523, 161091987, 309353240, 418166969, 277158439, 19632302, 885279296, 315163288, 109907115, 134037734, 490957858, 334912315, 759789699, 821106947, 790080217, 508354032, 788265326, 166179195, 46428056, 127360309, 969150035, 428985556, 442426537, 114747461, 108422470, 121438295, 511055709, 573632757, 130074603, 347994154, 896030291, 275805151, 293240892, 709403162, 789231835, 147000026, 629202942, 340230527, 276925015, 773337233, 491253369, 40190223, 824126019, 920518938, 386709896, 966415546, 842265609, 942056027, 16797786, 423789732, 717181785, 708143319, 728375893, 575136544, 489926927, 17356885, 408649729, 114523927, 115176387, 799262912, 533015565, 653882012, 429841858, 543975157, 929186999, 9551184, 582543314, 829109578, 838118599, 701620730, 95620067, 906988581, 409759096, 1610244, 911244105, 281742792, 46094571, 203726127, 889375905, 763983320, 899363961, 610274601, 581664648, 446699392, 558344056, 380725037, 60371947, 776480368, 448200318, 693453455, 985071801, 707670706, 162178156, 257539905, 129177303, 504234540, 73942196, 797407701, 553519502, 475064516, 544938330, 49857939, 464536254, 898067890, 816580462, 40624047, 419498851, 726878144, 398658636, 847451969, 364127412, 99725453, 497133988, 121808075, 187341542, 540862801, 877508698, 715702820, 831190853, 136455613, 318247781, 769767531, 321819635, 347819965, 346056698, 565027084, 276954722, 935235072, 316996458, 935595601, 396267910, 516424484, 24430764, 308444899, 717750346, 285800507, 803314735, 534350978, 470368125, 396743250, 633389605, 792543540, 741040243, 258099033, 285295693, 968746791, 308444164, 951658107, 304792768, 685233088, 596987022, 415725915, 695447189, 31377486, 967783514, 735422655, 652034100, 783457018, 69764362, 459988216, 14843894, 95388999, 633200406, 162900760, 61710343, 122849065, 255153802, 840827044, 774551329, 543454645, 772847172, 921050413, 489203714, 716845817, 949080054, 975948221, 608117572, 811572872, 921833578, 799823048, 865362865, 628365228, 79224089, 274898342, 206840753, 865512503, 536089268, 508614726, 303253693, 242407617, 635970916, 26812602, 433583542, 917623621, 426504444, 964009033, 272042594, 706606482, 834631781, 439723659, 406371472, 330471301, 529951483, 539869715, 877671590, 626362120, 775853881, 323489767, 838732323, 258650560, 453814718, 88808179, 850239733, 885863752, 642545190, 693474880, 330964496, 355765280, 955598460, 11317036, 652392655, 230264255, 849506057, 176176438, 946187786, 42087638, 371821994, 478719852, 431194802, 143731182, 110111628, 805040074, 485407497, 645154258, 413634354, 485521969, 78783692, 866203279, 547909182, 602357816, 754486084, 607732729, 363650522, 102221179, 688453947, 925553019, 504796782, 275350427, 835289304, 26511617, 333113878, 465838459, 495752653, 813280273, 541598157, 465136484, 489667655, 680689661, 318474518, 443181609, 796380704, 192871127, 86259608, 973790359, 804481539, 611180581, 990521385, 410691543, 690492473, 554249287, 916686658, 371579241, 851686269, 156044101, 309302130, 366224928, 133697695, 48725678, 777619151, 144395089, 546556018, 464297873, 602357471, 467405195, 756881778, 420635793, 162197896, 829154734, 340882823, 813366979, 924553948, 759257498, 381762133, 947913735, 809874746, 653655802, 97366215, 684923905, 411067059, 433053829, 156389055, 81397573, 423763382, 786089571, 940546247, 486031481, 849211189, 129364039, 671468017, 343332446, 348385142, 93085887, 7723339, 177001949, 357553833, 501921702, 671181309, 485724235, 697724641, 544187368, 616417065, 965056446, 355343235, 392485004, 597769817, 539128677, 909611996, 425448886, 288607219, 530328410, 57561936, 690963663, 190754017, 126477081, 655864207, 188484477, 774013508, 297876334, 759506978, 875309806, 188500473, 561440443, 55806552, 387324176, 755980959, 83357379, 750330287, 961682716, 426398989, 500062001, 509040739, 358879243, 531305314, 730872665, 804997231, 412234525, 798624981, 806447961, 61143125, 810865044, 139142699, 889417619, 802850629, 665450142, 877993628, 346908937, 605142569, 299696769, 724083608, 203313641, 789967146, 289793466, 987251551, 866515412, 47586346, 268308263, 94867964, 353883497, 293261760, 481786289, 279915260, 390071064, 415504269, 837699628, 65758421, 722199570, 75016713, 895492323, 85678919, 424415594, 342100807, 887158274, 841351006, 959632327, 120700751, 838697739, 720955065, 49157212, 540388302, 298289303, 975503141, 824206823, 723213125, 180215999, 537504488, 222376523, 188682823, 917378515, 545560398, 906172268, 588944941, 854376298, 128895639, 94247768, 312109532, 300891772, 671708196, 741977264, 471782481, 290324637, 886446938, 510577842, 788083272, 805104446, 538841771, 691009521, 5243007, 216501678, 379506643, 703017239, 295714895, 917381911, 674309729, 73555330, 216441103, 398029736, 141517437, 436461230, 517116617, 465031183, 570397464, 494243375, 206832534, 865515317, 700175393, 947146994, 112195516, 30179310, 131119352, 69927413, 327329902, 354678906, 676123083, 580347837, 601410415, 918591300, 484234468, 636129383, 668322842, 878082471, 962913603, 606540151, 873306700, 47740091, 660550456, 701390781, 576752229, 921541705, 521892695, 945685654, 69865404, 881812303, 412342981, 840590193, 183221577, 615554645, 956442831, 467424132, 75721515, 620332720, 509115602, 180419051, 220225537, 153305296, 832031378, 664577230, 506396645, 77462626, 403913491, 894492823, 300769766, 476321330, 937096253, 219454538, 91871586, 111228008, 302137250, 714182943, 274450869, 642576850, 80935616, 248298922, 19765989, 543869561, 99324173, 889833910, 555021511, 197043540, 283567283, 926892011, 934870671, 511314234, 968235705, 283212050, 771954115, 571932045, 789931811, 806149983, 529328280, 33392280, 179943215, 749341272, 776379778, 352354247, 763169868, 519271637, 730220124, 392929528, 594857255, 951223800, 403376613, 886474951, 81534363, 338971033, 650231361, 356532118, 127568806, 369558098, 206744148, 971397206, 579534224, 802695961, 679355857, 37300864, 671216766, 320500304, 813588766, 489735788, 743940037, 546481086, 454876392, 811703552, 947243256, 135831084, 427117844, 405271975, 192292107, 525878747, 425673460, 663266855, 567226129, 386016775, 272851682, 921700685, 9338337, 259683344, 722002648, 921529915, 959680298, 674322345, 957596840, 831259113, 780015987, 199485835, 787110810, 538358971, 912033823, 244194239, 275727922, 449713478, 940523841, 594186394, 668559304, 303696914, 557491539, 41032862, 797916768, 878214981, 432866880, 234221370, 647754566, 426807403, 867279455, 384332742, 340747173, 543524804, 368787001, 20758669, 306819004, 44363355, 361282261, 777405093, 227093380, 173819217, 761264520, 155863798, 3693398, 262986017, 335661233, 751912856, 148510264, 558047652, 276339585, 67261303, 540926020, 356373794, 233447165, 668573485, 932691039, 503930866, 941782116, 343893180, 708794339, 29791350, 290725986, 358244419, 876568812, 230517131, 184775332, 627438212, 571966510, 370825003, 297752391, 630835239, 471249044, 397347552, 763112938, 791113283, 227348364, 264815394, 776046051, 448335722, 14532594, 830891411, 73241142, 331784116, 607080614, 765669539, 458119251, 823802689, 944330476, 971704011, 719225981, 791113852, 386598983, 227813882, 774959161, 845011737, 515115978, 481996490, 279673891, 214261097, 480781143, 64366283, 932070158, 214327313, 322817877, 60165298, 775779811, 310919346, 399473779, 215103761, 273796126, 916519695, 468674228, 44641268, 533930472, 492016031, 970294271, 324821752, 121209861, 551287636, 886320416, 538567870, 657838999, 760321223, 595036758, 703301827, 543983734, 584103724, 477835516, 932216799, 938329161, 660502113, 406206184, 628066899, 298512582, 718776666, 428575504, 265735857, 414740377, 156621559, 598443933, 973704849, 397674945, 628758320, 155789491, 442684801, 999391268, 787861375, 342611713, 752115662, 747179635, 400235361, 811167050, 849394338, 78360050, 142977114, 964909425, 647971010, 676633812, 829859527, 482151670, 33373335, 739690767, 106061566, 410207803, 539251701, 325718577, 775728299, 278974007, 648309173, 480049106, 227169893, 872950214, 369187781, 976413558, 786030810, 669219286, 26090570, 614483102, 813878171, 771554881, 510397319, 657580701, 326631500, 504312668, 100739795, 389166878, 564172469, 983271378, 598438106, 585388813, 810952119, 92754175, 805090265, 175288232, 75116491, 1414733, 475556531, 244216589, 199697044, 24866722, 944389718, 336678008, 974697392, 928316970, 300665119, 269761657, 135419022, 509369679, 60919556, 295091432, 179377765, 526184023, 332382936, 169387460, 176493144, 257845613, 173141793, 352125528, 937047327, 678304220, 466194054, 312867892, 103844375, 926521270, 561490846, 663382539, 703274267, 244264593, 807893034, 188373761, 286319852, 831573794, 382493230, 187367251, 911850627, 835239780, 368334196, 259734830, 691703580, 791947992, 659856332, 375728654, 582824132, 50219125, 988668303, 375369026, 877061745, 782183061, 556552663, 251820704, 10233808, 519344547, 651722453, 688458030, 871808158, 811673537, 513739366, 311393360, 892453693, 959026429, 902224448, 970577408, 44475527, 185454284, 910532275, 92653603, 581251127, 955024857, 543399714, 673972595, 881136457, 231368767, 262775944, 13270206, 602144295, 867934818, 564178933, 520526107, 694347131, 423880508, 526093865, 12829995, 44383848, 197627165, 498416724, 901067163, 23248980, 283433550, 843839591, 837109692, 693759276, 290180431, 519538897, 271373385, 179027683, 775956362, 211748187, 515429128, 742866787, 783908749, 323210836, 210259943, 476801301, 450625979, 226339397, 872167022, 524333444, 115822742, 850459276, 311986037, 574937502, 979141747, 696845130, 189831537, 587776462, 16531927, 294693206, 495052824, 818283542, 122195468, 184683403, 340861595, 955760221, 764667969, 66138449, 213676694, 788938168, 139458798, 312358191, 676146566, 478412165, 723685451, 4100836, 53304543, 913207934, 693846665, 917493451, 815629393, 116758028, 339005398, 127008850, 419843304, 176162756, 465146639, 605016762, 19719680, 831274704, 362369645, 160000296, 800758726, 597251846, 694150660, 920289815, 27530847, 172581945, 582849845, 807299082, 283618092, 152015005, 531684512, 285150484, 461435271, 6878094, 180721975, 719000723, 141335001, 4510187, 779056225, 740079131, 973645785, 813280746, 366382183, 56409620, 619886764, 502871252, 247968250, 133590517, 767123146, 151807682, 683443582, 826538830, 70419785, 956764781, 513240943, 951663320, 97610347, 455192217, 831451661, 923195275, 741111287, 998967114, 238072376, 980086302, 894128685, 794505297, 421942793, 185189047, 116438265, 140298577, 291195009, 910699929, 546959875, 99927941, 675154604, 704737127, 652185204, 946431671, 613594355, 74515145, 1765009, 290344139, 337561205, 223234020, 565313061, 449292182, 466939302, 90985435, 468088661, 949016865, 580226139, 16334039, 483957516, 272268239, 616265992, 881530194, 376887680, 205563644, 151311595, 16330655, 218575767, 509199319, 169193371, 167372788, 506646966, 81998738, 894123104, 586127840, 693081306, 773725167, 383366615, 161525622, 377239409, 533694646, 673527246, 875185909, 773572444, 651175710, 323665227, 491660579, 315548447, 547222346, 317458369, 719258277, 56011600, 475260807, 143368748, 256529085, 31586923, 924958248, 516860922, 195215322, 413926946, 99733821, 671692293, 472806917, 28945967, 47410640, 866585748, 499474083, 770553837, 711530824, 988083730, 130629301, 502758066, 860560107, 333067349, 176375857, 658460971, 761105618, 474115526, 703509794, 806908423, 39997493, 417611255, 662228692, 119533485, 467265920, 821458223, 278247874, 129357666, 677339093, 460329448, 24434187, 40205081, 19013193, 106632717, 491961093, 149025816, 830468962, 104520819, 937956846, 423603729, 968146887, 898608205, 573967561, 815038676, 552101496, 185291165, 440998463, 842681277, 355590739, 412711641, 783714410, 868524168, 435521056, 625949025, 872530859, 941461391, 55210414, 737193757, 835861370, 555915708, 838951434, 379822899, 729155042, 427465130, 343010427, 720503101, 743533943, 377018741, 899308655, 586925745, 988841405, 74991715, 392574452, 709792123, 245826828, 174320152, 442006692, 610089306, 340242162, 528764820, 703778655, 630071135, 373275986, 608368062, 370202736, 586197840, 938392097, 356623117, 743847486, 668741055, 175018879, 381842370, 874039334, 407174319, 896236257, 998519538, 828055756, 896705544, 58751335, 59523289, 782767984, 460335435, 636642434, 120235445, 420488003, 853900952, 267228515, 242227997, 131817609, 354960265, 70902524, 887878397, 261713032, 450467844, 627182730, 859158740, 301894614, 260673906, 69730203, 923259619, 11420674, 206273624, 558526511, 649393953, 414288192, 478426624, 469670760, 612159337, 844264458, 32821925, 550599235, 160142741, 65686885, 362492935, 692348340, 723711670, 591466312, 907265559, 842385193, 940067414, 124210650, 667305872, 337314844, 234787207, 846202427, 226182137, 833313608, 356337512, 809720304, 548136893, 767052755, 294039469, 786947893, 948732625, 158515602, 848604143, 587695372, 70197455, 504960334, 189146723, 696454122, 493061361, 843802482, 92388141, 24764835, 650261496, 615260708, 264412889, 543004208, 359541719, 435382756, 394307108, 7562623, 26025512, 928017166, 578213757, 955005261, 171417714, 761837213, 870958651, 55236235, 142944952, 480940341, 83601176, 493135876, 456354090, 404186747, 327348133, 999498788, 710943420, 486410167, 380861442, 780786143, 491069651, 819710003, 274991280, 391221477, 768013288, 735589641, 836229327, 861272006, 357780680, 304273359, 412935117, 478903100, 76148407, 2426839, 27642460, 384769262, 843200505, 463473358, 997471673, 884898092, 408691424, 99889375, 999409653, 777306153, 279035160, 756272509, 531751031, 48312942, 854380404, 942369103, 482136002, 935882352, 759435938, 267025805, 198242367, 75537880, 492069488, 72925343, 308435231, 440483134, 427985260, 716486195, 731349382, 193772964, 116132578, 547845263, 608247624, 864277911, 894188808, 366529177, 473889211, 953773955, 784027858, 220540863, 615318481, 745193042, 850836720, 365328105, 411991034, 463800018, 723317231, 660662969, 39541049, 421498233, 235049691, 966416109, 519756156, 810808451, 378500988, 227296319, 541458551, 443293953, 175896197, 49774084, 962570709, 419068434, 252886235, 152447308, 900562198, 584319770, 633384648, 612680786, 788525963, 239825851, 962295365, 286101487, 901062708, 924528805, 814321690, 324952937, 111689454, 248914741, 452834538, 104983434, 891436485, 661142273, 676266862, 904890852, 327754738, 84860366, 523971304, 339941076, 399724747, 747468974, 633212706, 510108271, 727075946, 480984991, 331076636, 140570317, 902422010, 936634224, 195135698, 143619313, 254246347, 627049731, 537933989, 572893193, 893865222, 791989205, 258524187, 417210404, 799001288, 265047568, 158330822, 915642146, 164085572, 419484480, 698173759, 788921537, 261484464, 696750755, 275850390, 11529471, 350177798, 210332108, 2461456, 548757390, 633125755, 379551872, 647761500, 741822912, 18550215, 844072249, 29633236, 400215103, 480835073, 714252539, 639433459, 800885024, 728499760, 968496380, 591685291, 468556821, 370686373, 503667088, 142417141, 538041831, 719142016, 85835942, 573207515, 734821802, 126009370, 554921149, 133769019, 799025635, 39668459, 161170378, 928207529, 32328172, 437483490, 175918523, 263482190, 579024426, 164991843, 435624876, 602461372, 34267893, 654689541, 609582510, 346747975, 121721145, 156422641, 364677726, 826824493, 422233587, 740420534, 222091064, 207139023, 368200724, 415460676, 380867922, 827077562, 789020795, 58417071, 428988392, 712061590, 448331941, 794569865, 825548999, 191886708, 602596303, 414731869, 459426910, 483439892, 924922234, 382349959, 558933470, 352531747, 547770060, 267579736, 984341849, 834549979, 683863413, 292077261, 776665996, 206493323, 750443779, 332543412, 693025710, 612373049, 2741841, 168039194, 375377858, 873999574, 134553565, 960822564, 66165778, 549239424, 643257361, 634511065, 324076775, 874829099, 626790300, 101935679, 42246798, 436668575, 468748691, 121141069, 592243017, 977514124, 376842401, 552531365, 576052880, 553917780, 185514912, 266634024, 816321374, 145908884, 943158052, 513315352, 462428588, 604706214, 353365402, 300111399, 373405703, 893706278, 49540792, 218011269, 944715844, 902808409, 475505109, 773917688, 37191433, 745963543, 999557530, 40671800, 847240835, 155429444, 25189259, 82896567, 43016759, 111874543, 255527391, 479291433, 830922478, 136940953, 509452559, 108910834, 245436434, 140306001, 205242530, 693025949, 280741792, 281967226, 140202473, 270022019, 160255889, 653657592, 497828476, 168203499, 697237991, 607443923, 704547170, 929132168, 521969406, 364926176, 424341402, 604423879, 449901374, 815886879, 836047372, 655040828, 885077744, 134686379, 828526613, 464607770, 960126892, 766389874, 578754297, 643035891, 693282139, 187779891, 761400731, 74584448, 916830750, 258669094, 774520742, 242467672, 782219470, 414813428, 301396245, 643417505, 694525646, 246687277, 590568584, 245219360, 571881552, 348743989, 848919775, 562619192, 657551651, 677543880, 967330983, 222617831, 300455586, 733906732, 730807353, 627391400, 440088038, 416994469, 953833058, 160252877, 2348095, 553651390, 648959545, 150017070, 871602961, 722044354, 339035642, 270569932, 802737920, 697010771, 862749491, 285065340, 876532480, 708910947, 210196651, 785991397, 371472449, 812891970, 131690889, 737979356, 106038717, 962864843, 688368722, 646626626, 330124331, 609789822, 557284911, 824310350, 364312755, 499507755, 691574834, 521565554, 339022316, 268622047, 621563428, 624135490, 237636086, 805434682, 793502082, 383556616, 537703894, 310299048, 3444569, 261817275, 966738902, 881384646, 139750009, 204638452, 198238278, 945955402, 390984496, 891182754, 782042361, 466530464, 317538767, 253674973, 595005923, 331120412, 734933475, 539947808, 145181001, 760962057, 776356761, 273868974, 70220998, 180394613, 210291163, 769180207, 889567788, 243265220, 564236098, 883350824, 596907120, 392776088, 378349138, 822818026, 75966821, 341478786, 468561775, 736101633, 199739261, 194152102, 531102311, 975828516, 416973102, 64596311, 786878372, 837833827, 620332032, 864191575, 326803642, 865702818, 533027321, 720667203, 186861612, 484843802, 822076946, 402429253, 511766467, 291706712, 208637565, 266431006, 110483847, 715453314, 915512192, 803859189, 434555835, 642338142, 830232264, 798926244, 406059839, 517699575, 255329838, 655673372, 307751742, 89503345, 227440684, 236182180, 436621051, 625917877, 208643083, 346680842, 383456059, 703990046, 969982469, 270417221, 545502427, 46222304, 810009275, 931655559, 640704013, 962390619, 603684966, 835838601, 122225337, 312705379, 318292810, 747195984, 189244739, 432590583, 191408405, 103501997, 785584732, 414151648, 909778047, 256673822, 784668758, 330488734, 743411086, 381197590, 830107032, 510512706, 213338767, 661668538, 728177973, 665311634, 288500580, 773407433, 94561719, 506621690, 672938232, 4356547, 213701220, 364040083, 572142453, 155737014, 88620842, 268744521, 922120764, 14016640, 900781034, 592729811, 506616088, 776226461, 359478478, 473088175, 499342653, 283701722, 385919376, 719271680, 908726664, 315017014, 668241369, 732916856, 762584987, 315294754, 954406991, 351545781, 372755036, 828019177, 163423130, 682081953, 309969356, 458561116, 356462685, 604867683, 913047549, 226193101, 566859826, 854341447, 184720654, 331710637, 822591323, 861310984, 744026148, 472343487, 283436018, 584223404, 723530228, 251820097, 221105620, 155399720, 559897152, 602514441, 271788183, 446009129, 227134047, 177492315, 133974103, 918576082, 502511528, 455847573, 946048082, 407981623, 813302864, 409820309, 590865963, 344095865, 388094056, 577749635, 5213582, 543183294, 852912964, 925834507, 671936060, 639113452, 525706894, 637219363, 951053660, 478129632, 79945860, 682190102, 57962152, 823582809, 837609715, 878396645, 597563037, 296021133, 319702145, 565375263, 745432665, 783567042, 327138518, 288320317, 970860392, 469087107, 923961865, 960067626, 832388939, 998160916, 95645507, 210606781, 692677290, 52810727, 100344782, 834601053, 818944858, 432521167, 799929393, 499686507, 227879960, 693196412, 626196260, 224245956, 591311414, 492844050, 922479112, 493312066, 227396845, 566990908, 286791378, 823910927, 406540441, 110319624, 364430371, 554335308, 290582623, 527480894, 107166586, 133705684, 359989869, 562263815, 226506374, 785471568, 498158981, 703215215, 302782477, 892365860, 882956982, 928335322, 706776904, 549533994, 231198891, 368205215, 190128320, 544110979, 522896911, 415171506, 204541498, 756832434, 680461807, 316193827, 822055008, 58641601, 509413085, 615616411, 344475319, 260242539, 654493068, 982844787, 766264308, 655113194, 374943703, 157613489, 724397327, 176013203, 381258011, 566810217, 412259081, 765518705, 354047612, 255755584, 574738587, 986288270, 951826789, 309506188, 664396388, 169615442, 276849796, 503094180, 848200335, 780467558, 261709163, 118973450, 818085855, 374110421, 989646461, 845904975, 129521124, 328290114, 220672673, 932458386, 731699750, 304798724, 532646417, 36913627, 309813333, 147318758, 668642605, 241215019, 830858326, 311398356, 944432069, 238718696, 78031981, 451100302, 634997976, 61182246, 488123749, 216638639, 212591288, 155998795, 276201857, 224742779, 633777769, 342670148, 946239287, 427682576, 114964826, 821161628, 805011950, 896829795, 623992740, 162501012, 61154323, 39207746, 674158491, 506715889, 649496240, 679909214, 277223148, 207765202, 85440790, 870570950, 883169273, 587541644, 430731077, 409599609, 731857004, 252218071, 844528679, 869896735, 264084500, 430245610, 507062613, 234314820, 886042857, 609240113, 718545687, 845836058, 312855232, 889440421, 137620215, 663134664, 894610682, 703860325, 925771110, 537486804, 123330342, 288492391, 907391346, 893286826, 158008452, 104636036, 587172972, 509000349, 764253896, 48223155, 255179757, 293922705, 710076693, 958453859, 872632085, 192114454, 539486906, 973301776, 573940183, 250067038, 671384437, 181306997, 307125221, 696656382, 96954714, 646505682, 515000865, 969195855, 987859129, 607687119, 720414904, 80063322, 106637398, 352752710, 373435073, 704890058, 601317692, 450967238, 338198354, 854672508, 840137963, 98888896, 527474397, 309915388, 750178231, 936271634, 157496084, 977098264, 262238125, 643607037, 800136540, 911268733, 930792592, 669038509, 134366741, 951879838, 842486104, 91045700, 114091578, 399505213, 939349341, 42209140, 594883065, 372109068, 134525150, 692778379, 687363838, 89452422, 559011895, 194145780, 663720711, 189427498, 548369794, 711577229, 786453090, 85757347, 275657231, 122142914, 626378886, 991884302, 542940356, 321327431, 849425112, 882615763, 780830063, 121552418, 285341613, 703698843, 759001817, 216602550, 333691581, 928508195, 461459317, 381913908, 91323539, 554680034, 825951485, 506263891, 241423469, 50806547, 367216514, 535479690, 933629882, 707071844, 570847973, 216052052, 11667439, 394514765, 443090164, 530312937, 611186344, 789756262, 903554100, 818993304, 681322392, 904954415, 313671179, 626975039, 536741591, 445411309, 299888314, 763380583, 569143416, 236782519, 862731925, 420529892, 486810172, 738093048, 535484345, 648351862, 699266783, 719980517, 526448152, 391913496, 146658167, 479238696, 447726014, 459049235, 955332678, 530721683, 483173010, 644307833, 725029655, 790501190, 766815133, 911137578, 279755670, 467662089, 714781015, 701586546, 784673681, 743608728, 454526227, 126100677, 531292620, 421203713, 318219870, 131930551, 126340621, 609108920, 925974244, 504893806, 509853973, 191709912, 248335102, 716526026, 531268688, 855864301, 354401289, 173517889, 764939162, 161969480, 855704316, 609518191, 546706219, 941057516, 351815036, 17206760, 931271856, 343271096, 292164975, 481417329, 88454311, 510900165, 727878965, 97221855, 873695763, 359450639, 159953651, 285129339, 559234303, 581617918, 831475038, 166643544, 414564354, 158236607, 320861064, 147366908, 526937324, 827900664, 541080245, 883487952, 155403976, 418963021, 133965863, 561866334, 774890045, 67070203, 647637771, 799654577, 800915769, 631201432, 931231670, 1973514, 592705967, 509918020, 855673284, 456021615, 248895439, 287157793, 496272685, 244589260, 693427573, 154205001, 488471460, 146733552, 636690216, 825800378, 322811804, 545765092, 220975967, 509296415, 142683773, 996476408, 805266597, 304233367, 425818732, 935648658, 122442590, 303427901, 501197342, 470267573, 730166841, 387895704, 179430338, 521676868, 901904452, 792068999, 788203506, 375250687, 31249841, 874040139, 941791219, 742163256, 989010823, 972159110, 484945904, 674602362, 691054758, 48355648, 450153634, 198489476, 807467312, 724363384, 104825084, 566281849, 51932615, 18137238, 960255831, 242316938, 632578615, 802735338, 245780304, 559595994, 802595312, 986234725, 97687650, 876903369, 598887388, 923314316, 873934394, 462258238, 862483989, 1645270, 751270921, 691196019, 190538548, 312694962, 468059412, 537369348, 491865176, 787425522, 926730997, 456563296, 808472882, 551410428, 761119051, 560497340, 657373465, 446388035, 26624617, 451969423, 60583470, 449457993, 386559415, 880975884, 740788762, 177358273, 132519667, 32119130, 531524826, 738434639, 920231278, 305336869, 665244405, 922155389, 887244422, 127281687, 534277932, 666693487, 772531662, 415415602, 113280258, 695017685, 213321529, 485046272, 168320332, 591563076, 706050951, 660686975, 494270105, 801606402, 662374287, 423231261, 840621934, 595111452, 817686273, 521711641, 185733139, 360177935, 962624688, 217748089, 142591039, 685632857, 219329735, 879178283, 904464044, 725781678, 420822928, 20599257, 296708853, 728743282, 157816153, 654704187, 567473330, 32786395, 686111247, 118207427, 459491553, 688483583, 818628982, 453714876, 673052614, 832570103, 559185077, 995977091, 518513347, 95321130, 403961366, 263118330, 982734248, 568527215, 286879186, 950335216, 435045725, 179941407, 113506585, 923902262, 212243544, 990647783, 613129668, 915518914, 800079572, 129086877, 330463965, 495656569, 165960913, 978550206, 469915436, 607838994, 465204053, 832858623, 200748453, 146196006, 459480895, 537964234, 861708654, 65051977, 412851691, 475767646, 542273161, 400465130, 717798291, 129143863, 916013982, 668731772, 953474366, 30247859, 613519146, 356222069, 140323244, 349866709, 525635330, 401726544, 828169388, 719057272, 186412059, 558844971, 757439590, 390187396, 223068358, 252685420, 737951536, 924030566, 699683662, 266927717, 232162071, 297617174, 768932821, 956484992, 93626506, 383086957, 377103152, 847370256, 292369859, 763243048, 142840010, 444824575, 52679542, 300367746, 353448238, 644590816, 106941253, 289017216, 790067073, 217445058, 769427469, 935750833, 706928154, 610229126, 478071453, 629990187, 161749792, 719659690, 988635255, 135828946, 459135713, 655640167, 617923740, 585893892, 280520458, 229554859, 601053993, 870802058, 337796374, 344941936, 290850846, 618148181, 349419099, 610209405, 753273843, 804751579, 489132770, 434444963, 432358650, 408086252, 685964401, 781062964, 825304560, 64145336, 108848595, 885888489, 474081545, 787867597, 216720245, 884695535, 273449783, 429935396, 246120533, 481876053, 858882512, 410629696, 155665233, 55953077, 478730804, 712563146, 672471620, 843167129, 342250878, 39854990, 757889176, 301240213, 182883941, 447008896, 325868405, 974165448, 525336900, 890724877, 326473833, 468452236, 827632816, 539499962, 595877403, 229804029, 88541268, 829569176, 223589795, 356137795, 189425065, 569983140, 968455089, 815979138, 166100772, 937592748, 563326964, 415594120, 835491823, 809247866, 975649167, 679581790, 356239336, 579400000, 450272017, 905961902, 203847549, 134853018, 326804278, 195407325, 764221636, 460274423, 929878434, 659533046, 530923270, 204937297, 214448568, 827445094, 542422894, 275705879, 224372924, 859177111, 31445528, 560991081, 724775603, 377950797, 598229247, 562479274, 741236352, 970140202, 346947086, 236387503, 385157599, 504885080, 431020000, 76145945, 500633856, 796586238, 88723696, 921022679, 772749342, 9736213, 761979285, 156381551, 995060003, 232559614, 214077157, 423154719, 942645575, 105804194, 863637425, 926869045, 103967730, 856708245, 437337699, 442759353, 230470504, 207584744, 543822453, 129923522, 253348242, 520733011, 827294674, 865584808, 341061621, 973292860, 614684924, 614993590, 133799245, 770382937, 881607876, 423078149, 402364387, 352614769, 33356727, 755827618, 234364639, 641838133, 904301956, 601489627, 122616529, 773514693, 874393877, 961341584, 792681180, 120436943, 637904544, 67374518, 803260055, 454698148, 174512216, 92896907, 964314961, 195779195, 228574681, 532227065, 486912865, 486840389, 554771370, 787601964, 668853985, 249752887, 70155483, 31587482, 145115322, 858273711, 231509712, 384478773, 216469010, 388604180, 790918596, 286146229, 318687556, 100750311, 245107412, 833556514, 206114569, 473972006, 14919324, 927588930, 914432136, 267041655, 873689085, 342915052, 359546775, 159406390, 130189661, 909829840, 283880998, 777804771, 3869963, 176123522, 707448656, 81876125, 715234919, 415654076, 4985287, 943073444, 648449900, 781519109, 324626115, 183196779, 219519329, 907734303, 969368118, 878378974, 388513369, 723885048, 720825493, 971967033, 152507636, 590264921, 824527640, 439088608, 73046886, 369005906, 364208697, 491187439, 973962460, 873064191, 678368200, 528606699, 979732528, 55606311, 345104758, 299965513, 45415993, 328552344, 481200147, 662490075, 213538039, 44436399, 361815262, 925514614, 649572751, 324237478, 974409485, 298840635, 760381369, 185241208, 771979466, 5553782, 60769817, 543857926, 891358370, 547292038, 917206602, 199349856, 865126853, 207392304, 894760724, 114867361, 782492682, 151099695, 886331748, 554560377, 810401626, 791135214, 881437610, 215358143, 631785359, 182758325, 374284863, 148504342, 924658738, 387640203, 533065099, 303257843, 835444493, 614635956, 97459417, 143275124, 109874983, 69815563, 437636137, 846399041, 304936441, 998419668, 64474317, 157185882, 116144615, 802022279, 568208754, 312674921, 26849784, 541592997, 238525488, 804301924, 256790866, 346036118, 775189807, 654161252, 620538084, 408031693, 357013928, 541014234, 621245420, 653635580, 711623470, 693655454, 982529743, 475929342, 103263139, 32764802, 320077799, 785777322, 441560204, 531943869, 176371107, 533623314, 641295436, 759660232, 126926806, 355109585, 800777091, 898240410, 235763007, 924197081, 291366698, 666271448, 143886017, 290052114, 192049755, 352827446, 718329687, 674793618, 398896119, 73148487, 23661182, 21913013, 752289923, 994831118, 289603960, 893350271, 233861137, 291452231, 852836292, 59943027, 983993713, 328320912, 199166261, 616177172, 561329377, 952275226, 918358246, 118417884, 163086363, 650256024, 331776885, 944895268, 141329173, 905626888, 626356070, 810353461, 92439108, 102674641, 459705975, 598007747, 38521901, 245584514, 671821415, 634358156, 885496837, 930643506, 389516415, 755169871, 484427319, 10819411, 46368120, 397148627, 965076135, 89765940, 141281235, 672306840, 464629381, 731919762, 907665186, 548066868, 211385572, 509862060, 882488439, 105654590, 952829440, 96227690, 343819174, 989281574, 103162987, 574100569, 734935741, 34591697, 73331615, 430425405, 960807119, 260758774, 292196039, 630803162, 344526427, 163664177, 715942311, 488455851, 59496031, 182422148, 315676512, 139959797, 858217048, 557600893, 158633868, 733551619, 168283736, 548664320, 853132614, 947025091, 667009257, 108322959, 62993260, 424493200, 660763318, 855376408, 38654806, 541084101, 493135800, 930067781, 106009184, 583981939, 892002144, 24488106, 514110887, 496443578, 752149099, 976114941, 963446130, 722703390, 71604540, 417305889, 315373124, 176821757, 11941089, 77699535, 838064972, 86871788, 698702660, 145511849, 148499221, 535435458, 906513286, 693734842, 338543528, 907630542, 455889262, 215643474, 388283443, 300293609, 190491344, 169520454, 556927981, 106260643, 25741873, 208080657, 171641354, 128879580, 290844740, 252006708, 397208179, 161818650, 536277019, 790490625, 468406308, 177806187, 466520175, 788731484, 387609708, 104228844, 447289688, 833665692, 477856777, 663107449, 720001984, 219248387, 516131920, 32822371, 622728432, 156099231, 590601018, 498449899, 658354093, 428537034, 95221051, 407475343, 454534882, 181992143, 417476493, 217998371, 31356048, 422748295, 817271249, 344350741, 8121166, 486626589, 23734088, 543653945, 902852481, 355459834, 519828959, 57971816, 111039825, 888535316, 826627482, 655324287, 92534826, 530320071, 244638768, 69475785, 250004370, 567495695, 386684982, 450112665, 915037153, 217993144, 406737398, 132974051, 490166634, 216105077, 174311848, 40580608, 734910203, 478468222, 476085911, 53871398, 365915775, 777837455, 150745085, 741905337, 579516631, 999215966, 952263247, 512457561, 324337264, 465999398, 740740008, 105215811, 285076143, 686779490, 883633047, 803010215, 581111272, 954145547, 120849428, 586507169, 307823115, 286066438, 118487785, 961469075, 690757664, 714370401, 73394199, 479418531, 74528208, 803833003, 718825058, 449188080, 955364074, 355687621, 411234202, 179157017, 379827599, 306739570, 933523914, 504459520, 54040914, 887740131, 381851876, 283096029, 801969192, 256540595, 289410694, 233123062, 125531139, 307291988, 748329442, 341337933, 773064222, 843375746, 518256816, 274341395, 203601614, 51772356, 485863607, 891670128, 647850139, 556058363, 496426350, 346344746, 344372216, 715710944, 134560875, 59876062, 671770573, 246269789, 542303435, 247751428, 628895683, 704331936, 532123585, 519499271, 433517975, 329749579, 376237709, 382033891, 793848946, 298727794, 766989057, 758312523, 688047114, 5745813, 684160616, 822351324, 369039771, 895993106, 153876383, 485481841, 901095171, 712042439, 842409466, 733274344, 195099316, 441210284, 552896715, 577967670, 295597240, 766376321, 554638151, 50769954, 958213815, 65886140, 988307961, 394927648, 969268507, 403140867, 812457595, 13108953, 795171974, 479022102, 414382654, 519012872, 757695730, 682517162, 906011219, 734619214, 378174725, 351756674, 481527873, 578066931, 303819319, 931661251, 606985477, 567684616, 260242808, 682399519, 316916677, 659059614, 374724445, 181315448, 470863068, 242893026, 608471161, 546996782, 63911838, 172839651, 227971058, 958945823, 393901178, 191688964, 407728443, 654034734, 307517602, 483209789, 767239128, 844902110, 260577209, 331893242, 630957257, 571801606, 588882065, 753099826, 707256820, 33804667, 165694565, 170149204, 349341801, 584805695, 843663137, 421300502, 569530247, 502368100, 99531671, 18328305, 427542749, 439983419, 736508905, 818892410, 618871835, 635066580, 602740983, 381166435, 319523137, 449065469, 973691179, 542679083, 759926650, 114433050, 685811015, 801029005, 53277889, 375120848, 26854396, 338842576, 781230497, 564906117, 881432885, 488308884, 418612994, 470641196, 542899846, 913622168, 747947068, 728696339, 792310074, 505578143, 13875753, 674423615, 49690600, 84958691, 630040944, 271291009, 232341677, 648412335, 5188174, 987957587, 431598902, 478564804, 175334733, 62851516, 529248474, 538813207, 419439923, 641801312, 756671508, 26220087, 961698543, 617156212, 943475391, 465101831, 945263622, 683136202, 856329514, 395471256, 34182177, 402734728, 312809035, 925091334, 266213676, 559705946, 779640691, 382599102, 467049813, 251202765, 668560874, 377691091, 285223221, 467613670, 491673518, 250372424, 830674212, 266731021, 476235060, 917362057, 547197723, 151387427, 635576182, 459839872, 712287341, 759425596, 926468990, 486817591, 267605156, 301841333, 219065839, 84059048, 251384338, 351249541, 92237640, 764708324, 986692804, 484463371, 23557831, 607030820, 401038185, 132119131, 566368536, 885744229, 924407405, 291512238, 647685469, 899997589, 884778318, 180138315, 839092341, 45169320, 721633126, 16315935, 229939614, 635601909, 495006120, 994554134, 164304811, 89890274, 273060227, 860934090, 911988892, 769434179, 70370143, 577128421, 590137066, 178964312, 875144975, 613487987, 908031133, 755953008, 481974258, 3710702, 216200708, 122033573, 329632425, 423704220, 951885387, 674265925, 483524556, 64182385, 923945240, 610546609, 973534797, 720618652, 511236753, 673586358, 981837428, 798819702, 284544617, 501155970, 959764479, 153118989, 847431344, 362980437, 459037424, 583432421, 905030000, 55015969, 275772152, 307155019, 405583310, 866693495, 924496083, 770698885, 903922105, 385107461, 331096973, 671892986, 582490942, 108579554, 862109203, 972027688, 125447785, 329275196, 612356642, 241047393, 994202678, 378867493, 589890636, 661276334, 445538696, 311806515, 935830861, 411304724, 972487601, 682256887, 943199008, 117710015, 597218322, 505493786, 619328493, 393386207, 539161218, 986223643, 376158917, 764035404, 999735482, 409034159, 927959488, 735126430, 646229062, 376836736, 660133314, 295646359, 566883794, 273574290, 139407658, 424876686, 917651843, 394949798, 355738700, 888518867, 845613407, 192251479, 379849617, 717242961, 622924070, 326469190, 275487186, 266304998, 408313793, 686675788, 256579862, 208663078, 697902490, 767504868, 316099088, 899351062, 827034512, 555427735, 652431812, 528012477, 68140126, 786681503, 15141815, 442609210, 353169432, 705037494, 224165849, 105889472, 343574288, 272179176, 597556697, 887869605, 862400064, 956332065, 405085514, 634609004, 494959327, 52646162, 249254383, 867299947, 72664181, 128918136, 438558350, 601111069, 751456456, 584766656, 516694315, 791205922, 484196960, 444878062, 370541553, 116377155, 65580655, 652299290, 428076709, 888884064, 554726350, 762156381, 913497645, 887584643, 780698881, 878738898, 154674249, 759940196, 61672383, 798964664, 832732513, 299864265, 537098116, 778515964, 659810419, 163684313, 882968303, 823248263, 627007444, 609594324, 188947912, 555352155, 951495776, 297892555, 644839299, 168227788, 318031452, 613012349, 6552005, 525403156, 953659608, 393803871, 695170189, 295034501, 777953251, 403691071, 864819563, 23586268, 495179142, 851492737, 747554758, 951979055, 717697066, 779512307, 224614248, 586086177, 954683813, 84746808, 109587609, 994167603, 172942844, 873797228, 712199695, 418002512, 339110929, 74069519, 70942488, 868807546, 687356832, 449355961, 548808406, 434158372, 219600150, 683436687, 965520254, 228472547, 525959549, 630729638, 816831693, 365074663, 615549421, 458220677, 961256138, 590502685, 897109056, 309598866, 551292526, 801730542, 981259605, 147041311, 322873190, 128855981, 642205285, 111332523, 248760303, 261718162, 523147603, 119844783, 533440680, 268395664, 259418812, 836953172, 171966020, 327456308, 301895733, 973509432, 416856944, 968392027, 648537038, 101417432, 763438239, 444641350, 60574134, 410361718, 499917770, 240414570, 282044921, 728406444, 842737956, 344068738, 901463013, 165044068, 446387946, 276381422, 756836679, 170546203, 508579508, 293200246, 220270824, 74849773, 668868644, 257343942, 172094510, 198010342, 310594929, 902866978, 907134676, 266359029, 750913234, 609023914, 835011124, 567563529, 901202009, 530281307, 565777250, 421869708, 531472121, 808314594, 192828682, 811412040, 760858539, 502830585, 595097941, 323485151, 131002021, 19089823, 179221993, 721411057, 937185175, 918430268, 805357486, 460280368, 720771291, 550330443, 118175818, 404934718, 277571080, 179900650, 939872072, 649797226, 829149696, 26791228, 652178090, 239690700, 472501825, 235528136, 674778854, 723532751, 348825641, 326623766, 137431237, 617681827, 654421723, 550230280, 391616547, 123780927, 486544899, 503153145, 563725495, 57513988, 78648161, 382410518, 944438701, 302186077, 762274254, 510805089, 303192412, 760988301, 461370283, 773587104, 473241163, 290148438, 426262290, 286056056, 310197362, 813882712, 658578148, 696930921, 476272897, 761083420, 552442459, 955779438, 431031961, 48181372, 690136584, 525097374, 719234802, 505373501, 670439577, 64939787, 477107312, 369895, 31680897, 590131963, 20609296, 253883464, 240920157, 681580183, 891893617, 945111343, 240733681, 718442007, 991566754, 127975967, 657138910, 707794239, 850882761, 658855813, 994138894, 350727314, 958233401, 293346048, 223480742, 37535927, 914776483, 15660805, 794321468, 119908024, 869992842, 476251364, 340936205, 842686724, 448486248, 650734688, 219403639, 192642955, 121045949, 838303150, 877304729, 767364408, 199466780, 677895450, 345270497, 44178289, 878717344, 930553575, 391050891, 170464494, 598004647, 770576374, 304717116, 383156798, 106268367, 180922653, 33797673, 370404600, 444391120, 548091950, 75605960, 71493613, 799509732, 615629898, 695443613, 851799251, 879463633, 136424198, 342578122, 58712063, 791031125, 239103081, 148433165, 189224398, 854084544, 294061646, 240809893, 715217272, 69157827, 672949576, 283919722, 602932638, 97977013, 972555801, 502313540, 367416514, 430692251, 240657530, 394905689, 626219404, 927324389, 314197494, 496708321, 315168380, 551433081, 128163765, 225087072, 931926449, 611767681, 856941934, 911662260, 152779931, 388990944, 289529885, 953684272, 787457938, 2723484, 566558373, 114618340, 391865838, 760599628, 825608149, 848139443, 549290063, 942010135, 504602245, 326742801, 686248621, 948735124, 505502301, 785663351, 757244702, 613228511, 741038798, 920438432, 674532789, 771004042, 89288939, 545651810, 111053214, 435615183, 507257605, 845844959, 864087435, 765030847, 643251081, 383969771, 159917430, 260675901, 970435213, 251432676, 752334080, 560779611, 125796308, 285145101, 891184202, 374416148, 757851722, 980277349, 298817390, 126764891, 848160849, 648000842, 973708840, 837830319, 377183986, 724245746, 602285016, 326886330, 104587417, 974434692, 872592181, 266844754, 121625288, 758075754, 987554405, 472582202, 607040693, 400199716, 881552743, 9643830, 714790250, 877111439, 772891796, 83211498, 99044616, 842984917, 718565590, 774847038, 214026434, 173884519, 551927610, 806808248, 277891536, 542001376, 833506301, 5020227, 512809039, 558336445, 795281620, 238985401, 207275856, 274084877, 356124766, 832254729, 649144757, 513013628, 827082782, 121046950, 957159819, 227083757, 185810451, 972129997, 679199002, 576028294, 241574060, 267415920, 301477539, 804821270, 64457307, 610619702, 828930421, 548954018, 628054574, 14065979, 686848226, 966972631, 799304857, 484907975, 728158831, 667622118, 841243756, 885844308, 958048761, 242197426, 87521958, 41539599, 273908297, 228930115, 81384472, 800875331, 739633250, 477337799, 768539783, 422604247, 137477463, 563808149, 509726880, 265592242, 356305983, 546263813, 174230701, 822693882, 345738591, 197185356, 341483025, 658297379, 679593053, 166810331, 386180644, 765567886, 881210523, 848908620, 798213849, 325211549, 573887410, 39668580, 225613101, 666307160, 787955944, 872561891, 202737130, 603000952, 427501813, 93738673, 800895857, 97747671, 998863104, 915032524, 358611159, 179090748, 567087379, 423333586, 656083772, 961692912, 159266340, 432578969, 744880838, 471460011, 207371392, 521817282, 729320318, 308175694, 754659399, 604668421, 996789000, 659959104, 89520957, 795555775, 357870744, 528114, 552501576, 346990974, 557251621, 845683189, 768017379, 472348574, 300144326, 591984062, 691808630, 815212584, 601781053, 714414304, 271561593, 589623584, 923919259, 865800817, 634216342, 391185709, 74236840, 390485854, 702844311, 196283999, 658294336, 458862397, 61660509, 981711527, 48311345, 743816514, 948843818, 398482854, 409876149, 931707003, 904694293, 100526308, 684141217, 865827475, 963540335, 649027046, 872497845, 53508145, 291327284, 847818363, 363823897, 868179150, 554818179, 148095780, 807826783, 324280939, 20945445, 206827963, 526461907, 925631616, 161764592, 284244442, 403169600, 880532613, 925381567, 773915185, 62939670, 116520749, 153424024, 618860804, 731845433, 55680734, 262443116, 402713035, 133329417, 226502246, 377834706, 946707242, 351940076, 226126776, 201824465, 166555627, 924085074, 571508708, 928686695, 716038119, 947775361, 479385372, 263981409, 219844974, 341805059, 932764478, 116928369, 688504332, 514225748, 512586219, 391151534, 129887336, 583016294, 843305459, 128309912, 189345395, 633516093, 118386504, 695101616, 772169898, 76877729, 159847751, 43795085, 690943971, 454901490, 346989696, 607077084, 24197122, 57405637, 760933213, 975392705, 866321439, 666433838, 958592515, 396605734, 279948847, 940132142, 312635296, 321225015, 489514324, 513881926, 273224729, 881928292, 954350870, 262718659, 667414567, 572648514, 270118848, 525630848, 936493866, 837688789, 31643750, 411729952, 154364679, 434834798, 924333443, 9294129, 498508365, 909036260, 644841176, 474825782, 896438505, 340469803, 899095609, 434099144, 467908376, 525136864, 504896396, 609373856, 497195930, 301216937, 331967882, 33683963, 438181734, 122183519, 21125689, 926119488, 660404065, 195116955, 172426575, 390631443, 862139370, 515100147, 673219275, 36192494, 185274746, 304035106, 141397463, 815179938, 69904855, 292044191, 149779787, 609775647, 804025296, 901185490, 485343137, 962795070, 215924549, 387665615, 108604229, 74486775, 47667552, 951287166, 130194282, 578021364, 135163216, 745905395, 481337855, 263289620, 468990804, 974284510, 627519211, 842702197, 857943439, 305086502, 739669617, 991844430, 279490946, 257706756, 279533234, 812660662, 718691975, 318782135, 48023608, 857423429, 987799029, 570364431, 729267487, 337628156, 488530733, 756570722, 925118296, 237929490, 321913337, 805166275, 656511655, 947743197, 602859547, 537063999, 870229797, 124209839, 502710910, 43051189, 298825533, 48024673, 569520940, 537493787, 226992657, 801356516, 849522824, 892014932, 351375058, 999714304, 423716631, 473108909, 450495331, 159689034, 969605438, 968105736, 165110376, 623105038, 726966108, 260373223, 275591896, 795326695, 727084094, 732756314, 272873209, 905069117, 816166169, 619721697, 46058653, 315080651, 277032861, 180030196, 958875920, 330227271, 422419170, 479014653, 452415228, 371172606, 905847671, 490011072, 443471204, 867942479, 417169346, 673375916, 277952449, 819071516, 465811847, 364049511, 111904422, 45017225, 113229423, 139565128, 242772018, 137183323, 193067820, 294233537, 196976798, 802190403, 709993070, 336619529, 803949879, 671436207, 612950278, 370724250, 726353646, 733275539, 827317752, 608557340, 961172443, 369138349, 590872160, 223952366, 561044646, 421523480, 879254934, 454815010, 820187641, 925442162, 753159624, 471872997, 858843180, 388365412, 26231210, 627251528, 240936263, 613868475, 80768522, 79908206, 261153542, 766386143, 412458523, 300661728, 730782957, 403889102, 880664138, 186257679, 63117042, 902002286, 789470999, 297508429, 74334246, 576951906, 964628590, 70085926, 498209230, 453610220, 865636217, 311315058, 341112069, 283337310, 858296953, 938723357, 183366527, 561006437, 742216115, 626969949, 856386655, 463373413, 192162770, 962669736, 15660810, 241349461, 100104624, 569161880, 400303056, 787537988, 275966360, 747233995, 550354990, 155787444, 933580921, 114966894, 844635977, 933352538, 993469244, 796740868, 449549677, 778790210, 258510837, 614371154, 585377749, 43126175, 671159277, 862380533, 973508952, 498070274, 453199716, 389872912, 246148765, 358849530, 647812088, 131765187, 161947975, 128432223, 865094822, 657908616, 291861155, 89408953, 17995934, 480117413, 176416948, 566858633, 94249672, 344800131, 753635062, 411794631, 813078806, 355268725, 298810504, 909315045, 290594328, 834416442, 596015791, 788441311, 868516709, 547522190, 879597232, 609321831, 726637225, 478786909, 234926583, 235121295, 398336116, 938975208, 15334743, 819548299, 892497902, 764704325, 842837918, 544915396, 477548248, 717515822, 837969556, 986572215, 959212789, 913115865, 383101764, 504840641, 446993257, 398566804, 696091361, 629412522, 141799999, 148585404, 524580988, 695915482, 679211955, 560647954, 429680572, 789950001, 642618941, 58650671, 503254610, 586695508, 602209164, 613007005, 958172012, 571805528, 529730436, 213308332, 408640826, 973806469, 685354464, 254441722, 24777578, 945338, 928629566, 484940465, 706087268, 27674590, 704851300, 779595672, 993695969, 628603087, 552972375, 495997250, 86223371, 134147998, 402058021, 714771678, 27927884, 987701348, 744599342, 219754884, 205525105, 285166379, 420642778, 787996177, 950363317, 459810832, 457859028, 956081022, 826747105, 275336875, 767685675, 55656716, 747019351, 390699549, 251621992, 662730025, 523666545, 594724052, 27336991, 538360722, 880479140, 803907860, 790447604, 794043864, 585192821, 152235060, 847217164, 457794975, 413084779, 665803886, 269240408, 236154550, 633126573, 686170487, 690354408, 65806063, 883230506, 190263482, 698085243, 129060479, 589237497, 664784137, 205978308, 937685664, 493751799, 190150993, 429599524, 221539816, 418265569, 59686515, 580173182, 55963257, 458856706, 230066713, 820719787, 592374927, 759010256, 343314778, 770231270, 811285806, 838809919, 108085882, 850641353, 259049147, 250869252, 106928822, 80391691, 919963500, 798246281, 845407691, 230508184, 464191575, 356581434, 178930829, 601887064, 200581241, 435064614, 568786962, 859447844, 568541326, 145200764, 378128745, 323305636, 247486556, 862210047, 488867332, 443704707, 478261000, 966538136, 125475856, 757253419, 324035553, 802672267, 251047611, 384088137, 40956761, 926408988, 286066089, 96195932, 208926, 90508071, 860386650, 39965081, 572620274, 178631324, 451500536, 663695349, 388059577, 797354895, 954577553, 708326714, 538528712, 682284792, 295096444, 788319797, 385177026, 277365248, 437162244, 304629308, 18368935, 650140471, 498135564, 570456483, 406399785, 231310490, 340696542, 848030971, 618094047, 99269767, 566679727, 864758652, 30728743, 94445114, 524945702, 695615807, 66446996, 214528120, 481913427, 124393795, 372777672, 237426492, 474666364, 496367973, 744589303, 880907797, 962105899, 318201194, 374170731, 43195815, 981385180, 221888243, 215117239, 374604361, 510198938, 404212156, 238708640, 880299709, 607059276, 894560463, 203322172, 324724066, 108614593, 785706884, 36482971, 236274954, 813676516, 985269260, 704474682, 357981510, 648983085, 708091419, 95743942, 731307445, 871679699, 350050393, 959006315, 413424085, 247619500, 724979746, 441516180, 47169579, 855372347, 704912604, 906487434, 984477765, 963174684, 362342404, 20480908, 228952619, 394905368, 131748925, 950814159, 423097284, 553116564, 97290608, 559870703, 402040442, 647833034, 27149767, 169619588, 599380466, 721205239, 562257879, 107791394, 82383203, 270790861, 690132569, 741020014, 402365282, 957162468, 905380028, 661089892, 661986711, 549122953, 95786833, 241868290, 1928732, 106813994, 594330364, 606662975, 933928634, 106339610, 259652237, 197953139, 854924886, 170168898, 863139739, 73095319, 212540769, 923891031, 866640156, 53267878, 55079118, 212313226, 815303568, 70910373, 20203655, 788124381, 870677562, 279154945, 15099282, 109574929, 83147297, 244594745, 309559655, 344309621, 977223986, 762846746, 95955443, 698312036, 927456288, 870662110, 201365277, 944430026, 669640080, 815792457, 580017384, 235590941, 524802448, 910978129, 300810225, 960734216, 183568061, 104822764, 912317914, 974292225, 873562353, 984886311, 646048272, 579638404, 419074216, 402497029, 979943955, 500407890, 598719727, 408607260, 314965153, 99110807, 76557803, 714734280, 340320643, 738949199, 650907639, 517154526, 67945967, 837397671, 687576700, 224930999, 751707828, 259362894, 475024959, 910920432, 898639103, 960616104, 137129452, 232444906, 351586924, 817330101, 224619575, 575002207, 475107123, 596005310, 89013990, 92497605, 160561599, 661403050, 819831767, 319583886, 582442338, 421974980, 243461840, 261575910, 607658424, 534439239, 896078964, 65317259, 73101744, 605097891, 920071621, 357017571, 211997482, 554508766, 963596320, 966054876, 329836681, 973329669, 715882081, 199670616, 817756039, 23864840, 167397533, 490293891, 736903121, 196977905, 867092896, 645233057, 639400563, 891296630, 178172134, 78273385, 985164351, 511631915, 79110201, 894647695, 845880878, 526561029, 727950733, 500218422, 784207738, 575207184, 81449959, 229342372, 606055847, 710840861, 902587733, 208006324, 153680958, 136550426, 662986137, 653929461, 654019558, 448234312, 329870926, 594712802, 585929472, 830418335, 77383126, 495621001, 505631391, 661010532, 118816629, 448184627, 591867519, 247985198, 181859762, 744683697, 869761307, 454248601, 476786843, 576508713, 289854359, 456083706, 589452637, 482731578, 936952783, 919154971, 718219941, 591916629, 200372387, 769789317, 187293774, 656230474, 815971280, 527221994, 978836988, 668502602, 833305221, 637652383, 874774788, 491856991, 735876885, 246208026, 55084223, 249852297, 73627294, 190758648, 402493551, 697680583, 7407826, 111925996, 724243714, 190080918, 750728241, 544109759, 837405288, 690250152, 448184421, 707288772, 532687344, 807476196, 484010184, 317423743, 226790873, 311462095, 673334135, 682637437, 359591886, 469826622, 352200820, 958899978, 444511158, 412521470, 372778655, 582661006, 612039402, 39163177, 722866949, 658824606, 689579087, 390351062, 246799978, 591712341, 751450161, 614403444, 689958249, 899246496, 319650203, 228698721, 549904759, 861618905, 633098715, 692555860, 605628035, 130206833, 322487185, 546620353, 409056951, 977869616, 191699071, 950552151, 493446305, 203766416, 129994701, 848428632, 454396256, 689913012, 240887540, 515301446, 757154618, 411531812, 636713229, 516777193, 694638727, 684987725, 949773860, 223716281, 604484930, 345035377, 913280145, 581917744, 156911157, 775783732, 500356640, 22759385, 282189578, 622449044, 972474117, 442363887, 684016183, 284455279, 122224390, 549960967, 388763570, 198365757, 577026320, 365944866, 60910267, 223727404, 826132251, 193596177, 945627250, 924941614, 385559434, 720695829, 986892136, 991018086, 178214580, 656398757, 294323034, 99935402, 709404462, 695025638, 929560815, 627463617, 27533811, 875573998, 868673285, 739227965, 118093425, 345760390, 850736258, 495367699, 902736756, 359815990, 698406366, 176658464, 895162460, 697459097, 343523881, 474405248, 324957370, 240289893, 228955615, 609671250, 963692899, 279205812, 231954610, 401877896, 271855510, 409537171, 626718306, 988112615, 109133376, 582752102, 249435232, 194706786, 131298967, 976174255, 402536459, 289166826, 801732506, 23612499, 412511911, 446243222, 160314086, 957113992, 343982908, 760402658, 9223399, 683409154, 458868931, 783160405, 584892218, 305910218, 122423708, 477314212, 998463418, 69130792, 237022461, 959722480, 63845786, 798409776, 898154841, 1921827, 417186579, 310810327, 868155874, 527330841, 736518044, 193584780, 476892582, 711215294, 68443651, 945442550, 941563857, 884685301, 23367346, 404259562, 542692071, 654186672, 974078467, 774002610, 751353237, 733115583, 386460973, 811434118, 520527142, 246881697, 696955714, 369755166, 472085109, 583352034, 108104789, 839856461, 640540453, 297071407, 39084525, 113873047, 326217174, 862813268, 519214372, 192987267, 453828402, 504360068, 535028192, 665452530, 281326031, 726250850, 325104383, 200054679, 272372232, 585354507, 552894272, 619034569, 712378103, 435747644, 318311794, 767481285, 99154765, 184167058, 997176285, 173232548, 515923048, 428041550, 218137939, 520941137, 403615528, 483297854, 455632809, 526006030, 306129232, 608822959, 865391880, 684343467, 390327228, 376476468, 164104627, 245737950, 444053503, 755974350, 978792096, 696501442, 868550157, 321349106, 143578841, 975236463, 841805876, 389172800, 135034159, 277689206, 51713787, 299668508, 746328947, 379414755, 634037635, 283039103, 659696808, 419374957, 188262936, 932739221, 882347310, 814885354, 94694255, 552730658, 931322001, 777024144, 773198653, 360284662, 351658575, 328244584, 329260508, 140076070, 729827923, 919995848, 332273374, 945746419, 951463879, 268854752, 906645427, 192947434, 953962262, 29760170, 867757898, 562317829, 730087858, 415604948, 269540419, 824865031, 456396845, 480185917, 13510802, 180948801, 571909655, 47048405, 128722315, 836622847, 548591865, 161884684, 725756567, 110520591, 111603545, 401737379, 870542302, 915900438, 546832671, 399776609, 609920430, 683444948, 67873757, 433642881, 871208054, 87458090, 300733961, 219479760, 252650671, 694956519, 522875158, 330753861, 337317849, 268313520, 22746196, 100441373, 731158905, 223323199, 373992516, 71462964, 792613053, 526979947, 753339660, 915282077, 540904358, 903000623, 355802346, 767048155, 329699029, 351360329, 778294378, 761377099, 440094120, 81701296, 826909230, 657041519, 36664152, 939188664, 825112477, 11958279, 616497134, 487956319, 572649637, 709859241, 137134717, 651054461, 724297974, 4610967, 861440811, 949507183, 571176532, 385280795, 594358271, 891011663, 42270016, 755347077, 277540338, 552022640, 734666330, 288312669, 584048118, 577977548, 221634561, 30260073, 832810985, 361451045, 906719316, 716340854, 787730041, 770027258, 759316536, 842776659, 819242179, 800410694, 458245106, 832810509, 841077976, 541109296, 172334656, 143760413, 259961877, 420631306, 815828660, 269317684, 523418573, 493361860, 376977898, 683705140, 104326539, 801137168, 334079745, 204110498, 900135421, 565490926, 411873926, 837260302, 784120102, 955942012, 51497922, 777564492, 783178464, 859521131, 953194914, 50970200, 237702256, 24798786, 279490116, 335018444, 313124517, 288136381, 427752021, 466796281, 454141120, 382864301, 421217659, 381274435, 476331492, 272822898, 399445002, 169153416, 454186751, 685928052, 325723249, 905392905, 445352229, 104236018, 351513118, 813898376, 467696999, 227162551, 412709198, 909490242, 197293313, 530537644, 699973156, 901074526, 74853485, 174682181, 487414967, 228621716, 35085612, 575274148, 209763975, 266940915, 577338772, 668813133, 210947915, 488302617, 436205065, 278414080, 768112235, 783175169, 865208974, 967396837, 553857493, 84096781, 926714457, 874528810, 711364689, 347308929, 105097592, 97042369, 544816841, 860721324, 496923815, 779120936, 482409653, 158599944, 460708046, 209045012, 585136442, 363217603, 940854733, 305297369, 817528783, 388752698, 683592922, 604724390, 19795646, 597847486, 245947707, 536195726, 877725626, 75551958, 668949424, 338410162, 805297099, 982339043, 788395266, 309554874, 454811258, 200512045, 941864882, 431874113, 625256496, 159090810, 87110459, 964504787, 750409769, 408183489, 735869658, 741749493, 7054001, 237753523, 586912961, 803186467, 856355325, 365994999, 566799792, 243822982, 302752591, 287644716, 515294240, 649335948, 227204677, 886339459, 838417541, 918872041, 184051683, 476494437, 293782667, 302843680, 163490539, 570348566, 657890535, 562815973, 350426497, 518212315, 481097000, 833070496, 43474817, 23619802, 71630112, 128466310, 727299524, 966652853, 475536748, 302141422, 492776207, 711558894, 825886168, 177571172, 751462000, 366004162, 259383928, 350179819, 534358213, 284945014, 146875190, 167848616, 883417006, 297680927, 729629888, 120050192, 979672165, 811543039, 5923236, 234728077, 272024092, 644894559, 517914502, 848275734, 763570674, 750921851, 538763684, 289725193, 847911981, 369009296, 108674828, 946383303, 648340223, 108513301, 981968868, 907415796, 10749443, 491052986, 481626748, 934477274, 986157605, 713712628, 255759869, 461734473, 999365338, 988412604, 144824329, 317585914, 537591209, 766112877, 134696796, 579261968, 124042533, 807681314, 921888895, 396916258, 34699636, 290202869, 414106148, 195233965, 517936855, 861889924, 857727375, 27904999, 85910341, 732096080, 309545364, 683243129, 241640399, 603876765, 2284774, 359057210, 284331552, 73417630, 936322626, 413254086, 543377835, 506043036, 120586644, 296046003, 413176723, 815220437, 968170229, 130518954, 760686196, 931476696, 448780206, 709372095, 727741728, 411041688, 20429171, 88094821, 320101129, 431586736, 204246846, 976824926, 696844356, 763261679, 658555725, 225785718, 934971128, 669768211, 993344125, 716001298, 277637539, 567773974, 872961576, 431310834, 194010888, 146482781, 110176608, 809866989, 99530021, 236162296, 60187718, 127226892, 730361528, 402618540, 662577440, 108634629, 567930582, 555872217, 536306462, 9682, 538888482, 650931661, 887021043, 513976583, 613695578, 614294668, 272626995, 840787841, 288139920, 916281912, 175956187, 756086501, 584232022, 731094376, 907794457, 542491360, 226117734, 614559625, 984662324, 994465297, 200723640, 220385678, 168564680, 676285350, 875353714, 746455250, 702200666, 278241122, 775262830, 153523896, 86049993, 982664849, 907557975, 846535835, 517306873, 492079309, 226089943, 611527596, 337651172, 587419248, 269559747, 15458681, 657609979, 970896104, 321130302, 998442475, 954314627, 654946060, 464711458, 490701014, 853987691, 644787592, 897174387, 424243178, 717572440, 120880127, 526461946, 231702473, 419832379, 246799138, 579974668, 388511947, 141791666, 87309810, 585226941, 186332357, 157569162, 926544491, 993637206, 325711671, 906438158, 911387078, 500473480, 206390839, 731585559, 601716336, 578022884, 932754754, 33591938, 104835867, 699777225, 583677602, 658399643, 936591695, 792121434, 622906939, 854764198, 128474555, 839087498, 349674212, 997753397, 479941980, 470674948, 505071163, 20860326, 865819325, 1501943, 136656975, 37600679, 474086022, 331880169, 556391472, 85779899, 540914659, 961011215, 644624532, 438471474, 195900339, 213143717, 583790355, 813205372, 595619208, 222883944, 412923689, 835404490, 60210556, 762599582, 37334171, 349639145, 896578332, 57449845, 164993232, 448088764, 977352661, 561139686, 825507403, 843902525, 84693136, 173183039, 602987716, 927221350, 734970550, 150713312, 55420592, 451985317, 118487228, 521765554, 971336921, 847025631, 821690082, 250792275, 453095478, 357755277, 699433313, 80938285, 525862832, 92405866, 939415946, 765289492, 535044297, 805007355, 972598062, 812990615, 621614611, 411850683, 156381702, 766701776, 100680156, 533909329, 611314039, 304294381, 296957691, 693926798, 589628932, 482050761, 814128283, 73445209, 284089155, 702465439, 424280433, 726750104, 967265957, 149440119, 916493403, 402161820, 820013863, 498349653, 892137831, 539917885, 573895599, 532854514, 318864305, 900909460, 482694284, 899735107, 533292635, 237783809, 783257858, 330810722, 981600230, 425550525, 790857767, 588230802, 583394768, 745005216, 364559489, 950474513, 915316675, 627594419, 947799047, 453612768, 468303415, 874610122, 241943742, 285740637, 358461235, 690643179, 186123676, 597697355, 879301339, 326639376, 876982730, 1924068, 955390566, 149671262, 236304526, 851761390, 211911853, 894396996, 875809658, 510101986, 837681316, 207953623, 977212450, 477153434, 157745035, 939446888, 585738706, 91651620, 640445805, 715027835, 857305342, 847630036, 65924143, 656018164, 4403819, 515691524, 519245019, 94123468, 607491779, 844045116, 689541538, 757809926, 442909054, 157125921, 215826616, 831874259, 275716959, 543829470, 684353409, 459806678, 937983017, 739650159, 373455915, 347794484, 519337516, 703819121, 162078864, 941176844, 37322900, 489926870, 395369491, 685186271, 681837919, 129512469, 50014440, 162137948, 818445401, 10657404, 183680126, 679204771, 5189986, 895715018, 15735076, 34250869, 827086686, 842961546, 77709682, 206231707, 498129468, 523447884, 503843770, 150004768, 842607791, 775267788, 346378872, 914692767, 806044380, 51772716, 284632932, 285600068, 349546830, 638444683, 369695108, 770474805, 472801652, 15567723, 605071476, 143493473, 213396855, 805459414, 924378712, 199717318, 843243119, 305146123, 435679338, 265529659, 963258851, 949545398, 712024296, 96185743, 924813899, 339531273, 975891056, 988047246, 609946716, 804003265, 24159915, 771177744, 936051443, 906001696, 369400463, 654594993, 707005964, 362855100, 649770368, 977516451, 114196122, 354479996, 822217935, 772160988, 251767091, 230787772, 478674582, 81750437, 771813944, 903040614, 711977260, 641060102, 603532104, 313621329, 719789700, 166281684, 849160454, 586247955, 93893222, 704070623, 204743114, 274986955, 196482639, 533709812, 655726969, 486032288, 910477513, 160782529, 380751601, 489959864, 762340708, 551441270, 853516773, 346358486, 961450499, 231031220, 944417693, 390118034, 826445171, 623848413, 241727340, 710823788, 211948568, 618110275, 359573710, 825351449, 221705182, 705584078, 341186605, 865773011, 679958428, 678859748, 114934839, 948276859, 187276648, 202260420, 697488715, 854802718, 680236093, 547634247, 561101027, 516850909, 989126897, 215904509, 124368162, 443749157, 553029007, 274879378, 619375802, 940060526, 843479273, 658122419, 778977081, 518566747, 600733538, 25522993, 127720812, 880479867, 58406552, 488345427, 245703998, 971780764, 857891928, 788437111, 20000899, 238175433, 948258841, 648819630, 216564464, 966462568, 491163314, 322228162, 952063544, 615313908, 983907012, 950626069, 20464860, 382172157, 956392328, 991813146, 805331447, 689629955, 159013816, 696900497, 370397829, 580558790, 195719436, 593160142, 850270425, 425991206, 547782759, 751673014, 689604244, 594574957, 473230574, 791447467, 443368480, 258626631, 52644846, 455940010, 990088261, 696170090, 812029015, 981273230, 544144733, 10576802, 499573170, 892864615, 290890778, 596301903, 659267508, 856611835, 694533334, 467852469, 485538227, 144052794, 716468879, 290359069, 92544355, 837430854, 566605659, 313592554, 446227945, 855118228, 810629272, 907484722, 412392800, 662126906, 765662952, 305724008, 491911111, 836495327, 200910679, 935551790, 878940466, 606513170, 722252711, 991901727, 25177498, 546827250, 248549236, 551213274, 60614459, 750909630, 148095730, 691399406, 124220481, 460981805, 575576941, 273088662, 626364122, 414873831, 661768436, 38434316, 690852714, 825923376, 899083066, 609204831, 479861810, 267775407, 979553890, 255909763, 957640230, 644270601, 691241479, 166455511, 876536335, 979849276, 778030058, 530418342, 865974348, 137383768, 885597919, 415872306, 710741763, 652365119, 789076568, 926829155, 313969030, 959467389, 338191613, 260456318, 891725158, 691715561, 953177296, 759753939, 329919659, 851423728, 61605859, 158793023, 787023223, 967311474, 428013570, 826845882, 446734911, 987835111, 24147362, 994806240, 824751815, 699314298, 267324433, 251759261, 750902119, 773442285, 548180740, 592107122, 462031947, 1380763, 62635597, 656969908, 889130423, 38258685, 590889762, 226390657, 227284513, 140099375, 355678932, 397428543, 944901306, 782596837, 968155464, 119245082, 944880005, 718977177, 51111421, 998022560, 578972388, 207541341, 433894042, 778407245, 918925346, 980964523, 954409237, 150065074, 353005533, 602369177, 666582512, 638068138, 938113603, 684693658, 940371568, 127414247, 151827233, 243259510, 536630543, 597016472, 31315306, 642535316, 253134183, 511591606, 650533571, 128664760, 839860802, 804979734, 847360029, 774919013, 167091309, 576518902, 167110914, 576220953, 996442214, 145694491, 538239371, 9239890, 767643964, 647549395, 424641362, 91294501, 436134414, 199121038, 213047705, 324679747, 154063784, 904746371, 340836338, 273195691, 15473031, 143010344, 972274164, 577072929, 702945209, 230076164, 784522115, 308430064, 800064816, 430258810, 344906995, 810581431, 573578391, 742034003, 370060741, 513154953, 531199234, 21615856, 199453944, 419597112, 239137292, 322574908, 528420094, 466883563, 972021655, 636143533, 544531290, 95165732, 205842966, 883488829, 707365012, 105836205, 849626550, 106014908, 343724116, 15460642, 767682556, 871005413, 11302924, 435756658, 456339106, 365868452, 844530480, 509455075, 111823149, 420194860, 608704568, 328433568, 221299629, 726340397, 962725035, 503245775, 276224426, 114156276, 114013895, 771128520, 906253893, 830751390, 6116772, 28292624, 778527029, 895744756, 404292878, 69206576, 660289417, 373622206, 782816755, 928059261, 24188351, 428495251, 412591268, 261325473, 566800133, 715218294, 239205156, 767383230, 334988370, 356201839, 691249570, 295380903, 372667808, 260868339, 693294740, 960902123, 412663371, 970455390, 608918261, 121778217, 660895888, 609353983, 902859491, 607411758, 925634937, 969540268, 709131034, 472335235, 168119503, 84265430, 271677247, 805210384, 394603623, 560539559, 794453918, 67988576, 671882674, 357758858, 776923687, 386307177, 58448564, 348191365, 629648263, 607928444, 322558098, 640031586, 291108431, 253003332, 59721858, 384103133, 782490205, 254768220, 852458232, 887485967, 423208806, 769141411, 433177809, 96862641, 292996471, 934199061, 300739191, 857416674, 878304666, 342000580, 269523466, 578715256, 529856886, 98459094, 167828497, 130823039, 895393155, 468132402, 213237493, 754649928, 93309847, 840877960, 393389450, 313381461, 645774471, 526630215, 778643202, 360192852, 952408060, 960740487, 879917070, 703779917, 869250284, 616073783, 800309240, 533614306, 410167309, 924141877, 721543837, 853549812, 462360414, 876109590, 536946786, 533482040, 688520423, 18807013, 338341429, 448646129, 740491771, 471828939, 262075412, 246078451, 27647902, 103422433, 730981052, 297349771, 106532577, 663733546, 629007822, 687928824, 206941402, 315621587, 566420470, 639681723, 808603634, 957635244, 169754209, 940312708, 646098458, 675282769, 477625286, 725046405, 716603704, 515106348, 460714994, 864948537, 442354697, 613437573, 204402761, 524989779, 479588185, 605717304, 479656481, 983702693, 278165840, 532322953, 854515136, 158735070, 548468658, 267664419, 973732556, 97583418, 713414421, 165049857, 977245188, 497020988, 993330660, 927044330, 300965884, 552628798, 971750018, 462712612, 437223571, 829463359, 613884514, 666182190, 957108933, 921848396, 751701873, 148257485, 54577245, 313759021, 3177884, 396331986, 40806291, 416668559, 848314384, 605753154, 427101366, 447198329, 225139925, 392173705, 254190421, 258827395, 802956202, 27853214, 477093872, 183283611, 653392457, 904537288, 133105080, 107341137, 219415803, 643611182, 856120087, 65776379, 685960352, 946177043, 919836456, 242760287, 860938468, 736067489, 39271590, 254595362, 638753381, 112807468, 858549256, 136922112, 162420848, 46591692, 262735162, 862515411, 476522939, 528631622, 740297021, 573378139, 977321049, 390349667, 646111848, 268687054, 499257838, 47257430, 518936840, 518406220, 414189223, 457728684, 129649719, 838775461, 870807734, 766939002, 263017250, 83401395, 702601601, 806183387, 887254586, 94546258, 269720004, 19952807, 839642862, 436662003, 700052734, 327840360, 184935484, 311855521, 12212685, 315475249, 976795190, 162102358, 196395263, 63349648, 631519820, 877808450, 822770000, 792743039, 636232978, 201357365, 262812811, 914635789, 632258692, 542453586, 41735849, 321428684, 345835513, 176203565, 653215117, 262767417, 819197062, 956794745, 616646076, 776545223, 202639161, 932600484, 910430399, 284018620, 527317445, 71747542, 641082246, 99066063, 474768213, 659550488, 466669220, 174225462, 312233909, 3247345, 101485953, 910943930, 843124685, 508324775, 777208272, 74420251, 771824888, 702779933, 414701261, 834481862, 587123141, 48802450, 747480754, 868048162, 34765782, 844518515, 709767645, 399634870, 804709818, 443426452, 148859184, 651693573, 123690691, 369905636, 828385700, 293396034, 676633084, 676800716, 315648773, 110567078, 489989743, 805102924, 455252171, 689639262, 829818689, 708199480, 846706155, 345899456, 808954078, 61892674, 597569033, 975626544, 277630276, 451549639, 152021997, 216782475, 490095005, 36738626, 435222125, 859021724, 495360353, 898965485, 409182301, 890246042, 546166900, 684676873, 230701423, 13526883, 593095625, 370804520, 126506768, 170238833, 973536661, 687871794, 445967516, 573128998, 261430671, 108833420, 709816489, 386506494, 563539961, 196006381, 305133235, 608565543, 652845126, 781440733, 710755915, 63057871, 942809618, 377575195, 791940998, 74140469, 468828278, 808009272, 761308327, 440208203, 934665030, 991285793, 55174481, 612705503, 524524913, 311714510, 616865600, 953142045, 541896118, 788251049, 692087654, 270138941, 732766842, 635210897, 65040963, 85965368, 217625977, 348207036, 588271174, 290938556, 378659297, 714383384, 779691790, 675755853, 124798724, 880830715, 996983436, 9764423, 858201335, 526349534, 888719559, 264130652, 933381274, 648794145, 891207820, 818090310, 478317138, 734129707, 666804280, 357413877, 104087697, 924970794, 207788797, 271513474, 923005835, 477079577, 912850081, 917332199, 46826048, 563946785, 21316688, 824323387, 221247789, 631120247, 768561111, 738925726, 610373479, 57283819, 629224317, 37958474, 895532522, 192861559, 14487695, 33061050, 766319548, 385246034, 490299226, 428160810, 352203640, 422049365, 632994831, 529978453, 270429706, 106734851, 373099144, 999955574, 322549692, 167854797, 244255839, 17009551, 840060248, 145367397, 934316845, 577620869, 970822966, 365269045, 41887280, 294099036, 515497835, 287410159, 439497981, 343269827, 817931067, 686209049, 930697737, 970337543, 404590192, 437465978, 880328792, 507432277, 777060253, 512081666, 388186629, 627742494, 423126196, 396112106, 175981626, 154331252, 796142901, 341147374, 428167502, 623861831, 426398941, 580923064, 480023049, 333791549, 152275946, 617126076, 180172921, 652579916, 633309547, 198998050, 704933796, 891386288, 849162415, 967799085, 561271701, 918935572, 4322014, 26585074, 793270371, 13303467, 147372822, 705087755, 636428027, 288790391, 658459337, 298834481, 383203733, 34371777, 347509738, 922975716, 826193171, 251204891, 695072035, 303822930, 447873532, 172930596, 229435537, 931659165, 290065845, 783832272, 981264609, 93257727, 781246580, 760295267, 789540334, 227432467, 747125200, 51358336, 625748745, 794455242, 937475968, 292872663, 588682936, 792485840, 880624455, 818384029, 144440381, 590686595, 526602370, 876067299, 444847569, 27382775, 764396674, 503965718, 903392531, 303623078, 170533721, 47049924, 159606127, 356322662, 345321021, 90955500, 809600364, 406816996, 555774796, 233935034, 365322535, 427241422, 563218474, 363433359, 107687869, 376726634, 120980364, 256892503, 965559261, 653663885, 564948143, 564009537, 937269912, 508922963, 827777440, 807504661, 294224572, 321880488, 649392964, 914401906, 356813747, 36887163, 214008620, 142337273, 431470948, 164507436, 621265417, 836484777, 101583384, 875438450, 956267553, 656202252, 135213936, 190007061, 894923639, 956727386, 214731867, 441071917, 176883483, 778376630, 321526067, 24994014, 284728960, 964546915, 731637587, 922375118, 229270683, 360664152, 658655684, 803291671, 902354382, 475712930, 303409645, 997219206, 927339697, 689640131, 641416219, 251820846, 45123620, 493948715, 492882789, 376629936, 680796205, 410937374, 547305610, 960426111, 638845599, 653172515, 659900817, 307562479, 952693684, 863005257, 210927079, 262338824, 336665326, 646091382, 423353417, 756187361, 241037424, 684871755, 153248178, 375786959, 353776588, 812083175, 194200735, 626274248, 978677518, 642946339, 169725232, 567096783, 103645872, 130428580, 456448039, 808047428, 906902339, 817444840, 444993930, 141436467, 186438548, 341847954, 232150401, 539277406, 310624769, 559224648, 424285663, 516640053, 614738803, 233103557, 759774121, 914929276, 850376672, 46552631, 882723086, 363710218, 22442677, 171714674, 978496413, 965628656, 70238583, 901952816, 38778498, 348836642, 28364020, 547353229, 998880844, 942526003, 270886423, 679151984, 18250298, 649560629, 18294500, 17579210, 259548794, 908932424, 978093402, 832470494, 63964500, 778609510, 967993227, 984359425, 584078947, 177158077, 356896501, 194833542, 650918025, 916758829, 111679545, 383579041, 819467839, 355648914, 227689002, 875818866, 979931154, 721610907, 797716472, 612222715, 456590519, 654669951, 993602021, 500622050, 787145764, 933712680, 162187086, 903401274, 579738737, 301352745, 85220756, 814901424, 954659200, 825915454, 506133276, 254615683, 672619833, 498475213, 245215099, 3462120, 213212115, 751200929, 982509676, 348632788, 675942702, 106888424, 643863329, 283635871, 530420724, 926511197, 818428542, 533571728, 540850230, 532190843, 375789630, 136160689, 8911158, 959735808, 446547464, 340933329, 943745503, 365197762, 734448896, 452714547, 570569207, 486091995, 868752038, 691011413, 507727289, 629915288, 109071791, 115284891, 410995193, 594934206, 702728932, 386354169, 831794131, 865800973, 728420830, 434131219, 787303780, 831827469, 494446434, 627915661, 162472761, 56137066, 989988983, 395502363, 675831061, 490503973, 808675071, 620950038, 10643044, 819844921, 55939991, 228317831, 302252172, 265528876, 93914016, 101808425, 894764203, 852356768, 766837787, 865999068, 674406855, 894541528, 973685825, 796152100, 353694316, 571069151, 724184367, 629507240, 259539266, 242013010, 709191937, 557791325, 136542256, 852325613, 497782285, 585675362, 251432157, 710850743, 84354515, 725015937, 903937523, 580669380, 502305537, 468957970, 652087263, 214100589, 935267188, 7268668, 948581493, 894002886, 874148507, 903505778, 686782318, 404260582, 223433674, 618837032, 443827323, 89566278, 929758268, 602525180, 182234166, 909957153, 351949686, 66976894, 787156228, 98373433, 977861273, 254743575, 909104896, 302438245, 338343935, 926099958, 388751025, 493016497, 811141050, 8625131, 587268979, 534601205, 687974877, 340039190, 410709334, 769008553, 851758964, 542644972, 250397522, 410440579, 995701858, 825994833, 706204817, 64887611, 581889612, 810814685, 455489078, 396897628, 145010777, 611031191, 87100218, 403950001, 776550459, 396526890, 527765065, 765307216, 232606237, 627848520, 904587627, 84270819, 85445218, 479266453, 813138998, 334546339, 431296534, 711980672, 226686276, 677561762, 21302313, 84164975, 883706448, 225306420, 977038859, 79894575, 626376872, 204162713, 859898493, 332138020, 630477835, 617504576, 787240670, 794733402, 156184954, 968600791, 268426193, 99935574, 947181185, 204434433, 796883609, 87403780, 548176581, 520926741, 60865966, 795474953, 411110069, 402303496, 805961606, 502788207, 786457899, 298367791, 221438905, 565752104, 481224877, 136861895, 706431757, 330624182, 247806636, 851559563, 833471860, 7175942, 439298109, 16690749, 920735717, 915011618, 950860477, 949531536, 396343076, 122892178, 10006705, 544312900, 347225316, 414749243, 187879973, 283705949, 250588003, 897829057, 796090838, 934256579, 381937968, 184402153, 986287744, 630007421, 591989868, 783101403, 908231954, 644425725, 177714231, 627874881, 198572167, 449758790, 933415671, 462367174, 373130858, 144720339, 691773392, 494441018, 404757485, 409548854, 682626129, 418695611, 822380349, 243758053, 489925796, 52446214, 994391552, 797544196, 234991992, 85338782, 927884893, 658273058, 279744546, 199751040, 800226609, 75277372, 631331577, 424403703, 157293247, 211780620, 222537364, 504107872, 801620192, 717805564, 519055302, 656476462, 298179811, 728543712, 24924993, 778430892, 425589955, 161611434, 323312644, 679731525, 974653075, 141623411, 586636579, 173416429, 97156259, 132564848, 926077079, 894094423, 598199949, 708093934, 119801100, 237137041, 448052324, 531968453, 847430774, 970540091, 995591971, 431154218, 92983511, 36844375, 147827768, 313392581, 546232475, 57191922, 873189797, 266174692, 292743551, 144135, 920448220, 358725206, 740269167, 236434856, 288996297, 453263709, 983662626, 934835568, 56806894, 527928500, 58532620, 79295876, 433034637, 810195874, 406120091, 560589537, 366792089, 258353219, 21487759, 168495050, 651191989, 913301093, 540970597, 823984051, 72349194, 244422287, 985954264, 488139891, 802398925, 930491313, 201838562, 790378857, 75385744, 847792983, 775748037, 720581665, 250351675, 635588880, 487929939, 560671212, 397478307, 269893042, 924185614, 95986816, 246006283, 798540791, 747836129, 328128224, 714510142, 249539809, 913306625, 624599742, 530358098, 558245431, 510760118, 78879341, 340277969, 943201567, 965996604, 95644020, 599630666, 731010333, 973417749, 476550220, 932746348, 464646766, 291279556, 668221032, 464824864, 280746811, 433030211, 862984557, 875278234, 837898013, 225248757, 227390015, 581659512, 28034894, 647131809, 208767555, 432024155, 63316826, 233720157, 893150241, 560814283, 745378631, 164159224, 247971316, 629414300, 800439668, 107930824, 185745355, 550616331, 238312641, 356792151, 8618626, 803952021, 181695415, 75587659, 663597001, 903803608, 235833554, 14735376, 199526296, 323296141, 67324929, 408876932, 697793876, 881056906, 602296068, 422257566, 384041580, 945857539, 79672915, 810003798, 971182619, 788239357, 573569469, 896377476, 331217709, 844541703, 568131985, 790581372, 614229369, 22260660, 541719661, 392117690, 946185863, 883937646, 187735020, 490259733, 198705463, 279907733, 604457483, 54680033, 457656149, 297945761, 134404399, 653465676, 347863511, 719120393, 567119287, 974760379, 221247938, 228886072, 789846873, 100219842, 444090541, 381264555, 268062472, 483270362, 295817821, 193715698, 52369611, 321406965, 838656519, 857067829, 210295472, 516425829, 864479812, 85253061, 45357064, 298992884, 903681471, 589622248, 589928600, 57646082, 655222872, 242078587, 673737740, 867694765, 379549616, 578981615, 574051821, 519524277, 708255945, 514127085, 87481056, 795108291, 250918962, 411087215, 451001496, 255684319, 841259291, 860328194, 567639816, 295647754, 529891147, 538226844, 90773969, 621709205, 835267212, 75675880, 857785550, 678405684, 383192510, 37533491, 534981400, 303842443, 780428220, 231901676, 776436956, 98404451, 189081007, 351750516, 537522854, 782098108, 378344965, 890737234, 457152950, 760019785, 115240746, 516393328, 479197503, 293790267, 906464446, 84152924, 845697977, 211054471, 162325850, 818177771, 221121646, 856454248, 283585410, 21227122, 149824106, 895090503, 536276950, 412320669, 375964590, 257941741, 540145878, 34919472, 103334175, 187672087, 947309654, 724026398, 392503659, 482702633, 979995615, 932369347, 508273838, 654059263, 429695727, 246724938, 566052471, 694652828, 880596734, 380486288, 742391765, 421711545, 989905846, 948163121, 614621536, 201032102, 698371369, 813121524, 501211506, 111211517, 796219419, 999074080, 595056889, 115127934, 96033877, 431824231, 715828466, 689051509, 383606632, 737565811, 320375871, 215810925, 510722647, 925914377, 981834769, 976926002, 136192160, 429219611, 250949206, 121445240, 876260392, 482478764, 941669209, 81941844, 684285753, 399349536, 383687875, 74466328, 410427733, 511154204, 355641533, 551615648, 186085083, 426191544, 833601005, 350404931, 227758925, 133307983, 240799922, 616149385, 193468316, 507326404, 613109473, 482491636, 850197177, 568344435, 58080106, 786523876, 465967067, 60834925, 585668554, 410680958, 191424488, 284774078, 814528494, 122313378, 183777371, 735841502, 244056962, 963512129, 145934900, 560039828, 839692055, 958302500, 917138478, 698974522, 458389609, 50663157, 371962074, 672681470, 244209020, 888191930, 608181381, 585871057, 894177272, 982655113, 174604599, 643499271, 259401111, 750266237, 270616273, 911694277, 186400960, 385155018, 618278157, 269703911, 407187625, 180139194, 127210512, 616122301, 645635515, 601642019, 643971620, 697355847, 508622396, 123532816, 779717924, 740155609, 522476281, 740675982, 26989560, 997061898, 530889859, 958904268, 941435575, 970050931, 794923273, 529619883, 7842794, 602377774, 38686113, 771960939, 978923916, 483375437, 249897753, 157251842, 818828108, 704031258, 597115236, 327568066, 927266511, 947094590, 73499694, 314447129, 927562474, 612940514, 777713315, 532863379, 130658096, 561739638, 532697475, 505283251, 656046053, 127442743, 670184794, 595279499, 122289005, 981823701, 416369180, 550235709, 992976142, 715275134, 99257711, 762687596, 987709651, 809960363, 57946378, 699237680, 206141824, 64319414, 406556553, 450485119, 919425029, 987519546, 166486047, 576252844, 536538311, 413929089, 810125575, 119433819, 224832202, 262091158, 569285291, 812282225, 766940564, 945013970, 944719376, 902074363, 296948709, 467844535, 340336570, 108346461, 534115535, 598215836, 335747535, 411001540, 976892913, 876277023, 112633751, 134205626, 189836914, 70380086, 896315076, 652586355, 451221061, 713402138, 13388585, 29056107, 584094040, 465254671, 443826741, 527957330, 586076332, 985394956, 755757867, 107082334, 803345996, 215009372, 749856883, 130417744, 56932873, 205056837, 889522343, 987406519, 659236140, 979331331, 739513030, 363053411, 162573489, 532701275, 83771035, 165242933, 656118260, 345599611, 476220687, 941047398, 454289262, 904572634, 841686383, 221907937, 288474526, 516975938, 887877614, 983448531, 519046468, 578023471, 442467127, 944204651, 203397138, 725143281, 80696266, 420012330, 566668788, 138960464, 628103809, 665197530, 13442506, 586648540, 80624471, 651119643, 785703768, 384757876, 13230512, 902574302, 296814104, 350063717, 823098580, 390295644, 488672363, 940679491, 177279750, 400471196, 801653468, 18193643, 402717256, 932527981, 445983932, 683598480, 497458659, 656109806, 168619369, 127991379, 901731850, 599539338, 155718494, 18957271, 621074717, 981490701, 589452605, 585450361, 15766583, 958298579, 307878009, 581771133, 156351400, 135591827, 187485955, 984669806, 244340961, 367134030, 407154178, 835581549, 246688439, 180376634, 988776699, 101344847, 521385567, 349829657, 648864271, 890688872, 863779130, 860725467, 848530197, 493616428, 537595762, 49336543, 224546718, 977264042, 749605028, 409745722, 457988953, 178461556, 677001026, 615382401, 428700084, 336652011, 403389892, 924307335, 996813667, 727315426, 525867056, 403292426, 826839930, 300080275, 142941154, 417681251, 951831245, 860029500, 588025116, 713057748, 362248950, 480310228, 175094403, 257141851, 288697575, 533711079, 489824960, 695825668, 61932726, 309339664, 694426909, 862081829, 575252091, 118982353, 498595401, 479518077, 676683707, 9474094, 706388278, 820369042, 812913623, 433361572, 192818775, 709545983, 289932590, 638167110, 548514988, 543026960, 399534542, 466365609, 111969914, 678329681, 585484952, 795692948, 214739486, 760255300, 609981951, 931430049, 716668370, 975725397, 782514712, 66703863, 419466253, 346861696, 158699639, 354320965, 565870930, 556940440, 620133027, 478936970, 606798249, 354619458, 867426753, 631704165, 391662201, 745698739, 981114501, 550515346, 943254588, 214398414, 392790966, 821131314, 693911648, 300926343, 78801742, 493940657, 925038831, 162312890, 193741496, 908050817, 225871085, 70772805, 741741570, 439760354, 799954922, 842479838, 229419769, 633675637, 214912753, 289308405, 224520714, 98101818, 560158983, 256798122, 526598647, 703662548, 800719629, 952004020, 333698176, 128491001, 916521330, 377705890, 550582571, 543995863, 712683011, 917259501, 850086496, 136406074, 36686137, 267203492, 622760845, 988944872, 882863462, 874747808, 188264492, 39739017, 270296545, 117066910, 708988314, 988731587, 528799181, 387295216, 569215254, 110163891, 546766924, 409419764, 424133257, 980289604, 841561531, 858387477, 555290207, 151550904, 123149012, 898185419, 256324571, 210403215, 700698113, 395740105, 77915443, 638749907, 300691060, 475019497, 869103391, 302911049, 218700399, 81841052, 403543481, 550942203, 483636268, 984083894, 44850756, 440579383, 993305621, 785883405, 45653053, 671714196, 27352098, 86671355, 669018960, 545638182, 327170806, 191383638, 111805576, 846894361, 104425662, 6048531, 992156431, 864514765, 280594586, 306816148, 516804504, 415124973, 964646477, 133803406, 807393019, 232801518, 784577559, 95067599, 168827226, 280285978, 801125017, 702796289, 663267707, 798312923, 365767291, 320740823, 888001641, 107309077, 176819069, 780209778, 253009830, 567647554, 248625975, 710410762, 947661481, 776155415, 10627731, 579095246, 6026395, 204720720, 290966067, 42445374, 73643743, 289183678, 510475640, 647830185, 764143748, 711057822, 955668724, 570658940, 346777261, 844199996, 287312909, 303176065, 363463032, 557671736, 59770209, 918092915, 727644711, 401403535, 428983056, 521002873, 727044491, 575356775, 329970175, 425193893, 978916964, 498083173, 298378800, 209451999, 957197708, 384588058, 901060852, 472731273, 754112006, 582307769, 21031082, 134341418, 132665469, 688056162, 935712855, 837019471, 859425373, 81607579, 261615973, 196781486, 41664813, 136863830, 653810080, 319232798, 820445686, 43669774, 797124558, 398286681, 829973137, 68961735, 904878351, 254018352, 705014530, 1341435, 750105604, 646824033, 826192092, 484513977, 3498090, 621748255, 744059827, 404241046, 88507018, 344309404, 676175287, 49709238, 370721275, 283226180, 910218300, 577874701, 397539557, 312211286, 184127549, 308354179, 136944850, 217401114, 30486022, 521629427, 207791987, 723167416, 587785495, 529033324, 696207699, 127978857, 246167971, 912232659, 674779278, 916024048, 620195735, 448978553, 181453811, 732389483, 286459717, 37614377, 266248287, 174862230, 300395641, 216983559, 340890303, 195585413, 75530414, 456116068, 85350924, 708543294, 575590714, 401273942, 830648905, 80640078, 623940900, 669059717, 954466277, 687221057, 457168730, 872343055, 965890184, 384039683, 434447597, 716246992, 649412880, 281377528, 190521207, 635716732, 420806340, 457243607, 467874819, 792291168, 453253942, 606768550, 711383017, 773360244, 267603807, 101889630, 742196829, 640632718, 342109535, 465982659, 341001613, 251419345, 323104713, 17412905, 320257776, 790947276, 455426466, 523642592, 50628658, 199322718, 582295132, 620745233, 717264144, 818920674, 978165446, 225649491, 887152041, 885036138, 296958439, 994011812, 885621039, 306150483, 730439496, 806275041, 171631919, 171487444, 41156878, 771598802, 505072381, 899123572, 946918666, 460455898, 767243014, 250615443, 669384533, 560415686, 926476251, 80146288, 790146067, 326931478, 269202141, 367816747, 705400443, 315606500, 872155061, 840825364, 630046095, 809578521, 213408925, 640487915, 930167359, 605051615, 540288592, 101864787, 287182864, 4408246, 570507916, 876401453, 357480046, 417650547, 25273008, 860628559, 590724471, 694359538, 821311155, 580793085, 11510869, 147749785, 986821247, 13756835, 273387100, 295047871, 399171651, 147560898, 979522603, 956896572, 75543736, 79901097, 745649256, 556817244, 946207144, 412026834, 400035388, 129423814, 941394734, 510413236, 405210202, 241256495, 588962140, 544522939, 152341047, 754786316, 224305564, 267921166, 45297427, 960570024, 21397880, 355438914, 355923050, 905221441, 743823388, 713064877, 599688095, 395519952, 340160656, 191057584, 934698453, 973234908, 103563586, 187635823, 436544100, 163903059, 431533206, 618625972, 495288077, 234549059, 524669060, 482198028, 680231311, 891507338, 26381039, 216232083, 390804594, 867801426, 99567755, 407045382, 983001847, 54664717, 308785817, 764883209, 364672864, 516736232, 528457770, 917987995, 944192468, 289630245, 209010860, 818082590, 484789823, 383999476, 284967194, 672620979, 155456450, 471456229, 535021040, 298299509, 96078430, 870487768, 372314818, 275176217, 534706893, 953761072, 279886950, 270342902, 778665925, 959639172, 601484752, 275851024, 773128196, 510679874, 404944447, 677299174, 223218684, 792253794, 818219221, 367847113, 447376754, 224622162, 333840878, 599490444, 598645497, 636785183, 499192696, 754763413, 447116654, 633069519, 993422405, 848149982, 139363609, 605459164, 869546931, 304135143, 298414283, 207384383, 556390259, 596802503, 245989861, 268464874, 746184375, 348696877, 684665465, 164440420, 721036061, 966870616, 360838217, 146261347, 464448576, 369251621, 991098978, 619751916, 930048565, 703983924, 874148536, 315965019, 579638767, 188017825, 446609069, 564992073, 472303421, 303631695, 364584958, 279067397, 723182432, 719797929, 410938193, 564064899, 659776212, 846539126, 693264541, 315174540, 424166090, 888829785, 251133568, 404948579, 855385813, 203405282, 269787041, 165654107, 218171679, 551042865, 771968106, 235799059, 444924225, 111505281, 397550769, 761195624, 380993125, 658817150, 89409770, 11436387, 782273747, 702289991, 662413166, 789848961, 683724842, 841237205, 18933213, 573692951, 453152788, 685295629, 681525821, 334519264, 922767592, 56503370, 239287426, 777205293, 61785287, 363106497, 891137967, 784777681, 267168358, 64170658, 848089725, 446031137, 798940731, 359350169, 682694959, 26321738, 918739942, 727426587, 624947790, 90158372, 730693331, 690402329, 845288202, 723464523, 208697235, 379048647, 387033704, 912225106, 462266577, 933565918, 75507661, 346082145, 681262828, 180808157, 397121367, 118655735, 65027894, 518258363, 124792148, 577228654, 293973530, 175910354, 461793165, 721087330, 377619514, 657624032, 402130381, 55992739, 643534674, 230428193, 587822002, 3572608, 162803271, 304121082, 808526009, 325086954, 498081504, 407240385, 474914024, 87099878, 387947671, 495739424, 954836345, 854205226, 932836146, 432716299, 820444311, 188102199, 864722915, 705907217, 131719923, 326488909, 727311593, 29518642, 734635159, 133441182, 468265530, 845377174, 885508685, 546116255, 601760937, 862284054, 895230013, 883167270, 889246614, 699313333, 224103729, 554400975, 550111856, 898082648, 765797684, 787560463, 592555000, 289887426, 79825653, 769561982, 803789296, 718502566, 20756214, 178969763, 596432143, 459224937, 367045281, 729754383, 388835116, 76881266, 884135151, 556773429, 545057707, 695006085, 483569766, 730966616, 842511075, 586730918, 334151121, 766052333, 538506869, 304064682, 647577358, 106736458, 948627233, 970063169, 693031215, 948112837, 56702352, 376374381, 852254118, 803330326, 634066938, 709687391, 16752297, 354658237, 774691964, 969708628, 786893137, 803734046, 384254416, 128673578, 638686301, 126760175, 711584720, 428016203, 73160432, 895751596, 725537735, 42794421, 135008114, 651931642, 269277758, 826657836, 449738951, 232056429, 836897707, 214475866, 994858900, 781410675, 253203159, 352995527, 240787484, 733510618, 845272361, 64129210, 503291097, 763186827, 704865709, 81402370, 568525043, 683997075, 455749401, 118409822, 888099159, 694197664, 539691970, 803289132, 808911500, 349522411, 337730668, 333492374, 491359962, 563028104, 508476529, 143352802, 4246390, 348305777, 737769176, 802916568, 564700798, 4148113, 911758056, 220577812, 256365967, 199294787, 460582278, 426085807, 760314623, 250763348, 721335024, 507294768, 1244306, 695987001, 185585328, 60169628, 583761373, 459522709, 423552635, 868492820, 448815413, 89388806, 375109117, 425665630, 97783067, 869788408, 118941204, 126552971, 19983232, 172410425, 261231876, 450936682, 566019297, 492790633, 210416559, 944411346, 612697310, 46950122, 651301957, 743308819, 227648047, 631453799, 544283126, 837022671, 150640691, 22130072, 970572474, 351344197, 760081157, 581665370, 477627796, 93713963, 315828147, 894343693, 19144292, 398047569, 512418935, 455374458, 489077363, 982640841, 154772459, 861060765, 395448331, 104494583, 907599467, 875092363, 202922229, 141463378, 973176278, 369099201, 742252276, 38521070, 253090999, 107853137, 199545556, 546056848, 971259124, 658551754, 739897386, 577767332, 533329983, 714154592, 143907365, 81348239, 431642301, 705903393, 15208932, 474422918, 808074826, 368452426, 660953921, 423324153, 971404775, 785787206, 852491467, 278667939, 866581776, 97704643, 687129360, 471513640, 343567571, 585299654, 914622213, 398665716, 736676579, 908042819, 895347596, 225002581, 211032121, 696574976, 172689817, 755158767, 823949386, 931293644, 670623429, 985388318, 845839249, 394532891, 479925144, 419733667, 35365044, 383803487, 192317306, 526526388, 566199091, 839368715, 669805383, 19369312, 923243901, 81882350, 121065749, 241020538, 670140997, 132266528, 82080939, 12326600, 391626772, 876098358, 9751783, 272855830, 99669149, 106511673, 719992223, 547900217, 153490726, 490601877, 74558486, 446040775, 989837788, 209667149, 120850757, 501928950, 948894574, 409616574, 648351814, 131376368, 580219089, 858308019, 32750765, 263103341, 823336771, 26838752, 56578679, 62818905, 104965872, 748207713, 226222940, 358730915, 787246406, 196876204, 117212864, 712417214, 311970227, 290949385, 934857878, 392763125, 230806496, 403085517, 876101301, 96334197, 720036732, 164407941, 439081309, 143878430, 324978412, 519560735, 482708705, 313191028, 445406539, 866506802, 143549042, 68836428, 580051559, 476916809, 832731576, 615458960, 188943324, 317130733, 758103712, 266730719, 753985728, 909240051, 524178811, 491020125, 37514579, 844062258, 97384370, 357984313, 773694531, 690322324, 160723891, 343713481, 413608063, 643554015, 650992686, 809408766, 679496617, 806515754, 730815749, 936207195, 322053369, 322140844, 301272174, 347229618, 975547550, 686796096, 869310268, 41318275, 440732461, 380922009, 959036843, 669279005, 793530836, 846259557, 551276064, 352523836, 785031741, 938804977, 455736854, 20418420, 570634942, 76890833, 191828171, 946604257, 531889218, 582023654, 530055663, 351306405, 449279712, 862888162, 673868022, 363412832, 76615130, 16110428, 610954708, 387512266, 930937981, 921309819, 328205256, 892628874, 569671107, 734029452, 939010699, 964098754, 11126664, 800190088, 67853083, 195895120, 773193278, 183504279, 454791843, 972324822, 218578949, 101147708, 635857547, 146124356, 98040547, 612044891, 95435955, 331834198, 238098453, 771586736, 285134020, 37325640, 597928600, 267287795, 756131501, 302977891, 834546910, 223836268, 269916402, 590826674, 445197149, 908620319, 48107218, 617653229, 604372315, 376710182, 736992225, 788152624, 57100743, 855945894, 362216090, 991196990, 258794248, 233535366, 251537486, 269742242, 267825723, 810517022, 310374811, 215504093, 378581438, 996449332, 207793153, 598593901, 168009019, 806542052, 181643480, 294525048, 529585995, 72507955, 877820268, 129176982, 423182294, 246971063, 799559182, 213150306, 121098132, 391287991, 280518797, 49357941, 777974376, 516703845, 635452293, 42298240, 113017351, 40070523, 730648402, 251397295, 269054032, 792574630, 942128619, 846629092, 533335251, 22846911, 178404643, 787558308, 48593379, 688974005, 729264571, 666055561, 767916659, 46283287, 678886902, 754297059, 961851658, 441238194, 476473462, 983947055, 597472262, 692696874, 915291956, 888432785, 934036840, 994149722, 648553541, 399845287, 7018365, 28714483, 987103762, 490795688, 9442457, 10589677, 940722113, 370660123, 614587483, 331284182, 716285112, 198238429, 238768707, 411248627, 696104344, 341541884, 546433790, 858892914, 885798340, 704984489, 812273483, 136905115, 276626222, 318611501, 116258643, 989735192, 171581022, 264624339, 475285904, 437480057, 317617496, 754106997, 435566233, 195375460, 406992612, 108841532, 126034456, 473926807, 596732243, 40871742, 833008149, 416809982, 118804033, 941804884, 987746424, 172184917, 407525311, 316111791, 963385282, 29148858, 70586818, 324103212, 293467857, 135094861, 537167251, 504043744, 9895656, 18122575, 919183229, 728593248, 485455564, 713728022, 319181282, 750155037, 501468799, 546640653, 234363511, 359636629, 233526276, 337146875, 241703195, 583219347, 151401018, 220323796, 710420852, 746683485, 99227055, 719398496, 239404166, 190775114, 82176966, 126824041, 891584678, 606662425, 171874726, 313479991, 53512584, 993594416, 462569651, 207595317, 913647150, 454406700, 101391447, 591102331, 176780112, 273923443, 655891449, 794931820, 113382548, 830525943, 94162875, 444835644, 773757352, 698302824, 156112840, 24842902, 449421022, 263380168, 752005057, 772290880, 689420223, 72099301, 720891866, 683451287, 259807138, 168444286, 963603196, 10895066, 206450956, 368102280, 244130901, 748979292, 583052826, 726268025, 894896633, 182178796, 211994821, 387285680, 369574967, 240816723, 76185236, 492412236, 914005457, 137478739, 36760035, 566181843, 197619904, 347928484, 329004107, 755650738, 710163658, 78043555, 566701410, 196431032, 237585226, 321021143, 685927541, 122153770, 398671096, 395308117, 20751521, 427081637, 206522562, 542201704, 824280654, 900448264, 866176347, 53603644, 756914072, 836442472, 348104180, 921967315, 714841880, 347512721, 389896309, 503373445, 82676386, 762133983, 439725558, 499762136, 56992667, 578826452, 947007171, 303330459, 400801819, 818206898, 712647116, 256657704, 992128196, 993999023, 660711441, 318423120, 696417927, 969493606, 26538623, 819740753, 759967939, 79341675, 453260115, 3249166, 632858499, 472702638, 501223945, 790547949, 460813062, 637024061, 900017774, 219508970, 989024256, 710100279, 422494567, 709236615, 752833967, 282536443, 52272977, 618406883, 197926998, 878790886, 962023376, 399064613, 148955441, 761616279, 304728504, 959420450, 157651782, 327837874, 316008328, 961730378, 613311135, 411865468, 108064457, 500690189, 526485250, 579970775, 337834935, 898856345, 894256818, 955801284, 919446233, 736466546, 469486089, 969900674, 929210309, 635233227, 19041, 304048307, 828653365, 586199071, 132803243, 577437819, 327559014, 947993413, 74650354, 942795956, 523938657, 256842051, 781852825, 676236096, 881845232, 299041358, 221778634, 115157737, 364207746, 238788456, 791939664, 222715472, 105092502, 47161194, 910416948, 665096332, 244736951, 817314629, 831806633, 388238618, 708023538, 538631631, 584294931, 184911574, 902479750, 714981504, 571939719, 929314505, 951471549, 525832844, 811761821, 179136823, 64139356, 117236459, 926539865, 22204506, 617217200, 641944322, 891903384, 716707379, 879406708, 756445123, 462246498, 537017338, 202254427, 807389237, 576378181, 977572820, 479696013, 337832798, 29736103, 438885686, 727971109, 526621305, 77163646, 351199093, 54300547, 312921147, 411530046, 533907347, 490153643, 899870613, 784014688, 526575482, 763087592, 617722460, 747963538, 876259857, 334803152, 631967378, 27286937, 38782868, 695843020, 954574599, 362644254, 982961278, 195835637, 582167676, 574555376, 216542385, 867576794, 673010157, 149954597, 530165556, 530925917, 797100118, 854595245, 572563147, 547037852, 359962767, 712864549, 657297437, 486077857, 638940410, 619105335, 444159432, 994756210, 2720134, 339327384, 965141009, 42106040, 480893341, 71885571, 43452334, 981809924, 66964387, 160543011, 17482486, 335098900, 337508740, 528162016, 699321218, 516606180, 675021349, 794098444, 353845797, 973711124, 628633926, 242344981, 674112146, 255453093, 311078072, 356188105, 963622135, 620759671, 7829642, 512362114, 711982255, 684736298, 587882252, 588809049, 272673867, 306521564, 550300330, 841631591, 46936667, 621994384, 817400988, 343889074, 442733237, 168610990, 170609752, 401769103, 937404882, 86060801, 94462205, 795984457, 405187068, 873543899, 779112577, 434554083, 923036503, 697432405, 530170905, 917813395, 6271520, 762603294, 393709669, 363742367, 747076508, 365894390, 791811213, 326829297, 96085776, 869099055, 87614000, 55848247, 323055830, 978883906, 479144125, 401445108, 276101382, 219071901, 578372959, 955261568, 834301094, 913746009, 670005832, 357719834, 395615096, 680330417, 54650886, 370418606, 644836464, 303074581, 65748255, 585973862, 703238745, 835425433, 42204526, 547362406, 247261196, 48043529, 417580515, 925251115, 936444872, 238929302, 882353719, 798709845, 260280968, 974649432, 522880974, 814783098, 33548780, 565795498, 211292476, 232243841, 742095142, 273745494, 305105921, 131238238, 352901288, 3718461, 286984181, 154112307, 482306410, 192175821, 324020701, 914543664, 666147183, 718791687, 266341970, 483210902, 404917893, 409290843, 854834354, 670806649, 880236896, 203029057, 70769498, 566948553, 167786752, 784057193, 779403437, 331466670, 948982546, 845413612, 595469556, 171183750, 243295396, 878800694, 873610524, 553499885, 65336892, 294829899, 129712893, 339416642, 148962105, 999882795, 393599007, 802627730, 434910768, 546185827, 9022563, 411032852, 547539032, 173878636, 263071639, 228317955, 798213986, 577956726, 844595960, 709340521, 527160073, 22565939, 813871376, 614659492, 975945997, 897016889, 278359515, 637941206, 66140462, 23986652, 654729841, 757140797, 338178402, 364561743, 526294040, 792631238, 831749840, 725856269, 114770455, 593486202, 909638937, 594077248, 836875944, 927406469, 285708811, 287833496, 6604703, 791704376, 194432762, 535898146, 965501301, 274949716, 963621235, 530675125, 98826013, 803073821, 756181551, 944176921, 930850917, 638324993, 124647827, 88019410, 758915654, 537155302, 819754750, 53207085, 4436149, 225127232, 844492522, 60621549, 79423029, 605781725, 590132021, 381800227, 242623289, 645140229, 432107214, 450248825, 145119418, 955324534, 529656330, 390472020, 178732154, 994178972, 212339478, 164899846, 494254699, 435995243, 261885457, 403603177, 502508187, 225999622, 614626859, 202937028, 801605858, 875103187, 482812770, 30444087, 276580898, 20850626, 707788224, 233736088, 882215669, 438689760, 575327369, 195042319, 486281598, 48399939, 183418651, 566923801, 442730019, 844184515, 886367070, 482101396, 885766419, 74642715, 512389657, 201573085, 814025542, 944995089, 408965341, 719310568, 164952828, 316003986, 184149401, 712400903, 149893717, 305864778, 73296645, 888107806, 746613299, 974232027, 631129441, 987509111, 508109301, 279320967, 1675327, 958586365, 200808824, 302419690, 857096048, 899821308, 966685022, 615447815, 264332759, 803513110, 930847419, 949575081, 51715406, 888126570, 643246509, 519032398, 284029644, 920922425, 450547423, 409297097, 231742695, 955660869, 273560325, 44180897, 679716456, 794915021, 160448003, 13692388, 875637590, 866976845, 97135774, 928591452, 9642294, 787340634, 299364466, 898692507, 859691400, 46967599, 597637264, 846773330, 434531312, 671609238, 135167635, 362247932, 226156972, 667671791, 287542380, 545278476, 415763640, 601061480, 804390638, 805869314, 523811187, 478971497, 469641532, 511798434, 849217946, 194157741, 818707074, 929051643, 276637489, 105389874, 816750215, 79402519, 285250870, 121638894, 56037586, 205965259, 77292573, 830092111, 839143704, 795070959, 151656639, 649449930, 658452225, 448025985, 461620542, 610021789, 667352542, 286865743, 89425159, 344174704, 36240307, 895500875, 34193090, 635115332, 503651392, 526573409, 800526256, 765996703, 719358421, 302525990, 613218606, 554356394, 790578812, 410548068, 809026625, 100824255, 399609574, 353550192, 964665827, 462800313, 998304652, 631393939, 539883537, 324284488, 187053159, 311851115, 925954148, 880637342, 500420164, 210603363, 549300759, 494607872, 85426911, 274658928, 115268544, 451953802, 867683603, 190611185, 475406717, 155431327, 62256618, 306398608, 984866640, 391399307, 616550568, 477088289, 859220432, 186200887, 795762366, 698489393, 889594979, 984674523, 472569296, 778312858, 621307402, 603465193, 434399852, 5583264, 169570503, 569392162, 212757852, 919557573, 412742606, 567304756, 730565037, 647793999, 300722305, 698276876, 595308965, 469058720, 714783540, 807486464, 424712699, 471546647, 395050167, 891154880, 244152392, 858785651, 503687865, 122240241, 703035418, 38038910, 330963365, 811173563, 419742780, 127648051, 457801335, 488436921, 261716795, 169616531, 31665168, 77049441, 119919908, 349013508, 688956780, 717737008, 76670579, 986125282, 34233678, 617540399, 441048661, 789875638, 868082108, 258051736, 259261870, 506982397, 599812168, 640190167, 424459578, 460898619, 265632550, 339070221, 690768816, 57044379, 761177860, 717911810, 845821859, 325548814, 30546960, 391868192, 490870169, 102222756, 382220941, 100601729, 338570418, 15965630, 788464373, 52462553, 813459639, 90382898, 167511636, 200202687, 129879724, 727840433, 807572286, 547126872, 271722424, 891913535, 363845580, 409049630, 974867777, 613609889, 65092637, 312745710, 860253223, 163434232, 102801715, 322224074, 639359989, 53137025, 104395034, 440010501, 53203674, 492260937, 729995107, 283661132, 428166667, 181190407, 328915046, 610019705, 907914708, 471889278, 862167814, 964566188, 496330533, 682529851, 410871327, 27991814, 831666644, 897176077, 250641319, 808827361, 631613981, 52065682, 588125462, 515550056, 985020331, 226728751, 439795148, 509937757, 423126426, 959565804, 601596740, 151888082, 665510571, 927434936, 762512767, 186610199, 887545920, 921673181, 160383445, 565916225, 351972349, 901438177, 603347669, 312114615, 691644082, 849347604, 37251575, 746228840, 696197851, 216417634, 790442755, 787499687, 962550963, 725912198, 627417866, 83372536, 750729065, 774412493, 49588652, 104487974, 329730072, 468222309, 55895333, 564883821, 35051619, 346137171, 520904173, 841983372, 6004039, 86035166, 121967352, 274739567, 746226375, 437720918, 914257977, 341369353, 472868974, 26139485, 232240126, 526484093, 429032603, 71798364, 753300452, 793186370, 883000136, 302035710, 320535993, 782602436, 262143075, 624771039, 154405506, 538102631, 787878353, 799064203, 591443623, 529105793, 128601263, 882720057, 410689013, 829715596, 877964752, 547702209, 70988053, 902456287, 156057548, 415554951, 984972641, 730885331, 117317243, 344808832, 387364427, 938021054, 135860328, 512446524, 554055051, 522656032, 951253034, 319916510, 303619319, 322236617, 730529150, 937708649, 238524654, 461532106, 981521950, 46826089, 196140745, 219960188, 577436078, 462496504, 215575320, 806994737, 106377089, 671207105, 591635357, 46572904, 779205078, 697770940, 79109889, 221925488, 255236915, 133362203, 838143618, 826613953, 334584357, 872269827, 572939685, 514732432, 440223990, 314700876, 710296643, 809475138, 908237483, 621431156, 113308766, 900361243, 543095176, 784657076, 310342467, 704237072, 620345833, 227117820, 802218090, 861627774, 152305130, 868099115, 339987223, 297376370, 294976990, 400189262, 908832544, 939774412, 151017698, 724381999, 763015137, 235327257, 243582725, 125674227, 566761917, 159581367, 954308899, 407961542, 263646401, 406957594, 655340785, 66269778, 677716732, 197711725, 246920462, 575221375, 238648782, 90527450, 613117680, 369989709, 608998705, 811318276, 759339277, 296798107, 867551373, 496484718, 816054550, 986436110, 36444463, 269051221, 206168349, 658886540, 984633779, 781205708, 526223221, 873476331, 241018271, 739363447, 264996608, 687751757, 932688452, 426821532, 400938636, 950877670, 166877490, 516183105, 297509976, 462974422, 202526968, 988564443, 786859583, 405150859, 735331389, 884891337, 220969779, 534685925, 817519509, 338792576, 656655754, 243744071, 603472017, 884263013, 367666242, 307580862, 94393377, 843835989, 205721175, 778325200, 624487071, 473268626, 793773266, 333885009, 14140745, 709148447, 99358447, 326662861, 618748279, 857494626, 665697951, 378670705, 593320654, 88928438, 446020326, 392722349, 440075871, 781329272, 690059882, 116091392, 44481276, 756438064, 381809592, 52892621, 168716969, 288209093, 765142604, 285878612, 545952325, 212782783, 77343079, 448300652, 55898011, 901049816, 174775774, 264111294, 103209854, 491169881, 295777669, 504868948, 582774153, 844238130, 316971972, 755447617, 925099918, 619504103, 126563791, 475233612, 166564734, 419580565, 434470555, 460897787, 247680165, 188201177, 162130823, 636345388, 769156748, 740067126, 827926284, 66692452, 926481900, 388553999, 953407537, 19185817, 108883326, 291765563, 641884962, 451579660, 22612874, 22737825, 951320738, 842558675, 489828675, 351542594, 468393362, 684839630, 281031726, 654520980, 542413836, 539128077, 417907242, 705803551, 603247837, 89780532, 805603558, 903968060, 22392187, 43333558, 228665863, 754733614, 807326921, 866197710, 599268092, 557008091, 250227717, 125562730, 125453812, 932576775, 999266010, 867363825, 643152139, 249284879, 157552483, 338745160, 776826251, 133839867, 741793368, 466396548, 995591670, 156593295, 393715121, 329798204, 181300384, 555788600, 953738856, 144143985, 433862162, 596629835, 994542309, 218823963, 784147953, 102713269, 535141969, 992775505, 461763597, 738650785, 687194260, 639251925, 630744240, 768645044, 458558414, 289532676, 294752158, 303434446, 428966272, 327965952, 231973491, 377564184, 184628566, 286474246, 737680147, 777931144, 45106960, 768623362, 438046083, 331227670, 237217943, 811446901, 101985572, 262197876, 263797265, 90191724, 62964659, 472560870, 516014083, 887382174, 551708973, 949514969, 256137031, 976203315, 707004427, 376056307, 208709657, 156502081, 409280428, 924373284, 647039557, 161443522, 970990201, 645197539, 488478520, 979586976, 464454024, 465698528, 417306407, 320407479, 623594837, 737589008, 911552931, 467806786, 793777907, 25876034, 646738789, 761697952, 529148923, 564149289, 246168548, 33268460, 507673579, 948214228, 87272217, 751456555, 990885526, 923478679, 91473870, 443326005, 925300132, 605047605, 372719395, 644813256, 72951220, 566377701, 727533576, 158370460, 238782504, 364612985, 675781929, 550840198, 332381838, 169861970, 842971950, 421383275, 747930876, 816897061, 844160086, 842790438, 347547653, 687237051, 878915401, 14995368, 319621484, 438334734, 578377241, 229561475, 934330289, 777107741, 529464759, 482932234, 68598836, 988081434, 354704708, 105002016, 157269273, 853454454, 544818234, 245442843, 497464268, 916763949, 219004928, 47620866, 782603758, 245605522, 370575430, 486371520, 172235792, 600112872, 15256342, 133944827, 321454511, 918707513, 372876316, 388427599, 310887919, 560895356, 201563221, 285662241, 74809112, 292606364, 666847996, 416645641, 579056832, 647370804, 693527471, 491083643, 825439668, 634241731, 215067319, 427891154, 22380721, 945195759, 365069864, 205761728, 576153217, 803738222, 849212227, 464937846, 112577165, 39431669, 73279619, 1746768, 756199631, 515220640, 706627446, 184451578, 240922883, 232131286, 574749567, 935837216, 757086426, 471101240, 152056113, 453173265, 595706718, 589182644, 582820972, 101444674, 559897978, 949168728, 583093786, 436833121, 774884468, 393248989, 753138192, 908513572, 832745666, 239022296, 139628482, 127126264, 675348140, 616357008, 46845137, 899427706, 684418270, 437579481, 530236872, 264699977, 906190021, 58116812, 135243366, 134316055, 452593572, 67872851, 586630311, 798541164, 525476282, 905998743, 90338335, 423273979, 933964260, 644852287, 324502773, 754676425, 567497278, 93413750, 618821019, 20283707, 218534656, 609799628, 993594230, 944504405, 795970354, 223007249, 696628670, 229486684, 34208122, 455147269, 451798016, 615755827, 469127591, 850425507, 66759674, 493778225, 953544668, 846011408, 133804553, 748502963, 444813837, 530895850, 511621171, 669452796, 384776428, 898400365, 439677850, 222568368, 996227866, 294963272, 674454808, 4467492, 44879231, 917713487, 819709992, 518664502, 971401428, 532948703, 418444552, 472665241, 512838154, 386203299, 645350909, 14548664, 711735905, 719826318, 613740111, 631950432, 396346384, 295484994, 446006792, 663181000, 497537959, 238091427, 647658640, 87197918, 969944652, 410965879, 23011912, 262531090, 96138416, 714918531, 550091002, 552523729, 923798369, 11285841, 552722810, 336693103, 497581949, 766274797, 559917043, 406252030, 976286195, 373692050, 425463160, 719186577, 248911288, 490890958, 113576580, 224474557, 259722388, 620718000, 980921559, 172441214, 337236401, 629263266, 44838825, 505106194, 800542118, 351741544, 692211373, 553743154, 801179658, 859602642, 632824210, 630110915, 47578100, 555956315, 256773071, 493237342, 648157272, 912394018, 907489469, 555124762, 583042127, 257027701, 342427009, 587437779, 319429364, 319185843, 714018896, 714833724, 577280857, 811858612, 130090606, 163335759, 866769706, 256705884, 326632285, 217192761, 723831651, 586074280, 80038922, 91205042, 229242320, 724129487, 504836786, 158658414, 73857478, 8422992, 517648583, 241101182, 462509024, 483674702, 742233878, 837605030, 24173026, 912472066, 608882409, 219830110, 698841214, 208904340, 893968894, 270560516, 986615653, 571741244, 988935034, 515349465, 524466420, 964804372, 539765337, 422823466, 883742421, 1598966, 432100232, 813385712, 928951082, 112725763, 990033131, 317486675, 484075377, 594842724, 578914884, 809856240, 169698781, 102571175, 192463617, 772639004, 384113377, 642323279, 244950777, 537105731, 215795670, 125934572, 991333656, 596441808, 303008952, 215578788, 241159687, 256208684, 650454602, 907425459, 194576558, 241975206, 560521436, 374203815, 463590105, 356031617, 598787615, 212192089, 754051616, 335276228, 335786722, 46344640, 212737971, 424413451, 213464575, 87070230, 934952536, 915086272, 168408365, 65058361, 181328008, 302277365, 929074603, 905625996, 204851263, 920916000, 338048889, 767802752, 958561124, 553726792, 701237132, 389168638, 701520771, 486417018, 364008284, 291643336, 16380481, 95449234, 8854993, 403067706, 678649021, 694417632, 10682142, 801439254, 42120731, 424645125, 576723676, 107262412, 923021711, 244003889, 577383764, 132727775, 118190849, 310197837, 834582836, 364190835, 707856420, 903917554, 670233355, 173490717, 620662729, 992180026, 191560189, 411437179, 701802158, 55984604, 17963472, 190724488, 323475572, 495067149, 975391601, 337662404, 948719281, 63403109, 363829728, 614632470, 18712047, 910349792, 624653779, 756338061, 435217022, 316863781, 398982182, 237050666, 954815941, 220248055, 517738735, 23627378, 226391264, 563890398, 838453626, 929538757, 927503071, 134821590, 70022275, 440015300, 690007945, 461426414, 93489073, 248696815, 929218295, 403632468, 166613215, 870552195, 893431202, 909531953, 411658920, 686913451, 639929541, 205069498, 646201749, 790877497, 70431197, 734627020, 822743969, 154710717, 952394342, 200915697, 794462947, 996812143, 367747052, 942090091, 153720157, 522045695, 144592687, 695242038, 199968778, 174435364, 965684975, 73968452, 98295484, 855109855, 474342985, 857076118, 805226339, 589367121, 121511865, 261952270, 216556954, 366330179, 911258722, 145513209, 962002640, 752050315, 410526815, 242802206, 699246919, 733099673, 612067816, 947281922, 20554008, 661665986, 550247517, 492511672, 915989866, 177789090, 633194047, 815964264, 577932997, 458377030, 150065145, 244874486, 824968262, 910360304, 478876851, 164741988, 878271956, 172963301, 402573925, 560786932, 275813840, 813758730, 254719679, 140398169, 838346196, 893881761, 431189250, 392344421, 688050238, 361881481, 11784028, 614611370, 581876833, 988677414, 101302294, 431869828, 394836721, 796154530, 629206501, 346266286, 426569943, 338031226, 203798314, 257010326, 377817429, 238252311, 982537078, 500216089, 675430801, 120465890, 685834023, 469278013, 220650997, 797910516, 739958813, 71941961, 584494340, 430322999, 557318080, 392940355, 276583377, 465286428, 459682235, 77641357, 74420162, 260757534, 953708832, 485356042, 335186447, 747269910, 386664257, 295147321, 432675852, 385012684, 639973071, 686061194, 743092507, 780408840, 310601841, 62026571, 289466572, 900489912, 968047249, 245524639, 726523255, 320081326, 917503065, 741791937, 132732016, 18515949, 132875128, 470816687, 740239827, 610139250, 210642418, 758047837, 431991763, 737110827, 909146165, 392395035, 982298466, 279574698, 644276871, 958649218, 449551028, 408694569, 159352389, 682608029, 900980917, 906895779, 971515123, 17865203, 492052790, 477690890, 524078411, 46661060, 770161210, 974405962, 230326116, 177269355, 909229195, 205897553, 567046143, 245840965, 817358739, 447723582, 495456319, 625636240, 153895844, 799173326, 560137087, 359098524, 292747380, 659708716, 841710584, 425012315, 880191462, 628707537, 44246725, 11728172, 461879022, 741986097, 386194030, 850294765, 183008772, 63580839, 359904025, 579150611, 621049390, 281613546, 639936715, 466997224, 450823175, 740159512, 338756488, 420035620, 539563476, 900850797, 227981180, 638765486, 158981405, 773729165, 843260829, 604614704, 207561094, 391085686, 737144994, 352765358, 537322038, 553783930, 365420319, 677081446, 519273518, 679518893, 624975298, 102918565, 938556436, 322847300, 686014369, 964527615, 717076445, 732761706, 360072262, 573944601, 607689600, 794597055, 18156345, 13465008, 960434929, 681242387, 67397459, 465095255, 401876136, 86522982, 979526648, 876499344, 29436068, 934799301, 214465476, 773627977, 871531476, 605975480, 315678809, 559385781, 92110858, 23963738, 920107950, 527231354, 237365313, 842432636, 154368615, 909915979, 446423526, 570870045, 204804312, 922000864, 724898600, 89077444, 895672228, 95031855, 246996413, 650553037, 331720128, 798454609, 223873633, 968684295, 960125600, 338372166, 81578453, 181493661, 962848306, 101902416, 364463095, 632640882, 409910168, 222112243, 585011982, 433056169, 810901017, 518880429, 459060933, 808894709, 757628067, 282694228, 57118338, 550961854, 697234001, 500437795, 408887860, 624238737, 592990671, 542491145, 259891870, 943287259, 690642409, 569964903, 335276791, 13100008, 614848197, 656149154, 220046097, 417178456, 710430242, 267341572, 529108316, 190364549, 677937981, 258566338, 39990347, 394739973, 300619654, 699855640, 172505965, 225762630, 283334529, 863401362, 254839562, 582264756, 346938289, 103364219, 213958239, 243628390, 894302909, 150179065, 838021130, 975441274, 45675660, 870431911, 419154732, 679453458, 586227444, 734378287, 442894167, 532302444, 655006243, 62649634, 632827738, 407112924, 514740152, 164987970, 669518240, 772745942, 988371464, 31745356, 750907003, 530520343, 472923770, 643114472, 158134461, 983747329, 29299172, 629948267, 553880268, 417580969, 17157581, 138084056, 225736090, 47998575, 287755022, 344433613, 383280993, 697132847, 552412188, 820050985, 165105044, 109092804, 914062351, 472041069, 949115890, 419413569, 117033924, 579513822, 655131783, 637364576, 378958497, 600959487, 950688284, 274909337, 436852475, 714406466, 929995477, 859233808, 19791994, 704555488, 16180189, 697010274, 581229993, 366902808, 513388237, 429915884, 884363343, 451956193, 861568931, 715923789, 107558147, 856357745, 830409401, 211977338, 502786820, 996069632, 386939751, 868495830, 138575395, 914393073, 604690507, 401957977, 238131522, 205445812, 771173646, 290690868, 469620794, 857519703, 269911494, 613699089, 253226087, 240045051, 560507113, 614133323, 265438478, 814083956, 37231145, 238633183, 445729262, 175530613, 20701017, 895585348, 553069690, 511882347, 327372134, 778971017, 151858251, 120361625, 59952406, 647791146, 243258879, 328259153, 880089748, 762083010, 657621980, 681207570, 649582005, 630319986, 465100802, 955461937, 145353589, 563271959, 649310560, 366395187, 606517622, 213963436, 118687435, 873272563, 992030042, 725312001, 360763730, 609095511, 628203072, 912279991, 498193831, 376794045, 58972296, 675821836, 76889774, 723032095, 628489963, 896051513, 156455863, 634531247, 882739244, 482928448, 897737499, 545922991, 978130596, 857049731, 858483652, 244925117, 350772868, 751154611, 384233365, 394730680, 37176658, 168306746, 788811810, 51713059, 299690131, 694704021, 388368486, 983399405, 248443389, 941699549, 875065085, 545107886, 582862152, 86486927, 609147847, 398606117, 832274318, 744817564, 368052023, 271943976, 54286014, 550490732, 784771040, 885212286, 190720431, 235748512, 636321131, 699793298, 335804894, 540502032, 760614850, 548426843, 271863368, 571504000, 152561579, 95987507, 707975853, 575033007, 250960918, 45758206, 239028034, 622009154, 982817365, 431258140, 147884310, 869951348, 266411979, 98725918, 521326177, 464219950, 919171820, 76138057, 380060154, 891316914, 362155595, 108562377, 589315410, 429729790, 429314576, 396556812, 775767559, 157124833, 644290774, 194438019, 463451779, 815208654, 43035236, 86338044, 72622022, 278381748, 83504935, 584483377, 23546907, 261863296, 254271320, 456469078, 170410876, 438695609, 237252009, 647663343, 793525562, 117906657, 982447126, 48436128, 40381104, 479468495, 209528007, 703436265, 64216829, 875274664, 635890649, 38740840, 887999904, 597799508, 521939308, 674883350, 517616255, 575602681, 18656177, 309204280, 764710961, 781052812, 431559658, 792998950, 850135316, 147781373, 148968486, 519167798, 83685080, 24580212, 123945015, 707011842, 873330315, 363615187, 534356956, 888176027, 997811716, 232847206, 876977931, 219563140, 107082690, 49718176, 459621473, 960130093, 333217408, 78573704, 325859003, 408839153, 12554076, 162049015, 708545606, 876867447, 226845729, 39260465, 375831068, 370810420, 638620195, 264932025, 851627687, 513136175, 809703458, 842825616, 200114319, 408890131, 351736816, 551110525, 113001438, 243254387, 618048312, 457706104, 984920626, 537484219, 676392127, 18310757, 242619724, 795669267, 97447864, 950343644, 959216156, 670962544, 407079106, 446521237, 467277801, 383440956, 466267803, 248732734, 995235676, 528109799, 952393602, 58120411, 67164665, 624588319, 627633843, 966888089, 856458608, 614246612, 427082233, 154264737, 626574056, 405191389, 761858833, 852576214, 552064312, 231446132, 312150400, 13609715, 541765276, 410562498, 740805849, 941660293, 979159669, 997786070, 278907449, 648426752, 124468701, 97270950, 987328516, 143052547, 948748842, 982893871, 860894283, 879350120, 913802268, 141107655, 671239115, 172575812, 892446692, 933137191, 828008597, 548366108, 779655447, 270162186, 753454890, 502422788, 819982971, 21884355, 257527555, 356071420, 230639779, 68179203, 631708116, 609430759, 986924738, 503337082, 547932689, 564046788, 399474850, 278628443, 558394886, 15583174, 266710892, 474517998, 417324913, 594741517, 190820495, 215897541, 92150496, 110360984, 367108034, 752577325, 586801998, 397733893, 811444527, 769102549, 70836484, 733770607, 347853673, 100829567, 321190777, 840236018, 29173780, 929116633, 889691894, 94595460, 77209178, 635045668, 738186758, 194081769, 946558364, 31530142, 42013570, 767732865, 973400901, 293281177, 950025180, 129563366, 51723098, 142415003, 989146058, 943973706, 500956585, 176741586, 686089143, 444996054, 999689994, 327733464, 202318482, 982458850, 93895349, 141182732, 513072637, 448690031, 523599651, 865864612, 141220670, 174981125, 230750324, 731768808, 661942742, 500692417, 827477317, 871961719, 298020698, 521864261, 198479227, 402564250, 487241861, 537935566, 293547961, 935309544, 147681494, 359353824, 604363821, 727964149, 689328084, 678507871, 344742466, 844407624, 669651878, 564561488, 686967955, 103419644, 241473105, 483909005, 181276014, 785084273, 533742902, 191910657, 909000470, 338670449, 729473175, 411800822, 858246983, 673904253, 705238244, 661602153, 436095973, 832467065, 586691214, 173755238, 845193983, 738079396, 804067036, 520539328, 821214587, 679032220, 280763233, 497143989, 892359993, 772231982, 384123084, 678115053, 18914188, 637479445, 531833471, 883045989, 821869572, 79061846, 154587638, 218052795, 762044004, 140916314, 373234123, 165989960, 487020519, 772793475, 182234830, 527387057, 183429831, 366778721, 317697645, 772657350, 144385836, 311399353, 224775436, 935068128, 947992947, 238578757, 71811797, 268313951, 616750648, 939331531, 917451297, 347537551, 393409001, 877467707, 944505749, 521393543, 885034712, 361494106, 588331481, 95805866, 895430290, 289012197, 10935750, 717650204, 423241535, 540540547, 345790865, 693492326, 987175643, 579758971, 939115782, 75136962, 301286994, 258770397, 539699886, 189188260, 630501270, 595538340, 890652624, 587966909, 205498616, 289717047, 356793649, 980579156, 990349863, 62277351, 614889974, 798706366, 780416138, 906522101, 451501210, 151573969, 11100321, 898864731, 158444754, 44911221, 243156577, 860800036, 988653536, 761014587, 701723402, 538841538, 698088218, 457492133, 855735434, 75973606, 999691153, 109218354, 45856050, 640510425, 251693272, 740872624, 91064147, 385850225, 185383800, 682861688, 680453193, 513688319, 621914778, 663035452, 763769247, 634475929, 310056227, 209684464, 864467608, 112148772, 329072, 597460912, 150223032, 981594941, 492081683, 19408088, 236540137, 754420535, 928598110, 163227314, 889162874, 914857266, 22020440, 734070993, 609780994, 410836954, 478961240, 623946279, 63141277, 597577481, 737444558, 639169611, 823319838, 512648540, 701770555, 492132393, 869379331, 965646337, 758909575, 148913748, 681021323, 776320488, 138644137, 565740134, 217875541, 979854507, 860539392, 806812155, 394066731, 406227488, 550900897, 891141250, 746273023, 538746259, 742708827, 620019010, 652645042, 333392426, 151474615, 363440309, 32859271, 776206552, 235630584, 914625073, 50275245, 688786794, 973447908, 597438240, 368570455, 798381896, 470134613, 322426209, 768103420, 239472437, 478926512, 521893754, 633586133, 843875303, 812385566, 233436468, 141184335, 718923238, 856961780, 611311471, 434577364, 174723274, 372736726, 274061645, 603922475, 615239488, 546259219, 741493285, 166169270, 944575127, 598101419, 280114894, 808625977, 835570366, 818358742, 316666919, 130654212, 901809387, 1180379, 859977771, 384487432, 138779154, 606985508, 729506184, 353818960, 797925430, 592994100, 726082469, 689102981, 108227140, 530660250, 515686901, 274494826, 341159629, 442277382, 836833285, 262842424, 694755400, 905884515, 834361810, 626476465, 995739660, 848987558, 979515492, 800048160, 931929778, 125538993, 155823955, 587011125, 501987375, 877079803, 714188278, 437909519, 723079543, 98806878, 700936780, 986530904, 148200923, 170357662, 634248616, 500785892, 588662346, 907169582, 698094484, 399263939, 994171975, 930952872, 876008155, 649531077, 780135282, 273735132, 122146841, 862482393, 261194326, 824374041, 891649151, 956967426, 587912519, 692712175, 433647356, 251614198, 821005972, 403512570, 693801211, 921336357, 553600792, 558237719, 981933753, 39096289, 981836502, 271778783, 674934105, 142647413, 923026376, 104470504, 29589537, 996047939, 698826968, 355267686, 704518719, 764681932, 487719169, 671676167, 41175940, 667881160, 609835960, 934891004, 386913952, 355614908, 211261316, 343922354, 510217094, 999403872, 270124161, 553273218, 235773790, 123894211, 379817283, 350522887, 936873985, 752193303, 5953254, 61455442, 500175385, 42648873, 141506716, 524836978, 400302652, 731584330, 905070339, 67224709, 848416714, 970889566, 421327736, 273465797, 122160658, 629170162, 315219069, 124459846, 132902005, 780380668, 567946721, 186217217, 753547323, 110172445, 86912372, 760341029, 794041579, 41919403, 232768400, 313170300, 924516463, 646158986, 51342565, 135555170, 308228529, 927914192, 490529690, 767312135, 400478106, 602129770, 627789410, 309407066, 562333797, 924527164, 772803829, 349383486, 523986499, 316901672, 748531262, 25607974, 8304875, 182019468, 10051662, 365217139, 432717904, 693625065, 267603522, 228080651, 74379903, 485618499, 224373728, 274320520, 448724744, 496878805, 66045521, 349594963, 373643630, 195087135, 393635827, 117886588, 370302973, 948221487, 551618886, 519374064, 152598457, 403152246, 809831317, 854905503, 541524370, 927908468, 565740658, 822274067, 589951660, 82416625, 199552591, 963560333, 908757714, 520695776, 20399448, 210075277, 602622540, 576951382, 614191885, 207943182, 909685668, 791277379, 24586062, 508522207, 341410520, 767806054, 239037094, 732475929, 837094021, 109072094, 170634690, 360096941, 114921158, 263374750, 812846940, 447823401, 365937636, 923236556, 347465315, 146116405, 638100844, 85951672, 656567289, 137903688, 443369684, 981507407, 834643435, 701241100, 108298872, 44436282, 358144588, 144017315, 889262944, 687201228, 47665842, 723850255, 981824208, 344864719, 390019101, 849320131, 792272072, 244284142, 978788048, 142306997, 617989220, 403828071, 444122861, 142035586, 900020475, 938346483, 975044948, 562164537, 401085601, 95985890, 434845558, 940102633, 867781263, 242804901, 775711547, 589664765, 729293084, 753905996, 676284880, 543210748, 357723036, 912350087, 330723269, 971734405, 255020595, 164496342, 376081599, 600749370, 947303291, 343156137, 302850295, 186741686, 9350195, 32975269, 889562441, 756038687, 478258812, 280155036, 853970282, 655495488, 511711697, 959440544, 539717040, 691146065, 660377397, 957104928, 114428626, 183807130, 904486629, 333346166, 996775413, 690563501, 806381637, 297942727, 344090987, 792320210, 36618631, 7035213, 766996862, 456226288, 463317714, 136712705, 886642200, 43478551, 105916841, 330128246, 859373390, 571032365, 809266105, 307881347, 708863278, 933026510, 138309955, 523832023, 216583233, 327894246, 761872434, 358880888, 51877902, 840236146, 180953178, 950248539, 204022397, 436384556, 592690130, 53735313, 833843898, 322348930, 730632065, 471462077, 966073411, 97736226, 536879649, 587079302, 896080812, 111390439, 174648519, 285371758, 916842840, 623137848, 695550540, 383229852, 29544652, 28020992, 862957334, 439939601, 5691752, 832383034, 259487223, 256981848, 598605148, 515039251, 923478558, 216158336, 111113574, 413802044, 187497516, 269214559, 472446264, 445685254, 855506189, 863146836, 732858020, 209949613, 760787256, 246467980, 531318881, 792349477, 762068741, 726437277, 920836481, 833413346, 974418546, 829363895, 333353441, 405108681, 592037273, 52087360, 552323256, 963033873, 961243625, 928452763, 589325023, 168575242, 433471604, 782409129, 759831580, 465063033, 754220647, 551583810, 419755495, 200951455, 186536541, 679517530, 494252810, 570376129, 634581407, 917156791, 551427483, 255340741, 286046555, 519060746, 132534769, 331497926, 320755279, 270030174, 387955417, 804454737, 320398719, 854329534, 407506208, 965952785, 936287689, 812118784, 722466364, 690109480, 480733595, 44834205, 894488186, 782133913, 216731299, 867177526, 98903774, 888603646, 209287012, 178815930, 929761505, 818471308, 487642071, 509041547, 728288496, 882482375, 779457581, 943143924, 245419365, 397844721, 102357436, 140632778, 516363644, 33302374, 31509948, 91669382, 910477571, 46479721, 75861090, 302345592, 828691783, 36845115, 253098367, 57633253, 772028546, 807394466, 28457679, 432312569, 107797556, 867542061, 136936044, 830656534, 884697853, 494717970, 474965453, 121024068, 461607208, 471131879, 925282039, 819740986, 410943742, 79312257, 716846802, 205833168, 592188890, 681254426, 660347603, 319847667, 688563710, 78507894, 105470488, 54508694, 955407720, 45750367, 886732907, 180378420, 837993603, 976970709, 973997595, 384290896, 535167622, 577420895, 824224702, 596719597, 50708077, 187936578, 265643802, 343815092, 844869417, 456500150, 181868018, 396401937, 557227086, 843799385, 763475536, 567356633, 2793860, 616914401, 269186486, 712129814, 494489574, 849220593, 677478023, 563566596, 341674271, 843970306, 374553996, 535637593, 786682685, 629289752, 392893053, 983406803, 771853201, 4180165, 717973842, 292330882, 991541178, 727772524, 309467619, 69424805, 522006769, 909096485, 293387383, 493975670, 631650342, 171081800, 411074930, 451120918, 149355607, 820839075, 351468696, 577432186, 456064984, 762862171, 221724970, 373183042, 414287094, 609206893, 468692129, 242445888, 364261123, 951395442, 585938603, 808632964, 406266188, 327224440, 920465783, 466921401, 887989551, 557962611, 97590257, 851595016, 231962241, 59082568, 570245670, 819376015, 96853245, 911196720, 412543926, 719943647, 503194916, 143625587, 97268298, 4078552, 687903722, 656680334, 67646826, 74389376, 424157849, 159003936, 878038212, 20142587, 571040252, 77517451, 967600982, 557359075, 700320849, 745276376, 594351588, 108511456, 364182701, 635277401, 133750196, 510715279, 796249138, 380625414, 244137927, 188933544, 740096745, 186539915, 257948356, 322525042, 888864352, 724016379, 730221352, 928143903, 103543716, 989584358, 357648134, 998710636, 964315285, 305568273, 322939579, 998188190, 760751629, 291914779, 802706465, 203957625, 548078939, 911131020, 303271316, 803782909, 267676556, 386647920, 679161965, 257558539, 786472774, 306067285, 826715988, 174995835, 280628460, 396440569, 703418059, 465867448, 465448209, 911552638, 758562024, 377725855, 256990764, 970142260, 948727269, 455192343, 658640752, 229651731, 891853857, 656939469, 921826929, 956708314, 856401279, 256902427, 539744677, 975081333, 489762590, 74510200, 111620751, 898601596, 8702687, 851980258, 469968262, 834317458, 857120234, 88006610, 926286164, 361334861, 798223100, 63316369, 5782445, 996350348, 364928079, 522600057, 462783858, 167971402, 154507005, 907493993, 585038934, 853845265, 377793278, 997435695, 969292244, 259901767, 503838589, 337630476, 17418345, 426699011, 313919, 492500747, 368856651, 961212767, 328642301, 485096288, 824639964, 626396738, 846631941, 755531985, 351037754, 933700050, 339684080, 254204644, 497655956, 261326286, 403349387, 616265041, 652130343, 358861654, 129893775, 502928011, 425318660, 131995599, 673517660, 135672735, 385300612, 40210632, 951184022, 101144629, 583116601, 386981462, 900910632, 549804433, 218479043, 650166056, 715980450, 112596978, 468565088, 216968175, 525669109, 859093391, 400904727, 343567874, 321109942, 262320903, 524740145, 241664069, 926986089, 292450054, 402893863, 317315678, 285661089, 447898386, 737132478, 775892186, 894396167, 19675576, 38707859, 161204644, 725362884, 217761453, 900975393, 646750808, 685918690, 738103960, 652860142, 817762126, 295374770, 547692887, 406658400, 19714183, 655992120, 135763507, 690695070, 667978888, 817420924, 728897855, 238751199, 241515138, 576960093, 932521513, 781926031, 34584045, 697251223, 144939463, 178872830, 586401866, 423654166, 517043842, 77934427, 293788990, 282371456, 818204296, 65400154, 333692742, 425873208, 236548980, 14820328, 764418841, 840765874, 979550027, 483762316, 251554387, 8731598, 205585303, 863727805, 315781123, 704087011, 686813938, 589784077, 712365286, 431189995, 732728975, 939808271, 593460736, 262581716, 269839113, 895603089, 779618391, 241068410, 485636535, 569232496, 467175308, 626436695, 345978015, 299136654, 285040794, 561036814, 13360629, 984748360, 911280790, 203029507, 954698434, 991651457, 781237295, 468401523, 330896440, 172018761, 279537738, 123409488, 182316992, 617667110, 133425805, 367168686, 137585700, 553089137, 104026698, 101181581, 385313871, 339075543, 402374999, 751662446, 585148842, 222217170, 509485788, 119214773, 801891846, 20366716, 714124739, 865282549, 316425318, 223952151, 861377292, 8789223, 495670935, 697149977, 759584205, 65200737, 803398876, 553816973, 264095829, 935768705, 102352576, 27529526, 519614680, 722518293, 223954384, 318161699, 465307535, 802875983, 545148959, 934994490, 736082824, 328037466, 510391673, 93193048, 241418543, 475202923, 149092091, 882212636, 668014876, 695919879, 141917693, 950204939, 89834614, 860884207, 344313584, 566693052, 960469190, 120970177, 847736602, 538592870, 280052696, 399271262, 188872344, 850533135, 987163171, 77603522, 557861037, 151784181, 854894205, 470680569, 534111171, 697755576, 413931055, 547900577, 285568157, 799492828, 13643822, 223695713, 630149887, 434342584, 942206330, 772351102, 891172897, 837469443, 119876100, 144303048, 153073433, 247133824, 25054218, 810779692, 78254813, 786919985, 838260934, 50198544, 26044936, 427371788, 292872025, 435575186, 573340370, 998462418, 455106228, 695377622, 99604935, 235756630, 396614203, 413867437, 466734549, 57710590, 742101931, 600702782, 898344568, 27666313, 846419530, 119373876, 415735225, 174554391, 701879214, 844668351, 831299429, 817986616, 700589271, 385653375, 680059721, 69224923, 810154508, 117337469, 775485563, 210897443, 49568494, 520411836, 822856772, 462883562, 841381387, 184579538, 801230592, 747459416, 793891214, 415204607, 964591275, 880286677, 360267274, 830949225, 88501983, 436804166, 883222005, 459087690, 708976533, 723299470, 450392695, 153824461, 548605836, 782047456, 32105620, 247797659, 161053431, 871118503, 590716571, 704869603, 441748979, 745432861, 111787114, 561061732, 674874102, 675479468, 148902915, 160482275, 898231830, 169967823, 135763218, 433364120, 217490401, 275972937, 807476451, 559565090, 164957691, 660551394, 54418148, 129831638, 56730415, 660262671, 511825382, 776489858, 456555861, 926112382, 673703502, 319971670, 534212871, 545940913, 677962685, 401437261, 686805382, 916143372, 161785565, 850954421, 161802757, 824346821, 909311057, 817208962, 102483972, 338589376, 493401208, 54427114, 485103441, 926596349, 915925171, 948175212, 998563096, 541780888, 394938180, 359068185, 220129938, 817097496, 257876541, 626592425, 945926590, 165162356, 65031907, 705291709, 211965150, 679321735, 583187219, 367202358, 214648292, 922996296, 611175152, 160115522, 865921759, 247484912, 876364121, 833358359, 245344762, 847043618, 311046284, 700263667, 670908254, 374703040, 113585808, 124610011, 482943412, 348801316, 702420403, 119256631, 760634134, 797287812, 515797352, 577071036, 918245060, 252059027, 562447823, 191115133, 848023083, 804821923, 306224010, 321689310, 336614181, 270229239, 378491187, 252591006, 383422569, 186430759, 912285075, 926810154, 866194349, 910073242, 880269979, 557106027, 875614275, 101547285, 653068670, 794608022, 953636020, 24908498, 318228038, 943115473, 944217452, 382371967, 610373379, 880726902, 929949161, 413662453, 818080722, 30934014, 834628938, 404032332, 319848099, 41068113, 860294655, 84397297, 399565528, 687043703, 504933795, 159272867, 302735122, 837083661, 219388660, 290033659, 769914038, 195461171, 788557038, 912742770, 127763643, 565601302, 333519688, 782662945, 80380529, 783135846, 447949605, 487522464, 178390775, 121736835, 666257036, 959730467, 349063969, 93742855, 626304955, 318570845, 400634821, 778197005, 17110236, 529235915, 329754879, 670036471, 406521507, 690896714, 903688774, 873037143, 985139738, 254893890, 788548302, 952689978, 506981035, 65703092, 518988804, 918104482, 345209172, 462326724, 623111215, 219696120, 642080494, 953367008, 351222736, 956053925, 811740978, 600332114, 558304506, 885934822, 477741831, 897941386, 983757886, 832346962, 88569300, 584231379, 920651932, 487529842, 604610969, 146742661, 756850388, 396044515, 396055807, 141174993, 322852981, 262459628, 56195012, 665283433, 702383615, 16968721, 42787148, 624367100, 123335750, 44334430, 732238728, 414128004, 834922300, 326446680, 647787634, 964991674, 16302166, 550685127, 390299521, 94235123, 608185830, 10295345, 711732349, 493475855, 451836918, 183008849, 599920237, 875546865, 720004071, 845517868, 367089353, 332347161, 72260717, 500498879, 947622726, 66456123, 352589786, 576224565, 671826739, 80800042, 810104094, 828126266, 212697675, 472398688, 702187072, 874369436, 535155980, 84794781, 724211703, 141695576, 811913055, 343924202, 831335872, 353041314, 185654893, 876710554, 823491280, 39371376, 238595687, 757193942, 198528378, 227072742, 880903807, 880826158, 108554362, 76022352, 242117718, 832675798, 323192683, 70838551, 181171625, 548576675, 236052080, 397685918, 922159109, 741523394, 367808733, 520832530, 659888186, 481162453, 470758281, 960503008, 577882544, 4186907, 423461628, 720709226, 80096978, 998837841, 313036533, 675552312, 920135017, 43125281, 472591384, 470333206, 587028927, 944052447, 442730445, 626326856, 264790721, 384716916, 221868078, 971373682, 935794372, 842001487, 778558108, 287077109, 533804373, 274663166, 132311278, 665040378, 536226451, 473102732, 188140810, 259837948, 963205103, 860811232, 732308190, 594443069, 983641179, 137967103, 726521848, 761864933, 264256101, 758695581, 600793269, 754149553, 457745340, 135447323, 613289926, 220468865, 246148371, 990747749, 406972992, 800222326, 978541329, 644967351, 839587902, 725164359, 914946684, 84408649, 954537639, 689425091, 712903662, 994740887, 46975650, 456076986, 542265965, 893493105, 511491457, 422088446, 152307686, 546220678, 778125706, 899954271, 908068180, 912129091, 855186938, 99825935, 452284479, 58839801, 596880524, 266910687, 873095052, 125378358, 588449787, 389729794, 46548539, 454175743, 540187918, 433632355, 568807202, 521946475, 414587190, 677944783, 30399396, 923382222, 524623654, 314769198, 988666811, 966259483, 940476641, 363225066, 219105226, 772860028, 346824806, 608962568, 847436500, 177983676, 764157829, 972051915, 867058136, 832074244, 364990326, 900208948, 612808718, 419903328, 236746876, 275089718, 1751989, 646274654, 109586544, 972461296, 751152290, 166623186, 843508179, 266171406, 181755543, 16702096, 165420926, 248073092, 137587913, 314190645, 199359615, 11334020, 393474682, 413427433, 437931898, 707428638, 398725089, 949359430, 123033999, 703534600, 947193562, 306616349, 398520496, 926640209, 652072908, 497472250, 172331549, 853763039, 906640800, 256149980, 671079373, 512440350, 28892844, 658499581, 247187378, 984110538, 846308572, 777493544, 999225599, 586848533, 281420965, 934382923, 462125960, 97627198, 42688149, 791503191, 121727510, 271113865, 806812099, 429415136, 348178574, 668409331, 351567949, 708280464, 567585367, 142998382, 504806726, 885716880, 10394591, 598001988, 493774252, 666675598, 979156549, 251817765, 129753192, 880163629, 100634474, 966214913, 369559997, 390296845, 867014260, 884961430, 145490115, 214620651, 744446890, 784833392, 935088526, 289690466, 465031462, 157425691, 82145582, 379595616, 395636598, 363946532, 658228491, 291280492, 61211405, 421352932, 821213957, 458473594, 306201246, 219637224, 446506577, 566950849, 317794924, 733235896, 128568399, 460690310, 71844427, 295298251, 378397056, 279489621, 913788196, 858620491, 399483956, 677042690, 886456507, 171125631, 733948647, 841598606, 997292771, 240790545, 570353651, 466600972, 790373664, 695623393, 575661347, 223384318, 739225596, 933963975, 706788546, 274091032, 683317074, 872388748, 80544014, 630600799, 358826539, 455810717, 740039296, 226273119, 141765207, 569071344, 595521052, 54098046, 155684163, 825158527, 764303886, 417065249, 705684142, 862390386, 359150141, 593817909, 961227429, 885673487, 679921829, 915760864, 514657981, 263326221, 996278810, 338737044, 55216353, 290835200, 534489280, 638151803, 916384574, 151178912, 700041697, 309441299, 214903865, 423450976, 450935787, 859533198, 234230768, 653324014, 680427407, 27241667, 37203809, 660500727, 15495363, 288556245, 328419706, 810099988, 283320310, 869209327, 346300497, 600212954, 974673846, 291332556, 418354184, 177361782, 72404729, 137385528, 527451773, 803983575, 838021325, 620994517, 663886775, 965025103, 116457038, 464587981, 746070383, 610828185, 191063244, 398676795, 387018269, 469108914, 285412531, 421509557, 244318617, 499485785, 261243851, 373891514, 997275917, 867862849, 379703695, 104154954, 686531138, 771938804, 559614824, 964260993, 290562233, 841986543, 369038690, 975041394, 266183386, 819650236, 71706004, 918720409, 866600598, 299539019, 260980376, 272401322, 107289856, 141413142, 294818785, 440085092, 147761122, 654263735, 237419558, 597125595, 660364758, 672781773, 248410339, 42013543, 718929739, 760248282, 604314706, 567962857, 285680294, 113893503, 685791733, 466414750, 848450554, 718916871, 448170685, 476731205, 731456697, 944653792, 809023517, 857474897, 934709343, 458698528, 748776749, 77088987, 508843682, 242536307, 221645537, 496079407, 8389172, 671259628, 217481618, 290765079, 498286831, 928122963, 635733314, 773822317, 588519654, 35154958, 853556542, 542618882, 576302718, 694681881, 7107779, 748844167, 484568511, 569924662, 101845434, 86237247, 169635329, 16228489, 298496055, 304915383, 746349215, 110024923, 407204208, 734210852, 397984788, 105473134, 160461382, 794700771, 165978846, 606822405, 740282829, 852745945, 408262846, 856103797, 188208620, 945823137, 88684799, 668518839, 281406983, 407839478, 653202049, 414383494, 836465887, 358431808, 550382535, 279905181, 654716966, 618485865, 361953857, 836756822, 590047710, 159885674, 166606619, 799895524, 595190817, 362437713, 465614460, 227239634, 482054946, 395782555, 659154727, 793953243, 670393005, 80252714, 776852886, 270417873, 572524461, 991909334, 521397179, 645809695, 574307009, 210796566, 394699968, 929679678, 896210244, 677295118, 502049036, 534250113, 520932808, 340916866, 858129945, 637861321, 106981066, 973162594, 637504638, 859977429, 787444451, 212952346, 677376767, 485388897, 832634216, 49683189, 433001980, 100044969, 776070811, 74779557, 903033034, 409464259, 528231944, 63296198, 444970440, 263922770, 22753934, 688859382, 52982166, 255055407, 670108553, 728626375, 863461656, 970173760, 944529677, 28847753, 139154811, 988837504, 822206322, 537384596, 13709991, 95328732, 770635787, 327056760, 291327055, 641843196, 756511309, 460087552, 614636233, 730967079, 174471504, 870784740, 35346891, 126715067, 791970982, 397842030, 548562499, 458671823, 376636139, 946042577, 153277431, 434907153, 360024119, 658166572, 66327079, 517775770, 30917211, 942454485, 803050869, 250301883, 351319432, 710613932, 889462518, 96235213, 322919366, 314622947, 849812052, 808417767, 204869508, 855849522, 626363341, 903790856, 774761272, 446559852, 755188238, 709805309, 191924727, 643353192, 368830525, 586489584, 610968056, 581630310, 206710229, 544046472, 735121899, 923972431, 404529535, 89819951, 219465784, 167233224, 169144174, 279166480, 958167062, 729723962, 297261238, 530358240, 264228360, 35041148, 409430893, 679347027, 240916719, 467776212, 74500389, 567220668, 920410328, 562483922, 64190458, 986500397, 542652806, 365265307, 21110726, 857162436, 298648983, 839838550, 129992058, 666815462, 775655402, 476710593, 771572603, 768653136, 772816170, 452347223, 385822092, 300847691, 729604988, 258679116, 679839449, 32618880, 51710259, 904105821, 51315342, 446129814, 171331956, 309643541, 264513432, 526337483, 414693767, 397336719, 330711551, 900601328, 385769357, 49223602, 477690338, 521368803, 662031537, 656191143, 132189664, 224348195, 635076709, 333108044, 995194068, 292760100, 619511596, 610049471, 891574150, 766096368, 936072731, 842542052, 809349629, 915343705, 120632224, 416721008, 605887117, 517639038, 677954197, 312258593, 195368235, 486002986, 337056779, 457451176, 789672363, 638823648, 248738865, 776868030, 630042886, 92634733, 791596056, 212735090, 402631378, 140745338, 684593536, 438602218, 831614005, 301649571, 63949861, 930672755, 647207468, 474962271, 237302439, 758516738, 95256334, 793498418, 812753760, 198007119, 93236985, 154687897, 272489216, 50344031, 741517686, 233021371, 638571041, 373647719, 571170915, 565827527, 316775594, 158552339, 912834036, 984919741, 654203946, 925026221, 976933759, 415429787, 820145679, 105457101, 831179993, 985855999, 477867745, 1438881, 204007328, 180210667, 955628533, 858966193, 848150536, 783915446, 217656740, 800157960, 874481106, 540246431, 238735878, 905084974, 825427572, 100789889, 258468052, 980760645, 57547889, 614099820, 868234818, 525294814, 476457388, 944114462, 724651991, 950524217, 191215098, 248619128, 58048356, 580821095, 261142225, 716351647, 370502551, 398198777, 449592180, 307529413, 754509439, 406812348, 244998684, 680183949, 908613197, 753996801, 369520899, 974075430, 5072308, 667164478, 652670046, 167987646, 14100945, 706996584, 632981439, 168037271, 711055181, 495018920, 799594299, 268956211, 422104279, 782843431, 289089607, 877000528, 257166554, 511885046, 298853330, 599558319, 358416482, 507792440, 321466412, 397675039, 715692021, 751306068, 442589521, 714938407, 408583125, 356963380, 982048278, 103428836, 110252821, 785779026, 950085753, 535567625, 287871852, 383499474, 822924424, 647728025, 304408269, 822930669, 927231203, 902645920, 170517563, 487237794, 660719390, 122992330, 789715533, 231972049, 273755346, 389485362, 648063049, 163694683, 520694915, 82432305, 506128764, 247222034, 750788121, 902066326, 708266714, 502574131, 594433730, 580074280, 94877391, 751619125, 883267216, 791148439, 478231899, 187672188, 256584111, 373510101, 605042824, 555436249, 121766531, 985529182, 301620534, 673063851, 868687396, 811939493, 385121934, 556870635, 895501834, 554221942, 488655855, 203315483, 773191448, 20019130, 184989862, 778340727, 157252322, 12668888, 929695236, 903688419, 493511508, 515365571, 300527223, 905860569, 363539279, 49049539, 125563821, 239135294, 104888195, 812969096, 442079994, 279251477, 442530971, 262948438, 280888687, 31700781, 209249171, 911115115, 295841268, 701485261, 446545710, 671555640, 622476146, 400684084, 130847791, 496592487, 64980602, 873678287, 529058965, 539111502, 543204358, 431995391, 12809495, 321560684, 147089058, 327446422, 659470784, 602371179, 766127396, 836252499, 727668013, 553302953, 632008300, 707813025, 426999768, 138402702, 288238525, 858438225, 517438115, 674847355, 95471722, 941566445, 756966747, 683668648, 883538886, 417483098, 541167114, 24899677, 203232954, 166955853, 634000110, 990121881, 919443085, 565671736, 308598534, 550723175, 438332032, 92457778, 148806287, 535347582, 887502774, 57098273, 469388258, 779010598, 121167315, 528045852, 437224328, 895937205, 156988617, 706338631, 766370275, 620680627, 657022464, 464130784, 991351503, 907321660, 188308062, 135681733, 957272097, 909292295, 331363531, 732690306, 449838923, 708416585, 110242771, 821523301, 606045477, 872905358, 307218071, 511445818, 854397342, 856375331, 208304017, 130061072, 34766271, 441668175, 562256371, 2253055, 577253312, 348893380, 889442421, 143903036, 880835980, 323743689, 91530597, 798963403, 667942360, 499937825, 854065867, 63277060, 158608043, 645209384, 277221631, 245722816, 459843633, 20387248, 385993570, 142391592, 677967442, 147388322, 940426979, 141061511, 554719554, 966149356, 862299562, 708857218, 236862800, 457775469, 356247896, 903004883, 18821070, 304631478, 953799151, 606432847, 745006432, 864582992, 822345495, 676606608, 291116747, 146827652, 58776547, 101685800, 309737341, 683187602, 384901440, 422255046, 755926283, 726804428, 290056311, 704182703, 127599358, 283650441, 735880299, 32607499, 485614633, 630842894, 241683641, 164194108, 647037299, 62705185, 729831417, 981646604, 520034916, 585095852, 252368014, 263453005, 961486565, 482070262, 868763120, 894838037, 855946231, 137404882, 270567031, 16915285, 256205500, 227291858, 594383715, 563771649, 377074966, 748162677, 389305916, 44629987, 771105540, 519577062, 126379212, 347392416, 398431854, 868766655, 271520230, 811384206, 890260829, 543424354, 930710440, 397602576, 713782629, 362438369, 583752019, 955932132, 33783368, 94950982, 531365824, 617846836, 416926442, 155888810, 186231176, 624221790, 919814605, 884910665, 57413867, 88568270, 113465968, 922564255, 920670582, 49647301, 922727356, 545402298, 698519139, 856532607, 148112968, 288775851, 181881744, 701382548, 391763308, 198944525, 991818363, 30038409, 662013634, 31264570, 761005803, 702078761, 123299987, 472850315, 948915620, 550680581, 99138912, 98966372, 221648226, 647044379, 162036747, 850115030, 57574708, 787399675, 328247793, 738522193, 426707776, 177987944, 700193145, 268637164, 171662034, 990087597, 363332509, 82620056, 576213111, 410950206, 634010877, 198198693, 740526335, 247356379, 23696207, 303149665, 12266817, 153775041, 359458443, 295012842, 635319318, 535450258, 896241703, 85429902, 980657918, 137527198, 832711628, 913126753, 157731018, 617585369, 77381523, 720693514, 788399956, 712090842, 117551469, 423934775, 115421167, 210874615, 478757831, 268652035, 611188317, 268048722, 661348571, 211457320, 670544130, 491470586, 167250700, 823826850, 516670130, 251244760, 84905638, 984044324, 787310893, 148208657, 787825704, 880735690, 830770104, 683965433, 805022301, 480282744, 597364155, 453671800, 915298792, 385130515, 916844620, 909974082, 421168367, 104771345, 524194299, 534911093, 348632835, 505601249, 773587811, 14870699, 145532436, 526695557, 718564848, 635762744, 851282000, 428024171, 306503139, 85252670, 849563918, 921550780, 485184463, 232873756, 485342844, 164255039, 768732603, 26808640, 820820360, 102126590, 200108243, 143229074, 407111910, 198297708, 316485693, 23873150, 676550126, 134875786, 912120349, 672428009, 956414289, 701840056, 8843761, 855492828, 570214737, 127017370, 500404132, 100592847, 366126058, 334938664, 85878850, 789830652, 675597359, 508033582, 358306714, 723077412, 531843565, 417062036, 375999780, 680775314, 763647598, 15923364, 801540912, 842066277, 812050131, 723481343, 979184361, 570004897, 584842499, 823135997, 998164458, 88201473, 245779974, 674290628, 500428220, 446225990, 473326445, 249173203, 433041590, 601308906, 944684226, 240622913, 938575427, 245705324, 553387498, 59336086, 667155281, 696173446, 687925502, 849502851, 757537292, 182254307, 951629510, 996603255, 770184235, 663000917, 652730676, 786438587, 44990557, 292754688, 562667805, 921571811, 53030128, 326928627, 262886096, 158786920, 968497190, 1970842, 387347406, 757744385, 71339779, 797103903, 413804806, 279172061, 130513706, 390668319, 969838358, 34719672, 918889381, 537233488, 909701876, 942649022, 413931823, 837631669, 737025645, 559647493, 612705118, 57493742, 904765689, 977645900, 514323546, 304942432, 779742088, 483176453, 359842540, 171126149, 279328462, 297456136, 227632214, 759183206, 675744336, 647231877, 175307457, 608200013, 893533644, 320173633, 613054149, 594842479, 429389739, 340616097, 656496672, 384458567, 664537236, 712031944, 715218974, 701339472, 475976888, 661692962, 63542743, 554954737, 674484273, 60903172, 933968060, 893019265, 606518213, 365092676, 432486216, 815645733, 682489598, 328063226, 338958484, 510638533, 879935720, 822537843, 554529995, 689723781, 867332756, 818283732, 515073495, 371644192, 604508184, 20989574, 671958038, 917739406, 758605691, 387907108, 704410699, 63701574, 928216921, 973365360, 777157742, 86601161, 950362906, 989393119, 840209354, 423374145, 589542371, 969710225, 667455686, 130456367, 915858654, 932658557, 22219362, 496248750, 777596719, 663298808, 31714405, 103298874, 47517385, 672930811, 443942925, 233162522, 417293510, 592881255, 84018921, 979254721, 163954516, 177375038, 304314099, 284967046, 491731551, 381865474, 161699606, 939336562, 21551672, 464278372, 141500645, 458300565, 457259052, 142023811, 888021801, 513513790, 642483437, 489103983, 290754489, 41698756, 484405202, 823328213, 469045443, 822068971, 814543191, 210082256, 671376888, 912713652, 824527721, 870200513, 671403097, 548034334, 179500449, 988726, 169218414, 151343980, 535014009, 673485131, 163385815, 840692605, 968689669, 116936656, 41233137, 407376333, 532919964, 585796500, 6680030, 950992265, 686835070, 622680008, 337157987, 690048841, 214985696, 925363739, 556924569, 264005633, 44269504, 691209296, 462600488, 710921864, 946578441, 628840190, 594921123, 243338291, 512074740, 738741838, 152488029, 354632195, 273772584, 327044267, 104766723, 602476090, 685388864, 577841725, 150343593, 395434379, 595323841, 644123074, 34780446, 805151037, 116124133, 677881653, 587565385, 739190621, 641784327, 920466137, 18807658, 402743284, 34129086, 624689858, 863961391, 870297684, 119852586, 233447721, 982706947, 397580265, 682301782, 224915088, 850792287, 979505236, 289350935, 500860457, 63099409, 516739912, 968734560, 487289782, 194944579, 631413959, 723260531, 106475729, 86348424, 137463723, 697992634, 73799178, 110586137, 137288211, 431878143, 189096738, 454215533, 802284996, 224855490, 389652408, 44946738, 302286914, 793699290, 478320483, 87442309, 340330990, 33537222, 491137745, 92715016, 960649567, 964279258, 841836945, 502245545, 941557004, 933590262, 572627065, 48584458, 643390136, 809137274, 706015864, 879866871, 731637732, 624147231, 137835454, 727124268, 523562750, 838659049, 715298164, 568746577, 532251433, 329852769, 798505524, 319615497, 480414534, 334062869, 413497480, 549047638, 486824475, 444084937, 428134927, 77905170, 142980781, 640528869, 105685775, 69554739, 610739623, 803249914, 142336335, 573142779, 60043172, 574561206, 623932832, 540542840, 532490692, 83578626, 347007285, 432363015, 453641644, 861457907, 122048525, 776594125, 463341813, 17891152, 690145433, 306613437, 648451832, 363627045, 823228043, 937708511, 543884328, 569202899, 192421934, 675439430, 598086213, 672110576, 260407790, 933929057, 862647780, 330334839, 750980268, 882732329, 737852608, 286634407, 362537612, 330498258, 959254301, 788218595, 273797822, 108596769, 911555769, 59590463, 930368557, 215902309, 181051959, 200205180, 335495137, 289319672, 793750783, 460930446, 207330672, 504905224, 140906672, 931876958, 471312211, 317827858, 855526678, 637145452, 291919673, 901600716, 170390685, 133110625, 653164791, 18805356, 377172499, 97166577, 111615784, 679488518, 371888105, 653989354, 937398716, 985381664, 867344621, 624091897, 496452832, 822444977, 795063184, 337213969, 449934219, 944116562, 630781650, 206331425, 148283744, 784011705, 659093551, 774983156, 108660790, 895067808, 220259923, 482190789, 981694017, 338434016, 582285175, 910676707, 460380358, 243348192, 662070487, 643499470, 59133482, 491974265, 263900660, 459593091, 352170897, 335672051, 562834151, 612641649, 391205957, 760019854, 126548427, 95932779, 797900963, 867678085, 355916772, 818108321, 808236029, 895142792, 570507261, 548898619, 734663328, 518998689, 244092602, 811058676, 44973552, 312345559, 295427451, 900106645, 174926409, 595445377, 137495253, 369856903, 604618348, 634353443, 413402505, 276319695, 110274477, 443004641, 504008519, 985897675, 431061669, 643663602, 552879836, 475017672, 344840541, 863985306, 117238796, 775065378, 127984528, 196938436, 233235946, 381886298, 145890669, 642530134, 848655494, 271178575, 500414553, 867119510, 756860036, 583011033, 201908150, 929024243, 906041424, 353430117, 930736315, 871020298, 890862317, 262857350, 957305892, 785472742, 592304023, 393642374, 814391357, 499215560, 645153230, 513264145, 539380336, 605452336, 514768368, 151153985, 527964295, 900941889, 745561906, 208580921, 311926035, 119989865, 950009982, 604779152, 953183836, 693846988, 684942344, 935832641, 908939431, 994227816, 199648312, 394139941, 583811960, 324934665, 558822691, 144201949, 88301694, 627214816, 632467540, 552801072, 791892746, 800575583, 749353905, 893411242, 709797594, 198736382, 23737065, 602155243, 752198493, 969962319, 92237609, 619231097, 469890140, 32537367, 794257268, 792908431, 823432698, 549191954, 417616308, 636673451, 956324058, 522524225, 818977649, 607307041, 910987471, 139241146, 96327131, 573192332, 388377929, 72539141, 21377326, 662995896, 909006445, 136848150, 301083247, 966495995, 248613749, 820452545, 709012347, 306557177, 302706489, 512392939, 475901222, 604783324, 587354427, 407633072, 435586538, 6831808, 975070909, 117522612, 438440145, 122398996, 618173509, 864102686, 264552778, 712063952, 873939319, 546866305, 464779299, 469266362, 7160204, 566138345, 844102866, 190140755, 525743802, 837310756, 682884819, 260718026, 972346405, 814757745, 220904169, 453101138, 314349884, 723421447, 396507791, 239177242, 772201350, 196897378, 970229449, 909030408, 606655230, 415090499, 51918122, 715231775, 337748567, 646096875, 494226615, 929142557, 737136383, 222416894, 10880332, 12393211, 163031916, 468196784, 462966759, 108711702, 729754544, 4264194, 713787182, 99235203] 907909284)," 0 (countGood [517941044, 229380073, 103836370, 344819678, 233695574, 318502540, 142803802, 102355502, 501181094, 29697741, 552840508, 804199286, 32621082, 152263863, 627628942, 985216972, 594021418, 128193036, 311837886, 86593152, 630633829, 601579890, 249136541, 918722655, 330987735, 976288276, 998683988, 990129392, 507610086, 238819662, 781091154, 779698874, 807957786, 245765103, 850045560, 529256851, 337101010, 434328670, 404826293, 2244465, 269194486, 424415744, 382895468, 346387097, 611084214, 901557584, 559174989, 149314435, 842059658, 828568332, 130871115, 688967881, 477349760, 215412277, 955557200, 780794613, 754277039, 608488880, 973506471, 313665972, 635099126, 379948822, 414841866, 234685068, 545458705, 407539502, 276408618, 302199301, 711708581, 674198792, 609433579, 853440843, 108913433, 4845978, 350512141, 360832258, 993467473, 316259931, 361077266, 170240680, 271995674, 808967557, 620615086, 184695100, 437202875, 229849511, 912979240, 309612351, 605683310, 570517367, 733267668, 902832713, 607648938, 859276116, 939844049, 294478843, 685456484, 438193164, 653285813, 45133845, 457267536, 376360359, 566423500, 605108921, 633340433, 82675912, 773912134, 48344290, 615326359, 857719619, 508114993, 291705768, 318914100, 72890507, 259051840, 113584467, 519349245, 398418435, 932400817, 290653997, 902384377, 62267883, 800189947, 28232789, 458869112, 380647621, 474730235, 724441715, 741984959, 607932830, 417905815, 546586515, 927035547, 797988599, 945398883, 138928471, 866803343, 283749581, 961442165, 924535969, 786779517, 825634053, 494897817, 250639984, 682669290, 227206204, 578320582, 343605245, 692645021, 979669420, 386540353, 161313172, 457172882, 566259113, 855351600, 920233623, 475846895, 115904727, 475223253, 712604774, 277748257, 561069675, 857178285, 736993801, 239412716, 656602110, 216275731, 450683978, 759774709, 473121227, 36544013, 965856737, 936003352, 512430080, 562654618, 81298953, 986611089, 799943212, 696880098, 271456495, 608442203, 39326121, 848991672, 409350428, 741911610, 829732488, 602481023, 673349070, 890484532, 282597677, 963813618, 303956777, 868404281, 429829273, 959667437, 434097206, 400453780, 165875823, 950209811, 113493839, 475904207, 335246212, 951870441, 885777667, 197976750, 561473033, 765372459, 546926460, 818920755, 998703583, 554882009, 41213175, 659436981, 255324023, 788038556, 457970021, 388988912, 451208005, 542025643, 342837823, 173530108, 538590729, 763913205, 140893166, 523378129, 559850251, 924321783, 397355260, 780989399, 709489813, 229489241, 963291121, 524383815, 66617311, 588965393, 596225477, 272022624, 39843684, 624720443, 981539921, 187958832, 346948102, 660938103, 152475754, 131851577, 144385374, 864464199, 790637915, 130812162, 904578269, 502176266, 595240703, 347127575, 634499930, 905434469, 570318651, 693524173, 949351405, 915254686, 824775720, 261457901, 752153357, 23548031, 760919491, 843319069, 98581374, 495272919, 279811345, 120168983, 445963177, 343802585, 825846692, 42807990, 871257782, 478116680, 284065095, 528634620, 253739677, 55064061, 206238153, 429513200, 242290772, 241887607, 936209280, 21530402, 57534981, 913384166, 57270443, 492256985, 690288856, 789043079, 934924693, 1966657, 433344792, 538325769, 414928743, 956456456, 583693652, 33028777, 890440251, 277068404, 394008611, 262725412, 711013143, 955401461, 151303777, 295214406, 239532163, 158565224, 139358428, 591328279, 400481282, 739425572, 123080749, 181435293, 215644925, 49225799, 845827013, 444718858, 493621306, 548698881, 360310067, 19855834, 681509939, 555551064, 771651263, 29678001, 68337557, 180037547, 237728565, 401688672, 55753122, 249723875, 608002994, 902852266, 415164495, 67002245, 367141034, 243873968, 969790293, 429738792, 722887611, 500586055, 965280505, 29973186, 485885059, 166498446, 281096416, 983387044, 750312628, 278637709, 626794448, 850202304, 435717501, 482268193, 384073717, 42223020, 284767768, 728244264, 359638938, 998423105, 834578864, 681117118, 468268563, 241168975, 509278113, 672494443, 814545202, 89403837, 184270258, 688609558, 627191891, 118663605, 909514607, 929399229, 791028233, 901957962, 805293683, 729690342, 83488820, 737806256, 324720188, 148975294, 817798189, 238759200, 555736830, 643810047, 939214620, 745457784, 348984080, 910034584, 81271895, 416702911, 904723959, 419435444, 923338087, 529547778, 976774537, 969533989, 54413981, 412985574, 545775355, 714960900, 423192073, 205061086, 296448996, 586354773, 971675148, 141686572, 102502505, 205560506, 349511226, 333964575, 983560392, 416758774, 144918800, 638429401, 540016005, 249474130, 515091634, 863482062, 140512011, 731212175, 798308249, 188703087, 706667163, 974655013, 690088741, 69719111, 847579255, 953522799, 791298717, 92651937, 728445850, 706232361, 416338082, 721980026, 756819320, 191048990, 463509496, 571451715, 353141261, 677056956, 604562763, 224211742, 330172192, 377298719, 641150233, 141745019, 643502389, 934001197, 442790814, 413156857, 900288342, 798846076, 673594225, 355193139, 729718367, 391936538, 83577163, 41001236, 971213100, 901170435, 56293592, 745889632, 850650609, 276995736, 671740510, 207501876, 905382527, 657483421, 572953896, 99342142, 596570445, 330918431, 82941032, 871223891, 881038975, 712682643, 747723041, 360050721, 180466050, 762718170, 956746628, 412715169, 701818276, 961185343, 903941998, 811354248, 64925646, 432071575, 852293745, 785410550, 379396983, 389544708, 946390222, 405208572, 872499694, 1777583, 845782252, 92227647, 794702229, 1049413, 218381166, 535615850, 703851829, 115360146, 891814882, 508609153, 525225501, 542971332, 951727966, 183190730, 165239769, 262706844, 262918458, 888227605, 430728384, 270406079, 60380100, 578056866, 49758563, 512256137, 785288255, 885164353, 344342952, 517796029, 297018139, 448348039, 800908183, 312770393, 622015776, 752787461, 154201686, 277689704, 317516937, 530536451, 989484237, 529923339, 564680590, 144104688, 531774947, 459358378, 751734679, 196502942, 865107156, 217131725, 138924819, 37065792, 888852305, 764825896, 27904870, 192514179, 286674618, 823244331, 906054232, 261894533, 228729036, 691007760, 768076138, 23923193, 633659403, 960514902, 272228640, 5417814, 994187184, 772597428, 690541517, 731968834, 578719860, 743100414, 879593205, 226798509, 710739218, 786697532, 550280518, 837898567, 50785969, 678818353, 234826760, 305846, 607718464, 723879374, 135130156, 949853925, 329165301, 27093896, 809129349, 564270256, 679059829, 305045026, 154378029, 324302900, 678226482, 591063102, 812767185, 676421149, 469556819, 843736807, 902375758, 119004728, 728889009, 828917068, 815081078, 57964391, 461881484, 141884691, 11766180, 72745349, 923790066, 240326540, 533494463, 816871560, 981958408, 809309521, 632304477, 313824604, 686140140, 265574632, 159342404, 689421137, 578265235, 83292225, 942873614, 708552091, 559170677, 73507266, 897453546, 494367766, 835059128, 533946906, 771232436, 941720249, 753753520, 917033904, 724730524, 413424435, 598495794, 755289232, 303289810, 988362528, 64557717, 404009513, 593505960, 313308051, 476554790, 943122476, 972029151, 927225727, 437691588, 454457578, 567695386, 469579292, 697436689, 820868985, 891276059, 74131304, 21862428, 670266270, 320896055, 288906931, 43918576, 746175292, 330473929, 549346021, 251067121, 916518994, 647824273, 764939468, 726043893, 142892103, 539919136, 451429625, 927992479, 153363515, 454787712, 793505662, 731838472, 205081935, 759492753, 461668099, 457822207, 343690117, 817379381, 993241546, 157136774, 162927659, 933544408, 957855493, 262688713, 976918437, 482819153, 552659814, 954986622, 273491818, 524969187, 381207034, 758165457, 33052375, 935204341, 934575668, 718940484, 557418241, 947969767, 177172230, 279964772, 966970940, 675620617, 395483445, 561217360, 96846683, 36884052, 91665045, 885042858, 411384859, 505200283, 33138620, 587081674, 309893963, 324819962, 915159045, 73587732, 617658606, 763470059, 731102725, 876576039, 877117735, 260622944, 614194137, 652820248, 40446815, 106255388, 426883090, 554376318, 181633348, 359608309, 571121312, 399597513, 198422498, 746373705, 827162019, 804601109, 549419538, 86028663, 894119531, 385495786, 998737425, 882267057, 746357252, 250798269, 895558244, 248346459, 620187377, 971577098, 15487468, 365857023, 885700436, 842224500, 920083002, 469582702, 972304508, 306679409, 829239268, 671445193, 409194218, 987807445, 95882127, 41123398, 792974119, 241558971, 634515977, 393964985, 568441236, 409105062, 591514659, 633724935, 238056690, 562328879, 230424429, 835932284, 484557833, 592164756, 196920447, 338336327, 85919822, 882310072, 297839328, 947218198, 30788523, 571839607, 22495712, 177495943, 892964985, 221953314, 980673565, 607921929, 831287435, 812781713, 585051794, 729192243, 223856598, 769636504, 835676457, 811791604, 921993325, 96447671, 360498714, 357173012, 115290824, 293773206, 427344383, 111490543, 68189737, 966602794, 654222265, 156120889, 319718357, 307940227, 949363887, 852070823, 763568685, 870143728, 365049187, 772553172, 631795577, 360673203, 1889278, 648288087, 294346351, 362033192, 897612478, 740265812, 735174589, 820372142, 906537111, 355956489, 824364738, 61422588, 870466760, 214494518, 679294126, 662383292, 545124407, 174526320, 257374547, 363531937, 971720436, 514595088, 746370337, 985322368, 4717234, 446885836, 856144199, 241542273, 464883480, 969244959, 863842875, 257831597, 734378393, 657541642, 125203470, 968853053, 122885018, 201966556, 707602431, 831114369, 158001060, 701722624, 563734894, 858907984, 524924132, 135714935, 727640941, 978491317, 60018121, 327071637, 976315827, 128388484, 715476006, 186616728, 574172672, 11632248, 111737670, 425123445, 467121806, 76902859, 659703484, 590805840, 299519180, 18770163, 870461496, 968149810, 725913660, 860934623, 364366738, 484446505, 412348861, 778998117, 619732721, 141720256, 782904784, 437268023, 868815668, 744956434, 33690006, 88766863, 255106457, 715589169, 123166535, 806926616, 463632317, 338400831, 962786628, 948732595, 91636068, 123383989, 505896934, 590365747, 607904285, 331809578, 226433797, 533394824, 559268167, 975873366, 456189980, 858899646, 945772650, 323910489, 599515410, 658076356, 865241698, 828969924, 912712474, 887807051, 982565443, 226267453, 231187637, 770759175, 325233880, 115272528, 819090397, 735013432, 14917614, 674151510, 51039645, 947460810, 336548326, 332162767, 537321779, 697627856, 748795234, 822842717, 959643316, 615387161, 138685336, 26996525, 534766, 427920342, 447398636, 448721935, 671984215, 34102124, 740500847, 73387652, 539478692, 995481563, 603133586, 221290998, 995638492, 283363769, 813557753, 197936249, 409102331, 898932017, 106530692, 305255310, 77398575, 679066588, 422329787, 75480657, 743426265, 724484288, 532066940, 855173538, 747162461, 741074933, 464945473, 351920279, 556600729, 119165196, 483323641, 535389534, 380932609, 797785136, 97377917, 108441226, 211140780, 989229513, 778171382, 644251380, 854360960, 13720213, 724826524, 68439120, 913684311, 215124761, 306995068, 255574340, 355522791, 289460956, 735444434, 521865912, 422432264, 695171834, 315072407, 434747168, 102237834, 534867995, 896131746, 526736046, 208582053, 217632811, 992195198, 693335212, 828395602, 73690645, 597467422, 204970480, 206967670, 926963161, 173171460, 86804994, 334131695, 824762568, 899885000, 238283698, 243474463, 234550425, 461886649, 183484994, 837770317, 407371919, 704170143, 505739092, 791343647, 330198941, 207071303, 655803095, 652518824, 194902917, 965476419, 939729738, 152382747, 976152434, 62638053, 134914300, 416155455, 372078387, 655851121, 663962205, 715862228, 774405407, 724885717, 872305876, 676189623, 177763574, 438557095, 486605309, 761553459, 403302902, 814411626, 355022102, 131485099, 687486509, 878388655, 345633038, 464323973, 399831630, 44380634, 146002778, 899422754, 574850706, 649812330, 722676342, 874372003, 232854753, 255838073, 149433502, 31639204, 964969732, 339800533, 241559255, 841873899, 215617324, 925566337, 669389115, 635485474, 306997894, 662120709, 877954927, 9973152, 774938215, 302867856, 800540205, 725828071, 231884521, 94501514, 277474105, 807948409, 830267030, 596943406, 473977423, 457485673, 173709075, 199822917, 855754755, 95567003, 862580711, 339334131, 239946147, 185014574, 911516462, 523128100, 688080156, 990315171, 211187103, 447551612, 896226311, 194623100, 597398341, 715377919, 236634940, 945601098, 814138221, 541877435, 882835960, 927955297, 518855667, 602448544, 434829496, 407709212, 853369223, 179731629, 485203645, 85367542, 439972347, 377910328, 261054019, 513658911, 596276969, 949299199, 299121467, 870068505, 850904419, 349632896, 477613040, 841956709, 32842655, 738978837, 526247325, 73955353, 461643761, 164390041, 888623029, 560351822, 484886589, 670537866, 756418866, 188581168, 53860682, 567893971, 97471062, 347285214, 953223340, 962067048, 19752902, 48491040, 883994571, 923470812, 361154321, 564905518, 687785841, 542284487, 65538005, 367897273, 863507261, 853984917, 235039223, 414902579, 905339795, 611567853, 986280387, 735157031, 878881466, 495950029, 300709253, 622085588, 427059134, 598013651, 57637413, 54976415, 339141091, 584666806, 768411525, 528225919, 644690733, 594082898, 210417848, 725295351, 386477314, 126434280, 951231071, 973117472, 392612599, 700757786, 897598912, 230861725, 22003673, 674440342, 94825983, 903197537, 571942928, 487720277, 190318539, 281318021, 475308404, 322242959, 349949006, 276631502, 448787535, 944453304, 643921420, 511272343, 287485397, 434973389, 103131484, 453123526, 683109685, 519094903, 468204233, 338790321, 986497196, 340435669, 321567013, 905820366, 517315593, 736810535, 836948382, 726822040, 254993327, 344869318, 846851471, 812972542, 139438652, 431788859, 650147844, 500740171, 849424101, 285125345, 218895777, 663404859, 469503128, 246691785, 12932861, 613497758, 441343568, 59685213, 146790267, 92885157, 801157784, 199122588, 549248680, 825602675, 678498382, 449899090, 620506338, 465362954, 310269573, 39906771, 879536238, 470220557, 588778737, 973299915, 650010367, 597153692, 943079440, 899309289, 354649921, 180028983, 288847277, 158962449, 424898844, 800687146, 614436424, 408008558, 737862317, 191719064, 529298356, 487092697, 286294604, 628728756, 841561866, 271348296, 832482575, 590475575, 341818404, 855094403, 526866883, 265596632, 884248194, 572524174, 281870055, 774112666, 953439939, 760588861, 252640436, 978875686, 451370806, 543768458, 331285835, 779707462, 804566110, 112835631, 570092541, 124036739, 521002529, 336547905, 58773829, 919346964, 324088080, 690665664, 730895449, 95229480, 191377598, 214735341, 517888080, 214963951, 578942467, 458965079, 554949614, 843196187, 683172561, 15457609, 236598657, 489270737, 887199269, 423895732, 380343143, 231658553, 406975479, 700282607, 991072060, 143761665, 205982259, 30642776, 275375479, 245605564, 766737406, 407851470, 191062190, 525544453, 153780530, 10421766, 140799051, 392928928, 280843058, 821236007, 631333434, 635215453, 248402321, 937788815, 72044985, 890611621, 10147858, 676754560, 345534656, 32559440, 844262575, 471094814, 668380883, 152923508, 864887442, 899147803, 146522142, 619893269, 904063993, 980959299, 17150378, 528214395, 444716040, 990071608, 927389943, 378599249, 446621607, 841972469, 32795226, 722282104, 720261168, 467172106, 246005510, 455378815, 825125912, 457469651, 233738488, 636262416, 988515068, 610880712, 240708682, 464614072, 508121064, 273734715, 724018460, 406248114, 819573316, 389480123, 754423666, 269632111, 484351060, 377506662, 836846918, 334200284, 996755336, 83810651, 508330135, 405635337, 526617590, 47372767, 848216741, 258066641, 158948863, 974101866, 368918931, 118097675, 813438795, 619022760, 486371176, 803576005, 842550323, 743163740, 750240714, 476470279, 11364309, 357570110, 660183537, 541629835, 932447001, 531834079, 960099610, 293174493, 403373460, 899679282, 395704691, 129158990, 425619118, 322278534, 69162083, 854374699, 160790968, 568505992, 375937160, 292226864, 489602891, 592318467, 665874541, 32410786, 541200510, 735175232, 645616187, 950214884, 541284883, 401592703, 231399784, 937313666, 90216720, 228580602, 485555374, 166538342, 265462323, 23756766, 525417941, 701955833, 844324218, 713044453, 445574502, 635154860, 178156544, 247923951, 317993182, 408997205, 430323575, 190753544, 501682675, 507576536, 231724313, 216129339, 276572210, 787047829, 448877830, 350399397, 740251685, 2029556, 125827364, 9720103, 613413502, 662423514, 923025333, 41438773, 732985370, 348679909, 61953944, 964351693, 410153055, 57866157, 966134364, 711537040, 101211651, 257982247, 143578616, 398988814, 552709927, 451018242, 584710128, 924583727, 131558786, 153012350, 137005425, 135912238, 61862659, 8316760, 789510064, 531319985, 151758476, 934330954, 261081578, 456775597, 757866027, 980445506, 767581562, 506218578, 529221351, 83488313, 170479781, 515864736, 566517428, 853956136, 640562823, 837595294, 740226930, 819097646, 188901923, 305840696, 872888504, 261108027, 909240493, 372742861, 905000897, 244161418, 927668965, 916721776, 719840232, 932571658, 210953855, 596632606, 549127667, 361573946, 456148879, 28103745, 644080117, 853679358, 735666210, 617399189, 616553771, 386903702, 309078903, 996612425, 730238287, 250237548, 219650787, 684363436, 899662855, 974059561, 538105865, 396537964, 756632688, 529105993, 196851213, 746691323, 791603510, 961211942, 61143769, 186115353, 648618053, 513560917, 882096103, 88234541, 205840694, 406674654, 311719722, 849857064, 299504283, 749639404, 257264649, 182199771, 396099271, 208873983, 405175777, 875934703, 341655925, 962753860, 822114661, 578819847, 381209260, 266925405, 912737611, 416707475, 612658208, 31803521, 739120346, 578539318, 504071236, 806260420, 285253180, 538009871, 730383202, 332274253, 996086978, 725669422, 439470908, 688128076, 850264051, 605845975, 76867300, 205272873, 724324932, 943070788, 725363719, 676780928, 97266156, 428404864, 943520247, 441515836, 201106961, 36098041, 4739314, 493912644, 832735567, 163481532, 582041783, 170764592, 650221198, 946018612, 322314229, 748571077, 379816572, 586661292, 428006558, 370132161, 802282623, 444248675, 181759840, 351265130, 749121583, 852052034, 725417673, 164285684, 770047162, 334483899, 430362845, 390123182, 870135413, 803584225, 793437067, 824312937, 970146068, 788311136, 543506023, 804301167, 752622039, 540301731, 640017965, 499767210, 843048397, 854089291, 712137856, 88531335, 476199734, 152335167, 956907969, 538971803, 770665917, 190208944, 868352979, 192498771, 443251189, 590147482, 549023396, 248740373, 153209675, 631651963, 773747506, 340955872, 350965671, 92697539, 258451474, 869579626, 326258365, 983455425, 183976154, 648924781, 244890518, 774592863, 31192952, 547129396, 494322110, 456923182, 263883266, 435220227, 420002985, 290307697, 986299954, 87249600, 294350773, 434451708, 508543693, 779211925, 818313330, 707932192, 290469089, 668197130, 900043361, 73035275, 506878982, 252985310, 345295428, 789562656, 287394615, 797451620, 925785767, 792558285, 159977711, 78925352, 993487453, 334177970, 342921094, 511448829, 15850479, 776429566, 433027852, 520831252, 727224928, 691273211, 264928031, 169300263, 83417090, 53288926, 305562350, 885439117, 491111409, 964145974, 639261782, 345535362, 20613281, 614466950, 328868180, 766003555, 255544456, 756740863, 386727787, 748172967, 65815221, 555817059, 95220081, 15853131, 919942678, 863602419, 45544613, 926697787, 860789673, 446891794, 941664860, 744698469, 45025348, 441219268, 140509801, 45336732, 656410701, 242395616, 921269896, 846672053, 429427950, 669496324, 835883336, 278021621, 248465988, 581092471, 775167250, 251539924, 915093262, 542097875, 417291982, 817104046, 478433663, 674094814, 869122582, 446417409, 433630711, 928868810, 448614954, 505643948, 282447173, 695869564, 529581387, 47988822, 639371426, 24777752, 514961251, 93649069, 497893770, 22316839, 137350887, 444335474, 488663110, 986766162, 333978433, 905809792, 187054730, 930825084, 873574930, 176134506, 512099051, 246838058, 656184581, 23252154, 439178962, 15755469, 969389312, 391412123, 152620629, 303968963, 363219254, 287298276, 743640890, 274396361, 713703030, 383468542, 203082923, 595418052, 667770669, 748193089, 92017290, 19659217, 113184924, 208004857, 716355491, 116107415, 337616305, 871079396, 897634781, 100558424, 674189619, 591295890, 306773205, 651004782, 952699771, 142735597, 91390389, 471245802, 820774578, 296208289, 291575718, 294639800, 245714237, 386135540, 5294268, 796335947, 720693962, 957583684, 189972791, 208698220, 171684462, 74297060, 7469724, 859129268, 251397320, 601173843, 390711530, 817822477, 379734590, 243180935, 347927862, 741668655, 559320876, 909820770, 511447022, 796338637, 774371799, 293354888, 522226980, 738335346, 346275787, 737868918, 227879827, 891281094, 74251130, 24927070, 550970274, 63423825, 489209221, 178570911, 612641408, 7422008, 200856837, 189608648, 794916968, 449390510, 878934609, 955832656, 471630374, 91144625, 308824664, 479970041, 210700549, 622641693, 124916219, 553879896, 956028250, 802617161, 236645684, 808178082, 777969925, 733591597, 182245557, 233888318, 939181044, 134595223, 355279242, 999944373, 387919187, 744953800, 821063828, 275084509, 709818802, 333682414, 615537007, 419706286, 818903042, 982048258, 262090312, 177257137, 621449714, 33701540, 602683951, 16452984, 982145135, 394688684, 316606461, 936675536, 708799782, 524603168, 396693413, 986516729, 660723780, 79286277, 572727270, 2726978, 240725203, 162789439, 315240206, 56726029, 116512732, 586698407, 962959964, 140263454, 638553615, 774049295, 672290686, 971317601, 313594448, 449511041, 505142517, 34251915, 75063920, 241481976, 962308364, 443754540, 134385064, 11195150, 163984102, 4740512, 491365924, 203896091, 882164216, 395923652, 495885679, 87821624, 770745437, 391137795, 533274034, 901137904, 996697947, 992062520, 432535533, 12599682, 500649994, 412300859, 735178663, 218888479, 415938128, 571357170, 285727230, 515340697, 164038464, 43533991, 776869848, 249863371, 312161875, 402999224, 895312893, 763569504, 733952035, 846793158, 771129590, 268090959, 787051341, 148336928, 473088661, 197069026, 38229997, 730148584, 297718281, 958736504, 748458521, 594161184, 671721124, 533534159, 950038524, 74756281, 79135860, 319825991, 645331207, 371068393, 695822088, 302270652, 767638409, 688358464, 837868861, 849780734, 962237991, 522558006, 395484758, 682766097, 16361089, 816937412, 611939951, 771498203, 53621569, 291977802, 413357154, 635002443, 195239440, 888726287, 639019404, 495608347, 708070220, 808840523, 724732485, 113975238, 74843776, 124503920, 214391321, 610896627, 692497913, 474725934, 559371529, 97275277, 230836638, 347402227, 245694742, 765378777, 618414039, 753746797, 132968405, 267081447, 779649269, 800771578, 921938820, 409362623, 969828205, 890654565, 395576007, 803703956, 242756250, 270789849, 603119367, 116825181, 343561710, 912692738, 618158550, 608251798, 456437572, 231751207, 31005240, 295249523, 988314356, 462559127, 184808831, 852136864, 694443621, 819461345, 939776453, 315110599, 480273991, 999783923, 253575699, 711589164, 259392032, 859096024, 344587124, 338845850, 643174941, 526973938, 881429444, 647523630, 136080655, 345792269, 670669505, 261953461, 806988588, 243885670, 89074968, 251508045, 123990352, 355717592, 373224070, 350011399, 45148301, 17813173, 164960026, 177159562, 473271673, 303880953, 734332434, 372784867, 16400546, 190003751, 125437115, 188150537, 703131213, 326726922, 452036396, 713697149, 493496752, 681882033, 984853838, 27323121, 157303719, 557053130, 774742937, 463003592, 532121852, 39080311, 525733950, 967257685, 567953936, 358737195, 73273666, 463690716, 193975314, 888463742, 468880215, 706607046, 935760140, 785475617, 776411565, 70836758, 437325962, 772126328, 894284762, 650183427, 270758350, 435376331, 366629299, 957134091, 79119975, 811363375, 75298555, 219172023, 521819137, 776693441, 115826538, 417083191, 816404524, 768678807, 468158489, 611540046, 837202708, 124146330, 638173974, 959833994, 825204655, 225522033, 67138757, 573628640, 818177130, 24416892, 646103445, 282525871, 786904601, 985675157, 410944775, 896948863, 153565371, 109080698, 203284910, 941002385, 148295523, 18528309, 581733580, 923449471, 15437561, 596873007, 547799823, 761818431, 936184776, 563609848, 1308902, 998617150, 94095691, 48982007, 804373653, 352191837, 371809712, 575068048, 886492383, 267247708, 563456277, 734135647, 833266225, 936698277, 91933289, 771727185, 200339196, 306169634, 332934076, 357294183, 822442030, 964102641, 407529302, 371396372, 220226037, 343755268, 954890262, 88747962, 874475836, 194094536, 910803884, 56537510, 102384885, 663183802, 120827874, 578897199, 279997250, 733267979, 174469010, 414424500, 525908301, 725061590, 605172742, 809544525, 139333497, 224771982, 717294498, 512276004, 193885389, 775554451, 105763857, 468754783, 414557985, 882471326, 827221775, 500836905, 638381517, 60475790, 103151579, 469143485, 936544308, 146524581, 81866401, 740101186, 969633949, 325798399, 578522458, 202469898, 235885151, 939507516, 376009849, 767439757, 291384868, 478001368, 615616258, 365282993, 669890695, 467478772, 734273660, 557774538, 170584927, 881747930, 467743870, 442909211, 824224610, 632567989, 657039792, 268578583, 931835391, 403476323, 570772594, 443933013, 272847372, 645732218, 210044015, 742193848, 436340814, 118186002, 582174359, 544720065, 801115746, 777671852, 623558757, 869994653, 428643606, 875194441, 572054508, 183439514, 523025886, 769222341, 190609087, 22739637, 979781033, 485595592, 865280597, 778266911, 9342579, 171241817, 573798180, 238125379, 953304220, 450124162, 98163058, 797252025, 461616112, 667235662, 372042198, 819016394, 385146022, 320767184, 531139172, 735202589, 628464069, 512675241, 771942912, 764277019, 904796809, 711230592, 374357834, 163713171, 145793072, 914399036, 498387216, 691938080, 747795292, 720558281, 101872978, 683289749, 157987221, 660215200, 700944821, 106973117, 304066205, 116254904, 193486252, 459057911, 637392529, 247926939, 225046692, 441379297, 572856727, 341291842, 500520246, 677726802, 780755629, 27326501, 312569409, 674292442, 957432785, 706762126, 307559752, 963344965, 578196513, 38165466, 795634680, 124713744, 77348197, 597564905, 11248521, 19966129, 12904531, 936251698, 477237950, 569752229, 386342691, 239402359, 811201508, 286743747, 810712440, 746477220, 943370251, 28773731, 531432119, 971239789, 856111477, 47535991, 228913436, 985197257, 261769297, 66491843, 783730602, 874641795, 363011645, 690040530, 161776039, 481282672, 993731245, 347330386, 999419656, 761374725, 374898652, 525020419, 689278608, 693498760, 103280479, 495359812, 254281105, 415478985, 286154429, 198788705, 672669508, 18907284, 827300254, 444788721, 946892535, 702506291, 856979387, 616270732, 277808218, 516086014, 293331019, 700120643, 340366773, 768237747, 345892779, 886896310, 94156298, 460091118, 67635884, 111489831, 961638285, 633342594, 487818631, 401882813, 361022353, 4741423, 512093324, 172006304, 264470615, 778821705, 584035285, 218790850, 291807706, 918774413, 284877859, 365149299, 359198909, 61502194, 217102765, 199268424, 132904604, 578176025, 823317120, 31698291, 273871716, 184107416, 628405196, 404809581, 807696550, 900404616, 207273508, 621269746, 82459999, 227083480, 303386118, 804292328, 669513551, 132529845, 351125898, 476009963, 568227391, 125548270, 37450086, 585492516, 549598410, 383935354, 306007563, 736118080, 63358795, 475388118, 432827859, 578163832, 227400522, 545673970, 920560168, 680712023, 904908656, 497855397, 158298627, 153056903, 651279858, 716909531, 150745270, 980106004, 866009884, 541981208, 554582634, 838940931, 168308186, 906877991, 582777507, 610986307, 404051157, 452808940, 947904766, 547076732, 56365405, 416857196, 704678172, 98406193, 923382135, 525205003, 421352948, 33182597, 341931115, 736047393, 875828447, 707611339, 781310867, 671543651, 621336815, 763850320, 379647931, 87953949, 239208326, 425240153, 762601614, 977071013, 274243585, 188688423, 753192009, 95254331, 565184248, 533998256, 664776200, 259327873, 15315868, 509194929, 708020909, 903480374, 577885984, 325795035, 280684933, 537823941, 598961854, 338755630, 37637137, 672650863, 471780445, 812757869, 681240043, 665725229, 102174080, 42292607, 377499880, 540012138, 129226408, 40154655, 774054050, 381466278, 350898260, 366733710, 344226188, 499687266, 482230356, 912063005, 277557616, 61656313, 859915225, 992495038, 413870396, 612231986, 722729598, 50638139, 675562891, 986316500, 251241396, 876878276, 218404821, 525302962, 125367725, 329163963, 741403165, 992040021, 365660473, 125739701, 997968259, 782440029, 774526571, 435664423, 314157187, 290117539, 13952527, 830435777, 950001601, 660036508, 467212272, 860958686, 452520275, 691386949, 456654675, 261332633, 919161872, 809609105, 680062353, 367029625, 49542602, 401103159, 673264224, 504636814, 843417052, 734449567, 990865679, 207367628, 538261839, 456077462, 198919878, 739090900, 869918371, 656163239, 952244540, 911418500, 642080723, 350498977, 244782485, 910241605, 799239451, 501632167, 409555123, 144400747, 844753750, 283785929, 4173308, 323357722, 823479867, 324965153, 793243293, 276691601, 808438059, 3281846, 875349389, 730308192, 150810011, 387226065, 506658274, 288715654, 323110351, 146950497, 648779082, 180159557, 296087035, 296271878, 506948932, 567197614, 452463299, 174597069, 33292814, 585649597, 91474573, 138020769, 482819081, 432865626, 321197628, 2886362, 908035030, 483823609, 462850633, 101153297, 639894833, 425596445, 295327255, 505262432, 944309212, 48681306, 48718169, 335237280, 931923963, 962351135, 214482413, 812411434, 838847499, 992776077, 219282560, 454265805, 168485632, 896727156, 441156067, 273904320, 126808874, 281599382, 155104785, 200127013, 284684230, 139724142, 513540990, 839065980, 782174405, 44228578, 613209503, 379522442, 219560983, 211186397, 647134044, 847868491, 684301397, 296202598, 871065193, 733731867, 438701577, 678411429, 475023110, 119364071, 764919230, 347210024, 87019795, 744052329, 392976664, 271883482, 306165651, 805909638, 534299423, 874841274, 6828585, 634589078, 667308915, 279813852, 704241054, 652227408, 1614326, 739079039, 636522289, 556286652, 738283406, 265181198, 160984179, 698859532, 403698731, 715669230, 970996642, 188534277, 408897714, 812666454, 847574147, 457814403, 275443128, 38185239, 827757202, 927311241, 982636682, 167001997, 874099600, 210040637, 613235210, 269283093, 167699395, 607459984, 298775704, 365541270, 72434761, 351029812, 806803507, 181625451, 625650379, 188156669, 858954681, 471249059, 13466540, 428284661, 763089680, 325386220, 614604084, 721509160, 722822172, 973161288, 545012456, 190730320, 383852758, 398207300, 542539145, 928760372, 319268649, 915628894, 997865339, 182679674, 718448037, 136147762, 47145648, 302092280, 93367414, 949792306, 563942879, 781410385, 120752464, 992840124, 145718807, 726623406, 177506726, 731579636, 565252491, 264693739, 503673858, 109310659, 777072993, 319112990, 333880705, 996119154, 778022976, 970385538, 230947093, 909431712, 379002431, 643416566, 359451875, 486968759, 123825809, 206635333, 271883387, 950440731, 346347980, 262377791, 593295679, 710940709, 882391157, 711428011, 250356985, 736631543, 10356909, 103899879, 15813471, 618002643, 69414573, 800005026, 328139084, 794229752, 422311852, 131027644, 929371485, 797038235, 46322499, 801433840, 6558369, 667293686, 659137526, 588985971, 180848056, 609460268, 142573644, 813458828, 214596344, 144550552, 631266129, 424363514, 407743670, 952172089, 834626903, 423688998, 895534681, 491845087, 709808919, 12459090, 992377737, 343258527, 391634415, 278311470, 300081844, 51270685, 629104085, 54482902, 78551068, 584964749, 699084490, 576068982, 19058576, 409656022, 197127468, 473481684, 731955272, 471765979, 801762552, 952737855, 979816431, 633605975, 581445995, 505851196, 395823780, 246785367, 503652083, 508637724, 725383239, 993435550, 538731525, 956957156, 552708661, 924850014, 462853336, 444439742, 87446781, 727458445, 38320020, 36671746, 115204844, 202238406, 347292502, 171180421, 386642362, 500456810, 934113742, 854435605, 777705164, 576520296, 260112655, 905629567, 812491290, 753331074, 903022037, 652836948, 31104681, 629940819, 166897397, 886636029, 493110497, 304664285, 105779413, 219044877, 631119367, 191383959, 828445065, 857831740, 689421535, 447225042, 227805061, 587504462, 805211232, 148768865, 372462264, 219677492, 960950965, 829993546, 528964310, 320154993, 947011351, 369774587, 66812485, 732518214, 57593619, 911587584, 742997392, 386921474, 573370516, 728697045, 854186016, 638574540, 236661121, 476089652, 266026356, 397796153, 332537293, 678377484, 284386469, 340915401, 941373972, 40025987, 639009437, 603909736, 38933994, 586168782, 113257000, 203508612, 860880800, 500534748, 424614870, 968467236, 770195745, 95234854, 91442004, 157629335, 739885045, 119326123, 288360126, 901452812, 972195734, 981475532, 851036124, 121955998, 778696465, 61453922, 914464927, 714216008, 73604002, 885147651, 300904332, 21661649, 722704185, 235467674, 54560071, 804973502, 10450977, 846797643, 686915502, 561480489, 494846242, 303774905, 130965248, 532715038, 732648768, 901436768, 43150797, 935639404, 478782774, 257836868, 764434247, 761544994, 433477780, 849978003, 457922964, 810813028, 658240779, 584956513, 65790954, 219854634, 904617536, 708107373, 667840074, 31614874, 615187792, 316076381, 976010563, 511733268, 117010101, 1292606, 560813703, 942276056, 698079328, 594511896, 119300251, 154950650, 945850289, 504263788, 205008557, 377489257, 667256472, 175034649, 152879964, 251736818, 112656014, 391202766, 415723578, 905649447, 118948527, 550562270, 480965627, 375678388, 131080362, 250901869, 935100903, 51846293, 619945275, 250809867, 480017684, 828634136, 529520506, 475677776, 398375741, 864889281, 494606168, 442834514, 466647942, 472862711, 456188664, 281911103, 951213216, 318087863, 233359795, 610673749, 420165678, 758714910, 346488071, 752674169, 162943617, 154565109, 370746914, 173633915, 909033317, 28450764, 55670036, 668516678, 612769868, 583213979, 449473498, 931259482, 693641491, 231755199, 939188441, 653921879, 65011084, 52895272, 803729326, 9586877, 206603123, 678832142, 700552707, 569213252, 381267935, 861455641, 618832427, 116287121, 751153593, 237366289, 43873260, 951589064, 681358945, 579904839, 609022318, 436152159, 251445660, 974016264, 429581017, 247505609, 851031698, 817388570, 196024231, 952477523, 351280234, 388425801, 956067601, 754162608, 943382672, 453923534, 116867739, 910948578, 941367448, 215110481, 673853563, 189392957, 581141292, 958153298, 46127430, 622768555, 433398900, 117171927, 212151445, 528075919, 934233203, 770159452, 657635015, 804088552, 176197443, 302962126, 36186348, 440354211, 289620259, 721043532, 115315345, 246019686, 249473643, 487739654, 55559175, 215558696, 510826942, 470747763, 90398917, 232449158, 429543925, 959052625, 203775240, 468141788, 730490332, 602765164, 11773026, 323725289, 595754818, 582476176, 358365956, 995629554, 680395094, 105845147, 348263099, 431300280, 879600419, 302610514, 29732262, 553681565, 932427827, 237957927, 865148877, 232523551, 682475954, 979390965, 229368229, 26360570, 116242371, 828888227, 320209203, 734772277, 852803970, 302014516, 512335057, 221480844, 248099226, 799735578, 954085926, 553536015, 761036762, 107990690, 651105288, 587246802, 204952894, 361105638, 790354143, 180278959, 60381180, 212451925, 902007238, 921870770, 279126332, 814839603, 92177996, 637631802, 610074326, 937379062, 137032331, 304972664, 512393775, 324160089, 836867040, 786163813, 453203323, 110393808, 193497763, 241882349, 727311755, 28221252, 508403456, 334746295, 177487303, 91462779, 805513814, 29431800, 527185960, 563343885, 978438645, 538323264, 549260650, 14874566, 639459964, 239697967, 873507965, 733486447, 20085977, 92307584, 114340161, 13138609, 719497218, 868316651, 290988561, 256770239, 363649440, 847210765, 480414596, 539462598, 499116711, 409254856, 286017419, 650058223, 287238789, 699834521, 270926940, 182820975, 313710972, 970859785, 856814551, 656338026, 602818868, 96775278, 127445212, 636341906, 722917462, 965145553, 897364420, 504396218, 777285133, 432599706, 181141054, 733206405, 607366814, 75907181, 895747552, 810792325, 515632398, 225327567, 949128705, 99222460, 407408100, 483146402, 678340923, 695573852, 919956035, 559588634, 104511822, 65680753, 576297824, 261712887, 144868617, 662026610, 998510501, 777907990, 517333863, 572675298, 891712907, 972574561, 743510749, 943354271, 345466485, 615886785, 291199249, 498809707, 848652126, 214131802, 814217990, 967373931, 706100198, 446080420, 267741250, 316967629, 167220605, 3178762, 36415014, 252113733, 250154199, 348883691, 13708362, 675436544, 782753160, 518384150, 991621216, 282763668, 654180469, 926216919, 121641279, 279960576, 705942658, 918479310, 54624889, 604563073, 977470982, 273012623, 310161307, 773398779, 104524466, 962054305, 347991844, 277969641, 112623080, 162724401, 839576431, 405592221, 434512985, 530765168, 427801523, 328710612, 757505195, 123515440, 87678820, 316612436, 97763919, 121123138, 898150743, 414576112, 414149919, 722575463, 421896490, 413314194, 202425277, 250622499, 417426446, 411582548, 419860211, 194003021, 158924727, 981926763, 941780406, 389458974, 787873981, 845188776, 13566419, 582638586, 746396024, 325660982, 923621322, 467527458, 17818849, 852593631, 263086441, 45753567, 490726169, 237520541, 380011844, 774317335, 336547522, 269586792, 151008625, 740255617, 931428257, 609880130, 288096361, 746637595, 612018192, 641271337, 227249234, 756120102, 748958187, 302049196, 32007000, 809386542, 158615615, 754400011, 607022563, 377599773, 372702169, 263783945, 840440052, 852129992, 565938786, 382330964, 286007911, 785319183, 593950854, 770413809, 793635746, 310936922, 304828871, 31957641, 516755351, 903577238, 92467336, 314103951, 764323686, 792163727, 94081814, 514942048, 475285747, 283490258, 262758507, 329771430, 363219535, 847365448, 356798728, 848163611, 893807770, 85954412, 744126810, 171110327, 121359554, 972825547, 8445835, 687563728, 48635913, 656423681, 355884515, 187107455, 387546295, 299658347, 511290540, 263346770, 887759033, 422290240, 361089437, 8163312, 221030083, 627019253, 653314071, 900130846, 634367720, 831311405, 222655595, 744042066, 173440680, 625260596, 946327937, 776942952, 610786018, 755989691, 62069772, 443132903, 843153893, 587579624, 45371046, 719465587, 124024647, 223032255, 137314976, 300667916, 893211863, 395724731, 334410165, 176441014, 95923563, 376878521, 261738472, 205290095, 501620150, 945626942, 547251130, 419489936, 926610688, 321236092, 4236328, 377980392, 626925884, 289968609, 627029437, 599533113, 288561448, 518505559, 9147511, 487492857, 765394963, 864152528, 411982317, 109668007, 768500566, 44825601, 99231078, 926210818, 44993340, 908515, 624500352, 168913121, 997667177, 863378081, 526522814, 165702724, 342319667, 586688983, 408340652, 757505783, 615584855, 805797154, 809978326, 952937658, 288222693, 965117803, 582485662, 561822755, 45558329, 251172642, 22432428, 870554529, 326162129, 747000026, 237414523, 58847311, 453195873, 48380823, 260586145, 852676687, 594346504, 244648051, 264899687, 799324535, 593619599, 84395101, 884591462, 845568986, 998095839, 595915468, 868654614, 664182998, 480796496, 647153516, 719862953, 661984358, 170354532, 793742913, 357299700, 188435057, 235756830, 194405279, 236770536, 257133360, 293037042, 863977236, 651346447, 991430794, 286100808, 926643536, 756084206, 345935782, 982899412, 977923230, 196345232, 630335142, 807278270, 268830178, 93889089, 484093842, 666079102, 516298948, 406568144, 409605619, 796462949, 237664246, 111154420, 960506509, 991437812, 559423848, 465931725, 250017006, 746803006, 563384317, 358420260, 580727756, 408980340, 241609705, 580191923, 188519983, 228118097, 177007167, 523052855, 808598981, 431832022, 423673902, 248528135, 327671949, 426891675, 611981642, 892566593, 7307647, 533773911, 686774148, 249569766, 163867373, 283744701, 82721918, 654080737, 909270194, 903140968, 385455295, 671477071, 491542334, 920637261, 236986646, 766080349, 585165756, 838314528, 816476133, 388175881, 514335999, 437588520, 417414189, 631682722, 675205970, 457411379, 959453668, 961209223, 769384693, 819523313, 873141058, 116447198, 728417923, 753371459, 154949945, 542735613, 487060943, 882812110, 142565477, 800205371, 358590264, 321280648, 102450646, 300882588, 614492721, 456309200, 817692202, 854605164, 101124969, 740781265, 116100176, 957743873, 680075775, 758721253, 54489248, 524149223, 239717428, 252172685, 340525691, 125510251, 918553289, 488042626, 108801582, 780799243, 352111897, 181622311, 811024627, 535749964, 324736157, 248258340, 351073554, 389106812, 927510314, 437770620, 854529822, 754131203, 7757931, 604161376, 468277743, 655604627, 569434724, 522567835, 541616188, 982456857, 504098449, 106509763, 847769641, 67891405, 651104871, 735935946, 532257383, 848953301, 994007369, 610245690, 734533700, 857391902, 538665366, 982098535, 79343308, 294349734, 641058829, 937035649, 859296659, 314677301, 239054246, 939107102, 930400261, 728356721, 933926359, 98100127, 137447457, 61815460, 335141963, 596183239, 1187022, 710953056, 25592530, 44612064, 953909775, 529971536, 792046137, 110481442, 175578895, 818948302, 246925447, 398000332, 851655331, 404666359, 917464499, 96982756, 711193540, 89260413, 47067766, 327384333, 383607991, 186061891, 942912815, 523051586, 214222380, 742640466, 874934640, 243398170, 231737669, 184886801, 739514818, 218425261, 279510148, 959787098, 877874132, 881987745, 679400311, 901969281, 585212232, 948232720, 961710174, 403921139, 492296035, 194071736, 597079811, 374134034, 878384932, 874006747, 581848941, 900936814, 880393453, 25667541, 278261704, 222085322, 720550001, 953055197, 914358473, 435626095, 630020120, 769701290, 633845749, 98269108, 713365129, 103979240, 367164642, 557876963, 944102529, 753606546, 289332769, 70465398, 603272370, 459386114, 673094460, 43838395, 297341867, 964786667, 232772909, 622263677, 144829348, 501684068, 896388393, 924969257, 936915746, 516481408, 405569183, 29558662, 495646991, 289431512, 557699616, 7501238, 727012277, 948147501, 34145683, 137401428, 974160178, 318165600, 107313564, 107406030, 393021878, 340286212, 666424799, 296444505, 566368293, 266873575, 446355346, 924304095, 964072263, 968874652, 959618286, 232282141, 452028839, 826400427, 532283986, 818818791, 382176056, 478098245, 67882647, 308092028, 260856876, 3457481, 985368990, 261441690, 581712704, 546436609, 809705213, 545994031, 276093631, 747095232, 382513057, 230886434, 438457193, 436102064, 374225527, 439731591, 60647842, 905925665, 785270879, 965331315, 159180134, 587963709, 953436598, 926204028, 370392469, 966283173, 37003108, 747142544, 158861735, 475047295, 83663503, 739324351, 433906572, 521638365, 278404615, 251119225, 364091501, 338536656, 139441639, 42735594, 809566988, 21093943, 924022478, 180869269, 270352803, 256027856, 566078048, 977909478, 623709839, 300363026, 948237158, 658481210, 981378974, 511775637, 122486036, 763784148, 124151564, 723847934, 13268154, 90383777, 323758762, 773793386, 565154912, 836470905, 725190378, 569415589, 677126853, 536556818, 104684668, 858329008, 419739683, 688645326, 41860298, 48032538, 45904702, 395185842, 1640228, 345937286, 674020041, 16511659, 844621541, 174002318, 936536402, 676546453, 407745788, 953891355, 78878659, 562728643, 77135100, 368034838, 479284688, 404162490, 311175989, 718162204, 104689624, 713096437, 204784851, 34372940, 198425513, 499722287, 670299088, 945120283, 635655700, 27302165, 359473227, 803185010, 588911438, 55575673, 398644645, 777110027, 422533784, 924844046, 790377972, 654566452, 702052308, 848372942, 294034546, 666728692, 235768147, 696379602, 81489489, 326639784, 284373271, 695243422, 316951219, 479521523, 640677205, 863065325, 90930448, 168711740, 16843037, 915943279, 148376702, 109753840, 527291303, 367409286, 34822599, 702644237, 874755643, 217631356, 965211867, 449739939, 64548407, 267981586, 366172901, 40822324, 767966957, 884729004, 145385261, 697343929, 733231933, 926913228, 955280859, 470528608, 710845132, 982414687, 479798064, 246943271, 507795372, 17241474, 64518151, 798854512, 330055312, 808017883, 426193365, 68162668, 291852792, 260435993, 306446533, 714876174, 70388460, 552029744, 281480685, 94417272, 430110919, 917084240, 12938678, 181059049, 973154529, 845349582, 265236303, 557347214, 511271848, 507504978, 401702677, 246018341, 152516763, 622880501, 199564864, 176245725, 839872241, 618732496, 497385206, 639982398, 436871079, 861447484, 875257226, 565783044, 71065747, 839515178, 967951118, 812508925, 901430311, 590520787, 821781088, 851340042, 554256785, 701087946, 968011512, 865229319, 182229331, 116866204, 886748327, 770519673, 930679327, 842887427, 569863667, 612256079, 656683931, 130210047, 981761661, 780347359, 251629071, 439898275, 939274651, 611681530, 250930355, 544357562, 694224198, 932519560, 997166517, 646808064, 655465947, 630457442, 455456943, 346628156, 874007566, 99320080, 696522974, 979023826, 376705062, 438076113, 265524720, 275821890, 376292867, 515070372, 736311621, 510575944, 946676288, 429560765, 615919007, 833670957, 382311166, 844582364, 536117514, 413878435, 853188460, 370867564, 66110392, 318599706, 75975578, 692105133, 525208823, 42497257, 503845430, 189481251, 905562611, 519580585, 41242770, 502129013, 924307135, 167575824, 138759470, 372501640, 942829308, 186116292, 304670391, 501952292, 115171217, 153077942, 612710653, 922289003, 197269705, 621545443, 656243097, 970264032, 844948212, 818700517, 174476272, 207771132, 759667224, 504383985, 361080600, 521980256, 356992871, 855088290, 862723238, 657427431, 179980347, 928468188, 412759140, 922548902, 755184409, 487738407, 695984106, 112272952, 296257549, 650844035, 449918874, 486925342, 688446394, 642391750, 795224552, 147770469, 508901234, 837072549, 559603851, 577605399, 396266032, 52001228, 254139571, 699675475, 169404752, 144599070, 309352598, 51618838, 876154176, 538509454, 864381232, 421154320, 246712725, 453756946, 345405532, 822474994, 316938768, 633470870, 445802341, 539113621, 886293781, 628205606, 992315558, 769866220, 738683230, 612005824, 56540630, 717704787, 21482208, 907250819, 357130, 502687581, 79502010, 230288558, 138634138, 169593090, 255265523, 748235270, 752937271, 51596506, 541946888, 102292915, 532098777, 182759947, 605221563, 326256103, 817936537, 973086478, 784184016, 82259282, 235728721, 981784189, 337786545, 361536570, 190380152, 685203910, 781579318, 183296984, 582232104, 360395579, 798133757, 691016473, 543722916, 484454691, 108653181, 571522355, 992980307, 309485069, 525326817, 632672603, 264566648, 719653176, 309433444, 151728885, 231957623, 107857136, 514824071, 431842894, 68518660, 916242510, 701204075, 85973906, 213832517, 103640321, 369877194, 85729101, 346303850, 315015703, 672978270, 287377814, 202134729, 611393636, 403562409, 165842018, 584995614, 295452305, 309519274, 170870911, 683872506, 886883806, 235053826, 227293911, 943628195, 600224401, 7122259, 972929122, 645599351, 454004453, 233332719, 889730525, 248198610, 458417832, 682186820, 869013205, 54365894, 709009404, 799798115, 410846442, 4417835, 711182514, 378837885, 650522744, 918371365, 647590678, 579026969, 943728025, 66011418, 10169057, 818346426, 333834745, 472990778, 685565933, 232464859, 246584808, 743949618, 453971377, 276498849, 209746466, 680827135, 428463270, 838870436, 435986140, 368730351, 822843823, 218470313, 884795899, 669993875, 678701200, 941669540, 688715247, 833113471, 838660794, 305437209, 656915902, 743556817, 687695305, 299689091, 930034036, 210111369, 141028115, 341423089, 472783949, 497221735, 230407912, 26077260, 505828066, 729417310, 143576420, 282689481, 469725505, 701287021, 128110628, 433695197, 394061857, 194998492, 45993487, 912571898, 440634275, 665013495, 972337863, 211764963, 928077407, 245008083, 575628889, 322899592, 760233415, 405831724, 804687759, 501107951, 502389022, 971665126, 442221281, 298853439, 101360727, 584569469, 498411739, 344377724, 875156790, 993802358, 752775020, 106859738, 452738907, 193298189, 361331455, 235836124, 399510995, 654818230, 714476965, 300681220, 473584257, 890448435, 383918534, 656254603, 138328291, 178210209, 592213984, 975289560, 685445819, 757205261, 948915729, 608094660, 380966425, 95448214, 520009842, 476053742, 709055571, 616303535, 868276977, 363667008, 841300276, 684213122, 415125470, 949854475, 943266552, 488814093, 101704105, 761723612, 145856845, 774918522, 710210703, 477033366, 458019695, 938515386, 34086585, 750193004, 995077123, 728322838, 381814060, 223336442, 415384026, 163567863, 132922109, 899747478, 686984986, 913637605, 941862777, 321293554, 869307310, 984163877, 691320939, 218640365, 938987215, 652240258, 542426412, 351882474, 573598337, 856440352, 39955291, 554049881, 817332453, 171056717, 72608332, 375190576, 361283705, 205884792, 745829892, 579994310, 41996303, 313747054, 880542480, 75853112, 369057838, 329509298, 74171897, 657955769, 571855200, 452836329, 422928031, 604220068, 555300283, 991751282, 580325719, 978018366, 259049723, 247988103, 249334673, 663807970, 309493521, 237539417, 712837801, 963843781, 1504769, 4900461, 329554218, 224874884, 76840670, 679038935, 439421484, 76460929, 251576189, 92535668, 440252831, 441710748, 132091696, 605816222, 723533063, 442798172, 431365449, 51800673, 284312277, 174083327, 211393229, 518024919, 363059959, 871685585, 266814661, 380647651, 315508757, 130789700, 457657857, 773116230, 796561670, 789966640, 261094257, 836404133, 729119724, 62213247, 347303472, 11458673, 25978952, 281169068, 608047470, 135767236, 982294323, 585233951, 416915313, 411717239, 598394785, 571780076, 672411729, 279578568, 833597794, 471998112, 123008043, 799039724, 802808834, 830270224, 184529328, 456569999, 954821984, 486293206, 278463011, 7685246, 84819281, 140556017, 692203678, 133567598, 564999305, 78419778, 236996598, 274247841, 887553557, 498140852, 481399598, 374757549, 485270835, 488789957, 509747260, 774783243, 123158113, 99190323, 787298970, 170058738, 997104959, 491498789, 544272001, 621450454, 354564728, 166132663, 692982589, 396437731, 913858217, 31223235, 419375383, 778317334, 99897709, 204956801, 952452182, 286639708, 487114935, 669399968, 873978064, 85292815, 554069006, 266760061, 340731430, 629540703, 217419010, 951570643, 65703842, 497860903, 270203872, 77957575, 201039482, 588673246, 126236701, 412613576, 214928523, 886776058, 514615244, 938371254, 508860954, 440148133, 181545473, 124266116, 294398110, 33886736, 820610484, 952955050, 513862081, 134177093, 64805392, 551142458, 556259701, 155161075, 791685422, 139847128, 395047866, 845478392, 983347673, 591919447, 224379994, 123106172, 281648961, 296006183, 241355467, 805850064, 179872237, 172751918, 830072528, 290415939, 179674743, 360678056, 932905737, 836323716, 860234088, 625267055, 735604296, 304746452, 450608117, 285156403, 477632951, 776423577, 463404671, 77003067, 231309941, 360929576, 315377904, 41300306, 377299964, 740772103, 670120582, 693307824, 32653860, 316794472, 487490095, 976499140, 58837768, 765813670, 844906676, 997295699, 679869129, 809587171, 690036902, 923119201, 695479987, 545173200, 486814701, 992916215, 824220257, 936457743, 72587498, 333059137, 924119848, 847948637, 832769483, 308702941, 62934569, 477855923, 955735990, 773841647, 988950488, 158221971, 636466098, 766102571, 741292900, 797670999, 715145201, 78801434, 374350861, 423381810, 919242655, 447709583, 828525243, 752928203, 291906123, 63985669, 700009979, 782112731, 494579385, 594020573, 333038724, 660867508, 191135361, 177869284, 555658350, 456809464, 660836584, 614908071, 465766100, 706835585, 111726452, 30201436, 608702093, 587348492, 196104151, 187062608, 181601722, 107434541, 250289434, 120171008, 498746495, 423065753, 285060756, 970242052, 207306741, 124769435, 834013136, 978213059, 741787666, 673445827, 33453939, 743489333, 614947698, 54220667, 806714326, 563894678, 444610396, 501043815, 215568915, 836417968, 695684892, 968287713, 184721167, 763328087, 991697667, 463423572, 176687400, 943213498, 96959835, 817309843, 390815770, 588313737, 702412558, 540838815, 326271915, 619630438, 666853220, 628283115, 737875853, 929370336, 345172996, 377185283, 241929081, 549711706, 235951918, 374295076, 154799994, 906109924, 633235263, 506036687, 213334009, 443131661, 313786402, 743592066, 93965869, 54011101, 663388583, 832946726, 580291197, 230019171, 177105228, 967122909, 564507974, 695682604, 170852800, 50441463, 434353679, 898206137, 907926027, 968737417, 140016772, 439093860, 752239060, 896481239, 43126702, 801993311, 308823126, 927029225, 481558953, 226101813, 127572935, 310221865, 635430167, 209969622, 639560312, 853972884, 641901144, 828608676, 106484630, 97043790, 860100845, 840952004, 957368580, 791915887, 483150727, 37982188, 991128064, 826842565, 432647175, 82628819, 655302287, 855184692, 429580845, 695554729, 316129324, 190915055, 409066245, 156059220, 23328261, 693862253, 939324802, 818392641, 216866080, 258569309, 936066410, 274063781, 390792172, 311504975, 263245672, 146924578, 50414399, 804937945, 115034625, 292717504, 3581614, 563259115, 180522000, 713513417, 589439067, 336517437, 387238760, 548603835, 892050661, 183227171, 954607149, 16641428, 908179944, 776724800, 718683860, 404185342, 116349323, 71282275, 279080700, 720620948, 956295173, 106145807, 423577804, 507790392, 321171137, 134408365, 403785983, 111066392, 283115458, 342501550, 839511071, 377677430, 82262042, 961566703, 507155105, 243782003, 248632711, 982094863, 268915551, 191222223, 736093402, 919200039, 596971678, 898165772, 799546243, 388848709, 56947441, 114238162, 666727135, 181786516, 615180255, 46390363, 311474212, 888937163, 101663317, 252768093, 116374437, 367908512, 92602292, 538048559, 596587862, 232418297, 560426833, 30948006, 982367176, 632192425, 894250933, 184947115, 302641906, 224338523, 943937001, 923218516, 86553936, 57059441, 194528482, 489213864, 568560835, 299370158, 987627967, 412507449, 227981404, 127645081, 133648539, 448934653, 125525298, 161726646, 3988256, 433682136, 164787142, 493261597, 598549991, 624288291, 322971763, 670821070, 193920533, 121808120, 383098824, 113921537, 231440112, 276361555, 625864405, 162707929, 537353202, 29330952, 475901080, 316318333, 165729942, 355266475, 183468202, 237509723, 259312159, 379654805, 233599855, 588667992, 817673823, 378056676, 591882471, 669866551, 832121830, 966815975, 907758575, 725607848, 794183776, 766898010, 785067573, 281129553, 70121071, 542014830, 923092187, 475549552, 612687591, 456587960, 692467844, 560973748, 768028082, 868314381, 423380178, 343952479, 788488968, 107513307, 745255644, 889911229, 475571736, 68154597, 990800257, 879207008, 870048315, 381077525, 685759209, 807055398, 122896350, 895019248, 768559884, 243257168, 410219062, 687988805, 537606088, 673530160, 92602796, 315659416, 980366244, 587952697, 643961042, 277975869, 662672302, 355201721, 396566413, 915777372, 673888402, 615882245, 86903733, 696973208, 519000491, 473073639, 686696314, 772683107, 347825758, 35035802, 838880883, 909700181, 934097731, 840377560, 860793273, 875991807, 744972257, 105903817, 181118811, 90715197, 917631616, 366163849, 124153419, 17181545, 368545551, 305480864, 154959180, 277344400, 75530929, 364138054, 970151396, 301377274, 563404168, 177720993, 199708042, 744037695, 887510871, 105202447, 368386697, 456176036, 329632864, 236215712, 457295169, 661086960, 204999369, 832901009, 49901591, 175952914, 441636434, 824281056, 666709597, 530432608, 485095725, 257494862, 198811896, 357634048, 989352127, 213344348, 329353362, 514014083, 438136199, 783672780, 705975089, 651391872, 599493257, 426485491, 257794239, 698569089, 764217065, 281645846, 717899771, 165507135, 718785377, 653014819, 868034494, 223126461, 354776977, 595519402, 270268827, 643280707, 865405545, 235171385, 907684801, 911005116, 549310160, 823269151, 327061029, 660953071, 180257620, 301915010, 387045850, 874024549, 664283964, 596087201, 533252782, 857211409, 387256061, 541723442, 288172969, 695856962, 73163050, 150856689, 775420213, 6399321, 764752821, 577439727, 41233976, 139028658, 248458157, 334689368, 967580678, 478965901, 556646358, 711453128, 150214723, 83256808, 864044670, 31529309, 300114102, 819472474, 755005071, 693460060, 470639469, 280488666, 43316501, 571562252, 872194005, 789221166, 400965956, 386988589, 833874181, 732711192, 948155093, 770154090, 72414715, 925821956, 377938614, 712140488, 278041873, 436104253, 727682386, 827311343, 749132740, 83816967, 266754221, 380450663, 276492790, 406742501, 417780151, 81807465, 249728346, 360591487, 66584004, 594991338, 526768106, 208120945, 230234926, 349867847, 325685030, 651836317, 63923340, 208599078, 772457394, 622250236, 664309561, 30224394, 591807390, 946814373, 309976935, 199033009, 700296798, 47106422, 616529883, 773601528, 991707896, 350842887, 657392307, 217472867, 766434094, 888241934, 952374932, 382963957, 114419531, 805597296, 928857925, 755668264, 376778899, 877429008, 180817329, 467024723, 335329636, 715378643, 605809971, 128402276, 294596546, 462860890, 123006903, 783044006, 861449681, 798370176, 580041097, 772611254, 342374849, 377437460, 621879392, 63811658, 846776522, 866542965, 950205336, 838690464, 488825816, 46258136, 915723913, 867361137, 638024501, 439414102, 890418843, 54389783, 909842410, 811335228, 361373785, 116530036, 954982642, 404035481, 345901676, 638014007, 409021867, 103424335, 99775255, 414733344, 301943495, 231503677, 921592442, 45289403, 427221103, 500107044, 575442664, 269057969, 668087969, 567564553, 732920419, 752196222, 420925183, 117445683, 143276270, 24951741, 253544186, 580929615, 788722128, 73161046, 728888491, 622375375, 422940093, 242284330, 649259282, 207442697, 56265562, 84291079, 931283816, 523110996, 843945080, 227113398, 614132939, 834648060, 601414843, 112483676, 940830443, 232679362, 886653642, 429473053, 910602608, 22925988, 714829594, 689647441, 844840803, 546608275, 89553005, 531162346, 208247302, 611735134, 378016817, 714123144, 520245192, 378442327, 483258550, 153010045, 109647497, 18180217, 75658583, 633084730, 398323174, 834230711, 458833859, 635981016, 918081667, 738733347, 9029765, 63799980, 920805390, 619997875, 526265164, 814140331, 29004181, 227984904, 952267722, 208501377, 962126097, 431938534, 287577970, 77074224, 235730990, 837710194, 372948777, 32932408, 522310968, 266155717, 655595386, 666026855, 356876889, 735004114, 410253849, 173353379, 241468445, 166309658, 187901233, 191131312, 311604481, 746122397, 82451490, 823973168, 79272055, 337757020, 973785260, 26996081, 598910387, 555736520, 428578873, 437582857, 542010620, 524344664, 525981304, 376452806, 912466848, 350486742, 238976516, 844222542, 29648121, 376659410, 399402529, 839696841, 822971024, 460109829, 196490902, 298024993, 601192451, 930688368, 436739701, 578264996, 875436687, 896085633, 588740042, 567781195, 133511727, 56006255, 70669361, 627417697, 929704188, 375393258, 513702455, 67779882, 965640108, 669739700, 945164892, 301112393, 220138841, 423670368, 520630270, 761828386, 349792517, 93727052, 936692853, 521245377, 706829200, 286718537, 774865643, 455683228, 881441550, 45917580, 848216276, 508770648, 200757500, 651890829, 912597952, 892355278, 507231245, 658631135, 501142569, 181933197, 586889422, 155858310, 326607338, 464035008, 102760334, 886465109, 731272167, 425810136, 632086583, 593972870, 156384795, 636999764, 247593416, 41280168, 39685660, 610480927, 463255413, 705238870, 913481465, 218042010, 287642540, 221578694, 597437781, 407727767, 864469128, 142780226, 263131335, 408122810, 80733475, 196754669, 318206976, 223054869, 145637898, 862644778, 95593115, 403782770, 263256034, 189468801, 288025846, 283692079, 800887542, 113710583, 673107204, 20884890, 543298526, 415169140, 627473783, 464069727, 218537778, 479761172, 422803247, 282370492, 869726455, 842498837, 637733739, 307610144, 351032490, 94168978, 987771622, 839218065, 851461806, 932019750, 97757128, 136005579, 155288645, 63738586, 58192551, 924962965, 794856567, 722455802, 752286193, 737818683, 688077946, 478059040, 692195459, 382515199, 17499821, 121054059, 597848960, 449282859, 517011620, 261723480, 968129631, 886312943, 315334745, 335732002, 177967100, 839654040, 212621673, 310426012, 618753075, 696564769, 739088099, 34467422, 643659074, 214090080, 623681404, 550178012, 386086133, 759835072, 118811166, 949713657, 518976761, 782662650, 527562355, 74885339, 195923018, 341532352, 767883986, 104804072, 247520895, 238089180, 314266941, 425393517, 667967987, 270772933, 239984777, 217774000, 251271604, 642492079, 310491484, 275923745, 842677095, 291561877, 400052493, 575613245, 893246953, 663769687, 157295288, 590749144, 568305081, 999778852, 814175118, 388183541, 1745540, 333202274, 342538261, 550784548, 414454185, 472111439, 1337653, 331566682, 553185243, 354946543, 721145697, 109029997, 923764748, 598835238, 896091175, 647497993, 721814969, 545746592, 420291436, 239986537, 268112198, 743028947, 466910308, 889969806, 407561164, 928837227, 195080395, 407656766, 203261371, 647966709, 451052589, 673226199, 354300410, 589683798, 499391653, 55346036, 718276209, 558685475, 430996407, 438923054, 448958267, 21188383, 244473616, 895454747, 853172687, 677484598, 83546095, 378858155, 292337492, 617473822, 232548937, 738980596, 755996078, 510885980, 755986268, 550642647, 818378971, 440981613, 292507116, 521574620, 697967796, 245555360, 663860425, 503862679, 927975251, 771630348, 96434873, 621803170, 506504024, 651635011, 860148284, 293985186, 183818494, 459883119, 202424346, 681015639, 138603747, 345024727, 744836816, 713040223, 360384872, 715063369, 821676688, 203256246, 482869646, 41685255, 707434779, 631487182, 693002645, 155533188, 997161942, 258921631, 706141346, 587136554, 974274834, 979941718, 962040768, 696288331, 1490680, 417206025, 353524582, 797246402, 662227128, 643660255, 883237807, 31393715, 183138060, 284252036, 972588955, 796978149, 432197315, 303924041, 908973529, 668966439, 343854243, 181953994, 225348931, 537931148, 654026997, 33677357, 82165060, 415760337, 205366201, 456985050, 967763077, 529488574, 575762331, 30338482, 291138165, 744623232, 915248918, 131760614, 934989941, 634759657, 178368789, 929027458, 785095091, 736050307, 974714550, 154712934, 463290235, 290121421, 524532997, 397924718, 784264208, 640269118, 273554472, 43572965, 370210770, 959715691, 248998885, 836962803, 521621552, 324168562, 575440709, 253981792, 83534396, 283859919, 235590717, 551556713, 53593677, 318433832, 624138949, 170322397, 517091659, 160907601, 554642215, 346920712, 685996606, 589303427, 752273726, 667286967, 705343321, 234907167, 96228032, 351590763, 4357880, 676906513, 479924485, 458872149, 701775282, 247365814, 50731359, 420206456, 909125527, 879676947, 123883801, 644519395, 837380565, 533590214, 512555936, 70708940, 366700960, 8984802, 930028067, 86280039, 919459587, 760504324, 692116038, 146309510, 704641706, 885644835, 140578709, 156748667, 68154756, 669347757, 716419300, 621340506, 513026593, 279242306, 266076138, 252601245, 968986543, 14194966, 817354996, 751200032, 314212629, 507387874, 650168153, 305619780, 973474405, 417337719, 559364748, 460018552, 172218225, 736402438, 817353348, 605283287, 489266735, 127621040, 633425017, 733812148, 244084955, 368257930, 75379410, 945811580, 273212271, 91214516, 589429354, 380755596, 641791042, 240622080, 124310494, 195826036, 196613657, 768007497, 380183031, 450929936, 492851621, 205063241, 550799287, 553145514, 751542229, 742832784, 788514818, 345501399, 904443793, 645285151, 551998578, 938158396, 156870597, 238312008, 457326990, 106628962, 4017689, 552976136, 930122556, 990712309, 409735187, 294343310, 140949609, 979707902, 523503591, 669283153, 428669071, 632363838, 621977933, 178672246, 200457293, 490335142, 610291799, 531434163, 240937043, 50186441, 21150580, 702560035, 732411506, 388237868, 901912042, 55422331, 158203689, 20723312, 897014930, 10245374, 508750581, 6026008, 211445082, 543809460, 221404863, 247089396, 926248944, 60694982, 741022062, 262738517, 472670807, 821628541, 55954420, 151310766, 983399396, 671086751, 584945898, 41125030, 443788155, 115963382, 674863351, 698058312, 554566724, 262286234, 534455470, 64018329, 639110075, 809019468, 833535871, 843522667, 483199489, 962088668, 381418100, 900432599, 483879275, 918415790, 275442544, 850401357, 546767860, 648250829, 35452498, 474981715, 754616729, 455464415, 308525250, 323762362, 467362316, 276611299, 188429050, 706508104, 41692251, 646330356, 298790824, 282361661, 448448165, 739962753, 713759734, 379680505, 745983851, 257101460, 48874705, 407553997, 951328244, 440175036, 618067978, 482246485, 35743102, 152444988, 677705533, 264119852, 297968137, 962070402, 227036385, 279392617, 468344301, 213130068, 832058768, 389651045, 561124408, 718024464, 477697006, 208542404, 753113134, 386118340, 935168114, 698365608, 299436661, 85070560, 270703619, 297178649, 174196061, 894433141, 309847554, 889344933, 406636190, 784819507, 248763309, 109802916, 658482123, 702784885, 758734771, 457880001, 270629344, 411488366, 289845921, 569257801, 967240464, 424134827, 395921808, 325943841, 105773944, 21725420, 510282807, 796204430, 133208628, 853746529, 431100546, 459333875, 459423590, 897534735, 400355977, 768617285, 523067921, 95303270, 238765710, 113806094, 846955206, 560625540, 475087165, 531363400, 310741838, 735771129, 809352401, 484769123, 798859210, 504766497, 551705663, 159073520, 918573476, 382143539, 175638839, 391689210, 307169190, 169797676, 507704006, 571681107, 249465332, 832932132, 894843262, 356160287, 57754255, 35398651, 610355748, 231665003, 341709721, 307826326, 307622648, 449882280, 745401579, 134758606, 43848569, 107391188, 135101301, 109635574, 851399555, 47464238, 405556740, 632732648, 267240762, 104079944, 790007953, 925977388, 961944976, 374750781, 323206204, 386931723, 935734024, 958337548, 135098835, 598370732, 783303040, 616518035, 148427597, 626010215, 284405227, 201221825, 716506726, 196477562, 171991942, 217879721, 840341301, 657567018, 595058837, 732495634, 143717966, 576816218, 522393582, 454862134, 299897429, 840304134, 545001924, 163405576, 112101630, 429798470, 564138135, 477020724, 851883538, 659006467, 694584752, 334633771, 9290287, 388894565, 528853322, 319864401, 496439288, 498678068, 19281688, 722566624, 530034257, 960066540, 190694752, 36786926, 916403771, 946250811, 550154613, 625905278, 41452310, 421603386, 909460223, 55466161, 246836783, 240540603, 822151015, 667812841, 401146346, 146885143, 319953520, 587359837, 72067181, 467835461, 912407745, 70839299, 908747845, 888511893, 13541127, 517685789, 300500264, 756463748, 885967034, 95355945, 182944591, 833274331, 322513579, 155247267, 360022656, 469980339, 824272905, 639790170, 184157715, 956789249, 561493251, 144369050, 546479732, 717492802, 398730823, 896383135, 107495827, 836987306, 940171735, 432076379, 451401818, 578654373, 530345937, 21319849, 398881563, 571953305, 57603384, 385170773, 676365082, 590139705, 385400661, 347353976, 96310171, 218065914, 746845758, 833216151, 790848606, 912719942, 410908855, 157474757, 909239457, 817510513, 333384151, 509607545, 78548931, 570289517, 667761551, 914869445, 292307568, 154681347, 182888161, 312442576, 240158923, 360990610, 533564959, 37646497, 76222765, 408197122, 915967366, 958746951, 928292173, 68483730, 992840873, 999352124, 371648070, 629018258, 590551082, 418739042, 48008492, 74642880, 767953851, 267392669, 280144906, 175197031, 830138695, 436414889, 286131566, 203647955, 308962350, 897686646, 143855619, 621210782, 374738109, 429416182, 516590157, 540266334, 216341425, 667268740, 366785605, 532625840, 830142312, 70375510, 172108135, 600430285, 564185056, 662084398, 644545126, 549576427, 322157295, 373121489, 988921209, 279982064, 645529728, 178182954, 346051885, 41297434, 401755959, 821118420, 160211559, 699697318, 158395383, 634541685, 447607465, 577810322, 299827354, 83380848, 136673673, 563940271, 200603842, 728205844, 738018619, 255189583, 636562118, 955033335, 247351376, 372441359, 344668033, 147471599, 798557226, 873565766, 135723857, 210491363, 420437228, 984044107, 483763111, 266908530, 708338566, 177289606, 394563555, 775196108, 795109048, 106393684, 388172337, 331857543, 747974408, 248514873, 482339437, 362997907, 350536517, 801634308, 799498164, 618319684, 648875778, 543118108, 735423224, 148396539, 173035347, 109100519, 186485090, 442419785, 699089042, 717546071, 488753088, 495643753, 290233838, 304934223, 160606268, 554955733, 554350574, 814482721, 333888971, 848293511, 42273044, 622373089, 67831571, 602791936, 135019608, 568950881, 258999812, 520965608, 747787589, 618815785, 457233525, 365561643, 482191085, 147399120, 464980507, 734913785, 644802675, 840541995, 86897355, 583131540, 582764622, 179478606, 692164442, 386677961, 634417942, 270655269, 830937708, 627937736, 964754699, 149405845, 576620114, 782193540, 407119085, 751992262, 111581004, 471061545, 950422413, 527448093, 104720794, 61782780, 592896285, 731607503, 151761465, 877061245, 927004055, 480852728, 254094719, 913276813, 156629625, 56927784, 144902532, 784351719, 358266201, 284930015, 831546844, 206026441, 770533131, 682091035, 135283743, 977268241, 680054243, 160257433, 547024374, 228807955, 30821605, 1153598, 368733683, 353838467, 214179815, 480366387, 740220254, 90767168, 273056210, 349833469, 42738608, 375092811, 410092262, 441306542, 49356807, 824379116, 540056931, 890546833, 23622733, 423515516, 118399549, 330660146, 221601240, 453860882, 909055643, 396232715, 49879685, 561922165, 145949144, 730388127, 367245232, 402959531, 784463577, 534825585, 118521261, 556448172, 404266407, 782995712, 928557422, 598372118, 984086999, 840750864, 238962977, 445068554, 914069648, 260955341, 779897511, 544770135, 261007674, 334735884, 915620425, 452517648, 501276593, 280162812, 543950468, 69473247, 966683098, 714615404, 452449967, 497062330, 768838318, 150230809, 760681337, 818872811, 216420467, 361042484, 915360108, 966641336, 33638839, 806014028, 841867816, 889682103, 589153067, 899871469, 269023252, 28501038, 517431538, 941007689, 267184104, 178591121, 299689297, 7799827, 281986243, 72924986, 991281167, 309221343, 996132513, 623035295, 535401303, 893733146, 152065197, 26754324, 522327689, 40000156, 446028337, 805610003, 946821867, 787565460, 328071811, 94869003, 797729986, 441817924, 24127051, 410905412, 16974420, 46662866, 424820675, 483803204, 407155053, 550332179, 349452088, 934776838, 349336307, 792074370, 142931999, 488793256, 209063030, 776716422, 143582227, 185367492, 513963435, 982172380, 683526146, 666560278, 938786508, 483311923, 461808049, 755563125, 270640893, 891903142, 956739464, 70452951, 306261607, 889103842, 617936068, 407516322, 975364665, 13428180, 238568688, 204683457, 263271695, 829153624, 263013883, 320783280, 594928163, 125962965, 194476897, 402185996, 283779716, 934805330, 997978804, 970283453, 765395968, 645581112, 735955545, 388256306, 963023647, 50218743, 382836807, 749746234, 254679889, 265867842, 846397068, 716992038, 529646536, 707085074, 906797853, 325000641, 90452421, 609190080, 873520755, 598469675, 96973809, 107023179, 656332956, 255279349, 898635848, 432791245, 684970708, 732382640, 719530126, 458547032, 255964957, 393567162, 375729843, 645635911, 270754911, 815905617, 820048184, 10396920, 927065231, 966203716, 630796601, 166624537, 194412017, 954303268, 707632081, 406033284, 896065272, 773284891, 806394320, 998372191, 652010596, 735707032, 281778000, 837346487, 430048414, 536257497, 935440022, 267995770, 193220845, 575791850, 438113973, 699253950, 41752913, 552154310, 425262637, 735375653, 320270851, 457244681, 668937667, 812858331, 888876862, 242630108, 842489266, 920441885, 359461305, 732507503, 664534702, 220983635, 259154190, 362199849, 755119840, 560982855, 241985869, 962358604, 456800524, 588189755, 794770599, 611802485, 281274728, 923807684, 771595455, 905611889, 943317156, 175309257, 615019447, 323578008, 708810811, 686391023, 757645062, 709307668, 567935136, 121353508, 189488255, 414400349, 224350160, 661490379, 174552907, 544091763, 195143821, 687716619, 600568315, 543961684, 811201242, 264490115, 824234141, 798959269, 958723359, 834971615, 249175253, 716928816, 334005020, 203553901, 63258845, 280962358, 170162023, 390460054, 958023675, 934420825, 164925362, 443404118, 393074529, 149480785, 244830150, 325435329, 803523400, 71743241, 770329475, 67544378, 902044555, 297898167, 802438823, 682612450, 157096040, 652026299, 667156019, 719895095, 960402242, 960615919, 517331263, 562435035, 121908608, 431754438, 92319423, 470201314, 19612659, 939424483, 32771010, 686812965, 880645159, 354490118, 604852522, 667081263, 409089586, 623689463, 644564174, 830982938, 625364821, 930458915, 379178755, 928418356, 132615766, 548913617, 859686900, 514769289, 713765908, 452439371, 213168771, 501068089, 647184063, 218028207, 759380726, 472283187, 34608476, 514786078, 795762207, 381675140, 103629234, 925262281, 956634499, 378579034, 203409329, 268337394, 592329887, 124623244, 299772068, 192834854, 831471031, 780580311, 456322245, 366720677, 645167000, 203850804, 961625327, 910728195, 415364271, 122791318, 505017618, 988141847, 737087305, 485505648, 849253602, 417103134, 380269102, 962836363, 789760006, 989218067, 837007199, 257362487, 122978697, 617390904, 341446283, 467980584, 547494744, 832250026, 937518249, 397936859, 440410900, 615758374, 769375284, 121444750, 12129087, 670026525, 958839505, 408964293, 377516908, 849269387, 868394763, 19701388, 605370039, 621446478, 59468615, 237719113, 824999212, 852297846, 760536504, 790561110, 74433813, 388002753, 752051695, 583144702, 852918117, 186352976, 634229334, 944154806, 684945818, 663555212, 923398720, 682016777, 366729572, 41497204, 131875653, 503979282, 337016425, 206328067, 672172336, 895595722, 624841936, 284356599, 189913233, 796290155, 722146003, 263607736, 172512682, 350704079, 83873063, 738315906, 534822876, 994131485, 77609423, 931359086, 629966298, 169073476, 426918571, 9526877, 401407800, 522147348, 747139334, 815608280, 262581658, 148338505, 121448308, 131020725, 249694036, 172943639, 140408303, 448169626, 951146641, 632223103, 733078489, 611429281, 778215991, 1142517, 88793786, 332686363, 394665863, 364323390, 303347591, 54854382, 790210469, 434247772, 312844354, 697640527, 381940115, 257137205, 670257802, 487392451, 560224239, 267115273, 710789792, 23536801, 657442299, 435569809, 228013060, 357924246, 43710186, 908894105, 26259431, 356145739, 883584578, 972418948, 419546085, 507156410, 931282809, 395621600, 907334611, 205623480, 190348584, 410225460, 357758278, 659373403, 157116331, 187504662, 515583623, 861874769, 968065021, 699601757, 152379723, 300263948, 474142194, 285741797, 387140350, 240396311, 609159790, 134652808, 235969686, 347694674, 271913585, 732978056, 760967325, 202705300, 647651700, 731166218, 449801713, 553023715, 742445313, 406317725, 1011126, 328491561, 363321519, 360871968, 275779407, 288644138, 925156190, 201649505, 13417121, 686991157, 338388820, 248612360, 111348602, 702303139, 59311619, 419418507, 278391984, 725602486, 398833911, 720748233, 650713868, 360455999, 246447232, 674316100, 143137353, 720524770, 824768674, 403606058, 221561911, 886417953, 688713994, 998900237, 726547176, 55724445, 33095517, 430265912, 523040820, 883386875, 872047743, 99596000, 804509406, 71256015, 800547898, 653044023, 718059417, 101048474, 468605466, 646538896, 366054637, 837466569, 892320917, 387678859, 395064259, 763662038, 471388063, 348210963, 775897266, 192322186, 486181158, 178807154, 49449902, 46835849, 395037803, 331474784, 883624604, 96450196, 986102423, 579172051, 939204518, 652857621, 315092105, 752545428, 741733113, 10652047, 205617073, 834228918, 544069150, 731831911, 329223669, 175318497, 701280151, 624664000, 989609206, 664159660, 103251197, 312998941, 851880404, 303814508, 29232246, 777902628, 685570239, 652375517, 233596861, 728668506, 905510715, 653827646, 678725990, 543386128, 22108915, 690115736, 426560003, 275229246, 487607404, 306768995, 802285621, 953538026, 840537399, 489990715, 731706996, 139813549, 873716174, 43932186, 819059578, 162792954, 253305714, 710660826, 502055570, 810801481, 660177941, 44443762, 383219772, 629312725, 200372522, 243851963, 442736973, 490578230, 401605284, 352079604, 85325165, 481447246, 509597883, 50130411, 748350103, 310606782, 68459903, 808480123, 913704087, 389795034, 64617846, 476776514, 402052113, 615208100, 408331396, 446127600, 568426820, 918766702, 487140040, 23030685, 938348254, 72927646, 49896300, 2888499, 855133131, 50635742, 28451366, 487554311, 409923200, 286395045, 737479807, 464894487, 974093521, 140927033, 253359247, 137654427, 707038191, 111415802, 808774668, 199231986, 56470455, 11980139, 360350743, 89657819, 560279237, 28823047, 469403918, 317109122, 645061071, 77641560, 659511026, 561263349, 489586124, 901928751, 819369429, 339174403, 516330035, 406444539, 353679259, 205974586, 631446537, 643614523, 69397340, 570397257, 689729334, 527902624, 735837002, 501230637, 809811077, 611544513, 296914004, 370631400, 433365725, 412706713, 399660947, 488991741, 83628381, 734301847, 74865809, 898782370, 875197029, 270047554, 859239786, 987710891, 764020212, 848620400, 561282734, 625525234, 952130016, 214022646, 714683735, 41540965, 149500430, 497814168, 122975237, 524278238, 785626739, 375806044, 218947675, 405969108, 290656827, 450716915, 374821889, 857439919, 216639598, 8520586, 503973019, 395054511, 765483500, 647516990, 134826867, 215402755, 217040737, 305200485, 152175722, 667326059, 795095828, 273217383, 805824479, 695314483, 890111317, 760131896, 361472277, 532624383, 516977114, 860507320, 337926968, 718973863, 196188147, 733883056, 23864254, 77372651, 824308253, 191422523, 186148522, 842841489, 886909553, 503783966, 777775429, 260446020, 982341620, 131710841, 96242123, 869834234, 329336158, 105231292, 259641760, 480516407, 187705421, 83322002, 153689151, 737154265, 462461066, 936624374, 699147589, 869484751, 830367738, 65363603, 473344031, 548449264, 450084832, 978123121, 439592242, 358585359, 343298886, 721483435, 103918468, 341303109, 494140829, 802571617, 80600809, 348918524, 56352302, 785733895, 663019721, 647972871, 336739688, 459299903, 248571259, 194733821, 234000420, 996735767, 593059695, 448351802, 132191428, 498495148, 383663972, 693915924, 293754071, 968536275, 953992886, 321005636, 409678684, 196369302, 9219353, 633790369, 897865296, 810504821, 676752120, 768962149, 454174159, 332391118, 967961963, 569992624, 282688436, 941047093, 621228268, 988947006, 783309595, 292246244, 604260806, 118749653, 337509510, 548214668, 77593140, 637271381, 512309446, 864719322, 321989747, 430756436, 360017676, 301553873, 643129162, 246843314, 242805109, 213599143, 585204506, 246623697, 345414079, 400891158, 210855471, 720302472, 481216283, 963208634, 664101325, 713449241, 128234078, 644783700, 955205719, 713192382, 87302266, 176515902, 859742692, 692317274, 130391512, 486728924, 696621048, 748649907, 530103192, 590090404, 390645662, 79391590, 934446428, 754850593, 966595087, 874796964, 347630962, 345092657, 110732367, 274486131, 837888857, 605431632, 496335324, 283545928, 519975696, 907681615, 749359679, 22625646, 432689016, 379855606, 930303278, 516775539, 947785873, 609172512, 305384583, 776114152, 353971442, 103931073, 226169383, 318352841, 300151647, 38235574, 124130812, 414046865, 107847265, 971538625, 395609254, 594907789, 259787910, 169923926, 113285405, 386967424, 816634974, 31145852, 601685106, 782651404, 611633663, 196951189, 585752738, 791245465, 616444734, 874110561, 300179982, 906374448, 760346623, 161762771, 273547379, 58171396, 441774875, 672365302, 712837816, 399371601, 728316903, 36048164, 976132943, 231061517, 57792232, 644048427, 572702610, 946291745, 351780075, 783849430, 39817714, 433874230, 186159993, 460048930, 406941597, 417596788, 514283939, 767719482, 550163399, 274889893, 57104887, 417395237, 33154592, 172038099, 891164732, 295972675, 794581881, 520268702, 625366184, 67972589, 309001897, 204579599, 632551752, 319216172, 393656112, 246888923, 520617209, 876203841, 898689474, 329174783, 524222534, 975608303, 658805136, 475829558, 845421783, 378254013, 387334088, 478647568, 445185377, 825912544, 733506828, 598952203, 639011722, 412073255, 288040487, 944356111, 141677750, 309072386, 888234039, 843541277, 526145771, 261243358, 266753080, 12653490, 517053173, 2759071, 372161483, 903505943, 382250840, 926876299, 237253119, 622440151, 680458391, 907974941, 151901720, 739829496, 378802795, 179310478, 704328347, 12940060, 898105135, 847886061, 285739845, 903757389, 95029268, 422608297, 581650511, 318570032, 287407676, 638265420, 416180315, 524849405, 372815303, 498098776, 163632523, 100507727, 809913151, 195498037, 215615251, 449599377, 575169268, 59129059, 692393120, 482176376, 332598654, 355905716, 518000460, 965177614, 663840994, 869793838, 702172394, 323282948, 139023896, 567996662, 224858452, 245993982, 915035420, 499439876, 87156123, 456206224, 978158072, 831080203, 885689098, 902246078, 931531227, 464570858, 638758685, 731329917, 374411932, 243398782, 400521874, 741261159, 350099128, 588019279, 302145341, 535572567, 261429530, 969312624, 396297848, 864292859, 220927911, 915702808, 432356160, 317773625, 941354404, 44245774, 781484530, 857537979, 356498315, 897538901, 662444470, 437502593, 212184382, 434097611, 398057990, 691705033, 234601294, 820827754, 703625556, 568487077, 693509691, 546856021, 649177288, 108678486, 24869244, 358541842, 564364967, 317377299, 768558253, 578488625, 166832191, 714790165, 662790453, 623908009, 366784054, 112189232, 935124755, 822347426, 703632162, 336064353, 828976792, 783066621, 336416138, 280630562, 739272678, 128242938, 133052657, 675678954, 593843762, 289049914, 410916225, 628872558, 812362488, 208805940, 805563369, 977825623, 960989243, 381285321, 82281963, 921858714, 479299, 769388170, 428966937, 680495123, 473717548, 132469309, 805414272, 594201455, 10424836, 421347909, 976525438, 223255905, 124040760, 723702932, 792048652, 324491233, 161474019, 199781441, 237251386, 487273493, 237121411, 538612674, 852695063, 805103146, 441842643, 531103925, 136664035, 560322816, 77895879, 148601187, 263110792, 188955691, 998471886, 686579815, 669059579, 936678185, 242679579, 204615641, 935751854, 231124633, 294197442, 56580534, 295846542, 788817633, 376784886, 841729207, 170839371, 39926650, 544579555, 611335450, 230995184, 542492768, 344783934, 903812068, 400996259, 306798313, 753253550, 170636592, 265249892, 395452664, 667981420, 601414341, 181990229, 846585012, 760939157, 565182674, 460627167, 221405888, 603952595, 708268322, 828412979, 904313713, 80396978, 867970016, 263258161, 739032057, 223695893, 964958684, 153955545, 3797783, 534693479, 352593617, 834175736, 288502847, 502787146, 85777376, 241484937, 158429751, 830060523, 510141583, 17973291, 152288228, 543583434, 858275275, 340808286, 867939355, 707138640, 265890065, 309848332, 856061549, 854463410, 117233959, 685633689, 685596947, 801352284, 568619371, 874881985, 853107316, 449332350, 84618317, 441538597, 650159752, 100988294, 36794538, 910078572, 706377495, 811329257, 35456793, 802622885, 685748706, 973545501, 446526053, 538640869, 357111786, 576840448, 55467608, 820743764, 482384662, 259812413, 457437640, 374030689, 82198986, 265258237, 264463906, 156168508, 90892016, 44329729, 816545932, 88068929, 365294550, 605568425, 845016959, 144097949, 467274393, 279714276, 59364221, 236551463, 164027390, 515733734, 918356578, 897128983, 173140918, 741113315, 903314296, 822431436, 420126144, 442587895, 869856245, 346559929, 484281339, 99308110, 133627960, 324485985, 997912170, 592702714, 827018955, 301967739, 400651353, 83384396, 103643676, 707236422, 58660542, 196576117, 386960524, 316819344, 427988306, 833837184, 368203646, 627446695, 705540764, 739775392, 503847552, 614118700, 746035526, 12830896, 417836977, 41209100, 863965758, 509389238, 383384690, 344229285, 904646053, 856789357, 359328327, 107638881, 997139870, 237388915, 85539857, 525859039, 583298248, 606513196, 353148437, 399014392, 627020316, 305475659, 728838986, 615564116, 872120068, 289239637, 817968635, 720595221, 913555346, 326844453, 373389245, 246513449, 20409391, 273544769, 409824415, 985819057, 252291157, 61975359, 992060852, 429072055, 796461484, 608759151, 650180191, 340924112, 123214659, 763651284, 258606028, 569589950, 352810937, 805403660, 51151550, 280013237, 436234881, 896065826, 269625450, 310755739, 297801770, 359671842, 643060790, 911009453, 631339327, 523440083, 135306394, 221588802, 946102457, 741534538, 755283620, 292468321, 937367886, 711232189, 312236293, 461813401, 536703126, 3259805, 893765492, 854689089, 504436845, 992412558, 886038955, 711848214, 522807243, 230522386, 112594490, 921524598, 239015780, 520410763, 805999592, 96253297, 11955579, 873722199, 256970703, 65622966, 491289458, 568774574, 966493285, 724524959, 89192657, 971295961, 326941834, 719430577, 395789269, 455837405, 386187699, 488323861, 39880365, 994135583, 384952653, 505341331, 296923553, 247569573, 162522066, 727813183, 940948723, 273578368, 813367408, 906329422, 931740162, 908688847, 610488276, 802666376, 324336687, 405716258, 256861055, 490074991, 211104020, 205309321, 757701159, 619824655, 553822099, 599498423, 760520001, 577089441, 56864716, 475644345, 712217341, 923344174, 968249083, 736949865, 291194083, 625155089, 599893161, 766703220, 959235188, 616063679, 221324524, 167476894, 348889414, 726415637, 34585814, 475907659, 699336432, 900055463, 167161900, 186580729, 17286562, 581542762, 426658468, 254407818, 897551285, 641511750, 616871266, 268811615, 681907361, 837584800, 566505034, 571540793, 146780222, 675312424, 768102338, 621557373, 252778319, 458068774, 238543677, 651632739, 628458068, 690393284, 578306240, 183448590, 139575263, 316701088, 928736447, 560848695, 452198064, 191699171, 308193116, 744153944, 320227755, 50998103, 225147552, 636543188, 231125176, 876864657, 21667691, 993152732, 276972560, 48230708, 383854966, 881624272, 332233966, 403794316, 471942850, 568675176, 113536636, 230177234, 222917330, 677196725, 708749189, 824547550, 778808199, 121606452, 53530232, 910944597, 314475454, 422084192, 399494789, 762319216, 764967738, 825064997, 555116310, 277195738, 746080156, 978185233, 34693595, 897345640, 570126294, 949571703, 284980322, 684373038, 191854860, 407554771, 296682366, 390513414, 2996399, 671988877, 629138781, 107995589, 192288809, 58920229, 304080401, 759279742, 735325495, 44746037, 140143973, 695525294, 430738075, 537583533, 26063954, 822967837, 21340529, 412206680, 293931406, 599850249, 556284798, 106705448, 218174670, 319731816, 903553460, 337860710, 790979391, 736217637, 148716732, 461996201, 554132331, 66651684, 144945842, 395941440, 6482307, 268441185, 524454061, 545991333, 74234436, 494963918, 514861022, 691900955, 302348213, 168779855, 686818131, 587034581, 960277702, 759366688, 125493256, 602132209, 523418517, 48680626, 357488704, 949415478, 343004273, 913983847, 201777855, 230979217, 121541284, 858255504, 377284388, 842970406, 566986662, 52685495, 467107798, 677783590, 838782706, 385946449, 526396403, 411375618, 809337502, 20377672, 413124842, 346808007, 869571432, 827347118, 462570639, 882016005, 433751414, 800316389, 954311941, 713786094, 401910345, 125117949, 849759597, 677084461, 481945606, 197388733, 615710483, 873397146, 184015124, 77256732, 37759441, 331843224, 334736229, 828072991, 507924424, 149779233, 778257573, 932564919, 839919634, 166844263, 872023783, 629239827, 101660188, 440821407, 315684585, 97158945, 278825745, 981110060, 525045866, 944728408, 189412553, 401609593, 483178638, 908792680, 746512304, 439031119, 387339042, 495826268, 288651258, 773642014, 503579611, 385351253, 935732782, 129465004, 791907030, 305689476, 396578369, 575222192, 843293960, 790189805, 781067192, 598353621, 701418877, 721962435, 472194698, 653549406, 191923009, 720290324, 163267653, 802821525, 487102465, 418067740, 765104701, 322765166, 281482320, 980907200, 713995480, 753808545, 786413038, 163873057, 751865275, 209229810, 585121799, 73051895, 491780782, 727777558, 604837128, 474249004, 618306066, 67731307, 286870154, 45564152, 583446731, 977833579, 349108793, 728785739, 438476699, 420443487, 61799658, 196831415, 52996781, 232218993, 339900398, 216198947, 35439957, 546030526, 397870761, 586450581, 799280329, 366246648, 64471988, 908301677, 971824196, 622136169, 141034998, 58592445, 331673386, 555450594, 264348446, 470979640, 987139094, 826484195, 531744824, 672365968, 808384199, 753862915, 759008834, 652140295, 557529513, 656293583, 3942622, 657890956, 203535101, 968387938, 225603152, 802803482, 40221143, 175050636, 608897941, 334634407, 110396804, 900467997, 572034145, 292207886, 392084135, 926169454, 407575473, 114562091, 428489235, 362409179, 491809107, 324895830, 747626796, 461908361, 234135871, 955165251, 934339105, 834162925, 65897761, 315926138, 779829403, 20366405, 542173846, 878923212, 408049388, 55000310, 257862082, 799399626, 953711412, 539760130, 403744419, 453233142, 811683388, 455933460, 323682858, 103541770, 275487635, 586542227, 774514064, 844869726, 544844669, 474373599, 950401400, 601434065, 242711639, 978343419, 956153867, 575242875, 248299993, 117949598, 862428332, 422642815, 623651391, 580693258, 168307102, 369713559, 860457318, 788136883, 167115119, 488738848, 830028009, 611002956, 621713472, 773751766, 322770260, 727189443, 919566669, 145582735, 276581752, 849229725, 741909275, 585685288, 791301336, 605758668, 20352422, 592908720, 881295681, 472698337, 62496042, 17154854, 79587217, 581011510, 176666354, 995189253, 270707901, 36047140, 880967897, 413136879, 821713428, 567458197, 732652698, 595428580, 965588310, 105359795, 538745019, 148253687, 146539135, 592579850, 433382889, 966300659, 826378009, 621840512, 383005099, 211594753, 441575008, 40289098, 604594489, 720149717, 73422711, 643726313, 755594022, 589289381, 98774920, 113831457, 681536034, 562501958, 437886911, 820214202, 821675568, 595657017, 635802717, 36565581, 911306996, 743870692, 144231543, 540828550, 677698117, 142178743, 810579569, 673413749, 87453008, 885893672, 956513359, 123616466, 563879747, 85040029, 375396914, 651106121, 713615521, 475819835, 102364756, 142161001, 100382442, 633798753, 922426688, 32700902, 30061846, 722366175, 78549844, 149564604, 714869719, 174663633, 405955179, 8970480, 708155870, 585210458, 422528406, 300904537, 503121867, 573306421, 64814428, 524746422, 249187387, 891433958, 300083297, 456793741, 132531813, 365404585, 431542462, 575449385, 966589468, 695676107, 543523118, 236448470, 981432531, 833763741, 607303464, 29000102, 593218243, 396425777, 273327670, 122097111, 650161668, 692176638, 78130469, 528178195, 595403040, 29033583, 928463817, 971621669, 81989211, 520327079, 88923124, 976256863, 397636282, 490221264, 364699802, 366576093, 153521367, 267897655, 690055174, 205911538, 663567875, 796812920, 893136838, 657890105, 870698590, 405889677, 49059663, 926336102, 656669692, 63465648, 264477881, 987384728, 513037888, 315533718, 938466947, 784134940, 845846856, 270239222, 683263838, 524955053, 737812787, 610493944, 391166265, 713364227, 632507671, 710541675, 815790971, 815447527, 946456414, 920950862, 103615431, 415968830, 928639919, 331890675, 202574389, 666588019, 391322087, 133263666, 475158782, 772144148, 179978218, 246135609, 979747280, 149565880, 462403245, 729587886, 371426841, 607225940, 56855971, 466682509, 121659878, 6004373, 400425465, 923015251, 796532734, 953219781, 644673111, 73897011, 611480232, 861765102, 53100100, 38911684, 124778699, 428365766, 599926458, 40474259, 740927093, 356147681, 462208787, 936765681, 470768323, 700814462, 356230459, 52601374, 327248717, 315233855, 937457986, 562365716, 869328477, 82597829, 525989357, 795429392, 270340832, 452026970, 616084772, 148969025, 794786392, 104888804, 443689484, 692059232, 930349532, 206222129, 667588690, 256172026, 975611721, 829945935, 905996067, 587042382, 205337080, 367049327, 905249045, 296197623, 819570803, 203254884, 991807972, 593768411, 82055872, 677761044, 314566361, 296362391, 868106305, 94664814, 386995934, 539285319, 183889214, 410971825, 553681987, 163953328, 958863759, 896022770, 147266946, 221829458, 471626159, 779709960, 241905249, 549977171, 63499127, 32455577, 496580315, 791231564, 275230868, 747635397, 730227636, 881725615, 675335248, 85784152, 627078932, 231559397, 198209118, 74473271, 891992456, 907575471, 369126370, 944337119, 175186364, 559031707, 329849403, 987374663, 415006257, 308024691, 667851858, 436956735, 524158183, 352215869, 938142986, 229295043, 438442008, 757210850, 639292075, 345394515, 9891682, 893066843, 616733049, 229473504, 62093981, 718224804, 734023785, 897373834, 416181342, 288540932, 350789891, 602998931, 493188077, 800201193, 2780849, 138128122, 368656721, 628751559, 93570689, 224289260, 816999297, 148759432, 286869903, 582076486, 547626703, 219319137, 817041416, 976862518, 228901338, 748754428, 813212694, 833887245, 482542837, 193324730, 58544933, 272675805, 779283827, 516152717, 990613008, 525016709, 125961215, 629775746, 409973491, 898831067, 140797921, 913343603, 553190669, 884926887, 580130570, 142104147, 295939712, 185342911, 294190493, 767333564, 632518318, 430514029, 134998512, 264684718, 59175710, 382844969, 11748803, 576151542, 725700131, 713118185, 120682787, 917434245, 521074690, 882099462, 727669147, 922362155, 681226715, 953854367, 988005782, 796095185, 872779082, 896714891, 998978173, 588877767, 322804341, 8710233, 507349085, 163541873, 155429883, 796776608, 385429153, 631777526, 896447762, 752537967, 422487470, 45613634, 126856994, 670986194, 22006694, 600284686, 158277307, 748621666, 272742060, 694716555, 559787444, 385271793, 662926336, 366116630, 768783983, 894890473, 339378874, 611909854, 571850742, 747041394, 487322355, 939104540, 793837041, 149847554, 746425379, 500107842, 579618894, 752822458, 401140504, 658091364, 711145221, 210094401, 291933066, 286141545, 632600353, 496395896, 514710954, 401018160, 790613660, 254421535, 46493917, 828118134, 166918381, 294782461, 517729839, 286278351, 788374080, 279383545, 885430983, 716223299, 273932864, 832972654, 48214034, 135576687, 77824539, 209757924, 648283533, 223532828, 462177161, 639510943, 27905089, 914335028, 504156579, 321155345, 440049937, 834661132, 253821274, 475987539, 468853612, 680082292, 45674454, 16250396, 608491880, 644111894, 760233123, 9462255, 257896937, 259214350, 465258342, 311474548, 518654206, 100784778, 980181328, 369100248, 107079491, 136311188, 535052170, 554554783, 184566642, 30476653, 13082149, 458907637, 656742590, 395367354, 244811610, 389513021, 336504331, 702571983, 980252781, 407037727, 36737461, 216780900, 430800565, 89788396, 524376756, 166175327, 507172927, 326651432, 113502128, 224985825, 77772540, 916838264, 932401550, 362566661, 130227011, 169395924, 458243054, 836789330, 586540262, 801465506, 155803754, 998885747, 243403343, 318170027, 629147850, 138683401, 687753621, 444587835, 930709094, 486980538, 903366079, 620142953, 168133035, 562659475, 512251121, 424213955, 349489060, 88281343, 608882995, 397210656, 236051941, 794507316, 447498071, 847295705, 611200317, 665848676, 26882564, 137208444, 905027672, 876328959, 794214011, 291928267, 50231488, 127466280, 236293874, 841126056, 7158204, 399336872, 274221317, 874541219, 455487654, 780118624, 244400035, 452830531, 951059347, 199353141, 295514443, 101155256, 809043234, 725405253, 226619822, 882133773, 725764188, 763728294, 603737554, 970649404, 299788191, 395128001, 540903388, 36931035, 251311141, 157454772, 873570896, 623822201, 540655739, 683946187, 949441324, 550200649, 9622680, 868208461, 664455262, 899249485, 724732908, 669083310, 959600879, 567764196, 394391779, 505256624, 805954782, 194150546, 4085572, 728887263, 993262116, 420436935, 475943802, 594874538, 443379775, 508357942, 894656344, 62524601, 92238422, 755400776, 995554129, 111094043, 772383294, 348267467, 184216556, 623076386, 361964804, 690957803, 820133302, 780929026, 434198548, 625901594, 428692387, 44150416, 679477014, 373453260, 612888818, 888752910, 23764295, 178627974, 292318758, 858537497, 328855926, 235396087, 403418303, 649405571, 220463372, 520735298, 934234735, 445172336, 7946528, 876072351, 574760432, 135317811, 152863911, 71112630, 516863353, 134368099, 119821432, 63106649, 693834311, 134497525, 700388778, 95584553, 522286277, 998093721, 953081988, 650188106, 601862864, 696972807, 453144812, 769591674, 474009045, 118389027, 50339212, 785975363, 780118225, 948088144, 901403338, 364248085, 610988637, 479289542, 798111132, 160485427, 864881267, 665281841, 43266608, 968878426, 33877545, 2379943, 247596063, 507898695, 111393572, 608491009, 606343463, 726819638, 397507240, 584298123, 42108456, 648471873, 415996295, 29798799, 941629686, 309170030, 830107944, 502046658, 456290370, 282707985, 569122776, 322785272, 747595817, 235462684, 599149081, 173082644, 904806798, 590711609, 761580840, 746933561, 984255720, 718986694, 541324410, 984329126, 568631412, 930692803, 750252008, 854630295, 385069449, 488508053, 164334170, 298322003, 357320094, 942868507, 137352248, 819558267, 588065097, 554896963, 520125694, 108827943, 603053518, 46839748, 296482433, 209160893, 328520194, 498596493, 929358883, 822872211, 926170340, 371963463, 463027328, 139686498, 699033748, 44610201, 227177553, 589509520, 458256456, 306279599, 449250005, 527237708, 457610897, 66723446, 376117337, 751300284, 166094101, 549068554, 130342519, 598956778, 145055911, 978773825, 211086730, 486223605, 478053502, 790382132, 443281836, 168005246, 610644711, 99782006, 913929734, 308607295, 324446402, 33773329, 585358931, 565253191, 715754414, 426216884, 305774389, 236140563, 953218863, 696921746, 971882860, 545126360, 617854904, 675651748, 857079527, 429617125, 464607236, 392442566, 8982934, 729058674, 21432408, 459946853, 417495636, 953593244, 865740203, 813307320, 676545966, 393086421, 756152729, 745475902, 148630779, 770413420, 243162209, 411899289, 167177215, 752459479, 588512600, 6342649, 729259487, 11744815, 850764862, 22518996, 552144517, 988620254, 3926540, 51237670, 474473783, 465902758, 930042139, 292756837, 824000515, 541774132, 439320452, 76492350, 965216234, 862793420, 228489748, 979255372, 425080033, 389412677, 990644280, 52582001, 481304806, 830777991, 786231275, 681011996, 330556287, 605976240, 143149391, 402110989, 59207904, 287886278, 803604787, 74308750, 642201755, 86007445, 452778671, 410734655, 580999209, 879863072, 44158140, 699276289, 775085048, 160734521, 382870678, 609390501, 109656861, 988551916, 483765706, 126144859, 779870039, 292787921, 74114741, 561601755, 95537055, 836072111, 238792082, 762278306, 276377628, 758097566, 698037933, 890878983, 328535526, 919108465, 413581866, 479966998, 872665485, 498637047, 738936766, 523890541, 529996160, 916820520, 428068855, 631701009, 955398370, 265344893, 29960413, 31996570, 770224400, 22108613, 223221584, 609295753, 314107465, 947012160, 61338176, 350713915, 100875899, 731803446, 850934286, 783397838, 770812418, 945696980, 460668398, 376603710, 708194020, 488978099, 926150332, 720088391, 234654771, 107445568, 531892525, 110488844, 724624253, 826020042, 450912478, 561128717, 857126167, 863122310, 997442731, 287860608, 114256485, 438419687, 711482704, 574660392, 412618542, 746703475, 867570416, 103573749, 909977362, 781938782, 732787218, 799310106, 361947759, 390786252, 781611489, 919935273, 249561362, 197202747, 407109048, 999889619, 568880166, 742260408, 708883397, 887104034, 925439375, 342870845, 732929203, 392753444, 188145574, 568775805, 171042802, 594771476, 483104313, 492521066, 785295946, 991935682, 699811881, 379872474, 800296770, 373972699, 50406896, 993456903, 273630656, 290483271, 885955911, 61996272, 761689373, 699909899, 241642927, 799969005, 306061722, 62571331, 818624735, 699386224, 814295352, 427992028, 682519744, 909462471, 751010297, 361358649, 759417779, 221327406, 836634785, 369513340, 112302054, 910869943, 616897201, 274876699, 524079589, 614751572, 908005981, 964602547, 595644950, 891823313, 250839295, 932928913, 329865578, 317791838, 194635676, 430586891, 609738860, 521025745, 394665022, 776701916, 621201189, 469277324, 725316938, 195205638, 773568682, 655563670, 210661297, 146142101, 247450292, 489394222, 329609386, 510113526, 512780996, 928066519, 926072827, 917029789, 32216908, 314578377, 266016880, 451408125, 2299165, 716243810, 523078604, 299308218, 463862672, 325246685, 56745963, 891885611, 580965293, 175138507, 905517687, 926318248, 914781684, 893360675, 135379671, 738791488, 401448864, 452050075, 838860962, 68051099, 137109208, 664663860, 390258089, 23395436, 814550887, 742842509, 559676785, 94270816, 243582399, 169923457, 762969408, 998136953, 302730516, 587980898, 915893210, 682059576, 74398694, 605819814, 859999435, 649869448, 393441213, 404665557, 481027586, 763057967, 379558846, 314096455, 166132200, 91565852, 989443596, 867858555, 231825369, 826654362, 535154933, 285849526, 538463539, 872510674, 368276168, 530664836, 338814436, 728866837, 28080080, 846556091, 66611780, 239374258, 685934600, 66893091, 244246531, 356283698, 227558923, 612238949, 193632357, 587863429, 991882445, 547735494, 110560638, 174784917, 932014570, 751664085, 446582777, 615841214, 69043812, 561062070, 988032391, 206014486, 673728149, 943143107, 845383416, 878511018, 732635616, 277702616, 354424529, 568212922, 315614856, 349925108, 661924128, 926892332, 344439039, 78503039, 287943002, 509403175, 773894097, 308523127, 266421633, 503997894, 951251947, 516360213, 554090733, 511839478, 335966971, 630263663, 513260149, 168082117, 75157026, 707422166, 873922403, 187131051, 604344286, 418246475, 498464982, 543219269, 891341367, 535015316, 687749001, 203478090, 556831128, 936004669, 323557748, 328263819, 307129297, 875284365, 343834081, 45252967, 755156997, 994466208, 476756110, 315999572, 823655280, 170437252, 340244507, 490333036, 863045761, 377053966, 426031875, 683937557, 726599804, 803753382, 937021720, 152788583, 829529096, 804322026, 798476180, 569965588, 781705506, 401781994, 285286806, 52957060, 313194112, 260641126, 453671016, 176814010, 744570189, 358982453, 214682291, 245619405, 535690698, 558716693, 358217065, 100343527, 551728458, 434762376, 890096335, 560119803, 381169845, 244472330, 789767423, 510343549, 430139506, 350057532, 171977710, 285708559, 644751300, 214933658, 947402891, 725889660, 389850783, 650165038, 904585990, 40341174, 655183343, 266196993, 687261492, 927544219, 235109351, 595536081, 233890051, 849120632, 928470472, 704173609, 89689630, 375493940, 653648801, 390689515, 786416257, 710890673, 293646445, 764681568, 998326176, 587434969, 493424885, 969538097, 190125778, 756257772, 203556623, 544339870, 327439379, 294701208, 480398807, 269338327, 35387955, 293873253, 692815156, 58182390, 700787143, 277554003, 353184033, 516914696, 302368308, 61273667, 22895964, 413953143, 553149919, 782801001, 285034192, 280984347, 383690954, 234584794, 798304289, 484545104, 336835841, 782696950, 696770159, 755083663, 635595329, 920971067, 104403205, 746263149, 689555619, 898245410, 137956046, 464003333, 271686476, 962404770, 48733236, 831873161, 181420393, 647307512, 520345620, 879906591, 353608380, 226681483, 226715566, 113480883, 667560603, 143593152, 54657257, 602377400, 251258235, 224251298, 746368896, 726726705, 633174575, 942796754, 159420356, 133869600, 707323549, 832046755, 203760915, 296322946, 523200304, 486556117, 224314322, 397681446, 881942485, 882908562, 540225265, 524210503, 569680985, 295101100, 970629482, 436561044, 463314026, 863205618, 230428061, 966650827, 547682797, 878189513, 108075759, 615314463, 475535658, 936979885, 655171861, 1625425, 420066177, 840972924, 443074695, 168299312, 728639181, 662356653, 697001031, 39023331, 277636330, 958932063, 166783950, 760219984, 730335540, 341134200, 903297444, 672147142, 757192697, 612159987, 693449650, 542166225, 397907208, 936524647, 306376221, 403107774, 271792540, 168721673, 129471378, 275238213, 73834303, 551746181, 95426039, 73055717, 5957567, 450011852, 426249418, 486162880, 270503882, 489643211, 682008626, 98733861, 210140052, 274124726, 656340248, 281106139, 202934862, 786381499, 166054489, 950595555, 593409621, 92167038, 490968506, 633751440, 646050009, 409779392, 595285683, 600741589, 223604801, 605660408, 435445511, 647989314, 459411360, 886564084, 363907976, 935909206, 565390278, 955466350, 495127929, 180340718, 796925570, 135194800, 336270082, 412544718, 92791586, 596087276, 983657221, 369250531, 654038947, 68499048, 540594606, 868316387, 399448711, 671828178, 351935510, 927612337, 108796016, 311326729, 204684481, 630939198, 475121059, 697022635, 932075048, 823365047, 541660551, 552822165, 899272453, 371201405, 370591694, 631721051, 361833670, 296646509, 766010327, 293183950, 6959723, 885509808, 702185772, 371665324, 66402451, 275999841, 163165764, 623941269, 156097206, 447184941, 88656699, 313701651, 241538249, 946404394, 741166041, 480078239, 76335252, 997747465, 625922032, 495498664, 168216382, 429813184, 290669700, 26998844, 269308593, 749024654, 757427644, 96038885, 190213410, 112281474, 12369583, 443613488, 461366431, 364467254, 791138982, 308246339, 11582820, 935922143, 47541687, 143739658, 998141976, 586970747, 271820427, 689852561, 8264343, 333527743, 683336889, 748759766, 541959115, 239555431, 950877474, 745101167, 611615914, 957553569, 326156780, 825645783, 904760241, 403629235, 430757472, 827364267, 942204945, 363725711, 719645502, 724584617, 572306477, 804170816, 297029048, 639248611, 162091032, 507669175, 46131183, 680348293, 963374572, 115906414, 553966337, 720685156, 590231449, 500811058, 780023542, 558080361, 826597551, 272190612, 71597029, 218073263, 901314846, 134307396, 607589068, 836789539, 362613370, 164750925, 49789816, 116031580, 543486143, 548602589, 733762993, 689140802, 13284929, 781136346, 536302089, 171686953, 31614697, 185120703, 700078172, 603282522, 308354919, 52641555, 749437548, 395202827, 567188715, 498008890, 433591032, 888609562, 7730070, 121992063, 367258878, 650079916, 674418617, 113215565, 176109281, 300779081, 136235734, 123837550, 162687174, 792076981, 510025047, 323849824, 239754807, 829722554, 178372875, 771702713, 987530164, 659130910, 126816106, 622364121, 890694670, 745288961, 880185416, 333142975, 479744342, 351739326, 13809105, 388295323, 95881579, 250219303, 320685582, 581607595, 373699037, 257245952, 33879807, 537057867, 510550649, 968382568, 968041313, 90870925, 213774232, 326919053, 681526666, 422063152, 172030368, 619714454, 62920980, 904728794, 662630846, 338237389, 895758564, 335890847, 677626750, 623299770, 897561139, 127290272, 186867494, 84664895, 754390481, 428477547, 486178588, 681643936, 124235259, 335451961, 552059906, 86420000, 409337084, 158331272, 719356481, 359631442, 572788348, 703642702, 826892379, 546174661, 293007977, 486856072, 488119965, 885929984, 690207854, 473293984, 80847646, 658984768, 535627622, 668787285, 1030274, 97463330, 763400453, 569834826, 596811924, 89044126, 990855755, 558174078, 506612857, 472399039, 331439114, 312906026, 257403295, 564913727, 999352219, 883208281, 349421392, 498608935, 373446320, 295085391, 925989381, 623193680, 319879653, 766092309, 129291927, 686127102, 196649658, 93248646, 624011592, 652911518, 922660071, 165650225, 4953971, 664793070, 310867134, 409189642, 356530858, 186300432, 179552868, 81853386, 784186435, 158737966, 574570549, 743177125, 929557773, 16869899, 386989690, 390469317, 246162216, 342548173, 235701046, 307636713, 469419631, 16530661, 441753318, 179306913, 381167083, 684808057, 626389281, 839779359, 615973964, 752050870, 722194069, 960922056, 434597764, 137382625, 77615505, 937204582, 84642959, 931658444, 614738857, 911303787, 162881211, 6529969, 884814999, 258107591, 675060884, 315892516, 695384850, 399417468, 899119877, 773298344, 681799091, 420305545, 789164056, 559355035, 650886865, 901329622, 381640152, 249815309, 130461849, 657938453, 268054785, 272145299, 692232058, 411354185, 696998443, 267629226, 359057739, 355890885, 415265055, 538451951, 91976553, 967770516, 327005250, 899885729, 771036927, 469094691, 926844360, 980819754, 845093858, 912430714, 603048447, 87958944, 547208070, 238913891, 611044981, 73251585, 496965715, 588601024, 87412670, 314381884, 985625902, 24557005, 868511808, 669327059, 247750975, 816215276, 621445797, 680976479, 643248511, 485506754, 103173661, 184815355, 164327563, 656547010, 423596455, 466946446, 211895114, 272447487, 741565031, 528701056, 781500551, 684764393, 930186863, 790899884, 795885532, 608892176, 258521817, 610762892, 709357750, 317620112, 50678952, 955180533, 742878238, 64189522, 498778867, 731711215, 64940539, 730285109, 902456864, 511753234, 113855169, 152708138, 776812176, 200708104, 781527464, 735125421, 726114322, 81006507, 568003427, 823955520, 226921140, 129816061, 828507805, 741425559, 983397508, 690614989, 884623382, 23412897, 719552994, 117734305, 788184066, 592868869, 29752457, 839596869, 227469496, 585260980, 968470078, 703591379, 885875523, 456185807, 457130876, 204899998, 955900297, 64885800, 379874113, 357711221, 608336808, 197439537, 648101118, 815216334, 577321860, 384257186, 454354931, 492071687, 516570805, 775769807, 891972333, 29443248, 958606236, 200349984, 137963930, 347163418, 716678420, 545584866, 133581417, 837362566, 658961825, 200391655, 185877868, 902702127, 435753403, 24129578, 211030010, 66593388, 893642182, 910468023, 129996711, 252784141, 797489066, 105199339, 127638921, 656216899, 204056820, 611755757, 544074713, 139898785, 292626243, 720017993, 277025466, 628859236, 946954477, 961611123, 117875736, 501155224, 265516435, 299378942, 596053516, 63227885, 745119159, 92566714, 540787741, 638160104, 150807365, 255745224, 626913060, 525233418, 595427402, 48991782, 387075145, 260536329, 612724545, 825389610, 690004908, 416106191, 752728918, 211953411, 918223303, 127461090, 425661392, 848255004, 185693624, 974097698, 228254421, 97440032, 997102296, 716716828, 924549024, 970540339, 595970759, 12889230, 602889549, 80488064, 373291824, 470841671, 75509081, 917141880, 138877057, 595019802, 629969658, 357212795, 529118854, 442172501, 500392744, 506559285, 517457603, 658082222, 348765651, 327741385, 373223474, 449020112, 206362393, 474395648, 130632732, 677525242, 3584395, 262831452, 601731446, 152080506, 905235771, 425391916, 596175189, 189958622, 132140154, 676674094, 181217790, 894099661, 418833818, 60855971, 293967011, 614549658, 281282339, 142599524, 823725515, 700021960, 352086547, 534684354, 190215926, 627509434, 78744705, 421433750, 658602401, 126687235, 878535374, 404334963, 180451282, 835870119, 336154529, 449342139, 869353622, 828524842, 992374832, 950196984, 523968726, 395945064, 826532949, 969878720, 579511274, 333179474, 783368008, 66347660, 652780213, 29921682, 630434989, 914700321, 676938529, 605901873, 384503135, 120238842, 689936494, 878798288, 352343687, 563658995, 44299351, 814583659, 687607320, 324730946, 262524028, 930977559, 136853781, 722085372, 735675193, 645053150, 625434108, 383603034, 954324442, 357111464, 112390557, 80051073, 907566309, 79943859, 61290820, 746725986, 136927692, 612871234, 180525326, 579722790, 651699908, 670176421, 912018884, 10871275, 40627998, 187246592, 580992848, 561703321, 262712278, 100922893, 986305979, 180389734, 909884468, 308867111, 512067840, 517798464, 924251468, 613017594, 711224376, 760183198, 205647854, 869180414, 97791472, 303075330, 554734440, 3221789, 557762295, 488201735, 227531043, 718940826, 937304988, 378528231, 587749449, 304030949, 547602089, 76165051, 779272162, 822130981, 438621250, 664308606, 47509413, 154277496, 933016163, 396747665, 777132612, 9749052, 612876884, 979380114, 427758530, 24723631, 913694109, 599233438, 235551587, 145120227, 966291317, 53841101, 94175992, 947512734, 95174355, 450609401, 913071412, 107593911, 563221527, 594629414, 481707592, 392929753, 335333447, 313349518, 749830865, 908151886, 839712427, 502996470, 108267099, 286086896, 277554047, 465392174, 421245032, 859357521, 148294323, 583556956, 769640359, 885821047, 648411522, 883787724, 565215571, 551900903, 227381717, 179337799, 215579061, 277768082, 278693776, 1026239, 584583087, 528371462, 27881546, 465620689, 200347228, 564039971, 35181096, 751134920, 755914020, 687547183, 162545303, 738876029, 122568150, 545180164, 180560379, 636716987, 629069532, 510607579, 931638610, 372950545, 161638197, 129598635, 289600872, 582577175, 265271503, 519271160, 337978431, 513825134, 182797289, 553890911, 219382974, 279910065, 146311603, 673743133, 159595467, 124724360, 720233782, 321393619, 906884864, 90926297, 755159125, 849308334, 149686146, 136123939, 793812586, 66218686, 640522610, 630339840, 217702532, 603654024, 362542712, 886598550, 565187380, 45018716, 212390860, 134883046, 758521100, 191210934, 451932049, 215850361, 892572290, 818611148, 209620804, 502275128, 726487412, 291028230, 740682259, 877053525, 219571800, 171330483, 253962049, 727432708, 573056403, 777403197, 914105575, 750305226, 559679635, 561091119, 547577751, 796039775, 971738079, 29905273, 701265228, 759589061, 646642961, 32414453, 555224262, 730056879, 521295703, 202883014, 755998276, 434296667, 816869801, 522006294, 169420067, 895512846, 55939321, 413255446, 1932990, 566791972, 779464792, 909375144, 136244709, 56983629, 968422601, 167817775, 205758987, 262367428, 982289837, 335033228, 727349034, 617541588, 218160552, 879535082, 137183478, 449664955, 649648520, 326003018, 307092994, 981178957, 232457573, 205756936, 531339011, 367310368, 614050915, 374043031, 824751732, 243501226, 963979284, 885413760, 162593816, 266583069, 262007442, 929768126, 524240241, 704521420, 672731936, 63069349, 691358339, 498107543, 732140003, 996339573, 853864280, 8199845, 841400995, 113284341, 696294438, 946021267, 842405338, 155602539, 389287475, 882406311, 299552752, 694176621, 76375646, 375446300, 99700770, 301371350, 680178774, 947986291, 216343896, 923926103, 197498381, 880089955, 682832351, 931299132, 2291854, 411495653, 471131894, 338299517, 467822996, 372298362, 95431939, 524637902, 484706733, 79319468, 728352801, 182406658, 438291293, 240323456, 32807331, 813448324, 388081943, 951627688, 472253822, 226928870, 964921536, 449339131, 652420411, 207889655, 793872474, 649228648, 309651489, 89946019, 945686697, 316091287, 299468881, 759378650, 840185565, 650402416, 199844845, 660382763, 46230231, 190167695, 682845053, 527648497, 895369336, 928605055, 78160345, 277749080, 739220543, 160658503, 255953763, 485874857, 724057010, 206669927, 567042081, 605305394, 989064566, 375561671, 324269624, 820663966, 565569459, 353942730, 332711124, 730876310, 211438830, 560825978, 10880540, 123036380, 717360380, 162993261, 154636101, 798053149, 641884840, 463856691, 245548445, 786403917, 993549722, 856462645, 15295526, 617172314, 245775578, 705873606, 271770260, 94311296, 779699197, 378971812, 696922473, 176139531, 497457604, 584690066, 549640892, 900414950, 929986963, 33196076, 271676298, 210162793, 539367568, 202745220, 65010558, 562426437, 728679498, 172186506, 171334862, 584946673, 359619231, 303977426, 65230784, 252085497, 253876013, 701227005, 128986136, 885427572, 191682412, 377308475, 420902788, 179712760, 725658526, 947535762, 228900794, 256797037, 100213668, 50699736, 563265711, 523101136, 309323731, 62344563, 708267488, 57372597, 553288769, 335681761, 515715235, 113764173, 202754125, 215928382, 413925734, 948301104, 752049806, 69682961, 371955952, 149258948, 824024679, 7000754, 855356995, 955499409, 157586384, 824087867, 70916440, 889068377, 869052279, 26942440, 579303134, 150288214, 480127660, 14786410, 132250984, 768418743, 795316757, 207277247, 963222774, 963198716, 576082704, 857329948, 565389667, 168700653, 402999095, 472246007, 240535579, 136542961, 447368047, 993494432, 396920176, 191884789, 351868965, 64155272, 48322549, 526104909, 132762905, 548651585, 811303194, 950096165, 855550479, 573288513, 277084447, 950144194, 693392938, 624036629, 622616386, 669630360, 704193554, 591939030, 519582001, 695525486, 325628746, 961468805, 533654550, 237560440, 990116913, 658961637, 780379989, 343470601, 219657886, 68943320, 51240894, 624426920, 608347460, 325190579, 293955618, 958857590, 34673312, 225345699, 67923645, 748255536, 827632207, 618633790, 682814202, 38653109, 51003159, 416790156, 927001870, 4843472, 758635726, 103460839, 465828046, 581174801, 284309944, 485987846, 405045476, 320370416, 73143641, 915632623, 1673401, 506078222, 600369427, 770578218, 691367179, 573936140, 345920038, 620755520, 685002275, 454229858, 360814251, 49117107, 143996143, 264254144, 571929996, 47940988, 891888199, 288531746, 427118187, 256712101, 981515345, 85841278, 731450737, 615920333, 844862758, 10209715, 96180445, 757098004, 770866239, 785278617, 825461973, 281286875, 407570741, 139428614, 553487410, 87228230, 590877565, 784880470, 90598589, 40452052, 534711315, 176434382, 955927041, 586106303, 579785638, 155358895, 766181225, 984922029, 438517676, 940004131, 466658744, 847732488, 369593137, 587165877, 877175551, 252324441, 726397362, 373195963, 808957444, 486781397, 740638266, 209862744, 469448217, 494755214, 925120007, 814590019, 245796270, 467509929, 383793345, 624905027, 243894364, 564474821, 113275478, 211436728, 346218392, 462551377, 274340743, 776167844, 530390944, 214240677, 648676161, 651063523, 671774825, 851074799, 478902472, 219901936, 186189885, 640083671, 119484219, 452697116, 144000194, 863037539, 445781175, 994577626, 195777681, 55396941, 677437414, 594069728, 544191844, 34895253, 453281206, 181642393, 867663397, 405877745, 879678106, 445565606, 219437394, 294435913, 871725860, 225336336, 633114662, 174670895, 787559160, 306656437, 960710660, 717208976, 991188529, 97719311, 471220471, 920459882, 97069384, 792130292, 830644206, 429378405, 737218732, 853878125, 523325221, 632668188, 306138379, 54869548, 904830680, 221558975, 8737038, 273895230, 124096195, 717663339, 20861037, 325552626, 37375914, 917466766, 581096325, 525493738, 663286074, 857587858, 353070081, 25944121, 317758961, 946136076, 490370774, 380437284, 259950475, 758261283, 515550247, 327645520, 457795934, 876330508, 713924717, 337006884, 196362031, 255745980, 939323594, 416243846, 80074232, 131037661, 423128491, 238184174, 529798744, 221872770, 535172836, 45193096, 404674896, 73134628, 598416294, 304799985, 964112805, 727084234, 30793647, 929171366, 600464365, 985669253, 117500676, 911895709, 58563335, 974646084, 277598344, 308724974, 557980030, 40880428, 166798507, 781618107, 794235797, 458552605, 20657536, 993278967, 886606311, 562047912, 561860663, 232593431, 747922664, 5459379, 83227078, 395855316, 702583528, 169560403, 749130927, 998815653, 98854320, 72219236, 807416602, 263239594, 965966779, 263470458, 296662703, 111554269, 974552937, 79122957, 303792318, 350165235, 742037021, 4154518, 49750932, 20285562, 53826164, 562467279, 55167286, 469856687, 240991096, 459638691, 111603934, 502479863, 903226983, 574949596, 557380014, 472890615, 86518745, 504447914, 511601832, 8157476, 603468449, 300626425, 891794264, 587847533, 359684525, 555085963, 694983770, 587130367, 141220582, 348638767, 67042578, 686234010, 303374670, 749585339, 10050164, 105301447, 729663263, 476689006, 607135697, 262234419, 789119231, 294478241, 162331272, 659077420, 31525393, 720465659, 735332751, 197115272, 882900851, 667622672, 906600566, 976017673, 814403651, 150041678, 365124610, 654762938, 43528208, 885607303, 489738162, 344743049, 91568512, 16811990, 290006168, 81716164, 485254443, 871675164, 651347275, 481496455, 394434154, 202047619, 722067184, 516743775, 921318432, 539658266, 533446956, 636187761, 580332916, 775251200, 565721407, 411544427, 631108925, 231764000, 383716529, 427994889, 36564662, 108560820, 277685687, 519260415, 351827180, 983368499, 367012544, 425462701, 478347925, 588240383, 216373993, 789258245, 168840447, 124875822, 124938974, 471500893, 687997184, 494435127, 452801396, 348196158, 637460526, 613852951, 67035626, 435694858, 422675205, 202202193, 788519297, 597157693, 738363900, 42136931, 115986582, 901015240, 241072582, 930837940, 874175665, 65482394, 904388329, 747643519, 320084523, 601973098, 379766443, 708905846, 363568140, 720807446, 905246551, 509463445, 660147362, 587693417, 559240353, 263777273, 548889016, 421730945, 599058604, 176003984, 924529862, 502076401, 271942684, 162806317, 568978338, 166958299, 9649071, 115594430, 128957728, 690109308, 551721028, 9383013, 580209654, 769389398, 455186677, 911846438, 454807537, 302797519, 114631389, 702546060, 524577890, 319649914, 375656128, 852945955, 83571093, 695209890, 196506812, 721218516, 606235773, 129836886, 548663025, 265791324, 666708673, 922293786, 623513696, 860710529, 777564418, 845337611, 934654564, 471378674, 432384043, 132538616, 114046268, 809946190, 818723517, 283258802, 693486023, 317243928, 850297010, 81645797, 283411480, 550679287, 767235459, 799046412, 759079842, 583415547, 660527451, 810698860, 484845285, 681816372, 325904739, 955906233, 809202058, 158128549, 913758330, 112712956, 369329559, 433729542, 670495786, 240803513, 860140250, 156272641, 962935905, 419523092, 110029817, 364879333, 162575530, 324782531, 331277335, 141738528, 423534154, 46764790, 481479332, 354120825, 906396208, 964555240, 357000976, 59641766, 486314276, 693520945, 288796553, 749099015, 10759251, 176956905, 857756218, 80827183, 59953503, 682255473, 2381243, 469626649, 277863697, 55102999, 721540690, 855814989, 846988285, 103895767, 505770420, 766059469, 925582402, 701557364, 332424845, 251619142, 828904420, 137444072, 842054878, 28910580, 519120080, 94576497, 562213048, 284726613, 122503535, 105639278, 21120304, 368831421, 989783399, 797513707, 25583415, 145717787, 443124094, 762967548, 731058666, 311308253, 367982965, 377679071, 386484466, 259109615, 799968491, 526443037, 771009350, 971395738, 492454579, 789118017, 363171636, 185904455, 150918733, 232535022, 720363421, 519317708, 197394439, 925825548, 316766281, 526809071, 303334665, 343960510, 168630397, 8187195, 548658771, 791548993, 629387249, 998987026, 19895419, 911344183, 396562254, 381705957, 308235776, 167426455, 908186431, 456340900, 75634104, 400135809, 470930996, 805229484, 469838530, 814364909, 924006687, 797073968, 871300292, 521131620, 152603967, 718046425, 384642287, 794208640, 945079675, 968812255, 34019163, 357037151, 962066701, 328722876, 887283575, 508548692, 232417650, 923974071, 39956870, 409801919, 861671326, 454397471, 462547923, 765375913, 172717550, 418419039, 776352497, 875387370, 37488753, 431439348, 646465863, 406219328, 384667450, 75154559, 303151089, 309899991, 522120916, 785996288, 849611270, 506018677, 629971951, 686968087, 388278502, 597144410, 960327621, 716135765, 601136701, 387509946, 634931410, 949204194, 267750588, 564044294, 233502301, 588908365, 622997794, 777299645, 311135199, 422815915, 30825977, 470131465, 768023135, 721914038, 924217613, 479876121, 677840336, 952336424, 530077473, 524062659, 365924988, 745675734, 849451267, 440047101, 942706320, 620069563, 510047993, 820297875, 155905928, 630955180, 46184373, 74147552, 726922237, 845197600, 726116551, 923878260, 832289345, 652538682, 851352802, 750259860, 706876680, 438874876, 985650633, 349716865, 744038045, 703021210, 223289203, 933229321, 137053780, 41248733, 312319683, 162171586, 158570139, 106818310, 733236410, 5747707, 489014755, 4893366, 643313816, 634875442, 55387775, 481460389, 299654462, 338629995, 596023014, 822526526, 424661120, 731341946, 489599793, 232488623, 835554891, 282047536, 866932499, 492177253, 101036573, 834389950, 533037000, 199042797, 264525425, 523653486, 803024792, 54411242, 116935533, 514300633, 916235762, 838586778, 794076949, 653480771, 320662258, 897021798, 300555967, 869647716, 943693616, 967613960, 22238268, 552753628, 791315247, 136182305, 495348529, 410578192, 599826490, 130990930, 885581284, 4192866, 438779561, 904919864, 809882416, 45368934, 71504288, 563291873, 937644328, 774557337, 743846937, 893293387, 571716078, 473866281, 641506400, 757131486, 939762335, 669357284, 55732135, 167440853, 459865908, 844342581, 918358878, 342821635, 452813176, 318155332, 602939002, 432226818, 737178750, 712425326, 957351279, 910199344, 933499241, 782123607, 875800129, 967176737, 329638625, 825757024, 177727030, 93061971, 828682632, 483736049, 905905831, 191135426, 322153359, 190141672, 874822487, 251923092, 452554399, 55211557, 479929701, 262079971, 13007838, 102178687, 608283311, 925874121, 731095059, 242036093, 777330736, 902949360, 511519284, 727633577, 551800283, 223340363, 389094355, 224381125, 276892740, 449016450, 902796978, 230647426, 421782694, 720544968, 610712440, 579599929, 59353277, 854839522, 787016179, 256068249, 389871162, 940260068, 468816457, 64043553, 537093376, 382331039, 826159478, 659761268, 11510807, 635809656, 945449068, 948686399, 467360451, 835989858, 483678503, 875199295, 393101186, 657977076, 444446494, 581795599, 129068786, 684936930, 646372987, 933126129, 713153971, 846082920, 489920051, 333796721, 620046410, 210020014, 363579120, 380312255, 194386610, 6674001, 571682292, 326325670, 193694927, 490085523, 648295977, 834602537, 149494496, 119406553, 51495365, 347144130, 442977305, 807760759, 165604812, 235972306, 243891366, 105326436, 280404575, 109111680, 747169513, 404461710, 573118577, 109656609, 528516718, 976887712, 693358216, 38683504, 517194821, 521523192, 48579624, 544227584, 826843812, 855435298, 629171361, 807760259, 12522258, 668096641, 329160873, 194237271, 336836258, 589336826, 227806051, 95339346, 414960141, 158689409, 316339601, 643069643, 943657841, 512124231, 708634729, 416076414, 558722946, 666636428, 162614186, 77983086, 543049004, 648150219, 567652605, 9308141, 807023363, 221083517, 731096984, 283346105, 155784880, 717877749, 310201989, 625180319, 983343597, 663510519, 712074694, 912942730, 596871642, 271441999, 953379652, 286318111, 552500531, 604711387, 730219747, 124478436, 584931382, 734796132, 336109819, 333864493, 585071234, 37214523, 92413667, 105917865, 53086192, 769639147, 556015600, 520619778, 720815059, 353193066, 776829977, 867757918, 266242034, 919602474, 880067065, 993626165, 320142211, 877620869, 748665395, 445104305, 900806716, 261447860, 799209058, 69435706, 161785093, 925325580, 151123589, 518645847, 73667068, 388940881, 653258811, 610779229, 152211567, 830856552, 912760117, 341963036, 654685363, 341088237, 827302873, 983040367, 532590096, 865745570, 595253263, 62843680, 954778478, 273719603, 156244788, 327007765, 534113031, 356751392, 557021749, 627493073, 58732674, 259836396, 812286398, 175256776, 2404527, 845286443, 11894875, 920692034, 358312178, 781605285, 849588917, 769039719, 202750077, 107944877, 890636136, 18756295, 759938150, 24766797, 876994388, 882612794, 667392551, 634964409, 851619216, 988482237, 127817297, 695581257, 804744417, 835706955, 246211560, 721479678, 228768960, 374663135, 944755896, 173834511, 531791147, 119916540, 603069208, 726731416, 162815533, 836494221, 143849481, 216532660, 596562365, 644496777, 52751261, 975944600, 640084125, 116270272, 896622134, 71830572, 243351138, 545929565, 160426811, 419584043, 70655846, 682568513, 714968448, 234835602, 655340058, 617526345, 526526396, 300499564, 506643095, 2301160, 822469588, 465856238, 796017271, 750513192, 855197909, 353204643, 896828952, 373145353, 785408877, 283598939, 143813937, 222248637, 32115506, 611697187, 244400252, 456206623, 964897201, 10383796, 348508420, 244679767, 57536453, 534799239, 790986674, 320686837, 896048053, 373545254, 692295585, 457662575, 324900372, 651694674, 579155749, 800650169, 177436433, 994221136, 207416340, 11113481, 179825081, 195281417, 818975565, 470783820, 209019262, 641033620, 729026333, 681742599, 694456317, 694460189, 252036545, 913993842, 218067239, 145382415, 262541207, 214461157, 775315565, 30737723, 63974719, 861998028, 534490378, 786424286, 268991687, 147420657, 13495270, 895425419, 578897008, 578262061, 800229305, 491411603, 892777318, 851833195, 57884514, 854488120, 909928912, 788846125, 213230468, 758263248, 377022205, 850705167, 220644944, 279942837, 951210679, 438039789, 423755433, 494885430, 957637736, 995408914, 270212793, 176096511, 430075380, 722369810, 108016341, 83203569, 146318918, 540276724, 645191838, 898574807, 65249177, 226743149, 641376641, 953705151, 779198562, 541572677, 98403603, 754212686, 897696360, 9415448, 61787708, 9111044, 189540852, 168510667, 17888601, 287786267, 565969451, 506562578, 750030166, 139789830, 166539297, 995089729, 675802827, 102397057, 741910931, 154741923, 226609397, 634230311, 686164807, 163491855, 391985846, 352895145, 226088473, 244249976, 934558825, 417751153, 91133541, 287836938, 37908240, 558723062, 429579339, 330901542, 101048894, 774488319, 189716155, 749212489, 822116455, 629702608, 805896320, 388364797, 471701529, 272650279, 650982539, 337532921, 287759581, 827463140, 7009381, 910735664, 68270091, 969492081, 614016261, 562420273, 369134699, 28283293, 137644096, 870155705, 691606302, 737082800, 147585893, 435312736, 456846962, 90098348, 970558829, 829255120, 35360610, 388531310, 922114877, 463489575, 54367471, 952238556, 682428857, 149675315, 95185812, 4675630, 933183077, 448270727, 707812609, 767728469, 963849845, 101052092, 71806393, 489297868, 390920736, 977587250, 556915450, 264733932, 394562182, 378411767, 518928347, 240021253, 749569497, 349338911, 442042927, 487907342, 182663935, 498684248, 816660544, 294697324, 804702729, 48606227, 727520775, 580489500, 759952738, 498140751, 639167170, 846032802, 720029958, 760671377, 241453602, 945123293, 913948523, 14541462, 63062868, 414949696, 72594923, 865867278, 878454626, 218972035, 35908768, 350878395, 24505844, 697787707, 319808562, 183574629, 408919603, 625132797, 709668629, 605007297, 657843279, 857857988, 361544282, 278607656, 589245199, 76079823, 397580017, 772222653, 279978788, 756142077, 503943651, 521032184, 987076262, 97873147, 868973279, 527978697, 42718736, 607833781, 731820234, 483300806, 786769936, 342367670, 901597049, 24434773, 479753980, 201493212, 423089125, 732457425, 476095062, 539585406, 530583558, 593585194, 352155627, 813779254, 321796043, 201771318, 637270081, 893463084, 168290807, 142437417, 881775902, 695892180, 399407650, 205183788, 570896049, 648429091, 145192383, 330510351, 192081506, 771118283, 50060645, 364994558, 170039893, 717742189, 138314026, 318753208, 857705099, 57561320, 978460897, 769666785, 306055182, 980510368, 520397168, 976676144, 902020734, 492085571, 748872621, 192926066, 917031008, 845244083, 716150466, 63156343, 899918957, 466516598, 445521126, 167495407, 682836445, 742906315, 850072358, 328161145, 530116499, 706044649, 779589576, 421075763, 845540729, 35577712, 657394905, 821789288, 288457336, 824723219, 32261797, 238326731, 18260, 293243174, 103660449, 55359406, 445112581, 567977565, 459593660, 550214428, 709800843, 321689932, 555614772, 359477539, 693691528, 511296426, 563094366, 487125841, 15656349, 179429638, 55710080, 38546366, 998878664, 400515304, 555408954, 645647415, 673389898, 752333791, 841422625, 213640792, 732409374, 811192808, 237205923, 81018473, 767235662, 591449873, 833721899, 212088935, 467233986, 131429950, 612247660, 697019708, 332018073, 603769052, 660367592, 200545046, 578770432, 662677236, 857505470, 695520183, 166617305, 141108696, 809121892, 858255626, 875545738, 196839209, 20542613, 678996575, 858117661, 443146810, 18473261, 748334621, 95262507, 31991300, 645679183, 145093179, 985981275, 368700163, 237020812, 672487816, 449086535, 857160737, 823882041, 99432543, 906871546, 103191920, 644156619, 576936275, 98676457, 837991959, 350785453, 17857977, 663838787, 741919093, 740679896, 378972250, 374203455, 347079826, 110000263, 250555949, 55072078, 293859791, 186450418, 269384489, 428286561, 350876115, 293091469, 948728132, 911375053, 388654737, 922305267, 761841227, 235220125, 171345822, 139831396, 784473113, 333384232, 603176339, 439376964, 170752592, 937667456, 957032239, 678955736, 461976797, 759001081, 562627940, 336103574, 257766346, 713197720, 986127164, 472008409, 633249772, 998233952, 269464063, 61982664, 284787763, 842227964, 586852187, 932190154, 768208775, 881131507, 586169798, 274463646, 101900596, 988485979, 80981980, 469016392, 208688842, 307335214, 454974902, 489003403, 342983769, 286011657, 585838603, 55913500, 245764011, 218206758, 710448113, 634414123, 836663737, 220860548, 866499868, 343106156, 980271187, 908903195, 906575985, 900919181, 13865154, 996292455, 637583375, 596513463, 467538040, 292401674, 478274926, 58058278, 984688075, 94079979, 877201666, 705663465, 543746541, 474060890, 515587786, 973220043, 315551241, 917616820, 946444067, 729592736, 879055742, 214085984, 638436943, 86762697, 454797896, 541379768, 648654200, 383094656, 513094877, 632576349, 386409273, 737107187, 969722542, 480135116, 534333596, 720588362, 342059801, 994330150, 638175231, 783692184, 640138787, 649190807, 32309320, 857348071, 743882549, 992574858, 508445864, 47831666, 249070053, 181261489, 640437593, 119303700, 378383281, 202563138, 492031829, 391201829, 105536271, 685318430, 708117200, 77563126, 8371422, 413669006, 615998721, 452217236, 551738880, 991796856, 362336921, 403778382, 904434001, 263024609, 917921353, 866026249, 847189600, 256958217, 934102126, 931690713, 427141032, 468686391, 420549357, 122254659, 536855618, 27256515, 970535536, 198008661, 299042106, 191462360, 59151141, 159209885, 693023030, 922701726, 421775869, 269231581, 351563964, 175246361, 768501197, 972570681, 449123207, 67751497, 637158532, 690328380, 352896161, 274119093, 793619754, 707240821, 74644290, 806672285, 846142467, 781107702, 317510678, 576317692, 442270613, 725681775, 631900226, 228092108, 578152366, 978736085, 241577821, 442663181, 195987837, 679979578, 453918890, 304230998, 805061131, 275830798, 461669807, 121519172, 769884928, 421987798, 145150763, 138716563, 467456002, 100487028, 383695827, 204255416, 366381417, 263670193, 606508238, 978081882, 51225567, 652080579, 894843137, 786413845, 790569701, 569320768, 571207253, 934564782, 526791901, 842969607, 785718890, 607694149, 217173423, 137481138, 737049957, 837357984, 221697624, 938295588, 155672047, 318598521, 248631263, 401905818, 623741818, 135060185, 921731824, 526648608, 563058618, 849604279, 187873481, 135423967, 169029216, 361676923, 784403392, 549144223, 251248336, 536634986, 837956182, 23231509, 729946810, 309806198, 469716158, 882701964, 824537885, 586586606, 205795448, 444484602, 730450441, 561865152, 263061096, 172483978, 522578876, 778357825, 409099190, 151766587, 780468546, 337927191, 265499442, 856661299, 1394251, 80856485, 114134706, 525887312, 515004071, 561414751, 563891065, 420115388, 457670972, 577223776, 521114001, 2934913, 502398141, 106069733, 205695730, 116437247, 195216110, 304232414, 264693950, 496130715, 311508175, 958158390, 942853486, 623543842, 927839469, 87872275, 178348232, 101681328, 195203363, 152377918, 828230062, 865667823, 242647486, 272624894, 836418407, 50187086, 197062546, 273248035, 81254136, 543908051, 66122985, 356404909, 386699509, 95536886, 732423842, 717831803, 116419965, 982452167, 42710267, 643058368, 163683946, 239103742, 921857091, 720078174, 725983367, 932318794, 280649074, 63997382, 61243793, 706160985, 964200691, 649259340, 972223941, 580081552, 600552643, 968280514, 49216421, 757589056, 37567752, 357043348, 262171963, 661553279, 577726223, 955859685, 463230354, 959653079, 827428782, 719401255, 2569414, 425796434, 367538634, 637206285, 934183696, 626105769, 474044195, 813002006, 552695983, 291185765, 35600352, 258758900, 151947678, 190115898, 364623319, 901495084, 664684679, 999505452, 187267445, 279958029, 201253394, 730486242, 364151641, 769275977, 465633843, 874981252, 131293218, 532211890, 833796744, 977913361, 497996372, 85373383, 623598939, 446253783, 776873912, 494219750, 115309506, 408687535, 584559464, 31534370, 450594357, 47881375, 280170495, 788303847, 134351948, 681249752, 560715547, 977312997, 923838854, 519676119, 804720456, 127468553, 473330005, 399540912, 150383864, 601413927, 887892687, 343515321, 708944670, 720212067, 61506451, 980754004, 231708426, 517714796, 705832419, 937933344, 684758571, 928784375, 623452470, 276578194, 909081914, 268085240, 288316398, 297229204, 86339447, 756285908, 635027767, 938615973, 359537975, 142646694, 990124506, 163617464, 556306732, 311153717, 652539412, 733035681, 270088860, 447372457, 173482233, 776349433, 118239219, 51767685, 125460914, 262963442, 365393763, 600757462, 937186203, 970369111, 477586324, 879529388, 248804310, 625747773, 38425585, 96400573, 281673158, 221138419, 242895088, 726576738, 432468123, 267529500, 335322381, 335536083, 786546225, 825167725, 466799827, 77715718, 13512773, 97285259, 990544091, 737087268, 708100916, 461516001, 216384852, 601136054, 549944420, 297691060, 180815673, 16471110, 99215510, 923275643, 705350332, 239251993, 245800258, 279414447, 322243512, 75262836, 812001412, 124061121, 430087336, 497334782, 861308011, 771034249, 802033890, 901342146, 231562618, 220847247, 607480965, 923959366, 324921077, 129856701, 80596265, 759576405, 454959281, 490579027, 868933938, 381655335, 217000136, 883853925, 94935510, 386375444, 479089002, 299627084, 288237422, 755779728, 744263712, 905043099, 159283522, 994681169, 640962338, 767252120, 450362016, 870390593, 972318359, 284741460, 64409448, 263505887, 319001453, 257453880, 2842780, 426938950, 715844736, 469602321, 668381605, 911492587, 81275691, 268510678, 648831681, 225887400, 827261525, 558307113, 878343341, 634399575, 194165756, 677946449, 53873210, 885766479, 622660773, 406166107, 992875611, 244123267, 623248537, 417003766, 728645744, 941253213, 531436981, 223613202, 444243460, 615226458, 960558780, 224674462, 595756816, 223532756, 307280868, 247927813, 747162801, 892122877, 194570928, 296218542, 546313150, 616199646, 86743386, 140903998, 234682501, 382613809, 491870386, 80247005, 873154494, 280791653, 489030447, 167512790, 341681456, 363193383, 468897832, 854748510, 524171180, 818991988, 664159015, 263535988, 695635016, 543530251, 45953529, 778416548, 149058238, 138530868, 672099484, 750873430, 722114814, 753322639, 720039177, 140835118, 451767621, 910257828, 219427606, 92898961, 480616062, 609647102, 966547907, 758277768, 500263551, 521870031, 888898943, 479613082, 515501522, 418223962, 69022553, 74539409, 99535524, 277251822, 704768987, 355622893, 597499174, 383227198, 41751671, 888441088, 63100576, 16049150, 791332458, 631268038, 323422766, 529110229, 739827710, 116362195, 975088560, 342849749, 921770383, 8807833, 608960070, 903494462, 614577131, 211970090, 494617023, 758509954, 138095561, 935922175, 747881914, 111553058, 296760731, 927308292, 114633751, 292052257, 680492314, 670867667, 369727012, 810575133, 896192078, 754060832, 153454033, 902425184, 162614261, 924044845, 761625092, 982759078, 441057256, 152934166, 621425310, 675857261, 850576022, 755760170, 240353016, 344859623, 828884485, 854470112, 935262031, 418822573, 708859028, 728492088, 520137151, 798008279, 29053262, 332989505, 577454263, 513439417, 266216497, 150807358, 357061697, 241155022, 296149738, 949653667, 857360649, 277547505, 12032924, 720943718, 770263207, 513595359, 742127048, 194927951, 150558129, 486725130, 262374809, 751637620, 464213654, 172666197, 755221094, 722710384, 667007078, 783677716, 816090331, 428860085, 968762054, 655128853, 959563035, 938418542, 669516577, 939723552, 836411102, 367090141, 325151765, 167505141, 951219890, 940500400, 81392320, 407489667, 389212184, 470605770, 614339196, 815358857, 466347618, 883600245, 262189151, 554665415, 383633882, 363622149, 855353892, 205304093, 2228393, 118835755, 124127203, 769118506, 39036799, 944926340, 917413434, 983104951, 136938911, 652575896, 26848935, 518214023, 338871681, 78860205, 624509720, 240392995, 909419244, 473081505, 803595723, 277217768, 66468200, 716785354, 329619216, 48500986, 798676038, 939674053, 182118174, 437093817, 267619280, 946208494, 667855732, 173906004, 618410046, 886231519, 834274728, 235552632, 856110240, 363550144, 161828154, 868656721, 631531070, 329174444, 898342453, 40113463, 368917185, 2159290, 788510769, 420083323, 924508669, 671965247, 476441002, 644050601, 999882306, 590847880, 915155032, 800441775, 453551568, 799666338, 128057424, 310878492, 822306417, 307061928, 760223596, 66598814, 629058950, 179244616, 805932346, 71050953, 11690073, 352660312, 594396308, 137047895, 855286925, 725375122, 769488055, 467816820, 803267451, 410183668, 313505319, 80788621, 841465607, 645562386, 666315060, 464563103, 772196078, 468291000, 121702433, 813539703, 91445342, 825475795, 402351863, 276147520, 727571620, 347235558, 416370894, 223259575, 650399170, 669803702, 995334884, 695701717, 695768976, 819243162, 41840769, 983435405, 673902811, 919962580, 861778884, 140331373, 937791460, 145038861, 882611250, 733707374, 97237429, 843823528, 68903956, 605559301, 732343015, 362114632, 668304517, 190172603, 230799483, 786403818, 543647274, 768960072, 630878559, 6704828, 199247172, 724063703, 379251356, 632224326, 402895556, 622596908, 975741201, 311533734, 10888135, 854395126, 923889141, 768843235, 384416426, 5048158, 932891365, 724910038, 588376725, 886222816, 231710898, 996277666, 194822623, 491273793, 244188839, 102328628, 408443586, 980976385, 511750824, 737247791, 808228662, 322264436, 7728119, 368999099, 224808744, 503002027, 266441822, 614403159, 460615009, 439279448, 70791993, 539746372, 682537993, 838883729, 727432255, 917091822, 937005626, 224821415, 882714531, 455964492, 438705287, 744279680, 939016959, 969897386, 811975434, 707056299, 28465969, 518532113, 44047520, 939939890, 124045652, 727743750, 278906559, 979103363, 395964261, 938291839, 669976982, 638329124, 261864431, 225080144, 999420454, 73220070, 418732478, 615348496, 200386077, 389497151, 549381022, 995376014, 693816665, 86201648, 957840968, 678633649, 36245086, 685677613, 87234598, 760960473, 135830255, 118424122, 636959491, 175009784, 548653284, 477510266, 283239142, 935723245, 535324332, 457270853, 760084543, 713872793, 361225423, 684337215, 643322847, 874923765, 45356532, 334320478, 708659982, 281920044, 447891415, 47612293, 412220162, 96382760, 906235796, 354504989, 362952289, 469680996, 455975947, 514728806, 821732591, 780357278, 359653887, 322278494, 159142543, 957016970, 309628585, 403363932, 277194224, 411374783, 962696191, 160212831, 978775735, 732599887, 264539850, 310948548, 977354408, 468703903, 959717298, 149039326, 734188114, 106092476, 75118842, 498226026, 571231955, 618710812, 574956485, 267877218, 93077414, 256280396, 791663481, 765041991, 347762599, 208158788, 537777192, 235663120, 463575828, 889010930, 551722394, 383901419, 610099252, 224360025, 821238571, 489614484, 623661233, 196543733, 92832440, 175411028, 340365701, 788802318, 793818953, 519841618, 66047330, 448487961, 550143313, 786266031, 111771000, 691099510, 748007987, 177515117, 66492459, 598395640, 850304745, 6962070, 38443827, 958434102, 792886226, 364901519, 110982537, 443301355, 843570004, 792397810, 481782430, 223078306, 948212900, 752483398, 181625857, 429071989, 836839597, 312812875, 998138774, 645716124, 507754267, 533162443, 510544201, 654786600, 859258635, 646793912, 827356245, 86385354, 614240885, 898560407, 857669069, 612593454, 668654087, 51630048, 760137102, 624791077, 815687819, 603587397, 168641939, 57923252, 567610426, 507086402, 98812766, 806717338, 15189597, 448727840, 904549008, 658492091, 229744719, 779462075, 436770824, 799750424, 856561144, 782841688, 310168376, 964332996, 712589072, 958984907, 485381651, 565408232, 75018694, 751693269, 228119549, 653046765, 200292909, 206846983, 268295380, 293943808, 284727240, 881220393, 711293188, 248391510, 911033595, 644065935, 530131948, 118592035, 371428265, 192632173, 74028667, 637846574, 303399615, 183614596, 953058622, 400502275, 292777945, 775476421, 684702920, 365358483, 374629044, 18803402, 245309491, 581964923, 502635872, 847391007, 801414257, 339292262, 699222997, 372465482, 96665443, 795327921, 164598911, 234536908, 466394088, 878933287, 250825448, 314499320, 567557167, 742875575, 37914577, 896208621, 643280003, 118394754, 629474438, 919623053, 904381764, 76965615, 182161054, 27094505, 124032383, 574672686, 65904289, 920186408, 244292897, 918312544, 697995914, 224682779, 304685705, 779626008, 555093546, 228312083, 422438796, 553605561, 210607249, 49682526, 939820469, 461250950, 573387469, 358873831, 25124526, 679911407, 139799481, 647087095, 761401146, 944312869, 353666513, 121956755, 877361664, 700304939, 457481319, 306694161, 347824482, 494620438, 465127796, 59078100, 290172919, 716228270, 848898308, 780307803, 121632222, 651011063, 446155522, 250535087, 400312680, 133770102, 708840583, 972169962, 722661409, 498198567, 872399623, 945581904, 254206460, 126016050, 724148, 144004242, 916568305, 344218361, 479896580, 385741373, 751646651, 889443650, 93280610, 941427402, 416888287, 72338567, 325497786, 762431488, 195821797, 491112487, 884133717, 908003429, 999596047, 627684523, 808060107, 923854765, 177890794, 589799948, 202127206, 41123245, 93864266, 251061958, 285077278, 871146132, 73572174, 448334603, 68887983, 508579959, 638995078, 883043858, 294844466, 742485649, 313346740, 275666655, 203228711, 651860568, 65043222, 526190592, 892572163, 927094728, 25435767, 884650303, 862032627, 968082494, 887765711, 31445820, 77573713, 686163979, 625446972, 160609564, 932632521, 401418014, 867048969, 532042577, 908807752, 729150109, 267425465, 757892613, 384006691, 19260393, 77377432, 190361460, 647172321, 902349140, 442929934, 625346358, 183864679, 987377692, 65489853, 119296855, 744733610, 115393055, 217257204, 928393168, 767250633, 939709481, 605449047, 2835499, 989638599, 846590279, 692250728, 35414405, 43091658, 424464770, 989708021, 702589679, 146344082, 432806932, 66873231, 891398940, 434371896, 697745588, 953076616, 346030533, 475606862, 349325914, 990428749, 397406234, 494878378, 209574212, 836422021, 76892306, 91352656, 829994637, 647112443, 558095873, 394441604, 569299222, 561909741, 16608083, 77089726, 388767200, 293833169, 97785916, 368413163, 36585492, 298189056, 929226017, 444132177, 916341793, 637514096, 875138642, 723678671, 710644722, 429449064, 639474809, 728128093, 151222412, 965811998, 120986673, 958709628, 787643578, 415035123, 149824095, 149173636, 553489732, 943148428, 838260791, 422660239, 925363587, 91251133, 428329787, 314428009, 904112932, 444918765, 992032036, 696023602, 558727401, 354791309, 977617336, 788535124, 940785601, 301489321, 468121703, 655870387, 285454623, 558047715, 499646055, 781350786, 833824867, 597146700, 237902994, 238970447, 58148847, 240185956, 880713891, 199345690, 857806263, 502521120, 119913934, 600545629, 968981449, 909159257, 716466420, 870771471, 396388533, 672970049, 61807624, 768006038, 775807163, 817020325, 686594106, 579661656, 153090518, 842039059, 152158232, 635325747, 473047790, 955370870, 318543198, 33699338, 200540187, 120849820, 715132731, 829985497, 453651690, 303287299, 59505733, 113507107, 847198743, 23471575, 375263546, 513707815, 418810791, 185609318, 133090275, 688279484, 903305260, 404571564, 557411547, 326028571, 800510584, 290613779, 329159149, 941477237, 698918569, 235189671, 815086955, 95356252, 191269666, 61357574, 762209090, 814216514, 264389097, 492411810, 234351775, 745870083, 123161348, 296145865, 595610598, 538121809, 430088091, 233931031, 749390088, 497952039, 515195971, 892782431, 666060474, 910839922, 39892766, 927160025, 66125941, 508901323, 626525800, 588530710, 980889567, 632754637, 48618518, 725111970, 266515964, 778451409, 67840918, 222244768, 841328855, 32798158, 163901121, 17716581, 303548899, 267265543, 5177680, 283515191, 834002525, 470885761, 263954602, 389479099, 634152850, 344438551, 860110796, 725895096, 581009708, 693277357, 735517368, 309387443, 131803534, 980751310, 616748176, 801212515, 880740097, 452397611, 962362361, 62566458, 951566097, 158416935, 376436928, 553085495, 591316173, 101971536, 471558619, 334958569, 940065912, 495452424, 134885967, 414798004, 592032434, 725137748, 711141355, 500851549, 350114478, 129750782, 47332964, 922895488, 450967718, 114003203, 213400653, 935947177, 323476837, 920216117, 565497293, 324366891, 825688902, 301347755, 841478191, 372911427, 315821692, 178059158, 861938274, 281784524, 32959292, 837895822, 875240109, 596464620, 748322926, 146102027, 159065092, 701075258, 287999161, 945141166, 743230045, 51643347, 125534601, 758056202, 804768722, 566698921, 293020982, 485707394, 582325315, 296649382, 743461430, 303000815, 381148646, 827024380, 385506882, 839313565, 167492799, 723733108, 568773558, 263232410, 693667700, 60120020, 567895342, 967569809, 298508124, 379545296, 234791281, 928680916, 929629095, 810263713, 858724685, 645377032, 461712163, 654338866, 772248099, 589687023, 722299501, 499595359, 174908919, 123706878, 307232486, 99639616, 455075587, 491541322, 858381904, 540298657, 556178360, 370624315, 245199457, 158105323, 837886875, 684278229, 81387810, 646528203, 830888771, 247173658, 448591847, 501878956, 350487153, 607089696, 145391196, 16634868, 236263061, 688920529, 247962341, 315163564, 919030137, 579653887, 238498179, 978822111, 722261250, 217237026, 296856509, 396978015, 982001969, 107303011, 476082046, 486973814, 673396206, 809286858, 363092320, 270274531, 146409534, 355947284, 568251815, 23145419, 46239062, 259450382, 250507276, 147773270, 359244144, 537783640, 312099277, 979221141, 638195895, 507396070, 713289412, 544410587, 267772779, 651061714, 938512413, 784328413, 566762936, 557878796, 362373002, 212618029, 858770376, 266968968, 698139722, 65396922, 643783235, 447862548, 868026222, 527426022, 564219689, 886381065, 295003335, 969780662, 166261276, 335625680, 735402223, 718571995, 283709076, 398070534, 338735938, 958154601, 446448638, 569935888, 244333122, 266968534, 554532679, 752649185, 903398710, 270490763, 426452795, 82521048, 932675308, 703175021, 59895821, 329747556, 259011717, 268224285, 821798357, 426556459, 561976630, 213898432, 632431997, 149804668, 809766544, 814011235, 577507070, 761696214, 966570511, 816320720, 408726954, 556154979, 53252392, 691249506, 664446029, 877667753, 437297389, 297926127, 872106419, 820333000, 750907841, 151528264, 716286241, 807661621, 124868202, 342850480, 139091375, 163476709, 449878898, 860355571, 416042001, 785653451, 673107214, 757038407, 851878098, 615046998, 226343856, 241211350, 211390221, 755631369, 210679434, 997740238, 245601575, 124430374, 960209091, 151553470, 438677036, 295212660, 863617629, 945508547, 64084797, 25211918, 163369201, 94257858, 687282118, 72032696, 771168317, 861044474, 665505912, 322004067, 605922103, 736362927, 176203636, 769157424, 3644038, 254103661, 525249496, 589106585, 959122628, 455441739, 415659514, 624512788, 180021290, 371844947, 290235362, 343903094, 271149214, 903686292, 477992342, 977801604, 548871482, 860196860, 923372349, 435314325, 637038768, 180159207, 167830444, 52096347, 666585610, 236236448, 590390724, 933335460, 951903078, 36522136, 337233045, 864322711, 484256598, 558794805, 943586728, 146930646, 399885803, 197140160, 705805228, 238184247, 62368785, 257073492, 270657584, 300012252, 251433836, 459809076, 148882369, 366655794, 125324380, 672133657, 597705499, 567035419, 316683469, 113672383, 623520735, 212710894, 305009079, 954905297, 399130485, 291746838, 864908407, 734272701, 884800058, 81758819, 325893217, 209291218, 407327313, 866804972, 375731169, 249872115, 305295393, 480119789, 102302105, 910889123, 788217879, 542974710, 689881751, 768072212, 125738976, 260985695, 801532127, 886614442, 594692091, 877554214, 605265573, 798376453, 674978587, 427788658, 59713099, 384515824, 731973878, 888829503, 479579025, 355758154, 393115892, 286800827, 456059899, 661698073, 234410898, 461975103, 97991428, 222900398, 4846883, 49400720, 308091877, 91698575, 928396363, 991275566, 112519110, 891284937, 138813720, 679578379, 296413306, 293781351, 272333428, 984854877, 760676774, 593959214, 872157065, 637332544, 481092521, 562415744, 368764802, 839481713, 970173335, 833875989, 692168913, 577266083, 287830028, 554903834, 235101297, 831816526, 211295253, 682662155, 448861824, 615804415, 953807179, 803535442, 132655423, 61049857, 375691391, 636937939, 824638011, 217554368, 968816998, 801674804, 373047154, 251423214, 285191581, 554411704, 172626300, 697297943, 894060950, 436412074, 214201302, 355957741, 128120825, 662907206, 210800642, 715037229, 413979499, 469384130, 744893798, 361067317, 906675802, 316026164, 759956829, 675608472, 572439634, 184318114, 842504301, 141869513, 386243, 977831891, 259226095, 123218933, 314941173, 36101301, 789315042, 369588322, 77141939, 88430484, 332241095, 669051079, 544731115, 366917963, 954181348, 353845807, 201785367, 616850496, 757730541, 123516015, 768073154, 380066390, 689895836, 978240358, 125252855, 618273490, 38076265, 402621810, 822079377, 986637751, 169007939, 719831856, 714240810, 788531057, 567371723, 383967336, 468207053, 988302224, 521516107, 974074080, 862760610, 460963383, 16388311, 953102405, 310026297, 207869441, 875471376, 616119507, 808614862, 633629066, 207872922, 599963217, 698980873, 609042288, 151972129, 274572746, 367974501, 136735769, 828171118, 892487514, 1748445, 258686566, 80191664, 159689139, 162226471, 595703485, 395445758, 757155554, 456644543, 595888199, 26967093, 796330280, 804194274, 37303972, 657583838, 880500042, 591890609, 943955984, 854912703, 693631101, 224035517, 14729531, 598507878, 937818976, 48466110, 194021367, 661503880, 820781755, 31333271, 388863985, 711119051, 442455806, 232549264, 742774054, 435044692, 990201962, 607923978, 44345710, 145730187, 886599346, 452865855, 434117449, 828591270, 988672141, 167992726, 812009704, 745147741, 575965118, 843226653, 56989598, 180915782, 479728463, 856182996, 996211073, 700123759, 108521902, 995131633, 882876926, 599655892, 822253290, 797696446, 152694252, 752738852, 4205870, 547638430, 477032185, 397628763, 419937200, 867028744, 415408202, 722612776, 696801827, 445327677, 25750929, 788521971, 466439533, 387214721, 627781375, 282988857, 983747644, 790673721, 74428791, 672968422, 244925199, 553412267, 486379150, 638697605, 767714736, 107987679, 139863326, 660356645, 339641132, 514380487, 589640981, 142380880, 839239569, 643417233, 847506641, 129195708, 62950777, 779745638, 546795605, 127536123, 137048551, 118329545, 936798010, 136356349, 825912204, 382523957, 718028297, 941339338, 736890248, 260264321, 373869361, 505454798, 230186970, 385032337, 754887530, 704277825, 585929662, 198720376, 466475348, 46019848, 830369468, 971246752, 8853383, 390569444, 91831864, 694829044, 442500977, 204866242, 289965411, 776415064, 274681398, 308316461, 20632716, 717861461, 441157217, 341949929, 553715537, 776797999, 265832055, 709423020, 27899473, 49495807, 608737427, 482739944, 794085924, 365630881, 102130068, 683682661, 861214311, 444063054, 177224876, 432420050, 413338612, 48255471, 700221217, 24374929, 879805025, 111126566, 233359956, 244900634, 524953442, 674433032, 862226750, 24620539, 22021774, 621174877, 53138058, 487984179, 983815836, 684112362, 661158516, 586039970, 773264983, 277551123, 447852322, 462940796, 267429599, 941837724, 896808403, 461188224, 818978815, 140913404, 311075077, 524108700, 259283463, 795964038, 179185555, 877226045, 269801860, 51257855, 142996974, 993692465, 691804966, 116051442, 104265312, 176776616, 413893393, 472945813, 175716083, 547262182, 448732617, 228292989, 807110090, 748908427, 530659407, 786562824, 48917625, 263344489, 677655658, 895928710, 433713174, 550483302, 661997720, 342058031, 452597413, 576369695, 938851926, 289451896, 252777992, 252931744, 355191133, 799310337, 527376151, 292985855, 415631442, 171296411, 121305382, 375861864, 779085123, 552256691, 854819592, 824550861, 753241329, 471191386, 607628351, 747378414, 798330782, 311343491, 481888329, 21125480, 534262528, 342623606, 308167630, 556422696, 221141154, 897826798, 876553476, 502770322, 286801213, 332364316, 954198917, 85481458, 127174635, 369670012, 91163991, 46057904, 918829459, 197861366, 248221014, 731363783, 916255861, 823291081, 484120116, 7209360, 833045739, 949338667, 629115267, 543137707, 501111150, 264941182, 208194644, 995593253, 237607592, 951149708, 352291687, 164281733, 424987100, 567976512, 552517378, 767042451, 448750883, 381462354, 384226358, 426634175, 905601360, 143755233, 231982261, 493593517, 153622079, 501636273, 405274143, 920963862, 679821976, 896385783, 947444088, 387335094, 860973798, 469643136, 937304470, 663902900, 531768995, 756164299, 800378346, 587873474, 460000347, 163078808, 383427251, 512320309, 555317531, 527069719, 804400777, 471379347, 312851996, 736964451, 756934072, 937403482, 823858447, 125717025, 701255033, 510962449, 56452978, 89455975, 915525037, 975901637, 57365727, 755183894, 789859730, 418732596, 831932929, 849926765, 893753079, 470366280, 251030758, 920898334, 379140407, 396770725, 29090572, 334478949, 817488361, 741167841, 241095835, 667441631, 828231336, 388215200, 382200406, 864860235, 919127669, 538458150, 529225285, 767359693, 609451540, 531328522, 226858309, 961896558, 885653456, 782399360, 278826677, 865870480, 725422114, 882796487, 121390852, 966058978, 533177349, 943927567, 971234227, 33928945, 846805338, 293166209, 248332291, 752040509, 582739597, 127666707, 587876709, 418020136, 982764092, 786921126, 680567159, 462966051, 990466236, 24656569, 904589009, 40763553, 704997988, 869811328, 351473931, 338695076, 189384803, 689632185, 698911517, 712384524, 764831976, 452210105, 716435946, 75240747, 104974831, 417417745, 806871630, 109625506, 816064861, 754486570, 107822030, 161799881, 492255458, 747891308, 491850504, 706659468, 734132339, 731862237, 193030648, 8473453, 238234421, 387650330, 376988986, 975932928, 379408034, 81549011, 170319262, 134709727, 260195864, 594264695, 228380770, 924292613, 308641934, 970504400, 250085770, 510722743, 44444285, 116149409, 14100938, 292065625, 930822544, 638296692, 148316215, 139483661, 236259683, 773443530, 227492146, 131784168, 943656038, 141868722, 95038338, 771258879, 64921072, 271867103, 393143060, 179910292, 438307873, 93651291, 524609212, 208600951, 353682332, 866087266, 180747791, 105789780, 248810566, 234777824, 52525202, 914329572, 392500261, 682003186, 272385061, 606315275, 512728361, 774138255, 280440506, 361306200, 995481923, 506693124, 747693493, 220182279, 236540147, 721560645, 44224180, 18471638, 58907449, 156149459, 304873108, 663971418, 742685742, 484520180, 565439527, 160176458, 954608562, 881272368, 711156985, 230527895, 543342820, 209948870, 721632281, 326976702, 549974874, 836714881, 634050704, 682169827, 138099692, 650569667, 204108247, 188814387, 830332170, 756489477, 201744905, 562798987, 3389405, 279571194, 604309321, 727439497, 949573335, 615887825, 357252290, 145171268, 219955320, 603591266, 370837226, 721843152, 768210048, 598125036, 750392829, 257904768, 664731652, 282770266, 424805809, 174149732, 425948966, 90050775, 221911930, 251908718, 197476000, 854827594, 873216949, 1529726, 438703221, 435046651, 756205280, 756778946, 736128084, 827228497, 275344020, 272434171, 694015948, 962187481, 691409540, 172505918, 129109428, 958263016, 879869825, 680712050, 552403481, 820061802, 299539304, 50529349, 582904010, 353437079, 909835133, 815882720, 511452755, 969964547, 830338065, 39380984, 422663976, 935405938, 521422481, 168577497, 53986147, 655716621, 336387844, 456006207, 632240715, 968981488, 578008361, 532276902, 531544375, 498968391, 892464446, 283178272, 853550748, 519649367, 257948619, 789610046, 588768006, 45623361, 278552286, 867501596, 629020579, 843429186, 471462963, 881089346, 455755325, 950107619, 814868771, 702817977, 233213399, 538671670, 189958914, 422881864, 14334166, 742741452, 195561215, 654020852, 295248891, 331488719, 209584742, 700943737, 646672375, 682457884, 538090962, 379188454, 397652054, 369346166, 635086625, 659629527, 648440462, 514289706, 714115582, 975828472, 951717660, 351299591, 403049879, 830480510, 224521797, 360197270, 480591271, 649779306, 2336072, 663244308, 159861376, 198010033, 509131968, 743421661, 481823649, 634187627, 409364741, 144441608, 133340475, 133025078, 808968035, 56564771, 138408412, 833469929, 605578607, 504274136, 59614549, 359017824, 184529196, 131857818, 8870573, 340608650, 790518714, 443952621, 374621246, 166665642, 651337126, 28921394, 308634737, 213675650, 910390269, 789775508, 514184057, 150999742, 451553404, 677730023, 751770196, 384644782, 302711587, 691010590, 110631893, 803590974, 300990780, 111125925, 832446925, 408925824, 848116526, 579180443, 677519932, 689111311, 655473777, 133855590, 636241392, 150239049, 361928531, 79274238, 198920871, 907589539, 923113585, 195198054, 355239382, 774873337, 11234384, 54718318, 573886240, 602144754, 437134287, 853459571, 175025169, 585435753, 198848952, 64290181, 553353544, 135335721, 486987793, 961062058, 8451488, 10892235, 461954772, 63286428, 150404877, 488479165, 587148805, 733147744, 785048771, 719550649, 111251386, 117402930, 864035468, 698339593, 916432447, 500901676, 905842346, 566497365, 104611580, 22960013, 717436593, 143298030, 448699932, 631262844, 258965792, 751364196, 618741638, 890335702, 429551996, 733069516, 902189082, 452769732, 240020544, 285160826, 452388103, 52372594, 386115181, 258907570, 33514894, 322383961, 301573386, 573077054, 805882295, 722966041, 868842879, 804626732, 845958532, 566421954, 65511078, 650548534, 794640643, 922744398, 706479302, 333255928, 530149328, 513862149, 494002469, 984924153, 648491921, 137805429, 277993168, 137095409, 343681914, 18136808, 328882838, 904628387, 693334914, 180895788, 997893495, 415071631, 519974721, 819469181, 781318452, 97058755, 405896487, 740212311, 470840604, 40918994, 580205332, 254581110, 472602240, 742989671, 179119233, 3169967, 186664946, 346885867, 743399539, 650585280, 429845307, 141792759, 709328566, 616416857, 607066292, 867059383, 604570583, 763658514, 20162082, 641079679, 28814795, 68210952, 498122049, 700970332, 130418278, 917228212, 844749278, 414384627, 935913322, 330462538, 697311452, 525832165, 815871480, 449734417, 95926970, 125459252, 627091674, 273049522, 320678521, 366035717, 776945609, 521366167, 222328939, 117275381, 727721604, 867327933, 805268729, 992245910, 10543030, 937754216, 892283384, 421933870, 50824504, 767110628, 992116931, 665422283, 863339231, 19919950, 473577511, 996503430, 256995039, 301222597, 470169754, 436878601, 831461374, 79970133, 86172770, 124810919, 8034865, 528337727, 450481925, 621682866, 304662773, 453098294, 438443457, 828292855, 521040822, 234781885, 281820791, 859653222, 191032603, 31295632, 448448392, 715693488, 56753842, 756854064, 650899361, 925305069, 947868891, 361632935, 237225628, 56174516, 920110558, 907893175, 687347943, 480528953, 650734457, 812741052, 653380700, 611972506, 897386896, 234251908, 829151451, 157935910, 645152507, 16628449, 240002073, 129291996, 533595299, 100736969, 787471686, 79030789, 425778200, 210095028, 406191670, 216326054, 493908522, 490286990, 520051685, 394835958, 397824277, 179232987, 728054364, 459386853, 920277232, 861738003, 534962189, 262558868, 161496499, 531963803, 768371036, 396456739, 879385675, 781937421, 677202055, 89650600, 151746352, 891676427, 382240822, 971290702, 403801308, 324573688, 576640231, 750799545, 547361496, 270944220, 921531277, 695656513, 500715739, 10061638, 699637513, 284346524, 716654315, 907822156, 991721408, 706725654, 578606646, 762703509, 200818843, 462482212, 865900211, 694387666, 715058632, 907956837, 317773229, 649808968, 247475877, 486244957, 125141541, 213304020, 33743451, 508010517, 825046827, 552918218, 231475510, 1638944, 986836137, 186496439, 281009808, 817824771, 300761265, 981967992, 500821860, 351430865, 866526715, 776440609, 259893790, 114617205, 855772327, 725135015, 241302173, 12374883, 885806078, 968272083, 88286924, 413930728, 987979453, 667468331, 421951006, 525052235, 969113820, 407050553, 705538121, 53432089, 844194164, 321239130, 591807413, 876393553, 690421378, 995276547, 852883460, 569305467, 713963020, 273324010, 605471914, 212058356, 528026739, 711938054, 680811416, 726108688, 605984562, 831864802, 510597606, 278246221, 476020321, 577964907, 841938043, 661711753, 721422765, 207124703, 153663489, 513072510, 877081333, 159186063, 132520316, 487976402, 50522396, 289828064, 287875162, 489482838, 28645572, 861707894, 37617819, 293402064, 20366932, 499098620, 429796193, 754776093, 114844069, 587889584, 55652930, 853461378, 608435814, 847819378, 485449381, 239394978, 185932556, 299227483, 906419660, 435792189, 322495497, 448004553, 792622563, 685647051, 400743983, 492316549, 833895223, 32971866, 204712752, 799419097, 29543583, 883727561, 984532367, 485215678, 160978620, 273132593, 276617958, 65024874, 102885398, 871517665, 849375240, 593570908, 706142844, 29884818, 397148139, 685367227, 619886139, 464265623, 46074283, 572880457, 456605045, 324869425, 49520690, 381052934, 926584525, 749069817, 962554845, 669465572, 517680539, 788884757, 971648210, 547963147, 294348840, 194343209, 462458069, 569350718, 933456990, 566229432, 18521256, 271306385, 842030456, 943107572, 510189824, 812387604, 879508431, 6726839, 356718445, 581424168, 126957179, 244489629, 280060111, 655018435, 842732989, 540470592, 442003923, 97629778, 703932053, 335447151, 666379298, 420867847, 342322039, 822318517, 665745283, 865030659, 428836801, 723634903, 699796085, 755944607, 341246771, 36939714, 359027867, 370469210, 648717963, 465869917, 911264704, 626084, 380615085, 879281184, 71434042, 392066495, 220526750, 404535432, 668418529, 54657708, 780412658, 607983000, 830185683, 410507233, 395830852, 72003168, 197249628, 660187513, 742345295, 973528937, 783755461, 708503225, 337769458, 488382265, 869291778, 721449611, 333218570, 600729119, 698142860, 162603160, 899905740, 232845390, 459879839, 581243134, 862039226, 89826026, 667880105, 680593799, 747524470, 732865738, 413067239, 757745853, 631545043, 366977838, 59825607, 581131042, 350383395, 908187649, 412575025, 60809600, 356175771, 883406059, 301561935, 401010333, 511514778, 256063879, 408183785, 288515001, 260014598, 170517128, 510206533, 40709665, 764859660, 967982535, 505401415, 463262311, 848676128, 279838101, 627699891, 1634573, 887778748, 489132529, 115607016, 212739808, 811320845, 931647455, 237994864, 377530503, 871957828, 382525047, 690833632, 751689894, 105369807, 169650544, 345427119, 935802057, 483708854, 849812509, 312509531, 139507713, 297937520, 450289669, 666717491, 571457449, 318942527, 322850649, 684609776, 43349308, 218632056, 837052522, 400662165, 817447705, 334544545, 422657297, 405838156, 313899326, 175121282, 961961122, 119297443, 753288995, 265167250, 870631475, 689001523, 920803725, 720328350, 524954737, 826580380, 892176802, 567615043, 685007393, 105748967, 276223162, 527980861, 443429246, 726412644, 303395805, 797613843, 44052454, 222499371, 680301136, 146616288, 723376726, 663493957, 154703230, 954901156, 396297987, 9162244, 137485018, 597648870, 317897777, 992421786, 455181926, 616713892, 529074986, 175493893, 294729568, 719852758, 677747696, 658575624, 826451341, 727129273, 811273836, 686175438, 859965311, 141370684, 210153473, 395749172, 852892541, 771931223, 760189515, 302625134, 58536459, 517210294, 641578990, 146591582, 522917561, 572667000, 618124165, 509838035, 511666488, 149750707, 410887789, 317895419, 592072568, 519605393, 575068378, 164424515, 225606467, 284926595, 315867299, 797283310, 93818771, 700016876, 639476882, 201907207, 330987976, 161431034, 416557774, 378020569, 95767340, 6240859, 910931610, 528368384, 936634119, 565663985, 732749983, 764809421, 344717787, 944042959, 467509423, 612312739, 489241163, 597937847, 719215446, 280912734, 594137501, 401627609, 878938136, 199495616, 555239515, 259752987, 547286795, 553157899, 416257896, 114631736, 14677274, 902952767, 703003211, 305378819, 245498823, 195739464, 513869536, 998042894, 931667856, 264511426, 426217202, 233546494, 653809820, 950537847, 882778519, 97499232, 871348521, 778484513, 372977467, 312201664, 974294193, 140352916, 382947076, 539284100, 449940757, 409866570, 261673123, 990355011, 843522603, 571112356, 694174901, 999889292, 131522719, 393534062, 222638272, 847234834, 283859471, 695508918, 517057052, 147425227, 628594792, 510249443, 206448834, 387978931, 935969408, 300252572, 489071969, 224167082, 728899011, 57262865, 450635732, 139585925, 645606536, 581697807, 62987776, 958795189, 638772008, 349492950, 931517333, 612830142, 203816430, 123768853, 50579408, 630590809, 690576928, 55209500, 868528598, 334246237, 522511, 129846414, 992874081, 342606497, 43935059, 986470845, 43576314, 689132225, 273687474, 495438259, 747848918, 798315762, 163396077, 251337325, 113869871, 437431892, 84121873, 477832670, 321102193, 614565865, 552506427, 972805745, 145000228, 315247979, 964476790, 838801239, 414932609, 127087313, 462493785, 756193010, 45105929, 152385603, 116313124, 394251793, 703565912, 793125699, 967012657, 956753701, 205206529, 659650574, 864800033, 817183051, 502049103, 337667520, 140139907, 33517416, 546977482, 593056568, 577117097, 263834326, 467133050, 564565863, 221716097, 812865108, 344830523, 830225573, 878276864, 656540740, 75821225, 240780125, 7402149, 41779674, 365608784, 595754318, 841087436, 880974689, 165174267, 944528269, 365341753, 46184935, 330257552, 913003940, 810435059, 317857988, 386602572, 919110582, 500360049, 891738716, 608973889, 908262076, 975193961, 404189930, 566167946, 285521224, 542810968, 726294716, 188015112, 566295784, 977307274, 914293140, 960295359, 169012682, 551682265, 706645501, 98020714, 702753102, 922073686, 636506720, 909058041, 600650752, 239075626, 374770093, 83886745, 40220904, 382746116, 711854958, 773094887, 275875922, 904001885, 834554808, 639973873, 311926365, 186349705, 942975214, 357057370, 227078923, 884849711, 650910018, 199603540, 395411253, 992317699, 100394605, 369732403, 3913935, 395913358, 600243810, 614900413, 361993887, 345043658, 947849120, 986154371, 560096329, 120430702, 788771570, 827532582, 817179447, 775455672, 913167600, 852321820, 829359719, 704381627, 812271812, 375488112, 926196402, 4484747, 420210288, 530939329, 168189771, 485113510, 647580813, 976794478, 526544140, 937177349, 630011555, 664329972, 469634538, 285266379, 553621782, 785879298, 815525018, 449629001, 48066527, 372966316, 739030323, 857356184, 504391086, 433010986, 476761399, 347639705, 693422161, 920131963, 614891877, 956866005, 551084591, 376742469, 898073788, 114541402, 156023224, 956461786, 655419481, 229342602, 28105804, 773458218, 434593315, 945917211, 130703065, 412861526, 523963898, 5959044, 89577991, 152301292, 564513557, 821156474, 631166266, 703166261, 583109788, 992974978, 757485580, 567466768, 377622083, 923487373, 417721441, 152849382, 358965073, 551580064, 806741965, 263618050, 927052782, 790896725, 911235270, 526690623, 809871932, 466254656, 599618069, 29776827, 477940545, 451402132, 228198995, 759169255, 316325756, 843241218, 193438873, 790095359, 764584217, 576215588, 855443815, 992637981, 973077873, 242519230, 819106733, 631476462, 272526138, 798602279, 877257889, 898490, 240129105, 142160327, 311179866, 525207604, 347920947, 700259043, 779353378, 875711360, 51237020, 346235893, 147659986, 419825830, 800968760, 721945798, 240100186, 988003914, 789420563, 489146298, 249537867, 798461359, 134170716, 680267367, 660095397, 441476857, 431894707, 897491219, 729460394, 936705118, 885255878, 924170990, 707484703, 600568102, 573145174, 970976989, 622098710, 116100747, 362304077, 718694509, 95591145, 828443405, 493551138, 428072376, 729612195, 579456041, 87585230, 895790106, 291513101, 958926982, 297083320, 385855314, 341464900, 867972580, 924887984, 419877270, 227195891, 234984913, 572409737, 255231038, 169218791, 689298119, 671154761, 219167535, 205707672, 978367482, 167020308, 964678573, 497942877, 163173583, 77814031, 883711742, 68968237, 647405178, 389081458, 495281618, 623264754, 739946395, 443329688, 561516085, 642419529, 696873522, 556240839, 295152217, 219619638, 282462364, 88315344, 573198815, 680908363, 405037751, 67320932, 302385466, 153627234, 230649536, 358144274, 26335244, 294020906, 2009709, 367555836, 796485357, 771987985, 863696580, 101055395, 740637520, 566425631, 800837167, 430578285, 9830397, 382965593, 567499193, 683129158, 747437417, 617057459, 483274412, 901940563, 259082869, 8768580, 846407564, 985207227, 997293133, 210653948, 965654174, 274386382, 148810351, 570360496, 113557560, 306624415, 470567946, 46647514, 414335922, 165847810, 693505490, 865983308, 15674759, 135436126, 312410641, 875606055, 916184038, 240876288, 998224015, 252936313, 53300312, 231283623, 354722614, 514080790, 830242886, 516523048, 577683014, 377997957, 400353381, 949910212, 656857810, 472710913, 629970258, 805806722, 698034298, 326069541, 842444843, 204247099, 162060287, 533559923, 665713909, 984354355, 433358946, 323481625, 881279763, 861107172, 258385615, 843034813, 474568242, 365457691, 966496125, 782474652, 233629075, 33081089, 375457648, 150680263, 531547273, 844228900, 539319458, 77792118, 713086472, 608579981, 741213895, 233323518, 557670270, 703660044, 83992515, 793659462, 908771981, 599507726, 838707244, 559433247, 437415772, 475406302, 459686647, 661315149, 983686940, 758717517, 788440429, 238507583, 248065598, 774717541, 93304944, 288490785, 502118064, 866774847, 813602061, 953886303, 983325936, 448580869, 195230004, 515255450, 481327966, 361876145, 942576218, 267940917, 535420142, 194424421, 437751707, 889567091, 38553500, 696812449, 64200163, 219372180, 680593489, 415575222, 741627258, 366593973, 458175654, 177492482, 390565646, 334521936, 984763899, 92051309, 485942463, 171273273, 50299693, 61436072, 179201549, 233803893, 125867424, 563503355, 220494152, 779693132, 399332106, 490608623, 819095877, 606783650, 771533595, 35523498, 959081416, 364613026, 219536416, 454699806, 310997495, 461967583, 592353046, 524313656, 958485933, 620100092, 646590678, 254183944, 143309677, 671094766, 816563839, 726094121, 632617223, 274099183, 962381739, 207009432, 223707730, 941898295, 594321043, 930672787, 382991262, 119913511, 412252903, 576871580, 581565144, 38459178, 173797798, 808624900, 468698038, 992039579, 703179365, 407892568, 976307168, 699974967, 634018915, 992042590, 622927583, 486819400, 798263312, 710111768, 818333642, 281277218, 476940948, 559561884, 977198683, 878548077, 835139552, 622884021, 891120205, 241961391, 446094979, 750629220, 632777184, 314348597, 974447340, 865610560, 579833415, 694686064, 755242930, 431825563, 192816481, 142661153, 965362125, 970412697, 953142037, 415609223, 916074244, 67670717, 932886734, 668891570, 837946435, 925317549, 767025515, 157622050, 456597657, 767020678, 414397591, 281291823, 43585611, 495065758, 516268377, 421980783, 757337830, 659934736, 362383932, 832684723, 892580925, 46268010, 92828435, 99698561, 187885918, 311056901, 769120101, 955471827, 631187281, 613056136, 205231377, 48860237, 942937137, 253818944, 311296303, 777801197, 857256708, 391245756, 624535005, 188808243, 384237328, 712593576, 763257968, 284733676, 229335537, 749317500, 348722755, 208413325, 595360285, 631280930, 827919462, 910029807, 11088480, 745906773, 745661455, 792062293, 976788799, 449970676, 905161003, 303730965, 291016182, 847798382, 524852503, 828741578, 370597342, 366650673, 983595381, 329278393, 466220094, 61395993, 798433998, 390644344, 324243437, 877647443, 486884970, 821351495, 768156367, 333626229, 244273130, 358049554, 964691807, 818346420, 700636103, 103897781, 751017164, 805762977, 510465175, 375081694, 491229263, 238423728, 250823395, 55700593, 767693163, 136109388, 341222583, 756103563, 740814956, 532104470, 884880009, 686789374, 870496914, 780589180, 283679628, 925210148, 625319663, 332101222, 482608067, 796011389, 22738546, 399945847, 326884774, 134094921, 971036189, 718071371, 396303212, 683830001, 46527785, 462784045, 191323256, 798582919, 196584261, 844823290, 322228378, 83886441, 799059571, 773004933, 720872194, 340762351, 147453875, 575342100, 919177314, 363118825, 248318265, 194683592, 586647503, 275103684, 970897178, 980958557, 639551548, 874793020, 605291982, 907923292, 302401722, 964372227, 409719287, 51359192, 746346401, 197311401, 178137766, 40493606, 788798318, 454061416, 204783032, 924115858, 131034062, 680027119, 224517920, 415305634, 693312371, 659850498, 698466091, 923520491, 698132533, 620051265, 451998929, 785418353, 829354888, 373217690, 891465786, 562953906, 972420975, 784685562, 551746516, 365956803, 102028354, 419671955, 369364290, 951891324, 482574408, 291897068, 515299963, 807772631, 755514804, 398917003, 323122360, 634809577, 290271523, 514151006, 199282855, 344690374, 821675612, 112780780, 126372866, 289801274, 330768727, 778589723, 893634035, 676283032, 710563702, 272222954, 849063054, 941149077, 127138566, 299301583, 573823912, 846057776, 672511110, 446902066, 645623041, 804001791, 596600075, 775223573, 640183194, 909184908, 325698131, 38826741, 250866982, 677122924, 545140875, 792048671, 491344773, 245455401, 522317427, 460845029, 612457679, 845371685, 446221485, 737791928, 729235721, 518598948, 306154170, 651182206, 501584055, 798602141, 809213778, 639757752, 95505768, 419157233, 755052628, 166601543, 26258771, 957568491, 924513510, 838351865, 680430506, 776806596, 670172, 611180701, 426024095, 595859296, 441701917, 837511017, 493800760, 307262369, 333966412, 270279896, 518931336, 540691260, 684796194, 353857974, 478008359, 357238508, 341004428, 598881724, 494295390, 50401759, 819601332, 315715021, 627841358, 151831814, 159037677, 495299020, 684530944, 159712602, 661595628, 389504232, 775458902, 766590125, 110927915, 652810292, 352975423, 201764533, 727756941, 835705445, 771537007, 806181839, 680464166, 817369931, 23370160, 493942296, 664742605, 675039576, 145852286, 201506613, 583970537, 756159262, 250410841, 506044271, 844387924, 892020119, 808734805, 254173759, 16361415, 205676828, 78313236, 59780507, 37521733, 70882559, 7226348, 298504450, 237092442, 267740828, 243650420, 593066895, 540033199, 78372495, 667897940, 815839885, 648217817, 113643522, 525542940, 822648635, 99975343, 636004953, 516413287, 387183367, 580603965, 524432355, 795195443, 957631626, 10131634, 892156703, 100367959, 194093809, 283869079, 403079015, 49706621, 841384544, 251037939, 511713069, 776994846, 576486770, 271600803, 870268887, 264956871, 664211196, 140670756, 34119966, 294845472, 874787100, 123867792, 271998816, 650312768, 323355357, 955550934, 38031385, 636817978, 630620568, 50976557, 170550888, 319161446, 138197800, 581375165, 555398839, 794703966, 988453962, 833506943, 304985337, 464844283, 142563572, 974293646, 844889460, 348011570, 691099018, 205158179, 7946185, 819729296, 823196283, 305162287, 430783534, 73628155, 591271695, 149984524, 338542459, 187890154, 252807919, 483149770, 320404498, 62222332, 532423930, 532427655, 67245975, 543320669, 909785280, 828983133, 981454277, 624224022, 246076889, 975733441, 81669023, 450516410, 493671011, 833884179, 154873683, 299799732, 549207653, 700312640, 241353074, 924883837, 782873046, 433190647, 564257387, 322412048, 707025734, 99753033, 310001093, 370367977, 220767221, 249075681, 371120760, 163979581, 157498072, 530080613, 709104202, 309924211, 239359841, 404340633, 512677517, 644151301, 42733619, 81555578, 114536314, 444730231, 676148731, 718061331, 559441716, 155783984, 410840089, 180642048, 227304727, 870946127, 456142519, 360178769, 554932980, 232704444, 929589100, 324118427, 111133708, 900847853, 682792259, 921559826, 937205612, 64009478, 765959320, 671399285, 985607408, 721506287, 791452334, 415341192, 618775148, 984960347, 730088281, 914007341, 813106564, 531349967, 5665922, 421894549, 995513305, 916473107, 197109460, 212399369, 320558202, 752654935, 356439272, 231978242, 792244623, 662027549, 127602625, 252949056, 153288750, 671750405, 842135272, 657727993, 370012929, 431898198, 392805825, 425162462, 268489933, 537730482, 174662135, 278990498, 507229586, 489068696, 390972618, 92215890, 226915406, 428138959, 502101452, 315855447, 242675746, 47534996, 847991991, 117836237, 792147285, 547935377, 951364359, 88532390, 474263886, 713592740, 174203671, 755051773, 314184928, 456180578, 82427839, 708474137, 889128420, 80178622, 259692286, 937613054, 995340085, 134202279, 462190805, 57135942, 541210761, 933452979, 911641347, 515419590, 747880585, 867113429, 517982593, 914546758, 727968195, 247510770, 342701056, 873276797, 944970872, 437313327, 212124482, 400952934, 735830330, 793205347, 912743879, 916534149, 69836997, 558995326, 9411885, 548345661, 945752401, 421306476, 980921114, 682607252, 254424896, 641998857, 274757745, 655709063, 560478876, 130221125, 104064683, 257900065, 442593067, 224881157, 692286232, 227564152, 79357724, 970896318, 122637199, 550202521, 80094440, 699927768, 291515686, 337894578, 574837041, 708049405, 636780999, 925204679, 361849241, 636710186, 756416573, 966950776, 981818536, 874438593, 590317357, 597968761, 257305815, 617335516, 187104233, 829860798, 380434125, 335254112, 146850267, 219931732, 586121410, 202828316, 639984123, 969793240, 549427464, 940541145, 513803260, 568127439, 912311043, 834386969, 40490645, 490357783, 555705613, 666471365, 595314526, 27354433, 314525872, 206201528, 126165667, 910873994, 3343967, 166974574, 162099856, 104410511, 590034575, 595926941, 113720549, 693244645, 421558158, 173585905, 695439795, 704622264, 532768587, 531458395, 398060225, 33958980, 50072953, 613040286, 40411581, 880301330, 312800314, 33646488, 236210365, 855369432, 81122212, 916990157, 586056541, 81893071, 856099984, 269709715, 613002303, 618666864, 386565995, 292327364, 962010891, 502610627, 376818614, 753230358, 509213549, 502544121, 711512227, 935744196, 812287685, 256257508, 849612273, 176780095, 910380694, 780042733, 350324341, 236373415, 604190957, 923623393, 469009129, 238335824, 729084395, 489496680, 658768821, 133897864, 779568470, 250097516, 872281711, 591567783, 76801005, 450525182, 877572707, 967814303, 304453093, 980090867, 306009083, 649201219, 109437547, 974680113, 869847620, 937038522, 89480373, 34559559, 497361902, 314916508, 148442625, 616276480, 742649967, 657676882, 939473989, 828845585, 533388762, 809015480, 639853888, 552069399, 639003998, 98322815, 587083027, 218651095, 655695444, 274894556, 669549028, 335843715, 764143815, 457448062, 285524288, 423786327, 690792218, 683683494, 975037804, 879079573, 910235226, 873087673, 436711930, 476249356, 900248598, 249064527, 30381604, 451414054, 527324804, 763363146, 250515352, 587040703, 512556375, 330990710, 711456741, 156781270, 965310796, 635244169, 700446381, 224911513, 719259751, 227953942, 873539690, 723194876, 538716154, 853812681, 344469658, 555005291, 699001927, 357148398, 424767601, 968787156, 368659724, 749990903, 66025044, 227634319, 704205640, 828924791, 401873442, 510141696, 785990879, 531965676, 329857225, 328308370, 16260761, 769216866, 924360353, 55256579, 381064068, 350865361, 810153433, 97677174, 235477522, 360483625, 673434302, 375096380, 735268231, 813596964, 244123968, 608503843, 561931674, 85620686, 774167426, 724631712, 967378589, 710297700, 196541720, 868860900, 993185973, 841244124, 659336871, 588593302, 359804611, 182747753, 955431530, 656111811, 73274195, 210679985, 802457643, 930165090, 994992451, 608369593, 549785755, 380131886, 48378304, 550786525, 942686130, 661146891, 57307887, 535204556, 379984234, 544462812, 417709316, 847472848, 607458279, 219766502, 135730711, 616354060, 846684867, 920893533, 58405904, 835262397, 307676106, 750978741, 629545194, 927172660, 178633565, 142090486, 990104012, 152397477, 513495188, 476933628, 982438307, 812330292, 131691336, 606535878, 875718284, 291393958, 918374428, 216762722, 451493949, 132090734, 998124789, 248769839, 65224715, 67587849, 97201404, 760746510, 342778078, 324854658, 639010432, 92043013, 32279662, 938637862, 766455567, 145042123, 869090524, 909906533, 794748470, 323933373, 962492872, 739295290, 286577148, 620124120, 225353536, 746777665, 432045850, 637148777, 448878645, 146898345, 590027415, 772673870, 217069613, 598845782, 473775225, 110912431, 214165152, 289939136, 372315911, 789348588, 850819550, 644207808, 212024434, 229027063, 354488056, 39221194, 710606330, 669494317, 702827356, 811775728, 976404319, 296119766, 256296966, 745103962, 984269960, 740785680, 691595113, 795179445, 317624914, 881978317, 398629743, 199711619, 282380703, 183270393, 76566853, 688131324, 546744943, 60706000, 802603092, 553916346, 409742792, 172209889, 683840678, 409166121, 623035365, 461683413, 521084796, 848465478, 504123577, 893614132, 587406123, 606952447, 846958236, 991465202, 107636255, 553627934, 833907562, 970369827, 1927265, 583201807, 998699862, 165041163, 379102915, 527096322, 734540207, 274931653, 674260929, 702209295, 871481999, 466089662, 363008159, 140247883, 451156143, 313410987, 137678491, 548246096, 985299031, 541976217, 531023345, 711234368, 520805852, 950086051, 688619460, 521937380, 67513178, 328814833, 718407711, 770100972, 215173820, 139834162, 411783922, 405188386, 532997841, 750673262, 615780789, 626960591, 915486680, 286103411, 187044165, 877484249, 274585143, 343449060, 632683369, 522675276, 869813858, 731890322, 190340728, 769744965, 656916857, 697195247, 378240007, 488689526, 802957726, 910207450, 50566988, 235621195, 914079715, 973661335, 79737017, 497860643, 552114882, 148407533, 654287856, 60144876, 74449210, 923497958, 198544355, 394598931, 710015739, 895928002, 693037852, 685266401, 317754041, 783114468, 236485976, 244398974, 215288656, 813474824, 769520935, 62774805, 13904969, 858189063, 304629991, 579520934, 964941990, 724152802, 937026470, 952404028, 175576763, 588924036, 846474855, 492891355, 336965313, 156635709, 144524921, 829396729, 423873023, 961796214, 480873082, 674370008, 835812518, 62792268, 941329790, 430708228, 906734004, 181716127, 398409164, 299895535, 261300078, 506141713, 384454681, 931208702, 810393829, 411887228, 612748164, 448563460, 432657246, 90941953, 163117217, 633753261, 57773587, 409548191, 68530919, 991012851, 513751807, 872249169, 741499009, 799809950, 333968498, 182030253, 676790431, 259927125, 498836409, 256443509, 282072391, 376689701, 962727142, 48625594, 545278574, 820082034, 875668437, 394188285, 468479308, 455317138, 533922714, 443592459, 55512107, 732519114, 257150203, 351228595, 335162217, 435512845, 500999523, 161091987, 309353240, 418166969, 277158439, 19632302, 885279296, 315163288, 109907115, 134037734, 490957858, 334912315, 759789699, 821106947, 790080217, 508354032, 788265326, 166179195, 46428056, 127360309, 969150035, 428985556, 442426537, 114747461, 108422470, 121438295, 511055709, 573632757, 130074603, 347994154, 896030291, 275805151, 293240892, 709403162, 789231835, 147000026, 629202942, 340230527, 276925015, 773337233, 491253369, 40190223, 824126019, 920518938, 386709896, 966415546, 842265609, 942056027, 16797786, 423789732, 717181785, 708143319, 728375893, 575136544, 489926927, 17356885, 408649729, 114523927, 115176387, 799262912, 533015565, 653882012, 429841858, 543975157, 929186999, 9551184, 582543314, 829109578, 838118599, 701620730, 95620067, 906988581, 409759096, 1610244, 911244105, 281742792, 46094571, 203726127, 889375905, 763983320, 899363961, 610274601, 581664648, 446699392, 558344056, 380725037, 60371947, 776480368, 448200318, 693453455, 985071801, 707670706, 162178156, 257539905, 129177303, 504234540, 73942196, 797407701, 553519502, 475064516, 544938330, 49857939, 464536254, 898067890, 816580462, 40624047, 419498851, 726878144, 398658636, 847451969, 364127412, 99725453, 497133988, 121808075, 187341542, 540862801, 877508698, 715702820, 831190853, 136455613, 318247781, 769767531, 321819635, 347819965, 346056698, 565027084, 276954722, 935235072, 316996458, 935595601, 396267910, 516424484, 24430764, 308444899, 717750346, 285800507, 803314735, 534350978, 470368125, 396743250, 633389605, 792543540, 741040243, 258099033, 285295693, 968746791, 308444164, 951658107, 304792768, 685233088, 596987022, 415725915, 695447189, 31377486, 967783514, 735422655, 652034100, 783457018, 69764362, 459988216, 14843894, 95388999, 633200406, 162900760, 61710343, 122849065, 255153802, 840827044, 774551329, 543454645, 772847172, 921050413, 489203714, 716845817, 949080054, 975948221, 608117572, 811572872, 921833578, 799823048, 865362865, 628365228, 79224089, 274898342, 206840753, 865512503, 536089268, 508614726, 303253693, 242407617, 635970916, 26812602, 433583542, 917623621, 426504444, 964009033, 272042594, 706606482, 834631781, 439723659, 406371472, 330471301, 529951483, 539869715, 877671590, 626362120, 775853881, 323489767, 838732323, 258650560, 453814718, 88808179, 850239733, 885863752, 642545190, 693474880, 330964496, 355765280, 955598460, 11317036, 652392655, 230264255, 849506057, 176176438, 946187786, 42087638, 371821994, 478719852, 431194802, 143731182, 110111628, 805040074, 485407497, 645154258, 413634354, 485521969, 78783692, 866203279, 547909182, 602357816, 754486084, 607732729, 363650522, 102221179, 688453947, 925553019, 504796782, 275350427, 835289304, 26511617, 333113878, 465838459, 495752653, 813280273, 541598157, 465136484, 489667655, 680689661, 318474518, 443181609, 796380704, 192871127, 86259608, 973790359, 804481539, 611180581, 990521385, 410691543, 690492473, 554249287, 916686658, 371579241, 851686269, 156044101, 309302130, 366224928, 133697695, 48725678, 777619151, 144395089, 546556018, 464297873, 602357471, 467405195, 756881778, 420635793, 162197896, 829154734, 340882823, 813366979, 924553948, 759257498, 381762133, 947913735, 809874746, 653655802, 97366215, 684923905, 411067059, 433053829, 156389055, 81397573, 423763382, 786089571, 940546247, 486031481, 849211189, 129364039, 671468017, 343332446, 348385142, 93085887, 7723339, 177001949, 357553833, 501921702, 671181309, 485724235, 697724641, 544187368, 616417065, 965056446, 355343235, 392485004, 597769817, 539128677, 909611996, 425448886, 288607219, 530328410, 57561936, 690963663, 190754017, 126477081, 655864207, 188484477, 774013508, 297876334, 759506978, 875309806, 188500473, 561440443, 55806552, 387324176, 755980959, 83357379, 750330287, 961682716, 426398989, 500062001, 509040739, 358879243, 531305314, 730872665, 804997231, 412234525, 798624981, 806447961, 61143125, 810865044, 139142699, 889417619, 802850629, 665450142, 877993628, 346908937, 605142569, 299696769, 724083608, 203313641, 789967146, 289793466, 987251551, 866515412, 47586346, 268308263, 94867964, 353883497, 293261760, 481786289, 279915260, 390071064, 415504269, 837699628, 65758421, 722199570, 75016713, 895492323, 85678919, 424415594, 342100807, 887158274, 841351006, 959632327, 120700751, 838697739, 720955065, 49157212, 540388302, 298289303, 975503141, 824206823, 723213125, 180215999, 537504488, 222376523, 188682823, 917378515, 545560398, 906172268, 588944941, 854376298, 128895639, 94247768, 312109532, 300891772, 671708196, 741977264, 471782481, 290324637, 886446938, 510577842, 788083272, 805104446, 538841771, 691009521, 5243007, 216501678, 379506643, 703017239, 295714895, 917381911, 674309729, 73555330, 216441103, 398029736, 141517437, 436461230, 517116617, 465031183, 570397464, 494243375, 206832534, 865515317, 700175393, 947146994, 112195516, 30179310, 131119352, 69927413, 327329902, 354678906, 676123083, 580347837, 601410415, 918591300, 484234468, 636129383, 668322842, 878082471, 962913603, 606540151, 873306700, 47740091, 660550456, 701390781, 576752229, 921541705, 521892695, 945685654, 69865404, 881812303, 412342981, 840590193, 183221577, 615554645, 956442831, 467424132, 75721515, 620332720, 509115602, 180419051, 220225537, 153305296, 832031378, 664577230, 506396645, 77462626, 403913491, 894492823, 300769766, 476321330, 937096253, 219454538, 91871586, 111228008, 302137250, 714182943, 274450869, 642576850, 80935616, 248298922, 19765989, 543869561, 99324173, 889833910, 555021511, 197043540, 283567283, 926892011, 934870671, 511314234, 968235705, 283212050, 771954115, 571932045, 789931811, 806149983, 529328280, 33392280, 179943215, 749341272, 776379778, 352354247, 763169868, 519271637, 730220124, 392929528, 594857255, 951223800, 403376613, 886474951, 81534363, 338971033, 650231361, 356532118, 127568806, 369558098, 206744148, 971397206, 579534224, 802695961, 679355857, 37300864, 671216766, 320500304, 813588766, 489735788, 743940037, 546481086, 454876392, 811703552, 947243256, 135831084, 427117844, 405271975, 192292107, 525878747, 425673460, 663266855, 567226129, 386016775, 272851682, 921700685, 9338337, 259683344, 722002648, 921529915, 959680298, 674322345, 957596840, 831259113, 780015987, 199485835, 787110810, 538358971, 912033823, 244194239, 275727922, 449713478, 940523841, 594186394, 668559304, 303696914, 557491539, 41032862, 797916768, 878214981, 432866880, 234221370, 647754566, 426807403, 867279455, 384332742, 340747173, 543524804, 368787001, 20758669, 306819004, 44363355, 361282261, 777405093, 227093380, 173819217, 761264520, 155863798, 3693398, 262986017, 335661233, 751912856, 148510264, 558047652, 276339585, 67261303, 540926020, 356373794, 233447165, 668573485, 932691039, 503930866, 941782116, 343893180, 708794339, 29791350, 290725986, 358244419, 876568812, 230517131, 184775332, 627438212, 571966510, 370825003, 297752391, 630835239, 471249044, 397347552, 763112938, 791113283, 227348364, 264815394, 776046051, 448335722, 14532594, 830891411, 73241142, 331784116, 607080614, 765669539, 458119251, 823802689, 944330476, 971704011, 719225981, 791113852, 386598983, 227813882, 774959161, 845011737, 515115978, 481996490, 279673891, 214261097, 480781143, 64366283, 932070158, 214327313, 322817877, 60165298, 775779811, 310919346, 399473779, 215103761, 273796126, 916519695, 468674228, 44641268, 533930472, 492016031, 970294271, 324821752, 121209861, 551287636, 886320416, 538567870, 657838999, 760321223, 595036758, 703301827, 543983734, 584103724, 477835516, 932216799, 938329161, 660502113, 406206184, 628066899, 298512582, 718776666, 428575504, 265735857, 414740377, 156621559, 598443933, 973704849, 397674945, 628758320, 155789491, 442684801, 999391268, 787861375, 342611713, 752115662, 747179635, 400235361, 811167050, 849394338, 78360050, 142977114, 964909425, 647971010, 676633812, 829859527, 482151670, 33373335, 739690767, 106061566, 410207803, 539251701, 325718577, 775728299, 278974007, 648309173, 480049106, 227169893, 872950214, 369187781, 976413558, 786030810, 669219286, 26090570, 614483102, 813878171, 771554881, 510397319, 657580701, 326631500, 504312668, 100739795, 389166878, 564172469, 983271378, 598438106, 585388813, 810952119, 92754175, 805090265, 175288232, 75116491, 1414733, 475556531, 244216589, 199697044, 24866722, 944389718, 336678008, 974697392, 928316970, 300665119, 269761657, 135419022, 509369679, 60919556, 295091432, 179377765, 526184023, 332382936, 169387460, 176493144, 257845613, 173141793, 352125528, 937047327, 678304220, 466194054, 312867892, 103844375, 926521270, 561490846, 663382539, 703274267, 244264593, 807893034, 188373761, 286319852, 831573794, 382493230, 187367251, 911850627, 835239780, 368334196, 259734830, 691703580, 791947992, 659856332, 375728654, 582824132, 50219125, 988668303, 375369026, 877061745, 782183061, 556552663, 251820704, 10233808, 519344547, 651722453, 688458030, 871808158, 811673537, 513739366, 311393360, 892453693, 959026429, 902224448, 970577408, 44475527, 185454284, 910532275, 92653603, 581251127, 955024857, 543399714, 673972595, 881136457, 231368767, 262775944, 13270206, 602144295, 867934818, 564178933, 520526107, 694347131, 423880508, 526093865, 12829995, 44383848, 197627165, 498416724, 901067163, 23248980, 283433550, 843839591, 837109692, 693759276, 290180431, 519538897, 271373385, 179027683, 775956362, 211748187, 515429128, 742866787, 783908749, 323210836, 210259943, 476801301, 450625979, 226339397, 872167022, 524333444, 115822742, 850459276, 311986037, 574937502, 979141747, 696845130, 189831537, 587776462, 16531927, 294693206, 495052824, 818283542, 122195468, 184683403, 340861595, 955760221, 764667969, 66138449, 213676694, 788938168, 139458798, 312358191, 676146566, 478412165, 723685451, 4100836, 53304543, 913207934, 693846665, 917493451, 815629393, 116758028, 339005398, 127008850, 419843304, 176162756, 465146639, 605016762, 19719680, 831274704, 362369645, 160000296, 800758726, 597251846, 694150660, 920289815, 27530847, 172581945, 582849845, 807299082, 283618092, 152015005, 531684512, 285150484, 461435271, 6878094, 180721975, 719000723, 141335001, 4510187, 779056225, 740079131, 973645785, 813280746, 366382183, 56409620, 619886764, 502871252, 247968250, 133590517, 767123146, 151807682, 683443582, 826538830, 70419785, 956764781, 513240943, 951663320, 97610347, 455192217, 831451661, 923195275, 741111287, 998967114, 238072376, 980086302, 894128685, 794505297, 421942793, 185189047, 116438265, 140298577, 291195009, 910699929, 546959875, 99927941, 675154604, 704737127, 652185204, 946431671, 613594355, 74515145, 1765009, 290344139, 337561205, 223234020, 565313061, 449292182, 466939302, 90985435, 468088661, 949016865, 580226139, 16334039, 483957516, 272268239, 616265992, 881530194, 376887680, 205563644, 151311595, 16330655, 218575767, 509199319, 169193371, 167372788, 506646966, 81998738, 894123104, 586127840, 693081306, 773725167, 383366615, 161525622, 377239409, 533694646, 673527246, 875185909, 773572444, 651175710, 323665227, 491660579, 315548447, 547222346, 317458369, 719258277, 56011600, 475260807, 143368748, 256529085, 31586923, 924958248, 516860922, 195215322, 413926946, 99733821, 671692293, 472806917, 28945967, 47410640, 866585748, 499474083, 770553837, 711530824, 988083730, 130629301, 502758066, 860560107, 333067349, 176375857, 658460971, 761105618, 474115526, 703509794, 806908423, 39997493, 417611255, 662228692, 119533485, 467265920, 821458223, 278247874, 129357666, 677339093, 460329448, 24434187, 40205081, 19013193, 106632717, 491961093, 149025816, 830468962, 104520819, 937956846, 423603729, 968146887, 898608205, 573967561, 815038676, 552101496, 185291165, 440998463, 842681277, 355590739, 412711641, 783714410, 868524168, 435521056, 625949025, 872530859, 941461391, 55210414, 737193757, 835861370, 555915708, 838951434, 379822899, 729155042, 427465130, 343010427, 720503101, 743533943, 377018741, 899308655, 586925745, 988841405, 74991715, 392574452, 709792123, 245826828, 174320152, 442006692, 610089306, 340242162, 528764820, 703778655, 630071135, 373275986, 608368062, 370202736, 586197840, 938392097, 356623117, 743847486, 668741055, 175018879, 381842370, 874039334, 407174319, 896236257, 998519538, 828055756, 896705544, 58751335, 59523289, 782767984, 460335435, 636642434, 120235445, 420488003, 853900952, 267228515, 242227997, 131817609, 354960265, 70902524, 887878397, 261713032, 450467844, 627182730, 859158740, 301894614, 260673906, 69730203, 923259619, 11420674, 206273624, 558526511, 649393953, 414288192, 478426624, 469670760, 612159337, 844264458, 32821925, 550599235, 160142741, 65686885, 362492935, 692348340, 723711670, 591466312, 907265559, 842385193, 940067414, 124210650, 667305872, 337314844, 234787207, 846202427, 226182137, 833313608, 356337512, 809720304, 548136893, 767052755, 294039469, 786947893, 948732625, 158515602, 848604143, 587695372, 70197455, 504960334, 189146723, 696454122, 493061361, 843802482, 92388141, 24764835, 650261496, 615260708, 264412889, 543004208, 359541719, 435382756, 394307108, 7562623, 26025512, 928017166, 578213757, 955005261, 171417714, 761837213, 870958651, 55236235, 142944952, 480940341, 83601176, 493135876, 456354090, 404186747, 327348133, 999498788, 710943420, 486410167, 380861442, 780786143, 491069651, 819710003, 274991280, 391221477, 768013288, 735589641, 836229327, 861272006, 357780680, 304273359, 412935117, 478903100, 76148407, 2426839, 27642460, 384769262, 843200505, 463473358, 997471673, 884898092, 408691424, 99889375, 999409653, 777306153, 279035160, 756272509, 531751031, 48312942, 854380404, 942369103, 482136002, 935882352, 759435938, 267025805, 198242367, 75537880, 492069488, 72925343, 308435231, 440483134, 427985260, 716486195, 731349382, 193772964, 116132578, 547845263, 608247624, 864277911, 894188808, 366529177, 473889211, 953773955, 784027858, 220540863, 615318481, 745193042, 850836720, 365328105, 411991034, 463800018, 723317231, 660662969, 39541049, 421498233, 235049691, 966416109, 519756156, 810808451, 378500988, 227296319, 541458551, 443293953, 175896197, 49774084, 962570709, 419068434, 252886235, 152447308, 900562198, 584319770, 633384648, 612680786, 788525963, 239825851, 962295365, 286101487, 901062708, 924528805, 814321690, 324952937, 111689454, 248914741, 452834538, 104983434, 891436485, 661142273, 676266862, 904890852, 327754738, 84860366, 523971304, 339941076, 399724747, 747468974, 633212706, 510108271, 727075946, 480984991, 331076636, 140570317, 902422010, 936634224, 195135698, 143619313, 254246347, 627049731, 537933989, 572893193, 893865222, 791989205, 258524187, 417210404, 799001288, 265047568, 158330822, 915642146, 164085572, 419484480, 698173759, 788921537, 261484464, 696750755, 275850390, 11529471, 350177798, 210332108, 2461456, 548757390, 633125755, 379551872, 647761500, 741822912, 18550215, 844072249, 29633236, 400215103, 480835073, 714252539, 639433459, 800885024, 728499760, 968496380, 591685291, 468556821, 370686373, 503667088, 142417141, 538041831, 719142016, 85835942, 573207515, 734821802, 126009370, 554921149, 133769019, 799025635, 39668459, 161170378, 928207529, 32328172, 437483490, 175918523, 263482190, 579024426, 164991843, 435624876, 602461372, 34267893, 654689541, 609582510, 346747975, 121721145, 156422641, 364677726, 826824493, 422233587, 740420534, 222091064, 207139023, 368200724, 415460676, 380867922, 827077562, 789020795, 58417071, 428988392, 712061590, 448331941, 794569865, 825548999, 191886708, 602596303, 414731869, 459426910, 483439892, 924922234, 382349959, 558933470, 352531747, 547770060, 267579736, 984341849, 834549979, 683863413, 292077261, 776665996, 206493323, 750443779, 332543412, 693025710, 612373049, 2741841, 168039194, 375377858, 873999574, 134553565, 960822564, 66165778, 549239424, 643257361, 634511065, 324076775, 874829099, 626790300, 101935679, 42246798, 436668575, 468748691, 121141069, 592243017, 977514124, 376842401, 552531365, 576052880, 553917780, 185514912, 266634024, 816321374, 145908884, 943158052, 513315352, 462428588, 604706214, 353365402, 300111399, 373405703, 893706278, 49540792, 218011269, 944715844, 902808409, 475505109, 773917688, 37191433, 745963543, 999557530, 40671800, 847240835, 155429444, 25189259, 82896567, 43016759, 111874543, 255527391, 479291433, 830922478, 136940953, 509452559, 108910834, 245436434, 140306001, 205242530, 693025949, 280741792, 281967226, 140202473, 270022019, 160255889, 653657592, 497828476, 168203499, 697237991, 607443923, 704547170, 929132168, 521969406, 364926176, 424341402, 604423879, 449901374, 815886879, 836047372, 655040828, 885077744, 134686379, 828526613, 464607770, 960126892, 766389874, 578754297, 643035891, 693282139, 187779891, 761400731, 74584448, 916830750, 258669094, 774520742, 242467672, 782219470, 414813428, 301396245, 643417505, 694525646, 246687277, 590568584, 245219360, 571881552, 348743989, 848919775, 562619192, 657551651, 677543880, 967330983, 222617831, 300455586, 733906732, 730807353, 627391400, 440088038, 416994469, 953833058, 160252877, 2348095, 553651390, 648959545, 150017070, 871602961, 722044354, 339035642, 270569932, 802737920, 697010771, 862749491, 285065340, 876532480, 708910947, 210196651, 785991397, 371472449, 812891970, 131690889, 737979356, 106038717, 962864843, 688368722, 646626626, 330124331, 609789822, 557284911, 824310350, 364312755, 499507755, 691574834, 521565554, 339022316, 268622047, 621563428, 624135490, 237636086, 805434682, 793502082, 383556616, 537703894, 310299048, 3444569, 261817275, 966738902, 881384646, 139750009, 204638452, 198238278, 945955402, 390984496, 891182754, 782042361, 466530464, 317538767, 253674973, 595005923, 331120412, 734933475, 539947808, 145181001, 760962057, 776356761, 273868974, 70220998, 180394613, 210291163, 769180207, 889567788, 243265220, 564236098, 883350824, 596907120, 392776088, 378349138, 822818026, 75966821, 341478786, 468561775, 736101633, 199739261, 194152102, 531102311, 975828516, 416973102, 64596311, 786878372, 837833827, 620332032, 864191575, 326803642, 865702818, 533027321, 720667203, 186861612, 484843802, 822076946, 402429253, 511766467, 291706712, 208637565, 266431006, 110483847, 715453314, 915512192, 803859189, 434555835, 642338142, 830232264, 798926244, 406059839, 517699575, 255329838, 655673372, 307751742, 89503345, 227440684, 236182180, 436621051, 625917877, 208643083, 346680842, 383456059, 703990046, 969982469, 270417221, 545502427, 46222304, 810009275, 931655559, 640704013, 962390619, 603684966, 835838601, 122225337, 312705379, 318292810, 747195984, 189244739, 432590583, 191408405, 103501997, 785584732, 414151648, 909778047, 256673822, 784668758, 330488734, 743411086, 381197590, 830107032, 510512706, 213338767, 661668538, 728177973, 665311634, 288500580, 773407433, 94561719, 506621690, 672938232, 4356547, 213701220, 364040083, 572142453, 155737014, 88620842, 268744521, 922120764, 14016640, 900781034, 592729811, 506616088, 776226461, 359478478, 473088175, 499342653, 283701722, 385919376, 719271680, 908726664, 315017014, 668241369, 732916856, 762584987, 315294754, 954406991, 351545781, 372755036, 828019177, 163423130, 682081953, 309969356, 458561116, 356462685, 604867683, 913047549, 226193101, 566859826, 854341447, 184720654, 331710637, 822591323, 861310984, 744026148, 472343487, 283436018, 584223404, 723530228, 251820097, 221105620, 155399720, 559897152, 602514441, 271788183, 446009129, 227134047, 177492315, 133974103, 918576082, 502511528, 455847573, 946048082, 407981623, 813302864, 409820309, 590865963, 344095865, 388094056, 577749635, 5213582, 543183294, 852912964, 925834507, 671936060, 639113452, 525706894, 637219363, 951053660, 478129632, 79945860, 682190102, 57962152, 823582809, 837609715, 878396645, 597563037, 296021133, 319702145, 565375263, 745432665, 783567042, 327138518, 288320317, 970860392, 469087107, 923961865, 960067626, 832388939, 998160916, 95645507, 210606781, 692677290, 52810727, 100344782, 834601053, 818944858, 432521167, 799929393, 499686507, 227879960, 693196412, 626196260, 224245956, 591311414, 492844050, 922479112, 493312066, 227396845, 566990908, 286791378, 823910927, 406540441, 110319624, 364430371, 554335308, 290582623, 527480894, 107166586, 133705684, 359989869, 562263815, 226506374, 785471568, 498158981, 703215215, 302782477, 892365860, 882956982, 928335322, 706776904, 549533994, 231198891, 368205215, 190128320, 544110979, 522896911, 415171506, 204541498, 756832434, 680461807, 316193827, 822055008, 58641601, 509413085, 615616411, 344475319, 260242539, 654493068, 982844787, 766264308, 655113194, 374943703, 157613489, 724397327, 176013203, 381258011, 566810217, 412259081, 765518705, 354047612, 255755584, 574738587, 986288270, 951826789, 309506188, 664396388, 169615442, 276849796, 503094180, 848200335, 780467558, 261709163, 118973450, 818085855, 374110421, 989646461, 845904975, 129521124, 328290114, 220672673, 932458386, 731699750, 304798724, 532646417, 36913627, 309813333, 147318758, 668642605, 241215019, 830858326, 311398356, 944432069, 238718696, 78031981, 451100302, 634997976, 61182246, 488123749, 216638639, 212591288, 155998795, 276201857, 224742779, 633777769, 342670148, 946239287, 427682576, 114964826, 821161628, 805011950, 896829795, 623992740, 162501012, 61154323, 39207746, 674158491, 506715889, 649496240, 679909214, 277223148, 207765202, 85440790, 870570950, 883169273, 587541644, 430731077, 409599609, 731857004, 252218071, 844528679, 869896735, 264084500, 430245610, 507062613, 234314820, 886042857, 609240113, 718545687, 845836058, 312855232, 889440421, 137620215, 663134664, 894610682, 703860325, 925771110, 537486804, 123330342, 288492391, 907391346, 893286826, 158008452, 104636036, 587172972, 509000349, 764253896, 48223155, 255179757, 293922705, 710076693, 958453859, 872632085, 192114454, 539486906, 973301776, 573940183, 250067038, 671384437, 181306997, 307125221, 696656382, 96954714, 646505682, 515000865, 969195855, 987859129, 607687119, 720414904, 80063322, 106637398, 352752710, 373435073, 704890058, 601317692, 450967238, 338198354, 854672508, 840137963, 98888896, 527474397, 309915388, 750178231, 936271634, 157496084, 977098264, 262238125, 643607037, 800136540, 911268733, 930792592, 669038509, 134366741, 951879838, 842486104, 91045700, 114091578, 399505213, 939349341, 42209140, 594883065, 372109068, 134525150, 692778379, 687363838, 89452422, 559011895, 194145780, 663720711, 189427498, 548369794, 711577229, 786453090, 85757347, 275657231, 122142914, 626378886, 991884302, 542940356, 321327431, 849425112, 882615763, 780830063, 121552418, 285341613, 703698843, 759001817, 216602550, 333691581, 928508195, 461459317, 381913908, 91323539, 554680034, 825951485, 506263891, 241423469, 50806547, 367216514, 535479690, 933629882, 707071844, 570847973, 216052052, 11667439, 394514765, 443090164, 530312937, 611186344, 789756262, 903554100, 818993304, 681322392, 904954415, 313671179, 626975039, 536741591, 445411309, 299888314, 763380583, 569143416, 236782519, 862731925, 420529892, 486810172, 738093048, 535484345, 648351862, 699266783, 719980517, 526448152, 391913496, 146658167, 479238696, 447726014, 459049235, 955332678, 530721683, 483173010, 644307833, 725029655, 790501190, 766815133, 911137578, 279755670, 467662089, 714781015, 701586546, 784673681, 743608728, 454526227, 126100677, 531292620, 421203713, 318219870, 131930551, 126340621, 609108920, 925974244, 504893806, 509853973, 191709912, 248335102, 716526026, 531268688, 855864301, 354401289, 173517889, 764939162, 161969480, 855704316, 609518191, 546706219, 941057516, 351815036, 17206760, 931271856, 343271096, 292164975, 481417329, 88454311, 510900165, 727878965, 97221855, 873695763, 359450639, 159953651, 285129339, 559234303, 581617918, 831475038, 166643544, 414564354, 158236607, 320861064, 147366908, 526937324, 827900664, 541080245, 883487952, 155403976, 418963021, 133965863, 561866334, 774890045, 67070203, 647637771, 799654577, 800915769, 631201432, 931231670, 1973514, 592705967, 509918020, 855673284, 456021615, 248895439, 287157793, 496272685, 244589260, 693427573, 154205001, 488471460, 146733552, 636690216, 825800378, 322811804, 545765092, 220975967, 509296415, 142683773, 996476408, 805266597, 304233367, 425818732, 935648658, 122442590, 303427901, 501197342, 470267573, 730166841, 387895704, 179430338, 521676868, 901904452, 792068999, 788203506, 375250687, 31249841, 874040139, 941791219, 742163256, 989010823, 972159110, 484945904, 674602362, 691054758, 48355648, 450153634, 198489476, 807467312, 724363384, 104825084, 566281849, 51932615, 18137238, 960255831, 242316938, 632578615, 802735338, 245780304, 559595994, 802595312, 986234725, 97687650, 876903369, 598887388, 923314316, 873934394, 462258238, 862483989, 1645270, 751270921, 691196019, 190538548, 312694962, 468059412, 537369348, 491865176, 787425522, 926730997, 456563296, 808472882, 551410428, 761119051, 560497340, 657373465, 446388035, 26624617, 451969423, 60583470, 449457993, 386559415, 880975884, 740788762, 177358273, 132519667, 32119130, 531524826, 738434639, 920231278, 305336869, 665244405, 922155389, 887244422, 127281687, 534277932, 666693487, 772531662, 415415602, 113280258, 695017685, 213321529, 485046272, 168320332, 591563076, 706050951, 660686975, 494270105, 801606402, 662374287, 423231261, 840621934, 595111452, 817686273, 521711641, 185733139, 360177935, 962624688, 217748089, 142591039, 685632857, 219329735, 879178283, 904464044, 725781678, 420822928, 20599257, 296708853, 728743282, 157816153, 654704187, 567473330, 32786395, 686111247, 118207427, 459491553, 688483583, 818628982, 453714876, 673052614, 832570103, 559185077, 995977091, 518513347, 95321130, 403961366, 263118330, 982734248, 568527215, 286879186, 950335216, 435045725, 179941407, 113506585, 923902262, 212243544, 990647783, 613129668, 915518914, 800079572, 129086877, 330463965, 495656569, 165960913, 978550206, 469915436, 607838994, 465204053, 832858623, 200748453, 146196006, 459480895, 537964234, 861708654, 65051977, 412851691, 475767646, 542273161, 400465130, 717798291, 129143863, 916013982, 668731772, 953474366, 30247859, 613519146, 356222069, 140323244, 349866709, 525635330, 401726544, 828169388, 719057272, 186412059, 558844971, 757439590, 390187396, 223068358, 252685420, 737951536, 924030566, 699683662, 266927717, 232162071, 297617174, 768932821, 956484992, 93626506, 383086957, 377103152, 847370256, 292369859, 763243048, 142840010, 444824575, 52679542, 300367746, 353448238, 644590816, 106941253, 289017216, 790067073, 217445058, 769427469, 935750833, 706928154, 610229126, 478071453, 629990187, 161749792, 719659690, 988635255, 135828946, 459135713, 655640167, 617923740, 585893892, 280520458, 229554859, 601053993, 870802058, 337796374, 344941936, 290850846, 618148181, 349419099, 610209405, 753273843, 804751579, 489132770, 434444963, 432358650, 408086252, 685964401, 781062964, 825304560, 64145336, 108848595, 885888489, 474081545, 787867597, 216720245, 884695535, 273449783, 429935396, 246120533, 481876053, 858882512, 410629696, 155665233, 55953077, 478730804, 712563146, 672471620, 843167129, 342250878, 39854990, 757889176, 301240213, 182883941, 447008896, 325868405, 974165448, 525336900, 890724877, 326473833, 468452236, 827632816, 539499962, 595877403, 229804029, 88541268, 829569176, 223589795, 356137795, 189425065, 569983140, 968455089, 815979138, 166100772, 937592748, 563326964, 415594120, 835491823, 809247866, 975649167, 679581790, 356239336, 579400000, 450272017, 905961902, 203847549, 134853018, 326804278, 195407325, 764221636, 460274423, 929878434, 659533046, 530923270, 204937297, 214448568, 827445094, 542422894, 275705879, 224372924, 859177111, 31445528, 560991081, 724775603, 377950797, 598229247, 562479274, 741236352, 970140202, 346947086, 236387503, 385157599, 504885080, 431020000, 76145945, 500633856, 796586238, 88723696, 921022679, 772749342, 9736213, 761979285, 156381551, 995060003, 232559614, 214077157, 423154719, 942645575, 105804194, 863637425, 926869045, 103967730, 856708245, 437337699, 442759353, 230470504, 207584744, 543822453, 129923522, 253348242, 520733011, 827294674, 865584808, 341061621, 973292860, 614684924, 614993590, 133799245, 770382937, 881607876, 423078149, 402364387, 352614769, 33356727, 755827618, 234364639, 641838133, 904301956, 601489627, 122616529, 773514693, 874393877, 961341584, 792681180, 120436943, 637904544, 67374518, 803260055, 454698148, 174512216, 92896907, 964314961, 195779195, 228574681, 532227065, 486912865, 486840389, 554771370, 787601964, 668853985, 249752887, 70155483, 31587482, 145115322, 858273711, 231509712, 384478773, 216469010, 388604180, 790918596, 286146229, 318687556, 100750311, 245107412, 833556514, 206114569, 473972006, 14919324, 927588930, 914432136, 267041655, 873689085, 342915052, 359546775, 159406390, 130189661, 909829840, 283880998, 777804771, 3869963, 176123522, 707448656, 81876125, 715234919, 415654076, 4985287, 943073444, 648449900, 781519109, 324626115, 183196779, 219519329, 907734303, 969368118, 878378974, 388513369, 723885048, 720825493, 971967033, 152507636, 590264921, 824527640, 439088608, 73046886, 369005906, 364208697, 491187439, 973962460, 873064191, 678368200, 528606699, 979732528, 55606311, 345104758, 299965513, 45415993, 328552344, 481200147, 662490075, 213538039, 44436399, 361815262, 925514614, 649572751, 324237478, 974409485, 298840635, 760381369, 185241208, 771979466, 5553782, 60769817, 543857926, 891358370, 547292038, 917206602, 199349856, 865126853, 207392304, 894760724, 114867361, 782492682, 151099695, 886331748, 554560377, 810401626, 791135214, 881437610, 215358143, 631785359, 182758325, 374284863, 148504342, 924658738, 387640203, 533065099, 303257843, 835444493, 614635956, 97459417, 143275124, 109874983, 69815563, 437636137, 846399041, 304936441, 998419668, 64474317, 157185882, 116144615, 802022279, 568208754, 312674921, 26849784, 541592997, 238525488, 804301924, 256790866, 346036118, 775189807, 654161252, 620538084, 408031693, 357013928, 541014234, 621245420, 653635580, 711623470, 693655454, 982529743, 475929342, 103263139, 32764802, 320077799, 785777322, 441560204, 531943869, 176371107, 533623314, 641295436, 759660232, 126926806, 355109585, 800777091, 898240410, 235763007, 924197081, 291366698, 666271448, 143886017, 290052114, 192049755, 352827446, 718329687, 674793618, 398896119, 73148487, 23661182, 21913013, 752289923, 994831118, 289603960, 893350271, 233861137, 291452231, 852836292, 59943027, 983993713, 328320912, 199166261, 616177172, 561329377, 952275226, 918358246, 118417884, 163086363, 650256024, 331776885, 944895268, 141329173, 905626888, 626356070, 810353461, 92439108, 102674641, 459705975, 598007747, 38521901, 245584514, 671821415, 634358156, 885496837, 930643506, 389516415, 755169871, 484427319, 10819411, 46368120, 397148627, 965076135, 89765940, 141281235, 672306840, 464629381, 731919762, 907665186, 548066868, 211385572, 509862060, 882488439, 105654590, 952829440, 96227690, 343819174, 989281574, 103162987, 574100569, 734935741, 34591697, 73331615, 430425405, 960807119, 260758774, 292196039, 630803162, 344526427, 163664177, 715942311, 488455851, 59496031, 182422148, 315676512, 139959797, 858217048, 557600893, 158633868, 733551619, 168283736, 548664320, 853132614, 947025091, 667009257, 108322959, 62993260, 424493200, 660763318, 855376408, 38654806, 541084101, 493135800, 930067781, 106009184, 583981939, 892002144, 24488106, 514110887, 496443578, 752149099, 976114941, 963446130, 722703390, 71604540, 417305889, 315373124, 176821757, 11941089, 77699535, 838064972, 86871788, 698702660, 145511849, 148499221, 535435458, 906513286, 693734842, 338543528, 907630542, 455889262, 215643474, 388283443, 300293609, 190491344, 169520454, 556927981, 106260643, 25741873, 208080657, 171641354, 128879580, 290844740, 252006708, 397208179, 161818650, 536277019, 790490625, 468406308, 177806187, 466520175, 788731484, 387609708, 104228844, 447289688, 833665692, 477856777, 663107449, 720001984, 219248387, 516131920, 32822371, 622728432, 156099231, 590601018, 498449899, 658354093, 428537034, 95221051, 407475343, 454534882, 181992143, 417476493, 217998371, 31356048, 422748295, 817271249, 344350741, 8121166, 486626589, 23734088, 543653945, 902852481, 355459834, 519828959, 57971816, 111039825, 888535316, 826627482, 655324287, 92534826, 530320071, 244638768, 69475785, 250004370, 567495695, 386684982, 450112665, 915037153, 217993144, 406737398, 132974051, 490166634, 216105077, 174311848, 40580608, 734910203, 478468222, 476085911, 53871398, 365915775, 777837455, 150745085, 741905337, 579516631, 999215966, 952263247, 512457561, 324337264, 465999398, 740740008, 105215811, 285076143, 686779490, 883633047, 803010215, 581111272, 954145547, 120849428, 586507169, 307823115, 286066438, 118487785, 961469075, 690757664, 714370401, 73394199, 479418531, 74528208, 803833003, 718825058, 449188080, 955364074, 355687621, 411234202, 179157017, 379827599, 306739570, 933523914, 504459520, 54040914, 887740131, 381851876, 283096029, 801969192, 256540595, 289410694, 233123062, 125531139, 307291988, 748329442, 341337933, 773064222, 843375746, 518256816, 274341395, 203601614, 51772356, 485863607, 891670128, 647850139, 556058363, 496426350, 346344746, 344372216, 715710944, 134560875, 59876062, 671770573, 246269789, 542303435, 247751428, 628895683, 704331936, 532123585, 519499271, 433517975, 329749579, 376237709, 382033891, 793848946, 298727794, 766989057, 758312523, 688047114, 5745813, 684160616, 822351324, 369039771, 895993106, 153876383, 485481841, 901095171, 712042439, 842409466, 733274344, 195099316, 441210284, 552896715, 577967670, 295597240, 766376321, 554638151, 50769954, 958213815, 65886140, 988307961, 394927648, 969268507, 403140867, 812457595, 13108953, 795171974, 479022102, 414382654, 519012872, 757695730, 682517162, 906011219, 734619214, 378174725, 351756674, 481527873, 578066931, 303819319, 931661251, 606985477, 567684616, 260242808, 682399519, 316916677, 659059614, 374724445, 181315448, 470863068, 242893026, 608471161, 546996782, 63911838, 172839651, 227971058, 958945823, 393901178, 191688964, 407728443, 654034734, 307517602, 483209789, 767239128, 844902110, 260577209, 331893242, 630957257, 571801606, 588882065, 753099826, 707256820, 33804667, 165694565, 170149204, 349341801, 584805695, 843663137, 421300502, 569530247, 502368100, 99531671, 18328305, 427542749, 439983419, 736508905, 818892410, 618871835, 635066580, 602740983, 381166435, 319523137, 449065469, 973691179, 542679083, 759926650, 114433050, 685811015, 801029005, 53277889, 375120848, 26854396, 338842576, 781230497, 564906117, 881432885, 488308884, 418612994, 470641196, 542899846, 913622168, 747947068, 728696339, 792310074, 505578143, 13875753, 674423615, 49690600, 84958691, 630040944, 271291009, 232341677, 648412335, 5188174, 987957587, 431598902, 478564804, 175334733, 62851516, 529248474, 538813207, 419439923, 641801312, 756671508, 26220087, 961698543, 617156212, 943475391, 465101831, 945263622, 683136202, 856329514, 395471256, 34182177, 402734728, 312809035, 925091334, 266213676, 559705946, 779640691, 382599102, 467049813, 251202765, 668560874, 377691091, 285223221, 467613670, 491673518, 250372424, 830674212, 266731021, 476235060, 917362057, 547197723, 151387427, 635576182, 459839872, 712287341, 759425596, 926468990, 486817591, 267605156, 301841333, 219065839, 84059048, 251384338, 351249541, 92237640, 764708324, 986692804, 484463371, 23557831, 607030820, 401038185, 132119131, 566368536, 885744229, 924407405, 291512238, 647685469, 899997589, 884778318, 180138315, 839092341, 45169320, 721633126, 16315935, 229939614, 635601909, 495006120, 994554134, 164304811, 89890274, 273060227, 860934090, 911988892, 769434179, 70370143, 577128421, 590137066, 178964312, 875144975, 613487987, 908031133, 755953008, 481974258, 3710702, 216200708, 122033573, 329632425, 423704220, 951885387, 674265925, 483524556, 64182385, 923945240, 610546609, 973534797, 720618652, 511236753, 673586358, 981837428, 798819702, 284544617, 501155970, 959764479, 153118989, 847431344, 362980437, 459037424, 583432421, 905030000, 55015969, 275772152, 307155019, 405583310, 866693495, 924496083, 770698885, 903922105, 385107461, 331096973, 671892986, 582490942, 108579554, 862109203, 972027688, 125447785, 329275196, 612356642, 241047393, 994202678, 378867493, 589890636, 661276334, 445538696, 311806515, 935830861, 411304724, 972487601, 682256887, 943199008, 117710015, 597218322, 505493786, 619328493, 393386207, 539161218, 986223643, 376158917, 764035404, 999735482, 409034159, 927959488, 735126430, 646229062, 376836736, 660133314, 295646359, 566883794, 273574290, 139407658, 424876686, 917651843, 394949798, 355738700, 888518867, 845613407, 192251479, 379849617, 717242961, 622924070, 326469190, 275487186, 266304998, 408313793, 686675788, 256579862, 208663078, 697902490, 767504868, 316099088, 899351062, 827034512, 555427735, 652431812, 528012477, 68140126, 786681503, 15141815, 442609210, 353169432, 705037494, 224165849, 105889472, 343574288, 272179176, 597556697, 887869605, 862400064, 956332065, 405085514, 634609004, 494959327, 52646162, 249254383, 867299947, 72664181, 128918136, 438558350, 601111069, 751456456, 584766656, 516694315, 791205922, 484196960, 444878062, 370541553, 116377155, 65580655, 652299290, 428076709, 888884064, 554726350, 762156381, 913497645, 887584643, 780698881, 878738898, 154674249, 759940196, 61672383, 798964664, 832732513, 299864265, 537098116, 778515964, 659810419, 163684313, 882968303, 823248263, 627007444, 609594324, 188947912, 555352155, 951495776, 297892555, 644839299, 168227788, 318031452, 613012349, 6552005, 525403156, 953659608, 393803871, 695170189, 295034501, 777953251, 403691071, 864819563, 23586268, 495179142, 851492737, 747554758, 951979055, 717697066, 779512307, 224614248, 586086177, 954683813, 84746808, 109587609, 994167603, 172942844, 873797228, 712199695, 418002512, 339110929, 74069519, 70942488, 868807546, 687356832, 449355961, 548808406, 434158372, 219600150, 683436687, 965520254, 228472547, 525959549, 630729638, 816831693, 365074663, 615549421, 458220677, 961256138, 590502685, 897109056, 309598866, 551292526, 801730542, 981259605, 147041311, 322873190, 128855981, 642205285, 111332523, 248760303, 261718162, 523147603, 119844783, 533440680, 268395664, 259418812, 836953172, 171966020, 327456308, 301895733, 973509432, 416856944, 968392027, 648537038, 101417432, 763438239, 444641350, 60574134, 410361718, 499917770, 240414570, 282044921, 728406444, 842737956, 344068738, 901463013, 165044068, 446387946, 276381422, 756836679, 170546203, 508579508, 293200246, 220270824, 74849773, 668868644, 257343942, 172094510, 198010342, 310594929, 902866978, 907134676, 266359029, 750913234, 609023914, 835011124, 567563529, 901202009, 530281307, 565777250, 421869708, 531472121, 808314594, 192828682, 811412040, 760858539, 502830585, 595097941, 323485151, 131002021, 19089823, 179221993, 721411057, 937185175, 918430268, 805357486, 460280368, 720771291, 550330443, 118175818, 404934718, 277571080, 179900650, 939872072, 649797226, 829149696, 26791228, 652178090, 239690700, 472501825, 235528136, 674778854, 723532751, 348825641, 326623766, 137431237, 617681827, 654421723, 550230280, 391616547, 123780927, 486544899, 503153145, 563725495, 57513988, 78648161, 382410518, 944438701, 302186077, 762274254, 510805089, 303192412, 760988301, 461370283, 773587104, 473241163, 290148438, 426262290, 286056056, 310197362, 813882712, 658578148, 696930921, 476272897, 761083420, 552442459, 955779438, 431031961, 48181372, 690136584, 525097374, 719234802, 505373501, 670439577, 64939787, 477107312, 369895, 31680897, 590131963, 20609296, 253883464, 240920157, 681580183, 891893617, 945111343, 240733681, 718442007, 991566754, 127975967, 657138910, 707794239, 850882761, 658855813, 994138894, 350727314, 958233401, 293346048, 223480742, 37535927, 914776483, 15660805, 794321468, 119908024, 869992842, 476251364, 340936205, 842686724, 448486248, 650734688, 219403639, 192642955, 121045949, 838303150, 877304729, 767364408, 199466780, 677895450, 345270497, 44178289, 878717344, 930553575, 391050891, 170464494, 598004647, 770576374, 304717116, 383156798, 106268367, 180922653, 33797673, 370404600, 444391120, 548091950, 75605960, 71493613, 799509732, 615629898, 695443613, 851799251, 879463633, 136424198, 342578122, 58712063, 791031125, 239103081, 148433165, 189224398, 854084544, 294061646, 240809893, 715217272, 69157827, 672949576, 283919722, 602932638, 97977013, 972555801, 502313540, 367416514, 430692251, 240657530, 394905689, 626219404, 927324389, 314197494, 496708321, 315168380, 551433081, 128163765, 225087072, 931926449, 611767681, 856941934, 911662260, 152779931, 388990944, 289529885, 953684272, 787457938, 2723484, 566558373, 114618340, 391865838, 760599628, 825608149, 848139443, 549290063, 942010135, 504602245, 326742801, 686248621, 948735124, 505502301, 785663351, 757244702, 613228511, 741038798, 920438432, 674532789, 771004042, 89288939, 545651810, 111053214, 435615183, 507257605, 845844959, 864087435, 765030847, 643251081, 383969771, 159917430, 260675901, 970435213, 251432676, 752334080, 560779611, 125796308, 285145101, 891184202, 374416148, 757851722, 980277349, 298817390, 126764891, 848160849, 648000842, 973708840, 837830319, 377183986, 724245746, 602285016, 326886330, 104587417, 974434692, 872592181, 266844754, 121625288, 758075754, 987554405, 472582202, 607040693, 400199716, 881552743, 9643830, 714790250, 877111439, 772891796, 83211498, 99044616, 842984917, 718565590, 774847038, 214026434, 173884519, 551927610, 806808248, 277891536, 542001376, 833506301, 5020227, 512809039, 558336445, 795281620, 238985401, 207275856, 274084877, 356124766, 832254729, 649144757, 513013628, 827082782, 121046950, 957159819, 227083757, 185810451, 972129997, 679199002, 576028294, 241574060, 267415920, 301477539, 804821270, 64457307, 610619702, 828930421, 548954018, 628054574, 14065979, 686848226, 966972631, 799304857, 484907975, 728158831, 667622118, 841243756, 885844308, 958048761, 242197426, 87521958, 41539599, 273908297, 228930115, 81384472, 800875331, 739633250, 477337799, 768539783, 422604247, 137477463, 563808149, 509726880, 265592242, 356305983, 546263813, 174230701, 822693882, 345738591, 197185356, 341483025, 658297379, 679593053, 166810331, 386180644, 765567886, 881210523, 848908620, 798213849, 325211549, 573887410, 39668580, 225613101, 666307160, 787955944, 872561891, 202737130, 603000952, 427501813, 93738673, 800895857, 97747671, 998863104, 915032524, 358611159, 179090748, 567087379, 423333586, 656083772, 961692912, 159266340, 432578969, 744880838, 471460011, 207371392, 521817282, 729320318, 308175694, 754659399, 604668421, 996789000, 659959104, 89520957, 795555775, 357870744, 528114, 552501576, 346990974, 557251621, 845683189, 768017379, 472348574, 300144326, 591984062, 691808630, 815212584, 601781053, 714414304, 271561593, 589623584, 923919259, 865800817, 634216342, 391185709, 74236840, 390485854, 702844311, 196283999, 658294336, 458862397, 61660509, 981711527, 48311345, 743816514, 948843818, 398482854, 409876149, 931707003, 904694293, 100526308, 684141217, 865827475, 963540335, 649027046, 872497845, 53508145, 291327284, 847818363, 363823897, 868179150, 554818179, 148095780, 807826783, 324280939, 20945445, 206827963, 526461907, 925631616, 161764592, 284244442, 403169600, 880532613, 925381567, 773915185, 62939670, 116520749, 153424024, 618860804, 731845433, 55680734, 262443116, 402713035, 133329417, 226502246, 377834706, 946707242, 351940076, 226126776, 201824465, 166555627, 924085074, 571508708, 928686695, 716038119, 947775361, 479385372, 263981409, 219844974, 341805059, 932764478, 116928369, 688504332, 514225748, 512586219, 391151534, 129887336, 583016294, 843305459, 128309912, 189345395, 633516093, 118386504, 695101616, 772169898, 76877729, 159847751, 43795085, 690943971, 454901490, 346989696, 607077084, 24197122, 57405637, 760933213, 975392705, 866321439, 666433838, 958592515, 396605734, 279948847, 940132142, 312635296, 321225015, 489514324, 513881926, 273224729, 881928292, 954350870, 262718659, 667414567, 572648514, 270118848, 525630848, 936493866, 837688789, 31643750, 411729952, 154364679, 434834798, 924333443, 9294129, 498508365, 909036260, 644841176, 474825782, 896438505, 340469803, 899095609, 434099144, 467908376, 525136864, 504896396, 609373856, 497195930, 301216937, 331967882, 33683963, 438181734, 122183519, 21125689, 926119488, 660404065, 195116955, 172426575, 390631443, 862139370, 515100147, 673219275, 36192494, 185274746, 304035106, 141397463, 815179938, 69904855, 292044191, 149779787, 609775647, 804025296, 901185490, 485343137, 962795070, 215924549, 387665615, 108604229, 74486775, 47667552, 951287166, 130194282, 578021364, 135163216, 745905395, 481337855, 263289620, 468990804, 974284510, 627519211, 842702197, 857943439, 305086502, 739669617, 991844430, 279490946, 257706756, 279533234, 812660662, 718691975, 318782135, 48023608, 857423429, 987799029, 570364431, 729267487, 337628156, 488530733, 756570722, 925118296, 237929490, 321913337, 805166275, 656511655, 947743197, 602859547, 537063999, 870229797, 124209839, 502710910, 43051189, 298825533, 48024673, 569520940, 537493787, 226992657, 801356516, 849522824, 892014932, 351375058, 999714304, 423716631, 473108909, 450495331, 159689034, 969605438, 968105736, 165110376, 623105038, 726966108, 260373223, 275591896, 795326695, 727084094, 732756314, 272873209, 905069117, 816166169, 619721697, 46058653, 315080651, 277032861, 180030196, 958875920, 330227271, 422419170, 479014653, 452415228, 371172606, 905847671, 490011072, 443471204, 867942479, 417169346, 673375916, 277952449, 819071516, 465811847, 364049511, 111904422, 45017225, 113229423, 139565128, 242772018, 137183323, 193067820, 294233537, 196976798, 802190403, 709993070, 336619529, 803949879, 671436207, 612950278, 370724250, 726353646, 733275539, 827317752, 608557340, 961172443, 369138349, 590872160, 223952366, 561044646, 421523480, 879254934, 454815010, 820187641, 925442162, 753159624, 471872997, 858843180, 388365412, 26231210, 627251528, 240936263, 613868475, 80768522, 79908206, 261153542, 766386143, 412458523, 300661728, 730782957, 403889102, 880664138, 186257679, 63117042, 902002286, 789470999, 297508429, 74334246, 576951906, 964628590, 70085926, 498209230, 453610220, 865636217, 311315058, 341112069, 283337310, 858296953, 938723357, 183366527, 561006437, 742216115, 626969949, 856386655, 463373413, 192162770, 962669736, 15660810, 241349461, 100104624, 569161880, 400303056, 787537988, 275966360, 747233995, 550354990, 155787444, 933580921, 114966894, 844635977, 933352538, 993469244, 796740868, 449549677, 778790210, 258510837, 614371154, 585377749, 43126175, 671159277, 862380533, 973508952, 498070274, 453199716, 389872912, 246148765, 358849530, 647812088, 131765187, 161947975, 128432223, 865094822, 657908616, 291861155, 89408953, 17995934, 480117413, 176416948, 566858633, 94249672, 344800131, 753635062, 411794631, 813078806, 355268725, 298810504, 909315045, 290594328, 834416442, 596015791, 788441311, 868516709, 547522190, 879597232, 609321831, 726637225, 478786909, 234926583, 235121295, 398336116, 938975208, 15334743, 819548299, 892497902, 764704325, 842837918, 544915396, 477548248, 717515822, 837969556, 986572215, 959212789, 913115865, 383101764, 504840641, 446993257, 398566804, 696091361, 629412522, 141799999, 148585404, 524580988, 695915482, 679211955, 560647954, 429680572, 789950001, 642618941, 58650671, 503254610, 586695508, 602209164, 613007005, 958172012, 571805528, 529730436, 213308332, 408640826, 973806469, 685354464, 254441722, 24777578, 945338, 928629566, 484940465, 706087268, 27674590, 704851300, 779595672, 993695969, 628603087, 552972375, 495997250, 86223371, 134147998, 402058021, 714771678, 27927884, 987701348, 744599342, 219754884, 205525105, 285166379, 420642778, 787996177, 950363317, 459810832, 457859028, 956081022, 826747105, 275336875, 767685675, 55656716, 747019351, 390699549, 251621992, 662730025, 523666545, 594724052, 27336991, 538360722, 880479140, 803907860, 790447604, 794043864, 585192821, 152235060, 847217164, 457794975, 413084779, 665803886, 269240408, 236154550, 633126573, 686170487, 690354408, 65806063, 883230506, 190263482, 698085243, 129060479, 589237497, 664784137, 205978308, 937685664, 493751799, 190150993, 429599524, 221539816, 418265569, 59686515, 580173182, 55963257, 458856706, 230066713, 820719787, 592374927, 759010256, 343314778, 770231270, 811285806, 838809919, 108085882, 850641353, 259049147, 250869252, 106928822, 80391691, 919963500, 798246281, 845407691, 230508184, 464191575, 356581434, 178930829, 601887064, 200581241, 435064614, 568786962, 859447844, 568541326, 145200764, 378128745, 323305636, 247486556, 862210047, 488867332, 443704707, 478261000, 966538136, 125475856, 757253419, 324035553, 802672267, 251047611, 384088137, 40956761, 926408988, 286066089, 96195932, 208926, 90508071, 860386650, 39965081, 572620274, 178631324, 451500536, 663695349, 388059577, 797354895, 954577553, 708326714, 538528712, 682284792, 295096444, 788319797, 385177026, 277365248, 437162244, 304629308, 18368935, 650140471, 498135564, 570456483, 406399785, 231310490, 340696542, 848030971, 618094047, 99269767, 566679727, 864758652, 30728743, 94445114, 524945702, 695615807, 66446996, 214528120, 481913427, 124393795, 372777672, 237426492, 474666364, 496367973, 744589303, 880907797, 962105899, 318201194, 374170731, 43195815, 981385180, 221888243, 215117239, 374604361, 510198938, 404212156, 238708640, 880299709, 607059276, 894560463, 203322172, 324724066, 108614593, 785706884, 36482971, 236274954, 813676516, 985269260, 704474682, 357981510, 648983085, 708091419, 95743942, 731307445, 871679699, 350050393, 959006315, 413424085, 247619500, 724979746, 441516180, 47169579, 855372347, 704912604, 906487434, 984477765, 963174684, 362342404, 20480908, 228952619, 394905368, 131748925, 950814159, 423097284, 553116564, 97290608, 559870703, 402040442, 647833034, 27149767, 169619588, 599380466, 721205239, 562257879, 107791394, 82383203, 270790861, 690132569, 741020014, 402365282, 957162468, 905380028, 661089892, 661986711, 549122953, 95786833, 241868290, 1928732, 106813994, 594330364, 606662975, 933928634, 106339610, 259652237, 197953139, 854924886, 170168898, 863139739, 73095319, 212540769, 923891031, 866640156, 53267878, 55079118, 212313226, 815303568, 70910373, 20203655, 788124381, 870677562, 279154945, 15099282, 109574929, 83147297, 244594745, 309559655, 344309621, 977223986, 762846746, 95955443, 698312036, 927456288, 870662110, 201365277, 944430026, 669640080, 815792457, 580017384, 235590941, 524802448, 910978129, 300810225, 960734216, 183568061, 104822764, 912317914, 974292225, 873562353, 984886311, 646048272, 579638404, 419074216, 402497029, 979943955, 500407890, 598719727, 408607260, 314965153, 99110807, 76557803, 714734280, 340320643, 738949199, 650907639, 517154526, 67945967, 837397671, 687576700, 224930999, 751707828, 259362894, 475024959, 910920432, 898639103, 960616104, 137129452, 232444906, 351586924, 817330101, 224619575, 575002207, 475107123, 596005310, 89013990, 92497605, 160561599, 661403050, 819831767, 319583886, 582442338, 421974980, 243461840, 261575910, 607658424, 534439239, 896078964, 65317259, 73101744, 605097891, 920071621, 357017571, 211997482, 554508766, 963596320, 966054876, 329836681, 973329669, 715882081, 199670616, 817756039, 23864840, 167397533, 490293891, 736903121, 196977905, 867092896, 645233057, 639400563, 891296630, 178172134, 78273385, 985164351, 511631915, 79110201, 894647695, 845880878, 526561029, 727950733, 500218422, 784207738, 575207184, 81449959, 229342372, 606055847, 710840861, 902587733, 208006324, 153680958, 136550426, 662986137, 653929461, 654019558, 448234312, 329870926, 594712802, 585929472, 830418335, 77383126, 495621001, 505631391, 661010532, 118816629, 448184627, 591867519, 247985198, 181859762, 744683697, 869761307, 454248601, 476786843, 576508713, 289854359, 456083706, 589452637, 482731578, 936952783, 919154971, 718219941, 591916629, 200372387, 769789317, 187293774, 656230474, 815971280, 527221994, 978836988, 668502602, 833305221, 637652383, 874774788, 491856991, 735876885, 246208026, 55084223, 249852297, 73627294, 190758648, 402493551, 697680583, 7407826, 111925996, 724243714, 190080918, 750728241, 544109759, 837405288, 690250152, 448184421, 707288772, 532687344, 807476196, 484010184, 317423743, 226790873, 311462095, 673334135, 682637437, 359591886, 469826622, 352200820, 958899978, 444511158, 412521470, 372778655, 582661006, 612039402, 39163177, 722866949, 658824606, 689579087, 390351062, 246799978, 591712341, 751450161, 614403444, 689958249, 899246496, 319650203, 228698721, 549904759, 861618905, 633098715, 692555860, 605628035, 130206833, 322487185, 546620353, 409056951, 977869616, 191699071, 950552151, 493446305, 203766416, 129994701, 848428632, 454396256, 689913012, 240887540, 515301446, 757154618, 411531812, 636713229, 516777193, 694638727, 684987725, 949773860, 223716281, 604484930, 345035377, 913280145, 581917744, 156911157, 775783732, 500356640, 22759385, 282189578, 622449044, 972474117, 442363887, 684016183, 284455279, 122224390, 549960967, 388763570, 198365757, 577026320, 365944866, 60910267, 223727404, 826132251, 193596177, 945627250, 924941614, 385559434, 720695829, 986892136, 991018086, 178214580, 656398757, 294323034, 99935402, 709404462, 695025638, 929560815, 627463617, 27533811, 875573998, 868673285, 739227965, 118093425, 345760390, 850736258, 495367699, 902736756, 359815990, 698406366, 176658464, 895162460, 697459097, 343523881, 474405248, 324957370, 240289893, 228955615, 609671250, 963692899, 279205812, 231954610, 401877896, 271855510, 409537171, 626718306, 988112615, 109133376, 582752102, 249435232, 194706786, 131298967, 976174255, 402536459, 289166826, 801732506, 23612499, 412511911, 446243222, 160314086, 957113992, 343982908, 760402658, 9223399, 683409154, 458868931, 783160405, 584892218, 305910218, 122423708, 477314212, 998463418, 69130792, 237022461, 959722480, 63845786, 798409776, 898154841, 1921827, 417186579, 310810327, 868155874, 527330841, 736518044, 193584780, 476892582, 711215294, 68443651, 945442550, 941563857, 884685301, 23367346, 404259562, 542692071, 654186672, 974078467, 774002610, 751353237, 733115583, 386460973, 811434118, 520527142, 246881697, 696955714, 369755166, 472085109, 583352034, 108104789, 839856461, 640540453, 297071407, 39084525, 113873047, 326217174, 862813268, 519214372, 192987267, 453828402, 504360068, 535028192, 665452530, 281326031, 726250850, 325104383, 200054679, 272372232, 585354507, 552894272, 619034569, 712378103, 435747644, 318311794, 767481285, 99154765, 184167058, 997176285, 173232548, 515923048, 428041550, 218137939, 520941137, 403615528, 483297854, 455632809, 526006030, 306129232, 608822959, 865391880, 684343467, 390327228, 376476468, 164104627, 245737950, 444053503, 755974350, 978792096, 696501442, 868550157, 321349106, 143578841, 975236463, 841805876, 389172800, 135034159, 277689206, 51713787, 299668508, 746328947, 379414755, 634037635, 283039103, 659696808, 419374957, 188262936, 932739221, 882347310, 814885354, 94694255, 552730658, 931322001, 777024144, 773198653, 360284662, 351658575, 328244584, 329260508, 140076070, 729827923, 919995848, 332273374, 945746419, 951463879, 268854752, 906645427, 192947434, 953962262, 29760170, 867757898, 562317829, 730087858, 415604948, 269540419, 824865031, 456396845, 480185917, 13510802, 180948801, 571909655, 47048405, 128722315, 836622847, 548591865, 161884684, 725756567, 110520591, 111603545, 401737379, 870542302, 915900438, 546832671, 399776609, 609920430, 683444948, 67873757, 433642881, 871208054, 87458090, 300733961, 219479760, 252650671, 694956519, 522875158, 330753861, 337317849, 268313520, 22746196, 100441373, 731158905, 223323199, 373992516, 71462964, 792613053, 526979947, 753339660, 915282077, 540904358, 903000623, 355802346, 767048155, 329699029, 351360329, 778294378, 761377099, 440094120, 81701296, 826909230, 657041519, 36664152, 939188664, 825112477, 11958279, 616497134, 487956319, 572649637, 709859241, 137134717, 651054461, 724297974, 4610967, 861440811, 949507183, 571176532, 385280795, 594358271, 891011663, 42270016, 755347077, 277540338, 552022640, 734666330, 288312669, 584048118, 577977548, 221634561, 30260073, 832810985, 361451045, 906719316, 716340854, 787730041, 770027258, 759316536, 842776659, 819242179, 800410694, 458245106, 832810509, 841077976, 541109296, 172334656, 143760413, 259961877, 420631306, 815828660, 269317684, 523418573, 493361860, 376977898, 683705140, 104326539, 801137168, 334079745, 204110498, 900135421, 565490926, 411873926, 837260302, 784120102, 955942012, 51497922, 777564492, 783178464, 859521131, 953194914, 50970200, 237702256, 24798786, 279490116, 335018444, 313124517, 288136381, 427752021, 466796281, 454141120, 382864301, 421217659, 381274435, 476331492, 272822898, 399445002, 169153416, 454186751, 685928052, 325723249, 905392905, 445352229, 104236018, 351513118, 813898376, 467696999, 227162551, 412709198, 909490242, 197293313, 530537644, 699973156, 901074526, 74853485, 174682181, 487414967, 228621716, 35085612, 575274148, 209763975, 266940915, 577338772, 668813133, 210947915, 488302617, 436205065, 278414080, 768112235, 783175169, 865208974, 967396837, 553857493, 84096781, 926714457, 874528810, 711364689, 347308929, 105097592, 97042369, 544816841, 860721324, 496923815, 779120936, 482409653, 158599944, 460708046, 209045012, 585136442, 363217603, 940854733, 305297369, 817528783, 388752698, 683592922, 604724390, 19795646, 597847486, 245947707, 536195726, 877725626, 75551958, 668949424, 338410162, 805297099, 982339043, 788395266, 309554874, 454811258, 200512045, 941864882, 431874113, 625256496, 159090810, 87110459, 964504787, 750409769, 408183489, 735869658, 741749493, 7054001, 237753523, 586912961, 803186467, 856355325, 365994999, 566799792, 243822982, 302752591, 287644716, 515294240, 649335948, 227204677, 886339459, 838417541, 918872041, 184051683, 476494437, 293782667, 302843680, 163490539, 570348566, 657890535, 562815973, 350426497, 518212315, 481097000, 833070496, 43474817, 23619802, 71630112, 128466310, 727299524, 966652853, 475536748, 302141422, 492776207, 711558894, 825886168, 177571172, 751462000, 366004162, 259383928, 350179819, 534358213, 284945014, 146875190, 167848616, 883417006, 297680927, 729629888, 120050192, 979672165, 811543039, 5923236, 234728077, 272024092, 644894559, 517914502, 848275734, 763570674, 750921851, 538763684, 289725193, 847911981, 369009296, 108674828, 946383303, 648340223, 108513301, 981968868, 907415796, 10749443, 491052986, 481626748, 934477274, 986157605, 713712628, 255759869, 461734473, 999365338, 988412604, 144824329, 317585914, 537591209, 766112877, 134696796, 579261968, 124042533, 807681314, 921888895, 396916258, 34699636, 290202869, 414106148, 195233965, 517936855, 861889924, 857727375, 27904999, 85910341, 732096080, 309545364, 683243129, 241640399, 603876765, 2284774, 359057210, 284331552, 73417630, 936322626, 413254086, 543377835, 506043036, 120586644, 296046003, 413176723, 815220437, 968170229, 130518954, 760686196, 931476696, 448780206, 709372095, 727741728, 411041688, 20429171, 88094821, 320101129, 431586736, 204246846, 976824926, 696844356, 763261679, 658555725, 225785718, 934971128, 669768211, 993344125, 716001298, 277637539, 567773974, 872961576, 431310834, 194010888, 146482781, 110176608, 809866989, 99530021, 236162296, 60187718, 127226892, 730361528, 402618540, 662577440, 108634629, 567930582, 555872217, 536306462, 9682, 538888482, 650931661, 887021043, 513976583, 613695578, 614294668, 272626995, 840787841, 288139920, 916281912, 175956187, 756086501, 584232022, 731094376, 907794457, 542491360, 226117734, 614559625, 984662324, 994465297, 200723640, 220385678, 168564680, 676285350, 875353714, 746455250, 702200666, 278241122, 775262830, 153523896, 86049993, 982664849, 907557975, 846535835, 517306873, 492079309, 226089943, 611527596, 337651172, 587419248, 269559747, 15458681, 657609979, 970896104, 321130302, 998442475, 954314627, 654946060, 464711458, 490701014, 853987691, 644787592, 897174387, 424243178, 717572440, 120880127, 526461946, 231702473, 419832379, 246799138, 579974668, 388511947, 141791666, 87309810, 585226941, 186332357, 157569162, 926544491, 993637206, 325711671, 906438158, 911387078, 500473480, 206390839, 731585559, 601716336, 578022884, 932754754, 33591938, 104835867, 699777225, 583677602, 658399643, 936591695, 792121434, 622906939, 854764198, 128474555, 839087498, 349674212, 997753397, 479941980, 470674948, 505071163, 20860326, 865819325, 1501943, 136656975, 37600679, 474086022, 331880169, 556391472, 85779899, 540914659, 961011215, 644624532, 438471474, 195900339, 213143717, 583790355, 813205372, 595619208, 222883944, 412923689, 835404490, 60210556, 762599582, 37334171, 349639145, 896578332, 57449845, 164993232, 448088764, 977352661, 561139686, 825507403, 843902525, 84693136, 173183039, 602987716, 927221350, 734970550, 150713312, 55420592, 451985317, 118487228, 521765554, 971336921, 847025631, 821690082, 250792275, 453095478, 357755277, 699433313, 80938285, 525862832, 92405866, 939415946, 765289492, 535044297, 805007355, 972598062, 812990615, 621614611, 411850683, 156381702, 766701776, 100680156, 533909329, 611314039, 304294381, 296957691, 693926798, 589628932, 482050761, 814128283, 73445209, 284089155, 702465439, 424280433, 726750104, 967265957, 149440119, 916493403, 402161820, 820013863, 498349653, 892137831, 539917885, 573895599, 532854514, 318864305, 900909460, 482694284, 899735107, 533292635, 237783809, 783257858, 330810722, 981600230, 425550525, 790857767, 588230802, 583394768, 745005216, 364559489, 950474513, 915316675, 627594419, 947799047, 453612768, 468303415, 874610122, 241943742, 285740637, 358461235, 690643179, 186123676, 597697355, 879301339, 326639376, 876982730, 1924068, 955390566, 149671262, 236304526, 851761390, 211911853, 894396996, 875809658, 510101986, 837681316, 207953623, 977212450, 477153434, 157745035, 939446888, 585738706, 91651620, 640445805, 715027835, 857305342, 847630036, 65924143, 656018164, 4403819, 515691524, 519245019, 94123468, 607491779, 844045116, 689541538, 757809926, 442909054, 157125921, 215826616, 831874259, 275716959, 543829470, 684353409, 459806678, 937983017, 739650159, 373455915, 347794484, 519337516, 703819121, 162078864, 941176844, 37322900, 489926870, 395369491, 685186271, 681837919, 129512469, 50014440, 162137948, 818445401, 10657404, 183680126, 679204771, 5189986, 895715018, 15735076, 34250869, 827086686, 842961546, 77709682, 206231707, 498129468, 523447884, 503843770, 150004768, 842607791, 775267788, 346378872, 914692767, 806044380, 51772716, 284632932, 285600068, 349546830, 638444683, 369695108, 770474805, 472801652, 15567723, 605071476, 143493473, 213396855, 805459414, 924378712, 199717318, 843243119, 305146123, 435679338, 265529659, 963258851, 949545398, 712024296, 96185743, 924813899, 339531273, 975891056, 988047246, 609946716, 804003265, 24159915, 771177744, 936051443, 906001696, 369400463, 654594993, 707005964, 362855100, 649770368, 977516451, 114196122, 354479996, 822217935, 772160988, 251767091, 230787772, 478674582, 81750437, 771813944, 903040614, 711977260, 641060102, 603532104, 313621329, 719789700, 166281684, 849160454, 586247955, 93893222, 704070623, 204743114, 274986955, 196482639, 533709812, 655726969, 486032288, 910477513, 160782529, 380751601, 489959864, 762340708, 551441270, 853516773, 346358486, 961450499, 231031220, 944417693, 390118034, 826445171, 623848413, 241727340, 710823788, 211948568, 618110275, 359573710, 825351449, 221705182, 705584078, 341186605, 865773011, 679958428, 678859748, 114934839, 948276859, 187276648, 202260420, 697488715, 854802718, 680236093, 547634247, 561101027, 516850909, 989126897, 215904509, 124368162, 443749157, 553029007, 274879378, 619375802, 940060526, 843479273, 658122419, 778977081, 518566747, 600733538, 25522993, 127720812, 880479867, 58406552, 488345427, 245703998, 971780764, 857891928, 788437111, 20000899, 238175433, 948258841, 648819630, 216564464, 966462568, 491163314, 322228162, 952063544, 615313908, 983907012, 950626069, 20464860, 382172157, 956392328, 991813146, 805331447, 689629955, 159013816, 696900497, 370397829, 580558790, 195719436, 593160142, 850270425, 425991206, 547782759, 751673014, 689604244, 594574957, 473230574, 791447467, 443368480, 258626631, 52644846, 455940010, 990088261, 696170090, 812029015, 981273230, 544144733, 10576802, 499573170, 892864615, 290890778, 596301903, 659267508, 856611835, 694533334, 467852469, 485538227, 144052794, 716468879, 290359069, 92544355, 837430854, 566605659, 313592554, 446227945, 855118228, 810629272, 907484722, 412392800, 662126906, 765662952, 305724008, 491911111, 836495327, 200910679, 935551790, 878940466, 606513170, 722252711, 991901727, 25177498, 546827250, 248549236, 551213274, 60614459, 750909630, 148095730, 691399406, 124220481, 460981805, 575576941, 273088662, 626364122, 414873831, 661768436, 38434316, 690852714, 825923376, 899083066, 609204831, 479861810, 267775407, 979553890, 255909763, 957640230, 644270601, 691241479, 166455511, 876536335, 979849276, 778030058, 530418342, 865974348, 137383768, 885597919, 415872306, 710741763, 652365119, 789076568, 926829155, 313969030, 959467389, 338191613, 260456318, 891725158, 691715561, 953177296, 759753939, 329919659, 851423728, 61605859, 158793023, 787023223, 967311474, 428013570, 826845882, 446734911, 987835111, 24147362, 994806240, 824751815, 699314298, 267324433, 251759261, 750902119, 773442285, 548180740, 592107122, 462031947, 1380763, 62635597, 656969908, 889130423, 38258685, 590889762, 226390657, 227284513, 140099375, 355678932, 397428543, 944901306, 782596837, 968155464, 119245082, 944880005, 718977177, 51111421, 998022560, 578972388, 207541341, 433894042, 778407245, 918925346, 980964523, 954409237, 150065074, 353005533, 602369177, 666582512, 638068138, 938113603, 684693658, 940371568, 127414247, 151827233, 243259510, 536630543, 597016472, 31315306, 642535316, 253134183, 511591606, 650533571, 128664760, 839860802, 804979734, 847360029, 774919013, 167091309, 576518902, 167110914, 576220953, 996442214, 145694491, 538239371, 9239890, 767643964, 647549395, 424641362, 91294501, 436134414, 199121038, 213047705, 324679747, 154063784, 904746371, 340836338, 273195691, 15473031, 143010344, 972274164, 577072929, 702945209, 230076164, 784522115, 308430064, 800064816, 430258810, 344906995, 810581431, 573578391, 742034003, 370060741, 513154953, 531199234, 21615856, 199453944, 419597112, 239137292, 322574908, 528420094, 466883563, 972021655, 636143533, 544531290, 95165732, 205842966, 883488829, 707365012, 105836205, 849626550, 106014908, 343724116, 15460642, 767682556, 871005413, 11302924, 435756658, 456339106, 365868452, 844530480, 509455075, 111823149, 420194860, 608704568, 328433568, 221299629, 726340397, 962725035, 503245775, 276224426, 114156276, 114013895, 771128520, 906253893, 830751390, 6116772, 28292624, 778527029, 895744756, 404292878, 69206576, 660289417, 373622206, 782816755, 928059261, 24188351, 428495251, 412591268, 261325473, 566800133, 715218294, 239205156, 767383230, 334988370, 356201839, 691249570, 295380903, 372667808, 260868339, 693294740, 960902123, 412663371, 970455390, 608918261, 121778217, 660895888, 609353983, 902859491, 607411758, 925634937, 969540268, 709131034, 472335235, 168119503, 84265430, 271677247, 805210384, 394603623, 560539559, 794453918, 67988576, 671882674, 357758858, 776923687, 386307177, 58448564, 348191365, 629648263, 607928444, 322558098, 640031586, 291108431, 253003332, 59721858, 384103133, 782490205, 254768220, 852458232, 887485967, 423208806, 769141411, 433177809, 96862641, 292996471, 934199061, 300739191, 857416674, 878304666, 342000580, 269523466, 578715256, 529856886, 98459094, 167828497, 130823039, 895393155, 468132402, 213237493, 754649928, 93309847, 840877960, 393389450, 313381461, 645774471, 526630215, 778643202, 360192852, 952408060, 960740487, 879917070, 703779917, 869250284, 616073783, 800309240, 533614306, 410167309, 924141877, 721543837, 853549812, 462360414, 876109590, 536946786, 533482040, 688520423, 18807013, 338341429, 448646129, 740491771, 471828939, 262075412, 246078451, 27647902, 103422433, 730981052, 297349771, 106532577, 663733546, 629007822, 687928824, 206941402, 315621587, 566420470, 639681723, 808603634, 957635244, 169754209, 940312708, 646098458, 675282769, 477625286, 725046405, 716603704, 515106348, 460714994, 864948537, 442354697, 613437573, 204402761, 524989779, 479588185, 605717304, 479656481, 983702693, 278165840, 532322953, 854515136, 158735070, 548468658, 267664419, 973732556, 97583418, 713414421, 165049857, 977245188, 497020988, 993330660, 927044330, 300965884, 552628798, 971750018, 462712612, 437223571, 829463359, 613884514, 666182190, 957108933, 921848396, 751701873, 148257485, 54577245, 313759021, 3177884, 396331986, 40806291, 416668559, 848314384, 605753154, 427101366, 447198329, 225139925, 392173705, 254190421, 258827395, 802956202, 27853214, 477093872, 183283611, 653392457, 904537288, 133105080, 107341137, 219415803, 643611182, 856120087, 65776379, 685960352, 946177043, 919836456, 242760287, 860938468, 736067489, 39271590, 254595362, 638753381, 112807468, 858549256, 136922112, 162420848, 46591692, 262735162, 862515411, 476522939, 528631622, 740297021, 573378139, 977321049, 390349667, 646111848, 268687054, 499257838, 47257430, 518936840, 518406220, 414189223, 457728684, 129649719, 838775461, 870807734, 766939002, 263017250, 83401395, 702601601, 806183387, 887254586, 94546258, 269720004, 19952807, 839642862, 436662003, 700052734, 327840360, 184935484, 311855521, 12212685, 315475249, 976795190, 162102358, 196395263, 63349648, 631519820, 877808450, 822770000, 792743039, 636232978, 201357365, 262812811, 914635789, 632258692, 542453586, 41735849, 321428684, 345835513, 176203565, 653215117, 262767417, 819197062, 956794745, 616646076, 776545223, 202639161, 932600484, 910430399, 284018620, 527317445, 71747542, 641082246, 99066063, 474768213, 659550488, 466669220, 174225462, 312233909, 3247345, 101485953, 910943930, 843124685, 508324775, 777208272, 74420251, 771824888, 702779933, 414701261, 834481862, 587123141, 48802450, 747480754, 868048162, 34765782, 844518515, 709767645, 399634870, 804709818, 443426452, 148859184, 651693573, 123690691, 369905636, 828385700, 293396034, 676633084, 676800716, 315648773, 110567078, 489989743, 805102924, 455252171, 689639262, 829818689, 708199480, 846706155, 345899456, 808954078, 61892674, 597569033, 975626544, 277630276, 451549639, 152021997, 216782475, 490095005, 36738626, 435222125, 859021724, 495360353, 898965485, 409182301, 890246042, 546166900, 684676873, 230701423, 13526883, 593095625, 370804520, 126506768, 170238833, 973536661, 687871794, 445967516, 573128998, 261430671, 108833420, 709816489, 386506494, 563539961, 196006381, 305133235, 608565543, 652845126, 781440733, 710755915, 63057871, 942809618, 377575195, 791940998, 74140469, 468828278, 808009272, 761308327, 440208203, 934665030, 991285793, 55174481, 612705503, 524524913, 311714510, 616865600, 953142045, 541896118, 788251049, 692087654, 270138941, 732766842, 635210897, 65040963, 85965368, 217625977, 348207036, 588271174, 290938556, 378659297, 714383384, 779691790, 675755853, 124798724, 880830715, 996983436, 9764423, 858201335, 526349534, 888719559, 264130652, 933381274, 648794145, 891207820, 818090310, 478317138, 734129707, 666804280, 357413877, 104087697, 924970794, 207788797, 271513474, 923005835, 477079577, 912850081, 917332199, 46826048, 563946785, 21316688, 824323387, 221247789, 631120247, 768561111, 738925726, 610373479, 57283819, 629224317, 37958474, 895532522, 192861559, 14487695, 33061050, 766319548, 385246034, 490299226, 428160810, 352203640, 422049365, 632994831, 529978453, 270429706, 106734851, 373099144, 999955574, 322549692, 167854797, 244255839, 17009551, 840060248, 145367397, 934316845, 577620869, 970822966, 365269045, 41887280, 294099036, 515497835, 287410159, 439497981, 343269827, 817931067, 686209049, 930697737, 970337543, 404590192, 437465978, 880328792, 507432277, 777060253, 512081666, 388186629, 627742494, 423126196, 396112106, 175981626, 154331252, 796142901, 341147374, 428167502, 623861831, 426398941, 580923064, 480023049, 333791549, 152275946, 617126076, 180172921, 652579916, 633309547, 198998050, 704933796, 891386288, 849162415, 967799085, 561271701, 918935572, 4322014, 26585074, 793270371, 13303467, 147372822, 705087755, 636428027, 288790391, 658459337, 298834481, 383203733, 34371777, 347509738, 922975716, 826193171, 251204891, 695072035, 303822930, 447873532, 172930596, 229435537, 931659165, 290065845, 783832272, 981264609, 93257727, 781246580, 760295267, 789540334, 227432467, 747125200, 51358336, 625748745, 794455242, 937475968, 292872663, 588682936, 792485840, 880624455, 818384029, 144440381, 590686595, 526602370, 876067299, 444847569, 27382775, 764396674, 503965718, 903392531, 303623078, 170533721, 47049924, 159606127, 356322662, 345321021, 90955500, 809600364, 406816996, 555774796, 233935034, 365322535, 427241422, 563218474, 363433359, 107687869, 376726634, 120980364, 256892503, 965559261, 653663885, 564948143, 564009537, 937269912, 508922963, 827777440, 807504661, 294224572, 321880488, 649392964, 914401906, 356813747, 36887163, 214008620, 142337273, 431470948, 164507436, 621265417, 836484777, 101583384, 875438450, 956267553, 656202252, 135213936, 190007061, 894923639, 956727386, 214731867, 441071917, 176883483, 778376630, 321526067, 24994014, 284728960, 964546915, 731637587, 922375118, 229270683, 360664152, 658655684, 803291671, 902354382, 475712930, 303409645, 997219206, 927339697, 689640131, 641416219, 251820846, 45123620, 493948715, 492882789, 376629936, 680796205, 410937374, 547305610, 960426111, 638845599, 653172515, 659900817, 307562479, 952693684, 863005257, 210927079, 262338824, 336665326, 646091382, 423353417, 756187361, 241037424, 684871755, 153248178, 375786959, 353776588, 812083175, 194200735, 626274248, 978677518, 642946339, 169725232, 567096783, 103645872, 130428580, 456448039, 808047428, 906902339, 817444840, 444993930, 141436467, 186438548, 341847954, 232150401, 539277406, 310624769, 559224648, 424285663, 516640053, 614738803, 233103557, 759774121, 914929276, 850376672, 46552631, 882723086, 363710218, 22442677, 171714674, 978496413, 965628656, 70238583, 901952816, 38778498, 348836642, 28364020, 547353229, 998880844, 942526003, 270886423, 679151984, 18250298, 649560629, 18294500, 17579210, 259548794, 908932424, 978093402, 832470494, 63964500, 778609510, 967993227, 984359425, 584078947, 177158077, 356896501, 194833542, 650918025, 916758829, 111679545, 383579041, 819467839, 355648914, 227689002, 875818866, 979931154, 721610907, 797716472, 612222715, 456590519, 654669951, 993602021, 500622050, 787145764, 933712680, 162187086, 903401274, 579738737, 301352745, 85220756, 814901424, 954659200, 825915454, 506133276, 254615683, 672619833, 498475213, 245215099, 3462120, 213212115, 751200929, 982509676, 348632788, 675942702, 106888424, 643863329, 283635871, 530420724, 926511197, 818428542, 533571728, 540850230, 532190843, 375789630, 136160689, 8911158, 959735808, 446547464, 340933329, 943745503, 365197762, 734448896, 452714547, 570569207, 486091995, 868752038, 691011413, 507727289, 629915288, 109071791, 115284891, 410995193, 594934206, 702728932, 386354169, 831794131, 865800973, 728420830, 434131219, 787303780, 831827469, 494446434, 627915661, 162472761, 56137066, 989988983, 395502363, 675831061, 490503973, 808675071, 620950038, 10643044, 819844921, 55939991, 228317831, 302252172, 265528876, 93914016, 101808425, 894764203, 852356768, 766837787, 865999068, 674406855, 894541528, 973685825, 796152100, 353694316, 571069151, 724184367, 629507240, 259539266, 242013010, 709191937, 557791325, 136542256, 852325613, 497782285, 585675362, 251432157, 710850743, 84354515, 725015937, 903937523, 580669380, 502305537, 468957970, 652087263, 214100589, 935267188, 7268668, 948581493, 894002886, 874148507, 903505778, 686782318, 404260582, 223433674, 618837032, 443827323, 89566278, 929758268, 602525180, 182234166, 909957153, 351949686, 66976894, 787156228, 98373433, 977861273, 254743575, 909104896, 302438245, 338343935, 926099958, 388751025, 493016497, 811141050, 8625131, 587268979, 534601205, 687974877, 340039190, 410709334, 769008553, 851758964, 542644972, 250397522, 410440579, 995701858, 825994833, 706204817, 64887611, 581889612, 810814685, 455489078, 396897628, 145010777, 611031191, 87100218, 403950001, 776550459, 396526890, 527765065, 765307216, 232606237, 627848520, 904587627, 84270819, 85445218, 479266453, 813138998, 334546339, 431296534, 711980672, 226686276, 677561762, 21302313, 84164975, 883706448, 225306420, 977038859, 79894575, 626376872, 204162713, 859898493, 332138020, 630477835, 617504576, 787240670, 794733402, 156184954, 968600791, 268426193, 99935574, 947181185, 204434433, 796883609, 87403780, 548176581, 520926741, 60865966, 795474953, 411110069, 402303496, 805961606, 502788207, 786457899, 298367791, 221438905, 565752104, 481224877, 136861895, 706431757, 330624182, 247806636, 851559563, 833471860, 7175942, 439298109, 16690749, 920735717, 915011618, 950860477, 949531536, 396343076, 122892178, 10006705, 544312900, 347225316, 414749243, 187879973, 283705949, 250588003, 897829057, 796090838, 934256579, 381937968, 184402153, 986287744, 630007421, 591989868, 783101403, 908231954, 644425725, 177714231, 627874881, 198572167, 449758790, 933415671, 462367174, 373130858, 144720339, 691773392, 494441018, 404757485, 409548854, 682626129, 418695611, 822380349, 243758053, 489925796, 52446214, 994391552, 797544196, 234991992, 85338782, 927884893, 658273058, 279744546, 199751040, 800226609, 75277372, 631331577, 424403703, 157293247, 211780620, 222537364, 504107872, 801620192, 717805564, 519055302, 656476462, 298179811, 728543712, 24924993, 778430892, 425589955, 161611434, 323312644, 679731525, 974653075, 141623411, 586636579, 173416429, 97156259, 132564848, 926077079, 894094423, 598199949, 708093934, 119801100, 237137041, 448052324, 531968453, 847430774, 970540091, 995591971, 431154218, 92983511, 36844375, 147827768, 313392581, 546232475, 57191922, 873189797, 266174692, 292743551, 144135, 920448220, 358725206, 740269167, 236434856, 288996297, 453263709, 983662626, 934835568, 56806894, 527928500, 58532620, 79295876, 433034637, 810195874, 406120091, 560589537, 366792089, 258353219, 21487759, 168495050, 651191989, 913301093, 540970597, 823984051, 72349194, 244422287, 985954264, 488139891, 802398925, 930491313, 201838562, 790378857, 75385744, 847792983, 775748037, 720581665, 250351675, 635588880, 487929939, 560671212, 397478307, 269893042, 924185614, 95986816, 246006283, 798540791, 747836129, 328128224, 714510142, 249539809, 913306625, 624599742, 530358098, 558245431, 510760118, 78879341, 340277969, 943201567, 965996604, 95644020, 599630666, 731010333, 973417749, 476550220, 932746348, 464646766, 291279556, 668221032, 464824864, 280746811, 433030211, 862984557, 875278234, 837898013, 225248757, 227390015, 581659512, 28034894, 647131809, 208767555, 432024155, 63316826, 233720157, 893150241, 560814283, 745378631, 164159224, 247971316, 629414300, 800439668, 107930824, 185745355, 550616331, 238312641, 356792151, 8618626, 803952021, 181695415, 75587659, 663597001, 903803608, 235833554, 14735376, 199526296, 323296141, 67324929, 408876932, 697793876, 881056906, 602296068, 422257566, 384041580, 945857539, 79672915, 810003798, 971182619, 788239357, 573569469, 896377476, 331217709, 844541703, 568131985, 790581372, 614229369, 22260660, 541719661, 392117690, 946185863, 883937646, 187735020, 490259733, 198705463, 279907733, 604457483, 54680033, 457656149, 297945761, 134404399, 653465676, 347863511, 719120393, 567119287, 974760379, 221247938, 228886072, 789846873, 100219842, 444090541, 381264555, 268062472, 483270362, 295817821, 193715698, 52369611, 321406965, 838656519, 857067829, 210295472, 516425829, 864479812, 85253061, 45357064, 298992884, 903681471, 589622248, 589928600, 57646082, 655222872, 242078587, 673737740, 867694765, 379549616, 578981615, 574051821, 519524277, 708255945, 514127085, 87481056, 795108291, 250918962, 411087215, 451001496, 255684319, 841259291, 860328194, 567639816, 295647754, 529891147, 538226844, 90773969, 621709205, 835267212, 75675880, 857785550, 678405684, 383192510, 37533491, 534981400, 303842443, 780428220, 231901676, 776436956, 98404451, 189081007, 351750516, 537522854, 782098108, 378344965, 890737234, 457152950, 760019785, 115240746, 516393328, 479197503, 293790267, 906464446, 84152924, 845697977, 211054471, 162325850, 818177771, 221121646, 856454248, 283585410, 21227122, 149824106, 895090503, 536276950, 412320669, 375964590, 257941741, 540145878, 34919472, 103334175, 187672087, 947309654, 724026398, 392503659, 482702633, 979995615, 932369347, 508273838, 654059263, 429695727, 246724938, 566052471, 694652828, 880596734, 380486288, 742391765, 421711545, 989905846, 948163121, 614621536, 201032102, 698371369, 813121524, 501211506, 111211517, 796219419, 999074080, 595056889, 115127934, 96033877, 431824231, 715828466, 689051509, 383606632, 737565811, 320375871, 215810925, 510722647, 925914377, 981834769, 976926002, 136192160, 429219611, 250949206, 121445240, 876260392, 482478764, 941669209, 81941844, 684285753, 399349536, 383687875, 74466328, 410427733, 511154204, 355641533, 551615648, 186085083, 426191544, 833601005, 350404931, 227758925, 133307983, 240799922, 616149385, 193468316, 507326404, 613109473, 482491636, 850197177, 568344435, 58080106, 786523876, 465967067, 60834925, 585668554, 410680958, 191424488, 284774078, 814528494, 122313378, 183777371, 735841502, 244056962, 963512129, 145934900, 560039828, 839692055, 958302500, 917138478, 698974522, 458389609, 50663157, 371962074, 672681470, 244209020, 888191930, 608181381, 585871057, 894177272, 982655113, 174604599, 643499271, 259401111, 750266237, 270616273, 911694277, 186400960, 385155018, 618278157, 269703911, 407187625, 180139194, 127210512, 616122301, 645635515, 601642019, 643971620, 697355847, 508622396, 123532816, 779717924, 740155609, 522476281, 740675982, 26989560, 997061898, 530889859, 958904268, 941435575, 970050931, 794923273, 529619883, 7842794, 602377774, 38686113, 771960939, 978923916, 483375437, 249897753, 157251842, 818828108, 704031258, 597115236, 327568066, 927266511, 947094590, 73499694, 314447129, 927562474, 612940514, 777713315, 532863379, 130658096, 561739638, 532697475, 505283251, 656046053, 127442743, 670184794, 595279499, 122289005, 981823701, 416369180, 550235709, 992976142, 715275134, 99257711, 762687596, 987709651, 809960363, 57946378, 699237680, 206141824, 64319414, 406556553, 450485119, 919425029, 987519546, 166486047, 576252844, 536538311, 413929089, 810125575, 119433819, 224832202, 262091158, 569285291, 812282225, 766940564, 945013970, 944719376, 902074363, 296948709, 467844535, 340336570, 108346461, 534115535, 598215836, 335747535, 411001540, 976892913, 876277023, 112633751, 134205626, 189836914, 70380086, 896315076, 652586355, 451221061, 713402138, 13388585, 29056107, 584094040, 465254671, 443826741, 527957330, 586076332, 985394956, 755757867, 107082334, 803345996, 215009372, 749856883, 130417744, 56932873, 205056837, 889522343, 987406519, 659236140, 979331331, 739513030, 363053411, 162573489, 532701275, 83771035, 165242933, 656118260, 345599611, 476220687, 941047398, 454289262, 904572634, 841686383, 221907937, 288474526, 516975938, 887877614, 983448531, 519046468, 578023471, 442467127, 944204651, 203397138, 725143281, 80696266, 420012330, 566668788, 138960464, 628103809, 665197530, 13442506, 586648540, 80624471, 651119643, 785703768, 384757876, 13230512, 902574302, 296814104, 350063717, 823098580, 390295644, 488672363, 940679491, 177279750, 400471196, 801653468, 18193643, 402717256, 932527981, 445983932, 683598480, 497458659, 656109806, 168619369, 127991379, 901731850, 599539338, 155718494, 18957271, 621074717, 981490701, 589452605, 585450361, 15766583, 958298579, 307878009, 581771133, 156351400, 135591827, 187485955, 984669806, 244340961, 367134030, 407154178, 835581549, 246688439, 180376634, 988776699, 101344847, 521385567, 349829657, 648864271, 890688872, 863779130, 860725467, 848530197, 493616428, 537595762, 49336543, 224546718, 977264042, 749605028, 409745722, 457988953, 178461556, 677001026, 615382401, 428700084, 336652011, 403389892, 924307335, 996813667, 727315426, 525867056, 403292426, 826839930, 300080275, 142941154, 417681251, 951831245, 860029500, 588025116, 713057748, 362248950, 480310228, 175094403, 257141851, 288697575, 533711079, 489824960, 695825668, 61932726, 309339664, 694426909, 862081829, 575252091, 118982353, 498595401, 479518077, 676683707, 9474094, 706388278, 820369042, 812913623, 433361572, 192818775, 709545983, 289932590, 638167110, 548514988, 543026960, 399534542, 466365609, 111969914, 678329681, 585484952, 795692948, 214739486, 760255300, 609981951, 931430049, 716668370, 975725397, 782514712, 66703863, 419466253, 346861696, 158699639, 354320965, 565870930, 556940440, 620133027, 478936970, 606798249, 354619458, 867426753, 631704165, 391662201, 745698739, 981114501, 550515346, 943254588, 214398414, 392790966, 821131314, 693911648, 300926343, 78801742, 493940657, 925038831, 162312890, 193741496, 908050817, 225871085, 70772805, 741741570, 439760354, 799954922, 842479838, 229419769, 633675637, 214912753, 289308405, 224520714, 98101818, 560158983, 256798122, 526598647, 703662548, 800719629, 952004020, 333698176, 128491001, 916521330, 377705890, 550582571, 543995863, 712683011, 917259501, 850086496, 136406074, 36686137, 267203492, 622760845, 988944872, 882863462, 874747808, 188264492, 39739017, 270296545, 117066910, 708988314, 988731587, 528799181, 387295216, 569215254, 110163891, 546766924, 409419764, 424133257, 980289604, 841561531, 858387477, 555290207, 151550904, 123149012, 898185419, 256324571, 210403215, 700698113, 395740105, 77915443, 638749907, 300691060, 475019497, 869103391, 302911049, 218700399, 81841052, 403543481, 550942203, 483636268, 984083894, 44850756, 440579383, 993305621, 785883405, 45653053, 671714196, 27352098, 86671355, 669018960, 545638182, 327170806, 191383638, 111805576, 846894361, 104425662, 6048531, 992156431, 864514765, 280594586, 306816148, 516804504, 415124973, 964646477, 133803406, 807393019, 232801518, 784577559, 95067599, 168827226, 280285978, 801125017, 702796289, 663267707, 798312923, 365767291, 320740823, 888001641, 107309077, 176819069, 780209778, 253009830, 567647554, 248625975, 710410762, 947661481, 776155415, 10627731, 579095246, 6026395, 204720720, 290966067, 42445374, 73643743, 289183678, 510475640, 647830185, 764143748, 711057822, 955668724, 570658940, 346777261, 844199996, 287312909, 303176065, 363463032, 557671736, 59770209, 918092915, 727644711, 401403535, 428983056, 521002873, 727044491, 575356775, 329970175, 425193893, 978916964, 498083173, 298378800, 209451999, 957197708, 384588058, 901060852, 472731273, 754112006, 582307769, 21031082, 134341418, 132665469, 688056162, 935712855, 837019471, 859425373, 81607579, 261615973, 196781486, 41664813, 136863830, 653810080, 319232798, 820445686, 43669774, 797124558, 398286681, 829973137, 68961735, 904878351, 254018352, 705014530, 1341435, 750105604, 646824033, 826192092, 484513977, 3498090, 621748255, 744059827, 404241046, 88507018, 344309404, 676175287, 49709238, 370721275, 283226180, 910218300, 577874701, 397539557, 312211286, 184127549, 308354179, 136944850, 217401114, 30486022, 521629427, 207791987, 723167416, 587785495, 529033324, 696207699, 127978857, 246167971, 912232659, 674779278, 916024048, 620195735, 448978553, 181453811, 732389483, 286459717, 37614377, 266248287, 174862230, 300395641, 216983559, 340890303, 195585413, 75530414, 456116068, 85350924, 708543294, 575590714, 401273942, 830648905, 80640078, 623940900, 669059717, 954466277, 687221057, 457168730, 872343055, 965890184, 384039683, 434447597, 716246992, 649412880, 281377528, 190521207, 635716732, 420806340, 457243607, 467874819, 792291168, 453253942, 606768550, 711383017, 773360244, 267603807, 101889630, 742196829, 640632718, 342109535, 465982659, 341001613, 251419345, 323104713, 17412905, 320257776, 790947276, 455426466, 523642592, 50628658, 199322718, 582295132, 620745233, 717264144, 818920674, 978165446, 225649491, 887152041, 885036138, 296958439, 994011812, 885621039, 306150483, 730439496, 806275041, 171631919, 171487444, 41156878, 771598802, 505072381, 899123572, 946918666, 460455898, 767243014, 250615443, 669384533, 560415686, 926476251, 80146288, 790146067, 326931478, 269202141, 367816747, 705400443, 315606500, 872155061, 840825364, 630046095, 809578521, 213408925, 640487915, 930167359, 605051615, 540288592, 101864787, 287182864, 4408246, 570507916, 876401453, 357480046, 417650547, 25273008, 860628559, 590724471, 694359538, 821311155, 580793085, 11510869, 147749785, 986821247, 13756835, 273387100, 295047871, 399171651, 147560898, 979522603, 956896572, 75543736, 79901097, 745649256, 556817244, 946207144, 412026834, 400035388, 129423814, 941394734, 510413236, 405210202, 241256495, 588962140, 544522939, 152341047, 754786316, 224305564, 267921166, 45297427, 960570024, 21397880, 355438914, 355923050, 905221441, 743823388, 713064877, 599688095, 395519952, 340160656, 191057584, 934698453, 973234908, 103563586, 187635823, 436544100, 163903059, 431533206, 618625972, 495288077, 234549059, 524669060, 482198028, 680231311, 891507338, 26381039, 216232083, 390804594, 867801426, 99567755, 407045382, 983001847, 54664717, 308785817, 764883209, 364672864, 516736232, 528457770, 917987995, 944192468, 289630245, 209010860, 818082590, 484789823, 383999476, 284967194, 672620979, 155456450, 471456229, 535021040, 298299509, 96078430, 870487768, 372314818, 275176217, 534706893, 953761072, 279886950, 270342902, 778665925, 959639172, 601484752, 275851024, 773128196, 510679874, 404944447, 677299174, 223218684, 792253794, 818219221, 367847113, 447376754, 224622162, 333840878, 599490444, 598645497, 636785183, 499192696, 754763413, 447116654, 633069519, 993422405, 848149982, 139363609, 605459164, 869546931, 304135143, 298414283, 207384383, 556390259, 596802503, 245989861, 268464874, 746184375, 348696877, 684665465, 164440420, 721036061, 966870616, 360838217, 146261347, 464448576, 369251621, 991098978, 619751916, 930048565, 703983924, 874148536, 315965019, 579638767, 188017825, 446609069, 564992073, 472303421, 303631695, 364584958, 279067397, 723182432, 719797929, 410938193, 564064899, 659776212, 846539126, 693264541, 315174540, 424166090, 888829785, 251133568, 404948579, 855385813, 203405282, 269787041, 165654107, 218171679, 551042865, 771968106, 235799059, 444924225, 111505281, 397550769, 761195624, 380993125, 658817150, 89409770, 11436387, 782273747, 702289991, 662413166, 789848961, 683724842, 841237205, 18933213, 573692951, 453152788, 685295629, 681525821, 334519264, 922767592, 56503370, 239287426, 777205293, 61785287, 363106497, 891137967, 784777681, 267168358, 64170658, 848089725, 446031137, 798940731, 359350169, 682694959, 26321738, 918739942, 727426587, 624947790, 90158372, 730693331, 690402329, 845288202, 723464523, 208697235, 379048647, 387033704, 912225106, 462266577, 933565918, 75507661, 346082145, 681262828, 180808157, 397121367, 118655735, 65027894, 518258363, 124792148, 577228654, 293973530, 175910354, 461793165, 721087330, 377619514, 657624032, 402130381, 55992739, 643534674, 230428193, 587822002, 3572608, 162803271, 304121082, 808526009, 325086954, 498081504, 407240385, 474914024, 87099878, 387947671, 495739424, 954836345, 854205226, 932836146, 432716299, 820444311, 188102199, 864722915, 705907217, 131719923, 326488909, 727311593, 29518642, 734635159, 133441182, 468265530, 845377174, 885508685, 546116255, 601760937, 862284054, 895230013, 883167270, 889246614, 699313333, 224103729, 554400975, 550111856, 898082648, 765797684, 787560463, 592555000, 289887426, 79825653, 769561982, 803789296, 718502566, 20756214, 178969763, 596432143, 459224937, 367045281, 729754383, 388835116, 76881266, 884135151, 556773429, 545057707, 695006085, 483569766, 730966616, 842511075, 586730918, 334151121, 766052333, 538506869, 304064682, 647577358, 106736458, 948627233, 970063169, 693031215, 948112837, 56702352, 376374381, 852254118, 803330326, 634066938, 709687391, 16752297, 354658237, 774691964, 969708628, 786893137, 803734046, 384254416, 128673578, 638686301, 126760175, 711584720, 428016203, 73160432, 895751596, 725537735, 42794421, 135008114, 651931642, 269277758, 826657836, 449738951, 232056429, 836897707, 214475866, 994858900, 781410675, 253203159, 352995527, 240787484, 733510618, 845272361, 64129210, 503291097, 763186827, 704865709, 81402370, 568525043, 683997075, 455749401, 118409822, 888099159, 694197664, 539691970, 803289132, 808911500, 349522411, 337730668, 333492374, 491359962, 563028104, 508476529, 143352802, 4246390, 348305777, 737769176, 802916568, 564700798, 4148113, 911758056, 220577812, 256365967, 199294787, 460582278, 426085807, 760314623, 250763348, 721335024, 507294768, 1244306, 695987001, 185585328, 60169628, 583761373, 459522709, 423552635, 868492820, 448815413, 89388806, 375109117, 425665630, 97783067, 869788408, 118941204, 126552971, 19983232, 172410425, 261231876, 450936682, 566019297, 492790633, 210416559, 944411346, 612697310, 46950122, 651301957, 743308819, 227648047, 631453799, 544283126, 837022671, 150640691, 22130072, 970572474, 351344197, 760081157, 581665370, 477627796, 93713963, 315828147, 894343693, 19144292, 398047569, 512418935, 455374458, 489077363, 982640841, 154772459, 861060765, 395448331, 104494583, 907599467, 875092363, 202922229, 141463378, 973176278, 369099201, 742252276, 38521070, 253090999, 107853137, 199545556, 546056848, 971259124, 658551754, 739897386, 577767332, 533329983, 714154592, 143907365, 81348239, 431642301, 705903393, 15208932, 474422918, 808074826, 368452426, 660953921, 423324153, 971404775, 785787206, 852491467, 278667939, 866581776, 97704643, 687129360, 471513640, 343567571, 585299654, 914622213, 398665716, 736676579, 908042819, 895347596, 225002581, 211032121, 696574976, 172689817, 755158767, 823949386, 931293644, 670623429, 985388318, 845839249, 394532891, 479925144, 419733667, 35365044, 383803487, 192317306, 526526388, 566199091, 839368715, 669805383, 19369312, 923243901, 81882350, 121065749, 241020538, 670140997, 132266528, 82080939, 12326600, 391626772, 876098358, 9751783, 272855830, 99669149, 106511673, 719992223, 547900217, 153490726, 490601877, 74558486, 446040775, 989837788, 209667149, 120850757, 501928950, 948894574, 409616574, 648351814, 131376368, 580219089, 858308019, 32750765, 263103341, 823336771, 26838752, 56578679, 62818905, 104965872, 748207713, 226222940, 358730915, 787246406, 196876204, 117212864, 712417214, 311970227, 290949385, 934857878, 392763125, 230806496, 403085517, 876101301, 96334197, 720036732, 164407941, 439081309, 143878430, 324978412, 519560735, 482708705, 313191028, 445406539, 866506802, 143549042, 68836428, 580051559, 476916809, 832731576, 615458960, 188943324, 317130733, 758103712, 266730719, 753985728, 909240051, 524178811, 491020125, 37514579, 844062258, 97384370, 357984313, 773694531, 690322324, 160723891, 343713481, 413608063, 643554015, 650992686, 809408766, 679496617, 806515754, 730815749, 936207195, 322053369, 322140844, 301272174, 347229618, 975547550, 686796096, 869310268, 41318275, 440732461, 380922009, 959036843, 669279005, 793530836, 846259557, 551276064, 352523836, 785031741, 938804977, 455736854, 20418420, 570634942, 76890833, 191828171, 946604257, 531889218, 582023654, 530055663, 351306405, 449279712, 862888162, 673868022, 363412832, 76615130, 16110428, 610954708, 387512266, 930937981, 921309819, 328205256, 892628874, 569671107, 734029452, 939010699, 964098754, 11126664, 800190088, 67853083, 195895120, 773193278, 183504279, 454791843, 972324822, 218578949, 101147708, 635857547, 146124356, 98040547, 612044891, 95435955, 331834198, 238098453, 771586736, 285134020, 37325640, 597928600, 267287795, 756131501, 302977891, 834546910, 223836268, 269916402, 590826674, 445197149, 908620319, 48107218, 617653229, 604372315, 376710182, 736992225, 788152624, 57100743, 855945894, 362216090, 991196990, 258794248, 233535366, 251537486, 269742242, 267825723, 810517022, 310374811, 215504093, 378581438, 996449332, 207793153, 598593901, 168009019, 806542052, 181643480, 294525048, 529585995, 72507955, 877820268, 129176982, 423182294, 246971063, 799559182, 213150306, 121098132, 391287991, 280518797, 49357941, 777974376, 516703845, 635452293, 42298240, 113017351, 40070523, 730648402, 251397295, 269054032, 792574630, 942128619, 846629092, 533335251, 22846911, 178404643, 787558308, 48593379, 688974005, 729264571, 666055561, 767916659, 46283287, 678886902, 754297059, 961851658, 441238194, 476473462, 983947055, 597472262, 692696874, 915291956, 888432785, 934036840, 994149722, 648553541, 399845287, 7018365, 28714483, 987103762, 490795688, 9442457, 10589677, 940722113, 370660123, 614587483, 331284182, 716285112, 198238429, 238768707, 411248627, 696104344, 341541884, 546433790, 858892914, 885798340, 704984489, 812273483, 136905115, 276626222, 318611501, 116258643, 989735192, 171581022, 264624339, 475285904, 437480057, 317617496, 754106997, 435566233, 195375460, 406992612, 108841532, 126034456, 473926807, 596732243, 40871742, 833008149, 416809982, 118804033, 941804884, 987746424, 172184917, 407525311, 316111791, 963385282, 29148858, 70586818, 324103212, 293467857, 135094861, 537167251, 504043744, 9895656, 18122575, 919183229, 728593248, 485455564, 713728022, 319181282, 750155037, 501468799, 546640653, 234363511, 359636629, 233526276, 337146875, 241703195, 583219347, 151401018, 220323796, 710420852, 746683485, 99227055, 719398496, 239404166, 190775114, 82176966, 126824041, 891584678, 606662425, 171874726, 313479991, 53512584, 993594416, 462569651, 207595317, 913647150, 454406700, 101391447, 591102331, 176780112, 273923443, 655891449, 794931820, 113382548, 830525943, 94162875, 444835644, 773757352, 698302824, 156112840, 24842902, 449421022, 263380168, 752005057, 772290880, 689420223, 72099301, 720891866, 683451287, 259807138, 168444286, 963603196, 10895066, 206450956, 368102280, 244130901, 748979292, 583052826, 726268025, 894896633, 182178796, 211994821, 387285680, 369574967, 240816723, 76185236, 492412236, 914005457, 137478739, 36760035, 566181843, 197619904, 347928484, 329004107, 755650738, 710163658, 78043555, 566701410, 196431032, 237585226, 321021143, 685927541, 122153770, 398671096, 395308117, 20751521, 427081637, 206522562, 542201704, 824280654, 900448264, 866176347, 53603644, 756914072, 836442472, 348104180, 921967315, 714841880, 347512721, 389896309, 503373445, 82676386, 762133983, 439725558, 499762136, 56992667, 578826452, 947007171, 303330459, 400801819, 818206898, 712647116, 256657704, 992128196, 993999023, 660711441, 318423120, 696417927, 969493606, 26538623, 819740753, 759967939, 79341675, 453260115, 3249166, 632858499, 472702638, 501223945, 790547949, 460813062, 637024061, 900017774, 219508970, 989024256, 710100279, 422494567, 709236615, 752833967, 282536443, 52272977, 618406883, 197926998, 878790886, 962023376, 399064613, 148955441, 761616279, 304728504, 959420450, 157651782, 327837874, 316008328, 961730378, 613311135, 411865468, 108064457, 500690189, 526485250, 579970775, 337834935, 898856345, 894256818, 955801284, 919446233, 736466546, 469486089, 969900674, 929210309, 635233227, 19041, 304048307, 828653365, 586199071, 132803243, 577437819, 327559014, 947993413, 74650354, 942795956, 523938657, 256842051, 781852825, 676236096, 881845232, 299041358, 221778634, 115157737, 364207746, 238788456, 791939664, 222715472, 105092502, 47161194, 910416948, 665096332, 244736951, 817314629, 831806633, 388238618, 708023538, 538631631, 584294931, 184911574, 902479750, 714981504, 571939719, 929314505, 951471549, 525832844, 811761821, 179136823, 64139356, 117236459, 926539865, 22204506, 617217200, 641944322, 891903384, 716707379, 879406708, 756445123, 462246498, 537017338, 202254427, 807389237, 576378181, 977572820, 479696013, 337832798, 29736103, 438885686, 727971109, 526621305, 77163646, 351199093, 54300547, 312921147, 411530046, 533907347, 490153643, 899870613, 784014688, 526575482, 763087592, 617722460, 747963538, 876259857, 334803152, 631967378, 27286937, 38782868, 695843020, 954574599, 362644254, 982961278, 195835637, 582167676, 574555376, 216542385, 867576794, 673010157, 149954597, 530165556, 530925917, 797100118, 854595245, 572563147, 547037852, 359962767, 712864549, 657297437, 486077857, 638940410, 619105335, 444159432, 994756210, 2720134, 339327384, 965141009, 42106040, 480893341, 71885571, 43452334, 981809924, 66964387, 160543011, 17482486, 335098900, 337508740, 528162016, 699321218, 516606180, 675021349, 794098444, 353845797, 973711124, 628633926, 242344981, 674112146, 255453093, 311078072, 356188105, 963622135, 620759671, 7829642, 512362114, 711982255, 684736298, 587882252, 588809049, 272673867, 306521564, 550300330, 841631591, 46936667, 621994384, 817400988, 343889074, 442733237, 168610990, 170609752, 401769103, 937404882, 86060801, 94462205, 795984457, 405187068, 873543899, 779112577, 434554083, 923036503, 697432405, 530170905, 917813395, 6271520, 762603294, 393709669, 363742367, 747076508, 365894390, 791811213, 326829297, 96085776, 869099055, 87614000, 55848247, 323055830, 978883906, 479144125, 401445108, 276101382, 219071901, 578372959, 955261568, 834301094, 913746009, 670005832, 357719834, 395615096, 680330417, 54650886, 370418606, 644836464, 303074581, 65748255, 585973862, 703238745, 835425433, 42204526, 547362406, 247261196, 48043529, 417580515, 925251115, 936444872, 238929302, 882353719, 798709845, 260280968, 974649432, 522880974, 814783098, 33548780, 565795498, 211292476, 232243841, 742095142, 273745494, 305105921, 131238238, 352901288, 3718461, 286984181, 154112307, 482306410, 192175821, 324020701, 914543664, 666147183, 718791687, 266341970, 483210902, 404917893, 409290843, 854834354, 670806649, 880236896, 203029057, 70769498, 566948553, 167786752, 784057193, 779403437, 331466670, 948982546, 845413612, 595469556, 171183750, 243295396, 878800694, 873610524, 553499885, 65336892, 294829899, 129712893, 339416642, 148962105, 999882795, 393599007, 802627730, 434910768, 546185827, 9022563, 411032852, 547539032, 173878636, 263071639, 228317955, 798213986, 577956726, 844595960, 709340521, 527160073, 22565939, 813871376, 614659492, 975945997, 897016889, 278359515, 637941206, 66140462, 23986652, 654729841, 757140797, 338178402, 364561743, 526294040, 792631238, 831749840, 725856269, 114770455, 593486202, 909638937, 594077248, 836875944, 927406469, 285708811, 287833496, 6604703, 791704376, 194432762, 535898146, 965501301, 274949716, 963621235, 530675125, 98826013, 803073821, 756181551, 944176921, 930850917, 638324993, 124647827, 88019410, 758915654, 537155302, 819754750, 53207085, 4436149, 225127232, 844492522, 60621549, 79423029, 605781725, 590132021, 381800227, 242623289, 645140229, 432107214, 450248825, 145119418, 955324534, 529656330, 390472020, 178732154, 994178972, 212339478, 164899846, 494254699, 435995243, 261885457, 403603177, 502508187, 225999622, 614626859, 202937028, 801605858, 875103187, 482812770, 30444087, 276580898, 20850626, 707788224, 233736088, 882215669, 438689760, 575327369, 195042319, 486281598, 48399939, 183418651, 566923801, 442730019, 844184515, 886367070, 482101396, 885766419, 74642715, 512389657, 201573085, 814025542, 944995089, 408965341, 719310568, 164952828, 316003986, 184149401, 712400903, 149893717, 305864778, 73296645, 888107806, 746613299, 974232027, 631129441, 987509111, 508109301, 279320967, 1675327, 958586365, 200808824, 302419690, 857096048, 899821308, 966685022, 615447815, 264332759, 803513110, 930847419, 949575081, 51715406, 888126570, 643246509, 519032398, 284029644, 920922425, 450547423, 409297097, 231742695, 955660869, 273560325, 44180897, 679716456, 794915021, 160448003, 13692388, 875637590, 866976845, 97135774, 928591452, 9642294, 787340634, 299364466, 898692507, 859691400, 46967599, 597637264, 846773330, 434531312, 671609238, 135167635, 362247932, 226156972, 667671791, 287542380, 545278476, 415763640, 601061480, 804390638, 805869314, 523811187, 478971497, 469641532, 511798434, 849217946, 194157741, 818707074, 929051643, 276637489, 105389874, 816750215, 79402519, 285250870, 121638894, 56037586, 205965259, 77292573, 830092111, 839143704, 795070959, 151656639, 649449930, 658452225, 448025985, 461620542, 610021789, 667352542, 286865743, 89425159, 344174704, 36240307, 895500875, 34193090, 635115332, 503651392, 526573409, 800526256, 765996703, 719358421, 302525990, 613218606, 554356394, 790578812, 410548068, 809026625, 100824255, 399609574, 353550192, 964665827, 462800313, 998304652, 631393939, 539883537, 324284488, 187053159, 311851115, 925954148, 880637342, 500420164, 210603363, 549300759, 494607872, 85426911, 274658928, 115268544, 451953802, 867683603, 190611185, 475406717, 155431327, 62256618, 306398608, 984866640, 391399307, 616550568, 477088289, 859220432, 186200887, 795762366, 698489393, 889594979, 984674523, 472569296, 778312858, 621307402, 603465193, 434399852, 5583264, 169570503, 569392162, 212757852, 919557573, 412742606, 567304756, 730565037, 647793999, 300722305, 698276876, 595308965, 469058720, 714783540, 807486464, 424712699, 471546647, 395050167, 891154880, 244152392, 858785651, 503687865, 122240241, 703035418, 38038910, 330963365, 811173563, 419742780, 127648051, 457801335, 488436921, 261716795, 169616531, 31665168, 77049441, 119919908, 349013508, 688956780, 717737008, 76670579, 986125282, 34233678, 617540399, 441048661, 789875638, 868082108, 258051736, 259261870, 506982397, 599812168, 640190167, 424459578, 460898619, 265632550, 339070221, 690768816, 57044379, 761177860, 717911810, 845821859, 325548814, 30546960, 391868192, 490870169, 102222756, 382220941, 100601729, 338570418, 15965630, 788464373, 52462553, 813459639, 90382898, 167511636, 200202687, 129879724, 727840433, 807572286, 547126872, 271722424, 891913535, 363845580, 409049630, 974867777, 613609889, 65092637, 312745710, 860253223, 163434232, 102801715, 322224074, 639359989, 53137025, 104395034, 440010501, 53203674, 492260937, 729995107, 283661132, 428166667, 181190407, 328915046, 610019705, 907914708, 471889278, 862167814, 964566188, 496330533, 682529851, 410871327, 27991814, 831666644, 897176077, 250641319, 808827361, 631613981, 52065682, 588125462, 515550056, 985020331, 226728751, 439795148, 509937757, 423126426, 959565804, 601596740, 151888082, 665510571, 927434936, 762512767, 186610199, 887545920, 921673181, 160383445, 565916225, 351972349, 901438177, 603347669, 312114615, 691644082, 849347604, 37251575, 746228840, 696197851, 216417634, 790442755, 787499687, 962550963, 725912198, 627417866, 83372536, 750729065, 774412493, 49588652, 104487974, 329730072, 468222309, 55895333, 564883821, 35051619, 346137171, 520904173, 841983372, 6004039, 86035166, 121967352, 274739567, 746226375, 437720918, 914257977, 341369353, 472868974, 26139485, 232240126, 526484093, 429032603, 71798364, 753300452, 793186370, 883000136, 302035710, 320535993, 782602436, 262143075, 624771039, 154405506, 538102631, 787878353, 799064203, 591443623, 529105793, 128601263, 882720057, 410689013, 829715596, 877964752, 547702209, 70988053, 902456287, 156057548, 415554951, 984972641, 730885331, 117317243, 344808832, 387364427, 938021054, 135860328, 512446524, 554055051, 522656032, 951253034, 319916510, 303619319, 322236617, 730529150, 937708649, 238524654, 461532106, 981521950, 46826089, 196140745, 219960188, 577436078, 462496504, 215575320, 806994737, 106377089, 671207105, 591635357, 46572904, 779205078, 697770940, 79109889, 221925488, 255236915, 133362203, 838143618, 826613953, 334584357, 872269827, 572939685, 514732432, 440223990, 314700876, 710296643, 809475138, 908237483, 621431156, 113308766, 900361243, 543095176, 784657076, 310342467, 704237072, 620345833, 227117820, 802218090, 861627774, 152305130, 868099115, 339987223, 297376370, 294976990, 400189262, 908832544, 939774412, 151017698, 724381999, 763015137, 235327257, 243582725, 125674227, 566761917, 159581367, 954308899, 407961542, 263646401, 406957594, 655340785, 66269778, 677716732, 197711725, 246920462, 575221375, 238648782, 90527450, 613117680, 369989709, 608998705, 811318276, 759339277, 296798107, 867551373, 496484718, 816054550, 986436110, 36444463, 269051221, 206168349, 658886540, 984633779, 781205708, 526223221, 873476331, 241018271, 739363447, 264996608, 687751757, 932688452, 426821532, 400938636, 950877670, 166877490, 516183105, 297509976, 462974422, 202526968, 988564443, 786859583, 405150859, 735331389, 884891337, 220969779, 534685925, 817519509, 338792576, 656655754, 243744071, 603472017, 884263013, 367666242, 307580862, 94393377, 843835989, 205721175, 778325200, 624487071, 473268626, 793773266, 333885009, 14140745, 709148447, 99358447, 326662861, 618748279, 857494626, 665697951, 378670705, 593320654, 88928438, 446020326, 392722349, 440075871, 781329272, 690059882, 116091392, 44481276, 756438064, 381809592, 52892621, 168716969, 288209093, 765142604, 285878612, 545952325, 212782783, 77343079, 448300652, 55898011, 901049816, 174775774, 264111294, 103209854, 491169881, 295777669, 504868948, 582774153, 844238130, 316971972, 755447617, 925099918, 619504103, 126563791, 475233612, 166564734, 419580565, 434470555, 460897787, 247680165, 188201177, 162130823, 636345388, 769156748, 740067126, 827926284, 66692452, 926481900, 388553999, 953407537, 19185817, 108883326, 291765563, 641884962, 451579660, 22612874, 22737825, 951320738, 842558675, 489828675, 351542594, 468393362, 684839630, 281031726, 654520980, 542413836, 539128077, 417907242, 705803551, 603247837, 89780532, 805603558, 903968060, 22392187, 43333558, 228665863, 754733614, 807326921, 866197710, 599268092, 557008091, 250227717, 125562730, 125453812, 932576775, 999266010, 867363825, 643152139, 249284879, 157552483, 338745160, 776826251, 133839867, 741793368, 466396548, 995591670, 156593295, 393715121, 329798204, 181300384, 555788600, 953738856, 144143985, 433862162, 596629835, 994542309, 218823963, 784147953, 102713269, 535141969, 992775505, 461763597, 738650785, 687194260, 639251925, 630744240, 768645044, 458558414, 289532676, 294752158, 303434446, 428966272, 327965952, 231973491, 377564184, 184628566, 286474246, 737680147, 777931144, 45106960, 768623362, 438046083, 331227670, 237217943, 811446901, 101985572, 262197876, 263797265, 90191724, 62964659, 472560870, 516014083, 887382174, 551708973, 949514969, 256137031, 976203315, 707004427, 376056307, 208709657, 156502081, 409280428, 924373284, 647039557, 161443522, 970990201, 645197539, 488478520, 979586976, 464454024, 465698528, 417306407, 320407479, 623594837, 737589008, 911552931, 467806786, 793777907, 25876034, 646738789, 761697952, 529148923, 564149289, 246168548, 33268460, 507673579, 948214228, 87272217, 751456555, 990885526, 923478679, 91473870, 443326005, 925300132, 605047605, 372719395, 644813256, 72951220, 566377701, 727533576, 158370460, 238782504, 364612985, 675781929, 550840198, 332381838, 169861970, 842971950, 421383275, 747930876, 816897061, 844160086, 842790438, 347547653, 687237051, 878915401, 14995368, 319621484, 438334734, 578377241, 229561475, 934330289, 777107741, 529464759, 482932234, 68598836, 988081434, 354704708, 105002016, 157269273, 853454454, 544818234, 245442843, 497464268, 916763949, 219004928, 47620866, 782603758, 245605522, 370575430, 486371520, 172235792, 600112872, 15256342, 133944827, 321454511, 918707513, 372876316, 388427599, 310887919, 560895356, 201563221, 285662241, 74809112, 292606364, 666847996, 416645641, 579056832, 647370804, 693527471, 491083643, 825439668, 634241731, 215067319, 427891154, 22380721, 945195759, 365069864, 205761728, 576153217, 803738222, 849212227, 464937846, 112577165, 39431669, 73279619, 1746768, 756199631, 515220640, 706627446, 184451578, 240922883, 232131286, 574749567, 935837216, 757086426, 471101240, 152056113, 453173265, 595706718, 589182644, 582820972, 101444674, 559897978, 949168728, 583093786, 436833121, 774884468, 393248989, 753138192, 908513572, 832745666, 239022296, 139628482, 127126264, 675348140, 616357008, 46845137, 899427706, 684418270, 437579481, 530236872, 264699977, 906190021, 58116812, 135243366, 134316055, 452593572, 67872851, 586630311, 798541164, 525476282, 905998743, 90338335, 423273979, 933964260, 644852287, 324502773, 754676425, 567497278, 93413750, 618821019, 20283707, 218534656, 609799628, 993594230, 944504405, 795970354, 223007249, 696628670, 229486684, 34208122, 455147269, 451798016, 615755827, 469127591, 850425507, 66759674, 493778225, 953544668, 846011408, 133804553, 748502963, 444813837, 530895850, 511621171, 669452796, 384776428, 898400365, 439677850, 222568368, 996227866, 294963272, 674454808, 4467492, 44879231, 917713487, 819709992, 518664502, 971401428, 532948703, 418444552, 472665241, 512838154, 386203299, 645350909, 14548664, 711735905, 719826318, 613740111, 631950432, 396346384, 295484994, 446006792, 663181000, 497537959, 238091427, 647658640, 87197918, 969944652, 410965879, 23011912, 262531090, 96138416, 714918531, 550091002, 552523729, 923798369, 11285841, 552722810, 336693103, 497581949, 766274797, 559917043, 406252030, 976286195, 373692050, 425463160, 719186577, 248911288, 490890958, 113576580, 224474557, 259722388, 620718000, 980921559, 172441214, 337236401, 629263266, 44838825, 505106194, 800542118, 351741544, 692211373, 553743154, 801179658, 859602642, 632824210, 630110915, 47578100, 555956315, 256773071, 493237342, 648157272, 912394018, 907489469, 555124762, 583042127, 257027701, 342427009, 587437779, 319429364, 319185843, 714018896, 714833724, 577280857, 811858612, 130090606, 163335759, 866769706, 256705884, 326632285, 217192761, 723831651, 586074280, 80038922, 91205042, 229242320, 724129487, 504836786, 158658414, 73857478, 8422992, 517648583, 241101182, 462509024, 483674702, 742233878, 837605030, 24173026, 912472066, 608882409, 219830110, 698841214, 208904340, 893968894, 270560516, 986615653, 571741244, 988935034, 515349465, 524466420, 964804372, 539765337, 422823466, 883742421, 1598966, 432100232, 813385712, 928951082, 112725763, 990033131, 317486675, 484075377, 594842724, 578914884, 809856240, 169698781, 102571175, 192463617, 772639004, 384113377, 642323279, 244950777, 537105731, 215795670, 125934572, 991333656, 596441808, 303008952, 215578788, 241159687, 256208684, 650454602, 907425459, 194576558, 241975206, 560521436, 374203815, 463590105, 356031617, 598787615, 212192089, 754051616, 335276228, 335786722, 46344640, 212737971, 424413451, 213464575, 87070230, 934952536, 915086272, 168408365, 65058361, 181328008, 302277365, 929074603, 905625996, 204851263, 920916000, 338048889, 767802752, 958561124, 553726792, 701237132, 389168638, 701520771, 486417018, 364008284, 291643336, 16380481, 95449234, 8854993, 403067706, 678649021, 694417632, 10682142, 801439254, 42120731, 424645125, 576723676, 107262412, 923021711, 244003889, 577383764, 132727775, 118190849, 310197837, 834582836, 364190835, 707856420, 903917554, 670233355, 173490717, 620662729, 992180026, 191560189, 411437179, 701802158, 55984604, 17963472, 190724488, 323475572, 495067149, 975391601, 337662404, 948719281, 63403109, 363829728, 614632470, 18712047, 910349792, 624653779, 756338061, 435217022, 316863781, 398982182, 237050666, 954815941, 220248055, 517738735, 23627378, 226391264, 563890398, 838453626, 929538757, 927503071, 134821590, 70022275, 440015300, 690007945, 461426414, 93489073, 248696815, 929218295, 403632468, 166613215, 870552195, 893431202, 909531953, 411658920, 686913451, 639929541, 205069498, 646201749, 790877497, 70431197, 734627020, 822743969, 154710717, 952394342, 200915697, 794462947, 996812143, 367747052, 942090091, 153720157, 522045695, 144592687, 695242038, 199968778, 174435364, 965684975, 73968452, 98295484, 855109855, 474342985, 857076118, 805226339, 589367121, 121511865, 261952270, 216556954, 366330179, 911258722, 145513209, 962002640, 752050315, 410526815, 242802206, 699246919, 733099673, 612067816, 947281922, 20554008, 661665986, 550247517, 492511672, 915989866, 177789090, 633194047, 815964264, 577932997, 458377030, 150065145, 244874486, 824968262, 910360304, 478876851, 164741988, 878271956, 172963301, 402573925, 560786932, 275813840, 813758730, 254719679, 140398169, 838346196, 893881761, 431189250, 392344421, 688050238, 361881481, 11784028, 614611370, 581876833, 988677414, 101302294, 431869828, 394836721, 796154530, 629206501, 346266286, 426569943, 338031226, 203798314, 257010326, 377817429, 238252311, 982537078, 500216089, 675430801, 120465890, 685834023, 469278013, 220650997, 797910516, 739958813, 71941961, 584494340, 430322999, 557318080, 392940355, 276583377, 465286428, 459682235, 77641357, 74420162, 260757534, 953708832, 485356042, 335186447, 747269910, 386664257, 295147321, 432675852, 385012684, 639973071, 686061194, 743092507, 780408840, 310601841, 62026571, 289466572, 900489912, 968047249, 245524639, 726523255, 320081326, 917503065, 741791937, 132732016, 18515949, 132875128, 470816687, 740239827, 610139250, 210642418, 758047837, 431991763, 737110827, 909146165, 392395035, 982298466, 279574698, 644276871, 958649218, 449551028, 408694569, 159352389, 682608029, 900980917, 906895779, 971515123, 17865203, 492052790, 477690890, 524078411, 46661060, 770161210, 974405962, 230326116, 177269355, 909229195, 205897553, 567046143, 245840965, 817358739, 447723582, 495456319, 625636240, 153895844, 799173326, 560137087, 359098524, 292747380, 659708716, 841710584, 425012315, 880191462, 628707537, 44246725, 11728172, 461879022, 741986097, 386194030, 850294765, 183008772, 63580839, 359904025, 579150611, 621049390, 281613546, 639936715, 466997224, 450823175, 740159512, 338756488, 420035620, 539563476, 900850797, 227981180, 638765486, 158981405, 773729165, 843260829, 604614704, 207561094, 391085686, 737144994, 352765358, 537322038, 553783930, 365420319, 677081446, 519273518, 679518893, 624975298, 102918565, 938556436, 322847300, 686014369, 964527615, 717076445, 732761706, 360072262, 573944601, 607689600, 794597055, 18156345, 13465008, 960434929, 681242387, 67397459, 465095255, 401876136, 86522982, 979526648, 876499344, 29436068, 934799301, 214465476, 773627977, 871531476, 605975480, 315678809, 559385781, 92110858, 23963738, 920107950, 527231354, 237365313, 842432636, 154368615, 909915979, 446423526, 570870045, 204804312, 922000864, 724898600, 89077444, 895672228, 95031855, 246996413, 650553037, 331720128, 798454609, 223873633, 968684295, 960125600, 338372166, 81578453, 181493661, 962848306, 101902416, 364463095, 632640882, 409910168, 222112243, 585011982, 433056169, 810901017, 518880429, 459060933, 808894709, 757628067, 282694228, 57118338, 550961854, 697234001, 500437795, 408887860, 624238737, 592990671, 542491145, 259891870, 943287259, 690642409, 569964903, 335276791, 13100008, 614848197, 656149154, 220046097, 417178456, 710430242, 267341572, 529108316, 190364549, 677937981, 258566338, 39990347, 394739973, 300619654, 699855640, 172505965, 225762630, 283334529, 863401362, 254839562, 582264756, 346938289, 103364219, 213958239, 243628390, 894302909, 150179065, 838021130, 975441274, 45675660, 870431911, 419154732, 679453458, 586227444, 734378287, 442894167, 532302444, 655006243, 62649634, 632827738, 407112924, 514740152, 164987970, 669518240, 772745942, 988371464, 31745356, 750907003, 530520343, 472923770, 643114472, 158134461, 983747329, 29299172, 629948267, 553880268, 417580969, 17157581, 138084056, 225736090, 47998575, 287755022, 344433613, 383280993, 697132847, 552412188, 820050985, 165105044, 109092804, 914062351, 472041069, 949115890, 419413569, 117033924, 579513822, 655131783, 637364576, 378958497, 600959487, 950688284, 274909337, 436852475, 714406466, 929995477, 859233808, 19791994, 704555488, 16180189, 697010274, 581229993, 366902808, 513388237, 429915884, 884363343, 451956193, 861568931, 715923789, 107558147, 856357745, 830409401, 211977338, 502786820, 996069632, 386939751, 868495830, 138575395, 914393073, 604690507, 401957977, 238131522, 205445812, 771173646, 290690868, 469620794, 857519703, 269911494, 613699089, 253226087, 240045051, 560507113, 614133323, 265438478, 814083956, 37231145, 238633183, 445729262, 175530613, 20701017, 895585348, 553069690, 511882347, 327372134, 778971017, 151858251, 120361625, 59952406, 647791146, 243258879, 328259153, 880089748, 762083010, 657621980, 681207570, 649582005, 630319986, 465100802, 955461937, 145353589, 563271959, 649310560, 366395187, 606517622, 213963436, 118687435, 873272563, 992030042, 725312001, 360763730, 609095511, 628203072, 912279991, 498193831, 376794045, 58972296, 675821836, 76889774, 723032095, 628489963, 896051513, 156455863, 634531247, 882739244, 482928448, 897737499, 545922991, 978130596, 857049731, 858483652, 244925117, 350772868, 751154611, 384233365, 394730680, 37176658, 168306746, 788811810, 51713059, 299690131, 694704021, 388368486, 983399405, 248443389, 941699549, 875065085, 545107886, 582862152, 86486927, 609147847, 398606117, 832274318, 744817564, 368052023, 271943976, 54286014, 550490732, 784771040, 885212286, 190720431, 235748512, 636321131, 699793298, 335804894, 540502032, 760614850, 548426843, 271863368, 571504000, 152561579, 95987507, 707975853, 575033007, 250960918, 45758206, 239028034, 622009154, 982817365, 431258140, 147884310, 869951348, 266411979, 98725918, 521326177, 464219950, 919171820, 76138057, 380060154, 891316914, 362155595, 108562377, 589315410, 429729790, 429314576, 396556812, 775767559, 157124833, 644290774, 194438019, 463451779, 815208654, 43035236, 86338044, 72622022, 278381748, 83504935, 584483377, 23546907, 261863296, 254271320, 456469078, 170410876, 438695609, 237252009, 647663343, 793525562, 117906657, 982447126, 48436128, 40381104, 479468495, 209528007, 703436265, 64216829, 875274664, 635890649, 38740840, 887999904, 597799508, 521939308, 674883350, 517616255, 575602681, 18656177, 309204280, 764710961, 781052812, 431559658, 792998950, 850135316, 147781373, 148968486, 519167798, 83685080, 24580212, 123945015, 707011842, 873330315, 363615187, 534356956, 888176027, 997811716, 232847206, 876977931, 219563140, 107082690, 49718176, 459621473, 960130093, 333217408, 78573704, 325859003, 408839153, 12554076, 162049015, 708545606, 876867447, 226845729, 39260465, 375831068, 370810420, 638620195, 264932025, 851627687, 513136175, 809703458, 842825616, 200114319, 408890131, 351736816, 551110525, 113001438, 243254387, 618048312, 457706104, 984920626, 537484219, 676392127, 18310757, 242619724, 795669267, 97447864, 950343644, 959216156, 670962544, 407079106, 446521237, 467277801, 383440956, 466267803, 248732734, 995235676, 528109799, 952393602, 58120411, 67164665, 624588319, 627633843, 966888089, 856458608, 614246612, 427082233, 154264737, 626574056, 405191389, 761858833, 852576214, 552064312, 231446132, 312150400, 13609715, 541765276, 410562498, 740805849, 941660293, 979159669, 997786070, 278907449, 648426752, 124468701, 97270950, 987328516, 143052547, 948748842, 982893871, 860894283, 879350120, 913802268, 141107655, 671239115, 172575812, 892446692, 933137191, 828008597, 548366108, 779655447, 270162186, 753454890, 502422788, 819982971, 21884355, 257527555, 356071420, 230639779, 68179203, 631708116, 609430759, 986924738, 503337082, 547932689, 564046788, 399474850, 278628443, 558394886, 15583174, 266710892, 474517998, 417324913, 594741517, 190820495, 215897541, 92150496, 110360984, 367108034, 752577325, 586801998, 397733893, 811444527, 769102549, 70836484, 733770607, 347853673, 100829567, 321190777, 840236018, 29173780, 929116633, 889691894, 94595460, 77209178, 635045668, 738186758, 194081769, 946558364, 31530142, 42013570, 767732865, 973400901, 293281177, 950025180, 129563366, 51723098, 142415003, 989146058, 943973706, 500956585, 176741586, 686089143, 444996054, 999689994, 327733464, 202318482, 982458850, 93895349, 141182732, 513072637, 448690031, 523599651, 865864612, 141220670, 174981125, 230750324, 731768808, 661942742, 500692417, 827477317, 871961719, 298020698, 521864261, 198479227, 402564250, 487241861, 537935566, 293547961, 935309544, 147681494, 359353824, 604363821, 727964149, 689328084, 678507871, 344742466, 844407624, 669651878, 564561488, 686967955, 103419644, 241473105, 483909005, 181276014, 785084273, 533742902, 191910657, 909000470, 338670449, 729473175, 411800822, 858246983, 673904253, 705238244, 661602153, 436095973, 832467065, 586691214, 173755238, 845193983, 738079396, 804067036, 520539328, 821214587, 679032220, 280763233, 497143989, 892359993, 772231982, 384123084, 678115053, 18914188, 637479445, 531833471, 883045989, 821869572, 79061846, 154587638, 218052795, 762044004, 140916314, 373234123, 165989960, 487020519, 772793475, 182234830, 527387057, 183429831, 366778721, 317697645, 772657350, 144385836, 311399353, 224775436, 935068128, 947992947, 238578757, 71811797, 268313951, 616750648, 939331531, 917451297, 347537551, 393409001, 877467707, 944505749, 521393543, 885034712, 361494106, 588331481, 95805866, 895430290, 289012197, 10935750, 717650204, 423241535, 540540547, 345790865, 693492326, 987175643, 579758971, 939115782, 75136962, 301286994, 258770397, 539699886, 189188260, 630501270, 595538340, 890652624, 587966909, 205498616, 289717047, 356793649, 980579156, 990349863, 62277351, 614889974, 798706366, 780416138, 906522101, 451501210, 151573969, 11100321, 898864731, 158444754, 44911221, 243156577, 860800036, 988653536, 761014587, 701723402, 538841538, 698088218, 457492133, 855735434, 75973606, 999691153, 109218354, 45856050, 640510425, 251693272, 740872624, 91064147, 385850225, 185383800, 682861688, 680453193, 513688319, 621914778, 663035452, 763769247, 634475929, 310056227, 209684464, 864467608, 112148772, 329072, 597460912, 150223032, 981594941, 492081683, 19408088, 236540137, 754420535, 928598110, 163227314, 889162874, 914857266, 22020440, 734070993, 609780994, 410836954, 478961240, 623946279, 63141277, 597577481, 737444558, 639169611, 823319838, 512648540, 701770555, 492132393, 869379331, 965646337, 758909575, 148913748, 681021323, 776320488, 138644137, 565740134, 217875541, 979854507, 860539392, 806812155, 394066731, 406227488, 550900897, 891141250, 746273023, 538746259, 742708827, 620019010, 652645042, 333392426, 151474615, 363440309, 32859271, 776206552, 235630584, 914625073, 50275245, 688786794, 973447908, 597438240, 368570455, 798381896, 470134613, 322426209, 768103420, 239472437, 478926512, 521893754, 633586133, 843875303, 812385566, 233436468, 141184335, 718923238, 856961780, 611311471, 434577364, 174723274, 372736726, 274061645, 603922475, 615239488, 546259219, 741493285, 166169270, 944575127, 598101419, 280114894, 808625977, 835570366, 818358742, 316666919, 130654212, 901809387, 1180379, 859977771, 384487432, 138779154, 606985508, 729506184, 353818960, 797925430, 592994100, 726082469, 689102981, 108227140, 530660250, 515686901, 274494826, 341159629, 442277382, 836833285, 262842424, 694755400, 905884515, 834361810, 626476465, 995739660, 848987558, 979515492, 800048160, 931929778, 125538993, 155823955, 587011125, 501987375, 877079803, 714188278, 437909519, 723079543, 98806878, 700936780, 986530904, 148200923, 170357662, 634248616, 500785892, 588662346, 907169582, 698094484, 399263939, 994171975, 930952872, 876008155, 649531077, 780135282, 273735132, 122146841, 862482393, 261194326, 824374041, 891649151, 956967426, 587912519, 692712175, 433647356, 251614198, 821005972, 403512570, 693801211, 921336357, 553600792, 558237719, 981933753, 39096289, 981836502, 271778783, 674934105, 142647413, 923026376, 104470504, 29589537, 996047939, 698826968, 355267686, 704518719, 764681932, 487719169, 671676167, 41175940, 667881160, 609835960, 934891004, 386913952, 355614908, 211261316, 343922354, 510217094, 999403872, 270124161, 553273218, 235773790, 123894211, 379817283, 350522887, 936873985, 752193303, 5953254, 61455442, 500175385, 42648873, 141506716, 524836978, 400302652, 731584330, 905070339, 67224709, 848416714, 970889566, 421327736, 273465797, 122160658, 629170162, 315219069, 124459846, 132902005, 780380668, 567946721, 186217217, 753547323, 110172445, 86912372, 760341029, 794041579, 41919403, 232768400, 313170300, 924516463, 646158986, 51342565, 135555170, 308228529, 927914192, 490529690, 767312135, 400478106, 602129770, 627789410, 309407066, 562333797, 924527164, 772803829, 349383486, 523986499, 316901672, 748531262, 25607974, 8304875, 182019468, 10051662, 365217139, 432717904, 693625065, 267603522, 228080651, 74379903, 485618499, 224373728, 274320520, 448724744, 496878805, 66045521, 349594963, 373643630, 195087135, 393635827, 117886588, 370302973, 948221487, 551618886, 519374064, 152598457, 403152246, 809831317, 854905503, 541524370, 927908468, 565740658, 822274067, 589951660, 82416625, 199552591, 963560333, 908757714, 520695776, 20399448, 210075277, 602622540, 576951382, 614191885, 207943182, 909685668, 791277379, 24586062, 508522207, 341410520, 767806054, 239037094, 732475929, 837094021, 109072094, 170634690, 360096941, 114921158, 263374750, 812846940, 447823401, 365937636, 923236556, 347465315, 146116405, 638100844, 85951672, 656567289, 137903688, 443369684, 981507407, 834643435, 701241100, 108298872, 44436282, 358144588, 144017315, 889262944, 687201228, 47665842, 723850255, 981824208, 344864719, 390019101, 849320131, 792272072, 244284142, 978788048, 142306997, 617989220, 403828071, 444122861, 142035586, 900020475, 938346483, 975044948, 562164537, 401085601, 95985890, 434845558, 940102633, 867781263, 242804901, 775711547, 589664765, 729293084, 753905996, 676284880, 543210748, 357723036, 912350087, 330723269, 971734405, 255020595, 164496342, 376081599, 600749370, 947303291, 343156137, 302850295, 186741686, 9350195, 32975269, 889562441, 756038687, 478258812, 280155036, 853970282, 655495488, 511711697, 959440544, 539717040, 691146065, 660377397, 957104928, 114428626, 183807130, 904486629, 333346166, 996775413, 690563501, 806381637, 297942727, 344090987, 792320210, 36618631, 7035213, 766996862, 456226288, 463317714, 136712705, 886642200, 43478551, 105916841, 330128246, 859373390, 571032365, 809266105, 307881347, 708863278, 933026510, 138309955, 523832023, 216583233, 327894246, 761872434, 358880888, 51877902, 840236146, 180953178, 950248539, 204022397, 436384556, 592690130, 53735313, 833843898, 322348930, 730632065, 471462077, 966073411, 97736226, 536879649, 587079302, 896080812, 111390439, 174648519, 285371758, 916842840, 623137848, 695550540, 383229852, 29544652, 28020992, 862957334, 439939601, 5691752, 832383034, 259487223, 256981848, 598605148, 515039251, 923478558, 216158336, 111113574, 413802044, 187497516, 269214559, 472446264, 445685254, 855506189, 863146836, 732858020, 209949613, 760787256, 246467980, 531318881, 792349477, 762068741, 726437277, 920836481, 833413346, 974418546, 829363895, 333353441, 405108681, 592037273, 52087360, 552323256, 963033873, 961243625, 928452763, 589325023, 168575242, 433471604, 782409129, 759831580, 465063033, 754220647, 551583810, 419755495, 200951455, 186536541, 679517530, 494252810, 570376129, 634581407, 917156791, 551427483, 255340741, 286046555, 519060746, 132534769, 331497926, 320755279, 270030174, 387955417, 804454737, 320398719, 854329534, 407506208, 965952785, 936287689, 812118784, 722466364, 690109480, 480733595, 44834205, 894488186, 782133913, 216731299, 867177526, 98903774, 888603646, 209287012, 178815930, 929761505, 818471308, 487642071, 509041547, 728288496, 882482375, 779457581, 943143924, 245419365, 397844721, 102357436, 140632778, 516363644, 33302374, 31509948, 91669382, 910477571, 46479721, 75861090, 302345592, 828691783, 36845115, 253098367, 57633253, 772028546, 807394466, 28457679, 432312569, 107797556, 867542061, 136936044, 830656534, 884697853, 494717970, 474965453, 121024068, 461607208, 471131879, 925282039, 819740986, 410943742, 79312257, 716846802, 205833168, 592188890, 681254426, 660347603, 319847667, 688563710, 78507894, 105470488, 54508694, 955407720, 45750367, 886732907, 180378420, 837993603, 976970709, 973997595, 384290896, 535167622, 577420895, 824224702, 596719597, 50708077, 187936578, 265643802, 343815092, 844869417, 456500150, 181868018, 396401937, 557227086, 843799385, 763475536, 567356633, 2793860, 616914401, 269186486, 712129814, 494489574, 849220593, 677478023, 563566596, 341674271, 843970306, 374553996, 535637593, 786682685, 629289752, 392893053, 983406803, 771853201, 4180165, 717973842, 292330882, 991541178, 727772524, 309467619, 69424805, 522006769, 909096485, 293387383, 493975670, 631650342, 171081800, 411074930, 451120918, 149355607, 820839075, 351468696, 577432186, 456064984, 762862171, 221724970, 373183042, 414287094, 609206893, 468692129, 242445888, 364261123, 951395442, 585938603, 808632964, 406266188, 327224440, 920465783, 466921401, 887989551, 557962611, 97590257, 851595016, 231962241, 59082568, 570245670, 819376015, 96853245, 911196720, 412543926, 719943647, 503194916, 143625587, 97268298, 4078552, 687903722, 656680334, 67646826, 74389376, 424157849, 159003936, 878038212, 20142587, 571040252, 77517451, 967600982, 557359075, 700320849, 745276376, 594351588, 108511456, 364182701, 635277401, 133750196, 510715279, 796249138, 380625414, 244137927, 188933544, 740096745, 186539915, 257948356, 322525042, 888864352, 724016379, 730221352, 928143903, 103543716, 989584358, 357648134, 998710636, 964315285, 305568273, 322939579, 998188190, 760751629, 291914779, 802706465, 203957625, 548078939, 911131020, 303271316, 803782909, 267676556, 386647920, 679161965, 257558539, 786472774, 306067285, 826715988, 174995835, 280628460, 396440569, 703418059, 465867448, 465448209, 911552638, 758562024, 377725855, 256990764, 970142260, 948727269, 455192343, 658640752, 229651731, 891853857, 656939469, 921826929, 956708314, 856401279, 256902427, 539744677, 975081333, 489762590, 74510200, 111620751, 898601596, 8702687, 851980258, 469968262, 834317458, 857120234, 88006610, 926286164, 361334861, 798223100, 63316369, 5782445, 996350348, 364928079, 522600057, 462783858, 167971402, 154507005, 907493993, 585038934, 853845265, 377793278, 997435695, 969292244, 259901767, 503838589, 337630476, 17418345, 426699011, 313919, 492500747, 368856651, 961212767, 328642301, 485096288, 824639964, 626396738, 846631941, 755531985, 351037754, 933700050, 339684080, 254204644, 497655956, 261326286, 403349387, 616265041, 652130343, 358861654, 129893775, 502928011, 425318660, 131995599, 673517660, 135672735, 385300612, 40210632, 951184022, 101144629, 583116601, 386981462, 900910632, 549804433, 218479043, 650166056, 715980450, 112596978, 468565088, 216968175, 525669109, 859093391, 400904727, 343567874, 321109942, 262320903, 524740145, 241664069, 926986089, 292450054, 402893863, 317315678, 285661089, 447898386, 737132478, 775892186, 894396167, 19675576, 38707859, 161204644, 725362884, 217761453, 900975393, 646750808, 685918690, 738103960, 652860142, 817762126, 295374770, 547692887, 406658400, 19714183, 655992120, 135763507, 690695070, 667978888, 817420924, 728897855, 238751199, 241515138, 576960093, 932521513, 781926031, 34584045, 697251223, 144939463, 178872830, 586401866, 423654166, 517043842, 77934427, 293788990, 282371456, 818204296, 65400154, 333692742, 425873208, 236548980, 14820328, 764418841, 840765874, 979550027, 483762316, 251554387, 8731598, 205585303, 863727805, 315781123, 704087011, 686813938, 589784077, 712365286, 431189995, 732728975, 939808271, 593460736, 262581716, 269839113, 895603089, 779618391, 241068410, 485636535, 569232496, 467175308, 626436695, 345978015, 299136654, 285040794, 561036814, 13360629, 984748360, 911280790, 203029507, 954698434, 991651457, 781237295, 468401523, 330896440, 172018761, 279537738, 123409488, 182316992, 617667110, 133425805, 367168686, 137585700, 553089137, 104026698, 101181581, 385313871, 339075543, 402374999, 751662446, 585148842, 222217170, 509485788, 119214773, 801891846, 20366716, 714124739, 865282549, 316425318, 223952151, 861377292, 8789223, 495670935, 697149977, 759584205, 65200737, 803398876, 553816973, 264095829, 935768705, 102352576, 27529526, 519614680, 722518293, 223954384, 318161699, 465307535, 802875983, 545148959, 934994490, 736082824, 328037466, 510391673, 93193048, 241418543, 475202923, 149092091, 882212636, 668014876, 695919879, 141917693, 950204939, 89834614, 860884207, 344313584, 566693052, 960469190, 120970177, 847736602, 538592870, 280052696, 399271262, 188872344, 850533135, 987163171, 77603522, 557861037, 151784181, 854894205, 470680569, 534111171, 697755576, 413931055, 547900577, 285568157, 799492828, 13643822, 223695713, 630149887, 434342584, 942206330, 772351102, 891172897, 837469443, 119876100, 144303048, 153073433, 247133824, 25054218, 810779692, 78254813, 786919985, 838260934, 50198544, 26044936, 427371788, 292872025, 435575186, 573340370, 998462418, 455106228, 695377622, 99604935, 235756630, 396614203, 413867437, 466734549, 57710590, 742101931, 600702782, 898344568, 27666313, 846419530, 119373876, 415735225, 174554391, 701879214, 844668351, 831299429, 817986616, 700589271, 385653375, 680059721, 69224923, 810154508, 117337469, 775485563, 210897443, 49568494, 520411836, 822856772, 462883562, 841381387, 184579538, 801230592, 747459416, 793891214, 415204607, 964591275, 880286677, 360267274, 830949225, 88501983, 436804166, 883222005, 459087690, 708976533, 723299470, 450392695, 153824461, 548605836, 782047456, 32105620, 247797659, 161053431, 871118503, 590716571, 704869603, 441748979, 745432861, 111787114, 561061732, 674874102, 675479468, 148902915, 160482275, 898231830, 169967823, 135763218, 433364120, 217490401, 275972937, 807476451, 559565090, 164957691, 660551394, 54418148, 129831638, 56730415, 660262671, 511825382, 776489858, 456555861, 926112382, 673703502, 319971670, 534212871, 545940913, 677962685, 401437261, 686805382, 916143372, 161785565, 850954421, 161802757, 824346821, 909311057, 817208962, 102483972, 338589376, 493401208, 54427114, 485103441, 926596349, 915925171, 948175212, 998563096, 541780888, 394938180, 359068185, 220129938, 817097496, 257876541, 626592425, 945926590, 165162356, 65031907, 705291709, 211965150, 679321735, 583187219, 367202358, 214648292, 922996296, 611175152, 160115522, 865921759, 247484912, 876364121, 833358359, 245344762, 847043618, 311046284, 700263667, 670908254, 374703040, 113585808, 124610011, 482943412, 348801316, 702420403, 119256631, 760634134, 797287812, 515797352, 577071036, 918245060, 252059027, 562447823, 191115133, 848023083, 804821923, 306224010, 321689310, 336614181, 270229239, 378491187, 252591006, 383422569, 186430759, 912285075, 926810154, 866194349, 910073242, 880269979, 557106027, 875614275, 101547285, 653068670, 794608022, 953636020, 24908498, 318228038, 943115473, 944217452, 382371967, 610373379, 880726902, 929949161, 413662453, 818080722, 30934014, 834628938, 404032332, 319848099, 41068113, 860294655, 84397297, 399565528, 687043703, 504933795, 159272867, 302735122, 837083661, 219388660, 290033659, 769914038, 195461171, 788557038, 912742770, 127763643, 565601302, 333519688, 782662945, 80380529, 783135846, 447949605, 487522464, 178390775, 121736835, 666257036, 959730467, 349063969, 93742855, 626304955, 318570845, 400634821, 778197005, 17110236, 529235915, 329754879, 670036471, 406521507, 690896714, 903688774, 873037143, 985139738, 254893890, 788548302, 952689978, 506981035, 65703092, 518988804, 918104482, 345209172, 462326724, 623111215, 219696120, 642080494, 953367008, 351222736, 956053925, 811740978, 600332114, 558304506, 885934822, 477741831, 897941386, 983757886, 832346962, 88569300, 584231379, 920651932, 487529842, 604610969, 146742661, 756850388, 396044515, 396055807, 141174993, 322852981, 262459628, 56195012, 665283433, 702383615, 16968721, 42787148, 624367100, 123335750, 44334430, 732238728, 414128004, 834922300, 326446680, 647787634, 964991674, 16302166, 550685127, 390299521, 94235123, 608185830, 10295345, 711732349, 493475855, 451836918, 183008849, 599920237, 875546865, 720004071, 845517868, 367089353, 332347161, 72260717, 500498879, 947622726, 66456123, 352589786, 576224565, 671826739, 80800042, 810104094, 828126266, 212697675, 472398688, 702187072, 874369436, 535155980, 84794781, 724211703, 141695576, 811913055, 343924202, 831335872, 353041314, 185654893, 876710554, 823491280, 39371376, 238595687, 757193942, 198528378, 227072742, 880903807, 880826158, 108554362, 76022352, 242117718, 832675798, 323192683, 70838551, 181171625, 548576675, 236052080, 397685918, 922159109, 741523394, 367808733, 520832530, 659888186, 481162453, 470758281, 960503008, 577882544, 4186907, 423461628, 720709226, 80096978, 998837841, 313036533, 675552312, 920135017, 43125281, 472591384, 470333206, 587028927, 944052447, 442730445, 626326856, 264790721, 384716916, 221868078, 971373682, 935794372, 842001487, 778558108, 287077109, 533804373, 274663166, 132311278, 665040378, 536226451, 473102732, 188140810, 259837948, 963205103, 860811232, 732308190, 594443069, 983641179, 137967103, 726521848, 761864933, 264256101, 758695581, 600793269, 754149553, 457745340, 135447323, 613289926, 220468865, 246148371, 990747749, 406972992, 800222326, 978541329, 644967351, 839587902, 725164359, 914946684, 84408649, 954537639, 689425091, 712903662, 994740887, 46975650, 456076986, 542265965, 893493105, 511491457, 422088446, 152307686, 546220678, 778125706, 899954271, 908068180, 912129091, 855186938, 99825935, 452284479, 58839801, 596880524, 266910687, 873095052, 125378358, 588449787, 389729794, 46548539, 454175743, 540187918, 433632355, 568807202, 521946475, 414587190, 677944783, 30399396, 923382222, 524623654, 314769198, 988666811, 966259483, 940476641, 363225066, 219105226, 772860028, 346824806, 608962568, 847436500, 177983676, 764157829, 972051915, 867058136, 832074244, 364990326, 900208948, 612808718, 419903328, 236746876, 275089718, 1751989, 646274654, 109586544, 972461296, 751152290, 166623186, 843508179, 266171406, 181755543, 16702096, 165420926, 248073092, 137587913, 314190645, 199359615, 11334020, 393474682, 413427433, 437931898, 707428638, 398725089, 949359430, 123033999, 703534600, 947193562, 306616349, 398520496, 926640209, 652072908, 497472250, 172331549, 853763039, 906640800, 256149980, 671079373, 512440350, 28892844, 658499581, 247187378, 984110538, 846308572, 777493544, 999225599, 586848533, 281420965, 934382923, 462125960, 97627198, 42688149, 791503191, 121727510, 271113865, 806812099, 429415136, 348178574, 668409331, 351567949, 708280464, 567585367, 142998382, 504806726, 885716880, 10394591, 598001988, 493774252, 666675598, 979156549, 251817765, 129753192, 880163629, 100634474, 966214913, 369559997, 390296845, 867014260, 884961430, 145490115, 214620651, 744446890, 784833392, 935088526, 289690466, 465031462, 157425691, 82145582, 379595616, 395636598, 363946532, 658228491, 291280492, 61211405, 421352932, 821213957, 458473594, 306201246, 219637224, 446506577, 566950849, 317794924, 733235896, 128568399, 460690310, 71844427, 295298251, 378397056, 279489621, 913788196, 858620491, 399483956, 677042690, 886456507, 171125631, 733948647, 841598606, 997292771, 240790545, 570353651, 466600972, 790373664, 695623393, 575661347, 223384318, 739225596, 933963975, 706788546, 274091032, 683317074, 872388748, 80544014, 630600799, 358826539, 455810717, 740039296, 226273119, 141765207, 569071344, 595521052, 54098046, 155684163, 825158527, 764303886, 417065249, 705684142, 862390386, 359150141, 593817909, 961227429, 885673487, 679921829, 915760864, 514657981, 263326221, 996278810, 338737044, 55216353, 290835200, 534489280, 638151803, 916384574, 151178912, 700041697, 309441299, 214903865, 423450976, 450935787, 859533198, 234230768, 653324014, 680427407, 27241667, 37203809, 660500727, 15495363, 288556245, 328419706, 810099988, 283320310, 869209327, 346300497, 600212954, 974673846, 291332556, 418354184, 177361782, 72404729, 137385528, 527451773, 803983575, 838021325, 620994517, 663886775, 965025103, 116457038, 464587981, 746070383, 610828185, 191063244, 398676795, 387018269, 469108914, 285412531, 421509557, 244318617, 499485785, 261243851, 373891514, 997275917, 867862849, 379703695, 104154954, 686531138, 771938804, 559614824, 964260993, 290562233, 841986543, 369038690, 975041394, 266183386, 819650236, 71706004, 918720409, 866600598, 299539019, 260980376, 272401322, 107289856, 141413142, 294818785, 440085092, 147761122, 654263735, 237419558, 597125595, 660364758, 672781773, 248410339, 42013543, 718929739, 760248282, 604314706, 567962857, 285680294, 113893503, 685791733, 466414750, 848450554, 718916871, 448170685, 476731205, 731456697, 944653792, 809023517, 857474897, 934709343, 458698528, 748776749, 77088987, 508843682, 242536307, 221645537, 496079407, 8389172, 671259628, 217481618, 290765079, 498286831, 928122963, 635733314, 773822317, 588519654, 35154958, 853556542, 542618882, 576302718, 694681881, 7107779, 748844167, 484568511, 569924662, 101845434, 86237247, 169635329, 16228489, 298496055, 304915383, 746349215, 110024923, 407204208, 734210852, 397984788, 105473134, 160461382, 794700771, 165978846, 606822405, 740282829, 852745945, 408262846, 856103797, 188208620, 945823137, 88684799, 668518839, 281406983, 407839478, 653202049, 414383494, 836465887, 358431808, 550382535, 279905181, 654716966, 618485865, 361953857, 836756822, 590047710, 159885674, 166606619, 799895524, 595190817, 362437713, 465614460, 227239634, 482054946, 395782555, 659154727, 793953243, 670393005, 80252714, 776852886, 270417873, 572524461, 991909334, 521397179, 645809695, 574307009, 210796566, 394699968, 929679678, 896210244, 677295118, 502049036, 534250113, 520932808, 340916866, 858129945, 637861321, 106981066, 973162594, 637504638, 859977429, 787444451, 212952346, 677376767, 485388897, 832634216, 49683189, 433001980, 100044969, 776070811, 74779557, 903033034, 409464259, 528231944, 63296198, 444970440, 263922770, 22753934, 688859382, 52982166, 255055407, 670108553, 728626375, 863461656, 970173760, 944529677, 28847753, 139154811, 988837504, 822206322, 537384596, 13709991, 95328732, 770635787, 327056760, 291327055, 641843196, 756511309, 460087552, 614636233, 730967079, 174471504, 870784740, 35346891, 126715067, 791970982, 397842030, 548562499, 458671823, 376636139, 946042577, 153277431, 434907153, 360024119, 658166572, 66327079, 517775770, 30917211, 942454485, 803050869, 250301883, 351319432, 710613932, 889462518, 96235213, 322919366, 314622947, 849812052, 808417767, 204869508, 855849522, 626363341, 903790856, 774761272, 446559852, 755188238, 709805309, 191924727, 643353192, 368830525, 586489584, 610968056, 581630310, 206710229, 544046472, 735121899, 923972431, 404529535, 89819951, 219465784, 167233224, 169144174, 279166480, 958167062, 729723962, 297261238, 530358240, 264228360, 35041148, 409430893, 679347027, 240916719, 467776212, 74500389, 567220668, 920410328, 562483922, 64190458, 986500397, 542652806, 365265307, 21110726, 857162436, 298648983, 839838550, 129992058, 666815462, 775655402, 476710593, 771572603, 768653136, 772816170, 452347223, 385822092, 300847691, 729604988, 258679116, 679839449, 32618880, 51710259, 904105821, 51315342, 446129814, 171331956, 309643541, 264513432, 526337483, 414693767, 397336719, 330711551, 900601328, 385769357, 49223602, 477690338, 521368803, 662031537, 656191143, 132189664, 224348195, 635076709, 333108044, 995194068, 292760100, 619511596, 610049471, 891574150, 766096368, 936072731, 842542052, 809349629, 915343705, 120632224, 416721008, 605887117, 517639038, 677954197, 312258593, 195368235, 486002986, 337056779, 457451176, 789672363, 638823648, 248738865, 776868030, 630042886, 92634733, 791596056, 212735090, 402631378, 140745338, 684593536, 438602218, 831614005, 301649571, 63949861, 930672755, 647207468, 474962271, 237302439, 758516738, 95256334, 793498418, 812753760, 198007119, 93236985, 154687897, 272489216, 50344031, 741517686, 233021371, 638571041, 373647719, 571170915, 565827527, 316775594, 158552339, 912834036, 984919741, 654203946, 925026221, 976933759, 415429787, 820145679, 105457101, 831179993, 985855999, 477867745, 1438881, 204007328, 180210667, 955628533, 858966193, 848150536, 783915446, 217656740, 800157960, 874481106, 540246431, 238735878, 905084974, 825427572, 100789889, 258468052, 980760645, 57547889, 614099820, 868234818, 525294814, 476457388, 944114462, 724651991, 950524217, 191215098, 248619128, 58048356, 580821095, 261142225, 716351647, 370502551, 398198777, 449592180, 307529413, 754509439, 406812348, 244998684, 680183949, 908613197, 753996801, 369520899, 974075430, 5072308, 667164478, 652670046, 167987646, 14100945, 706996584, 632981439, 168037271, 711055181, 495018920, 799594299, 268956211, 422104279, 782843431, 289089607, 877000528, 257166554, 511885046, 298853330, 599558319, 358416482, 507792440, 321466412, 397675039, 715692021, 751306068, 442589521, 714938407, 408583125, 356963380, 982048278, 103428836, 110252821, 785779026, 950085753, 535567625, 287871852, 383499474, 822924424, 647728025, 304408269, 822930669, 927231203, 902645920, 170517563, 487237794, 660719390, 122992330, 789715533, 231972049, 273755346, 389485362, 648063049, 163694683, 520694915, 82432305, 506128764, 247222034, 750788121, 902066326, 708266714, 502574131, 594433730, 580074280, 94877391, 751619125, 883267216, 791148439, 478231899, 187672188, 256584111, 373510101, 605042824, 555436249, 121766531, 985529182, 301620534, 673063851, 868687396, 811939493, 385121934, 556870635, 895501834, 554221942, 488655855, 203315483, 773191448, 20019130, 184989862, 778340727, 157252322, 12668888, 929695236, 903688419, 493511508, 515365571, 300527223, 905860569, 363539279, 49049539, 125563821, 239135294, 104888195, 812969096, 442079994, 279251477, 442530971, 262948438, 280888687, 31700781, 209249171, 911115115, 295841268, 701485261, 446545710, 671555640, 622476146, 400684084, 130847791, 496592487, 64980602, 873678287, 529058965, 539111502, 543204358, 431995391, 12809495, 321560684, 147089058, 327446422, 659470784, 602371179, 766127396, 836252499, 727668013, 553302953, 632008300, 707813025, 426999768, 138402702, 288238525, 858438225, 517438115, 674847355, 95471722, 941566445, 756966747, 683668648, 883538886, 417483098, 541167114, 24899677, 203232954, 166955853, 634000110, 990121881, 919443085, 565671736, 308598534, 550723175, 438332032, 92457778, 148806287, 535347582, 887502774, 57098273, 469388258, 779010598, 121167315, 528045852, 437224328, 895937205, 156988617, 706338631, 766370275, 620680627, 657022464, 464130784, 991351503, 907321660, 188308062, 135681733, 957272097, 909292295, 331363531, 732690306, 449838923, 708416585, 110242771, 821523301, 606045477, 872905358, 307218071, 511445818, 854397342, 856375331, 208304017, 130061072, 34766271, 441668175, 562256371, 2253055, 577253312, 348893380, 889442421, 143903036, 880835980, 323743689, 91530597, 798963403, 667942360, 499937825, 854065867, 63277060, 158608043, 645209384, 277221631, 245722816, 459843633, 20387248, 385993570, 142391592, 677967442, 147388322, 940426979, 141061511, 554719554, 966149356, 862299562, 708857218, 236862800, 457775469, 356247896, 903004883, 18821070, 304631478, 953799151, 606432847, 745006432, 864582992, 822345495, 676606608, 291116747, 146827652, 58776547, 101685800, 309737341, 683187602, 384901440, 422255046, 755926283, 726804428, 290056311, 704182703, 127599358, 283650441, 735880299, 32607499, 485614633, 630842894, 241683641, 164194108, 647037299, 62705185, 729831417, 981646604, 520034916, 585095852, 252368014, 263453005, 961486565, 482070262, 868763120, 894838037, 855946231, 137404882, 270567031, 16915285, 256205500, 227291858, 594383715, 563771649, 377074966, 748162677, 389305916, 44629987, 771105540, 519577062, 126379212, 347392416, 398431854, 868766655, 271520230, 811384206, 890260829, 543424354, 930710440, 397602576, 713782629, 362438369, 583752019, 955932132, 33783368, 94950982, 531365824, 617846836, 416926442, 155888810, 186231176, 624221790, 919814605, 884910665, 57413867, 88568270, 113465968, 922564255, 920670582, 49647301, 922727356, 545402298, 698519139, 856532607, 148112968, 288775851, 181881744, 701382548, 391763308, 198944525, 991818363, 30038409, 662013634, 31264570, 761005803, 702078761, 123299987, 472850315, 948915620, 550680581, 99138912, 98966372, 221648226, 647044379, 162036747, 850115030, 57574708, 787399675, 328247793, 738522193, 426707776, 177987944, 700193145, 268637164, 171662034, 990087597, 363332509, 82620056, 576213111, 410950206, 634010877, 198198693, 740526335, 247356379, 23696207, 303149665, 12266817, 153775041, 359458443, 295012842, 635319318, 535450258, 896241703, 85429902, 980657918, 137527198, 832711628, 913126753, 157731018, 617585369, 77381523, 720693514, 788399956, 712090842, 117551469, 423934775, 115421167, 210874615, 478757831, 268652035, 611188317, 268048722, 661348571, 211457320, 670544130, 491470586, 167250700, 823826850, 516670130, 251244760, 84905638, 984044324, 787310893, 148208657, 787825704, 880735690, 830770104, 683965433, 805022301, 480282744, 597364155, 453671800, 915298792, 385130515, 916844620, 909974082, 421168367, 104771345, 524194299, 534911093, 348632835, 505601249, 773587811, 14870699, 145532436, 526695557, 718564848, 635762744, 851282000, 428024171, 306503139, 85252670, 849563918, 921550780, 485184463, 232873756, 485342844, 164255039, 768732603, 26808640, 820820360, 102126590, 200108243, 143229074, 407111910, 198297708, 316485693, 23873150, 676550126, 134875786, 912120349, 672428009, 956414289, 701840056, 8843761, 855492828, 570214737, 127017370, 500404132, 100592847, 366126058, 334938664, 85878850, 789830652, 675597359, 508033582, 358306714, 723077412, 531843565, 417062036, 375999780, 680775314, 763647598, 15923364, 801540912, 842066277, 812050131, 723481343, 979184361, 570004897, 584842499, 823135997, 998164458, 88201473, 245779974, 674290628, 500428220, 446225990, 473326445, 249173203, 433041590, 601308906, 944684226, 240622913, 938575427, 245705324, 553387498, 59336086, 667155281, 696173446, 687925502, 849502851, 757537292, 182254307, 951629510, 996603255, 770184235, 663000917, 652730676, 786438587, 44990557, 292754688, 562667805, 921571811, 53030128, 326928627, 262886096, 158786920, 968497190, 1970842, 387347406, 757744385, 71339779, 797103903, 413804806, 279172061, 130513706, 390668319, 969838358, 34719672, 918889381, 537233488, 909701876, 942649022, 413931823, 837631669, 737025645, 559647493, 612705118, 57493742, 904765689, 977645900, 514323546, 304942432, 779742088, 483176453, 359842540, 171126149, 279328462, 297456136, 227632214, 759183206, 675744336, 647231877, 175307457, 608200013, 893533644, 320173633, 613054149, 594842479, 429389739, 340616097, 656496672, 384458567, 664537236, 712031944, 715218974, 701339472, 475976888, 661692962, 63542743, 554954737, 674484273, 60903172, 933968060, 893019265, 606518213, 365092676, 432486216, 815645733, 682489598, 328063226, 338958484, 510638533, 879935720, 822537843, 554529995, 689723781, 867332756, 818283732, 515073495, 371644192, 604508184, 20989574, 671958038, 917739406, 758605691, 387907108, 704410699, 63701574, 928216921, 973365360, 777157742, 86601161, 950362906, 989393119, 840209354, 423374145, 589542371, 969710225, 667455686, 130456367, 915858654, 932658557, 22219362, 496248750, 777596719, 663298808, 31714405, 103298874, 47517385, 672930811, 443942925, 233162522, 417293510, 592881255, 84018921, 979254721, 163954516, 177375038, 304314099, 284967046, 491731551, 381865474, 161699606, 939336562, 21551672, 464278372, 141500645, 458300565, 457259052, 142023811, 888021801, 513513790, 642483437, 489103983, 290754489, 41698756, 484405202, 823328213, 469045443, 822068971, 814543191, 210082256, 671376888, 912713652, 824527721, 870200513, 671403097, 548034334, 179500449, 988726, 169218414, 151343980, 535014009, 673485131, 163385815, 840692605, 968689669, 116936656, 41233137, 407376333, 532919964, 585796500, 6680030, 950992265, 686835070, 622680008, 337157987, 690048841, 214985696, 925363739, 556924569, 264005633, 44269504, 691209296, 462600488, 710921864, 946578441, 628840190, 594921123, 243338291, 512074740, 738741838, 152488029, 354632195, 273772584, 327044267, 104766723, 602476090, 685388864, 577841725, 150343593, 395434379, 595323841, 644123074, 34780446, 805151037, 116124133, 677881653, 587565385, 739190621, 641784327, 920466137, 18807658, 402743284, 34129086, 624689858, 863961391, 870297684, 119852586, 233447721, 982706947, 397580265, 682301782, 224915088, 850792287, 979505236, 289350935, 500860457, 63099409, 516739912, 968734560, 487289782, 194944579, 631413959, 723260531, 106475729, 86348424, 137463723, 697992634, 73799178, 110586137, 137288211, 431878143, 189096738, 454215533, 802284996, 224855490, 389652408, 44946738, 302286914, 793699290, 478320483, 87442309, 340330990, 33537222, 491137745, 92715016, 960649567, 964279258, 841836945, 502245545, 941557004, 933590262, 572627065, 48584458, 643390136, 809137274, 706015864, 879866871, 731637732, 624147231, 137835454, 727124268, 523562750, 838659049, 715298164, 568746577, 532251433, 329852769, 798505524, 319615497, 480414534, 334062869, 413497480, 549047638, 486824475, 444084937, 428134927, 77905170, 142980781, 640528869, 105685775, 69554739, 610739623, 803249914, 142336335, 573142779, 60043172, 574561206, 623932832, 540542840, 532490692, 83578626, 347007285, 432363015, 453641644, 861457907, 122048525, 776594125, 463341813, 17891152, 690145433, 306613437, 648451832, 363627045, 823228043, 937708511, 543884328, 569202899, 192421934, 675439430, 598086213, 672110576, 260407790, 933929057, 862647780, 330334839, 750980268, 882732329, 737852608, 286634407, 362537612, 330498258, 959254301, 788218595, 273797822, 108596769, 911555769, 59590463, 930368557, 215902309, 181051959, 200205180, 335495137, 289319672, 793750783, 460930446, 207330672, 504905224, 140906672, 931876958, 471312211, 317827858, 855526678, 637145452, 291919673, 901600716, 170390685, 133110625, 653164791, 18805356, 377172499, 97166577, 111615784, 679488518, 371888105, 653989354, 937398716, 985381664, 867344621, 624091897, 496452832, 822444977, 795063184, 337213969, 449934219, 944116562, 630781650, 206331425, 148283744, 784011705, 659093551, 774983156, 108660790, 895067808, 220259923, 482190789, 981694017, 338434016, 582285175, 910676707, 460380358, 243348192, 662070487, 643499470, 59133482, 491974265, 263900660, 459593091, 352170897, 335672051, 562834151, 612641649, 391205957, 760019854, 126548427, 95932779, 797900963, 867678085, 355916772, 818108321, 808236029, 895142792, 570507261, 548898619, 734663328, 518998689, 244092602, 811058676, 44973552, 312345559, 295427451, 900106645, 174926409, 595445377, 137495253, 369856903, 604618348, 634353443, 413402505, 276319695, 110274477, 443004641, 504008519, 985897675, 431061669, 643663602, 552879836, 475017672, 344840541, 863985306, 117238796, 775065378, 127984528, 196938436, 233235946, 381886298, 145890669, 642530134, 848655494, 271178575, 500414553, 867119510, 756860036, 583011033, 201908150, 929024243, 906041424, 353430117, 930736315, 871020298, 890862317, 262857350, 957305892, 785472742, 592304023, 393642374, 814391357, 499215560, 645153230, 513264145, 539380336, 605452336, 514768368, 151153985, 527964295, 900941889, 745561906, 208580921, 311926035, 119989865, 950009982, 604779152, 953183836, 693846988, 684942344, 935832641, 908939431, 994227816, 199648312, 394139941, 583811960, 324934665, 558822691, 144201949, 88301694, 627214816, 632467540, 552801072, 791892746, 800575583, 749353905, 893411242, 709797594, 198736382, 23737065, 602155243, 752198493, 969962319, 92237609, 619231097, 469890140, 32537367, 794257268, 792908431, 823432698, 549191954, 417616308, 636673451, 956324058, 522524225, 818977649, 607307041, 910987471, 139241146, 96327131, 573192332, 388377929, 72539141, 21377326, 662995896, 909006445, 136848150, 301083247, 966495995, 248613749, 820452545, 709012347, 306557177, 302706489, 512392939, 475901222, 604783324, 587354427, 407633072, 435586538, 6831808, 975070909, 117522612, 438440145, 122398996, 618173509, 864102686, 264552778, 712063952, 873939319, 546866305, 464779299, 469266362, 7160204, 566138345, 844102866, 190140755, 525743802, 837310756, 682884819, 260718026, 972346405, 814757745, 220904169, 453101138, 314349884, 723421447, 396507791, 239177242, 772201350, 196897378, 970229449, 909030408, 606655230, 415090499, 51918122, 715231775, 337748567, 646096875, 494226615, 929142557, 737136383, 222416894, 10880332, 12393211, 163031916, 468196784, 462966759, 108711702, 729754544, 4264194, 713787182, 99235203] 907909284))
+
+test8 :: Test
+test8 = TestCase (assertEqual "for (countGood [545422775, 850851772, 186447348, 572264082, 643409027, 997686213, 336765769, 997995744, 490221770, 144951954, 759346104, 329684729, 672880796, 896658001, 139472718, 987854440, 480638560, 504038335, 970577570, 36619028, 671690092, 75740469, 255068878, 443125182, 808952002, 196272467, 61189628, 860584532, 341241819, 438275841, 506459373, 315301748, 340153380, 471811956, 935310299, 191910219, 765602206, 350075628, 902181663, 453089381, 570507497, 417787742, 500826374, 802378693, 556846751, 570697473, 564586214, 585695080, 409440939, 706593810, 12545970, 228019597, 814094801, 118441768, 310679290, 169964358, 640229488, 429226116, 944597360, 59255817, 766372665, 333185924, 711095430, 304555535, 482711071, 457784046, 837561235, 134939030, 508877662, 362477791, 394743862, 493480221, 552921226, 581240227, 89370343, 783394378, 489291549, 289401480, 731209421, 225478379, 764696677, 601773292, 473784064, 546161311, 123588555, 220796282, 33522420, 509914753, 757333229, 298436698, 276447504, 229716491, 726749973, 500727097, 82033677, 280414898, 464257605, 284528371, 126688389, 648496681, 539955164, 624381293, 843363964, 600360757, 700426065, 60514178, 795375966, 249263855, 410965775, 119860212, 357383438, 576444974, 699509403, 909683931, 367650552, 990835479, 234487758, 391021832, 401179273, 800391678, 79944336, 721436566, 954826653, 604072994, 73978026, 90451581, 643782449, 481525557, 307723993, 241936737, 788109220, 873809593, 61958447, 301744610, 925201002, 613183132, 976345369, 654262814, 592156088, 373411833, 943934031, 313466961, 322710727, 795864514, 736045235, 226280807, 274870308, 531890507, 116491212, 129325017, 70159116, 416749316, 509964272, 477772610, 974539278, 602113268, 62874810, 496863316, 296131507, 78922232, 187186131, 867727406, 25837457, 774848580, 528994, 29777737, 165193859, 963164118, 488497570, 495277484, 208127880, 151871715, 51667726, 929155600, 605198933, 662080709, 241409792, 873930784, 620763119, 505989800, 429957898, 733197064, 43030535, 211625654, 783422701, 550005146, 559640203, 249404943, 796980691, 532605008, 691550280, 512245421, 164025522, 417532777, 199416417, 160329031, 604417835, 854618756, 525766424, 885703259, 705366540, 971099265, 631780838, 345283448, 632669557, 387361197, 324965240, 528793359, 20117670, 467849676, 349980059, 114529430, 302662326, 792321158, 114067145, 765784144, 927429774, 250969618, 836004614, 661039272, 929137502, 753530520, 768966430, 581034649, 673361577, 569756240, 799118911, 896345727, 715570726, 619424239, 897367901, 436472337, 60675985, 945089529, 685496146, 995830110, 134592959, 332375976, 995447834, 17513169, 111599247, 423249385, 997963177, 684968086, 164113150, 874888071, 488751068, 994974602, 130875215, 679898984, 206940633, 777909321, 175844016, 826886290, 941090431, 815866820, 543493433, 743867473, 111158193, 492807455, 683370375, 77419580, 845324690, 871271398, 544679798, 924577079, 287771993, 649534465, 499278945, 844365295, 851314464, 219796270, 394327128, 97761333, 488561128, 669460429, 92872140, 872772303, 339879062, 381633402, 907396253, 686941406, 995918091, 139688345, 297015647, 92195220, 408556567, 35830520, 400814415, 619412163, 754336844, 50206578, 299996746, 758095394, 546689824, 872843615, 211540069, 726428537, 817621453, 560154947, 462120497, 971011985, 472033793, 130501809, 409460244, 51512057, 31392147, 431278349, 684576555, 556197674, 574187728, 707342184, 406053622, 578573117, 257516078, 160861296, 762813946, 350962173, 146682238, 391829709, 844964292, 503905306, 878525185, 308488226, 282729746, 314363283, 494442849, 298059633, 416778555, 311118031, 35887266, 607641976, 245614270, 491192962, 631445142, 998767209, 817287496, 777829091, 417263569, 143553691, 703217389, 539898665, 637290647, 640855135, 3521157, 567217309, 913543945, 962856325, 639066304, 352865461, 255590618, 145870048, 618751594, 278797546, 958824590, 844572207, 938233014, 1697977, 573999751, 803702852, 850661557, 867730247, 816951875, 414712811, 622030360, 974794195, 90245850, 215018084, 399569528, 752745227, 350867270, 269497209, 717351166, 366268440, 648959929, 254292388, 789535449, 229618885, 496346147, 648498777, 632904349, 809144932, 232390474, 422969363, 36356573, 138703580, 491711356, 204332804, 737178408, 193345970, 375204382, 414177894, 95150500, 263095803, 123216289, 122243709, 856286196, 938619000, 570047745, 668733767, 979545265, 218150494, 465793701, 992322266, 34982301, 863505309, 730461224, 872398365, 547406649, 577378447, 830866557, 453625826, 190247196, 612646594, 128619253, 713527150, 456725848, 731887749, 788498918, 251590289, 959121941, 161468782, 301524563, 920511932, 559345763, 87531591, 738719431, 405994520, 511486144, 223959633, 107694598, 254640957, 760578146, 478132594, 341840229, 933712985, 636516631, 742778244, 142970559, 355968963, 97259563, 624952906, 523568488, 934380596, 86309597, 864122978, 391970343, 280391249, 48181141, 671540839, 150959668, 5861371, 173480747, 716184530, 368827834, 277301157, 388249566, 511727040, 243497113, 131080344, 51463878, 683467465, 831560235, 710836473, 724236479, 497625939, 489801116, 739013848, 622060099, 728818602, 557747795, 927805797, 129280245, 295489037, 50339961, 394789470, 688782562, 246631632, 589246419, 338758580, 273231347, 263692663, 704648981, 420313139, 54985967, 372930909, 279291860, 300088667, 418473032, 129911943, 173446057, 36899698, 823806272, 385702356, 814906402, 355732308, 578216584, 257307641, 805118560, 158274926, 337362226, 763640779, 108651709, 875018818, 650806600, 149230928, 672326491, 843231564, 489144774, 378796858, 450883106, 902008646, 374954408, 126640647, 411595364, 986460332, 79447669, 829159927, 626785906, 464268642, 273592897, 106978857, 722003889, 549308049, 101115003, 774307743, 746287847, 628651044, 354038064, 90805044, 887835658, 373004146, 451939065, 947016417, 144146571, 679439941, 762868133, 20665209, 563460281, 136731449, 977515878, 317371338, 645445655, 279957168, 53317835, 85713824, 585926232, 87899880, 821166093, 587273957, 584781515, 624084201, 405743971, 523779141, 215408841, 806031783, 993570491, 910924550, 971535275, 407324406, 628205386, 40041178, 757360280, 992460337, 976546504, 468956542, 697371770, 627603421, 512224549, 330566310, 831055582, 779913046, 690424925, 599526447, 849020640, 827546443, 609235419, 620723826, 729438671, 823769976, 411515189, 313443235, 722607166, 936026381, 947262847, 966148962, 905320861, 630815911, 843800081, 309401959, 423963625, 590692611, 771671777, 412354117, 890413627, 2836197, 92975677, 392781403, 816806350, 286629377, 642485058, 486767252, 113743877, 631102724, 733784051, 731016348, 28507754, 333055984, 680598483, 292782664, 808740109, 602080658, 384227759, 250654828, 27038348, 745903361, 15428205, 235795024, 707981118, 952585462, 172241510, 456016952, 590885162, 476292000, 859327255, 762433553, 760263464, 993980796, 796847511, 757380450, 880309177, 4065351, 332923021, 576356023, 620964405, 186193756, 231916030, 250679030, 384879649, 369567903, 689872420, 82156654, 429447304, 264871857, 985557788, 159168455, 704951609, 285825761, 462817447, 975035875, 792858500, 761379083, 64660280, 105038232, 840085517, 977918956, 277178359, 3552999, 360477209, 837524661, 362845246, 465470799, 494298637, 61305887, 313106429, 516777944, 604526885, 6764350, 778440454, 418324032, 295309898, 669005309, 972351607, 885088888, 985752645, 318862031, 20575282, 454101858, 789833048, 177546307, 288590077, 301932723, 750849933, 331420637, 176296439, 289304637, 488123258, 606583990, 166120989, 212152370, 206838061, 965867749, 118010483, 770205060, 928911884, 311509032, 331231217, 319811217, 119533757, 830774676, 575860692, 33667882, 293542286, 961342818, 869030748, 438620277, 757297577, 990108183, 247379510, 407286354, 854222268, 84345275, 642946839, 716037501, 491819275, 757974131, 644851535, 50000197, 130966435, 477887577, 390538604, 369784545, 636259819, 286920190, 748697672, 943005761, 386040363, 408063129, 328626326, 342338993, 72457654, 916718793, 22487458, 505567517, 465892059, 875277473, 200159709, 348228871, 354613873, 807686777, 8019738, 402759119, 82049665, 318629593, 780345764, 663314876, 653635375, 816329035, 365491793, 665331356, 838968519, 647621379, 196985945, 552076875, 323864643, 780821958, 989930743, 347863536, 978910107, 538138409, 642494934, 758697495, 175339573, 38213657, 460847833, 762551582, 481278208, 453720443, 825189887, 684216343, 6900656, 496574404, 974775993, 389184910, 579206394, 870376703, 84944218, 453307722, 119120889, 264043092, 40773090, 559769249, 367598455, 135275873, 698268069, 506943911, 784942693, 393585076, 550604125, 568730210, 773595568, 19457340, 614903384, 132833403, 926107592, 126072134, 797118878, 516498682, 212150831, 668443231, 76134252, 100401555, 408932122, 43096783, 98821201, 161340776, 710690381, 471755614, 986162245, 74585234, 988804569, 264684511, 192365787, 552001006, 139030200, 168262364, 691770231, 640976692, 580086014, 909235950, 827816048, 874237563, 657441031, 568367611, 437942194, 945162780, 861466806, 41838990, 160845694, 946289021, 401285091, 242014922, 809207772, 435876647, 427383360, 37858065, 797907300, 178292562, 409639118, 427565473, 442579920, 675662096, 697702868, 404490643, 90967026, 74982833, 509160982, 633409386, 144907588, 25465768, 959320595, 57019753, 265277222, 916550960, 933666641, 887807856, 918515180, 406304758, 370649527, 581535226, 191942580, 446585358, 619645055, 429946085, 963805600, 641839521, 624929864, 83794675, 517488074, 880824423, 603134194, 80012002, 986015714, 801492014, 637065665, 980305484, 768983768, 840455971, 727897050, 375174353, 517974100, 379369285, 380906332, 347343735, 738502081, 59718474, 981624910, 202578375, 781007041, 103845964, 493143497, 237939440, 931948995, 664966527, 977075768, 603145666, 309091751, 496866250, 48587706, 871827608, 750797052, 896979545, 354057755, 523867028, 403308052, 735926294, 550523567, 177328113, 723723278, 9962562, 148117146, 801836733, 775395512, 723479938, 461919820, 534360601, 964293863, 672049250, 393697474, 201821347, 855446753, 268486740, 620006997, 134480089, 663297647, 797423188, 956885523, 63606930, 326468909, 484956108, 863482587, 808964931, 141476316, 32140488, 391212357, 690874676, 575571363, 866126719, 452028719, 24401779, 677328838, 170832327, 202103368, 113199675, 280395742, 101892874, 544642558, 620162746, 473713521, 661571422, 698285546, 145801470, 418855273, 574088918, 982073636, 824475449, 167889571, 126246887, 133924260, 610545782, 386024539, 968681641, 191442415, 163317774, 405067210, 12432547, 388168642, 933687216, 45765938, 747866310, 993747263, 904199627, 489897486, 252446431, 75439988, 500298936, 232389460, 401255352, 384888279, 277108059, 878952414, 500388978, 536762513, 195761990, 861513639, 272441806, 271640530, 114530081, 534190102, 657863556, 664934681, 406064019, 443643084, 574707633, 751730035, 749291500, 822168966, 895705267, 600488499, 45061567, 701884587, 670658856, 479882018, 502674829, 792261698, 716799220, 11477578, 775094978, 543728419, 510015965, 649775138, 436047810, 576046502, 264011600, 487684469, 216107862, 964933029, 220109461, 102463940, 331366977, 456413760, 742291552, 210127097, 316292794, 35394155, 534629648, 550974001, 314134345, 327596320, 914636961, 644989786, 824087229, 566642401, 537879246, 688297989, 485165753, 496076665, 350812153, 436250567, 673830404, 40736766, 212018047, 673057098, 750040048, 893345277, 579164109, 832929854, 476806419, 70627410, 575164470, 588342804, 444639659, 313240935, 660751183, 794009121, 39146253, 617419957, 962913493, 301849461, 649197413, 779391903, 296231693, 315864332, 513299459, 946044681, 142059943, 737567682, 354515474, 816876646, 653895480, 750330687, 135016000, 655989315, 778253819, 117830496, 536110891, 276794699, 435152258, 541452837, 419865755, 770059331, 809248175, 441207040, 629440689, 363103162, 262804950, 358810751, 77725435, 380780807, 321990455, 581584607, 353979206, 716825667, 347323621, 967615756, 818185266, 927809971, 45844877, 811596877, 183065530, 455557132, 568473144, 520746485, 744306701, 38511582, 395317655, 747666546, 173898441, 420063183, 638671543, 292332643, 4290255, 47534796, 141577201, 402317345, 285765154, 67321393, 879508750, 129527785, 211063805, 812426018, 864407939, 648440684, 809586344, 283462586, 490546181, 106809710, 887154897, 704641640, 57175429, 419516668, 453925474, 694132510, 714990898, 728090625, 153458165, 925469828, 673352539, 158083659, 921807731, 129454936, 465982077, 121881680, 731834859, 497030127, 11585887, 262079725, 242335707, 483488424, 749976334, 281441334, 340908639, 743493387, 193784121, 821054680, 470469032, 660738222, 605515464, 617223250, 921041012, 544061852, 606447389, 560686944, 569341746, 473870930, 724439587, 580576879, 186864263, 618731215, 382220571, 706927370, 116844783, 599049752, 816358810, 341458576, 993762186, 643832642, 351549193, 878319690, 313157814, 675390105, 613021447, 902346935, 773612240, 837519632, 407601770, 551348663, 179828911, 845558609, 580570739, 239092405, 659906574, 286162111, 625241534, 799484166, 307069371, 203824841, 885158714, 888487516, 145498669, 599238156, 275781271, 182287334, 704601917, 941583866, 303971935, 786180658, 431328568, 174082546, 368384159, 750043213, 460716096, 489765336, 538863803, 208370372, 383042279, 405984086, 103940697, 276588205, 349405858, 659711108, 146741291, 735001678, 347532159, 784709002, 337941224, 680596470, 476866253, 264588644, 421247908, 9629088, 474868635, 809107199, 791277029, 699223283, 966097010, 188745745, 556019509, 979549035, 280661432, 445930502, 227733413, 897289840, 769901642, 539495965, 574649823, 384673249, 9821274, 965748936, 62530796, 983631239, 956953355, 784473828, 591587807, 734395957, 732154315, 752058690, 754890589, 753346861, 626100953, 253269259, 846686672, 370894205, 695875813, 143354403, 748594096, 462021711, 766741969, 680281268, 843724923, 564923639, 86170608, 48063774, 463925756, 159611940, 827755638, 855123641, 447576814, 308410516, 768240902, 85167348, 891863376, 593550445, 151756616, 91659284, 147925686, 816162448, 352682699, 771998823, 766189763, 21686146, 94094008, 300550921, 495991317, 879543165, 525322268, 423421044, 582848555, 523827339, 394378445, 974530140, 221379995, 792732666, 604845103, 951761158, 635123596, 549439458, 695736124, 405932055, 667938378, 364629761, 124987569, 806267165, 109651198, 853036037, 969869759, 775826665, 630165675, 395802993, 438930179, 825968378, 638015266, 238530668, 897275668, 975847618, 575344910, 899420725, 240292786, 481594184, 957778358, 488594336, 423701155, 655842750, 744190433, 355204425, 719804796, 320323144, 540874341, 631144769, 127208493, 943382105, 508149375, 664234769, 208551965, 60954242, 14787780, 113953484, 420372756, 338793126, 467972556, 175219085, 745274246, 596192990, 546957216, 520116097, 788667782, 124245111, 585058115, 530242704, 151868310, 755381937, 593592617, 842446099, 518043390, 346056895, 594804538, 350894568, 936024453, 345649200, 614854953, 812296411, 535528282, 410218038, 551714040, 848288803, 734721409, 38360210, 212997894, 753074477, 341628355, 867582955, 673983303, 772734230, 217724226, 474086904, 976434501, 631321485, 436322798, 660757778, 715046412, 888699796, 725642198, 455003370, 285387900, 59536021, 768802554, 77731192, 704893735, 374474686, 358097401, 424731745, 426428834, 282208282, 888887850, 455314167, 444218639, 270615225, 616174293, 471754227, 585193473, 613523046, 531117590, 444175153, 478750677, 762210800, 609561862, 746139441, 297563995, 387422876, 299089565, 747227689, 665339239, 474383290, 72066139, 231720681, 165059185, 967399500, 756922632, 901960330, 474535312, 117041361, 689354717, 919135137, 107785367, 495430347, 98383057, 213814082, 764924316, 936873926, 212414263, 891102881, 733564362, 939763483, 898965792, 180595853, 578824087, 683455477, 940143008, 991708608, 118815651, 213396633, 601267071, 108565350, 209680856, 667227073, 306877570, 183684948, 703757664, 654732184, 11082789, 919075375, 214284444, 639199383, 800757194, 911032706, 284517600, 307867010, 512476565, 458605737, 463338883, 81869952, 254748308, 428719100, 537712171, 119725853, 345961240, 188289759, 855212890, 300236557, 306030675, 491322491, 763264827, 518583926, 397604121, 346269912, 116231541, 959198724, 684278264, 201805194, 197645166, 882982781, 750217832, 460900025, 905085342, 480665971, 267141408, 664601584, 86840672, 432002950, 72828903, 805121515, 818753799, 539666302, 26029424, 610585054, 311103501, 10582367, 605385892, 308124170, 250857540, 33308461, 204615576, 240825080, 587621483, 205072124, 779471595, 739695031, 582851378, 8535540, 585631720, 373272667, 19814036, 158210727, 509919023, 150345222, 791129603, 539982237, 766418179, 249953042, 362454016, 366720775, 597564974, 358744343, 929680378, 350889186, 831254566, 672467990, 614695485, 244314102, 18974751, 444563913, 387282519, 688241122, 328067893, 768161827, 455971518, 647819058, 284776112, 36797273, 98330035, 856171236, 773790395, 615090517, 203544914, 290347859, 86392450, 509471581, 417578070, 27621853, 348126356, 114898188, 852120275, 43489497, 571103585, 702683299, 531911871, 729993330, 918569018, 78022183, 674315554, 734645025, 667274993, 468801383, 111846952, 994078631, 702653499, 151097595, 754533740, 871908294, 264164603, 758484032, 249993012, 75089017, 689173346, 493058695, 99677002, 280747395, 219311224, 454572377, 288540040, 344604496, 48921070, 857740942, 386229266, 28413860, 573366998, 309844520, 463442812, 406976293, 603983108, 724089017, 280580487, 950159434, 223001137, 308605153, 280878560, 477412224, 932892890, 277068266, 132507881, 512757118, 429482766, 69559805, 298124437, 675101234, 263317531, 424879663, 321220075, 962530372, 149069034, 880999763, 909476792, 235659640, 158442188, 12824712, 28246261, 187300720, 534111262, 568769984, 198136628, 64586714, 533958522, 705191712, 211722068, 46735683, 477421441, 300060162, 404133203, 219350214, 809534431, 578994170, 888551589, 952350400, 141447911, 482509723, 904710058, 795467158, 14966178, 338547286, 491337619, 682996937, 585590686, 893365605, 644518111, 497080584, 122031102, 233105815, 211743690, 431598809, 124907463, 583340417, 319705953, 108807324, 733660365, 91933800, 619311472, 508985342, 675661337, 779451784, 318430445, 198470323, 511504007, 183178648, 203846249, 691889484, 801304788, 966112639, 424244303, 1139375, 970469802, 77385509, 613046865, 204029533, 466422754, 510337346, 87885620, 24246373, 785254450, 594398246, 149691298, 399238159, 167779471, 408467171, 227132621, 996662768, 902405899, 835191130, 246122022, 442259705, 642991919, 932148003, 567378859, 843041932, 630350946, 137534470, 425158977, 200685705, 705951386, 610286849, 837490004, 573443322, 468712115, 209565956, 6817447, 445679267, 491027089, 430817515, 464314635, 825479318, 444609699, 970627980, 366724585, 771653958, 259204253, 769731146, 241849908, 477454158, 246067171, 813593874, 229250948, 919298866, 676617379, 130902694, 957679197, 791739349, 881692727, 198773941, 331227829, 27371817, 953736673, 265115678, 439319895, 381039854, 983081836, 256447816, 235526630, 516517058, 19715245, 646063946, 65177572, 189813039, 284356091, 318445653, 727094028, 546555644, 302423917, 763368252, 173789155, 49133481, 890549391, 747671157, 42019429, 667031164, 408459541, 679990090, 906484157, 123686385, 229484063, 360360797, 159031440, 56263347, 392194706, 257348308, 257209070, 35628673, 311176180, 861736990, 529450672, 815771760, 151821931, 455750427, 906769158, 716345371, 932379077, 143178420, 253801520, 91261649, 786213471, 819591076, 11804760, 544769575, 554569038, 361593702, 295925448, 531155508, 530191249, 785124496, 599927477, 309592150, 475165929, 405090048, 222979893, 722198476, 562676465, 95178050, 733689484, 537481515, 456305614, 54159782, 909198190, 477878212, 204241186, 573807848, 241076702, 401117924, 800866420, 773463211, 780122321, 696562241, 339265480, 858813805, 148355004, 888926119, 493287043, 449190125, 947921197, 201553961, 153773535, 84152980, 242630344, 175733770, 122600985, 967513220, 80474389, 430382992, 103481163, 541792034, 783967072, 965865716, 517884451, 11617296, 953741971, 766344506, 371835628, 413821615, 921514918, 84451834, 543697955, 56722716, 382524813, 775537729, 223255264, 394814771, 719075779, 10047804, 873140682, 454141823, 177739019, 123923777, 990091604, 563459405, 576146643, 204811318, 575960895, 511568752, 161553821, 322747403, 543841479, 780594199, 599929898, 918985637, 894457881, 310007000, 667315509, 324032572, 633456999, 32038329, 327084835, 177081548, 565385808, 410492017, 18306780, 432414025, 8692023, 902262428, 941807098, 235213003, 450068587, 101724635, 260309802, 998209979, 18217590, 784263670, 62390105, 377263626, 635975297, 96914147, 785066425, 883050090, 307740174, 40577770, 401161568, 441104149, 656174879, 764678044, 865480386, 239825299, 759809956, 943137240, 195330058, 945992760, 425368340, 896778335, 372337557, 617200308, 319400371, 651950157, 975690672, 633172236, 309724542, 933340397, 436564546, 587506362, 622618381, 897951982, 943380215, 478243198, 698789433, 704515972, 673033998, 178509018, 308049715, 828906326, 148183757, 750166764, 626658849, 873753189, 593325452, 986795841, 922704083, 132859279, 439630290, 806113974, 914397116, 566027088, 748988349, 832612851, 682812821, 990222242, 704428362, 499686754, 370973613, 279045622, 912996563, 541995405, 857146946, 981614136, 636361334, 50699630, 288158275, 828258786, 94852105, 880748141, 253667002, 300065963, 719459889, 720432269, 2199432, 89965339, 286969232, 601350895, 203839066, 243332281, 993219781, 399565819, 421976412, 801638993, 654186903, 867509310, 478383744, 577651013, 966790123, 58823299, 996256081, 898485957, 2753082, 503876162, 851394136, 164869997, 870307613, 144256215, 997947833, 311623841, 413618107, 418462082, 624210278, 256032115, 100063104, 695255800, 746029402, 785234158, 258501985, 897733333, 874090862, 739652432, 690055286, 177521259, 803840068, 847128915, 218286070, 907767541, 707733965, 750919260, 847435967, 739629638, 481076300, 493364591, 644220746, 318278762, 242738235, 468254443, 227820905, 126999811, 962280915, 906734885, 280145803, 457175578, 345708214, 751909403, 992602999, 515865083, 735116508, 354440772, 506969833, 708086608, 364382425, 652467190, 482099886, 614814047, 461732767, 833709014, 919086320, 56670634, 82587728, 391993741, 595837402, 689542826, 335913364, 333283552, 236443452, 300238625, 621710855, 943689130, 312420970, 677244071, 98038510, 734109765, 439099017, 300813551, 684078945, 778708502, 815545753, 380024512, 793974883, 847689711, 820060155, 786650596, 846710749, 136926835, 907844334, 698978216, 874353568, 116724223, 100414418, 546245270, 381106673, 311078013, 618203782, 828429621, 360915213, 161881615, 606470416, 30963604, 110127436, 774402341, 716163855, 415358971, 68238871, 338275847, 19173944, 819449680, 895534012, 168400797, 212445067, 862081785, 938916410, 687135509, 544413254, 206562646, 31487612, 705492480, 944835799, 264353031, 278758077, 109099728, 911235059, 581854241, 837899101, 447905503, 341916342, 379519482, 954239979, 991176307, 5780730, 943520997, 971739996, 10312857, 818620017, 314352679, 62304748, 860165244, 929297809, 876256446, 67073294, 859695164, 906522349, 396357264, 954180520, 632151323, 632557276, 671459310, 169375963, 933851789, 103012564, 136787196, 415302259, 225073859, 645812282, 7324086, 415717560, 745594142, 90332009, 227525375, 576037002, 256197581, 930255389, 227178593, 289293497, 460256605, 8720946, 495202656, 493036684, 607451506, 736151403, 574204876, 419736582, 306713819, 437141717, 505029293, 390615347, 258538565, 222452365, 270869411, 618703098, 370141263, 202475575, 314301959, 931695300, 766202649, 251332638, 267494005, 306874503, 743087729, 347646784, 379559736, 487099985, 145137507, 829889904, 456828656, 472295458, 609949639, 672576043, 518823979, 247236084, 83485618, 107134139, 65746935, 170478248, 14901586, 250765547, 43393495, 697072245, 902572791, 672621455, 723170803, 783290476, 547823801, 932797348, 398669344, 471668704, 284928974, 891585053, 79456103, 773624198, 271496879, 873091475, 12617550, 280669624, 557991063, 419285738, 392674934, 580293429, 843121181, 258436860, 989330300, 915460688, 571980477, 716616776, 86983769, 386464456, 655576653, 599438198, 768596445, 953674333, 117507269, 685813704, 157307513, 875556048, 41707865, 267048592, 346926010, 808814442, 468718501, 864964113, 466065533, 31183326, 562981678, 755097958, 218351108, 92613133, 422103819, 512175581, 721148582, 636514423, 336202172, 557618633, 225569742, 952109925, 976371228, 688931258, 441524671, 340642498, 914259859, 355731293, 227502838, 376269796, 549855560, 29348373, 538637286, 89089427, 911320994, 282830286, 583304266, 387491219, 53552656, 955245128, 834869287, 384030298, 101884320, 225877630, 430940868, 775188767, 814973981, 844307976, 829920896, 445484820, 57150575, 235872721, 745480370, 525394073, 254413200, 319991637, 758535955, 899103830, 910809765, 659533926, 421426081, 359866845, 745947582, 267340150, 373356431, 412398067, 877638922, 104012347, 71728225, 499347396, 333052701, 492255920, 285459889, 614037219, 960367096, 421431400, 239969818, 512032502, 340969519, 724642848, 290829407, 388794178, 578245323, 147852850, 672547882, 790089052, 512293292, 223485479, 257808288, 38569657, 73643970, 385292738, 283156867, 315830894, 753579306, 435483845, 996899356, 516700334, 781279677, 418226790, 560632711, 900973459, 51679512, 35896445, 145291503, 102278971, 643714411, 525079841, 72914449, 721625515, 435220219, 57255458, 648335395, 115364525, 325091494, 707206927, 832579151, 646948095, 38602688, 274133007, 433839473, 948597451, 912826887, 143411705, 408365386, 801446373, 46814919, 279262783, 32228184, 813725973, 120197497, 782223812, 246757101, 569306526, 736426256, 157078268, 74461261, 629618743, 246716156, 269802583, 363603376, 78359813, 553671831, 22356454, 944511323, 3648544, 577908074, 619901143, 345050114, 958166962, 911443934, 279743883, 637856026, 71444662, 101467906, 198068586, 356174356, 477692265, 120970964, 749394926, 833177093, 430376071, 299359930, 606789760, 809587998, 665051200, 808763042, 235589049, 881211950, 495313827, 615148604, 243203649, 339782833, 635213567, 67953902, 882693982, 869786136, 118963013, 399291459, 586668304, 518271326, 85797019, 869507768, 505593924, 924861909, 685885648, 87762881, 24743280, 885142918, 582454855, 798166930, 637574122, 245266468, 165749748, 319924550, 883982994, 458332922, 896420663, 570984868, 703532187, 145652953, 923314581, 565088606, 137765878, 647022315, 11783132, 683725821, 729107591, 901913499, 735766703, 537468075, 7316772, 610298193, 990425467, 655027477, 872391989, 521038894, 912332389, 623823954, 566047141, 703374657, 569813891, 357955676, 175152559, 491923261, 70691268, 686188536, 621592075, 787387106, 31779185, 658267275, 101856132, 91062925, 264961673, 281466835, 813330516, 869405949, 140079444, 219073455, 422471171, 353136049, 958602967, 253266580, 734745048, 97642918, 680738093, 469188110, 50648652, 759168624, 368022167, 646796296, 993293123, 596748426, 516032884, 526056975, 547516421, 884520154, 111995675, 842839464, 446465567, 335497952, 280403907, 747808423, 217749982, 688078818, 568511844, 4249169, 651685635, 398924519, 305883711, 78966024, 432722336, 905047227, 950625086, 596347217, 360181573, 598699739, 343592825, 776832314, 337544029, 65611686, 480112840, 502939181, 890882570, 766959173, 134433734, 761549033, 123222440, 8904951, 80469718, 554335007, 525068976, 445062045, 299870762, 384092393, 229322869, 374478294, 669532230, 341171700, 974236014, 412848439, 677118052, 362274021, 267499617, 289685262, 86897179, 317980106, 924718221, 936251116, 542758387, 514289036, 617518098, 383076753, 846352356, 47800078, 703603826, 434381176, 528095345, 507334818, 677995000, 828072407, 653508269, 35662728, 277535641, 940608606, 581894851, 434442748, 616837013, 788346116, 258923504, 27352220, 560112161, 923365844, 234534398, 574786358, 756721261, 929170317, 90596045, 917339033, 540789761, 348169438, 803017782, 583113479, 697754713, 251819681, 373908911, 362068513, 763020655, 744093830, 301990383, 650045093, 234310541, 715181998, 953578724, 35508184, 100507256, 482490766, 677917290, 152593169, 682824812, 99231728, 439397253, 765591757, 698656495, 561163540, 192590658, 449610925, 86004286, 898127470, 802982995, 746573016, 124445343, 859877470, 656854048, 889034291, 127915493, 218986951, 518811888, 639591249, 622794881, 734951088, 450206700, 54624026, 384114115, 375844909, 475307126, 110744606, 57058763, 789519117, 402994241, 801328743, 173879358, 9602151, 904914976, 601430889, 708134003, 553784329, 91679945, 189603528, 361194506, 721316176, 738688442, 594304669, 991480326, 592433577, 687786728, 247118088, 259181222, 500501479, 805453804, 184355519, 685061363, 703248921, 55653804, 549732120, 613570417, 144192074, 224016329, 838588441, 516003100, 368419054, 470592948, 4200135, 767121973, 187922908, 25787393, 97660076, 107357025, 636114518, 630287928, 820627153, 580530718, 324018704, 461630794, 865834556, 589494857, 280294045, 661454242, 235498383, 996777835, 868859153, 534065376, 313577690, 828942347, 980269535, 510859705, 268587287, 154405411, 123394814, 493587898, 808870303, 766510596, 858775700, 841542926, 119207215, 523472998, 952150280, 705850980, 964943304, 417851126, 994157911, 865476297, 984939959, 120106710, 588226110, 48838281, 357823763, 360559460, 630010152, 170057895, 154844065, 258178897, 850741809, 690469377, 743903291, 846900819, 946529767, 152751041, 240825403, 588165091, 710040129, 448600581, 935174489, 435596162, 701903792, 413018839, 612853362, 541026511, 636063321, 155529239, 565016157, 750489472, 369461314, 574985566, 318019212, 375026675, 840463813, 536369019, 870753090, 807288828, 541054077, 861429614, 224712871, 349747787, 890264951, 143603164, 379202777, 902139172, 597117166, 877098893, 542932894, 737516327, 753812642, 590439328, 395799101, 411548977, 83663227, 319965553, 603663285, 429789412, 231134023, 915531286, 206707954, 217500856, 140926189, 307430219, 694910371, 234065564, 582185596, 980100627, 876351341, 137237205, 401876040, 417391014, 85527745, 417841753, 422469919, 398627728, 851727501, 96041582, 846682193, 163731882, 512135364, 226143666, 291647091, 989052734, 790168398, 403803869, 627422387, 436169962, 608577201, 336919524, 406077243, 791551768, 882608837, 199185112, 98387306, 610832893, 56067981, 638909920, 967617188, 143033438, 930946401, 380486726, 496651704, 112317749, 91939654, 784647158, 77981058, 28819055, 761436789, 544573149, 687023287, 411104586, 936016783, 902725693, 648389783, 86896328, 409496230, 762173533, 731240882, 639716434, 870411196, 396946844, 219100774, 478725059, 972810274, 634989024, 55752559, 161074447, 468167987, 195682401, 973323856, 881228938, 392853561, 929177726, 773635890, 325882544, 585613471, 34308221, 842166960, 689134169, 108927027, 584702248, 77521530, 183499988, 828116171, 135565453, 645842426, 249376126, 803521283, 231295354, 493640852, 238360069, 831130906, 106240137, 717356843, 959838107, 958545393, 112065769, 997194573, 628833587, 271685438, 709015124, 182047360, 815326443, 305921123, 538700755, 124325564, 911196666, 341035296, 55889791, 349496403, 359193689, 821038997, 711974526, 865983812, 446217209, 940454209, 386836723, 663757429, 756649259, 788786307, 877202299, 418897519, 65823024, 143339865, 665209955, 429325920, 688706365, 612727075, 196232397, 756881848, 620469114, 750996588, 851419292, 121827521, 109023486, 30905161, 664310173, 519608858, 102463743, 799335086, 715884402, 128670862, 231135701, 826744701, 201034778, 483375434, 76951432, 54498085, 24198638, 689342738, 214104279, 184114987, 628008926, 212278296, 332559567, 119748367, 270788982, 423177924, 492719183, 74842311, 53502787, 687125929, 895597307, 375249067, 149727981, 734511570, 396733023, 522362404, 40111475, 626505659, 24429577, 887007104, 392648170, 166581488, 17412644, 172348634, 374544653, 268946906, 565421465, 749861764, 694612257, 323056011, 427372556, 757327527, 315074870, 99477951, 585787458, 366397614, 832279384, 596021733, 541582396, 402786521, 438142609, 117230934, 927602333, 583007209, 281687737, 529408287, 862013142, 22903723, 473018709, 313999095, 631694444, 286210044, 190644976, 137349673, 452032664, 480368059, 41493546, 81530345, 263947389, 324884767, 92730814, 207901271, 522351498, 920791264, 339083694, 642598366, 200770770, 151132925, 86782687, 972810472, 38371485, 838746068, 970262669, 687176886, 658743721, 176391678, 926678887, 286640203, 424639370, 535332363, 522812700, 733303511, 819025563, 254203546, 495661447, 813440448, 565681879, 454951058, 642249477, 760576602, 524573520, 750292403, 930477008, 144628982, 877384360, 762644136, 478255697, 386736870, 371256919, 670363923, 710918618, 253297600, 341021116, 700165281, 525803569, 762339077, 378119284, 249285059, 49176995, 113983161, 471405967, 42548153, 71388044, 96871644, 921948601, 967438247, 899991909, 121381432, 195051003, 534737187, 426915975, 882135355, 115479022, 197393245, 24828008, 830019259, 854127276, 84072739, 878562607, 183494478, 495529172, 202252854, 618878249, 684285204, 174857999, 394594768, 36194637, 830501184, 492666623, 291241613, 90538540, 83681528, 894078986, 884134365, 516327066, 547861862, 190983973, 618872547, 974959359, 16390329, 575715669, 932815494, 382875697, 376351768, 888757019, 481996356, 367414505, 693342811, 431544534, 269540036, 45762524, 112536660, 703890508, 584152137, 870114965, 188143970, 279627017, 539978896, 942492172, 378520291, 458038300, 452810018, 87012725, 155480136, 755027551, 255665929, 697515414, 485198745, 500169921, 61692758, 880892948, 146667227, 192191169, 113642506, 274055601, 630768768, 242818520, 880879940, 178599537, 242651168, 30248679, 641328534, 344114937, 123962918, 577686519, 798231923, 81433761, 573796433, 14657244, 928780295, 540216474, 705923824, 902965430, 961766450, 535924157, 377996328, 673710417, 121058301, 503641644, 741800572, 484285137, 717625333, 975373223, 275809002, 855724940, 454621742, 40333512, 128213743, 934477239, 951382571, 354872644, 513979361, 127836362, 928972887, 681667953, 72603342, 958223749, 369447158, 754398494, 523873752, 876220583, 776160186, 37204103, 229403140, 584400732, 65991053, 240349943, 913936852, 814466228, 135652045, 558647157, 147280750, 687024108, 32119081, 413236447, 226552262, 377490083, 183931024, 250099305, 480033355, 947776874, 141504477, 869218218, 737838153, 786248243, 567874468, 258844697, 457034516, 803823245, 954604026, 93015906, 270920076, 293296339, 431178398, 738743645, 989186993, 758686119, 227015493, 862875071, 80404058, 235505307, 129808403, 477786700, 390202971, 426401226, 971098983, 1318466, 294576131, 658796871, 823202561, 783432026, 928585938, 592580621, 212015020, 21051684, 100816843, 803202429, 402352425, 847829072, 515798931, 490593663, 520265078, 767022832, 212973718, 863656128, 492068713, 741334154, 651484124, 506224708, 639909303, 704795773, 851886969, 815765483, 69287258, 118799730, 612307221, 638307906, 227564930, 87550524, 404071385, 720878164, 510305386, 708596563, 631376248, 786244915, 504700799, 195113075, 958703907, 128998987, 299935432, 763982580, 534088275, 775341216, 19363457, 156604399, 97398692, 358098317, 94353461, 864793064, 193244954, 801304616, 422179188, 18609657, 702538944, 455644375, 804166110, 354874619, 725559289, 371537854, 728702136, 541614872, 879157619, 96527222, 4992792, 607105966, 524571910, 489282775, 886724650, 87990029, 413769084, 407750304, 980209414, 143282156, 824912945, 979812530, 782672553, 946938901, 542632890, 756016753, 136609857, 200593133, 733429111, 312306426, 147281874, 720057337, 185773088, 236444216, 163840756, 679044807, 428609818, 708639800, 573090831, 22144253, 8006595, 584384963, 366240978, 595350639, 717674562, 144538414, 973873787, 117006268, 736323522, 874657829, 161531123, 126013932, 262212920, 937642394, 800568490, 229385832, 686852254, 678187463, 896145028, 11322277, 995550910, 586967847, 42027762, 124227955, 119989936, 548995358, 32148493, 816243988, 351461240, 347780445, 598636413, 966334028, 202043723, 343059485, 274697155, 132716962, 645833703, 293231516, 469193990, 669844276, 134209966, 977803221, 885635888, 645076861, 680161293, 905750210, 382244404, 657154051, 58252329, 465477437, 949045472, 72717215, 565353569, 442202329, 150416885, 180425910, 806440598, 700496752, 472575874, 625634540, 794279629, 141442643, 630742025, 270151357, 89320939, 115522094, 609118858, 781261738, 181078219, 205898034, 17716800, 666677402, 520104449, 193621784, 39404236, 261849737, 410649123, 69719389, 578045887, 122338091, 442399756, 346652265, 616006106, 129130688, 98051392, 899357890, 78825874, 702903752, 803833411, 507512156, 199892565, 117225794, 107502027, 189860438, 59049285, 247331086, 494515190, 470016038, 592263304, 44542250, 330313649, 627212371, 857829559, 646837820, 517407590, 239731857, 69894388, 434082639, 912371941, 798912541, 250699010, 334129407, 839568557, 897495037, 907988751, 4605793, 242607182, 640195391, 794707170, 603363602, 237814754, 519383265, 932591209, 4522727, 687136612, 580060667, 515809050, 340558574, 917900513, 247795243, 547534491, 206130375, 409836364, 448850557, 826784320, 36068113, 930024798, 364964187, 301672552, 752356018, 831251996, 431431931, 719637750, 699528467, 72712414, 285011381, 656349161, 878842177, 633393564, 193335063, 456252203, 848930410, 845261879, 830058754, 926403524, 483064414, 175458682, 539378191, 232930487, 48551418, 767290768, 592900064, 793043181, 400895273, 114048474, 540733667, 546599666, 606189113, 400659110, 273954745, 130456954, 389146951, 186504592, 867354607, 983459429, 503182813, 858681896, 382079818, 828327034, 108628626, 510587828, 410688368, 323660650, 305567860, 189475983, 62655427, 221226489, 633026643, 773810696, 413243739, 386245086, 718154422, 936390448, 811440976, 648358011, 885913005, 970247997, 409164268, 445159234, 776798312, 272912111, 745382075, 934683920, 472271431, 112542213, 165649641, 454082744, 779093130, 192411932, 747246895, 890650369, 816201396, 554479999, 657405926, 631391060, 17725220, 240651243, 647562643, 769346941, 562575702, 693426841, 410114977, 210602587, 473906045, 424978530, 17090476, 20143122, 341347254, 404835784, 394883421, 784702859, 982569628, 264434817, 332091746, 649056930, 298597370, 894449294, 212086646, 903959061, 512299704, 180874784, 927795459, 415793924, 32148928, 797357493, 236142254, 68157316, 498043346, 355000258, 957297719, 796702071, 50301937, 824815111, 717605447, 184413493, 458521204, 424393366, 659988263, 581644460, 617526163, 487980397, 557100263, 558433257, 732119386, 466336674, 868718543, 921935258, 467456033, 253946533, 701898364, 300193042, 795339503, 117771030, 563977367, 166374104, 559310467, 974810918, 210433798, 967191721, 806348191, 159020039, 800266296, 288906897, 386612693, 447427517, 540193709, 854373888, 545263178, 528707484, 376498211, 197823867, 746350342, 372046414, 9304848, 428498269, 508708936, 829406095, 854047582, 575193159, 784509484, 700338705, 797856932, 686874867, 277812071, 121890484, 652649452, 522248915, 660996843, 729257269, 657297181, 785895501, 790531377, 712901426, 882398660, 786763762, 302200532, 232905427, 242131786, 243032675, 750353461, 856809698, 310416912, 157881758, 570528522, 332631882, 850619861, 113442216, 515492523, 110625705, 925713577, 804636674, 711497082, 910210344, 467846005, 81707808, 196485890, 102970048, 77054936, 619196060, 875002861, 677501309, 147937162, 851134307, 581979737, 603264333, 272255826, 45836301, 111934118, 292671908, 665845360, 35785196, 657771996, 678236935, 670185887, 186490313, 401266000, 533921517, 301705807, 714811715, 475364556, 371982455, 588538782, 650332864, 15344901, 882951697, 243870174, 838295811, 633927667, 543037115, 895269761, 55161442, 134954311, 668787566, 317254621, 260494026, 794541592, 287554561, 996330560, 643098227, 254516012, 850379333, 810735244, 761288471, 530144560, 422894431, 176355128, 895342559, 296995766, 410449857, 460621216, 797161099, 942674376, 584376478, 12142913, 734121879, 559325576, 490233742, 67380643, 998039392, 257352403, 197200038, 556979030, 274937909, 240904141, 122785289, 801053517, 332002494, 786668954, 941529679, 571717269, 654967741, 458379369, 295236073, 864673159, 292354796, 157412792, 51264432, 623770813, 862011965, 659012116, 926560128, 925131506, 733517733, 816829196, 135007071, 475740969, 509543844, 588559872, 346247852, 825263319, 23454129, 779754430, 531343320, 56740682, 203454572, 370748058, 885237713, 249487228, 16830025, 202287877, 686441441, 438598353, 609596102, 20544705, 817664876, 711917313, 301631523, 953426447, 786862063, 609414900, 952125910, 79284483, 885311878, 701059060, 286133988, 37568580, 908007008, 689489125, 977471653, 191949006, 624421160, 319930479, 361465027, 660231948, 653463097, 951860780, 606593599, 688665613, 919199720, 427164350, 633605193, 693475075, 502972070, 883411381, 733027961, 125132532, 383617379, 14613829, 929298214, 277732498, 515511798, 299888294, 945484553, 308386660, 34093321, 642910523, 945086799, 734003204, 966452473, 926191503, 707252199, 571206033, 386204515, 439204563, 414457950, 823794416, 163443231, 917386500, 954327970, 302351588, 384666095, 69287964, 908827981, 426093681, 153523822, 929754867, 322856246, 946623041, 398007980, 772349051, 531402430, 248640647, 593380656, 757773432, 107123600, 494273323, 256490087, 252784535, 740480987, 779182029, 348815524, 92506094, 220111548, 958265452, 589559827, 276194762, 299510210, 150919597, 395463293, 551713000, 383162662, 495304119, 184165853, 173016161, 253856891, 23436942, 466849094, 276896565, 115080242, 935551702, 857115978, 790668397, 753394402, 882095470, 980244935, 837566740, 869676674, 556290661, 249698569, 300808064, 306382762, 568390691, 461256912, 629890416, 644376116, 10388229, 535814582, 218929843, 117329118, 138317604, 668594059, 130047852, 941334238, 264653053, 527665318, 690399807, 170651475, 190561219, 320950219, 321268829, 707064999, 5311835, 674143807, 671052109, 271970107, 955969100, 752540842, 666935201, 323520062, 602928816, 15513230, 440081474, 264612105, 364253852, 851947702, 284807201, 723614675, 619541988, 402765046, 189319184, 506569661, 10364297, 318095283, 824817816, 205631411, 774673227, 410890668, 362260686, 492163807, 58096837, 545789244, 424129768, 291779949, 202816729, 160815230, 600098682, 688052939, 603923438, 110866177, 469483696, 567356029, 56144603, 139691919, 25125892, 711823341, 706026597, 214322076, 727909422, 552556935, 175080977, 201672114, 684602251, 676214640, 895547813, 924228088, 373887531, 23838822, 849125696, 51386185, 89453019, 443250340, 826398219, 557572139, 676767524, 182656732, 272004253, 100384283, 213920344, 911587485, 171512472, 884755104, 863499190, 716912646, 218917237, 470470863, 978151965, 719994460, 392789838, 746896568, 565528958, 700327091, 912637070, 260738934, 901159775, 25383559, 898777313, 105632627, 184011278, 53415831, 987908091, 172193103, 775141728, 14414384, 629393491, 669008676, 139425110, 164093031, 34375295, 201885073, 533724498, 229687400, 859577144, 374632281, 992039376, 183575366, 838198250, 97820485, 252984999, 725131911, 658247593, 730130919, 771738654, 174032814, 208335643, 642550459, 360690059, 279769876, 461205588, 770701379, 164080834, 423645821, 3436909, 938241177, 90696428, 157686143, 795739806, 227141698, 715361790, 789564241, 473203185, 117104060, 469352716, 355106515, 947559194, 986871480, 2193810, 206194254, 861114017, 341802322, 300365671, 753588068, 131401054, 159242964, 740154011, 575505160, 800707882, 56472149, 769370482, 370114067, 24280704, 249123930, 469593142, 359101225, 786182731, 823880488, 618386067, 584754791, 336161417, 984779160, 253024868, 703450055, 185884033, 169065117, 125636903, 440256593, 115330699, 58448571, 70410418, 690943709, 639919100, 877207187, 400888349, 400101044, 34609587, 301443866, 561221419, 484925362, 358824184, 267608285, 498786741, 380043880, 326887623, 370476514, 703359125, 295297566, 586892482, 524400736, 868255540, 366228019, 792089025, 803774367, 298301542, 274634001, 298079900, 927655710, 833151029, 242276219, 371021789, 488775163, 880691650, 865497216, 873954376, 584722210, 275538150, 611344364, 615937936, 374881582, 683526010, 834336029, 519236097, 404856429, 985241904, 735471944, 882602934, 670116655, 837954918, 2310158, 758749690, 552090267, 703584503, 547239300, 178582516, 498225726, 389429935, 712678946, 890398529, 676266132, 76378002, 945527073, 424526371, 424226706, 126244702, 793666857, 333925939, 997244384, 686354769, 582016840, 185641433, 707120128, 76683585, 963956771, 634674268, 3547860, 110109839, 685422778, 520355495, 115068947, 204988876, 414790969, 11007018, 925320304, 320313054, 350494334, 84389281, 237527580, 692909767, 911582326, 195369799, 312038642, 668239673, 741637689, 644270273, 56516341, 89233904, 234773578, 225621083, 362401419, 459447846, 754366755, 505165963, 665595905, 680472029, 335092323, 8850593, 209977102, 98586522, 844981725, 797121231, 367138925, 65489499, 235918385, 842592418, 125798236, 640763357, 550193639, 121274923, 939000355, 668830247, 468379748, 252917053, 975962516, 905592146, 231632502, 237199785, 692643573, 776805346, 539834551, 52539945, 404781360, 548286411, 93797641, 732045940, 878697932, 620792104, 287412158, 891666185, 411367991, 551677129, 202839761, 278971319, 982666881, 299656124, 817538629, 212839192, 916063359, 289255812, 332907011, 134939567, 124326636, 339281820, 596246266, 995961351, 163990899, 19052345, 221697798, 593913479, 693106950, 789133363, 851959960, 47341069, 95825000, 741973644, 155336901, 719252191, 256249473, 114669412, 3071702, 123332299, 711949497, 647789171, 784391057, 83439913, 82925817, 427614538, 226377971, 552258752, 800638147, 500012248, 405738767, 928216752, 848331334, 973465234, 469630114, 515961746, 263923981, 345489588, 892162318, 352161342, 146093848, 912308914, 168340379, 990376730, 712771191, 139425961, 963902742, 63007106, 927265049, 118894153, 21693733, 286523866, 640757615, 553616196, 844144944, 71898591, 212496363, 481172133, 816248160, 261463911, 752324788, 534266420, 378293490, 547428069, 710701642, 155925172, 298024587, 255772021, 468140239, 835832918, 652909576, 711093926, 825401225, 971531188, 420102480, 592713741, 1013486, 60774407, 399205476, 327216084, 194375609, 539028519, 938647058, 871240874, 317501582, 647532841, 886662847, 804566104, 904263706, 29041877, 388653667, 304928158, 417417770, 950040507, 143956170, 475014765, 823747217, 433887367, 402959371, 824085671, 412061351, 293817190, 812386653, 569473128, 149872659, 819589281, 91637443, 255756532, 121735113, 285807954, 526937203, 10946231, 201895263, 927767879, 552088196, 687709805, 971188920, 353972469, 811588449, 543906566, 376240291, 892814147, 522896573, 964949146, 657248159, 616555060, 652004128, 371694713, 629693723, 244732458, 712204693, 944535774, 223141955, 618980300, 596895466, 65179294, 684859, 98587909, 455273739, 696176266, 570416244, 921505044, 857818985, 92565227, 120566133, 217596108, 751825570, 188425924, 694264322, 809271329, 283336736, 401761003, 237457963, 407585621, 696973705, 396599454, 592736216, 729276591, 679981687, 745071381, 432988664, 880936999, 436069016, 661379065, 790303507, 264831810, 228326870, 783464251, 790592954, 358997294, 988598376, 565740008, 523773854, 165933676, 361067053, 162809505, 665125461, 592508713, 278048581, 857268176, 796207894, 705411204, 637307890, 284036579, 102754394, 664033556, 331337097, 208155307, 768933676, 422104969, 198201859, 733445042, 665805107, 146220338, 538981044, 470191549, 30511616, 903966196, 963855571, 383851501, 545702429, 732632912, 742397763, 368618475, 343672018, 849611770, 945132334, 64607503, 10408244, 793861547, 320974430, 635650695, 758053715, 219716373, 603898221, 754234462, 538455425, 277692486, 584997298, 501991489, 776034537, 783690696, 144336123, 819200643, 728036639, 90227569, 381743083, 205951302, 104934599, 741103324, 467040576, 651085081, 856881296, 417060504, 342608609, 731449729, 661218909, 550181759, 881975419, 990643002, 332316701, 105337592, 674129735, 397941615, 325525619, 839960288, 511352585, 17291734, 321080297, 961985252, 274912537, 280503671, 258266379, 603707997, 74636347, 642291119, 773707299, 965150317, 972897033, 432493290, 577471192, 323790326, 777960261, 279787241, 53586365, 204518566, 424647918, 643528625, 278650673, 742141696, 767881274, 370481658, 654447415, 423508462, 184949083, 511367570, 999828473, 228378751, 804315359, 516603944, 345503819, 82813333, 124832929, 959134012, 386162165, 128511510, 335475976, 217988965, 811235078, 739770270, 488294789, 852987634, 232894508, 512784825, 65571665, 337163401, 762017806, 78947378, 353717111, 2081262, 212076857, 528280759, 168334527, 582020904, 862977946, 342372705, 887921221, 397557708, 843986698, 817070422, 684177761, 755254872, 850452628, 769755689, 564923907, 973140165, 625110178, 881910243, 772532965, 289624334, 743527590, 141218068, 720739543, 342331516, 8112642, 408333387, 704038156, 625027207, 954086962, 484450665, 380794317, 738160490, 655858538, 246727737, 989009252, 740826752, 630897126, 953447872, 465099601, 5733928, 243257582, 895362982, 690115236, 129112950, 795027452, 154703297, 930016915, 704011223, 903904096, 728399973, 484183225, 55270638, 613919305, 995108315, 838174193, 503238932, 843350489, 2001760, 636341273, 527770861, 67422600, 413738237, 92359573, 63195335, 457764771, 426626527, 790181010, 463021778, 724376448, 724658086, 329337092, 826924091, 470407035, 574185105, 288252850, 711146005, 996257835, 928072382, 117415377, 158451261, 526259110, 256546325, 804489956, 527246354, 878383250, 4586067, 523551093, 82393290, 627592773, 128418632, 369978365, 295007029, 588445583, 228558880, 6256161, 795573462, 374869837, 411178446, 231977079, 146204484, 569520851, 509801834, 721344148, 219712892, 867033560, 70319128, 8609220, 661242074, 273610329, 771947148, 449278518, 270195430, 796214318, 359366767, 293356226, 897884278, 822992818, 248697561, 897214279, 36103519, 315290953, 30618877, 72596641, 756818703, 823218620, 52310413, 863582688, 549329056, 343241850, 895371403, 381262912, 396444977, 937919271, 684530650, 418219403, 276409085, 589693729, 967927994, 646211732, 650964727, 530584814, 297517262, 66285537, 543711852, 287926405, 112618343, 773596359, 392176109, 967929273, 358835350, 494889639, 706872845, 561212180, 26832744, 230114702, 922690243, 599249430, 745657730, 478489393, 883034701, 38454744, 457240718, 97938235, 718454092, 875520875, 301435515, 656221360, 828355049, 151316356, 166724316, 628951763, 781617948, 64237381, 829980217, 750384341, 816685305, 796772438, 497467916, 332753961, 539129895, 485824407, 468932209, 530953698, 773318636, 317486515, 900188035, 203713359, 738485351, 727905702, 47057754, 217030670, 351330949, 429465453, 395516439, 220282097, 367375677, 398414464, 350082393, 752700514, 786986163, 345564211, 682824472, 705570228, 163045483, 180066924, 799052862, 678856438, 389278948, 398735787, 800376610, 167037551, 984762029, 221196881, 562156188, 182671061, 547491346, 963882529, 190193459, 1110446, 710812463, 420672611, 85386718, 721460598, 122447568, 75143481, 140697049, 585358991, 468867942, 67874012, 673863482, 409330895, 989323207, 65307910, 322509324, 504219159, 511295729, 589831496, 193087652, 341810248, 225795385, 210159244, 538688851, 530315463, 326817508, 385394526, 875894069, 433733450, 523239516, 915280976, 579862998, 306662379, 682492566, 775024470, 430041635, 217687455, 177906683, 720776355, 339641463, 179463188, 685971726, 893227369, 590326487, 325915839, 3539420, 923963665, 334060499, 241802078, 219735923, 957606031, 810666333, 995588246, 561372005, 384378788, 385921218, 427981, 923036157, 495002506, 937579468, 608611116, 512408797, 961144049, 867293093, 697468386, 420368276, 816698979, 627359403, 423587108, 973171430, 71844175, 347366814, 691477530, 939860837, 859178324, 719865334, 139507229, 229755081, 18691081, 25531176, 22087180, 264445177, 337162973, 119045142, 104568096, 532632547, 483136558, 427599875, 712246320, 820674524, 497678546, 966101302, 702012256, 999888329, 514093496, 551745438, 27476561, 321839564, 606295223, 975072537, 336550855, 605644813, 26968020, 632408260, 509432838, 57629648, 807046423, 902629896, 509459475, 902076374, 934347318, 380935914, 211767204, 719570703, 39667229, 201632792, 633900215, 775524344, 555614003, 5245195, 215913028, 991845054, 381791357, 337860075, 129817606, 962506428, 357306045, 111909243, 287689453, 158176134, 99521361, 509529201, 69778346, 417749885, 813725321, 905170004, 141512355, 655387262, 964831436, 184851757, 238367974, 255061573, 885655344, 564191656, 711997177, 11806844, 372504341, 772851391, 238698863, 208104383, 725704736, 542888538, 753875150, 541081948, 243055325, 256488091, 525660089, 682735634, 63267367, 566807982, 889087443, 343931885, 507053727, 96661309, 45186271, 857376990, 497697733, 703092211, 343203707, 449839449, 574827890, 269567362, 882352763, 166141675, 775845325, 483055510, 252797649, 14252546, 987304829, 752091736, 896794247, 966077045, 796917182, 735578417, 160356344, 498560826, 454032558, 466582764, 441120837, 53449561, 613312824, 342914309, 666242594, 874470119, 629013585, 820173864, 68333639, 605359979, 374331305, 947802535, 33201158, 687417906, 432742132, 460239727, 581721054, 864542675, 109662278, 884866166, 204559174, 128380750, 847933292, 143614036, 262084961, 548429592, 692355924, 125115599, 214772461, 915556746, 263170051, 112107707, 407460924, 261729693, 732374843, 99098701, 370900227, 920113914, 580510019, 745942164, 33884000, 662200458, 356630961, 927997214, 186104057, 302443488, 276332736, 685843193, 130451432, 632787439, 670510821, 947584714, 728888900, 167465840, 916376571, 656605557, 878560770, 227664882, 430905449, 52613451, 636528008, 108676757, 673723148, 44281621, 375141227, 456007693, 798913047, 336658430, 706525408, 123917466, 52924986, 621778052, 173942055, 784496669, 928512132, 678518106, 692914477, 154651568, 965291424, 107091235, 941956493, 963631295, 628021697, 415049608, 299016453, 991940471, 970877628, 905810186, 828827423, 48447458, 440341064, 483496803, 333579082, 830732219, 243260914, 312254342, 940220570, 978797821, 544347106, 265622010, 146779427, 258941795, 101541255, 724876586, 902122129, 342934730, 162967713, 830971807, 685288147, 925563384, 631545577, 717900079, 177025731, 46111899, 884295965, 332797634, 866666496, 438732036, 403636800, 482420913, 47405486, 526798576, 361843020, 793182800, 966657998, 687375958, 620613263, 129842537, 42059935, 347645417, 5209329, 697870972, 677177182, 741415556, 608321206, 4868240, 5140983, 889224754, 14273511, 528695654, 117566739, 659041225, 752487665, 902200210, 491470566, 372186077, 625214971, 509546952, 975620312, 904738432, 142491279, 456550622, 855385372, 65217572, 414631488, 251571163, 700257068, 298778935, 909601628, 134847508, 943013359, 91350475, 819857949, 505520374, 109646071, 83330392, 921627193, 613799573, 830367583, 183865914, 450484830, 736585194, 984911461, 184612137, 607187395, 897591505, 814369830, 807964123, 466392528, 812601625, 278303859, 582931928, 422036293, 676344049, 506045069, 23290450, 782947567, 751647689, 239220853, 579145666, 316941595, 61156037, 348129724, 507576069, 327179585, 152367278, 808587830, 304771413, 742616660, 12907251, 157975553, 791067629, 821032281, 313438289, 217860800, 161968472, 520207714, 296629206, 959112246, 925999894, 722318995, 974847179, 507552208, 856751128, 899386308, 627301855, 669136892, 273875531, 271154576, 679303911, 938261878, 865968430, 507620599, 715630393, 938621439, 468863667, 577406621, 709938678, 513757622, 8767479, 893874777, 989023528, 542300586, 41142485, 825224885, 499604675, 588641949, 236550570, 822119084, 931515913, 916402350, 981772949, 384782369, 383035324, 653546153, 765570926, 586250156, 481593092, 576402252, 644195090, 266305349, 3333523, 333583648, 724928300, 833646094, 431973404, 315377722, 892903548, 207538457, 211428012, 652682001, 220867805, 288770860, 170696085, 267775878, 163577233, 801459846, 617443705, 853759204, 397986448, 1817319, 28132669, 61596377, 904847560, 407211294, 716940328, 603476758, 755531392, 929220605, 423987892, 949732034, 684937300, 853708908, 373437536, 935736846, 462187375, 930130669, 226321526, 348565112, 140730356, 327677328, 685656356, 965525440, 369783561, 51220263, 326921455, 803567143, 117593393, 461892425, 306964801, 362532321, 122321886, 292918261, 864952750, 606945998, 404499402, 636141629, 783891317, 192728025, 700614679, 464916066, 199172063, 635931841, 332732705, 556236551, 671228590, 621339563, 751075276, 807299844, 147702316, 896261550, 411012987, 6772116, 217504737, 86874685, 701836420, 439459387, 853182850, 549562696, 678432697, 807525721, 323746075, 311914307, 710238319, 849222798, 165914641, 179993342, 574526264, 692157755, 986188243, 567685125, 93344063, 251373890, 384973786, 329062120, 650496530, 398016801, 836480893, 548848282, 749986895, 689501909, 734910336, 331967138, 718435175, 345552865, 678347519, 823047649, 17815766, 777182886, 422871773, 323137848, 864169379, 925800802, 495178734, 841163814, 647917344, 492765891, 399349948, 495935998, 987221222, 277162158, 954281792, 517327964, 646496145, 280733970, 931584775, 365316905, 606220100, 278763925, 967281200, 507908418, 651841284, 570987943, 650128125, 312011125, 368315566, 271075115, 41779368, 328120120, 640567142, 729970412, 839771216, 695564327, 727243926, 74471401, 147040049, 615769384, 737455198, 510837327, 914912955, 980414127, 613507488, 280384587, 453918922, 426743441, 334709310, 735703459, 377733111, 532305879, 515439983, 888363615, 408196586, 103497203, 238670224, 824245945, 872851106, 689977710, 753233886, 155742484, 890714950, 676735528, 268746146, 18453879, 231941668, 986899231, 923202407, 424571424, 984905254, 554357317, 674013784, 360238600, 95320224, 842154372, 151739660, 595467479, 350636843, 913941229, 302207941, 988260203, 527479128, 867145799, 18524058, 863031877, 352037786, 856860138, 611521400, 918782050, 68407474, 676516358, 562915595, 535911556, 445402824, 671510033, 849692426, 851538308, 800288517, 952248871, 260834672, 263353399, 706673485, 818207843, 393388716, 561198753, 465903673, 325825893, 17662283, 183281422, 879403419, 384787139, 972770066, 504656052, 249751655, 246972906, 285008501, 190683261, 544658635, 335255993, 726766538, 982962242, 961330207, 363543748, 515464716, 623083699, 599533059, 673533280, 372740471, 513497835, 187952409, 288963236, 927977193, 350805366, 857683632, 585423247, 735171025, 482062602, 193097706, 156745588, 746025430, 798770042, 796953901, 703742275, 565569464, 931175933, 932238365, 869621980, 161609279, 393961465, 642771429, 541111900, 546866379, 976414945, 589789530, 394279570, 369389387, 310898186, 664992368, 438018784, 777221319, 951349605, 262739483, 710938832, 485664760, 399012714, 293228695, 175173495, 243309782, 178635443, 591825804, 100076442, 944353316, 917788964, 242735823, 917210458, 965367805, 105255731, 244760438, 207478706, 916757541, 166667582, 928329389, 773220029, 21470468, 484111040, 315358209, 506375798, 783818592, 51633258, 425559960, 962879334, 414654212, 736845457, 556044511, 565194952, 963981796, 286870490, 882904701, 884904437, 164645608, 620000787, 211915019, 943086893, 303601073, 649860772, 834107087, 75332081, 986633302, 521574214, 535535541, 357061963, 256512919, 158246183, 782513755, 670692026, 110562129, 166216151, 290459470, 531327366, 12202697, 450154420, 37417411, 514470944, 557175186, 2622349, 10059083, 506542710, 563455235, 667154015, 195431374, 902638868, 72533582, 509172208, 957615196, 611099282, 758658307, 933361108, 548449852, 812004524, 295282063, 638828646, 145069093, 592724731, 903178882, 64225107, 381519233, 567066414, 475655734, 316999040, 872019608, 659966977, 808158570, 64068250, 309220431, 297520672, 973206758, 614882156, 947363894, 597509858, 427703758, 605140175, 237258805, 697568513, 812892709, 739347250, 246224472, 165156262, 672059802, 465868136, 432081972, 625209708, 138389005, 647862922, 109653050, 159878860, 687840007, 376071925, 382349735, 825439158, 962600484, 624240181, 261294654, 393384550, 567814493, 400262360, 135628355, 233292235, 187777196, 95780145, 911041860, 110755545, 146114685, 135226145, 873278329, 799651565, 793620394, 504559581, 396513566, 412973818, 842227914, 761192789, 201306330, 326747478, 385023491, 376950069, 307586660, 890676046, 221236049, 86729857, 89297300, 628499849, 515654288, 822502166, 159821366, 396595837, 41638462, 306555007, 55821318, 860531224, 312497755, 754342031, 756863619, 35142148, 666855407, 65567213, 102703292, 685175747, 878827242, 914038068, 844023516, 522376157, 543962942, 206592550, 804001641, 430700452, 363733719, 471508450, 19312614, 508247607, 62821975, 7170786, 577164487, 213888365, 107356287, 368652036, 97932206, 182659628, 867804829, 230468976, 143890603, 303256638, 673071097, 378337549, 704683824, 580488802, 597700420, 403691277, 466860313, 104250236, 736563030, 410195859, 93771754, 333398234, 196242538, 723022776, 684321090, 875663662, 604936315, 579258049, 342074413, 57412540, 448347642, 53255625, 372117799, 146731433, 223271603, 414966223, 775423701, 351886951, 17345633, 253529584, 609970979, 839491925, 748262269, 414297273, 815423927, 322728808, 248407595, 937497478, 50799004, 943454208, 771694948, 503909197, 127085120, 714057417, 480301838, 422037593, 355277857, 802338879, 860551672, 348341161, 353210988, 544356420, 273282437, 657118811, 300360359, 993246381, 55186378, 301889068, 338868023, 399297399, 222464718, 803252918, 356831907, 516197656, 608156641, 415489928, 616576041, 787483162, 514919657, 662336059, 590240234, 480348094, 785515636, 194509260, 789976650, 559802995, 82490330, 287843204, 127836230, 34175998, 461152455, 451175873, 992543721, 694243016, 97858192, 722761823, 451331105, 377701253, 842540146, 483269177, 990302980, 269862915, 29361487, 518441331, 883550740, 672245473, 598810501, 766471434, 317125177, 185132043, 828371277, 450896867, 374441710, 129890948, 251123035, 654662466, 329477871, 391748870, 709415720, 725378100, 595896093, 577474583, 227691279, 566472784, 161588762, 439649828, 713233366, 156466824, 725552744, 105093141, 139309219, 753926373, 159393717, 821764935, 182429321, 455658034, 862126290, 680556506, 128267436, 792113162, 556183367, 278316960, 76358831, 925802672, 462022242, 20816971, 266852361, 812813502, 35494277, 116294256, 243953948, 62383998, 919362102, 414347981, 698674207, 177040325, 929396284, 927420399, 670934955, 204368332, 72728453, 533379806, 59897559, 738881577, 491821035, 37274133, 954979497, 467362480, 939431322, 126143930, 306014478, 490211051, 661840435, 522417360, 650952251, 125643399, 550154968, 974194070, 548086823, 736921016, 120536368, 982695380, 841193275, 571635723, 339580701, 354131573, 562342266, 718781416, 139959902, 795271031, 532642224, 616696039, 132499817, 725179738, 132250691, 134680038, 621580356, 133401900, 631901138, 258532864, 602173040, 922277045, 232449869, 468108896, 904545359, 912510800, 292605529, 319710507, 616262323, 179741435, 277526638, 647599342, 968385919, 623852017, 715016270, 255616679, 669042204, 261152956, 569933564, 487994102, 100195209, 991651907, 674480319, 17671917, 888307642, 709736875, 16094472, 927261081, 951429620, 695178549, 153404514, 318057451, 219548296, 921851417, 246788765, 45678461, 25392427, 84915939, 118045914, 606446495, 550664967, 696925800, 106905471, 673271012, 446059110, 125696505, 622973656, 506752110, 372255741, 731067297, 871715639, 207389883, 440597080, 718869010, 867145768, 699643026, 53012427, 828810218, 953417999, 962093280, 49820139, 865186507, 840913065, 562967476, 189713967, 612200095, 653123309, 936216482, 300003401, 382484335, 912424407, 454842838, 206784964, 210803602, 169780818, 913153055, 25730049, 765893610, 817967259, 836236904, 715244403, 345471510, 719379111, 138771704, 240456471, 836160923, 630241370, 585659802, 965006491, 606212719, 559892531, 813270003, 953285584, 954738878, 398780134, 491797067, 196070751, 30734402, 582330077, 873385097, 276019624, 792423762, 404996833, 66991656, 800488940, 978862522, 573885446, 444927759, 488370976, 725564258, 525378740, 206073117, 895751671, 513568591, 575146290, 801020163, 153939708, 701822565, 29415642, 147274561, 372337232, 344881871, 725232511, 282836835, 427889208, 594295715, 90920978, 574992829, 965458303, 979334305, 150970726, 926985069, 93313239, 311839932, 628538367, 560850291, 906739449, 321018781, 478189060, 703320326, 542485977, 960838188, 827199462, 729174520, 328269568, 9416128, 392891245, 975518857, 902802009, 493950846, 485897931, 388694182, 828095717, 997940520, 835422395, 182410677, 577993483, 124900810, 973795488, 297362192, 947974849, 654943712, 76807749, 383155613, 45068398, 961555419, 97454001, 824323548, 21892715, 462047209, 551898405, 536181610, 406959132, 2022367, 838788790, 937985800, 198330857, 50857646, 635370626, 709564852, 359118401, 431034979, 770537383, 407545146, 879852158, 746048119, 790574033, 62090209, 805501350, 638953472, 16929916, 554556026, 485893822, 577567335, 20011047, 43949853, 440986614, 317927230, 845619710, 346202100, 792951421, 231715927, 430789907, 382013043, 454638443, 79141805, 146641761, 948792960, 761121113, 584427166, 475533776, 271762417, 282299545, 224525062, 592534584, 307993360, 96993973, 251890589, 480935123, 719086222, 127839012, 537193911, 463358493, 912539409, 678038304, 896687576, 930951395, 429517848, 529413745, 168646457, 131380211, 949185752, 299734683, 774608686, 120890007, 206750997, 610789159, 659773331, 803867580, 4070307, 565739202, 586297073, 431836354, 502945033, 913078152, 199212613, 419119997, 53494285, 406822787, 840619486, 542561087, 55753983, 376481584, 869820666, 692413229, 878282770, 693189852, 117282256, 936026989, 900270906, 539474062, 959848178, 705472183, 550212659, 63120076, 152714814, 512191896, 321774801, 80234256, 439327978, 213850452, 199521423, 583262231, 309520958, 7458679, 427548701, 962354831, 331075675, 736516847, 504917058, 949844322, 591420072, 103226815, 829413407, 578556449, 65028388, 937838313, 413655885, 932056486, 550754389, 627002354, 38715074, 952737156, 343331458, 850857624, 462808980, 249846062, 815181240, 553410999, 51353566, 829953527, 832836200, 390862773, 588423712, 234380913, 21140648, 888049316, 590932602, 193474187, 731198987, 178261195, 422215887, 22161311, 918150389, 98363505, 304750254, 775160915, 748813299, 888936753, 975674869, 791372948, 261768166, 366367268, 833977360, 903836845, 538831750, 877399850, 724440977, 81028744, 514046045, 449734403, 852824571, 755863233, 913071174, 32015252, 67735087, 241725304, 825256124, 263466742, 105862359, 229188140, 69674825, 959703933, 184739787, 104857265, 360110604, 172291613, 657303771, 594117146, 786209409, 649368393, 142323769, 598074901, 642497208, 850712245, 449117504, 924090723, 311303975, 86471626, 957128087, 307636187, 224348021, 778490230, 177226794, 878784499, 434279650, 799066092, 932230706, 749980299, 294726473, 594770591, 64075141, 462055350, 245486151, 458693226, 625232856, 690656400, 693347310, 152172992, 687942079, 165364143, 344143302, 269942848, 682463531, 370387228, 201772087, 850118303, 488422511, 287636886, 610329869, 604963845, 950233790, 605369319, 417673360, 182754982, 364137830, 445453674, 822434528, 58028962, 50192501, 500423635, 515476004, 287437877, 213415261, 798258502, 267715729, 297102363, 857549056, 360203303, 399321014, 577907653, 197569957, 514062756, 479049688, 556915325, 422672674, 409208153, 847125032, 836028361, 923798729, 551219576, 222722018, 96774116, 899179563, 696294447, 477373903, 18678865, 237984059, 92449112, 297921852, 649388729, 956342427, 882508792, 318120640, 413826079, 9454921, 877826469, 173185104, 928851617, 416094014, 672939398, 225470486, 557442414, 611221464, 976706464, 271799796, 94294730, 716786475, 310803584, 638182394, 183960417, 695514379, 885879099, 107720650, 186182789, 250026995, 280020283, 76420703, 955560919, 531732511, 742063632, 421549993, 23794491, 815435499, 899420609, 894697455, 308977943, 409682565, 953966981, 845959232, 757276263, 170963806, 174746853, 515567906, 61851228, 683548355, 455684336, 503837235, 908111441, 382559935, 734148497, 163474539, 251313913, 593929182, 914035840, 741426018, 484275440, 101078067, 565257844, 790367200, 975047684, 315457372, 268672743, 893935186, 602049132, 594883844, 261090636, 686161276, 260536313, 114657040, 265655511, 859428281, 620927296, 357104793, 127999587, 528036115, 504060758, 390205724, 49519050, 236231162, 579017028, 573148561, 602832426, 123477662, 893180198, 420606001, 576025693, 545184154, 322002473, 772694971, 635880122, 889372374, 140059846, 592528675, 618381145, 972501440, 679744595, 706857648, 70517202, 801546712, 360082611, 855297501, 332981644, 135861643, 948584676, 195016185, 841296920, 92691147, 625719786, 715403342, 793382441, 891571979, 494676887, 178953236, 772586429, 797545834, 131530038, 824063199, 648749593, 396134014, 879079759, 544981313, 809057362, 295925563, 851548557, 882005760, 379391529, 494681807, 529582596, 24352541, 480385504, 802293081, 28933014, 670800688, 736386947, 163083564, 787465926, 308161638, 474970363, 165422410, 540966349, 473922264, 789379162, 602905140, 29525763, 864132490, 827054349, 567594109, 974077822, 918631251, 748627277, 552622901, 868457007, 387537476, 500835174, 42999583, 510276131, 468544731, 922105632, 703148261, 223093264, 290914943, 360903012, 808871690, 551472416, 93487068, 304746644, 651899534, 744571298, 59760269, 338075033, 442245362, 669333552, 846169696, 625230961, 43720975, 725991525, 150610329, 109902176, 894789356, 901356879, 86041650, 255044134, 489901726, 57934755, 478027223, 510300207, 718556948, 122390583, 340971669, 791528005, 791642135, 916677134, 587039302, 223143268, 427028684, 920543759, 141239830, 902775575, 438331654, 77592811, 497831543, 697969883, 380447130, 101590042, 991486521, 882711439, 375429060, 427523982, 484668075, 392653054, 378280357, 142471161, 902133844, 417908999, 112275433, 55541630, 580359748, 2579793, 692918076, 332181287, 240821764, 365568680, 999055481, 375828697, 430429207, 80445937, 157736733, 291447151, 848922316, 644864784, 274270954, 58870265, 656522520, 303179671, 982078013, 341299424, 843155127, 265544850, 866442118, 122780363, 73264437, 669102759, 513490872, 388633243, 856546026, 426066722, 960112328, 366387458, 655908072, 118995343, 656876664, 349901681, 518416784, 920908668, 298810290, 860109350, 373611284, 246105474, 692143553, 679955775, 490926444, 89145085, 474371058, 623701268, 768331460, 442535044, 225663977, 97256986, 917957892, 769254183, 874660980, 563840853, 509491020, 237153063, 765745512, 506056267, 48653981, 359539806, 275537756, 38178387, 220384917, 418269366, 35949142, 170124951, 678430212, 660896084, 477818635, 33440603, 736413998, 846229145, 596999950, 22908318, 623322361, 526637626, 382969582, 45510677, 173158146, 149643207, 806652703, 844890568, 995618685, 562121942, 713870105, 471393732, 122306293, 906001765, 977403912, 281679702, 396087277, 104022854, 729950011, 158482011, 413936961, 145861227, 589524721, 196498383, 945125978, 778840891, 927192804, 553237091, 582724684, 435066004, 848124046, 806841841, 179482270, 938357871, 940960657, 681331578, 856466513, 780917522, 572807110, 800935044, 668587563, 270579109, 689296916, 426664572, 209038777, 629438671, 740847525, 243931050, 286804946, 271411508, 449991910, 19579812, 380101752, 346949569, 700950164, 295845279, 346573452, 853809968, 362279082, 263238406, 335533477, 256804347, 113221841, 411863520, 696059229, 978247799, 937146569, 615221553, 425689348, 569692831, 164497101, 28760116, 35170843, 849438523, 464381709, 23496277, 708409833, 816016953, 211784693, 681998359, 265562169, 862351221, 53895135, 110749751, 189366355, 458016648, 914735235, 305673403, 112063273, 892514113, 647109866, 385282949, 678868584, 173755354, 979252049, 257696751, 583999676, 419021043, 291421348, 459890644, 174515240, 838950754, 635715843, 816266565, 451117552, 697044058, 267347031, 509496103, 438632197, 664129374, 267786559, 999988406, 222594781, 170890468, 669785259, 58767560, 82490766, 295394215, 340416587, 328160299, 876210545, 569026961, 271227664, 484508858, 380466881, 593687585, 515445101, 884607182, 830330772, 884881633, 832441720, 747898399, 3229113, 253193418, 102312130, 933574694, 700834099, 552744517, 834837095, 592034112, 861878636, 89113126, 318683368, 76080501, 131247026, 472277263, 612165130, 146407119, 491404351, 33140036, 812650786, 833636391, 175532900, 11410787, 221642424, 225726032, 16199577, 730697789, 47299306, 849508960, 547425699, 756702905, 37218155, 413153602, 749134700, 463049404, 639826454, 322526910, 565698313, 57972248, 891808868, 745333651, 297169017, 221731436, 610503549, 529560538, 910624439, 337810349, 566208915, 496761965, 340334774, 189486215, 569166217, 893540260, 420570053, 681009828, 134687573, 935819461, 22431093, 59810368, 46271250, 635244432, 33822921, 111662789, 645306687, 322000569, 106900229, 582040792, 8558176, 745783361, 643991511, 943443875, 80616342, 755726329, 801095401, 567797673, 23165532, 437932443, 370378708, 855670484, 323610745, 986613348, 570752383, 616938139, 973788536, 118617534, 61284944, 671060146, 638566345, 271293889, 108641627, 216402146, 222933426, 364173747, 878516678, 41436647, 52581966, 114588395, 421462450, 593570615, 508849246, 707337387, 23045369, 409086967, 289615209, 822395435, 30459718, 589896569, 532852310, 831259072, 188530285, 132476819, 894020571, 957011570, 863070426, 344207408, 719545525, 897548529, 794241038, 403847228, 226664698, 486630030, 243551878, 177705049, 788638744, 375483779, 623919993, 484686409, 359050732, 60115686, 217792579, 209914474, 719773135, 741557069, 926072562, 199356779, 532647105, 269289449, 253720596, 734598550, 582612548, 508522084, 798131602, 836162846, 261947169, 80887185, 481765568, 808957605, 233341112, 174532100, 527213396, 380506036, 694645269, 435221560, 192020083, 112170336, 586136689, 550320929, 934717110, 883443240, 104377574, 346229154, 547853856, 227315308, 617077367, 405499143, 791137300, 161214118, 149655063, 789678726, 609025524, 101534747, 227319533, 927854357, 483891088, 263693586, 381816685, 619768866, 444687956, 267810880, 672862845, 96322433, 425748807, 191982598, 975864253, 566899027, 808921158, 509520019, 800934126, 622993991, 757575450, 679517412, 406996994, 223759218, 425150134, 704670356, 969090660, 817323005, 611032328, 540193121, 80260659, 300695124, 592908519, 554569615, 748420990, 510752135, 178267781, 185197061, 392950126, 777661589, 169373280, 268116388, 558259098, 849126637, 893699919, 364502658, 797499055, 648727080, 777315420, 859885907, 977671, 729114300, 861052047, 599027055, 684584813, 952021014, 572832108, 270655895, 770432824, 655902634, 958215875, 759052034, 889103645, 777699907, 119693241, 197323977, 163167172, 240923419, 998223676, 688654386, 905455570, 267808759, 675078755, 78702938, 501594407, 301483184, 990669856, 562346556, 525247745, 78694776, 634494599, 990863233, 399772068, 467137372, 539477975, 539893781, 907270772, 517054872, 342229678, 577153080, 118716945, 793541871, 175889660, 742169903, 824866783, 764202370, 341638149, 272555364, 256038661, 818026834, 206219895, 660526284, 546425021, 669875083, 428257594, 922026425, 395880809, 514302274, 215202276, 292717465, 701952018, 924049309, 982972027, 183514809, 784888606, 367764930, 830341804, 959376958, 240700952, 987151047, 276897144, 257328355, 62059373, 298862164, 775406097, 263023461, 714155813, 355389851, 706922876, 527305550, 816803612, 573397867, 706171104, 998248572, 105525242, 637966487, 867884850, 374737137, 254598591, 992191949, 494355012, 650279770, 890050216, 750096877, 768812247, 351381790, 21336459, 152546403, 301009784, 809601220, 165299693, 682072604, 75780094, 556530263, 86037918, 868245776, 86135543, 977954648, 847844910, 957616470, 595731750, 625431756, 877605299, 652053729, 68004195, 657366566, 605698916, 687483048, 847128228, 611532149, 247058969, 502800635, 359237107, 132766522, 394800593, 433701011, 608312920, 790665767, 199049055, 162400610, 198648697, 315865499, 804011856, 299160121, 331366928, 614065540, 73498616, 252647673, 111525598, 731024250, 23545289, 221839951, 659913653, 31983814, 184866876, 157545719, 567400368, 428108455, 753755132, 694881416, 52601039, 94657286, 972483618, 539546715, 846021562, 862246928, 277726825, 181304936, 308139323, 112996076, 903538616, 991802909, 252977574, 389739649, 373565935, 858055871, 382597359, 516642787, 784113483, 370889977, 239714900, 26527836, 832000885, 77440570, 192810180, 520772662, 679949585, 262245040, 736864065, 538395783, 279945631, 377286611, 665571858, 427511582, 382355064, 286428078, 914230893, 313841736, 373976863, 790662242, 280758155, 644820097, 639635973, 997026504, 230336806, 923298016, 176786927, 954330606, 688534606, 508469293, 500246961, 971312811, 643440248, 594136567, 208585957, 958099608, 55617077, 638294611, 174475794, 238421763, 132811289, 852457402, 227173147, 697812858, 750256834, 938904932, 630172088, 905779762, 426287245, 61424845, 46589493, 474201596, 104782945, 488590873, 65219071, 904493511, 256591531, 675477528, 219466306, 3191245, 783381087, 62023216, 767397190, 357486399, 552704238, 635261241, 863708140, 455619179, 881171605, 194380279, 284990574, 668978610, 16722076, 352753313, 686498855, 69588360, 483388608, 592019676, 152449075, 632289330, 46686115, 22334888, 401812235, 561225612, 417222739, 871570661, 181490328, 824548006, 910844214, 570293291, 822789409, 388620731, 607370620, 488110977, 604539537, 406539653, 593537534, 267313383, 615246006, 223758562, 251527584, 134740527, 617237548, 540729956, 65568396, 356862265, 347537840, 361825542, 847055521, 863243345, 815521361, 904932254, 155307397, 38152354, 750949470, 64578891, 290961980, 702302331, 57215790, 542042082, 732348626, 871690236, 803008029, 27243089, 802074336, 944612950, 85173852, 341577120, 939513957, 871589899, 104921573, 252210722, 916830574, 144880165, 309404509, 10520903, 937231707, 906300688, 861693006, 913495696, 959064547, 178043757, 461776929, 795176341, 204697926, 428487385, 156642327, 216954992, 855812007, 264905576, 898523719, 172967457, 330219863, 308897842, 701002162, 456124493, 858006795, 119794056, 266720267, 917463804, 29202440, 373584338, 262923347, 864331330, 257310566, 227227462, 881645935, 147961185, 871823754, 262741260, 368709204, 255333952, 936697097, 673665811, 306392773, 366022215, 20362061, 538865308, 743540635, 845181938, 581059208, 73801192, 431463092, 569856744, 535968029, 961709438, 417909612, 557110770, 685380008, 585590982, 148051300, 59449747, 184510360, 976733928, 842812803, 878069915, 294008694, 232562664, 647725841, 948690189, 476979027, 613291767, 965467044, 738212414, 792459550, 730296964, 420932610, 876909443, 395481094, 765516482, 940688304, 382604530, 700797402, 755255102, 505127653, 758752186, 282258553, 366814549, 965519533, 302173242, 819225849, 17538995, 543679805, 615952680, 889376149, 72453230, 978187504, 808341255, 336109789, 804518323, 246953379, 100467285, 810197835, 597289839, 404909490, 740582895, 414885267, 461867150, 118123321, 91553301, 315370497, 217691946, 801901056, 476875952, 817789315, 361079602, 335876374, 647367689, 841088488, 790779804, 5275271, 279458829, 885225452, 462014265, 23928883, 175043344, 77395715, 643032027, 468656387, 37935727, 524241176, 146592861, 874597009, 20701612, 719983309, 309818106, 715373130, 345220682, 727761005, 32907920, 541867425, 117521694, 728040076, 562015964, 487015712, 823709020, 834093130, 843066271, 185417573, 827379114, 812851873, 58624793, 44135541, 201822202, 546341783, 788926217, 627778020, 895468925, 711349448, 47181349, 946061373, 378979777, 57985429, 712440820, 469776039, 186023934, 288995715, 253106443, 706870640, 453537373, 650312705, 42987794, 501963925, 294083941, 742463742, 944653056, 135074696, 602085554, 645307423, 345973753, 434830860, 740572448, 425598107, 47796870, 104055513, 237407060, 600356678, 422851696, 703862515, 303868265, 710923478, 282519353, 244452129, 376392282, 583563983, 335014037, 430138520, 440399582, 540320207, 802732207, 513609491, 530580632, 799205168, 594415393, 257756904, 438652813, 731321686, 585646126, 20433313, 499902672, 793625048, 557788128, 950439462, 614858226, 526326967, 376517218, 986852469, 661821021, 162790339, 423224015, 867252221, 688767718, 905195383, 979832354, 926342, 513140539, 146774733, 30480620, 871676388, 766778603, 276618508, 685931714, 48074220, 121904962, 593775932, 176714053, 154228014, 547476588, 960274867, 272467977, 954824831, 426164462, 933919085, 819191621, 767321521, 733479587, 354711320, 50167039, 455204682, 380399663, 388198494, 247140754, 938758210, 999296283, 921683319, 202652742, 898864017, 221592622, 905353448, 225455592, 523518978, 357742392, 400884416, 10793804, 645844696, 63195975, 816644688, 143723842, 755500796, 458045696, 864093995, 349609975, 103868379, 363145758, 32885992, 350617580, 341190433, 988056144, 983254987, 328804225, 130316880, 707770514, 960690764, 720715824, 64726230, 142486196, 42660564, 81999741, 926314961, 285652856, 81244517, 400923165, 933608232, 838228802, 863808945, 292726490, 95888516, 106174765, 884728858, 805286213, 924596322, 364909355, 312453135, 58556198, 475760994, 759456845, 640393545, 394806891, 271378319, 777832901, 459216024, 535686774, 928547057, 669508747, 175136864, 357140296, 262533851, 954946265, 542859152, 337968539, 240870555, 339891049, 842939654, 335373483, 364503881, 948074396, 121212224, 906917464, 148792201, 944719528, 218038449, 962271453, 527296703, 593739983, 439647511, 944133501, 239928609, 424951142, 729979366, 490154220, 411779860, 675757626, 637586870, 997374406, 648649286, 333785967, 633628682, 152176967, 111302038, 790663726, 878378946, 784952516, 783346662, 734341211, 163854710, 184215227, 860824763, 461504668, 275948874, 587313879, 172028707, 380616207, 4854961, 903166800, 478292151, 652415167, 832736343, 792119644, 286386691, 443612364, 558742241, 979811903, 489767308, 886307157, 413298013, 637116072, 881451303, 476296510, 229974077, 231351212, 102428137, 851633656, 271270140, 723606952, 137985012, 339045480, 492861830, 920207490, 17655769, 513210791, 969631261, 678780141, 242235759, 974904683, 382891123, 969785454, 44254198, 945573140, 276347297, 571758059, 620688322, 854012415, 149203362, 288545123, 719405465, 575194347, 839963947, 333656314, 107911954, 641153850, 305107725, 139492512, 140271599, 934922414, 554781901, 79445336, 288349742, 21846252, 582995359, 900564262, 364014238, 349163317, 101275264, 556431842, 196481360, 509899408, 913291135, 534032792, 864085374, 993207004, 404401271, 416084212, 851397485, 889264798, 393432764, 254939046, 500088634, 391749903, 799962484, 512218167, 63045186, 338628896, 134895936, 932291323, 847100599, 783040082, 255059353, 499231244, 19803088, 219534874, 281715732, 350827571, 919388412, 763911278, 811507248, 967457671, 463783596, 405462859, 83671508, 707980976, 75754444, 780568240, 104920124, 280854818, 71941528, 87438449, 466081219, 646554955, 94907738, 92730718, 140679967, 301621052, 681843489, 488618075, 929056554, 897884036, 269574864, 251481569, 882836901, 54757121, 537315303, 749064830, 773632894, 323831670, 327345157, 546203354, 726038804, 577441912, 184867829, 61320533, 172715325, 131384118, 8206941, 807348312, 673766361, 620210431, 752117700, 255202204, 462819035, 856044648, 310897036, 379228198, 739633029, 645532659, 508124446, 440227237, 701263479, 379652037, 256763431, 733767303, 381672383, 990740156, 478696284, 576365973, 817918041, 80389948, 739325822, 888983384, 968023425, 545621054, 255727435, 47250795, 75992063, 649280649, 326321271, 49148758, 787811090, 542095101, 921284817, 356162751, 146858006, 326998335, 209930237, 384744294, 956205147, 970408015, 369415614, 431160206, 28799992, 287130106, 549849972, 464680213, 586256514, 936209229, 1077451, 674079471, 41266695, 723293709, 904545606, 622638545, 923256319, 66552118, 654027359, 374666048, 352429791, 929695162, 66877260, 156208268, 495063188, 784327683, 340891109, 981661271, 760044406, 513192161, 896114074, 901023882, 737563546, 701079214, 558346813, 432021845, 275360716, 546366262, 209335998, 261880141, 54476857, 950119050, 563480867, 249995074, 357763786, 246322668, 57094861, 808073116, 861570097, 375565043, 367029373, 34066056, 945074217, 424091677, 144377661, 623582268, 472284407, 218698127, 593120117, 159943046, 556981317, 340346515, 351304074, 156117030, 824911340, 822775855, 934855072, 133431782, 392181838, 543370888, 216977992, 30080926, 106764257, 340572390, 234136969, 55281010, 450365550, 151771829, 111055917, 334011766, 584836338, 284361408, 268045451, 473378079, 576985039, 13807807, 687192120, 519585729, 675632297, 452413725, 257613973, 944869049, 719943753, 433342188, 867368487, 193528086, 51913587, 138812685, 94733398, 977285616, 480989535, 273673305, 575885883, 788116448, 464299161, 387241218, 974871786, 165267415, 892335956, 968174430, 924810468, 433622592, 540048912, 868781630, 255022570, 576777786, 407643716, 78920292, 156782080, 312261863, 857630340, 209203013, 195527272, 683500529, 941290142, 511448988, 518655163, 843543377, 420646103, 856194217, 84893993, 71051334, 497757759, 403602410, 24633976, 186880862, 261734952, 244984810, 44572913, 834603099, 278175385, 189095855, 511954513, 649913309, 838946248, 9765464, 846894960, 364226373, 952296029, 69156861, 839025398, 980330003, 663684862, 338755724, 153158088, 768280297, 878103595, 641072570, 132303074, 95565324, 946357506, 307391679, 275560650, 280902859, 757278733, 810844057, 698316948, 189197963, 13570557, 805033942, 881250550, 623950277, 479758770, 287869950, 943221295, 813771465, 331558446, 151320151, 230647918, 358796052, 787686643, 976296872, 613261955, 196765350, 866495902, 392630949, 438215002, 372066380, 70531926, 783503863, 244064921, 565356425, 9278514, 469639198, 107657355, 906924355, 676130228, 311748051, 725109802, 691352815, 708620207, 588672914, 987619257, 493893711, 677880985, 936827263, 733429332, 478726186, 839733388, 221375191, 537617649, 544022540, 837284478, 137172335, 228552183, 208843959, 27428449, 129866841, 880109351, 631810564, 740074991, 738164204, 805924021, 619320924, 370782545, 529756391, 779454095, 943625383, 282833049, 949737799, 182529655, 434854424, 484423194, 164200170, 49668403, 25603550, 447904823, 579179431, 92356288, 977757437, 190854814, 639502008, 691235419, 609095349, 511637307, 874226803, 145271077, 190979724, 987727336, 41927026, 966065200, 498058044, 490262283, 572357673, 427719682, 857593794, 779007933, 663483512, 461434048, 259759735, 331503567, 442270385, 431695279, 423326732, 721185524, 462482057, 931100150, 982043425, 940143049, 166018309, 908794214, 989068370, 224128120, 98591536, 775355427, 758815626, 334694744, 243905180, 42795391, 11933132, 655629775, 919782522, 185191186, 818450675, 416407198, 502855808, 113808968, 238361939, 487710135, 607732425, 206095653, 856822897, 641076353, 725644827, 946140414, 309559856, 307452699, 985489923, 195486790, 462613445, 639465674, 701559636, 362275854, 689782446, 329564958, 952442600, 708155793, 161183692, 929351442, 966528600, 553775063, 179109826, 489930021, 631307218, 731883293, 45747412, 374791452, 618241780, 529669644, 680478069, 161653820, 441323329, 993747909, 462405113, 628895305, 710119632, 992293009, 835352557, 282561748, 619616102, 633400039, 660179898, 561756565, 248421462, 973654030, 621414743, 569501441, 120918491, 731753249, 142012820, 783345730, 461000417, 538050871, 372367102, 436442986, 896863111, 787837290, 507235660, 886466218, 928860670, 240912494, 459657587, 622370810, 36843112, 995134381, 555584595, 267830564, 434851424, 884435023, 63786722, 495143029, 418133782, 832626489, 957605112, 131024466, 365418124, 715975779, 214856316, 560913469, 454881766, 807149435, 488771254, 862342910, 890455038, 653108521, 385496290, 175572577, 736785860, 798928748, 74679405, 611465872, 767117575, 417481255, 682173504, 815201293, 419138845, 654459912, 223845850, 703586027, 973237689, 314283601, 213808918, 802725734, 725596603, 625068153, 471854296, 691720903, 978139768, 832864387, 636481789, 923076678, 454753578, 917732970, 467626346, 904084139, 270968189, 965481163, 737576882, 823888651, 490258811, 22933336, 313137487, 731288555, 692506, 472232115, 980512353, 592337575, 133154940, 942885731, 751498910, 800743025, 904239994, 325788354, 557137294, 575763541, 398645558, 30332508, 796252341, 899414927, 247347878, 968178642, 970458961, 698150931, 534509692, 185667045, 474990392, 784726802, 644695652, 453289227, 373304173, 626213924, 175364894, 309363733, 539492851, 80857216, 853984475, 218310997, 758715310, 182927231, 394941703, 416484138, 368587053, 430585081, 260383419, 523941823, 821438741, 360355212, 717792053, 262937227, 883360500, 421273491, 883134295, 927992342, 764679202, 783128777, 587547368, 664147750, 593134530, 620381487, 787235585, 157380189, 593936546, 284230785, 152359512, 244157248, 797663427, 803154452, 396947840, 432556780, 905762718, 446691366, 642735825, 251114258, 720006853, 11742363, 875675144, 482348159, 739833204, 134613213, 267158200, 922307428, 67245973, 763387386, 909233244, 747899713, 619717246, 640009623, 390341347, 944338455, 130762508, 173084303, 447186422, 156464945, 300081726, 897280773, 146048955, 544255810, 693116963, 2175873, 516231014, 965644779, 901249122, 897772050, 758137588, 958440803, 790566764, 649359076, 399355814, 577913764, 726016418, 235297293, 636156024, 776930769, 304969246, 286015427, 942908219, 978321433, 797596060, 568693474, 927678554, 781929741, 717574063, 999179957, 877066325, 78383349, 25818787, 355429580, 878087796, 305659143, 888322685, 775905870, 517079985, 135728578, 269615744, 693461012, 641871550, 547861556, 219905525, 326545273, 903556371, 750561343, 187811906, 259673772, 649095401, 889752918, 148937375, 991131963, 974984529, 598122620, 559024290, 471785192, 451356993, 288517588, 690220010, 962089525, 676439475, 311129353, 261677159, 9725836, 532168285, 549603462, 985887510, 772338359, 659346296, 747692511, 366160232, 251635361, 804932491, 750239456, 425588312, 689923912, 316187722, 932897241, 61441269, 737931489, 93006961, 726544725, 411613414, 303450185, 338874777, 934415226, 503485967, 484399465, 390488130, 331683015, 676679115, 527538577, 626971279, 175106378, 857431248, 302413270, 280538236, 306589975, 152538597, 655608129, 445512631, 804222845, 491947174, 239718250, 38096631, 301004490, 459226779, 710099674, 222793657, 74430101, 383699761, 213243547, 797300894, 577452473, 793388134, 220652678, 861353739, 592950726, 396639390, 886748976, 822392000, 905701984, 949695271, 927696163, 589438645, 382373, 479121374, 300128704, 451725039, 348153858, 139321940, 107910930, 553786737, 785534597, 634616630, 753463139, 368212193, 250148983, 498954583, 341042859, 306264761, 155250540, 172054816, 805674314, 865289126, 470971413, 897372807, 894496675, 106622864, 801950154, 147370425, 258172768, 985356632, 610532554, 31334478, 164129662, 679423512, 847663049, 121150805, 420351043, 890863574, 506369871, 635135408, 863476496, 581123827, 718950493, 337003774, 107106678, 581102623, 724961937, 409816544, 389757428, 398945753, 390417373, 542182729, 914562212, 363403414, 970135870, 176761139, 888906757, 892774976, 603134144, 709633361, 150157676, 439693257, 231013532, 1842304, 204525398, 853179827, 781261343, 412114628, 816411951, 670645507, 151579494, 848974179, 351390801, 969076719, 16984720, 840330313, 427507828, 303392480, 376289288, 191001402, 261504831, 678784976, 824035769, 885228531, 213332139, 987773846, 8422194, 227053114, 313229621, 855698278, 106083062, 692945768, 206661826, 871205301, 162867873, 166346742, 371457424, 398133838, 243605841, 101284975, 668340015, 212703379, 450978755, 166320758, 592078007, 331294292, 35032575, 736235153, 795466726, 165509461, 499322271, 238517394, 79914683, 681596638, 20978646, 189516068, 463310652, 605626764, 22155220, 775541964, 630413112, 426182338, 463717509, 72138085, 324726204, 572610900, 928777063, 925079621, 23176058, 308472642, 769247206, 902316385, 29020793, 913170279, 225907854, 174953196, 707621881, 887826596, 380788760, 178532534, 632954836, 948089864, 766810784, 981414752, 121886767, 598971904, 27912291, 695209519, 732950173, 557238087, 915599661, 557264438, 511417975, 418470255, 764466035, 229516325, 964827032, 778863818, 347550711, 80496540, 260877339, 494279452, 980560496, 557754142, 157614031, 359310957, 46576626, 625158602, 92839490, 493825621, 415449438, 740289990, 249351384, 810014363, 366830785, 741852238, 978461965, 835129356, 617712871, 630650126, 302331751, 838877078, 151917026, 516441432, 74015299, 240407790, 850089193, 545624223, 530075661, 220658122, 214314593, 999815339, 941869441, 547217970, 716845281, 829967225, 276688982, 87573170, 833252889, 237008896, 453461674, 56248480, 138059795, 362105544, 59471347, 133593287, 331508962, 618151144, 290679677, 451573256, 731083722, 231837373, 569869950, 500009846, 740544509, 673525268, 353572238, 735103255, 963757725, 320097356, 450729734, 813538088, 247136829, 590219947, 273033490, 978078879, 782884693, 521672112, 974557084, 348875775, 618419225, 747600074, 268340163, 636913320, 940404858, 208065168, 791175407, 40740080, 927460314, 329435657, 685747493, 637864938, 991493420, 584833171, 627358321, 143309675, 397127791, 716302435, 199173684, 135718745, 898225019, 799173138, 466889834, 309006453, 152328800, 752848829, 326494852, 826907822, 833730804, 122691370, 805034535, 675758498, 960378695, 959060212, 316871745, 216649432, 582016589, 587525093, 186943692, 51894490, 359095766, 358767967, 579922366, 699620181, 158509261, 87661134, 323334470, 494375833, 986801906, 614588954, 443281633, 697304373, 221970578, 666324747, 843991136, 641340862, 475848103, 64408291, 603964480, 312354103, 67499476, 786582004, 915971400, 724535282, 339815309, 508648914, 500372601, 130275944, 473117058, 314134830, 209525812, 53654927, 897317906, 422045258, 651748628, 462182827, 305502852, 348895670, 41504694, 375859351, 110443013, 567320758, 639122375, 857408691, 658066722, 500847447, 163687186, 338262827, 351078203, 573241518, 191154887, 435849019, 374253772, 749048561, 576952971, 618357995, 116077039, 342049879, 392497203, 137593750, 188426222, 930212315, 766226073, 506780124, 655910215, 655483108, 961250836, 16761838, 961264223, 408374952, 469084483, 774062150, 882777901, 182218351, 157152678, 154947558, 924233666, 291955270, 427162815, 246625978, 684424386, 324412337, 201617235, 713479492, 751594880, 907765552, 805630171, 414545204, 313554687, 908979260, 110025358, 575293850, 182757156, 743521372, 732249370, 194451327, 420947700, 823389468, 548850524, 543613297, 280224369, 613616410, 505544839, 762599471, 853851146, 553455390, 587834682, 285695999, 573343565, 30905935, 333132924, 769127856, 112994217, 457370736, 297033909, 783693672, 605309318, 235280156, 258540535, 829837066, 474771326, 699519581, 111827460, 121446367, 652337976, 499201921, 232299213, 890813245, 900574570, 264217261, 84222077, 449016911, 383832851, 854565671, 991854170, 597691729, 930384231, 132346560, 132246921, 320695916, 905403887, 324777122, 227047319, 578569936, 231131511, 376336823, 850804102, 38567321, 756390659, 558289941, 990745383, 754688436, 6165374, 836623751, 334600460, 711778941, 703853142, 230401952, 500940998, 694987701, 271369196, 838341299, 110621317, 926888530, 232571365, 559894984, 380074127, 594798869, 81450476, 272197927, 197266814, 685918913, 250117051, 602938640, 873111291, 814816586, 555940842, 371031644, 49066402, 749403353, 488204323, 124930375, 677201945, 160596528, 262622656, 938837623, 881387592, 446524635, 827872155, 111433842, 27164396, 156837537, 516799551, 92632364, 911922676, 319383969, 982395889, 138777935, 925980357, 669097809, 199844788, 195552493, 277311812, 617416575, 680772835, 670929010, 92447393, 37876360, 439205789, 210192166, 944088194, 511032298, 100253480, 845872245, 645429196, 512482275, 296546157, 273107493, 599569066, 184922073, 165799927, 603895323, 554126782, 950298210, 14662536, 832184921, 211088248, 290032415, 807027111, 665901136, 117383177, 802156349, 659484932, 309405881, 300927771, 578240594, 106252933, 56110820, 591819608, 75168912, 34819540, 477002539, 985393548, 706482149, 396875882, 861882655, 138429375, 95798620, 697551185, 986528647, 849086993, 266726791, 907448331, 83037357, 915010433, 247487647, 208881390, 302296566, 605275501, 645357407, 327811913, 900786976, 326363893, 975364493, 655091740, 68119556, 89987737, 6515154, 975068029, 619853432, 577667374, 441860644, 237722791, 901676001, 773290693, 48801214, 263818676, 608388988, 454659796, 795985824, 239960204, 26763923, 957087460, 6344102, 981903742, 344234795, 257053033, 270044073, 613934660, 707286665, 940719250, 830762627, 885812479, 853369510, 544522038, 141633824, 427168392, 276395133, 164496190, 184156468, 776802764, 905867163, 893564834, 134184267, 538100436, 978793359, 796124681, 184033531, 452024713, 644155094, 592764929, 195386100, 150714575, 519526349, 300927173, 3510708, 613971840, 959326950, 949933019, 314256479, 897064251, 906014418, 327859142, 809233277, 377363659, 349261686, 443592309, 646503773, 21335118, 414845185, 380860621, 386911547, 685607472, 919607308, 729336451, 272144706, 245724052, 283247064, 399641091, 990361579, 937156796, 720255450, 95182083, 259775286, 121888743, 796526049, 350824370, 100824517, 431057527, 968549315, 468447814, 541876066, 49619623, 990042215, 580698577, 360225781, 216710544, 105572325, 361282692, 119262944, 692328325, 979550018, 542790880, 399148973, 254955396, 342687782, 722130855, 179839753, 376767947, 925904614, 305627136, 791786408, 408359301, 792910478, 715239779, 905510707, 514842032, 744178363, 210454106, 364259446, 353916743, 61348050, 72069950, 98419954, 322876527, 540944911, 353200430, 540578799, 618613188, 489351875, 711514694, 887410754, 642517890, 859054688, 36113955, 330968972, 301193045, 652101719, 906630982, 325150126, 154489370, 825330474, 831907304, 70461790, 235982372, 134309747, 818994411, 30862088, 545508909, 942884619, 854070338, 334878003, 683628136, 918021194, 497256617, 362355224, 263591350, 617889212, 200267179, 777628054, 223246535, 241580001, 345308473, 434773673, 950525079, 207276717, 873896967, 170361647, 657234449, 309107325, 830157717, 871854079, 476474942, 790551413, 406964265, 515850534, 76436820, 125794785, 437678186, 352043993, 454422365, 41818790, 49360248, 849110306, 807906517, 294161998, 553333633, 609770335, 246097314, 418166309, 81359425, 757049280, 550654789, 945008691, 146391386, 942195067, 407250527, 94741020, 683109733, 721759464, 211041261, 381751629, 822778812, 122478828, 227832233, 187137743, 273677221, 916160211, 511249341, 622635383, 154588067, 383049704, 641484119, 392635077, 507200810, 925011957, 725463089, 683180503, 519600521, 336946855, 165764494, 322238593, 730635467, 983251022, 829130210, 482650872, 127522524, 198756945, 547885204, 726665278, 52664879, 987594463, 399461612, 128421051, 853862951, 173599473, 495119386, 561214083, 468495190, 513700835, 631722537, 607329221, 168750410, 633944226, 25445569, 757863491, 666257382, 609318126, 497666845, 56473778, 477691398, 518517908, 694792422, 340319587, 518036052, 716363765, 694980505, 273423153, 841713765, 563284215, 689385873, 750296518, 488706143, 200668232, 636605844, 583398005, 523031383, 689104026, 37958479, 615581085, 991952325, 165242008, 673882832, 980155459, 621295492, 392420323, 840176691, 152758635, 557612652, 925512923, 758931284, 516610862, 507727331, 358384847, 672310471, 944240713, 901147084, 29015350, 328774332, 710383105, 963185551, 646548739, 105415935, 380927680, 667505331, 472169360, 912032040, 712699000, 861563400, 544523785, 688846632, 930655760, 428987572, 244842562, 526591555, 989687633, 339198347, 149632568, 904391253, 832858367, 618992940, 398457895, 662309571, 773917512, 258094045, 373998982, 837821739, 494169944, 823318604, 200304767, 801371005, 78784209, 523022275, 62919729, 585056171, 463637884, 599003440, 561922713, 952668969, 837694560, 81935028, 98910912, 602651115, 66469833, 448712776, 453336346, 192471658, 306373535, 942186905, 585822678, 339218161, 804618484, 564221531, 128653196, 656344184, 813026976, 268447775, 946758014, 444244796, 972798253, 285903799, 780813942, 707623608, 296951405, 932216296, 842567024, 123196496, 306871019, 42373320, 355843486, 654703501, 82388745, 618053953, 68971548, 918775568, 243416955, 402187464, 682982222, 448026447, 175204903, 632591672, 911338986, 952823024, 537898520, 163277479, 612447937, 627771617, 332061187, 438434765, 293708091, 254470583, 302705266, 428163775, 609809150, 788286293, 211529213, 578983345, 663060817, 892406899, 585059442, 184245886, 754274674, 360442139, 365743457, 764233870, 264420049, 664096300, 97593207, 796645865, 516727260, 232122416, 926940209, 991069091, 232744386, 895043732, 953289657, 454544044, 189895032, 762693903, 814406724, 20445070, 560613022, 156596562, 607540207, 697068697, 927676617, 813533323, 35364925, 39882048, 701705926, 176869111, 254625354, 465119129, 668708809, 788945644, 463022135, 693056281, 744683974, 197370899, 721635207, 368951964, 597033561, 977147876, 133099970, 633986191, 670678334, 496983765, 510262204, 175830074, 212647448, 128698903, 423836392, 945991644, 280381655, 398747947, 339776589, 871963355, 64676642, 901816627, 835798020, 175892821, 659313674, 83977841, 175465472, 951042299, 947875355, 131874230, 861391147, 278937361, 172611276, 966992063, 779680357, 454498750, 529997221, 815269124, 252189834, 431378182, 116589910, 851579463, 505489208, 562598253, 123785420, 993307978, 606829093, 428800565, 329691505, 788389027, 964765010, 867013419, 98479392, 337545523, 23502243, 288442881, 740230195, 44635551, 57549933, 429606546, 519199527, 257905415, 832475096, 132218505, 495409033, 550612752, 126933824, 142593691, 301656179, 872525536, 307554406, 511882873, 758166588, 757361908, 367148351, 412924328, 623169086, 695262792, 735600005, 142616214, 929474857, 660494965, 123889997, 521387114, 570966735, 815657301, 870429450, 576572394, 425152335, 985318881, 845637899, 713807675, 606624048, 210621993, 283812869, 748597203, 590852066, 632434693, 916104919, 462538233, 870737842, 366514377, 873308067, 166723522, 510866483, 188443311, 239741164, 243783913, 331045027, 635141626, 744367594, 1826168, 912135459, 170465785, 708438096, 574696619, 658003084, 583277804, 99214837, 491947564, 234077790, 645302568, 720616035, 658321546, 595163180, 557044085, 888460509, 359444345, 214052723, 735722303, 420956869, 38837567, 305740004, 114845999, 173886281, 385425750, 115493369, 329450351, 917937663, 571261614, 845797423, 301762117, 67927566, 374870932, 159134555, 969844278, 344575624, 754040973, 690957111, 684365070, 494993662, 141764419, 580169179, 835241110, 857582930, 428816040, 451625767, 171824111, 485562543, 100938366, 411007821, 659282065, 679977807, 943411716, 596174936, 109756204, 535855144, 128152575, 723363404, 609679764, 609724006, 947555872, 859911825, 775258081, 94162028, 270017797, 542233919, 578192021, 225075283, 380728912, 58314624, 994540759, 318288210, 47764489, 321395564, 683566924, 539824872, 862435847, 637189338, 940044241, 489561, 349194086, 955249905, 697491763, 63871565, 128069028, 674207913, 624320539, 643582718, 665501023, 622160104, 610295835, 878644640, 18297086, 210645864, 939841702, 181614640, 952380016, 747648311, 996238922, 956992000, 50074988, 582498472, 499218440, 621459300, 138302305, 40916639, 91635548, 410687070, 94338071, 622328862, 336378446, 517744705, 398306741, 974667398, 95861868, 504047432, 915540489, 559886166, 639171298, 792543915, 343828200, 598563645, 161751622, 603841919, 454305739, 303136205, 802110652, 988074121, 428004373, 544669126, 657760496, 157992315, 692135975, 938877066, 53078374, 612796755, 509265603, 560479302, 369064316, 39427233, 873056525, 355811641, 847901464, 811236186, 939540638, 341284318, 78855546, 717877570, 262012188, 79103075, 620388598, 621658363, 20644976, 7004187, 449905970, 256063320, 335505451, 894699947, 492515409, 644867089, 303173267, 40831062, 946314430, 785016368, 886878049, 156058608, 486176860, 762124532, 818422817, 860346030, 113493592, 405976486, 107225982, 827239292, 849271695, 908684460, 618181061, 415703832, 655530000, 401410450, 587681735, 456189579, 513853402, 416553712, 220473837, 921738804, 434967886, 727937570, 486069914, 847225604, 835548026, 187252754, 734888977, 51117517, 233459538, 434792502, 533875932, 928957478, 629936958, 508758677, 727759226, 234686050, 497485633, 793360896, 907014751, 853953682, 502660947, 551049664, 394631292, 105506412, 168800120, 987870265, 730265302, 87126477, 802364797, 885277544, 951951022, 629435014, 497691745, 588459370, 175692772, 807139126, 497666431, 493838445, 515567895, 655298114, 172086899, 630796916, 116263316, 79076881, 782604545, 396524931, 44721849, 426804245, 53161391, 407437111, 619460649, 752348099, 366292561, 782612452, 83424650, 869437345, 637700590, 798895994, 847768685, 896412461, 793396381, 56100231, 966044263, 544525309, 476487142, 334553621, 606069352, 711828940, 584969983, 651554635, 47661521, 374933709, 804864774, 777375614, 622160964, 516909039, 230459923, 470701759, 559592552, 677374325, 88706652, 140687103, 697674747, 988075661, 871567682, 779347566, 446667539, 670043505, 806266478, 670538553, 686890276, 953136848, 901171818, 4967856, 539866058, 736387983, 361821665, 119778378, 337661882, 653334904, 588366213, 281405596, 128166304, 535506924, 868693210, 261904702, 272663476, 212794905, 85363507, 712314377, 668051961, 580711820, 195206459, 376808983, 682634194, 596586479, 818561920, 932909354, 258662763, 918373747, 723315408, 552894104, 176735141, 968308373, 521450416, 967025275, 627502533, 214045639, 772186551, 563064869, 257023209, 173993890, 68985220, 296583280, 164788190, 597906810, 806935649, 90203156, 384926700, 306752783, 438976192, 306157304, 103999922, 800624028, 103686548, 722631749, 629517658, 794595897, 948012326, 876659245, 624707506, 867916300, 627308719, 573858522, 306331606, 374922933, 508469820, 254826582, 805491738, 194854185, 467708445, 220908204, 944408694, 59284855, 502126115, 280890902, 951993683, 241986643, 238158949, 760890472, 126426183, 109665494, 92153540, 199000418, 449065150, 509187391, 861935710, 135584495, 271739487, 718736929, 378896280, 641263592, 161378765, 107844845, 475826832, 626065640, 628096766, 38191909, 246815345, 959639296, 742973003, 447360375, 911335313, 376935200, 813281054, 580360138, 407815999, 63945263, 64920589, 410656675, 318628935, 186013596, 201770313, 743555379, 93048529, 393619095, 184467786, 9559655, 42325554, 208750418, 899980965, 927109070, 849026397, 382206850, 46210573, 702480882, 997757659, 203387805, 977532944, 360867278, 835608812, 694144516, 711687984, 686678826, 626870806, 28641826, 776173090, 969423437, 836431851, 588472295, 993894649, 234090348, 228348623, 213443634, 354941623, 74962554, 683252143, 714604477, 391418351, 293688575, 17082895, 326140276, 56343036, 348507185, 498674628, 14887253, 94590761, 874863226, 421632293, 796133120, 567736392, 959284847, 177023281, 37208219, 981468531, 260040085, 76379924, 834008461, 320250427, 303161890, 647284745, 817179797, 162980897, 553711509, 435664839, 219408947, 202186064, 593127383, 145828037, 786039059, 350599888, 624331076, 878494901, 554666306, 975677381, 476157452, 604179412, 940761734, 465775804, 684955255, 457118089, 769606867, 170503859, 204474361, 900470643, 517882269, 140855214, 113251925, 543971083, 10052496, 590141978, 138626032, 525024999, 790562560, 495365725, 452256769, 711878798, 1677098, 141265974, 895823805, 81243131, 644014945, 350916459, 670448026, 512585398, 260440897, 354445319, 812017211, 107112887, 512200651, 182303470, 375584737, 102033728, 270817038, 226489161, 803369774, 101632198, 899795942, 682687845, 665046148, 195062866, 775574140, 598808689, 723001888, 208118368, 862030374, 424326645, 623707180, 684259259, 38744214, 118174609, 343637877, 810929847, 180487031, 607081328, 217933444, 23253588, 374210030, 491595507, 439284659, 941592599, 907671340, 870949135, 740995384, 12015927, 383644365, 561863829, 613212656, 251675924, 5422182, 536181128, 32849208, 166762360, 533171996, 135509255, 885966910, 238562654, 829150507, 864974760, 200413729, 124800251, 197299467, 771966432, 828846376, 358733725, 710090143, 644919955, 367047837, 266544444, 801387672, 213946045, 478451996, 75309030, 27279428, 120802543, 171989364, 935586789, 244587520, 919234921, 593289121, 401468717, 987658755, 187651885, 233091736, 346111736, 410666583, 228243876, 649457930, 98733044, 774994658, 932152560, 506700298, 734856892, 880736616, 841567770, 785165894, 383939190, 479569924, 114393384, 299510670, 245634091, 691007868, 343525171, 749957838, 496630887, 672015113, 958741253, 809356360, 251999858, 794176088, 433200937, 197013473, 253464479, 492150969, 15037846, 53478768, 821158969, 696843189, 758676200, 585222520, 697486953, 2637016, 101248803, 767415172, 950783514, 453448550, 489362200, 219730169, 530725144, 753946095, 700023059, 483836823, 382194479, 311653152, 195503517, 894483410, 551693368, 66106034, 467393148, 783424621, 425159376, 616702732, 777667728, 196366091, 937697761, 984526694, 378724465, 220400177, 407952486, 774643540, 393212076, 632218990, 585568329, 426559516, 714396518, 945619250, 225030973, 113275673, 406498045, 654081360, 396075663, 993357942, 768216400, 779945141, 44822674, 426311892, 267100627, 632381889, 519961064, 646324168, 22366273, 827442712, 529829727, 575475299, 539178706, 252851733, 23598530, 791735367, 849362836, 109951906, 668544149, 78160182, 544675449, 296004031, 960915932, 52515998, 736400677, 792145598, 257332595, 362894522, 19770696, 371688766, 683157193, 287689954, 497792730, 591373316, 259335540, 147789526, 413241352, 820565843, 168185430, 214857962, 147513891, 445523360, 736527086, 847865712, 332633001, 806196691, 40062762, 354899554, 707067504, 259071301, 403734639, 159855803, 184658767, 583539935, 320801242, 896857139, 896733558, 383815760, 611984388, 208012553, 460207465, 71352178, 161475638, 235407192, 363965774, 991883983, 441923451, 530246562, 917303868, 440009779, 121232220, 559931089, 841210712, 361718205, 392465866, 702435796, 851903042, 221680510, 571732179, 743864102, 931112189, 690322855, 167833591, 521561820, 962545073, 510787323, 102633790, 697721475, 94687486, 332907959, 925810709, 706801850, 212427981, 385581878, 391672747, 245258735, 81180198, 279318634, 933737088, 316279491, 940718607, 895489241, 708151542, 247394540, 121000531, 254720073, 722827037, 968237363, 195702384, 567978448, 799469849, 874918829, 583120753, 971267845, 472769414, 490993171, 851766679, 12909721, 118074270, 775602799, 106606027, 350245824, 151069019, 933725313, 139094459, 592051018, 127813409, 110519534, 426711388, 318283552, 507406632, 674339237, 609177689, 663519559, 814259068, 823733984, 99022461, 201115362, 116215833, 906577588, 671104554, 60757989, 229950541, 388803473, 898666909, 93013339, 254363180, 677748260, 562433598, 649642068, 289376208, 225520724, 789821000, 139326528, 703544576, 516098072, 499917495, 868885557, 153444854, 730769165, 30404077, 383648754, 767153114, 351840542, 474952231, 569652623, 406274208, 359206976, 143337515, 236576615, 934297675, 429854929, 732465965, 462352574, 23872315, 892257413, 921862884, 899376297, 674455605, 578510963, 21925705, 982645120, 79409145, 203563214, 58339047, 781243799, 326845210, 465891918, 836160213, 520816963, 228296299, 863735647, 650051352, 543799222, 929041245, 620870343, 107055421, 344185897, 845983612, 283532787, 406920127, 163161640, 33689777, 765613764, 164899977, 643048792, 265976761, 427864566, 626710748, 570619449, 376488589, 145924069, 208762466, 443054577, 596179611, 27233800, 841339289, 209544945, 833819914, 155050355, 913257545, 31637432, 199613096, 765457245, 664971048, 991002818, 661854655, 567291394, 792154601, 519616739, 121728742, 126540249, 312565674, 788856041, 4547649, 903354853, 217253142, 650062630, 852425675, 516727835, 966607614, 20752964, 729882521, 314683056, 421882610, 732923193, 55893134, 88289333, 43620370, 754450615, 977288946, 767093015, 243129422, 662826209, 373496783, 473270159, 951443316, 616383699, 335913030, 625133589, 245291138, 813765126, 779519322, 384300747, 727896539, 807165407, 73541192, 387006956, 945769120, 720376141, 762982205, 400936703, 122693095, 649815026, 452643150, 608656788, 565444072, 411915934, 419200166, 556225159, 165015211, 897887595, 547526352, 485819239, 627316520, 435437805, 922905626, 691545492, 858083247, 57541909, 533347163, 210327418, 729765838, 591295033, 71944557, 332798025, 981578199, 423926229, 133771577, 175031617, 252204121, 426846944, 927034481, 740223295, 791392861, 103511755, 174644901, 71608199, 560261802, 1326402, 784752172, 494117482, 683912510, 111274837, 139751978, 789613350, 574430317, 648987721, 945858925, 452207013, 645867559, 15238294, 789034537, 67019269, 663699080, 576601376, 350043117, 560968537, 51212250, 485728381, 684074979, 519153285, 747018497, 387593282, 49457340, 953694333, 588534833, 723283394, 935999727, 141080663, 814506050, 494594539, 965262924, 501265620, 361760816, 235789884, 837084919, 543829824, 181645700, 75161526, 333759933, 926494316, 204652894, 545224844, 239827681, 599377224, 503332024, 622583930, 222270411, 594935021, 152397541, 867812481, 240956541, 646169883, 481028913, 361519783, 813983880, 519054672, 983315605, 679999754, 517442863, 249909510, 83119861, 384317472, 823721848, 675609836, 546819072, 644302477, 169113992, 790591809, 857161162, 583814597, 353073846, 506346781, 756140437, 416918763, 911867368, 136737357, 29650019, 331090401, 486166844, 189497252, 580095551, 968578817, 527485332, 870776098, 466860332, 540694298, 421860267, 561529336, 480233563, 144680539, 537061390, 33515026, 445898432, 801470198, 479103509, 393383090, 140406054, 371733178, 313781381, 436732715, 111127201, 757048218, 282438892, 607759201, 49678004, 44842126, 162410396, 782515983, 197784936, 353628495, 840233519, 684392896, 725324441, 24414297, 318625584, 135304973, 690027472, 969237144, 861587422, 459003554, 243862697, 633394513, 663453796, 87763168, 303153342, 130690418, 426688851, 202536113, 582230386, 583580604, 769261603, 465951731, 946571101, 928439262, 224753388, 309713248, 407551462, 121189587, 705510981, 394911578, 624097589, 103576030, 522336728, 218601324, 521458008, 731172839, 216721549, 876977534, 687802057, 893849571, 794755621, 426069939, 548530221, 309464834, 196789254, 229120990, 959134516, 938552253, 756041440, 814383029, 852388166, 524760780, 23474640, 120280788, 950109477, 610641623, 360108001, 231909660, 206418908, 961188958, 111458334, 831298722, 140018209, 820831642, 683327021, 378216923, 763492103, 690441389, 14991098, 652819993, 224541890, 286328887, 271004768, 315487610, 645980617, 201068189, 385391105, 908210169, 903118562, 671406182, 427979958, 315671488, 857609084, 70516609, 69548354, 717292953, 29846925, 948117137, 481481789, 216661542, 636405076, 426132381, 48104748, 687831166, 966593913, 806591475, 418542052, 807020201, 225771755, 71358577, 912706219, 978557385, 635955763, 787217131, 818125758, 669427198, 556646799, 351238486, 87204030, 420395789, 324739020, 142115498, 289778180, 845399344, 620570817, 202231158, 340746703, 705778925, 462462706, 307653690, 287300289, 152627523, 582335128, 254968250, 631234950, 222595032, 501104273, 361402709, 863879898, 784746497, 348668553, 551334912, 615891156, 484819755, 720662785, 52217855, 941930061, 335904558, 923313708, 840395098, 579815420, 82340450, 195407584, 139984223, 857948594, 441588104, 512581345, 649048627, 67384596, 494885609, 558884168, 814033010, 724305050, 456476306, 337590408, 213551785, 664471436, 567669215, 521258474, 466026705, 433530436, 528665138, 183937024, 648487856, 248998011, 658897766, 746864271, 432017143, 769644087, 879298290, 544721304, 963433610, 660993968, 780140835, 842194942, 567580793, 485361707, 939396086, 535799687, 798454779, 480755769, 780377177, 380160830, 468875048, 702076927, 36069104, 881384011, 297770800, 697454176, 523729049, 90394699, 12260660, 371657464, 484114660, 466351312, 5431068, 915356612, 732307072, 123784481, 530292741, 636676102, 395530843, 877642505, 971361172, 534982300, 963023153, 186320964, 419551793, 224637099, 71101001, 53719584, 372009419, 57298792, 737329774, 701135136, 897228716, 294643215, 45328031, 295506862, 674133137, 984569539, 436149897, 661123110, 517241438, 209077197, 497907508, 434959187, 673294670, 2417343, 213619604, 391538046, 895215362, 486003740, 630162655, 18532005, 414857485, 173055081, 411589007, 272953517, 107459713, 761334951, 900689725, 176130563, 52033327, 735798615, 629903386, 489223761, 754329585, 698568176, 297527383, 590680448, 759337480, 737727451, 219648343, 349007014, 712246667, 42344879, 949685780, 942837985, 896093243, 512423153, 55493232, 26169368, 412769479, 33222345, 216428582, 662251761, 76292403, 237284828, 432707003, 394735037, 271445391, 453348518, 469858439, 45203476, 281102202, 11712547, 838280059, 170922426, 479888617, 388909855, 235361985, 400500935, 990074305, 312594813, 126025366, 42607478, 23091171, 76919886, 934753827, 263981542, 943721300, 880524496, 378880570, 605787559, 542205271, 126231913, 125709795, 158966469, 140917691, 599332422, 565432974, 353864680, 173396841, 97137547, 7845922, 62128419, 476513637, 412504733, 660443146, 136968213, 362411136, 391494199, 103601573, 737763068, 508264028, 368841986, 290575963, 825013838, 821203707, 512290225, 46928187, 395908699, 637858717, 726064052, 750492068, 473402325, 30458970, 317931013, 725738855, 64062794, 730086680, 617863669, 505880870, 673176758, 331267413, 751404896, 545948418, 705962354, 478915202, 527057350, 44218870, 767962799, 809253157, 194802453, 135936491, 470985956, 795051986, 964348757, 757124483, 751461204, 849659729, 68563674, 782827169, 870488992, 487608880, 739320155, 138409492, 869940152, 77549200, 915660035, 342313340, 929311380, 233972589, 115432871, 999741111, 425991973, 295775830, 15992988, 378405855, 474835705, 696100079, 681666443, 974893838, 74102947, 752416913, 207467270, 32746901, 905402406, 755201784, 549620893, 757689286, 997298492, 439120079, 617742429, 514637224, 62052213, 411200891, 253911334, 179499939, 298033145, 187150107, 254740550, 480953825, 858143933, 650960894, 223218005, 270020610, 443682090, 814013481, 285578905, 587419615, 300409985, 716209723, 338329546, 363315594, 41285975, 586133809, 121744592, 258022176, 726361005, 926210503, 706320598, 789561259, 624548689, 899926508, 559689852, 219161821, 959862218, 265799617, 911330900, 589344807, 855107808, 369464760, 348673239, 942179259, 762437786, 728576624, 726456816, 565754279, 602676737, 167633758, 131034158, 851012961, 434217242, 840648908, 279806001, 82727209, 302587098, 303841814, 505886090, 58625134, 900032787, 194062480, 201101935, 74981261, 610647840, 320326189, 102008585, 899624912, 340317489, 396153213, 720240285, 412269527, 227814542, 931968356, 950982584, 779029212, 406198286, 957855194, 424250552, 195559715, 314481295, 944622377, 12523039, 846473724, 336582408, 180246401, 657229362, 438033755, 53812462, 604133460, 189671926, 724919159, 111308807, 400438286, 671981182, 964408798, 825597895, 713677547, 51432096, 963042575, 454305356, 453128687, 43136723, 963247492, 935675914, 504074805, 810134330, 67947285, 450900816, 908952747, 401892736, 992181955, 674782960, 227895502, 268253240, 844061043, 52689204, 368179099, 605667406, 206585761, 403042900, 460911626, 725684662, 260750196, 955586747, 132638051, 591408391, 297729579, 482227872, 438682717, 173125977, 799488326, 918435770, 912289189, 475438535, 48308635, 101906524, 8723715, 376934681, 368686087, 763464631, 234819693, 602580262, 136336744, 667802914, 560864277, 847083861, 952291203, 277913523, 641839588, 45231634, 955594953, 177871488, 296394782, 603596135, 649202899, 718878469, 700484114, 886598066, 703218203, 333751115, 112353943, 390551136, 314696393, 487774972, 828605508, 79521048, 789475588, 830572266, 797148347, 381672664, 110945420, 408199304, 234276098, 71223074, 967728290, 6600234, 647157439, 774173451, 160290564, 947444563, 193944551, 725541361, 155997054, 461150208, 955484749, 480257980, 887619872, 529597975, 705717251, 653020986, 352220505, 52963466, 859601019, 361459660, 464530844, 480662927, 379738451, 516677411, 315513590, 956239294, 77448559, 36266379, 136290496, 501408076, 740463168, 244248036, 101950017, 373167759, 711728798, 164376960, 271348425, 279523781, 643364400, 984232990, 602360576, 814459996, 465549950, 162031643, 470331778, 235701102, 940625328, 237359945, 857347651, 724556093, 280111216, 234548323, 192920995, 233414251, 563461992, 260722492, 79763962, 166414625, 117192476, 739081099, 87307339, 976111939, 344965282, 272607284, 906215306, 399139043, 556318639, 502630598, 78327294, 172924444, 583876070, 363684364, 267083624, 50106720, 365119283, 363110245, 647031052, 982866591, 159721751, 709456812, 68580263, 659004251, 494972325, 459796472, 839691931, 814205799, 419003686, 970094622, 574934709, 499813361, 986315508, 232517520, 803267474, 278177422, 325949215, 799936440, 975236056, 391094685, 160604002, 108594145, 959911002, 985228684, 434462813, 18199652, 62826487, 321257587, 498991377, 902005010, 301617234, 210874782, 344499230, 492264959, 172635883, 733602762, 351435445, 571845250, 365391973, 435946593, 599534761, 390657540, 961390217, 163915756, 265261264, 485903193, 848079915, 967059625, 588196759, 153016801, 423876888, 670017678, 793861318, 896630757, 420933947, 298257952, 584639640, 802158621, 158712274, 70019185, 157418017, 881420978, 269308105, 107686446, 15065762, 595947712, 876568316, 959551384, 858999755, 761701408, 5671905, 727385373, 51080359, 313157581, 524526130, 170052966, 546403703, 753701613, 976418503, 585963317, 176759679, 424680657, 519860138, 766307585, 661000616, 298719023, 553520796, 627234359, 558508493, 801416933, 714558426, 577626897, 186523784, 464713646, 208179850, 247770665, 678190320, 164934839, 751840436, 961747849, 352476452, 867680588, 829461754, 830173056, 23070757, 612296498, 147044313, 654822385, 426818381, 523083687, 739074628, 556140296, 128968069, 240089905, 915980136, 736112948, 562350219, 353591958, 947548389, 333732834, 853552198, 221197097, 337640984, 951075408, 336741221, 130018561, 813966185, 203589757, 65591284, 917116621, 296399216, 744554756, 803735641, 215032008, 670167295, 790793127, 361526943, 208795792, 167326529, 146168420, 533041533, 752976292, 649645663, 328170641, 985034569, 925085724, 71846168, 392580607, 341705616, 659759756, 905450078, 808094727, 599148239, 255924515, 23167568, 721357297, 505629340, 750859907, 68685443, 63705358, 734420603, 716581444, 488073755, 521427770, 850904808, 645299013, 826751912, 403340851, 3314264, 634736158, 984479746, 704044652, 395956031, 264129630, 323370079, 911268436, 428137173, 570967890, 760218600, 902652831, 8463385, 489948331, 989479604, 903280237, 336873420, 24684324, 272663241, 708597011, 437693558, 349033919, 133182377, 229987987, 38722617, 543570916, 161346104, 272881055, 920179376, 792804954, 197140264, 657094953, 686384502, 773001926, 904231961, 180085508, 396081227, 70354171, 893554570, 100683266, 113627162, 910357171, 99248413, 925522940, 406636932, 148471082, 710165976, 456150722, 170024638, 895442067, 164552792, 535815214, 841929591, 6884669, 189476575, 5262145, 705146915, 922689086, 799525525, 675184912, 784455788, 919127292, 645325661, 463865500, 691492116, 486844129, 85599374, 659284763, 125691582, 165846229, 809724512, 534555267, 149043183, 307028114, 514262189, 824497808, 368093233, 685146966, 844353009, 180554283, 801709428, 635491472, 797109415, 948388340, 183361040, 124074660, 714239879, 751839127, 762486887, 818918525, 147469088, 353728924, 225101235, 333722108, 211657191, 697843859, 275335389, 596706017, 700831150, 51538022, 654434373, 546577198, 839787284, 312048697, 468281786, 485620399, 42976757, 60876908, 638668178, 389800204, 111249196, 280194734, 169561628, 447463191, 146355852, 9017220, 856897301, 266912823, 464699978, 754347192, 152500996, 783360584, 541443777, 635422736, 239714268, 347864288, 102555991, 483027632, 585634595, 279280366, 189976927, 735813394, 89022857, 211781685, 278012936, 948905922, 129006268, 239733077, 708865545, 45938454, 545677571, 957118136, 313422915, 536733358, 557452024, 56392496, 383550653, 170373194, 577586307, 198818672, 250378590, 75373164, 420324335, 148364843, 448226067, 68729240, 708396763, 836649880, 881472507, 959816669, 155943291, 869334900, 197690521, 722532112, 307485405, 184515199, 247242404, 450596793, 282970375, 96287416, 661377968, 833455341, 701561986, 369769482, 872410856, 938858946, 490676306, 767238458, 123476708, 502810675, 9773147, 700980973, 790037674, 292576083, 137606458, 822319789, 897317328, 483945952, 520077653, 769526806, 712482920, 245262329, 854235160, 828263880, 962178765, 440125136, 915352492, 838610999, 355110790, 558356990, 940773952, 120182490, 354760028, 715318231, 154107666, 427733235, 961594737, 617850689, 116732994, 935789735, 662195967, 449941035, 76533349, 760688617, 169915219, 855662115, 840948902, 771573195, 633264119, 409278906, 854634762, 40516368, 960993438, 667591277, 216773007, 97299910, 107513298, 227443999, 784947737, 975356373, 971812031, 511566690, 459395919, 190279108, 192591215, 274533801, 717012427, 808473109, 130055841, 965282578, 89094631, 113412020, 420084161, 318099232, 133278360, 93879221, 188513843, 664655293, 193683178, 838399082, 803421964, 614684972, 978554952, 16028359, 633234586, 478400114, 661826541, 85283751, 593251200, 741429376, 349174925, 99897365, 985895055, 789421480, 655352561, 456546697, 859172587, 421239642, 574992352, 572458514, 91132847, 33392286, 454715624, 660004857, 673353798, 345710211, 36678195, 228729639, 185461318, 333623016, 535219867, 642647968, 578165534, 182002715, 551682580, 145009960, 772769208, 423251529, 172637364, 52065680, 399662159, 924192669, 591784253, 488921004, 813083868, 548359349, 265915606, 134262127, 995081081, 380748662, 614363062, 346359688, 813436594, 398981320, 512223177, 968155462, 537150299, 484621098, 7342388, 16647885, 374523840, 372962469, 519841489, 729977250, 840233756, 793231400, 397818035, 91489991, 526445857, 114422252, 962889000, 261100151, 543453349, 200697470, 944658542, 779343603, 696052674, 906844722, 827517295, 627436703, 958286654, 670860645, 630207940, 878274706, 946618575, 642812404, 764165340, 788098896, 13433741, 208842816, 482628496, 119457411, 716677996, 789502993, 750546978, 648220240, 588432678, 212047910, 844848199, 131877794, 760721910, 532063359, 770385212, 752414492, 296600258, 906391116, 120832824, 944896038, 692533960, 679967666, 240788337, 401963372, 359634934, 865771938, 789664491, 670920085, 73017676, 841343861, 317519799, 688107818, 951181285, 907403511, 469762759, 191174182, 226499131, 158122593, 614401380, 374725720, 691973689, 248126419, 220808093, 71169122, 138224561, 863791420, 762798482, 820818117, 896288552, 477293020, 69048388, 460001315, 628117215, 864413207, 912244715, 266568155, 214336060, 993230631, 697957259, 112267066, 520699641, 614451995, 381411342, 319780648, 790004109, 973450405, 119046087, 110747857, 354185004, 550904616, 421391581, 379217512, 849506455, 612749642, 714628068, 431747082, 524416946, 825899472, 591378925, 494764835, 754950409, 733316244, 332987769, 324324177, 2824169, 942652066, 143888497, 720316210, 29355767, 418120650, 781753798, 208005101, 178615341, 808924618, 368678606, 416075895, 723678281, 259469359, 343500858, 190626730, 424714985, 920556959, 216141030, 641606264, 825814372, 784940188, 261578357, 676818903, 555765364, 217803767, 619797528, 329691229, 161216092, 457994191, 231876632, 461700076, 933887302, 903024655, 826725148, 202514174, 596858515, 493080479, 706169167, 94680971, 587118555, 443340987, 512590493, 9476245, 355504528, 243027356, 260605410, 397331507, 910308866, 149488351, 233800563, 863394188, 672908195, 745031129, 995347999, 966720077, 253762605, 374692575, 897407859, 940777200, 28299461, 887994164, 790820693, 438235658, 624713138, 309883603, 385042307, 49580018, 239944583, 512807546, 629701784, 373617401, 750406552, 390417230, 129706287, 829558283, 580614556, 235497909, 919051926, 592621807, 913757766, 4131716, 20706893, 201277944, 873445653, 26740262, 44059997, 791453361, 670286733, 494373890, 896222445, 473599618, 900080349, 947747753, 419009912, 460366421, 334740992, 921602071, 207034089, 912014236, 85771724, 628160554, 404828852, 157065166, 320564145, 43080751, 731032633, 441483946, 770358071, 320751629, 55813171, 882935409, 527182698, 687288900, 26143826, 216849637, 107817061, 901431162, 505991980, 211986513, 859748734, 436375087, 320974252, 538350935, 195301024, 448245497, 634095862, 748833947, 918293047, 931867706, 860905978, 53759189, 501350538, 976696596, 604333509, 587903068, 220454383, 895074366, 773049686, 1264391, 260349923, 560755037, 822202863, 367009987, 649719527, 362923208, 798545364, 6013466, 800067826, 556801025, 673429633, 26594317, 442591621, 679425792, 539285131, 979793876, 24400921, 180606372, 981916667, 431870923, 960612209, 971019956, 606833194, 504411380, 575186720, 960202892, 978008220, 325344089, 834955182, 499059129, 293245115, 415167168, 459667514, 922706404, 407566907, 803994187, 444291647, 776083003, 395195174, 520770957, 376188421, 939518407, 157806900, 630554065, 106668348, 755728402, 917772867, 2528923, 988073725, 67884048, 609725214, 723335512, 181643333, 876545210, 720260902, 100877145, 687079158, 432698358, 391940487, 289313430, 697271112, 517336041, 347869577, 725138115, 926348814, 920708756, 650130832, 133727089, 753661893, 142433284, 850784759, 162885455, 499312352, 785459769, 450615563, 314556759, 185001370, 298104398, 745887967, 350606962, 617657400, 921864711, 447812869, 510837081, 922636601, 545717222, 114902021, 534275901, 379647447, 171509386, 35772890, 167022930, 295664541, 682927088, 219163410, 827780029, 17048898, 825529155, 294703875, 795017536, 454807675, 937759576, 119799672, 551974669, 419550173, 529252474, 302377600, 502871276, 126636495, 702696552, 813888266, 428591795, 641421541, 6507162, 826867264, 47783797, 758632783, 878453443, 375394485, 160307155, 833899242, 252972643, 273984375, 235244368, 24154636, 574585440, 697493722, 890375556, 406300598, 456718805, 31681213, 162416989, 148738037, 128925521, 4313904, 83407615, 18808047, 606012768, 670665585, 135472522, 791167540, 946505846, 414371856, 326172720, 109113552, 886516487, 331625959, 316787161, 872266021, 371794351, 907450238, 972950169, 562757674, 848108032, 635032424, 906076992, 760054995, 817407982, 960308748, 396376008, 175722470, 667308927, 725464831, 403790643, 51681859, 957316508, 809643604, 345890086, 388795277, 900035179, 115812871, 168371069, 841449951, 814372555, 518496009, 439093858, 169289223, 18163398, 29284602, 447686208, 100376946, 444830364, 323981776, 511517472, 974610926, 981690277, 747504041, 421413006, 112121273, 232987358, 249377924, 454328621, 770296261, 966827707, 172836816, 416452553, 271038388, 238085060, 6597290, 110095031, 335551572, 679511760, 983029169, 384589746, 184582847, 376339817, 905003426, 498796659, 569959947, 91860491, 228128300, 597308822, 804056397, 811547232, 762441372, 316654599, 137191310, 371767313, 385061501, 929599170, 475663063, 175581044, 382398321, 893132039, 55606744, 496519186, 216099070, 41150813, 836499794, 932598886, 487489005, 383504751, 908956668, 417716037, 959476284, 907159576, 968588344, 4467068, 731723580, 36838166, 534496676, 35581131, 391342139, 211023170, 77011316, 472138912, 981709234, 844641665, 960374208, 195833450, 549576510, 626469643, 373247131, 549522469, 852910861, 245851188, 435004774, 295185662, 18830903, 64728516, 542004655, 742445779, 306973557, 983569925, 527351398, 195772563, 115965730, 684277475, 686481746, 981349468, 767447651, 442590109, 641824276, 674611073, 37074970, 865716390, 60395245, 342301499, 866737890, 24488422, 903904246, 966644010, 60878616, 46903134, 85635346, 453655674, 321623841, 767878420, 305753867, 557197234, 482371059, 904015331, 149183898, 380175150, 543334770, 695307095, 717522807, 141506127, 260661148, 433281147, 633280502, 694809183, 120795510, 648065311, 597568122, 830473402, 447404834, 668499181, 512416784, 593870646, 201417817, 486921501, 999159950, 773225951, 949160126, 853142515, 385698296, 699758340, 853490637, 275400318, 124646666, 949357456, 15952011, 8914333, 493072690, 400777981, 395249809, 87398683, 435376593, 349959460, 871423861, 137644083, 896006619, 222536905, 437058701, 320686275, 860102073, 734697902, 388679826, 690666970, 9538177, 921753207, 696793920, 348401254, 230762706, 303499221, 989883083, 924037475, 754047585, 691198655, 145817992, 603331972, 249580854, 818884223, 330595123, 24128615, 998639499, 651812079, 138198494, 920561261, 887517402, 570910157, 484763105, 971074422, 136089611, 992811797, 216303231, 364589358, 275058350, 614542408, 967908099, 252961935, 310029619, 705873258, 736066728, 826765273, 621120486, 783944628, 69038532, 170899550, 201889621, 789566594, 267085830, 251720219, 183881891, 100534315, 670595886, 848491276, 396228030, 86532606, 603327758, 619009012, 196699031, 770510348, 165079807, 716154545, 645408584, 852179522, 671667869, 480704620, 406858192, 644771159, 736837466, 896161611, 463560748, 605624934, 506286938, 440025195, 3108627, 40723655, 123681843, 89610760, 652204597, 407479122, 905747330, 743858075, 485078791, 917697314, 37325596, 364252192, 410739419, 90174060, 650834920, 425396530, 175039515, 397709131, 794813264, 549793828, 38212476, 707815197, 725882715, 971474683, 335307913, 200782903, 486564673, 442804062, 162830130, 6409440, 269897803, 561759548, 114866008, 734279043, 483328547, 789020917, 3830974, 174258974, 981608123, 906834123, 329091102, 372057211, 222531176, 165840785, 468541182, 836014975, 113658276, 937195615, 82046521, 581675106, 97398711, 515031330, 437888765, 362222620, 956482811, 814926868, 425682779, 310359542, 182384669, 455449973, 344304734, 88936808, 706464333, 149837682, 668172459, 284937361, 237170280, 949238109, 527055858, 667026668, 29438788, 429242141, 848409520, 376299949, 420180312, 428810881, 820301704, 282103341, 64219246, 345368368, 853709056, 282288517, 101008844, 383988007, 934532502, 730715466, 746136745, 45601416, 724292316, 990504525, 860042270, 555397425, 237300738, 603171606, 867516687, 580009731, 223479234, 467563700, 502077941, 998040749, 414433488, 657971357, 580890541, 348025129, 617667435, 839222833, 558299850, 81791419, 575344117, 686065625, 869138407, 758566913, 103485330, 835979551, 786244401, 805061285, 787289967, 851606274, 241191729, 400692538, 22901391, 862592122, 237440797, 95574256, 5788115, 476343073, 554474546, 642458833, 109195216, 567936517, 69719267, 992168595, 579658417, 897966080, 279475160, 60198581, 498949043, 46443128, 893664578, 173594797, 651148339, 602876556, 731189003, 741826649, 135007636, 740604983, 126039120, 619658185, 78142846, 279002224, 94028484, 296339380, 696615089, 805433671, 847724270, 119021690, 166307759, 943275948, 369366613, 907428902, 87552220, 323012440, 719869313, 543195897, 99905289, 669912173, 211353721, 698229920, 187821367, 575128974, 304467776, 3093986, 873532552, 264534110, 478219532, 638620002, 28485946, 445338761, 961313997, 731719254, 85900591, 369209497, 112285635, 299123653, 940924792, 62326807, 587047632, 396842882, 272577169, 407628833, 783322573, 36533232, 877945306, 335968181, 905487513, 355878230, 631586702, 273722894, 325141092, 617141074, 978873370, 127639901, 102170446, 322407747, 311520397, 481669342, 147789655, 26786875, 867393202, 246055871, 605378480, 417520619, 793673012, 186336127, 475720285, 751118905, 51175971, 627555709, 796985335, 229667867, 733895128, 229848419, 636145035, 550561850, 728946935, 400351161, 857572677, 444651548, 559457278, 73427517, 746784841, 938794905, 106084403, 277590917, 589266110, 256679191, 851522864, 741889052, 738676921, 306467713, 116899967, 868777260, 414670193, 536220659, 62094429, 930351135, 772510851, 238003533, 770841578, 635820747, 710680050, 460037763, 185594909, 334803332, 651004627, 448449488, 840571075, 821594804, 413133342, 21666330, 95571669, 614650, 485832453, 650995958, 587007485, 368528675, 154061056, 851110433, 431391405, 816477282, 701197169, 882298444, 807889161, 887721251, 462887235, 361858185, 310159591, 924164745, 617142435, 233348931, 888434845, 784478766, 604409729, 462583724, 216789922, 539724586, 962707288, 938204773, 258532322, 926882512, 95941321, 428662055, 673510544, 594358827, 507690099, 112018779, 168325653, 134994335, 758657180, 607782539, 59504738, 586261486, 30408893, 484803042, 338092178, 136428496, 480443849, 496466081, 163031533, 334749710, 102836349, 298866630, 698145093, 282388761, 285728285, 851693507, 478739436, 649103687, 765374195, 893228644, 493755922, 986579263, 311622731, 628105237, 585904467, 199018665, 239158619, 974453272, 862365167, 68404949, 49535948, 358731421, 453580128, 677005822, 631083101, 524648876, 125419601, 882339341, 406651455, 891928240, 268901333, 209872067, 419442203, 800667275, 69665238, 28983333, 803694239, 55863878, 993003576, 338250979, 404112186, 931765704, 64981814, 878989718, 699266872, 559845389, 90000706, 101003582, 130664416, 971271113, 601816926, 38124457, 298750046, 750587390, 349935903, 969103604, 119171085, 440835153, 327280138, 753658803, 241304148, 373622338, 822198419, 395384127, 582328958, 474451935, 824531772, 894819010, 678087219, 474745061, 473442236, 837511393, 622184006, 691027955, 130701724, 576611942, 727766790, 907131103, 994823761, 476111636, 1238246, 519991592, 43662701, 432281664, 219993664, 355649991, 514274231, 634329246, 386666463, 760666436, 407549153, 800106321, 241616093, 10244009, 875931307, 414813155, 420063264, 108683058, 376046060, 539104036, 10880661, 115102003, 677323969, 682925177, 476808246, 203554317, 764266159, 88189235, 360633851, 109174461, 279074323, 268278809, 609566523, 272133793, 858386257, 475649422, 445312576, 621166486, 227814776, 900214554, 334453391, 945694786, 232804738, 67423613, 397025327, 946567908, 665018645, 440595974, 615725140, 160835252, 275162034, 47544351, 590259013, 897394378, 194145209, 744346110, 689217774, 681829951, 277173999, 931748821, 912227719, 834182764, 87362735, 914649484, 603795524, 753187728, 511034837, 307513966, 108881984, 519305430, 320935299, 820468690, 998697879, 227711450, 630408500, 951510461, 927857512, 587503543, 315470867, 860566829, 669653586, 245680316, 495051703, 597450916, 840050859, 794842999, 69195827, 268557518, 633901225, 910449052, 615298382, 694145843, 594112661, 359798012, 454949003, 11132959, 732704725, 402034522, 421883535, 584296119, 694445031, 192397083, 728503821, 654406948, 862086306, 268963391, 308073903, 242687785, 258130403, 873833282, 501113139, 201368591, 240241459, 152510621, 771284198, 821984602, 946486130, 833006165, 109293049, 732651749, 602621231, 40069809, 669533989, 534333601, 27009102, 795552259, 193980268, 673356267, 274788486, 371777117, 826315777, 809901404, 360612558, 970972246, 210888714, 135533663, 14863594, 605880992, 236115194, 248933313, 955185403, 711031247, 312544662, 634691572, 755473931, 566558379, 200681979, 93464141, 297040123, 251635176, 57489870, 211062947, 403961372, 488657774, 28113693, 594810987, 265617209, 287470161, 162717846, 527884989, 120226358, 119335528, 630087130, 813262557, 56885394, 927012454, 408850981, 255682968, 440576791, 282252391, 855041665, 655201173, 744944428, 792097452, 453929649, 745888639, 164475188, 908029360, 951726794, 128687221, 173465164, 137720538, 574494976, 784702655, 860294516, 99912169, 216585934, 384331672, 450697112, 116596856, 890948177, 691182995, 199412955, 920882718, 970080938, 995149445, 526082082, 879420104, 596311131, 69243925, 376657589, 536571691, 633258022, 60902241, 900124895, 809050047, 137182010, 955927609, 113323517, 721883858, 129884768, 414870658, 358060068, 316652892, 108323733, 709240248, 5823287, 61453915, 104321781, 378692936, 785289835, 969509579, 809988037, 253647792, 137041563, 171960757, 672667635, 489772249, 349655203, 639985162, 679421065, 738941831, 125673685, 876525099, 111307794, 355148568, 212137840, 273286137, 493097995, 288037591, 432765029, 819860144, 811987078, 81091806, 113528462, 135362867, 839361246, 950843636, 48845045, 993764639, 802636125, 705906943, 772812818, 190389127, 147311264, 568443867, 881932392, 328218668, 969951787, 294345897, 777416680, 983645987, 616982241, 592602698, 660863627, 861465120, 937814064, 922642050, 468280795, 929525761, 298162466, 458680442, 413492241, 700097418, 917168582, 995844920, 721600405, 353008977, 53878172, 335172146, 16970598, 277509282, 375148266, 298734339, 882687177, 198220244, 470377580, 655505275, 136434079, 275481491, 325748176, 975288682, 720825749, 34101875, 955040707, 866155583, 40872371, 132938386, 172424319, 664217976, 586704347, 963044021, 688497466, 628451418, 905190597, 335770652, 511195893, 14312950, 280655259, 946099004, 667027760, 377590351, 466094410, 778636479, 954850743, 940168967, 56802767, 292915127, 962035369, 386161780, 708120662, 860413207, 723124242, 490911830, 296634257, 550542703, 840965828, 308106264, 348866991, 699886028, 358478280, 402393304, 188551837, 19348281, 733979310, 383123026, 358253103, 856319168, 145244375, 585786847, 926357201, 121425698, 567355355, 78258259, 470655786, 574584465, 270408684, 175627327, 559985101, 918580181, 569832953, 662323472, 111698687, 362703302, 115027654, 149748160, 909476057, 273487460, 444512782, 249459579, 71387307, 274576641, 72178442, 948966276, 928108940, 708095106, 257157238, 779068170, 465021711, 694078850, 540471985, 93931838, 183156850, 549788866, 906279566, 920291979, 466606465, 978084086, 196559737, 881672894, 24194332, 673967278, 690151232, 622810563, 494020161, 643179374, 880734396, 611219167, 87890720, 628054820, 588719743, 727642442, 748115185, 15261254, 505300250, 156339549, 780696649, 626393006, 700310767, 931106040, 704947687, 306029114, 87588059, 387339607, 863427316, 433659189, 598335133, 452892561, 690947821, 404042360, 885199715, 926041215, 270849133, 64399124, 661600414, 79519886, 95592613, 820155098, 107805040, 136914006, 156873201, 935574820, 729696083, 420922115, 817366808, 434267558, 885000570, 441674835, 274131389, 119435799, 754118562, 892498378, 918677417, 592702483, 219151080, 918421299, 311900643, 854962411, 584680948, 331065895, 964457672, 448275741, 409313832, 647017152, 209988388, 919198025, 83822522, 165594002, 416523911, 222247752, 416378975, 996076012, 339055994, 303894852, 992884552, 131614793, 284815821, 90882513, 156814478, 190846726, 559660704, 691951488, 911176221, 160562312, 191415001, 70426725, 297288024, 398116575, 975467391, 48266358, 470133188, 881785260, 947520256, 879886388, 45112314, 756974486, 999467375, 812912162, 624429967, 218875971, 202121788, 802030279, 729422382, 962325345, 827783916, 55636270, 714519985, 76082474, 78928338, 977871364, 419112639, 947492846, 663586688, 568349920, 575399132, 12470501, 110887853, 344096225, 478827936, 252421994, 195306154, 983287691, 732379540, 452359500, 68587638, 802701518, 442909131, 374111, 308859234, 225001135, 376506615, 821276276, 746964507, 273612364, 323018352, 465021330, 962781714, 278079398, 995328016, 256386081, 28404384, 79253944, 203101725, 983283947, 241763612, 482699506, 97693144, 216683188, 79910756, 944454215, 779672981, 904941800, 792706004, 621607518, 731367805, 33709103, 599184837, 922052145, 464577823, 702160027, 469411037, 826222319, 635059465, 312375270, 753278654, 679360366, 581032025, 315278089, 949768452, 315136960, 377325824, 947651131, 303208225, 699827612, 143601967, 66674758, 575938785, 743130650, 386790564, 696185726, 494722340, 452006744, 41167559, 186762535, 783577904, 402379619, 636455991, 853122107, 169573242, 141596988, 560704504, 199330633, 895662708, 881672300, 845838298, 730367943, 723490154, 25869545, 457845370, 250758100, 217535140, 344120411, 646968499, 364867478, 206598421, 805124236, 549506397, 856194060, 416536027, 371496840, 118913289, 760949173, 466835602, 21337292, 466020361, 618385811, 720917610, 583823966, 546635779, 999571166, 839012924, 423301823, 444639011, 453789608, 584251653, 117793809, 763177096, 655489719, 31771758, 277554336, 402689193, 162358199, 530263881, 435012260, 432962428, 588808349, 885642069, 428191220, 36373335, 96660695, 859432106, 537092152, 669298115, 668143438, 706138631, 268952068, 5739165, 410894022, 514020568, 385785962, 273639685, 813071786, 248634696, 778663327, 812817568, 857748630, 143708342, 113710860, 76163703, 774518406, 482022201, 44574850, 430022757, 725915526, 756880635, 975158250, 546009480, 725525876, 893703269, 535140327, 654231720, 310195159, 942583747, 862670987, 584519078, 875574338, 867497297, 865708987, 263945519, 812507871, 495753445, 128278439, 499929647, 272817397, 629497445, 455503105, 647625962, 694759085, 472682789, 827247297, 383170790, 900336463, 122835487, 135263074, 136480283, 355415537, 56625114, 682533140, 587835807, 148768957, 159387195, 377238030, 658904944, 775245817, 983785166, 521620765, 468141002, 821076818, 406318271, 642555181, 802776032, 242232834, 507763890, 677400397, 359123893, 28836983, 959022037, 438504917, 693884007, 566700391, 72544326, 138763183, 539653710, 360055283, 725322478, 288467230, 223930043, 650005477, 708496465, 616785440, 883617800, 761859357, 580437363, 471938419, 192608981, 828643601, 523016514, 61836057, 28647414, 660384999, 950642270, 320041577, 272475603, 913078715, 492401301, 969758740, 193798920, 307260369, 496358440, 651306621, 105613664, 54698199, 729933507, 105369731, 239996815, 71194733, 769750717, 829106699, 811012379, 802756344, 467357170, 789109713, 201092072, 881827591, 371295005, 481271516, 415143335, 5699430, 832748829, 365713966, 470947562, 485157748, 695538411, 10517707, 122394229, 14234170, 624559932, 79966027, 866831360, 418946887, 738002446, 559444953, 360974824, 264936736, 80958612, 249685939, 946484720, 626136830, 46138916, 423558294, 972289448, 542766789, 182434888, 238551861, 348631237, 614561547, 138348141, 164569652, 446540223, 986725578, 803450673, 495875705, 283092493, 902908630, 791421801, 184867234, 746782305, 977934613, 534066166, 344252334, 707871648, 383614829, 881201850, 925256225, 835656931, 131677301, 918771913, 762968741, 486299393, 636587155, 372722795, 878595842, 32479919, 261311774, 11227587, 943753585, 668715974, 595643070, 443967419, 747364006, 868724149, 842488579, 835400554, 5871881, 722003743, 166266059, 499244668, 875599298, 72421592, 807111547, 741949013, 571105674, 532620794, 945837903, 286562712, 465635189, 186399147, 478950356, 809022797, 382114063, 83810890, 942437142, 836961145, 395247654, 755308303, 813284306, 433331208, 302294965, 232345987, 644899847, 68196328, 643145725, 631026049, 839670140, 598080806, 453192499, 704856218, 514891332, 983444620, 542035821, 869384391, 672965790, 124611218, 202516125, 305560229, 926113244, 626426931, 661692033, 78014671, 257981780, 57925391, 356725649, 72365547, 98226463, 838417403, 608801902, 667112551, 707115745, 136159410, 991523735, 440771827, 364915600, 693672440, 343048297, 639059878, 753138601, 999636090, 763207436, 211940623, 515814567, 650883215, 252770917, 165298895, 442477457, 525404529, 623678105, 377402456, 358671873, 635675669, 901123009, 183593566, 989138565, 70334924, 153631271, 184212916, 635863017, 98100203, 468796733, 762291869, 243831578, 63785393, 864379603, 532824933, 394525500, 369765089, 625706703, 574841812, 218852864, 713994198, 34750620, 863498746, 521676801, 509211385, 474199994, 764896170, 710337875, 338940944, 564008553, 76279632, 739062800, 33682760, 320681567, 139035833, 687731135, 955000123, 348149487, 932063147, 610878906, 688602875, 16628831, 291827857, 288526923, 127781345, 581983620, 268692476, 757920246, 756867314, 258340725, 823834714, 85386412, 175239876, 387726921, 721584548, 357711047, 219319815, 530112101, 258605027, 922776079, 578205960, 671056625, 972700193, 8528208, 849696722, 359106065, 70425246, 968877970, 818064308, 313033231, 8291956, 616391202, 680478287, 951758647, 773143429, 324264213, 39566613, 107713340, 275160995, 630847300, 456811269, 535209796, 814772007, 512429691, 347843742, 174421460, 6700815, 399946178, 561887952, 863496062, 938489467, 353980736, 187518441, 895285307, 581602937, 284497900, 514323498, 32119651, 736395793, 380316815, 128713351, 427461099, 926545398, 773594334, 842878045, 527007065, 980354437, 688427308, 479658720, 43326064, 438569949, 204848287, 505825506, 160910389, 808295851, 566845144, 389602346, 428557085, 350757202, 262309870, 961678650, 95120557, 900824152, 961887866, 705579639, 95926718, 775239001, 780153483, 886195022, 684221941, 870276047, 934474934, 683694034, 441875695, 118938511, 583354592, 922191030, 242365085, 996202625, 29269885, 978460422, 32831949, 36151788, 303956470, 524743755, 896349598, 291801802, 912855225, 753142915, 453297748, 342919928, 159089688, 672426437, 740391979, 956865151, 700235373, 813065445, 627699893, 625082586, 449783443, 485007264, 161065440, 621424404, 524289385, 121751919, 321272604, 609884916, 771292783, 445754295, 148811683, 593687792, 264450694, 275516565, 286045854, 441717205, 161913443, 161852939, 695551884, 98784994, 690033610, 478363778, 651270080, 923381712, 812711539, 627258137, 694605475, 231674588, 906857304, 442125924, 312406813, 530974340, 316024942, 914096326, 616212955, 708093969, 378445993, 131476781, 116848455, 219493142, 359592099, 720143733, 749964565, 446802050, 436179053, 534335806, 720460426, 776999064, 829461987, 405604335, 283382868, 189665812, 680941443, 760375254, 64631282, 194715446, 19182901, 489851386, 126865356, 951396465, 103434562, 125107544, 697539217, 306729750, 398968972, 73251825, 393263649, 829310437, 590322779, 728322847, 609355604, 929561038, 158370666, 380431863, 866440770, 849618545, 824815080, 246790343, 351825772, 829038582, 696874253, 239464548, 556512744, 472465811, 762502506, 60784719, 730773962, 94316590, 915638546, 28462059, 63891222, 858505799, 138042224, 83344471, 228571211, 267171023, 326618684, 480972671, 809583011, 127950999, 241007683, 458714472, 884024548, 447795983, 693690407, 59586624, 119489941, 646378215, 285286103, 71732232, 448622141, 210482142, 513333584, 152299484, 525975998, 928924383, 90736587, 278406612, 934262040, 276474275, 968467784, 795999487, 447848964, 279250212, 649773639, 673879112, 102061747, 849286469, 42477735, 174886455, 645804579, 735152512, 390331549, 268188929, 580032560, 466121677, 144906160, 685623455, 167696535, 974868732, 919177221, 956642668, 94171438, 829934934, 417677258, 9848090, 364617060, 513949106, 597071068, 750749615, 405996001, 444801341, 126800696, 956673045, 722489425, 222916443, 763918841, 949764862, 358127324, 974012561, 4342315, 905606038, 182198927, 966882183, 665766870, 158347519, 313981030, 948005963, 250699972, 766306694, 414479682, 203499347, 94253903, 819945233, 620782044, 958358413, 113428095, 860383762, 923103042, 788017847, 441414720, 628844153, 160463090, 571352435, 689877107, 579993009, 503205579, 491189178, 332959611, 444829065, 317497658, 404281708, 153240118, 1518438, 687899147, 131051553, 515115442, 360015166, 456483717, 500770897, 530000378, 46924178, 151526551, 152250142, 635970237, 112607133, 450614699, 618548436, 972156789, 467189021, 928813277, 69991656, 364757082, 983563391, 124002866, 789461286, 844725721, 440103882, 427141464, 846439690, 32214882, 91920036, 333940913, 843346469, 463281322, 127433000, 169067282, 446526071, 5178016, 754547455, 210281926, 621072688, 689395547, 702743066, 351367899, 434360527, 268382035, 385498935, 908678422, 590087791, 278870857, 842428291, 15462934, 105456744, 56258908, 459555638, 340010659, 33958758, 243432973, 654482487, 115058876, 653531328, 76642918, 587885889, 994320820, 342993738, 968415036, 5319234, 215684021, 860731989, 105265919, 65195888, 165909489, 312364968, 562680071, 220603317, 835339764, 308252259, 538396729, 753251592, 968305682, 565937961, 611343249, 557060647, 513858937, 344680365, 409113673, 585696017, 272770903, 914415222, 807173925, 750542167, 70067765, 754967012, 464210230, 678137818, 110749561, 975918521, 878225634, 460362154, 244680617, 995587679, 288719712, 780029836, 858021302, 102488526, 463657491, 300846570, 951589679, 212109217, 273474434, 966323647, 161310889, 548501145, 60760598, 892209471, 465618204, 586116131, 26243212, 818447717, 368878694, 675485210, 627796584, 381287959, 751933782, 534378378, 343188701, 429979095, 423538320, 261031230, 403997203, 116037055, 211545869, 997292011, 170075902, 340236307, 119076199, 177130958, 504083994, 998502476, 509028616, 189651862, 893974365, 964045695, 208533139, 157864246, 253014900, 434596679, 524781516, 10747058, 355833837, 367823661, 424943695, 981773735, 466293251, 621912892, 952823205, 7749097, 188711505, 850224310, 839523788, 60169565, 614354270, 953159427, 366067316, 409163582, 216737461, 826382784, 990254336, 978132747, 896703841, 746637986, 400878354, 428332306, 767710120, 716403137, 289991977, 216867526, 364912375, 17585145, 839620610, 88296038, 936425550, 91824934, 318682904, 627880590, 253175221, 883823225, 989405979, 767038379, 906488655, 118171611, 451726409, 566151244, 364678884, 297867397, 163286013, 925275217, 253643002, 190160409, 247983178, 317029242, 540859778, 52936056, 800646038, 582286021, 589721133, 541084227, 123788684, 481859348, 328550928, 603430886, 834648448, 923254692, 996048907, 458705937, 789448471, 220199680, 677721717, 678069367, 368857175, 24045872, 178400819, 923743633, 254956107, 74729086, 180001680, 497929058, 233506591, 979271909, 948598353, 714339444, 608327175, 559355961, 518698520, 947867066, 390428001, 17357277, 623222878, 181295647, 537446540, 606133581, 893071852, 21240809, 95108034, 325683185, 365355410, 260211136, 574860471, 579440856, 38204748, 242444079, 940799629, 156025398, 521184123, 788547013, 420428397, 604085056, 510201445, 909962468, 332968936, 911189791, 158764288, 377263055, 128208220, 938053122, 64577952, 841157029, 239549490, 323938985, 325427224, 743141868, 481411767, 87776447, 878613804, 858183015, 124230851, 521778495, 757040627, 278409576, 920348583, 260557633, 646202408, 57206172, 246021583, 490323949, 615779014, 80682669, 18601416, 347567037, 766931673, 651286018, 780826010, 94895892, 468177546, 690917448, 375121497, 22796954, 549728004, 974248056, 143719192, 623384039, 112534273, 941174608, 430483367, 487346416, 317340849, 960751299, 814190603, 762051684, 972739078, 766061912, 511364179, 274679992, 140985246, 471499324, 307167110, 444547726, 507472719, 984943005, 888707511, 481773852, 883220801, 298856674, 136074326, 486979530, 453687379, 740813125, 108469897, 418917875, 925457555, 350371928, 452045067, 482635759, 279194018, 546472064, 891067936, 458757483, 883450682, 683853022, 474135390, 416016564, 747437721, 906493679, 298963915, 881470902, 57639190, 770067006, 163628554, 711759395, 92530436, 639801380, 483344443, 503718369, 935253987, 402466400, 586748044, 717731762, 286609333, 623561645, 894838625, 459208258, 436830973, 138639314, 119971072, 536488997, 561458695, 235396221, 876019717, 956121628, 942245110, 444135682, 840470650, 289988958, 42970369, 778344260, 848800420, 731494565, 153869406, 662159045, 500353543, 174796997, 475160731, 405348740, 477468304, 256243557, 529580834, 998798759, 367134922, 698492178, 691230507, 587628846, 952785534, 566451056, 68959352, 381994655, 779286906, 1786160, 155850960, 75403530, 890063132, 586165089, 100823460, 823834154, 656767945, 249663328, 173822297, 684502063, 682927312, 678715531, 552772186, 168635202, 164441640, 387157936, 932882700, 276654934, 753042950, 817640618, 618538195, 13029037, 838188294, 807737943, 646418456, 833410522, 513882589, 960245771, 197262146, 97871348, 747406368, 471219755, 524313294, 293635081, 622079985, 509205404, 141176359, 499380544, 344614249, 783235230, 517539624, 563385641, 416505752, 818256291, 204030022, 343986725, 98170219, 845603820, 765021023, 566084679, 831875221, 789262821, 747870690, 776011195, 703691521, 783184206, 179108511, 330853504, 227383395, 531450278, 472312674, 986710033, 809350876, 413876855, 226756856, 322563161, 832935959, 46444555, 150488961, 355139040, 253247634, 541879203, 608589742, 311810141, 319119001, 252546397, 555397090, 486078452, 693378139, 927671286, 575398615, 637301780, 976582982, 632018885, 931723176, 474199717, 648117599, 185752768, 72759537, 627997969, 840126474, 355897678, 117822166, 201188780, 685351748, 963353028, 4059861, 172499839, 982802347, 661564945, 381079975, 989648665, 236525682, 579165695, 613457842, 76921036, 871113011, 627651410, 653925070, 366089313, 918269938, 506370922, 876712359, 640546558, 853142301, 512467999, 965886778, 667794329, 630083847, 153708346, 824581453, 183125529, 451041548, 323288131, 562060983, 193857512, 360206620, 63076360, 24301330, 726892870, 397399734, 558464786, 893953112, 638814685, 465105744, 594368190, 793980872, 817112930, 536580558, 257158526, 186106602, 599296934, 311788999, 589535179, 967185399, 123963242, 346512555, 380406175, 564107650, 766030404, 534818223, 518276646, 955586212, 567472928, 681213575, 354642450, 820036241, 761327286, 692512030, 687213866, 258084845, 161399849, 413137699, 446608490, 863898207, 505389449, 367970895, 655103076, 882938306, 809348304, 171816956, 259992304, 686953056, 75577976, 504265720, 720879799, 678425126, 744512889, 701610250, 562696538, 837399430, 475736857, 965430588, 402845074, 648271557, 949715185, 771616986, 590289081, 403578892, 113698434, 643613239, 360405383, 429991543, 239546703, 992216672, 57469871, 69082183, 407382480, 251221176, 812141741, 754383897, 895160489, 793554691, 443818712, 2735103, 183839984, 514318179, 193642434, 407018443, 60343492, 77439966, 674890659, 278276712, 164616870, 32749541, 795052514, 958420835, 747579999, 483963586, 947692149, 914359219, 50847814, 153081606, 807680343, 334953674, 782194254, 947965079, 365410094, 711124356, 246403107, 936284042, 788714155, 719344805, 254497965, 235700781, 649526125, 675730300, 85988447, 701020297, 343434203, 198375456, 61374516, 585350800, 288823236, 978103583, 627245088, 949602475, 942222891, 139637076, 766895278, 461729511, 834681767, 385313721, 15322476, 637712238, 747674383, 500237647, 526231730, 161309492, 964596195, 5110894, 59198786, 57363410, 208645350, 218428546, 595912932, 89061582, 381662862, 167097035, 822370444, 723400143, 615440375, 4535389, 284073984, 822157874, 995476030, 714671111, 785641993, 568739059, 131817701, 196634723, 680252789, 146354491, 40327405, 182515067, 392170221, 442562396, 310227454, 967123718, 518225822, 814272963, 189045385, 176615819, 299554518, 696767103, 922881319, 648281130, 558629607, 234562592, 72186429, 441108624, 514990411, 890117321, 608899414, 350981853, 226563362, 49670099, 221554162, 781151796, 839686550, 634330047, 911104314, 230361975, 716605015, 698299592, 13318873, 174581726, 663666533, 367075236, 849420958, 941884901, 955734387, 899343970, 45372877, 723784026, 909527537, 717086718, 523143908, 97844470, 942439461, 1263338, 884649575, 267172083, 867882280, 313060906, 261053444, 824776884, 978406015, 812004270, 501706058, 610455271, 925363054, 720815998, 974851266, 5782332, 259988136, 690163452, 177420799, 372316998, 727080982, 298445561, 938273854, 182453301, 793776166, 336265795, 458230341, 175413781, 435278040, 231536838, 263375020, 803958596, 711366154, 972993652, 569105359, 490363803, 21410098, 368651509, 939027651, 790220588, 412759944, 141729526, 947231597, 541840129, 439736991, 558052043, 721150215, 421933493, 136197515, 853195559, 286985228, 20648760, 26681209, 161542425, 289544388, 884820291, 829150043, 947262217, 577233791, 577896006, 270871273, 414190455, 377300499, 725056949, 304663436, 15059013, 841285384, 70703416, 802556975, 436876466, 143637247, 221138198, 635524493, 805753341, 6896647, 581744466, 446367600, 289097954, 868192729, 352325198, 715997388, 428947315, 102053681, 895743605, 297613820, 151651905, 265230501, 454028502, 733684196, 358327060, 687421116, 431580984, 293704839, 525026654, 502292980, 246415969, 492739769, 293547127, 43928554, 115962776, 234591885, 689283186, 973893149, 797932980, 302992938, 386782153, 449234055, 556471768, 796679037, 38405502, 222735421, 160893729, 478073211, 32058795, 236657548, 980864736, 643281455, 566835974, 137409492, 210002841, 659753249, 770544344, 704950971, 334383209, 19149861, 770930516, 129340379, 272045809, 202001829, 298126028, 206196323, 103199798, 177004671, 672075931, 836191206, 420612658, 395351603, 800575458, 909655374, 331701155, 288094477, 314296282, 328090662, 25864309, 696444505, 923075488, 594195789, 365305737, 765237711, 760362036, 323058938, 800238106, 706134050, 636453849, 776892399, 612855423, 256198838, 358845132, 124240080, 915927967, 457944118, 772035673, 957032601, 386529472, 752557159, 159649039, 75123158, 310160526, 205446391, 846360299, 973695237, 500496823, 123987709, 296214527, 751930237, 269304434, 942567713, 476256209, 572656936, 989007724, 122126342, 625058137, 293016526, 272944772, 841804527, 779885081, 946219162, 784633819, 775684020, 55711448, 363935764, 41434359, 950823684, 415287079, 270368147, 949741238, 202755625, 881230258, 729320012, 754651023, 572214826, 244241597, 833193900, 732192978, 342647030, 335882273, 886329464, 721453628, 462660037, 159165971, 918873459, 599313737, 825905066, 520394206, 91417221, 532602663, 534194185, 237381643, 836445816, 314572630, 63793496, 78618410, 48057293, 456308285, 468131833, 656673485, 593683908, 459694664, 989417684, 736539276, 133743532, 714583647, 156615494, 139438610, 323193444, 244021144, 507897221, 984865747, 811912241, 233734571, 186899969, 164167701, 995847581, 403762078, 84314038, 869943221, 511936925, 454334263, 456796335, 801995539, 396997286, 716566022, 131181495, 500019458, 47791594, 225473723, 695011238, 387858212, 163721603, 10777064, 37186973, 802684624, 350814783, 170333909, 302520832, 563717179, 709686318, 24999778, 259840087, 347519670, 966740048, 5435927, 817684961, 144020, 886012258, 845024341, 988719843, 135245784, 84912607, 217022850, 677797951, 923425140, 268801899, 780356750, 35258239, 359607805, 999587112, 381987218, 905161064, 671059228, 450134802, 619592077, 665901673, 699610246, 829693129, 616405672, 84628599, 577765522, 657134721, 30196240, 360990309, 519686703, 50513448, 57985291, 984249680, 798222354, 114801673, 857305020, 466481072, 574433222, 684260958, 50012229, 236002495, 335024601, 517025076, 455619471, 868490876, 256640314, 942073728, 940352281, 964038957, 37128183, 454940862, 259408365, 130944640, 864031447, 752453001, 482044459, 495527918, 568600161, 679625566, 671051133, 660851013, 658664482, 84549593, 735961486, 203322105, 59380905, 39750389, 415796171, 917569819, 368340862, 155112664, 533371199, 327174563, 3807570, 864017883, 480804777, 623962356, 38442393, 246722596, 596919705, 780439950, 248773269, 441910421, 248190803, 682628250, 938212841, 90066934, 14690952, 122879744, 628836167, 558529735, 137750129, 797018743, 64160339, 626828422, 723396681, 367541803, 170648405, 513737451, 217753559, 537682200, 318875511, 698156193, 519029902, 234932292, 606192404, 504347626, 482651974, 948583313, 918959309, 112614557, 87919851, 684375903, 848061127, 916393938, 893444543, 201820985, 443595233, 308628674, 745109685, 656912419, 280620439, 320031775, 981936022, 465622477, 856504971, 985552435, 555426793, 836187995, 23035785, 196989669, 678107093, 342949517, 700439214, 755370269, 84023196, 442140319, 463010072, 192923867, 690713745, 17090546, 901267027, 797364799, 282563537, 247767514, 815944479, 484265933, 299298853, 708460525, 471042831, 729121270, 770172376, 135447745, 291572174, 639019142, 54535425, 253778100, 395198494, 128429195, 601594574, 923971090, 600055223, 817308417, 791102594, 68174056, 895073840, 570986485, 221240489, 649746089, 689366928, 827745715, 13472021, 278679954, 127962242, 14627911, 367928010, 121671545, 403449912, 537051197, 737818008, 472917424, 683587181, 55148604, 416658242, 620209340, 348648573, 80952680, 52913071, 47862966, 145520356, 172954995, 77273009, 16987604, 197126086, 452495937, 170424602, 922011164, 74432601, 125517312, 559737151, 655509516, 547823157, 818717459, 663072098, 491615706, 443731819, 706174917, 967265838, 407488272, 549230340, 382955792, 227282821, 454771210, 239947686, 800820598, 765005150, 583010882, 13255650, 31222229, 888159866, 145179778, 432921691, 888053634, 383408273, 317067420, 160258817, 229235945, 363727504, 754041107, 322784557, 463563292, 618297522, 870704644, 264448954, 505085737, 464553552, 823854402, 216951830, 319807751, 31764243, 284405007, 405047074, 259090092, 294152949, 9291378, 993700419, 466045775, 784682147, 94579745, 706284283, 841328526, 772182411, 793988538, 108397195, 295536442, 104463687, 195958852, 76297568, 199338960, 70453647, 214876612, 924366526, 789899193, 584868186, 226862463, 136818109, 539709506, 750966860, 191509832, 291014652, 588282798, 884096191, 450711041, 330564535, 629161822, 156246887, 748929708, 923667375, 210703875, 693922569, 603474802, 663361652, 631073446, 976574011, 88542706, 108154899, 378011049, 723243503, 596258594, 29549033, 621224366, 331030477, 248642435, 472073727, 951552255, 976267491, 190102361, 37221068, 332893185, 638127746, 647133048, 736019700, 822440719, 799626834, 828507741, 6753707, 871181422, 579343564, 727145236, 929376210, 189155280, 563092205, 294748611, 445328002, 989020113, 48904038, 48316242, 539277753, 568279519, 300946712, 464482394, 752636284, 464736369, 624155118, 866852071, 334460192, 756380775, 955022933, 101842090, 295068338, 812933078, 451314190, 657810746, 371321381, 730164031, 133545749, 737882383, 502732386, 557766606, 29389080, 820793505, 695320238, 795288910, 476558346, 461157803, 889008381, 191081782, 472132340, 269217736, 370975769, 572493869, 541272146, 408721839, 960893713, 707049609, 442795644, 385517023, 538621082, 976823095, 394446050, 778312802, 866421369, 809999223, 337451712, 796394239, 652606504, 699670055, 377510084, 143850946, 376768297, 592574900, 773460314, 6167238, 165093924, 417135800, 219060018, 70543606, 860932546, 763900940, 646081802, 377774890, 914577657, 241677641, 705475107, 449054756, 648613488, 1435590, 151066996, 112280133, 499930755, 166142716, 86122425, 601990973, 935583584, 52151185, 746353299, 16780408, 187201434, 720036190, 341923510, 658246150, 95424532, 11720408, 38210620, 815406587, 439806140, 412031864, 184569811, 432154335, 181674085, 747321713, 613021535, 553524284, 702014839, 237517893, 237867488, 135837561, 467384549, 861867607, 778697518, 620647420, 649280820, 412607484, 141370338, 234403158, 959260622, 195639739, 763380132, 33192252, 610547185, 81242125, 685321373, 616451365, 842953602, 338975158, 861370534, 517369247, 18139823, 346400870, 541658079, 77297460, 590977709, 590165288, 784697282, 864802885, 29502767, 138801974, 579176588, 96482318, 37098948, 151662059, 759854413, 991054578, 424486530, 493478725, 388932607, 949160996, 687791600, 301516442, 83588252, 723778784, 371670383, 936240683, 516735604, 304203875, 642820345, 773073856, 586584692, 260846101, 165011589, 632094616, 224551361, 926387446, 208555573, 485139469, 556640581, 791601230, 471298188, 147982207, 990366986, 612781878, 704217723, 985737221, 209751873, 40124159, 317811212, 737003441, 529465132, 822003120, 41673945, 931882865, 962248260, 890757231, 979506631, 535618168, 317907351, 4022152, 893748153, 994618826, 723803914, 972288929, 732856611, 948029475, 13945475, 920399885, 848421975, 147610798, 784485968, 690434757, 580524584, 309612657, 789668079, 671748652, 321759163, 392025462, 625462791, 406856154, 293140678, 140629679, 124081788, 341494490, 236848384, 621837846, 377415656, 792850210, 98968382, 383099165, 809222384, 74983616, 163923008, 815175258, 432399169, 49422462, 486884299, 289798743, 190498771, 705577925, 13113274, 599308223, 315140422, 357277662, 61935659, 163291786, 819221546, 903769273, 384476019, 647161085, 649474911, 556096140, 662278332, 85945293, 956994936, 101317261, 680439248, 496058598, 365118142, 185282544, 69538489, 972140409, 266315000, 430449819, 145023896, 603143559, 985069269, 877943793, 699931364, 803258009, 250337747, 957033609, 118069550, 234103002, 964855277, 373206632, 519457508, 712910610, 158201760, 978372250, 414605102, 255054271, 509554042, 371743461, 452150355, 647042875, 982126717, 447901475, 599010945, 655531088, 182036908, 207761285, 712899459, 622852930, 5874130, 861270093, 312861817, 122234127, 779559744, 894286855, 781470733, 94179285, 150979176, 370046922, 892710532, 889721039, 927315846, 946389662, 357470350, 11828945, 448715818, 814108967, 370841616, 413603221, 836172127, 361016844, 179120167, 585422832, 249564322, 674860533, 672406772, 433141074, 40548674, 464930232, 300361447, 627977456, 620656053, 423071844, 978965521, 740786581, 683175689, 413717554, 774503461, 84175989, 206579116, 940732480, 589146163, 960635076, 713520310, 551245300, 525807378, 508605648, 152820818, 413541578, 252040971, 506572863, 946278945, 514903147, 875076952, 824985029, 310063422, 713633070, 924370464, 671939754, 24723906, 280377471, 384161831, 586982478, 692574776, 635154439, 72332856, 122700695, 531499439, 164598902, 308914778, 80084583, 803928654, 987766908, 55321807, 299132734, 66150538, 190105544, 799371221, 644785891, 573499379, 558549719, 889900925, 170337946, 963707499, 325576110, 147023772, 592146735, 131043638, 516982296, 694797976, 712504399, 471430691, 439602945, 2046719, 514925631, 109536051, 271187850, 85474795, 768562194, 614952376, 970202901, 507814207, 922601928, 377993290, 707894805, 71582405, 717339219, 709467898, 778075311, 396127366, 510077112, 138828354, 726074238, 562405936, 685054374, 816793667, 618557789, 638052386, 602102340, 666018842, 704151867, 53288736, 392736461, 941793700, 527244743, 958125676, 351558507, 828458977, 334127564, 990269853, 597818194, 978370223, 975527228, 500320807, 354654063, 22910802, 51791067, 229586527, 947672919, 90411141, 50244760, 905038893, 622970558, 685898633, 256775045, 178348788, 301619220, 980480471, 914111020, 25395270, 901805739, 735111226, 309203717, 232520973, 509184495, 271560155, 106027011, 268671561, 319578411, 563301430, 616933509, 820215398, 331781153, 372652746, 23462585, 326144691, 429406752, 160513735, 64634227, 90333096, 568048911, 780417907, 208288366, 183054536, 229516956, 949456347, 883757266, 299861689, 597200428, 969306223, 586009689, 840663529, 121625456, 781368927, 772437622, 771869852, 549373657, 163159129, 931901689, 87116740, 110760280, 903260464, 996602534, 355176235, 292405372, 421054229, 272304686, 18404930, 600931412, 161785193, 955407696, 480551321, 168246310, 534933166, 286023328, 809935402, 131964779, 319749226, 354538274, 334613702, 576615298, 618201805, 913133239, 981448944, 827120418, 80735658, 719043454, 104698179, 580769015, 272890960, 925916018, 580607073, 467229360, 103487613, 153075320, 321041646, 136068703, 682803764, 425713964, 212394427, 246723589, 405541520, 528694802, 61255393, 238681809, 945524179, 264473533, 942277877, 112164694, 245973972, 960153304, 79667651, 312098251, 379049847, 311532766, 623885589, 812776679, 790601172, 583050426, 481909168, 848381558, 262139604, 705141234, 358568593, 612095536, 465387259, 213226659, 120455585, 240346258, 290732954, 474317137, 124579877, 622363635, 527356195, 340893998, 30896816, 592241140, 34260535, 206615504, 469160833, 318047781, 765765085, 277737296, 604462594, 389782686, 857428012, 487795444, 708330646, 519058819, 340097373, 157389279, 574939217, 691891866, 616907659, 438953960, 906329024, 407381283, 971902642, 28723098, 392797140, 466680764, 242570473, 292518960, 42136943, 251457024, 439631637, 701490333, 873415279, 228214210, 818672486, 967244666, 268812135, 792553028, 679488793, 193763246, 512224809, 85794961, 292064929, 73788602, 672954857, 299880468, 448018068, 966287559, 443927382, 50622800, 831985608, 611244838, 825095607, 555488224, 653189415, 559386888, 219864079, 914195374, 495959951, 777227430, 258216723, 356924003, 870477514, 4147574, 703962204, 57575210, 560928579, 199325727, 719472591, 279458981, 774657428, 44983295, 154386521, 805096781, 711771319, 318482279, 388108417, 234516647, 229007109, 739215688, 225967195, 171750730, 138036578, 544865967, 701474709, 834900253, 142782086, 694786944, 348107804, 845108134, 408858377, 666421351, 794856891, 477797504, 495500750, 244416226, 406397918, 754004826, 251577716, 926486257, 981591889, 570425860, 314859948, 648637881, 338459875, 208129074, 243726471, 951919174, 438339300, 604489063, 664462113, 929125078, 723329609, 823803012, 614928354, 800713874, 416407607, 491718574, 54546828, 700191345, 871182638, 178072828, 524076943, 842523848, 719642172, 203061961, 884081672, 995245769, 748401078, 781905372, 440525571, 657271066, 59333597, 817318253, 927007199, 852263199, 865796322, 434399361, 61594608, 758769764, 549428584, 879213544, 495553101, 827311255, 596963246, 575112798, 695327016, 626452206, 209141191, 257505326, 832728592, 812250308, 785758255, 735547081, 542239199, 300228327, 89491571, 493877458, 628072312, 665155748, 265204461, 251484193, 174094070, 12416855, 992447959, 9668114, 449841417, 147512083, 786593964, 836764560, 606815683, 214681290, 260789267, 458426546, 323277775, 606294226, 815225519, 732683721, 841352409, 607851697, 947534708, 949094001, 425407946, 689420719, 368248541, 437949995, 558999656, 217000586, 302466204, 366822266, 74478680, 113217156, 825357941, 128583841, 21614877, 419191234, 87110509, 490276037, 990946615, 135227744, 41716871, 260119359, 199630377, 510880521, 553500207, 62394922, 37953895, 626858462, 852174787, 504480156, 75786819, 808743096, 272356556, 419066623, 471048445, 851633682, 724100585, 260998995, 29972169, 496511220, 177228626, 137674391, 572111597, 305950805, 79900595, 200728837, 728108813, 42289260, 698532674, 169499943, 265957640, 840013927, 88713291, 164751461, 602834022, 173903781, 264449792, 63114502, 239225303, 256678659, 360002315, 607245243, 334630233, 248513041, 107441414, 388303532, 851417911, 524410987, 267100884, 662684284, 253883345, 234247365, 713460389, 839829893, 580479377, 177680349, 165849066, 903763568, 205522814, 995240354, 603974700, 876279673, 334226456, 246774340, 138328132, 361319680, 313957442, 658182659, 488655947, 210795360, 506507993, 816649091, 989056020, 696917222, 61732206, 507053481, 487207136, 626576235, 578644914, 229560364, 563944702, 374883104, 35983551, 296480853, 203522031, 541583228, 664192074, 853678678, 541130049, 430764602, 401914271, 639533119, 823541042, 72509455, 755005082, 231030849, 443978522, 629790268, 480422001, 697598521, 879838300, 803707128, 732345658, 798167860, 590856266, 303420269, 662119230, 410228688, 528712913, 169138084, 360957307, 475134900, 147345772, 905052200, 84448068, 357389902, 214901184, 720242103, 545396203, 708990648, 219889222, 45893246, 553437284, 470924522, 796073551, 203996723, 121140755, 188890003, 4142499, 377756425, 368703433, 449662382, 535327182, 757413629, 892627101, 680019547, 170821632, 227361650, 191244423, 803281418, 338223895, 172002098, 962292084, 228558360, 537013983, 327413067, 716973815, 110175353, 442053796, 864078570, 185138215, 367270324, 900394510, 621975054, 251156044, 414836560, 519708597, 479310990, 718257798, 902317407, 449900617, 574346075, 856676360, 806281824, 802513119, 671706990, 384941124, 748543897, 370276950, 359158515, 499752097, 904013769, 666384577, 643759881, 410444520, 47701079, 972623730, 202969015, 540646069, 578712086, 293761388, 247672927, 346692901, 967704511, 632683587, 237356212, 248092729, 607707615, 940068818, 681169388, 71261436, 61510979, 588379415, 583429177, 932268126, 330113183, 712368458, 454924715, 443972424, 435698773, 495374173, 183388466, 923857981, 921318496, 425927840, 367853449, 647356988, 508336863, 362830214, 590754236, 12760413, 802320977, 835740095, 5798628, 617799568, 873934124, 671732426, 23219728, 707951145, 85739190, 937529496, 428666543, 998309319, 111994949, 168761513, 788585027, 615678140, 233190327, 175889868, 423307399, 771309886, 917870088, 270049094, 560661282, 542209625, 434366949, 91017084, 640056822, 826099799, 852584617, 120168303, 212353606, 857036993, 910247801, 960185257, 530253572, 965934027, 265557771, 126708472, 43441872, 363607492, 599391029, 219328072, 960828676, 923529601, 102158639, 712584577, 931458367, 564117813, 547222531, 361163028, 116484471, 43777149, 371454194, 35815872, 159442979, 981608531, 829953163, 574785460, 662277551, 85391370, 124286142, 938405674, 631763338, 703217301, 121990175, 665929992, 407281860, 805891000, 821407120, 925533583, 808418756, 370322279, 439513259, 408857517, 175698417, 231049650, 622449943, 637555538, 652971866, 610104770, 506640777, 947251929, 338103524, 511362, 629706813, 188336056, 288783855, 743642664, 884298922, 257049038, 426039237, 927744822, 186903220, 678943390, 464553704, 509999856, 932761678, 312761517, 239025192, 824434318, 445746909, 425417278, 109360400, 106106243, 710817334, 206363914, 726966397, 267391589, 518989119, 478434213, 63210822, 829896691, 799092820, 295879300, 175915166, 717297378, 123895279, 20587468, 382035966, 225378202, 254985189, 611424713, 594936924, 311225336, 162909971, 967233873, 800122091, 990269741, 58021172, 322269161, 297015072, 819672431, 302098602, 825681125, 474857584, 955308151, 603164419, 535044397, 557310719, 185532464, 311191685, 312637329, 714448362, 258826193, 127724227, 629658197, 290710252, 173151677, 364288771, 339373563, 835318173, 930369189, 815445364, 363477242, 78883409, 327670618, 666931253, 302231554, 334331989, 252111400, 723408787, 503258066, 695192752, 940455820, 124414756, 229779294, 273424302, 926968841, 692222033, 887468135, 276285795, 634834643, 895617495, 940282167, 305256531, 230183223, 495013763, 23057753, 994671314, 873538770, 938989418, 407112357, 127112713, 784420457, 607757640, 720595820, 319190995, 55491426, 97539998, 944046199, 436927955, 774769789, 856226780, 911627308, 271124307, 598464183, 506434463, 726829438, 705895810, 674038346, 491354653, 519592096, 856115300, 299120090, 605318498, 59906822, 359721473, 838086132, 484894502, 955679926, 10792951, 664722157, 747409012, 85940043, 838632970, 358364628, 995457080, 670214042, 203391773, 867591909, 999845390, 515092269, 4501535, 865888783, 29221103, 74746555, 315869476, 845703539, 745278300, 378518707, 87940081, 838458933, 703285150, 58433905, 447039498, 724559840, 74179083, 555401261, 829216052, 269943439, 983513386, 798256744, 852394709, 313052845, 838677507, 314630313, 263645940, 504037234, 822611887, 660483678, 384991109, 529498681, 730187641, 249291788, 516767887, 954633829, 476600447, 210507989, 386279211, 488985657, 630312367, 580841723, 737512774, 699400423, 656875369, 98684996, 329137614, 939255563, 992634705, 35176723, 337696023, 940583056, 469621876, 100030648, 769820885, 43548296, 751274231, 128895134, 183134759, 170887303, 61867468, 936626787, 717191791, 425381834, 568483780, 178335105, 237929799, 920996128, 941055509, 106066547, 122868396, 688949522, 337212965, 304817561, 755685040, 870049549, 560895424, 778944635, 995958345, 910103133, 169110419, 813626695, 873162722, 405869683, 802185229, 223196111, 446558191, 18412112, 139468418, 48541116, 268961614, 817159834, 347203209, 708554234, 439077981, 408746175, 972122408, 961693160, 211169034, 866284927, 97006530, 171303210, 938257631, 932128275, 240121395, 258501405, 516642613, 185965807, 210936109, 802523070, 625314438, 692990710, 492372693, 542666364, 477237720, 890835272, 909971702, 868799771, 402221765, 738329591, 778115486, 979590564, 206550729, 751903169, 121854905, 554279688, 81848237, 843957114, 709849615, 525691964, 409527302, 491626432, 906578671, 329675424, 289650006, 999010475, 240651192, 29210888, 519644047, 835960901, 490548346, 404772596, 768053573, 810454264, 945666388, 972469850, 489634130, 656969260, 255550033, 207191175, 186354230, 83623181, 181214333, 34768479, 573085154, 637707373, 204340778, 453610774, 337632, 318841691, 765880968, 539580546, 214809728, 92011418, 942538481, 561066421, 900489657, 240224853, 382266133, 666617037, 821108303, 559476537, 112835552, 535045737, 192246888, 812681349, 706336334, 198871183, 637913, 395999239, 61770931, 271489831, 165160669, 498461872, 568660655, 801639011, 312795016, 381065745, 732079368, 343064834, 307472349, 976854065, 47732711, 206511037, 893883103, 823190107, 578757432, 118811390, 800284646, 326964924, 168892788, 396684336, 908534614, 391689, 931545438, 442423626, 493853075, 65408443, 988140568, 736977222, 205956927, 270501731, 921702185, 676242651, 827136236, 76800435, 373190895, 536494098, 159906243, 138984225, 860946360, 352744822, 840343437, 237060603, 498639338, 357763429, 653666279, 340380982, 763067734, 610942277, 525504972, 984082706, 247068103, 552921204, 692906741, 83181330, 507647063, 396301314, 947899474, 355963760, 173848960, 656285224, 627176766, 400021143, 411150114, 98173099, 468108308, 710268090, 176433101, 147648996, 773196714, 715519893, 588194699, 815296376, 257448144, 92320713, 902704951, 786585216, 791636208, 49457423, 481194667, 732561934, 809479759, 923333106, 571231040, 180375019, 599562090, 612899045, 36380462, 606525149, 717554401, 473756109, 41566706, 36492677, 263756798, 194992606, 519960834, 966242527, 358465785, 462913834, 807967917, 605344068, 287119870, 728046568, 665224079, 682408123, 333748, 214057565, 993207518, 224906297, 660695974, 607073539, 269148491, 378358213, 966584667, 580535955, 685061596, 866671110, 775683715, 401104641, 529300465, 355607223, 982734938, 858400042, 820775290, 140841612, 207186331, 98531073, 543701828, 106245018, 64524671, 551701839, 756282438, 548743864, 952860063, 579215204, 184593368, 997892682, 891423292, 632178103, 292866393, 758847910, 682392063, 614516606, 916119956, 731009859, 908766927, 471945864, 828657719, 652777750, 25167794, 48841336, 62594881, 471981935, 853843195, 399690407, 150741170, 853530215, 327485680, 976763052, 10346096, 212134850, 539909818, 713180895, 660809046, 924406283, 91675219, 170981553, 948211245, 921412439, 741349418, 115597700, 138006537, 312092028, 551497983, 410362848, 600946315, 48124934, 527354269, 559980919, 610182961, 938503462, 825122133, 173144757, 361071747, 478238332, 816311151, 208823258, 323310947, 506857393, 895014544, 493797972, 893535974, 872491961, 373438720, 975764278, 392999953, 665573279, 46721522, 439464920, 331159722, 454518514, 227843318, 870537626, 693238698, 168584488, 560254142, 621112987, 259393313, 124888119, 304498238, 907640199, 883990384, 957199647, 812669282, 938050204, 519886056, 21209837, 540013759, 121978330, 35982748, 888422754, 186853903, 425440894, 49892696, 540888049, 38257236, 942418302, 120412328, 886981815, 89241980, 417681200, 205078757, 63628173, 921433104, 718493300, 229507024, 721161891, 419782850, 68144055, 494632387, 525686752, 421814444, 750056365, 820154571, 363272794, 953443007, 794474255, 258716907, 639089542, 125107218, 62938142, 791537582, 344777058, 646968731, 779931364, 990733799, 959528511, 584422598, 486345387, 826840712, 456536853, 357133209, 757611776, 706955880, 224483263, 841895618, 777001649, 885145523, 770135470, 491035409, 86511551, 285270706, 299487474, 427930872, 77322157, 109382534, 112588727, 242669735, 189913217, 472226301, 702459823, 491409060, 109655230, 696307217, 511992694, 782349144, 534749868, 551722504, 728079129, 786839152, 676856499, 509538633, 457275639, 348465472, 405422597, 8819353, 667636116, 432350369, 150392382, 896820954, 389545445, 191983468, 989989119, 569201474, 671970347, 629476050, 608695815, 15338977, 136815589, 159254470, 178838285, 791583828, 590907458, 348568577, 534346048, 621359210, 549002867, 1938580, 151455150, 449027472, 356642664, 236324145, 234878706, 953746686, 398327458, 394587673, 281650301, 33606803, 836760248, 401456721, 140659117, 476034460, 390881461, 424677910, 105026913, 733810136, 742527042, 679455939, 576797607, 135954964, 961606961, 231731304, 219905941, 1058828, 669402430, 913113436, 313730101, 549545367, 75336340, 295804686, 354953512, 398847511, 688725133, 206031730, 700703882, 457159005, 358940134, 553280749, 732045089, 796504466, 281894735, 368001233, 329981543, 914164576, 841846014, 807928641, 50238348, 850138948, 16743241, 840531294, 552330386, 413363225, 865994924, 805642132, 410893671, 498128039, 431655363, 382112672, 883954045, 630509883, 60134076, 680592654, 51103743, 927762944, 382332025, 273945973, 52940397, 973603868, 511194391, 814533484, 755319943, 41837114, 344968865, 19398431, 893403410, 842468970, 399819669, 151408626, 364558402, 456119723, 399826496, 347998898, 842866569, 26733861, 158861487, 626227702, 126497195, 537597050, 32138164, 505972555, 394032543, 863244631, 105323022, 654005528, 397655603, 714618025, 881344031, 683794902, 186628357, 660257079, 851631773, 741149053, 891611672, 891701979, 415162899, 968881176, 715845222, 505699835, 604849139, 40504459, 587096050, 887069461, 40588576, 687963544, 98985787, 532764544, 313085911, 236987932, 808614181, 581333359, 705833908, 769846804, 187050504, 205755125, 373387526, 306808327, 778713872, 950551052, 885878152, 448355679, 705726775, 139075014, 23479784, 252106298, 549480861, 965920215, 554565212, 400121103, 152405009, 642091199, 694091698, 874496852, 50091676, 37609696, 936409549, 32820527, 983010012, 833990684, 408046954, 293192475, 599262393, 752141513, 98965758, 42542345, 197921923, 391681736, 488406896, 868329895, 474882858, 267149227, 989944204, 671503456, 378239212, 308268799, 398785086, 183218495, 820934784, 100491804, 872109953, 124998786, 299342720, 113522648, 949263951, 519782728, 97523072, 412046325, 806139221, 417559225, 586469487, 501604763, 275899951, 109768267, 641016248, 449769416, 788285674, 984470413, 337367904, 164099710, 209068577, 470160020, 872700797, 786410042, 109007956, 425992219, 224573886, 92923906, 359450462, 646082370, 352595533, 743196659, 497459440, 638537723, 746979996, 600381031, 48768681, 102184814, 790706873, 723808664, 18147439, 449150209, 605825706, 910360533, 893503828, 379705763, 345333762, 134806421, 842536743, 474857927, 235483665, 690233474, 524432782, 442279553, 726169834, 411269921, 535904169, 367320489, 437406941, 366632419, 112232707, 271553318, 832084205, 262362515, 383953162, 219549161, 126869155, 624374689, 163701912, 921810022, 980403784, 272163046, 971909424, 177482058, 314117146, 195654538, 670972632, 733123147, 827930785, 867898901, 744553801, 955521273, 223414185, 853737406, 810872949, 960122528, 330383948, 268646588, 744673071, 570584218, 536535810, 109898227, 143000330, 465095441, 586579170, 594652765, 44666, 855877143, 543308345, 271408031, 755344408, 852344114, 469439231, 69857010, 212910562, 941147546, 200898430, 416614585, 372421766, 561173708, 686718707, 403078373, 419384757, 367087977, 761879671, 75932494, 927741862, 406649552, 947518835, 861654610, 779073489, 358975404, 29152207, 641946415, 986372723, 557384437, 668886314, 788640611, 439009536, 64254141, 196438789, 204461970, 64486644, 133031564, 166262418, 670190051, 641448531, 923254823, 636324259, 291575530, 93383785, 396271716, 819619087, 742397222, 503746639, 501600711, 541581055, 214027862, 773228157, 136790535, 159086420, 735390919, 118103633, 802133644, 192284905, 412455880, 901851904, 29679303, 550277751, 218667118, 270569006, 261318747, 990787576, 914158894, 362992969, 985164968, 331950381, 728031376, 703057972, 454212481, 428559096, 522911774, 468309346, 115645336, 977589272, 10336883, 829084929, 271585289, 581407634, 830539066, 324309536, 213786246, 920121081, 453178849, 25210498, 36954007, 758785371, 854756596, 480196043, 54943868, 260631644, 550905479, 675506156, 90519454, 321164726, 534964133, 144424630, 122364996, 444123419, 343226165, 151150470, 490794351, 759771637, 754197492, 630921266, 884431877, 218999854, 110482964, 531355164, 980807592, 517121448, 873264407, 1146887, 642568702, 256784084, 581599668, 7012245, 310123660, 308846321, 877050673, 763473683, 249739195, 807695486, 676228092, 266049868, 981295164, 532780586, 192608524, 602152388, 697916169, 71229713, 100506425, 742068398, 932639508, 848200036, 984379230, 885747231, 509393013, 76551570, 608992716, 337267433, 204397111, 212617042, 828484378, 315713416, 930476415, 841175850, 687883491, 404956103, 802813270, 735840720, 169289521, 922416838, 571468720, 566471802, 434814130, 473814277, 334433213, 274192504, 544745374, 619773568, 970051307, 410622130, 889459191, 358697455, 550782106, 586965242, 861183470, 196257234, 219948986, 306055076, 788372749, 440064276, 913523843, 73744758, 466606835, 90308050, 694358941, 577150815, 209897341, 461410703, 231955425, 261165273, 736187496, 989821195, 917259537, 377431842, 261130934, 719351757, 350123996, 926946316, 775358332, 357965929, 570403524, 283557144, 447523811, 753242628, 61728311, 742582798, 962331490, 742551609, 418041159, 162482438, 673073888, 107715803, 626095671, 704334639, 321388446, 753563845, 414713617, 827529440, 824912029, 683562387, 136878284, 11510812, 660045648, 45891039, 246639104, 317458649, 556197695, 505650520, 389349604, 296848316, 174838730, 887408705, 268937148, 738936828, 570133968, 459832078, 462584806, 777566091, 71685968, 657971191, 649085136, 258708467, 431534084, 879575233, 84130755, 146901308, 830061062, 495797937, 304081492, 861843335, 677034838, 922687465, 753056637, 448745130, 933461298, 534326774, 851855105, 573603093, 844114293, 936148651, 805074892, 750199951, 978625673, 568900677, 864441089, 840861459, 489480797, 400701216, 78362539, 491586308, 948690402, 885035435, 577099709, 254216414, 432755270, 781673091, 788072217, 263411790, 797691866, 112261027, 654714894, 441504144, 183530300, 415120900, 806596586, 73927282, 662001549, 615306309, 904416802, 582858188, 338908326, 538935277, 764652324, 954499742, 112880704, 657591784, 687328667, 562922316, 703014205, 851125620, 169484797, 359111448, 816833141, 424857692, 293875052, 308501846, 612097047, 477895578, 50768061, 577850157, 962162577, 395913732, 798972668, 799780350, 397425624, 494773720, 427138629, 145482532, 647900138, 381009158, 456668191, 510413469, 30512419, 296236617, 52548583, 153953229, 294100490, 299776585, 140938895, 440628378, 845202378, 426416359, 475443274, 238642028, 887061899, 816338632, 197455511, 366428039, 406528051, 375155638, 219958838, 728525067, 918522103, 455313712, 670106162, 235538265, 408232930, 873116167, 471416661, 930112875, 858448437, 41692105, 259382134, 847534835, 545610227, 981857861, 582668580, 612104512, 575492929, 468114135, 787628759, 9509122, 22129873, 427768356, 911132921, 374302327, 730128376, 94386000, 803896732, 513884760, 785738778, 332480044, 397385326, 489015571, 218880715, 658084537, 361632281, 840809429, 713983545, 436184121, 995913710, 75919028, 72860976, 233891793, 448639729, 323578509, 906959519, 624071620, 652350603, 268439607, 589267355, 764562682, 324196195, 825422449, 418638820, 174479301, 990008205, 574757855, 785284392, 455024191, 866569093, 391532445, 207774661, 496774921, 563436992, 114073011, 481606803, 698977464, 899398620, 559379579, 581320971, 894667201, 223292444, 87752078, 813575555, 550502064, 287681276, 126373172, 758689867, 197357147, 811815262, 517931746, 950977861, 383149943, 605336292, 445377028, 416518085, 180782952, 29013359, 458246738, 119334439, 981434996, 138738842, 90953733, 938667068, 199797249, 686426394, 907567515, 1212337, 86287741, 939364341, 81523057, 879724144, 55199212, 746365812, 139694078, 156850072, 661071564, 31682201, 943865640, 884107215, 131449523, 68816844, 906430558, 356853224, 823582454, 439792733, 316585155, 327178429, 658863596, 985482384, 639501306, 160331660, 158431337, 919427826, 904304762, 562021574, 675489906, 70269641, 578714107, 154287003, 982148952, 30886988, 80474153, 134604677, 388122331, 213452210, 701948642, 355409071, 37457786, 734866150, 756515475, 67547084, 637661401, 970336415, 443753037, 563618635, 454007321, 372363391, 27821413, 814976617, 404329971, 929836450, 222111800, 934199347, 416621106, 501015126, 778359730, 42557676, 115050871, 767018049, 835124210, 956941775, 220668397, 771532515, 312187414, 126346062, 963204177, 136671614, 216055911, 528729563, 448561557, 862343828, 481377308, 20850733, 812272968, 572364378, 610384357, 823153725, 768531631, 251895614, 890758341, 66304123, 724715272, 508338796, 320382405, 629005018, 290672542, 55615869, 473700499, 524221453, 614591122, 372770414, 92948568, 950131747, 311177668, 70705001, 915209198, 766164670, 255989588, 512440286, 995329555, 866429485, 98871077, 861754254, 246195325, 709408796, 641714255, 818270382, 590967787, 52439825, 879794734, 438546529, 189966548, 836638203, 340451222, 913290230, 808722190, 909695751, 816124612, 443693066, 955019224, 689858329, 493812997, 843629699, 665030541, 970226429, 369533877, 97890419, 605412560, 386807284, 101081313, 553933259, 276032072, 936470313, 490538289, 32305342, 9899004, 247880693, 138466094, 265218092, 504734048, 921190964, 286678107, 170923857, 643526906, 534000139, 973563404, 161841974, 417765136, 487359084, 783877050, 41256003, 845735991, 307636752, 926663913, 459207612, 906260507, 123684378, 939584408, 412720758, 114546097, 395515548, 304211419, 561444109, 565496732, 443910110, 538408043, 504059861, 420343778, 889453326, 303378342, 733432566, 555747085, 806095946, 96041868, 511497585, 28147311, 573752465, 858575129, 469712873, 963823372, 438426095, 354816158, 217104616, 846537565, 651979345, 539102842, 456415005, 911516361, 814266839, 394150643, 143829994, 82208783, 833009760, 258768073, 658773108, 796461312, 821348366, 222985529, 731837581, 347339962, 245438983, 779352851, 748701718, 946224989, 332558181, 845749905, 459086749, 501991584, 615885927, 528758888, 75642738, 250375325, 984171514, 102641189, 377614016, 108395588, 533613877, 700923828, 129149551, 123758537, 686900812, 977704084, 183658537, 551236600, 852268038, 264733510, 292425107, 743995682, 797020148, 968296002, 171124939, 221847157, 45794774, 604719755, 724705461, 134052059, 545632550, 910719883, 586471547, 941201348, 987372921, 784687042, 228905971, 926108314, 927472604, 818131029, 414497930, 135615979, 650100166, 164037768, 7024485, 316416350, 765790771, 985997852, 569435878, 532107754, 524879181, 795814542, 679735708, 415349945, 8947973, 242280980, 134255838, 376003245, 934809638, 617572638, 246416611, 572301197, 571546007, 63350088, 376165866, 855510917, 977987107, 153880895, 732071460, 921557883, 279677197, 629455825, 482808960, 387259101, 74026728, 926339642, 362934382, 381931452, 195159172, 84703399, 530433335, 902458365, 745467953, 925461323, 990741763, 446603826, 639654246, 139635649, 295001294, 719702157, 444388713, 993618633, 419590037, 373753309, 561302817, 369949925, 13770094, 820949768, 385794305, 606614251, 137693865, 719990166, 10733302, 829308145, 814912377, 124615710, 224365504, 302075752, 540744920, 705438469, 61652132, 93453652, 238681764, 404123638, 555478182, 3634714, 872105051, 239574978, 18978851, 264283171, 715075835, 373634371, 263962694, 332543269, 671054507, 488546246, 249466061, 945030496, 366208904, 205512407, 632174715, 842447180, 124885502, 195378658, 66090834, 237378972, 13638485, 305545345, 432438614, 421557915, 138186154, 325837215, 668571403, 965882200, 904160121, 585974762, 430503864, 721424509, 390578342, 427895619, 203649648, 860211386, 416120264, 156035330, 121490836, 540295655, 894099743, 28638469, 532381890, 360998305, 192650351, 38910980, 10308504, 937591128, 718266096, 657369867, 880678035, 934364327, 575877159, 234163433, 70989642, 378611467, 69245638, 719706512, 404543830, 982156849, 658561408, 617810398, 730718070, 806026795, 166992309, 201171726, 782105103, 496017753, 515354344, 321719181, 427334951, 109750667, 595098906, 234241177, 72571315, 799209364, 297931113, 262279905, 706334248, 126356922, 805224689, 173370339, 276776095, 111821170, 969633721, 432202034, 638906844, 89449467, 272700449, 529127874, 965538145, 847986622, 337512871, 789478163, 163699653, 307846917, 453103450, 527526682, 177424974, 887986206, 656503894, 528162443, 672015042, 477331702, 89726170, 791819600, 300095431, 283232652, 998139277, 943260964, 865703715, 470842652, 891739632, 974294322, 324510224, 379873133, 2186748, 173870273, 55236594, 863356930, 472012233, 504739700, 934246887, 353273481, 628115671, 667561009, 860343164, 11937496, 741961478, 600132637, 68997121, 376575210, 459371245, 573718455, 323689554, 823786020, 953734315, 74372274, 426663050, 280708613, 638287106, 532333228, 523515490, 733982421, 47194743, 61340972, 13427799, 446140194, 953424528, 458316204, 752299910, 802979557, 770541415, 190847442, 747786780, 528320493, 960662461, 107629671, 764760966, 71859167, 343478313, 640172415, 754097086, 220959003, 836379531, 571948466, 654688266, 467099160, 651280591, 541852858, 781965158, 730317069, 153998247, 128700121, 402438568, 461196430, 133231865, 397313185, 499559763, 944213289, 802936845, 745789143, 120034589, 664541075, 817826446, 17570364, 838057217, 267784188, 917621703, 805916099, 200469570, 999473118, 343232888, 993210701, 799294191, 800689535, 585949399, 911892986, 235048485, 754324520, 364679483, 908715242, 790373657, 876562275, 788276399, 212390445, 351278780, 230248762, 363740201, 126877952, 70676096, 637400793, 832812965, 953603365, 570281436, 126049161, 3081188, 880119487, 350993290, 772306103, 681948036, 376154700, 818930049, 888951023, 645139405, 490561949, 244026221, 871612921, 545496135, 51030783, 38423967, 262292469, 108492458, 588695772, 540483003, 739591473, 773081314, 865697057, 604170292, 298969268, 278227819, 58410283, 56951022, 329398421, 233832260, 691258742, 79910027, 592624675, 943221482, 582140054, 351274028, 682007372, 505241068, 696703750, 28731139, 133498462, 97965402, 764009889, 400808317, 297882860, 864218654, 510582062, 533092433, 401642406, 910882753, 822875903, 347078662, 887895513, 42474440, 830228918, 614984920, 250653768, 210490225, 582064344, 810593268, 21116371, 583642859, 310549560, 602084179, 618540044, 278811734, 471875992, 707293901, 620606660, 992000225, 666864093, 622756309, 667226693, 998704364, 154199396, 760422418, 413376930, 691679195, 686271712, 855549640, 132497309, 339153681, 815124907, 357185440, 180136579, 792401066, 18090534, 334384682, 180730728, 674882182, 607304814, 923449052, 100468718, 95888611, 489162625, 356329125, 632555921, 831441852, 27335250, 607899022, 320326284, 225507921, 167670270, 681979296, 152486251, 642334717, 137451527, 335142693, 346132959, 431484673, 488125218, 571849707, 296256387, 521595689, 393161615, 520221691, 471529779, 82628838, 391507678, 477678707, 426083342, 306050794, 170292369, 954160513, 835950905, 225660628, 828474235, 441523761, 222544809, 484934230, 364183034, 394396013, 631137465, 789572677, 341016536, 558676552, 104673539, 547687863, 323292641, 820263640, 633260080, 372348760, 658575261, 601137242, 433179977, 689476643, 852024723, 728506758, 213633797, 858693219, 945373968, 364272268, 968793400, 183946977, 769477708, 103940704, 762281542, 384166430, 263396924, 780073720, 220872712, 674222059, 773250662, 580978878, 824230734, 855827672, 689887714, 172918848, 151582721, 413934188, 565504178, 695557626, 79622995, 4529992, 845001547, 173710139, 249730526, 577397558, 120963061, 657565521, 94550573, 744760665, 845246937, 722623972, 683255422, 885882715, 192755242, 730426960, 771092643, 241151087, 464379573, 549848278, 185682386, 647210745, 127396405, 351422970, 931331255, 297626330, 19547013, 401078269, 402735045, 644854785, 433928177, 73935485, 197881804, 104191225, 573735258, 77583350, 571937888, 487265086, 167681199, 971474497, 291608594, 488836727, 459906938, 951727803, 771338006, 378898511, 494446291, 174187216, 118428313, 577343019, 322116410, 115042516, 386531750, 684169279, 851274513, 231168719, 368970164, 618735196, 652122511, 974498441, 384383243, 142914067, 311729054, 193812305, 592685210, 851615145, 96964689, 764201096, 862274867, 731356525, 328913696, 662398591, 35867310, 503222610, 218947994, 689405167, 580494140, 361676529, 713593426, 543904672, 174476662, 378125595, 638639026, 951836832, 157324277, 706746292, 95049631, 38174389, 232492901, 46295217, 236492334, 250610327, 393919905, 646632281, 309160582, 946628842, 343712341, 76935576, 7264287, 662200937, 991435719, 714458158, 684324097, 239969810, 995883142, 992335124, 584355679, 845363625, 661224229, 546267754, 427521655, 751434535, 474599156, 844821563, 401016685, 403237369, 207670679, 893843124, 910743280, 882218184, 211977043, 375727968, 416685688, 490430283, 24838447, 785844623, 640003600, 559103364, 136305868, 521757130, 966201774, 519010445, 690428040, 571194680, 510440116, 60912806, 641052416, 312890304, 823490549, 947793482, 257818810, 981512327, 713610775, 919562773, 550625777, 652872983, 676877315, 892385460, 919888610, 707299043, 728980878, 101208878, 196928672, 464755927, 639114927, 747085092, 722880811, 386056357, 845070554, 114857346, 482935587, 612913117, 606394693, 168981834, 769777630, 977339727, 977952025, 951305711, 927396088, 670633970, 200551113, 796614543, 227065380, 119393120, 756544599, 943230027, 659546506, 895666588, 380740450, 155116742, 845929734, 242818292, 871262357, 410982700, 776935578, 478991732, 196608644, 120162003, 809688142, 763794166, 250806331, 715232722, 16812213, 986676641, 383073698, 22182105, 741587732, 136051937, 264172544, 499070424, 717773834, 708123828, 910261422, 33797530, 445994178, 521008939, 206484379, 359372472, 206788019, 58567244, 428120442, 604787513, 259863249, 212372129, 141827178, 700655911, 955633775, 184973520, 771897546, 178631376, 521750160, 122262809, 682599989, 345318319, 691134894, 889631622, 599960038, 512469108, 132504727, 83008688, 160463469, 600081969, 67885499, 856580104, 87293044, 153338734, 678575432, 114013491, 52687347, 628560826, 144049790, 200347195, 586969741, 584459608, 344296303, 17407014, 242450817, 995511607, 79424577, 797368313, 286500246, 561367624, 47924308, 901093374, 689333561, 517514889, 609570579, 953222972, 794238251, 874359201, 756900959, 429963501, 687751051, 971733028, 339549519, 657969286, 803580991, 747198293, 133348255, 410214498, 755213106, 966325581, 790983360, 30835226, 646070111, 135901875, 77670635, 996541869, 445771666, 258143375, 141554885, 161607760, 971886624, 138522815, 508258601, 525916877, 44530926, 818663649, 993536228, 703690137, 180696289, 73913631, 751809247, 893040012, 282285893, 656845795, 322643931, 156679853, 948315432, 805967815, 409137734, 39952245, 48024132, 778458145, 548093129, 759139644, 887550418, 505511755, 260703124, 447006980, 626155682, 635506115, 66188275, 143841822, 616289225, 620897370, 615057045, 148961583, 490068972, 237709300, 781968793, 906576062, 319120112, 70626741, 123361659, 62682629, 366305397, 358545381, 658188822, 96130693, 276373759, 137260111, 662660060, 847767234, 884321875, 266282579, 179052828, 402763921, 415012970, 635884253, 532471034, 451610231, 194270331, 739700179, 513278047, 582580571, 966668394, 604931451, 901183599, 609708436, 539376833, 322309704, 390433028, 265538583, 765590653, 670528288, 278058709, 591764429, 694501312, 512842113, 218489735, 661317185, 574877217, 497048512, 153993405, 970939511, 265723441, 543562581, 757373408, 342657307, 561673480, 71991987, 99985035, 679826046, 772439073, 926767573, 225660513, 263095961, 735272159, 937095902, 411908066, 428993167, 524417432, 286551093, 308221567, 569814621, 806960417, 659125131, 909950961, 583113737, 516858559, 658681339, 674542369, 480668829, 539766785, 758644536, 433413764, 699568364, 19880326, 328187543, 298230379, 563330939, 759193942, 866780440, 543541898, 583630428, 727437780, 698909943, 779334573, 52648241, 33775888, 389941286, 202601401, 112679664, 339344720, 308484357, 971710583, 32917007, 155067148, 111641710, 892133262, 711649051, 974742845, 427198735, 278572899, 290216639, 148573875, 512623253, 572846503, 413867420, 136548510, 269204965, 427711018, 597066331, 111796172, 297935864, 683655797, 223124358, 484537315, 805535333, 258212552, 883501334, 285106051, 777507765, 527582946, 426758847, 26971587, 675025600, 879558624, 537056382, 372071768, 663817094, 300540948, 76951910, 341502346, 431284780, 507929344, 4941858, 597895322, 336856167, 829386269, 116368873, 624261488, 152778567, 108896019, 439454819, 742981269, 522733961, 911714176, 471580342, 706727182, 539032847, 68429570, 659784015, 318437159, 366492105, 351373811, 72680651, 280160606, 641759462, 399409966, 881048138, 225585013, 290589222, 319195885, 581945982, 152386447, 310507922, 598907055, 423291374, 371330598, 657979715, 146682661, 828371640, 704855280, 394651568, 174955756, 965315700, 837336920, 427999486, 857273181, 946116970, 317112197, 879024995, 441364457, 360526863, 453704095, 156540667, 622207710, 159534808, 383839715, 957251637, 345740068, 158955872, 573233992, 809905770, 246458874, 215824471, 852392794, 640678549, 928720653, 473887233, 941777879, 639051252, 507769381, 904104354, 525185827, 667147955, 111117479, 460357858, 80918872, 48898041, 490491318, 77152297, 134616381, 424539595, 739022927, 911486625, 14363609, 960230442, 711707043, 133198262, 313465284, 352763848, 497370548, 244459728, 211957723, 985049150, 242638170, 900132843, 788707340, 293224606, 576286177, 653876011, 14046908, 145163472, 549786408, 750315677, 116203757, 272096533, 766690336, 400156891, 709638556, 204709923, 866711282, 335358574, 981711095, 241857352, 682325308, 943332195, 614441078, 395389924, 891156409, 697129872, 819263388, 250503036, 973442235, 935198202, 184601162, 249008707, 731644312, 359166625, 189547604, 579417926, 736768993, 828902887, 813881805, 602616368, 771271776, 656889170, 102238504, 247211273, 537527618, 885578778, 383773495, 830121272, 953647281, 957893510, 225895693, 560323187, 758030300, 134670140, 158483506, 388776594, 170969996, 95515665, 684070654, 509182203, 824973039, 935838343, 266197946, 594000793, 49186463, 103312758, 707092686, 141244962, 621362566, 639103203, 2688976, 18248322, 895884484, 52307305, 67274883, 697454944, 756976824, 137110149, 123238800, 573624589, 600907888, 387169841, 431093377, 132837964, 463505971, 721020285, 49478458, 742084901, 365095932, 937702968, 93913266, 706116859, 28835810, 525613854, 493588101, 539044232, 947215976, 993714028, 920783948, 684779794, 915795060, 475998915, 937815299, 5219692, 771472463, 391080778, 309330367, 739484341, 25668939, 872560999, 366356097, 392131480, 605971023, 425135143, 488067706, 999822355, 696234816, 222077092, 196633013, 859075029, 454340733, 88587375, 287271889, 823715823, 866826184, 609880170, 129477678, 926653218, 190679262, 774987795, 520074715, 769435707, 58993272, 298883801, 880880192, 472377557, 255566704, 260742079, 346002236, 501989558, 204584621, 793936744, 738386575, 789148840, 749537504, 948968731, 986296738, 881419616, 294085448, 761276032, 693444039, 652057291, 307595042, 570371105, 719770204, 359369871, 666415926, 669940549, 8943605, 742441687, 328547756, 101698097, 249700481, 918628550, 317766730, 673566080, 389655197, 648468410, 508079290, 941557634, 321202298, 586653663, 849551554, 702554473, 380328270, 192574595, 784081777, 7545897, 54750577, 797619153, 659764236, 94425830, 95691519, 158041165, 61602053, 63230185, 975900068, 151569763, 893809431, 531427344, 983822161, 508403969, 555859105, 737578118, 183046967, 829124393, 673645043, 596994130, 405977330, 920241999, 517785114, 891806514, 48000914, 853915194, 53693970, 554732673, 68249873, 771804280, 410365746, 113500327, 481892540, 854139985, 560817538, 226746695, 445448359, 766312866, 294762173, 48474485, 981747331, 781251458, 41515726, 11951463, 139908356, 616567046, 706755686, 675590249, 951876703, 240574569, 648898117, 89690151, 284262432, 906423643, 539289165, 98207676, 979392575, 927895696, 325615851, 925536751, 537406404, 285702000, 939653280, 875694792, 525841925, 686812083, 291822919, 545358289, 251659373, 36451703, 868754411, 277527125, 493610475, 657834690, 109506943, 967844686, 90512623, 852497438, 850515488, 539076141, 214980007, 824592827, 445739337, 660631706, 522993022, 578420216, 176433103, 687754952, 382176818, 909559654, 934713746, 302711923, 901125459, 469047380, 14367054, 701245010, 500644381, 303667705, 129886459, 40810725, 6266462, 640157760, 184039699, 118427126, 28608288, 846849920, 341362184, 275120942, 890941906, 2689877, 328593977, 437769253, 769641718, 344532560, 144487233, 921192030, 890556056, 305860985, 814375849, 372899021, 739229165, 185392017, 74178416, 143574193, 183516951, 638118551, 136755749, 589207588, 183097610, 997524071, 447019366, 73560769, 848717187, 904182882, 427731087, 321052903, 197800803, 957476882, 382274474, 517522019, 962238653, 992267042, 336054951, 186465522, 378204894, 602331350, 655604550, 538700469, 923945924, 316561939, 361799731, 332530431, 271333131, 515575563, 460261862, 210317081, 754586798, 791370497, 605090412, 934008048, 971230331, 81754864, 650413582, 96081537, 938945146, 700082448, 792086804, 203001715, 344208775, 380936720, 851401632, 314051229, 797131462, 64856221, 943914323, 978069469, 781244429, 570902482, 485019619, 818389555, 106495227, 298742273, 862718359, 12345831, 637207210, 978814207, 584462803, 796993031, 421855608, 728528524, 364091762, 51128703, 817074877, 137024504, 944001596, 470326199, 970938852, 788448650, 996667934, 78155353, 162540124, 846996351, 170371961, 268575956, 269834039, 269028751, 453366254, 821292511, 608564793, 427323664, 974345981, 746521116, 328903281, 884729924, 523764495, 494097855, 843743353, 683740919, 488952485, 842052226, 823246561, 630393700, 757764262, 90216238, 865943934, 563489561, 329437970, 698488328, 193251869, 767028570, 249217758, 329880454, 169883000, 849846581, 767362554, 901587458, 122033528, 894877687, 428398869, 842108719, 161382506, 873551886, 185892540, 226150510, 696833227, 939791991, 245273585, 520115397, 470309427, 320679032, 186708560, 290653026, 602952059, 886959202, 524566056, 853550512, 152753826, 390772704, 863863213, 506107699, 816734860, 353975631, 403021998, 947309363, 694692165, 651936298, 126739488, 11167070, 771169488, 637866773, 298429472, 870733647, 558097389, 939719856, 698290279, 215578957, 621448654, 589280646, 70295838, 770124575, 866207996, 550879713, 575455074, 881190956, 390569079, 179414820, 869753809, 407611331, 118747542, 522576020, 773310020, 816890228, 256111847, 14956918, 896332715, 699511379, 661942469, 391127635, 368325689, 593783739, 591273304, 601039121, 357000506, 678885867, 162660418, 533257192, 829589626, 982283699, 561580080, 714636886, 977540487, 980730910, 482968022, 48739553, 640467367, 896759563, 267028328, 166048873, 364441544, 204829804, 19380444, 248504118, 576398852, 420952613, 696517489, 177814555, 379839008, 516020224, 351669417, 337307949, 285007697, 886313625, 31069301, 404131034, 667427833, 585314818, 271491332, 192617023, 798722784, 316369166, 414667449, 994673932, 808333305, 313463230, 550611769, 187134656, 492496525, 811980844, 659280638, 888336630, 56693997, 324904850, 956604777, 615339878, 286383592, 972661783, 944778660, 192005626, 519397656, 468965493, 365688603, 998682692, 67920171, 536971674, 640160145, 95960644, 905149432, 735458199, 918193577, 138035909, 754684050, 731748937, 77123975, 208188854, 419267502, 220067739, 907234990, 524405908, 333075724, 449668987, 255186208, 669578949, 347388762, 294594866, 39661196, 294843238, 257236996, 981131515, 297312730, 755427025, 94299476, 651241841, 85138807, 448217487, 628454521, 815563071, 673133891, 517247015, 612366273, 163670082, 384785316, 399508431, 622854208, 267277698, 669963975, 381839487, 883551598, 55725417, 161742236, 701571924, 684924172, 253430476, 318157671, 836470462, 37511654, 210741767, 508512663, 693040806, 909232618, 216684930, 592209335, 674565797, 186075948, 327992703, 520879928, 217264445, 590921879, 794369937, 581339079, 28326603, 382920930, 393169386, 946227623, 582167728, 467269057, 911734571, 764943972, 458585019, 437909431, 439211228, 783594273, 533516287, 696090841, 132880657, 635440266, 571258728, 854782450, 218185992, 802984850, 191633392, 502627892, 8837095, 750975314, 12351343, 204532555, 423335599, 89428174, 232627749, 3347448, 565540866, 809820657, 682812420, 96288555, 619473511, 129100496, 485278304, 375957248, 410799798, 432380015, 704618532, 234923354, 478465139, 487089657, 12783359, 724712525, 117540364, 640190197, 110132012, 813662854, 684849719, 340866316, 629469740, 929286482, 834087343, 294693838, 600009919, 604977205, 918544545, 956635861, 948432881, 409185055, 512062922, 831974038, 437324868, 466682779, 140216161, 929723379, 756023844, 647020628, 855799715, 424029592, 200184445, 553076271, 222582453, 456608045, 838896940, 629277164, 46087237, 692528821, 630642547, 28613150, 219993170, 519712244, 942497339, 42932821, 536552037, 994968342, 172327405, 243986641, 638641971, 784118623, 271326772, 94488051, 533994137, 118612053, 661001207, 845684429, 615202713, 994801047, 628412354, 107137541, 864523507, 200394544, 746961909, 668006918, 219052477, 465062339, 24954510, 422307133, 627247991, 63207178, 849338653, 348262061, 239995131, 824052018, 682768935, 990578169, 751276687, 466886977, 898063953, 309028414, 346147037, 217869163, 902407428, 509507792, 607704710, 730050241, 544410697, 897010317, 277554899, 823623125, 752940564, 155389279, 656436074, 555447020, 39558952, 268520349, 101718054, 936587095, 809058381, 859121918, 611267995, 809134836, 513027601, 614291634, 42020186, 50364213, 928094532, 924354963, 53269116, 200591019, 415539767, 871406789, 428237000, 304464166, 436988563, 972083065, 652803185, 600002365, 978441764, 462239740, 139678837, 230805434, 969618288, 568462672, 718882464, 327469125, 390202942, 637551101, 912016596, 924122064, 710442147, 30690407, 602388629, 425858012, 101776494, 647532996, 346364536, 312010177, 440045113, 737994639, 454525190, 438409376, 727777233, 870234069, 964591171, 90313393, 583359658, 888130904, 886323142, 23326568, 798685310, 183502544, 798568260, 810847257, 996037011, 647245021, 549019754, 920485652, 858383750, 676817952, 13993046, 4116594, 103965317, 394089441, 32833040, 826049121, 200348777, 796996012, 568206158, 645424482, 838547192, 668783401, 288256830, 398565941, 412723827, 638462131, 562691863, 7272389, 307297017, 938334824, 206758433, 828193458, 760279654, 744048412, 894840683, 439093613, 804915646, 248340561, 822744603, 534622760, 564713806, 732276494, 448473968, 629093529, 260473959, 452386446, 153781890, 917545213, 271174475, 468386885, 74306984, 23670398, 149985488, 578317514, 325676030, 292547232, 381724711, 435055952, 640078812, 335189239, 329206831, 332442069, 70560724, 91038591, 528680929, 202644831, 44291915, 401855161, 292885687, 36325033, 250401214, 186998926, 931946204, 389717300, 504774202, 797477973, 225400666, 118684135, 387295445, 433500567, 974838317, 331570253, 643491152, 753145234, 519937456, 612358952, 790050782, 713743074, 769019787, 403570867, 604535913, 438899974, 471283762, 831305741, 261121648, 477863173, 799033919, 206028131, 937887036, 893166493, 16083837, 677250296, 95854494, 477787384, 984776833, 577685173, 895604067, 788020581, 518604232, 161348990, 315893272, 8860721, 558437178, 593091945, 167128719, 670936777, 698114107, 615873743, 99081202, 712615116, 462983715, 919132045, 836340936, 844477151, 621484118, 538648117, 208101671, 833061332, 37184211, 475217680, 15148923, 569725327, 962861810, 985744113, 452486156, 24046037, 469248071, 906196352, 747858917, 367275881, 725372948, 467242123, 209173036, 302812077, 890967393, 6241343, 349587305, 993262911, 961578141, 51715775, 821316844, 100077490, 347794021, 491993697, 933751735, 512017059, 209073102, 268282360, 122575042, 605830380, 264495578, 761383103, 598476786, 978634480, 882411860, 968702303, 287931901, 893765258, 230458125, 45470958, 425300932, 183338598, 298980738, 293382479, 11564989, 601846178, 904544235, 92994147, 721369511, 395115492, 931375407, 164586323, 564147151, 152751811, 894627607, 605148586, 962814406, 12308658, 878935403, 620219178, 570231280, 951404872, 589865005, 850394622, 299102348, 411267074, 90089270, 554737317, 161312588, 81924285, 829227471, 494689952, 196513780, 290932476, 65146935, 730062483, 397907738, 799026808, 133835880, 950838738, 564825343, 769345878, 732130756, 68202077, 80126265, 318462096, 277432554, 756376673, 103710041, 866211953, 233161380, 807013361, 573405249, 424350494, 849144354, 533078466, 928124627, 375900223, 48091671, 491146005, 432420989, 267043618, 332710620, 712763158, 939415162, 902769571, 328065566, 634348847, 636480072, 319778639, 600253448, 649498169, 25783819, 943359649, 260304343, 87245825, 884037208, 190708056, 105351458, 397067574, 362468766, 426420902, 772922105, 485299749, 514559794, 34540004, 61850976, 906713561, 268936211, 597595909, 898115183, 519314924, 474633682, 17128194, 982686374, 602274720, 20772298, 878098538, 247646349, 717991455, 125859558, 577043567, 962408366, 483478343, 174263684, 428699176, 818369441, 13139214, 266536183, 836902522, 699549246, 560470473, 572628773, 816579759, 825067921, 50894050, 468373575, 550820475, 866384371, 238519819, 35945384, 661155534, 392625109, 293331738, 533641836, 375444473, 262346637, 862778698, 721390356, 223207825, 533760435, 888512226, 448628358, 312792010, 488706707, 357848777, 451424674, 558449967, 444075825, 627503399, 821862963, 782439342, 901384572, 677172863, 8169338, 192013553, 468317519, 246223703, 626217002, 82492754, 691055001, 83103431, 145739269, 736269412, 45647506, 703425545, 588156068, 128048533, 601478128, 129127243, 814467942, 371164852, 393291844, 971089937, 519356114, 823943842, 771549190, 40253444, 230030486, 782350399, 572838805, 836016367, 163606594, 112446133, 99064496, 730715355, 887998594, 956143623, 941385110, 343326736, 226092019, 816850981, 981040798, 212914253, 893804778, 424881732, 636759868, 170783120, 596676847, 657408542, 547854506, 683277679, 387754890, 115037148, 526075309, 781709528, 51828017, 621727736, 283253430, 795594005, 302084111, 473757706, 596234758, 566445640, 215358541, 559186653, 779246411, 268199855, 750832227, 156155927, 292760851, 825093982, 782300423, 767926133, 519082274, 716052248, 367681884, 289298258, 132515712, 976415720, 664634482, 671707532, 484524098, 446471561, 932753090, 809549642, 172278687, 864256330, 956624117, 39628196, 978732570, 60051068, 637553993, 780272567, 416611807, 975988022, 667023945, 151594169, 287440333, 471784964, 400702146, 725612347, 84213694, 428623783, 852697185, 431755967, 555926203, 531397734, 62161177, 783887114, 584444652, 367663806, 252714728, 299553484, 795588611, 581044025, 551366309, 644047430, 802408628, 671388699, 633028318, 608387151, 495117672, 243782285, 693895688, 621271322, 314153321, 164966640, 431104866, 268576268, 863535667, 629431620, 651960097, 922221811, 881399028, 488925899, 423635062, 927762647, 697674540, 414423731, 162180981, 472617895, 863276677, 202715769, 302992363, 642125254, 258326838, 649116878, 239466814, 504084050, 520013672, 587138323, 410394275, 772041058, 999172644, 893657169, 823541834, 195634769, 854736457, 816752342, 903845515, 485519425, 42880967, 599913492, 477860935, 578487015, 766631717, 379390658, 906585449, 434354737, 956442022, 975461615, 482154498, 646140288, 681891575, 796216558, 729258050, 663124456, 460641645, 136098608, 72191645, 528761184, 892256220, 339641545, 418676038, 163010886, 331624914, 952860851, 215555120, 491391681, 759871084, 427383100, 576093766, 228922445, 3154222, 312047012, 899155659, 799736467, 896184964, 389480681, 862301478, 946550985, 48209282, 163552377, 132975696, 656116766, 479781432, 447196524, 988789764, 395694858, 309345584, 337239107, 905391447, 702273874, 669205780, 92449009, 122614489, 521305020, 825346419, 516462135, 312018697, 100459835, 826763754, 212684438, 267802906, 871267623, 302857831, 309703417, 128631654, 63338436, 613823349, 233652544, 320902102, 224948927, 281454562, 839518768, 398364076, 81881085, 412541170, 965207997, 424131122, 815452645, 412695496, 62431260, 64315575, 656530019, 339318522, 360694030, 34279333, 345486330, 561921918, 839317952, 205782275, 240691805, 966878185, 917179663, 205599961, 875679611, 179259410, 507376943, 720183284, 153510759, 120998024, 480435174, 638775073, 518997817, 975471700, 708726161, 912892446, 523146539, 298149278, 115675288, 638111032, 752129201, 589191229, 170581866, 72568612, 667447390, 922560836, 725112417, 959672500, 401119719, 676922633, 311497095, 969412159, 94099904, 18971559, 71771376, 417609886, 566438277, 96768806, 796903600, 279816284, 27860739, 133892273, 874029799, 937104419, 474236867, 949295423, 921902826, 267975377, 160592117, 973558368, 479356728, 713242820, 452966874, 713847808, 150327643, 181006354, 880271613, 122957529, 548839304, 551090802, 744633323, 883118890, 617094339, 151238704, 271839243, 935843088, 407513608, 120904574, 398350786, 648731211, 7791339, 696818444, 885070206, 100387911, 434074915, 621191205, 233680354, 455221454, 602986761, 613321670, 526338688, 605410599, 886517638, 570374548, 474972653, 8527143, 357290989, 177591976, 146984427, 534676842, 678728749, 672576948, 475628067, 187341503, 456880849, 886176836, 539392748, 134083719, 132292480, 539741126, 967705922, 593601374, 762393335, 515072910, 911827989, 377513376, 711947588, 738043148, 454475360, 830896545, 957786535, 412852924, 236839359, 904369331, 668982476, 792614197, 686429233, 487114354, 512589070, 36766325, 756681824, 184317581, 762464151, 927557815, 699316682, 892053445, 924901900, 758052188, 150997538, 942059421, 289775806, 685615255, 879152839, 522867911, 1737795, 235493206, 548615025, 348167253, 117679377, 344082951, 72851202, 596044176, 11557199, 696815987, 579101759, 419063934, 235668341, 377194511, 961975324, 948907802, 546194301, 577075700, 280103443, 84395768, 142276908, 228917048, 762970054, 641271236, 980833346, 266897538, 228182084, 603070803, 986722594, 842252700, 566299871, 954690875, 359296538, 631285750, 457053803, 931676193, 594795077, 69045070, 400246083, 218687631, 197857398, 792469485, 6861664, 815396499, 95990288, 966245943, 479442447, 43162711, 386986409, 933478801, 427304650, 949888734, 590640694, 541773033, 5803282, 857012764, 96176159, 29705907, 731971158, 963838339, 188002663, 299321946, 976617675, 496291407, 571370122, 8363078, 424242916, 665227373, 690287135, 573372270, 947376497, 830628669, 107861945, 424061756, 749078013, 671533961, 870541431, 200915439, 807534556, 460059746, 960958812, 221623067, 207897534, 471357547, 367094321, 464218034, 248844722, 370837136, 261799373, 624163503, 11169961, 463104721, 403368198, 347018253, 51614207, 888035758, 488919858, 829037548, 850152780, 183879742, 119227560, 94779378, 431900156, 979731556, 326233635, 117466360, 61097158, 362345416, 415151456, 35286032, 978718703, 976371466, 382404052, 551048228, 961428389, 434882355, 260816967, 881710642, 454282715, 806950926, 674817050, 293751862, 481233089, 268796424, 66850695, 85687189, 310904965, 952511687, 932910622, 736291054, 21868025, 662319586, 339920347, 281170425, 206277746, 313272611, 433316661, 715282014, 554629932, 889307661, 214078175, 196973843, 936125245, 430893286, 843343939, 760237675, 147146497, 545667068, 787922229, 476113341, 370844032, 162010232, 770352882, 932966403, 264049239, 795037661, 897910625, 735630483, 635415050, 45485207, 119147286, 524513133, 841982878, 578028129, 261266000, 380899552, 690914333, 954061041, 224527535, 788339207, 172134566, 94867754, 211568696, 62359940, 120845659, 201190058, 36337139, 111413563, 647294863, 172606238, 706768249, 681505083, 152369175, 902905434, 194279779, 198143083, 795401624, 888561900, 127052716, 781940051, 44796590, 372329247, 464675455, 274683164, 851196363, 597646739, 540689057, 836287671, 146656257, 188095000, 880771927, 38934007, 944256009, 958430153, 401859748, 975045041, 325175412, 227082156, 413017532, 942716127, 406809228, 847580558, 629442890, 551586402, 107319943, 157236433, 839252592, 633451450, 764627849, 762073314, 322960335, 979734343, 652836681, 497417605, 213504259, 332307073, 132589835, 843501667, 895230518, 116055972, 841677556, 185840178, 513237190, 15922952, 517026459, 949203343, 601781214, 935149387, 594734333, 309781076, 482363397, 812546056, 987573122, 27661130, 527602107, 261741348, 333495601, 304238869, 32161086, 89187376, 105548799, 963775467, 100390896, 32271408, 844561398, 749211422, 3439134, 52045709, 143103878, 996796495, 461031402, 621553922, 446807674, 974875426, 515547332, 693045297, 631978472, 585043699, 540577725, 32735459, 562282882, 883324391, 7890467, 144538259, 118195572, 306924808, 964551347, 899808404, 921584297, 755646517, 835385843, 56809478, 111042313, 947969681, 865046180, 713053593, 248392154, 446301258, 704394765, 216431153, 868663302, 113762068, 436348080, 480553803, 763824472, 381892904, 107165445, 887486768, 702454855, 57071478, 78646963, 10213412, 4662593, 777633960, 196820885, 611202157, 648843287, 766029831, 415235468, 14129443, 202692097, 646549050, 679930155, 558330207, 727352382, 548478269, 476997788, 797187860, 182209842, 612520514, 50287275, 565403722, 251545139, 938073059, 82314199, 85697233, 694907782, 890654260, 571348890, 465386476, 493492224, 162771032, 546853402, 785526173, 858082836, 273250404, 451255839, 670938470, 856202329, 672627798, 161341219, 310929712, 887660229, 988481106, 51478100, 607455448, 121074093, 607620903, 686571280, 919943248, 696485889, 524353410, 461540769, 884198174, 938811555, 492419740, 149734439, 449228258, 701383189, 814818686, 79948991, 242032956, 365849881, 327294957, 180903645, 693963933, 108971143, 114719903, 788978475, 593847730, 770731076, 131292454, 688238437, 423956256, 213546346, 175112694, 817377002, 972590663, 57040941, 700139987, 762014783, 266955376, 405629695, 705184953, 1708919, 759267754, 473690576, 832488696, 913561305, 525028565, 608191701, 717065766, 814907156, 874807415, 299590594, 287247899, 38821321, 340788243, 40092723, 776523703, 864553454, 408357204, 153819038, 912526793, 794885765, 81589111, 189471962, 636380474, 447909334, 957694064, 839741718, 333465394, 45211813, 972847067, 301570763, 102932555, 542978283, 693152229, 680550328, 700687497, 735541821, 624695034, 11421075, 590535761, 458364466, 879569765, 128005359, 469221096, 825292682, 115820071, 843382562, 74518306, 837603266, 261626208, 944740816, 803124744, 369580303, 229788852, 729282493, 366894146, 21969455, 788859654, 612187285, 594337330, 77517672, 876244483, 370292252, 126053433, 801520618, 405848003, 281774045, 959237602, 149321928, 972010936, 41537476, 157081018, 726867975, 338912810, 339652253, 63492102, 866560067, 638278459, 272414045, 117464951, 306147557, 346846809, 88617415, 712162465, 181496323, 118781459, 803276790, 62973018, 997718291, 467312582, 735135390, 660278468, 980278854, 200921910, 457079648, 5120953, 425767426, 608851222, 750849634, 263347296, 432158957, 990180325, 493467005, 707525334, 499908498, 962492585, 469762844, 347761377, 69676240, 38105414, 500538990, 431183867, 372370349, 660568272, 318828856, 227008786, 544827002, 749504768, 467437240, 404492657, 274630209, 443828542, 507568626, 296086038, 373763620, 228002678, 286484442, 704837344, 631109671, 608124202, 448794490, 113399260, 332736416, 39488496, 655283961, 658444675, 248631092, 258039571, 252322081, 601127263, 356991453, 630748798, 12535612, 471573596, 280832584, 596140050, 806342488, 362236581, 479502506, 101524599, 312953508, 412392642, 926034975, 571686062, 109971441, 207054541, 118230583, 185165342, 924150220, 335454534, 853272117, 671871309, 486504586, 701903871, 386580071, 19666778, 725833627, 895346992, 355848141, 361541450, 707086041, 470863991, 308832486, 700165563, 142601067, 10388061, 756409915, 523783148, 958648360, 582259250, 626067497, 946143341, 223207820, 451026321, 694836666, 414385630, 141221684, 504532693, 107383619, 252035837, 146178969, 887147203, 249435874, 810681403, 375723737, 495910527, 220828164, 807640895, 488034851, 940914383, 81460120, 1333804, 8586209, 46585399, 597282280, 762611466, 903297542, 620884810, 92873050, 594107184, 146022392, 114054539, 124173025, 587745476, 344379558, 360228354, 538105086, 139206355, 597768258, 298504080, 280501565, 73388702, 41233109, 48782169, 773803406, 916107188, 361633992, 503832636, 465776223, 186925480, 428038723, 611880413, 921790404, 493659425, 378049221, 463780690, 461907845, 809556962, 95596925, 869900283, 402243851, 470558373, 738012112, 765742079, 669524907, 267506199, 755731054, 937832298, 319126114, 505211684, 622407127, 555959735, 444570358, 194720724, 125564361, 442716203, 651485184, 853837016, 960105913, 936443120, 87857338, 171865378, 293889356, 365936230, 689380200, 90864777, 683393148, 177948323, 814429228, 77595596, 531313498, 965586124, 378445475, 340609979, 747077533, 149796998, 397829690, 172580539, 796361843, 310762166, 825519995, 213711696, 858773137, 416371968, 942387504, 172812485, 165367772, 624809609, 862508792, 415462608, 551693769, 203987104, 294041204, 830384019, 94843276, 11732026, 415284368, 328748862, 873383607, 395104651, 109866607, 264821448, 752331467, 447843600, 75714503, 354756611, 299279746, 281371097, 90736074, 84387760, 755234852, 259910916, 728470694, 615123430, 515638613, 684449847, 360211435, 833011208, 308463400, 849746362, 126611588, 559437249, 156491499, 580447734, 571452160, 881600537, 65126817, 289110783, 925031617, 942093293, 178773037, 374278493, 956605781, 667994327, 911700223, 724929029, 632315529, 32363954, 874132891, 663313597, 262061031, 413031812, 95697087, 71656900, 384150905, 726676595, 829137391, 599659282, 920348857, 249191852, 94288065, 382591398, 981212625, 188666502, 874896920, 300907528, 832824152, 827723161, 604338856, 267746452, 90660896, 646211763, 538831409, 914566961, 233686075, 801507602, 532073306, 479461444, 541778797, 251535018, 845712451, 258389426, 769577677, 546822326, 322851797, 223020434, 372592817, 135318346, 782231074, 932440317, 475822050, 892181944, 750835161, 321412554, 948525793, 636514100, 253338661, 653915289, 422683306, 589191024, 580630628, 216591195, 427080499, 119401271, 772025400, 722614483, 892103742, 364142694, 398022639, 236537234, 834036841, 55236464, 276518232, 503394591, 895932513, 940373191, 695573771, 179127429, 313703434, 729862067, 442760934, 368680573, 859053485, 640599214, 899985749, 470186374, 432695912, 939511584, 531873838, 858619621, 813245978, 877218800, 234006369, 934467175, 921156599, 636708887, 50655436, 79337099, 152291346, 362815112, 811798953, 181749524, 275788184, 287042963, 129720515, 95479672, 31679496, 368424194, 536014296, 242558814, 189804830, 629933548, 703706914, 382310135, 481270781, 925951505, 173210972, 766053527, 917413588, 853957847, 162875553, 920431680, 40283777, 364964310, 731274048, 767147300, 106605939, 213334901, 589438906, 623137376, 147297131, 237627358, 57590104, 305182081, 341810469, 463257233, 347303361, 532936311, 641823859, 113263486, 790207950, 764445897, 149012895, 53280399, 15789817, 795127393, 122619658, 43990106, 116415045, 30668980, 159048237, 251735171, 607986757, 60602755, 654527939, 45024233, 313774797, 121604112, 756129856, 699589235, 565672551, 649091510, 603215830, 402975987, 88878013, 976008407, 148582554, 87890956, 696110194, 313867117, 129568174, 144193891, 168990672, 446512622, 48459525, 295736419, 609894015, 919091650, 948919981, 956004565, 961370744, 330239337, 133593149, 565264874, 433309063, 36334016, 876104284, 216173451, 983254945, 76185383, 520486145, 952127573, 409371299, 635916633, 875793658, 19332268, 307559374, 115703994, 489894720, 925081372, 304886675, 568501640, 202369479, 468460114, 609160735, 927184765, 161136477, 380965969, 816960165, 69465808, 278519104, 118117378, 390007312, 751568659, 745350834, 940382813, 45248499, 520637267, 567518843, 403613256, 678571467, 444411949, 51339466, 935438524, 412480608, 822450491, 594974783, 187881189, 443518776, 274604999, 173312242, 272791790, 115841012, 342254015, 10527086, 970203515, 247301267, 527761090, 409736843, 911868863, 787555331, 573397907, 245069137, 994309529, 183129121, 319806196, 414507360, 55747308, 47404583, 84142863, 44752511, 740200485, 390615318, 23127150, 767161170, 792795141, 579413212, 814430508, 137004163, 760242293, 266650060, 323940977, 890962885, 992955355, 524253290, 910148076, 821256120, 133413446, 739829378, 577565363, 25118716, 704586052, 822006965, 985964464, 930112322, 121507668, 901541581, 845890182, 697480754, 61583744, 463903059, 453439695, 479648814, 601040923, 509832481, 417689578, 82208954, 651210148, 659083935, 226295236, 893258566, 151197634, 937111979, 460159628, 472200519, 198942374, 476103119, 424504843, 990566750, 247756601, 117435419, 61529891, 66648115, 29529587, 647314059, 985500812, 57978012, 316396742, 763993057, 495515513, 209829072, 120258521, 885012799, 650845294, 855695469, 364285854, 719999983, 923907021, 576076913, 636412045, 693763942, 751006042, 494819928, 461248654, 39486715, 213387515, 689711527, 620529591, 462361335, 490515508, 371615203, 744581491, 23616618, 231887162, 773576092, 159755477, 508886544, 800266668, 824313546, 413284239, 918051541, 758642038, 472566008, 521719938, 713567185, 736800044, 175642521, 833238700, 714233636, 977953310, 7843635, 42264236, 958587619, 41886426, 922422437, 502553828, 116090173, 512824482, 631775260, 451105054, 955274370, 350257017, 285975702, 174799908, 648957889, 879524563, 846602402, 42096363, 49754695, 624035989, 211952576, 551471431, 991026240, 513620432, 716701284, 314152473, 717741754, 419634625, 545779193, 180440454, 157231809, 184648037, 481853981, 748831450, 551713878, 677234833, 71125050, 555130498, 950518056, 492514128, 363815360, 887768564, 603443889, 38446751, 196832259, 674770585, 340893880, 995473100, 175879411, 92581225, 794336691, 268453847, 331941484, 676333197, 772355349, 20596243, 136598845, 605282253, 551751298, 112576839, 39462300, 407193334, 539486067, 835897040, 204627100, 229185031, 773410372, 562738408, 436803061, 491573351, 371802347, 108446912, 436453777, 746075629, 772269461, 4994861, 581621893, 992439894, 475296227, 527508614, 812626063, 892948213, 571793872, 91605261, 703008244, 28694340, 8402477, 514945086, 310662080, 532128840, 349066949, 419695687, 22712518, 689942585, 668919828, 292474462, 687220134, 506628119, 833932026, 120522642, 344851007, 741944234, 461878953, 456272286, 323051740, 347365634, 491439444, 575092677, 65738899, 450338206, 465422038, 647647610, 248671220, 87819892, 922865141, 546343796, 130674175, 470806005, 775963588, 46062793, 847581430, 145286015, 365930902, 201040017, 834089043, 60802503, 808359017, 77123058, 657483010, 994034852, 333665424, 880305365, 206138297, 622085257, 478773504, 149273449, 291900719, 595268122, 48169405, 673388303, 189059511, 596673506, 3224490, 827715797, 406830254, 19062403, 105931294, 875478705, 304981212, 541295708, 988439758, 230516781, 269559673, 683435945, 348536005, 3473640, 876986874, 569392061, 220860952, 261138070, 192970350, 796679281, 145962649, 241894012, 875123697, 583329186, 605858431, 800814277, 125042662, 374042892, 944437936, 472059378, 886585601, 539299675, 214339722, 588582906, 422388961, 551588141, 908891618, 828076448, 680106130, 593266496, 640350802, 562368497, 740987903, 129822849, 630534282, 470034835, 415046330, 784591881, 860098328, 191735703, 82350055, 41166589, 623415216, 493267866, 689331252, 208222610, 792321357, 53685421, 921459913, 505662281, 585010974, 516426855, 278742332, 412437706, 15615515, 612295924, 433595084, 44297592, 428351240, 316940453, 109729714, 324171120, 370014036, 694420550, 447183991, 780024642, 338349349, 988973699, 374477080, 972431569, 706305278, 945026728, 111726632, 582529222, 470404680, 752947010, 544297591, 421407698, 152684037, 681595246, 455578515, 843958815, 555872249, 826924586, 263373717, 645736652, 864245754, 110018386, 91895562, 876824231, 373642720, 284695492, 868285591, 651728310, 54536871, 225623394, 176993219, 721111752, 19548877, 170668052, 692877926, 426277572, 238708788, 758346524, 468200179, 119107794, 729217378, 339314867, 383792898, 206518882, 315963968, 853176430, 688895853, 535735917, 967982755, 555798787, 193835407, 192845188, 89724769, 692492716, 809120192, 500794631, 17107959, 822456171, 223753059, 535993720, 746603218, 349796994, 322934010, 48666869, 134555461, 719221541, 646331779, 737701850, 430727635, 623748374, 500366987, 279743082, 366937863, 292038165, 867160955, 121752882, 605029540, 37694982, 508251030, 524700848, 334078257, 124696079, 468297936, 618197002, 382902529, 149190345, 131487941, 468066830, 957894200, 799358995, 783130917, 953633074, 524506038, 318283198, 831317601, 676520507, 531756622, 461523907, 96182804, 607176264, 28655916, 166591225, 864420749, 751952878, 579958694, 110789287, 19299829, 116408831, 187445406, 604905383, 725427922, 232123825, 685960326, 232737233, 770567001, 758777048, 894818449, 365832318, 886692333, 867804990, 945131103, 665071245, 958311466, 211325698, 38042074, 464318407, 962012626, 967616826, 473747736, 406786951, 768642171, 222926097, 188053021, 503244869, 323222806, 8337186, 419383706, 950574995, 507982103, 428315546, 267402637, 520093916, 559409113, 209242046, 322498517, 529520775, 421708986, 279656799, 103961286, 513758125, 359018958, 895608835, 85106098, 364833908, 830733758, 939729301, 273345566, 318356060, 689188537, 670160569, 555601058, 303080141, 939660929, 128922333, 183224209, 261086181, 805525947, 475622130, 467896298, 28266244, 226297743, 665496893, 516298883, 920974256, 140390201, 699347426, 811511947, 930510057, 240745276, 314431162, 709163190, 854302163, 106002425, 804062844, 948790134, 37418980, 902037779, 503945778, 644689953, 636799778, 825562909, 119006361, 991437353, 556862154, 504753117, 113579027, 808240299, 395172308, 728630779, 879725160, 979584045, 169740291, 889658290, 301096835, 425854966, 899307180, 424620185, 387245950, 374939339, 460638274, 765874306, 267777403, 5889282, 169848328, 206904946, 180867314, 412254512, 794041922, 992570068, 464054520, 435213756, 363646728, 670435065, 296051416, 416340659, 909520462, 694363736, 241983274, 43180274, 992841521, 2026195, 827620129, 826424432, 767493161, 801528684, 531335724, 896990836, 569163489, 797989003, 732945343, 556109815, 687635060, 888138626, 667676073, 401287287, 818418829, 272661664, 885552264, 238683684, 318533959, 887459100, 297416889, 252032125, 878172651, 341007459, 441472037, 69543633, 739837901, 783066400, 818152695, 6031266, 141820687, 644100295, 19594632, 747554025, 316274246, 408390628, 688059681, 627387829, 825801358, 651635716, 52983231, 924021527, 132263538, 384786515, 222527677, 441215403, 123835447, 616445134, 331125238, 328858038, 322951841, 549248768, 378247622, 807972900, 909851645, 671143373, 731629428, 706657801, 712632336, 126889549, 332640479, 89962278, 562755557, 891414785, 615441534, 220159086, 214123328, 434918555, 919260084, 825585611, 268428929, 551831603, 900356722, 500144586, 235622572, 833507694, 805297051, 722595614, 177308164, 482167443, 692326951, 589152519, 908798705, 185008770, 619279488, 332113455, 393092327, 978215738, 467802545, 728937283, 392940763, 42407456, 647298190, 677251892, 749332059, 152134377, 900699263, 405502094, 2612118, 237313462, 64368728, 547784528, 5599912, 226544059, 148972136, 346622688, 891295074, 673073715, 351200994, 762569540, 342611090, 563619139, 389888181, 143996605, 178455646, 976388086, 889418720, 205805420, 47792722, 676176416, 394053078, 212953007, 719509103, 254608427, 160605666, 116382360, 309770548, 337299624, 833839154, 157720208, 929339163, 282960488, 469735977, 271997347, 311166957, 351028053, 7718966, 999592530, 773838247, 856995868, 157599804, 226830304, 203028971, 379368514, 507192863, 97308528, 919904526, 480388919, 129954558, 338479444, 638484067, 551115952, 451511974, 420901120, 187406901, 38488290, 376322822, 38749099, 754314114, 619670131, 622535943, 764034923, 503571546, 738866451, 528817602, 19643506, 392337058, 786818164, 275504810, 527053480, 76811230, 447763645, 96465699, 793604468, 477612104, 22428200, 727643394, 76578235, 989180876, 310317484, 278191652, 941650320, 804057820, 306551756, 589854217, 720572964, 197504385, 772905652, 652774600, 898020137, 491470778, 958983590, 196874636, 490961996, 63178518, 16465693, 278894627, 463184691, 334462422, 683322281, 459738785, 406696875, 657035948, 792836426, 6095206, 821660164, 308912781, 214100375, 811705336, 181436791, 360144358, 932671479, 318778355, 784981935, 897470679, 294798949, 9936665, 955308881, 385774862, 510594323, 913995785, 205713266, 778302797, 664965433, 594100468, 118628377, 592574282, 193313866, 957530840, 617252794, 991196011, 418979251, 526005793, 231349480, 874696836, 391224579, 262700433, 690774738, 432682858, 38327653, 334281562, 333331478, 316927751, 71166403, 176833478, 940666563, 471323672, 55679531, 165113938, 297889094, 286938188, 185864450, 819221915, 6203033, 839862208, 251957853, 129944413, 399844991, 530688406, 538058219, 796808003, 399296259, 118596255, 57789777, 465757915, 307296308, 193221263, 127040643, 327600591, 4671297, 577858663, 959112994, 997019101, 555272207, 280471509, 841517860, 281174641, 702751569, 143571098, 241082488, 765301517, 329069772, 949445852, 381673319, 387971694, 864146014, 134046819, 922982563, 775278923, 648689990, 364630311, 561403306, 168705895, 222804539, 790779161, 44268469, 200126238, 843501251, 141418682, 995545327, 139545428, 42807928, 230100019, 801090749, 158115458, 954937524, 740675473, 318746621, 64138291, 659576768, 513593772, 250237696, 782941125, 779011867, 437213414, 602451910, 631152194, 919496991, 865965197, 738601884, 473663554, 836803508, 713857421, 935421855, 788485192, 982967919, 838726423, 998830583, 126115482, 213744976, 804141838, 158690762, 357804787, 8047323, 966039857, 385613606, 260536643, 177086350, 267623220, 619086366, 396357517, 55115626, 79310657, 903089920, 214981061, 30513535, 468323755, 78476913, 623788538, 358458908, 983370337, 520480262, 496556272, 686703894, 263480904, 786152477, 170587028, 91245332, 543138781, 944480173, 798471959, 523099376, 35173127, 200392451, 312464225, 278674292, 656992778, 480947422, 59022604, 653169165, 324235274, 91317349, 691973685, 31805790, 41151366, 228212297, 218608915, 286370327, 971793632, 128395765, 427283367, 705093891, 609111816, 95946489, 110495490, 924817356, 5656461, 275310250, 714402629, 222634945, 533200874, 148826391, 419729443, 643041464, 229115391, 590263902, 427461622, 879411801, 964234998, 73807973, 487864258, 678648417, 530373052, 929121839, 415393556, 413724892, 778039695, 777750742, 556082835, 32121622, 486792470, 507907863, 497258145, 730992409, 318936075, 288903253, 810680383, 539848936, 539420790, 471175587, 123749186, 721956621, 760811172, 564453875, 154327392, 708327764, 402095609, 6167527, 814997135, 215118979, 387091, 286986505, 26416686, 641758847, 856494797, 954312037, 518653125, 999094143, 277593724, 317224281, 320140666, 522008475, 119813842, 38329611, 791040142, 385508405, 527351450, 875485518, 209268819, 511815355, 407785127, 332862577, 659738384, 262341755, 387439775, 428519412, 507388620, 197513847, 257429865, 545792335, 682222773, 426736362, 274112614, 531633570, 826986409, 801728400, 388074708, 765565863, 111352030, 92821681, 72784047, 446826405, 403083558, 353884155, 963828890, 246288052, 683917605, 514377449, 258211269, 107177861, 500792213, 916186998, 353074488, 932102764, 76877039, 451056836, 422282302, 773884638, 76549431, 586505795, 817949917, 552429043, 58347668, 971219138, 19978971, 163629497, 434729396, 445760264, 110566019, 51392546, 372172491, 557658788, 329893080, 47577728, 853595859, 309006224, 907727795, 851298842, 394559725, 184986900, 495375813, 344044834, 739744120, 601900696, 31378622, 971194038, 845545116, 903732273, 154279703, 923232963, 402864113, 352084244, 626544202, 201585594, 203203990, 55234545, 352247396, 273707704, 515138184, 709378292, 525400634, 556006132, 833015055, 919936756, 541018826, 324263823, 830259837, 684312994, 523869622, 200547624, 954355376, 34813293, 169157844, 229553692, 239514146, 88445052, 22628281, 163484810, 15850881, 769664707, 265534154, 272530793, 353790575, 59035122, 361353076, 4513877, 828631374, 307247063, 694140426, 726100515, 527286377, 120203657, 310319381, 324845624, 228991425, 563476027, 242805589, 235051286, 994712369, 877145434, 821817953, 243338416, 558531808, 838559369, 434179544, 138690307, 103084681, 99653782, 130780033, 324535082, 597729554, 730266761, 834069703, 173361065, 702728414, 961010988, 704135911, 676795659, 192781633, 810795025, 897784738, 433148072, 356829603, 829593914, 818259786, 408833129, 826471187, 797845682, 146494865, 301438549, 860619634, 869691392, 860440766, 153221846, 53251706, 434874417, 257143360, 719887094, 383607291, 184366053, 178766314, 466793235, 558955036, 699674956, 448980085, 630895737, 594418832, 909188018, 647020137, 791796570, 666074751, 142314718, 464491346, 752745850, 782462539, 98217408, 259593631, 324667313, 835056299, 407272278, 971236988, 397268694, 603124957, 153045867, 865510253, 468602445, 519708874, 125329728, 730731992, 38728758, 854699812, 31512574, 665385162, 831278691, 603406268, 111016465, 377481311, 486919302, 590931984, 84770117, 224327203, 767218238, 976059242, 118576016, 889057368, 49063862, 458773403, 920487082, 205591703, 55186262, 792928178, 91185059, 647359613, 124620884, 979567651, 481170129, 822041828, 925397756, 262509741, 248048475, 322878598, 261522241, 617143626, 216615639, 432553758, 306386029, 621463558, 887064271, 328216804, 48491324, 115497025, 456210939, 334400666, 736250913, 617504075, 635202746, 247995240, 38667002, 396364443, 781840272, 520270594, 353091337, 847236537, 392194434, 868791569, 654908521, 446639438, 539714759, 135753794, 130183157, 640319564, 813446849, 428492341, 946967706, 514061760, 757346301, 782187173, 897651850, 16314709, 643810539, 995108873, 691978440, 245826646, 548201016, 516304642, 456689609, 36835334, 688695102, 129049587, 201397586, 303298302, 83204050, 62813856, 155747061, 921001632, 589720279, 360773155, 711968762, 726437664, 672554283, 399905339, 924459603, 633482303, 87883100, 357370576, 380414204, 89335014, 566831833, 288518166, 631954232, 193819344, 381760684, 410644349, 636132466, 148331637, 98979542, 485153702, 156725275, 953421351, 323780476, 26932532, 47241324, 636417675, 190487450, 63353573, 976091308, 83913755, 800046796, 47940006, 267299032, 151148048, 209979886, 316798116, 680635553, 448295059, 427648012, 893482227, 674174959, 812260399, 993061954, 232862736, 817950104, 798519617, 996529365, 141239050, 261242727, 898929057, 176311115, 871196043, 481333574, 293452630, 625265056, 167077825, 654246779, 329675158, 966027449, 344038936, 755955303, 266773729, 184075293, 993672645, 281622296, 671798242, 557426384, 368610188, 373226333, 928515959, 684856139, 212626070, 431135704, 876915491, 368891519, 952564737, 324206592, 603691193, 508880121, 396484560, 373817435, 895382861, 502719250, 252281637, 693228375, 716682952, 678295696, 153783142, 569111909, 315842353, 169406176, 796730426, 855576377, 252546259, 690050983, 784318400, 593956491, 172513576, 654971933, 102624991, 715467902, 860822644, 465386384, 319774985, 813538227, 720431100, 889625826, 171633149, 592607064, 515834335, 642634562, 374537608, 256859700, 123380120, 415665734, 559246460, 206761592, 91997156, 907596055, 641667880, 918443216, 376814743, 490940396, 938366307, 984803999, 727898979, 246145853, 362050116, 305503326, 317647705, 857437644, 491865801, 289608724, 32142635, 958859387, 505804113, 647488522, 373684680, 143459899, 927884864, 126449074, 708076388, 806940208, 408930280, 735593987, 315524037, 882531914, 464886387, 72311918, 788970072, 524480725, 547502641, 329356630, 766000989, 227173428, 896994529, 280982270, 1494787, 140466346, 120257407, 582221344, 697752955, 422348600, 361756620, 177709040, 139203684, 959271882, 547973108, 904429460, 339478459, 235749124, 397855694, 996734004, 756851, 831498010, 219658116, 872522255, 135117511, 930338785, 652056150, 835137513, 232567907, 972576084, 683865105, 833025049, 845386517, 285354617, 492361398, 739119986, 94707724, 650581193, 497555581, 233359894, 693569958, 752318453, 740949941, 345817829, 296209470, 122110029, 832229557, 589621832, 395367171, 330047943, 789240122, 536509403, 923611945, 469322294, 479804810, 245758539, 120335467, 916532126, 256522393, 295792307, 107194664, 62019628, 675167154, 264253669, 695894709, 391533943, 761315700, 193202999, 165274730, 868427104, 779581538, 993006463, 543488525, 201086839, 648594539, 212031485, 142567166, 978728690, 641760415, 352809132, 686959954, 381588200, 294411304, 967698919, 985017183, 230669576, 990925159, 823349971, 293624214, 170951911, 346686533, 47311537, 665304920, 240368241, 254548223, 441114261, 839980410, 891187075, 156261447, 293141022, 759331933, 35599603, 617831129, 838347872, 63742145, 871384061, 324390277, 800515089, 2057973, 230450828, 320172408, 830492701, 450490995, 367274408, 509937681, 618218674, 859254979, 659287139, 728775668, 892976023, 495416765, 606735740, 704319202, 58262434, 717974289, 707366830, 828307289, 247212670, 411486614, 862585727, 314203147, 327955034, 123764617, 695899266, 953449651, 403284439, 420285145, 686607016, 929914682, 35365645, 675668333, 888271826, 635345561, 453066099, 578789881, 3599423, 554600454, 104380270, 314980931, 246586704, 438986401, 30675475, 184085528, 618059228, 147100141, 204018032, 126409612, 373728874, 585410605, 208542014, 451286071, 975243850, 914533600, 778561800, 679695248, 329184327, 369653332, 133265313, 820796127, 199632743, 625536537, 735825051, 121224527, 651989605, 953614203, 794381191, 983272038, 371120773, 666021031, 98543348, 462257499, 781645940, 589490260, 522501866, 966762065, 639372960, 749359783, 595738995, 722317190, 18896349, 695400428, 319246439, 510433014, 847126400, 898959426, 511184052, 681152339, 230618760, 749050879, 34085403, 157284675, 131192110, 825217050, 58426688, 987218189, 105985947, 542712204, 320730180, 302688021, 331337567, 428843123, 552690971, 66368761, 776968044, 897735023, 36461524, 892780899, 470372740, 941341724, 242885290, 200281124, 707729111, 157343535, 74919311, 871682808, 161570845, 826312791, 150376377, 457571878, 872500096, 776279480, 360593156, 287930490, 607104831, 395923527, 631458477, 678422707, 856986390, 237863812, 728624217, 323695011, 851241135, 890197097, 391934806, 722222889, 131546107, 708546075, 43678396, 824264148, 856033595, 102716564, 109055175, 376504398, 505912408, 67714063, 562362883, 93996127, 725858157, 162715697, 780801327, 861726215, 309356854, 409105984, 118166559, 573782003, 431091710, 166489249, 231501690, 598878812, 45429587, 784002878, 145990160, 723124791, 581911242, 512528366, 875925944, 334320466, 535090707, 812294864, 295524195, 831169727, 37034423, 988337647, 62393636, 189313728, 656814850, 442749667, 70769702, 334535913, 919437199, 24502441, 525830288, 811392010, 213954345, 57864461, 160227007, 964402401, 8612091, 265139300, 660935059, 540956961, 208167695, 871392438, 475589158, 627203728, 426289899, 458236542, 331967740, 716774254, 82495074, 679918786, 863222070, 642367718, 235353394, 924436177, 514763654, 160091863, 542116882, 386635811, 764935141, 709499967, 963735245, 698486798, 615341787, 452823444, 618394986, 492631990, 124350736, 824418183, 157857943, 331181331, 707748636, 852546645, 835002509, 360894628, 646284479, 643642066, 381116350, 717644863, 149381429, 674518152, 57605138, 907744601, 935815674, 590999755, 464466578, 248371006, 283681050, 364027502, 599240803, 818187791, 679391713, 443648002, 564668899, 707779919, 402234181, 858021535, 230430794, 982491607, 180376648, 849812542, 72891361, 337079834, 835032037, 971144715, 556248115, 737668744, 212891819, 441053047, 118599628, 691994586, 645379628, 342760407, 660102319, 148190898, 713018495, 98131871, 778573302, 807981515, 74336983, 981688970, 859517915, 576044031, 710905062, 516081533, 105795286, 841458893, 863164346, 716412643, 855821622, 347197456, 770446439, 326957035, 958862781, 470202391, 81338128, 734784471, 170412030, 965823021, 985448130, 44270390, 589981158, 531586654, 4901375, 472250823, 682183574, 308464125, 403267988, 193547604, 988286849, 793844057, 440956890, 53600331, 202183997, 806054923, 168740590, 509009412, 274896909, 433454535, 863721823, 36761969, 242515617, 666181550, 69248037, 605969588, 182687108, 103086372, 763971008, 130553179, 576572669, 202526205, 58634129, 527498400, 929082960, 429721002, 251054394, 777407618, 881187084, 80821781, 178891905, 871163357, 497267889, 245079939, 796092469, 92973373, 156880421, 230103701, 813041008, 571198930, 454011405, 888690156, 516975914, 879431373, 115053606, 947985406, 207956906, 642687368, 316164123, 342973480, 456122046, 760532774, 809637834, 640568605, 33756900, 155898039, 224070574, 130295818, 102467380, 45366832, 903083024, 510878005, 508694691, 673693805, 679218142, 473596120, 171282984, 199461303, 799297714, 768623107, 858591608, 737254249, 786332931, 291576330, 750455700, 547078743, 122560241, 891479481, 257065294, 583262721, 483700762, 160300133, 779379770, 648984152, 916372389, 920435084, 668528625, 274941651, 588208037, 226872791, 484538549, 97331178, 544250502, 68058121, 462071991, 832959688, 172851434, 996545631, 648030829, 586890485, 152390330, 959469360, 8199213, 775217498, 790190301, 613322682, 290095263, 648883170, 803545940, 842591192, 88508048, 50503003, 428272882, 486921199, 759925010, 243329471, 155502398, 695653202, 461655238, 251402846, 170787184, 800394889, 559755529, 486527534, 447610886, 162092889, 262855599, 875461968, 673986515, 893357420, 483011101, 700990861, 645999859, 871329069, 589952901, 92598925, 690523019, 448822457, 861812982, 402539192, 771838368, 516165388, 774143597, 228562338, 109550117, 823789188, 643106043, 358648738, 18282994, 958069143, 541432229, 173675976, 977447309, 914856183, 341151422, 897210782, 775236274, 595708237, 15686382, 373750065, 284488051, 96502227, 37676317, 466950140, 102432073, 985711377, 869768463, 229383618, 366399625, 510264169, 521071690, 16016984, 204558187, 78977860, 887573295, 342136263, 920519482, 708821872, 78554122, 274330362, 321033093, 125044924, 631202941, 829487180, 623978716, 790770755, 460542037, 265465546, 742110229, 403838255, 958734862, 981746117, 624194877, 130961334, 129076101, 86174331, 605244079, 657885849, 371422292, 830925976, 709180756, 23728025, 596264904, 911580376, 883882388, 266606969, 794667820, 23478727, 540785666, 932850662, 214777206, 201193597, 143232282, 129542224, 508296136, 101604813, 894005330, 324207581, 588485089, 381903286, 167275157, 317418034, 129980332, 940814467, 813933974, 187411730, 319870329, 487635687, 918817702, 716620162, 208733993, 589133853, 748779556, 179698841, 499624675, 852696090, 61616856, 258758606, 192147649, 714620200, 545527043, 692690667, 499634595, 319328185, 793101648, 900427728, 623314396, 738443288, 48798467, 845520193, 8024755, 16862271, 603798538, 278927616, 49245205, 965963272, 377412826, 312719161, 310166416, 819934082, 459521714, 266602255, 258032906, 67713421, 996343551, 839086740, 197131824, 414064715, 853399618, 703673028, 289393644, 426091916, 712470855, 887175996, 75775967, 673761713, 701761803, 656237603, 213039639, 394778953, 978143370, 190366244, 559585091, 125064860, 800451197, 250568096, 224118038, 889912449, 829035307, 104565060, 200131362, 672578484, 993220115, 236513058, 545081734, 524058077, 57190419, 2105872, 109133248, 496897956, 768391095, 385961633, 654548055, 147572745, 869057126, 229274796, 880525579, 402136588, 733383420, 580692848, 472678116, 718873469, 956692574, 481995034, 865338071, 255911790, 692123293, 543449674, 14996663, 701446923, 752598954, 866037035, 684548779, 198264339, 531065526, 844774989, 236120906, 222001874, 987023073, 627495418, 87960684, 50045124, 77412232, 556790019, 174285808, 92489313, 483735543, 761324146, 802084455, 476451344, 532770639, 21696902, 463702461, 712012350, 591572636, 563264984, 944111730, 968226356, 421144478, 869121637, 411097468, 67640442, 191207707, 685311468, 156568233, 221349129, 37788063, 567629277, 271622037, 749624687, 480481085, 556663615, 129510326, 58639655, 169383426, 245071315, 51171533, 294373698, 185816361, 292519030, 742102876, 380670123, 666686647, 575647106, 582684266, 34822037, 788970391, 837482390, 431885998, 981845171, 942697402, 926070605, 583687085, 399024144, 982886051, 732906073, 155854332, 401178535, 207129444, 736075529, 209881635, 750756593, 753317390, 137506646, 122529454, 419947507, 279822247, 882215939, 351992104, 197926476, 207668791, 239808649, 828339766, 129941896, 286296328, 8582505, 363075954, 696499662, 838350657, 836821039, 935219001, 88580325, 919632257, 721938506, 671038038, 394260924, 612307619, 498339448, 822994476, 359722022, 223201116, 760147488, 264296551, 235374550, 781668427, 632733668, 833073139, 10573280, 113771825, 945173820, 110119198, 596460710, 265656145, 404236631, 768021760, 353119489, 167520678, 835354080, 258203383, 177867806, 587365237, 643523361, 969752163, 510025228, 739101638, 87505924, 394906947, 173736328, 200461792, 573972218, 423353483, 965939431, 187646361, 752172612, 74772509, 715089403, 191648736, 506542752, 523442945, 978034181, 77174591, 140119923, 71024357, 200127287, 295975276, 599511663, 368699075, 159228312, 163448056, 808712747, 151935388, 792533735, 127670863, 136164445, 499750343, 644093218, 805251475, 305294975, 754623435, 388738721, 267043857, 819835517, 940998967, 368073479, 840857147, 63822179, 605390392, 676874392, 241176273, 604039800, 701159445, 750330237, 609441022, 7703116, 897957019, 467645364, 881806959, 637002178, 153474012, 744810585, 287372820, 973144721, 410912893, 687513275, 690286510, 979687050, 511544981, 356496650, 310352822, 517903189, 467213209, 264725679, 319289450, 826429882, 153237712, 386677958, 520645977, 113546627, 280709190, 424060288, 32314343, 976704603, 321285082, 668810418, 87273302, 225043184, 937745367, 140724988, 953576797, 772189936, 378323811, 581978633, 590993708, 645327184, 620119909, 261529942, 780876739, 673697518, 481623919, 40277308, 771981079, 916533483, 21838097, 724312112, 905838219, 533731163, 772128481, 377916256, 374692679, 265692351, 321840187, 526924762, 666952397, 656022502, 325215988, 512666126, 264757580, 2457678, 616648908, 733673946, 944371997, 219404024, 93665400, 469551581, 414011231, 145478869, 971638192, 698718831, 391304961, 489332878, 944704655, 279099242, 977152351, 839228914, 707204235, 526540188, 809581489, 950159820, 94054675, 537893268, 896569022, 339045981, 703138044, 624030690, 309566875, 705699251, 972828715, 981280937, 268381970, 583877941, 663274347, 250631373, 438261289, 86567012, 209494688, 897257415, 252808218, 43495562, 699290536, 639235719, 782273466, 853483838, 37959935, 936632420, 530336584, 695419560, 420284307, 542446899, 1368989, 642757981, 58060849, 16878021, 837529899, 396630824, 456968356, 320993020, 278280132, 599021234, 755496776, 167199015, 857706924, 53366129, 461653710, 648018699, 160447843, 497580068, 108088108, 928459162, 17757589, 835329057, 251282669, 674053372, 28787123, 643620499, 311493508, 937014857, 521567812, 544383590, 107873044, 874730534, 21752375, 758412880, 163636541, 748152166, 78579317, 619820244, 812708375, 785990925, 561351621, 792415148, 59160493, 520152249, 561316053, 249472016, 646735744, 27652666, 603624914, 925332501, 321597813, 63545034, 881506416, 156405819, 599132848, 170666619, 793050721, 132379761, 10917644, 165791066, 857637663, 660028296, 820369091, 823650817, 411518785, 834595848, 773000463, 320111071, 515758739, 693583884, 780364220, 223701672, 56228138, 452571046, 581867329, 615551192, 795447367, 483447546, 466469978, 679434995, 572787002, 463932202, 11193255, 171896510, 682126318, 590072634, 810353334, 884365869, 624851723, 306429666, 909847483, 463552964, 610371995, 611671113, 571465768, 770054281, 373693449, 207124628, 392105028, 604954767, 935152638, 942607371, 869077922, 748568100, 580215499, 771599184, 225765024, 608239575, 143991891, 690675612, 225080482, 69277571, 646314387, 596987800, 935494945, 174375397, 660690670, 72363963, 764411392, 544413504, 795998820, 489529729, 176268954, 5051381, 262792988, 164950484, 327082263, 687428864, 982196231, 529976241, 180910490, 962659298, 409937778, 110592717, 771671029, 894793166, 242394040, 288783767, 782725228, 80837930, 784357859, 832664752, 814602713, 653574387, 458732513, 770046500, 214691097, 543989551, 603950117, 265002934, 474513731, 680182660, 317350999, 968327276, 220162797, 524792611, 833867796, 741179550, 613876667, 710670293, 127416411, 755095304, 212742610, 826008204, 837597815, 938558703, 647450577, 691012014, 130990141, 130852603, 974348970, 272321812, 74679212, 44089380, 370021384, 451290693, 857197013, 21861286, 56219113, 422232863, 838212945, 62415679, 134933260, 83681515, 944118749, 561512099, 704742901, 28674384, 427702253, 523402543, 364061894, 553092414, 135911376, 398782118, 175244223, 134936844, 76766641, 855992074, 234173225, 358026552, 71717099, 411398565, 651124795, 745615525, 148350534, 194612274, 353694229, 474778546, 877215941, 312901858, 944884801, 344164854, 812403491, 756331591, 249821377, 565097326, 428947867, 388745767, 592602862, 713246129, 126734505, 836480816, 730845094, 856062333, 127767629, 909693085, 770333627, 382291432, 496862639, 602549408, 940747050, 539116311, 641760430, 41040021, 449768998, 943921974, 354951336, 191886295, 498480235, 367447477, 218056055, 308901165, 842175206, 126812418, 961627571, 916785588, 315628989, 165164586, 329660544, 662152519, 135120049, 462957726, 411093698, 468580972, 423079630, 351888874, 139284542, 236494180, 299190165, 691734433, 806727336, 94056414, 733111160, 820316677, 559573439, 772934078, 667057059, 273900626, 131280049, 222326861, 22659464, 473365543, 556820186, 533277233, 782096899, 812549708, 244922056, 378582990, 846459142, 410446123, 806125948, 261904769, 946799625, 76473370, 120453407, 73071410, 753403082, 993424227, 376881130, 924354447, 349344145, 909384475, 457968996, 429433810, 231990200, 819110873, 538178034, 940760050, 604293678, 174039399, 553587450, 62352965, 830441918, 919970494, 422978404, 321627356, 301591978, 530460463, 980185291, 718191927, 909416214, 862588034, 238025745, 487731016, 225308453, 651938700, 568299093, 646758405, 237947410, 90848214, 140958490, 216826819, 129188855, 952856967, 295349093, 797165737, 816191905, 795018000, 878097340, 227037228, 916468870, 288268252, 571653955, 302942178, 24653277, 628865342, 942977078, 731859097, 769432001, 467265380, 774558484, 336473696, 125501678, 665687112, 310283809, 899022253, 537169276, 756732344, 85960129, 690057378, 279986914, 338534760, 298073773, 364823110, 511045956, 506284907, 751669225, 327996262, 327220884, 648210281, 370822461, 802224560, 206224767, 404732483, 447489637, 41693683, 941487001, 106533628, 226276193, 950704328, 25376776, 921375636, 271862292, 253266010, 535795856, 188181301, 776898709, 193485455, 755420065, 205681978, 232259804, 352691498, 135286771, 612091734, 572363970, 16536947, 969545691, 388217239, 407121653, 202377848, 778503719, 379004049, 39431467, 842848251, 637866278, 263450913, 470022310, 786715867, 712767197, 472115017, 471357883, 270215412, 772795814, 423705153, 866560930, 507400612, 713147602, 795797543, 216333050, 160735731, 654836176, 506551750, 409217459, 133302452, 433886796, 481130707, 788582688, 871102860, 774630431, 161042410, 109836463, 282767382, 870912711, 693083468, 77038066, 643642972, 235513252, 590305228, 674495965, 439123102, 16279572, 304548313, 204025945, 128000673, 781767975, 475379851, 229186121, 171972548, 470865962, 151864626, 490975863, 401119346, 380829910, 480143135, 10654923, 255382056, 775839249, 176875454, 996590336, 838963961, 267823231, 429284231, 662930127, 896634280, 672267616, 391016829, 754850404, 48328415, 867243255, 364056003, 413070022, 134458849, 331842951, 941854320, 702972985, 819034737, 484951326, 949496121, 740222836, 30771452, 657788788, 229966694, 118170301, 110252009, 842696432, 64164525, 598569496, 39300034, 943747201, 717548968, 708981342, 327819229, 314507435, 450192749, 29111481, 454489383, 617291826, 590001778, 347132933, 442357299, 953924949, 674778818, 434373341, 60688856, 155450813, 291826642, 614633163, 481486476, 440950228, 995129412, 146263623, 774145354, 422004162, 459739094, 295176867, 842050485, 253887073, 754385981, 330094230, 326134971, 477044168, 685709867, 664291667, 618311578, 714730998, 846239951, 672632700, 91094955, 227190807, 298974151, 207586326, 134500974, 90353482, 460994075, 829461303, 71384393, 771986594, 896824858, 411097012, 934487737, 473472244, 832902668, 305396103, 860813780, 421129205, 738226159, 22077097, 340570602, 35003815, 986543921, 682422479, 10830207, 425181951, 153706857, 823899400, 819142389, 795689570, 507430885, 526638566, 855364960, 837144594, 82065512, 842372974, 895171337, 849583896, 277516966, 789994540, 19695962, 798669716, 669590972, 579525217, 142508872, 975880542, 333212788, 588555193, 110908191, 787445956, 896088257, 69568604, 248121827, 948760238, 324949422, 48253420, 728039129, 681267339, 912539755, 902713353, 415550357, 900469949, 951112942, 240227809, 760395374, 965573881, 111744390, 887304504, 398162545, 892547384, 890572198, 297476258, 912738833, 760909615, 475827188, 951085413, 544044108, 352532904, 645920644, 459378381, 434343389, 798731449, 90859835, 438199988, 763664939, 694869437, 404391419, 102769860, 354645649, 348578915, 834701912, 27060798, 85679111, 487012362, 747470456, 576309086, 92847766, 919038896, 523770835, 656263785, 283969970, 412020655, 716792691, 314495650, 974031182, 200747551, 251840730, 627277259, 611044872, 808623906, 551470293, 24574484, 984994870, 981215170, 137617941, 435703778, 455311155, 344315178, 862171983, 773727022, 370450964, 925782880, 181554009, 61958868, 353600366, 673289890, 706862591, 543205964, 433668, 607065186, 368688968, 326181678, 186530885, 947732639, 6965826, 326795144, 429461182, 869727131, 752378868, 566678886, 898234660, 180947791, 906816679, 519829895, 890893083, 782114506, 665054223, 711508362, 976563816, 877196644, 190179802, 598410381, 566007568, 525227159, 332999758, 794487555, 106478665, 932154866, 450796308, 159700294, 689646625, 171115921, 402266568, 87410579, 711917612, 813685252, 353919953, 44842277, 965942781, 871629498, 221300080, 300578150, 728940639, 273747418, 304599701, 429095710, 103143829, 773914595, 17181576, 985417318, 242881590, 789401830, 316855494, 92836077, 600411162, 728440414, 470433852, 271937480, 927570748, 9083893, 600293619, 587311063, 936579694, 100804937, 695775542, 778447362, 526546493, 148945779, 899680479, 189009924, 202527268, 202374553, 699439536, 780692, 309789946, 202377354, 564046025, 115215929, 619321208, 379328279, 302854627, 5421250, 861850434, 759057396, 199970572, 723036836, 686880541, 10921078, 287951715, 450739676, 479801254, 923592054, 71805485, 712065584, 459754645, 387714757, 734887364, 150299555, 128503568, 69220874, 113305670, 911237097, 918996943, 126161131, 54481003, 471915264, 512616470, 471095332, 568275318, 801371113, 486266654, 587699112, 364408715, 671558047, 27762607, 185043364, 74768596, 55257314, 505481421, 923906611, 253487906, 988339, 943132260, 174758444, 409016469, 936565936, 297210159, 190994831, 818670234, 881047300, 453672204, 369526736, 666706888, 41277532, 438099506, 769145728, 892127224, 764178611, 924277936, 980133320, 718510552, 813290417, 365605710, 762588867, 64470465, 829962256, 30679000, 448298186, 983293814, 849210617, 460347708, 49009866, 296101994, 225232199, 864191671, 918181777, 409020120, 151749821, 382089144, 690944363, 55082531, 92453188, 816118363, 466894417, 296265993, 923427327, 558593920, 591941569, 733196463, 120575467, 691318699, 16340883, 423429373, 423111936, 668454517, 241676104, 360611263, 660737481, 911835893, 327099981, 330978497, 543654981, 967673805, 213293936, 573204122, 699493292, 574833965, 60634488, 904919118, 336785306, 691013140, 379294114, 890953880, 708239515, 801829726, 839760864, 700685289, 597467694, 437395404, 700842128, 960066090, 65324499, 524459623, 751726506, 918151548, 409237559, 136645555, 929815216, 367750837, 157097922, 633824602, 518021490, 956164311, 597751330, 813887604, 812790972, 119014980, 803390059, 115797757, 13169835, 563366706, 142417496, 356623706, 675912740, 539220590, 326462766, 967260284, 785833872, 813915810, 395435682, 525953993, 633593337, 274762980, 971100078, 160216504, 18561979, 426938089, 567500474, 955464389, 313682975, 399074014, 449696550, 431193918, 65761894, 609336703, 637990593, 908902135, 176365553, 669858049, 518190793, 281431001, 105010170, 545225314, 7082617, 696622116, 414776167, 454432541, 21508866, 465294730, 216144421, 357145146, 523146935, 762045851, 334756073, 679757801, 661422983, 276792063, 657610152, 586303429, 139164280, 309047691, 737441932, 126915191, 904581467, 998306119, 464664378, 283513883, 31998267, 784846231, 819816884, 342468932, 271953880, 438357149, 307952636, 656800279, 509039953, 363998948, 598072983, 148247904, 358205879, 906032176, 638418594, 81398807, 871340260, 796315659, 996353599, 147625393, 918417172, 974195506, 10979098, 990385372, 486968256, 618440894, 855100932, 807573269, 848167237, 694099288, 436367983, 573755461, 714833128, 236566739, 8553115, 315136909, 288833351, 807460742, 877502387, 829811314, 606323993, 298544690, 609294952, 680492720, 51437092, 364468008, 414766251, 166757497, 311253708, 588996191, 722390962, 403270586, 541947736, 678944686, 488252530, 947983678, 52593980, 621691453, 951835577, 86157857, 165252414, 100560608, 731595852, 601781455, 486092556, 300619703, 617396145, 205611507, 781364311, 704167304, 296349218, 789697185, 57797611, 865876805, 543172965, 870874557, 292605114, 226791189, 148690991, 785949907, 135607915, 126133981, 748235602, 541061889, 753234767, 594497059, 915959040, 834029669, 493002885, 266624127, 764206459, 481390259, 111335012, 769946874, 145498675, 47638835, 626998784, 79880759, 579556392, 378385732, 755108402, 728045451, 294096024, 751847369, 716388900, 111587141, 410630415, 341095462, 994831516, 718868745, 763417474, 572623070, 335148349, 987946124, 645986249, 412639323, 423732922, 902823353, 839054289, 371653439, 746951166, 912436569, 775580184, 985304842, 946561809, 698716399, 969349052, 314722362, 508287181, 321817216, 190417475, 284697844, 175486380, 509752774, 185254961, 904715244, 155250896, 536302968, 358190640, 760401667, 112942295, 378930738, 998181199, 152862760, 298374745, 270965720, 367543764, 550632672, 804280238, 483720517, 913909259, 314312168, 831540346, 664316412, 969180557, 949674708, 688763655, 135249536, 630046936, 555640544, 215964364, 996083140, 485325148, 595532586, 824289770, 891068920, 53121272, 477140924, 954705489, 987069281, 38927575, 1043995, 771118390, 656630430, 95306557, 797388440, 686589109, 493130709, 963148088, 461648450, 494472060, 752555877, 894351222, 950385673, 176174854, 242153160, 734956569, 575053105, 186422079, 325703894, 149034734, 554203005, 217749129, 664464476, 72206121, 189700904, 249542657, 210910148, 626146576, 674260052, 537059725, 952061914, 395019926, 180618300, 611741727, 474265999, 57791017, 324414690, 847865070, 326048011, 124025965, 243628018, 91383314, 388744856, 373447479, 625305805, 594784054, 520407823, 937578860, 740605712, 243765589, 760980024, 657928351, 989905749, 390113472, 741351947, 430893170, 149388415, 985223530, 686251078, 980229150, 348078473, 250900171, 474129020, 519821516, 151462329, 489070673, 447752475, 131575972, 373837140, 15315454, 317570947, 958282608, 239391981, 416606860, 408152714, 245358865, 213457157, 267933836, 813941845, 540277797, 109443561, 106818361, 597152418, 267354906, 678241528, 130534369, 153532062, 664219814, 346301791, 521557808, 432478429, 353082296, 512222480, 925088217, 209778232, 890452954, 460746265, 233629104, 522931776, 290074837, 277212553, 439332062, 93147598, 530115748, 197559993, 987748689, 360826195, 348900874, 67145425, 807416334, 650574078, 742851234, 564907744, 317019932, 677568320, 909846889, 764297588, 328826400, 571817565, 876604134, 66751849, 779790533, 672278830, 824900078, 505089145, 30975042, 571690790, 491245190, 34119166, 920176028, 727393643, 890167562, 445189852, 972604154, 23971090, 963150046, 209505515, 70322663, 911724376, 113601389, 124736784, 597063845, 191896771, 451469319, 490559853, 956404080, 61916881, 929551592, 341624470, 568132223, 66206719, 697360043, 294316970, 947104394, 432959257, 903702204, 20675227, 602826761, 684045471, 836946821, 106159291, 746239023, 483760590, 161515330, 255557113, 447849164, 380594967, 332362008, 240646520, 953322734, 592606415, 753931691, 131760731, 626901391, 47721193, 600108280, 693704726, 142670821, 992865688, 679460857, 606300678, 998652339, 522200299, 447971442, 538205401, 203533950, 681583717, 333427921, 564142787, 225396764, 89584320, 324230920, 468651851, 5041026, 160692533, 498335094, 245994286, 848559742, 640108885, 952909781, 380539407, 541825357, 814886608, 98770273, 55446013, 205083952, 433960234, 538592279, 549903688, 470754323, 758554598, 26384234, 463643253, 355791400, 4291608, 855051052, 894661484, 550488623, 776832896, 745576400, 62213624, 386396482, 256282788, 172276542, 390666003, 827957223, 690070291, 733879323, 355865414, 588395659, 907260033, 676974082, 3700796, 763504876, 121146879, 692376485, 303239169, 135742763, 735633298, 85227551, 263215222, 271570138, 335209282, 95259937, 225852923, 702824328, 579568615, 575907145, 729964579, 116333531, 164284461, 181531268, 761738155, 835478983, 993236222, 974404447, 432574815, 593400675, 640101352, 795567821, 243675012, 107927290, 636911110, 476854554, 859117477, 262267319, 309130347, 101498242, 14807815, 496831544, 366976925, 712395638, 3847069, 258099517, 534120510, 611747415, 76418523, 904133207, 19842892, 747875267, 67243649, 567177031, 502476451, 473737403, 221971634, 612219541, 850049738, 824900913, 616294712, 174691986, 838505736, 601899330, 506023550, 756232196, 45931127, 570848128, 240153191, 112362583, 874594495, 840820576, 176254935, 843975548, 607788049, 518151550, 608997738, 459001954, 632816639, 938051932, 512379008, 34150968, 294426767, 52442901, 40713092, 311537520, 368405404, 200464889, 433551554, 187417796, 37609286, 265015471, 227890907, 261492003, 202655194, 150248952, 956948148, 544344802, 162032518, 429683537, 713542021, 26278002, 82369752, 354475786, 683134539, 893138040, 185805541, 219280328, 711776197, 198602702, 731061022, 854995263, 310532979, 114753347, 558192981, 20797474, 498591265, 857152517, 23371078, 615719232, 681782495, 196153244, 842032272, 295506647, 427091460, 771288876, 590179254, 279081169, 349597231, 984915359, 166671757, 960225100, 156713493, 143499410, 234997770, 930247300, 989007385, 384330171, 763204723, 174562399, 58781289, 221446279, 191060563, 675754284, 604167286, 233948105, 469495354, 404471417, 591450423, 73785027, 158441697, 198897051, 965003245, 867442687, 100499666, 674896559, 536914123, 715648096, 72681305, 736542159, 857303007, 801263408, 966643513, 731894105, 998879372, 367883140, 824170937, 488158807, 224636975, 888274758, 157689675, 805682944, 580209587, 368140102, 617477627, 265471005, 322212102, 10134150, 900590709, 973327097, 656830778, 163705490, 604784802, 715998642, 703354687, 1038506, 347538241, 329223088, 351832004, 699452087, 226166571, 609267829, 386937370, 114606504, 998063130, 120369544, 426735085, 493759195, 211068644, 790373442, 649319698, 82867656, 664796909, 357767284, 364333451, 687962792, 386484851, 809057521, 357392416, 563586577, 728171143, 127702985, 872947775, 398967235, 836496418, 775198319, 157646610, 50366791, 804945290, 391528510, 417629974, 710485009, 216737438, 362252242, 516099199, 171714770, 136148940, 605997339, 18212352, 837877476, 731363823, 341631176, 383059259, 727013253, 975093654, 990711577, 356916165, 696294392, 999655851, 522680566, 876309953, 368760671, 714911614, 953188453, 422276743, 683606816, 451631813, 929365636, 546467211, 101930486, 115396291, 226089868, 911576459, 446130321, 160564425, 593989185, 680872784, 340083544, 731934108, 852788770, 463267592, 300818525, 680771680, 208155972, 351473283, 102220032, 147570890, 306077054, 50774133, 588634733, 373985780, 690147736, 662074177, 299439008, 354238467, 289287068, 790307627, 868807356, 418716039, 363265760, 712162644, 4883328, 146840801, 976338517, 59368703, 94031158, 550127982, 840486771, 833269267, 999003781, 583458403, 108871472, 391219196, 807611853, 299630383, 454540901, 987375940, 306038101, 826962031, 38432630, 174054556, 364498411, 484126909, 463495145, 773644055, 524427874, 144666583, 94928969, 12576915, 539395345, 841939158, 129263002, 324076059, 888014708, 768403235, 107106113, 454094610, 5345636, 988451927, 366279188, 236530078, 702898490, 628707076, 657782427, 464012403, 850796162, 612208225, 658459798, 856715652, 905167054, 351995751, 411319134, 565774901, 435916377, 935942493, 968731249, 257743925, 275544258, 71634197, 129732335, 649596904, 918418411, 809258031, 13442755, 188612981, 503592815, 582026468, 54071715, 152974375, 59136143, 293020701, 941646191, 40094595, 32927101, 11968506, 524779313, 167835377, 648146036, 897290731, 91916097, 272450755, 70335972, 203679669, 742027263, 35566048, 159696404, 904506679, 445924124, 909847953, 402349675, 439533965, 965713566, 476924954, 112800137, 760056275, 183235350, 778131282, 62471124, 461758583, 428373891, 901278825, 80773026, 297099241, 35942911, 816011474, 90830624, 589513647, 551931238, 851298744, 903214010, 12285331, 546457216, 415040505, 4072357, 45221324, 134078339, 851947210, 192317879, 479258767, 557020897, 639415333, 530455794, 582768084, 8643572, 338130600, 774521139, 146036125, 27763293, 931749339, 367543094, 846524693, 427797010, 500977599, 698901615, 836300495, 114575944, 356262729, 784723276, 830697163, 145923837, 422831821, 685146459, 489145681, 96939648, 63004552, 919273903, 425160092, 440498928, 189078878, 293154204, 598974728, 552137049, 164748236, 317239484, 488864938, 366709708, 403537272, 326938654, 45911254, 115704188, 212209802, 567937955, 977086563, 774688994, 710563331, 830570070, 916951490, 508997859, 628342409, 402094530, 258191680, 969082105, 599953227, 398100120, 724665366, 139562226, 890991276, 693730452, 282970979, 383812440, 904631485, 826744051, 631820576, 918502628, 727576258, 443244616, 731651477, 2667292, 861175327, 387637677, 867680159, 706737939, 56540571, 11020120, 128691345, 95303217, 501552486, 148030861, 651195604, 172462096, 254276446, 405005206, 304138744, 225307189, 548884101, 903163447, 16806029, 276033718, 92983808, 197458101, 879766653, 75630304, 352188050, 308044417, 882148803, 999749347, 644737506, 279582426, 250553408, 541634055, 863526336, 888521838, 965423561, 516044, 212848944, 988752200, 223177460, 294402341, 397785586, 936498615, 155232689, 155550540, 657392725, 703247028, 79650520, 663610862, 53637543, 808041651, 392350013, 280127554, 27944160, 317994921, 862116014, 780122455, 543606381, 209326460, 867340127, 174939764, 984773375, 611963083, 36241307, 316578380, 233090475, 185720695, 950104898, 243292825, 737544740, 354236231, 261498971, 506358561, 589744579, 824861873, 688240550, 857353584, 666426493, 126605438, 80483423, 230471248, 880505293, 929434058, 168281981, 266942641, 214703139, 810706506, 713785933, 271955688, 666039933, 897279986, 688845771, 828934774, 210594228, 692791014, 140851387, 710548339, 153724904, 599224912, 3072848, 85127171, 608586280, 378023749, 228002452, 952383616, 505141711, 596537298, 122895867, 911854589, 8636428, 897096094, 462228443, 454532471, 498381023, 415844174, 949517655, 486173349, 106090194, 321386433, 903688248, 439860905, 618389649, 799987680, 477902133, 92518102, 485123133, 163178330, 30961638, 306737222, 760790467, 400282681, 194631004, 457855347, 399980409, 15024965, 396279436, 921544773, 759350864, 186197754, 933729242, 103920543, 767575915, 124341079, 472719662, 416994693, 924192366, 948023768, 583879241, 107861766, 978078000, 210343544, 38104971, 849447725, 131723922, 884709898, 450154857, 693063805, 225905628, 41413398, 57827076, 284418426, 822408565, 652129484, 633917950, 120327141, 455982641, 602169323, 575503250, 311589396, 622121746, 366390962, 97222458, 727534944, 776519969, 956715634, 494330215, 890464234, 999957884, 841498841, 167258148, 550840834, 807836292, 715553532, 807969711, 742847394, 372958655, 768592567, 376019741, 865988266, 815272816, 673156849, 53639330, 137768134, 163462605, 467718724, 42199486, 588049708, 5670424, 854622005, 47260835, 543271147, 890622425, 724197174, 614730119, 820674340, 542148444, 881563372, 872672603, 99287654, 857396023, 698867717, 215157633, 839340055, 799880653, 173067361, 454034098, 911805540, 738029488, 868500779, 312580419, 972122188, 9088445, 165255892, 271048135, 101845541, 280672654, 246752324, 584270676, 160172033, 611101992, 947853991, 444171754, 389516583, 811041958, 341034498, 784160046, 818497991, 531829836, 356937285, 43407052, 903469722, 724191687, 504398137, 390276653, 915041516, 991735325, 297757892, 757874435, 464091378, 612701069, 904913888, 29741365, 415071458, 221801140, 387023851, 874552537, 45899922, 480405955, 628570577, 622149313, 762375745, 503860731, 103678195, 495670523, 409989074, 874585171, 954952886, 849220187, 588371870, 397388559, 363826341, 205739790, 543196301, 344476663, 478927289, 71029971, 618901879, 183673899, 515183505, 552156382, 55156351, 621733366, 28685189, 386541774, 163761588, 401618607, 924759980, 852387218, 817739626, 366002476, 795720512, 822278490, 269454417, 980066228, 216271017, 322258794, 803076265, 743566928, 939549053, 430740209, 838387441, 869776979, 772541886, 577124249, 477084864, 749198546, 436192497, 255908505, 197873699, 164489828, 459326507, 455568429, 463491506, 16059735, 867511857, 948636414, 224165674, 649675035, 178286707, 659944739, 109018360, 300920489, 240265253, 468610134, 852327497, 514302980, 39335276, 672570948, 915755666, 294024226, 909004454, 707685819, 601902747, 541612734, 481769480, 431394886, 738957186, 817207376, 232842485, 69461345, 536348955, 93667121, 780847093, 194094970, 918832075, 699327747, 480439917, 623110215, 419758455, 321429874, 22665925, 277178569, 553844292, 622553996, 405864231, 370538385, 46944763, 120841828, 491436601, 130692144, 189444768, 758783245, 70026414, 779266139, 840004693, 325363263, 177263382, 165156914, 244963453, 173934179, 788788906, 150241796, 656366401, 684281619, 15588490, 585562807, 640921648, 339120635, 630223223, 116771629, 952575015, 811233801, 507954100, 146939702, 797986810, 652299004, 531966102, 863802671, 998546687, 873082438, 16815457, 599645648, 136540520, 312402786, 931072738, 620934351, 102667992, 649849336, 237109527, 601534819, 926462884, 881910199, 907912738, 385792628, 19982441, 711387643, 463515102, 176277550, 468194683, 395601526, 257486775, 103777422, 941467749, 839005524, 90783237, 733128826, 72309869, 469448846, 8153539, 105165859, 692831971, 327834472, 983760962, 854680454, 145034436, 698798880, 934901570, 906781997, 434691925, 766267296, 384024404, 889165250, 906666846, 192548698, 272518435, 673341724, 564869857, 154551747, 628200622, 718224935, 254700209, 512182487, 894406851, 65149307, 151715107, 905242384, 915616910, 910621321, 321117067, 240591962, 108443117, 701087070, 862128372, 851674503, 517195322, 653871325, 514794633, 289756223, 887784198, 611919590, 42156898, 529193227, 527258968, 164721086, 78098039, 710263577, 375800303, 447588572, 251081719, 90091699, 299371165, 182082143, 298366715, 24313738, 526863479, 820826301, 551253920, 607486080, 755633833, 875859742, 506477805, 232447730, 110959314, 603348271, 379040800, 58744018, 230380657, 98973204, 538037660, 564521144, 196016841, 381738884, 17337887, 383709739, 421531779, 774617240, 104184693, 745234673, 504744225, 479892441, 430146112, 639518822, 287144945, 133644201, 338876779, 457591017, 859454445, 387403438, 283450363, 756318841, 993282340, 246424298, 311476742, 279063794, 182478443, 211647920, 737317401, 662592662, 495703726, 205876648, 42074980, 347623288, 132274820, 17660580, 992424310, 553419167, 437120501, 84515877, 513925425, 415468734, 696678443, 997507712, 682030104, 661921053, 341629420, 792669675, 207266223, 379702144, 637618475, 92515924, 341701946, 686916141, 686612467, 916145612, 233678029, 390447699, 618473461, 292872403, 545877302, 546327263, 650530914, 699178545, 255438518, 944581127, 356012523, 827697607, 659118505, 992166612, 448192079, 201957055, 128553528, 403054335, 233123423, 339298974, 99647048, 185942351, 118328161, 816991666, 64298465, 150201729, 867155670, 815133702, 201270623, 438434981, 218111561, 899572610, 71906065, 263328031, 373003684, 743260822, 313212493, 420997341, 260358973, 322340689, 712340921, 287783665, 59480620, 422621797, 331488731, 89706689, 766144311, 6605746, 123135805, 832327607, 587794750, 824252276, 958864188, 7513780, 580796461, 280812418, 635149154, 633430748, 887728598, 881558184, 818057814, 307200594, 540343657, 738265646, 892357689, 97627228, 367121835, 416488403, 644530867, 866921692, 645776625, 78365078, 931769710, 417880488, 19996794, 383779031, 426604664, 959249422, 377220204, 552572458, 563647343, 5241223, 417134309, 209416512, 249014071, 102314535, 189142181, 224914568, 10788326, 841058698, 745077087, 975923905, 958775568, 915116542, 836896535, 644550454, 987629623, 206153714, 765848007, 889668732, 989478209, 334995359, 653372937, 396909940, 128366101, 351103287, 274888597, 757559040, 775146626, 899498257, 566873117, 629110328, 620035164, 265606714, 812319830, 202466158, 357913425, 799411937, 755130399, 144541577, 737825890, 317582197, 144795659, 850651499, 767624197, 503553526, 873378838, 328066194, 193357882, 723546722, 43828586, 922769784, 763906475, 474109859, 176017088, 162066343, 87720280, 697659168, 63659400, 548247368, 18069541, 409367731, 934012880, 92744574, 980517859, 352908985, 987831826, 501449382, 166954630, 936622119, 634086146, 707658880, 80454330, 991728155, 885937029, 496545670, 58471088, 581912030, 286246046, 973627988, 51396623, 944341598, 307791631, 550681497, 973792624, 755594803, 292516462, 885054296, 58100322, 784783387, 902605999, 168440387, 971113459, 120077001, 302726207, 18879608, 602193000, 590318886, 998468079, 895965386, 848063345, 341534572, 853972754, 658261247, 269550220, 772835336, 912039639, 485273001, 372372008, 946446600, 706523627, 264488802, 802354604, 290871382, 363848960, 954175193, 667874128, 477875826, 552654966, 990024611, 873462084, 701589180, 241066072, 429067330, 43806878, 600695963, 68538720, 742493540, 451728676, 693243552, 208622298, 160282107, 541358275, 794923079, 888565775, 311446809, 437615286, 143459719, 202166926, 435085297, 501350670, 392960322, 393613206, 564154319, 406552361, 937061657, 55030478, 361943268, 814877466, 125788344, 948152495, 262737116, 835751112, 939088525, 672499289, 673270253, 305742199, 444777864, 393984489, 977542617, 38826386, 507256772, 967838375, 379299575, 488711874, 690334224, 444022153, 400774482, 206828908, 318909489, 967786388, 466796021, 893733634, 363530599, 137049485, 542421297, 816636652, 643720280, 113076949, 746890836, 747071563, 824335360, 521329130, 238542053, 250209583, 12077975, 263895672, 269409961, 898017915, 188312998, 253793755, 712457867, 154691569, 250248343, 315515788, 217492283, 37080606, 541814088, 533663578, 166005798, 763034630, 196633696, 621094827, 437165132, 169702071, 36982174, 946987348, 566482255, 202343653, 366562376, 80453687, 805255585, 63540792, 550748140, 796711711, 514767058, 477607046, 832885739, 745506018, 373434277, 624595173, 654304309, 929460560, 407468768, 785691136, 730771131, 220366856, 471557041, 134931636, 900006127, 240652007, 881634118, 229425121, 640655615, 149025621, 377490850, 113227435, 689143465, 59464994, 564104578, 963354678, 532354778, 653660988, 448478969, 135349798, 726647814, 271997686, 622014755, 542267209, 80061113, 573429089, 884185941, 73442092, 772010994, 453894149, 513316507, 468264850, 360998287, 340011784, 515441589, 847637544, 666137774, 614661411, 542744736, 880325574, 114491355, 254977129, 924225156, 772463812, 84417861, 628669165, 515890053, 523701411, 296348730, 856750628, 658083249, 782935018, 192210121, 961887482, 338332790, 684034771, 324362577, 256855072, 830396785, 574466643, 527919958, 635223690, 240305020, 508553731, 130961181, 436503304, 288321340, 291980413, 922759285, 561031421, 407422740, 225757889, 492984901, 859984465, 13095534, 34137883, 109708966, 577397916, 637205084, 594917706, 925358412, 351205379, 381490641, 2657300, 54690266, 234532955, 213787018, 325758775, 82092237, 589021272, 300144924, 279254422, 555512810, 540184968, 288511419, 547124487, 364274295, 363473218, 526929692, 872193074, 845453845, 38355542, 356018033, 262867514, 838856453, 904965353, 886794469, 603720342, 125622801, 226072121, 829961127, 221478682, 774087204, 356024276, 30096945, 738227447, 527802061, 982822951, 750476840, 746985766, 462782393, 849578071, 701358955, 438260253, 161111480, 379285654, 953223485, 416445990, 507475528, 157281199, 395988293, 727116364, 230116881, 717257960, 537544541, 244767162, 764038362, 232320502, 469659501, 55210637, 317177021, 395423628, 222381738, 358391862, 527506760, 6028178, 141419706, 965561218, 810520013, 706141604, 552568816, 556442592, 99239814, 452603740, 574326007, 616170008, 268429063, 578697606, 852798951, 327023532, 320902763, 666520204, 258000632, 839643336, 432392165, 35280983, 513513177, 379405055, 291330687, 429750153, 155264390, 912265562, 4535489, 86073999, 452815205, 236820298, 924358019, 345646465, 608983113, 676003626, 746817895, 576955010, 563124923, 259246037, 640719785, 294112853, 217848302, 328103500, 909095000, 261275869, 218809661, 28214351, 481840031, 239973855, 859550761, 634093693, 641958364, 446700200, 401798538, 331604223, 450599119, 839060621, 780621484, 696845879, 853846694, 445302091, 343787981, 693536180, 477947449, 142690842, 325673983, 302556315, 990910906, 670307344, 691510477, 294448347, 426862150, 640423797, 276539913, 934244908, 341543523, 595835390, 548133012, 521879235, 449565207, 361666573, 152185386, 920740995, 974829261, 690551680, 302922937, 975436841, 692322304, 213997094, 966762026, 818360058, 325318826, 830791246, 440836699, 49514893, 91967589, 797606554, 788093925, 696738451, 847237021, 905169194, 261845161, 526057506, 342783361, 659118742, 976290065, 292714050, 629087687, 996864193, 283041089, 499251204, 171761485, 612292682, 621760541, 641503363, 337551747, 58086384, 210735484, 485376844, 290574436, 707227874, 124433476, 614771019, 560874916, 306420903, 187366485, 52581720, 555471196, 740244516, 170829110, 914917096, 253060973, 13106502, 8140166, 667688528, 289831650, 150839494, 397757890, 358278728, 524400958, 500505691, 978509217, 192746343, 688242734, 85665153, 281618782, 722823452, 786884639, 492484840, 84098025, 109606172, 870428231, 246025406, 865816324, 264515413, 508185872, 147953098, 650571794, 461377209, 439750651, 42498545, 496324979, 13060590, 985834550, 491204979, 625751492, 572552308, 72412806, 261582687, 827694400, 865220564, 496874566, 25842516, 699902244, 552609372, 48644689, 377586888, 353311486, 26789001, 574326354, 351280891, 854642299, 894129898, 236750802, 74833524, 539710053, 354800341, 214589523, 440586237, 207397008, 343533535, 747299775, 308444463, 810795475, 90188510, 598897171, 774742968, 134823879, 761987345, 608985622, 624061740, 530747352, 120826760, 38383707, 569574243, 262902455, 189554261, 704214636, 758962956, 84089656, 563498809, 386433480, 597823065, 755035816, 404292649, 909067599, 606400897, 700466853, 337629650, 150897558, 198210783, 510720106, 868162072, 44017364, 366468603, 448793731, 522074794, 618726858, 598524303, 780151362, 168179824, 837048557, 487671549, 964962956, 789980187, 543352062, 928224848, 626076330, 845973339, 924088785, 976209907, 504160752, 991904150, 210025305, 717181593, 266155457, 490185392, 201724355, 579079085, 133969594, 738982033, 165120449, 872309644, 272033806, 329206344, 606305522, 305999922, 90402192, 675424057, 499407244, 352685849, 57073909, 164934321, 164949510, 179457971, 317418018, 463581906, 972818511, 768008186, 318179183, 953460524, 931371107, 706202549, 395220396, 321217581, 991451446, 570729323, 710909669, 670041256, 752770168, 667116262, 232926825, 937339138, 815489391, 58228485, 897294763, 699042551, 688804085, 313704630, 596314211, 990587711, 105151478, 742495385, 284819991, 572752636, 720530720, 423918606, 371271969, 868888535, 442874564, 983733951, 932130437, 461125254, 260506975, 904171501, 6898877, 678965692, 596029494, 647884108, 511373934, 428880893, 963931192, 296996112, 882688045, 580915053, 668543008, 458294847, 986361710, 84485365, 100296830, 238802753, 685673921, 846004502, 532308708, 762043666, 413844893, 783051168, 767630979, 862362257, 818006973, 483833043, 933252752, 397788522, 374251708, 336956817, 190103966, 569674714, 897709094, 913787707, 624849763, 235792292, 693586655, 119673301, 230483972, 289594251, 608223880, 451424835, 244181138, 657531397, 655848198, 690268710, 58494081, 960128379, 464186807, 447360836, 648627477, 812754967, 171959221, 588347933, 422578849, 776945596, 258688708, 572349883, 409946322, 549722293, 618491450, 306792988, 340005702, 835253229, 538668046, 918623998, 208146671, 973872783, 23114214, 594763337, 834575228, 844292289, 545212575, 68885355, 519882278, 184552886, 727136453, 514020364, 912319671, 308030804, 706129014, 747850280, 344361152, 634239420, 402127072, 747954584, 503709317, 410807992, 378848579, 959323241, 432081848, 91666808, 889576732, 969992894, 196720710, 490142410, 713118784, 835030250, 317659808, 182321223, 153258429, 428644416, 656391943, 689388031, 822224402, 691099001, 174886697, 564996120, 260010895, 795064101, 545099522, 115425593, 752597967, 686510635, 318627364, 237812861, 475958000, 469834295, 586470264, 52487452, 426255855, 963203384, 517440299, 234768293, 815145988, 102238657, 681911635, 665747029, 670314510, 99767223, 967264773, 538964895, 260803566, 479065866, 793767902, 62251652, 449047417, 142603587, 862372643, 62768414, 753240278, 480621597, 981078803, 374857727, 148069447, 664912829, 438463527, 841357294, 51382087, 55637467, 402360683, 74182757, 123548927, 958888856, 298391660, 38122422, 878252123, 517607106, 431929800, 320564877, 689792141, 948162720, 638930115, 144513690, 88732943, 719601864, 79451831, 552534966, 286827892, 71282327, 870604147, 712536053, 565697535, 627544391, 117219463, 76660094, 458531860, 31927178, 688033915, 372509022, 835043525, 929054170, 378064741, 36407879, 823680655, 681453631, 794631371, 630436010, 244054167, 18339560, 175938208, 247526670, 286238477, 369054408, 259834454, 358060846, 225770612, 215396638, 216255044, 913861506, 216444296, 366929368, 46125709, 385237727, 342534587, 574598711, 756702845, 666678540, 918790712, 705929954, 861370672, 578234043, 173238849, 464026273, 311170364, 867349621, 119465968, 307352712, 23943363, 277304832, 207802322, 524591009, 560836959, 309680089, 922900457, 821887376, 496609021, 105144046, 77558590, 441341191, 44904932, 913199763, 662987843, 484186200, 981704228, 737749689, 244585601, 240883645, 182918181, 25807630, 305123324, 796059206, 984480162, 627109382, 702883610, 536840189, 251862420, 121955202, 123432017, 216762934, 409781368, 374492722, 911658635, 495739654, 29115331, 689484630, 799860021, 790851951, 266572843, 973414753, 737847854, 56348531, 408981092, 113926837, 796938989, 420810294, 520222041, 687635403, 644242381, 324320374, 379191568, 671119257, 22629263, 759552187, 441248739, 673186107, 502322309, 639411334, 294377048, 466382224, 797832702, 792999817, 21928756, 871631403, 574943727, 752569217, 27763756, 385414901, 221215977, 658670192, 359083932, 284458152, 651314364, 337950098, 1959732, 493319905, 762382013, 993443466, 807876258, 159737645, 832777780, 943182934, 539674093, 195543032, 576616988, 665777144, 353694037, 185351383, 226217393, 32629066, 689302990, 610392767, 671995078, 220690693, 340668510, 532940968, 295013222, 460661735, 901932798, 725808324, 311648644, 639991830, 572676783, 965466028, 945299857, 335577429, 855199297, 351592157, 652596681, 820943285, 677542645, 337518593, 330438818, 785007394, 855383702, 973975399, 731202172, 518425554, 264931475, 381909773, 171697724, 443175623, 10355506, 12374040, 826326445, 219615492, 317643272, 398085327, 159658824, 522392152, 618329690, 426393540, 23595719, 971192932, 375936618, 561113443, 783626738, 96700818, 811348202, 993630165, 653719202, 799996878, 4926884, 391396214, 177815894, 260672925, 253119442, 948586615, 786876910, 30254233, 805170499, 846437698, 215457610, 702074614, 540685448, 869026226, 688577125, 820797147, 519610960, 675343285, 700244457, 767921030, 528673346, 231649006, 94573767, 299260129, 725183541, 971560120, 45569551, 2502401, 697021261, 536123047, 122500645, 932913489, 465558761, 114096422, 166925934, 835501078, 999460926, 355671991, 294006753, 435311603, 411026636, 520268211, 267666682, 414886412, 893073641, 290266270, 542612353, 871605272, 790063245, 465813159, 226399275, 725783501, 905941319, 920252635, 56557092, 779306545, 641510145, 991881337, 55160287, 900162643, 28235289, 760739293, 169083597, 765765243, 533241878, 593794854, 525728445, 308577372, 761344382, 252709958, 715263131, 3347902, 507450603, 146562543, 131409726, 974974042, 434110007, 889161609, 152182294, 34754749, 160370236, 521112939, 899185164, 853725938, 303374749, 462865270, 847724641, 559894380, 527069470, 683377639, 424020835, 575610431, 807343848, 527806121, 16653212, 786254005, 439940338, 940900867, 663850443, 740448188, 278457851, 220157349, 522107518, 454946011, 982564882, 136649200, 666636306, 39917203, 762598526, 775078967, 280272005, 347513627, 763619205, 862014146, 752778850, 1684336, 267291552, 865847427, 399328095, 443090263, 98219691, 358698000, 701064213, 806833552, 826994460, 683445614, 657099370, 160848778, 188535705, 65018303, 342808743, 213041169, 262901963, 742745439, 669568674, 263892406, 475677676, 750898583, 716101341, 496487818, 43906753, 47049343, 113414912, 750354177, 477767093, 608930997, 191330514, 386262780, 16101423, 341930429, 309308536, 868352036, 840844155, 693021143, 619229359, 547474601, 212072266, 661201050, 193321772, 133874466, 495854438, 317848324, 183902649, 238271257, 293907450, 194830802, 797111674, 152237513, 435647292, 543047027, 140789123, 787194019, 499093682, 886295066, 619491283, 998277757, 156257644, 330051898, 136326756, 116077914, 472783421, 406989990, 261013249, 260517064, 846942030, 406323907, 409513456, 295400840, 195773580, 519892671, 262363341, 272850873, 428636223, 923879822, 493507033, 360909538, 952090304, 476959516, 696743407, 784832430, 865360271, 162853377, 370958346, 975950437, 240221613, 843179504, 668065841, 10522536, 436513894, 56421571, 790268896, 236843419, 919960177, 111780701, 618129809, 928763788, 976295598, 326470781, 130306184, 652476997, 791432695, 466747393, 707221501, 438779066, 616567575, 901392988, 108076456, 948058735, 962278436, 563110172, 5984407, 539090101, 295495547, 765154624, 418406859, 369048560, 479200315, 458546289, 179634851, 3908174, 617065733, 770714025, 910352695, 376848649, 869818764, 461578651, 974681480, 481545668, 42385778, 39297414, 15224906, 230465637, 926360496, 315637691, 707941226, 472325626, 936489543, 359251824, 743582829, 809393215, 998435572, 781338107, 442081701, 74179890, 214123713, 893280702, 430028647, 405050310, 418523804, 486742656, 411429601, 646630148, 906196625, 429006548, 708070009, 921824907, 98200770, 638897090, 26372963, 989032566, 861990723, 402933552, 57603215, 94064183, 304065824, 100342740, 667135246, 478750908, 930776768, 139085689, 354359066, 664137106, 48517197, 979661019, 382187431, 714585845, 255230874, 758660620, 374129349, 513075098, 94333862, 149988639, 795632057, 576399874, 41474049, 215898374, 738495585, 810470876, 774324848, 242382509, 322883208, 446467238, 238286392, 724945039, 673397125, 38192806, 936729078, 753900333, 569989552, 462452540, 206564703, 574960837, 27889989, 8161147, 153341572, 790270593, 326418766, 879432399, 473572376, 841308902, 505463994, 426393774, 396429570, 484735840, 474842389, 518829941, 349137060, 362396232, 453277105, 255692242, 827162520, 239958419, 21016308, 933753458, 760954007, 193979673, 685983668, 474211717, 872614465, 633830650, 811170718, 331045903, 532915140, 21249131, 991464658, 338863559, 65750101, 867652935, 994934658, 996016468, 129219095, 135975633, 944159926, 804597201, 603444700, 454570920, 982706217, 255067961, 111708398, 458886214, 470643608, 213881957, 309691170, 448503453, 971013000, 559582790, 739977443, 229785395, 944208611, 185558986, 932347869, 382685895, 747135627, 365998999, 990414993, 659839264, 142904414, 101604853, 553070896, 768990522, 229724698, 534703626, 522069536, 592510731, 621933386, 942230421, 571807565, 837845204, 483728519, 433848010, 601423222, 29477590, 638543341, 611602833, 615373338, 953492908, 632699301, 271827716, 756176658, 166862898, 71706135, 963282807, 966298991, 57391745, 393092896, 179370989, 736840298, 549852956, 84412171, 960574221, 991160708, 71772279, 792727436, 214813697, 603312055, 673324005, 700182746, 505543874, 478936004, 302035006, 710941091, 619913170, 194435129, 616147325, 442280615, 201636411, 917923069, 839570329, 328958723, 622286515, 542743405, 821673140, 435335647, 984805011, 270593978, 608826360, 554818714, 67470116, 553599023, 489855987, 470984931, 601129450, 496997029, 390095345, 747792847, 832707444, 931040000, 982011463, 582966849, 323343151, 125914544, 684671891, 965016617, 691451687, 681449216, 585212190, 447015119, 621882251, 828522303, 505300699, 719809355, 189769475, 654689027, 509083580, 387128388, 913053820, 862666927, 429519125, 650663860, 442379241, 931460003, 433554259, 505307513, 209036295, 442730963, 923287814, 837223609, 962341104, 390440681, 795731435, 191323865, 769498167, 129188461, 110013288, 740160868, 381972260, 494922735, 946276723, 814829903, 246190189, 812495679, 779890155, 529875448, 16839921, 874724958, 940133383, 763656240, 706406150, 799553235, 196819766, 206667963, 244241682, 34483891, 181306087, 551630380, 910667300, 52571418, 844869435, 661666315, 638940700, 4932480, 686504958, 849197477, 981974279, 72986380, 713441429, 83844160, 296573421, 78378693, 540074784, 878910916, 478115186, 382112271, 52380749, 154758807, 98299329, 484731106, 687726279, 153918707, 431614571, 365717699, 667984813, 831510546, 491858204, 140104433, 379461233, 500684374, 468185062, 182396387, 428320942, 171786550, 924202397, 332546977, 882233236, 721795499, 601388116, 728107197, 757861567, 330178200, 36152564, 452826614, 613310735, 419389577, 737739416, 570198427, 64336355, 530275505, 336232031, 972449948, 56408659, 714597773, 904116785, 961892700, 203220211, 567022329, 476343010, 993353899, 716090116, 86286613, 57231634, 18581737, 560537365, 641382941, 963707377, 602057786, 289581171, 826246878, 858128213, 589228118, 186750675, 485066489, 123479873, 787338929, 863539733, 586922061, 72751660, 551795383, 237237107, 210390710, 616545402, 277033247, 52372, 36334119, 149185445, 920398415, 554963834, 986067870, 887658345, 982757103, 472029583, 493018777, 123384345, 521621681, 449112702, 294669915, 555227230, 858265425, 562990175, 805725712, 189497886, 353222773, 684191149, 26796364, 543669962, 631348666, 3381929, 992446322, 160859046, 354306210, 954682972, 260833587, 807504026, 694656038, 325156837, 816324296, 384951966, 629617263, 179722587, 999904721, 950245282, 749391162, 83853909, 994575268, 914230060, 642539884, 475822477, 727192061, 625545457, 775563755, 846453127, 275807202, 537421695, 273083042, 772085495, 320487534, 655424262, 129232513, 693390673, 92964953, 87090877, 36939791, 164693038, 720528863, 562541416, 742196070, 491216518, 594741970, 508620546, 273658873, 80137135, 511655785, 4995091, 178950435, 973938056, 328324976, 522558010, 754683729, 292572525, 463556272, 239783738, 237621223, 318280450, 899127503, 975000323, 926284504, 212855485, 521027666, 885694636, 929823933, 522244003, 40684199, 847340254, 486905657, 95023956, 172062441, 130078820, 712500713, 299822626, 717726978, 98484566, 744883230, 716111199, 337723881, 523972798, 578775248, 1597144, 210443688, 108852931, 564769780, 601867433, 393096130, 368183157, 354001535, 353682220, 767453423, 411635261, 746274653, 920235300, 948974727, 977330397, 567793998, 694452886, 57413681, 934536704, 397546874, 410497373, 53918754, 571429366, 265229137, 434417664, 935423024, 166752271, 633785324, 136570318, 132788000, 230300718, 589922221, 294431226, 964366087, 864130187, 881535535, 955500824, 304188693, 51176596, 284637710, 659509324, 116112856, 206163066, 805791794, 65995217, 167479626, 554138215, 59883013, 162475669, 490909862, 646304539, 638804879, 215940382, 522689502, 672525415, 983454003, 851047394, 462904171, 630892814, 568935819, 89410426, 564897524, 722668850, 841363997, 371826990, 376716148, 381516644, 626231075, 322999434, 155101643, 513528772, 469575597, 881826693, 558878196, 590112754, 255456518, 269304212, 748521590, 482153794, 410809658, 871697759, 514519248, 227174429, 781429263, 782524085, 754491700, 992894345, 956007642, 499980318, 190899212, 886982348, 921476885, 722625207, 89848503, 364590651, 220412261, 979924735, 359329713, 606284088, 847167629, 741534872, 893818412, 500506997, 19416473, 622145294, 609360915, 231548514, 514162165, 852550167, 244172022, 222248927, 676173697, 523266945, 453421735, 415586905, 117568847, 199270961, 355024038, 202032688, 820588507, 673831638, 461370923, 651411203, 801114677, 124344073, 671935136, 696436840, 974137076, 799140524, 940144797, 982131090, 42176827, 702923284, 124921319, 556219602, 22272816, 900707566, 845231149, 789328742, 333517041, 708538003, 713647609, 472119871, 833208754, 36960040, 869020642, 81752445, 266826183, 734520529, 486831259, 765109456, 470781672, 607573141, 455667832, 511203114, 7643564, 537688416, 731338514, 757362259, 759305800, 452370805, 518899200, 115994842, 838444098, 819332456, 914885924, 192605599, 398715083, 663229117, 146715965, 745794681, 308328527, 36673313, 335244055, 537792830, 667933814, 656958913, 245782220, 618759170, 517046389, 191429017, 408818809, 275202030, 849998127, 779219376, 953431422, 412505244, 731764404, 603415610, 554819106, 681612417, 980617522, 874834060, 93987253, 862254182, 967942554, 835131257, 520004233, 899310686, 451148098, 194528507, 940495499, 351876296, 896109816, 164300701, 203654679, 71823622, 337160155, 160697260, 280728811, 348119070, 304058823, 856774931, 397715841, 865101722, 454356569, 914052064, 10521721, 843252345, 635207216, 34420875, 728612202, 738841572, 445306470, 466082335, 462891000, 968206033, 817941999, 336494308, 123056524, 573333816, 772863633, 920129598, 231521457, 245020672, 185756104, 49217938, 646632800, 892354980, 824759101, 58992073, 932992433, 726059196, 361425480, 247344116, 663375098, 786904715, 851115496, 59472912, 554962776, 178592761, 724735160, 21677027, 929867807, 836656660, 401049430, 573124341, 213027232, 138264573, 928756913, 872934669, 427948280, 881825440, 483700164, 571658923, 107699782, 564357851, 91711947, 497152135, 94019064, 205412784, 556554358, 467468975, 346297687, 987990888, 384206643, 119006040, 750694383, 161889846, 821353823, 853527854, 931814930, 934128395, 908514647, 111744938, 423886321, 651227891, 809688438, 896307873, 281991282, 988441058, 837248737, 330100442, 311069840, 801824373, 426037921, 201366060, 54919586, 794987053, 420977058, 73764889, 745876601, 492862362, 777077576, 466078696, 963006392, 433846588, 436672270, 920809349, 596441285, 759545589, 474264137, 722660150, 964706064, 238020496, 943577292, 578357366, 357536265, 547984513, 103964612, 386573117, 121795286, 925180995, 61856776, 463121482, 832258013, 914503277, 168492142, 349897799, 114231103, 484006183, 691813807, 246725511, 201448005, 561524167, 684727874, 962258647, 973797074, 68664010, 782073530, 894868580, 460509583, 251748881, 680723301, 822343964, 273361502, 120147315, 228505661, 491114122, 722903448, 567476953, 291197804, 85664723, 395925554, 552744468, 410787829, 127722909, 709320142, 35342488, 962549599, 677381800, 503598883, 648857148, 997116035, 207737926, 685861792, 103246585, 931459038, 16508052, 474752371, 481694802, 733586780, 38738497, 495216949, 645782151, 347896775, 704497252, 676999175, 867810818, 709415456, 568154763, 792436238, 377785649, 721302972, 411682511, 203669818, 603579305, 942989006, 390774971, 866534565, 692239728, 275562833, 654135116, 467646988, 508387789, 595150428, 6717741, 406142309, 700218558, 994881519, 200739069, 286243109, 702922351, 932638563, 350404669, 849706748, 40964219, 804920371, 957495717, 592912517, 478038928, 930935968, 810024566, 348432680, 938505915, 537568905, 703982629, 501164820, 875910379, 189631352, 143755722, 145613947, 210705321, 955069280, 993319595, 955041406, 355830735, 869195531, 282890978, 736535819, 594804841, 51118775, 354962213, 746415353, 864813754, 463949108, 575009241, 435929100, 755809452, 165813149, 630948151, 173442526, 693378227, 298528849, 811853090, 326830502, 568592075, 289962644, 821597053, 426042624, 844334547, 23627649, 8568632, 190854189, 294140509, 291476816, 505873502, 862721931, 726810605, 741706229, 644245409, 397356023, 876692370, 734789903, 956650202, 142414602, 80962840, 75225129, 8817020, 531903301, 569593032, 993348139, 720893345, 708099410, 677652104, 718965463, 436576991, 686414389, 559737017, 644384958, 890977897, 61287336, 720696195, 574995904, 950169395, 980930363, 247881889, 95460391, 9537508, 607986788, 290564060, 179144592, 619599185, 954196873, 908840251, 821716834, 652866828, 156856085, 212884474, 143274060, 603774239, 483574395, 860488813, 217080263, 960621586, 309308600, 114537183, 419974033, 238003051, 662369758, 130668199, 369604090, 147423530, 175216907, 269982473, 863198936, 927227159, 66164539, 116767888, 482086438, 819383160, 549475358, 51918270, 545852751, 332275793, 872169574, 874808862, 507313213, 636729519, 434827974, 616952185, 234622082, 783948814, 668910239, 446915980, 334645660, 936233786, 96639685, 390751454, 33642431, 670591962, 463095012, 686888523, 487257308, 29377677, 23498305, 769987225, 542883170, 652140418, 311426147, 221877000, 373315365, 79017039, 224854482, 408064680, 961422135, 371705464, 848271167, 30509273, 252103197, 28902527, 91801513, 630885496, 690287521, 723390696, 331987565, 895572458, 891771705, 494970437, 814605162, 444596371, 725522198, 729189469, 980350082, 664183777, 850710910, 753645403, 559860074, 50694555, 857434417, 413349590, 788372423, 641772991, 669497017, 170684775, 107129765, 560767609, 831535853, 38233125, 999934046, 421164110, 78269978, 644854203, 547084946, 286540202, 387103504, 413693270, 780656623, 756319245, 121687163, 590770932, 864652166, 624994000, 985124406, 288557318, 486256620, 230629090, 906666065, 998401699, 161044110, 912366551, 769416793, 531797673, 682731947, 238589289, 172354304, 552846929, 908600525, 619991471, 610573548, 786901745, 802990332, 533360265, 438518209, 962292127, 346106880, 549742946, 503181947, 651370767, 146207237, 826743736, 889787255, 637415802, 411966819, 458186580, 260619311, 986209117, 892666295, 507261924, 949365685, 175211889, 909263504, 211585979, 834110344, 636809221, 515693857, 596141303, 9945645, 481051819, 662546637, 229857019, 279013828, 979336081, 541953633, 592188197, 266834956, 802436353, 135643302, 723359758, 696304354, 751895913, 735100717, 134398979, 134143437, 67881374, 790180758, 311746574, 830283204, 792115306, 77933473, 989560701, 504818678, 590365845, 405905227, 655299811, 265261449, 648440603, 756862479, 586181408, 256763772, 479562995, 731368649, 450046585, 400691028, 469163208, 739823243, 178614524, 900024459, 209033451, 271225085, 696246238, 220014075, 117178214, 159078650, 559662512, 873106247, 589678500, 439036354, 917288689, 852784701, 176964224, 584882172, 872782467, 194834249, 484728114, 312410675, 394772513, 81696210, 371954683, 519216462, 47147089, 714397124, 957436437, 328621561, 189824155, 291374482, 951332298, 498982429, 447115066, 444453587, 799046472, 269052546, 344495818, 16766120, 444381982, 182220433, 992647651, 169712483, 377453840, 444935579, 904440819, 310397777, 945951428, 445741445, 570891093, 457877879, 522023787, 235072294, 805223054, 362461597, 808525166, 629952668, 965720905, 529022912, 876433178, 893678749, 457011492, 457786579, 236278676, 505314366, 638974369, 647436813, 521632722, 956932033, 593965083, 255329091, 983814990, 856532637, 306449408, 61825492, 816744894, 890634758, 506887070, 124915754, 77035817, 273824512, 500084823, 195334288, 760678696, 415797250, 721559245, 155793281, 494828746, 511810670, 582863776, 118044952, 869173244, 967632209, 994888484, 522824884, 758364978, 387756336, 907794016, 965781678, 757185871, 780197077, 557035081, 723186340, 578839390, 470128074, 692836331, 411860014, 342894232, 765111822, 190880184, 969714815, 477503648, 390048920, 702524091, 59459602, 150481441, 388825251, 412012734, 876886347, 854649090, 766083792, 306082934, 146862372, 972845600, 391473734, 188865414, 203725975, 890627365, 589649452, 863165224, 274920400, 371281017, 985642554, 179683712, 755770222, 702755839, 429272086, 410312704, 704522201, 708808823, 897378891, 751984367, 9310059, 562357498, 302595489, 132249771, 310253253, 400817274, 139117874, 657485837, 118470732, 502913173, 895390869, 722370256, 568221463, 378732951, 166471559, 535255828, 687697950, 585944717, 355184818, 272162645, 145057442, 501822020, 131731222, 535797464, 931721670, 324466153, 147544451, 909057512, 449584002, 182584904, 775191296, 443296615, 172255116, 361232282, 223761260, 949200845, 717313047, 955688380, 310038443, 283970267, 955102493, 909145854, 560722480, 999906780, 755820425, 242951907, 193956578, 657605934, 654100700, 904706732, 609534658, 52170118, 704073260, 755164711, 629366326, 623877187, 467081528, 607788360, 484673868, 806191168, 619449044, 800565874, 248885379, 997834004, 838151331, 281879707, 994057894, 861953811, 734866164, 124705419, 282093740, 468070520, 486906040, 394360457, 6498814, 700309678, 800127144, 618179029, 64202518, 522542104, 894217916, 749525901, 553671872, 388753381, 862448329, 659553372, 221558538, 976680280, 67348139, 413960341, 150885329, 70761859, 530571090, 897900398, 253701792, 755575694, 712642405, 665465126, 746030419, 809008710, 23488576, 208194279, 708683886, 955288672, 646536139, 921212952, 821971244, 827939037, 689147353, 743719035, 642268033, 23374295, 353555640, 828990255, 627564018, 853301490, 939380861, 81511036, 441282888, 972573187, 423842730, 124617816, 610878564, 18318783, 942254573, 656865431, 324602010, 65663118, 442571930, 560173181, 136309853, 909855393, 798384052, 481093481, 647820081, 609554764, 498113738, 248899859, 298416881, 578998203, 699898421, 702376808, 430825502, 624555369, 556442689, 348555566, 252507901, 122507197, 519769049, 658969012, 611607283, 373251612, 308618976, 303276108, 91283883, 389703308, 825327801, 312694018, 53334675, 817349222, 463233568, 640855670, 511238535, 944906378, 245722939, 67876587, 160153872, 840940305, 549476283, 793631574, 952943437, 386447622, 589431763, 653805911, 757391119, 68521486, 563121433, 521356422, 234106467, 434492489, 717331273, 151865675, 315661950, 413917202, 783121411, 158197655, 492878659, 775173557, 293055181, 782536290, 912967075, 957136266, 239757009, 97873962, 419667518, 857573531, 925158485, 416648722, 452091563, 77470414, 633860348, 735275134, 446138081, 462721194, 953154410, 300067035, 881070941, 688246712, 317042611, 992936333, 928155092, 359045324, 225463012, 147029688, 432470480, 776597414, 416937462, 35072253, 79704014, 714237033, 240893441, 696414359, 576258824, 129939007, 869847191, 683681161, 352254813, 818772836, 983210170, 969461269, 724213586, 91153104, 572417235, 491549365, 2649348, 801275167, 247361925, 300035627, 882638329, 422623770, 758191512, 198650905, 633612620, 530496891, 662343089, 327966669, 293553859, 21636109, 699644720, 826932211, 484766414, 407270582, 632622070, 198024651, 724365108, 933894558, 389957526, 771990149, 378162901, 349668871, 725831522, 371412054, 299674316, 526981149, 57354205, 132779562, 652553077, 281488935, 619227715, 907175165, 340647767, 885158365, 442711822, 517081275, 687553926, 118568595, 949879044, 423962702, 817500825, 524207138, 605253082, 451103824, 851889998, 912003909, 197803803, 428662143, 7424720, 308182645, 937064444, 843237657, 743250998, 726979782, 755052366, 936302447, 563602811, 728509924, 904055754, 246016155, 452385953, 77654712, 356920200, 446933462, 432221447, 675700108, 865999945, 792902737, 316575620, 284666805, 717103413, 529201508, 613185039, 999260991, 237007420, 218907453, 776228954, 712002937, 755606154, 163413668, 632885732, 324070622, 421903564, 502519782, 501037889, 596153905, 812561279, 412698403, 872812591, 671649400, 587718536, 558095245, 543776566, 985074562, 887719783, 41003341, 248658371, 897001227, 855609065, 696326632, 542835606, 833429457, 875374403, 592474823, 927396340, 5039137, 909939439, 292609367, 557650794, 282531164, 629443968, 354635653, 784390338, 794625299, 575381818, 418674785, 330628219, 839953856, 573042508, 881048538, 667491698, 70326896, 770412071, 596219256, 923477221, 808874937, 179556608, 936300737, 261569472, 472599309, 663435877, 884188890, 369184333, 919361199, 275435506, 431227565, 6227046, 250665507, 180747915, 218123647, 832340540, 371006061, 263258915, 551054179, 604021601, 377640860, 934009784, 283446342, 123435556, 1485622, 778302296, 847540817, 744334204, 570787630, 267893868, 188147137, 977918690, 119184610, 221313908, 585941247, 576123842, 570208076, 453075168, 147030769, 976439467, 776674111, 826663381, 224083185, 989631270, 998259887, 371167963, 333417563, 396801209, 880054233, 671665805, 64248307, 516717748, 370127910, 443989069, 51461345, 84056828, 575897512, 212667635, 959035001, 57765931, 918475647, 203644008, 650476285, 96402566, 732567446, 950962937, 177095213, 304629385, 763497523, 611995276, 812892376, 848428601, 157912110, 162885517, 940085888, 958764548, 555861998, 406276017, 932414273, 384883000, 681680566, 681679047, 377171827, 963588858, 72068991, 579492081, 795923651, 259683184, 860924255, 17406738, 974427488, 394140981, 66829794, 931134103, 585780667, 750866678, 382393677, 680619255, 339246647, 787148196, 223565946, 795224702, 261487525, 230796472, 805172557, 117705196, 452493228, 85139119, 911053873, 951277084, 337025348, 611897232, 503413607, 634902911, 348934302, 9843156, 491165788, 249900458, 311396398, 480398154, 502516379, 105347896, 341391409, 895565697, 607344852, 223342720, 457865234, 839697057, 294650689, 996061294, 755759006, 806309269, 116462842, 695379414, 804448069, 124079783, 5203439, 88828240, 277583164, 784815509, 869065483, 880605902, 848499073, 964535352, 900604012, 229411074, 272732272, 779760484, 381820159, 173538808, 212670897, 166688991, 214440693, 227310810, 937374534, 810841582, 874019598, 486549876, 605615741, 219088534, 25604190, 918016676, 702532829, 54674786, 496978302, 310008493, 22847159, 363088246, 361321094, 365986934, 789599193, 979377552, 138275259, 580592532, 951712827, 491011636, 64685198, 788457056, 530856867, 500268290, 300627674, 201113216, 241572793, 62029995, 403257984, 49249539, 85864466, 898541462, 177428377, 38952714, 291461376, 147046954, 692802847, 973305733, 959748533, 234786054, 470089625, 642429315, 607016744, 736749164, 776027434, 537409137, 907808292, 696152478, 332007085, 910423207, 836363539, 781353044, 128358451, 605098497, 615030706, 162235805, 964769341, 92535642, 563184424, 738758910, 908469977, 997742997, 662234519, 215426377, 317546918, 342863796, 898656171, 466004748, 664759242, 787357669, 518103177, 414406541, 718896730, 730935245, 56027651, 746036328, 853359051, 537976203, 824650709, 785058033, 440593997, 938797240, 263540878, 118647156, 160290731, 66776047, 112285208, 336381960, 536503496, 15024056, 946774113, 906326863, 448143645, 269110542, 718416879, 774585402, 393750160, 348381608, 789430233, 600103446, 207134537, 139455660, 514190211, 636807671, 1911261, 162119020, 503593377, 655356448, 33866659, 867866455, 470380193, 141578173, 828101608, 277938027, 31282755, 445400622, 222830668, 660265297, 115392575, 447970662, 143153424, 615557131, 649675019, 81146907, 393178409, 122589267, 397624486, 325511149, 156312368, 437132964, 298781775, 776321216, 158032455, 755783846, 856309382, 702628223, 492224160, 444339261, 582603875, 170189380, 442541738, 780670937, 248911381, 772069571, 592175094, 905833754, 153192990, 233039297, 395216292, 773946304, 277562685, 347196751, 534479657, 671504266, 753124811, 490618571, 411271047, 281676501, 6628648, 202619319, 214798547, 989755918, 77183623, 550428840, 150351669, 31918723, 382641787, 51316770, 40856505, 545022142, 355668262, 689843095, 662543643, 419407191, 999740460, 593440391, 377901905, 838463647, 767216955, 201409024, 727522662, 36700076, 880431459, 210370169, 928060601, 217010987, 834388935, 354847559, 406410417, 371365086, 186655585, 889134210, 308455888, 179200033, 431372027, 740517073, 48541502, 845628614, 862594505, 190657200, 88645452, 300271497, 481111423, 418972976, 105496848, 230089274, 7914655, 742460471, 467126588, 616514661, 18333226, 970729732, 629542836, 109804086, 705827966, 274014563, 636462348, 888501030, 77984588, 513772713, 468816660, 702785477, 686027535, 225735057, 443956612, 900890403, 370467755, 324223111, 770280596, 51016651, 900142242, 654831669, 525289876, 792409339, 110444317, 145699947, 861700882, 984425598, 89327229, 642435842, 339580785, 659831288, 316848165, 153361819, 369039155, 511474442, 763047295, 7191009, 268366765, 634607094, 211975055, 308153767, 972541568, 977253471, 390836395, 701471031, 94854735, 945889561, 557001987, 210598562, 198172211, 325784409, 744204962, 744491804, 48289820, 37319157, 969839478, 887372892, 871012035, 136826292, 915064569, 28482687, 274898902, 139326842, 777439808, 720239356, 617143649, 956912822, 931092189, 929496936, 716219887, 197681253, 528664937, 870420380, 190693507, 985815912, 931402941, 414570254, 411553406, 261281867, 908987001, 723204844, 950670317, 497532540, 515792449, 324415430, 28312247, 651201075, 262434915, 587911717, 105067571, 611834580, 489068579, 971391968, 281004626, 244827348, 566005414, 871320016, 646320163, 534217746, 5152078, 270517131, 285562333, 495329600, 145909323, 654953994, 958418469, 574000593, 128018361, 999664323, 66816683, 538723846, 265857331, 343275845, 535887975, 430453080, 502128595, 635240710, 454628748, 63082148, 864262906, 362245505, 655185845, 317612145, 964781139, 645718935, 698157766, 244063120, 46792669, 976422957, 852778619, 567728632, 888226772, 173175386, 982390090, 8893328, 9565006, 411000704, 764603803, 483666244, 540456936, 299681430, 721290503, 509125010, 986035296, 67072665, 712321409, 13235891, 278706788, 456305331, 860340077, 543657285, 959343352, 180752898, 534558276, 994101614, 744028107, 61197197, 728119048, 511675387, 889587799, 507934519, 267774377, 238438340, 549121551, 556990208, 616432782, 65772176, 283712581, 796799381, 134454780, 805738205, 71424319, 864907615, 47920034, 552708009, 438774933, 469120005, 51409143, 139720418, 277456002, 816582155, 370559457, 422849074, 610101340, 115288384, 534421651, 706206514, 136324977, 122392082, 479944705, 110882506, 369888726, 774744810, 556559967, 73752532, 499705531, 257951015, 930087079, 908016085, 70665683, 423182730, 461140905, 738154451, 234845527, 463701982, 65808425, 286800720, 962198510, 129964085, 739988060, 89016581, 107443669, 882407316, 963089478, 364664341, 16934994, 674323703, 172638692, 255646533, 558629186, 107295606, 714732347, 241495043, 860986568, 746557333, 620634466, 488996736, 878324412, 430782928, 285728599, 563659169, 485907984, 351170227, 774507834, 254633272, 72355808, 615004546, 671212737, 585418035, 235326870, 40980770, 623120127, 650110982, 618653647, 753421597, 628087231, 54681196, 695741476, 526367515, 356671612, 196624805, 422053045, 641230449, 661079102, 867551765, 241312098, 380156376, 135108049, 463049118, 775230383, 299700657, 404436966, 221210329, 317129295, 89537561, 113927269, 691316531, 339430800, 651041199, 200669705, 58423631, 953699822, 843298657, 826363929, 482010596, 536038149, 371057060, 656254738, 886462479, 943758345, 893461361, 917883163, 107074123, 691944603, 910177994, 968218317, 645261786, 639091660, 862516014, 562665526, 48412331, 972698314, 662904258, 176996705, 212700220, 689143066, 755562762, 835132536, 211111, 404729052, 807960733, 441926524, 380544516, 286116224, 401322841, 548250967, 848791526, 563892167, 440489546, 398157942, 748825980, 749242254, 362879273, 635440881, 223392982, 353416613, 644672753, 299053195, 504300756, 59948224, 341777053, 415485051, 513530401, 63653559, 108307703, 40634771, 352449559, 431347938, 646548809, 436204950, 978784128, 875667271, 274320348, 840629683, 529939482, 841633664, 989981473, 422903383, 378525723, 245622651, 483203724, 699571685, 238835984, 630304953, 112299510, 705577780, 933950591, 241903693, 254738981, 386319820, 970266075, 449613172, 508235971, 895580334, 656792514, 973208058, 604525281, 822927920, 821326695, 824099214, 249219483, 410444159, 838297290, 648866438, 40610413, 951080059, 495575689, 271077889, 282753751, 612001695, 213921963, 649095818, 959752867, 148875401, 808983735, 274304, 971599179, 358497043, 541383640, 195360700, 482426786, 722150175, 541389115, 462807219, 125169286, 750784430, 343388161, 100968814, 114998463, 500989846, 812328596, 300710012, 347881112, 866742278, 947548841, 511724487, 279538152, 638760781, 87407192, 820451963, 400114027, 799310563, 269475249, 395695074, 897861248, 478034758, 262035978, 485987554, 87350601, 343163642, 600004307, 906815576, 399075480, 573958687, 195900567, 511294238, 28565700, 296227502, 726116268, 608216745, 469439097, 932276966, 111586631, 219174390, 931855554, 215664761, 890775409, 437584519, 538533813, 213416944, 201514558, 664159635, 987054439, 994726725, 885368763, 424231635, 479103249, 874766678, 811168019, 814503369, 645188050, 920630464, 804178658, 285502242, 900623804, 885289026, 774406084, 501100946, 424198741, 483502352, 282432760, 399611470, 192900063, 634351380, 741586457, 98372478, 667144699, 743984645, 641176533, 179723724, 676262681, 519466589, 269342599, 270491996, 462921464, 835474785, 842285866, 984303717, 968058266, 333182147, 297573802, 366196653, 87806274, 509639699, 495320768, 609026773, 605130957, 129419367, 857657416, 570810415, 760870835, 14297663, 107295730, 512846629, 30327688, 679887134, 592482241, 11054510, 279544877, 281332569, 939542783, 268436753, 408161107, 869078969, 883933099, 874293108, 17126557, 538561332, 80263398, 225261616, 272605079, 960195580, 880755194, 104628675, 386802270, 243850116, 128975170, 201121625, 282867975, 303384094, 989340586, 681042771, 232714079, 152717266, 776685129, 351746483, 168680408, 374363770, 333376315, 654757395, 779326381, 421052333, 610863274, 786290449, 260382601, 295000321, 865450552, 729520644, 99207382, 466372981, 59332097, 499386058, 218398684, 29598424, 316112185, 227890354, 637951305, 726829229, 708236635, 183925476, 878221470, 868279148, 907678240, 671725487, 415546179, 63890999, 931246772, 395587397, 145555626, 726670341, 866485260, 325623117, 250469822, 638262399, 604915506, 960134837, 406694216, 530436824, 844298164, 62754913, 78346005, 594420199, 438327689, 446002364, 34680891, 805617781, 919743894, 95833470, 263218644, 144222281, 813016906, 956686688, 373687724, 198997990, 165494871, 233087651, 502526010, 413242462, 31925994, 617365826, 242745282, 255383483, 806911894, 587585443, 260304535, 758950962, 568306274, 686350140, 200631833, 48370822, 553395499, 673953190, 895484202, 717455208, 825712566, 266208942, 12261084, 867259699, 956417303, 458051549, 722132841, 179448602, 430553336, 633573903, 914351512, 435431617, 255628967, 522013125, 315888467, 687546106, 717725174, 400936028, 449415673, 393014841, 92073629, 217317526, 43032580, 543399709, 517242351, 666176010, 226274876, 490036182, 749701325, 103175452, 300539410, 472926183, 340315226, 893716040, 454551636, 133960178, 931390802, 885785252, 375500336, 896746705, 698872093, 881438621, 631827514, 540902670, 94314311, 433774271, 414626372, 737219956, 311149786, 797563381, 13299637, 232093856, 132147615, 331210320, 764036728, 799465249, 384709343, 736403993, 954441245, 84382108, 458532041, 795361976, 155994389, 560606445, 918597064, 204684408, 697738121, 562777047, 719485857, 537967021, 89854082, 787733091, 86270317, 286792880, 548488138, 858431363, 372391274, 848465737, 718141096, 898892898, 641066805, 43087249, 255723937, 242301068, 807950580, 321077483, 186015636, 837242986, 476031725, 147078937, 618017237, 187533054, 788196654, 826324706, 23610814, 931012344, 69702462, 163408355, 758218403, 203963597, 977032547, 314370072, 691664703, 400346732, 293174375, 803853540, 745325277, 773625841, 549600335, 431642404, 24066700, 804541390, 87149637, 704951348, 315073111, 294448094, 375292990, 712829421, 628318136, 887725621, 326121651, 551258801, 340858231, 783891133, 240936346, 509471533, 488735007, 627859048, 362948765, 64612001, 781760828, 522072953, 656453435, 487904809, 731052633, 59542600, 310643035, 705427766, 93483358, 246514650, 559518884, 191479272, 587758565, 616185739, 124357169, 109590798, 848854655, 954199772, 64255882, 451460183, 864156064, 621178768, 968138733, 126245, 340291370, 585800158, 792806851, 608347810, 461652775, 944084114, 520916650, 151405503, 876928770, 893195229, 109609233, 777851994, 54525489, 286804899, 958916030, 880039434, 573492758, 218829363, 231559921, 648301553, 269717420, 224053070, 113624950, 934713298, 830231752, 182816570, 338841334, 767309139, 947086496, 481758377, 871973111, 163491216, 105458298, 738625769, 624961337, 360634020, 729505625, 519587758, 269397238, 591658573, 411600935, 54461557, 844492716, 798606353, 727038606, 645249024, 348771306, 473557094, 366335343, 426025406, 453017474, 934094114, 29779683, 652712020, 728377716, 545583986, 274428253, 676001777, 808757673, 795364042, 627323465, 63419072, 368176850, 198560620, 235539412, 205137998, 967999465, 752008245, 635881783, 902136972, 546370110, 218982854, 445711900, 284926116, 882654801, 555001348, 605505782, 246699373, 57548557, 324967805, 900013916, 502970527, 168395021, 854332894, 847991532, 555094756, 785736226, 349850094, 174498312, 273090414, 38520597, 43088254, 168092988, 617267862, 826009908, 804501676, 276845606, 331600330, 723298448, 555042484, 735043829, 533337921, 212944710, 433197755, 922380749, 838072693, 156745693, 438272963, 98576509, 775792195, 243389019, 98758786, 964629476, 816733743, 677547177, 622704282, 77883331, 715057331, 769835567, 343114167, 278227996, 376967457, 833112310, 546013037, 364551042, 136394724, 133364717, 896437505, 618494877, 701686643, 766342052, 800522021, 636363803, 228949786, 228809553, 933236851, 591356177, 796872069, 221669564, 810542932, 265161796, 321843366, 269965312, 925226988, 162584271, 956314771, 88478137, 932188201, 304920886, 783192614, 113895293, 968620411, 969853412, 371964317, 549313656, 796627232, 436939724, 113075369, 771139008, 609256093, 227834203, 203187331, 444820316, 187663270, 427093443, 591443086, 646496583, 929776406, 488443851, 469633794, 425340184, 572538930, 832210515, 378342949, 122478403, 56541122, 4876847, 452183304, 876273486, 461610294, 651107129, 820406766, 285444934, 985500793, 676245966, 796455134, 500461194, 56505600, 847250601, 90484637, 910732892, 14229511, 319350233, 219528916, 128749094, 326812681, 190613927, 276282592, 813152964, 148205484, 65060232, 743257844, 317974916, 75449523, 946752887, 452156040, 905082453, 317011202, 387212563, 149559753, 299894490, 48446374, 121006739, 328793071, 882689386, 957956132, 422555640, 21608287, 567355339, 252711962, 207957603, 11087362, 657668795, 783459992, 211738767, 170716860, 67533085, 97086664, 916660542, 860963478, 547361650, 374241906, 710130414, 535229151, 834050768, 647684946, 466027194, 48944548, 880267632, 874263620, 265548520, 325763081, 397814958, 172796002, 910292108, 236395178, 134214101, 397612234, 882603016, 675814607, 450739022, 494550945, 562426907, 600630977, 42889628, 203767052, 777834626, 526644292, 124624278, 151797274, 891872690, 989859172, 826944546, 541753668, 839513489, 870618705, 79051467, 516009201, 953997915, 863002231, 522399768, 839070994, 495721937, 129072746, 467749435, 225506802, 373654374, 646088692, 894228400, 764633768, 597204673, 386254053, 568175022, 520292906, 301029407, 151801010, 1561607, 626861368, 53908364, 871648105, 947321965, 753468564, 28930690, 595388435, 86681642, 510874924, 15697154, 423822028, 657183617, 694016963, 111423420, 153050170, 990725978, 804427149, 212103527, 723990750, 259754513, 270481778, 249165297, 829726249, 153634440, 868322785, 762837134, 161550575, 410550480, 377290292, 279035921, 159844083, 391937796, 699576404, 992934577, 272261052, 818752372, 259590701, 662365068, 483673339, 400505713, 920150361, 143617582, 684505848, 40704400, 851640647, 820322367, 625040093, 435707358, 349903374, 837033128, 452496320, 1283555, 984169037, 486532592, 21186104, 261764762, 170292672, 636955257, 608668303, 360044799, 925966894, 978803571, 527575950, 626932873, 916737876, 571524154, 97619036, 382162945, 883540084, 113834097, 22304474, 496129972, 199412194, 773232957, 559086782, 84605511, 293788243, 75860441, 615216032, 844084953, 58633873, 397586228, 806490469, 711443937, 491444434, 322613805, 63117089, 573888470, 898521103, 386353514, 747016110, 912114135, 528982948, 435395631, 325046418, 124765914, 756864023, 884173976, 181848217, 481245285, 510780226, 898038648, 56940552, 28237126, 490611308, 973445301, 581490240, 468099922, 852606556, 228209547, 195152765, 599926945, 958883797, 989908407, 674693428, 528973814, 685478067, 652434243, 349333661, 535875081, 98701827, 435666712, 343502835, 488047029, 545013415, 581645718, 739032049, 250697916, 699738929, 810891097, 991310971, 490187769, 445733522, 635266406, 463641855, 978470935, 849702038, 865214664, 355670309, 203768019, 90664528, 132530279, 522523636, 921733277, 600563728, 793491162, 432021111, 171819675, 389468319, 737134208, 550143314, 155942810, 717610770, 37422305, 820409743, 559426002, 302351433, 839421931, 565396828, 321532672, 770335821, 320852992, 998449509, 742936196, 837503326, 146546661, 619217303, 15036923, 665414222, 425948304, 207889307, 52849436, 969370817, 579325295, 149155930, 572462381, 613133048, 350363912, 576849624, 808149756, 584914442, 874043713, 860375824, 434228644, 697261661, 309135734, 677258866, 331133774, 878444598, 107916751, 767167464, 746183729, 76948381, 894196044, 666708410, 955554632, 73211675, 677153670, 211264462, 31791452, 530536328, 141661888, 740519336, 262282133, 217429323, 132651477, 955293374, 176237409, 436932230, 494434538, 348298904, 408694196, 372225931, 375637713, 779083763, 167500022, 531094605, 463442155, 95039702, 961630986, 419799350, 806741590, 573296780, 963971807, 94178750, 570893005, 149881193, 958277182, 71324381, 300449193, 874263985, 38096275, 862933875, 116024328, 40925077, 771701548, 279968840, 630056839, 989592178, 899833631, 89675713, 986009452, 908804400, 650158547, 247893797, 387713526, 143326216, 419136708, 993260719, 148022152, 204141663, 28405512, 723211988, 943772282, 732353564, 457919265, 84640774, 934017736, 927264843, 94985916, 383625730, 347833336, 797312269, 567027160, 32219969, 881300181, 964378374, 113027499, 654487224, 237465182, 625149796, 204331132, 251149569, 770096010, 500449648, 971172793, 519638367, 730298508, 998269668, 551962890, 305419098, 821174046, 396211433, 253764976, 160235620, 627819375, 443486511, 804950123, 668029589, 629771256, 683633746, 602323124, 255026858, 481374479, 307760751, 635846005, 451605393, 553863688, 643077347, 661766220, 470228334, 81186964, 519211082, 280167509, 894352394, 88379166, 227438677, 556226391, 983174332, 825774325, 925785180, 300485144, 834962221, 576756785, 356226621, 415634752, 396323699, 399875791, 788938166, 546300544, 207114315, 803837981, 353371850, 424112239, 125285737, 513288674, 763674860, 662819446, 114145586, 542617906, 637782193, 112942055, 636710686, 731407343, 887654319, 791876422, 648709341, 100352851, 434734515, 429466432, 120265886, 283217886, 892257565, 394763054, 876007848, 69658120, 507466381, 298257485, 933627402, 954018128, 623257528, 892099080, 434056707, 524710991, 590816432, 694025972, 46811110, 233867862, 945483907, 404438207, 845880060, 588163653, 591018920, 767601282, 113656897, 359443344, 773571944, 28988770, 412198878, 339950317, 230497548, 475338215, 509816392, 970975794, 561267717, 178355449, 627109249, 475845454, 954669105, 902229483, 519823240, 332802200, 173624378, 958448500, 673682095, 71803230, 202561649, 353343211, 922574253, 938771142, 189459761, 902456718, 212652544, 123182097, 174623147, 675466957, 718469111, 841598739, 249513174, 481910855, 634785271, 536413948, 882591747, 906029965, 596327303, 531470806, 897830105, 273866612, 607334052, 401490654, 175020586, 674756865, 284647924, 589070943, 906488452, 234796598, 941005458, 499143840, 28621379, 366469637, 62191812, 842703150, 134711032, 682989448, 456688161, 139348148, 36625778, 939279744, 197703053, 224830783, 863238179, 608539404, 83278846, 364784386, 923732412, 351624203, 913392072, 421292625, 24095421, 737027606, 558078368, 327470324, 794862248, 423353244, 919612963, 485135736, 79158077, 891643992, 282862757, 819386469, 162132883, 177649411, 353718305, 277847615, 872768158, 273066715, 457882641, 230231064, 618068587, 430100641, 358244605, 830233538, 473104163, 360834630, 237258161, 494012110, 222931, 910278723, 309105056, 133124623, 412302017, 205124378, 853210060, 404130317, 467743946, 877211349, 296196524, 269196069, 306197216, 720877656, 922522606, 488035332, 791517609, 689931660, 222421884, 781565119, 424234083, 616131626, 469900885, 131121143, 30060290, 813574913, 366497590, 333160449, 269387095, 629519128, 200006429, 748252914, 631579743, 815603871, 218764706, 904286673, 152598906, 584755762, 361042543, 897463862, 253333814, 520501612, 969813900, 811740911, 62058691, 686079478, 85336205, 303166665, 983324394, 772285853, 292231334, 96018728, 246669596, 811449772, 786302895, 722014104, 960594594, 83153467, 85126869, 746031882, 675849289, 201883861, 192836585, 749196990, 382966257, 538123744, 560095434, 439295640, 112696498, 510360185, 545243499, 838497486, 105991273, 891523071, 172454304, 887797778, 367402846, 775020387, 418072137, 463861367, 712458375, 233942117, 984031247, 983301831, 643653162, 931773477, 382029360, 35395346, 700837878, 356981594, 688204234, 366257430, 441266283, 739178949, 408263146, 326446214, 285801558, 56169428, 541733040, 423603482, 335756552, 662962951, 42223005, 182299141, 416512020, 17249259, 744405919, 179443005, 93060278, 544471187, 718119498, 500587847, 242594712, 295891352, 869577556, 570807472, 563677312, 807183123, 963443036, 713362779, 333182135, 310232487, 886533366, 390919537, 923353106, 202222811, 507969734, 641614818, 5546278, 810134875, 711225049, 525620983, 843201188, 355585639, 792116443, 660489433, 300698319, 115683643, 981367331, 768844530, 499925013, 886151766, 733989435, 615117370, 851983095, 657041931, 700539676, 274331683, 417606008, 368632055, 50473675, 652192995, 157712011, 358463640, 791584227, 680494970, 969930479, 15990889, 343806107, 98363967, 431996813, 730786828, 409859447, 243634201, 374238839, 442652055, 725121274, 854943179, 951527177, 327434418, 539884353, 755774947, 615392864, 805883927, 200258523, 63384657, 404959697, 485328086, 963181056, 954593696, 662372870, 415144332, 809024610, 208346856, 498701150, 345975702, 321119685, 25614732, 239983933, 844904652, 266084695, 102517302, 625525771, 340021402, 893612766, 913280558, 395284561, 33268106, 140802846, 621676978, 749938880, 582371449, 312767962, 872596001, 244191734, 980840193, 331606791, 216996243, 307217935, 271163904, 107161101, 865697637, 93804129, 317853281, 389953371, 268081241, 570536312, 519735369, 761372464, 604387438, 188576118, 577543681, 40704433, 554456647, 448072688, 88404613, 714875884, 270896601, 657883228, 678840365, 694620357, 318093769, 120238052, 26903692, 432596557, 624540065, 743744960, 96347360, 32837239, 146812182, 955727433, 572356815, 749146970, 181149343, 318718840, 153381301, 521269370, 539261082, 299065126, 434576736, 170762949, 579896715, 30604196, 296698086, 195236285, 886349375, 245860637, 222134728, 739396711, 246610162, 350896755, 840864392, 427221486, 968643959, 424285799, 801232341, 962114047, 841828133, 990542078, 927315307, 389245600, 5465762, 901073359, 803597879, 180466587, 522387520, 265666686, 938703644, 623878868, 571308910, 151998798, 546696252, 411593614, 608638446, 279533929, 771672659, 273400210, 384593022, 220141950, 737277438, 690300204, 851809202, 390649027, 510355924, 290604107, 608496291, 378090242, 862289672, 256239829, 23158405, 480311896, 397760820, 526060179, 734270842, 274461552, 495788073, 320134346, 106498675, 160766755, 276847922, 579426489, 41245864, 976123060, 30811617, 450330986, 830873026, 97982659, 624477939, 831064320, 820572642, 612458980, 919570516, 237889580, 316452066, 228347424, 246968978, 215120338, 699149551, 701730559, 558943938, 158472527, 965898796, 581025231, 905372514, 126663156, 68617347, 698934613, 426137727, 30801138, 96901712, 550497822, 679108896, 511917718, 776723688, 572321450, 592485981, 776681448, 602172704, 499807276, 127507741, 969841712, 671008207, 118214218, 78983145, 950580872, 145288062, 814410007, 420076339, 547712201, 395835918, 251817452, 861794492, 361115, 158432073, 491319715, 643396820, 451077860, 301014299, 403235054, 972274729, 528682078, 47372186, 356798412, 456348398, 485137143, 341943896, 680679789, 445111158, 271918322, 950636340, 530190264, 349795352, 447143943, 584444261, 337248281, 273495574, 596617039, 445966637, 462134361, 231029516, 47313635, 607296421, 185814089, 555768829, 314836152, 73180217, 821572311, 308547236, 249536788, 740367107, 705280697, 299493914, 723394935, 255319304, 451417481, 63682454, 714847377, 653037587, 977846482, 350294875, 104806718, 574675722, 80991085, 26539219, 593969865, 259850001, 180513041, 5212891, 443577820, 192776925, 828002552, 725687499, 123700879, 786743586, 893447302, 856753502, 321830705, 817062994, 142856609, 331740475, 68843567, 838852367, 70248518, 220817516, 945190960, 212638401, 960914642, 8987747, 392082310, 378942412, 43937891, 312508319, 129865905, 442339566, 806891969, 812736692, 973895068, 4702474, 370133487, 353695463, 390021311, 919547574, 197242901, 506109703, 761674609, 321962704, 8869433, 398070494, 53963480, 969530383, 463963385, 761026860, 714323321, 799557035, 80701205, 695252509, 998664361, 901690307, 352809335, 646824177, 298643743, 659069191, 900993176, 663394199, 233729435, 346086323, 180645647, 277352639, 62433347, 445870935, 461639978, 838548058, 620979918, 680686228, 349248703, 116316858, 193026298, 490636679, 644979442, 562602240, 212323582, 122881576, 656956834, 505913289, 220543092, 865977109, 961143262, 150849049, 336913606, 701939640, 42424068, 685250021, 21822695, 518533604, 425154778, 577293114, 938409440, 435532346, 471757607, 677513282, 852948840, 558138854, 524890146, 352359364, 143813980, 917822512, 64530446, 79938266, 118328603, 687548965, 539819584, 671723033, 346024447, 199700273, 622683324, 29507625, 635613456, 789081116, 14961015, 809350502, 278309985, 699594851, 431315208, 656762909, 23407710, 682998987, 657888223, 325799027, 100720465, 978814305, 556463150, 229304752, 412493003, 848755386, 999859134, 520712851, 191397433, 323256962, 137773236, 424214506, 45489579, 843635397, 135895127, 891629884, 325011494, 354385443, 159618824, 438667623, 212111908, 274789289, 797975218, 922665947, 94763777, 394975720, 716098208, 13153840, 626844287, 168157036, 792820081, 991172325, 694403159, 490212286, 546335290, 406110901, 362665586, 814416418, 36687530, 951346007, 746347167, 447623317, 176690853, 441647649, 645756569, 558520366, 301071294, 523893506, 972317320, 462549236, 146328443, 963435389, 410191204, 216283634, 360722469, 483802450, 667797784, 450421383, 626516057, 200369213, 506259234, 530642317, 764560805, 713636616, 171177580, 389451472, 904159639, 752997238, 234018742, 597752156, 255068440, 407194641, 823481123, 734070788, 215507144, 853419613, 230100355, 816316914, 473676105, 633347536, 664612516, 361298852, 771153972, 907515221, 435724299, 950526950, 269201612, 662350161, 833234987, 111986857, 752880542, 57581839, 130421544, 343626261, 343754569, 359689687, 464468590, 428365554, 799822684, 153925184, 619770734, 482446516, 171500882, 241577642, 385223023, 306789418, 94715670, 940788987, 522396201, 506791900, 271032607, 601108951, 392717571, 460439736, 216643546, 864907324, 871833270, 605698262, 42784806, 15975468, 808365695, 585853529, 524871514, 529705589, 377659586, 747633065, 766144622, 733890015, 511555934, 135973510, 571975403, 598082607, 116668306, 706056426, 415435038, 78060410, 74266630, 322678864, 196639400, 106246762, 45771762, 733811215, 620712707, 164132585, 308531701, 501653436, 284983773, 60235185, 579782806, 165243396, 863014422, 942958620, 214958132, 363888300, 651999094, 107734441, 151436546, 123709348, 417271801, 283382120, 424096705, 341996610, 853294886, 546128015, 415668828, 301247359, 38375867, 473132485, 589249122, 887814744, 218100267, 23818843, 700140149, 689470753, 294571204, 842560398, 980231544, 378033247, 46284214, 404968767, 727126252, 529099688, 160562746, 123036541, 797767585, 914529269, 636584886, 765284736, 766502407, 369735423, 965623441, 283116663, 965258223, 582181294, 630923943, 80139494, 887518632, 802831578, 574183762, 643516806, 952825189, 722333679, 306927409, 190318604, 742972069, 522379729, 913037801, 602713456, 592938387, 107246185, 448678948, 947421333, 826352195, 934694259, 846671438, 686569455, 967269247, 515218108, 289066168, 708218063, 320964871, 130210440, 19057129, 143969067, 956586294, 396831599, 908581001, 392381991, 871517078, 132227874, 601128309, 211621320, 559505101, 547381599, 382477060, 489815189, 872830169, 148563096, 135236861, 879976577, 501658759, 615763913, 676340190, 972765856, 248652958, 893937738, 263890020, 75897574, 786830777, 660931230, 461445239, 522955587, 724472690, 972126729, 228048195, 436850858, 704651846, 767286220, 957308950, 46656985, 925465822, 243322337, 663518376, 545344372, 968858226, 496842968, 629481194, 550925110, 526316507, 576183204, 235448152, 445932252, 355957961, 598530739, 107804956, 371734003, 4804994, 492836844, 481557282, 905469861, 659224985, 864697266, 698999332, 25636609, 203213960, 813933654, 809055780, 59486742, 421876829, 991678132, 613956424, 404081365, 347957337, 650810034, 630394485, 725225817, 83761055, 517128114, 953097118, 750436155, 980721977, 617793582, 561886973, 594280068, 91597376, 11756901, 179746579, 898165613, 5261598, 630370876, 823417312, 234213692, 277602006, 798854008, 145181905, 609121259, 136302766, 609184683, 594963941, 568233583, 745498794, 102354611, 813526721, 10403691, 480309743, 490187339, 966119365, 417282610, 391126273, 177492783, 485089406, 356024876, 22995332, 585998788, 186557096, 622651006, 536023231, 453168938, 931491709, 477474408, 532215111, 710416904, 386570080, 21176212, 921689067, 593145132, 901937868, 496881082, 586512503, 120663834, 572482605, 380575431, 274725571, 584860442, 818935316, 707539056, 179729722, 269301102, 644679940, 145734450, 32701896, 680070939, 578801670, 645571547, 544115213, 735042357, 93456212, 548589416, 341881507, 655894571, 396898328, 526470575, 492229801, 12311814, 261001337, 827323556, 895376307, 659257279, 123104690, 386855657, 712289605, 742562120, 847652119, 930680258, 799488068, 735640964, 995932974, 951934402, 758544652, 873599695, 947426473, 718865315, 976323356, 469302077, 8240136, 875878957, 455455611, 250466926, 986963651, 891512262, 807434236, 146136504, 41109865, 394536413, 868422653, 861288928, 744962190, 103996262, 294112582, 607069247, 82791029, 272786031, 337622400, 361568972, 262520521, 395202250, 913209201, 937494929, 373001243, 789600742, 284807072, 918717868, 911226117, 667681206, 774686378, 550251444, 560139667, 761365777, 95695112, 201046681, 921071964, 883658038, 647613625, 48691737, 871777988, 166133248, 185397163, 904790968, 296081072, 979189540, 536359975, 153142938, 458043192, 187423340, 547907982, 693796740, 331303391, 310637465, 251492449, 365543002, 957714464, 285968463, 461032460, 596461819, 296164978, 188949761, 653149066, 757806224, 401988957, 480171675, 544375304, 93573718, 405185872, 86553335, 3705878, 712635036, 590401788, 910828519, 142680663, 477967039, 96749497, 637704091, 38847342, 949094145, 476565532, 400122932, 813529249, 779361550, 973531676, 121404213, 267801900, 528714246, 426060404, 535529274, 464962690, 9679065, 820272823, 243548280, 567007662, 767907423, 538362822, 597720778, 519154804, 78831313, 264827256, 523560925, 499031423, 699439981, 516206109, 764421305, 802007244, 530847639, 182716658, 621075205, 687711238, 392122661, 918762117, 963420328, 681924458, 50324040, 668576140, 650818873, 635037830, 842584850, 705083723, 302236097, 848778374, 165118220, 757662293, 506507257, 69323769, 544648588, 565016634, 99052569, 11724615, 867554847, 138096706, 877922008, 278430479, 496499779, 590552530, 325615023, 670488008, 809167178, 651041846, 165245336, 230699544, 516281742, 928579388, 956901922, 23463876, 880574411, 387464465, 803484831, 788871505, 875457284, 194237889, 22887252, 12164373, 743903371, 418802774, 436632348, 70242023, 545649399, 43110868, 549611937, 621200062, 666972575, 500726481, 127933550, 182669107, 785083458, 523253199, 214173705, 718017604, 442115692, 732170700, 508437660, 989727198, 860551236, 342315456, 74479139, 26623659, 839670977, 818385622, 677111413, 232513740, 592009372, 761116367, 446059363, 652633955, 254953377, 401030093, 198963359, 211141071, 882194387, 778740050, 939096912, 167224989, 622231774, 503728879, 447050804, 882428663, 597590493, 231670302, 376760656, 715772782, 34781638, 683414668, 947817015, 461865185, 426722763, 240288954, 636720583, 975764297, 78798928, 843423351, 472777950, 102517146, 46070877, 293390409, 224879964, 832970690, 702744573, 606149071, 708216533, 353659479, 705992158, 501409171, 462717105, 754431068, 821112719, 376177494, 508313708, 464339187, 444175949, 561329918, 753287037, 445361804, 225795905, 597141805, 296183844, 112283350, 884626357, 548562548, 242519216, 391134775, 778895156, 582613215, 552634241, 490365227, 598866698, 848850060, 521172411, 930557663, 82646389, 97336149, 831289680, 592987199, 471340647, 223218691, 322458483, 181975905, 234792222, 974533180, 717711279, 778271983, 547509846, 787030217, 513413101, 379268018, 545225684, 627856008, 771718206, 944594050, 64634755, 497301566, 634949799, 160114082, 498790963, 205010294, 967866804, 488332521, 684338678, 74471905, 528780176, 777448920, 850608346, 52730627, 612719876, 408136567, 583955001, 802350166, 479246859, 87819878, 91519540, 543414634, 801069267, 460650161, 305895448, 650070912, 571761048, 356155822, 305599712, 384695007, 132984271, 716976593, 303641060, 539558601, 774660524, 249517326, 926134924, 149209272, 692774656, 420128390, 24540164, 15271070, 652531715, 640769506, 916447567, 280493882, 983633266, 679403344, 709474212, 364816518, 153192438, 426917219, 455259604, 295448266, 835415972, 103595658, 829735682, 792110826, 909690119, 992714791, 25754936, 317623733, 539549423, 393468003, 231069707, 974381359, 480688379, 567105752, 705128085, 302728621, 802729825, 728176965, 848796681, 490055022, 941802914, 129117495, 315814220, 870956145, 482242982, 949905859, 952751872, 639529559, 134932160, 509133289, 135677478, 697075717, 402898758, 593683386, 455068825, 451914211, 61631537, 358298589, 129359110, 271608636, 814438150, 612877394, 102721914, 180939353, 419602405, 853048575, 640144750, 655865101, 638328952, 120653442, 396978639, 960084401, 19687453, 486489128, 712002206, 914424611, 137356038, 922577887, 41236352, 806516984, 718393930, 100730073, 521801242, 341194535, 890312672, 53298589, 748191346, 54417566, 500841935, 778129114, 550656042, 875908040, 584545532, 976993152, 399580684, 237596235, 424823137, 375282403, 199840753, 225113179, 905872415, 265410281, 782409627, 149533686, 154141961, 628589882, 23970907, 154086341, 641313186, 323057051, 713219465, 850962177, 588962508, 875288652, 710851787, 417098244, 45916135, 427666740, 100426566, 475128356, 209062186, 833478185, 724402196, 234570805, 670005801, 623902619, 232433477, 386910128, 806319435, 405175084, 160950157, 999578565, 764573165, 895741418, 57959132, 568211854, 241048556, 30358947, 883152882, 567741072, 111680452, 523484454, 256653120, 698261533, 755990943, 411163185, 821712938, 233527276, 500934011, 213134769, 31505981, 845961554, 150199180, 880176960, 110331625, 230633238, 381258284, 226873348, 529562519, 519452022, 688083495, 391018433, 776420531, 496050602, 647025134, 590790634, 490257038, 744834568, 22791593, 871888122, 789696004, 102905543, 285961758, 175192595, 436801022, 440093798, 935595835, 13460676, 808370882, 409029180, 659959576, 443559879, 879549530, 34897528, 823160355, 659948800, 840919093, 377863377, 969587249, 993724084, 203978712, 751896989, 251583526, 463284947, 935745558, 350138882, 699310599, 81441080, 95840008, 146349290, 629290861, 985276339, 443040483, 17855133, 545821001, 666196195, 723991022, 741036773, 807169201, 516790883, 62162646, 994523871, 260664085, 704731853, 142179884, 881618793, 65847800, 55965152, 251147495, 976851206, 775985480, 388707428, 562819296, 508597981, 948622110, 662298473, 321673595, 125922640, 346414940, 413831271, 976240260, 965092105, 296217448, 990955292, 451280516, 18405146, 774428929, 89939906, 413556710, 440623874, 454058698, 977316579, 309238952, 616982825, 958129920, 840347639, 312370228, 946311680, 623377722, 207923358, 779085085, 807408221, 59300525, 848540886, 523727423, 324743601, 674125148, 105878027, 299493260, 385804280, 3697437, 756598167, 502318808, 980447655, 146564282, 435657530, 730630288, 265329557, 343514380, 3233277, 321961719, 346201370, 663813376, 502979230, 413734421, 383530894, 171406797, 741168670, 661685179, 914543267, 829170983, 734004709, 290611765, 378187432, 117478729, 603982011, 170425643, 916658888, 381743847, 541915529, 860628572, 485284162, 735627980, 404327501, 309369489, 541818044, 418478134, 182816601, 387498869, 838161228, 393790920, 245672639, 961698973, 388014405, 20625395, 574684758, 163547119, 163326971, 969225655, 853069146, 820815408, 878148388, 69144841, 540430109, 531549194, 768205194, 116799722, 688745582, 711316966, 495944585, 490739471, 286285406, 155663366, 161063654, 363469666, 915063680, 262652894, 159912427, 105631077, 763331486, 419523466, 234266245, 875271602, 988969137, 31018889, 864290500, 22554780, 614302891, 762032584, 500584958, 569664265, 671167964, 168240850, 23314960, 19802982, 955604350, 559751254, 328445981, 614740111, 411806477, 975171408, 859921460, 883390363, 361247773, 895123243, 196720473, 977878537, 873315202, 165143014, 187228498, 740077415, 674838258, 714591627, 16561703, 367582556, 572838989, 938032993, 421059120, 243118178, 976069515, 126032360, 697610305, 702014983, 181715580, 421159997, 604346830, 479539028, 787836106, 968911287, 704294368, 804992454, 846393621, 203192019, 935445936, 956936293, 904079256, 167082452, 144452619, 723611131, 243685266, 981993146, 358285264, 209431963, 611884024, 181127021, 507413537, 715815649, 265267824, 559579148, 320177245, 931664212, 908587556, 843002223, 104207154, 526331931, 859156713, 778850637, 468463070, 766138538, 136840743, 143472053, 523088811, 534344844, 736040384, 256105299, 985496332, 547346277, 759040417, 382807061, 350918027, 682681740, 734610698, 553996974, 47012408, 318046039, 649577273, 598756534, 668028261, 116895209, 899200897, 85341751, 154499670, 842109701, 310039047, 821997132, 119481598, 538091146, 652686476, 484005803, 982519491, 389651394, 483290931, 74078590, 554268416, 66300108, 650491307, 601921394, 972536053, 305242859, 73621508, 487974533, 43401592, 206958592, 157864488, 463013250, 818153184, 635015981, 164770060, 852437006, 590889115, 651039079, 337392114, 456924335, 405445377, 692550108, 637706366, 947806068, 771930632, 154756435, 649240985, 960470873, 231894941, 462855046, 565907120, 791982672, 620658443, 992609336, 226996201, 317363061, 707756603, 723516483, 219024494, 628169838, 696366219, 917707744, 705951724, 262940731, 110787585, 831438528, 477540386, 40159757, 576460643, 167391278, 987711092, 765013838, 904032325, 301968359, 764119341, 218692353, 378894060, 528476406, 794692006, 8457799, 254359270, 556432879, 935503558, 384458954, 30475824, 781336468, 389093050, 323657769, 452974801, 180407267, 513989550, 319891272, 884475554, 64039127, 72540808, 280227781, 524108264, 738373461, 299758499, 979978868, 80132042, 753943668, 759915746, 676743108, 760500130, 639933535, 939307703, 709919132, 80526431, 943972217, 89699863, 99668731, 125336230, 736868384, 632191760, 801895814, 226673436, 294496795, 800746268, 677864220, 338723747, 880159067, 695824231, 658400368, 801083901, 993831108, 638555720, 301914206, 847242609, 423597261, 882354893, 690285611, 515029092, 665776717, 13271836, 87357143, 145947142, 270403311, 477385159, 176680840, 911513291, 861253657, 482756019, 24214053, 676589861, 958972976, 197898888, 820466539, 871316247, 698357218, 594169834, 310540948, 833547476, 567791234, 627093468, 139327625, 569373268, 748320110, 275458961, 769356450, 847773092, 462715676, 682313022, 359897972, 415286290, 480999671, 958363654, 271108936, 316364043, 628753442, 269980647, 906282304, 796935814, 393072579, 357979029, 766380981, 176962605, 274176618, 142764132, 644255183, 529701058, 809921344, 490018773, 917228789, 247792437, 721050024, 137721859, 842436778, 453254660, 382898595, 435056639, 536298696, 656388666, 731237987, 538503911, 21952670, 432958444, 636312932, 899189373, 657813339, 200533068, 568226648, 309773097, 766047440, 987709237, 336672998, 563890413, 850473447, 947869380, 580316784, 276798615, 651114095, 832690959, 66732098, 312003875, 846122995, 345889842, 476809969, 268328258, 243588533, 345914815, 387318123, 482647116, 56544082, 91248077, 776290891, 235520499, 723067693, 353699018, 662911564, 827970390, 682812391, 198757703, 259307983, 961161084, 903307472, 743001629, 31442258, 372019732, 727485744, 86249160, 463766478, 186812683, 144122186, 623490540, 793536099, 192195356, 915741801, 141999568, 58279689, 892760807, 957789973, 477506618, 844772492, 828546596, 249703070, 182324651, 954221910, 938097954, 896358144, 399340887, 192594321, 436020415, 315560565, 918774930, 970167719, 633003324, 246166614, 936652991, 529821409, 785503893, 868570332, 748771772, 667106165, 896261458, 540764326, 136408928, 937740115, 227741252, 615891834, 303733429, 692836757, 617111582, 255952884, 187590482, 22028725, 117221114, 463601297, 457379959, 953172956, 324158283, 387868006, 438782186, 874104994, 115233054, 207517051, 419679846, 714134717, 806237505, 730395217, 98489983, 641680273, 196594535, 297113052, 750858329, 252097141, 321011503, 772241114, 185348274, 345513239, 896266872, 85924476, 313246681, 557212029, 944754455, 525099327, 285285076, 694290451, 702318948, 739121406, 362899813, 572290414, 871097075, 278755039, 878380660, 998225820, 33848218, 780608848, 557973433, 359680922, 183201173, 234114320, 674248140, 568525727, 910761447, 675837708, 431701987, 327465395, 184512395, 545036874, 489066186, 723791458, 645076993, 435339571, 975330887, 796054965, 451936497, 867764959, 322604752, 503257990, 7785224, 109489865, 198103825, 724978475, 648714784, 617097593, 995426163, 413177237, 623946812, 50052627, 907732868, 281222773, 585759331, 26604777, 603434212, 305536371, 648649266, 967047111, 245798210, 664095862, 268800594, 9795843, 867127426, 103578175, 568005914, 283196307, 440976182, 18361056, 529978955, 562991722, 850028545, 470769204, 602917361, 703463332, 471376889, 924142323, 613688168, 200939848, 752361489, 98486119, 636269842, 921518262, 462345864, 256990581, 74313554, 291902588, 993796420, 433910562, 912572428, 148734447, 739414352, 789499480, 521551023, 599347101, 518299956, 475964146, 822314384, 774604478, 919554655, 740495925, 267629005, 480206703, 433714534, 689425874, 353470069, 612437199, 198760085, 840056148, 268829841, 734327748, 243040563, 734520137, 596113060, 878707934, 397805918, 540860522, 598216147, 281201060, 767431064, 958578965, 579804407, 783703847, 158678286, 602216396, 431615360, 107663298, 10502731, 858174969, 503416514, 562593115, 762088592, 510052361, 951190480, 619941281, 25987907, 176257316, 178608380, 784437368, 859524848, 855059534, 401732707, 125640795, 860545977, 366625268, 540678396, 776980920, 823265155, 217699260, 812489733, 127774067, 18765248, 909795469, 409169732, 916079380, 330010622, 885421567, 183391622, 449382765, 407564349, 56065578, 455297127, 122027179, 532071109, 866576384, 482559277, 201352235, 441063347, 521033542, 750890220, 639708109, 141131058, 669767361, 52805875, 837196704, 977303913, 903034998, 540928881, 420242750, 541909932, 457961330, 422646356, 343764704, 307142674, 815596854, 188536066, 709516167, 994133707, 351969465, 222029471, 320558078, 423112908, 160856481, 264175801, 820676249, 366483521, 227672062, 659096828, 144268431, 5784236, 369936582, 553887554, 238995458, 396296216, 427239733, 241453822, 630928332, 30369884, 390546673, 663562185, 482921321, 914980105, 699657264, 866521504, 398485476, 356190239, 682886497, 920504015, 585474089, 760699624, 188832705, 903064914, 203436767, 404513732, 689614711, 466721810, 913947259, 132962143, 983591247, 295074656, 672945515, 44444446, 147399087, 549961799, 291667110, 465977933, 131035634, 493272114, 269715598, 476911349, 748200063, 416165193, 969560473, 57914627, 452596847, 920012965, 493706208, 864749255, 981140605, 692043360, 586060138, 446394245, 318994266, 172441428, 132908469, 190666380, 539928834, 758338591, 790543350, 412510677, 113735521, 60261953, 385484175, 99239116, 260846942, 626522442, 928525096, 665832588, 149914800, 724743261, 134104018, 888942047, 431958503, 22853567, 112902487, 298626843, 376393244, 384352533, 875246851, 532637174, 296880980, 409299795, 484096046, 109925032, 469905746, 899743754, 334364508, 350265665, 6595239, 484658207, 498154009, 949915357, 987211393, 27347042, 26708191, 62662990, 582188723, 877083417, 47755962, 995315874, 917311255, 498167370, 994493264, 102241661, 694320048, 421775132, 796497779, 533414938, 431650138, 540441773, 470008284, 907529678, 151710135, 531257818, 545166466, 442186375, 275357193, 84405103, 338334829, 301645381, 9014972, 970622832, 570226083, 39156554, 250806992, 912620370, 118633547, 131027926, 684827657, 386237060, 669150463, 705628475, 176955792, 994383961, 539151397, 863531669, 535939418, 658278889, 625879022, 997482854, 394574543, 380240751, 144760045, 388721246, 289007537, 857914305, 980140612, 934998943, 204013913, 888040544, 340952428, 997999210, 824941107, 787964794, 938910663, 231865809, 380955432, 616189296, 375634683, 322665742, 745780023, 476540205, 54740886, 736355397, 607995185, 665547490, 160604139, 21500403, 870060324, 298482408, 500957967, 633757623, 339479848, 767167761, 258019914, 978343776, 928259554, 917098909, 127400622, 795924791, 799801944, 207076774, 636036310, 516325971, 628844761, 604152638, 578736224, 37336102, 705151003, 470625526, 203592957, 779428118, 880207654, 169925502, 565665119, 348055500, 959608728, 922525333, 473116215, 205053664, 169338842, 782614826, 62137097, 747534164, 138863036, 444581161, 285258598, 720451974, 737200155, 460291227, 394898885, 899550051, 339520651, 657032166, 134066524, 88184047, 264007477, 478399018, 317938719, 327330020, 728594304, 377668601, 754684981, 890523233, 739582494, 108277941, 733495955, 789054041, 720757939, 136779383, 835357227, 85551225, 145753867, 539154350, 830910615, 834160812, 899068346, 510538639, 419906139, 903626634, 886875233, 852442919, 656051004, 607925657, 374325226, 989112293, 889075474, 558210868, 266151675, 747277348, 722543729, 481216823, 863808196, 272152869, 599141930, 262325777, 425924574, 234272791, 783141594, 256716730, 15134739, 420687851, 949043705, 897543612, 346087649, 221149167, 110097058, 539528634, 308215759, 384049111, 143019138, 352520046, 920760465, 310064300, 862030855, 442689441, 466178541, 213253814, 898481614, 281262497, 295246368, 187400903, 430057158, 865266854, 850764793, 196018411, 802948666, 453879209, 935551720, 256261066, 92843654, 277102553, 227872340, 45537531, 40979247, 545473438, 860007329, 995410405, 109964421, 717328375, 158695546, 308927047, 98206551, 248796040, 885603117, 867942256, 373493406, 138869138, 340434841, 335748621, 918210501, 399575157, 601073589, 651038747, 244127850, 697145, 640811471, 148816674, 157679450, 551062248, 250462117, 303121898, 644422128, 228718628, 123112190, 716101589, 809985258, 744581636, 330364735, 956364090, 814277595, 520402133, 369853130, 761460018, 117191791, 920528951, 318207510, 505200783, 388568813, 309538912, 668643126, 406022457, 278037726, 614397950, 297980200, 474097939, 608977557, 626107434, 887474373, 138328696, 178382760, 190680645, 231628406, 544302763, 236027814, 850374786, 329223505, 237208476, 329470306, 339446588, 753989192, 343046807, 220225786, 482910268, 593240911, 152339543, 390813139, 396962521, 173316331, 923635601, 787457020, 907547364, 803015784, 871762980, 978375138, 596709474, 306429173, 67272348, 113917180, 813718415, 872702848, 433981932, 918547226, 295695617, 98363963, 674059013, 375391147, 400876486, 184778463, 411398149, 492355871, 162500103, 480538428, 221591766, 393151019, 565831624, 413022918, 442985312, 405743508, 843121556, 952768945, 951929740, 609269711, 575007157, 987632987, 302585716, 503440078, 748983139, 234952238, 234459365, 984864818, 806083154, 754862259, 106067433, 239192815, 436975392, 802888071, 918784919, 609001077, 913515109, 736559386, 351836157, 241988785, 434625466, 298970576, 4694024, 115915414, 830787797, 147176055, 440842587, 768020706, 514344587, 358489565, 385617707, 726751454, 444903491, 38005225, 283477260, 136488232, 794233785, 10951792, 445195241, 258268129, 904954215, 891467267, 763896212, 894546734, 281403761, 851057424, 27013027, 716517770, 356727689, 192707745, 780295302, 394436962, 883498898, 81034945, 137624001, 661627029, 244511686, 971821789, 512230553, 571800404, 284105685, 932002442, 83391708, 758523898, 70638766, 317538537, 177214287, 558314455, 861883577, 202304440, 602191317, 163975159, 688532291, 918624341, 444473480, 688481758, 561083817, 54930585, 812573913, 92135025, 375345769, 224375055, 276091533, 723810785, 634274427, 128788195, 231653451, 138582462, 166559743, 647962515, 740661686, 428171947, 434090868, 980926836, 403058568, 613622697, 192316336, 263006664, 695357154, 487897344, 598493936, 331356897, 172245845, 431737902, 305738322, 244239374, 272767515, 572559185, 860418087, 760973667, 687637400, 519984181, 312278580, 942277879, 347884114, 247602587, 495579211, 131278421, 97052833, 697740382, 711263787, 852547652, 137729080, 229845158, 350467768, 568043521, 987398095, 917145063, 926782721, 715217683, 940668228, 582461149, 625928778, 580292537, 579897740, 300359341, 181598358, 785186502, 786679548, 372876113, 865342903, 959113546, 196796157, 291973038, 701623491, 89864659, 979501912, 423319698, 456758377, 939379536, 724235037, 391272553, 239762347, 802830262, 314275437, 338519971, 884897927, 603489234, 852473946, 192580242, 353672242, 747699944, 552067671, 574854664, 126990135, 826050115, 427299516, 466182771, 245974935, 691695303, 718328131, 768278203, 530098825, 533635799, 666425493, 309371413, 478385747, 304345157, 592331641, 627280745, 696040576, 418272673, 246964707, 805941212, 720132335, 495601965, 417108916, 869394935, 860547788, 734219102, 168534690, 737838905, 534540761, 289951359, 505924065, 812355274, 477060041, 357610360, 774904867, 203429181, 541406917, 70440189, 974906001, 967105686, 750675440, 590552532, 181049898, 740563780, 347900206, 654358738, 494805116, 223500408, 651919264, 857466755, 303572123, 878165270, 193921115, 941971950, 841839733, 82542970, 611243028, 197185738, 305788119, 959854220, 703297338, 593771227, 288212451, 979566460, 319935860, 312768546, 276942887, 607612699, 563360477, 597895283, 963232882, 279302036, 393129864, 69868926, 469155330, 505942691, 942021314, 820647493, 369824927, 77829498, 164559436, 761319427, 177202505, 279773157, 246298411, 6348775, 497214541, 237549779, 155101827, 966082675, 893438591, 972917043, 219059051, 514186808, 660194907, 189442878, 575748378, 114635879, 814090914, 689640111, 325582643, 310107812, 348119710, 693468611, 409639074, 224640185, 543702891, 688729076, 997675457, 968561482, 816421829, 685460004, 392195309, 830595482, 713852536, 582801052, 716464430, 331320373, 568543368, 778928035, 565784819, 755031015, 804762260, 407888486, 521609333, 487725772, 882134509, 876338004, 120454321, 196099771, 923999045, 758160613, 15970337, 934682440, 460651226, 302986213, 792356830, 632300401, 259762648, 443075671, 96358374, 98994472, 997432268, 17785538, 191918284, 404415084, 651967004, 555566496, 29361658, 690935032, 555673447, 27444505, 422006528, 235622847, 900548851, 593786524, 404982998, 10624419, 115013235, 637661488, 722593188, 59081471, 972732837, 287447295, 911188631, 639093584, 207481697, 881982654, 423905246, 280104775, 662686509, 411648921, 659233993, 795879475, 622542332, 273785399, 209697467, 198288826, 590284224, 658759317, 220648772, 124190595, 29463712, 338610146, 36211014, 286788938, 945814383, 345985360, 238207391, 823810543, 551778311, 393204531, 853629822, 855103282, 201978878, 749493292, 23394004, 287534576, 150377334, 350394593, 526330759, 585787751, 603102984, 651915589, 8995249, 761794288, 523437622, 141943878, 152789204, 967544575, 929021756, 757262800, 179051497, 535601383, 809524252, 213095458, 497643827, 716839082, 565630669, 395596790, 817248870, 952014520, 154309347, 506361285, 918497025, 328563589, 628099805, 562911732, 549712382, 6500068, 940857623, 164727637, 894255995, 440625804, 655784783, 682348860, 718194322, 595834098, 166982149, 596839370, 448682897, 258196380, 168412126, 739829686, 115349857, 928126934, 90167011, 834562947, 857126956, 570611244, 210711835, 217390519, 509767412, 287693355, 910342743, 143842260, 130476354, 567368726, 845335402, 322433259, 809832029, 813937867, 721847290, 716916455, 297070904, 708690650, 7946543, 518222588, 458257786, 125200396, 857569485, 319667248, 584223985, 90756134, 438898605, 348029828, 11886756, 350452943, 566425909, 261557250, 168477705, 159991791, 633749430, 44872618, 752794164, 752388865, 374145889, 126238811, 985637575, 540293614, 30503972, 658442336, 703274487, 261595642, 824524304, 882559830, 537991068, 48880670, 457321847, 785238622, 748890672, 618502585, 872681946, 98611579, 83652470, 855399419, 326631161, 762958248, 144543392, 754685230, 630958596, 457649716, 671666205, 762446896, 85935835, 776327611, 845579150, 704758674, 298472484, 733303708, 315238250, 891730285, 942096447, 509901178, 787211666, 77608072, 839272989, 822960019, 499226637, 803747109, 736801052, 968125759, 302815977, 745957104, 590509242, 994026700, 581984421, 793519574, 301672505, 354911507, 982410823, 938276641, 731500031, 626495001, 675456020, 454410834, 516004267, 487201358, 9579554, 248805845, 702597087, 744965934, 300412132, 997502273, 845841439, 971079953, 153883577, 604608863, 124946801, 271175891, 574366233, 44745581, 228997601, 117436419, 516475244, 317443804, 442222135, 340590142, 397868887, 337302146, 246070534, 267440060, 922732116, 263009897, 73117020, 381712462, 909236865, 997905363, 844069085, 857433914, 432051038, 585901016, 614587941, 902947365, 278137493, 112478817, 665532034, 686541768, 133328977, 973536964, 657570361, 814874437, 57516776, 852303039, 92270458, 651623488, 118159442, 145336090, 523752619, 949286080, 812402935, 127007095, 973556351, 206895019, 145057829, 117909958, 961349639, 193854426, 908065682, 30507101, 505026751, 822137978, 852687715, 773596750, 94888532, 640443768, 636596332, 502290090, 350652687, 215079197, 57111792, 526713886, 121264823, 124018538, 167054151, 503067993, 791296728, 555827518, 252260015, 725425201, 65179222, 263176575, 367210373, 750778928, 165210132, 205514673, 561770363, 7885502, 71274054, 432442387, 714540341, 144477930, 530095081, 642758762, 777893994, 81739870, 465391665, 313299068, 654679722, 601122938, 991985634, 748760492, 507812704, 645393879, 494391514, 555668278, 653228696, 378806382, 867250198, 21356975, 367374336, 424533666, 310146523, 565140688, 206467957, 475666236, 859016517, 440332130, 949487436, 953086409, 596306915, 871878680, 928862427, 492412710, 9814753, 318389956, 503740874, 375942467, 53719227, 681514803, 840227652, 70365055, 953073936, 880776217, 433193317, 899810247, 374825068, 223979570, 229661103, 915464096, 764581662, 667870158, 443936650, 911065107, 286872352, 841772765, 849233139, 542717211, 105364166, 733605018, 520486076, 822300108, 213406831, 612832569, 482837341, 118068603, 491422064, 896657912, 626476957, 940295998, 718256677, 958061688, 849635826, 742032886, 51844829, 642467379, 382014635, 380444556, 801964027, 544083207, 756186583, 291221878, 733053942, 148489791, 466904249, 621777829, 873259661, 647825558, 860472395, 520177157, 196551629, 145685549, 346413671, 213059890, 683031066, 277873035, 471059138, 583980145, 476780807, 691671048, 672375302, 355945995, 635764773, 460807189, 870914778, 521224343, 426483271, 758186967, 708567201, 317800407, 825989719, 759247459, 444564238, 281793470, 186699180, 171035821, 3562785, 36748897, 311805958, 470257385, 844033309, 318745271, 292173981, 728593352, 778760890, 415793812, 578538854, 203099880, 401302532, 426308791, 358988648, 892793003, 172668287, 32119457, 333072578, 882294066, 691702502, 392509224, 524472097, 657071006, 21032583, 427549670, 443494660, 478012476, 405798289, 109348256, 373713662, 314758610, 230403496, 262574958, 907326320, 791374900, 780662548, 51479979, 11357533, 843684823, 201179964, 496316415, 22781552, 834292855, 684367749, 451154501, 946474529, 812400294, 383458436, 833576539, 445231323, 727452150, 333585560, 674455768, 460725700, 183940723, 561951944, 649831318, 365310061, 443480776, 992121330, 976850238, 93849461, 227713829, 469653503, 129947455, 51254696, 524012627, 164267001, 563307317, 275353636, 920348009, 785483825, 961857424, 121877154, 833585527, 918939634, 680288157, 26454894, 460916417, 954488827, 155861872, 784081430, 25511839, 675059628, 7450728, 552172466, 328140284, 957981941, 24485013, 116108464, 521716498, 664959285, 841503832, 247384557, 822115570, 561449665, 835320418, 141211950, 952667833, 235723796, 427682481, 591477363, 171965966, 983676169, 416529796, 888463934, 854029001, 237010414, 288829225, 126179545, 122256386, 939737274, 403066700, 348354423, 42833119, 460455925, 664112644, 144955718, 925664113, 168337707, 106356996, 340674909, 710942695, 633030148, 823290655, 295857845, 888382578, 414984545, 910727267, 579969204, 341001685, 239372968, 186650269, 777270623, 407332419, 555859283, 11829811, 990828624, 863913582, 951142673, 215865855, 302638620, 962857810, 86622219, 410112853, 499419238, 166642645, 741626064, 372135731, 689717751, 783038228, 796268596, 760977811, 653797231, 166782413, 785010204, 449944617, 674853726, 731385834, 355879547, 864478154, 39662046, 527800064, 891058995, 919360888, 645912522, 473517587, 571260143, 260358896, 455445521, 343120202, 36433464, 447776539, 362142447, 115431928, 642733647, 856894441, 467479268, 565235218, 522843433, 496415360, 106895169, 227997143, 994184953, 337850339, 619776467, 685809271, 540414815, 815862422, 781790171, 953626550, 50577879, 449201671, 334796537, 104186513, 650845634, 109506894, 465826799, 48370961, 606704055, 567464492, 791821450, 699759962, 857870430, 653403463, 249964064, 710637092, 475530118, 631703442, 841884963, 537960730, 297425647, 284203810, 195736061, 501787701, 905959181, 400634199, 742002191, 732051846, 1857350, 664173956, 670485516, 96509049, 454487091, 330218233, 752287211, 267554871, 322625898, 172013863, 32902600, 270687290, 384717663, 500843343, 969234518, 814450020, 524547246, 166419995, 627406617, 454359623, 729413193, 552129015, 598272846, 178246127, 423811462, 364057577, 853449978, 320439292, 304033506, 553626748, 660369503, 96727304, 334089538, 559446976, 159699481, 266443443, 409729130, 838632219, 270995214, 175176959, 405110251, 49855770, 248931535, 835983299, 88334537, 516610557, 120838697, 274683738, 414116719, 462237960, 780526306, 613273791, 141212143, 367687297, 891229254, 518993079, 438132095, 14367869, 887216853, 151287368, 706130208, 452180451, 936223007, 439276077, 801333029, 85488256, 577927701, 702443624, 62068972, 189231853, 364826036, 349685286, 848722893, 645809851, 309404322, 711335904, 301212948, 421064419, 82143522, 707453429, 399411995, 708451271, 59951690, 43841231, 250272989, 918440461, 722124511, 350860212, 97324831, 69855485, 837911278, 906722647, 113988471, 215700999, 294864146, 91744962, 691911144, 889110138, 640572345, 508638945, 647625893, 138876648, 168295525, 120047098, 373204384, 17205341, 316309679, 278294304, 866439982, 493450473, 114366241, 50455925, 73800842, 746489262, 173916412, 297001981, 291917145, 101099825, 336779218, 829482198, 107668543, 734595219, 520883731, 645777337, 541120504, 390518007, 219221527, 772901480, 254856879, 587069420, 653272277, 920576467, 782124348, 90846914, 524349277, 491937345, 300812116, 350614991, 470140588, 759255200, 430699335, 201836272, 515141341, 916623911, 399436239, 994907031, 698133892, 627170617, 678550720, 689180201, 186516416, 42793900, 92031327, 448537933, 94432528, 234130454, 995735798, 672575077, 216865923, 58814316, 558324684, 326340715, 484962920, 376944263, 860888980, 821926925, 335026211, 751340005, 500325208, 103406615, 912425884, 967578016, 722233413, 667801502, 565314039, 952601513, 941740990, 98358898, 974555751, 604421610, 230453263, 840693411, 615087008, 245780538, 305265905, 811741109, 55683679, 921370389, 351279524, 30811140, 704961815, 978016819, 369652749, 897463961, 879844068, 566768718, 163250135, 170105467, 216740710, 772156206, 144366983, 751958796, 623366925, 717880870, 504712054, 529232335, 191240743, 741230086, 368797312, 449872712, 294258011, 877665884, 808657995, 803450950, 26709069, 876357013, 272237554, 872830829, 456014392, 311692975, 118949011, 716297676, 289189652, 169388124, 902375956, 831500478, 295473704, 552132848, 330724807, 301300364, 73886907, 657434427, 343844607, 458411783, 920477735, 395062112, 163448098, 306696655, 825542477, 251637953, 684786142, 294464206, 118716873, 988410915, 856338738, 108069453, 285044605, 441623068, 660753463, 567473056, 779044397, 703237233, 504057326, 357638854, 494231375, 897259958, 82949284, 721934223, 832224934, 590635908, 154826360, 273869846, 636751197, 879169207, 40181440, 405506288, 854154075, 544267361, 774153701, 749612747, 875877324, 562856811, 67290738, 362030872, 420488279, 138660772, 741658433, 708936804, 245951024, 784697293, 552125053, 278893946, 480267955, 699490097, 83472912, 66811232, 240087040, 544142869, 506175780, 863385337, 412643656, 29701871, 931798771, 388089073, 406087690, 257574729, 488409742, 608263497, 920466205, 801510318, 253233248, 189789620, 822612304, 349796436, 571687857, 368471851, 851871050, 572277453, 886737714, 438923924, 965664518, 690795872, 418945585, 366002362, 566650116, 757247688, 791188885, 178155068, 522411485, 656159908, 646619714, 701476919, 641103054, 603585109, 927117381, 670703326, 722724401, 83170505, 118670919, 565334281, 592994358, 456481989, 187258029, 353340024, 191731304, 700283199, 553718629, 902851437, 627412181, 191478099, 745918050, 627813627, 468175657, 434230809, 926643094, 877710490, 822763995, 491385785, 130746585, 725352334, 22369713, 345664201, 229828911, 282722908, 832549251, 830395526, 241717366, 282605762, 786544609, 247369370, 523343485, 876767656, 4697063, 350056950, 450968618, 614879367, 327194154, 274562116, 880675170, 826793406, 400880060, 217320492, 168595584, 749065439, 678505769, 177760457, 558741037, 385916069, 268666515, 245889770, 689329052, 30115303, 303004051, 793928962, 906791629, 482398985, 35732983, 88744336, 728277542, 403990535, 240574916, 522751022, 355855100, 695186658, 596632726, 39171120, 683944317, 347703510, 569660672, 761611338, 687715312, 579179539, 118581297, 167372307, 849164658, 904615838, 66951024, 536548909, 39865096, 924801686, 991356774, 22193933, 717454451, 907653742, 277482910, 164320632, 673752294, 533506091, 693324148, 663943522, 878856340, 403738935, 871711093, 790906185, 816872103, 999985470, 43661439, 276836002, 406711073, 367024391, 731003118, 168366703, 849692792, 159180641, 359083877, 676858174, 301860763, 918985852, 689997512, 831728119, 288733296, 428755059, 831196505, 988359967, 199669304, 58445193, 709946, 784077877, 508008717, 87902958, 111323883, 911246111, 425961494, 291061951, 439461137, 575190940, 851465866, 919626040, 662973075, 879447975, 482424636, 966548867, 358459147, 319346887, 279219078, 53419995, 913006358, 622107680, 361919523, 193469635, 83924707, 633725292, 812757589, 571274483, 589903039, 499315515, 75844647, 392752774, 30710142, 967295878, 229131591, 203087229, 54197778, 980767647, 565649833, 179346123, 171005364, 231942328, 449726609, 854276891, 919362897, 391560432, 998143861, 334975740, 575920410, 931195282, 963327735, 947630332, 408069879, 654452452, 282086530, 276881625, 617523344, 532391301, 338856914, 31518804, 119303911, 460762930, 241942437, 894883225, 90184138, 270349160, 895588125, 780197212, 983583963, 803744502, 73788263, 412854836, 430042712, 547928400, 697985946, 813735602, 431439080, 624378049, 480718683, 672233919, 859831114, 466643210, 849246416, 275566250, 932802086, 454373145, 437496326, 689894841, 792927960, 793176145, 2192329, 556166063, 127695881, 337694904, 412954195, 329173618, 677699805, 21361127, 332640432, 226907903, 450629668, 737639072, 549285627, 882540656, 379684877, 983207160, 77370152, 378144760, 938707752, 486482529, 440047221, 990757175, 910414676, 480712670, 883171791, 223210726, 362509725, 599160129, 849972693, 399039558, 409519197, 895079575, 308664020, 215707502, 692096295, 917176168, 341058916, 509296233, 766129125, 698077836, 177151670, 862819206, 682669405, 8024248, 58462200, 410062131, 865537144, 706600184, 568487661, 280972624, 63396867, 988459965, 471422645, 476779751, 366495827, 133306941, 358760314, 48022068, 156559666, 69628862, 343240455, 182549655, 109299, 263320993, 92165943, 988364663, 873442396, 54681748, 100281831, 990552937, 43606056, 515604601, 401621175, 913230473, 775252344, 666120447, 996693626, 716549075, 542351695, 695822373, 415045237, 10138737, 716347279, 733104125, 735602058, 717952816, 794338506, 808382712, 658514059, 762250315, 528227398, 96839547, 407448252, 746511528, 658694512, 462959896, 659407478, 542611060, 756339961, 693321658, 600599890, 909457712, 292788490, 761165226, 436365388, 200747682, 865513462, 323727592, 510535374, 306378026, 361875868, 278051720, 995580255, 546406160, 373063670, 275303349, 747135487, 631943490, 463461044, 421190787, 227938540, 432636881, 159376024, 783626345, 710884398, 131826368, 770558185, 712069131, 198964707, 703948093, 624534540, 335670435, 182742070, 595530095, 931132535, 563501529, 876811337, 780399401, 567585458, 935601869, 918117731, 856011501, 816142582, 194732252, 271563361, 643389560, 734909334, 231326106, 311038227, 640697870, 406051792, 889128613, 732938550, 73845625, 102876140, 104357980, 199622450, 297215212, 215415060, 319612078, 723483321, 394508430, 38858878, 239202645, 504943634, 241074218, 667793578, 905632717, 304805679, 85578327, 772266002, 897950750, 873834143, 239732921, 336301163, 582826308, 726906973, 963669090, 350957133, 947155288, 618356229, 427004980, 936224940, 976396356, 845998783, 746602493, 684348542, 639927014, 224755912, 564778950, 705021044, 45847547, 609448079, 663606735, 252325313, 464840260, 107295208, 605647000, 794297803, 763736181, 708741208, 693052477, 550863170, 881098422, 803707597, 570566598, 613737122, 316760495, 481104355, 774377017, 575092161, 33956690, 304256208, 440986503, 150628587, 86289334, 169514751, 917244331, 944730119, 30878602, 542583809, 724760512, 719131361, 307900814, 871419964, 384507671, 980736776, 348553435, 410784161, 447848661, 578494665, 838439244, 847295113, 231574196, 8224410, 374423343, 989136878, 276650097, 219537171, 542333021, 477016547, 189136822, 549081225, 995180742, 39680546, 457756136, 959544182, 123343111, 512595873, 616440399, 378974950, 760029564, 724786011, 147662165, 500614166, 733219048, 589849742, 623871148, 446117250, 285856693, 292216798, 387581405, 655818778, 886381569, 445280546, 108861665, 605104828, 859506523, 910190640, 870332775, 996763600, 551360638, 944686933, 874940904, 536827196, 87692205, 876841383, 684495259, 214504919, 213959026, 894306030, 759265093, 973695087, 732312103, 904324071, 301691972, 91860127, 148014236, 872828252, 92301317, 181137675, 855459407, 962945110, 961533323, 715711687, 421650867, 986807537, 593311806, 287884169, 893104440, 947933978, 566464096, 957357918, 957650234, 773184015, 211915728, 970873901, 619043982, 261078624, 56168954, 695449582, 707519359, 207779099, 810315558, 796719862, 164507139, 977249275, 112708343, 190599827, 589815349, 349379861, 446622728, 293403907, 95081158, 562340826, 40738864, 655207479, 259094989, 375623663, 18172671, 65763753, 251948371, 513672394, 154321829, 254792655, 744909213, 449708099, 522641333, 938946955, 277366069, 381467380, 175246959, 936813850, 399390331, 918221428, 736792772, 3596597, 825370925, 908480295, 915822415, 863686099, 183347724, 25355933, 700849800, 35855643, 610274576, 866545174, 399645740, 623862802, 919862496, 927878077, 285947668, 8460690, 746843379, 709382611, 927262359, 549067123, 27052786, 320301626, 408129228, 118055033, 519989118, 596847885, 686289402, 61938481, 905075703, 343557765, 935887854, 943677060, 431298811, 44595045, 101048094, 778618825, 305633704, 470726627, 56195807, 110641114, 147670697, 264279653, 588362541, 534018532, 946846787, 661110364, 607182292, 294024270, 256280028, 232248805, 59720690, 578811576, 685988107, 3529913, 557340314, 600444355, 330905285, 134952325, 275236872, 684293428, 621443103, 102638730, 544835501, 296150218, 62888268, 230935657, 886578517, 369035849, 248813560, 786703672, 154807526, 490542629, 447249670, 83463273, 419706833, 493071836, 170380148, 855292037, 31625966, 770840034, 661196354, 951144072, 409896604, 548908153, 174413810, 23371930, 582213178, 15044562, 534579490, 730476586, 679628990, 678697003, 296447618, 912762723, 729741972, 696753037, 217482338, 93457354, 492148678, 36946207, 262908471, 50351123, 379924770, 742455512, 672304890, 813141155, 822840253, 718594880, 906640241, 869535006, 735444687, 256466882, 451059475, 748726971, 822444669, 437329438, 242095099, 398785190, 626606952, 880796788, 102174826, 55699001, 858937823, 697641608, 869234957, 493994804, 448436455, 285619963, 851817035, 17454073, 561458303, 578920713, 266947055, 850750970, 657302347, 504082045, 982914283, 486237371, 692435596, 21691887, 847850076, 355590112, 768625070, 542871482, 641842932, 503248446, 787801373, 512667422, 305502623, 65116718, 240027979, 172427262, 554879661, 321167336, 710386489, 524103636, 94479006, 619183263, 558120057, 981033804, 610369181, 409587197, 2643337, 624395393, 237808779, 84941309, 254273490, 420705588, 713177643, 253239211, 742201686, 536438069, 466229646, 333842024, 123615042, 4487484, 137386111, 413156612, 791296861, 584494316, 595582372, 579669498, 725958920, 211884104, 818003042, 425295898, 945664748, 828558821, 122701055, 22534369, 124193780, 744796654, 227344289, 379099261, 859035177, 980698695, 793733818, 776168519, 38696041, 465176859, 881919644, 857576249, 339965922, 810054465, 943923787, 152795710, 456064474, 819522317, 528420892, 666026248, 437245863, 567501968, 623361091, 755384535, 751660585, 295245071, 863609395, 505726489, 875201036, 767383424, 272199728, 803267122, 98652464, 319159157, 86380222, 666094995, 801876866, 530736373, 285510070, 888627018, 647977848, 425165558, 66122548, 610281885, 961960924, 35985070, 260146608, 625796124, 274183523, 460697446, 806023856, 518501507, 909793917, 817146491, 129225500, 173920705, 166789642, 5697673, 692162480, 105998991, 975968246, 863414406, 219049945, 879854032, 859421466, 620585246, 946237497, 194093154, 967628204, 198523873, 755755008, 760829822, 140138712, 647088632, 679413832, 415187021, 487649503, 864080262, 197539354, 146340971, 464939924, 417610885, 477803934, 164850227, 524206470, 919380887, 446637257, 672801039, 154342559, 485634062, 850445620, 177577631, 794786761, 308007917, 46559214, 904361180, 711138489, 261216907, 308203611, 50977488, 92308594, 50877689, 623416675, 734823783, 583463985, 318985030, 262343076, 686867641, 214036029, 733072097, 10790128, 18431929, 30278750, 806435133, 334585463, 558020596, 172154631, 314905589, 553989218, 527067383, 327113579, 626900952, 996829303, 53092262, 546700873, 350134169, 867205694, 567296097, 108810905, 867799549, 571819267, 750641533, 609580180, 600949194, 128069508, 812899267, 132086891, 398880872, 259497327, 490810599, 770102961, 607969376, 386548737, 559686992, 701899547, 147697964, 962974666, 358469968, 579739094, 792194271, 948383633, 452269485, 985322053, 142906630, 765261933, 865442247, 24901070, 640659014, 504691564, 790868868, 992887705, 760772280, 315275793, 917638227, 443963330, 315416964, 984636260, 210552879, 186340747, 52683343, 729074118, 885026984, 467015727, 389154236, 598674913, 969147039, 128941910, 955427017, 850772017, 853709361, 853788884, 248132766, 164319912, 198619024, 979662378, 436815703, 44052492, 158522164, 115678325, 289476857, 928547587, 278400954, 737207579, 687210440, 376646790, 905337313, 58375312, 997081779, 478790489, 703566907, 713087316, 990195666, 774898736, 490447442, 110802942, 427942982, 753808811, 159291104, 428572734, 225976229, 595375390, 33739544, 237287026, 15578407, 381971012, 879003906, 499979648, 134278446, 643565016, 415772766, 197802205, 772501369, 986681234, 53436377, 815802431, 575245579, 617463663, 595129260, 464743847, 241535983, 464150514, 613279072, 854697665, 872988690, 117835288, 579736369, 385286870, 204761363, 352311711, 584172768, 911540923, 292009458, 368532307, 335585471, 163428706, 957334162, 994517833, 343714002, 632647804, 426074254, 933301929, 121853386, 204151790, 490337109, 395767658, 947739954, 291566013, 461842897, 686541112, 766270816, 677369475, 907975750, 480727609, 759790687, 603288470, 108468380, 514784459, 522097576, 860968484, 743724872, 284677181, 210425043, 949832395, 434593387, 826836423, 77631270, 117119590, 43493942, 146053109, 45910927, 795428421, 208534855, 889096486, 543306162, 846918791, 982388772, 658743735, 485100369, 640794371, 892534121, 193228972, 778999006, 626782503, 24339705, 795102871, 486788647, 107148568, 809910204, 450651807, 846503712, 281689811, 460913754, 971582374, 982094448, 359748164, 361347216, 213657578, 264086190, 488947884, 918472908, 511156846, 214306093, 479903089, 143185370, 610865113, 402180758, 921787002, 43024351, 759123160, 537754344, 292111431, 506181710, 286189028, 567517058, 273585795, 940286329, 10106395, 428571152, 791145058, 428521519, 612196749, 821267290, 836764783, 609374928, 748047115, 979479227, 92815257, 374124676, 321710124, 858452273, 826167549, 36046994, 660161281, 848021851, 433405237, 697456703, 954151442, 599571067, 347003598, 847409358, 741328632, 740193393, 565362890, 287346041, 147714291, 92820230, 497586491, 970288572, 515845684, 705275652, 273621821, 968403927, 949522721, 218878904, 525913345, 452777395, 301496059, 586249209, 119832041, 477106805, 488249771, 554885902, 228769972, 107036995, 638002875, 818909983, 761635848, 800705331, 760804097, 598259239, 787664303, 629391802, 965234172, 672311055, 985661675, 730022316, 954134178, 777683468, 32948385, 435569150, 948983862, 293633720, 966842697, 44490851, 963102251, 5530628, 281998003, 39781547, 931755424, 892491908, 827501235, 608793493, 541589857, 338762665, 595018146, 461801316, 417550578, 381532550, 815551030, 960905651, 48715402, 403424330, 762359507, 724214981, 649199432, 979581839, 7203577, 627850561, 608900496, 764800233, 387571659, 350046958, 777951948, 163429228, 75104166, 950559473, 743295534, 783062783, 13111562, 463247889, 67827862, 893705265, 225086578, 127098193, 609092993, 855404163, 327688588, 948794934, 146415559, 546140882, 892678984, 327458964, 185495478, 748891236, 249156857, 394991679, 947347131, 874062074, 380203769, 613901374, 990778423, 348966526, 263785199, 909423663, 573164793, 310603176, 859908336, 942366588, 488452684, 93794758, 524099841, 970003024, 948272119, 468627352, 255606759, 554038101, 550023752, 517040308, 273739246, 922669505, 23314301, 14432124, 490992451, 347757039, 925284073, 8702128, 663327398, 801555597, 728913431, 899381411, 509882528, 415005125, 370480637, 878997511, 339510868, 906470205, 282441231, 392518141, 217105358, 766295353, 258908695, 641772634, 252884089, 148979641, 549358905, 253364798, 160943825, 200742256, 694078561, 223114845, 458534977, 184209330, 844710312, 527102435, 375936024, 114151588, 963120924, 471696978, 845387354, 109473728, 714496618, 157905721, 752293952, 763467468, 160173275, 286153055, 1744220, 682813564, 392465296, 715598991, 837694317, 236812743, 703669606, 877107484, 76131514, 435571174, 389254202, 301479527, 660551216, 446001073, 101796176, 536550332, 615538795, 419039581, 590409205, 899650903, 713042342, 886595938, 239906313, 105869726, 828981619, 275208032, 966716375, 360868619, 690314537, 792916093, 628361306, 994715377, 248936758, 753973278, 408763765, 561485140, 729232605, 69602126, 36748919, 536236941, 970469235, 562384686, 195484833, 25727379, 518256100, 417657900, 756898001, 541832323, 639693380, 158081324, 284725318, 850251684, 178003424, 309094230, 220203338, 345791763, 394039430, 65506372, 246819454, 125203455, 41282677, 958068191, 69915317, 906787283, 122044649, 468304082, 689266701, 250838533, 414489138, 681402407, 591771270, 192606812, 701962951, 449502946, 501848629, 699787899, 99269160, 471608708, 653780855, 46446246, 255374343, 56963223, 962073022, 235992686, 937521035, 701262678, 882391351, 591601799, 445584597, 319006718, 282156229, 437893400, 974834152, 599766848, 839449099, 720124989, 662050329, 40326444, 916771397, 961006186, 905140165, 545602186, 699564633, 845000798, 747247918, 366710351, 161758287, 573917182, 364800892, 910088084, 888982550, 442671375, 148343718, 308722439, 643836788, 627858546, 750666782, 928829476, 598749756, 93973621, 994820955, 858615997, 184911923, 245518054, 827780577, 90351422, 474977486, 236147693, 189699127, 467145218, 557954164, 275055779, 315287529, 360179944, 994777943, 201825341, 786731690, 867328983, 482175367, 142212789, 806897413, 221329256, 619055755, 889929699, 669302880, 251626356, 612798327, 908526498, 405448579, 292819477, 817534760, 603054471, 125293214, 803743527, 731015701, 575895960, 436478815, 696864388, 585661123, 508443987, 785844007, 296596315, 609958362, 120565167, 870546162, 712608181, 58218937, 952635303, 337097460, 773845958, 789201926, 893043944, 18293000, 230143856, 492134298, 336056163, 794415523, 489860715, 250428805, 188053535, 376841187, 795814422, 787946839, 458842171, 999848582, 728550114, 785370790, 709113941, 322799677, 856207104, 254542257, 934504297, 177198964, 240109312, 666080198, 397467436, 585874543, 235932261, 955402552, 695666140, 547245632, 180097327, 255684327, 839990199, 434868962, 448444165, 475910658, 156763399, 798911760, 985138427, 907775911, 695022348, 982484791, 95709742, 843923544, 751277780, 37699628, 322516341, 649031945, 917093031, 323609568, 779739125, 869642004, 777322162, 468771876, 473678609, 880362192, 932815173, 957774165, 534378529, 179495191, 22808350, 85733452, 11046935, 986175195, 693002782, 999341866, 900881169, 592384694, 765667290, 570088791, 493537286, 834963225, 271153122, 532823998, 797245270, 696376739, 629129892, 942245938, 723915809, 525117021, 552350384, 558677534, 968516714, 831772406, 824657141, 861150509, 387355437, 791808832, 413073389, 228555939, 983425061, 199675369, 940734540, 853662643, 183791387, 988924532, 864273777, 178154920, 660602972, 177031318, 837342163, 531578517, 594675546, 168725401, 184991535, 538494571, 623610590, 263033016, 908979287, 261580728, 709738285, 125410599, 942950529, 166911173, 628809167, 935055564, 576922812, 689133474, 636804702, 536214357, 598234392, 432725637, 21027434, 406409004, 115663796, 932310162, 934192846, 310633903, 571153820, 281494900, 666938924, 91026297, 37057537, 152114182, 144303031, 96955832, 371741997, 294832969, 399411093, 345427301, 190211843, 339280089, 735499177, 518620767, 222828509, 246451949, 317445747, 111811888, 455903636, 209303805, 555780751, 959511613, 227562927, 431252521, 910078638, 197891032, 703329125, 99465650, 372461797, 865973875, 174516089, 597998504, 89838435, 799332312, 544720214, 815445212, 277369312, 39028208, 620579755, 827014357, 936531054, 506644022, 385085105, 449752844, 3498825, 965604175, 619262100, 239909761, 49091583, 596200924, 856510728, 321789371, 146353041, 528563327, 736623978, 422314115, 377329993, 554252832, 495872863, 386378316, 571645788, 38906000, 802897334, 428338995, 153223103, 93184494, 188197525, 75504798, 309037291, 527921943, 70860296, 127631018, 591130667, 156310445, 939615065, 337432235, 245816624, 666986985, 629449049, 178875859, 844735119, 154046653, 570109872, 26264743, 50415239, 878952226, 285960938, 94095629, 807705466, 228955389, 105749343, 748607534, 744217036, 367763130, 887239556, 308518985, 717051006, 930075610, 739617429, 526511080, 51924533, 255766095, 460783310, 397532424, 119275914, 564658145, 689653680, 903029054, 372143939, 24274661, 267822316, 740594463, 442605735, 579730747, 18482465, 577464496, 515366032, 460352774, 918203754, 492722332, 208870442, 856982696, 727596396, 220496143, 262069838, 244403754, 814967355, 540882349, 50292308, 860853695, 594462494, 489947984, 251358460, 582173206, 37901347, 200056601, 970385993, 816677957, 507470881, 94316172, 18341927, 771552665, 979813421, 664001, 847839380, 148814762, 528411786, 383815187, 742905413, 171873472, 60845554, 156951933, 786752353, 410156785, 888716090, 951581579, 496424798, 899911542, 366247900, 209124630, 434595671, 850917812, 487889643, 635025129, 280483182, 535275610, 562132343, 659897645, 528872326, 709174538, 792126436, 98561214, 916236031, 366757735, 312103273, 55344810, 656202464, 221909251, 677157991, 481015176, 184402326, 378592034, 120311695, 985079247, 623275346, 98470338, 813057353, 691733963, 686774211, 409819391, 636988774, 915291066, 272860305, 118462331, 764682287, 939827077, 790743069, 937545737, 981225064, 827944940, 671413140, 648415610, 963613943, 515015286, 341670932, 462723359, 90255805, 336878776, 113624211, 237453631, 150590520, 671411348, 484973019, 665468182, 679332624, 915100415, 455752169, 601357740, 671842399, 913133548, 904494386, 108535558, 114350211, 428275258, 360406072, 412470655, 42550248, 551032869, 697368613, 773651133, 751659914, 836238273, 595423465, 927663859, 55232866, 913923270, 589174804, 54883188, 425738316, 658429265, 637679122, 459672732, 781762306, 189174209, 263081481, 327050156, 849435710, 582941012, 806170530, 556714581, 38278745, 880903445, 43777284, 26480594, 77176657, 872172260, 409617160, 462926168, 605680298, 272983208, 701317286, 842721158, 228909924, 466225222, 654246797, 352967576, 916180026, 128742363, 55524326, 997281430, 842432404, 184296953, 456306394, 248063823, 984164170, 810161391, 911829156, 131917008, 666692862, 102573244, 837081861, 625180137, 480440139, 887920475, 824253132, 186519345, 750584539, 117312064, 157889359, 146170965, 687562786, 601238612, 364648192, 540516027, 857090398, 330766043, 69186680, 79384237, 461830672, 531656911, 93688875, 312963825, 666393323, 900945238, 639133059, 954745682, 697345281, 494948385, 413276890, 870220875, 24118096, 840276466, 751021153, 827766255, 297421245, 402486250, 953475087, 268274659, 826370096, 767829329, 248168246, 346969893, 383519818, 523589090, 71922831, 718177178, 165957518, 890668957, 757647551, 213731464, 167687987, 254460365, 705393061, 97677515, 786757658, 63135809, 814995321, 416609268, 938799741, 893720225, 977295511, 909405932, 871443976, 912642625, 983659710, 353818660, 20885610, 14500702, 939038570, 817533906, 415886387, 8379390, 46981471, 827005207, 562508374, 128389717, 92801746, 552087438, 975768382, 837417914, 367685911, 890799529, 153166444, 888730013, 625541902, 967200827, 890012892, 170302432, 836446036, 269125554, 541823810, 360884673, 303371420, 487665522, 788711370, 516970573, 833555740, 685109317, 147088220, 512215198, 212340242, 896340754, 505007122, 845187251, 952464229, 406349379, 657744762, 366867217, 366676183, 665480463, 91216701, 255618856, 349032497, 818755310, 786950683, 365577139, 364975737, 336124780, 93718343, 897028332, 709361745, 191480447, 190800099, 728116797, 637373537, 281863179, 465448315, 440590270, 908109226, 862960172, 824977431, 668024892, 11814378, 117988818, 71094667, 859023035, 721838891, 535291517, 18760939, 925410351, 760407583, 767157856, 380041095, 574448090, 660069030, 901052721, 46165171, 119598209, 161042570, 575704956, 981341941, 262571736, 231466527, 336056740, 857161546, 226741582, 403691529, 82623285, 956232638, 823972997, 932378518, 257428070, 109105844, 851567191, 795708800, 268052043, 238648743, 424041618, 128470842, 215007344, 358840599, 833971108, 402757642, 531658501, 466348903, 733668203, 104941219, 203213954, 981088214, 148176953, 40537162, 366079613, 982592605, 743846084, 800746353, 968014295, 321696753, 729890342, 786504499, 725176297, 23149070, 226887877, 74857764, 862567435, 272867065, 979396444, 645705294, 789426164, 562215088, 893191231, 211584325, 199203434, 306292220, 48194724, 794512346, 441337356, 443197833, 368116708, 547780135, 173924595, 477172608, 632307418, 916053650, 432137166, 689442533, 408203317, 155610902, 464327457, 614021237, 878524877, 33579193, 117224476, 892761490, 863260225, 112468681, 380770231, 499859295, 476696915, 254179531, 969308787, 542135196, 742205000, 855922074, 251889321, 407874725, 276913485, 886184574, 772249190, 483926119, 959764088, 158779416, 874368858, 859081445, 959236103, 261186877, 352252187, 282847745, 156982510, 269539761, 768698703, 419889906, 673849980, 265513110, 8479126, 554911967, 961164672, 646963059, 566174323, 5670503, 322477825, 678703458, 27609643, 861422686, 370800130, 501869099, 717730523, 741907339, 307324224, 599186164, 656723260, 339750279, 943071246, 324282495, 233261105, 519105879, 689628950, 243027005, 262272141, 292042485, 861113186, 939990807, 861279673, 204414555, 978572134, 162618486, 782464885, 548625556, 187276117, 651459183, 152997823, 146396387, 495982107, 484867367, 216487588, 556307439, 644217558, 63569379, 295333412, 697236900, 261362274, 181956771, 635038781, 627225095, 685141589, 864630658, 45092446, 999054853, 116444693, 756529742, 155478581, 925366968, 44486557, 500874919, 771237195, 926412134, 918891891, 359415679, 33928169, 952446169, 186962216, 52824337, 932684209, 767120773, 127529182, 674814898, 511428768, 62615523, 68787559, 805828800, 968012615, 242941973, 798575370, 960827950, 975670317, 915998864, 662873708, 241564021, 773689917, 970089566, 73199797, 202623504, 351408297, 974077857, 891128416, 461721780, 569191519, 776959459, 37006275, 852718264, 709901848, 225135782, 260149379, 570822304, 957890512, 194446407, 903303584, 67563985, 638625060, 720985513, 831573495, 983857838, 446126543, 847062977, 830292105, 832968395, 508544066, 398084500, 943199730, 829623218, 249019520, 834870992, 106650162, 27789025, 749138451, 277046484, 537570544, 847360719, 495093020, 860861606, 642870342, 45573748, 303300600, 657514087, 30956911, 648556256, 522851039, 714002119, 272846537, 112685271, 625363540, 911574829, 918347353, 419540843, 557533353, 44972402, 847932372, 721317211, 547415063, 789349042, 413082117, 251641175, 193402135, 255805207, 337985181, 318319764, 546261281, 409556801, 406313796, 627041195, 996343086, 39611481, 421193386, 785045551, 213851922, 967234112, 89077267, 616983388, 3773368, 609214298, 468698122, 231609505, 97734054, 64166843, 767248957, 235140421, 452751481, 921047683, 709304556, 636418291, 691176119, 890092855, 386644700, 245074099, 675434907, 621977420, 982814134, 652833369, 626704190, 482160240, 275838376, 395448132, 132176162, 820107301, 171088557, 98836158, 940583720, 813571190, 929441391, 943467276, 135206696, 648408194, 935783642, 549748176, 952234903, 487668988, 951971432, 374345302, 748595385, 962732076, 940729540, 543557951, 244075159, 656419948, 414568447, 88922990, 844658035, 787340213, 60936166, 96687227, 591894232, 724561804, 617273127, 11238303, 341643748, 124853720, 531946893, 770951509, 145682731, 98382749, 709871266, 817187760, 903314435, 690819144, 795317068, 929612300, 55513530, 705749530, 643070112, 902325136, 214932489, 369625647, 594315859, 982288051, 788655640, 447977528, 939448197, 832606544, 873203538, 567092262, 586843465, 393973106, 435394330, 387698062, 921616313, 961964844, 487039174, 614204191, 784662893, 180813243, 626120194, 472016793, 102128911, 248699959, 136509081, 211121576, 954204299, 155966607, 280210850, 268801213, 109761827, 633868248, 176476691, 196674696, 477363157, 890883173, 490873885, 102775485, 382456808, 119772999, 186779240, 926437373, 367929859, 14159412, 43581315, 61359272, 585669348, 700257326, 358942908, 915532928, 344913695, 160919637, 770148190, 271568769, 330718384, 264065897, 941263047, 376807114, 436883639, 336053950, 384932223, 272622141, 407948117, 751956632, 886662202, 918461294, 545989394, 883722564, 405715273, 632482044, 158771520, 875645574, 93427730, 792320595, 358955457, 765285412, 291409924, 656493628, 803079680, 382861371, 749960884, 72640820, 81965091, 203556074, 539492343, 351222445, 534078775, 823852254, 515146862, 506868892, 213679791, 199759133, 671757574, 635210619, 767306000, 15403660, 402467896, 505800467, 194874199, 953589136, 236829591, 61083567, 165896366, 239531590, 167501570, 936090133, 239750151, 314700075, 942263044, 113828633, 329619579, 998568293, 55703965, 193189627, 554242377, 521635427, 515370226, 566463395, 325225572, 591636426, 949416005, 187259793, 688202124, 305751023, 915315965, 431619358, 340914357, 850374384, 158072945, 91684273, 711204167, 795809854, 460173006, 305699126, 486280089, 801172136, 991885984, 548782379, 839454545, 256748325, 412784942, 94389367, 394169502, 483914821, 406259611, 813895828, 204190404, 324187793, 385486224, 475471060, 43416629, 333514452, 792729557, 860632366, 49531629, 626714512, 145480179, 359666641, 410016745, 327935139, 993613310, 770008232, 152815399, 662502666, 253950185, 90173315, 814566129, 161860074, 418479209, 63930281, 148825195, 35674671, 782414604, 438970295, 108556674, 59843515, 734725666, 620931492, 646262018, 697171977, 217269910, 656550200, 818806203, 268824408, 8474563, 272907577, 96090391, 953236237, 236838277, 596210925, 77410836, 662923167, 411282102, 486448412, 110543791, 175980987, 54327035, 78830802, 377248896, 568473805, 681473685, 33956634, 167569030, 773400129, 633013727, 602679081, 462523979, 101421515, 57940555, 889180455, 754086926, 481997772, 750366456, 774782169, 691174902, 849160789, 350329390, 206397828, 961626101, 379536281, 267670140, 153106319, 52623145, 160660366, 685583425, 945393206, 647173761, 751398303, 955235871, 108958883, 434417068, 944155853, 316718133, 886614115, 745202362, 792291001, 733477643, 7446058, 993953383, 538567717, 70290806, 243678558, 267906874, 864077462, 83154497, 394714205, 165844374, 615334811, 531501207, 537762400, 798648393, 864328576, 974191495, 277230755, 42123905, 700080911, 516313981, 546491705, 247395559, 283737045, 476859425, 434867396, 557007691, 743965086, 903013477, 585180240, 54505935, 512385391, 12096437, 132189862, 397156742, 818679204, 607691559, 397744287, 186832066, 492947316, 686267562, 769985417, 666628992, 493286612, 435362729, 930899475, 358007763, 231362768, 971399361, 48367032, 127232585, 703446172, 258282617, 501478459, 29036987, 528325790, 59757032, 415530378, 658268730, 301704759, 48875695, 738202222, 529016981, 555374710, 771829543, 470792351, 807940385, 913322472, 772266715, 280452003, 231300136, 923367228, 634080044, 729682256, 836782944, 902791147, 704913680, 2724727, 917744564, 75896877, 932960585, 762329664, 855943790, 749359946, 829884424, 973267975, 929802373, 502894385, 746204739, 762616034, 719931543, 139501594, 3508598, 194077452, 797887102, 650847794, 739668485, 773561557, 48453424, 320238308, 38641742, 706004002, 59431604, 793292229, 402612841, 983978216, 504440820, 428988800, 34530042, 61338045, 792950350, 533959037, 596669937, 289126890, 960358474, 525817876, 470883967, 387221796, 947531419, 27623637, 714666440, 196022765, 346039414, 821953864, 927642777, 483754959, 231974217, 776714170, 244213818, 718746302, 753658353, 121456546, 626878074, 158227702, 918024353, 515141399, 574210215, 830993983, 669779324, 416984784, 794107836, 139847676, 157356274, 137897627, 743433123, 571258579, 528342992, 254653867, 50038665, 709836829, 324776079, 641125554, 707510538, 789910096, 168370813, 9640651, 84873633, 250591496, 428092888, 853180283, 854174751, 792606033, 429955931, 978186716, 572039122, 730791683, 88381369, 198552003, 130064011, 823723726, 355809721, 969631350, 714721764, 101976996, 847197322, 549129392, 832928169, 757125046, 554242321, 361750320, 698346617, 707087165, 111766664, 776053079, 875650212, 24458438, 167043736, 334926090, 994425975, 259033137, 786167014, 796640385, 822140452, 999084005, 627893624, 323988209, 743306118, 383660918, 492432683, 62194765, 599577230, 427807319, 248464839, 561492110, 484357419, 98593697, 160644528, 919393575, 556292720, 151595207, 210689224, 738895005, 370115874, 902601398, 226366784, 797684452, 760255976, 503569916, 540719892, 977645524, 515842143, 79034817, 369758359, 898393350, 476387300, 557201398, 349139258, 463842733, 612062883, 134588453, 204637905, 328990067, 939580428, 204265818, 852761375, 779508802, 302921373, 629761175, 211743213, 506996192, 873326560, 327336020, 818884251, 759491823, 924540351, 357816535, 454821164, 322971460, 548071875, 391562209, 550300833, 618996816, 711657281, 608964959, 266613165, 386719253, 438123058, 745873058, 872258581, 837423442, 472028669, 420490156, 277635162, 754145203, 789522220, 306986679, 262318267, 627460309, 416615681, 625716391, 126720818, 609759490, 893411837, 148361421, 880112967, 594318063, 430066204, 97842706, 271300412, 799347767, 714681065, 415510894, 786901188, 684091592, 91686852, 364207890, 22173944, 778267045, 113100142, 265385640, 285657470, 544606864, 104605477, 749864827, 359170259, 61560595, 157434218, 706562571, 757862060, 791975396, 385788439, 617874200, 237701454, 97241811, 382713908, 215283118, 77661215, 309905954, 818040562, 856169207, 818642181, 13695630, 690947289, 235724646, 846360226, 744436899, 503659169, 771302557, 131098620, 811092125, 832918236, 322356378, 91957507, 639083687, 582152001, 971633372, 707951903, 174975575, 223790355, 194521824, 165932275, 936242326, 527843881, 531624613, 496052845, 321894569, 589808889, 702137874, 586844947, 256836499, 4431296, 334636829, 814862722, 545543062, 689377420, 646086622, 257583321, 783407090, 945226109, 325070489, 964775123, 187994594, 877814040, 677586178, 272003927, 783726505, 348234195, 836555818, 449726375, 74332256, 679628939, 249936503, 678722008, 498265505, 935148297, 930656540, 707679332, 349415504, 382296974, 93662040, 502245759, 332747488, 481146901, 230403781, 577066925, 234515980, 820735427, 692875711, 381776567, 530797133, 334667880, 466192539, 475497375, 253643847, 955389975, 749984526, 315637740, 435303172, 951719730, 667303813, 602918116, 26773178, 784932245, 974981266, 839088284, 319020465, 625697464, 165641587, 637579797, 259731244, 206858392, 498224760, 415470169, 418226468, 907410758, 317334870, 299245048, 508869043, 787663086, 63869370, 697191906, 353194633, 322935020, 758259486, 500888592, 53736544, 702029550, 505575895, 991498992, 713077, 294748376, 313824798, 182394435, 832526141, 886175506, 795288656, 33919358, 1536113, 743428555, 223938059, 151204140, 664526733, 267281399, 628457989, 850932762, 951711673, 311161317, 418033041, 250076132, 88802228, 734506898, 942972848, 119999925, 313541184, 197083928, 439345901, 508636079, 422204443, 759354959, 571801441, 964802207, 714241211, 243347197, 500876138, 599345018, 368701750, 867446919, 228119046, 567321007, 21800865, 794155346, 523529414, 992407171, 408145747, 488753379, 187536944, 681963031, 172127025, 47259481, 162811864, 765745872, 549854413, 840037097, 297791563, 102197010, 528318790, 216700014, 761934007, 330798707, 724502429, 320485279, 461894081, 31665275, 404047189, 462817069, 575748048, 569423536, 318527278, 534124406, 687442121, 498559003, 607880944, 497263964, 381026539, 431743111, 206637439, 423713759, 93531133, 294480361, 387346966, 961729230, 430813425, 475508457, 459944201, 219086159, 584271028, 413116848, 977479265, 44390779, 561653067, 562477527, 136953273, 300778506, 950814428, 547718722, 878288498, 849705115, 452392251, 714746079, 388357013, 546512155, 4308185, 561209140, 120710660, 196329951, 729581988, 185277217, 882914704, 725764092, 31863502, 774989961, 621123455, 616174306, 595488706, 276084065, 709468400, 91219478, 645938447, 961665660, 887875732, 53736202, 185414205, 707264867, 981745483, 534199859, 783152211, 722123219, 966113168, 917338093, 299505020, 168645973, 218731404, 291842333, 867391713, 238218489, 362012309, 293695441, 810087, 836294922, 625346445, 179662733, 240611409, 37150764, 397725266, 467481000, 455778930, 349283464, 952565992, 364118260, 721357493, 266570717, 653969682, 8458024, 531104869, 477823560, 993662818, 219868002, 50523918, 5896769, 457885880, 451375892, 890557078, 189364362, 78057226, 188692105, 719048825, 592609392, 497773597, 860549414, 342548008, 604640991, 132976356, 89926940, 143871210, 288226843, 526314683, 933578615, 544411763, 78532564, 599519934, 963083915, 602867376, 162454587, 331079806, 220752104, 82755218, 275941742, 771461506, 643733036, 591227862, 119391887, 544034553, 97232042, 475061417, 543258573, 661280242, 555823788, 886704581, 321196211, 244777811, 431779283, 105493793, 400155216, 481995964, 674127476, 142319802, 321527309, 121039883, 142587758, 736440365, 381830788, 844062427, 923958619, 405818852, 800584753, 708405862, 683422002, 76724584, 540444076, 496352681, 447277344, 969939796, 351846328, 594773473, 14017251, 972572884, 258234279, 401061111, 232840509, 930094485, 654045887, 141125335, 379886992, 103983915, 252169613, 309077463, 597310093, 385457974, 62026605, 256303204, 748807458, 854118732, 868015995, 14560666, 519356460, 995442051, 544731232, 987146466, 56570999, 928346086, 411803945, 502133809, 83088823, 923281503, 256298091, 784966666, 289706101, 468534414, 532382440, 810945208, 320645668, 752942066, 670817133, 532460272, 629326651, 39234795, 81861863, 429402356, 522509995, 489795846, 855597205, 756291701, 911779483, 764156081, 78888277, 319323256, 237132454, 388307167, 157211699, 437142062, 745149834, 201250390, 35264884, 62441897, 485569149, 517924258, 290885409, 878468681, 274984033, 632071341, 388543485, 260441800, 901202618, 930118765, 850012014, 329130860, 30949501, 15829433, 549327931, 514131653, 735107911, 747271001, 467062840, 827452686, 334262117, 376756766, 998143346, 330420055, 162484971, 840384451, 336851298, 880704862, 906845396, 489727670, 225330331, 379023679, 755420990, 667118872, 492640914, 999191035, 506046258, 647995516, 779255337, 252368621, 278567057, 800751232, 435856993, 73045769, 49731283, 492706057, 653382841, 284399892, 532871037, 980598617, 815636377, 815123376, 765772026, 3881078, 132597347, 629529406, 595875897, 867408225, 573177768, 166222908, 452433108, 101690736, 632788398, 447078416, 271496450, 610292092, 46249616, 494123802, 750460178, 407088100, 656146554, 791386435, 558847094, 441376771, 688628972, 770499907, 623592871, 711404104, 993286976, 257057435, 623894614, 721453658, 908664429, 443794443, 761539387, 593458722, 835720197, 114175373, 394959772, 704745424, 548247144, 986197825, 203079570, 357777316, 790069769, 409938406, 411358812, 15573506, 422793430, 436379438, 378691924, 588825915, 449208598, 75027496, 382714589, 757483852, 233737283, 218513912, 478260706, 405379787, 787787834, 358454440, 845914255, 421639124, 321445188, 808509295, 162924376, 560548544, 271256989, 928553781, 137234995, 256508461, 569283611, 316896339, 304176288, 846536423, 637204306, 956887292, 613118785, 13990015, 306905177, 47383938, 487770598, 609489526, 507148284, 738397425, 460298362, 752038562, 431196102, 393650637, 624390391, 350692573, 336690094, 709048068, 926577211, 702656829, 336187177, 532373739, 639805086, 236601807, 26320501, 121847752, 100105887, 984825857, 815697351, 396675270, 972061744, 258535709, 949675072, 875228562, 80938071, 287119657, 893286093, 106022561, 732487296, 600715263, 150815844, 596179947, 843707600, 660028295, 328801109, 138656315, 19251133, 699832428, 731734584, 29443269, 373935200, 857532765, 17696615, 492309774, 523130236, 47801796, 718831138, 437838373, 801110383, 652536840, 751611289, 333052120, 359488473, 522920469, 518125172, 112276725, 737299353, 286777475, 461338803, 769337413, 906900519, 590545062, 82367193, 592035014, 548756622, 794300593, 353697958, 114574426, 34824746, 447115564, 802921221, 504852808, 40524671, 228586886, 865528262, 39948908, 802094117, 728628791, 284839101, 72568791, 63783720, 691345016, 724700894, 913977395, 196641200, 725903267, 799520170, 231432471, 437804600, 384091301, 935960505, 850912589, 835624502, 304740254, 910507050, 703955220, 189502304, 793848241, 263297903, 998433186, 475316247, 663379873, 744284921, 554711579, 438701678, 556605565, 891849374, 821639422, 193630279, 259409854, 65304049, 811774701, 689753472, 828219249, 958876802, 616714464, 501906136, 217775135, 463109013, 460067778, 253564140, 972913561, 147002277, 794537925, 321750719, 2787430, 934940334, 995315714, 199902346, 2713605, 57954386, 732365462, 62216328, 198939032, 969123703, 129371358, 56911360, 947163824, 454727072, 491846089, 939449160, 379008765, 146280196, 342813942, 178115465, 980702795, 770739917, 247618281, 610620137, 656138990, 977750735, 289670929, 925229137, 442181787, 348636539, 620868029, 763838500, 8616548, 23358274, 458408318, 493437528, 977926339, 414863259, 194295713, 671827829, 618704486, 550865121, 573515944, 879385370, 428093864, 389531436, 594093569, 682875091, 476900817, 681082142, 798332707, 142764350, 831533823, 54519096, 661893620, 23111595, 879575171, 358876959, 60023391, 324618527, 672781689, 886241692, 808326408, 608446536, 793082107, 633803101, 753055278, 273889854, 973474223, 631530069, 77346705, 822590832, 643070786, 860768209, 811459246, 459268894, 395095137, 144083445, 422562584, 921046534, 257388028, 12030565, 392743640, 197377818, 839903726, 687266488, 835997219, 861486678, 605003672, 928063525, 676529612, 265173590, 262287619, 520712311, 871098260, 641861373, 238817087, 926106258, 735790803, 453651368, 385989123, 14008520, 283582340, 167589501, 183185764, 127699197, 713848113, 874911695, 138691906, 655909606, 527183484, 489957314, 375983975, 272978391, 427816255, 168079813, 832538004, 53399065, 191723943, 23394827, 501262716, 357989828, 776309080, 934906860, 360052157, 471275402, 564785262, 945101948, 964191046, 189833401, 726541272, 139151635, 178670686, 607595038, 298949615, 481771341, 866688509, 829120448, 295858662, 527708000, 71163738, 322357707, 640340621, 558501132, 700489235, 918885126, 350869664, 160480129, 665316900, 259634327, 93259877, 558366789, 43249828, 979301198, 172694532, 968118452, 169970716, 647107844, 561385893, 859120519, 480486763, 935997880, 885908486, 669915323, 947862863, 272566277, 151466074, 360130957, 59568278, 640270760, 234125346, 953798118, 826502569, 770658992, 244861873, 595648826, 500333967, 765541923, 245553434, 849263538, 983229686, 788066683, 501510240, 592783074, 20347338, 288260588, 162415093, 363231987, 423369108, 665017607, 424830722, 57004407, 740421380, 958613632, 442671314, 257993776, 456856411, 106673140, 395868804, 228327043, 888763108, 226662094, 295522969, 361576263, 838610957, 352323190, 195763694, 228539601, 639412874, 856539050, 1914092, 795770193, 487293468, 286595507, 622720533, 215401647, 338605100, 982941575, 122127324, 28422993, 161402635, 985913551, 377956107, 197881662, 321180355, 944258833, 763699736, 536527390, 573101770, 176168714, 691000560, 901713011, 362133204, 408846109, 392200887, 774305670, 561321286, 96153755, 102757041, 402246266, 345072562, 451577143, 448130149, 810329670, 549397224, 608970000, 697183971, 756316459, 898981184, 154953319, 978801497, 966244848, 445459787, 86999685, 196027003, 131233854, 288833433, 524196741, 585574660, 737978349, 681899177, 155623667, 547549180, 301722717, 994334457, 756011519, 706993399, 502788873, 280622209, 580532431, 189235596, 407678614, 82452951, 305781911, 181968197, 474943516, 38205735, 21283714, 819579664, 880696459, 554987291, 590193715, 549347667, 892013219, 611319507, 645846846, 577991472, 20758167, 455569219, 887762260, 479103321, 386629416, 610758538, 433168929, 714138793, 591261684, 962638864, 225946952, 693217217, 211616980, 132750895, 817391385, 71682247, 451459684, 81642807, 314324771, 658239866, 310070005, 723356460, 374341233, 276206341, 528353074, 972319982, 869313108, 864012005, 225681643, 698363605, 669176736, 705572923, 662658958, 735257394, 221714683, 373354884, 464866373, 13694167, 486711165, 597131923, 343210277, 410432763, 479055010, 248360019, 165170531, 432422509, 914108089, 806953807, 764076622, 814690983, 487236340, 220412143, 231869426, 203936595, 606388762, 26597149, 189635041, 827309397, 614248261, 719628931, 507742606, 112581939, 763863098, 602397632, 328550449, 670302235, 829689395, 936650206, 200414658, 551101720, 347102432, 984403836, 245323200, 4244490, 24425824, 502670025, 81855834, 139797631, 25163179, 756784914, 466068409, 505952592, 25089475, 760583894, 710505344, 79600435, 926630068, 737800951, 238666290, 421801493, 657628338, 112334170, 898029062, 789494174, 792647541, 297122816, 315650356, 102507108, 556527954, 236352924, 859538463, 263735349, 522080392, 933864360, 589711212, 1513705, 709908648, 479086257, 914055927, 503026856, 486225820, 218357559, 252704776, 929170602, 313870716, 393939764, 945633539, 700388799, 774245675, 420288287, 789338080, 516410782, 888500080, 707297515, 631054214, 131694431, 671883564, 86090500, 257044514, 724409224, 714764930, 34244433, 621249245, 699099862, 523640328, 235015974, 48047820, 569673305, 627775934, 385688749, 693309742, 777753389, 55091964, 781293117, 481833923, 326574973, 336438009, 128191392, 345223079, 837491548, 842767095, 274211224, 905263540, 542706656, 407401204, 401817585, 112305716, 776999, 850016164, 599803361, 381387570, 593289432, 972008700, 926262403, 967366565, 918649594, 144848697, 176384462, 554631195, 504496670, 397653645, 487581427, 310335150, 907880821, 555123472, 137537924, 715370157, 986275130, 286900007, 564205184, 290814902, 560814532, 172634867, 534955086, 858148101, 67550427, 785861069, 57067181, 425455411, 697190818, 988088541, 287448484, 256474788, 233430584, 446646420, 880281893, 562028380, 754304196, 682346388, 197906421, 186881022, 219750331, 61313310, 714704185, 918330123, 549963771, 485316747, 276790042, 819745293, 113701558, 30485336, 311520474, 592583040, 876204812, 779716866, 72277808, 644612633, 898880325, 595267733, 354799565, 380795606, 982828695, 699065825, 655492324, 533467162, 234322979, 301127157, 622828043, 485368313, 395724573, 321251085, 689656609, 190171903, 660575643, 620825667, 958894393, 457535912, 77039022, 758393976, 837287101, 816184624, 275941976, 167887912, 243281731, 238600721, 734546589, 167993238, 604794876, 212582538, 375497055, 230093926, 652983260, 184244462, 70474607, 720305604, 398313672, 479717993, 836350476, 158837925, 146703121, 294042781, 609871745, 854040052, 903194688, 232955929, 723370454, 74388020, 485635040, 879026846, 619241739, 672954602, 728102826, 706493977, 656510650, 326208025, 576241956, 784544752, 37244995, 61733380, 38059215, 134072525, 633051489, 374293360, 305475948, 324936577, 987747598, 849815120, 847180269, 592937556, 150022816, 589564535, 933286454, 825308117, 169365192, 567604981, 256337590, 194315774, 725799311, 160476568, 147153212, 131677635, 418392707, 452822883, 945778072, 150855428, 763856521, 454936656, 785203207, 877669299, 549593244, 382925952, 988679098, 987274777, 746837238, 46889174, 181271288, 773526620, 422995045, 590303664, 793598170, 63871612, 234726494, 941090483, 260756591, 882431860, 562485783, 468576187, 688472585, 791767854, 899721505, 610497882, 340848870, 40592697, 606799810, 256367847, 807808336, 611936445, 936680471, 521438525, 734794861, 31431253, 270586428, 90631505, 239665376, 844101084, 58830068, 521035360, 498747685, 289648094, 310072436, 984869059, 955506802, 589762050, 11222082, 806040546, 571758842, 615694375, 78426551, 907966767, 291840037, 403141798, 425302627, 526199131, 565822236, 994892092, 640315550, 92256621, 318414169, 326810268, 227489084, 24170652, 523315621, 971894767, 963073712, 604236857, 945831438, 491936696, 22649341, 567018357, 477761763, 800254556, 43657487, 627364179, 288261009, 369552339, 547334134, 405847698, 443955098, 975845079, 910644949, 999738685, 987765023, 593693680, 345656605, 249885851, 718460930, 332330690, 58712455, 84271882, 463709718, 993892610, 58344128, 57231459, 516854903, 100094870, 20708404, 905364508, 603330148, 92090524, 182645523, 779410714, 504442635, 84878864, 331301476, 438903424, 651975458, 921769120, 592965210, 134127188, 35171500, 583051731, 247458831, 372465525, 811292032, 486879449, 268642871, 228010225, 423192863, 314829153, 279469006, 615865110, 935861081, 526557173, 997762323, 842716709, 408226046, 676426831, 664661724, 296323437, 218655061, 254983360, 439694851, 573884253, 944662124, 166128772, 549713408, 480414792, 832635300, 48691139, 160974928, 959143297, 302209319, 888638166, 44761464, 556930727, 409458811, 533194838, 600746939, 955946677, 684845108, 520048837, 843993864, 532734759, 952634567, 44555795, 198002898, 835327312, 491594463, 725018745, 700163652, 554279876, 642550874, 926034376, 760170055, 289562261, 833176140, 110740752, 288140854, 165626202, 9289607, 579972425, 412479310, 959907525, 564649145, 268551318, 61057998, 141715369, 952342109, 646061793, 628117854, 926325658, 803833908, 361704332, 88517126, 126114305, 473335083, 450146379, 838148237, 998993970, 322171808, 558766985, 839333484, 556165876, 682747431, 501740220, 167364522, 161662866, 807870614, 578281109, 631161690, 207675982, 180379234, 109864333, 552507299, 675626416, 693517171, 223696696, 711284524, 262848298, 472146029, 216083248, 283104828, 333290796, 506693663, 502573229, 866823341, 172459806, 520566740, 778539693, 30556395, 34039073, 107145829, 832739325, 38609259, 86638367, 615468907, 187353513, 150358261, 879457890, 878055266, 231425417, 236001389, 251809669, 193225940, 741109702, 968820513, 348086364, 793882596, 773849528, 846534549, 268718985, 714455157, 768789426, 813993609, 411042173, 508493618, 264763893, 368894515, 361483719, 336647588, 652985450, 828763725, 662582359, 405383289, 318474922, 447893897, 132693730, 902114365, 678690192, 727717873, 255916570, 71468668, 275731176, 262160671, 443161835, 831086388, 573164950, 884537970, 112200609, 309308491, 65241415, 330018152, 217175387, 972378697, 880394309, 957243120, 25107699, 388299639, 820751953, 768174286, 140397521, 488896480, 218914087, 397631083, 270631267, 794729702, 145948869, 465285547, 551523090, 982887847, 589948247, 382453617, 957620179, 553790003, 441943002, 851982963, 170791995, 225472834, 475858018, 877824558, 927597438, 451448885, 356236765, 265347796, 810674087, 650323955, 505747681, 180450287, 346794061, 788216729, 160686243, 7821874, 512947667, 134783075, 141906604, 524828532, 625173937, 870716924, 646358630, 493990322, 537388983, 545738540, 993863330, 900758379, 104415708, 732821808, 840736687, 950828962, 779849936, 956752550, 823162823, 260636775, 666282231, 86843532, 126274048, 234173332, 749723202, 238990309, 780482801, 500625853, 895729117, 481046274, 77522751, 213475276, 259158350, 975262143, 645774731, 892883642, 522845233, 142714201, 76757466, 24411623, 845164028, 998931629, 878603870, 207607529, 111257186, 55433525, 498744626, 364110299, 992352192, 269095361, 525708017, 994710669, 180249306, 206993647, 169537568, 242991097, 193578484, 47271512, 707227707, 919703096, 271432081, 979637061, 354280569, 270343681, 656109288, 306448422, 986744492, 324953277, 562201763, 22775593, 582277232, 611253657, 166357338, 205478699, 767400141, 809326826, 13775249, 776889404, 326686326, 14842531, 335714795, 266716807, 902750502, 745100502, 800395177, 812409800, 478672650, 858663413, 528994190, 604799373, 269125018, 968839532, 460123048, 72132466, 53097923, 938299418, 875128210, 764174644, 100802885, 630440846, 340717739, 836288965, 730049803, 865514538, 716914426, 628086476, 12218730, 896028834, 830270021, 677110897, 7098560, 240533530, 473148815, 394951021, 664871971, 118631514, 562075830, 552082758, 482129164, 616723564, 448377723, 444451146, 491441322, 303364229, 222123739, 569242225, 509330421, 732685053, 959386616, 176428822, 191857051, 877669241, 949569444, 576961367, 782499806, 303455234, 329517163, 666115777, 703752166, 167850779, 546234409, 430083258, 535912403, 389080361, 480481518, 534666766, 783025895, 123112682, 256142311, 650495100, 52247528, 386150532, 510329020, 415780572, 526325057, 11781619, 937789478, 323836794, 904472570, 333301189, 964975980, 620137920, 37166623, 998517909, 447065808, 720687016, 234242199, 782223397, 569385603, 281305807, 32304091, 923393008, 175969639, 8576178, 25202485, 100970879, 250840004, 675265108, 880276161, 311317036, 642139991, 927204243, 988448651, 195684632, 688085568, 296298235, 566673866, 968284960, 247652740, 674619360, 453608866, 648379077, 544165036, 791398624, 466052213, 268100038, 335414449, 337580132, 70784262, 48830311, 560015846, 746981429, 526224727, 423493341, 220583294, 761386649, 550463151, 75914680, 442242097, 386253715, 570889290, 340675381, 717246461, 983887228, 490469122, 425580099, 856133520, 354507509, 231049324, 581093435, 382405806, 556775086, 599038676, 74823779, 845984783, 446773587, 313337412, 319415274, 19160793, 896806928, 101445336, 442865585, 920886401, 665520583, 469057707, 234334774, 412593438, 916083904, 142213148, 230192244, 602124462, 928633194, 493909407, 680944358, 194855299, 110667462, 970146320, 48742501, 469769385, 810678105, 545716600, 700952752, 136465395, 359434938, 857402735, 160883827, 857954026, 199894403, 730249158, 258083303, 770561357, 650315886, 981196308, 559117032, 832921920, 247944460, 250067469, 412095869, 418078655, 934874120, 202726443, 502387751, 947609353, 443008450, 321090002, 622299814, 329368499, 516634897, 777331917, 613915987, 261671091, 711290952, 217420062, 749083229, 971231760, 326595779, 118113382, 775179371, 212889574, 508697239, 340748054, 902157636, 502923046, 971826363, 782699391, 646435400, 634345114, 794397998, 86040789, 451771866, 245197217, 794592465, 436986260, 204779661, 418870116, 776978499, 516955997, 964818172, 671512480, 880941123, 464898026, 264207201, 447437738, 768113780, 742984054, 847554853, 394669964, 41031357, 308083884, 326832566, 526591262, 143593931, 57247961, 488404936, 652431925, 405122380, 311024911, 327145336, 266190454, 149072153, 522839642, 778657277, 780706233, 246016181, 595189007, 743690445, 271082925, 285974535, 609654395, 583642304, 376553089, 840876374, 121932696, 584889388, 714379974, 23223026, 379177813, 279876595, 708143085, 593807364, 619725692, 195434635, 554986288, 450774798, 43259794, 25242776, 365529582, 217188776, 112754330, 620533333, 474858096, 7530009, 497048206, 217263856, 997523279, 89688916, 335117716, 861404759, 748785272, 205212689, 24478502, 736727903, 816888167, 78264014, 806226582, 674272406, 525776015, 891417080, 985416706, 239715887, 831593233, 430520759, 741505772, 590865654, 289829002, 963448285, 349964118, 705849844, 958961539, 992807511, 364288968, 840515442, 894619814, 449427816, 111746953, 387637219, 364376041, 141568159, 198411823, 635007834, 918561613, 122682433, 27536590, 764590568, 522638892, 90579953, 184258977, 530425046, 228480660, 152003529, 459640131, 453006834, 900409603, 576348840, 228032547, 735738363, 254647461, 21452432, 355741070, 615518290, 984114663, 82522, 58517572, 307721735, 616420045, 400602264, 95087227, 759454962, 750807406, 980383419, 672513591, 285571451, 823356591, 437194728, 265558333, 876707969, 850583001, 260448181, 170613680, 123867547, 620958803, 77019401, 506841741, 993055544, 303840766, 360582501, 396184310, 686363011, 783564943, 371811417, 532456486, 700109589, 715490468, 227851873, 847042516, 96399898, 928665541, 626345208, 572062567, 926745853, 719945023, 510470354, 474212620, 299120520, 66846332, 137142142, 476639659, 562815726, 270016988, 90318433, 782778192, 165038524, 53607529, 103476318, 20496071, 346951801, 216480005, 422335537, 474626656, 336119301, 346427624, 831793628, 743040790, 309960424, 827751734, 476392094, 214564905, 817096154, 187364488, 349812019, 536706515, 679318138, 6328307, 103855284, 351122748, 590772233, 803657738, 774687405, 431245023, 468487186, 158754142, 608359661, 952593912, 311849635, 433052078, 388777720, 289247133, 6104540, 149032717, 100428234, 216918048, 557141595, 850245183, 774479916, 266806469, 61916988, 183699574, 809942320, 410105791, 18298030, 506670547, 502103719, 672008386, 391757747, 460706905, 598178639, 53165362, 786843879, 312122626, 880339363, 752504103, 615934710, 838554030, 575746294, 244485519, 322268257, 100092753, 58470808, 304141770, 613142199, 73738765, 331715094, 10982270, 733718049, 366732648, 814228966, 97753082, 610426119, 538302182, 903739981, 732120714, 648444129, 672668140, 533728554, 345842807, 965249161, 827181471, 444343847, 549855972, 946136128, 872421802, 601448430, 226548254, 395524977, 765656306, 776144217, 645272186, 913604657, 188994996, 84213902, 46446078, 706448535, 569819843, 680762774, 629549255, 276772268, 720419407, 41099884, 337928968, 86658166, 838097798, 285465888, 30075181, 239111274, 581940680, 828113164, 254464396, 800791137, 881919069, 150471676, 470332473, 940254132, 657469433, 503451942, 654484828, 967216930, 310109319, 295926697, 689965585, 813152262, 97844558, 249274186, 618824278, 877340454, 893252767, 216815498, 230511972, 520956630, 242346356, 978197349, 915975112, 614392947, 534916814, 798648523, 986738573, 212570102, 181314541, 335857995, 370800724, 469999314, 823908435, 805954193, 491263032, 707174372, 133850737, 530279948, 853543942, 802304632, 345898431, 781187412, 326643197, 372145540, 354337284, 418841488, 292335266, 642466879, 948075934, 312608483, 709631919, 699980051, 971113882, 875477587, 112954025, 16386722, 352471815, 315229234, 458756290, 655986716, 961194631, 639958202, 403763158, 293769023, 189783585, 878743638, 252613053, 262424014, 660609680, 532463397, 407635358, 998568283, 122279600, 210173036, 459022372, 756199688, 707261372, 374790837, 827979082, 436000930, 628388493, 966793295, 642104900, 430969463, 635687968, 583749522, 85917971, 181153796, 706265896, 505305888, 16153547, 703371646, 392759049, 686021174, 675112488, 682858241, 266276140, 508637091, 708286459, 349343823, 247334987, 79924995, 491656205, 73862375, 935390669, 186161033, 679670882, 601711775, 923955685, 36499879, 123943693, 340545844, 225033074, 737136188, 570331970, 968049597, 550007557, 456301404, 259108048, 660700164, 49103072, 285427052, 675860551, 828311615, 699127377, 780287782, 169125541, 151455886, 207385800, 680170762, 985808767, 909091773, 763260867, 824936337, 558431006, 224412988, 718090691, 527960883, 622609781, 319433640, 536629915, 322789618, 227642622, 947942787, 216284474, 511885190, 138204710, 993802903, 80821766, 568589658, 477165193, 144418440, 822005490, 743951122, 536318285, 414532654, 261538445, 896669310, 13972087, 682226765, 610171656, 276708447, 270704896, 618097806, 828526990, 768813457, 160897299, 36656276, 713133370, 389360394, 545555610, 558516398, 770777901, 548844713, 232230386, 946003960, 918067337, 719748229, 205372719, 439473842, 280947186, 289746080, 317954056, 264786629, 257112407, 547632585, 85936506, 627468453, 729177680, 333003033, 751982455, 360622541, 609408581, 70885307, 259624907, 600021647, 545979676, 905748402, 114645856, 55578889, 495410219, 738865062, 214663840, 508285307, 612771957, 358357864, 488479826, 425040303, 801378454, 505246366, 206282747, 262563098, 996320048, 415978844, 801980651, 808179951, 273527594, 275925514, 156209125, 751607188, 259266181, 806984029, 86657466, 766807001, 648667847, 49462220, 224452665, 963198528, 956987583, 918970307, 761265791, 937447813, 230306860, 522649014, 670186797, 298980451, 80865912, 399546730, 390004724, 859326683, 414883368, 737982690, 377820252, 954661958, 532242157, 981785544, 376419143, 337417845, 590347442, 379612834, 132336761, 178441898, 350448778, 652728283, 753994179, 96134432, 993504401, 325012010, 792668555, 934486022, 360384145, 182638983, 544454226, 422355027, 459568189, 811456562, 12521821, 160607725, 670907189, 383665999, 843941310, 632547053, 806618933, 875364013, 916733555, 802922832, 608893655, 751215118, 440837697, 28482231, 568565513, 938672483, 494289990, 322191217, 519695727, 806320420, 975068414, 387774009, 87609343, 776709566, 570999878, 819414563, 677273499, 930074998, 660815042, 188805153, 664560737, 668957856, 276264166, 16956338, 615246743, 983447371, 361749734, 764480667, 9047948, 504084697, 71333366, 48395094, 745394398, 31245684, 213616087, 366640357, 827550774, 290511199, 293514322, 150223238, 185874566, 475111553, 89308617, 318319823, 645712698, 379491904, 409608043, 474097832, 409830587, 142696266, 756673647, 731277695, 742230061, 233978069, 154540828, 854092119, 915914172, 455382433, 528341256, 531836018, 859363075, 603636678, 915940927, 614192217, 91753758, 22452286, 873034723, 657603011, 657770208, 287563222, 219475156, 865792061, 167369106, 542069349, 651560740, 55397784, 560493650, 241126973, 753675540, 541245098, 18286768, 254001745, 422409150, 774129887, 951842274, 547642819, 51923867, 44373254, 388822051, 737389579, 705821269, 573274296, 512819675, 905689811, 614787508, 772956363, 447314879, 916803287, 216093279, 302993973, 172254407, 300113199, 434891406, 489101419, 864044907, 464840454, 265430844, 689512196, 985563703, 617555671, 825288356, 319176016, 295850388, 843789704, 69003257, 465352748, 488323653, 50322412, 498549918, 168049251, 974501609, 613708562, 586476162, 150898919, 225290806, 696598343, 228489613, 960267793, 353461955, 869186457, 701717613, 524924173, 855252039, 670988641, 538610961, 221016523, 293181521, 697100844, 486742225, 853944925, 211320316, 794979977, 13352114, 471468290, 100056139, 2586161, 745920126, 950870531, 12721536, 573362973, 145599234, 956722851, 351024746, 57845230, 477258475, 797939525, 392849884, 455980570, 602377926, 212283890, 317405244, 392792419, 118491732, 755060640, 766810338, 48350276, 525812121, 961916469, 976785880, 343273193, 135081306, 30242749, 316316199, 605634712, 643934328, 47296599, 823398907, 118654412, 829854396, 769836640, 547178246, 800995045, 955448384, 143274009, 957420609, 917400708, 980283578, 888754054, 391356030, 565329928, 314103169, 892235248, 92243777, 650088440, 135272809, 849085281, 427197491, 209693046, 199782226, 704689212, 613816665, 800466329, 198158027, 70214663, 274004597, 749099196, 149981041, 403133003, 526552921, 494137728, 877232664, 803816619, 411304621, 690348029, 53316177, 211833997, 212940458, 777990262, 537011125, 305192833, 485372905, 534763784, 543201060, 998942751, 348117333, 914870950, 88739121, 337671689, 21433246, 612471057, 250909624, 508894713, 995252932, 838296213, 838366998, 898226766, 499222702, 231456296, 938054290, 208047179, 414084404, 484666451, 576850887, 149069183, 791335826, 266912590, 444792901, 905434088, 840323898, 296523444, 295428191, 93154377, 573164581, 927935046, 610774074, 543591526, 213563591, 459301351, 702953202, 431601383, 111207241, 181387529, 347988104, 534243548, 5354467, 292160032, 927959900, 307305974, 839188204, 275223492, 161432321, 349104754, 239858011, 752655392, 870540446, 835998679, 817745953, 281525525, 491589525, 357940538, 476327294, 431784324, 841299235, 265391587, 883818790, 445846521, 178178839, 453722579, 544211569, 555366461, 257294174, 204095754, 885884891, 547345927, 901692575, 625577154, 312658282, 391764493, 789401057, 345041665, 705045075, 105410753, 405942272, 794861003, 255388321, 134036977, 914257237, 148820582, 603737238, 430275819, 699293089, 786602576, 759545698, 61228414, 825995336, 939264493, 178677633, 999868878, 542161453, 574107750, 972602852, 625619653, 524388966, 39631503, 107564197, 669767834, 376162164, 765043012, 216756423, 615739315, 420716186, 341741610, 922313047, 350448843, 38370783, 896705681, 456803343, 638569313, 847698649, 356176240, 781728321, 66704100, 755342669, 710081290, 435043673, 462027821, 846743667, 3339741, 399065532, 603666240, 38542752, 668231654, 492873043, 290581469, 752183103, 693443216, 374678477, 283285495, 547237778, 464733478, 776423433, 212555202, 144202395, 841128257, 355260972, 183905340, 73919930, 782835652, 129871720, 628026145, 862448358, 823805244, 146754036, 380899191, 683895945, 10069154, 533163009, 905554048, 859046224, 287361601, 266853515, 340723797, 650029656, 17554220, 219509430, 122229147, 494728443, 369022323, 536038241, 310223772, 389773503, 395041190, 912807471, 853828484, 640375996, 247651588, 117773224, 533974916, 703794466, 103336901, 679112786, 35550723, 790616760, 723011636, 400206378, 131832738, 663312742, 966474184, 16680373, 733488245, 659948752, 290489772, 572902631, 613445916, 93318183, 179174333, 266287500, 907634602, 448122658, 328732879, 135739347, 627924652, 741380166, 780070004, 418658331, 846242090, 542375044, 156503989, 972525994, 334938183, 404507604, 44930178, 939369407, 51261036, 30170848, 238172681, 370606511, 19061249, 876768943, 276501771, 416539152, 369475776, 952572050, 996073121, 229578923, 365961911, 1320576, 22080528, 910965437, 320214608, 727577599, 286769351, 502346480, 713877764, 107548067, 666695895, 336563734, 961291363, 151068310, 734383012, 697309471, 345239228, 244971342, 293100911, 909780182, 634112728, 440505858, 250749045, 557805876, 193928323, 498322527, 18992159, 490385797, 745100533, 632536537, 790193783, 43386364, 17561047, 418659516, 33470700, 517769252, 317260444, 694640462, 183894491, 456442062, 940401021, 616770354, 699105316, 406134985, 225774244, 698312794, 552154479, 322582870, 558699527, 109026379, 400243352, 702729765, 781642843, 962121777, 25468880, 434666919, 471476848, 589167259, 888071790, 34261047, 683290279, 838947080, 219398942, 576828180, 154178846, 534468697, 639143507, 387094955, 70406489, 816286371, 814834912, 709201964, 265245171, 922421, 126343060, 683285466, 610111967, 655433959, 399354391, 569370776, 241618874, 42535340, 935790159, 650528370, 714363150, 57066884, 591040340, 580818800, 538545577, 262206536, 605453590, 643493718, 654830164, 19478970, 389130995, 251159615, 662399790, 879118976, 428240094, 321041174, 310896385, 206811525, 945231143, 53524909, 663411590, 247052069, 706226736, 712320885, 34983179, 221369522, 792813240, 568656908, 421074854, 444689461, 765527445, 389902794, 427784669, 592566637, 773556756, 386512950, 887362454, 590346653, 472315874, 709021691, 756941944, 294718633, 30493092, 62165410, 762913795, 276433675, 583920474, 827560546, 817702707, 829600217, 811551786, 381596795, 363649969, 662914198, 782193524, 239718949, 29806828, 525080961, 441889048, 467512538, 576512340, 587221946, 331173451, 883757535, 899709103, 698940216, 621203549, 804742482, 681882545, 46645434, 876568638, 323332559, 876133647, 222299329, 272686877, 273261744, 848963917, 287976647, 182172261, 314691309, 547280886, 4317508, 190143683, 942138565, 823994071, 257352277, 668642390, 812832826, 585864366, 217029662, 607351652, 116832619, 485665099, 18687930, 706002932, 389249205, 360878514, 723949677, 682876432, 884303953, 690623295, 156699304, 738297030, 1250068, 891415859, 924435702, 208853003, 809541047, 152757324, 937972060, 859444353, 570481094, 245675521, 138258467, 781467454, 390365679, 803707992, 641205283, 581547760, 47915716, 50724223, 503485779, 941805618, 326290820, 214662760, 885122723, 679563810, 575021239, 764499499, 725979996, 140485963, 940672077, 491528620, 260404542, 697198199, 892578553, 420533564, 220024589, 451737177, 538892218, 60952122, 76650908, 428774225, 928258914, 647519384, 339933078, 48952926, 457881264, 435320770, 198199903, 584269475, 614413327, 357344551, 591664083, 733686543, 72111645, 229942943, 686291947, 826605903, 508414217, 570341267, 887925305, 619382268, 50551943, 973078686, 92740296, 407872340, 450437684, 454038807, 967439778, 515364010, 540351945, 508782010, 96846427, 751721702, 263025311, 273792762, 114468300, 735419469, 24596851, 534182221, 904973315, 563296552, 792766126, 934318094, 217637847, 592083803, 43108063, 225865973, 561956810, 226940060, 728266919, 25087093, 409761960, 358412323, 626545953, 851198314, 160658981, 372936209, 944761820, 649878102, 66876637, 761146379, 417260465, 857928605, 127684088, 283786345, 840936990, 462979781, 12484803, 98964938, 38416137, 645214064, 62751860, 510344763, 405574091, 78284879, 634418424, 33864716, 561426654, 639157185, 648443381, 15150141, 156194253, 473084924, 557155018, 86180455, 99762950, 933084767, 615056162, 455834208, 365891147, 485608298, 621793826, 567283146, 812963598, 682451139, 77724417, 702742577, 637571291, 820404870, 649541302, 815430919, 944835222, 708678012, 585381090, 390658952, 560278280, 882832104, 976146636, 348247997, 921827493, 979410437, 421292868, 734080516, 888154606, 75733900, 37745440, 823323054, 650018287, 341351200, 280907226, 33202500, 739854614, 665721648, 507453195, 779215840, 463134011, 193072118, 450992240, 435889273, 493358563, 488085242, 681688018, 899107993, 569847853, 878003748, 983589666, 994462134, 33129586, 276718110, 348811846, 67918308, 742762980, 820050111, 791129428, 392266666, 44884295, 834625500, 258919492, 694906402, 266141775, 843297604, 54611289, 319991442, 911022683, 409484309, 887659202, 628670431, 388003037, 728501438, 439733470, 42492463, 8253714, 321356461, 943916314, 142069949, 795056434, 946512147, 885644842, 514413468, 592895612, 332839315, 672691818, 210545083, 320839981, 344583383, 808931741, 562302789, 926597642, 596821090, 526079238, 782096075, 311796297, 394822418, 338181886, 200880899, 330315453, 651564196, 637360802, 545140341, 843493370, 522785351, 500127416, 674532624, 933400792, 361152467, 860416160, 310723021, 956212109, 932801018, 435769990, 183321185, 946895819, 365343588, 625348376, 958485067, 499349837, 342636497, 727671584, 251478219, 250437110, 129476954, 258767153, 136743688, 306622559, 176945778, 401285135, 904180964, 864768752, 960192773, 430676857, 42935092, 361508426, 684520150, 594704484, 677071154, 214618031, 423803823, 387105008, 375062239, 153871536, 427171596, 331623557, 872635671, 395040754, 523399713, 30334035, 972169447, 445148270, 455018061, 536497217, 92960676, 569862988, 286771649, 385102002, 587741733, 199049934, 64007661, 299382606, 305424208, 52951738, 178994186, 405511013, 937284465, 515929296, 988286099, 948444241, 597834206, 929262202, 837059581, 204393329, 257354569, 702866027, 601503493, 148268846, 862621283, 642676369, 644000786, 182354439, 194862983, 51563691, 854087124, 730036708, 685168394, 131799626, 584277757, 120207986, 914729522, 961759383, 212553818, 972007396, 361781507, 72012988, 637589063, 264864566, 910207551, 740034856, 379915976, 558215648, 927971820, 11790013, 532819841, 795224458, 920990829, 490772026, 527308808, 166429191, 891256445, 693246703, 928833258, 904947989, 294898545, 863369861, 211562076, 543512571, 779332092, 597476484, 274405997, 957909645, 232773342, 300786668, 187976795, 660176453, 672938689, 55562907, 871378265, 557074678, 14143248, 880030257, 884941348, 31067102, 773074876, 342437745, 573694174, 807893407, 794394180, 525304821, 533255925, 609551092, 468910260, 316145380, 974506884, 411232277, 1251539, 700497712, 361529715, 226754131, 474538722, 551757793, 598009038, 662609711, 722373009, 180678386, 512041255, 663217833, 452072145, 358512028, 485503184, 344815393, 168721583, 587286277, 380156174, 139865175, 823017810, 694394302, 565245597, 311631042, 61800035, 744707753, 312823793, 498480840, 717052816, 915037100, 874721595, 939145274, 247759290, 689296905, 393536527, 978495770, 595959167, 771767067, 289900219, 98125761, 101308101, 324307836, 228878992, 113762752, 353318816, 997030954, 848991553, 141655712, 195956771, 154755058, 643222133, 357882533, 59718084, 740954614, 386306358, 477836493, 228714168, 80246608, 971451647, 314819421, 703537329, 792064721, 682790371, 526739266, 447138653, 478656512, 252489782, 285689625, 230014834, 774396933, 846907046, 609588120, 11315996, 639419869, 991935000, 308424520, 966316754, 503316183, 694989988, 616056174, 90903959, 259830800, 848330473, 271216624, 541088658, 606963158, 301639817, 728308536, 837543889, 968254228, 928521009, 199662322, 400960449, 588871718, 39678326, 882878334, 391413217, 46277566, 283789051, 941825212, 534017353, 141829946, 832035191, 49655251, 227651593, 883414567, 167567409, 395540548, 339814369, 323722107, 758572172, 718337688, 159492014, 703193159, 676588890, 575287209, 884852479, 725941388, 694526407, 634349884, 561821613, 236945380, 486661906, 627973873, 109016505, 175052966, 264421393, 278764207, 642299541, 941632181, 488860061, 413443364, 550743403, 669439776, 717122416, 239491263, 776568821, 535273674, 811845975, 22821476, 961512115, 120920949, 463052769, 697632159, 80949047, 215415473, 624294376, 179417940, 897076440, 782775337, 585565553, 553170743, 715581582, 188352273, 617140555, 366028868, 772714489, 346750557, 594455576, 837383012, 50433372, 514818807, 279319195, 765790146, 968471643, 635329811, 649544613, 104237393, 483525576, 694838665, 288547917, 414667615, 276742693, 895968378, 772358149, 649588088, 126731261, 851559939, 829731227, 987360043, 892775845, 348960284, 430038672, 659123119, 328746563, 785734067, 88034279, 676020428, 707011370, 911832474, 365637538, 125559027, 928095924, 334759554, 166657374, 219357163, 298969312, 418975495, 384919175, 722125989, 328539960, 626887756, 997281479, 170142243, 27111801, 319512436, 639823319, 291290146, 226603302, 672074218, 190239378, 101344868, 829178081, 114949931, 904034108, 884476290, 16785937, 71946054, 878666257, 463627996, 499726051, 880879306, 941420759, 862778292, 247306878, 297350867, 587545142, 713914745, 226249450, 214367229, 947100113, 280992869, 188336438, 709833439, 690747878, 952609782, 969725785, 789729728, 360160503, 653585707, 187656006, 687149934, 503199319, 63776926, 62633967, 950835999, 256685259, 643231158, 185559850, 926129496, 706925278, 416309224, 598265188, 638659946, 537982115, 398587789, 926851250, 57306456, 763197156, 417392705, 14987150, 957874853, 750027335, 485637366, 569999398, 77341631, 730722508, 881420814, 397843127, 975427547, 891924329, 534758430, 573551102, 642445912, 567866526, 244365529, 718714984, 559845759, 811269666, 346320614, 119657110, 764973769, 477638371, 415268719, 483573578, 576305602, 407509978, 455026519, 701064265, 820395837, 686899063, 740594641, 46758887, 20807271, 247156228, 1639035, 280287658, 108904456, 169483375, 868197611, 825451098, 440224799, 867748626, 625071217, 315962794, 732060826, 284104146, 809051040, 501331030, 535015461, 607597496, 132927624, 918386404, 815867145, 447649453, 278787674, 983379712, 53675949, 788533216, 853815779, 128979082, 143203131, 480846484, 637134618, 689921701, 699652369, 513257981, 904086312, 558245387, 988916772, 323304205, 951229642, 388912142, 917864066, 972425391, 944863432, 94514806, 128447629, 134036142, 842526138, 825853011, 578956628, 172452788, 987657386, 824303107, 134333427, 609759868, 215162120, 306156584, 763978113, 413075802, 167731330, 6554907, 287430546, 279869285, 560242657, 638915805, 152380950, 42310483, 579138006, 520422451, 251362726, 886764734, 637749842, 12695566, 379873064, 706160624, 167356026, 35891447, 349376985, 742699157, 189227437, 585418831, 511699189, 777863967, 957012493, 187503573, 668383734, 906582224, 868857303, 820362841, 216239104, 309658259, 535319859, 377693427, 852644473, 771676028, 492532301, 366787390, 542005293, 799921010, 801866901, 275728521, 985273175, 276038556, 943951200, 186424614, 519190152, 476873003, 921438388, 463361882, 477824874, 298831505, 298639965, 531121472, 655746136, 647624758, 996463232, 869755159, 883062975, 787911659, 59412519, 511290402, 150796465, 48069088, 624920798, 319960631, 615158949, 128978619, 218586135, 224668010, 105168437, 643751558, 538340754, 855865420, 306235485, 821064712, 367231762, 223655433, 311185907, 796036889, 638870338, 437335448, 20443252, 931549196, 393524148, 387293957, 67436842, 717736727, 637555000, 165014639, 150144543, 796724353, 812581166, 493763640, 209608831, 719193062, 188016721, 812071153, 606134303, 188196661, 993666009, 212867158, 874553293, 278251370, 132428655, 494041470, 132685523, 622296401, 323960595, 12508131, 424310815, 442222223, 143290784, 835836745, 513411871, 423475567, 152927304, 6645132, 171255831, 561943243, 788563672, 245243085, 952266858, 646762793, 405173264, 680605906, 564817846, 840956239, 241690667, 525065430, 196227261, 100990347, 688026871, 755427020, 51064716, 545824713, 662903581, 146312710, 900865362, 801337802, 222378159, 75184163, 863056726, 899617979, 364609486, 867855199, 390796645, 517637640, 471364007, 262771004, 21122736, 667740600, 572728928, 361633423, 630712105, 206233012, 270283291, 624785604, 466217244, 75103129, 36698423, 388472198, 325655621, 887392501, 647313804, 964378297, 605303810, 280405133, 901530235, 611100384, 280638630, 804834772, 74799674, 527294827, 508577277, 479527131, 232993254, 292996419, 967943856, 783212040, 444675469, 293409185, 874518525, 409826147, 305985986, 366635208, 576993562, 274947439, 771013901, 372194191, 117171792, 485474145, 521295270, 867060001, 878108285, 626293797, 197531600, 180313193, 393983276, 337894690, 422982818, 377253497, 282226986, 946951422, 718592272, 644744295, 439624935, 511759914, 634943911, 696789436, 69862799, 554063714, 532325427, 636910158, 461973441, 400554951, 495574664, 869545705, 593083453, 169506115, 264566871, 233121821, 827376286, 61602680, 200472246, 709102252, 212072444, 218245395, 126963801, 118371083, 973163490, 12996486, 869539650, 625746862, 787060843, 892548754, 389672303, 530278855, 552981904, 215770411, 973414826, 915093589, 325945679, 571846609, 290001251, 725570207, 111845840, 272218803, 363136846, 824683015, 465186493, 668877344, 754952791, 617374512, 393805806, 585257506, 51066155, 928759653, 237775405, 734712927, 477635008, 694939143, 25807830, 300727038, 390661158, 747178403, 597501511, 131966034, 308140446, 53759182, 615702849, 466399964, 105220705, 275739790, 110856603, 913263959, 329080309, 14336452, 293300587, 503268043, 506830955, 352735590, 98826333, 754981797, 322238379, 285763801, 84464514, 263394950, 57533259, 823297989, 272438494, 170636198, 891837338, 68800180, 300724989, 825183747, 617538813, 996065304, 725156903, 345400332, 635659774, 247518861, 844715645, 946380866, 740326694, 693940367, 632567875, 308335904, 398740010, 211887258, 176909797, 329059051, 982277645, 928490288, 851201265, 420883893, 288535974, 425643580, 729808414, 560438781, 687530129, 788882998, 990926445, 460014678, 867543982, 148091434, 750359641, 789455718, 454075543, 176169268, 702796166, 873354979, 794932986, 553828678, 811030088, 248413863, 931645242, 808282586, 476758777, 462614437, 410895272, 239534572, 618664626, 737634637, 695464798, 607894668, 261001870, 658195361, 797014468, 543639769, 538592662, 720922841, 372234633, 275079780, 819479925, 66208594, 390973241, 295311732, 84317603, 191137787, 912422429, 621260866, 610316236, 241382597, 829293692, 359343691, 326033832, 975701434, 722806606, 364716675, 482167325, 718863606, 122970179, 199483252, 790067226, 918806122, 623424599, 453338979, 222831766, 536212010, 154119678, 350567692, 7776104, 89723904, 432307604, 569043900, 612914870, 51599330, 696827794, 999887907, 267735570, 845923568, 840924878, 747859752, 707882392, 222946278, 667340517, 487566772, 570474618, 62111613, 715397185, 249512448, 458813954, 35283099, 350467187, 432990373, 590815901, 435732492, 386342994, 23211303, 916827192, 282954594, 445536812, 439553433, 730442806, 454858738, 98727130, 359508173, 22151291, 800081521, 127339953, 154570469, 846664719, 74497277, 883781260, 865392028, 766033015, 499221304, 414215704, 708244041, 342833504, 276146191, 984396177, 607717088, 605703829, 273130953, 955971419, 104003905, 444525376, 11415758, 960408004, 73844571, 548578848, 769185403, 170455368, 713315014, 445583043, 451301052, 56877627, 980606706, 987072057, 475664761, 188729199, 971955252, 566995555, 752354460, 260700341, 111489016, 641760555, 811263666, 39455740, 335503320, 91762370, 542985557, 668934673, 557074339, 790402199, 982678954, 258198593, 873816420, 917071128, 645861089, 798487014, 291445509, 390684108, 382656844, 502616807, 839953098, 973333235, 118454866, 493379195, 39312541, 864109591, 513330421, 562477963, 751092839, 638498548, 232654174, 65518738, 783794514, 321948839, 63248452, 781385712, 831569886, 553879199, 313779162, 565577341, 430098410, 373555899, 676479659, 171294953, 732586798, 283944672, 501016697, 174593991, 220792149, 749869370, 246506993, 368827559, 511332637, 469076277, 344414334, 378842904, 736484586, 123216471, 594966937, 620845352, 689308914, 732818616, 4460741, 835263887, 164071927, 254413260, 692590788, 406393360, 415402856, 128756771, 710532238, 479601078, 549347722, 517410627, 82352607, 766365578, 420409412, 855197055, 479302217, 14044981, 377812092, 719373984, 423336270, 501267127, 932876138, 827583480, 15086506, 922647018, 345679889, 337068482, 145650810, 942378664, 657235330, 517443428, 844447443, 111753442, 643236629, 33349438, 839890518, 172560433, 161392415, 188534205, 940525600, 442912888, 874708998, 466549944, 570289568, 237657943, 842240712, 873734530, 617812738, 621626103, 554133610, 148499750, 138195313, 666945952, 291397663, 962781513, 204501822, 558075871, 515418826, 652731759, 418528908, 126982760, 107682146, 624781582, 25107442, 114932525, 632449893, 405226090, 133183869, 952064691, 679351089, 527121541, 296381500, 54804879, 936534362, 484206631, 108010579, 178740000, 884351854, 869449891, 355103671, 840596087, 774819542, 944613529, 589804267, 408831954, 467374074, 749310651, 894764432, 239925620, 460376738, 117546673, 783461520, 3063410, 145464989, 289462602, 409270598, 152397852, 923177361, 342327913, 55263857, 147100617, 589818097, 150910203, 841701646, 467371805, 702151957, 817478511, 903032826, 126425764, 838758929, 769882648, 677459317, 542140592, 61234809, 544511095, 968574281, 608602830, 147250868, 100374233, 170993948, 592995949, 991387080, 702110918, 173365161, 430302422, 928272902, 224617394, 473233120, 202172745, 538568411, 505852722, 484822353, 234123421, 729378722, 71191425, 313183828, 939113946, 239167831, 410605901, 590046322, 518580553, 771731511, 759398153, 45743039, 205368362, 698418690, 672916960, 291354827, 165353140, 723746500, 44431907, 151435704, 778863352, 44605789, 961221971, 313661527, 518320643, 27012640, 750682097, 777394147, 686774209, 171411740, 694425217, 360201348, 565739526, 218523742, 118439170, 200104951, 193932070, 717975146, 185791078, 545252608, 634596411, 100812022, 43230046, 860997406, 499053660, 983777659, 351635062, 866946461, 204313194, 318375167, 193455323, 373500959, 243837958, 721442650, 550489635, 773424983, 211372040, 73506476, 142561858, 942180414, 226008092, 368496996, 836458004, 131354663, 102779491, 711930906, 140152695, 852089152, 321525015, 706310052, 196571802, 845922937, 848365297, 166397909, 887271164, 723160625, 235765023, 433918418, 445426999, 646901766, 449480777, 734305425, 360988341, 444814036, 361918955, 64916499, 550929949, 389677860, 48670505, 273602108, 68168632, 425268734, 448459285, 31402098, 283417709, 576045063, 870530250, 611222632, 777758334, 813616758, 475292774, 295552577, 132541912, 798668370, 152087426, 628452931, 914632682, 90668787, 920765774, 879402786, 120096955, 888473870, 145188372, 832723865, 678766893, 589137309, 634441431, 654620660, 728080881, 506581248, 403923528, 249798511, 379462759, 701825915, 343438014, 671721829, 170814510, 70102767, 262955431, 810149501, 141953422, 233781433, 100056115, 865634147, 434980264, 699971867, 715499428, 643596425, 150806901, 903334883, 468436876, 435037453, 262218593, 639139820, 956338099, 237510979, 293640783, 976264431, 336330960, 30939194, 883227020, 307933682, 264225100, 315875997, 316784265, 466182451, 466429746, 929983352, 11874652, 312214496, 238989773, 783186, 556005606, 833925596, 906277807, 142178648, 888336809, 200874217, 873706449, 785651536, 100125934, 635856280, 791074707, 902801986, 660237243, 938121725, 291548902, 576209422, 618800960, 131013343, 783133903, 107351574, 368810225, 674123916, 473690947, 360886124, 249371671, 734944594, 799279549, 252882572, 797949196, 690650163, 681009757, 71622742, 675065699, 19516311, 739141727, 113594011, 719069092, 884398574, 362981791, 734387774, 697346646, 895240000, 262142837, 108064196, 339253909, 63097466, 317419034, 551893224, 217217535, 203323632, 486172622, 768302093, 397505496, 48321666, 217479607, 670880788, 652638139, 815715774, 551695630, 422605138, 131762135, 280212728, 282539352, 642611131, 578820654, 328893608, 301434706, 432289612, 17488230, 671703752, 674697185, 484221540, 630641424, 311505265, 367664192, 572840919, 926504306, 410080455, 437195457, 769985362, 794185837, 748641784, 760416960, 851825708, 312765272, 527608278, 712884268, 922795996, 483523748, 463523630, 935420369, 600511464, 665878134, 487236850, 787921013, 592548197, 135094722, 109330203, 128717133, 314650016, 486839222, 763226407, 323183625, 759625057, 577486118, 850227560, 240250924, 538684042, 866479144, 36555133, 390984390, 494198270, 842597420, 517536648, 629920174, 701664340, 693580338, 959917339, 873459453, 632897420, 393748405, 471556755, 323273694, 627176695, 336669519, 680992611, 155574389, 491970321, 324273431, 335320609, 514546433, 51305453, 599049331, 841698464, 515631838, 59362926, 703260239, 25555412, 730486804, 686059854, 894382135, 541603447, 115634226, 936745028, 392352308, 465513483, 924077692, 901491312, 114141039, 935298253, 422637354, 16168482, 812712386, 117821539, 574384999, 759197812, 998940701, 892056661, 734954641, 917863537, 924000664, 253036430, 457600185, 18104945, 354785572, 714893218, 928448736, 512974074, 118336211, 476410242, 712490905, 491535321, 12596639, 233064307, 824373511, 181187065, 735777520, 535880586, 296335436, 796599611, 207584967, 464678127, 916743560, 519523996, 90531043, 998633895, 15421367, 700579258, 399723390, 355857440, 656583977, 628185589, 219416371, 586639388, 453982796, 805416454, 203448458, 843790442, 849699360, 474074280, 387954357, 704177535, 350388300, 150340477, 83953836, 251906043, 269735709, 547200582, 49244156, 816959480, 196685903, 624176998, 748215008, 628426462, 144852231, 10910300, 709528498, 706650962, 360969374, 4793790, 442626408, 344944888, 517883959, 99848938, 952950830, 962179147, 891897320, 350886292, 370751102, 377201922, 163144687, 412766955, 721311615, 793371633, 196632656, 92598377, 282389517, 896940349, 23498184, 101215058, 824026597, 258294905, 338510323, 690795034, 892491154, 405828115, 545996862, 170706336, 567247895, 913943900, 520172717, 130917150, 888352487, 500294112, 469170394, 974336488, 245310980, 156004769, 57490013, 2813002, 953244318, 52817398, 48018337, 643408996, 54997549, 763447404, 890704090, 207602550, 617471159, 619640933, 552819504, 625442190, 824830611, 24306787, 898066125, 188175501, 911319519, 25255385, 655969362, 320247108, 46430837, 62245288, 613446439, 40637774, 536996925, 298979860, 451386455, 217268750, 783597480, 993907884, 381652506, 724383282, 794507215, 631310538, 903791274, 125219280, 806565106, 268387029, 199968158, 255590172, 359839979, 978521892, 28342751, 286242892, 929295390, 18318651, 577046190, 403649583, 352362794, 672058819, 900231294, 899234130, 211414717, 256006694, 221830344, 847983097, 721489966, 149921141, 928089209, 53737132, 303026944, 236959980, 281596990, 817063061, 237223212, 74981387, 781991779, 11413465, 643047990, 902755626, 461318914, 340765318, 815940483, 992407081, 919526642, 131091591, 556273492, 474291413, 550428941, 964962272, 667785990, 77786437, 816058810, 101967973, 433831730, 424936547, 671744959, 241683402, 465007851, 633160238, 161848020, 690353826, 602075079, 362059098, 375443585, 167304395, 301672915, 238278760, 581603108, 122560666, 209470354, 635779142, 197953912, 695239364, 879215033, 513274988, 650165852, 434853720, 196392286, 324929440, 87156216, 664300178, 923828990, 353599024, 520996882, 101492178, 582995663, 587561841, 398872191, 706061137, 693315880, 973664064, 902584124, 748268772, 666976979, 436191829, 910949897, 294796256, 158559201, 118631207, 808096781, 54472473, 929444364, 811501663, 48515649, 827605478, 138077387, 27648341, 514415732, 928505504, 564422013, 120626912, 168951750, 498774613, 537508936, 137187723, 223590894, 947318401, 798259605, 455255288, 665854080, 608192838, 945285929, 609309754, 191678759, 86944928, 289025420, 877074945, 891970927, 811726444, 565427774, 358219013, 2047945, 155660867, 558487120, 44785253, 392414749, 980999982, 818043224, 314281173, 232022967, 225965537, 981205286, 859131405, 769620304, 860698019, 108767852, 327073620, 280517887, 419178012, 287722493, 886846966, 593181230, 181556152, 982782864, 622688722, 497926309, 119649120, 737606802, 305826418, 485426373, 454590098, 291558779, 577809172, 430798542, 919818732, 178820870, 595301009, 397718836, 715424097, 291607322, 666617353, 331914694, 142297439, 852376195, 66797269, 772795800, 663090878, 143019297, 915152258, 205775506, 623087580, 125750266, 663281430, 936991939, 203599203, 592998487, 420165233, 914191236, 161796370, 873352290, 113346419, 669163243, 421535013, 4452562, 108470694, 696913463, 70983395, 564935583, 746332688, 59423907, 306929986, 668528217, 575528161, 536408136, 437568781, 675014807, 554360732, 62245991, 599294657, 380558137, 771510539, 464435604, 355762193, 698549662, 414996752, 198878213, 394484705, 387373770, 688400297, 35486111, 231458622, 961697521, 993679024, 809770542, 85729787, 902765610, 114855093, 587981460, 902484297, 396059856, 425663046, 201067972, 717879161, 91680974, 32081275, 409747844, 490401616, 641027255, 302384042, 992307799, 892169930, 35786771, 263285694, 615604671, 671642961, 717190658, 986884420, 513151861, 492311426, 790125276, 633208650, 107094449, 752646756, 198367298, 433882948, 213232448, 618044647, 660341374, 727134240, 535196582, 132194406, 467625951, 713282714, 793698119, 956270480, 426427104, 416230463, 111557684, 534586807, 241947306, 119092932, 598319539, 618736676, 23123482, 933095351, 988959690, 790541730, 13415940, 551218586, 388020530, 196145091, 116280497, 577067683, 758568459, 351634636, 415743385, 712244274, 522090390, 666345426, 823770556, 714064916, 665519311, 164668956, 780504141, 646866676, 658382503, 924707213, 878602059, 177441244, 318499314, 37455773, 402967139, 624809665, 279484105, 253800481, 548279920, 114407211, 978786980, 533262692, 494083665, 171394691, 805696500, 445874174, 576066757, 765479577, 681132796, 513225193, 754347189, 788890444, 787332653, 282645393, 947093337, 96477115, 654933279, 459237519, 955143402, 810792280, 40718098, 470770625, 482726539, 275974303, 336186055, 309502790, 739325297, 456047561, 705534063, 698760052, 36133841, 787333907, 645973475, 796630815, 955869944, 195023395, 16145398, 655445751, 493994173, 617127769, 45907716, 415728431, 322033520, 848379633, 470723785, 114337836, 776907403, 608009749, 20206759, 289296182, 268836798, 641565378, 620465811, 909544795, 638951056, 437222741, 939410886, 238381185, 12861602, 723062327, 533134013, 395984708, 810203444, 9695656, 583138462, 456048803, 589966395, 780041000, 841701429, 784829035, 149918145, 857012294, 65601586, 962529586, 502574315, 421760574, 325339089, 760293942, 308120492, 233806499, 558423724, 325600302, 681183639, 770980347, 633677617, 193791170, 660484945, 435680895, 805187665, 410770308, 28277046, 546108479, 349948334, 889910189, 778887053, 675546285, 490378776, 947748353, 655361104, 438105855, 238320096, 870439591, 355351185, 95839025, 482902310, 248748395, 484412780, 657322759, 585237433, 108657513, 730620177, 19722770, 486265801, 196669555, 158330692, 127739504, 723735906, 704275207, 802218648, 712341580, 560138649, 2255630, 784903839, 999128565, 606937522, 610773969, 648601341, 185234161, 310227557, 381569011, 783182284, 133930565, 510041238, 907517102, 588340669, 16307890, 202625825, 535357955, 308468501, 124575102, 234279839, 10658869, 909765917, 410285596, 865021223, 285016050, 86934872, 436478241, 987628433, 391545396, 190421487, 168927792, 952211061, 702152545, 543658108, 645390125, 102100604, 509219555, 403498118, 590909055, 159095470, 541554583, 846657836, 520330384, 864663038, 888686173, 479196327, 583606078, 771929756, 483600514, 932734703, 590051695, 903614590, 279092080, 44666745, 610849223, 346035455, 241728375, 741019558, 582633098, 658441992, 736159920, 382592196, 755622410, 600495374, 749470518, 260393910, 509767641, 133821475, 524121747, 359707704, 281614645, 424858517, 353155257, 997031295, 621272767, 464645553, 318623581, 495331056, 5552568, 831794306, 962858513, 405078035, 426906034, 819290480, 709044413, 661335938, 253108132, 605669094, 537958918, 652548265, 572448868, 402569712, 471113946, 912167913, 354330737, 947519588, 465054799, 236424505, 431640722, 292223553, 836284547, 72755092, 313515392, 706901344, 809864018, 483141795, 157006494, 999754055, 789912633, 369289113, 95724714, 347155432, 606324905, 348123772, 504432652, 764755347, 303993786, 440454490, 289811231, 79653522, 691282839, 917843997, 847662602, 92646184, 442572804, 640304625, 217475773, 948844434, 6427537, 704337924, 836939677, 222080472, 384758371, 117744760, 579547521, 863049611, 599686704, 351531854, 145619762, 872942584, 51469308, 334732259, 930278699, 464290398, 915403171, 882961867, 565840791, 409828574, 538871995, 272701243, 731117222, 838462743, 95564716, 611870749, 340024601, 830773776, 592775279, 225979693, 236624100, 984672139, 473997338, 728363992, 203008663, 598094808, 79084814, 806092453, 582030814, 572095005, 868922168, 268919524, 460398015, 44196122, 696397129, 254709999, 811098041, 530211162, 500353676, 895725358, 117294903, 447454694, 278264819, 648756685, 68647716, 607620573, 305954814, 469777678, 594111539, 24395587, 970139917, 755500303, 978032235, 959257304, 34219458, 162239309, 979536349, 60344713, 667795942, 42507875, 881660494, 893868179, 321158635, 893002385, 170512120, 514696673, 263494560, 707440175, 298992872, 273725520, 970988664, 915197856, 480509820, 572303204, 593532736, 854303220, 619156218, 121034102, 902401353, 518637827, 171078993, 343101556, 129929044, 682782144, 989255820, 788869686, 167091033, 197464115, 552112437, 715702532, 783811128, 399066875, 646638943, 473554131, 843641837, 27101715, 515362223, 584068243, 549658505, 622555065, 43116905, 766774600, 808781203, 476306539, 654262939, 933452681, 904244849, 30473312, 935301410, 573807519, 333593284, 486495489, 91474384, 689044817, 197112850, 534255293, 370590841, 550642205, 689199959, 146327351, 469932277, 92132767, 93385530, 558173456, 202270553, 86792452, 496909786, 320053981, 750649472, 273122906, 751881148, 716337872, 931218182, 675106224, 338999516, 483381422, 600618173, 25226801, 612728807, 387555547, 89454411, 517756817, 714405005, 287594964, 570607093, 752290929, 536005362, 472145959, 377530629, 551029686, 862449997, 983677027, 318948414, 590758916, 95102587, 683895504, 913714728, 793944546, 874559882, 451895157, 638252485, 991135698, 186911847, 595977840, 458738698, 369896351, 206560894, 769832899, 391544048, 387099620, 954710557, 194452321, 339596957, 838651376, 755055951, 192608370, 835651069, 997609831, 612550065, 461907883, 731976082, 624646863, 685618978, 605685935, 703462536, 717100278, 944550033, 167828035, 939677190, 883018267, 235062266, 201831523, 480704919, 168674799, 664856680, 607486743, 5982376, 10400437, 598248613, 54272278, 41791707, 90043232, 754567573, 890454786, 864853060, 346952074, 894544321, 976880461, 835878552, 234460272, 533353355, 144170887, 591345808, 243060190, 482311944, 576427071, 373297734, 850014507, 949742858, 234362466, 298614245, 395650007, 105941128, 45399976, 938692803, 351925751, 566804498, 136200315, 382059190, 826127197, 529780074, 21995758, 533249896, 661207149, 376723397, 755244857, 477644330, 218102750, 136797352, 67958673, 870126593, 957616138, 916702713, 365137035, 407574344, 373355717, 154947062, 127559650, 462184081, 615180260, 632507238, 556459888, 41415297, 185797998, 249493839, 621577140, 317296540, 56155808, 493030096, 307392736, 285382060, 627624562, 170747518, 272094643, 689786546, 305891469, 149379919, 730513608, 88913360, 609606458, 453700528, 623017076, 818289424, 711465618, 346783208, 849322507, 427938635, 275846240, 263163563, 479505134, 144537796, 815394722, 678319056, 722753931, 506504510, 613521679, 51006409, 1631102, 320061005, 919907032, 485574918, 600763410, 456804486, 677816857, 523372934, 649394074, 727302333, 217931159, 674254579, 361103415, 820292882, 994855749, 808765596, 937656925, 406149748, 257291773, 633431762, 422403169, 794158417, 197358530, 680919698, 369659122, 348340492, 734743378, 226279908, 932288401, 256209691, 405128828, 448857269, 617713479, 263268411, 525931379, 224340346, 867090512, 248632474, 19571975, 57115344, 399634305, 290622928, 580215474, 641904194, 250645482, 264145919, 962619729, 61822362, 826276105, 874198019, 63469176, 238148648, 480441196, 590718801, 182394906, 408760252, 752065925, 637714546, 984887500, 347974240, 392187648, 81399014, 387685462, 708136063, 937850201, 299962138, 250388597, 518142813, 657973013, 594340542, 860778701, 101439850, 158561300, 920157686, 958997227, 585347273, 264267456, 662446790, 576395967, 561197178, 887901345, 465646303, 925705234, 942587011, 704294709, 12693081, 563618532, 343040677, 470924018, 122918772, 702871752, 466842074, 649405393, 457912978, 431426045, 643575686, 88915929, 236277309, 591523308, 726229814, 290792779, 446565740, 947537050, 168686374, 787988603, 597952323, 204208919, 600360078, 220770155, 5326942, 955828050, 308598046, 793771545, 360772238, 680956789, 298939910, 796680762, 486667762, 104632606, 911281462, 329288632, 489490417, 26213686, 623191495, 279275294, 945548253, 393718804, 366363817, 367347131, 366664350, 20822707, 400914775, 525097367, 26095534, 898108384, 327835850, 920537769, 944332430, 28155438, 252186898, 147738506, 533042462, 445988575, 553414099, 296151288, 776324156, 115315452, 768720488, 338320233, 220156824, 36692392, 425744078, 727097207, 459009284, 155297152, 496254954, 990876594, 998410485, 700759345, 563742240, 818385877, 753208806, 417469924, 43497466, 773027676, 867221187, 854094116, 422207202, 647713014, 107708089, 839556832, 894176185, 958879534, 989332642, 342501457, 906074916, 398801568, 410737818, 491650226, 105793299, 232043669, 515557987, 892821461, 74619, 913972343, 456993174, 708361319, 71001497, 904689347, 484015907, 90319893, 611125068, 440326961, 704071315, 679535111, 634133951, 859925101, 357169873, 28705157, 405827755, 729561842, 105013966, 205387460, 826659739, 775023747, 133054368, 395714486, 289224235, 45475925, 889474906, 682800449, 263681187, 834494178, 144378144, 105272931, 810791794, 767518650, 569283030, 109375910, 628950472, 358252055, 937790003, 983899428, 209582592, 780608779, 997626782, 431901558, 564678196, 970207366, 586298967, 987460337, 818216842, 565777116, 272816680, 678539928, 484959835, 87530961, 925763850, 649830126, 749528809, 519753880, 386359866, 509611274, 180193740, 328712298, 338960242, 181569057, 959155007, 844956926, 146885971, 350439150, 413313331, 677344516, 124946506, 809200230, 204348131, 938732201, 144005799, 475044343, 106572340, 681909718, 899641300, 67491623, 814286898, 263516146, 761890873, 917393079, 510603639, 737313291, 297791003, 875064948, 543238255, 598212627, 376786130, 143018935, 603167399, 226364789, 281044247, 485767108, 794538642, 430135551, 563569120, 145675324, 111459462, 164385380, 235596838, 941869263, 347086350, 65594131, 29344556, 265427602, 813798024, 172837515, 937581241, 977972794, 855931810, 825841836, 997328674, 772209557, 188615384, 932050496, 216550318, 653967572, 814040638, 795825431, 172501361, 190699162, 353009737, 341631119, 12343873, 372561368, 596288759, 54571754, 893791177, 441221674, 981500238, 690397199, 487159131, 862416146, 481804550, 816322702, 868994864, 339221368, 294567296, 5766700, 43938265, 768850261, 859136830, 145563462, 866491023, 817896561, 886135313, 836733510, 622513441, 732432037, 308873522, 50427172, 400504789, 205019954, 772311553, 923185489, 176614584, 287265757, 756746278, 853610410, 543821126, 213590974, 910371958, 72427271, 582705893, 198513357, 164682501, 283855814, 181606039, 655867960, 202186989, 351462563, 170268083, 744748759, 451067994, 343179986, 279994709, 238596605, 532914467, 960578340, 398391902, 84272081, 347828012, 764105355, 666723952, 649508505, 722776333, 33833299, 31540704, 379546488, 913300699, 958037639, 987302149, 336149293, 999159860, 931377186, 548008887, 366218203, 32261596, 436124744, 176755817, 21796091, 466381074, 780524895, 55216967, 775341858, 27824264, 964761576, 753126506, 469564362, 578521978, 237778228, 333922045, 610401427, 78249231, 551760228, 895402995, 743274330, 633321868, 522085333, 897187725, 627703044, 357370230, 776442562, 934215899, 897407042, 776706969, 302413341, 323203003, 515125568, 106729060, 882173780, 227463398, 819143228, 344313501, 206992927, 869431496, 590410867, 722010026, 267884309, 555478553, 80188153, 405381365, 139576563, 536902362, 533273015, 147302388, 667871034, 485877128, 887067878, 93209232, 884434080, 110034665, 126338606, 837729943, 422762134, 809308686, 967485818, 968160580, 44955322, 568761586, 397833677, 508302808, 570601643, 788129213, 315506520, 411103540, 596622882, 130709730, 277816441, 856017749, 947246731, 9148393, 271931057, 951774020, 335033195, 842126529, 910742525, 648430373, 11579651, 523369319, 686532974, 754523719, 433403678, 145686703, 80533180, 807695532, 301042751, 772926602, 327364015, 347051337, 197698592, 955192343, 429316733, 887694143, 433594071, 554775356, 694660055, 135028, 341400123, 3248790, 982663755, 206160242, 505887355, 93134492, 787835024, 196767943, 759298599, 318625339, 646174309, 374944509, 746726477, 942041631, 649895276, 295371999, 558765158, 228550585, 929541124, 282178420, 427802664, 881477003, 924286039, 68664362, 345903600, 803309874, 255721952, 931084556, 885124416, 772375722, 124632384, 977242295, 111695836, 360037904, 983725407, 968695949, 191117352, 728195539, 608128145, 135885624, 175913570, 898912959, 395045812, 643129925, 422177923, 804199576, 698412000, 156570009, 541236933, 542644826, 428610864, 936922561, 212453897, 689885126, 138216774, 767246981, 694332640, 38293836, 925159289, 132179076, 808715641, 250208846, 117155755, 765349541, 454751767, 313106519, 546028859, 845888761, 866585920, 792815617, 702162857, 977829480, 542667595, 990901230, 811941433, 97845410, 297678686, 789210654, 507156183, 977499418, 477747947, 239089081, 885669086, 127107136, 219656800, 530190344, 163820832, 380284774, 221093109, 399061788, 855705870, 153183888, 896602841, 61056470, 913548345, 492356273, 708446064, 96160543, 797941867, 593337441, 963464341, 969611176, 655340967, 374308329, 889993103, 605774052, 339836969, 946132052, 264541975, 949636732, 785252943, 442664389, 280169107, 905751038, 654565046, 174737062, 461725919, 853353559, 549812318, 491059385, 496854701, 227124831, 669293914, 205044740, 494584983, 191328246, 508459238, 613230208, 855773441, 405413132, 618870005, 685378476, 222758729, 161806855, 943425363, 238011110, 968484325, 869393918, 118906020, 313863476, 644626638, 845612065, 139549783, 49511771, 994260066, 891342080, 734841818, 866307018, 226183110, 802980873, 435466431, 523287340, 4845057, 921295950, 797396038, 676190297, 294817944, 757178825, 460078482, 879687297, 255312576, 422962897, 571738159, 937488752, 79207989, 846241875, 100911114, 11868413, 503609413, 245118778, 36965862, 625289778, 937493152, 735306707, 317942104, 348967792, 236823028, 91000681, 114604979, 613051363, 698843334, 899807170, 964221285, 634665152, 380000525, 479158425, 512993134, 954998543, 1984239, 650069239, 515886144, 3604078, 193418829, 26485521, 348442051, 113766603, 601308445, 588387034, 315393856, 439702619, 319607426, 471106826, 81826414, 862611619, 197889152, 596475008, 309916029, 111395351, 523530758, 853272409, 489519187, 134866933, 348602129, 731852887, 379497554, 962286674, 743578737, 793901056, 69006891, 987865726, 415485636, 653883094, 956318356, 820324817, 160426926, 376712204, 842025556, 831254289, 891361563, 628327446, 337188852, 890879137, 667453670, 101377172, 161941069, 492906087, 795833513, 41137909, 596234161, 827685907, 615417245, 261074019, 862285714, 834150312, 67491008, 366655796, 827679971, 663480636, 500252786, 408201339, 905863185, 111940523, 809755144, 948633933, 353978867, 467691999, 3438949, 40833494, 377609407, 404093902, 692141129, 793814331, 49754233, 870632011, 152961467, 47392126, 824948356, 153708454, 69738242, 644122435, 692036583, 889759544, 719125483, 622396166, 938226536, 470988777, 132736941, 231327959, 37507558, 17791851, 968656483, 296063533, 608291321, 233850784, 115160797, 965138489, 84776128, 92746316, 231523768, 361637913, 518016693, 519357953, 421489399, 75354683, 866381414, 939296985, 282355107, 368464591, 572498151, 877037361, 186103944, 104437277, 359741188, 212074507, 572789158, 185799220, 3553245, 656097490, 455761529, 265255038, 627087208, 218171334, 63492955, 829292205, 883837663, 570996132, 559118244, 614270751, 403425388, 993130415, 505288302, 781942441, 861610943, 669332038, 808953299, 838889134, 393208308, 781234605, 968622037, 743591723, 502107181, 579837898, 130647433, 378836873, 478164749, 139593633, 833785786, 345457748, 998648740, 704066767, 752303946, 804432888, 632470627, 958430378, 804081647, 573832820, 923985969, 320857539, 238851270, 523503192, 724354261, 658878809, 538349727, 327073387, 6014021, 367983765, 861461107, 398159398, 681285663, 876847946, 541826634, 622213021, 609946695, 491762836, 884882324, 419850661, 946665873, 720636700, 580996106, 513161218, 852211429, 191161397, 452868418, 773944877, 135301245, 877752215, 212946028, 596563850, 23822547, 650752333, 251746646, 33091404, 655722083, 751604670, 373863876, 445503075, 839992722, 520995808, 948550085, 177803090, 807683248, 862149658, 819434021, 191476286, 657841427, 46963832, 99188, 459997335, 195916559, 284963305, 258832069, 895022996, 749280966, 765181553, 813344066, 817515290, 706619271, 859123110, 96875171, 436706273, 553077198, 581976726, 236076115, 287707018, 295690699, 753309957, 978151792, 26061570, 738229578, 47054888, 872538338, 247038805, 956152958, 847044447, 434433426, 630479436, 162975224, 712650787, 546256810, 666853141, 621401777, 331776179, 914524342, 321625925, 610032384, 777341481, 910756306, 980106549, 120223504, 821799634, 148743174, 70787684, 813136033, 961107956, 561870833, 895117049, 93220815, 451509363, 901739041, 5649601, 463599878, 132800793, 973259878, 407140695, 401937174, 222675303, 43836787, 737335613, 812488294, 651292647, 81596861, 253469708, 783384102, 813994193, 583758710, 256070054, 750077764, 155467419, 108671105, 915680785, 476616040, 311242840, 79425686, 136953172, 70713052, 224404070, 637078234, 347133712, 565426818, 794357015, 439593535, 973115932, 135772519, 866661720, 502511152, 792382035, 931553154, 859146360, 823779132, 877271389, 746744245, 730029582, 364988305, 469967925, 366669233, 409202690, 786849532, 887092643, 938373088, 291587488, 240907878, 533623126, 650734993, 348085978, 715599795, 466048652, 456662145, 875578164, 682508498, 486160417, 981867975, 937905560, 365273069, 467288817, 953121904, 34195821, 932608448, 173312784, 566677879, 83494007, 415945122, 805802164, 975469511, 251345081, 681723174, 624085748, 39090286, 376672945, 45349402, 983353770, 398545759, 854440485, 898009976, 413475328, 451969490, 302205300, 867775640, 154804715, 928458685, 137664118, 332714894, 182365449, 517539892, 113564737, 633811769, 412482874, 715735632, 454935839, 631527749, 240422967, 421324299, 372470044, 400708934, 994236116, 415715782, 591045266, 369452053, 880273374, 891876003, 396956072, 439055156, 832955638, 711581824, 673376871, 266013931, 254319121, 756440667, 288635232, 487695894, 35089686, 91469706, 856213474, 220902178, 890003979, 392727695, 961707400, 675621495, 682747754, 169262213, 91423898, 860081508, 704345999, 429126474, 128210690, 837755518, 909494264, 245941547, 983995417, 858372873, 631632012, 567106730, 638681226, 511366915, 445102823, 590738549, 35090019, 825863235, 883287656, 856051480, 129715613, 712468062, 539502325, 924420274, 178017335, 930634794, 45619985, 726153959, 560487415, 378274389, 362375462, 989720855, 905556814, 299672948, 969612192, 433526122, 314064005, 428750807, 674967656, 769353771, 748310074, 274294104, 906783000, 241432196, 6576846, 407094793, 33456134, 999972779, 755102909, 989668113, 359468060, 568532786, 363906605, 606864829, 643842123, 704078428, 114885347, 70576731, 357473112, 133785246, 214498946, 529703560, 635562308, 513063581, 882002439, 441196569, 764927764, 876927465, 853227208, 545985486, 429394472, 970762369, 760930834, 145963847, 189283, 265601926, 263527157, 638418388, 225185891, 223707494, 374236356, 770195528, 143725378, 728205356, 415130515, 975752195, 275292380, 307490934, 952812436, 929260551, 248679755, 29200340, 148499620, 302804956, 83248573, 629115419, 610203116, 353488965, 581197840, 468328684, 908719238, 405834678, 534116270, 925567813, 665234836, 384599348, 915308337, 590206419, 63600749, 654329377, 267993614, 589009551, 158268336, 254872356, 633738021, 184182423, 728059727, 485778275, 772308585, 291505335, 566436353, 421296203, 423222685, 548126519, 355976700, 935374571, 927307188, 354959760, 874799430, 175691085, 654749820, 880689726, 896372590, 13289537, 194597208, 149602836, 703586218, 135228696, 979883669, 718857051, 724495468, 269803829, 254993468, 463107877, 485018180, 142095188, 357716014, 137960864, 149732759, 928818450, 605977293, 17605214, 69319148, 892800367, 970039700, 211116148, 99916362, 623852690, 882671720, 550662424, 226765652, 483805912, 731909040, 169369832, 983107597, 977589058, 790364524, 890933724, 421897128, 923718733, 406704474, 335179845, 788030038, 512409902, 508255284, 147949257, 144752345, 822043237, 878200127, 63668004, 775870650, 271952824, 942215146, 815763960, 605484967, 688461590, 128617610, 538095349, 839033698, 802302758, 964329708, 508229943, 255015151, 832645133, 752823554, 496906096, 651157202, 651873405, 686288873, 914577133, 83624810, 25179596, 74164622, 902261976, 231470476, 935764996, 949276818, 311184191, 458560517, 208534615, 863161201, 249775824, 905713461, 149468007, 230272703, 134955867, 535696536, 115648702, 385777645, 596681602, 249883426, 699039855, 610986590, 522865388, 278427941, 150756335, 903855777, 426498956, 939873265, 469306492, 907439227, 454235428, 397511421, 331808703, 145592682, 671686927, 866716971, 845028458, 876980783, 894888165, 949643810, 175756282, 130306423, 10329830, 152294214, 455101550, 994188439, 975063685, 185148379, 300345488, 248204257, 899581036, 700172059, 236435064, 143742363, 343825010, 609515090, 183760793, 307897300, 300652470, 768920071, 925247071, 675124164, 691031581, 17447898, 453063700, 871250412, 807291158, 625467870, 161203782, 960448101, 432565759, 221317533, 541610852, 503183618, 93495042, 417540866, 336019335, 397740057, 407639153, 180504840, 546071106, 234748350, 41965092, 586079364, 615419869, 321367401, 166421014, 328212424, 126173883, 774414606, 114214245, 630091431, 334491057, 351484580, 613331608, 253532711, 468259046, 217491726, 566253532, 547995986, 785371882, 783552742, 226541556, 715976230, 520370557, 786839183, 47837111, 586886538, 501729976, 171900156, 393382208, 560848127, 552071124, 876383315, 225417372, 181670484, 786535207, 284704276, 679244681, 801708127, 628894699, 748530854, 877433692, 987764353, 829132816, 784511769, 616211072, 609034989, 350225451, 15848959, 69631772, 412214792, 616406308, 972925367, 142756673, 129536446, 392997315, 314443665, 926677382, 165494754, 967724016, 329208028, 516792611, 431021784, 440061066, 98963028, 546294246, 693805636, 382588467, 874128453, 506377073, 395635172, 700559449, 889183194, 609028252, 16914646, 40036550, 714521258, 902662627, 199323912, 288379200, 147992579, 339902415, 636025994, 333062589, 624946822, 405832186, 248100050, 778467927, 938307075, 987553953, 255590838, 689144449, 220432168, 261650968, 468279452, 84588467, 913964294, 475419431, 459467863, 829245554, 129371954, 534757721, 850402225, 575297738, 115022462, 509275765, 282337911, 553378235, 74545730, 390120559, 735879872, 496667700, 786365487, 3889415, 240388227, 893409995, 43955802, 167361834, 124087298, 437339425, 520176036, 574919354, 960593195, 521885025, 623065550, 527104570, 430569448, 133029711, 97055183, 885818498, 942128182, 725473222, 15517080, 509327641, 268489416, 72146478, 941821757, 986889402, 771611026, 899023470, 262933805, 928394080, 268748488, 78782362, 397360288, 21230669, 146401024, 592926216, 991928428, 138001350, 916407663, 967119671, 180240734, 317165869, 869594409, 995754643, 963361268, 267139119, 924774387, 521905870, 359593898, 995146929, 184817461, 950768305, 210716654, 157726082, 953906201, 580772363, 811933375, 3513831, 411698871, 279982983, 365285002, 809849849, 5946822, 201264796, 990584630, 45381789, 22426963, 191849510, 462472827, 112257230, 924243262, 520766570, 39399374, 108142875, 625566309, 216757502, 841309106, 862757666, 990484173, 47113365, 660310153, 77865858, 488690085, 822873629, 356931972, 315501536, 839497844, 527336374, 448803453, 337205150, 172310706, 733908592, 971510355, 596541456, 246230625, 395291614, 922812032, 333593682, 856905799, 355291187, 615429583, 870896357, 744586818, 670857883, 221473963, 422384081, 282186825, 355558768, 175796014, 820867279, 900829880, 651314746, 769162908, 456055101, 763227894, 324886708, 877263288, 687350239, 592108357, 708670547, 680400616, 428059743, 738184873, 945574721, 495910153, 460163001, 351082040, 428771412, 61542551, 610466399, 789307443, 68225176, 164780009, 521299167, 433205568, 343171479, 120208788, 855234066, 294586489, 98183161, 258643612, 826819604, 376829975, 204083533, 20096527, 51247229, 619923549, 274573473, 85107164, 818722571, 301725670, 368906978, 509154309, 394878920, 539899258, 407331119, 749943915, 611554948, 24521679, 588342040, 256329659, 459048979, 770916011, 875659847, 751379491, 917504804, 691256116, 754275159, 538105358, 644218534, 897328902, 653318753, 85863839, 392170539, 291740277, 977151174, 753334752, 622903438, 86079313, 130632723, 286009182, 545841985, 677531123, 394741326, 619681146, 28266305, 467545528, 624213525, 398559329, 564309950, 550143587, 299364020, 562287929, 498073707, 574665790, 913196988, 679515044, 920494798, 79459210, 605057337, 619122567, 571021815, 599170289, 267676323, 584484394, 858301899, 714177205, 186879312, 949136976, 661628659, 140121766, 166252117, 615076036, 835529024, 761558388, 708984756, 738162840, 974452063, 945434674, 498741975, 290878632, 341645576, 469962298, 699184059, 312632546, 88305267, 187246887, 211311158, 160551552, 98900659, 78429380, 693377154, 411755809, 341850928, 968003565, 530566396, 620559006, 807300788, 449310614, 666850815, 608291108, 398769896, 21815905, 452293067, 719217208, 652807207, 274161326, 914792153, 217125028, 712334015, 664738984, 83090002, 814754840, 735336588, 450496729, 253278704, 570535926, 705458070, 630705928, 393827311, 717437229, 1574473, 815419205, 356530937, 99696380, 454537778, 799580502, 125145256, 750841895, 591402082, 287521635, 600402963, 279644207, 348594129, 240412589, 133503526, 312001668, 955853655, 646808618, 615331544, 760921414, 310450567, 850923225, 906325450, 732802710, 328345086, 350118419, 447888901, 708214564, 740387047, 934240185, 983475273, 310971703, 180855213, 695069039, 162180582, 990740377, 385054046, 533534509, 959005746, 553638162, 213918808, 779800923, 259815307, 465013089, 883832734, 708644446, 778562600, 259494899, 230597956, 604050454, 907914054, 432569076, 894047218, 797976543, 14227933, 62244003, 156865529, 965272458, 203951170, 389343509, 435720632, 843089557, 416908077, 988393940, 279433493, 953584282, 882488845, 301761644, 867686354, 753333028, 974477415, 414031917, 640863520, 928459294, 181451881, 826253960, 809601963, 86137939, 747836364, 68258236, 996927407, 870521105, 60688814, 180429791, 420228852, 226234426, 500229019, 704766260, 528446408, 287046508, 335912339, 11490326, 638473442, 66605135, 759698641, 282403565, 79906390, 796509377, 388939953, 646027740, 387421952, 859152969, 142880844, 823942802, 266466614, 625201461, 66887727, 18765354, 605121254, 423127290, 308676171, 959197023, 313522104, 181763192, 303837454, 220082996, 270821008, 254058570, 376119924, 909056473, 888148019, 261242790, 86502844, 79044276, 26212489, 944913186, 504726068, 199959149, 94360231, 413196356, 423687804, 553388982, 663291839, 748028376, 266626084, 404834628, 199065531, 138782872, 604781556, 769741116, 12531117, 128445657, 873523175, 325891081, 223629246, 879633185, 111484460, 97684701, 770056386, 486755885, 536717748, 355831740, 126049807, 580522338, 484931693, 335222615, 285111238, 22989779, 116339470, 648805921, 814268110, 662734439, 602142695, 660111466, 634295438, 91576797, 330996924, 962597951, 69750722, 969002866, 58357198, 689611133, 593947803, 105672875, 708839620, 214024144, 671170913, 913730992, 681401947, 104708768, 249309913, 739395784, 302753350, 965054193, 915639196, 916030167, 191433477, 508107718, 304850854, 953320948, 285083511, 307981374, 579121068, 716152343, 723825075, 379844467, 186060655, 420969322, 486232699, 634316711, 228534771, 489337365, 384879009, 215490807, 485561413, 26508459, 831735138, 351873992, 691663184, 911430506, 349888618, 217239857, 967487450, 337859406, 308499212, 803181036, 779216156, 382377942, 47536321, 118813863, 147950663, 40282713, 64047446, 906917052, 29428051, 234270290, 366004050, 559755365, 550773155, 241559497, 681417477, 486135127, 789761286, 868885071, 543880921, 807182054, 593156725, 736190824, 329963476, 280235575, 43273481, 490341684, 708317770, 925997277, 643183847, 347909671, 551966755, 902911336, 893857362, 356007368, 996455373, 453816774, 144145191, 511615442, 10804480, 348569636, 36553687, 964451065, 281884859, 577479906, 404444258, 174515019, 163500972, 246657336, 307652697, 809314594, 320239081, 70028059, 558895804, 409915338, 987824394, 180081339, 623365218, 63189884, 411892945, 833452211, 98196008, 826410432, 202738457, 534465940, 262311178, 397202124, 891661335, 521174331, 260119594, 493972892, 568480987, 776691441, 590429580, 307312216, 140171954, 864125490, 112694334, 491225882, 594679530, 458101013, 957181997, 407739816, 596941793, 647022513, 953911006, 281907001, 505354448, 686568015, 209792399, 969817109, 916673536, 524613477, 745634227, 32701409, 508480601, 700754, 28731346, 485412080, 332331801, 140939936, 157623880, 967662638, 143812383, 901210819, 157202364, 685697577, 861142031, 151739403, 455684291, 77671008, 50627264, 845598377, 954566483, 121989622, 562895094, 266608641, 206527428, 675581485, 587790891, 301058350, 781370730, 120161806, 938001203, 798208999, 401630968, 907710920, 277329940, 394163996, 496194333, 199168612, 622162472, 437228186, 907509041, 317581030, 58707347, 682578968, 953534613, 991574312, 97807487, 54508743, 830020674, 530727731, 176261403, 586813457, 197700189, 612851047, 226517076, 859930323, 230844835, 482850416, 110323621, 51340022, 711370549, 166140604, 475860133, 816952309, 532911104, 236910973, 149898455, 91261710, 204124812, 27183456, 514969121, 878573855, 992039716, 826798212, 523134546, 317682065, 401824720, 350399905, 316744345, 480595452, 572369028, 526161850, 974021615, 477477631, 204168894, 347330994, 274248795, 250445139, 450080779, 369648606, 379285149, 747092470, 50705822, 999513644, 492265363, 124550075, 182692996, 208343481, 278153418, 963607751, 11134602, 173186928, 335466666, 379575886, 878688143, 671054072, 504269773, 716223296, 171637806, 867591064, 89227462, 472508575, 694450613, 309678310, 227918161, 369235556, 900237367, 548230572, 452010895, 764784582, 22555787, 55622766, 634452435, 403249969, 74875608, 939372813, 746168268, 754923479, 727688578, 27989077, 640747118, 248280186, 237724460, 333682839, 411519246, 502570824, 900101988, 436904333, 981618053, 419628931, 60739642, 135983774, 146846595, 30663496, 724562418, 625218379, 992701055, 616811247, 841172634, 983090437, 13084687, 280013081, 214167479, 776059012, 948696459, 91683366, 775754966, 871004020, 711013396, 870426485, 415169280, 466549824, 336878700, 159537852, 188261405, 752670926, 726867175, 89204094, 444753331, 512101094, 184866731, 30009182, 157159358, 176795819, 3385027, 62581158, 124917232, 505365841, 187090711, 885172166, 556664877, 938215321, 908756114, 566757900, 402220725, 908209107, 787704916, 665985928, 974013365, 805186203, 461096132, 288079002, 876575968, 867101085, 984151407, 361424455, 992076699, 614531245, 668018764, 566643231, 6176956, 368152353, 890931359, 553820696, 800057422, 39554644, 400108914, 496255186, 817218280, 876057211, 439789882, 196659236, 385469757, 616657799, 718349934, 860646962, 167403288, 964021403, 64537841, 29650230, 533289736, 926515481, 694279821, 904929526, 4595371, 845970888, 497675288, 239890267, 334232012, 403821238, 930999504, 565745114, 19811351, 997301363, 348120123, 363156786, 128719569, 402639015, 97599410, 909074174, 784290334, 26372306, 960837941, 676332433, 413006151, 8215947, 333429815, 482391423, 419659042, 581980361, 241900119, 317101057, 65550696, 971839912, 14823214, 749203805, 109975482, 764969439, 139001009, 568100911, 260008813, 311913236, 621537351, 398939089, 736641574, 154366315, 676552886, 942525476, 923090095, 68485779, 839835612, 387289214, 452177508, 241573976, 980730902, 538372139, 741221589, 816305350, 407737439, 692720157, 923287754, 292082343, 842919529, 332120200, 359906142, 275926115, 868396801, 168368505, 749065841, 423835263, 211633881, 738298571, 115060515, 573579379, 58418208, 975856473, 803919622, 124048366, 163952518, 327161513, 993740875, 178591658, 326206673, 214794257, 391359573, 29653578, 670161185, 813887591, 40251241, 448072434, 848788660, 743636578, 685935983, 217677526, 302976987, 140795853, 277568813, 841697812, 575043741, 117956393, 446939812, 963374220, 490990008, 802466683, 238776142, 23813844, 981560433, 624217708, 820403388, 134387858, 863059594, 59009033, 762612082, 644275643, 985281324, 64006947, 845490639, 958245827, 379975166, 755605985, 607538624, 97827457, 594944179, 457349468, 571024533, 635514107, 536602090, 73400372, 159400544, 787310247, 278002017, 138935025, 976145181, 529377582, 494589162, 459825903, 672982413, 604449622, 57430246, 767057899, 207271506, 408141380, 354602398, 125903933, 210232194, 284789708, 420382881, 428715351, 390187430, 415972657, 488494618, 467901096, 783533454, 754502718, 358945296, 362526103, 17715373, 132863682, 754506573, 567888723, 415703195, 868885692, 296358432, 365867167, 262982364, 410994631, 525389568, 169940341, 211073318, 118749692, 92996137, 242593301, 432713950, 474564468, 170682729, 89299997, 5408179, 190799122, 793515396, 469077249, 956300988, 158782088, 300265836, 64507125, 922668063, 291923097, 460496402, 976061130, 104129830, 557863564, 154330098, 857013924, 766049220, 22378644, 958160682, 482513399, 800248353, 20085645, 817227481, 564629712, 728885693, 804200736, 428657929, 934507209, 171426144, 922848305, 342339151, 602275844, 462268127, 563755719, 388875587, 111412381, 228292691, 26541383, 934651501, 352708156, 634283896, 773622823, 657701759, 18183647, 839246059, 562804131, 90229223, 431515341, 230617043, 948234839, 144057, 853377997, 118383669, 684399155, 78990214, 788002917, 721458081, 652124282, 224607234, 80850011, 437734226, 452242058, 738477714, 483511313, 260080013, 272895998, 494759999, 241480970, 790112397, 806016915, 61520733, 412757944, 843555551, 779253809, 860877366, 190188860, 93364808, 544252397, 276423054, 301000378, 69519041, 953647539, 107717770, 523470268, 854114415, 470087599, 880625683, 581539627, 499445818, 680750952, 395180674, 641284965, 534408651, 400085543, 696478673, 231549654, 864509160, 416434512, 777190254, 614601509, 71704814, 387885279, 370196195, 20130394, 693076602, 963300090, 539314369, 187214198, 227640498, 100684646, 899956444, 667440601, 943205783, 454756854, 925220216, 163681888, 399704331, 575667086, 471645811, 87342088, 97921886, 257268743, 6558817, 656083998, 650538475, 78160134, 509131980, 406228401, 710493629, 5287999, 630280613, 850439695, 323541214, 290306426, 169177652, 821850293, 330229830, 824912545, 164279463, 996326454, 643261086, 522910127, 811942593, 822196046, 327307117, 100666888, 261659742, 764859355, 364465693, 414993872, 226035683, 19864596, 372266727, 843980711, 112800006, 932336106, 491584139, 931413766, 988369334, 476467010, 320056634, 799719619, 260836094, 573496207, 164478322, 582815436, 529775124, 500927628, 313471303, 585121033, 208152284, 176164614, 461950954, 825563156, 583321687, 467454128, 51063326, 259212632, 681973791, 875382806, 582693716, 681154739, 226191417, 281262623, 711848402, 866414819, 672031945, 465136443, 626641870, 102937452, 634253505, 371572810, 424647738, 979886679, 72672274, 558848608, 83334625, 841491873, 150908110, 177529882, 607145182, 539593186, 426861817, 792629983, 659191210, 642055154, 557874437, 320746868, 881854333, 593321299, 566123925, 138934441, 857002785, 16939770, 149217861, 707772619, 612856090, 701557889, 286461592, 302455250, 493355527, 303805573, 359842144, 925524030, 691333169, 374317456, 732794189, 173096300, 870266162, 935165170, 763566769, 738353268, 970042592, 816669529, 646346039, 496191381, 913901155, 883234059, 238670996, 90635044, 432853007, 989528772, 22196869, 739533100, 777513900, 552219719, 290294297, 434795134, 956375868, 660566433, 947729623, 403505308, 86836692, 679517974, 332725074, 109676701, 127535045, 871856819, 461689963, 600817385, 712655359, 491538165, 901624635, 671275053, 528315032, 54103912, 860354884, 744912759, 655637758, 285808122, 81706047, 146309458, 990543103, 777959736, 354352573, 376732302, 154381551, 529481205, 408166807, 265189490, 487040397, 648423382, 684066796, 397633278, 518157064, 281446745, 512868236, 494330204, 85979572, 728958435, 419188169, 457171345, 90164404, 697562009, 73331387, 768720251, 777446607, 212602713, 399031865, 257893647, 910671935, 969253379, 356800998, 65758105, 323142461, 809873215, 798934662, 485754859, 921516407, 160617990, 375952058, 862423016, 493882289, 175420570, 318763950, 211835607, 482966767, 575472174, 101872269, 976149679, 588499681, 504271095, 547326517, 403717375, 493041946, 217155057, 689655315, 898157257, 670061849, 743524421, 332241873, 639455277, 75720790, 941890431, 511553851, 492964003, 943686384, 9916661, 124623727, 983737710, 290373296, 693697250, 409991792, 104841209, 307453929, 33012287, 963315933, 372888332, 911878644, 381635808, 362256008, 632096288, 221545126, 493304987, 198674842, 566317771, 309074948, 97760215, 797460463, 426088640, 441762959, 149782839, 365720728, 151335272, 57659392, 682264956, 443209927, 80162402, 843981901, 896245377, 929342779, 264748672, 691076872, 217330711, 40542727, 637955808, 779379891, 330183895, 920181424, 302762035, 746975616, 385482101, 962052172, 506774984, 873308139, 541485016, 463840334, 767767849, 656936416, 945591867, 791320286, 356288929, 205090795, 577154400, 364873781, 787389378, 621587090, 741233538, 389688115, 546128655, 125535007, 250047580, 578754464, 249848570, 183601813, 872362657, 876305707, 940820078, 758259226, 292845668, 920009878, 917492029, 101435332, 854354227, 602765116, 532710623, 159726931, 832535916, 775373468, 286364221, 649454731, 323547021, 744762396, 1966576, 602298165, 411091380, 432975082, 386858480, 840335975, 787425695, 191586935, 89707473, 10237771, 314782442, 977532948, 407012789, 712790017, 781627720, 904656849, 798519532, 456889765, 542742647, 591631906, 763172025, 781567257, 689226841, 766483211, 404899652, 692242064, 582379322, 764342403, 588481419, 215147014, 15297268, 612446075, 772817915, 675367883, 112575427, 503882989, 99815129, 712102758, 825217879, 441574993, 970735925, 523121012, 563777687, 917996827, 397560897, 801796538, 707817839, 210157181, 521949459, 32546017, 660909032, 821379195, 861955948, 230701321, 650451881, 303907315, 466924543, 129206116, 213422109, 177058855, 811497756, 808202473, 50000146, 377112130, 188559669, 613256213, 410187484, 43186096, 8288986, 534849724, 642777622, 5314493, 155481098, 235959669, 861550301, 621798130, 473222475, 237964948, 376712977, 158865319, 80894252, 140740696, 988950424, 360406040, 586810887, 73149991, 526224162, 432073677, 839578759, 612437227, 807536088, 622170625, 485696410, 398684579, 373275894, 746064043, 906907161, 247778627, 759403052, 517524618, 877609637, 437564349, 362484002, 210968784, 780260181, 536613489, 838384769, 451780242, 848988010, 618765267, 501557357, 391427124, 455997243, 305607296, 465078376, 608146544, 314074397, 840946776, 949136186, 825203923, 594522973, 227657811, 694850577, 131445854, 434392659, 280374739, 823112216, 771637023, 899320131, 846330422, 407559241, 908226997, 764997511, 841605590, 50729501, 235035875, 914497806, 590353014, 886711009, 723660632, 260603462, 644524495, 211856759, 317428088, 674250479, 476326846, 168715002, 431167457, 662085167, 33074363, 91751033, 448014016, 554395213, 228109717, 91099678, 688137342, 883039991, 594513534, 865628107, 436448186, 313770518, 884432720, 874776849, 573393374, 327517591, 782090123, 900156119, 596990201, 506615699, 731917325, 187772596, 442792774, 735365781, 940241879, 3177191, 949462694, 294912915, 219549323, 457911799, 354740883, 718063399, 837498564, 946975443, 10685805, 892688828, 382154560, 581084785, 970359352, 449306101, 595963076, 57665592, 357502644, 941208355, 353164972, 138130093, 902235616, 393788697, 761638062, 598302416, 663811675, 756587086, 177002476, 19489391, 328856569, 337970160, 550810343, 395920021, 208476202, 9479582, 854851629, 387342563, 811769832, 816723388, 601518965, 747521309, 393012873, 250541278, 672275269, 440640903, 975527873, 779570278, 167701857, 701582961, 826731621, 684179406, 934681239, 968121619, 45023885, 744422353, 934804241, 494192311, 815752665, 614010540, 580978986, 727571679, 761157452, 176450623, 694738670, 738832777, 408902658, 911504971, 315050395, 321457198, 638395579, 118212141, 972313009, 935778009, 806777941, 624298660, 788551495, 693193851, 990266076, 217675009, 286386224, 273528168, 121049450, 423274843, 763820163, 347321901, 952280686, 513944577, 11175473, 382955841, 126063131, 113588529, 672944363, 414817680, 733042704, 394083300, 981300076, 223927205, 716869813, 287884645, 911545958, 442950421, 394350558, 118345017, 25537415, 645453169, 334569603, 652545320, 198286411, 861708381, 260647029, 164044027, 952381974, 16875792, 278112924, 92002554, 181570767, 326493150, 974004829, 99589774, 754948017, 174469058, 595687097, 222938359, 511023279, 917143845, 534569473, 630865871, 796655157, 644608753, 958290102, 439824567, 749984911, 39547416, 68305712, 534113421, 296925382, 536098121, 853576827, 67579363, 276291507, 760016141, 552856664, 467555454, 483362763, 996683902, 892401344, 614847536, 608603222, 639391290, 160897493, 617517171, 83057265, 520304190, 295605996, 345224822, 545159536, 993876930, 144045849, 26258872, 595665213, 31125333, 54980974, 445940796, 873882525, 77780461, 289209774, 874013071, 464812806, 341975452, 345573100, 704967393, 486153379, 164197363, 66130664, 124075863, 949641801, 484616859, 5077900, 892908273, 600792216, 296091299, 137435096, 162444443, 794598307, 737252894, 633226006, 242827486, 679782268, 782113492, 866520598, 984236927, 986128926, 446418477, 691014157, 208096858, 349872016, 323463598, 276520089, 519139498, 850594312, 939727629, 733997245, 684058381, 919606860, 180003598, 792254206, 630289451, 776768671, 728464778, 842703997, 711966826, 838318375, 332725229, 250864066, 428973436, 691147577, 434291484, 236288742, 334712577, 979334453, 458533078, 642528757, 10385472, 79633322, 985989621, 58933739, 560830556, 682273878, 705555298, 675078649, 808569420, 668108838, 413890118, 174844752, 818478033, 482627804, 846192339, 240914082, 60256045, 307294002, 206511989, 367644146, 414588908, 393807750, 856358022, 281471339, 966353781, 887448181, 362443952, 687566425, 587315255, 78344829, 349641646, 229188038, 444903780, 608358039, 600376586, 229416436, 565327885, 763627952, 671891478, 502800316, 788844316, 953804953, 706805724, 770412226, 364322368, 243681985, 750460927, 575806462, 610886287, 273489946, 28358923, 12948292, 926243130, 445445852, 452640421, 517227296, 719247932, 132583550, 907323978, 306441821, 352255862, 211313454, 21297738, 253951784, 75323406, 284878708, 955426196, 176876814, 302213945, 15920244, 277798306, 526936029, 700155679, 150993793, 713001021, 572819381, 454209448, 246922841, 78534402, 743141366, 456226988, 610333608, 671871362, 745742538, 848536675, 499154926, 593995301, 454286223, 93517812, 306033276, 289169113, 678013427, 989787447, 952078401, 46474989, 701904349, 658903528, 841953437, 944224409, 319245257, 783600471, 446198770, 270494842, 398272451, 623710899, 908872585, 161862577, 841882787, 245896668, 290024360, 814717696, 6096718, 830049793, 692112547, 963745897, 32030586, 458262704, 272213827, 390192616, 169845596, 489187345, 460493046, 885617058, 912401719, 5458122, 498517495, 14852383, 701530868, 939549460, 302859987, 247875047, 219813160, 788574097, 757188767, 239272193, 734590834, 924144951, 513711197, 980906528, 547077929, 264672022, 805500225, 683305854, 537601039, 505114082, 94304798, 647787499, 924600278, 396101638, 78657947, 11703458, 650303136, 273207881, 450398828, 384685858, 497573931, 743533895, 656256908, 926527306, 288331327, 539777107, 127352012, 166823898, 784968113, 522673362, 867073346, 577574065, 559066832, 552034037, 95871079, 841330148, 605717880, 619517193, 988384236, 450469892, 676566663, 801534449, 544508427, 311394208, 440184693, 358672503, 347414632, 726723945, 47073137, 179376582, 131841735, 810651544, 48518378, 885572452, 737439938, 185711628, 896525053, 204879003, 395874540, 346880123, 226736737, 997486334, 837276135, 671773209, 440635101, 365028522, 28673128, 970148998, 631643195, 675257622, 899802486, 230447299, 613349904, 158705243, 998046017, 522525240, 271428680, 155276776, 593158682, 168907583, 860931488, 34860156, 662296855, 261190479, 848842415, 738116739, 872100236, 229921350, 891064561, 871899447, 233011362, 529393350, 18516350, 552155770, 797919828, 14693929, 261547724, 496873230, 86987791, 889787574, 222335049, 633218941, 555591602, 798265553, 595292676, 472069315, 274280509, 550406951, 703057307, 661961864, 701685000, 359729313, 40742633, 282928710, 77738609, 627961871, 425995532, 715798784, 847488420, 284986310, 700165863, 720590186, 990320290, 411524353, 656989956, 21848580, 196576252, 409735222, 174460655, 558114141, 882291837, 758985722, 867671650, 976935692, 947305935, 404818396, 898108730, 331094232, 261816425, 951180013, 348526773, 918891731, 382229753, 822775216, 506449501, 969013325, 377553123, 265757530, 124652565, 831779767, 70660673, 287684295, 484415308, 659275925, 631192298, 284171015, 457456225, 393442760, 411020044, 635063567, 934547237, 56519350, 605873823, 319337083, 439927735, 277580318, 349066301, 342159935, 141363559, 294999463, 4226718, 634929546, 645721690, 405522940, 758124165, 752793901, 513385917, 194498566, 990963305, 922100099, 771876305, 546384838, 864120024, 784355866, 317715689, 364506548, 37479355, 95170101, 813757672, 773839588, 43220830, 757849139, 486935200, 272035217, 388034405, 24251623, 691399692, 145625604, 522010526, 709991166, 324240800, 272475092, 349917965, 851914037, 331649136, 342600029, 476284449, 560127645, 602831847, 711467292, 904601116, 900496444, 375323650, 185849883, 586035580, 503782207, 448320925, 44897441, 593163438, 473621619, 611471217, 218555923, 18333359, 277017652, 999777080, 497030891, 758885716, 996962049, 507533286, 771764101, 571225524, 865595489, 430932750, 478102056, 931668156, 335114492, 285316659, 751235098, 437585778, 752636115, 451901858, 107095699, 768119560, 453479956, 256487231, 34709888, 235378926, 269871054, 962729552, 717780138, 721006202, 228419537, 804959934, 240854255, 790531335, 94154051, 292795543, 788557498, 457343256, 156284724, 160343414, 267083076, 913015260, 547662401, 432187641, 361845260, 281619017, 58805090, 937438812, 594687057, 93420767, 566445952, 914172567, 574845579, 428262685, 206010801, 354011292, 701787801, 905997838, 620600564, 659443963, 800042922, 847763438, 516855141, 548271935, 721887857, 320096218, 230438671, 157393355, 787157881, 532450500, 607212677, 771671017, 254750524, 229838183, 179693161, 575169017, 951657491, 460545024, 925442152, 841752222, 930382257, 945796014, 552477398, 871226678, 947649302, 120462433, 509418229, 95720384, 693477714, 865811254, 425275391, 390712563, 470122192, 445810705, 98002023, 672890236, 347426759, 550754675, 10559720, 320975699, 589264561, 875543040, 217508460, 298215143, 520114125, 632256349, 710606673, 168993252, 415742332, 39857397, 16500620, 147474382, 38386431, 394765783, 408010582, 824751143, 799056412, 596613595, 671492634, 389493367, 650153292, 907686036, 258364236, 997081319, 905520050, 655450990, 963254700, 671920521, 43714208, 494698237, 309016687, 540855219, 579548711, 458321677, 54256678, 900096971, 807314144, 58146423, 288762447, 535489597, 582490764, 800738777, 498615544, 709914510, 870541890, 61491704, 350769894, 124082836, 274922984, 29338549, 311928973, 353776715, 502138122, 385473639, 157659873, 277518980, 492714519, 144180372, 775454422, 760075370, 929165530, 99291496, 28462164, 519960055, 801818120, 350380366, 199744632, 457664606, 262911591, 480389231, 593170404, 659277447, 657391495, 232513382, 632460830, 327245621, 691246877, 367765899, 640160687, 385546866, 981477273, 144172706, 113094227, 822788604, 242932666, 959550033, 280691037, 891134734, 154006242, 738716753, 590263850, 896121139, 397523952, 928400501, 638488075, 861292002, 822098937, 834710779, 830735535, 394382590, 993757619, 741567926, 465221257, 194233969, 899322585, 903398387, 942460289, 20897486, 90785714, 150567998, 385582869, 570359502, 961251097, 376902097, 86288648, 300123148, 919824001, 936397884, 798694660, 441884470, 205795385, 771165945, 118071145, 195950035, 695003229, 985421348, 262824122, 605180349, 628447087, 666855273, 507382185, 239518843, 802606698, 510442763, 114510601, 233489631, 259063464, 28923119, 293516403, 574184081, 328471208, 434580271, 307259061, 699344701, 105390423, 741691322, 605941377, 989348485, 487424165, 662200599, 298588669, 28823393, 990715253, 206309994, 771816891, 286614276, 482676177, 115326489, 878802061, 42532864, 699818055, 597584424, 902425384, 252213705, 659771647, 662119942, 801467997, 69472682, 355396548, 833767980, 414197451, 189705600, 225639090, 768225156, 924836079, 614016894, 865565976, 232261696, 94065565, 670896574, 394786615, 315286609, 451103007, 454525230, 379089496, 995969951, 17154859, 94022734, 277370752, 195080728, 492435203, 491902142, 154588179, 20032829, 600368771, 860491018, 947481239, 921754711, 854510433, 359277592, 371361360, 497558705, 100022880, 333688555, 882271505, 917608290, 944762565, 695541812, 608679584, 808778543, 420931379, 904768505, 515356682, 607552464, 342646630, 684556432, 125960761, 142142368, 300936003, 25961733, 762517379, 922691430, 708023431, 416319652, 966536339, 116473730, 407313235, 908864066, 9273503, 368028571, 203074028, 151127725, 898784672, 796772924, 325512274, 312078632, 348493018, 912201756, 955223308, 707879035, 678034273, 768199448, 617585119, 995924574, 753709733, 797691480, 394031540, 844915187, 229259269, 276937338, 288618012, 925686670, 364246171, 366473715, 755262330, 621237618, 701783446, 212791853, 662991930, 812330306, 973864187, 989436606, 180654371, 902160684, 641458753, 992837205, 413246546, 802334199, 276376185, 578387377, 87958422, 454937789, 683625151, 316329901, 8166678, 266377855, 276768794, 223306245, 876231647, 843561509, 338456932, 349842153, 871531376, 769557065, 53185954, 498547992, 179236224, 882208446, 639324435, 50899156, 985281564, 768548637, 531325321, 119897459, 960084064, 835568026, 6899792, 940552393, 662970879, 427689789, 399185005, 32927687, 922386296, 701526476, 46618657, 395047839, 476136342, 355934430, 337525479, 719260398, 94896484, 252986585, 861185034, 832611778, 650401724, 743490967, 899493283, 948821250, 602306450, 480008549, 833697932, 766492198, 571220461, 139362071, 583343857, 615474456, 614176783, 107831092, 498320944, 57039311, 475579512, 80872547, 715014080, 694303403, 124415759, 724156513, 641202469, 352063942, 812415986, 978202643, 287853215, 444114199, 114067728, 488711903, 202544828, 455120781, 123176442, 624699266, 61972221, 19103526, 307067063, 465586930, 123870621, 853695973, 527009387, 964914967, 502111883, 32086671, 711902349, 325041073, 190363959, 593747259, 300678981, 112857537, 42435265, 995676257, 405569594, 617093189, 507171669, 534216093, 15112084, 909117533, 788476317, 469972109, 581539000, 227371973, 51789207, 969150708, 295241954, 892491087, 128976593, 881596350, 993628161, 605511396, 781273067, 331692957, 247717858, 89714215, 979138907, 133348145, 990823099, 679274679, 408643785, 832667505, 131342150, 925109998, 33597272, 894940394, 187708642, 978814674, 985422548, 432802099, 59106992, 789962250, 743030008, 956803067, 115613821, 539416309, 906216160, 564238779, 562901775, 783802558, 233607860, 96120367, 282175886, 235630686, 9950014, 918385265, 89824525, 14423513, 508897942, 911933152, 585547903, 315201069, 518523457, 450060227, 362923418, 137396640, 911536914, 2731731, 94298172, 334418740, 372395074, 124928657, 162580763, 50892360, 625831540, 330428636, 367486, 716541284, 273927411, 510963104, 425541377, 574667977, 454492865, 26096447, 689989079, 429647574, 17752433, 566859203, 299666003, 621370196, 20974153, 771349307, 787243628, 453262815, 912916114, 64121652, 823239552, 82050299, 61846074, 934102349, 939788758, 234708411, 853866104, 249660341, 683377863, 223124202, 631791896, 755321963, 167656254, 743622415, 734746456, 881183477, 533248207, 696486058, 428756572, 353966428, 765141271, 669927661, 565801009, 151368791, 371011659, 175484116, 181508571, 185583604, 809333095, 660629417, 979594104, 759091718, 148430147, 798504929, 345124428, 583330737, 274534962, 757491327, 430679595, 188940463, 805465450, 395103664, 470335761, 6007521, 760760243, 939976054, 289672677, 499706090, 558909339, 638288037, 961390422, 879747070, 779439048, 898133157, 553206078, 663249828, 80635580, 519681362, 793574560, 843154289, 513855468, 382523197, 544253062, 744383257, 665344765, 636180709, 30618433, 864749668, 385341554, 113971622, 984168855, 656358868, 565380158, 673495024, 329794754, 907763152, 326710245, 635178859, 234645018, 215452917, 765577600, 873023163, 585958789, 406737282, 656929686, 817149945, 691975717, 192610288, 403294837, 804547968, 120567033, 989977247, 292232881, 764681534, 923415037, 928568087, 886814637, 744332600, 655649455, 649565464, 395312715, 106112680, 562507020, 902442450, 961716684, 309529178, 6411705, 511560050, 437856562, 585354090, 416041171, 15822409, 714896879, 220918673, 600578886, 386044870, 478607220, 497544660, 145960678, 327229001, 222752517, 548884521, 961323711, 368631968, 418551690, 34761898, 276200307, 36876717, 599754195, 995725186, 240146482, 978905882, 144981972, 981311218, 933522099, 573130405, 373382960, 952322308, 371429196, 976214425, 200579724, 183723915, 469751525, 952731400, 562208345, 639111505, 247068175, 971070179, 188419373, 696405198, 801635473, 864756962, 45424222, 100937646, 655710432, 648865064, 119057220, 640854040, 23248204, 66468638, 499228984, 788063807, 855827582, 911409193, 811273668, 268928225, 281221045, 480959373, 239738628, 779555032, 718972140, 669065105, 347959290, 463033055, 288675154, 182108163, 887406675, 593748846, 327070951, 599167268, 439409543, 536212658, 760033648, 988149342, 60862725, 501623211, 740504372, 237638807, 676410268, 217991932, 758140619, 27020468, 505807149, 27208637, 585516980, 925154520, 175190384, 68111890, 433046420, 332716443, 472512866, 194589861, 585026024, 610466150, 12910510, 73117624, 685046031, 837557588, 467992975, 49292820, 80183216, 179823131, 893260528, 291550700, 703400467, 603860227, 938746910, 580062755, 232971218, 647270051, 318212986, 985672915, 31483896, 918766135, 443529308, 26345647, 59444160, 332588929, 974975571, 345412933, 156384526, 16637700, 584511665, 326708326, 293717261, 792688462, 652060427, 988763708, 446506558, 711659249, 691366773, 646312324, 744304579, 103342771, 871648508, 372770310, 239216371, 90395562, 233309076, 707941948, 66208764, 188210450, 650309504, 876852057, 870729756, 296917990, 603910734, 476983205, 440850211, 45692851, 376826693, 196353820, 359629921, 958741343, 484742230, 464202412, 414226060, 953622736, 9668708, 91798511, 876488067, 574478976, 873145477, 674455882, 338061058, 890110584, 981699591, 389588987, 684119570, 458824230, 683095378, 835139700, 636221257, 480883616, 59001936, 902398414, 96660671, 897963252, 865365468, 551405320, 242433346, 758917195, 336425081, 123765041, 579902013, 569006542, 902021404, 461279222, 113724535, 953949439, 22152780, 622859405, 656197525, 320683838, 707211752, 570054841, 386606981, 23636763, 463410775, 990347838, 123101610, 981671043, 787397595, 576144775, 684282691, 167793136, 33846832, 102516335, 698440336, 385863393, 627404856, 936596636, 550722818, 525287792, 423432271, 625589515, 621342955, 471312692, 683813515, 202351881, 377569084, 913280464, 139142690, 346139970, 165361999, 574215604, 998020423, 853373936, 967645388, 766677419, 941747588, 536256626, 52639147, 898741503, 226171942, 878435933, 558839085, 475103142, 231635980, 416123409, 312895922, 259517847, 346200557, 389731328, 441800037, 469504306, 483611227, 236975707, 815896781, 341705680, 768403390, 850887429, 50373356, 444752225, 223097880, 623785860, 341545584, 26876772, 576889666, 743416825, 310679034, 608288964, 654964573, 364403710, 246490240, 614379156, 678277135, 694031500, 308736212, 584462220, 937659629, 369371534, 615750398, 125143847, 856786516, 845366818, 810627472, 385927160, 471058131, 16889435, 951769878, 507267662, 568662909, 600697574, 269540758, 386548946, 470025805, 54964530, 546166260, 527015823, 583083782, 811438230, 995412925, 854867587, 137629528, 268519037, 24855674, 193878312, 128124408, 955260183, 158586837, 181054348, 337716042, 863069368, 327672245, 133421745, 550945464, 426683830, 976469081, 802948504, 59248179, 705158469, 371752482, 63243953, 932135802, 828197671, 581028759, 657786220, 259797093, 369874638, 639952680, 486980567, 426074201, 9694299, 271193227, 339345887, 188019278, 612871790, 632328097, 827451257, 156782973, 860358856, 330222703, 119082357, 57907730, 336432596, 907938532, 380825093, 729350678, 516669878, 895998983, 655163956, 54160441, 855586596, 940264048, 458865480, 700008273, 516925482, 33268354, 798416813, 236583694, 781214745, 123809267, 936794800, 974221454, 839827487, 208048313, 841478706, 668317915, 168969787, 533088232, 345451628, 742234324, 436263982, 957377208, 1110186, 535814679, 328659434, 806853359, 723875855, 653178999, 111812242, 219631107, 728795255, 237665590, 527131229, 639092739, 497786788, 599361544, 983851611, 741512798, 799622070, 309073795, 492326008, 825906953, 338705132, 394678991, 54464801, 837840760, 828467449, 743739487, 967919506, 461394528, 342801783, 527282472, 557233360, 905219966, 987447567, 783103605, 15849043, 451800421, 781132897, 530409068, 517047318, 971189502, 724386451, 893661435, 692515743, 193482547, 450353353, 155317193, 540506892, 392312122, 661867869, 561428434, 442973401, 620292811, 33141390, 626338698, 553196276, 886912742, 628651593, 972455730, 328823822, 395709700, 209780908, 600139559, 122937301, 120904250, 673736304, 927527930, 905655750, 190934758, 477999721, 123495324, 127777124, 414813358, 155945719, 16996597, 304701810, 183841978, 997100168, 431320448, 766351223, 815536430, 14760084, 930101845, 726216218, 487973365, 246843786, 986307040, 896869059, 67585147, 887349227, 299230293, 48519599, 16455283, 187061373, 732326767, 732731301, 645564703, 566695818, 619709365, 218182149, 992760734, 768383662, 879922784, 436591947, 816506115, 956725210, 822390656, 10400704, 901367326, 243133670, 213635529, 805974459, 458034469, 642292207, 351812743, 733206797, 582699104, 193164290, 469753942, 487646083, 928489790, 71355243, 601703529, 59487782, 223250637, 316091336, 909602380, 367776023, 517212118, 734066926, 755793342, 230926363, 935066144, 320516267, 271596571, 829892088, 350532402, 375347569, 721323481, 320597429, 438090035, 979006000, 287752472, 902139555, 615951992, 244267652, 106197645, 71386984, 472322842, 639757818, 179178891, 48303448, 795457373, 308048606, 689300821, 732688828, 720552288, 211277911, 139044229, 512147992, 30943221, 284665463, 701866101, 555381389, 730853665, 355718722, 775191121, 766848225, 217112799, 208895234, 543267602, 91207009, 21670734, 863706519, 45324419, 990609595, 875637612, 110052888, 498034983, 830661632, 142492015, 836503966, 659714897, 150345973, 460445895, 691218058, 428156494, 141972039, 519541959, 120661920, 34777676, 128923966, 347123396, 560371839, 817948717, 592810688, 269197059, 498570751, 707644599, 779519345, 756303121, 458983360, 672112084, 804705149, 943526771, 824474940, 66417624, 555672315, 416722911, 857394972, 847267459, 823903222, 31332923, 506806037, 646035379, 560485056, 734175652, 965575573, 972668995, 643672285, 794000003, 511233539, 889327001, 512038200, 980282659, 53735454, 921932290, 566394330, 900612851, 797298475, 430965391, 793132423, 414534895, 26832690, 949431703, 244675316, 532051239, 906079734, 160143767, 826318839, 906455562, 996063126, 739664446, 447164169, 453760442, 178282716, 964571580, 537939081, 999751539, 334282304, 962829857, 27204068, 823929244, 829206293, 672434017, 19583449, 352356504, 394610564, 288220857, 873645241, 165616602, 848172354, 226579182, 587420007, 806442802, 350371954, 286573521, 442195411, 714762620, 362678552, 286270848, 995621892, 567840268, 234549288, 604360588, 156661091, 186535369, 44715691, 496072457, 446476849, 453714096, 899027370, 332400886, 547544294, 38121894, 670767254, 843379714, 277436621, 213106027, 769637194, 244206956, 672217097, 497416684, 196550503, 779094537, 991592678, 430572353, 956726573, 255722013, 492632530, 160784343, 597942872, 396886439, 369250219, 276330038, 427202307, 402294210, 205044865, 144316057, 488359890, 715894528, 348316179, 672096560, 430045809, 116444265, 8125001, 220079396, 703654088, 901027384, 678177506, 609222590, 395500724, 163200428, 970714386, 744437616, 527290402, 972082689, 928223917, 256233468, 276230348, 310754042, 601518231, 762068986, 989757642, 950686665, 685759001, 463409287, 538139210, 142322332, 623261292, 81876593, 512312867, 37079294, 744218197, 161974066, 423893835, 986125357, 102294729, 71391802, 684241854, 381127850, 706854340, 791582775, 29330935, 277297411, 976457695, 797477017, 941473378, 1715380, 298261315, 358924569, 980801407, 895089604, 279948622, 549981042, 948840563, 331190361, 809895708, 956649602, 11964419, 28717875, 227219115, 384581914, 823677401, 745901571, 965548356, 122019892, 402086856, 600661758, 510058497, 207036831, 681805364, 95138565, 401638109, 656627141, 346017913, 993472589, 668407772, 855732586, 360559642, 65347012, 335933824, 544389701, 534974199, 588616772, 452732839, 383198489, 917375811, 545158962, 882326519, 185117937, 539317611, 52043606, 117690226, 835966722, 735379719, 318784195, 682975392, 968726415, 708487062, 52898165, 704341758, 403525525, 226820372, 841544087, 28342187, 695101023, 971578059, 72673562, 928204709, 301630124, 661286368, 253315286, 812332684, 351532457, 730482184, 838592237, 815159027, 885160389, 795211531, 519702899, 171148334, 392812287, 749348781, 489595904, 129314393, 649607515, 316893021, 484879544, 832710519, 485007178, 587458305, 270455999, 621010630, 612157367, 366849385, 250960712, 585791778, 72122472, 467033047, 879997759, 824253444, 781163871, 913784169, 911188694, 329850495, 511273112, 434791745, 880751249, 217988935, 448764175, 584925978, 604483962, 216604832, 333376536, 770414110, 383242431, 517738689, 528904032, 462350720, 579041537, 491311010, 382526648, 162908310, 908001266, 609037815, 924594361, 898094905, 683777431, 316009717, 858422270, 408388801, 803648741, 671482178, 379723257, 478643747, 686468072, 445733330, 887716107, 292285561, 32645549, 141799647, 581250222, 172694454, 676315991, 134586425, 354543947, 819487481, 923303156, 278664763, 307409940, 114812675, 487058643, 332151267, 293053543, 746157714, 52473428, 15688153, 11984325, 371805338, 256899808, 504544386, 753011762, 155135618, 495830682, 141399647, 395809298, 819486230, 936011423, 112069368, 155767716, 978106564, 4438516, 55819019, 436164464, 187926422, 875080635, 783202522, 111287968, 504295185, 561339375, 159518267, 843855310, 547740586, 779063885, 46713513, 282768101, 676508530, 382121949, 164282310, 369100320, 901842418, 643453352, 270285135, 336030013, 553596126, 786930616, 408568670, 986847447, 153121455, 576106045, 717207372, 178526095, 489453455, 412569149, 535645878, 524329057, 849303499, 650395386, 829576301, 120782905, 487290673, 513497510, 938177977, 376774767, 981284094, 294989156, 714682795, 390123931, 15840019, 320536568, 674392886, 90540624, 588252903, 347708451, 458198307, 412847727, 387024664, 3102503, 718794904, 431218012, 991332461, 91365061, 230045512, 829318257, 74876815, 489489970, 349953731, 275604142, 45283404, 287164205, 11332661, 566066088, 464860256, 851398367, 124635259, 1963449, 445493403, 911700403, 596220626, 605795918, 470932963, 347337790, 413903182, 539412968, 628098853, 198113280, 923242711, 933779903, 20883586, 312087668, 212169861, 184431919, 559190778, 876145897, 131585735, 679613929, 146182247, 420124196, 351343802, 258084517, 631650722, 158650567, 485900820, 366756110, 907861052, 387453703, 874083366, 358876938, 967467692, 306077373, 997380844, 915841661, 266417249, 407040203, 968712084, 585309788, 225975656, 763631232, 234989985, 345564835, 282061551, 51654836, 276250849, 848605762, 178978785, 433246476, 689234707, 295664773, 450135365, 750292992, 754390198, 323466358, 993188693, 679273915, 437361702, 47926309, 69451443, 735957761, 214741999, 391523547, 316426051, 493237366, 343607848, 197784067, 365191294, 395041621, 621128669, 942194910, 651532947, 6801582, 815602590, 122440176, 636618689, 788604690, 898709224, 187036018, 157544093, 644248363, 709819714, 688728718, 333839002, 680001957, 431405663, 414982595, 530018225, 277309367, 380442364, 919124748, 599463194, 165000751, 838220785, 506313784, 119136927, 442973318, 278337418, 382289242, 457123201, 163007535, 474340551, 282685821, 840530679, 217011119, 70591999, 743120417, 191241602, 741747576, 891923777, 479370460, 820208000, 274355653, 750067061, 623157727, 609114587, 799127879, 351832825, 976059483, 416627341, 626019223, 709948835, 8578023, 646081734, 89846284, 298199448, 40374889, 518343840, 177425953, 892080580, 370380746, 630741734, 53450520, 655219389, 234643912, 329203230, 631751166, 68155004, 691552488, 181629348, 505899929, 690045209, 775868661, 941259886, 373406796, 610956852, 604335749, 917390499, 79230555, 427307620, 587770737, 225634335, 576348713, 586588109, 615551056, 673296238, 151042961, 429506052, 523539815, 552511637, 535629099, 369372989, 941172733, 2090222, 13921866, 527204011, 97569039, 701582056, 240079401, 62443559, 785288774, 270545839, 820167451, 478347131, 783325535, 483654778, 825077992, 889900812, 929452912, 974405871, 995441851, 211395139, 799532995, 229490155, 336423220, 963466354, 301163291, 30512721, 798890691, 860531218, 402772108, 227402706, 729300602, 752674649, 91848345, 545468505, 642669828, 206318872, 750812864, 346122959, 520058530, 777102871, 560551587, 294625228, 716444316, 438575736, 631222800, 324800425, 460085085, 712526188, 594597070, 474256043, 619975198, 122146423, 222467314, 520491492, 990732867, 177156718, 263165837, 387076934, 850980806, 375304434, 184274804, 1075682, 85093661, 679444195, 881141577, 412440651, 886945743, 11066051, 37623010, 961706366, 70985778, 282728280, 525321752, 440013080, 789288542, 897226253, 542448316, 600265937, 998756338, 997749442, 305950189, 302728067, 734881415, 982171577, 693954949, 882669315, 832633785, 139742123, 360176193, 538482997, 795394467, 53065657, 119947534, 172127206, 872821584, 918076581, 598314851, 798570522, 335127749, 377661087, 423902040, 428124001, 519346027, 364562640, 281983429, 303432544, 50384318, 543104967, 153576625, 959592183, 931277334, 963487150, 866793828, 589818090, 744732224, 926965501, 180568513, 915874078, 865313287, 927466338, 773919956, 426297144, 19110123, 885927841, 310299181, 130482613, 15579707, 826531372, 849795174, 440045343, 754602435, 645952961, 147639160, 816043211, 749375121, 778671446, 962317574, 274033048, 55201385, 442721091, 173710580, 895650331, 482071644, 603611397, 347623390, 183749886, 795699968, 492987625, 806353803, 179886205, 508913127, 611494436, 858452782, 111898274, 667790761, 183956392, 577930727, 709894472, 715175592, 480632134, 264373534, 292617867, 563713379, 866237010, 603038994, 98721347, 202294313, 226283251, 966108714, 905455721, 962326248, 35640210, 518677259, 942042091, 368943110, 126627987, 872113700, 491415818, 706882162, 915004630, 718528132, 138124944, 261021165, 2953277, 356212536, 737143249, 219150830, 720009978, 749613942, 643870878, 355899210, 596740472, 359141583, 480907464, 973051366, 848604978, 724114931, 71546572, 171447580, 660411592, 698119329, 505195580, 287915474, 387257050, 566705338, 856026036, 212042779, 854516891, 257434755, 528218226, 709561413, 863184776, 9760162, 972533547, 521925442, 713272305, 51314198, 912851604, 763422830, 98798550, 713227807, 166083369, 660579678, 524581529, 303159974, 909233965, 192729739, 620334425, 162042251, 281087190, 505182342, 324550600, 63652874, 88392599, 570275246, 658077976, 617349892, 477685909, 435699931, 186734457, 600956222, 620753147, 244749152, 538780928, 594549620, 895584864, 910491926, 860706147, 782041800, 33512696, 422443429, 161750247, 530681598, 514164066, 97781991, 235991305, 101270608, 503874149, 799553656, 840441287, 254060415, 295652442, 688304525, 923203875, 506048901, 35355740, 251406644, 944638721, 261433575, 892880884, 921703105, 896034291, 517862894, 723544685, 879890579, 267998625, 67029882, 822393469, 777918855, 408884940, 161134822, 143568176, 930896719, 807544743, 264661683, 447289932, 888382790, 420296510, 75388557, 378127971, 571373182, 797820930, 518888253, 631920381, 395158190, 269502137, 710467076, 944017187, 43225846, 105772441, 725347416, 143685116, 747333795, 402237361, 886077694, 875369994, 438631594, 731882348, 929763604, 465675535, 760876096, 518442667, 866965020, 959947186, 120892337, 964870909, 199366651, 273611397, 272232826, 992621975, 907910255, 954033455, 765288115, 560996854, 119148569, 698574150, 517105878, 699036728, 700728034, 671007695, 656845369, 382198016, 389330565, 637728950, 306546441, 7271873, 446894942, 704717757, 473587005, 431713142, 604380488, 711779183, 718357106, 222096140, 810852600, 566168927, 632166745, 369893402, 486584219, 586216005, 804173467, 211902237, 934608568, 940634990, 313567077, 775134791, 917063541, 590907946, 115966977, 838584270, 216916074, 936609966, 128697791, 35266133, 373553882, 645197399, 583662426, 376770982, 179998897, 186616617, 766828661, 906301234, 348706172, 971526097, 699046886, 768173214, 652141696, 181261651, 730504158, 337021555, 428137212, 417457087, 747090173, 804002573, 838436162, 183726095, 165117985, 257206749, 368939264, 605670574, 14495713, 355407764, 385141796, 704278062, 237326657, 103112808, 171645199, 151054012, 808846755, 387088778, 27659050, 850553751, 963052316, 179040094, 78693456, 166257905, 355245049, 655385699, 618119079, 327823836, 493578377, 613645799, 605043587, 389622588, 95617203, 285369330, 190917307, 568773060, 442052376, 259222661, 695151050, 341006475, 556677732, 382957251, 401863770, 299706998, 964161085, 420535153, 671856416, 664536412, 132619212, 634980493, 812293329, 832629388, 458918863, 926921804, 667603922, 69647881, 46165157, 243679094, 744949625, 61547936, 272151845, 430390665, 848952986, 28398255, 399736392, 939073940, 394961187, 442850890, 209891948, 99265190, 632353915, 902148277, 679319631, 87201188, 649423625, 256528209, 615349413, 928095961, 296015573, 458171277, 778376998, 846640489, 760477800, 709287283, 571962750, 271722167, 348127492, 794349925, 669103181, 315588874, 372638993, 431061930, 484450145, 374053174, 515349381, 919709059, 336270101, 169027053, 25746484, 798430781, 973283554, 280120400, 845536647, 580446021, 59574603, 810103583, 526656339, 554030093, 242155649, 52699572, 329702418, 662848945, 575530042, 419879023, 999196363, 363533383, 502231407, 68963702, 76900829, 772773315, 463336072, 13968566, 743335598, 782611399, 884069480, 38937913, 794584576, 655121205, 365500420, 798387366, 594909145, 94238684, 353274357, 184742741, 859320841, 732979025, 934003691, 23131118, 967203348, 942844010, 740183722, 360561454, 960561466, 789410805, 698362847, 594334657, 197562286, 356542925, 224851988, 983352325, 107961643, 368407384, 187850029, 242284104, 587804769, 960193973, 11780117, 714978054, 196483465, 509567610, 676622662, 909726933, 799606360, 954523315, 240147568, 735343598, 887329017, 641626756, 773562515, 486636574, 650761969, 413402718, 610735395, 903074768, 354814774, 430770801, 262882253, 710296908, 728199561, 27610977, 807889318, 227888115, 135992331, 930489478, 55006926, 60625662, 944213576, 607342651, 135648669, 105501379, 854630596, 124118571, 891953294, 98197797, 811484885, 703427254, 603131876, 492489809, 878206696, 420272289, 328174767, 332448171, 786569087, 12125196, 426700492, 461634132, 266615446, 222633337, 747295647, 815219309, 934021085, 1649813, 282144754, 932583545, 892185267, 523326811, 187972589, 343674222, 492739313, 56802419, 808610237, 339157766, 931622971, 143946055, 14803194, 155796618, 185678792, 231058825, 743554604, 332959171, 20807711, 822419479, 620686820, 877632356, 896779906, 399001590, 742072242, 526890691, 838112423, 384937656, 23587663, 506962143, 122124683, 688785158, 599573808, 989802235, 971427279, 24494333, 925621351, 865610779, 376113574, 220215126, 399070429, 337511790, 368682717, 220843417, 292202397, 404866375, 416349321, 126913987, 581074776, 236062766, 887029175, 446965845, 256902306, 56859184, 823665560, 231163738, 637063317, 951143706, 775477003, 448845228, 607629874, 995285313, 737411335, 576760556, 529409807, 652385687, 953671499, 260795169, 791435026, 415164476, 200563601, 85516905, 376110469, 945056465, 296974562, 386974241, 902620249, 110589195, 275476719, 79804435, 549651842, 672223746, 932033129, 412372942, 907731607, 550956725, 87730116, 796286332, 246059213, 551093840, 909421417, 769095812, 199646402, 431815895, 872578086, 466766900, 105165609, 910274094, 864194332, 429518243, 558244711, 185581009, 1459033, 668290837, 457878977, 356837612, 38333752, 386278655, 682461001, 130504589, 85458580, 904507822, 599561188, 811058232, 920092785, 574350225, 95256923, 715537179, 807977021, 473485677, 817508611, 84975428, 131431163, 31527400, 44356485, 80110238, 362301145, 784546624, 150854264, 587033087, 625886499, 219240582, 163114601, 300068949, 915288909, 117898693, 682220134, 718227341, 45865928, 533542239, 97418962, 688210957, 336158957, 894980731, 918933525, 636953057, 234533573, 415790255, 131333519, 514936968, 67796935, 333858829, 156012267, 37929080, 22430115, 231835604, 888181598, 698192406, 613476804, 397757884, 81999390, 93166844, 664134865, 286707669, 860445545, 458530685, 399580661, 815844401, 168736551, 595731595, 952739897, 733682357, 501924301, 733646742, 829060957, 76790121, 123212295, 586770557, 79115397, 950131470, 541823972, 368607032, 651813028, 512081343, 279330770, 626955937, 770083248, 890313443, 993883719, 594190183, 728326140, 512405987, 137626548, 4950947, 282792490, 648433993, 730749979, 799606989, 187251027, 44750328, 549132307, 5965217, 860194815, 21747773, 489439535, 353095515, 459367871, 82284878, 725050772, 430153210, 263127066, 89306804, 464723183, 76639974, 734232088, 154867710, 331733378, 260037820, 461529987, 562643485, 620308058, 747818733, 241389377, 950339829, 177456424, 758758230, 349396489, 300290821, 171431956, 637846535, 621130306, 109545162, 765880298, 256614984, 531023592, 531350192, 634647876, 315177022, 269737514, 654362177, 584554132, 935659779, 803757545, 590032812, 210947160, 320509829, 380895904, 43266282, 126360311, 466707605, 974304243, 86800965, 289581424, 62891322, 505406121, 369126990, 840242200, 606310639, 891197577, 604302301, 160169347, 301555685, 963983406, 941040402, 999346623, 603552706, 952387052, 33600473, 750686664, 764006077, 718365435, 888697198, 392021572, 38333667, 411633606, 229075439, 486812782, 306988391, 467684116, 228998273, 113138233, 48971510, 505541580, 791427652, 347450819, 430690122, 99606085, 616580426, 409476123, 921779433, 421270392, 935173164, 780055680, 300668809, 664297052, 383568846, 799812320, 185893924, 686755718, 831436073, 803074804, 240230128, 952461132, 688082562, 222966480, 52971856, 620433772, 839168109, 914529517, 416477460, 557397070, 855530743, 901839462, 962755639, 957394519, 795469425, 601913284, 592654854, 209887706, 877023855, 84580640, 879305638, 763868365, 584676298, 683833022, 534341577, 503744644, 81604307, 56994505, 656049735, 359741017, 770838854, 762822418, 338768061, 338112125, 923589714, 645890974, 623755076, 982776005, 927839205, 953556015, 61550362, 221090224, 753733161, 608468332, 719283707, 363393995, 781894834, 522203703, 103337123, 518538776, 460252378, 6703722, 173086663, 405927066, 609460951, 218697993, 464920851, 474306682, 392664801, 333190719, 597451584, 553660081, 60101300, 450879133, 101283039, 794986302, 180224104, 378529234, 537303939, 761182754, 296419463, 246120652, 644529209, 991614265, 400782111, 241278938, 227434277, 182879856, 246590358, 637584994, 564246159, 646648731, 73162070, 780367359, 848642803, 990431911, 830015574, 719877927, 671492442, 744213036, 292347524, 257749323, 150345015, 315895051, 116522907, 609811398, 150048653, 373085867, 654971234, 10811152, 253170903, 472933316, 513736859, 76018947, 911972089, 747431041, 229191449, 4151851, 915393401, 696194656, 533502905, 866169901, 174639286, 752355192, 271402469, 476788283, 863888160, 980697299, 348602904, 612798914, 250028017, 482322031, 515257467, 633400162, 31226526, 503706386, 489420337, 512279587, 828373761, 81119933, 627420648, 919520914, 652417029, 401650272, 697455223, 339316391, 889351740, 594358564, 976836394, 410044012, 268376410, 339712004, 830463115, 901731331, 887213128, 431539583, 296471107, 28764599, 724058855, 178530326, 199229070, 56225206, 856192057, 304875187, 463434468, 534298164, 278355222, 594532285, 396903386, 597675076, 730173165, 975762206, 916186169, 454118359, 595005693, 138699374, 695981563, 402618575, 173448684, 663368961, 690469469, 744374114, 969825234, 446641949, 628737352, 978196586, 786627694, 441198363, 195109713, 483471005, 618401622, 413525503, 689044148, 298968054, 616107891, 305913812, 223615140, 386240139, 909905368, 218556450, 661526242, 144267626, 231913018, 570036600, 106144578, 910282667, 882560955, 900114029, 721515085, 10540152, 844570388, 916285139, 648122708, 857239550, 985882717, 924592347, 392006604, 28563510, 714908630, 337014883, 641996577, 556085268, 621770580, 688687846, 916292571, 31166477, 165313313, 113876627, 184844532, 84795352, 622597317, 729091618, 638954075, 452904557, 438134588, 133023349, 618985503, 154382986, 704058159, 746831786, 362079389, 104647033, 408139576, 49828097, 256682357, 113726514, 825225586, 930736033, 933895937, 547947289, 831639114, 206066159, 843838342, 295874456, 792352410, 220454884, 707735293, 715598197, 434180805, 766668171, 250026588, 351941588, 921365405, 5176636, 494129692, 801316591, 457373411, 872671464, 3457032, 229854274, 638853650, 457232007, 17201753, 908213161, 583595508, 801535922, 659451082, 633749966, 370498692, 968055123, 207376295, 177088688, 153901322, 704479150, 719247504, 433743161, 142925962, 127071653, 75702413, 44263703, 870844802, 174801872, 900357460, 208559660, 407312147, 922052382, 549576913, 367567770, 292791884, 186018523, 330706968, 599115138, 333657347, 986413525, 199423201, 925547609, 686205982, 168559577, 911698482, 467691898, 188074771, 226884232, 263070649, 820188393, 152305583, 113325797, 271951656, 422912974, 153063603, 888525159, 153410438, 520769737, 895680012, 83672492, 549620649, 889281469, 357857102, 651385354, 391802241, 347525938, 9049397, 499983672, 311239238, 621520154, 62053113, 372061953, 592209262, 328781503, 850024801, 390106435, 547676572, 752544733, 91851287, 204747180, 203738888, 10534535, 405232253, 47330170, 577156789, 828791107, 438006744, 388904034, 67919658, 205650851, 990756422, 89313017, 50185162, 447944849, 452233180, 801678040, 695784447, 122092194, 844188964, 981411392, 406528605, 904634013, 736072801, 117451239, 480553779, 606969115, 7660485, 661736490, 286207149, 203922061, 854019024, 669933625, 836796578, 760177461, 154768791, 136782930, 474204065, 937101931, 418819766, 533374687, 973060604, 931942520, 442070703, 10411580, 122886922, 103445001, 589282697, 557121144, 971857796, 488626069, 766059726, 683166968, 868425849, 916938746, 436005797, 521083107, 876634009, 94872405, 723840239, 458645252, 650815963, 782713257, 419841840, 92671052, 29019810, 870933829, 892864200, 899510797, 80917331, 429465610, 840209867, 632358759, 295107748, 647195128, 386361520, 279902987, 609293793, 429297344, 830950916, 506771755, 741786506, 776941156, 116799968, 65673826, 583830523, 362442766, 95409084, 359710176, 227155077, 30974833, 96814427, 781700073, 892059801, 320189274, 379609319, 427145815, 775477230, 866407617, 233290457, 309186701, 621018670, 788831435, 52451054, 676719138, 831250943, 100263485, 121676377, 285825851, 846904512, 569513545, 645234940, 207574621, 794020957, 130495790, 764849046, 547532751, 192331004, 215543304, 697361700, 733001895, 210942023, 938210775, 403970544, 61075344, 125530267, 215538117, 471647064, 577873731, 634733937, 78555213, 173988352, 277579277, 363718899, 398847690, 751060058, 108073488, 511467184, 419380969, 661780185, 290840921, 178504322, 968770020, 303549406, 148274585, 234878111, 6118094, 257398429, 365977072, 157585749, 894732414, 182853115, 386196181, 218918168, 988312900, 877368229, 422800491, 451076106, 219781076, 689229994, 146230194, 365133843, 357904704, 98714570, 264052362, 375104150, 513337607, 106522077, 291822883, 503465607, 9281268, 918102778, 23193853, 742832402, 791391017, 733496587, 75753114, 844163009, 153644059, 455751026, 113550849, 265051012, 636717211, 257168151, 135069187, 780067714, 588720875, 830646389, 720534711, 188305221, 292638272, 867394522, 474709905, 723826475, 435940373, 386237186, 857581505, 884438767, 568018064, 603983720, 675695296, 445664095, 279318008, 891879890, 83967172, 892012077, 929447437, 716233964, 284153720, 904606453, 689861857, 149971696, 807490747, 765930205, 233880436, 889888143, 14165940, 232928332, 342187146, 57294117, 610236782, 163038799, 401797767, 817309681, 976136579, 939252636, 483439830, 495317983, 461949774, 848866902, 253282145, 955319908, 955295553, 596914489, 396601429, 917677840, 101729384, 406792727, 719177690, 622775559, 549494235, 276522839, 459259224, 204339072, 88578706, 311401356, 590855753, 498296146, 632881553, 662504348, 594293016, 477142145, 606820793, 52221468, 407003888, 452212564, 703919818, 490055094, 641670872, 627269146, 678014728, 557637338, 870854627, 27201431, 467969358, 965035872, 163465930, 185217223, 521387193, 104674368, 115959770, 151788009, 358389709, 694942652, 143284789, 674814044, 1239279, 911002015, 250436652, 895171212, 155577315, 316079626, 882904146, 274140370, 947170733, 894021782, 271529293, 124258197, 902307147, 707582227, 948257091, 135800781, 502858509, 175374468, 390240123, 122727863, 181938517, 420277334, 670101042, 93960377, 891681853, 968238509, 657388851, 762341575, 850007856, 243356863, 938275932, 1308739, 87903342, 960187719, 358685344, 830365509, 413876777, 934416953, 268927227, 62397924, 386597262, 130397182, 216425149, 132535453, 813005338, 571101081, 306708748, 575160957, 331364536, 926923493, 406772732, 992708007, 142875105, 761025232, 158544401, 36331717, 900477282, 35752950, 225149431, 638026580, 503544835, 701736576, 864466017, 440826527, 419675156, 348322470, 905359955, 186551312, 566281824, 192798872, 358579334, 677517601, 872451888, 791936265, 463950426, 179176733, 666792940, 473266689, 659914939, 78840155, 776061453, 864411645, 984344890, 748432029, 251025964, 161810148, 67399511, 282046224, 136639719, 232856819, 694018420, 163237833, 83047209, 486432225, 922229753, 63200063, 349021081, 576795465, 202679317, 254098679, 979751684, 399951019, 771700979, 741504714, 354993128, 999327552, 281694888, 882291661, 11441659, 367395361, 338050502, 632179771, 445779997, 977150062, 893725530, 792514435, 60625082, 466830927, 86577403, 316751559, 160785298, 306329291, 107919601, 443113822, 269122688, 514186159, 935300542, 916918483, 219554495, 459239247, 5245730, 881302929, 82496678, 853199897, 129415869, 490544495, 409351926, 698393676, 623316374, 778100963, 916595870, 692068128, 563690892, 647939145, 445414607, 654970851, 601181415, 655666680, 429649637, 814481183, 245502108, 628676980, 150549193, 192983543, 636177605, 230831724, 363289369, 612612713, 457373640, 590608501, 361454896, 359405474, 649487108, 71544962, 781230470, 28429987, 62175570, 601475875, 328236423, 602276102, 806858985, 741084795, 829902926, 277398985, 440162219, 81021065, 362291021, 13023799, 98899548, 504488196, 890865532, 136486529, 542420035, 722984135, 898308288, 81359359, 471471410, 789096905, 38216412, 692793827, 793688227, 500533811, 529801937, 848225307, 251667600, 192147735, 3007246, 915537201, 872911608, 226644688, 14413862, 600615686, 607322809, 462148590, 94681102, 228827058, 945333710, 522633724, 2800435, 106639178, 93194650, 795187422, 606498501, 871552227, 459264544, 705050983, 788700666, 487427743, 193102230, 239325148, 598527645, 12300905, 601555606, 760057967, 53154940, 919537017, 914098367, 829563880, 219108469, 608635284, 171031739, 21795820, 423271773, 17434004, 167647981, 123924756, 531303221, 935219164, 691331091, 969498099, 817192080, 923842401, 86970019, 528254321, 953331954, 617842221, 222880428, 354075802, 597941639, 559192431, 272021372, 391841539, 709463782, 685510583, 787579771, 971666802, 8486188, 337275300, 314359540, 348885656, 681161658, 843411854, 514471656, 483748919, 518804007, 493105979, 118268150, 956334745, 75152856, 221818719, 939987501, 283466335, 402114091, 711310193, 560483240, 251077365, 92716130, 102190167, 745676227, 16356454, 520071619, 85692518, 566595254, 601489587, 619919282, 682252635, 637954114, 467594762, 239776271, 662396482, 265330959, 81877289, 571882446, 159555810, 209688787, 671109298, 660508934, 550647755, 303790056, 536958434, 198701988, 739853975, 751975819, 668020050, 772092349, 382362073, 895106001, 368584502, 18218262, 697193689, 444233929, 175133942, 322631120, 29021482, 834938952, 296374755, 488969445, 908093516, 655592120, 787405563, 998104978, 320141749, 505661819, 721140899, 453296934, 211108288, 12910787, 702002704, 337285040, 102588924, 287147437, 941654887, 835651587, 16262412, 991319671, 416664647, 440000764, 110463574, 692036691, 906055088, 22576170, 349323092, 783800604, 676880257, 683514739, 527960587, 396714553, 341444068, 163388000, 118570074, 246303317, 41687266, 231931991, 335450423, 591315587, 603942992, 778057282, 205204166, 543284369, 145128379, 685176751, 698845300, 675959533, 894985831, 67553575, 385524002, 164668501, 377952464, 548170702, 689327374, 877214568, 944432645, 655046962, 191985358, 255883305, 934099402, 523131158, 734082437, 566309592, 125287299, 979803282, 497464827, 613454275, 738337385, 155768714, 411752781, 551535263, 351467499, 349960486, 685970066, 731336175, 315481812, 356050501, 14068429, 79378016, 28424078, 714649649, 812822791, 187244761, 283496008, 273208547, 809019360, 29092262, 296747464, 344413447, 65285761, 557202139, 261230648, 188313309, 907731581, 15670765, 299006338, 223924089, 23622583, 912360124, 742803727, 773099710, 696766008, 756002840, 469518472, 890885646, 93533139, 56141553, 395088325, 589732660, 971998529, 372952269, 994873207, 129319348, 479033085, 465624380, 307715502, 485044042, 974171643, 921269786, 203789637, 275406141, 260754521, 144341108, 342982297, 333558859, 150092961, 134510341, 224039329, 13333337, 741867951, 949180756, 299454708, 922809467, 335787551, 215808969, 625397722, 880357514, 329171067, 238318324, 593870749, 207809797, 621501466, 467306424, 434315966, 112061917, 408324161, 408901346, 538724175, 941205997, 494348559, 213700612, 459191468, 923945810, 330071318, 441256515, 151423433, 61144685, 42614285, 115914059, 783183506, 599848178, 84860525, 210164540, 934124636, 532421743, 344981500, 316568650, 913753597, 793588939, 137527734, 303307995, 700777550, 751566368, 349011378, 609030288, 961576516, 839931290, 458030531, 176000589, 846693764, 364463686, 270112941, 528191190, 279939837, 119150048, 900612910, 71591905, 989224283, 186112462, 253011126, 361910227, 55990184, 406624542, 646976930, 413633093, 694655683, 553387721, 832947088, 885371600, 718549145, 43760113, 652159805, 777865114, 606340268, 756635452, 417908132, 872102255, 673604196, 121475857, 996995866, 90084422, 82163067, 321546891, 886519111, 512321124, 439935412, 172088486, 21954582, 919006252, 963341274, 186529612, 737201796, 671391054, 748124443, 345654799, 220668039, 723296497, 127533436, 620871231, 754875554, 887896940, 909790807, 791869836, 526092224, 949959776, 220891500, 260424634, 632785690, 719414707, 734558242, 678189035, 431063386, 227778591, 964451987, 841216668, 934445931, 40069324, 978428299, 361086276, 531552252, 550625669, 64001398, 438090843, 36788346, 345187846, 957726930, 432598534, 953589580, 511665175, 791138119, 646461963, 897423520, 86771705, 293358876, 940335753, 627532797, 509296561, 583665704, 220525631, 661788948, 454967601, 711830780, 994987192, 467061018, 166760051, 726057632, 816848295, 536556919, 829095716, 734142940, 624172470, 98764287, 282702256, 175065008, 972856112, 739040075, 741418424, 221648518, 222183883, 666625763, 714718011, 667819620, 738914349, 178106337, 513391739, 322444203, 910679066, 552394284, 900729981, 446634352, 444811951, 720356061, 883091543, 797555129, 161763971, 877159255, 292248732, 202297966, 309500308, 97947601, 607401023, 122439406, 357553800, 985337904, 305243092, 934663731, 341058352, 5894762, 328358556, 544697609, 323675764, 562309715, 835636146, 755174795, 172445275, 309923469, 8526763, 193994169, 725124284, 614465683, 735158239, 949635501, 7072127, 380715073, 509272014, 728262354, 42025788, 481977651, 523973349, 493409320, 764019736, 288348893, 652817133, 125101166, 759742210, 800418066, 463943383, 618320119, 806845915, 758437539, 186760236, 314459260, 516340016, 631144417, 949933319, 667991806, 608901385, 124477392, 64867668, 348821489, 865879349, 996868589, 339589327, 550013360, 520686347, 134931860, 662253109, 401887503, 957289711, 511110768, 743573609, 900891356, 196959721, 534870194, 408743442, 910546584, 129440641, 944066685, 389715349, 474699923, 819580069, 605702568, 875168444, 339656040, 687697235, 375269635, 751663609, 595063043, 462557850, 810090760, 3693656, 71248, 851978166, 892241695, 413240482, 229443646, 676876262, 41478750, 87315201, 945447174, 52946519, 933409165, 863510509, 94231814, 508589792, 133055432, 492838258, 452703134, 365698633, 481186378, 662250592, 904641158, 380530383, 775590989, 470228985, 195538521, 182485350, 887930480, 123587945, 425824457, 421858867, 687307138, 560884496, 306145591, 978478124, 187030751, 384920126, 424937984, 794712999, 773055329, 274877882, 873375709, 962910189, 354355826, 788654966, 840657602, 230221544, 463726664, 407819208, 544580856, 123501883, 834836639, 926660898, 423411345, 10979610, 496482631, 784169472, 315744464, 369733456, 607218433, 498551123, 500937546, 581267792, 603634102, 440793407, 871222545, 716739886, 742276556, 97786229, 976575277, 353054606, 865451264, 602240849, 946630991, 532077432, 894401366, 528655006, 852523793, 23102319, 492735055, 920773130, 158561199, 284421742, 418280893, 182486326, 294555773, 817962840, 158738471, 206806988, 382096102, 898846045, 927303958, 131424505, 773240310, 412723379, 304876384, 828047224, 846246213, 129957226, 909421285, 481830675, 95528789, 457190059, 872719409, 38714348, 1419640, 422556282, 16169553, 536359918, 13386893, 565537460, 786024335, 484669588, 169964319, 712229831, 812576464, 627427190, 519697657, 464504883, 611339997, 473461160, 88242258, 359079641, 513877, 667947856, 554573082, 294816968, 979961861, 478277463, 256708953, 860580377, 698366563, 428186757, 797337400, 337432186, 240162327, 548069060, 306643608, 232084457, 556401974, 781938844, 252267792, 889541481, 724858473, 363533173, 326271217, 369651543, 480372890, 587393470, 620764390, 337747019, 498009691, 415520966, 509055433, 471796132, 744970450, 71010583, 106817402, 558344688, 327785613, 458274289, 720517466, 128868748, 194815837, 637952679, 302266835, 312729319, 328748142, 557069522, 724435448, 298282610, 279436844, 315482005, 475547319, 428762003, 186576144, 399664686, 168958919, 574639078, 788009947, 737493684, 240665830, 358155585, 485926413, 204299764, 429645015, 605489969, 856748025, 930747616, 63561636, 585424101, 601784061, 442525549, 932660604, 306743663, 984644465, 976713416, 792223181, 373087473, 29353527, 561080440, 806288721, 639107946, 246548876, 147188138, 393288328, 152972274, 63710689, 592225206, 380577417, 477107184, 171575543, 580360622, 357864816, 780569800, 607359313, 306293023, 379328721, 388259943, 740784349, 896020656, 142225464, 850487852, 172003881, 928485419, 435734788, 140604147, 688039339, 801509003, 542353090, 706505747, 748565377, 360106540, 764194266, 371992599, 32318446, 810225964, 244884761, 166636561, 55910251, 416898565, 936011117, 892786211, 153604282, 213505456, 683666650, 589699832, 237004564, 926327196, 733822462, 304390481, 495012988, 160170478, 841146227, 318584320, 393900147, 546489170, 185098754, 645451963, 221279794, 791685776, 320900871, 682190831, 193274967, 262505537, 674616088, 66845919, 219696184, 188727939, 247327829, 746636836, 292775665, 199138123, 139736068, 117341979, 673888044, 487703369, 912314944, 919675308, 430018499, 385159098, 596968135, 541627991, 361669054, 897851866, 20256210, 343027733, 613687574, 35483939, 391748563, 196402099, 698511828, 888953495, 744147390, 998946443, 195131391, 858729613, 686551651, 669556295, 399183071, 792239148, 803112175, 765455290, 102481525, 835917621, 268507311, 260306160, 719148206, 199465147, 444719124, 36974151, 32586865, 83527399, 942971127, 863784049, 730770426, 115505750, 70052178, 891693590, 795003368, 932597267, 881785582, 356430166, 796199614, 60723780, 263474489, 53823973, 242806446, 9051457, 580425148, 520130266, 212827991, 409395574, 788478329, 206120906, 836388614, 944750071, 332208482, 439440835, 12068238, 444849165, 75409591, 762281158, 77455767, 939551054, 358482359, 437482101, 729738353, 734693332, 484304990, 694744990, 187798827, 584693522, 195448163, 289794641, 530241686, 182222293, 62796310, 363110524, 817013156, 268705820, 773770918, 196183302, 342843054, 812105437, 927407211, 129001465, 530552710, 831858147, 892406687, 205520050, 594190599, 810948093, 719637518, 389635226, 497340742, 688358976, 572092842, 871458946, 282025699, 786510534, 747728829, 499100392, 80119355, 23093870, 550954458, 201393619, 85396625, 500616152, 248846287, 144151883, 992452536, 408248483, 595648717, 685415487, 925797156, 690552351, 995319448, 691842464, 164188343, 699040261, 223664, 91732477, 898707801, 566014676, 228773529, 901572347, 877456062, 990952996, 571302046, 348834231, 723615409, 539606325, 698653406, 768383450, 992547598, 135083412, 702688652, 669540720, 600131917, 686003324, 133411973, 907471326, 151014401, 953064953, 328253678, 758578242, 578583992, 184281809, 835889845, 510545607, 394909082, 483952513, 523170773, 355123992, 460361243, 453007333, 993960010, 707919569, 511404640, 241172928, 608797759, 665280699, 788439281, 977693365, 703445203, 118801132, 686030850, 3584697, 838471332, 761969823, 95278162, 569375350, 794983122, 445090916, 923347660, 4068442, 12522032, 205806840, 488217987, 973638064, 637932047, 626057225, 370971727, 694090938, 874794492, 263173688, 209294773, 897566970, 342179235, 560154985, 713922222, 477140040, 17326367, 821370896, 636438057, 553863069, 194157362, 883277904, 563836710, 967649509, 124820346, 454791301, 68015293, 436459626, 740961184, 202145008, 526346930, 423905111, 796125717, 753405734, 306033244, 953399434, 625972396, 772978628, 371539505, 505768220, 456851571, 894180021, 235550914, 24374436, 280251707, 623572001, 854426605, 121220794, 41344779, 261725345, 737105250, 100585685, 354642041, 806413714, 546763948, 548997596, 200692397, 249667482, 561230295, 991459761, 80274293, 441974901, 639094685, 254953687, 239470155, 825364295, 648107708, 588376114, 127696859, 247578386, 393820992, 446282922, 240699883, 43735242, 671683279, 790413110, 225665538, 957463528, 960988931, 858268395, 856764320, 204575028, 514471848, 192759200, 867288978, 603508100, 400855338, 58292947, 246121579, 660845911, 746360082, 632679414, 165364221, 220942169, 608846714, 91936286, 300488994, 236117704, 155039957, 939539327, 62486583, 910491637, 770171220, 643241259, 101384910, 828641712, 201677335, 2395374, 418226025, 125221421, 233765989, 815323246, 30723446, 426605564, 821637813, 894152467, 102701688, 250113831, 856677800, 787221836, 127074125, 535286753, 394467196, 456562404, 989529870, 465205172, 689059659, 338818652, 411536410, 156413115, 341326179, 191290202, 478498464, 287251969, 980955858, 575852973, 162884587, 55983340, 94592190, 158807436, 482993561, 728105084, 582312396, 925139697, 690594471, 400306709, 708356512, 185214983, 529443374, 284604050, 416506909, 941881269, 618873042, 23157917, 161178683, 608487405, 856724173, 880348072, 331008985, 822851489, 943355140, 114397739, 49887613, 850901341, 205778076, 653093101, 469525685, 37209107, 527663761, 902846515, 389547756, 595945784, 66097892, 35576390, 105140854, 57321580, 721425800, 586129756, 826749447, 75443220, 138101364, 807222835, 121281854, 208097403, 926619058, 361636682, 276094490, 798044148, 879957511, 936483091, 32385354, 15120480, 387786931, 956827083, 719976561, 563990375, 672491051, 904669600, 717863583, 129601184, 277591409, 774590652, 736422749, 798048882, 450690958, 663980415, 692531700, 903462317, 966429995, 609287768, 470775358, 70177358, 387744862, 565442427, 414919753, 563432641, 146484817, 980695827, 759489722, 332571480, 556379343, 735456704, 474478160, 493474061, 626637700, 430850647, 580496331, 41564069, 97411091, 575703816, 408921304, 970713854, 619537668, 513787422, 671430864, 986252175, 909383618, 121372976, 482333846, 849907607, 967749218, 697198946, 874895106, 994054049, 802628178, 900802811, 492676385, 326433932, 43601728, 515972043, 841217376, 948372323, 156346348, 896145260, 258676781, 793428397, 207746169, 468725634, 760374085, 249644448, 315557166, 840932397, 311747725, 351680264, 470342811, 775650499, 40846756, 753889306, 292886317, 153183946, 382525363, 593858760, 167244482, 683922717, 506388086, 466213533, 438924916, 615867381, 166215180, 353088531, 219069821, 167021922, 660013348, 56080919, 629515099, 975731785, 340869022, 149066539, 468603463, 761023184, 853344246, 402217044, 92368434, 427594416, 193062633, 27418225, 460214470, 317408602, 925239495, 920912155, 946574825, 999641237, 407999083, 246145837, 877343425, 430025778, 762791640, 230513719, 60509280, 364337732, 62270024, 53625086, 462963682, 550998360, 133906342, 881233476, 686206895, 574685204, 402301339, 4214009, 429680210, 903189327, 470003203, 464944651, 951327666, 510581807, 670145624, 36475157, 382322285, 784768345, 98893045, 945300388, 762432726, 76043174, 360533546, 929476546, 705186319, 604078257, 83973765, 398861459, 733399630, 197263731, 428172479, 148532314, 88356203, 836888017, 719748377, 305426013, 488344630, 172907032, 118495164, 672065170, 484430066, 83251386, 575106767, 420553391, 337894711, 839805339, 952619541, 302248797, 394800397, 301523906, 627205274, 700526226, 14542099, 56246474, 24293069, 236643415, 652404616, 537675286, 91198231, 188058177, 220120718, 106502675, 620960643, 738842777, 821729513, 44373460, 765076023, 69720608, 318273597, 611699397, 335121677, 522153135, 64230011, 748871741, 819270234, 271877019, 982743043, 22580408, 459443255, 447617262, 871446398, 199796650, 130946823, 217488994, 249223822, 522125088, 257209200, 593738464, 432282918, 702534580, 390671130, 301135351, 957164225, 714166874, 813407578, 574912389, 623665209, 39892079, 50914289, 78722716, 891085874, 980154013, 759684358, 941906858, 594038010, 27542153, 440894672, 974009442, 286992090, 417417833, 903177723, 285835653, 622801415, 591594232, 92777146, 964607437, 131614968, 194510609, 587733483, 592884178, 925392360, 131628496, 533848406, 62853604, 423467579, 745208070, 407768839, 545039107, 903532538, 2789271, 752995536, 640495240, 335107102, 436569892, 909687230, 670891445, 734083486, 449696179, 956025799, 741122124, 783164330, 61047017, 858507778, 9216143, 783823002, 314505135, 59504971, 30537057, 499575667, 419872324, 629106894, 336588508, 709877123, 173983868, 557937200, 110047495, 711620983, 851051241, 21734788, 479252264, 105580910, 434410258, 568494299, 983943651, 659614258, 84787412, 12861044, 796144190, 982615662, 48877431, 543558412, 214917413, 261147914, 618854029, 479148916, 679335612, 507617998, 618537212, 715483476, 849009130, 687623597, 458504240, 141804550, 921859991, 17509795, 446230396, 48371660, 712842676, 275614588, 258014244, 148029360, 741979473, 241262752, 924842484, 358034006, 199909993, 871362885, 252041787, 875661403, 565154466, 281622422, 76909091, 776261104, 685661077, 935666139, 277329568, 350775902, 869672360, 342507142, 3053058, 902692526, 372955128, 733172807, 271578945, 285945190, 145449948, 97142487, 367629309, 215411850, 71422692, 327177526, 198015752, 683257022, 956911608, 958740431, 773158996, 948591519, 953471322, 897043059, 378932662, 692376767, 209146536, 100507612, 461332604, 537713138, 710360118, 882709991, 395556627, 830019349, 160290040, 509844962, 324380493, 193911248, 611460085, 48363926, 844945452, 116435870, 619726240, 241369279, 786508028, 425965157, 139542179, 340931483, 772955021, 961157448, 838819637, 75049401, 169675599, 426931321, 936140653, 128022728, 359961421, 881826820, 4322832, 871141620, 218155761, 47894443, 29217079, 945889708, 647109377, 406364704, 422611349, 649128175, 697574635, 589253162, 664518757, 997366330, 541065120, 367049767, 913770916, 683132535, 689786306, 397961879, 314920450, 526930986, 783263682, 950409426, 566491464, 573189683, 296407860, 654016628, 517615719, 628407038, 413341559, 361790013, 435127254, 107865783, 889434851, 485978443, 171462055, 190415076, 71808469, 188508199, 13583585, 361869710, 286622018, 18860011, 498895041, 870759912, 788842243, 204271982, 152197860, 411272846, 497774252, 48574837, 333140926, 214686568, 560131995, 8610621, 733232967, 37283260, 7957868, 200772182, 937889794, 19489616, 826087383, 327780320, 805906875, 340696344, 876735131, 274469330, 135232777, 939364792, 78770829, 613080277, 575172023, 423756564, 930303145, 506880951, 912104683, 525185706, 177156643, 267287313, 664949114, 240214722, 446544283, 479127891, 304685169, 699162929, 953843555, 540052800, 799640032, 318266612, 627341886, 338578378, 476647006, 611215659, 783170543, 754624871, 647390422, 593247717, 223345210, 583482014, 174177710, 757710842, 107358718, 818380093, 991056149, 989202634, 987688989, 676269471, 836802924, 44192527, 543932923, 763836861, 287285007, 959586541, 272166359, 637694605, 82031715, 319326848, 508038696, 846075809, 748255787, 620096041, 23582269, 262154640, 584331302, 778482952, 634367017, 846886013, 429252577, 608920073, 733771912, 313630923, 285354669, 369578817, 582029700, 856038213, 824490123, 867688399, 103171688, 231988340, 551532185, 375218268, 474357593, 81799377, 882795359, 879550662, 976638274, 907937185, 348245804, 9848605, 12824852, 648018203, 464175746, 397302001, 445123770, 409252633, 537718584, 161268279, 61250854, 992625239, 39783299, 248378266, 21861342, 112872108, 399258430, 952659048, 902235163, 623801964, 315757707, 941349936, 749485332, 860890494, 711292349, 353602081, 576778750, 895949249, 594085890, 322153522, 322923346, 561176412, 487971239, 114367420, 381479725, 747678313, 773845142, 830463890, 998087032, 980943943, 427345274, 970734369, 652101143, 437095835, 525347384, 469894138, 947329788, 385573188, 54859693, 527355536, 562849569, 211882329, 920465090, 270879286, 475062437, 832033890, 166305532, 70550581, 112908924, 557920935, 789802034, 406548367, 422334593, 290702567, 649910883, 425815477, 310089064, 23758648, 871283053, 152054365, 687263421, 773644168, 245499255, 880413658, 844028841, 450266320, 73945955, 14788442, 445464837, 961443911, 92034959, 496522098, 778437550, 500847362, 23070041, 805568246, 678485063, 507046565, 793008255, 400901347, 838351226, 165926743, 301330813, 539253950, 830501588, 352995783, 840436725, 229916531, 986681003, 688814379, 16687011, 243716476, 691006184, 365753316, 612445312, 602874912, 875241894, 166587990, 983637177, 411792965, 776547017, 160954207, 169038363, 950014040, 675686415, 298847618, 794282928, 388979282, 759524999, 115254686, 694836671, 914355765, 795561482, 502387288, 691849697, 73918593, 361688053, 704092262, 52134907, 941071695, 838169396, 782009506, 174297621, 687379873, 411194095, 266639078, 377128005, 345045093, 329999829, 869728539, 375639180, 750330067, 827533453, 503578645, 765774789, 279572717, 911045164, 995911544, 443476081, 857482697, 391294366, 785654928, 529198368, 371523854, 286120152, 167238754, 712076065, 335920495, 176372627, 76613334, 557833049, 471080804, 968777704, 567710021, 153586781, 137335611, 582807925, 942481526, 717346543, 468480431, 669243316, 537265056, 307745999, 159928599, 520280669, 934852252, 980791979, 514940337, 499149783, 319219527, 315086120, 841314058, 145041058, 782458673, 304457254, 663293173, 217979738, 373784943, 437019409, 88282429, 580678168, 325298605, 379880106, 124317695, 966027895, 976464385, 341277057, 913544169, 376967187, 54759327, 942063364, 686827148, 94330561, 512331494, 835044409, 955644827, 299964521, 48666501, 694056042, 494035717, 804173016, 707438269, 458146621, 934457170, 496150482, 479764537, 618250926, 37421313, 386300216, 280888927, 739037280, 871486046, 155002737, 940172419, 414896318, 128573653, 644468801, 804164397, 201516259, 91096307, 729769135, 86407514, 653435690, 162904166, 193181329, 281103717, 103433217, 820543304, 579125886, 180137899, 443123777, 19089990, 841766116, 257913064, 293809603, 932229785, 850580652, 792345733, 250986130, 685191834, 525539836, 656796309, 135965667, 874845080, 790261881, 930735159, 961841674, 946315063, 202030728, 972135313, 424558769, 857820361, 94429223, 695223740, 988630816, 60196765, 181573116, 493737299, 42367010, 581406200, 781989928, 887633838, 682682018, 437696680, 586714489, 607103993, 75617952, 286575861, 709878650, 295643240, 123471465, 709239037, 961616183, 639471720, 401584693, 243617467, 586071916, 871563357, 509237010, 151851127, 332863911, 224500014, 118535310, 578101791, 546131114, 505778514, 221595642, 561268593, 294085235, 266894459, 308357386, 850711793, 417281016, 751454720, 734100536, 225525562, 577739406, 993658915, 283047353, 508597133, 126767081, 72367531, 609733681, 431689473, 931071404, 967519662, 24042278, 429923463, 488852006, 540105608, 889318297, 223217106, 435222628, 205638804, 347243974, 146628764, 725201247, 771979340, 303474825, 131173300, 570948260, 845592436, 82608256, 309885384, 934967400, 124378080, 982474764, 965136799, 639793452, 747968682, 565970667, 312350454, 594886392, 582846482, 963122431, 465534468, 334112921, 765816002, 592272311, 706689907, 536247305, 578391069, 99282182, 299143341, 241205168, 50789346, 790498830, 218614603, 697326673, 164486231, 275546181, 898476936, 441625131, 93168467, 767872682, 118891060, 541476985, 277913472, 232391410, 460836215, 68782246, 29277412, 840747435, 176527524, 453777848, 694549709, 304652506, 796541009, 765525159, 650989317, 859395646, 882504544, 806293195, 90874829, 773093575, 176418231, 734956825, 275252101, 790915429, 295849972, 54495554, 971254256, 283230581, 547421319, 143275583, 960147534, 482701105, 308706539, 584874680, 85915864, 161466277, 680036038, 84267238, 180571492, 167562224, 509450402, 501021887, 954467872, 371804364, 781050725, 926772960, 439813090, 897541288, 267307256, 340028195, 974795904, 784502131, 767249668, 659330167, 786859227, 832213961, 376582772, 478495030, 275043629, 515886781, 223863951, 98177545, 945263929, 58728794, 610426833, 149151011, 267044655, 224126777, 231286730, 84717033, 220533653, 274802566, 392732494, 84115639, 616572732, 710364077, 577406322, 511609557, 46966461, 989863490, 167936369, 804934528, 794995933, 85670661, 445551059, 82482452, 716328304, 859904425, 733259477, 551650379, 876639964, 650582357, 269168131, 517316412, 735784726, 957189366, 769578128, 55921364, 641479427, 618755563, 623899746, 786309009, 383041517, 794371979, 252980491, 952758615, 368959549, 290810034, 109235298, 209691708, 829744729, 812334764, 431190329, 479419802, 112529990, 593724799, 810008563, 218261006, 134330622, 679823302, 793127045, 345973293, 977258825, 911854713, 34714821, 954997337, 564039780, 158782574, 643117838, 299486654, 946584764, 945447303, 773315018, 934627743, 509616910, 251590990, 450063498, 42868689, 226960916, 142853122, 900426234, 361341287, 116872489, 760353215, 757227828, 744022290, 996876525, 494043805, 163023477, 526282169, 848820690, 414126468, 891760737, 351156427, 736924772, 987678744, 958950931, 883222933, 792357444, 172165159, 755003644, 194169645, 109965562, 998867148, 256292454, 317301873, 316753077, 14234125, 871630243, 117607528, 729809898, 325232354, 69222490, 529695352, 23856092, 894175403, 948730441, 849584286, 504110633, 231023011, 297404971, 531007370, 56495146, 666733099, 994949840, 171381898, 964289690, 308463528, 353758896, 938929004, 495477846, 29249108, 354637873, 880621425, 606590060, 723579026, 85254998, 648805909, 682992319, 447065639, 977948012, 410389622, 922672463, 498578879, 305947815, 920119901, 216401264, 757872558, 569756846, 100495072, 409715729, 186024019, 936602407, 74623905, 740707497, 50395371, 169542578, 530004380, 362399741, 597371233, 920398379, 898122135, 524294725, 932864394, 6890616, 380794784, 716742858, 315386669, 695018289, 777656962, 341532672, 92305079, 808770190, 853740230, 458775395, 559854842, 733090214, 587541025, 372953136, 220725287, 255152868, 236867276, 8807828, 427910848, 412805079, 512103391, 450862416, 931237821, 162160853, 314414959, 520183472, 132338373, 470877017, 393818596, 119575435, 704559514, 86679210, 926414112, 579439269, 146728081, 478578192, 560220572, 678701427, 792318568, 991095849, 39907575, 179670358, 530636228, 13918840, 710216344, 992008464, 865140351, 153349562, 836427898, 990876436, 863075113, 400373428, 1732109, 497951127, 85273925, 459138072, 484235731, 627030550, 292865179, 66101923, 931681629, 49031256, 773540693, 369930201, 208139025, 530511503, 377020893, 494739841, 886323459, 632921894, 729225285, 573184447, 896694641, 490951566, 665766907, 495823185, 970473092, 779601798, 491098731, 409466220, 697978000, 500602901, 607476439, 701233739, 441352278, 84709458, 940784626, 151421249, 752844902, 483486726, 618554432, 803836917, 789710292, 51540590, 207126681, 273460772, 745552742, 683900411, 211554586, 824284139, 395214309, 656202608, 569131211, 453269969, 544692934, 38071076, 119743822, 843629727, 528209519, 808119531, 760125161, 910888411, 457803010, 397032497, 135062065, 531125282, 729106060, 575921921, 892331263, 89337864, 921644561, 849944319, 860765319, 223241108, 466941875, 604542861, 932332921, 150417039, 139525089, 822343928, 122551348, 734812229, 518100498, 138580609, 850699948, 400084019, 229150718, 606965907, 287678813, 842278014, 800103952, 888173621, 994781859, 208194192, 451546610, 933645590, 17223873, 767534986, 185391791, 360730626, 388271429, 592031222, 884954732, 835191098, 599217716, 679755656, 899609270, 600018665, 46470560, 507081791, 55626178, 240227125, 498148921, 531562377, 737793858, 941344851, 492430043, 375618776, 838067801, 195998812, 880463552, 314971843, 354985941, 208567665, 88689320, 220101591, 924466237, 893081883, 689110252, 711309867, 868282894, 780975080, 196433145, 125846757, 645691787, 790645547, 264060528, 612777042, 422155482, 582884309, 145917454, 939496421, 57697327, 882037285, 114216528, 124886791, 122151562, 30465621, 17678679, 422850384, 400910385, 940161394, 696220369, 950879930, 830581049, 929337964, 169778958, 90649914, 124665536, 832903588, 798552060, 123123369, 725201407, 803275039, 198219797, 700221104, 102081340, 135520893, 567348375, 888854173, 879767033, 523703371, 551950782, 52700584, 303773039, 118352223, 404363149, 486593575, 744975276, 245259121, 272205975, 166873352, 90854571, 160550129, 997149825, 629302255, 328549943, 533114548, 527441011, 842621423, 445974516, 996573980, 872525676, 131567781, 363089858, 203767208, 742417508, 836122961, 642646569, 511780241, 382570622, 207273643, 986020949, 750283755, 425352043, 129785328, 304671155, 110215906, 24188771, 493799402, 929686732, 142395353, 146263494, 675038333, 140228337, 877873052, 746640769, 152040524, 306627333, 125065435, 819789328, 246702472, 212173975, 21401133, 585647442, 939818376, 728903600, 77141675, 703295497, 474539363, 831589224, 728660564, 655478702, 168291937, 270765007, 569354692, 218844964, 870564825, 560234901, 512498019, 370957130, 969740314, 763998238, 85407304, 625742919, 835281805, 660230609, 825809041, 377319500, 579617328, 646692882, 892687544, 35366316, 552200163, 828075599, 421173025, 988527458, 460167305, 428742028, 652225644, 318183412, 492359546, 633665395, 49624302, 31385544, 42191335, 43424415, 685813783, 751813238, 549433138, 741963388, 154056433, 888884804, 496866299, 979319941, 290836547, 339484532, 750491263, 56066932, 774748245, 954051393, 429774182, 270899643, 667634310, 643798550, 435744572, 915230776, 563983582, 114288413, 258784484, 258533740, 983132796, 173806184, 167913736, 290877351, 829595567, 542395490, 132401365, 959611454, 883778128, 228723448, 208306918, 326639669, 473716789, 834325770, 252767513, 481565943, 488670338, 460491881, 164220753, 367754995, 377484484, 583310693, 530175502, 220585159, 574655230, 576310694, 882871409, 619588655, 876095056, 244592042, 979776098, 24255437, 260075466, 646795821, 595284743, 569168389, 796939621, 462627352, 790744003, 740467560, 965317320, 922821336, 164879726, 23803430, 990489810, 282508560, 462392614, 798696872, 17332574, 36527490, 629490534, 122049459, 723210839, 370439952, 155037651, 582241418, 367117895, 419628807, 608766464, 651817926, 629285860, 140125127, 180164328, 229038226, 703550380, 587324968, 206870574, 313956000, 142440509, 710602979, 590811010, 1286028, 752964152, 590052375, 874455685, 291042251, 695199830, 161658065, 652201635, 660048795, 551739260, 549493998, 519679466, 643414535, 290185371, 496341209, 417740383, 223970471, 226094819, 263275837, 81790728, 441122939, 120502049, 434582061, 875896299, 204408712, 33457000, 334446039, 546553652, 769006219, 936839419, 308819564, 588057957, 146534332, 897032576, 746310898, 782681900, 516756406, 574506966, 582874618, 250590319, 138192303, 399995114, 672649331, 404595887, 236632891, 576372136, 523194484, 25098631, 789205827, 621710688, 224391457, 660337288, 137344162, 743533936, 601404590, 382912865, 506260484, 610202110, 828085582, 837498601, 74073844, 359557453, 151004159, 468751565, 395027924, 208301704, 542118965, 603597956, 379431558, 502953809, 853552876, 126195216, 510116403, 852238133, 758265231, 244501770, 317344965, 453544218, 320852067, 121478381, 928839028, 82746696, 615753868, 755244371, 655116527, 189861965, 27934404, 625578656, 62271098, 200761352, 362000784, 270247612, 685907859, 571635723, 962983690, 623652178, 781244412, 635150337, 700022668, 617941988, 25648868, 484600298, 86420608, 83178521, 761433703, 516494710, 249483378, 760121900, 521449648, 968586234, 667816277, 659681030, 836950583, 380343667, 299448312, 916506868, 258170708, 304739008, 687689386, 606723906, 161103553, 573261926, 608074736, 796406717, 446362202, 26327655, 985282914, 663893144, 300852080, 323403471, 910664715, 824768203, 464981440, 19846094, 141448698, 134433432, 686387602, 960291532, 991454262, 170760382, 660784584, 160599237, 74340263, 147735155, 167295390, 740494525, 973187703, 850695922, 819907457, 975589874, 495692197, 212505095, 634512140, 575032731, 774476966, 607812294, 513910772, 782644407, 258792136, 239373854, 244974661, 722539945, 381064630, 604604028, 618025244, 738710246, 782913067, 153347253, 828367017, 55751402, 509290858, 437370353, 846455767, 403323602, 271476411, 644586797, 750491205, 907481991, 980178563, 860484782, 502310928, 115157758, 727514823, 271498101, 30374452, 418249605, 307136159, 355370473, 79617986, 397398233, 942858426, 102321777, 350666525, 57419304, 753531253, 620492545, 133377353, 981278078, 62424465, 412631208, 92923107, 417241712, 931472689, 936041459, 603658205, 568835609, 388959417, 867590757, 511830624, 163157807, 632595093, 513759059, 534494791, 614443174, 972822040, 116721784, 774045194, 507761722, 651065972, 275151797, 433870539, 567876026, 645286856, 245560130, 970868995, 479765972, 511704137, 30091429, 953370586, 561655783, 768470468, 214107274, 680219486, 201227581, 344638918, 646986392, 320820508, 529893429, 313605585, 316651008, 875519544, 776275436, 240957554, 264487402, 749027257, 125620070, 993174147, 491285990, 992420945, 588358811, 792875477, 831553726, 137154632, 999990562, 521866584, 846652581, 557820329, 713713742, 918090775, 844521974, 196775846, 993327751, 192214826, 924794471, 932723089, 93751527, 428776253, 961753162, 980352491, 871923735, 136193014, 642788242, 960501048, 624541833, 503721064, 976989970, 888981137, 256554470, 429132785, 397608791, 124053387, 59332154, 149374829, 560039437, 718450560, 344399404, 692246885, 358828012, 116228280, 446851383, 78770886, 430460741, 501047251, 177273015, 197329146, 168849869, 377657776, 255864988, 448659764, 884359389, 400290140, 822409924, 407456368, 20843677, 626213167, 75369541, 466331520, 552208914, 831480894, 9131769, 398621105, 578252414, 698565640, 452436490, 698926969, 70719688, 679191367, 310279335, 145997216, 771160967, 354261367, 132132307, 496892191, 733308466, 408854450, 948772504, 437037533, 664077238, 467629902, 224737140, 908752604, 123864179, 271852651, 476217385, 337396241, 330372575, 617981996, 765652363, 977808482, 80412455, 998460173, 976342960, 805662381, 305979045, 91669987, 754991791, 153845868, 677101204, 19137428, 235974311, 411234684, 652736320, 992318805, 454033965, 116273064, 727329363, 572386483, 444804259, 954232318, 724132047, 351115968, 9703970, 610925506, 582381322, 904750439, 830639013, 80711474, 688038484, 290738578, 91907885, 214857733, 963252521, 925702220, 571997649, 73380924, 722508892, 154216640, 999894167, 977740216, 975045934, 706695995, 482658230, 419859629, 678103960, 38998954, 158478881, 993489591, 305150638, 538185325, 36744861, 580733417, 799783666, 943647422, 43234986, 547538826, 496628508, 790595694, 811667024, 954244795, 71379893, 11068239, 380304918, 893991695, 10818540, 800716560, 205702087, 951696787, 496790489, 206947711, 547604195, 831696230, 264825904, 72320851, 873809567, 606748874, 654423253, 237280771, 532203028, 441646909, 35487295, 929892499, 161782050, 915384620, 56522931, 910681140, 709537765, 342912462, 880998364, 125018766, 697466090, 266353314, 783464476, 671063392, 886281299, 237990139, 318644803, 210780828, 399833464, 38636413, 771621369, 177674390, 816555129, 485722525, 314140888, 83711793, 43047104, 146784368, 223114455, 403207208, 236314856, 860288215, 349887797, 627806080, 721654716, 801849009, 94015760, 587501314, 438724381, 994686650, 908282675, 514378359, 796970138, 892314708, 812642843, 654947836, 166084574, 835946625, 927262500, 964472192, 804664714, 871685246, 472138176, 96440336, 256334221, 127729632, 359849325, 888594830, 672606018, 273717748, 888355360, 161626430, 268582610, 169921531, 274954928, 632595636, 430329887, 809488194, 725563286, 533060724, 89393935, 541244141, 661995967, 701609302, 672217536, 223086618, 713035585, 549407005, 112577032, 611340181, 994877177, 32571741, 486139772, 276464453, 620898800, 198323643, 429620686, 176836459, 407066795, 924895056, 447538622, 52281871, 594580626, 84626680, 93527805, 849317143, 388158889, 943370300, 181097988, 15638157, 421934737, 877466977, 886852572, 664345780, 580871699, 219306405, 172466135, 762895169, 854183646, 236794188, 269304115, 720196522, 537513774, 365657854, 654755588, 558545405, 821045129, 670629717, 359518023, 324433145, 357761156, 225456527, 996076396, 929287421, 123204429, 671188653, 607211517, 460867393, 325192947, 226707811, 230396172, 444596840, 470540277, 80907585, 267248015, 282005951, 400793382, 21922534, 295072146, 583438558, 617023424, 591465597, 524885971, 544417781, 875123066, 501043285, 762531520, 619181657, 147475543, 934873313, 677689665, 675185372, 173999826, 115886871, 81218371, 793680048, 321616825, 449972116, 337913608, 312976326, 484816436, 171590022, 191551401, 113066244, 390303303, 421525235, 686273272, 32727019, 834517200, 914949727, 327203426, 401374407, 375995695, 532500984, 912383928, 706501862, 458407694, 347195655, 203604135, 449621397, 654114126, 255576653, 41896877, 678167848, 549263155, 917823467, 235958468, 138043943, 795373103, 874413223, 397077029, 648749586, 320365798, 938517879, 543728986, 985656829, 209573890, 887718109, 378221844, 33541146, 650269254, 762957476, 806605111, 875702525, 132003014, 342767515, 883171702, 485307621, 745634029, 679891175, 347990854, 691634494, 599256301, 583390118, 947434300, 293516125, 211717736, 935011583, 882801803, 48014749, 62788421, 383385052, 777106380, 991859826, 494117669, 295082739, 602791956, 143488835, 420769255, 972280676, 648968964, 705414716, 963958118, 700865842, 912447260, 60676759, 683745463, 638015192, 28049409, 411155173, 996840171, 400099809, 45625649, 37891004, 208239084, 753256742, 44479225, 603254079, 325917168, 688884925, 369365036, 187480402, 865192409, 306096474, 711561036, 567872416, 300930761, 904114254, 544684546, 214005427, 533210247, 477796226, 795228985, 283292003, 388339061, 996995276, 592443017, 699086428, 554674942, 816863739, 131862627, 638839758, 700410409, 853625622, 555994973, 227796574, 104963972, 184745856, 541366916, 2254543, 91096342, 793508330, 932371120, 843785240, 446539197, 119491145, 719886981, 712370366, 601886375, 869614951, 10148701, 766892034, 875381650, 977637172, 737416813, 330248362, 123403739, 141365143, 246504530, 47564392, 938056736, 266508803, 973069733, 955801643, 660913140, 658015025, 795067019, 823142332, 961227081, 602630407, 612471349, 729134630, 171438514, 454001464, 288441944, 765130167, 626465206, 47776460, 113029494, 22693541, 432635026, 788092882, 284836267, 945983244, 719415500, 45541721, 328578508, 420934228, 871197550, 367486556, 732502508, 480034718, 595496934, 54427061, 388533960, 121107247, 657110864, 846685115, 226816221, 734161079, 598938852, 608232927, 104071888, 615258824, 888406423, 237058448, 868048304, 253825860, 522290528, 484871851, 724384847, 675133068, 916833965, 910918113, 11755225, 791950730, 896982804, 241032463, 76015490, 854269762, 8657742, 172507916, 55584127, 148227676, 936270094, 57951500, 942433126, 355773143, 365031764, 964063391, 3704977, 115290898, 439267483, 812976536, 267347685, 624268528, 217913145, 723566846, 961505356, 257883570, 718097030, 763258782, 565499046, 788767051, 888242152, 819621931, 846906667, 333337299, 854429489, 487572116, 498387380, 623845495, 681594405, 490784864, 321740060, 405288378, 378612635, 616554969, 978231358, 980736332, 313757587, 514197749, 136106528, 523569897, 426016616, 14326046, 91805678, 964093679, 951646829, 45737627, 684628987, 199000628, 75352097, 888991893, 273418482, 551776569, 395883493, 194400187, 938639116, 182433402, 289331004, 869070285, 400030843, 295227096, 105724689, 676169182, 602133032, 549854161, 111310514, 473423823, 463311848, 298386550, 466111972, 984111090, 934150472, 757417261, 203570711, 469443850, 651244148, 607974945, 360713613, 630413173, 554596944, 286834877, 644194716, 581785064, 364592702, 249733392, 711055247, 647238840, 444216530, 676467808, 982938088, 656682247, 136652220, 664068767, 191220961, 650016566, 671122249, 13755556, 515960597, 907368552, 666922345, 904465504, 371940469, 824059295, 263927172, 583226409, 396548641, 102107196, 637115539, 722005803, 332027915, 830149940, 464776910, 59100724, 283312549, 448553144, 236892251, 508655794, 842837878, 666353893, 703829303, 736192818, 908915788, 52705407, 75747858, 298464582, 229944047, 95497040, 661197, 567772389, 25289588, 48012388, 441207666, 490882484, 811878228, 188078977, 858399091, 5119429, 61092002, 460259165, 435405572, 540893524, 597800041, 91016286, 946030363, 342862667, 100432424, 399484700, 259485984, 674631376, 743389652, 227474647, 887360287, 330331365, 77608868, 491601481, 978296507, 582916646, 586851505, 520210448, 76768263, 207912949, 162470560, 912731454, 626639087, 675947346, 874956638, 462337975, 213657358, 199598187, 81460979, 500419514, 815982234, 160254249, 745857608, 28038854, 106534786, 672490310, 887586847, 41882498, 368444865, 15601023, 185257380, 713200989, 788625010, 96245132, 207116339, 35396542, 21029694, 63850585, 26459210, 312557682, 769620304, 233558758, 741557581, 955399258, 933947282, 696019635, 198537025, 343937518, 420254709, 311488667, 432428352, 767874494, 977351201, 798630162, 724411328, 743666319, 862356630, 229854282, 102406611, 405053709, 607553915, 193895773, 456351958, 120543363, 224104003, 316070828, 111528857, 605209874, 6441919, 200498305, 798178620, 594346221, 176361041, 731387335, 555641315, 359345655, 542312538, 387289573, 681092297, 866472839, 187615215, 411366388, 400310314, 373910581, 197825751, 554430767, 898491188, 150749458, 256339225, 664570482, 563279065, 664903307, 887736742, 757945384, 117005094, 498863204, 223981293, 415757708, 610376997, 631704035, 687328469, 449770265, 459209962, 207224570, 990930827, 223544162, 102635833, 564482404, 233288188, 779938143, 715430245, 408054402, 949645562, 62413787, 192396873, 475892124, 227746524, 613402364, 428390147, 145130900, 600084798, 725126564, 447811926, 498707523, 322570433, 989586331, 884529220, 732318323, 513105271, 518118224, 862452693, 894931369, 589738003, 298904333, 346847197, 321430827, 361170908, 111380663, 878654428, 190951616, 176002550, 563725819, 817922489, 697664053, 849398284, 238461645, 986188823, 533812104, 524466207, 683971470, 697911124, 637650222, 103054175, 130192331, 372260231, 703896711, 423953401, 705985147, 805897088, 295128796, 848621817, 409224952, 597241967, 401031535, 418164547, 4450594, 24623626, 8370025, 844615287, 130231475, 457071718, 811557506, 600994577, 391913398, 497362153, 316953593, 948518475, 556824281, 964615194, 238060340, 544421002, 967258447, 373799764, 384024926, 322762134, 938514641, 606964747, 643717343, 634218463, 42455460, 791387257, 910120789, 886939796, 253887414, 173714687, 472344916, 586487030, 723999692, 862358645, 433259540, 553971442, 664999090, 547154371, 484610373, 387290611, 131341102, 59645182, 737310491, 590328965, 577028027, 278364440, 78195951, 649329788, 127356674, 342652591, 820966043, 245068966, 781342415, 742995419, 839826299, 918019160, 302046300, 633946466, 303613373, 366928522, 305483630, 832043000, 708443317, 76475171, 342648204, 21693652, 912323392, 468207501, 631272776, 23304834, 979807476, 993791775, 663246211, 903277056, 392542470, 875279899, 471821757, 333872534, 437228205, 919793626, 558627217, 877286101, 220998831, 393912581, 461042130, 744488944, 666771702, 203282804, 741039713, 328985206, 45196528, 234489297, 883718768, 675219640, 46573323, 482586670, 901682257, 390431220, 613656232, 823928697, 567445742, 792644829, 59568832, 843970005, 965389488, 69374470, 585732768, 857627481, 141901813, 688818728, 229912332, 529430340, 968918538, 19099953, 602509660, 797699100, 788519039, 430355647, 881294573, 688758701, 982247086, 144701540, 312709111, 969533926, 371281618, 969238522, 8429362, 377975565, 589147054, 804891188, 207961545, 450535753, 899080368, 641330541, 372874527, 744094408, 712719396, 693076219, 309528223, 247444121, 68008352, 29886682, 607503360, 316574969, 885310020, 457862941, 910346780, 140922734, 202606771, 689272053, 443996542, 126453032, 190040195, 502124004, 862635179, 409757440, 505028092, 577923709, 391490407, 637049685, 661285609, 651206291, 173628391, 508499990, 203054312, 124911257, 680432449, 157265776, 859428379, 809892419, 712856314, 746876836, 502937002, 159012600, 62848326, 653665529, 321373772, 770182010, 519293857, 852322902, 6566926, 396585449, 705968427, 772469156, 314740429, 316750242, 729667141, 873838577, 721042187, 644867961, 992036135, 272080205, 913959809, 83571379, 45155632, 3012134, 977880425, 485798199, 782572702, 857950926, 832113136, 322776399, 461374250, 670876421, 721537555, 345436649, 443539448, 486958373, 293502822, 510189964, 911045721, 970946703, 74552390, 835696368, 853413116, 102353980, 84605959, 128452224, 167906692, 235840538, 897445539, 71703506, 510139972, 668807386, 384559929, 493982584, 519175940, 222589150, 724132804, 279353649, 103239439, 681997499, 438201572, 445634713, 609881325, 46285974, 424618932, 796301443, 782552872, 591909372, 522366016, 269190646, 738828975, 116464035, 408788722, 868304236, 501893626, 879482165, 407208628, 491519470, 471467496, 249582966, 484880919, 349123880, 773042365, 253003359, 462783602, 796382267, 259023307, 846310689, 579547404, 39647639, 859789025, 995301681, 198718270, 92833574, 421087244, 215797963, 222635997, 918220326, 205293763, 819672382, 927933197, 707555624, 10168214, 926896080, 176402461, 788205625, 278385164, 161281694, 440177884, 301440389, 333462329, 922220936, 340664808, 30191567, 678816101, 709735196, 136187680, 452600505, 464256457, 530896059, 676958735, 963165151, 706728886, 329078486, 664990667, 800900151, 240714785, 969733378, 780996445, 434810180, 212169460, 416345560, 813117217, 748431499, 729460429, 465571329, 240655563, 676620901, 502994927, 668438458, 724460242, 828521344, 393304437, 261321196, 836482112, 584597420, 15348193, 295934497, 243869707, 665767643, 256828548, 580934609, 682427053, 145132226, 869083774, 968018625, 147658592, 300286266, 578954536, 852635945, 608746987, 37013251, 540287994, 429622695, 340317333, 367337599, 820476770, 90538250, 538111481, 217136434, 560091959, 375839271, 113676829, 3100935, 49345337, 905232102, 957828483, 216692315, 460579905, 426626103, 828524468, 807757421, 878389650, 796792254, 649052641, 23463277, 173427549, 262444674, 480179767, 577754600, 184218659, 201048629, 367237547, 354127272, 68829527, 290269957, 855397120, 886904908, 516563527, 33806007, 321580498, 229404735, 533043314, 643192313, 563646411, 599233292, 113275353, 811585952, 674309825, 555267136, 5581439, 965356345, 199824657, 378038741, 314383751, 450471531, 588103932, 512792570, 106449007, 127767693, 713319717, 799862140, 809786430, 535843200, 151549965, 867659300, 92526947, 665798263, 579939953, 656516451, 105897874, 256073177, 8615546, 629407703, 743787230, 890213671, 250453236, 36663498, 780635986, 296921610, 529300239, 467079685, 231468495, 933332877, 491351205, 310095017, 959334246, 137508105, 47472338, 898953689, 85483387, 410787031, 398145814, 357986938, 700291598, 361981658, 536154947, 161412613, 514157224, 429070813, 210769720, 21439343, 426702544, 778636283, 770515527, 843468087, 592839821, 820842416, 515590115, 969782270, 383182899, 114699332, 109440773, 470247508, 323766099, 686830619, 303133599, 245673597, 68410397, 769531991, 717770242, 872598713, 368306543, 102193966, 221255707, 725782034, 893721918, 1430169, 508783456, 950400883, 915734317, 856667752, 460604407, 804794946, 161591365, 759425506, 73089962, 923800490, 945020640, 785514573, 130768570, 678470184, 838021604, 227996825, 546653236, 956735082, 588788712, 799857585, 252701909, 809892472, 351361740, 148303143, 851221106, 204070557, 39348691, 784226642, 82469511, 157529625, 261560397, 487455973, 352224723, 181532865, 593676685, 335488828, 945553216, 597768833, 643982529, 465663749, 342159382, 581207205, 271746870, 683988032, 211462838, 702062019, 861159414, 348612653, 654347162, 549684887, 486931461, 940517615, 471145312, 6099647, 155870120, 869858858, 708177628, 764230569, 856775854, 992959845, 814949582, 395756013, 993433803, 552811329, 143980147, 614029633, 158884012, 347645935, 960287842, 91621385, 89277517, 38571779, 34789196, 868547886, 97163572, 546407791, 645578758, 927459088, 968017817, 873547407, 617368999, 51842839, 784268503, 937735956, 128127874, 163043783, 449593179, 808492912, 778188363, 858659593, 299391556, 122081801, 595079124, 624210878, 871200393, 348974521, 727605548, 403185292, 467666569, 437457506, 910622282, 983364577, 31117100, 730182054, 153496090, 303554188, 907404264, 523447883, 375279708, 935828480, 995017283, 553553295, 585686090, 78323197, 92974840, 638523159, 583619244, 295381470, 811370201, 966663598, 474569285, 245618134, 47376260, 875383203, 190512214, 813640238, 303225620, 460784733, 640414006, 354971927, 697755366, 968243470, 711381617, 318233101, 284715902, 300189060, 576755698, 332422527, 710802719, 215160610, 776283356, 931051986, 382286560, 202268441, 56808043, 913237074, 940886566, 726827688, 585668905, 529295655, 533157027, 925632116, 188059405, 352761017, 1674326, 565083171, 959819582, 325460032, 426400178, 831073995, 561433807, 523437286, 366767699, 648323963, 557646297, 511952727, 888782699, 63476706, 999996068, 536067035, 96378372, 678303038, 832488427, 278988730, 184048047, 107051194, 249189910, 859558249, 88989122, 263592541, 668106812, 646143998, 666920103, 212186559, 691487615, 690663023, 156669818, 905065730, 248366289, 324243015, 259894877, 654625080, 808551855, 475890861, 680105097, 95421213, 349887322, 605852552, 797820632, 552885824, 854948139, 448839449, 340138460, 372284722, 715274392, 536890577, 366718116, 526740413, 857208066, 486230179, 951264928, 412415860, 822075803, 369166741, 218594277, 553035734, 432279652, 283067750, 845132974, 625299635, 830049333, 451446613, 530196282, 196062851, 349710693, 132919987, 647555537, 361470554, 474678356, 827798273, 175750760, 601846290, 478180684, 279903756, 537480941, 529612096, 337672273, 277406605, 852977221, 551217865, 818819792, 452969215, 634474861, 795922, 260801434, 198587613, 241400341, 942849903, 892506224, 869824074, 421099287, 919995131, 792070675, 290841655, 802952331, 165301796, 745942173, 650351729, 286461116, 350380283, 783104395, 78379469, 654295357, 164001088, 539282642, 925972611, 584958200, 886124836, 334912803, 573619758, 542418877, 774452806, 652782619, 645225387, 832050988, 250080486, 100127239, 332597393, 35680597, 317353344, 599560763, 841207679, 310840420, 337211687, 618847286, 977506767, 460554845, 270202013, 772473825, 236130341, 523828348, 525368600, 82519452, 876115497, 323664986, 511956028, 400016265, 548564645, 795027022, 335658033, 694102160, 447063883, 333452555, 796160558, 62088774, 408356453, 917213909, 416293145, 768612024, 378636001, 736804897, 265194322, 671850147, 650537308, 169285338, 552714889, 818782505, 825293037, 979423740, 477964758, 991149753, 194847762, 552567938, 294318504, 905915458, 770811406, 981075228, 526444141, 205754868, 636906776, 88376022, 447754821, 318603453, 641267088, 115272865, 392205530, 777985630, 733407210, 248437968, 672475479, 733009847, 628584622, 95916484, 2667063, 171239835, 910352577, 617084413, 138096249, 261756409, 739445354, 514370236, 279913755, 512879307, 979636394, 904875422, 959136505, 976788679, 337272810, 264536485, 465354210, 744607953, 17866360, 332832096, 73492264, 845284309, 322676181, 356291778, 192262623, 721207647, 820154771, 380702752, 975372502, 466121745, 446574943, 664877722, 482122870, 353745805, 638591936, 247597982, 809677281, 885928404, 740887862, 272798885, 74300812, 99927948, 892977823, 3451342, 585996230, 954058369, 369541770, 536790789, 588664357, 16647158, 510720090, 438695205, 553963193, 982879977, 225352373, 107457666, 460448453, 110618543, 945941365, 138881123, 68697718, 892345457, 493117005, 995315355, 606667719, 898113330, 14452153, 355111285, 729687211, 903260455, 74829245, 391342169, 531593499, 137255631, 348430425, 471235584, 495061088, 397002563, 610227571, 122755239, 262994431, 725984671, 523757, 564096769, 491723291, 264945731, 904503057, 521606834, 137459034, 746029102, 242550298, 914356147, 114228076, 707089776, 756584259, 680516605, 369123973, 2109644, 9628926, 987596415, 230587062, 968106704, 169383385, 602498799, 319891183, 818141450, 403427740, 150664303, 895800999, 734049740, 666258106, 86206860, 990920480, 356912867, 651383090, 840363685, 720298892, 41160924, 816569085, 643903227, 701003678, 766006686, 75958917, 508157998, 527264001, 52275880, 118705127, 347244288, 952805605, 939574197, 573480000, 8028025, 285191936, 235028426, 829451501, 754166582, 313373236, 848322851, 943064771, 608158120, 979911062, 910450295, 156317869, 556627875, 907461507, 44096192, 520921701, 197855954, 812367711, 378921448, 320760521, 804588146, 303094037, 307609371, 233779885, 303160363, 165678829, 808270968, 296702155, 636825850, 641577655, 99448761, 744328427, 27303663, 227967405, 250915524, 388433980, 692259578, 813923475, 745597400, 813520644, 472134288, 514089461, 202670627, 667448307, 378117204, 593081259, 2443572, 381602211, 150750346, 221404942, 289333239, 123376445, 57062487, 284396084, 567338965, 855285987, 787061319, 708879273, 663985627, 88658223, 225086811, 494426730, 667830180, 245153326, 341383053, 861689462, 753630180, 254903203, 511738379, 606916377, 388427979, 627191411, 992984146, 502504347, 622154307, 248824556, 109160788, 529942230, 369452774, 869606607, 469126975, 662266148, 59870619, 782114835, 703405019, 816749175, 44007574, 970054710, 987807280, 866599596, 921698348, 58846118, 106866295, 783980558, 319149597, 527167316, 453054247, 492598744, 225950381, 485143654, 529428725, 186859603, 81115570, 288998009, 463384663, 276495294, 939257968, 302386359, 372018166, 75691336, 132555003, 127970382, 601734004, 242810685, 123584170, 26719517, 534633510, 702130233, 732796776, 670973394, 733181056, 401885642, 422096265, 610946625, 418991884, 954536572, 101826030, 576906725, 834232708, 657944924, 133068252, 627987755, 823526252, 149314113, 376980141, 217451352, 715872422, 340871380, 432810386, 677362107, 118986530, 600816815, 559984605, 16372088, 414493926, 193192259, 666688337, 482693193, 657698170, 51180154, 600374377, 783797665, 238104948, 133769628, 448129814, 641654751, 262479991, 671473622, 725844648, 741129009, 443628220, 788422457, 169755596, 647163871, 721216431, 291212570, 346900857, 552846074, 852909912, 604732445, 101045998, 338413965, 951451345, 582691501, 435135513, 827919622, 277548809, 156163878, 689521038, 330327849, 398159822, 924943822, 478982650, 508641710, 950950518, 849417966, 240950128, 493836364, 627458707, 704885612, 542064743, 354920875, 460458979, 144544638, 699367998, 214625416, 408387415, 251148298, 102163130, 219527985, 760624980, 158984887, 172876837, 313247093, 178426487, 754278881, 61390857, 211204887, 190766955, 956978987, 887837489, 466725720, 305313989, 26613569, 32251897, 860307004, 999743640, 35339496, 876478203, 599274117, 345690928, 280909920, 419804156, 682156203, 960057306, 484338426, 647079960, 857205143, 26381434, 121944219, 167150118, 845508576, 454284040, 614880993, 298165059, 311316103, 761149156, 698213111, 154709737, 877762153, 976787201, 888358886, 177595062, 771349742, 466176405, 377716224, 967463810, 180052627, 917161442, 919476879, 365726457, 226937430, 930967146, 624541319, 1896314, 604569164, 768703013, 314898404, 915870017, 93196225, 657787967, 702495033, 846781220, 82950488, 212463003, 451022348, 547236239, 543656614, 657337044, 932750074, 108501143, 950092039, 828159569, 181113131, 451313978, 654761424, 583372635, 810924471, 992587065, 455681236, 641632071, 393826948, 227780395, 902584671, 86220448, 331432202, 810058385, 726353065, 7668521, 92422391, 953427235, 633397564, 312105506, 441782704, 131069698, 343713702, 79685877, 704564451, 160128963, 502658804, 115125475, 158804541, 183563646, 575398147, 381285457, 62246975, 875202709, 867851127, 852204225, 768565824, 355046083, 425232054, 300043452, 785011178, 61203926, 190611226, 905253124, 270704842, 503890603, 206332926, 144429443, 46806570, 976712291, 704049284, 197192856, 85214613, 577599635, 701076300, 577041720, 896910957, 705375347, 753111505, 13441703, 538411155, 111979782, 525907780, 742948844, 717974208, 818908331, 911931103, 762408505, 564248089, 586144594, 689048211, 45843624, 468315428, 401307563, 928938478, 373553387, 163681611, 55903808, 275906065, 974108828, 962528474, 671307827, 244551854, 852590562, 729331360, 484413339, 663945760, 758768626, 300473664, 180527317, 266799949, 84693346, 629073656, 701405810, 970224420, 238537626, 776251035, 593823141, 84019829, 172315098, 10907538, 204828251, 932099080, 253235833, 299800875, 997413217, 136262306, 291033058, 101088347, 87099374, 163620401, 530565088, 342717914, 329856929, 314759974, 276077260, 981078344, 187553299, 759905448, 527432960, 20123432, 541981902, 277737515, 491958477, 137407943, 162256486, 56107615, 428258891, 23704746, 15722801, 292886785, 263864469, 70661593, 33681713, 847601370, 461204737, 639823143, 315550488, 296370953, 658640621, 379722221, 608703915, 905544046, 830131039, 816021151, 711844395, 126691108, 672601869, 888177403, 476589645, 803635669, 430082343, 818852332, 851421263, 309149088, 373633403, 847564227, 545350431, 219363611, 756987817, 306673674, 923252432, 804992499, 895334571, 569653695, 949903885, 938064876, 156507973, 727689257, 331273424, 764119670, 92273267, 951718686, 932655543, 388358440, 730177204, 268629587, 926784835, 43153392, 481004348, 190140887, 404482855, 923005495, 872912175, 977572536, 823398370, 38933111, 949190523, 39155229, 798568561, 539621955, 607800128, 645975992, 57526043, 247402058, 336158622, 187734854, 536657447, 660362532, 348325613, 385706515, 696688197, 277612118, 87768424, 65681924, 966661369, 770236085, 176059849, 590186776, 293352188, 772812118, 724495916, 883176025, 688822544, 356275964, 386927091, 665405620, 673376114, 227864004, 722382285, 172567673, 124711979, 109073739, 580563128, 704284610, 195432368, 788172149, 134431569, 936134531, 275107933, 789450258, 419641120, 821709672, 80737593, 685119436, 309039873, 982957176, 873400493, 825624497, 995699554, 376051139, 351363541, 200323622, 58941940, 820732085, 408681427, 352659967, 21601992, 955409542, 350268343, 351162475, 908112429, 6296128, 31722121, 854488134, 193528085, 579577381, 362296122, 956060334, 53097164, 973698772, 391334710, 214819716, 472898797, 378966092, 648127715, 208251625, 981005483, 576422597, 47401237, 796322739, 413779023, 417068812, 505804931, 928076704, 387822006, 321541982, 303757765, 129929417, 50985069, 130189664, 651011197, 424832032, 236157805, 135870501, 277577758, 433761361, 90645420, 621563988, 465878721, 751945980, 749261260, 130090344, 613498061, 893745322, 501574375, 282805200, 485269261, 420597299, 225761091, 537070373, 992817999, 716379936, 340194182, 858505325, 938801527, 906966232, 912963718, 71380774, 515686735, 392995865, 337513371, 713490798, 521225660, 129062036, 944175579, 442541982, 668414336, 969971437, 821822746, 175889713, 452137772, 491431914, 459887146, 939669559, 267982473, 234985098, 427984077, 337802560, 396763924, 830629226, 337520034, 569050906, 374763250, 748712714, 734716029, 699615038, 213954206, 200956384, 198429277, 162998165, 935437040, 811760449, 37876738, 669675922, 782216279, 424425255, 247582286, 921902832, 777928208, 503957891, 389025002, 339193362, 571384280, 148077383, 695389410, 726897212, 594192985, 659997840, 944074163, 981238740, 339439370, 27439622, 556572299, 845160874, 843942973, 233882893, 846500842, 858782343, 126877177, 292532957, 121966467, 644829218, 880877669, 941973667, 619100860, 234345093, 791437002, 291430733, 102969063, 201343842, 541365900, 969057753, 582566595, 78416358, 742541970, 975506788, 96241450, 172805723, 268439746, 257506630, 162196138, 552541274, 500595943, 88363720, 732386931, 22832823, 26117248, 619723508, 282830170, 31031644, 327366774, 763187719, 491759518, 129567110, 745060622, 391522614, 39172508, 389141023, 678589804, 943081845, 241272962, 574898952, 48682002, 196747359, 843330064, 987280108, 476633648, 98358330, 429138287, 798956718, 793828527, 746391075, 498698819, 315961509, 568739652, 428366203, 599371274, 959709625, 554923870, 11217048, 753216534, 553878729, 277959905, 304673331, 688830965, 968867493, 884310475, 445789153, 773890926, 81379505, 385273786, 339999155, 579980628, 983645846, 952335837, 53025550, 641116104, 174475026, 957253884, 140379504, 335426662, 732809270, 362372131, 240791516, 584425431, 365613679, 616961065, 279111613, 425258972, 574795320, 136667352, 640799311, 945820035, 480700225, 279912638, 500917387, 700491742, 32046549, 620709256, 462681056, 997517161, 818474220, 414351354, 807646107, 732955516, 222389103, 699564344, 73827101, 535375445, 684502016, 861280351, 963713538, 550732471, 468675563, 569960129, 452196339, 683327804, 835902707, 363519465, 898373924, 126685566, 681051154, 884242509, 265230231, 764578080, 555339208, 854199884, 223655909, 688222303, 143477703, 323390663, 600365496, 964764974, 625179584, 102918323, 705246355, 193667997, 627690013, 428178670, 270553288, 250559471, 189854906, 797976629, 931374210, 510887268, 20333001, 73393606, 126425385, 793935118, 955516190, 886958273, 537447550, 591542768, 267535095, 39368385, 950584020, 429765097, 768133069, 346635829, 729740543, 862460256, 955432543, 888834393, 400380475, 944682429, 341730339, 885817723, 828301087, 660277152, 714615933, 698343254, 291432848, 859150657, 182028107, 867250616, 596787324, 270003897, 756948096, 84616077, 914315237, 544871006, 438050254, 554650676, 125372964, 175813716, 964607252, 128148200, 635191022, 335915197, 935261402, 65054478, 652336304, 561342346, 891510200, 214741237, 10789882, 422413680, 581518252, 844450532, 518580357, 192316769, 394709741, 689306655, 383325386, 666371785, 802568899, 83649105, 741730685, 328684123, 41752863, 966972563, 843026870, 842595830, 99826110, 8990880, 389991517, 79691062, 145162545, 871334495, 852741267, 578163623, 970512948, 814054755, 511203515, 727509507, 682376014, 331798481, 319248769, 711332822, 130832442, 557201348, 288180215, 777573420, 332396966, 342141558, 816749651, 21017951, 130507997, 783656777, 436575506, 963348183, 448456539, 687340158, 722839766, 519434095, 911318467, 110469275, 85107352, 756399091, 861124817, 944926852, 731262223, 394323292, 448320050, 176491146, 426232675, 31116595, 988498658, 771579776, 909379479, 66289503, 16927127, 885497506, 290654374, 876477198, 69106942, 508676289, 489809865, 715019368, 126651414, 676288001, 972154984, 802668555, 473873629, 904837350, 543179211, 242462178, 799547799, 961483743, 668732920, 179136984, 790437203, 52164729, 871587481, 640795156, 332865105, 743810264, 762357513, 627909974, 155619423, 76696704, 559064997, 446849168, 20032129, 455795009, 984234290, 501945080, 12348569, 426395198, 197019225, 631300100, 697603860, 743405203, 64412405, 625823863, 45585060, 600182880, 312037790, 278487405, 946771103, 767730076, 559173067, 13304182, 37388779, 901949296, 713612168, 957668375, 232479354, 34944328, 759331181, 261149780, 283070746, 872982117, 874411907, 273078744, 535102386, 726805233, 299699273, 871887023, 393953161, 35119122, 446408805, 424018000, 814050178, 955839630, 948226884, 250723, 310803551, 754751124, 139915976, 957351773, 275279702, 274002589, 799056374, 456426794, 173424200, 103590127, 930796453, 120864283, 818074365, 67720665, 308341345, 965327952, 998917653, 615221178, 320921749, 285625929, 974593616, 993593129, 483575345, 703768134, 861713440, 497385512, 769065628, 607714561, 981736980, 448590788, 372320832, 859784997, 562611785, 806611088, 226283432, 275011176, 453320657, 285318433, 425863208, 489392771, 918756823, 292700677, 463894892, 542343923, 411562170, 930792656, 866306848, 414184878, 193619619, 172151396, 933299688, 649666779, 241287922, 956178964, 591151830, 430977681, 533701657, 868667905, 568509861, 950050051, 657377123, 329821960, 526579474, 557691100, 14166407, 334613983, 296262409, 595685540, 931269846, 685892286, 774139505, 47449298, 403680048, 520113594, 187948772, 829320586, 383621300, 907032982, 684212455, 274764388, 311428624, 673994999, 168818091, 231288319, 888447727, 127498555, 879019666, 392511907, 137105938, 224546795, 736458448, 425233081, 4380801, 613717871, 493980152, 421200899, 325390451, 120380026, 705381794, 479791622, 137578784, 429089181, 610015453, 179431454, 417900137, 570392981, 691421325, 263163384, 546795740, 441919086, 636022451, 605024489, 801825256, 932380552, 652326276, 94598287, 529512731, 356356223, 595654110, 635480956, 440262936, 835911335, 556163347, 574228909, 151161005, 466928275, 886694485, 438626272, 605050966, 223092820, 639825916, 138327165, 412671036, 694716170, 725787291, 36675634, 13966921, 979620846, 99943574, 980192116, 469380814, 885249016, 168467077, 493985111, 913641278, 765634055, 606686793, 781327546, 374299960, 446704596, 813732875, 7443399, 207258585, 259847737, 91454385, 182964559, 433860214, 292101801, 52467446, 505969880, 344688065, 160341122, 930559275, 249144622, 3564148, 735803400, 25498172, 516035276, 750312507, 315974427, 643083954, 826046670, 66740256, 350127535, 175646054, 879780894, 109271045, 306883569, 312737715, 193343874, 784903031, 514014774, 725908725, 488848375, 175771211, 802757432, 614046177, 233715986, 237776882, 853121552, 338611136, 829665627, 466568156, 140858792, 622232887, 79028102, 300108560, 178595806, 703711560, 781036362, 27763024, 950395231, 115543614, 479663027, 617617505, 808845690, 72874873, 898920252, 753461434, 970928426, 8763897, 243553733, 852305212, 515170614, 74198080, 332350896, 924623957, 617576097, 403971209, 76861552, 795623133, 308836803, 516361838, 520847605, 162460708, 144579012, 782216695, 584898719, 728510936, 314232367, 685578133, 528527701, 219794025, 161880266, 778885336, 652154280, 557375865, 771793244, 158343946, 542070387, 835680299, 476038773, 36520796, 198245029, 208434190, 847196993, 901407944, 678168479, 318279839, 977576440, 803639172, 177795023, 950991067, 556687731, 362958543, 366335412, 22433959, 670439856, 467229473, 49619066, 306163377, 896302197, 842809213, 893730897, 483321057, 822786975, 383672080, 963458330, 969109245, 338032880, 265070359, 957190938, 623841398, 63362262, 383655830, 939278504, 912142300, 404354373, 459871138, 24639356, 977215175, 725326725, 488959667, 271534617, 124291436, 511477269, 933078508, 738089550, 721502035, 231301821, 68107974, 615995225, 790799989, 813552863, 215897176, 544240866, 369429070, 921630899, 860547509, 90645555, 833818414, 959258007, 93510247, 758616069, 878059902, 24865496, 263127693, 151169361, 663416957, 342915207, 626791112, 809026601, 36935226, 492392625, 465273482, 822407342, 105635744, 257147600, 800583961, 598763983, 303272435, 811985514, 260883871, 99585088, 108929250, 3030196, 360962779, 651189815, 625025219, 804275554, 258086434, 943729847, 697058728, 353943052, 847814914, 777507290, 941547558, 966832852, 725328388, 453123581, 974406443, 198543767, 778753901, 903320719, 18074915, 638153416, 18984793, 515062127, 80323601, 474423017, 216642264, 373508725, 66682811, 699539242, 478231210, 635124651, 974230149, 406158779, 431685061, 495225064, 429571639, 74839137, 859812793, 382264122, 430019802, 966899034, 11593142, 319101146, 537672858, 777322270, 409343884, 272630738, 844604418, 60834105, 725784676, 410766343, 501878018, 375382969, 876634570, 115031536, 10490900, 208220399, 473800181, 784004395, 950756288, 721114536, 131810109, 131790794, 839281615, 779375147, 137960444, 97087390, 786366983, 145163482, 9274, 734456313, 126560229, 868518857, 589136589, 295758424, 85566472, 961138351, 339257633, 118296796, 646458840, 4368056, 571908428, 823639216, 17726808, 264675145, 320503245, 525023834, 687112519, 273669726, 34536793, 227978157, 232494053, 499594927, 896888029, 298014480, 508853441, 63098198, 698035568, 815324287, 290963207, 688451553, 837460194, 987958054, 619758005, 35953128, 896282747, 502012227, 424617101, 81494156, 833384235, 253357846, 310331581, 650558636, 888101193, 697532842, 44165655, 496440683, 305975367, 419203610, 5367122, 233668439, 495681093, 973766718, 348720448, 642448769, 784772105, 864228551, 327297001, 167492453, 844215161, 578258245, 310656159, 252094883, 156920046, 218311955, 476342576, 718371652, 988922007, 557088776, 644171822, 564901332, 272968079, 555359457, 729684203, 221592484, 543157814, 802660546, 253187454, 877825449, 932685100, 36434229, 925219051, 200505728, 289712287, 133664453, 532584870, 625552504, 488247869, 159460349, 259425901, 683692243, 682250256, 597279747, 849855679, 512034043, 116172331, 171474047, 135752037, 48403082, 549658422, 604592424, 393052808, 750781381, 249000978, 720264128, 640427499, 823045410, 376903518, 435637301, 233158133, 182923482, 186725573, 909061370, 496019630, 773730404, 203693961, 242444636, 893158935, 742494405, 15790995, 220419181, 40952651, 973239759, 87162141, 399793167, 394255293, 431985729, 689992145, 69382344, 798308944, 866121955, 302191490, 558459806, 123143265, 596279960, 377266150, 582234243, 794690033, 492869981, 451520850, 252460094, 141588735, 198310902, 74663122, 792131149, 27249324, 898830660, 905990397, 359614828, 255897690, 535900964, 229898873, 379865475, 211897105, 153196189, 475391536, 690146946, 675210517, 822646628, 75244873, 48945708, 647387937, 203299906, 110701429, 513792373, 312483901, 460339766, 856637917, 498142057, 382704882, 674958412, 804963914, 317117477, 174633698, 588447972, 338958520, 995906144, 386210672, 845968134, 284755463, 247032277, 451832595, 238788954, 512997083, 649428071, 745865840, 326888937, 989929329, 180233316, 195174874, 792395439, 37983557, 931417477, 439867422, 444186941, 797888536, 625861610, 736987259, 191196300, 887768298, 905158222, 164858448, 711967098, 277577063, 20380243, 444733262, 353548451, 639989032, 595063207, 357479738, 519559468, 966206475, 53208678, 392569114, 56990052, 743489027, 189630329, 84617299, 730288293, 300881285, 313294509, 312632602, 879782195, 492249530, 375901570, 733928646, 117035414, 973323030, 332248369, 121985292, 322456850, 381833808, 274867874, 39556215, 337269492, 686772029, 515888363, 904472673, 433504162, 804401295, 403870262, 138978213, 303857956, 64140545, 660155388, 132109069, 345316568, 754808812, 980680646, 197091631, 20001927, 378653499, 940690036, 949364005, 682262296, 96185150, 34839931, 396602088, 740343676, 183414176, 337499466, 873941331, 781150001, 625470793, 640864911, 219378710, 902459263, 703754029, 41545931, 693180843, 458291300, 811855961, 188417428, 376874673, 459310566, 746510926, 440345607, 301908907, 239353484, 808143626, 525817866, 247450661, 955733, 238879305, 370391715, 992518442, 913154078, 305851118, 727743244, 374959137, 734626018, 2483997, 896958672, 842445971, 118217193, 171720866, 493037922, 269292728, 609505771, 717413053, 625406452, 436339085, 522286256, 493609611, 177201931, 755280500, 848468287, 555298890, 426464463, 435492080, 120648329, 251612259, 920622598, 536270005, 57875199, 929623521, 593185024, 654095922, 405341177, 106126624, 656081037, 759259578, 732574557, 377046939, 251285532, 315917710, 798355532, 918253772, 16856877, 826185177, 417427203, 899876641, 737101435, 946061089, 983513202, 922605647, 177616729, 539895881, 215524149, 511696511, 21518872, 863084288, 668212816, 589268730, 125671037, 971687562, 180607927, 592393698, 115450733, 659757421, 956441147, 487976984, 481568832, 199447571, 676035261, 217129267, 222686766, 3557535, 745937247, 190677656, 497253244, 276914959, 989683840, 162033105, 991154729, 446827515, 443519999, 705874954, 52912275, 990864412, 732472523, 959231982, 672909070, 349652682, 862512109, 570123058, 713344173, 659159475, 269093730, 988230945, 477902773, 469480778, 915297261, 23182108, 622683030, 954613051, 496808677, 381539444, 817853033, 254678094, 42050914, 43324185, 655083389, 245364993, 142444621, 602307856, 10524673, 787549620, 967353524, 352804608, 630311682, 609522619, 459860117, 188749689, 993575785, 921339947, 900935107, 48991708, 170514886, 1596438, 781497494, 588171306, 887687641, 310886224, 402788920, 712604879, 951942160, 133413334, 477126833, 224677324, 467569926, 498762284, 877303815, 891274975, 739261009, 652966612, 417215694, 816145366, 127412212, 872920252, 502912286, 740357810, 220661013, 54423134, 30187220, 473650402, 279687327, 890815897, 616168695, 365132263, 333626893, 645034822, 721671931, 74498193, 988195684, 330887152, 798870379, 563065010, 193027007, 493401680, 921888582, 277537064, 692284403, 992654000, 762019341, 915704598, 222059706, 739093353, 566769162, 639058091, 976114002, 768399232, 991555637, 773034877, 219659338, 342707027, 601625662, 185461060, 200674162, 283843199, 36022995, 392720372, 662604766, 151699522, 972981040, 412815188, 683290099, 811647853, 640292387, 686205778, 531702100, 153430296, 208674991, 323277724, 342104635, 17381797, 819762572, 230538009, 843054691, 434492379, 850578750, 154255940, 21089170, 971195463, 452431966, 882472481, 696761862, 980331314, 54603688, 322787429, 725442761, 643333287, 670361643, 39800184, 457450016, 986431918, 598378597, 27856892, 767043161, 468412928, 689687889, 840804006, 81933339, 242064101, 659380317, 525337099, 379762830, 415428363, 596973318, 40049605, 286185392, 440850274, 199749857, 940509799, 843799363, 202223543, 570917463, 213180149, 413310298, 187379005, 768101232, 78929934, 828572447, 701296675, 758375117, 407266234, 600645255, 799501860, 793259668, 645445205, 628415602, 625138310, 397284162, 653091617, 639215245, 780874612, 479448685, 328747548, 953748338, 205089670, 436103967, 71576474, 421651006, 546821373, 435918927, 239768929, 179720561, 346122237, 467954153, 813558761, 425907209, 630650546, 547885313, 489787761, 518614906, 800897500, 810409343, 116006608, 969619637, 206524036, 251620829, 820176287, 47469356, 119172790, 794367870, 1512684, 497923424, 183116954, 736201968, 904461882, 584451524, 125919366, 40869925, 876034363, 246066279, 792141338, 81080116, 184800761, 442091703, 872867187, 858595994, 710390539, 361103984, 703682569, 806765683, 780697858, 550427894, 964173767, 191596207, 802984161, 234621911, 358761910, 762899480, 680831208, 287641875, 350656620, 820277548, 298695931, 483731582, 700097382, 472926471, 310951676, 239493898, 232354695, 32292619, 200510776, 494542844, 868371712, 917168410, 345776099, 170288609, 322296135, 912896231, 517911600, 411489480, 634429535, 153747610, 260800717, 986152231, 612074051, 588208894, 763578413, 273325076, 865328908, 960214381, 371418007, 386686456, 827981978, 45404080, 895920218, 991857262, 803499070, 226062388, 569866713, 985627797, 371990315, 934321465, 745671927, 349048887, 427394511, 855861828, 954264970, 670233003, 106790280, 697634646, 661038330, 234156731, 642596971, 682458092, 973974826, 569675401, 480807215, 14786177, 342104098, 889401841, 861501811, 933184196, 543674768, 796616305, 241592544, 261698287, 976199587, 996067774, 870466848, 808276337, 680185323, 944550028, 625886588, 964513866, 968167237, 307090626, 507808757, 161361574, 525974086, 570907737, 469829875, 371869672, 223202246, 938872904, 795975670, 662167918, 974160522, 475685401, 755552311, 926633689, 51359938, 603908545, 139919562, 256351042, 84291017, 793393307, 390468560, 48254491, 518865855, 478484633, 480362112, 829112472, 566594961, 53016709, 789061663, 483019186, 851801836, 233280224, 836470167, 385762895, 581758324, 662762387, 226762902, 350011379, 723295702, 981874556, 749430595, 445396352, 230313744, 609308310, 177054269, 346118757, 94335049, 360359169, 512528415, 809994513, 479991652, 569616629, 582883080, 438050490, 356164345, 554634177, 878562818, 13921900, 501304471, 777335957, 661931574, 722740903, 991628465, 101871933, 372218589, 406362548, 65258233, 158026215, 114257348, 624370591, 391688892, 767264391, 142392509, 55570167, 253347674, 447064406, 779714795, 540398968, 189458083, 873436714, 77227105, 119352239, 759730423, 348870755, 706093265, 691943181, 701289182, 199610709, 616339666, 607680991, 741580149, 9773166, 693055197, 149403059, 511087200, 194308574, 4317402, 588814921, 72437644, 66106688, 145495622, 884329662, 476315506, 46751413, 827857017, 623567284, 869846596, 296303510, 398274053, 254021508, 460151662, 112581256, 934409942, 86351696, 437351063, 573769150, 576170535, 458834620, 867852500, 822609720, 135009651, 226630302, 465271816, 874459834, 717502101, 502420081, 771828534, 128673019, 9878855, 962893065, 152966529, 352431241, 179193784, 727607888, 198190572, 875498375, 252097206, 849542397, 352288325, 658588691, 930894918, 406740598, 151654343, 420621753, 293615412, 951476804, 106085026, 897430536, 856465591, 612116909, 507081986, 625702466, 925881289, 933330005, 311626579, 545090413, 700118136, 199093326, 593247473, 160335262, 465647699, 283009054, 1113943, 237263167, 611621929, 631148482, 40238914, 143249210, 859397096, 351717530, 301626234, 612122607, 810176658, 38273644, 205884683, 637383839, 204604780, 760619338, 407978798, 36336094, 580813646, 875690184, 25318997, 265020699, 247510411, 95787868, 379825296, 727600117, 365864824, 860942165, 287963294, 167529221, 106544080, 418564676, 52381371, 754651441, 253090257, 127171069, 773903526, 792344801, 23830125, 126498830, 553507610, 692889246, 917123634, 404275865, 295552993, 316218902, 40526413, 166491930, 920488127, 189990617, 276989871, 128395874, 224373145, 583829997, 560573957, 688165738, 160273165, 686230908, 319452923, 845739596, 722739801, 634442158, 754250582, 634295611, 645004825, 294007044, 820453204, 467076396, 394786974, 227084622, 365976514, 455599237, 707635033, 987953153, 297686935, 432118004, 543491531, 169413058, 982422504, 153220152, 436878490, 267897451, 18627896, 120081196, 581028421, 367332137, 936468144, 445317387, 871329067, 177802070, 472618953, 392767176, 44575521, 322957911, 511451517, 99769918, 137098231, 400583058, 631232768, 480836407, 79141089, 132154600, 66339357, 89782314, 442941730, 906784705, 631206797, 841389954, 418537340, 177055297, 413996200, 780149387, 337816225, 425510084, 982597069, 320073739, 99266686, 972621034, 328368738, 748180588, 715282578, 85595259, 579920947, 432403712, 441398876, 611296055, 549298739, 662698007, 359461819, 729914199, 101321384, 195712787, 887100477, 473950644, 485246226, 665318860, 72930949, 45859435, 781759892, 426100176, 307146695, 665512429, 75300555, 748675753, 729576467, 398094533, 946698223, 530745555, 904668288, 279719074, 843895539, 584788528, 359245492, 7265977, 446052225, 182756620, 64557066, 955320516, 841265463, 528238098, 939863019, 775456754, 365938092, 92424370, 713602857, 422677159, 156527793, 437787452, 378614759, 661474585, 613274653, 748174329, 771763005, 137548965, 428662199, 255423068, 702214436, 505554980, 899936952, 266461398, 966940664, 101196185, 411881887, 287331356, 91707364, 232072993, 718628105, 691362485, 752783177, 97826797, 703621491, 838574389, 582999833, 707129824, 793102550, 942773554, 671206228, 278841283, 534805414, 518915081, 968368223, 515742456, 98488218, 930922235, 115022660, 105062777, 174637070, 925594598, 248513594, 619987147, 450924209, 60085560, 154168636, 110782291, 536135388, 719727590, 165075254, 758038493, 662086767, 875119995, 968571886, 501567476, 907070633, 735264509, 633493821, 930516754, 65439628, 656638573, 285306275, 228407880, 674475072, 291625074, 452731014, 408905585, 350405743, 918666599, 624203307, 473492363, 52613338, 784274286, 715732883, 602244121, 223052723, 578910736, 700952586, 837500556, 549579308, 956549213, 526422862, 681779870, 771877701, 98983454, 444825768, 366628476, 923948275, 514533524, 850660338, 875400574, 837618581, 681283792, 653467439, 777881486, 865156430, 764506826, 151217268, 147521568, 498061182, 829590896, 693393093, 335376136, 83592384, 916426777, 132770998, 689254734, 360340559, 615213460, 515948753, 175727015, 994751119, 825672087, 446328096, 379654854, 812281635, 389295682, 272063059, 613838775, 105749735, 828436902, 96545959, 453797299, 275341816, 182757367, 470051325, 682985314, 518588020, 824173745, 997981730, 700418093, 419694420, 789819901, 937685990, 66991211, 2106664, 364593820, 436257859, 997748984, 815966569, 848768932, 920544142, 295018265, 716564100, 977197118, 920146429, 636433458, 700948989, 588596203, 645902478, 612115336, 232793377, 354515130, 406995928, 866828901, 286214645, 329704671, 963130921, 764909740, 968036323, 654449915, 912054862, 778344681, 451909535, 318268730, 448974279, 562071558, 669264656, 482100625, 860260663, 289879076, 511233531, 472682047, 586601652, 409207518, 677002804, 195126570, 456407941, 872219720, 88339264, 1023648, 526773674, 982146942, 575542586, 698305893, 374824225, 424472858, 622469866, 908979458, 319688392, 159895858, 332757242, 712668239, 485846636, 340817104, 985239624, 705784547, 872017156, 57983432, 384571624, 102923354, 856424483, 415291225, 495377755, 236656856, 692716240, 675139958, 334430457, 478826030, 545420434, 620134777, 747132764, 299921159, 61641612, 827567281, 356370787, 234447987, 231120579, 219582305, 442544918, 420022220, 701616648, 147658102, 912522077, 5586404, 792773655, 922135603, 947855259, 676559750, 504441686, 337499612, 683639272, 933835671, 261965159, 769169796, 26539151, 986298440, 707446185, 384430375, 542576138, 354144899, 728221482, 176339933, 915805219, 192445200, 259659841, 687587543, 821674233, 155184858, 806877093, 120083429, 610150036, 215039587, 634787163, 163144808, 864530642, 413785871, 752361571, 122457300, 129671590, 418867911, 572725353, 542016037, 749263945, 908397740, 711521169, 573240465, 239468797, 14492867, 379012132, 45800173, 702025884, 280627153, 394307643, 852165880, 116831528, 705275092, 404372495, 960986632, 371406676, 905712814, 840401997, 547952643, 281501126, 111448372, 721288136, 318962254, 291278021, 239584976, 425082987, 975064646, 313650762, 667911035, 2452476, 7156912, 770957336, 750214633, 269192256, 452428578, 760440691, 879284354, 112299115, 532898277, 639141508, 917991749, 224495107, 541857046, 887278373, 667404362, 934963035, 411054840, 968483277, 713721876, 32551842, 293309243, 790130184, 400665251, 877690619, 892154521, 238188680, 59840121, 255943087, 867065394, 841720836, 960055647, 278867938, 431062379, 582376238, 252904320, 506649933, 290664313, 239182900, 971713662, 470130535, 315698361, 27205423, 438445560, 865685133, 862967901, 49801349, 816926739, 771545352, 611116506, 969442511, 253774548, 47865969, 198293147, 704262740, 70704601, 620004163, 7693048, 996394628, 280201492, 470546308, 995758513, 62918520, 33688337, 970067362, 683422899, 588539333, 949540893, 39180182, 768933432, 887883456, 596091790, 761190706, 68210974, 666884429, 896541399, 953042216, 845461326, 133127164, 536145142, 882357756, 272535442, 589904880, 598980000, 613832163, 459242282, 119845608, 789016256, 842813357, 101913721, 347219294, 825116257, 506949038, 729913060, 547986599, 819113631, 596761061, 559421411, 470532294, 217320435, 894767368, 369940297, 590711144, 91912580, 65166088, 674537823, 442062623, 241266058, 251342572, 800168497, 38235735, 555094877, 701946448, 13369478, 569718918, 82793569, 982680786, 172153689, 611573486, 534120433, 857962212, 812171961, 711673709, 910395941, 43741716, 9201485, 788453221, 830187999, 307767186, 474668383, 568022682, 202604383, 814012105, 795914946, 299763002, 790972370, 616977846, 423578597, 787887804, 281006931, 780282396, 959769991, 564116648, 96437227, 481387612, 182445908, 864170727, 216986846, 73230928, 852588106, 322752099, 554426850, 304741133, 765642354, 431122600, 288037250, 181317581, 644012169, 460753893, 729127201, 100101789, 79306052, 517615352, 68863297, 988399369, 72529618, 634120508, 21149985, 929076539, 926990789, 115821668, 172243149, 755638978, 556249849, 275837599, 474206309, 631897055, 720614686, 552548575, 591056817, 65405323, 114412308, 936039021, 966189671, 607285997, 72093691, 480253414, 209458878, 846840262, 700446973, 220148496, 54906121, 330660057, 934455337, 357102236, 894435446, 550826664, 720924437, 657743333, 774695438, 159469420, 252283284, 476178977, 497558729, 79743731, 627079856, 449442284, 845373604, 230089705, 71721486, 219603004, 784892865, 876116792, 680173073, 11167835, 808200756, 689014124, 202027836, 877724006, 770499604, 48469012, 960372855, 985495590, 678711283, 363696340, 611426535, 982716205, 284143697, 240970499, 566705873, 200435161, 974690963, 486893897, 344298350, 784754165, 927024126, 494506002, 738227449, 497615618, 773513725, 975666125, 423154350, 335618717, 116601227, 717144670, 41391288, 157545325, 603346453, 384757715, 68806393, 221751378, 44477097, 130372505, 922566350, 37148321, 106713739, 60507641, 581789769, 857547227, 683970712, 740058857, 293641226, 365962338, 42507991, 896491469, 370561469, 755980270, 57945750, 945527026, 865325464, 660955272, 400398336, 572299065, 877898856, 926756883, 579087708, 722511930, 780594362, 458556320, 230118284, 644597472, 46146045, 691303142, 963093595, 714244352, 329724046, 210211463, 69982889, 257220191, 92544761, 549472730, 944750112, 279116583, 168949667, 75071291, 269116048, 975597168, 842952920, 657044385, 129887477, 945378904, 253312837, 634057252, 258381583, 4590640, 680234868, 343794420, 30501452, 770931430, 528542352, 348264582, 653932706, 367174181, 894472268, 493883873, 960391246, 213045095, 394258898, 6108579, 167954965, 46562504, 956721526, 503402326, 567394691, 490007503, 932559560, 846580878, 887208250, 614393659, 131807958, 706139208, 435903828, 848814688, 798016233, 358921488, 412771292, 542400538, 945890366, 598406766, 667728897, 382251689, 537694377, 994812143, 553316397, 734854973, 911124509, 799658851, 470593965, 334751028, 827024910, 32421102, 45086706, 26198281, 339408431, 671618661, 881987874, 234539763, 636468641, 807497664, 231337904, 382788156, 531194141, 559630735, 344828376, 306816712, 415497033, 170693555, 426964632, 113350719, 970688338, 711604045, 178950006, 264794711, 837774998, 361782867, 686711027, 989460438, 569634246, 659480859, 226745718, 742601659, 295221427, 267189687, 534370896, 522381732, 194032233, 227705769, 556767818, 298632298, 756693696, 352073782, 689796950, 602026430, 761429617, 770988018, 681902734, 95420532, 7839170, 328567779, 795140395, 676145915, 17498243, 672980773, 719639413, 708801527, 109802643, 225463218, 471079463, 710193025, 169322529, 73843688, 487624190, 947888033, 871142160, 622459575, 282866465, 232730319, 505197861, 819152179, 991549300, 735966983, 608680425, 527618127, 911605382, 547757719, 95612498, 684880343, 843442558, 452221252, 55743883, 715467170, 104350896, 203736318, 124000188, 715927586, 347996622, 57157811, 608197504, 603985532, 435642462, 934201807, 532994047, 936305788, 177036713, 625802589, 55047542, 772807700, 109044003, 141431132, 170545849, 154426583, 404501449, 382196738, 69473811, 689814096, 80308083, 567155632, 915973969, 715514954, 620060537, 102089963, 564898713, 346144968, 372414841, 687818892, 697866856, 635635589, 260968836, 845912119, 894390184, 753562709, 635681371, 119047033, 112439112, 145006676, 907253924, 973524120, 86522618, 207423320, 697322322, 143690551, 67332237, 806192744, 947384492, 737908863, 85654211, 62371117, 758745472, 153017926, 222554718, 845217135, 888342108, 884056541, 967684623, 548557550, 377092664, 941498554, 74367022, 470471793, 769433663, 51025904, 162237443, 263495682, 34368484, 606049219, 158888936, 392105521, 48001553, 197100592, 183238338, 481143943, 974162822, 206192105, 804065771, 270447381, 723306117, 689779578, 223412834, 835205852, 528050151, 260644922, 626386296, 68832559, 326585227, 312814821, 132858564, 56728384, 243250861, 555767647, 595134477, 914103178, 921594935, 877553534, 430489299, 485111, 646766217, 75745457, 288039109, 544392579, 641718193, 250962405, 764201308, 183800984, 403934651, 404897899, 376688454, 601157340, 246601118, 79158924, 551891661, 940704377, 199481908, 397372771, 781484520, 845790443, 214843725, 293463189, 345563899, 472239387, 174812831, 31021935, 838150251, 848307820, 790241080, 410887312, 743311905, 22270613, 763576962, 477398994, 77509887, 15054048, 252803314, 88891965, 875877408, 384711374, 68807178, 155378946, 986121263, 702375896, 174072360, 285305202, 956271323, 708027198, 511997993, 611846324, 718157560, 339945925, 894949858, 464560567, 379092722, 485734011, 508973200, 1392136, 260363664, 977270302, 861046132, 438803896, 330463872, 739805682, 11351329, 262669549, 605256632, 549538444, 561799719, 97142373, 724728939, 517090439, 376664568, 881640447, 592502262, 779041171, 26034276, 452892029, 14291113, 906653857, 986761718, 251595197, 384960958, 61293592, 449626446, 65086833, 416961786, 980296013, 142170619, 917299087, 473033126, 409313172, 630742118, 582972682, 136837867, 682468967, 784194555, 607497696, 578261790, 842780525, 954984267, 685034345, 503750959, 459451401, 170094178, 146218456, 124616757, 866454213, 723672003, 182167053, 455481873, 511893753, 156058128, 282681347, 578178392, 73383272, 568814315, 798500796, 99941920, 627103337, 920302439, 114545536, 11413924, 370371831, 882012061, 302134053, 765770206, 822697356, 120065847, 246587723, 420561864, 814017142, 432236242, 21490341, 45485221, 972062444, 604712062, 584130187, 474608356, 527558462, 984747157, 216286131, 822815126, 596630829, 835244251, 723614332, 861979506, 340121626, 555605461, 840197382, 270716396, 486407212, 74118531, 381376545, 720505784, 940127242, 627276968, 244320033, 79235277, 864664359, 271245792, 729816630, 723193037, 521418349, 551900500, 505674545, 216908497, 127085874, 956592723, 158943278, 279044013, 434788815, 489720286, 882571562, 62677462, 392103046, 869223216, 671709151, 543836159, 480195233, 589746821, 883038635, 225808692, 15164431, 440855329, 623843300, 588873960, 795731157, 941386682, 416852103, 550515863, 316413275, 82649187, 619784655, 953039222, 468585036, 580789153, 977598847, 797923686, 982263381, 809410152, 247560345, 22520996, 721011259, 59520059, 105891155, 685443824, 419063271, 305028915, 261464119, 822293168, 144419719, 949195667, 856075601, 98876564, 325468152, 961678025, 818690692, 487448953, 607289338, 866433319, 619329593, 336568185, 555601440, 587264390, 641848552, 710702558, 505493246, 354836407, 779998107, 571437468, 733875248, 347282310, 247361746, 856643758, 477181031, 255940386, 203739697, 948296121, 966145014, 42192502, 895150348, 605038506, 824791820, 896395508, 34469792, 288407009, 781365851, 895485504, 577677201, 85797468, 797338432, 695653414, 840801181, 345696059, 458977510, 290844133, 566370531, 353128604, 507196035, 362959042, 680683443, 752021577, 482396754, 519113800, 183850761, 997269956, 352929584, 849548189, 192866152, 329654401, 36224703, 157647874, 153151947, 819729541, 64847469, 6664138, 288567049, 836181460, 620122239, 816151684, 910329430, 817028642, 405861810, 99620666, 28674477, 84463578, 972196172, 154249673, 755819696, 401667598, 463627555, 495159946, 799302895, 518331228, 127656746, 875481941, 598056907, 263571013, 344690196, 108695374, 666323886, 347520496, 627604456, 732810011, 785911252, 172294662, 822277157, 417850618, 743183784, 715621394, 13374088, 963108917, 755480889, 904802515, 730008068, 17211908, 708500243, 3107901, 941197642, 319605054, 881117341, 216706261, 951475723, 707087905, 233730446, 287806802, 830486782, 797439815, 112091349, 853373276, 488445777, 703791206, 338555837, 751381610, 250224619, 824293357, 942670023, 594596506, 897502892, 699412138, 527177261, 181969248, 120902311, 229144763, 920379963, 458745855, 10186335, 392211915, 518351181, 768915447, 326549713, 875228181, 209088522, 734135321, 387293542, 505229152, 744270879, 374516568, 457928188, 80058812, 131386512, 707408590, 351622983, 736540849, 991895223, 377857483, 770061195, 747148402, 563240008, 910698995, 293699801, 634163059, 569884223, 692999781, 666921869, 456481638, 658846655, 553489114, 532121654, 193355886, 754459614, 266074431, 481687942, 747755149, 393879889, 42766302, 643523986, 931914154, 5886248, 782357362, 950903810, 858938583, 542499398, 325900917, 346935352, 236778789, 163487410, 357145092, 226099461, 159132197, 944475866, 545814303, 7954658, 47768230, 368033812, 99927844, 30939401, 713544233, 288763094, 467180440, 452812538, 661089561, 317156895, 965176888, 979833554, 404612588, 976906162, 137320252, 264761267, 438616997, 797970820, 683242140, 497823919, 382150176, 868481790, 927165217, 114578751, 679113721, 68260257, 113990651, 26734048, 362285944, 40884335, 822682785, 266438723, 998519363, 148240414, 84902540, 208570427, 258416766, 966516296, 38323287, 502565301, 794450554, 693789087, 88002794, 836836164, 545367568, 827825470, 874697249, 79289306, 644345594, 710977306, 180345458, 99759663, 554987476, 995322292, 924357095, 301689723, 330431255, 332100375, 663276421, 555964477, 354983994, 665123199, 929017562, 958501999, 937583780, 597353580, 49623144, 558894352, 877339803, 358082580, 217695830, 381622310, 569594512, 126678243, 636321747, 644924654, 923683020, 906515903, 322232480, 519367985, 415036316, 23228431, 906733753, 202784419, 152267828, 528146899, 353902125, 2184219, 355262629, 247222390, 598752638, 930894205, 333342272, 611818152, 471654705, 432518463, 973389792, 829165781, 51031270, 950324786, 21156502, 333155246, 290719984, 944571643, 335664113, 549738763, 24138517, 741172045, 716513150, 393222494, 248804791, 103115367, 639313845, 55544854, 242462778, 142121499, 484004067, 413924172, 404278524, 112110374, 975212906, 753481078, 848263423, 887304154, 979470059, 887768926, 666892224, 446867749, 105966251, 334706578, 49033608, 757550181, 669998656, 525939169, 528479377, 523835604, 555077055, 590280207, 421950893, 221486868, 812953880, 460830219, 210056548, 931305051, 104119840, 189131577, 127189192, 662534786, 888251615, 579043896, 334833258, 982277371, 248518501, 244860627, 238114919, 248218554, 249179466, 491393484, 563026437, 707206818, 633665614, 151879124, 870931273, 518837822, 980636127, 136007601, 79435633, 296759272, 767804733, 691330960, 636597827, 482047218, 815049981, 696101106, 480008420, 275982569, 888719805, 242684752, 900039010, 246164972, 370822900, 379177377, 38007742, 176519767, 495033939, 616158867, 774668244, 437236760, 907149039, 757060463, 823772622, 841785418, 301998343, 127954114, 896700655, 752864198, 677067598, 293036861, 273727517, 497739570, 419094011, 35585499, 377991542, 775014566, 706846280, 974259924, 348519330, 535649571, 752665215, 105527829, 980686325, 429091543, 787812213, 411274685, 499499451, 457171041, 839516140, 133807979, 296728958, 194498042, 458116819, 138157558, 2855914, 146327864, 568513923, 818833826, 334388002, 80693395, 148595844, 302921700, 992639538, 591280215, 55670596, 9019390, 526199339, 461774209, 285350567, 605563980, 877476653, 928201911, 443180586, 998155471, 351410264, 158355187, 874107833, 320816493, 733567378, 318132176, 922192022, 566911014, 315660627, 599773240, 550005944, 644892725, 618737066, 31771629, 173699562, 459619910, 436832839, 623413233, 53324220, 934633287, 454661997, 335977144, 721986515, 346693093, 130406579, 989549643, 189620737, 470002906, 709515637, 113091430, 826323923, 936475263, 335832787, 143997158, 533315029, 122287040, 674228266, 619587705, 832558066, 275413249, 251955770, 998062782, 253415807, 382687472, 475082373, 187743292, 564664805, 634458425, 362708259, 131821180, 617461319, 100481393, 272780276, 329310595, 556020340, 864283523, 821627213, 660514201, 870738607, 838378281, 48121415, 692677308, 234140448, 521274496, 868390421, 133708542, 890592319, 532077331, 775384714, 178199023, 205731690, 652085709, 408698468, 777361335, 667289642, 444258608, 48011796, 786771898, 493261279, 177759951, 549867052, 279752859, 259264433, 8718828, 448008823, 263009931, 96067216, 788426643, 570946242, 403034397, 86288372, 924646379, 519464145, 554309262, 184968252, 330316389, 831423638, 493264871, 129450233, 503173365, 867017992, 267184767, 137063453, 56031464, 87526399, 830998370, 727079440, 633434303, 174194039, 477168372, 66839117, 18691001, 649268890, 128989121, 355238981, 30378082, 74775746, 538259448, 453579219, 759674947, 870623424, 914600813, 619506997, 527754287, 625939969, 432122578, 409684444, 560258737, 65634547, 957555723, 239348778, 917097163, 326034359, 888430882, 136553110, 730847027, 568739720, 602458695, 444756223, 552999745, 118515824, 773952209, 939046136, 462973253, 719734086, 55841598, 898068184, 784535855, 343484311, 154260715, 960511727, 805945277, 452621262, 905585316, 692103994, 252547839, 179710521, 970027720, 11808654, 301230430, 361010954, 334334771, 466557876, 691067875, 934337735, 827438028, 319662380, 298941495, 34351876, 619955306, 958006143, 188989877, 722154932, 179994985, 194284701, 355308428, 467031336, 682556059, 830356922, 972986875, 824170431, 531094758, 597413541, 430611404, 944695813, 932307525, 63148332, 703884138, 385452204, 680078091, 165444130, 251672989, 25325309, 534599344, 320234463, 600850149, 260553584, 992680541, 91295893, 71808724, 406610766, 16086471, 804489952, 543128955, 648019621, 676418033, 69055302, 907225842, 315137762, 618736899, 582512876, 246190423, 66407252, 137927677, 750791912, 861161015, 839024007, 182171244, 458212927, 751983829, 163864356, 644989310, 617376619, 193136820, 472469720, 547831787, 552404129, 650061568, 473430812, 185692283, 604253801, 325870164, 726643411, 653760674, 236445142, 960754104, 138230083, 525990724, 713915607, 92841460, 133028682, 49155994, 94791779, 223003072, 485056674, 357232552, 910842183, 89126684, 687124438, 48621089, 992041227, 928269187, 283220227, 195205014, 35806053, 49041912, 314018314, 121701226, 290549084, 609139232, 1421532, 22479133, 505254759, 410344407, 19422835, 325986208, 615895303, 765911250, 205990104, 692498291, 583833453, 836961762, 519808147, 530716337, 873103531, 91434089, 915908560, 982557872, 510391674, 772793783, 595817857, 549576040, 920789903, 112862896, 138046429, 995134732, 661162572, 443074052, 444756927, 938961050, 974238989, 731677613, 833752468, 798652832, 759850047, 937636773, 705739332, 733519473, 551077566, 869158573, 517458475, 230225544, 413500939, 654501309, 807807014, 583545083, 879892173, 125151604, 900623594, 222174084, 257299560, 394006381, 324260931, 870458231, 997985808, 535718199, 873047759, 4468185, 707391437, 368920631, 144665629, 119658536, 441100646, 44373541, 523479053, 940170051, 31373486, 273370573, 545880215, 426985672, 959582448, 921821094, 952588162, 629112383, 873157788, 373393051, 520902558, 937812448, 691898389, 892481483, 4373867, 448550319, 418182343, 902490001, 365370352, 108053678, 441717169, 788537440, 479043461, 219130693, 334189322, 971124740, 61921722, 27241757, 427152098, 65053180, 951492462, 201456624, 509486702, 729386213, 970902350, 760398302, 672389597, 393835729, 961353243, 143177237, 117667916, 815332199, 514070071, 546720386, 175004276, 393603219, 407322862, 225861461, 716725384, 758102429, 731529750, 862281700, 271270326, 731967350, 926818090, 22648117, 426033350, 262150336, 829740893, 174984873, 161238389, 599481891, 356103865, 430907881, 221175232, 847376796, 185924708, 923910340, 39540708, 422292286, 957953195, 175377158, 365026277, 906733609, 659129942, 285867363, 814650342, 823255770, 813316033, 753092852, 620377977, 291899560, 875432539, 554206859, 601778846, 397374356, 737391772, 252062333, 613857065, 77533109, 714542379, 146061187, 336790139, 285266099, 541168822, 743817027, 905902763, 7167738, 520086726, 472573107, 559808807, 623550832, 391222205, 763512063, 464932612, 905317627, 409796840, 87398556, 401215899, 331086304, 171950293, 498548651, 796724034, 599020022, 978090186, 64779676, 197872564, 947933555, 551929865, 960077645, 41313475, 941816231, 328521257, 128322492, 262722539, 437831996, 565575672, 730164921, 819980629, 333564170, 128367994, 426068532, 718685064, 38834943, 18852894, 806847990, 301974668, 599833483, 632707802, 330367117, 209715772, 41698806, 364287096, 742918656, 893317015, 83279168, 987837551, 481772193, 36306529, 873722434, 460482823, 319571635, 194556972, 583892639, 469447620, 256667450, 462764939, 65401398, 581938174, 669097604, 823512388, 304462971, 63304500, 68198731, 936040104, 177860014, 534989198, 399897385, 845479222, 664090174, 664458667, 551737247, 548515310, 550310004, 805515392, 628543544, 978337774, 342446931, 311736512, 68551060, 841615162, 824398163, 473698743, 777063164, 291994121, 528893537, 912672013, 208688260, 600603352, 831114822, 397470315, 843015192, 299008845, 963893551, 118975435, 543927561, 127607315, 362148853, 774273663, 960962726, 89487797, 335966, 288897458, 878559828, 433470305, 108903963, 17504321, 581405199, 572402977, 791983289, 270149156, 544666513, 721062645, 532942406, 103905914, 841151028, 688017502, 721246428, 303088570, 938561959, 344053283, 408118332, 633609713, 649512259, 206396183, 129323028, 247713385, 927388911, 966095523, 143688876, 688954021, 555421378, 299465411, 753336163, 249682949, 120680960, 29155361, 819459610, 838670416, 825983682, 605387410, 3770309, 540476444, 110228645, 178298569, 648231396, 718745444, 281131496, 645920224, 224881590, 799106476, 384748928, 250866521, 749492022, 863187188, 115034562, 284125814, 528272806, 193650784, 707981403, 453260456, 32790480, 143664408, 427741865, 832716899, 518702410, 800650948, 15019057, 623996149, 830957258, 569101566, 2109009, 95027318, 478561964, 147871382, 287902985, 228119832, 437473433, 463784659, 32343853, 458219701, 619574144, 91251682, 575990199, 50502388, 491136285, 171448716, 264559655, 611718534, 46609772, 87668793, 788681434, 115058524, 956459204, 705053925, 320043339, 182421592, 271074149, 564057860, 374982408, 456687857, 560928496, 497441875, 853295821, 363478547, 703831632, 924326140, 150314107, 172962439, 471210154, 409384512, 440637482, 601487041, 325885921, 982972685, 844067651, 4809627, 961428510, 248108303, 889795126, 372266751, 37393617, 407122765, 832531628, 139566856, 18292150, 310943296, 511029152, 878034028, 824616229, 547628114, 893106657, 676653924, 660480247, 190644912, 435374495, 989633084, 981659608, 271864600, 879545031, 655348751, 153383360, 901433155, 236287216, 414458483, 760893290, 903129818, 853097515, 746528936, 794962591, 301765281, 49892893, 933699322, 787973593, 350765926, 436764280, 828666453, 430356286, 792158871, 363128025, 911592594, 126141375, 65366161, 133808518, 861351316, 90319630, 967714351, 940678111, 726246164, 971954217, 227594148, 223402226, 200727268, 15380483, 536191453, 466125754, 115992984, 533369635, 893253021, 697573504, 369916872, 501004022, 228538259, 862148582, 284915226, 656051836, 184953093, 401625983, 143750064, 461948532, 711836184, 46565132, 2818515, 275237023, 295501259, 625740628, 180655799, 428645299, 545925010, 866963296, 438245801, 656932136, 813723316, 923907122, 621908905, 616661746, 228893998, 48828241, 818295777, 580270319, 6242576, 74353896, 255282377, 609913044, 305329566, 866446033, 676926717, 546742021, 957552389, 886314596, 665715421, 811226876, 964684256, 696439295, 299835115, 961632526, 813428081, 526136285, 563284683, 414086683, 459438050, 148766661, 352168897, 507721319, 793177283, 338686086, 939234239, 275040440, 966854461, 572744319, 496297284, 663424842, 797541452, 574697190, 77032042, 10827481, 260717481, 563840804, 50566143, 961337719, 27267940, 845828936, 439328207, 262302189, 933685335, 976348281, 800620439, 744095505, 630433954, 535524229, 951081837, 470690311, 42094382, 307121211, 102275878, 408344434, 412092884, 928646676, 803264853, 433885795, 307850114, 696679619, 128745225, 906108914, 859931875, 614733872, 228338303, 238877256, 835116260, 706279555, 838504154, 127311025, 930103433, 532893154, 77791108, 477347248, 977012011, 929257528, 181494426, 755903223, 191049348, 577166579, 303120532, 977535933, 23576390, 101210309, 794796742, 787301341, 713563798, 287259723, 87429687, 905948067, 887590352, 168390662, 239530902, 221428804, 561360800, 619027946, 170589118, 795424485, 249026244, 696917574, 47860825, 40167800, 745776403, 88486907, 168890100, 868496692, 214613379, 697053912, 802026332, 44155276, 60714456, 228520049, 530874034, 902573193, 445452598, 809763798, 158298148, 635306941, 261406696, 32884609, 622937979, 755083522, 270537666, 179382762, 450386048, 703328635, 756861416, 291808666, 576246896, 106531378, 291838709, 720837313, 232031712, 326125886, 668753652, 847692431, 216169689, 304876963, 308993780, 352290351, 235202728, 973588123, 755219514, 697878849, 38072155, 432136268, 590827584, 534227291, 994728197, 678666726, 49049573, 289582618, 630243846, 367903377, 345724882, 892233127, 781870649, 828084120, 430420944, 119941527, 106595886, 739942216, 718432656, 616861836, 613310831, 276361450, 780341214, 237806364, 747262280, 592952416, 941974364, 630592279, 864597692, 707282565, 73012255, 815747526, 492930859, 768068667, 683570197, 334063331, 83427082, 889097406, 738391045, 850665044, 118137053, 741368210, 33177648, 782228280, 38574025, 367221358, 187523999, 506542735, 905443886, 42616720, 459539202, 139933921, 437533, 918061264, 130825691, 246895915, 873435414, 671130936, 599073005, 366030552, 669952967, 586812210, 129979857, 5220432, 694860839, 115868965, 692772063, 52035123, 773857517, 907412200, 890750645, 194246093, 347425584, 852711170, 153290274, 274261999, 78927740, 366610847, 816112256, 371755373, 748489353, 873714375, 979500042, 971599971, 466925992, 577358409, 268103218, 184325452, 134066745, 504772827, 843184453, 979652575, 280483334, 372869579, 463580831, 24083065, 450567915, 919985304, 484789338, 55630227, 60833902, 771569031, 848374155, 285987716, 638451084, 175373512, 483790117, 292299674, 826834704, 898695724, 668476532, 241194055, 71267539, 372531011, 444197490, 795722950, 525396328, 910052300, 189851662, 443087024, 992444669, 536271379, 602491157, 309247852, 933990629, 840672809, 137972568, 15796372, 768176507, 557896033, 343521762, 116533108, 439901035, 135537167, 333561375, 874334635, 839840907, 784884845, 455263814, 909561135, 515398615, 727334788, 20554337, 925402798, 387707738, 750476364, 763297061, 756975611, 315192998, 766417051, 28929428, 688448304, 798644289, 726660420, 128754292, 534442116, 995158353, 288017731, 411513843, 438960731, 615483838, 805322717, 455715277, 264257174, 633943443, 595487444, 217364093, 890938227, 677752981, 878021751, 651761897, 355245983, 467008407, 215590095, 994461601, 136936798, 530329464, 313188788, 555129508, 798535700, 404934571, 939137505, 641898783, 799200577, 23595461, 701054501, 480172908, 120993806, 53558926, 244785250, 683780739, 426909290, 803062212, 462383421, 458153049, 6481979, 306984224, 280674280, 508740335, 241070259, 490085414, 133288054, 483541470, 45317810, 567893990, 510506191, 377398212, 340077062, 858330576, 278371484, 392384265, 653407713, 714546987, 461958596, 816174363, 30459984, 518103886, 687949029, 589833278, 111489684, 693169868, 43189334, 75617476, 334384914, 235185192, 172477614, 718672036, 151474659, 997262845, 237859266, 473006462, 848818287, 499132437, 975669296, 853320091, 87600182, 495398111, 28403105, 224865485, 443649794, 415532578, 675784606, 218843640, 713904440, 328471184, 628261428, 680532348, 709381647, 849196682, 270412365, 666184151, 397556948, 492939960, 197893385, 121431881, 587078693, 275595025, 202198857, 549132599, 562246589, 275632182, 372140813, 796693920, 716715964, 936327272, 831029076, 246620684, 97560954, 293327676, 181555693, 827380436, 379619759, 462520541, 96993989, 149906241, 322958138, 12595081, 817474333, 484240408, 22438662, 745094486, 295481137, 540275756, 23054777, 69275210, 115192781, 879424318, 923456493, 467274059, 582455567, 561230844, 8228171, 267344527, 889488561, 87715767, 764644562, 279694055, 488691596, 501755407, 484154008, 606429515, 18177000, 28501712, 83972872, 678806978, 963181396, 882390065, 527461179, 706152488, 216677862, 319156354, 140537198, 264973121, 407663780, 228315747, 533285570, 104848378, 394333681, 777563395, 759462720, 186880221, 933034544, 954083367, 490877965, 528717633, 440665554, 468604289, 647258446, 40178330, 724590931, 608997047, 843017383, 305762964, 333179738, 599078051, 503288602, 762753423, 32447267, 207895939, 956443821, 897372811, 968680459, 843387128, 308036055, 644359591, 711699506, 345001042, 639620734, 805498907, 676956718, 389757158, 44193007, 434663011, 432225204, 161092531, 292894111, 120416664, 385609096, 296273173, 820385807, 33500846, 386016497, 586868582, 601676539, 66727400, 677058084, 775422386, 215672803, 335198975, 171254048, 684171467, 175725484, 204282717, 824025066, 328374207, 573038838, 442652000, 321542371, 684518641, 515863366, 532444066, 471289372, 278512441, 101601145, 671628170, 743239857, 662526657, 892081389, 895918701, 560712017, 179359037, 430937988, 878291689, 385156681, 565831764, 137663156, 992269405, 642491272, 685063353, 571583921, 658336890, 657935357, 360014514, 762914432, 631424812, 230954150, 429998102, 762929524, 718272098, 565348792, 426649924, 175526352, 227590351, 268810392, 26394612, 417942354, 572599221, 227908807, 904172579, 386310064, 960949237, 351080782, 854770740, 621538435, 835427432, 813867006, 118706589, 312599374, 991890161, 281715669, 454112913, 462173154, 104585636, 973464322, 998129593, 665521537, 164169307, 649776872, 859006521, 456400602, 905730244, 97256184, 581332979, 349549418, 73231897, 934804767, 997039043, 832456395, 490541270, 67527928, 209300738, 352345376, 566333252, 84763865, 49385560, 200892661, 160640836, 155692443, 746176674, 891955251, 619266188, 402493088, 839216984, 561254011, 919582094, 755130008, 271024574, 991140960, 368213956, 863546238, 497883847, 399314593, 932310940, 787424902, 34968085, 987874030, 440163131, 293549207, 978899635, 85249639, 33625257, 561627162, 698874161, 778342243, 702995088, 403964818, 500764949, 898287342, 286274883, 986760560, 243852705, 273592558, 187225500, 595554064, 196496981, 371595815, 102189221, 559746665, 203995151, 32570381, 556441667, 990959866, 607382090, 854390727, 300402471, 308683913, 836440105, 363813215, 230689443, 551651417, 613369967, 534552644, 680970011, 218895646, 566661430, 532244890, 293800553, 648024884, 236521822, 684125474, 878431245, 695715871, 535552445, 766388061, 212062961, 259597249, 116160213, 840608065, 269224683, 363770133, 325520325, 419398495, 854011470, 641800284, 124899370, 79418861, 212737266, 712220752, 965794888, 891825132, 516277445, 347943348, 113524063, 836160833, 372749673, 870352829, 463030486, 417035300, 209034935, 152452365, 816495819, 398451360, 984372348, 184076168, 83883070, 21534987, 866771061, 2130589, 485057864, 338953079, 777648909, 938158572, 745378870, 698473667, 467785269, 43566176, 799159942, 821898730, 789480092, 670730656, 346379693, 477169380, 711190037, 550892105, 185210083, 412429878, 973764723, 841331304, 668291877, 314852537, 864033625, 813976236, 177397158, 887489936, 434874322, 401145965, 453064956, 957653059, 25535751, 408534197, 537846481, 996415189, 779184598, 150234095, 813250359, 423195825, 278295404, 738739875, 938175518, 197956946, 262601691, 939078361, 507309014, 284967065, 93314212, 23436095, 677648969, 237725498, 407190614, 727657163, 210629019, 57015973, 903466890, 318796162, 330679251, 694325537, 810150051, 715915918, 119394097, 875581772, 395995889, 436044696, 885704726, 544960681, 347998298, 277113873, 620565149, 601473165, 418503048, 84493126, 50045625, 761278495, 826896722, 939655572, 679833661, 446756629, 526408135, 712867254, 96696756, 696348724, 775754750, 490343432, 20511693, 841788319, 462357929, 414169536, 321046651, 761762526, 6760179, 768315685, 38143328, 407139577, 855168901, 730890050, 456824685, 198900096, 309363634, 964612714, 36380278, 112617216, 654135405, 792774044, 548878487, 695207681, 292371670, 589260857, 66135567, 847282208, 446074549, 788950942, 312823190, 294906183, 471170985, 598427652, 138878111, 374854504, 112499887, 611683736, 836336776, 367936005, 728171501, 432341677, 468683546, 416946805, 497720481, 507718117, 54489487, 309963680, 521749315, 617400519, 874809775, 864504179, 520226354, 897179987, 320673936, 588135123, 838860344, 126596465, 767682597, 386039164, 203935791, 781521793, 383065213, 868896351, 47589679, 853217104, 818367985, 173210064, 694355518, 857308984, 202329237, 569205164, 116398631, 812532860, 976490253, 740555299, 857218020, 266766926, 305191303, 45271386, 73079343, 215998673, 681671563, 151915611, 333953625, 988657056, 207929424, 471767890, 390942064, 76769903, 513090009, 81856267, 7616003, 813938064, 883570029, 443415554, 731850794, 203827318, 557111673, 79043481, 195362615, 770381278, 790174458, 541462419, 387387740, 223456299, 691475007, 278943820, 809833979, 620922194, 902743646, 208415099, 444781527, 485415219, 622862543, 529146568, 916242245, 687200295, 892268211, 101352242, 794868522, 521573927, 123166929, 718032937, 336290531, 46111840, 463585393, 989957140, 580344227, 312974660, 10735623, 298456291, 951160666, 666388531, 444917575, 763309100, 984775539, 686489651, 586448197, 129248286, 140569851, 675462565, 794821709, 576966169, 846654348, 85385677, 704358712, 404848462, 656341384, 785744126, 123870631, 426953425, 580626484, 849463466, 789738830, 266074203, 253915569, 962081791, 865323078, 111368879, 5277859, 604022959, 996994028, 63293583, 124635489, 960821995, 625896884, 922274427, 98618904, 90067641, 164464325, 779346732, 775662799, 709987988, 867122803, 295198506, 73115122, 540515233, 368838371, 502760523, 295417787, 729358851, 852056897, 579026755, 953663437, 256418645, 989042109, 961367779, 98751060, 2999944, 351050560, 829778073, 569743528, 656277132, 379847572, 218625683, 275041083, 217515489, 608830592, 269260602, 858260294, 496597787, 563728885, 910825434, 50696011, 667039060, 106883275, 559732017, 548712770, 386068885, 740274702, 106953520, 470180609, 380628407, 974311043, 716307986, 375560587, 223992693, 810016714, 82956594, 242495275, 555519592, 996918247, 57435003, 622638347, 93164607, 778822683, 944757006, 44191168, 781288010, 152099596, 16913282, 856058007, 878394189, 377410831, 558332841, 271581020, 753948482, 778157677, 353666507, 83951454, 447848997, 271632929, 420454131, 955638606, 55511542, 669039760, 259609883, 289005387, 850785364, 774028088, 51842022, 840683683, 649956234, 327632799, 474727212, 414242676, 672483278, 829108470, 256786991, 359749522, 762471881, 319011914, 382271611, 406375695, 308719671, 925175293, 529859792, 650787860, 516274621, 84790372, 319133772, 661612047, 677463259, 652995013, 697879753, 220228825, 88437540, 89995413, 267265015, 294938542, 236592451, 193486481, 971120409, 957976805, 948667897, 454884751, 831807879, 881877572, 517360377, 597965813, 117940119, 441281290, 632073277, 614087709, 505115494, 461395325, 482739447, 381893321, 893304448, 20524091, 691559357, 256723595, 15167240, 762653131, 496186581, 31154413, 70829485, 591074606, 351682844, 715588765, 653657826, 850524783, 330106613, 362335507, 636142186, 503363219, 40218980, 228575859, 766925578, 508716806, 750156838, 206974252, 190483718, 557472839, 201700328, 961126254, 131295571, 914086086, 963657443, 232071094, 26687865, 131581834, 808457494, 35443545, 607399800, 850392587, 101940767, 122209541, 662564288, 876203333, 60044427, 417611844, 964473896, 384276357, 650670747, 736950257, 766951830, 868234554, 465385890, 382331377, 971457723, 345412378, 87689912, 917865639, 882750261, 427104088, 322728441, 879087957, 323761619, 329722497, 142753347, 136096024, 38989687, 5572120, 12749553, 11107003, 654083001, 570621593, 896615525, 640256639, 104360280, 319644544, 46714802, 106896227, 364651750, 886266337, 324922563, 618085847, 934581516, 891411470, 555908152, 429682896, 285720554, 539361248, 840762621, 895943625, 126984713, 249289763, 423623393, 395596148, 728147922, 501548770, 443140929, 984306287, 801420729, 881238821, 818928898, 351777352, 306538228, 901475631, 5939090, 406515339, 826359958, 236981165, 159103834, 632794594, 3774085, 368584909, 382793110, 18573504, 823931923, 869571088, 640587082, 305175199, 697977794, 345774818, 802155800, 476019311, 226940522, 916240673, 424104576, 336855805, 703375163, 429690713, 698434011, 198057481, 717569382, 804057718, 359238548, 875748434, 429692128, 558039299, 773279479, 684662610, 819553991, 650083775, 328446936, 385296043, 143735872, 197114948, 970851530, 738466187, 746961972, 487225096, 525170800, 689866075, 988358698, 618001639, 896561186, 765470451, 755233015, 82075729, 598925599, 359095205, 597504871, 997707238, 28732874, 9753387, 120759974, 777960475, 638388334, 489829078, 341651947, 378217037, 799059650, 899535566, 906760379, 963685845, 162237857, 291239296, 163005163, 970947079, 173005247, 571954707, 225790511, 792725188, 587530779, 873743810, 560094319, 258352802, 431419989, 910173924, 571045320, 149313129, 342406750, 847940727, 145935815, 384393586, 667878042, 499196065, 436858427, 487264364, 290154566, 382093990, 50205065, 395838233, 506206919, 468472836, 391716145, 363845134, 716270673, 757969509, 185273113, 655252396, 674468480, 529312520, 920328262, 483017394, 540857871, 183210860, 68533148, 911355055, 814335549, 409182055, 968374110, 754309600, 660199608, 165821415, 707825508, 282300050, 437781892, 656588973, 517388864, 343443452, 258785794, 317957117, 566864079, 858260994, 192582213, 601668139, 276109349, 379327615, 981963760, 946621294, 691589269, 674352052, 239698374, 598963000, 343232845, 115258429, 962297154, 511487722, 617316950, 67877989, 518168920, 264707252, 38823907, 288746366, 789848427, 703008320, 374065200, 504518721, 158076385, 845251129, 279518702, 508551233, 159469329, 182566340, 470853427, 674298646, 453751809, 663086768, 871553492, 921470218, 646762517, 177839757, 577172154, 215248693, 579852182, 51189062, 963454330, 600880288, 77991408, 710879292, 568856481, 760195623, 424065184, 210446344, 220784970, 424340972, 605822701, 925061164, 251745434, 651279726, 491919995, 850083751, 719536127, 395956978, 318264601, 815497430, 228804220, 649003691, 665070534, 970725442, 65367056, 704651904, 434369250, 258730796, 116922220, 651168789, 972144057, 706317141, 1918776, 381449054, 306135653, 827198661, 203766730, 883165374, 502096223, 373093703, 613669862, 320715242, 543909183, 400105890, 464395112, 429058066, 704541614, 429845084, 321961047, 201235164, 387597923, 428081265, 552594956, 837727096, 944169049, 829460637, 873188673, 303525942, 592568866, 139667577, 564456879, 405627034, 859729934, 880720365, 463193821, 217722078, 943704171, 302226572, 698791203, 522569084, 691645507, 730362916, 856924895, 309015303, 362283664, 883308008, 492836264, 427746238, 577582309, 845566633, 715664724, 19220966, 19898041, 921748928, 778122503, 890918750, 731924320, 37143482, 578216758, 597628879, 912902418, 753959056, 470808441, 385268617, 833987705, 425851067, 797009247, 602512044, 937439868, 150716900, 241791996, 898658539, 87298029, 755038422, 23503834, 938141001, 540428061, 609629084, 277206697, 532834741, 292988339, 501153602, 415838084, 805468624, 507750157, 834694189, 580030957, 854815517, 651723227, 291354558, 471179161, 872162985, 862652998, 631636603, 436912999, 740109603, 830772577, 207789162, 773297566, 437068580, 390603450, 52349613, 296191523, 352121057, 310876590, 375078978, 83025939, 887337831, 237830000, 275708696, 561580909, 443337734, 172604553, 66487931, 493182886, 552287679, 91459026, 969899272, 837659864, 249394909, 800230612, 524027184, 650485483, 417972660, 518127168, 115917969, 656143365, 491112921, 124861552, 506002772, 280381996, 508941489, 241639215, 725156387, 815136630, 387169163, 956734469, 184049207, 362416321, 992458619, 431251953, 744097431, 634250413, 606267414, 816894681, 505582182, 311688428, 747880729, 47160373, 642672497, 15822599, 72218093, 883807486, 506376562, 933984527, 340964280, 778599919, 315915569, 938996015, 313090466, 751869890, 158672556, 272130158, 551122342, 461166954, 629160507, 345690578, 751439408, 561888564, 865791145, 741188151, 25203335, 514756677, 511707179, 649314481, 281590336, 205364097, 597924113, 468091386, 975764215, 13680965, 958499196, 124188145, 405568300, 999314842, 618587832, 975875518, 496405638, 57126824, 155228667, 55931533, 539140666, 316027436, 673003346, 733932772, 185120331, 162755666, 818310300, 656082892, 678328384, 138353397, 593214399, 3858181, 328637919, 70632699, 304233830, 870712260, 681187413, 520531796, 466072466, 440126498, 459599143, 445192164, 829350555, 541443489, 224953449, 201599289, 463201504, 865806627, 877549364, 543631802, 789336558, 376626258, 127295162, 246061797, 967828563, 617139028, 711906158, 734526180, 117197198, 741002076, 382046262, 61733221, 256966534, 17425302, 228295103, 56860676, 583134413, 253385721, 357717597, 954143051, 308780502, 682891125, 962315795, 434188683, 276650462, 302619460, 173004396, 417980240, 990758246, 717616349, 470916267, 895882705, 157231570, 333887768, 204008944, 498558259, 138501911, 421707552, 995232108, 413184745, 933495316, 277981053, 86959440, 338161474, 233243625, 609945215, 990783710, 511316677, 511906283, 403238436, 512317254, 322898309, 65233416, 472998791, 512801393, 838355139, 461981449, 459571328, 573536583, 399232064, 792007072, 437830888, 748772260, 49941353, 21219147, 593758625, 88119920, 395950432, 382249482, 216335523, 148214660, 43252212, 250705091, 912973504, 649369349, 26941510, 266848293, 978395288, 507648641, 432487202, 171499098, 606085110, 879398240, 554484839, 223820746, 598848270, 241580441, 598716696, 998936900, 135263824, 888078820, 185275204, 124802075, 871529413, 824851165, 252043586, 800915636, 911842208, 203462185, 746321821, 195476961, 667389619, 892192300, 547075458, 471353234, 245541601, 894202338, 25041397, 446217318, 250276289, 870627350, 514887326, 769714671, 772288320, 558448159, 237837358, 13481993, 94162410, 942796396, 892224368, 612952243, 304952667, 277389533, 620844532, 931225069, 140722559, 396839141, 946884082, 14793586, 801372214, 564161708, 55159638, 160926599, 764931781, 820361947, 756648297, 251724148, 323763517, 492480909, 534999576, 635915005, 519525584, 986060119, 438166799, 795687872, 793599488, 975038687, 979160663, 65492637, 531316090, 842642393, 107339381, 610412588, 735259762, 387125918, 599449998, 328303800, 257654086, 896223452, 364325125, 674105024, 393748497, 76555813, 200680551, 789813131, 234081937, 923658271, 191856890, 571315279, 392568320, 155962373, 223145348, 661931150, 55161268, 365538217, 803102989, 28773425, 820927673, 650580572, 561593517, 641050660, 736155507, 165383423, 541044661, 337500734, 238373866, 384233495, 635400365, 431175535, 12785176, 457301761, 213784754, 722743141, 323763256, 599315921, 925185523, 947108072, 954442581, 723173490, 288941858, 999816464, 474791226, 468741987, 555953759, 543334511, 397990273, 35877622, 850587529, 886610603, 294364429, 834013531, 856918771, 279788170, 153127916, 794661142, 438871600, 37990848, 667841726, 607001754, 599502644, 993548763, 745645367, 876310684, 434667626, 847650239, 846680550, 664693795, 886170016, 783222206, 470405020, 553381561, 238957141, 49625415, 360295124, 389470713, 637347224, 652309133, 477368246, 710466518, 335566958, 549292616, 945995566, 682220397, 461595809, 504179575, 566761328, 588031886, 971924373, 613283940, 23929037, 904338439, 347207511, 612343993, 79490051, 351119804, 618517060, 368738955, 556840445, 718360575, 85760577, 338592658, 132472478, 179732917, 352805042, 518229588, 647928588, 13962566, 171811823, 706806586, 836111234, 345872163, 633088549, 161229698, 699328303, 884907662, 955905972, 37333233, 943555884, 365273917, 441956591, 855719948, 718108450, 996977622, 54220310, 70960760, 987633602, 489086998, 362634734, 65396209, 967785573, 753344498, 211577690, 460351617, 436471536, 953772106, 806177830, 721756539, 57151833, 809021921, 944872331, 30365879, 255418734, 85457894, 322852661, 709532315, 11082840, 5871264, 949679924, 65181486, 655234319, 457728079, 638269962, 200437909, 294424624, 448205518, 175204435, 72811089, 480415267, 809429528, 328181203, 176605650, 178075831, 110803641, 38393282, 401155135, 757597078, 663743558, 559991610, 263690844, 206823858, 603598384, 499103495, 735790443, 640448022, 527105020, 112938866, 235843637, 745653998, 236337260, 178026176, 449701129, 565309400, 349746913, 936521674, 474707249, 917211051, 179728307, 643221033, 352027272, 333255891, 449688772, 877062008, 793672089, 780330103, 288792834, 586314768, 569140698, 328112077, 682615403, 783395996, 246062594, 450793209, 819968434, 857906152, 776533593, 156566361, 868056189, 464076353, 309304542, 110436166, 437043322, 58995811, 408641265, 240539023, 339465933, 322364770, 621545143, 312568052, 72462180, 965751597, 748073457, 209143103, 378011294, 903757478, 721660567, 221155486, 39330111, 529844432, 308714509, 303302412, 267660248, 600338251, 100721917, 799403315, 8242878, 275827595, 782141835, 463018360, 616389813, 198270485, 469645273, 591955736, 324191002, 340332527, 745095856, 690843926, 348615046, 672205801, 125269362, 797890405, 818472307, 103076817, 410657300, 231367607, 43727482, 44630899, 115539150, 277166712, 982979402, 767462571, 864877511, 848934032, 487320535, 460382761, 152669235, 47207967, 115689835, 380034777, 402504405, 201532623, 282133661, 431801043, 622059291, 729461422, 451413617, 247559165, 568748484, 42579331, 386644404, 66954587, 573082659, 388558085, 814220098, 257430842, 366300610, 282182459, 651869205, 760181879, 752436199, 137886124, 84434265, 656234460, 177606981, 490800396, 583023315, 312017685, 525897599, 41807089, 543237736, 66656401, 829841539, 732957315, 906521774, 449209386, 918709292, 580023930, 50543472, 873069403, 49208182, 543632631, 416614197, 160105136, 944888159, 905027472, 668502758, 545199294, 404001314, 184077106, 68745133, 811673051, 735863080, 519121900, 40161489, 316812617, 803305769, 828156916, 509263665, 884929976, 390939304, 824592456, 461648729, 814244312, 920812452, 225275834, 821945289, 352837361, 300517815, 630559894, 469458642, 907772955, 249881149, 846563026, 870543399, 608577162, 92842949, 692524918, 289393597, 733756752, 323970437, 389241933, 166170294, 993755169, 927559845, 866820952, 946448906, 424604602, 859996742, 393962485, 565196690, 512557689, 183825623, 484359537, 716892598, 887794517, 870169846, 240185245, 229281679, 968274590, 992614100, 544763628, 763693193, 104590590, 568409127, 125120636, 315678329, 397397998, 105030733, 334950048, 376767313, 982824452, 874404981, 874976043, 403732437, 877480262, 890915389, 258463663, 341397194, 939245872, 297223177, 623464113, 10356227, 655570627, 77371923, 548769092, 934218931, 549065563, 237664586, 449150310, 969883199, 929357795, 307286929, 627572536, 136618034, 46697322, 342571585, 391576610, 41924865, 123081741, 393857071, 329603580, 585816362, 350586547, 479800285, 74163737, 853099741, 423118001, 870547416, 286899312, 649384881, 184741253, 258376837, 301221935, 585531173, 323793825, 422441904, 51034134, 339020036, 151555696, 525925878, 648373487, 345019093, 568290643, 417335431, 506510989, 417635367, 674496966, 350027016, 751079945, 325004851, 59939097, 195936112, 380964951, 484033457, 659431667, 798051597, 954967569, 271026608, 874427674, 351882749, 583986713, 105758921, 478118683, 423138260, 877719274, 135971501, 240707261, 745554008, 691267963, 746711228, 865973695, 197750128, 927020196, 561031075, 375723867, 570984133, 270984323, 925230686, 657955523, 884410711, 467175112, 563443904, 852869603, 146557255, 447247475, 389987169, 188342384, 45144537, 930075400, 288949390, 829523530, 349802314, 164832409, 324147229, 576385675, 727740141, 335664565, 911312527, 843050465, 648174206, 201110964, 783065005, 455289681, 266806803, 89968796, 499643449, 295895584, 697725592, 801676557, 613296526, 588651721, 651108177, 589684988, 668468886, 731678311, 107200641, 597401905, 629828938, 781043618, 900339285, 910450458, 85818999, 797911069, 570475967, 407150881, 890079902, 818116988, 946994409, 814697709, 476204072, 106558601, 837136184, 346462281, 852819163, 663895495, 80531931, 551206614, 304942966, 728385605, 29848594, 846393888, 137524352, 510526407, 915636912, 259706686, 914776791, 731186601, 119561693, 673673479, 907162124, 26956409, 185943577, 999972403, 885241649, 360269700, 710190402, 168886085, 216801586, 780416052, 770498817, 375180565, 396063264, 450824413, 242725523, 913574367, 639005008, 328761999, 780928138, 572603758, 901640635, 868284112, 395341960, 456012379, 631777851, 156167081, 263017582, 49517239, 437897526, 11366140, 530532948, 716871639, 871874498, 263343160, 419826201, 776960521, 500814092, 541813340, 747822905, 375462338, 814897126, 192956369, 318116327, 726155466, 516342219, 449388251, 866332713, 102607233, 814106287, 915851404, 972855958, 806617888, 148798252, 910048250, 438794222, 982585919, 248385286, 295527492, 622404350, 10763450, 902978709, 17940924, 966556971, 188254712, 559318575, 174160545, 990668732, 119730220, 799476274, 927682740, 458840671, 606838390, 520894473, 974623047, 351476279, 148811884, 712695721, 916021040, 677334259, 330909082, 40343514, 831746266, 511321614, 509679855, 405671423, 111455143, 480175571, 771696630, 817160162, 881982831, 314036279, 490380809, 303559840, 92323570, 667411825, 349683591, 986537928, 48942012, 941553932, 579769344, 303236933, 634307608, 597062518, 290192017, 737793158, 728874294, 370187062, 401449146, 813998357, 655385448, 954560593, 630682103, 31204174, 516169272, 316416925, 851655370, 642092657, 687625820, 539836887, 977233957, 934224774, 925257192, 940524880, 948831072, 717483499, 381720058, 864798810, 274552375, 332074101, 744963075, 944764017, 797355471, 558380823, 865831008, 103616280, 183486037, 54810273, 747837321, 867517523, 369845572, 825479439, 525468111, 94605929, 347270248, 287772998, 749957442, 882342778, 244048465, 752399950, 293058570, 278621565, 570569237, 115543589, 274276739, 649509937, 43323772, 376278223, 605910955, 520673586, 840624674, 510717810, 766125816, 360832482, 4963501, 617291848, 92400276, 225154617, 767412705, 729237522, 495059040, 633911896, 827109365, 488842461, 751194734, 776132279, 492565453, 633437821, 110187692, 377766623, 44456641, 824591586, 381918939, 116677519, 647835473, 967636804, 602765870, 162349164, 744688164, 543414571, 569352754, 147893936, 41261867, 168848257, 178613791, 153492062, 69426353, 790302815, 835119618, 379723791, 683397630, 845106768, 427064443, 787394291, 254514438, 275165055, 901942252, 957626050, 178143657, 274820226, 407788205, 919335072, 919167488, 477655167, 198084359, 167456767, 626993436, 996383790, 741643520, 201369216, 595229032, 156285657, 582872014, 178932540, 408470717, 798213882, 747916403, 271628234, 509461623, 973729066, 979026771, 976468388, 664012154, 383741131, 746401220, 149622917, 86528493, 12508910, 973243174, 543272824, 773775210, 796407684, 462109473, 505429297, 428869707, 483756107, 611351967, 280637155, 564870756, 328279404, 407146020, 573230414, 447512374, 67403151, 984727949, 170424774, 973083138, 719044050, 313307994, 489383176, 389888158, 490962648, 8491210, 942308039, 584972588, 160865077, 233141930, 974546808, 968843673, 98496144, 611888973, 182587744, 719043777, 37804425, 881358694, 427881213, 360355089, 846345243, 562573789, 956413800, 653695776, 866971609, 793651639, 414248047, 718570518, 624722133, 25394363, 329775986, 628406911, 364643857, 41613597, 361702230, 279140279, 58829003, 537680513, 116094870, 407618034, 391969023, 658181775, 346936573, 154180275, 658027158, 992794686, 560601465, 655027020, 844683648, 393741985, 422549838, 232651057, 771682467, 28801975, 318698187, 494420047, 591700766, 370440715, 202711142, 811881688, 741162685, 422212828, 129151440, 788276300, 37531725, 616675599, 403316525, 307209170, 29079341, 619038873, 123237094, 524964141, 273338659, 58316587, 113671193, 321570917, 407804546, 109425255, 563675851, 770959694, 785267853, 149050225, 76300812, 559432316, 976606908, 852337246, 901330513, 793647171, 496221915, 376455300, 974923592, 402468856, 835313277, 502293492, 802400776, 770055265, 513248798, 25449779, 901746579, 539330049, 7105722, 369137406, 723635926, 153986755, 699601660, 518143523, 433134537, 743265393, 51384241, 369162287, 299409004, 718884412, 599461542, 297157755, 115015235, 484228381, 707232239, 249701915, 213351886, 15325344, 96690453, 114228481, 67159370, 118322135, 860292513, 319654608, 731601920, 3414600, 329465492, 938676058, 889923295, 273344852, 617342431, 730613606, 23862935, 838494488, 199356821, 758388013, 886240131, 230056072, 739689618, 293098994, 224540184, 266385825, 56126234, 730619872, 86072346, 579343622, 243427085, 463687023, 363326748, 745065902, 147675264, 342161580, 892947945, 37253780, 383013738, 359978615, 191596220, 149894660, 103928462, 321866414, 582837625, 837338863, 691676551, 776893397, 408924532, 695152378, 24561783, 587203289, 30501551, 903468137, 129609447, 50569235, 456520598, 61919331, 180327494, 593336562, 953096822, 489861018, 85697281, 778593736, 818346453, 229817049, 857156484, 284414725, 986783831, 253751560, 864429526, 834699895, 633129559, 159877184, 132352968, 60223554, 681439841, 620642008, 225141332, 712030856, 440549249, 603059148, 534035310, 328636579, 218090499, 169995047, 639022652, 398461903, 211646069, 163007157, 355216667, 803339452, 926004097, 237189454, 504651951, 246907839, 622368547, 177647815, 134253855, 881035682, 95865997, 70694768, 926937084, 451535411, 794914500, 660644387, 649658689, 571921343, 783338743, 814895362, 970358480, 636075804, 895592344, 428240345, 726757978, 594670989, 567398778, 130389235, 801296746, 955990739, 555094515, 483724154, 169032562, 375983596, 699021102, 332837892, 657103825, 887820799, 387501649, 443760594, 207522131, 714245930, 469535916, 656221302, 373207006, 914998810, 577156099, 94034456, 713174525, 2300573, 692950638, 311442973, 184983954, 174129581, 993690504, 825751149, 274994899, 829787529, 897951516, 136129310, 822467484, 476550994, 235683160, 691267146, 325224733, 465610641, 301438795, 600827543, 262326270, 251687166, 640527791, 581062866, 157404512, 734327421, 619195428, 95353885, 884768439, 41495229, 294172288, 81167980, 422412737, 672599606, 169953867, 972837821, 635376746, 150064796, 746873035, 908509929, 818828728, 114142603, 637476907, 986240118, 853553454, 828124135, 333371310, 180580235, 634319162, 184306786, 40641452, 141432449, 849158182, 411181578, 617228276, 740128532, 817258525, 992301768, 466738481, 110571431, 489403251, 986217212, 49122271, 454481207, 863933689, 599964867, 9877911, 73871881, 226301529, 577077572, 361594243, 882368659, 112804444, 511568551, 169331485, 287453748, 194433640, 542745044, 280634239, 728132894, 618913126, 600473535, 276877167, 782680751, 672104392, 948523325, 622285286, 821117851, 570869920, 386450657, 862931810, 878528573, 796117879, 202036941, 756497976, 82943541, 25555459, 412630919, 987882637, 880711984, 62507946, 123686648, 626652551, 752326880, 657988669, 25369886, 81130183, 908135492, 454736748, 758130829, 884339057, 326487891, 246431377, 810541542, 373468732, 688157816, 886297416, 282242631, 563416180, 890172490, 302209058, 884547978, 622280317, 895670260, 946831107, 268412681, 180129632, 299408271, 951456097, 799282296, 910877029, 179389264, 509160273, 112905971, 148583677, 435583852, 909755463, 3304916, 792353376, 191845075, 579463794, 137312241, 232643955, 774818312, 784528868, 384809674, 869600692, 944688532, 470329687, 894511514, 565048500, 534732364, 741659453, 321426606, 313984690, 254375381, 779916934, 24411696, 654729954, 812404069, 221727471, 283679133, 738642035, 658135071, 314680130, 725699643, 639393585, 218188728, 361589235, 139914196, 445713680, 803070905, 219397801, 43727234, 466631583, 90382798, 396030597, 266965985, 797275606, 797748325, 857088545, 108093137, 583247277, 67836760, 353897305, 915595832, 638089612, 648397394, 497040291, 555848584, 749493718, 584627472, 777924872, 351586950, 261701555, 949283481, 964994010, 196171069, 922142409, 662208825, 771507627, 623614105, 177974675, 668328302, 464582473, 222077666, 501431228, 203349254, 983783693, 150258735, 112604637, 218782802, 166962235, 986630865, 361304315, 173823594, 725779887, 848751449, 556172766, 291978563, 998525910, 445442639, 467940186, 38600751, 956097106, 421694374, 616282191, 757909625, 615306562, 163967572, 869109571, 830736799, 387286532, 801017044, 4848980, 939505685, 682586064, 931241954, 909959490, 720710210, 107122682, 821511747, 879564191, 858866297, 7804694, 377155422, 574409140, 135195665, 136007562, 656539790, 700307667, 198316027, 817431228, 601486255, 224539939, 652503189, 823744043, 280468703, 391888943, 873221525, 334114529, 68173842, 335946352, 235260049, 367641883, 548818353, 138060818, 225525065, 345948335, 576678851, 735591363, 177498287, 555427866, 428212789, 98228002, 379217589, 389997567, 71604979, 81344455, 222638662, 959230927, 62159484, 157796926, 896354948, 133203294, 167543455, 623015342, 544558066, 619548534, 972489102, 339014234, 771336131, 68171831, 758581177, 728938108, 637822442, 195674212, 917692353, 12729782, 19272533, 783333554, 887244572, 462586575, 42200200, 224164555, 568049937, 245846896, 1198202, 257971716, 113562126, 846150118, 189343166, 428621335, 505525750, 201311124, 317129535, 954627292, 182965962, 834310140, 600617415, 299534147, 399774054, 21132494, 13246419, 801984146, 57839626, 578382689, 617463407, 173069128, 348783518, 122613318, 339295420, 696918932, 670999287, 814892306, 702250568, 359882164, 743096227, 861824765, 977279933, 690270748, 506563751, 324383878, 777748546, 264296482, 101857069, 658170340, 516807959, 653446697, 27010851, 35272644, 100135436, 160271960, 795887188, 65186071, 755859362, 96012282, 679946029, 864489807, 382841521, 813799720, 37511660, 496236915, 145089388, 105016090, 957149787, 171433110, 212090033, 808075845, 273465711, 166456273, 839626991, 710930870, 559945724, 93539784, 41353094, 108231830, 504038975, 922397193, 502402005, 118008940, 472456422, 767056539, 99084090, 841897800, 329312044, 262615709, 702627911, 503161777, 426825723, 213297155, 270385145, 453314842, 523493866, 944764322, 772555915, 617660329, 213076102, 560303996, 702650386, 240206266, 392480563, 365420858, 920054582, 28034036, 610786679, 841980744, 670448699, 742330610, 975531700, 920827235, 48215241, 198552008, 60493703, 458455249, 597427254, 269477404, 436067836, 973838844, 669338751, 416926098, 341418848, 74937997, 66934541, 544137741, 645040266, 420060168, 207695134, 702621915, 155070887, 832099109, 5516967, 333213598, 874879660, 856226687, 343191436, 979943374, 438708550, 762388915, 691940567, 315763702, 580322296, 659288749, 513287711, 753116162, 870855613, 754700317, 34965594, 792477261, 38913698, 963034830, 626154324, 986145860, 501244257, 772727698, 897768343, 321177724, 83701682, 771398935, 253868009, 20587968, 605415306, 681514540, 829664442, 352741156, 152813867, 782896956, 428865276, 929350327, 203340138, 777854052, 331808588, 905199287, 549420452, 225978195, 818013152, 409160453, 421283985, 75449642, 400485882, 95238486, 780760031, 634850111, 22220688, 605430256, 134094389, 766439401, 795305915, 292061842, 162652333, 905542088, 467024404, 808278748, 193614413, 453859562, 811923919, 276943672, 636641252, 745063939, 296575902, 820449639, 236227700, 639681037, 943614940, 982105912, 291524469, 532201590, 691461570, 477065718, 357695279, 636577898, 88391853, 12215383, 54311449, 390491491, 475112713, 283643722, 201375330, 792367580, 744958761, 722498266, 355046631, 91976055, 73187297, 653034141, 347709510, 586721356, 898809939, 719240287, 951156709, 814799719, 780121124, 714604962, 231009526, 81022425, 224680050, 899353742, 794421797, 952700240, 456347024, 378095135, 20969683, 171844235, 127131718, 259644698, 800998015, 572253798, 920843884, 459804477, 153998490, 201165510, 249399102, 116303804, 962589125, 393360947, 97968380, 597860643, 671417032, 915205523, 799823934, 317730416, 50849711, 425628347, 494904715, 908377804, 567963237, 454943474, 684877532, 875253528, 225985729, 900994211, 93871439, 57926616, 492022665, 294587310, 88015292, 920430397, 572381930, 314925639, 430833243, 462428828, 678132014, 636076268, 152576865, 725587767, 315824631, 268452939, 74656728, 293124129, 964601091, 218356985, 499740916, 434826060, 734906438, 230203203, 645387450, 209668435, 975628662, 538985605, 410959014, 569145308, 853766203, 780313767, 818969718, 55784225, 740618181, 466902956, 336084465, 137380038, 853624321, 385231519, 376828879, 144944914, 604522827, 880075887, 672128132, 701957745, 639077584, 832993683, 63623304, 259428546, 50789272, 620967027, 219598428, 985888827, 454576602, 783461579, 444899083, 430154124, 245371566, 913053276, 232083010, 960617131, 391398080, 902279839, 551373522, 294210795, 575813588, 589140447, 552292218, 560173701, 260602544, 243159275, 958246019, 182851754, 606042388, 381417641, 107875715, 690714739, 251975609, 818973932, 133303135, 458204740, 802082835, 197887803, 410219173, 819261950, 758186194, 422012513, 413915645, 154254751, 353245889, 129921800, 917260002, 676211524, 909402146, 471596888, 469496499, 689931030, 892658345, 745420820, 211366981, 456182316, 690354802, 198031265, 291838650, 84647443, 785437921, 172417976, 585245757, 246078260, 91052503, 616810980, 608041966, 123927408, 8477322, 462292749, 218173564, 502588543, 429430075, 87399195, 401381984, 303022813, 274063283, 928898763, 643277185, 825913583, 15342633, 794197425, 605086370, 375963643, 815608664, 331925248, 261437396, 357387360, 458022462, 234887195, 289111188, 92230340, 341130489, 49307227, 885712406, 71360007, 239447136, 919280824, 411083452, 173468232, 479912134, 676316413, 218402500, 868035912, 122452061, 830559272, 833872113, 498216750, 187619129, 979244088, 162139563, 959894756, 735699838, 759982086, 495406621, 827284624, 501579126, 515199183, 371144132, 614563578, 320675162, 536366723, 696120717, 56903347, 442554518, 724504303, 993358160, 983918492, 231826767, 218309809, 784713993, 975934568, 388950864, 473702996, 981488585, 434263153, 455392901, 95235297, 786678936, 899596170, 255203992, 517752846, 509514500, 559550439, 939758879, 11513685, 423365226, 678798876, 467923554, 866842151, 354206942, 635696487, 725952317, 366964361, 806764126, 442690770, 568026079, 825599071, 196719026, 676467203, 11374498, 181663690, 96021185, 403232455, 159700022, 981239743, 738483492, 717141236, 711162591, 970390418, 244147496, 788255259, 98165640, 115087892, 925074881, 807583068, 159877695, 316482600, 520820532, 474567165, 364790033, 648326989, 317575494, 833642205, 381657200, 656181058, 15169818, 439405653, 219265561, 97722512, 927152149, 564348043, 676419648, 854341324, 699616129, 642171412, 270632868, 882597691, 364963657, 463927943, 81525491, 727521447, 855235129, 133599442, 819942452, 31838009, 66327983, 257193905, 78399768, 678016070, 183106653, 454796384, 892395491, 472790908, 352016605, 106307091, 651469662, 538007858, 386802324, 734807695, 351448517, 178319793, 520469905, 702606528, 799401612, 479004328, 224944032, 223280723, 337408107, 436668938, 863250667, 841639037, 786820991, 174371629, 139991225, 826073982, 991870542, 173934820, 716971655, 288168306, 909634323, 99624183, 748875553, 438978705, 551045371, 576956781, 972795178, 149010347, 540267421, 731165579, 752615413, 513229426, 924017740, 390254782, 173251854, 70975284, 806184787, 253943961, 114168715, 513340188, 771278382, 856909086, 188461098, 52636695, 956452617, 429050106, 730308650, 797536175, 745656989, 870360942, 983595584, 279388857, 450091700, 630378590, 823707501, 822871748, 373990434, 328435048, 423457654, 373064037, 943301359, 16335333, 629305209, 104184698, 773842074, 819705260, 675113486, 751155550, 49342038, 832126701, 968017380, 832008229, 791468146, 210974543, 425446959, 731144348, 804304278, 938597557, 424519811, 483080299, 935303756, 27841615, 918757261, 498501741, 986256273, 848987995, 753009046, 605515613, 741856384, 806651758, 122941780, 248774305, 839817103, 157208986, 464512454, 380320977, 914155610, 248017282, 641904363, 712930303, 49332740, 324060366, 245529507, 288786363, 306794426, 390500356, 692590963, 35420955, 984383387, 322848465, 551216974, 37452183, 984911104, 22970798, 196424402, 340461018, 73889550, 180244285, 543433630, 192009410, 298267978, 242866401, 385043441, 467277579, 378017954, 256698052, 819357573, 406687644, 813049877, 351071149, 368684667, 291938960, 765426959, 797541778, 316445304, 60430868, 665447976, 860348668, 211574202, 602755057, 402601301, 450665993, 223667188, 905786882, 883170252, 368448646, 781906839, 777869773, 610590326, 273740676, 33053129, 836750652, 120516366, 455948197, 21493325, 307052116, 218212545, 909206284, 935452344, 434544822, 390865010, 613223763, 41507078, 972974675, 429443960, 999116553, 872508528, 155419089, 18674854, 993095365, 427245762, 699237062, 294876704, 61787840, 99216730, 158505398, 109939051, 711357623, 404229779, 131845482, 923894661, 156774917, 829026935, 781898336, 642565091, 662284115, 163593691, 555750405, 804722849, 467932788, 85861093, 966150521, 610648665, 638208210, 569374216, 497182001, 864234558, 70061869, 199627965, 187773182, 350175179, 247251640, 241645777, 797662825, 879156209, 858224503, 268977877, 280764390, 233693841, 430545241, 294437020, 34586404, 137731123, 790704788, 428993643, 428904611, 723759332, 507123944, 580672379, 757926888, 804091056, 427693408, 464870442, 40667820, 283164706, 151721395, 482252414, 290902425, 428805937, 88069523, 331116508, 655419858, 588714669, 504507138, 553256692, 862768583, 46570595, 4889448, 596591929, 6176431, 567504480, 72680267, 541640312, 979589926, 525065451, 249006234, 807371174, 537690655, 770648180, 687011619, 363128450, 978791203, 893507026, 191412961, 492838569, 496705230, 417861248, 363088578, 550220712, 216979382, 817178842, 181620861, 71145466, 38329455, 14157105, 333425300, 262746006, 806700006, 160645227, 882681172, 917919648, 10082636, 987938658, 581006002, 510470960, 165404359, 573215686, 672825544, 894232954, 743870923, 321089258, 962190699, 214296624, 246127221, 450498169, 333189135, 183503686, 241786041, 825334000, 927633166, 344247346, 582161370, 436559878, 828577139, 191803095, 405120425, 30763455, 908051524, 626688312, 811421410, 186008018, 828746538, 545296991, 131462521, 910740598, 864426043, 480731968, 684935568, 843022848, 136798943, 301830196, 29020244, 400291132, 262692544, 657717399, 237369229, 579047712, 911601275, 289154308, 76813235, 41073262, 714793539, 119457983, 404578502, 279829948, 519937151, 378202535, 914183761, 707446055, 112578015, 160780517, 340473646, 911034316, 538946955, 152043957, 476098590, 942012434, 980222746, 933341171, 594833256, 368899203, 942594932, 502707433, 512075835, 860921646, 769479560, 69593359, 187271118, 334462684, 824222526, 393715875, 241243986, 555364979, 636846083, 228234823, 703420255, 519752323, 919861657, 346568256, 423659080, 356696107, 305509095, 824710537, 470804148, 222476926, 770420190, 979465348, 473299542, 653910543, 33817985, 185479694, 389847184, 661967148, 360847117, 496585335, 479942064, 887597296, 442422048, 648756591, 304641283, 816199233, 66538943, 247564525, 766766584, 198503286, 293004086, 165907690, 758790235, 625632330, 136719579, 147012724, 808242882, 633734369, 921338776, 953284696, 414457718, 805891786, 600824698, 450008692, 950031549, 999832029, 637176089, 165801041, 508782099, 110123720, 196111083, 605129097, 953791286, 908204766, 826232199, 213686462, 900590851, 16559435, 763115714, 987404806, 420696656, 70568885, 427819579, 436186618, 792482800, 537748717, 538764300, 17833063, 498964264, 825429266, 91834659, 612180706, 987628831, 912259818, 442207117, 389889517, 633545456, 886286531, 693954668, 876031598, 880962112, 837933455, 433545423, 750366142, 947643626, 552369108, 627431070, 711396097, 31507366, 501491118, 687198843, 426568441, 137394590, 177824798, 873459384, 600445019, 561256459, 185294398, 345195643, 331057979, 62999189, 239516702, 59957485, 717613122, 432264466, 83184246, 372153601, 987061787, 571444446, 286237458, 570699108, 131874964, 472208042, 863120383, 766145326, 188207766, 894215652, 554540827, 30147447, 938144682, 428252700, 714839127, 959528317, 536358682, 860773597, 215821136, 537709043, 862822162, 893878665, 43310560, 244509546, 66042241, 529197558, 394439587, 345034291, 358184158, 351824912, 165207253, 446419261, 964621075, 866608948, 78061601, 47200443, 68643709, 460154730, 642471799, 142709347, 876845200, 546089327, 685828981, 371368832, 971986924, 692411266, 583188073, 598966343, 577136271, 741680935, 845892548, 77962942, 872258006, 584392136, 9985024, 437652933, 25260417, 45198434, 432256615, 165966705, 719448176, 226240421, 605258118, 391570432, 280550780, 746720353, 511967767, 196658467, 97834967, 916682886, 617511031, 462060324, 624949532, 802351014, 213838128, 134210346, 111373251, 358188896, 654193515, 259199097, 804981433, 151334336, 996980471, 993477689, 927715115, 914793242, 333634278, 236207982, 560152284, 873864096, 757949152, 169816261, 735452637, 464160417, 703147524, 853769002, 153357962, 720262398, 583507980, 582518961, 226100485, 758521807, 693354425, 43508943, 420135368, 44906722, 461046367, 56426683, 138527433, 156928416, 442864598, 602532768, 230561882, 895043105, 295601813, 672727513, 475310398, 382292576, 788842252, 842580504, 13816227, 366470543, 73810734, 255979487, 623483841, 209559142, 790737221, 546481816, 932970306, 574372743, 126699944, 998834281, 343419308, 374127700, 244501360, 298150409, 296240220, 886141331, 571467732, 429357171, 637910693, 950417304, 535653474, 295403364, 730220519, 476307110, 748625224, 670523572, 460227239, 976572512, 752750119, 754524036, 269912051, 102556959, 671572211, 332506182, 458719793, 755820761, 659026007, 857015278, 970064806, 48589243, 127952098, 165017201, 12485475, 300505171, 588234328, 536146232, 303446165, 803350628, 252923631, 340327905, 990116689, 76382776, 814212616, 604403919, 312266897, 332065132, 433258279, 933139573, 618874089, 239967410, 648131692, 538433836, 963058092, 365502963, 301886610, 912925516, 8268610, 570257687, 508375305, 224585325, 226328000, 768928972, 607752471, 526762878, 308856387, 218403478, 54557728, 324780654, 570942303, 968286768, 667032161, 3452757, 565686171, 183514434, 615775323, 865744226, 496221992, 558597291, 10647599, 548442486, 187762218, 375914467, 236819957, 760481249, 844690301, 488069841, 438720989, 977156133, 175389903, 906420187, 825211314, 968818067, 771994246, 819015989, 88632203, 684523743, 214938036, 247189960, 471608257, 599901896, 124820643, 322577817, 413049494, 938767161, 45777440, 511283619, 630402092, 224848320, 916179326, 861934900, 741216530, 536668409, 554362527, 749789577, 6860441, 590835086, 241337087, 395745104, 946847232, 320823925, 43428046, 895481510, 584590064, 917975539, 598442179, 729313343, 332875325, 124679722, 124345477, 225810800, 468484800, 190336856, 184194188, 345663752, 989326337, 213713634, 486152430, 954419532, 881799280, 465434090, 824843788, 914069487, 539271508, 217048006, 680672547, 127938606, 666748261, 858075928, 199229943, 852315398, 236238387, 459007044, 485343329, 778190576, 290756388, 556154150, 671060241, 854294432, 588085559, 421281912, 740097526, 680621391, 298500563, 126139707, 666018593, 104973157, 37675534, 877015257, 220338964, 543143261, 341606725, 327655480, 660076305, 769706055, 632745588, 678628259, 625614010, 57613224, 788118706, 802572607, 8926697, 596781968, 715722545, 176476753, 739021568, 141774896, 442040641, 44185713, 50005251, 186050090, 487342056, 873571440, 333941778, 47313237, 717271131, 310356723, 114266318, 655979151, 374889367, 59258555, 584535562, 460153213, 969057446, 186856194, 466521922, 812313065, 223219965, 746896844, 132608344, 449847464, 671330102, 660421294, 855931962, 901964280, 788636978, 628765599, 260280102, 931184378, 94479313, 497042438, 143714886, 781291627, 281263021, 364881095, 395399915, 178173571, 97052576, 51163298, 458617806, 687865793, 203834633, 580252087, 557323624, 869183181, 693284536, 528298922, 275009038, 63738997, 236920023, 967216541, 811013971, 474591627, 618085727, 763864426, 638620162, 942576823, 440997895, 546280234, 621351537, 269898100, 843865361, 232622204, 691645656, 60329017, 494425657, 794016629, 264052091, 851624751, 171553511, 938131491, 91686426, 598828065, 578536962, 979389693, 702611411, 981318889, 169082699, 907914802, 249606890, 810153322, 97278311, 81552383, 256972700, 948424499, 109283056, 412194461, 288317774, 704166972, 819007401, 770223773, 918846373, 350269841, 986523506, 338352533, 428362130, 224907383, 303934835, 241890941, 69786016, 819297632, 328412343, 689291450, 278481277, 39507533, 449294495, 683847105, 368093863, 512905062, 976630934, 173377401, 87479022, 634919794, 6354238, 748347529, 351811391, 538778984, 316537779, 557694657, 924009884, 223216169, 778062306, 403631451, 792539866, 112508851, 297349267, 862275722, 772407910, 332527811, 487685519, 550791778, 906588967, 242061632, 526637134, 408847804, 808351429, 458455771, 127573631, 8246559, 941305980, 57264404, 244054428, 840515634, 52126873, 159291519, 655130848, 925360445, 801556134, 18829208, 159594258, 139527516, 44857524, 638514906, 556688504, 754166112, 325999542, 94865995, 247739899, 649218997, 242726687, 829426526, 675936721, 798909792, 354595797, 794896324, 708856466, 582448532, 422610521, 450646794, 573424933, 61856265, 330606739, 532346227, 845808219, 247381410, 618026621, 4957833, 867531900, 602529524, 690977143, 249203093, 125395571, 142421184, 874009645, 12412956, 730430753, 281249618, 493388512, 864818453, 381123277, 557358148, 298947167, 434820216, 472334414, 219832888, 8106373, 980221222, 58900459, 222099157, 727588777, 896376337, 257164767, 970419518, 773558365, 316562536, 461525207, 196086923, 638138176, 403328797, 451943988, 692810920, 367486690, 998324081, 854301243, 88058164, 15942519, 251026026, 229369429, 703020783, 575763695, 255264998, 426536991, 62454171, 928010296, 39239641, 305341883, 458966547, 466586272, 864867856, 837985011, 694438927, 739348920, 562873584, 917962921, 710440997, 766577690, 552697258, 648707757, 255709264, 577502885, 47505142, 359045726, 104035385, 738337479, 446770525, 694661145, 267980177, 113646027, 937361857, 758333709, 133949528, 501924476, 587568829, 847542857, 319039317, 86595685, 355434160, 505717899, 836070584, 885145147, 537988168, 404172944, 155543722, 661636573, 294063486, 63009576, 819436610, 876395288, 57514379, 77714464, 451662125, 77293932, 138616390, 36952940, 514223715, 485293070, 550246125, 169386513, 401903431, 619100066, 337230871, 353041790, 488172546, 731019171, 393111339, 643151851, 711308320, 187794288, 959267934, 80147288, 393529607, 940238029, 899176686, 716344580, 993265800, 324798076, 947731442, 457148011, 197196139, 841893512, 691518828, 792568873, 789189020, 136351886, 479488941, 228538581, 612772816, 365537358, 20075971, 819296626, 49049655, 589018600, 503232415, 79335005, 476446724, 243677973, 568913738, 975827364, 733607254, 154164311, 361593943, 394469228, 733410422, 27882457, 717533728, 665039556, 289793840, 418055142, 794465125, 209234773, 109487811, 868863444, 853422343, 117656288, 205476793, 241199326, 822478563, 911394027, 345834403, 570393415, 301894046, 720610564, 308544812, 289036992, 919851461, 824273607, 170359260, 237325788, 193431425, 810743771, 439267000, 369913883, 744626399, 394168767, 217594898, 499500172, 375290527, 915483196, 278643360, 986207673, 276769784, 147223407, 742314876, 108272308, 68188178, 4462069, 951174855, 91247578, 199456189, 650109793, 736321555, 498416454, 631214831, 677546798, 130785065, 202541408, 230454075, 155854729, 769336632, 474753822, 801483625, 357141385, 639172251, 568989218, 584923074, 553698048, 470495077, 152630313, 620209764, 710508492, 161360332, 600881601, 408309569, 264856938, 842577425, 73908538, 774217957, 401786190, 149482212, 803146076, 772603365, 169960999, 27480827, 95426247, 914685070, 754167634, 965970005, 361658618, 823698223, 929540740, 263258605, 270444370, 654152649, 112362139, 904499705, 12749176, 261814014, 80561608, 585640724, 93953849, 478345259, 374954532, 678065337, 899103095, 335959097, 598797815, 429557403, 238425966, 39177272, 836704057, 134101963, 433994529, 453950306, 790044300, 411739217, 600157875, 952748277, 48163626, 429391753, 762569848, 126548255, 543972047, 810177060, 757371133, 924039179, 453872525, 10950710, 806607679, 544910661, 709365675, 439931898, 974877343, 737624742, 190304118, 789250019, 182681907, 346557004, 493115329, 995094761, 402932709, 864781153, 860745570, 476104578, 816810122, 347272797, 433941384, 375660438, 534487380, 605558673, 593673833, 374953987, 869560778, 892337717, 388278050, 600495646, 776596588, 660877548, 551336907, 467206553, 973426083, 805099549, 923145592, 812461106, 416090611, 517568990, 653241114, 66320663, 702926343, 495181108, 214002311, 361413553, 951967754, 69468136, 121857354, 685952203, 304811223, 91213266, 629935704, 510248642, 468961021, 582090986, 853239148, 764851506, 659432645, 68196878, 216220984, 80634528, 285556319, 914406491, 943239302, 412236994, 758833195, 798522085, 885460919, 815085914, 553661139, 203259002, 971217150, 801048753, 671895609, 224191938, 544143101, 368261968, 479558825, 827516340, 705549841, 303611529, 441684324, 369656329, 811458495, 268500593, 852937328, 239468118, 297901322, 524161909, 318291819, 933063860, 488409104, 564606257, 738309362, 850617000, 935981327, 26840927, 269915026, 453681810, 227869270, 379795264, 255244866, 440886386, 879251958, 937858252, 183542524, 590592912, 783902973, 749136198, 651960489, 313678087, 421133325, 981512596, 522767888, 340632364, 180714923, 536261017, 895889598, 419600893, 941147527, 365999124, 204809378, 538886213, 393910044, 192034625, 666917408, 699721313, 825427101, 324067465, 140460760, 423948112, 228261131, 709703000, 703801414, 911152034, 85920649, 637276163, 882711050, 296627796, 184128240, 419544387, 634016291, 5400904, 271043892, 197480554, 827852297, 194019048, 224483113, 571896113, 857408974, 127150169, 181566732, 659924356, 187033657, 701218828, 958457620, 252337333, 365773944, 555305886, 790829690, 827224614, 995008051, 82365319, 116698078, 840773655, 419701821, 842876489, 474152779, 292609644, 163562821, 565868595, 471838777, 941743469, 332254219, 106370472, 517612664, 685774706, 126315025, 293407268, 970763797, 519025935, 754152286, 371525486, 536650807, 793051417, 932295444, 508138488, 905564390, 301833754, 279807662, 380808092, 474059066, 455475379, 142640114, 443166402, 389407025, 58461026, 838509793, 74616413, 604824939, 27078239, 976365319, 323615068, 698179566, 444696857, 520363169, 922817491, 634040536, 593072571, 49469721, 642441221, 773884734, 639354263, 458038670, 196148143, 458826566, 567498972, 370557479, 929039377, 450039612, 653466311, 644088313, 307370294, 344671001, 592974682, 749137505, 975760613, 804649864, 443588144, 258885410, 42776603, 338679542, 431581847, 925500360, 41114920, 516188923, 238567210, 838102905, 497309941, 230523609, 446801453, 135832922, 162581826, 453148162, 873350367, 997177723, 197167351, 976097380, 638575400, 376733132, 691960253, 292701205, 628042837, 118177483, 490657093, 810172117, 513961201, 955300794, 504182458, 445173258, 701419529, 987653688, 322619595, 704023413, 279046053, 104137548, 70053754, 745134065, 264074360, 673282222, 621468166, 933756259, 586961449, 814467978, 153992503, 511794498, 564590962, 711539026, 881101097, 995641017, 31064799, 139080574, 343319209, 399482123, 355992305, 107395498, 150964326, 874730522, 322671290, 601222947, 912099124, 414740563, 445638586, 543626752, 638653607, 491782803, 460472983, 127946451, 162313238, 238817580, 20457215, 611319805, 407825487, 991722045, 112200648, 481438531, 672816596, 118135101, 103713644, 194154619, 401928319, 482047609, 58001434, 259685259, 446367537, 197759099, 610600399, 863905519, 479372918, 961518803, 187456395, 751743895, 579645112, 274854805, 970897264, 422511298, 624562869, 996649181, 735269081, 373502863, 945238933, 995362056, 894606474, 822358412, 809304160, 417061802, 830668884, 959054269, 937333904, 53766080, 575713639, 125246169, 239852522, 655333318, 948846995, 746046730, 85301435, 679691129, 710762997, 931682068, 138033405, 512191151, 651164665, 285114594, 850844621, 978128056, 133062887, 277070535, 728138582, 817789463, 10429678, 959053192, 231236453, 736707326, 553909293, 486614993, 825981733, 110137294, 353354877, 497528426, 632185163, 532593264, 316989764, 495640849, 382884488, 677478576, 362022030, 19843905, 533370685, 612706855, 10842383, 878695747, 726464041, 915424625, 844203114, 66923757, 117748623, 353681927, 928211491, 168390480, 874658510, 679435740, 245969638, 401684036, 703657506, 214479962, 568633731, 407536260, 242275771, 220165488, 584294914, 790939384, 64606319, 994355524, 685525069, 190612846, 166665140, 270868343, 773033420, 606159374, 540615713, 25029466, 928833168, 782542331, 319847297, 559878622, 649955098, 990166307, 285707950, 283715547, 650506277, 663757021, 957968579, 773099380, 300243802, 342238520, 388415289, 734696677, 371880415, 864952395, 984763436, 177605250, 726200026, 853356715, 38811187, 441398922, 992377073, 675226092, 781549580, 981370568, 77620739, 121436756, 926106394, 726985519, 823454732, 107034542, 648119783, 694930241, 521745450, 863557835, 888536853, 144231789, 844331424, 614384205, 765027870, 451679480, 205778313, 200410188, 451885270, 897947666, 429955259, 866097062, 805408012, 948764908, 283883446, 424982923, 665777339, 771940364, 919064884, 460010833, 951058546, 364467955, 607415208, 519076462, 572281023, 269973253, 179218079, 531695270, 654133194, 320138667, 880879491, 318753624, 175496518, 78377482, 944572445, 838670630, 711468105, 675526814, 33051491, 718201582, 280992551, 707692053, 572465644, 831119410, 758829122, 461793067, 74275318, 172373283, 664275913, 885745875, 924713427, 249340829, 885633223, 232922032, 564583713, 655233332, 542416409, 913249099, 252217938, 718640364, 577818144, 228864319, 886611141, 239251647, 105464109, 336940020, 614482328, 141421556, 353077830, 342979851, 821345397, 470861534, 192495168, 964592980, 385173119, 879628114, 934751207, 309430652, 911449576, 881413148, 500850694, 914089715, 543320712, 482271109, 55841324, 497842440, 901032075, 621305027, 109389656, 731999391, 794365243, 348013029, 736501148, 499283974, 790907249, 305152652, 989557113, 68299412, 773656225, 869516545, 428250692, 156074817, 584765783, 510963343, 383866060, 55717645, 577005449, 756855704, 218556830, 76429955, 439809529, 489637652, 287755575, 2997031, 388651676, 724011221, 464894799, 231314592, 551381035, 605816333, 511264354, 136265212, 11184698, 137683703, 575648692, 948117948, 328953915, 398420565, 953278886, 720057970, 393432579, 534545544, 804087531, 215465939, 564436445, 892166150, 681124418, 930112297, 917693249, 619608643, 670253008, 860523144, 432329186, 574801224, 907413123, 543676017, 514072946, 788968002, 502228137, 949033996, 942192810, 676200376, 231782713, 606236670, 875644360, 397339541, 828558395, 574042087, 316320004, 77947113, 368737368, 414234936, 651543905, 528060612, 723571658, 616773343, 273464096, 765441389, 422465440, 930526177, 126094210, 308961386, 614946959, 76463821, 972491894, 116017200, 944120071, 105608039, 273806458, 918649435, 183141496, 3263491, 627297556, 313471169, 239872841, 751080159, 86128788, 459269185, 9903870, 198168977, 35763058, 734505283, 576487226, 961468280, 253156148, 254002860, 389276408, 444660912, 87176947, 719298785, 768793119, 75715616, 918739020, 49486397, 859378170, 330362234, 660158476, 903181037, 8065387, 688730979, 393620360, 707893903, 298719151, 958411192, 485573518, 835835077, 394844262, 607304827, 65895074, 667450773, 818081051, 284634495, 661860140, 734917156, 120534097, 704859314, 161019427, 415563830, 370280546, 898225914, 641172042, 788936637, 971020460, 402288791, 832166314, 314135005, 493675450, 60932312, 717987926, 703761726, 206645470, 811282353, 351799089, 475623996, 410217735, 154911542, 641626665, 881502090, 948773603, 322264189, 450954014, 984637574, 414258700, 504609419, 855426974, 269686477, 75605492, 192375689, 461942506, 177646972, 381584654, 906784847, 379698656, 803580794, 764276418, 445019267, 43857112, 641283198, 255628140, 591620442, 350904622, 852567175, 402009210, 251599065, 816775977, 676801140, 71699029, 645636582, 408370512, 488865802, 152613382, 99808073, 533320909, 876090708, 422636413, 628510945, 825973252, 793810243, 93534668, 385860431, 691508877, 463230387, 478838163, 375328586, 463835900, 52272483, 846165570, 183703383, 226365707, 582326575, 639244389, 336893205, 735154738, 249097013, 43213742, 297361260, 167884204, 248940538, 27604252, 376082065, 526180509, 341555400, 639463906, 244334158, 130302093, 159111350, 253917412, 901206510, 875168455, 396017124, 162747248, 420213313, 617951086, 468348729, 965547024, 540598863, 705579799, 6797292, 409973156, 97380275, 346422266, 410031359, 537862400, 86424302, 772040482, 436662333, 323297634, 324765915, 923002546, 355697956, 313388929, 420557227, 725070349, 328579868, 249001697, 341525133, 828947630, 623646293, 331778597, 337339617, 155406547, 964187827, 480523183, 181154604, 812157279, 624485843, 594865343, 812008152, 740052243, 417057184, 152788691, 515172727, 76725074, 996188542, 702640027, 710647755, 356926183, 915720820, 142769184, 580383268, 949395239, 803836494, 269191680, 852605389, 156774830, 471852637, 369578605, 139865708, 967344184, 350475014, 739131014, 456549546, 709481688, 141658951, 823814102, 103968677, 861660681, 408151237, 746234971, 867242610, 188869560, 266690164, 56591079, 261159904, 305439415, 807588710, 347858456, 451489571, 887948438, 834543491, 155395975, 730590775, 471098819, 887618953, 210773583, 617235492, 259876619, 284413573, 742170224, 494228852, 919793167, 565818974, 544901299, 456040244, 513166171, 301308912, 362901372, 369691294, 154132612, 111106325, 592820007, 703348300, 149824556, 611831626, 801664835, 207610527, 590040014, 874246435, 579763938, 455282105, 219837070, 649226276, 250601830, 505367682, 390074143, 219063147, 73018594, 206891940, 350445981, 663683683, 938321132, 74622027, 643776095, 541200808, 739741161, 939885977, 988141827, 149780828, 716753225, 113368453, 30410160, 184927782, 339493906, 655234252, 965000889, 878244532, 257773434, 501528569, 978033375, 196639610, 779032442, 611898187, 845881722, 456836517, 318882380, 776989855, 815662193, 893857897, 135384650, 146407445, 176284724, 708180438, 872309057, 193207872, 825063414, 116696302, 587437119, 359338201, 801652578, 539633822, 686489836, 434454626, 745705659, 234684425, 387439185, 256212814, 62552804, 886781185, 468593468, 989259945, 592442830, 99121187, 20803704, 421119344, 752733997, 967500358, 755713202, 366006086, 765345024, 869950494, 673901374, 885746778, 274432840, 779035639, 417548438, 22198161, 308440281, 893693418, 229695653, 494424952, 70778805, 621528796, 204005973, 646046053, 678010843, 782931747, 393081404, 73616787, 872882606, 686221672, 888121698, 778390248, 415646146, 702360535, 917268496, 986835985, 708980313, 179156437, 698670321, 75640184, 477014805, 479166154, 533873194, 448071325, 354997616, 743300245, 506119314, 75831373, 100305302, 738416748, 698486502, 447015865, 43734288, 388311466, 997705242, 878705883, 464566466, 802865031, 768271951, 442912798, 538984997, 778215019, 792588061, 315033296, 882020036, 716489567, 257075782, 16024514, 317078389, 675044840, 456015726, 34335975, 721040480, 355578829, 81232374, 30218078, 91002643, 831099220, 660134327, 390685028, 123025930, 749120148, 388848462, 233288732, 273713510, 911907701, 313551933, 565845364, 371894101, 428765900, 892845469, 850619022, 364942921, 884829874, 542458541, 980143410, 481100250, 819645663, 205971742, 296363258, 415091530, 237986887, 813807582, 536561465, 510829414, 435997544, 163685081, 273092039, 676280737, 460428352, 504583937, 848619984, 552721348, 328163073, 119329552, 414947972, 429942298, 808936906, 530053981, 199788931, 537487400, 533926823, 666998651, 546081383, 770477145, 776017189, 988023018, 24583193, 930710884, 79609493, 268511564, 240435086, 823133296, 964456492, 50822703, 763858005, 635449988, 645244457, 486543416, 928094777, 565838790, 626056606, 944095061, 868578435, 850095027, 291608278, 384388832, 426786971, 533302237, 635214093, 898963497, 627603043, 278665680, 562717474, 139447076, 661811142, 548871743, 711758733, 626115064, 992569243, 845951475, 123584272, 631415335, 739321447, 568227687, 555257303, 798186283, 199472751, 55255783, 111424703, 241305647, 58127936, 506662930, 453728155, 545615165, 627911188, 57154982, 295721625, 552426202, 770290166, 230337139, 383594469, 351020726, 597502556, 304284964, 186957258, 880533747, 339461343, 180466292, 425131928, 446061869, 988343039, 41531570, 971554415, 470796746, 305207249, 970611750, 418248718, 940558665, 655238955, 864260225, 940287471, 710612280, 696144957, 644679698, 170458844, 279664300, 20787155, 921014641, 130642959, 356398780, 907924034, 220312990, 169368149, 775240269, 995487089, 470216054, 616231727, 281701814, 688000818, 233604557, 351591686, 491803460, 948996684, 527084378, 388748151, 383197571, 353019676, 835765989, 689014436, 745219000, 812569501, 499119541, 418809010, 930230793, 494410294, 881836319, 477289853, 514300592, 509806030, 13075278, 30999123, 940351870, 528595536, 617760353, 70150949, 248798775, 711811997, 758444746, 200738415, 142526718, 904425788, 678830023, 214063450, 508411228, 509967074, 503059497, 240962263, 445378586, 233968257, 806641343, 159423897, 64629905, 443877047, 798359557, 560856345, 214856741, 240210057, 933414624, 855534455, 421004039, 647980695, 726044306, 226880623, 973580264, 954831654, 22252661, 48856758, 287166355, 876709586, 46885843, 900276141, 698731173, 947235684, 573540900, 896731194, 242247423, 147988728, 95046972, 385364929, 401979845, 895862389, 611992671, 276710468, 939678574, 331154057, 196755529, 355425889, 682515945, 374163701, 834648465, 205929230, 479070298, 903171501, 400674843, 424622323, 599082759, 357215015, 486250372, 538307691, 31417133, 56291566, 984503435, 823095614, 2668651, 798723821, 942014092, 373886748, 159836953, 964316770, 613345319, 526808790, 651029478, 138883176, 183159390, 604214663, 218199398, 542068922, 854430597, 534321469, 392747213, 189729958, 639052274, 726357977, 788025765, 801095843, 151897361, 123018599, 104884610, 729265406, 429208644, 248031406, 92415935, 624636732, 981898991, 722065457, 948120473, 273049046, 920223307, 592485737, 432923542, 287582840, 724937916, 156774362, 265149530, 967545397, 926073321, 795082430, 38826160, 440987062, 698124183, 991574758, 224224295, 864780557, 666910460, 327640067, 399264395, 314241827, 742765437, 241273450, 552105060, 602271730, 699567701, 286582228, 220177823, 154136151, 249580672, 883742851, 875992697, 225981900, 633349596, 820085911, 776305355, 189930452, 538243, 525128739, 430493474, 138427021, 851261226, 515013941, 702260804, 438356119, 240049091, 695416773, 471151084, 596663551, 376655585, 482806055, 588117275, 889817235, 338580757, 839950596, 614874595, 274108358, 277942599, 375990226, 765023750, 612757708, 216732238, 903628587, 522491994, 817430359, 693078063, 273384034, 297737651, 103076893, 683403579, 790843719, 572068491, 176733010, 310611329, 995450593, 809941473, 530182500, 132449671, 838583272, 155846716, 399748508, 242158949, 869169274, 290969204, 92796969, 391056072, 981111870, 660295735, 246108459, 898825067, 15589234, 372054057, 723991130, 489081263, 418600894, 811376921, 920127313, 719131200, 136084637, 902717174, 291385517, 343774097, 881853005, 334756836, 869397316, 794242337, 358536245, 25312700, 228020373, 709715424, 190760206, 14542079, 266931748, 24469971, 529863740, 427224944, 511780514, 593570642, 341738948, 262982584, 968523607, 310269429, 325006543, 906136698, 962139332, 472957046, 304907305, 918812082, 503197314, 186605834, 765900735, 722515806, 335398160, 616410555, 329983567, 637803578, 443773996, 266323690, 27652616, 740549381, 938842232, 859103782, 79392090, 454003721, 313725284, 937216358, 777925463, 793756050, 206552357, 756826108, 836391904, 427170305, 818832698, 238433926, 489257420, 979294715, 218223927, 476765948, 758268090, 819182100, 188049105, 535938204, 370464199, 432695290, 866871975, 674026206, 491865530, 532308386, 36760333, 346282535, 813146729, 97866156, 468413875, 995017619, 525108491, 736994576, 431087919, 528583524, 797274502, 877586401, 176402295, 576651791, 74683879, 221726474, 371672716, 111474935, 350113429, 86325428, 490542439, 580094284, 886047817, 74892723, 564971904, 402660379, 269653031, 598020996, 411027734, 464846150, 161217333, 301565650, 77546065, 820159533, 680003535, 571064599, 536920261, 826825878, 334687767, 982967727, 207904681, 311886282, 624098992, 60926886, 965959040, 169689060, 401414360, 485693538, 417709527, 231441702, 918876928, 152043411, 632360108, 968711923, 614755493, 737028183, 608648413, 664053487, 714897713, 358916162, 889295252, 151730631, 575325719, 897102877, 146171897, 82198698, 23174130, 277535949, 905820452, 111108213, 990297067, 749802201, 45977357, 778672265, 32240577, 374251775, 872014708, 71236985, 662241622, 575810325, 734422317, 553021775, 111611398, 763228435, 711350560, 301717921, 980283390, 551732135, 735036727, 891329138, 766360383, 380491405, 482932210, 196862332, 736953118, 883579517, 397789551, 49886184, 123799817, 926326997, 302272700, 370578515, 633953354, 851144540, 348307096, 421831935, 473721687, 286075274, 800995372, 150988704, 976856124, 403995363, 372209876, 430377636, 93046328, 603381387, 486592260, 56137857, 503160964, 14530958, 548875673, 637352710, 640734582, 387444517, 278565474, 292200491, 561888784, 487430432, 804800462, 485699777, 272094953, 923907442, 29117406, 974877829, 906907172, 180556252, 456061546, 974069982, 297982894, 166432398, 213664790, 201408662, 451518844, 692628284, 242132271, 136526094, 398101882, 836769127, 905543946, 783666379, 269336171, 268430166, 397152687, 32618912, 712890189, 307735654, 686425710, 517766449, 649211873, 552433358, 517238304, 17427973, 94270576, 715205617, 887560218, 305876306, 48729333, 740652558, 804421058, 338993387, 414427380, 695845217, 880042688, 335060349, 696996658, 751979136, 85482504, 538459139, 684412629, 940517020, 334171550, 120679959, 235851176, 268794519, 93826817, 731136189, 93483323, 453830107, 890102226, 840957929, 248947535, 425891978, 529835929, 49611228, 407739470, 656013701, 454704473, 918151788, 890198679, 329047560, 907106461, 760841438, 275114121, 383839342, 473014280, 18759555, 628127851, 86572978, 606348831, 758322742, 856873196, 829493678, 266775052, 51399232, 964234728, 150245870, 412438283, 58934507, 234977404, 999498510, 94276529, 702737126, 131142176, 652802396, 295710560, 25184796, 907022837, 661567309, 61777893, 549176028, 136660866, 27178945, 86443264, 376038156, 892141083, 396155876, 117211193, 106484539, 766543607, 343039177, 205036449, 89486057, 734939223, 677738092, 596296252, 381097867, 490349342, 314115761, 199834894, 304986834, 455095492, 55510496, 578426827, 446246527, 294974379, 387650549, 46687161, 438648522, 305730341, 560831643, 79445302, 628004325, 476195159, 957492655, 25485349, 31747392, 545801026, 467196667, 874398531, 136426798, 52211484, 950080515, 900458361, 350238306, 812791073, 42061024, 822503915, 941863173, 178403436, 145388484, 813738588, 927429742, 887850228, 353808429, 942260488, 948171809, 457260649, 511805284, 143443315, 731052803, 755131963, 831252803, 501733325, 940222475, 956265358, 821368633, 174207856, 807208704, 994620486, 356639172, 600496838, 749362806, 560648072, 971535563, 241424537, 881283035, 630784227, 224304003, 472017588, 310809637, 638976376, 406101738, 549469392, 655218653, 951252491, 967387746, 935127303, 333506316, 978798142, 401550754, 169248906, 379237243, 587032391, 127732572, 605617558, 344831266, 220067599, 265633469, 461639758, 53001808, 303298927, 603558456, 199521606, 20112294, 683177431, 518148380, 784093084, 765758349, 361984514, 673822092, 396699089, 858943868, 522197309, 818335325, 118136966, 716791240, 251727378, 720582219, 160552615, 144539157, 940013756, 126707320, 843122729, 819558455, 307256585, 432190648, 71035418, 85607046, 25880649, 345551022, 242315277, 968246304, 121785071, 684435524, 601068608, 197673058, 191922037, 53178052, 286212184, 773589771, 217311359, 494114147, 193258090, 340505354, 230653553, 464078430, 125893619, 119514865, 342333849, 623078096, 728381637, 846596444, 917305468, 318077918, 505790057, 542356505, 423849362, 447807722, 453134935, 570741911, 119281818, 850297193, 1508124, 343768901, 349573412, 394799108, 81841711, 115341222, 875218889, 658353225, 272184918, 534636810, 679964352, 806684290, 233255730, 368160418, 909700511, 828269050, 584091856, 756649392, 207041809, 305905548, 351521257, 528973766, 591947669, 212975113, 365507608, 22899933, 403817301, 689107646, 771721606, 414378772, 549306424, 825871985, 471526053, 923328266, 370231932, 367422222, 203697431, 516212979, 276150109, 249563011, 116128258, 636718196, 822022881, 817909264, 590699693, 261993668, 424760805, 13766118, 575301793, 327548630, 767288429, 971344987, 293675171, 850841331, 423106740, 172981067, 908535946, 663213014, 662686170, 968522885, 922210369, 229584348, 436789085, 949376366, 93549408, 275924569, 822693484, 679237995, 168395183, 760123483, 369411106, 72298687, 338098943, 559758459, 432847842, 211799181, 410424724, 540913703, 674637210, 583258467, 51447163, 425130701, 738908769, 825491881, 989128042, 240535075, 250985732, 707312513, 673301793, 18307657, 493514412, 740581017, 764619966, 993829405, 369447079, 651474094, 164233166, 592830518, 982555252, 54992054, 696488131, 363434026, 677403937, 370214870, 504156179, 585914037, 402329050, 679468988, 916217179, 528502378, 49448811, 373947636, 867843693, 871248006, 399918173, 592016942, 26704791, 527794584, 65293665, 394761524, 596839834, 453160619, 70831670, 890164142, 378995084, 167941171, 129968746, 699016089, 935545628, 973635584, 152712740, 391454130, 974465966, 163303230, 4789256, 962625781, 279916096, 312497272, 475020053, 830310938, 968460348, 252008494, 325065286, 115260785, 755682121, 907781963, 393794596, 997102266, 943716591, 122391464, 947291482, 195274268, 211543013, 842023550, 531648277, 694750167, 215528584, 489820735, 594591002, 67439548, 625855535, 374959673, 660796764, 453167583, 370022139, 233934591, 758457825, 641545554, 918330393, 213722348, 497178234, 198616687, 887915506, 792345195, 1757924, 335181788, 877325294, 697717734, 869079464, 59344267, 471418088, 715706176, 932867823, 272293653, 907414282, 245793352, 497594394, 417456710, 703002899, 374659023, 96805298, 136515371, 502550606, 869497272, 943406645, 570184019, 848894027, 366723566, 644140428, 730626474, 506011674, 736900366, 348106758, 668040126, 839864182, 185853460, 585324454, 229010225, 992215203, 920715584, 192815245, 867696485, 114431153, 707524177, 957912229, 49474512, 272605288, 710313185, 807818836, 787993786, 158055286, 713706940, 716086615, 147147635, 209523613, 395739721, 485243821, 910062634, 249677240, 627482216, 563204344, 43313538, 986531955, 469112949, 742603826, 848653019, 959609056, 200927281, 94836446, 870221184, 220717831, 662891493, 823392913, 752903717, 454125167, 610656112, 513044660, 53599239, 318449875, 862804107, 578767021, 692296742, 670982176, 556639346, 265488778, 220652277, 494562592, 417626614, 564876077, 771146718, 593286373, 331454806, 104849417, 398292229, 904580799, 404829540, 251038482, 26175437, 686156270, 879010173, 235961048, 924717052, 86667055, 130344706, 818720442, 525617818, 840261277, 723159881, 820570979, 802601611, 956289590, 981598985, 89796182, 955955446, 472156604, 921575639, 144878158, 600153816, 365514759, 74394008, 771834095, 115743446, 338053105, 630798041, 294173316, 443111115, 773284698, 467342349, 566445757, 907745547, 352911953, 536110091, 447682106, 39475548, 739212211, 852118635, 544916761, 474872815, 410528268, 846529488, 242158841, 810051223, 495459887, 286741971, 204246646, 962016575, 175811325, 689441229, 345745857, 587048304, 916741018, 308919332, 780316782, 584646119, 614781305, 570207614, 741290130, 661663951, 451557409, 698689689, 534827192, 27037678, 274489356, 608567961, 575947582, 69311394, 126667149, 566700267, 274094970, 365565778, 976459668, 919867742, 348450260, 156922443, 638107074, 29607726, 665522744, 574794705, 767414925, 669516251, 194159217, 120105611, 102271032, 510689527, 449088344, 671386482, 942110641, 508056984, 594600559, 110696728, 500539328, 774491856, 961529263, 729104349, 217213953, 777563517, 730039350, 167988786, 69789493, 901866217, 365841752, 242431113, 486718316, 886833900, 23036054, 6044950, 519802229, 34021983, 394513245, 34245462, 604897050, 165282609, 655872781, 494165671, 570941334, 267794397, 930320468, 271668900, 238613685, 476540250, 112599395, 916247729, 565537846, 509276094, 349944364, 736755227, 599045099, 420841957, 59699261, 140297921, 307591780, 413488456, 657933674, 869982371, 919572667, 484780544, 309927077, 857239635, 324784758, 828922484, 980739329, 659365451, 806186580, 779540855, 915889650, 777602792, 675418493, 755760374, 450473339, 641315451, 537640097, 958773500, 561031620, 589239133, 174505397, 42485573, 639556359, 227695373, 790669744, 960643037, 73013874, 384764395, 966604527, 308467980, 881847777, 923865411, 28057538, 125713896, 531674972, 461141661, 756197930, 393249536, 486157249, 397041914, 889251167, 62154607, 805097400, 847014484, 147647701, 278193612, 815008068, 471735584, 302539518, 926959813, 156805303, 927742614, 164612028, 595447463, 819027258, 432111243, 118975976, 829633820, 353434006, 277536928, 906947320, 900185339, 78519585, 493403280, 52234812, 58604728, 874883307, 770599057, 997978793, 706382062, 831373185, 632133419, 698722758, 331826953, 814243088, 529262438, 292827270, 744478394, 11693898, 847456656, 464107780, 432855351, 171380254, 245620970, 887461213, 735917659, 869068859, 495933095, 132384084, 530395294, 637147046, 877859449, 172076158, 841839748, 641645129, 916878843, 931597690, 376708617, 201335198, 619714804, 268006953, 845623414, 680631379, 487885170, 320227432, 651792880, 442620300, 915408969, 720914235, 9277944, 792973932, 96569108, 876075976, 425775818, 431364343, 508272474, 445557334, 376939283, 684407877, 998002251, 363802115, 252400236, 685028840, 591054962, 925403683, 783668679, 265042652, 138870173, 342671158, 607877337, 989070437, 917886647, 542622175, 421474383, 998963304, 695998037, 726380937, 826800886, 729036073, 131513206, 708672600, 714181798, 170682756, 19512865, 340838521, 895643645, 815378221, 202191012, 599057472, 776093893, 211819108, 525050827, 231345562, 77752194, 956697100, 532059417, 818584786, 869589583, 306240917, 248477683, 550674124, 118983187, 125720136, 621600640, 235544144, 197330988, 272247544, 558658815, 500496726, 109841092, 107222559, 580432570, 405268031, 198115424, 296881543, 409097925, 549950090, 787873309, 156599855, 839139883, 53518808, 632861311, 840591104, 632598562, 183533104, 984881272, 771011915, 702607903, 839622958, 195385789, 562322960, 447607360, 306857946, 732382748, 337425986, 245597256, 497992383, 926651085, 494776117, 13757657, 465708451, 277313253, 124498945, 195031888, 446708968, 833188134, 566673384, 719564367, 28800782, 923813134, 565416902, 893174511, 880636327, 676755746, 17017167, 105455564, 3499601, 744614511, 536355616, 281078829, 143526483, 645802788, 647581755, 136108731, 210605376, 601168782, 40906012, 421818046, 349017041, 990134359, 955622304, 366679572, 242448854, 512369089, 296906986, 352807179, 547628274, 487099607, 205303601, 729018465, 31417363, 170773842, 251970465, 783891670, 590384744, 500261149, 662563641, 345600155, 803687071, 872388463, 440261272, 902155287, 209438813, 471346192, 662215373, 242866195, 551283400, 538829704, 978418621, 939532580, 444109609, 677261110, 664379397, 860751250, 932893404, 714798707, 325932027, 949382975, 509453680, 634761952, 421386683, 516907463, 26941006, 388988941, 536432206, 465924642, 246717884, 727158447, 47834463, 132585383, 279301889, 982733897, 113991855, 838791785, 337725135, 287293294, 315854172, 222943385, 963434514, 258054335, 142048258, 673676029, 948713986, 457005775, 151707553, 923501050, 605375403, 89451514, 503681499, 316248161, 918249830, 606874071, 245380153, 252111167, 808104611, 810464795, 740007953, 120276533, 423163637, 395518748, 793239279, 805678034, 171817249, 337939259, 140187282, 468828975, 769637507, 912981580, 608463759, 518343431, 65964049, 653921102, 103548747, 202592110, 561980033, 589806422, 558010288, 512560010, 539637276, 998524739, 801787075, 190264438, 442971296, 964369329, 185665006, 845316730, 929800746, 450321886, 890975277, 61640695, 74560715, 723108919, 258869983, 921524159, 263640447, 927588024, 464913488, 377981884, 781394331, 584497680, 395846663, 106946846, 215477588, 140344310, 60457187, 86965079, 538493749, 639255339, 614389637, 32134814, 279222019, 886418059, 563861693, 633463986, 779001572, 175535122, 718080594, 569435230, 464454163, 76810211, 98349379, 373603306, 967485003, 252798969, 274990904, 377600772, 379752653, 259377445, 870533383, 384491388, 134120357, 692311466, 285328086, 783311154, 876720036, 145830252, 622621677, 465412138, 545289339, 761336226, 533756895, 292094252, 340718630, 177609629, 61089379, 332425466, 438925741, 311840372, 533610405, 387503502, 774764216, 214458544, 315786081, 887889043, 482501087, 659868414, 636618946, 58918930, 555402389, 535219166, 793122869, 780042947, 950072615, 705078541, 648885941, 312416163, 692369392, 325710940, 968310318, 916854741, 347896665, 982201888, 130245682, 111092352, 839812584, 755260169, 232955970, 818940471, 738152457, 531934045, 487850836, 474056456, 525654907, 500786008, 478935718, 9411664, 466711262, 397437887, 844224117, 250482830, 716002240, 773276273, 404108829, 71527717, 372636107, 762936909, 498506897, 595346084, 278467945, 421863380, 602215028, 157881691, 912560994, 859284969, 710007834, 981350233, 706669118, 132320887, 464296419, 845207653, 240045708, 725005195, 863425888, 461792628, 194554246, 874838237, 364034292, 37186692, 408995196, 66020635, 501132734, 505816254, 872595469, 506417962, 755595657, 58119468, 615510707, 4944016, 496626826, 191793541, 741908379, 857725151, 812615595, 407881311, 611519679, 142913475, 230963941, 562799382, 6132093, 720910438, 118175551, 654023685, 805237448, 751945209, 50986295, 834144829, 115704955, 804597412, 282753559, 443213222, 524116128, 286929496, 294863732, 79026036, 186960931, 265008835, 52678090, 361522269, 937353956, 100346530, 615337105, 800544608, 672975845, 694231206, 414471083, 454289905, 804110865, 195186970, 663955816, 23153108, 164868142, 521858930, 174562654, 812515895, 767885260, 53335038, 551165468, 476437183, 299308823, 580820944, 161359574, 858101934, 298554665, 345960761, 554858476, 952494153, 499483570, 257899647, 40292398, 577042195, 276239485, 660039834, 661274252, 254817250, 855496183, 880565207, 886590300, 464094039, 134933699, 447738467, 229545101, 835233697, 977160848, 896138262, 828802671, 474013780, 241678421, 677898222, 144068067, 882845088, 420918861, 436304600, 842959771, 73603176, 270020312, 164257979, 650092059, 501401098, 216054817, 337003187, 914057239, 932176125, 863853327, 405424903, 195490630, 447967057, 712527549, 835623292, 551516064, 506493974, 587141412, 265664261, 614624394, 415791536, 399910861, 785959350, 670488954, 311666856, 296023550, 488328771, 901924890, 664470112, 920756071, 524199619, 109408965, 616404265, 122384533, 669687498, 556799161, 795069279, 668568703, 323807919, 400955885, 845797825, 991158124, 82179425, 400877069, 920640769, 161728826, 839057758, 19315600, 952553783, 900611469, 486587107, 20299835, 681910125, 690882952, 34002837, 375651536, 46405704, 625940821, 571229639, 938115166, 185691783, 335919320, 533451859, 29913087, 625946067, 271374188, 362663083, 674992051, 443910606, 78692745, 310630100, 250581356, 973023438, 730599819, 244274622, 309355004, 420629480, 303850351, 501198351, 897847512, 777621275, 711419299, 366485141, 645537709, 470299176, 544738230, 693571676, 792730794, 986085268, 62292220, 688088779, 317077100, 15333613, 464794281, 737443453, 35448641, 636709464, 553383089, 281452328, 383268317, 314318425, 954631292, 200848499, 978220785, 643881942, 845662298, 355800345, 211342726, 20676228, 123085950, 278296378, 432856941, 155603825, 850983448, 839459214, 24821828, 570256383, 381667189, 993433368, 294382790, 961021906, 229575541, 894631729, 727289160, 795931539, 954878353, 584854966, 746694926, 302198012, 722881448, 466709433, 248901221, 397935262, 328317723, 408705120, 443989271, 964120316, 420430655, 255831716, 96796739, 523860674, 29547529, 170411374, 956706446, 99087057, 969543745, 316716637, 384009502, 23113045, 539021774, 44733086, 119409025, 860462810, 744127267, 667537041, 611185619, 362527034, 969722892, 196269874, 339811480, 371868862, 422996385, 890243911, 476731883, 174527633, 503675368, 27946791, 413079461, 523536397, 30970482, 491645897, 720857255, 686801087, 781419753, 494305439, 845947311, 39598400, 253070308, 643469877, 646601699, 942683442, 420094264, 274137266, 122929534, 510413472, 469026472, 530935974, 314846709, 369244296, 228928946, 251140348, 462876211, 658701614, 713879073, 655624753, 655673079, 128766409, 630670222, 8734880, 800705083, 675940049, 909393231, 165844739, 615269482, 749349517, 164724706, 420553031, 847227328, 536672900, 229540586, 767205497, 429968214, 460958870, 657916501, 985269110, 799883116, 837840123, 926366255, 69435594, 722012603, 928603968, 221489834, 804017356, 959732349, 816079949, 691000509, 767125854, 546211161, 286358688, 190838042, 640275537, 257748509, 489281379, 317872445, 507558748, 943850008, 701108796, 649213558, 953000234, 415115361, 380069855, 42441960, 989226311, 206045754, 996276439, 588578317, 502500914, 968922478, 632775050, 272390857, 698885471, 620427726, 256209102, 9321242, 990099724, 714842389, 425825059, 175543144, 580139818, 991728704, 694325097, 178112024, 3147254, 82575240, 748370560, 603531294, 594230736, 968685418, 273720850, 963456561, 539227364, 967398793, 753365569, 867128999, 797130282, 836359748, 980095001, 827422743, 804048040, 604589291, 201426652, 439997232, 206239197, 765198761, 638726569, 325019715, 628390578, 994624316, 657983552, 485273954, 77139776, 340180332, 886312794, 290453130, 603081723, 462007671, 444996175, 450319482, 754545409, 101367422, 130215941, 622797380, 619791439, 66010042, 785185611, 573323853, 753597672, 360092991, 436710176, 437714278, 944725012, 270967503, 104653492, 49339676, 21588931, 84538290, 719743187, 242245872, 661598785, 965628614, 660409551, 585312280, 783351674, 729310669, 134128891, 340027018, 401192671, 595900820, 14573469, 971490865, 487186828, 418723725, 953357672, 499852938, 633972214, 159216351, 614091546, 271222858, 536412521, 569124708, 133339217, 629910399, 923989057, 646172771, 912336082, 563796494, 615583907, 292124603, 895007414, 623159469, 248499727, 877883211, 318481963, 95366304, 914401424, 708135151, 636297923, 777303772, 690164823, 781118205, 44715312, 18571712, 833558542, 764911181, 701709614, 392807815, 483946802, 355999789, 690677376, 244991399, 78383302, 523019545, 704626058, 453438032, 172094737, 560082235, 408892594, 148152139, 784622758, 672951308, 881235002, 88558443, 417318371, 975818084, 352583853, 402463443, 10044632, 516948976, 866523649, 367617381, 352870397, 324861910, 763334013, 606446796, 374664035, 186541231, 803047582, 471757459, 724617393, 772519307, 96137400, 681703337, 485224050, 694223605, 466074320, 824699534, 649283611, 631968535, 389512081, 490568115, 115974093, 155730800, 665500343, 408490659, 690364200, 201029936, 927031648, 902350063, 902751591, 187671336, 74907582, 712262356, 976640454, 687019725, 734425020, 664321388, 501729222, 361571249, 104953363, 138849522, 571363568, 309945668, 571398621, 32213583, 477599956, 299107940, 449452792, 68876956, 441391073, 78113117, 85258383, 72447023, 865022267, 170224979, 603294345, 492938517, 596398624, 516519334, 624636136, 501493804, 881763035, 744673243, 938199358, 914029546, 539144131, 632170464, 475301964, 269933087, 868705184, 240402314, 629270599, 798549159, 863656254, 462746676, 849629535, 632475242, 373474461, 26467898, 519858152, 185900228, 658763810, 917385701, 881214489, 643862037, 866059344, 811092137, 636518244, 851842423, 376795449, 841923716, 112551129, 79300387, 189341551, 583435282, 739749384, 373694223, 499061397, 374610600, 668101933, 495196427, 114253943, 346284268, 339658663, 563779567, 338034988, 194680542, 412073152, 188300233, 368033289, 513078436, 558392388, 430001150, 316564870, 565233895, 409944324, 37354141, 781313109, 663417443, 375509590, 344405283, 921409075, 408027921, 120030739, 384115156, 38758427, 321174992, 447080895, 595318979, 263552935, 455381742, 567281340, 207282879, 108317196, 29791812, 70431399, 423670562, 158018320, 663174979, 914544626, 621936687, 377165106, 879382385, 888097887, 287513661, 105766240, 940613477, 652089719, 697115384, 426035291, 293240204, 629009124, 865459781, 535377751, 568996251, 948332403, 298982274, 361026303, 403145336, 752089917, 215126717, 833237768, 14537374, 138330719, 973795797, 511787318, 826886573, 497501364, 577677733, 166450861, 836075210, 442437396, 741532104, 333524237, 20692385, 998117606, 994675120, 588672123, 947524567, 332302198, 527791569, 636271277, 165261312, 368758565, 574014921, 880273713, 798721242, 589241378, 946056667, 415764654, 768331915, 682954887, 460892338, 735288751, 873823838, 540315505, 662513840, 103070334, 969236188, 652210704, 696484951, 516126041, 403120914, 957200218, 967703564, 409570835, 835056120, 60339429, 855230302, 93829411, 358558688, 847095908, 445888276, 140722708, 36783486, 591757213, 777184296, 931357504, 747548186, 266176783, 730657965, 712322538, 650804765, 722918455, 170939062, 504182678, 99588552, 410840635, 904836375, 74938174, 462624093, 366538813, 796178503, 628508616, 376893956, 203036822, 297018598, 825351934, 317470296, 621604198, 986678328, 934950327, 915201055, 797453187, 634596569, 387805177, 290106463, 841643685, 691301948, 589634368, 596314884, 21890537, 869752223, 748537929, 269033796, 925028859, 993797695, 891395792, 310770127, 260477739, 330012603, 271299751, 819090086, 41432830, 896840389, 685864574, 420233108, 494073079, 995780216, 188450591, 485184156, 331644897, 585185688, 800057904, 849526750, 969592746, 373777215, 741766661, 221877659, 446878474, 717062138, 217206728, 684402509, 31523014, 228479513, 680743202, 93573599, 122624623, 912593725, 526471056, 979856695, 815905701, 857302188, 167223715, 15596544, 577629408, 860985565, 230728153, 718115609, 790363439, 78873972, 170270800, 85512519, 18065593, 473029880, 865655912, 567640172, 861913146, 932871460, 22951319, 676032106, 214488688, 495504390, 231822719, 931714533, 317006358, 870327892, 971468109, 309541203, 490579811, 923229031, 830909650, 509445100, 224408974, 862965117, 473648312, 200879933, 157909655, 164308878, 557753965, 50259940, 710950031, 473491817, 924923263, 285678248, 253713739, 831491178, 277765919, 785985930, 629660519, 417634190, 548271459, 664679688, 153721438, 587060374, 873087696, 756858919, 426030727, 936341723, 415279511, 95088032, 717597918, 907606993, 143861526, 308256300, 675841781, 493714117, 791072450, 431614286, 952468961, 684033351, 87645865, 591008132, 380405503, 495258143, 26258981, 148890376, 570383046, 689199062, 32109212, 874523729, 454639275, 746609295, 217743999, 2173936, 506279375, 168856049, 248313726, 727281281, 513643777, 269441928, 497230499, 913843129, 772538275, 869332217, 135511744, 75861761, 538856761, 913294347, 190491743, 735660795, 341505557, 418584902, 199751929, 272384878, 689145316, 333183796, 186769692, 427209006, 895475727, 716243429, 276473002, 65885298, 40494682, 517716988, 246416860, 456361710, 18294610, 15707446, 424163095, 680294319, 883217170, 555038383, 186937296, 964732415, 349812210, 964246412, 767720227, 411026588, 475190242, 958186398, 420389496, 871363462, 689994729, 520042241, 777946338, 770647236, 155325661, 956879166, 92028297, 664145746, 617457742, 729044532, 364783603, 259617312, 389265324, 366640161, 506697335, 646407045, 136966968, 774867971, 369014729, 12238705, 699423236, 348350413, 117775333, 368961572, 438639337, 104326799, 785233999, 96085368, 202491313, 130315633, 113954820, 942796989, 822233354, 962402519, 402634949, 915116658, 575479277, 156718897, 948575566, 178834027, 861618332, 323421273, 489466653, 608037061, 949302577, 519418849, 355353951, 259618020, 78796036, 40582716, 491935440, 704275204, 896874602, 567003519, 992139114, 435017508, 415354002, 336702407, 515919840, 103115413, 460892600, 872803495, 63653253, 191223138, 687183250, 909055898, 881518193, 548781901, 717688961, 194121405, 585012375, 425564305, 554862186, 988238445, 814863667, 513034401, 75246589, 264979860, 449550365, 810154248, 997281319, 872450426, 283801438, 127109326, 666689048, 732756422, 66075376, 596046039, 631431313, 927235447, 269732879, 161162376, 205906077, 594588870, 347923402, 730444994, 771648940, 182112772, 462295640, 232754148, 960717910, 67225135, 178704784, 116004271, 697496481, 961766205, 570893658, 531311951, 355146063, 495179078, 286823217, 648161849, 801679006, 438321398, 338233499, 259697568, 165363798, 548484923, 956816206, 823095434, 776106065, 360609902, 831349271, 70430116, 972321645, 234852184, 776835502, 83549375, 859820251, 967206476, 543775164, 755804259, 126216140, 200486319, 986689451, 900833645, 947454476, 163174535, 263614083, 947827124, 282273738, 841735750, 866292657, 63817194, 677377681, 700995382, 726666203, 507483398, 448311660, 665494135, 681692846, 352031047, 559005954, 573143157, 929593713, 144920829, 578103523, 918718683, 294595945, 340659293, 53320351, 389501356, 320272715, 822003890, 427588573, 201923885, 40742308, 301375067, 909868400, 182459425, 188199257, 691896459, 469183652, 754565529, 788851454, 79989605, 971807861, 170989558, 67965961, 290766925, 901424026, 422478523, 327744142, 693092323, 624452449, 908334123, 95715896, 728610057, 840048382, 220988635, 145922666, 642039476, 652446344, 567786316, 827383935, 899914610, 732856648, 541521016, 267265736, 41880229, 715275845, 731471954, 562118655, 533993881, 483495882, 779049791, 204765771, 326197527, 114525792, 399587581, 468951166, 733855673, 325513297, 352763440, 244609520, 463394297, 915611404, 630426547, 946595202, 261888206, 327045439, 376409525, 944926318, 806386916, 846033526, 385454911, 173029099, 378673177, 226741740, 74461359, 447625354, 53161963, 331593274, 359925382, 533072276, 316932911, 489421733, 385219105, 448949964, 241808866, 190821912, 261387213, 988833416, 758962149, 144642135, 485067081, 861187575, 810257466, 524733966, 756559028, 211555836, 240771208, 760263086, 469455089, 543044300, 722465893, 251527026, 816604864, 493697741, 365372500, 701737285, 452055766, 514364882, 541014423, 320406927, 618367972, 986082174, 32235345, 549935722, 390150850, 914250844, 918178848, 756150667, 200989373, 391905994, 748800651, 342925601, 505904054, 41129895, 375001666, 786957996, 908903737, 334876406, 849440915, 502678039, 392166923, 422345242, 915528429, 167394564, 793156718, 649715748, 321171889, 460140649, 592996812, 650305645, 147185509, 262759253, 197109486, 395283540, 485721356, 207369379, 962249137, 731632322, 422482238, 300042567, 800638417, 29240421, 626673947, 754817774, 846757676, 751405346, 841730359, 122450787, 867018753, 574043245, 136441168, 964506421, 818549312, 501028479, 979375133, 19036576, 71880950, 361662154, 144272885, 159510093, 33892542, 282570625, 650248984, 396405379, 759231234, 545432774, 567271625, 283346053, 776661420, 354495462, 834463923, 592534144, 706882960, 913758300, 749734083, 414200521, 514015575, 32608741, 84387634, 22240307, 512368887, 981987953, 403831760, 852735378, 87800314, 371827073, 528576827, 126434146, 698766768, 980704643, 597316272, 233426095, 208668703, 985699633, 493529863, 241928422, 355782595, 280095047, 7587616, 440220741, 63075363, 796713505, 856608925, 17158787, 103462931, 428352287, 612621413, 562467763, 113550679, 460763185, 505149325, 320407275, 694834752, 382043871, 280878030, 214861857, 888093523, 372166781, 388065452, 150552700, 77949797, 206149721, 253135759, 578907702, 39877764, 492535526, 2385841, 802375553, 2040157, 686505091, 290352817, 949425445, 627924880, 684588888, 395685704, 406556335, 850204928, 737021120, 87663264, 465735771, 944318554, 452059360, 121277449, 983425019, 345625307, 849644855, 580520220, 889359010, 402416193, 266689461, 958034343, 36442116, 451523524, 318338711, 979990666, 666169091, 183416987, 871864018, 5664871, 327256356, 257160396, 709735730, 855796412, 956212810, 657212876, 506862700, 962292114, 957612750, 29773681, 274076564, 955117437, 933008757, 996419494, 231378013, 520230486, 986990572, 672964191, 966356771, 946200398, 423309250, 313470963, 742124501, 305889872, 862135469, 71075902, 907057199, 70819471, 436937079, 752273536, 390081635, 755751490, 63157815, 954276269, 492023597, 173634006, 357353874, 435372851, 607174595, 555889809, 105454602, 824788637, 248049787, 3095568, 534124446, 555557556, 41729941, 457547331, 900174741, 386734121, 60627646, 989786479, 522782197, 100549494, 7286648, 524239030, 678164664, 304596634, 332418502, 726221772, 474390892, 177584209, 764664722, 904148371, 981149948, 784395857, 797478928, 868255936, 240897827, 206125261, 999759683, 785092553, 544744633, 838088902, 507071979, 282066505, 845786652, 641990834, 242711083, 280245113, 268764789, 529636183, 946968239, 239237035, 962206081, 610045300, 984249423, 529699984, 539014365, 971215738, 122204045, 163580825, 119296434, 929676413, 916984220, 184938865, 227435040, 864698197, 610750796, 386064196, 56456347, 442550586, 300911993, 699293646, 310527197, 47068668, 526139177, 461805326, 502036127, 451925366, 479777188, 569246086, 931204942, 803517273, 973079998, 975580201, 145292053, 202809275, 911414114, 216476073, 332111208, 274423565, 405962066, 862136238, 353566484, 820526266, 758956979, 867661232, 760256470, 685415100, 908174720, 588362326, 650238707, 658588445, 524464238, 432746245, 959117828, 270057638, 548449510, 330024542, 929219868, 945125780, 242183167, 943356557, 805055944, 186387114, 894380633, 333250358, 217618553, 86877440, 81572678, 999666822, 568700870, 269155148, 613242765, 257541569, 533610259, 776381511, 855967143, 232691827, 344151599, 846376323, 839278708, 700553170, 633090737, 283972738, 697707107, 780558216, 284927979, 415733318, 11601804, 82551467, 336514237, 988039014, 15751347, 24654157, 518045386, 49357511, 396794207, 721178377, 446870545, 17596271, 717540407, 199370983, 999058199, 281283011, 288580164, 965109157, 670361932, 406036216, 27310420, 741581570, 986704150, 546382326, 458084707, 27099153, 571616484, 282430137, 999065674, 384792560, 389349677, 186541585, 461897904, 776990778, 309458564, 172025488, 907161448, 603822418, 991423461, 548446014, 101178605, 785314246, 278852411, 681539837, 995098033, 47000610, 706067942, 614076661, 703285060, 58462147, 436508645, 323794018, 98382646, 380303219, 532209882, 826641090, 219519739, 505941219, 555163577, 306162763, 1536671, 280469609, 205345866, 948215452, 56060197, 722293861, 369202958, 750141161, 707325967, 179464907, 241996751, 894307981, 583208916, 681787735, 394178048, 625427010, 740535575, 875321792, 727619642, 467232202, 964746660, 291810085, 219419586, 326376768, 956505234, 470841835, 560236484, 399659336, 353175803, 589083170, 646887843, 883290185, 63582908, 499482806, 588037167, 350577390, 305063689, 16133339, 753822457, 793855011, 681162234, 621279985, 430081767, 381104951, 844777984, 668087214, 623072373, 610611275, 854431798, 757298624, 797712889, 99225008, 581865940, 479740969, 155776441, 594126337, 260497772, 956596670, 951454899, 546231324, 326773289, 685405243, 90791185, 962171291, 201960026, 414140805, 465981121, 728283117, 623520309, 889697839, 209438037, 673814402, 150940528, 402924122, 622999358, 649028224, 377626074, 233013267, 765043619, 340881005, 311016370, 540267204, 259139129, 965448348, 192139552, 563517712, 981548358, 754553883, 360949733, 962071608, 537306470, 349078377, 186643182, 126810489, 757854557, 522244114, 933972652, 632999965, 670464594, 447743457, 812107911, 588636721, 555302598, 372966366, 142736093, 156341870, 163794394, 348119984, 453609765, 254849109, 220667597, 973706036, 381676017, 758014718, 710737335, 735514750, 769466834, 545575982, 888835879, 637291830, 775420610, 587435445, 243883024, 459013138, 320144146, 162882820, 902637774, 988542414, 328408130, 260800042, 156054941, 61353909, 503545798, 843464518, 742969813, 738134664, 217363146, 152032707, 634063727, 390773104, 437103710, 962109847, 415027341, 548610049, 486431374, 978712223, 746728918, 469228533, 111514496, 603236807, 784781331, 88920120, 719905004, 423596759, 808636048, 117173367, 908428407, 531412555, 513957593, 451733471, 981689339, 931871554, 122877745, 852405207, 467080055, 943701667, 96356643, 15444853, 895938030, 875791633, 782365353, 443782503, 629331653, 768987668, 254553306, 708430142, 818559319, 277647099, 799161134, 400711741, 812095661, 862715249, 765263364, 612450461, 716083717, 723016666, 779451295, 66442065, 444825330, 221565282, 847352482, 807955442, 961823825, 439864480, 855589205, 491434017, 748365773, 634676445, 96561058, 252984089, 666445434, 200879121, 140698044, 809644800, 477366179, 783013248, 466632872, 354717277, 57932361, 662253331, 769840780, 166675647, 505164692, 635036508, 818586595, 520078559, 450368672, 822090094, 559368971, 350522582, 879617587, 337573901, 787625415, 528732177, 456806921, 449938284, 326839407, 510202993, 707988370, 751990588, 169055961, 106731283, 195215230, 2611308, 865076971, 899233340, 544066869, 298257358, 882954962, 776781632, 735861019, 401613311, 327989692, 717820478, 841796571, 110295816, 853967623, 982140838, 25306935, 587119768, 24843056, 638577715, 597634715, 469647036, 19178287, 976564307, 906746822, 271307708, 535587735, 131219569, 145332856, 16200123, 974783826, 392900272, 765686379, 152652497, 550307742, 106312548, 583078156, 740873031, 843490171, 220839772, 909151633, 611805481, 174892375, 11571946, 464124736, 350681660, 940830525, 458691052, 52070190, 974987291, 880191279, 302336304, 382006527, 496662032, 30504369, 697470848, 850007798, 496174007, 212938314, 777102653, 179700179, 201048815, 63537938, 894730332, 10161479, 955723025, 721153959, 941205582, 157389294, 484594353, 729315080, 701339267, 681439680, 770013546, 625260200, 657277406, 311304886, 432802494, 472384963, 148578621, 41846533, 128534665, 16420789, 618089984, 700031453, 594566359, 854681405, 324461894, 116843921, 981200909, 384113489, 181546694, 572778797, 81487967, 987480048, 476759865, 600632457, 393333901, 333016032, 187763527, 847301527, 520120599, 947976591, 900217854, 178611990, 899018778, 668652707, 595660415, 260288995, 146326665, 549680452, 927686243, 87195271, 294942736, 463947680, 328265780, 356731843, 734294673, 251197093, 21639204, 139882126, 994298850, 36769612, 791234618, 21404474, 299979075, 260884689, 540160395, 607404008, 682509327, 62905091, 782414505, 532863681, 424608723, 522380529, 636447260, 690322811, 679994266, 197384235, 438076100, 914920116, 708115618, 969701026, 523304381, 205850030, 788479931, 60416818, 722905733, 635129483, 864159321, 809135186, 902905724, 536114779, 250776193, 598102654, 810076540, 102235902, 861868686, 249840926, 102686197, 627157225, 796324380, 353224137, 617773300, 19954488, 768656714, 841323485, 451597662, 102766975, 364011338, 293177954, 753308159, 684629172, 227422015, 671018909, 919263659, 868872347, 902266845, 199648231, 506964404, 83893426, 883120366, 552382999, 826031408, 373610062, 655147589, 885307541, 22353091, 517893014, 124270162, 629260940, 578833563, 159189659, 582072368, 412956585, 874515326, 188145281, 20996179, 485398504, 5762973, 326710878, 52946098, 190300695, 22714058, 224574365, 942663637, 115503612, 270556680, 879044647, 643169135, 349185466, 272054105, 708582131, 955912917, 701236278, 98558170, 437076824, 50522786, 907583141, 246102527, 337752953, 575731410, 537718025, 739053497, 434269850, 593923066, 156064590, 475167006, 583588355, 268694328, 196523833, 275548201, 750297799, 64541131, 399519360, 536473264, 984964845, 763116635, 157687607, 926529716, 631277058, 974238558, 117991774, 647662588, 295827923, 946183638, 676960224, 92337927, 48396981, 544717294, 823299082, 754294761, 818670065, 210335821, 296445802, 484254162, 17206189, 616138091, 205636197, 727876125, 446926878, 53587812, 587009076, 420652132, 767388379, 126338224, 570246102, 967286480, 633847356, 950500377, 323100438, 113800483, 858960584, 645781092, 817751704, 807583617, 918080897, 410888900, 833320914, 34561826, 439649695, 316216224, 156034592, 383350171, 651767199, 457811199, 145243175, 768397987, 71958721, 513110781, 576992161, 303594468, 301194964, 81771096, 534247894, 501104398, 432271273, 772056997, 653301276, 290027280, 22541805, 241667978, 367132246, 828774700, 831311673, 537320966, 969360866, 267163363, 772347117, 489439301, 237240132, 681895787, 894215347, 479651113, 160642977, 930417236, 887235138, 561284489, 757607765, 379210979, 321352548, 645180488, 735320485, 806840424, 399869688, 564495831, 45920484, 65251388, 852753861, 111296084, 292375599, 321271185, 690629829, 532132557, 363623063, 774069508, 809011390, 348823986, 514981708, 915487731, 228454029, 127925490, 186491398, 890407966, 603784320, 453968552, 671276940, 954225108, 876020932, 263119178, 431115801, 481513669, 962327840, 718027647, 645021476, 686744978, 998796878, 859024760, 271414205, 517336403, 716929727, 66692875, 598924492, 470105232, 50132334, 157078147, 678031860, 692183124, 11982961, 860985604, 832898623, 217754322, 215703223, 641014233, 907974677, 610260152, 10793616, 264263351, 39363118, 190898207, 242941515, 732234607, 578140309, 187941594, 241066324, 484640192, 821472942, 108133004, 694532387, 618260089, 621238966, 740643067, 192993228, 388034089, 399122353, 506246014, 575728967, 97543038, 72057149, 485336015, 950811780, 706463981, 8360978, 772189775, 564611538, 358104386, 869033135, 175673734, 454711489, 930140665, 804248161, 123515577, 767430288, 694375501, 173966984, 62978003, 344574007, 264489194, 156233084, 759106090, 570482219, 267126863, 174922037, 946029610, 41240547, 553503532, 416692598, 671261008, 643768468, 931620980, 338778647, 679380431, 557865411, 21655688, 931116213, 698428460, 121186271, 749437781, 66074968, 235928548, 46035510, 596702413, 855371145, 246043685, 106342342, 415585703, 984403021, 913219474, 291322163, 124383111, 794570390, 926309243, 768429401, 628427895, 106827241, 398240455, 679114449, 386211151, 332838228, 221195391, 965155238, 951345441, 703592765, 29417883, 287132382, 709584225, 765124827, 554572116, 493993451, 186336962, 803614675, 73742034, 711971516, 327410038, 15629369, 508493952, 497880207, 548468839, 463817906, 432818100, 650468274, 775317240, 679033197, 761152456, 712230459, 27985680, 668184646, 708556423, 734032267, 992201576, 39844613, 366547248, 633540999, 183101460, 888165753, 747099970, 823926528, 268854714, 69893653, 533120276, 853367760, 44154063, 719044398, 59064337, 859343891, 691518715, 12607212, 795524942, 157830922, 279504532, 200606784, 522790658, 495964289, 382838972, 50287760, 713301757, 72826832, 245473486, 505799752, 274285474, 62217299, 163837515, 109296822, 719375677, 409024607, 398956900, 528999076, 931791194, 631887250, 730670022, 299806347, 696673041, 557346234, 250258611, 756262136, 886116826, 945535098, 579779652, 525210330, 303962323, 847001036, 625082938, 659370081, 706260488, 351805410, 942974018, 906871537, 169789157, 661186056, 519353599, 522453315, 533296687, 639981867, 140943607, 68931332, 333225064, 347429444, 332372032, 138556034, 726323732, 577565203, 796882087, 136668687, 544391704, 554855242, 108642207, 624454309, 569504471, 127818574, 669839024, 560550698, 194473808, 799066313, 11047443, 49967971, 966446138, 760128623, 211578905, 437973233, 590554917, 756631479, 356607360, 913793442, 925230634, 913416797, 388704841, 87247223, 124074524, 775354655, 25001994, 50391708, 870673342, 733488838, 911663879, 790474564, 24832679, 154771057, 64302511, 363109145, 839737039, 662401594, 667694844, 722923721, 953058288, 169054084, 958264068, 645732327, 991239173, 387112316, 271592612, 415086115, 157595142, 321037849, 996574816, 55370528, 936588505, 620521320, 539023788, 731328797, 68263143, 377163107, 924155493, 213715634, 299776143, 138913264, 242958811, 152399625, 479818860, 343440957, 656492750, 424677639, 303456650, 598397389, 485624827, 310350810, 131234901, 452411076, 347898991, 409867447, 862920091, 230162491, 726512231, 375840766, 807546499, 779262391, 134550383, 824106613, 840396526, 642515174, 769212197, 382327582, 572392257, 764162825, 5356423, 660310138, 426853335, 604286623, 657593386, 644487739, 140580315, 630008926, 932170015, 603859469, 240088774, 340536370, 939665403, 574692827, 40233461, 184360366, 882596238, 38303608, 697547847, 774963316, 345992300, 481442306, 981955211, 346470797, 485484285, 790600201, 925565250, 432915431, 294174035, 142267970, 772358725, 79270072, 998174378, 661793737, 453729697, 372953586, 411040237, 998205445, 526515105, 493830325, 376242500, 985987692, 712157970, 966451541, 205668324, 532174403, 551510294, 280319592, 422115971, 455684669, 350578390, 661307341, 475273362, 640131505, 329547359, 886517420, 555458573, 295398621, 888648582, 169567184, 541319770, 674794654, 594101984, 151275035, 670226745, 821174012, 383699741, 266789925, 369022615, 326512765, 471915702, 967588307, 614676959, 869517085, 106403391, 219911863, 422237121, 664924787, 474709978, 542506655, 936681464, 267187356, 679452824, 672101119, 302757617, 956248286, 779672970, 963360627, 910263620, 789495317, 578008303, 901457133, 588680717, 123476193, 88506512, 625387182, 210865115, 385846723, 831853562, 156308950, 757894928, 10285143, 398308336, 58227833, 647273820, 823456365, 578611651, 455162579, 740309418, 961260759, 93099250, 812881510, 423539679, 315838226, 900701852, 813269543, 914620788, 886485417, 8355618, 261816331, 941665961, 102566642, 965793750, 258258069, 165631570, 521367492, 109270794, 594136948, 244325635, 528737628, 180851881, 928310919, 775669164, 532435437, 782860262, 240887206, 878108776, 591002822, 556518110, 554674508, 25574397, 33130788, 568476222, 570875717, 672320329, 380033675, 490711190, 595528208, 477923040, 625963405, 416810140, 759668195, 982628865, 597903677, 815885163, 682935135, 385705222, 377819595, 869378586, 804057212, 1443738, 680903151, 637905821, 237592558, 958557320, 241794154, 448916475, 13824206, 391592361, 362833983, 128550246, 22404422, 2194002, 804286143, 323901134, 501834099, 674180261, 704332434, 916084887, 230177525, 366934882, 887302069, 785288601, 841830520, 9815973, 976010707, 985712035, 348125218, 388200030, 781877540, 280279020, 718111446, 642473814, 482678630, 200929801, 112971363, 938080956, 920843701, 767081791, 662087211, 770609060, 446466829, 854486453, 7814498, 95907760, 866038314, 708674517, 641629417, 295236153, 54381684, 983421791, 583742178, 474817099, 342109907, 2425797, 360562603, 10306933, 414249418, 211575623, 605272203, 572541769, 580082489, 25330871, 571839772, 239200323, 999435641, 547028963, 428844717, 23836356, 51829671, 618960612, 272694882, 676362224, 246232905, 882285018, 867754285, 177838026, 478788080, 981251483, 272777350, 430868082, 126187137, 684123891, 26550500, 831709896, 687661283, 948307863, 650354961, 725930218, 944371429, 699746402, 412563626, 568649754, 771921651, 860155852, 627869223, 186829620, 728035628, 548454137, 988517192, 778619928, 378607234, 66251794, 719130140, 527528851, 493218967, 973423958, 419569129, 454743583, 989611892, 949546137, 587721960, 823704339, 309560512, 444863172, 108215488, 609324606, 406607639, 241430845, 565559610, 706109278, 319925729, 548340913, 719685644, 747166308, 690601194, 829542178, 220569099, 55987461, 16636597, 139638659, 662781588, 26712500, 607591210, 895826957, 995458579, 27421723, 524192166, 977886614, 865231078, 773724583, 506194733, 98569599, 627119647, 624789415, 187154948, 568250546, 495529822, 800152644, 695285240, 519813938, 803142748, 707450894, 988825313, 702476049, 453717325, 664405356, 301420597, 407993311, 663602591, 45901402, 196162965, 801500129, 148431556, 109628488, 622676288, 693579462, 888037293, 685623770, 474704984, 816424725, 452970730, 812726261, 381363331, 472630702, 843704578, 54046003, 802233087, 507744066, 563333356, 512701778, 260282107, 954745577, 953079450, 150436736, 922958067, 444025328, 641000571, 651545713, 498622077, 476077031, 835623132, 163608934, 612590875, 998941644, 609673603, 519710527, 3432132, 401369699, 674809500, 307978195, 722241146, 459755678, 461908346, 382360582, 317995340, 764893560, 692972832, 808358746, 785231503, 895490742, 520101242, 40231722, 994879130, 682971885, 668353731, 418370163, 419236828, 205026408, 4366788, 829203797, 331400916, 760685914, 115263625, 751389274, 565859090, 135454048, 226492950, 435188410, 714975154, 90923987, 630696974, 972133676, 354813170, 525034790, 168018670, 26283917, 39259121, 603648664, 804062042, 335631367, 564680914, 740047417, 839173230, 181048787, 145327457, 942111259, 791021261, 330931061, 246822993, 685595282, 843232839, 787355369, 374634573, 200061450, 153181746, 97882883, 569375700, 634854621, 289881441, 349627729, 938005907, 65596825, 390413233, 236615281, 374920281, 389678596, 265421057, 61402651, 251503415, 512470336, 584664066, 843384781, 213328272, 416941000, 573510769, 159660919, 736873121, 660478295, 913340116, 279998458, 605292229, 980132273, 509906745, 190639707, 350968311, 178850571, 389000375, 672642836, 260541758, 665982900, 380880284, 778330022, 392703272, 493256988, 417492716, 646232402, 824392003, 160523072, 864197518, 254580820, 30265365, 469159626, 38032345, 993372056, 548303506, 984519723, 611454487, 744317496, 675893095, 275326150, 458436278, 874174995, 909922047, 66076556, 421996951, 178355647, 658593120, 246388321, 918278123, 392499128, 400996734, 202689058, 192913079, 775991482, 249619894, 736849105, 705678807, 62787345, 373382739, 272586645, 76893016, 771487370, 922390233, 789819040, 697284840, 460859241, 240736950, 753986506, 48372673, 99582056, 502725432, 719133471, 817104912, 551535045, 669127915, 809576281, 814706991, 260314267, 926157853, 339586477, 862959113, 312011316, 424103529, 645300200, 529693224, 516358733, 990146754, 776894095, 22585035, 763348129, 568151251, 147524584, 765222198, 911922317, 654174957, 94543518, 619851524, 364581928, 227715056, 349756807, 787836204, 208366809, 360772998, 23429605, 49759275, 847732342, 768055716, 710721974, 534845538, 872546005, 865805025, 678579189, 206867950, 460887239, 269293419, 779510046, 25891893, 817590980, 481743698, 765104532, 881801357, 986022626, 907447863, 98229843, 123929447, 997393102, 304596386, 17611186, 614791376, 107798057, 394852199, 415130668, 921739069, 321463914, 648447442, 624734285, 837859495, 580202791, 800993703, 688133908, 1255893, 405521298, 888908195, 892803648, 494596436, 78009334, 188463172, 939304062, 793212530, 582256474, 827818629, 752025840, 403010727, 37622891, 952172219, 98404902, 319834576, 832073223, 753976947, 409300680, 35288571, 519340350, 898307112, 745943628, 255659303, 393923701, 596690686, 537583342, 332784638, 827665210, 606797284, 826836704, 54918626, 554984355, 326300940, 100011297, 859017412, 148358059, 767840834, 285561834, 915830796, 798785522, 433479485, 730947797, 364668038, 502111887, 635202740, 870640430, 801266516, 163641293, 298751608, 986645048, 792760986, 10875903, 998461614, 865337721, 623458288, 975057550, 712147276, 355125302, 770042664, 423174739, 795489579, 328814200, 986696585, 574023058, 709542966, 49864332, 782143420, 236533949, 220671953, 600666189, 263880207, 245246466, 867670106, 874733075, 552094510, 529811727, 407658745, 986637848, 936924422, 255260106, 483452488, 745599003, 141115053, 497630696, 961344784, 979831826, 973903369, 6668473, 943277252, 632364637, 843540836, 989112474, 455816415, 728625293, 592347132, 447705601, 190469503, 49895923, 826659252, 74661117, 794442809, 520822620, 345052784, 480406589, 632991628, 28975095, 521875039, 979586340, 11641157, 733107392, 887758130, 557213877, 58754269, 323486423, 656541983, 663941067, 960943881, 915551460, 526442767, 966654547, 134753192, 70897956, 43443896, 864848073, 54713139, 217985653, 344436388, 386974578, 296805041, 191587997, 975764487, 975948063, 147555908, 555707266, 840925810, 553404679, 214082328, 833544773, 533463048, 285455907, 925566041, 398395903, 112257578, 854834626, 960443358, 541712021, 980871347, 728468503, 209702017, 103312712, 33315614, 106621177, 48452194, 9614946, 913288846, 82987011, 189364265, 944711167, 815056848, 274837463, 584930225, 345470120, 864260097, 120845662, 214102295, 964026358, 297231345, 834361693, 191678425, 100864745, 948846752, 188660199, 430802041, 590496019, 500943760, 318547626, 814926229, 226381426, 813362606, 887480739, 200919103, 910685776, 116988528, 330641249, 733715108, 475673288, 677540422, 880418338, 155542251, 796874487, 248965369, 423169507, 635674161, 608731733, 190810821, 851445084, 878877836, 289378456, 336816617, 203635169, 720669920, 541308071, 992797518, 547887300, 212602329, 963240758, 876510268, 765935200, 100812815, 986672958, 304215932, 610860453, 147399364, 590116871, 312775000, 962874857, 977820994, 935859437, 223986414, 157922337, 838421819, 706837420, 882425368, 78023137, 54388551, 274985835, 1861740, 95712756, 736338248, 298082276, 979837457, 193013561, 227861083, 645309958, 138156871, 212317383, 898618983, 563912204, 764886449, 554143350, 66283979, 798509899, 949246730, 948303478, 868907288, 219389679, 333356239, 161849975, 684050762, 591834566, 377539394, 981328956, 410944566, 828703321, 905590438, 214312799, 415549672, 607864788, 65069422, 245780170, 724100939, 488702788, 498123758, 536772704, 562932148, 483234385, 576977395, 423438047, 267828003, 898087116, 301973176, 790528152, 962030035, 243027923, 622150991, 513140662, 417078715, 786756884, 415998391, 225576881, 770387183, 676101358, 475640925, 101294198, 259800916, 915165127, 389240627, 531099402, 675922998, 581681148, 919035815, 503369717, 638423422, 5785498, 829250868, 907071075, 866967087, 277607716, 6972808, 667578819, 144094636, 380998392, 855127864, 893608065, 217906399, 507967568, 838855290, 813474909, 810508739, 306712811, 708763190, 152364837, 978165917, 31906489, 965879064, 424663516, 581624439, 564958002, 124107139, 957103460, 38027917, 217858771, 911887242, 880579857, 122799951, 551390044, 687554167, 197877058, 766890689, 601641737, 318706272, 847224045, 666858929, 638560832, 106354843, 737395181, 139781531, 611691634, 813241934, 815124127, 569986003, 789328370, 343958601, 255726614, 469045393, 227999246, 503359201, 755128897, 622993766, 92617516, 422918308, 185676524, 97535085, 649499602, 170346705, 122602701, 229294161, 414942191, 961023189, 158164539, 930068631, 565452938, 285518103, 173642589, 742529365, 637855686, 929240141, 461576567, 877023987, 244868298, 547525915, 834301637, 477326805, 898482776, 22577283, 16082841, 896089270, 866361883, 340317565, 939038324, 238824173, 976066480, 95713623, 700865159, 37142621, 941217109, 938908417, 139902585, 193317798, 87324372, 502681980, 127874736, 794307876, 258848596, 166363514, 799870645, 398953957, 529868673, 194728010, 122228262, 804688920, 261381270, 338855871, 644111914, 822884627, 713831609, 488701769, 601630093, 480590164, 570197981, 798415577, 79357556, 755289431, 380888258, 777047750, 782643222, 442372953, 487025001, 686744149, 514658689, 849636108, 230014997, 546201414, 326506492, 539770622, 84770201, 321878666, 170443352, 925580867, 240889282, 201015956, 766261232, 29986947, 734046313, 462366405, 33151445, 86775833, 950552220, 755277334, 97186584, 78312780, 118873759, 692718639, 985712350, 41066215, 473728060, 159715754, 788940299, 709000424, 71582709, 520056875, 125877249, 57688351, 379625150, 235570764, 666313457, 40807502, 972318718, 895160400, 523217830, 730255268, 384355610, 504176362, 614994686, 849642096, 639734415, 696809274, 786851876, 451063351, 946060886, 146935787, 519086381, 78801164, 443067820, 242066332, 499157485, 326324256, 32992621, 7953353, 320630932, 253400554, 322690995, 662012134, 87947331, 726526345, 958103938, 567934800, 425935193, 549290275, 206431781, 197770582, 533926445, 607246411, 725138652, 929260966, 693494719, 145309818, 276955039, 145010517, 458618977, 181097357, 40512490, 586403223, 378251383, 651887559, 867858472, 503547161, 366019988, 760675367, 368676507, 93327094, 736617727, 876129877, 27297101, 139420593, 625578983, 540930444, 809485974, 654005795, 82292350, 450432549, 674541577, 911794490, 332571396, 838099209, 287520912, 782077878, 280057433, 309498166, 23710022, 709985652, 948469518, 775403548, 849280655, 723796008, 498888799, 495684451, 670803188, 33697044, 421798224, 487498597, 58219322, 851552835, 758997627, 944145271, 556872887, 747122854, 601630845, 252099652, 81286220, 29631588, 297284187, 497285155, 786711598, 863063090, 253378008, 459638271, 468966633, 17312884, 951539122, 517815364, 615501899, 850091861, 559079735, 845695154, 726055112, 865577506, 559014397, 272667393, 565635803, 9853341, 763444547, 452391582, 366109201, 236565644, 232316889, 748387642, 563652610, 575613276, 167584826, 329708825, 687715416, 378865889, 916499234, 699759742, 320580846, 165971427, 226355470, 224735327, 121433832, 614307451, 238541903, 927627042, 186797919, 684361390, 35464651, 430833825, 783581570, 337061314, 522607549, 142132555, 379114783, 990471847, 808912560, 611918480, 330600683, 21234491, 350712530, 778913893, 967280616, 855734658, 324548749, 870556228, 420197896, 53800612, 828088, 824204189, 811123696, 506863704, 804443720, 42174952, 387825387, 572663957, 383451458, 328417072, 230492622, 228010066, 654984966, 174983216, 922079206, 616498159, 907923003, 327221588, 171503696, 737326156, 739810387, 39938463, 646569203, 463888042, 830093418, 642334844, 192313580, 23922013, 714056634, 721902477, 428235293, 414760668, 281983275, 817736608, 928221422, 845668582, 691070599, 122838403, 893164508, 80787564, 767385515, 624159200, 495525668, 328294802, 725635671, 842989559, 422866939, 556172025, 966828769, 767791463, 152326458, 188579968, 402763672, 646430788, 782704072, 679376341, 866847535, 384390608, 41291573, 53851809, 249711977, 419575093, 850081615, 190168000, 957652727, 139689497, 1064396, 629253658, 879262395, 422321401, 982849440, 906039831, 715260438, 18936447, 462076070, 290789587, 493050298, 913968070, 386098798, 595148331, 241688790, 673381503, 817032878, 704138207, 314122090, 121137775, 149028957, 879535142, 741808021, 648199104, 814706309, 116260807, 866282352, 35236427, 865604732, 95742664, 455669005, 50235066, 744204518, 171840895, 960998364, 248863202, 922350415, 760046326, 905930951, 258607109, 257495211, 434080764, 174156966, 105472170, 109991879, 198550094, 916877329, 389724120, 780605062, 379443288, 525081999, 285723360, 881750844, 532816593, 677525414, 271553449, 462418404, 197834284, 693420048, 61492497, 102606117, 809646484, 927327829, 543412243, 986059099, 154245065, 391404752, 442345896, 52691084, 383319278, 11986590, 122174724, 625375773, 242668713, 736997739, 320591566, 667598661, 307206721, 422286031, 527672224, 226373294, 233536102, 476714810, 547358036, 735924764, 400697928, 194140183, 413825631, 876774157, 242103457, 288336704, 381832063, 555640086, 908114686, 423620204, 911176414, 810676659, 274249233, 76720805, 31329405, 107000757, 24407242, 558253585, 441943574, 889382866, 877562889, 499895250, 478102010, 841509057, 479622910, 546994542, 66817755, 333184598, 698459824, 618487713, 859269565, 612409731, 465343997, 753001124, 853246811, 352989471, 35107728, 488123463, 151320123, 321485733, 319254217, 135707147, 929794763, 162428122, 661146125, 999243134, 87568252, 918902555, 490468360, 372024767, 823778583, 859631060, 401340230, 77584882, 313559573, 229941760, 722250000, 205595744, 735213301, 298164562, 37674617, 208289784, 28604263, 339242318, 835801459, 142676941, 550430301, 903152360, 120066760, 807944089, 244495806, 313674015, 90916170, 349942374, 312771201, 775592590, 687980531, 857232273, 455052038, 559435187, 900789778, 123519132, 43941696, 131399198, 892768131, 967411032, 626108545, 72163062, 934995386, 819494503, 541983399, 484936249, 498919353, 141225369, 84366100, 316719197, 852323492, 359894535, 775158839, 629105944, 857600283, 819417402, 614902874, 291834479, 70518155, 417529988, 489997896, 320989866, 513372533, 202604486, 934248233, 37847941, 190808057, 339771481, 337758405, 356302248, 94161991, 750883933, 63159729, 736843567, 165822626, 261885259, 214710350, 348320527, 964562975, 711585374, 118292794, 205675995, 854299582, 62586230, 147023918, 86665691, 416220752, 120317978, 494169205, 419917749, 245236600, 500240872, 902547051, 316578427, 805861556, 833360993, 351560444, 315951211, 943245691, 287573668, 648654613, 10800219, 437597351, 915255226, 502360059, 588368086, 788028382, 944304302, 36929408, 374136172, 226592613, 79989259, 912778711, 716923951, 109291066, 728795455, 766132267, 214436593, 923523579, 217280720, 290485915, 548856086, 138620046, 451916355, 597428677, 652062267, 189304431, 665020551, 365480329, 823013586, 356081313, 798635093, 526375831, 722883440, 759192418, 407299383, 835909127, 724811231, 461103924, 415816699, 595648564, 138271135, 923964106, 962712714, 988800738, 653163769, 148565192, 579998962, 34023304, 797402264, 392191132, 567254082, 995624163, 568537197, 564717799, 692891299, 917895886, 844230272, 705591478, 130496303, 592664446, 870456472, 737489585, 702013364, 477722306, 762161048, 517906640, 564025648, 974120727, 402356779, 217839260, 916892473, 459099589, 103835563, 695456760, 596094253, 828106447, 259483982, 267172317, 703794129, 80640975, 113347834, 276497326, 929456241, 497103819, 612782878, 690242583, 239784337, 241525997, 173180873, 633012219, 643552444, 925695159, 114054579, 231061640, 611786252, 699362065, 88746995, 136585737, 12129639, 309003565, 179787539, 440206846, 791751346, 147043186, 288936985, 125704101, 655513505, 781096709, 108801989, 775170132, 211391089, 889636215, 643354784, 56714307, 339916061, 7722600, 711860522, 919334061, 580647167, 797443626, 301322827, 346833053, 535003642, 71271742, 741855400, 350840912, 255195796, 547619515, 959642855, 542071477, 724097110, 602671, 138226024, 573224188, 472737874, 411641944, 717135368, 128870604, 105235212, 379780199, 746324337, 147045508, 975448399, 238497902, 129111871, 265164280, 271949664, 780399536, 350589394, 620160235, 34411021, 662879770, 477681652, 256181912, 909077169, 188491730, 172038775, 27358940, 712259695, 125131894, 396984517, 187372775, 888063212, 12364207, 392288185, 906354937, 77157975, 116619903, 622181009, 198372732, 102124894, 877142847, 973911450, 865242101, 569329798, 548955178, 67495006, 129334816, 703239876, 756246925, 478596240, 885748731, 502621435, 491028998, 727290738, 377913408, 360121283, 617654894, 121499033, 979397904, 507015563, 630597011, 359763421, 254080439, 861054002, 394498821, 512023604, 796383640, 419275252, 116965415, 542252596, 487131189, 617237971, 334572508, 258726508, 899484692, 78945810, 408096578, 310470211, 180542849, 458339433, 572557489, 566645650, 295341634, 289061185, 815035800, 761835505, 61381328, 466040131, 230417443, 173936988, 559041218, 620585452, 826306690, 306155423, 543435636, 954095006, 987230276, 564760082, 911752923, 859362090, 51266288, 54067858, 827560017, 72708740, 506120533, 619550338, 168430049, 812135753, 428485346, 370453493, 675082504, 199313936, 693508929, 670200559, 633376622, 319470212, 588541901, 545249269, 507788937, 41391625, 34553949, 39797587, 212456537, 742776840, 817730082, 653625764, 293499787, 14313351, 574272578, 228632796, 159246675, 95623860, 974983783, 898588773, 585377517, 912271734, 554396352, 9682858, 169687534, 83782203, 253440068, 444745817, 506254167, 404574921, 659096161, 136663059, 924925865, 85614407, 389413435, 23864600, 608011772, 58493978, 965072856, 528530193, 520132953, 894338021, 444298251, 127856761, 333729319, 655639688, 452855022, 979459631, 454661271, 612271891, 563795593, 896960635, 621868509, 343748383, 431976881, 216106294, 616724479, 847357602, 989047522, 787183926, 204374839, 957853780, 166983949, 405926439, 70150636, 62527053, 244302680, 885723095, 381939783, 798986930, 936739382, 893718443, 562763934, 478010712, 636796179, 488339143, 341888600, 443860046, 931131613, 617002094, 592376781, 48899887, 217879704, 23399533, 283577860, 926954715, 437073821, 350247565, 851933378, 992717992, 441718631, 851458025, 803746119, 624061133, 115408901, 478148579, 806218694, 875468874, 381751467, 820290517, 969480522, 580243374, 162099001, 709480220, 550149881, 310504545, 541890691, 795683504, 842495683, 670500014, 126531678, 469664792, 870754724, 812006659, 108680291, 754837793, 553421992, 999182979, 651373644, 308593472, 535411486, 356740980, 497294253, 689755913, 851982949, 475352594, 870138653, 683111345, 853503118, 595560460, 474890984, 164186560, 548230082, 902092201, 763145744, 43506904, 448637832, 43153161, 511026364, 703448459, 493409603, 384281091, 588468685, 672033076, 876599979, 282993576, 455804948, 196835651, 560869177, 152793328, 603526248, 758102352, 921441343, 369519847, 700174033, 208035536, 909252264, 364191606, 801578485, 455900972, 476057118, 680953409, 726541595, 348873111, 832731410, 667520030, 648695810, 110453065, 194815215, 472663689, 839418986, 507601325, 240046413, 958017687, 116894543, 277174496, 756572040, 237229001, 217053304, 390462701, 179784178, 897420760, 716301022, 234107416, 169659440, 329817396, 351393602, 522417970, 729706116, 962230331, 229772750, 310618836, 239316288, 66203611, 920481514, 924737022, 631947834, 152566202, 288180150, 901203137, 943435169, 625369250, 413721048, 41017780, 493398937, 371961917, 482485702, 913337128, 220395237, 930198682, 551988816, 420709616, 111954984, 538756478, 380669704, 413529900, 743728109, 777102121, 299981138, 849775456, 671628083, 849432935, 500687806, 488463696, 539471236, 818718308, 27817992, 372052246, 587611024, 459498248, 832720603, 891657802, 675171047, 18426903, 957283412, 273053304, 490958444, 37948473, 849240063, 770387015, 611608306, 932849725, 766254054, 407599198, 592720555, 730908353, 159980995, 309436713, 193231766, 782525853, 141695096, 150181579, 913000441, 137161750, 646752950, 517747067, 364220926, 350423732, 286707716, 125233328, 394241398, 847100140, 241201487, 635477748, 560281826, 365522231, 237645808, 140119622, 38401147, 958841630, 821668257, 477315585, 445643567, 627758738, 796442814, 815948274, 26005777, 90585258, 743666984, 196722774, 34377758, 610371405, 246331335, 510626505, 171616536, 308927519, 664231342, 534251410, 486296339, 330013737, 276244022, 967220688, 683387858, 273670556, 507492921, 8578337, 536991220, 657084109, 636072768, 205069666, 265522764, 261525894, 111244603, 535203194, 65483473, 925908713, 698418001, 400576052, 562020714, 911487236, 401416964, 700849751, 433918771, 421656613, 947854481, 587807061, 696434345, 513690693, 317849379, 652123543, 749959057, 140624536, 325502777, 417576089, 775390017, 743964257, 814160379, 540831038, 38092937, 988767342, 117723322, 802365440, 312759818, 892155656, 437809138, 145265202, 169428646, 433047381, 509696599, 507874671, 624081182, 927003194, 746360060, 700115728, 74019089, 547631865, 36227078, 245558773, 273764611, 786799171, 191769965, 389496025, 392750400, 3357185, 548933718, 949567502, 126709391, 404081995, 547624746, 861846058, 870529283, 64110928, 562556171, 932740300, 872594707, 103635919, 452443939, 133733109, 401958517, 699612559, 726474080, 364366424, 657259926, 248837692, 126277606, 353908389, 864444456, 559877750, 217986823, 377299505, 612657292, 679695906, 136058272, 266264593, 318121251, 3095694, 938278718, 215371112, 355991447, 666530562, 976209150, 381865671, 778235737, 994874853, 115357403, 770879061, 768822507, 758825707, 759759531, 695609207, 319016216, 902150404, 286135106, 307405415, 292592529, 433355917, 902045990, 738199055, 841688958, 527710457, 643813989, 93896013, 897224854, 569235446, 354058681, 847517554, 53867014, 737271469, 861355623, 367115379, 268636784, 595132314, 327958624, 687086328, 94285594, 272864407, 230968061, 416691687, 698929187, 943243637, 132512226, 397318089, 481157307, 779771358, 168381984, 348774416, 859129876, 79257495, 201203626, 49457042, 618890800, 925324316, 443646392, 793557855, 219205409, 103046644, 209185343, 293725162, 859775532, 131201064, 472920439, 451136667, 500852240, 712328951, 942180436, 279157601, 763612339, 670514686, 905903651, 163464030, 940518949, 425342920, 704241530, 631735045, 372109108, 386586500, 907707624, 711717230, 500915287, 570195214, 309355582, 965536261, 307099233, 86911356, 191830559, 697198926, 910401055, 865480651, 888431153, 407746478, 484677823, 375150703, 113508168, 527421130, 593967231, 553010933, 124444783, 476360660, 274692602, 170727338, 330759462, 610527662, 41797936, 312437034, 508381973, 578269209, 118297366, 215643241, 425818655, 642332069, 773515274, 693490404, 741845701, 473526061, 938365343, 482045533, 125009124, 88704191, 335506970, 535407923, 6075861, 170651434, 688437593, 523880292, 351684680, 6826995, 917319515, 866733838, 721346798, 531158412, 856690537, 334848090, 587183891, 75859869, 809534700, 890256961, 3006612, 492568691, 373216975, 917453325, 884933105, 524640368, 192789870, 433708876, 772997794, 697623436, 553360259, 15279599, 664741667, 524920648, 411816161, 689173907, 851050333, 752446423, 557291905, 742509296, 61318186, 436920124, 900586096, 145955538, 349474025, 709649397, 532670961, 911556482, 56387062, 244131359, 842013807, 309489161, 265850012, 764240206, 29490590, 68415578, 664059029, 528230275, 124433704, 179220462, 471277207, 713962112, 485279636, 143368999, 549320465, 2964596, 987986052, 942217414, 526038227, 230864240, 725908299, 537897498, 391643383, 744689028, 64260034, 484128862, 634538202, 374295010, 243266824, 957151141, 4101106, 377458645, 648055003, 646918461, 950932514, 775434441, 722295017, 865659986, 777674129, 692302608, 267565891, 219202528, 806834592, 101207218, 107654936, 200540688, 987581851, 429542210, 286079393, 886006370, 634516143, 284109948, 377684990, 601959508, 975200928, 837227976, 449278608, 438443520, 631809634, 202442488, 457604377, 890211864, 184493339, 436612337, 621145375, 429294278, 391556471, 229452203, 884928160, 437258338, 34986590, 33670648, 79024673, 236654469, 924590565, 555568674, 96643904, 130203947, 145167335, 801680992, 603056135, 568333462, 300394056, 510514598, 737254580, 304618625, 257967521, 67166485, 867176818, 34475244, 861153761, 55765183, 268540413, 543874532, 881504862, 470192930, 185556080, 309267114, 448238702, 680048995, 16708699, 42628606, 142745040, 933105352, 10281231, 381135288, 869439229, 477933906, 243968771, 122879857, 674342944, 971748431, 988113704, 253195124, 623495611, 823498974, 935801736, 422403278, 599209762, 537610010, 56864596, 182112936, 273593387, 634235646, 507445051, 712395222, 966866157, 765648052, 144129859, 200854159, 747491930, 212558632, 637139318, 686555950, 413141794, 962517142, 949165078, 819439182, 150639851, 277591722, 906315698, 632817941, 582575674, 554819072, 182574896, 903443142, 842906827, 242893514, 907908024, 623180756, 589205595, 151050815, 496694221, 984602, 655009014, 624305091, 52264379, 422041230, 127201346, 994222425, 449747683, 556057628, 159063474, 535329491, 528033238, 582195574, 295259580, 994214701, 310906879, 897530658, 778378512, 732071274, 570030938, 1012433, 140000553, 150354523, 250652926, 907166792, 960772093, 667775572, 54669452, 626514018, 629265599, 371824876, 710651040, 181372821, 365242629, 531079081, 919635196, 145128147, 408690686, 28992983, 177744252, 706358808, 740886712, 57952833, 314906178, 627285496, 344957515, 677385495, 64023524, 200613806, 170676045, 518819028, 865697192, 199095909, 454851631, 58907865, 912242922, 819231949, 402664609, 928345145, 261001402, 804648785, 977741970, 165074230, 38203740, 122833768, 564363851, 202095793, 793296325, 973925366, 257781698, 120055417, 977291917, 658380607, 799020361, 418303226, 35835400, 613463685, 38755535, 379528546, 196116905, 993398493, 901237416, 461122895, 514026951, 192079331, 250750113, 909017822, 790216969, 210583730, 338096081, 688242863, 511559569, 373377916, 700310316, 804458417, 263341090, 47465981, 419087574, 704248227, 289797711, 310722219, 354568930, 848771668, 695624895, 338953118, 978179949, 178385617, 295519388, 959206770, 906001197, 858292839, 25150707, 391937557, 253033549, 561229041, 817228764, 995085142, 506940172, 836739055, 269107482, 598367118, 81363363, 669730522, 949620997, 872028394, 940792608, 527259440, 846976149, 472293506, 938305540, 529705996, 380762713, 305222626, 145946246, 81121442, 548276203, 311246707, 135309225, 231083487, 119908703, 325679596, 430323433, 39631093, 382081138, 577695279, 374273864, 615755360, 669703962, 924042207, 879713010, 198796144, 818526955, 198672406, 757265791, 132099298, 567864638, 557987517, 939316025, 706568268, 918693990, 803328473, 22001981, 897775779, 363117328, 417296485, 668345605, 224180059, 993018741, 151535593, 799078773, 838471730, 787869229, 769186612, 336582630, 804979899, 631002984, 272476926, 614680509, 544892391, 244473111, 5807563, 272587234, 60260594, 437328085, 976834682, 341678633, 401687690, 771596655, 648180827, 74538310, 547373533, 778856786, 917437772, 10270493, 217215597, 98938118, 82156432, 890743747, 645536881, 371293047, 835660465, 823138829, 774654146, 450629266, 313205201, 442483959, 722995063, 495850503, 240703343, 80902578, 222260904, 274780779, 339547380, 82958272, 627855054, 84688124, 386008861, 263579751, 314297020, 659335356, 234700627, 791005294, 261959552, 370271407, 524470058, 603961650, 643575309, 392494040, 38706442, 493671790, 136754052, 179870595, 215228773, 91432547, 421458032, 638516422, 198130026, 805522738, 235475575, 46709196, 316994878, 497101649, 998366423, 54224570, 340446709, 250824053, 178361364, 790011876, 835007497, 195005384, 572632299, 714628395, 102718781, 915845672, 930396626, 404382004, 457173026, 619476492, 159527487, 732954449, 997579371, 192402050, 770392180, 964903657, 473112735, 403232621, 951096584, 787989649, 829140076, 768706827, 407693179, 623443887, 41425497, 633028856, 90345214, 425324896, 933717278, 980168455, 876660850, 165219377, 492119967, 400311930, 691372748, 385104200, 761108722, 914330073, 498398758, 11499341, 459038112, 675276042, 300613374, 661187369, 977273721, 748102067, 979706868, 856191514, 379897898, 144369242, 670223168, 148690807, 697157264, 199561642, 760972246, 379922509, 431505137, 635349350, 968194000, 235792459, 472271392, 905158486, 20298148, 174185302, 72125918, 398193723, 232231114, 836601522, 553065964, 682196304, 254519776, 680130451, 547189058, 622758225, 185609994, 482685688, 423005333, 184282157, 877484978, 522114259, 582191325, 293340157, 151467117, 941158506, 879270917, 452651468, 856849482, 691405409, 470298394, 62664972, 704226512, 729794597, 730411862, 658471502, 149084095, 46988283, 241336618, 553287119, 180455744, 383860988, 592502829, 570500671, 321846011, 488635457, 590156184, 255008210, 894537254, 477928104, 379785545, 484919935, 307260575, 111452506, 828529532, 272312797, 732448672, 232817963, 446579928, 708324227, 233591457, 160765368, 813033073, 873263577, 863454870, 500195314, 201433508, 601240887, 842573216, 144976311, 917002046, 127503934, 945077224, 718220952, 162096398, 269683551, 204316109, 881376191, 54245869, 93222699, 25087568, 827413983, 576662598, 17263141, 371811766, 262493407, 909042663, 747837751, 704521804, 471790274, 908229879, 80523006, 428426928, 98913947, 107209837, 105780430, 443377613, 420863481, 331803222, 84184878, 248857273, 356057855, 394531466, 344676217, 152280436, 418185869, 963511716, 161736759, 578570487, 711138846, 946061909, 786665214, 397946371, 414561113, 933777776, 405174850, 131170431, 624518107, 627738910, 709347608, 280902129, 219088504, 693911528, 168410613, 302596487, 355517264, 938234128, 417743997, 99580155, 520722397, 316664261, 481000196, 275600704, 591623007, 817762099, 659893796, 847147668, 980164577, 417690235, 790406225, 164989223, 489174918, 392027489, 148301205, 792798815, 770289744, 93139632, 366317161, 906278870, 908918420, 198039586, 964309546, 477651081, 672797094, 804337466, 380207894, 995118831, 790578229, 215036990, 291376348, 70232087, 404832291, 579131105, 992986037, 556400472, 719745801, 811258206, 617420020, 670109630, 882507666, 412818417, 932205130, 370066396, 677311770, 543273866, 534042305, 631061646, 209156338, 843837596, 994581489, 931875073, 566159412, 377006714, 907512956, 119526649, 276953459, 448327376, 506406863, 389924605, 4141303, 153785542, 983609501, 636148858, 254700294, 125522284, 967691365, 708501969, 545666902, 985804986, 390201731, 762239773, 33109248, 755768577, 310768973, 539842790, 472944359, 948549686, 235365662, 409388477, 275144027, 686440594, 506752561, 162736071, 22564093, 943003130, 106493374, 572591291, 995018301, 261316432, 604609793, 103376377, 288924154, 513574667, 332510441, 349448946, 208535595, 512186865, 720543467, 383956300, 299792000, 229100704, 369931459, 458764228, 537318893, 977348882, 983804088, 443947015, 475258124, 140199483, 257149490, 187244859, 64174656, 392720139, 514654112, 370543112, 998156105, 39836136, 370750450, 244618709, 224682417, 765953909, 794942304, 16595811, 841621248, 816804409, 149694771, 564230744, 872319349, 616037948, 155588193, 238369156, 47138597, 966004228, 955931147, 818523234, 342402372, 8952220, 767771315, 703917343, 262666951, 948387318, 7243331, 976471315, 599192208, 743950845, 344616711, 125262362, 162076295, 841703595, 774080263, 478754609, 816882935, 366233984, 694623456, 13022653, 961600682, 299052818, 660973237, 883602842, 463353996, 510193591, 877699980, 558698729, 151137759, 822575543, 284597188, 249773551, 402969535, 10284937, 622828530, 659587043, 489197048, 851731959, 733972396, 854524277, 885522489, 141391623, 346683879, 312542407, 959046396, 704466691, 324270869, 98045178, 115404315, 741946007, 655240048, 615302962, 219972488, 994811179, 193470448, 625681075, 902460120, 141576354, 383482407, 186148238, 886191009, 629852243, 519614382, 999683643, 758368080, 689173065, 362680258, 467475142, 826035006, 939034169, 284562256, 673273749, 817138567, 368256613, 818391553, 179456141, 530607955, 620021163, 763854126, 539194109, 271148137, 702802736, 624173371, 796926853, 607275346, 259799947, 264973618, 954704439, 796688899, 856398578, 942848404, 719192113, 986351441, 316391830, 315457714, 403940058, 728865802, 2196223, 492765390, 22255307, 381343874, 854908835, 385568806, 829115446, 794073940, 249770985, 395056040, 904953017, 754766394, 635852769, 148567718, 909158926, 132686479, 623286785, 786268131, 200761353, 473211571, 137390724, 978373245, 385961828, 986692747, 602608320, 561185916, 533355363, 314806641, 105166607, 334040333, 544528758, 672919958, 917856755, 872113222, 251452154, 6228258, 329629478, 220844113, 27539862, 935648014, 813160133, 488907418, 465019738, 477349147, 224244668, 246895307, 853407198, 442268108, 298835024, 655108392, 969439994, 76657411, 174292498, 682851942, 298083500, 749430587, 741056464, 100195129, 577400748, 278434131, 74590207, 686253071, 284064146, 816298385, 743575041, 774618362, 685643550, 232010034, 783268998, 820654525, 115647599, 196633955, 375711091, 763111377, 173194738, 580320507, 793632086, 91609947, 717873845, 406078786, 246690533, 687939219, 653721463, 243421094, 340547932, 129611459, 10048646, 636960631, 460101482, 120596911, 704610489, 751516390, 712362105, 563721097, 692663427, 648097071, 439601535, 429941374, 298396713, 84845955, 597134922, 936483350, 731729960, 907263662, 477116190, 283249677, 489523760, 92408717, 86112596, 729933638, 698727843, 184471122, 927134354, 479933016, 749980635, 601376950, 584220761, 841302520, 915732678, 526389859, 994450779, 989682694, 204882683, 109254603, 345677684, 410081095, 258773947, 665605292, 187794619, 990244386, 431413964, 95828086, 731860440, 861687396, 202851879, 216989214, 113508392, 371762678, 198877925, 526047360, 923630677, 533456694, 828555670, 629977934, 311759151, 457728922, 526913441, 558898717, 988891726, 242164867, 189763839, 854860168, 772855832, 222213666, 302325218, 587202957, 378870588, 984030459, 61694872, 138540844, 640447419, 981936981, 874513735, 689274409, 762475763, 229876654, 854701370, 283295554, 921156638, 225678778, 971526245, 627960024, 982222279, 712619792, 513001514, 307747357, 486480367, 457835158, 878379780, 627858558, 337032180, 796921418, 856510783, 144735953, 196511530, 697372383, 928276694, 295197914, 93509075, 250768763, 16252112, 678924454, 849519939, 103497753, 731442290, 403927481, 839687717, 414455711, 420646731, 991893813, 123205155, 180733716, 197223627, 562242395, 16637329, 453868560, 576061198, 949604136, 753312812, 437132632, 545639952, 488189496, 331870373, 865189710, 751005912, 455160418, 551848718, 444082883, 98934828, 396817328, 566957406, 323085302, 888394987, 292322716, 430782360, 905830360, 58248846, 447066744, 334232472, 181704330, 143441631, 784245012, 891315450, 742167590, 987570133, 239387420, 608556354, 434569047, 308354945, 396522805, 848797459, 158484119, 934060383, 508243013, 680161276, 449644659, 69942391, 748907665, 543271482, 854971520, 173916675, 692895441, 595877387, 668483108, 429265054, 112270576, 24812748, 983132403, 811947186, 684876506, 207194602, 961107799, 674093830, 719749750, 295617773, 820154035, 651273289, 402958609, 948011113, 67205510, 201138422, 13346869, 110673197, 727046377, 515603057, 859609370, 871571992, 474095033, 737588710, 471318855, 486017384, 813167303, 684044941, 123782461, 767355345, 812719300, 32859002, 499239285, 922380768, 442443688, 374675830, 934104989, 371067379, 580324697, 579084593, 587152305, 958470297, 127146869, 430890792, 52661130, 425451182, 166609132, 944434280, 871543966, 915159512, 471887560, 961700917, 609502602, 236966940, 721239651, 748401722, 240345137, 59675838, 615725677, 693379350, 460943603, 889043495, 844392531, 112403710, 735272472, 245486437, 687610531, 898280073, 624361618, 692989567, 162399257, 771770082, 651667886, 771699910, 668864043, 763375006, 788457805, 176633228, 592450264, 283148865, 90859862, 743292132, 658388056, 555260152, 259924483, 312323737, 612961491, 496144951, 992463105, 458973597, 87766643, 661688126, 788297175, 644608429, 474875752, 3838493, 259916863, 520188593, 355431931, 411152904, 951650391, 168984165, 980164060, 287890728, 160584948, 566162535, 937895650, 196933085, 51745210, 531495726, 323122580, 705391282, 923592778, 926712137, 876942504, 669640945, 629021155, 894873140, 706540899, 782893283, 609915611, 470137253, 999733002, 834909421, 537437405, 52718132, 505794394, 293858305, 631585244, 42087772, 334036478, 899074733, 586513553, 712293817, 327073126, 9557827, 944466424, 345154868, 163933021, 42330511, 67018783, 749541318, 303666341, 65511624, 642747901, 267010077, 551686562, 971559022, 942527117, 260411438, 410655270, 213354587, 579726575, 835058990, 298492669, 989044796, 827471887, 419345520, 27985670, 384045602, 603175238, 752682859, 179881850, 648960273, 71362918, 594444914, 628368598, 248852177, 399185377, 66266810, 926191704, 54865363, 54038273, 872468706, 250004701, 291219393, 658401282, 271191067, 988720372, 69328958, 637462965, 713361862, 472856061, 788807370, 552651437, 929998962, 420243167, 370620256, 383092005, 991947249, 366416578, 544494224, 420295317, 646566696, 258998609, 857941989, 399694753, 564737130, 467818477, 28638678, 264028838, 257932714, 239604318, 76671999, 551624228, 475544860, 988432324, 261744218, 377676822, 161825659, 448160699, 112277627, 323698377, 607784834, 390125950, 955221087, 411485925, 308021255, 802849981, 891693414, 557596938, 406320847, 923819450, 944718499, 634304583, 745312396, 666542841, 562335378, 584488944, 520834917, 412923802, 590344907, 570699105, 825841448, 208859617, 111788451, 675894773, 528068095, 119418565, 13506823, 279869857, 856229097, 984624845, 475463130, 158977836, 245068742, 610969195, 758864401, 310836092, 992369572, 92733509, 113789287, 984700591, 425864737, 393094470, 131550616, 890802456, 798688213, 396589265, 919208837, 878652923, 410327134, 101209858, 40694890, 958246381, 40521317, 548245795, 513327171, 398812950, 87958728, 464215263, 917531537, 225929928, 761983705, 165076425, 545600080, 780588963, 373777020, 519219936, 828414498, 762059067, 581028113, 948964172, 605474794, 426140101, 786364883, 136368497, 596496481, 99168981, 247696445, 619533363, 997444231, 502104211, 566879803, 472842217, 619485130, 832045627, 35782182, 409853299, 225167618, 710091260, 71388759, 373569251, 100750507, 289133791, 373888127, 502432765, 400583143, 789550069, 982182503, 542481466, 477902778, 273806463, 42135570, 593546592, 258792252, 861586965, 894045388, 342491109, 404142965, 201397841, 395897552, 640340921, 620080315, 228949049, 690571177, 595332387, 427569900, 283637688, 453116747, 205842964, 622757045, 735678268, 61867624, 21547150, 686385253, 582423063, 435202914, 210034354, 746373575, 848038902, 427172928, 309389480, 755385214, 40960910, 850068860, 556410518, 105596571, 407090370, 372769889, 89023768, 47364063, 48476343, 766908248, 305847423, 174219409, 711333098, 602501496, 509335010, 218688308, 110461693, 909845794, 215966336, 27325306, 693820321, 117159632, 759178646, 239295239, 584082972, 295821453, 704879582, 774140878, 655282448, 281028632, 817928550, 357464886, 728274439, 533121703, 537043332, 749509025, 68574531, 637638094, 388520325, 185698742, 367730700, 557000959, 617008362, 116524322, 825870159, 399808467, 953594973, 101876665, 18195154, 885869138, 887459767, 734551159, 8340541, 251122010, 844702127, 833768501, 674611049, 755334193, 197829874, 829660175, 652192938, 506875757, 54737528, 178057562, 672613625, 603347362, 943526950, 935732192, 100296779, 661221538, 512840127, 246210919, 72298018, 828827622, 157961415, 562121762, 585805772, 798429003, 129146152, 799775280, 149881565, 745610314, 284744453, 671076764, 242245659, 623470560, 809428512, 66572798, 525776788, 654624996, 397895684, 323191354, 14621279, 877971562, 731050990, 463256257, 135723126, 628274192, 339591674, 332645971, 193689287, 781678977, 979026203, 613634407, 541072426, 300004921, 189535089, 295482940, 810455545, 394958842, 678639809, 193060741, 302935453, 658337344, 300471466, 693243812, 942081915, 57102651, 895501638, 209713727, 691667366, 340631324, 764992164, 277249656, 771100169, 110889680, 158891163, 230731257, 827535088, 228001038, 427995910, 188956156, 704336647, 629237093, 295278889, 22669613, 241311988, 148450181, 395863323, 670267592, 606896584, 845657279, 490778016, 991338810, 3449521, 742634777, 351711837, 152384548, 286398626, 608939438, 13784161, 269371161, 894554678, 509185991, 675970225, 367299040, 328818092, 290559767, 413762261, 481720651, 822442413, 479183144, 893431394, 52957798, 52836670, 967863033, 831484234, 189162227, 594542976, 157444225, 888598077, 75763742, 535205383, 702808516, 675232859, 998424598, 441581746, 760241960, 418983174, 674603667, 17684101, 264587001, 105279906, 335877211, 808404537, 256153374, 29093688, 7147216, 716734773, 610137700, 488010027, 793804766, 195500134, 69535001, 401280234, 357383636, 221051925, 456791334, 806175908, 741284417, 361488225, 838197931, 820874795, 50638330, 318635650, 317248286, 748952859, 228821490, 275839476, 401941315, 772549080, 506755313, 419781369, 827458882, 982716013, 939875027, 120832619, 305432928, 117570025, 6302874, 163171677, 977013471, 361787583, 140239754, 790462203, 15640786, 412537075, 3914287, 441211879, 134693284, 656363996, 371295952, 817971780, 883813336, 527545439, 671697929, 613430368, 301656742, 99490273, 472648071, 331298918, 358125961, 366957015, 479889065, 390761655, 428225340, 79524624, 119379565, 166518514, 113402309, 744008945, 441230201, 421268893, 728703593, 552397335, 461888904, 961539863, 864746951, 858700995, 25022237, 359044944, 380227993, 47255281, 632154687, 734515180, 47608938, 938344480, 656808746, 27696387, 924751044, 602755458, 706620766, 178301692, 332827728, 319727400, 709355575, 363810888, 667804050, 849167663, 567695473, 195639327, 782815548, 40843111, 375316170, 678028524, 83210655, 421012664, 934162755, 250643100, 467598370, 172700144, 630254593, 628936802, 831689535, 672374904, 616956217, 791367167, 423364631, 696070588, 802757033, 68430075, 708674511, 787438077, 930686668, 411657848, 788652925, 109153701, 577661173, 609335942, 837186630, 372218898, 394432192, 862620905, 497831239, 111615358, 869192986, 289848842, 169505805, 287946757, 228815008, 495999995, 105101695, 857686131, 10778624, 586817895, 50838557, 468438533, 667996968, 640939752, 488878974, 247045263, 570817842, 479385598, 177927261, 545266498, 383422924, 261173990, 207688685, 614544744, 746753877, 816497139, 70676242, 296946448, 769602486, 957072153, 39112743, 964586909, 186525174, 46213450, 621511820, 349877009, 821120869, 358719252, 373607084, 778791156, 901637872, 161610668, 167226827, 727863537, 953263164, 999775918, 511836545, 845289860, 986339059, 826398122, 948863904, 862912009, 971510379, 684891114, 512447564, 713020361, 516437132, 620724041, 483192730, 816384576, 498175505, 220627074, 645756379, 142222834, 68103753, 74483339, 580987127, 759173657, 241972584, 57216086, 206490233, 465927280, 70710249, 784134387, 550003016, 953381040, 719046778, 571383720, 782716418, 786928281, 550483831, 252900106, 499687695, 785429916, 578312392, 874954339, 119775730, 711074060, 851729165, 674970610, 119186363, 718453138, 366401490, 440677032, 760427570, 235762604, 471609136, 761462354, 124890285, 879419224, 262343208, 327367563, 783332767, 834733102, 324249250, 787578267, 764865066, 852509274, 53035731, 277462227, 3785267, 481425604, 878771281, 231734857, 906055568, 233639207, 768333308, 601977218, 868859785, 113052587, 769243986, 884115305, 968515444, 540887029, 876229336, 113009054, 814863907, 860789498, 586840663, 748597916, 203473428, 769577649, 347598240, 42836112, 684681686, 457399433, 284297318, 34615513, 61742913, 297225844, 951939063, 528095549, 514913168, 635792096, 960194435, 611516637, 592161402, 931182674, 244382690, 605969173, 902172661, 280555653, 482433180, 5275481, 936499850, 681995950, 33317789, 620096310, 137857260, 332999058, 722054696, 993497088, 972499643, 728128773, 28425246, 174636232, 137069477, 748230087, 827762629, 452995196, 369540359, 257105036, 311005298, 126895479, 358029469, 863155198, 474844528, 886638541, 368357624, 492550250, 454990233, 899947810, 275122347, 482388449, 209302245, 628218643, 332938639, 869238180, 330765164, 35385803, 110200331, 981236117, 854347231, 496827279, 651593296, 391670783, 349704544, 607325875, 577328461, 72458465, 632534822, 148131411, 924516085, 480587673, 35741980, 508107842, 11367114, 527224579, 87398598, 373213516, 965650603, 884665800, 806669404, 268661094, 981033908, 124756342, 217962142, 253724167, 926436845, 42528582, 860752812, 221186117, 424928317, 713859120, 927882655, 522913369, 686583281, 504511764, 641373061, 305460115, 351340650, 674100943, 272357973, 835996012, 102755994, 403636580, 763436870, 252671320, 246565891, 653694405, 600486217, 461216451, 956669940, 42806551, 465249903, 299685280, 852779892, 617905415, 137862011, 618852415, 229628030, 790672924, 934525042, 755720265, 20586522, 972473873, 585813757, 785324255, 397883529, 444260811, 967856020, 398945894, 114689711, 641827332, 626403777, 749459946, 522750895, 778408839, 760304692, 375816838, 750257253, 644058644, 951558986, 674211960, 50701606, 885063194, 202176004, 7428811, 644813297, 120858024, 721013088, 677597612, 230094160, 932364516, 18661747, 808071782, 335366195, 367493721, 630903984, 126737421, 743049072, 679848901, 843905754, 596909987, 270768091, 925421467, 780345963, 284377777, 895405840, 287340297, 69650037, 937830440, 911673723, 866196988, 757517347, 364086442, 319677614, 90524663, 323799659, 481244766, 845206752, 849438964, 432022589, 977196147, 467234035, 691814977, 808326826, 823665676, 692351135, 599497817, 973262248, 550057134, 403850237, 776559537, 126578440, 590905052, 562696501, 561549752, 363340922, 83133467, 426785247, 164405662, 341204126, 353552590, 240171156, 845293829, 201171163, 674003859, 480714204, 479078616, 73789142, 283407307, 32621447, 428792602, 517734653, 283320492, 254339444, 481624211, 456400175, 580773742, 715252, 746902775, 352579552, 847996356, 579143646, 205279977, 170446918, 590691517, 78913431, 606912393, 714307378, 961665841, 539233487, 174008117, 403333419, 974165971, 914757707, 788384670, 124020073, 232349409, 137283146, 110988904, 619041245, 82302049, 398889546, 374230067, 410181889, 265997409, 195456700, 842678986, 284885049, 753230782, 551273855, 336053036, 833362427, 556656783, 450748061, 995017389, 381196415, 820950589, 889802253, 203571647, 135116860, 480476626, 886864786, 306592452, 579132644, 448658325, 647876221, 890546291, 967066804, 901490370, 315090063, 780345926, 928554055, 743702197, 771742730, 63916540, 785780961, 704139901, 161595351, 273729179, 646150829, 726478561, 853911140, 190413183, 146726085, 167953617, 116589495, 150391514, 551036460, 563184779, 689702897, 669150050, 677918879, 217856109, 635089870, 252437464, 764182809, 534462569, 95307904, 465494242, 655578664, 970724671, 551845653, 685629141, 775850787, 527358573, 747728905, 92515913, 783266733, 310546160, 159052164, 958078995, 591014946, 21527823, 889725617, 181451705, 730969938, 89677781, 86025179, 162464818, 485049011, 673563343, 662480996, 774348636, 337033055, 237166914, 261437995, 22497060, 717155010, 639657905, 844481536, 257956662, 222620828, 442382290, 534294575, 168346673, 222682636, 872119618, 529725058, 602933103, 948806317, 282444635, 602303634, 226111482, 474923553, 458326660, 32215730, 730618133, 370506795, 615386894, 851062810, 547353532, 450964527, 20953011, 3059492, 115057403, 551064184, 854683456, 317446562, 332015204, 444569029, 585748861, 612650040, 967824283, 455202825, 511249921, 389440958, 181804845, 73054757, 737647181, 844955418, 432112995, 517946489, 949825096, 983208410, 719119580, 911328098, 432648529, 851755594, 181778029, 188162825, 225494195, 348084040, 227135080, 248843791, 173491710, 934012516, 183416590, 293223200, 575579724, 182655374, 600194054, 167871429, 535076431, 26374061, 955924413, 305421085, 919047910, 237029173, 982557516, 896763231, 296616994, 926148420, 61806242, 832800599, 671963401, 171552472, 82712636, 567138705, 706161765, 149271042, 238070478, 350923202, 498352499, 786788960, 299623118, 565990095, 88897235, 978510953, 221687942, 124878845, 981653588, 681274561, 444766012, 372523650, 300337712, 290194086, 904179133, 579324274, 526762535, 380491455, 683212479, 970337420, 927884094, 101195799, 265614399, 839304807, 778514885, 992225811, 878689951, 125247248, 408407802, 156253598, 359459382, 634194407, 328717231, 849050503, 402688162, 868568917, 913661862, 743713668, 736139850, 616475095, 388322869, 732964042, 212283607, 621643652, 622225732, 889401486, 648011959, 196446481, 149470960, 810005672, 763099132, 303038062, 640526962, 75619432, 313323060, 350881238, 381498779, 948155940, 914427033, 507563339, 18467502, 593230743, 880292728, 639991456, 204451031, 768616902, 733525064, 924660305, 559523436, 204719737, 602839649, 754341523, 139626012, 774086232, 197950166, 860917744, 820479771, 394110963, 636247417, 971440745, 867430979, 115329080, 52651318, 190443640, 590051691, 970275427, 743423736, 737130763, 894440045, 63159749, 660676125, 735103073, 262788580, 112608643, 287166898, 477455137, 899726363, 615764657, 677706288, 669995234, 155832089, 948645164, 256666358, 6760752, 797496526, 921465783, 762845020, 720564815, 231912039, 984529603, 750445254, 501577829, 936846676, 44825106, 194243777, 196615233, 364830055, 780942633, 661247150, 281227471, 867249774, 418470473, 202961213, 548508413, 25751857, 176183450, 4718036, 398160580, 942935614, 159711610, 731816282, 397999455, 431402231, 263571139, 429976616, 871449101, 377750643, 429018603, 827886032, 246561442, 850379906, 234806569, 278937442, 943033582, 654375614, 750289558, 755624806, 483824877, 586014158, 31517360, 625664399, 522528944, 216291409, 393769614, 280061051, 317487851, 557095805, 207932535, 415718726, 533384982, 806716129, 161217401, 401711893, 112713073, 816028217, 308116187, 302117556, 248133937, 315178175, 159653370, 525974491, 906733029, 239522321, 994141023, 527213430, 37163677, 34495086, 658355512, 179196079, 219721554, 715315929, 909417511, 337458378, 430563531, 788480359, 949434841, 165650103, 461518742, 781025162, 569835288, 580727640, 12293743, 28664167, 324010492, 903264833, 67398697, 52105237, 243683104, 503684022, 130454249, 39424082, 405806983, 396042708, 83626994, 474171830, 391188708, 201555539, 838763487, 75877526, 521161192, 151944893, 708946374, 899871997, 276909399, 708101781, 620631381, 193779418, 883611237, 577039732, 331528202, 478140029, 408433308, 193397947, 435922642, 758082930, 544428517, 216428779, 852430563, 774406, 325837119, 900995424, 836933420, 801943352, 656921275, 174970815, 265809852, 916715272, 593415972, 529993333, 814103841, 718020011, 186751934, 535159812, 169228679, 412898173, 112394169, 711700016, 722193179, 134366905, 433736383, 464033520, 61502293, 118542174, 427215498, 436163155, 803188007, 96744103, 326673552, 584953682, 294457817, 561027006, 392676874, 239201399, 790263266, 190269595, 982846410, 847718685, 794802168, 506532130, 603463648, 701075206, 7202655, 608012993, 555482084, 854981015, 144358921, 409799970, 51458602, 187426447, 99828440, 126216830, 200083473, 145894776, 325524843, 591988711, 966981423, 6551776, 795192999, 132571687, 582391062, 899672414, 632415529, 824572492, 602823106, 868680324, 16221035, 769558090, 884376267, 575626921, 666076403, 503738814, 681959915, 733336936, 314920560, 802555187, 704657571, 167422316, 925222850, 338293907, 214480360, 124048337, 533346391, 871163582, 79302567, 498625234, 860217910, 429528892, 397477031, 310480891, 808198575, 11166724, 831437619, 404840689, 529253364, 207076856, 389206610, 765035242, 879867747, 981911214, 255308112, 202332809, 444780831, 822605464, 372401292, 55828302, 974727510, 265497835, 877813239, 669970205, 793513629, 456021428, 400607490, 851097156, 327273391, 840767249, 334118197, 310339757, 493536575, 574853655, 338699903, 235426910, 590971660, 651363703, 457029461, 225776282, 713837502, 355238424, 927282578, 946147178, 800775328, 586883821, 712022021, 194960925, 894290922, 800043184, 573643794, 969473798, 539177467, 879231643, 92241408, 798356563, 93079688, 136165347, 535304516, 66271786, 635622514, 989556092, 473377091, 557630924, 573772871, 627304098, 524479289, 903495706, 670058878, 736806024, 337800974, 897261093, 477392722, 125062321, 558418202, 650910885, 316702526, 59394886, 778322515, 532962129, 698457025, 203981044, 156426191, 369785621, 25713101, 66884327, 888287898, 131868415, 192729703, 887976510, 845890396, 720226154, 523909663, 352381055, 443016190, 243787235, 727139487, 474137838, 281490118, 856366839, 777594286, 545249623, 824823869, 456410745, 515832272, 29249892, 342609735, 128484661, 953387669, 131906067, 85591878, 915770831, 706690470, 452112801, 418311760, 176280263, 113342993, 625457967, 773073339, 64884822, 953781322, 548053722, 315965225, 806188068, 737946932, 451030334, 743270247, 2803604, 170925863, 627008302, 190312887, 941151545, 254816241, 947753500, 422977945, 426142207, 604394795, 303917530, 977342520, 340994089, 227528742, 62248961, 688211326, 242985754, 827518675, 551915040, 408441144, 505939930, 623759533, 270526708, 658290152, 44929333, 258594885, 402479893, 637799613, 650319987, 289047284, 397525891, 365984544, 323563716, 388339566, 178306778, 399165619, 262901020, 864154815, 214764838, 613223840, 568188191, 942455261, 414260761, 865695221, 194674242, 643976777, 516741911, 780680278, 437472674, 878547910, 793086299, 638762911, 89964192, 423327468, 995281167, 862751875, 667900834, 748827737, 69675329, 852345564, 11688688, 257365643, 404929813, 379517269, 186322254, 126505324, 297871407, 880231335, 835162997, 203661965, 162260212, 217863378, 894577511, 275555611, 741004500, 58171891, 566990882, 521566044, 901404734, 683600003, 865554092, 443491078, 380718426, 778220262, 469340155, 263621484, 502129938, 836386270, 678906354, 120253107, 868199818, 225169311, 67409419, 299597858, 811087333, 223779389, 43609524, 822743040, 975201288, 611098462, 835615138, 414084353, 773772821, 311503358, 243381488, 204591599, 928602752, 712750499, 685680804, 670562253, 853545764, 805140463, 317234769, 486263662, 767246661, 442568593, 151733110, 631175189, 8364235, 75758833, 365019166, 130149731, 651269944, 972175362, 856093196, 115106191, 752610844, 170793780, 658137858, 154361767, 815940438, 893790869, 125656951, 79311507, 674101911, 314224352, 817803088, 380463692, 960741375, 832245607, 212322057, 59554901, 749298081, 556511584, 946802864, 622406335, 129403974, 16013046, 72989518, 759874389, 150192491, 402389851, 998648541, 175952248, 192700478, 835701892, 989447230, 892331019, 879494735, 607995233, 199833434, 261719249, 725302020, 352716989, 636667029, 342302184, 15381524, 661074389, 185875760, 871011103, 550515344, 86687267, 649231807, 154724580, 835505472, 633910143, 592871122, 648478716, 349616118, 946834360, 381800441, 567348751, 590002124, 463091302, 21905466, 630377747, 156077131, 922609915, 535333578, 665629234, 871150108, 310589621, 269329621, 389860128, 194716215, 434655109, 88327099, 486946430, 855578087, 986762969, 79432289, 369709929, 559253673, 26245213, 923092607, 647218894, 480331828, 995258367, 632792166, 155629722, 796952493, 484327189, 307520321, 451093889, 132591347, 907459639, 821907579, 706277251, 404582651, 115958765, 271234822, 355271253, 125853998, 434170125, 909916595, 920102696, 809656566, 800238793, 28814451, 942239660, 801960827, 610837556, 246991251, 160410810, 305922824, 255478, 762889283, 392517779, 494212685, 560378685, 35902575, 595473674, 729727888, 74741134, 223978208, 897047066, 278787438, 428494699, 89550651, 294540359, 179725966, 866086106, 892390875, 398339051, 231153640, 954632087, 162965739, 845695561, 677547395, 283407484, 237571591, 966451354, 472263137, 949155431, 887377373, 804708179, 726228164, 407345239, 108216398, 308953869, 186853050, 456669785, 634159456, 11101486, 509793004, 794338193, 669724771, 829944484, 894141670, 337082615, 796146964, 611899540, 487085849, 379451646, 76430423, 8906282, 890497068, 903257944, 713297233, 433611259, 847392800, 252982393, 333781504, 896211566, 248559655, 432520566, 316164672, 628658898, 381869392, 407963399, 121421197, 323149587, 53712010, 509140305, 829581545, 303153560, 459443733, 825888062, 988428895, 182320458, 190122934, 543095866, 637253476, 187177563, 537136633, 565709511, 660900477, 997714271, 569704759, 268694023, 685394129, 447028898, 330209851, 269318792, 256698253, 725237936, 410501754, 378453320, 915724931, 56147024, 413066166, 108914857, 657995818, 247116829, 869214263, 365973260, 180550756, 970694560, 3247598, 69225129, 37842627, 659332884, 606192042, 768195973, 698700310, 571676961, 737382725, 363150441, 765513250, 477613170, 671291305, 547826506, 16722118, 764907640, 544486785, 302470877, 461828104, 185719610, 123484947, 816660680, 515461648, 102184894, 449688997, 680559214, 73822285, 571953901, 926348313, 547157451, 942377784, 846593320, 915233679, 806233889, 579438990, 30104837, 449398830, 513538968, 513624538, 646819328, 264572364, 743251554, 118330768, 449836209, 702934482, 976699906, 110066098, 469325715, 485399989, 988541218, 178385811, 370155631, 136940553, 88665943, 329793221, 457814194, 913274502, 397730988, 707741894, 460295978, 255555486, 177611612, 141067122, 530710226, 663193295, 799615912, 241935258, 999542904, 865088350, 298082094, 587525236, 53661574, 22513696, 523188743, 231129713, 425634937, 820038282, 409624355, 321516290, 793381247, 679231011, 85408252, 664343435, 876238053, 471984354, 163207744, 276872128, 937281654, 64940871, 860760387, 95083899, 514656764, 538196399, 617347778, 603393694, 187141399, 899322116, 9994635, 107889313, 946066977, 216610587, 516403120, 221098655, 367360132, 381116215, 951622316, 434021794, 50133169, 352547237, 283000270, 686398235, 522308443, 299573862, 187150477, 742401704, 786157090, 133413199, 474013841, 95685209, 573130108, 244864020, 127868782, 26287728, 696393984, 103477724, 906088393, 878960422, 483289900, 703878830, 486468835, 263831663, 954679003, 131110282, 735274788, 426732598, 758844428, 726054171, 435661686, 193389668, 35232645, 654654870, 916971774, 185864110, 307817866, 320949051, 675939276, 140652437, 156948675, 683844974, 87277799, 121092961, 356714863, 842102915, 291055131, 934592340, 480197795, 994972283, 342454067, 684230328, 744957652, 949155263, 11883920, 890698918, 209560766, 722162519, 687940876, 146904170, 535021944, 993578936, 562374079, 359655216, 717210398, 299943660, 568838941, 178557282, 107264281, 9258758, 2236636, 899032760, 846862019, 907918018, 831314415, 895000757, 80641625, 498820671, 929414348, 212287847, 785976460, 825304708, 120488920, 830554211, 475974347, 728215868, 18612113, 504539634, 373648157, 543229324, 193088451, 916747883, 282252235, 945325420, 85300807, 361520393, 718813440, 347406140, 227134305, 284192706, 71837456, 463551801, 436345810, 384089858, 726332023, 190778028, 235968207, 309553957, 308256092, 75891972, 918508475, 850759026, 342461633, 99163086, 512563495, 882351364, 274859269, 622499949, 948507458, 229133448, 594375979, 550704198, 54604680, 98481959, 945804172, 681441393, 391950887, 85164009, 590364326, 755048604, 385097367, 28476478, 538170394, 754814987, 365778860, 877737688, 669185657, 85563269, 694661972, 170358375, 594443598, 51947340, 12295988, 148684507, 113585837, 252876092, 75954844, 240546323, 127788263, 432691776, 926949423, 840636670, 26764622, 393256391, 256328868, 348762292, 658317362, 436447261, 303470791, 286654120, 942249227, 796858928, 785601319, 888799537, 887940134, 642557367, 384624222, 17771427, 148777956, 34161348, 714348911, 135181671, 499335151, 330515161, 451197889, 502678916, 617994877, 83866703, 749788129, 714605923, 152772495, 846072016, 976892839, 828351058, 513185878, 12514572, 359676527, 541735888, 966780783, 551582407, 957140737, 642156472, 963848305, 722460222, 756590209, 140781212, 390852187, 870884082, 765405522, 656529187, 139563559, 177334087, 700358510, 678297164, 207546821, 323953131, 24165515, 474061195, 709943866, 859701033, 427221381, 982478872, 192080811, 447274051, 24390035, 291490319, 754482751, 980946497, 240160546, 958093287, 530282738, 802835102, 645258885, 246458567, 517051901, 41927183, 234014614, 954178006, 404711692, 205712281, 548149657, 15539520, 834648716, 176840388, 812146971, 571022254, 472552618, 83696441, 677093892, 159396009, 192372726, 633602523, 563287913, 148428812, 822173479, 649486683, 129666740, 878524467, 717490623, 422697322, 95409996, 967314784, 756845835, 792633671, 225920645, 991245122, 881057082, 703270295, 490005492, 746245677, 410768171, 340773210, 196396842, 832332650, 253107018, 463920694, 906960395, 487702254, 317133298, 163987435, 61771605, 461308611, 813959045, 448503990, 49953988, 218851877, 430968700, 117441249, 467676487, 803453004, 919707170, 977651606, 82803899, 305901547, 763753089, 269861909, 830097669, 421174347, 553998047, 851639942, 783250657, 82941888, 373978023, 926119321, 395422621, 434514363, 82572537, 11671036, 204010797, 584976796, 34057620, 224416240, 171872704, 776357457, 125075184, 453986061, 798546597, 218067232, 573208845, 695081061, 66976490, 880251419, 743875745, 230124570, 687451922, 744378683, 888463613, 833419661, 369785814, 363115053, 402643001, 213023682, 144435818, 924778420, 564848731, 959848642, 482791148, 242966978, 32296695, 101075425, 371234941, 991027758, 576218624, 230128579, 897442863, 47107127, 103663405, 738428025, 584306476, 729369084, 47412430, 742004021, 914946200, 45003994, 933392719, 322181524, 193410229, 76328113, 403342784, 319852227, 15014274, 336753617, 312931362, 9302034, 202133305, 270828815, 67923834, 958111907, 29827232, 808291849, 803243288, 313831437, 710929997, 263035037, 614365417, 41815729, 618250463, 902846509, 903939151, 433705327, 624193333, 349668346, 986309544, 211444239, 506105719, 871621572, 523806737, 519544036, 334436487, 216813325, 308722609, 109655970, 594383197, 420017580, 408913746, 235797672, 55872091, 776036975, 671264609, 835994594, 569487826, 673888952, 825172253, 972152652, 536854322, 453448303, 26764149, 153614761, 971274046, 921703354, 223512339, 596127053, 896538830, 441637554, 999396250, 772046862, 664609131, 507702696, 989336330, 560876408, 221674985, 225848574, 731302507, 111651399, 709802296, 627191798, 374047108, 883614854, 405625425, 16240145, 552830163, 238384731, 668944630, 483697181, 344609449, 931843032, 197725864, 320777035, 308280021, 85950809, 818993708, 868223542, 660066151, 198049726, 561862575, 84466764, 701218505, 279756035, 939386264, 345805112, 544158891, 879597805, 193390260, 86980371, 633964822, 239767186, 614701944, 480182064, 825209576, 706871048, 888909085, 354565369, 973089253, 905220087, 568580949, 780935902, 723912954, 257205716, 399034350, 725259561, 708974980, 571517305, 656696851, 818068363, 164880009, 658097706, 64695767, 40805664, 606924748, 713074097, 834977723, 212314422, 996883520, 850559227, 164137028, 160989679, 350022636, 802248853, 161086265, 436660502, 48335350, 969183486, 836400956, 587499170, 381241251, 615187438, 198817208, 651853762, 809612954, 282211925, 64775022, 73879579, 486372581, 259597156, 11574972, 565457794, 201596905, 19307976, 499639794, 797942658, 129789679, 546938201, 902937445, 747897781, 32128744, 187876524, 601593166, 500121565, 421516991, 601975524, 237082182, 839789036, 713725666, 7487067, 505042426, 236861951, 621348442, 106714851, 734114832, 729774231, 170924135, 179194607, 722310837, 395525223, 165768798, 101029426, 175845665, 394735446, 25565848, 746840072, 26281759, 801531748, 606337508, 249551555, 967301123, 237018368, 201705529, 973669601, 409304446, 957946449, 20219495, 949590099, 384325065, 759351130, 742846496, 574218010, 938947427, 815715198, 898801310, 991630018, 565259416, 831489266, 586633553, 264540402, 97556925, 307603285, 4155116, 304719997, 287990936, 310362885, 794714570, 481221646, 159841668, 796644062, 612376916, 696183118, 570055931, 467889616, 198105630, 245456256, 979188967, 599891358, 464268486, 890643397, 897923734, 427158979, 661311737, 888922470, 11595892, 951909999, 694588693, 665168830, 485806809, 4107991, 629060388, 981570233, 602418896, 574310443, 425818592, 814150362, 595595792, 804226855, 515525168, 916116752, 752181910, 279101154, 725218197, 722479112, 89785959, 942942774, 303711048, 763932039, 981731664, 305670907, 873757866, 446567219, 226376535, 1365037, 663444152, 427113670, 874889660, 495813750, 497819486, 563690724, 694747428, 634702309, 19907038, 249537812, 589550057, 356121170, 937859217, 208164738, 648778828, 762140823, 571832638, 33597770, 152081134, 404782120, 156280095, 414706449, 491124329, 940013712, 205328224, 873155248, 933754708, 44120019, 809933254, 706457402, 846402471, 129767315, 371741889, 400747804, 606745379, 64334429, 277867735, 447476803, 913773861, 802853371, 362848354, 586467911, 793238505, 641643768, 188149847, 928276039, 425597353, 302306141, 580882520, 239804938, 959267006, 303728346, 728305147, 502445269, 264101592, 279299320, 115447813, 190938810, 482457598, 589039655, 425634126, 30497103, 819795701, 129082952, 656869603, 901170324, 975367980, 917299654, 435312074, 998550111, 993345917, 579128639, 699652680, 495127421, 44475638, 893104455, 263291619, 703019443, 281490708, 447912351, 730279280, 545149888, 754130845, 491965205, 463912877, 209931135, 751267666, 704444822, 681661159, 453866550, 544759257, 948491934, 364050135, 256637678, 421992218, 300509504, 260064286, 270441813, 204859284, 804813744, 30913656, 492370054, 273430724, 547823362, 333027429, 208250374, 240920075, 401495596, 57008354, 656680586, 804679808, 352649032, 63553008, 205034650, 441281323, 792890149, 590088360, 998821630, 229651382, 667670397, 405702275, 425363786, 808409778, 603430686, 708705808, 525725904, 317892435, 649746415, 482942347, 707511653, 917755170, 534297922, 620997445, 995593289, 662220542, 547321346, 105301988, 112053616, 356947132, 287561360, 932380044, 846794535, 516225256, 729036845, 57801032, 334956999, 750419287, 111622191, 390620501, 703108801, 320905257, 812565725, 19724339, 356945283, 857030453, 631465997, 131626794, 523452334, 138853460, 421145464, 280101924, 464084148, 517382647, 165575481, 338676075, 402199388, 314165310, 504154024, 126600438, 399776649, 397075456, 833259647, 754209126, 612092573, 532750763, 171565719, 101520119, 910767233, 470745079, 845976494, 544526797, 292403042, 305453758, 548967757, 680392550, 483193093, 697344474, 387001186, 639924322, 244797107, 491658167, 897916053, 722198414, 253479375, 931812061, 500777787, 287512678, 678611330, 57640031, 744936548, 393288177, 480962153, 674194732, 556565668, 244423740, 757333970, 498965849, 648382081, 239970811, 473391833, 932940012, 606845260, 865550067, 169305254, 81662165, 336920473, 97872811, 247926743, 366201548, 765280938, 266005840, 559824288, 586174038, 807716577, 662196250, 952462405, 679013313, 173655950, 910489471, 422628247, 31267088, 273543641, 809140329, 675945627, 707740738, 508069627, 860320367, 183332220, 365831905, 332768538, 44026186, 651147742, 818069160, 126655319, 554495943, 973690694, 375274041, 766502810, 339365478, 664814383, 574464079, 760875014, 103172859, 314972301, 271095638, 774586363, 507803131, 762332934, 255485138, 668995115, 412173196, 590070582, 548723434, 655501790, 523892240, 708851843, 907364447, 727254136, 401272107, 955408196, 655153762, 278735331, 123916434, 999134254, 287419923, 345586215, 576199709, 353120867, 217428439, 400223025, 403630593, 725777285, 615224949, 593524695, 742405140, 90046315, 878313123, 876232445, 661778134, 155028006, 271089323, 845398065, 331217303, 641713989, 606634178, 960072085, 208970185, 356519794, 877363150, 919344791, 857852246, 157282911, 493438058, 904740533, 468111991, 399480159, 936144801, 266853206, 859083497, 464168339, 972625931, 660214569, 263368402, 497423044, 298448580, 484222666, 796674333, 96104869, 750576955, 290843047, 423466976, 599725365, 199164761, 629825601, 999192697, 465263400, 788496166, 555031374, 846509430, 400016235, 446766994, 3015076, 69524987, 567570429, 562779573, 489761129, 893534998, 142194464, 907170432, 234359935, 166317648, 528508726, 827342496, 111587843, 359859138, 529558734, 367939040, 34386224, 854758502, 635787697, 376736267, 526855040, 931242832, 749774056, 741587324, 779096192, 333134724, 196720760, 809039687, 156672071, 395240117, 357191243, 402091702, 239491297, 99959784, 150310870, 415522978, 174391819, 908869253, 524745722, 450081073, 263055577, 939674244, 175705165, 749464682, 499163511, 19683496, 979623289, 213428053, 775004845, 787285751, 378399501, 771241404, 772544486, 937296793, 773405111, 485459838, 345242849, 226252767, 721322333, 4683974, 643454246, 508928667, 461800277, 955757599, 110500411, 592062520, 562127400, 210581712, 248446946, 411719080, 352853741, 511211920, 371810051, 562990535, 230531233, 226444175, 433618036, 817342484, 880621131, 509811220, 717525968, 790762573, 299558998, 202627196, 787486803, 43738593, 548856128, 22254919, 909236786, 854899334, 184294137, 582023724, 350878658, 832571449, 691736812, 66528252, 936069421, 73328263, 99234081, 854588555, 954009377, 68935441, 857243039, 519465429, 277730143, 643018590, 409686614, 353801669, 975464743, 129084986, 76336504, 999530034, 872822738, 299350972, 459498828, 269177443, 110771433, 814393975, 617946651, 658372918, 943768772, 760457800, 685789118, 958313970, 418949500, 448059242, 478544262, 522598625, 511117301, 455850889, 166358661, 477916721, 487091223, 246881813, 311961636, 638700395, 858733027, 971919400, 318043312, 147156804, 365718727, 855152227, 218959367, 302597921, 28725121, 728076326, 369967229, 750363535, 62688476, 209015495, 473942765, 626256193, 862432978, 633245869, 723965148, 65135488, 927543643, 268008497, 556359021, 843077864, 244939186, 448601583, 347400705, 906731388, 294982914, 476252222, 575949673, 666903391, 208084812, 550216041, 953746122, 278887278, 306893551, 637932305, 580278778, 556390868, 197076551, 698368921, 882378153, 83436941, 50160418, 21048886, 886147421, 79115396, 679974804, 968099786, 418556406, 811114582, 190442601, 580954459, 268983131, 518444482, 333640181, 234427563, 7718372, 354719326, 269061093, 518526060, 34776821, 100166408, 906148359, 240496144, 882611294, 744671444, 215648033, 713039078, 563023076, 389081136, 139530795, 879066437, 532113670, 968307531, 576856847, 6778129, 853899288, 182796880, 995003928, 155207105, 455639162, 737661963, 152107294, 111454577, 139596776, 132520737, 556500231, 237079038, 506960191, 464122020, 159544510, 754697532, 117397360, 851880472, 832609957, 603250173, 858628769, 724427433, 919274968, 633722494, 248940470, 927964215, 692234910, 822022516, 595732332, 432234407, 912089623, 172283353, 93069738, 406141962, 515975307, 427301083, 165570141, 364920602, 336025900, 357829243, 151445524, 480984944, 664901378, 768652863, 883052456, 975358225, 188032058, 136821145, 740811523, 951263221, 299056621, 762842851, 215730854, 380029713, 905375241, 451284241, 335257747, 415497462, 336639627, 863868061, 535288706, 105448823, 259457997, 6738356, 88842601, 234697615, 712758061, 616645702, 214124893, 71874917, 876816122, 765662554, 466155823, 24418258, 514229851, 742226343, 762657741, 22590152, 273341584, 107248630, 312092972, 556633490, 225894467, 217948290, 425148329, 16465185, 501070403, 985083304, 327145745, 974211329, 536050854, 930779537, 44629268, 167471659, 751440878, 294203930, 772282707, 853981758, 265259962, 912316222, 318969218, 315800900, 549464232, 42804378, 240399554, 39516682, 296644876, 168289011, 27987937, 474466254, 802018822, 342111670, 436576930, 851419960, 286926193, 967175520, 286562522, 126077233, 86479313, 889544138, 33921001, 264601023, 486309890, 310600996, 389521968, 508979896, 305299481, 766352705, 38893942, 25589698, 629706351, 201996007, 207080171, 548443146, 661220360, 667403360, 850480651, 426562622, 727708063, 725993188, 97645433, 391932697, 749021787, 412098608, 896240769, 441253697, 771958792, 183813607, 25565496, 261817137, 161489693, 98475870, 52946047, 28026667, 974095134, 22503039, 20436182, 254219757, 647023796, 183691236, 830431976, 263403012, 343765299, 24029743, 384679211, 366918681, 912094085, 121738890, 997523546, 430607939, 474337490, 348026629, 178246899, 391593606, 754807462, 976833024, 81081062, 604895942, 286215179, 271546857, 764889643, 479481026, 890727118, 679119890, 665520672, 463280096, 530250013, 959892857, 508322069, 686372872, 7359761, 576224094, 342943093, 843579414, 797132362, 623137179, 574757281, 687917601, 839657286, 563281784, 598493663, 737774126, 673002618, 731863757, 418618944, 597485626, 335681121, 564133383, 366392578, 626002889, 641623938, 89868834, 474909248, 805886844, 884253110, 312168521, 542335269, 957586347, 977902941, 523917272, 211382300, 250960846, 762329954, 347745564, 295287358, 714829442, 722901929, 324850358, 543392330, 328360465, 800978566, 257421146, 64805162, 32364133, 209882051, 80361192, 885685049, 410618514, 159634156, 768630449, 897654265, 619098164, 592759013, 125555199, 386211683, 795966909, 372268947, 205261324, 650719540, 158118157, 175201019, 576618173, 265563222, 14638515, 984909765, 556231447, 636503347, 216990691, 216812659, 147867835, 767894142, 814527928, 325608287, 918160904, 630688258, 886676492, 512253230, 471169696, 954383512, 992465098, 158882676, 705289938, 388747488, 96847043, 614429024, 983265684, 178707557, 478922978, 244214476, 217755629, 933029519, 686435852, 704355245, 120891849, 358566597, 867657270, 207645820, 760667139, 267087248, 382389520, 185132693, 512181339, 875639504, 670708279, 325712809, 34527682, 866690652, 217608020, 554488292, 89152169, 40082012, 923766894, 558161184, 783930394, 649925354, 958863963, 944515584, 872237444, 207460768, 293296035, 904777275, 413962425, 838168892, 141160969, 312075693, 246516628, 327676119, 900904070, 961330306, 170342720, 575924110, 456401777, 121973639, 780858718, 624015745, 154354708, 217912339, 663864619, 376905032, 167726650, 139849641, 305556524, 841908325, 441357046, 970847304, 706333573, 885984677, 41057251, 139131414, 465835411, 479873372, 671279906, 345988373, 445897171, 198765468, 615588083, 74755226, 982446598, 878864238, 404151464, 44058390, 302077722, 345669330, 686251513, 625824300, 683683314, 508462175, 299825721, 556885560, 372208732, 713510788, 213047041, 443674285, 810549901, 467266206, 948369988, 334785687, 634559707, 347973485, 958444665, 878203354, 897064590, 998762817, 717386861, 684327982, 711306663, 334006619, 5385698, 930092552, 969557543, 69207525, 963426708, 883061445, 63591500, 224694112, 173449185, 96021824, 385696007, 634251179, 497340680, 773326493, 230143289, 314705536, 154900391, 182765811, 927378129, 550981912, 655686405, 380751899, 854284690, 258749768, 470606716, 558412290, 106400977, 927106262, 383149212, 260855207, 472028138, 932605168, 816874112, 412067943, 357679290, 1712519, 314598101, 265371940, 53981730, 917967260, 858699035, 832226365, 967909692, 811329172, 308613306, 981702610, 200925225, 830124884, 124555464, 316641548, 680870415, 96650508, 518519326, 948303979, 58985721, 555981837, 454342400, 160687470, 740923862, 418909435, 167718077, 445698775, 42959927, 312021789, 307647699, 250366401, 343017143, 99807096, 715468624, 561897313, 385765443, 952667248, 746434961, 610590234, 970151982, 391867972, 818207493, 20111076, 781475880, 477057761, 992948148, 316038780, 933197720, 311646452, 698316712, 712677621, 837403768, 122874067, 939289464, 293823438, 171644354, 951874570, 178576799, 487162616, 789012756, 583686683, 774510201, 296501658, 234447072, 746651834, 166667902, 739406040, 975740190, 369044731, 68949222, 946873209, 324904654, 340782524, 610705652, 966071587, 483510033, 429280614, 596623988, 664416599, 926713432, 287968442, 104346557, 615275428, 989703277, 201384737, 917465775, 79868317, 829968607, 81852161, 814836740, 121296967, 923583332, 710961770, 495668974, 455745885, 219780985, 950718627, 984300813, 527020017, 88834241, 805682275, 619986977, 611833272, 322079014, 210833552, 314323375, 369923096, 131979437, 437146888, 704736140, 326315631, 672104362, 821578188, 724737017, 973115851, 42116217, 840717108, 115328822, 797262707, 856142463, 312317437, 702270080, 713647600, 305006552, 306361410, 128677363, 278471444, 581918897, 450283182, 264987145, 100617385, 295085982, 263149400, 11658329, 312920501, 681733207, 216082101, 480180843, 705967025, 154913484, 979706240, 139161308, 576925464, 809226694, 346864965, 780479787, 599578644, 374165014, 803152361, 919639500, 215045193, 675059182, 667866703, 796548524, 352764229, 156520642, 19415425, 69969928, 38873642, 581265201, 626545472, 116400149, 996040957, 166254730, 778443152, 525696401, 702194601, 421274797, 934389192, 479047096, 507914288, 532456969, 183054670, 535745216, 73354207, 121058473, 185905907, 997052595, 478865038, 444715345, 596142765, 906800978, 913742315, 67715138, 831535434, 909340504, 212259513, 23071846, 352986989, 217946011, 69340819, 829025842, 319145815, 596122609, 98331157, 195679323, 526662183, 348717796, 210709719, 485120682, 324875367, 279365115, 491686964, 494094081, 501383148, 802434737, 136048275, 403135774, 674179198, 12348046, 729686540, 344558353, 592514743, 165763716, 675478523, 20175279, 917089576, 859293445, 723281524, 574849529, 125358414, 486434496, 799394735, 120250622, 736859914, 460048777, 380553141, 259905175, 588212209, 168784380, 992371739, 554309470, 966248666, 414204427, 880980208, 320795525, 740698252, 336172562, 607062620, 289753200, 448447383, 511829276, 955560460, 636554600, 925802015, 419803404, 452101802, 563689640, 556236713, 989081061, 461456590, 546538194, 62822816, 424153344, 136236427, 237867149, 810340348, 777764947, 206253945, 645268957, 88391276, 969690330, 229083143, 380361521, 764486892, 650048771, 283212193, 587187017, 936776024, 163494191, 121173647, 189166557, 173337932, 374151343, 718038108, 997117148, 208828244, 6205433, 815731650, 189719961, 123658620, 115661532, 333422480, 444407344, 617520398, 216438043, 364809286, 457530708, 827052279, 901449210, 177802769, 455130507, 902517659, 61390214, 472966416, 104608837, 759059864, 373122270, 155336521, 664761528, 920672414, 840519372, 884904231, 80441117, 259442106, 509858298, 156858238, 519408479, 556100237, 995055782, 152132011, 161781446, 617864791, 451863264, 960148598, 816736770, 790656867, 290906685, 646279426, 861699288, 901350815, 335269893, 514220735, 717800738, 631516088, 412028099, 143224325, 505256066, 196125404, 734357897, 251562138, 335139174, 391522396, 956719161, 832763470, 394083321, 248339215, 826762888, 864346398, 340818645, 687671775, 933606323, 77015394, 432130306, 796381659, 577059788, 4679256, 911888572, 847096664, 592475336, 805949364, 38613560, 206337830, 383207747, 698906156, 275624435, 717376268, 873530801, 98320231, 399851245, 773839034, 917226792, 257940514, 867418614, 383652692, 195932383, 650905458, 53522377, 966144219, 92662556, 972572305, 213876906, 875289004, 470788933, 312546607, 501720061, 218554928, 952641808, 425726261, 311124899, 299564526, 270433254, 773023353, 709782736, 376463887, 932830126, 897929349, 666523770, 93027503, 290059943, 626472890, 957175999, 582772620, 59420438, 345164585, 269976261, 1018555, 120525858, 886887024, 878766691, 210032007, 881300876, 482812897, 957452354, 193478375, 356573203, 845201196, 819352930, 816378566, 68043235, 731348806, 892934912, 686872082, 753420021, 661213196, 81371305, 540135722, 62189251, 478469139, 93649928, 645086105, 960823590, 543561143, 836749889, 728201581, 90312039, 560852166, 707377549, 802174543, 552726306, 187698850, 922613745, 637676809, 174937591, 96175866, 27750644, 341412725, 416067224, 470580086, 213812431, 658882668, 792511247, 225900430, 799352943, 891891173, 550561837, 44240632, 25843868, 235265662, 23830866, 326759334, 288131627, 91462888, 455578874, 193937506, 152405205, 709001012, 698050589, 185491924, 964829003, 163838652, 38866758, 527346146, 802422934, 390512529, 124268194, 6582928, 511063943, 585005461, 793980381, 73119549, 470597296, 375662513, 106123014, 247087261, 241734255, 335431675, 499481544, 426080302, 566642573, 744313493, 282161515, 77988238, 993637125, 839078412, 492288641, 632699733, 280336570, 291907370, 155206356, 28387040, 67789630, 136464500, 714395910, 325866492, 679538015, 91714477, 54368733, 655371043, 270737900, 487815968, 379401670, 852951510, 774475864, 234190199, 670121001, 796120732, 865581740, 90861427, 584886500, 553354586, 932856455, 205819742, 426437880, 871666550, 379386615, 8830303, 162442568, 304313376, 172690209, 691807361, 907061334, 577064495, 593186694, 318852799, 574372142, 90180532, 226411213, 598361000, 399564813, 601755596, 752710344, 865965697, 780981868, 828379694, 630707066, 891143019, 591838463, 439729162, 196018431, 6959468, 564249649, 444420551, 65442827, 818286961, 976803446, 374392073, 140650501, 581047341, 489937282, 702195196, 780719147, 853121728, 202213222, 436121691, 793095008, 984878926, 798514459, 727466356, 105044733, 59197257, 28712937, 772969365, 906713155, 396674879, 549303647, 890922227, 813063155, 720907353, 441043773, 90628843, 391923871, 430599454, 568998268, 793499562, 563798478, 753053119, 117714216, 31749367, 503247882, 271311184, 279911436, 390379638, 834596542, 317770542, 42941581, 361502851, 725799414, 118393006, 675362717, 651457566, 912580396, 358583331, 40906793, 305887693, 546879982, 730606836, 347555072, 592475585, 888430909, 131263831, 206018790, 787509842, 68082822, 495625561, 850535256, 829291466, 182940510, 45968323, 26176127, 91489912, 776084455, 118132774, 23101584, 592753888, 894920192, 383315390, 912455884, 525054399, 138604829, 677666478, 247199404, 43205492, 123667349, 195460235, 969105583, 858810044, 116619531, 94017256, 758072671, 196886746, 154289138, 607802339, 421568175, 5392383, 91400372, 108001163, 371036987, 307609127, 43215305, 372651471, 511256875, 396927662, 594839854, 297620676, 439919885, 290275041, 352461601, 952250009, 623207465, 850685032, 150614466, 98967418, 708593629, 128684701, 5606603, 120619559, 231496244, 811305838, 300697154, 662058, 149146447, 648447847, 807035528, 267740567, 196151081, 710478223, 871469088, 279318814, 533187187, 557857614, 502487146, 174865684, 399727654, 550502821, 855176701, 916307220, 259632324, 774614707, 457413183, 781653957, 303762047, 753177454, 654378331, 456271819, 218075055, 968839388, 662509020, 218232039, 370426044, 241239901, 837879136, 458938435, 846651054, 407210683, 700235907, 196007062, 825917610, 358676180, 314060389, 433459228, 285008929, 294247740, 57699235, 318682376, 661092246, 846826335, 891747048, 972837684, 195398509, 458471828, 638486477, 587492457, 392934426, 670145093, 367082123, 303579892, 587409590, 367871209, 487101033, 648496882, 649066910, 127591853, 971647819, 359769211, 667856717, 563923094, 273965097, 375808430, 764146873, 619527090, 569498808, 185691934, 201096024, 533321913, 155732167, 773746770, 829525200, 12704995, 324036646, 519135377, 218759573, 851211328, 972653591, 860432388, 341073787, 682321552, 874816717, 474241532, 741707949, 698767573, 665450439, 314318819, 543025726, 671360259, 343429482, 374205649, 66280333, 417174827, 66733627, 34402780, 827627515, 622610078, 468527659, 608522576, 553829909, 81142438, 350440224, 600804587, 291652375, 719447607, 667014106, 484366927, 9832563, 289040403, 955812336, 184870454, 962995234, 681863091, 930555095, 438546657, 186611733, 263791856, 134924568, 916498230, 609915058, 921144623, 57768779, 540171059, 405181060, 845157368, 883042092, 730200495, 846252703, 102729796, 486140864, 42447510, 163255333, 654856308, 917003722, 403006961, 503858815, 538599290, 675934636, 936111909, 976418568, 200362306, 611539664, 39070953, 738462202, 743875722, 241859874, 86435041, 757793426, 982402508, 488240430, 482842128, 243714532, 416876628, 314576054, 41010666, 418953234, 294359027, 207616777, 26788133, 665404921, 767796171, 524913770, 366098380, 377805212, 481939401, 528554373, 869677543, 553512815, 616041375, 396458470, 550688074, 568267372, 713549012, 386417663, 340123730, 379004262, 356059942, 226294874, 851798200, 360515710, 915401661, 154489727, 331290182, 537142736, 724635893, 764936566, 36867064, 486991815, 732159684, 480819820, 317156030, 414819963, 10016064, 284570321, 73473225, 149060841, 867013019, 742192556, 462441031, 984065928, 761948115, 319198395, 984219625, 39225119, 543631175, 606085594, 776068222, 357970662, 982389708, 527391514, 925697961, 632909341, 641384538, 90181203, 470964050, 208080834, 953965170, 335975073, 894853448, 551653016, 437086748, 351605762, 626452027, 31621754, 195073886, 225758913, 618296343, 55102818, 334278314, 7917897, 538106521, 287729755, 383082035, 206212480, 462575901, 220507873, 252604834, 721432937, 191134678, 436018837, 790009747, 515250124, 920092289, 19503635, 923443136, 495220738, 296949612, 499502416, 529587784, 588190820, 380734938, 7673109, 353822881, 617294784, 990877302, 365741249, 767116027, 975108080, 113666952, 583716893, 218327265, 19853496, 582026769, 809194827, 428202960, 389018100, 763957594, 110451641, 52901237, 298601510, 483326178, 229895715, 800796509, 341330265, 180134857, 922125075, 22222695, 398709893, 947604247, 295610348, 712174446, 105664902, 683496116, 826689277, 618879679, 57596535, 376548683, 353121407, 961604189, 673926525, 577964494, 48000897, 365127944, 620334038, 326710914, 668792661, 901298634, 822488650, 794946355, 429411583, 910362980, 228958156, 452191162, 636364310, 879875554, 808140056, 237246168, 198997819, 367495508, 548807281, 972544801, 249580346, 684235576, 212463328, 923846095, 561953842, 405337479, 881571243, 668877112, 16660947, 226244183, 376959597, 893298186, 449289764, 191318581, 80957429, 33511474, 675842242, 996241835, 952632695, 919670753, 175269708, 601647580, 592320107, 479414408, 902981250, 591930367, 144311335, 580886039, 973499131, 130107036, 492784579, 489121401, 629273101, 983902159, 489008324, 811265436, 597599805, 238761746, 444007418, 969747416, 864733530, 433182420, 483637295, 73498815, 626196120, 129041756, 880471100, 480680984, 586519419, 459369412, 521041404, 777648634, 117751318, 163997202, 667041785, 297989835, 710370803, 94561169, 381711416, 317266594, 774390056, 914744581, 883002584, 491893296, 833386647, 838281323, 949308724, 372811195, 116808615, 402242444, 179912794, 145706194, 701575475, 106692995, 776417674, 314294528, 679173257, 631593114, 224987625, 465722210, 985425561, 796824345, 857440220, 461821714, 953176833, 828541700, 796940027, 135498339, 605623037, 656854369, 444065039, 396458514, 171258516, 556031370, 469741682, 7397230, 4219904, 351475805, 789146615, 236364028, 843756364, 74443189, 179770669, 397624158, 742603231, 889495339, 201427596, 5327477, 745894600, 63996448, 253135428, 846989016, 790300779, 951732393, 915915804, 175927359, 906336756, 123797243, 245447158, 452585175, 547053068, 347968338, 909229602, 185582117, 820371683, 916446643, 711914451, 687446554, 49897982, 730651734, 563153769, 870096154, 558074612, 859661960, 194444350, 876941697, 347945894, 202454467, 855635230, 950871654, 273766173, 866743283, 595629952, 980743066, 181203002, 582264567, 548478633, 255199325, 170671284, 185398562, 453345284, 512336371, 86183090, 738548395, 70766412, 870043105, 867550859, 166077018, 917620517, 517787900, 724080071, 762764487, 31997107, 789546888, 447833651, 588435600, 367234626, 182184899, 470464761, 160659203, 359936480, 45083361, 641578289, 180387523, 440660628, 151494036, 556293303, 226497298, 334408873, 907172166, 828509239, 297236443, 41296330, 540675921, 159535303, 131730619, 782233904, 411700535, 476409781, 498490620, 890145264, 317753981, 22970112, 885527673, 264046689, 57178584, 694014832, 198128186, 30695887, 811926600, 28774880, 580359712, 57043878, 409829884, 46124248, 847810066, 515881569, 643844292, 377165565, 22948327, 976482811, 660656499, 200887910, 387864455, 933607765, 902422673, 281539824, 272625510, 860430362, 977121259, 73096174, 620593897, 185657507, 988445606, 741203806, 635719818, 575357481, 576720582, 349859154, 985534735, 521907350, 646671393, 249517211, 930094002, 297514818, 661265136, 980285616, 461842141, 939580308, 339047235, 809090028, 628256057, 279489132, 901888856, 112971530, 374521482, 613954060, 561894501, 856248154, 894977908, 847033127, 354125631, 409771776, 228625693, 296629132, 8117768, 104282401, 678572599, 839387840, 486450280, 456039268, 71739024, 464140687, 644358671, 927239779, 475176379, 681482526, 961758881, 377356443, 501026596, 202898036, 510585546, 169072035, 83937670, 4595799, 977964674, 126513318, 406698925, 330831011, 176312697, 132085104, 482965805, 810260854, 881697755, 309990223, 99632950, 272228587, 872366526, 125603819, 2742574, 225607444, 23145879, 94490556, 787042847, 52851301, 862809997, 792699737, 108522160, 20942442, 306428892, 163104000, 4661450, 338723835, 100777029, 504728952, 925632455, 883092859, 862522080, 728745911, 821042410, 113748306, 423043218, 985481976, 474969036, 278306531, 816497211, 135757576, 926325856, 15041179, 797017291, 723675866, 221956385, 996164513, 192846703, 856619905, 530157886, 845110458, 54259074, 270342140, 34870765, 40664998, 510098287, 252829193, 840010128, 559609517, 761978436, 848942762, 698897065, 297576479, 275509301, 132725015, 600053994, 260477123, 447920643, 33550505, 335402271, 419804315, 466274013, 106546213, 7529163, 388615235, 749221967, 426031085, 519230967, 514739233, 954877551, 584844218, 774420370, 447252620, 870440162, 677523067, 601455663, 391840327, 88471678, 161008517, 780156447, 336952090, 336628184, 337283056, 653724324, 563139167, 588273541, 406658416, 482502685, 372362244, 256223426, 409359964, 296581178, 802182322, 408385770, 134752209, 651496078, 534625947, 816432599, 757926787, 405859894, 688369059, 762657910, 632568526, 393604446, 715925460, 685022046, 676682167, 133285741, 31454709, 105260765, 287929372, 98767480, 474406154, 635822053, 247729182, 916745539, 24831511, 753266867, 920549734, 285459780, 583757843, 845683549, 618965195, 268000951, 471387087, 801385687, 124190190, 446238836, 510866529, 885039959, 835214864, 671631057, 289633712, 659502431, 676978182, 605938497, 699221668, 292094042, 66522209, 826123030, 96440501, 693020866, 617453224, 109434966, 145491868, 245859268, 125711799, 241558474, 969680759, 288181130, 359344248, 643998815, 437012749, 196646952, 987454187, 284591148, 617953402, 724809160, 950475454, 164004520, 53163086, 631914509, 203019362, 680012499, 486116711, 327398822, 344669571, 322455415, 440257485, 219210613, 613098551, 733114827, 966845655, 368150981, 472997049, 832746053, 314709901, 356848495, 45310103, 11495101, 116088379, 750915118, 602441172, 242201815, 729091162, 112834686, 250321012, 294799336, 772171979, 552616743, 928700273, 292461327, 130709905, 982619242, 104156562, 601703329, 124541087, 970144206, 197792046, 884361342, 452832993, 169537468, 219593812, 501728297, 491597095, 929434050, 130867816, 201257434, 894556046, 483482374, 32883887, 139366535, 737617356, 688953550, 671592528, 641385013, 584531965, 900399981, 125681137, 233394656, 274536766, 595881705, 409942393, 192621321, 491564440, 797220862, 382783583, 234278869, 36553456, 940891120, 36819341, 527113079, 858562935, 205433759, 123048110, 600826128, 859411036, 448907849, 670831254, 176251243, 532097284, 59616782, 900539634, 889977413, 647181117, 898018787, 924494055, 890289457, 110219462, 225516025, 921200494, 182512810, 785871351, 316394213, 227596901, 808554732, 71703732, 69148396, 626726128, 1798557, 933857878, 607006426, 748999151, 4321383, 305760124, 804705132, 767288300, 678052927, 553284908, 573663636, 741777042, 165267129, 903839259, 120447644, 217925224, 52430468, 740552407, 930473456, 845426805, 520508704, 628541459, 318569498, 839059096, 868280752, 423943197, 817389675, 469595531, 223080730, 666219349, 665722186, 448499114, 303451800, 972154163, 972479279, 678565303, 653835275, 640398416, 813677280, 954211185, 559012781, 958919332, 286088331, 625048582, 514708691, 552455713, 309227984, 873292082, 114684743, 334211309, 499050015, 296956512, 184988105, 687088582, 234856724, 430227954, 134682257, 228872474, 848097322, 826822322, 109860416, 422221014, 988852142, 483716959, 235292441, 243600819, 488760846, 271992603, 740334265, 244268581, 691407980, 838137667, 202956240, 505962167, 850324694, 3349762, 553301611, 505254221, 722324538, 78601730, 569969653, 277259333, 285499814, 837051945, 216699390, 637406658, 376208177, 367570998, 413661212, 645496411, 458415977, 482192890, 880342763, 206999997, 414982358, 275223772, 50155015, 259469436, 426621261, 336326639, 291023206, 143926585, 225946478, 765965796, 236336601, 389694926, 381127283, 774151632, 588500792, 849457117, 243390443, 130827739, 356763102, 824771450, 87030658, 986917369, 439029920, 237808951, 621182029, 910314896, 905883793, 873682096, 19242787, 640826214, 205896220, 458974965, 395028511, 539442647, 873332839, 717461274, 781828381, 26428472, 21153563, 420663862, 275239080, 913751720, 281420450, 574323149, 748010259, 300004029, 983578714, 289425554, 223677541, 696847298, 174736207, 357746892, 293586102, 798679170, 80489296, 49203521, 444606354, 517579096, 890362, 540864560, 97303844, 83003913, 437918731, 686557714, 427765563, 404571157, 583356583, 121767329, 307250834, 67730423, 114378140, 667581224, 770549951, 389737291, 395690499, 839999034, 787109808, 585220517, 391274859, 666248469, 747717465, 183465755, 225113917, 600005044, 342415898, 966510085, 614913071, 705767272, 451448482, 30344064, 780733398, 105792361, 414472504, 760140901, 840536392, 40085320, 818321515, 50397349, 955004606, 507217007, 101988130, 488607273, 593449019, 66371307, 253091136, 348929162, 955489919, 285918813, 282975631, 658595287, 409231728, 58037122, 675011486, 127180205, 670699126, 947041699, 194080518, 693189736, 185250129, 334071912, 967392144, 65493604, 928764664, 303252248, 954365315, 572010347, 576359153, 391222567, 802902666, 758911763, 392617843, 86039599, 802781024, 693493902, 981122953, 213813093, 641777514, 501284357, 723199664, 727339629, 477367497, 759729243, 146747192, 444717074, 973569123, 19756226, 223381607, 565488572, 604843051, 154805992, 215198352, 773212449, 930572549, 545061838, 467941895, 521336076, 701466521, 697073507, 957819095, 409120419, 53759854, 281513048, 733266615, 4910806, 40910833, 944652834, 978605087, 825052224, 918531286, 713061914, 785066264, 56390282, 360426274, 373349386, 981069491, 524326342, 394247191, 98960435, 878347566, 711292623, 782691781, 236419327, 681126817, 814341160, 551714376, 909167471, 326292833, 716967455, 101698517, 472856111, 111247948, 839616281, 159523398, 630298072, 127990918, 891226469, 971800985, 132449749, 840029759, 269039752, 913908785, 236184071, 730409819, 559948447, 476590933, 461326704, 221151854, 572741138, 83477005, 670353105, 682806114, 907596298, 632771854, 603302546, 32886548, 910657183, 174170901, 718136293, 992008755, 855045301, 911149995, 595985489, 307714586, 296666108, 620953656, 553545282, 44215538, 764289353, 437869353, 652565133, 548776981, 624371928, 304510727, 735348659, 764989076, 703715115, 454303815, 199832372, 289464370, 46548203, 381115850, 482409240, 35978902, 149164644, 868889705, 264799525, 565771304, 812999009, 469411215, 809816419, 160437232, 637526657, 384578962, 679566640, 564663216, 504588511, 865925422, 29587467, 950408418, 409742411, 695690912, 150455994, 796945065, 537295991, 464160776, 28958948, 505090176, 746323068, 469127001, 536821268, 482649347, 416632822, 62791056, 895752106, 854181370, 791644428, 79841183, 856344430, 826254587, 226385028, 418438653, 67917395, 345845848, 292174679, 986006583, 559425015, 367531302, 860971582, 790650748, 49317265, 380665090, 710847768, 288004331, 838059416, 896196119, 459404025, 164319372, 572560578, 5943830, 49485371, 843705200, 499364473, 218905253, 414167994, 605172940, 49228608, 917072389, 632896329, 971409546, 981969270, 498936392, 771327816, 729453855, 953617847, 933845562, 783027208, 278727887, 704623467, 873295439, 479398287, 876634917, 808110052, 703418274, 416676476, 314518350, 990561521, 852347051, 431994872, 461307215, 541707199, 740515128, 493976775, 725182566, 936649233, 958352979, 634429020, 685685747, 791104406, 34382681, 196538391, 973234092, 351650745, 345889621, 86410884, 352313118, 606676155, 679874097, 730936564, 201986400, 871906801, 927518447, 750256044, 570391195, 105667717, 654128049, 885222156, 687684113, 341940086, 316855415, 735760478, 705600508, 637894636, 210879259, 769822496, 119103462, 550539254, 333340353, 725845607, 174681440, 433247493, 638557674, 887099369, 652481864, 95646192, 360268839, 15955113, 923175130, 181935554, 505088335, 16491360, 603147841, 9288260, 821797539, 300312201, 722923897, 890432301, 137284260, 691741435, 149706566, 691511572, 769116979, 61969019, 460078229, 630549663, 694316263, 319662608, 104562049, 461081254, 386100012, 661128038, 908213403, 48041314, 661208216, 986587935, 134675772, 530728656, 828820069, 179027029, 279018548, 97640576, 983059275, 340252855, 624689365, 503055932, 973129303, 528637317, 421095680, 278295349, 642041209, 939021899, 390274696, 322290460, 860438092, 112738244, 762205294, 555726569, 268052326, 203216584, 669205560, 556306054, 749735574, 344580910, 505501134, 262766513, 835048030, 943446984, 90828088, 536857971, 423194284, 67833057, 525100934, 79960703, 389503131, 338483308, 491745598, 377048760, 956591711, 485672305, 184248167, 414036985, 342422481, 128634550, 826732250, 342904711, 821432949, 410408595, 923145832, 808419766, 820746292, 123056101, 159409537, 540184669, 943230537, 555799281, 710852613, 787672388, 817950462, 492171118, 221902451, 344133191, 466564251, 194397658, 904997399, 144217127, 806127641, 833805314, 948393596, 606334435, 538629988, 909469702, 76036661, 749349291, 263522953, 854480219, 134694354, 291331006, 752579238, 29062063, 371960640, 394687799, 322649177, 651352068, 37732590, 888157838, 319910846, 771517761, 643885115, 458942439, 695343007, 398758037, 621110599, 309804837, 238673791, 856255292, 345941426, 208013511, 592503474, 902772098, 358282202, 642853710, 467250413, 612289238, 301552794, 154222321, 95093949, 195130427, 50523602, 943070449, 217020775, 358374187, 133557566, 738068678, 539039130, 565556441, 555412908, 338843807, 439613602, 202812134, 885993412, 595877238, 278231593, 997838, 500187968, 166595810, 638586893, 515812053, 188300332, 855229899, 871528443, 130886270, 116518331, 849864864, 965131394, 798553897, 331847007, 994952886, 421995641, 476623065, 480669366, 82358760, 78036479, 402781168, 380932997, 169670953, 519363053, 566001954, 581995171, 241622037, 157648577, 965441588, 612135753, 780178461, 599726211, 459326904, 915836690, 602779896, 112140350, 456423045, 349782424, 736444539, 119661560, 222143840, 684482421, 998291294, 165298808, 770169259, 954108310, 231252306, 737301406, 57848756, 360225415, 345911722, 543698896, 157852617, 490650056, 431049609, 911560495, 825096320, 675745013, 859162873, 198529891, 912320941, 690359806, 363237608, 691321816, 105982303, 125197319, 862436071, 139152477, 725459976, 921033438, 432298987, 772879296, 225212789, 20950410, 613513404, 432368867, 209738028, 291782599, 875176014, 804438598, 390691163, 239875313, 98760622, 551975745, 532697518, 105056754, 349776781, 781700800, 659111405, 814575300, 743404864, 739079188, 514699840, 804143217, 45364360, 334740023, 978979622, 950136967, 899594829, 336901138, 336203818, 543201571, 140780247, 151744781, 945649362, 617217204, 630735148, 727586314, 490507323, 237734096, 498903434, 599979152, 282346108, 828288270, 985293504, 764253930, 887694761, 118217935, 211875695, 234251843, 10846381, 471783375, 383902524, 185004101, 638933348, 20677419, 46314637, 411553130, 816224774, 575512227, 357724543, 290333190, 721525481, 902516420, 694694770, 967814971, 286034969, 841975341, 354070098, 912516618, 818681805, 478964684, 558919400, 439700605, 832116761, 78545697, 809688127, 221307383, 762900447, 321893098, 994657298, 24050401, 115333034, 948004637, 226522466, 421146368, 938428405, 856962571, 457512206, 298795358, 705814317, 747074629, 21228376, 110677274, 746741180, 738116987, 806559158, 232329030, 643051145, 907336445, 274744220, 837532937, 447079665, 662686619, 259318725, 799138610, 485997987, 660217053, 933255629, 8341985, 691637318, 680174990, 28286320, 277199968, 957597187, 503674190, 355678435, 583150280, 578488888, 173050782, 356160870, 272766889, 788769798, 613874650, 181071525, 768227955, 613620265, 844399132, 651441904, 745499022, 389402757, 34287391, 87573708, 425450813, 373817438, 559397340, 798025027, 663884874, 870941742, 376060394, 818874591, 987521105, 456322473, 337465632, 536426008, 646094503, 279024863, 202786552, 928973838, 587162111, 8429221, 647637822, 424699661, 589632519, 760543189, 48252634, 370554614, 291807795, 304007348, 137676343, 821940483, 810829822, 513664098, 555492136, 512338234, 990397981, 560797927, 565239395, 715639866, 91524072, 405465832, 488492651, 441539634, 72145902, 289681499, 859694498, 242113879, 38886684, 283735977, 683663134, 799659506, 835436816, 110595009, 314122949, 903760102, 22067498, 206763432, 562060807, 106396445, 295499436, 613840029, 466551265, 346002768, 680924679, 258012048, 816645268, 275254233, 585483240, 149682394, 755818049, 328914047, 221499693, 707575074, 587765055, 369437643, 58085309, 593478057, 917168857, 235122881, 721189667, 868451074, 674181995, 204318573, 971631273, 587639507, 454333542, 114537172, 874288176, 629309547, 945749805, 825754442, 877899969, 844743981, 486077053, 247134248, 904109391, 594232523, 607330933, 60748620, 14406065, 5566852, 22239358, 407190185, 923881596, 180113533, 835639918, 50470171, 54440417, 647176874, 610242836, 691984243, 266176250, 824068704, 821982808, 698217839, 225370685, 63518883, 952146662, 19657490, 419932757, 571220793, 900836556, 861589379, 476021213, 965793140, 797555721, 116457912, 293261432, 197817137, 534155213, 490447102, 733809577, 77844804, 171381719, 260601824, 928527557, 244247797, 820553431, 204773163, 52360176, 101972413, 171360852, 867606768, 82165652, 526387722, 985631026, 290106072, 759855402, 807110527, 317674205, 881674003, 423856579, 848029640, 972866653, 136334119, 136559370, 188463765, 768932210, 603127921, 613174942, 106678716, 514669162, 193243324, 806673394, 595212036, 806269040, 376718278, 157047787, 77613923, 152364447, 884126242, 175918582, 47349028, 59724266, 546964648, 57920770, 11649154, 307161174, 800271947, 959775225, 720039586, 870406532, 146826486, 426961609, 177195848, 804487503, 516748787, 244954215, 35709188, 490776006, 150915680, 213367083, 721368191, 774135925, 260685473, 220104800, 472708911, 135714188, 383187876, 53833603, 524432219, 80006580, 480410995, 148044318, 680693558, 8586433, 253248078, 457890364, 766940868, 257725607, 548957002, 716719887, 810811760, 671524251, 202386948, 88833046, 150519682, 922953352, 347813392, 435240347, 202587742, 93839713, 13389153, 57678313, 564720428, 183038246, 564132429, 704467733, 355476753, 908141745, 449078475, 918688047, 975332906, 593670707, 307076699, 85209204, 390017776, 959132141, 473579778, 562671400, 893081691, 79445535, 230027991, 719671494, 965579250, 875102964, 856907308, 658983928, 683474607, 55860287, 253074879, 18195435, 557051844, 271769533, 242428763, 966472315, 221773383, 10187325, 994326022, 924088331, 280164032, 549775492, 220695223, 5935796, 98245626, 653694498, 299877552, 12730345, 782156317, 174715576, 568102857, 177580844, 637450897, 824093476, 482727698, 847740988, 336609075, 621795591, 384674326, 136859435, 674358444, 476540217, 971275049, 99492352, 427427542, 937202132, 422252832, 146785784, 67535817, 383910161, 491480272, 254011856, 436333050, 82755129, 117154447, 385082049, 136271296, 988748912, 546611964, 383804073, 887131933, 45151721, 380189921, 932472524, 277011637, 716469536, 680991030, 269679694, 991258949, 176615894, 17848481, 435140172, 260254920, 230403270, 806470406, 39772746, 938738535, 257921557, 492540317, 82245532, 759057151, 14149720, 395216121, 437347485, 311507049, 882587167, 647949106, 574911325, 741818117, 369680553, 665518829, 160771262, 669326095, 63223708, 608628001, 612850383, 90694529, 708243723, 543995122, 9209906, 262325093, 137157594, 42555553, 291935867, 414567606, 227175997, 100458958, 203757346, 504846195, 360363930, 151027964, 630675399, 634851570, 201821330, 123277950, 434756967, 747547905, 416867089, 882307725, 583599663, 475878034, 994058731, 546231854, 457192237, 983414512, 669069375, 855001571, 936106192, 326052715, 946808357, 754699321, 390765667, 840326069, 108869970, 127026639, 692234220, 650050779, 95759900, 293574388, 570782694, 526935413, 648999508, 754311583, 214199957, 744028519, 2304376, 726168141, 475541854, 102287863, 969256118, 506518449, 75577967, 554455292, 503034289, 589589630, 861881821, 657012121, 514592576, 583460693, 378698819, 36028169, 691386015, 265052856, 104135172, 509562845, 89207967, 892482165, 565132366, 732971426, 403600249, 313473211, 232142287, 909328457, 774539011, 796340021, 420162188, 27699558, 945769706, 521386974, 699084015, 569844064, 32195462, 145197302, 642453169, 468493954, 445520908, 651461231, 458248100, 584757412, 334213607, 292159922, 725233185, 492984528, 101991714, 627240544, 766905790, 146068322, 559799179, 950266577, 926894461, 856201297, 886963573, 273745742, 467524539, 576441682, 880914033, 948626084, 427053829, 65258471, 137685114, 362760266, 860803823, 642320900, 931925641, 859753493, 428283504, 112458531, 903321851, 85650061, 735776755, 269406872, 309530367, 340617417, 114380725, 707953050, 760009743, 530671511, 473515676, 95600707, 525392749, 985865135, 638182885, 829854427, 366370253, 362202081, 55235577, 465415577, 169378517, 818087595, 441592080, 258366899, 513898218, 245121834, 68184269, 115224273, 787290003, 159580737, 869537237, 898236406, 892347526, 970367335, 899698428, 984744348, 657152235, 7363587, 515271277, 484200785, 532555829, 275278136, 116324293, 749936481, 124127560, 353605246, 46370184, 63202707, 370889449, 379511661, 501921903, 868416257, 506782284, 912390534, 884795451, 636230636, 678356308, 103644459, 348294591, 543320365, 242767690, 149479300, 195946807, 745323443, 7216518, 851283052, 366804198, 368974071, 705562967, 153518813, 114926258, 648364568, 583506564, 298330907, 181180761, 702721907, 137851351, 710263543, 69354365, 705882748, 220923563, 974896599, 738566654, 639989257, 955948129, 140850334, 214033467, 820952564, 416419010, 847052002, 669903894, 163740643, 349551190, 174248521, 213665898, 523284567, 924303256, 853386511, 60184732, 445178658, 567731729, 534390462, 561520004, 979769005, 932171805, 773097747, 34357031, 316403543, 417081338, 735412862, 199082204, 581426460, 979360032, 715187034, 233068558, 83943100, 683759560, 130228751, 766964379, 879425989, 653869498, 528901189, 107368811, 59425738, 229922493, 892495044, 498236613, 18143948, 92660556, 975641339, 115068012, 855953476, 298126797, 257684600, 77169612, 499521751, 478895060, 264222632, 466122319, 433211568, 293168106, 496419801, 549051806, 409281199, 170688542, 156880158, 766590699, 661521286, 803283306, 745217998, 403863913, 943107221, 617760209, 795309020, 720875721, 872589730, 729839916, 740205226, 327454719, 202358411, 668662336, 855501028, 974178232, 924855711, 323003065, 395950820, 70049937, 944279318, 235055303, 554134171, 83735568, 292011708, 49387106, 318167373, 688151010, 34949517, 824242771, 845060380, 570343917, 759083058, 707538060, 884743745, 189323169, 210819071, 885590227, 968142327, 538390328, 35635346, 325658756, 467180583, 825985223, 63249766, 731693602, 776634886, 700332387, 324859279, 330340226, 301799609, 424276967, 38788988, 634717331, 213422863, 869285908, 771772551, 424447633, 686834388, 192793150, 110427689, 421066872, 209456923, 554077108, 35853865, 271088511, 950328874, 184829257, 390325820, 872071978, 98916136, 81552763, 574089113, 277857582, 732168773, 454410956, 454538162, 455351644, 236144580, 1659457, 176675623, 820912686, 640242954, 818779024, 371952997, 392898626, 91028079, 567123672, 256269082, 61820401, 258716796, 555378281, 126265018, 469487830, 435339616, 768075780, 70968156, 876105811, 371183512, 500151502, 324546295, 47778727, 50337072, 442679933, 474472837, 690074591, 927272434, 228427782, 364528393, 637423291, 980089571, 583276353, 695690639, 558185162, 560321472, 112244078, 392865247, 706516733, 1656220, 301376287, 205462660, 130598688, 760877984, 220368876, 217919318, 951648062, 645909697, 17474576, 689710760, 890362596, 375205433, 376192839, 132528688, 461951919, 757104989, 724473182, 201776532, 789325430, 464557449, 659250166, 333513947, 966993822, 881263999, 815291444, 913592750, 709679605, 748796784, 82829789, 981770720, 542796769, 871137420, 770133026, 667621315, 439574751, 211609952, 15849313, 14928787, 36810430, 643974683, 854599615, 841687364, 785968862, 468125314, 910138025, 892694944, 499313696, 762698695, 714442871, 595664782, 682265691, 141930260, 525223351, 66393620, 614553709, 883345846, 392703851, 254444664, 225232690, 959942403, 562830936, 539060386, 912544770, 570022475, 700253021, 788937068, 325693846, 72504614, 443153637, 179828399, 875025950, 899201023, 694724759, 500370607, 935451366, 671149078, 611126471, 726211252, 545326521, 487370688, 624871720, 827046844, 524705311, 892501857, 230433073, 827208306, 594136075, 538403061, 899292747, 414664621, 311041070, 340742686, 253240631, 493936611, 675345380, 874560121, 85315334, 932527581, 352039737, 241189109, 525908691, 872543759, 545989814, 50022275, 541296573, 477173609, 115364959, 231054863, 319870221, 292449731, 131150743, 44932674, 915181829, 921158680, 693286406, 93385091, 322058882, 830883148, 588227288, 947429181, 588548669, 626359636, 286039825, 749479910, 208508512, 806448281, 333900185, 471427354, 395658046, 780062248, 472008926, 610397618, 229806023, 374426893, 935282657, 462577939, 329384861, 388572206, 497670248, 848225897, 547428468, 881782401, 824764778, 247550611, 653416322, 382089272, 708622038, 515799440, 341910432, 783560193, 801958685, 260277932, 734225484, 58571710, 968234331, 950679564, 40882327, 18013510, 350684687, 304793769, 535542062, 102905832, 979203410, 945585518, 363959263, 957699593, 59995644, 411531503, 888266082, 229699695, 466385135, 573259930, 371575018, 74383622, 902184992, 550715783, 288073628, 421047061, 151886996, 250283484, 820218107, 766390764, 885829088, 634266381, 455238864, 637366487, 176686085, 540812841, 328968709, 176004607, 231899726, 206072983, 900738122, 138638097, 622907281, 591976426, 787117516, 535145501, 575444631, 27725670, 807880621, 469439073, 668587202, 166149648, 223411827, 378963165, 304550695, 123260375, 418491674, 922956338, 343027861, 536631160, 749228358, 207932264, 158016901, 705971590, 444177388, 726613016, 784131472, 116679968, 938414849, 16367477, 839745756, 407845471, 106695849, 593878176, 97356939, 314893976, 2846514, 968268488, 522628479, 64377992, 621618561, 855274227, 734763803, 767151458, 670815194, 42029422, 258588342, 170603394, 81700595, 978778015, 992081609, 57464663, 177126987, 776135248, 865631391, 593617203, 851523444, 773824165, 530510106, 779469747, 498707049, 119433100, 137352230, 44216490, 286785875, 71504542, 580360531, 975455207, 468408904, 405568612, 694527315, 898360512, 149935983, 449108722, 427355409, 327962366, 489937337, 693436784, 333433819, 719297385, 769490185, 776200899, 934956318, 158569034, 253020288, 609106240, 732846629, 84663874, 471371648, 720382108, 958998990, 507723267, 419829295, 80225311, 487150532, 950738926, 3430117, 516585994, 29142767, 643058330, 186998545, 535575652, 448191150, 121286426, 399645281, 599765259, 307308142, 986804728, 560757730, 87236170, 312320140, 139438494, 232692573, 917688073, 921790919, 643384352, 546527237, 579090022, 672527305, 712905698, 30052355, 628967414, 482379736, 193719946, 112832345, 243505395, 358504750, 24075559, 99548599, 758350951, 40489715, 587020259, 711902830, 121622733, 991181638, 633322347, 448098176, 351872113, 620258171, 941019160, 91161752, 884770882, 302263958, 691741439, 255440173, 266519561, 868695145, 181289207, 884569588, 448753541, 278386382, 284245954, 970953939, 563633677, 508670467, 679989832, 319290798, 11801001, 108017570, 456854893, 266437298, 555669671, 991547963, 532451302, 960551919, 326846073, 456536437, 66276165, 439668258, 985112083, 126179431, 309577683, 419438398, 882987168, 555156767, 958429322, 169054784, 451934911, 539483127, 729069190, 696651651, 860358192, 308747659, 642305120, 458383730, 260510331, 298520398, 270742503, 183716021, 269919265, 337010906, 513430455, 415985173, 631474877, 487506409, 832258382, 544495751, 981544004, 276171933, 576375244, 868544121, 948782522, 133279796, 194472743, 642826463, 942179255, 266807784, 587529394, 901415034, 929267839, 304449273, 735351637, 80090406, 885441773, 172139801, 702067046, 103275760, 237330117, 552583032, 56528879, 808239634, 144966216, 206857902, 290674099, 85742924, 58982834, 796374944, 79731924, 885749807, 262686532, 966719064, 292734274, 881304802, 433235623, 537888688, 954009770, 899203755, 828655006, 776755052, 1640305, 445514844, 375676120, 793014763, 424663698, 714839472, 360245305, 458463238, 390456519, 480695832, 194554506, 797429904, 869196094, 485182581, 672850488, 249054402, 479767955, 710170579, 886252867, 887220724, 554197520, 873243211, 910424585, 47537497, 610349096, 366002715, 802307285, 738538115, 467610997, 423770258, 954644317, 684592324, 705665793, 372926940, 179867106, 183710997, 307119506, 98923337, 433293027, 735926330, 627600774, 670447739, 366627820, 533029743, 764410816, 447078597, 358641666, 733554720, 558429025, 787114366, 584658444, 152806148, 521662336, 495977383, 967533333, 568439445, 77498217, 747986989, 273625379, 389085302, 951879217, 274811098, 271186816, 510690350, 985949637, 59584883, 93444095, 123697588, 219102102, 267447424, 433179110, 828062261, 567270738, 743702449, 385890690, 399356642, 969201907, 99213397, 60979064, 352989121, 145345896, 665062409, 257686693, 595007060, 423396808, 100168047, 920318490, 184347211, 110323543, 57001415, 140938667, 568489613, 335773341, 895372793, 119440823, 995639148, 233013901, 613393549, 543219909, 206936789, 307507512, 275143189, 631854910, 451157202, 957270270, 70784487, 774010358, 973925312, 635786672, 635830223, 475616917, 652204546, 606119472, 482837571, 97510842, 55474597, 506624402, 198119621, 351042923, 668017966, 980428654, 631997552, 778083995, 972609456, 273192073, 921171267, 657034977, 615405942, 970238036, 991519368, 94095573, 698823338, 447845233, 591163093, 571954615, 105215583, 310502912, 77905150, 867750460, 488618652, 967094310, 40464037, 846935141, 941164019, 356102489, 651963731, 6581141, 994354608, 446671283, 822955993, 805366672, 598428618, 145505227, 513553007, 309723983, 165042571, 453054383, 562110516, 875041805, 982455263, 321886292, 883670114, 763242352, 456153066, 472060838, 7694718, 337278401, 491263545, 438924010, 132550381, 894544756, 161497010, 578554682, 776271620, 173693672, 409440823, 383316325, 889960780, 283999912, 299242116, 836119371, 779477969, 952345007, 1822695, 780723747, 713080760, 86048811, 75027027, 833422506, 616533921, 192618947, 477527418, 299937115, 103812986, 417557276, 237446074, 196692687, 331363292, 506577868, 963666839, 842913865, 578674580, 993171949, 920378068, 419746648, 108767772, 987110604, 255783249, 855161158, 937897954, 223684498, 906829785, 751350480, 556616670, 428263000, 187802756, 369535168, 22409050, 608599937, 377348119, 203877753, 498270685, 356016524, 284793323, 379957457, 606398771, 676232392, 951854943, 226056479, 15214552, 129658903, 378507923, 930625094, 548240350, 864966259, 687846877, 417755409, 435326027, 517071990, 515916956, 616943564, 254768048, 460391539, 6864041, 588562541, 355939381, 288970036, 651986402, 41974164, 906744755, 902734476, 112046412, 949955707, 696444998, 187062165, 345795892, 424678796, 340598699, 524948301, 436807114, 531193319, 963470308, 95332154, 678494, 320247713, 521835661, 442933984, 37044894, 93065878, 523214246, 713982384, 386228639, 91100065, 765952518, 291473594, 232666143, 934964327, 175785672, 519728603, 237001126, 389465806, 565507093, 272402094, 261536197, 717387700, 955060270, 297227441, 521334422, 892188165, 715397030, 108225671, 779563045, 980838937, 317390814, 640185686, 910456731, 978920065, 302428314, 807272364, 7396458, 636394723, 146751457, 963430689, 390052477, 564551528, 595326216, 882805077, 788631235, 265080355, 462365221, 493738036, 517694527, 158275312, 366784662, 322554012, 207316595, 744829110, 656852493, 840395999, 281640970, 790180811, 111631846, 240592073, 542908201, 914405062, 212193152, 862381010, 966154767, 139357650, 48306951, 19475070, 49389253, 19206660, 65732259, 463097181, 899369707, 698671060, 995873494, 705849805, 479058271, 447231419, 643086455, 682501270, 119852560, 872845083, 790712417, 143470199, 135706664, 483309646, 363431818, 945740601, 163478453, 141798578, 574538163, 702460667, 877201479, 904778641, 322102672, 932270289, 630042072, 495832682, 693915574, 952125000, 287905787, 304148848, 652946821, 835074170, 561377551, 736168301, 146083540, 376907967, 850298809, 392490909, 151750316, 704579621, 181950923, 180492138, 921061895, 528951091, 168926287, 246855845, 248518134, 135201308, 925979845, 536981869, 930263165, 532242300, 403665954, 141172132, 575348962, 831574975, 969446864, 16108215, 591697570, 978663069, 350410349, 104240580, 612196289, 232106382, 30265274, 418829924, 15271022, 91623646, 828826811, 336660646, 944823689, 814296022, 584524647, 113959689, 592918500, 919925271, 92268890, 136161402, 676893957, 882875255, 687466714, 997404824, 264401395, 251939028, 508283141, 486692434, 963118156, 622941553, 828584826, 560811358, 505098521, 339978712, 72171785, 423118143, 375018048, 51956455, 160255989, 803562895, 596441865, 274530900, 512160471, 94469376, 653871935, 621589351, 551499856, 882319715, 690293583, 386741161, 770347171, 652166950, 440321041, 817756727, 722025010, 243539685, 798193956, 46930266, 793065396, 847129961, 746929258, 861800377, 498695272, 841816455, 116461079, 686325084, 144874362, 953450875, 833900322, 591271968, 395747787, 401686608, 225556733, 516240302, 144979124, 157676674, 607107569, 3432750, 949948017, 745392729, 63542942, 659642152, 25117567, 886711964, 475606311, 91616962, 743467914, 61982482, 690974422, 138278389, 770779882, 388760211, 561617718, 607551183, 814668189, 48811564, 944517479, 751611178, 181188012, 698447667, 921864430, 989393815, 804169204, 886465091, 4387282, 274994456, 716297876, 577037532, 874157217, 774758921, 115555542, 313107152, 733863515, 810029767, 296523874, 870718943, 992647024, 854368664, 255400373, 869503914, 809990388, 224301561, 258867384, 620207327, 884297498, 832671236, 159501282, 332840833, 959969738, 693028047, 967015808, 916676212, 284524462, 532519596, 945768753, 493636490, 362548430, 467642394, 781247093, 224812698, 695422093, 803004582, 995686573, 858884124, 195081841, 371480183, 394169937, 144116012, 711390215, 530670288, 177078281, 881327104, 121433004, 770085133, 153204672, 955231892, 526263573, 839452711, 788134836, 555991436, 329472069, 707560300, 210264620, 805486672, 895831690, 394873045, 392934552, 576923413, 583161310, 570606215, 70503153, 822823210, 665104746, 94920270, 642022586, 513913730, 495235283, 369102101, 609077285, 368221387, 571495548, 35334214, 873274120, 986814245, 856316143, 381252008, 100609334, 689881690, 74604615, 629591717, 325719955, 310872557, 611304417, 726766727, 545721172, 368041401, 88204103, 154737100, 148139423, 470661186, 649853036, 182243513, 74737695, 151355991, 894461051, 29659168, 320651003, 981512410, 314726936, 56144783, 445494332, 153986407, 128926050, 966133246, 950792303, 223656292, 150264472, 641198251, 733866688, 131885652, 353358916, 922048390, 853314598, 668935139, 166639345, 914057094, 349524314, 60462785, 92467363, 837453478, 362631547, 221621319, 423012988, 637028201, 618518387, 738750798, 372154872, 799993132, 415120339, 561383398, 88925474, 820494978, 10899583, 234119662, 345350503, 378467238, 147557989, 424814279, 545713361, 123523479, 289853388, 152830254, 434139310, 400319918, 424557023, 236042522, 954474412, 462994095, 828302752, 581927112, 704542424, 632336669, 858016091, 719659656, 57083315, 504854839, 999804147, 742314772, 982430809, 147753224, 908867605, 652400858, 37544173, 745444242, 907938658, 531312267, 568754806, 368062200, 907359768, 883082959, 198725600, 796810940, 799280573, 679181684, 923917684, 107228158, 35217827, 526309800, 267967457, 127729356, 979658525, 938030672, 293764509, 421772526, 811188271, 920767480, 885135259, 34766920, 917979805, 963194062, 204999334, 924015343, 149114695, 480928707, 239562850, 299527827, 399328486, 302894911, 67580434, 717850837, 747585250, 624346814, 738639410, 991989849, 632673558, 587551502, 378297625, 679613555, 269272833, 687440043, 206438986, 39668953, 196185142, 473507543, 894038368, 508951305, 524045414, 72733531, 245184278, 604661201, 866201575, 411130913, 896203750, 953912436, 427306860, 19866617, 667465041, 260552312, 292019987, 926229608, 26759030, 207070298, 514610940, 166796552, 917714569, 640007719, 272218503, 4597287, 491179699, 906931951, 463091417, 132892671, 85102585, 370579793, 324146645, 361831684, 619476102, 334038744, 983259417, 291301567, 609087148, 398560472, 408818465, 787801656, 586697615, 406360524, 832246073, 523714337, 635510968, 534266701, 373772858, 962299414, 578366985, 815019476, 724021607, 294203763, 364271537, 391174523, 126429611, 285527406, 86821739, 655742104, 265558015, 153546345, 788235956, 490046629, 241181594, 722735463, 803394234, 163808599, 146229773, 227283438, 58867878, 38346869, 329407225, 123651859, 868183109, 414730506, 43879381, 476831716, 428711514, 910284705, 142706388, 196307539, 432632714, 542798442, 877682885, 216328893, 832151080, 319709459, 233765328, 326083365, 163326539, 491059235, 956980624, 611642624, 338076427, 165813792, 561578910, 241721406, 796918389, 244815394, 334672285, 472539996, 898754533, 202444708, 784277526, 278167097, 448200616, 674250306, 724145841, 484699195, 420267206, 150786425, 581293310, 885094717, 414629154, 555275662, 133557870, 377427790, 291098209, 898192025, 823249061, 842842143, 445126544, 397661994, 424963644, 745410415, 508824224, 700595147, 122181631, 787874844, 232980128, 549090463, 149809765, 879631952, 469516616, 620542162, 809442621, 589783613, 421849187, 544625527, 516492741, 33831176, 825491522, 599095260, 40709903, 473332836, 103145381, 207119510, 795027050, 84204844, 39950258, 893090428, 110596398, 114901715, 941632401, 425804493, 472523318, 298550752, 880177501, 12473290, 156208959, 236296481, 266097990, 844039930, 509351427, 302792335, 165374307, 166470241, 265524680, 866115923, 838777377, 707056586, 493203129, 72956163, 55902063, 286040398, 448059451, 621056266, 538082217, 598728978, 319869940, 301912472, 293536909, 233057995, 602703016, 619908138, 267514911, 627152641, 225538197, 754629052, 382315027, 571584223, 641358940, 302247112, 604430680, 749919411, 589925466, 181445279, 534278055, 556553124, 488285658, 200661929, 98342706, 155397252, 9021193, 140458782, 718891510, 367477087, 68376954, 805971623, 858376239, 866185668, 440684837, 973655912, 635919368, 586655668, 833376015, 591519996, 787864799, 964317923, 892487850, 11599050, 801944243, 579172522, 648930516, 178991711, 622467715, 293885626, 871844038, 272721736, 179483051, 442119993, 129700711, 456306043, 482882176, 780089176, 433840362, 670554388, 608732459, 735479003, 575146514, 937742681, 739505228, 348990345, 305334206, 485412220, 762800245, 480697380, 658454823, 923798667, 256970248, 680189068, 37636149, 440938159, 834266444, 95884343, 370360320, 645915211, 454162816, 967392992, 365839982, 903000133, 145765442, 927640532, 638338891, 266441311, 202623879, 793130415, 256894220, 257631253, 457741237, 431727403, 970282182, 897949930, 985300223, 132670971, 331127632, 556209084, 311402446, 501701199, 596407850, 301391186, 192343275, 444894232, 87672957, 165272137, 446226718, 288183703, 514291581, 305974118, 385252367, 349281705, 629808030, 231815123, 11287835, 800692246, 941063064, 959644771, 993982166, 902510165, 433188547, 382307751, 795072631, 76227188, 946719109, 656610378, 363517976, 220647518, 675859711, 618157585, 871741823, 872565625, 618635039, 638594634, 660099276, 453189706, 183872699, 540625816, 439116372, 565707134, 622113578, 774162586, 825907126, 324323272, 388943370, 505606266, 412159469, 735348062, 513483467, 81850395, 512232857, 311450230, 531830771, 974052892, 411227079, 603780940, 373263019, 509218741, 545612908, 886859106, 196977323, 662699448, 302032628, 944564479, 384506444, 488996038, 546116948, 809579210, 995232937, 468270477, 728381769, 82696677, 900453105, 969148145, 454848546, 22883066, 344072144, 965565691, 602901591, 138656677, 327092176, 917342360, 998258752, 373197919, 259326045, 450660759, 994469174, 89599819, 947973068, 670190307, 837160430, 888616978, 285700723, 840693851, 490215546, 297128686, 913445582, 217515222, 244264505, 751395994, 758810134, 915654708, 536099760, 254581020, 624416967, 880232173, 185954925, 543632249, 995469485, 105617258, 597240425, 258241905, 556734907, 984676320, 987356805, 421329825, 599474824, 967360915, 727045330, 181483502, 824614087, 166147642, 293294125, 916824041, 567519903, 785761901, 552464942, 143809581, 789407012, 406787517, 811986331, 209767119, 823222158, 529769634, 873870003, 611798913, 627916917, 366666234, 786893389, 582774405, 731991491, 578758121, 797966041, 975466734, 710296024, 527643379, 720527602, 616917856, 330291796, 282703823, 448804916, 291831906, 452353619, 550375831, 516743368, 593065074, 272899779, 775200403, 606709336, 601193919, 524576405, 918191729, 46274617, 499115412, 927017556, 35132116, 627310871, 758021729, 192199320, 989968870, 942351983, 57074338, 330654830, 206471272, 534303447, 636793561, 452296832, 438276140, 491297770, 329935092, 770202898, 438794124, 1748615, 91392819, 47543183, 453403321, 820904466, 150981415, 301968537, 452701801, 886006434, 475514856, 640602762, 326574615, 72712000, 898377184, 808480662, 774863579, 653684284, 299529130, 127873417, 455034352, 129231090, 977094209, 998044321, 267004815, 400445525, 252342482, 477952781, 368753976, 40659893, 278483676, 785405112, 664426059, 479078933, 864772132, 823099488, 124793523, 250556105, 853613125, 534880591, 435290757, 627123341, 471384628, 252574535, 928561847, 811036158, 886156174, 217573385, 73391910, 5505919, 75425741, 40618093, 252244973, 848502670, 246806849, 808263902, 610362235, 275272001, 996574938, 8946166, 988285147, 2887146, 108115327, 727941921, 518891386, 541950592, 377955623, 283778718, 28361190, 394010463, 440926209, 133271317, 480671549, 347626672, 546604599, 445105024, 381050273, 460113693, 254800761, 383360571, 101159329, 258395720, 175298100, 90532682, 901634580, 682386488, 847459001, 39061628, 213636320, 129840593, 310733600, 930874834, 990327784, 645320437, 488850986, 914826755, 800895225, 895579068, 625563154, 405249289, 806471739, 37214808, 160252333, 837352297, 543644521, 355666544, 653664054, 936372224, 306574863, 154013153, 577540065, 188899322, 691823352, 718113005, 365385828, 266291174, 13858503, 265349436, 530234235, 412231078, 331933624, 375168971, 63666899, 802313416, 527720516, 459587150, 672778956, 301089501, 423081710, 901225090, 593499454, 392334742, 795902287, 689734199, 842275526, 900128484, 211063434, 300347702, 677787197, 248435593, 154416032, 357307746, 394028545, 521016929, 633282185, 170427675, 463820956, 473591409, 195985107, 660297455, 981866028, 575589227, 874467081, 463944015, 897028387, 778746614, 719658636, 288630464, 142828894, 801057459, 184690451, 612379290, 951924032, 521031062, 555609168, 391286282, 75354190, 53974246, 66229650, 112385912, 458952530, 885625171, 23021275, 124176744, 986229494, 76523628, 298757638, 343807058, 863839035, 264530292, 986225908, 876365248, 314758115, 879353321, 547039977, 220052745, 512796213, 722931437, 316794015, 171692649, 842881864, 342236657, 917975472, 882131647, 798465187, 495863907, 809939768, 516760452, 794482617, 494376039, 798044156, 609584441, 838100295, 382666506, 809468425, 364668816, 639698159, 628070617, 180985719, 352514844, 787458800, 515827473, 642325691, 214946426, 709477929, 592445003, 806173107, 446161167, 876013435, 50007548, 297799083, 11908512, 37295296, 717996791, 490767125, 874294893, 498148772, 43362778, 618327620, 38298237, 234337735, 464047536, 184747405, 129420053, 348994397, 477051933, 86383902, 151959423, 340812107, 298676307, 14079519, 699660772, 523479428, 952470170, 125569431, 536237253, 751087842, 608074532, 664524512, 68129372, 9952674, 49873519, 380510512, 203422621, 987072174, 570789444, 182246862, 720492066, 89630060, 301926964, 204684736, 428160456, 837484358, 14802017, 287680419, 842677202, 850589827, 869200526, 574415787, 247704157, 148834752, 66040982, 123877551, 467221399, 695839313, 187814205, 940050030, 650770606, 892883758, 940148431, 546549758, 188653710, 255290844, 373589852, 41231012, 740933796, 461105205, 391277908, 603152949, 270075551, 535898091, 885461344, 356561999, 132291423, 508045646, 780307560, 627122574, 311592502, 975815665, 971798504, 799269356, 229476148, 433929623, 545579048, 520406933, 792285903, 262926647, 868834617, 866327702, 431162924, 430712191, 922931634, 57934821, 56939843, 901697136, 634933538, 435735818, 890779075, 895787103, 740592899, 795718413, 73770894, 411971232, 616779171, 686631320, 17434940, 901082226, 990355630, 26073092, 893290752, 718741982, 15817275, 396159623, 439769192, 536687688, 409041321, 375460237, 726903754, 744583089, 95176535, 271096027, 794708694, 412146867, 962417877, 676618997, 802287983, 314971139, 982995668, 824348349, 972048244, 398007832, 874301221, 417259764, 311844891, 266544947, 584075787, 646931530, 397519138, 769418646, 486765023, 214259652, 425888144, 303576294, 271531483, 601533151, 613339182, 733404296, 9037117, 281688442, 237754585, 224655655, 633105198, 144223196, 132576346, 177602999, 399775620, 11388012, 546557989, 336952206, 448420545, 423168116, 943473857, 552410916, 72685954, 300330885, 290226116, 711962458, 780947784, 821849596, 37340619, 610668379, 384188274, 162832941, 615346970, 983287822, 399999889, 827734067, 600904655, 827182963, 72835723, 1882420, 545429456, 73491434, 114618822, 433267756, 116888631, 589387650, 845301372, 264743483, 625153601, 69944367, 476754039, 92788613, 684096680, 702463541, 795706332, 116976674, 959473333, 978152659, 443230374, 632497579, 848217106, 311570505, 657215954, 694136184, 570011564, 742659393, 221826734, 768384054, 749266861, 529266899, 742761722, 888098930, 792141086, 810344667, 383861085, 541791435, 594637530, 214321276, 6984070, 912973937, 808715057, 761545155, 795428989, 23030397, 429017170, 688580868, 340779581, 182014525, 205130348, 405033927, 875857301, 310859184, 401900222, 351614880, 443651237, 521054434, 711838904, 491484205, 366201873, 545606480, 942126991, 71694912, 21067186, 780789212, 293240400, 620345274, 604082622, 349965163, 765718018, 668186108, 509558467, 513007567, 605441828, 410904600, 90405754, 850707225, 791898558, 549506723, 561456968, 964345611, 616873596, 316829414, 167034092, 960471006, 243921860, 614598432, 60426610, 721470774, 913804889, 636560575, 117160897, 79078865, 506129953, 782962495, 580100759, 183769530, 350907176, 327715291, 772787953, 412679142, 448137890, 969887211, 676345825, 468362466, 457561512, 164637160, 436103656, 466716692, 828382635, 969168693, 189198730, 34098184, 3936758, 681157714, 634728414, 872721254, 19357754, 314547457, 675841139, 904492518, 507740453, 220285964, 182135160, 802458941, 551774821, 625545370, 431876775, 486249991, 100675084, 39329790, 162578671, 983965383, 29880211, 695044460, 808763743, 275758821, 188858033, 700043065, 307968769, 394560728, 59484228, 908746993, 686939191, 269557123, 667157071, 540637765, 928007816, 247782077, 601783824, 44112449, 455801232, 695013943, 694296254, 912364252, 365819073, 959506829, 550247855, 533812956, 527508777, 446235493, 456201014, 104505397, 644669223, 78856818, 2823817, 869569880, 535827997, 287856424, 676223169, 998463186, 232853364, 84877932, 351611229, 870951645, 580869385, 128295189, 665838561, 656999584, 986680065, 663912516, 982237972, 397312061, 334839261, 793560253, 489321895, 673524807, 874975187, 733336535, 10656562, 785979102, 586598088, 401169500, 480047996, 683142738, 488467739, 331800255, 819107208, 308291766, 919263145, 368892775, 702418498, 941156596, 843230716, 168303138, 339200830, 151238269, 293811828, 636546226, 915190445, 520779519, 361500850, 632764460, 961378241, 791689907, 164452298, 952277767, 764566567, 340192460, 967883740, 822832603, 671768829, 470879563, 923413731, 25469199, 395722862, 236615763, 158796580, 253969848, 475790578, 301309177, 213654090, 332021664, 497547795, 437212269, 273358068, 189921272, 916385024, 207310048, 289618102, 60426327, 218231185, 195344930, 720643675, 546482435, 907899725, 351847449, 655873359, 139708810, 696992767, 708644321, 171692055, 881991635, 799665838, 106927263, 647008223, 726201694, 397925443, 191874191, 984364530, 221886364, 556254583, 742728273, 401321467, 214876464, 111009628, 17206575, 125800790, 718917939, 152347749, 670369029, 333297101, 696308007, 288863174, 34517868, 101442393, 992619071, 768161222, 924551465, 950211572, 493114986, 160677183, 211901592, 888750564, 47618918, 213008077, 433645396, 215817435, 392178034, 206054879, 401233372, 155475931, 668611310, 12821259, 463284122, 346230224, 601861501, 58793622, 661529293, 648724007, 614368842, 149991499, 656102564, 672639642, 341567825, 502547036, 304236456, 897374338, 883070938, 428403912, 395261413, 197960785, 129980510, 180010531, 428459985, 716399338, 311689209, 149002891, 572802555, 343489154, 343021814, 898955973, 666543661, 941382000, 818325545, 126481719, 114324926, 982304227, 298783203, 745503651, 86086994, 161986264, 370765615, 698533623, 162726222, 738160, 433263040, 475053811, 310664236, 335411774, 178588684, 223073608, 772885567, 741947484, 12290239, 26253301, 404429884, 598404125, 899949247, 900571022, 32856945, 998378771, 32076170, 958600479, 921129482, 510466177, 646357604, 564420342, 42132468, 224195589, 896221288, 349686319, 954673529, 365360133, 992899817, 487070882, 665646282, 604773642, 1460249, 305550267, 151913172, 800448573, 14036045, 290321947, 72406835, 826003256, 722790567, 152241456, 229143652, 544978378, 315019194, 392159707, 579030142, 505781024, 396742972, 74800308, 199008712, 298603643, 688307947, 586591358, 150633435, 403114930, 47947623, 446769450, 176238795, 655817105, 499348563, 444935006, 788678218, 662967083, 490996986, 251842920, 943590129, 179630074, 854523420, 644109561, 527176433, 183772572, 304044887, 899887787, 540756633, 781006572, 600559505, 424861304, 804667207, 209414697, 737701331, 503556648, 906817629, 708922232, 541901006, 219625270, 309847175, 973405048, 195108353, 211013935, 740946229, 554436000, 288766619, 116581453, 99091325, 634095317, 743289980, 363307103, 767602166, 78846441, 949331330, 776849247, 346677500, 339483782, 757233173, 531334873, 248098655, 74848433, 787281203, 483042081, 108785200, 14219189, 467252231, 598123755, 584137330, 618786693, 76122061, 280267310, 53597258, 50433, 654872353, 903418784, 766408580, 928366249, 901395623, 253894243, 883034621, 615278209, 133688832, 421993531, 999018179, 149193276, 67638395, 410232611, 442958617, 785534753, 77637401, 230040367, 479898234, 592610609, 396099784, 218254833, 35755201, 331498140, 217067918, 835130370, 193482687, 880456923, 404852749, 195940842, 493339561, 922818668, 820949284, 737475283, 128041611, 103211608, 270139456, 14657653, 379386365, 374941182, 500435173, 78007237, 472931379, 82973594, 671761292, 70693774, 376850305, 105767505, 304037986, 682672402, 131354088, 174391381, 980423116, 91125335, 443242881, 305949450, 880410432, 292589045, 331332955, 619290473, 291590523, 423541466, 362100794, 736900387, 996613634, 115860406, 535466247, 965948402, 637207533, 933530493, 774421891, 801250329, 661513075, 759458728, 371670755, 286000082, 886156773, 795134825, 219369784, 819246072, 346580453, 944022174, 300419973, 192416786, 994106014, 358001539, 520636341, 123761905, 617317945, 931184747, 794536486, 136865201, 920340874, 580998900, 912869313, 870758940, 29992511, 129485203, 326484779, 964556322, 798926643, 342241933, 534966597, 124463606, 440725577, 773725945, 760332137, 733795198, 957475303, 924525101, 603629045, 54918110, 883432961, 39902531, 631827353, 671016870, 375508762, 271911117, 508465664, 569131029, 799070652, 409156375, 960015883, 777650744, 332839557, 243917160, 694670980, 211898915, 903705106, 218469681, 375559666, 324848344, 702507170, 691176882, 363229748, 198457096, 546393996, 885361019, 609200056, 625961947, 685921736, 279682649, 686726864, 505113256, 408516041, 148329846, 165978143, 138414547, 69655709, 586375818, 887197533, 676359569, 497595236, 904006824, 358498106, 516998418, 935561268, 639818292, 375938374, 277095901, 375995861, 17005462, 40445699, 856273067, 93498457, 346598611, 577731049, 64583873, 994212105, 659663450, 595891342, 844431411, 663309197, 637968806, 174483447, 513380276, 290946521, 438382391, 814999036, 239155666, 610362153, 790519741, 577287939, 639331173, 944621688, 726768070, 239255543, 338682043, 768088012, 607063683, 665298424, 368576887, 572801090, 335807413, 426584624, 435773950, 910730713, 305467628, 648849761, 678709970, 626490891, 464200164, 70741406, 796058874, 824884178, 738293702, 679344135, 63326532, 273896295, 356762371, 377311173, 280646572, 483266298, 752554585, 213947707, 657309684, 64911532, 954620878, 811473857, 213983233, 77482118, 99628467, 899493599, 575879863, 605679706, 662625655, 69729878, 129229421, 452111255, 281007894, 313549087, 273788629, 108674048, 75959654, 879478982, 519650375, 615372462, 139655937, 918360455, 146960176, 791588028, 910399417, 415392346, 359736088, 255086754, 283480667, 410732249, 895110302, 911459787, 919933740, 65431407, 403073541, 430036526, 905790089, 79396407, 682499236, 167154571, 607000550, 804016076, 625519789, 928047637, 936532140, 901643602, 26720944, 676613180, 471436224, 49933686, 297324987, 233956336, 22129611, 794780607, 918537993, 523751141, 938579852, 376957581, 611406753, 477927167, 222696332, 271305893, 441693984, 143029511, 810972822, 276750446, 321055159, 344401480, 448742598, 619688596, 343080708, 339181696, 294737224, 463973433, 960057776, 269592995, 507248204, 76571901, 178750008, 864340241, 574898443, 483960010, 289954778, 497838627, 853955021, 748445065, 569820404, 543330594, 208672938, 422070037, 748509560, 519151625, 17385087, 719120883, 652821490, 931902317, 838515551, 741547470, 289317732, 275068783, 441468735, 93846130, 693527201, 497714943, 373257452, 194090028, 674883654, 669929382, 136719254, 733851459, 946640749, 154276204, 626140289, 50971535, 146593409, 847125238, 13552481, 264244105, 90694158, 654490466, 280889241, 201016917, 903650490, 295188707, 309426262, 638636276, 396325123, 962520707, 923345196, 822841181, 380769599, 455961062, 999725331, 636192306, 199402403, 827671442, 673041276, 842922546, 237433195, 104761135, 223271237, 638587592, 188038520, 797837043, 847627243, 533043627, 489754229, 716453475, 525611192, 989919750, 95325611, 955172076, 101616556, 429510399, 388871883, 19586955, 571647659, 125797802, 293410195, 159716827, 198461715, 635370187, 930424018, 991799994, 241644123, 412298026, 132276558, 376286947, 205156727, 80558342, 44829025, 951931587, 958770975, 489470582, 531873901, 988387269, 310182346, 61474329, 980863399, 685534612, 692584015, 765445331, 863290921, 454516435, 224011572, 721585223, 908660042, 105470106, 68514893, 463351585, 261646247, 278292638, 204380228, 551615909, 674839502, 241970704, 581101112, 293935148, 434447651, 988896418, 569242090, 764709062, 315320549, 437659134, 783709708, 127704439, 716388362, 211326767, 333938654, 541168286, 685541654, 370393190, 255725586, 8893496, 62872005, 847342482, 551774194, 683354662, 66553395, 156459029, 172397137, 168906778, 583568339, 462724340, 536287852, 331989100, 634625191, 49228659, 680208548, 887978957, 951239241, 510596860, 999158628, 460738144, 530634364, 38982663, 651011682, 835827155, 421319911, 303065814, 832916271, 6050587, 13846289, 712448018, 823916272, 98777961, 291839000, 422147718, 653444134, 761849787, 517575219, 419449888, 323095579, 400554889, 177396677, 517415247, 241120896, 511433096, 959880267, 629126861, 338640531, 408131218, 81177141, 909485691, 700667988, 926702780, 115795199, 720522834, 180094153, 38782772, 384881592, 12511436, 311219493, 672282046, 621007104, 166741549, 952644572, 24913865, 682716803, 149062035, 462340922, 199075798, 26804309, 767075080, 105418231, 913943459, 667230213, 856665141, 227727181, 322745531, 544268719, 70979046, 269768693, 561155050, 697603842, 728329100, 12110230, 87901922, 794481070, 371949680, 349557075, 414028142, 554644361, 525459991, 10118179, 218996193, 550753069, 68690847, 405786394, 590623793, 690281826, 299624392, 641476728, 186062903, 427876269, 556699292, 90827153, 254529764, 76448192, 58626746, 894784969, 237502058, 414914067, 846908037, 410315037, 28142863, 31329956, 801845595, 754702154, 376178684, 628207947, 381382525, 447251018, 284405322, 271062214, 56133800, 292013256, 682170452, 738165855, 858787481, 855357450, 416860527, 364340461, 184541618, 561022938, 252951136, 267572225, 460694378, 875575753, 753493851, 258450717, 597519669, 700612851, 601158630, 916438192, 641077486, 656423550, 22252651, 226087878, 131260791, 240906970, 317045123, 119723954, 166098720, 195992370, 444903541, 437897218, 44827118, 716118441, 381948945, 761209146, 443227941, 486623214, 611834393, 332447121, 228493287, 973806621, 819904428, 511521344, 881948390, 131923683, 209379351, 505052162, 266036243, 166592801, 712178986, 736268010, 653308054, 262084944, 821885157, 666673440, 713641571, 627266225, 112471364, 209371879, 804741543, 744361944, 132630387, 95221373, 271849332, 987035534, 967444465, 67982162, 795081122, 918827024, 941028497, 182381077, 864339740, 910768127, 286630749, 863465483, 845974014, 862540317, 118138316, 355834318, 206765204, 771898792, 411476977, 235176627, 780530546, 258158566, 159330900, 990454778, 716420018, 663935911, 57813671, 524698374, 558699861, 880785065, 347731648, 902335221, 837214244, 673860608, 86688260, 410732329, 555069253, 377140157, 819287456, 751106451, 795847026, 372882617, 197127629, 240630482, 268067386, 532016953, 357585902, 153314804, 767981330, 965579128, 67237623, 677531904, 738594042, 405583994, 500379918, 598998450, 492452769, 354614282, 663594202, 575652612, 981469393, 682922365, 284528613, 845172222, 514513371, 441257139, 606497071, 644581541, 127103713, 297081306, 986034290, 626976914, 87079739, 858680296, 517661094, 899445476, 451119850, 840949042, 98162062, 631766070, 883402986, 755621240, 897651921, 253753529, 547515114, 728526342, 36610742, 729900816, 870512987, 642388420, 696443642, 841631900, 280402127, 881318253, 546709055, 741269194, 839050921, 286673707, 380998572, 577533871, 899041661, 658902204, 553494749, 917849700, 301043018, 416835579, 188084781, 333184088, 83782853, 74959928, 550593416, 410435428, 423228123, 620186139, 405336576, 398136752, 238786087, 123026884, 452546620, 482232435, 627808545, 208023342, 698724327, 419858151, 367093967, 162366386, 415665732, 968454208, 105905229, 573220847, 900967457, 134537768, 561394427, 107955419, 325372000, 195523567, 205661693, 87640724, 928588384, 444596737, 883012296, 497195069, 191417356, 219372579, 838174267, 673340110, 160680407, 714183442, 663325544, 946232681, 761246386, 141615665, 632009517, 635405561, 255739305, 270583368, 6944142, 681557621, 573870163, 414443635, 208372401, 298441957, 269170877, 561364130, 87721945, 693421826, 252275985, 174708161, 469653640, 430923183, 441083119, 945533193, 402908285, 560287630, 454874936, 217653437, 293468427, 461873338, 88216183, 334312852, 899278308, 337485539, 396731771, 610455615, 860801047, 945183959, 961273306, 583788079, 531335757, 639198311, 142805099, 909879525, 56684068, 972955898, 383010318, 607567242, 893686454, 189610923, 535372950, 894081626, 495055506, 650907982, 817658155, 349254229, 34198369, 735451633, 134110135, 989271421, 827903203, 902380669, 547880057, 750107407, 298153804, 882615383, 914483754, 66332731, 640587755, 81591074, 842616307, 444203697, 200761439, 45314613, 726515575, 316054017, 66256224, 956210915, 979747849, 929468409, 918759870, 665054446, 806990525, 74142709, 346278783, 92644597, 269590534, 120429939, 434396313, 902231352, 843156542, 781832105, 415341446, 839467572, 733530776, 587179384, 743508669, 567105516, 999697132, 627628762, 925188168, 72476184, 624152952, 177522627, 717418657, 443193142, 645850974, 798532585, 258106406, 322208100, 730161695, 480612445, 551451680, 66338743, 253996567, 14591279, 768096111, 679621195, 944344902, 127556130, 397322805, 308251137, 825763326, 62690554, 394306103, 565840757, 585417733, 978146697, 51323027, 897146886, 680298996, 743211814, 425890723, 986045401, 79385801, 800607579, 590046893, 918530227, 880214361, 248008268, 136451223, 414462709, 106246156, 760339822, 222763663, 412206048, 548964361, 734455910, 512053442, 357198455, 145185777, 496233824, 585730543, 827546901, 652452552, 664339678, 653544641, 896606895, 424508389, 10467801, 985880238, 175410638, 574536484, 596291562, 651437510, 983078692, 326565071, 113996189, 847860218, 423716923, 627642701, 365351782, 226428374, 932169939, 960210570, 421739310, 28770625, 454406572, 805715140, 803571613, 238256145, 148728136, 9282402, 456072206, 66415103, 624613891, 656039714, 462014960, 250177827, 475493920, 231780914, 818210545, 478591414, 115545679, 771692702, 796758438, 327752691, 859037348, 270791036, 605897851, 52048956, 420854182, 261797950, 714169887, 950807361, 627195349, 68060776, 631753392, 230170385, 955831605, 328152179, 729762500, 310387070, 437654612, 566094822, 97911755, 44859308, 968631313, 684461643, 531398224, 919544240, 710886735, 493679247, 723002848, 723869410, 648725168, 749146416, 409447894, 165318127, 991963035, 96180763, 331647014, 154600813, 292849511, 105580956, 90291943, 959698216, 409913325, 997919630, 480800483, 749015222, 546388853, 617986451, 57793326, 586572287, 576968617, 117965959, 630201430, 382825744, 799344490, 85723407, 560855590, 234226442, 416339500, 621822316, 619723654, 812202653, 568010177, 647993810, 674848194, 713444706, 466517203, 857780345, 155927926, 229949410, 814423837, 763805298, 928479430, 364541547, 668404485, 483509723, 923225243, 332916744, 346868506, 370905457, 774757, 738749918, 489737661, 280927732, 180909091, 78465236, 109782126, 902887017, 339849969, 129463468, 51499631, 187508184, 449199152, 794989349, 577005586, 284508908, 939624244, 26757668, 703439159, 81678396, 358808565, 296162318, 137613777, 288382971, 148855372, 998848209, 227235588, 387021303, 280472482, 354506741, 580729944, 382917430, 830110564, 729092905, 121585280, 769147090, 592813374, 584912320, 317255748, 179163968, 51686420, 25027308, 934512264, 161702098, 443793277, 967184172, 250632330, 724825868, 955516663, 607872580, 831652022, 997584260, 667329734, 229629883, 696949903, 148841464, 373969723, 191661210, 865002772, 632493178, 377069407, 489176238, 139321969, 471667631, 679936205, 294692109, 484684200, 236848339, 445290650, 21481850, 478704493, 815328488, 961342637, 779085658, 871205853, 600448913, 964124785, 308879408, 436286816, 503197179, 154573994, 333199332, 932684795, 430299443, 831797701, 133853473, 79805511, 2957623, 533579579, 271696463, 460394083, 38245317, 755041915, 279505932, 861229958, 85755052, 678943403, 84921958, 348882605, 865647289, 269463282, 865794749, 987761222, 134655446, 562714220, 524563194, 997530874, 713306637, 882457536, 814062791, 572121666, 706300820, 140700616, 243414769, 817553472, 907101496, 291580875, 952428579, 91103102, 150213636, 699057774, 350604182, 950183485, 761756574, 304011818, 282055193, 909849605, 772751748, 478045714, 434939564, 829572665, 458015878, 605528600, 858087874, 939452883, 257000464, 929155288, 716382514, 267639922, 860640687, 919680395, 891680002, 646593821, 700755280, 169813518, 705567982, 89040041, 377190611, 712577161, 59977817, 843854663, 920294646, 919699024, 405836113, 421616541, 152360476, 742982875, 246350456, 589119990, 603264725, 432509959, 729412246, 286326821, 348689195, 180320846, 725467912, 593201291, 338795482, 105592593, 577378975, 327127689, 149253668, 573747178, 917142148, 152044372, 165155847, 798956217, 6754372, 635577738, 748828010, 690806017, 630603209, 408538797, 722224080, 407713195, 639059364, 556605569, 528579662, 571309180, 146763969, 141411045, 868095025, 773004146, 264339757, 172535109, 711281046, 455643273, 163397539, 707677818, 262559722, 634759254, 750784854, 281419435, 26689411, 362445558, 347359438, 506588166, 601267926, 272994952, 894590050, 945417765, 805100948, 426291912, 441232638, 178889998, 447167830, 505277314, 82126734, 598175621, 388241784, 815612342, 681593279, 235678354, 987490217, 685662353, 155987852, 665140861, 322746162, 19009625, 582499412, 76943483, 454966841, 351063775, 64378182, 247962183, 923932147, 40712142, 169615885, 251403906, 801152861, 445334835, 715750943, 537800502, 435624035, 553435885, 280275742, 862205554, 714139973, 309008246, 957306054, 913937341, 459807089, 321425787, 14377390, 616524825, 930579681, 186750103, 804193627, 970063341, 314389447, 341502069, 297567414, 539120035, 696618859, 974439982, 278918242, 867329038, 52559546, 407423816, 913320606, 463913781, 869855007, 110328915, 749648578, 352085281, 172110500, 811279626, 707040128, 575291067, 274644773, 421798516, 138055488, 714059631, 358641686, 31108639, 969260200, 76446700, 575986560, 42673169, 507748876, 579493141, 126605704, 475268049, 218975265, 654921667, 380314714, 67210208, 653247289, 687506230, 670131761, 853437425, 932967341, 411773250, 482642928, 347975419, 446417704, 868871362, 633250792, 227558268, 194315109, 902535671, 30753509, 92179937, 315567681, 321612594, 163048023, 843874771, 597368613, 422889911, 597005354, 302373091, 215250205, 350091493, 279311612, 396956662, 49429569, 250530386, 607454801, 805130917, 774415350, 97992021, 757233575, 882160538, 410618725, 844309617, 78595223, 947006516, 142019060, 705312635, 520594591, 551099259, 923516653, 37550014, 685733788, 531091027, 809380809, 172684263, 297424478, 140376136, 831141561, 503969832, 252510512, 768242558, 239550028, 838180278, 351562077, 255946236, 774412537, 617021504, 610600452, 645846334, 408818778, 964620999, 386519924, 632993836, 528967777, 502797743, 125320227, 805100217, 52158745, 773747072, 386202458, 368185807, 418805071, 949877430, 356930419, 232286758, 558453910, 671398524, 517999239, 780067891, 883237774, 545739954, 521801900, 809248199, 92759117, 639360963, 82790783, 308306800, 38804586, 551605660, 670102272, 208747103, 717074191, 663283430, 722890317, 167669664, 329645605, 386517912, 643125445, 575920044, 637390198, 422979317, 884795076, 284626594, 904358884, 578961772, 173429777, 136065688, 274934418, 557860441, 750661134, 781412693, 850166783, 774608855, 748427089, 398827379, 845549541, 820325808, 2226789, 62909618, 998953733, 205562447, 373729232, 79071585, 338593096, 96968858, 921906242, 379335254, 347100638, 327574859, 308987486, 846288825, 938361819, 46395038, 848072685, 754149018, 754540491, 777678312, 719821672, 810822783, 468719333, 63634516, 134133409, 70291646, 820537187, 680787069, 827675381, 697197975, 897044308, 698307109, 531754554, 683290419, 179397544, 731677904, 330925749, 8157117, 28285013, 327037365, 548365871, 258728384, 657911983, 40234074, 191087357, 982131566, 925037681, 122501877, 650583750, 704487043, 102443924, 735044254, 470980629, 380462710, 999883877, 42302898, 428221963, 60347611, 782560468, 508789469, 963864496, 459618518, 821412155, 309057994, 169877025, 506535880, 898907192, 641653419, 683316314, 249270288, 498629971, 992140051, 539938076, 433240106, 713872828, 963050748, 183513846, 803109432, 507946393, 997360019, 514557237, 437013867, 400819643, 199064046, 931268171, 878817652, 976244162, 137169269, 41582229, 68604460, 215777811, 439186676, 264270034, 426871234, 567858329, 634202496, 366698338, 681534882, 444240647, 173503475, 245255096, 688286397, 867368473, 352620196, 559487542, 754688589, 100716715, 130670377, 519767463, 314566772, 721825737, 494415147, 125904272, 276419453, 212443326, 976937967, 848232267, 486580358, 1267188, 25648194, 152759561, 359561042, 435275523, 614304503, 266378064, 467840527, 992307779, 54710807, 537392510, 595264074, 53931630, 961537620, 623307202, 992686224, 101851080, 466322282, 472509403, 888630045, 88687959, 245455745, 512016061, 567274150, 172747548, 346360133, 344635801, 839101778, 444178192, 4089147, 535683133, 18939640, 5944156, 37649656, 32765368, 118628500, 967604727, 980117993, 392946405, 25437039, 790936628, 299616286, 622439695, 843674799, 137132807, 336238236, 679142302, 884674536, 48454099, 393101958, 92890140, 772209115, 622588679, 265052102, 185414425, 710468344, 925327518, 735442391, 81756254, 949274129, 316542632, 933526914, 814693020, 746169328, 181982531, 661367283, 412548749, 58510848, 628400683, 880198061, 762668769, 382798869, 850032108, 974940186, 535948692, 244532371, 711341268, 447476756, 287614802, 745425920, 850214491, 843838776, 116837828, 419625300, 573574933, 456603656, 894793317, 796677215, 705764973, 544195843, 880179797, 824228109, 49960291, 8033149, 777721825, 271070256, 273068264, 962857877, 369677307, 932910095, 359677510, 968307817, 280065628, 43937824, 403605157, 899029341, 909415293, 242320298, 42675820, 551101890, 758458401, 971417456, 190712577, 85763875, 529020233, 475790964, 883415585, 95603245, 318469004, 326190724, 216259953, 606175591, 975032174, 158869010, 179809632, 704482650, 387077311, 283721354, 642503493, 496738351, 685725232, 898946261, 895952948, 762311312, 591710471, 418266692, 477312469, 70269443, 315919320, 526407959, 69504653, 384620325, 134652964, 886367240, 678237263, 183751003, 104056683, 851864103, 697017852, 693953719, 823419602, 284892206, 472177537, 172338323, 220228366, 713569920, 673711039, 424792902, 326909035, 302321676, 427180305, 752117612, 398675927, 911194088, 849579946, 739089049, 100103658, 955260157, 455617476, 833399280, 356541714, 297494720, 177306634, 308670162, 840110387, 765265191, 562835024, 563701408, 220239031, 508318138, 984108008, 267366748, 154335048, 578964149, 545238924, 951239811, 74039892, 41761631, 937372982, 357488840, 884977611, 417002054, 262360122, 772946159, 204337807, 933137264, 940374513, 108266547, 161712833, 21565623, 754803658, 722047499, 24856871, 527957006, 652489221, 301795836, 638348436, 505515470, 136400270, 7825719, 424818704, 728530348, 3918746, 652020228, 395157712, 183345232, 434228075, 122776053, 809444195, 568921018, 229148055, 3794360, 332391099, 376888270, 843758646, 756574889, 956727274, 347244236, 460031958, 235526834, 501010012, 452049755, 796697191, 39993632, 200085860, 391336282, 564388645, 878761098, 646485694, 559306039, 486593022, 734488323, 271725095, 649935731, 502638493, 585141357, 431533539, 818358988, 112465967, 475052963, 639482296, 636827380, 591562546, 332442755, 565884375, 272301432, 706362725, 617583500, 894091145, 856179598, 367537659, 841868645, 772467206, 463599641, 417376085, 199793494, 877890560, 915056365, 293867980, 835450061, 408836177, 282842870, 569080421, 468779871, 237570213, 934730525, 31496661, 456253720, 819428001, 407910862, 795238055, 771853039, 819094260, 511963906, 212044599, 485424020, 982088783, 123678139, 780392891, 753200084, 886860467, 547284180, 376489740, 234141859, 611810609, 656872892, 626862667, 295863221, 236407562, 794563586, 235595227, 729367261, 437834339, 437878807, 398679578, 532893469, 972077256, 209933414, 986081511, 346570550, 16887397, 298825433, 465372864, 111056826, 96876125, 9616377, 699442048, 297867513, 277029844, 952517377, 160544736, 203699047, 771851693, 885381977, 907906432, 41249757, 795741555, 835742937, 299252276, 505428819, 560202665, 89008875, 385752820, 50071706, 379944283, 198474893, 389239260, 515380930, 354958816, 41096645, 991510957, 624104295, 450888115, 57629690, 432469322, 449464908, 414914728, 64482356, 609534715, 835114429, 65397407, 314763470, 329636356, 35476120, 129608659, 552071642, 958225085, 323529430, 663448890, 851733307, 340284441, 410497834, 269086015, 481353075, 574180822, 769390164, 794914927, 781851403, 464708377, 715819678, 879230467, 881216330, 179238768, 472202015, 999000204, 864361807, 825363064, 316240152, 894191647, 974800777, 150860257, 148566195, 263965760, 327097434, 850321194, 99049824, 171326415, 911694197, 696580859, 353768809, 856147500, 304338549, 791429399, 94413519, 253083284, 65521456, 718755077, 565436199, 968894712, 509421111, 250891651, 800248467, 914230417, 459864213, 227712505, 598271784, 854577442, 227819992, 892123268, 219904581, 753881229, 6549793, 127969386, 268526011, 886462322, 426264002, 864716833, 381078960, 111614585, 287952285, 406408088, 451062905, 274114415, 347442750, 86541392, 858380272, 438882019, 421064572, 694523443, 507653283, 197960078, 87794470, 728135046, 680529235, 265492588, 535978045, 308955329, 85627505, 143101359, 796036420, 497452618, 415954954, 469729651, 672435903, 212753415, 607118028, 779480490, 171653969, 388376476, 581147172, 564328704, 189424118, 878805981, 569816190, 703863027, 875316553, 571075059, 967382113, 972144669, 50047324, 934044852, 579976680, 697751379, 366246321, 518281121, 149783808, 593297274, 295249702, 363776328, 596237094, 806952148, 660668629, 931798720, 26395663, 297376574, 296373375, 88444158, 851885674, 860151960, 584187081, 515713301, 626649266, 320097361, 9614131, 619161021, 270193559, 816289673, 436246887, 470115533, 633769965, 986412584, 751944881, 498608747, 715877049, 429642453, 130856640, 745131855, 150074628, 85982726, 486123260, 154575457, 455125319, 862871719, 724897306, 867730828, 128278357, 550255358, 617378919, 743597693, 684003992, 196682027, 915239089, 227179257, 788108747, 3571899, 277014626, 688464054, 369086131, 334451819, 793389349, 621435851, 408747446, 616964253, 383587708, 883193988, 1123183, 554111185, 532731235, 584501813, 414659259, 680515974, 134436327, 780941494, 502296804, 355174404, 214012622, 864390546, 775527180, 677709926, 887989611, 288814048, 67447220, 541438088, 14411424, 309828136, 730809202, 748229115, 501346224, 646098576, 608646261, 349811892, 565579750, 602775133, 99631783, 218921770, 995806781, 408783900, 804727842, 848915411, 154349963, 568731860, 397200824, 800370906, 469426062, 727644688, 304258901, 466941386, 556856025, 465266282, 276348011, 226420400, 685088354, 569882528, 410036164, 153200331, 720410890, 283582842, 410491908, 355604228, 137833499, 24308355, 724172696, 22620618, 590707438, 213167788, 588972955, 794398213, 312169768, 249957053, 95942801, 664080226, 811684589, 622000326, 447799848, 202674552, 214735186, 329113125, 997285222, 547010096, 677960511, 906645064, 919735440, 272200399, 363126867, 480481012, 285785711, 134012151, 144376510, 971086017, 154031215, 40464026, 652439668, 337360049, 248837160, 795383977, 424262258, 900293157, 986697570, 373262585, 794480290, 52400997, 648265437, 96196394, 63381398, 268358370, 85492495, 102159894, 955724891, 106868005, 655863468, 65734366, 152202448, 515496534, 441215846, 582442314, 157210512, 681004420, 157811659, 427563536, 901211481, 171029700, 898970412, 75770440, 354104895, 586971377, 86218221, 886609507, 100093062, 67482854, 489560206, 33496659, 635779978, 605998081, 915756909, 57768915, 439044954, 432337777, 114458886, 279061481, 741451809, 543919207, 204494946, 169354229, 693731920, 202206562, 74320726, 898391780, 455584595, 422818864, 919186486, 420827606, 493278672, 258547600, 526940063, 62588912, 883104876, 619800099, 31796507, 287923246, 208278315, 673850985, 526219511, 52666544, 366403791, 114617634, 993018813, 812549199, 988068556, 421044703, 107194387, 562102257, 685757969, 725541261, 683238443, 228025421, 54928069, 716616699, 861313271, 50903863, 437114093, 155344622, 921992003, 859815180, 246572704, 180737386, 149931888, 526269890, 134282010, 93224319, 979166109, 720281486, 499182947, 489168581, 433577038, 120801732, 483815410, 14833913, 626617936, 897804914, 801744981, 691346886, 280606835, 926559175, 601113551, 695812435, 598692813, 869203682, 969241779, 982550861, 567005832, 222387548, 821356180, 863639158, 109418514, 22530277, 421695699, 345462376, 638866688, 927500296, 182164032, 894339136, 733216953, 839566659, 41381720, 75642676, 396771986, 638488606, 806513623, 996431246, 296248124, 833559763, 285862439, 644206173, 869624830, 599709409, 917282337, 180185219, 86036131, 250510045, 244299078, 618023531, 963661621, 544666575, 518781856, 695498983, 323880189, 494266375, 164874342, 75809794, 922877456, 654478827, 392187569, 155288086, 544089849, 462091105, 698332048, 692415319, 79979586, 856387342, 66741421, 263370733, 719096636, 280938548, 565021149, 726747173, 885553939, 543224617, 493599536, 743793576, 247279136, 724943779, 171637256, 412260593, 722848013, 334784177, 311554450, 342143255, 374900955, 364729940, 7203908, 754046039, 488012192, 880457951, 513726520, 673237266, 230532038, 779101867, 868494497, 37247431, 147879020, 15640825, 90537158, 744377654, 111585423, 634628906, 303348504, 420375855, 825724330, 544994670, 147669783, 608199267, 902285748, 616738943, 835514266, 702460595, 464522922, 440164101, 875337077, 284063469, 422041753, 631516957, 515020451, 856728432, 685816269, 381300511, 94041857, 125340166, 499468761, 57979926, 923109699, 14000930, 634699583, 839107601, 27158058, 402334539, 624987067, 91531497, 94069438, 713664746, 930986381, 353545137, 702855844, 779370139, 552861663, 919184986, 523429652, 179136934, 277547561, 128588729, 816866211, 867993943, 175996664, 198361767, 306534287, 250141888, 83674692, 784207865, 871164706, 85291116, 556174042, 816260868, 490355595, 361148402, 705794788, 515229151, 626749515, 813950379, 342696567, 671813416, 290917409, 870041164, 916762062, 657852034, 781473021, 891049045, 864547830, 125563609, 9298256, 921484864, 27059916, 519659623, 900132480, 728916772, 665677844, 580187951, 134736029, 941502153, 643818825, 937355340, 474338695, 874782009, 432455104, 408663663, 44499553, 260969857, 753562714, 797043843, 289847273, 944961666, 806385224, 642572747, 844594414, 41500171, 551889431, 65573978, 924429782, 779477821, 495509485, 295330584, 27550671, 15122757, 4292631, 663445141, 149423922, 58886008, 971235360, 722337327, 869618787, 762281453, 493302176, 388180012, 79731287, 750579360, 916145956, 787214552, 217914062, 209624473, 450606758, 194795548, 503760779, 100741620, 608411245, 603376445, 838638985, 876371923, 639296303, 781730795, 672109053, 53537371, 411568445, 524417518, 457911631, 64725062, 303719928, 375883124, 994178740, 900747922, 114862163, 333356973, 728908347, 800994810, 336270117, 641246680, 768166341, 831748064, 895649861, 657530045, 695065858, 648617820, 371371211, 976388625, 687934547, 185973637, 520461947, 292864376, 850482963, 590963530, 878222281, 731768744, 184295216, 836771801, 221312218, 908849240, 726560386, 918743838, 988783325, 766810216, 514144979, 167957706, 408693655, 372190291, 697922887, 22337770, 806274108, 635308776, 989501188, 150349237, 578624490, 525073972, 516785914, 47128492, 616496432, 298349115, 53211954, 525213458, 589347190, 364711339, 214060624, 761766600, 413326963, 231652671, 934537904, 262895798, 99662886, 477903394, 199688112, 261113148, 978032911, 26868463, 915715766, 988649394, 306279836, 57098167, 464199917, 538515386, 24179666, 298872736, 911310958, 717680215, 276048073, 290134283, 669168552, 887044417, 636175611, 969092596, 65010028, 416014470, 248042900, 533959769, 987439083, 529174942, 495985635, 586439145, 363338199, 559711601, 538065186, 745464163, 257836812, 432646759, 57897921, 693175613, 808132743, 723697401, 230262787, 731170379, 699853154, 414914646, 175720896, 880317470, 796086404, 991240440, 485859834, 615451537, 334306707, 309024936, 757521731, 105987454, 358287938, 600556844, 885128137, 994669289, 772179496, 192183848, 333965219, 330065682, 61770227, 162707211, 20536545, 218945039, 683674818, 166630640, 829252116, 2845299, 789140902, 67324773, 384149000, 401060540, 402194662, 601508083, 170922107, 204391990, 926126267, 266636192, 135400116, 469972821, 875403171, 316058802, 54767569, 392657547, 197440991, 308274489, 954028476, 913850660, 105464907, 368287590, 273068162, 922487413, 35175674, 637470740, 317840204, 819775906, 745913217, 113102443, 400181969, 928895608, 420161816, 576203367, 7537433, 787056926, 569895057, 931840875, 480256840, 2001635, 77502521, 455820789, 609741093, 138877101, 272242438, 843844714, 797770831, 718369554, 134151770, 652302528, 617653434, 88735921, 117855365, 735915569, 365686482, 630804717, 642634588, 681956778, 392181098, 723961220, 21819345, 327425428, 578828071, 949361456, 260128475, 663516064, 786394053, 649871298, 938700278, 754931123, 730565620, 623618724, 726289045, 600340881, 755525705, 799372856, 613248770, 349295813, 557725855, 676878148, 216064521, 555912731, 445251631, 940067215, 317439345, 459579722, 414993277, 560169512, 725709116, 547485775, 814125450, 868227221, 202880215, 39030043, 475314717, 832846163, 194182638, 715185211, 849688326, 908124467, 321623609, 779432888, 496176571, 512210267, 231010967, 442708682, 120989434, 585582571, 145794990, 468996996, 50883604, 559878472, 346345582, 512269370, 970160396, 204312455, 459065748, 766358743, 678478767, 950027195, 604904282, 485349922, 293289445, 980347973, 349644510, 30434396, 92687321, 160025092, 810636066, 219209885, 730216015, 132600979, 381617323, 314360411, 436769423, 285473646, 464550614, 652450631, 449948643, 573390732, 911745867, 272216613, 672472100, 768410078, 534267970, 72048476, 770475751, 433211747, 890090102, 307267877, 469436680, 990039792, 714551475, 65204336, 818244747, 203830082, 980708030, 883038358, 292266880, 953269417, 163343647, 889368892, 121132404, 437112847, 849507005, 222345375, 246192487, 805604607, 814134679, 446905144, 917928689, 110179387, 93573028, 398847030, 399623808, 320612448, 477275905, 422867793, 544831671, 747218670, 858752103, 200209134, 511898040, 369298085, 507467774, 278895307, 896615099, 607881996, 481688354, 396870944, 156375621, 733928944, 122806038, 533667650, 822849389, 609296326, 747501792, 837249601, 159899382, 445041866, 553121693, 737480646, 728044363, 234366860, 718794084, 955038712, 810964193, 887084990, 504056301, 781716317, 734033550, 828197758, 277554439, 636806861, 846659683, 595560902, 735343718, 759967137, 94288568, 756492959, 983327460, 771699537, 664270430, 425165560, 356411160, 406249834, 36173647, 828581152, 371920765, 206277363, 712346503, 83908231, 259022213, 75820249, 21408615, 814616851, 126720838, 44200658, 554847430, 297365937, 786768225, 485583460, 349165201, 797595163, 461058346, 705411798, 651123787, 429400284, 376575912, 715221261, 31514229, 107439317, 471915090, 528247495, 825835953, 681211951, 868796897, 818350590, 652469814, 929493783, 981080253, 665645444, 630244272, 325271539, 296156183, 544172765, 482309481, 644175794, 724527481, 423493406, 750972385, 140898193, 786413728, 542076014, 112863858, 427285081, 713085351, 194661374, 512563035, 705346429, 612954891, 708235775, 379461604, 882583986, 679802618, 276762502, 403047765, 323634852, 21783077, 883909530, 304145393, 237671663, 842550067, 817380601, 165141510, 385204709, 556527271, 376453097, 185282962, 729327287, 675182513, 330388875, 898285851, 38583063, 748125847, 646391791, 459336717, 446648253, 601237180, 221900303, 763042652, 200565368, 98948109, 526976815, 39148750, 18301837, 750990583, 332778544, 384404909, 274004252, 715810491, 189885027, 200146568, 513510180, 947616090, 50911446, 177198116, 844562434, 361275406, 604781995, 275713756, 476717240, 537493560, 711055245, 343035661, 5289471, 712747965, 358820006, 179679415, 596105009, 764711878, 414813217, 156691345, 782762707, 48733515, 374923344, 68713698, 117373383, 554669450, 322987055, 82596896, 699467974, 664262635, 343798701, 960183192, 782824846, 516923083, 814238253, 840984451, 811520499, 488739315, 48336951, 406065966, 953879349, 921704751, 178683246, 688424933, 389887343, 295476263, 841494567, 9313958, 498872628, 415993572, 183759237, 834775102, 283139518, 147888558, 585206120, 617420683, 388773084, 820928328, 985503186, 336707117, 315256320, 242012869, 665481684, 538795364, 73879662, 33446534, 592952870, 314388918, 22996561, 529346578, 856212377, 323575727, 437799841, 905775967, 990761168, 603555051, 910032254, 218825060, 881604863, 555840616, 843661669, 52166175, 373695044, 137340661, 73786154, 982991049, 618588136, 22722811, 288924395, 541971097, 570878151, 983716749, 94769488, 932461477, 250887942, 210384882, 603473067, 214341056, 435340900, 25336267, 554632912, 458961612, 645739416, 394139856, 759522323, 643607543, 409203517, 260759674, 54563540, 578748253, 72878678, 236233678, 536634579, 75679693, 679180232, 630411121, 190750349, 898469653, 896511450, 143302191, 740137064, 251978514, 513057631, 551841299, 480510151, 460717313, 781903942, 429010315, 647291206, 934051996, 737203557, 302339246, 848119084, 199598161, 736806964, 186687173, 458238081, 784045568, 344161506, 532999307, 155093884, 674092678, 464482191, 154689615, 424783303, 952829353, 591903245, 956392250, 356859250, 473432417, 757950955, 103097743, 531768216, 943508160, 403472269, 93904172, 343286679, 371949770, 293182715, 838000023, 989425840, 628153203, 194260185, 879747204, 855681587, 726787018, 323438313, 688803340, 537147825, 105583318, 604541979, 443146298, 510095467, 558547092, 248372187, 720602229, 190862613, 490921691, 765110293, 561791292, 988040351, 824634967, 69875102, 521005739, 158183173, 915752008, 819268807, 753642909, 737930479, 765274285, 570904666, 478192134, 464358388, 99614435, 697795212, 508036432, 827437175, 929381534, 875480118, 536893210, 82513894, 552387617, 436745604, 140269833, 84716332, 444973359, 757731635, 594950568, 972006594, 756533264, 516215222, 77810563, 45418082, 270271885, 533405088, 878900328, 763594796, 818666487, 824604250, 392437583, 813367120, 921353778, 965863912, 502976115, 869809888, 726079363, 846557892, 121036826, 644190533, 522600525, 71894048, 771014147, 870955569, 145546966, 207297596, 513476386, 337575884, 55228075, 357351173, 835538757, 276952566, 104455453, 339198979, 887496746, 723503102, 622048225, 165570298, 499589082, 549526933, 311699518, 925681198, 812468474, 616291542, 910914849, 414274579, 425675202, 612443929, 997402315, 661192814, 622246130, 724198581, 654692914, 517011398, 198559748, 103394238, 655759834, 846254462, 125373939, 185069342, 144446613, 726502457, 730417482, 721590531, 638925057, 291500733, 515065272, 111244578, 596684814, 902673683, 813645225, 466770173, 97121037, 931971607, 219240642, 678766460, 111676956, 284455076, 897536242, 14025872, 899550715, 967561711, 568804483, 533766643, 398559591, 95746477, 622305363, 319693065, 597833089, 396108114, 804027967, 313389189, 928114706, 241983224, 473923526, 636031582, 957832647, 515903713, 66465733, 972942778, 222803863, 31825910, 388216074, 117962347, 295374085, 582410797, 536025957, 974170476, 378879302, 792393976, 960726525, 921906974, 271945679, 568092546, 831010479, 491236618, 767621585, 748228867, 769197762, 294616397, 192728754, 147449336, 976339925, 881672698, 328374036, 759442624, 785522733, 761163175, 666967801, 666669878, 464543559, 739778886, 297146063, 413279133, 165055677, 56314852, 801763066, 107727841, 372699653, 420429543, 519908445, 450936728, 918681023, 990558026, 111135976, 489576081, 928896934, 331058796, 773271178, 150033572, 198995131, 501035118, 444392182, 367316803, 434715646, 627240432, 684016276, 145210290, 412814637, 732557009, 130236232, 589489231, 922145695, 530702606, 887574989, 571561358, 500105646, 209062421, 890591626, 110457941, 213269760, 515916117, 201751830, 382304854, 670153410, 676170898, 98430322, 365215648, 809190601, 823646304, 686652177, 101028255, 937334802, 615655841, 368656965, 385095962, 887201205, 255724044, 466385762, 858537617, 102713510, 450626810, 69206676, 529148628, 878502035, 522448987, 490909602, 985659255, 781819996, 869024002, 627462289, 761584009, 253406949, 514996441, 361671537, 943427948, 845243800, 804430537, 519439175, 942451974, 592737883, 201178705, 527523063, 111261003, 446010705, 277346005, 916361092, 717429757, 452132552, 792496126, 375199045, 53944596, 349967573, 406330895, 137641134, 986179139, 48491375, 575804434, 937413000, 753590296, 920309953, 428178271, 420045813, 62391509, 706702139, 809295852, 471577460, 729630378, 624254295, 767129094, 807611863, 15264258, 175372113, 424716015, 475169348, 805780030, 575692469, 780503100, 383868716, 514152599, 443628965, 394381965, 218069882, 258534345, 810031256, 813158705, 528442462, 588208269, 11799850, 835352496, 768278457, 772393884, 648316779, 419640838, 655640766, 50798315, 333913021, 389826335, 658437652, 180131734, 207357789, 498002775, 254074061, 406917690, 811414469, 385169970, 149079005, 203619376, 101484666, 784678784, 603839225, 101078574, 486054645, 984105635, 191586059, 313759056, 66305975, 451024674, 612810514, 932990575, 57900022, 308428926, 590258082, 700396602, 876745934, 627447774, 753382658, 596983828, 849536397, 646722412, 148958789, 271151599, 491068023, 259755360, 213166833, 122128569, 508869531, 20563567, 405218909, 919488940, 702836248, 964612311, 202822969, 408186731, 49907186, 224863865, 718064747, 565432047, 567569593, 55591890, 407239430, 23513837, 769341897, 774153801, 28388132, 620500699, 184787131, 991992049, 334349114, 36972636, 974065792, 529247943, 599767013, 767310102, 265805193, 104649777, 384923079, 18542193, 998182347, 763728609, 977432054, 813385447, 524108648, 269387302, 895510798, 484737610, 885008234, 919811506, 662945840, 410406640, 70100867, 513199455, 320837426, 436209969, 13124544, 72379370, 658561194, 227510822, 541586532, 129269244, 949336543, 637641326, 945408067, 694706011, 998741526, 710970520, 278066519, 302831912, 751192825, 874746075, 252074162, 793342777, 950878069, 190763164, 358975852, 531335522, 777835336, 11564827, 236476525, 375874778, 119304879, 674967856, 557376986, 177512027, 180178734, 456272588, 667329517, 397336925, 973944517, 31160946, 942769523, 426187250, 596139349, 195305989, 635984907, 386490882, 660587907, 999611383, 619824676, 17227084, 55938837, 333266572, 881707428, 397577459, 321559865, 40824951, 383234606, 22987119, 752707189, 839747119, 187554454, 678987405, 251959508, 557060737, 214629797, 315791040, 910560028, 240838293, 446875569, 943605136, 426154240, 213893100, 956773134, 345771132, 485900458, 368834695, 89977431, 469284986, 231348406, 218469471, 787709898, 195763921, 620914208, 210591482, 362447974, 497456326, 683254754, 795475109, 256857259, 823970075, 79849383, 579699490, 337952698, 676760936, 288932561, 885048254, 517350124, 444102446, 385670992, 823160203, 703387602, 511748385, 314211643, 774890922, 18364557, 800342020, 363947757, 863672861, 131046816, 320633740, 394993229, 842239764, 852288972, 959387948, 844259009, 403553237, 964300374, 350186880, 906521954, 29606744, 678510281, 450921622, 684842344, 682643635, 228926788, 859191446, 406710617, 185072101, 987603698, 884973648, 789458845, 847323490, 379724598, 46520556, 582539708, 581895921, 630969596, 356482744, 78791390, 880948333, 219774240, 922849013, 772614649, 491395904, 937978028, 682209121, 745903076, 149836782, 774991991, 542995660, 936947400, 569362820, 425132034, 750522631, 8053278, 642531660, 418092392, 901846740, 30749447, 714847652, 68994235, 737881721, 366919420, 927135647, 94149480, 772583868, 448648624, 739315000, 872036716, 797044540, 380899023, 557821705, 437768520, 616595419, 863764830, 888568151, 183122386, 500195434, 414188553, 90661852, 484672618, 212190949, 661281183, 322026367, 63813502, 686618626, 139750428, 613171540, 991294544, 774277680, 865514860, 873999060, 288565634, 140579339, 611853532, 949881854, 62818717, 88365210, 344683889, 852129909, 517557206, 899159488, 709155586, 527219007, 66893349, 893890530, 26409467, 712799304, 471072908, 628368222, 202626984, 729816088, 415099392, 843183206, 795748968, 525599510, 282171242, 295955252, 620054303, 740125138, 113258783, 882223957, 406466960, 738348319, 483879138, 355693084, 519921805, 411886179, 582516467, 234492457, 187636266, 365958619, 154044401, 231891697, 612452441, 703298969, 710973630, 834781229, 910037240, 660688960, 74215216, 533067406, 772024495, 153169444, 350301528, 584414854, 481338995, 99756572, 250267924, 131635962, 77018840, 51566604, 625254813, 730795998, 480980360, 644616561, 786881235, 896780863, 674041057, 401361464, 719956758, 443594180, 335994319, 758556739, 135125719, 947404233, 819442245, 616399178, 592164286, 601390915, 82061734, 90272207, 971953433, 400779596, 566262313, 498279959, 574551810, 856920831, 439842083, 362431466, 761842844, 778901493, 147354169, 229573464, 78251283, 833454705, 460850306, 745984145, 917020514, 786098516, 156977047, 203985742, 324425655, 63323267, 14984899, 769253549, 375549864, 854870726, 268755830, 688940619, 179509673, 233624472, 426927794, 836218291, 891174944, 161726483, 660221818, 878174574, 845738020, 898858723, 727496308, 930610062, 520492229, 895390653, 972075104, 576732916, 760365157, 831397725, 241571212, 97176089, 842401755, 246188801, 577218982, 712791208, 869250865, 819151094, 967531460, 294404446, 186325268, 964143157, 964067655, 888538749, 314865748, 618217892, 509476422, 538730237, 400010618, 588107382, 525303110, 446539441, 440537862, 435814594, 638897819, 688413194, 402959171, 796696703, 476738624, 431791037, 922500207, 638346687, 994511884, 371763437, 218717422, 480222708, 698783115, 692475179, 593570986, 591252809, 319780532, 446400944, 946044013, 642587954, 639298061, 924510435, 457274475, 739994469, 337320416, 969271553, 618332256, 637221252, 850515743, 245695562, 667338934, 192595497, 838565030, 346840920, 75454987, 976212325, 46167529, 973188218, 26935053, 639882119, 504571208, 807119354, 675404662, 117053705, 829569596, 813071960, 264478902, 675365989, 577704543, 402264409, 693396404, 783309043, 205468206, 217588732, 288022041, 763892804, 745889021, 627241879, 794694433, 177506269, 872664144, 107701241, 682298251, 333290728, 949442199, 176461539, 637272053, 94132778, 464763205, 24525621, 754890023, 273050286, 370686514, 185250195, 609867705, 744384501, 684153048, 297229337, 974423319, 852221180, 74571943, 57799220, 561175438, 456402495, 807927340, 997838019, 410181854, 868964047, 278556548, 996586315, 166097897, 888543251, 710985565, 565316738, 955696721, 111118387, 485737844, 632671630, 899784418, 938483132, 472248502, 114550534, 847851770, 857490900, 573058159, 47634549, 119105388, 450661747, 422510938, 907416351, 41626342, 439729827, 415084868, 725796589, 649113862, 110883571, 864120503, 48867988, 487052451, 869562148, 586984334, 221533861, 414892107, 36217538, 548968436, 491854578, 722399686, 205231990, 626088131, 912659282, 359201407, 114833861, 897339023, 58893204, 243484702, 350902928, 237299456, 697775854, 773267909, 38615310, 786351599, 362940790, 354127590, 169644169, 492647753, 766915005, 360069369, 327369860, 588671735, 622752148, 704571876, 605373328, 324948891, 915069023, 427412194, 682161526, 423852732, 794094389, 417220766, 217041663, 121535548, 680887944, 446518591, 806165014, 899966921, 875060986, 641403547, 182964602, 410958499, 80692081, 334911902, 350438829, 850225837, 294090827, 908992749, 12516229, 704407435, 212315330, 496478542, 387926378, 376745426, 450318616, 740093994, 579235393, 463643947, 563619172, 393253286, 600776799, 989805164, 355755345, 106546738, 393820638, 456371064, 880803493, 900136298, 589052869, 803460364, 998515071, 157099592, 368658476, 902456569, 954828322, 296489776, 941118405, 954556651, 899618741, 286577624, 183045828, 426635932, 478636610, 987582592, 989432886, 207804794, 8132227, 929226975, 98170260, 203698041, 300969642, 3823501, 655407822, 832787784, 839831729, 723826411, 44110063, 45805773, 768780727, 803915527, 101802923, 228500655, 710042918, 520592495, 232577172, 65912897, 799661902, 596928463, 515334047, 399676264, 168697467, 885788323, 331516501, 597542709, 970741020, 731945143, 861386611, 228494442, 163595485, 688245915, 632540986, 37880769, 692485828, 966902707, 450444058, 917793789, 722793314, 273419247, 316501551, 601917799, 425943693, 372656221, 753220504, 57809936, 404304354, 699771344, 596335268, 369265377, 547928431, 255761378, 405407459, 41882974, 909758279, 168670133, 19643920, 530039352, 652065505, 136301445, 915122819, 585831022, 954664677, 240524813, 231300904, 299404613, 870297353, 974762033, 551163020, 886123309, 442120106, 236753548, 318715772, 184405781, 759773030, 16880044, 655734418, 193841363, 366804316, 258793190, 149901864, 597821982, 690855743, 433549716, 348563263, 202832092, 469252175, 649202445, 663582358, 999078798, 524236764, 216681664, 788926750, 882993119, 112836231, 699435634, 922184037, 849706669, 538467682, 30726055, 210211707, 8888794, 799672528, 252210460, 904276822, 251174180, 17395358, 945966861, 522392551, 400224174, 410338540, 391474940, 38571767, 232153778, 507652928, 333008134, 568079298, 80337932, 625062224, 69944929, 708873360, 425458898, 945669785, 724807062, 98933874, 863125421, 982197485, 893120151, 150004934, 228571307, 898155887, 869983913, 633457104, 187936621, 42225577, 773756223, 169460675, 713830794, 658975519, 110850054, 644009287, 819099077, 268938697, 465292481, 571929995, 369774152, 789873551, 678343772, 169560073, 367767432, 811547821, 418030696, 254131098, 164404986, 20371692, 427436465, 593264119, 991049267, 334039813, 94914523, 964793500, 460784353, 971903540, 427277371, 881812463, 656388271, 842155776, 688781518, 754697183, 97677342, 31943217, 963847166, 712101156, 305017474, 548679335, 989557168, 861793087, 779783724, 807510812, 993927925, 784429571, 898493714, 221123409, 353884412, 485131881, 438102851, 183188095, 93265599, 389209212, 285878914, 328063811, 553437851, 75390495, 974450583, 311937828, 787182762, 210207942, 853210146, 459247448, 267016172, 296335897, 200920242, 315680760, 96291555, 549760036, 183556561, 37871203, 29858490, 427084306, 209381041, 138316236, 343267566, 27032621, 255988707, 332409240, 253786400, 236546026, 825897621, 67914894, 422323199, 279156400, 749712197, 150083144, 198453898, 93295368, 101668381, 962265110, 165586375, 341573929, 627789120, 329505960, 854251517, 391490038, 251839354, 361374860, 670880069, 57485911, 390458209, 544530829, 375381566, 687707717, 166124832, 989417535, 800248089, 741012027, 553452331, 421589320, 854639687, 443831714, 266918798, 601519399, 648691003, 198747642, 516854115, 446185291, 493335073, 448842437, 506293932, 921860490, 85765824, 419982755, 715526694, 721129183, 728364065, 401144083, 239530932, 578586989, 49329536, 675056694, 771286093, 112290543, 652376783, 514907295, 584706103, 932426271, 342746277, 44551523, 228824609, 822648035, 762280236, 621390381, 893880397, 700385632, 590416865, 289931086, 328187740, 545520453, 127730155, 500967407, 196756404, 173311151, 217631156, 978167392, 629580806, 228434632, 814104943, 186843630, 199898242, 574670682, 197185732, 812484544, 557947539, 262939443, 363849908, 482689368, 989413739, 953692152, 426407674, 548732971, 943678253, 684031596, 347233558, 924665004, 542043096, 266487354, 542010578, 478814644, 208939525, 277144313, 386522659, 144577104, 929097900, 934484186, 944314882, 140784856, 541625909, 637942917, 48397770, 455875265, 152432416, 467136451, 741002302, 686605357, 50419471, 371258262, 222299554, 566936, 217205304, 686891686, 511756754, 385816610, 459106997, 172596977, 617080575, 476038395, 412728929, 478768549, 220674105, 252888005, 624907918, 550053367, 158688791, 280276396, 221264037, 49502604, 123285953, 324677419, 437468168, 137069864, 799204746, 767155159, 129316792, 60148347, 502303056, 249783013, 291284918, 168465853, 779449577, 381054693, 761522369, 147452443, 106886232, 479925986, 924152299, 780481438, 122574695, 54739232, 620783370, 310684745, 775555814, 157305929, 196232409, 223292692, 495534166, 362216063, 323100092, 833683483, 572766857, 807889129, 641491591, 781913099, 584466844, 662858408, 454337316, 649560342, 726806137, 634914087, 508463614, 449248180, 11183004, 150839714, 495156724, 720202447, 412079322, 151186145, 266175085, 510301017, 605266870, 228205838, 748785821, 223040520, 591308296, 272985112, 790443544, 631129645, 803668551, 157588155, 755027926, 785267011, 629342476, 76990134, 836854126, 563562207, 643348601, 977786438, 284127175, 695637976, 536592865, 109817656, 387745795, 372835792, 759991800, 631530287, 324265210, 895546265, 13031024, 14973166, 653005205, 794112325, 320268875, 213717943, 970325708, 336693427, 710058955, 650398108, 102108838, 417143283, 643071118, 336840771, 194604446, 838162778, 654137494, 244857738, 774040505, 308293345, 441965371, 530762912, 90836350, 703660966, 819697056, 678875294, 782361816, 154356404, 464722887, 114140639, 464804207, 119846210, 266871330, 196230212, 169041868, 962699300, 57286395, 440671374, 496350800, 39026723, 746029658, 435596839, 213508737, 813810042, 523460390, 2118771, 157468464, 764051323, 624979224, 816513669, 789823233, 582867533, 980318823, 543163786, 894847250, 955624385, 986025994, 832004511, 697404861, 81777347, 959061132, 33808683, 977431064, 910582490, 95355634, 991664912, 847627285, 24772718, 227704221, 433145535, 397341545, 713125581, 772014322, 886943802, 960165891, 23992155, 943392828, 685125321, 900047241, 564879951, 785798819, 162416269, 730403098, 908421357, 450272276, 966686626, 360628319, 823843546, 6839819, 968812764, 894742070, 982235871, 267643076, 341686559, 926868928, 361116367, 615964627, 176626953, 369605489, 850274493, 43443442, 845635152, 276910805, 899633172, 998746277, 327297665, 797217716, 424069493, 137105911, 398591960, 921107998, 239047275, 110314007, 17178971, 341146077, 747492041, 17077932, 796133496, 866998824, 985017503, 70260048, 686859901, 626343804, 477432492, 902196617, 250345253, 730647113, 130021163, 777204511, 253440981, 387260113, 992228332, 84591614, 873099435, 284820513, 224910503, 174520586, 710531670, 422062024, 929637278, 69718709, 174883250, 561778415, 151600452, 500094737, 197319847, 342705876, 95600850, 218359762, 622379192, 247459271, 982082114, 183023243, 983996250, 410306135, 534406998, 291329868, 949489390, 743171622, 270934735, 686510135, 65703307, 6994976, 429115275, 328107508, 44739233, 439103047, 897113326, 201873040, 377397888, 976814911, 619329752, 900076761, 145897527, 883498749, 647640976, 184134817, 588283598, 665872726, 393735449, 601227220, 660052571, 322565722, 55193278, 221932891, 199394298, 336402798, 151590920, 882903141, 230955641, 905786553, 576209975, 335967688, 994743087, 51265791, 671274453, 62663517, 277741322, 856517436, 227232469, 702744549, 240818105, 114641740, 891016714, 141452558, 466565065, 254501671, 806003798, 789986271, 902807113, 800670519, 775981980, 484390684, 120037595, 664870759, 545718458, 454699502, 567366638, 71582476, 994155588, 259401769, 312274679, 631568981, 844049848, 406725894, 546120103, 454515594, 374589004, 25119455, 433824976, 825458071, 518262776, 32522998, 516279764, 756658698, 169229677, 166894786, 358440738, 241769550, 470835682, 123645990, 470581256, 587011549, 841307401, 702126701, 774722366, 115551721, 226101344, 137117952, 613544296, 698064860, 957920356, 40860624, 57569196, 443359981, 332553387, 870911162, 277934673, 458806068, 426442117, 293126854, 895978900, 823172117, 226136032, 529139245, 491863195, 62448037, 445887051, 583637659, 514536367, 492843554, 657821748, 165299222, 70073990, 896267861, 230481195, 450861048, 500854247, 223409843, 644584150, 173287857, 141612517, 184703135, 174957236, 735422444, 720275575, 863539489, 376661020, 262272242, 266667269, 691955746, 179151059, 419873821, 588750152, 643779745, 870648184, 209232204, 421182120, 560826082, 99675939, 673296300, 999594206, 707698779, 329564891, 203895731, 450731865, 361216052, 213126849, 506421791, 465578342, 896970633, 247584423, 31393371, 634876215, 825959695, 822258686, 797300243, 175691437, 832709403, 7207614, 379894646, 435576516, 677394968, 553856713, 98082438, 903786742, 356761705, 832048378, 259427821, 342083339, 940750184, 642366328, 885300238, 875627987, 584453439, 700837520, 150896522, 632538186, 238580437, 986518242, 444973624, 893325910, 652606484, 2977114, 107935055, 289408428, 372706301, 94742248, 735904892, 500379806, 537007156, 416893428, 659514510, 791342129, 522986753, 413101943, 257197472, 509925900, 50646323, 191992854, 296706223, 796137199, 137522692, 446829356, 959168302, 953480405, 139384398, 561519859, 545816282, 840915943, 320793834, 297494079, 176517180, 983933658, 874978429, 500539909, 560061994, 354891980, 208575436, 184819729, 80549564, 260812276, 752100824, 200468608, 768781572, 681818763, 373292541, 273575896, 250934106, 674043006, 849095076, 55613012, 77105946, 934765385, 464659790, 192215458, 907161259, 760687810, 388825065, 883598347, 771501478, 390820579, 236786328, 21392166, 151142796, 600209892, 955361289, 164323205, 171156161, 322921158, 895967446, 645680848, 908065720, 313241811, 879325552, 681091265, 605925778, 424199617, 377384520, 651814390, 999660070, 930887906, 245962263, 889671971, 349520971, 244058479, 651749166, 213117222, 622263435, 758309236, 932372220, 498864859, 387807495, 874087069, 558648268, 907472759, 41223118, 45629934, 109039188, 124123173, 969754030, 220574184, 660247440, 751285429, 718277955, 867446757, 580253579, 845079371, 581518861, 273556699, 181448393, 431270208, 592077722, 163175109, 306979845, 4120845, 309457261, 485692552, 718311564, 654040824, 542137028, 321777758, 614513020, 701828217, 438307378, 520003683, 599675816, 878006339, 556786082, 624617757, 918861764, 620997180, 712178441, 524179721, 133893474, 355778502, 586602140, 404346988, 700197813, 12356782, 396178147, 382728073, 680543605, 958659116, 533022607, 71369672, 226407412, 551235456, 804291489, 885848088, 786238907, 36148532, 591106232, 106729691, 636340847, 787874578, 931230632, 346511637, 657207544, 855763309, 342150050, 180027463, 251376454, 451930948, 842140694, 680669376, 473063332, 317805406, 521988405, 810116309, 316086949, 590967297, 475321342, 987748974, 565154965, 839516315, 217144909, 531157107, 950395937, 889317996, 298141973, 322598825, 208395802, 142303872, 95133460, 381297164, 165562527, 427154859, 356223914, 633638204, 165585818, 169718604, 266127569, 839353668, 223315581, 465370950, 554708829, 610205293, 404785376, 946085599, 395518881, 753925004, 449807209, 534344447, 888726171, 333094570, 570299700, 379887172, 998437826, 265881485, 213430502, 682466324, 934115037, 501206279, 366469257, 548287992, 223078357, 843953970, 842014875, 363384451, 375949137, 256285979, 610722535, 168991264, 475013986, 776063001, 221007153, 516056686, 43995273, 726478986, 353158681, 634455027, 535961839, 200541903, 875005895, 258681601, 460587436, 78284526, 180464078, 852235395, 639436821, 773064620, 312597111, 970429694, 994173640, 643172076, 518623734, 433692869, 356326203, 167189699, 355884382, 408642908, 67755375, 236123646, 410122790, 685023258, 471554834, 377517303, 589716682, 747224868, 366962344, 807919057, 755975251, 352346557, 233818894, 101074843, 519806990, 160196670, 432755977, 383896523, 124138270, 46868821, 848098751, 985697851, 637840228, 35059255, 289659132, 208502158, 614390788, 45140440, 552019822, 479374844, 775428573, 525113681, 929413646, 557579853, 522313345, 849445836, 110531057, 192133445, 82994894, 909069176, 484161593, 8699164, 64134618, 356811244, 470833816, 963930611, 146484512, 380086345, 788508366, 521752819, 574320640, 55233556, 744996299, 395641796, 434652414, 693420849, 583454461, 202563485, 809790088, 138489352, 439057296, 730997931, 364507006, 275602212, 241890243, 46242675, 924536431, 389086468, 900996806, 849736235, 353529719, 650440041, 579965062, 771471728, 701472461, 734692645, 669403884, 745351431, 54521446, 558283172, 940484876, 815533117, 624277764, 674537864, 47048003, 688411134, 835262006, 167485189, 618304663, 127523214, 750002422, 435506090, 691398661, 507290302, 293139233, 736003488, 565610085, 686514810, 82028784, 830377969, 512812294, 655066197, 974047977, 424807508, 821147056, 765316241, 133135442, 704454896, 367583622, 653321354, 709769723, 465270823, 27463467, 773501075, 950013955, 738334018, 937096100, 950509418, 348251169, 75899824, 219223605, 282732171, 211440482, 113201580, 724622070, 243380088, 165376780, 452335897, 501888861, 402142176, 19851510, 551416115, 5529080, 284248677, 770450366, 552171105, 577182017, 971989184, 772391181, 858162022, 188834625, 933275271, 822095506, 390128177, 318877573, 429178458, 646931526, 554224490, 558157537, 702016200, 693552624, 494866277, 362926491, 787985578, 99348030, 69240758, 829106771, 895904343, 24772418, 973252251, 215615066, 324121770, 618963800, 720860125, 997004862, 271547972, 244199613, 187154956, 971652736, 685813826, 561595710, 661810003, 92110625, 615406882, 395588080, 877685962, 40876742, 215808116, 109270616, 905916516, 576818300, 652811049, 507561827, 635341948, 162314353, 592790829, 228146329, 243843832, 369081095, 917716223, 752915691, 450358688, 180257343, 679580082, 297551611, 377966097, 460386020, 731656244, 42808536, 507055356, 18916441, 96896990, 370101232, 797580685, 353153810, 90430916, 326831425, 886671531, 694518861, 200444488, 76609066, 757633149, 467737119, 345485175, 661765722, 974375017, 891077366, 179198782, 979309124, 937456149, 854592077, 535478576, 539827334, 556891032, 912579466, 698993667, 593242260, 307471183, 945673572, 9500254, 927586436, 145652055, 728034469, 664784309, 947349070, 547669345, 897730730, 481723937, 103462812, 238752857, 105453368, 375042998, 486022148, 849618772, 584088133, 774356708, 918335174, 875862935, 237203968, 159537922, 228888917, 517682146, 366972894, 453396630, 842045575, 188398121, 383740162, 790752655, 438450173, 663691903, 216603685, 522436409, 502917358, 363082074, 796168855, 243235761, 949944848, 886056841, 723770597, 373701929, 770820336, 881349269, 393889690, 212121486, 375168929, 336829088, 552684108, 763432017, 994684031, 859400912, 555831408, 951602722, 932987985, 419330719, 752731858, 172912127, 965950461, 352344379, 596959918, 725013857, 488873133, 815111599, 684000182, 980236212, 197003299, 995003151, 264839907, 974529140, 975817532, 894423306, 261940817, 721603571, 202282361, 116851493, 371061115, 498664108, 411448462, 631832957, 504608559, 36497312, 395225570, 525294199, 600790158, 282841648, 901170034, 901798867, 243306656, 340487092, 211685357, 165919985, 956059348, 764852086, 179695917, 585233406, 749610642, 157265587, 986727436, 462586048, 452445017, 910692720, 849139455, 463931718, 881102670, 574823436, 343530090, 392871915, 456426507, 265444450, 756251042, 72024126, 645093212, 199680299, 242199528, 585297460, 643707914, 496696874, 326237404, 1797069, 442336294, 224425385, 863136981, 890542067, 474918155, 254807060, 35024559, 728484976, 328702329, 63058783, 389671113, 93176129, 851232449, 666417199, 54121110, 304724300, 462111078, 263938511, 809998272, 375460048, 629773175, 305168764, 478545056, 769494378, 165460413, 162085793, 285008766, 51503446, 740819729, 263462081, 703679566, 896982920, 460197992, 515490526, 362055684, 338394656, 327233041, 280969661, 852652484, 778231201, 746208100, 878306190, 195152509, 445641640, 734416701, 577244314, 457547546, 265722609, 576266872, 726016265, 457890795, 692618226, 448822309, 204186546, 392202405, 269988380, 211338336, 501265761, 899330764, 866555314, 428713431, 659308852, 124773563, 273222394, 296215851, 249820841, 551221599, 557719250, 880172319, 855088510, 796056935, 347197720, 65081460, 388453469, 628985471, 392979862, 632686769, 90507302, 468320712, 787249582, 462198523, 457168349, 962843287, 52343002, 678681287, 711433572, 221393534, 989657966, 373149490, 51213629, 17213454, 442213104, 977437662, 382924304, 842207782, 347921138, 669428294, 418918267, 583632467, 150074163, 299868190, 414107430, 949146016, 687874240, 487576531, 558730121, 805638694, 874651454, 653640353, 470451855, 696666248, 558212632, 590230338, 315620292, 29314395, 460039822, 860646258, 17531640, 35727339, 556824454, 260348752, 428457725, 336676297, 189605760, 848262778, 73453425, 528910466, 130971674, 390078218, 947217592, 210329734, 112245182, 147120260, 996572434, 21046953, 743670486, 339785298, 733264559, 397122028, 826754964, 489202724, 32205536, 511555301, 710845599, 116698434, 118073498, 139513292, 103541252, 472773140, 584367088, 37552125, 692591414, 719956891, 820510196, 9574103, 659057669, 271553665, 207210321, 964727, 982760530, 704728428, 260892261, 595414108, 842253246, 281506025, 782057714, 385428733, 164788274, 315238892, 163054008, 754857586, 928109594, 25863444, 58094466, 392775182, 714903335, 750901075, 910350938, 27902636, 408681850, 448204714, 632176330, 734921787, 601077623, 402386858, 642316747, 725269887, 521107774, 313222529, 166840115, 370574328, 445026237, 913315835, 985054608, 540299757, 925522443, 54641495, 605562613, 538085215, 738070598, 546078696, 613307755, 465554812, 698635228, 694173083, 310893820, 754837441, 476090144, 619010073, 370836612, 221847750, 368508688, 592531247, 874537634, 457457241, 848720571, 67822747, 989803022, 365989945, 617290412, 461250749, 30471995, 121803131, 953200808, 166109212, 490281784, 288087635, 100997739, 900236636, 775131474, 979427580, 418604153, 698891433, 562581516, 472102489, 134818840, 116468696, 835120462, 840593384, 786336978, 983338300, 351258424, 661578788, 230549001, 356182337, 209197884, 844340308, 452070970, 138560204, 521236306, 20607471, 190725612, 199132585, 773261700, 755923753, 915879718, 12674169, 904671175, 738961313, 707977202, 502711733, 780233276, 551867396, 620777076, 521274969, 984512906, 815306713, 41359211, 486096904, 243064491, 391627994, 365314165, 210847952, 90736946, 323868236, 416489677, 734502002, 352901279, 329035456, 948226295, 780563059, 801381852, 606526333, 930963054, 213744788, 17204705, 51190249, 184562261, 759899027, 586244526, 776982839, 823771068, 628031550, 164931646, 499751876, 138290512, 847216736, 484388260, 634778022, 898628034, 259641550, 185497984, 382184084, 652669586, 679274463, 643992030, 668580196, 173220992, 569964543, 596825624, 423596, 786697370, 961059860, 596164623, 443518266, 564833685, 364670346, 453209028, 637395826, 702405688, 325199442, 209673833, 626407594, 215932070, 583476050, 63707125, 875252707, 114559363, 714045909, 341899538, 67684485, 394943032, 120583258, 464108789, 806435770, 222530314, 330095338, 647785985, 36152370, 859930691, 501634585, 318488086, 410659851, 787022084, 626665913, 53793528, 206976481, 491753589, 999743110, 309965535, 52206173, 155265487, 402732778, 402292460, 535886903, 326971424, 221258504, 946296633, 555885987, 127682528, 642234185, 942318652, 809600466, 493551944, 541424688, 334745890, 446321809, 264207663, 916444931, 592045128, 225606794, 530371259, 93835334, 856167349, 308147109, 641674764, 166658275, 921961226, 127532677, 66618548, 599102553, 930031951, 117567207, 768777113, 760613171, 529562614, 133351152, 817111614, 770021620, 617517446, 656749922, 192611048, 635526432, 385163778, 774629885, 744672742, 2503741, 620619854, 793822422, 797267381, 195217878, 182720359, 24367643, 226515466, 85320420, 416641997, 706315610, 81013046, 432721086, 815186812, 908927101, 214382058, 605360629, 839974265, 523601174, 379588171, 23319178, 77003472, 65887818, 610071109, 835772243, 910540147, 639895007, 42972658, 929471010, 135523888, 549973767, 12425749, 215853511, 191878661, 252784418, 920324894, 169843407, 741599232, 288327240, 845139339, 764815743, 760030604, 253310030, 956419959, 406421034, 648606487, 34585011, 821512696, 790168238, 880789794, 297595863, 805985474, 621674178, 358062375, 513279505, 317304186, 233530326, 870108191, 621933198, 913631175, 749083375, 870898231, 795619074, 279885713, 491156948, 652243494, 107635884, 800844444, 973835123, 533264636, 113453254, 617893426, 685714793, 717197305, 753990707, 870208396, 377203180, 421543256, 217160634, 81857275, 405914481, 920558655, 649884848, 117152719, 765627709, 749473308, 661587780, 50414858, 785719496, 144559642, 957230691, 636054347, 595656095, 678662278, 60555321, 850946775, 465000621, 870789224, 226286019, 438247027, 959991114, 892069174, 907446207, 988572300, 110853380, 512755568, 40361659, 468401504, 501531887, 194620293, 802264854, 365315251, 814660036, 391454426, 804424015, 841621579, 24024850, 929418086, 875220496, 249020421, 676490582, 983363543, 536573384, 671250230, 462463128, 5576058, 458828435, 430840672, 717171344, 264445147, 181752147, 962421997, 868195365, 246960407, 136802797, 574604079, 748984934, 378503701, 290947059, 912741202, 682329058, 380070849, 789978907, 180282651, 326487718, 17443910, 621010347, 155753208, 641801145, 216429417, 378751946, 720141284, 347364375, 132431855, 789660404, 8893264, 505533741, 216961694, 585213550, 709061745, 150658291, 634001620, 179807923, 580053388, 607815046, 401257276, 801219167, 154837637, 835100111, 627874452, 349303348, 902583068, 144247805, 452257914, 868384585, 620388058, 483419001, 228254023, 252095974, 210681142, 328477410, 552016563, 95279991, 304608194, 946162238, 4880353, 211089475, 864854336, 500922294, 810547698, 144633306, 28467159, 360955316, 763344110, 159430977, 340727559, 443500702, 952165909, 177185616, 137214938, 621041658, 26576749, 314783004, 193651446, 384816284, 160139144, 355044087, 270017479, 907071259, 895283651, 176453829, 116537221, 726260261, 674407014, 547968113, 341723765, 565665290, 836141441, 509612069, 155149390, 246542217, 263992210, 366592043, 675220656, 615982874, 512086485, 243710366, 367091657, 536204712, 183338386, 748438982, 227416591, 641623980, 824399484, 843496187, 551898387, 519904177, 206590829, 807072219, 795626272, 810889420, 323440405, 337052619, 202616160, 856294612, 430919105, 883262582, 296561477, 445932219, 909436138, 383289653, 456561947, 332666169, 590363385, 27391433, 617351680, 829972062, 169197684, 895986460, 183805888, 888961354, 542459912, 253741494, 276046608, 327985512, 684349422, 978216094, 333642180, 712838346, 639129155, 789716387, 223129103, 980390689, 83411509, 842242044, 49443494, 860309414, 400774343, 447778242, 654560964, 608822963, 708986710, 500131488, 505841522, 586315974, 513766323, 15702770, 475034847, 124036566, 277909866, 835381442, 771108221, 42749521, 288912400, 486660315, 288616122, 152897230, 856792073, 707955416, 189773723, 942158113, 7779112, 178403645, 203456594, 256116222, 218441542, 494714556, 785577600, 50706730, 915614800, 368437861, 990775107, 351611566, 178993439, 122419670, 468815069, 901134316, 915308825, 373793464, 393836968, 373292730, 20297069, 584720549, 240982444, 966797230, 81789125, 746164992, 392902632, 749921595, 402943464, 481365534, 639867911, 755985524, 424063377, 533924929, 504305586, 16603842, 397486523, 368907875, 41625009, 985800623, 223520644, 668850237, 547294705, 464619338, 714380789, 871763692, 322494032, 586687613, 476281097, 957160064, 812405867, 288829864, 30840180, 47179657, 375397421, 631534214, 106686948, 439705725, 255512974, 938151496, 124339276, 980925975, 997220071, 706423496, 397825600, 751013655, 620951729, 105689364, 864757034, 584336760, 461785159, 446739438, 590684320, 146650161, 820339508, 950896380, 56715963, 673522769, 629816966, 104712428, 839350721, 912253596, 531272526, 44078264, 614859549, 88608204, 108657401, 485129553, 666766766, 876510473, 432614622, 770811279, 527047585, 950697483, 387060323, 68202486, 120097613, 534600812, 487589085, 441732933, 886251253, 22145006, 554558378, 381404224, 710554933, 345310380, 958846375, 436605925, 432881786, 870442186, 349262109, 709119461, 738036530, 544289472, 292048892, 40729621, 821454651, 920256510, 100036354, 802094769, 204408700, 19884939, 993061128, 934833480, 750432284, 366006315, 923948, 341105478, 288054864, 67845288, 323921456, 462689570, 328314709, 793476953, 718492520, 958543478, 132934943, 666965844, 84128778, 166746211, 751432103, 122575048, 839412036, 421386135, 347592718, 351906209, 485172287, 905684909, 652286538, 734711972, 814355054, 579906773, 827352140, 888806694, 432027276, 557419161, 82926835, 464644301, 910436307, 619107093, 531917350, 49336339, 117081497, 98218584, 272591821, 930656583, 423504715, 486576336, 269302040, 416191479, 642272441, 563717786, 282626233, 183016409, 683069170, 57233194, 658349582, 648795283, 88531288, 24513343, 715617299, 848636386, 209472658, 186714549, 509324195, 831417242, 824238732, 107423761, 273077500, 54967314, 315786873, 296787524, 950378867, 413182126, 937509536, 807982800, 555140235, 518848785, 509338356, 564205703, 378223546, 123805018, 985016907, 847109216, 387530035, 639682968, 273260713, 952909779, 831153715, 852007491, 974736222, 436180266, 629242026, 596178785, 556154634, 827354788, 18421767, 765720402, 97236815, 348715891, 90427776, 342830106, 854281471, 613637132, 187088662, 81649043, 522424850, 968652493, 754194582, 539868092, 557504393, 398564303, 151040347, 330516744, 474347377, 431005987, 881268348, 806556908, 953374690, 879904705, 316861239, 597041192, 157689420, 486893840, 105126408, 658841104, 954785310, 381247152, 254931456, 65154336, 544995309, 153628417, 850361261, 261639979, 970042999, 536288806, 625306917, 198159120, 230630717, 919707668, 710485710, 305205587, 105246415, 97111297, 488556008, 219856894, 557511667, 916265675, 706133254, 300657469, 747472724, 165518101, 809699696, 851069680, 899005432, 24813638, 572697821, 793807300, 181991857, 946862076, 216722728, 855267694, 607689191, 584149054, 235015967, 799965193, 875385139, 343871771, 785396202, 639861048, 532690063, 481892065, 735376071, 519599107, 14302945, 357944836, 747039201, 924755850, 977903602, 876948063, 643016127, 655823645, 699349778, 653421341, 123008354, 943780970, 842922071, 85918757, 317766932, 366516333, 700491881, 526160472, 448772451, 483553343, 6363286, 789441907, 145352080, 596150559, 690358204, 506480392, 927678538, 87801363, 553583652, 490422402, 67142214, 620644119, 119191516, 648112815, 155468396, 904027665, 373387567, 303542741, 286783371, 590758484, 910508155, 696119106, 740577176, 905846464, 318729704, 808189691, 243943471, 127684665, 325775062, 604433734, 689930183, 693694730, 528606291, 260025379, 189256696, 236269738, 212367109, 511075493, 491098713, 907602040, 195005970, 452244640, 305878466, 276299692, 155067202, 846211356, 21697603, 814766361, 744518422, 326668862, 931270299, 73851009, 575052402, 19057726, 124727993, 665699067, 213480903, 435471932, 750840023, 399496028, 245812698, 934490213, 923697014, 684046097, 333810644, 635574277, 572768872, 547736530, 190925777, 450444088, 536483507, 545058395, 715794233, 76498664, 259419534, 231451160, 32839068, 197480225, 906634436, 984660537, 220308657, 357414746, 194490770, 793588957, 367114663, 425154982, 634235873, 228464263, 886114379, 759936967, 394652818, 967988331, 660770166, 803178613, 214354655, 971222679, 233266721, 851408981, 51506700, 86542741, 44055335, 276143454, 113792633, 261072213, 50167572, 168385221, 93709563, 707589560, 198557934, 871791214, 623597135, 681508332, 897506818, 849022951, 939054187, 878094484, 663390217, 5378544, 216445273, 942536470, 478596736, 393153199, 410018542, 58074366, 809717569, 175557384, 522581441, 833747817, 550903728, 339870210, 464762045, 908815770, 946401367, 357416897, 342023690, 958113805, 694134000, 767849348, 400464568, 832129680, 181310320, 54919157, 546793027, 682137258, 664878313, 48353512, 138831619, 818032815, 221386558, 423861356, 529072820, 734989968, 456359338, 274688908, 725448919, 561285000, 534240728, 43611719, 982578137, 500905480, 858817462, 129322633, 822719165, 899973366, 633919106, 470503801, 871885549, 853062199, 853200478, 882682278, 887738404, 526326297, 355567700, 438076193, 34374587, 329254288, 920299527, 103242044, 315963323, 743827256, 472491413, 761417978, 680337779, 917669450, 133541677] 293858445)," 0 (countGood [545422775, 850851772, 186447348, 572264082, 643409027, 997686213, 336765769, 997995744, 490221770, 144951954, 759346104, 329684729, 672880796, 896658001, 139472718, 987854440, 480638560, 504038335, 970577570, 36619028, 671690092, 75740469, 255068878, 443125182, 808952002, 196272467, 61189628, 860584532, 341241819, 438275841, 506459373, 315301748, 340153380, 471811956, 935310299, 191910219, 765602206, 350075628, 902181663, 453089381, 570507497, 417787742, 500826374, 802378693, 556846751, 570697473, 564586214, 585695080, 409440939, 706593810, 12545970, 228019597, 814094801, 118441768, 310679290, 169964358, 640229488, 429226116, 944597360, 59255817, 766372665, 333185924, 711095430, 304555535, 482711071, 457784046, 837561235, 134939030, 508877662, 362477791, 394743862, 493480221, 552921226, 581240227, 89370343, 783394378, 489291549, 289401480, 731209421, 225478379, 764696677, 601773292, 473784064, 546161311, 123588555, 220796282, 33522420, 509914753, 757333229, 298436698, 276447504, 229716491, 726749973, 500727097, 82033677, 280414898, 464257605, 284528371, 126688389, 648496681, 539955164, 624381293, 843363964, 600360757, 700426065, 60514178, 795375966, 249263855, 410965775, 119860212, 357383438, 576444974, 699509403, 909683931, 367650552, 990835479, 234487758, 391021832, 401179273, 800391678, 79944336, 721436566, 954826653, 604072994, 73978026, 90451581, 643782449, 481525557, 307723993, 241936737, 788109220, 873809593, 61958447, 301744610, 925201002, 613183132, 976345369, 654262814, 592156088, 373411833, 943934031, 313466961, 322710727, 795864514, 736045235, 226280807, 274870308, 531890507, 116491212, 129325017, 70159116, 416749316, 509964272, 477772610, 974539278, 602113268, 62874810, 496863316, 296131507, 78922232, 187186131, 867727406, 25837457, 774848580, 528994, 29777737, 165193859, 963164118, 488497570, 495277484, 208127880, 151871715, 51667726, 929155600, 605198933, 662080709, 241409792, 873930784, 620763119, 505989800, 429957898, 733197064, 43030535, 211625654, 783422701, 550005146, 559640203, 249404943, 796980691, 532605008, 691550280, 512245421, 164025522, 417532777, 199416417, 160329031, 604417835, 854618756, 525766424, 885703259, 705366540, 971099265, 631780838, 345283448, 632669557, 387361197, 324965240, 528793359, 20117670, 467849676, 349980059, 114529430, 302662326, 792321158, 114067145, 765784144, 927429774, 250969618, 836004614, 661039272, 929137502, 753530520, 768966430, 581034649, 673361577, 569756240, 799118911, 896345727, 715570726, 619424239, 897367901, 436472337, 60675985, 945089529, 685496146, 995830110, 134592959, 332375976, 995447834, 17513169, 111599247, 423249385, 997963177, 684968086, 164113150, 874888071, 488751068, 994974602, 130875215, 679898984, 206940633, 777909321, 175844016, 826886290, 941090431, 815866820, 543493433, 743867473, 111158193, 492807455, 683370375, 77419580, 845324690, 871271398, 544679798, 924577079, 287771993, 649534465, 499278945, 844365295, 851314464, 219796270, 394327128, 97761333, 488561128, 669460429, 92872140, 872772303, 339879062, 381633402, 907396253, 686941406, 995918091, 139688345, 297015647, 92195220, 408556567, 35830520, 400814415, 619412163, 754336844, 50206578, 299996746, 758095394, 546689824, 872843615, 211540069, 726428537, 817621453, 560154947, 462120497, 971011985, 472033793, 130501809, 409460244, 51512057, 31392147, 431278349, 684576555, 556197674, 574187728, 707342184, 406053622, 578573117, 257516078, 160861296, 762813946, 350962173, 146682238, 391829709, 844964292, 503905306, 878525185, 308488226, 282729746, 314363283, 494442849, 298059633, 416778555, 311118031, 35887266, 607641976, 245614270, 491192962, 631445142, 998767209, 817287496, 777829091, 417263569, 143553691, 703217389, 539898665, 637290647, 640855135, 3521157, 567217309, 913543945, 962856325, 639066304, 352865461, 255590618, 145870048, 618751594, 278797546, 958824590, 844572207, 938233014, 1697977, 573999751, 803702852, 850661557, 867730247, 816951875, 414712811, 622030360, 974794195, 90245850, 215018084, 399569528, 752745227, 350867270, 269497209, 717351166, 366268440, 648959929, 254292388, 789535449, 229618885, 496346147, 648498777, 632904349, 809144932, 232390474, 422969363, 36356573, 138703580, 491711356, 204332804, 737178408, 193345970, 375204382, 414177894, 95150500, 263095803, 123216289, 122243709, 856286196, 938619000, 570047745, 668733767, 979545265, 218150494, 465793701, 992322266, 34982301, 863505309, 730461224, 872398365, 547406649, 577378447, 830866557, 453625826, 190247196, 612646594, 128619253, 713527150, 456725848, 731887749, 788498918, 251590289, 959121941, 161468782, 301524563, 920511932, 559345763, 87531591, 738719431, 405994520, 511486144, 223959633, 107694598, 254640957, 760578146, 478132594, 341840229, 933712985, 636516631, 742778244, 142970559, 355968963, 97259563, 624952906, 523568488, 934380596, 86309597, 864122978, 391970343, 280391249, 48181141, 671540839, 150959668, 5861371, 173480747, 716184530, 368827834, 277301157, 388249566, 511727040, 243497113, 131080344, 51463878, 683467465, 831560235, 710836473, 724236479, 497625939, 489801116, 739013848, 622060099, 728818602, 557747795, 927805797, 129280245, 295489037, 50339961, 394789470, 688782562, 246631632, 589246419, 338758580, 273231347, 263692663, 704648981, 420313139, 54985967, 372930909, 279291860, 300088667, 418473032, 129911943, 173446057, 36899698, 823806272, 385702356, 814906402, 355732308, 578216584, 257307641, 805118560, 158274926, 337362226, 763640779, 108651709, 875018818, 650806600, 149230928, 672326491, 843231564, 489144774, 378796858, 450883106, 902008646, 374954408, 126640647, 411595364, 986460332, 79447669, 829159927, 626785906, 464268642, 273592897, 106978857, 722003889, 549308049, 101115003, 774307743, 746287847, 628651044, 354038064, 90805044, 887835658, 373004146, 451939065, 947016417, 144146571, 679439941, 762868133, 20665209, 563460281, 136731449, 977515878, 317371338, 645445655, 279957168, 53317835, 85713824, 585926232, 87899880, 821166093, 587273957, 584781515, 624084201, 405743971, 523779141, 215408841, 806031783, 993570491, 910924550, 971535275, 407324406, 628205386, 40041178, 757360280, 992460337, 976546504, 468956542, 697371770, 627603421, 512224549, 330566310, 831055582, 779913046, 690424925, 599526447, 849020640, 827546443, 609235419, 620723826, 729438671, 823769976, 411515189, 313443235, 722607166, 936026381, 947262847, 966148962, 905320861, 630815911, 843800081, 309401959, 423963625, 590692611, 771671777, 412354117, 890413627, 2836197, 92975677, 392781403, 816806350, 286629377, 642485058, 486767252, 113743877, 631102724, 733784051, 731016348, 28507754, 333055984, 680598483, 292782664, 808740109, 602080658, 384227759, 250654828, 27038348, 745903361, 15428205, 235795024, 707981118, 952585462, 172241510, 456016952, 590885162, 476292000, 859327255, 762433553, 760263464, 993980796, 796847511, 757380450, 880309177, 4065351, 332923021, 576356023, 620964405, 186193756, 231916030, 250679030, 384879649, 369567903, 689872420, 82156654, 429447304, 264871857, 985557788, 159168455, 704951609, 285825761, 462817447, 975035875, 792858500, 761379083, 64660280, 105038232, 840085517, 977918956, 277178359, 3552999, 360477209, 837524661, 362845246, 465470799, 494298637, 61305887, 313106429, 516777944, 604526885, 6764350, 778440454, 418324032, 295309898, 669005309, 972351607, 885088888, 985752645, 318862031, 20575282, 454101858, 789833048, 177546307, 288590077, 301932723, 750849933, 331420637, 176296439, 289304637, 488123258, 606583990, 166120989, 212152370, 206838061, 965867749, 118010483, 770205060, 928911884, 311509032, 331231217, 319811217, 119533757, 830774676, 575860692, 33667882, 293542286, 961342818, 869030748, 438620277, 757297577, 990108183, 247379510, 407286354, 854222268, 84345275, 642946839, 716037501, 491819275, 757974131, 644851535, 50000197, 130966435, 477887577, 390538604, 369784545, 636259819, 286920190, 748697672, 943005761, 386040363, 408063129, 328626326, 342338993, 72457654, 916718793, 22487458, 505567517, 465892059, 875277473, 200159709, 348228871, 354613873, 807686777, 8019738, 402759119, 82049665, 318629593, 780345764, 663314876, 653635375, 816329035, 365491793, 665331356, 838968519, 647621379, 196985945, 552076875, 323864643, 780821958, 989930743, 347863536, 978910107, 538138409, 642494934, 758697495, 175339573, 38213657, 460847833, 762551582, 481278208, 453720443, 825189887, 684216343, 6900656, 496574404, 974775993, 389184910, 579206394, 870376703, 84944218, 453307722, 119120889, 264043092, 40773090, 559769249, 367598455, 135275873, 698268069, 506943911, 784942693, 393585076, 550604125, 568730210, 773595568, 19457340, 614903384, 132833403, 926107592, 126072134, 797118878, 516498682, 212150831, 668443231, 76134252, 100401555, 408932122, 43096783, 98821201, 161340776, 710690381, 471755614, 986162245, 74585234, 988804569, 264684511, 192365787, 552001006, 139030200, 168262364, 691770231, 640976692, 580086014, 909235950, 827816048, 874237563, 657441031, 568367611, 437942194, 945162780, 861466806, 41838990, 160845694, 946289021, 401285091, 242014922, 809207772, 435876647, 427383360, 37858065, 797907300, 178292562, 409639118, 427565473, 442579920, 675662096, 697702868, 404490643, 90967026, 74982833, 509160982, 633409386, 144907588, 25465768, 959320595, 57019753, 265277222, 916550960, 933666641, 887807856, 918515180, 406304758, 370649527, 581535226, 191942580, 446585358, 619645055, 429946085, 963805600, 641839521, 624929864, 83794675, 517488074, 880824423, 603134194, 80012002, 986015714, 801492014, 637065665, 980305484, 768983768, 840455971, 727897050, 375174353, 517974100, 379369285, 380906332, 347343735, 738502081, 59718474, 981624910, 202578375, 781007041, 103845964, 493143497, 237939440, 931948995, 664966527, 977075768, 603145666, 309091751, 496866250, 48587706, 871827608, 750797052, 896979545, 354057755, 523867028, 403308052, 735926294, 550523567, 177328113, 723723278, 9962562, 148117146, 801836733, 775395512, 723479938, 461919820, 534360601, 964293863, 672049250, 393697474, 201821347, 855446753, 268486740, 620006997, 134480089, 663297647, 797423188, 956885523, 63606930, 326468909, 484956108, 863482587, 808964931, 141476316, 32140488, 391212357, 690874676, 575571363, 866126719, 452028719, 24401779, 677328838, 170832327, 202103368, 113199675, 280395742, 101892874, 544642558, 620162746, 473713521, 661571422, 698285546, 145801470, 418855273, 574088918, 982073636, 824475449, 167889571, 126246887, 133924260, 610545782, 386024539, 968681641, 191442415, 163317774, 405067210, 12432547, 388168642, 933687216, 45765938, 747866310, 993747263, 904199627, 489897486, 252446431, 75439988, 500298936, 232389460, 401255352, 384888279, 277108059, 878952414, 500388978, 536762513, 195761990, 861513639, 272441806, 271640530, 114530081, 534190102, 657863556, 664934681, 406064019, 443643084, 574707633, 751730035, 749291500, 822168966, 895705267, 600488499, 45061567, 701884587, 670658856, 479882018, 502674829, 792261698, 716799220, 11477578, 775094978, 543728419, 510015965, 649775138, 436047810, 576046502, 264011600, 487684469, 216107862, 964933029, 220109461, 102463940, 331366977, 456413760, 742291552, 210127097, 316292794, 35394155, 534629648, 550974001, 314134345, 327596320, 914636961, 644989786, 824087229, 566642401, 537879246, 688297989, 485165753, 496076665, 350812153, 436250567, 673830404, 40736766, 212018047, 673057098, 750040048, 893345277, 579164109, 832929854, 476806419, 70627410, 575164470, 588342804, 444639659, 313240935, 660751183, 794009121, 39146253, 617419957, 962913493, 301849461, 649197413, 779391903, 296231693, 315864332, 513299459, 946044681, 142059943, 737567682, 354515474, 816876646, 653895480, 750330687, 135016000, 655989315, 778253819, 117830496, 536110891, 276794699, 435152258, 541452837, 419865755, 770059331, 809248175, 441207040, 629440689, 363103162, 262804950, 358810751, 77725435, 380780807, 321990455, 581584607, 353979206, 716825667, 347323621, 967615756, 818185266, 927809971, 45844877, 811596877, 183065530, 455557132, 568473144, 520746485, 744306701, 38511582, 395317655, 747666546, 173898441, 420063183, 638671543, 292332643, 4290255, 47534796, 141577201, 402317345, 285765154, 67321393, 879508750, 129527785, 211063805, 812426018, 864407939, 648440684, 809586344, 283462586, 490546181, 106809710, 887154897, 704641640, 57175429, 419516668, 453925474, 694132510, 714990898, 728090625, 153458165, 925469828, 673352539, 158083659, 921807731, 129454936, 465982077, 121881680, 731834859, 497030127, 11585887, 262079725, 242335707, 483488424, 749976334, 281441334, 340908639, 743493387, 193784121, 821054680, 470469032, 660738222, 605515464, 617223250, 921041012, 544061852, 606447389, 560686944, 569341746, 473870930, 724439587, 580576879, 186864263, 618731215, 382220571, 706927370, 116844783, 599049752, 816358810, 341458576, 993762186, 643832642, 351549193, 878319690, 313157814, 675390105, 613021447, 902346935, 773612240, 837519632, 407601770, 551348663, 179828911, 845558609, 580570739, 239092405, 659906574, 286162111, 625241534, 799484166, 307069371, 203824841, 885158714, 888487516, 145498669, 599238156, 275781271, 182287334, 704601917, 941583866, 303971935, 786180658, 431328568, 174082546, 368384159, 750043213, 460716096, 489765336, 538863803, 208370372, 383042279, 405984086, 103940697, 276588205, 349405858, 659711108, 146741291, 735001678, 347532159, 784709002, 337941224, 680596470, 476866253, 264588644, 421247908, 9629088, 474868635, 809107199, 791277029, 699223283, 966097010, 188745745, 556019509, 979549035, 280661432, 445930502, 227733413, 897289840, 769901642, 539495965, 574649823, 384673249, 9821274, 965748936, 62530796, 983631239, 956953355, 784473828, 591587807, 734395957, 732154315, 752058690, 754890589, 753346861, 626100953, 253269259, 846686672, 370894205, 695875813, 143354403, 748594096, 462021711, 766741969, 680281268, 843724923, 564923639, 86170608, 48063774, 463925756, 159611940, 827755638, 855123641, 447576814, 308410516, 768240902, 85167348, 891863376, 593550445, 151756616, 91659284, 147925686, 816162448, 352682699, 771998823, 766189763, 21686146, 94094008, 300550921, 495991317, 879543165, 525322268, 423421044, 582848555, 523827339, 394378445, 974530140, 221379995, 792732666, 604845103, 951761158, 635123596, 549439458, 695736124, 405932055, 667938378, 364629761, 124987569, 806267165, 109651198, 853036037, 969869759, 775826665, 630165675, 395802993, 438930179, 825968378, 638015266, 238530668, 897275668, 975847618, 575344910, 899420725, 240292786, 481594184, 957778358, 488594336, 423701155, 655842750, 744190433, 355204425, 719804796, 320323144, 540874341, 631144769, 127208493, 943382105, 508149375, 664234769, 208551965, 60954242, 14787780, 113953484, 420372756, 338793126, 467972556, 175219085, 745274246, 596192990, 546957216, 520116097, 788667782, 124245111, 585058115, 530242704, 151868310, 755381937, 593592617, 842446099, 518043390, 346056895, 594804538, 350894568, 936024453, 345649200, 614854953, 812296411, 535528282, 410218038, 551714040, 848288803, 734721409, 38360210, 212997894, 753074477, 341628355, 867582955, 673983303, 772734230, 217724226, 474086904, 976434501, 631321485, 436322798, 660757778, 715046412, 888699796, 725642198, 455003370, 285387900, 59536021, 768802554, 77731192, 704893735, 374474686, 358097401, 424731745, 426428834, 282208282, 888887850, 455314167, 444218639, 270615225, 616174293, 471754227, 585193473, 613523046, 531117590, 444175153, 478750677, 762210800, 609561862, 746139441, 297563995, 387422876, 299089565, 747227689, 665339239, 474383290, 72066139, 231720681, 165059185, 967399500, 756922632, 901960330, 474535312, 117041361, 689354717, 919135137, 107785367, 495430347, 98383057, 213814082, 764924316, 936873926, 212414263, 891102881, 733564362, 939763483, 898965792, 180595853, 578824087, 683455477, 940143008, 991708608, 118815651, 213396633, 601267071, 108565350, 209680856, 667227073, 306877570, 183684948, 703757664, 654732184, 11082789, 919075375, 214284444, 639199383, 800757194, 911032706, 284517600, 307867010, 512476565, 458605737, 463338883, 81869952, 254748308, 428719100, 537712171, 119725853, 345961240, 188289759, 855212890, 300236557, 306030675, 491322491, 763264827, 518583926, 397604121, 346269912, 116231541, 959198724, 684278264, 201805194, 197645166, 882982781, 750217832, 460900025, 905085342, 480665971, 267141408, 664601584, 86840672, 432002950, 72828903, 805121515, 818753799, 539666302, 26029424, 610585054, 311103501, 10582367, 605385892, 308124170, 250857540, 33308461, 204615576, 240825080, 587621483, 205072124, 779471595, 739695031, 582851378, 8535540, 585631720, 373272667, 19814036, 158210727, 509919023, 150345222, 791129603, 539982237, 766418179, 249953042, 362454016, 366720775, 597564974, 358744343, 929680378, 350889186, 831254566, 672467990, 614695485, 244314102, 18974751, 444563913, 387282519, 688241122, 328067893, 768161827, 455971518, 647819058, 284776112, 36797273, 98330035, 856171236, 773790395, 615090517, 203544914, 290347859, 86392450, 509471581, 417578070, 27621853, 348126356, 114898188, 852120275, 43489497, 571103585, 702683299, 531911871, 729993330, 918569018, 78022183, 674315554, 734645025, 667274993, 468801383, 111846952, 994078631, 702653499, 151097595, 754533740, 871908294, 264164603, 758484032, 249993012, 75089017, 689173346, 493058695, 99677002, 280747395, 219311224, 454572377, 288540040, 344604496, 48921070, 857740942, 386229266, 28413860, 573366998, 309844520, 463442812, 406976293, 603983108, 724089017, 280580487, 950159434, 223001137, 308605153, 280878560, 477412224, 932892890, 277068266, 132507881, 512757118, 429482766, 69559805, 298124437, 675101234, 263317531, 424879663, 321220075, 962530372, 149069034, 880999763, 909476792, 235659640, 158442188, 12824712, 28246261, 187300720, 534111262, 568769984, 198136628, 64586714, 533958522, 705191712, 211722068, 46735683, 477421441, 300060162, 404133203, 219350214, 809534431, 578994170, 888551589, 952350400, 141447911, 482509723, 904710058, 795467158, 14966178, 338547286, 491337619, 682996937, 585590686, 893365605, 644518111, 497080584, 122031102, 233105815, 211743690, 431598809, 124907463, 583340417, 319705953, 108807324, 733660365, 91933800, 619311472, 508985342, 675661337, 779451784, 318430445, 198470323, 511504007, 183178648, 203846249, 691889484, 801304788, 966112639, 424244303, 1139375, 970469802, 77385509, 613046865, 204029533, 466422754, 510337346, 87885620, 24246373, 785254450, 594398246, 149691298, 399238159, 167779471, 408467171, 227132621, 996662768, 902405899, 835191130, 246122022, 442259705, 642991919, 932148003, 567378859, 843041932, 630350946, 137534470, 425158977, 200685705, 705951386, 610286849, 837490004, 573443322, 468712115, 209565956, 6817447, 445679267, 491027089, 430817515, 464314635, 825479318, 444609699, 970627980, 366724585, 771653958, 259204253, 769731146, 241849908, 477454158, 246067171, 813593874, 229250948, 919298866, 676617379, 130902694, 957679197, 791739349, 881692727, 198773941, 331227829, 27371817, 953736673, 265115678, 439319895, 381039854, 983081836, 256447816, 235526630, 516517058, 19715245, 646063946, 65177572, 189813039, 284356091, 318445653, 727094028, 546555644, 302423917, 763368252, 173789155, 49133481, 890549391, 747671157, 42019429, 667031164, 408459541, 679990090, 906484157, 123686385, 229484063, 360360797, 159031440, 56263347, 392194706, 257348308, 257209070, 35628673, 311176180, 861736990, 529450672, 815771760, 151821931, 455750427, 906769158, 716345371, 932379077, 143178420, 253801520, 91261649, 786213471, 819591076, 11804760, 544769575, 554569038, 361593702, 295925448, 531155508, 530191249, 785124496, 599927477, 309592150, 475165929, 405090048, 222979893, 722198476, 562676465, 95178050, 733689484, 537481515, 456305614, 54159782, 909198190, 477878212, 204241186, 573807848, 241076702, 401117924, 800866420, 773463211, 780122321, 696562241, 339265480, 858813805, 148355004, 888926119, 493287043, 449190125, 947921197, 201553961, 153773535, 84152980, 242630344, 175733770, 122600985, 967513220, 80474389, 430382992, 103481163, 541792034, 783967072, 965865716, 517884451, 11617296, 953741971, 766344506, 371835628, 413821615, 921514918, 84451834, 543697955, 56722716, 382524813, 775537729, 223255264, 394814771, 719075779, 10047804, 873140682, 454141823, 177739019, 123923777, 990091604, 563459405, 576146643, 204811318, 575960895, 511568752, 161553821, 322747403, 543841479, 780594199, 599929898, 918985637, 894457881, 310007000, 667315509, 324032572, 633456999, 32038329, 327084835, 177081548, 565385808, 410492017, 18306780, 432414025, 8692023, 902262428, 941807098, 235213003, 450068587, 101724635, 260309802, 998209979, 18217590, 784263670, 62390105, 377263626, 635975297, 96914147, 785066425, 883050090, 307740174, 40577770, 401161568, 441104149, 656174879, 764678044, 865480386, 239825299, 759809956, 943137240, 195330058, 945992760, 425368340, 896778335, 372337557, 617200308, 319400371, 651950157, 975690672, 633172236, 309724542, 933340397, 436564546, 587506362, 622618381, 897951982, 943380215, 478243198, 698789433, 704515972, 673033998, 178509018, 308049715, 828906326, 148183757, 750166764, 626658849, 873753189, 593325452, 986795841, 922704083, 132859279, 439630290, 806113974, 914397116, 566027088, 748988349, 832612851, 682812821, 990222242, 704428362, 499686754, 370973613, 279045622, 912996563, 541995405, 857146946, 981614136, 636361334, 50699630, 288158275, 828258786, 94852105, 880748141, 253667002, 300065963, 719459889, 720432269, 2199432, 89965339, 286969232, 601350895, 203839066, 243332281, 993219781, 399565819, 421976412, 801638993, 654186903, 867509310, 478383744, 577651013, 966790123, 58823299, 996256081, 898485957, 2753082, 503876162, 851394136, 164869997, 870307613, 144256215, 997947833, 311623841, 413618107, 418462082, 624210278, 256032115, 100063104, 695255800, 746029402, 785234158, 258501985, 897733333, 874090862, 739652432, 690055286, 177521259, 803840068, 847128915, 218286070, 907767541, 707733965, 750919260, 847435967, 739629638, 481076300, 493364591, 644220746, 318278762, 242738235, 468254443, 227820905, 126999811, 962280915, 906734885, 280145803, 457175578, 345708214, 751909403, 992602999, 515865083, 735116508, 354440772, 506969833, 708086608, 364382425, 652467190, 482099886, 614814047, 461732767, 833709014, 919086320, 56670634, 82587728, 391993741, 595837402, 689542826, 335913364, 333283552, 236443452, 300238625, 621710855, 943689130, 312420970, 677244071, 98038510, 734109765, 439099017, 300813551, 684078945, 778708502, 815545753, 380024512, 793974883, 847689711, 820060155, 786650596, 846710749, 136926835, 907844334, 698978216, 874353568, 116724223, 100414418, 546245270, 381106673, 311078013, 618203782, 828429621, 360915213, 161881615, 606470416, 30963604, 110127436, 774402341, 716163855, 415358971, 68238871, 338275847, 19173944, 819449680, 895534012, 168400797, 212445067, 862081785, 938916410, 687135509, 544413254, 206562646, 31487612, 705492480, 944835799, 264353031, 278758077, 109099728, 911235059, 581854241, 837899101, 447905503, 341916342, 379519482, 954239979, 991176307, 5780730, 943520997, 971739996, 10312857, 818620017, 314352679, 62304748, 860165244, 929297809, 876256446, 67073294, 859695164, 906522349, 396357264, 954180520, 632151323, 632557276, 671459310, 169375963, 933851789, 103012564, 136787196, 415302259, 225073859, 645812282, 7324086, 415717560, 745594142, 90332009, 227525375, 576037002, 256197581, 930255389, 227178593, 289293497, 460256605, 8720946, 495202656, 493036684, 607451506, 736151403, 574204876, 419736582, 306713819, 437141717, 505029293, 390615347, 258538565, 222452365, 270869411, 618703098, 370141263, 202475575, 314301959, 931695300, 766202649, 251332638, 267494005, 306874503, 743087729, 347646784, 379559736, 487099985, 145137507, 829889904, 456828656, 472295458, 609949639, 672576043, 518823979, 247236084, 83485618, 107134139, 65746935, 170478248, 14901586, 250765547, 43393495, 697072245, 902572791, 672621455, 723170803, 783290476, 547823801, 932797348, 398669344, 471668704, 284928974, 891585053, 79456103, 773624198, 271496879, 873091475, 12617550, 280669624, 557991063, 419285738, 392674934, 580293429, 843121181, 258436860, 989330300, 915460688, 571980477, 716616776, 86983769, 386464456, 655576653, 599438198, 768596445, 953674333, 117507269, 685813704, 157307513, 875556048, 41707865, 267048592, 346926010, 808814442, 468718501, 864964113, 466065533, 31183326, 562981678, 755097958, 218351108, 92613133, 422103819, 512175581, 721148582, 636514423, 336202172, 557618633, 225569742, 952109925, 976371228, 688931258, 441524671, 340642498, 914259859, 355731293, 227502838, 376269796, 549855560, 29348373, 538637286, 89089427, 911320994, 282830286, 583304266, 387491219, 53552656, 955245128, 834869287, 384030298, 101884320, 225877630, 430940868, 775188767, 814973981, 844307976, 829920896, 445484820, 57150575, 235872721, 745480370, 525394073, 254413200, 319991637, 758535955, 899103830, 910809765, 659533926, 421426081, 359866845, 745947582, 267340150, 373356431, 412398067, 877638922, 104012347, 71728225, 499347396, 333052701, 492255920, 285459889, 614037219, 960367096, 421431400, 239969818, 512032502, 340969519, 724642848, 290829407, 388794178, 578245323, 147852850, 672547882, 790089052, 512293292, 223485479, 257808288, 38569657, 73643970, 385292738, 283156867, 315830894, 753579306, 435483845, 996899356, 516700334, 781279677, 418226790, 560632711, 900973459, 51679512, 35896445, 145291503, 102278971, 643714411, 525079841, 72914449, 721625515, 435220219, 57255458, 648335395, 115364525, 325091494, 707206927, 832579151, 646948095, 38602688, 274133007, 433839473, 948597451, 912826887, 143411705, 408365386, 801446373, 46814919, 279262783, 32228184, 813725973, 120197497, 782223812, 246757101, 569306526, 736426256, 157078268, 74461261, 629618743, 246716156, 269802583, 363603376, 78359813, 553671831, 22356454, 944511323, 3648544, 577908074, 619901143, 345050114, 958166962, 911443934, 279743883, 637856026, 71444662, 101467906, 198068586, 356174356, 477692265, 120970964, 749394926, 833177093, 430376071, 299359930, 606789760, 809587998, 665051200, 808763042, 235589049, 881211950, 495313827, 615148604, 243203649, 339782833, 635213567, 67953902, 882693982, 869786136, 118963013, 399291459, 586668304, 518271326, 85797019, 869507768, 505593924, 924861909, 685885648, 87762881, 24743280, 885142918, 582454855, 798166930, 637574122, 245266468, 165749748, 319924550, 883982994, 458332922, 896420663, 570984868, 703532187, 145652953, 923314581, 565088606, 137765878, 647022315, 11783132, 683725821, 729107591, 901913499, 735766703, 537468075, 7316772, 610298193, 990425467, 655027477, 872391989, 521038894, 912332389, 623823954, 566047141, 703374657, 569813891, 357955676, 175152559, 491923261, 70691268, 686188536, 621592075, 787387106, 31779185, 658267275, 101856132, 91062925, 264961673, 281466835, 813330516, 869405949, 140079444, 219073455, 422471171, 353136049, 958602967, 253266580, 734745048, 97642918, 680738093, 469188110, 50648652, 759168624, 368022167, 646796296, 993293123, 596748426, 516032884, 526056975, 547516421, 884520154, 111995675, 842839464, 446465567, 335497952, 280403907, 747808423, 217749982, 688078818, 568511844, 4249169, 651685635, 398924519, 305883711, 78966024, 432722336, 905047227, 950625086, 596347217, 360181573, 598699739, 343592825, 776832314, 337544029, 65611686, 480112840, 502939181, 890882570, 766959173, 134433734, 761549033, 123222440, 8904951, 80469718, 554335007, 525068976, 445062045, 299870762, 384092393, 229322869, 374478294, 669532230, 341171700, 974236014, 412848439, 677118052, 362274021, 267499617, 289685262, 86897179, 317980106, 924718221, 936251116, 542758387, 514289036, 617518098, 383076753, 846352356, 47800078, 703603826, 434381176, 528095345, 507334818, 677995000, 828072407, 653508269, 35662728, 277535641, 940608606, 581894851, 434442748, 616837013, 788346116, 258923504, 27352220, 560112161, 923365844, 234534398, 574786358, 756721261, 929170317, 90596045, 917339033, 540789761, 348169438, 803017782, 583113479, 697754713, 251819681, 373908911, 362068513, 763020655, 744093830, 301990383, 650045093, 234310541, 715181998, 953578724, 35508184, 100507256, 482490766, 677917290, 152593169, 682824812, 99231728, 439397253, 765591757, 698656495, 561163540, 192590658, 449610925, 86004286, 898127470, 802982995, 746573016, 124445343, 859877470, 656854048, 889034291, 127915493, 218986951, 518811888, 639591249, 622794881, 734951088, 450206700, 54624026, 384114115, 375844909, 475307126, 110744606, 57058763, 789519117, 402994241, 801328743, 173879358, 9602151, 904914976, 601430889, 708134003, 553784329, 91679945, 189603528, 361194506, 721316176, 738688442, 594304669, 991480326, 592433577, 687786728, 247118088, 259181222, 500501479, 805453804, 184355519, 685061363, 703248921, 55653804, 549732120, 613570417, 144192074, 224016329, 838588441, 516003100, 368419054, 470592948, 4200135, 767121973, 187922908, 25787393, 97660076, 107357025, 636114518, 630287928, 820627153, 580530718, 324018704, 461630794, 865834556, 589494857, 280294045, 661454242, 235498383, 996777835, 868859153, 534065376, 313577690, 828942347, 980269535, 510859705, 268587287, 154405411, 123394814, 493587898, 808870303, 766510596, 858775700, 841542926, 119207215, 523472998, 952150280, 705850980, 964943304, 417851126, 994157911, 865476297, 984939959, 120106710, 588226110, 48838281, 357823763, 360559460, 630010152, 170057895, 154844065, 258178897, 850741809, 690469377, 743903291, 846900819, 946529767, 152751041, 240825403, 588165091, 710040129, 448600581, 935174489, 435596162, 701903792, 413018839, 612853362, 541026511, 636063321, 155529239, 565016157, 750489472, 369461314, 574985566, 318019212, 375026675, 840463813, 536369019, 870753090, 807288828, 541054077, 861429614, 224712871, 349747787, 890264951, 143603164, 379202777, 902139172, 597117166, 877098893, 542932894, 737516327, 753812642, 590439328, 395799101, 411548977, 83663227, 319965553, 603663285, 429789412, 231134023, 915531286, 206707954, 217500856, 140926189, 307430219, 694910371, 234065564, 582185596, 980100627, 876351341, 137237205, 401876040, 417391014, 85527745, 417841753, 422469919, 398627728, 851727501, 96041582, 846682193, 163731882, 512135364, 226143666, 291647091, 989052734, 790168398, 403803869, 627422387, 436169962, 608577201, 336919524, 406077243, 791551768, 882608837, 199185112, 98387306, 610832893, 56067981, 638909920, 967617188, 143033438, 930946401, 380486726, 496651704, 112317749, 91939654, 784647158, 77981058, 28819055, 761436789, 544573149, 687023287, 411104586, 936016783, 902725693, 648389783, 86896328, 409496230, 762173533, 731240882, 639716434, 870411196, 396946844, 219100774, 478725059, 972810274, 634989024, 55752559, 161074447, 468167987, 195682401, 973323856, 881228938, 392853561, 929177726, 773635890, 325882544, 585613471, 34308221, 842166960, 689134169, 108927027, 584702248, 77521530, 183499988, 828116171, 135565453, 645842426, 249376126, 803521283, 231295354, 493640852, 238360069, 831130906, 106240137, 717356843, 959838107, 958545393, 112065769, 997194573, 628833587, 271685438, 709015124, 182047360, 815326443, 305921123, 538700755, 124325564, 911196666, 341035296, 55889791, 349496403, 359193689, 821038997, 711974526, 865983812, 446217209, 940454209, 386836723, 663757429, 756649259, 788786307, 877202299, 418897519, 65823024, 143339865, 665209955, 429325920, 688706365, 612727075, 196232397, 756881848, 620469114, 750996588, 851419292, 121827521, 109023486, 30905161, 664310173, 519608858, 102463743, 799335086, 715884402, 128670862, 231135701, 826744701, 201034778, 483375434, 76951432, 54498085, 24198638, 689342738, 214104279, 184114987, 628008926, 212278296, 332559567, 119748367, 270788982, 423177924, 492719183, 74842311, 53502787, 687125929, 895597307, 375249067, 149727981, 734511570, 396733023, 522362404, 40111475, 626505659, 24429577, 887007104, 392648170, 166581488, 17412644, 172348634, 374544653, 268946906, 565421465, 749861764, 694612257, 323056011, 427372556, 757327527, 315074870, 99477951, 585787458, 366397614, 832279384, 596021733, 541582396, 402786521, 438142609, 117230934, 927602333, 583007209, 281687737, 529408287, 862013142, 22903723, 473018709, 313999095, 631694444, 286210044, 190644976, 137349673, 452032664, 480368059, 41493546, 81530345, 263947389, 324884767, 92730814, 207901271, 522351498, 920791264, 339083694, 642598366, 200770770, 151132925, 86782687, 972810472, 38371485, 838746068, 970262669, 687176886, 658743721, 176391678, 926678887, 286640203, 424639370, 535332363, 522812700, 733303511, 819025563, 254203546, 495661447, 813440448, 565681879, 454951058, 642249477, 760576602, 524573520, 750292403, 930477008, 144628982, 877384360, 762644136, 478255697, 386736870, 371256919, 670363923, 710918618, 253297600, 341021116, 700165281, 525803569, 762339077, 378119284, 249285059, 49176995, 113983161, 471405967, 42548153, 71388044, 96871644, 921948601, 967438247, 899991909, 121381432, 195051003, 534737187, 426915975, 882135355, 115479022, 197393245, 24828008, 830019259, 854127276, 84072739, 878562607, 183494478, 495529172, 202252854, 618878249, 684285204, 174857999, 394594768, 36194637, 830501184, 492666623, 291241613, 90538540, 83681528, 894078986, 884134365, 516327066, 547861862, 190983973, 618872547, 974959359, 16390329, 575715669, 932815494, 382875697, 376351768, 888757019, 481996356, 367414505, 693342811, 431544534, 269540036, 45762524, 112536660, 703890508, 584152137, 870114965, 188143970, 279627017, 539978896, 942492172, 378520291, 458038300, 452810018, 87012725, 155480136, 755027551, 255665929, 697515414, 485198745, 500169921, 61692758, 880892948, 146667227, 192191169, 113642506, 274055601, 630768768, 242818520, 880879940, 178599537, 242651168, 30248679, 641328534, 344114937, 123962918, 577686519, 798231923, 81433761, 573796433, 14657244, 928780295, 540216474, 705923824, 902965430, 961766450, 535924157, 377996328, 673710417, 121058301, 503641644, 741800572, 484285137, 717625333, 975373223, 275809002, 855724940, 454621742, 40333512, 128213743, 934477239, 951382571, 354872644, 513979361, 127836362, 928972887, 681667953, 72603342, 958223749, 369447158, 754398494, 523873752, 876220583, 776160186, 37204103, 229403140, 584400732, 65991053, 240349943, 913936852, 814466228, 135652045, 558647157, 147280750, 687024108, 32119081, 413236447, 226552262, 377490083, 183931024, 250099305, 480033355, 947776874, 141504477, 869218218, 737838153, 786248243, 567874468, 258844697, 457034516, 803823245, 954604026, 93015906, 270920076, 293296339, 431178398, 738743645, 989186993, 758686119, 227015493, 862875071, 80404058, 235505307, 129808403, 477786700, 390202971, 426401226, 971098983, 1318466, 294576131, 658796871, 823202561, 783432026, 928585938, 592580621, 212015020, 21051684, 100816843, 803202429, 402352425, 847829072, 515798931, 490593663, 520265078, 767022832, 212973718, 863656128, 492068713, 741334154, 651484124, 506224708, 639909303, 704795773, 851886969, 815765483, 69287258, 118799730, 612307221, 638307906, 227564930, 87550524, 404071385, 720878164, 510305386, 708596563, 631376248, 786244915, 504700799, 195113075, 958703907, 128998987, 299935432, 763982580, 534088275, 775341216, 19363457, 156604399, 97398692, 358098317, 94353461, 864793064, 193244954, 801304616, 422179188, 18609657, 702538944, 455644375, 804166110, 354874619, 725559289, 371537854, 728702136, 541614872, 879157619, 96527222, 4992792, 607105966, 524571910, 489282775, 886724650, 87990029, 413769084, 407750304, 980209414, 143282156, 824912945, 979812530, 782672553, 946938901, 542632890, 756016753, 136609857, 200593133, 733429111, 312306426, 147281874, 720057337, 185773088, 236444216, 163840756, 679044807, 428609818, 708639800, 573090831, 22144253, 8006595, 584384963, 366240978, 595350639, 717674562, 144538414, 973873787, 117006268, 736323522, 874657829, 161531123, 126013932, 262212920, 937642394, 800568490, 229385832, 686852254, 678187463, 896145028, 11322277, 995550910, 586967847, 42027762, 124227955, 119989936, 548995358, 32148493, 816243988, 351461240, 347780445, 598636413, 966334028, 202043723, 343059485, 274697155, 132716962, 645833703, 293231516, 469193990, 669844276, 134209966, 977803221, 885635888, 645076861, 680161293, 905750210, 382244404, 657154051, 58252329, 465477437, 949045472, 72717215, 565353569, 442202329, 150416885, 180425910, 806440598, 700496752, 472575874, 625634540, 794279629, 141442643, 630742025, 270151357, 89320939, 115522094, 609118858, 781261738, 181078219, 205898034, 17716800, 666677402, 520104449, 193621784, 39404236, 261849737, 410649123, 69719389, 578045887, 122338091, 442399756, 346652265, 616006106, 129130688, 98051392, 899357890, 78825874, 702903752, 803833411, 507512156, 199892565, 117225794, 107502027, 189860438, 59049285, 247331086, 494515190, 470016038, 592263304, 44542250, 330313649, 627212371, 857829559, 646837820, 517407590, 239731857, 69894388, 434082639, 912371941, 798912541, 250699010, 334129407, 839568557, 897495037, 907988751, 4605793, 242607182, 640195391, 794707170, 603363602, 237814754, 519383265, 932591209, 4522727, 687136612, 580060667, 515809050, 340558574, 917900513, 247795243, 547534491, 206130375, 409836364, 448850557, 826784320, 36068113, 930024798, 364964187, 301672552, 752356018, 831251996, 431431931, 719637750, 699528467, 72712414, 285011381, 656349161, 878842177, 633393564, 193335063, 456252203, 848930410, 845261879, 830058754, 926403524, 483064414, 175458682, 539378191, 232930487, 48551418, 767290768, 592900064, 793043181, 400895273, 114048474, 540733667, 546599666, 606189113, 400659110, 273954745, 130456954, 389146951, 186504592, 867354607, 983459429, 503182813, 858681896, 382079818, 828327034, 108628626, 510587828, 410688368, 323660650, 305567860, 189475983, 62655427, 221226489, 633026643, 773810696, 413243739, 386245086, 718154422, 936390448, 811440976, 648358011, 885913005, 970247997, 409164268, 445159234, 776798312, 272912111, 745382075, 934683920, 472271431, 112542213, 165649641, 454082744, 779093130, 192411932, 747246895, 890650369, 816201396, 554479999, 657405926, 631391060, 17725220, 240651243, 647562643, 769346941, 562575702, 693426841, 410114977, 210602587, 473906045, 424978530, 17090476, 20143122, 341347254, 404835784, 394883421, 784702859, 982569628, 264434817, 332091746, 649056930, 298597370, 894449294, 212086646, 903959061, 512299704, 180874784, 927795459, 415793924, 32148928, 797357493, 236142254, 68157316, 498043346, 355000258, 957297719, 796702071, 50301937, 824815111, 717605447, 184413493, 458521204, 424393366, 659988263, 581644460, 617526163, 487980397, 557100263, 558433257, 732119386, 466336674, 868718543, 921935258, 467456033, 253946533, 701898364, 300193042, 795339503, 117771030, 563977367, 166374104, 559310467, 974810918, 210433798, 967191721, 806348191, 159020039, 800266296, 288906897, 386612693, 447427517, 540193709, 854373888, 545263178, 528707484, 376498211, 197823867, 746350342, 372046414, 9304848, 428498269, 508708936, 829406095, 854047582, 575193159, 784509484, 700338705, 797856932, 686874867, 277812071, 121890484, 652649452, 522248915, 660996843, 729257269, 657297181, 785895501, 790531377, 712901426, 882398660, 786763762, 302200532, 232905427, 242131786, 243032675, 750353461, 856809698, 310416912, 157881758, 570528522, 332631882, 850619861, 113442216, 515492523, 110625705, 925713577, 804636674, 711497082, 910210344, 467846005, 81707808, 196485890, 102970048, 77054936, 619196060, 875002861, 677501309, 147937162, 851134307, 581979737, 603264333, 272255826, 45836301, 111934118, 292671908, 665845360, 35785196, 657771996, 678236935, 670185887, 186490313, 401266000, 533921517, 301705807, 714811715, 475364556, 371982455, 588538782, 650332864, 15344901, 882951697, 243870174, 838295811, 633927667, 543037115, 895269761, 55161442, 134954311, 668787566, 317254621, 260494026, 794541592, 287554561, 996330560, 643098227, 254516012, 850379333, 810735244, 761288471, 530144560, 422894431, 176355128, 895342559, 296995766, 410449857, 460621216, 797161099, 942674376, 584376478, 12142913, 734121879, 559325576, 490233742, 67380643, 998039392, 257352403, 197200038, 556979030, 274937909, 240904141, 122785289, 801053517, 332002494, 786668954, 941529679, 571717269, 654967741, 458379369, 295236073, 864673159, 292354796, 157412792, 51264432, 623770813, 862011965, 659012116, 926560128, 925131506, 733517733, 816829196, 135007071, 475740969, 509543844, 588559872, 346247852, 825263319, 23454129, 779754430, 531343320, 56740682, 203454572, 370748058, 885237713, 249487228, 16830025, 202287877, 686441441, 438598353, 609596102, 20544705, 817664876, 711917313, 301631523, 953426447, 786862063, 609414900, 952125910, 79284483, 885311878, 701059060, 286133988, 37568580, 908007008, 689489125, 977471653, 191949006, 624421160, 319930479, 361465027, 660231948, 653463097, 951860780, 606593599, 688665613, 919199720, 427164350, 633605193, 693475075, 502972070, 883411381, 733027961, 125132532, 383617379, 14613829, 929298214, 277732498, 515511798, 299888294, 945484553, 308386660, 34093321, 642910523, 945086799, 734003204, 966452473, 926191503, 707252199, 571206033, 386204515, 439204563, 414457950, 823794416, 163443231, 917386500, 954327970, 302351588, 384666095, 69287964, 908827981, 426093681, 153523822, 929754867, 322856246, 946623041, 398007980, 772349051, 531402430, 248640647, 593380656, 757773432, 107123600, 494273323, 256490087, 252784535, 740480987, 779182029, 348815524, 92506094, 220111548, 958265452, 589559827, 276194762, 299510210, 150919597, 395463293, 551713000, 383162662, 495304119, 184165853, 173016161, 253856891, 23436942, 466849094, 276896565, 115080242, 935551702, 857115978, 790668397, 753394402, 882095470, 980244935, 837566740, 869676674, 556290661, 249698569, 300808064, 306382762, 568390691, 461256912, 629890416, 644376116, 10388229, 535814582, 218929843, 117329118, 138317604, 668594059, 130047852, 941334238, 264653053, 527665318, 690399807, 170651475, 190561219, 320950219, 321268829, 707064999, 5311835, 674143807, 671052109, 271970107, 955969100, 752540842, 666935201, 323520062, 602928816, 15513230, 440081474, 264612105, 364253852, 851947702, 284807201, 723614675, 619541988, 402765046, 189319184, 506569661, 10364297, 318095283, 824817816, 205631411, 774673227, 410890668, 362260686, 492163807, 58096837, 545789244, 424129768, 291779949, 202816729, 160815230, 600098682, 688052939, 603923438, 110866177, 469483696, 567356029, 56144603, 139691919, 25125892, 711823341, 706026597, 214322076, 727909422, 552556935, 175080977, 201672114, 684602251, 676214640, 895547813, 924228088, 373887531, 23838822, 849125696, 51386185, 89453019, 443250340, 826398219, 557572139, 676767524, 182656732, 272004253, 100384283, 213920344, 911587485, 171512472, 884755104, 863499190, 716912646, 218917237, 470470863, 978151965, 719994460, 392789838, 746896568, 565528958, 700327091, 912637070, 260738934, 901159775, 25383559, 898777313, 105632627, 184011278, 53415831, 987908091, 172193103, 775141728, 14414384, 629393491, 669008676, 139425110, 164093031, 34375295, 201885073, 533724498, 229687400, 859577144, 374632281, 992039376, 183575366, 838198250, 97820485, 252984999, 725131911, 658247593, 730130919, 771738654, 174032814, 208335643, 642550459, 360690059, 279769876, 461205588, 770701379, 164080834, 423645821, 3436909, 938241177, 90696428, 157686143, 795739806, 227141698, 715361790, 789564241, 473203185, 117104060, 469352716, 355106515, 947559194, 986871480, 2193810, 206194254, 861114017, 341802322, 300365671, 753588068, 131401054, 159242964, 740154011, 575505160, 800707882, 56472149, 769370482, 370114067, 24280704, 249123930, 469593142, 359101225, 786182731, 823880488, 618386067, 584754791, 336161417, 984779160, 253024868, 703450055, 185884033, 169065117, 125636903, 440256593, 115330699, 58448571, 70410418, 690943709, 639919100, 877207187, 400888349, 400101044, 34609587, 301443866, 561221419, 484925362, 358824184, 267608285, 498786741, 380043880, 326887623, 370476514, 703359125, 295297566, 586892482, 524400736, 868255540, 366228019, 792089025, 803774367, 298301542, 274634001, 298079900, 927655710, 833151029, 242276219, 371021789, 488775163, 880691650, 865497216, 873954376, 584722210, 275538150, 611344364, 615937936, 374881582, 683526010, 834336029, 519236097, 404856429, 985241904, 735471944, 882602934, 670116655, 837954918, 2310158, 758749690, 552090267, 703584503, 547239300, 178582516, 498225726, 389429935, 712678946, 890398529, 676266132, 76378002, 945527073, 424526371, 424226706, 126244702, 793666857, 333925939, 997244384, 686354769, 582016840, 185641433, 707120128, 76683585, 963956771, 634674268, 3547860, 110109839, 685422778, 520355495, 115068947, 204988876, 414790969, 11007018, 925320304, 320313054, 350494334, 84389281, 237527580, 692909767, 911582326, 195369799, 312038642, 668239673, 741637689, 644270273, 56516341, 89233904, 234773578, 225621083, 362401419, 459447846, 754366755, 505165963, 665595905, 680472029, 335092323, 8850593, 209977102, 98586522, 844981725, 797121231, 367138925, 65489499, 235918385, 842592418, 125798236, 640763357, 550193639, 121274923, 939000355, 668830247, 468379748, 252917053, 975962516, 905592146, 231632502, 237199785, 692643573, 776805346, 539834551, 52539945, 404781360, 548286411, 93797641, 732045940, 878697932, 620792104, 287412158, 891666185, 411367991, 551677129, 202839761, 278971319, 982666881, 299656124, 817538629, 212839192, 916063359, 289255812, 332907011, 134939567, 124326636, 339281820, 596246266, 995961351, 163990899, 19052345, 221697798, 593913479, 693106950, 789133363, 851959960, 47341069, 95825000, 741973644, 155336901, 719252191, 256249473, 114669412, 3071702, 123332299, 711949497, 647789171, 784391057, 83439913, 82925817, 427614538, 226377971, 552258752, 800638147, 500012248, 405738767, 928216752, 848331334, 973465234, 469630114, 515961746, 263923981, 345489588, 892162318, 352161342, 146093848, 912308914, 168340379, 990376730, 712771191, 139425961, 963902742, 63007106, 927265049, 118894153, 21693733, 286523866, 640757615, 553616196, 844144944, 71898591, 212496363, 481172133, 816248160, 261463911, 752324788, 534266420, 378293490, 547428069, 710701642, 155925172, 298024587, 255772021, 468140239, 835832918, 652909576, 711093926, 825401225, 971531188, 420102480, 592713741, 1013486, 60774407, 399205476, 327216084, 194375609, 539028519, 938647058, 871240874, 317501582, 647532841, 886662847, 804566104, 904263706, 29041877, 388653667, 304928158, 417417770, 950040507, 143956170, 475014765, 823747217, 433887367, 402959371, 824085671, 412061351, 293817190, 812386653, 569473128, 149872659, 819589281, 91637443, 255756532, 121735113, 285807954, 526937203, 10946231, 201895263, 927767879, 552088196, 687709805, 971188920, 353972469, 811588449, 543906566, 376240291, 892814147, 522896573, 964949146, 657248159, 616555060, 652004128, 371694713, 629693723, 244732458, 712204693, 944535774, 223141955, 618980300, 596895466, 65179294, 684859, 98587909, 455273739, 696176266, 570416244, 921505044, 857818985, 92565227, 120566133, 217596108, 751825570, 188425924, 694264322, 809271329, 283336736, 401761003, 237457963, 407585621, 696973705, 396599454, 592736216, 729276591, 679981687, 745071381, 432988664, 880936999, 436069016, 661379065, 790303507, 264831810, 228326870, 783464251, 790592954, 358997294, 988598376, 565740008, 523773854, 165933676, 361067053, 162809505, 665125461, 592508713, 278048581, 857268176, 796207894, 705411204, 637307890, 284036579, 102754394, 664033556, 331337097, 208155307, 768933676, 422104969, 198201859, 733445042, 665805107, 146220338, 538981044, 470191549, 30511616, 903966196, 963855571, 383851501, 545702429, 732632912, 742397763, 368618475, 343672018, 849611770, 945132334, 64607503, 10408244, 793861547, 320974430, 635650695, 758053715, 219716373, 603898221, 754234462, 538455425, 277692486, 584997298, 501991489, 776034537, 783690696, 144336123, 819200643, 728036639, 90227569, 381743083, 205951302, 104934599, 741103324, 467040576, 651085081, 856881296, 417060504, 342608609, 731449729, 661218909, 550181759, 881975419, 990643002, 332316701, 105337592, 674129735, 397941615, 325525619, 839960288, 511352585, 17291734, 321080297, 961985252, 274912537, 280503671, 258266379, 603707997, 74636347, 642291119, 773707299, 965150317, 972897033, 432493290, 577471192, 323790326, 777960261, 279787241, 53586365, 204518566, 424647918, 643528625, 278650673, 742141696, 767881274, 370481658, 654447415, 423508462, 184949083, 511367570, 999828473, 228378751, 804315359, 516603944, 345503819, 82813333, 124832929, 959134012, 386162165, 128511510, 335475976, 217988965, 811235078, 739770270, 488294789, 852987634, 232894508, 512784825, 65571665, 337163401, 762017806, 78947378, 353717111, 2081262, 212076857, 528280759, 168334527, 582020904, 862977946, 342372705, 887921221, 397557708, 843986698, 817070422, 684177761, 755254872, 850452628, 769755689, 564923907, 973140165, 625110178, 881910243, 772532965, 289624334, 743527590, 141218068, 720739543, 342331516, 8112642, 408333387, 704038156, 625027207, 954086962, 484450665, 380794317, 738160490, 655858538, 246727737, 989009252, 740826752, 630897126, 953447872, 465099601, 5733928, 243257582, 895362982, 690115236, 129112950, 795027452, 154703297, 930016915, 704011223, 903904096, 728399973, 484183225, 55270638, 613919305, 995108315, 838174193, 503238932, 843350489, 2001760, 636341273, 527770861, 67422600, 413738237, 92359573, 63195335, 457764771, 426626527, 790181010, 463021778, 724376448, 724658086, 329337092, 826924091, 470407035, 574185105, 288252850, 711146005, 996257835, 928072382, 117415377, 158451261, 526259110, 256546325, 804489956, 527246354, 878383250, 4586067, 523551093, 82393290, 627592773, 128418632, 369978365, 295007029, 588445583, 228558880, 6256161, 795573462, 374869837, 411178446, 231977079, 146204484, 569520851, 509801834, 721344148, 219712892, 867033560, 70319128, 8609220, 661242074, 273610329, 771947148, 449278518, 270195430, 796214318, 359366767, 293356226, 897884278, 822992818, 248697561, 897214279, 36103519, 315290953, 30618877, 72596641, 756818703, 823218620, 52310413, 863582688, 549329056, 343241850, 895371403, 381262912, 396444977, 937919271, 684530650, 418219403, 276409085, 589693729, 967927994, 646211732, 650964727, 530584814, 297517262, 66285537, 543711852, 287926405, 112618343, 773596359, 392176109, 967929273, 358835350, 494889639, 706872845, 561212180, 26832744, 230114702, 922690243, 599249430, 745657730, 478489393, 883034701, 38454744, 457240718, 97938235, 718454092, 875520875, 301435515, 656221360, 828355049, 151316356, 166724316, 628951763, 781617948, 64237381, 829980217, 750384341, 816685305, 796772438, 497467916, 332753961, 539129895, 485824407, 468932209, 530953698, 773318636, 317486515, 900188035, 203713359, 738485351, 727905702, 47057754, 217030670, 351330949, 429465453, 395516439, 220282097, 367375677, 398414464, 350082393, 752700514, 786986163, 345564211, 682824472, 705570228, 163045483, 180066924, 799052862, 678856438, 389278948, 398735787, 800376610, 167037551, 984762029, 221196881, 562156188, 182671061, 547491346, 963882529, 190193459, 1110446, 710812463, 420672611, 85386718, 721460598, 122447568, 75143481, 140697049, 585358991, 468867942, 67874012, 673863482, 409330895, 989323207, 65307910, 322509324, 504219159, 511295729, 589831496, 193087652, 341810248, 225795385, 210159244, 538688851, 530315463, 326817508, 385394526, 875894069, 433733450, 523239516, 915280976, 579862998, 306662379, 682492566, 775024470, 430041635, 217687455, 177906683, 720776355, 339641463, 179463188, 685971726, 893227369, 590326487, 325915839, 3539420, 923963665, 334060499, 241802078, 219735923, 957606031, 810666333, 995588246, 561372005, 384378788, 385921218, 427981, 923036157, 495002506, 937579468, 608611116, 512408797, 961144049, 867293093, 697468386, 420368276, 816698979, 627359403, 423587108, 973171430, 71844175, 347366814, 691477530, 939860837, 859178324, 719865334, 139507229, 229755081, 18691081, 25531176, 22087180, 264445177, 337162973, 119045142, 104568096, 532632547, 483136558, 427599875, 712246320, 820674524, 497678546, 966101302, 702012256, 999888329, 514093496, 551745438, 27476561, 321839564, 606295223, 975072537, 336550855, 605644813, 26968020, 632408260, 509432838, 57629648, 807046423, 902629896, 509459475, 902076374, 934347318, 380935914, 211767204, 719570703, 39667229, 201632792, 633900215, 775524344, 555614003, 5245195, 215913028, 991845054, 381791357, 337860075, 129817606, 962506428, 357306045, 111909243, 287689453, 158176134, 99521361, 509529201, 69778346, 417749885, 813725321, 905170004, 141512355, 655387262, 964831436, 184851757, 238367974, 255061573, 885655344, 564191656, 711997177, 11806844, 372504341, 772851391, 238698863, 208104383, 725704736, 542888538, 753875150, 541081948, 243055325, 256488091, 525660089, 682735634, 63267367, 566807982, 889087443, 343931885, 507053727, 96661309, 45186271, 857376990, 497697733, 703092211, 343203707, 449839449, 574827890, 269567362, 882352763, 166141675, 775845325, 483055510, 252797649, 14252546, 987304829, 752091736, 896794247, 966077045, 796917182, 735578417, 160356344, 498560826, 454032558, 466582764, 441120837, 53449561, 613312824, 342914309, 666242594, 874470119, 629013585, 820173864, 68333639, 605359979, 374331305, 947802535, 33201158, 687417906, 432742132, 460239727, 581721054, 864542675, 109662278, 884866166, 204559174, 128380750, 847933292, 143614036, 262084961, 548429592, 692355924, 125115599, 214772461, 915556746, 263170051, 112107707, 407460924, 261729693, 732374843, 99098701, 370900227, 920113914, 580510019, 745942164, 33884000, 662200458, 356630961, 927997214, 186104057, 302443488, 276332736, 685843193, 130451432, 632787439, 670510821, 947584714, 728888900, 167465840, 916376571, 656605557, 878560770, 227664882, 430905449, 52613451, 636528008, 108676757, 673723148, 44281621, 375141227, 456007693, 798913047, 336658430, 706525408, 123917466, 52924986, 621778052, 173942055, 784496669, 928512132, 678518106, 692914477, 154651568, 965291424, 107091235, 941956493, 963631295, 628021697, 415049608, 299016453, 991940471, 970877628, 905810186, 828827423, 48447458, 440341064, 483496803, 333579082, 830732219, 243260914, 312254342, 940220570, 978797821, 544347106, 265622010, 146779427, 258941795, 101541255, 724876586, 902122129, 342934730, 162967713, 830971807, 685288147, 925563384, 631545577, 717900079, 177025731, 46111899, 884295965, 332797634, 866666496, 438732036, 403636800, 482420913, 47405486, 526798576, 361843020, 793182800, 966657998, 687375958, 620613263, 129842537, 42059935, 347645417, 5209329, 697870972, 677177182, 741415556, 608321206, 4868240, 5140983, 889224754, 14273511, 528695654, 117566739, 659041225, 752487665, 902200210, 491470566, 372186077, 625214971, 509546952, 975620312, 904738432, 142491279, 456550622, 855385372, 65217572, 414631488, 251571163, 700257068, 298778935, 909601628, 134847508, 943013359, 91350475, 819857949, 505520374, 109646071, 83330392, 921627193, 613799573, 830367583, 183865914, 450484830, 736585194, 984911461, 184612137, 607187395, 897591505, 814369830, 807964123, 466392528, 812601625, 278303859, 582931928, 422036293, 676344049, 506045069, 23290450, 782947567, 751647689, 239220853, 579145666, 316941595, 61156037, 348129724, 507576069, 327179585, 152367278, 808587830, 304771413, 742616660, 12907251, 157975553, 791067629, 821032281, 313438289, 217860800, 161968472, 520207714, 296629206, 959112246, 925999894, 722318995, 974847179, 507552208, 856751128, 899386308, 627301855, 669136892, 273875531, 271154576, 679303911, 938261878, 865968430, 507620599, 715630393, 938621439, 468863667, 577406621, 709938678, 513757622, 8767479, 893874777, 989023528, 542300586, 41142485, 825224885, 499604675, 588641949, 236550570, 822119084, 931515913, 916402350, 981772949, 384782369, 383035324, 653546153, 765570926, 586250156, 481593092, 576402252, 644195090, 266305349, 3333523, 333583648, 724928300, 833646094, 431973404, 315377722, 892903548, 207538457, 211428012, 652682001, 220867805, 288770860, 170696085, 267775878, 163577233, 801459846, 617443705, 853759204, 397986448, 1817319, 28132669, 61596377, 904847560, 407211294, 716940328, 603476758, 755531392, 929220605, 423987892, 949732034, 684937300, 853708908, 373437536, 935736846, 462187375, 930130669, 226321526, 348565112, 140730356, 327677328, 685656356, 965525440, 369783561, 51220263, 326921455, 803567143, 117593393, 461892425, 306964801, 362532321, 122321886, 292918261, 864952750, 606945998, 404499402, 636141629, 783891317, 192728025, 700614679, 464916066, 199172063, 635931841, 332732705, 556236551, 671228590, 621339563, 751075276, 807299844, 147702316, 896261550, 411012987, 6772116, 217504737, 86874685, 701836420, 439459387, 853182850, 549562696, 678432697, 807525721, 323746075, 311914307, 710238319, 849222798, 165914641, 179993342, 574526264, 692157755, 986188243, 567685125, 93344063, 251373890, 384973786, 329062120, 650496530, 398016801, 836480893, 548848282, 749986895, 689501909, 734910336, 331967138, 718435175, 345552865, 678347519, 823047649, 17815766, 777182886, 422871773, 323137848, 864169379, 925800802, 495178734, 841163814, 647917344, 492765891, 399349948, 495935998, 987221222, 277162158, 954281792, 517327964, 646496145, 280733970, 931584775, 365316905, 606220100, 278763925, 967281200, 507908418, 651841284, 570987943, 650128125, 312011125, 368315566, 271075115, 41779368, 328120120, 640567142, 729970412, 839771216, 695564327, 727243926, 74471401, 147040049, 615769384, 737455198, 510837327, 914912955, 980414127, 613507488, 280384587, 453918922, 426743441, 334709310, 735703459, 377733111, 532305879, 515439983, 888363615, 408196586, 103497203, 238670224, 824245945, 872851106, 689977710, 753233886, 155742484, 890714950, 676735528, 268746146, 18453879, 231941668, 986899231, 923202407, 424571424, 984905254, 554357317, 674013784, 360238600, 95320224, 842154372, 151739660, 595467479, 350636843, 913941229, 302207941, 988260203, 527479128, 867145799, 18524058, 863031877, 352037786, 856860138, 611521400, 918782050, 68407474, 676516358, 562915595, 535911556, 445402824, 671510033, 849692426, 851538308, 800288517, 952248871, 260834672, 263353399, 706673485, 818207843, 393388716, 561198753, 465903673, 325825893, 17662283, 183281422, 879403419, 384787139, 972770066, 504656052, 249751655, 246972906, 285008501, 190683261, 544658635, 335255993, 726766538, 982962242, 961330207, 363543748, 515464716, 623083699, 599533059, 673533280, 372740471, 513497835, 187952409, 288963236, 927977193, 350805366, 857683632, 585423247, 735171025, 482062602, 193097706, 156745588, 746025430, 798770042, 796953901, 703742275, 565569464, 931175933, 932238365, 869621980, 161609279, 393961465, 642771429, 541111900, 546866379, 976414945, 589789530, 394279570, 369389387, 310898186, 664992368, 438018784, 777221319, 951349605, 262739483, 710938832, 485664760, 399012714, 293228695, 175173495, 243309782, 178635443, 591825804, 100076442, 944353316, 917788964, 242735823, 917210458, 965367805, 105255731, 244760438, 207478706, 916757541, 166667582, 928329389, 773220029, 21470468, 484111040, 315358209, 506375798, 783818592, 51633258, 425559960, 962879334, 414654212, 736845457, 556044511, 565194952, 963981796, 286870490, 882904701, 884904437, 164645608, 620000787, 211915019, 943086893, 303601073, 649860772, 834107087, 75332081, 986633302, 521574214, 535535541, 357061963, 256512919, 158246183, 782513755, 670692026, 110562129, 166216151, 290459470, 531327366, 12202697, 450154420, 37417411, 514470944, 557175186, 2622349, 10059083, 506542710, 563455235, 667154015, 195431374, 902638868, 72533582, 509172208, 957615196, 611099282, 758658307, 933361108, 548449852, 812004524, 295282063, 638828646, 145069093, 592724731, 903178882, 64225107, 381519233, 567066414, 475655734, 316999040, 872019608, 659966977, 808158570, 64068250, 309220431, 297520672, 973206758, 614882156, 947363894, 597509858, 427703758, 605140175, 237258805, 697568513, 812892709, 739347250, 246224472, 165156262, 672059802, 465868136, 432081972, 625209708, 138389005, 647862922, 109653050, 159878860, 687840007, 376071925, 382349735, 825439158, 962600484, 624240181, 261294654, 393384550, 567814493, 400262360, 135628355, 233292235, 187777196, 95780145, 911041860, 110755545, 146114685, 135226145, 873278329, 799651565, 793620394, 504559581, 396513566, 412973818, 842227914, 761192789, 201306330, 326747478, 385023491, 376950069, 307586660, 890676046, 221236049, 86729857, 89297300, 628499849, 515654288, 822502166, 159821366, 396595837, 41638462, 306555007, 55821318, 860531224, 312497755, 754342031, 756863619, 35142148, 666855407, 65567213, 102703292, 685175747, 878827242, 914038068, 844023516, 522376157, 543962942, 206592550, 804001641, 430700452, 363733719, 471508450, 19312614, 508247607, 62821975, 7170786, 577164487, 213888365, 107356287, 368652036, 97932206, 182659628, 867804829, 230468976, 143890603, 303256638, 673071097, 378337549, 704683824, 580488802, 597700420, 403691277, 466860313, 104250236, 736563030, 410195859, 93771754, 333398234, 196242538, 723022776, 684321090, 875663662, 604936315, 579258049, 342074413, 57412540, 448347642, 53255625, 372117799, 146731433, 223271603, 414966223, 775423701, 351886951, 17345633, 253529584, 609970979, 839491925, 748262269, 414297273, 815423927, 322728808, 248407595, 937497478, 50799004, 943454208, 771694948, 503909197, 127085120, 714057417, 480301838, 422037593, 355277857, 802338879, 860551672, 348341161, 353210988, 544356420, 273282437, 657118811, 300360359, 993246381, 55186378, 301889068, 338868023, 399297399, 222464718, 803252918, 356831907, 516197656, 608156641, 415489928, 616576041, 787483162, 514919657, 662336059, 590240234, 480348094, 785515636, 194509260, 789976650, 559802995, 82490330, 287843204, 127836230, 34175998, 461152455, 451175873, 992543721, 694243016, 97858192, 722761823, 451331105, 377701253, 842540146, 483269177, 990302980, 269862915, 29361487, 518441331, 883550740, 672245473, 598810501, 766471434, 317125177, 185132043, 828371277, 450896867, 374441710, 129890948, 251123035, 654662466, 329477871, 391748870, 709415720, 725378100, 595896093, 577474583, 227691279, 566472784, 161588762, 439649828, 713233366, 156466824, 725552744, 105093141, 139309219, 753926373, 159393717, 821764935, 182429321, 455658034, 862126290, 680556506, 128267436, 792113162, 556183367, 278316960, 76358831, 925802672, 462022242, 20816971, 266852361, 812813502, 35494277, 116294256, 243953948, 62383998, 919362102, 414347981, 698674207, 177040325, 929396284, 927420399, 670934955, 204368332, 72728453, 533379806, 59897559, 738881577, 491821035, 37274133, 954979497, 467362480, 939431322, 126143930, 306014478, 490211051, 661840435, 522417360, 650952251, 125643399, 550154968, 974194070, 548086823, 736921016, 120536368, 982695380, 841193275, 571635723, 339580701, 354131573, 562342266, 718781416, 139959902, 795271031, 532642224, 616696039, 132499817, 725179738, 132250691, 134680038, 621580356, 133401900, 631901138, 258532864, 602173040, 922277045, 232449869, 468108896, 904545359, 912510800, 292605529, 319710507, 616262323, 179741435, 277526638, 647599342, 968385919, 623852017, 715016270, 255616679, 669042204, 261152956, 569933564, 487994102, 100195209, 991651907, 674480319, 17671917, 888307642, 709736875, 16094472, 927261081, 951429620, 695178549, 153404514, 318057451, 219548296, 921851417, 246788765, 45678461, 25392427, 84915939, 118045914, 606446495, 550664967, 696925800, 106905471, 673271012, 446059110, 125696505, 622973656, 506752110, 372255741, 731067297, 871715639, 207389883, 440597080, 718869010, 867145768, 699643026, 53012427, 828810218, 953417999, 962093280, 49820139, 865186507, 840913065, 562967476, 189713967, 612200095, 653123309, 936216482, 300003401, 382484335, 912424407, 454842838, 206784964, 210803602, 169780818, 913153055, 25730049, 765893610, 817967259, 836236904, 715244403, 345471510, 719379111, 138771704, 240456471, 836160923, 630241370, 585659802, 965006491, 606212719, 559892531, 813270003, 953285584, 954738878, 398780134, 491797067, 196070751, 30734402, 582330077, 873385097, 276019624, 792423762, 404996833, 66991656, 800488940, 978862522, 573885446, 444927759, 488370976, 725564258, 525378740, 206073117, 895751671, 513568591, 575146290, 801020163, 153939708, 701822565, 29415642, 147274561, 372337232, 344881871, 725232511, 282836835, 427889208, 594295715, 90920978, 574992829, 965458303, 979334305, 150970726, 926985069, 93313239, 311839932, 628538367, 560850291, 906739449, 321018781, 478189060, 703320326, 542485977, 960838188, 827199462, 729174520, 328269568, 9416128, 392891245, 975518857, 902802009, 493950846, 485897931, 388694182, 828095717, 997940520, 835422395, 182410677, 577993483, 124900810, 973795488, 297362192, 947974849, 654943712, 76807749, 383155613, 45068398, 961555419, 97454001, 824323548, 21892715, 462047209, 551898405, 536181610, 406959132, 2022367, 838788790, 937985800, 198330857, 50857646, 635370626, 709564852, 359118401, 431034979, 770537383, 407545146, 879852158, 746048119, 790574033, 62090209, 805501350, 638953472, 16929916, 554556026, 485893822, 577567335, 20011047, 43949853, 440986614, 317927230, 845619710, 346202100, 792951421, 231715927, 430789907, 382013043, 454638443, 79141805, 146641761, 948792960, 761121113, 584427166, 475533776, 271762417, 282299545, 224525062, 592534584, 307993360, 96993973, 251890589, 480935123, 719086222, 127839012, 537193911, 463358493, 912539409, 678038304, 896687576, 930951395, 429517848, 529413745, 168646457, 131380211, 949185752, 299734683, 774608686, 120890007, 206750997, 610789159, 659773331, 803867580, 4070307, 565739202, 586297073, 431836354, 502945033, 913078152, 199212613, 419119997, 53494285, 406822787, 840619486, 542561087, 55753983, 376481584, 869820666, 692413229, 878282770, 693189852, 117282256, 936026989, 900270906, 539474062, 959848178, 705472183, 550212659, 63120076, 152714814, 512191896, 321774801, 80234256, 439327978, 213850452, 199521423, 583262231, 309520958, 7458679, 427548701, 962354831, 331075675, 736516847, 504917058, 949844322, 591420072, 103226815, 829413407, 578556449, 65028388, 937838313, 413655885, 932056486, 550754389, 627002354, 38715074, 952737156, 343331458, 850857624, 462808980, 249846062, 815181240, 553410999, 51353566, 829953527, 832836200, 390862773, 588423712, 234380913, 21140648, 888049316, 590932602, 193474187, 731198987, 178261195, 422215887, 22161311, 918150389, 98363505, 304750254, 775160915, 748813299, 888936753, 975674869, 791372948, 261768166, 366367268, 833977360, 903836845, 538831750, 877399850, 724440977, 81028744, 514046045, 449734403, 852824571, 755863233, 913071174, 32015252, 67735087, 241725304, 825256124, 263466742, 105862359, 229188140, 69674825, 959703933, 184739787, 104857265, 360110604, 172291613, 657303771, 594117146, 786209409, 649368393, 142323769, 598074901, 642497208, 850712245, 449117504, 924090723, 311303975, 86471626, 957128087, 307636187, 224348021, 778490230, 177226794, 878784499, 434279650, 799066092, 932230706, 749980299, 294726473, 594770591, 64075141, 462055350, 245486151, 458693226, 625232856, 690656400, 693347310, 152172992, 687942079, 165364143, 344143302, 269942848, 682463531, 370387228, 201772087, 850118303, 488422511, 287636886, 610329869, 604963845, 950233790, 605369319, 417673360, 182754982, 364137830, 445453674, 822434528, 58028962, 50192501, 500423635, 515476004, 287437877, 213415261, 798258502, 267715729, 297102363, 857549056, 360203303, 399321014, 577907653, 197569957, 514062756, 479049688, 556915325, 422672674, 409208153, 847125032, 836028361, 923798729, 551219576, 222722018, 96774116, 899179563, 696294447, 477373903, 18678865, 237984059, 92449112, 297921852, 649388729, 956342427, 882508792, 318120640, 413826079, 9454921, 877826469, 173185104, 928851617, 416094014, 672939398, 225470486, 557442414, 611221464, 976706464, 271799796, 94294730, 716786475, 310803584, 638182394, 183960417, 695514379, 885879099, 107720650, 186182789, 250026995, 280020283, 76420703, 955560919, 531732511, 742063632, 421549993, 23794491, 815435499, 899420609, 894697455, 308977943, 409682565, 953966981, 845959232, 757276263, 170963806, 174746853, 515567906, 61851228, 683548355, 455684336, 503837235, 908111441, 382559935, 734148497, 163474539, 251313913, 593929182, 914035840, 741426018, 484275440, 101078067, 565257844, 790367200, 975047684, 315457372, 268672743, 893935186, 602049132, 594883844, 261090636, 686161276, 260536313, 114657040, 265655511, 859428281, 620927296, 357104793, 127999587, 528036115, 504060758, 390205724, 49519050, 236231162, 579017028, 573148561, 602832426, 123477662, 893180198, 420606001, 576025693, 545184154, 322002473, 772694971, 635880122, 889372374, 140059846, 592528675, 618381145, 972501440, 679744595, 706857648, 70517202, 801546712, 360082611, 855297501, 332981644, 135861643, 948584676, 195016185, 841296920, 92691147, 625719786, 715403342, 793382441, 891571979, 494676887, 178953236, 772586429, 797545834, 131530038, 824063199, 648749593, 396134014, 879079759, 544981313, 809057362, 295925563, 851548557, 882005760, 379391529, 494681807, 529582596, 24352541, 480385504, 802293081, 28933014, 670800688, 736386947, 163083564, 787465926, 308161638, 474970363, 165422410, 540966349, 473922264, 789379162, 602905140, 29525763, 864132490, 827054349, 567594109, 974077822, 918631251, 748627277, 552622901, 868457007, 387537476, 500835174, 42999583, 510276131, 468544731, 922105632, 703148261, 223093264, 290914943, 360903012, 808871690, 551472416, 93487068, 304746644, 651899534, 744571298, 59760269, 338075033, 442245362, 669333552, 846169696, 625230961, 43720975, 725991525, 150610329, 109902176, 894789356, 901356879, 86041650, 255044134, 489901726, 57934755, 478027223, 510300207, 718556948, 122390583, 340971669, 791528005, 791642135, 916677134, 587039302, 223143268, 427028684, 920543759, 141239830, 902775575, 438331654, 77592811, 497831543, 697969883, 380447130, 101590042, 991486521, 882711439, 375429060, 427523982, 484668075, 392653054, 378280357, 142471161, 902133844, 417908999, 112275433, 55541630, 580359748, 2579793, 692918076, 332181287, 240821764, 365568680, 999055481, 375828697, 430429207, 80445937, 157736733, 291447151, 848922316, 644864784, 274270954, 58870265, 656522520, 303179671, 982078013, 341299424, 843155127, 265544850, 866442118, 122780363, 73264437, 669102759, 513490872, 388633243, 856546026, 426066722, 960112328, 366387458, 655908072, 118995343, 656876664, 349901681, 518416784, 920908668, 298810290, 860109350, 373611284, 246105474, 692143553, 679955775, 490926444, 89145085, 474371058, 623701268, 768331460, 442535044, 225663977, 97256986, 917957892, 769254183, 874660980, 563840853, 509491020, 237153063, 765745512, 506056267, 48653981, 359539806, 275537756, 38178387, 220384917, 418269366, 35949142, 170124951, 678430212, 660896084, 477818635, 33440603, 736413998, 846229145, 596999950, 22908318, 623322361, 526637626, 382969582, 45510677, 173158146, 149643207, 806652703, 844890568, 995618685, 562121942, 713870105, 471393732, 122306293, 906001765, 977403912, 281679702, 396087277, 104022854, 729950011, 158482011, 413936961, 145861227, 589524721, 196498383, 945125978, 778840891, 927192804, 553237091, 582724684, 435066004, 848124046, 806841841, 179482270, 938357871, 940960657, 681331578, 856466513, 780917522, 572807110, 800935044, 668587563, 270579109, 689296916, 426664572, 209038777, 629438671, 740847525, 243931050, 286804946, 271411508, 449991910, 19579812, 380101752, 346949569, 700950164, 295845279, 346573452, 853809968, 362279082, 263238406, 335533477, 256804347, 113221841, 411863520, 696059229, 978247799, 937146569, 615221553, 425689348, 569692831, 164497101, 28760116, 35170843, 849438523, 464381709, 23496277, 708409833, 816016953, 211784693, 681998359, 265562169, 862351221, 53895135, 110749751, 189366355, 458016648, 914735235, 305673403, 112063273, 892514113, 647109866, 385282949, 678868584, 173755354, 979252049, 257696751, 583999676, 419021043, 291421348, 459890644, 174515240, 838950754, 635715843, 816266565, 451117552, 697044058, 267347031, 509496103, 438632197, 664129374, 267786559, 999988406, 222594781, 170890468, 669785259, 58767560, 82490766, 295394215, 340416587, 328160299, 876210545, 569026961, 271227664, 484508858, 380466881, 593687585, 515445101, 884607182, 830330772, 884881633, 832441720, 747898399, 3229113, 253193418, 102312130, 933574694, 700834099, 552744517, 834837095, 592034112, 861878636, 89113126, 318683368, 76080501, 131247026, 472277263, 612165130, 146407119, 491404351, 33140036, 812650786, 833636391, 175532900, 11410787, 221642424, 225726032, 16199577, 730697789, 47299306, 849508960, 547425699, 756702905, 37218155, 413153602, 749134700, 463049404, 639826454, 322526910, 565698313, 57972248, 891808868, 745333651, 297169017, 221731436, 610503549, 529560538, 910624439, 337810349, 566208915, 496761965, 340334774, 189486215, 569166217, 893540260, 420570053, 681009828, 134687573, 935819461, 22431093, 59810368, 46271250, 635244432, 33822921, 111662789, 645306687, 322000569, 106900229, 582040792, 8558176, 745783361, 643991511, 943443875, 80616342, 755726329, 801095401, 567797673, 23165532, 437932443, 370378708, 855670484, 323610745, 986613348, 570752383, 616938139, 973788536, 118617534, 61284944, 671060146, 638566345, 271293889, 108641627, 216402146, 222933426, 364173747, 878516678, 41436647, 52581966, 114588395, 421462450, 593570615, 508849246, 707337387, 23045369, 409086967, 289615209, 822395435, 30459718, 589896569, 532852310, 831259072, 188530285, 132476819, 894020571, 957011570, 863070426, 344207408, 719545525, 897548529, 794241038, 403847228, 226664698, 486630030, 243551878, 177705049, 788638744, 375483779, 623919993, 484686409, 359050732, 60115686, 217792579, 209914474, 719773135, 741557069, 926072562, 199356779, 532647105, 269289449, 253720596, 734598550, 582612548, 508522084, 798131602, 836162846, 261947169, 80887185, 481765568, 808957605, 233341112, 174532100, 527213396, 380506036, 694645269, 435221560, 192020083, 112170336, 586136689, 550320929, 934717110, 883443240, 104377574, 346229154, 547853856, 227315308, 617077367, 405499143, 791137300, 161214118, 149655063, 789678726, 609025524, 101534747, 227319533, 927854357, 483891088, 263693586, 381816685, 619768866, 444687956, 267810880, 672862845, 96322433, 425748807, 191982598, 975864253, 566899027, 808921158, 509520019, 800934126, 622993991, 757575450, 679517412, 406996994, 223759218, 425150134, 704670356, 969090660, 817323005, 611032328, 540193121, 80260659, 300695124, 592908519, 554569615, 748420990, 510752135, 178267781, 185197061, 392950126, 777661589, 169373280, 268116388, 558259098, 849126637, 893699919, 364502658, 797499055, 648727080, 777315420, 859885907, 977671, 729114300, 861052047, 599027055, 684584813, 952021014, 572832108, 270655895, 770432824, 655902634, 958215875, 759052034, 889103645, 777699907, 119693241, 197323977, 163167172, 240923419, 998223676, 688654386, 905455570, 267808759, 675078755, 78702938, 501594407, 301483184, 990669856, 562346556, 525247745, 78694776, 634494599, 990863233, 399772068, 467137372, 539477975, 539893781, 907270772, 517054872, 342229678, 577153080, 118716945, 793541871, 175889660, 742169903, 824866783, 764202370, 341638149, 272555364, 256038661, 818026834, 206219895, 660526284, 546425021, 669875083, 428257594, 922026425, 395880809, 514302274, 215202276, 292717465, 701952018, 924049309, 982972027, 183514809, 784888606, 367764930, 830341804, 959376958, 240700952, 987151047, 276897144, 257328355, 62059373, 298862164, 775406097, 263023461, 714155813, 355389851, 706922876, 527305550, 816803612, 573397867, 706171104, 998248572, 105525242, 637966487, 867884850, 374737137, 254598591, 992191949, 494355012, 650279770, 890050216, 750096877, 768812247, 351381790, 21336459, 152546403, 301009784, 809601220, 165299693, 682072604, 75780094, 556530263, 86037918, 868245776, 86135543, 977954648, 847844910, 957616470, 595731750, 625431756, 877605299, 652053729, 68004195, 657366566, 605698916, 687483048, 847128228, 611532149, 247058969, 502800635, 359237107, 132766522, 394800593, 433701011, 608312920, 790665767, 199049055, 162400610, 198648697, 315865499, 804011856, 299160121, 331366928, 614065540, 73498616, 252647673, 111525598, 731024250, 23545289, 221839951, 659913653, 31983814, 184866876, 157545719, 567400368, 428108455, 753755132, 694881416, 52601039, 94657286, 972483618, 539546715, 846021562, 862246928, 277726825, 181304936, 308139323, 112996076, 903538616, 991802909, 252977574, 389739649, 373565935, 858055871, 382597359, 516642787, 784113483, 370889977, 239714900, 26527836, 832000885, 77440570, 192810180, 520772662, 679949585, 262245040, 736864065, 538395783, 279945631, 377286611, 665571858, 427511582, 382355064, 286428078, 914230893, 313841736, 373976863, 790662242, 280758155, 644820097, 639635973, 997026504, 230336806, 923298016, 176786927, 954330606, 688534606, 508469293, 500246961, 971312811, 643440248, 594136567, 208585957, 958099608, 55617077, 638294611, 174475794, 238421763, 132811289, 852457402, 227173147, 697812858, 750256834, 938904932, 630172088, 905779762, 426287245, 61424845, 46589493, 474201596, 104782945, 488590873, 65219071, 904493511, 256591531, 675477528, 219466306, 3191245, 783381087, 62023216, 767397190, 357486399, 552704238, 635261241, 863708140, 455619179, 881171605, 194380279, 284990574, 668978610, 16722076, 352753313, 686498855, 69588360, 483388608, 592019676, 152449075, 632289330, 46686115, 22334888, 401812235, 561225612, 417222739, 871570661, 181490328, 824548006, 910844214, 570293291, 822789409, 388620731, 607370620, 488110977, 604539537, 406539653, 593537534, 267313383, 615246006, 223758562, 251527584, 134740527, 617237548, 540729956, 65568396, 356862265, 347537840, 361825542, 847055521, 863243345, 815521361, 904932254, 155307397, 38152354, 750949470, 64578891, 290961980, 702302331, 57215790, 542042082, 732348626, 871690236, 803008029, 27243089, 802074336, 944612950, 85173852, 341577120, 939513957, 871589899, 104921573, 252210722, 916830574, 144880165, 309404509, 10520903, 937231707, 906300688, 861693006, 913495696, 959064547, 178043757, 461776929, 795176341, 204697926, 428487385, 156642327, 216954992, 855812007, 264905576, 898523719, 172967457, 330219863, 308897842, 701002162, 456124493, 858006795, 119794056, 266720267, 917463804, 29202440, 373584338, 262923347, 864331330, 257310566, 227227462, 881645935, 147961185, 871823754, 262741260, 368709204, 255333952, 936697097, 673665811, 306392773, 366022215, 20362061, 538865308, 743540635, 845181938, 581059208, 73801192, 431463092, 569856744, 535968029, 961709438, 417909612, 557110770, 685380008, 585590982, 148051300, 59449747, 184510360, 976733928, 842812803, 878069915, 294008694, 232562664, 647725841, 948690189, 476979027, 613291767, 965467044, 738212414, 792459550, 730296964, 420932610, 876909443, 395481094, 765516482, 940688304, 382604530, 700797402, 755255102, 505127653, 758752186, 282258553, 366814549, 965519533, 302173242, 819225849, 17538995, 543679805, 615952680, 889376149, 72453230, 978187504, 808341255, 336109789, 804518323, 246953379, 100467285, 810197835, 597289839, 404909490, 740582895, 414885267, 461867150, 118123321, 91553301, 315370497, 217691946, 801901056, 476875952, 817789315, 361079602, 335876374, 647367689, 841088488, 790779804, 5275271, 279458829, 885225452, 462014265, 23928883, 175043344, 77395715, 643032027, 468656387, 37935727, 524241176, 146592861, 874597009, 20701612, 719983309, 309818106, 715373130, 345220682, 727761005, 32907920, 541867425, 117521694, 728040076, 562015964, 487015712, 823709020, 834093130, 843066271, 185417573, 827379114, 812851873, 58624793, 44135541, 201822202, 546341783, 788926217, 627778020, 895468925, 711349448, 47181349, 946061373, 378979777, 57985429, 712440820, 469776039, 186023934, 288995715, 253106443, 706870640, 453537373, 650312705, 42987794, 501963925, 294083941, 742463742, 944653056, 135074696, 602085554, 645307423, 345973753, 434830860, 740572448, 425598107, 47796870, 104055513, 237407060, 600356678, 422851696, 703862515, 303868265, 710923478, 282519353, 244452129, 376392282, 583563983, 335014037, 430138520, 440399582, 540320207, 802732207, 513609491, 530580632, 799205168, 594415393, 257756904, 438652813, 731321686, 585646126, 20433313, 499902672, 793625048, 557788128, 950439462, 614858226, 526326967, 376517218, 986852469, 661821021, 162790339, 423224015, 867252221, 688767718, 905195383, 979832354, 926342, 513140539, 146774733, 30480620, 871676388, 766778603, 276618508, 685931714, 48074220, 121904962, 593775932, 176714053, 154228014, 547476588, 960274867, 272467977, 954824831, 426164462, 933919085, 819191621, 767321521, 733479587, 354711320, 50167039, 455204682, 380399663, 388198494, 247140754, 938758210, 999296283, 921683319, 202652742, 898864017, 221592622, 905353448, 225455592, 523518978, 357742392, 400884416, 10793804, 645844696, 63195975, 816644688, 143723842, 755500796, 458045696, 864093995, 349609975, 103868379, 363145758, 32885992, 350617580, 341190433, 988056144, 983254987, 328804225, 130316880, 707770514, 960690764, 720715824, 64726230, 142486196, 42660564, 81999741, 926314961, 285652856, 81244517, 400923165, 933608232, 838228802, 863808945, 292726490, 95888516, 106174765, 884728858, 805286213, 924596322, 364909355, 312453135, 58556198, 475760994, 759456845, 640393545, 394806891, 271378319, 777832901, 459216024, 535686774, 928547057, 669508747, 175136864, 357140296, 262533851, 954946265, 542859152, 337968539, 240870555, 339891049, 842939654, 335373483, 364503881, 948074396, 121212224, 906917464, 148792201, 944719528, 218038449, 962271453, 527296703, 593739983, 439647511, 944133501, 239928609, 424951142, 729979366, 490154220, 411779860, 675757626, 637586870, 997374406, 648649286, 333785967, 633628682, 152176967, 111302038, 790663726, 878378946, 784952516, 783346662, 734341211, 163854710, 184215227, 860824763, 461504668, 275948874, 587313879, 172028707, 380616207, 4854961, 903166800, 478292151, 652415167, 832736343, 792119644, 286386691, 443612364, 558742241, 979811903, 489767308, 886307157, 413298013, 637116072, 881451303, 476296510, 229974077, 231351212, 102428137, 851633656, 271270140, 723606952, 137985012, 339045480, 492861830, 920207490, 17655769, 513210791, 969631261, 678780141, 242235759, 974904683, 382891123, 969785454, 44254198, 945573140, 276347297, 571758059, 620688322, 854012415, 149203362, 288545123, 719405465, 575194347, 839963947, 333656314, 107911954, 641153850, 305107725, 139492512, 140271599, 934922414, 554781901, 79445336, 288349742, 21846252, 582995359, 900564262, 364014238, 349163317, 101275264, 556431842, 196481360, 509899408, 913291135, 534032792, 864085374, 993207004, 404401271, 416084212, 851397485, 889264798, 393432764, 254939046, 500088634, 391749903, 799962484, 512218167, 63045186, 338628896, 134895936, 932291323, 847100599, 783040082, 255059353, 499231244, 19803088, 219534874, 281715732, 350827571, 919388412, 763911278, 811507248, 967457671, 463783596, 405462859, 83671508, 707980976, 75754444, 780568240, 104920124, 280854818, 71941528, 87438449, 466081219, 646554955, 94907738, 92730718, 140679967, 301621052, 681843489, 488618075, 929056554, 897884036, 269574864, 251481569, 882836901, 54757121, 537315303, 749064830, 773632894, 323831670, 327345157, 546203354, 726038804, 577441912, 184867829, 61320533, 172715325, 131384118, 8206941, 807348312, 673766361, 620210431, 752117700, 255202204, 462819035, 856044648, 310897036, 379228198, 739633029, 645532659, 508124446, 440227237, 701263479, 379652037, 256763431, 733767303, 381672383, 990740156, 478696284, 576365973, 817918041, 80389948, 739325822, 888983384, 968023425, 545621054, 255727435, 47250795, 75992063, 649280649, 326321271, 49148758, 787811090, 542095101, 921284817, 356162751, 146858006, 326998335, 209930237, 384744294, 956205147, 970408015, 369415614, 431160206, 28799992, 287130106, 549849972, 464680213, 586256514, 936209229, 1077451, 674079471, 41266695, 723293709, 904545606, 622638545, 923256319, 66552118, 654027359, 374666048, 352429791, 929695162, 66877260, 156208268, 495063188, 784327683, 340891109, 981661271, 760044406, 513192161, 896114074, 901023882, 737563546, 701079214, 558346813, 432021845, 275360716, 546366262, 209335998, 261880141, 54476857, 950119050, 563480867, 249995074, 357763786, 246322668, 57094861, 808073116, 861570097, 375565043, 367029373, 34066056, 945074217, 424091677, 144377661, 623582268, 472284407, 218698127, 593120117, 159943046, 556981317, 340346515, 351304074, 156117030, 824911340, 822775855, 934855072, 133431782, 392181838, 543370888, 216977992, 30080926, 106764257, 340572390, 234136969, 55281010, 450365550, 151771829, 111055917, 334011766, 584836338, 284361408, 268045451, 473378079, 576985039, 13807807, 687192120, 519585729, 675632297, 452413725, 257613973, 944869049, 719943753, 433342188, 867368487, 193528086, 51913587, 138812685, 94733398, 977285616, 480989535, 273673305, 575885883, 788116448, 464299161, 387241218, 974871786, 165267415, 892335956, 968174430, 924810468, 433622592, 540048912, 868781630, 255022570, 576777786, 407643716, 78920292, 156782080, 312261863, 857630340, 209203013, 195527272, 683500529, 941290142, 511448988, 518655163, 843543377, 420646103, 856194217, 84893993, 71051334, 497757759, 403602410, 24633976, 186880862, 261734952, 244984810, 44572913, 834603099, 278175385, 189095855, 511954513, 649913309, 838946248, 9765464, 846894960, 364226373, 952296029, 69156861, 839025398, 980330003, 663684862, 338755724, 153158088, 768280297, 878103595, 641072570, 132303074, 95565324, 946357506, 307391679, 275560650, 280902859, 757278733, 810844057, 698316948, 189197963, 13570557, 805033942, 881250550, 623950277, 479758770, 287869950, 943221295, 813771465, 331558446, 151320151, 230647918, 358796052, 787686643, 976296872, 613261955, 196765350, 866495902, 392630949, 438215002, 372066380, 70531926, 783503863, 244064921, 565356425, 9278514, 469639198, 107657355, 906924355, 676130228, 311748051, 725109802, 691352815, 708620207, 588672914, 987619257, 493893711, 677880985, 936827263, 733429332, 478726186, 839733388, 221375191, 537617649, 544022540, 837284478, 137172335, 228552183, 208843959, 27428449, 129866841, 880109351, 631810564, 740074991, 738164204, 805924021, 619320924, 370782545, 529756391, 779454095, 943625383, 282833049, 949737799, 182529655, 434854424, 484423194, 164200170, 49668403, 25603550, 447904823, 579179431, 92356288, 977757437, 190854814, 639502008, 691235419, 609095349, 511637307, 874226803, 145271077, 190979724, 987727336, 41927026, 966065200, 498058044, 490262283, 572357673, 427719682, 857593794, 779007933, 663483512, 461434048, 259759735, 331503567, 442270385, 431695279, 423326732, 721185524, 462482057, 931100150, 982043425, 940143049, 166018309, 908794214, 989068370, 224128120, 98591536, 775355427, 758815626, 334694744, 243905180, 42795391, 11933132, 655629775, 919782522, 185191186, 818450675, 416407198, 502855808, 113808968, 238361939, 487710135, 607732425, 206095653, 856822897, 641076353, 725644827, 946140414, 309559856, 307452699, 985489923, 195486790, 462613445, 639465674, 701559636, 362275854, 689782446, 329564958, 952442600, 708155793, 161183692, 929351442, 966528600, 553775063, 179109826, 489930021, 631307218, 731883293, 45747412, 374791452, 618241780, 529669644, 680478069, 161653820, 441323329, 993747909, 462405113, 628895305, 710119632, 992293009, 835352557, 282561748, 619616102, 633400039, 660179898, 561756565, 248421462, 973654030, 621414743, 569501441, 120918491, 731753249, 142012820, 783345730, 461000417, 538050871, 372367102, 436442986, 896863111, 787837290, 507235660, 886466218, 928860670, 240912494, 459657587, 622370810, 36843112, 995134381, 555584595, 267830564, 434851424, 884435023, 63786722, 495143029, 418133782, 832626489, 957605112, 131024466, 365418124, 715975779, 214856316, 560913469, 454881766, 807149435, 488771254, 862342910, 890455038, 653108521, 385496290, 175572577, 736785860, 798928748, 74679405, 611465872, 767117575, 417481255, 682173504, 815201293, 419138845, 654459912, 223845850, 703586027, 973237689, 314283601, 213808918, 802725734, 725596603, 625068153, 471854296, 691720903, 978139768, 832864387, 636481789, 923076678, 454753578, 917732970, 467626346, 904084139, 270968189, 965481163, 737576882, 823888651, 490258811, 22933336, 313137487, 731288555, 692506, 472232115, 980512353, 592337575, 133154940, 942885731, 751498910, 800743025, 904239994, 325788354, 557137294, 575763541, 398645558, 30332508, 796252341, 899414927, 247347878, 968178642, 970458961, 698150931, 534509692, 185667045, 474990392, 784726802, 644695652, 453289227, 373304173, 626213924, 175364894, 309363733, 539492851, 80857216, 853984475, 218310997, 758715310, 182927231, 394941703, 416484138, 368587053, 430585081, 260383419, 523941823, 821438741, 360355212, 717792053, 262937227, 883360500, 421273491, 883134295, 927992342, 764679202, 783128777, 587547368, 664147750, 593134530, 620381487, 787235585, 157380189, 593936546, 284230785, 152359512, 244157248, 797663427, 803154452, 396947840, 432556780, 905762718, 446691366, 642735825, 251114258, 720006853, 11742363, 875675144, 482348159, 739833204, 134613213, 267158200, 922307428, 67245973, 763387386, 909233244, 747899713, 619717246, 640009623, 390341347, 944338455, 130762508, 173084303, 447186422, 156464945, 300081726, 897280773, 146048955, 544255810, 693116963, 2175873, 516231014, 965644779, 901249122, 897772050, 758137588, 958440803, 790566764, 649359076, 399355814, 577913764, 726016418, 235297293, 636156024, 776930769, 304969246, 286015427, 942908219, 978321433, 797596060, 568693474, 927678554, 781929741, 717574063, 999179957, 877066325, 78383349, 25818787, 355429580, 878087796, 305659143, 888322685, 775905870, 517079985, 135728578, 269615744, 693461012, 641871550, 547861556, 219905525, 326545273, 903556371, 750561343, 187811906, 259673772, 649095401, 889752918, 148937375, 991131963, 974984529, 598122620, 559024290, 471785192, 451356993, 288517588, 690220010, 962089525, 676439475, 311129353, 261677159, 9725836, 532168285, 549603462, 985887510, 772338359, 659346296, 747692511, 366160232, 251635361, 804932491, 750239456, 425588312, 689923912, 316187722, 932897241, 61441269, 737931489, 93006961, 726544725, 411613414, 303450185, 338874777, 934415226, 503485967, 484399465, 390488130, 331683015, 676679115, 527538577, 626971279, 175106378, 857431248, 302413270, 280538236, 306589975, 152538597, 655608129, 445512631, 804222845, 491947174, 239718250, 38096631, 301004490, 459226779, 710099674, 222793657, 74430101, 383699761, 213243547, 797300894, 577452473, 793388134, 220652678, 861353739, 592950726, 396639390, 886748976, 822392000, 905701984, 949695271, 927696163, 589438645, 382373, 479121374, 300128704, 451725039, 348153858, 139321940, 107910930, 553786737, 785534597, 634616630, 753463139, 368212193, 250148983, 498954583, 341042859, 306264761, 155250540, 172054816, 805674314, 865289126, 470971413, 897372807, 894496675, 106622864, 801950154, 147370425, 258172768, 985356632, 610532554, 31334478, 164129662, 679423512, 847663049, 121150805, 420351043, 890863574, 506369871, 635135408, 863476496, 581123827, 718950493, 337003774, 107106678, 581102623, 724961937, 409816544, 389757428, 398945753, 390417373, 542182729, 914562212, 363403414, 970135870, 176761139, 888906757, 892774976, 603134144, 709633361, 150157676, 439693257, 231013532, 1842304, 204525398, 853179827, 781261343, 412114628, 816411951, 670645507, 151579494, 848974179, 351390801, 969076719, 16984720, 840330313, 427507828, 303392480, 376289288, 191001402, 261504831, 678784976, 824035769, 885228531, 213332139, 987773846, 8422194, 227053114, 313229621, 855698278, 106083062, 692945768, 206661826, 871205301, 162867873, 166346742, 371457424, 398133838, 243605841, 101284975, 668340015, 212703379, 450978755, 166320758, 592078007, 331294292, 35032575, 736235153, 795466726, 165509461, 499322271, 238517394, 79914683, 681596638, 20978646, 189516068, 463310652, 605626764, 22155220, 775541964, 630413112, 426182338, 463717509, 72138085, 324726204, 572610900, 928777063, 925079621, 23176058, 308472642, 769247206, 902316385, 29020793, 913170279, 225907854, 174953196, 707621881, 887826596, 380788760, 178532534, 632954836, 948089864, 766810784, 981414752, 121886767, 598971904, 27912291, 695209519, 732950173, 557238087, 915599661, 557264438, 511417975, 418470255, 764466035, 229516325, 964827032, 778863818, 347550711, 80496540, 260877339, 494279452, 980560496, 557754142, 157614031, 359310957, 46576626, 625158602, 92839490, 493825621, 415449438, 740289990, 249351384, 810014363, 366830785, 741852238, 978461965, 835129356, 617712871, 630650126, 302331751, 838877078, 151917026, 516441432, 74015299, 240407790, 850089193, 545624223, 530075661, 220658122, 214314593, 999815339, 941869441, 547217970, 716845281, 829967225, 276688982, 87573170, 833252889, 237008896, 453461674, 56248480, 138059795, 362105544, 59471347, 133593287, 331508962, 618151144, 290679677, 451573256, 731083722, 231837373, 569869950, 500009846, 740544509, 673525268, 353572238, 735103255, 963757725, 320097356, 450729734, 813538088, 247136829, 590219947, 273033490, 978078879, 782884693, 521672112, 974557084, 348875775, 618419225, 747600074, 268340163, 636913320, 940404858, 208065168, 791175407, 40740080, 927460314, 329435657, 685747493, 637864938, 991493420, 584833171, 627358321, 143309675, 397127791, 716302435, 199173684, 135718745, 898225019, 799173138, 466889834, 309006453, 152328800, 752848829, 326494852, 826907822, 833730804, 122691370, 805034535, 675758498, 960378695, 959060212, 316871745, 216649432, 582016589, 587525093, 186943692, 51894490, 359095766, 358767967, 579922366, 699620181, 158509261, 87661134, 323334470, 494375833, 986801906, 614588954, 443281633, 697304373, 221970578, 666324747, 843991136, 641340862, 475848103, 64408291, 603964480, 312354103, 67499476, 786582004, 915971400, 724535282, 339815309, 508648914, 500372601, 130275944, 473117058, 314134830, 209525812, 53654927, 897317906, 422045258, 651748628, 462182827, 305502852, 348895670, 41504694, 375859351, 110443013, 567320758, 639122375, 857408691, 658066722, 500847447, 163687186, 338262827, 351078203, 573241518, 191154887, 435849019, 374253772, 749048561, 576952971, 618357995, 116077039, 342049879, 392497203, 137593750, 188426222, 930212315, 766226073, 506780124, 655910215, 655483108, 961250836, 16761838, 961264223, 408374952, 469084483, 774062150, 882777901, 182218351, 157152678, 154947558, 924233666, 291955270, 427162815, 246625978, 684424386, 324412337, 201617235, 713479492, 751594880, 907765552, 805630171, 414545204, 313554687, 908979260, 110025358, 575293850, 182757156, 743521372, 732249370, 194451327, 420947700, 823389468, 548850524, 543613297, 280224369, 613616410, 505544839, 762599471, 853851146, 553455390, 587834682, 285695999, 573343565, 30905935, 333132924, 769127856, 112994217, 457370736, 297033909, 783693672, 605309318, 235280156, 258540535, 829837066, 474771326, 699519581, 111827460, 121446367, 652337976, 499201921, 232299213, 890813245, 900574570, 264217261, 84222077, 449016911, 383832851, 854565671, 991854170, 597691729, 930384231, 132346560, 132246921, 320695916, 905403887, 324777122, 227047319, 578569936, 231131511, 376336823, 850804102, 38567321, 756390659, 558289941, 990745383, 754688436, 6165374, 836623751, 334600460, 711778941, 703853142, 230401952, 500940998, 694987701, 271369196, 838341299, 110621317, 926888530, 232571365, 559894984, 380074127, 594798869, 81450476, 272197927, 197266814, 685918913, 250117051, 602938640, 873111291, 814816586, 555940842, 371031644, 49066402, 749403353, 488204323, 124930375, 677201945, 160596528, 262622656, 938837623, 881387592, 446524635, 827872155, 111433842, 27164396, 156837537, 516799551, 92632364, 911922676, 319383969, 982395889, 138777935, 925980357, 669097809, 199844788, 195552493, 277311812, 617416575, 680772835, 670929010, 92447393, 37876360, 439205789, 210192166, 944088194, 511032298, 100253480, 845872245, 645429196, 512482275, 296546157, 273107493, 599569066, 184922073, 165799927, 603895323, 554126782, 950298210, 14662536, 832184921, 211088248, 290032415, 807027111, 665901136, 117383177, 802156349, 659484932, 309405881, 300927771, 578240594, 106252933, 56110820, 591819608, 75168912, 34819540, 477002539, 985393548, 706482149, 396875882, 861882655, 138429375, 95798620, 697551185, 986528647, 849086993, 266726791, 907448331, 83037357, 915010433, 247487647, 208881390, 302296566, 605275501, 645357407, 327811913, 900786976, 326363893, 975364493, 655091740, 68119556, 89987737, 6515154, 975068029, 619853432, 577667374, 441860644, 237722791, 901676001, 773290693, 48801214, 263818676, 608388988, 454659796, 795985824, 239960204, 26763923, 957087460, 6344102, 981903742, 344234795, 257053033, 270044073, 613934660, 707286665, 940719250, 830762627, 885812479, 853369510, 544522038, 141633824, 427168392, 276395133, 164496190, 184156468, 776802764, 905867163, 893564834, 134184267, 538100436, 978793359, 796124681, 184033531, 452024713, 644155094, 592764929, 195386100, 150714575, 519526349, 300927173, 3510708, 613971840, 959326950, 949933019, 314256479, 897064251, 906014418, 327859142, 809233277, 377363659, 349261686, 443592309, 646503773, 21335118, 414845185, 380860621, 386911547, 685607472, 919607308, 729336451, 272144706, 245724052, 283247064, 399641091, 990361579, 937156796, 720255450, 95182083, 259775286, 121888743, 796526049, 350824370, 100824517, 431057527, 968549315, 468447814, 541876066, 49619623, 990042215, 580698577, 360225781, 216710544, 105572325, 361282692, 119262944, 692328325, 979550018, 542790880, 399148973, 254955396, 342687782, 722130855, 179839753, 376767947, 925904614, 305627136, 791786408, 408359301, 792910478, 715239779, 905510707, 514842032, 744178363, 210454106, 364259446, 353916743, 61348050, 72069950, 98419954, 322876527, 540944911, 353200430, 540578799, 618613188, 489351875, 711514694, 887410754, 642517890, 859054688, 36113955, 330968972, 301193045, 652101719, 906630982, 325150126, 154489370, 825330474, 831907304, 70461790, 235982372, 134309747, 818994411, 30862088, 545508909, 942884619, 854070338, 334878003, 683628136, 918021194, 497256617, 362355224, 263591350, 617889212, 200267179, 777628054, 223246535, 241580001, 345308473, 434773673, 950525079, 207276717, 873896967, 170361647, 657234449, 309107325, 830157717, 871854079, 476474942, 790551413, 406964265, 515850534, 76436820, 125794785, 437678186, 352043993, 454422365, 41818790, 49360248, 849110306, 807906517, 294161998, 553333633, 609770335, 246097314, 418166309, 81359425, 757049280, 550654789, 945008691, 146391386, 942195067, 407250527, 94741020, 683109733, 721759464, 211041261, 381751629, 822778812, 122478828, 227832233, 187137743, 273677221, 916160211, 511249341, 622635383, 154588067, 383049704, 641484119, 392635077, 507200810, 925011957, 725463089, 683180503, 519600521, 336946855, 165764494, 322238593, 730635467, 983251022, 829130210, 482650872, 127522524, 198756945, 547885204, 726665278, 52664879, 987594463, 399461612, 128421051, 853862951, 173599473, 495119386, 561214083, 468495190, 513700835, 631722537, 607329221, 168750410, 633944226, 25445569, 757863491, 666257382, 609318126, 497666845, 56473778, 477691398, 518517908, 694792422, 340319587, 518036052, 716363765, 694980505, 273423153, 841713765, 563284215, 689385873, 750296518, 488706143, 200668232, 636605844, 583398005, 523031383, 689104026, 37958479, 615581085, 991952325, 165242008, 673882832, 980155459, 621295492, 392420323, 840176691, 152758635, 557612652, 925512923, 758931284, 516610862, 507727331, 358384847, 672310471, 944240713, 901147084, 29015350, 328774332, 710383105, 963185551, 646548739, 105415935, 380927680, 667505331, 472169360, 912032040, 712699000, 861563400, 544523785, 688846632, 930655760, 428987572, 244842562, 526591555, 989687633, 339198347, 149632568, 904391253, 832858367, 618992940, 398457895, 662309571, 773917512, 258094045, 373998982, 837821739, 494169944, 823318604, 200304767, 801371005, 78784209, 523022275, 62919729, 585056171, 463637884, 599003440, 561922713, 952668969, 837694560, 81935028, 98910912, 602651115, 66469833, 448712776, 453336346, 192471658, 306373535, 942186905, 585822678, 339218161, 804618484, 564221531, 128653196, 656344184, 813026976, 268447775, 946758014, 444244796, 972798253, 285903799, 780813942, 707623608, 296951405, 932216296, 842567024, 123196496, 306871019, 42373320, 355843486, 654703501, 82388745, 618053953, 68971548, 918775568, 243416955, 402187464, 682982222, 448026447, 175204903, 632591672, 911338986, 952823024, 537898520, 163277479, 612447937, 627771617, 332061187, 438434765, 293708091, 254470583, 302705266, 428163775, 609809150, 788286293, 211529213, 578983345, 663060817, 892406899, 585059442, 184245886, 754274674, 360442139, 365743457, 764233870, 264420049, 664096300, 97593207, 796645865, 516727260, 232122416, 926940209, 991069091, 232744386, 895043732, 953289657, 454544044, 189895032, 762693903, 814406724, 20445070, 560613022, 156596562, 607540207, 697068697, 927676617, 813533323, 35364925, 39882048, 701705926, 176869111, 254625354, 465119129, 668708809, 788945644, 463022135, 693056281, 744683974, 197370899, 721635207, 368951964, 597033561, 977147876, 133099970, 633986191, 670678334, 496983765, 510262204, 175830074, 212647448, 128698903, 423836392, 945991644, 280381655, 398747947, 339776589, 871963355, 64676642, 901816627, 835798020, 175892821, 659313674, 83977841, 175465472, 951042299, 947875355, 131874230, 861391147, 278937361, 172611276, 966992063, 779680357, 454498750, 529997221, 815269124, 252189834, 431378182, 116589910, 851579463, 505489208, 562598253, 123785420, 993307978, 606829093, 428800565, 329691505, 788389027, 964765010, 867013419, 98479392, 337545523, 23502243, 288442881, 740230195, 44635551, 57549933, 429606546, 519199527, 257905415, 832475096, 132218505, 495409033, 550612752, 126933824, 142593691, 301656179, 872525536, 307554406, 511882873, 758166588, 757361908, 367148351, 412924328, 623169086, 695262792, 735600005, 142616214, 929474857, 660494965, 123889997, 521387114, 570966735, 815657301, 870429450, 576572394, 425152335, 985318881, 845637899, 713807675, 606624048, 210621993, 283812869, 748597203, 590852066, 632434693, 916104919, 462538233, 870737842, 366514377, 873308067, 166723522, 510866483, 188443311, 239741164, 243783913, 331045027, 635141626, 744367594, 1826168, 912135459, 170465785, 708438096, 574696619, 658003084, 583277804, 99214837, 491947564, 234077790, 645302568, 720616035, 658321546, 595163180, 557044085, 888460509, 359444345, 214052723, 735722303, 420956869, 38837567, 305740004, 114845999, 173886281, 385425750, 115493369, 329450351, 917937663, 571261614, 845797423, 301762117, 67927566, 374870932, 159134555, 969844278, 344575624, 754040973, 690957111, 684365070, 494993662, 141764419, 580169179, 835241110, 857582930, 428816040, 451625767, 171824111, 485562543, 100938366, 411007821, 659282065, 679977807, 943411716, 596174936, 109756204, 535855144, 128152575, 723363404, 609679764, 609724006, 947555872, 859911825, 775258081, 94162028, 270017797, 542233919, 578192021, 225075283, 380728912, 58314624, 994540759, 318288210, 47764489, 321395564, 683566924, 539824872, 862435847, 637189338, 940044241, 489561, 349194086, 955249905, 697491763, 63871565, 128069028, 674207913, 624320539, 643582718, 665501023, 622160104, 610295835, 878644640, 18297086, 210645864, 939841702, 181614640, 952380016, 747648311, 996238922, 956992000, 50074988, 582498472, 499218440, 621459300, 138302305, 40916639, 91635548, 410687070, 94338071, 622328862, 336378446, 517744705, 398306741, 974667398, 95861868, 504047432, 915540489, 559886166, 639171298, 792543915, 343828200, 598563645, 161751622, 603841919, 454305739, 303136205, 802110652, 988074121, 428004373, 544669126, 657760496, 157992315, 692135975, 938877066, 53078374, 612796755, 509265603, 560479302, 369064316, 39427233, 873056525, 355811641, 847901464, 811236186, 939540638, 341284318, 78855546, 717877570, 262012188, 79103075, 620388598, 621658363, 20644976, 7004187, 449905970, 256063320, 335505451, 894699947, 492515409, 644867089, 303173267, 40831062, 946314430, 785016368, 886878049, 156058608, 486176860, 762124532, 818422817, 860346030, 113493592, 405976486, 107225982, 827239292, 849271695, 908684460, 618181061, 415703832, 655530000, 401410450, 587681735, 456189579, 513853402, 416553712, 220473837, 921738804, 434967886, 727937570, 486069914, 847225604, 835548026, 187252754, 734888977, 51117517, 233459538, 434792502, 533875932, 928957478, 629936958, 508758677, 727759226, 234686050, 497485633, 793360896, 907014751, 853953682, 502660947, 551049664, 394631292, 105506412, 168800120, 987870265, 730265302, 87126477, 802364797, 885277544, 951951022, 629435014, 497691745, 588459370, 175692772, 807139126, 497666431, 493838445, 515567895, 655298114, 172086899, 630796916, 116263316, 79076881, 782604545, 396524931, 44721849, 426804245, 53161391, 407437111, 619460649, 752348099, 366292561, 782612452, 83424650, 869437345, 637700590, 798895994, 847768685, 896412461, 793396381, 56100231, 966044263, 544525309, 476487142, 334553621, 606069352, 711828940, 584969983, 651554635, 47661521, 374933709, 804864774, 777375614, 622160964, 516909039, 230459923, 470701759, 559592552, 677374325, 88706652, 140687103, 697674747, 988075661, 871567682, 779347566, 446667539, 670043505, 806266478, 670538553, 686890276, 953136848, 901171818, 4967856, 539866058, 736387983, 361821665, 119778378, 337661882, 653334904, 588366213, 281405596, 128166304, 535506924, 868693210, 261904702, 272663476, 212794905, 85363507, 712314377, 668051961, 580711820, 195206459, 376808983, 682634194, 596586479, 818561920, 932909354, 258662763, 918373747, 723315408, 552894104, 176735141, 968308373, 521450416, 967025275, 627502533, 214045639, 772186551, 563064869, 257023209, 173993890, 68985220, 296583280, 164788190, 597906810, 806935649, 90203156, 384926700, 306752783, 438976192, 306157304, 103999922, 800624028, 103686548, 722631749, 629517658, 794595897, 948012326, 876659245, 624707506, 867916300, 627308719, 573858522, 306331606, 374922933, 508469820, 254826582, 805491738, 194854185, 467708445, 220908204, 944408694, 59284855, 502126115, 280890902, 951993683, 241986643, 238158949, 760890472, 126426183, 109665494, 92153540, 199000418, 449065150, 509187391, 861935710, 135584495, 271739487, 718736929, 378896280, 641263592, 161378765, 107844845, 475826832, 626065640, 628096766, 38191909, 246815345, 959639296, 742973003, 447360375, 911335313, 376935200, 813281054, 580360138, 407815999, 63945263, 64920589, 410656675, 318628935, 186013596, 201770313, 743555379, 93048529, 393619095, 184467786, 9559655, 42325554, 208750418, 899980965, 927109070, 849026397, 382206850, 46210573, 702480882, 997757659, 203387805, 977532944, 360867278, 835608812, 694144516, 711687984, 686678826, 626870806, 28641826, 776173090, 969423437, 836431851, 588472295, 993894649, 234090348, 228348623, 213443634, 354941623, 74962554, 683252143, 714604477, 391418351, 293688575, 17082895, 326140276, 56343036, 348507185, 498674628, 14887253, 94590761, 874863226, 421632293, 796133120, 567736392, 959284847, 177023281, 37208219, 981468531, 260040085, 76379924, 834008461, 320250427, 303161890, 647284745, 817179797, 162980897, 553711509, 435664839, 219408947, 202186064, 593127383, 145828037, 786039059, 350599888, 624331076, 878494901, 554666306, 975677381, 476157452, 604179412, 940761734, 465775804, 684955255, 457118089, 769606867, 170503859, 204474361, 900470643, 517882269, 140855214, 113251925, 543971083, 10052496, 590141978, 138626032, 525024999, 790562560, 495365725, 452256769, 711878798, 1677098, 141265974, 895823805, 81243131, 644014945, 350916459, 670448026, 512585398, 260440897, 354445319, 812017211, 107112887, 512200651, 182303470, 375584737, 102033728, 270817038, 226489161, 803369774, 101632198, 899795942, 682687845, 665046148, 195062866, 775574140, 598808689, 723001888, 208118368, 862030374, 424326645, 623707180, 684259259, 38744214, 118174609, 343637877, 810929847, 180487031, 607081328, 217933444, 23253588, 374210030, 491595507, 439284659, 941592599, 907671340, 870949135, 740995384, 12015927, 383644365, 561863829, 613212656, 251675924, 5422182, 536181128, 32849208, 166762360, 533171996, 135509255, 885966910, 238562654, 829150507, 864974760, 200413729, 124800251, 197299467, 771966432, 828846376, 358733725, 710090143, 644919955, 367047837, 266544444, 801387672, 213946045, 478451996, 75309030, 27279428, 120802543, 171989364, 935586789, 244587520, 919234921, 593289121, 401468717, 987658755, 187651885, 233091736, 346111736, 410666583, 228243876, 649457930, 98733044, 774994658, 932152560, 506700298, 734856892, 880736616, 841567770, 785165894, 383939190, 479569924, 114393384, 299510670, 245634091, 691007868, 343525171, 749957838, 496630887, 672015113, 958741253, 809356360, 251999858, 794176088, 433200937, 197013473, 253464479, 492150969, 15037846, 53478768, 821158969, 696843189, 758676200, 585222520, 697486953, 2637016, 101248803, 767415172, 950783514, 453448550, 489362200, 219730169, 530725144, 753946095, 700023059, 483836823, 382194479, 311653152, 195503517, 894483410, 551693368, 66106034, 467393148, 783424621, 425159376, 616702732, 777667728, 196366091, 937697761, 984526694, 378724465, 220400177, 407952486, 774643540, 393212076, 632218990, 585568329, 426559516, 714396518, 945619250, 225030973, 113275673, 406498045, 654081360, 396075663, 993357942, 768216400, 779945141, 44822674, 426311892, 267100627, 632381889, 519961064, 646324168, 22366273, 827442712, 529829727, 575475299, 539178706, 252851733, 23598530, 791735367, 849362836, 109951906, 668544149, 78160182, 544675449, 296004031, 960915932, 52515998, 736400677, 792145598, 257332595, 362894522, 19770696, 371688766, 683157193, 287689954, 497792730, 591373316, 259335540, 147789526, 413241352, 820565843, 168185430, 214857962, 147513891, 445523360, 736527086, 847865712, 332633001, 806196691, 40062762, 354899554, 707067504, 259071301, 403734639, 159855803, 184658767, 583539935, 320801242, 896857139, 896733558, 383815760, 611984388, 208012553, 460207465, 71352178, 161475638, 235407192, 363965774, 991883983, 441923451, 530246562, 917303868, 440009779, 121232220, 559931089, 841210712, 361718205, 392465866, 702435796, 851903042, 221680510, 571732179, 743864102, 931112189, 690322855, 167833591, 521561820, 962545073, 510787323, 102633790, 697721475, 94687486, 332907959, 925810709, 706801850, 212427981, 385581878, 391672747, 245258735, 81180198, 279318634, 933737088, 316279491, 940718607, 895489241, 708151542, 247394540, 121000531, 254720073, 722827037, 968237363, 195702384, 567978448, 799469849, 874918829, 583120753, 971267845, 472769414, 490993171, 851766679, 12909721, 118074270, 775602799, 106606027, 350245824, 151069019, 933725313, 139094459, 592051018, 127813409, 110519534, 426711388, 318283552, 507406632, 674339237, 609177689, 663519559, 814259068, 823733984, 99022461, 201115362, 116215833, 906577588, 671104554, 60757989, 229950541, 388803473, 898666909, 93013339, 254363180, 677748260, 562433598, 649642068, 289376208, 225520724, 789821000, 139326528, 703544576, 516098072, 499917495, 868885557, 153444854, 730769165, 30404077, 383648754, 767153114, 351840542, 474952231, 569652623, 406274208, 359206976, 143337515, 236576615, 934297675, 429854929, 732465965, 462352574, 23872315, 892257413, 921862884, 899376297, 674455605, 578510963, 21925705, 982645120, 79409145, 203563214, 58339047, 781243799, 326845210, 465891918, 836160213, 520816963, 228296299, 863735647, 650051352, 543799222, 929041245, 620870343, 107055421, 344185897, 845983612, 283532787, 406920127, 163161640, 33689777, 765613764, 164899977, 643048792, 265976761, 427864566, 626710748, 570619449, 376488589, 145924069, 208762466, 443054577, 596179611, 27233800, 841339289, 209544945, 833819914, 155050355, 913257545, 31637432, 199613096, 765457245, 664971048, 991002818, 661854655, 567291394, 792154601, 519616739, 121728742, 126540249, 312565674, 788856041, 4547649, 903354853, 217253142, 650062630, 852425675, 516727835, 966607614, 20752964, 729882521, 314683056, 421882610, 732923193, 55893134, 88289333, 43620370, 754450615, 977288946, 767093015, 243129422, 662826209, 373496783, 473270159, 951443316, 616383699, 335913030, 625133589, 245291138, 813765126, 779519322, 384300747, 727896539, 807165407, 73541192, 387006956, 945769120, 720376141, 762982205, 400936703, 122693095, 649815026, 452643150, 608656788, 565444072, 411915934, 419200166, 556225159, 165015211, 897887595, 547526352, 485819239, 627316520, 435437805, 922905626, 691545492, 858083247, 57541909, 533347163, 210327418, 729765838, 591295033, 71944557, 332798025, 981578199, 423926229, 133771577, 175031617, 252204121, 426846944, 927034481, 740223295, 791392861, 103511755, 174644901, 71608199, 560261802, 1326402, 784752172, 494117482, 683912510, 111274837, 139751978, 789613350, 574430317, 648987721, 945858925, 452207013, 645867559, 15238294, 789034537, 67019269, 663699080, 576601376, 350043117, 560968537, 51212250, 485728381, 684074979, 519153285, 747018497, 387593282, 49457340, 953694333, 588534833, 723283394, 935999727, 141080663, 814506050, 494594539, 965262924, 501265620, 361760816, 235789884, 837084919, 543829824, 181645700, 75161526, 333759933, 926494316, 204652894, 545224844, 239827681, 599377224, 503332024, 622583930, 222270411, 594935021, 152397541, 867812481, 240956541, 646169883, 481028913, 361519783, 813983880, 519054672, 983315605, 679999754, 517442863, 249909510, 83119861, 384317472, 823721848, 675609836, 546819072, 644302477, 169113992, 790591809, 857161162, 583814597, 353073846, 506346781, 756140437, 416918763, 911867368, 136737357, 29650019, 331090401, 486166844, 189497252, 580095551, 968578817, 527485332, 870776098, 466860332, 540694298, 421860267, 561529336, 480233563, 144680539, 537061390, 33515026, 445898432, 801470198, 479103509, 393383090, 140406054, 371733178, 313781381, 436732715, 111127201, 757048218, 282438892, 607759201, 49678004, 44842126, 162410396, 782515983, 197784936, 353628495, 840233519, 684392896, 725324441, 24414297, 318625584, 135304973, 690027472, 969237144, 861587422, 459003554, 243862697, 633394513, 663453796, 87763168, 303153342, 130690418, 426688851, 202536113, 582230386, 583580604, 769261603, 465951731, 946571101, 928439262, 224753388, 309713248, 407551462, 121189587, 705510981, 394911578, 624097589, 103576030, 522336728, 218601324, 521458008, 731172839, 216721549, 876977534, 687802057, 893849571, 794755621, 426069939, 548530221, 309464834, 196789254, 229120990, 959134516, 938552253, 756041440, 814383029, 852388166, 524760780, 23474640, 120280788, 950109477, 610641623, 360108001, 231909660, 206418908, 961188958, 111458334, 831298722, 140018209, 820831642, 683327021, 378216923, 763492103, 690441389, 14991098, 652819993, 224541890, 286328887, 271004768, 315487610, 645980617, 201068189, 385391105, 908210169, 903118562, 671406182, 427979958, 315671488, 857609084, 70516609, 69548354, 717292953, 29846925, 948117137, 481481789, 216661542, 636405076, 426132381, 48104748, 687831166, 966593913, 806591475, 418542052, 807020201, 225771755, 71358577, 912706219, 978557385, 635955763, 787217131, 818125758, 669427198, 556646799, 351238486, 87204030, 420395789, 324739020, 142115498, 289778180, 845399344, 620570817, 202231158, 340746703, 705778925, 462462706, 307653690, 287300289, 152627523, 582335128, 254968250, 631234950, 222595032, 501104273, 361402709, 863879898, 784746497, 348668553, 551334912, 615891156, 484819755, 720662785, 52217855, 941930061, 335904558, 923313708, 840395098, 579815420, 82340450, 195407584, 139984223, 857948594, 441588104, 512581345, 649048627, 67384596, 494885609, 558884168, 814033010, 724305050, 456476306, 337590408, 213551785, 664471436, 567669215, 521258474, 466026705, 433530436, 528665138, 183937024, 648487856, 248998011, 658897766, 746864271, 432017143, 769644087, 879298290, 544721304, 963433610, 660993968, 780140835, 842194942, 567580793, 485361707, 939396086, 535799687, 798454779, 480755769, 780377177, 380160830, 468875048, 702076927, 36069104, 881384011, 297770800, 697454176, 523729049, 90394699, 12260660, 371657464, 484114660, 466351312, 5431068, 915356612, 732307072, 123784481, 530292741, 636676102, 395530843, 877642505, 971361172, 534982300, 963023153, 186320964, 419551793, 224637099, 71101001, 53719584, 372009419, 57298792, 737329774, 701135136, 897228716, 294643215, 45328031, 295506862, 674133137, 984569539, 436149897, 661123110, 517241438, 209077197, 497907508, 434959187, 673294670, 2417343, 213619604, 391538046, 895215362, 486003740, 630162655, 18532005, 414857485, 173055081, 411589007, 272953517, 107459713, 761334951, 900689725, 176130563, 52033327, 735798615, 629903386, 489223761, 754329585, 698568176, 297527383, 590680448, 759337480, 737727451, 219648343, 349007014, 712246667, 42344879, 949685780, 942837985, 896093243, 512423153, 55493232, 26169368, 412769479, 33222345, 216428582, 662251761, 76292403, 237284828, 432707003, 394735037, 271445391, 453348518, 469858439, 45203476, 281102202, 11712547, 838280059, 170922426, 479888617, 388909855, 235361985, 400500935, 990074305, 312594813, 126025366, 42607478, 23091171, 76919886, 934753827, 263981542, 943721300, 880524496, 378880570, 605787559, 542205271, 126231913, 125709795, 158966469, 140917691, 599332422, 565432974, 353864680, 173396841, 97137547, 7845922, 62128419, 476513637, 412504733, 660443146, 136968213, 362411136, 391494199, 103601573, 737763068, 508264028, 368841986, 290575963, 825013838, 821203707, 512290225, 46928187, 395908699, 637858717, 726064052, 750492068, 473402325, 30458970, 317931013, 725738855, 64062794, 730086680, 617863669, 505880870, 673176758, 331267413, 751404896, 545948418, 705962354, 478915202, 527057350, 44218870, 767962799, 809253157, 194802453, 135936491, 470985956, 795051986, 964348757, 757124483, 751461204, 849659729, 68563674, 782827169, 870488992, 487608880, 739320155, 138409492, 869940152, 77549200, 915660035, 342313340, 929311380, 233972589, 115432871, 999741111, 425991973, 295775830, 15992988, 378405855, 474835705, 696100079, 681666443, 974893838, 74102947, 752416913, 207467270, 32746901, 905402406, 755201784, 549620893, 757689286, 997298492, 439120079, 617742429, 514637224, 62052213, 411200891, 253911334, 179499939, 298033145, 187150107, 254740550, 480953825, 858143933, 650960894, 223218005, 270020610, 443682090, 814013481, 285578905, 587419615, 300409985, 716209723, 338329546, 363315594, 41285975, 586133809, 121744592, 258022176, 726361005, 926210503, 706320598, 789561259, 624548689, 899926508, 559689852, 219161821, 959862218, 265799617, 911330900, 589344807, 855107808, 369464760, 348673239, 942179259, 762437786, 728576624, 726456816, 565754279, 602676737, 167633758, 131034158, 851012961, 434217242, 840648908, 279806001, 82727209, 302587098, 303841814, 505886090, 58625134, 900032787, 194062480, 201101935, 74981261, 610647840, 320326189, 102008585, 899624912, 340317489, 396153213, 720240285, 412269527, 227814542, 931968356, 950982584, 779029212, 406198286, 957855194, 424250552, 195559715, 314481295, 944622377, 12523039, 846473724, 336582408, 180246401, 657229362, 438033755, 53812462, 604133460, 189671926, 724919159, 111308807, 400438286, 671981182, 964408798, 825597895, 713677547, 51432096, 963042575, 454305356, 453128687, 43136723, 963247492, 935675914, 504074805, 810134330, 67947285, 450900816, 908952747, 401892736, 992181955, 674782960, 227895502, 268253240, 844061043, 52689204, 368179099, 605667406, 206585761, 403042900, 460911626, 725684662, 260750196, 955586747, 132638051, 591408391, 297729579, 482227872, 438682717, 173125977, 799488326, 918435770, 912289189, 475438535, 48308635, 101906524, 8723715, 376934681, 368686087, 763464631, 234819693, 602580262, 136336744, 667802914, 560864277, 847083861, 952291203, 277913523, 641839588, 45231634, 955594953, 177871488, 296394782, 603596135, 649202899, 718878469, 700484114, 886598066, 703218203, 333751115, 112353943, 390551136, 314696393, 487774972, 828605508, 79521048, 789475588, 830572266, 797148347, 381672664, 110945420, 408199304, 234276098, 71223074, 967728290, 6600234, 647157439, 774173451, 160290564, 947444563, 193944551, 725541361, 155997054, 461150208, 955484749, 480257980, 887619872, 529597975, 705717251, 653020986, 352220505, 52963466, 859601019, 361459660, 464530844, 480662927, 379738451, 516677411, 315513590, 956239294, 77448559, 36266379, 136290496, 501408076, 740463168, 244248036, 101950017, 373167759, 711728798, 164376960, 271348425, 279523781, 643364400, 984232990, 602360576, 814459996, 465549950, 162031643, 470331778, 235701102, 940625328, 237359945, 857347651, 724556093, 280111216, 234548323, 192920995, 233414251, 563461992, 260722492, 79763962, 166414625, 117192476, 739081099, 87307339, 976111939, 344965282, 272607284, 906215306, 399139043, 556318639, 502630598, 78327294, 172924444, 583876070, 363684364, 267083624, 50106720, 365119283, 363110245, 647031052, 982866591, 159721751, 709456812, 68580263, 659004251, 494972325, 459796472, 839691931, 814205799, 419003686, 970094622, 574934709, 499813361, 986315508, 232517520, 803267474, 278177422, 325949215, 799936440, 975236056, 391094685, 160604002, 108594145, 959911002, 985228684, 434462813, 18199652, 62826487, 321257587, 498991377, 902005010, 301617234, 210874782, 344499230, 492264959, 172635883, 733602762, 351435445, 571845250, 365391973, 435946593, 599534761, 390657540, 961390217, 163915756, 265261264, 485903193, 848079915, 967059625, 588196759, 153016801, 423876888, 670017678, 793861318, 896630757, 420933947, 298257952, 584639640, 802158621, 158712274, 70019185, 157418017, 881420978, 269308105, 107686446, 15065762, 595947712, 876568316, 959551384, 858999755, 761701408, 5671905, 727385373, 51080359, 313157581, 524526130, 170052966, 546403703, 753701613, 976418503, 585963317, 176759679, 424680657, 519860138, 766307585, 661000616, 298719023, 553520796, 627234359, 558508493, 801416933, 714558426, 577626897, 186523784, 464713646, 208179850, 247770665, 678190320, 164934839, 751840436, 961747849, 352476452, 867680588, 829461754, 830173056, 23070757, 612296498, 147044313, 654822385, 426818381, 523083687, 739074628, 556140296, 128968069, 240089905, 915980136, 736112948, 562350219, 353591958, 947548389, 333732834, 853552198, 221197097, 337640984, 951075408, 336741221, 130018561, 813966185, 203589757, 65591284, 917116621, 296399216, 744554756, 803735641, 215032008, 670167295, 790793127, 361526943, 208795792, 167326529, 146168420, 533041533, 752976292, 649645663, 328170641, 985034569, 925085724, 71846168, 392580607, 341705616, 659759756, 905450078, 808094727, 599148239, 255924515, 23167568, 721357297, 505629340, 750859907, 68685443, 63705358, 734420603, 716581444, 488073755, 521427770, 850904808, 645299013, 826751912, 403340851, 3314264, 634736158, 984479746, 704044652, 395956031, 264129630, 323370079, 911268436, 428137173, 570967890, 760218600, 902652831, 8463385, 489948331, 989479604, 903280237, 336873420, 24684324, 272663241, 708597011, 437693558, 349033919, 133182377, 229987987, 38722617, 543570916, 161346104, 272881055, 920179376, 792804954, 197140264, 657094953, 686384502, 773001926, 904231961, 180085508, 396081227, 70354171, 893554570, 100683266, 113627162, 910357171, 99248413, 925522940, 406636932, 148471082, 710165976, 456150722, 170024638, 895442067, 164552792, 535815214, 841929591, 6884669, 189476575, 5262145, 705146915, 922689086, 799525525, 675184912, 784455788, 919127292, 645325661, 463865500, 691492116, 486844129, 85599374, 659284763, 125691582, 165846229, 809724512, 534555267, 149043183, 307028114, 514262189, 824497808, 368093233, 685146966, 844353009, 180554283, 801709428, 635491472, 797109415, 948388340, 183361040, 124074660, 714239879, 751839127, 762486887, 818918525, 147469088, 353728924, 225101235, 333722108, 211657191, 697843859, 275335389, 596706017, 700831150, 51538022, 654434373, 546577198, 839787284, 312048697, 468281786, 485620399, 42976757, 60876908, 638668178, 389800204, 111249196, 280194734, 169561628, 447463191, 146355852, 9017220, 856897301, 266912823, 464699978, 754347192, 152500996, 783360584, 541443777, 635422736, 239714268, 347864288, 102555991, 483027632, 585634595, 279280366, 189976927, 735813394, 89022857, 211781685, 278012936, 948905922, 129006268, 239733077, 708865545, 45938454, 545677571, 957118136, 313422915, 536733358, 557452024, 56392496, 383550653, 170373194, 577586307, 198818672, 250378590, 75373164, 420324335, 148364843, 448226067, 68729240, 708396763, 836649880, 881472507, 959816669, 155943291, 869334900, 197690521, 722532112, 307485405, 184515199, 247242404, 450596793, 282970375, 96287416, 661377968, 833455341, 701561986, 369769482, 872410856, 938858946, 490676306, 767238458, 123476708, 502810675, 9773147, 700980973, 790037674, 292576083, 137606458, 822319789, 897317328, 483945952, 520077653, 769526806, 712482920, 245262329, 854235160, 828263880, 962178765, 440125136, 915352492, 838610999, 355110790, 558356990, 940773952, 120182490, 354760028, 715318231, 154107666, 427733235, 961594737, 617850689, 116732994, 935789735, 662195967, 449941035, 76533349, 760688617, 169915219, 855662115, 840948902, 771573195, 633264119, 409278906, 854634762, 40516368, 960993438, 667591277, 216773007, 97299910, 107513298, 227443999, 784947737, 975356373, 971812031, 511566690, 459395919, 190279108, 192591215, 274533801, 717012427, 808473109, 130055841, 965282578, 89094631, 113412020, 420084161, 318099232, 133278360, 93879221, 188513843, 664655293, 193683178, 838399082, 803421964, 614684972, 978554952, 16028359, 633234586, 478400114, 661826541, 85283751, 593251200, 741429376, 349174925, 99897365, 985895055, 789421480, 655352561, 456546697, 859172587, 421239642, 574992352, 572458514, 91132847, 33392286, 454715624, 660004857, 673353798, 345710211, 36678195, 228729639, 185461318, 333623016, 535219867, 642647968, 578165534, 182002715, 551682580, 145009960, 772769208, 423251529, 172637364, 52065680, 399662159, 924192669, 591784253, 488921004, 813083868, 548359349, 265915606, 134262127, 995081081, 380748662, 614363062, 346359688, 813436594, 398981320, 512223177, 968155462, 537150299, 484621098, 7342388, 16647885, 374523840, 372962469, 519841489, 729977250, 840233756, 793231400, 397818035, 91489991, 526445857, 114422252, 962889000, 261100151, 543453349, 200697470, 944658542, 779343603, 696052674, 906844722, 827517295, 627436703, 958286654, 670860645, 630207940, 878274706, 946618575, 642812404, 764165340, 788098896, 13433741, 208842816, 482628496, 119457411, 716677996, 789502993, 750546978, 648220240, 588432678, 212047910, 844848199, 131877794, 760721910, 532063359, 770385212, 752414492, 296600258, 906391116, 120832824, 944896038, 692533960, 679967666, 240788337, 401963372, 359634934, 865771938, 789664491, 670920085, 73017676, 841343861, 317519799, 688107818, 951181285, 907403511, 469762759, 191174182, 226499131, 158122593, 614401380, 374725720, 691973689, 248126419, 220808093, 71169122, 138224561, 863791420, 762798482, 820818117, 896288552, 477293020, 69048388, 460001315, 628117215, 864413207, 912244715, 266568155, 214336060, 993230631, 697957259, 112267066, 520699641, 614451995, 381411342, 319780648, 790004109, 973450405, 119046087, 110747857, 354185004, 550904616, 421391581, 379217512, 849506455, 612749642, 714628068, 431747082, 524416946, 825899472, 591378925, 494764835, 754950409, 733316244, 332987769, 324324177, 2824169, 942652066, 143888497, 720316210, 29355767, 418120650, 781753798, 208005101, 178615341, 808924618, 368678606, 416075895, 723678281, 259469359, 343500858, 190626730, 424714985, 920556959, 216141030, 641606264, 825814372, 784940188, 261578357, 676818903, 555765364, 217803767, 619797528, 329691229, 161216092, 457994191, 231876632, 461700076, 933887302, 903024655, 826725148, 202514174, 596858515, 493080479, 706169167, 94680971, 587118555, 443340987, 512590493, 9476245, 355504528, 243027356, 260605410, 397331507, 910308866, 149488351, 233800563, 863394188, 672908195, 745031129, 995347999, 966720077, 253762605, 374692575, 897407859, 940777200, 28299461, 887994164, 790820693, 438235658, 624713138, 309883603, 385042307, 49580018, 239944583, 512807546, 629701784, 373617401, 750406552, 390417230, 129706287, 829558283, 580614556, 235497909, 919051926, 592621807, 913757766, 4131716, 20706893, 201277944, 873445653, 26740262, 44059997, 791453361, 670286733, 494373890, 896222445, 473599618, 900080349, 947747753, 419009912, 460366421, 334740992, 921602071, 207034089, 912014236, 85771724, 628160554, 404828852, 157065166, 320564145, 43080751, 731032633, 441483946, 770358071, 320751629, 55813171, 882935409, 527182698, 687288900, 26143826, 216849637, 107817061, 901431162, 505991980, 211986513, 859748734, 436375087, 320974252, 538350935, 195301024, 448245497, 634095862, 748833947, 918293047, 931867706, 860905978, 53759189, 501350538, 976696596, 604333509, 587903068, 220454383, 895074366, 773049686, 1264391, 260349923, 560755037, 822202863, 367009987, 649719527, 362923208, 798545364, 6013466, 800067826, 556801025, 673429633, 26594317, 442591621, 679425792, 539285131, 979793876, 24400921, 180606372, 981916667, 431870923, 960612209, 971019956, 606833194, 504411380, 575186720, 960202892, 978008220, 325344089, 834955182, 499059129, 293245115, 415167168, 459667514, 922706404, 407566907, 803994187, 444291647, 776083003, 395195174, 520770957, 376188421, 939518407, 157806900, 630554065, 106668348, 755728402, 917772867, 2528923, 988073725, 67884048, 609725214, 723335512, 181643333, 876545210, 720260902, 100877145, 687079158, 432698358, 391940487, 289313430, 697271112, 517336041, 347869577, 725138115, 926348814, 920708756, 650130832, 133727089, 753661893, 142433284, 850784759, 162885455, 499312352, 785459769, 450615563, 314556759, 185001370, 298104398, 745887967, 350606962, 617657400, 921864711, 447812869, 510837081, 922636601, 545717222, 114902021, 534275901, 379647447, 171509386, 35772890, 167022930, 295664541, 682927088, 219163410, 827780029, 17048898, 825529155, 294703875, 795017536, 454807675, 937759576, 119799672, 551974669, 419550173, 529252474, 302377600, 502871276, 126636495, 702696552, 813888266, 428591795, 641421541, 6507162, 826867264, 47783797, 758632783, 878453443, 375394485, 160307155, 833899242, 252972643, 273984375, 235244368, 24154636, 574585440, 697493722, 890375556, 406300598, 456718805, 31681213, 162416989, 148738037, 128925521, 4313904, 83407615, 18808047, 606012768, 670665585, 135472522, 791167540, 946505846, 414371856, 326172720, 109113552, 886516487, 331625959, 316787161, 872266021, 371794351, 907450238, 972950169, 562757674, 848108032, 635032424, 906076992, 760054995, 817407982, 960308748, 396376008, 175722470, 667308927, 725464831, 403790643, 51681859, 957316508, 809643604, 345890086, 388795277, 900035179, 115812871, 168371069, 841449951, 814372555, 518496009, 439093858, 169289223, 18163398, 29284602, 447686208, 100376946, 444830364, 323981776, 511517472, 974610926, 981690277, 747504041, 421413006, 112121273, 232987358, 249377924, 454328621, 770296261, 966827707, 172836816, 416452553, 271038388, 238085060, 6597290, 110095031, 335551572, 679511760, 983029169, 384589746, 184582847, 376339817, 905003426, 498796659, 569959947, 91860491, 228128300, 597308822, 804056397, 811547232, 762441372, 316654599, 137191310, 371767313, 385061501, 929599170, 475663063, 175581044, 382398321, 893132039, 55606744, 496519186, 216099070, 41150813, 836499794, 932598886, 487489005, 383504751, 908956668, 417716037, 959476284, 907159576, 968588344, 4467068, 731723580, 36838166, 534496676, 35581131, 391342139, 211023170, 77011316, 472138912, 981709234, 844641665, 960374208, 195833450, 549576510, 626469643, 373247131, 549522469, 852910861, 245851188, 435004774, 295185662, 18830903, 64728516, 542004655, 742445779, 306973557, 983569925, 527351398, 195772563, 115965730, 684277475, 686481746, 981349468, 767447651, 442590109, 641824276, 674611073, 37074970, 865716390, 60395245, 342301499, 866737890, 24488422, 903904246, 966644010, 60878616, 46903134, 85635346, 453655674, 321623841, 767878420, 305753867, 557197234, 482371059, 904015331, 149183898, 380175150, 543334770, 695307095, 717522807, 141506127, 260661148, 433281147, 633280502, 694809183, 120795510, 648065311, 597568122, 830473402, 447404834, 668499181, 512416784, 593870646, 201417817, 486921501, 999159950, 773225951, 949160126, 853142515, 385698296, 699758340, 853490637, 275400318, 124646666, 949357456, 15952011, 8914333, 493072690, 400777981, 395249809, 87398683, 435376593, 349959460, 871423861, 137644083, 896006619, 222536905, 437058701, 320686275, 860102073, 734697902, 388679826, 690666970, 9538177, 921753207, 696793920, 348401254, 230762706, 303499221, 989883083, 924037475, 754047585, 691198655, 145817992, 603331972, 249580854, 818884223, 330595123, 24128615, 998639499, 651812079, 138198494, 920561261, 887517402, 570910157, 484763105, 971074422, 136089611, 992811797, 216303231, 364589358, 275058350, 614542408, 967908099, 252961935, 310029619, 705873258, 736066728, 826765273, 621120486, 783944628, 69038532, 170899550, 201889621, 789566594, 267085830, 251720219, 183881891, 100534315, 670595886, 848491276, 396228030, 86532606, 603327758, 619009012, 196699031, 770510348, 165079807, 716154545, 645408584, 852179522, 671667869, 480704620, 406858192, 644771159, 736837466, 896161611, 463560748, 605624934, 506286938, 440025195, 3108627, 40723655, 123681843, 89610760, 652204597, 407479122, 905747330, 743858075, 485078791, 917697314, 37325596, 364252192, 410739419, 90174060, 650834920, 425396530, 175039515, 397709131, 794813264, 549793828, 38212476, 707815197, 725882715, 971474683, 335307913, 200782903, 486564673, 442804062, 162830130, 6409440, 269897803, 561759548, 114866008, 734279043, 483328547, 789020917, 3830974, 174258974, 981608123, 906834123, 329091102, 372057211, 222531176, 165840785, 468541182, 836014975, 113658276, 937195615, 82046521, 581675106, 97398711, 515031330, 437888765, 362222620, 956482811, 814926868, 425682779, 310359542, 182384669, 455449973, 344304734, 88936808, 706464333, 149837682, 668172459, 284937361, 237170280, 949238109, 527055858, 667026668, 29438788, 429242141, 848409520, 376299949, 420180312, 428810881, 820301704, 282103341, 64219246, 345368368, 853709056, 282288517, 101008844, 383988007, 934532502, 730715466, 746136745, 45601416, 724292316, 990504525, 860042270, 555397425, 237300738, 603171606, 867516687, 580009731, 223479234, 467563700, 502077941, 998040749, 414433488, 657971357, 580890541, 348025129, 617667435, 839222833, 558299850, 81791419, 575344117, 686065625, 869138407, 758566913, 103485330, 835979551, 786244401, 805061285, 787289967, 851606274, 241191729, 400692538, 22901391, 862592122, 237440797, 95574256, 5788115, 476343073, 554474546, 642458833, 109195216, 567936517, 69719267, 992168595, 579658417, 897966080, 279475160, 60198581, 498949043, 46443128, 893664578, 173594797, 651148339, 602876556, 731189003, 741826649, 135007636, 740604983, 126039120, 619658185, 78142846, 279002224, 94028484, 296339380, 696615089, 805433671, 847724270, 119021690, 166307759, 943275948, 369366613, 907428902, 87552220, 323012440, 719869313, 543195897, 99905289, 669912173, 211353721, 698229920, 187821367, 575128974, 304467776, 3093986, 873532552, 264534110, 478219532, 638620002, 28485946, 445338761, 961313997, 731719254, 85900591, 369209497, 112285635, 299123653, 940924792, 62326807, 587047632, 396842882, 272577169, 407628833, 783322573, 36533232, 877945306, 335968181, 905487513, 355878230, 631586702, 273722894, 325141092, 617141074, 978873370, 127639901, 102170446, 322407747, 311520397, 481669342, 147789655, 26786875, 867393202, 246055871, 605378480, 417520619, 793673012, 186336127, 475720285, 751118905, 51175971, 627555709, 796985335, 229667867, 733895128, 229848419, 636145035, 550561850, 728946935, 400351161, 857572677, 444651548, 559457278, 73427517, 746784841, 938794905, 106084403, 277590917, 589266110, 256679191, 851522864, 741889052, 738676921, 306467713, 116899967, 868777260, 414670193, 536220659, 62094429, 930351135, 772510851, 238003533, 770841578, 635820747, 710680050, 460037763, 185594909, 334803332, 651004627, 448449488, 840571075, 821594804, 413133342, 21666330, 95571669, 614650, 485832453, 650995958, 587007485, 368528675, 154061056, 851110433, 431391405, 816477282, 701197169, 882298444, 807889161, 887721251, 462887235, 361858185, 310159591, 924164745, 617142435, 233348931, 888434845, 784478766, 604409729, 462583724, 216789922, 539724586, 962707288, 938204773, 258532322, 926882512, 95941321, 428662055, 673510544, 594358827, 507690099, 112018779, 168325653, 134994335, 758657180, 607782539, 59504738, 586261486, 30408893, 484803042, 338092178, 136428496, 480443849, 496466081, 163031533, 334749710, 102836349, 298866630, 698145093, 282388761, 285728285, 851693507, 478739436, 649103687, 765374195, 893228644, 493755922, 986579263, 311622731, 628105237, 585904467, 199018665, 239158619, 974453272, 862365167, 68404949, 49535948, 358731421, 453580128, 677005822, 631083101, 524648876, 125419601, 882339341, 406651455, 891928240, 268901333, 209872067, 419442203, 800667275, 69665238, 28983333, 803694239, 55863878, 993003576, 338250979, 404112186, 931765704, 64981814, 878989718, 699266872, 559845389, 90000706, 101003582, 130664416, 971271113, 601816926, 38124457, 298750046, 750587390, 349935903, 969103604, 119171085, 440835153, 327280138, 753658803, 241304148, 373622338, 822198419, 395384127, 582328958, 474451935, 824531772, 894819010, 678087219, 474745061, 473442236, 837511393, 622184006, 691027955, 130701724, 576611942, 727766790, 907131103, 994823761, 476111636, 1238246, 519991592, 43662701, 432281664, 219993664, 355649991, 514274231, 634329246, 386666463, 760666436, 407549153, 800106321, 241616093, 10244009, 875931307, 414813155, 420063264, 108683058, 376046060, 539104036, 10880661, 115102003, 677323969, 682925177, 476808246, 203554317, 764266159, 88189235, 360633851, 109174461, 279074323, 268278809, 609566523, 272133793, 858386257, 475649422, 445312576, 621166486, 227814776, 900214554, 334453391, 945694786, 232804738, 67423613, 397025327, 946567908, 665018645, 440595974, 615725140, 160835252, 275162034, 47544351, 590259013, 897394378, 194145209, 744346110, 689217774, 681829951, 277173999, 931748821, 912227719, 834182764, 87362735, 914649484, 603795524, 753187728, 511034837, 307513966, 108881984, 519305430, 320935299, 820468690, 998697879, 227711450, 630408500, 951510461, 927857512, 587503543, 315470867, 860566829, 669653586, 245680316, 495051703, 597450916, 840050859, 794842999, 69195827, 268557518, 633901225, 910449052, 615298382, 694145843, 594112661, 359798012, 454949003, 11132959, 732704725, 402034522, 421883535, 584296119, 694445031, 192397083, 728503821, 654406948, 862086306, 268963391, 308073903, 242687785, 258130403, 873833282, 501113139, 201368591, 240241459, 152510621, 771284198, 821984602, 946486130, 833006165, 109293049, 732651749, 602621231, 40069809, 669533989, 534333601, 27009102, 795552259, 193980268, 673356267, 274788486, 371777117, 826315777, 809901404, 360612558, 970972246, 210888714, 135533663, 14863594, 605880992, 236115194, 248933313, 955185403, 711031247, 312544662, 634691572, 755473931, 566558379, 200681979, 93464141, 297040123, 251635176, 57489870, 211062947, 403961372, 488657774, 28113693, 594810987, 265617209, 287470161, 162717846, 527884989, 120226358, 119335528, 630087130, 813262557, 56885394, 927012454, 408850981, 255682968, 440576791, 282252391, 855041665, 655201173, 744944428, 792097452, 453929649, 745888639, 164475188, 908029360, 951726794, 128687221, 173465164, 137720538, 574494976, 784702655, 860294516, 99912169, 216585934, 384331672, 450697112, 116596856, 890948177, 691182995, 199412955, 920882718, 970080938, 995149445, 526082082, 879420104, 596311131, 69243925, 376657589, 536571691, 633258022, 60902241, 900124895, 809050047, 137182010, 955927609, 113323517, 721883858, 129884768, 414870658, 358060068, 316652892, 108323733, 709240248, 5823287, 61453915, 104321781, 378692936, 785289835, 969509579, 809988037, 253647792, 137041563, 171960757, 672667635, 489772249, 349655203, 639985162, 679421065, 738941831, 125673685, 876525099, 111307794, 355148568, 212137840, 273286137, 493097995, 288037591, 432765029, 819860144, 811987078, 81091806, 113528462, 135362867, 839361246, 950843636, 48845045, 993764639, 802636125, 705906943, 772812818, 190389127, 147311264, 568443867, 881932392, 328218668, 969951787, 294345897, 777416680, 983645987, 616982241, 592602698, 660863627, 861465120, 937814064, 922642050, 468280795, 929525761, 298162466, 458680442, 413492241, 700097418, 917168582, 995844920, 721600405, 353008977, 53878172, 335172146, 16970598, 277509282, 375148266, 298734339, 882687177, 198220244, 470377580, 655505275, 136434079, 275481491, 325748176, 975288682, 720825749, 34101875, 955040707, 866155583, 40872371, 132938386, 172424319, 664217976, 586704347, 963044021, 688497466, 628451418, 905190597, 335770652, 511195893, 14312950, 280655259, 946099004, 667027760, 377590351, 466094410, 778636479, 954850743, 940168967, 56802767, 292915127, 962035369, 386161780, 708120662, 860413207, 723124242, 490911830, 296634257, 550542703, 840965828, 308106264, 348866991, 699886028, 358478280, 402393304, 188551837, 19348281, 733979310, 383123026, 358253103, 856319168, 145244375, 585786847, 926357201, 121425698, 567355355, 78258259, 470655786, 574584465, 270408684, 175627327, 559985101, 918580181, 569832953, 662323472, 111698687, 362703302, 115027654, 149748160, 909476057, 273487460, 444512782, 249459579, 71387307, 274576641, 72178442, 948966276, 928108940, 708095106, 257157238, 779068170, 465021711, 694078850, 540471985, 93931838, 183156850, 549788866, 906279566, 920291979, 466606465, 978084086, 196559737, 881672894, 24194332, 673967278, 690151232, 622810563, 494020161, 643179374, 880734396, 611219167, 87890720, 628054820, 588719743, 727642442, 748115185, 15261254, 505300250, 156339549, 780696649, 626393006, 700310767, 931106040, 704947687, 306029114, 87588059, 387339607, 863427316, 433659189, 598335133, 452892561, 690947821, 404042360, 885199715, 926041215, 270849133, 64399124, 661600414, 79519886, 95592613, 820155098, 107805040, 136914006, 156873201, 935574820, 729696083, 420922115, 817366808, 434267558, 885000570, 441674835, 274131389, 119435799, 754118562, 892498378, 918677417, 592702483, 219151080, 918421299, 311900643, 854962411, 584680948, 331065895, 964457672, 448275741, 409313832, 647017152, 209988388, 919198025, 83822522, 165594002, 416523911, 222247752, 416378975, 996076012, 339055994, 303894852, 992884552, 131614793, 284815821, 90882513, 156814478, 190846726, 559660704, 691951488, 911176221, 160562312, 191415001, 70426725, 297288024, 398116575, 975467391, 48266358, 470133188, 881785260, 947520256, 879886388, 45112314, 756974486, 999467375, 812912162, 624429967, 218875971, 202121788, 802030279, 729422382, 962325345, 827783916, 55636270, 714519985, 76082474, 78928338, 977871364, 419112639, 947492846, 663586688, 568349920, 575399132, 12470501, 110887853, 344096225, 478827936, 252421994, 195306154, 983287691, 732379540, 452359500, 68587638, 802701518, 442909131, 374111, 308859234, 225001135, 376506615, 821276276, 746964507, 273612364, 323018352, 465021330, 962781714, 278079398, 995328016, 256386081, 28404384, 79253944, 203101725, 983283947, 241763612, 482699506, 97693144, 216683188, 79910756, 944454215, 779672981, 904941800, 792706004, 621607518, 731367805, 33709103, 599184837, 922052145, 464577823, 702160027, 469411037, 826222319, 635059465, 312375270, 753278654, 679360366, 581032025, 315278089, 949768452, 315136960, 377325824, 947651131, 303208225, 699827612, 143601967, 66674758, 575938785, 743130650, 386790564, 696185726, 494722340, 452006744, 41167559, 186762535, 783577904, 402379619, 636455991, 853122107, 169573242, 141596988, 560704504, 199330633, 895662708, 881672300, 845838298, 730367943, 723490154, 25869545, 457845370, 250758100, 217535140, 344120411, 646968499, 364867478, 206598421, 805124236, 549506397, 856194060, 416536027, 371496840, 118913289, 760949173, 466835602, 21337292, 466020361, 618385811, 720917610, 583823966, 546635779, 999571166, 839012924, 423301823, 444639011, 453789608, 584251653, 117793809, 763177096, 655489719, 31771758, 277554336, 402689193, 162358199, 530263881, 435012260, 432962428, 588808349, 885642069, 428191220, 36373335, 96660695, 859432106, 537092152, 669298115, 668143438, 706138631, 268952068, 5739165, 410894022, 514020568, 385785962, 273639685, 813071786, 248634696, 778663327, 812817568, 857748630, 143708342, 113710860, 76163703, 774518406, 482022201, 44574850, 430022757, 725915526, 756880635, 975158250, 546009480, 725525876, 893703269, 535140327, 654231720, 310195159, 942583747, 862670987, 584519078, 875574338, 867497297, 865708987, 263945519, 812507871, 495753445, 128278439, 499929647, 272817397, 629497445, 455503105, 647625962, 694759085, 472682789, 827247297, 383170790, 900336463, 122835487, 135263074, 136480283, 355415537, 56625114, 682533140, 587835807, 148768957, 159387195, 377238030, 658904944, 775245817, 983785166, 521620765, 468141002, 821076818, 406318271, 642555181, 802776032, 242232834, 507763890, 677400397, 359123893, 28836983, 959022037, 438504917, 693884007, 566700391, 72544326, 138763183, 539653710, 360055283, 725322478, 288467230, 223930043, 650005477, 708496465, 616785440, 883617800, 761859357, 580437363, 471938419, 192608981, 828643601, 523016514, 61836057, 28647414, 660384999, 950642270, 320041577, 272475603, 913078715, 492401301, 969758740, 193798920, 307260369, 496358440, 651306621, 105613664, 54698199, 729933507, 105369731, 239996815, 71194733, 769750717, 829106699, 811012379, 802756344, 467357170, 789109713, 201092072, 881827591, 371295005, 481271516, 415143335, 5699430, 832748829, 365713966, 470947562, 485157748, 695538411, 10517707, 122394229, 14234170, 624559932, 79966027, 866831360, 418946887, 738002446, 559444953, 360974824, 264936736, 80958612, 249685939, 946484720, 626136830, 46138916, 423558294, 972289448, 542766789, 182434888, 238551861, 348631237, 614561547, 138348141, 164569652, 446540223, 986725578, 803450673, 495875705, 283092493, 902908630, 791421801, 184867234, 746782305, 977934613, 534066166, 344252334, 707871648, 383614829, 881201850, 925256225, 835656931, 131677301, 918771913, 762968741, 486299393, 636587155, 372722795, 878595842, 32479919, 261311774, 11227587, 943753585, 668715974, 595643070, 443967419, 747364006, 868724149, 842488579, 835400554, 5871881, 722003743, 166266059, 499244668, 875599298, 72421592, 807111547, 741949013, 571105674, 532620794, 945837903, 286562712, 465635189, 186399147, 478950356, 809022797, 382114063, 83810890, 942437142, 836961145, 395247654, 755308303, 813284306, 433331208, 302294965, 232345987, 644899847, 68196328, 643145725, 631026049, 839670140, 598080806, 453192499, 704856218, 514891332, 983444620, 542035821, 869384391, 672965790, 124611218, 202516125, 305560229, 926113244, 626426931, 661692033, 78014671, 257981780, 57925391, 356725649, 72365547, 98226463, 838417403, 608801902, 667112551, 707115745, 136159410, 991523735, 440771827, 364915600, 693672440, 343048297, 639059878, 753138601, 999636090, 763207436, 211940623, 515814567, 650883215, 252770917, 165298895, 442477457, 525404529, 623678105, 377402456, 358671873, 635675669, 901123009, 183593566, 989138565, 70334924, 153631271, 184212916, 635863017, 98100203, 468796733, 762291869, 243831578, 63785393, 864379603, 532824933, 394525500, 369765089, 625706703, 574841812, 218852864, 713994198, 34750620, 863498746, 521676801, 509211385, 474199994, 764896170, 710337875, 338940944, 564008553, 76279632, 739062800, 33682760, 320681567, 139035833, 687731135, 955000123, 348149487, 932063147, 610878906, 688602875, 16628831, 291827857, 288526923, 127781345, 581983620, 268692476, 757920246, 756867314, 258340725, 823834714, 85386412, 175239876, 387726921, 721584548, 357711047, 219319815, 530112101, 258605027, 922776079, 578205960, 671056625, 972700193, 8528208, 849696722, 359106065, 70425246, 968877970, 818064308, 313033231, 8291956, 616391202, 680478287, 951758647, 773143429, 324264213, 39566613, 107713340, 275160995, 630847300, 456811269, 535209796, 814772007, 512429691, 347843742, 174421460, 6700815, 399946178, 561887952, 863496062, 938489467, 353980736, 187518441, 895285307, 581602937, 284497900, 514323498, 32119651, 736395793, 380316815, 128713351, 427461099, 926545398, 773594334, 842878045, 527007065, 980354437, 688427308, 479658720, 43326064, 438569949, 204848287, 505825506, 160910389, 808295851, 566845144, 389602346, 428557085, 350757202, 262309870, 961678650, 95120557, 900824152, 961887866, 705579639, 95926718, 775239001, 780153483, 886195022, 684221941, 870276047, 934474934, 683694034, 441875695, 118938511, 583354592, 922191030, 242365085, 996202625, 29269885, 978460422, 32831949, 36151788, 303956470, 524743755, 896349598, 291801802, 912855225, 753142915, 453297748, 342919928, 159089688, 672426437, 740391979, 956865151, 700235373, 813065445, 627699893, 625082586, 449783443, 485007264, 161065440, 621424404, 524289385, 121751919, 321272604, 609884916, 771292783, 445754295, 148811683, 593687792, 264450694, 275516565, 286045854, 441717205, 161913443, 161852939, 695551884, 98784994, 690033610, 478363778, 651270080, 923381712, 812711539, 627258137, 694605475, 231674588, 906857304, 442125924, 312406813, 530974340, 316024942, 914096326, 616212955, 708093969, 378445993, 131476781, 116848455, 219493142, 359592099, 720143733, 749964565, 446802050, 436179053, 534335806, 720460426, 776999064, 829461987, 405604335, 283382868, 189665812, 680941443, 760375254, 64631282, 194715446, 19182901, 489851386, 126865356, 951396465, 103434562, 125107544, 697539217, 306729750, 398968972, 73251825, 393263649, 829310437, 590322779, 728322847, 609355604, 929561038, 158370666, 380431863, 866440770, 849618545, 824815080, 246790343, 351825772, 829038582, 696874253, 239464548, 556512744, 472465811, 762502506, 60784719, 730773962, 94316590, 915638546, 28462059, 63891222, 858505799, 138042224, 83344471, 228571211, 267171023, 326618684, 480972671, 809583011, 127950999, 241007683, 458714472, 884024548, 447795983, 693690407, 59586624, 119489941, 646378215, 285286103, 71732232, 448622141, 210482142, 513333584, 152299484, 525975998, 928924383, 90736587, 278406612, 934262040, 276474275, 968467784, 795999487, 447848964, 279250212, 649773639, 673879112, 102061747, 849286469, 42477735, 174886455, 645804579, 735152512, 390331549, 268188929, 580032560, 466121677, 144906160, 685623455, 167696535, 974868732, 919177221, 956642668, 94171438, 829934934, 417677258, 9848090, 364617060, 513949106, 597071068, 750749615, 405996001, 444801341, 126800696, 956673045, 722489425, 222916443, 763918841, 949764862, 358127324, 974012561, 4342315, 905606038, 182198927, 966882183, 665766870, 158347519, 313981030, 948005963, 250699972, 766306694, 414479682, 203499347, 94253903, 819945233, 620782044, 958358413, 113428095, 860383762, 923103042, 788017847, 441414720, 628844153, 160463090, 571352435, 689877107, 579993009, 503205579, 491189178, 332959611, 444829065, 317497658, 404281708, 153240118, 1518438, 687899147, 131051553, 515115442, 360015166, 456483717, 500770897, 530000378, 46924178, 151526551, 152250142, 635970237, 112607133, 450614699, 618548436, 972156789, 467189021, 928813277, 69991656, 364757082, 983563391, 124002866, 789461286, 844725721, 440103882, 427141464, 846439690, 32214882, 91920036, 333940913, 843346469, 463281322, 127433000, 169067282, 446526071, 5178016, 754547455, 210281926, 621072688, 689395547, 702743066, 351367899, 434360527, 268382035, 385498935, 908678422, 590087791, 278870857, 842428291, 15462934, 105456744, 56258908, 459555638, 340010659, 33958758, 243432973, 654482487, 115058876, 653531328, 76642918, 587885889, 994320820, 342993738, 968415036, 5319234, 215684021, 860731989, 105265919, 65195888, 165909489, 312364968, 562680071, 220603317, 835339764, 308252259, 538396729, 753251592, 968305682, 565937961, 611343249, 557060647, 513858937, 344680365, 409113673, 585696017, 272770903, 914415222, 807173925, 750542167, 70067765, 754967012, 464210230, 678137818, 110749561, 975918521, 878225634, 460362154, 244680617, 995587679, 288719712, 780029836, 858021302, 102488526, 463657491, 300846570, 951589679, 212109217, 273474434, 966323647, 161310889, 548501145, 60760598, 892209471, 465618204, 586116131, 26243212, 818447717, 368878694, 675485210, 627796584, 381287959, 751933782, 534378378, 343188701, 429979095, 423538320, 261031230, 403997203, 116037055, 211545869, 997292011, 170075902, 340236307, 119076199, 177130958, 504083994, 998502476, 509028616, 189651862, 893974365, 964045695, 208533139, 157864246, 253014900, 434596679, 524781516, 10747058, 355833837, 367823661, 424943695, 981773735, 466293251, 621912892, 952823205, 7749097, 188711505, 850224310, 839523788, 60169565, 614354270, 953159427, 366067316, 409163582, 216737461, 826382784, 990254336, 978132747, 896703841, 746637986, 400878354, 428332306, 767710120, 716403137, 289991977, 216867526, 364912375, 17585145, 839620610, 88296038, 936425550, 91824934, 318682904, 627880590, 253175221, 883823225, 989405979, 767038379, 906488655, 118171611, 451726409, 566151244, 364678884, 297867397, 163286013, 925275217, 253643002, 190160409, 247983178, 317029242, 540859778, 52936056, 800646038, 582286021, 589721133, 541084227, 123788684, 481859348, 328550928, 603430886, 834648448, 923254692, 996048907, 458705937, 789448471, 220199680, 677721717, 678069367, 368857175, 24045872, 178400819, 923743633, 254956107, 74729086, 180001680, 497929058, 233506591, 979271909, 948598353, 714339444, 608327175, 559355961, 518698520, 947867066, 390428001, 17357277, 623222878, 181295647, 537446540, 606133581, 893071852, 21240809, 95108034, 325683185, 365355410, 260211136, 574860471, 579440856, 38204748, 242444079, 940799629, 156025398, 521184123, 788547013, 420428397, 604085056, 510201445, 909962468, 332968936, 911189791, 158764288, 377263055, 128208220, 938053122, 64577952, 841157029, 239549490, 323938985, 325427224, 743141868, 481411767, 87776447, 878613804, 858183015, 124230851, 521778495, 757040627, 278409576, 920348583, 260557633, 646202408, 57206172, 246021583, 490323949, 615779014, 80682669, 18601416, 347567037, 766931673, 651286018, 780826010, 94895892, 468177546, 690917448, 375121497, 22796954, 549728004, 974248056, 143719192, 623384039, 112534273, 941174608, 430483367, 487346416, 317340849, 960751299, 814190603, 762051684, 972739078, 766061912, 511364179, 274679992, 140985246, 471499324, 307167110, 444547726, 507472719, 984943005, 888707511, 481773852, 883220801, 298856674, 136074326, 486979530, 453687379, 740813125, 108469897, 418917875, 925457555, 350371928, 452045067, 482635759, 279194018, 546472064, 891067936, 458757483, 883450682, 683853022, 474135390, 416016564, 747437721, 906493679, 298963915, 881470902, 57639190, 770067006, 163628554, 711759395, 92530436, 639801380, 483344443, 503718369, 935253987, 402466400, 586748044, 717731762, 286609333, 623561645, 894838625, 459208258, 436830973, 138639314, 119971072, 536488997, 561458695, 235396221, 876019717, 956121628, 942245110, 444135682, 840470650, 289988958, 42970369, 778344260, 848800420, 731494565, 153869406, 662159045, 500353543, 174796997, 475160731, 405348740, 477468304, 256243557, 529580834, 998798759, 367134922, 698492178, 691230507, 587628846, 952785534, 566451056, 68959352, 381994655, 779286906, 1786160, 155850960, 75403530, 890063132, 586165089, 100823460, 823834154, 656767945, 249663328, 173822297, 684502063, 682927312, 678715531, 552772186, 168635202, 164441640, 387157936, 932882700, 276654934, 753042950, 817640618, 618538195, 13029037, 838188294, 807737943, 646418456, 833410522, 513882589, 960245771, 197262146, 97871348, 747406368, 471219755, 524313294, 293635081, 622079985, 509205404, 141176359, 499380544, 344614249, 783235230, 517539624, 563385641, 416505752, 818256291, 204030022, 343986725, 98170219, 845603820, 765021023, 566084679, 831875221, 789262821, 747870690, 776011195, 703691521, 783184206, 179108511, 330853504, 227383395, 531450278, 472312674, 986710033, 809350876, 413876855, 226756856, 322563161, 832935959, 46444555, 150488961, 355139040, 253247634, 541879203, 608589742, 311810141, 319119001, 252546397, 555397090, 486078452, 693378139, 927671286, 575398615, 637301780, 976582982, 632018885, 931723176, 474199717, 648117599, 185752768, 72759537, 627997969, 840126474, 355897678, 117822166, 201188780, 685351748, 963353028, 4059861, 172499839, 982802347, 661564945, 381079975, 989648665, 236525682, 579165695, 613457842, 76921036, 871113011, 627651410, 653925070, 366089313, 918269938, 506370922, 876712359, 640546558, 853142301, 512467999, 965886778, 667794329, 630083847, 153708346, 824581453, 183125529, 451041548, 323288131, 562060983, 193857512, 360206620, 63076360, 24301330, 726892870, 397399734, 558464786, 893953112, 638814685, 465105744, 594368190, 793980872, 817112930, 536580558, 257158526, 186106602, 599296934, 311788999, 589535179, 967185399, 123963242, 346512555, 380406175, 564107650, 766030404, 534818223, 518276646, 955586212, 567472928, 681213575, 354642450, 820036241, 761327286, 692512030, 687213866, 258084845, 161399849, 413137699, 446608490, 863898207, 505389449, 367970895, 655103076, 882938306, 809348304, 171816956, 259992304, 686953056, 75577976, 504265720, 720879799, 678425126, 744512889, 701610250, 562696538, 837399430, 475736857, 965430588, 402845074, 648271557, 949715185, 771616986, 590289081, 403578892, 113698434, 643613239, 360405383, 429991543, 239546703, 992216672, 57469871, 69082183, 407382480, 251221176, 812141741, 754383897, 895160489, 793554691, 443818712, 2735103, 183839984, 514318179, 193642434, 407018443, 60343492, 77439966, 674890659, 278276712, 164616870, 32749541, 795052514, 958420835, 747579999, 483963586, 947692149, 914359219, 50847814, 153081606, 807680343, 334953674, 782194254, 947965079, 365410094, 711124356, 246403107, 936284042, 788714155, 719344805, 254497965, 235700781, 649526125, 675730300, 85988447, 701020297, 343434203, 198375456, 61374516, 585350800, 288823236, 978103583, 627245088, 949602475, 942222891, 139637076, 766895278, 461729511, 834681767, 385313721, 15322476, 637712238, 747674383, 500237647, 526231730, 161309492, 964596195, 5110894, 59198786, 57363410, 208645350, 218428546, 595912932, 89061582, 381662862, 167097035, 822370444, 723400143, 615440375, 4535389, 284073984, 822157874, 995476030, 714671111, 785641993, 568739059, 131817701, 196634723, 680252789, 146354491, 40327405, 182515067, 392170221, 442562396, 310227454, 967123718, 518225822, 814272963, 189045385, 176615819, 299554518, 696767103, 922881319, 648281130, 558629607, 234562592, 72186429, 441108624, 514990411, 890117321, 608899414, 350981853, 226563362, 49670099, 221554162, 781151796, 839686550, 634330047, 911104314, 230361975, 716605015, 698299592, 13318873, 174581726, 663666533, 367075236, 849420958, 941884901, 955734387, 899343970, 45372877, 723784026, 909527537, 717086718, 523143908, 97844470, 942439461, 1263338, 884649575, 267172083, 867882280, 313060906, 261053444, 824776884, 978406015, 812004270, 501706058, 610455271, 925363054, 720815998, 974851266, 5782332, 259988136, 690163452, 177420799, 372316998, 727080982, 298445561, 938273854, 182453301, 793776166, 336265795, 458230341, 175413781, 435278040, 231536838, 263375020, 803958596, 711366154, 972993652, 569105359, 490363803, 21410098, 368651509, 939027651, 790220588, 412759944, 141729526, 947231597, 541840129, 439736991, 558052043, 721150215, 421933493, 136197515, 853195559, 286985228, 20648760, 26681209, 161542425, 289544388, 884820291, 829150043, 947262217, 577233791, 577896006, 270871273, 414190455, 377300499, 725056949, 304663436, 15059013, 841285384, 70703416, 802556975, 436876466, 143637247, 221138198, 635524493, 805753341, 6896647, 581744466, 446367600, 289097954, 868192729, 352325198, 715997388, 428947315, 102053681, 895743605, 297613820, 151651905, 265230501, 454028502, 733684196, 358327060, 687421116, 431580984, 293704839, 525026654, 502292980, 246415969, 492739769, 293547127, 43928554, 115962776, 234591885, 689283186, 973893149, 797932980, 302992938, 386782153, 449234055, 556471768, 796679037, 38405502, 222735421, 160893729, 478073211, 32058795, 236657548, 980864736, 643281455, 566835974, 137409492, 210002841, 659753249, 770544344, 704950971, 334383209, 19149861, 770930516, 129340379, 272045809, 202001829, 298126028, 206196323, 103199798, 177004671, 672075931, 836191206, 420612658, 395351603, 800575458, 909655374, 331701155, 288094477, 314296282, 328090662, 25864309, 696444505, 923075488, 594195789, 365305737, 765237711, 760362036, 323058938, 800238106, 706134050, 636453849, 776892399, 612855423, 256198838, 358845132, 124240080, 915927967, 457944118, 772035673, 957032601, 386529472, 752557159, 159649039, 75123158, 310160526, 205446391, 846360299, 973695237, 500496823, 123987709, 296214527, 751930237, 269304434, 942567713, 476256209, 572656936, 989007724, 122126342, 625058137, 293016526, 272944772, 841804527, 779885081, 946219162, 784633819, 775684020, 55711448, 363935764, 41434359, 950823684, 415287079, 270368147, 949741238, 202755625, 881230258, 729320012, 754651023, 572214826, 244241597, 833193900, 732192978, 342647030, 335882273, 886329464, 721453628, 462660037, 159165971, 918873459, 599313737, 825905066, 520394206, 91417221, 532602663, 534194185, 237381643, 836445816, 314572630, 63793496, 78618410, 48057293, 456308285, 468131833, 656673485, 593683908, 459694664, 989417684, 736539276, 133743532, 714583647, 156615494, 139438610, 323193444, 244021144, 507897221, 984865747, 811912241, 233734571, 186899969, 164167701, 995847581, 403762078, 84314038, 869943221, 511936925, 454334263, 456796335, 801995539, 396997286, 716566022, 131181495, 500019458, 47791594, 225473723, 695011238, 387858212, 163721603, 10777064, 37186973, 802684624, 350814783, 170333909, 302520832, 563717179, 709686318, 24999778, 259840087, 347519670, 966740048, 5435927, 817684961, 144020, 886012258, 845024341, 988719843, 135245784, 84912607, 217022850, 677797951, 923425140, 268801899, 780356750, 35258239, 359607805, 999587112, 381987218, 905161064, 671059228, 450134802, 619592077, 665901673, 699610246, 829693129, 616405672, 84628599, 577765522, 657134721, 30196240, 360990309, 519686703, 50513448, 57985291, 984249680, 798222354, 114801673, 857305020, 466481072, 574433222, 684260958, 50012229, 236002495, 335024601, 517025076, 455619471, 868490876, 256640314, 942073728, 940352281, 964038957, 37128183, 454940862, 259408365, 130944640, 864031447, 752453001, 482044459, 495527918, 568600161, 679625566, 671051133, 660851013, 658664482, 84549593, 735961486, 203322105, 59380905, 39750389, 415796171, 917569819, 368340862, 155112664, 533371199, 327174563, 3807570, 864017883, 480804777, 623962356, 38442393, 246722596, 596919705, 780439950, 248773269, 441910421, 248190803, 682628250, 938212841, 90066934, 14690952, 122879744, 628836167, 558529735, 137750129, 797018743, 64160339, 626828422, 723396681, 367541803, 170648405, 513737451, 217753559, 537682200, 318875511, 698156193, 519029902, 234932292, 606192404, 504347626, 482651974, 948583313, 918959309, 112614557, 87919851, 684375903, 848061127, 916393938, 893444543, 201820985, 443595233, 308628674, 745109685, 656912419, 280620439, 320031775, 981936022, 465622477, 856504971, 985552435, 555426793, 836187995, 23035785, 196989669, 678107093, 342949517, 700439214, 755370269, 84023196, 442140319, 463010072, 192923867, 690713745, 17090546, 901267027, 797364799, 282563537, 247767514, 815944479, 484265933, 299298853, 708460525, 471042831, 729121270, 770172376, 135447745, 291572174, 639019142, 54535425, 253778100, 395198494, 128429195, 601594574, 923971090, 600055223, 817308417, 791102594, 68174056, 895073840, 570986485, 221240489, 649746089, 689366928, 827745715, 13472021, 278679954, 127962242, 14627911, 367928010, 121671545, 403449912, 537051197, 737818008, 472917424, 683587181, 55148604, 416658242, 620209340, 348648573, 80952680, 52913071, 47862966, 145520356, 172954995, 77273009, 16987604, 197126086, 452495937, 170424602, 922011164, 74432601, 125517312, 559737151, 655509516, 547823157, 818717459, 663072098, 491615706, 443731819, 706174917, 967265838, 407488272, 549230340, 382955792, 227282821, 454771210, 239947686, 800820598, 765005150, 583010882, 13255650, 31222229, 888159866, 145179778, 432921691, 888053634, 383408273, 317067420, 160258817, 229235945, 363727504, 754041107, 322784557, 463563292, 618297522, 870704644, 264448954, 505085737, 464553552, 823854402, 216951830, 319807751, 31764243, 284405007, 405047074, 259090092, 294152949, 9291378, 993700419, 466045775, 784682147, 94579745, 706284283, 841328526, 772182411, 793988538, 108397195, 295536442, 104463687, 195958852, 76297568, 199338960, 70453647, 214876612, 924366526, 789899193, 584868186, 226862463, 136818109, 539709506, 750966860, 191509832, 291014652, 588282798, 884096191, 450711041, 330564535, 629161822, 156246887, 748929708, 923667375, 210703875, 693922569, 603474802, 663361652, 631073446, 976574011, 88542706, 108154899, 378011049, 723243503, 596258594, 29549033, 621224366, 331030477, 248642435, 472073727, 951552255, 976267491, 190102361, 37221068, 332893185, 638127746, 647133048, 736019700, 822440719, 799626834, 828507741, 6753707, 871181422, 579343564, 727145236, 929376210, 189155280, 563092205, 294748611, 445328002, 989020113, 48904038, 48316242, 539277753, 568279519, 300946712, 464482394, 752636284, 464736369, 624155118, 866852071, 334460192, 756380775, 955022933, 101842090, 295068338, 812933078, 451314190, 657810746, 371321381, 730164031, 133545749, 737882383, 502732386, 557766606, 29389080, 820793505, 695320238, 795288910, 476558346, 461157803, 889008381, 191081782, 472132340, 269217736, 370975769, 572493869, 541272146, 408721839, 960893713, 707049609, 442795644, 385517023, 538621082, 976823095, 394446050, 778312802, 866421369, 809999223, 337451712, 796394239, 652606504, 699670055, 377510084, 143850946, 376768297, 592574900, 773460314, 6167238, 165093924, 417135800, 219060018, 70543606, 860932546, 763900940, 646081802, 377774890, 914577657, 241677641, 705475107, 449054756, 648613488, 1435590, 151066996, 112280133, 499930755, 166142716, 86122425, 601990973, 935583584, 52151185, 746353299, 16780408, 187201434, 720036190, 341923510, 658246150, 95424532, 11720408, 38210620, 815406587, 439806140, 412031864, 184569811, 432154335, 181674085, 747321713, 613021535, 553524284, 702014839, 237517893, 237867488, 135837561, 467384549, 861867607, 778697518, 620647420, 649280820, 412607484, 141370338, 234403158, 959260622, 195639739, 763380132, 33192252, 610547185, 81242125, 685321373, 616451365, 842953602, 338975158, 861370534, 517369247, 18139823, 346400870, 541658079, 77297460, 590977709, 590165288, 784697282, 864802885, 29502767, 138801974, 579176588, 96482318, 37098948, 151662059, 759854413, 991054578, 424486530, 493478725, 388932607, 949160996, 687791600, 301516442, 83588252, 723778784, 371670383, 936240683, 516735604, 304203875, 642820345, 773073856, 586584692, 260846101, 165011589, 632094616, 224551361, 926387446, 208555573, 485139469, 556640581, 791601230, 471298188, 147982207, 990366986, 612781878, 704217723, 985737221, 209751873, 40124159, 317811212, 737003441, 529465132, 822003120, 41673945, 931882865, 962248260, 890757231, 979506631, 535618168, 317907351, 4022152, 893748153, 994618826, 723803914, 972288929, 732856611, 948029475, 13945475, 920399885, 848421975, 147610798, 784485968, 690434757, 580524584, 309612657, 789668079, 671748652, 321759163, 392025462, 625462791, 406856154, 293140678, 140629679, 124081788, 341494490, 236848384, 621837846, 377415656, 792850210, 98968382, 383099165, 809222384, 74983616, 163923008, 815175258, 432399169, 49422462, 486884299, 289798743, 190498771, 705577925, 13113274, 599308223, 315140422, 357277662, 61935659, 163291786, 819221546, 903769273, 384476019, 647161085, 649474911, 556096140, 662278332, 85945293, 956994936, 101317261, 680439248, 496058598, 365118142, 185282544, 69538489, 972140409, 266315000, 430449819, 145023896, 603143559, 985069269, 877943793, 699931364, 803258009, 250337747, 957033609, 118069550, 234103002, 964855277, 373206632, 519457508, 712910610, 158201760, 978372250, 414605102, 255054271, 509554042, 371743461, 452150355, 647042875, 982126717, 447901475, 599010945, 655531088, 182036908, 207761285, 712899459, 622852930, 5874130, 861270093, 312861817, 122234127, 779559744, 894286855, 781470733, 94179285, 150979176, 370046922, 892710532, 889721039, 927315846, 946389662, 357470350, 11828945, 448715818, 814108967, 370841616, 413603221, 836172127, 361016844, 179120167, 585422832, 249564322, 674860533, 672406772, 433141074, 40548674, 464930232, 300361447, 627977456, 620656053, 423071844, 978965521, 740786581, 683175689, 413717554, 774503461, 84175989, 206579116, 940732480, 589146163, 960635076, 713520310, 551245300, 525807378, 508605648, 152820818, 413541578, 252040971, 506572863, 946278945, 514903147, 875076952, 824985029, 310063422, 713633070, 924370464, 671939754, 24723906, 280377471, 384161831, 586982478, 692574776, 635154439, 72332856, 122700695, 531499439, 164598902, 308914778, 80084583, 803928654, 987766908, 55321807, 299132734, 66150538, 190105544, 799371221, 644785891, 573499379, 558549719, 889900925, 170337946, 963707499, 325576110, 147023772, 592146735, 131043638, 516982296, 694797976, 712504399, 471430691, 439602945, 2046719, 514925631, 109536051, 271187850, 85474795, 768562194, 614952376, 970202901, 507814207, 922601928, 377993290, 707894805, 71582405, 717339219, 709467898, 778075311, 396127366, 510077112, 138828354, 726074238, 562405936, 685054374, 816793667, 618557789, 638052386, 602102340, 666018842, 704151867, 53288736, 392736461, 941793700, 527244743, 958125676, 351558507, 828458977, 334127564, 990269853, 597818194, 978370223, 975527228, 500320807, 354654063, 22910802, 51791067, 229586527, 947672919, 90411141, 50244760, 905038893, 622970558, 685898633, 256775045, 178348788, 301619220, 980480471, 914111020, 25395270, 901805739, 735111226, 309203717, 232520973, 509184495, 271560155, 106027011, 268671561, 319578411, 563301430, 616933509, 820215398, 331781153, 372652746, 23462585, 326144691, 429406752, 160513735, 64634227, 90333096, 568048911, 780417907, 208288366, 183054536, 229516956, 949456347, 883757266, 299861689, 597200428, 969306223, 586009689, 840663529, 121625456, 781368927, 772437622, 771869852, 549373657, 163159129, 931901689, 87116740, 110760280, 903260464, 996602534, 355176235, 292405372, 421054229, 272304686, 18404930, 600931412, 161785193, 955407696, 480551321, 168246310, 534933166, 286023328, 809935402, 131964779, 319749226, 354538274, 334613702, 576615298, 618201805, 913133239, 981448944, 827120418, 80735658, 719043454, 104698179, 580769015, 272890960, 925916018, 580607073, 467229360, 103487613, 153075320, 321041646, 136068703, 682803764, 425713964, 212394427, 246723589, 405541520, 528694802, 61255393, 238681809, 945524179, 264473533, 942277877, 112164694, 245973972, 960153304, 79667651, 312098251, 379049847, 311532766, 623885589, 812776679, 790601172, 583050426, 481909168, 848381558, 262139604, 705141234, 358568593, 612095536, 465387259, 213226659, 120455585, 240346258, 290732954, 474317137, 124579877, 622363635, 527356195, 340893998, 30896816, 592241140, 34260535, 206615504, 469160833, 318047781, 765765085, 277737296, 604462594, 389782686, 857428012, 487795444, 708330646, 519058819, 340097373, 157389279, 574939217, 691891866, 616907659, 438953960, 906329024, 407381283, 971902642, 28723098, 392797140, 466680764, 242570473, 292518960, 42136943, 251457024, 439631637, 701490333, 873415279, 228214210, 818672486, 967244666, 268812135, 792553028, 679488793, 193763246, 512224809, 85794961, 292064929, 73788602, 672954857, 299880468, 448018068, 966287559, 443927382, 50622800, 831985608, 611244838, 825095607, 555488224, 653189415, 559386888, 219864079, 914195374, 495959951, 777227430, 258216723, 356924003, 870477514, 4147574, 703962204, 57575210, 560928579, 199325727, 719472591, 279458981, 774657428, 44983295, 154386521, 805096781, 711771319, 318482279, 388108417, 234516647, 229007109, 739215688, 225967195, 171750730, 138036578, 544865967, 701474709, 834900253, 142782086, 694786944, 348107804, 845108134, 408858377, 666421351, 794856891, 477797504, 495500750, 244416226, 406397918, 754004826, 251577716, 926486257, 981591889, 570425860, 314859948, 648637881, 338459875, 208129074, 243726471, 951919174, 438339300, 604489063, 664462113, 929125078, 723329609, 823803012, 614928354, 800713874, 416407607, 491718574, 54546828, 700191345, 871182638, 178072828, 524076943, 842523848, 719642172, 203061961, 884081672, 995245769, 748401078, 781905372, 440525571, 657271066, 59333597, 817318253, 927007199, 852263199, 865796322, 434399361, 61594608, 758769764, 549428584, 879213544, 495553101, 827311255, 596963246, 575112798, 695327016, 626452206, 209141191, 257505326, 832728592, 812250308, 785758255, 735547081, 542239199, 300228327, 89491571, 493877458, 628072312, 665155748, 265204461, 251484193, 174094070, 12416855, 992447959, 9668114, 449841417, 147512083, 786593964, 836764560, 606815683, 214681290, 260789267, 458426546, 323277775, 606294226, 815225519, 732683721, 841352409, 607851697, 947534708, 949094001, 425407946, 689420719, 368248541, 437949995, 558999656, 217000586, 302466204, 366822266, 74478680, 113217156, 825357941, 128583841, 21614877, 419191234, 87110509, 490276037, 990946615, 135227744, 41716871, 260119359, 199630377, 510880521, 553500207, 62394922, 37953895, 626858462, 852174787, 504480156, 75786819, 808743096, 272356556, 419066623, 471048445, 851633682, 724100585, 260998995, 29972169, 496511220, 177228626, 137674391, 572111597, 305950805, 79900595, 200728837, 728108813, 42289260, 698532674, 169499943, 265957640, 840013927, 88713291, 164751461, 602834022, 173903781, 264449792, 63114502, 239225303, 256678659, 360002315, 607245243, 334630233, 248513041, 107441414, 388303532, 851417911, 524410987, 267100884, 662684284, 253883345, 234247365, 713460389, 839829893, 580479377, 177680349, 165849066, 903763568, 205522814, 995240354, 603974700, 876279673, 334226456, 246774340, 138328132, 361319680, 313957442, 658182659, 488655947, 210795360, 506507993, 816649091, 989056020, 696917222, 61732206, 507053481, 487207136, 626576235, 578644914, 229560364, 563944702, 374883104, 35983551, 296480853, 203522031, 541583228, 664192074, 853678678, 541130049, 430764602, 401914271, 639533119, 823541042, 72509455, 755005082, 231030849, 443978522, 629790268, 480422001, 697598521, 879838300, 803707128, 732345658, 798167860, 590856266, 303420269, 662119230, 410228688, 528712913, 169138084, 360957307, 475134900, 147345772, 905052200, 84448068, 357389902, 214901184, 720242103, 545396203, 708990648, 219889222, 45893246, 553437284, 470924522, 796073551, 203996723, 121140755, 188890003, 4142499, 377756425, 368703433, 449662382, 535327182, 757413629, 892627101, 680019547, 170821632, 227361650, 191244423, 803281418, 338223895, 172002098, 962292084, 228558360, 537013983, 327413067, 716973815, 110175353, 442053796, 864078570, 185138215, 367270324, 900394510, 621975054, 251156044, 414836560, 519708597, 479310990, 718257798, 902317407, 449900617, 574346075, 856676360, 806281824, 802513119, 671706990, 384941124, 748543897, 370276950, 359158515, 499752097, 904013769, 666384577, 643759881, 410444520, 47701079, 972623730, 202969015, 540646069, 578712086, 293761388, 247672927, 346692901, 967704511, 632683587, 237356212, 248092729, 607707615, 940068818, 681169388, 71261436, 61510979, 588379415, 583429177, 932268126, 330113183, 712368458, 454924715, 443972424, 435698773, 495374173, 183388466, 923857981, 921318496, 425927840, 367853449, 647356988, 508336863, 362830214, 590754236, 12760413, 802320977, 835740095, 5798628, 617799568, 873934124, 671732426, 23219728, 707951145, 85739190, 937529496, 428666543, 998309319, 111994949, 168761513, 788585027, 615678140, 233190327, 175889868, 423307399, 771309886, 917870088, 270049094, 560661282, 542209625, 434366949, 91017084, 640056822, 826099799, 852584617, 120168303, 212353606, 857036993, 910247801, 960185257, 530253572, 965934027, 265557771, 126708472, 43441872, 363607492, 599391029, 219328072, 960828676, 923529601, 102158639, 712584577, 931458367, 564117813, 547222531, 361163028, 116484471, 43777149, 371454194, 35815872, 159442979, 981608531, 829953163, 574785460, 662277551, 85391370, 124286142, 938405674, 631763338, 703217301, 121990175, 665929992, 407281860, 805891000, 821407120, 925533583, 808418756, 370322279, 439513259, 408857517, 175698417, 231049650, 622449943, 637555538, 652971866, 610104770, 506640777, 947251929, 338103524, 511362, 629706813, 188336056, 288783855, 743642664, 884298922, 257049038, 426039237, 927744822, 186903220, 678943390, 464553704, 509999856, 932761678, 312761517, 239025192, 824434318, 445746909, 425417278, 109360400, 106106243, 710817334, 206363914, 726966397, 267391589, 518989119, 478434213, 63210822, 829896691, 799092820, 295879300, 175915166, 717297378, 123895279, 20587468, 382035966, 225378202, 254985189, 611424713, 594936924, 311225336, 162909971, 967233873, 800122091, 990269741, 58021172, 322269161, 297015072, 819672431, 302098602, 825681125, 474857584, 955308151, 603164419, 535044397, 557310719, 185532464, 311191685, 312637329, 714448362, 258826193, 127724227, 629658197, 290710252, 173151677, 364288771, 339373563, 835318173, 930369189, 815445364, 363477242, 78883409, 327670618, 666931253, 302231554, 334331989, 252111400, 723408787, 503258066, 695192752, 940455820, 124414756, 229779294, 273424302, 926968841, 692222033, 887468135, 276285795, 634834643, 895617495, 940282167, 305256531, 230183223, 495013763, 23057753, 994671314, 873538770, 938989418, 407112357, 127112713, 784420457, 607757640, 720595820, 319190995, 55491426, 97539998, 944046199, 436927955, 774769789, 856226780, 911627308, 271124307, 598464183, 506434463, 726829438, 705895810, 674038346, 491354653, 519592096, 856115300, 299120090, 605318498, 59906822, 359721473, 838086132, 484894502, 955679926, 10792951, 664722157, 747409012, 85940043, 838632970, 358364628, 995457080, 670214042, 203391773, 867591909, 999845390, 515092269, 4501535, 865888783, 29221103, 74746555, 315869476, 845703539, 745278300, 378518707, 87940081, 838458933, 703285150, 58433905, 447039498, 724559840, 74179083, 555401261, 829216052, 269943439, 983513386, 798256744, 852394709, 313052845, 838677507, 314630313, 263645940, 504037234, 822611887, 660483678, 384991109, 529498681, 730187641, 249291788, 516767887, 954633829, 476600447, 210507989, 386279211, 488985657, 630312367, 580841723, 737512774, 699400423, 656875369, 98684996, 329137614, 939255563, 992634705, 35176723, 337696023, 940583056, 469621876, 100030648, 769820885, 43548296, 751274231, 128895134, 183134759, 170887303, 61867468, 936626787, 717191791, 425381834, 568483780, 178335105, 237929799, 920996128, 941055509, 106066547, 122868396, 688949522, 337212965, 304817561, 755685040, 870049549, 560895424, 778944635, 995958345, 910103133, 169110419, 813626695, 873162722, 405869683, 802185229, 223196111, 446558191, 18412112, 139468418, 48541116, 268961614, 817159834, 347203209, 708554234, 439077981, 408746175, 972122408, 961693160, 211169034, 866284927, 97006530, 171303210, 938257631, 932128275, 240121395, 258501405, 516642613, 185965807, 210936109, 802523070, 625314438, 692990710, 492372693, 542666364, 477237720, 890835272, 909971702, 868799771, 402221765, 738329591, 778115486, 979590564, 206550729, 751903169, 121854905, 554279688, 81848237, 843957114, 709849615, 525691964, 409527302, 491626432, 906578671, 329675424, 289650006, 999010475, 240651192, 29210888, 519644047, 835960901, 490548346, 404772596, 768053573, 810454264, 945666388, 972469850, 489634130, 656969260, 255550033, 207191175, 186354230, 83623181, 181214333, 34768479, 573085154, 637707373, 204340778, 453610774, 337632, 318841691, 765880968, 539580546, 214809728, 92011418, 942538481, 561066421, 900489657, 240224853, 382266133, 666617037, 821108303, 559476537, 112835552, 535045737, 192246888, 812681349, 706336334, 198871183, 637913, 395999239, 61770931, 271489831, 165160669, 498461872, 568660655, 801639011, 312795016, 381065745, 732079368, 343064834, 307472349, 976854065, 47732711, 206511037, 893883103, 823190107, 578757432, 118811390, 800284646, 326964924, 168892788, 396684336, 908534614, 391689, 931545438, 442423626, 493853075, 65408443, 988140568, 736977222, 205956927, 270501731, 921702185, 676242651, 827136236, 76800435, 373190895, 536494098, 159906243, 138984225, 860946360, 352744822, 840343437, 237060603, 498639338, 357763429, 653666279, 340380982, 763067734, 610942277, 525504972, 984082706, 247068103, 552921204, 692906741, 83181330, 507647063, 396301314, 947899474, 355963760, 173848960, 656285224, 627176766, 400021143, 411150114, 98173099, 468108308, 710268090, 176433101, 147648996, 773196714, 715519893, 588194699, 815296376, 257448144, 92320713, 902704951, 786585216, 791636208, 49457423, 481194667, 732561934, 809479759, 923333106, 571231040, 180375019, 599562090, 612899045, 36380462, 606525149, 717554401, 473756109, 41566706, 36492677, 263756798, 194992606, 519960834, 966242527, 358465785, 462913834, 807967917, 605344068, 287119870, 728046568, 665224079, 682408123, 333748, 214057565, 993207518, 224906297, 660695974, 607073539, 269148491, 378358213, 966584667, 580535955, 685061596, 866671110, 775683715, 401104641, 529300465, 355607223, 982734938, 858400042, 820775290, 140841612, 207186331, 98531073, 543701828, 106245018, 64524671, 551701839, 756282438, 548743864, 952860063, 579215204, 184593368, 997892682, 891423292, 632178103, 292866393, 758847910, 682392063, 614516606, 916119956, 731009859, 908766927, 471945864, 828657719, 652777750, 25167794, 48841336, 62594881, 471981935, 853843195, 399690407, 150741170, 853530215, 327485680, 976763052, 10346096, 212134850, 539909818, 713180895, 660809046, 924406283, 91675219, 170981553, 948211245, 921412439, 741349418, 115597700, 138006537, 312092028, 551497983, 410362848, 600946315, 48124934, 527354269, 559980919, 610182961, 938503462, 825122133, 173144757, 361071747, 478238332, 816311151, 208823258, 323310947, 506857393, 895014544, 493797972, 893535974, 872491961, 373438720, 975764278, 392999953, 665573279, 46721522, 439464920, 331159722, 454518514, 227843318, 870537626, 693238698, 168584488, 560254142, 621112987, 259393313, 124888119, 304498238, 907640199, 883990384, 957199647, 812669282, 938050204, 519886056, 21209837, 540013759, 121978330, 35982748, 888422754, 186853903, 425440894, 49892696, 540888049, 38257236, 942418302, 120412328, 886981815, 89241980, 417681200, 205078757, 63628173, 921433104, 718493300, 229507024, 721161891, 419782850, 68144055, 494632387, 525686752, 421814444, 750056365, 820154571, 363272794, 953443007, 794474255, 258716907, 639089542, 125107218, 62938142, 791537582, 344777058, 646968731, 779931364, 990733799, 959528511, 584422598, 486345387, 826840712, 456536853, 357133209, 757611776, 706955880, 224483263, 841895618, 777001649, 885145523, 770135470, 491035409, 86511551, 285270706, 299487474, 427930872, 77322157, 109382534, 112588727, 242669735, 189913217, 472226301, 702459823, 491409060, 109655230, 696307217, 511992694, 782349144, 534749868, 551722504, 728079129, 786839152, 676856499, 509538633, 457275639, 348465472, 405422597, 8819353, 667636116, 432350369, 150392382, 896820954, 389545445, 191983468, 989989119, 569201474, 671970347, 629476050, 608695815, 15338977, 136815589, 159254470, 178838285, 791583828, 590907458, 348568577, 534346048, 621359210, 549002867, 1938580, 151455150, 449027472, 356642664, 236324145, 234878706, 953746686, 398327458, 394587673, 281650301, 33606803, 836760248, 401456721, 140659117, 476034460, 390881461, 424677910, 105026913, 733810136, 742527042, 679455939, 576797607, 135954964, 961606961, 231731304, 219905941, 1058828, 669402430, 913113436, 313730101, 549545367, 75336340, 295804686, 354953512, 398847511, 688725133, 206031730, 700703882, 457159005, 358940134, 553280749, 732045089, 796504466, 281894735, 368001233, 329981543, 914164576, 841846014, 807928641, 50238348, 850138948, 16743241, 840531294, 552330386, 413363225, 865994924, 805642132, 410893671, 498128039, 431655363, 382112672, 883954045, 630509883, 60134076, 680592654, 51103743, 927762944, 382332025, 273945973, 52940397, 973603868, 511194391, 814533484, 755319943, 41837114, 344968865, 19398431, 893403410, 842468970, 399819669, 151408626, 364558402, 456119723, 399826496, 347998898, 842866569, 26733861, 158861487, 626227702, 126497195, 537597050, 32138164, 505972555, 394032543, 863244631, 105323022, 654005528, 397655603, 714618025, 881344031, 683794902, 186628357, 660257079, 851631773, 741149053, 891611672, 891701979, 415162899, 968881176, 715845222, 505699835, 604849139, 40504459, 587096050, 887069461, 40588576, 687963544, 98985787, 532764544, 313085911, 236987932, 808614181, 581333359, 705833908, 769846804, 187050504, 205755125, 373387526, 306808327, 778713872, 950551052, 885878152, 448355679, 705726775, 139075014, 23479784, 252106298, 549480861, 965920215, 554565212, 400121103, 152405009, 642091199, 694091698, 874496852, 50091676, 37609696, 936409549, 32820527, 983010012, 833990684, 408046954, 293192475, 599262393, 752141513, 98965758, 42542345, 197921923, 391681736, 488406896, 868329895, 474882858, 267149227, 989944204, 671503456, 378239212, 308268799, 398785086, 183218495, 820934784, 100491804, 872109953, 124998786, 299342720, 113522648, 949263951, 519782728, 97523072, 412046325, 806139221, 417559225, 586469487, 501604763, 275899951, 109768267, 641016248, 449769416, 788285674, 984470413, 337367904, 164099710, 209068577, 470160020, 872700797, 786410042, 109007956, 425992219, 224573886, 92923906, 359450462, 646082370, 352595533, 743196659, 497459440, 638537723, 746979996, 600381031, 48768681, 102184814, 790706873, 723808664, 18147439, 449150209, 605825706, 910360533, 893503828, 379705763, 345333762, 134806421, 842536743, 474857927, 235483665, 690233474, 524432782, 442279553, 726169834, 411269921, 535904169, 367320489, 437406941, 366632419, 112232707, 271553318, 832084205, 262362515, 383953162, 219549161, 126869155, 624374689, 163701912, 921810022, 980403784, 272163046, 971909424, 177482058, 314117146, 195654538, 670972632, 733123147, 827930785, 867898901, 744553801, 955521273, 223414185, 853737406, 810872949, 960122528, 330383948, 268646588, 744673071, 570584218, 536535810, 109898227, 143000330, 465095441, 586579170, 594652765, 44666, 855877143, 543308345, 271408031, 755344408, 852344114, 469439231, 69857010, 212910562, 941147546, 200898430, 416614585, 372421766, 561173708, 686718707, 403078373, 419384757, 367087977, 761879671, 75932494, 927741862, 406649552, 947518835, 861654610, 779073489, 358975404, 29152207, 641946415, 986372723, 557384437, 668886314, 788640611, 439009536, 64254141, 196438789, 204461970, 64486644, 133031564, 166262418, 670190051, 641448531, 923254823, 636324259, 291575530, 93383785, 396271716, 819619087, 742397222, 503746639, 501600711, 541581055, 214027862, 773228157, 136790535, 159086420, 735390919, 118103633, 802133644, 192284905, 412455880, 901851904, 29679303, 550277751, 218667118, 270569006, 261318747, 990787576, 914158894, 362992969, 985164968, 331950381, 728031376, 703057972, 454212481, 428559096, 522911774, 468309346, 115645336, 977589272, 10336883, 829084929, 271585289, 581407634, 830539066, 324309536, 213786246, 920121081, 453178849, 25210498, 36954007, 758785371, 854756596, 480196043, 54943868, 260631644, 550905479, 675506156, 90519454, 321164726, 534964133, 144424630, 122364996, 444123419, 343226165, 151150470, 490794351, 759771637, 754197492, 630921266, 884431877, 218999854, 110482964, 531355164, 980807592, 517121448, 873264407, 1146887, 642568702, 256784084, 581599668, 7012245, 310123660, 308846321, 877050673, 763473683, 249739195, 807695486, 676228092, 266049868, 981295164, 532780586, 192608524, 602152388, 697916169, 71229713, 100506425, 742068398, 932639508, 848200036, 984379230, 885747231, 509393013, 76551570, 608992716, 337267433, 204397111, 212617042, 828484378, 315713416, 930476415, 841175850, 687883491, 404956103, 802813270, 735840720, 169289521, 922416838, 571468720, 566471802, 434814130, 473814277, 334433213, 274192504, 544745374, 619773568, 970051307, 410622130, 889459191, 358697455, 550782106, 586965242, 861183470, 196257234, 219948986, 306055076, 788372749, 440064276, 913523843, 73744758, 466606835, 90308050, 694358941, 577150815, 209897341, 461410703, 231955425, 261165273, 736187496, 989821195, 917259537, 377431842, 261130934, 719351757, 350123996, 926946316, 775358332, 357965929, 570403524, 283557144, 447523811, 753242628, 61728311, 742582798, 962331490, 742551609, 418041159, 162482438, 673073888, 107715803, 626095671, 704334639, 321388446, 753563845, 414713617, 827529440, 824912029, 683562387, 136878284, 11510812, 660045648, 45891039, 246639104, 317458649, 556197695, 505650520, 389349604, 296848316, 174838730, 887408705, 268937148, 738936828, 570133968, 459832078, 462584806, 777566091, 71685968, 657971191, 649085136, 258708467, 431534084, 879575233, 84130755, 146901308, 830061062, 495797937, 304081492, 861843335, 677034838, 922687465, 753056637, 448745130, 933461298, 534326774, 851855105, 573603093, 844114293, 936148651, 805074892, 750199951, 978625673, 568900677, 864441089, 840861459, 489480797, 400701216, 78362539, 491586308, 948690402, 885035435, 577099709, 254216414, 432755270, 781673091, 788072217, 263411790, 797691866, 112261027, 654714894, 441504144, 183530300, 415120900, 806596586, 73927282, 662001549, 615306309, 904416802, 582858188, 338908326, 538935277, 764652324, 954499742, 112880704, 657591784, 687328667, 562922316, 703014205, 851125620, 169484797, 359111448, 816833141, 424857692, 293875052, 308501846, 612097047, 477895578, 50768061, 577850157, 962162577, 395913732, 798972668, 799780350, 397425624, 494773720, 427138629, 145482532, 647900138, 381009158, 456668191, 510413469, 30512419, 296236617, 52548583, 153953229, 294100490, 299776585, 140938895, 440628378, 845202378, 426416359, 475443274, 238642028, 887061899, 816338632, 197455511, 366428039, 406528051, 375155638, 219958838, 728525067, 918522103, 455313712, 670106162, 235538265, 408232930, 873116167, 471416661, 930112875, 858448437, 41692105, 259382134, 847534835, 545610227, 981857861, 582668580, 612104512, 575492929, 468114135, 787628759, 9509122, 22129873, 427768356, 911132921, 374302327, 730128376, 94386000, 803896732, 513884760, 785738778, 332480044, 397385326, 489015571, 218880715, 658084537, 361632281, 840809429, 713983545, 436184121, 995913710, 75919028, 72860976, 233891793, 448639729, 323578509, 906959519, 624071620, 652350603, 268439607, 589267355, 764562682, 324196195, 825422449, 418638820, 174479301, 990008205, 574757855, 785284392, 455024191, 866569093, 391532445, 207774661, 496774921, 563436992, 114073011, 481606803, 698977464, 899398620, 559379579, 581320971, 894667201, 223292444, 87752078, 813575555, 550502064, 287681276, 126373172, 758689867, 197357147, 811815262, 517931746, 950977861, 383149943, 605336292, 445377028, 416518085, 180782952, 29013359, 458246738, 119334439, 981434996, 138738842, 90953733, 938667068, 199797249, 686426394, 907567515, 1212337, 86287741, 939364341, 81523057, 879724144, 55199212, 746365812, 139694078, 156850072, 661071564, 31682201, 943865640, 884107215, 131449523, 68816844, 906430558, 356853224, 823582454, 439792733, 316585155, 327178429, 658863596, 985482384, 639501306, 160331660, 158431337, 919427826, 904304762, 562021574, 675489906, 70269641, 578714107, 154287003, 982148952, 30886988, 80474153, 134604677, 388122331, 213452210, 701948642, 355409071, 37457786, 734866150, 756515475, 67547084, 637661401, 970336415, 443753037, 563618635, 454007321, 372363391, 27821413, 814976617, 404329971, 929836450, 222111800, 934199347, 416621106, 501015126, 778359730, 42557676, 115050871, 767018049, 835124210, 956941775, 220668397, 771532515, 312187414, 126346062, 963204177, 136671614, 216055911, 528729563, 448561557, 862343828, 481377308, 20850733, 812272968, 572364378, 610384357, 823153725, 768531631, 251895614, 890758341, 66304123, 724715272, 508338796, 320382405, 629005018, 290672542, 55615869, 473700499, 524221453, 614591122, 372770414, 92948568, 950131747, 311177668, 70705001, 915209198, 766164670, 255989588, 512440286, 995329555, 866429485, 98871077, 861754254, 246195325, 709408796, 641714255, 818270382, 590967787, 52439825, 879794734, 438546529, 189966548, 836638203, 340451222, 913290230, 808722190, 909695751, 816124612, 443693066, 955019224, 689858329, 493812997, 843629699, 665030541, 970226429, 369533877, 97890419, 605412560, 386807284, 101081313, 553933259, 276032072, 936470313, 490538289, 32305342, 9899004, 247880693, 138466094, 265218092, 504734048, 921190964, 286678107, 170923857, 643526906, 534000139, 973563404, 161841974, 417765136, 487359084, 783877050, 41256003, 845735991, 307636752, 926663913, 459207612, 906260507, 123684378, 939584408, 412720758, 114546097, 395515548, 304211419, 561444109, 565496732, 443910110, 538408043, 504059861, 420343778, 889453326, 303378342, 733432566, 555747085, 806095946, 96041868, 511497585, 28147311, 573752465, 858575129, 469712873, 963823372, 438426095, 354816158, 217104616, 846537565, 651979345, 539102842, 456415005, 911516361, 814266839, 394150643, 143829994, 82208783, 833009760, 258768073, 658773108, 796461312, 821348366, 222985529, 731837581, 347339962, 245438983, 779352851, 748701718, 946224989, 332558181, 845749905, 459086749, 501991584, 615885927, 528758888, 75642738, 250375325, 984171514, 102641189, 377614016, 108395588, 533613877, 700923828, 129149551, 123758537, 686900812, 977704084, 183658537, 551236600, 852268038, 264733510, 292425107, 743995682, 797020148, 968296002, 171124939, 221847157, 45794774, 604719755, 724705461, 134052059, 545632550, 910719883, 586471547, 941201348, 987372921, 784687042, 228905971, 926108314, 927472604, 818131029, 414497930, 135615979, 650100166, 164037768, 7024485, 316416350, 765790771, 985997852, 569435878, 532107754, 524879181, 795814542, 679735708, 415349945, 8947973, 242280980, 134255838, 376003245, 934809638, 617572638, 246416611, 572301197, 571546007, 63350088, 376165866, 855510917, 977987107, 153880895, 732071460, 921557883, 279677197, 629455825, 482808960, 387259101, 74026728, 926339642, 362934382, 381931452, 195159172, 84703399, 530433335, 902458365, 745467953, 925461323, 990741763, 446603826, 639654246, 139635649, 295001294, 719702157, 444388713, 993618633, 419590037, 373753309, 561302817, 369949925, 13770094, 820949768, 385794305, 606614251, 137693865, 719990166, 10733302, 829308145, 814912377, 124615710, 224365504, 302075752, 540744920, 705438469, 61652132, 93453652, 238681764, 404123638, 555478182, 3634714, 872105051, 239574978, 18978851, 264283171, 715075835, 373634371, 263962694, 332543269, 671054507, 488546246, 249466061, 945030496, 366208904, 205512407, 632174715, 842447180, 124885502, 195378658, 66090834, 237378972, 13638485, 305545345, 432438614, 421557915, 138186154, 325837215, 668571403, 965882200, 904160121, 585974762, 430503864, 721424509, 390578342, 427895619, 203649648, 860211386, 416120264, 156035330, 121490836, 540295655, 894099743, 28638469, 532381890, 360998305, 192650351, 38910980, 10308504, 937591128, 718266096, 657369867, 880678035, 934364327, 575877159, 234163433, 70989642, 378611467, 69245638, 719706512, 404543830, 982156849, 658561408, 617810398, 730718070, 806026795, 166992309, 201171726, 782105103, 496017753, 515354344, 321719181, 427334951, 109750667, 595098906, 234241177, 72571315, 799209364, 297931113, 262279905, 706334248, 126356922, 805224689, 173370339, 276776095, 111821170, 969633721, 432202034, 638906844, 89449467, 272700449, 529127874, 965538145, 847986622, 337512871, 789478163, 163699653, 307846917, 453103450, 527526682, 177424974, 887986206, 656503894, 528162443, 672015042, 477331702, 89726170, 791819600, 300095431, 283232652, 998139277, 943260964, 865703715, 470842652, 891739632, 974294322, 324510224, 379873133, 2186748, 173870273, 55236594, 863356930, 472012233, 504739700, 934246887, 353273481, 628115671, 667561009, 860343164, 11937496, 741961478, 600132637, 68997121, 376575210, 459371245, 573718455, 323689554, 823786020, 953734315, 74372274, 426663050, 280708613, 638287106, 532333228, 523515490, 733982421, 47194743, 61340972, 13427799, 446140194, 953424528, 458316204, 752299910, 802979557, 770541415, 190847442, 747786780, 528320493, 960662461, 107629671, 764760966, 71859167, 343478313, 640172415, 754097086, 220959003, 836379531, 571948466, 654688266, 467099160, 651280591, 541852858, 781965158, 730317069, 153998247, 128700121, 402438568, 461196430, 133231865, 397313185, 499559763, 944213289, 802936845, 745789143, 120034589, 664541075, 817826446, 17570364, 838057217, 267784188, 917621703, 805916099, 200469570, 999473118, 343232888, 993210701, 799294191, 800689535, 585949399, 911892986, 235048485, 754324520, 364679483, 908715242, 790373657, 876562275, 788276399, 212390445, 351278780, 230248762, 363740201, 126877952, 70676096, 637400793, 832812965, 953603365, 570281436, 126049161, 3081188, 880119487, 350993290, 772306103, 681948036, 376154700, 818930049, 888951023, 645139405, 490561949, 244026221, 871612921, 545496135, 51030783, 38423967, 262292469, 108492458, 588695772, 540483003, 739591473, 773081314, 865697057, 604170292, 298969268, 278227819, 58410283, 56951022, 329398421, 233832260, 691258742, 79910027, 592624675, 943221482, 582140054, 351274028, 682007372, 505241068, 696703750, 28731139, 133498462, 97965402, 764009889, 400808317, 297882860, 864218654, 510582062, 533092433, 401642406, 910882753, 822875903, 347078662, 887895513, 42474440, 830228918, 614984920, 250653768, 210490225, 582064344, 810593268, 21116371, 583642859, 310549560, 602084179, 618540044, 278811734, 471875992, 707293901, 620606660, 992000225, 666864093, 622756309, 667226693, 998704364, 154199396, 760422418, 413376930, 691679195, 686271712, 855549640, 132497309, 339153681, 815124907, 357185440, 180136579, 792401066, 18090534, 334384682, 180730728, 674882182, 607304814, 923449052, 100468718, 95888611, 489162625, 356329125, 632555921, 831441852, 27335250, 607899022, 320326284, 225507921, 167670270, 681979296, 152486251, 642334717, 137451527, 335142693, 346132959, 431484673, 488125218, 571849707, 296256387, 521595689, 393161615, 520221691, 471529779, 82628838, 391507678, 477678707, 426083342, 306050794, 170292369, 954160513, 835950905, 225660628, 828474235, 441523761, 222544809, 484934230, 364183034, 394396013, 631137465, 789572677, 341016536, 558676552, 104673539, 547687863, 323292641, 820263640, 633260080, 372348760, 658575261, 601137242, 433179977, 689476643, 852024723, 728506758, 213633797, 858693219, 945373968, 364272268, 968793400, 183946977, 769477708, 103940704, 762281542, 384166430, 263396924, 780073720, 220872712, 674222059, 773250662, 580978878, 824230734, 855827672, 689887714, 172918848, 151582721, 413934188, 565504178, 695557626, 79622995, 4529992, 845001547, 173710139, 249730526, 577397558, 120963061, 657565521, 94550573, 744760665, 845246937, 722623972, 683255422, 885882715, 192755242, 730426960, 771092643, 241151087, 464379573, 549848278, 185682386, 647210745, 127396405, 351422970, 931331255, 297626330, 19547013, 401078269, 402735045, 644854785, 433928177, 73935485, 197881804, 104191225, 573735258, 77583350, 571937888, 487265086, 167681199, 971474497, 291608594, 488836727, 459906938, 951727803, 771338006, 378898511, 494446291, 174187216, 118428313, 577343019, 322116410, 115042516, 386531750, 684169279, 851274513, 231168719, 368970164, 618735196, 652122511, 974498441, 384383243, 142914067, 311729054, 193812305, 592685210, 851615145, 96964689, 764201096, 862274867, 731356525, 328913696, 662398591, 35867310, 503222610, 218947994, 689405167, 580494140, 361676529, 713593426, 543904672, 174476662, 378125595, 638639026, 951836832, 157324277, 706746292, 95049631, 38174389, 232492901, 46295217, 236492334, 250610327, 393919905, 646632281, 309160582, 946628842, 343712341, 76935576, 7264287, 662200937, 991435719, 714458158, 684324097, 239969810, 995883142, 992335124, 584355679, 845363625, 661224229, 546267754, 427521655, 751434535, 474599156, 844821563, 401016685, 403237369, 207670679, 893843124, 910743280, 882218184, 211977043, 375727968, 416685688, 490430283, 24838447, 785844623, 640003600, 559103364, 136305868, 521757130, 966201774, 519010445, 690428040, 571194680, 510440116, 60912806, 641052416, 312890304, 823490549, 947793482, 257818810, 981512327, 713610775, 919562773, 550625777, 652872983, 676877315, 892385460, 919888610, 707299043, 728980878, 101208878, 196928672, 464755927, 639114927, 747085092, 722880811, 386056357, 845070554, 114857346, 482935587, 612913117, 606394693, 168981834, 769777630, 977339727, 977952025, 951305711, 927396088, 670633970, 200551113, 796614543, 227065380, 119393120, 756544599, 943230027, 659546506, 895666588, 380740450, 155116742, 845929734, 242818292, 871262357, 410982700, 776935578, 478991732, 196608644, 120162003, 809688142, 763794166, 250806331, 715232722, 16812213, 986676641, 383073698, 22182105, 741587732, 136051937, 264172544, 499070424, 717773834, 708123828, 910261422, 33797530, 445994178, 521008939, 206484379, 359372472, 206788019, 58567244, 428120442, 604787513, 259863249, 212372129, 141827178, 700655911, 955633775, 184973520, 771897546, 178631376, 521750160, 122262809, 682599989, 345318319, 691134894, 889631622, 599960038, 512469108, 132504727, 83008688, 160463469, 600081969, 67885499, 856580104, 87293044, 153338734, 678575432, 114013491, 52687347, 628560826, 144049790, 200347195, 586969741, 584459608, 344296303, 17407014, 242450817, 995511607, 79424577, 797368313, 286500246, 561367624, 47924308, 901093374, 689333561, 517514889, 609570579, 953222972, 794238251, 874359201, 756900959, 429963501, 687751051, 971733028, 339549519, 657969286, 803580991, 747198293, 133348255, 410214498, 755213106, 966325581, 790983360, 30835226, 646070111, 135901875, 77670635, 996541869, 445771666, 258143375, 141554885, 161607760, 971886624, 138522815, 508258601, 525916877, 44530926, 818663649, 993536228, 703690137, 180696289, 73913631, 751809247, 893040012, 282285893, 656845795, 322643931, 156679853, 948315432, 805967815, 409137734, 39952245, 48024132, 778458145, 548093129, 759139644, 887550418, 505511755, 260703124, 447006980, 626155682, 635506115, 66188275, 143841822, 616289225, 620897370, 615057045, 148961583, 490068972, 237709300, 781968793, 906576062, 319120112, 70626741, 123361659, 62682629, 366305397, 358545381, 658188822, 96130693, 276373759, 137260111, 662660060, 847767234, 884321875, 266282579, 179052828, 402763921, 415012970, 635884253, 532471034, 451610231, 194270331, 739700179, 513278047, 582580571, 966668394, 604931451, 901183599, 609708436, 539376833, 322309704, 390433028, 265538583, 765590653, 670528288, 278058709, 591764429, 694501312, 512842113, 218489735, 661317185, 574877217, 497048512, 153993405, 970939511, 265723441, 543562581, 757373408, 342657307, 561673480, 71991987, 99985035, 679826046, 772439073, 926767573, 225660513, 263095961, 735272159, 937095902, 411908066, 428993167, 524417432, 286551093, 308221567, 569814621, 806960417, 659125131, 909950961, 583113737, 516858559, 658681339, 674542369, 480668829, 539766785, 758644536, 433413764, 699568364, 19880326, 328187543, 298230379, 563330939, 759193942, 866780440, 543541898, 583630428, 727437780, 698909943, 779334573, 52648241, 33775888, 389941286, 202601401, 112679664, 339344720, 308484357, 971710583, 32917007, 155067148, 111641710, 892133262, 711649051, 974742845, 427198735, 278572899, 290216639, 148573875, 512623253, 572846503, 413867420, 136548510, 269204965, 427711018, 597066331, 111796172, 297935864, 683655797, 223124358, 484537315, 805535333, 258212552, 883501334, 285106051, 777507765, 527582946, 426758847, 26971587, 675025600, 879558624, 537056382, 372071768, 663817094, 300540948, 76951910, 341502346, 431284780, 507929344, 4941858, 597895322, 336856167, 829386269, 116368873, 624261488, 152778567, 108896019, 439454819, 742981269, 522733961, 911714176, 471580342, 706727182, 539032847, 68429570, 659784015, 318437159, 366492105, 351373811, 72680651, 280160606, 641759462, 399409966, 881048138, 225585013, 290589222, 319195885, 581945982, 152386447, 310507922, 598907055, 423291374, 371330598, 657979715, 146682661, 828371640, 704855280, 394651568, 174955756, 965315700, 837336920, 427999486, 857273181, 946116970, 317112197, 879024995, 441364457, 360526863, 453704095, 156540667, 622207710, 159534808, 383839715, 957251637, 345740068, 158955872, 573233992, 809905770, 246458874, 215824471, 852392794, 640678549, 928720653, 473887233, 941777879, 639051252, 507769381, 904104354, 525185827, 667147955, 111117479, 460357858, 80918872, 48898041, 490491318, 77152297, 134616381, 424539595, 739022927, 911486625, 14363609, 960230442, 711707043, 133198262, 313465284, 352763848, 497370548, 244459728, 211957723, 985049150, 242638170, 900132843, 788707340, 293224606, 576286177, 653876011, 14046908, 145163472, 549786408, 750315677, 116203757, 272096533, 766690336, 400156891, 709638556, 204709923, 866711282, 335358574, 981711095, 241857352, 682325308, 943332195, 614441078, 395389924, 891156409, 697129872, 819263388, 250503036, 973442235, 935198202, 184601162, 249008707, 731644312, 359166625, 189547604, 579417926, 736768993, 828902887, 813881805, 602616368, 771271776, 656889170, 102238504, 247211273, 537527618, 885578778, 383773495, 830121272, 953647281, 957893510, 225895693, 560323187, 758030300, 134670140, 158483506, 388776594, 170969996, 95515665, 684070654, 509182203, 824973039, 935838343, 266197946, 594000793, 49186463, 103312758, 707092686, 141244962, 621362566, 639103203, 2688976, 18248322, 895884484, 52307305, 67274883, 697454944, 756976824, 137110149, 123238800, 573624589, 600907888, 387169841, 431093377, 132837964, 463505971, 721020285, 49478458, 742084901, 365095932, 937702968, 93913266, 706116859, 28835810, 525613854, 493588101, 539044232, 947215976, 993714028, 920783948, 684779794, 915795060, 475998915, 937815299, 5219692, 771472463, 391080778, 309330367, 739484341, 25668939, 872560999, 366356097, 392131480, 605971023, 425135143, 488067706, 999822355, 696234816, 222077092, 196633013, 859075029, 454340733, 88587375, 287271889, 823715823, 866826184, 609880170, 129477678, 926653218, 190679262, 774987795, 520074715, 769435707, 58993272, 298883801, 880880192, 472377557, 255566704, 260742079, 346002236, 501989558, 204584621, 793936744, 738386575, 789148840, 749537504, 948968731, 986296738, 881419616, 294085448, 761276032, 693444039, 652057291, 307595042, 570371105, 719770204, 359369871, 666415926, 669940549, 8943605, 742441687, 328547756, 101698097, 249700481, 918628550, 317766730, 673566080, 389655197, 648468410, 508079290, 941557634, 321202298, 586653663, 849551554, 702554473, 380328270, 192574595, 784081777, 7545897, 54750577, 797619153, 659764236, 94425830, 95691519, 158041165, 61602053, 63230185, 975900068, 151569763, 893809431, 531427344, 983822161, 508403969, 555859105, 737578118, 183046967, 829124393, 673645043, 596994130, 405977330, 920241999, 517785114, 891806514, 48000914, 853915194, 53693970, 554732673, 68249873, 771804280, 410365746, 113500327, 481892540, 854139985, 560817538, 226746695, 445448359, 766312866, 294762173, 48474485, 981747331, 781251458, 41515726, 11951463, 139908356, 616567046, 706755686, 675590249, 951876703, 240574569, 648898117, 89690151, 284262432, 906423643, 539289165, 98207676, 979392575, 927895696, 325615851, 925536751, 537406404, 285702000, 939653280, 875694792, 525841925, 686812083, 291822919, 545358289, 251659373, 36451703, 868754411, 277527125, 493610475, 657834690, 109506943, 967844686, 90512623, 852497438, 850515488, 539076141, 214980007, 824592827, 445739337, 660631706, 522993022, 578420216, 176433103, 687754952, 382176818, 909559654, 934713746, 302711923, 901125459, 469047380, 14367054, 701245010, 500644381, 303667705, 129886459, 40810725, 6266462, 640157760, 184039699, 118427126, 28608288, 846849920, 341362184, 275120942, 890941906, 2689877, 328593977, 437769253, 769641718, 344532560, 144487233, 921192030, 890556056, 305860985, 814375849, 372899021, 739229165, 185392017, 74178416, 143574193, 183516951, 638118551, 136755749, 589207588, 183097610, 997524071, 447019366, 73560769, 848717187, 904182882, 427731087, 321052903, 197800803, 957476882, 382274474, 517522019, 962238653, 992267042, 336054951, 186465522, 378204894, 602331350, 655604550, 538700469, 923945924, 316561939, 361799731, 332530431, 271333131, 515575563, 460261862, 210317081, 754586798, 791370497, 605090412, 934008048, 971230331, 81754864, 650413582, 96081537, 938945146, 700082448, 792086804, 203001715, 344208775, 380936720, 851401632, 314051229, 797131462, 64856221, 943914323, 978069469, 781244429, 570902482, 485019619, 818389555, 106495227, 298742273, 862718359, 12345831, 637207210, 978814207, 584462803, 796993031, 421855608, 728528524, 364091762, 51128703, 817074877, 137024504, 944001596, 470326199, 970938852, 788448650, 996667934, 78155353, 162540124, 846996351, 170371961, 268575956, 269834039, 269028751, 453366254, 821292511, 608564793, 427323664, 974345981, 746521116, 328903281, 884729924, 523764495, 494097855, 843743353, 683740919, 488952485, 842052226, 823246561, 630393700, 757764262, 90216238, 865943934, 563489561, 329437970, 698488328, 193251869, 767028570, 249217758, 329880454, 169883000, 849846581, 767362554, 901587458, 122033528, 894877687, 428398869, 842108719, 161382506, 873551886, 185892540, 226150510, 696833227, 939791991, 245273585, 520115397, 470309427, 320679032, 186708560, 290653026, 602952059, 886959202, 524566056, 853550512, 152753826, 390772704, 863863213, 506107699, 816734860, 353975631, 403021998, 947309363, 694692165, 651936298, 126739488, 11167070, 771169488, 637866773, 298429472, 870733647, 558097389, 939719856, 698290279, 215578957, 621448654, 589280646, 70295838, 770124575, 866207996, 550879713, 575455074, 881190956, 390569079, 179414820, 869753809, 407611331, 118747542, 522576020, 773310020, 816890228, 256111847, 14956918, 896332715, 699511379, 661942469, 391127635, 368325689, 593783739, 591273304, 601039121, 357000506, 678885867, 162660418, 533257192, 829589626, 982283699, 561580080, 714636886, 977540487, 980730910, 482968022, 48739553, 640467367, 896759563, 267028328, 166048873, 364441544, 204829804, 19380444, 248504118, 576398852, 420952613, 696517489, 177814555, 379839008, 516020224, 351669417, 337307949, 285007697, 886313625, 31069301, 404131034, 667427833, 585314818, 271491332, 192617023, 798722784, 316369166, 414667449, 994673932, 808333305, 313463230, 550611769, 187134656, 492496525, 811980844, 659280638, 888336630, 56693997, 324904850, 956604777, 615339878, 286383592, 972661783, 944778660, 192005626, 519397656, 468965493, 365688603, 998682692, 67920171, 536971674, 640160145, 95960644, 905149432, 735458199, 918193577, 138035909, 754684050, 731748937, 77123975, 208188854, 419267502, 220067739, 907234990, 524405908, 333075724, 449668987, 255186208, 669578949, 347388762, 294594866, 39661196, 294843238, 257236996, 981131515, 297312730, 755427025, 94299476, 651241841, 85138807, 448217487, 628454521, 815563071, 673133891, 517247015, 612366273, 163670082, 384785316, 399508431, 622854208, 267277698, 669963975, 381839487, 883551598, 55725417, 161742236, 701571924, 684924172, 253430476, 318157671, 836470462, 37511654, 210741767, 508512663, 693040806, 909232618, 216684930, 592209335, 674565797, 186075948, 327992703, 520879928, 217264445, 590921879, 794369937, 581339079, 28326603, 382920930, 393169386, 946227623, 582167728, 467269057, 911734571, 764943972, 458585019, 437909431, 439211228, 783594273, 533516287, 696090841, 132880657, 635440266, 571258728, 854782450, 218185992, 802984850, 191633392, 502627892, 8837095, 750975314, 12351343, 204532555, 423335599, 89428174, 232627749, 3347448, 565540866, 809820657, 682812420, 96288555, 619473511, 129100496, 485278304, 375957248, 410799798, 432380015, 704618532, 234923354, 478465139, 487089657, 12783359, 724712525, 117540364, 640190197, 110132012, 813662854, 684849719, 340866316, 629469740, 929286482, 834087343, 294693838, 600009919, 604977205, 918544545, 956635861, 948432881, 409185055, 512062922, 831974038, 437324868, 466682779, 140216161, 929723379, 756023844, 647020628, 855799715, 424029592, 200184445, 553076271, 222582453, 456608045, 838896940, 629277164, 46087237, 692528821, 630642547, 28613150, 219993170, 519712244, 942497339, 42932821, 536552037, 994968342, 172327405, 243986641, 638641971, 784118623, 271326772, 94488051, 533994137, 118612053, 661001207, 845684429, 615202713, 994801047, 628412354, 107137541, 864523507, 200394544, 746961909, 668006918, 219052477, 465062339, 24954510, 422307133, 627247991, 63207178, 849338653, 348262061, 239995131, 824052018, 682768935, 990578169, 751276687, 466886977, 898063953, 309028414, 346147037, 217869163, 902407428, 509507792, 607704710, 730050241, 544410697, 897010317, 277554899, 823623125, 752940564, 155389279, 656436074, 555447020, 39558952, 268520349, 101718054, 936587095, 809058381, 859121918, 611267995, 809134836, 513027601, 614291634, 42020186, 50364213, 928094532, 924354963, 53269116, 200591019, 415539767, 871406789, 428237000, 304464166, 436988563, 972083065, 652803185, 600002365, 978441764, 462239740, 139678837, 230805434, 969618288, 568462672, 718882464, 327469125, 390202942, 637551101, 912016596, 924122064, 710442147, 30690407, 602388629, 425858012, 101776494, 647532996, 346364536, 312010177, 440045113, 737994639, 454525190, 438409376, 727777233, 870234069, 964591171, 90313393, 583359658, 888130904, 886323142, 23326568, 798685310, 183502544, 798568260, 810847257, 996037011, 647245021, 549019754, 920485652, 858383750, 676817952, 13993046, 4116594, 103965317, 394089441, 32833040, 826049121, 200348777, 796996012, 568206158, 645424482, 838547192, 668783401, 288256830, 398565941, 412723827, 638462131, 562691863, 7272389, 307297017, 938334824, 206758433, 828193458, 760279654, 744048412, 894840683, 439093613, 804915646, 248340561, 822744603, 534622760, 564713806, 732276494, 448473968, 629093529, 260473959, 452386446, 153781890, 917545213, 271174475, 468386885, 74306984, 23670398, 149985488, 578317514, 325676030, 292547232, 381724711, 435055952, 640078812, 335189239, 329206831, 332442069, 70560724, 91038591, 528680929, 202644831, 44291915, 401855161, 292885687, 36325033, 250401214, 186998926, 931946204, 389717300, 504774202, 797477973, 225400666, 118684135, 387295445, 433500567, 974838317, 331570253, 643491152, 753145234, 519937456, 612358952, 790050782, 713743074, 769019787, 403570867, 604535913, 438899974, 471283762, 831305741, 261121648, 477863173, 799033919, 206028131, 937887036, 893166493, 16083837, 677250296, 95854494, 477787384, 984776833, 577685173, 895604067, 788020581, 518604232, 161348990, 315893272, 8860721, 558437178, 593091945, 167128719, 670936777, 698114107, 615873743, 99081202, 712615116, 462983715, 919132045, 836340936, 844477151, 621484118, 538648117, 208101671, 833061332, 37184211, 475217680, 15148923, 569725327, 962861810, 985744113, 452486156, 24046037, 469248071, 906196352, 747858917, 367275881, 725372948, 467242123, 209173036, 302812077, 890967393, 6241343, 349587305, 993262911, 961578141, 51715775, 821316844, 100077490, 347794021, 491993697, 933751735, 512017059, 209073102, 268282360, 122575042, 605830380, 264495578, 761383103, 598476786, 978634480, 882411860, 968702303, 287931901, 893765258, 230458125, 45470958, 425300932, 183338598, 298980738, 293382479, 11564989, 601846178, 904544235, 92994147, 721369511, 395115492, 931375407, 164586323, 564147151, 152751811, 894627607, 605148586, 962814406, 12308658, 878935403, 620219178, 570231280, 951404872, 589865005, 850394622, 299102348, 411267074, 90089270, 554737317, 161312588, 81924285, 829227471, 494689952, 196513780, 290932476, 65146935, 730062483, 397907738, 799026808, 133835880, 950838738, 564825343, 769345878, 732130756, 68202077, 80126265, 318462096, 277432554, 756376673, 103710041, 866211953, 233161380, 807013361, 573405249, 424350494, 849144354, 533078466, 928124627, 375900223, 48091671, 491146005, 432420989, 267043618, 332710620, 712763158, 939415162, 902769571, 328065566, 634348847, 636480072, 319778639, 600253448, 649498169, 25783819, 943359649, 260304343, 87245825, 884037208, 190708056, 105351458, 397067574, 362468766, 426420902, 772922105, 485299749, 514559794, 34540004, 61850976, 906713561, 268936211, 597595909, 898115183, 519314924, 474633682, 17128194, 982686374, 602274720, 20772298, 878098538, 247646349, 717991455, 125859558, 577043567, 962408366, 483478343, 174263684, 428699176, 818369441, 13139214, 266536183, 836902522, 699549246, 560470473, 572628773, 816579759, 825067921, 50894050, 468373575, 550820475, 866384371, 238519819, 35945384, 661155534, 392625109, 293331738, 533641836, 375444473, 262346637, 862778698, 721390356, 223207825, 533760435, 888512226, 448628358, 312792010, 488706707, 357848777, 451424674, 558449967, 444075825, 627503399, 821862963, 782439342, 901384572, 677172863, 8169338, 192013553, 468317519, 246223703, 626217002, 82492754, 691055001, 83103431, 145739269, 736269412, 45647506, 703425545, 588156068, 128048533, 601478128, 129127243, 814467942, 371164852, 393291844, 971089937, 519356114, 823943842, 771549190, 40253444, 230030486, 782350399, 572838805, 836016367, 163606594, 112446133, 99064496, 730715355, 887998594, 956143623, 941385110, 343326736, 226092019, 816850981, 981040798, 212914253, 893804778, 424881732, 636759868, 170783120, 596676847, 657408542, 547854506, 683277679, 387754890, 115037148, 526075309, 781709528, 51828017, 621727736, 283253430, 795594005, 302084111, 473757706, 596234758, 566445640, 215358541, 559186653, 779246411, 268199855, 750832227, 156155927, 292760851, 825093982, 782300423, 767926133, 519082274, 716052248, 367681884, 289298258, 132515712, 976415720, 664634482, 671707532, 484524098, 446471561, 932753090, 809549642, 172278687, 864256330, 956624117, 39628196, 978732570, 60051068, 637553993, 780272567, 416611807, 975988022, 667023945, 151594169, 287440333, 471784964, 400702146, 725612347, 84213694, 428623783, 852697185, 431755967, 555926203, 531397734, 62161177, 783887114, 584444652, 367663806, 252714728, 299553484, 795588611, 581044025, 551366309, 644047430, 802408628, 671388699, 633028318, 608387151, 495117672, 243782285, 693895688, 621271322, 314153321, 164966640, 431104866, 268576268, 863535667, 629431620, 651960097, 922221811, 881399028, 488925899, 423635062, 927762647, 697674540, 414423731, 162180981, 472617895, 863276677, 202715769, 302992363, 642125254, 258326838, 649116878, 239466814, 504084050, 520013672, 587138323, 410394275, 772041058, 999172644, 893657169, 823541834, 195634769, 854736457, 816752342, 903845515, 485519425, 42880967, 599913492, 477860935, 578487015, 766631717, 379390658, 906585449, 434354737, 956442022, 975461615, 482154498, 646140288, 681891575, 796216558, 729258050, 663124456, 460641645, 136098608, 72191645, 528761184, 892256220, 339641545, 418676038, 163010886, 331624914, 952860851, 215555120, 491391681, 759871084, 427383100, 576093766, 228922445, 3154222, 312047012, 899155659, 799736467, 896184964, 389480681, 862301478, 946550985, 48209282, 163552377, 132975696, 656116766, 479781432, 447196524, 988789764, 395694858, 309345584, 337239107, 905391447, 702273874, 669205780, 92449009, 122614489, 521305020, 825346419, 516462135, 312018697, 100459835, 826763754, 212684438, 267802906, 871267623, 302857831, 309703417, 128631654, 63338436, 613823349, 233652544, 320902102, 224948927, 281454562, 839518768, 398364076, 81881085, 412541170, 965207997, 424131122, 815452645, 412695496, 62431260, 64315575, 656530019, 339318522, 360694030, 34279333, 345486330, 561921918, 839317952, 205782275, 240691805, 966878185, 917179663, 205599961, 875679611, 179259410, 507376943, 720183284, 153510759, 120998024, 480435174, 638775073, 518997817, 975471700, 708726161, 912892446, 523146539, 298149278, 115675288, 638111032, 752129201, 589191229, 170581866, 72568612, 667447390, 922560836, 725112417, 959672500, 401119719, 676922633, 311497095, 969412159, 94099904, 18971559, 71771376, 417609886, 566438277, 96768806, 796903600, 279816284, 27860739, 133892273, 874029799, 937104419, 474236867, 949295423, 921902826, 267975377, 160592117, 973558368, 479356728, 713242820, 452966874, 713847808, 150327643, 181006354, 880271613, 122957529, 548839304, 551090802, 744633323, 883118890, 617094339, 151238704, 271839243, 935843088, 407513608, 120904574, 398350786, 648731211, 7791339, 696818444, 885070206, 100387911, 434074915, 621191205, 233680354, 455221454, 602986761, 613321670, 526338688, 605410599, 886517638, 570374548, 474972653, 8527143, 357290989, 177591976, 146984427, 534676842, 678728749, 672576948, 475628067, 187341503, 456880849, 886176836, 539392748, 134083719, 132292480, 539741126, 967705922, 593601374, 762393335, 515072910, 911827989, 377513376, 711947588, 738043148, 454475360, 830896545, 957786535, 412852924, 236839359, 904369331, 668982476, 792614197, 686429233, 487114354, 512589070, 36766325, 756681824, 184317581, 762464151, 927557815, 699316682, 892053445, 924901900, 758052188, 150997538, 942059421, 289775806, 685615255, 879152839, 522867911, 1737795, 235493206, 548615025, 348167253, 117679377, 344082951, 72851202, 596044176, 11557199, 696815987, 579101759, 419063934, 235668341, 377194511, 961975324, 948907802, 546194301, 577075700, 280103443, 84395768, 142276908, 228917048, 762970054, 641271236, 980833346, 266897538, 228182084, 603070803, 986722594, 842252700, 566299871, 954690875, 359296538, 631285750, 457053803, 931676193, 594795077, 69045070, 400246083, 218687631, 197857398, 792469485, 6861664, 815396499, 95990288, 966245943, 479442447, 43162711, 386986409, 933478801, 427304650, 949888734, 590640694, 541773033, 5803282, 857012764, 96176159, 29705907, 731971158, 963838339, 188002663, 299321946, 976617675, 496291407, 571370122, 8363078, 424242916, 665227373, 690287135, 573372270, 947376497, 830628669, 107861945, 424061756, 749078013, 671533961, 870541431, 200915439, 807534556, 460059746, 960958812, 221623067, 207897534, 471357547, 367094321, 464218034, 248844722, 370837136, 261799373, 624163503, 11169961, 463104721, 403368198, 347018253, 51614207, 888035758, 488919858, 829037548, 850152780, 183879742, 119227560, 94779378, 431900156, 979731556, 326233635, 117466360, 61097158, 362345416, 415151456, 35286032, 978718703, 976371466, 382404052, 551048228, 961428389, 434882355, 260816967, 881710642, 454282715, 806950926, 674817050, 293751862, 481233089, 268796424, 66850695, 85687189, 310904965, 952511687, 932910622, 736291054, 21868025, 662319586, 339920347, 281170425, 206277746, 313272611, 433316661, 715282014, 554629932, 889307661, 214078175, 196973843, 936125245, 430893286, 843343939, 760237675, 147146497, 545667068, 787922229, 476113341, 370844032, 162010232, 770352882, 932966403, 264049239, 795037661, 897910625, 735630483, 635415050, 45485207, 119147286, 524513133, 841982878, 578028129, 261266000, 380899552, 690914333, 954061041, 224527535, 788339207, 172134566, 94867754, 211568696, 62359940, 120845659, 201190058, 36337139, 111413563, 647294863, 172606238, 706768249, 681505083, 152369175, 902905434, 194279779, 198143083, 795401624, 888561900, 127052716, 781940051, 44796590, 372329247, 464675455, 274683164, 851196363, 597646739, 540689057, 836287671, 146656257, 188095000, 880771927, 38934007, 944256009, 958430153, 401859748, 975045041, 325175412, 227082156, 413017532, 942716127, 406809228, 847580558, 629442890, 551586402, 107319943, 157236433, 839252592, 633451450, 764627849, 762073314, 322960335, 979734343, 652836681, 497417605, 213504259, 332307073, 132589835, 843501667, 895230518, 116055972, 841677556, 185840178, 513237190, 15922952, 517026459, 949203343, 601781214, 935149387, 594734333, 309781076, 482363397, 812546056, 987573122, 27661130, 527602107, 261741348, 333495601, 304238869, 32161086, 89187376, 105548799, 963775467, 100390896, 32271408, 844561398, 749211422, 3439134, 52045709, 143103878, 996796495, 461031402, 621553922, 446807674, 974875426, 515547332, 693045297, 631978472, 585043699, 540577725, 32735459, 562282882, 883324391, 7890467, 144538259, 118195572, 306924808, 964551347, 899808404, 921584297, 755646517, 835385843, 56809478, 111042313, 947969681, 865046180, 713053593, 248392154, 446301258, 704394765, 216431153, 868663302, 113762068, 436348080, 480553803, 763824472, 381892904, 107165445, 887486768, 702454855, 57071478, 78646963, 10213412, 4662593, 777633960, 196820885, 611202157, 648843287, 766029831, 415235468, 14129443, 202692097, 646549050, 679930155, 558330207, 727352382, 548478269, 476997788, 797187860, 182209842, 612520514, 50287275, 565403722, 251545139, 938073059, 82314199, 85697233, 694907782, 890654260, 571348890, 465386476, 493492224, 162771032, 546853402, 785526173, 858082836, 273250404, 451255839, 670938470, 856202329, 672627798, 161341219, 310929712, 887660229, 988481106, 51478100, 607455448, 121074093, 607620903, 686571280, 919943248, 696485889, 524353410, 461540769, 884198174, 938811555, 492419740, 149734439, 449228258, 701383189, 814818686, 79948991, 242032956, 365849881, 327294957, 180903645, 693963933, 108971143, 114719903, 788978475, 593847730, 770731076, 131292454, 688238437, 423956256, 213546346, 175112694, 817377002, 972590663, 57040941, 700139987, 762014783, 266955376, 405629695, 705184953, 1708919, 759267754, 473690576, 832488696, 913561305, 525028565, 608191701, 717065766, 814907156, 874807415, 299590594, 287247899, 38821321, 340788243, 40092723, 776523703, 864553454, 408357204, 153819038, 912526793, 794885765, 81589111, 189471962, 636380474, 447909334, 957694064, 839741718, 333465394, 45211813, 972847067, 301570763, 102932555, 542978283, 693152229, 680550328, 700687497, 735541821, 624695034, 11421075, 590535761, 458364466, 879569765, 128005359, 469221096, 825292682, 115820071, 843382562, 74518306, 837603266, 261626208, 944740816, 803124744, 369580303, 229788852, 729282493, 366894146, 21969455, 788859654, 612187285, 594337330, 77517672, 876244483, 370292252, 126053433, 801520618, 405848003, 281774045, 959237602, 149321928, 972010936, 41537476, 157081018, 726867975, 338912810, 339652253, 63492102, 866560067, 638278459, 272414045, 117464951, 306147557, 346846809, 88617415, 712162465, 181496323, 118781459, 803276790, 62973018, 997718291, 467312582, 735135390, 660278468, 980278854, 200921910, 457079648, 5120953, 425767426, 608851222, 750849634, 263347296, 432158957, 990180325, 493467005, 707525334, 499908498, 962492585, 469762844, 347761377, 69676240, 38105414, 500538990, 431183867, 372370349, 660568272, 318828856, 227008786, 544827002, 749504768, 467437240, 404492657, 274630209, 443828542, 507568626, 296086038, 373763620, 228002678, 286484442, 704837344, 631109671, 608124202, 448794490, 113399260, 332736416, 39488496, 655283961, 658444675, 248631092, 258039571, 252322081, 601127263, 356991453, 630748798, 12535612, 471573596, 280832584, 596140050, 806342488, 362236581, 479502506, 101524599, 312953508, 412392642, 926034975, 571686062, 109971441, 207054541, 118230583, 185165342, 924150220, 335454534, 853272117, 671871309, 486504586, 701903871, 386580071, 19666778, 725833627, 895346992, 355848141, 361541450, 707086041, 470863991, 308832486, 700165563, 142601067, 10388061, 756409915, 523783148, 958648360, 582259250, 626067497, 946143341, 223207820, 451026321, 694836666, 414385630, 141221684, 504532693, 107383619, 252035837, 146178969, 887147203, 249435874, 810681403, 375723737, 495910527, 220828164, 807640895, 488034851, 940914383, 81460120, 1333804, 8586209, 46585399, 597282280, 762611466, 903297542, 620884810, 92873050, 594107184, 146022392, 114054539, 124173025, 587745476, 344379558, 360228354, 538105086, 139206355, 597768258, 298504080, 280501565, 73388702, 41233109, 48782169, 773803406, 916107188, 361633992, 503832636, 465776223, 186925480, 428038723, 611880413, 921790404, 493659425, 378049221, 463780690, 461907845, 809556962, 95596925, 869900283, 402243851, 470558373, 738012112, 765742079, 669524907, 267506199, 755731054, 937832298, 319126114, 505211684, 622407127, 555959735, 444570358, 194720724, 125564361, 442716203, 651485184, 853837016, 960105913, 936443120, 87857338, 171865378, 293889356, 365936230, 689380200, 90864777, 683393148, 177948323, 814429228, 77595596, 531313498, 965586124, 378445475, 340609979, 747077533, 149796998, 397829690, 172580539, 796361843, 310762166, 825519995, 213711696, 858773137, 416371968, 942387504, 172812485, 165367772, 624809609, 862508792, 415462608, 551693769, 203987104, 294041204, 830384019, 94843276, 11732026, 415284368, 328748862, 873383607, 395104651, 109866607, 264821448, 752331467, 447843600, 75714503, 354756611, 299279746, 281371097, 90736074, 84387760, 755234852, 259910916, 728470694, 615123430, 515638613, 684449847, 360211435, 833011208, 308463400, 849746362, 126611588, 559437249, 156491499, 580447734, 571452160, 881600537, 65126817, 289110783, 925031617, 942093293, 178773037, 374278493, 956605781, 667994327, 911700223, 724929029, 632315529, 32363954, 874132891, 663313597, 262061031, 413031812, 95697087, 71656900, 384150905, 726676595, 829137391, 599659282, 920348857, 249191852, 94288065, 382591398, 981212625, 188666502, 874896920, 300907528, 832824152, 827723161, 604338856, 267746452, 90660896, 646211763, 538831409, 914566961, 233686075, 801507602, 532073306, 479461444, 541778797, 251535018, 845712451, 258389426, 769577677, 546822326, 322851797, 223020434, 372592817, 135318346, 782231074, 932440317, 475822050, 892181944, 750835161, 321412554, 948525793, 636514100, 253338661, 653915289, 422683306, 589191024, 580630628, 216591195, 427080499, 119401271, 772025400, 722614483, 892103742, 364142694, 398022639, 236537234, 834036841, 55236464, 276518232, 503394591, 895932513, 940373191, 695573771, 179127429, 313703434, 729862067, 442760934, 368680573, 859053485, 640599214, 899985749, 470186374, 432695912, 939511584, 531873838, 858619621, 813245978, 877218800, 234006369, 934467175, 921156599, 636708887, 50655436, 79337099, 152291346, 362815112, 811798953, 181749524, 275788184, 287042963, 129720515, 95479672, 31679496, 368424194, 536014296, 242558814, 189804830, 629933548, 703706914, 382310135, 481270781, 925951505, 173210972, 766053527, 917413588, 853957847, 162875553, 920431680, 40283777, 364964310, 731274048, 767147300, 106605939, 213334901, 589438906, 623137376, 147297131, 237627358, 57590104, 305182081, 341810469, 463257233, 347303361, 532936311, 641823859, 113263486, 790207950, 764445897, 149012895, 53280399, 15789817, 795127393, 122619658, 43990106, 116415045, 30668980, 159048237, 251735171, 607986757, 60602755, 654527939, 45024233, 313774797, 121604112, 756129856, 699589235, 565672551, 649091510, 603215830, 402975987, 88878013, 976008407, 148582554, 87890956, 696110194, 313867117, 129568174, 144193891, 168990672, 446512622, 48459525, 295736419, 609894015, 919091650, 948919981, 956004565, 961370744, 330239337, 133593149, 565264874, 433309063, 36334016, 876104284, 216173451, 983254945, 76185383, 520486145, 952127573, 409371299, 635916633, 875793658, 19332268, 307559374, 115703994, 489894720, 925081372, 304886675, 568501640, 202369479, 468460114, 609160735, 927184765, 161136477, 380965969, 816960165, 69465808, 278519104, 118117378, 390007312, 751568659, 745350834, 940382813, 45248499, 520637267, 567518843, 403613256, 678571467, 444411949, 51339466, 935438524, 412480608, 822450491, 594974783, 187881189, 443518776, 274604999, 173312242, 272791790, 115841012, 342254015, 10527086, 970203515, 247301267, 527761090, 409736843, 911868863, 787555331, 573397907, 245069137, 994309529, 183129121, 319806196, 414507360, 55747308, 47404583, 84142863, 44752511, 740200485, 390615318, 23127150, 767161170, 792795141, 579413212, 814430508, 137004163, 760242293, 266650060, 323940977, 890962885, 992955355, 524253290, 910148076, 821256120, 133413446, 739829378, 577565363, 25118716, 704586052, 822006965, 985964464, 930112322, 121507668, 901541581, 845890182, 697480754, 61583744, 463903059, 453439695, 479648814, 601040923, 509832481, 417689578, 82208954, 651210148, 659083935, 226295236, 893258566, 151197634, 937111979, 460159628, 472200519, 198942374, 476103119, 424504843, 990566750, 247756601, 117435419, 61529891, 66648115, 29529587, 647314059, 985500812, 57978012, 316396742, 763993057, 495515513, 209829072, 120258521, 885012799, 650845294, 855695469, 364285854, 719999983, 923907021, 576076913, 636412045, 693763942, 751006042, 494819928, 461248654, 39486715, 213387515, 689711527, 620529591, 462361335, 490515508, 371615203, 744581491, 23616618, 231887162, 773576092, 159755477, 508886544, 800266668, 824313546, 413284239, 918051541, 758642038, 472566008, 521719938, 713567185, 736800044, 175642521, 833238700, 714233636, 977953310, 7843635, 42264236, 958587619, 41886426, 922422437, 502553828, 116090173, 512824482, 631775260, 451105054, 955274370, 350257017, 285975702, 174799908, 648957889, 879524563, 846602402, 42096363, 49754695, 624035989, 211952576, 551471431, 991026240, 513620432, 716701284, 314152473, 717741754, 419634625, 545779193, 180440454, 157231809, 184648037, 481853981, 748831450, 551713878, 677234833, 71125050, 555130498, 950518056, 492514128, 363815360, 887768564, 603443889, 38446751, 196832259, 674770585, 340893880, 995473100, 175879411, 92581225, 794336691, 268453847, 331941484, 676333197, 772355349, 20596243, 136598845, 605282253, 551751298, 112576839, 39462300, 407193334, 539486067, 835897040, 204627100, 229185031, 773410372, 562738408, 436803061, 491573351, 371802347, 108446912, 436453777, 746075629, 772269461, 4994861, 581621893, 992439894, 475296227, 527508614, 812626063, 892948213, 571793872, 91605261, 703008244, 28694340, 8402477, 514945086, 310662080, 532128840, 349066949, 419695687, 22712518, 689942585, 668919828, 292474462, 687220134, 506628119, 833932026, 120522642, 344851007, 741944234, 461878953, 456272286, 323051740, 347365634, 491439444, 575092677, 65738899, 450338206, 465422038, 647647610, 248671220, 87819892, 922865141, 546343796, 130674175, 470806005, 775963588, 46062793, 847581430, 145286015, 365930902, 201040017, 834089043, 60802503, 808359017, 77123058, 657483010, 994034852, 333665424, 880305365, 206138297, 622085257, 478773504, 149273449, 291900719, 595268122, 48169405, 673388303, 189059511, 596673506, 3224490, 827715797, 406830254, 19062403, 105931294, 875478705, 304981212, 541295708, 988439758, 230516781, 269559673, 683435945, 348536005, 3473640, 876986874, 569392061, 220860952, 261138070, 192970350, 796679281, 145962649, 241894012, 875123697, 583329186, 605858431, 800814277, 125042662, 374042892, 944437936, 472059378, 886585601, 539299675, 214339722, 588582906, 422388961, 551588141, 908891618, 828076448, 680106130, 593266496, 640350802, 562368497, 740987903, 129822849, 630534282, 470034835, 415046330, 784591881, 860098328, 191735703, 82350055, 41166589, 623415216, 493267866, 689331252, 208222610, 792321357, 53685421, 921459913, 505662281, 585010974, 516426855, 278742332, 412437706, 15615515, 612295924, 433595084, 44297592, 428351240, 316940453, 109729714, 324171120, 370014036, 694420550, 447183991, 780024642, 338349349, 988973699, 374477080, 972431569, 706305278, 945026728, 111726632, 582529222, 470404680, 752947010, 544297591, 421407698, 152684037, 681595246, 455578515, 843958815, 555872249, 826924586, 263373717, 645736652, 864245754, 110018386, 91895562, 876824231, 373642720, 284695492, 868285591, 651728310, 54536871, 225623394, 176993219, 721111752, 19548877, 170668052, 692877926, 426277572, 238708788, 758346524, 468200179, 119107794, 729217378, 339314867, 383792898, 206518882, 315963968, 853176430, 688895853, 535735917, 967982755, 555798787, 193835407, 192845188, 89724769, 692492716, 809120192, 500794631, 17107959, 822456171, 223753059, 535993720, 746603218, 349796994, 322934010, 48666869, 134555461, 719221541, 646331779, 737701850, 430727635, 623748374, 500366987, 279743082, 366937863, 292038165, 867160955, 121752882, 605029540, 37694982, 508251030, 524700848, 334078257, 124696079, 468297936, 618197002, 382902529, 149190345, 131487941, 468066830, 957894200, 799358995, 783130917, 953633074, 524506038, 318283198, 831317601, 676520507, 531756622, 461523907, 96182804, 607176264, 28655916, 166591225, 864420749, 751952878, 579958694, 110789287, 19299829, 116408831, 187445406, 604905383, 725427922, 232123825, 685960326, 232737233, 770567001, 758777048, 894818449, 365832318, 886692333, 867804990, 945131103, 665071245, 958311466, 211325698, 38042074, 464318407, 962012626, 967616826, 473747736, 406786951, 768642171, 222926097, 188053021, 503244869, 323222806, 8337186, 419383706, 950574995, 507982103, 428315546, 267402637, 520093916, 559409113, 209242046, 322498517, 529520775, 421708986, 279656799, 103961286, 513758125, 359018958, 895608835, 85106098, 364833908, 830733758, 939729301, 273345566, 318356060, 689188537, 670160569, 555601058, 303080141, 939660929, 128922333, 183224209, 261086181, 805525947, 475622130, 467896298, 28266244, 226297743, 665496893, 516298883, 920974256, 140390201, 699347426, 811511947, 930510057, 240745276, 314431162, 709163190, 854302163, 106002425, 804062844, 948790134, 37418980, 902037779, 503945778, 644689953, 636799778, 825562909, 119006361, 991437353, 556862154, 504753117, 113579027, 808240299, 395172308, 728630779, 879725160, 979584045, 169740291, 889658290, 301096835, 425854966, 899307180, 424620185, 387245950, 374939339, 460638274, 765874306, 267777403, 5889282, 169848328, 206904946, 180867314, 412254512, 794041922, 992570068, 464054520, 435213756, 363646728, 670435065, 296051416, 416340659, 909520462, 694363736, 241983274, 43180274, 992841521, 2026195, 827620129, 826424432, 767493161, 801528684, 531335724, 896990836, 569163489, 797989003, 732945343, 556109815, 687635060, 888138626, 667676073, 401287287, 818418829, 272661664, 885552264, 238683684, 318533959, 887459100, 297416889, 252032125, 878172651, 341007459, 441472037, 69543633, 739837901, 783066400, 818152695, 6031266, 141820687, 644100295, 19594632, 747554025, 316274246, 408390628, 688059681, 627387829, 825801358, 651635716, 52983231, 924021527, 132263538, 384786515, 222527677, 441215403, 123835447, 616445134, 331125238, 328858038, 322951841, 549248768, 378247622, 807972900, 909851645, 671143373, 731629428, 706657801, 712632336, 126889549, 332640479, 89962278, 562755557, 891414785, 615441534, 220159086, 214123328, 434918555, 919260084, 825585611, 268428929, 551831603, 900356722, 500144586, 235622572, 833507694, 805297051, 722595614, 177308164, 482167443, 692326951, 589152519, 908798705, 185008770, 619279488, 332113455, 393092327, 978215738, 467802545, 728937283, 392940763, 42407456, 647298190, 677251892, 749332059, 152134377, 900699263, 405502094, 2612118, 237313462, 64368728, 547784528, 5599912, 226544059, 148972136, 346622688, 891295074, 673073715, 351200994, 762569540, 342611090, 563619139, 389888181, 143996605, 178455646, 976388086, 889418720, 205805420, 47792722, 676176416, 394053078, 212953007, 719509103, 254608427, 160605666, 116382360, 309770548, 337299624, 833839154, 157720208, 929339163, 282960488, 469735977, 271997347, 311166957, 351028053, 7718966, 999592530, 773838247, 856995868, 157599804, 226830304, 203028971, 379368514, 507192863, 97308528, 919904526, 480388919, 129954558, 338479444, 638484067, 551115952, 451511974, 420901120, 187406901, 38488290, 376322822, 38749099, 754314114, 619670131, 622535943, 764034923, 503571546, 738866451, 528817602, 19643506, 392337058, 786818164, 275504810, 527053480, 76811230, 447763645, 96465699, 793604468, 477612104, 22428200, 727643394, 76578235, 989180876, 310317484, 278191652, 941650320, 804057820, 306551756, 589854217, 720572964, 197504385, 772905652, 652774600, 898020137, 491470778, 958983590, 196874636, 490961996, 63178518, 16465693, 278894627, 463184691, 334462422, 683322281, 459738785, 406696875, 657035948, 792836426, 6095206, 821660164, 308912781, 214100375, 811705336, 181436791, 360144358, 932671479, 318778355, 784981935, 897470679, 294798949, 9936665, 955308881, 385774862, 510594323, 913995785, 205713266, 778302797, 664965433, 594100468, 118628377, 592574282, 193313866, 957530840, 617252794, 991196011, 418979251, 526005793, 231349480, 874696836, 391224579, 262700433, 690774738, 432682858, 38327653, 334281562, 333331478, 316927751, 71166403, 176833478, 940666563, 471323672, 55679531, 165113938, 297889094, 286938188, 185864450, 819221915, 6203033, 839862208, 251957853, 129944413, 399844991, 530688406, 538058219, 796808003, 399296259, 118596255, 57789777, 465757915, 307296308, 193221263, 127040643, 327600591, 4671297, 577858663, 959112994, 997019101, 555272207, 280471509, 841517860, 281174641, 702751569, 143571098, 241082488, 765301517, 329069772, 949445852, 381673319, 387971694, 864146014, 134046819, 922982563, 775278923, 648689990, 364630311, 561403306, 168705895, 222804539, 790779161, 44268469, 200126238, 843501251, 141418682, 995545327, 139545428, 42807928, 230100019, 801090749, 158115458, 954937524, 740675473, 318746621, 64138291, 659576768, 513593772, 250237696, 782941125, 779011867, 437213414, 602451910, 631152194, 919496991, 865965197, 738601884, 473663554, 836803508, 713857421, 935421855, 788485192, 982967919, 838726423, 998830583, 126115482, 213744976, 804141838, 158690762, 357804787, 8047323, 966039857, 385613606, 260536643, 177086350, 267623220, 619086366, 396357517, 55115626, 79310657, 903089920, 214981061, 30513535, 468323755, 78476913, 623788538, 358458908, 983370337, 520480262, 496556272, 686703894, 263480904, 786152477, 170587028, 91245332, 543138781, 944480173, 798471959, 523099376, 35173127, 200392451, 312464225, 278674292, 656992778, 480947422, 59022604, 653169165, 324235274, 91317349, 691973685, 31805790, 41151366, 228212297, 218608915, 286370327, 971793632, 128395765, 427283367, 705093891, 609111816, 95946489, 110495490, 924817356, 5656461, 275310250, 714402629, 222634945, 533200874, 148826391, 419729443, 643041464, 229115391, 590263902, 427461622, 879411801, 964234998, 73807973, 487864258, 678648417, 530373052, 929121839, 415393556, 413724892, 778039695, 777750742, 556082835, 32121622, 486792470, 507907863, 497258145, 730992409, 318936075, 288903253, 810680383, 539848936, 539420790, 471175587, 123749186, 721956621, 760811172, 564453875, 154327392, 708327764, 402095609, 6167527, 814997135, 215118979, 387091, 286986505, 26416686, 641758847, 856494797, 954312037, 518653125, 999094143, 277593724, 317224281, 320140666, 522008475, 119813842, 38329611, 791040142, 385508405, 527351450, 875485518, 209268819, 511815355, 407785127, 332862577, 659738384, 262341755, 387439775, 428519412, 507388620, 197513847, 257429865, 545792335, 682222773, 426736362, 274112614, 531633570, 826986409, 801728400, 388074708, 765565863, 111352030, 92821681, 72784047, 446826405, 403083558, 353884155, 963828890, 246288052, 683917605, 514377449, 258211269, 107177861, 500792213, 916186998, 353074488, 932102764, 76877039, 451056836, 422282302, 773884638, 76549431, 586505795, 817949917, 552429043, 58347668, 971219138, 19978971, 163629497, 434729396, 445760264, 110566019, 51392546, 372172491, 557658788, 329893080, 47577728, 853595859, 309006224, 907727795, 851298842, 394559725, 184986900, 495375813, 344044834, 739744120, 601900696, 31378622, 971194038, 845545116, 903732273, 154279703, 923232963, 402864113, 352084244, 626544202, 201585594, 203203990, 55234545, 352247396, 273707704, 515138184, 709378292, 525400634, 556006132, 833015055, 919936756, 541018826, 324263823, 830259837, 684312994, 523869622, 200547624, 954355376, 34813293, 169157844, 229553692, 239514146, 88445052, 22628281, 163484810, 15850881, 769664707, 265534154, 272530793, 353790575, 59035122, 361353076, 4513877, 828631374, 307247063, 694140426, 726100515, 527286377, 120203657, 310319381, 324845624, 228991425, 563476027, 242805589, 235051286, 994712369, 877145434, 821817953, 243338416, 558531808, 838559369, 434179544, 138690307, 103084681, 99653782, 130780033, 324535082, 597729554, 730266761, 834069703, 173361065, 702728414, 961010988, 704135911, 676795659, 192781633, 810795025, 897784738, 433148072, 356829603, 829593914, 818259786, 408833129, 826471187, 797845682, 146494865, 301438549, 860619634, 869691392, 860440766, 153221846, 53251706, 434874417, 257143360, 719887094, 383607291, 184366053, 178766314, 466793235, 558955036, 699674956, 448980085, 630895737, 594418832, 909188018, 647020137, 791796570, 666074751, 142314718, 464491346, 752745850, 782462539, 98217408, 259593631, 324667313, 835056299, 407272278, 971236988, 397268694, 603124957, 153045867, 865510253, 468602445, 519708874, 125329728, 730731992, 38728758, 854699812, 31512574, 665385162, 831278691, 603406268, 111016465, 377481311, 486919302, 590931984, 84770117, 224327203, 767218238, 976059242, 118576016, 889057368, 49063862, 458773403, 920487082, 205591703, 55186262, 792928178, 91185059, 647359613, 124620884, 979567651, 481170129, 822041828, 925397756, 262509741, 248048475, 322878598, 261522241, 617143626, 216615639, 432553758, 306386029, 621463558, 887064271, 328216804, 48491324, 115497025, 456210939, 334400666, 736250913, 617504075, 635202746, 247995240, 38667002, 396364443, 781840272, 520270594, 353091337, 847236537, 392194434, 868791569, 654908521, 446639438, 539714759, 135753794, 130183157, 640319564, 813446849, 428492341, 946967706, 514061760, 757346301, 782187173, 897651850, 16314709, 643810539, 995108873, 691978440, 245826646, 548201016, 516304642, 456689609, 36835334, 688695102, 129049587, 201397586, 303298302, 83204050, 62813856, 155747061, 921001632, 589720279, 360773155, 711968762, 726437664, 672554283, 399905339, 924459603, 633482303, 87883100, 357370576, 380414204, 89335014, 566831833, 288518166, 631954232, 193819344, 381760684, 410644349, 636132466, 148331637, 98979542, 485153702, 156725275, 953421351, 323780476, 26932532, 47241324, 636417675, 190487450, 63353573, 976091308, 83913755, 800046796, 47940006, 267299032, 151148048, 209979886, 316798116, 680635553, 448295059, 427648012, 893482227, 674174959, 812260399, 993061954, 232862736, 817950104, 798519617, 996529365, 141239050, 261242727, 898929057, 176311115, 871196043, 481333574, 293452630, 625265056, 167077825, 654246779, 329675158, 966027449, 344038936, 755955303, 266773729, 184075293, 993672645, 281622296, 671798242, 557426384, 368610188, 373226333, 928515959, 684856139, 212626070, 431135704, 876915491, 368891519, 952564737, 324206592, 603691193, 508880121, 396484560, 373817435, 895382861, 502719250, 252281637, 693228375, 716682952, 678295696, 153783142, 569111909, 315842353, 169406176, 796730426, 855576377, 252546259, 690050983, 784318400, 593956491, 172513576, 654971933, 102624991, 715467902, 860822644, 465386384, 319774985, 813538227, 720431100, 889625826, 171633149, 592607064, 515834335, 642634562, 374537608, 256859700, 123380120, 415665734, 559246460, 206761592, 91997156, 907596055, 641667880, 918443216, 376814743, 490940396, 938366307, 984803999, 727898979, 246145853, 362050116, 305503326, 317647705, 857437644, 491865801, 289608724, 32142635, 958859387, 505804113, 647488522, 373684680, 143459899, 927884864, 126449074, 708076388, 806940208, 408930280, 735593987, 315524037, 882531914, 464886387, 72311918, 788970072, 524480725, 547502641, 329356630, 766000989, 227173428, 896994529, 280982270, 1494787, 140466346, 120257407, 582221344, 697752955, 422348600, 361756620, 177709040, 139203684, 959271882, 547973108, 904429460, 339478459, 235749124, 397855694, 996734004, 756851, 831498010, 219658116, 872522255, 135117511, 930338785, 652056150, 835137513, 232567907, 972576084, 683865105, 833025049, 845386517, 285354617, 492361398, 739119986, 94707724, 650581193, 497555581, 233359894, 693569958, 752318453, 740949941, 345817829, 296209470, 122110029, 832229557, 589621832, 395367171, 330047943, 789240122, 536509403, 923611945, 469322294, 479804810, 245758539, 120335467, 916532126, 256522393, 295792307, 107194664, 62019628, 675167154, 264253669, 695894709, 391533943, 761315700, 193202999, 165274730, 868427104, 779581538, 993006463, 543488525, 201086839, 648594539, 212031485, 142567166, 978728690, 641760415, 352809132, 686959954, 381588200, 294411304, 967698919, 985017183, 230669576, 990925159, 823349971, 293624214, 170951911, 346686533, 47311537, 665304920, 240368241, 254548223, 441114261, 839980410, 891187075, 156261447, 293141022, 759331933, 35599603, 617831129, 838347872, 63742145, 871384061, 324390277, 800515089, 2057973, 230450828, 320172408, 830492701, 450490995, 367274408, 509937681, 618218674, 859254979, 659287139, 728775668, 892976023, 495416765, 606735740, 704319202, 58262434, 717974289, 707366830, 828307289, 247212670, 411486614, 862585727, 314203147, 327955034, 123764617, 695899266, 953449651, 403284439, 420285145, 686607016, 929914682, 35365645, 675668333, 888271826, 635345561, 453066099, 578789881, 3599423, 554600454, 104380270, 314980931, 246586704, 438986401, 30675475, 184085528, 618059228, 147100141, 204018032, 126409612, 373728874, 585410605, 208542014, 451286071, 975243850, 914533600, 778561800, 679695248, 329184327, 369653332, 133265313, 820796127, 199632743, 625536537, 735825051, 121224527, 651989605, 953614203, 794381191, 983272038, 371120773, 666021031, 98543348, 462257499, 781645940, 589490260, 522501866, 966762065, 639372960, 749359783, 595738995, 722317190, 18896349, 695400428, 319246439, 510433014, 847126400, 898959426, 511184052, 681152339, 230618760, 749050879, 34085403, 157284675, 131192110, 825217050, 58426688, 987218189, 105985947, 542712204, 320730180, 302688021, 331337567, 428843123, 552690971, 66368761, 776968044, 897735023, 36461524, 892780899, 470372740, 941341724, 242885290, 200281124, 707729111, 157343535, 74919311, 871682808, 161570845, 826312791, 150376377, 457571878, 872500096, 776279480, 360593156, 287930490, 607104831, 395923527, 631458477, 678422707, 856986390, 237863812, 728624217, 323695011, 851241135, 890197097, 391934806, 722222889, 131546107, 708546075, 43678396, 824264148, 856033595, 102716564, 109055175, 376504398, 505912408, 67714063, 562362883, 93996127, 725858157, 162715697, 780801327, 861726215, 309356854, 409105984, 118166559, 573782003, 431091710, 166489249, 231501690, 598878812, 45429587, 784002878, 145990160, 723124791, 581911242, 512528366, 875925944, 334320466, 535090707, 812294864, 295524195, 831169727, 37034423, 988337647, 62393636, 189313728, 656814850, 442749667, 70769702, 334535913, 919437199, 24502441, 525830288, 811392010, 213954345, 57864461, 160227007, 964402401, 8612091, 265139300, 660935059, 540956961, 208167695, 871392438, 475589158, 627203728, 426289899, 458236542, 331967740, 716774254, 82495074, 679918786, 863222070, 642367718, 235353394, 924436177, 514763654, 160091863, 542116882, 386635811, 764935141, 709499967, 963735245, 698486798, 615341787, 452823444, 618394986, 492631990, 124350736, 824418183, 157857943, 331181331, 707748636, 852546645, 835002509, 360894628, 646284479, 643642066, 381116350, 717644863, 149381429, 674518152, 57605138, 907744601, 935815674, 590999755, 464466578, 248371006, 283681050, 364027502, 599240803, 818187791, 679391713, 443648002, 564668899, 707779919, 402234181, 858021535, 230430794, 982491607, 180376648, 849812542, 72891361, 337079834, 835032037, 971144715, 556248115, 737668744, 212891819, 441053047, 118599628, 691994586, 645379628, 342760407, 660102319, 148190898, 713018495, 98131871, 778573302, 807981515, 74336983, 981688970, 859517915, 576044031, 710905062, 516081533, 105795286, 841458893, 863164346, 716412643, 855821622, 347197456, 770446439, 326957035, 958862781, 470202391, 81338128, 734784471, 170412030, 965823021, 985448130, 44270390, 589981158, 531586654, 4901375, 472250823, 682183574, 308464125, 403267988, 193547604, 988286849, 793844057, 440956890, 53600331, 202183997, 806054923, 168740590, 509009412, 274896909, 433454535, 863721823, 36761969, 242515617, 666181550, 69248037, 605969588, 182687108, 103086372, 763971008, 130553179, 576572669, 202526205, 58634129, 527498400, 929082960, 429721002, 251054394, 777407618, 881187084, 80821781, 178891905, 871163357, 497267889, 245079939, 796092469, 92973373, 156880421, 230103701, 813041008, 571198930, 454011405, 888690156, 516975914, 879431373, 115053606, 947985406, 207956906, 642687368, 316164123, 342973480, 456122046, 760532774, 809637834, 640568605, 33756900, 155898039, 224070574, 130295818, 102467380, 45366832, 903083024, 510878005, 508694691, 673693805, 679218142, 473596120, 171282984, 199461303, 799297714, 768623107, 858591608, 737254249, 786332931, 291576330, 750455700, 547078743, 122560241, 891479481, 257065294, 583262721, 483700762, 160300133, 779379770, 648984152, 916372389, 920435084, 668528625, 274941651, 588208037, 226872791, 484538549, 97331178, 544250502, 68058121, 462071991, 832959688, 172851434, 996545631, 648030829, 586890485, 152390330, 959469360, 8199213, 775217498, 790190301, 613322682, 290095263, 648883170, 803545940, 842591192, 88508048, 50503003, 428272882, 486921199, 759925010, 243329471, 155502398, 695653202, 461655238, 251402846, 170787184, 800394889, 559755529, 486527534, 447610886, 162092889, 262855599, 875461968, 673986515, 893357420, 483011101, 700990861, 645999859, 871329069, 589952901, 92598925, 690523019, 448822457, 861812982, 402539192, 771838368, 516165388, 774143597, 228562338, 109550117, 823789188, 643106043, 358648738, 18282994, 958069143, 541432229, 173675976, 977447309, 914856183, 341151422, 897210782, 775236274, 595708237, 15686382, 373750065, 284488051, 96502227, 37676317, 466950140, 102432073, 985711377, 869768463, 229383618, 366399625, 510264169, 521071690, 16016984, 204558187, 78977860, 887573295, 342136263, 920519482, 708821872, 78554122, 274330362, 321033093, 125044924, 631202941, 829487180, 623978716, 790770755, 460542037, 265465546, 742110229, 403838255, 958734862, 981746117, 624194877, 130961334, 129076101, 86174331, 605244079, 657885849, 371422292, 830925976, 709180756, 23728025, 596264904, 911580376, 883882388, 266606969, 794667820, 23478727, 540785666, 932850662, 214777206, 201193597, 143232282, 129542224, 508296136, 101604813, 894005330, 324207581, 588485089, 381903286, 167275157, 317418034, 129980332, 940814467, 813933974, 187411730, 319870329, 487635687, 918817702, 716620162, 208733993, 589133853, 748779556, 179698841, 499624675, 852696090, 61616856, 258758606, 192147649, 714620200, 545527043, 692690667, 499634595, 319328185, 793101648, 900427728, 623314396, 738443288, 48798467, 845520193, 8024755, 16862271, 603798538, 278927616, 49245205, 965963272, 377412826, 312719161, 310166416, 819934082, 459521714, 266602255, 258032906, 67713421, 996343551, 839086740, 197131824, 414064715, 853399618, 703673028, 289393644, 426091916, 712470855, 887175996, 75775967, 673761713, 701761803, 656237603, 213039639, 394778953, 978143370, 190366244, 559585091, 125064860, 800451197, 250568096, 224118038, 889912449, 829035307, 104565060, 200131362, 672578484, 993220115, 236513058, 545081734, 524058077, 57190419, 2105872, 109133248, 496897956, 768391095, 385961633, 654548055, 147572745, 869057126, 229274796, 880525579, 402136588, 733383420, 580692848, 472678116, 718873469, 956692574, 481995034, 865338071, 255911790, 692123293, 543449674, 14996663, 701446923, 752598954, 866037035, 684548779, 198264339, 531065526, 844774989, 236120906, 222001874, 987023073, 627495418, 87960684, 50045124, 77412232, 556790019, 174285808, 92489313, 483735543, 761324146, 802084455, 476451344, 532770639, 21696902, 463702461, 712012350, 591572636, 563264984, 944111730, 968226356, 421144478, 869121637, 411097468, 67640442, 191207707, 685311468, 156568233, 221349129, 37788063, 567629277, 271622037, 749624687, 480481085, 556663615, 129510326, 58639655, 169383426, 245071315, 51171533, 294373698, 185816361, 292519030, 742102876, 380670123, 666686647, 575647106, 582684266, 34822037, 788970391, 837482390, 431885998, 981845171, 942697402, 926070605, 583687085, 399024144, 982886051, 732906073, 155854332, 401178535, 207129444, 736075529, 209881635, 750756593, 753317390, 137506646, 122529454, 419947507, 279822247, 882215939, 351992104, 197926476, 207668791, 239808649, 828339766, 129941896, 286296328, 8582505, 363075954, 696499662, 838350657, 836821039, 935219001, 88580325, 919632257, 721938506, 671038038, 394260924, 612307619, 498339448, 822994476, 359722022, 223201116, 760147488, 264296551, 235374550, 781668427, 632733668, 833073139, 10573280, 113771825, 945173820, 110119198, 596460710, 265656145, 404236631, 768021760, 353119489, 167520678, 835354080, 258203383, 177867806, 587365237, 643523361, 969752163, 510025228, 739101638, 87505924, 394906947, 173736328, 200461792, 573972218, 423353483, 965939431, 187646361, 752172612, 74772509, 715089403, 191648736, 506542752, 523442945, 978034181, 77174591, 140119923, 71024357, 200127287, 295975276, 599511663, 368699075, 159228312, 163448056, 808712747, 151935388, 792533735, 127670863, 136164445, 499750343, 644093218, 805251475, 305294975, 754623435, 388738721, 267043857, 819835517, 940998967, 368073479, 840857147, 63822179, 605390392, 676874392, 241176273, 604039800, 701159445, 750330237, 609441022, 7703116, 897957019, 467645364, 881806959, 637002178, 153474012, 744810585, 287372820, 973144721, 410912893, 687513275, 690286510, 979687050, 511544981, 356496650, 310352822, 517903189, 467213209, 264725679, 319289450, 826429882, 153237712, 386677958, 520645977, 113546627, 280709190, 424060288, 32314343, 976704603, 321285082, 668810418, 87273302, 225043184, 937745367, 140724988, 953576797, 772189936, 378323811, 581978633, 590993708, 645327184, 620119909, 261529942, 780876739, 673697518, 481623919, 40277308, 771981079, 916533483, 21838097, 724312112, 905838219, 533731163, 772128481, 377916256, 374692679, 265692351, 321840187, 526924762, 666952397, 656022502, 325215988, 512666126, 264757580, 2457678, 616648908, 733673946, 944371997, 219404024, 93665400, 469551581, 414011231, 145478869, 971638192, 698718831, 391304961, 489332878, 944704655, 279099242, 977152351, 839228914, 707204235, 526540188, 809581489, 950159820, 94054675, 537893268, 896569022, 339045981, 703138044, 624030690, 309566875, 705699251, 972828715, 981280937, 268381970, 583877941, 663274347, 250631373, 438261289, 86567012, 209494688, 897257415, 252808218, 43495562, 699290536, 639235719, 782273466, 853483838, 37959935, 936632420, 530336584, 695419560, 420284307, 542446899, 1368989, 642757981, 58060849, 16878021, 837529899, 396630824, 456968356, 320993020, 278280132, 599021234, 755496776, 167199015, 857706924, 53366129, 461653710, 648018699, 160447843, 497580068, 108088108, 928459162, 17757589, 835329057, 251282669, 674053372, 28787123, 643620499, 311493508, 937014857, 521567812, 544383590, 107873044, 874730534, 21752375, 758412880, 163636541, 748152166, 78579317, 619820244, 812708375, 785990925, 561351621, 792415148, 59160493, 520152249, 561316053, 249472016, 646735744, 27652666, 603624914, 925332501, 321597813, 63545034, 881506416, 156405819, 599132848, 170666619, 793050721, 132379761, 10917644, 165791066, 857637663, 660028296, 820369091, 823650817, 411518785, 834595848, 773000463, 320111071, 515758739, 693583884, 780364220, 223701672, 56228138, 452571046, 581867329, 615551192, 795447367, 483447546, 466469978, 679434995, 572787002, 463932202, 11193255, 171896510, 682126318, 590072634, 810353334, 884365869, 624851723, 306429666, 909847483, 463552964, 610371995, 611671113, 571465768, 770054281, 373693449, 207124628, 392105028, 604954767, 935152638, 942607371, 869077922, 748568100, 580215499, 771599184, 225765024, 608239575, 143991891, 690675612, 225080482, 69277571, 646314387, 596987800, 935494945, 174375397, 660690670, 72363963, 764411392, 544413504, 795998820, 489529729, 176268954, 5051381, 262792988, 164950484, 327082263, 687428864, 982196231, 529976241, 180910490, 962659298, 409937778, 110592717, 771671029, 894793166, 242394040, 288783767, 782725228, 80837930, 784357859, 832664752, 814602713, 653574387, 458732513, 770046500, 214691097, 543989551, 603950117, 265002934, 474513731, 680182660, 317350999, 968327276, 220162797, 524792611, 833867796, 741179550, 613876667, 710670293, 127416411, 755095304, 212742610, 826008204, 837597815, 938558703, 647450577, 691012014, 130990141, 130852603, 974348970, 272321812, 74679212, 44089380, 370021384, 451290693, 857197013, 21861286, 56219113, 422232863, 838212945, 62415679, 134933260, 83681515, 944118749, 561512099, 704742901, 28674384, 427702253, 523402543, 364061894, 553092414, 135911376, 398782118, 175244223, 134936844, 76766641, 855992074, 234173225, 358026552, 71717099, 411398565, 651124795, 745615525, 148350534, 194612274, 353694229, 474778546, 877215941, 312901858, 944884801, 344164854, 812403491, 756331591, 249821377, 565097326, 428947867, 388745767, 592602862, 713246129, 126734505, 836480816, 730845094, 856062333, 127767629, 909693085, 770333627, 382291432, 496862639, 602549408, 940747050, 539116311, 641760430, 41040021, 449768998, 943921974, 354951336, 191886295, 498480235, 367447477, 218056055, 308901165, 842175206, 126812418, 961627571, 916785588, 315628989, 165164586, 329660544, 662152519, 135120049, 462957726, 411093698, 468580972, 423079630, 351888874, 139284542, 236494180, 299190165, 691734433, 806727336, 94056414, 733111160, 820316677, 559573439, 772934078, 667057059, 273900626, 131280049, 222326861, 22659464, 473365543, 556820186, 533277233, 782096899, 812549708, 244922056, 378582990, 846459142, 410446123, 806125948, 261904769, 946799625, 76473370, 120453407, 73071410, 753403082, 993424227, 376881130, 924354447, 349344145, 909384475, 457968996, 429433810, 231990200, 819110873, 538178034, 940760050, 604293678, 174039399, 553587450, 62352965, 830441918, 919970494, 422978404, 321627356, 301591978, 530460463, 980185291, 718191927, 909416214, 862588034, 238025745, 487731016, 225308453, 651938700, 568299093, 646758405, 237947410, 90848214, 140958490, 216826819, 129188855, 952856967, 295349093, 797165737, 816191905, 795018000, 878097340, 227037228, 916468870, 288268252, 571653955, 302942178, 24653277, 628865342, 942977078, 731859097, 769432001, 467265380, 774558484, 336473696, 125501678, 665687112, 310283809, 899022253, 537169276, 756732344, 85960129, 690057378, 279986914, 338534760, 298073773, 364823110, 511045956, 506284907, 751669225, 327996262, 327220884, 648210281, 370822461, 802224560, 206224767, 404732483, 447489637, 41693683, 941487001, 106533628, 226276193, 950704328, 25376776, 921375636, 271862292, 253266010, 535795856, 188181301, 776898709, 193485455, 755420065, 205681978, 232259804, 352691498, 135286771, 612091734, 572363970, 16536947, 969545691, 388217239, 407121653, 202377848, 778503719, 379004049, 39431467, 842848251, 637866278, 263450913, 470022310, 786715867, 712767197, 472115017, 471357883, 270215412, 772795814, 423705153, 866560930, 507400612, 713147602, 795797543, 216333050, 160735731, 654836176, 506551750, 409217459, 133302452, 433886796, 481130707, 788582688, 871102860, 774630431, 161042410, 109836463, 282767382, 870912711, 693083468, 77038066, 643642972, 235513252, 590305228, 674495965, 439123102, 16279572, 304548313, 204025945, 128000673, 781767975, 475379851, 229186121, 171972548, 470865962, 151864626, 490975863, 401119346, 380829910, 480143135, 10654923, 255382056, 775839249, 176875454, 996590336, 838963961, 267823231, 429284231, 662930127, 896634280, 672267616, 391016829, 754850404, 48328415, 867243255, 364056003, 413070022, 134458849, 331842951, 941854320, 702972985, 819034737, 484951326, 949496121, 740222836, 30771452, 657788788, 229966694, 118170301, 110252009, 842696432, 64164525, 598569496, 39300034, 943747201, 717548968, 708981342, 327819229, 314507435, 450192749, 29111481, 454489383, 617291826, 590001778, 347132933, 442357299, 953924949, 674778818, 434373341, 60688856, 155450813, 291826642, 614633163, 481486476, 440950228, 995129412, 146263623, 774145354, 422004162, 459739094, 295176867, 842050485, 253887073, 754385981, 330094230, 326134971, 477044168, 685709867, 664291667, 618311578, 714730998, 846239951, 672632700, 91094955, 227190807, 298974151, 207586326, 134500974, 90353482, 460994075, 829461303, 71384393, 771986594, 896824858, 411097012, 934487737, 473472244, 832902668, 305396103, 860813780, 421129205, 738226159, 22077097, 340570602, 35003815, 986543921, 682422479, 10830207, 425181951, 153706857, 823899400, 819142389, 795689570, 507430885, 526638566, 855364960, 837144594, 82065512, 842372974, 895171337, 849583896, 277516966, 789994540, 19695962, 798669716, 669590972, 579525217, 142508872, 975880542, 333212788, 588555193, 110908191, 787445956, 896088257, 69568604, 248121827, 948760238, 324949422, 48253420, 728039129, 681267339, 912539755, 902713353, 415550357, 900469949, 951112942, 240227809, 760395374, 965573881, 111744390, 887304504, 398162545, 892547384, 890572198, 297476258, 912738833, 760909615, 475827188, 951085413, 544044108, 352532904, 645920644, 459378381, 434343389, 798731449, 90859835, 438199988, 763664939, 694869437, 404391419, 102769860, 354645649, 348578915, 834701912, 27060798, 85679111, 487012362, 747470456, 576309086, 92847766, 919038896, 523770835, 656263785, 283969970, 412020655, 716792691, 314495650, 974031182, 200747551, 251840730, 627277259, 611044872, 808623906, 551470293, 24574484, 984994870, 981215170, 137617941, 435703778, 455311155, 344315178, 862171983, 773727022, 370450964, 925782880, 181554009, 61958868, 353600366, 673289890, 706862591, 543205964, 433668, 607065186, 368688968, 326181678, 186530885, 947732639, 6965826, 326795144, 429461182, 869727131, 752378868, 566678886, 898234660, 180947791, 906816679, 519829895, 890893083, 782114506, 665054223, 711508362, 976563816, 877196644, 190179802, 598410381, 566007568, 525227159, 332999758, 794487555, 106478665, 932154866, 450796308, 159700294, 689646625, 171115921, 402266568, 87410579, 711917612, 813685252, 353919953, 44842277, 965942781, 871629498, 221300080, 300578150, 728940639, 273747418, 304599701, 429095710, 103143829, 773914595, 17181576, 985417318, 242881590, 789401830, 316855494, 92836077, 600411162, 728440414, 470433852, 271937480, 927570748, 9083893, 600293619, 587311063, 936579694, 100804937, 695775542, 778447362, 526546493, 148945779, 899680479, 189009924, 202527268, 202374553, 699439536, 780692, 309789946, 202377354, 564046025, 115215929, 619321208, 379328279, 302854627, 5421250, 861850434, 759057396, 199970572, 723036836, 686880541, 10921078, 287951715, 450739676, 479801254, 923592054, 71805485, 712065584, 459754645, 387714757, 734887364, 150299555, 128503568, 69220874, 113305670, 911237097, 918996943, 126161131, 54481003, 471915264, 512616470, 471095332, 568275318, 801371113, 486266654, 587699112, 364408715, 671558047, 27762607, 185043364, 74768596, 55257314, 505481421, 923906611, 253487906, 988339, 943132260, 174758444, 409016469, 936565936, 297210159, 190994831, 818670234, 881047300, 453672204, 369526736, 666706888, 41277532, 438099506, 769145728, 892127224, 764178611, 924277936, 980133320, 718510552, 813290417, 365605710, 762588867, 64470465, 829962256, 30679000, 448298186, 983293814, 849210617, 460347708, 49009866, 296101994, 225232199, 864191671, 918181777, 409020120, 151749821, 382089144, 690944363, 55082531, 92453188, 816118363, 466894417, 296265993, 923427327, 558593920, 591941569, 733196463, 120575467, 691318699, 16340883, 423429373, 423111936, 668454517, 241676104, 360611263, 660737481, 911835893, 327099981, 330978497, 543654981, 967673805, 213293936, 573204122, 699493292, 574833965, 60634488, 904919118, 336785306, 691013140, 379294114, 890953880, 708239515, 801829726, 839760864, 700685289, 597467694, 437395404, 700842128, 960066090, 65324499, 524459623, 751726506, 918151548, 409237559, 136645555, 929815216, 367750837, 157097922, 633824602, 518021490, 956164311, 597751330, 813887604, 812790972, 119014980, 803390059, 115797757, 13169835, 563366706, 142417496, 356623706, 675912740, 539220590, 326462766, 967260284, 785833872, 813915810, 395435682, 525953993, 633593337, 274762980, 971100078, 160216504, 18561979, 426938089, 567500474, 955464389, 313682975, 399074014, 449696550, 431193918, 65761894, 609336703, 637990593, 908902135, 176365553, 669858049, 518190793, 281431001, 105010170, 545225314, 7082617, 696622116, 414776167, 454432541, 21508866, 465294730, 216144421, 357145146, 523146935, 762045851, 334756073, 679757801, 661422983, 276792063, 657610152, 586303429, 139164280, 309047691, 737441932, 126915191, 904581467, 998306119, 464664378, 283513883, 31998267, 784846231, 819816884, 342468932, 271953880, 438357149, 307952636, 656800279, 509039953, 363998948, 598072983, 148247904, 358205879, 906032176, 638418594, 81398807, 871340260, 796315659, 996353599, 147625393, 918417172, 974195506, 10979098, 990385372, 486968256, 618440894, 855100932, 807573269, 848167237, 694099288, 436367983, 573755461, 714833128, 236566739, 8553115, 315136909, 288833351, 807460742, 877502387, 829811314, 606323993, 298544690, 609294952, 680492720, 51437092, 364468008, 414766251, 166757497, 311253708, 588996191, 722390962, 403270586, 541947736, 678944686, 488252530, 947983678, 52593980, 621691453, 951835577, 86157857, 165252414, 100560608, 731595852, 601781455, 486092556, 300619703, 617396145, 205611507, 781364311, 704167304, 296349218, 789697185, 57797611, 865876805, 543172965, 870874557, 292605114, 226791189, 148690991, 785949907, 135607915, 126133981, 748235602, 541061889, 753234767, 594497059, 915959040, 834029669, 493002885, 266624127, 764206459, 481390259, 111335012, 769946874, 145498675, 47638835, 626998784, 79880759, 579556392, 378385732, 755108402, 728045451, 294096024, 751847369, 716388900, 111587141, 410630415, 341095462, 994831516, 718868745, 763417474, 572623070, 335148349, 987946124, 645986249, 412639323, 423732922, 902823353, 839054289, 371653439, 746951166, 912436569, 775580184, 985304842, 946561809, 698716399, 969349052, 314722362, 508287181, 321817216, 190417475, 284697844, 175486380, 509752774, 185254961, 904715244, 155250896, 536302968, 358190640, 760401667, 112942295, 378930738, 998181199, 152862760, 298374745, 270965720, 367543764, 550632672, 804280238, 483720517, 913909259, 314312168, 831540346, 664316412, 969180557, 949674708, 688763655, 135249536, 630046936, 555640544, 215964364, 996083140, 485325148, 595532586, 824289770, 891068920, 53121272, 477140924, 954705489, 987069281, 38927575, 1043995, 771118390, 656630430, 95306557, 797388440, 686589109, 493130709, 963148088, 461648450, 494472060, 752555877, 894351222, 950385673, 176174854, 242153160, 734956569, 575053105, 186422079, 325703894, 149034734, 554203005, 217749129, 664464476, 72206121, 189700904, 249542657, 210910148, 626146576, 674260052, 537059725, 952061914, 395019926, 180618300, 611741727, 474265999, 57791017, 324414690, 847865070, 326048011, 124025965, 243628018, 91383314, 388744856, 373447479, 625305805, 594784054, 520407823, 937578860, 740605712, 243765589, 760980024, 657928351, 989905749, 390113472, 741351947, 430893170, 149388415, 985223530, 686251078, 980229150, 348078473, 250900171, 474129020, 519821516, 151462329, 489070673, 447752475, 131575972, 373837140, 15315454, 317570947, 958282608, 239391981, 416606860, 408152714, 245358865, 213457157, 267933836, 813941845, 540277797, 109443561, 106818361, 597152418, 267354906, 678241528, 130534369, 153532062, 664219814, 346301791, 521557808, 432478429, 353082296, 512222480, 925088217, 209778232, 890452954, 460746265, 233629104, 522931776, 290074837, 277212553, 439332062, 93147598, 530115748, 197559993, 987748689, 360826195, 348900874, 67145425, 807416334, 650574078, 742851234, 564907744, 317019932, 677568320, 909846889, 764297588, 328826400, 571817565, 876604134, 66751849, 779790533, 672278830, 824900078, 505089145, 30975042, 571690790, 491245190, 34119166, 920176028, 727393643, 890167562, 445189852, 972604154, 23971090, 963150046, 209505515, 70322663, 911724376, 113601389, 124736784, 597063845, 191896771, 451469319, 490559853, 956404080, 61916881, 929551592, 341624470, 568132223, 66206719, 697360043, 294316970, 947104394, 432959257, 903702204, 20675227, 602826761, 684045471, 836946821, 106159291, 746239023, 483760590, 161515330, 255557113, 447849164, 380594967, 332362008, 240646520, 953322734, 592606415, 753931691, 131760731, 626901391, 47721193, 600108280, 693704726, 142670821, 992865688, 679460857, 606300678, 998652339, 522200299, 447971442, 538205401, 203533950, 681583717, 333427921, 564142787, 225396764, 89584320, 324230920, 468651851, 5041026, 160692533, 498335094, 245994286, 848559742, 640108885, 952909781, 380539407, 541825357, 814886608, 98770273, 55446013, 205083952, 433960234, 538592279, 549903688, 470754323, 758554598, 26384234, 463643253, 355791400, 4291608, 855051052, 894661484, 550488623, 776832896, 745576400, 62213624, 386396482, 256282788, 172276542, 390666003, 827957223, 690070291, 733879323, 355865414, 588395659, 907260033, 676974082, 3700796, 763504876, 121146879, 692376485, 303239169, 135742763, 735633298, 85227551, 263215222, 271570138, 335209282, 95259937, 225852923, 702824328, 579568615, 575907145, 729964579, 116333531, 164284461, 181531268, 761738155, 835478983, 993236222, 974404447, 432574815, 593400675, 640101352, 795567821, 243675012, 107927290, 636911110, 476854554, 859117477, 262267319, 309130347, 101498242, 14807815, 496831544, 366976925, 712395638, 3847069, 258099517, 534120510, 611747415, 76418523, 904133207, 19842892, 747875267, 67243649, 567177031, 502476451, 473737403, 221971634, 612219541, 850049738, 824900913, 616294712, 174691986, 838505736, 601899330, 506023550, 756232196, 45931127, 570848128, 240153191, 112362583, 874594495, 840820576, 176254935, 843975548, 607788049, 518151550, 608997738, 459001954, 632816639, 938051932, 512379008, 34150968, 294426767, 52442901, 40713092, 311537520, 368405404, 200464889, 433551554, 187417796, 37609286, 265015471, 227890907, 261492003, 202655194, 150248952, 956948148, 544344802, 162032518, 429683537, 713542021, 26278002, 82369752, 354475786, 683134539, 893138040, 185805541, 219280328, 711776197, 198602702, 731061022, 854995263, 310532979, 114753347, 558192981, 20797474, 498591265, 857152517, 23371078, 615719232, 681782495, 196153244, 842032272, 295506647, 427091460, 771288876, 590179254, 279081169, 349597231, 984915359, 166671757, 960225100, 156713493, 143499410, 234997770, 930247300, 989007385, 384330171, 763204723, 174562399, 58781289, 221446279, 191060563, 675754284, 604167286, 233948105, 469495354, 404471417, 591450423, 73785027, 158441697, 198897051, 965003245, 867442687, 100499666, 674896559, 536914123, 715648096, 72681305, 736542159, 857303007, 801263408, 966643513, 731894105, 998879372, 367883140, 824170937, 488158807, 224636975, 888274758, 157689675, 805682944, 580209587, 368140102, 617477627, 265471005, 322212102, 10134150, 900590709, 973327097, 656830778, 163705490, 604784802, 715998642, 703354687, 1038506, 347538241, 329223088, 351832004, 699452087, 226166571, 609267829, 386937370, 114606504, 998063130, 120369544, 426735085, 493759195, 211068644, 790373442, 649319698, 82867656, 664796909, 357767284, 364333451, 687962792, 386484851, 809057521, 357392416, 563586577, 728171143, 127702985, 872947775, 398967235, 836496418, 775198319, 157646610, 50366791, 804945290, 391528510, 417629974, 710485009, 216737438, 362252242, 516099199, 171714770, 136148940, 605997339, 18212352, 837877476, 731363823, 341631176, 383059259, 727013253, 975093654, 990711577, 356916165, 696294392, 999655851, 522680566, 876309953, 368760671, 714911614, 953188453, 422276743, 683606816, 451631813, 929365636, 546467211, 101930486, 115396291, 226089868, 911576459, 446130321, 160564425, 593989185, 680872784, 340083544, 731934108, 852788770, 463267592, 300818525, 680771680, 208155972, 351473283, 102220032, 147570890, 306077054, 50774133, 588634733, 373985780, 690147736, 662074177, 299439008, 354238467, 289287068, 790307627, 868807356, 418716039, 363265760, 712162644, 4883328, 146840801, 976338517, 59368703, 94031158, 550127982, 840486771, 833269267, 999003781, 583458403, 108871472, 391219196, 807611853, 299630383, 454540901, 987375940, 306038101, 826962031, 38432630, 174054556, 364498411, 484126909, 463495145, 773644055, 524427874, 144666583, 94928969, 12576915, 539395345, 841939158, 129263002, 324076059, 888014708, 768403235, 107106113, 454094610, 5345636, 988451927, 366279188, 236530078, 702898490, 628707076, 657782427, 464012403, 850796162, 612208225, 658459798, 856715652, 905167054, 351995751, 411319134, 565774901, 435916377, 935942493, 968731249, 257743925, 275544258, 71634197, 129732335, 649596904, 918418411, 809258031, 13442755, 188612981, 503592815, 582026468, 54071715, 152974375, 59136143, 293020701, 941646191, 40094595, 32927101, 11968506, 524779313, 167835377, 648146036, 897290731, 91916097, 272450755, 70335972, 203679669, 742027263, 35566048, 159696404, 904506679, 445924124, 909847953, 402349675, 439533965, 965713566, 476924954, 112800137, 760056275, 183235350, 778131282, 62471124, 461758583, 428373891, 901278825, 80773026, 297099241, 35942911, 816011474, 90830624, 589513647, 551931238, 851298744, 903214010, 12285331, 546457216, 415040505, 4072357, 45221324, 134078339, 851947210, 192317879, 479258767, 557020897, 639415333, 530455794, 582768084, 8643572, 338130600, 774521139, 146036125, 27763293, 931749339, 367543094, 846524693, 427797010, 500977599, 698901615, 836300495, 114575944, 356262729, 784723276, 830697163, 145923837, 422831821, 685146459, 489145681, 96939648, 63004552, 919273903, 425160092, 440498928, 189078878, 293154204, 598974728, 552137049, 164748236, 317239484, 488864938, 366709708, 403537272, 326938654, 45911254, 115704188, 212209802, 567937955, 977086563, 774688994, 710563331, 830570070, 916951490, 508997859, 628342409, 402094530, 258191680, 969082105, 599953227, 398100120, 724665366, 139562226, 890991276, 693730452, 282970979, 383812440, 904631485, 826744051, 631820576, 918502628, 727576258, 443244616, 731651477, 2667292, 861175327, 387637677, 867680159, 706737939, 56540571, 11020120, 128691345, 95303217, 501552486, 148030861, 651195604, 172462096, 254276446, 405005206, 304138744, 225307189, 548884101, 903163447, 16806029, 276033718, 92983808, 197458101, 879766653, 75630304, 352188050, 308044417, 882148803, 999749347, 644737506, 279582426, 250553408, 541634055, 863526336, 888521838, 965423561, 516044, 212848944, 988752200, 223177460, 294402341, 397785586, 936498615, 155232689, 155550540, 657392725, 703247028, 79650520, 663610862, 53637543, 808041651, 392350013, 280127554, 27944160, 317994921, 862116014, 780122455, 543606381, 209326460, 867340127, 174939764, 984773375, 611963083, 36241307, 316578380, 233090475, 185720695, 950104898, 243292825, 737544740, 354236231, 261498971, 506358561, 589744579, 824861873, 688240550, 857353584, 666426493, 126605438, 80483423, 230471248, 880505293, 929434058, 168281981, 266942641, 214703139, 810706506, 713785933, 271955688, 666039933, 897279986, 688845771, 828934774, 210594228, 692791014, 140851387, 710548339, 153724904, 599224912, 3072848, 85127171, 608586280, 378023749, 228002452, 952383616, 505141711, 596537298, 122895867, 911854589, 8636428, 897096094, 462228443, 454532471, 498381023, 415844174, 949517655, 486173349, 106090194, 321386433, 903688248, 439860905, 618389649, 799987680, 477902133, 92518102, 485123133, 163178330, 30961638, 306737222, 760790467, 400282681, 194631004, 457855347, 399980409, 15024965, 396279436, 921544773, 759350864, 186197754, 933729242, 103920543, 767575915, 124341079, 472719662, 416994693, 924192366, 948023768, 583879241, 107861766, 978078000, 210343544, 38104971, 849447725, 131723922, 884709898, 450154857, 693063805, 225905628, 41413398, 57827076, 284418426, 822408565, 652129484, 633917950, 120327141, 455982641, 602169323, 575503250, 311589396, 622121746, 366390962, 97222458, 727534944, 776519969, 956715634, 494330215, 890464234, 999957884, 841498841, 167258148, 550840834, 807836292, 715553532, 807969711, 742847394, 372958655, 768592567, 376019741, 865988266, 815272816, 673156849, 53639330, 137768134, 163462605, 467718724, 42199486, 588049708, 5670424, 854622005, 47260835, 543271147, 890622425, 724197174, 614730119, 820674340, 542148444, 881563372, 872672603, 99287654, 857396023, 698867717, 215157633, 839340055, 799880653, 173067361, 454034098, 911805540, 738029488, 868500779, 312580419, 972122188, 9088445, 165255892, 271048135, 101845541, 280672654, 246752324, 584270676, 160172033, 611101992, 947853991, 444171754, 389516583, 811041958, 341034498, 784160046, 818497991, 531829836, 356937285, 43407052, 903469722, 724191687, 504398137, 390276653, 915041516, 991735325, 297757892, 757874435, 464091378, 612701069, 904913888, 29741365, 415071458, 221801140, 387023851, 874552537, 45899922, 480405955, 628570577, 622149313, 762375745, 503860731, 103678195, 495670523, 409989074, 874585171, 954952886, 849220187, 588371870, 397388559, 363826341, 205739790, 543196301, 344476663, 478927289, 71029971, 618901879, 183673899, 515183505, 552156382, 55156351, 621733366, 28685189, 386541774, 163761588, 401618607, 924759980, 852387218, 817739626, 366002476, 795720512, 822278490, 269454417, 980066228, 216271017, 322258794, 803076265, 743566928, 939549053, 430740209, 838387441, 869776979, 772541886, 577124249, 477084864, 749198546, 436192497, 255908505, 197873699, 164489828, 459326507, 455568429, 463491506, 16059735, 867511857, 948636414, 224165674, 649675035, 178286707, 659944739, 109018360, 300920489, 240265253, 468610134, 852327497, 514302980, 39335276, 672570948, 915755666, 294024226, 909004454, 707685819, 601902747, 541612734, 481769480, 431394886, 738957186, 817207376, 232842485, 69461345, 536348955, 93667121, 780847093, 194094970, 918832075, 699327747, 480439917, 623110215, 419758455, 321429874, 22665925, 277178569, 553844292, 622553996, 405864231, 370538385, 46944763, 120841828, 491436601, 130692144, 189444768, 758783245, 70026414, 779266139, 840004693, 325363263, 177263382, 165156914, 244963453, 173934179, 788788906, 150241796, 656366401, 684281619, 15588490, 585562807, 640921648, 339120635, 630223223, 116771629, 952575015, 811233801, 507954100, 146939702, 797986810, 652299004, 531966102, 863802671, 998546687, 873082438, 16815457, 599645648, 136540520, 312402786, 931072738, 620934351, 102667992, 649849336, 237109527, 601534819, 926462884, 881910199, 907912738, 385792628, 19982441, 711387643, 463515102, 176277550, 468194683, 395601526, 257486775, 103777422, 941467749, 839005524, 90783237, 733128826, 72309869, 469448846, 8153539, 105165859, 692831971, 327834472, 983760962, 854680454, 145034436, 698798880, 934901570, 906781997, 434691925, 766267296, 384024404, 889165250, 906666846, 192548698, 272518435, 673341724, 564869857, 154551747, 628200622, 718224935, 254700209, 512182487, 894406851, 65149307, 151715107, 905242384, 915616910, 910621321, 321117067, 240591962, 108443117, 701087070, 862128372, 851674503, 517195322, 653871325, 514794633, 289756223, 887784198, 611919590, 42156898, 529193227, 527258968, 164721086, 78098039, 710263577, 375800303, 447588572, 251081719, 90091699, 299371165, 182082143, 298366715, 24313738, 526863479, 820826301, 551253920, 607486080, 755633833, 875859742, 506477805, 232447730, 110959314, 603348271, 379040800, 58744018, 230380657, 98973204, 538037660, 564521144, 196016841, 381738884, 17337887, 383709739, 421531779, 774617240, 104184693, 745234673, 504744225, 479892441, 430146112, 639518822, 287144945, 133644201, 338876779, 457591017, 859454445, 387403438, 283450363, 756318841, 993282340, 246424298, 311476742, 279063794, 182478443, 211647920, 737317401, 662592662, 495703726, 205876648, 42074980, 347623288, 132274820, 17660580, 992424310, 553419167, 437120501, 84515877, 513925425, 415468734, 696678443, 997507712, 682030104, 661921053, 341629420, 792669675, 207266223, 379702144, 637618475, 92515924, 341701946, 686916141, 686612467, 916145612, 233678029, 390447699, 618473461, 292872403, 545877302, 546327263, 650530914, 699178545, 255438518, 944581127, 356012523, 827697607, 659118505, 992166612, 448192079, 201957055, 128553528, 403054335, 233123423, 339298974, 99647048, 185942351, 118328161, 816991666, 64298465, 150201729, 867155670, 815133702, 201270623, 438434981, 218111561, 899572610, 71906065, 263328031, 373003684, 743260822, 313212493, 420997341, 260358973, 322340689, 712340921, 287783665, 59480620, 422621797, 331488731, 89706689, 766144311, 6605746, 123135805, 832327607, 587794750, 824252276, 958864188, 7513780, 580796461, 280812418, 635149154, 633430748, 887728598, 881558184, 818057814, 307200594, 540343657, 738265646, 892357689, 97627228, 367121835, 416488403, 644530867, 866921692, 645776625, 78365078, 931769710, 417880488, 19996794, 383779031, 426604664, 959249422, 377220204, 552572458, 563647343, 5241223, 417134309, 209416512, 249014071, 102314535, 189142181, 224914568, 10788326, 841058698, 745077087, 975923905, 958775568, 915116542, 836896535, 644550454, 987629623, 206153714, 765848007, 889668732, 989478209, 334995359, 653372937, 396909940, 128366101, 351103287, 274888597, 757559040, 775146626, 899498257, 566873117, 629110328, 620035164, 265606714, 812319830, 202466158, 357913425, 799411937, 755130399, 144541577, 737825890, 317582197, 144795659, 850651499, 767624197, 503553526, 873378838, 328066194, 193357882, 723546722, 43828586, 922769784, 763906475, 474109859, 176017088, 162066343, 87720280, 697659168, 63659400, 548247368, 18069541, 409367731, 934012880, 92744574, 980517859, 352908985, 987831826, 501449382, 166954630, 936622119, 634086146, 707658880, 80454330, 991728155, 885937029, 496545670, 58471088, 581912030, 286246046, 973627988, 51396623, 944341598, 307791631, 550681497, 973792624, 755594803, 292516462, 885054296, 58100322, 784783387, 902605999, 168440387, 971113459, 120077001, 302726207, 18879608, 602193000, 590318886, 998468079, 895965386, 848063345, 341534572, 853972754, 658261247, 269550220, 772835336, 912039639, 485273001, 372372008, 946446600, 706523627, 264488802, 802354604, 290871382, 363848960, 954175193, 667874128, 477875826, 552654966, 990024611, 873462084, 701589180, 241066072, 429067330, 43806878, 600695963, 68538720, 742493540, 451728676, 693243552, 208622298, 160282107, 541358275, 794923079, 888565775, 311446809, 437615286, 143459719, 202166926, 435085297, 501350670, 392960322, 393613206, 564154319, 406552361, 937061657, 55030478, 361943268, 814877466, 125788344, 948152495, 262737116, 835751112, 939088525, 672499289, 673270253, 305742199, 444777864, 393984489, 977542617, 38826386, 507256772, 967838375, 379299575, 488711874, 690334224, 444022153, 400774482, 206828908, 318909489, 967786388, 466796021, 893733634, 363530599, 137049485, 542421297, 816636652, 643720280, 113076949, 746890836, 747071563, 824335360, 521329130, 238542053, 250209583, 12077975, 263895672, 269409961, 898017915, 188312998, 253793755, 712457867, 154691569, 250248343, 315515788, 217492283, 37080606, 541814088, 533663578, 166005798, 763034630, 196633696, 621094827, 437165132, 169702071, 36982174, 946987348, 566482255, 202343653, 366562376, 80453687, 805255585, 63540792, 550748140, 796711711, 514767058, 477607046, 832885739, 745506018, 373434277, 624595173, 654304309, 929460560, 407468768, 785691136, 730771131, 220366856, 471557041, 134931636, 900006127, 240652007, 881634118, 229425121, 640655615, 149025621, 377490850, 113227435, 689143465, 59464994, 564104578, 963354678, 532354778, 653660988, 448478969, 135349798, 726647814, 271997686, 622014755, 542267209, 80061113, 573429089, 884185941, 73442092, 772010994, 453894149, 513316507, 468264850, 360998287, 340011784, 515441589, 847637544, 666137774, 614661411, 542744736, 880325574, 114491355, 254977129, 924225156, 772463812, 84417861, 628669165, 515890053, 523701411, 296348730, 856750628, 658083249, 782935018, 192210121, 961887482, 338332790, 684034771, 324362577, 256855072, 830396785, 574466643, 527919958, 635223690, 240305020, 508553731, 130961181, 436503304, 288321340, 291980413, 922759285, 561031421, 407422740, 225757889, 492984901, 859984465, 13095534, 34137883, 109708966, 577397916, 637205084, 594917706, 925358412, 351205379, 381490641, 2657300, 54690266, 234532955, 213787018, 325758775, 82092237, 589021272, 300144924, 279254422, 555512810, 540184968, 288511419, 547124487, 364274295, 363473218, 526929692, 872193074, 845453845, 38355542, 356018033, 262867514, 838856453, 904965353, 886794469, 603720342, 125622801, 226072121, 829961127, 221478682, 774087204, 356024276, 30096945, 738227447, 527802061, 982822951, 750476840, 746985766, 462782393, 849578071, 701358955, 438260253, 161111480, 379285654, 953223485, 416445990, 507475528, 157281199, 395988293, 727116364, 230116881, 717257960, 537544541, 244767162, 764038362, 232320502, 469659501, 55210637, 317177021, 395423628, 222381738, 358391862, 527506760, 6028178, 141419706, 965561218, 810520013, 706141604, 552568816, 556442592, 99239814, 452603740, 574326007, 616170008, 268429063, 578697606, 852798951, 327023532, 320902763, 666520204, 258000632, 839643336, 432392165, 35280983, 513513177, 379405055, 291330687, 429750153, 155264390, 912265562, 4535489, 86073999, 452815205, 236820298, 924358019, 345646465, 608983113, 676003626, 746817895, 576955010, 563124923, 259246037, 640719785, 294112853, 217848302, 328103500, 909095000, 261275869, 218809661, 28214351, 481840031, 239973855, 859550761, 634093693, 641958364, 446700200, 401798538, 331604223, 450599119, 839060621, 780621484, 696845879, 853846694, 445302091, 343787981, 693536180, 477947449, 142690842, 325673983, 302556315, 990910906, 670307344, 691510477, 294448347, 426862150, 640423797, 276539913, 934244908, 341543523, 595835390, 548133012, 521879235, 449565207, 361666573, 152185386, 920740995, 974829261, 690551680, 302922937, 975436841, 692322304, 213997094, 966762026, 818360058, 325318826, 830791246, 440836699, 49514893, 91967589, 797606554, 788093925, 696738451, 847237021, 905169194, 261845161, 526057506, 342783361, 659118742, 976290065, 292714050, 629087687, 996864193, 283041089, 499251204, 171761485, 612292682, 621760541, 641503363, 337551747, 58086384, 210735484, 485376844, 290574436, 707227874, 124433476, 614771019, 560874916, 306420903, 187366485, 52581720, 555471196, 740244516, 170829110, 914917096, 253060973, 13106502, 8140166, 667688528, 289831650, 150839494, 397757890, 358278728, 524400958, 500505691, 978509217, 192746343, 688242734, 85665153, 281618782, 722823452, 786884639, 492484840, 84098025, 109606172, 870428231, 246025406, 865816324, 264515413, 508185872, 147953098, 650571794, 461377209, 439750651, 42498545, 496324979, 13060590, 985834550, 491204979, 625751492, 572552308, 72412806, 261582687, 827694400, 865220564, 496874566, 25842516, 699902244, 552609372, 48644689, 377586888, 353311486, 26789001, 574326354, 351280891, 854642299, 894129898, 236750802, 74833524, 539710053, 354800341, 214589523, 440586237, 207397008, 343533535, 747299775, 308444463, 810795475, 90188510, 598897171, 774742968, 134823879, 761987345, 608985622, 624061740, 530747352, 120826760, 38383707, 569574243, 262902455, 189554261, 704214636, 758962956, 84089656, 563498809, 386433480, 597823065, 755035816, 404292649, 909067599, 606400897, 700466853, 337629650, 150897558, 198210783, 510720106, 868162072, 44017364, 366468603, 448793731, 522074794, 618726858, 598524303, 780151362, 168179824, 837048557, 487671549, 964962956, 789980187, 543352062, 928224848, 626076330, 845973339, 924088785, 976209907, 504160752, 991904150, 210025305, 717181593, 266155457, 490185392, 201724355, 579079085, 133969594, 738982033, 165120449, 872309644, 272033806, 329206344, 606305522, 305999922, 90402192, 675424057, 499407244, 352685849, 57073909, 164934321, 164949510, 179457971, 317418018, 463581906, 972818511, 768008186, 318179183, 953460524, 931371107, 706202549, 395220396, 321217581, 991451446, 570729323, 710909669, 670041256, 752770168, 667116262, 232926825, 937339138, 815489391, 58228485, 897294763, 699042551, 688804085, 313704630, 596314211, 990587711, 105151478, 742495385, 284819991, 572752636, 720530720, 423918606, 371271969, 868888535, 442874564, 983733951, 932130437, 461125254, 260506975, 904171501, 6898877, 678965692, 596029494, 647884108, 511373934, 428880893, 963931192, 296996112, 882688045, 580915053, 668543008, 458294847, 986361710, 84485365, 100296830, 238802753, 685673921, 846004502, 532308708, 762043666, 413844893, 783051168, 767630979, 862362257, 818006973, 483833043, 933252752, 397788522, 374251708, 336956817, 190103966, 569674714, 897709094, 913787707, 624849763, 235792292, 693586655, 119673301, 230483972, 289594251, 608223880, 451424835, 244181138, 657531397, 655848198, 690268710, 58494081, 960128379, 464186807, 447360836, 648627477, 812754967, 171959221, 588347933, 422578849, 776945596, 258688708, 572349883, 409946322, 549722293, 618491450, 306792988, 340005702, 835253229, 538668046, 918623998, 208146671, 973872783, 23114214, 594763337, 834575228, 844292289, 545212575, 68885355, 519882278, 184552886, 727136453, 514020364, 912319671, 308030804, 706129014, 747850280, 344361152, 634239420, 402127072, 747954584, 503709317, 410807992, 378848579, 959323241, 432081848, 91666808, 889576732, 969992894, 196720710, 490142410, 713118784, 835030250, 317659808, 182321223, 153258429, 428644416, 656391943, 689388031, 822224402, 691099001, 174886697, 564996120, 260010895, 795064101, 545099522, 115425593, 752597967, 686510635, 318627364, 237812861, 475958000, 469834295, 586470264, 52487452, 426255855, 963203384, 517440299, 234768293, 815145988, 102238657, 681911635, 665747029, 670314510, 99767223, 967264773, 538964895, 260803566, 479065866, 793767902, 62251652, 449047417, 142603587, 862372643, 62768414, 753240278, 480621597, 981078803, 374857727, 148069447, 664912829, 438463527, 841357294, 51382087, 55637467, 402360683, 74182757, 123548927, 958888856, 298391660, 38122422, 878252123, 517607106, 431929800, 320564877, 689792141, 948162720, 638930115, 144513690, 88732943, 719601864, 79451831, 552534966, 286827892, 71282327, 870604147, 712536053, 565697535, 627544391, 117219463, 76660094, 458531860, 31927178, 688033915, 372509022, 835043525, 929054170, 378064741, 36407879, 823680655, 681453631, 794631371, 630436010, 244054167, 18339560, 175938208, 247526670, 286238477, 369054408, 259834454, 358060846, 225770612, 215396638, 216255044, 913861506, 216444296, 366929368, 46125709, 385237727, 342534587, 574598711, 756702845, 666678540, 918790712, 705929954, 861370672, 578234043, 173238849, 464026273, 311170364, 867349621, 119465968, 307352712, 23943363, 277304832, 207802322, 524591009, 560836959, 309680089, 922900457, 821887376, 496609021, 105144046, 77558590, 441341191, 44904932, 913199763, 662987843, 484186200, 981704228, 737749689, 244585601, 240883645, 182918181, 25807630, 305123324, 796059206, 984480162, 627109382, 702883610, 536840189, 251862420, 121955202, 123432017, 216762934, 409781368, 374492722, 911658635, 495739654, 29115331, 689484630, 799860021, 790851951, 266572843, 973414753, 737847854, 56348531, 408981092, 113926837, 796938989, 420810294, 520222041, 687635403, 644242381, 324320374, 379191568, 671119257, 22629263, 759552187, 441248739, 673186107, 502322309, 639411334, 294377048, 466382224, 797832702, 792999817, 21928756, 871631403, 574943727, 752569217, 27763756, 385414901, 221215977, 658670192, 359083932, 284458152, 651314364, 337950098, 1959732, 493319905, 762382013, 993443466, 807876258, 159737645, 832777780, 943182934, 539674093, 195543032, 576616988, 665777144, 353694037, 185351383, 226217393, 32629066, 689302990, 610392767, 671995078, 220690693, 340668510, 532940968, 295013222, 460661735, 901932798, 725808324, 311648644, 639991830, 572676783, 965466028, 945299857, 335577429, 855199297, 351592157, 652596681, 820943285, 677542645, 337518593, 330438818, 785007394, 855383702, 973975399, 731202172, 518425554, 264931475, 381909773, 171697724, 443175623, 10355506, 12374040, 826326445, 219615492, 317643272, 398085327, 159658824, 522392152, 618329690, 426393540, 23595719, 971192932, 375936618, 561113443, 783626738, 96700818, 811348202, 993630165, 653719202, 799996878, 4926884, 391396214, 177815894, 260672925, 253119442, 948586615, 786876910, 30254233, 805170499, 846437698, 215457610, 702074614, 540685448, 869026226, 688577125, 820797147, 519610960, 675343285, 700244457, 767921030, 528673346, 231649006, 94573767, 299260129, 725183541, 971560120, 45569551, 2502401, 697021261, 536123047, 122500645, 932913489, 465558761, 114096422, 166925934, 835501078, 999460926, 355671991, 294006753, 435311603, 411026636, 520268211, 267666682, 414886412, 893073641, 290266270, 542612353, 871605272, 790063245, 465813159, 226399275, 725783501, 905941319, 920252635, 56557092, 779306545, 641510145, 991881337, 55160287, 900162643, 28235289, 760739293, 169083597, 765765243, 533241878, 593794854, 525728445, 308577372, 761344382, 252709958, 715263131, 3347902, 507450603, 146562543, 131409726, 974974042, 434110007, 889161609, 152182294, 34754749, 160370236, 521112939, 899185164, 853725938, 303374749, 462865270, 847724641, 559894380, 527069470, 683377639, 424020835, 575610431, 807343848, 527806121, 16653212, 786254005, 439940338, 940900867, 663850443, 740448188, 278457851, 220157349, 522107518, 454946011, 982564882, 136649200, 666636306, 39917203, 762598526, 775078967, 280272005, 347513627, 763619205, 862014146, 752778850, 1684336, 267291552, 865847427, 399328095, 443090263, 98219691, 358698000, 701064213, 806833552, 826994460, 683445614, 657099370, 160848778, 188535705, 65018303, 342808743, 213041169, 262901963, 742745439, 669568674, 263892406, 475677676, 750898583, 716101341, 496487818, 43906753, 47049343, 113414912, 750354177, 477767093, 608930997, 191330514, 386262780, 16101423, 341930429, 309308536, 868352036, 840844155, 693021143, 619229359, 547474601, 212072266, 661201050, 193321772, 133874466, 495854438, 317848324, 183902649, 238271257, 293907450, 194830802, 797111674, 152237513, 435647292, 543047027, 140789123, 787194019, 499093682, 886295066, 619491283, 998277757, 156257644, 330051898, 136326756, 116077914, 472783421, 406989990, 261013249, 260517064, 846942030, 406323907, 409513456, 295400840, 195773580, 519892671, 262363341, 272850873, 428636223, 923879822, 493507033, 360909538, 952090304, 476959516, 696743407, 784832430, 865360271, 162853377, 370958346, 975950437, 240221613, 843179504, 668065841, 10522536, 436513894, 56421571, 790268896, 236843419, 919960177, 111780701, 618129809, 928763788, 976295598, 326470781, 130306184, 652476997, 791432695, 466747393, 707221501, 438779066, 616567575, 901392988, 108076456, 948058735, 962278436, 563110172, 5984407, 539090101, 295495547, 765154624, 418406859, 369048560, 479200315, 458546289, 179634851, 3908174, 617065733, 770714025, 910352695, 376848649, 869818764, 461578651, 974681480, 481545668, 42385778, 39297414, 15224906, 230465637, 926360496, 315637691, 707941226, 472325626, 936489543, 359251824, 743582829, 809393215, 998435572, 781338107, 442081701, 74179890, 214123713, 893280702, 430028647, 405050310, 418523804, 486742656, 411429601, 646630148, 906196625, 429006548, 708070009, 921824907, 98200770, 638897090, 26372963, 989032566, 861990723, 402933552, 57603215, 94064183, 304065824, 100342740, 667135246, 478750908, 930776768, 139085689, 354359066, 664137106, 48517197, 979661019, 382187431, 714585845, 255230874, 758660620, 374129349, 513075098, 94333862, 149988639, 795632057, 576399874, 41474049, 215898374, 738495585, 810470876, 774324848, 242382509, 322883208, 446467238, 238286392, 724945039, 673397125, 38192806, 936729078, 753900333, 569989552, 462452540, 206564703, 574960837, 27889989, 8161147, 153341572, 790270593, 326418766, 879432399, 473572376, 841308902, 505463994, 426393774, 396429570, 484735840, 474842389, 518829941, 349137060, 362396232, 453277105, 255692242, 827162520, 239958419, 21016308, 933753458, 760954007, 193979673, 685983668, 474211717, 872614465, 633830650, 811170718, 331045903, 532915140, 21249131, 991464658, 338863559, 65750101, 867652935, 994934658, 996016468, 129219095, 135975633, 944159926, 804597201, 603444700, 454570920, 982706217, 255067961, 111708398, 458886214, 470643608, 213881957, 309691170, 448503453, 971013000, 559582790, 739977443, 229785395, 944208611, 185558986, 932347869, 382685895, 747135627, 365998999, 990414993, 659839264, 142904414, 101604853, 553070896, 768990522, 229724698, 534703626, 522069536, 592510731, 621933386, 942230421, 571807565, 837845204, 483728519, 433848010, 601423222, 29477590, 638543341, 611602833, 615373338, 953492908, 632699301, 271827716, 756176658, 166862898, 71706135, 963282807, 966298991, 57391745, 393092896, 179370989, 736840298, 549852956, 84412171, 960574221, 991160708, 71772279, 792727436, 214813697, 603312055, 673324005, 700182746, 505543874, 478936004, 302035006, 710941091, 619913170, 194435129, 616147325, 442280615, 201636411, 917923069, 839570329, 328958723, 622286515, 542743405, 821673140, 435335647, 984805011, 270593978, 608826360, 554818714, 67470116, 553599023, 489855987, 470984931, 601129450, 496997029, 390095345, 747792847, 832707444, 931040000, 982011463, 582966849, 323343151, 125914544, 684671891, 965016617, 691451687, 681449216, 585212190, 447015119, 621882251, 828522303, 505300699, 719809355, 189769475, 654689027, 509083580, 387128388, 913053820, 862666927, 429519125, 650663860, 442379241, 931460003, 433554259, 505307513, 209036295, 442730963, 923287814, 837223609, 962341104, 390440681, 795731435, 191323865, 769498167, 129188461, 110013288, 740160868, 381972260, 494922735, 946276723, 814829903, 246190189, 812495679, 779890155, 529875448, 16839921, 874724958, 940133383, 763656240, 706406150, 799553235, 196819766, 206667963, 244241682, 34483891, 181306087, 551630380, 910667300, 52571418, 844869435, 661666315, 638940700, 4932480, 686504958, 849197477, 981974279, 72986380, 713441429, 83844160, 296573421, 78378693, 540074784, 878910916, 478115186, 382112271, 52380749, 154758807, 98299329, 484731106, 687726279, 153918707, 431614571, 365717699, 667984813, 831510546, 491858204, 140104433, 379461233, 500684374, 468185062, 182396387, 428320942, 171786550, 924202397, 332546977, 882233236, 721795499, 601388116, 728107197, 757861567, 330178200, 36152564, 452826614, 613310735, 419389577, 737739416, 570198427, 64336355, 530275505, 336232031, 972449948, 56408659, 714597773, 904116785, 961892700, 203220211, 567022329, 476343010, 993353899, 716090116, 86286613, 57231634, 18581737, 560537365, 641382941, 963707377, 602057786, 289581171, 826246878, 858128213, 589228118, 186750675, 485066489, 123479873, 787338929, 863539733, 586922061, 72751660, 551795383, 237237107, 210390710, 616545402, 277033247, 52372, 36334119, 149185445, 920398415, 554963834, 986067870, 887658345, 982757103, 472029583, 493018777, 123384345, 521621681, 449112702, 294669915, 555227230, 858265425, 562990175, 805725712, 189497886, 353222773, 684191149, 26796364, 543669962, 631348666, 3381929, 992446322, 160859046, 354306210, 954682972, 260833587, 807504026, 694656038, 325156837, 816324296, 384951966, 629617263, 179722587, 999904721, 950245282, 749391162, 83853909, 994575268, 914230060, 642539884, 475822477, 727192061, 625545457, 775563755, 846453127, 275807202, 537421695, 273083042, 772085495, 320487534, 655424262, 129232513, 693390673, 92964953, 87090877, 36939791, 164693038, 720528863, 562541416, 742196070, 491216518, 594741970, 508620546, 273658873, 80137135, 511655785, 4995091, 178950435, 973938056, 328324976, 522558010, 754683729, 292572525, 463556272, 239783738, 237621223, 318280450, 899127503, 975000323, 926284504, 212855485, 521027666, 885694636, 929823933, 522244003, 40684199, 847340254, 486905657, 95023956, 172062441, 130078820, 712500713, 299822626, 717726978, 98484566, 744883230, 716111199, 337723881, 523972798, 578775248, 1597144, 210443688, 108852931, 564769780, 601867433, 393096130, 368183157, 354001535, 353682220, 767453423, 411635261, 746274653, 920235300, 948974727, 977330397, 567793998, 694452886, 57413681, 934536704, 397546874, 410497373, 53918754, 571429366, 265229137, 434417664, 935423024, 166752271, 633785324, 136570318, 132788000, 230300718, 589922221, 294431226, 964366087, 864130187, 881535535, 955500824, 304188693, 51176596, 284637710, 659509324, 116112856, 206163066, 805791794, 65995217, 167479626, 554138215, 59883013, 162475669, 490909862, 646304539, 638804879, 215940382, 522689502, 672525415, 983454003, 851047394, 462904171, 630892814, 568935819, 89410426, 564897524, 722668850, 841363997, 371826990, 376716148, 381516644, 626231075, 322999434, 155101643, 513528772, 469575597, 881826693, 558878196, 590112754, 255456518, 269304212, 748521590, 482153794, 410809658, 871697759, 514519248, 227174429, 781429263, 782524085, 754491700, 992894345, 956007642, 499980318, 190899212, 886982348, 921476885, 722625207, 89848503, 364590651, 220412261, 979924735, 359329713, 606284088, 847167629, 741534872, 893818412, 500506997, 19416473, 622145294, 609360915, 231548514, 514162165, 852550167, 244172022, 222248927, 676173697, 523266945, 453421735, 415586905, 117568847, 199270961, 355024038, 202032688, 820588507, 673831638, 461370923, 651411203, 801114677, 124344073, 671935136, 696436840, 974137076, 799140524, 940144797, 982131090, 42176827, 702923284, 124921319, 556219602, 22272816, 900707566, 845231149, 789328742, 333517041, 708538003, 713647609, 472119871, 833208754, 36960040, 869020642, 81752445, 266826183, 734520529, 486831259, 765109456, 470781672, 607573141, 455667832, 511203114, 7643564, 537688416, 731338514, 757362259, 759305800, 452370805, 518899200, 115994842, 838444098, 819332456, 914885924, 192605599, 398715083, 663229117, 146715965, 745794681, 308328527, 36673313, 335244055, 537792830, 667933814, 656958913, 245782220, 618759170, 517046389, 191429017, 408818809, 275202030, 849998127, 779219376, 953431422, 412505244, 731764404, 603415610, 554819106, 681612417, 980617522, 874834060, 93987253, 862254182, 967942554, 835131257, 520004233, 899310686, 451148098, 194528507, 940495499, 351876296, 896109816, 164300701, 203654679, 71823622, 337160155, 160697260, 280728811, 348119070, 304058823, 856774931, 397715841, 865101722, 454356569, 914052064, 10521721, 843252345, 635207216, 34420875, 728612202, 738841572, 445306470, 466082335, 462891000, 968206033, 817941999, 336494308, 123056524, 573333816, 772863633, 920129598, 231521457, 245020672, 185756104, 49217938, 646632800, 892354980, 824759101, 58992073, 932992433, 726059196, 361425480, 247344116, 663375098, 786904715, 851115496, 59472912, 554962776, 178592761, 724735160, 21677027, 929867807, 836656660, 401049430, 573124341, 213027232, 138264573, 928756913, 872934669, 427948280, 881825440, 483700164, 571658923, 107699782, 564357851, 91711947, 497152135, 94019064, 205412784, 556554358, 467468975, 346297687, 987990888, 384206643, 119006040, 750694383, 161889846, 821353823, 853527854, 931814930, 934128395, 908514647, 111744938, 423886321, 651227891, 809688438, 896307873, 281991282, 988441058, 837248737, 330100442, 311069840, 801824373, 426037921, 201366060, 54919586, 794987053, 420977058, 73764889, 745876601, 492862362, 777077576, 466078696, 963006392, 433846588, 436672270, 920809349, 596441285, 759545589, 474264137, 722660150, 964706064, 238020496, 943577292, 578357366, 357536265, 547984513, 103964612, 386573117, 121795286, 925180995, 61856776, 463121482, 832258013, 914503277, 168492142, 349897799, 114231103, 484006183, 691813807, 246725511, 201448005, 561524167, 684727874, 962258647, 973797074, 68664010, 782073530, 894868580, 460509583, 251748881, 680723301, 822343964, 273361502, 120147315, 228505661, 491114122, 722903448, 567476953, 291197804, 85664723, 395925554, 552744468, 410787829, 127722909, 709320142, 35342488, 962549599, 677381800, 503598883, 648857148, 997116035, 207737926, 685861792, 103246585, 931459038, 16508052, 474752371, 481694802, 733586780, 38738497, 495216949, 645782151, 347896775, 704497252, 676999175, 867810818, 709415456, 568154763, 792436238, 377785649, 721302972, 411682511, 203669818, 603579305, 942989006, 390774971, 866534565, 692239728, 275562833, 654135116, 467646988, 508387789, 595150428, 6717741, 406142309, 700218558, 994881519, 200739069, 286243109, 702922351, 932638563, 350404669, 849706748, 40964219, 804920371, 957495717, 592912517, 478038928, 930935968, 810024566, 348432680, 938505915, 537568905, 703982629, 501164820, 875910379, 189631352, 143755722, 145613947, 210705321, 955069280, 993319595, 955041406, 355830735, 869195531, 282890978, 736535819, 594804841, 51118775, 354962213, 746415353, 864813754, 463949108, 575009241, 435929100, 755809452, 165813149, 630948151, 173442526, 693378227, 298528849, 811853090, 326830502, 568592075, 289962644, 821597053, 426042624, 844334547, 23627649, 8568632, 190854189, 294140509, 291476816, 505873502, 862721931, 726810605, 741706229, 644245409, 397356023, 876692370, 734789903, 956650202, 142414602, 80962840, 75225129, 8817020, 531903301, 569593032, 993348139, 720893345, 708099410, 677652104, 718965463, 436576991, 686414389, 559737017, 644384958, 890977897, 61287336, 720696195, 574995904, 950169395, 980930363, 247881889, 95460391, 9537508, 607986788, 290564060, 179144592, 619599185, 954196873, 908840251, 821716834, 652866828, 156856085, 212884474, 143274060, 603774239, 483574395, 860488813, 217080263, 960621586, 309308600, 114537183, 419974033, 238003051, 662369758, 130668199, 369604090, 147423530, 175216907, 269982473, 863198936, 927227159, 66164539, 116767888, 482086438, 819383160, 549475358, 51918270, 545852751, 332275793, 872169574, 874808862, 507313213, 636729519, 434827974, 616952185, 234622082, 783948814, 668910239, 446915980, 334645660, 936233786, 96639685, 390751454, 33642431, 670591962, 463095012, 686888523, 487257308, 29377677, 23498305, 769987225, 542883170, 652140418, 311426147, 221877000, 373315365, 79017039, 224854482, 408064680, 961422135, 371705464, 848271167, 30509273, 252103197, 28902527, 91801513, 630885496, 690287521, 723390696, 331987565, 895572458, 891771705, 494970437, 814605162, 444596371, 725522198, 729189469, 980350082, 664183777, 850710910, 753645403, 559860074, 50694555, 857434417, 413349590, 788372423, 641772991, 669497017, 170684775, 107129765, 560767609, 831535853, 38233125, 999934046, 421164110, 78269978, 644854203, 547084946, 286540202, 387103504, 413693270, 780656623, 756319245, 121687163, 590770932, 864652166, 624994000, 985124406, 288557318, 486256620, 230629090, 906666065, 998401699, 161044110, 912366551, 769416793, 531797673, 682731947, 238589289, 172354304, 552846929, 908600525, 619991471, 610573548, 786901745, 802990332, 533360265, 438518209, 962292127, 346106880, 549742946, 503181947, 651370767, 146207237, 826743736, 889787255, 637415802, 411966819, 458186580, 260619311, 986209117, 892666295, 507261924, 949365685, 175211889, 909263504, 211585979, 834110344, 636809221, 515693857, 596141303, 9945645, 481051819, 662546637, 229857019, 279013828, 979336081, 541953633, 592188197, 266834956, 802436353, 135643302, 723359758, 696304354, 751895913, 735100717, 134398979, 134143437, 67881374, 790180758, 311746574, 830283204, 792115306, 77933473, 989560701, 504818678, 590365845, 405905227, 655299811, 265261449, 648440603, 756862479, 586181408, 256763772, 479562995, 731368649, 450046585, 400691028, 469163208, 739823243, 178614524, 900024459, 209033451, 271225085, 696246238, 220014075, 117178214, 159078650, 559662512, 873106247, 589678500, 439036354, 917288689, 852784701, 176964224, 584882172, 872782467, 194834249, 484728114, 312410675, 394772513, 81696210, 371954683, 519216462, 47147089, 714397124, 957436437, 328621561, 189824155, 291374482, 951332298, 498982429, 447115066, 444453587, 799046472, 269052546, 344495818, 16766120, 444381982, 182220433, 992647651, 169712483, 377453840, 444935579, 904440819, 310397777, 945951428, 445741445, 570891093, 457877879, 522023787, 235072294, 805223054, 362461597, 808525166, 629952668, 965720905, 529022912, 876433178, 893678749, 457011492, 457786579, 236278676, 505314366, 638974369, 647436813, 521632722, 956932033, 593965083, 255329091, 983814990, 856532637, 306449408, 61825492, 816744894, 890634758, 506887070, 124915754, 77035817, 273824512, 500084823, 195334288, 760678696, 415797250, 721559245, 155793281, 494828746, 511810670, 582863776, 118044952, 869173244, 967632209, 994888484, 522824884, 758364978, 387756336, 907794016, 965781678, 757185871, 780197077, 557035081, 723186340, 578839390, 470128074, 692836331, 411860014, 342894232, 765111822, 190880184, 969714815, 477503648, 390048920, 702524091, 59459602, 150481441, 388825251, 412012734, 876886347, 854649090, 766083792, 306082934, 146862372, 972845600, 391473734, 188865414, 203725975, 890627365, 589649452, 863165224, 274920400, 371281017, 985642554, 179683712, 755770222, 702755839, 429272086, 410312704, 704522201, 708808823, 897378891, 751984367, 9310059, 562357498, 302595489, 132249771, 310253253, 400817274, 139117874, 657485837, 118470732, 502913173, 895390869, 722370256, 568221463, 378732951, 166471559, 535255828, 687697950, 585944717, 355184818, 272162645, 145057442, 501822020, 131731222, 535797464, 931721670, 324466153, 147544451, 909057512, 449584002, 182584904, 775191296, 443296615, 172255116, 361232282, 223761260, 949200845, 717313047, 955688380, 310038443, 283970267, 955102493, 909145854, 560722480, 999906780, 755820425, 242951907, 193956578, 657605934, 654100700, 904706732, 609534658, 52170118, 704073260, 755164711, 629366326, 623877187, 467081528, 607788360, 484673868, 806191168, 619449044, 800565874, 248885379, 997834004, 838151331, 281879707, 994057894, 861953811, 734866164, 124705419, 282093740, 468070520, 486906040, 394360457, 6498814, 700309678, 800127144, 618179029, 64202518, 522542104, 894217916, 749525901, 553671872, 388753381, 862448329, 659553372, 221558538, 976680280, 67348139, 413960341, 150885329, 70761859, 530571090, 897900398, 253701792, 755575694, 712642405, 665465126, 746030419, 809008710, 23488576, 208194279, 708683886, 955288672, 646536139, 921212952, 821971244, 827939037, 689147353, 743719035, 642268033, 23374295, 353555640, 828990255, 627564018, 853301490, 939380861, 81511036, 441282888, 972573187, 423842730, 124617816, 610878564, 18318783, 942254573, 656865431, 324602010, 65663118, 442571930, 560173181, 136309853, 909855393, 798384052, 481093481, 647820081, 609554764, 498113738, 248899859, 298416881, 578998203, 699898421, 702376808, 430825502, 624555369, 556442689, 348555566, 252507901, 122507197, 519769049, 658969012, 611607283, 373251612, 308618976, 303276108, 91283883, 389703308, 825327801, 312694018, 53334675, 817349222, 463233568, 640855670, 511238535, 944906378, 245722939, 67876587, 160153872, 840940305, 549476283, 793631574, 952943437, 386447622, 589431763, 653805911, 757391119, 68521486, 563121433, 521356422, 234106467, 434492489, 717331273, 151865675, 315661950, 413917202, 783121411, 158197655, 492878659, 775173557, 293055181, 782536290, 912967075, 957136266, 239757009, 97873962, 419667518, 857573531, 925158485, 416648722, 452091563, 77470414, 633860348, 735275134, 446138081, 462721194, 953154410, 300067035, 881070941, 688246712, 317042611, 992936333, 928155092, 359045324, 225463012, 147029688, 432470480, 776597414, 416937462, 35072253, 79704014, 714237033, 240893441, 696414359, 576258824, 129939007, 869847191, 683681161, 352254813, 818772836, 983210170, 969461269, 724213586, 91153104, 572417235, 491549365, 2649348, 801275167, 247361925, 300035627, 882638329, 422623770, 758191512, 198650905, 633612620, 530496891, 662343089, 327966669, 293553859, 21636109, 699644720, 826932211, 484766414, 407270582, 632622070, 198024651, 724365108, 933894558, 389957526, 771990149, 378162901, 349668871, 725831522, 371412054, 299674316, 526981149, 57354205, 132779562, 652553077, 281488935, 619227715, 907175165, 340647767, 885158365, 442711822, 517081275, 687553926, 118568595, 949879044, 423962702, 817500825, 524207138, 605253082, 451103824, 851889998, 912003909, 197803803, 428662143, 7424720, 308182645, 937064444, 843237657, 743250998, 726979782, 755052366, 936302447, 563602811, 728509924, 904055754, 246016155, 452385953, 77654712, 356920200, 446933462, 432221447, 675700108, 865999945, 792902737, 316575620, 284666805, 717103413, 529201508, 613185039, 999260991, 237007420, 218907453, 776228954, 712002937, 755606154, 163413668, 632885732, 324070622, 421903564, 502519782, 501037889, 596153905, 812561279, 412698403, 872812591, 671649400, 587718536, 558095245, 543776566, 985074562, 887719783, 41003341, 248658371, 897001227, 855609065, 696326632, 542835606, 833429457, 875374403, 592474823, 927396340, 5039137, 909939439, 292609367, 557650794, 282531164, 629443968, 354635653, 784390338, 794625299, 575381818, 418674785, 330628219, 839953856, 573042508, 881048538, 667491698, 70326896, 770412071, 596219256, 923477221, 808874937, 179556608, 936300737, 261569472, 472599309, 663435877, 884188890, 369184333, 919361199, 275435506, 431227565, 6227046, 250665507, 180747915, 218123647, 832340540, 371006061, 263258915, 551054179, 604021601, 377640860, 934009784, 283446342, 123435556, 1485622, 778302296, 847540817, 744334204, 570787630, 267893868, 188147137, 977918690, 119184610, 221313908, 585941247, 576123842, 570208076, 453075168, 147030769, 976439467, 776674111, 826663381, 224083185, 989631270, 998259887, 371167963, 333417563, 396801209, 880054233, 671665805, 64248307, 516717748, 370127910, 443989069, 51461345, 84056828, 575897512, 212667635, 959035001, 57765931, 918475647, 203644008, 650476285, 96402566, 732567446, 950962937, 177095213, 304629385, 763497523, 611995276, 812892376, 848428601, 157912110, 162885517, 940085888, 958764548, 555861998, 406276017, 932414273, 384883000, 681680566, 681679047, 377171827, 963588858, 72068991, 579492081, 795923651, 259683184, 860924255, 17406738, 974427488, 394140981, 66829794, 931134103, 585780667, 750866678, 382393677, 680619255, 339246647, 787148196, 223565946, 795224702, 261487525, 230796472, 805172557, 117705196, 452493228, 85139119, 911053873, 951277084, 337025348, 611897232, 503413607, 634902911, 348934302, 9843156, 491165788, 249900458, 311396398, 480398154, 502516379, 105347896, 341391409, 895565697, 607344852, 223342720, 457865234, 839697057, 294650689, 996061294, 755759006, 806309269, 116462842, 695379414, 804448069, 124079783, 5203439, 88828240, 277583164, 784815509, 869065483, 880605902, 848499073, 964535352, 900604012, 229411074, 272732272, 779760484, 381820159, 173538808, 212670897, 166688991, 214440693, 227310810, 937374534, 810841582, 874019598, 486549876, 605615741, 219088534, 25604190, 918016676, 702532829, 54674786, 496978302, 310008493, 22847159, 363088246, 361321094, 365986934, 789599193, 979377552, 138275259, 580592532, 951712827, 491011636, 64685198, 788457056, 530856867, 500268290, 300627674, 201113216, 241572793, 62029995, 403257984, 49249539, 85864466, 898541462, 177428377, 38952714, 291461376, 147046954, 692802847, 973305733, 959748533, 234786054, 470089625, 642429315, 607016744, 736749164, 776027434, 537409137, 907808292, 696152478, 332007085, 910423207, 836363539, 781353044, 128358451, 605098497, 615030706, 162235805, 964769341, 92535642, 563184424, 738758910, 908469977, 997742997, 662234519, 215426377, 317546918, 342863796, 898656171, 466004748, 664759242, 787357669, 518103177, 414406541, 718896730, 730935245, 56027651, 746036328, 853359051, 537976203, 824650709, 785058033, 440593997, 938797240, 263540878, 118647156, 160290731, 66776047, 112285208, 336381960, 536503496, 15024056, 946774113, 906326863, 448143645, 269110542, 718416879, 774585402, 393750160, 348381608, 789430233, 600103446, 207134537, 139455660, 514190211, 636807671, 1911261, 162119020, 503593377, 655356448, 33866659, 867866455, 470380193, 141578173, 828101608, 277938027, 31282755, 445400622, 222830668, 660265297, 115392575, 447970662, 143153424, 615557131, 649675019, 81146907, 393178409, 122589267, 397624486, 325511149, 156312368, 437132964, 298781775, 776321216, 158032455, 755783846, 856309382, 702628223, 492224160, 444339261, 582603875, 170189380, 442541738, 780670937, 248911381, 772069571, 592175094, 905833754, 153192990, 233039297, 395216292, 773946304, 277562685, 347196751, 534479657, 671504266, 753124811, 490618571, 411271047, 281676501, 6628648, 202619319, 214798547, 989755918, 77183623, 550428840, 150351669, 31918723, 382641787, 51316770, 40856505, 545022142, 355668262, 689843095, 662543643, 419407191, 999740460, 593440391, 377901905, 838463647, 767216955, 201409024, 727522662, 36700076, 880431459, 210370169, 928060601, 217010987, 834388935, 354847559, 406410417, 371365086, 186655585, 889134210, 308455888, 179200033, 431372027, 740517073, 48541502, 845628614, 862594505, 190657200, 88645452, 300271497, 481111423, 418972976, 105496848, 230089274, 7914655, 742460471, 467126588, 616514661, 18333226, 970729732, 629542836, 109804086, 705827966, 274014563, 636462348, 888501030, 77984588, 513772713, 468816660, 702785477, 686027535, 225735057, 443956612, 900890403, 370467755, 324223111, 770280596, 51016651, 900142242, 654831669, 525289876, 792409339, 110444317, 145699947, 861700882, 984425598, 89327229, 642435842, 339580785, 659831288, 316848165, 153361819, 369039155, 511474442, 763047295, 7191009, 268366765, 634607094, 211975055, 308153767, 972541568, 977253471, 390836395, 701471031, 94854735, 945889561, 557001987, 210598562, 198172211, 325784409, 744204962, 744491804, 48289820, 37319157, 969839478, 887372892, 871012035, 136826292, 915064569, 28482687, 274898902, 139326842, 777439808, 720239356, 617143649, 956912822, 931092189, 929496936, 716219887, 197681253, 528664937, 870420380, 190693507, 985815912, 931402941, 414570254, 411553406, 261281867, 908987001, 723204844, 950670317, 497532540, 515792449, 324415430, 28312247, 651201075, 262434915, 587911717, 105067571, 611834580, 489068579, 971391968, 281004626, 244827348, 566005414, 871320016, 646320163, 534217746, 5152078, 270517131, 285562333, 495329600, 145909323, 654953994, 958418469, 574000593, 128018361, 999664323, 66816683, 538723846, 265857331, 343275845, 535887975, 430453080, 502128595, 635240710, 454628748, 63082148, 864262906, 362245505, 655185845, 317612145, 964781139, 645718935, 698157766, 244063120, 46792669, 976422957, 852778619, 567728632, 888226772, 173175386, 982390090, 8893328, 9565006, 411000704, 764603803, 483666244, 540456936, 299681430, 721290503, 509125010, 986035296, 67072665, 712321409, 13235891, 278706788, 456305331, 860340077, 543657285, 959343352, 180752898, 534558276, 994101614, 744028107, 61197197, 728119048, 511675387, 889587799, 507934519, 267774377, 238438340, 549121551, 556990208, 616432782, 65772176, 283712581, 796799381, 134454780, 805738205, 71424319, 864907615, 47920034, 552708009, 438774933, 469120005, 51409143, 139720418, 277456002, 816582155, 370559457, 422849074, 610101340, 115288384, 534421651, 706206514, 136324977, 122392082, 479944705, 110882506, 369888726, 774744810, 556559967, 73752532, 499705531, 257951015, 930087079, 908016085, 70665683, 423182730, 461140905, 738154451, 234845527, 463701982, 65808425, 286800720, 962198510, 129964085, 739988060, 89016581, 107443669, 882407316, 963089478, 364664341, 16934994, 674323703, 172638692, 255646533, 558629186, 107295606, 714732347, 241495043, 860986568, 746557333, 620634466, 488996736, 878324412, 430782928, 285728599, 563659169, 485907984, 351170227, 774507834, 254633272, 72355808, 615004546, 671212737, 585418035, 235326870, 40980770, 623120127, 650110982, 618653647, 753421597, 628087231, 54681196, 695741476, 526367515, 356671612, 196624805, 422053045, 641230449, 661079102, 867551765, 241312098, 380156376, 135108049, 463049118, 775230383, 299700657, 404436966, 221210329, 317129295, 89537561, 113927269, 691316531, 339430800, 651041199, 200669705, 58423631, 953699822, 843298657, 826363929, 482010596, 536038149, 371057060, 656254738, 886462479, 943758345, 893461361, 917883163, 107074123, 691944603, 910177994, 968218317, 645261786, 639091660, 862516014, 562665526, 48412331, 972698314, 662904258, 176996705, 212700220, 689143066, 755562762, 835132536, 211111, 404729052, 807960733, 441926524, 380544516, 286116224, 401322841, 548250967, 848791526, 563892167, 440489546, 398157942, 748825980, 749242254, 362879273, 635440881, 223392982, 353416613, 644672753, 299053195, 504300756, 59948224, 341777053, 415485051, 513530401, 63653559, 108307703, 40634771, 352449559, 431347938, 646548809, 436204950, 978784128, 875667271, 274320348, 840629683, 529939482, 841633664, 989981473, 422903383, 378525723, 245622651, 483203724, 699571685, 238835984, 630304953, 112299510, 705577780, 933950591, 241903693, 254738981, 386319820, 970266075, 449613172, 508235971, 895580334, 656792514, 973208058, 604525281, 822927920, 821326695, 824099214, 249219483, 410444159, 838297290, 648866438, 40610413, 951080059, 495575689, 271077889, 282753751, 612001695, 213921963, 649095818, 959752867, 148875401, 808983735, 274304, 971599179, 358497043, 541383640, 195360700, 482426786, 722150175, 541389115, 462807219, 125169286, 750784430, 343388161, 100968814, 114998463, 500989846, 812328596, 300710012, 347881112, 866742278, 947548841, 511724487, 279538152, 638760781, 87407192, 820451963, 400114027, 799310563, 269475249, 395695074, 897861248, 478034758, 262035978, 485987554, 87350601, 343163642, 600004307, 906815576, 399075480, 573958687, 195900567, 511294238, 28565700, 296227502, 726116268, 608216745, 469439097, 932276966, 111586631, 219174390, 931855554, 215664761, 890775409, 437584519, 538533813, 213416944, 201514558, 664159635, 987054439, 994726725, 885368763, 424231635, 479103249, 874766678, 811168019, 814503369, 645188050, 920630464, 804178658, 285502242, 900623804, 885289026, 774406084, 501100946, 424198741, 483502352, 282432760, 399611470, 192900063, 634351380, 741586457, 98372478, 667144699, 743984645, 641176533, 179723724, 676262681, 519466589, 269342599, 270491996, 462921464, 835474785, 842285866, 984303717, 968058266, 333182147, 297573802, 366196653, 87806274, 509639699, 495320768, 609026773, 605130957, 129419367, 857657416, 570810415, 760870835, 14297663, 107295730, 512846629, 30327688, 679887134, 592482241, 11054510, 279544877, 281332569, 939542783, 268436753, 408161107, 869078969, 883933099, 874293108, 17126557, 538561332, 80263398, 225261616, 272605079, 960195580, 880755194, 104628675, 386802270, 243850116, 128975170, 201121625, 282867975, 303384094, 989340586, 681042771, 232714079, 152717266, 776685129, 351746483, 168680408, 374363770, 333376315, 654757395, 779326381, 421052333, 610863274, 786290449, 260382601, 295000321, 865450552, 729520644, 99207382, 466372981, 59332097, 499386058, 218398684, 29598424, 316112185, 227890354, 637951305, 726829229, 708236635, 183925476, 878221470, 868279148, 907678240, 671725487, 415546179, 63890999, 931246772, 395587397, 145555626, 726670341, 866485260, 325623117, 250469822, 638262399, 604915506, 960134837, 406694216, 530436824, 844298164, 62754913, 78346005, 594420199, 438327689, 446002364, 34680891, 805617781, 919743894, 95833470, 263218644, 144222281, 813016906, 956686688, 373687724, 198997990, 165494871, 233087651, 502526010, 413242462, 31925994, 617365826, 242745282, 255383483, 806911894, 587585443, 260304535, 758950962, 568306274, 686350140, 200631833, 48370822, 553395499, 673953190, 895484202, 717455208, 825712566, 266208942, 12261084, 867259699, 956417303, 458051549, 722132841, 179448602, 430553336, 633573903, 914351512, 435431617, 255628967, 522013125, 315888467, 687546106, 717725174, 400936028, 449415673, 393014841, 92073629, 217317526, 43032580, 543399709, 517242351, 666176010, 226274876, 490036182, 749701325, 103175452, 300539410, 472926183, 340315226, 893716040, 454551636, 133960178, 931390802, 885785252, 375500336, 896746705, 698872093, 881438621, 631827514, 540902670, 94314311, 433774271, 414626372, 737219956, 311149786, 797563381, 13299637, 232093856, 132147615, 331210320, 764036728, 799465249, 384709343, 736403993, 954441245, 84382108, 458532041, 795361976, 155994389, 560606445, 918597064, 204684408, 697738121, 562777047, 719485857, 537967021, 89854082, 787733091, 86270317, 286792880, 548488138, 858431363, 372391274, 848465737, 718141096, 898892898, 641066805, 43087249, 255723937, 242301068, 807950580, 321077483, 186015636, 837242986, 476031725, 147078937, 618017237, 187533054, 788196654, 826324706, 23610814, 931012344, 69702462, 163408355, 758218403, 203963597, 977032547, 314370072, 691664703, 400346732, 293174375, 803853540, 745325277, 773625841, 549600335, 431642404, 24066700, 804541390, 87149637, 704951348, 315073111, 294448094, 375292990, 712829421, 628318136, 887725621, 326121651, 551258801, 340858231, 783891133, 240936346, 509471533, 488735007, 627859048, 362948765, 64612001, 781760828, 522072953, 656453435, 487904809, 731052633, 59542600, 310643035, 705427766, 93483358, 246514650, 559518884, 191479272, 587758565, 616185739, 124357169, 109590798, 848854655, 954199772, 64255882, 451460183, 864156064, 621178768, 968138733, 126245, 340291370, 585800158, 792806851, 608347810, 461652775, 944084114, 520916650, 151405503, 876928770, 893195229, 109609233, 777851994, 54525489, 286804899, 958916030, 880039434, 573492758, 218829363, 231559921, 648301553, 269717420, 224053070, 113624950, 934713298, 830231752, 182816570, 338841334, 767309139, 947086496, 481758377, 871973111, 163491216, 105458298, 738625769, 624961337, 360634020, 729505625, 519587758, 269397238, 591658573, 411600935, 54461557, 844492716, 798606353, 727038606, 645249024, 348771306, 473557094, 366335343, 426025406, 453017474, 934094114, 29779683, 652712020, 728377716, 545583986, 274428253, 676001777, 808757673, 795364042, 627323465, 63419072, 368176850, 198560620, 235539412, 205137998, 967999465, 752008245, 635881783, 902136972, 546370110, 218982854, 445711900, 284926116, 882654801, 555001348, 605505782, 246699373, 57548557, 324967805, 900013916, 502970527, 168395021, 854332894, 847991532, 555094756, 785736226, 349850094, 174498312, 273090414, 38520597, 43088254, 168092988, 617267862, 826009908, 804501676, 276845606, 331600330, 723298448, 555042484, 735043829, 533337921, 212944710, 433197755, 922380749, 838072693, 156745693, 438272963, 98576509, 775792195, 243389019, 98758786, 964629476, 816733743, 677547177, 622704282, 77883331, 715057331, 769835567, 343114167, 278227996, 376967457, 833112310, 546013037, 364551042, 136394724, 133364717, 896437505, 618494877, 701686643, 766342052, 800522021, 636363803, 228949786, 228809553, 933236851, 591356177, 796872069, 221669564, 810542932, 265161796, 321843366, 269965312, 925226988, 162584271, 956314771, 88478137, 932188201, 304920886, 783192614, 113895293, 968620411, 969853412, 371964317, 549313656, 796627232, 436939724, 113075369, 771139008, 609256093, 227834203, 203187331, 444820316, 187663270, 427093443, 591443086, 646496583, 929776406, 488443851, 469633794, 425340184, 572538930, 832210515, 378342949, 122478403, 56541122, 4876847, 452183304, 876273486, 461610294, 651107129, 820406766, 285444934, 985500793, 676245966, 796455134, 500461194, 56505600, 847250601, 90484637, 910732892, 14229511, 319350233, 219528916, 128749094, 326812681, 190613927, 276282592, 813152964, 148205484, 65060232, 743257844, 317974916, 75449523, 946752887, 452156040, 905082453, 317011202, 387212563, 149559753, 299894490, 48446374, 121006739, 328793071, 882689386, 957956132, 422555640, 21608287, 567355339, 252711962, 207957603, 11087362, 657668795, 783459992, 211738767, 170716860, 67533085, 97086664, 916660542, 860963478, 547361650, 374241906, 710130414, 535229151, 834050768, 647684946, 466027194, 48944548, 880267632, 874263620, 265548520, 325763081, 397814958, 172796002, 910292108, 236395178, 134214101, 397612234, 882603016, 675814607, 450739022, 494550945, 562426907, 600630977, 42889628, 203767052, 777834626, 526644292, 124624278, 151797274, 891872690, 989859172, 826944546, 541753668, 839513489, 870618705, 79051467, 516009201, 953997915, 863002231, 522399768, 839070994, 495721937, 129072746, 467749435, 225506802, 373654374, 646088692, 894228400, 764633768, 597204673, 386254053, 568175022, 520292906, 301029407, 151801010, 1561607, 626861368, 53908364, 871648105, 947321965, 753468564, 28930690, 595388435, 86681642, 510874924, 15697154, 423822028, 657183617, 694016963, 111423420, 153050170, 990725978, 804427149, 212103527, 723990750, 259754513, 270481778, 249165297, 829726249, 153634440, 868322785, 762837134, 161550575, 410550480, 377290292, 279035921, 159844083, 391937796, 699576404, 992934577, 272261052, 818752372, 259590701, 662365068, 483673339, 400505713, 920150361, 143617582, 684505848, 40704400, 851640647, 820322367, 625040093, 435707358, 349903374, 837033128, 452496320, 1283555, 984169037, 486532592, 21186104, 261764762, 170292672, 636955257, 608668303, 360044799, 925966894, 978803571, 527575950, 626932873, 916737876, 571524154, 97619036, 382162945, 883540084, 113834097, 22304474, 496129972, 199412194, 773232957, 559086782, 84605511, 293788243, 75860441, 615216032, 844084953, 58633873, 397586228, 806490469, 711443937, 491444434, 322613805, 63117089, 573888470, 898521103, 386353514, 747016110, 912114135, 528982948, 435395631, 325046418, 124765914, 756864023, 884173976, 181848217, 481245285, 510780226, 898038648, 56940552, 28237126, 490611308, 973445301, 581490240, 468099922, 852606556, 228209547, 195152765, 599926945, 958883797, 989908407, 674693428, 528973814, 685478067, 652434243, 349333661, 535875081, 98701827, 435666712, 343502835, 488047029, 545013415, 581645718, 739032049, 250697916, 699738929, 810891097, 991310971, 490187769, 445733522, 635266406, 463641855, 978470935, 849702038, 865214664, 355670309, 203768019, 90664528, 132530279, 522523636, 921733277, 600563728, 793491162, 432021111, 171819675, 389468319, 737134208, 550143314, 155942810, 717610770, 37422305, 820409743, 559426002, 302351433, 839421931, 565396828, 321532672, 770335821, 320852992, 998449509, 742936196, 837503326, 146546661, 619217303, 15036923, 665414222, 425948304, 207889307, 52849436, 969370817, 579325295, 149155930, 572462381, 613133048, 350363912, 576849624, 808149756, 584914442, 874043713, 860375824, 434228644, 697261661, 309135734, 677258866, 331133774, 878444598, 107916751, 767167464, 746183729, 76948381, 894196044, 666708410, 955554632, 73211675, 677153670, 211264462, 31791452, 530536328, 141661888, 740519336, 262282133, 217429323, 132651477, 955293374, 176237409, 436932230, 494434538, 348298904, 408694196, 372225931, 375637713, 779083763, 167500022, 531094605, 463442155, 95039702, 961630986, 419799350, 806741590, 573296780, 963971807, 94178750, 570893005, 149881193, 958277182, 71324381, 300449193, 874263985, 38096275, 862933875, 116024328, 40925077, 771701548, 279968840, 630056839, 989592178, 899833631, 89675713, 986009452, 908804400, 650158547, 247893797, 387713526, 143326216, 419136708, 993260719, 148022152, 204141663, 28405512, 723211988, 943772282, 732353564, 457919265, 84640774, 934017736, 927264843, 94985916, 383625730, 347833336, 797312269, 567027160, 32219969, 881300181, 964378374, 113027499, 654487224, 237465182, 625149796, 204331132, 251149569, 770096010, 500449648, 971172793, 519638367, 730298508, 998269668, 551962890, 305419098, 821174046, 396211433, 253764976, 160235620, 627819375, 443486511, 804950123, 668029589, 629771256, 683633746, 602323124, 255026858, 481374479, 307760751, 635846005, 451605393, 553863688, 643077347, 661766220, 470228334, 81186964, 519211082, 280167509, 894352394, 88379166, 227438677, 556226391, 983174332, 825774325, 925785180, 300485144, 834962221, 576756785, 356226621, 415634752, 396323699, 399875791, 788938166, 546300544, 207114315, 803837981, 353371850, 424112239, 125285737, 513288674, 763674860, 662819446, 114145586, 542617906, 637782193, 112942055, 636710686, 731407343, 887654319, 791876422, 648709341, 100352851, 434734515, 429466432, 120265886, 283217886, 892257565, 394763054, 876007848, 69658120, 507466381, 298257485, 933627402, 954018128, 623257528, 892099080, 434056707, 524710991, 590816432, 694025972, 46811110, 233867862, 945483907, 404438207, 845880060, 588163653, 591018920, 767601282, 113656897, 359443344, 773571944, 28988770, 412198878, 339950317, 230497548, 475338215, 509816392, 970975794, 561267717, 178355449, 627109249, 475845454, 954669105, 902229483, 519823240, 332802200, 173624378, 958448500, 673682095, 71803230, 202561649, 353343211, 922574253, 938771142, 189459761, 902456718, 212652544, 123182097, 174623147, 675466957, 718469111, 841598739, 249513174, 481910855, 634785271, 536413948, 882591747, 906029965, 596327303, 531470806, 897830105, 273866612, 607334052, 401490654, 175020586, 674756865, 284647924, 589070943, 906488452, 234796598, 941005458, 499143840, 28621379, 366469637, 62191812, 842703150, 134711032, 682989448, 456688161, 139348148, 36625778, 939279744, 197703053, 224830783, 863238179, 608539404, 83278846, 364784386, 923732412, 351624203, 913392072, 421292625, 24095421, 737027606, 558078368, 327470324, 794862248, 423353244, 919612963, 485135736, 79158077, 891643992, 282862757, 819386469, 162132883, 177649411, 353718305, 277847615, 872768158, 273066715, 457882641, 230231064, 618068587, 430100641, 358244605, 830233538, 473104163, 360834630, 237258161, 494012110, 222931, 910278723, 309105056, 133124623, 412302017, 205124378, 853210060, 404130317, 467743946, 877211349, 296196524, 269196069, 306197216, 720877656, 922522606, 488035332, 791517609, 689931660, 222421884, 781565119, 424234083, 616131626, 469900885, 131121143, 30060290, 813574913, 366497590, 333160449, 269387095, 629519128, 200006429, 748252914, 631579743, 815603871, 218764706, 904286673, 152598906, 584755762, 361042543, 897463862, 253333814, 520501612, 969813900, 811740911, 62058691, 686079478, 85336205, 303166665, 983324394, 772285853, 292231334, 96018728, 246669596, 811449772, 786302895, 722014104, 960594594, 83153467, 85126869, 746031882, 675849289, 201883861, 192836585, 749196990, 382966257, 538123744, 560095434, 439295640, 112696498, 510360185, 545243499, 838497486, 105991273, 891523071, 172454304, 887797778, 367402846, 775020387, 418072137, 463861367, 712458375, 233942117, 984031247, 983301831, 643653162, 931773477, 382029360, 35395346, 700837878, 356981594, 688204234, 366257430, 441266283, 739178949, 408263146, 326446214, 285801558, 56169428, 541733040, 423603482, 335756552, 662962951, 42223005, 182299141, 416512020, 17249259, 744405919, 179443005, 93060278, 544471187, 718119498, 500587847, 242594712, 295891352, 869577556, 570807472, 563677312, 807183123, 963443036, 713362779, 333182135, 310232487, 886533366, 390919537, 923353106, 202222811, 507969734, 641614818, 5546278, 810134875, 711225049, 525620983, 843201188, 355585639, 792116443, 660489433, 300698319, 115683643, 981367331, 768844530, 499925013, 886151766, 733989435, 615117370, 851983095, 657041931, 700539676, 274331683, 417606008, 368632055, 50473675, 652192995, 157712011, 358463640, 791584227, 680494970, 969930479, 15990889, 343806107, 98363967, 431996813, 730786828, 409859447, 243634201, 374238839, 442652055, 725121274, 854943179, 951527177, 327434418, 539884353, 755774947, 615392864, 805883927, 200258523, 63384657, 404959697, 485328086, 963181056, 954593696, 662372870, 415144332, 809024610, 208346856, 498701150, 345975702, 321119685, 25614732, 239983933, 844904652, 266084695, 102517302, 625525771, 340021402, 893612766, 913280558, 395284561, 33268106, 140802846, 621676978, 749938880, 582371449, 312767962, 872596001, 244191734, 980840193, 331606791, 216996243, 307217935, 271163904, 107161101, 865697637, 93804129, 317853281, 389953371, 268081241, 570536312, 519735369, 761372464, 604387438, 188576118, 577543681, 40704433, 554456647, 448072688, 88404613, 714875884, 270896601, 657883228, 678840365, 694620357, 318093769, 120238052, 26903692, 432596557, 624540065, 743744960, 96347360, 32837239, 146812182, 955727433, 572356815, 749146970, 181149343, 318718840, 153381301, 521269370, 539261082, 299065126, 434576736, 170762949, 579896715, 30604196, 296698086, 195236285, 886349375, 245860637, 222134728, 739396711, 246610162, 350896755, 840864392, 427221486, 968643959, 424285799, 801232341, 962114047, 841828133, 990542078, 927315307, 389245600, 5465762, 901073359, 803597879, 180466587, 522387520, 265666686, 938703644, 623878868, 571308910, 151998798, 546696252, 411593614, 608638446, 279533929, 771672659, 273400210, 384593022, 220141950, 737277438, 690300204, 851809202, 390649027, 510355924, 290604107, 608496291, 378090242, 862289672, 256239829, 23158405, 480311896, 397760820, 526060179, 734270842, 274461552, 495788073, 320134346, 106498675, 160766755, 276847922, 579426489, 41245864, 976123060, 30811617, 450330986, 830873026, 97982659, 624477939, 831064320, 820572642, 612458980, 919570516, 237889580, 316452066, 228347424, 246968978, 215120338, 699149551, 701730559, 558943938, 158472527, 965898796, 581025231, 905372514, 126663156, 68617347, 698934613, 426137727, 30801138, 96901712, 550497822, 679108896, 511917718, 776723688, 572321450, 592485981, 776681448, 602172704, 499807276, 127507741, 969841712, 671008207, 118214218, 78983145, 950580872, 145288062, 814410007, 420076339, 547712201, 395835918, 251817452, 861794492, 361115, 158432073, 491319715, 643396820, 451077860, 301014299, 403235054, 972274729, 528682078, 47372186, 356798412, 456348398, 485137143, 341943896, 680679789, 445111158, 271918322, 950636340, 530190264, 349795352, 447143943, 584444261, 337248281, 273495574, 596617039, 445966637, 462134361, 231029516, 47313635, 607296421, 185814089, 555768829, 314836152, 73180217, 821572311, 308547236, 249536788, 740367107, 705280697, 299493914, 723394935, 255319304, 451417481, 63682454, 714847377, 653037587, 977846482, 350294875, 104806718, 574675722, 80991085, 26539219, 593969865, 259850001, 180513041, 5212891, 443577820, 192776925, 828002552, 725687499, 123700879, 786743586, 893447302, 856753502, 321830705, 817062994, 142856609, 331740475, 68843567, 838852367, 70248518, 220817516, 945190960, 212638401, 960914642, 8987747, 392082310, 378942412, 43937891, 312508319, 129865905, 442339566, 806891969, 812736692, 973895068, 4702474, 370133487, 353695463, 390021311, 919547574, 197242901, 506109703, 761674609, 321962704, 8869433, 398070494, 53963480, 969530383, 463963385, 761026860, 714323321, 799557035, 80701205, 695252509, 998664361, 901690307, 352809335, 646824177, 298643743, 659069191, 900993176, 663394199, 233729435, 346086323, 180645647, 277352639, 62433347, 445870935, 461639978, 838548058, 620979918, 680686228, 349248703, 116316858, 193026298, 490636679, 644979442, 562602240, 212323582, 122881576, 656956834, 505913289, 220543092, 865977109, 961143262, 150849049, 336913606, 701939640, 42424068, 685250021, 21822695, 518533604, 425154778, 577293114, 938409440, 435532346, 471757607, 677513282, 852948840, 558138854, 524890146, 352359364, 143813980, 917822512, 64530446, 79938266, 118328603, 687548965, 539819584, 671723033, 346024447, 199700273, 622683324, 29507625, 635613456, 789081116, 14961015, 809350502, 278309985, 699594851, 431315208, 656762909, 23407710, 682998987, 657888223, 325799027, 100720465, 978814305, 556463150, 229304752, 412493003, 848755386, 999859134, 520712851, 191397433, 323256962, 137773236, 424214506, 45489579, 843635397, 135895127, 891629884, 325011494, 354385443, 159618824, 438667623, 212111908, 274789289, 797975218, 922665947, 94763777, 394975720, 716098208, 13153840, 626844287, 168157036, 792820081, 991172325, 694403159, 490212286, 546335290, 406110901, 362665586, 814416418, 36687530, 951346007, 746347167, 447623317, 176690853, 441647649, 645756569, 558520366, 301071294, 523893506, 972317320, 462549236, 146328443, 963435389, 410191204, 216283634, 360722469, 483802450, 667797784, 450421383, 626516057, 200369213, 506259234, 530642317, 764560805, 713636616, 171177580, 389451472, 904159639, 752997238, 234018742, 597752156, 255068440, 407194641, 823481123, 734070788, 215507144, 853419613, 230100355, 816316914, 473676105, 633347536, 664612516, 361298852, 771153972, 907515221, 435724299, 950526950, 269201612, 662350161, 833234987, 111986857, 752880542, 57581839, 130421544, 343626261, 343754569, 359689687, 464468590, 428365554, 799822684, 153925184, 619770734, 482446516, 171500882, 241577642, 385223023, 306789418, 94715670, 940788987, 522396201, 506791900, 271032607, 601108951, 392717571, 460439736, 216643546, 864907324, 871833270, 605698262, 42784806, 15975468, 808365695, 585853529, 524871514, 529705589, 377659586, 747633065, 766144622, 733890015, 511555934, 135973510, 571975403, 598082607, 116668306, 706056426, 415435038, 78060410, 74266630, 322678864, 196639400, 106246762, 45771762, 733811215, 620712707, 164132585, 308531701, 501653436, 284983773, 60235185, 579782806, 165243396, 863014422, 942958620, 214958132, 363888300, 651999094, 107734441, 151436546, 123709348, 417271801, 283382120, 424096705, 341996610, 853294886, 546128015, 415668828, 301247359, 38375867, 473132485, 589249122, 887814744, 218100267, 23818843, 700140149, 689470753, 294571204, 842560398, 980231544, 378033247, 46284214, 404968767, 727126252, 529099688, 160562746, 123036541, 797767585, 914529269, 636584886, 765284736, 766502407, 369735423, 965623441, 283116663, 965258223, 582181294, 630923943, 80139494, 887518632, 802831578, 574183762, 643516806, 952825189, 722333679, 306927409, 190318604, 742972069, 522379729, 913037801, 602713456, 592938387, 107246185, 448678948, 947421333, 826352195, 934694259, 846671438, 686569455, 967269247, 515218108, 289066168, 708218063, 320964871, 130210440, 19057129, 143969067, 956586294, 396831599, 908581001, 392381991, 871517078, 132227874, 601128309, 211621320, 559505101, 547381599, 382477060, 489815189, 872830169, 148563096, 135236861, 879976577, 501658759, 615763913, 676340190, 972765856, 248652958, 893937738, 263890020, 75897574, 786830777, 660931230, 461445239, 522955587, 724472690, 972126729, 228048195, 436850858, 704651846, 767286220, 957308950, 46656985, 925465822, 243322337, 663518376, 545344372, 968858226, 496842968, 629481194, 550925110, 526316507, 576183204, 235448152, 445932252, 355957961, 598530739, 107804956, 371734003, 4804994, 492836844, 481557282, 905469861, 659224985, 864697266, 698999332, 25636609, 203213960, 813933654, 809055780, 59486742, 421876829, 991678132, 613956424, 404081365, 347957337, 650810034, 630394485, 725225817, 83761055, 517128114, 953097118, 750436155, 980721977, 617793582, 561886973, 594280068, 91597376, 11756901, 179746579, 898165613, 5261598, 630370876, 823417312, 234213692, 277602006, 798854008, 145181905, 609121259, 136302766, 609184683, 594963941, 568233583, 745498794, 102354611, 813526721, 10403691, 480309743, 490187339, 966119365, 417282610, 391126273, 177492783, 485089406, 356024876, 22995332, 585998788, 186557096, 622651006, 536023231, 453168938, 931491709, 477474408, 532215111, 710416904, 386570080, 21176212, 921689067, 593145132, 901937868, 496881082, 586512503, 120663834, 572482605, 380575431, 274725571, 584860442, 818935316, 707539056, 179729722, 269301102, 644679940, 145734450, 32701896, 680070939, 578801670, 645571547, 544115213, 735042357, 93456212, 548589416, 341881507, 655894571, 396898328, 526470575, 492229801, 12311814, 261001337, 827323556, 895376307, 659257279, 123104690, 386855657, 712289605, 742562120, 847652119, 930680258, 799488068, 735640964, 995932974, 951934402, 758544652, 873599695, 947426473, 718865315, 976323356, 469302077, 8240136, 875878957, 455455611, 250466926, 986963651, 891512262, 807434236, 146136504, 41109865, 394536413, 868422653, 861288928, 744962190, 103996262, 294112582, 607069247, 82791029, 272786031, 337622400, 361568972, 262520521, 395202250, 913209201, 937494929, 373001243, 789600742, 284807072, 918717868, 911226117, 667681206, 774686378, 550251444, 560139667, 761365777, 95695112, 201046681, 921071964, 883658038, 647613625, 48691737, 871777988, 166133248, 185397163, 904790968, 296081072, 979189540, 536359975, 153142938, 458043192, 187423340, 547907982, 693796740, 331303391, 310637465, 251492449, 365543002, 957714464, 285968463, 461032460, 596461819, 296164978, 188949761, 653149066, 757806224, 401988957, 480171675, 544375304, 93573718, 405185872, 86553335, 3705878, 712635036, 590401788, 910828519, 142680663, 477967039, 96749497, 637704091, 38847342, 949094145, 476565532, 400122932, 813529249, 779361550, 973531676, 121404213, 267801900, 528714246, 426060404, 535529274, 464962690, 9679065, 820272823, 243548280, 567007662, 767907423, 538362822, 597720778, 519154804, 78831313, 264827256, 523560925, 499031423, 699439981, 516206109, 764421305, 802007244, 530847639, 182716658, 621075205, 687711238, 392122661, 918762117, 963420328, 681924458, 50324040, 668576140, 650818873, 635037830, 842584850, 705083723, 302236097, 848778374, 165118220, 757662293, 506507257, 69323769, 544648588, 565016634, 99052569, 11724615, 867554847, 138096706, 877922008, 278430479, 496499779, 590552530, 325615023, 670488008, 809167178, 651041846, 165245336, 230699544, 516281742, 928579388, 956901922, 23463876, 880574411, 387464465, 803484831, 788871505, 875457284, 194237889, 22887252, 12164373, 743903371, 418802774, 436632348, 70242023, 545649399, 43110868, 549611937, 621200062, 666972575, 500726481, 127933550, 182669107, 785083458, 523253199, 214173705, 718017604, 442115692, 732170700, 508437660, 989727198, 860551236, 342315456, 74479139, 26623659, 839670977, 818385622, 677111413, 232513740, 592009372, 761116367, 446059363, 652633955, 254953377, 401030093, 198963359, 211141071, 882194387, 778740050, 939096912, 167224989, 622231774, 503728879, 447050804, 882428663, 597590493, 231670302, 376760656, 715772782, 34781638, 683414668, 947817015, 461865185, 426722763, 240288954, 636720583, 975764297, 78798928, 843423351, 472777950, 102517146, 46070877, 293390409, 224879964, 832970690, 702744573, 606149071, 708216533, 353659479, 705992158, 501409171, 462717105, 754431068, 821112719, 376177494, 508313708, 464339187, 444175949, 561329918, 753287037, 445361804, 225795905, 597141805, 296183844, 112283350, 884626357, 548562548, 242519216, 391134775, 778895156, 582613215, 552634241, 490365227, 598866698, 848850060, 521172411, 930557663, 82646389, 97336149, 831289680, 592987199, 471340647, 223218691, 322458483, 181975905, 234792222, 974533180, 717711279, 778271983, 547509846, 787030217, 513413101, 379268018, 545225684, 627856008, 771718206, 944594050, 64634755, 497301566, 634949799, 160114082, 498790963, 205010294, 967866804, 488332521, 684338678, 74471905, 528780176, 777448920, 850608346, 52730627, 612719876, 408136567, 583955001, 802350166, 479246859, 87819878, 91519540, 543414634, 801069267, 460650161, 305895448, 650070912, 571761048, 356155822, 305599712, 384695007, 132984271, 716976593, 303641060, 539558601, 774660524, 249517326, 926134924, 149209272, 692774656, 420128390, 24540164, 15271070, 652531715, 640769506, 916447567, 280493882, 983633266, 679403344, 709474212, 364816518, 153192438, 426917219, 455259604, 295448266, 835415972, 103595658, 829735682, 792110826, 909690119, 992714791, 25754936, 317623733, 539549423, 393468003, 231069707, 974381359, 480688379, 567105752, 705128085, 302728621, 802729825, 728176965, 848796681, 490055022, 941802914, 129117495, 315814220, 870956145, 482242982, 949905859, 952751872, 639529559, 134932160, 509133289, 135677478, 697075717, 402898758, 593683386, 455068825, 451914211, 61631537, 358298589, 129359110, 271608636, 814438150, 612877394, 102721914, 180939353, 419602405, 853048575, 640144750, 655865101, 638328952, 120653442, 396978639, 960084401, 19687453, 486489128, 712002206, 914424611, 137356038, 922577887, 41236352, 806516984, 718393930, 100730073, 521801242, 341194535, 890312672, 53298589, 748191346, 54417566, 500841935, 778129114, 550656042, 875908040, 584545532, 976993152, 399580684, 237596235, 424823137, 375282403, 199840753, 225113179, 905872415, 265410281, 782409627, 149533686, 154141961, 628589882, 23970907, 154086341, 641313186, 323057051, 713219465, 850962177, 588962508, 875288652, 710851787, 417098244, 45916135, 427666740, 100426566, 475128356, 209062186, 833478185, 724402196, 234570805, 670005801, 623902619, 232433477, 386910128, 806319435, 405175084, 160950157, 999578565, 764573165, 895741418, 57959132, 568211854, 241048556, 30358947, 883152882, 567741072, 111680452, 523484454, 256653120, 698261533, 755990943, 411163185, 821712938, 233527276, 500934011, 213134769, 31505981, 845961554, 150199180, 880176960, 110331625, 230633238, 381258284, 226873348, 529562519, 519452022, 688083495, 391018433, 776420531, 496050602, 647025134, 590790634, 490257038, 744834568, 22791593, 871888122, 789696004, 102905543, 285961758, 175192595, 436801022, 440093798, 935595835, 13460676, 808370882, 409029180, 659959576, 443559879, 879549530, 34897528, 823160355, 659948800, 840919093, 377863377, 969587249, 993724084, 203978712, 751896989, 251583526, 463284947, 935745558, 350138882, 699310599, 81441080, 95840008, 146349290, 629290861, 985276339, 443040483, 17855133, 545821001, 666196195, 723991022, 741036773, 807169201, 516790883, 62162646, 994523871, 260664085, 704731853, 142179884, 881618793, 65847800, 55965152, 251147495, 976851206, 775985480, 388707428, 562819296, 508597981, 948622110, 662298473, 321673595, 125922640, 346414940, 413831271, 976240260, 965092105, 296217448, 990955292, 451280516, 18405146, 774428929, 89939906, 413556710, 440623874, 454058698, 977316579, 309238952, 616982825, 958129920, 840347639, 312370228, 946311680, 623377722, 207923358, 779085085, 807408221, 59300525, 848540886, 523727423, 324743601, 674125148, 105878027, 299493260, 385804280, 3697437, 756598167, 502318808, 980447655, 146564282, 435657530, 730630288, 265329557, 343514380, 3233277, 321961719, 346201370, 663813376, 502979230, 413734421, 383530894, 171406797, 741168670, 661685179, 914543267, 829170983, 734004709, 290611765, 378187432, 117478729, 603982011, 170425643, 916658888, 381743847, 541915529, 860628572, 485284162, 735627980, 404327501, 309369489, 541818044, 418478134, 182816601, 387498869, 838161228, 393790920, 245672639, 961698973, 388014405, 20625395, 574684758, 163547119, 163326971, 969225655, 853069146, 820815408, 878148388, 69144841, 540430109, 531549194, 768205194, 116799722, 688745582, 711316966, 495944585, 490739471, 286285406, 155663366, 161063654, 363469666, 915063680, 262652894, 159912427, 105631077, 763331486, 419523466, 234266245, 875271602, 988969137, 31018889, 864290500, 22554780, 614302891, 762032584, 500584958, 569664265, 671167964, 168240850, 23314960, 19802982, 955604350, 559751254, 328445981, 614740111, 411806477, 975171408, 859921460, 883390363, 361247773, 895123243, 196720473, 977878537, 873315202, 165143014, 187228498, 740077415, 674838258, 714591627, 16561703, 367582556, 572838989, 938032993, 421059120, 243118178, 976069515, 126032360, 697610305, 702014983, 181715580, 421159997, 604346830, 479539028, 787836106, 968911287, 704294368, 804992454, 846393621, 203192019, 935445936, 956936293, 904079256, 167082452, 144452619, 723611131, 243685266, 981993146, 358285264, 209431963, 611884024, 181127021, 507413537, 715815649, 265267824, 559579148, 320177245, 931664212, 908587556, 843002223, 104207154, 526331931, 859156713, 778850637, 468463070, 766138538, 136840743, 143472053, 523088811, 534344844, 736040384, 256105299, 985496332, 547346277, 759040417, 382807061, 350918027, 682681740, 734610698, 553996974, 47012408, 318046039, 649577273, 598756534, 668028261, 116895209, 899200897, 85341751, 154499670, 842109701, 310039047, 821997132, 119481598, 538091146, 652686476, 484005803, 982519491, 389651394, 483290931, 74078590, 554268416, 66300108, 650491307, 601921394, 972536053, 305242859, 73621508, 487974533, 43401592, 206958592, 157864488, 463013250, 818153184, 635015981, 164770060, 852437006, 590889115, 651039079, 337392114, 456924335, 405445377, 692550108, 637706366, 947806068, 771930632, 154756435, 649240985, 960470873, 231894941, 462855046, 565907120, 791982672, 620658443, 992609336, 226996201, 317363061, 707756603, 723516483, 219024494, 628169838, 696366219, 917707744, 705951724, 262940731, 110787585, 831438528, 477540386, 40159757, 576460643, 167391278, 987711092, 765013838, 904032325, 301968359, 764119341, 218692353, 378894060, 528476406, 794692006, 8457799, 254359270, 556432879, 935503558, 384458954, 30475824, 781336468, 389093050, 323657769, 452974801, 180407267, 513989550, 319891272, 884475554, 64039127, 72540808, 280227781, 524108264, 738373461, 299758499, 979978868, 80132042, 753943668, 759915746, 676743108, 760500130, 639933535, 939307703, 709919132, 80526431, 943972217, 89699863, 99668731, 125336230, 736868384, 632191760, 801895814, 226673436, 294496795, 800746268, 677864220, 338723747, 880159067, 695824231, 658400368, 801083901, 993831108, 638555720, 301914206, 847242609, 423597261, 882354893, 690285611, 515029092, 665776717, 13271836, 87357143, 145947142, 270403311, 477385159, 176680840, 911513291, 861253657, 482756019, 24214053, 676589861, 958972976, 197898888, 820466539, 871316247, 698357218, 594169834, 310540948, 833547476, 567791234, 627093468, 139327625, 569373268, 748320110, 275458961, 769356450, 847773092, 462715676, 682313022, 359897972, 415286290, 480999671, 958363654, 271108936, 316364043, 628753442, 269980647, 906282304, 796935814, 393072579, 357979029, 766380981, 176962605, 274176618, 142764132, 644255183, 529701058, 809921344, 490018773, 917228789, 247792437, 721050024, 137721859, 842436778, 453254660, 382898595, 435056639, 536298696, 656388666, 731237987, 538503911, 21952670, 432958444, 636312932, 899189373, 657813339, 200533068, 568226648, 309773097, 766047440, 987709237, 336672998, 563890413, 850473447, 947869380, 580316784, 276798615, 651114095, 832690959, 66732098, 312003875, 846122995, 345889842, 476809969, 268328258, 243588533, 345914815, 387318123, 482647116, 56544082, 91248077, 776290891, 235520499, 723067693, 353699018, 662911564, 827970390, 682812391, 198757703, 259307983, 961161084, 903307472, 743001629, 31442258, 372019732, 727485744, 86249160, 463766478, 186812683, 144122186, 623490540, 793536099, 192195356, 915741801, 141999568, 58279689, 892760807, 957789973, 477506618, 844772492, 828546596, 249703070, 182324651, 954221910, 938097954, 896358144, 399340887, 192594321, 436020415, 315560565, 918774930, 970167719, 633003324, 246166614, 936652991, 529821409, 785503893, 868570332, 748771772, 667106165, 896261458, 540764326, 136408928, 937740115, 227741252, 615891834, 303733429, 692836757, 617111582, 255952884, 187590482, 22028725, 117221114, 463601297, 457379959, 953172956, 324158283, 387868006, 438782186, 874104994, 115233054, 207517051, 419679846, 714134717, 806237505, 730395217, 98489983, 641680273, 196594535, 297113052, 750858329, 252097141, 321011503, 772241114, 185348274, 345513239, 896266872, 85924476, 313246681, 557212029, 944754455, 525099327, 285285076, 694290451, 702318948, 739121406, 362899813, 572290414, 871097075, 278755039, 878380660, 998225820, 33848218, 780608848, 557973433, 359680922, 183201173, 234114320, 674248140, 568525727, 910761447, 675837708, 431701987, 327465395, 184512395, 545036874, 489066186, 723791458, 645076993, 435339571, 975330887, 796054965, 451936497, 867764959, 322604752, 503257990, 7785224, 109489865, 198103825, 724978475, 648714784, 617097593, 995426163, 413177237, 623946812, 50052627, 907732868, 281222773, 585759331, 26604777, 603434212, 305536371, 648649266, 967047111, 245798210, 664095862, 268800594, 9795843, 867127426, 103578175, 568005914, 283196307, 440976182, 18361056, 529978955, 562991722, 850028545, 470769204, 602917361, 703463332, 471376889, 924142323, 613688168, 200939848, 752361489, 98486119, 636269842, 921518262, 462345864, 256990581, 74313554, 291902588, 993796420, 433910562, 912572428, 148734447, 739414352, 789499480, 521551023, 599347101, 518299956, 475964146, 822314384, 774604478, 919554655, 740495925, 267629005, 480206703, 433714534, 689425874, 353470069, 612437199, 198760085, 840056148, 268829841, 734327748, 243040563, 734520137, 596113060, 878707934, 397805918, 540860522, 598216147, 281201060, 767431064, 958578965, 579804407, 783703847, 158678286, 602216396, 431615360, 107663298, 10502731, 858174969, 503416514, 562593115, 762088592, 510052361, 951190480, 619941281, 25987907, 176257316, 178608380, 784437368, 859524848, 855059534, 401732707, 125640795, 860545977, 366625268, 540678396, 776980920, 823265155, 217699260, 812489733, 127774067, 18765248, 909795469, 409169732, 916079380, 330010622, 885421567, 183391622, 449382765, 407564349, 56065578, 455297127, 122027179, 532071109, 866576384, 482559277, 201352235, 441063347, 521033542, 750890220, 639708109, 141131058, 669767361, 52805875, 837196704, 977303913, 903034998, 540928881, 420242750, 541909932, 457961330, 422646356, 343764704, 307142674, 815596854, 188536066, 709516167, 994133707, 351969465, 222029471, 320558078, 423112908, 160856481, 264175801, 820676249, 366483521, 227672062, 659096828, 144268431, 5784236, 369936582, 553887554, 238995458, 396296216, 427239733, 241453822, 630928332, 30369884, 390546673, 663562185, 482921321, 914980105, 699657264, 866521504, 398485476, 356190239, 682886497, 920504015, 585474089, 760699624, 188832705, 903064914, 203436767, 404513732, 689614711, 466721810, 913947259, 132962143, 983591247, 295074656, 672945515, 44444446, 147399087, 549961799, 291667110, 465977933, 131035634, 493272114, 269715598, 476911349, 748200063, 416165193, 969560473, 57914627, 452596847, 920012965, 493706208, 864749255, 981140605, 692043360, 586060138, 446394245, 318994266, 172441428, 132908469, 190666380, 539928834, 758338591, 790543350, 412510677, 113735521, 60261953, 385484175, 99239116, 260846942, 626522442, 928525096, 665832588, 149914800, 724743261, 134104018, 888942047, 431958503, 22853567, 112902487, 298626843, 376393244, 384352533, 875246851, 532637174, 296880980, 409299795, 484096046, 109925032, 469905746, 899743754, 334364508, 350265665, 6595239, 484658207, 498154009, 949915357, 987211393, 27347042, 26708191, 62662990, 582188723, 877083417, 47755962, 995315874, 917311255, 498167370, 994493264, 102241661, 694320048, 421775132, 796497779, 533414938, 431650138, 540441773, 470008284, 907529678, 151710135, 531257818, 545166466, 442186375, 275357193, 84405103, 338334829, 301645381, 9014972, 970622832, 570226083, 39156554, 250806992, 912620370, 118633547, 131027926, 684827657, 386237060, 669150463, 705628475, 176955792, 994383961, 539151397, 863531669, 535939418, 658278889, 625879022, 997482854, 394574543, 380240751, 144760045, 388721246, 289007537, 857914305, 980140612, 934998943, 204013913, 888040544, 340952428, 997999210, 824941107, 787964794, 938910663, 231865809, 380955432, 616189296, 375634683, 322665742, 745780023, 476540205, 54740886, 736355397, 607995185, 665547490, 160604139, 21500403, 870060324, 298482408, 500957967, 633757623, 339479848, 767167761, 258019914, 978343776, 928259554, 917098909, 127400622, 795924791, 799801944, 207076774, 636036310, 516325971, 628844761, 604152638, 578736224, 37336102, 705151003, 470625526, 203592957, 779428118, 880207654, 169925502, 565665119, 348055500, 959608728, 922525333, 473116215, 205053664, 169338842, 782614826, 62137097, 747534164, 138863036, 444581161, 285258598, 720451974, 737200155, 460291227, 394898885, 899550051, 339520651, 657032166, 134066524, 88184047, 264007477, 478399018, 317938719, 327330020, 728594304, 377668601, 754684981, 890523233, 739582494, 108277941, 733495955, 789054041, 720757939, 136779383, 835357227, 85551225, 145753867, 539154350, 830910615, 834160812, 899068346, 510538639, 419906139, 903626634, 886875233, 852442919, 656051004, 607925657, 374325226, 989112293, 889075474, 558210868, 266151675, 747277348, 722543729, 481216823, 863808196, 272152869, 599141930, 262325777, 425924574, 234272791, 783141594, 256716730, 15134739, 420687851, 949043705, 897543612, 346087649, 221149167, 110097058, 539528634, 308215759, 384049111, 143019138, 352520046, 920760465, 310064300, 862030855, 442689441, 466178541, 213253814, 898481614, 281262497, 295246368, 187400903, 430057158, 865266854, 850764793, 196018411, 802948666, 453879209, 935551720, 256261066, 92843654, 277102553, 227872340, 45537531, 40979247, 545473438, 860007329, 995410405, 109964421, 717328375, 158695546, 308927047, 98206551, 248796040, 885603117, 867942256, 373493406, 138869138, 340434841, 335748621, 918210501, 399575157, 601073589, 651038747, 244127850, 697145, 640811471, 148816674, 157679450, 551062248, 250462117, 303121898, 644422128, 228718628, 123112190, 716101589, 809985258, 744581636, 330364735, 956364090, 814277595, 520402133, 369853130, 761460018, 117191791, 920528951, 318207510, 505200783, 388568813, 309538912, 668643126, 406022457, 278037726, 614397950, 297980200, 474097939, 608977557, 626107434, 887474373, 138328696, 178382760, 190680645, 231628406, 544302763, 236027814, 850374786, 329223505, 237208476, 329470306, 339446588, 753989192, 343046807, 220225786, 482910268, 593240911, 152339543, 390813139, 396962521, 173316331, 923635601, 787457020, 907547364, 803015784, 871762980, 978375138, 596709474, 306429173, 67272348, 113917180, 813718415, 872702848, 433981932, 918547226, 295695617, 98363963, 674059013, 375391147, 400876486, 184778463, 411398149, 492355871, 162500103, 480538428, 221591766, 393151019, 565831624, 413022918, 442985312, 405743508, 843121556, 952768945, 951929740, 609269711, 575007157, 987632987, 302585716, 503440078, 748983139, 234952238, 234459365, 984864818, 806083154, 754862259, 106067433, 239192815, 436975392, 802888071, 918784919, 609001077, 913515109, 736559386, 351836157, 241988785, 434625466, 298970576, 4694024, 115915414, 830787797, 147176055, 440842587, 768020706, 514344587, 358489565, 385617707, 726751454, 444903491, 38005225, 283477260, 136488232, 794233785, 10951792, 445195241, 258268129, 904954215, 891467267, 763896212, 894546734, 281403761, 851057424, 27013027, 716517770, 356727689, 192707745, 780295302, 394436962, 883498898, 81034945, 137624001, 661627029, 244511686, 971821789, 512230553, 571800404, 284105685, 932002442, 83391708, 758523898, 70638766, 317538537, 177214287, 558314455, 861883577, 202304440, 602191317, 163975159, 688532291, 918624341, 444473480, 688481758, 561083817, 54930585, 812573913, 92135025, 375345769, 224375055, 276091533, 723810785, 634274427, 128788195, 231653451, 138582462, 166559743, 647962515, 740661686, 428171947, 434090868, 980926836, 403058568, 613622697, 192316336, 263006664, 695357154, 487897344, 598493936, 331356897, 172245845, 431737902, 305738322, 244239374, 272767515, 572559185, 860418087, 760973667, 687637400, 519984181, 312278580, 942277879, 347884114, 247602587, 495579211, 131278421, 97052833, 697740382, 711263787, 852547652, 137729080, 229845158, 350467768, 568043521, 987398095, 917145063, 926782721, 715217683, 940668228, 582461149, 625928778, 580292537, 579897740, 300359341, 181598358, 785186502, 786679548, 372876113, 865342903, 959113546, 196796157, 291973038, 701623491, 89864659, 979501912, 423319698, 456758377, 939379536, 724235037, 391272553, 239762347, 802830262, 314275437, 338519971, 884897927, 603489234, 852473946, 192580242, 353672242, 747699944, 552067671, 574854664, 126990135, 826050115, 427299516, 466182771, 245974935, 691695303, 718328131, 768278203, 530098825, 533635799, 666425493, 309371413, 478385747, 304345157, 592331641, 627280745, 696040576, 418272673, 246964707, 805941212, 720132335, 495601965, 417108916, 869394935, 860547788, 734219102, 168534690, 737838905, 534540761, 289951359, 505924065, 812355274, 477060041, 357610360, 774904867, 203429181, 541406917, 70440189, 974906001, 967105686, 750675440, 590552532, 181049898, 740563780, 347900206, 654358738, 494805116, 223500408, 651919264, 857466755, 303572123, 878165270, 193921115, 941971950, 841839733, 82542970, 611243028, 197185738, 305788119, 959854220, 703297338, 593771227, 288212451, 979566460, 319935860, 312768546, 276942887, 607612699, 563360477, 597895283, 963232882, 279302036, 393129864, 69868926, 469155330, 505942691, 942021314, 820647493, 369824927, 77829498, 164559436, 761319427, 177202505, 279773157, 246298411, 6348775, 497214541, 237549779, 155101827, 966082675, 893438591, 972917043, 219059051, 514186808, 660194907, 189442878, 575748378, 114635879, 814090914, 689640111, 325582643, 310107812, 348119710, 693468611, 409639074, 224640185, 543702891, 688729076, 997675457, 968561482, 816421829, 685460004, 392195309, 830595482, 713852536, 582801052, 716464430, 331320373, 568543368, 778928035, 565784819, 755031015, 804762260, 407888486, 521609333, 487725772, 882134509, 876338004, 120454321, 196099771, 923999045, 758160613, 15970337, 934682440, 460651226, 302986213, 792356830, 632300401, 259762648, 443075671, 96358374, 98994472, 997432268, 17785538, 191918284, 404415084, 651967004, 555566496, 29361658, 690935032, 555673447, 27444505, 422006528, 235622847, 900548851, 593786524, 404982998, 10624419, 115013235, 637661488, 722593188, 59081471, 972732837, 287447295, 911188631, 639093584, 207481697, 881982654, 423905246, 280104775, 662686509, 411648921, 659233993, 795879475, 622542332, 273785399, 209697467, 198288826, 590284224, 658759317, 220648772, 124190595, 29463712, 338610146, 36211014, 286788938, 945814383, 345985360, 238207391, 823810543, 551778311, 393204531, 853629822, 855103282, 201978878, 749493292, 23394004, 287534576, 150377334, 350394593, 526330759, 585787751, 603102984, 651915589, 8995249, 761794288, 523437622, 141943878, 152789204, 967544575, 929021756, 757262800, 179051497, 535601383, 809524252, 213095458, 497643827, 716839082, 565630669, 395596790, 817248870, 952014520, 154309347, 506361285, 918497025, 328563589, 628099805, 562911732, 549712382, 6500068, 940857623, 164727637, 894255995, 440625804, 655784783, 682348860, 718194322, 595834098, 166982149, 596839370, 448682897, 258196380, 168412126, 739829686, 115349857, 928126934, 90167011, 834562947, 857126956, 570611244, 210711835, 217390519, 509767412, 287693355, 910342743, 143842260, 130476354, 567368726, 845335402, 322433259, 809832029, 813937867, 721847290, 716916455, 297070904, 708690650, 7946543, 518222588, 458257786, 125200396, 857569485, 319667248, 584223985, 90756134, 438898605, 348029828, 11886756, 350452943, 566425909, 261557250, 168477705, 159991791, 633749430, 44872618, 752794164, 752388865, 374145889, 126238811, 985637575, 540293614, 30503972, 658442336, 703274487, 261595642, 824524304, 882559830, 537991068, 48880670, 457321847, 785238622, 748890672, 618502585, 872681946, 98611579, 83652470, 855399419, 326631161, 762958248, 144543392, 754685230, 630958596, 457649716, 671666205, 762446896, 85935835, 776327611, 845579150, 704758674, 298472484, 733303708, 315238250, 891730285, 942096447, 509901178, 787211666, 77608072, 839272989, 822960019, 499226637, 803747109, 736801052, 968125759, 302815977, 745957104, 590509242, 994026700, 581984421, 793519574, 301672505, 354911507, 982410823, 938276641, 731500031, 626495001, 675456020, 454410834, 516004267, 487201358, 9579554, 248805845, 702597087, 744965934, 300412132, 997502273, 845841439, 971079953, 153883577, 604608863, 124946801, 271175891, 574366233, 44745581, 228997601, 117436419, 516475244, 317443804, 442222135, 340590142, 397868887, 337302146, 246070534, 267440060, 922732116, 263009897, 73117020, 381712462, 909236865, 997905363, 844069085, 857433914, 432051038, 585901016, 614587941, 902947365, 278137493, 112478817, 665532034, 686541768, 133328977, 973536964, 657570361, 814874437, 57516776, 852303039, 92270458, 651623488, 118159442, 145336090, 523752619, 949286080, 812402935, 127007095, 973556351, 206895019, 145057829, 117909958, 961349639, 193854426, 908065682, 30507101, 505026751, 822137978, 852687715, 773596750, 94888532, 640443768, 636596332, 502290090, 350652687, 215079197, 57111792, 526713886, 121264823, 124018538, 167054151, 503067993, 791296728, 555827518, 252260015, 725425201, 65179222, 263176575, 367210373, 750778928, 165210132, 205514673, 561770363, 7885502, 71274054, 432442387, 714540341, 144477930, 530095081, 642758762, 777893994, 81739870, 465391665, 313299068, 654679722, 601122938, 991985634, 748760492, 507812704, 645393879, 494391514, 555668278, 653228696, 378806382, 867250198, 21356975, 367374336, 424533666, 310146523, 565140688, 206467957, 475666236, 859016517, 440332130, 949487436, 953086409, 596306915, 871878680, 928862427, 492412710, 9814753, 318389956, 503740874, 375942467, 53719227, 681514803, 840227652, 70365055, 953073936, 880776217, 433193317, 899810247, 374825068, 223979570, 229661103, 915464096, 764581662, 667870158, 443936650, 911065107, 286872352, 841772765, 849233139, 542717211, 105364166, 733605018, 520486076, 822300108, 213406831, 612832569, 482837341, 118068603, 491422064, 896657912, 626476957, 940295998, 718256677, 958061688, 849635826, 742032886, 51844829, 642467379, 382014635, 380444556, 801964027, 544083207, 756186583, 291221878, 733053942, 148489791, 466904249, 621777829, 873259661, 647825558, 860472395, 520177157, 196551629, 145685549, 346413671, 213059890, 683031066, 277873035, 471059138, 583980145, 476780807, 691671048, 672375302, 355945995, 635764773, 460807189, 870914778, 521224343, 426483271, 758186967, 708567201, 317800407, 825989719, 759247459, 444564238, 281793470, 186699180, 171035821, 3562785, 36748897, 311805958, 470257385, 844033309, 318745271, 292173981, 728593352, 778760890, 415793812, 578538854, 203099880, 401302532, 426308791, 358988648, 892793003, 172668287, 32119457, 333072578, 882294066, 691702502, 392509224, 524472097, 657071006, 21032583, 427549670, 443494660, 478012476, 405798289, 109348256, 373713662, 314758610, 230403496, 262574958, 907326320, 791374900, 780662548, 51479979, 11357533, 843684823, 201179964, 496316415, 22781552, 834292855, 684367749, 451154501, 946474529, 812400294, 383458436, 833576539, 445231323, 727452150, 333585560, 674455768, 460725700, 183940723, 561951944, 649831318, 365310061, 443480776, 992121330, 976850238, 93849461, 227713829, 469653503, 129947455, 51254696, 524012627, 164267001, 563307317, 275353636, 920348009, 785483825, 961857424, 121877154, 833585527, 918939634, 680288157, 26454894, 460916417, 954488827, 155861872, 784081430, 25511839, 675059628, 7450728, 552172466, 328140284, 957981941, 24485013, 116108464, 521716498, 664959285, 841503832, 247384557, 822115570, 561449665, 835320418, 141211950, 952667833, 235723796, 427682481, 591477363, 171965966, 983676169, 416529796, 888463934, 854029001, 237010414, 288829225, 126179545, 122256386, 939737274, 403066700, 348354423, 42833119, 460455925, 664112644, 144955718, 925664113, 168337707, 106356996, 340674909, 710942695, 633030148, 823290655, 295857845, 888382578, 414984545, 910727267, 579969204, 341001685, 239372968, 186650269, 777270623, 407332419, 555859283, 11829811, 990828624, 863913582, 951142673, 215865855, 302638620, 962857810, 86622219, 410112853, 499419238, 166642645, 741626064, 372135731, 689717751, 783038228, 796268596, 760977811, 653797231, 166782413, 785010204, 449944617, 674853726, 731385834, 355879547, 864478154, 39662046, 527800064, 891058995, 919360888, 645912522, 473517587, 571260143, 260358896, 455445521, 343120202, 36433464, 447776539, 362142447, 115431928, 642733647, 856894441, 467479268, 565235218, 522843433, 496415360, 106895169, 227997143, 994184953, 337850339, 619776467, 685809271, 540414815, 815862422, 781790171, 953626550, 50577879, 449201671, 334796537, 104186513, 650845634, 109506894, 465826799, 48370961, 606704055, 567464492, 791821450, 699759962, 857870430, 653403463, 249964064, 710637092, 475530118, 631703442, 841884963, 537960730, 297425647, 284203810, 195736061, 501787701, 905959181, 400634199, 742002191, 732051846, 1857350, 664173956, 670485516, 96509049, 454487091, 330218233, 752287211, 267554871, 322625898, 172013863, 32902600, 270687290, 384717663, 500843343, 969234518, 814450020, 524547246, 166419995, 627406617, 454359623, 729413193, 552129015, 598272846, 178246127, 423811462, 364057577, 853449978, 320439292, 304033506, 553626748, 660369503, 96727304, 334089538, 559446976, 159699481, 266443443, 409729130, 838632219, 270995214, 175176959, 405110251, 49855770, 248931535, 835983299, 88334537, 516610557, 120838697, 274683738, 414116719, 462237960, 780526306, 613273791, 141212143, 367687297, 891229254, 518993079, 438132095, 14367869, 887216853, 151287368, 706130208, 452180451, 936223007, 439276077, 801333029, 85488256, 577927701, 702443624, 62068972, 189231853, 364826036, 349685286, 848722893, 645809851, 309404322, 711335904, 301212948, 421064419, 82143522, 707453429, 399411995, 708451271, 59951690, 43841231, 250272989, 918440461, 722124511, 350860212, 97324831, 69855485, 837911278, 906722647, 113988471, 215700999, 294864146, 91744962, 691911144, 889110138, 640572345, 508638945, 647625893, 138876648, 168295525, 120047098, 373204384, 17205341, 316309679, 278294304, 866439982, 493450473, 114366241, 50455925, 73800842, 746489262, 173916412, 297001981, 291917145, 101099825, 336779218, 829482198, 107668543, 734595219, 520883731, 645777337, 541120504, 390518007, 219221527, 772901480, 254856879, 587069420, 653272277, 920576467, 782124348, 90846914, 524349277, 491937345, 300812116, 350614991, 470140588, 759255200, 430699335, 201836272, 515141341, 916623911, 399436239, 994907031, 698133892, 627170617, 678550720, 689180201, 186516416, 42793900, 92031327, 448537933, 94432528, 234130454, 995735798, 672575077, 216865923, 58814316, 558324684, 326340715, 484962920, 376944263, 860888980, 821926925, 335026211, 751340005, 500325208, 103406615, 912425884, 967578016, 722233413, 667801502, 565314039, 952601513, 941740990, 98358898, 974555751, 604421610, 230453263, 840693411, 615087008, 245780538, 305265905, 811741109, 55683679, 921370389, 351279524, 30811140, 704961815, 978016819, 369652749, 897463961, 879844068, 566768718, 163250135, 170105467, 216740710, 772156206, 144366983, 751958796, 623366925, 717880870, 504712054, 529232335, 191240743, 741230086, 368797312, 449872712, 294258011, 877665884, 808657995, 803450950, 26709069, 876357013, 272237554, 872830829, 456014392, 311692975, 118949011, 716297676, 289189652, 169388124, 902375956, 831500478, 295473704, 552132848, 330724807, 301300364, 73886907, 657434427, 343844607, 458411783, 920477735, 395062112, 163448098, 306696655, 825542477, 251637953, 684786142, 294464206, 118716873, 988410915, 856338738, 108069453, 285044605, 441623068, 660753463, 567473056, 779044397, 703237233, 504057326, 357638854, 494231375, 897259958, 82949284, 721934223, 832224934, 590635908, 154826360, 273869846, 636751197, 879169207, 40181440, 405506288, 854154075, 544267361, 774153701, 749612747, 875877324, 562856811, 67290738, 362030872, 420488279, 138660772, 741658433, 708936804, 245951024, 784697293, 552125053, 278893946, 480267955, 699490097, 83472912, 66811232, 240087040, 544142869, 506175780, 863385337, 412643656, 29701871, 931798771, 388089073, 406087690, 257574729, 488409742, 608263497, 920466205, 801510318, 253233248, 189789620, 822612304, 349796436, 571687857, 368471851, 851871050, 572277453, 886737714, 438923924, 965664518, 690795872, 418945585, 366002362, 566650116, 757247688, 791188885, 178155068, 522411485, 656159908, 646619714, 701476919, 641103054, 603585109, 927117381, 670703326, 722724401, 83170505, 118670919, 565334281, 592994358, 456481989, 187258029, 353340024, 191731304, 700283199, 553718629, 902851437, 627412181, 191478099, 745918050, 627813627, 468175657, 434230809, 926643094, 877710490, 822763995, 491385785, 130746585, 725352334, 22369713, 345664201, 229828911, 282722908, 832549251, 830395526, 241717366, 282605762, 786544609, 247369370, 523343485, 876767656, 4697063, 350056950, 450968618, 614879367, 327194154, 274562116, 880675170, 826793406, 400880060, 217320492, 168595584, 749065439, 678505769, 177760457, 558741037, 385916069, 268666515, 245889770, 689329052, 30115303, 303004051, 793928962, 906791629, 482398985, 35732983, 88744336, 728277542, 403990535, 240574916, 522751022, 355855100, 695186658, 596632726, 39171120, 683944317, 347703510, 569660672, 761611338, 687715312, 579179539, 118581297, 167372307, 849164658, 904615838, 66951024, 536548909, 39865096, 924801686, 991356774, 22193933, 717454451, 907653742, 277482910, 164320632, 673752294, 533506091, 693324148, 663943522, 878856340, 403738935, 871711093, 790906185, 816872103, 999985470, 43661439, 276836002, 406711073, 367024391, 731003118, 168366703, 849692792, 159180641, 359083877, 676858174, 301860763, 918985852, 689997512, 831728119, 288733296, 428755059, 831196505, 988359967, 199669304, 58445193, 709946, 784077877, 508008717, 87902958, 111323883, 911246111, 425961494, 291061951, 439461137, 575190940, 851465866, 919626040, 662973075, 879447975, 482424636, 966548867, 358459147, 319346887, 279219078, 53419995, 913006358, 622107680, 361919523, 193469635, 83924707, 633725292, 812757589, 571274483, 589903039, 499315515, 75844647, 392752774, 30710142, 967295878, 229131591, 203087229, 54197778, 980767647, 565649833, 179346123, 171005364, 231942328, 449726609, 854276891, 919362897, 391560432, 998143861, 334975740, 575920410, 931195282, 963327735, 947630332, 408069879, 654452452, 282086530, 276881625, 617523344, 532391301, 338856914, 31518804, 119303911, 460762930, 241942437, 894883225, 90184138, 270349160, 895588125, 780197212, 983583963, 803744502, 73788263, 412854836, 430042712, 547928400, 697985946, 813735602, 431439080, 624378049, 480718683, 672233919, 859831114, 466643210, 849246416, 275566250, 932802086, 454373145, 437496326, 689894841, 792927960, 793176145, 2192329, 556166063, 127695881, 337694904, 412954195, 329173618, 677699805, 21361127, 332640432, 226907903, 450629668, 737639072, 549285627, 882540656, 379684877, 983207160, 77370152, 378144760, 938707752, 486482529, 440047221, 990757175, 910414676, 480712670, 883171791, 223210726, 362509725, 599160129, 849972693, 399039558, 409519197, 895079575, 308664020, 215707502, 692096295, 917176168, 341058916, 509296233, 766129125, 698077836, 177151670, 862819206, 682669405, 8024248, 58462200, 410062131, 865537144, 706600184, 568487661, 280972624, 63396867, 988459965, 471422645, 476779751, 366495827, 133306941, 358760314, 48022068, 156559666, 69628862, 343240455, 182549655, 109299, 263320993, 92165943, 988364663, 873442396, 54681748, 100281831, 990552937, 43606056, 515604601, 401621175, 913230473, 775252344, 666120447, 996693626, 716549075, 542351695, 695822373, 415045237, 10138737, 716347279, 733104125, 735602058, 717952816, 794338506, 808382712, 658514059, 762250315, 528227398, 96839547, 407448252, 746511528, 658694512, 462959896, 659407478, 542611060, 756339961, 693321658, 600599890, 909457712, 292788490, 761165226, 436365388, 200747682, 865513462, 323727592, 510535374, 306378026, 361875868, 278051720, 995580255, 546406160, 373063670, 275303349, 747135487, 631943490, 463461044, 421190787, 227938540, 432636881, 159376024, 783626345, 710884398, 131826368, 770558185, 712069131, 198964707, 703948093, 624534540, 335670435, 182742070, 595530095, 931132535, 563501529, 876811337, 780399401, 567585458, 935601869, 918117731, 856011501, 816142582, 194732252, 271563361, 643389560, 734909334, 231326106, 311038227, 640697870, 406051792, 889128613, 732938550, 73845625, 102876140, 104357980, 199622450, 297215212, 215415060, 319612078, 723483321, 394508430, 38858878, 239202645, 504943634, 241074218, 667793578, 905632717, 304805679, 85578327, 772266002, 897950750, 873834143, 239732921, 336301163, 582826308, 726906973, 963669090, 350957133, 947155288, 618356229, 427004980, 936224940, 976396356, 845998783, 746602493, 684348542, 639927014, 224755912, 564778950, 705021044, 45847547, 609448079, 663606735, 252325313, 464840260, 107295208, 605647000, 794297803, 763736181, 708741208, 693052477, 550863170, 881098422, 803707597, 570566598, 613737122, 316760495, 481104355, 774377017, 575092161, 33956690, 304256208, 440986503, 150628587, 86289334, 169514751, 917244331, 944730119, 30878602, 542583809, 724760512, 719131361, 307900814, 871419964, 384507671, 980736776, 348553435, 410784161, 447848661, 578494665, 838439244, 847295113, 231574196, 8224410, 374423343, 989136878, 276650097, 219537171, 542333021, 477016547, 189136822, 549081225, 995180742, 39680546, 457756136, 959544182, 123343111, 512595873, 616440399, 378974950, 760029564, 724786011, 147662165, 500614166, 733219048, 589849742, 623871148, 446117250, 285856693, 292216798, 387581405, 655818778, 886381569, 445280546, 108861665, 605104828, 859506523, 910190640, 870332775, 996763600, 551360638, 944686933, 874940904, 536827196, 87692205, 876841383, 684495259, 214504919, 213959026, 894306030, 759265093, 973695087, 732312103, 904324071, 301691972, 91860127, 148014236, 872828252, 92301317, 181137675, 855459407, 962945110, 961533323, 715711687, 421650867, 986807537, 593311806, 287884169, 893104440, 947933978, 566464096, 957357918, 957650234, 773184015, 211915728, 970873901, 619043982, 261078624, 56168954, 695449582, 707519359, 207779099, 810315558, 796719862, 164507139, 977249275, 112708343, 190599827, 589815349, 349379861, 446622728, 293403907, 95081158, 562340826, 40738864, 655207479, 259094989, 375623663, 18172671, 65763753, 251948371, 513672394, 154321829, 254792655, 744909213, 449708099, 522641333, 938946955, 277366069, 381467380, 175246959, 936813850, 399390331, 918221428, 736792772, 3596597, 825370925, 908480295, 915822415, 863686099, 183347724, 25355933, 700849800, 35855643, 610274576, 866545174, 399645740, 623862802, 919862496, 927878077, 285947668, 8460690, 746843379, 709382611, 927262359, 549067123, 27052786, 320301626, 408129228, 118055033, 519989118, 596847885, 686289402, 61938481, 905075703, 343557765, 935887854, 943677060, 431298811, 44595045, 101048094, 778618825, 305633704, 470726627, 56195807, 110641114, 147670697, 264279653, 588362541, 534018532, 946846787, 661110364, 607182292, 294024270, 256280028, 232248805, 59720690, 578811576, 685988107, 3529913, 557340314, 600444355, 330905285, 134952325, 275236872, 684293428, 621443103, 102638730, 544835501, 296150218, 62888268, 230935657, 886578517, 369035849, 248813560, 786703672, 154807526, 490542629, 447249670, 83463273, 419706833, 493071836, 170380148, 855292037, 31625966, 770840034, 661196354, 951144072, 409896604, 548908153, 174413810, 23371930, 582213178, 15044562, 534579490, 730476586, 679628990, 678697003, 296447618, 912762723, 729741972, 696753037, 217482338, 93457354, 492148678, 36946207, 262908471, 50351123, 379924770, 742455512, 672304890, 813141155, 822840253, 718594880, 906640241, 869535006, 735444687, 256466882, 451059475, 748726971, 822444669, 437329438, 242095099, 398785190, 626606952, 880796788, 102174826, 55699001, 858937823, 697641608, 869234957, 493994804, 448436455, 285619963, 851817035, 17454073, 561458303, 578920713, 266947055, 850750970, 657302347, 504082045, 982914283, 486237371, 692435596, 21691887, 847850076, 355590112, 768625070, 542871482, 641842932, 503248446, 787801373, 512667422, 305502623, 65116718, 240027979, 172427262, 554879661, 321167336, 710386489, 524103636, 94479006, 619183263, 558120057, 981033804, 610369181, 409587197, 2643337, 624395393, 237808779, 84941309, 254273490, 420705588, 713177643, 253239211, 742201686, 536438069, 466229646, 333842024, 123615042, 4487484, 137386111, 413156612, 791296861, 584494316, 595582372, 579669498, 725958920, 211884104, 818003042, 425295898, 945664748, 828558821, 122701055, 22534369, 124193780, 744796654, 227344289, 379099261, 859035177, 980698695, 793733818, 776168519, 38696041, 465176859, 881919644, 857576249, 339965922, 810054465, 943923787, 152795710, 456064474, 819522317, 528420892, 666026248, 437245863, 567501968, 623361091, 755384535, 751660585, 295245071, 863609395, 505726489, 875201036, 767383424, 272199728, 803267122, 98652464, 319159157, 86380222, 666094995, 801876866, 530736373, 285510070, 888627018, 647977848, 425165558, 66122548, 610281885, 961960924, 35985070, 260146608, 625796124, 274183523, 460697446, 806023856, 518501507, 909793917, 817146491, 129225500, 173920705, 166789642, 5697673, 692162480, 105998991, 975968246, 863414406, 219049945, 879854032, 859421466, 620585246, 946237497, 194093154, 967628204, 198523873, 755755008, 760829822, 140138712, 647088632, 679413832, 415187021, 487649503, 864080262, 197539354, 146340971, 464939924, 417610885, 477803934, 164850227, 524206470, 919380887, 446637257, 672801039, 154342559, 485634062, 850445620, 177577631, 794786761, 308007917, 46559214, 904361180, 711138489, 261216907, 308203611, 50977488, 92308594, 50877689, 623416675, 734823783, 583463985, 318985030, 262343076, 686867641, 214036029, 733072097, 10790128, 18431929, 30278750, 806435133, 334585463, 558020596, 172154631, 314905589, 553989218, 527067383, 327113579, 626900952, 996829303, 53092262, 546700873, 350134169, 867205694, 567296097, 108810905, 867799549, 571819267, 750641533, 609580180, 600949194, 128069508, 812899267, 132086891, 398880872, 259497327, 490810599, 770102961, 607969376, 386548737, 559686992, 701899547, 147697964, 962974666, 358469968, 579739094, 792194271, 948383633, 452269485, 985322053, 142906630, 765261933, 865442247, 24901070, 640659014, 504691564, 790868868, 992887705, 760772280, 315275793, 917638227, 443963330, 315416964, 984636260, 210552879, 186340747, 52683343, 729074118, 885026984, 467015727, 389154236, 598674913, 969147039, 128941910, 955427017, 850772017, 853709361, 853788884, 248132766, 164319912, 198619024, 979662378, 436815703, 44052492, 158522164, 115678325, 289476857, 928547587, 278400954, 737207579, 687210440, 376646790, 905337313, 58375312, 997081779, 478790489, 703566907, 713087316, 990195666, 774898736, 490447442, 110802942, 427942982, 753808811, 159291104, 428572734, 225976229, 595375390, 33739544, 237287026, 15578407, 381971012, 879003906, 499979648, 134278446, 643565016, 415772766, 197802205, 772501369, 986681234, 53436377, 815802431, 575245579, 617463663, 595129260, 464743847, 241535983, 464150514, 613279072, 854697665, 872988690, 117835288, 579736369, 385286870, 204761363, 352311711, 584172768, 911540923, 292009458, 368532307, 335585471, 163428706, 957334162, 994517833, 343714002, 632647804, 426074254, 933301929, 121853386, 204151790, 490337109, 395767658, 947739954, 291566013, 461842897, 686541112, 766270816, 677369475, 907975750, 480727609, 759790687, 603288470, 108468380, 514784459, 522097576, 860968484, 743724872, 284677181, 210425043, 949832395, 434593387, 826836423, 77631270, 117119590, 43493942, 146053109, 45910927, 795428421, 208534855, 889096486, 543306162, 846918791, 982388772, 658743735, 485100369, 640794371, 892534121, 193228972, 778999006, 626782503, 24339705, 795102871, 486788647, 107148568, 809910204, 450651807, 846503712, 281689811, 460913754, 971582374, 982094448, 359748164, 361347216, 213657578, 264086190, 488947884, 918472908, 511156846, 214306093, 479903089, 143185370, 610865113, 402180758, 921787002, 43024351, 759123160, 537754344, 292111431, 506181710, 286189028, 567517058, 273585795, 940286329, 10106395, 428571152, 791145058, 428521519, 612196749, 821267290, 836764783, 609374928, 748047115, 979479227, 92815257, 374124676, 321710124, 858452273, 826167549, 36046994, 660161281, 848021851, 433405237, 697456703, 954151442, 599571067, 347003598, 847409358, 741328632, 740193393, 565362890, 287346041, 147714291, 92820230, 497586491, 970288572, 515845684, 705275652, 273621821, 968403927, 949522721, 218878904, 525913345, 452777395, 301496059, 586249209, 119832041, 477106805, 488249771, 554885902, 228769972, 107036995, 638002875, 818909983, 761635848, 800705331, 760804097, 598259239, 787664303, 629391802, 965234172, 672311055, 985661675, 730022316, 954134178, 777683468, 32948385, 435569150, 948983862, 293633720, 966842697, 44490851, 963102251, 5530628, 281998003, 39781547, 931755424, 892491908, 827501235, 608793493, 541589857, 338762665, 595018146, 461801316, 417550578, 381532550, 815551030, 960905651, 48715402, 403424330, 762359507, 724214981, 649199432, 979581839, 7203577, 627850561, 608900496, 764800233, 387571659, 350046958, 777951948, 163429228, 75104166, 950559473, 743295534, 783062783, 13111562, 463247889, 67827862, 893705265, 225086578, 127098193, 609092993, 855404163, 327688588, 948794934, 146415559, 546140882, 892678984, 327458964, 185495478, 748891236, 249156857, 394991679, 947347131, 874062074, 380203769, 613901374, 990778423, 348966526, 263785199, 909423663, 573164793, 310603176, 859908336, 942366588, 488452684, 93794758, 524099841, 970003024, 948272119, 468627352, 255606759, 554038101, 550023752, 517040308, 273739246, 922669505, 23314301, 14432124, 490992451, 347757039, 925284073, 8702128, 663327398, 801555597, 728913431, 899381411, 509882528, 415005125, 370480637, 878997511, 339510868, 906470205, 282441231, 392518141, 217105358, 766295353, 258908695, 641772634, 252884089, 148979641, 549358905, 253364798, 160943825, 200742256, 694078561, 223114845, 458534977, 184209330, 844710312, 527102435, 375936024, 114151588, 963120924, 471696978, 845387354, 109473728, 714496618, 157905721, 752293952, 763467468, 160173275, 286153055, 1744220, 682813564, 392465296, 715598991, 837694317, 236812743, 703669606, 877107484, 76131514, 435571174, 389254202, 301479527, 660551216, 446001073, 101796176, 536550332, 615538795, 419039581, 590409205, 899650903, 713042342, 886595938, 239906313, 105869726, 828981619, 275208032, 966716375, 360868619, 690314537, 792916093, 628361306, 994715377, 248936758, 753973278, 408763765, 561485140, 729232605, 69602126, 36748919, 536236941, 970469235, 562384686, 195484833, 25727379, 518256100, 417657900, 756898001, 541832323, 639693380, 158081324, 284725318, 850251684, 178003424, 309094230, 220203338, 345791763, 394039430, 65506372, 246819454, 125203455, 41282677, 958068191, 69915317, 906787283, 122044649, 468304082, 689266701, 250838533, 414489138, 681402407, 591771270, 192606812, 701962951, 449502946, 501848629, 699787899, 99269160, 471608708, 653780855, 46446246, 255374343, 56963223, 962073022, 235992686, 937521035, 701262678, 882391351, 591601799, 445584597, 319006718, 282156229, 437893400, 974834152, 599766848, 839449099, 720124989, 662050329, 40326444, 916771397, 961006186, 905140165, 545602186, 699564633, 845000798, 747247918, 366710351, 161758287, 573917182, 364800892, 910088084, 888982550, 442671375, 148343718, 308722439, 643836788, 627858546, 750666782, 928829476, 598749756, 93973621, 994820955, 858615997, 184911923, 245518054, 827780577, 90351422, 474977486, 236147693, 189699127, 467145218, 557954164, 275055779, 315287529, 360179944, 994777943, 201825341, 786731690, 867328983, 482175367, 142212789, 806897413, 221329256, 619055755, 889929699, 669302880, 251626356, 612798327, 908526498, 405448579, 292819477, 817534760, 603054471, 125293214, 803743527, 731015701, 575895960, 436478815, 696864388, 585661123, 508443987, 785844007, 296596315, 609958362, 120565167, 870546162, 712608181, 58218937, 952635303, 337097460, 773845958, 789201926, 893043944, 18293000, 230143856, 492134298, 336056163, 794415523, 489860715, 250428805, 188053535, 376841187, 795814422, 787946839, 458842171, 999848582, 728550114, 785370790, 709113941, 322799677, 856207104, 254542257, 934504297, 177198964, 240109312, 666080198, 397467436, 585874543, 235932261, 955402552, 695666140, 547245632, 180097327, 255684327, 839990199, 434868962, 448444165, 475910658, 156763399, 798911760, 985138427, 907775911, 695022348, 982484791, 95709742, 843923544, 751277780, 37699628, 322516341, 649031945, 917093031, 323609568, 779739125, 869642004, 777322162, 468771876, 473678609, 880362192, 932815173, 957774165, 534378529, 179495191, 22808350, 85733452, 11046935, 986175195, 693002782, 999341866, 900881169, 592384694, 765667290, 570088791, 493537286, 834963225, 271153122, 532823998, 797245270, 696376739, 629129892, 942245938, 723915809, 525117021, 552350384, 558677534, 968516714, 831772406, 824657141, 861150509, 387355437, 791808832, 413073389, 228555939, 983425061, 199675369, 940734540, 853662643, 183791387, 988924532, 864273777, 178154920, 660602972, 177031318, 837342163, 531578517, 594675546, 168725401, 184991535, 538494571, 623610590, 263033016, 908979287, 261580728, 709738285, 125410599, 942950529, 166911173, 628809167, 935055564, 576922812, 689133474, 636804702, 536214357, 598234392, 432725637, 21027434, 406409004, 115663796, 932310162, 934192846, 310633903, 571153820, 281494900, 666938924, 91026297, 37057537, 152114182, 144303031, 96955832, 371741997, 294832969, 399411093, 345427301, 190211843, 339280089, 735499177, 518620767, 222828509, 246451949, 317445747, 111811888, 455903636, 209303805, 555780751, 959511613, 227562927, 431252521, 910078638, 197891032, 703329125, 99465650, 372461797, 865973875, 174516089, 597998504, 89838435, 799332312, 544720214, 815445212, 277369312, 39028208, 620579755, 827014357, 936531054, 506644022, 385085105, 449752844, 3498825, 965604175, 619262100, 239909761, 49091583, 596200924, 856510728, 321789371, 146353041, 528563327, 736623978, 422314115, 377329993, 554252832, 495872863, 386378316, 571645788, 38906000, 802897334, 428338995, 153223103, 93184494, 188197525, 75504798, 309037291, 527921943, 70860296, 127631018, 591130667, 156310445, 939615065, 337432235, 245816624, 666986985, 629449049, 178875859, 844735119, 154046653, 570109872, 26264743, 50415239, 878952226, 285960938, 94095629, 807705466, 228955389, 105749343, 748607534, 744217036, 367763130, 887239556, 308518985, 717051006, 930075610, 739617429, 526511080, 51924533, 255766095, 460783310, 397532424, 119275914, 564658145, 689653680, 903029054, 372143939, 24274661, 267822316, 740594463, 442605735, 579730747, 18482465, 577464496, 515366032, 460352774, 918203754, 492722332, 208870442, 856982696, 727596396, 220496143, 262069838, 244403754, 814967355, 540882349, 50292308, 860853695, 594462494, 489947984, 251358460, 582173206, 37901347, 200056601, 970385993, 816677957, 507470881, 94316172, 18341927, 771552665, 979813421, 664001, 847839380, 148814762, 528411786, 383815187, 742905413, 171873472, 60845554, 156951933, 786752353, 410156785, 888716090, 951581579, 496424798, 899911542, 366247900, 209124630, 434595671, 850917812, 487889643, 635025129, 280483182, 535275610, 562132343, 659897645, 528872326, 709174538, 792126436, 98561214, 916236031, 366757735, 312103273, 55344810, 656202464, 221909251, 677157991, 481015176, 184402326, 378592034, 120311695, 985079247, 623275346, 98470338, 813057353, 691733963, 686774211, 409819391, 636988774, 915291066, 272860305, 118462331, 764682287, 939827077, 790743069, 937545737, 981225064, 827944940, 671413140, 648415610, 963613943, 515015286, 341670932, 462723359, 90255805, 336878776, 113624211, 237453631, 150590520, 671411348, 484973019, 665468182, 679332624, 915100415, 455752169, 601357740, 671842399, 913133548, 904494386, 108535558, 114350211, 428275258, 360406072, 412470655, 42550248, 551032869, 697368613, 773651133, 751659914, 836238273, 595423465, 927663859, 55232866, 913923270, 589174804, 54883188, 425738316, 658429265, 637679122, 459672732, 781762306, 189174209, 263081481, 327050156, 849435710, 582941012, 806170530, 556714581, 38278745, 880903445, 43777284, 26480594, 77176657, 872172260, 409617160, 462926168, 605680298, 272983208, 701317286, 842721158, 228909924, 466225222, 654246797, 352967576, 916180026, 128742363, 55524326, 997281430, 842432404, 184296953, 456306394, 248063823, 984164170, 810161391, 911829156, 131917008, 666692862, 102573244, 837081861, 625180137, 480440139, 887920475, 824253132, 186519345, 750584539, 117312064, 157889359, 146170965, 687562786, 601238612, 364648192, 540516027, 857090398, 330766043, 69186680, 79384237, 461830672, 531656911, 93688875, 312963825, 666393323, 900945238, 639133059, 954745682, 697345281, 494948385, 413276890, 870220875, 24118096, 840276466, 751021153, 827766255, 297421245, 402486250, 953475087, 268274659, 826370096, 767829329, 248168246, 346969893, 383519818, 523589090, 71922831, 718177178, 165957518, 890668957, 757647551, 213731464, 167687987, 254460365, 705393061, 97677515, 786757658, 63135809, 814995321, 416609268, 938799741, 893720225, 977295511, 909405932, 871443976, 912642625, 983659710, 353818660, 20885610, 14500702, 939038570, 817533906, 415886387, 8379390, 46981471, 827005207, 562508374, 128389717, 92801746, 552087438, 975768382, 837417914, 367685911, 890799529, 153166444, 888730013, 625541902, 967200827, 890012892, 170302432, 836446036, 269125554, 541823810, 360884673, 303371420, 487665522, 788711370, 516970573, 833555740, 685109317, 147088220, 512215198, 212340242, 896340754, 505007122, 845187251, 952464229, 406349379, 657744762, 366867217, 366676183, 665480463, 91216701, 255618856, 349032497, 818755310, 786950683, 365577139, 364975737, 336124780, 93718343, 897028332, 709361745, 191480447, 190800099, 728116797, 637373537, 281863179, 465448315, 440590270, 908109226, 862960172, 824977431, 668024892, 11814378, 117988818, 71094667, 859023035, 721838891, 535291517, 18760939, 925410351, 760407583, 767157856, 380041095, 574448090, 660069030, 901052721, 46165171, 119598209, 161042570, 575704956, 981341941, 262571736, 231466527, 336056740, 857161546, 226741582, 403691529, 82623285, 956232638, 823972997, 932378518, 257428070, 109105844, 851567191, 795708800, 268052043, 238648743, 424041618, 128470842, 215007344, 358840599, 833971108, 402757642, 531658501, 466348903, 733668203, 104941219, 203213954, 981088214, 148176953, 40537162, 366079613, 982592605, 743846084, 800746353, 968014295, 321696753, 729890342, 786504499, 725176297, 23149070, 226887877, 74857764, 862567435, 272867065, 979396444, 645705294, 789426164, 562215088, 893191231, 211584325, 199203434, 306292220, 48194724, 794512346, 441337356, 443197833, 368116708, 547780135, 173924595, 477172608, 632307418, 916053650, 432137166, 689442533, 408203317, 155610902, 464327457, 614021237, 878524877, 33579193, 117224476, 892761490, 863260225, 112468681, 380770231, 499859295, 476696915, 254179531, 969308787, 542135196, 742205000, 855922074, 251889321, 407874725, 276913485, 886184574, 772249190, 483926119, 959764088, 158779416, 874368858, 859081445, 959236103, 261186877, 352252187, 282847745, 156982510, 269539761, 768698703, 419889906, 673849980, 265513110, 8479126, 554911967, 961164672, 646963059, 566174323, 5670503, 322477825, 678703458, 27609643, 861422686, 370800130, 501869099, 717730523, 741907339, 307324224, 599186164, 656723260, 339750279, 943071246, 324282495, 233261105, 519105879, 689628950, 243027005, 262272141, 292042485, 861113186, 939990807, 861279673, 204414555, 978572134, 162618486, 782464885, 548625556, 187276117, 651459183, 152997823, 146396387, 495982107, 484867367, 216487588, 556307439, 644217558, 63569379, 295333412, 697236900, 261362274, 181956771, 635038781, 627225095, 685141589, 864630658, 45092446, 999054853, 116444693, 756529742, 155478581, 925366968, 44486557, 500874919, 771237195, 926412134, 918891891, 359415679, 33928169, 952446169, 186962216, 52824337, 932684209, 767120773, 127529182, 674814898, 511428768, 62615523, 68787559, 805828800, 968012615, 242941973, 798575370, 960827950, 975670317, 915998864, 662873708, 241564021, 773689917, 970089566, 73199797, 202623504, 351408297, 974077857, 891128416, 461721780, 569191519, 776959459, 37006275, 852718264, 709901848, 225135782, 260149379, 570822304, 957890512, 194446407, 903303584, 67563985, 638625060, 720985513, 831573495, 983857838, 446126543, 847062977, 830292105, 832968395, 508544066, 398084500, 943199730, 829623218, 249019520, 834870992, 106650162, 27789025, 749138451, 277046484, 537570544, 847360719, 495093020, 860861606, 642870342, 45573748, 303300600, 657514087, 30956911, 648556256, 522851039, 714002119, 272846537, 112685271, 625363540, 911574829, 918347353, 419540843, 557533353, 44972402, 847932372, 721317211, 547415063, 789349042, 413082117, 251641175, 193402135, 255805207, 337985181, 318319764, 546261281, 409556801, 406313796, 627041195, 996343086, 39611481, 421193386, 785045551, 213851922, 967234112, 89077267, 616983388, 3773368, 609214298, 468698122, 231609505, 97734054, 64166843, 767248957, 235140421, 452751481, 921047683, 709304556, 636418291, 691176119, 890092855, 386644700, 245074099, 675434907, 621977420, 982814134, 652833369, 626704190, 482160240, 275838376, 395448132, 132176162, 820107301, 171088557, 98836158, 940583720, 813571190, 929441391, 943467276, 135206696, 648408194, 935783642, 549748176, 952234903, 487668988, 951971432, 374345302, 748595385, 962732076, 940729540, 543557951, 244075159, 656419948, 414568447, 88922990, 844658035, 787340213, 60936166, 96687227, 591894232, 724561804, 617273127, 11238303, 341643748, 124853720, 531946893, 770951509, 145682731, 98382749, 709871266, 817187760, 903314435, 690819144, 795317068, 929612300, 55513530, 705749530, 643070112, 902325136, 214932489, 369625647, 594315859, 982288051, 788655640, 447977528, 939448197, 832606544, 873203538, 567092262, 586843465, 393973106, 435394330, 387698062, 921616313, 961964844, 487039174, 614204191, 784662893, 180813243, 626120194, 472016793, 102128911, 248699959, 136509081, 211121576, 954204299, 155966607, 280210850, 268801213, 109761827, 633868248, 176476691, 196674696, 477363157, 890883173, 490873885, 102775485, 382456808, 119772999, 186779240, 926437373, 367929859, 14159412, 43581315, 61359272, 585669348, 700257326, 358942908, 915532928, 344913695, 160919637, 770148190, 271568769, 330718384, 264065897, 941263047, 376807114, 436883639, 336053950, 384932223, 272622141, 407948117, 751956632, 886662202, 918461294, 545989394, 883722564, 405715273, 632482044, 158771520, 875645574, 93427730, 792320595, 358955457, 765285412, 291409924, 656493628, 803079680, 382861371, 749960884, 72640820, 81965091, 203556074, 539492343, 351222445, 534078775, 823852254, 515146862, 506868892, 213679791, 199759133, 671757574, 635210619, 767306000, 15403660, 402467896, 505800467, 194874199, 953589136, 236829591, 61083567, 165896366, 239531590, 167501570, 936090133, 239750151, 314700075, 942263044, 113828633, 329619579, 998568293, 55703965, 193189627, 554242377, 521635427, 515370226, 566463395, 325225572, 591636426, 949416005, 187259793, 688202124, 305751023, 915315965, 431619358, 340914357, 850374384, 158072945, 91684273, 711204167, 795809854, 460173006, 305699126, 486280089, 801172136, 991885984, 548782379, 839454545, 256748325, 412784942, 94389367, 394169502, 483914821, 406259611, 813895828, 204190404, 324187793, 385486224, 475471060, 43416629, 333514452, 792729557, 860632366, 49531629, 626714512, 145480179, 359666641, 410016745, 327935139, 993613310, 770008232, 152815399, 662502666, 253950185, 90173315, 814566129, 161860074, 418479209, 63930281, 148825195, 35674671, 782414604, 438970295, 108556674, 59843515, 734725666, 620931492, 646262018, 697171977, 217269910, 656550200, 818806203, 268824408, 8474563, 272907577, 96090391, 953236237, 236838277, 596210925, 77410836, 662923167, 411282102, 486448412, 110543791, 175980987, 54327035, 78830802, 377248896, 568473805, 681473685, 33956634, 167569030, 773400129, 633013727, 602679081, 462523979, 101421515, 57940555, 889180455, 754086926, 481997772, 750366456, 774782169, 691174902, 849160789, 350329390, 206397828, 961626101, 379536281, 267670140, 153106319, 52623145, 160660366, 685583425, 945393206, 647173761, 751398303, 955235871, 108958883, 434417068, 944155853, 316718133, 886614115, 745202362, 792291001, 733477643, 7446058, 993953383, 538567717, 70290806, 243678558, 267906874, 864077462, 83154497, 394714205, 165844374, 615334811, 531501207, 537762400, 798648393, 864328576, 974191495, 277230755, 42123905, 700080911, 516313981, 546491705, 247395559, 283737045, 476859425, 434867396, 557007691, 743965086, 903013477, 585180240, 54505935, 512385391, 12096437, 132189862, 397156742, 818679204, 607691559, 397744287, 186832066, 492947316, 686267562, 769985417, 666628992, 493286612, 435362729, 930899475, 358007763, 231362768, 971399361, 48367032, 127232585, 703446172, 258282617, 501478459, 29036987, 528325790, 59757032, 415530378, 658268730, 301704759, 48875695, 738202222, 529016981, 555374710, 771829543, 470792351, 807940385, 913322472, 772266715, 280452003, 231300136, 923367228, 634080044, 729682256, 836782944, 902791147, 704913680, 2724727, 917744564, 75896877, 932960585, 762329664, 855943790, 749359946, 829884424, 973267975, 929802373, 502894385, 746204739, 762616034, 719931543, 139501594, 3508598, 194077452, 797887102, 650847794, 739668485, 773561557, 48453424, 320238308, 38641742, 706004002, 59431604, 793292229, 402612841, 983978216, 504440820, 428988800, 34530042, 61338045, 792950350, 533959037, 596669937, 289126890, 960358474, 525817876, 470883967, 387221796, 947531419, 27623637, 714666440, 196022765, 346039414, 821953864, 927642777, 483754959, 231974217, 776714170, 244213818, 718746302, 753658353, 121456546, 626878074, 158227702, 918024353, 515141399, 574210215, 830993983, 669779324, 416984784, 794107836, 139847676, 157356274, 137897627, 743433123, 571258579, 528342992, 254653867, 50038665, 709836829, 324776079, 641125554, 707510538, 789910096, 168370813, 9640651, 84873633, 250591496, 428092888, 853180283, 854174751, 792606033, 429955931, 978186716, 572039122, 730791683, 88381369, 198552003, 130064011, 823723726, 355809721, 969631350, 714721764, 101976996, 847197322, 549129392, 832928169, 757125046, 554242321, 361750320, 698346617, 707087165, 111766664, 776053079, 875650212, 24458438, 167043736, 334926090, 994425975, 259033137, 786167014, 796640385, 822140452, 999084005, 627893624, 323988209, 743306118, 383660918, 492432683, 62194765, 599577230, 427807319, 248464839, 561492110, 484357419, 98593697, 160644528, 919393575, 556292720, 151595207, 210689224, 738895005, 370115874, 902601398, 226366784, 797684452, 760255976, 503569916, 540719892, 977645524, 515842143, 79034817, 369758359, 898393350, 476387300, 557201398, 349139258, 463842733, 612062883, 134588453, 204637905, 328990067, 939580428, 204265818, 852761375, 779508802, 302921373, 629761175, 211743213, 506996192, 873326560, 327336020, 818884251, 759491823, 924540351, 357816535, 454821164, 322971460, 548071875, 391562209, 550300833, 618996816, 711657281, 608964959, 266613165, 386719253, 438123058, 745873058, 872258581, 837423442, 472028669, 420490156, 277635162, 754145203, 789522220, 306986679, 262318267, 627460309, 416615681, 625716391, 126720818, 609759490, 893411837, 148361421, 880112967, 594318063, 430066204, 97842706, 271300412, 799347767, 714681065, 415510894, 786901188, 684091592, 91686852, 364207890, 22173944, 778267045, 113100142, 265385640, 285657470, 544606864, 104605477, 749864827, 359170259, 61560595, 157434218, 706562571, 757862060, 791975396, 385788439, 617874200, 237701454, 97241811, 382713908, 215283118, 77661215, 309905954, 818040562, 856169207, 818642181, 13695630, 690947289, 235724646, 846360226, 744436899, 503659169, 771302557, 131098620, 811092125, 832918236, 322356378, 91957507, 639083687, 582152001, 971633372, 707951903, 174975575, 223790355, 194521824, 165932275, 936242326, 527843881, 531624613, 496052845, 321894569, 589808889, 702137874, 586844947, 256836499, 4431296, 334636829, 814862722, 545543062, 689377420, 646086622, 257583321, 783407090, 945226109, 325070489, 964775123, 187994594, 877814040, 677586178, 272003927, 783726505, 348234195, 836555818, 449726375, 74332256, 679628939, 249936503, 678722008, 498265505, 935148297, 930656540, 707679332, 349415504, 382296974, 93662040, 502245759, 332747488, 481146901, 230403781, 577066925, 234515980, 820735427, 692875711, 381776567, 530797133, 334667880, 466192539, 475497375, 253643847, 955389975, 749984526, 315637740, 435303172, 951719730, 667303813, 602918116, 26773178, 784932245, 974981266, 839088284, 319020465, 625697464, 165641587, 637579797, 259731244, 206858392, 498224760, 415470169, 418226468, 907410758, 317334870, 299245048, 508869043, 787663086, 63869370, 697191906, 353194633, 322935020, 758259486, 500888592, 53736544, 702029550, 505575895, 991498992, 713077, 294748376, 313824798, 182394435, 832526141, 886175506, 795288656, 33919358, 1536113, 743428555, 223938059, 151204140, 664526733, 267281399, 628457989, 850932762, 951711673, 311161317, 418033041, 250076132, 88802228, 734506898, 942972848, 119999925, 313541184, 197083928, 439345901, 508636079, 422204443, 759354959, 571801441, 964802207, 714241211, 243347197, 500876138, 599345018, 368701750, 867446919, 228119046, 567321007, 21800865, 794155346, 523529414, 992407171, 408145747, 488753379, 187536944, 681963031, 172127025, 47259481, 162811864, 765745872, 549854413, 840037097, 297791563, 102197010, 528318790, 216700014, 761934007, 330798707, 724502429, 320485279, 461894081, 31665275, 404047189, 462817069, 575748048, 569423536, 318527278, 534124406, 687442121, 498559003, 607880944, 497263964, 381026539, 431743111, 206637439, 423713759, 93531133, 294480361, 387346966, 961729230, 430813425, 475508457, 459944201, 219086159, 584271028, 413116848, 977479265, 44390779, 561653067, 562477527, 136953273, 300778506, 950814428, 547718722, 878288498, 849705115, 452392251, 714746079, 388357013, 546512155, 4308185, 561209140, 120710660, 196329951, 729581988, 185277217, 882914704, 725764092, 31863502, 774989961, 621123455, 616174306, 595488706, 276084065, 709468400, 91219478, 645938447, 961665660, 887875732, 53736202, 185414205, 707264867, 981745483, 534199859, 783152211, 722123219, 966113168, 917338093, 299505020, 168645973, 218731404, 291842333, 867391713, 238218489, 362012309, 293695441, 810087, 836294922, 625346445, 179662733, 240611409, 37150764, 397725266, 467481000, 455778930, 349283464, 952565992, 364118260, 721357493, 266570717, 653969682, 8458024, 531104869, 477823560, 993662818, 219868002, 50523918, 5896769, 457885880, 451375892, 890557078, 189364362, 78057226, 188692105, 719048825, 592609392, 497773597, 860549414, 342548008, 604640991, 132976356, 89926940, 143871210, 288226843, 526314683, 933578615, 544411763, 78532564, 599519934, 963083915, 602867376, 162454587, 331079806, 220752104, 82755218, 275941742, 771461506, 643733036, 591227862, 119391887, 544034553, 97232042, 475061417, 543258573, 661280242, 555823788, 886704581, 321196211, 244777811, 431779283, 105493793, 400155216, 481995964, 674127476, 142319802, 321527309, 121039883, 142587758, 736440365, 381830788, 844062427, 923958619, 405818852, 800584753, 708405862, 683422002, 76724584, 540444076, 496352681, 447277344, 969939796, 351846328, 594773473, 14017251, 972572884, 258234279, 401061111, 232840509, 930094485, 654045887, 141125335, 379886992, 103983915, 252169613, 309077463, 597310093, 385457974, 62026605, 256303204, 748807458, 854118732, 868015995, 14560666, 519356460, 995442051, 544731232, 987146466, 56570999, 928346086, 411803945, 502133809, 83088823, 923281503, 256298091, 784966666, 289706101, 468534414, 532382440, 810945208, 320645668, 752942066, 670817133, 532460272, 629326651, 39234795, 81861863, 429402356, 522509995, 489795846, 855597205, 756291701, 911779483, 764156081, 78888277, 319323256, 237132454, 388307167, 157211699, 437142062, 745149834, 201250390, 35264884, 62441897, 485569149, 517924258, 290885409, 878468681, 274984033, 632071341, 388543485, 260441800, 901202618, 930118765, 850012014, 329130860, 30949501, 15829433, 549327931, 514131653, 735107911, 747271001, 467062840, 827452686, 334262117, 376756766, 998143346, 330420055, 162484971, 840384451, 336851298, 880704862, 906845396, 489727670, 225330331, 379023679, 755420990, 667118872, 492640914, 999191035, 506046258, 647995516, 779255337, 252368621, 278567057, 800751232, 435856993, 73045769, 49731283, 492706057, 653382841, 284399892, 532871037, 980598617, 815636377, 815123376, 765772026, 3881078, 132597347, 629529406, 595875897, 867408225, 573177768, 166222908, 452433108, 101690736, 632788398, 447078416, 271496450, 610292092, 46249616, 494123802, 750460178, 407088100, 656146554, 791386435, 558847094, 441376771, 688628972, 770499907, 623592871, 711404104, 993286976, 257057435, 623894614, 721453658, 908664429, 443794443, 761539387, 593458722, 835720197, 114175373, 394959772, 704745424, 548247144, 986197825, 203079570, 357777316, 790069769, 409938406, 411358812, 15573506, 422793430, 436379438, 378691924, 588825915, 449208598, 75027496, 382714589, 757483852, 233737283, 218513912, 478260706, 405379787, 787787834, 358454440, 845914255, 421639124, 321445188, 808509295, 162924376, 560548544, 271256989, 928553781, 137234995, 256508461, 569283611, 316896339, 304176288, 846536423, 637204306, 956887292, 613118785, 13990015, 306905177, 47383938, 487770598, 609489526, 507148284, 738397425, 460298362, 752038562, 431196102, 393650637, 624390391, 350692573, 336690094, 709048068, 926577211, 702656829, 336187177, 532373739, 639805086, 236601807, 26320501, 121847752, 100105887, 984825857, 815697351, 396675270, 972061744, 258535709, 949675072, 875228562, 80938071, 287119657, 893286093, 106022561, 732487296, 600715263, 150815844, 596179947, 843707600, 660028295, 328801109, 138656315, 19251133, 699832428, 731734584, 29443269, 373935200, 857532765, 17696615, 492309774, 523130236, 47801796, 718831138, 437838373, 801110383, 652536840, 751611289, 333052120, 359488473, 522920469, 518125172, 112276725, 737299353, 286777475, 461338803, 769337413, 906900519, 590545062, 82367193, 592035014, 548756622, 794300593, 353697958, 114574426, 34824746, 447115564, 802921221, 504852808, 40524671, 228586886, 865528262, 39948908, 802094117, 728628791, 284839101, 72568791, 63783720, 691345016, 724700894, 913977395, 196641200, 725903267, 799520170, 231432471, 437804600, 384091301, 935960505, 850912589, 835624502, 304740254, 910507050, 703955220, 189502304, 793848241, 263297903, 998433186, 475316247, 663379873, 744284921, 554711579, 438701678, 556605565, 891849374, 821639422, 193630279, 259409854, 65304049, 811774701, 689753472, 828219249, 958876802, 616714464, 501906136, 217775135, 463109013, 460067778, 253564140, 972913561, 147002277, 794537925, 321750719, 2787430, 934940334, 995315714, 199902346, 2713605, 57954386, 732365462, 62216328, 198939032, 969123703, 129371358, 56911360, 947163824, 454727072, 491846089, 939449160, 379008765, 146280196, 342813942, 178115465, 980702795, 770739917, 247618281, 610620137, 656138990, 977750735, 289670929, 925229137, 442181787, 348636539, 620868029, 763838500, 8616548, 23358274, 458408318, 493437528, 977926339, 414863259, 194295713, 671827829, 618704486, 550865121, 573515944, 879385370, 428093864, 389531436, 594093569, 682875091, 476900817, 681082142, 798332707, 142764350, 831533823, 54519096, 661893620, 23111595, 879575171, 358876959, 60023391, 324618527, 672781689, 886241692, 808326408, 608446536, 793082107, 633803101, 753055278, 273889854, 973474223, 631530069, 77346705, 822590832, 643070786, 860768209, 811459246, 459268894, 395095137, 144083445, 422562584, 921046534, 257388028, 12030565, 392743640, 197377818, 839903726, 687266488, 835997219, 861486678, 605003672, 928063525, 676529612, 265173590, 262287619, 520712311, 871098260, 641861373, 238817087, 926106258, 735790803, 453651368, 385989123, 14008520, 283582340, 167589501, 183185764, 127699197, 713848113, 874911695, 138691906, 655909606, 527183484, 489957314, 375983975, 272978391, 427816255, 168079813, 832538004, 53399065, 191723943, 23394827, 501262716, 357989828, 776309080, 934906860, 360052157, 471275402, 564785262, 945101948, 964191046, 189833401, 726541272, 139151635, 178670686, 607595038, 298949615, 481771341, 866688509, 829120448, 295858662, 527708000, 71163738, 322357707, 640340621, 558501132, 700489235, 918885126, 350869664, 160480129, 665316900, 259634327, 93259877, 558366789, 43249828, 979301198, 172694532, 968118452, 169970716, 647107844, 561385893, 859120519, 480486763, 935997880, 885908486, 669915323, 947862863, 272566277, 151466074, 360130957, 59568278, 640270760, 234125346, 953798118, 826502569, 770658992, 244861873, 595648826, 500333967, 765541923, 245553434, 849263538, 983229686, 788066683, 501510240, 592783074, 20347338, 288260588, 162415093, 363231987, 423369108, 665017607, 424830722, 57004407, 740421380, 958613632, 442671314, 257993776, 456856411, 106673140, 395868804, 228327043, 888763108, 226662094, 295522969, 361576263, 838610957, 352323190, 195763694, 228539601, 639412874, 856539050, 1914092, 795770193, 487293468, 286595507, 622720533, 215401647, 338605100, 982941575, 122127324, 28422993, 161402635, 985913551, 377956107, 197881662, 321180355, 944258833, 763699736, 536527390, 573101770, 176168714, 691000560, 901713011, 362133204, 408846109, 392200887, 774305670, 561321286, 96153755, 102757041, 402246266, 345072562, 451577143, 448130149, 810329670, 549397224, 608970000, 697183971, 756316459, 898981184, 154953319, 978801497, 966244848, 445459787, 86999685, 196027003, 131233854, 288833433, 524196741, 585574660, 737978349, 681899177, 155623667, 547549180, 301722717, 994334457, 756011519, 706993399, 502788873, 280622209, 580532431, 189235596, 407678614, 82452951, 305781911, 181968197, 474943516, 38205735, 21283714, 819579664, 880696459, 554987291, 590193715, 549347667, 892013219, 611319507, 645846846, 577991472, 20758167, 455569219, 887762260, 479103321, 386629416, 610758538, 433168929, 714138793, 591261684, 962638864, 225946952, 693217217, 211616980, 132750895, 817391385, 71682247, 451459684, 81642807, 314324771, 658239866, 310070005, 723356460, 374341233, 276206341, 528353074, 972319982, 869313108, 864012005, 225681643, 698363605, 669176736, 705572923, 662658958, 735257394, 221714683, 373354884, 464866373, 13694167, 486711165, 597131923, 343210277, 410432763, 479055010, 248360019, 165170531, 432422509, 914108089, 806953807, 764076622, 814690983, 487236340, 220412143, 231869426, 203936595, 606388762, 26597149, 189635041, 827309397, 614248261, 719628931, 507742606, 112581939, 763863098, 602397632, 328550449, 670302235, 829689395, 936650206, 200414658, 551101720, 347102432, 984403836, 245323200, 4244490, 24425824, 502670025, 81855834, 139797631, 25163179, 756784914, 466068409, 505952592, 25089475, 760583894, 710505344, 79600435, 926630068, 737800951, 238666290, 421801493, 657628338, 112334170, 898029062, 789494174, 792647541, 297122816, 315650356, 102507108, 556527954, 236352924, 859538463, 263735349, 522080392, 933864360, 589711212, 1513705, 709908648, 479086257, 914055927, 503026856, 486225820, 218357559, 252704776, 929170602, 313870716, 393939764, 945633539, 700388799, 774245675, 420288287, 789338080, 516410782, 888500080, 707297515, 631054214, 131694431, 671883564, 86090500, 257044514, 724409224, 714764930, 34244433, 621249245, 699099862, 523640328, 235015974, 48047820, 569673305, 627775934, 385688749, 693309742, 777753389, 55091964, 781293117, 481833923, 326574973, 336438009, 128191392, 345223079, 837491548, 842767095, 274211224, 905263540, 542706656, 407401204, 401817585, 112305716, 776999, 850016164, 599803361, 381387570, 593289432, 972008700, 926262403, 967366565, 918649594, 144848697, 176384462, 554631195, 504496670, 397653645, 487581427, 310335150, 907880821, 555123472, 137537924, 715370157, 986275130, 286900007, 564205184, 290814902, 560814532, 172634867, 534955086, 858148101, 67550427, 785861069, 57067181, 425455411, 697190818, 988088541, 287448484, 256474788, 233430584, 446646420, 880281893, 562028380, 754304196, 682346388, 197906421, 186881022, 219750331, 61313310, 714704185, 918330123, 549963771, 485316747, 276790042, 819745293, 113701558, 30485336, 311520474, 592583040, 876204812, 779716866, 72277808, 644612633, 898880325, 595267733, 354799565, 380795606, 982828695, 699065825, 655492324, 533467162, 234322979, 301127157, 622828043, 485368313, 395724573, 321251085, 689656609, 190171903, 660575643, 620825667, 958894393, 457535912, 77039022, 758393976, 837287101, 816184624, 275941976, 167887912, 243281731, 238600721, 734546589, 167993238, 604794876, 212582538, 375497055, 230093926, 652983260, 184244462, 70474607, 720305604, 398313672, 479717993, 836350476, 158837925, 146703121, 294042781, 609871745, 854040052, 903194688, 232955929, 723370454, 74388020, 485635040, 879026846, 619241739, 672954602, 728102826, 706493977, 656510650, 326208025, 576241956, 784544752, 37244995, 61733380, 38059215, 134072525, 633051489, 374293360, 305475948, 324936577, 987747598, 849815120, 847180269, 592937556, 150022816, 589564535, 933286454, 825308117, 169365192, 567604981, 256337590, 194315774, 725799311, 160476568, 147153212, 131677635, 418392707, 452822883, 945778072, 150855428, 763856521, 454936656, 785203207, 877669299, 549593244, 382925952, 988679098, 987274777, 746837238, 46889174, 181271288, 773526620, 422995045, 590303664, 793598170, 63871612, 234726494, 941090483, 260756591, 882431860, 562485783, 468576187, 688472585, 791767854, 899721505, 610497882, 340848870, 40592697, 606799810, 256367847, 807808336, 611936445, 936680471, 521438525, 734794861, 31431253, 270586428, 90631505, 239665376, 844101084, 58830068, 521035360, 498747685, 289648094, 310072436, 984869059, 955506802, 589762050, 11222082, 806040546, 571758842, 615694375, 78426551, 907966767, 291840037, 403141798, 425302627, 526199131, 565822236, 994892092, 640315550, 92256621, 318414169, 326810268, 227489084, 24170652, 523315621, 971894767, 963073712, 604236857, 945831438, 491936696, 22649341, 567018357, 477761763, 800254556, 43657487, 627364179, 288261009, 369552339, 547334134, 405847698, 443955098, 975845079, 910644949, 999738685, 987765023, 593693680, 345656605, 249885851, 718460930, 332330690, 58712455, 84271882, 463709718, 993892610, 58344128, 57231459, 516854903, 100094870, 20708404, 905364508, 603330148, 92090524, 182645523, 779410714, 504442635, 84878864, 331301476, 438903424, 651975458, 921769120, 592965210, 134127188, 35171500, 583051731, 247458831, 372465525, 811292032, 486879449, 268642871, 228010225, 423192863, 314829153, 279469006, 615865110, 935861081, 526557173, 997762323, 842716709, 408226046, 676426831, 664661724, 296323437, 218655061, 254983360, 439694851, 573884253, 944662124, 166128772, 549713408, 480414792, 832635300, 48691139, 160974928, 959143297, 302209319, 888638166, 44761464, 556930727, 409458811, 533194838, 600746939, 955946677, 684845108, 520048837, 843993864, 532734759, 952634567, 44555795, 198002898, 835327312, 491594463, 725018745, 700163652, 554279876, 642550874, 926034376, 760170055, 289562261, 833176140, 110740752, 288140854, 165626202, 9289607, 579972425, 412479310, 959907525, 564649145, 268551318, 61057998, 141715369, 952342109, 646061793, 628117854, 926325658, 803833908, 361704332, 88517126, 126114305, 473335083, 450146379, 838148237, 998993970, 322171808, 558766985, 839333484, 556165876, 682747431, 501740220, 167364522, 161662866, 807870614, 578281109, 631161690, 207675982, 180379234, 109864333, 552507299, 675626416, 693517171, 223696696, 711284524, 262848298, 472146029, 216083248, 283104828, 333290796, 506693663, 502573229, 866823341, 172459806, 520566740, 778539693, 30556395, 34039073, 107145829, 832739325, 38609259, 86638367, 615468907, 187353513, 150358261, 879457890, 878055266, 231425417, 236001389, 251809669, 193225940, 741109702, 968820513, 348086364, 793882596, 773849528, 846534549, 268718985, 714455157, 768789426, 813993609, 411042173, 508493618, 264763893, 368894515, 361483719, 336647588, 652985450, 828763725, 662582359, 405383289, 318474922, 447893897, 132693730, 902114365, 678690192, 727717873, 255916570, 71468668, 275731176, 262160671, 443161835, 831086388, 573164950, 884537970, 112200609, 309308491, 65241415, 330018152, 217175387, 972378697, 880394309, 957243120, 25107699, 388299639, 820751953, 768174286, 140397521, 488896480, 218914087, 397631083, 270631267, 794729702, 145948869, 465285547, 551523090, 982887847, 589948247, 382453617, 957620179, 553790003, 441943002, 851982963, 170791995, 225472834, 475858018, 877824558, 927597438, 451448885, 356236765, 265347796, 810674087, 650323955, 505747681, 180450287, 346794061, 788216729, 160686243, 7821874, 512947667, 134783075, 141906604, 524828532, 625173937, 870716924, 646358630, 493990322, 537388983, 545738540, 993863330, 900758379, 104415708, 732821808, 840736687, 950828962, 779849936, 956752550, 823162823, 260636775, 666282231, 86843532, 126274048, 234173332, 749723202, 238990309, 780482801, 500625853, 895729117, 481046274, 77522751, 213475276, 259158350, 975262143, 645774731, 892883642, 522845233, 142714201, 76757466, 24411623, 845164028, 998931629, 878603870, 207607529, 111257186, 55433525, 498744626, 364110299, 992352192, 269095361, 525708017, 994710669, 180249306, 206993647, 169537568, 242991097, 193578484, 47271512, 707227707, 919703096, 271432081, 979637061, 354280569, 270343681, 656109288, 306448422, 986744492, 324953277, 562201763, 22775593, 582277232, 611253657, 166357338, 205478699, 767400141, 809326826, 13775249, 776889404, 326686326, 14842531, 335714795, 266716807, 902750502, 745100502, 800395177, 812409800, 478672650, 858663413, 528994190, 604799373, 269125018, 968839532, 460123048, 72132466, 53097923, 938299418, 875128210, 764174644, 100802885, 630440846, 340717739, 836288965, 730049803, 865514538, 716914426, 628086476, 12218730, 896028834, 830270021, 677110897, 7098560, 240533530, 473148815, 394951021, 664871971, 118631514, 562075830, 552082758, 482129164, 616723564, 448377723, 444451146, 491441322, 303364229, 222123739, 569242225, 509330421, 732685053, 959386616, 176428822, 191857051, 877669241, 949569444, 576961367, 782499806, 303455234, 329517163, 666115777, 703752166, 167850779, 546234409, 430083258, 535912403, 389080361, 480481518, 534666766, 783025895, 123112682, 256142311, 650495100, 52247528, 386150532, 510329020, 415780572, 526325057, 11781619, 937789478, 323836794, 904472570, 333301189, 964975980, 620137920, 37166623, 998517909, 447065808, 720687016, 234242199, 782223397, 569385603, 281305807, 32304091, 923393008, 175969639, 8576178, 25202485, 100970879, 250840004, 675265108, 880276161, 311317036, 642139991, 927204243, 988448651, 195684632, 688085568, 296298235, 566673866, 968284960, 247652740, 674619360, 453608866, 648379077, 544165036, 791398624, 466052213, 268100038, 335414449, 337580132, 70784262, 48830311, 560015846, 746981429, 526224727, 423493341, 220583294, 761386649, 550463151, 75914680, 442242097, 386253715, 570889290, 340675381, 717246461, 983887228, 490469122, 425580099, 856133520, 354507509, 231049324, 581093435, 382405806, 556775086, 599038676, 74823779, 845984783, 446773587, 313337412, 319415274, 19160793, 896806928, 101445336, 442865585, 920886401, 665520583, 469057707, 234334774, 412593438, 916083904, 142213148, 230192244, 602124462, 928633194, 493909407, 680944358, 194855299, 110667462, 970146320, 48742501, 469769385, 810678105, 545716600, 700952752, 136465395, 359434938, 857402735, 160883827, 857954026, 199894403, 730249158, 258083303, 770561357, 650315886, 981196308, 559117032, 832921920, 247944460, 250067469, 412095869, 418078655, 934874120, 202726443, 502387751, 947609353, 443008450, 321090002, 622299814, 329368499, 516634897, 777331917, 613915987, 261671091, 711290952, 217420062, 749083229, 971231760, 326595779, 118113382, 775179371, 212889574, 508697239, 340748054, 902157636, 502923046, 971826363, 782699391, 646435400, 634345114, 794397998, 86040789, 451771866, 245197217, 794592465, 436986260, 204779661, 418870116, 776978499, 516955997, 964818172, 671512480, 880941123, 464898026, 264207201, 447437738, 768113780, 742984054, 847554853, 394669964, 41031357, 308083884, 326832566, 526591262, 143593931, 57247961, 488404936, 652431925, 405122380, 311024911, 327145336, 266190454, 149072153, 522839642, 778657277, 780706233, 246016181, 595189007, 743690445, 271082925, 285974535, 609654395, 583642304, 376553089, 840876374, 121932696, 584889388, 714379974, 23223026, 379177813, 279876595, 708143085, 593807364, 619725692, 195434635, 554986288, 450774798, 43259794, 25242776, 365529582, 217188776, 112754330, 620533333, 474858096, 7530009, 497048206, 217263856, 997523279, 89688916, 335117716, 861404759, 748785272, 205212689, 24478502, 736727903, 816888167, 78264014, 806226582, 674272406, 525776015, 891417080, 985416706, 239715887, 831593233, 430520759, 741505772, 590865654, 289829002, 963448285, 349964118, 705849844, 958961539, 992807511, 364288968, 840515442, 894619814, 449427816, 111746953, 387637219, 364376041, 141568159, 198411823, 635007834, 918561613, 122682433, 27536590, 764590568, 522638892, 90579953, 184258977, 530425046, 228480660, 152003529, 459640131, 453006834, 900409603, 576348840, 228032547, 735738363, 254647461, 21452432, 355741070, 615518290, 984114663, 82522, 58517572, 307721735, 616420045, 400602264, 95087227, 759454962, 750807406, 980383419, 672513591, 285571451, 823356591, 437194728, 265558333, 876707969, 850583001, 260448181, 170613680, 123867547, 620958803, 77019401, 506841741, 993055544, 303840766, 360582501, 396184310, 686363011, 783564943, 371811417, 532456486, 700109589, 715490468, 227851873, 847042516, 96399898, 928665541, 626345208, 572062567, 926745853, 719945023, 510470354, 474212620, 299120520, 66846332, 137142142, 476639659, 562815726, 270016988, 90318433, 782778192, 165038524, 53607529, 103476318, 20496071, 346951801, 216480005, 422335537, 474626656, 336119301, 346427624, 831793628, 743040790, 309960424, 827751734, 476392094, 214564905, 817096154, 187364488, 349812019, 536706515, 679318138, 6328307, 103855284, 351122748, 590772233, 803657738, 774687405, 431245023, 468487186, 158754142, 608359661, 952593912, 311849635, 433052078, 388777720, 289247133, 6104540, 149032717, 100428234, 216918048, 557141595, 850245183, 774479916, 266806469, 61916988, 183699574, 809942320, 410105791, 18298030, 506670547, 502103719, 672008386, 391757747, 460706905, 598178639, 53165362, 786843879, 312122626, 880339363, 752504103, 615934710, 838554030, 575746294, 244485519, 322268257, 100092753, 58470808, 304141770, 613142199, 73738765, 331715094, 10982270, 733718049, 366732648, 814228966, 97753082, 610426119, 538302182, 903739981, 732120714, 648444129, 672668140, 533728554, 345842807, 965249161, 827181471, 444343847, 549855972, 946136128, 872421802, 601448430, 226548254, 395524977, 765656306, 776144217, 645272186, 913604657, 188994996, 84213902, 46446078, 706448535, 569819843, 680762774, 629549255, 276772268, 720419407, 41099884, 337928968, 86658166, 838097798, 285465888, 30075181, 239111274, 581940680, 828113164, 254464396, 800791137, 881919069, 150471676, 470332473, 940254132, 657469433, 503451942, 654484828, 967216930, 310109319, 295926697, 689965585, 813152262, 97844558, 249274186, 618824278, 877340454, 893252767, 216815498, 230511972, 520956630, 242346356, 978197349, 915975112, 614392947, 534916814, 798648523, 986738573, 212570102, 181314541, 335857995, 370800724, 469999314, 823908435, 805954193, 491263032, 707174372, 133850737, 530279948, 853543942, 802304632, 345898431, 781187412, 326643197, 372145540, 354337284, 418841488, 292335266, 642466879, 948075934, 312608483, 709631919, 699980051, 971113882, 875477587, 112954025, 16386722, 352471815, 315229234, 458756290, 655986716, 961194631, 639958202, 403763158, 293769023, 189783585, 878743638, 252613053, 262424014, 660609680, 532463397, 407635358, 998568283, 122279600, 210173036, 459022372, 756199688, 707261372, 374790837, 827979082, 436000930, 628388493, 966793295, 642104900, 430969463, 635687968, 583749522, 85917971, 181153796, 706265896, 505305888, 16153547, 703371646, 392759049, 686021174, 675112488, 682858241, 266276140, 508637091, 708286459, 349343823, 247334987, 79924995, 491656205, 73862375, 935390669, 186161033, 679670882, 601711775, 923955685, 36499879, 123943693, 340545844, 225033074, 737136188, 570331970, 968049597, 550007557, 456301404, 259108048, 660700164, 49103072, 285427052, 675860551, 828311615, 699127377, 780287782, 169125541, 151455886, 207385800, 680170762, 985808767, 909091773, 763260867, 824936337, 558431006, 224412988, 718090691, 527960883, 622609781, 319433640, 536629915, 322789618, 227642622, 947942787, 216284474, 511885190, 138204710, 993802903, 80821766, 568589658, 477165193, 144418440, 822005490, 743951122, 536318285, 414532654, 261538445, 896669310, 13972087, 682226765, 610171656, 276708447, 270704896, 618097806, 828526990, 768813457, 160897299, 36656276, 713133370, 389360394, 545555610, 558516398, 770777901, 548844713, 232230386, 946003960, 918067337, 719748229, 205372719, 439473842, 280947186, 289746080, 317954056, 264786629, 257112407, 547632585, 85936506, 627468453, 729177680, 333003033, 751982455, 360622541, 609408581, 70885307, 259624907, 600021647, 545979676, 905748402, 114645856, 55578889, 495410219, 738865062, 214663840, 508285307, 612771957, 358357864, 488479826, 425040303, 801378454, 505246366, 206282747, 262563098, 996320048, 415978844, 801980651, 808179951, 273527594, 275925514, 156209125, 751607188, 259266181, 806984029, 86657466, 766807001, 648667847, 49462220, 224452665, 963198528, 956987583, 918970307, 761265791, 937447813, 230306860, 522649014, 670186797, 298980451, 80865912, 399546730, 390004724, 859326683, 414883368, 737982690, 377820252, 954661958, 532242157, 981785544, 376419143, 337417845, 590347442, 379612834, 132336761, 178441898, 350448778, 652728283, 753994179, 96134432, 993504401, 325012010, 792668555, 934486022, 360384145, 182638983, 544454226, 422355027, 459568189, 811456562, 12521821, 160607725, 670907189, 383665999, 843941310, 632547053, 806618933, 875364013, 916733555, 802922832, 608893655, 751215118, 440837697, 28482231, 568565513, 938672483, 494289990, 322191217, 519695727, 806320420, 975068414, 387774009, 87609343, 776709566, 570999878, 819414563, 677273499, 930074998, 660815042, 188805153, 664560737, 668957856, 276264166, 16956338, 615246743, 983447371, 361749734, 764480667, 9047948, 504084697, 71333366, 48395094, 745394398, 31245684, 213616087, 366640357, 827550774, 290511199, 293514322, 150223238, 185874566, 475111553, 89308617, 318319823, 645712698, 379491904, 409608043, 474097832, 409830587, 142696266, 756673647, 731277695, 742230061, 233978069, 154540828, 854092119, 915914172, 455382433, 528341256, 531836018, 859363075, 603636678, 915940927, 614192217, 91753758, 22452286, 873034723, 657603011, 657770208, 287563222, 219475156, 865792061, 167369106, 542069349, 651560740, 55397784, 560493650, 241126973, 753675540, 541245098, 18286768, 254001745, 422409150, 774129887, 951842274, 547642819, 51923867, 44373254, 388822051, 737389579, 705821269, 573274296, 512819675, 905689811, 614787508, 772956363, 447314879, 916803287, 216093279, 302993973, 172254407, 300113199, 434891406, 489101419, 864044907, 464840454, 265430844, 689512196, 985563703, 617555671, 825288356, 319176016, 295850388, 843789704, 69003257, 465352748, 488323653, 50322412, 498549918, 168049251, 974501609, 613708562, 586476162, 150898919, 225290806, 696598343, 228489613, 960267793, 353461955, 869186457, 701717613, 524924173, 855252039, 670988641, 538610961, 221016523, 293181521, 697100844, 486742225, 853944925, 211320316, 794979977, 13352114, 471468290, 100056139, 2586161, 745920126, 950870531, 12721536, 573362973, 145599234, 956722851, 351024746, 57845230, 477258475, 797939525, 392849884, 455980570, 602377926, 212283890, 317405244, 392792419, 118491732, 755060640, 766810338, 48350276, 525812121, 961916469, 976785880, 343273193, 135081306, 30242749, 316316199, 605634712, 643934328, 47296599, 823398907, 118654412, 829854396, 769836640, 547178246, 800995045, 955448384, 143274009, 957420609, 917400708, 980283578, 888754054, 391356030, 565329928, 314103169, 892235248, 92243777, 650088440, 135272809, 849085281, 427197491, 209693046, 199782226, 704689212, 613816665, 800466329, 198158027, 70214663, 274004597, 749099196, 149981041, 403133003, 526552921, 494137728, 877232664, 803816619, 411304621, 690348029, 53316177, 211833997, 212940458, 777990262, 537011125, 305192833, 485372905, 534763784, 543201060, 998942751, 348117333, 914870950, 88739121, 337671689, 21433246, 612471057, 250909624, 508894713, 995252932, 838296213, 838366998, 898226766, 499222702, 231456296, 938054290, 208047179, 414084404, 484666451, 576850887, 149069183, 791335826, 266912590, 444792901, 905434088, 840323898, 296523444, 295428191, 93154377, 573164581, 927935046, 610774074, 543591526, 213563591, 459301351, 702953202, 431601383, 111207241, 181387529, 347988104, 534243548, 5354467, 292160032, 927959900, 307305974, 839188204, 275223492, 161432321, 349104754, 239858011, 752655392, 870540446, 835998679, 817745953, 281525525, 491589525, 357940538, 476327294, 431784324, 841299235, 265391587, 883818790, 445846521, 178178839, 453722579, 544211569, 555366461, 257294174, 204095754, 885884891, 547345927, 901692575, 625577154, 312658282, 391764493, 789401057, 345041665, 705045075, 105410753, 405942272, 794861003, 255388321, 134036977, 914257237, 148820582, 603737238, 430275819, 699293089, 786602576, 759545698, 61228414, 825995336, 939264493, 178677633, 999868878, 542161453, 574107750, 972602852, 625619653, 524388966, 39631503, 107564197, 669767834, 376162164, 765043012, 216756423, 615739315, 420716186, 341741610, 922313047, 350448843, 38370783, 896705681, 456803343, 638569313, 847698649, 356176240, 781728321, 66704100, 755342669, 710081290, 435043673, 462027821, 846743667, 3339741, 399065532, 603666240, 38542752, 668231654, 492873043, 290581469, 752183103, 693443216, 374678477, 283285495, 547237778, 464733478, 776423433, 212555202, 144202395, 841128257, 355260972, 183905340, 73919930, 782835652, 129871720, 628026145, 862448358, 823805244, 146754036, 380899191, 683895945, 10069154, 533163009, 905554048, 859046224, 287361601, 266853515, 340723797, 650029656, 17554220, 219509430, 122229147, 494728443, 369022323, 536038241, 310223772, 389773503, 395041190, 912807471, 853828484, 640375996, 247651588, 117773224, 533974916, 703794466, 103336901, 679112786, 35550723, 790616760, 723011636, 400206378, 131832738, 663312742, 966474184, 16680373, 733488245, 659948752, 290489772, 572902631, 613445916, 93318183, 179174333, 266287500, 907634602, 448122658, 328732879, 135739347, 627924652, 741380166, 780070004, 418658331, 846242090, 542375044, 156503989, 972525994, 334938183, 404507604, 44930178, 939369407, 51261036, 30170848, 238172681, 370606511, 19061249, 876768943, 276501771, 416539152, 369475776, 952572050, 996073121, 229578923, 365961911, 1320576, 22080528, 910965437, 320214608, 727577599, 286769351, 502346480, 713877764, 107548067, 666695895, 336563734, 961291363, 151068310, 734383012, 697309471, 345239228, 244971342, 293100911, 909780182, 634112728, 440505858, 250749045, 557805876, 193928323, 498322527, 18992159, 490385797, 745100533, 632536537, 790193783, 43386364, 17561047, 418659516, 33470700, 517769252, 317260444, 694640462, 183894491, 456442062, 940401021, 616770354, 699105316, 406134985, 225774244, 698312794, 552154479, 322582870, 558699527, 109026379, 400243352, 702729765, 781642843, 962121777, 25468880, 434666919, 471476848, 589167259, 888071790, 34261047, 683290279, 838947080, 219398942, 576828180, 154178846, 534468697, 639143507, 387094955, 70406489, 816286371, 814834912, 709201964, 265245171, 922421, 126343060, 683285466, 610111967, 655433959, 399354391, 569370776, 241618874, 42535340, 935790159, 650528370, 714363150, 57066884, 591040340, 580818800, 538545577, 262206536, 605453590, 643493718, 654830164, 19478970, 389130995, 251159615, 662399790, 879118976, 428240094, 321041174, 310896385, 206811525, 945231143, 53524909, 663411590, 247052069, 706226736, 712320885, 34983179, 221369522, 792813240, 568656908, 421074854, 444689461, 765527445, 389902794, 427784669, 592566637, 773556756, 386512950, 887362454, 590346653, 472315874, 709021691, 756941944, 294718633, 30493092, 62165410, 762913795, 276433675, 583920474, 827560546, 817702707, 829600217, 811551786, 381596795, 363649969, 662914198, 782193524, 239718949, 29806828, 525080961, 441889048, 467512538, 576512340, 587221946, 331173451, 883757535, 899709103, 698940216, 621203549, 804742482, 681882545, 46645434, 876568638, 323332559, 876133647, 222299329, 272686877, 273261744, 848963917, 287976647, 182172261, 314691309, 547280886, 4317508, 190143683, 942138565, 823994071, 257352277, 668642390, 812832826, 585864366, 217029662, 607351652, 116832619, 485665099, 18687930, 706002932, 389249205, 360878514, 723949677, 682876432, 884303953, 690623295, 156699304, 738297030, 1250068, 891415859, 924435702, 208853003, 809541047, 152757324, 937972060, 859444353, 570481094, 245675521, 138258467, 781467454, 390365679, 803707992, 641205283, 581547760, 47915716, 50724223, 503485779, 941805618, 326290820, 214662760, 885122723, 679563810, 575021239, 764499499, 725979996, 140485963, 940672077, 491528620, 260404542, 697198199, 892578553, 420533564, 220024589, 451737177, 538892218, 60952122, 76650908, 428774225, 928258914, 647519384, 339933078, 48952926, 457881264, 435320770, 198199903, 584269475, 614413327, 357344551, 591664083, 733686543, 72111645, 229942943, 686291947, 826605903, 508414217, 570341267, 887925305, 619382268, 50551943, 973078686, 92740296, 407872340, 450437684, 454038807, 967439778, 515364010, 540351945, 508782010, 96846427, 751721702, 263025311, 273792762, 114468300, 735419469, 24596851, 534182221, 904973315, 563296552, 792766126, 934318094, 217637847, 592083803, 43108063, 225865973, 561956810, 226940060, 728266919, 25087093, 409761960, 358412323, 626545953, 851198314, 160658981, 372936209, 944761820, 649878102, 66876637, 761146379, 417260465, 857928605, 127684088, 283786345, 840936990, 462979781, 12484803, 98964938, 38416137, 645214064, 62751860, 510344763, 405574091, 78284879, 634418424, 33864716, 561426654, 639157185, 648443381, 15150141, 156194253, 473084924, 557155018, 86180455, 99762950, 933084767, 615056162, 455834208, 365891147, 485608298, 621793826, 567283146, 812963598, 682451139, 77724417, 702742577, 637571291, 820404870, 649541302, 815430919, 944835222, 708678012, 585381090, 390658952, 560278280, 882832104, 976146636, 348247997, 921827493, 979410437, 421292868, 734080516, 888154606, 75733900, 37745440, 823323054, 650018287, 341351200, 280907226, 33202500, 739854614, 665721648, 507453195, 779215840, 463134011, 193072118, 450992240, 435889273, 493358563, 488085242, 681688018, 899107993, 569847853, 878003748, 983589666, 994462134, 33129586, 276718110, 348811846, 67918308, 742762980, 820050111, 791129428, 392266666, 44884295, 834625500, 258919492, 694906402, 266141775, 843297604, 54611289, 319991442, 911022683, 409484309, 887659202, 628670431, 388003037, 728501438, 439733470, 42492463, 8253714, 321356461, 943916314, 142069949, 795056434, 946512147, 885644842, 514413468, 592895612, 332839315, 672691818, 210545083, 320839981, 344583383, 808931741, 562302789, 926597642, 596821090, 526079238, 782096075, 311796297, 394822418, 338181886, 200880899, 330315453, 651564196, 637360802, 545140341, 843493370, 522785351, 500127416, 674532624, 933400792, 361152467, 860416160, 310723021, 956212109, 932801018, 435769990, 183321185, 946895819, 365343588, 625348376, 958485067, 499349837, 342636497, 727671584, 251478219, 250437110, 129476954, 258767153, 136743688, 306622559, 176945778, 401285135, 904180964, 864768752, 960192773, 430676857, 42935092, 361508426, 684520150, 594704484, 677071154, 214618031, 423803823, 387105008, 375062239, 153871536, 427171596, 331623557, 872635671, 395040754, 523399713, 30334035, 972169447, 445148270, 455018061, 536497217, 92960676, 569862988, 286771649, 385102002, 587741733, 199049934, 64007661, 299382606, 305424208, 52951738, 178994186, 405511013, 937284465, 515929296, 988286099, 948444241, 597834206, 929262202, 837059581, 204393329, 257354569, 702866027, 601503493, 148268846, 862621283, 642676369, 644000786, 182354439, 194862983, 51563691, 854087124, 730036708, 685168394, 131799626, 584277757, 120207986, 914729522, 961759383, 212553818, 972007396, 361781507, 72012988, 637589063, 264864566, 910207551, 740034856, 379915976, 558215648, 927971820, 11790013, 532819841, 795224458, 920990829, 490772026, 527308808, 166429191, 891256445, 693246703, 928833258, 904947989, 294898545, 863369861, 211562076, 543512571, 779332092, 597476484, 274405997, 957909645, 232773342, 300786668, 187976795, 660176453, 672938689, 55562907, 871378265, 557074678, 14143248, 880030257, 884941348, 31067102, 773074876, 342437745, 573694174, 807893407, 794394180, 525304821, 533255925, 609551092, 468910260, 316145380, 974506884, 411232277, 1251539, 700497712, 361529715, 226754131, 474538722, 551757793, 598009038, 662609711, 722373009, 180678386, 512041255, 663217833, 452072145, 358512028, 485503184, 344815393, 168721583, 587286277, 380156174, 139865175, 823017810, 694394302, 565245597, 311631042, 61800035, 744707753, 312823793, 498480840, 717052816, 915037100, 874721595, 939145274, 247759290, 689296905, 393536527, 978495770, 595959167, 771767067, 289900219, 98125761, 101308101, 324307836, 228878992, 113762752, 353318816, 997030954, 848991553, 141655712, 195956771, 154755058, 643222133, 357882533, 59718084, 740954614, 386306358, 477836493, 228714168, 80246608, 971451647, 314819421, 703537329, 792064721, 682790371, 526739266, 447138653, 478656512, 252489782, 285689625, 230014834, 774396933, 846907046, 609588120, 11315996, 639419869, 991935000, 308424520, 966316754, 503316183, 694989988, 616056174, 90903959, 259830800, 848330473, 271216624, 541088658, 606963158, 301639817, 728308536, 837543889, 968254228, 928521009, 199662322, 400960449, 588871718, 39678326, 882878334, 391413217, 46277566, 283789051, 941825212, 534017353, 141829946, 832035191, 49655251, 227651593, 883414567, 167567409, 395540548, 339814369, 323722107, 758572172, 718337688, 159492014, 703193159, 676588890, 575287209, 884852479, 725941388, 694526407, 634349884, 561821613, 236945380, 486661906, 627973873, 109016505, 175052966, 264421393, 278764207, 642299541, 941632181, 488860061, 413443364, 550743403, 669439776, 717122416, 239491263, 776568821, 535273674, 811845975, 22821476, 961512115, 120920949, 463052769, 697632159, 80949047, 215415473, 624294376, 179417940, 897076440, 782775337, 585565553, 553170743, 715581582, 188352273, 617140555, 366028868, 772714489, 346750557, 594455576, 837383012, 50433372, 514818807, 279319195, 765790146, 968471643, 635329811, 649544613, 104237393, 483525576, 694838665, 288547917, 414667615, 276742693, 895968378, 772358149, 649588088, 126731261, 851559939, 829731227, 987360043, 892775845, 348960284, 430038672, 659123119, 328746563, 785734067, 88034279, 676020428, 707011370, 911832474, 365637538, 125559027, 928095924, 334759554, 166657374, 219357163, 298969312, 418975495, 384919175, 722125989, 328539960, 626887756, 997281479, 170142243, 27111801, 319512436, 639823319, 291290146, 226603302, 672074218, 190239378, 101344868, 829178081, 114949931, 904034108, 884476290, 16785937, 71946054, 878666257, 463627996, 499726051, 880879306, 941420759, 862778292, 247306878, 297350867, 587545142, 713914745, 226249450, 214367229, 947100113, 280992869, 188336438, 709833439, 690747878, 952609782, 969725785, 789729728, 360160503, 653585707, 187656006, 687149934, 503199319, 63776926, 62633967, 950835999, 256685259, 643231158, 185559850, 926129496, 706925278, 416309224, 598265188, 638659946, 537982115, 398587789, 926851250, 57306456, 763197156, 417392705, 14987150, 957874853, 750027335, 485637366, 569999398, 77341631, 730722508, 881420814, 397843127, 975427547, 891924329, 534758430, 573551102, 642445912, 567866526, 244365529, 718714984, 559845759, 811269666, 346320614, 119657110, 764973769, 477638371, 415268719, 483573578, 576305602, 407509978, 455026519, 701064265, 820395837, 686899063, 740594641, 46758887, 20807271, 247156228, 1639035, 280287658, 108904456, 169483375, 868197611, 825451098, 440224799, 867748626, 625071217, 315962794, 732060826, 284104146, 809051040, 501331030, 535015461, 607597496, 132927624, 918386404, 815867145, 447649453, 278787674, 983379712, 53675949, 788533216, 853815779, 128979082, 143203131, 480846484, 637134618, 689921701, 699652369, 513257981, 904086312, 558245387, 988916772, 323304205, 951229642, 388912142, 917864066, 972425391, 944863432, 94514806, 128447629, 134036142, 842526138, 825853011, 578956628, 172452788, 987657386, 824303107, 134333427, 609759868, 215162120, 306156584, 763978113, 413075802, 167731330, 6554907, 287430546, 279869285, 560242657, 638915805, 152380950, 42310483, 579138006, 520422451, 251362726, 886764734, 637749842, 12695566, 379873064, 706160624, 167356026, 35891447, 349376985, 742699157, 189227437, 585418831, 511699189, 777863967, 957012493, 187503573, 668383734, 906582224, 868857303, 820362841, 216239104, 309658259, 535319859, 377693427, 852644473, 771676028, 492532301, 366787390, 542005293, 799921010, 801866901, 275728521, 985273175, 276038556, 943951200, 186424614, 519190152, 476873003, 921438388, 463361882, 477824874, 298831505, 298639965, 531121472, 655746136, 647624758, 996463232, 869755159, 883062975, 787911659, 59412519, 511290402, 150796465, 48069088, 624920798, 319960631, 615158949, 128978619, 218586135, 224668010, 105168437, 643751558, 538340754, 855865420, 306235485, 821064712, 367231762, 223655433, 311185907, 796036889, 638870338, 437335448, 20443252, 931549196, 393524148, 387293957, 67436842, 717736727, 637555000, 165014639, 150144543, 796724353, 812581166, 493763640, 209608831, 719193062, 188016721, 812071153, 606134303, 188196661, 993666009, 212867158, 874553293, 278251370, 132428655, 494041470, 132685523, 622296401, 323960595, 12508131, 424310815, 442222223, 143290784, 835836745, 513411871, 423475567, 152927304, 6645132, 171255831, 561943243, 788563672, 245243085, 952266858, 646762793, 405173264, 680605906, 564817846, 840956239, 241690667, 525065430, 196227261, 100990347, 688026871, 755427020, 51064716, 545824713, 662903581, 146312710, 900865362, 801337802, 222378159, 75184163, 863056726, 899617979, 364609486, 867855199, 390796645, 517637640, 471364007, 262771004, 21122736, 667740600, 572728928, 361633423, 630712105, 206233012, 270283291, 624785604, 466217244, 75103129, 36698423, 388472198, 325655621, 887392501, 647313804, 964378297, 605303810, 280405133, 901530235, 611100384, 280638630, 804834772, 74799674, 527294827, 508577277, 479527131, 232993254, 292996419, 967943856, 783212040, 444675469, 293409185, 874518525, 409826147, 305985986, 366635208, 576993562, 274947439, 771013901, 372194191, 117171792, 485474145, 521295270, 867060001, 878108285, 626293797, 197531600, 180313193, 393983276, 337894690, 422982818, 377253497, 282226986, 946951422, 718592272, 644744295, 439624935, 511759914, 634943911, 696789436, 69862799, 554063714, 532325427, 636910158, 461973441, 400554951, 495574664, 869545705, 593083453, 169506115, 264566871, 233121821, 827376286, 61602680, 200472246, 709102252, 212072444, 218245395, 126963801, 118371083, 973163490, 12996486, 869539650, 625746862, 787060843, 892548754, 389672303, 530278855, 552981904, 215770411, 973414826, 915093589, 325945679, 571846609, 290001251, 725570207, 111845840, 272218803, 363136846, 824683015, 465186493, 668877344, 754952791, 617374512, 393805806, 585257506, 51066155, 928759653, 237775405, 734712927, 477635008, 694939143, 25807830, 300727038, 390661158, 747178403, 597501511, 131966034, 308140446, 53759182, 615702849, 466399964, 105220705, 275739790, 110856603, 913263959, 329080309, 14336452, 293300587, 503268043, 506830955, 352735590, 98826333, 754981797, 322238379, 285763801, 84464514, 263394950, 57533259, 823297989, 272438494, 170636198, 891837338, 68800180, 300724989, 825183747, 617538813, 996065304, 725156903, 345400332, 635659774, 247518861, 844715645, 946380866, 740326694, 693940367, 632567875, 308335904, 398740010, 211887258, 176909797, 329059051, 982277645, 928490288, 851201265, 420883893, 288535974, 425643580, 729808414, 560438781, 687530129, 788882998, 990926445, 460014678, 867543982, 148091434, 750359641, 789455718, 454075543, 176169268, 702796166, 873354979, 794932986, 553828678, 811030088, 248413863, 931645242, 808282586, 476758777, 462614437, 410895272, 239534572, 618664626, 737634637, 695464798, 607894668, 261001870, 658195361, 797014468, 543639769, 538592662, 720922841, 372234633, 275079780, 819479925, 66208594, 390973241, 295311732, 84317603, 191137787, 912422429, 621260866, 610316236, 241382597, 829293692, 359343691, 326033832, 975701434, 722806606, 364716675, 482167325, 718863606, 122970179, 199483252, 790067226, 918806122, 623424599, 453338979, 222831766, 536212010, 154119678, 350567692, 7776104, 89723904, 432307604, 569043900, 612914870, 51599330, 696827794, 999887907, 267735570, 845923568, 840924878, 747859752, 707882392, 222946278, 667340517, 487566772, 570474618, 62111613, 715397185, 249512448, 458813954, 35283099, 350467187, 432990373, 590815901, 435732492, 386342994, 23211303, 916827192, 282954594, 445536812, 439553433, 730442806, 454858738, 98727130, 359508173, 22151291, 800081521, 127339953, 154570469, 846664719, 74497277, 883781260, 865392028, 766033015, 499221304, 414215704, 708244041, 342833504, 276146191, 984396177, 607717088, 605703829, 273130953, 955971419, 104003905, 444525376, 11415758, 960408004, 73844571, 548578848, 769185403, 170455368, 713315014, 445583043, 451301052, 56877627, 980606706, 987072057, 475664761, 188729199, 971955252, 566995555, 752354460, 260700341, 111489016, 641760555, 811263666, 39455740, 335503320, 91762370, 542985557, 668934673, 557074339, 790402199, 982678954, 258198593, 873816420, 917071128, 645861089, 798487014, 291445509, 390684108, 382656844, 502616807, 839953098, 973333235, 118454866, 493379195, 39312541, 864109591, 513330421, 562477963, 751092839, 638498548, 232654174, 65518738, 783794514, 321948839, 63248452, 781385712, 831569886, 553879199, 313779162, 565577341, 430098410, 373555899, 676479659, 171294953, 732586798, 283944672, 501016697, 174593991, 220792149, 749869370, 246506993, 368827559, 511332637, 469076277, 344414334, 378842904, 736484586, 123216471, 594966937, 620845352, 689308914, 732818616, 4460741, 835263887, 164071927, 254413260, 692590788, 406393360, 415402856, 128756771, 710532238, 479601078, 549347722, 517410627, 82352607, 766365578, 420409412, 855197055, 479302217, 14044981, 377812092, 719373984, 423336270, 501267127, 932876138, 827583480, 15086506, 922647018, 345679889, 337068482, 145650810, 942378664, 657235330, 517443428, 844447443, 111753442, 643236629, 33349438, 839890518, 172560433, 161392415, 188534205, 940525600, 442912888, 874708998, 466549944, 570289568, 237657943, 842240712, 873734530, 617812738, 621626103, 554133610, 148499750, 138195313, 666945952, 291397663, 962781513, 204501822, 558075871, 515418826, 652731759, 418528908, 126982760, 107682146, 624781582, 25107442, 114932525, 632449893, 405226090, 133183869, 952064691, 679351089, 527121541, 296381500, 54804879, 936534362, 484206631, 108010579, 178740000, 884351854, 869449891, 355103671, 840596087, 774819542, 944613529, 589804267, 408831954, 467374074, 749310651, 894764432, 239925620, 460376738, 117546673, 783461520, 3063410, 145464989, 289462602, 409270598, 152397852, 923177361, 342327913, 55263857, 147100617, 589818097, 150910203, 841701646, 467371805, 702151957, 817478511, 903032826, 126425764, 838758929, 769882648, 677459317, 542140592, 61234809, 544511095, 968574281, 608602830, 147250868, 100374233, 170993948, 592995949, 991387080, 702110918, 173365161, 430302422, 928272902, 224617394, 473233120, 202172745, 538568411, 505852722, 484822353, 234123421, 729378722, 71191425, 313183828, 939113946, 239167831, 410605901, 590046322, 518580553, 771731511, 759398153, 45743039, 205368362, 698418690, 672916960, 291354827, 165353140, 723746500, 44431907, 151435704, 778863352, 44605789, 961221971, 313661527, 518320643, 27012640, 750682097, 777394147, 686774209, 171411740, 694425217, 360201348, 565739526, 218523742, 118439170, 200104951, 193932070, 717975146, 185791078, 545252608, 634596411, 100812022, 43230046, 860997406, 499053660, 983777659, 351635062, 866946461, 204313194, 318375167, 193455323, 373500959, 243837958, 721442650, 550489635, 773424983, 211372040, 73506476, 142561858, 942180414, 226008092, 368496996, 836458004, 131354663, 102779491, 711930906, 140152695, 852089152, 321525015, 706310052, 196571802, 845922937, 848365297, 166397909, 887271164, 723160625, 235765023, 433918418, 445426999, 646901766, 449480777, 734305425, 360988341, 444814036, 361918955, 64916499, 550929949, 389677860, 48670505, 273602108, 68168632, 425268734, 448459285, 31402098, 283417709, 576045063, 870530250, 611222632, 777758334, 813616758, 475292774, 295552577, 132541912, 798668370, 152087426, 628452931, 914632682, 90668787, 920765774, 879402786, 120096955, 888473870, 145188372, 832723865, 678766893, 589137309, 634441431, 654620660, 728080881, 506581248, 403923528, 249798511, 379462759, 701825915, 343438014, 671721829, 170814510, 70102767, 262955431, 810149501, 141953422, 233781433, 100056115, 865634147, 434980264, 699971867, 715499428, 643596425, 150806901, 903334883, 468436876, 435037453, 262218593, 639139820, 956338099, 237510979, 293640783, 976264431, 336330960, 30939194, 883227020, 307933682, 264225100, 315875997, 316784265, 466182451, 466429746, 929983352, 11874652, 312214496, 238989773, 783186, 556005606, 833925596, 906277807, 142178648, 888336809, 200874217, 873706449, 785651536, 100125934, 635856280, 791074707, 902801986, 660237243, 938121725, 291548902, 576209422, 618800960, 131013343, 783133903, 107351574, 368810225, 674123916, 473690947, 360886124, 249371671, 734944594, 799279549, 252882572, 797949196, 690650163, 681009757, 71622742, 675065699, 19516311, 739141727, 113594011, 719069092, 884398574, 362981791, 734387774, 697346646, 895240000, 262142837, 108064196, 339253909, 63097466, 317419034, 551893224, 217217535, 203323632, 486172622, 768302093, 397505496, 48321666, 217479607, 670880788, 652638139, 815715774, 551695630, 422605138, 131762135, 280212728, 282539352, 642611131, 578820654, 328893608, 301434706, 432289612, 17488230, 671703752, 674697185, 484221540, 630641424, 311505265, 367664192, 572840919, 926504306, 410080455, 437195457, 769985362, 794185837, 748641784, 760416960, 851825708, 312765272, 527608278, 712884268, 922795996, 483523748, 463523630, 935420369, 600511464, 665878134, 487236850, 787921013, 592548197, 135094722, 109330203, 128717133, 314650016, 486839222, 763226407, 323183625, 759625057, 577486118, 850227560, 240250924, 538684042, 866479144, 36555133, 390984390, 494198270, 842597420, 517536648, 629920174, 701664340, 693580338, 959917339, 873459453, 632897420, 393748405, 471556755, 323273694, 627176695, 336669519, 680992611, 155574389, 491970321, 324273431, 335320609, 514546433, 51305453, 599049331, 841698464, 515631838, 59362926, 703260239, 25555412, 730486804, 686059854, 894382135, 541603447, 115634226, 936745028, 392352308, 465513483, 924077692, 901491312, 114141039, 935298253, 422637354, 16168482, 812712386, 117821539, 574384999, 759197812, 998940701, 892056661, 734954641, 917863537, 924000664, 253036430, 457600185, 18104945, 354785572, 714893218, 928448736, 512974074, 118336211, 476410242, 712490905, 491535321, 12596639, 233064307, 824373511, 181187065, 735777520, 535880586, 296335436, 796599611, 207584967, 464678127, 916743560, 519523996, 90531043, 998633895, 15421367, 700579258, 399723390, 355857440, 656583977, 628185589, 219416371, 586639388, 453982796, 805416454, 203448458, 843790442, 849699360, 474074280, 387954357, 704177535, 350388300, 150340477, 83953836, 251906043, 269735709, 547200582, 49244156, 816959480, 196685903, 624176998, 748215008, 628426462, 144852231, 10910300, 709528498, 706650962, 360969374, 4793790, 442626408, 344944888, 517883959, 99848938, 952950830, 962179147, 891897320, 350886292, 370751102, 377201922, 163144687, 412766955, 721311615, 793371633, 196632656, 92598377, 282389517, 896940349, 23498184, 101215058, 824026597, 258294905, 338510323, 690795034, 892491154, 405828115, 545996862, 170706336, 567247895, 913943900, 520172717, 130917150, 888352487, 500294112, 469170394, 974336488, 245310980, 156004769, 57490013, 2813002, 953244318, 52817398, 48018337, 643408996, 54997549, 763447404, 890704090, 207602550, 617471159, 619640933, 552819504, 625442190, 824830611, 24306787, 898066125, 188175501, 911319519, 25255385, 655969362, 320247108, 46430837, 62245288, 613446439, 40637774, 536996925, 298979860, 451386455, 217268750, 783597480, 993907884, 381652506, 724383282, 794507215, 631310538, 903791274, 125219280, 806565106, 268387029, 199968158, 255590172, 359839979, 978521892, 28342751, 286242892, 929295390, 18318651, 577046190, 403649583, 352362794, 672058819, 900231294, 899234130, 211414717, 256006694, 221830344, 847983097, 721489966, 149921141, 928089209, 53737132, 303026944, 236959980, 281596990, 817063061, 237223212, 74981387, 781991779, 11413465, 643047990, 902755626, 461318914, 340765318, 815940483, 992407081, 919526642, 131091591, 556273492, 474291413, 550428941, 964962272, 667785990, 77786437, 816058810, 101967973, 433831730, 424936547, 671744959, 241683402, 465007851, 633160238, 161848020, 690353826, 602075079, 362059098, 375443585, 167304395, 301672915, 238278760, 581603108, 122560666, 209470354, 635779142, 197953912, 695239364, 879215033, 513274988, 650165852, 434853720, 196392286, 324929440, 87156216, 664300178, 923828990, 353599024, 520996882, 101492178, 582995663, 587561841, 398872191, 706061137, 693315880, 973664064, 902584124, 748268772, 666976979, 436191829, 910949897, 294796256, 158559201, 118631207, 808096781, 54472473, 929444364, 811501663, 48515649, 827605478, 138077387, 27648341, 514415732, 928505504, 564422013, 120626912, 168951750, 498774613, 537508936, 137187723, 223590894, 947318401, 798259605, 455255288, 665854080, 608192838, 945285929, 609309754, 191678759, 86944928, 289025420, 877074945, 891970927, 811726444, 565427774, 358219013, 2047945, 155660867, 558487120, 44785253, 392414749, 980999982, 818043224, 314281173, 232022967, 225965537, 981205286, 859131405, 769620304, 860698019, 108767852, 327073620, 280517887, 419178012, 287722493, 886846966, 593181230, 181556152, 982782864, 622688722, 497926309, 119649120, 737606802, 305826418, 485426373, 454590098, 291558779, 577809172, 430798542, 919818732, 178820870, 595301009, 397718836, 715424097, 291607322, 666617353, 331914694, 142297439, 852376195, 66797269, 772795800, 663090878, 143019297, 915152258, 205775506, 623087580, 125750266, 663281430, 936991939, 203599203, 592998487, 420165233, 914191236, 161796370, 873352290, 113346419, 669163243, 421535013, 4452562, 108470694, 696913463, 70983395, 564935583, 746332688, 59423907, 306929986, 668528217, 575528161, 536408136, 437568781, 675014807, 554360732, 62245991, 599294657, 380558137, 771510539, 464435604, 355762193, 698549662, 414996752, 198878213, 394484705, 387373770, 688400297, 35486111, 231458622, 961697521, 993679024, 809770542, 85729787, 902765610, 114855093, 587981460, 902484297, 396059856, 425663046, 201067972, 717879161, 91680974, 32081275, 409747844, 490401616, 641027255, 302384042, 992307799, 892169930, 35786771, 263285694, 615604671, 671642961, 717190658, 986884420, 513151861, 492311426, 790125276, 633208650, 107094449, 752646756, 198367298, 433882948, 213232448, 618044647, 660341374, 727134240, 535196582, 132194406, 467625951, 713282714, 793698119, 956270480, 426427104, 416230463, 111557684, 534586807, 241947306, 119092932, 598319539, 618736676, 23123482, 933095351, 988959690, 790541730, 13415940, 551218586, 388020530, 196145091, 116280497, 577067683, 758568459, 351634636, 415743385, 712244274, 522090390, 666345426, 823770556, 714064916, 665519311, 164668956, 780504141, 646866676, 658382503, 924707213, 878602059, 177441244, 318499314, 37455773, 402967139, 624809665, 279484105, 253800481, 548279920, 114407211, 978786980, 533262692, 494083665, 171394691, 805696500, 445874174, 576066757, 765479577, 681132796, 513225193, 754347189, 788890444, 787332653, 282645393, 947093337, 96477115, 654933279, 459237519, 955143402, 810792280, 40718098, 470770625, 482726539, 275974303, 336186055, 309502790, 739325297, 456047561, 705534063, 698760052, 36133841, 787333907, 645973475, 796630815, 955869944, 195023395, 16145398, 655445751, 493994173, 617127769, 45907716, 415728431, 322033520, 848379633, 470723785, 114337836, 776907403, 608009749, 20206759, 289296182, 268836798, 641565378, 620465811, 909544795, 638951056, 437222741, 939410886, 238381185, 12861602, 723062327, 533134013, 395984708, 810203444, 9695656, 583138462, 456048803, 589966395, 780041000, 841701429, 784829035, 149918145, 857012294, 65601586, 962529586, 502574315, 421760574, 325339089, 760293942, 308120492, 233806499, 558423724, 325600302, 681183639, 770980347, 633677617, 193791170, 660484945, 435680895, 805187665, 410770308, 28277046, 546108479, 349948334, 889910189, 778887053, 675546285, 490378776, 947748353, 655361104, 438105855, 238320096, 870439591, 355351185, 95839025, 482902310, 248748395, 484412780, 657322759, 585237433, 108657513, 730620177, 19722770, 486265801, 196669555, 158330692, 127739504, 723735906, 704275207, 802218648, 712341580, 560138649, 2255630, 784903839, 999128565, 606937522, 610773969, 648601341, 185234161, 310227557, 381569011, 783182284, 133930565, 510041238, 907517102, 588340669, 16307890, 202625825, 535357955, 308468501, 124575102, 234279839, 10658869, 909765917, 410285596, 865021223, 285016050, 86934872, 436478241, 987628433, 391545396, 190421487, 168927792, 952211061, 702152545, 543658108, 645390125, 102100604, 509219555, 403498118, 590909055, 159095470, 541554583, 846657836, 520330384, 864663038, 888686173, 479196327, 583606078, 771929756, 483600514, 932734703, 590051695, 903614590, 279092080, 44666745, 610849223, 346035455, 241728375, 741019558, 582633098, 658441992, 736159920, 382592196, 755622410, 600495374, 749470518, 260393910, 509767641, 133821475, 524121747, 359707704, 281614645, 424858517, 353155257, 997031295, 621272767, 464645553, 318623581, 495331056, 5552568, 831794306, 962858513, 405078035, 426906034, 819290480, 709044413, 661335938, 253108132, 605669094, 537958918, 652548265, 572448868, 402569712, 471113946, 912167913, 354330737, 947519588, 465054799, 236424505, 431640722, 292223553, 836284547, 72755092, 313515392, 706901344, 809864018, 483141795, 157006494, 999754055, 789912633, 369289113, 95724714, 347155432, 606324905, 348123772, 504432652, 764755347, 303993786, 440454490, 289811231, 79653522, 691282839, 917843997, 847662602, 92646184, 442572804, 640304625, 217475773, 948844434, 6427537, 704337924, 836939677, 222080472, 384758371, 117744760, 579547521, 863049611, 599686704, 351531854, 145619762, 872942584, 51469308, 334732259, 930278699, 464290398, 915403171, 882961867, 565840791, 409828574, 538871995, 272701243, 731117222, 838462743, 95564716, 611870749, 340024601, 830773776, 592775279, 225979693, 236624100, 984672139, 473997338, 728363992, 203008663, 598094808, 79084814, 806092453, 582030814, 572095005, 868922168, 268919524, 460398015, 44196122, 696397129, 254709999, 811098041, 530211162, 500353676, 895725358, 117294903, 447454694, 278264819, 648756685, 68647716, 607620573, 305954814, 469777678, 594111539, 24395587, 970139917, 755500303, 978032235, 959257304, 34219458, 162239309, 979536349, 60344713, 667795942, 42507875, 881660494, 893868179, 321158635, 893002385, 170512120, 514696673, 263494560, 707440175, 298992872, 273725520, 970988664, 915197856, 480509820, 572303204, 593532736, 854303220, 619156218, 121034102, 902401353, 518637827, 171078993, 343101556, 129929044, 682782144, 989255820, 788869686, 167091033, 197464115, 552112437, 715702532, 783811128, 399066875, 646638943, 473554131, 843641837, 27101715, 515362223, 584068243, 549658505, 622555065, 43116905, 766774600, 808781203, 476306539, 654262939, 933452681, 904244849, 30473312, 935301410, 573807519, 333593284, 486495489, 91474384, 689044817, 197112850, 534255293, 370590841, 550642205, 689199959, 146327351, 469932277, 92132767, 93385530, 558173456, 202270553, 86792452, 496909786, 320053981, 750649472, 273122906, 751881148, 716337872, 931218182, 675106224, 338999516, 483381422, 600618173, 25226801, 612728807, 387555547, 89454411, 517756817, 714405005, 287594964, 570607093, 752290929, 536005362, 472145959, 377530629, 551029686, 862449997, 983677027, 318948414, 590758916, 95102587, 683895504, 913714728, 793944546, 874559882, 451895157, 638252485, 991135698, 186911847, 595977840, 458738698, 369896351, 206560894, 769832899, 391544048, 387099620, 954710557, 194452321, 339596957, 838651376, 755055951, 192608370, 835651069, 997609831, 612550065, 461907883, 731976082, 624646863, 685618978, 605685935, 703462536, 717100278, 944550033, 167828035, 939677190, 883018267, 235062266, 201831523, 480704919, 168674799, 664856680, 607486743, 5982376, 10400437, 598248613, 54272278, 41791707, 90043232, 754567573, 890454786, 864853060, 346952074, 894544321, 976880461, 835878552, 234460272, 533353355, 144170887, 591345808, 243060190, 482311944, 576427071, 373297734, 850014507, 949742858, 234362466, 298614245, 395650007, 105941128, 45399976, 938692803, 351925751, 566804498, 136200315, 382059190, 826127197, 529780074, 21995758, 533249896, 661207149, 376723397, 755244857, 477644330, 218102750, 136797352, 67958673, 870126593, 957616138, 916702713, 365137035, 407574344, 373355717, 154947062, 127559650, 462184081, 615180260, 632507238, 556459888, 41415297, 185797998, 249493839, 621577140, 317296540, 56155808, 493030096, 307392736, 285382060, 627624562, 170747518, 272094643, 689786546, 305891469, 149379919, 730513608, 88913360, 609606458, 453700528, 623017076, 818289424, 711465618, 346783208, 849322507, 427938635, 275846240, 263163563, 479505134, 144537796, 815394722, 678319056, 722753931, 506504510, 613521679, 51006409, 1631102, 320061005, 919907032, 485574918, 600763410, 456804486, 677816857, 523372934, 649394074, 727302333, 217931159, 674254579, 361103415, 820292882, 994855749, 808765596, 937656925, 406149748, 257291773, 633431762, 422403169, 794158417, 197358530, 680919698, 369659122, 348340492, 734743378, 226279908, 932288401, 256209691, 405128828, 448857269, 617713479, 263268411, 525931379, 224340346, 867090512, 248632474, 19571975, 57115344, 399634305, 290622928, 580215474, 641904194, 250645482, 264145919, 962619729, 61822362, 826276105, 874198019, 63469176, 238148648, 480441196, 590718801, 182394906, 408760252, 752065925, 637714546, 984887500, 347974240, 392187648, 81399014, 387685462, 708136063, 937850201, 299962138, 250388597, 518142813, 657973013, 594340542, 860778701, 101439850, 158561300, 920157686, 958997227, 585347273, 264267456, 662446790, 576395967, 561197178, 887901345, 465646303, 925705234, 942587011, 704294709, 12693081, 563618532, 343040677, 470924018, 122918772, 702871752, 466842074, 649405393, 457912978, 431426045, 643575686, 88915929, 236277309, 591523308, 726229814, 290792779, 446565740, 947537050, 168686374, 787988603, 597952323, 204208919, 600360078, 220770155, 5326942, 955828050, 308598046, 793771545, 360772238, 680956789, 298939910, 796680762, 486667762, 104632606, 911281462, 329288632, 489490417, 26213686, 623191495, 279275294, 945548253, 393718804, 366363817, 367347131, 366664350, 20822707, 400914775, 525097367, 26095534, 898108384, 327835850, 920537769, 944332430, 28155438, 252186898, 147738506, 533042462, 445988575, 553414099, 296151288, 776324156, 115315452, 768720488, 338320233, 220156824, 36692392, 425744078, 727097207, 459009284, 155297152, 496254954, 990876594, 998410485, 700759345, 563742240, 818385877, 753208806, 417469924, 43497466, 773027676, 867221187, 854094116, 422207202, 647713014, 107708089, 839556832, 894176185, 958879534, 989332642, 342501457, 906074916, 398801568, 410737818, 491650226, 105793299, 232043669, 515557987, 892821461, 74619, 913972343, 456993174, 708361319, 71001497, 904689347, 484015907, 90319893, 611125068, 440326961, 704071315, 679535111, 634133951, 859925101, 357169873, 28705157, 405827755, 729561842, 105013966, 205387460, 826659739, 775023747, 133054368, 395714486, 289224235, 45475925, 889474906, 682800449, 263681187, 834494178, 144378144, 105272931, 810791794, 767518650, 569283030, 109375910, 628950472, 358252055, 937790003, 983899428, 209582592, 780608779, 997626782, 431901558, 564678196, 970207366, 586298967, 987460337, 818216842, 565777116, 272816680, 678539928, 484959835, 87530961, 925763850, 649830126, 749528809, 519753880, 386359866, 509611274, 180193740, 328712298, 338960242, 181569057, 959155007, 844956926, 146885971, 350439150, 413313331, 677344516, 124946506, 809200230, 204348131, 938732201, 144005799, 475044343, 106572340, 681909718, 899641300, 67491623, 814286898, 263516146, 761890873, 917393079, 510603639, 737313291, 297791003, 875064948, 543238255, 598212627, 376786130, 143018935, 603167399, 226364789, 281044247, 485767108, 794538642, 430135551, 563569120, 145675324, 111459462, 164385380, 235596838, 941869263, 347086350, 65594131, 29344556, 265427602, 813798024, 172837515, 937581241, 977972794, 855931810, 825841836, 997328674, 772209557, 188615384, 932050496, 216550318, 653967572, 814040638, 795825431, 172501361, 190699162, 353009737, 341631119, 12343873, 372561368, 596288759, 54571754, 893791177, 441221674, 981500238, 690397199, 487159131, 862416146, 481804550, 816322702, 868994864, 339221368, 294567296, 5766700, 43938265, 768850261, 859136830, 145563462, 866491023, 817896561, 886135313, 836733510, 622513441, 732432037, 308873522, 50427172, 400504789, 205019954, 772311553, 923185489, 176614584, 287265757, 756746278, 853610410, 543821126, 213590974, 910371958, 72427271, 582705893, 198513357, 164682501, 283855814, 181606039, 655867960, 202186989, 351462563, 170268083, 744748759, 451067994, 343179986, 279994709, 238596605, 532914467, 960578340, 398391902, 84272081, 347828012, 764105355, 666723952, 649508505, 722776333, 33833299, 31540704, 379546488, 913300699, 958037639, 987302149, 336149293, 999159860, 931377186, 548008887, 366218203, 32261596, 436124744, 176755817, 21796091, 466381074, 780524895, 55216967, 775341858, 27824264, 964761576, 753126506, 469564362, 578521978, 237778228, 333922045, 610401427, 78249231, 551760228, 895402995, 743274330, 633321868, 522085333, 897187725, 627703044, 357370230, 776442562, 934215899, 897407042, 776706969, 302413341, 323203003, 515125568, 106729060, 882173780, 227463398, 819143228, 344313501, 206992927, 869431496, 590410867, 722010026, 267884309, 555478553, 80188153, 405381365, 139576563, 536902362, 533273015, 147302388, 667871034, 485877128, 887067878, 93209232, 884434080, 110034665, 126338606, 837729943, 422762134, 809308686, 967485818, 968160580, 44955322, 568761586, 397833677, 508302808, 570601643, 788129213, 315506520, 411103540, 596622882, 130709730, 277816441, 856017749, 947246731, 9148393, 271931057, 951774020, 335033195, 842126529, 910742525, 648430373, 11579651, 523369319, 686532974, 754523719, 433403678, 145686703, 80533180, 807695532, 301042751, 772926602, 327364015, 347051337, 197698592, 955192343, 429316733, 887694143, 433594071, 554775356, 694660055, 135028, 341400123, 3248790, 982663755, 206160242, 505887355, 93134492, 787835024, 196767943, 759298599, 318625339, 646174309, 374944509, 746726477, 942041631, 649895276, 295371999, 558765158, 228550585, 929541124, 282178420, 427802664, 881477003, 924286039, 68664362, 345903600, 803309874, 255721952, 931084556, 885124416, 772375722, 124632384, 977242295, 111695836, 360037904, 983725407, 968695949, 191117352, 728195539, 608128145, 135885624, 175913570, 898912959, 395045812, 643129925, 422177923, 804199576, 698412000, 156570009, 541236933, 542644826, 428610864, 936922561, 212453897, 689885126, 138216774, 767246981, 694332640, 38293836, 925159289, 132179076, 808715641, 250208846, 117155755, 765349541, 454751767, 313106519, 546028859, 845888761, 866585920, 792815617, 702162857, 977829480, 542667595, 990901230, 811941433, 97845410, 297678686, 789210654, 507156183, 977499418, 477747947, 239089081, 885669086, 127107136, 219656800, 530190344, 163820832, 380284774, 221093109, 399061788, 855705870, 153183888, 896602841, 61056470, 913548345, 492356273, 708446064, 96160543, 797941867, 593337441, 963464341, 969611176, 655340967, 374308329, 889993103, 605774052, 339836969, 946132052, 264541975, 949636732, 785252943, 442664389, 280169107, 905751038, 654565046, 174737062, 461725919, 853353559, 549812318, 491059385, 496854701, 227124831, 669293914, 205044740, 494584983, 191328246, 508459238, 613230208, 855773441, 405413132, 618870005, 685378476, 222758729, 161806855, 943425363, 238011110, 968484325, 869393918, 118906020, 313863476, 644626638, 845612065, 139549783, 49511771, 994260066, 891342080, 734841818, 866307018, 226183110, 802980873, 435466431, 523287340, 4845057, 921295950, 797396038, 676190297, 294817944, 757178825, 460078482, 879687297, 255312576, 422962897, 571738159, 937488752, 79207989, 846241875, 100911114, 11868413, 503609413, 245118778, 36965862, 625289778, 937493152, 735306707, 317942104, 348967792, 236823028, 91000681, 114604979, 613051363, 698843334, 899807170, 964221285, 634665152, 380000525, 479158425, 512993134, 954998543, 1984239, 650069239, 515886144, 3604078, 193418829, 26485521, 348442051, 113766603, 601308445, 588387034, 315393856, 439702619, 319607426, 471106826, 81826414, 862611619, 197889152, 596475008, 309916029, 111395351, 523530758, 853272409, 489519187, 134866933, 348602129, 731852887, 379497554, 962286674, 743578737, 793901056, 69006891, 987865726, 415485636, 653883094, 956318356, 820324817, 160426926, 376712204, 842025556, 831254289, 891361563, 628327446, 337188852, 890879137, 667453670, 101377172, 161941069, 492906087, 795833513, 41137909, 596234161, 827685907, 615417245, 261074019, 862285714, 834150312, 67491008, 366655796, 827679971, 663480636, 500252786, 408201339, 905863185, 111940523, 809755144, 948633933, 353978867, 467691999, 3438949, 40833494, 377609407, 404093902, 692141129, 793814331, 49754233, 870632011, 152961467, 47392126, 824948356, 153708454, 69738242, 644122435, 692036583, 889759544, 719125483, 622396166, 938226536, 470988777, 132736941, 231327959, 37507558, 17791851, 968656483, 296063533, 608291321, 233850784, 115160797, 965138489, 84776128, 92746316, 231523768, 361637913, 518016693, 519357953, 421489399, 75354683, 866381414, 939296985, 282355107, 368464591, 572498151, 877037361, 186103944, 104437277, 359741188, 212074507, 572789158, 185799220, 3553245, 656097490, 455761529, 265255038, 627087208, 218171334, 63492955, 829292205, 883837663, 570996132, 559118244, 614270751, 403425388, 993130415, 505288302, 781942441, 861610943, 669332038, 808953299, 838889134, 393208308, 781234605, 968622037, 743591723, 502107181, 579837898, 130647433, 378836873, 478164749, 139593633, 833785786, 345457748, 998648740, 704066767, 752303946, 804432888, 632470627, 958430378, 804081647, 573832820, 923985969, 320857539, 238851270, 523503192, 724354261, 658878809, 538349727, 327073387, 6014021, 367983765, 861461107, 398159398, 681285663, 876847946, 541826634, 622213021, 609946695, 491762836, 884882324, 419850661, 946665873, 720636700, 580996106, 513161218, 852211429, 191161397, 452868418, 773944877, 135301245, 877752215, 212946028, 596563850, 23822547, 650752333, 251746646, 33091404, 655722083, 751604670, 373863876, 445503075, 839992722, 520995808, 948550085, 177803090, 807683248, 862149658, 819434021, 191476286, 657841427, 46963832, 99188, 459997335, 195916559, 284963305, 258832069, 895022996, 749280966, 765181553, 813344066, 817515290, 706619271, 859123110, 96875171, 436706273, 553077198, 581976726, 236076115, 287707018, 295690699, 753309957, 978151792, 26061570, 738229578, 47054888, 872538338, 247038805, 956152958, 847044447, 434433426, 630479436, 162975224, 712650787, 546256810, 666853141, 621401777, 331776179, 914524342, 321625925, 610032384, 777341481, 910756306, 980106549, 120223504, 821799634, 148743174, 70787684, 813136033, 961107956, 561870833, 895117049, 93220815, 451509363, 901739041, 5649601, 463599878, 132800793, 973259878, 407140695, 401937174, 222675303, 43836787, 737335613, 812488294, 651292647, 81596861, 253469708, 783384102, 813994193, 583758710, 256070054, 750077764, 155467419, 108671105, 915680785, 476616040, 311242840, 79425686, 136953172, 70713052, 224404070, 637078234, 347133712, 565426818, 794357015, 439593535, 973115932, 135772519, 866661720, 502511152, 792382035, 931553154, 859146360, 823779132, 877271389, 746744245, 730029582, 364988305, 469967925, 366669233, 409202690, 786849532, 887092643, 938373088, 291587488, 240907878, 533623126, 650734993, 348085978, 715599795, 466048652, 456662145, 875578164, 682508498, 486160417, 981867975, 937905560, 365273069, 467288817, 953121904, 34195821, 932608448, 173312784, 566677879, 83494007, 415945122, 805802164, 975469511, 251345081, 681723174, 624085748, 39090286, 376672945, 45349402, 983353770, 398545759, 854440485, 898009976, 413475328, 451969490, 302205300, 867775640, 154804715, 928458685, 137664118, 332714894, 182365449, 517539892, 113564737, 633811769, 412482874, 715735632, 454935839, 631527749, 240422967, 421324299, 372470044, 400708934, 994236116, 415715782, 591045266, 369452053, 880273374, 891876003, 396956072, 439055156, 832955638, 711581824, 673376871, 266013931, 254319121, 756440667, 288635232, 487695894, 35089686, 91469706, 856213474, 220902178, 890003979, 392727695, 961707400, 675621495, 682747754, 169262213, 91423898, 860081508, 704345999, 429126474, 128210690, 837755518, 909494264, 245941547, 983995417, 858372873, 631632012, 567106730, 638681226, 511366915, 445102823, 590738549, 35090019, 825863235, 883287656, 856051480, 129715613, 712468062, 539502325, 924420274, 178017335, 930634794, 45619985, 726153959, 560487415, 378274389, 362375462, 989720855, 905556814, 299672948, 969612192, 433526122, 314064005, 428750807, 674967656, 769353771, 748310074, 274294104, 906783000, 241432196, 6576846, 407094793, 33456134, 999972779, 755102909, 989668113, 359468060, 568532786, 363906605, 606864829, 643842123, 704078428, 114885347, 70576731, 357473112, 133785246, 214498946, 529703560, 635562308, 513063581, 882002439, 441196569, 764927764, 876927465, 853227208, 545985486, 429394472, 970762369, 760930834, 145963847, 189283, 265601926, 263527157, 638418388, 225185891, 223707494, 374236356, 770195528, 143725378, 728205356, 415130515, 975752195, 275292380, 307490934, 952812436, 929260551, 248679755, 29200340, 148499620, 302804956, 83248573, 629115419, 610203116, 353488965, 581197840, 468328684, 908719238, 405834678, 534116270, 925567813, 665234836, 384599348, 915308337, 590206419, 63600749, 654329377, 267993614, 589009551, 158268336, 254872356, 633738021, 184182423, 728059727, 485778275, 772308585, 291505335, 566436353, 421296203, 423222685, 548126519, 355976700, 935374571, 927307188, 354959760, 874799430, 175691085, 654749820, 880689726, 896372590, 13289537, 194597208, 149602836, 703586218, 135228696, 979883669, 718857051, 724495468, 269803829, 254993468, 463107877, 485018180, 142095188, 357716014, 137960864, 149732759, 928818450, 605977293, 17605214, 69319148, 892800367, 970039700, 211116148, 99916362, 623852690, 882671720, 550662424, 226765652, 483805912, 731909040, 169369832, 983107597, 977589058, 790364524, 890933724, 421897128, 923718733, 406704474, 335179845, 788030038, 512409902, 508255284, 147949257, 144752345, 822043237, 878200127, 63668004, 775870650, 271952824, 942215146, 815763960, 605484967, 688461590, 128617610, 538095349, 839033698, 802302758, 964329708, 508229943, 255015151, 832645133, 752823554, 496906096, 651157202, 651873405, 686288873, 914577133, 83624810, 25179596, 74164622, 902261976, 231470476, 935764996, 949276818, 311184191, 458560517, 208534615, 863161201, 249775824, 905713461, 149468007, 230272703, 134955867, 535696536, 115648702, 385777645, 596681602, 249883426, 699039855, 610986590, 522865388, 278427941, 150756335, 903855777, 426498956, 939873265, 469306492, 907439227, 454235428, 397511421, 331808703, 145592682, 671686927, 866716971, 845028458, 876980783, 894888165, 949643810, 175756282, 130306423, 10329830, 152294214, 455101550, 994188439, 975063685, 185148379, 300345488, 248204257, 899581036, 700172059, 236435064, 143742363, 343825010, 609515090, 183760793, 307897300, 300652470, 768920071, 925247071, 675124164, 691031581, 17447898, 453063700, 871250412, 807291158, 625467870, 161203782, 960448101, 432565759, 221317533, 541610852, 503183618, 93495042, 417540866, 336019335, 397740057, 407639153, 180504840, 546071106, 234748350, 41965092, 586079364, 615419869, 321367401, 166421014, 328212424, 126173883, 774414606, 114214245, 630091431, 334491057, 351484580, 613331608, 253532711, 468259046, 217491726, 566253532, 547995986, 785371882, 783552742, 226541556, 715976230, 520370557, 786839183, 47837111, 586886538, 501729976, 171900156, 393382208, 560848127, 552071124, 876383315, 225417372, 181670484, 786535207, 284704276, 679244681, 801708127, 628894699, 748530854, 877433692, 987764353, 829132816, 784511769, 616211072, 609034989, 350225451, 15848959, 69631772, 412214792, 616406308, 972925367, 142756673, 129536446, 392997315, 314443665, 926677382, 165494754, 967724016, 329208028, 516792611, 431021784, 440061066, 98963028, 546294246, 693805636, 382588467, 874128453, 506377073, 395635172, 700559449, 889183194, 609028252, 16914646, 40036550, 714521258, 902662627, 199323912, 288379200, 147992579, 339902415, 636025994, 333062589, 624946822, 405832186, 248100050, 778467927, 938307075, 987553953, 255590838, 689144449, 220432168, 261650968, 468279452, 84588467, 913964294, 475419431, 459467863, 829245554, 129371954, 534757721, 850402225, 575297738, 115022462, 509275765, 282337911, 553378235, 74545730, 390120559, 735879872, 496667700, 786365487, 3889415, 240388227, 893409995, 43955802, 167361834, 124087298, 437339425, 520176036, 574919354, 960593195, 521885025, 623065550, 527104570, 430569448, 133029711, 97055183, 885818498, 942128182, 725473222, 15517080, 509327641, 268489416, 72146478, 941821757, 986889402, 771611026, 899023470, 262933805, 928394080, 268748488, 78782362, 397360288, 21230669, 146401024, 592926216, 991928428, 138001350, 916407663, 967119671, 180240734, 317165869, 869594409, 995754643, 963361268, 267139119, 924774387, 521905870, 359593898, 995146929, 184817461, 950768305, 210716654, 157726082, 953906201, 580772363, 811933375, 3513831, 411698871, 279982983, 365285002, 809849849, 5946822, 201264796, 990584630, 45381789, 22426963, 191849510, 462472827, 112257230, 924243262, 520766570, 39399374, 108142875, 625566309, 216757502, 841309106, 862757666, 990484173, 47113365, 660310153, 77865858, 488690085, 822873629, 356931972, 315501536, 839497844, 527336374, 448803453, 337205150, 172310706, 733908592, 971510355, 596541456, 246230625, 395291614, 922812032, 333593682, 856905799, 355291187, 615429583, 870896357, 744586818, 670857883, 221473963, 422384081, 282186825, 355558768, 175796014, 820867279, 900829880, 651314746, 769162908, 456055101, 763227894, 324886708, 877263288, 687350239, 592108357, 708670547, 680400616, 428059743, 738184873, 945574721, 495910153, 460163001, 351082040, 428771412, 61542551, 610466399, 789307443, 68225176, 164780009, 521299167, 433205568, 343171479, 120208788, 855234066, 294586489, 98183161, 258643612, 826819604, 376829975, 204083533, 20096527, 51247229, 619923549, 274573473, 85107164, 818722571, 301725670, 368906978, 509154309, 394878920, 539899258, 407331119, 749943915, 611554948, 24521679, 588342040, 256329659, 459048979, 770916011, 875659847, 751379491, 917504804, 691256116, 754275159, 538105358, 644218534, 897328902, 653318753, 85863839, 392170539, 291740277, 977151174, 753334752, 622903438, 86079313, 130632723, 286009182, 545841985, 677531123, 394741326, 619681146, 28266305, 467545528, 624213525, 398559329, 564309950, 550143587, 299364020, 562287929, 498073707, 574665790, 913196988, 679515044, 920494798, 79459210, 605057337, 619122567, 571021815, 599170289, 267676323, 584484394, 858301899, 714177205, 186879312, 949136976, 661628659, 140121766, 166252117, 615076036, 835529024, 761558388, 708984756, 738162840, 974452063, 945434674, 498741975, 290878632, 341645576, 469962298, 699184059, 312632546, 88305267, 187246887, 211311158, 160551552, 98900659, 78429380, 693377154, 411755809, 341850928, 968003565, 530566396, 620559006, 807300788, 449310614, 666850815, 608291108, 398769896, 21815905, 452293067, 719217208, 652807207, 274161326, 914792153, 217125028, 712334015, 664738984, 83090002, 814754840, 735336588, 450496729, 253278704, 570535926, 705458070, 630705928, 393827311, 717437229, 1574473, 815419205, 356530937, 99696380, 454537778, 799580502, 125145256, 750841895, 591402082, 287521635, 600402963, 279644207, 348594129, 240412589, 133503526, 312001668, 955853655, 646808618, 615331544, 760921414, 310450567, 850923225, 906325450, 732802710, 328345086, 350118419, 447888901, 708214564, 740387047, 934240185, 983475273, 310971703, 180855213, 695069039, 162180582, 990740377, 385054046, 533534509, 959005746, 553638162, 213918808, 779800923, 259815307, 465013089, 883832734, 708644446, 778562600, 259494899, 230597956, 604050454, 907914054, 432569076, 894047218, 797976543, 14227933, 62244003, 156865529, 965272458, 203951170, 389343509, 435720632, 843089557, 416908077, 988393940, 279433493, 953584282, 882488845, 301761644, 867686354, 753333028, 974477415, 414031917, 640863520, 928459294, 181451881, 826253960, 809601963, 86137939, 747836364, 68258236, 996927407, 870521105, 60688814, 180429791, 420228852, 226234426, 500229019, 704766260, 528446408, 287046508, 335912339, 11490326, 638473442, 66605135, 759698641, 282403565, 79906390, 796509377, 388939953, 646027740, 387421952, 859152969, 142880844, 823942802, 266466614, 625201461, 66887727, 18765354, 605121254, 423127290, 308676171, 959197023, 313522104, 181763192, 303837454, 220082996, 270821008, 254058570, 376119924, 909056473, 888148019, 261242790, 86502844, 79044276, 26212489, 944913186, 504726068, 199959149, 94360231, 413196356, 423687804, 553388982, 663291839, 748028376, 266626084, 404834628, 199065531, 138782872, 604781556, 769741116, 12531117, 128445657, 873523175, 325891081, 223629246, 879633185, 111484460, 97684701, 770056386, 486755885, 536717748, 355831740, 126049807, 580522338, 484931693, 335222615, 285111238, 22989779, 116339470, 648805921, 814268110, 662734439, 602142695, 660111466, 634295438, 91576797, 330996924, 962597951, 69750722, 969002866, 58357198, 689611133, 593947803, 105672875, 708839620, 214024144, 671170913, 913730992, 681401947, 104708768, 249309913, 739395784, 302753350, 965054193, 915639196, 916030167, 191433477, 508107718, 304850854, 953320948, 285083511, 307981374, 579121068, 716152343, 723825075, 379844467, 186060655, 420969322, 486232699, 634316711, 228534771, 489337365, 384879009, 215490807, 485561413, 26508459, 831735138, 351873992, 691663184, 911430506, 349888618, 217239857, 967487450, 337859406, 308499212, 803181036, 779216156, 382377942, 47536321, 118813863, 147950663, 40282713, 64047446, 906917052, 29428051, 234270290, 366004050, 559755365, 550773155, 241559497, 681417477, 486135127, 789761286, 868885071, 543880921, 807182054, 593156725, 736190824, 329963476, 280235575, 43273481, 490341684, 708317770, 925997277, 643183847, 347909671, 551966755, 902911336, 893857362, 356007368, 996455373, 453816774, 144145191, 511615442, 10804480, 348569636, 36553687, 964451065, 281884859, 577479906, 404444258, 174515019, 163500972, 246657336, 307652697, 809314594, 320239081, 70028059, 558895804, 409915338, 987824394, 180081339, 623365218, 63189884, 411892945, 833452211, 98196008, 826410432, 202738457, 534465940, 262311178, 397202124, 891661335, 521174331, 260119594, 493972892, 568480987, 776691441, 590429580, 307312216, 140171954, 864125490, 112694334, 491225882, 594679530, 458101013, 957181997, 407739816, 596941793, 647022513, 953911006, 281907001, 505354448, 686568015, 209792399, 969817109, 916673536, 524613477, 745634227, 32701409, 508480601, 700754, 28731346, 485412080, 332331801, 140939936, 157623880, 967662638, 143812383, 901210819, 157202364, 685697577, 861142031, 151739403, 455684291, 77671008, 50627264, 845598377, 954566483, 121989622, 562895094, 266608641, 206527428, 675581485, 587790891, 301058350, 781370730, 120161806, 938001203, 798208999, 401630968, 907710920, 277329940, 394163996, 496194333, 199168612, 622162472, 437228186, 907509041, 317581030, 58707347, 682578968, 953534613, 991574312, 97807487, 54508743, 830020674, 530727731, 176261403, 586813457, 197700189, 612851047, 226517076, 859930323, 230844835, 482850416, 110323621, 51340022, 711370549, 166140604, 475860133, 816952309, 532911104, 236910973, 149898455, 91261710, 204124812, 27183456, 514969121, 878573855, 992039716, 826798212, 523134546, 317682065, 401824720, 350399905, 316744345, 480595452, 572369028, 526161850, 974021615, 477477631, 204168894, 347330994, 274248795, 250445139, 450080779, 369648606, 379285149, 747092470, 50705822, 999513644, 492265363, 124550075, 182692996, 208343481, 278153418, 963607751, 11134602, 173186928, 335466666, 379575886, 878688143, 671054072, 504269773, 716223296, 171637806, 867591064, 89227462, 472508575, 694450613, 309678310, 227918161, 369235556, 900237367, 548230572, 452010895, 764784582, 22555787, 55622766, 634452435, 403249969, 74875608, 939372813, 746168268, 754923479, 727688578, 27989077, 640747118, 248280186, 237724460, 333682839, 411519246, 502570824, 900101988, 436904333, 981618053, 419628931, 60739642, 135983774, 146846595, 30663496, 724562418, 625218379, 992701055, 616811247, 841172634, 983090437, 13084687, 280013081, 214167479, 776059012, 948696459, 91683366, 775754966, 871004020, 711013396, 870426485, 415169280, 466549824, 336878700, 159537852, 188261405, 752670926, 726867175, 89204094, 444753331, 512101094, 184866731, 30009182, 157159358, 176795819, 3385027, 62581158, 124917232, 505365841, 187090711, 885172166, 556664877, 938215321, 908756114, 566757900, 402220725, 908209107, 787704916, 665985928, 974013365, 805186203, 461096132, 288079002, 876575968, 867101085, 984151407, 361424455, 992076699, 614531245, 668018764, 566643231, 6176956, 368152353, 890931359, 553820696, 800057422, 39554644, 400108914, 496255186, 817218280, 876057211, 439789882, 196659236, 385469757, 616657799, 718349934, 860646962, 167403288, 964021403, 64537841, 29650230, 533289736, 926515481, 694279821, 904929526, 4595371, 845970888, 497675288, 239890267, 334232012, 403821238, 930999504, 565745114, 19811351, 997301363, 348120123, 363156786, 128719569, 402639015, 97599410, 909074174, 784290334, 26372306, 960837941, 676332433, 413006151, 8215947, 333429815, 482391423, 419659042, 581980361, 241900119, 317101057, 65550696, 971839912, 14823214, 749203805, 109975482, 764969439, 139001009, 568100911, 260008813, 311913236, 621537351, 398939089, 736641574, 154366315, 676552886, 942525476, 923090095, 68485779, 839835612, 387289214, 452177508, 241573976, 980730902, 538372139, 741221589, 816305350, 407737439, 692720157, 923287754, 292082343, 842919529, 332120200, 359906142, 275926115, 868396801, 168368505, 749065841, 423835263, 211633881, 738298571, 115060515, 573579379, 58418208, 975856473, 803919622, 124048366, 163952518, 327161513, 993740875, 178591658, 326206673, 214794257, 391359573, 29653578, 670161185, 813887591, 40251241, 448072434, 848788660, 743636578, 685935983, 217677526, 302976987, 140795853, 277568813, 841697812, 575043741, 117956393, 446939812, 963374220, 490990008, 802466683, 238776142, 23813844, 981560433, 624217708, 820403388, 134387858, 863059594, 59009033, 762612082, 644275643, 985281324, 64006947, 845490639, 958245827, 379975166, 755605985, 607538624, 97827457, 594944179, 457349468, 571024533, 635514107, 536602090, 73400372, 159400544, 787310247, 278002017, 138935025, 976145181, 529377582, 494589162, 459825903, 672982413, 604449622, 57430246, 767057899, 207271506, 408141380, 354602398, 125903933, 210232194, 284789708, 420382881, 428715351, 390187430, 415972657, 488494618, 467901096, 783533454, 754502718, 358945296, 362526103, 17715373, 132863682, 754506573, 567888723, 415703195, 868885692, 296358432, 365867167, 262982364, 410994631, 525389568, 169940341, 211073318, 118749692, 92996137, 242593301, 432713950, 474564468, 170682729, 89299997, 5408179, 190799122, 793515396, 469077249, 956300988, 158782088, 300265836, 64507125, 922668063, 291923097, 460496402, 976061130, 104129830, 557863564, 154330098, 857013924, 766049220, 22378644, 958160682, 482513399, 800248353, 20085645, 817227481, 564629712, 728885693, 804200736, 428657929, 934507209, 171426144, 922848305, 342339151, 602275844, 462268127, 563755719, 388875587, 111412381, 228292691, 26541383, 934651501, 352708156, 634283896, 773622823, 657701759, 18183647, 839246059, 562804131, 90229223, 431515341, 230617043, 948234839, 144057, 853377997, 118383669, 684399155, 78990214, 788002917, 721458081, 652124282, 224607234, 80850011, 437734226, 452242058, 738477714, 483511313, 260080013, 272895998, 494759999, 241480970, 790112397, 806016915, 61520733, 412757944, 843555551, 779253809, 860877366, 190188860, 93364808, 544252397, 276423054, 301000378, 69519041, 953647539, 107717770, 523470268, 854114415, 470087599, 880625683, 581539627, 499445818, 680750952, 395180674, 641284965, 534408651, 400085543, 696478673, 231549654, 864509160, 416434512, 777190254, 614601509, 71704814, 387885279, 370196195, 20130394, 693076602, 963300090, 539314369, 187214198, 227640498, 100684646, 899956444, 667440601, 943205783, 454756854, 925220216, 163681888, 399704331, 575667086, 471645811, 87342088, 97921886, 257268743, 6558817, 656083998, 650538475, 78160134, 509131980, 406228401, 710493629, 5287999, 630280613, 850439695, 323541214, 290306426, 169177652, 821850293, 330229830, 824912545, 164279463, 996326454, 643261086, 522910127, 811942593, 822196046, 327307117, 100666888, 261659742, 764859355, 364465693, 414993872, 226035683, 19864596, 372266727, 843980711, 112800006, 932336106, 491584139, 931413766, 988369334, 476467010, 320056634, 799719619, 260836094, 573496207, 164478322, 582815436, 529775124, 500927628, 313471303, 585121033, 208152284, 176164614, 461950954, 825563156, 583321687, 467454128, 51063326, 259212632, 681973791, 875382806, 582693716, 681154739, 226191417, 281262623, 711848402, 866414819, 672031945, 465136443, 626641870, 102937452, 634253505, 371572810, 424647738, 979886679, 72672274, 558848608, 83334625, 841491873, 150908110, 177529882, 607145182, 539593186, 426861817, 792629983, 659191210, 642055154, 557874437, 320746868, 881854333, 593321299, 566123925, 138934441, 857002785, 16939770, 149217861, 707772619, 612856090, 701557889, 286461592, 302455250, 493355527, 303805573, 359842144, 925524030, 691333169, 374317456, 732794189, 173096300, 870266162, 935165170, 763566769, 738353268, 970042592, 816669529, 646346039, 496191381, 913901155, 883234059, 238670996, 90635044, 432853007, 989528772, 22196869, 739533100, 777513900, 552219719, 290294297, 434795134, 956375868, 660566433, 947729623, 403505308, 86836692, 679517974, 332725074, 109676701, 127535045, 871856819, 461689963, 600817385, 712655359, 491538165, 901624635, 671275053, 528315032, 54103912, 860354884, 744912759, 655637758, 285808122, 81706047, 146309458, 990543103, 777959736, 354352573, 376732302, 154381551, 529481205, 408166807, 265189490, 487040397, 648423382, 684066796, 397633278, 518157064, 281446745, 512868236, 494330204, 85979572, 728958435, 419188169, 457171345, 90164404, 697562009, 73331387, 768720251, 777446607, 212602713, 399031865, 257893647, 910671935, 969253379, 356800998, 65758105, 323142461, 809873215, 798934662, 485754859, 921516407, 160617990, 375952058, 862423016, 493882289, 175420570, 318763950, 211835607, 482966767, 575472174, 101872269, 976149679, 588499681, 504271095, 547326517, 403717375, 493041946, 217155057, 689655315, 898157257, 670061849, 743524421, 332241873, 639455277, 75720790, 941890431, 511553851, 492964003, 943686384, 9916661, 124623727, 983737710, 290373296, 693697250, 409991792, 104841209, 307453929, 33012287, 963315933, 372888332, 911878644, 381635808, 362256008, 632096288, 221545126, 493304987, 198674842, 566317771, 309074948, 97760215, 797460463, 426088640, 441762959, 149782839, 365720728, 151335272, 57659392, 682264956, 443209927, 80162402, 843981901, 896245377, 929342779, 264748672, 691076872, 217330711, 40542727, 637955808, 779379891, 330183895, 920181424, 302762035, 746975616, 385482101, 962052172, 506774984, 873308139, 541485016, 463840334, 767767849, 656936416, 945591867, 791320286, 356288929, 205090795, 577154400, 364873781, 787389378, 621587090, 741233538, 389688115, 546128655, 125535007, 250047580, 578754464, 249848570, 183601813, 872362657, 876305707, 940820078, 758259226, 292845668, 920009878, 917492029, 101435332, 854354227, 602765116, 532710623, 159726931, 832535916, 775373468, 286364221, 649454731, 323547021, 744762396, 1966576, 602298165, 411091380, 432975082, 386858480, 840335975, 787425695, 191586935, 89707473, 10237771, 314782442, 977532948, 407012789, 712790017, 781627720, 904656849, 798519532, 456889765, 542742647, 591631906, 763172025, 781567257, 689226841, 766483211, 404899652, 692242064, 582379322, 764342403, 588481419, 215147014, 15297268, 612446075, 772817915, 675367883, 112575427, 503882989, 99815129, 712102758, 825217879, 441574993, 970735925, 523121012, 563777687, 917996827, 397560897, 801796538, 707817839, 210157181, 521949459, 32546017, 660909032, 821379195, 861955948, 230701321, 650451881, 303907315, 466924543, 129206116, 213422109, 177058855, 811497756, 808202473, 50000146, 377112130, 188559669, 613256213, 410187484, 43186096, 8288986, 534849724, 642777622, 5314493, 155481098, 235959669, 861550301, 621798130, 473222475, 237964948, 376712977, 158865319, 80894252, 140740696, 988950424, 360406040, 586810887, 73149991, 526224162, 432073677, 839578759, 612437227, 807536088, 622170625, 485696410, 398684579, 373275894, 746064043, 906907161, 247778627, 759403052, 517524618, 877609637, 437564349, 362484002, 210968784, 780260181, 536613489, 838384769, 451780242, 848988010, 618765267, 501557357, 391427124, 455997243, 305607296, 465078376, 608146544, 314074397, 840946776, 949136186, 825203923, 594522973, 227657811, 694850577, 131445854, 434392659, 280374739, 823112216, 771637023, 899320131, 846330422, 407559241, 908226997, 764997511, 841605590, 50729501, 235035875, 914497806, 590353014, 886711009, 723660632, 260603462, 644524495, 211856759, 317428088, 674250479, 476326846, 168715002, 431167457, 662085167, 33074363, 91751033, 448014016, 554395213, 228109717, 91099678, 688137342, 883039991, 594513534, 865628107, 436448186, 313770518, 884432720, 874776849, 573393374, 327517591, 782090123, 900156119, 596990201, 506615699, 731917325, 187772596, 442792774, 735365781, 940241879, 3177191, 949462694, 294912915, 219549323, 457911799, 354740883, 718063399, 837498564, 946975443, 10685805, 892688828, 382154560, 581084785, 970359352, 449306101, 595963076, 57665592, 357502644, 941208355, 353164972, 138130093, 902235616, 393788697, 761638062, 598302416, 663811675, 756587086, 177002476, 19489391, 328856569, 337970160, 550810343, 395920021, 208476202, 9479582, 854851629, 387342563, 811769832, 816723388, 601518965, 747521309, 393012873, 250541278, 672275269, 440640903, 975527873, 779570278, 167701857, 701582961, 826731621, 684179406, 934681239, 968121619, 45023885, 744422353, 934804241, 494192311, 815752665, 614010540, 580978986, 727571679, 761157452, 176450623, 694738670, 738832777, 408902658, 911504971, 315050395, 321457198, 638395579, 118212141, 972313009, 935778009, 806777941, 624298660, 788551495, 693193851, 990266076, 217675009, 286386224, 273528168, 121049450, 423274843, 763820163, 347321901, 952280686, 513944577, 11175473, 382955841, 126063131, 113588529, 672944363, 414817680, 733042704, 394083300, 981300076, 223927205, 716869813, 287884645, 911545958, 442950421, 394350558, 118345017, 25537415, 645453169, 334569603, 652545320, 198286411, 861708381, 260647029, 164044027, 952381974, 16875792, 278112924, 92002554, 181570767, 326493150, 974004829, 99589774, 754948017, 174469058, 595687097, 222938359, 511023279, 917143845, 534569473, 630865871, 796655157, 644608753, 958290102, 439824567, 749984911, 39547416, 68305712, 534113421, 296925382, 536098121, 853576827, 67579363, 276291507, 760016141, 552856664, 467555454, 483362763, 996683902, 892401344, 614847536, 608603222, 639391290, 160897493, 617517171, 83057265, 520304190, 295605996, 345224822, 545159536, 993876930, 144045849, 26258872, 595665213, 31125333, 54980974, 445940796, 873882525, 77780461, 289209774, 874013071, 464812806, 341975452, 345573100, 704967393, 486153379, 164197363, 66130664, 124075863, 949641801, 484616859, 5077900, 892908273, 600792216, 296091299, 137435096, 162444443, 794598307, 737252894, 633226006, 242827486, 679782268, 782113492, 866520598, 984236927, 986128926, 446418477, 691014157, 208096858, 349872016, 323463598, 276520089, 519139498, 850594312, 939727629, 733997245, 684058381, 919606860, 180003598, 792254206, 630289451, 776768671, 728464778, 842703997, 711966826, 838318375, 332725229, 250864066, 428973436, 691147577, 434291484, 236288742, 334712577, 979334453, 458533078, 642528757, 10385472, 79633322, 985989621, 58933739, 560830556, 682273878, 705555298, 675078649, 808569420, 668108838, 413890118, 174844752, 818478033, 482627804, 846192339, 240914082, 60256045, 307294002, 206511989, 367644146, 414588908, 393807750, 856358022, 281471339, 966353781, 887448181, 362443952, 687566425, 587315255, 78344829, 349641646, 229188038, 444903780, 608358039, 600376586, 229416436, 565327885, 763627952, 671891478, 502800316, 788844316, 953804953, 706805724, 770412226, 364322368, 243681985, 750460927, 575806462, 610886287, 273489946, 28358923, 12948292, 926243130, 445445852, 452640421, 517227296, 719247932, 132583550, 907323978, 306441821, 352255862, 211313454, 21297738, 253951784, 75323406, 284878708, 955426196, 176876814, 302213945, 15920244, 277798306, 526936029, 700155679, 150993793, 713001021, 572819381, 454209448, 246922841, 78534402, 743141366, 456226988, 610333608, 671871362, 745742538, 848536675, 499154926, 593995301, 454286223, 93517812, 306033276, 289169113, 678013427, 989787447, 952078401, 46474989, 701904349, 658903528, 841953437, 944224409, 319245257, 783600471, 446198770, 270494842, 398272451, 623710899, 908872585, 161862577, 841882787, 245896668, 290024360, 814717696, 6096718, 830049793, 692112547, 963745897, 32030586, 458262704, 272213827, 390192616, 169845596, 489187345, 460493046, 885617058, 912401719, 5458122, 498517495, 14852383, 701530868, 939549460, 302859987, 247875047, 219813160, 788574097, 757188767, 239272193, 734590834, 924144951, 513711197, 980906528, 547077929, 264672022, 805500225, 683305854, 537601039, 505114082, 94304798, 647787499, 924600278, 396101638, 78657947, 11703458, 650303136, 273207881, 450398828, 384685858, 497573931, 743533895, 656256908, 926527306, 288331327, 539777107, 127352012, 166823898, 784968113, 522673362, 867073346, 577574065, 559066832, 552034037, 95871079, 841330148, 605717880, 619517193, 988384236, 450469892, 676566663, 801534449, 544508427, 311394208, 440184693, 358672503, 347414632, 726723945, 47073137, 179376582, 131841735, 810651544, 48518378, 885572452, 737439938, 185711628, 896525053, 204879003, 395874540, 346880123, 226736737, 997486334, 837276135, 671773209, 440635101, 365028522, 28673128, 970148998, 631643195, 675257622, 899802486, 230447299, 613349904, 158705243, 998046017, 522525240, 271428680, 155276776, 593158682, 168907583, 860931488, 34860156, 662296855, 261190479, 848842415, 738116739, 872100236, 229921350, 891064561, 871899447, 233011362, 529393350, 18516350, 552155770, 797919828, 14693929, 261547724, 496873230, 86987791, 889787574, 222335049, 633218941, 555591602, 798265553, 595292676, 472069315, 274280509, 550406951, 703057307, 661961864, 701685000, 359729313, 40742633, 282928710, 77738609, 627961871, 425995532, 715798784, 847488420, 284986310, 700165863, 720590186, 990320290, 411524353, 656989956, 21848580, 196576252, 409735222, 174460655, 558114141, 882291837, 758985722, 867671650, 976935692, 947305935, 404818396, 898108730, 331094232, 261816425, 951180013, 348526773, 918891731, 382229753, 822775216, 506449501, 969013325, 377553123, 265757530, 124652565, 831779767, 70660673, 287684295, 484415308, 659275925, 631192298, 284171015, 457456225, 393442760, 411020044, 635063567, 934547237, 56519350, 605873823, 319337083, 439927735, 277580318, 349066301, 342159935, 141363559, 294999463, 4226718, 634929546, 645721690, 405522940, 758124165, 752793901, 513385917, 194498566, 990963305, 922100099, 771876305, 546384838, 864120024, 784355866, 317715689, 364506548, 37479355, 95170101, 813757672, 773839588, 43220830, 757849139, 486935200, 272035217, 388034405, 24251623, 691399692, 145625604, 522010526, 709991166, 324240800, 272475092, 349917965, 851914037, 331649136, 342600029, 476284449, 560127645, 602831847, 711467292, 904601116, 900496444, 375323650, 185849883, 586035580, 503782207, 448320925, 44897441, 593163438, 473621619, 611471217, 218555923, 18333359, 277017652, 999777080, 497030891, 758885716, 996962049, 507533286, 771764101, 571225524, 865595489, 430932750, 478102056, 931668156, 335114492, 285316659, 751235098, 437585778, 752636115, 451901858, 107095699, 768119560, 453479956, 256487231, 34709888, 235378926, 269871054, 962729552, 717780138, 721006202, 228419537, 804959934, 240854255, 790531335, 94154051, 292795543, 788557498, 457343256, 156284724, 160343414, 267083076, 913015260, 547662401, 432187641, 361845260, 281619017, 58805090, 937438812, 594687057, 93420767, 566445952, 914172567, 574845579, 428262685, 206010801, 354011292, 701787801, 905997838, 620600564, 659443963, 800042922, 847763438, 516855141, 548271935, 721887857, 320096218, 230438671, 157393355, 787157881, 532450500, 607212677, 771671017, 254750524, 229838183, 179693161, 575169017, 951657491, 460545024, 925442152, 841752222, 930382257, 945796014, 552477398, 871226678, 947649302, 120462433, 509418229, 95720384, 693477714, 865811254, 425275391, 390712563, 470122192, 445810705, 98002023, 672890236, 347426759, 550754675, 10559720, 320975699, 589264561, 875543040, 217508460, 298215143, 520114125, 632256349, 710606673, 168993252, 415742332, 39857397, 16500620, 147474382, 38386431, 394765783, 408010582, 824751143, 799056412, 596613595, 671492634, 389493367, 650153292, 907686036, 258364236, 997081319, 905520050, 655450990, 963254700, 671920521, 43714208, 494698237, 309016687, 540855219, 579548711, 458321677, 54256678, 900096971, 807314144, 58146423, 288762447, 535489597, 582490764, 800738777, 498615544, 709914510, 870541890, 61491704, 350769894, 124082836, 274922984, 29338549, 311928973, 353776715, 502138122, 385473639, 157659873, 277518980, 492714519, 144180372, 775454422, 760075370, 929165530, 99291496, 28462164, 519960055, 801818120, 350380366, 199744632, 457664606, 262911591, 480389231, 593170404, 659277447, 657391495, 232513382, 632460830, 327245621, 691246877, 367765899, 640160687, 385546866, 981477273, 144172706, 113094227, 822788604, 242932666, 959550033, 280691037, 891134734, 154006242, 738716753, 590263850, 896121139, 397523952, 928400501, 638488075, 861292002, 822098937, 834710779, 830735535, 394382590, 993757619, 741567926, 465221257, 194233969, 899322585, 903398387, 942460289, 20897486, 90785714, 150567998, 385582869, 570359502, 961251097, 376902097, 86288648, 300123148, 919824001, 936397884, 798694660, 441884470, 205795385, 771165945, 118071145, 195950035, 695003229, 985421348, 262824122, 605180349, 628447087, 666855273, 507382185, 239518843, 802606698, 510442763, 114510601, 233489631, 259063464, 28923119, 293516403, 574184081, 328471208, 434580271, 307259061, 699344701, 105390423, 741691322, 605941377, 989348485, 487424165, 662200599, 298588669, 28823393, 990715253, 206309994, 771816891, 286614276, 482676177, 115326489, 878802061, 42532864, 699818055, 597584424, 902425384, 252213705, 659771647, 662119942, 801467997, 69472682, 355396548, 833767980, 414197451, 189705600, 225639090, 768225156, 924836079, 614016894, 865565976, 232261696, 94065565, 670896574, 394786615, 315286609, 451103007, 454525230, 379089496, 995969951, 17154859, 94022734, 277370752, 195080728, 492435203, 491902142, 154588179, 20032829, 600368771, 860491018, 947481239, 921754711, 854510433, 359277592, 371361360, 497558705, 100022880, 333688555, 882271505, 917608290, 944762565, 695541812, 608679584, 808778543, 420931379, 904768505, 515356682, 607552464, 342646630, 684556432, 125960761, 142142368, 300936003, 25961733, 762517379, 922691430, 708023431, 416319652, 966536339, 116473730, 407313235, 908864066, 9273503, 368028571, 203074028, 151127725, 898784672, 796772924, 325512274, 312078632, 348493018, 912201756, 955223308, 707879035, 678034273, 768199448, 617585119, 995924574, 753709733, 797691480, 394031540, 844915187, 229259269, 276937338, 288618012, 925686670, 364246171, 366473715, 755262330, 621237618, 701783446, 212791853, 662991930, 812330306, 973864187, 989436606, 180654371, 902160684, 641458753, 992837205, 413246546, 802334199, 276376185, 578387377, 87958422, 454937789, 683625151, 316329901, 8166678, 266377855, 276768794, 223306245, 876231647, 843561509, 338456932, 349842153, 871531376, 769557065, 53185954, 498547992, 179236224, 882208446, 639324435, 50899156, 985281564, 768548637, 531325321, 119897459, 960084064, 835568026, 6899792, 940552393, 662970879, 427689789, 399185005, 32927687, 922386296, 701526476, 46618657, 395047839, 476136342, 355934430, 337525479, 719260398, 94896484, 252986585, 861185034, 832611778, 650401724, 743490967, 899493283, 948821250, 602306450, 480008549, 833697932, 766492198, 571220461, 139362071, 583343857, 615474456, 614176783, 107831092, 498320944, 57039311, 475579512, 80872547, 715014080, 694303403, 124415759, 724156513, 641202469, 352063942, 812415986, 978202643, 287853215, 444114199, 114067728, 488711903, 202544828, 455120781, 123176442, 624699266, 61972221, 19103526, 307067063, 465586930, 123870621, 853695973, 527009387, 964914967, 502111883, 32086671, 711902349, 325041073, 190363959, 593747259, 300678981, 112857537, 42435265, 995676257, 405569594, 617093189, 507171669, 534216093, 15112084, 909117533, 788476317, 469972109, 581539000, 227371973, 51789207, 969150708, 295241954, 892491087, 128976593, 881596350, 993628161, 605511396, 781273067, 331692957, 247717858, 89714215, 979138907, 133348145, 990823099, 679274679, 408643785, 832667505, 131342150, 925109998, 33597272, 894940394, 187708642, 978814674, 985422548, 432802099, 59106992, 789962250, 743030008, 956803067, 115613821, 539416309, 906216160, 564238779, 562901775, 783802558, 233607860, 96120367, 282175886, 235630686, 9950014, 918385265, 89824525, 14423513, 508897942, 911933152, 585547903, 315201069, 518523457, 450060227, 362923418, 137396640, 911536914, 2731731, 94298172, 334418740, 372395074, 124928657, 162580763, 50892360, 625831540, 330428636, 367486, 716541284, 273927411, 510963104, 425541377, 574667977, 454492865, 26096447, 689989079, 429647574, 17752433, 566859203, 299666003, 621370196, 20974153, 771349307, 787243628, 453262815, 912916114, 64121652, 823239552, 82050299, 61846074, 934102349, 939788758, 234708411, 853866104, 249660341, 683377863, 223124202, 631791896, 755321963, 167656254, 743622415, 734746456, 881183477, 533248207, 696486058, 428756572, 353966428, 765141271, 669927661, 565801009, 151368791, 371011659, 175484116, 181508571, 185583604, 809333095, 660629417, 979594104, 759091718, 148430147, 798504929, 345124428, 583330737, 274534962, 757491327, 430679595, 188940463, 805465450, 395103664, 470335761, 6007521, 760760243, 939976054, 289672677, 499706090, 558909339, 638288037, 961390422, 879747070, 779439048, 898133157, 553206078, 663249828, 80635580, 519681362, 793574560, 843154289, 513855468, 382523197, 544253062, 744383257, 665344765, 636180709, 30618433, 864749668, 385341554, 113971622, 984168855, 656358868, 565380158, 673495024, 329794754, 907763152, 326710245, 635178859, 234645018, 215452917, 765577600, 873023163, 585958789, 406737282, 656929686, 817149945, 691975717, 192610288, 403294837, 804547968, 120567033, 989977247, 292232881, 764681534, 923415037, 928568087, 886814637, 744332600, 655649455, 649565464, 395312715, 106112680, 562507020, 902442450, 961716684, 309529178, 6411705, 511560050, 437856562, 585354090, 416041171, 15822409, 714896879, 220918673, 600578886, 386044870, 478607220, 497544660, 145960678, 327229001, 222752517, 548884521, 961323711, 368631968, 418551690, 34761898, 276200307, 36876717, 599754195, 995725186, 240146482, 978905882, 144981972, 981311218, 933522099, 573130405, 373382960, 952322308, 371429196, 976214425, 200579724, 183723915, 469751525, 952731400, 562208345, 639111505, 247068175, 971070179, 188419373, 696405198, 801635473, 864756962, 45424222, 100937646, 655710432, 648865064, 119057220, 640854040, 23248204, 66468638, 499228984, 788063807, 855827582, 911409193, 811273668, 268928225, 281221045, 480959373, 239738628, 779555032, 718972140, 669065105, 347959290, 463033055, 288675154, 182108163, 887406675, 593748846, 327070951, 599167268, 439409543, 536212658, 760033648, 988149342, 60862725, 501623211, 740504372, 237638807, 676410268, 217991932, 758140619, 27020468, 505807149, 27208637, 585516980, 925154520, 175190384, 68111890, 433046420, 332716443, 472512866, 194589861, 585026024, 610466150, 12910510, 73117624, 685046031, 837557588, 467992975, 49292820, 80183216, 179823131, 893260528, 291550700, 703400467, 603860227, 938746910, 580062755, 232971218, 647270051, 318212986, 985672915, 31483896, 918766135, 443529308, 26345647, 59444160, 332588929, 974975571, 345412933, 156384526, 16637700, 584511665, 326708326, 293717261, 792688462, 652060427, 988763708, 446506558, 711659249, 691366773, 646312324, 744304579, 103342771, 871648508, 372770310, 239216371, 90395562, 233309076, 707941948, 66208764, 188210450, 650309504, 876852057, 870729756, 296917990, 603910734, 476983205, 440850211, 45692851, 376826693, 196353820, 359629921, 958741343, 484742230, 464202412, 414226060, 953622736, 9668708, 91798511, 876488067, 574478976, 873145477, 674455882, 338061058, 890110584, 981699591, 389588987, 684119570, 458824230, 683095378, 835139700, 636221257, 480883616, 59001936, 902398414, 96660671, 897963252, 865365468, 551405320, 242433346, 758917195, 336425081, 123765041, 579902013, 569006542, 902021404, 461279222, 113724535, 953949439, 22152780, 622859405, 656197525, 320683838, 707211752, 570054841, 386606981, 23636763, 463410775, 990347838, 123101610, 981671043, 787397595, 576144775, 684282691, 167793136, 33846832, 102516335, 698440336, 385863393, 627404856, 936596636, 550722818, 525287792, 423432271, 625589515, 621342955, 471312692, 683813515, 202351881, 377569084, 913280464, 139142690, 346139970, 165361999, 574215604, 998020423, 853373936, 967645388, 766677419, 941747588, 536256626, 52639147, 898741503, 226171942, 878435933, 558839085, 475103142, 231635980, 416123409, 312895922, 259517847, 346200557, 389731328, 441800037, 469504306, 483611227, 236975707, 815896781, 341705680, 768403390, 850887429, 50373356, 444752225, 223097880, 623785860, 341545584, 26876772, 576889666, 743416825, 310679034, 608288964, 654964573, 364403710, 246490240, 614379156, 678277135, 694031500, 308736212, 584462220, 937659629, 369371534, 615750398, 125143847, 856786516, 845366818, 810627472, 385927160, 471058131, 16889435, 951769878, 507267662, 568662909, 600697574, 269540758, 386548946, 470025805, 54964530, 546166260, 527015823, 583083782, 811438230, 995412925, 854867587, 137629528, 268519037, 24855674, 193878312, 128124408, 955260183, 158586837, 181054348, 337716042, 863069368, 327672245, 133421745, 550945464, 426683830, 976469081, 802948504, 59248179, 705158469, 371752482, 63243953, 932135802, 828197671, 581028759, 657786220, 259797093, 369874638, 639952680, 486980567, 426074201, 9694299, 271193227, 339345887, 188019278, 612871790, 632328097, 827451257, 156782973, 860358856, 330222703, 119082357, 57907730, 336432596, 907938532, 380825093, 729350678, 516669878, 895998983, 655163956, 54160441, 855586596, 940264048, 458865480, 700008273, 516925482, 33268354, 798416813, 236583694, 781214745, 123809267, 936794800, 974221454, 839827487, 208048313, 841478706, 668317915, 168969787, 533088232, 345451628, 742234324, 436263982, 957377208, 1110186, 535814679, 328659434, 806853359, 723875855, 653178999, 111812242, 219631107, 728795255, 237665590, 527131229, 639092739, 497786788, 599361544, 983851611, 741512798, 799622070, 309073795, 492326008, 825906953, 338705132, 394678991, 54464801, 837840760, 828467449, 743739487, 967919506, 461394528, 342801783, 527282472, 557233360, 905219966, 987447567, 783103605, 15849043, 451800421, 781132897, 530409068, 517047318, 971189502, 724386451, 893661435, 692515743, 193482547, 450353353, 155317193, 540506892, 392312122, 661867869, 561428434, 442973401, 620292811, 33141390, 626338698, 553196276, 886912742, 628651593, 972455730, 328823822, 395709700, 209780908, 600139559, 122937301, 120904250, 673736304, 927527930, 905655750, 190934758, 477999721, 123495324, 127777124, 414813358, 155945719, 16996597, 304701810, 183841978, 997100168, 431320448, 766351223, 815536430, 14760084, 930101845, 726216218, 487973365, 246843786, 986307040, 896869059, 67585147, 887349227, 299230293, 48519599, 16455283, 187061373, 732326767, 732731301, 645564703, 566695818, 619709365, 218182149, 992760734, 768383662, 879922784, 436591947, 816506115, 956725210, 822390656, 10400704, 901367326, 243133670, 213635529, 805974459, 458034469, 642292207, 351812743, 733206797, 582699104, 193164290, 469753942, 487646083, 928489790, 71355243, 601703529, 59487782, 223250637, 316091336, 909602380, 367776023, 517212118, 734066926, 755793342, 230926363, 935066144, 320516267, 271596571, 829892088, 350532402, 375347569, 721323481, 320597429, 438090035, 979006000, 287752472, 902139555, 615951992, 244267652, 106197645, 71386984, 472322842, 639757818, 179178891, 48303448, 795457373, 308048606, 689300821, 732688828, 720552288, 211277911, 139044229, 512147992, 30943221, 284665463, 701866101, 555381389, 730853665, 355718722, 775191121, 766848225, 217112799, 208895234, 543267602, 91207009, 21670734, 863706519, 45324419, 990609595, 875637612, 110052888, 498034983, 830661632, 142492015, 836503966, 659714897, 150345973, 460445895, 691218058, 428156494, 141972039, 519541959, 120661920, 34777676, 128923966, 347123396, 560371839, 817948717, 592810688, 269197059, 498570751, 707644599, 779519345, 756303121, 458983360, 672112084, 804705149, 943526771, 824474940, 66417624, 555672315, 416722911, 857394972, 847267459, 823903222, 31332923, 506806037, 646035379, 560485056, 734175652, 965575573, 972668995, 643672285, 794000003, 511233539, 889327001, 512038200, 980282659, 53735454, 921932290, 566394330, 900612851, 797298475, 430965391, 793132423, 414534895, 26832690, 949431703, 244675316, 532051239, 906079734, 160143767, 826318839, 906455562, 996063126, 739664446, 447164169, 453760442, 178282716, 964571580, 537939081, 999751539, 334282304, 962829857, 27204068, 823929244, 829206293, 672434017, 19583449, 352356504, 394610564, 288220857, 873645241, 165616602, 848172354, 226579182, 587420007, 806442802, 350371954, 286573521, 442195411, 714762620, 362678552, 286270848, 995621892, 567840268, 234549288, 604360588, 156661091, 186535369, 44715691, 496072457, 446476849, 453714096, 899027370, 332400886, 547544294, 38121894, 670767254, 843379714, 277436621, 213106027, 769637194, 244206956, 672217097, 497416684, 196550503, 779094537, 991592678, 430572353, 956726573, 255722013, 492632530, 160784343, 597942872, 396886439, 369250219, 276330038, 427202307, 402294210, 205044865, 144316057, 488359890, 715894528, 348316179, 672096560, 430045809, 116444265, 8125001, 220079396, 703654088, 901027384, 678177506, 609222590, 395500724, 163200428, 970714386, 744437616, 527290402, 972082689, 928223917, 256233468, 276230348, 310754042, 601518231, 762068986, 989757642, 950686665, 685759001, 463409287, 538139210, 142322332, 623261292, 81876593, 512312867, 37079294, 744218197, 161974066, 423893835, 986125357, 102294729, 71391802, 684241854, 381127850, 706854340, 791582775, 29330935, 277297411, 976457695, 797477017, 941473378, 1715380, 298261315, 358924569, 980801407, 895089604, 279948622, 549981042, 948840563, 331190361, 809895708, 956649602, 11964419, 28717875, 227219115, 384581914, 823677401, 745901571, 965548356, 122019892, 402086856, 600661758, 510058497, 207036831, 681805364, 95138565, 401638109, 656627141, 346017913, 993472589, 668407772, 855732586, 360559642, 65347012, 335933824, 544389701, 534974199, 588616772, 452732839, 383198489, 917375811, 545158962, 882326519, 185117937, 539317611, 52043606, 117690226, 835966722, 735379719, 318784195, 682975392, 968726415, 708487062, 52898165, 704341758, 403525525, 226820372, 841544087, 28342187, 695101023, 971578059, 72673562, 928204709, 301630124, 661286368, 253315286, 812332684, 351532457, 730482184, 838592237, 815159027, 885160389, 795211531, 519702899, 171148334, 392812287, 749348781, 489595904, 129314393, 649607515, 316893021, 484879544, 832710519, 485007178, 587458305, 270455999, 621010630, 612157367, 366849385, 250960712, 585791778, 72122472, 467033047, 879997759, 824253444, 781163871, 913784169, 911188694, 329850495, 511273112, 434791745, 880751249, 217988935, 448764175, 584925978, 604483962, 216604832, 333376536, 770414110, 383242431, 517738689, 528904032, 462350720, 579041537, 491311010, 382526648, 162908310, 908001266, 609037815, 924594361, 898094905, 683777431, 316009717, 858422270, 408388801, 803648741, 671482178, 379723257, 478643747, 686468072, 445733330, 887716107, 292285561, 32645549, 141799647, 581250222, 172694454, 676315991, 134586425, 354543947, 819487481, 923303156, 278664763, 307409940, 114812675, 487058643, 332151267, 293053543, 746157714, 52473428, 15688153, 11984325, 371805338, 256899808, 504544386, 753011762, 155135618, 495830682, 141399647, 395809298, 819486230, 936011423, 112069368, 155767716, 978106564, 4438516, 55819019, 436164464, 187926422, 875080635, 783202522, 111287968, 504295185, 561339375, 159518267, 843855310, 547740586, 779063885, 46713513, 282768101, 676508530, 382121949, 164282310, 369100320, 901842418, 643453352, 270285135, 336030013, 553596126, 786930616, 408568670, 986847447, 153121455, 576106045, 717207372, 178526095, 489453455, 412569149, 535645878, 524329057, 849303499, 650395386, 829576301, 120782905, 487290673, 513497510, 938177977, 376774767, 981284094, 294989156, 714682795, 390123931, 15840019, 320536568, 674392886, 90540624, 588252903, 347708451, 458198307, 412847727, 387024664, 3102503, 718794904, 431218012, 991332461, 91365061, 230045512, 829318257, 74876815, 489489970, 349953731, 275604142, 45283404, 287164205, 11332661, 566066088, 464860256, 851398367, 124635259, 1963449, 445493403, 911700403, 596220626, 605795918, 470932963, 347337790, 413903182, 539412968, 628098853, 198113280, 923242711, 933779903, 20883586, 312087668, 212169861, 184431919, 559190778, 876145897, 131585735, 679613929, 146182247, 420124196, 351343802, 258084517, 631650722, 158650567, 485900820, 366756110, 907861052, 387453703, 874083366, 358876938, 967467692, 306077373, 997380844, 915841661, 266417249, 407040203, 968712084, 585309788, 225975656, 763631232, 234989985, 345564835, 282061551, 51654836, 276250849, 848605762, 178978785, 433246476, 689234707, 295664773, 450135365, 750292992, 754390198, 323466358, 993188693, 679273915, 437361702, 47926309, 69451443, 735957761, 214741999, 391523547, 316426051, 493237366, 343607848, 197784067, 365191294, 395041621, 621128669, 942194910, 651532947, 6801582, 815602590, 122440176, 636618689, 788604690, 898709224, 187036018, 157544093, 644248363, 709819714, 688728718, 333839002, 680001957, 431405663, 414982595, 530018225, 277309367, 380442364, 919124748, 599463194, 165000751, 838220785, 506313784, 119136927, 442973318, 278337418, 382289242, 457123201, 163007535, 474340551, 282685821, 840530679, 217011119, 70591999, 743120417, 191241602, 741747576, 891923777, 479370460, 820208000, 274355653, 750067061, 623157727, 609114587, 799127879, 351832825, 976059483, 416627341, 626019223, 709948835, 8578023, 646081734, 89846284, 298199448, 40374889, 518343840, 177425953, 892080580, 370380746, 630741734, 53450520, 655219389, 234643912, 329203230, 631751166, 68155004, 691552488, 181629348, 505899929, 690045209, 775868661, 941259886, 373406796, 610956852, 604335749, 917390499, 79230555, 427307620, 587770737, 225634335, 576348713, 586588109, 615551056, 673296238, 151042961, 429506052, 523539815, 552511637, 535629099, 369372989, 941172733, 2090222, 13921866, 527204011, 97569039, 701582056, 240079401, 62443559, 785288774, 270545839, 820167451, 478347131, 783325535, 483654778, 825077992, 889900812, 929452912, 974405871, 995441851, 211395139, 799532995, 229490155, 336423220, 963466354, 301163291, 30512721, 798890691, 860531218, 402772108, 227402706, 729300602, 752674649, 91848345, 545468505, 642669828, 206318872, 750812864, 346122959, 520058530, 777102871, 560551587, 294625228, 716444316, 438575736, 631222800, 324800425, 460085085, 712526188, 594597070, 474256043, 619975198, 122146423, 222467314, 520491492, 990732867, 177156718, 263165837, 387076934, 850980806, 375304434, 184274804, 1075682, 85093661, 679444195, 881141577, 412440651, 886945743, 11066051, 37623010, 961706366, 70985778, 282728280, 525321752, 440013080, 789288542, 897226253, 542448316, 600265937, 998756338, 997749442, 305950189, 302728067, 734881415, 982171577, 693954949, 882669315, 832633785, 139742123, 360176193, 538482997, 795394467, 53065657, 119947534, 172127206, 872821584, 918076581, 598314851, 798570522, 335127749, 377661087, 423902040, 428124001, 519346027, 364562640, 281983429, 303432544, 50384318, 543104967, 153576625, 959592183, 931277334, 963487150, 866793828, 589818090, 744732224, 926965501, 180568513, 915874078, 865313287, 927466338, 773919956, 426297144, 19110123, 885927841, 310299181, 130482613, 15579707, 826531372, 849795174, 440045343, 754602435, 645952961, 147639160, 816043211, 749375121, 778671446, 962317574, 274033048, 55201385, 442721091, 173710580, 895650331, 482071644, 603611397, 347623390, 183749886, 795699968, 492987625, 806353803, 179886205, 508913127, 611494436, 858452782, 111898274, 667790761, 183956392, 577930727, 709894472, 715175592, 480632134, 264373534, 292617867, 563713379, 866237010, 603038994, 98721347, 202294313, 226283251, 966108714, 905455721, 962326248, 35640210, 518677259, 942042091, 368943110, 126627987, 872113700, 491415818, 706882162, 915004630, 718528132, 138124944, 261021165, 2953277, 356212536, 737143249, 219150830, 720009978, 749613942, 643870878, 355899210, 596740472, 359141583, 480907464, 973051366, 848604978, 724114931, 71546572, 171447580, 660411592, 698119329, 505195580, 287915474, 387257050, 566705338, 856026036, 212042779, 854516891, 257434755, 528218226, 709561413, 863184776, 9760162, 972533547, 521925442, 713272305, 51314198, 912851604, 763422830, 98798550, 713227807, 166083369, 660579678, 524581529, 303159974, 909233965, 192729739, 620334425, 162042251, 281087190, 505182342, 324550600, 63652874, 88392599, 570275246, 658077976, 617349892, 477685909, 435699931, 186734457, 600956222, 620753147, 244749152, 538780928, 594549620, 895584864, 910491926, 860706147, 782041800, 33512696, 422443429, 161750247, 530681598, 514164066, 97781991, 235991305, 101270608, 503874149, 799553656, 840441287, 254060415, 295652442, 688304525, 923203875, 506048901, 35355740, 251406644, 944638721, 261433575, 892880884, 921703105, 896034291, 517862894, 723544685, 879890579, 267998625, 67029882, 822393469, 777918855, 408884940, 161134822, 143568176, 930896719, 807544743, 264661683, 447289932, 888382790, 420296510, 75388557, 378127971, 571373182, 797820930, 518888253, 631920381, 395158190, 269502137, 710467076, 944017187, 43225846, 105772441, 725347416, 143685116, 747333795, 402237361, 886077694, 875369994, 438631594, 731882348, 929763604, 465675535, 760876096, 518442667, 866965020, 959947186, 120892337, 964870909, 199366651, 273611397, 272232826, 992621975, 907910255, 954033455, 765288115, 560996854, 119148569, 698574150, 517105878, 699036728, 700728034, 671007695, 656845369, 382198016, 389330565, 637728950, 306546441, 7271873, 446894942, 704717757, 473587005, 431713142, 604380488, 711779183, 718357106, 222096140, 810852600, 566168927, 632166745, 369893402, 486584219, 586216005, 804173467, 211902237, 934608568, 940634990, 313567077, 775134791, 917063541, 590907946, 115966977, 838584270, 216916074, 936609966, 128697791, 35266133, 373553882, 645197399, 583662426, 376770982, 179998897, 186616617, 766828661, 906301234, 348706172, 971526097, 699046886, 768173214, 652141696, 181261651, 730504158, 337021555, 428137212, 417457087, 747090173, 804002573, 838436162, 183726095, 165117985, 257206749, 368939264, 605670574, 14495713, 355407764, 385141796, 704278062, 237326657, 103112808, 171645199, 151054012, 808846755, 387088778, 27659050, 850553751, 963052316, 179040094, 78693456, 166257905, 355245049, 655385699, 618119079, 327823836, 493578377, 613645799, 605043587, 389622588, 95617203, 285369330, 190917307, 568773060, 442052376, 259222661, 695151050, 341006475, 556677732, 382957251, 401863770, 299706998, 964161085, 420535153, 671856416, 664536412, 132619212, 634980493, 812293329, 832629388, 458918863, 926921804, 667603922, 69647881, 46165157, 243679094, 744949625, 61547936, 272151845, 430390665, 848952986, 28398255, 399736392, 939073940, 394961187, 442850890, 209891948, 99265190, 632353915, 902148277, 679319631, 87201188, 649423625, 256528209, 615349413, 928095961, 296015573, 458171277, 778376998, 846640489, 760477800, 709287283, 571962750, 271722167, 348127492, 794349925, 669103181, 315588874, 372638993, 431061930, 484450145, 374053174, 515349381, 919709059, 336270101, 169027053, 25746484, 798430781, 973283554, 280120400, 845536647, 580446021, 59574603, 810103583, 526656339, 554030093, 242155649, 52699572, 329702418, 662848945, 575530042, 419879023, 999196363, 363533383, 502231407, 68963702, 76900829, 772773315, 463336072, 13968566, 743335598, 782611399, 884069480, 38937913, 794584576, 655121205, 365500420, 798387366, 594909145, 94238684, 353274357, 184742741, 859320841, 732979025, 934003691, 23131118, 967203348, 942844010, 740183722, 360561454, 960561466, 789410805, 698362847, 594334657, 197562286, 356542925, 224851988, 983352325, 107961643, 368407384, 187850029, 242284104, 587804769, 960193973, 11780117, 714978054, 196483465, 509567610, 676622662, 909726933, 799606360, 954523315, 240147568, 735343598, 887329017, 641626756, 773562515, 486636574, 650761969, 413402718, 610735395, 903074768, 354814774, 430770801, 262882253, 710296908, 728199561, 27610977, 807889318, 227888115, 135992331, 930489478, 55006926, 60625662, 944213576, 607342651, 135648669, 105501379, 854630596, 124118571, 891953294, 98197797, 811484885, 703427254, 603131876, 492489809, 878206696, 420272289, 328174767, 332448171, 786569087, 12125196, 426700492, 461634132, 266615446, 222633337, 747295647, 815219309, 934021085, 1649813, 282144754, 932583545, 892185267, 523326811, 187972589, 343674222, 492739313, 56802419, 808610237, 339157766, 931622971, 143946055, 14803194, 155796618, 185678792, 231058825, 743554604, 332959171, 20807711, 822419479, 620686820, 877632356, 896779906, 399001590, 742072242, 526890691, 838112423, 384937656, 23587663, 506962143, 122124683, 688785158, 599573808, 989802235, 971427279, 24494333, 925621351, 865610779, 376113574, 220215126, 399070429, 337511790, 368682717, 220843417, 292202397, 404866375, 416349321, 126913987, 581074776, 236062766, 887029175, 446965845, 256902306, 56859184, 823665560, 231163738, 637063317, 951143706, 775477003, 448845228, 607629874, 995285313, 737411335, 576760556, 529409807, 652385687, 953671499, 260795169, 791435026, 415164476, 200563601, 85516905, 376110469, 945056465, 296974562, 386974241, 902620249, 110589195, 275476719, 79804435, 549651842, 672223746, 932033129, 412372942, 907731607, 550956725, 87730116, 796286332, 246059213, 551093840, 909421417, 769095812, 199646402, 431815895, 872578086, 466766900, 105165609, 910274094, 864194332, 429518243, 558244711, 185581009, 1459033, 668290837, 457878977, 356837612, 38333752, 386278655, 682461001, 130504589, 85458580, 904507822, 599561188, 811058232, 920092785, 574350225, 95256923, 715537179, 807977021, 473485677, 817508611, 84975428, 131431163, 31527400, 44356485, 80110238, 362301145, 784546624, 150854264, 587033087, 625886499, 219240582, 163114601, 300068949, 915288909, 117898693, 682220134, 718227341, 45865928, 533542239, 97418962, 688210957, 336158957, 894980731, 918933525, 636953057, 234533573, 415790255, 131333519, 514936968, 67796935, 333858829, 156012267, 37929080, 22430115, 231835604, 888181598, 698192406, 613476804, 397757884, 81999390, 93166844, 664134865, 286707669, 860445545, 458530685, 399580661, 815844401, 168736551, 595731595, 952739897, 733682357, 501924301, 733646742, 829060957, 76790121, 123212295, 586770557, 79115397, 950131470, 541823972, 368607032, 651813028, 512081343, 279330770, 626955937, 770083248, 890313443, 993883719, 594190183, 728326140, 512405987, 137626548, 4950947, 282792490, 648433993, 730749979, 799606989, 187251027, 44750328, 549132307, 5965217, 860194815, 21747773, 489439535, 353095515, 459367871, 82284878, 725050772, 430153210, 263127066, 89306804, 464723183, 76639974, 734232088, 154867710, 331733378, 260037820, 461529987, 562643485, 620308058, 747818733, 241389377, 950339829, 177456424, 758758230, 349396489, 300290821, 171431956, 637846535, 621130306, 109545162, 765880298, 256614984, 531023592, 531350192, 634647876, 315177022, 269737514, 654362177, 584554132, 935659779, 803757545, 590032812, 210947160, 320509829, 380895904, 43266282, 126360311, 466707605, 974304243, 86800965, 289581424, 62891322, 505406121, 369126990, 840242200, 606310639, 891197577, 604302301, 160169347, 301555685, 963983406, 941040402, 999346623, 603552706, 952387052, 33600473, 750686664, 764006077, 718365435, 888697198, 392021572, 38333667, 411633606, 229075439, 486812782, 306988391, 467684116, 228998273, 113138233, 48971510, 505541580, 791427652, 347450819, 430690122, 99606085, 616580426, 409476123, 921779433, 421270392, 935173164, 780055680, 300668809, 664297052, 383568846, 799812320, 185893924, 686755718, 831436073, 803074804, 240230128, 952461132, 688082562, 222966480, 52971856, 620433772, 839168109, 914529517, 416477460, 557397070, 855530743, 901839462, 962755639, 957394519, 795469425, 601913284, 592654854, 209887706, 877023855, 84580640, 879305638, 763868365, 584676298, 683833022, 534341577, 503744644, 81604307, 56994505, 656049735, 359741017, 770838854, 762822418, 338768061, 338112125, 923589714, 645890974, 623755076, 982776005, 927839205, 953556015, 61550362, 221090224, 753733161, 608468332, 719283707, 363393995, 781894834, 522203703, 103337123, 518538776, 460252378, 6703722, 173086663, 405927066, 609460951, 218697993, 464920851, 474306682, 392664801, 333190719, 597451584, 553660081, 60101300, 450879133, 101283039, 794986302, 180224104, 378529234, 537303939, 761182754, 296419463, 246120652, 644529209, 991614265, 400782111, 241278938, 227434277, 182879856, 246590358, 637584994, 564246159, 646648731, 73162070, 780367359, 848642803, 990431911, 830015574, 719877927, 671492442, 744213036, 292347524, 257749323, 150345015, 315895051, 116522907, 609811398, 150048653, 373085867, 654971234, 10811152, 253170903, 472933316, 513736859, 76018947, 911972089, 747431041, 229191449, 4151851, 915393401, 696194656, 533502905, 866169901, 174639286, 752355192, 271402469, 476788283, 863888160, 980697299, 348602904, 612798914, 250028017, 482322031, 515257467, 633400162, 31226526, 503706386, 489420337, 512279587, 828373761, 81119933, 627420648, 919520914, 652417029, 401650272, 697455223, 339316391, 889351740, 594358564, 976836394, 410044012, 268376410, 339712004, 830463115, 901731331, 887213128, 431539583, 296471107, 28764599, 724058855, 178530326, 199229070, 56225206, 856192057, 304875187, 463434468, 534298164, 278355222, 594532285, 396903386, 597675076, 730173165, 975762206, 916186169, 454118359, 595005693, 138699374, 695981563, 402618575, 173448684, 663368961, 690469469, 744374114, 969825234, 446641949, 628737352, 978196586, 786627694, 441198363, 195109713, 483471005, 618401622, 413525503, 689044148, 298968054, 616107891, 305913812, 223615140, 386240139, 909905368, 218556450, 661526242, 144267626, 231913018, 570036600, 106144578, 910282667, 882560955, 900114029, 721515085, 10540152, 844570388, 916285139, 648122708, 857239550, 985882717, 924592347, 392006604, 28563510, 714908630, 337014883, 641996577, 556085268, 621770580, 688687846, 916292571, 31166477, 165313313, 113876627, 184844532, 84795352, 622597317, 729091618, 638954075, 452904557, 438134588, 133023349, 618985503, 154382986, 704058159, 746831786, 362079389, 104647033, 408139576, 49828097, 256682357, 113726514, 825225586, 930736033, 933895937, 547947289, 831639114, 206066159, 843838342, 295874456, 792352410, 220454884, 707735293, 715598197, 434180805, 766668171, 250026588, 351941588, 921365405, 5176636, 494129692, 801316591, 457373411, 872671464, 3457032, 229854274, 638853650, 457232007, 17201753, 908213161, 583595508, 801535922, 659451082, 633749966, 370498692, 968055123, 207376295, 177088688, 153901322, 704479150, 719247504, 433743161, 142925962, 127071653, 75702413, 44263703, 870844802, 174801872, 900357460, 208559660, 407312147, 922052382, 549576913, 367567770, 292791884, 186018523, 330706968, 599115138, 333657347, 986413525, 199423201, 925547609, 686205982, 168559577, 911698482, 467691898, 188074771, 226884232, 263070649, 820188393, 152305583, 113325797, 271951656, 422912974, 153063603, 888525159, 153410438, 520769737, 895680012, 83672492, 549620649, 889281469, 357857102, 651385354, 391802241, 347525938, 9049397, 499983672, 311239238, 621520154, 62053113, 372061953, 592209262, 328781503, 850024801, 390106435, 547676572, 752544733, 91851287, 204747180, 203738888, 10534535, 405232253, 47330170, 577156789, 828791107, 438006744, 388904034, 67919658, 205650851, 990756422, 89313017, 50185162, 447944849, 452233180, 801678040, 695784447, 122092194, 844188964, 981411392, 406528605, 904634013, 736072801, 117451239, 480553779, 606969115, 7660485, 661736490, 286207149, 203922061, 854019024, 669933625, 836796578, 760177461, 154768791, 136782930, 474204065, 937101931, 418819766, 533374687, 973060604, 931942520, 442070703, 10411580, 122886922, 103445001, 589282697, 557121144, 971857796, 488626069, 766059726, 683166968, 868425849, 916938746, 436005797, 521083107, 876634009, 94872405, 723840239, 458645252, 650815963, 782713257, 419841840, 92671052, 29019810, 870933829, 892864200, 899510797, 80917331, 429465610, 840209867, 632358759, 295107748, 647195128, 386361520, 279902987, 609293793, 429297344, 830950916, 506771755, 741786506, 776941156, 116799968, 65673826, 583830523, 362442766, 95409084, 359710176, 227155077, 30974833, 96814427, 781700073, 892059801, 320189274, 379609319, 427145815, 775477230, 866407617, 233290457, 309186701, 621018670, 788831435, 52451054, 676719138, 831250943, 100263485, 121676377, 285825851, 846904512, 569513545, 645234940, 207574621, 794020957, 130495790, 764849046, 547532751, 192331004, 215543304, 697361700, 733001895, 210942023, 938210775, 403970544, 61075344, 125530267, 215538117, 471647064, 577873731, 634733937, 78555213, 173988352, 277579277, 363718899, 398847690, 751060058, 108073488, 511467184, 419380969, 661780185, 290840921, 178504322, 968770020, 303549406, 148274585, 234878111, 6118094, 257398429, 365977072, 157585749, 894732414, 182853115, 386196181, 218918168, 988312900, 877368229, 422800491, 451076106, 219781076, 689229994, 146230194, 365133843, 357904704, 98714570, 264052362, 375104150, 513337607, 106522077, 291822883, 503465607, 9281268, 918102778, 23193853, 742832402, 791391017, 733496587, 75753114, 844163009, 153644059, 455751026, 113550849, 265051012, 636717211, 257168151, 135069187, 780067714, 588720875, 830646389, 720534711, 188305221, 292638272, 867394522, 474709905, 723826475, 435940373, 386237186, 857581505, 884438767, 568018064, 603983720, 675695296, 445664095, 279318008, 891879890, 83967172, 892012077, 929447437, 716233964, 284153720, 904606453, 689861857, 149971696, 807490747, 765930205, 233880436, 889888143, 14165940, 232928332, 342187146, 57294117, 610236782, 163038799, 401797767, 817309681, 976136579, 939252636, 483439830, 495317983, 461949774, 848866902, 253282145, 955319908, 955295553, 596914489, 396601429, 917677840, 101729384, 406792727, 719177690, 622775559, 549494235, 276522839, 459259224, 204339072, 88578706, 311401356, 590855753, 498296146, 632881553, 662504348, 594293016, 477142145, 606820793, 52221468, 407003888, 452212564, 703919818, 490055094, 641670872, 627269146, 678014728, 557637338, 870854627, 27201431, 467969358, 965035872, 163465930, 185217223, 521387193, 104674368, 115959770, 151788009, 358389709, 694942652, 143284789, 674814044, 1239279, 911002015, 250436652, 895171212, 155577315, 316079626, 882904146, 274140370, 947170733, 894021782, 271529293, 124258197, 902307147, 707582227, 948257091, 135800781, 502858509, 175374468, 390240123, 122727863, 181938517, 420277334, 670101042, 93960377, 891681853, 968238509, 657388851, 762341575, 850007856, 243356863, 938275932, 1308739, 87903342, 960187719, 358685344, 830365509, 413876777, 934416953, 268927227, 62397924, 386597262, 130397182, 216425149, 132535453, 813005338, 571101081, 306708748, 575160957, 331364536, 926923493, 406772732, 992708007, 142875105, 761025232, 158544401, 36331717, 900477282, 35752950, 225149431, 638026580, 503544835, 701736576, 864466017, 440826527, 419675156, 348322470, 905359955, 186551312, 566281824, 192798872, 358579334, 677517601, 872451888, 791936265, 463950426, 179176733, 666792940, 473266689, 659914939, 78840155, 776061453, 864411645, 984344890, 748432029, 251025964, 161810148, 67399511, 282046224, 136639719, 232856819, 694018420, 163237833, 83047209, 486432225, 922229753, 63200063, 349021081, 576795465, 202679317, 254098679, 979751684, 399951019, 771700979, 741504714, 354993128, 999327552, 281694888, 882291661, 11441659, 367395361, 338050502, 632179771, 445779997, 977150062, 893725530, 792514435, 60625082, 466830927, 86577403, 316751559, 160785298, 306329291, 107919601, 443113822, 269122688, 514186159, 935300542, 916918483, 219554495, 459239247, 5245730, 881302929, 82496678, 853199897, 129415869, 490544495, 409351926, 698393676, 623316374, 778100963, 916595870, 692068128, 563690892, 647939145, 445414607, 654970851, 601181415, 655666680, 429649637, 814481183, 245502108, 628676980, 150549193, 192983543, 636177605, 230831724, 363289369, 612612713, 457373640, 590608501, 361454896, 359405474, 649487108, 71544962, 781230470, 28429987, 62175570, 601475875, 328236423, 602276102, 806858985, 741084795, 829902926, 277398985, 440162219, 81021065, 362291021, 13023799, 98899548, 504488196, 890865532, 136486529, 542420035, 722984135, 898308288, 81359359, 471471410, 789096905, 38216412, 692793827, 793688227, 500533811, 529801937, 848225307, 251667600, 192147735, 3007246, 915537201, 872911608, 226644688, 14413862, 600615686, 607322809, 462148590, 94681102, 228827058, 945333710, 522633724, 2800435, 106639178, 93194650, 795187422, 606498501, 871552227, 459264544, 705050983, 788700666, 487427743, 193102230, 239325148, 598527645, 12300905, 601555606, 760057967, 53154940, 919537017, 914098367, 829563880, 219108469, 608635284, 171031739, 21795820, 423271773, 17434004, 167647981, 123924756, 531303221, 935219164, 691331091, 969498099, 817192080, 923842401, 86970019, 528254321, 953331954, 617842221, 222880428, 354075802, 597941639, 559192431, 272021372, 391841539, 709463782, 685510583, 787579771, 971666802, 8486188, 337275300, 314359540, 348885656, 681161658, 843411854, 514471656, 483748919, 518804007, 493105979, 118268150, 956334745, 75152856, 221818719, 939987501, 283466335, 402114091, 711310193, 560483240, 251077365, 92716130, 102190167, 745676227, 16356454, 520071619, 85692518, 566595254, 601489587, 619919282, 682252635, 637954114, 467594762, 239776271, 662396482, 265330959, 81877289, 571882446, 159555810, 209688787, 671109298, 660508934, 550647755, 303790056, 536958434, 198701988, 739853975, 751975819, 668020050, 772092349, 382362073, 895106001, 368584502, 18218262, 697193689, 444233929, 175133942, 322631120, 29021482, 834938952, 296374755, 488969445, 908093516, 655592120, 787405563, 998104978, 320141749, 505661819, 721140899, 453296934, 211108288, 12910787, 702002704, 337285040, 102588924, 287147437, 941654887, 835651587, 16262412, 991319671, 416664647, 440000764, 110463574, 692036691, 906055088, 22576170, 349323092, 783800604, 676880257, 683514739, 527960587, 396714553, 341444068, 163388000, 118570074, 246303317, 41687266, 231931991, 335450423, 591315587, 603942992, 778057282, 205204166, 543284369, 145128379, 685176751, 698845300, 675959533, 894985831, 67553575, 385524002, 164668501, 377952464, 548170702, 689327374, 877214568, 944432645, 655046962, 191985358, 255883305, 934099402, 523131158, 734082437, 566309592, 125287299, 979803282, 497464827, 613454275, 738337385, 155768714, 411752781, 551535263, 351467499, 349960486, 685970066, 731336175, 315481812, 356050501, 14068429, 79378016, 28424078, 714649649, 812822791, 187244761, 283496008, 273208547, 809019360, 29092262, 296747464, 344413447, 65285761, 557202139, 261230648, 188313309, 907731581, 15670765, 299006338, 223924089, 23622583, 912360124, 742803727, 773099710, 696766008, 756002840, 469518472, 890885646, 93533139, 56141553, 395088325, 589732660, 971998529, 372952269, 994873207, 129319348, 479033085, 465624380, 307715502, 485044042, 974171643, 921269786, 203789637, 275406141, 260754521, 144341108, 342982297, 333558859, 150092961, 134510341, 224039329, 13333337, 741867951, 949180756, 299454708, 922809467, 335787551, 215808969, 625397722, 880357514, 329171067, 238318324, 593870749, 207809797, 621501466, 467306424, 434315966, 112061917, 408324161, 408901346, 538724175, 941205997, 494348559, 213700612, 459191468, 923945810, 330071318, 441256515, 151423433, 61144685, 42614285, 115914059, 783183506, 599848178, 84860525, 210164540, 934124636, 532421743, 344981500, 316568650, 913753597, 793588939, 137527734, 303307995, 700777550, 751566368, 349011378, 609030288, 961576516, 839931290, 458030531, 176000589, 846693764, 364463686, 270112941, 528191190, 279939837, 119150048, 900612910, 71591905, 989224283, 186112462, 253011126, 361910227, 55990184, 406624542, 646976930, 413633093, 694655683, 553387721, 832947088, 885371600, 718549145, 43760113, 652159805, 777865114, 606340268, 756635452, 417908132, 872102255, 673604196, 121475857, 996995866, 90084422, 82163067, 321546891, 886519111, 512321124, 439935412, 172088486, 21954582, 919006252, 963341274, 186529612, 737201796, 671391054, 748124443, 345654799, 220668039, 723296497, 127533436, 620871231, 754875554, 887896940, 909790807, 791869836, 526092224, 949959776, 220891500, 260424634, 632785690, 719414707, 734558242, 678189035, 431063386, 227778591, 964451987, 841216668, 934445931, 40069324, 978428299, 361086276, 531552252, 550625669, 64001398, 438090843, 36788346, 345187846, 957726930, 432598534, 953589580, 511665175, 791138119, 646461963, 897423520, 86771705, 293358876, 940335753, 627532797, 509296561, 583665704, 220525631, 661788948, 454967601, 711830780, 994987192, 467061018, 166760051, 726057632, 816848295, 536556919, 829095716, 734142940, 624172470, 98764287, 282702256, 175065008, 972856112, 739040075, 741418424, 221648518, 222183883, 666625763, 714718011, 667819620, 738914349, 178106337, 513391739, 322444203, 910679066, 552394284, 900729981, 446634352, 444811951, 720356061, 883091543, 797555129, 161763971, 877159255, 292248732, 202297966, 309500308, 97947601, 607401023, 122439406, 357553800, 985337904, 305243092, 934663731, 341058352, 5894762, 328358556, 544697609, 323675764, 562309715, 835636146, 755174795, 172445275, 309923469, 8526763, 193994169, 725124284, 614465683, 735158239, 949635501, 7072127, 380715073, 509272014, 728262354, 42025788, 481977651, 523973349, 493409320, 764019736, 288348893, 652817133, 125101166, 759742210, 800418066, 463943383, 618320119, 806845915, 758437539, 186760236, 314459260, 516340016, 631144417, 949933319, 667991806, 608901385, 124477392, 64867668, 348821489, 865879349, 996868589, 339589327, 550013360, 520686347, 134931860, 662253109, 401887503, 957289711, 511110768, 743573609, 900891356, 196959721, 534870194, 408743442, 910546584, 129440641, 944066685, 389715349, 474699923, 819580069, 605702568, 875168444, 339656040, 687697235, 375269635, 751663609, 595063043, 462557850, 810090760, 3693656, 71248, 851978166, 892241695, 413240482, 229443646, 676876262, 41478750, 87315201, 945447174, 52946519, 933409165, 863510509, 94231814, 508589792, 133055432, 492838258, 452703134, 365698633, 481186378, 662250592, 904641158, 380530383, 775590989, 470228985, 195538521, 182485350, 887930480, 123587945, 425824457, 421858867, 687307138, 560884496, 306145591, 978478124, 187030751, 384920126, 424937984, 794712999, 773055329, 274877882, 873375709, 962910189, 354355826, 788654966, 840657602, 230221544, 463726664, 407819208, 544580856, 123501883, 834836639, 926660898, 423411345, 10979610, 496482631, 784169472, 315744464, 369733456, 607218433, 498551123, 500937546, 581267792, 603634102, 440793407, 871222545, 716739886, 742276556, 97786229, 976575277, 353054606, 865451264, 602240849, 946630991, 532077432, 894401366, 528655006, 852523793, 23102319, 492735055, 920773130, 158561199, 284421742, 418280893, 182486326, 294555773, 817962840, 158738471, 206806988, 382096102, 898846045, 927303958, 131424505, 773240310, 412723379, 304876384, 828047224, 846246213, 129957226, 909421285, 481830675, 95528789, 457190059, 872719409, 38714348, 1419640, 422556282, 16169553, 536359918, 13386893, 565537460, 786024335, 484669588, 169964319, 712229831, 812576464, 627427190, 519697657, 464504883, 611339997, 473461160, 88242258, 359079641, 513877, 667947856, 554573082, 294816968, 979961861, 478277463, 256708953, 860580377, 698366563, 428186757, 797337400, 337432186, 240162327, 548069060, 306643608, 232084457, 556401974, 781938844, 252267792, 889541481, 724858473, 363533173, 326271217, 369651543, 480372890, 587393470, 620764390, 337747019, 498009691, 415520966, 509055433, 471796132, 744970450, 71010583, 106817402, 558344688, 327785613, 458274289, 720517466, 128868748, 194815837, 637952679, 302266835, 312729319, 328748142, 557069522, 724435448, 298282610, 279436844, 315482005, 475547319, 428762003, 186576144, 399664686, 168958919, 574639078, 788009947, 737493684, 240665830, 358155585, 485926413, 204299764, 429645015, 605489969, 856748025, 930747616, 63561636, 585424101, 601784061, 442525549, 932660604, 306743663, 984644465, 976713416, 792223181, 373087473, 29353527, 561080440, 806288721, 639107946, 246548876, 147188138, 393288328, 152972274, 63710689, 592225206, 380577417, 477107184, 171575543, 580360622, 357864816, 780569800, 607359313, 306293023, 379328721, 388259943, 740784349, 896020656, 142225464, 850487852, 172003881, 928485419, 435734788, 140604147, 688039339, 801509003, 542353090, 706505747, 748565377, 360106540, 764194266, 371992599, 32318446, 810225964, 244884761, 166636561, 55910251, 416898565, 936011117, 892786211, 153604282, 213505456, 683666650, 589699832, 237004564, 926327196, 733822462, 304390481, 495012988, 160170478, 841146227, 318584320, 393900147, 546489170, 185098754, 645451963, 221279794, 791685776, 320900871, 682190831, 193274967, 262505537, 674616088, 66845919, 219696184, 188727939, 247327829, 746636836, 292775665, 199138123, 139736068, 117341979, 673888044, 487703369, 912314944, 919675308, 430018499, 385159098, 596968135, 541627991, 361669054, 897851866, 20256210, 343027733, 613687574, 35483939, 391748563, 196402099, 698511828, 888953495, 744147390, 998946443, 195131391, 858729613, 686551651, 669556295, 399183071, 792239148, 803112175, 765455290, 102481525, 835917621, 268507311, 260306160, 719148206, 199465147, 444719124, 36974151, 32586865, 83527399, 942971127, 863784049, 730770426, 115505750, 70052178, 891693590, 795003368, 932597267, 881785582, 356430166, 796199614, 60723780, 263474489, 53823973, 242806446, 9051457, 580425148, 520130266, 212827991, 409395574, 788478329, 206120906, 836388614, 944750071, 332208482, 439440835, 12068238, 444849165, 75409591, 762281158, 77455767, 939551054, 358482359, 437482101, 729738353, 734693332, 484304990, 694744990, 187798827, 584693522, 195448163, 289794641, 530241686, 182222293, 62796310, 363110524, 817013156, 268705820, 773770918, 196183302, 342843054, 812105437, 927407211, 129001465, 530552710, 831858147, 892406687, 205520050, 594190599, 810948093, 719637518, 389635226, 497340742, 688358976, 572092842, 871458946, 282025699, 786510534, 747728829, 499100392, 80119355, 23093870, 550954458, 201393619, 85396625, 500616152, 248846287, 144151883, 992452536, 408248483, 595648717, 685415487, 925797156, 690552351, 995319448, 691842464, 164188343, 699040261, 223664, 91732477, 898707801, 566014676, 228773529, 901572347, 877456062, 990952996, 571302046, 348834231, 723615409, 539606325, 698653406, 768383450, 992547598, 135083412, 702688652, 669540720, 600131917, 686003324, 133411973, 907471326, 151014401, 953064953, 328253678, 758578242, 578583992, 184281809, 835889845, 510545607, 394909082, 483952513, 523170773, 355123992, 460361243, 453007333, 993960010, 707919569, 511404640, 241172928, 608797759, 665280699, 788439281, 977693365, 703445203, 118801132, 686030850, 3584697, 838471332, 761969823, 95278162, 569375350, 794983122, 445090916, 923347660, 4068442, 12522032, 205806840, 488217987, 973638064, 637932047, 626057225, 370971727, 694090938, 874794492, 263173688, 209294773, 897566970, 342179235, 560154985, 713922222, 477140040, 17326367, 821370896, 636438057, 553863069, 194157362, 883277904, 563836710, 967649509, 124820346, 454791301, 68015293, 436459626, 740961184, 202145008, 526346930, 423905111, 796125717, 753405734, 306033244, 953399434, 625972396, 772978628, 371539505, 505768220, 456851571, 894180021, 235550914, 24374436, 280251707, 623572001, 854426605, 121220794, 41344779, 261725345, 737105250, 100585685, 354642041, 806413714, 546763948, 548997596, 200692397, 249667482, 561230295, 991459761, 80274293, 441974901, 639094685, 254953687, 239470155, 825364295, 648107708, 588376114, 127696859, 247578386, 393820992, 446282922, 240699883, 43735242, 671683279, 790413110, 225665538, 957463528, 960988931, 858268395, 856764320, 204575028, 514471848, 192759200, 867288978, 603508100, 400855338, 58292947, 246121579, 660845911, 746360082, 632679414, 165364221, 220942169, 608846714, 91936286, 300488994, 236117704, 155039957, 939539327, 62486583, 910491637, 770171220, 643241259, 101384910, 828641712, 201677335, 2395374, 418226025, 125221421, 233765989, 815323246, 30723446, 426605564, 821637813, 894152467, 102701688, 250113831, 856677800, 787221836, 127074125, 535286753, 394467196, 456562404, 989529870, 465205172, 689059659, 338818652, 411536410, 156413115, 341326179, 191290202, 478498464, 287251969, 980955858, 575852973, 162884587, 55983340, 94592190, 158807436, 482993561, 728105084, 582312396, 925139697, 690594471, 400306709, 708356512, 185214983, 529443374, 284604050, 416506909, 941881269, 618873042, 23157917, 161178683, 608487405, 856724173, 880348072, 331008985, 822851489, 943355140, 114397739, 49887613, 850901341, 205778076, 653093101, 469525685, 37209107, 527663761, 902846515, 389547756, 595945784, 66097892, 35576390, 105140854, 57321580, 721425800, 586129756, 826749447, 75443220, 138101364, 807222835, 121281854, 208097403, 926619058, 361636682, 276094490, 798044148, 879957511, 936483091, 32385354, 15120480, 387786931, 956827083, 719976561, 563990375, 672491051, 904669600, 717863583, 129601184, 277591409, 774590652, 736422749, 798048882, 450690958, 663980415, 692531700, 903462317, 966429995, 609287768, 470775358, 70177358, 387744862, 565442427, 414919753, 563432641, 146484817, 980695827, 759489722, 332571480, 556379343, 735456704, 474478160, 493474061, 626637700, 430850647, 580496331, 41564069, 97411091, 575703816, 408921304, 970713854, 619537668, 513787422, 671430864, 986252175, 909383618, 121372976, 482333846, 849907607, 967749218, 697198946, 874895106, 994054049, 802628178, 900802811, 492676385, 326433932, 43601728, 515972043, 841217376, 948372323, 156346348, 896145260, 258676781, 793428397, 207746169, 468725634, 760374085, 249644448, 315557166, 840932397, 311747725, 351680264, 470342811, 775650499, 40846756, 753889306, 292886317, 153183946, 382525363, 593858760, 167244482, 683922717, 506388086, 466213533, 438924916, 615867381, 166215180, 353088531, 219069821, 167021922, 660013348, 56080919, 629515099, 975731785, 340869022, 149066539, 468603463, 761023184, 853344246, 402217044, 92368434, 427594416, 193062633, 27418225, 460214470, 317408602, 925239495, 920912155, 946574825, 999641237, 407999083, 246145837, 877343425, 430025778, 762791640, 230513719, 60509280, 364337732, 62270024, 53625086, 462963682, 550998360, 133906342, 881233476, 686206895, 574685204, 402301339, 4214009, 429680210, 903189327, 470003203, 464944651, 951327666, 510581807, 670145624, 36475157, 382322285, 784768345, 98893045, 945300388, 762432726, 76043174, 360533546, 929476546, 705186319, 604078257, 83973765, 398861459, 733399630, 197263731, 428172479, 148532314, 88356203, 836888017, 719748377, 305426013, 488344630, 172907032, 118495164, 672065170, 484430066, 83251386, 575106767, 420553391, 337894711, 839805339, 952619541, 302248797, 394800397, 301523906, 627205274, 700526226, 14542099, 56246474, 24293069, 236643415, 652404616, 537675286, 91198231, 188058177, 220120718, 106502675, 620960643, 738842777, 821729513, 44373460, 765076023, 69720608, 318273597, 611699397, 335121677, 522153135, 64230011, 748871741, 819270234, 271877019, 982743043, 22580408, 459443255, 447617262, 871446398, 199796650, 130946823, 217488994, 249223822, 522125088, 257209200, 593738464, 432282918, 702534580, 390671130, 301135351, 957164225, 714166874, 813407578, 574912389, 623665209, 39892079, 50914289, 78722716, 891085874, 980154013, 759684358, 941906858, 594038010, 27542153, 440894672, 974009442, 286992090, 417417833, 903177723, 285835653, 622801415, 591594232, 92777146, 964607437, 131614968, 194510609, 587733483, 592884178, 925392360, 131628496, 533848406, 62853604, 423467579, 745208070, 407768839, 545039107, 903532538, 2789271, 752995536, 640495240, 335107102, 436569892, 909687230, 670891445, 734083486, 449696179, 956025799, 741122124, 783164330, 61047017, 858507778, 9216143, 783823002, 314505135, 59504971, 30537057, 499575667, 419872324, 629106894, 336588508, 709877123, 173983868, 557937200, 110047495, 711620983, 851051241, 21734788, 479252264, 105580910, 434410258, 568494299, 983943651, 659614258, 84787412, 12861044, 796144190, 982615662, 48877431, 543558412, 214917413, 261147914, 618854029, 479148916, 679335612, 507617998, 618537212, 715483476, 849009130, 687623597, 458504240, 141804550, 921859991, 17509795, 446230396, 48371660, 712842676, 275614588, 258014244, 148029360, 741979473, 241262752, 924842484, 358034006, 199909993, 871362885, 252041787, 875661403, 565154466, 281622422, 76909091, 776261104, 685661077, 935666139, 277329568, 350775902, 869672360, 342507142, 3053058, 902692526, 372955128, 733172807, 271578945, 285945190, 145449948, 97142487, 367629309, 215411850, 71422692, 327177526, 198015752, 683257022, 956911608, 958740431, 773158996, 948591519, 953471322, 897043059, 378932662, 692376767, 209146536, 100507612, 461332604, 537713138, 710360118, 882709991, 395556627, 830019349, 160290040, 509844962, 324380493, 193911248, 611460085, 48363926, 844945452, 116435870, 619726240, 241369279, 786508028, 425965157, 139542179, 340931483, 772955021, 961157448, 838819637, 75049401, 169675599, 426931321, 936140653, 128022728, 359961421, 881826820, 4322832, 871141620, 218155761, 47894443, 29217079, 945889708, 647109377, 406364704, 422611349, 649128175, 697574635, 589253162, 664518757, 997366330, 541065120, 367049767, 913770916, 683132535, 689786306, 397961879, 314920450, 526930986, 783263682, 950409426, 566491464, 573189683, 296407860, 654016628, 517615719, 628407038, 413341559, 361790013, 435127254, 107865783, 889434851, 485978443, 171462055, 190415076, 71808469, 188508199, 13583585, 361869710, 286622018, 18860011, 498895041, 870759912, 788842243, 204271982, 152197860, 411272846, 497774252, 48574837, 333140926, 214686568, 560131995, 8610621, 733232967, 37283260, 7957868, 200772182, 937889794, 19489616, 826087383, 327780320, 805906875, 340696344, 876735131, 274469330, 135232777, 939364792, 78770829, 613080277, 575172023, 423756564, 930303145, 506880951, 912104683, 525185706, 177156643, 267287313, 664949114, 240214722, 446544283, 479127891, 304685169, 699162929, 953843555, 540052800, 799640032, 318266612, 627341886, 338578378, 476647006, 611215659, 783170543, 754624871, 647390422, 593247717, 223345210, 583482014, 174177710, 757710842, 107358718, 818380093, 991056149, 989202634, 987688989, 676269471, 836802924, 44192527, 543932923, 763836861, 287285007, 959586541, 272166359, 637694605, 82031715, 319326848, 508038696, 846075809, 748255787, 620096041, 23582269, 262154640, 584331302, 778482952, 634367017, 846886013, 429252577, 608920073, 733771912, 313630923, 285354669, 369578817, 582029700, 856038213, 824490123, 867688399, 103171688, 231988340, 551532185, 375218268, 474357593, 81799377, 882795359, 879550662, 976638274, 907937185, 348245804, 9848605, 12824852, 648018203, 464175746, 397302001, 445123770, 409252633, 537718584, 161268279, 61250854, 992625239, 39783299, 248378266, 21861342, 112872108, 399258430, 952659048, 902235163, 623801964, 315757707, 941349936, 749485332, 860890494, 711292349, 353602081, 576778750, 895949249, 594085890, 322153522, 322923346, 561176412, 487971239, 114367420, 381479725, 747678313, 773845142, 830463890, 998087032, 980943943, 427345274, 970734369, 652101143, 437095835, 525347384, 469894138, 947329788, 385573188, 54859693, 527355536, 562849569, 211882329, 920465090, 270879286, 475062437, 832033890, 166305532, 70550581, 112908924, 557920935, 789802034, 406548367, 422334593, 290702567, 649910883, 425815477, 310089064, 23758648, 871283053, 152054365, 687263421, 773644168, 245499255, 880413658, 844028841, 450266320, 73945955, 14788442, 445464837, 961443911, 92034959, 496522098, 778437550, 500847362, 23070041, 805568246, 678485063, 507046565, 793008255, 400901347, 838351226, 165926743, 301330813, 539253950, 830501588, 352995783, 840436725, 229916531, 986681003, 688814379, 16687011, 243716476, 691006184, 365753316, 612445312, 602874912, 875241894, 166587990, 983637177, 411792965, 776547017, 160954207, 169038363, 950014040, 675686415, 298847618, 794282928, 388979282, 759524999, 115254686, 694836671, 914355765, 795561482, 502387288, 691849697, 73918593, 361688053, 704092262, 52134907, 941071695, 838169396, 782009506, 174297621, 687379873, 411194095, 266639078, 377128005, 345045093, 329999829, 869728539, 375639180, 750330067, 827533453, 503578645, 765774789, 279572717, 911045164, 995911544, 443476081, 857482697, 391294366, 785654928, 529198368, 371523854, 286120152, 167238754, 712076065, 335920495, 176372627, 76613334, 557833049, 471080804, 968777704, 567710021, 153586781, 137335611, 582807925, 942481526, 717346543, 468480431, 669243316, 537265056, 307745999, 159928599, 520280669, 934852252, 980791979, 514940337, 499149783, 319219527, 315086120, 841314058, 145041058, 782458673, 304457254, 663293173, 217979738, 373784943, 437019409, 88282429, 580678168, 325298605, 379880106, 124317695, 966027895, 976464385, 341277057, 913544169, 376967187, 54759327, 942063364, 686827148, 94330561, 512331494, 835044409, 955644827, 299964521, 48666501, 694056042, 494035717, 804173016, 707438269, 458146621, 934457170, 496150482, 479764537, 618250926, 37421313, 386300216, 280888927, 739037280, 871486046, 155002737, 940172419, 414896318, 128573653, 644468801, 804164397, 201516259, 91096307, 729769135, 86407514, 653435690, 162904166, 193181329, 281103717, 103433217, 820543304, 579125886, 180137899, 443123777, 19089990, 841766116, 257913064, 293809603, 932229785, 850580652, 792345733, 250986130, 685191834, 525539836, 656796309, 135965667, 874845080, 790261881, 930735159, 961841674, 946315063, 202030728, 972135313, 424558769, 857820361, 94429223, 695223740, 988630816, 60196765, 181573116, 493737299, 42367010, 581406200, 781989928, 887633838, 682682018, 437696680, 586714489, 607103993, 75617952, 286575861, 709878650, 295643240, 123471465, 709239037, 961616183, 639471720, 401584693, 243617467, 586071916, 871563357, 509237010, 151851127, 332863911, 224500014, 118535310, 578101791, 546131114, 505778514, 221595642, 561268593, 294085235, 266894459, 308357386, 850711793, 417281016, 751454720, 734100536, 225525562, 577739406, 993658915, 283047353, 508597133, 126767081, 72367531, 609733681, 431689473, 931071404, 967519662, 24042278, 429923463, 488852006, 540105608, 889318297, 223217106, 435222628, 205638804, 347243974, 146628764, 725201247, 771979340, 303474825, 131173300, 570948260, 845592436, 82608256, 309885384, 934967400, 124378080, 982474764, 965136799, 639793452, 747968682, 565970667, 312350454, 594886392, 582846482, 963122431, 465534468, 334112921, 765816002, 592272311, 706689907, 536247305, 578391069, 99282182, 299143341, 241205168, 50789346, 790498830, 218614603, 697326673, 164486231, 275546181, 898476936, 441625131, 93168467, 767872682, 118891060, 541476985, 277913472, 232391410, 460836215, 68782246, 29277412, 840747435, 176527524, 453777848, 694549709, 304652506, 796541009, 765525159, 650989317, 859395646, 882504544, 806293195, 90874829, 773093575, 176418231, 734956825, 275252101, 790915429, 295849972, 54495554, 971254256, 283230581, 547421319, 143275583, 960147534, 482701105, 308706539, 584874680, 85915864, 161466277, 680036038, 84267238, 180571492, 167562224, 509450402, 501021887, 954467872, 371804364, 781050725, 926772960, 439813090, 897541288, 267307256, 340028195, 974795904, 784502131, 767249668, 659330167, 786859227, 832213961, 376582772, 478495030, 275043629, 515886781, 223863951, 98177545, 945263929, 58728794, 610426833, 149151011, 267044655, 224126777, 231286730, 84717033, 220533653, 274802566, 392732494, 84115639, 616572732, 710364077, 577406322, 511609557, 46966461, 989863490, 167936369, 804934528, 794995933, 85670661, 445551059, 82482452, 716328304, 859904425, 733259477, 551650379, 876639964, 650582357, 269168131, 517316412, 735784726, 957189366, 769578128, 55921364, 641479427, 618755563, 623899746, 786309009, 383041517, 794371979, 252980491, 952758615, 368959549, 290810034, 109235298, 209691708, 829744729, 812334764, 431190329, 479419802, 112529990, 593724799, 810008563, 218261006, 134330622, 679823302, 793127045, 345973293, 977258825, 911854713, 34714821, 954997337, 564039780, 158782574, 643117838, 299486654, 946584764, 945447303, 773315018, 934627743, 509616910, 251590990, 450063498, 42868689, 226960916, 142853122, 900426234, 361341287, 116872489, 760353215, 757227828, 744022290, 996876525, 494043805, 163023477, 526282169, 848820690, 414126468, 891760737, 351156427, 736924772, 987678744, 958950931, 883222933, 792357444, 172165159, 755003644, 194169645, 109965562, 998867148, 256292454, 317301873, 316753077, 14234125, 871630243, 117607528, 729809898, 325232354, 69222490, 529695352, 23856092, 894175403, 948730441, 849584286, 504110633, 231023011, 297404971, 531007370, 56495146, 666733099, 994949840, 171381898, 964289690, 308463528, 353758896, 938929004, 495477846, 29249108, 354637873, 880621425, 606590060, 723579026, 85254998, 648805909, 682992319, 447065639, 977948012, 410389622, 922672463, 498578879, 305947815, 920119901, 216401264, 757872558, 569756846, 100495072, 409715729, 186024019, 936602407, 74623905, 740707497, 50395371, 169542578, 530004380, 362399741, 597371233, 920398379, 898122135, 524294725, 932864394, 6890616, 380794784, 716742858, 315386669, 695018289, 777656962, 341532672, 92305079, 808770190, 853740230, 458775395, 559854842, 733090214, 587541025, 372953136, 220725287, 255152868, 236867276, 8807828, 427910848, 412805079, 512103391, 450862416, 931237821, 162160853, 314414959, 520183472, 132338373, 470877017, 393818596, 119575435, 704559514, 86679210, 926414112, 579439269, 146728081, 478578192, 560220572, 678701427, 792318568, 991095849, 39907575, 179670358, 530636228, 13918840, 710216344, 992008464, 865140351, 153349562, 836427898, 990876436, 863075113, 400373428, 1732109, 497951127, 85273925, 459138072, 484235731, 627030550, 292865179, 66101923, 931681629, 49031256, 773540693, 369930201, 208139025, 530511503, 377020893, 494739841, 886323459, 632921894, 729225285, 573184447, 896694641, 490951566, 665766907, 495823185, 970473092, 779601798, 491098731, 409466220, 697978000, 500602901, 607476439, 701233739, 441352278, 84709458, 940784626, 151421249, 752844902, 483486726, 618554432, 803836917, 789710292, 51540590, 207126681, 273460772, 745552742, 683900411, 211554586, 824284139, 395214309, 656202608, 569131211, 453269969, 544692934, 38071076, 119743822, 843629727, 528209519, 808119531, 760125161, 910888411, 457803010, 397032497, 135062065, 531125282, 729106060, 575921921, 892331263, 89337864, 921644561, 849944319, 860765319, 223241108, 466941875, 604542861, 932332921, 150417039, 139525089, 822343928, 122551348, 734812229, 518100498, 138580609, 850699948, 400084019, 229150718, 606965907, 287678813, 842278014, 800103952, 888173621, 994781859, 208194192, 451546610, 933645590, 17223873, 767534986, 185391791, 360730626, 388271429, 592031222, 884954732, 835191098, 599217716, 679755656, 899609270, 600018665, 46470560, 507081791, 55626178, 240227125, 498148921, 531562377, 737793858, 941344851, 492430043, 375618776, 838067801, 195998812, 880463552, 314971843, 354985941, 208567665, 88689320, 220101591, 924466237, 893081883, 689110252, 711309867, 868282894, 780975080, 196433145, 125846757, 645691787, 790645547, 264060528, 612777042, 422155482, 582884309, 145917454, 939496421, 57697327, 882037285, 114216528, 124886791, 122151562, 30465621, 17678679, 422850384, 400910385, 940161394, 696220369, 950879930, 830581049, 929337964, 169778958, 90649914, 124665536, 832903588, 798552060, 123123369, 725201407, 803275039, 198219797, 700221104, 102081340, 135520893, 567348375, 888854173, 879767033, 523703371, 551950782, 52700584, 303773039, 118352223, 404363149, 486593575, 744975276, 245259121, 272205975, 166873352, 90854571, 160550129, 997149825, 629302255, 328549943, 533114548, 527441011, 842621423, 445974516, 996573980, 872525676, 131567781, 363089858, 203767208, 742417508, 836122961, 642646569, 511780241, 382570622, 207273643, 986020949, 750283755, 425352043, 129785328, 304671155, 110215906, 24188771, 493799402, 929686732, 142395353, 146263494, 675038333, 140228337, 877873052, 746640769, 152040524, 306627333, 125065435, 819789328, 246702472, 212173975, 21401133, 585647442, 939818376, 728903600, 77141675, 703295497, 474539363, 831589224, 728660564, 655478702, 168291937, 270765007, 569354692, 218844964, 870564825, 560234901, 512498019, 370957130, 969740314, 763998238, 85407304, 625742919, 835281805, 660230609, 825809041, 377319500, 579617328, 646692882, 892687544, 35366316, 552200163, 828075599, 421173025, 988527458, 460167305, 428742028, 652225644, 318183412, 492359546, 633665395, 49624302, 31385544, 42191335, 43424415, 685813783, 751813238, 549433138, 741963388, 154056433, 888884804, 496866299, 979319941, 290836547, 339484532, 750491263, 56066932, 774748245, 954051393, 429774182, 270899643, 667634310, 643798550, 435744572, 915230776, 563983582, 114288413, 258784484, 258533740, 983132796, 173806184, 167913736, 290877351, 829595567, 542395490, 132401365, 959611454, 883778128, 228723448, 208306918, 326639669, 473716789, 834325770, 252767513, 481565943, 488670338, 460491881, 164220753, 367754995, 377484484, 583310693, 530175502, 220585159, 574655230, 576310694, 882871409, 619588655, 876095056, 244592042, 979776098, 24255437, 260075466, 646795821, 595284743, 569168389, 796939621, 462627352, 790744003, 740467560, 965317320, 922821336, 164879726, 23803430, 990489810, 282508560, 462392614, 798696872, 17332574, 36527490, 629490534, 122049459, 723210839, 370439952, 155037651, 582241418, 367117895, 419628807, 608766464, 651817926, 629285860, 140125127, 180164328, 229038226, 703550380, 587324968, 206870574, 313956000, 142440509, 710602979, 590811010, 1286028, 752964152, 590052375, 874455685, 291042251, 695199830, 161658065, 652201635, 660048795, 551739260, 549493998, 519679466, 643414535, 290185371, 496341209, 417740383, 223970471, 226094819, 263275837, 81790728, 441122939, 120502049, 434582061, 875896299, 204408712, 33457000, 334446039, 546553652, 769006219, 936839419, 308819564, 588057957, 146534332, 897032576, 746310898, 782681900, 516756406, 574506966, 582874618, 250590319, 138192303, 399995114, 672649331, 404595887, 236632891, 576372136, 523194484, 25098631, 789205827, 621710688, 224391457, 660337288, 137344162, 743533936, 601404590, 382912865, 506260484, 610202110, 828085582, 837498601, 74073844, 359557453, 151004159, 468751565, 395027924, 208301704, 542118965, 603597956, 379431558, 502953809, 853552876, 126195216, 510116403, 852238133, 758265231, 244501770, 317344965, 453544218, 320852067, 121478381, 928839028, 82746696, 615753868, 755244371, 655116527, 189861965, 27934404, 625578656, 62271098, 200761352, 362000784, 270247612, 685907859, 571635723, 962983690, 623652178, 781244412, 635150337, 700022668, 617941988, 25648868, 484600298, 86420608, 83178521, 761433703, 516494710, 249483378, 760121900, 521449648, 968586234, 667816277, 659681030, 836950583, 380343667, 299448312, 916506868, 258170708, 304739008, 687689386, 606723906, 161103553, 573261926, 608074736, 796406717, 446362202, 26327655, 985282914, 663893144, 300852080, 323403471, 910664715, 824768203, 464981440, 19846094, 141448698, 134433432, 686387602, 960291532, 991454262, 170760382, 660784584, 160599237, 74340263, 147735155, 167295390, 740494525, 973187703, 850695922, 819907457, 975589874, 495692197, 212505095, 634512140, 575032731, 774476966, 607812294, 513910772, 782644407, 258792136, 239373854, 244974661, 722539945, 381064630, 604604028, 618025244, 738710246, 782913067, 153347253, 828367017, 55751402, 509290858, 437370353, 846455767, 403323602, 271476411, 644586797, 750491205, 907481991, 980178563, 860484782, 502310928, 115157758, 727514823, 271498101, 30374452, 418249605, 307136159, 355370473, 79617986, 397398233, 942858426, 102321777, 350666525, 57419304, 753531253, 620492545, 133377353, 981278078, 62424465, 412631208, 92923107, 417241712, 931472689, 936041459, 603658205, 568835609, 388959417, 867590757, 511830624, 163157807, 632595093, 513759059, 534494791, 614443174, 972822040, 116721784, 774045194, 507761722, 651065972, 275151797, 433870539, 567876026, 645286856, 245560130, 970868995, 479765972, 511704137, 30091429, 953370586, 561655783, 768470468, 214107274, 680219486, 201227581, 344638918, 646986392, 320820508, 529893429, 313605585, 316651008, 875519544, 776275436, 240957554, 264487402, 749027257, 125620070, 993174147, 491285990, 992420945, 588358811, 792875477, 831553726, 137154632, 999990562, 521866584, 846652581, 557820329, 713713742, 918090775, 844521974, 196775846, 993327751, 192214826, 924794471, 932723089, 93751527, 428776253, 961753162, 980352491, 871923735, 136193014, 642788242, 960501048, 624541833, 503721064, 976989970, 888981137, 256554470, 429132785, 397608791, 124053387, 59332154, 149374829, 560039437, 718450560, 344399404, 692246885, 358828012, 116228280, 446851383, 78770886, 430460741, 501047251, 177273015, 197329146, 168849869, 377657776, 255864988, 448659764, 884359389, 400290140, 822409924, 407456368, 20843677, 626213167, 75369541, 466331520, 552208914, 831480894, 9131769, 398621105, 578252414, 698565640, 452436490, 698926969, 70719688, 679191367, 310279335, 145997216, 771160967, 354261367, 132132307, 496892191, 733308466, 408854450, 948772504, 437037533, 664077238, 467629902, 224737140, 908752604, 123864179, 271852651, 476217385, 337396241, 330372575, 617981996, 765652363, 977808482, 80412455, 998460173, 976342960, 805662381, 305979045, 91669987, 754991791, 153845868, 677101204, 19137428, 235974311, 411234684, 652736320, 992318805, 454033965, 116273064, 727329363, 572386483, 444804259, 954232318, 724132047, 351115968, 9703970, 610925506, 582381322, 904750439, 830639013, 80711474, 688038484, 290738578, 91907885, 214857733, 963252521, 925702220, 571997649, 73380924, 722508892, 154216640, 999894167, 977740216, 975045934, 706695995, 482658230, 419859629, 678103960, 38998954, 158478881, 993489591, 305150638, 538185325, 36744861, 580733417, 799783666, 943647422, 43234986, 547538826, 496628508, 790595694, 811667024, 954244795, 71379893, 11068239, 380304918, 893991695, 10818540, 800716560, 205702087, 951696787, 496790489, 206947711, 547604195, 831696230, 264825904, 72320851, 873809567, 606748874, 654423253, 237280771, 532203028, 441646909, 35487295, 929892499, 161782050, 915384620, 56522931, 910681140, 709537765, 342912462, 880998364, 125018766, 697466090, 266353314, 783464476, 671063392, 886281299, 237990139, 318644803, 210780828, 399833464, 38636413, 771621369, 177674390, 816555129, 485722525, 314140888, 83711793, 43047104, 146784368, 223114455, 403207208, 236314856, 860288215, 349887797, 627806080, 721654716, 801849009, 94015760, 587501314, 438724381, 994686650, 908282675, 514378359, 796970138, 892314708, 812642843, 654947836, 166084574, 835946625, 927262500, 964472192, 804664714, 871685246, 472138176, 96440336, 256334221, 127729632, 359849325, 888594830, 672606018, 273717748, 888355360, 161626430, 268582610, 169921531, 274954928, 632595636, 430329887, 809488194, 725563286, 533060724, 89393935, 541244141, 661995967, 701609302, 672217536, 223086618, 713035585, 549407005, 112577032, 611340181, 994877177, 32571741, 486139772, 276464453, 620898800, 198323643, 429620686, 176836459, 407066795, 924895056, 447538622, 52281871, 594580626, 84626680, 93527805, 849317143, 388158889, 943370300, 181097988, 15638157, 421934737, 877466977, 886852572, 664345780, 580871699, 219306405, 172466135, 762895169, 854183646, 236794188, 269304115, 720196522, 537513774, 365657854, 654755588, 558545405, 821045129, 670629717, 359518023, 324433145, 357761156, 225456527, 996076396, 929287421, 123204429, 671188653, 607211517, 460867393, 325192947, 226707811, 230396172, 444596840, 470540277, 80907585, 267248015, 282005951, 400793382, 21922534, 295072146, 583438558, 617023424, 591465597, 524885971, 544417781, 875123066, 501043285, 762531520, 619181657, 147475543, 934873313, 677689665, 675185372, 173999826, 115886871, 81218371, 793680048, 321616825, 449972116, 337913608, 312976326, 484816436, 171590022, 191551401, 113066244, 390303303, 421525235, 686273272, 32727019, 834517200, 914949727, 327203426, 401374407, 375995695, 532500984, 912383928, 706501862, 458407694, 347195655, 203604135, 449621397, 654114126, 255576653, 41896877, 678167848, 549263155, 917823467, 235958468, 138043943, 795373103, 874413223, 397077029, 648749586, 320365798, 938517879, 543728986, 985656829, 209573890, 887718109, 378221844, 33541146, 650269254, 762957476, 806605111, 875702525, 132003014, 342767515, 883171702, 485307621, 745634029, 679891175, 347990854, 691634494, 599256301, 583390118, 947434300, 293516125, 211717736, 935011583, 882801803, 48014749, 62788421, 383385052, 777106380, 991859826, 494117669, 295082739, 602791956, 143488835, 420769255, 972280676, 648968964, 705414716, 963958118, 700865842, 912447260, 60676759, 683745463, 638015192, 28049409, 411155173, 996840171, 400099809, 45625649, 37891004, 208239084, 753256742, 44479225, 603254079, 325917168, 688884925, 369365036, 187480402, 865192409, 306096474, 711561036, 567872416, 300930761, 904114254, 544684546, 214005427, 533210247, 477796226, 795228985, 283292003, 388339061, 996995276, 592443017, 699086428, 554674942, 816863739, 131862627, 638839758, 700410409, 853625622, 555994973, 227796574, 104963972, 184745856, 541366916, 2254543, 91096342, 793508330, 932371120, 843785240, 446539197, 119491145, 719886981, 712370366, 601886375, 869614951, 10148701, 766892034, 875381650, 977637172, 737416813, 330248362, 123403739, 141365143, 246504530, 47564392, 938056736, 266508803, 973069733, 955801643, 660913140, 658015025, 795067019, 823142332, 961227081, 602630407, 612471349, 729134630, 171438514, 454001464, 288441944, 765130167, 626465206, 47776460, 113029494, 22693541, 432635026, 788092882, 284836267, 945983244, 719415500, 45541721, 328578508, 420934228, 871197550, 367486556, 732502508, 480034718, 595496934, 54427061, 388533960, 121107247, 657110864, 846685115, 226816221, 734161079, 598938852, 608232927, 104071888, 615258824, 888406423, 237058448, 868048304, 253825860, 522290528, 484871851, 724384847, 675133068, 916833965, 910918113, 11755225, 791950730, 896982804, 241032463, 76015490, 854269762, 8657742, 172507916, 55584127, 148227676, 936270094, 57951500, 942433126, 355773143, 365031764, 964063391, 3704977, 115290898, 439267483, 812976536, 267347685, 624268528, 217913145, 723566846, 961505356, 257883570, 718097030, 763258782, 565499046, 788767051, 888242152, 819621931, 846906667, 333337299, 854429489, 487572116, 498387380, 623845495, 681594405, 490784864, 321740060, 405288378, 378612635, 616554969, 978231358, 980736332, 313757587, 514197749, 136106528, 523569897, 426016616, 14326046, 91805678, 964093679, 951646829, 45737627, 684628987, 199000628, 75352097, 888991893, 273418482, 551776569, 395883493, 194400187, 938639116, 182433402, 289331004, 869070285, 400030843, 295227096, 105724689, 676169182, 602133032, 549854161, 111310514, 473423823, 463311848, 298386550, 466111972, 984111090, 934150472, 757417261, 203570711, 469443850, 651244148, 607974945, 360713613, 630413173, 554596944, 286834877, 644194716, 581785064, 364592702, 249733392, 711055247, 647238840, 444216530, 676467808, 982938088, 656682247, 136652220, 664068767, 191220961, 650016566, 671122249, 13755556, 515960597, 907368552, 666922345, 904465504, 371940469, 824059295, 263927172, 583226409, 396548641, 102107196, 637115539, 722005803, 332027915, 830149940, 464776910, 59100724, 283312549, 448553144, 236892251, 508655794, 842837878, 666353893, 703829303, 736192818, 908915788, 52705407, 75747858, 298464582, 229944047, 95497040, 661197, 567772389, 25289588, 48012388, 441207666, 490882484, 811878228, 188078977, 858399091, 5119429, 61092002, 460259165, 435405572, 540893524, 597800041, 91016286, 946030363, 342862667, 100432424, 399484700, 259485984, 674631376, 743389652, 227474647, 887360287, 330331365, 77608868, 491601481, 978296507, 582916646, 586851505, 520210448, 76768263, 207912949, 162470560, 912731454, 626639087, 675947346, 874956638, 462337975, 213657358, 199598187, 81460979, 500419514, 815982234, 160254249, 745857608, 28038854, 106534786, 672490310, 887586847, 41882498, 368444865, 15601023, 185257380, 713200989, 788625010, 96245132, 207116339, 35396542, 21029694, 63850585, 26459210, 312557682, 769620304, 233558758, 741557581, 955399258, 933947282, 696019635, 198537025, 343937518, 420254709, 311488667, 432428352, 767874494, 977351201, 798630162, 724411328, 743666319, 862356630, 229854282, 102406611, 405053709, 607553915, 193895773, 456351958, 120543363, 224104003, 316070828, 111528857, 605209874, 6441919, 200498305, 798178620, 594346221, 176361041, 731387335, 555641315, 359345655, 542312538, 387289573, 681092297, 866472839, 187615215, 411366388, 400310314, 373910581, 197825751, 554430767, 898491188, 150749458, 256339225, 664570482, 563279065, 664903307, 887736742, 757945384, 117005094, 498863204, 223981293, 415757708, 610376997, 631704035, 687328469, 449770265, 459209962, 207224570, 990930827, 223544162, 102635833, 564482404, 233288188, 779938143, 715430245, 408054402, 949645562, 62413787, 192396873, 475892124, 227746524, 613402364, 428390147, 145130900, 600084798, 725126564, 447811926, 498707523, 322570433, 989586331, 884529220, 732318323, 513105271, 518118224, 862452693, 894931369, 589738003, 298904333, 346847197, 321430827, 361170908, 111380663, 878654428, 190951616, 176002550, 563725819, 817922489, 697664053, 849398284, 238461645, 986188823, 533812104, 524466207, 683971470, 697911124, 637650222, 103054175, 130192331, 372260231, 703896711, 423953401, 705985147, 805897088, 295128796, 848621817, 409224952, 597241967, 401031535, 418164547, 4450594, 24623626, 8370025, 844615287, 130231475, 457071718, 811557506, 600994577, 391913398, 497362153, 316953593, 948518475, 556824281, 964615194, 238060340, 544421002, 967258447, 373799764, 384024926, 322762134, 938514641, 606964747, 643717343, 634218463, 42455460, 791387257, 910120789, 886939796, 253887414, 173714687, 472344916, 586487030, 723999692, 862358645, 433259540, 553971442, 664999090, 547154371, 484610373, 387290611, 131341102, 59645182, 737310491, 590328965, 577028027, 278364440, 78195951, 649329788, 127356674, 342652591, 820966043, 245068966, 781342415, 742995419, 839826299, 918019160, 302046300, 633946466, 303613373, 366928522, 305483630, 832043000, 708443317, 76475171, 342648204, 21693652, 912323392, 468207501, 631272776, 23304834, 979807476, 993791775, 663246211, 903277056, 392542470, 875279899, 471821757, 333872534, 437228205, 919793626, 558627217, 877286101, 220998831, 393912581, 461042130, 744488944, 666771702, 203282804, 741039713, 328985206, 45196528, 234489297, 883718768, 675219640, 46573323, 482586670, 901682257, 390431220, 613656232, 823928697, 567445742, 792644829, 59568832, 843970005, 965389488, 69374470, 585732768, 857627481, 141901813, 688818728, 229912332, 529430340, 968918538, 19099953, 602509660, 797699100, 788519039, 430355647, 881294573, 688758701, 982247086, 144701540, 312709111, 969533926, 371281618, 969238522, 8429362, 377975565, 589147054, 804891188, 207961545, 450535753, 899080368, 641330541, 372874527, 744094408, 712719396, 693076219, 309528223, 247444121, 68008352, 29886682, 607503360, 316574969, 885310020, 457862941, 910346780, 140922734, 202606771, 689272053, 443996542, 126453032, 190040195, 502124004, 862635179, 409757440, 505028092, 577923709, 391490407, 637049685, 661285609, 651206291, 173628391, 508499990, 203054312, 124911257, 680432449, 157265776, 859428379, 809892419, 712856314, 746876836, 502937002, 159012600, 62848326, 653665529, 321373772, 770182010, 519293857, 852322902, 6566926, 396585449, 705968427, 772469156, 314740429, 316750242, 729667141, 873838577, 721042187, 644867961, 992036135, 272080205, 913959809, 83571379, 45155632, 3012134, 977880425, 485798199, 782572702, 857950926, 832113136, 322776399, 461374250, 670876421, 721537555, 345436649, 443539448, 486958373, 293502822, 510189964, 911045721, 970946703, 74552390, 835696368, 853413116, 102353980, 84605959, 128452224, 167906692, 235840538, 897445539, 71703506, 510139972, 668807386, 384559929, 493982584, 519175940, 222589150, 724132804, 279353649, 103239439, 681997499, 438201572, 445634713, 609881325, 46285974, 424618932, 796301443, 782552872, 591909372, 522366016, 269190646, 738828975, 116464035, 408788722, 868304236, 501893626, 879482165, 407208628, 491519470, 471467496, 249582966, 484880919, 349123880, 773042365, 253003359, 462783602, 796382267, 259023307, 846310689, 579547404, 39647639, 859789025, 995301681, 198718270, 92833574, 421087244, 215797963, 222635997, 918220326, 205293763, 819672382, 927933197, 707555624, 10168214, 926896080, 176402461, 788205625, 278385164, 161281694, 440177884, 301440389, 333462329, 922220936, 340664808, 30191567, 678816101, 709735196, 136187680, 452600505, 464256457, 530896059, 676958735, 963165151, 706728886, 329078486, 664990667, 800900151, 240714785, 969733378, 780996445, 434810180, 212169460, 416345560, 813117217, 748431499, 729460429, 465571329, 240655563, 676620901, 502994927, 668438458, 724460242, 828521344, 393304437, 261321196, 836482112, 584597420, 15348193, 295934497, 243869707, 665767643, 256828548, 580934609, 682427053, 145132226, 869083774, 968018625, 147658592, 300286266, 578954536, 852635945, 608746987, 37013251, 540287994, 429622695, 340317333, 367337599, 820476770, 90538250, 538111481, 217136434, 560091959, 375839271, 113676829, 3100935, 49345337, 905232102, 957828483, 216692315, 460579905, 426626103, 828524468, 807757421, 878389650, 796792254, 649052641, 23463277, 173427549, 262444674, 480179767, 577754600, 184218659, 201048629, 367237547, 354127272, 68829527, 290269957, 855397120, 886904908, 516563527, 33806007, 321580498, 229404735, 533043314, 643192313, 563646411, 599233292, 113275353, 811585952, 674309825, 555267136, 5581439, 965356345, 199824657, 378038741, 314383751, 450471531, 588103932, 512792570, 106449007, 127767693, 713319717, 799862140, 809786430, 535843200, 151549965, 867659300, 92526947, 665798263, 579939953, 656516451, 105897874, 256073177, 8615546, 629407703, 743787230, 890213671, 250453236, 36663498, 780635986, 296921610, 529300239, 467079685, 231468495, 933332877, 491351205, 310095017, 959334246, 137508105, 47472338, 898953689, 85483387, 410787031, 398145814, 357986938, 700291598, 361981658, 536154947, 161412613, 514157224, 429070813, 210769720, 21439343, 426702544, 778636283, 770515527, 843468087, 592839821, 820842416, 515590115, 969782270, 383182899, 114699332, 109440773, 470247508, 323766099, 686830619, 303133599, 245673597, 68410397, 769531991, 717770242, 872598713, 368306543, 102193966, 221255707, 725782034, 893721918, 1430169, 508783456, 950400883, 915734317, 856667752, 460604407, 804794946, 161591365, 759425506, 73089962, 923800490, 945020640, 785514573, 130768570, 678470184, 838021604, 227996825, 546653236, 956735082, 588788712, 799857585, 252701909, 809892472, 351361740, 148303143, 851221106, 204070557, 39348691, 784226642, 82469511, 157529625, 261560397, 487455973, 352224723, 181532865, 593676685, 335488828, 945553216, 597768833, 643982529, 465663749, 342159382, 581207205, 271746870, 683988032, 211462838, 702062019, 861159414, 348612653, 654347162, 549684887, 486931461, 940517615, 471145312, 6099647, 155870120, 869858858, 708177628, 764230569, 856775854, 992959845, 814949582, 395756013, 993433803, 552811329, 143980147, 614029633, 158884012, 347645935, 960287842, 91621385, 89277517, 38571779, 34789196, 868547886, 97163572, 546407791, 645578758, 927459088, 968017817, 873547407, 617368999, 51842839, 784268503, 937735956, 128127874, 163043783, 449593179, 808492912, 778188363, 858659593, 299391556, 122081801, 595079124, 624210878, 871200393, 348974521, 727605548, 403185292, 467666569, 437457506, 910622282, 983364577, 31117100, 730182054, 153496090, 303554188, 907404264, 523447883, 375279708, 935828480, 995017283, 553553295, 585686090, 78323197, 92974840, 638523159, 583619244, 295381470, 811370201, 966663598, 474569285, 245618134, 47376260, 875383203, 190512214, 813640238, 303225620, 460784733, 640414006, 354971927, 697755366, 968243470, 711381617, 318233101, 284715902, 300189060, 576755698, 332422527, 710802719, 215160610, 776283356, 931051986, 382286560, 202268441, 56808043, 913237074, 940886566, 726827688, 585668905, 529295655, 533157027, 925632116, 188059405, 352761017, 1674326, 565083171, 959819582, 325460032, 426400178, 831073995, 561433807, 523437286, 366767699, 648323963, 557646297, 511952727, 888782699, 63476706, 999996068, 536067035, 96378372, 678303038, 832488427, 278988730, 184048047, 107051194, 249189910, 859558249, 88989122, 263592541, 668106812, 646143998, 666920103, 212186559, 691487615, 690663023, 156669818, 905065730, 248366289, 324243015, 259894877, 654625080, 808551855, 475890861, 680105097, 95421213, 349887322, 605852552, 797820632, 552885824, 854948139, 448839449, 340138460, 372284722, 715274392, 536890577, 366718116, 526740413, 857208066, 486230179, 951264928, 412415860, 822075803, 369166741, 218594277, 553035734, 432279652, 283067750, 845132974, 625299635, 830049333, 451446613, 530196282, 196062851, 349710693, 132919987, 647555537, 361470554, 474678356, 827798273, 175750760, 601846290, 478180684, 279903756, 537480941, 529612096, 337672273, 277406605, 852977221, 551217865, 818819792, 452969215, 634474861, 795922, 260801434, 198587613, 241400341, 942849903, 892506224, 869824074, 421099287, 919995131, 792070675, 290841655, 802952331, 165301796, 745942173, 650351729, 286461116, 350380283, 783104395, 78379469, 654295357, 164001088, 539282642, 925972611, 584958200, 886124836, 334912803, 573619758, 542418877, 774452806, 652782619, 645225387, 832050988, 250080486, 100127239, 332597393, 35680597, 317353344, 599560763, 841207679, 310840420, 337211687, 618847286, 977506767, 460554845, 270202013, 772473825, 236130341, 523828348, 525368600, 82519452, 876115497, 323664986, 511956028, 400016265, 548564645, 795027022, 335658033, 694102160, 447063883, 333452555, 796160558, 62088774, 408356453, 917213909, 416293145, 768612024, 378636001, 736804897, 265194322, 671850147, 650537308, 169285338, 552714889, 818782505, 825293037, 979423740, 477964758, 991149753, 194847762, 552567938, 294318504, 905915458, 770811406, 981075228, 526444141, 205754868, 636906776, 88376022, 447754821, 318603453, 641267088, 115272865, 392205530, 777985630, 733407210, 248437968, 672475479, 733009847, 628584622, 95916484, 2667063, 171239835, 910352577, 617084413, 138096249, 261756409, 739445354, 514370236, 279913755, 512879307, 979636394, 904875422, 959136505, 976788679, 337272810, 264536485, 465354210, 744607953, 17866360, 332832096, 73492264, 845284309, 322676181, 356291778, 192262623, 721207647, 820154771, 380702752, 975372502, 466121745, 446574943, 664877722, 482122870, 353745805, 638591936, 247597982, 809677281, 885928404, 740887862, 272798885, 74300812, 99927948, 892977823, 3451342, 585996230, 954058369, 369541770, 536790789, 588664357, 16647158, 510720090, 438695205, 553963193, 982879977, 225352373, 107457666, 460448453, 110618543, 945941365, 138881123, 68697718, 892345457, 493117005, 995315355, 606667719, 898113330, 14452153, 355111285, 729687211, 903260455, 74829245, 391342169, 531593499, 137255631, 348430425, 471235584, 495061088, 397002563, 610227571, 122755239, 262994431, 725984671, 523757, 564096769, 491723291, 264945731, 904503057, 521606834, 137459034, 746029102, 242550298, 914356147, 114228076, 707089776, 756584259, 680516605, 369123973, 2109644, 9628926, 987596415, 230587062, 968106704, 169383385, 602498799, 319891183, 818141450, 403427740, 150664303, 895800999, 734049740, 666258106, 86206860, 990920480, 356912867, 651383090, 840363685, 720298892, 41160924, 816569085, 643903227, 701003678, 766006686, 75958917, 508157998, 527264001, 52275880, 118705127, 347244288, 952805605, 939574197, 573480000, 8028025, 285191936, 235028426, 829451501, 754166582, 313373236, 848322851, 943064771, 608158120, 979911062, 910450295, 156317869, 556627875, 907461507, 44096192, 520921701, 197855954, 812367711, 378921448, 320760521, 804588146, 303094037, 307609371, 233779885, 303160363, 165678829, 808270968, 296702155, 636825850, 641577655, 99448761, 744328427, 27303663, 227967405, 250915524, 388433980, 692259578, 813923475, 745597400, 813520644, 472134288, 514089461, 202670627, 667448307, 378117204, 593081259, 2443572, 381602211, 150750346, 221404942, 289333239, 123376445, 57062487, 284396084, 567338965, 855285987, 787061319, 708879273, 663985627, 88658223, 225086811, 494426730, 667830180, 245153326, 341383053, 861689462, 753630180, 254903203, 511738379, 606916377, 388427979, 627191411, 992984146, 502504347, 622154307, 248824556, 109160788, 529942230, 369452774, 869606607, 469126975, 662266148, 59870619, 782114835, 703405019, 816749175, 44007574, 970054710, 987807280, 866599596, 921698348, 58846118, 106866295, 783980558, 319149597, 527167316, 453054247, 492598744, 225950381, 485143654, 529428725, 186859603, 81115570, 288998009, 463384663, 276495294, 939257968, 302386359, 372018166, 75691336, 132555003, 127970382, 601734004, 242810685, 123584170, 26719517, 534633510, 702130233, 732796776, 670973394, 733181056, 401885642, 422096265, 610946625, 418991884, 954536572, 101826030, 576906725, 834232708, 657944924, 133068252, 627987755, 823526252, 149314113, 376980141, 217451352, 715872422, 340871380, 432810386, 677362107, 118986530, 600816815, 559984605, 16372088, 414493926, 193192259, 666688337, 482693193, 657698170, 51180154, 600374377, 783797665, 238104948, 133769628, 448129814, 641654751, 262479991, 671473622, 725844648, 741129009, 443628220, 788422457, 169755596, 647163871, 721216431, 291212570, 346900857, 552846074, 852909912, 604732445, 101045998, 338413965, 951451345, 582691501, 435135513, 827919622, 277548809, 156163878, 689521038, 330327849, 398159822, 924943822, 478982650, 508641710, 950950518, 849417966, 240950128, 493836364, 627458707, 704885612, 542064743, 354920875, 460458979, 144544638, 699367998, 214625416, 408387415, 251148298, 102163130, 219527985, 760624980, 158984887, 172876837, 313247093, 178426487, 754278881, 61390857, 211204887, 190766955, 956978987, 887837489, 466725720, 305313989, 26613569, 32251897, 860307004, 999743640, 35339496, 876478203, 599274117, 345690928, 280909920, 419804156, 682156203, 960057306, 484338426, 647079960, 857205143, 26381434, 121944219, 167150118, 845508576, 454284040, 614880993, 298165059, 311316103, 761149156, 698213111, 154709737, 877762153, 976787201, 888358886, 177595062, 771349742, 466176405, 377716224, 967463810, 180052627, 917161442, 919476879, 365726457, 226937430, 930967146, 624541319, 1896314, 604569164, 768703013, 314898404, 915870017, 93196225, 657787967, 702495033, 846781220, 82950488, 212463003, 451022348, 547236239, 543656614, 657337044, 932750074, 108501143, 950092039, 828159569, 181113131, 451313978, 654761424, 583372635, 810924471, 992587065, 455681236, 641632071, 393826948, 227780395, 902584671, 86220448, 331432202, 810058385, 726353065, 7668521, 92422391, 953427235, 633397564, 312105506, 441782704, 131069698, 343713702, 79685877, 704564451, 160128963, 502658804, 115125475, 158804541, 183563646, 575398147, 381285457, 62246975, 875202709, 867851127, 852204225, 768565824, 355046083, 425232054, 300043452, 785011178, 61203926, 190611226, 905253124, 270704842, 503890603, 206332926, 144429443, 46806570, 976712291, 704049284, 197192856, 85214613, 577599635, 701076300, 577041720, 896910957, 705375347, 753111505, 13441703, 538411155, 111979782, 525907780, 742948844, 717974208, 818908331, 911931103, 762408505, 564248089, 586144594, 689048211, 45843624, 468315428, 401307563, 928938478, 373553387, 163681611, 55903808, 275906065, 974108828, 962528474, 671307827, 244551854, 852590562, 729331360, 484413339, 663945760, 758768626, 300473664, 180527317, 266799949, 84693346, 629073656, 701405810, 970224420, 238537626, 776251035, 593823141, 84019829, 172315098, 10907538, 204828251, 932099080, 253235833, 299800875, 997413217, 136262306, 291033058, 101088347, 87099374, 163620401, 530565088, 342717914, 329856929, 314759974, 276077260, 981078344, 187553299, 759905448, 527432960, 20123432, 541981902, 277737515, 491958477, 137407943, 162256486, 56107615, 428258891, 23704746, 15722801, 292886785, 263864469, 70661593, 33681713, 847601370, 461204737, 639823143, 315550488, 296370953, 658640621, 379722221, 608703915, 905544046, 830131039, 816021151, 711844395, 126691108, 672601869, 888177403, 476589645, 803635669, 430082343, 818852332, 851421263, 309149088, 373633403, 847564227, 545350431, 219363611, 756987817, 306673674, 923252432, 804992499, 895334571, 569653695, 949903885, 938064876, 156507973, 727689257, 331273424, 764119670, 92273267, 951718686, 932655543, 388358440, 730177204, 268629587, 926784835, 43153392, 481004348, 190140887, 404482855, 923005495, 872912175, 977572536, 823398370, 38933111, 949190523, 39155229, 798568561, 539621955, 607800128, 645975992, 57526043, 247402058, 336158622, 187734854, 536657447, 660362532, 348325613, 385706515, 696688197, 277612118, 87768424, 65681924, 966661369, 770236085, 176059849, 590186776, 293352188, 772812118, 724495916, 883176025, 688822544, 356275964, 386927091, 665405620, 673376114, 227864004, 722382285, 172567673, 124711979, 109073739, 580563128, 704284610, 195432368, 788172149, 134431569, 936134531, 275107933, 789450258, 419641120, 821709672, 80737593, 685119436, 309039873, 982957176, 873400493, 825624497, 995699554, 376051139, 351363541, 200323622, 58941940, 820732085, 408681427, 352659967, 21601992, 955409542, 350268343, 351162475, 908112429, 6296128, 31722121, 854488134, 193528085, 579577381, 362296122, 956060334, 53097164, 973698772, 391334710, 214819716, 472898797, 378966092, 648127715, 208251625, 981005483, 576422597, 47401237, 796322739, 413779023, 417068812, 505804931, 928076704, 387822006, 321541982, 303757765, 129929417, 50985069, 130189664, 651011197, 424832032, 236157805, 135870501, 277577758, 433761361, 90645420, 621563988, 465878721, 751945980, 749261260, 130090344, 613498061, 893745322, 501574375, 282805200, 485269261, 420597299, 225761091, 537070373, 992817999, 716379936, 340194182, 858505325, 938801527, 906966232, 912963718, 71380774, 515686735, 392995865, 337513371, 713490798, 521225660, 129062036, 944175579, 442541982, 668414336, 969971437, 821822746, 175889713, 452137772, 491431914, 459887146, 939669559, 267982473, 234985098, 427984077, 337802560, 396763924, 830629226, 337520034, 569050906, 374763250, 748712714, 734716029, 699615038, 213954206, 200956384, 198429277, 162998165, 935437040, 811760449, 37876738, 669675922, 782216279, 424425255, 247582286, 921902832, 777928208, 503957891, 389025002, 339193362, 571384280, 148077383, 695389410, 726897212, 594192985, 659997840, 944074163, 981238740, 339439370, 27439622, 556572299, 845160874, 843942973, 233882893, 846500842, 858782343, 126877177, 292532957, 121966467, 644829218, 880877669, 941973667, 619100860, 234345093, 791437002, 291430733, 102969063, 201343842, 541365900, 969057753, 582566595, 78416358, 742541970, 975506788, 96241450, 172805723, 268439746, 257506630, 162196138, 552541274, 500595943, 88363720, 732386931, 22832823, 26117248, 619723508, 282830170, 31031644, 327366774, 763187719, 491759518, 129567110, 745060622, 391522614, 39172508, 389141023, 678589804, 943081845, 241272962, 574898952, 48682002, 196747359, 843330064, 987280108, 476633648, 98358330, 429138287, 798956718, 793828527, 746391075, 498698819, 315961509, 568739652, 428366203, 599371274, 959709625, 554923870, 11217048, 753216534, 553878729, 277959905, 304673331, 688830965, 968867493, 884310475, 445789153, 773890926, 81379505, 385273786, 339999155, 579980628, 983645846, 952335837, 53025550, 641116104, 174475026, 957253884, 140379504, 335426662, 732809270, 362372131, 240791516, 584425431, 365613679, 616961065, 279111613, 425258972, 574795320, 136667352, 640799311, 945820035, 480700225, 279912638, 500917387, 700491742, 32046549, 620709256, 462681056, 997517161, 818474220, 414351354, 807646107, 732955516, 222389103, 699564344, 73827101, 535375445, 684502016, 861280351, 963713538, 550732471, 468675563, 569960129, 452196339, 683327804, 835902707, 363519465, 898373924, 126685566, 681051154, 884242509, 265230231, 764578080, 555339208, 854199884, 223655909, 688222303, 143477703, 323390663, 600365496, 964764974, 625179584, 102918323, 705246355, 193667997, 627690013, 428178670, 270553288, 250559471, 189854906, 797976629, 931374210, 510887268, 20333001, 73393606, 126425385, 793935118, 955516190, 886958273, 537447550, 591542768, 267535095, 39368385, 950584020, 429765097, 768133069, 346635829, 729740543, 862460256, 955432543, 888834393, 400380475, 944682429, 341730339, 885817723, 828301087, 660277152, 714615933, 698343254, 291432848, 859150657, 182028107, 867250616, 596787324, 270003897, 756948096, 84616077, 914315237, 544871006, 438050254, 554650676, 125372964, 175813716, 964607252, 128148200, 635191022, 335915197, 935261402, 65054478, 652336304, 561342346, 891510200, 214741237, 10789882, 422413680, 581518252, 844450532, 518580357, 192316769, 394709741, 689306655, 383325386, 666371785, 802568899, 83649105, 741730685, 328684123, 41752863, 966972563, 843026870, 842595830, 99826110, 8990880, 389991517, 79691062, 145162545, 871334495, 852741267, 578163623, 970512948, 814054755, 511203515, 727509507, 682376014, 331798481, 319248769, 711332822, 130832442, 557201348, 288180215, 777573420, 332396966, 342141558, 816749651, 21017951, 130507997, 783656777, 436575506, 963348183, 448456539, 687340158, 722839766, 519434095, 911318467, 110469275, 85107352, 756399091, 861124817, 944926852, 731262223, 394323292, 448320050, 176491146, 426232675, 31116595, 988498658, 771579776, 909379479, 66289503, 16927127, 885497506, 290654374, 876477198, 69106942, 508676289, 489809865, 715019368, 126651414, 676288001, 972154984, 802668555, 473873629, 904837350, 543179211, 242462178, 799547799, 961483743, 668732920, 179136984, 790437203, 52164729, 871587481, 640795156, 332865105, 743810264, 762357513, 627909974, 155619423, 76696704, 559064997, 446849168, 20032129, 455795009, 984234290, 501945080, 12348569, 426395198, 197019225, 631300100, 697603860, 743405203, 64412405, 625823863, 45585060, 600182880, 312037790, 278487405, 946771103, 767730076, 559173067, 13304182, 37388779, 901949296, 713612168, 957668375, 232479354, 34944328, 759331181, 261149780, 283070746, 872982117, 874411907, 273078744, 535102386, 726805233, 299699273, 871887023, 393953161, 35119122, 446408805, 424018000, 814050178, 955839630, 948226884, 250723, 310803551, 754751124, 139915976, 957351773, 275279702, 274002589, 799056374, 456426794, 173424200, 103590127, 930796453, 120864283, 818074365, 67720665, 308341345, 965327952, 998917653, 615221178, 320921749, 285625929, 974593616, 993593129, 483575345, 703768134, 861713440, 497385512, 769065628, 607714561, 981736980, 448590788, 372320832, 859784997, 562611785, 806611088, 226283432, 275011176, 453320657, 285318433, 425863208, 489392771, 918756823, 292700677, 463894892, 542343923, 411562170, 930792656, 866306848, 414184878, 193619619, 172151396, 933299688, 649666779, 241287922, 956178964, 591151830, 430977681, 533701657, 868667905, 568509861, 950050051, 657377123, 329821960, 526579474, 557691100, 14166407, 334613983, 296262409, 595685540, 931269846, 685892286, 774139505, 47449298, 403680048, 520113594, 187948772, 829320586, 383621300, 907032982, 684212455, 274764388, 311428624, 673994999, 168818091, 231288319, 888447727, 127498555, 879019666, 392511907, 137105938, 224546795, 736458448, 425233081, 4380801, 613717871, 493980152, 421200899, 325390451, 120380026, 705381794, 479791622, 137578784, 429089181, 610015453, 179431454, 417900137, 570392981, 691421325, 263163384, 546795740, 441919086, 636022451, 605024489, 801825256, 932380552, 652326276, 94598287, 529512731, 356356223, 595654110, 635480956, 440262936, 835911335, 556163347, 574228909, 151161005, 466928275, 886694485, 438626272, 605050966, 223092820, 639825916, 138327165, 412671036, 694716170, 725787291, 36675634, 13966921, 979620846, 99943574, 980192116, 469380814, 885249016, 168467077, 493985111, 913641278, 765634055, 606686793, 781327546, 374299960, 446704596, 813732875, 7443399, 207258585, 259847737, 91454385, 182964559, 433860214, 292101801, 52467446, 505969880, 344688065, 160341122, 930559275, 249144622, 3564148, 735803400, 25498172, 516035276, 750312507, 315974427, 643083954, 826046670, 66740256, 350127535, 175646054, 879780894, 109271045, 306883569, 312737715, 193343874, 784903031, 514014774, 725908725, 488848375, 175771211, 802757432, 614046177, 233715986, 237776882, 853121552, 338611136, 829665627, 466568156, 140858792, 622232887, 79028102, 300108560, 178595806, 703711560, 781036362, 27763024, 950395231, 115543614, 479663027, 617617505, 808845690, 72874873, 898920252, 753461434, 970928426, 8763897, 243553733, 852305212, 515170614, 74198080, 332350896, 924623957, 617576097, 403971209, 76861552, 795623133, 308836803, 516361838, 520847605, 162460708, 144579012, 782216695, 584898719, 728510936, 314232367, 685578133, 528527701, 219794025, 161880266, 778885336, 652154280, 557375865, 771793244, 158343946, 542070387, 835680299, 476038773, 36520796, 198245029, 208434190, 847196993, 901407944, 678168479, 318279839, 977576440, 803639172, 177795023, 950991067, 556687731, 362958543, 366335412, 22433959, 670439856, 467229473, 49619066, 306163377, 896302197, 842809213, 893730897, 483321057, 822786975, 383672080, 963458330, 969109245, 338032880, 265070359, 957190938, 623841398, 63362262, 383655830, 939278504, 912142300, 404354373, 459871138, 24639356, 977215175, 725326725, 488959667, 271534617, 124291436, 511477269, 933078508, 738089550, 721502035, 231301821, 68107974, 615995225, 790799989, 813552863, 215897176, 544240866, 369429070, 921630899, 860547509, 90645555, 833818414, 959258007, 93510247, 758616069, 878059902, 24865496, 263127693, 151169361, 663416957, 342915207, 626791112, 809026601, 36935226, 492392625, 465273482, 822407342, 105635744, 257147600, 800583961, 598763983, 303272435, 811985514, 260883871, 99585088, 108929250, 3030196, 360962779, 651189815, 625025219, 804275554, 258086434, 943729847, 697058728, 353943052, 847814914, 777507290, 941547558, 966832852, 725328388, 453123581, 974406443, 198543767, 778753901, 903320719, 18074915, 638153416, 18984793, 515062127, 80323601, 474423017, 216642264, 373508725, 66682811, 699539242, 478231210, 635124651, 974230149, 406158779, 431685061, 495225064, 429571639, 74839137, 859812793, 382264122, 430019802, 966899034, 11593142, 319101146, 537672858, 777322270, 409343884, 272630738, 844604418, 60834105, 725784676, 410766343, 501878018, 375382969, 876634570, 115031536, 10490900, 208220399, 473800181, 784004395, 950756288, 721114536, 131810109, 131790794, 839281615, 779375147, 137960444, 97087390, 786366983, 145163482, 9274, 734456313, 126560229, 868518857, 589136589, 295758424, 85566472, 961138351, 339257633, 118296796, 646458840, 4368056, 571908428, 823639216, 17726808, 264675145, 320503245, 525023834, 687112519, 273669726, 34536793, 227978157, 232494053, 499594927, 896888029, 298014480, 508853441, 63098198, 698035568, 815324287, 290963207, 688451553, 837460194, 987958054, 619758005, 35953128, 896282747, 502012227, 424617101, 81494156, 833384235, 253357846, 310331581, 650558636, 888101193, 697532842, 44165655, 496440683, 305975367, 419203610, 5367122, 233668439, 495681093, 973766718, 348720448, 642448769, 784772105, 864228551, 327297001, 167492453, 844215161, 578258245, 310656159, 252094883, 156920046, 218311955, 476342576, 718371652, 988922007, 557088776, 644171822, 564901332, 272968079, 555359457, 729684203, 221592484, 543157814, 802660546, 253187454, 877825449, 932685100, 36434229, 925219051, 200505728, 289712287, 133664453, 532584870, 625552504, 488247869, 159460349, 259425901, 683692243, 682250256, 597279747, 849855679, 512034043, 116172331, 171474047, 135752037, 48403082, 549658422, 604592424, 393052808, 750781381, 249000978, 720264128, 640427499, 823045410, 376903518, 435637301, 233158133, 182923482, 186725573, 909061370, 496019630, 773730404, 203693961, 242444636, 893158935, 742494405, 15790995, 220419181, 40952651, 973239759, 87162141, 399793167, 394255293, 431985729, 689992145, 69382344, 798308944, 866121955, 302191490, 558459806, 123143265, 596279960, 377266150, 582234243, 794690033, 492869981, 451520850, 252460094, 141588735, 198310902, 74663122, 792131149, 27249324, 898830660, 905990397, 359614828, 255897690, 535900964, 229898873, 379865475, 211897105, 153196189, 475391536, 690146946, 675210517, 822646628, 75244873, 48945708, 647387937, 203299906, 110701429, 513792373, 312483901, 460339766, 856637917, 498142057, 382704882, 674958412, 804963914, 317117477, 174633698, 588447972, 338958520, 995906144, 386210672, 845968134, 284755463, 247032277, 451832595, 238788954, 512997083, 649428071, 745865840, 326888937, 989929329, 180233316, 195174874, 792395439, 37983557, 931417477, 439867422, 444186941, 797888536, 625861610, 736987259, 191196300, 887768298, 905158222, 164858448, 711967098, 277577063, 20380243, 444733262, 353548451, 639989032, 595063207, 357479738, 519559468, 966206475, 53208678, 392569114, 56990052, 743489027, 189630329, 84617299, 730288293, 300881285, 313294509, 312632602, 879782195, 492249530, 375901570, 733928646, 117035414, 973323030, 332248369, 121985292, 322456850, 381833808, 274867874, 39556215, 337269492, 686772029, 515888363, 904472673, 433504162, 804401295, 403870262, 138978213, 303857956, 64140545, 660155388, 132109069, 345316568, 754808812, 980680646, 197091631, 20001927, 378653499, 940690036, 949364005, 682262296, 96185150, 34839931, 396602088, 740343676, 183414176, 337499466, 873941331, 781150001, 625470793, 640864911, 219378710, 902459263, 703754029, 41545931, 693180843, 458291300, 811855961, 188417428, 376874673, 459310566, 746510926, 440345607, 301908907, 239353484, 808143626, 525817866, 247450661, 955733, 238879305, 370391715, 992518442, 913154078, 305851118, 727743244, 374959137, 734626018, 2483997, 896958672, 842445971, 118217193, 171720866, 493037922, 269292728, 609505771, 717413053, 625406452, 436339085, 522286256, 493609611, 177201931, 755280500, 848468287, 555298890, 426464463, 435492080, 120648329, 251612259, 920622598, 536270005, 57875199, 929623521, 593185024, 654095922, 405341177, 106126624, 656081037, 759259578, 732574557, 377046939, 251285532, 315917710, 798355532, 918253772, 16856877, 826185177, 417427203, 899876641, 737101435, 946061089, 983513202, 922605647, 177616729, 539895881, 215524149, 511696511, 21518872, 863084288, 668212816, 589268730, 125671037, 971687562, 180607927, 592393698, 115450733, 659757421, 956441147, 487976984, 481568832, 199447571, 676035261, 217129267, 222686766, 3557535, 745937247, 190677656, 497253244, 276914959, 989683840, 162033105, 991154729, 446827515, 443519999, 705874954, 52912275, 990864412, 732472523, 959231982, 672909070, 349652682, 862512109, 570123058, 713344173, 659159475, 269093730, 988230945, 477902773, 469480778, 915297261, 23182108, 622683030, 954613051, 496808677, 381539444, 817853033, 254678094, 42050914, 43324185, 655083389, 245364993, 142444621, 602307856, 10524673, 787549620, 967353524, 352804608, 630311682, 609522619, 459860117, 188749689, 993575785, 921339947, 900935107, 48991708, 170514886, 1596438, 781497494, 588171306, 887687641, 310886224, 402788920, 712604879, 951942160, 133413334, 477126833, 224677324, 467569926, 498762284, 877303815, 891274975, 739261009, 652966612, 417215694, 816145366, 127412212, 872920252, 502912286, 740357810, 220661013, 54423134, 30187220, 473650402, 279687327, 890815897, 616168695, 365132263, 333626893, 645034822, 721671931, 74498193, 988195684, 330887152, 798870379, 563065010, 193027007, 493401680, 921888582, 277537064, 692284403, 992654000, 762019341, 915704598, 222059706, 739093353, 566769162, 639058091, 976114002, 768399232, 991555637, 773034877, 219659338, 342707027, 601625662, 185461060, 200674162, 283843199, 36022995, 392720372, 662604766, 151699522, 972981040, 412815188, 683290099, 811647853, 640292387, 686205778, 531702100, 153430296, 208674991, 323277724, 342104635, 17381797, 819762572, 230538009, 843054691, 434492379, 850578750, 154255940, 21089170, 971195463, 452431966, 882472481, 696761862, 980331314, 54603688, 322787429, 725442761, 643333287, 670361643, 39800184, 457450016, 986431918, 598378597, 27856892, 767043161, 468412928, 689687889, 840804006, 81933339, 242064101, 659380317, 525337099, 379762830, 415428363, 596973318, 40049605, 286185392, 440850274, 199749857, 940509799, 843799363, 202223543, 570917463, 213180149, 413310298, 187379005, 768101232, 78929934, 828572447, 701296675, 758375117, 407266234, 600645255, 799501860, 793259668, 645445205, 628415602, 625138310, 397284162, 653091617, 639215245, 780874612, 479448685, 328747548, 953748338, 205089670, 436103967, 71576474, 421651006, 546821373, 435918927, 239768929, 179720561, 346122237, 467954153, 813558761, 425907209, 630650546, 547885313, 489787761, 518614906, 800897500, 810409343, 116006608, 969619637, 206524036, 251620829, 820176287, 47469356, 119172790, 794367870, 1512684, 497923424, 183116954, 736201968, 904461882, 584451524, 125919366, 40869925, 876034363, 246066279, 792141338, 81080116, 184800761, 442091703, 872867187, 858595994, 710390539, 361103984, 703682569, 806765683, 780697858, 550427894, 964173767, 191596207, 802984161, 234621911, 358761910, 762899480, 680831208, 287641875, 350656620, 820277548, 298695931, 483731582, 700097382, 472926471, 310951676, 239493898, 232354695, 32292619, 200510776, 494542844, 868371712, 917168410, 345776099, 170288609, 322296135, 912896231, 517911600, 411489480, 634429535, 153747610, 260800717, 986152231, 612074051, 588208894, 763578413, 273325076, 865328908, 960214381, 371418007, 386686456, 827981978, 45404080, 895920218, 991857262, 803499070, 226062388, 569866713, 985627797, 371990315, 934321465, 745671927, 349048887, 427394511, 855861828, 954264970, 670233003, 106790280, 697634646, 661038330, 234156731, 642596971, 682458092, 973974826, 569675401, 480807215, 14786177, 342104098, 889401841, 861501811, 933184196, 543674768, 796616305, 241592544, 261698287, 976199587, 996067774, 870466848, 808276337, 680185323, 944550028, 625886588, 964513866, 968167237, 307090626, 507808757, 161361574, 525974086, 570907737, 469829875, 371869672, 223202246, 938872904, 795975670, 662167918, 974160522, 475685401, 755552311, 926633689, 51359938, 603908545, 139919562, 256351042, 84291017, 793393307, 390468560, 48254491, 518865855, 478484633, 480362112, 829112472, 566594961, 53016709, 789061663, 483019186, 851801836, 233280224, 836470167, 385762895, 581758324, 662762387, 226762902, 350011379, 723295702, 981874556, 749430595, 445396352, 230313744, 609308310, 177054269, 346118757, 94335049, 360359169, 512528415, 809994513, 479991652, 569616629, 582883080, 438050490, 356164345, 554634177, 878562818, 13921900, 501304471, 777335957, 661931574, 722740903, 991628465, 101871933, 372218589, 406362548, 65258233, 158026215, 114257348, 624370591, 391688892, 767264391, 142392509, 55570167, 253347674, 447064406, 779714795, 540398968, 189458083, 873436714, 77227105, 119352239, 759730423, 348870755, 706093265, 691943181, 701289182, 199610709, 616339666, 607680991, 741580149, 9773166, 693055197, 149403059, 511087200, 194308574, 4317402, 588814921, 72437644, 66106688, 145495622, 884329662, 476315506, 46751413, 827857017, 623567284, 869846596, 296303510, 398274053, 254021508, 460151662, 112581256, 934409942, 86351696, 437351063, 573769150, 576170535, 458834620, 867852500, 822609720, 135009651, 226630302, 465271816, 874459834, 717502101, 502420081, 771828534, 128673019, 9878855, 962893065, 152966529, 352431241, 179193784, 727607888, 198190572, 875498375, 252097206, 849542397, 352288325, 658588691, 930894918, 406740598, 151654343, 420621753, 293615412, 951476804, 106085026, 897430536, 856465591, 612116909, 507081986, 625702466, 925881289, 933330005, 311626579, 545090413, 700118136, 199093326, 593247473, 160335262, 465647699, 283009054, 1113943, 237263167, 611621929, 631148482, 40238914, 143249210, 859397096, 351717530, 301626234, 612122607, 810176658, 38273644, 205884683, 637383839, 204604780, 760619338, 407978798, 36336094, 580813646, 875690184, 25318997, 265020699, 247510411, 95787868, 379825296, 727600117, 365864824, 860942165, 287963294, 167529221, 106544080, 418564676, 52381371, 754651441, 253090257, 127171069, 773903526, 792344801, 23830125, 126498830, 553507610, 692889246, 917123634, 404275865, 295552993, 316218902, 40526413, 166491930, 920488127, 189990617, 276989871, 128395874, 224373145, 583829997, 560573957, 688165738, 160273165, 686230908, 319452923, 845739596, 722739801, 634442158, 754250582, 634295611, 645004825, 294007044, 820453204, 467076396, 394786974, 227084622, 365976514, 455599237, 707635033, 987953153, 297686935, 432118004, 543491531, 169413058, 982422504, 153220152, 436878490, 267897451, 18627896, 120081196, 581028421, 367332137, 936468144, 445317387, 871329067, 177802070, 472618953, 392767176, 44575521, 322957911, 511451517, 99769918, 137098231, 400583058, 631232768, 480836407, 79141089, 132154600, 66339357, 89782314, 442941730, 906784705, 631206797, 841389954, 418537340, 177055297, 413996200, 780149387, 337816225, 425510084, 982597069, 320073739, 99266686, 972621034, 328368738, 748180588, 715282578, 85595259, 579920947, 432403712, 441398876, 611296055, 549298739, 662698007, 359461819, 729914199, 101321384, 195712787, 887100477, 473950644, 485246226, 665318860, 72930949, 45859435, 781759892, 426100176, 307146695, 665512429, 75300555, 748675753, 729576467, 398094533, 946698223, 530745555, 904668288, 279719074, 843895539, 584788528, 359245492, 7265977, 446052225, 182756620, 64557066, 955320516, 841265463, 528238098, 939863019, 775456754, 365938092, 92424370, 713602857, 422677159, 156527793, 437787452, 378614759, 661474585, 613274653, 748174329, 771763005, 137548965, 428662199, 255423068, 702214436, 505554980, 899936952, 266461398, 966940664, 101196185, 411881887, 287331356, 91707364, 232072993, 718628105, 691362485, 752783177, 97826797, 703621491, 838574389, 582999833, 707129824, 793102550, 942773554, 671206228, 278841283, 534805414, 518915081, 968368223, 515742456, 98488218, 930922235, 115022660, 105062777, 174637070, 925594598, 248513594, 619987147, 450924209, 60085560, 154168636, 110782291, 536135388, 719727590, 165075254, 758038493, 662086767, 875119995, 968571886, 501567476, 907070633, 735264509, 633493821, 930516754, 65439628, 656638573, 285306275, 228407880, 674475072, 291625074, 452731014, 408905585, 350405743, 918666599, 624203307, 473492363, 52613338, 784274286, 715732883, 602244121, 223052723, 578910736, 700952586, 837500556, 549579308, 956549213, 526422862, 681779870, 771877701, 98983454, 444825768, 366628476, 923948275, 514533524, 850660338, 875400574, 837618581, 681283792, 653467439, 777881486, 865156430, 764506826, 151217268, 147521568, 498061182, 829590896, 693393093, 335376136, 83592384, 916426777, 132770998, 689254734, 360340559, 615213460, 515948753, 175727015, 994751119, 825672087, 446328096, 379654854, 812281635, 389295682, 272063059, 613838775, 105749735, 828436902, 96545959, 453797299, 275341816, 182757367, 470051325, 682985314, 518588020, 824173745, 997981730, 700418093, 419694420, 789819901, 937685990, 66991211, 2106664, 364593820, 436257859, 997748984, 815966569, 848768932, 920544142, 295018265, 716564100, 977197118, 920146429, 636433458, 700948989, 588596203, 645902478, 612115336, 232793377, 354515130, 406995928, 866828901, 286214645, 329704671, 963130921, 764909740, 968036323, 654449915, 912054862, 778344681, 451909535, 318268730, 448974279, 562071558, 669264656, 482100625, 860260663, 289879076, 511233531, 472682047, 586601652, 409207518, 677002804, 195126570, 456407941, 872219720, 88339264, 1023648, 526773674, 982146942, 575542586, 698305893, 374824225, 424472858, 622469866, 908979458, 319688392, 159895858, 332757242, 712668239, 485846636, 340817104, 985239624, 705784547, 872017156, 57983432, 384571624, 102923354, 856424483, 415291225, 495377755, 236656856, 692716240, 675139958, 334430457, 478826030, 545420434, 620134777, 747132764, 299921159, 61641612, 827567281, 356370787, 234447987, 231120579, 219582305, 442544918, 420022220, 701616648, 147658102, 912522077, 5586404, 792773655, 922135603, 947855259, 676559750, 504441686, 337499612, 683639272, 933835671, 261965159, 769169796, 26539151, 986298440, 707446185, 384430375, 542576138, 354144899, 728221482, 176339933, 915805219, 192445200, 259659841, 687587543, 821674233, 155184858, 806877093, 120083429, 610150036, 215039587, 634787163, 163144808, 864530642, 413785871, 752361571, 122457300, 129671590, 418867911, 572725353, 542016037, 749263945, 908397740, 711521169, 573240465, 239468797, 14492867, 379012132, 45800173, 702025884, 280627153, 394307643, 852165880, 116831528, 705275092, 404372495, 960986632, 371406676, 905712814, 840401997, 547952643, 281501126, 111448372, 721288136, 318962254, 291278021, 239584976, 425082987, 975064646, 313650762, 667911035, 2452476, 7156912, 770957336, 750214633, 269192256, 452428578, 760440691, 879284354, 112299115, 532898277, 639141508, 917991749, 224495107, 541857046, 887278373, 667404362, 934963035, 411054840, 968483277, 713721876, 32551842, 293309243, 790130184, 400665251, 877690619, 892154521, 238188680, 59840121, 255943087, 867065394, 841720836, 960055647, 278867938, 431062379, 582376238, 252904320, 506649933, 290664313, 239182900, 971713662, 470130535, 315698361, 27205423, 438445560, 865685133, 862967901, 49801349, 816926739, 771545352, 611116506, 969442511, 253774548, 47865969, 198293147, 704262740, 70704601, 620004163, 7693048, 996394628, 280201492, 470546308, 995758513, 62918520, 33688337, 970067362, 683422899, 588539333, 949540893, 39180182, 768933432, 887883456, 596091790, 761190706, 68210974, 666884429, 896541399, 953042216, 845461326, 133127164, 536145142, 882357756, 272535442, 589904880, 598980000, 613832163, 459242282, 119845608, 789016256, 842813357, 101913721, 347219294, 825116257, 506949038, 729913060, 547986599, 819113631, 596761061, 559421411, 470532294, 217320435, 894767368, 369940297, 590711144, 91912580, 65166088, 674537823, 442062623, 241266058, 251342572, 800168497, 38235735, 555094877, 701946448, 13369478, 569718918, 82793569, 982680786, 172153689, 611573486, 534120433, 857962212, 812171961, 711673709, 910395941, 43741716, 9201485, 788453221, 830187999, 307767186, 474668383, 568022682, 202604383, 814012105, 795914946, 299763002, 790972370, 616977846, 423578597, 787887804, 281006931, 780282396, 959769991, 564116648, 96437227, 481387612, 182445908, 864170727, 216986846, 73230928, 852588106, 322752099, 554426850, 304741133, 765642354, 431122600, 288037250, 181317581, 644012169, 460753893, 729127201, 100101789, 79306052, 517615352, 68863297, 988399369, 72529618, 634120508, 21149985, 929076539, 926990789, 115821668, 172243149, 755638978, 556249849, 275837599, 474206309, 631897055, 720614686, 552548575, 591056817, 65405323, 114412308, 936039021, 966189671, 607285997, 72093691, 480253414, 209458878, 846840262, 700446973, 220148496, 54906121, 330660057, 934455337, 357102236, 894435446, 550826664, 720924437, 657743333, 774695438, 159469420, 252283284, 476178977, 497558729, 79743731, 627079856, 449442284, 845373604, 230089705, 71721486, 219603004, 784892865, 876116792, 680173073, 11167835, 808200756, 689014124, 202027836, 877724006, 770499604, 48469012, 960372855, 985495590, 678711283, 363696340, 611426535, 982716205, 284143697, 240970499, 566705873, 200435161, 974690963, 486893897, 344298350, 784754165, 927024126, 494506002, 738227449, 497615618, 773513725, 975666125, 423154350, 335618717, 116601227, 717144670, 41391288, 157545325, 603346453, 384757715, 68806393, 221751378, 44477097, 130372505, 922566350, 37148321, 106713739, 60507641, 581789769, 857547227, 683970712, 740058857, 293641226, 365962338, 42507991, 896491469, 370561469, 755980270, 57945750, 945527026, 865325464, 660955272, 400398336, 572299065, 877898856, 926756883, 579087708, 722511930, 780594362, 458556320, 230118284, 644597472, 46146045, 691303142, 963093595, 714244352, 329724046, 210211463, 69982889, 257220191, 92544761, 549472730, 944750112, 279116583, 168949667, 75071291, 269116048, 975597168, 842952920, 657044385, 129887477, 945378904, 253312837, 634057252, 258381583, 4590640, 680234868, 343794420, 30501452, 770931430, 528542352, 348264582, 653932706, 367174181, 894472268, 493883873, 960391246, 213045095, 394258898, 6108579, 167954965, 46562504, 956721526, 503402326, 567394691, 490007503, 932559560, 846580878, 887208250, 614393659, 131807958, 706139208, 435903828, 848814688, 798016233, 358921488, 412771292, 542400538, 945890366, 598406766, 667728897, 382251689, 537694377, 994812143, 553316397, 734854973, 911124509, 799658851, 470593965, 334751028, 827024910, 32421102, 45086706, 26198281, 339408431, 671618661, 881987874, 234539763, 636468641, 807497664, 231337904, 382788156, 531194141, 559630735, 344828376, 306816712, 415497033, 170693555, 426964632, 113350719, 970688338, 711604045, 178950006, 264794711, 837774998, 361782867, 686711027, 989460438, 569634246, 659480859, 226745718, 742601659, 295221427, 267189687, 534370896, 522381732, 194032233, 227705769, 556767818, 298632298, 756693696, 352073782, 689796950, 602026430, 761429617, 770988018, 681902734, 95420532, 7839170, 328567779, 795140395, 676145915, 17498243, 672980773, 719639413, 708801527, 109802643, 225463218, 471079463, 710193025, 169322529, 73843688, 487624190, 947888033, 871142160, 622459575, 282866465, 232730319, 505197861, 819152179, 991549300, 735966983, 608680425, 527618127, 911605382, 547757719, 95612498, 684880343, 843442558, 452221252, 55743883, 715467170, 104350896, 203736318, 124000188, 715927586, 347996622, 57157811, 608197504, 603985532, 435642462, 934201807, 532994047, 936305788, 177036713, 625802589, 55047542, 772807700, 109044003, 141431132, 170545849, 154426583, 404501449, 382196738, 69473811, 689814096, 80308083, 567155632, 915973969, 715514954, 620060537, 102089963, 564898713, 346144968, 372414841, 687818892, 697866856, 635635589, 260968836, 845912119, 894390184, 753562709, 635681371, 119047033, 112439112, 145006676, 907253924, 973524120, 86522618, 207423320, 697322322, 143690551, 67332237, 806192744, 947384492, 737908863, 85654211, 62371117, 758745472, 153017926, 222554718, 845217135, 888342108, 884056541, 967684623, 548557550, 377092664, 941498554, 74367022, 470471793, 769433663, 51025904, 162237443, 263495682, 34368484, 606049219, 158888936, 392105521, 48001553, 197100592, 183238338, 481143943, 974162822, 206192105, 804065771, 270447381, 723306117, 689779578, 223412834, 835205852, 528050151, 260644922, 626386296, 68832559, 326585227, 312814821, 132858564, 56728384, 243250861, 555767647, 595134477, 914103178, 921594935, 877553534, 430489299, 485111, 646766217, 75745457, 288039109, 544392579, 641718193, 250962405, 764201308, 183800984, 403934651, 404897899, 376688454, 601157340, 246601118, 79158924, 551891661, 940704377, 199481908, 397372771, 781484520, 845790443, 214843725, 293463189, 345563899, 472239387, 174812831, 31021935, 838150251, 848307820, 790241080, 410887312, 743311905, 22270613, 763576962, 477398994, 77509887, 15054048, 252803314, 88891965, 875877408, 384711374, 68807178, 155378946, 986121263, 702375896, 174072360, 285305202, 956271323, 708027198, 511997993, 611846324, 718157560, 339945925, 894949858, 464560567, 379092722, 485734011, 508973200, 1392136, 260363664, 977270302, 861046132, 438803896, 330463872, 739805682, 11351329, 262669549, 605256632, 549538444, 561799719, 97142373, 724728939, 517090439, 376664568, 881640447, 592502262, 779041171, 26034276, 452892029, 14291113, 906653857, 986761718, 251595197, 384960958, 61293592, 449626446, 65086833, 416961786, 980296013, 142170619, 917299087, 473033126, 409313172, 630742118, 582972682, 136837867, 682468967, 784194555, 607497696, 578261790, 842780525, 954984267, 685034345, 503750959, 459451401, 170094178, 146218456, 124616757, 866454213, 723672003, 182167053, 455481873, 511893753, 156058128, 282681347, 578178392, 73383272, 568814315, 798500796, 99941920, 627103337, 920302439, 114545536, 11413924, 370371831, 882012061, 302134053, 765770206, 822697356, 120065847, 246587723, 420561864, 814017142, 432236242, 21490341, 45485221, 972062444, 604712062, 584130187, 474608356, 527558462, 984747157, 216286131, 822815126, 596630829, 835244251, 723614332, 861979506, 340121626, 555605461, 840197382, 270716396, 486407212, 74118531, 381376545, 720505784, 940127242, 627276968, 244320033, 79235277, 864664359, 271245792, 729816630, 723193037, 521418349, 551900500, 505674545, 216908497, 127085874, 956592723, 158943278, 279044013, 434788815, 489720286, 882571562, 62677462, 392103046, 869223216, 671709151, 543836159, 480195233, 589746821, 883038635, 225808692, 15164431, 440855329, 623843300, 588873960, 795731157, 941386682, 416852103, 550515863, 316413275, 82649187, 619784655, 953039222, 468585036, 580789153, 977598847, 797923686, 982263381, 809410152, 247560345, 22520996, 721011259, 59520059, 105891155, 685443824, 419063271, 305028915, 261464119, 822293168, 144419719, 949195667, 856075601, 98876564, 325468152, 961678025, 818690692, 487448953, 607289338, 866433319, 619329593, 336568185, 555601440, 587264390, 641848552, 710702558, 505493246, 354836407, 779998107, 571437468, 733875248, 347282310, 247361746, 856643758, 477181031, 255940386, 203739697, 948296121, 966145014, 42192502, 895150348, 605038506, 824791820, 896395508, 34469792, 288407009, 781365851, 895485504, 577677201, 85797468, 797338432, 695653414, 840801181, 345696059, 458977510, 290844133, 566370531, 353128604, 507196035, 362959042, 680683443, 752021577, 482396754, 519113800, 183850761, 997269956, 352929584, 849548189, 192866152, 329654401, 36224703, 157647874, 153151947, 819729541, 64847469, 6664138, 288567049, 836181460, 620122239, 816151684, 910329430, 817028642, 405861810, 99620666, 28674477, 84463578, 972196172, 154249673, 755819696, 401667598, 463627555, 495159946, 799302895, 518331228, 127656746, 875481941, 598056907, 263571013, 344690196, 108695374, 666323886, 347520496, 627604456, 732810011, 785911252, 172294662, 822277157, 417850618, 743183784, 715621394, 13374088, 963108917, 755480889, 904802515, 730008068, 17211908, 708500243, 3107901, 941197642, 319605054, 881117341, 216706261, 951475723, 707087905, 233730446, 287806802, 830486782, 797439815, 112091349, 853373276, 488445777, 703791206, 338555837, 751381610, 250224619, 824293357, 942670023, 594596506, 897502892, 699412138, 527177261, 181969248, 120902311, 229144763, 920379963, 458745855, 10186335, 392211915, 518351181, 768915447, 326549713, 875228181, 209088522, 734135321, 387293542, 505229152, 744270879, 374516568, 457928188, 80058812, 131386512, 707408590, 351622983, 736540849, 991895223, 377857483, 770061195, 747148402, 563240008, 910698995, 293699801, 634163059, 569884223, 692999781, 666921869, 456481638, 658846655, 553489114, 532121654, 193355886, 754459614, 266074431, 481687942, 747755149, 393879889, 42766302, 643523986, 931914154, 5886248, 782357362, 950903810, 858938583, 542499398, 325900917, 346935352, 236778789, 163487410, 357145092, 226099461, 159132197, 944475866, 545814303, 7954658, 47768230, 368033812, 99927844, 30939401, 713544233, 288763094, 467180440, 452812538, 661089561, 317156895, 965176888, 979833554, 404612588, 976906162, 137320252, 264761267, 438616997, 797970820, 683242140, 497823919, 382150176, 868481790, 927165217, 114578751, 679113721, 68260257, 113990651, 26734048, 362285944, 40884335, 822682785, 266438723, 998519363, 148240414, 84902540, 208570427, 258416766, 966516296, 38323287, 502565301, 794450554, 693789087, 88002794, 836836164, 545367568, 827825470, 874697249, 79289306, 644345594, 710977306, 180345458, 99759663, 554987476, 995322292, 924357095, 301689723, 330431255, 332100375, 663276421, 555964477, 354983994, 665123199, 929017562, 958501999, 937583780, 597353580, 49623144, 558894352, 877339803, 358082580, 217695830, 381622310, 569594512, 126678243, 636321747, 644924654, 923683020, 906515903, 322232480, 519367985, 415036316, 23228431, 906733753, 202784419, 152267828, 528146899, 353902125, 2184219, 355262629, 247222390, 598752638, 930894205, 333342272, 611818152, 471654705, 432518463, 973389792, 829165781, 51031270, 950324786, 21156502, 333155246, 290719984, 944571643, 335664113, 549738763, 24138517, 741172045, 716513150, 393222494, 248804791, 103115367, 639313845, 55544854, 242462778, 142121499, 484004067, 413924172, 404278524, 112110374, 975212906, 753481078, 848263423, 887304154, 979470059, 887768926, 666892224, 446867749, 105966251, 334706578, 49033608, 757550181, 669998656, 525939169, 528479377, 523835604, 555077055, 590280207, 421950893, 221486868, 812953880, 460830219, 210056548, 931305051, 104119840, 189131577, 127189192, 662534786, 888251615, 579043896, 334833258, 982277371, 248518501, 244860627, 238114919, 248218554, 249179466, 491393484, 563026437, 707206818, 633665614, 151879124, 870931273, 518837822, 980636127, 136007601, 79435633, 296759272, 767804733, 691330960, 636597827, 482047218, 815049981, 696101106, 480008420, 275982569, 888719805, 242684752, 900039010, 246164972, 370822900, 379177377, 38007742, 176519767, 495033939, 616158867, 774668244, 437236760, 907149039, 757060463, 823772622, 841785418, 301998343, 127954114, 896700655, 752864198, 677067598, 293036861, 273727517, 497739570, 419094011, 35585499, 377991542, 775014566, 706846280, 974259924, 348519330, 535649571, 752665215, 105527829, 980686325, 429091543, 787812213, 411274685, 499499451, 457171041, 839516140, 133807979, 296728958, 194498042, 458116819, 138157558, 2855914, 146327864, 568513923, 818833826, 334388002, 80693395, 148595844, 302921700, 992639538, 591280215, 55670596, 9019390, 526199339, 461774209, 285350567, 605563980, 877476653, 928201911, 443180586, 998155471, 351410264, 158355187, 874107833, 320816493, 733567378, 318132176, 922192022, 566911014, 315660627, 599773240, 550005944, 644892725, 618737066, 31771629, 173699562, 459619910, 436832839, 623413233, 53324220, 934633287, 454661997, 335977144, 721986515, 346693093, 130406579, 989549643, 189620737, 470002906, 709515637, 113091430, 826323923, 936475263, 335832787, 143997158, 533315029, 122287040, 674228266, 619587705, 832558066, 275413249, 251955770, 998062782, 253415807, 382687472, 475082373, 187743292, 564664805, 634458425, 362708259, 131821180, 617461319, 100481393, 272780276, 329310595, 556020340, 864283523, 821627213, 660514201, 870738607, 838378281, 48121415, 692677308, 234140448, 521274496, 868390421, 133708542, 890592319, 532077331, 775384714, 178199023, 205731690, 652085709, 408698468, 777361335, 667289642, 444258608, 48011796, 786771898, 493261279, 177759951, 549867052, 279752859, 259264433, 8718828, 448008823, 263009931, 96067216, 788426643, 570946242, 403034397, 86288372, 924646379, 519464145, 554309262, 184968252, 330316389, 831423638, 493264871, 129450233, 503173365, 867017992, 267184767, 137063453, 56031464, 87526399, 830998370, 727079440, 633434303, 174194039, 477168372, 66839117, 18691001, 649268890, 128989121, 355238981, 30378082, 74775746, 538259448, 453579219, 759674947, 870623424, 914600813, 619506997, 527754287, 625939969, 432122578, 409684444, 560258737, 65634547, 957555723, 239348778, 917097163, 326034359, 888430882, 136553110, 730847027, 568739720, 602458695, 444756223, 552999745, 118515824, 773952209, 939046136, 462973253, 719734086, 55841598, 898068184, 784535855, 343484311, 154260715, 960511727, 805945277, 452621262, 905585316, 692103994, 252547839, 179710521, 970027720, 11808654, 301230430, 361010954, 334334771, 466557876, 691067875, 934337735, 827438028, 319662380, 298941495, 34351876, 619955306, 958006143, 188989877, 722154932, 179994985, 194284701, 355308428, 467031336, 682556059, 830356922, 972986875, 824170431, 531094758, 597413541, 430611404, 944695813, 932307525, 63148332, 703884138, 385452204, 680078091, 165444130, 251672989, 25325309, 534599344, 320234463, 600850149, 260553584, 992680541, 91295893, 71808724, 406610766, 16086471, 804489952, 543128955, 648019621, 676418033, 69055302, 907225842, 315137762, 618736899, 582512876, 246190423, 66407252, 137927677, 750791912, 861161015, 839024007, 182171244, 458212927, 751983829, 163864356, 644989310, 617376619, 193136820, 472469720, 547831787, 552404129, 650061568, 473430812, 185692283, 604253801, 325870164, 726643411, 653760674, 236445142, 960754104, 138230083, 525990724, 713915607, 92841460, 133028682, 49155994, 94791779, 223003072, 485056674, 357232552, 910842183, 89126684, 687124438, 48621089, 992041227, 928269187, 283220227, 195205014, 35806053, 49041912, 314018314, 121701226, 290549084, 609139232, 1421532, 22479133, 505254759, 410344407, 19422835, 325986208, 615895303, 765911250, 205990104, 692498291, 583833453, 836961762, 519808147, 530716337, 873103531, 91434089, 915908560, 982557872, 510391674, 772793783, 595817857, 549576040, 920789903, 112862896, 138046429, 995134732, 661162572, 443074052, 444756927, 938961050, 974238989, 731677613, 833752468, 798652832, 759850047, 937636773, 705739332, 733519473, 551077566, 869158573, 517458475, 230225544, 413500939, 654501309, 807807014, 583545083, 879892173, 125151604, 900623594, 222174084, 257299560, 394006381, 324260931, 870458231, 997985808, 535718199, 873047759, 4468185, 707391437, 368920631, 144665629, 119658536, 441100646, 44373541, 523479053, 940170051, 31373486, 273370573, 545880215, 426985672, 959582448, 921821094, 952588162, 629112383, 873157788, 373393051, 520902558, 937812448, 691898389, 892481483, 4373867, 448550319, 418182343, 902490001, 365370352, 108053678, 441717169, 788537440, 479043461, 219130693, 334189322, 971124740, 61921722, 27241757, 427152098, 65053180, 951492462, 201456624, 509486702, 729386213, 970902350, 760398302, 672389597, 393835729, 961353243, 143177237, 117667916, 815332199, 514070071, 546720386, 175004276, 393603219, 407322862, 225861461, 716725384, 758102429, 731529750, 862281700, 271270326, 731967350, 926818090, 22648117, 426033350, 262150336, 829740893, 174984873, 161238389, 599481891, 356103865, 430907881, 221175232, 847376796, 185924708, 923910340, 39540708, 422292286, 957953195, 175377158, 365026277, 906733609, 659129942, 285867363, 814650342, 823255770, 813316033, 753092852, 620377977, 291899560, 875432539, 554206859, 601778846, 397374356, 737391772, 252062333, 613857065, 77533109, 714542379, 146061187, 336790139, 285266099, 541168822, 743817027, 905902763, 7167738, 520086726, 472573107, 559808807, 623550832, 391222205, 763512063, 464932612, 905317627, 409796840, 87398556, 401215899, 331086304, 171950293, 498548651, 796724034, 599020022, 978090186, 64779676, 197872564, 947933555, 551929865, 960077645, 41313475, 941816231, 328521257, 128322492, 262722539, 437831996, 565575672, 730164921, 819980629, 333564170, 128367994, 426068532, 718685064, 38834943, 18852894, 806847990, 301974668, 599833483, 632707802, 330367117, 209715772, 41698806, 364287096, 742918656, 893317015, 83279168, 987837551, 481772193, 36306529, 873722434, 460482823, 319571635, 194556972, 583892639, 469447620, 256667450, 462764939, 65401398, 581938174, 669097604, 823512388, 304462971, 63304500, 68198731, 936040104, 177860014, 534989198, 399897385, 845479222, 664090174, 664458667, 551737247, 548515310, 550310004, 805515392, 628543544, 978337774, 342446931, 311736512, 68551060, 841615162, 824398163, 473698743, 777063164, 291994121, 528893537, 912672013, 208688260, 600603352, 831114822, 397470315, 843015192, 299008845, 963893551, 118975435, 543927561, 127607315, 362148853, 774273663, 960962726, 89487797, 335966, 288897458, 878559828, 433470305, 108903963, 17504321, 581405199, 572402977, 791983289, 270149156, 544666513, 721062645, 532942406, 103905914, 841151028, 688017502, 721246428, 303088570, 938561959, 344053283, 408118332, 633609713, 649512259, 206396183, 129323028, 247713385, 927388911, 966095523, 143688876, 688954021, 555421378, 299465411, 753336163, 249682949, 120680960, 29155361, 819459610, 838670416, 825983682, 605387410, 3770309, 540476444, 110228645, 178298569, 648231396, 718745444, 281131496, 645920224, 224881590, 799106476, 384748928, 250866521, 749492022, 863187188, 115034562, 284125814, 528272806, 193650784, 707981403, 453260456, 32790480, 143664408, 427741865, 832716899, 518702410, 800650948, 15019057, 623996149, 830957258, 569101566, 2109009, 95027318, 478561964, 147871382, 287902985, 228119832, 437473433, 463784659, 32343853, 458219701, 619574144, 91251682, 575990199, 50502388, 491136285, 171448716, 264559655, 611718534, 46609772, 87668793, 788681434, 115058524, 956459204, 705053925, 320043339, 182421592, 271074149, 564057860, 374982408, 456687857, 560928496, 497441875, 853295821, 363478547, 703831632, 924326140, 150314107, 172962439, 471210154, 409384512, 440637482, 601487041, 325885921, 982972685, 844067651, 4809627, 961428510, 248108303, 889795126, 372266751, 37393617, 407122765, 832531628, 139566856, 18292150, 310943296, 511029152, 878034028, 824616229, 547628114, 893106657, 676653924, 660480247, 190644912, 435374495, 989633084, 981659608, 271864600, 879545031, 655348751, 153383360, 901433155, 236287216, 414458483, 760893290, 903129818, 853097515, 746528936, 794962591, 301765281, 49892893, 933699322, 787973593, 350765926, 436764280, 828666453, 430356286, 792158871, 363128025, 911592594, 126141375, 65366161, 133808518, 861351316, 90319630, 967714351, 940678111, 726246164, 971954217, 227594148, 223402226, 200727268, 15380483, 536191453, 466125754, 115992984, 533369635, 893253021, 697573504, 369916872, 501004022, 228538259, 862148582, 284915226, 656051836, 184953093, 401625983, 143750064, 461948532, 711836184, 46565132, 2818515, 275237023, 295501259, 625740628, 180655799, 428645299, 545925010, 866963296, 438245801, 656932136, 813723316, 923907122, 621908905, 616661746, 228893998, 48828241, 818295777, 580270319, 6242576, 74353896, 255282377, 609913044, 305329566, 866446033, 676926717, 546742021, 957552389, 886314596, 665715421, 811226876, 964684256, 696439295, 299835115, 961632526, 813428081, 526136285, 563284683, 414086683, 459438050, 148766661, 352168897, 507721319, 793177283, 338686086, 939234239, 275040440, 966854461, 572744319, 496297284, 663424842, 797541452, 574697190, 77032042, 10827481, 260717481, 563840804, 50566143, 961337719, 27267940, 845828936, 439328207, 262302189, 933685335, 976348281, 800620439, 744095505, 630433954, 535524229, 951081837, 470690311, 42094382, 307121211, 102275878, 408344434, 412092884, 928646676, 803264853, 433885795, 307850114, 696679619, 128745225, 906108914, 859931875, 614733872, 228338303, 238877256, 835116260, 706279555, 838504154, 127311025, 930103433, 532893154, 77791108, 477347248, 977012011, 929257528, 181494426, 755903223, 191049348, 577166579, 303120532, 977535933, 23576390, 101210309, 794796742, 787301341, 713563798, 287259723, 87429687, 905948067, 887590352, 168390662, 239530902, 221428804, 561360800, 619027946, 170589118, 795424485, 249026244, 696917574, 47860825, 40167800, 745776403, 88486907, 168890100, 868496692, 214613379, 697053912, 802026332, 44155276, 60714456, 228520049, 530874034, 902573193, 445452598, 809763798, 158298148, 635306941, 261406696, 32884609, 622937979, 755083522, 270537666, 179382762, 450386048, 703328635, 756861416, 291808666, 576246896, 106531378, 291838709, 720837313, 232031712, 326125886, 668753652, 847692431, 216169689, 304876963, 308993780, 352290351, 235202728, 973588123, 755219514, 697878849, 38072155, 432136268, 590827584, 534227291, 994728197, 678666726, 49049573, 289582618, 630243846, 367903377, 345724882, 892233127, 781870649, 828084120, 430420944, 119941527, 106595886, 739942216, 718432656, 616861836, 613310831, 276361450, 780341214, 237806364, 747262280, 592952416, 941974364, 630592279, 864597692, 707282565, 73012255, 815747526, 492930859, 768068667, 683570197, 334063331, 83427082, 889097406, 738391045, 850665044, 118137053, 741368210, 33177648, 782228280, 38574025, 367221358, 187523999, 506542735, 905443886, 42616720, 459539202, 139933921, 437533, 918061264, 130825691, 246895915, 873435414, 671130936, 599073005, 366030552, 669952967, 586812210, 129979857, 5220432, 694860839, 115868965, 692772063, 52035123, 773857517, 907412200, 890750645, 194246093, 347425584, 852711170, 153290274, 274261999, 78927740, 366610847, 816112256, 371755373, 748489353, 873714375, 979500042, 971599971, 466925992, 577358409, 268103218, 184325452, 134066745, 504772827, 843184453, 979652575, 280483334, 372869579, 463580831, 24083065, 450567915, 919985304, 484789338, 55630227, 60833902, 771569031, 848374155, 285987716, 638451084, 175373512, 483790117, 292299674, 826834704, 898695724, 668476532, 241194055, 71267539, 372531011, 444197490, 795722950, 525396328, 910052300, 189851662, 443087024, 992444669, 536271379, 602491157, 309247852, 933990629, 840672809, 137972568, 15796372, 768176507, 557896033, 343521762, 116533108, 439901035, 135537167, 333561375, 874334635, 839840907, 784884845, 455263814, 909561135, 515398615, 727334788, 20554337, 925402798, 387707738, 750476364, 763297061, 756975611, 315192998, 766417051, 28929428, 688448304, 798644289, 726660420, 128754292, 534442116, 995158353, 288017731, 411513843, 438960731, 615483838, 805322717, 455715277, 264257174, 633943443, 595487444, 217364093, 890938227, 677752981, 878021751, 651761897, 355245983, 467008407, 215590095, 994461601, 136936798, 530329464, 313188788, 555129508, 798535700, 404934571, 939137505, 641898783, 799200577, 23595461, 701054501, 480172908, 120993806, 53558926, 244785250, 683780739, 426909290, 803062212, 462383421, 458153049, 6481979, 306984224, 280674280, 508740335, 241070259, 490085414, 133288054, 483541470, 45317810, 567893990, 510506191, 377398212, 340077062, 858330576, 278371484, 392384265, 653407713, 714546987, 461958596, 816174363, 30459984, 518103886, 687949029, 589833278, 111489684, 693169868, 43189334, 75617476, 334384914, 235185192, 172477614, 718672036, 151474659, 997262845, 237859266, 473006462, 848818287, 499132437, 975669296, 853320091, 87600182, 495398111, 28403105, 224865485, 443649794, 415532578, 675784606, 218843640, 713904440, 328471184, 628261428, 680532348, 709381647, 849196682, 270412365, 666184151, 397556948, 492939960, 197893385, 121431881, 587078693, 275595025, 202198857, 549132599, 562246589, 275632182, 372140813, 796693920, 716715964, 936327272, 831029076, 246620684, 97560954, 293327676, 181555693, 827380436, 379619759, 462520541, 96993989, 149906241, 322958138, 12595081, 817474333, 484240408, 22438662, 745094486, 295481137, 540275756, 23054777, 69275210, 115192781, 879424318, 923456493, 467274059, 582455567, 561230844, 8228171, 267344527, 889488561, 87715767, 764644562, 279694055, 488691596, 501755407, 484154008, 606429515, 18177000, 28501712, 83972872, 678806978, 963181396, 882390065, 527461179, 706152488, 216677862, 319156354, 140537198, 264973121, 407663780, 228315747, 533285570, 104848378, 394333681, 777563395, 759462720, 186880221, 933034544, 954083367, 490877965, 528717633, 440665554, 468604289, 647258446, 40178330, 724590931, 608997047, 843017383, 305762964, 333179738, 599078051, 503288602, 762753423, 32447267, 207895939, 956443821, 897372811, 968680459, 843387128, 308036055, 644359591, 711699506, 345001042, 639620734, 805498907, 676956718, 389757158, 44193007, 434663011, 432225204, 161092531, 292894111, 120416664, 385609096, 296273173, 820385807, 33500846, 386016497, 586868582, 601676539, 66727400, 677058084, 775422386, 215672803, 335198975, 171254048, 684171467, 175725484, 204282717, 824025066, 328374207, 573038838, 442652000, 321542371, 684518641, 515863366, 532444066, 471289372, 278512441, 101601145, 671628170, 743239857, 662526657, 892081389, 895918701, 560712017, 179359037, 430937988, 878291689, 385156681, 565831764, 137663156, 992269405, 642491272, 685063353, 571583921, 658336890, 657935357, 360014514, 762914432, 631424812, 230954150, 429998102, 762929524, 718272098, 565348792, 426649924, 175526352, 227590351, 268810392, 26394612, 417942354, 572599221, 227908807, 904172579, 386310064, 960949237, 351080782, 854770740, 621538435, 835427432, 813867006, 118706589, 312599374, 991890161, 281715669, 454112913, 462173154, 104585636, 973464322, 998129593, 665521537, 164169307, 649776872, 859006521, 456400602, 905730244, 97256184, 581332979, 349549418, 73231897, 934804767, 997039043, 832456395, 490541270, 67527928, 209300738, 352345376, 566333252, 84763865, 49385560, 200892661, 160640836, 155692443, 746176674, 891955251, 619266188, 402493088, 839216984, 561254011, 919582094, 755130008, 271024574, 991140960, 368213956, 863546238, 497883847, 399314593, 932310940, 787424902, 34968085, 987874030, 440163131, 293549207, 978899635, 85249639, 33625257, 561627162, 698874161, 778342243, 702995088, 403964818, 500764949, 898287342, 286274883, 986760560, 243852705, 273592558, 187225500, 595554064, 196496981, 371595815, 102189221, 559746665, 203995151, 32570381, 556441667, 990959866, 607382090, 854390727, 300402471, 308683913, 836440105, 363813215, 230689443, 551651417, 613369967, 534552644, 680970011, 218895646, 566661430, 532244890, 293800553, 648024884, 236521822, 684125474, 878431245, 695715871, 535552445, 766388061, 212062961, 259597249, 116160213, 840608065, 269224683, 363770133, 325520325, 419398495, 854011470, 641800284, 124899370, 79418861, 212737266, 712220752, 965794888, 891825132, 516277445, 347943348, 113524063, 836160833, 372749673, 870352829, 463030486, 417035300, 209034935, 152452365, 816495819, 398451360, 984372348, 184076168, 83883070, 21534987, 866771061, 2130589, 485057864, 338953079, 777648909, 938158572, 745378870, 698473667, 467785269, 43566176, 799159942, 821898730, 789480092, 670730656, 346379693, 477169380, 711190037, 550892105, 185210083, 412429878, 973764723, 841331304, 668291877, 314852537, 864033625, 813976236, 177397158, 887489936, 434874322, 401145965, 453064956, 957653059, 25535751, 408534197, 537846481, 996415189, 779184598, 150234095, 813250359, 423195825, 278295404, 738739875, 938175518, 197956946, 262601691, 939078361, 507309014, 284967065, 93314212, 23436095, 677648969, 237725498, 407190614, 727657163, 210629019, 57015973, 903466890, 318796162, 330679251, 694325537, 810150051, 715915918, 119394097, 875581772, 395995889, 436044696, 885704726, 544960681, 347998298, 277113873, 620565149, 601473165, 418503048, 84493126, 50045625, 761278495, 826896722, 939655572, 679833661, 446756629, 526408135, 712867254, 96696756, 696348724, 775754750, 490343432, 20511693, 841788319, 462357929, 414169536, 321046651, 761762526, 6760179, 768315685, 38143328, 407139577, 855168901, 730890050, 456824685, 198900096, 309363634, 964612714, 36380278, 112617216, 654135405, 792774044, 548878487, 695207681, 292371670, 589260857, 66135567, 847282208, 446074549, 788950942, 312823190, 294906183, 471170985, 598427652, 138878111, 374854504, 112499887, 611683736, 836336776, 367936005, 728171501, 432341677, 468683546, 416946805, 497720481, 507718117, 54489487, 309963680, 521749315, 617400519, 874809775, 864504179, 520226354, 897179987, 320673936, 588135123, 838860344, 126596465, 767682597, 386039164, 203935791, 781521793, 383065213, 868896351, 47589679, 853217104, 818367985, 173210064, 694355518, 857308984, 202329237, 569205164, 116398631, 812532860, 976490253, 740555299, 857218020, 266766926, 305191303, 45271386, 73079343, 215998673, 681671563, 151915611, 333953625, 988657056, 207929424, 471767890, 390942064, 76769903, 513090009, 81856267, 7616003, 813938064, 883570029, 443415554, 731850794, 203827318, 557111673, 79043481, 195362615, 770381278, 790174458, 541462419, 387387740, 223456299, 691475007, 278943820, 809833979, 620922194, 902743646, 208415099, 444781527, 485415219, 622862543, 529146568, 916242245, 687200295, 892268211, 101352242, 794868522, 521573927, 123166929, 718032937, 336290531, 46111840, 463585393, 989957140, 580344227, 312974660, 10735623, 298456291, 951160666, 666388531, 444917575, 763309100, 984775539, 686489651, 586448197, 129248286, 140569851, 675462565, 794821709, 576966169, 846654348, 85385677, 704358712, 404848462, 656341384, 785744126, 123870631, 426953425, 580626484, 849463466, 789738830, 266074203, 253915569, 962081791, 865323078, 111368879, 5277859, 604022959, 996994028, 63293583, 124635489, 960821995, 625896884, 922274427, 98618904, 90067641, 164464325, 779346732, 775662799, 709987988, 867122803, 295198506, 73115122, 540515233, 368838371, 502760523, 295417787, 729358851, 852056897, 579026755, 953663437, 256418645, 989042109, 961367779, 98751060, 2999944, 351050560, 829778073, 569743528, 656277132, 379847572, 218625683, 275041083, 217515489, 608830592, 269260602, 858260294, 496597787, 563728885, 910825434, 50696011, 667039060, 106883275, 559732017, 548712770, 386068885, 740274702, 106953520, 470180609, 380628407, 974311043, 716307986, 375560587, 223992693, 810016714, 82956594, 242495275, 555519592, 996918247, 57435003, 622638347, 93164607, 778822683, 944757006, 44191168, 781288010, 152099596, 16913282, 856058007, 878394189, 377410831, 558332841, 271581020, 753948482, 778157677, 353666507, 83951454, 447848997, 271632929, 420454131, 955638606, 55511542, 669039760, 259609883, 289005387, 850785364, 774028088, 51842022, 840683683, 649956234, 327632799, 474727212, 414242676, 672483278, 829108470, 256786991, 359749522, 762471881, 319011914, 382271611, 406375695, 308719671, 925175293, 529859792, 650787860, 516274621, 84790372, 319133772, 661612047, 677463259, 652995013, 697879753, 220228825, 88437540, 89995413, 267265015, 294938542, 236592451, 193486481, 971120409, 957976805, 948667897, 454884751, 831807879, 881877572, 517360377, 597965813, 117940119, 441281290, 632073277, 614087709, 505115494, 461395325, 482739447, 381893321, 893304448, 20524091, 691559357, 256723595, 15167240, 762653131, 496186581, 31154413, 70829485, 591074606, 351682844, 715588765, 653657826, 850524783, 330106613, 362335507, 636142186, 503363219, 40218980, 228575859, 766925578, 508716806, 750156838, 206974252, 190483718, 557472839, 201700328, 961126254, 131295571, 914086086, 963657443, 232071094, 26687865, 131581834, 808457494, 35443545, 607399800, 850392587, 101940767, 122209541, 662564288, 876203333, 60044427, 417611844, 964473896, 384276357, 650670747, 736950257, 766951830, 868234554, 465385890, 382331377, 971457723, 345412378, 87689912, 917865639, 882750261, 427104088, 322728441, 879087957, 323761619, 329722497, 142753347, 136096024, 38989687, 5572120, 12749553, 11107003, 654083001, 570621593, 896615525, 640256639, 104360280, 319644544, 46714802, 106896227, 364651750, 886266337, 324922563, 618085847, 934581516, 891411470, 555908152, 429682896, 285720554, 539361248, 840762621, 895943625, 126984713, 249289763, 423623393, 395596148, 728147922, 501548770, 443140929, 984306287, 801420729, 881238821, 818928898, 351777352, 306538228, 901475631, 5939090, 406515339, 826359958, 236981165, 159103834, 632794594, 3774085, 368584909, 382793110, 18573504, 823931923, 869571088, 640587082, 305175199, 697977794, 345774818, 802155800, 476019311, 226940522, 916240673, 424104576, 336855805, 703375163, 429690713, 698434011, 198057481, 717569382, 804057718, 359238548, 875748434, 429692128, 558039299, 773279479, 684662610, 819553991, 650083775, 328446936, 385296043, 143735872, 197114948, 970851530, 738466187, 746961972, 487225096, 525170800, 689866075, 988358698, 618001639, 896561186, 765470451, 755233015, 82075729, 598925599, 359095205, 597504871, 997707238, 28732874, 9753387, 120759974, 777960475, 638388334, 489829078, 341651947, 378217037, 799059650, 899535566, 906760379, 963685845, 162237857, 291239296, 163005163, 970947079, 173005247, 571954707, 225790511, 792725188, 587530779, 873743810, 560094319, 258352802, 431419989, 910173924, 571045320, 149313129, 342406750, 847940727, 145935815, 384393586, 667878042, 499196065, 436858427, 487264364, 290154566, 382093990, 50205065, 395838233, 506206919, 468472836, 391716145, 363845134, 716270673, 757969509, 185273113, 655252396, 674468480, 529312520, 920328262, 483017394, 540857871, 183210860, 68533148, 911355055, 814335549, 409182055, 968374110, 754309600, 660199608, 165821415, 707825508, 282300050, 437781892, 656588973, 517388864, 343443452, 258785794, 317957117, 566864079, 858260994, 192582213, 601668139, 276109349, 379327615, 981963760, 946621294, 691589269, 674352052, 239698374, 598963000, 343232845, 115258429, 962297154, 511487722, 617316950, 67877989, 518168920, 264707252, 38823907, 288746366, 789848427, 703008320, 374065200, 504518721, 158076385, 845251129, 279518702, 508551233, 159469329, 182566340, 470853427, 674298646, 453751809, 663086768, 871553492, 921470218, 646762517, 177839757, 577172154, 215248693, 579852182, 51189062, 963454330, 600880288, 77991408, 710879292, 568856481, 760195623, 424065184, 210446344, 220784970, 424340972, 605822701, 925061164, 251745434, 651279726, 491919995, 850083751, 719536127, 395956978, 318264601, 815497430, 228804220, 649003691, 665070534, 970725442, 65367056, 704651904, 434369250, 258730796, 116922220, 651168789, 972144057, 706317141, 1918776, 381449054, 306135653, 827198661, 203766730, 883165374, 502096223, 373093703, 613669862, 320715242, 543909183, 400105890, 464395112, 429058066, 704541614, 429845084, 321961047, 201235164, 387597923, 428081265, 552594956, 837727096, 944169049, 829460637, 873188673, 303525942, 592568866, 139667577, 564456879, 405627034, 859729934, 880720365, 463193821, 217722078, 943704171, 302226572, 698791203, 522569084, 691645507, 730362916, 856924895, 309015303, 362283664, 883308008, 492836264, 427746238, 577582309, 845566633, 715664724, 19220966, 19898041, 921748928, 778122503, 890918750, 731924320, 37143482, 578216758, 597628879, 912902418, 753959056, 470808441, 385268617, 833987705, 425851067, 797009247, 602512044, 937439868, 150716900, 241791996, 898658539, 87298029, 755038422, 23503834, 938141001, 540428061, 609629084, 277206697, 532834741, 292988339, 501153602, 415838084, 805468624, 507750157, 834694189, 580030957, 854815517, 651723227, 291354558, 471179161, 872162985, 862652998, 631636603, 436912999, 740109603, 830772577, 207789162, 773297566, 437068580, 390603450, 52349613, 296191523, 352121057, 310876590, 375078978, 83025939, 887337831, 237830000, 275708696, 561580909, 443337734, 172604553, 66487931, 493182886, 552287679, 91459026, 969899272, 837659864, 249394909, 800230612, 524027184, 650485483, 417972660, 518127168, 115917969, 656143365, 491112921, 124861552, 506002772, 280381996, 508941489, 241639215, 725156387, 815136630, 387169163, 956734469, 184049207, 362416321, 992458619, 431251953, 744097431, 634250413, 606267414, 816894681, 505582182, 311688428, 747880729, 47160373, 642672497, 15822599, 72218093, 883807486, 506376562, 933984527, 340964280, 778599919, 315915569, 938996015, 313090466, 751869890, 158672556, 272130158, 551122342, 461166954, 629160507, 345690578, 751439408, 561888564, 865791145, 741188151, 25203335, 514756677, 511707179, 649314481, 281590336, 205364097, 597924113, 468091386, 975764215, 13680965, 958499196, 124188145, 405568300, 999314842, 618587832, 975875518, 496405638, 57126824, 155228667, 55931533, 539140666, 316027436, 673003346, 733932772, 185120331, 162755666, 818310300, 656082892, 678328384, 138353397, 593214399, 3858181, 328637919, 70632699, 304233830, 870712260, 681187413, 520531796, 466072466, 440126498, 459599143, 445192164, 829350555, 541443489, 224953449, 201599289, 463201504, 865806627, 877549364, 543631802, 789336558, 376626258, 127295162, 246061797, 967828563, 617139028, 711906158, 734526180, 117197198, 741002076, 382046262, 61733221, 256966534, 17425302, 228295103, 56860676, 583134413, 253385721, 357717597, 954143051, 308780502, 682891125, 962315795, 434188683, 276650462, 302619460, 173004396, 417980240, 990758246, 717616349, 470916267, 895882705, 157231570, 333887768, 204008944, 498558259, 138501911, 421707552, 995232108, 413184745, 933495316, 277981053, 86959440, 338161474, 233243625, 609945215, 990783710, 511316677, 511906283, 403238436, 512317254, 322898309, 65233416, 472998791, 512801393, 838355139, 461981449, 459571328, 573536583, 399232064, 792007072, 437830888, 748772260, 49941353, 21219147, 593758625, 88119920, 395950432, 382249482, 216335523, 148214660, 43252212, 250705091, 912973504, 649369349, 26941510, 266848293, 978395288, 507648641, 432487202, 171499098, 606085110, 879398240, 554484839, 223820746, 598848270, 241580441, 598716696, 998936900, 135263824, 888078820, 185275204, 124802075, 871529413, 824851165, 252043586, 800915636, 911842208, 203462185, 746321821, 195476961, 667389619, 892192300, 547075458, 471353234, 245541601, 894202338, 25041397, 446217318, 250276289, 870627350, 514887326, 769714671, 772288320, 558448159, 237837358, 13481993, 94162410, 942796396, 892224368, 612952243, 304952667, 277389533, 620844532, 931225069, 140722559, 396839141, 946884082, 14793586, 801372214, 564161708, 55159638, 160926599, 764931781, 820361947, 756648297, 251724148, 323763517, 492480909, 534999576, 635915005, 519525584, 986060119, 438166799, 795687872, 793599488, 975038687, 979160663, 65492637, 531316090, 842642393, 107339381, 610412588, 735259762, 387125918, 599449998, 328303800, 257654086, 896223452, 364325125, 674105024, 393748497, 76555813, 200680551, 789813131, 234081937, 923658271, 191856890, 571315279, 392568320, 155962373, 223145348, 661931150, 55161268, 365538217, 803102989, 28773425, 820927673, 650580572, 561593517, 641050660, 736155507, 165383423, 541044661, 337500734, 238373866, 384233495, 635400365, 431175535, 12785176, 457301761, 213784754, 722743141, 323763256, 599315921, 925185523, 947108072, 954442581, 723173490, 288941858, 999816464, 474791226, 468741987, 555953759, 543334511, 397990273, 35877622, 850587529, 886610603, 294364429, 834013531, 856918771, 279788170, 153127916, 794661142, 438871600, 37990848, 667841726, 607001754, 599502644, 993548763, 745645367, 876310684, 434667626, 847650239, 846680550, 664693795, 886170016, 783222206, 470405020, 553381561, 238957141, 49625415, 360295124, 389470713, 637347224, 652309133, 477368246, 710466518, 335566958, 549292616, 945995566, 682220397, 461595809, 504179575, 566761328, 588031886, 971924373, 613283940, 23929037, 904338439, 347207511, 612343993, 79490051, 351119804, 618517060, 368738955, 556840445, 718360575, 85760577, 338592658, 132472478, 179732917, 352805042, 518229588, 647928588, 13962566, 171811823, 706806586, 836111234, 345872163, 633088549, 161229698, 699328303, 884907662, 955905972, 37333233, 943555884, 365273917, 441956591, 855719948, 718108450, 996977622, 54220310, 70960760, 987633602, 489086998, 362634734, 65396209, 967785573, 753344498, 211577690, 460351617, 436471536, 953772106, 806177830, 721756539, 57151833, 809021921, 944872331, 30365879, 255418734, 85457894, 322852661, 709532315, 11082840, 5871264, 949679924, 65181486, 655234319, 457728079, 638269962, 200437909, 294424624, 448205518, 175204435, 72811089, 480415267, 809429528, 328181203, 176605650, 178075831, 110803641, 38393282, 401155135, 757597078, 663743558, 559991610, 263690844, 206823858, 603598384, 499103495, 735790443, 640448022, 527105020, 112938866, 235843637, 745653998, 236337260, 178026176, 449701129, 565309400, 349746913, 936521674, 474707249, 917211051, 179728307, 643221033, 352027272, 333255891, 449688772, 877062008, 793672089, 780330103, 288792834, 586314768, 569140698, 328112077, 682615403, 783395996, 246062594, 450793209, 819968434, 857906152, 776533593, 156566361, 868056189, 464076353, 309304542, 110436166, 437043322, 58995811, 408641265, 240539023, 339465933, 322364770, 621545143, 312568052, 72462180, 965751597, 748073457, 209143103, 378011294, 903757478, 721660567, 221155486, 39330111, 529844432, 308714509, 303302412, 267660248, 600338251, 100721917, 799403315, 8242878, 275827595, 782141835, 463018360, 616389813, 198270485, 469645273, 591955736, 324191002, 340332527, 745095856, 690843926, 348615046, 672205801, 125269362, 797890405, 818472307, 103076817, 410657300, 231367607, 43727482, 44630899, 115539150, 277166712, 982979402, 767462571, 864877511, 848934032, 487320535, 460382761, 152669235, 47207967, 115689835, 380034777, 402504405, 201532623, 282133661, 431801043, 622059291, 729461422, 451413617, 247559165, 568748484, 42579331, 386644404, 66954587, 573082659, 388558085, 814220098, 257430842, 366300610, 282182459, 651869205, 760181879, 752436199, 137886124, 84434265, 656234460, 177606981, 490800396, 583023315, 312017685, 525897599, 41807089, 543237736, 66656401, 829841539, 732957315, 906521774, 449209386, 918709292, 580023930, 50543472, 873069403, 49208182, 543632631, 416614197, 160105136, 944888159, 905027472, 668502758, 545199294, 404001314, 184077106, 68745133, 811673051, 735863080, 519121900, 40161489, 316812617, 803305769, 828156916, 509263665, 884929976, 390939304, 824592456, 461648729, 814244312, 920812452, 225275834, 821945289, 352837361, 300517815, 630559894, 469458642, 907772955, 249881149, 846563026, 870543399, 608577162, 92842949, 692524918, 289393597, 733756752, 323970437, 389241933, 166170294, 993755169, 927559845, 866820952, 946448906, 424604602, 859996742, 393962485, 565196690, 512557689, 183825623, 484359537, 716892598, 887794517, 870169846, 240185245, 229281679, 968274590, 992614100, 544763628, 763693193, 104590590, 568409127, 125120636, 315678329, 397397998, 105030733, 334950048, 376767313, 982824452, 874404981, 874976043, 403732437, 877480262, 890915389, 258463663, 341397194, 939245872, 297223177, 623464113, 10356227, 655570627, 77371923, 548769092, 934218931, 549065563, 237664586, 449150310, 969883199, 929357795, 307286929, 627572536, 136618034, 46697322, 342571585, 391576610, 41924865, 123081741, 393857071, 329603580, 585816362, 350586547, 479800285, 74163737, 853099741, 423118001, 870547416, 286899312, 649384881, 184741253, 258376837, 301221935, 585531173, 323793825, 422441904, 51034134, 339020036, 151555696, 525925878, 648373487, 345019093, 568290643, 417335431, 506510989, 417635367, 674496966, 350027016, 751079945, 325004851, 59939097, 195936112, 380964951, 484033457, 659431667, 798051597, 954967569, 271026608, 874427674, 351882749, 583986713, 105758921, 478118683, 423138260, 877719274, 135971501, 240707261, 745554008, 691267963, 746711228, 865973695, 197750128, 927020196, 561031075, 375723867, 570984133, 270984323, 925230686, 657955523, 884410711, 467175112, 563443904, 852869603, 146557255, 447247475, 389987169, 188342384, 45144537, 930075400, 288949390, 829523530, 349802314, 164832409, 324147229, 576385675, 727740141, 335664565, 911312527, 843050465, 648174206, 201110964, 783065005, 455289681, 266806803, 89968796, 499643449, 295895584, 697725592, 801676557, 613296526, 588651721, 651108177, 589684988, 668468886, 731678311, 107200641, 597401905, 629828938, 781043618, 900339285, 910450458, 85818999, 797911069, 570475967, 407150881, 890079902, 818116988, 946994409, 814697709, 476204072, 106558601, 837136184, 346462281, 852819163, 663895495, 80531931, 551206614, 304942966, 728385605, 29848594, 846393888, 137524352, 510526407, 915636912, 259706686, 914776791, 731186601, 119561693, 673673479, 907162124, 26956409, 185943577, 999972403, 885241649, 360269700, 710190402, 168886085, 216801586, 780416052, 770498817, 375180565, 396063264, 450824413, 242725523, 913574367, 639005008, 328761999, 780928138, 572603758, 901640635, 868284112, 395341960, 456012379, 631777851, 156167081, 263017582, 49517239, 437897526, 11366140, 530532948, 716871639, 871874498, 263343160, 419826201, 776960521, 500814092, 541813340, 747822905, 375462338, 814897126, 192956369, 318116327, 726155466, 516342219, 449388251, 866332713, 102607233, 814106287, 915851404, 972855958, 806617888, 148798252, 910048250, 438794222, 982585919, 248385286, 295527492, 622404350, 10763450, 902978709, 17940924, 966556971, 188254712, 559318575, 174160545, 990668732, 119730220, 799476274, 927682740, 458840671, 606838390, 520894473, 974623047, 351476279, 148811884, 712695721, 916021040, 677334259, 330909082, 40343514, 831746266, 511321614, 509679855, 405671423, 111455143, 480175571, 771696630, 817160162, 881982831, 314036279, 490380809, 303559840, 92323570, 667411825, 349683591, 986537928, 48942012, 941553932, 579769344, 303236933, 634307608, 597062518, 290192017, 737793158, 728874294, 370187062, 401449146, 813998357, 655385448, 954560593, 630682103, 31204174, 516169272, 316416925, 851655370, 642092657, 687625820, 539836887, 977233957, 934224774, 925257192, 940524880, 948831072, 717483499, 381720058, 864798810, 274552375, 332074101, 744963075, 944764017, 797355471, 558380823, 865831008, 103616280, 183486037, 54810273, 747837321, 867517523, 369845572, 825479439, 525468111, 94605929, 347270248, 287772998, 749957442, 882342778, 244048465, 752399950, 293058570, 278621565, 570569237, 115543589, 274276739, 649509937, 43323772, 376278223, 605910955, 520673586, 840624674, 510717810, 766125816, 360832482, 4963501, 617291848, 92400276, 225154617, 767412705, 729237522, 495059040, 633911896, 827109365, 488842461, 751194734, 776132279, 492565453, 633437821, 110187692, 377766623, 44456641, 824591586, 381918939, 116677519, 647835473, 967636804, 602765870, 162349164, 744688164, 543414571, 569352754, 147893936, 41261867, 168848257, 178613791, 153492062, 69426353, 790302815, 835119618, 379723791, 683397630, 845106768, 427064443, 787394291, 254514438, 275165055, 901942252, 957626050, 178143657, 274820226, 407788205, 919335072, 919167488, 477655167, 198084359, 167456767, 626993436, 996383790, 741643520, 201369216, 595229032, 156285657, 582872014, 178932540, 408470717, 798213882, 747916403, 271628234, 509461623, 973729066, 979026771, 976468388, 664012154, 383741131, 746401220, 149622917, 86528493, 12508910, 973243174, 543272824, 773775210, 796407684, 462109473, 505429297, 428869707, 483756107, 611351967, 280637155, 564870756, 328279404, 407146020, 573230414, 447512374, 67403151, 984727949, 170424774, 973083138, 719044050, 313307994, 489383176, 389888158, 490962648, 8491210, 942308039, 584972588, 160865077, 233141930, 974546808, 968843673, 98496144, 611888973, 182587744, 719043777, 37804425, 881358694, 427881213, 360355089, 846345243, 562573789, 956413800, 653695776, 866971609, 793651639, 414248047, 718570518, 624722133, 25394363, 329775986, 628406911, 364643857, 41613597, 361702230, 279140279, 58829003, 537680513, 116094870, 407618034, 391969023, 658181775, 346936573, 154180275, 658027158, 992794686, 560601465, 655027020, 844683648, 393741985, 422549838, 232651057, 771682467, 28801975, 318698187, 494420047, 591700766, 370440715, 202711142, 811881688, 741162685, 422212828, 129151440, 788276300, 37531725, 616675599, 403316525, 307209170, 29079341, 619038873, 123237094, 524964141, 273338659, 58316587, 113671193, 321570917, 407804546, 109425255, 563675851, 770959694, 785267853, 149050225, 76300812, 559432316, 976606908, 852337246, 901330513, 793647171, 496221915, 376455300, 974923592, 402468856, 835313277, 502293492, 802400776, 770055265, 513248798, 25449779, 901746579, 539330049, 7105722, 369137406, 723635926, 153986755, 699601660, 518143523, 433134537, 743265393, 51384241, 369162287, 299409004, 718884412, 599461542, 297157755, 115015235, 484228381, 707232239, 249701915, 213351886, 15325344, 96690453, 114228481, 67159370, 118322135, 860292513, 319654608, 731601920, 3414600, 329465492, 938676058, 889923295, 273344852, 617342431, 730613606, 23862935, 838494488, 199356821, 758388013, 886240131, 230056072, 739689618, 293098994, 224540184, 266385825, 56126234, 730619872, 86072346, 579343622, 243427085, 463687023, 363326748, 745065902, 147675264, 342161580, 892947945, 37253780, 383013738, 359978615, 191596220, 149894660, 103928462, 321866414, 582837625, 837338863, 691676551, 776893397, 408924532, 695152378, 24561783, 587203289, 30501551, 903468137, 129609447, 50569235, 456520598, 61919331, 180327494, 593336562, 953096822, 489861018, 85697281, 778593736, 818346453, 229817049, 857156484, 284414725, 986783831, 253751560, 864429526, 834699895, 633129559, 159877184, 132352968, 60223554, 681439841, 620642008, 225141332, 712030856, 440549249, 603059148, 534035310, 328636579, 218090499, 169995047, 639022652, 398461903, 211646069, 163007157, 355216667, 803339452, 926004097, 237189454, 504651951, 246907839, 622368547, 177647815, 134253855, 881035682, 95865997, 70694768, 926937084, 451535411, 794914500, 660644387, 649658689, 571921343, 783338743, 814895362, 970358480, 636075804, 895592344, 428240345, 726757978, 594670989, 567398778, 130389235, 801296746, 955990739, 555094515, 483724154, 169032562, 375983596, 699021102, 332837892, 657103825, 887820799, 387501649, 443760594, 207522131, 714245930, 469535916, 656221302, 373207006, 914998810, 577156099, 94034456, 713174525, 2300573, 692950638, 311442973, 184983954, 174129581, 993690504, 825751149, 274994899, 829787529, 897951516, 136129310, 822467484, 476550994, 235683160, 691267146, 325224733, 465610641, 301438795, 600827543, 262326270, 251687166, 640527791, 581062866, 157404512, 734327421, 619195428, 95353885, 884768439, 41495229, 294172288, 81167980, 422412737, 672599606, 169953867, 972837821, 635376746, 150064796, 746873035, 908509929, 818828728, 114142603, 637476907, 986240118, 853553454, 828124135, 333371310, 180580235, 634319162, 184306786, 40641452, 141432449, 849158182, 411181578, 617228276, 740128532, 817258525, 992301768, 466738481, 110571431, 489403251, 986217212, 49122271, 454481207, 863933689, 599964867, 9877911, 73871881, 226301529, 577077572, 361594243, 882368659, 112804444, 511568551, 169331485, 287453748, 194433640, 542745044, 280634239, 728132894, 618913126, 600473535, 276877167, 782680751, 672104392, 948523325, 622285286, 821117851, 570869920, 386450657, 862931810, 878528573, 796117879, 202036941, 756497976, 82943541, 25555459, 412630919, 987882637, 880711984, 62507946, 123686648, 626652551, 752326880, 657988669, 25369886, 81130183, 908135492, 454736748, 758130829, 884339057, 326487891, 246431377, 810541542, 373468732, 688157816, 886297416, 282242631, 563416180, 890172490, 302209058, 884547978, 622280317, 895670260, 946831107, 268412681, 180129632, 299408271, 951456097, 799282296, 910877029, 179389264, 509160273, 112905971, 148583677, 435583852, 909755463, 3304916, 792353376, 191845075, 579463794, 137312241, 232643955, 774818312, 784528868, 384809674, 869600692, 944688532, 470329687, 894511514, 565048500, 534732364, 741659453, 321426606, 313984690, 254375381, 779916934, 24411696, 654729954, 812404069, 221727471, 283679133, 738642035, 658135071, 314680130, 725699643, 639393585, 218188728, 361589235, 139914196, 445713680, 803070905, 219397801, 43727234, 466631583, 90382798, 396030597, 266965985, 797275606, 797748325, 857088545, 108093137, 583247277, 67836760, 353897305, 915595832, 638089612, 648397394, 497040291, 555848584, 749493718, 584627472, 777924872, 351586950, 261701555, 949283481, 964994010, 196171069, 922142409, 662208825, 771507627, 623614105, 177974675, 668328302, 464582473, 222077666, 501431228, 203349254, 983783693, 150258735, 112604637, 218782802, 166962235, 986630865, 361304315, 173823594, 725779887, 848751449, 556172766, 291978563, 998525910, 445442639, 467940186, 38600751, 956097106, 421694374, 616282191, 757909625, 615306562, 163967572, 869109571, 830736799, 387286532, 801017044, 4848980, 939505685, 682586064, 931241954, 909959490, 720710210, 107122682, 821511747, 879564191, 858866297, 7804694, 377155422, 574409140, 135195665, 136007562, 656539790, 700307667, 198316027, 817431228, 601486255, 224539939, 652503189, 823744043, 280468703, 391888943, 873221525, 334114529, 68173842, 335946352, 235260049, 367641883, 548818353, 138060818, 225525065, 345948335, 576678851, 735591363, 177498287, 555427866, 428212789, 98228002, 379217589, 389997567, 71604979, 81344455, 222638662, 959230927, 62159484, 157796926, 896354948, 133203294, 167543455, 623015342, 544558066, 619548534, 972489102, 339014234, 771336131, 68171831, 758581177, 728938108, 637822442, 195674212, 917692353, 12729782, 19272533, 783333554, 887244572, 462586575, 42200200, 224164555, 568049937, 245846896, 1198202, 257971716, 113562126, 846150118, 189343166, 428621335, 505525750, 201311124, 317129535, 954627292, 182965962, 834310140, 600617415, 299534147, 399774054, 21132494, 13246419, 801984146, 57839626, 578382689, 617463407, 173069128, 348783518, 122613318, 339295420, 696918932, 670999287, 814892306, 702250568, 359882164, 743096227, 861824765, 977279933, 690270748, 506563751, 324383878, 777748546, 264296482, 101857069, 658170340, 516807959, 653446697, 27010851, 35272644, 100135436, 160271960, 795887188, 65186071, 755859362, 96012282, 679946029, 864489807, 382841521, 813799720, 37511660, 496236915, 145089388, 105016090, 957149787, 171433110, 212090033, 808075845, 273465711, 166456273, 839626991, 710930870, 559945724, 93539784, 41353094, 108231830, 504038975, 922397193, 502402005, 118008940, 472456422, 767056539, 99084090, 841897800, 329312044, 262615709, 702627911, 503161777, 426825723, 213297155, 270385145, 453314842, 523493866, 944764322, 772555915, 617660329, 213076102, 560303996, 702650386, 240206266, 392480563, 365420858, 920054582, 28034036, 610786679, 841980744, 670448699, 742330610, 975531700, 920827235, 48215241, 198552008, 60493703, 458455249, 597427254, 269477404, 436067836, 973838844, 669338751, 416926098, 341418848, 74937997, 66934541, 544137741, 645040266, 420060168, 207695134, 702621915, 155070887, 832099109, 5516967, 333213598, 874879660, 856226687, 343191436, 979943374, 438708550, 762388915, 691940567, 315763702, 580322296, 659288749, 513287711, 753116162, 870855613, 754700317, 34965594, 792477261, 38913698, 963034830, 626154324, 986145860, 501244257, 772727698, 897768343, 321177724, 83701682, 771398935, 253868009, 20587968, 605415306, 681514540, 829664442, 352741156, 152813867, 782896956, 428865276, 929350327, 203340138, 777854052, 331808588, 905199287, 549420452, 225978195, 818013152, 409160453, 421283985, 75449642, 400485882, 95238486, 780760031, 634850111, 22220688, 605430256, 134094389, 766439401, 795305915, 292061842, 162652333, 905542088, 467024404, 808278748, 193614413, 453859562, 811923919, 276943672, 636641252, 745063939, 296575902, 820449639, 236227700, 639681037, 943614940, 982105912, 291524469, 532201590, 691461570, 477065718, 357695279, 636577898, 88391853, 12215383, 54311449, 390491491, 475112713, 283643722, 201375330, 792367580, 744958761, 722498266, 355046631, 91976055, 73187297, 653034141, 347709510, 586721356, 898809939, 719240287, 951156709, 814799719, 780121124, 714604962, 231009526, 81022425, 224680050, 899353742, 794421797, 952700240, 456347024, 378095135, 20969683, 171844235, 127131718, 259644698, 800998015, 572253798, 920843884, 459804477, 153998490, 201165510, 249399102, 116303804, 962589125, 393360947, 97968380, 597860643, 671417032, 915205523, 799823934, 317730416, 50849711, 425628347, 494904715, 908377804, 567963237, 454943474, 684877532, 875253528, 225985729, 900994211, 93871439, 57926616, 492022665, 294587310, 88015292, 920430397, 572381930, 314925639, 430833243, 462428828, 678132014, 636076268, 152576865, 725587767, 315824631, 268452939, 74656728, 293124129, 964601091, 218356985, 499740916, 434826060, 734906438, 230203203, 645387450, 209668435, 975628662, 538985605, 410959014, 569145308, 853766203, 780313767, 818969718, 55784225, 740618181, 466902956, 336084465, 137380038, 853624321, 385231519, 376828879, 144944914, 604522827, 880075887, 672128132, 701957745, 639077584, 832993683, 63623304, 259428546, 50789272, 620967027, 219598428, 985888827, 454576602, 783461579, 444899083, 430154124, 245371566, 913053276, 232083010, 960617131, 391398080, 902279839, 551373522, 294210795, 575813588, 589140447, 552292218, 560173701, 260602544, 243159275, 958246019, 182851754, 606042388, 381417641, 107875715, 690714739, 251975609, 818973932, 133303135, 458204740, 802082835, 197887803, 410219173, 819261950, 758186194, 422012513, 413915645, 154254751, 353245889, 129921800, 917260002, 676211524, 909402146, 471596888, 469496499, 689931030, 892658345, 745420820, 211366981, 456182316, 690354802, 198031265, 291838650, 84647443, 785437921, 172417976, 585245757, 246078260, 91052503, 616810980, 608041966, 123927408, 8477322, 462292749, 218173564, 502588543, 429430075, 87399195, 401381984, 303022813, 274063283, 928898763, 643277185, 825913583, 15342633, 794197425, 605086370, 375963643, 815608664, 331925248, 261437396, 357387360, 458022462, 234887195, 289111188, 92230340, 341130489, 49307227, 885712406, 71360007, 239447136, 919280824, 411083452, 173468232, 479912134, 676316413, 218402500, 868035912, 122452061, 830559272, 833872113, 498216750, 187619129, 979244088, 162139563, 959894756, 735699838, 759982086, 495406621, 827284624, 501579126, 515199183, 371144132, 614563578, 320675162, 536366723, 696120717, 56903347, 442554518, 724504303, 993358160, 983918492, 231826767, 218309809, 784713993, 975934568, 388950864, 473702996, 981488585, 434263153, 455392901, 95235297, 786678936, 899596170, 255203992, 517752846, 509514500, 559550439, 939758879, 11513685, 423365226, 678798876, 467923554, 866842151, 354206942, 635696487, 725952317, 366964361, 806764126, 442690770, 568026079, 825599071, 196719026, 676467203, 11374498, 181663690, 96021185, 403232455, 159700022, 981239743, 738483492, 717141236, 711162591, 970390418, 244147496, 788255259, 98165640, 115087892, 925074881, 807583068, 159877695, 316482600, 520820532, 474567165, 364790033, 648326989, 317575494, 833642205, 381657200, 656181058, 15169818, 439405653, 219265561, 97722512, 927152149, 564348043, 676419648, 854341324, 699616129, 642171412, 270632868, 882597691, 364963657, 463927943, 81525491, 727521447, 855235129, 133599442, 819942452, 31838009, 66327983, 257193905, 78399768, 678016070, 183106653, 454796384, 892395491, 472790908, 352016605, 106307091, 651469662, 538007858, 386802324, 734807695, 351448517, 178319793, 520469905, 702606528, 799401612, 479004328, 224944032, 223280723, 337408107, 436668938, 863250667, 841639037, 786820991, 174371629, 139991225, 826073982, 991870542, 173934820, 716971655, 288168306, 909634323, 99624183, 748875553, 438978705, 551045371, 576956781, 972795178, 149010347, 540267421, 731165579, 752615413, 513229426, 924017740, 390254782, 173251854, 70975284, 806184787, 253943961, 114168715, 513340188, 771278382, 856909086, 188461098, 52636695, 956452617, 429050106, 730308650, 797536175, 745656989, 870360942, 983595584, 279388857, 450091700, 630378590, 823707501, 822871748, 373990434, 328435048, 423457654, 373064037, 943301359, 16335333, 629305209, 104184698, 773842074, 819705260, 675113486, 751155550, 49342038, 832126701, 968017380, 832008229, 791468146, 210974543, 425446959, 731144348, 804304278, 938597557, 424519811, 483080299, 935303756, 27841615, 918757261, 498501741, 986256273, 848987995, 753009046, 605515613, 741856384, 806651758, 122941780, 248774305, 839817103, 157208986, 464512454, 380320977, 914155610, 248017282, 641904363, 712930303, 49332740, 324060366, 245529507, 288786363, 306794426, 390500356, 692590963, 35420955, 984383387, 322848465, 551216974, 37452183, 984911104, 22970798, 196424402, 340461018, 73889550, 180244285, 543433630, 192009410, 298267978, 242866401, 385043441, 467277579, 378017954, 256698052, 819357573, 406687644, 813049877, 351071149, 368684667, 291938960, 765426959, 797541778, 316445304, 60430868, 665447976, 860348668, 211574202, 602755057, 402601301, 450665993, 223667188, 905786882, 883170252, 368448646, 781906839, 777869773, 610590326, 273740676, 33053129, 836750652, 120516366, 455948197, 21493325, 307052116, 218212545, 909206284, 935452344, 434544822, 390865010, 613223763, 41507078, 972974675, 429443960, 999116553, 872508528, 155419089, 18674854, 993095365, 427245762, 699237062, 294876704, 61787840, 99216730, 158505398, 109939051, 711357623, 404229779, 131845482, 923894661, 156774917, 829026935, 781898336, 642565091, 662284115, 163593691, 555750405, 804722849, 467932788, 85861093, 966150521, 610648665, 638208210, 569374216, 497182001, 864234558, 70061869, 199627965, 187773182, 350175179, 247251640, 241645777, 797662825, 879156209, 858224503, 268977877, 280764390, 233693841, 430545241, 294437020, 34586404, 137731123, 790704788, 428993643, 428904611, 723759332, 507123944, 580672379, 757926888, 804091056, 427693408, 464870442, 40667820, 283164706, 151721395, 482252414, 290902425, 428805937, 88069523, 331116508, 655419858, 588714669, 504507138, 553256692, 862768583, 46570595, 4889448, 596591929, 6176431, 567504480, 72680267, 541640312, 979589926, 525065451, 249006234, 807371174, 537690655, 770648180, 687011619, 363128450, 978791203, 893507026, 191412961, 492838569, 496705230, 417861248, 363088578, 550220712, 216979382, 817178842, 181620861, 71145466, 38329455, 14157105, 333425300, 262746006, 806700006, 160645227, 882681172, 917919648, 10082636, 987938658, 581006002, 510470960, 165404359, 573215686, 672825544, 894232954, 743870923, 321089258, 962190699, 214296624, 246127221, 450498169, 333189135, 183503686, 241786041, 825334000, 927633166, 344247346, 582161370, 436559878, 828577139, 191803095, 405120425, 30763455, 908051524, 626688312, 811421410, 186008018, 828746538, 545296991, 131462521, 910740598, 864426043, 480731968, 684935568, 843022848, 136798943, 301830196, 29020244, 400291132, 262692544, 657717399, 237369229, 579047712, 911601275, 289154308, 76813235, 41073262, 714793539, 119457983, 404578502, 279829948, 519937151, 378202535, 914183761, 707446055, 112578015, 160780517, 340473646, 911034316, 538946955, 152043957, 476098590, 942012434, 980222746, 933341171, 594833256, 368899203, 942594932, 502707433, 512075835, 860921646, 769479560, 69593359, 187271118, 334462684, 824222526, 393715875, 241243986, 555364979, 636846083, 228234823, 703420255, 519752323, 919861657, 346568256, 423659080, 356696107, 305509095, 824710537, 470804148, 222476926, 770420190, 979465348, 473299542, 653910543, 33817985, 185479694, 389847184, 661967148, 360847117, 496585335, 479942064, 887597296, 442422048, 648756591, 304641283, 816199233, 66538943, 247564525, 766766584, 198503286, 293004086, 165907690, 758790235, 625632330, 136719579, 147012724, 808242882, 633734369, 921338776, 953284696, 414457718, 805891786, 600824698, 450008692, 950031549, 999832029, 637176089, 165801041, 508782099, 110123720, 196111083, 605129097, 953791286, 908204766, 826232199, 213686462, 900590851, 16559435, 763115714, 987404806, 420696656, 70568885, 427819579, 436186618, 792482800, 537748717, 538764300, 17833063, 498964264, 825429266, 91834659, 612180706, 987628831, 912259818, 442207117, 389889517, 633545456, 886286531, 693954668, 876031598, 880962112, 837933455, 433545423, 750366142, 947643626, 552369108, 627431070, 711396097, 31507366, 501491118, 687198843, 426568441, 137394590, 177824798, 873459384, 600445019, 561256459, 185294398, 345195643, 331057979, 62999189, 239516702, 59957485, 717613122, 432264466, 83184246, 372153601, 987061787, 571444446, 286237458, 570699108, 131874964, 472208042, 863120383, 766145326, 188207766, 894215652, 554540827, 30147447, 938144682, 428252700, 714839127, 959528317, 536358682, 860773597, 215821136, 537709043, 862822162, 893878665, 43310560, 244509546, 66042241, 529197558, 394439587, 345034291, 358184158, 351824912, 165207253, 446419261, 964621075, 866608948, 78061601, 47200443, 68643709, 460154730, 642471799, 142709347, 876845200, 546089327, 685828981, 371368832, 971986924, 692411266, 583188073, 598966343, 577136271, 741680935, 845892548, 77962942, 872258006, 584392136, 9985024, 437652933, 25260417, 45198434, 432256615, 165966705, 719448176, 226240421, 605258118, 391570432, 280550780, 746720353, 511967767, 196658467, 97834967, 916682886, 617511031, 462060324, 624949532, 802351014, 213838128, 134210346, 111373251, 358188896, 654193515, 259199097, 804981433, 151334336, 996980471, 993477689, 927715115, 914793242, 333634278, 236207982, 560152284, 873864096, 757949152, 169816261, 735452637, 464160417, 703147524, 853769002, 153357962, 720262398, 583507980, 582518961, 226100485, 758521807, 693354425, 43508943, 420135368, 44906722, 461046367, 56426683, 138527433, 156928416, 442864598, 602532768, 230561882, 895043105, 295601813, 672727513, 475310398, 382292576, 788842252, 842580504, 13816227, 366470543, 73810734, 255979487, 623483841, 209559142, 790737221, 546481816, 932970306, 574372743, 126699944, 998834281, 343419308, 374127700, 244501360, 298150409, 296240220, 886141331, 571467732, 429357171, 637910693, 950417304, 535653474, 295403364, 730220519, 476307110, 748625224, 670523572, 460227239, 976572512, 752750119, 754524036, 269912051, 102556959, 671572211, 332506182, 458719793, 755820761, 659026007, 857015278, 970064806, 48589243, 127952098, 165017201, 12485475, 300505171, 588234328, 536146232, 303446165, 803350628, 252923631, 340327905, 990116689, 76382776, 814212616, 604403919, 312266897, 332065132, 433258279, 933139573, 618874089, 239967410, 648131692, 538433836, 963058092, 365502963, 301886610, 912925516, 8268610, 570257687, 508375305, 224585325, 226328000, 768928972, 607752471, 526762878, 308856387, 218403478, 54557728, 324780654, 570942303, 968286768, 667032161, 3452757, 565686171, 183514434, 615775323, 865744226, 496221992, 558597291, 10647599, 548442486, 187762218, 375914467, 236819957, 760481249, 844690301, 488069841, 438720989, 977156133, 175389903, 906420187, 825211314, 968818067, 771994246, 819015989, 88632203, 684523743, 214938036, 247189960, 471608257, 599901896, 124820643, 322577817, 413049494, 938767161, 45777440, 511283619, 630402092, 224848320, 916179326, 861934900, 741216530, 536668409, 554362527, 749789577, 6860441, 590835086, 241337087, 395745104, 946847232, 320823925, 43428046, 895481510, 584590064, 917975539, 598442179, 729313343, 332875325, 124679722, 124345477, 225810800, 468484800, 190336856, 184194188, 345663752, 989326337, 213713634, 486152430, 954419532, 881799280, 465434090, 824843788, 914069487, 539271508, 217048006, 680672547, 127938606, 666748261, 858075928, 199229943, 852315398, 236238387, 459007044, 485343329, 778190576, 290756388, 556154150, 671060241, 854294432, 588085559, 421281912, 740097526, 680621391, 298500563, 126139707, 666018593, 104973157, 37675534, 877015257, 220338964, 543143261, 341606725, 327655480, 660076305, 769706055, 632745588, 678628259, 625614010, 57613224, 788118706, 802572607, 8926697, 596781968, 715722545, 176476753, 739021568, 141774896, 442040641, 44185713, 50005251, 186050090, 487342056, 873571440, 333941778, 47313237, 717271131, 310356723, 114266318, 655979151, 374889367, 59258555, 584535562, 460153213, 969057446, 186856194, 466521922, 812313065, 223219965, 746896844, 132608344, 449847464, 671330102, 660421294, 855931962, 901964280, 788636978, 628765599, 260280102, 931184378, 94479313, 497042438, 143714886, 781291627, 281263021, 364881095, 395399915, 178173571, 97052576, 51163298, 458617806, 687865793, 203834633, 580252087, 557323624, 869183181, 693284536, 528298922, 275009038, 63738997, 236920023, 967216541, 811013971, 474591627, 618085727, 763864426, 638620162, 942576823, 440997895, 546280234, 621351537, 269898100, 843865361, 232622204, 691645656, 60329017, 494425657, 794016629, 264052091, 851624751, 171553511, 938131491, 91686426, 598828065, 578536962, 979389693, 702611411, 981318889, 169082699, 907914802, 249606890, 810153322, 97278311, 81552383, 256972700, 948424499, 109283056, 412194461, 288317774, 704166972, 819007401, 770223773, 918846373, 350269841, 986523506, 338352533, 428362130, 224907383, 303934835, 241890941, 69786016, 819297632, 328412343, 689291450, 278481277, 39507533, 449294495, 683847105, 368093863, 512905062, 976630934, 173377401, 87479022, 634919794, 6354238, 748347529, 351811391, 538778984, 316537779, 557694657, 924009884, 223216169, 778062306, 403631451, 792539866, 112508851, 297349267, 862275722, 772407910, 332527811, 487685519, 550791778, 906588967, 242061632, 526637134, 408847804, 808351429, 458455771, 127573631, 8246559, 941305980, 57264404, 244054428, 840515634, 52126873, 159291519, 655130848, 925360445, 801556134, 18829208, 159594258, 139527516, 44857524, 638514906, 556688504, 754166112, 325999542, 94865995, 247739899, 649218997, 242726687, 829426526, 675936721, 798909792, 354595797, 794896324, 708856466, 582448532, 422610521, 450646794, 573424933, 61856265, 330606739, 532346227, 845808219, 247381410, 618026621, 4957833, 867531900, 602529524, 690977143, 249203093, 125395571, 142421184, 874009645, 12412956, 730430753, 281249618, 493388512, 864818453, 381123277, 557358148, 298947167, 434820216, 472334414, 219832888, 8106373, 980221222, 58900459, 222099157, 727588777, 896376337, 257164767, 970419518, 773558365, 316562536, 461525207, 196086923, 638138176, 403328797, 451943988, 692810920, 367486690, 998324081, 854301243, 88058164, 15942519, 251026026, 229369429, 703020783, 575763695, 255264998, 426536991, 62454171, 928010296, 39239641, 305341883, 458966547, 466586272, 864867856, 837985011, 694438927, 739348920, 562873584, 917962921, 710440997, 766577690, 552697258, 648707757, 255709264, 577502885, 47505142, 359045726, 104035385, 738337479, 446770525, 694661145, 267980177, 113646027, 937361857, 758333709, 133949528, 501924476, 587568829, 847542857, 319039317, 86595685, 355434160, 505717899, 836070584, 885145147, 537988168, 404172944, 155543722, 661636573, 294063486, 63009576, 819436610, 876395288, 57514379, 77714464, 451662125, 77293932, 138616390, 36952940, 514223715, 485293070, 550246125, 169386513, 401903431, 619100066, 337230871, 353041790, 488172546, 731019171, 393111339, 643151851, 711308320, 187794288, 959267934, 80147288, 393529607, 940238029, 899176686, 716344580, 993265800, 324798076, 947731442, 457148011, 197196139, 841893512, 691518828, 792568873, 789189020, 136351886, 479488941, 228538581, 612772816, 365537358, 20075971, 819296626, 49049655, 589018600, 503232415, 79335005, 476446724, 243677973, 568913738, 975827364, 733607254, 154164311, 361593943, 394469228, 733410422, 27882457, 717533728, 665039556, 289793840, 418055142, 794465125, 209234773, 109487811, 868863444, 853422343, 117656288, 205476793, 241199326, 822478563, 911394027, 345834403, 570393415, 301894046, 720610564, 308544812, 289036992, 919851461, 824273607, 170359260, 237325788, 193431425, 810743771, 439267000, 369913883, 744626399, 394168767, 217594898, 499500172, 375290527, 915483196, 278643360, 986207673, 276769784, 147223407, 742314876, 108272308, 68188178, 4462069, 951174855, 91247578, 199456189, 650109793, 736321555, 498416454, 631214831, 677546798, 130785065, 202541408, 230454075, 155854729, 769336632, 474753822, 801483625, 357141385, 639172251, 568989218, 584923074, 553698048, 470495077, 152630313, 620209764, 710508492, 161360332, 600881601, 408309569, 264856938, 842577425, 73908538, 774217957, 401786190, 149482212, 803146076, 772603365, 169960999, 27480827, 95426247, 914685070, 754167634, 965970005, 361658618, 823698223, 929540740, 263258605, 270444370, 654152649, 112362139, 904499705, 12749176, 261814014, 80561608, 585640724, 93953849, 478345259, 374954532, 678065337, 899103095, 335959097, 598797815, 429557403, 238425966, 39177272, 836704057, 134101963, 433994529, 453950306, 790044300, 411739217, 600157875, 952748277, 48163626, 429391753, 762569848, 126548255, 543972047, 810177060, 757371133, 924039179, 453872525, 10950710, 806607679, 544910661, 709365675, 439931898, 974877343, 737624742, 190304118, 789250019, 182681907, 346557004, 493115329, 995094761, 402932709, 864781153, 860745570, 476104578, 816810122, 347272797, 433941384, 375660438, 534487380, 605558673, 593673833, 374953987, 869560778, 892337717, 388278050, 600495646, 776596588, 660877548, 551336907, 467206553, 973426083, 805099549, 923145592, 812461106, 416090611, 517568990, 653241114, 66320663, 702926343, 495181108, 214002311, 361413553, 951967754, 69468136, 121857354, 685952203, 304811223, 91213266, 629935704, 510248642, 468961021, 582090986, 853239148, 764851506, 659432645, 68196878, 216220984, 80634528, 285556319, 914406491, 943239302, 412236994, 758833195, 798522085, 885460919, 815085914, 553661139, 203259002, 971217150, 801048753, 671895609, 224191938, 544143101, 368261968, 479558825, 827516340, 705549841, 303611529, 441684324, 369656329, 811458495, 268500593, 852937328, 239468118, 297901322, 524161909, 318291819, 933063860, 488409104, 564606257, 738309362, 850617000, 935981327, 26840927, 269915026, 453681810, 227869270, 379795264, 255244866, 440886386, 879251958, 937858252, 183542524, 590592912, 783902973, 749136198, 651960489, 313678087, 421133325, 981512596, 522767888, 340632364, 180714923, 536261017, 895889598, 419600893, 941147527, 365999124, 204809378, 538886213, 393910044, 192034625, 666917408, 699721313, 825427101, 324067465, 140460760, 423948112, 228261131, 709703000, 703801414, 911152034, 85920649, 637276163, 882711050, 296627796, 184128240, 419544387, 634016291, 5400904, 271043892, 197480554, 827852297, 194019048, 224483113, 571896113, 857408974, 127150169, 181566732, 659924356, 187033657, 701218828, 958457620, 252337333, 365773944, 555305886, 790829690, 827224614, 995008051, 82365319, 116698078, 840773655, 419701821, 842876489, 474152779, 292609644, 163562821, 565868595, 471838777, 941743469, 332254219, 106370472, 517612664, 685774706, 126315025, 293407268, 970763797, 519025935, 754152286, 371525486, 536650807, 793051417, 932295444, 508138488, 905564390, 301833754, 279807662, 380808092, 474059066, 455475379, 142640114, 443166402, 389407025, 58461026, 838509793, 74616413, 604824939, 27078239, 976365319, 323615068, 698179566, 444696857, 520363169, 922817491, 634040536, 593072571, 49469721, 642441221, 773884734, 639354263, 458038670, 196148143, 458826566, 567498972, 370557479, 929039377, 450039612, 653466311, 644088313, 307370294, 344671001, 592974682, 749137505, 975760613, 804649864, 443588144, 258885410, 42776603, 338679542, 431581847, 925500360, 41114920, 516188923, 238567210, 838102905, 497309941, 230523609, 446801453, 135832922, 162581826, 453148162, 873350367, 997177723, 197167351, 976097380, 638575400, 376733132, 691960253, 292701205, 628042837, 118177483, 490657093, 810172117, 513961201, 955300794, 504182458, 445173258, 701419529, 987653688, 322619595, 704023413, 279046053, 104137548, 70053754, 745134065, 264074360, 673282222, 621468166, 933756259, 586961449, 814467978, 153992503, 511794498, 564590962, 711539026, 881101097, 995641017, 31064799, 139080574, 343319209, 399482123, 355992305, 107395498, 150964326, 874730522, 322671290, 601222947, 912099124, 414740563, 445638586, 543626752, 638653607, 491782803, 460472983, 127946451, 162313238, 238817580, 20457215, 611319805, 407825487, 991722045, 112200648, 481438531, 672816596, 118135101, 103713644, 194154619, 401928319, 482047609, 58001434, 259685259, 446367537, 197759099, 610600399, 863905519, 479372918, 961518803, 187456395, 751743895, 579645112, 274854805, 970897264, 422511298, 624562869, 996649181, 735269081, 373502863, 945238933, 995362056, 894606474, 822358412, 809304160, 417061802, 830668884, 959054269, 937333904, 53766080, 575713639, 125246169, 239852522, 655333318, 948846995, 746046730, 85301435, 679691129, 710762997, 931682068, 138033405, 512191151, 651164665, 285114594, 850844621, 978128056, 133062887, 277070535, 728138582, 817789463, 10429678, 959053192, 231236453, 736707326, 553909293, 486614993, 825981733, 110137294, 353354877, 497528426, 632185163, 532593264, 316989764, 495640849, 382884488, 677478576, 362022030, 19843905, 533370685, 612706855, 10842383, 878695747, 726464041, 915424625, 844203114, 66923757, 117748623, 353681927, 928211491, 168390480, 874658510, 679435740, 245969638, 401684036, 703657506, 214479962, 568633731, 407536260, 242275771, 220165488, 584294914, 790939384, 64606319, 994355524, 685525069, 190612846, 166665140, 270868343, 773033420, 606159374, 540615713, 25029466, 928833168, 782542331, 319847297, 559878622, 649955098, 990166307, 285707950, 283715547, 650506277, 663757021, 957968579, 773099380, 300243802, 342238520, 388415289, 734696677, 371880415, 864952395, 984763436, 177605250, 726200026, 853356715, 38811187, 441398922, 992377073, 675226092, 781549580, 981370568, 77620739, 121436756, 926106394, 726985519, 823454732, 107034542, 648119783, 694930241, 521745450, 863557835, 888536853, 144231789, 844331424, 614384205, 765027870, 451679480, 205778313, 200410188, 451885270, 897947666, 429955259, 866097062, 805408012, 948764908, 283883446, 424982923, 665777339, 771940364, 919064884, 460010833, 951058546, 364467955, 607415208, 519076462, 572281023, 269973253, 179218079, 531695270, 654133194, 320138667, 880879491, 318753624, 175496518, 78377482, 944572445, 838670630, 711468105, 675526814, 33051491, 718201582, 280992551, 707692053, 572465644, 831119410, 758829122, 461793067, 74275318, 172373283, 664275913, 885745875, 924713427, 249340829, 885633223, 232922032, 564583713, 655233332, 542416409, 913249099, 252217938, 718640364, 577818144, 228864319, 886611141, 239251647, 105464109, 336940020, 614482328, 141421556, 353077830, 342979851, 821345397, 470861534, 192495168, 964592980, 385173119, 879628114, 934751207, 309430652, 911449576, 881413148, 500850694, 914089715, 543320712, 482271109, 55841324, 497842440, 901032075, 621305027, 109389656, 731999391, 794365243, 348013029, 736501148, 499283974, 790907249, 305152652, 989557113, 68299412, 773656225, 869516545, 428250692, 156074817, 584765783, 510963343, 383866060, 55717645, 577005449, 756855704, 218556830, 76429955, 439809529, 489637652, 287755575, 2997031, 388651676, 724011221, 464894799, 231314592, 551381035, 605816333, 511264354, 136265212, 11184698, 137683703, 575648692, 948117948, 328953915, 398420565, 953278886, 720057970, 393432579, 534545544, 804087531, 215465939, 564436445, 892166150, 681124418, 930112297, 917693249, 619608643, 670253008, 860523144, 432329186, 574801224, 907413123, 543676017, 514072946, 788968002, 502228137, 949033996, 942192810, 676200376, 231782713, 606236670, 875644360, 397339541, 828558395, 574042087, 316320004, 77947113, 368737368, 414234936, 651543905, 528060612, 723571658, 616773343, 273464096, 765441389, 422465440, 930526177, 126094210, 308961386, 614946959, 76463821, 972491894, 116017200, 944120071, 105608039, 273806458, 918649435, 183141496, 3263491, 627297556, 313471169, 239872841, 751080159, 86128788, 459269185, 9903870, 198168977, 35763058, 734505283, 576487226, 961468280, 253156148, 254002860, 389276408, 444660912, 87176947, 719298785, 768793119, 75715616, 918739020, 49486397, 859378170, 330362234, 660158476, 903181037, 8065387, 688730979, 393620360, 707893903, 298719151, 958411192, 485573518, 835835077, 394844262, 607304827, 65895074, 667450773, 818081051, 284634495, 661860140, 734917156, 120534097, 704859314, 161019427, 415563830, 370280546, 898225914, 641172042, 788936637, 971020460, 402288791, 832166314, 314135005, 493675450, 60932312, 717987926, 703761726, 206645470, 811282353, 351799089, 475623996, 410217735, 154911542, 641626665, 881502090, 948773603, 322264189, 450954014, 984637574, 414258700, 504609419, 855426974, 269686477, 75605492, 192375689, 461942506, 177646972, 381584654, 906784847, 379698656, 803580794, 764276418, 445019267, 43857112, 641283198, 255628140, 591620442, 350904622, 852567175, 402009210, 251599065, 816775977, 676801140, 71699029, 645636582, 408370512, 488865802, 152613382, 99808073, 533320909, 876090708, 422636413, 628510945, 825973252, 793810243, 93534668, 385860431, 691508877, 463230387, 478838163, 375328586, 463835900, 52272483, 846165570, 183703383, 226365707, 582326575, 639244389, 336893205, 735154738, 249097013, 43213742, 297361260, 167884204, 248940538, 27604252, 376082065, 526180509, 341555400, 639463906, 244334158, 130302093, 159111350, 253917412, 901206510, 875168455, 396017124, 162747248, 420213313, 617951086, 468348729, 965547024, 540598863, 705579799, 6797292, 409973156, 97380275, 346422266, 410031359, 537862400, 86424302, 772040482, 436662333, 323297634, 324765915, 923002546, 355697956, 313388929, 420557227, 725070349, 328579868, 249001697, 341525133, 828947630, 623646293, 331778597, 337339617, 155406547, 964187827, 480523183, 181154604, 812157279, 624485843, 594865343, 812008152, 740052243, 417057184, 152788691, 515172727, 76725074, 996188542, 702640027, 710647755, 356926183, 915720820, 142769184, 580383268, 949395239, 803836494, 269191680, 852605389, 156774830, 471852637, 369578605, 139865708, 967344184, 350475014, 739131014, 456549546, 709481688, 141658951, 823814102, 103968677, 861660681, 408151237, 746234971, 867242610, 188869560, 266690164, 56591079, 261159904, 305439415, 807588710, 347858456, 451489571, 887948438, 834543491, 155395975, 730590775, 471098819, 887618953, 210773583, 617235492, 259876619, 284413573, 742170224, 494228852, 919793167, 565818974, 544901299, 456040244, 513166171, 301308912, 362901372, 369691294, 154132612, 111106325, 592820007, 703348300, 149824556, 611831626, 801664835, 207610527, 590040014, 874246435, 579763938, 455282105, 219837070, 649226276, 250601830, 505367682, 390074143, 219063147, 73018594, 206891940, 350445981, 663683683, 938321132, 74622027, 643776095, 541200808, 739741161, 939885977, 988141827, 149780828, 716753225, 113368453, 30410160, 184927782, 339493906, 655234252, 965000889, 878244532, 257773434, 501528569, 978033375, 196639610, 779032442, 611898187, 845881722, 456836517, 318882380, 776989855, 815662193, 893857897, 135384650, 146407445, 176284724, 708180438, 872309057, 193207872, 825063414, 116696302, 587437119, 359338201, 801652578, 539633822, 686489836, 434454626, 745705659, 234684425, 387439185, 256212814, 62552804, 886781185, 468593468, 989259945, 592442830, 99121187, 20803704, 421119344, 752733997, 967500358, 755713202, 366006086, 765345024, 869950494, 673901374, 885746778, 274432840, 779035639, 417548438, 22198161, 308440281, 893693418, 229695653, 494424952, 70778805, 621528796, 204005973, 646046053, 678010843, 782931747, 393081404, 73616787, 872882606, 686221672, 888121698, 778390248, 415646146, 702360535, 917268496, 986835985, 708980313, 179156437, 698670321, 75640184, 477014805, 479166154, 533873194, 448071325, 354997616, 743300245, 506119314, 75831373, 100305302, 738416748, 698486502, 447015865, 43734288, 388311466, 997705242, 878705883, 464566466, 802865031, 768271951, 442912798, 538984997, 778215019, 792588061, 315033296, 882020036, 716489567, 257075782, 16024514, 317078389, 675044840, 456015726, 34335975, 721040480, 355578829, 81232374, 30218078, 91002643, 831099220, 660134327, 390685028, 123025930, 749120148, 388848462, 233288732, 273713510, 911907701, 313551933, 565845364, 371894101, 428765900, 892845469, 850619022, 364942921, 884829874, 542458541, 980143410, 481100250, 819645663, 205971742, 296363258, 415091530, 237986887, 813807582, 536561465, 510829414, 435997544, 163685081, 273092039, 676280737, 460428352, 504583937, 848619984, 552721348, 328163073, 119329552, 414947972, 429942298, 808936906, 530053981, 199788931, 537487400, 533926823, 666998651, 546081383, 770477145, 776017189, 988023018, 24583193, 930710884, 79609493, 268511564, 240435086, 823133296, 964456492, 50822703, 763858005, 635449988, 645244457, 486543416, 928094777, 565838790, 626056606, 944095061, 868578435, 850095027, 291608278, 384388832, 426786971, 533302237, 635214093, 898963497, 627603043, 278665680, 562717474, 139447076, 661811142, 548871743, 711758733, 626115064, 992569243, 845951475, 123584272, 631415335, 739321447, 568227687, 555257303, 798186283, 199472751, 55255783, 111424703, 241305647, 58127936, 506662930, 453728155, 545615165, 627911188, 57154982, 295721625, 552426202, 770290166, 230337139, 383594469, 351020726, 597502556, 304284964, 186957258, 880533747, 339461343, 180466292, 425131928, 446061869, 988343039, 41531570, 971554415, 470796746, 305207249, 970611750, 418248718, 940558665, 655238955, 864260225, 940287471, 710612280, 696144957, 644679698, 170458844, 279664300, 20787155, 921014641, 130642959, 356398780, 907924034, 220312990, 169368149, 775240269, 995487089, 470216054, 616231727, 281701814, 688000818, 233604557, 351591686, 491803460, 948996684, 527084378, 388748151, 383197571, 353019676, 835765989, 689014436, 745219000, 812569501, 499119541, 418809010, 930230793, 494410294, 881836319, 477289853, 514300592, 509806030, 13075278, 30999123, 940351870, 528595536, 617760353, 70150949, 248798775, 711811997, 758444746, 200738415, 142526718, 904425788, 678830023, 214063450, 508411228, 509967074, 503059497, 240962263, 445378586, 233968257, 806641343, 159423897, 64629905, 443877047, 798359557, 560856345, 214856741, 240210057, 933414624, 855534455, 421004039, 647980695, 726044306, 226880623, 973580264, 954831654, 22252661, 48856758, 287166355, 876709586, 46885843, 900276141, 698731173, 947235684, 573540900, 896731194, 242247423, 147988728, 95046972, 385364929, 401979845, 895862389, 611992671, 276710468, 939678574, 331154057, 196755529, 355425889, 682515945, 374163701, 834648465, 205929230, 479070298, 903171501, 400674843, 424622323, 599082759, 357215015, 486250372, 538307691, 31417133, 56291566, 984503435, 823095614, 2668651, 798723821, 942014092, 373886748, 159836953, 964316770, 613345319, 526808790, 651029478, 138883176, 183159390, 604214663, 218199398, 542068922, 854430597, 534321469, 392747213, 189729958, 639052274, 726357977, 788025765, 801095843, 151897361, 123018599, 104884610, 729265406, 429208644, 248031406, 92415935, 624636732, 981898991, 722065457, 948120473, 273049046, 920223307, 592485737, 432923542, 287582840, 724937916, 156774362, 265149530, 967545397, 926073321, 795082430, 38826160, 440987062, 698124183, 991574758, 224224295, 864780557, 666910460, 327640067, 399264395, 314241827, 742765437, 241273450, 552105060, 602271730, 699567701, 286582228, 220177823, 154136151, 249580672, 883742851, 875992697, 225981900, 633349596, 820085911, 776305355, 189930452, 538243, 525128739, 430493474, 138427021, 851261226, 515013941, 702260804, 438356119, 240049091, 695416773, 471151084, 596663551, 376655585, 482806055, 588117275, 889817235, 338580757, 839950596, 614874595, 274108358, 277942599, 375990226, 765023750, 612757708, 216732238, 903628587, 522491994, 817430359, 693078063, 273384034, 297737651, 103076893, 683403579, 790843719, 572068491, 176733010, 310611329, 995450593, 809941473, 530182500, 132449671, 838583272, 155846716, 399748508, 242158949, 869169274, 290969204, 92796969, 391056072, 981111870, 660295735, 246108459, 898825067, 15589234, 372054057, 723991130, 489081263, 418600894, 811376921, 920127313, 719131200, 136084637, 902717174, 291385517, 343774097, 881853005, 334756836, 869397316, 794242337, 358536245, 25312700, 228020373, 709715424, 190760206, 14542079, 266931748, 24469971, 529863740, 427224944, 511780514, 593570642, 341738948, 262982584, 968523607, 310269429, 325006543, 906136698, 962139332, 472957046, 304907305, 918812082, 503197314, 186605834, 765900735, 722515806, 335398160, 616410555, 329983567, 637803578, 443773996, 266323690, 27652616, 740549381, 938842232, 859103782, 79392090, 454003721, 313725284, 937216358, 777925463, 793756050, 206552357, 756826108, 836391904, 427170305, 818832698, 238433926, 489257420, 979294715, 218223927, 476765948, 758268090, 819182100, 188049105, 535938204, 370464199, 432695290, 866871975, 674026206, 491865530, 532308386, 36760333, 346282535, 813146729, 97866156, 468413875, 995017619, 525108491, 736994576, 431087919, 528583524, 797274502, 877586401, 176402295, 576651791, 74683879, 221726474, 371672716, 111474935, 350113429, 86325428, 490542439, 580094284, 886047817, 74892723, 564971904, 402660379, 269653031, 598020996, 411027734, 464846150, 161217333, 301565650, 77546065, 820159533, 680003535, 571064599, 536920261, 826825878, 334687767, 982967727, 207904681, 311886282, 624098992, 60926886, 965959040, 169689060, 401414360, 485693538, 417709527, 231441702, 918876928, 152043411, 632360108, 968711923, 614755493, 737028183, 608648413, 664053487, 714897713, 358916162, 889295252, 151730631, 575325719, 897102877, 146171897, 82198698, 23174130, 277535949, 905820452, 111108213, 990297067, 749802201, 45977357, 778672265, 32240577, 374251775, 872014708, 71236985, 662241622, 575810325, 734422317, 553021775, 111611398, 763228435, 711350560, 301717921, 980283390, 551732135, 735036727, 891329138, 766360383, 380491405, 482932210, 196862332, 736953118, 883579517, 397789551, 49886184, 123799817, 926326997, 302272700, 370578515, 633953354, 851144540, 348307096, 421831935, 473721687, 286075274, 800995372, 150988704, 976856124, 403995363, 372209876, 430377636, 93046328, 603381387, 486592260, 56137857, 503160964, 14530958, 548875673, 637352710, 640734582, 387444517, 278565474, 292200491, 561888784, 487430432, 804800462, 485699777, 272094953, 923907442, 29117406, 974877829, 906907172, 180556252, 456061546, 974069982, 297982894, 166432398, 213664790, 201408662, 451518844, 692628284, 242132271, 136526094, 398101882, 836769127, 905543946, 783666379, 269336171, 268430166, 397152687, 32618912, 712890189, 307735654, 686425710, 517766449, 649211873, 552433358, 517238304, 17427973, 94270576, 715205617, 887560218, 305876306, 48729333, 740652558, 804421058, 338993387, 414427380, 695845217, 880042688, 335060349, 696996658, 751979136, 85482504, 538459139, 684412629, 940517020, 334171550, 120679959, 235851176, 268794519, 93826817, 731136189, 93483323, 453830107, 890102226, 840957929, 248947535, 425891978, 529835929, 49611228, 407739470, 656013701, 454704473, 918151788, 890198679, 329047560, 907106461, 760841438, 275114121, 383839342, 473014280, 18759555, 628127851, 86572978, 606348831, 758322742, 856873196, 829493678, 266775052, 51399232, 964234728, 150245870, 412438283, 58934507, 234977404, 999498510, 94276529, 702737126, 131142176, 652802396, 295710560, 25184796, 907022837, 661567309, 61777893, 549176028, 136660866, 27178945, 86443264, 376038156, 892141083, 396155876, 117211193, 106484539, 766543607, 343039177, 205036449, 89486057, 734939223, 677738092, 596296252, 381097867, 490349342, 314115761, 199834894, 304986834, 455095492, 55510496, 578426827, 446246527, 294974379, 387650549, 46687161, 438648522, 305730341, 560831643, 79445302, 628004325, 476195159, 957492655, 25485349, 31747392, 545801026, 467196667, 874398531, 136426798, 52211484, 950080515, 900458361, 350238306, 812791073, 42061024, 822503915, 941863173, 178403436, 145388484, 813738588, 927429742, 887850228, 353808429, 942260488, 948171809, 457260649, 511805284, 143443315, 731052803, 755131963, 831252803, 501733325, 940222475, 956265358, 821368633, 174207856, 807208704, 994620486, 356639172, 600496838, 749362806, 560648072, 971535563, 241424537, 881283035, 630784227, 224304003, 472017588, 310809637, 638976376, 406101738, 549469392, 655218653, 951252491, 967387746, 935127303, 333506316, 978798142, 401550754, 169248906, 379237243, 587032391, 127732572, 605617558, 344831266, 220067599, 265633469, 461639758, 53001808, 303298927, 603558456, 199521606, 20112294, 683177431, 518148380, 784093084, 765758349, 361984514, 673822092, 396699089, 858943868, 522197309, 818335325, 118136966, 716791240, 251727378, 720582219, 160552615, 144539157, 940013756, 126707320, 843122729, 819558455, 307256585, 432190648, 71035418, 85607046, 25880649, 345551022, 242315277, 968246304, 121785071, 684435524, 601068608, 197673058, 191922037, 53178052, 286212184, 773589771, 217311359, 494114147, 193258090, 340505354, 230653553, 464078430, 125893619, 119514865, 342333849, 623078096, 728381637, 846596444, 917305468, 318077918, 505790057, 542356505, 423849362, 447807722, 453134935, 570741911, 119281818, 850297193, 1508124, 343768901, 349573412, 394799108, 81841711, 115341222, 875218889, 658353225, 272184918, 534636810, 679964352, 806684290, 233255730, 368160418, 909700511, 828269050, 584091856, 756649392, 207041809, 305905548, 351521257, 528973766, 591947669, 212975113, 365507608, 22899933, 403817301, 689107646, 771721606, 414378772, 549306424, 825871985, 471526053, 923328266, 370231932, 367422222, 203697431, 516212979, 276150109, 249563011, 116128258, 636718196, 822022881, 817909264, 590699693, 261993668, 424760805, 13766118, 575301793, 327548630, 767288429, 971344987, 293675171, 850841331, 423106740, 172981067, 908535946, 663213014, 662686170, 968522885, 922210369, 229584348, 436789085, 949376366, 93549408, 275924569, 822693484, 679237995, 168395183, 760123483, 369411106, 72298687, 338098943, 559758459, 432847842, 211799181, 410424724, 540913703, 674637210, 583258467, 51447163, 425130701, 738908769, 825491881, 989128042, 240535075, 250985732, 707312513, 673301793, 18307657, 493514412, 740581017, 764619966, 993829405, 369447079, 651474094, 164233166, 592830518, 982555252, 54992054, 696488131, 363434026, 677403937, 370214870, 504156179, 585914037, 402329050, 679468988, 916217179, 528502378, 49448811, 373947636, 867843693, 871248006, 399918173, 592016942, 26704791, 527794584, 65293665, 394761524, 596839834, 453160619, 70831670, 890164142, 378995084, 167941171, 129968746, 699016089, 935545628, 973635584, 152712740, 391454130, 974465966, 163303230, 4789256, 962625781, 279916096, 312497272, 475020053, 830310938, 968460348, 252008494, 325065286, 115260785, 755682121, 907781963, 393794596, 997102266, 943716591, 122391464, 947291482, 195274268, 211543013, 842023550, 531648277, 694750167, 215528584, 489820735, 594591002, 67439548, 625855535, 374959673, 660796764, 453167583, 370022139, 233934591, 758457825, 641545554, 918330393, 213722348, 497178234, 198616687, 887915506, 792345195, 1757924, 335181788, 877325294, 697717734, 869079464, 59344267, 471418088, 715706176, 932867823, 272293653, 907414282, 245793352, 497594394, 417456710, 703002899, 374659023, 96805298, 136515371, 502550606, 869497272, 943406645, 570184019, 848894027, 366723566, 644140428, 730626474, 506011674, 736900366, 348106758, 668040126, 839864182, 185853460, 585324454, 229010225, 992215203, 920715584, 192815245, 867696485, 114431153, 707524177, 957912229, 49474512, 272605288, 710313185, 807818836, 787993786, 158055286, 713706940, 716086615, 147147635, 209523613, 395739721, 485243821, 910062634, 249677240, 627482216, 563204344, 43313538, 986531955, 469112949, 742603826, 848653019, 959609056, 200927281, 94836446, 870221184, 220717831, 662891493, 823392913, 752903717, 454125167, 610656112, 513044660, 53599239, 318449875, 862804107, 578767021, 692296742, 670982176, 556639346, 265488778, 220652277, 494562592, 417626614, 564876077, 771146718, 593286373, 331454806, 104849417, 398292229, 904580799, 404829540, 251038482, 26175437, 686156270, 879010173, 235961048, 924717052, 86667055, 130344706, 818720442, 525617818, 840261277, 723159881, 820570979, 802601611, 956289590, 981598985, 89796182, 955955446, 472156604, 921575639, 144878158, 600153816, 365514759, 74394008, 771834095, 115743446, 338053105, 630798041, 294173316, 443111115, 773284698, 467342349, 566445757, 907745547, 352911953, 536110091, 447682106, 39475548, 739212211, 852118635, 544916761, 474872815, 410528268, 846529488, 242158841, 810051223, 495459887, 286741971, 204246646, 962016575, 175811325, 689441229, 345745857, 587048304, 916741018, 308919332, 780316782, 584646119, 614781305, 570207614, 741290130, 661663951, 451557409, 698689689, 534827192, 27037678, 274489356, 608567961, 575947582, 69311394, 126667149, 566700267, 274094970, 365565778, 976459668, 919867742, 348450260, 156922443, 638107074, 29607726, 665522744, 574794705, 767414925, 669516251, 194159217, 120105611, 102271032, 510689527, 449088344, 671386482, 942110641, 508056984, 594600559, 110696728, 500539328, 774491856, 961529263, 729104349, 217213953, 777563517, 730039350, 167988786, 69789493, 901866217, 365841752, 242431113, 486718316, 886833900, 23036054, 6044950, 519802229, 34021983, 394513245, 34245462, 604897050, 165282609, 655872781, 494165671, 570941334, 267794397, 930320468, 271668900, 238613685, 476540250, 112599395, 916247729, 565537846, 509276094, 349944364, 736755227, 599045099, 420841957, 59699261, 140297921, 307591780, 413488456, 657933674, 869982371, 919572667, 484780544, 309927077, 857239635, 324784758, 828922484, 980739329, 659365451, 806186580, 779540855, 915889650, 777602792, 675418493, 755760374, 450473339, 641315451, 537640097, 958773500, 561031620, 589239133, 174505397, 42485573, 639556359, 227695373, 790669744, 960643037, 73013874, 384764395, 966604527, 308467980, 881847777, 923865411, 28057538, 125713896, 531674972, 461141661, 756197930, 393249536, 486157249, 397041914, 889251167, 62154607, 805097400, 847014484, 147647701, 278193612, 815008068, 471735584, 302539518, 926959813, 156805303, 927742614, 164612028, 595447463, 819027258, 432111243, 118975976, 829633820, 353434006, 277536928, 906947320, 900185339, 78519585, 493403280, 52234812, 58604728, 874883307, 770599057, 997978793, 706382062, 831373185, 632133419, 698722758, 331826953, 814243088, 529262438, 292827270, 744478394, 11693898, 847456656, 464107780, 432855351, 171380254, 245620970, 887461213, 735917659, 869068859, 495933095, 132384084, 530395294, 637147046, 877859449, 172076158, 841839748, 641645129, 916878843, 931597690, 376708617, 201335198, 619714804, 268006953, 845623414, 680631379, 487885170, 320227432, 651792880, 442620300, 915408969, 720914235, 9277944, 792973932, 96569108, 876075976, 425775818, 431364343, 508272474, 445557334, 376939283, 684407877, 998002251, 363802115, 252400236, 685028840, 591054962, 925403683, 783668679, 265042652, 138870173, 342671158, 607877337, 989070437, 917886647, 542622175, 421474383, 998963304, 695998037, 726380937, 826800886, 729036073, 131513206, 708672600, 714181798, 170682756, 19512865, 340838521, 895643645, 815378221, 202191012, 599057472, 776093893, 211819108, 525050827, 231345562, 77752194, 956697100, 532059417, 818584786, 869589583, 306240917, 248477683, 550674124, 118983187, 125720136, 621600640, 235544144, 197330988, 272247544, 558658815, 500496726, 109841092, 107222559, 580432570, 405268031, 198115424, 296881543, 409097925, 549950090, 787873309, 156599855, 839139883, 53518808, 632861311, 840591104, 632598562, 183533104, 984881272, 771011915, 702607903, 839622958, 195385789, 562322960, 447607360, 306857946, 732382748, 337425986, 245597256, 497992383, 926651085, 494776117, 13757657, 465708451, 277313253, 124498945, 195031888, 446708968, 833188134, 566673384, 719564367, 28800782, 923813134, 565416902, 893174511, 880636327, 676755746, 17017167, 105455564, 3499601, 744614511, 536355616, 281078829, 143526483, 645802788, 647581755, 136108731, 210605376, 601168782, 40906012, 421818046, 349017041, 990134359, 955622304, 366679572, 242448854, 512369089, 296906986, 352807179, 547628274, 487099607, 205303601, 729018465, 31417363, 170773842, 251970465, 783891670, 590384744, 500261149, 662563641, 345600155, 803687071, 872388463, 440261272, 902155287, 209438813, 471346192, 662215373, 242866195, 551283400, 538829704, 978418621, 939532580, 444109609, 677261110, 664379397, 860751250, 932893404, 714798707, 325932027, 949382975, 509453680, 634761952, 421386683, 516907463, 26941006, 388988941, 536432206, 465924642, 246717884, 727158447, 47834463, 132585383, 279301889, 982733897, 113991855, 838791785, 337725135, 287293294, 315854172, 222943385, 963434514, 258054335, 142048258, 673676029, 948713986, 457005775, 151707553, 923501050, 605375403, 89451514, 503681499, 316248161, 918249830, 606874071, 245380153, 252111167, 808104611, 810464795, 740007953, 120276533, 423163637, 395518748, 793239279, 805678034, 171817249, 337939259, 140187282, 468828975, 769637507, 912981580, 608463759, 518343431, 65964049, 653921102, 103548747, 202592110, 561980033, 589806422, 558010288, 512560010, 539637276, 998524739, 801787075, 190264438, 442971296, 964369329, 185665006, 845316730, 929800746, 450321886, 890975277, 61640695, 74560715, 723108919, 258869983, 921524159, 263640447, 927588024, 464913488, 377981884, 781394331, 584497680, 395846663, 106946846, 215477588, 140344310, 60457187, 86965079, 538493749, 639255339, 614389637, 32134814, 279222019, 886418059, 563861693, 633463986, 779001572, 175535122, 718080594, 569435230, 464454163, 76810211, 98349379, 373603306, 967485003, 252798969, 274990904, 377600772, 379752653, 259377445, 870533383, 384491388, 134120357, 692311466, 285328086, 783311154, 876720036, 145830252, 622621677, 465412138, 545289339, 761336226, 533756895, 292094252, 340718630, 177609629, 61089379, 332425466, 438925741, 311840372, 533610405, 387503502, 774764216, 214458544, 315786081, 887889043, 482501087, 659868414, 636618946, 58918930, 555402389, 535219166, 793122869, 780042947, 950072615, 705078541, 648885941, 312416163, 692369392, 325710940, 968310318, 916854741, 347896665, 982201888, 130245682, 111092352, 839812584, 755260169, 232955970, 818940471, 738152457, 531934045, 487850836, 474056456, 525654907, 500786008, 478935718, 9411664, 466711262, 397437887, 844224117, 250482830, 716002240, 773276273, 404108829, 71527717, 372636107, 762936909, 498506897, 595346084, 278467945, 421863380, 602215028, 157881691, 912560994, 859284969, 710007834, 981350233, 706669118, 132320887, 464296419, 845207653, 240045708, 725005195, 863425888, 461792628, 194554246, 874838237, 364034292, 37186692, 408995196, 66020635, 501132734, 505816254, 872595469, 506417962, 755595657, 58119468, 615510707, 4944016, 496626826, 191793541, 741908379, 857725151, 812615595, 407881311, 611519679, 142913475, 230963941, 562799382, 6132093, 720910438, 118175551, 654023685, 805237448, 751945209, 50986295, 834144829, 115704955, 804597412, 282753559, 443213222, 524116128, 286929496, 294863732, 79026036, 186960931, 265008835, 52678090, 361522269, 937353956, 100346530, 615337105, 800544608, 672975845, 694231206, 414471083, 454289905, 804110865, 195186970, 663955816, 23153108, 164868142, 521858930, 174562654, 812515895, 767885260, 53335038, 551165468, 476437183, 299308823, 580820944, 161359574, 858101934, 298554665, 345960761, 554858476, 952494153, 499483570, 257899647, 40292398, 577042195, 276239485, 660039834, 661274252, 254817250, 855496183, 880565207, 886590300, 464094039, 134933699, 447738467, 229545101, 835233697, 977160848, 896138262, 828802671, 474013780, 241678421, 677898222, 144068067, 882845088, 420918861, 436304600, 842959771, 73603176, 270020312, 164257979, 650092059, 501401098, 216054817, 337003187, 914057239, 932176125, 863853327, 405424903, 195490630, 447967057, 712527549, 835623292, 551516064, 506493974, 587141412, 265664261, 614624394, 415791536, 399910861, 785959350, 670488954, 311666856, 296023550, 488328771, 901924890, 664470112, 920756071, 524199619, 109408965, 616404265, 122384533, 669687498, 556799161, 795069279, 668568703, 323807919, 400955885, 845797825, 991158124, 82179425, 400877069, 920640769, 161728826, 839057758, 19315600, 952553783, 900611469, 486587107, 20299835, 681910125, 690882952, 34002837, 375651536, 46405704, 625940821, 571229639, 938115166, 185691783, 335919320, 533451859, 29913087, 625946067, 271374188, 362663083, 674992051, 443910606, 78692745, 310630100, 250581356, 973023438, 730599819, 244274622, 309355004, 420629480, 303850351, 501198351, 897847512, 777621275, 711419299, 366485141, 645537709, 470299176, 544738230, 693571676, 792730794, 986085268, 62292220, 688088779, 317077100, 15333613, 464794281, 737443453, 35448641, 636709464, 553383089, 281452328, 383268317, 314318425, 954631292, 200848499, 978220785, 643881942, 845662298, 355800345, 211342726, 20676228, 123085950, 278296378, 432856941, 155603825, 850983448, 839459214, 24821828, 570256383, 381667189, 993433368, 294382790, 961021906, 229575541, 894631729, 727289160, 795931539, 954878353, 584854966, 746694926, 302198012, 722881448, 466709433, 248901221, 397935262, 328317723, 408705120, 443989271, 964120316, 420430655, 255831716, 96796739, 523860674, 29547529, 170411374, 956706446, 99087057, 969543745, 316716637, 384009502, 23113045, 539021774, 44733086, 119409025, 860462810, 744127267, 667537041, 611185619, 362527034, 969722892, 196269874, 339811480, 371868862, 422996385, 890243911, 476731883, 174527633, 503675368, 27946791, 413079461, 523536397, 30970482, 491645897, 720857255, 686801087, 781419753, 494305439, 845947311, 39598400, 253070308, 643469877, 646601699, 942683442, 420094264, 274137266, 122929534, 510413472, 469026472, 530935974, 314846709, 369244296, 228928946, 251140348, 462876211, 658701614, 713879073, 655624753, 655673079, 128766409, 630670222, 8734880, 800705083, 675940049, 909393231, 165844739, 615269482, 749349517, 164724706, 420553031, 847227328, 536672900, 229540586, 767205497, 429968214, 460958870, 657916501, 985269110, 799883116, 837840123, 926366255, 69435594, 722012603, 928603968, 221489834, 804017356, 959732349, 816079949, 691000509, 767125854, 546211161, 286358688, 190838042, 640275537, 257748509, 489281379, 317872445, 507558748, 943850008, 701108796, 649213558, 953000234, 415115361, 380069855, 42441960, 989226311, 206045754, 996276439, 588578317, 502500914, 968922478, 632775050, 272390857, 698885471, 620427726, 256209102, 9321242, 990099724, 714842389, 425825059, 175543144, 580139818, 991728704, 694325097, 178112024, 3147254, 82575240, 748370560, 603531294, 594230736, 968685418, 273720850, 963456561, 539227364, 967398793, 753365569, 867128999, 797130282, 836359748, 980095001, 827422743, 804048040, 604589291, 201426652, 439997232, 206239197, 765198761, 638726569, 325019715, 628390578, 994624316, 657983552, 485273954, 77139776, 340180332, 886312794, 290453130, 603081723, 462007671, 444996175, 450319482, 754545409, 101367422, 130215941, 622797380, 619791439, 66010042, 785185611, 573323853, 753597672, 360092991, 436710176, 437714278, 944725012, 270967503, 104653492, 49339676, 21588931, 84538290, 719743187, 242245872, 661598785, 965628614, 660409551, 585312280, 783351674, 729310669, 134128891, 340027018, 401192671, 595900820, 14573469, 971490865, 487186828, 418723725, 953357672, 499852938, 633972214, 159216351, 614091546, 271222858, 536412521, 569124708, 133339217, 629910399, 923989057, 646172771, 912336082, 563796494, 615583907, 292124603, 895007414, 623159469, 248499727, 877883211, 318481963, 95366304, 914401424, 708135151, 636297923, 777303772, 690164823, 781118205, 44715312, 18571712, 833558542, 764911181, 701709614, 392807815, 483946802, 355999789, 690677376, 244991399, 78383302, 523019545, 704626058, 453438032, 172094737, 560082235, 408892594, 148152139, 784622758, 672951308, 881235002, 88558443, 417318371, 975818084, 352583853, 402463443, 10044632, 516948976, 866523649, 367617381, 352870397, 324861910, 763334013, 606446796, 374664035, 186541231, 803047582, 471757459, 724617393, 772519307, 96137400, 681703337, 485224050, 694223605, 466074320, 824699534, 649283611, 631968535, 389512081, 490568115, 115974093, 155730800, 665500343, 408490659, 690364200, 201029936, 927031648, 902350063, 902751591, 187671336, 74907582, 712262356, 976640454, 687019725, 734425020, 664321388, 501729222, 361571249, 104953363, 138849522, 571363568, 309945668, 571398621, 32213583, 477599956, 299107940, 449452792, 68876956, 441391073, 78113117, 85258383, 72447023, 865022267, 170224979, 603294345, 492938517, 596398624, 516519334, 624636136, 501493804, 881763035, 744673243, 938199358, 914029546, 539144131, 632170464, 475301964, 269933087, 868705184, 240402314, 629270599, 798549159, 863656254, 462746676, 849629535, 632475242, 373474461, 26467898, 519858152, 185900228, 658763810, 917385701, 881214489, 643862037, 866059344, 811092137, 636518244, 851842423, 376795449, 841923716, 112551129, 79300387, 189341551, 583435282, 739749384, 373694223, 499061397, 374610600, 668101933, 495196427, 114253943, 346284268, 339658663, 563779567, 338034988, 194680542, 412073152, 188300233, 368033289, 513078436, 558392388, 430001150, 316564870, 565233895, 409944324, 37354141, 781313109, 663417443, 375509590, 344405283, 921409075, 408027921, 120030739, 384115156, 38758427, 321174992, 447080895, 595318979, 263552935, 455381742, 567281340, 207282879, 108317196, 29791812, 70431399, 423670562, 158018320, 663174979, 914544626, 621936687, 377165106, 879382385, 888097887, 287513661, 105766240, 940613477, 652089719, 697115384, 426035291, 293240204, 629009124, 865459781, 535377751, 568996251, 948332403, 298982274, 361026303, 403145336, 752089917, 215126717, 833237768, 14537374, 138330719, 973795797, 511787318, 826886573, 497501364, 577677733, 166450861, 836075210, 442437396, 741532104, 333524237, 20692385, 998117606, 994675120, 588672123, 947524567, 332302198, 527791569, 636271277, 165261312, 368758565, 574014921, 880273713, 798721242, 589241378, 946056667, 415764654, 768331915, 682954887, 460892338, 735288751, 873823838, 540315505, 662513840, 103070334, 969236188, 652210704, 696484951, 516126041, 403120914, 957200218, 967703564, 409570835, 835056120, 60339429, 855230302, 93829411, 358558688, 847095908, 445888276, 140722708, 36783486, 591757213, 777184296, 931357504, 747548186, 266176783, 730657965, 712322538, 650804765, 722918455, 170939062, 504182678, 99588552, 410840635, 904836375, 74938174, 462624093, 366538813, 796178503, 628508616, 376893956, 203036822, 297018598, 825351934, 317470296, 621604198, 986678328, 934950327, 915201055, 797453187, 634596569, 387805177, 290106463, 841643685, 691301948, 589634368, 596314884, 21890537, 869752223, 748537929, 269033796, 925028859, 993797695, 891395792, 310770127, 260477739, 330012603, 271299751, 819090086, 41432830, 896840389, 685864574, 420233108, 494073079, 995780216, 188450591, 485184156, 331644897, 585185688, 800057904, 849526750, 969592746, 373777215, 741766661, 221877659, 446878474, 717062138, 217206728, 684402509, 31523014, 228479513, 680743202, 93573599, 122624623, 912593725, 526471056, 979856695, 815905701, 857302188, 167223715, 15596544, 577629408, 860985565, 230728153, 718115609, 790363439, 78873972, 170270800, 85512519, 18065593, 473029880, 865655912, 567640172, 861913146, 932871460, 22951319, 676032106, 214488688, 495504390, 231822719, 931714533, 317006358, 870327892, 971468109, 309541203, 490579811, 923229031, 830909650, 509445100, 224408974, 862965117, 473648312, 200879933, 157909655, 164308878, 557753965, 50259940, 710950031, 473491817, 924923263, 285678248, 253713739, 831491178, 277765919, 785985930, 629660519, 417634190, 548271459, 664679688, 153721438, 587060374, 873087696, 756858919, 426030727, 936341723, 415279511, 95088032, 717597918, 907606993, 143861526, 308256300, 675841781, 493714117, 791072450, 431614286, 952468961, 684033351, 87645865, 591008132, 380405503, 495258143, 26258981, 148890376, 570383046, 689199062, 32109212, 874523729, 454639275, 746609295, 217743999, 2173936, 506279375, 168856049, 248313726, 727281281, 513643777, 269441928, 497230499, 913843129, 772538275, 869332217, 135511744, 75861761, 538856761, 913294347, 190491743, 735660795, 341505557, 418584902, 199751929, 272384878, 689145316, 333183796, 186769692, 427209006, 895475727, 716243429, 276473002, 65885298, 40494682, 517716988, 246416860, 456361710, 18294610, 15707446, 424163095, 680294319, 883217170, 555038383, 186937296, 964732415, 349812210, 964246412, 767720227, 411026588, 475190242, 958186398, 420389496, 871363462, 689994729, 520042241, 777946338, 770647236, 155325661, 956879166, 92028297, 664145746, 617457742, 729044532, 364783603, 259617312, 389265324, 366640161, 506697335, 646407045, 136966968, 774867971, 369014729, 12238705, 699423236, 348350413, 117775333, 368961572, 438639337, 104326799, 785233999, 96085368, 202491313, 130315633, 113954820, 942796989, 822233354, 962402519, 402634949, 915116658, 575479277, 156718897, 948575566, 178834027, 861618332, 323421273, 489466653, 608037061, 949302577, 519418849, 355353951, 259618020, 78796036, 40582716, 491935440, 704275204, 896874602, 567003519, 992139114, 435017508, 415354002, 336702407, 515919840, 103115413, 460892600, 872803495, 63653253, 191223138, 687183250, 909055898, 881518193, 548781901, 717688961, 194121405, 585012375, 425564305, 554862186, 988238445, 814863667, 513034401, 75246589, 264979860, 449550365, 810154248, 997281319, 872450426, 283801438, 127109326, 666689048, 732756422, 66075376, 596046039, 631431313, 927235447, 269732879, 161162376, 205906077, 594588870, 347923402, 730444994, 771648940, 182112772, 462295640, 232754148, 960717910, 67225135, 178704784, 116004271, 697496481, 961766205, 570893658, 531311951, 355146063, 495179078, 286823217, 648161849, 801679006, 438321398, 338233499, 259697568, 165363798, 548484923, 956816206, 823095434, 776106065, 360609902, 831349271, 70430116, 972321645, 234852184, 776835502, 83549375, 859820251, 967206476, 543775164, 755804259, 126216140, 200486319, 986689451, 900833645, 947454476, 163174535, 263614083, 947827124, 282273738, 841735750, 866292657, 63817194, 677377681, 700995382, 726666203, 507483398, 448311660, 665494135, 681692846, 352031047, 559005954, 573143157, 929593713, 144920829, 578103523, 918718683, 294595945, 340659293, 53320351, 389501356, 320272715, 822003890, 427588573, 201923885, 40742308, 301375067, 909868400, 182459425, 188199257, 691896459, 469183652, 754565529, 788851454, 79989605, 971807861, 170989558, 67965961, 290766925, 901424026, 422478523, 327744142, 693092323, 624452449, 908334123, 95715896, 728610057, 840048382, 220988635, 145922666, 642039476, 652446344, 567786316, 827383935, 899914610, 732856648, 541521016, 267265736, 41880229, 715275845, 731471954, 562118655, 533993881, 483495882, 779049791, 204765771, 326197527, 114525792, 399587581, 468951166, 733855673, 325513297, 352763440, 244609520, 463394297, 915611404, 630426547, 946595202, 261888206, 327045439, 376409525, 944926318, 806386916, 846033526, 385454911, 173029099, 378673177, 226741740, 74461359, 447625354, 53161963, 331593274, 359925382, 533072276, 316932911, 489421733, 385219105, 448949964, 241808866, 190821912, 261387213, 988833416, 758962149, 144642135, 485067081, 861187575, 810257466, 524733966, 756559028, 211555836, 240771208, 760263086, 469455089, 543044300, 722465893, 251527026, 816604864, 493697741, 365372500, 701737285, 452055766, 514364882, 541014423, 320406927, 618367972, 986082174, 32235345, 549935722, 390150850, 914250844, 918178848, 756150667, 200989373, 391905994, 748800651, 342925601, 505904054, 41129895, 375001666, 786957996, 908903737, 334876406, 849440915, 502678039, 392166923, 422345242, 915528429, 167394564, 793156718, 649715748, 321171889, 460140649, 592996812, 650305645, 147185509, 262759253, 197109486, 395283540, 485721356, 207369379, 962249137, 731632322, 422482238, 300042567, 800638417, 29240421, 626673947, 754817774, 846757676, 751405346, 841730359, 122450787, 867018753, 574043245, 136441168, 964506421, 818549312, 501028479, 979375133, 19036576, 71880950, 361662154, 144272885, 159510093, 33892542, 282570625, 650248984, 396405379, 759231234, 545432774, 567271625, 283346053, 776661420, 354495462, 834463923, 592534144, 706882960, 913758300, 749734083, 414200521, 514015575, 32608741, 84387634, 22240307, 512368887, 981987953, 403831760, 852735378, 87800314, 371827073, 528576827, 126434146, 698766768, 980704643, 597316272, 233426095, 208668703, 985699633, 493529863, 241928422, 355782595, 280095047, 7587616, 440220741, 63075363, 796713505, 856608925, 17158787, 103462931, 428352287, 612621413, 562467763, 113550679, 460763185, 505149325, 320407275, 694834752, 382043871, 280878030, 214861857, 888093523, 372166781, 388065452, 150552700, 77949797, 206149721, 253135759, 578907702, 39877764, 492535526, 2385841, 802375553, 2040157, 686505091, 290352817, 949425445, 627924880, 684588888, 395685704, 406556335, 850204928, 737021120, 87663264, 465735771, 944318554, 452059360, 121277449, 983425019, 345625307, 849644855, 580520220, 889359010, 402416193, 266689461, 958034343, 36442116, 451523524, 318338711, 979990666, 666169091, 183416987, 871864018, 5664871, 327256356, 257160396, 709735730, 855796412, 956212810, 657212876, 506862700, 962292114, 957612750, 29773681, 274076564, 955117437, 933008757, 996419494, 231378013, 520230486, 986990572, 672964191, 966356771, 946200398, 423309250, 313470963, 742124501, 305889872, 862135469, 71075902, 907057199, 70819471, 436937079, 752273536, 390081635, 755751490, 63157815, 954276269, 492023597, 173634006, 357353874, 435372851, 607174595, 555889809, 105454602, 824788637, 248049787, 3095568, 534124446, 555557556, 41729941, 457547331, 900174741, 386734121, 60627646, 989786479, 522782197, 100549494, 7286648, 524239030, 678164664, 304596634, 332418502, 726221772, 474390892, 177584209, 764664722, 904148371, 981149948, 784395857, 797478928, 868255936, 240897827, 206125261, 999759683, 785092553, 544744633, 838088902, 507071979, 282066505, 845786652, 641990834, 242711083, 280245113, 268764789, 529636183, 946968239, 239237035, 962206081, 610045300, 984249423, 529699984, 539014365, 971215738, 122204045, 163580825, 119296434, 929676413, 916984220, 184938865, 227435040, 864698197, 610750796, 386064196, 56456347, 442550586, 300911993, 699293646, 310527197, 47068668, 526139177, 461805326, 502036127, 451925366, 479777188, 569246086, 931204942, 803517273, 973079998, 975580201, 145292053, 202809275, 911414114, 216476073, 332111208, 274423565, 405962066, 862136238, 353566484, 820526266, 758956979, 867661232, 760256470, 685415100, 908174720, 588362326, 650238707, 658588445, 524464238, 432746245, 959117828, 270057638, 548449510, 330024542, 929219868, 945125780, 242183167, 943356557, 805055944, 186387114, 894380633, 333250358, 217618553, 86877440, 81572678, 999666822, 568700870, 269155148, 613242765, 257541569, 533610259, 776381511, 855967143, 232691827, 344151599, 846376323, 839278708, 700553170, 633090737, 283972738, 697707107, 780558216, 284927979, 415733318, 11601804, 82551467, 336514237, 988039014, 15751347, 24654157, 518045386, 49357511, 396794207, 721178377, 446870545, 17596271, 717540407, 199370983, 999058199, 281283011, 288580164, 965109157, 670361932, 406036216, 27310420, 741581570, 986704150, 546382326, 458084707, 27099153, 571616484, 282430137, 999065674, 384792560, 389349677, 186541585, 461897904, 776990778, 309458564, 172025488, 907161448, 603822418, 991423461, 548446014, 101178605, 785314246, 278852411, 681539837, 995098033, 47000610, 706067942, 614076661, 703285060, 58462147, 436508645, 323794018, 98382646, 380303219, 532209882, 826641090, 219519739, 505941219, 555163577, 306162763, 1536671, 280469609, 205345866, 948215452, 56060197, 722293861, 369202958, 750141161, 707325967, 179464907, 241996751, 894307981, 583208916, 681787735, 394178048, 625427010, 740535575, 875321792, 727619642, 467232202, 964746660, 291810085, 219419586, 326376768, 956505234, 470841835, 560236484, 399659336, 353175803, 589083170, 646887843, 883290185, 63582908, 499482806, 588037167, 350577390, 305063689, 16133339, 753822457, 793855011, 681162234, 621279985, 430081767, 381104951, 844777984, 668087214, 623072373, 610611275, 854431798, 757298624, 797712889, 99225008, 581865940, 479740969, 155776441, 594126337, 260497772, 956596670, 951454899, 546231324, 326773289, 685405243, 90791185, 962171291, 201960026, 414140805, 465981121, 728283117, 623520309, 889697839, 209438037, 673814402, 150940528, 402924122, 622999358, 649028224, 377626074, 233013267, 765043619, 340881005, 311016370, 540267204, 259139129, 965448348, 192139552, 563517712, 981548358, 754553883, 360949733, 962071608, 537306470, 349078377, 186643182, 126810489, 757854557, 522244114, 933972652, 632999965, 670464594, 447743457, 812107911, 588636721, 555302598, 372966366, 142736093, 156341870, 163794394, 348119984, 453609765, 254849109, 220667597, 973706036, 381676017, 758014718, 710737335, 735514750, 769466834, 545575982, 888835879, 637291830, 775420610, 587435445, 243883024, 459013138, 320144146, 162882820, 902637774, 988542414, 328408130, 260800042, 156054941, 61353909, 503545798, 843464518, 742969813, 738134664, 217363146, 152032707, 634063727, 390773104, 437103710, 962109847, 415027341, 548610049, 486431374, 978712223, 746728918, 469228533, 111514496, 603236807, 784781331, 88920120, 719905004, 423596759, 808636048, 117173367, 908428407, 531412555, 513957593, 451733471, 981689339, 931871554, 122877745, 852405207, 467080055, 943701667, 96356643, 15444853, 895938030, 875791633, 782365353, 443782503, 629331653, 768987668, 254553306, 708430142, 818559319, 277647099, 799161134, 400711741, 812095661, 862715249, 765263364, 612450461, 716083717, 723016666, 779451295, 66442065, 444825330, 221565282, 847352482, 807955442, 961823825, 439864480, 855589205, 491434017, 748365773, 634676445, 96561058, 252984089, 666445434, 200879121, 140698044, 809644800, 477366179, 783013248, 466632872, 354717277, 57932361, 662253331, 769840780, 166675647, 505164692, 635036508, 818586595, 520078559, 450368672, 822090094, 559368971, 350522582, 879617587, 337573901, 787625415, 528732177, 456806921, 449938284, 326839407, 510202993, 707988370, 751990588, 169055961, 106731283, 195215230, 2611308, 865076971, 899233340, 544066869, 298257358, 882954962, 776781632, 735861019, 401613311, 327989692, 717820478, 841796571, 110295816, 853967623, 982140838, 25306935, 587119768, 24843056, 638577715, 597634715, 469647036, 19178287, 976564307, 906746822, 271307708, 535587735, 131219569, 145332856, 16200123, 974783826, 392900272, 765686379, 152652497, 550307742, 106312548, 583078156, 740873031, 843490171, 220839772, 909151633, 611805481, 174892375, 11571946, 464124736, 350681660, 940830525, 458691052, 52070190, 974987291, 880191279, 302336304, 382006527, 496662032, 30504369, 697470848, 850007798, 496174007, 212938314, 777102653, 179700179, 201048815, 63537938, 894730332, 10161479, 955723025, 721153959, 941205582, 157389294, 484594353, 729315080, 701339267, 681439680, 770013546, 625260200, 657277406, 311304886, 432802494, 472384963, 148578621, 41846533, 128534665, 16420789, 618089984, 700031453, 594566359, 854681405, 324461894, 116843921, 981200909, 384113489, 181546694, 572778797, 81487967, 987480048, 476759865, 600632457, 393333901, 333016032, 187763527, 847301527, 520120599, 947976591, 900217854, 178611990, 899018778, 668652707, 595660415, 260288995, 146326665, 549680452, 927686243, 87195271, 294942736, 463947680, 328265780, 356731843, 734294673, 251197093, 21639204, 139882126, 994298850, 36769612, 791234618, 21404474, 299979075, 260884689, 540160395, 607404008, 682509327, 62905091, 782414505, 532863681, 424608723, 522380529, 636447260, 690322811, 679994266, 197384235, 438076100, 914920116, 708115618, 969701026, 523304381, 205850030, 788479931, 60416818, 722905733, 635129483, 864159321, 809135186, 902905724, 536114779, 250776193, 598102654, 810076540, 102235902, 861868686, 249840926, 102686197, 627157225, 796324380, 353224137, 617773300, 19954488, 768656714, 841323485, 451597662, 102766975, 364011338, 293177954, 753308159, 684629172, 227422015, 671018909, 919263659, 868872347, 902266845, 199648231, 506964404, 83893426, 883120366, 552382999, 826031408, 373610062, 655147589, 885307541, 22353091, 517893014, 124270162, 629260940, 578833563, 159189659, 582072368, 412956585, 874515326, 188145281, 20996179, 485398504, 5762973, 326710878, 52946098, 190300695, 22714058, 224574365, 942663637, 115503612, 270556680, 879044647, 643169135, 349185466, 272054105, 708582131, 955912917, 701236278, 98558170, 437076824, 50522786, 907583141, 246102527, 337752953, 575731410, 537718025, 739053497, 434269850, 593923066, 156064590, 475167006, 583588355, 268694328, 196523833, 275548201, 750297799, 64541131, 399519360, 536473264, 984964845, 763116635, 157687607, 926529716, 631277058, 974238558, 117991774, 647662588, 295827923, 946183638, 676960224, 92337927, 48396981, 544717294, 823299082, 754294761, 818670065, 210335821, 296445802, 484254162, 17206189, 616138091, 205636197, 727876125, 446926878, 53587812, 587009076, 420652132, 767388379, 126338224, 570246102, 967286480, 633847356, 950500377, 323100438, 113800483, 858960584, 645781092, 817751704, 807583617, 918080897, 410888900, 833320914, 34561826, 439649695, 316216224, 156034592, 383350171, 651767199, 457811199, 145243175, 768397987, 71958721, 513110781, 576992161, 303594468, 301194964, 81771096, 534247894, 501104398, 432271273, 772056997, 653301276, 290027280, 22541805, 241667978, 367132246, 828774700, 831311673, 537320966, 969360866, 267163363, 772347117, 489439301, 237240132, 681895787, 894215347, 479651113, 160642977, 930417236, 887235138, 561284489, 757607765, 379210979, 321352548, 645180488, 735320485, 806840424, 399869688, 564495831, 45920484, 65251388, 852753861, 111296084, 292375599, 321271185, 690629829, 532132557, 363623063, 774069508, 809011390, 348823986, 514981708, 915487731, 228454029, 127925490, 186491398, 890407966, 603784320, 453968552, 671276940, 954225108, 876020932, 263119178, 431115801, 481513669, 962327840, 718027647, 645021476, 686744978, 998796878, 859024760, 271414205, 517336403, 716929727, 66692875, 598924492, 470105232, 50132334, 157078147, 678031860, 692183124, 11982961, 860985604, 832898623, 217754322, 215703223, 641014233, 907974677, 610260152, 10793616, 264263351, 39363118, 190898207, 242941515, 732234607, 578140309, 187941594, 241066324, 484640192, 821472942, 108133004, 694532387, 618260089, 621238966, 740643067, 192993228, 388034089, 399122353, 506246014, 575728967, 97543038, 72057149, 485336015, 950811780, 706463981, 8360978, 772189775, 564611538, 358104386, 869033135, 175673734, 454711489, 930140665, 804248161, 123515577, 767430288, 694375501, 173966984, 62978003, 344574007, 264489194, 156233084, 759106090, 570482219, 267126863, 174922037, 946029610, 41240547, 553503532, 416692598, 671261008, 643768468, 931620980, 338778647, 679380431, 557865411, 21655688, 931116213, 698428460, 121186271, 749437781, 66074968, 235928548, 46035510, 596702413, 855371145, 246043685, 106342342, 415585703, 984403021, 913219474, 291322163, 124383111, 794570390, 926309243, 768429401, 628427895, 106827241, 398240455, 679114449, 386211151, 332838228, 221195391, 965155238, 951345441, 703592765, 29417883, 287132382, 709584225, 765124827, 554572116, 493993451, 186336962, 803614675, 73742034, 711971516, 327410038, 15629369, 508493952, 497880207, 548468839, 463817906, 432818100, 650468274, 775317240, 679033197, 761152456, 712230459, 27985680, 668184646, 708556423, 734032267, 992201576, 39844613, 366547248, 633540999, 183101460, 888165753, 747099970, 823926528, 268854714, 69893653, 533120276, 853367760, 44154063, 719044398, 59064337, 859343891, 691518715, 12607212, 795524942, 157830922, 279504532, 200606784, 522790658, 495964289, 382838972, 50287760, 713301757, 72826832, 245473486, 505799752, 274285474, 62217299, 163837515, 109296822, 719375677, 409024607, 398956900, 528999076, 931791194, 631887250, 730670022, 299806347, 696673041, 557346234, 250258611, 756262136, 886116826, 945535098, 579779652, 525210330, 303962323, 847001036, 625082938, 659370081, 706260488, 351805410, 942974018, 906871537, 169789157, 661186056, 519353599, 522453315, 533296687, 639981867, 140943607, 68931332, 333225064, 347429444, 332372032, 138556034, 726323732, 577565203, 796882087, 136668687, 544391704, 554855242, 108642207, 624454309, 569504471, 127818574, 669839024, 560550698, 194473808, 799066313, 11047443, 49967971, 966446138, 760128623, 211578905, 437973233, 590554917, 756631479, 356607360, 913793442, 925230634, 913416797, 388704841, 87247223, 124074524, 775354655, 25001994, 50391708, 870673342, 733488838, 911663879, 790474564, 24832679, 154771057, 64302511, 363109145, 839737039, 662401594, 667694844, 722923721, 953058288, 169054084, 958264068, 645732327, 991239173, 387112316, 271592612, 415086115, 157595142, 321037849, 996574816, 55370528, 936588505, 620521320, 539023788, 731328797, 68263143, 377163107, 924155493, 213715634, 299776143, 138913264, 242958811, 152399625, 479818860, 343440957, 656492750, 424677639, 303456650, 598397389, 485624827, 310350810, 131234901, 452411076, 347898991, 409867447, 862920091, 230162491, 726512231, 375840766, 807546499, 779262391, 134550383, 824106613, 840396526, 642515174, 769212197, 382327582, 572392257, 764162825, 5356423, 660310138, 426853335, 604286623, 657593386, 644487739, 140580315, 630008926, 932170015, 603859469, 240088774, 340536370, 939665403, 574692827, 40233461, 184360366, 882596238, 38303608, 697547847, 774963316, 345992300, 481442306, 981955211, 346470797, 485484285, 790600201, 925565250, 432915431, 294174035, 142267970, 772358725, 79270072, 998174378, 661793737, 453729697, 372953586, 411040237, 998205445, 526515105, 493830325, 376242500, 985987692, 712157970, 966451541, 205668324, 532174403, 551510294, 280319592, 422115971, 455684669, 350578390, 661307341, 475273362, 640131505, 329547359, 886517420, 555458573, 295398621, 888648582, 169567184, 541319770, 674794654, 594101984, 151275035, 670226745, 821174012, 383699741, 266789925, 369022615, 326512765, 471915702, 967588307, 614676959, 869517085, 106403391, 219911863, 422237121, 664924787, 474709978, 542506655, 936681464, 267187356, 679452824, 672101119, 302757617, 956248286, 779672970, 963360627, 910263620, 789495317, 578008303, 901457133, 588680717, 123476193, 88506512, 625387182, 210865115, 385846723, 831853562, 156308950, 757894928, 10285143, 398308336, 58227833, 647273820, 823456365, 578611651, 455162579, 740309418, 961260759, 93099250, 812881510, 423539679, 315838226, 900701852, 813269543, 914620788, 886485417, 8355618, 261816331, 941665961, 102566642, 965793750, 258258069, 165631570, 521367492, 109270794, 594136948, 244325635, 528737628, 180851881, 928310919, 775669164, 532435437, 782860262, 240887206, 878108776, 591002822, 556518110, 554674508, 25574397, 33130788, 568476222, 570875717, 672320329, 380033675, 490711190, 595528208, 477923040, 625963405, 416810140, 759668195, 982628865, 597903677, 815885163, 682935135, 385705222, 377819595, 869378586, 804057212, 1443738, 680903151, 637905821, 237592558, 958557320, 241794154, 448916475, 13824206, 391592361, 362833983, 128550246, 22404422, 2194002, 804286143, 323901134, 501834099, 674180261, 704332434, 916084887, 230177525, 366934882, 887302069, 785288601, 841830520, 9815973, 976010707, 985712035, 348125218, 388200030, 781877540, 280279020, 718111446, 642473814, 482678630, 200929801, 112971363, 938080956, 920843701, 767081791, 662087211, 770609060, 446466829, 854486453, 7814498, 95907760, 866038314, 708674517, 641629417, 295236153, 54381684, 983421791, 583742178, 474817099, 342109907, 2425797, 360562603, 10306933, 414249418, 211575623, 605272203, 572541769, 580082489, 25330871, 571839772, 239200323, 999435641, 547028963, 428844717, 23836356, 51829671, 618960612, 272694882, 676362224, 246232905, 882285018, 867754285, 177838026, 478788080, 981251483, 272777350, 430868082, 126187137, 684123891, 26550500, 831709896, 687661283, 948307863, 650354961, 725930218, 944371429, 699746402, 412563626, 568649754, 771921651, 860155852, 627869223, 186829620, 728035628, 548454137, 988517192, 778619928, 378607234, 66251794, 719130140, 527528851, 493218967, 973423958, 419569129, 454743583, 989611892, 949546137, 587721960, 823704339, 309560512, 444863172, 108215488, 609324606, 406607639, 241430845, 565559610, 706109278, 319925729, 548340913, 719685644, 747166308, 690601194, 829542178, 220569099, 55987461, 16636597, 139638659, 662781588, 26712500, 607591210, 895826957, 995458579, 27421723, 524192166, 977886614, 865231078, 773724583, 506194733, 98569599, 627119647, 624789415, 187154948, 568250546, 495529822, 800152644, 695285240, 519813938, 803142748, 707450894, 988825313, 702476049, 453717325, 664405356, 301420597, 407993311, 663602591, 45901402, 196162965, 801500129, 148431556, 109628488, 622676288, 693579462, 888037293, 685623770, 474704984, 816424725, 452970730, 812726261, 381363331, 472630702, 843704578, 54046003, 802233087, 507744066, 563333356, 512701778, 260282107, 954745577, 953079450, 150436736, 922958067, 444025328, 641000571, 651545713, 498622077, 476077031, 835623132, 163608934, 612590875, 998941644, 609673603, 519710527, 3432132, 401369699, 674809500, 307978195, 722241146, 459755678, 461908346, 382360582, 317995340, 764893560, 692972832, 808358746, 785231503, 895490742, 520101242, 40231722, 994879130, 682971885, 668353731, 418370163, 419236828, 205026408, 4366788, 829203797, 331400916, 760685914, 115263625, 751389274, 565859090, 135454048, 226492950, 435188410, 714975154, 90923987, 630696974, 972133676, 354813170, 525034790, 168018670, 26283917, 39259121, 603648664, 804062042, 335631367, 564680914, 740047417, 839173230, 181048787, 145327457, 942111259, 791021261, 330931061, 246822993, 685595282, 843232839, 787355369, 374634573, 200061450, 153181746, 97882883, 569375700, 634854621, 289881441, 349627729, 938005907, 65596825, 390413233, 236615281, 374920281, 389678596, 265421057, 61402651, 251503415, 512470336, 584664066, 843384781, 213328272, 416941000, 573510769, 159660919, 736873121, 660478295, 913340116, 279998458, 605292229, 980132273, 509906745, 190639707, 350968311, 178850571, 389000375, 672642836, 260541758, 665982900, 380880284, 778330022, 392703272, 493256988, 417492716, 646232402, 824392003, 160523072, 864197518, 254580820, 30265365, 469159626, 38032345, 993372056, 548303506, 984519723, 611454487, 744317496, 675893095, 275326150, 458436278, 874174995, 909922047, 66076556, 421996951, 178355647, 658593120, 246388321, 918278123, 392499128, 400996734, 202689058, 192913079, 775991482, 249619894, 736849105, 705678807, 62787345, 373382739, 272586645, 76893016, 771487370, 922390233, 789819040, 697284840, 460859241, 240736950, 753986506, 48372673, 99582056, 502725432, 719133471, 817104912, 551535045, 669127915, 809576281, 814706991, 260314267, 926157853, 339586477, 862959113, 312011316, 424103529, 645300200, 529693224, 516358733, 990146754, 776894095, 22585035, 763348129, 568151251, 147524584, 765222198, 911922317, 654174957, 94543518, 619851524, 364581928, 227715056, 349756807, 787836204, 208366809, 360772998, 23429605, 49759275, 847732342, 768055716, 710721974, 534845538, 872546005, 865805025, 678579189, 206867950, 460887239, 269293419, 779510046, 25891893, 817590980, 481743698, 765104532, 881801357, 986022626, 907447863, 98229843, 123929447, 997393102, 304596386, 17611186, 614791376, 107798057, 394852199, 415130668, 921739069, 321463914, 648447442, 624734285, 837859495, 580202791, 800993703, 688133908, 1255893, 405521298, 888908195, 892803648, 494596436, 78009334, 188463172, 939304062, 793212530, 582256474, 827818629, 752025840, 403010727, 37622891, 952172219, 98404902, 319834576, 832073223, 753976947, 409300680, 35288571, 519340350, 898307112, 745943628, 255659303, 393923701, 596690686, 537583342, 332784638, 827665210, 606797284, 826836704, 54918626, 554984355, 326300940, 100011297, 859017412, 148358059, 767840834, 285561834, 915830796, 798785522, 433479485, 730947797, 364668038, 502111887, 635202740, 870640430, 801266516, 163641293, 298751608, 986645048, 792760986, 10875903, 998461614, 865337721, 623458288, 975057550, 712147276, 355125302, 770042664, 423174739, 795489579, 328814200, 986696585, 574023058, 709542966, 49864332, 782143420, 236533949, 220671953, 600666189, 263880207, 245246466, 867670106, 874733075, 552094510, 529811727, 407658745, 986637848, 936924422, 255260106, 483452488, 745599003, 141115053, 497630696, 961344784, 979831826, 973903369, 6668473, 943277252, 632364637, 843540836, 989112474, 455816415, 728625293, 592347132, 447705601, 190469503, 49895923, 826659252, 74661117, 794442809, 520822620, 345052784, 480406589, 632991628, 28975095, 521875039, 979586340, 11641157, 733107392, 887758130, 557213877, 58754269, 323486423, 656541983, 663941067, 960943881, 915551460, 526442767, 966654547, 134753192, 70897956, 43443896, 864848073, 54713139, 217985653, 344436388, 386974578, 296805041, 191587997, 975764487, 975948063, 147555908, 555707266, 840925810, 553404679, 214082328, 833544773, 533463048, 285455907, 925566041, 398395903, 112257578, 854834626, 960443358, 541712021, 980871347, 728468503, 209702017, 103312712, 33315614, 106621177, 48452194, 9614946, 913288846, 82987011, 189364265, 944711167, 815056848, 274837463, 584930225, 345470120, 864260097, 120845662, 214102295, 964026358, 297231345, 834361693, 191678425, 100864745, 948846752, 188660199, 430802041, 590496019, 500943760, 318547626, 814926229, 226381426, 813362606, 887480739, 200919103, 910685776, 116988528, 330641249, 733715108, 475673288, 677540422, 880418338, 155542251, 796874487, 248965369, 423169507, 635674161, 608731733, 190810821, 851445084, 878877836, 289378456, 336816617, 203635169, 720669920, 541308071, 992797518, 547887300, 212602329, 963240758, 876510268, 765935200, 100812815, 986672958, 304215932, 610860453, 147399364, 590116871, 312775000, 962874857, 977820994, 935859437, 223986414, 157922337, 838421819, 706837420, 882425368, 78023137, 54388551, 274985835, 1861740, 95712756, 736338248, 298082276, 979837457, 193013561, 227861083, 645309958, 138156871, 212317383, 898618983, 563912204, 764886449, 554143350, 66283979, 798509899, 949246730, 948303478, 868907288, 219389679, 333356239, 161849975, 684050762, 591834566, 377539394, 981328956, 410944566, 828703321, 905590438, 214312799, 415549672, 607864788, 65069422, 245780170, 724100939, 488702788, 498123758, 536772704, 562932148, 483234385, 576977395, 423438047, 267828003, 898087116, 301973176, 790528152, 962030035, 243027923, 622150991, 513140662, 417078715, 786756884, 415998391, 225576881, 770387183, 676101358, 475640925, 101294198, 259800916, 915165127, 389240627, 531099402, 675922998, 581681148, 919035815, 503369717, 638423422, 5785498, 829250868, 907071075, 866967087, 277607716, 6972808, 667578819, 144094636, 380998392, 855127864, 893608065, 217906399, 507967568, 838855290, 813474909, 810508739, 306712811, 708763190, 152364837, 978165917, 31906489, 965879064, 424663516, 581624439, 564958002, 124107139, 957103460, 38027917, 217858771, 911887242, 880579857, 122799951, 551390044, 687554167, 197877058, 766890689, 601641737, 318706272, 847224045, 666858929, 638560832, 106354843, 737395181, 139781531, 611691634, 813241934, 815124127, 569986003, 789328370, 343958601, 255726614, 469045393, 227999246, 503359201, 755128897, 622993766, 92617516, 422918308, 185676524, 97535085, 649499602, 170346705, 122602701, 229294161, 414942191, 961023189, 158164539, 930068631, 565452938, 285518103, 173642589, 742529365, 637855686, 929240141, 461576567, 877023987, 244868298, 547525915, 834301637, 477326805, 898482776, 22577283, 16082841, 896089270, 866361883, 340317565, 939038324, 238824173, 976066480, 95713623, 700865159, 37142621, 941217109, 938908417, 139902585, 193317798, 87324372, 502681980, 127874736, 794307876, 258848596, 166363514, 799870645, 398953957, 529868673, 194728010, 122228262, 804688920, 261381270, 338855871, 644111914, 822884627, 713831609, 488701769, 601630093, 480590164, 570197981, 798415577, 79357556, 755289431, 380888258, 777047750, 782643222, 442372953, 487025001, 686744149, 514658689, 849636108, 230014997, 546201414, 326506492, 539770622, 84770201, 321878666, 170443352, 925580867, 240889282, 201015956, 766261232, 29986947, 734046313, 462366405, 33151445, 86775833, 950552220, 755277334, 97186584, 78312780, 118873759, 692718639, 985712350, 41066215, 473728060, 159715754, 788940299, 709000424, 71582709, 520056875, 125877249, 57688351, 379625150, 235570764, 666313457, 40807502, 972318718, 895160400, 523217830, 730255268, 384355610, 504176362, 614994686, 849642096, 639734415, 696809274, 786851876, 451063351, 946060886, 146935787, 519086381, 78801164, 443067820, 242066332, 499157485, 326324256, 32992621, 7953353, 320630932, 253400554, 322690995, 662012134, 87947331, 726526345, 958103938, 567934800, 425935193, 549290275, 206431781, 197770582, 533926445, 607246411, 725138652, 929260966, 693494719, 145309818, 276955039, 145010517, 458618977, 181097357, 40512490, 586403223, 378251383, 651887559, 867858472, 503547161, 366019988, 760675367, 368676507, 93327094, 736617727, 876129877, 27297101, 139420593, 625578983, 540930444, 809485974, 654005795, 82292350, 450432549, 674541577, 911794490, 332571396, 838099209, 287520912, 782077878, 280057433, 309498166, 23710022, 709985652, 948469518, 775403548, 849280655, 723796008, 498888799, 495684451, 670803188, 33697044, 421798224, 487498597, 58219322, 851552835, 758997627, 944145271, 556872887, 747122854, 601630845, 252099652, 81286220, 29631588, 297284187, 497285155, 786711598, 863063090, 253378008, 459638271, 468966633, 17312884, 951539122, 517815364, 615501899, 850091861, 559079735, 845695154, 726055112, 865577506, 559014397, 272667393, 565635803, 9853341, 763444547, 452391582, 366109201, 236565644, 232316889, 748387642, 563652610, 575613276, 167584826, 329708825, 687715416, 378865889, 916499234, 699759742, 320580846, 165971427, 226355470, 224735327, 121433832, 614307451, 238541903, 927627042, 186797919, 684361390, 35464651, 430833825, 783581570, 337061314, 522607549, 142132555, 379114783, 990471847, 808912560, 611918480, 330600683, 21234491, 350712530, 778913893, 967280616, 855734658, 324548749, 870556228, 420197896, 53800612, 828088, 824204189, 811123696, 506863704, 804443720, 42174952, 387825387, 572663957, 383451458, 328417072, 230492622, 228010066, 654984966, 174983216, 922079206, 616498159, 907923003, 327221588, 171503696, 737326156, 739810387, 39938463, 646569203, 463888042, 830093418, 642334844, 192313580, 23922013, 714056634, 721902477, 428235293, 414760668, 281983275, 817736608, 928221422, 845668582, 691070599, 122838403, 893164508, 80787564, 767385515, 624159200, 495525668, 328294802, 725635671, 842989559, 422866939, 556172025, 966828769, 767791463, 152326458, 188579968, 402763672, 646430788, 782704072, 679376341, 866847535, 384390608, 41291573, 53851809, 249711977, 419575093, 850081615, 190168000, 957652727, 139689497, 1064396, 629253658, 879262395, 422321401, 982849440, 906039831, 715260438, 18936447, 462076070, 290789587, 493050298, 913968070, 386098798, 595148331, 241688790, 673381503, 817032878, 704138207, 314122090, 121137775, 149028957, 879535142, 741808021, 648199104, 814706309, 116260807, 866282352, 35236427, 865604732, 95742664, 455669005, 50235066, 744204518, 171840895, 960998364, 248863202, 922350415, 760046326, 905930951, 258607109, 257495211, 434080764, 174156966, 105472170, 109991879, 198550094, 916877329, 389724120, 780605062, 379443288, 525081999, 285723360, 881750844, 532816593, 677525414, 271553449, 462418404, 197834284, 693420048, 61492497, 102606117, 809646484, 927327829, 543412243, 986059099, 154245065, 391404752, 442345896, 52691084, 383319278, 11986590, 122174724, 625375773, 242668713, 736997739, 320591566, 667598661, 307206721, 422286031, 527672224, 226373294, 233536102, 476714810, 547358036, 735924764, 400697928, 194140183, 413825631, 876774157, 242103457, 288336704, 381832063, 555640086, 908114686, 423620204, 911176414, 810676659, 274249233, 76720805, 31329405, 107000757, 24407242, 558253585, 441943574, 889382866, 877562889, 499895250, 478102010, 841509057, 479622910, 546994542, 66817755, 333184598, 698459824, 618487713, 859269565, 612409731, 465343997, 753001124, 853246811, 352989471, 35107728, 488123463, 151320123, 321485733, 319254217, 135707147, 929794763, 162428122, 661146125, 999243134, 87568252, 918902555, 490468360, 372024767, 823778583, 859631060, 401340230, 77584882, 313559573, 229941760, 722250000, 205595744, 735213301, 298164562, 37674617, 208289784, 28604263, 339242318, 835801459, 142676941, 550430301, 903152360, 120066760, 807944089, 244495806, 313674015, 90916170, 349942374, 312771201, 775592590, 687980531, 857232273, 455052038, 559435187, 900789778, 123519132, 43941696, 131399198, 892768131, 967411032, 626108545, 72163062, 934995386, 819494503, 541983399, 484936249, 498919353, 141225369, 84366100, 316719197, 852323492, 359894535, 775158839, 629105944, 857600283, 819417402, 614902874, 291834479, 70518155, 417529988, 489997896, 320989866, 513372533, 202604486, 934248233, 37847941, 190808057, 339771481, 337758405, 356302248, 94161991, 750883933, 63159729, 736843567, 165822626, 261885259, 214710350, 348320527, 964562975, 711585374, 118292794, 205675995, 854299582, 62586230, 147023918, 86665691, 416220752, 120317978, 494169205, 419917749, 245236600, 500240872, 902547051, 316578427, 805861556, 833360993, 351560444, 315951211, 943245691, 287573668, 648654613, 10800219, 437597351, 915255226, 502360059, 588368086, 788028382, 944304302, 36929408, 374136172, 226592613, 79989259, 912778711, 716923951, 109291066, 728795455, 766132267, 214436593, 923523579, 217280720, 290485915, 548856086, 138620046, 451916355, 597428677, 652062267, 189304431, 665020551, 365480329, 823013586, 356081313, 798635093, 526375831, 722883440, 759192418, 407299383, 835909127, 724811231, 461103924, 415816699, 595648564, 138271135, 923964106, 962712714, 988800738, 653163769, 148565192, 579998962, 34023304, 797402264, 392191132, 567254082, 995624163, 568537197, 564717799, 692891299, 917895886, 844230272, 705591478, 130496303, 592664446, 870456472, 737489585, 702013364, 477722306, 762161048, 517906640, 564025648, 974120727, 402356779, 217839260, 916892473, 459099589, 103835563, 695456760, 596094253, 828106447, 259483982, 267172317, 703794129, 80640975, 113347834, 276497326, 929456241, 497103819, 612782878, 690242583, 239784337, 241525997, 173180873, 633012219, 643552444, 925695159, 114054579, 231061640, 611786252, 699362065, 88746995, 136585737, 12129639, 309003565, 179787539, 440206846, 791751346, 147043186, 288936985, 125704101, 655513505, 781096709, 108801989, 775170132, 211391089, 889636215, 643354784, 56714307, 339916061, 7722600, 711860522, 919334061, 580647167, 797443626, 301322827, 346833053, 535003642, 71271742, 741855400, 350840912, 255195796, 547619515, 959642855, 542071477, 724097110, 602671, 138226024, 573224188, 472737874, 411641944, 717135368, 128870604, 105235212, 379780199, 746324337, 147045508, 975448399, 238497902, 129111871, 265164280, 271949664, 780399536, 350589394, 620160235, 34411021, 662879770, 477681652, 256181912, 909077169, 188491730, 172038775, 27358940, 712259695, 125131894, 396984517, 187372775, 888063212, 12364207, 392288185, 906354937, 77157975, 116619903, 622181009, 198372732, 102124894, 877142847, 973911450, 865242101, 569329798, 548955178, 67495006, 129334816, 703239876, 756246925, 478596240, 885748731, 502621435, 491028998, 727290738, 377913408, 360121283, 617654894, 121499033, 979397904, 507015563, 630597011, 359763421, 254080439, 861054002, 394498821, 512023604, 796383640, 419275252, 116965415, 542252596, 487131189, 617237971, 334572508, 258726508, 899484692, 78945810, 408096578, 310470211, 180542849, 458339433, 572557489, 566645650, 295341634, 289061185, 815035800, 761835505, 61381328, 466040131, 230417443, 173936988, 559041218, 620585452, 826306690, 306155423, 543435636, 954095006, 987230276, 564760082, 911752923, 859362090, 51266288, 54067858, 827560017, 72708740, 506120533, 619550338, 168430049, 812135753, 428485346, 370453493, 675082504, 199313936, 693508929, 670200559, 633376622, 319470212, 588541901, 545249269, 507788937, 41391625, 34553949, 39797587, 212456537, 742776840, 817730082, 653625764, 293499787, 14313351, 574272578, 228632796, 159246675, 95623860, 974983783, 898588773, 585377517, 912271734, 554396352, 9682858, 169687534, 83782203, 253440068, 444745817, 506254167, 404574921, 659096161, 136663059, 924925865, 85614407, 389413435, 23864600, 608011772, 58493978, 965072856, 528530193, 520132953, 894338021, 444298251, 127856761, 333729319, 655639688, 452855022, 979459631, 454661271, 612271891, 563795593, 896960635, 621868509, 343748383, 431976881, 216106294, 616724479, 847357602, 989047522, 787183926, 204374839, 957853780, 166983949, 405926439, 70150636, 62527053, 244302680, 885723095, 381939783, 798986930, 936739382, 893718443, 562763934, 478010712, 636796179, 488339143, 341888600, 443860046, 931131613, 617002094, 592376781, 48899887, 217879704, 23399533, 283577860, 926954715, 437073821, 350247565, 851933378, 992717992, 441718631, 851458025, 803746119, 624061133, 115408901, 478148579, 806218694, 875468874, 381751467, 820290517, 969480522, 580243374, 162099001, 709480220, 550149881, 310504545, 541890691, 795683504, 842495683, 670500014, 126531678, 469664792, 870754724, 812006659, 108680291, 754837793, 553421992, 999182979, 651373644, 308593472, 535411486, 356740980, 497294253, 689755913, 851982949, 475352594, 870138653, 683111345, 853503118, 595560460, 474890984, 164186560, 548230082, 902092201, 763145744, 43506904, 448637832, 43153161, 511026364, 703448459, 493409603, 384281091, 588468685, 672033076, 876599979, 282993576, 455804948, 196835651, 560869177, 152793328, 603526248, 758102352, 921441343, 369519847, 700174033, 208035536, 909252264, 364191606, 801578485, 455900972, 476057118, 680953409, 726541595, 348873111, 832731410, 667520030, 648695810, 110453065, 194815215, 472663689, 839418986, 507601325, 240046413, 958017687, 116894543, 277174496, 756572040, 237229001, 217053304, 390462701, 179784178, 897420760, 716301022, 234107416, 169659440, 329817396, 351393602, 522417970, 729706116, 962230331, 229772750, 310618836, 239316288, 66203611, 920481514, 924737022, 631947834, 152566202, 288180150, 901203137, 943435169, 625369250, 413721048, 41017780, 493398937, 371961917, 482485702, 913337128, 220395237, 930198682, 551988816, 420709616, 111954984, 538756478, 380669704, 413529900, 743728109, 777102121, 299981138, 849775456, 671628083, 849432935, 500687806, 488463696, 539471236, 818718308, 27817992, 372052246, 587611024, 459498248, 832720603, 891657802, 675171047, 18426903, 957283412, 273053304, 490958444, 37948473, 849240063, 770387015, 611608306, 932849725, 766254054, 407599198, 592720555, 730908353, 159980995, 309436713, 193231766, 782525853, 141695096, 150181579, 913000441, 137161750, 646752950, 517747067, 364220926, 350423732, 286707716, 125233328, 394241398, 847100140, 241201487, 635477748, 560281826, 365522231, 237645808, 140119622, 38401147, 958841630, 821668257, 477315585, 445643567, 627758738, 796442814, 815948274, 26005777, 90585258, 743666984, 196722774, 34377758, 610371405, 246331335, 510626505, 171616536, 308927519, 664231342, 534251410, 486296339, 330013737, 276244022, 967220688, 683387858, 273670556, 507492921, 8578337, 536991220, 657084109, 636072768, 205069666, 265522764, 261525894, 111244603, 535203194, 65483473, 925908713, 698418001, 400576052, 562020714, 911487236, 401416964, 700849751, 433918771, 421656613, 947854481, 587807061, 696434345, 513690693, 317849379, 652123543, 749959057, 140624536, 325502777, 417576089, 775390017, 743964257, 814160379, 540831038, 38092937, 988767342, 117723322, 802365440, 312759818, 892155656, 437809138, 145265202, 169428646, 433047381, 509696599, 507874671, 624081182, 927003194, 746360060, 700115728, 74019089, 547631865, 36227078, 245558773, 273764611, 786799171, 191769965, 389496025, 392750400, 3357185, 548933718, 949567502, 126709391, 404081995, 547624746, 861846058, 870529283, 64110928, 562556171, 932740300, 872594707, 103635919, 452443939, 133733109, 401958517, 699612559, 726474080, 364366424, 657259926, 248837692, 126277606, 353908389, 864444456, 559877750, 217986823, 377299505, 612657292, 679695906, 136058272, 266264593, 318121251, 3095694, 938278718, 215371112, 355991447, 666530562, 976209150, 381865671, 778235737, 994874853, 115357403, 770879061, 768822507, 758825707, 759759531, 695609207, 319016216, 902150404, 286135106, 307405415, 292592529, 433355917, 902045990, 738199055, 841688958, 527710457, 643813989, 93896013, 897224854, 569235446, 354058681, 847517554, 53867014, 737271469, 861355623, 367115379, 268636784, 595132314, 327958624, 687086328, 94285594, 272864407, 230968061, 416691687, 698929187, 943243637, 132512226, 397318089, 481157307, 779771358, 168381984, 348774416, 859129876, 79257495, 201203626, 49457042, 618890800, 925324316, 443646392, 793557855, 219205409, 103046644, 209185343, 293725162, 859775532, 131201064, 472920439, 451136667, 500852240, 712328951, 942180436, 279157601, 763612339, 670514686, 905903651, 163464030, 940518949, 425342920, 704241530, 631735045, 372109108, 386586500, 907707624, 711717230, 500915287, 570195214, 309355582, 965536261, 307099233, 86911356, 191830559, 697198926, 910401055, 865480651, 888431153, 407746478, 484677823, 375150703, 113508168, 527421130, 593967231, 553010933, 124444783, 476360660, 274692602, 170727338, 330759462, 610527662, 41797936, 312437034, 508381973, 578269209, 118297366, 215643241, 425818655, 642332069, 773515274, 693490404, 741845701, 473526061, 938365343, 482045533, 125009124, 88704191, 335506970, 535407923, 6075861, 170651434, 688437593, 523880292, 351684680, 6826995, 917319515, 866733838, 721346798, 531158412, 856690537, 334848090, 587183891, 75859869, 809534700, 890256961, 3006612, 492568691, 373216975, 917453325, 884933105, 524640368, 192789870, 433708876, 772997794, 697623436, 553360259, 15279599, 664741667, 524920648, 411816161, 689173907, 851050333, 752446423, 557291905, 742509296, 61318186, 436920124, 900586096, 145955538, 349474025, 709649397, 532670961, 911556482, 56387062, 244131359, 842013807, 309489161, 265850012, 764240206, 29490590, 68415578, 664059029, 528230275, 124433704, 179220462, 471277207, 713962112, 485279636, 143368999, 549320465, 2964596, 987986052, 942217414, 526038227, 230864240, 725908299, 537897498, 391643383, 744689028, 64260034, 484128862, 634538202, 374295010, 243266824, 957151141, 4101106, 377458645, 648055003, 646918461, 950932514, 775434441, 722295017, 865659986, 777674129, 692302608, 267565891, 219202528, 806834592, 101207218, 107654936, 200540688, 987581851, 429542210, 286079393, 886006370, 634516143, 284109948, 377684990, 601959508, 975200928, 837227976, 449278608, 438443520, 631809634, 202442488, 457604377, 890211864, 184493339, 436612337, 621145375, 429294278, 391556471, 229452203, 884928160, 437258338, 34986590, 33670648, 79024673, 236654469, 924590565, 555568674, 96643904, 130203947, 145167335, 801680992, 603056135, 568333462, 300394056, 510514598, 737254580, 304618625, 257967521, 67166485, 867176818, 34475244, 861153761, 55765183, 268540413, 543874532, 881504862, 470192930, 185556080, 309267114, 448238702, 680048995, 16708699, 42628606, 142745040, 933105352, 10281231, 381135288, 869439229, 477933906, 243968771, 122879857, 674342944, 971748431, 988113704, 253195124, 623495611, 823498974, 935801736, 422403278, 599209762, 537610010, 56864596, 182112936, 273593387, 634235646, 507445051, 712395222, 966866157, 765648052, 144129859, 200854159, 747491930, 212558632, 637139318, 686555950, 413141794, 962517142, 949165078, 819439182, 150639851, 277591722, 906315698, 632817941, 582575674, 554819072, 182574896, 903443142, 842906827, 242893514, 907908024, 623180756, 589205595, 151050815, 496694221, 984602, 655009014, 624305091, 52264379, 422041230, 127201346, 994222425, 449747683, 556057628, 159063474, 535329491, 528033238, 582195574, 295259580, 994214701, 310906879, 897530658, 778378512, 732071274, 570030938, 1012433, 140000553, 150354523, 250652926, 907166792, 960772093, 667775572, 54669452, 626514018, 629265599, 371824876, 710651040, 181372821, 365242629, 531079081, 919635196, 145128147, 408690686, 28992983, 177744252, 706358808, 740886712, 57952833, 314906178, 627285496, 344957515, 677385495, 64023524, 200613806, 170676045, 518819028, 865697192, 199095909, 454851631, 58907865, 912242922, 819231949, 402664609, 928345145, 261001402, 804648785, 977741970, 165074230, 38203740, 122833768, 564363851, 202095793, 793296325, 973925366, 257781698, 120055417, 977291917, 658380607, 799020361, 418303226, 35835400, 613463685, 38755535, 379528546, 196116905, 993398493, 901237416, 461122895, 514026951, 192079331, 250750113, 909017822, 790216969, 210583730, 338096081, 688242863, 511559569, 373377916, 700310316, 804458417, 263341090, 47465981, 419087574, 704248227, 289797711, 310722219, 354568930, 848771668, 695624895, 338953118, 978179949, 178385617, 295519388, 959206770, 906001197, 858292839, 25150707, 391937557, 253033549, 561229041, 817228764, 995085142, 506940172, 836739055, 269107482, 598367118, 81363363, 669730522, 949620997, 872028394, 940792608, 527259440, 846976149, 472293506, 938305540, 529705996, 380762713, 305222626, 145946246, 81121442, 548276203, 311246707, 135309225, 231083487, 119908703, 325679596, 430323433, 39631093, 382081138, 577695279, 374273864, 615755360, 669703962, 924042207, 879713010, 198796144, 818526955, 198672406, 757265791, 132099298, 567864638, 557987517, 939316025, 706568268, 918693990, 803328473, 22001981, 897775779, 363117328, 417296485, 668345605, 224180059, 993018741, 151535593, 799078773, 838471730, 787869229, 769186612, 336582630, 804979899, 631002984, 272476926, 614680509, 544892391, 244473111, 5807563, 272587234, 60260594, 437328085, 976834682, 341678633, 401687690, 771596655, 648180827, 74538310, 547373533, 778856786, 917437772, 10270493, 217215597, 98938118, 82156432, 890743747, 645536881, 371293047, 835660465, 823138829, 774654146, 450629266, 313205201, 442483959, 722995063, 495850503, 240703343, 80902578, 222260904, 274780779, 339547380, 82958272, 627855054, 84688124, 386008861, 263579751, 314297020, 659335356, 234700627, 791005294, 261959552, 370271407, 524470058, 603961650, 643575309, 392494040, 38706442, 493671790, 136754052, 179870595, 215228773, 91432547, 421458032, 638516422, 198130026, 805522738, 235475575, 46709196, 316994878, 497101649, 998366423, 54224570, 340446709, 250824053, 178361364, 790011876, 835007497, 195005384, 572632299, 714628395, 102718781, 915845672, 930396626, 404382004, 457173026, 619476492, 159527487, 732954449, 997579371, 192402050, 770392180, 964903657, 473112735, 403232621, 951096584, 787989649, 829140076, 768706827, 407693179, 623443887, 41425497, 633028856, 90345214, 425324896, 933717278, 980168455, 876660850, 165219377, 492119967, 400311930, 691372748, 385104200, 761108722, 914330073, 498398758, 11499341, 459038112, 675276042, 300613374, 661187369, 977273721, 748102067, 979706868, 856191514, 379897898, 144369242, 670223168, 148690807, 697157264, 199561642, 760972246, 379922509, 431505137, 635349350, 968194000, 235792459, 472271392, 905158486, 20298148, 174185302, 72125918, 398193723, 232231114, 836601522, 553065964, 682196304, 254519776, 680130451, 547189058, 622758225, 185609994, 482685688, 423005333, 184282157, 877484978, 522114259, 582191325, 293340157, 151467117, 941158506, 879270917, 452651468, 856849482, 691405409, 470298394, 62664972, 704226512, 729794597, 730411862, 658471502, 149084095, 46988283, 241336618, 553287119, 180455744, 383860988, 592502829, 570500671, 321846011, 488635457, 590156184, 255008210, 894537254, 477928104, 379785545, 484919935, 307260575, 111452506, 828529532, 272312797, 732448672, 232817963, 446579928, 708324227, 233591457, 160765368, 813033073, 873263577, 863454870, 500195314, 201433508, 601240887, 842573216, 144976311, 917002046, 127503934, 945077224, 718220952, 162096398, 269683551, 204316109, 881376191, 54245869, 93222699, 25087568, 827413983, 576662598, 17263141, 371811766, 262493407, 909042663, 747837751, 704521804, 471790274, 908229879, 80523006, 428426928, 98913947, 107209837, 105780430, 443377613, 420863481, 331803222, 84184878, 248857273, 356057855, 394531466, 344676217, 152280436, 418185869, 963511716, 161736759, 578570487, 711138846, 946061909, 786665214, 397946371, 414561113, 933777776, 405174850, 131170431, 624518107, 627738910, 709347608, 280902129, 219088504, 693911528, 168410613, 302596487, 355517264, 938234128, 417743997, 99580155, 520722397, 316664261, 481000196, 275600704, 591623007, 817762099, 659893796, 847147668, 980164577, 417690235, 790406225, 164989223, 489174918, 392027489, 148301205, 792798815, 770289744, 93139632, 366317161, 906278870, 908918420, 198039586, 964309546, 477651081, 672797094, 804337466, 380207894, 995118831, 790578229, 215036990, 291376348, 70232087, 404832291, 579131105, 992986037, 556400472, 719745801, 811258206, 617420020, 670109630, 882507666, 412818417, 932205130, 370066396, 677311770, 543273866, 534042305, 631061646, 209156338, 843837596, 994581489, 931875073, 566159412, 377006714, 907512956, 119526649, 276953459, 448327376, 506406863, 389924605, 4141303, 153785542, 983609501, 636148858, 254700294, 125522284, 967691365, 708501969, 545666902, 985804986, 390201731, 762239773, 33109248, 755768577, 310768973, 539842790, 472944359, 948549686, 235365662, 409388477, 275144027, 686440594, 506752561, 162736071, 22564093, 943003130, 106493374, 572591291, 995018301, 261316432, 604609793, 103376377, 288924154, 513574667, 332510441, 349448946, 208535595, 512186865, 720543467, 383956300, 299792000, 229100704, 369931459, 458764228, 537318893, 977348882, 983804088, 443947015, 475258124, 140199483, 257149490, 187244859, 64174656, 392720139, 514654112, 370543112, 998156105, 39836136, 370750450, 244618709, 224682417, 765953909, 794942304, 16595811, 841621248, 816804409, 149694771, 564230744, 872319349, 616037948, 155588193, 238369156, 47138597, 966004228, 955931147, 818523234, 342402372, 8952220, 767771315, 703917343, 262666951, 948387318, 7243331, 976471315, 599192208, 743950845, 344616711, 125262362, 162076295, 841703595, 774080263, 478754609, 816882935, 366233984, 694623456, 13022653, 961600682, 299052818, 660973237, 883602842, 463353996, 510193591, 877699980, 558698729, 151137759, 822575543, 284597188, 249773551, 402969535, 10284937, 622828530, 659587043, 489197048, 851731959, 733972396, 854524277, 885522489, 141391623, 346683879, 312542407, 959046396, 704466691, 324270869, 98045178, 115404315, 741946007, 655240048, 615302962, 219972488, 994811179, 193470448, 625681075, 902460120, 141576354, 383482407, 186148238, 886191009, 629852243, 519614382, 999683643, 758368080, 689173065, 362680258, 467475142, 826035006, 939034169, 284562256, 673273749, 817138567, 368256613, 818391553, 179456141, 530607955, 620021163, 763854126, 539194109, 271148137, 702802736, 624173371, 796926853, 607275346, 259799947, 264973618, 954704439, 796688899, 856398578, 942848404, 719192113, 986351441, 316391830, 315457714, 403940058, 728865802, 2196223, 492765390, 22255307, 381343874, 854908835, 385568806, 829115446, 794073940, 249770985, 395056040, 904953017, 754766394, 635852769, 148567718, 909158926, 132686479, 623286785, 786268131, 200761353, 473211571, 137390724, 978373245, 385961828, 986692747, 602608320, 561185916, 533355363, 314806641, 105166607, 334040333, 544528758, 672919958, 917856755, 872113222, 251452154, 6228258, 329629478, 220844113, 27539862, 935648014, 813160133, 488907418, 465019738, 477349147, 224244668, 246895307, 853407198, 442268108, 298835024, 655108392, 969439994, 76657411, 174292498, 682851942, 298083500, 749430587, 741056464, 100195129, 577400748, 278434131, 74590207, 686253071, 284064146, 816298385, 743575041, 774618362, 685643550, 232010034, 783268998, 820654525, 115647599, 196633955, 375711091, 763111377, 173194738, 580320507, 793632086, 91609947, 717873845, 406078786, 246690533, 687939219, 653721463, 243421094, 340547932, 129611459, 10048646, 636960631, 460101482, 120596911, 704610489, 751516390, 712362105, 563721097, 692663427, 648097071, 439601535, 429941374, 298396713, 84845955, 597134922, 936483350, 731729960, 907263662, 477116190, 283249677, 489523760, 92408717, 86112596, 729933638, 698727843, 184471122, 927134354, 479933016, 749980635, 601376950, 584220761, 841302520, 915732678, 526389859, 994450779, 989682694, 204882683, 109254603, 345677684, 410081095, 258773947, 665605292, 187794619, 990244386, 431413964, 95828086, 731860440, 861687396, 202851879, 216989214, 113508392, 371762678, 198877925, 526047360, 923630677, 533456694, 828555670, 629977934, 311759151, 457728922, 526913441, 558898717, 988891726, 242164867, 189763839, 854860168, 772855832, 222213666, 302325218, 587202957, 378870588, 984030459, 61694872, 138540844, 640447419, 981936981, 874513735, 689274409, 762475763, 229876654, 854701370, 283295554, 921156638, 225678778, 971526245, 627960024, 982222279, 712619792, 513001514, 307747357, 486480367, 457835158, 878379780, 627858558, 337032180, 796921418, 856510783, 144735953, 196511530, 697372383, 928276694, 295197914, 93509075, 250768763, 16252112, 678924454, 849519939, 103497753, 731442290, 403927481, 839687717, 414455711, 420646731, 991893813, 123205155, 180733716, 197223627, 562242395, 16637329, 453868560, 576061198, 949604136, 753312812, 437132632, 545639952, 488189496, 331870373, 865189710, 751005912, 455160418, 551848718, 444082883, 98934828, 396817328, 566957406, 323085302, 888394987, 292322716, 430782360, 905830360, 58248846, 447066744, 334232472, 181704330, 143441631, 784245012, 891315450, 742167590, 987570133, 239387420, 608556354, 434569047, 308354945, 396522805, 848797459, 158484119, 934060383, 508243013, 680161276, 449644659, 69942391, 748907665, 543271482, 854971520, 173916675, 692895441, 595877387, 668483108, 429265054, 112270576, 24812748, 983132403, 811947186, 684876506, 207194602, 961107799, 674093830, 719749750, 295617773, 820154035, 651273289, 402958609, 948011113, 67205510, 201138422, 13346869, 110673197, 727046377, 515603057, 859609370, 871571992, 474095033, 737588710, 471318855, 486017384, 813167303, 684044941, 123782461, 767355345, 812719300, 32859002, 499239285, 922380768, 442443688, 374675830, 934104989, 371067379, 580324697, 579084593, 587152305, 958470297, 127146869, 430890792, 52661130, 425451182, 166609132, 944434280, 871543966, 915159512, 471887560, 961700917, 609502602, 236966940, 721239651, 748401722, 240345137, 59675838, 615725677, 693379350, 460943603, 889043495, 844392531, 112403710, 735272472, 245486437, 687610531, 898280073, 624361618, 692989567, 162399257, 771770082, 651667886, 771699910, 668864043, 763375006, 788457805, 176633228, 592450264, 283148865, 90859862, 743292132, 658388056, 555260152, 259924483, 312323737, 612961491, 496144951, 992463105, 458973597, 87766643, 661688126, 788297175, 644608429, 474875752, 3838493, 259916863, 520188593, 355431931, 411152904, 951650391, 168984165, 980164060, 287890728, 160584948, 566162535, 937895650, 196933085, 51745210, 531495726, 323122580, 705391282, 923592778, 926712137, 876942504, 669640945, 629021155, 894873140, 706540899, 782893283, 609915611, 470137253, 999733002, 834909421, 537437405, 52718132, 505794394, 293858305, 631585244, 42087772, 334036478, 899074733, 586513553, 712293817, 327073126, 9557827, 944466424, 345154868, 163933021, 42330511, 67018783, 749541318, 303666341, 65511624, 642747901, 267010077, 551686562, 971559022, 942527117, 260411438, 410655270, 213354587, 579726575, 835058990, 298492669, 989044796, 827471887, 419345520, 27985670, 384045602, 603175238, 752682859, 179881850, 648960273, 71362918, 594444914, 628368598, 248852177, 399185377, 66266810, 926191704, 54865363, 54038273, 872468706, 250004701, 291219393, 658401282, 271191067, 988720372, 69328958, 637462965, 713361862, 472856061, 788807370, 552651437, 929998962, 420243167, 370620256, 383092005, 991947249, 366416578, 544494224, 420295317, 646566696, 258998609, 857941989, 399694753, 564737130, 467818477, 28638678, 264028838, 257932714, 239604318, 76671999, 551624228, 475544860, 988432324, 261744218, 377676822, 161825659, 448160699, 112277627, 323698377, 607784834, 390125950, 955221087, 411485925, 308021255, 802849981, 891693414, 557596938, 406320847, 923819450, 944718499, 634304583, 745312396, 666542841, 562335378, 584488944, 520834917, 412923802, 590344907, 570699105, 825841448, 208859617, 111788451, 675894773, 528068095, 119418565, 13506823, 279869857, 856229097, 984624845, 475463130, 158977836, 245068742, 610969195, 758864401, 310836092, 992369572, 92733509, 113789287, 984700591, 425864737, 393094470, 131550616, 890802456, 798688213, 396589265, 919208837, 878652923, 410327134, 101209858, 40694890, 958246381, 40521317, 548245795, 513327171, 398812950, 87958728, 464215263, 917531537, 225929928, 761983705, 165076425, 545600080, 780588963, 373777020, 519219936, 828414498, 762059067, 581028113, 948964172, 605474794, 426140101, 786364883, 136368497, 596496481, 99168981, 247696445, 619533363, 997444231, 502104211, 566879803, 472842217, 619485130, 832045627, 35782182, 409853299, 225167618, 710091260, 71388759, 373569251, 100750507, 289133791, 373888127, 502432765, 400583143, 789550069, 982182503, 542481466, 477902778, 273806463, 42135570, 593546592, 258792252, 861586965, 894045388, 342491109, 404142965, 201397841, 395897552, 640340921, 620080315, 228949049, 690571177, 595332387, 427569900, 283637688, 453116747, 205842964, 622757045, 735678268, 61867624, 21547150, 686385253, 582423063, 435202914, 210034354, 746373575, 848038902, 427172928, 309389480, 755385214, 40960910, 850068860, 556410518, 105596571, 407090370, 372769889, 89023768, 47364063, 48476343, 766908248, 305847423, 174219409, 711333098, 602501496, 509335010, 218688308, 110461693, 909845794, 215966336, 27325306, 693820321, 117159632, 759178646, 239295239, 584082972, 295821453, 704879582, 774140878, 655282448, 281028632, 817928550, 357464886, 728274439, 533121703, 537043332, 749509025, 68574531, 637638094, 388520325, 185698742, 367730700, 557000959, 617008362, 116524322, 825870159, 399808467, 953594973, 101876665, 18195154, 885869138, 887459767, 734551159, 8340541, 251122010, 844702127, 833768501, 674611049, 755334193, 197829874, 829660175, 652192938, 506875757, 54737528, 178057562, 672613625, 603347362, 943526950, 935732192, 100296779, 661221538, 512840127, 246210919, 72298018, 828827622, 157961415, 562121762, 585805772, 798429003, 129146152, 799775280, 149881565, 745610314, 284744453, 671076764, 242245659, 623470560, 809428512, 66572798, 525776788, 654624996, 397895684, 323191354, 14621279, 877971562, 731050990, 463256257, 135723126, 628274192, 339591674, 332645971, 193689287, 781678977, 979026203, 613634407, 541072426, 300004921, 189535089, 295482940, 810455545, 394958842, 678639809, 193060741, 302935453, 658337344, 300471466, 693243812, 942081915, 57102651, 895501638, 209713727, 691667366, 340631324, 764992164, 277249656, 771100169, 110889680, 158891163, 230731257, 827535088, 228001038, 427995910, 188956156, 704336647, 629237093, 295278889, 22669613, 241311988, 148450181, 395863323, 670267592, 606896584, 845657279, 490778016, 991338810, 3449521, 742634777, 351711837, 152384548, 286398626, 608939438, 13784161, 269371161, 894554678, 509185991, 675970225, 367299040, 328818092, 290559767, 413762261, 481720651, 822442413, 479183144, 893431394, 52957798, 52836670, 967863033, 831484234, 189162227, 594542976, 157444225, 888598077, 75763742, 535205383, 702808516, 675232859, 998424598, 441581746, 760241960, 418983174, 674603667, 17684101, 264587001, 105279906, 335877211, 808404537, 256153374, 29093688, 7147216, 716734773, 610137700, 488010027, 793804766, 195500134, 69535001, 401280234, 357383636, 221051925, 456791334, 806175908, 741284417, 361488225, 838197931, 820874795, 50638330, 318635650, 317248286, 748952859, 228821490, 275839476, 401941315, 772549080, 506755313, 419781369, 827458882, 982716013, 939875027, 120832619, 305432928, 117570025, 6302874, 163171677, 977013471, 361787583, 140239754, 790462203, 15640786, 412537075, 3914287, 441211879, 134693284, 656363996, 371295952, 817971780, 883813336, 527545439, 671697929, 613430368, 301656742, 99490273, 472648071, 331298918, 358125961, 366957015, 479889065, 390761655, 428225340, 79524624, 119379565, 166518514, 113402309, 744008945, 441230201, 421268893, 728703593, 552397335, 461888904, 961539863, 864746951, 858700995, 25022237, 359044944, 380227993, 47255281, 632154687, 734515180, 47608938, 938344480, 656808746, 27696387, 924751044, 602755458, 706620766, 178301692, 332827728, 319727400, 709355575, 363810888, 667804050, 849167663, 567695473, 195639327, 782815548, 40843111, 375316170, 678028524, 83210655, 421012664, 934162755, 250643100, 467598370, 172700144, 630254593, 628936802, 831689535, 672374904, 616956217, 791367167, 423364631, 696070588, 802757033, 68430075, 708674511, 787438077, 930686668, 411657848, 788652925, 109153701, 577661173, 609335942, 837186630, 372218898, 394432192, 862620905, 497831239, 111615358, 869192986, 289848842, 169505805, 287946757, 228815008, 495999995, 105101695, 857686131, 10778624, 586817895, 50838557, 468438533, 667996968, 640939752, 488878974, 247045263, 570817842, 479385598, 177927261, 545266498, 383422924, 261173990, 207688685, 614544744, 746753877, 816497139, 70676242, 296946448, 769602486, 957072153, 39112743, 964586909, 186525174, 46213450, 621511820, 349877009, 821120869, 358719252, 373607084, 778791156, 901637872, 161610668, 167226827, 727863537, 953263164, 999775918, 511836545, 845289860, 986339059, 826398122, 948863904, 862912009, 971510379, 684891114, 512447564, 713020361, 516437132, 620724041, 483192730, 816384576, 498175505, 220627074, 645756379, 142222834, 68103753, 74483339, 580987127, 759173657, 241972584, 57216086, 206490233, 465927280, 70710249, 784134387, 550003016, 953381040, 719046778, 571383720, 782716418, 786928281, 550483831, 252900106, 499687695, 785429916, 578312392, 874954339, 119775730, 711074060, 851729165, 674970610, 119186363, 718453138, 366401490, 440677032, 760427570, 235762604, 471609136, 761462354, 124890285, 879419224, 262343208, 327367563, 783332767, 834733102, 324249250, 787578267, 764865066, 852509274, 53035731, 277462227, 3785267, 481425604, 878771281, 231734857, 906055568, 233639207, 768333308, 601977218, 868859785, 113052587, 769243986, 884115305, 968515444, 540887029, 876229336, 113009054, 814863907, 860789498, 586840663, 748597916, 203473428, 769577649, 347598240, 42836112, 684681686, 457399433, 284297318, 34615513, 61742913, 297225844, 951939063, 528095549, 514913168, 635792096, 960194435, 611516637, 592161402, 931182674, 244382690, 605969173, 902172661, 280555653, 482433180, 5275481, 936499850, 681995950, 33317789, 620096310, 137857260, 332999058, 722054696, 993497088, 972499643, 728128773, 28425246, 174636232, 137069477, 748230087, 827762629, 452995196, 369540359, 257105036, 311005298, 126895479, 358029469, 863155198, 474844528, 886638541, 368357624, 492550250, 454990233, 899947810, 275122347, 482388449, 209302245, 628218643, 332938639, 869238180, 330765164, 35385803, 110200331, 981236117, 854347231, 496827279, 651593296, 391670783, 349704544, 607325875, 577328461, 72458465, 632534822, 148131411, 924516085, 480587673, 35741980, 508107842, 11367114, 527224579, 87398598, 373213516, 965650603, 884665800, 806669404, 268661094, 981033908, 124756342, 217962142, 253724167, 926436845, 42528582, 860752812, 221186117, 424928317, 713859120, 927882655, 522913369, 686583281, 504511764, 641373061, 305460115, 351340650, 674100943, 272357973, 835996012, 102755994, 403636580, 763436870, 252671320, 246565891, 653694405, 600486217, 461216451, 956669940, 42806551, 465249903, 299685280, 852779892, 617905415, 137862011, 618852415, 229628030, 790672924, 934525042, 755720265, 20586522, 972473873, 585813757, 785324255, 397883529, 444260811, 967856020, 398945894, 114689711, 641827332, 626403777, 749459946, 522750895, 778408839, 760304692, 375816838, 750257253, 644058644, 951558986, 674211960, 50701606, 885063194, 202176004, 7428811, 644813297, 120858024, 721013088, 677597612, 230094160, 932364516, 18661747, 808071782, 335366195, 367493721, 630903984, 126737421, 743049072, 679848901, 843905754, 596909987, 270768091, 925421467, 780345963, 284377777, 895405840, 287340297, 69650037, 937830440, 911673723, 866196988, 757517347, 364086442, 319677614, 90524663, 323799659, 481244766, 845206752, 849438964, 432022589, 977196147, 467234035, 691814977, 808326826, 823665676, 692351135, 599497817, 973262248, 550057134, 403850237, 776559537, 126578440, 590905052, 562696501, 561549752, 363340922, 83133467, 426785247, 164405662, 341204126, 353552590, 240171156, 845293829, 201171163, 674003859, 480714204, 479078616, 73789142, 283407307, 32621447, 428792602, 517734653, 283320492, 254339444, 481624211, 456400175, 580773742, 715252, 746902775, 352579552, 847996356, 579143646, 205279977, 170446918, 590691517, 78913431, 606912393, 714307378, 961665841, 539233487, 174008117, 403333419, 974165971, 914757707, 788384670, 124020073, 232349409, 137283146, 110988904, 619041245, 82302049, 398889546, 374230067, 410181889, 265997409, 195456700, 842678986, 284885049, 753230782, 551273855, 336053036, 833362427, 556656783, 450748061, 995017389, 381196415, 820950589, 889802253, 203571647, 135116860, 480476626, 886864786, 306592452, 579132644, 448658325, 647876221, 890546291, 967066804, 901490370, 315090063, 780345926, 928554055, 743702197, 771742730, 63916540, 785780961, 704139901, 161595351, 273729179, 646150829, 726478561, 853911140, 190413183, 146726085, 167953617, 116589495, 150391514, 551036460, 563184779, 689702897, 669150050, 677918879, 217856109, 635089870, 252437464, 764182809, 534462569, 95307904, 465494242, 655578664, 970724671, 551845653, 685629141, 775850787, 527358573, 747728905, 92515913, 783266733, 310546160, 159052164, 958078995, 591014946, 21527823, 889725617, 181451705, 730969938, 89677781, 86025179, 162464818, 485049011, 673563343, 662480996, 774348636, 337033055, 237166914, 261437995, 22497060, 717155010, 639657905, 844481536, 257956662, 222620828, 442382290, 534294575, 168346673, 222682636, 872119618, 529725058, 602933103, 948806317, 282444635, 602303634, 226111482, 474923553, 458326660, 32215730, 730618133, 370506795, 615386894, 851062810, 547353532, 450964527, 20953011, 3059492, 115057403, 551064184, 854683456, 317446562, 332015204, 444569029, 585748861, 612650040, 967824283, 455202825, 511249921, 389440958, 181804845, 73054757, 737647181, 844955418, 432112995, 517946489, 949825096, 983208410, 719119580, 911328098, 432648529, 851755594, 181778029, 188162825, 225494195, 348084040, 227135080, 248843791, 173491710, 934012516, 183416590, 293223200, 575579724, 182655374, 600194054, 167871429, 535076431, 26374061, 955924413, 305421085, 919047910, 237029173, 982557516, 896763231, 296616994, 926148420, 61806242, 832800599, 671963401, 171552472, 82712636, 567138705, 706161765, 149271042, 238070478, 350923202, 498352499, 786788960, 299623118, 565990095, 88897235, 978510953, 221687942, 124878845, 981653588, 681274561, 444766012, 372523650, 300337712, 290194086, 904179133, 579324274, 526762535, 380491455, 683212479, 970337420, 927884094, 101195799, 265614399, 839304807, 778514885, 992225811, 878689951, 125247248, 408407802, 156253598, 359459382, 634194407, 328717231, 849050503, 402688162, 868568917, 913661862, 743713668, 736139850, 616475095, 388322869, 732964042, 212283607, 621643652, 622225732, 889401486, 648011959, 196446481, 149470960, 810005672, 763099132, 303038062, 640526962, 75619432, 313323060, 350881238, 381498779, 948155940, 914427033, 507563339, 18467502, 593230743, 880292728, 639991456, 204451031, 768616902, 733525064, 924660305, 559523436, 204719737, 602839649, 754341523, 139626012, 774086232, 197950166, 860917744, 820479771, 394110963, 636247417, 971440745, 867430979, 115329080, 52651318, 190443640, 590051691, 970275427, 743423736, 737130763, 894440045, 63159749, 660676125, 735103073, 262788580, 112608643, 287166898, 477455137, 899726363, 615764657, 677706288, 669995234, 155832089, 948645164, 256666358, 6760752, 797496526, 921465783, 762845020, 720564815, 231912039, 984529603, 750445254, 501577829, 936846676, 44825106, 194243777, 196615233, 364830055, 780942633, 661247150, 281227471, 867249774, 418470473, 202961213, 548508413, 25751857, 176183450, 4718036, 398160580, 942935614, 159711610, 731816282, 397999455, 431402231, 263571139, 429976616, 871449101, 377750643, 429018603, 827886032, 246561442, 850379906, 234806569, 278937442, 943033582, 654375614, 750289558, 755624806, 483824877, 586014158, 31517360, 625664399, 522528944, 216291409, 393769614, 280061051, 317487851, 557095805, 207932535, 415718726, 533384982, 806716129, 161217401, 401711893, 112713073, 816028217, 308116187, 302117556, 248133937, 315178175, 159653370, 525974491, 906733029, 239522321, 994141023, 527213430, 37163677, 34495086, 658355512, 179196079, 219721554, 715315929, 909417511, 337458378, 430563531, 788480359, 949434841, 165650103, 461518742, 781025162, 569835288, 580727640, 12293743, 28664167, 324010492, 903264833, 67398697, 52105237, 243683104, 503684022, 130454249, 39424082, 405806983, 396042708, 83626994, 474171830, 391188708, 201555539, 838763487, 75877526, 521161192, 151944893, 708946374, 899871997, 276909399, 708101781, 620631381, 193779418, 883611237, 577039732, 331528202, 478140029, 408433308, 193397947, 435922642, 758082930, 544428517, 216428779, 852430563, 774406, 325837119, 900995424, 836933420, 801943352, 656921275, 174970815, 265809852, 916715272, 593415972, 529993333, 814103841, 718020011, 186751934, 535159812, 169228679, 412898173, 112394169, 711700016, 722193179, 134366905, 433736383, 464033520, 61502293, 118542174, 427215498, 436163155, 803188007, 96744103, 326673552, 584953682, 294457817, 561027006, 392676874, 239201399, 790263266, 190269595, 982846410, 847718685, 794802168, 506532130, 603463648, 701075206, 7202655, 608012993, 555482084, 854981015, 144358921, 409799970, 51458602, 187426447, 99828440, 126216830, 200083473, 145894776, 325524843, 591988711, 966981423, 6551776, 795192999, 132571687, 582391062, 899672414, 632415529, 824572492, 602823106, 868680324, 16221035, 769558090, 884376267, 575626921, 666076403, 503738814, 681959915, 733336936, 314920560, 802555187, 704657571, 167422316, 925222850, 338293907, 214480360, 124048337, 533346391, 871163582, 79302567, 498625234, 860217910, 429528892, 397477031, 310480891, 808198575, 11166724, 831437619, 404840689, 529253364, 207076856, 389206610, 765035242, 879867747, 981911214, 255308112, 202332809, 444780831, 822605464, 372401292, 55828302, 974727510, 265497835, 877813239, 669970205, 793513629, 456021428, 400607490, 851097156, 327273391, 840767249, 334118197, 310339757, 493536575, 574853655, 338699903, 235426910, 590971660, 651363703, 457029461, 225776282, 713837502, 355238424, 927282578, 946147178, 800775328, 586883821, 712022021, 194960925, 894290922, 800043184, 573643794, 969473798, 539177467, 879231643, 92241408, 798356563, 93079688, 136165347, 535304516, 66271786, 635622514, 989556092, 473377091, 557630924, 573772871, 627304098, 524479289, 903495706, 670058878, 736806024, 337800974, 897261093, 477392722, 125062321, 558418202, 650910885, 316702526, 59394886, 778322515, 532962129, 698457025, 203981044, 156426191, 369785621, 25713101, 66884327, 888287898, 131868415, 192729703, 887976510, 845890396, 720226154, 523909663, 352381055, 443016190, 243787235, 727139487, 474137838, 281490118, 856366839, 777594286, 545249623, 824823869, 456410745, 515832272, 29249892, 342609735, 128484661, 953387669, 131906067, 85591878, 915770831, 706690470, 452112801, 418311760, 176280263, 113342993, 625457967, 773073339, 64884822, 953781322, 548053722, 315965225, 806188068, 737946932, 451030334, 743270247, 2803604, 170925863, 627008302, 190312887, 941151545, 254816241, 947753500, 422977945, 426142207, 604394795, 303917530, 977342520, 340994089, 227528742, 62248961, 688211326, 242985754, 827518675, 551915040, 408441144, 505939930, 623759533, 270526708, 658290152, 44929333, 258594885, 402479893, 637799613, 650319987, 289047284, 397525891, 365984544, 323563716, 388339566, 178306778, 399165619, 262901020, 864154815, 214764838, 613223840, 568188191, 942455261, 414260761, 865695221, 194674242, 643976777, 516741911, 780680278, 437472674, 878547910, 793086299, 638762911, 89964192, 423327468, 995281167, 862751875, 667900834, 748827737, 69675329, 852345564, 11688688, 257365643, 404929813, 379517269, 186322254, 126505324, 297871407, 880231335, 835162997, 203661965, 162260212, 217863378, 894577511, 275555611, 741004500, 58171891, 566990882, 521566044, 901404734, 683600003, 865554092, 443491078, 380718426, 778220262, 469340155, 263621484, 502129938, 836386270, 678906354, 120253107, 868199818, 225169311, 67409419, 299597858, 811087333, 223779389, 43609524, 822743040, 975201288, 611098462, 835615138, 414084353, 773772821, 311503358, 243381488, 204591599, 928602752, 712750499, 685680804, 670562253, 853545764, 805140463, 317234769, 486263662, 767246661, 442568593, 151733110, 631175189, 8364235, 75758833, 365019166, 130149731, 651269944, 972175362, 856093196, 115106191, 752610844, 170793780, 658137858, 154361767, 815940438, 893790869, 125656951, 79311507, 674101911, 314224352, 817803088, 380463692, 960741375, 832245607, 212322057, 59554901, 749298081, 556511584, 946802864, 622406335, 129403974, 16013046, 72989518, 759874389, 150192491, 402389851, 998648541, 175952248, 192700478, 835701892, 989447230, 892331019, 879494735, 607995233, 199833434, 261719249, 725302020, 352716989, 636667029, 342302184, 15381524, 661074389, 185875760, 871011103, 550515344, 86687267, 649231807, 154724580, 835505472, 633910143, 592871122, 648478716, 349616118, 946834360, 381800441, 567348751, 590002124, 463091302, 21905466, 630377747, 156077131, 922609915, 535333578, 665629234, 871150108, 310589621, 269329621, 389860128, 194716215, 434655109, 88327099, 486946430, 855578087, 986762969, 79432289, 369709929, 559253673, 26245213, 923092607, 647218894, 480331828, 995258367, 632792166, 155629722, 796952493, 484327189, 307520321, 451093889, 132591347, 907459639, 821907579, 706277251, 404582651, 115958765, 271234822, 355271253, 125853998, 434170125, 909916595, 920102696, 809656566, 800238793, 28814451, 942239660, 801960827, 610837556, 246991251, 160410810, 305922824, 255478, 762889283, 392517779, 494212685, 560378685, 35902575, 595473674, 729727888, 74741134, 223978208, 897047066, 278787438, 428494699, 89550651, 294540359, 179725966, 866086106, 892390875, 398339051, 231153640, 954632087, 162965739, 845695561, 677547395, 283407484, 237571591, 966451354, 472263137, 949155431, 887377373, 804708179, 726228164, 407345239, 108216398, 308953869, 186853050, 456669785, 634159456, 11101486, 509793004, 794338193, 669724771, 829944484, 894141670, 337082615, 796146964, 611899540, 487085849, 379451646, 76430423, 8906282, 890497068, 903257944, 713297233, 433611259, 847392800, 252982393, 333781504, 896211566, 248559655, 432520566, 316164672, 628658898, 381869392, 407963399, 121421197, 323149587, 53712010, 509140305, 829581545, 303153560, 459443733, 825888062, 988428895, 182320458, 190122934, 543095866, 637253476, 187177563, 537136633, 565709511, 660900477, 997714271, 569704759, 268694023, 685394129, 447028898, 330209851, 269318792, 256698253, 725237936, 410501754, 378453320, 915724931, 56147024, 413066166, 108914857, 657995818, 247116829, 869214263, 365973260, 180550756, 970694560, 3247598, 69225129, 37842627, 659332884, 606192042, 768195973, 698700310, 571676961, 737382725, 363150441, 765513250, 477613170, 671291305, 547826506, 16722118, 764907640, 544486785, 302470877, 461828104, 185719610, 123484947, 816660680, 515461648, 102184894, 449688997, 680559214, 73822285, 571953901, 926348313, 547157451, 942377784, 846593320, 915233679, 806233889, 579438990, 30104837, 449398830, 513538968, 513624538, 646819328, 264572364, 743251554, 118330768, 449836209, 702934482, 976699906, 110066098, 469325715, 485399989, 988541218, 178385811, 370155631, 136940553, 88665943, 329793221, 457814194, 913274502, 397730988, 707741894, 460295978, 255555486, 177611612, 141067122, 530710226, 663193295, 799615912, 241935258, 999542904, 865088350, 298082094, 587525236, 53661574, 22513696, 523188743, 231129713, 425634937, 820038282, 409624355, 321516290, 793381247, 679231011, 85408252, 664343435, 876238053, 471984354, 163207744, 276872128, 937281654, 64940871, 860760387, 95083899, 514656764, 538196399, 617347778, 603393694, 187141399, 899322116, 9994635, 107889313, 946066977, 216610587, 516403120, 221098655, 367360132, 381116215, 951622316, 434021794, 50133169, 352547237, 283000270, 686398235, 522308443, 299573862, 187150477, 742401704, 786157090, 133413199, 474013841, 95685209, 573130108, 244864020, 127868782, 26287728, 696393984, 103477724, 906088393, 878960422, 483289900, 703878830, 486468835, 263831663, 954679003, 131110282, 735274788, 426732598, 758844428, 726054171, 435661686, 193389668, 35232645, 654654870, 916971774, 185864110, 307817866, 320949051, 675939276, 140652437, 156948675, 683844974, 87277799, 121092961, 356714863, 842102915, 291055131, 934592340, 480197795, 994972283, 342454067, 684230328, 744957652, 949155263, 11883920, 890698918, 209560766, 722162519, 687940876, 146904170, 535021944, 993578936, 562374079, 359655216, 717210398, 299943660, 568838941, 178557282, 107264281, 9258758, 2236636, 899032760, 846862019, 907918018, 831314415, 895000757, 80641625, 498820671, 929414348, 212287847, 785976460, 825304708, 120488920, 830554211, 475974347, 728215868, 18612113, 504539634, 373648157, 543229324, 193088451, 916747883, 282252235, 945325420, 85300807, 361520393, 718813440, 347406140, 227134305, 284192706, 71837456, 463551801, 436345810, 384089858, 726332023, 190778028, 235968207, 309553957, 308256092, 75891972, 918508475, 850759026, 342461633, 99163086, 512563495, 882351364, 274859269, 622499949, 948507458, 229133448, 594375979, 550704198, 54604680, 98481959, 945804172, 681441393, 391950887, 85164009, 590364326, 755048604, 385097367, 28476478, 538170394, 754814987, 365778860, 877737688, 669185657, 85563269, 694661972, 170358375, 594443598, 51947340, 12295988, 148684507, 113585837, 252876092, 75954844, 240546323, 127788263, 432691776, 926949423, 840636670, 26764622, 393256391, 256328868, 348762292, 658317362, 436447261, 303470791, 286654120, 942249227, 796858928, 785601319, 888799537, 887940134, 642557367, 384624222, 17771427, 148777956, 34161348, 714348911, 135181671, 499335151, 330515161, 451197889, 502678916, 617994877, 83866703, 749788129, 714605923, 152772495, 846072016, 976892839, 828351058, 513185878, 12514572, 359676527, 541735888, 966780783, 551582407, 957140737, 642156472, 963848305, 722460222, 756590209, 140781212, 390852187, 870884082, 765405522, 656529187, 139563559, 177334087, 700358510, 678297164, 207546821, 323953131, 24165515, 474061195, 709943866, 859701033, 427221381, 982478872, 192080811, 447274051, 24390035, 291490319, 754482751, 980946497, 240160546, 958093287, 530282738, 802835102, 645258885, 246458567, 517051901, 41927183, 234014614, 954178006, 404711692, 205712281, 548149657, 15539520, 834648716, 176840388, 812146971, 571022254, 472552618, 83696441, 677093892, 159396009, 192372726, 633602523, 563287913, 148428812, 822173479, 649486683, 129666740, 878524467, 717490623, 422697322, 95409996, 967314784, 756845835, 792633671, 225920645, 991245122, 881057082, 703270295, 490005492, 746245677, 410768171, 340773210, 196396842, 832332650, 253107018, 463920694, 906960395, 487702254, 317133298, 163987435, 61771605, 461308611, 813959045, 448503990, 49953988, 218851877, 430968700, 117441249, 467676487, 803453004, 919707170, 977651606, 82803899, 305901547, 763753089, 269861909, 830097669, 421174347, 553998047, 851639942, 783250657, 82941888, 373978023, 926119321, 395422621, 434514363, 82572537, 11671036, 204010797, 584976796, 34057620, 224416240, 171872704, 776357457, 125075184, 453986061, 798546597, 218067232, 573208845, 695081061, 66976490, 880251419, 743875745, 230124570, 687451922, 744378683, 888463613, 833419661, 369785814, 363115053, 402643001, 213023682, 144435818, 924778420, 564848731, 959848642, 482791148, 242966978, 32296695, 101075425, 371234941, 991027758, 576218624, 230128579, 897442863, 47107127, 103663405, 738428025, 584306476, 729369084, 47412430, 742004021, 914946200, 45003994, 933392719, 322181524, 193410229, 76328113, 403342784, 319852227, 15014274, 336753617, 312931362, 9302034, 202133305, 270828815, 67923834, 958111907, 29827232, 808291849, 803243288, 313831437, 710929997, 263035037, 614365417, 41815729, 618250463, 902846509, 903939151, 433705327, 624193333, 349668346, 986309544, 211444239, 506105719, 871621572, 523806737, 519544036, 334436487, 216813325, 308722609, 109655970, 594383197, 420017580, 408913746, 235797672, 55872091, 776036975, 671264609, 835994594, 569487826, 673888952, 825172253, 972152652, 536854322, 453448303, 26764149, 153614761, 971274046, 921703354, 223512339, 596127053, 896538830, 441637554, 999396250, 772046862, 664609131, 507702696, 989336330, 560876408, 221674985, 225848574, 731302507, 111651399, 709802296, 627191798, 374047108, 883614854, 405625425, 16240145, 552830163, 238384731, 668944630, 483697181, 344609449, 931843032, 197725864, 320777035, 308280021, 85950809, 818993708, 868223542, 660066151, 198049726, 561862575, 84466764, 701218505, 279756035, 939386264, 345805112, 544158891, 879597805, 193390260, 86980371, 633964822, 239767186, 614701944, 480182064, 825209576, 706871048, 888909085, 354565369, 973089253, 905220087, 568580949, 780935902, 723912954, 257205716, 399034350, 725259561, 708974980, 571517305, 656696851, 818068363, 164880009, 658097706, 64695767, 40805664, 606924748, 713074097, 834977723, 212314422, 996883520, 850559227, 164137028, 160989679, 350022636, 802248853, 161086265, 436660502, 48335350, 969183486, 836400956, 587499170, 381241251, 615187438, 198817208, 651853762, 809612954, 282211925, 64775022, 73879579, 486372581, 259597156, 11574972, 565457794, 201596905, 19307976, 499639794, 797942658, 129789679, 546938201, 902937445, 747897781, 32128744, 187876524, 601593166, 500121565, 421516991, 601975524, 237082182, 839789036, 713725666, 7487067, 505042426, 236861951, 621348442, 106714851, 734114832, 729774231, 170924135, 179194607, 722310837, 395525223, 165768798, 101029426, 175845665, 394735446, 25565848, 746840072, 26281759, 801531748, 606337508, 249551555, 967301123, 237018368, 201705529, 973669601, 409304446, 957946449, 20219495, 949590099, 384325065, 759351130, 742846496, 574218010, 938947427, 815715198, 898801310, 991630018, 565259416, 831489266, 586633553, 264540402, 97556925, 307603285, 4155116, 304719997, 287990936, 310362885, 794714570, 481221646, 159841668, 796644062, 612376916, 696183118, 570055931, 467889616, 198105630, 245456256, 979188967, 599891358, 464268486, 890643397, 897923734, 427158979, 661311737, 888922470, 11595892, 951909999, 694588693, 665168830, 485806809, 4107991, 629060388, 981570233, 602418896, 574310443, 425818592, 814150362, 595595792, 804226855, 515525168, 916116752, 752181910, 279101154, 725218197, 722479112, 89785959, 942942774, 303711048, 763932039, 981731664, 305670907, 873757866, 446567219, 226376535, 1365037, 663444152, 427113670, 874889660, 495813750, 497819486, 563690724, 694747428, 634702309, 19907038, 249537812, 589550057, 356121170, 937859217, 208164738, 648778828, 762140823, 571832638, 33597770, 152081134, 404782120, 156280095, 414706449, 491124329, 940013712, 205328224, 873155248, 933754708, 44120019, 809933254, 706457402, 846402471, 129767315, 371741889, 400747804, 606745379, 64334429, 277867735, 447476803, 913773861, 802853371, 362848354, 586467911, 793238505, 641643768, 188149847, 928276039, 425597353, 302306141, 580882520, 239804938, 959267006, 303728346, 728305147, 502445269, 264101592, 279299320, 115447813, 190938810, 482457598, 589039655, 425634126, 30497103, 819795701, 129082952, 656869603, 901170324, 975367980, 917299654, 435312074, 998550111, 993345917, 579128639, 699652680, 495127421, 44475638, 893104455, 263291619, 703019443, 281490708, 447912351, 730279280, 545149888, 754130845, 491965205, 463912877, 209931135, 751267666, 704444822, 681661159, 453866550, 544759257, 948491934, 364050135, 256637678, 421992218, 300509504, 260064286, 270441813, 204859284, 804813744, 30913656, 492370054, 273430724, 547823362, 333027429, 208250374, 240920075, 401495596, 57008354, 656680586, 804679808, 352649032, 63553008, 205034650, 441281323, 792890149, 590088360, 998821630, 229651382, 667670397, 405702275, 425363786, 808409778, 603430686, 708705808, 525725904, 317892435, 649746415, 482942347, 707511653, 917755170, 534297922, 620997445, 995593289, 662220542, 547321346, 105301988, 112053616, 356947132, 287561360, 932380044, 846794535, 516225256, 729036845, 57801032, 334956999, 750419287, 111622191, 390620501, 703108801, 320905257, 812565725, 19724339, 356945283, 857030453, 631465997, 131626794, 523452334, 138853460, 421145464, 280101924, 464084148, 517382647, 165575481, 338676075, 402199388, 314165310, 504154024, 126600438, 399776649, 397075456, 833259647, 754209126, 612092573, 532750763, 171565719, 101520119, 910767233, 470745079, 845976494, 544526797, 292403042, 305453758, 548967757, 680392550, 483193093, 697344474, 387001186, 639924322, 244797107, 491658167, 897916053, 722198414, 253479375, 931812061, 500777787, 287512678, 678611330, 57640031, 744936548, 393288177, 480962153, 674194732, 556565668, 244423740, 757333970, 498965849, 648382081, 239970811, 473391833, 932940012, 606845260, 865550067, 169305254, 81662165, 336920473, 97872811, 247926743, 366201548, 765280938, 266005840, 559824288, 586174038, 807716577, 662196250, 952462405, 679013313, 173655950, 910489471, 422628247, 31267088, 273543641, 809140329, 675945627, 707740738, 508069627, 860320367, 183332220, 365831905, 332768538, 44026186, 651147742, 818069160, 126655319, 554495943, 973690694, 375274041, 766502810, 339365478, 664814383, 574464079, 760875014, 103172859, 314972301, 271095638, 774586363, 507803131, 762332934, 255485138, 668995115, 412173196, 590070582, 548723434, 655501790, 523892240, 708851843, 907364447, 727254136, 401272107, 955408196, 655153762, 278735331, 123916434, 999134254, 287419923, 345586215, 576199709, 353120867, 217428439, 400223025, 403630593, 725777285, 615224949, 593524695, 742405140, 90046315, 878313123, 876232445, 661778134, 155028006, 271089323, 845398065, 331217303, 641713989, 606634178, 960072085, 208970185, 356519794, 877363150, 919344791, 857852246, 157282911, 493438058, 904740533, 468111991, 399480159, 936144801, 266853206, 859083497, 464168339, 972625931, 660214569, 263368402, 497423044, 298448580, 484222666, 796674333, 96104869, 750576955, 290843047, 423466976, 599725365, 199164761, 629825601, 999192697, 465263400, 788496166, 555031374, 846509430, 400016235, 446766994, 3015076, 69524987, 567570429, 562779573, 489761129, 893534998, 142194464, 907170432, 234359935, 166317648, 528508726, 827342496, 111587843, 359859138, 529558734, 367939040, 34386224, 854758502, 635787697, 376736267, 526855040, 931242832, 749774056, 741587324, 779096192, 333134724, 196720760, 809039687, 156672071, 395240117, 357191243, 402091702, 239491297, 99959784, 150310870, 415522978, 174391819, 908869253, 524745722, 450081073, 263055577, 939674244, 175705165, 749464682, 499163511, 19683496, 979623289, 213428053, 775004845, 787285751, 378399501, 771241404, 772544486, 937296793, 773405111, 485459838, 345242849, 226252767, 721322333, 4683974, 643454246, 508928667, 461800277, 955757599, 110500411, 592062520, 562127400, 210581712, 248446946, 411719080, 352853741, 511211920, 371810051, 562990535, 230531233, 226444175, 433618036, 817342484, 880621131, 509811220, 717525968, 790762573, 299558998, 202627196, 787486803, 43738593, 548856128, 22254919, 909236786, 854899334, 184294137, 582023724, 350878658, 832571449, 691736812, 66528252, 936069421, 73328263, 99234081, 854588555, 954009377, 68935441, 857243039, 519465429, 277730143, 643018590, 409686614, 353801669, 975464743, 129084986, 76336504, 999530034, 872822738, 299350972, 459498828, 269177443, 110771433, 814393975, 617946651, 658372918, 943768772, 760457800, 685789118, 958313970, 418949500, 448059242, 478544262, 522598625, 511117301, 455850889, 166358661, 477916721, 487091223, 246881813, 311961636, 638700395, 858733027, 971919400, 318043312, 147156804, 365718727, 855152227, 218959367, 302597921, 28725121, 728076326, 369967229, 750363535, 62688476, 209015495, 473942765, 626256193, 862432978, 633245869, 723965148, 65135488, 927543643, 268008497, 556359021, 843077864, 244939186, 448601583, 347400705, 906731388, 294982914, 476252222, 575949673, 666903391, 208084812, 550216041, 953746122, 278887278, 306893551, 637932305, 580278778, 556390868, 197076551, 698368921, 882378153, 83436941, 50160418, 21048886, 886147421, 79115396, 679974804, 968099786, 418556406, 811114582, 190442601, 580954459, 268983131, 518444482, 333640181, 234427563, 7718372, 354719326, 269061093, 518526060, 34776821, 100166408, 906148359, 240496144, 882611294, 744671444, 215648033, 713039078, 563023076, 389081136, 139530795, 879066437, 532113670, 968307531, 576856847, 6778129, 853899288, 182796880, 995003928, 155207105, 455639162, 737661963, 152107294, 111454577, 139596776, 132520737, 556500231, 237079038, 506960191, 464122020, 159544510, 754697532, 117397360, 851880472, 832609957, 603250173, 858628769, 724427433, 919274968, 633722494, 248940470, 927964215, 692234910, 822022516, 595732332, 432234407, 912089623, 172283353, 93069738, 406141962, 515975307, 427301083, 165570141, 364920602, 336025900, 357829243, 151445524, 480984944, 664901378, 768652863, 883052456, 975358225, 188032058, 136821145, 740811523, 951263221, 299056621, 762842851, 215730854, 380029713, 905375241, 451284241, 335257747, 415497462, 336639627, 863868061, 535288706, 105448823, 259457997, 6738356, 88842601, 234697615, 712758061, 616645702, 214124893, 71874917, 876816122, 765662554, 466155823, 24418258, 514229851, 742226343, 762657741, 22590152, 273341584, 107248630, 312092972, 556633490, 225894467, 217948290, 425148329, 16465185, 501070403, 985083304, 327145745, 974211329, 536050854, 930779537, 44629268, 167471659, 751440878, 294203930, 772282707, 853981758, 265259962, 912316222, 318969218, 315800900, 549464232, 42804378, 240399554, 39516682, 296644876, 168289011, 27987937, 474466254, 802018822, 342111670, 436576930, 851419960, 286926193, 967175520, 286562522, 126077233, 86479313, 889544138, 33921001, 264601023, 486309890, 310600996, 389521968, 508979896, 305299481, 766352705, 38893942, 25589698, 629706351, 201996007, 207080171, 548443146, 661220360, 667403360, 850480651, 426562622, 727708063, 725993188, 97645433, 391932697, 749021787, 412098608, 896240769, 441253697, 771958792, 183813607, 25565496, 261817137, 161489693, 98475870, 52946047, 28026667, 974095134, 22503039, 20436182, 254219757, 647023796, 183691236, 830431976, 263403012, 343765299, 24029743, 384679211, 366918681, 912094085, 121738890, 997523546, 430607939, 474337490, 348026629, 178246899, 391593606, 754807462, 976833024, 81081062, 604895942, 286215179, 271546857, 764889643, 479481026, 890727118, 679119890, 665520672, 463280096, 530250013, 959892857, 508322069, 686372872, 7359761, 576224094, 342943093, 843579414, 797132362, 623137179, 574757281, 687917601, 839657286, 563281784, 598493663, 737774126, 673002618, 731863757, 418618944, 597485626, 335681121, 564133383, 366392578, 626002889, 641623938, 89868834, 474909248, 805886844, 884253110, 312168521, 542335269, 957586347, 977902941, 523917272, 211382300, 250960846, 762329954, 347745564, 295287358, 714829442, 722901929, 324850358, 543392330, 328360465, 800978566, 257421146, 64805162, 32364133, 209882051, 80361192, 885685049, 410618514, 159634156, 768630449, 897654265, 619098164, 592759013, 125555199, 386211683, 795966909, 372268947, 205261324, 650719540, 158118157, 175201019, 576618173, 265563222, 14638515, 984909765, 556231447, 636503347, 216990691, 216812659, 147867835, 767894142, 814527928, 325608287, 918160904, 630688258, 886676492, 512253230, 471169696, 954383512, 992465098, 158882676, 705289938, 388747488, 96847043, 614429024, 983265684, 178707557, 478922978, 244214476, 217755629, 933029519, 686435852, 704355245, 120891849, 358566597, 867657270, 207645820, 760667139, 267087248, 382389520, 185132693, 512181339, 875639504, 670708279, 325712809, 34527682, 866690652, 217608020, 554488292, 89152169, 40082012, 923766894, 558161184, 783930394, 649925354, 958863963, 944515584, 872237444, 207460768, 293296035, 904777275, 413962425, 838168892, 141160969, 312075693, 246516628, 327676119, 900904070, 961330306, 170342720, 575924110, 456401777, 121973639, 780858718, 624015745, 154354708, 217912339, 663864619, 376905032, 167726650, 139849641, 305556524, 841908325, 441357046, 970847304, 706333573, 885984677, 41057251, 139131414, 465835411, 479873372, 671279906, 345988373, 445897171, 198765468, 615588083, 74755226, 982446598, 878864238, 404151464, 44058390, 302077722, 345669330, 686251513, 625824300, 683683314, 508462175, 299825721, 556885560, 372208732, 713510788, 213047041, 443674285, 810549901, 467266206, 948369988, 334785687, 634559707, 347973485, 958444665, 878203354, 897064590, 998762817, 717386861, 684327982, 711306663, 334006619, 5385698, 930092552, 969557543, 69207525, 963426708, 883061445, 63591500, 224694112, 173449185, 96021824, 385696007, 634251179, 497340680, 773326493, 230143289, 314705536, 154900391, 182765811, 927378129, 550981912, 655686405, 380751899, 854284690, 258749768, 470606716, 558412290, 106400977, 927106262, 383149212, 260855207, 472028138, 932605168, 816874112, 412067943, 357679290, 1712519, 314598101, 265371940, 53981730, 917967260, 858699035, 832226365, 967909692, 811329172, 308613306, 981702610, 200925225, 830124884, 124555464, 316641548, 680870415, 96650508, 518519326, 948303979, 58985721, 555981837, 454342400, 160687470, 740923862, 418909435, 167718077, 445698775, 42959927, 312021789, 307647699, 250366401, 343017143, 99807096, 715468624, 561897313, 385765443, 952667248, 746434961, 610590234, 970151982, 391867972, 818207493, 20111076, 781475880, 477057761, 992948148, 316038780, 933197720, 311646452, 698316712, 712677621, 837403768, 122874067, 939289464, 293823438, 171644354, 951874570, 178576799, 487162616, 789012756, 583686683, 774510201, 296501658, 234447072, 746651834, 166667902, 739406040, 975740190, 369044731, 68949222, 946873209, 324904654, 340782524, 610705652, 966071587, 483510033, 429280614, 596623988, 664416599, 926713432, 287968442, 104346557, 615275428, 989703277, 201384737, 917465775, 79868317, 829968607, 81852161, 814836740, 121296967, 923583332, 710961770, 495668974, 455745885, 219780985, 950718627, 984300813, 527020017, 88834241, 805682275, 619986977, 611833272, 322079014, 210833552, 314323375, 369923096, 131979437, 437146888, 704736140, 326315631, 672104362, 821578188, 724737017, 973115851, 42116217, 840717108, 115328822, 797262707, 856142463, 312317437, 702270080, 713647600, 305006552, 306361410, 128677363, 278471444, 581918897, 450283182, 264987145, 100617385, 295085982, 263149400, 11658329, 312920501, 681733207, 216082101, 480180843, 705967025, 154913484, 979706240, 139161308, 576925464, 809226694, 346864965, 780479787, 599578644, 374165014, 803152361, 919639500, 215045193, 675059182, 667866703, 796548524, 352764229, 156520642, 19415425, 69969928, 38873642, 581265201, 626545472, 116400149, 996040957, 166254730, 778443152, 525696401, 702194601, 421274797, 934389192, 479047096, 507914288, 532456969, 183054670, 535745216, 73354207, 121058473, 185905907, 997052595, 478865038, 444715345, 596142765, 906800978, 913742315, 67715138, 831535434, 909340504, 212259513, 23071846, 352986989, 217946011, 69340819, 829025842, 319145815, 596122609, 98331157, 195679323, 526662183, 348717796, 210709719, 485120682, 324875367, 279365115, 491686964, 494094081, 501383148, 802434737, 136048275, 403135774, 674179198, 12348046, 729686540, 344558353, 592514743, 165763716, 675478523, 20175279, 917089576, 859293445, 723281524, 574849529, 125358414, 486434496, 799394735, 120250622, 736859914, 460048777, 380553141, 259905175, 588212209, 168784380, 992371739, 554309470, 966248666, 414204427, 880980208, 320795525, 740698252, 336172562, 607062620, 289753200, 448447383, 511829276, 955560460, 636554600, 925802015, 419803404, 452101802, 563689640, 556236713, 989081061, 461456590, 546538194, 62822816, 424153344, 136236427, 237867149, 810340348, 777764947, 206253945, 645268957, 88391276, 969690330, 229083143, 380361521, 764486892, 650048771, 283212193, 587187017, 936776024, 163494191, 121173647, 189166557, 173337932, 374151343, 718038108, 997117148, 208828244, 6205433, 815731650, 189719961, 123658620, 115661532, 333422480, 444407344, 617520398, 216438043, 364809286, 457530708, 827052279, 901449210, 177802769, 455130507, 902517659, 61390214, 472966416, 104608837, 759059864, 373122270, 155336521, 664761528, 920672414, 840519372, 884904231, 80441117, 259442106, 509858298, 156858238, 519408479, 556100237, 995055782, 152132011, 161781446, 617864791, 451863264, 960148598, 816736770, 790656867, 290906685, 646279426, 861699288, 901350815, 335269893, 514220735, 717800738, 631516088, 412028099, 143224325, 505256066, 196125404, 734357897, 251562138, 335139174, 391522396, 956719161, 832763470, 394083321, 248339215, 826762888, 864346398, 340818645, 687671775, 933606323, 77015394, 432130306, 796381659, 577059788, 4679256, 911888572, 847096664, 592475336, 805949364, 38613560, 206337830, 383207747, 698906156, 275624435, 717376268, 873530801, 98320231, 399851245, 773839034, 917226792, 257940514, 867418614, 383652692, 195932383, 650905458, 53522377, 966144219, 92662556, 972572305, 213876906, 875289004, 470788933, 312546607, 501720061, 218554928, 952641808, 425726261, 311124899, 299564526, 270433254, 773023353, 709782736, 376463887, 932830126, 897929349, 666523770, 93027503, 290059943, 626472890, 957175999, 582772620, 59420438, 345164585, 269976261, 1018555, 120525858, 886887024, 878766691, 210032007, 881300876, 482812897, 957452354, 193478375, 356573203, 845201196, 819352930, 816378566, 68043235, 731348806, 892934912, 686872082, 753420021, 661213196, 81371305, 540135722, 62189251, 478469139, 93649928, 645086105, 960823590, 543561143, 836749889, 728201581, 90312039, 560852166, 707377549, 802174543, 552726306, 187698850, 922613745, 637676809, 174937591, 96175866, 27750644, 341412725, 416067224, 470580086, 213812431, 658882668, 792511247, 225900430, 799352943, 891891173, 550561837, 44240632, 25843868, 235265662, 23830866, 326759334, 288131627, 91462888, 455578874, 193937506, 152405205, 709001012, 698050589, 185491924, 964829003, 163838652, 38866758, 527346146, 802422934, 390512529, 124268194, 6582928, 511063943, 585005461, 793980381, 73119549, 470597296, 375662513, 106123014, 247087261, 241734255, 335431675, 499481544, 426080302, 566642573, 744313493, 282161515, 77988238, 993637125, 839078412, 492288641, 632699733, 280336570, 291907370, 155206356, 28387040, 67789630, 136464500, 714395910, 325866492, 679538015, 91714477, 54368733, 655371043, 270737900, 487815968, 379401670, 852951510, 774475864, 234190199, 670121001, 796120732, 865581740, 90861427, 584886500, 553354586, 932856455, 205819742, 426437880, 871666550, 379386615, 8830303, 162442568, 304313376, 172690209, 691807361, 907061334, 577064495, 593186694, 318852799, 574372142, 90180532, 226411213, 598361000, 399564813, 601755596, 752710344, 865965697, 780981868, 828379694, 630707066, 891143019, 591838463, 439729162, 196018431, 6959468, 564249649, 444420551, 65442827, 818286961, 976803446, 374392073, 140650501, 581047341, 489937282, 702195196, 780719147, 853121728, 202213222, 436121691, 793095008, 984878926, 798514459, 727466356, 105044733, 59197257, 28712937, 772969365, 906713155, 396674879, 549303647, 890922227, 813063155, 720907353, 441043773, 90628843, 391923871, 430599454, 568998268, 793499562, 563798478, 753053119, 117714216, 31749367, 503247882, 271311184, 279911436, 390379638, 834596542, 317770542, 42941581, 361502851, 725799414, 118393006, 675362717, 651457566, 912580396, 358583331, 40906793, 305887693, 546879982, 730606836, 347555072, 592475585, 888430909, 131263831, 206018790, 787509842, 68082822, 495625561, 850535256, 829291466, 182940510, 45968323, 26176127, 91489912, 776084455, 118132774, 23101584, 592753888, 894920192, 383315390, 912455884, 525054399, 138604829, 677666478, 247199404, 43205492, 123667349, 195460235, 969105583, 858810044, 116619531, 94017256, 758072671, 196886746, 154289138, 607802339, 421568175, 5392383, 91400372, 108001163, 371036987, 307609127, 43215305, 372651471, 511256875, 396927662, 594839854, 297620676, 439919885, 290275041, 352461601, 952250009, 623207465, 850685032, 150614466, 98967418, 708593629, 128684701, 5606603, 120619559, 231496244, 811305838, 300697154, 662058, 149146447, 648447847, 807035528, 267740567, 196151081, 710478223, 871469088, 279318814, 533187187, 557857614, 502487146, 174865684, 399727654, 550502821, 855176701, 916307220, 259632324, 774614707, 457413183, 781653957, 303762047, 753177454, 654378331, 456271819, 218075055, 968839388, 662509020, 218232039, 370426044, 241239901, 837879136, 458938435, 846651054, 407210683, 700235907, 196007062, 825917610, 358676180, 314060389, 433459228, 285008929, 294247740, 57699235, 318682376, 661092246, 846826335, 891747048, 972837684, 195398509, 458471828, 638486477, 587492457, 392934426, 670145093, 367082123, 303579892, 587409590, 367871209, 487101033, 648496882, 649066910, 127591853, 971647819, 359769211, 667856717, 563923094, 273965097, 375808430, 764146873, 619527090, 569498808, 185691934, 201096024, 533321913, 155732167, 773746770, 829525200, 12704995, 324036646, 519135377, 218759573, 851211328, 972653591, 860432388, 341073787, 682321552, 874816717, 474241532, 741707949, 698767573, 665450439, 314318819, 543025726, 671360259, 343429482, 374205649, 66280333, 417174827, 66733627, 34402780, 827627515, 622610078, 468527659, 608522576, 553829909, 81142438, 350440224, 600804587, 291652375, 719447607, 667014106, 484366927, 9832563, 289040403, 955812336, 184870454, 962995234, 681863091, 930555095, 438546657, 186611733, 263791856, 134924568, 916498230, 609915058, 921144623, 57768779, 540171059, 405181060, 845157368, 883042092, 730200495, 846252703, 102729796, 486140864, 42447510, 163255333, 654856308, 917003722, 403006961, 503858815, 538599290, 675934636, 936111909, 976418568, 200362306, 611539664, 39070953, 738462202, 743875722, 241859874, 86435041, 757793426, 982402508, 488240430, 482842128, 243714532, 416876628, 314576054, 41010666, 418953234, 294359027, 207616777, 26788133, 665404921, 767796171, 524913770, 366098380, 377805212, 481939401, 528554373, 869677543, 553512815, 616041375, 396458470, 550688074, 568267372, 713549012, 386417663, 340123730, 379004262, 356059942, 226294874, 851798200, 360515710, 915401661, 154489727, 331290182, 537142736, 724635893, 764936566, 36867064, 486991815, 732159684, 480819820, 317156030, 414819963, 10016064, 284570321, 73473225, 149060841, 867013019, 742192556, 462441031, 984065928, 761948115, 319198395, 984219625, 39225119, 543631175, 606085594, 776068222, 357970662, 982389708, 527391514, 925697961, 632909341, 641384538, 90181203, 470964050, 208080834, 953965170, 335975073, 894853448, 551653016, 437086748, 351605762, 626452027, 31621754, 195073886, 225758913, 618296343, 55102818, 334278314, 7917897, 538106521, 287729755, 383082035, 206212480, 462575901, 220507873, 252604834, 721432937, 191134678, 436018837, 790009747, 515250124, 920092289, 19503635, 923443136, 495220738, 296949612, 499502416, 529587784, 588190820, 380734938, 7673109, 353822881, 617294784, 990877302, 365741249, 767116027, 975108080, 113666952, 583716893, 218327265, 19853496, 582026769, 809194827, 428202960, 389018100, 763957594, 110451641, 52901237, 298601510, 483326178, 229895715, 800796509, 341330265, 180134857, 922125075, 22222695, 398709893, 947604247, 295610348, 712174446, 105664902, 683496116, 826689277, 618879679, 57596535, 376548683, 353121407, 961604189, 673926525, 577964494, 48000897, 365127944, 620334038, 326710914, 668792661, 901298634, 822488650, 794946355, 429411583, 910362980, 228958156, 452191162, 636364310, 879875554, 808140056, 237246168, 198997819, 367495508, 548807281, 972544801, 249580346, 684235576, 212463328, 923846095, 561953842, 405337479, 881571243, 668877112, 16660947, 226244183, 376959597, 893298186, 449289764, 191318581, 80957429, 33511474, 675842242, 996241835, 952632695, 919670753, 175269708, 601647580, 592320107, 479414408, 902981250, 591930367, 144311335, 580886039, 973499131, 130107036, 492784579, 489121401, 629273101, 983902159, 489008324, 811265436, 597599805, 238761746, 444007418, 969747416, 864733530, 433182420, 483637295, 73498815, 626196120, 129041756, 880471100, 480680984, 586519419, 459369412, 521041404, 777648634, 117751318, 163997202, 667041785, 297989835, 710370803, 94561169, 381711416, 317266594, 774390056, 914744581, 883002584, 491893296, 833386647, 838281323, 949308724, 372811195, 116808615, 402242444, 179912794, 145706194, 701575475, 106692995, 776417674, 314294528, 679173257, 631593114, 224987625, 465722210, 985425561, 796824345, 857440220, 461821714, 953176833, 828541700, 796940027, 135498339, 605623037, 656854369, 444065039, 396458514, 171258516, 556031370, 469741682, 7397230, 4219904, 351475805, 789146615, 236364028, 843756364, 74443189, 179770669, 397624158, 742603231, 889495339, 201427596, 5327477, 745894600, 63996448, 253135428, 846989016, 790300779, 951732393, 915915804, 175927359, 906336756, 123797243, 245447158, 452585175, 547053068, 347968338, 909229602, 185582117, 820371683, 916446643, 711914451, 687446554, 49897982, 730651734, 563153769, 870096154, 558074612, 859661960, 194444350, 876941697, 347945894, 202454467, 855635230, 950871654, 273766173, 866743283, 595629952, 980743066, 181203002, 582264567, 548478633, 255199325, 170671284, 185398562, 453345284, 512336371, 86183090, 738548395, 70766412, 870043105, 867550859, 166077018, 917620517, 517787900, 724080071, 762764487, 31997107, 789546888, 447833651, 588435600, 367234626, 182184899, 470464761, 160659203, 359936480, 45083361, 641578289, 180387523, 440660628, 151494036, 556293303, 226497298, 334408873, 907172166, 828509239, 297236443, 41296330, 540675921, 159535303, 131730619, 782233904, 411700535, 476409781, 498490620, 890145264, 317753981, 22970112, 885527673, 264046689, 57178584, 694014832, 198128186, 30695887, 811926600, 28774880, 580359712, 57043878, 409829884, 46124248, 847810066, 515881569, 643844292, 377165565, 22948327, 976482811, 660656499, 200887910, 387864455, 933607765, 902422673, 281539824, 272625510, 860430362, 977121259, 73096174, 620593897, 185657507, 988445606, 741203806, 635719818, 575357481, 576720582, 349859154, 985534735, 521907350, 646671393, 249517211, 930094002, 297514818, 661265136, 980285616, 461842141, 939580308, 339047235, 809090028, 628256057, 279489132, 901888856, 112971530, 374521482, 613954060, 561894501, 856248154, 894977908, 847033127, 354125631, 409771776, 228625693, 296629132, 8117768, 104282401, 678572599, 839387840, 486450280, 456039268, 71739024, 464140687, 644358671, 927239779, 475176379, 681482526, 961758881, 377356443, 501026596, 202898036, 510585546, 169072035, 83937670, 4595799, 977964674, 126513318, 406698925, 330831011, 176312697, 132085104, 482965805, 810260854, 881697755, 309990223, 99632950, 272228587, 872366526, 125603819, 2742574, 225607444, 23145879, 94490556, 787042847, 52851301, 862809997, 792699737, 108522160, 20942442, 306428892, 163104000, 4661450, 338723835, 100777029, 504728952, 925632455, 883092859, 862522080, 728745911, 821042410, 113748306, 423043218, 985481976, 474969036, 278306531, 816497211, 135757576, 926325856, 15041179, 797017291, 723675866, 221956385, 996164513, 192846703, 856619905, 530157886, 845110458, 54259074, 270342140, 34870765, 40664998, 510098287, 252829193, 840010128, 559609517, 761978436, 848942762, 698897065, 297576479, 275509301, 132725015, 600053994, 260477123, 447920643, 33550505, 335402271, 419804315, 466274013, 106546213, 7529163, 388615235, 749221967, 426031085, 519230967, 514739233, 954877551, 584844218, 774420370, 447252620, 870440162, 677523067, 601455663, 391840327, 88471678, 161008517, 780156447, 336952090, 336628184, 337283056, 653724324, 563139167, 588273541, 406658416, 482502685, 372362244, 256223426, 409359964, 296581178, 802182322, 408385770, 134752209, 651496078, 534625947, 816432599, 757926787, 405859894, 688369059, 762657910, 632568526, 393604446, 715925460, 685022046, 676682167, 133285741, 31454709, 105260765, 287929372, 98767480, 474406154, 635822053, 247729182, 916745539, 24831511, 753266867, 920549734, 285459780, 583757843, 845683549, 618965195, 268000951, 471387087, 801385687, 124190190, 446238836, 510866529, 885039959, 835214864, 671631057, 289633712, 659502431, 676978182, 605938497, 699221668, 292094042, 66522209, 826123030, 96440501, 693020866, 617453224, 109434966, 145491868, 245859268, 125711799, 241558474, 969680759, 288181130, 359344248, 643998815, 437012749, 196646952, 987454187, 284591148, 617953402, 724809160, 950475454, 164004520, 53163086, 631914509, 203019362, 680012499, 486116711, 327398822, 344669571, 322455415, 440257485, 219210613, 613098551, 733114827, 966845655, 368150981, 472997049, 832746053, 314709901, 356848495, 45310103, 11495101, 116088379, 750915118, 602441172, 242201815, 729091162, 112834686, 250321012, 294799336, 772171979, 552616743, 928700273, 292461327, 130709905, 982619242, 104156562, 601703329, 124541087, 970144206, 197792046, 884361342, 452832993, 169537468, 219593812, 501728297, 491597095, 929434050, 130867816, 201257434, 894556046, 483482374, 32883887, 139366535, 737617356, 688953550, 671592528, 641385013, 584531965, 900399981, 125681137, 233394656, 274536766, 595881705, 409942393, 192621321, 491564440, 797220862, 382783583, 234278869, 36553456, 940891120, 36819341, 527113079, 858562935, 205433759, 123048110, 600826128, 859411036, 448907849, 670831254, 176251243, 532097284, 59616782, 900539634, 889977413, 647181117, 898018787, 924494055, 890289457, 110219462, 225516025, 921200494, 182512810, 785871351, 316394213, 227596901, 808554732, 71703732, 69148396, 626726128, 1798557, 933857878, 607006426, 748999151, 4321383, 305760124, 804705132, 767288300, 678052927, 553284908, 573663636, 741777042, 165267129, 903839259, 120447644, 217925224, 52430468, 740552407, 930473456, 845426805, 520508704, 628541459, 318569498, 839059096, 868280752, 423943197, 817389675, 469595531, 223080730, 666219349, 665722186, 448499114, 303451800, 972154163, 972479279, 678565303, 653835275, 640398416, 813677280, 954211185, 559012781, 958919332, 286088331, 625048582, 514708691, 552455713, 309227984, 873292082, 114684743, 334211309, 499050015, 296956512, 184988105, 687088582, 234856724, 430227954, 134682257, 228872474, 848097322, 826822322, 109860416, 422221014, 988852142, 483716959, 235292441, 243600819, 488760846, 271992603, 740334265, 244268581, 691407980, 838137667, 202956240, 505962167, 850324694, 3349762, 553301611, 505254221, 722324538, 78601730, 569969653, 277259333, 285499814, 837051945, 216699390, 637406658, 376208177, 367570998, 413661212, 645496411, 458415977, 482192890, 880342763, 206999997, 414982358, 275223772, 50155015, 259469436, 426621261, 336326639, 291023206, 143926585, 225946478, 765965796, 236336601, 389694926, 381127283, 774151632, 588500792, 849457117, 243390443, 130827739, 356763102, 824771450, 87030658, 986917369, 439029920, 237808951, 621182029, 910314896, 905883793, 873682096, 19242787, 640826214, 205896220, 458974965, 395028511, 539442647, 873332839, 717461274, 781828381, 26428472, 21153563, 420663862, 275239080, 913751720, 281420450, 574323149, 748010259, 300004029, 983578714, 289425554, 223677541, 696847298, 174736207, 357746892, 293586102, 798679170, 80489296, 49203521, 444606354, 517579096, 890362, 540864560, 97303844, 83003913, 437918731, 686557714, 427765563, 404571157, 583356583, 121767329, 307250834, 67730423, 114378140, 667581224, 770549951, 389737291, 395690499, 839999034, 787109808, 585220517, 391274859, 666248469, 747717465, 183465755, 225113917, 600005044, 342415898, 966510085, 614913071, 705767272, 451448482, 30344064, 780733398, 105792361, 414472504, 760140901, 840536392, 40085320, 818321515, 50397349, 955004606, 507217007, 101988130, 488607273, 593449019, 66371307, 253091136, 348929162, 955489919, 285918813, 282975631, 658595287, 409231728, 58037122, 675011486, 127180205, 670699126, 947041699, 194080518, 693189736, 185250129, 334071912, 967392144, 65493604, 928764664, 303252248, 954365315, 572010347, 576359153, 391222567, 802902666, 758911763, 392617843, 86039599, 802781024, 693493902, 981122953, 213813093, 641777514, 501284357, 723199664, 727339629, 477367497, 759729243, 146747192, 444717074, 973569123, 19756226, 223381607, 565488572, 604843051, 154805992, 215198352, 773212449, 930572549, 545061838, 467941895, 521336076, 701466521, 697073507, 957819095, 409120419, 53759854, 281513048, 733266615, 4910806, 40910833, 944652834, 978605087, 825052224, 918531286, 713061914, 785066264, 56390282, 360426274, 373349386, 981069491, 524326342, 394247191, 98960435, 878347566, 711292623, 782691781, 236419327, 681126817, 814341160, 551714376, 909167471, 326292833, 716967455, 101698517, 472856111, 111247948, 839616281, 159523398, 630298072, 127990918, 891226469, 971800985, 132449749, 840029759, 269039752, 913908785, 236184071, 730409819, 559948447, 476590933, 461326704, 221151854, 572741138, 83477005, 670353105, 682806114, 907596298, 632771854, 603302546, 32886548, 910657183, 174170901, 718136293, 992008755, 855045301, 911149995, 595985489, 307714586, 296666108, 620953656, 553545282, 44215538, 764289353, 437869353, 652565133, 548776981, 624371928, 304510727, 735348659, 764989076, 703715115, 454303815, 199832372, 289464370, 46548203, 381115850, 482409240, 35978902, 149164644, 868889705, 264799525, 565771304, 812999009, 469411215, 809816419, 160437232, 637526657, 384578962, 679566640, 564663216, 504588511, 865925422, 29587467, 950408418, 409742411, 695690912, 150455994, 796945065, 537295991, 464160776, 28958948, 505090176, 746323068, 469127001, 536821268, 482649347, 416632822, 62791056, 895752106, 854181370, 791644428, 79841183, 856344430, 826254587, 226385028, 418438653, 67917395, 345845848, 292174679, 986006583, 559425015, 367531302, 860971582, 790650748, 49317265, 380665090, 710847768, 288004331, 838059416, 896196119, 459404025, 164319372, 572560578, 5943830, 49485371, 843705200, 499364473, 218905253, 414167994, 605172940, 49228608, 917072389, 632896329, 971409546, 981969270, 498936392, 771327816, 729453855, 953617847, 933845562, 783027208, 278727887, 704623467, 873295439, 479398287, 876634917, 808110052, 703418274, 416676476, 314518350, 990561521, 852347051, 431994872, 461307215, 541707199, 740515128, 493976775, 725182566, 936649233, 958352979, 634429020, 685685747, 791104406, 34382681, 196538391, 973234092, 351650745, 345889621, 86410884, 352313118, 606676155, 679874097, 730936564, 201986400, 871906801, 927518447, 750256044, 570391195, 105667717, 654128049, 885222156, 687684113, 341940086, 316855415, 735760478, 705600508, 637894636, 210879259, 769822496, 119103462, 550539254, 333340353, 725845607, 174681440, 433247493, 638557674, 887099369, 652481864, 95646192, 360268839, 15955113, 923175130, 181935554, 505088335, 16491360, 603147841, 9288260, 821797539, 300312201, 722923897, 890432301, 137284260, 691741435, 149706566, 691511572, 769116979, 61969019, 460078229, 630549663, 694316263, 319662608, 104562049, 461081254, 386100012, 661128038, 908213403, 48041314, 661208216, 986587935, 134675772, 530728656, 828820069, 179027029, 279018548, 97640576, 983059275, 340252855, 624689365, 503055932, 973129303, 528637317, 421095680, 278295349, 642041209, 939021899, 390274696, 322290460, 860438092, 112738244, 762205294, 555726569, 268052326, 203216584, 669205560, 556306054, 749735574, 344580910, 505501134, 262766513, 835048030, 943446984, 90828088, 536857971, 423194284, 67833057, 525100934, 79960703, 389503131, 338483308, 491745598, 377048760, 956591711, 485672305, 184248167, 414036985, 342422481, 128634550, 826732250, 342904711, 821432949, 410408595, 923145832, 808419766, 820746292, 123056101, 159409537, 540184669, 943230537, 555799281, 710852613, 787672388, 817950462, 492171118, 221902451, 344133191, 466564251, 194397658, 904997399, 144217127, 806127641, 833805314, 948393596, 606334435, 538629988, 909469702, 76036661, 749349291, 263522953, 854480219, 134694354, 291331006, 752579238, 29062063, 371960640, 394687799, 322649177, 651352068, 37732590, 888157838, 319910846, 771517761, 643885115, 458942439, 695343007, 398758037, 621110599, 309804837, 238673791, 856255292, 345941426, 208013511, 592503474, 902772098, 358282202, 642853710, 467250413, 612289238, 301552794, 154222321, 95093949, 195130427, 50523602, 943070449, 217020775, 358374187, 133557566, 738068678, 539039130, 565556441, 555412908, 338843807, 439613602, 202812134, 885993412, 595877238, 278231593, 997838, 500187968, 166595810, 638586893, 515812053, 188300332, 855229899, 871528443, 130886270, 116518331, 849864864, 965131394, 798553897, 331847007, 994952886, 421995641, 476623065, 480669366, 82358760, 78036479, 402781168, 380932997, 169670953, 519363053, 566001954, 581995171, 241622037, 157648577, 965441588, 612135753, 780178461, 599726211, 459326904, 915836690, 602779896, 112140350, 456423045, 349782424, 736444539, 119661560, 222143840, 684482421, 998291294, 165298808, 770169259, 954108310, 231252306, 737301406, 57848756, 360225415, 345911722, 543698896, 157852617, 490650056, 431049609, 911560495, 825096320, 675745013, 859162873, 198529891, 912320941, 690359806, 363237608, 691321816, 105982303, 125197319, 862436071, 139152477, 725459976, 921033438, 432298987, 772879296, 225212789, 20950410, 613513404, 432368867, 209738028, 291782599, 875176014, 804438598, 390691163, 239875313, 98760622, 551975745, 532697518, 105056754, 349776781, 781700800, 659111405, 814575300, 743404864, 739079188, 514699840, 804143217, 45364360, 334740023, 978979622, 950136967, 899594829, 336901138, 336203818, 543201571, 140780247, 151744781, 945649362, 617217204, 630735148, 727586314, 490507323, 237734096, 498903434, 599979152, 282346108, 828288270, 985293504, 764253930, 887694761, 118217935, 211875695, 234251843, 10846381, 471783375, 383902524, 185004101, 638933348, 20677419, 46314637, 411553130, 816224774, 575512227, 357724543, 290333190, 721525481, 902516420, 694694770, 967814971, 286034969, 841975341, 354070098, 912516618, 818681805, 478964684, 558919400, 439700605, 832116761, 78545697, 809688127, 221307383, 762900447, 321893098, 994657298, 24050401, 115333034, 948004637, 226522466, 421146368, 938428405, 856962571, 457512206, 298795358, 705814317, 747074629, 21228376, 110677274, 746741180, 738116987, 806559158, 232329030, 643051145, 907336445, 274744220, 837532937, 447079665, 662686619, 259318725, 799138610, 485997987, 660217053, 933255629, 8341985, 691637318, 680174990, 28286320, 277199968, 957597187, 503674190, 355678435, 583150280, 578488888, 173050782, 356160870, 272766889, 788769798, 613874650, 181071525, 768227955, 613620265, 844399132, 651441904, 745499022, 389402757, 34287391, 87573708, 425450813, 373817438, 559397340, 798025027, 663884874, 870941742, 376060394, 818874591, 987521105, 456322473, 337465632, 536426008, 646094503, 279024863, 202786552, 928973838, 587162111, 8429221, 647637822, 424699661, 589632519, 760543189, 48252634, 370554614, 291807795, 304007348, 137676343, 821940483, 810829822, 513664098, 555492136, 512338234, 990397981, 560797927, 565239395, 715639866, 91524072, 405465832, 488492651, 441539634, 72145902, 289681499, 859694498, 242113879, 38886684, 283735977, 683663134, 799659506, 835436816, 110595009, 314122949, 903760102, 22067498, 206763432, 562060807, 106396445, 295499436, 613840029, 466551265, 346002768, 680924679, 258012048, 816645268, 275254233, 585483240, 149682394, 755818049, 328914047, 221499693, 707575074, 587765055, 369437643, 58085309, 593478057, 917168857, 235122881, 721189667, 868451074, 674181995, 204318573, 971631273, 587639507, 454333542, 114537172, 874288176, 629309547, 945749805, 825754442, 877899969, 844743981, 486077053, 247134248, 904109391, 594232523, 607330933, 60748620, 14406065, 5566852, 22239358, 407190185, 923881596, 180113533, 835639918, 50470171, 54440417, 647176874, 610242836, 691984243, 266176250, 824068704, 821982808, 698217839, 225370685, 63518883, 952146662, 19657490, 419932757, 571220793, 900836556, 861589379, 476021213, 965793140, 797555721, 116457912, 293261432, 197817137, 534155213, 490447102, 733809577, 77844804, 171381719, 260601824, 928527557, 244247797, 820553431, 204773163, 52360176, 101972413, 171360852, 867606768, 82165652, 526387722, 985631026, 290106072, 759855402, 807110527, 317674205, 881674003, 423856579, 848029640, 972866653, 136334119, 136559370, 188463765, 768932210, 603127921, 613174942, 106678716, 514669162, 193243324, 806673394, 595212036, 806269040, 376718278, 157047787, 77613923, 152364447, 884126242, 175918582, 47349028, 59724266, 546964648, 57920770, 11649154, 307161174, 800271947, 959775225, 720039586, 870406532, 146826486, 426961609, 177195848, 804487503, 516748787, 244954215, 35709188, 490776006, 150915680, 213367083, 721368191, 774135925, 260685473, 220104800, 472708911, 135714188, 383187876, 53833603, 524432219, 80006580, 480410995, 148044318, 680693558, 8586433, 253248078, 457890364, 766940868, 257725607, 548957002, 716719887, 810811760, 671524251, 202386948, 88833046, 150519682, 922953352, 347813392, 435240347, 202587742, 93839713, 13389153, 57678313, 564720428, 183038246, 564132429, 704467733, 355476753, 908141745, 449078475, 918688047, 975332906, 593670707, 307076699, 85209204, 390017776, 959132141, 473579778, 562671400, 893081691, 79445535, 230027991, 719671494, 965579250, 875102964, 856907308, 658983928, 683474607, 55860287, 253074879, 18195435, 557051844, 271769533, 242428763, 966472315, 221773383, 10187325, 994326022, 924088331, 280164032, 549775492, 220695223, 5935796, 98245626, 653694498, 299877552, 12730345, 782156317, 174715576, 568102857, 177580844, 637450897, 824093476, 482727698, 847740988, 336609075, 621795591, 384674326, 136859435, 674358444, 476540217, 971275049, 99492352, 427427542, 937202132, 422252832, 146785784, 67535817, 383910161, 491480272, 254011856, 436333050, 82755129, 117154447, 385082049, 136271296, 988748912, 546611964, 383804073, 887131933, 45151721, 380189921, 932472524, 277011637, 716469536, 680991030, 269679694, 991258949, 176615894, 17848481, 435140172, 260254920, 230403270, 806470406, 39772746, 938738535, 257921557, 492540317, 82245532, 759057151, 14149720, 395216121, 437347485, 311507049, 882587167, 647949106, 574911325, 741818117, 369680553, 665518829, 160771262, 669326095, 63223708, 608628001, 612850383, 90694529, 708243723, 543995122, 9209906, 262325093, 137157594, 42555553, 291935867, 414567606, 227175997, 100458958, 203757346, 504846195, 360363930, 151027964, 630675399, 634851570, 201821330, 123277950, 434756967, 747547905, 416867089, 882307725, 583599663, 475878034, 994058731, 546231854, 457192237, 983414512, 669069375, 855001571, 936106192, 326052715, 946808357, 754699321, 390765667, 840326069, 108869970, 127026639, 692234220, 650050779, 95759900, 293574388, 570782694, 526935413, 648999508, 754311583, 214199957, 744028519, 2304376, 726168141, 475541854, 102287863, 969256118, 506518449, 75577967, 554455292, 503034289, 589589630, 861881821, 657012121, 514592576, 583460693, 378698819, 36028169, 691386015, 265052856, 104135172, 509562845, 89207967, 892482165, 565132366, 732971426, 403600249, 313473211, 232142287, 909328457, 774539011, 796340021, 420162188, 27699558, 945769706, 521386974, 699084015, 569844064, 32195462, 145197302, 642453169, 468493954, 445520908, 651461231, 458248100, 584757412, 334213607, 292159922, 725233185, 492984528, 101991714, 627240544, 766905790, 146068322, 559799179, 950266577, 926894461, 856201297, 886963573, 273745742, 467524539, 576441682, 880914033, 948626084, 427053829, 65258471, 137685114, 362760266, 860803823, 642320900, 931925641, 859753493, 428283504, 112458531, 903321851, 85650061, 735776755, 269406872, 309530367, 340617417, 114380725, 707953050, 760009743, 530671511, 473515676, 95600707, 525392749, 985865135, 638182885, 829854427, 366370253, 362202081, 55235577, 465415577, 169378517, 818087595, 441592080, 258366899, 513898218, 245121834, 68184269, 115224273, 787290003, 159580737, 869537237, 898236406, 892347526, 970367335, 899698428, 984744348, 657152235, 7363587, 515271277, 484200785, 532555829, 275278136, 116324293, 749936481, 124127560, 353605246, 46370184, 63202707, 370889449, 379511661, 501921903, 868416257, 506782284, 912390534, 884795451, 636230636, 678356308, 103644459, 348294591, 543320365, 242767690, 149479300, 195946807, 745323443, 7216518, 851283052, 366804198, 368974071, 705562967, 153518813, 114926258, 648364568, 583506564, 298330907, 181180761, 702721907, 137851351, 710263543, 69354365, 705882748, 220923563, 974896599, 738566654, 639989257, 955948129, 140850334, 214033467, 820952564, 416419010, 847052002, 669903894, 163740643, 349551190, 174248521, 213665898, 523284567, 924303256, 853386511, 60184732, 445178658, 567731729, 534390462, 561520004, 979769005, 932171805, 773097747, 34357031, 316403543, 417081338, 735412862, 199082204, 581426460, 979360032, 715187034, 233068558, 83943100, 683759560, 130228751, 766964379, 879425989, 653869498, 528901189, 107368811, 59425738, 229922493, 892495044, 498236613, 18143948, 92660556, 975641339, 115068012, 855953476, 298126797, 257684600, 77169612, 499521751, 478895060, 264222632, 466122319, 433211568, 293168106, 496419801, 549051806, 409281199, 170688542, 156880158, 766590699, 661521286, 803283306, 745217998, 403863913, 943107221, 617760209, 795309020, 720875721, 872589730, 729839916, 740205226, 327454719, 202358411, 668662336, 855501028, 974178232, 924855711, 323003065, 395950820, 70049937, 944279318, 235055303, 554134171, 83735568, 292011708, 49387106, 318167373, 688151010, 34949517, 824242771, 845060380, 570343917, 759083058, 707538060, 884743745, 189323169, 210819071, 885590227, 968142327, 538390328, 35635346, 325658756, 467180583, 825985223, 63249766, 731693602, 776634886, 700332387, 324859279, 330340226, 301799609, 424276967, 38788988, 634717331, 213422863, 869285908, 771772551, 424447633, 686834388, 192793150, 110427689, 421066872, 209456923, 554077108, 35853865, 271088511, 950328874, 184829257, 390325820, 872071978, 98916136, 81552763, 574089113, 277857582, 732168773, 454410956, 454538162, 455351644, 236144580, 1659457, 176675623, 820912686, 640242954, 818779024, 371952997, 392898626, 91028079, 567123672, 256269082, 61820401, 258716796, 555378281, 126265018, 469487830, 435339616, 768075780, 70968156, 876105811, 371183512, 500151502, 324546295, 47778727, 50337072, 442679933, 474472837, 690074591, 927272434, 228427782, 364528393, 637423291, 980089571, 583276353, 695690639, 558185162, 560321472, 112244078, 392865247, 706516733, 1656220, 301376287, 205462660, 130598688, 760877984, 220368876, 217919318, 951648062, 645909697, 17474576, 689710760, 890362596, 375205433, 376192839, 132528688, 461951919, 757104989, 724473182, 201776532, 789325430, 464557449, 659250166, 333513947, 966993822, 881263999, 815291444, 913592750, 709679605, 748796784, 82829789, 981770720, 542796769, 871137420, 770133026, 667621315, 439574751, 211609952, 15849313, 14928787, 36810430, 643974683, 854599615, 841687364, 785968862, 468125314, 910138025, 892694944, 499313696, 762698695, 714442871, 595664782, 682265691, 141930260, 525223351, 66393620, 614553709, 883345846, 392703851, 254444664, 225232690, 959942403, 562830936, 539060386, 912544770, 570022475, 700253021, 788937068, 325693846, 72504614, 443153637, 179828399, 875025950, 899201023, 694724759, 500370607, 935451366, 671149078, 611126471, 726211252, 545326521, 487370688, 624871720, 827046844, 524705311, 892501857, 230433073, 827208306, 594136075, 538403061, 899292747, 414664621, 311041070, 340742686, 253240631, 493936611, 675345380, 874560121, 85315334, 932527581, 352039737, 241189109, 525908691, 872543759, 545989814, 50022275, 541296573, 477173609, 115364959, 231054863, 319870221, 292449731, 131150743, 44932674, 915181829, 921158680, 693286406, 93385091, 322058882, 830883148, 588227288, 947429181, 588548669, 626359636, 286039825, 749479910, 208508512, 806448281, 333900185, 471427354, 395658046, 780062248, 472008926, 610397618, 229806023, 374426893, 935282657, 462577939, 329384861, 388572206, 497670248, 848225897, 547428468, 881782401, 824764778, 247550611, 653416322, 382089272, 708622038, 515799440, 341910432, 783560193, 801958685, 260277932, 734225484, 58571710, 968234331, 950679564, 40882327, 18013510, 350684687, 304793769, 535542062, 102905832, 979203410, 945585518, 363959263, 957699593, 59995644, 411531503, 888266082, 229699695, 466385135, 573259930, 371575018, 74383622, 902184992, 550715783, 288073628, 421047061, 151886996, 250283484, 820218107, 766390764, 885829088, 634266381, 455238864, 637366487, 176686085, 540812841, 328968709, 176004607, 231899726, 206072983, 900738122, 138638097, 622907281, 591976426, 787117516, 535145501, 575444631, 27725670, 807880621, 469439073, 668587202, 166149648, 223411827, 378963165, 304550695, 123260375, 418491674, 922956338, 343027861, 536631160, 749228358, 207932264, 158016901, 705971590, 444177388, 726613016, 784131472, 116679968, 938414849, 16367477, 839745756, 407845471, 106695849, 593878176, 97356939, 314893976, 2846514, 968268488, 522628479, 64377992, 621618561, 855274227, 734763803, 767151458, 670815194, 42029422, 258588342, 170603394, 81700595, 978778015, 992081609, 57464663, 177126987, 776135248, 865631391, 593617203, 851523444, 773824165, 530510106, 779469747, 498707049, 119433100, 137352230, 44216490, 286785875, 71504542, 580360531, 975455207, 468408904, 405568612, 694527315, 898360512, 149935983, 449108722, 427355409, 327962366, 489937337, 693436784, 333433819, 719297385, 769490185, 776200899, 934956318, 158569034, 253020288, 609106240, 732846629, 84663874, 471371648, 720382108, 958998990, 507723267, 419829295, 80225311, 487150532, 950738926, 3430117, 516585994, 29142767, 643058330, 186998545, 535575652, 448191150, 121286426, 399645281, 599765259, 307308142, 986804728, 560757730, 87236170, 312320140, 139438494, 232692573, 917688073, 921790919, 643384352, 546527237, 579090022, 672527305, 712905698, 30052355, 628967414, 482379736, 193719946, 112832345, 243505395, 358504750, 24075559, 99548599, 758350951, 40489715, 587020259, 711902830, 121622733, 991181638, 633322347, 448098176, 351872113, 620258171, 941019160, 91161752, 884770882, 302263958, 691741439, 255440173, 266519561, 868695145, 181289207, 884569588, 448753541, 278386382, 284245954, 970953939, 563633677, 508670467, 679989832, 319290798, 11801001, 108017570, 456854893, 266437298, 555669671, 991547963, 532451302, 960551919, 326846073, 456536437, 66276165, 439668258, 985112083, 126179431, 309577683, 419438398, 882987168, 555156767, 958429322, 169054784, 451934911, 539483127, 729069190, 696651651, 860358192, 308747659, 642305120, 458383730, 260510331, 298520398, 270742503, 183716021, 269919265, 337010906, 513430455, 415985173, 631474877, 487506409, 832258382, 544495751, 981544004, 276171933, 576375244, 868544121, 948782522, 133279796, 194472743, 642826463, 942179255, 266807784, 587529394, 901415034, 929267839, 304449273, 735351637, 80090406, 885441773, 172139801, 702067046, 103275760, 237330117, 552583032, 56528879, 808239634, 144966216, 206857902, 290674099, 85742924, 58982834, 796374944, 79731924, 885749807, 262686532, 966719064, 292734274, 881304802, 433235623, 537888688, 954009770, 899203755, 828655006, 776755052, 1640305, 445514844, 375676120, 793014763, 424663698, 714839472, 360245305, 458463238, 390456519, 480695832, 194554506, 797429904, 869196094, 485182581, 672850488, 249054402, 479767955, 710170579, 886252867, 887220724, 554197520, 873243211, 910424585, 47537497, 610349096, 366002715, 802307285, 738538115, 467610997, 423770258, 954644317, 684592324, 705665793, 372926940, 179867106, 183710997, 307119506, 98923337, 433293027, 735926330, 627600774, 670447739, 366627820, 533029743, 764410816, 447078597, 358641666, 733554720, 558429025, 787114366, 584658444, 152806148, 521662336, 495977383, 967533333, 568439445, 77498217, 747986989, 273625379, 389085302, 951879217, 274811098, 271186816, 510690350, 985949637, 59584883, 93444095, 123697588, 219102102, 267447424, 433179110, 828062261, 567270738, 743702449, 385890690, 399356642, 969201907, 99213397, 60979064, 352989121, 145345896, 665062409, 257686693, 595007060, 423396808, 100168047, 920318490, 184347211, 110323543, 57001415, 140938667, 568489613, 335773341, 895372793, 119440823, 995639148, 233013901, 613393549, 543219909, 206936789, 307507512, 275143189, 631854910, 451157202, 957270270, 70784487, 774010358, 973925312, 635786672, 635830223, 475616917, 652204546, 606119472, 482837571, 97510842, 55474597, 506624402, 198119621, 351042923, 668017966, 980428654, 631997552, 778083995, 972609456, 273192073, 921171267, 657034977, 615405942, 970238036, 991519368, 94095573, 698823338, 447845233, 591163093, 571954615, 105215583, 310502912, 77905150, 867750460, 488618652, 967094310, 40464037, 846935141, 941164019, 356102489, 651963731, 6581141, 994354608, 446671283, 822955993, 805366672, 598428618, 145505227, 513553007, 309723983, 165042571, 453054383, 562110516, 875041805, 982455263, 321886292, 883670114, 763242352, 456153066, 472060838, 7694718, 337278401, 491263545, 438924010, 132550381, 894544756, 161497010, 578554682, 776271620, 173693672, 409440823, 383316325, 889960780, 283999912, 299242116, 836119371, 779477969, 952345007, 1822695, 780723747, 713080760, 86048811, 75027027, 833422506, 616533921, 192618947, 477527418, 299937115, 103812986, 417557276, 237446074, 196692687, 331363292, 506577868, 963666839, 842913865, 578674580, 993171949, 920378068, 419746648, 108767772, 987110604, 255783249, 855161158, 937897954, 223684498, 906829785, 751350480, 556616670, 428263000, 187802756, 369535168, 22409050, 608599937, 377348119, 203877753, 498270685, 356016524, 284793323, 379957457, 606398771, 676232392, 951854943, 226056479, 15214552, 129658903, 378507923, 930625094, 548240350, 864966259, 687846877, 417755409, 435326027, 517071990, 515916956, 616943564, 254768048, 460391539, 6864041, 588562541, 355939381, 288970036, 651986402, 41974164, 906744755, 902734476, 112046412, 949955707, 696444998, 187062165, 345795892, 424678796, 340598699, 524948301, 436807114, 531193319, 963470308, 95332154, 678494, 320247713, 521835661, 442933984, 37044894, 93065878, 523214246, 713982384, 386228639, 91100065, 765952518, 291473594, 232666143, 934964327, 175785672, 519728603, 237001126, 389465806, 565507093, 272402094, 261536197, 717387700, 955060270, 297227441, 521334422, 892188165, 715397030, 108225671, 779563045, 980838937, 317390814, 640185686, 910456731, 978920065, 302428314, 807272364, 7396458, 636394723, 146751457, 963430689, 390052477, 564551528, 595326216, 882805077, 788631235, 265080355, 462365221, 493738036, 517694527, 158275312, 366784662, 322554012, 207316595, 744829110, 656852493, 840395999, 281640970, 790180811, 111631846, 240592073, 542908201, 914405062, 212193152, 862381010, 966154767, 139357650, 48306951, 19475070, 49389253, 19206660, 65732259, 463097181, 899369707, 698671060, 995873494, 705849805, 479058271, 447231419, 643086455, 682501270, 119852560, 872845083, 790712417, 143470199, 135706664, 483309646, 363431818, 945740601, 163478453, 141798578, 574538163, 702460667, 877201479, 904778641, 322102672, 932270289, 630042072, 495832682, 693915574, 952125000, 287905787, 304148848, 652946821, 835074170, 561377551, 736168301, 146083540, 376907967, 850298809, 392490909, 151750316, 704579621, 181950923, 180492138, 921061895, 528951091, 168926287, 246855845, 248518134, 135201308, 925979845, 536981869, 930263165, 532242300, 403665954, 141172132, 575348962, 831574975, 969446864, 16108215, 591697570, 978663069, 350410349, 104240580, 612196289, 232106382, 30265274, 418829924, 15271022, 91623646, 828826811, 336660646, 944823689, 814296022, 584524647, 113959689, 592918500, 919925271, 92268890, 136161402, 676893957, 882875255, 687466714, 997404824, 264401395, 251939028, 508283141, 486692434, 963118156, 622941553, 828584826, 560811358, 505098521, 339978712, 72171785, 423118143, 375018048, 51956455, 160255989, 803562895, 596441865, 274530900, 512160471, 94469376, 653871935, 621589351, 551499856, 882319715, 690293583, 386741161, 770347171, 652166950, 440321041, 817756727, 722025010, 243539685, 798193956, 46930266, 793065396, 847129961, 746929258, 861800377, 498695272, 841816455, 116461079, 686325084, 144874362, 953450875, 833900322, 591271968, 395747787, 401686608, 225556733, 516240302, 144979124, 157676674, 607107569, 3432750, 949948017, 745392729, 63542942, 659642152, 25117567, 886711964, 475606311, 91616962, 743467914, 61982482, 690974422, 138278389, 770779882, 388760211, 561617718, 607551183, 814668189, 48811564, 944517479, 751611178, 181188012, 698447667, 921864430, 989393815, 804169204, 886465091, 4387282, 274994456, 716297876, 577037532, 874157217, 774758921, 115555542, 313107152, 733863515, 810029767, 296523874, 870718943, 992647024, 854368664, 255400373, 869503914, 809990388, 224301561, 258867384, 620207327, 884297498, 832671236, 159501282, 332840833, 959969738, 693028047, 967015808, 916676212, 284524462, 532519596, 945768753, 493636490, 362548430, 467642394, 781247093, 224812698, 695422093, 803004582, 995686573, 858884124, 195081841, 371480183, 394169937, 144116012, 711390215, 530670288, 177078281, 881327104, 121433004, 770085133, 153204672, 955231892, 526263573, 839452711, 788134836, 555991436, 329472069, 707560300, 210264620, 805486672, 895831690, 394873045, 392934552, 576923413, 583161310, 570606215, 70503153, 822823210, 665104746, 94920270, 642022586, 513913730, 495235283, 369102101, 609077285, 368221387, 571495548, 35334214, 873274120, 986814245, 856316143, 381252008, 100609334, 689881690, 74604615, 629591717, 325719955, 310872557, 611304417, 726766727, 545721172, 368041401, 88204103, 154737100, 148139423, 470661186, 649853036, 182243513, 74737695, 151355991, 894461051, 29659168, 320651003, 981512410, 314726936, 56144783, 445494332, 153986407, 128926050, 966133246, 950792303, 223656292, 150264472, 641198251, 733866688, 131885652, 353358916, 922048390, 853314598, 668935139, 166639345, 914057094, 349524314, 60462785, 92467363, 837453478, 362631547, 221621319, 423012988, 637028201, 618518387, 738750798, 372154872, 799993132, 415120339, 561383398, 88925474, 820494978, 10899583, 234119662, 345350503, 378467238, 147557989, 424814279, 545713361, 123523479, 289853388, 152830254, 434139310, 400319918, 424557023, 236042522, 954474412, 462994095, 828302752, 581927112, 704542424, 632336669, 858016091, 719659656, 57083315, 504854839, 999804147, 742314772, 982430809, 147753224, 908867605, 652400858, 37544173, 745444242, 907938658, 531312267, 568754806, 368062200, 907359768, 883082959, 198725600, 796810940, 799280573, 679181684, 923917684, 107228158, 35217827, 526309800, 267967457, 127729356, 979658525, 938030672, 293764509, 421772526, 811188271, 920767480, 885135259, 34766920, 917979805, 963194062, 204999334, 924015343, 149114695, 480928707, 239562850, 299527827, 399328486, 302894911, 67580434, 717850837, 747585250, 624346814, 738639410, 991989849, 632673558, 587551502, 378297625, 679613555, 269272833, 687440043, 206438986, 39668953, 196185142, 473507543, 894038368, 508951305, 524045414, 72733531, 245184278, 604661201, 866201575, 411130913, 896203750, 953912436, 427306860, 19866617, 667465041, 260552312, 292019987, 926229608, 26759030, 207070298, 514610940, 166796552, 917714569, 640007719, 272218503, 4597287, 491179699, 906931951, 463091417, 132892671, 85102585, 370579793, 324146645, 361831684, 619476102, 334038744, 983259417, 291301567, 609087148, 398560472, 408818465, 787801656, 586697615, 406360524, 832246073, 523714337, 635510968, 534266701, 373772858, 962299414, 578366985, 815019476, 724021607, 294203763, 364271537, 391174523, 126429611, 285527406, 86821739, 655742104, 265558015, 153546345, 788235956, 490046629, 241181594, 722735463, 803394234, 163808599, 146229773, 227283438, 58867878, 38346869, 329407225, 123651859, 868183109, 414730506, 43879381, 476831716, 428711514, 910284705, 142706388, 196307539, 432632714, 542798442, 877682885, 216328893, 832151080, 319709459, 233765328, 326083365, 163326539, 491059235, 956980624, 611642624, 338076427, 165813792, 561578910, 241721406, 796918389, 244815394, 334672285, 472539996, 898754533, 202444708, 784277526, 278167097, 448200616, 674250306, 724145841, 484699195, 420267206, 150786425, 581293310, 885094717, 414629154, 555275662, 133557870, 377427790, 291098209, 898192025, 823249061, 842842143, 445126544, 397661994, 424963644, 745410415, 508824224, 700595147, 122181631, 787874844, 232980128, 549090463, 149809765, 879631952, 469516616, 620542162, 809442621, 589783613, 421849187, 544625527, 516492741, 33831176, 825491522, 599095260, 40709903, 473332836, 103145381, 207119510, 795027050, 84204844, 39950258, 893090428, 110596398, 114901715, 941632401, 425804493, 472523318, 298550752, 880177501, 12473290, 156208959, 236296481, 266097990, 844039930, 509351427, 302792335, 165374307, 166470241, 265524680, 866115923, 838777377, 707056586, 493203129, 72956163, 55902063, 286040398, 448059451, 621056266, 538082217, 598728978, 319869940, 301912472, 293536909, 233057995, 602703016, 619908138, 267514911, 627152641, 225538197, 754629052, 382315027, 571584223, 641358940, 302247112, 604430680, 749919411, 589925466, 181445279, 534278055, 556553124, 488285658, 200661929, 98342706, 155397252, 9021193, 140458782, 718891510, 367477087, 68376954, 805971623, 858376239, 866185668, 440684837, 973655912, 635919368, 586655668, 833376015, 591519996, 787864799, 964317923, 892487850, 11599050, 801944243, 579172522, 648930516, 178991711, 622467715, 293885626, 871844038, 272721736, 179483051, 442119993, 129700711, 456306043, 482882176, 780089176, 433840362, 670554388, 608732459, 735479003, 575146514, 937742681, 739505228, 348990345, 305334206, 485412220, 762800245, 480697380, 658454823, 923798667, 256970248, 680189068, 37636149, 440938159, 834266444, 95884343, 370360320, 645915211, 454162816, 967392992, 365839982, 903000133, 145765442, 927640532, 638338891, 266441311, 202623879, 793130415, 256894220, 257631253, 457741237, 431727403, 970282182, 897949930, 985300223, 132670971, 331127632, 556209084, 311402446, 501701199, 596407850, 301391186, 192343275, 444894232, 87672957, 165272137, 446226718, 288183703, 514291581, 305974118, 385252367, 349281705, 629808030, 231815123, 11287835, 800692246, 941063064, 959644771, 993982166, 902510165, 433188547, 382307751, 795072631, 76227188, 946719109, 656610378, 363517976, 220647518, 675859711, 618157585, 871741823, 872565625, 618635039, 638594634, 660099276, 453189706, 183872699, 540625816, 439116372, 565707134, 622113578, 774162586, 825907126, 324323272, 388943370, 505606266, 412159469, 735348062, 513483467, 81850395, 512232857, 311450230, 531830771, 974052892, 411227079, 603780940, 373263019, 509218741, 545612908, 886859106, 196977323, 662699448, 302032628, 944564479, 384506444, 488996038, 546116948, 809579210, 995232937, 468270477, 728381769, 82696677, 900453105, 969148145, 454848546, 22883066, 344072144, 965565691, 602901591, 138656677, 327092176, 917342360, 998258752, 373197919, 259326045, 450660759, 994469174, 89599819, 947973068, 670190307, 837160430, 888616978, 285700723, 840693851, 490215546, 297128686, 913445582, 217515222, 244264505, 751395994, 758810134, 915654708, 536099760, 254581020, 624416967, 880232173, 185954925, 543632249, 995469485, 105617258, 597240425, 258241905, 556734907, 984676320, 987356805, 421329825, 599474824, 967360915, 727045330, 181483502, 824614087, 166147642, 293294125, 916824041, 567519903, 785761901, 552464942, 143809581, 789407012, 406787517, 811986331, 209767119, 823222158, 529769634, 873870003, 611798913, 627916917, 366666234, 786893389, 582774405, 731991491, 578758121, 797966041, 975466734, 710296024, 527643379, 720527602, 616917856, 330291796, 282703823, 448804916, 291831906, 452353619, 550375831, 516743368, 593065074, 272899779, 775200403, 606709336, 601193919, 524576405, 918191729, 46274617, 499115412, 927017556, 35132116, 627310871, 758021729, 192199320, 989968870, 942351983, 57074338, 330654830, 206471272, 534303447, 636793561, 452296832, 438276140, 491297770, 329935092, 770202898, 438794124, 1748615, 91392819, 47543183, 453403321, 820904466, 150981415, 301968537, 452701801, 886006434, 475514856, 640602762, 326574615, 72712000, 898377184, 808480662, 774863579, 653684284, 299529130, 127873417, 455034352, 129231090, 977094209, 998044321, 267004815, 400445525, 252342482, 477952781, 368753976, 40659893, 278483676, 785405112, 664426059, 479078933, 864772132, 823099488, 124793523, 250556105, 853613125, 534880591, 435290757, 627123341, 471384628, 252574535, 928561847, 811036158, 886156174, 217573385, 73391910, 5505919, 75425741, 40618093, 252244973, 848502670, 246806849, 808263902, 610362235, 275272001, 996574938, 8946166, 988285147, 2887146, 108115327, 727941921, 518891386, 541950592, 377955623, 283778718, 28361190, 394010463, 440926209, 133271317, 480671549, 347626672, 546604599, 445105024, 381050273, 460113693, 254800761, 383360571, 101159329, 258395720, 175298100, 90532682, 901634580, 682386488, 847459001, 39061628, 213636320, 129840593, 310733600, 930874834, 990327784, 645320437, 488850986, 914826755, 800895225, 895579068, 625563154, 405249289, 806471739, 37214808, 160252333, 837352297, 543644521, 355666544, 653664054, 936372224, 306574863, 154013153, 577540065, 188899322, 691823352, 718113005, 365385828, 266291174, 13858503, 265349436, 530234235, 412231078, 331933624, 375168971, 63666899, 802313416, 527720516, 459587150, 672778956, 301089501, 423081710, 901225090, 593499454, 392334742, 795902287, 689734199, 842275526, 900128484, 211063434, 300347702, 677787197, 248435593, 154416032, 357307746, 394028545, 521016929, 633282185, 170427675, 463820956, 473591409, 195985107, 660297455, 981866028, 575589227, 874467081, 463944015, 897028387, 778746614, 719658636, 288630464, 142828894, 801057459, 184690451, 612379290, 951924032, 521031062, 555609168, 391286282, 75354190, 53974246, 66229650, 112385912, 458952530, 885625171, 23021275, 124176744, 986229494, 76523628, 298757638, 343807058, 863839035, 264530292, 986225908, 876365248, 314758115, 879353321, 547039977, 220052745, 512796213, 722931437, 316794015, 171692649, 842881864, 342236657, 917975472, 882131647, 798465187, 495863907, 809939768, 516760452, 794482617, 494376039, 798044156, 609584441, 838100295, 382666506, 809468425, 364668816, 639698159, 628070617, 180985719, 352514844, 787458800, 515827473, 642325691, 214946426, 709477929, 592445003, 806173107, 446161167, 876013435, 50007548, 297799083, 11908512, 37295296, 717996791, 490767125, 874294893, 498148772, 43362778, 618327620, 38298237, 234337735, 464047536, 184747405, 129420053, 348994397, 477051933, 86383902, 151959423, 340812107, 298676307, 14079519, 699660772, 523479428, 952470170, 125569431, 536237253, 751087842, 608074532, 664524512, 68129372, 9952674, 49873519, 380510512, 203422621, 987072174, 570789444, 182246862, 720492066, 89630060, 301926964, 204684736, 428160456, 837484358, 14802017, 287680419, 842677202, 850589827, 869200526, 574415787, 247704157, 148834752, 66040982, 123877551, 467221399, 695839313, 187814205, 940050030, 650770606, 892883758, 940148431, 546549758, 188653710, 255290844, 373589852, 41231012, 740933796, 461105205, 391277908, 603152949, 270075551, 535898091, 885461344, 356561999, 132291423, 508045646, 780307560, 627122574, 311592502, 975815665, 971798504, 799269356, 229476148, 433929623, 545579048, 520406933, 792285903, 262926647, 868834617, 866327702, 431162924, 430712191, 922931634, 57934821, 56939843, 901697136, 634933538, 435735818, 890779075, 895787103, 740592899, 795718413, 73770894, 411971232, 616779171, 686631320, 17434940, 901082226, 990355630, 26073092, 893290752, 718741982, 15817275, 396159623, 439769192, 536687688, 409041321, 375460237, 726903754, 744583089, 95176535, 271096027, 794708694, 412146867, 962417877, 676618997, 802287983, 314971139, 982995668, 824348349, 972048244, 398007832, 874301221, 417259764, 311844891, 266544947, 584075787, 646931530, 397519138, 769418646, 486765023, 214259652, 425888144, 303576294, 271531483, 601533151, 613339182, 733404296, 9037117, 281688442, 237754585, 224655655, 633105198, 144223196, 132576346, 177602999, 399775620, 11388012, 546557989, 336952206, 448420545, 423168116, 943473857, 552410916, 72685954, 300330885, 290226116, 711962458, 780947784, 821849596, 37340619, 610668379, 384188274, 162832941, 615346970, 983287822, 399999889, 827734067, 600904655, 827182963, 72835723, 1882420, 545429456, 73491434, 114618822, 433267756, 116888631, 589387650, 845301372, 264743483, 625153601, 69944367, 476754039, 92788613, 684096680, 702463541, 795706332, 116976674, 959473333, 978152659, 443230374, 632497579, 848217106, 311570505, 657215954, 694136184, 570011564, 742659393, 221826734, 768384054, 749266861, 529266899, 742761722, 888098930, 792141086, 810344667, 383861085, 541791435, 594637530, 214321276, 6984070, 912973937, 808715057, 761545155, 795428989, 23030397, 429017170, 688580868, 340779581, 182014525, 205130348, 405033927, 875857301, 310859184, 401900222, 351614880, 443651237, 521054434, 711838904, 491484205, 366201873, 545606480, 942126991, 71694912, 21067186, 780789212, 293240400, 620345274, 604082622, 349965163, 765718018, 668186108, 509558467, 513007567, 605441828, 410904600, 90405754, 850707225, 791898558, 549506723, 561456968, 964345611, 616873596, 316829414, 167034092, 960471006, 243921860, 614598432, 60426610, 721470774, 913804889, 636560575, 117160897, 79078865, 506129953, 782962495, 580100759, 183769530, 350907176, 327715291, 772787953, 412679142, 448137890, 969887211, 676345825, 468362466, 457561512, 164637160, 436103656, 466716692, 828382635, 969168693, 189198730, 34098184, 3936758, 681157714, 634728414, 872721254, 19357754, 314547457, 675841139, 904492518, 507740453, 220285964, 182135160, 802458941, 551774821, 625545370, 431876775, 486249991, 100675084, 39329790, 162578671, 983965383, 29880211, 695044460, 808763743, 275758821, 188858033, 700043065, 307968769, 394560728, 59484228, 908746993, 686939191, 269557123, 667157071, 540637765, 928007816, 247782077, 601783824, 44112449, 455801232, 695013943, 694296254, 912364252, 365819073, 959506829, 550247855, 533812956, 527508777, 446235493, 456201014, 104505397, 644669223, 78856818, 2823817, 869569880, 535827997, 287856424, 676223169, 998463186, 232853364, 84877932, 351611229, 870951645, 580869385, 128295189, 665838561, 656999584, 986680065, 663912516, 982237972, 397312061, 334839261, 793560253, 489321895, 673524807, 874975187, 733336535, 10656562, 785979102, 586598088, 401169500, 480047996, 683142738, 488467739, 331800255, 819107208, 308291766, 919263145, 368892775, 702418498, 941156596, 843230716, 168303138, 339200830, 151238269, 293811828, 636546226, 915190445, 520779519, 361500850, 632764460, 961378241, 791689907, 164452298, 952277767, 764566567, 340192460, 967883740, 822832603, 671768829, 470879563, 923413731, 25469199, 395722862, 236615763, 158796580, 253969848, 475790578, 301309177, 213654090, 332021664, 497547795, 437212269, 273358068, 189921272, 916385024, 207310048, 289618102, 60426327, 218231185, 195344930, 720643675, 546482435, 907899725, 351847449, 655873359, 139708810, 696992767, 708644321, 171692055, 881991635, 799665838, 106927263, 647008223, 726201694, 397925443, 191874191, 984364530, 221886364, 556254583, 742728273, 401321467, 214876464, 111009628, 17206575, 125800790, 718917939, 152347749, 670369029, 333297101, 696308007, 288863174, 34517868, 101442393, 992619071, 768161222, 924551465, 950211572, 493114986, 160677183, 211901592, 888750564, 47618918, 213008077, 433645396, 215817435, 392178034, 206054879, 401233372, 155475931, 668611310, 12821259, 463284122, 346230224, 601861501, 58793622, 661529293, 648724007, 614368842, 149991499, 656102564, 672639642, 341567825, 502547036, 304236456, 897374338, 883070938, 428403912, 395261413, 197960785, 129980510, 180010531, 428459985, 716399338, 311689209, 149002891, 572802555, 343489154, 343021814, 898955973, 666543661, 941382000, 818325545, 126481719, 114324926, 982304227, 298783203, 745503651, 86086994, 161986264, 370765615, 698533623, 162726222, 738160, 433263040, 475053811, 310664236, 335411774, 178588684, 223073608, 772885567, 741947484, 12290239, 26253301, 404429884, 598404125, 899949247, 900571022, 32856945, 998378771, 32076170, 958600479, 921129482, 510466177, 646357604, 564420342, 42132468, 224195589, 896221288, 349686319, 954673529, 365360133, 992899817, 487070882, 665646282, 604773642, 1460249, 305550267, 151913172, 800448573, 14036045, 290321947, 72406835, 826003256, 722790567, 152241456, 229143652, 544978378, 315019194, 392159707, 579030142, 505781024, 396742972, 74800308, 199008712, 298603643, 688307947, 586591358, 150633435, 403114930, 47947623, 446769450, 176238795, 655817105, 499348563, 444935006, 788678218, 662967083, 490996986, 251842920, 943590129, 179630074, 854523420, 644109561, 527176433, 183772572, 304044887, 899887787, 540756633, 781006572, 600559505, 424861304, 804667207, 209414697, 737701331, 503556648, 906817629, 708922232, 541901006, 219625270, 309847175, 973405048, 195108353, 211013935, 740946229, 554436000, 288766619, 116581453, 99091325, 634095317, 743289980, 363307103, 767602166, 78846441, 949331330, 776849247, 346677500, 339483782, 757233173, 531334873, 248098655, 74848433, 787281203, 483042081, 108785200, 14219189, 467252231, 598123755, 584137330, 618786693, 76122061, 280267310, 53597258, 50433, 654872353, 903418784, 766408580, 928366249, 901395623, 253894243, 883034621, 615278209, 133688832, 421993531, 999018179, 149193276, 67638395, 410232611, 442958617, 785534753, 77637401, 230040367, 479898234, 592610609, 396099784, 218254833, 35755201, 331498140, 217067918, 835130370, 193482687, 880456923, 404852749, 195940842, 493339561, 922818668, 820949284, 737475283, 128041611, 103211608, 270139456, 14657653, 379386365, 374941182, 500435173, 78007237, 472931379, 82973594, 671761292, 70693774, 376850305, 105767505, 304037986, 682672402, 131354088, 174391381, 980423116, 91125335, 443242881, 305949450, 880410432, 292589045, 331332955, 619290473, 291590523, 423541466, 362100794, 736900387, 996613634, 115860406, 535466247, 965948402, 637207533, 933530493, 774421891, 801250329, 661513075, 759458728, 371670755, 286000082, 886156773, 795134825, 219369784, 819246072, 346580453, 944022174, 300419973, 192416786, 994106014, 358001539, 520636341, 123761905, 617317945, 931184747, 794536486, 136865201, 920340874, 580998900, 912869313, 870758940, 29992511, 129485203, 326484779, 964556322, 798926643, 342241933, 534966597, 124463606, 440725577, 773725945, 760332137, 733795198, 957475303, 924525101, 603629045, 54918110, 883432961, 39902531, 631827353, 671016870, 375508762, 271911117, 508465664, 569131029, 799070652, 409156375, 960015883, 777650744, 332839557, 243917160, 694670980, 211898915, 903705106, 218469681, 375559666, 324848344, 702507170, 691176882, 363229748, 198457096, 546393996, 885361019, 609200056, 625961947, 685921736, 279682649, 686726864, 505113256, 408516041, 148329846, 165978143, 138414547, 69655709, 586375818, 887197533, 676359569, 497595236, 904006824, 358498106, 516998418, 935561268, 639818292, 375938374, 277095901, 375995861, 17005462, 40445699, 856273067, 93498457, 346598611, 577731049, 64583873, 994212105, 659663450, 595891342, 844431411, 663309197, 637968806, 174483447, 513380276, 290946521, 438382391, 814999036, 239155666, 610362153, 790519741, 577287939, 639331173, 944621688, 726768070, 239255543, 338682043, 768088012, 607063683, 665298424, 368576887, 572801090, 335807413, 426584624, 435773950, 910730713, 305467628, 648849761, 678709970, 626490891, 464200164, 70741406, 796058874, 824884178, 738293702, 679344135, 63326532, 273896295, 356762371, 377311173, 280646572, 483266298, 752554585, 213947707, 657309684, 64911532, 954620878, 811473857, 213983233, 77482118, 99628467, 899493599, 575879863, 605679706, 662625655, 69729878, 129229421, 452111255, 281007894, 313549087, 273788629, 108674048, 75959654, 879478982, 519650375, 615372462, 139655937, 918360455, 146960176, 791588028, 910399417, 415392346, 359736088, 255086754, 283480667, 410732249, 895110302, 911459787, 919933740, 65431407, 403073541, 430036526, 905790089, 79396407, 682499236, 167154571, 607000550, 804016076, 625519789, 928047637, 936532140, 901643602, 26720944, 676613180, 471436224, 49933686, 297324987, 233956336, 22129611, 794780607, 918537993, 523751141, 938579852, 376957581, 611406753, 477927167, 222696332, 271305893, 441693984, 143029511, 810972822, 276750446, 321055159, 344401480, 448742598, 619688596, 343080708, 339181696, 294737224, 463973433, 960057776, 269592995, 507248204, 76571901, 178750008, 864340241, 574898443, 483960010, 289954778, 497838627, 853955021, 748445065, 569820404, 543330594, 208672938, 422070037, 748509560, 519151625, 17385087, 719120883, 652821490, 931902317, 838515551, 741547470, 289317732, 275068783, 441468735, 93846130, 693527201, 497714943, 373257452, 194090028, 674883654, 669929382, 136719254, 733851459, 946640749, 154276204, 626140289, 50971535, 146593409, 847125238, 13552481, 264244105, 90694158, 654490466, 280889241, 201016917, 903650490, 295188707, 309426262, 638636276, 396325123, 962520707, 923345196, 822841181, 380769599, 455961062, 999725331, 636192306, 199402403, 827671442, 673041276, 842922546, 237433195, 104761135, 223271237, 638587592, 188038520, 797837043, 847627243, 533043627, 489754229, 716453475, 525611192, 989919750, 95325611, 955172076, 101616556, 429510399, 388871883, 19586955, 571647659, 125797802, 293410195, 159716827, 198461715, 635370187, 930424018, 991799994, 241644123, 412298026, 132276558, 376286947, 205156727, 80558342, 44829025, 951931587, 958770975, 489470582, 531873901, 988387269, 310182346, 61474329, 980863399, 685534612, 692584015, 765445331, 863290921, 454516435, 224011572, 721585223, 908660042, 105470106, 68514893, 463351585, 261646247, 278292638, 204380228, 551615909, 674839502, 241970704, 581101112, 293935148, 434447651, 988896418, 569242090, 764709062, 315320549, 437659134, 783709708, 127704439, 716388362, 211326767, 333938654, 541168286, 685541654, 370393190, 255725586, 8893496, 62872005, 847342482, 551774194, 683354662, 66553395, 156459029, 172397137, 168906778, 583568339, 462724340, 536287852, 331989100, 634625191, 49228659, 680208548, 887978957, 951239241, 510596860, 999158628, 460738144, 530634364, 38982663, 651011682, 835827155, 421319911, 303065814, 832916271, 6050587, 13846289, 712448018, 823916272, 98777961, 291839000, 422147718, 653444134, 761849787, 517575219, 419449888, 323095579, 400554889, 177396677, 517415247, 241120896, 511433096, 959880267, 629126861, 338640531, 408131218, 81177141, 909485691, 700667988, 926702780, 115795199, 720522834, 180094153, 38782772, 384881592, 12511436, 311219493, 672282046, 621007104, 166741549, 952644572, 24913865, 682716803, 149062035, 462340922, 199075798, 26804309, 767075080, 105418231, 913943459, 667230213, 856665141, 227727181, 322745531, 544268719, 70979046, 269768693, 561155050, 697603842, 728329100, 12110230, 87901922, 794481070, 371949680, 349557075, 414028142, 554644361, 525459991, 10118179, 218996193, 550753069, 68690847, 405786394, 590623793, 690281826, 299624392, 641476728, 186062903, 427876269, 556699292, 90827153, 254529764, 76448192, 58626746, 894784969, 237502058, 414914067, 846908037, 410315037, 28142863, 31329956, 801845595, 754702154, 376178684, 628207947, 381382525, 447251018, 284405322, 271062214, 56133800, 292013256, 682170452, 738165855, 858787481, 855357450, 416860527, 364340461, 184541618, 561022938, 252951136, 267572225, 460694378, 875575753, 753493851, 258450717, 597519669, 700612851, 601158630, 916438192, 641077486, 656423550, 22252651, 226087878, 131260791, 240906970, 317045123, 119723954, 166098720, 195992370, 444903541, 437897218, 44827118, 716118441, 381948945, 761209146, 443227941, 486623214, 611834393, 332447121, 228493287, 973806621, 819904428, 511521344, 881948390, 131923683, 209379351, 505052162, 266036243, 166592801, 712178986, 736268010, 653308054, 262084944, 821885157, 666673440, 713641571, 627266225, 112471364, 209371879, 804741543, 744361944, 132630387, 95221373, 271849332, 987035534, 967444465, 67982162, 795081122, 918827024, 941028497, 182381077, 864339740, 910768127, 286630749, 863465483, 845974014, 862540317, 118138316, 355834318, 206765204, 771898792, 411476977, 235176627, 780530546, 258158566, 159330900, 990454778, 716420018, 663935911, 57813671, 524698374, 558699861, 880785065, 347731648, 902335221, 837214244, 673860608, 86688260, 410732329, 555069253, 377140157, 819287456, 751106451, 795847026, 372882617, 197127629, 240630482, 268067386, 532016953, 357585902, 153314804, 767981330, 965579128, 67237623, 677531904, 738594042, 405583994, 500379918, 598998450, 492452769, 354614282, 663594202, 575652612, 981469393, 682922365, 284528613, 845172222, 514513371, 441257139, 606497071, 644581541, 127103713, 297081306, 986034290, 626976914, 87079739, 858680296, 517661094, 899445476, 451119850, 840949042, 98162062, 631766070, 883402986, 755621240, 897651921, 253753529, 547515114, 728526342, 36610742, 729900816, 870512987, 642388420, 696443642, 841631900, 280402127, 881318253, 546709055, 741269194, 839050921, 286673707, 380998572, 577533871, 899041661, 658902204, 553494749, 917849700, 301043018, 416835579, 188084781, 333184088, 83782853, 74959928, 550593416, 410435428, 423228123, 620186139, 405336576, 398136752, 238786087, 123026884, 452546620, 482232435, 627808545, 208023342, 698724327, 419858151, 367093967, 162366386, 415665732, 968454208, 105905229, 573220847, 900967457, 134537768, 561394427, 107955419, 325372000, 195523567, 205661693, 87640724, 928588384, 444596737, 883012296, 497195069, 191417356, 219372579, 838174267, 673340110, 160680407, 714183442, 663325544, 946232681, 761246386, 141615665, 632009517, 635405561, 255739305, 270583368, 6944142, 681557621, 573870163, 414443635, 208372401, 298441957, 269170877, 561364130, 87721945, 693421826, 252275985, 174708161, 469653640, 430923183, 441083119, 945533193, 402908285, 560287630, 454874936, 217653437, 293468427, 461873338, 88216183, 334312852, 899278308, 337485539, 396731771, 610455615, 860801047, 945183959, 961273306, 583788079, 531335757, 639198311, 142805099, 909879525, 56684068, 972955898, 383010318, 607567242, 893686454, 189610923, 535372950, 894081626, 495055506, 650907982, 817658155, 349254229, 34198369, 735451633, 134110135, 989271421, 827903203, 902380669, 547880057, 750107407, 298153804, 882615383, 914483754, 66332731, 640587755, 81591074, 842616307, 444203697, 200761439, 45314613, 726515575, 316054017, 66256224, 956210915, 979747849, 929468409, 918759870, 665054446, 806990525, 74142709, 346278783, 92644597, 269590534, 120429939, 434396313, 902231352, 843156542, 781832105, 415341446, 839467572, 733530776, 587179384, 743508669, 567105516, 999697132, 627628762, 925188168, 72476184, 624152952, 177522627, 717418657, 443193142, 645850974, 798532585, 258106406, 322208100, 730161695, 480612445, 551451680, 66338743, 253996567, 14591279, 768096111, 679621195, 944344902, 127556130, 397322805, 308251137, 825763326, 62690554, 394306103, 565840757, 585417733, 978146697, 51323027, 897146886, 680298996, 743211814, 425890723, 986045401, 79385801, 800607579, 590046893, 918530227, 880214361, 248008268, 136451223, 414462709, 106246156, 760339822, 222763663, 412206048, 548964361, 734455910, 512053442, 357198455, 145185777, 496233824, 585730543, 827546901, 652452552, 664339678, 653544641, 896606895, 424508389, 10467801, 985880238, 175410638, 574536484, 596291562, 651437510, 983078692, 326565071, 113996189, 847860218, 423716923, 627642701, 365351782, 226428374, 932169939, 960210570, 421739310, 28770625, 454406572, 805715140, 803571613, 238256145, 148728136, 9282402, 456072206, 66415103, 624613891, 656039714, 462014960, 250177827, 475493920, 231780914, 818210545, 478591414, 115545679, 771692702, 796758438, 327752691, 859037348, 270791036, 605897851, 52048956, 420854182, 261797950, 714169887, 950807361, 627195349, 68060776, 631753392, 230170385, 955831605, 328152179, 729762500, 310387070, 437654612, 566094822, 97911755, 44859308, 968631313, 684461643, 531398224, 919544240, 710886735, 493679247, 723002848, 723869410, 648725168, 749146416, 409447894, 165318127, 991963035, 96180763, 331647014, 154600813, 292849511, 105580956, 90291943, 959698216, 409913325, 997919630, 480800483, 749015222, 546388853, 617986451, 57793326, 586572287, 576968617, 117965959, 630201430, 382825744, 799344490, 85723407, 560855590, 234226442, 416339500, 621822316, 619723654, 812202653, 568010177, 647993810, 674848194, 713444706, 466517203, 857780345, 155927926, 229949410, 814423837, 763805298, 928479430, 364541547, 668404485, 483509723, 923225243, 332916744, 346868506, 370905457, 774757, 738749918, 489737661, 280927732, 180909091, 78465236, 109782126, 902887017, 339849969, 129463468, 51499631, 187508184, 449199152, 794989349, 577005586, 284508908, 939624244, 26757668, 703439159, 81678396, 358808565, 296162318, 137613777, 288382971, 148855372, 998848209, 227235588, 387021303, 280472482, 354506741, 580729944, 382917430, 830110564, 729092905, 121585280, 769147090, 592813374, 584912320, 317255748, 179163968, 51686420, 25027308, 934512264, 161702098, 443793277, 967184172, 250632330, 724825868, 955516663, 607872580, 831652022, 997584260, 667329734, 229629883, 696949903, 148841464, 373969723, 191661210, 865002772, 632493178, 377069407, 489176238, 139321969, 471667631, 679936205, 294692109, 484684200, 236848339, 445290650, 21481850, 478704493, 815328488, 961342637, 779085658, 871205853, 600448913, 964124785, 308879408, 436286816, 503197179, 154573994, 333199332, 932684795, 430299443, 831797701, 133853473, 79805511, 2957623, 533579579, 271696463, 460394083, 38245317, 755041915, 279505932, 861229958, 85755052, 678943403, 84921958, 348882605, 865647289, 269463282, 865794749, 987761222, 134655446, 562714220, 524563194, 997530874, 713306637, 882457536, 814062791, 572121666, 706300820, 140700616, 243414769, 817553472, 907101496, 291580875, 952428579, 91103102, 150213636, 699057774, 350604182, 950183485, 761756574, 304011818, 282055193, 909849605, 772751748, 478045714, 434939564, 829572665, 458015878, 605528600, 858087874, 939452883, 257000464, 929155288, 716382514, 267639922, 860640687, 919680395, 891680002, 646593821, 700755280, 169813518, 705567982, 89040041, 377190611, 712577161, 59977817, 843854663, 920294646, 919699024, 405836113, 421616541, 152360476, 742982875, 246350456, 589119990, 603264725, 432509959, 729412246, 286326821, 348689195, 180320846, 725467912, 593201291, 338795482, 105592593, 577378975, 327127689, 149253668, 573747178, 917142148, 152044372, 165155847, 798956217, 6754372, 635577738, 748828010, 690806017, 630603209, 408538797, 722224080, 407713195, 639059364, 556605569, 528579662, 571309180, 146763969, 141411045, 868095025, 773004146, 264339757, 172535109, 711281046, 455643273, 163397539, 707677818, 262559722, 634759254, 750784854, 281419435, 26689411, 362445558, 347359438, 506588166, 601267926, 272994952, 894590050, 945417765, 805100948, 426291912, 441232638, 178889998, 447167830, 505277314, 82126734, 598175621, 388241784, 815612342, 681593279, 235678354, 987490217, 685662353, 155987852, 665140861, 322746162, 19009625, 582499412, 76943483, 454966841, 351063775, 64378182, 247962183, 923932147, 40712142, 169615885, 251403906, 801152861, 445334835, 715750943, 537800502, 435624035, 553435885, 280275742, 862205554, 714139973, 309008246, 957306054, 913937341, 459807089, 321425787, 14377390, 616524825, 930579681, 186750103, 804193627, 970063341, 314389447, 341502069, 297567414, 539120035, 696618859, 974439982, 278918242, 867329038, 52559546, 407423816, 913320606, 463913781, 869855007, 110328915, 749648578, 352085281, 172110500, 811279626, 707040128, 575291067, 274644773, 421798516, 138055488, 714059631, 358641686, 31108639, 969260200, 76446700, 575986560, 42673169, 507748876, 579493141, 126605704, 475268049, 218975265, 654921667, 380314714, 67210208, 653247289, 687506230, 670131761, 853437425, 932967341, 411773250, 482642928, 347975419, 446417704, 868871362, 633250792, 227558268, 194315109, 902535671, 30753509, 92179937, 315567681, 321612594, 163048023, 843874771, 597368613, 422889911, 597005354, 302373091, 215250205, 350091493, 279311612, 396956662, 49429569, 250530386, 607454801, 805130917, 774415350, 97992021, 757233575, 882160538, 410618725, 844309617, 78595223, 947006516, 142019060, 705312635, 520594591, 551099259, 923516653, 37550014, 685733788, 531091027, 809380809, 172684263, 297424478, 140376136, 831141561, 503969832, 252510512, 768242558, 239550028, 838180278, 351562077, 255946236, 774412537, 617021504, 610600452, 645846334, 408818778, 964620999, 386519924, 632993836, 528967777, 502797743, 125320227, 805100217, 52158745, 773747072, 386202458, 368185807, 418805071, 949877430, 356930419, 232286758, 558453910, 671398524, 517999239, 780067891, 883237774, 545739954, 521801900, 809248199, 92759117, 639360963, 82790783, 308306800, 38804586, 551605660, 670102272, 208747103, 717074191, 663283430, 722890317, 167669664, 329645605, 386517912, 643125445, 575920044, 637390198, 422979317, 884795076, 284626594, 904358884, 578961772, 173429777, 136065688, 274934418, 557860441, 750661134, 781412693, 850166783, 774608855, 748427089, 398827379, 845549541, 820325808, 2226789, 62909618, 998953733, 205562447, 373729232, 79071585, 338593096, 96968858, 921906242, 379335254, 347100638, 327574859, 308987486, 846288825, 938361819, 46395038, 848072685, 754149018, 754540491, 777678312, 719821672, 810822783, 468719333, 63634516, 134133409, 70291646, 820537187, 680787069, 827675381, 697197975, 897044308, 698307109, 531754554, 683290419, 179397544, 731677904, 330925749, 8157117, 28285013, 327037365, 548365871, 258728384, 657911983, 40234074, 191087357, 982131566, 925037681, 122501877, 650583750, 704487043, 102443924, 735044254, 470980629, 380462710, 999883877, 42302898, 428221963, 60347611, 782560468, 508789469, 963864496, 459618518, 821412155, 309057994, 169877025, 506535880, 898907192, 641653419, 683316314, 249270288, 498629971, 992140051, 539938076, 433240106, 713872828, 963050748, 183513846, 803109432, 507946393, 997360019, 514557237, 437013867, 400819643, 199064046, 931268171, 878817652, 976244162, 137169269, 41582229, 68604460, 215777811, 439186676, 264270034, 426871234, 567858329, 634202496, 366698338, 681534882, 444240647, 173503475, 245255096, 688286397, 867368473, 352620196, 559487542, 754688589, 100716715, 130670377, 519767463, 314566772, 721825737, 494415147, 125904272, 276419453, 212443326, 976937967, 848232267, 486580358, 1267188, 25648194, 152759561, 359561042, 435275523, 614304503, 266378064, 467840527, 992307779, 54710807, 537392510, 595264074, 53931630, 961537620, 623307202, 992686224, 101851080, 466322282, 472509403, 888630045, 88687959, 245455745, 512016061, 567274150, 172747548, 346360133, 344635801, 839101778, 444178192, 4089147, 535683133, 18939640, 5944156, 37649656, 32765368, 118628500, 967604727, 980117993, 392946405, 25437039, 790936628, 299616286, 622439695, 843674799, 137132807, 336238236, 679142302, 884674536, 48454099, 393101958, 92890140, 772209115, 622588679, 265052102, 185414425, 710468344, 925327518, 735442391, 81756254, 949274129, 316542632, 933526914, 814693020, 746169328, 181982531, 661367283, 412548749, 58510848, 628400683, 880198061, 762668769, 382798869, 850032108, 974940186, 535948692, 244532371, 711341268, 447476756, 287614802, 745425920, 850214491, 843838776, 116837828, 419625300, 573574933, 456603656, 894793317, 796677215, 705764973, 544195843, 880179797, 824228109, 49960291, 8033149, 777721825, 271070256, 273068264, 962857877, 369677307, 932910095, 359677510, 968307817, 280065628, 43937824, 403605157, 899029341, 909415293, 242320298, 42675820, 551101890, 758458401, 971417456, 190712577, 85763875, 529020233, 475790964, 883415585, 95603245, 318469004, 326190724, 216259953, 606175591, 975032174, 158869010, 179809632, 704482650, 387077311, 283721354, 642503493, 496738351, 685725232, 898946261, 895952948, 762311312, 591710471, 418266692, 477312469, 70269443, 315919320, 526407959, 69504653, 384620325, 134652964, 886367240, 678237263, 183751003, 104056683, 851864103, 697017852, 693953719, 823419602, 284892206, 472177537, 172338323, 220228366, 713569920, 673711039, 424792902, 326909035, 302321676, 427180305, 752117612, 398675927, 911194088, 849579946, 739089049, 100103658, 955260157, 455617476, 833399280, 356541714, 297494720, 177306634, 308670162, 840110387, 765265191, 562835024, 563701408, 220239031, 508318138, 984108008, 267366748, 154335048, 578964149, 545238924, 951239811, 74039892, 41761631, 937372982, 357488840, 884977611, 417002054, 262360122, 772946159, 204337807, 933137264, 940374513, 108266547, 161712833, 21565623, 754803658, 722047499, 24856871, 527957006, 652489221, 301795836, 638348436, 505515470, 136400270, 7825719, 424818704, 728530348, 3918746, 652020228, 395157712, 183345232, 434228075, 122776053, 809444195, 568921018, 229148055, 3794360, 332391099, 376888270, 843758646, 756574889, 956727274, 347244236, 460031958, 235526834, 501010012, 452049755, 796697191, 39993632, 200085860, 391336282, 564388645, 878761098, 646485694, 559306039, 486593022, 734488323, 271725095, 649935731, 502638493, 585141357, 431533539, 818358988, 112465967, 475052963, 639482296, 636827380, 591562546, 332442755, 565884375, 272301432, 706362725, 617583500, 894091145, 856179598, 367537659, 841868645, 772467206, 463599641, 417376085, 199793494, 877890560, 915056365, 293867980, 835450061, 408836177, 282842870, 569080421, 468779871, 237570213, 934730525, 31496661, 456253720, 819428001, 407910862, 795238055, 771853039, 819094260, 511963906, 212044599, 485424020, 982088783, 123678139, 780392891, 753200084, 886860467, 547284180, 376489740, 234141859, 611810609, 656872892, 626862667, 295863221, 236407562, 794563586, 235595227, 729367261, 437834339, 437878807, 398679578, 532893469, 972077256, 209933414, 986081511, 346570550, 16887397, 298825433, 465372864, 111056826, 96876125, 9616377, 699442048, 297867513, 277029844, 952517377, 160544736, 203699047, 771851693, 885381977, 907906432, 41249757, 795741555, 835742937, 299252276, 505428819, 560202665, 89008875, 385752820, 50071706, 379944283, 198474893, 389239260, 515380930, 354958816, 41096645, 991510957, 624104295, 450888115, 57629690, 432469322, 449464908, 414914728, 64482356, 609534715, 835114429, 65397407, 314763470, 329636356, 35476120, 129608659, 552071642, 958225085, 323529430, 663448890, 851733307, 340284441, 410497834, 269086015, 481353075, 574180822, 769390164, 794914927, 781851403, 464708377, 715819678, 879230467, 881216330, 179238768, 472202015, 999000204, 864361807, 825363064, 316240152, 894191647, 974800777, 150860257, 148566195, 263965760, 327097434, 850321194, 99049824, 171326415, 911694197, 696580859, 353768809, 856147500, 304338549, 791429399, 94413519, 253083284, 65521456, 718755077, 565436199, 968894712, 509421111, 250891651, 800248467, 914230417, 459864213, 227712505, 598271784, 854577442, 227819992, 892123268, 219904581, 753881229, 6549793, 127969386, 268526011, 886462322, 426264002, 864716833, 381078960, 111614585, 287952285, 406408088, 451062905, 274114415, 347442750, 86541392, 858380272, 438882019, 421064572, 694523443, 507653283, 197960078, 87794470, 728135046, 680529235, 265492588, 535978045, 308955329, 85627505, 143101359, 796036420, 497452618, 415954954, 469729651, 672435903, 212753415, 607118028, 779480490, 171653969, 388376476, 581147172, 564328704, 189424118, 878805981, 569816190, 703863027, 875316553, 571075059, 967382113, 972144669, 50047324, 934044852, 579976680, 697751379, 366246321, 518281121, 149783808, 593297274, 295249702, 363776328, 596237094, 806952148, 660668629, 931798720, 26395663, 297376574, 296373375, 88444158, 851885674, 860151960, 584187081, 515713301, 626649266, 320097361, 9614131, 619161021, 270193559, 816289673, 436246887, 470115533, 633769965, 986412584, 751944881, 498608747, 715877049, 429642453, 130856640, 745131855, 150074628, 85982726, 486123260, 154575457, 455125319, 862871719, 724897306, 867730828, 128278357, 550255358, 617378919, 743597693, 684003992, 196682027, 915239089, 227179257, 788108747, 3571899, 277014626, 688464054, 369086131, 334451819, 793389349, 621435851, 408747446, 616964253, 383587708, 883193988, 1123183, 554111185, 532731235, 584501813, 414659259, 680515974, 134436327, 780941494, 502296804, 355174404, 214012622, 864390546, 775527180, 677709926, 887989611, 288814048, 67447220, 541438088, 14411424, 309828136, 730809202, 748229115, 501346224, 646098576, 608646261, 349811892, 565579750, 602775133, 99631783, 218921770, 995806781, 408783900, 804727842, 848915411, 154349963, 568731860, 397200824, 800370906, 469426062, 727644688, 304258901, 466941386, 556856025, 465266282, 276348011, 226420400, 685088354, 569882528, 410036164, 153200331, 720410890, 283582842, 410491908, 355604228, 137833499, 24308355, 724172696, 22620618, 590707438, 213167788, 588972955, 794398213, 312169768, 249957053, 95942801, 664080226, 811684589, 622000326, 447799848, 202674552, 214735186, 329113125, 997285222, 547010096, 677960511, 906645064, 919735440, 272200399, 363126867, 480481012, 285785711, 134012151, 144376510, 971086017, 154031215, 40464026, 652439668, 337360049, 248837160, 795383977, 424262258, 900293157, 986697570, 373262585, 794480290, 52400997, 648265437, 96196394, 63381398, 268358370, 85492495, 102159894, 955724891, 106868005, 655863468, 65734366, 152202448, 515496534, 441215846, 582442314, 157210512, 681004420, 157811659, 427563536, 901211481, 171029700, 898970412, 75770440, 354104895, 586971377, 86218221, 886609507, 100093062, 67482854, 489560206, 33496659, 635779978, 605998081, 915756909, 57768915, 439044954, 432337777, 114458886, 279061481, 741451809, 543919207, 204494946, 169354229, 693731920, 202206562, 74320726, 898391780, 455584595, 422818864, 919186486, 420827606, 493278672, 258547600, 526940063, 62588912, 883104876, 619800099, 31796507, 287923246, 208278315, 673850985, 526219511, 52666544, 366403791, 114617634, 993018813, 812549199, 988068556, 421044703, 107194387, 562102257, 685757969, 725541261, 683238443, 228025421, 54928069, 716616699, 861313271, 50903863, 437114093, 155344622, 921992003, 859815180, 246572704, 180737386, 149931888, 526269890, 134282010, 93224319, 979166109, 720281486, 499182947, 489168581, 433577038, 120801732, 483815410, 14833913, 626617936, 897804914, 801744981, 691346886, 280606835, 926559175, 601113551, 695812435, 598692813, 869203682, 969241779, 982550861, 567005832, 222387548, 821356180, 863639158, 109418514, 22530277, 421695699, 345462376, 638866688, 927500296, 182164032, 894339136, 733216953, 839566659, 41381720, 75642676, 396771986, 638488606, 806513623, 996431246, 296248124, 833559763, 285862439, 644206173, 869624830, 599709409, 917282337, 180185219, 86036131, 250510045, 244299078, 618023531, 963661621, 544666575, 518781856, 695498983, 323880189, 494266375, 164874342, 75809794, 922877456, 654478827, 392187569, 155288086, 544089849, 462091105, 698332048, 692415319, 79979586, 856387342, 66741421, 263370733, 719096636, 280938548, 565021149, 726747173, 885553939, 543224617, 493599536, 743793576, 247279136, 724943779, 171637256, 412260593, 722848013, 334784177, 311554450, 342143255, 374900955, 364729940, 7203908, 754046039, 488012192, 880457951, 513726520, 673237266, 230532038, 779101867, 868494497, 37247431, 147879020, 15640825, 90537158, 744377654, 111585423, 634628906, 303348504, 420375855, 825724330, 544994670, 147669783, 608199267, 902285748, 616738943, 835514266, 702460595, 464522922, 440164101, 875337077, 284063469, 422041753, 631516957, 515020451, 856728432, 685816269, 381300511, 94041857, 125340166, 499468761, 57979926, 923109699, 14000930, 634699583, 839107601, 27158058, 402334539, 624987067, 91531497, 94069438, 713664746, 930986381, 353545137, 702855844, 779370139, 552861663, 919184986, 523429652, 179136934, 277547561, 128588729, 816866211, 867993943, 175996664, 198361767, 306534287, 250141888, 83674692, 784207865, 871164706, 85291116, 556174042, 816260868, 490355595, 361148402, 705794788, 515229151, 626749515, 813950379, 342696567, 671813416, 290917409, 870041164, 916762062, 657852034, 781473021, 891049045, 864547830, 125563609, 9298256, 921484864, 27059916, 519659623, 900132480, 728916772, 665677844, 580187951, 134736029, 941502153, 643818825, 937355340, 474338695, 874782009, 432455104, 408663663, 44499553, 260969857, 753562714, 797043843, 289847273, 944961666, 806385224, 642572747, 844594414, 41500171, 551889431, 65573978, 924429782, 779477821, 495509485, 295330584, 27550671, 15122757, 4292631, 663445141, 149423922, 58886008, 971235360, 722337327, 869618787, 762281453, 493302176, 388180012, 79731287, 750579360, 916145956, 787214552, 217914062, 209624473, 450606758, 194795548, 503760779, 100741620, 608411245, 603376445, 838638985, 876371923, 639296303, 781730795, 672109053, 53537371, 411568445, 524417518, 457911631, 64725062, 303719928, 375883124, 994178740, 900747922, 114862163, 333356973, 728908347, 800994810, 336270117, 641246680, 768166341, 831748064, 895649861, 657530045, 695065858, 648617820, 371371211, 976388625, 687934547, 185973637, 520461947, 292864376, 850482963, 590963530, 878222281, 731768744, 184295216, 836771801, 221312218, 908849240, 726560386, 918743838, 988783325, 766810216, 514144979, 167957706, 408693655, 372190291, 697922887, 22337770, 806274108, 635308776, 989501188, 150349237, 578624490, 525073972, 516785914, 47128492, 616496432, 298349115, 53211954, 525213458, 589347190, 364711339, 214060624, 761766600, 413326963, 231652671, 934537904, 262895798, 99662886, 477903394, 199688112, 261113148, 978032911, 26868463, 915715766, 988649394, 306279836, 57098167, 464199917, 538515386, 24179666, 298872736, 911310958, 717680215, 276048073, 290134283, 669168552, 887044417, 636175611, 969092596, 65010028, 416014470, 248042900, 533959769, 987439083, 529174942, 495985635, 586439145, 363338199, 559711601, 538065186, 745464163, 257836812, 432646759, 57897921, 693175613, 808132743, 723697401, 230262787, 731170379, 699853154, 414914646, 175720896, 880317470, 796086404, 991240440, 485859834, 615451537, 334306707, 309024936, 757521731, 105987454, 358287938, 600556844, 885128137, 994669289, 772179496, 192183848, 333965219, 330065682, 61770227, 162707211, 20536545, 218945039, 683674818, 166630640, 829252116, 2845299, 789140902, 67324773, 384149000, 401060540, 402194662, 601508083, 170922107, 204391990, 926126267, 266636192, 135400116, 469972821, 875403171, 316058802, 54767569, 392657547, 197440991, 308274489, 954028476, 913850660, 105464907, 368287590, 273068162, 922487413, 35175674, 637470740, 317840204, 819775906, 745913217, 113102443, 400181969, 928895608, 420161816, 576203367, 7537433, 787056926, 569895057, 931840875, 480256840, 2001635, 77502521, 455820789, 609741093, 138877101, 272242438, 843844714, 797770831, 718369554, 134151770, 652302528, 617653434, 88735921, 117855365, 735915569, 365686482, 630804717, 642634588, 681956778, 392181098, 723961220, 21819345, 327425428, 578828071, 949361456, 260128475, 663516064, 786394053, 649871298, 938700278, 754931123, 730565620, 623618724, 726289045, 600340881, 755525705, 799372856, 613248770, 349295813, 557725855, 676878148, 216064521, 555912731, 445251631, 940067215, 317439345, 459579722, 414993277, 560169512, 725709116, 547485775, 814125450, 868227221, 202880215, 39030043, 475314717, 832846163, 194182638, 715185211, 849688326, 908124467, 321623609, 779432888, 496176571, 512210267, 231010967, 442708682, 120989434, 585582571, 145794990, 468996996, 50883604, 559878472, 346345582, 512269370, 970160396, 204312455, 459065748, 766358743, 678478767, 950027195, 604904282, 485349922, 293289445, 980347973, 349644510, 30434396, 92687321, 160025092, 810636066, 219209885, 730216015, 132600979, 381617323, 314360411, 436769423, 285473646, 464550614, 652450631, 449948643, 573390732, 911745867, 272216613, 672472100, 768410078, 534267970, 72048476, 770475751, 433211747, 890090102, 307267877, 469436680, 990039792, 714551475, 65204336, 818244747, 203830082, 980708030, 883038358, 292266880, 953269417, 163343647, 889368892, 121132404, 437112847, 849507005, 222345375, 246192487, 805604607, 814134679, 446905144, 917928689, 110179387, 93573028, 398847030, 399623808, 320612448, 477275905, 422867793, 544831671, 747218670, 858752103, 200209134, 511898040, 369298085, 507467774, 278895307, 896615099, 607881996, 481688354, 396870944, 156375621, 733928944, 122806038, 533667650, 822849389, 609296326, 747501792, 837249601, 159899382, 445041866, 553121693, 737480646, 728044363, 234366860, 718794084, 955038712, 810964193, 887084990, 504056301, 781716317, 734033550, 828197758, 277554439, 636806861, 846659683, 595560902, 735343718, 759967137, 94288568, 756492959, 983327460, 771699537, 664270430, 425165560, 356411160, 406249834, 36173647, 828581152, 371920765, 206277363, 712346503, 83908231, 259022213, 75820249, 21408615, 814616851, 126720838, 44200658, 554847430, 297365937, 786768225, 485583460, 349165201, 797595163, 461058346, 705411798, 651123787, 429400284, 376575912, 715221261, 31514229, 107439317, 471915090, 528247495, 825835953, 681211951, 868796897, 818350590, 652469814, 929493783, 981080253, 665645444, 630244272, 325271539, 296156183, 544172765, 482309481, 644175794, 724527481, 423493406, 750972385, 140898193, 786413728, 542076014, 112863858, 427285081, 713085351, 194661374, 512563035, 705346429, 612954891, 708235775, 379461604, 882583986, 679802618, 276762502, 403047765, 323634852, 21783077, 883909530, 304145393, 237671663, 842550067, 817380601, 165141510, 385204709, 556527271, 376453097, 185282962, 729327287, 675182513, 330388875, 898285851, 38583063, 748125847, 646391791, 459336717, 446648253, 601237180, 221900303, 763042652, 200565368, 98948109, 526976815, 39148750, 18301837, 750990583, 332778544, 384404909, 274004252, 715810491, 189885027, 200146568, 513510180, 947616090, 50911446, 177198116, 844562434, 361275406, 604781995, 275713756, 476717240, 537493560, 711055245, 343035661, 5289471, 712747965, 358820006, 179679415, 596105009, 764711878, 414813217, 156691345, 782762707, 48733515, 374923344, 68713698, 117373383, 554669450, 322987055, 82596896, 699467974, 664262635, 343798701, 960183192, 782824846, 516923083, 814238253, 840984451, 811520499, 488739315, 48336951, 406065966, 953879349, 921704751, 178683246, 688424933, 389887343, 295476263, 841494567, 9313958, 498872628, 415993572, 183759237, 834775102, 283139518, 147888558, 585206120, 617420683, 388773084, 820928328, 985503186, 336707117, 315256320, 242012869, 665481684, 538795364, 73879662, 33446534, 592952870, 314388918, 22996561, 529346578, 856212377, 323575727, 437799841, 905775967, 990761168, 603555051, 910032254, 218825060, 881604863, 555840616, 843661669, 52166175, 373695044, 137340661, 73786154, 982991049, 618588136, 22722811, 288924395, 541971097, 570878151, 983716749, 94769488, 932461477, 250887942, 210384882, 603473067, 214341056, 435340900, 25336267, 554632912, 458961612, 645739416, 394139856, 759522323, 643607543, 409203517, 260759674, 54563540, 578748253, 72878678, 236233678, 536634579, 75679693, 679180232, 630411121, 190750349, 898469653, 896511450, 143302191, 740137064, 251978514, 513057631, 551841299, 480510151, 460717313, 781903942, 429010315, 647291206, 934051996, 737203557, 302339246, 848119084, 199598161, 736806964, 186687173, 458238081, 784045568, 344161506, 532999307, 155093884, 674092678, 464482191, 154689615, 424783303, 952829353, 591903245, 956392250, 356859250, 473432417, 757950955, 103097743, 531768216, 943508160, 403472269, 93904172, 343286679, 371949770, 293182715, 838000023, 989425840, 628153203, 194260185, 879747204, 855681587, 726787018, 323438313, 688803340, 537147825, 105583318, 604541979, 443146298, 510095467, 558547092, 248372187, 720602229, 190862613, 490921691, 765110293, 561791292, 988040351, 824634967, 69875102, 521005739, 158183173, 915752008, 819268807, 753642909, 737930479, 765274285, 570904666, 478192134, 464358388, 99614435, 697795212, 508036432, 827437175, 929381534, 875480118, 536893210, 82513894, 552387617, 436745604, 140269833, 84716332, 444973359, 757731635, 594950568, 972006594, 756533264, 516215222, 77810563, 45418082, 270271885, 533405088, 878900328, 763594796, 818666487, 824604250, 392437583, 813367120, 921353778, 965863912, 502976115, 869809888, 726079363, 846557892, 121036826, 644190533, 522600525, 71894048, 771014147, 870955569, 145546966, 207297596, 513476386, 337575884, 55228075, 357351173, 835538757, 276952566, 104455453, 339198979, 887496746, 723503102, 622048225, 165570298, 499589082, 549526933, 311699518, 925681198, 812468474, 616291542, 910914849, 414274579, 425675202, 612443929, 997402315, 661192814, 622246130, 724198581, 654692914, 517011398, 198559748, 103394238, 655759834, 846254462, 125373939, 185069342, 144446613, 726502457, 730417482, 721590531, 638925057, 291500733, 515065272, 111244578, 596684814, 902673683, 813645225, 466770173, 97121037, 931971607, 219240642, 678766460, 111676956, 284455076, 897536242, 14025872, 899550715, 967561711, 568804483, 533766643, 398559591, 95746477, 622305363, 319693065, 597833089, 396108114, 804027967, 313389189, 928114706, 241983224, 473923526, 636031582, 957832647, 515903713, 66465733, 972942778, 222803863, 31825910, 388216074, 117962347, 295374085, 582410797, 536025957, 974170476, 378879302, 792393976, 960726525, 921906974, 271945679, 568092546, 831010479, 491236618, 767621585, 748228867, 769197762, 294616397, 192728754, 147449336, 976339925, 881672698, 328374036, 759442624, 785522733, 761163175, 666967801, 666669878, 464543559, 739778886, 297146063, 413279133, 165055677, 56314852, 801763066, 107727841, 372699653, 420429543, 519908445, 450936728, 918681023, 990558026, 111135976, 489576081, 928896934, 331058796, 773271178, 150033572, 198995131, 501035118, 444392182, 367316803, 434715646, 627240432, 684016276, 145210290, 412814637, 732557009, 130236232, 589489231, 922145695, 530702606, 887574989, 571561358, 500105646, 209062421, 890591626, 110457941, 213269760, 515916117, 201751830, 382304854, 670153410, 676170898, 98430322, 365215648, 809190601, 823646304, 686652177, 101028255, 937334802, 615655841, 368656965, 385095962, 887201205, 255724044, 466385762, 858537617, 102713510, 450626810, 69206676, 529148628, 878502035, 522448987, 490909602, 985659255, 781819996, 869024002, 627462289, 761584009, 253406949, 514996441, 361671537, 943427948, 845243800, 804430537, 519439175, 942451974, 592737883, 201178705, 527523063, 111261003, 446010705, 277346005, 916361092, 717429757, 452132552, 792496126, 375199045, 53944596, 349967573, 406330895, 137641134, 986179139, 48491375, 575804434, 937413000, 753590296, 920309953, 428178271, 420045813, 62391509, 706702139, 809295852, 471577460, 729630378, 624254295, 767129094, 807611863, 15264258, 175372113, 424716015, 475169348, 805780030, 575692469, 780503100, 383868716, 514152599, 443628965, 394381965, 218069882, 258534345, 810031256, 813158705, 528442462, 588208269, 11799850, 835352496, 768278457, 772393884, 648316779, 419640838, 655640766, 50798315, 333913021, 389826335, 658437652, 180131734, 207357789, 498002775, 254074061, 406917690, 811414469, 385169970, 149079005, 203619376, 101484666, 784678784, 603839225, 101078574, 486054645, 984105635, 191586059, 313759056, 66305975, 451024674, 612810514, 932990575, 57900022, 308428926, 590258082, 700396602, 876745934, 627447774, 753382658, 596983828, 849536397, 646722412, 148958789, 271151599, 491068023, 259755360, 213166833, 122128569, 508869531, 20563567, 405218909, 919488940, 702836248, 964612311, 202822969, 408186731, 49907186, 224863865, 718064747, 565432047, 567569593, 55591890, 407239430, 23513837, 769341897, 774153801, 28388132, 620500699, 184787131, 991992049, 334349114, 36972636, 974065792, 529247943, 599767013, 767310102, 265805193, 104649777, 384923079, 18542193, 998182347, 763728609, 977432054, 813385447, 524108648, 269387302, 895510798, 484737610, 885008234, 919811506, 662945840, 410406640, 70100867, 513199455, 320837426, 436209969, 13124544, 72379370, 658561194, 227510822, 541586532, 129269244, 949336543, 637641326, 945408067, 694706011, 998741526, 710970520, 278066519, 302831912, 751192825, 874746075, 252074162, 793342777, 950878069, 190763164, 358975852, 531335522, 777835336, 11564827, 236476525, 375874778, 119304879, 674967856, 557376986, 177512027, 180178734, 456272588, 667329517, 397336925, 973944517, 31160946, 942769523, 426187250, 596139349, 195305989, 635984907, 386490882, 660587907, 999611383, 619824676, 17227084, 55938837, 333266572, 881707428, 397577459, 321559865, 40824951, 383234606, 22987119, 752707189, 839747119, 187554454, 678987405, 251959508, 557060737, 214629797, 315791040, 910560028, 240838293, 446875569, 943605136, 426154240, 213893100, 956773134, 345771132, 485900458, 368834695, 89977431, 469284986, 231348406, 218469471, 787709898, 195763921, 620914208, 210591482, 362447974, 497456326, 683254754, 795475109, 256857259, 823970075, 79849383, 579699490, 337952698, 676760936, 288932561, 885048254, 517350124, 444102446, 385670992, 823160203, 703387602, 511748385, 314211643, 774890922, 18364557, 800342020, 363947757, 863672861, 131046816, 320633740, 394993229, 842239764, 852288972, 959387948, 844259009, 403553237, 964300374, 350186880, 906521954, 29606744, 678510281, 450921622, 684842344, 682643635, 228926788, 859191446, 406710617, 185072101, 987603698, 884973648, 789458845, 847323490, 379724598, 46520556, 582539708, 581895921, 630969596, 356482744, 78791390, 880948333, 219774240, 922849013, 772614649, 491395904, 937978028, 682209121, 745903076, 149836782, 774991991, 542995660, 936947400, 569362820, 425132034, 750522631, 8053278, 642531660, 418092392, 901846740, 30749447, 714847652, 68994235, 737881721, 366919420, 927135647, 94149480, 772583868, 448648624, 739315000, 872036716, 797044540, 380899023, 557821705, 437768520, 616595419, 863764830, 888568151, 183122386, 500195434, 414188553, 90661852, 484672618, 212190949, 661281183, 322026367, 63813502, 686618626, 139750428, 613171540, 991294544, 774277680, 865514860, 873999060, 288565634, 140579339, 611853532, 949881854, 62818717, 88365210, 344683889, 852129909, 517557206, 899159488, 709155586, 527219007, 66893349, 893890530, 26409467, 712799304, 471072908, 628368222, 202626984, 729816088, 415099392, 843183206, 795748968, 525599510, 282171242, 295955252, 620054303, 740125138, 113258783, 882223957, 406466960, 738348319, 483879138, 355693084, 519921805, 411886179, 582516467, 234492457, 187636266, 365958619, 154044401, 231891697, 612452441, 703298969, 710973630, 834781229, 910037240, 660688960, 74215216, 533067406, 772024495, 153169444, 350301528, 584414854, 481338995, 99756572, 250267924, 131635962, 77018840, 51566604, 625254813, 730795998, 480980360, 644616561, 786881235, 896780863, 674041057, 401361464, 719956758, 443594180, 335994319, 758556739, 135125719, 947404233, 819442245, 616399178, 592164286, 601390915, 82061734, 90272207, 971953433, 400779596, 566262313, 498279959, 574551810, 856920831, 439842083, 362431466, 761842844, 778901493, 147354169, 229573464, 78251283, 833454705, 460850306, 745984145, 917020514, 786098516, 156977047, 203985742, 324425655, 63323267, 14984899, 769253549, 375549864, 854870726, 268755830, 688940619, 179509673, 233624472, 426927794, 836218291, 891174944, 161726483, 660221818, 878174574, 845738020, 898858723, 727496308, 930610062, 520492229, 895390653, 972075104, 576732916, 760365157, 831397725, 241571212, 97176089, 842401755, 246188801, 577218982, 712791208, 869250865, 819151094, 967531460, 294404446, 186325268, 964143157, 964067655, 888538749, 314865748, 618217892, 509476422, 538730237, 400010618, 588107382, 525303110, 446539441, 440537862, 435814594, 638897819, 688413194, 402959171, 796696703, 476738624, 431791037, 922500207, 638346687, 994511884, 371763437, 218717422, 480222708, 698783115, 692475179, 593570986, 591252809, 319780532, 446400944, 946044013, 642587954, 639298061, 924510435, 457274475, 739994469, 337320416, 969271553, 618332256, 637221252, 850515743, 245695562, 667338934, 192595497, 838565030, 346840920, 75454987, 976212325, 46167529, 973188218, 26935053, 639882119, 504571208, 807119354, 675404662, 117053705, 829569596, 813071960, 264478902, 675365989, 577704543, 402264409, 693396404, 783309043, 205468206, 217588732, 288022041, 763892804, 745889021, 627241879, 794694433, 177506269, 872664144, 107701241, 682298251, 333290728, 949442199, 176461539, 637272053, 94132778, 464763205, 24525621, 754890023, 273050286, 370686514, 185250195, 609867705, 744384501, 684153048, 297229337, 974423319, 852221180, 74571943, 57799220, 561175438, 456402495, 807927340, 997838019, 410181854, 868964047, 278556548, 996586315, 166097897, 888543251, 710985565, 565316738, 955696721, 111118387, 485737844, 632671630, 899784418, 938483132, 472248502, 114550534, 847851770, 857490900, 573058159, 47634549, 119105388, 450661747, 422510938, 907416351, 41626342, 439729827, 415084868, 725796589, 649113862, 110883571, 864120503, 48867988, 487052451, 869562148, 586984334, 221533861, 414892107, 36217538, 548968436, 491854578, 722399686, 205231990, 626088131, 912659282, 359201407, 114833861, 897339023, 58893204, 243484702, 350902928, 237299456, 697775854, 773267909, 38615310, 786351599, 362940790, 354127590, 169644169, 492647753, 766915005, 360069369, 327369860, 588671735, 622752148, 704571876, 605373328, 324948891, 915069023, 427412194, 682161526, 423852732, 794094389, 417220766, 217041663, 121535548, 680887944, 446518591, 806165014, 899966921, 875060986, 641403547, 182964602, 410958499, 80692081, 334911902, 350438829, 850225837, 294090827, 908992749, 12516229, 704407435, 212315330, 496478542, 387926378, 376745426, 450318616, 740093994, 579235393, 463643947, 563619172, 393253286, 600776799, 989805164, 355755345, 106546738, 393820638, 456371064, 880803493, 900136298, 589052869, 803460364, 998515071, 157099592, 368658476, 902456569, 954828322, 296489776, 941118405, 954556651, 899618741, 286577624, 183045828, 426635932, 478636610, 987582592, 989432886, 207804794, 8132227, 929226975, 98170260, 203698041, 300969642, 3823501, 655407822, 832787784, 839831729, 723826411, 44110063, 45805773, 768780727, 803915527, 101802923, 228500655, 710042918, 520592495, 232577172, 65912897, 799661902, 596928463, 515334047, 399676264, 168697467, 885788323, 331516501, 597542709, 970741020, 731945143, 861386611, 228494442, 163595485, 688245915, 632540986, 37880769, 692485828, 966902707, 450444058, 917793789, 722793314, 273419247, 316501551, 601917799, 425943693, 372656221, 753220504, 57809936, 404304354, 699771344, 596335268, 369265377, 547928431, 255761378, 405407459, 41882974, 909758279, 168670133, 19643920, 530039352, 652065505, 136301445, 915122819, 585831022, 954664677, 240524813, 231300904, 299404613, 870297353, 974762033, 551163020, 886123309, 442120106, 236753548, 318715772, 184405781, 759773030, 16880044, 655734418, 193841363, 366804316, 258793190, 149901864, 597821982, 690855743, 433549716, 348563263, 202832092, 469252175, 649202445, 663582358, 999078798, 524236764, 216681664, 788926750, 882993119, 112836231, 699435634, 922184037, 849706669, 538467682, 30726055, 210211707, 8888794, 799672528, 252210460, 904276822, 251174180, 17395358, 945966861, 522392551, 400224174, 410338540, 391474940, 38571767, 232153778, 507652928, 333008134, 568079298, 80337932, 625062224, 69944929, 708873360, 425458898, 945669785, 724807062, 98933874, 863125421, 982197485, 893120151, 150004934, 228571307, 898155887, 869983913, 633457104, 187936621, 42225577, 773756223, 169460675, 713830794, 658975519, 110850054, 644009287, 819099077, 268938697, 465292481, 571929995, 369774152, 789873551, 678343772, 169560073, 367767432, 811547821, 418030696, 254131098, 164404986, 20371692, 427436465, 593264119, 991049267, 334039813, 94914523, 964793500, 460784353, 971903540, 427277371, 881812463, 656388271, 842155776, 688781518, 754697183, 97677342, 31943217, 963847166, 712101156, 305017474, 548679335, 989557168, 861793087, 779783724, 807510812, 993927925, 784429571, 898493714, 221123409, 353884412, 485131881, 438102851, 183188095, 93265599, 389209212, 285878914, 328063811, 553437851, 75390495, 974450583, 311937828, 787182762, 210207942, 853210146, 459247448, 267016172, 296335897, 200920242, 315680760, 96291555, 549760036, 183556561, 37871203, 29858490, 427084306, 209381041, 138316236, 343267566, 27032621, 255988707, 332409240, 253786400, 236546026, 825897621, 67914894, 422323199, 279156400, 749712197, 150083144, 198453898, 93295368, 101668381, 962265110, 165586375, 341573929, 627789120, 329505960, 854251517, 391490038, 251839354, 361374860, 670880069, 57485911, 390458209, 544530829, 375381566, 687707717, 166124832, 989417535, 800248089, 741012027, 553452331, 421589320, 854639687, 443831714, 266918798, 601519399, 648691003, 198747642, 516854115, 446185291, 493335073, 448842437, 506293932, 921860490, 85765824, 419982755, 715526694, 721129183, 728364065, 401144083, 239530932, 578586989, 49329536, 675056694, 771286093, 112290543, 652376783, 514907295, 584706103, 932426271, 342746277, 44551523, 228824609, 822648035, 762280236, 621390381, 893880397, 700385632, 590416865, 289931086, 328187740, 545520453, 127730155, 500967407, 196756404, 173311151, 217631156, 978167392, 629580806, 228434632, 814104943, 186843630, 199898242, 574670682, 197185732, 812484544, 557947539, 262939443, 363849908, 482689368, 989413739, 953692152, 426407674, 548732971, 943678253, 684031596, 347233558, 924665004, 542043096, 266487354, 542010578, 478814644, 208939525, 277144313, 386522659, 144577104, 929097900, 934484186, 944314882, 140784856, 541625909, 637942917, 48397770, 455875265, 152432416, 467136451, 741002302, 686605357, 50419471, 371258262, 222299554, 566936, 217205304, 686891686, 511756754, 385816610, 459106997, 172596977, 617080575, 476038395, 412728929, 478768549, 220674105, 252888005, 624907918, 550053367, 158688791, 280276396, 221264037, 49502604, 123285953, 324677419, 437468168, 137069864, 799204746, 767155159, 129316792, 60148347, 502303056, 249783013, 291284918, 168465853, 779449577, 381054693, 761522369, 147452443, 106886232, 479925986, 924152299, 780481438, 122574695, 54739232, 620783370, 310684745, 775555814, 157305929, 196232409, 223292692, 495534166, 362216063, 323100092, 833683483, 572766857, 807889129, 641491591, 781913099, 584466844, 662858408, 454337316, 649560342, 726806137, 634914087, 508463614, 449248180, 11183004, 150839714, 495156724, 720202447, 412079322, 151186145, 266175085, 510301017, 605266870, 228205838, 748785821, 223040520, 591308296, 272985112, 790443544, 631129645, 803668551, 157588155, 755027926, 785267011, 629342476, 76990134, 836854126, 563562207, 643348601, 977786438, 284127175, 695637976, 536592865, 109817656, 387745795, 372835792, 759991800, 631530287, 324265210, 895546265, 13031024, 14973166, 653005205, 794112325, 320268875, 213717943, 970325708, 336693427, 710058955, 650398108, 102108838, 417143283, 643071118, 336840771, 194604446, 838162778, 654137494, 244857738, 774040505, 308293345, 441965371, 530762912, 90836350, 703660966, 819697056, 678875294, 782361816, 154356404, 464722887, 114140639, 464804207, 119846210, 266871330, 196230212, 169041868, 962699300, 57286395, 440671374, 496350800, 39026723, 746029658, 435596839, 213508737, 813810042, 523460390, 2118771, 157468464, 764051323, 624979224, 816513669, 789823233, 582867533, 980318823, 543163786, 894847250, 955624385, 986025994, 832004511, 697404861, 81777347, 959061132, 33808683, 977431064, 910582490, 95355634, 991664912, 847627285, 24772718, 227704221, 433145535, 397341545, 713125581, 772014322, 886943802, 960165891, 23992155, 943392828, 685125321, 900047241, 564879951, 785798819, 162416269, 730403098, 908421357, 450272276, 966686626, 360628319, 823843546, 6839819, 968812764, 894742070, 982235871, 267643076, 341686559, 926868928, 361116367, 615964627, 176626953, 369605489, 850274493, 43443442, 845635152, 276910805, 899633172, 998746277, 327297665, 797217716, 424069493, 137105911, 398591960, 921107998, 239047275, 110314007, 17178971, 341146077, 747492041, 17077932, 796133496, 866998824, 985017503, 70260048, 686859901, 626343804, 477432492, 902196617, 250345253, 730647113, 130021163, 777204511, 253440981, 387260113, 992228332, 84591614, 873099435, 284820513, 224910503, 174520586, 710531670, 422062024, 929637278, 69718709, 174883250, 561778415, 151600452, 500094737, 197319847, 342705876, 95600850, 218359762, 622379192, 247459271, 982082114, 183023243, 983996250, 410306135, 534406998, 291329868, 949489390, 743171622, 270934735, 686510135, 65703307, 6994976, 429115275, 328107508, 44739233, 439103047, 897113326, 201873040, 377397888, 976814911, 619329752, 900076761, 145897527, 883498749, 647640976, 184134817, 588283598, 665872726, 393735449, 601227220, 660052571, 322565722, 55193278, 221932891, 199394298, 336402798, 151590920, 882903141, 230955641, 905786553, 576209975, 335967688, 994743087, 51265791, 671274453, 62663517, 277741322, 856517436, 227232469, 702744549, 240818105, 114641740, 891016714, 141452558, 466565065, 254501671, 806003798, 789986271, 902807113, 800670519, 775981980, 484390684, 120037595, 664870759, 545718458, 454699502, 567366638, 71582476, 994155588, 259401769, 312274679, 631568981, 844049848, 406725894, 546120103, 454515594, 374589004, 25119455, 433824976, 825458071, 518262776, 32522998, 516279764, 756658698, 169229677, 166894786, 358440738, 241769550, 470835682, 123645990, 470581256, 587011549, 841307401, 702126701, 774722366, 115551721, 226101344, 137117952, 613544296, 698064860, 957920356, 40860624, 57569196, 443359981, 332553387, 870911162, 277934673, 458806068, 426442117, 293126854, 895978900, 823172117, 226136032, 529139245, 491863195, 62448037, 445887051, 583637659, 514536367, 492843554, 657821748, 165299222, 70073990, 896267861, 230481195, 450861048, 500854247, 223409843, 644584150, 173287857, 141612517, 184703135, 174957236, 735422444, 720275575, 863539489, 376661020, 262272242, 266667269, 691955746, 179151059, 419873821, 588750152, 643779745, 870648184, 209232204, 421182120, 560826082, 99675939, 673296300, 999594206, 707698779, 329564891, 203895731, 450731865, 361216052, 213126849, 506421791, 465578342, 896970633, 247584423, 31393371, 634876215, 825959695, 822258686, 797300243, 175691437, 832709403, 7207614, 379894646, 435576516, 677394968, 553856713, 98082438, 903786742, 356761705, 832048378, 259427821, 342083339, 940750184, 642366328, 885300238, 875627987, 584453439, 700837520, 150896522, 632538186, 238580437, 986518242, 444973624, 893325910, 652606484, 2977114, 107935055, 289408428, 372706301, 94742248, 735904892, 500379806, 537007156, 416893428, 659514510, 791342129, 522986753, 413101943, 257197472, 509925900, 50646323, 191992854, 296706223, 796137199, 137522692, 446829356, 959168302, 953480405, 139384398, 561519859, 545816282, 840915943, 320793834, 297494079, 176517180, 983933658, 874978429, 500539909, 560061994, 354891980, 208575436, 184819729, 80549564, 260812276, 752100824, 200468608, 768781572, 681818763, 373292541, 273575896, 250934106, 674043006, 849095076, 55613012, 77105946, 934765385, 464659790, 192215458, 907161259, 760687810, 388825065, 883598347, 771501478, 390820579, 236786328, 21392166, 151142796, 600209892, 955361289, 164323205, 171156161, 322921158, 895967446, 645680848, 908065720, 313241811, 879325552, 681091265, 605925778, 424199617, 377384520, 651814390, 999660070, 930887906, 245962263, 889671971, 349520971, 244058479, 651749166, 213117222, 622263435, 758309236, 932372220, 498864859, 387807495, 874087069, 558648268, 907472759, 41223118, 45629934, 109039188, 124123173, 969754030, 220574184, 660247440, 751285429, 718277955, 867446757, 580253579, 845079371, 581518861, 273556699, 181448393, 431270208, 592077722, 163175109, 306979845, 4120845, 309457261, 485692552, 718311564, 654040824, 542137028, 321777758, 614513020, 701828217, 438307378, 520003683, 599675816, 878006339, 556786082, 624617757, 918861764, 620997180, 712178441, 524179721, 133893474, 355778502, 586602140, 404346988, 700197813, 12356782, 396178147, 382728073, 680543605, 958659116, 533022607, 71369672, 226407412, 551235456, 804291489, 885848088, 786238907, 36148532, 591106232, 106729691, 636340847, 787874578, 931230632, 346511637, 657207544, 855763309, 342150050, 180027463, 251376454, 451930948, 842140694, 680669376, 473063332, 317805406, 521988405, 810116309, 316086949, 590967297, 475321342, 987748974, 565154965, 839516315, 217144909, 531157107, 950395937, 889317996, 298141973, 322598825, 208395802, 142303872, 95133460, 381297164, 165562527, 427154859, 356223914, 633638204, 165585818, 169718604, 266127569, 839353668, 223315581, 465370950, 554708829, 610205293, 404785376, 946085599, 395518881, 753925004, 449807209, 534344447, 888726171, 333094570, 570299700, 379887172, 998437826, 265881485, 213430502, 682466324, 934115037, 501206279, 366469257, 548287992, 223078357, 843953970, 842014875, 363384451, 375949137, 256285979, 610722535, 168991264, 475013986, 776063001, 221007153, 516056686, 43995273, 726478986, 353158681, 634455027, 535961839, 200541903, 875005895, 258681601, 460587436, 78284526, 180464078, 852235395, 639436821, 773064620, 312597111, 970429694, 994173640, 643172076, 518623734, 433692869, 356326203, 167189699, 355884382, 408642908, 67755375, 236123646, 410122790, 685023258, 471554834, 377517303, 589716682, 747224868, 366962344, 807919057, 755975251, 352346557, 233818894, 101074843, 519806990, 160196670, 432755977, 383896523, 124138270, 46868821, 848098751, 985697851, 637840228, 35059255, 289659132, 208502158, 614390788, 45140440, 552019822, 479374844, 775428573, 525113681, 929413646, 557579853, 522313345, 849445836, 110531057, 192133445, 82994894, 909069176, 484161593, 8699164, 64134618, 356811244, 470833816, 963930611, 146484512, 380086345, 788508366, 521752819, 574320640, 55233556, 744996299, 395641796, 434652414, 693420849, 583454461, 202563485, 809790088, 138489352, 439057296, 730997931, 364507006, 275602212, 241890243, 46242675, 924536431, 389086468, 900996806, 849736235, 353529719, 650440041, 579965062, 771471728, 701472461, 734692645, 669403884, 745351431, 54521446, 558283172, 940484876, 815533117, 624277764, 674537864, 47048003, 688411134, 835262006, 167485189, 618304663, 127523214, 750002422, 435506090, 691398661, 507290302, 293139233, 736003488, 565610085, 686514810, 82028784, 830377969, 512812294, 655066197, 974047977, 424807508, 821147056, 765316241, 133135442, 704454896, 367583622, 653321354, 709769723, 465270823, 27463467, 773501075, 950013955, 738334018, 937096100, 950509418, 348251169, 75899824, 219223605, 282732171, 211440482, 113201580, 724622070, 243380088, 165376780, 452335897, 501888861, 402142176, 19851510, 551416115, 5529080, 284248677, 770450366, 552171105, 577182017, 971989184, 772391181, 858162022, 188834625, 933275271, 822095506, 390128177, 318877573, 429178458, 646931526, 554224490, 558157537, 702016200, 693552624, 494866277, 362926491, 787985578, 99348030, 69240758, 829106771, 895904343, 24772418, 973252251, 215615066, 324121770, 618963800, 720860125, 997004862, 271547972, 244199613, 187154956, 971652736, 685813826, 561595710, 661810003, 92110625, 615406882, 395588080, 877685962, 40876742, 215808116, 109270616, 905916516, 576818300, 652811049, 507561827, 635341948, 162314353, 592790829, 228146329, 243843832, 369081095, 917716223, 752915691, 450358688, 180257343, 679580082, 297551611, 377966097, 460386020, 731656244, 42808536, 507055356, 18916441, 96896990, 370101232, 797580685, 353153810, 90430916, 326831425, 886671531, 694518861, 200444488, 76609066, 757633149, 467737119, 345485175, 661765722, 974375017, 891077366, 179198782, 979309124, 937456149, 854592077, 535478576, 539827334, 556891032, 912579466, 698993667, 593242260, 307471183, 945673572, 9500254, 927586436, 145652055, 728034469, 664784309, 947349070, 547669345, 897730730, 481723937, 103462812, 238752857, 105453368, 375042998, 486022148, 849618772, 584088133, 774356708, 918335174, 875862935, 237203968, 159537922, 228888917, 517682146, 366972894, 453396630, 842045575, 188398121, 383740162, 790752655, 438450173, 663691903, 216603685, 522436409, 502917358, 363082074, 796168855, 243235761, 949944848, 886056841, 723770597, 373701929, 770820336, 881349269, 393889690, 212121486, 375168929, 336829088, 552684108, 763432017, 994684031, 859400912, 555831408, 951602722, 932987985, 419330719, 752731858, 172912127, 965950461, 352344379, 596959918, 725013857, 488873133, 815111599, 684000182, 980236212, 197003299, 995003151, 264839907, 974529140, 975817532, 894423306, 261940817, 721603571, 202282361, 116851493, 371061115, 498664108, 411448462, 631832957, 504608559, 36497312, 395225570, 525294199, 600790158, 282841648, 901170034, 901798867, 243306656, 340487092, 211685357, 165919985, 956059348, 764852086, 179695917, 585233406, 749610642, 157265587, 986727436, 462586048, 452445017, 910692720, 849139455, 463931718, 881102670, 574823436, 343530090, 392871915, 456426507, 265444450, 756251042, 72024126, 645093212, 199680299, 242199528, 585297460, 643707914, 496696874, 326237404, 1797069, 442336294, 224425385, 863136981, 890542067, 474918155, 254807060, 35024559, 728484976, 328702329, 63058783, 389671113, 93176129, 851232449, 666417199, 54121110, 304724300, 462111078, 263938511, 809998272, 375460048, 629773175, 305168764, 478545056, 769494378, 165460413, 162085793, 285008766, 51503446, 740819729, 263462081, 703679566, 896982920, 460197992, 515490526, 362055684, 338394656, 327233041, 280969661, 852652484, 778231201, 746208100, 878306190, 195152509, 445641640, 734416701, 577244314, 457547546, 265722609, 576266872, 726016265, 457890795, 692618226, 448822309, 204186546, 392202405, 269988380, 211338336, 501265761, 899330764, 866555314, 428713431, 659308852, 124773563, 273222394, 296215851, 249820841, 551221599, 557719250, 880172319, 855088510, 796056935, 347197720, 65081460, 388453469, 628985471, 392979862, 632686769, 90507302, 468320712, 787249582, 462198523, 457168349, 962843287, 52343002, 678681287, 711433572, 221393534, 989657966, 373149490, 51213629, 17213454, 442213104, 977437662, 382924304, 842207782, 347921138, 669428294, 418918267, 583632467, 150074163, 299868190, 414107430, 949146016, 687874240, 487576531, 558730121, 805638694, 874651454, 653640353, 470451855, 696666248, 558212632, 590230338, 315620292, 29314395, 460039822, 860646258, 17531640, 35727339, 556824454, 260348752, 428457725, 336676297, 189605760, 848262778, 73453425, 528910466, 130971674, 390078218, 947217592, 210329734, 112245182, 147120260, 996572434, 21046953, 743670486, 339785298, 733264559, 397122028, 826754964, 489202724, 32205536, 511555301, 710845599, 116698434, 118073498, 139513292, 103541252, 472773140, 584367088, 37552125, 692591414, 719956891, 820510196, 9574103, 659057669, 271553665, 207210321, 964727, 982760530, 704728428, 260892261, 595414108, 842253246, 281506025, 782057714, 385428733, 164788274, 315238892, 163054008, 754857586, 928109594, 25863444, 58094466, 392775182, 714903335, 750901075, 910350938, 27902636, 408681850, 448204714, 632176330, 734921787, 601077623, 402386858, 642316747, 725269887, 521107774, 313222529, 166840115, 370574328, 445026237, 913315835, 985054608, 540299757, 925522443, 54641495, 605562613, 538085215, 738070598, 546078696, 613307755, 465554812, 698635228, 694173083, 310893820, 754837441, 476090144, 619010073, 370836612, 221847750, 368508688, 592531247, 874537634, 457457241, 848720571, 67822747, 989803022, 365989945, 617290412, 461250749, 30471995, 121803131, 953200808, 166109212, 490281784, 288087635, 100997739, 900236636, 775131474, 979427580, 418604153, 698891433, 562581516, 472102489, 134818840, 116468696, 835120462, 840593384, 786336978, 983338300, 351258424, 661578788, 230549001, 356182337, 209197884, 844340308, 452070970, 138560204, 521236306, 20607471, 190725612, 199132585, 773261700, 755923753, 915879718, 12674169, 904671175, 738961313, 707977202, 502711733, 780233276, 551867396, 620777076, 521274969, 984512906, 815306713, 41359211, 486096904, 243064491, 391627994, 365314165, 210847952, 90736946, 323868236, 416489677, 734502002, 352901279, 329035456, 948226295, 780563059, 801381852, 606526333, 930963054, 213744788, 17204705, 51190249, 184562261, 759899027, 586244526, 776982839, 823771068, 628031550, 164931646, 499751876, 138290512, 847216736, 484388260, 634778022, 898628034, 259641550, 185497984, 382184084, 652669586, 679274463, 643992030, 668580196, 173220992, 569964543, 596825624, 423596, 786697370, 961059860, 596164623, 443518266, 564833685, 364670346, 453209028, 637395826, 702405688, 325199442, 209673833, 626407594, 215932070, 583476050, 63707125, 875252707, 114559363, 714045909, 341899538, 67684485, 394943032, 120583258, 464108789, 806435770, 222530314, 330095338, 647785985, 36152370, 859930691, 501634585, 318488086, 410659851, 787022084, 626665913, 53793528, 206976481, 491753589, 999743110, 309965535, 52206173, 155265487, 402732778, 402292460, 535886903, 326971424, 221258504, 946296633, 555885987, 127682528, 642234185, 942318652, 809600466, 493551944, 541424688, 334745890, 446321809, 264207663, 916444931, 592045128, 225606794, 530371259, 93835334, 856167349, 308147109, 641674764, 166658275, 921961226, 127532677, 66618548, 599102553, 930031951, 117567207, 768777113, 760613171, 529562614, 133351152, 817111614, 770021620, 617517446, 656749922, 192611048, 635526432, 385163778, 774629885, 744672742, 2503741, 620619854, 793822422, 797267381, 195217878, 182720359, 24367643, 226515466, 85320420, 416641997, 706315610, 81013046, 432721086, 815186812, 908927101, 214382058, 605360629, 839974265, 523601174, 379588171, 23319178, 77003472, 65887818, 610071109, 835772243, 910540147, 639895007, 42972658, 929471010, 135523888, 549973767, 12425749, 215853511, 191878661, 252784418, 920324894, 169843407, 741599232, 288327240, 845139339, 764815743, 760030604, 253310030, 956419959, 406421034, 648606487, 34585011, 821512696, 790168238, 880789794, 297595863, 805985474, 621674178, 358062375, 513279505, 317304186, 233530326, 870108191, 621933198, 913631175, 749083375, 870898231, 795619074, 279885713, 491156948, 652243494, 107635884, 800844444, 973835123, 533264636, 113453254, 617893426, 685714793, 717197305, 753990707, 870208396, 377203180, 421543256, 217160634, 81857275, 405914481, 920558655, 649884848, 117152719, 765627709, 749473308, 661587780, 50414858, 785719496, 144559642, 957230691, 636054347, 595656095, 678662278, 60555321, 850946775, 465000621, 870789224, 226286019, 438247027, 959991114, 892069174, 907446207, 988572300, 110853380, 512755568, 40361659, 468401504, 501531887, 194620293, 802264854, 365315251, 814660036, 391454426, 804424015, 841621579, 24024850, 929418086, 875220496, 249020421, 676490582, 983363543, 536573384, 671250230, 462463128, 5576058, 458828435, 430840672, 717171344, 264445147, 181752147, 962421997, 868195365, 246960407, 136802797, 574604079, 748984934, 378503701, 290947059, 912741202, 682329058, 380070849, 789978907, 180282651, 326487718, 17443910, 621010347, 155753208, 641801145, 216429417, 378751946, 720141284, 347364375, 132431855, 789660404, 8893264, 505533741, 216961694, 585213550, 709061745, 150658291, 634001620, 179807923, 580053388, 607815046, 401257276, 801219167, 154837637, 835100111, 627874452, 349303348, 902583068, 144247805, 452257914, 868384585, 620388058, 483419001, 228254023, 252095974, 210681142, 328477410, 552016563, 95279991, 304608194, 946162238, 4880353, 211089475, 864854336, 500922294, 810547698, 144633306, 28467159, 360955316, 763344110, 159430977, 340727559, 443500702, 952165909, 177185616, 137214938, 621041658, 26576749, 314783004, 193651446, 384816284, 160139144, 355044087, 270017479, 907071259, 895283651, 176453829, 116537221, 726260261, 674407014, 547968113, 341723765, 565665290, 836141441, 509612069, 155149390, 246542217, 263992210, 366592043, 675220656, 615982874, 512086485, 243710366, 367091657, 536204712, 183338386, 748438982, 227416591, 641623980, 824399484, 843496187, 551898387, 519904177, 206590829, 807072219, 795626272, 810889420, 323440405, 337052619, 202616160, 856294612, 430919105, 883262582, 296561477, 445932219, 909436138, 383289653, 456561947, 332666169, 590363385, 27391433, 617351680, 829972062, 169197684, 895986460, 183805888, 888961354, 542459912, 253741494, 276046608, 327985512, 684349422, 978216094, 333642180, 712838346, 639129155, 789716387, 223129103, 980390689, 83411509, 842242044, 49443494, 860309414, 400774343, 447778242, 654560964, 608822963, 708986710, 500131488, 505841522, 586315974, 513766323, 15702770, 475034847, 124036566, 277909866, 835381442, 771108221, 42749521, 288912400, 486660315, 288616122, 152897230, 856792073, 707955416, 189773723, 942158113, 7779112, 178403645, 203456594, 256116222, 218441542, 494714556, 785577600, 50706730, 915614800, 368437861, 990775107, 351611566, 178993439, 122419670, 468815069, 901134316, 915308825, 373793464, 393836968, 373292730, 20297069, 584720549, 240982444, 966797230, 81789125, 746164992, 392902632, 749921595, 402943464, 481365534, 639867911, 755985524, 424063377, 533924929, 504305586, 16603842, 397486523, 368907875, 41625009, 985800623, 223520644, 668850237, 547294705, 464619338, 714380789, 871763692, 322494032, 586687613, 476281097, 957160064, 812405867, 288829864, 30840180, 47179657, 375397421, 631534214, 106686948, 439705725, 255512974, 938151496, 124339276, 980925975, 997220071, 706423496, 397825600, 751013655, 620951729, 105689364, 864757034, 584336760, 461785159, 446739438, 590684320, 146650161, 820339508, 950896380, 56715963, 673522769, 629816966, 104712428, 839350721, 912253596, 531272526, 44078264, 614859549, 88608204, 108657401, 485129553, 666766766, 876510473, 432614622, 770811279, 527047585, 950697483, 387060323, 68202486, 120097613, 534600812, 487589085, 441732933, 886251253, 22145006, 554558378, 381404224, 710554933, 345310380, 958846375, 436605925, 432881786, 870442186, 349262109, 709119461, 738036530, 544289472, 292048892, 40729621, 821454651, 920256510, 100036354, 802094769, 204408700, 19884939, 993061128, 934833480, 750432284, 366006315, 923948, 341105478, 288054864, 67845288, 323921456, 462689570, 328314709, 793476953, 718492520, 958543478, 132934943, 666965844, 84128778, 166746211, 751432103, 122575048, 839412036, 421386135, 347592718, 351906209, 485172287, 905684909, 652286538, 734711972, 814355054, 579906773, 827352140, 888806694, 432027276, 557419161, 82926835, 464644301, 910436307, 619107093, 531917350, 49336339, 117081497, 98218584, 272591821, 930656583, 423504715, 486576336, 269302040, 416191479, 642272441, 563717786, 282626233, 183016409, 683069170, 57233194, 658349582, 648795283, 88531288, 24513343, 715617299, 848636386, 209472658, 186714549, 509324195, 831417242, 824238732, 107423761, 273077500, 54967314, 315786873, 296787524, 950378867, 413182126, 937509536, 807982800, 555140235, 518848785, 509338356, 564205703, 378223546, 123805018, 985016907, 847109216, 387530035, 639682968, 273260713, 952909779, 831153715, 852007491, 974736222, 436180266, 629242026, 596178785, 556154634, 827354788, 18421767, 765720402, 97236815, 348715891, 90427776, 342830106, 854281471, 613637132, 187088662, 81649043, 522424850, 968652493, 754194582, 539868092, 557504393, 398564303, 151040347, 330516744, 474347377, 431005987, 881268348, 806556908, 953374690, 879904705, 316861239, 597041192, 157689420, 486893840, 105126408, 658841104, 954785310, 381247152, 254931456, 65154336, 544995309, 153628417, 850361261, 261639979, 970042999, 536288806, 625306917, 198159120, 230630717, 919707668, 710485710, 305205587, 105246415, 97111297, 488556008, 219856894, 557511667, 916265675, 706133254, 300657469, 747472724, 165518101, 809699696, 851069680, 899005432, 24813638, 572697821, 793807300, 181991857, 946862076, 216722728, 855267694, 607689191, 584149054, 235015967, 799965193, 875385139, 343871771, 785396202, 639861048, 532690063, 481892065, 735376071, 519599107, 14302945, 357944836, 747039201, 924755850, 977903602, 876948063, 643016127, 655823645, 699349778, 653421341, 123008354, 943780970, 842922071, 85918757, 317766932, 366516333, 700491881, 526160472, 448772451, 483553343, 6363286, 789441907, 145352080, 596150559, 690358204, 506480392, 927678538, 87801363, 553583652, 490422402, 67142214, 620644119, 119191516, 648112815, 155468396, 904027665, 373387567, 303542741, 286783371, 590758484, 910508155, 696119106, 740577176, 905846464, 318729704, 808189691, 243943471, 127684665, 325775062, 604433734, 689930183, 693694730, 528606291, 260025379, 189256696, 236269738, 212367109, 511075493, 491098713, 907602040, 195005970, 452244640, 305878466, 276299692, 155067202, 846211356, 21697603, 814766361, 744518422, 326668862, 931270299, 73851009, 575052402, 19057726, 124727993, 665699067, 213480903, 435471932, 750840023, 399496028, 245812698, 934490213, 923697014, 684046097, 333810644, 635574277, 572768872, 547736530, 190925777, 450444088, 536483507, 545058395, 715794233, 76498664, 259419534, 231451160, 32839068, 197480225, 906634436, 984660537, 220308657, 357414746, 194490770, 793588957, 367114663, 425154982, 634235873, 228464263, 886114379, 759936967, 394652818, 967988331, 660770166, 803178613, 214354655, 971222679, 233266721, 851408981, 51506700, 86542741, 44055335, 276143454, 113792633, 261072213, 50167572, 168385221, 93709563, 707589560, 198557934, 871791214, 623597135, 681508332, 897506818, 849022951, 939054187, 878094484, 663390217, 5378544, 216445273, 942536470, 478596736, 393153199, 410018542, 58074366, 809717569, 175557384, 522581441, 833747817, 550903728, 339870210, 464762045, 908815770, 946401367, 357416897, 342023690, 958113805, 694134000, 767849348, 400464568, 832129680, 181310320, 54919157, 546793027, 682137258, 664878313, 48353512, 138831619, 818032815, 221386558, 423861356, 529072820, 734989968, 456359338, 274688908, 725448919, 561285000, 534240728, 43611719, 982578137, 500905480, 858817462, 129322633, 822719165, 899973366, 633919106, 470503801, 871885549, 853062199, 853200478, 882682278, 887738404, 526326297, 355567700, 438076193, 34374587, 329254288, 920299527, 103242044, 315963323, 743827256, 472491413, 761417978, 680337779, 917669450, 133541677] 293858445))
+
+test9 :: Test
+test9 = TestCase (assertEqual "for (countGood [188749986, 43025141, 306806411, 885408463, 556260816, 483369158, 698256361, 814526941, 82297086, 399692927, 142440421, 4245511, 820838803, 309696682, 754534500, 554627895, 970778496, 686428872, 627071363, 351759234, 640474410, 29124833, 376472563, 122099150, 166904425, 188779876, 82771456, 921149156, 536810241, 404342138, 998779376, 874768811, 967529938, 841122969, 772449459, 119886029, 364198074, 408279935, 413267718, 685795278, 308407684, 753723671, 37725190, 161330137, 577209788, 525292491, 884135758, 456115239, 580118341, 442707785, 699046542, 813428173, 118134230, 60085235, 815838537, 360638699, 20099530, 323115449, 529231601, 665061552, 476011922, 230297999, 37184234, 712016941, 944573957, 973715861, 919854749, 732496221, 980887679, 407237583, 783332693, 597201608, 644080959, 588386248, 833580260, 347657083, 859957486, 711293338, 233028365, 828983473, 318065306, 281624978, 977991378, 497631478, 512133094, 476006560, 27935819, 932638161, 40970419, 887288597, 424914662, 91013203, 398934948, 233942963, 887011498, 549972358, 272178849, 318426727, 678641654, 401013937, 974293763, 728731321, 1573539, 976524852, 618943008, 449418051, 335159868, 510301350, 34468726, 906623001, 846907141, 372861192, 443103176, 692797275, 257905831, 145013620, 649563715, 909859837, 263337423, 486274036, 511631446, 687300339, 28385500, 404972471, 129566420, 539855715, 214982389, 821428158, 254158909, 464381983, 327543182, 655758792, 225215679, 660569487, 834459, 978177794, 62402508, 524411829, 189801436, 511659809, 993854145, 968482682, 954157984, 348334713, 161779150, 784770393, 786449594, 676556114, 584421615, 864319908, 415347006, 112073393, 823422770, 740198011, 363117025, 822686880, 49491132, 923669178, 849677668, 836484821, 232442420, 373326721, 234594638, 694976143, 948261060, 496495193, 281282633, 455703898, 167137622, 807095138, 863084498, 972072679, 646661778, 590674491, 506046888, 872936181, 886737330, 437195717, 160119874, 894881862, 239775484, 308705292, 245490091, 26834250, 8398195, 821484971, 743727362, 213365976, 241217052, 410252245, 889241902, 35658520, 175639084, 942326966, 853978024, 372030876, 336283719, 298745220, 763837975, 367161637, 397322919, 406621081, 141127532, 830321029, 838828761, 851923682, 611505957, 698939698, 959596109, 254761757, 858536339, 270168224, 947456212, 840174870, 273605789, 485409883, 244496304, 666750262, 709453149, 815497459, 562530642, 619962324, 508883188, 71210470, 53535972, 140832303, 695176857, 724249562, 880354188, 570710744, 241611876, 45738301, 420933432, 852723644, 581656721, 526005890, 888946534, 498606121, 437073042, 818692258, 135830747, 272781638, 547003819, 109986614, 771311331, 547573510, 732081486, 636399996, 866610586, 588751467, 946338988, 75022780, 532882083, 414869305, 193750052, 639763798, 77285136, 777016543, 341214107, 75153942, 839511394, 695589038, 467611420, 167330710, 608972063, 367905343, 575545709, 412231415, 241417964, 477425269, 558849472, 90775226, 141883975, 603506809, 140610226, 186260170, 598835769, 874972504, 771600898, 97669905, 712010511, 379497707, 983021074, 290327989, 419528891, 355421965, 571929045, 545295752, 238528092, 753807664, 731194233, 230917045, 623741812, 637020932, 119835360, 620168933, 227563298, 237390649, 755331705, 484075495, 813717546, 378470378, 732989366, 126699727, 33423146, 425458086, 7866727, 96589728, 549042574, 540550993, 384259117, 79333833, 415193520, 321821230, 38678313, 343430421, 710252378, 455488110, 204433088, 638041994, 255016033, 345096879, 290973109, 290367827, 871184255, 153423741, 62081036, 266461854, 199192490, 489528951, 153679814, 671068274, 8885007, 818145325, 904710031, 872346692, 640025865, 766145459, 888994217, 751845245, 186364794, 272667568, 818131505, 206824470, 838476591, 412116801, 987553422, 291585322, 450302893, 605906807, 689598994, 493583556, 451393072, 415422316, 970570407, 900754733, 611448635, 400438689, 336702964, 280744361, 796384448, 715358082, 575272003, 491671389, 379778145, 595812528, 558536691, 690107990, 790556773, 805351575, 174113266, 69386736, 926116746, 347978940, 66372807, 846108587, 318011546, 465151379, 823649570, 644556790, 541078342, 374245406, 570369339, 904449155, 462289756, 668560504, 782432886, 628460676, 61245663, 873457589, 471862855, 882946400, 805286733, 212330168, 315426610, 560245919, 941266279, 785619546, 478363150, 180006341, 607550439, 294860591, 697670189, 293191243, 207375105, 212856089, 490626593, 471335734, 919436938, 344157465, 387875568, 718897187, 300700694, 672489757, 374954741, 534090501, 203220197, 738594697, 448207740, 176826284, 535531868, 227949594, 140384735, 91433321, 339215321, 126542971, 844185331, 84989875, 65015795, 806744107, 76530884, 247814417, 872476406, 872285565, 858744552, 745926159, 70438638, 631117336, 556149783, 617039235, 370984641, 355820026, 140186574, 405159325, 780119558, 168935641, 587321291, 90452849, 999120110, 227960299, 51792250, 363736231, 617091235, 107636796, 143539708, 115063541, 561848909, 439088486, 55696864, 985072567, 27816428, 752517250, 124221394, 700590802, 821530475, 53467966, 717508198, 889635041, 742848050, 280074709, 293626124, 598607868, 729258688, 579562690, 462879738, 591686573, 520582070, 182059145, 540321587, 365393023, 639343076, 910374535, 37755537, 360848156, 368077304, 944366426, 167493318, 305819185, 796275659, 469086374, 157140010, 765436370, 483998534, 223904193, 213597563, 28769788, 338953315, 886341427, 221731666, 798010881, 557478641, 965851329, 129715853, 511009037, 382322539, 742966963, 330342448, 829104240, 582073383, 343825082, 998355181, 147813989, 647417248, 655239663, 628600267, 348428408, 204116440, 57600522, 937488871, 991357792, 781106359, 14423814, 808881397, 160826734, 975767325, 775377633, 171774629, 91649053, 493208618, 719883623, 102954455, 593679870, 417933198, 732625745, 44592295, 137978104, 898268144, 547942775, 517953029, 666220247, 732990442, 603861019, 677232286, 26363457, 587505941, 555195742, 563961887, 293456434, 505049440, 854745740, 60263395, 477282411, 315586306, 138603081, 294182943, 907787878, 905398850, 883949040, 116056431, 929254342, 971782094, 980525290, 321119150, 735608505, 959598332, 784020735, 365241711, 547441283, 589526597, 14589438, 904332668, 452378770, 47457268, 430989161, 143540890, 550953737, 802351133, 561727230, 544552861, 686051873, 596450333, 502686642, 816722654, 442121901, 861668165, 841528819, 118074227, 452783948, 875564922, 778757608, 468891727, 394383419, 259904679, 975027685, 938566635, 280101181, 549880144, 109975044, 790693347, 307270068, 178158165, 300695366, 690174296, 199408351, 697137014, 322897509, 450846425, 347710638, 31108697, 472504184, 672421292, 343391066, 351798544, 517262203, 791007743, 700363746, 846822829, 81579690, 198617402, 716345558, 354426048, 58378851, 758021632, 366664143, 40295936, 271276080, 859808757, 120218616, 367769325, 818567604, 525851326, 756076349, 832419826, 672213225, 92743779, 672876011, 699975068, 342091468, 610794078, 384986296, 33614820, 816523560, 56498407, 799252515, 842553621, 523360687, 702953835, 612780413, 768436163, 584845465, 982560604, 763736388, 423441666, 405843966, 591658376, 797900178, 722648557, 17451299, 505389771, 649875876, 999027995, 723787853, 70930611, 658526658, 387642165, 326569947, 438045367, 427223634, 295236877, 396780654, 383395126, 91729711, 470527593, 868880563, 188689712, 646698351, 101773026, 575682544, 418666131, 372623452, 348061654, 875860745, 97640648, 348347526, 821699237, 116076243, 117128762, 771122753, 568534822, 302500788, 653409643, 392486364, 689869540, 565640544, 830748308, 626264020, 632900066, 235905841, 820084972, 152978741, 908718995, 781521427, 984453578, 35855612, 938279138, 846840957, 566849592, 343938316, 8207952, 71019647, 149712078, 805125502, 78884648, 658039085, 633920567, 325821993, 890455682, 450254404, 813744187, 187082063, 815558106, 347041565, 929141270, 639582200, 258894364, 178862616, 587689799, 215456893, 259054239, 510097076, 531762567, 910088281, 396721605, 624468759, 869088219, 853478451, 606011603, 949643076, 683541074, 21593882, 29633373, 915948471, 665035028, 615418322, 350051138, 758545630, 546368706, 103862146, 292809778, 870310817, 215813834, 592157620, 104479398, 997059808, 926280919, 354273132, 774386362, 942438949, 585098340, 53764381, 809065591, 466928338, 935139635, 904384204, 537115802, 737499408, 808830688, 11187938, 26610539, 591474942, 456199610, 643948844, 269596648, 967385388, 802929928, 572718184, 654417040, 271189481, 539553739, 66439668, 23620387, 772522405, 145999334, 279646827, 40677164, 714543969, 290897818, 112934124, 450030507, 179556989, 128886341, 991532699, 224037406, 649992506, 174992060, 339409932, 836714578, 249230039, 771848186, 730871409, 344566800, 904354872, 387190893, 181087249, 342084958, 751530281, 680912857, 492845731, 83419657, 646864611, 777044142, 760418316, 790640068, 231940713, 119520490, 882822849, 743198902, 90750908, 577452772, 383468263, 992860554, 376186556, 177518995, 613284632, 978220082, 630474883, 19242432, 61836897, 575743151, 503189950, 845610688, 392918215, 357602489, 124128391, 182665371, 108235543, 694584882, 317471195, 375427241, 547416021, 646125273, 492300869, 83686464, 901885297, 975848741, 861712535, 179073314, 620692861, 170901800, 727999428, 15326635, 790158124, 191675946, 391476376, 717612319, 157916682, 923197076, 698439685, 819676880, 69474549, 558920686, 123078856, 286778962, 248315842, 772562668, 525241843, 756179415, 982694182, 672701907, 993082297, 633197676, 168100901, 806490757, 274622251, 71253831, 304980835, 996445433, 341603442, 696122556, 928464906, 462310917, 368555244, 614593302, 173634686, 340130875, 523878847, 313009819, 144658608, 879877437, 94428279, 591221285, 365709813, 654130784, 785479423, 973341199, 136509591, 184493659, 864234326, 955878678, 865853203, 165304166, 506836898, 771343773, 683686725, 533515338, 978504022, 283530784, 285857727, 13067368, 480371726, 251293913, 494943643, 658330913, 408033131, 211002390, 597152466, 618466221, 245988316, 935234172, 989246579, 192084157, 738154474, 876075146, 286665159, 222707556, 300763745, 328036058, 465078776, 518637895, 603412735, 25941082, 90259632, 689546239, 248817507, 282794583, 993073424, 186613538, 521868313, 607876533, 974409989, 340881849, 231284243, 457880675, 836247232, 282309706, 310432911, 99454925, 752922546, 937930959, 637673479, 349263362, 388381717, 531373510, 914301798, 222272678, 354779600, 851636465, 335909160, 182006697, 500036423, 575041659, 277206767, 345591072, 493575146, 593904927, 679275958, 269819791, 575674485, 227810028, 572883088, 34351407, 148146466, 320626677, 751619928, 995194739, 792510705, 125977067, 574380159, 783232977, 855450358, 622195928, 315105280, 550585808, 602591843, 607772757, 798870210, 267434347, 799516988, 99539582, 748257057, 258125542, 19416291, 743699325, 834243639, 201743073, 76425493, 231183251, 604890894, 19879958, 912558289, 374798770, 424089970, 963811141, 193125826, 14020884, 869876730, 597526897, 520827823, 347982684, 100032468, 560860621, 879619495, 152316379, 996122285, 44270128, 593029445, 308128806, 169598294, 485927339, 284299622, 545199516, 374164799, 912974636, 163234405, 475200246, 449401251, 563969496, 38691112, 252329215, 937255290, 443651705, 286011308, 831536818, 738359497, 641177931, 7496557, 868169197, 728910987, 395006297, 195597444, 957305260, 840412804, 785421058, 229565053, 271265165, 986522989, 809881074, 591483559, 592910651, 310358631, 796085982, 263183546, 90505475, 251945517, 631959543, 562366284, 214879891, 49622036, 443773876, 455114860, 624355544, 872331042, 943699529, 872173625, 375552299, 865429227, 266059996, 606636254, 44064586, 61736847, 533056490, 459008672, 924804739, 816492988, 179803594, 229039718, 213119614, 955036276, 244336967, 346494829, 128176524, 423276383, 497449484, 737231093, 194004067, 8450519, 869612638, 3060580, 681548430, 920978181, 146682402, 805662575, 377184806, 5447311, 556475093, 180283657, 333878681, 501441961, 904622141, 90094587, 766853862, 567027729, 435500292, 79388053, 822815265, 868174557, 377221132, 610408099, 982155190, 934357901, 915620943, 731470526, 55277755, 40216920, 642697458, 470047352, 313993206, 686406836, 328538470, 809920446, 443568126, 860775735, 787143423, 436912273, 8801233, 991390653, 334689247, 954713156, 741735422, 152141527, 495815455, 250638825, 644452855, 764949343, 746531449, 167119697, 176084944, 145828190, 345570817, 690643419, 708336107, 939417527, 900592515, 385194016, 963524539, 8761183, 136497928, 263143294, 226839250, 612781611, 44209766, 156341983, 271227338, 712259010, 288411254, 225404938, 349541637, 235388970, 468719882, 937840148, 530090493, 886054304, 298541382, 446978273, 85627746, 5227161, 218899412, 175864077, 980394999, 675210845, 593724875, 197490785, 222728226, 965717566, 894926909, 134540395, 1561832, 555631207, 245101843, 315760653, 170161965, 623955717, 892951478, 380295058, 387673753, 390856276, 183177551, 48770805, 633849989, 272712793, 721582885, 786003066, 723665979, 621388598, 787449366, 629273476, 34586127, 10581400, 379495101, 991205268, 119417158, 379815718, 594437074, 629665637, 706225250, 571904178, 348522377, 386590386, 271005147, 306233353, 389322291, 909265436, 317705000, 908426357, 72580175, 517455165, 449339567, 360248285, 802410037, 55618779, 799187541, 372852814, 358681446, 425775658, 787043870, 616131941, 285454567, 583529784, 462412064, 932109659, 215344886, 946661792, 461288201, 830522701, 738726519, 748078008, 218082424, 259052200, 872906456, 556905503, 244258468, 15132018, 54136765, 59748696, 898236789, 965192095, 413768332, 596936296, 178640919, 340256310, 674278649, 253331761, 422054626, 291606905, 673747784, 439622296, 663777844, 479206546, 487314339, 45387185, 332067262, 349290776, 181999041, 715631232, 145699883, 819106462, 301469902, 603060317, 962192767, 272061861, 360795262, 364420189, 699263424, 204701591, 69803661, 562766592, 177995700, 719773094, 664859684, 952864871, 184516294, 172629221, 899618970, 844813583, 214788894, 273694662, 467035843, 80653262, 967121196, 487307022, 373315634, 141864534, 68026757, 867625155, 499654026, 251329976, 355835437, 195562002, 767217782, 183550683, 425871286, 167557944, 230651935, 566098121, 64722137, 195370297, 215715162, 585753707, 202771836, 531576643, 323843120, 546863554, 272175728, 450806133, 507303782, 491354466, 402270106, 154275709, 531144975, 912033604, 272004719, 647026890, 37253863, 951818565, 945769859, 506508357, 987439523, 233657522, 610814810, 933239759, 238283261, 418381612, 284919857, 225871651, 653954689, 527012223, 524752391, 315386635, 505175794, 940218722, 915899303, 600141354, 821073887, 421441484, 237182799, 666770166, 40786045, 508630274, 665232550, 447247345, 99026989, 855010802, 310402921, 49656229, 246148623, 55452768, 972301402, 100358684, 927407109, 225117383, 875371086, 313884278, 350765826, 719133980, 888775071, 364766067, 618500125, 658812813, 296498627, 524245745, 271938095, 913770775, 972906139, 358782605, 830026376, 352158263, 882826455, 102670380, 123530628, 738926057, 935239977, 606485401, 13262110, 875693261, 61048173, 107669017, 789589207, 467516260, 29486557, 178000845, 169011360, 832315321, 150870310, 855996970, 525200318, 825611636, 312236377, 621063239, 88537582, 545178242, 730546503, 834478794, 434351456, 956499157, 747819223, 642443117, 29624069, 320105889, 81226588, 271635800, 924121738, 605352850, 955132937, 802118991, 637052142, 431716662, 803678144, 485328217, 501611031, 512378829, 749578967, 784980032, 215072718, 169269069, 686081443, 582488896, 656971594, 898872147, 227442103, 395361523, 752009470, 585763055, 758480415, 812440089, 404989963, 515648971, 457565311, 480285157, 499271225, 817086262, 117293099, 840216127, 475426236, 120282562, 162872721, 31771540, 858746394, 473305744, 203621869, 7634474, 483044162, 557373836, 671576182, 309942130, 582535706, 773339763, 390515644, 873957872, 264392179, 32001229, 133485276, 536352013, 447045308, 396254062, 302377415, 647092112, 713109140, 38765353, 727066725, 269112577, 26961998, 574309835, 489730796, 658697702, 841771859, 718609683, 916417075, 509450378, 71165455, 304915478, 359462341, 280901839, 385436662, 338002380, 659856448, 567691235, 699263778, 112705825, 907064617, 439456579, 702109120, 458688009, 141600188, 45495591, 706691211, 393626078, 674417730, 986946015, 153487601, 875015642, 517832485, 91051826, 709741474, 895645609, 804376091, 549844605, 259518026, 234997378, 110029818, 997183252, 191856366, 93909687, 424301454, 900831767, 907502519, 655870048, 559287543, 69564349, 572302285, 131135672, 800620961, 377997379, 281380095, 165518707, 57128766, 594702200, 89979640, 284225894, 324593824, 577652605, 440423360, 801708776, 446840643, 820279356, 567642605, 470003545, 473525594, 334866861, 914183849, 385117087, 669030798, 985273068, 441050785, 933482647, 306072970, 304245119, 827655811, 813880710, 55355010, 597794120, 717218416, 496297593, 120013475, 339555345, 333174124, 690430452, 874651079, 964884879, 709460227, 225505903, 738897750, 727728129, 89004676, 699813820, 855026300, 424508779, 643678523, 473858477, 363553586, 488688128, 582803674, 348587275, 910481196, 224850476, 361603464, 461963922, 641753789, 735158819, 195311177, 625382268, 377281274, 341095341, 758533591, 505913413, 230569969, 836546349, 580342930, 99486507, 161696841, 304941701, 654027334, 223998944, 731470940, 251485978, 161382766, 47645868, 68172679, 118104117, 849027198, 802862588, 320572430, 860390015, 941831247, 320860944, 541102282, 456490388, 990626378, 971372583, 465058749, 946591679, 873061380, 222586649, 234779281, 771087597, 756736654, 772755660, 462062687, 236069970, 887454582, 850817884, 590984306, 98137802, 894930846, 141217242, 282443794, 639001330, 345956760, 851153732, 888081677, 250475694, 237300932, 223247132, 593733736, 172398363, 340941548, 176073684, 108306293, 563169559, 706979553, 287640583, 748540508, 835209433, 435986002, 529816154, 537793492, 161428993, 962115465, 771226369, 574862655, 632040442, 323554743, 672953735, 224792457, 688044301, 503153007, 265520538, 29985815, 891688580, 804530177, 458122175, 793892813, 508825680, 614977208, 333913586, 775393675, 964888340, 988890282, 4670952, 55331441, 932472523, 67047902, 96300713, 268365102, 939016085, 139378602, 922592768, 670518693, 380224142, 183263565, 655298081, 509148151, 128567853, 69518274, 516943907, 34292530, 92693066, 110089822, 614083265, 288673936, 462237833, 676320675, 294701278, 161036105, 733679802, 845927863, 40708343, 388573119, 268528964, 615607193, 423059765, 463570647, 406912057, 27806094, 526308839, 814543732, 907271163, 138660918, 296254913, 753250839, 153179614, 128283075, 88385281, 581507562, 633165162, 767842375, 186602981, 125188798, 544202149, 124367639, 15184218, 857412987, 876657339, 412844150, 622430235, 934786625, 577626922, 22420771, 82825427, 743212636, 114980192, 862509262, 705872913, 160090291, 79857399, 613852652, 389906958, 834517680, 197439321, 536552508, 536981326, 76512868, 751243175, 200472110, 851468767, 457058292, 822201232, 836978263, 328196612, 746714791, 652432514, 695833385, 183701604, 466328571, 70695294, 283432166, 72892697, 326396710, 915875723, 448773429, 546201466, 468682347, 7294301, 606198598, 87251319, 264664582, 816674967, 886846893, 686303881, 207185822, 242062967, 620449631, 561080761, 110360682, 840184961, 47097631, 967486223, 399752541, 383756262, 567514594, 630527564, 889409508, 195109278, 799512173, 460015977, 86604447, 652616644, 776572123, 409288667, 935016360, 669575202, 960806458, 429944209, 18437295, 836611059, 778058337, 296768289, 701265651, 294473370, 377873320, 231950048, 856130657, 198990542, 404267203, 373933364, 803477711, 827150771, 593581459, 862237711, 35951903, 982826401, 409849959, 719574470, 853461495, 903872312, 124083677, 948986728, 948923449, 295734645, 836160715, 770087704, 561673296, 658237324, 763330355, 150071048, 490276168, 997744091, 862011424, 901905073, 301815065, 115463427, 28824870, 861123660, 345570703, 339801741, 862865414, 587012394, 773273632, 45790597, 502934042, 228575103, 586184226, 88106238, 553648522, 633612995, 888162312, 124610361, 631780052, 734386219, 737876170, 272420796, 912409413, 277505334, 66368860, 642514246, 248382514, 632856901, 715119231, 618961987, 41967494, 196878205, 687913706, 942436307, 822153534, 312492605, 678850778, 770837877, 800242365, 778725678, 655137135, 166441574, 324527929, 719742936, 599264102, 708459994, 196486543, 579264849, 223274538, 397208561, 533410883, 935204167, 320515635, 4586365, 86156236, 573504471, 555673158, 477081570, 452023939, 523707011, 726598730, 373105963, 229199941, 362238579, 504849264, 529548277, 511920156, 332187996, 393782934, 571004357, 657186911, 155777945, 280176229, 910090729, 206202000, 109809772, 814183133, 368115296, 993529862, 401449482, 642158363, 561351882, 261330946, 206379836, 178855647, 511375485, 534807337, 404164150, 760932730, 106369861, 141521679, 72850010, 204021139, 579555323, 540140397, 837845061, 672865986, 194153523, 937777429, 671892397, 168143422, 735507476, 112986156, 531681184, 394232765, 79181880, 508448828, 366285839, 190751732, 47614783, 91612852, 234519029, 868665761, 69950365, 879409929, 798469356, 20357246, 813209936, 802843449, 672118678, 253241542, 780279668, 937987392, 122402751, 939625539, 461517099, 27967626, 231718878, 552433507, 45750141, 944842601, 702735120, 656773500, 235152839, 140756167, 85208910, 832188590, 560482152, 773462927, 324991937, 966121530, 352538315, 986664385, 752304354, 999470659, 950437354, 376862926, 218874638, 871078903, 393898820, 453253250, 610889263, 354352533, 1320702, 435825935, 887113438, 191375013, 357399178, 436127938, 825075146, 2441104, 841193816, 507333815, 93876144, 68518560, 173717629, 675305022, 714016190, 40026078, 457343023, 353180883, 219452215, 586152480, 386616244, 365742876, 50902586, 218738750, 765188609, 497189880, 473356725, 80790917, 427310732, 264027099, 556336304, 940597609, 102588144, 718446227, 13826749, 132006886, 138931038, 170729657, 300982900, 527862920, 653340729, 872504596, 317234430, 267823596, 362629705, 104970793, 68166422, 399295846, 581193413, 305168519, 242498806, 454416193, 564962815, 35614774, 70561245, 512334719, 193656788, 886094660, 481026072, 698019517, 15303222, 420916369, 199312349, 401795424, 571547178, 642716553, 401012376, 717760041, 303228753, 972977967, 740017103, 322677445, 142699569, 556163384, 459453989, 409670947, 381539396, 730880516, 671577868, 356317618, 893038127, 445884295, 761011435, 221118019, 301974377, 671288312, 167948080, 963746138, 241770215, 687865321, 380581660, 667085229, 222724100, 601754222, 180163184, 89074914, 944364014, 787167789, 471120557, 302450320, 694741745, 550079930, 608915021, 627765222, 36657798, 626264189, 368974615, 753930997, 379638216, 78777247, 184012130, 444351021, 768432757, 797758713, 124016801, 348935343, 365231405, 906734335, 517205154, 422851497, 700283259, 864645611, 139714322, 797658955, 21091274, 288410405, 544347188, 535330913, 720830941, 233021712, 397054534, 392702321, 277698549, 208901381, 477536351, 629336345, 614546016, 392646297, 929204138, 591243532, 618816207, 35545709, 608696924, 384066883, 168946313, 27914900, 806410018, 973627019, 589935095, 723500089, 391693800, 115480268, 83638944, 878293846, 399992280, 270755503, 280072830, 205959301, 538547831, 614469970, 23597754, 368169147, 769407375, 718518871, 549508126, 747313813, 68254918, 273849068, 699907816, 424907367, 213505715, 821126809, 870163676, 557122947, 325068436, 207593239, 84787021, 946843032, 708927856, 728735599, 920113214, 851367531, 667973806, 45187344, 534897276, 713676870, 423048027, 652877162, 665579871, 144395181, 231804435, 631124547, 502584217, 369697865, 814122410, 971419934, 32349156, 278366398, 410295051, 72471204, 820915789, 728686363, 81491399, 374673698, 278781541, 388937801, 425577680, 589851604, 950986940, 516857693, 506228363, 980180649, 209172153, 522165993, 122200094, 501148128, 550782164, 271453248, 130320486, 978871994, 415236014, 346411006, 571684138, 990130923, 38621516, 870743488, 353543848, 372131359, 196317349, 995545718, 269081949, 605671372, 731888082, 942149538, 511620800, 952617814, 157607303, 641931848, 495573283, 171619400, 228012006, 865412287, 474773894, 967243478, 161364893, 319489296, 810500610, 423229851, 244041143, 111862321, 511851719, 300626019, 745249216, 68510537, 243745972, 167811758, 600843450, 683404978, 969495105, 92055311, 907940961, 346184234, 191979081, 217538085, 578697575, 556868444, 311550439, 850047353, 384428956, 262111036, 593301317, 664332037, 998975843, 867669867, 114080972, 164217859, 148961327, 388479266, 913873121, 65753268, 106292312, 252751952, 430590806, 725824546, 953566774, 549393121, 97064366, 363543174, 861709305, 202574899, 768052969, 693823212, 413573821, 803227423, 888564570, 677188017, 545713292, 350963950, 432550896, 202099554, 222015015, 302146942, 543580391, 522166299, 480258915, 61250715, 830168125, 125681891, 810122840, 382488252, 79483352, 403064238, 535273460, 493575974, 740241272, 974230199, 250677008, 436893375, 299970229, 956129276, 980505252, 358994994, 988174601, 262330544, 656872271, 692279723, 528839707, 475085772, 322315374, 908063364, 812430209, 722467100, 289181551, 945220058, 155554607, 782798811, 848759636, 219084767, 680294202, 273711165, 866124900, 557711331, 434402392, 975968947, 369816179, 698319222, 214595575, 858151032, 861439395, 958418702, 996076559, 699346099, 566456297, 701423118, 663591362, 888724403, 998748152, 718716428, 363681774, 259929412, 120779374, 818787894, 548842083, 565096353, 756711437, 37742864, 439282033, 208922978, 821663938, 685661536, 172255173, 734441345, 623448846, 118146407, 730353811, 547522760, 514698121, 668596007, 116951853, 735787407, 174337906, 63207511, 776354475, 787442091, 167726038, 536863988, 556078227, 58592262, 213401379, 734442891, 859644617, 487694311, 405517783, 131790021, 137635045, 648711838, 175362521, 867397296, 437908638, 421151195, 103423490, 548708602, 776132147, 697539224, 674115041, 392131454, 742284076, 792988014, 540925705, 119431659, 634096114, 825246178, 603715271, 700141547, 86813859, 968010633, 950094302, 892821945, 769243795, 466899212, 300590263, 407456130, 244930272, 900295658, 486724077, 272868160, 885053116, 217333757, 433037636, 418653010, 672157299, 568361049, 859097769, 172417488, 700765609, 499153169, 876515112, 386901442, 635668580, 507588556, 128740564, 237793396, 846524730, 44893187, 307828928, 747643908, 472781371, 31896267, 957226873, 70563517, 559578835, 386863251, 10454061, 87798253, 732210245, 261348105, 167795970, 954837070, 914859563, 782495411, 17662921, 736085985, 456127373, 121461285, 917733996, 186064870, 55879734, 873344082, 780497910, 545003510, 720277722, 839856741, 658303655, 602278772, 92510261, 812198770, 893422531, 643992143, 821916332, 761535201, 437032594, 169907011, 404317202, 345550129, 879256083, 250016516, 14419636, 638920687, 881743658, 543331995, 141838882, 205312943, 11688423, 304014243, 905772987, 478278764, 770600610, 525749599, 356959890, 796637996, 927895649, 210033346, 992782781, 532728854, 275618838, 120972505, 250696343, 369994121, 502998812, 952071945, 432573706, 659894301, 211750723, 327073727, 587112836, 228627350, 589728357, 781049823, 642953874, 244566149, 50958079, 606353343, 891252265, 973721562, 212882407, 428721918, 954827686, 838067377, 112775211, 331709154, 80739514, 990700483, 790757866, 499692618, 501021379, 535990276, 331237765, 412910766, 530467066, 491808925, 477482812, 351358312, 702983441, 248196320, 394269345, 381451422, 810972309, 724030870, 536759139, 652102231, 354822416, 832585775, 294801828, 614703017, 364992334, 229322089, 253418729, 15805468, 158926662, 93927926, 429912721, 833481278, 684982483, 568675517, 937722881, 545725932, 862704215, 813864998, 262076824, 310356815, 381754302, 164359696, 825774023, 104012238, 784291824, 755213969, 662472073, 291474393, 403215314, 319675222, 74935135, 403907936, 188468189, 940426081, 306535852, 865871341, 120235693, 35230197, 519412823, 135916786, 74311047, 509683143, 187498223, 95661248, 343255617, 227511519, 204935561, 112380940, 142257785, 403644876, 928153863, 813370820, 359377397, 186099205, 171757842, 634611945, 907789400, 336346283, 27390513, 47403167, 281650072, 396263592, 287089813, 842036912, 281498217, 821401028, 508492122, 615140282, 863782683, 812698257, 192388678, 468485971, 943850428, 237448424, 288123372, 24493201, 574103758, 230701879, 990996930, 515533298, 92367372, 976014291, 877270991, 347451058, 44331328, 11181192, 583089066, 632978635, 805166150, 320121323, 913628746, 450863358, 786026478, 790577697, 486446480, 176061666, 833022640, 586039237, 531900279, 978646031, 7704351, 515153925, 325094798, 461371808, 389284942, 494843990, 358979655, 835265048, 332359903, 971710194, 97378609, 144671637, 368825390, 216710765, 216515921, 499133780, 398945454, 971885268, 674371778, 421104858, 221823712, 663283337, 972863437, 427792511, 732399950, 653684377, 569945315, 236037829, 549785774, 692972180, 984768422, 271389385, 905742802, 862287825, 351317290, 578989390, 941648846, 676461893, 95989089, 283235279, 473785357, 369939902, 984024861, 144178197, 428688489, 704030684, 232437108, 419880288, 865816312, 845126321, 908434681, 112979952, 666667452, 9410045, 734474300, 432734440, 83695636, 464837662, 992208607, 157078969, 180768389, 734037330, 578212324, 698148671, 642345495, 141268308, 901670265, 357917857, 544058489, 838994585, 797754926, 1053705, 732702229, 199867029, 711876198, 864142730, 636054935, 71613242, 384389542, 557721665, 460188445, 572922087, 181068806, 586945841, 378006302, 572641271, 973366169, 365733172, 702267133, 953773838, 234226232, 17689306, 940202036, 78125228, 522779191, 84760009, 340637476, 8462272, 238706709, 88216611, 379843938, 721350904, 580484559, 455838950, 461481031, 837877999, 45670836, 193353592, 788918215, 351293726, 848725605, 554436178, 784177759, 847877311, 73977884, 100483312, 868645038, 407572186, 729789185, 132230175, 677954250, 709997454, 753620342, 434731549, 21277157, 90782639, 5664330, 342241196, 209982148, 540047478, 46593606, 974399544, 505374215, 610112992, 850044436, 121144533, 215393739, 838899901, 646328895, 171662537, 9306809, 987684889, 753294299, 446529223, 519722294, 467513773, 516857515, 836028062, 791990216, 788639786, 221277511, 98334970, 353738579, 78017696, 407467377, 955539851, 763830598, 18436607, 276987610, 162779865, 891239561, 362288521, 930501987, 924092581, 849245473, 53574101, 190842687, 902586402, 753028693, 866512028, 640004482, 150150399, 563084848, 818714519, 61742746, 355294744, 322876297, 500101348, 942396786, 997350853, 337687610, 224519203, 329477054, 615522247, 700383137, 148345327, 460448752, 900870134, 219399400, 195389496, 227862694, 577913985, 963676417, 440927992, 888838537, 778848882, 443646029, 45722369, 320137816, 348108348, 173917099, 242013966, 113953034, 821287706, 590384812, 684899768, 72816331, 82218520, 600737237, 832364465, 114785316, 862196499, 80763602, 118212969, 130695451, 515478796, 794953050, 46511360, 103072156, 705665766, 369638449, 894101406, 887683787, 270066547, 518522007, 923330492, 106460563, 889668721, 158958146, 8025417, 153700216, 587259573, 369404729, 835102004, 665769232, 178574446, 199895874, 56011613, 180242334, 508800600, 668570732, 381514979, 665654057, 64192372, 525948549, 727231362, 134539968, 641744618, 485265466, 582612599, 867455014, 887211214, 198163541, 529912311, 425557177, 261538448, 494635853, 661035858, 839424781, 882463499, 537093252, 650084869, 820554699, 769471059, 779397536, 517429987, 779668501, 501351941, 765809274, 962369896, 815694830, 471443532, 624384253, 341775738, 87651195, 706670902, 937644915, 651320083, 481961774, 508895302, 89562545, 519287732, 961079165, 200204760, 607103968, 619766058, 141287442, 792150639, 719721578, 317202792, 586911646, 713381689, 536401712, 719416419, 555146700, 203163134, 595126090, 940455494, 735808230, 757670799, 263510903, 250786249, 806653705, 426009943, 235175768, 770315082, 19573098, 446132289, 640744666, 231515638, 460772136, 305760021, 188881832, 743350600, 153253738, 488056998, 686427216, 16161784, 617348706, 33670852, 962753725, 247099432, 146070953, 188067281, 390637795, 259992338, 106411526, 18340737, 817079203, 64416729, 192579098, 23717114, 732794250, 317619225, 265014323, 752121160, 389512471, 51061728, 627357961, 284238119, 571173249, 210118348, 97742165, 143552910, 84476416, 788903243, 300593189, 29546423, 702943366, 777837646, 848042350, 657206139, 588920617, 759924318, 694430374, 225646528, 795007464, 3281251, 271123863, 805822639, 372103530, 427529946, 734837515, 780128898, 859386131, 517442603, 151837817, 418896443, 13031262, 480542174, 134393839, 709846168, 32039841, 816801072, 19764885, 585792871, 410450132, 337952452, 727105060, 420829470, 343335648, 105871770, 499327831, 100290901, 762287469, 435387077, 738072196, 676241119, 378963715, 503712908, 425183612, 218121480, 822276585, 521247657, 321712343, 602207482, 101999754, 439961703, 345541757, 522025915, 777348806, 149684856, 925430307, 713494126, 566544528, 973971489, 248255309, 131707363, 721145630, 888870314, 615344427, 8256160, 892490087, 926096834, 431961063, 439254982, 553980775, 746577668, 659004113, 491324901, 455892070, 103022620, 515503384, 318730058, 211792307, 198756289, 976816163, 445944792, 118771509, 211011049, 783406396, 655170301, 60264302, 342889892, 783956657, 760972930, 162965957, 944485650, 32700056, 891998851, 900915810, 963858203, 232148698, 844775744, 819435867, 284644666, 980190178, 907492113, 372909106, 907408858, 764087838, 864302483, 706559774, 859416105, 219492593, 216929442, 933025581, 950394400, 437185136, 803785635, 658116162, 549054718, 128142102, 671566060, 151122182, 220645360, 793245011, 357295918, 703519063, 476925401, 360856443, 164680929, 151318147, 695754341, 66859291, 117714114, 837610486, 997517354, 649877315, 197962020, 427678833, 908533643, 368273304, 401287364, 815996383, 357778186, 735851031, 709199762, 591240946, 37637617, 103921914, 931578159, 990065367, 778823634, 963597653, 909347738, 762071793, 505383911, 548322459, 989715943, 431217027, 657555567, 809675055, 446905680, 335645527, 607276024, 205770190, 533276301, 755017662, 170195334, 491076715, 308414801, 204988846, 495593065, 136358313, 67005643, 153210267, 471814181, 450101352, 807502968, 643708155, 919327024, 793457350, 504436440, 754647490, 776484878, 835699704, 520903642, 434072484, 800894215, 562429737, 144176502, 359832298, 417355758, 915950792, 943826818, 35832214, 643452628, 885386576, 422453696, 59430321, 170731114, 738579838, 579325325, 614662094, 757559933, 474468291, 331127886, 451307572, 827378870, 166216472, 810511780, 967751331, 252302171, 798355861, 667790540, 416999428, 466172239, 505173917, 198876342, 337569557, 682001786, 626908446, 850079474, 920275717, 910938832, 917486757, 571770326, 990987224, 902984088, 306541214, 9245553, 317387553, 660573143, 863723804, 483890023, 216714818, 494690217, 685021619, 521926507, 809405243, 963555890, 493124214, 93507108, 397520883, 858053709, 439528980, 53598975, 282190552, 687951970, 138475372, 880422731, 215155311, 706984194, 258573139, 1956568, 453433657, 708682004, 338823847, 787472134, 831785659, 453270270, 860053007, 789368390, 945186608, 313205531, 718874075, 451403773, 383021614, 660345384, 736670217, 736512023, 613009450, 894221786, 459488630, 253512392, 299813409, 846593778, 399950750, 358572598, 75663131, 632318117, 302817107, 550309584, 41217180, 201542645, 170964718, 579853026, 321493972, 563434911, 407128474, 876447043, 324769385, 883909708, 929053158, 322616006, 617415274, 733689550, 21083428, 149948694, 346304197, 347170355, 625057271, 276178428, 511505740, 719141170, 7075784, 59532135, 712190615, 413697858, 610078494, 852368703, 286737983, 503734685, 453439953, 217262566, 266038821, 620271259, 95075490, 533903338, 593916218, 970030031, 165512583, 855491032, 468199665, 328350201, 644636595, 282527907, 793684896, 952739749, 12119973, 571412086, 521010003, 268756647, 640652140, 841348031, 772808756, 708580713, 877794129, 956896043, 845432035, 102193862, 752833427, 909078120, 68476743, 977075671, 83886988, 642211165, 456621836, 800472419, 896520401, 973395853, 603144952, 37978450, 374159692, 500525648, 399031981, 395726599, 779726250, 654104093, 487176033, 818027111, 327670181, 825503778, 856375464, 141245743, 109994550, 48506703, 725523863, 791947286, 530436461, 569181122, 184684671, 901309646, 652981875, 18693758, 771477252, 731453061, 269687642, 14720667, 362382924, 552217140, 867833698, 195554693, 946526367, 186670605, 553651297, 872531303, 858657712, 616613208, 727616196, 920129329, 45088136, 305188625, 785712885, 179154601, 31993244, 862922278, 866872838, 776631570, 31245730, 755112892, 488667370, 606217250, 538659377, 436705324, 859411706, 979490511, 329555369, 626723596, 979612697, 648455468, 222513642, 149141799, 473256851, 631883486, 298697036, 762912934, 627170660, 191559622, 985271007, 564505776, 358376846, 776107406, 957609239, 216320114, 687536392, 320394473, 114822892, 474117717, 194197600, 349673098, 310907875, 244666978, 915716351, 607792604, 652137463, 896044778, 774512517, 184442378, 587900374, 7559917, 487662935, 336526300, 903234691, 439954446, 886297329, 368506117, 874918788, 523706438, 620358835, 510287534, 583565331, 838258358, 198151621, 228290589, 773473008, 179746990, 683154507, 947430252, 38817538, 211648760, 850841213, 425543779, 711921640, 468347536, 298846284, 459653297, 343947999, 552303486, 285601087, 898476657, 324025323, 508351251, 199806233, 641417862, 422858964, 699793121, 335738580, 75547771, 112990195, 929174834, 772231406, 913128516, 700480359, 887096324, 760306016, 12170504, 214282535, 864455667, 525141354, 311369768, 387512158, 926156806, 919262679, 838347802, 176969615, 737679146, 297317648, 426815315, 597156197, 245979309, 867031892, 812586557, 864534259, 319914560, 530232509, 970743094, 440969472, 626366103, 796707980, 6183838, 472793221, 814670786, 755999864, 989428358, 939131485, 679937210, 476328231, 292763114, 549858848, 310174074, 757316779, 271412416, 890204252, 221079355, 771267181, 31343877, 531089397, 668726507, 958717771, 753608874, 882902171, 991254288, 197570601, 339794189, 331751842, 132369076, 876284336, 92406772, 81129057, 760550456, 5915279, 734242351, 624546801, 398856343, 264027833, 801469244, 171713412, 416555224, 323326636, 393356724, 8018849, 21685248, 800812778, 778628957, 469776753, 915957627, 168459804, 446339121, 836750314, 186178756, 951052636, 606455685, 177954358, 847346815, 434368576, 254327757, 912615125, 135354273, 788685037, 610985443, 434305945, 338672482, 429538616, 183019196, 976218069, 206853161, 681199929, 98757258, 228302162, 458454318, 382111451, 142813186, 318557602, 90991524, 685740768, 700182257, 337351519, 594832476, 119074486, 539621487, 37446239, 19156983, 982360476, 548170989, 622062614, 98611338, 939786446, 384460899, 180201321, 54219525, 706681740, 635723471, 74470229, 423566515, 340151466, 968233895, 265261964, 75769447, 247525793, 446539444, 424839216, 947862861, 525777258, 469016223, 148933026, 138743624, 246868918, 631703704, 412663411, 818518819, 345341632, 486963755, 413261177, 782417344, 936796755, 66855064, 243180236, 611906556, 246699216, 337987729, 561691273, 752501180, 202027293, 183905494, 274566637, 466343829, 797872716, 318904859, 433537503, 367880653, 279917027, 267833328, 60774465, 512006306, 902180733, 952437964, 866161030, 51539845, 331830234, 379749169, 919143114, 529060771, 608492581, 434285199, 502626864, 32011291, 362439075, 262605870, 682758371, 968725854, 322542216, 405364864, 521793476, 322255800, 461113213, 972937455, 980700519, 186824005, 566815314, 706352744, 204257127, 396825651, 65594775, 212935550, 450797132, 490783360, 350192163, 893256774, 22736888, 508628281, 107584034, 547937171, 394161735, 614371221, 212295345, 70459309, 380901190, 352304395, 537504598, 74319995, 800915842, 391797909, 763668153, 585854750, 902821937, 690407521, 946503132, 401177804, 264693307, 691845718, 65925913, 35582168, 47749101, 531342328, 253411143, 636448911, 817547586, 200447708, 245010393, 997448846, 494082562, 417827854, 826901903, 244983958, 862383217, 624901432, 663427336, 164758749, 754687380, 916893148, 665091243, 145655932, 664480502, 550970532, 129392595, 658902596, 297648071, 471081280, 409827851, 714850991, 468883226, 112254969, 562650837, 633949322, 93953563, 348005962, 636686292, 141366129, 412822214, 494346133, 602624430, 660679363, 321413267, 303850031, 899602991, 797264600, 549691379, 556083543, 751660310, 677430279, 98963861, 211186651, 838042501, 530782544, 596182573, 607637187, 338718199, 929305526, 822977313, 683167847, 367554940, 895814907, 940950067, 828007994, 140181227, 924822814, 546445542, 473124003, 596689972, 91451807, 865545237, 514383890, 471942224, 723507508, 447172225, 892098918, 29947483, 120500228, 607697894, 684755474, 860352230, 934637857, 208004324, 898501605, 716273895, 508388128, 243856696, 983727507, 983354949, 286178676, 694099909, 992307947, 159184037, 748230505, 995293118, 321773230, 615303048, 685851682, 812406269, 44597279, 421830648, 324922813, 416877797, 580662105, 229982564, 239890878, 38523955, 341063021, 330967043, 664128111, 96255389, 798998871, 762110003, 624781948, 887457779, 961151838, 476889003, 581570571, 32452595, 874455259, 527056666, 726390889, 914228142, 860667448, 313057739, 854724387, 311572034, 562619873, 490570467, 121172469, 579984667, 563368366, 350358448, 34543284, 456404857, 798008016, 65573022, 658941178, 746844365, 231210331, 447077123, 530151198, 531465319, 115066986, 448767457, 965575604, 82981594, 695273951, 197230167, 376435944, 539019588, 952452023, 548324030, 514160222, 702588814, 696409163, 810539873, 799686205, 791286734, 939643279, 899107811, 467972361, 946081963, 885875975, 781189932, 972608132, 971593656, 18507577, 308035334, 826637638, 570777409, 292924805, 396090462, 920927620, 214501785, 325286798, 737193682, 623692036, 131690853, 72996476, 939868198, 508243785, 539580709, 975845688, 386739404, 470224232, 3617585, 666347350, 332375690, 944047529, 148681614, 112313318, 513088662, 730000423, 338308619, 464007380, 945963328, 92634977, 494977229, 976158605, 778822934, 128716603, 332058825, 125897118, 357873892, 204020069, 645336734, 402304156, 106366258, 359059503, 308108215, 762581444, 730834616, 662351469, 838665001, 285693123, 466544414, 252151950, 771004698, 246743370, 404926007, 114176282, 355110711, 709083525, 668230584, 176011217, 255149665, 935351464, 625844305, 527872717, 705661901, 12928549, 547739695, 910627658, 902319212, 686520521, 540165527, 198440280, 953329966, 377054737, 806848155, 418578072, 28108678, 854067033, 795952425, 670160647, 92537158, 592860439, 995894739, 834411692, 572279600, 144182151, 714441816, 174856557, 264886461, 198667438, 649756094, 175608910, 32542706, 555351851, 667177569, 769046837, 743100146, 334402122, 866073482, 443220273, 520860755, 550544521, 983548914, 633262163, 712750549, 592269438, 712136844, 815676994, 853666938, 428772959, 48218890, 839233148, 998774371, 795858632, 809110265, 155763433, 870011143, 503007859, 62981542, 440165979, 574664808, 175305048, 518890633, 997945220, 922962714, 195153881, 68149036, 10807536, 589570241, 272111852, 580692521, 102398745, 171215309, 639143081, 487021305, 2827841, 84306594, 201469039, 147146046, 128745720, 264757138, 446644482, 334361423, 821554069, 807043453, 890141402, 509708849, 205648648, 466662347, 320002276, 740618286, 789701852, 848029892, 489277161, 694988810, 879653363, 757849658, 454396501, 401078622, 958676772, 40779376, 863582639, 433906027, 725118637, 904739133, 974085754, 737414724, 486190191, 240876395, 782650761, 261289763, 71722805, 160177121, 682360495, 717360571, 501767253, 936682520, 907380271, 697372104, 915235678, 287527521, 909216101, 323120392, 146268838, 837696039, 944705459, 894511132, 200527295, 677288216, 570583204, 43029617, 252136015, 584971944, 341070172, 773589800, 503736523, 953001338, 490918833, 562662166, 53646966, 294425606, 217382829, 984915169, 405077523, 533236492, 663682192, 214426357, 905136901, 313973828, 940207652, 742972339, 561631802, 643628574, 792390659, 937953801, 291785671, 259659901, 412018216, 273686089, 752256183, 724430684, 263849877, 707288802, 602764182, 527595029, 223227211, 948901003, 336746514, 728385229, 936171671, 614797555, 564793483, 311392480, 639057631, 687123898, 933259475, 419385310, 918303091, 997518187, 456794998, 210895330, 629107867, 156964262, 719423936, 986284968, 610835594, 702443591, 120321634, 940477719, 792492372, 39405912, 606664262, 345834655, 589847823, 459193225, 46455752, 745743686, 125014325, 109957757, 611947689, 799525212, 13395544, 909993765, 269341917, 114471925, 228672971, 316624565, 437780111, 764105286, 673602735, 177761807, 823703890, 985648275, 672265245, 999678376, 310437730, 968663550, 808180345, 935389580, 4106277, 716168761, 887477678, 789632853, 37823155, 86273968, 306159874, 432571161, 505152904, 809492327, 529211082, 681791858, 239839145, 870095420, 146022938, 951543937, 830981550, 691779760, 519212919, 559543389, 527638458, 60113237, 612511339, 961290224, 584401206, 244904460, 880616541, 645854449, 824301052, 991834080, 193288526, 852238013, 682620092, 700596012, 752725628, 836050435, 432542013, 125711139, 108683825, 316353602, 304077562, 815821899, 211822543, 425005047, 680301623, 962945248, 931170361, 748949152, 95632129, 409374609, 765711251, 497348707, 225597175, 971596559, 695427847, 215952940, 657298481, 971172291, 902355136, 812203854, 438359035, 929515416, 155536311, 89237641, 574724676, 448668040, 935969721, 912787133, 719198094, 257978454, 628973267, 700013388, 202646880, 282691451, 766511748, 217866928, 876944699, 331029035, 344091132, 759462369, 909452475, 82035367, 554561189, 843112638, 151678237, 245308210, 27113082, 736105680, 380710180, 699741307, 287713237, 991144305, 464379299, 608370168, 329270566, 259939301, 995509696, 215150441, 595295974, 555724930, 324553397, 61677535, 166244625, 356032440, 878374896, 217147013, 480718675, 676511427, 831022027, 90984554, 943859967, 428835350, 897188884, 841730311, 807644709, 318136025, 773129205, 788716147, 512466884, 765843022, 949824931, 160120568, 177284645, 8559368, 542023515, 193080518, 479981355, 900763686, 239809437, 593382766, 459311445, 556545873, 748274439, 895262647, 321354532, 420683901, 661870565, 489162528, 508672261, 587992555, 242103688, 192745101, 889506224, 861430311, 90323738, 458527850, 192079474, 192482741, 415031261, 266594230, 854907394, 327229819, 653467995, 578032877, 496718469, 613206812, 730068273, 180344641, 669920657, 820156685, 67065087, 960946927, 178955010, 832525410, 303064599, 219299740, 813072745, 945473582, 376822695, 661420354, 5327240, 878298238, 671879087, 383796743, 616032884, 706948196, 371520862, 409546477, 611625450, 647608986, 727682412, 256929526, 779524883, 209063287, 688213887, 230821502, 929031034, 217019840, 927413974, 850278952, 816203148, 730414075, 487358081, 718237857, 938781332, 761269401, 957011319, 717439972, 986476987, 226650021, 196215411, 227310540, 204993434, 723029231, 500656187, 996158278, 120116628, 654358291, 715352355, 737480443, 632272546, 514090564, 463262247, 816201439, 801045117, 2609392, 576298259, 235901314, 508599619, 767152891, 164192783, 538829778, 130695717, 349951535, 982811548, 297144626, 334701611, 385192501, 210197918, 369584520, 19368276, 653423384, 718494644, 581731802, 554594087, 133697180, 898667946, 930916394, 469671471, 664165670, 814855202, 152473001, 733691916, 403853188, 47718259, 76152535, 820475441, 93084721, 453493769, 190508722, 43000194, 399858880, 635470411, 132759954, 933982633, 647176902, 388195707, 819918980, 667446795, 255214555, 483955694, 80243751, 687088125, 655317384, 589758066, 210938784, 199005101, 464083602, 353845264, 826364042, 792025407, 319781841, 537302661, 810326489, 671255025, 853924903, 817947416, 25080996, 596647360, 275539684, 141820640, 491439894, 831224059, 484130853, 586782380, 785527830, 763878664, 467375791, 179556223, 10982036, 517413960, 69326936, 534705162, 410434201, 717533971, 218515747, 641092891, 897819511, 854834599, 135177078, 697651971, 671781870, 85470054, 452870190, 871726095, 426386809, 912016741, 457828609, 509739765, 533215745, 653892664, 683599547, 37714202, 368109777, 662238207, 750794457, 867064874, 196878180, 456728264, 694216979, 416163301, 78580237, 538047358, 852399567, 977064829, 964246423, 667861018, 313148125, 681139386, 46824751, 152753467, 465071413, 632324471, 661849646, 282536254, 575636614, 925170291, 210535791, 931458703, 533356168, 419822586, 578376055, 436275898, 402613792, 8119232, 493039521, 259334313, 767977299, 743343210, 878075198, 681350807, 60452692, 166475429, 267641386, 291743651, 648206342, 308021633, 138700519, 884079044, 221946442, 339491836, 698037270, 155271445, 281180618, 634739975, 462556770, 69193805, 67131386, 118679757, 163100965, 630801272, 353843507, 73155691, 781286582, 874482134, 909031475, 743642634, 794957541, 210699358, 356835467, 504320828, 379786263, 998669429, 310597767, 589519955, 648887885, 157563051, 744428554, 258584259, 853595629, 691286986, 705819895, 679723561, 77077555, 921852572, 667357768, 951337677, 600870309, 369762294, 466325338, 348487260, 425596469, 871035679, 218761960, 947126218, 219388241, 295747734, 457608102, 475256254, 908850075, 573245876, 14484896, 446955325, 232820763, 684386006, 336156927, 619737851, 17853278, 861747393, 655846091, 699451008, 975024632, 738012931, 11873342, 845128999, 833591562, 328529272, 481533567, 151851852, 307031052, 805172286, 907194708, 91408935, 967528397, 598595899, 106522818, 300686502, 754363061, 839727548, 238984468, 259198451, 11542016, 728847923, 117914853, 660514545, 104889169, 53065775, 579652639, 732647830, 883830822, 462153696, 392856666, 49468106, 163041712, 970169827, 104459001, 669566658, 97704254, 563300533, 128042405, 577947849, 917270956, 137283609, 650388018, 255056093, 592412981, 720592080, 517675735, 288938674, 115996754, 736907722, 349890144, 533166203, 200805562, 832774298, 345840067, 205517752, 130032567, 292358776, 367076785, 217621923, 805636843, 677479421, 428705991, 561753914, 552531734, 543778726, 346679416, 155638212, 357841771, 149562244, 168619385, 304042816, 138946003, 826868675, 813795176, 442133906, 100544106, 883714491, 92852332, 694413453, 827175905, 585229280, 737239877, 774598657, 856125498, 780478183, 52226855, 955679461, 209856292, 633812298, 772195000, 410492540, 364484647, 250530175, 557132869, 592306158, 984982000, 160443900, 184576660, 666830602, 209248148, 605165963, 572244613, 456106220, 597376023, 377898488, 659052513, 409700530, 935778046, 459028754, 305789861, 33559014, 169631213, 970242274, 315445037, 649912562, 289107990, 178943773, 63341695, 184239924, 388369512, 374443606, 295747505, 91332503, 283768485, 317128108, 840339171, 98685859, 164925046, 420158631, 342488468, 368131850, 704194372, 52746111, 369545669, 421341388, 585502594, 677132612, 176652542, 436752879, 975986600, 416505779, 926915392, 972156876, 310829423, 534895869, 384500749, 818089402, 802877337, 681724221, 877309890, 544274298, 488091321, 9938641, 777051050, 950165805, 69302740, 315063524, 449734081, 420931941, 17395231, 954061176, 160175190, 538220159, 304603684, 844668959, 721106114, 871874483, 885569613, 719331907, 596648639, 375372264, 683138060, 480604737, 478770845, 6433478, 338579423, 527429380, 954292067, 206338385, 195088218, 876796755, 436675090, 551838203, 922265622, 568966941, 359171920, 423867060, 99074972, 862268892, 301440234, 557106107, 19841211, 869567307, 307018124, 914382371, 872723630, 851452142, 220610936, 904970241, 772160113, 7371974, 843810738, 653498814, 913190382, 462234632, 346996221, 525583716, 575945578, 172584892, 957364658, 635587686, 822450282, 601097233, 855115398, 403192318, 10774534, 104905110, 653552915, 822073844, 78281418, 346198842, 776160558, 618005333, 952596793, 630401638, 607574320, 859807756, 736292669, 788065952, 29273619, 539252120, 774599877, 683834450, 442283169, 978842799, 952431279, 592548085, 180067151, 10672354, 107884607, 334958062, 824479438, 982229010, 970668059, 643317810, 281641883, 363747247, 331492830, 85781546, 21463636, 718116094, 160141541, 532090160, 971880431, 503876505, 635926975, 149507759, 685239144, 28680886, 316662944, 10052322, 336725113, 210157288, 194754201, 791911114, 895827254, 866683208, 201986168, 41480083, 691798223, 446604025, 554131524, 193473332, 928863987, 514334973, 178650270, 632696770, 554044095, 831620949, 72147975, 678212083, 650485724, 349754574, 265031054, 847600053, 759915042, 84294308, 430245054, 545534887, 897379779, 232217301, 426966090, 43126143, 852078512, 100792490, 145244644, 953230568, 420373125, 615227693, 697164879, 789373667, 996593052, 580192017, 183560444, 16735240, 572143456, 69362610, 924353312, 724857747, 46557177, 179809842, 431113403, 567046305, 807843960, 190993905, 250671710, 400352995, 582470029, 912864487, 329124399, 319744365, 860475895, 566424105, 650381901, 46069614, 965280133, 262984414, 979218223, 397197066, 258104563, 766187296, 651246721, 4192882, 918405337, 798081138, 183984140, 623393558, 283585184, 712299364, 508612443, 220686206, 45347635, 692249921, 71382145, 140864811, 275339611, 403705366, 286929197, 727175250, 646519689, 93549258, 673498538, 403387142, 342250319, 127236995, 510132944, 212981156, 694925376, 608960525, 293782349, 873315371, 800680476, 715259350, 685859554, 260324498, 829131242, 447850631, 991671621, 695973020, 881875015, 463098193, 43600928, 228847161, 181194911, 445796645, 973672812, 570910716, 934252520, 73951775, 662714004, 819782406, 161789755, 80964312, 716269656, 528443145, 997061183, 898487129, 593912403, 945073325, 693145988, 137594699, 275502395, 643788863, 955661630, 669010876, 387168090, 540209298, 261385355, 597331542, 16100080, 500370731, 297202974, 272713352, 633559377, 704451363, 690607529, 122345575, 900019055, 924317299, 259823675, 810941022, 1914670, 251519072, 549399845, 858861947, 20929016, 422614112, 776374133, 38958667, 945435554, 930064952, 16666944, 594194297, 167037721, 757774452, 711704602, 664239028, 533485738, 954891337, 176607811, 218512726, 826565229, 109523478, 958101503, 25562169, 30620625, 600569468, 884430363, 292987939, 975500330, 158666238, 149330021, 608634699, 863555949, 429912243, 706878522, 388827967, 847353806, 991946458, 656550954, 685266084, 649868959, 123515534, 50352695, 831345060, 643663812, 776941665, 613430256, 10251195, 148009592, 698615650, 945032098, 414462329, 566170482, 343057773, 21370505, 44770023, 841996218, 546298688, 761100254, 177167733, 288978228, 115304455, 188478711, 1545056, 349382553, 163667182, 975295112, 65360984, 366571251, 726802273, 414491772, 278257948, 663928800, 533577738, 793039348, 250699757, 918539427, 811485161, 650850000, 390156466, 684426402, 711541560, 646598762, 522087195, 356742437, 257702958, 602608318, 367121510, 544894224, 831859403, 341425098, 305364760, 132351515, 858605356, 937948873, 118836709, 474717613, 672936132, 33119469, 307313522, 415003605, 418803364, 720120851, 906293391, 776589531, 287325339, 682669700, 210825636, 695512571, 769522162, 467782879, 652195224, 247933454, 523355371, 782464152, 722400764, 8108543, 166432282, 656751136, 184075031, 665465453, 293080622, 873798459, 921754518, 864232087, 579189532, 708248202, 392672944, 549753161, 993572388, 169676522, 435930469, 979088085, 625108220, 577088686, 677724154, 110634625, 504748267, 808228263, 90541304, 119320656, 150870711, 739844051, 29981320, 947345022, 482290134, 90858303, 281654147, 574567209, 241170714, 649237092, 639156873, 83417396, 796609048, 553351390, 188535017, 863174364, 606547142, 347412545, 130418999, 149893744, 4389348, 913816905, 804673878, 616042991, 714179067, 844027149, 603600967, 711165840, 126403809, 234815786, 60227380, 359867675, 735306289, 445324181, 682308164, 694685344, 896545077, 709694989, 192009656, 253019265, 565415067, 579571620, 19882019, 48699117, 423073156, 31256664, 862134905, 141908122, 532987217, 93724927, 269312847, 592131228, 489590058, 311195212, 370133405, 85153398, 493243440, 748389272, 637331703, 839021943, 797172769, 889942656, 59111219, 265361482, 228444944, 364813117, 788317709, 238175766, 891050330, 167529666, 135264466, 465569823, 49387098, 970079720, 468259260, 35086794, 180485115, 953625249, 389318991, 868547327, 126654635, 631752917, 485162368, 895549485, 167839246, 133798846, 714977657, 763115226, 4553547, 851637343, 713274586, 187783844, 543446879, 901035908, 32146729, 407087645, 541568557, 164907143, 761215688, 852948053, 511589277, 756610067, 337301518, 602826851, 390073724, 677505953, 283368302, 895777008, 882428396, 499082513, 639933836, 652844744, 78022899, 123538404, 787723011, 809816101, 477668546, 155952241, 864989774, 400514147, 321611644, 493933057, 116063827, 608548423, 106306318, 601132737, 365639326, 275850536, 79871748, 423398980, 332594695, 87987922, 877759519, 92173115, 321618292, 567024623, 475823194, 46375881, 883298157, 358348816, 920912179, 814050559, 806873149, 671852782, 220610071, 458017106, 343566289, 566389083, 344027348, 516786915, 139206926, 341111568, 994826013, 355063455, 123271044, 871486324, 316629138, 8685024, 882269961, 241825340, 47432479, 412149420, 256682347, 977208811, 688914733, 57206855, 322588522, 706505985, 52641702, 910142010, 823595055, 553458039, 77130836, 64873723, 389901462, 132942668, 48391539, 533475523, 914028852, 695569061, 574702725, 627911025, 836270225, 403287106, 862286084, 649344599, 981264116, 198330488, 173629993, 780302442, 857592142, 123837055, 91652873, 812669990, 729515583, 69377614, 248685925, 332690951, 676200008, 25549910, 716115013, 682428677, 624576110, 343167545, 429742254, 748701872, 924330907, 579204152, 758828454, 692098795, 973240216, 938625810, 273083611, 740551833, 238806342, 230943821, 685462077, 167257502, 654732497, 421288599, 253499187, 589085437, 481949945, 128885848, 778235549, 664209777, 841165875, 59428045, 872499506, 42623427, 71990301, 58672006, 101349998, 363793373, 835452503, 408951085, 880663696, 666407809, 462902963, 241708926, 573093973, 203181689, 153652106, 575450165, 433734963, 629470061, 904414461, 337300135, 85357052, 887397425, 77588905, 526096672, 112558719, 8521738, 37830069, 304953957, 625560387, 716006235, 138820459, 710135157, 539888298, 525800731, 90126781, 324319667, 477112589, 405397729, 265594117, 20829736, 304329481, 801768751, 480575729, 792427315, 739454847, 573564948, 117614174, 740840115, 263462105, 842145896, 550224278, 392983226, 221282557, 176226242, 23685901, 484069003, 71071443, 360257330, 701155946, 295971543, 103982695, 940325654, 293458404, 444230881, 949223932, 10648871, 584442447, 138053914, 683393576, 836333677, 870648574, 239357004, 153408660, 99355442, 897467097, 108592114, 923701376, 829022132, 641537587, 45657367, 363428266, 562680923, 618715071, 20085152, 737568442, 677279409, 797150209, 47085358, 369079241, 609238572, 718142260, 7472330, 84459093, 219444666, 975869183, 36342501, 863514054, 134254206, 218014090, 156123109, 16793644, 296390655, 27662562, 365517462, 82701227, 581541371, 650715883, 726192114, 403349543, 549798494, 264873220, 441963054, 656273453, 713533311, 546952031, 943089540, 552187197, 656943220, 963842229, 63922644, 553388831, 524344283, 471859283, 54322939, 511008678, 696386178, 219292888, 116937960, 77716557, 281538055, 929172062, 695724207, 999146309, 565866663, 756897534, 572584858, 827041224, 354718563, 746868241, 641788786, 834796227, 539988548, 239408475, 197643955, 374567074, 179955233, 387437006, 757901253, 44666305, 122570876, 685887029, 934092207, 998477581, 314436026, 787055595, 563002030, 399085446, 962327877, 63628418, 96436712, 595849098, 68487828, 714657932, 151601182, 483170402, 755657614, 661736049, 864022187, 406827599, 618672328, 815247396, 671017679, 256413551, 929744161, 990739694, 448462535, 12695194, 368406956, 400141083, 468848062, 508513452, 379624429, 263202355, 307387990, 269067668, 998847723, 149243310, 222026395, 917117161, 265165699, 249512534, 467871306, 914987993, 792384762, 353533175, 521947256, 865483249, 46110819, 803731558, 609355630, 923144842, 525729383, 398183770, 710281190, 36855048, 114256734, 243503856, 845876187, 550395999, 789388373, 274108050, 128348287, 757064715, 308080224, 346380440, 961506203, 407846959, 251226008, 943156917, 938225335, 176466985, 158325954, 661724464, 21798717, 627873290, 611758291, 666343415, 80223427, 609330668, 181738428, 620616017, 491440927, 177491647, 878182155, 331893397, 53059671, 346170214, 504614865, 165251073, 126504036, 958217656, 427308078, 886729257, 973821383, 428978145, 43881066, 678857861, 778577489, 380951752, 687090206, 568818060, 72745619, 483165804, 963597387, 950114975, 463068995, 512938102, 44114390, 710398203, 888516371, 177460636, 53881710, 731503063, 700144191, 570876004, 509882611, 199762984, 942974516, 254537589, 909625131, 229077490, 436578500, 137654283, 659580568, 599234428, 352306341, 686829707, 488268374, 530679378, 369974048, 873855044, 306298262, 931784677, 316993410, 511358465, 488843889, 835862325, 760194722, 559106116, 183854588, 109113611, 23938278, 437249435, 268897589, 364868589, 56492102, 278688047, 399936000, 387121904, 602879129, 87984262, 920056281, 49467794, 232158545, 278986638, 893054973, 783174914, 628803401, 526518697, 190200569, 716452612, 510082659, 449584376, 647078288, 262300156, 779730176, 771493293, 343312097, 213840883, 480058786, 517309158, 454760120, 308788913, 32828973, 195573505, 125315763, 563335171, 107200962, 273170317, 594618942, 217448520, 445043223, 127856952, 779260420, 108377618, 624218884, 709623531, 770867340, 818772762, 743265504, 671659445, 724370749, 58964581, 201843991, 704670234, 228625707, 505688689, 124470974, 205788217, 592155886, 102047854, 429573619, 501088597, 323736782, 836492830, 654784469, 167946548, 105707117, 276613928, 630409304, 590243178, 204535101, 39287453, 225544326, 653493025, 873617888, 701654588, 521163743, 185449175, 727904961, 155818038, 456466387, 395905708, 451827438, 730135235, 305474537, 552745401, 602543409, 564767951, 976039510, 180450476, 75402012, 835045103, 955842874, 83312376, 339873770, 595794567, 575991729, 548230218, 44929469, 515700401, 31768758, 296794422, 109144657, 663358519, 512513542, 194197997, 152535890, 152898556, 292632272, 899609164, 795954455, 936239060, 574758145, 958544730, 300630590, 709367646, 509888737, 69545961, 159995246, 477766146, 140408596, 63052847, 185921144, 302553327, 111133749, 463024230, 146773015, 362967675, 686944525, 963594058, 967660551, 931330487, 599883347, 45247849, 376591585, 868896014, 797461181, 291978761, 251756901, 176198683, 872741740, 327908880, 739232821, 693202986, 596079216, 19378204, 701794428, 134113633, 368969180, 971997615, 654530850, 559212045, 987506700, 430244963, 822286067, 453845499, 349067020, 543728878, 242633835, 124326109, 615306509, 409706802, 760341812, 462897851, 145761080, 38124093, 516385981, 198661200, 745204717, 909088547, 510249487, 494323891, 851606857, 675227574, 979524041, 158916321, 668023602, 803142471, 875314017, 481450954, 285169293, 493895848, 202802935, 763306501, 702829094, 898180635, 713913657, 65243239, 290913366, 460668347, 187915303, 232513019, 203275601, 221317765, 976787260, 426729853, 423488929, 352476265, 568223564, 111506564, 520927907, 328422950, 200868349, 331853802, 614798693, 346357081, 746599564, 661952731, 392128451, 25669376, 494007027, 235573494, 400179496, 968102146, 563831496, 416588107, 262167021, 984921389, 280667344, 833187400, 806763184, 162634689, 627831661, 125702922, 241391190, 320061200, 744164958, 899018498, 892280155, 623774520, 537715466, 675262455, 48501124, 789593769, 920381114, 279393688, 950060711, 972124262, 451206606, 770822074, 814361352, 277946217, 633948012, 451974035, 25446646, 581694273, 883489237, 355431873, 691864508, 150121431, 806013891, 611076189, 831339361, 893720139, 444434072, 104657649, 972963964, 994599317, 36787500, 472901364, 610177428, 295544235, 969432029, 751489773, 85966696, 632872547, 595893249, 804399494, 508592373, 87032757, 257623206, 55747859, 501563271, 65648637, 406217534, 696754658, 632801119, 921337199, 177859740, 390544477, 776913785, 352233561, 61949100, 696120255, 511105596, 284431540, 4787827, 404407500, 833061602, 925488913, 261191372, 640405296, 703331123, 842698197, 367137056, 389772569, 810368246, 325837137, 964090223, 54635108, 960531985, 491301597, 666434928, 741504154, 389600972, 353943355, 135586761, 59309921, 877110583, 472756034, 778972679, 318274635, 612121181, 973086734, 24156110, 605618698, 555203381, 450125933, 71643358, 54969265, 850912632, 585683651, 493110100, 470212202, 642191882, 104064232, 971876533, 412920936, 296526844, 786761362, 511056374, 3575737, 422611355, 712281979, 295821935, 873948709, 319827848, 16907925, 55195158, 861741562, 896301687, 632507249, 669135434, 270064285, 273987710, 813510095, 781124159, 15524438, 348748999, 807593468, 433672492, 342931545, 40298304, 449436507, 446228477, 890679048, 379536271, 711894339, 843366905, 965086068, 395155033, 63299099, 644938689, 740792572, 58540275, 37262896, 557842538, 238395619, 253635778, 767477347, 334869452, 57663820, 215178205, 77786780, 541661910, 596132636, 830364484, 151702390, 101080416, 138016364, 167951326, 378198378, 673598542, 266391757, 594664260, 645457917, 746159941, 690128267, 326925431, 20279454, 277054937, 47317677, 139870665, 406623648, 410441830, 22450388, 754963266, 880933195, 253251331, 803482962, 294597785, 81559647, 177929083, 482441780, 896732077, 16481752, 467679785, 72837974, 702687485, 168448618, 256857113, 883497894, 929083955, 165420082, 939528132, 529491308, 989972958, 789739383, 971554084, 416507586, 327957671, 964511362, 123217655, 877397792, 839821232, 588217283, 671036315, 997508096, 213024582, 327484283, 335925238, 192147080, 668206897, 717143409, 946467167, 139598966, 405454285, 358688717, 310711581, 120280469, 457593589, 701885855, 635433565, 885324654, 317933857, 764989178, 873259978, 844629696, 671424448, 520698848, 926542789, 706966089, 350228037, 255785024, 474619419, 898252426, 500196786, 442265288, 585804419, 501311001, 986777848, 395927423, 938192585, 700489154, 977503677, 580315920, 245906944, 622561449, 175126397, 251465656, 877723421, 496441935, 809866948, 837908211, 985627262, 543952558, 322789142, 199328407, 692192593, 34350899, 24734144, 992822617, 464481278, 28702405, 341031508, 582613564, 119013914, 377839962, 923840684, 60216905, 568045970, 55071500, 235191701, 789411817, 903601161, 394792031, 59592730, 861129675, 753478446, 277254458, 394020098, 821412556, 410191068, 868515153, 624775602, 589757387, 338780520, 117834992, 770526581, 91837370, 683444530, 22059631, 775266139, 868544380, 96074033, 10933185, 369113077, 100205578, 969626235, 131445624, 457332529, 993004782, 882536561, 540520133, 134089918, 469906043, 662395412, 641319257, 257003711, 784408931, 71511611, 330678551, 836169982, 635755384, 874437667, 893052213, 67220354, 952089692, 771019272, 306307120, 560979061, 675539010, 261696046, 62001444, 198558311, 961751765, 534444886, 964956655, 971168911, 150834615, 804892934, 701991563, 16191665, 316691995, 860364756, 497638078, 283892406, 783170727, 473761849, 670242330, 945473918, 85415863, 134017091, 644929503, 599644624, 998131003, 223149679, 353771143, 675415146, 895439566, 894827000, 820234294, 110963813, 342110860, 949567507, 373098507, 729540038, 734581080, 586706827, 417998916, 718955377, 903957209, 776578346, 518996763, 900391140, 57324891, 301167425, 902853129, 584947432, 898826437, 811410891, 309895949, 340034563, 626709124, 879794079, 63499035, 830847433, 40843755, 397692601, 828873300, 950588291, 476277202, 871291236, 156995170, 545525258, 783813005, 649792742, 228848057, 875550663, 701376627, 118026492, 134789383, 228360978, 834173431, 313757201, 694743782, 5923763, 970601587, 569602205, 325946223, 457916499, 772540678, 810320568, 886135427, 640959659, 291472345, 575096798, 905220802, 271902148, 107227860, 251906774, 707078892, 778807179, 855341656, 621723283, 449493808, 320834100, 7912829, 510587497, 941736877, 186640150, 861615510, 32092452, 949955673, 38239225, 466745030, 662614393, 53649259, 138091214, 384336374, 176897307, 390768289, 726830374, 96836487, 375365516, 28756161, 910011265, 357710338, 100212119, 611285068, 6549436, 273394018, 552725735, 840991065, 458481937, 701420927, 616685408, 479089841, 63349187, 906646954, 370095636, 57039404, 104717717, 344620899, 623360865, 201490818, 11676409, 120919356, 474460582, 369003572, 634959877, 735796794, 797252454, 46310713, 141316919, 70043810, 690241567, 803515113, 412699445, 663941510, 266134105, 756935906, 117003215, 801685077, 983450217, 405929794, 29433219, 142678654, 226337752, 143120100, 423915820, 236159266, 532123808, 529468441, 280022623, 518439964, 228940503, 23725244, 686429239, 769776112, 796265273, 939843191, 953529705, 765647196, 285228463, 454966610, 923541979, 25083917, 543969892, 948881297, 921001247, 955252304, 647911014, 234564830, 993406857, 785180448, 287460612, 172835850, 322523541, 824026536, 407066688, 898898240, 42995803, 647367283, 150771682, 801350031, 290927109, 376986011, 778745780, 715234344, 572130328, 60918167, 491243786, 745774061, 440244811, 777760956, 334615866, 228635694, 412599344, 727267354, 28859540, 124165557, 579329867, 530016520, 228948972, 706385580, 420270091, 748676026, 308437606, 74755240, 323102912, 219028540, 496250710, 799416148, 537817429, 826686038, 679954834, 358063243, 380556974, 141767598, 557523401, 115517538, 612894608, 20092953, 553915600, 37455292, 971092522, 462921025, 396352040, 723597358, 485555073, 411918420, 455428917, 496108387, 952117237, 60157057, 208537136, 809767620, 683690473, 394718953, 220528412, 322185087, 19098634, 701451601, 504686836, 563240849, 880295337, 343286400, 262317380, 321796637, 691502754, 550074949, 590680011, 950626781, 376833945, 341117312, 800207135, 688211771, 689065872, 936929506, 43031219, 841594767, 946222815, 612600273, 716243818, 907108708, 55576923, 773367635, 884624759, 690619707, 568356535, 482253942, 641660839, 42887950, 430559266, 455261266, 813727488, 804264091, 124106676, 590168877, 234694735, 487574316, 130255572, 645063156, 70296969, 402073035, 834713686, 659792448, 534788168, 425148366, 812187130, 599670181, 68905586, 151833224, 369603506, 14765312, 208509481, 311963224, 266918600, 204404155, 908774965, 213818393, 195241185, 87451103, 503015469, 843513543, 816780465, 294467967, 77831020, 903633335, 162600317, 893037192, 971323345, 304610858, 847441027, 323969042, 434602870, 22575838, 65738468, 841367714, 934338772, 225748318, 686296862, 957052779, 779415817, 301604943, 703471205, 907334367, 808849299, 648990802, 187725157, 129361299, 458928080, 968689567, 179000012, 613334298, 807710797, 262805808, 955231713, 622925632, 105591825, 790180603, 280087464, 268904104, 696305417, 105401620, 16423805, 61359705, 480394655, 918972356, 91759498, 402185589, 295960566, 628178983, 666311455, 728522986, 726499785, 280270619, 665356642, 2523392, 946967756, 482637139, 617793094, 178349803, 380480164, 674824234, 932487733, 211130311, 306049421, 443327981, 381857018, 193191278, 198823267, 712559655, 651014145, 551718282, 524337847, 329487597, 5039727, 802465377, 276792287, 172711772, 243545847, 516699879, 528571582, 580902981, 727466858, 806403749, 767735606, 966880808, 734022855, 54854027, 951106390, 533030378, 933912441, 435095372, 704121124, 25852585, 24745447, 86485382, 126487426, 688852436, 105170734, 503378062, 962145191, 35132024, 478434269, 676743061, 417535675, 784858021, 747384244, 143007330, 126306176, 458243717, 58848665, 253290067, 392681732, 459646729, 90919604, 446970108, 184032814, 826124826, 580457540, 931665039, 243160663, 717783291, 589354730, 538866918, 920849716, 771696210, 600783940, 612719439, 912533437, 374586150, 171305109, 541891120, 405071405, 706294161, 792927395, 421042610, 983693721, 213556468, 214775267, 189630777, 599203894, 363389878, 295399392, 441642683, 908025368, 678163102, 904426996, 719750592, 500496977, 355342555, 194442471, 273843668, 945372599, 518945457, 601446383, 957808082, 512225109, 658895251, 852891762, 921905306, 255165732, 913719739, 42750260, 630023614, 36210663, 217087832, 532427784, 856726144, 669851916, 819377892, 472679202, 586760278, 765752291, 442956656, 358489639, 78260797, 626931953, 818954979, 604811272, 629954539, 853668288, 735513710, 842063497, 972593793, 503054243, 541090722, 377581920, 382596438, 297477139, 955881256, 290956952, 334210, 992155351, 485790386, 699765676, 259830845, 780352717, 729279634, 436459958, 623686821, 830465634, 216881564, 578867357, 271789749, 893474578, 94837811, 771420941, 981052361, 32267781, 690754655, 907690745, 373830607, 680394946, 715802486, 507625279, 197488399, 917883703, 293360682, 160023880, 963594903, 743083968, 363690838, 218780454, 906409743, 61712189, 919436997, 934384281, 915326933, 410089154, 75704465, 871678105, 815129824, 513166796, 240613386, 96542246, 295126403, 893354858, 571890250, 217650323, 661378314, 4874573, 501970307, 514793366, 471015267, 354867759, 70083505, 934752258, 199767677, 998557945, 950320753, 481049373, 585511999, 584303570, 777218446, 902384304, 597441289, 574914067, 728211757, 560925347, 183966168, 422842089, 303854049, 396753055, 2183056, 720379209, 371102786, 347614898, 668207404, 81823269, 882523490, 404784249, 292143337, 530381730, 896114540, 871602619, 305304625, 854252079, 428330098, 24169962, 640340549, 803001359, 160048803, 828401624, 794479037, 595167488, 546910287, 910102245, 974359063, 679627540, 436404332, 348505239, 344212367, 450553750, 855540110, 262967689, 983471869, 333073749, 728318976, 710257289, 311573152, 614543618, 632826485, 614581736, 945768460, 809281627, 704924427, 968802436, 494332979, 7134439, 95994050, 136704761, 82403684, 694850128, 649623682, 830425362, 923772671, 179853197, 844506634, 151098168, 481543928, 402175311, 655761713, 383044602, 761450320, 211458088, 303839102, 421045923, 552878030, 389444669, 472606848, 80814252, 574488197, 486212075, 520900734, 271162524, 677056815, 938795070, 78998959, 455738688, 175169815, 31579838, 101526676, 678824125, 385591356, 705188085, 785991159, 881956970, 419619306, 18592972, 636308156, 621038841, 979270362, 759652432, 516238924, 134781277, 61828858, 223671402, 850779908, 81165330, 577881862, 260021465, 304021435, 263378049, 7066170, 755438313, 853945543, 367921773, 568449134, 704356760, 393845016, 732370578, 693276358, 849892767, 722036980, 884164738, 505310415, 663132469, 197131455, 576910570, 485900247, 637469926, 283726437, 313368902, 23154556, 140613369, 682081777, 428118113, 595134465, 625714835, 731108044, 366332235, 726163340, 195032005, 36068005, 893956444, 675522687, 638064276, 289371433, 895032322, 135989203, 723413953, 542487753, 740718187, 608688273, 727351484, 939776177, 420574308, 534198626, 503300400, 720386521, 304052083, 663428794, 396865245, 83356727, 200638056, 152124962, 243606471, 82526027, 321390929, 702428029, 97664980, 53321471, 246236798, 463718852, 530082575, 240348926, 581934619, 313694997, 60987255, 193023017, 391009672, 126837774, 894824264, 299069146, 179038758, 831074180, 114054912, 404209764, 736346545, 72054364, 49770388, 85295934, 957595424, 936078522, 786358037, 970525255, 117070508, 832505716, 379038025, 314951701, 380174568, 600615920, 917283903, 43718430, 893038474, 59920678, 944382666, 696116395, 350682776, 965532369, 904474244, 964682128, 121365609, 112883591, 290682780, 71039101, 541610924, 541820106, 942967481, 554586126, 868426620, 413978763, 859405813, 683416653, 770694255, 162002429, 245276150, 751832757, 917859144, 244485925, 597880737, 56567657, 875312759, 135252593, 433468754, 741001638, 373942441, 42588149, 482214870, 56587570, 384163649, 80585417, 471357602, 172362182, 578271642, 219966213, 220873024, 416962992, 378763852, 605093243, 244666837, 743736001, 886259360, 973963809, 562182152, 181192383, 409623114, 942142054, 91657675, 392542731, 322024810, 31985462, 886862166, 964910657, 363233279, 813586364, 207908303, 182927501, 203463110, 420055847, 844583882, 937252206, 59428683, 595604654, 846282577, 208794298, 890144934, 190933755, 231819424, 860624110, 998818487, 537279847, 621191950, 372835274, 870292595, 289877810, 531095644, 490112890, 16374014, 835285621, 387463495, 719709577, 524018960, 298095042, 891457573, 846231086, 693385908, 831598996, 840916004, 767829064, 731658344, 758810299, 941345695, 224966346, 45368090, 810511232, 183556412, 137698726, 979210941, 581836690, 913599238, 763096719, 324755831, 390535329, 741770661, 321175401, 495403270, 133779268, 732439598, 313105045, 971619616, 457350770, 68053288, 889487030, 532550060, 379649126, 114381384, 776914196, 386826304, 639171435, 337947430, 368013434, 23148747, 156707171, 736799432, 816364814, 946150937, 475836497, 963372216, 145902718, 823953255, 275936527, 491363833, 426756680, 476730116, 729356079, 536374490, 771709699, 893687019, 950787017, 230210869, 100610140, 122414247, 681657031, 213819278, 567423955, 412032426, 550782746, 699163121, 31050170, 203612192, 417570671, 326090021, 305453186, 483992728, 208642055, 947861741, 25761255, 61558915, 744887695, 666116827, 105184163, 948863547, 484216659, 767547533, 641836463, 695239459, 954135661, 629514189, 884213401, 546538169, 42805168, 356796050, 34444077, 540618797, 660768611, 349207550, 907072657, 762947440, 871964579, 523955868, 553944321, 708784313, 574680775, 730773456, 157011568, 831176259, 887533237, 556557127, 50360610, 413224275, 141812348, 890009491, 466862552, 478872277, 290909674, 378269963, 147660375, 537208742, 182028392, 647429099, 325027518, 273954733, 869751827, 687359483, 463963178, 843920556, 690817148, 350285464, 162432236, 591422345, 52940484, 399911403, 395686615, 140650044, 677946170, 344221093, 63911089, 393663308, 842007374, 869292570, 767998772, 69371034, 733587705, 101365280, 78118210, 110434822, 102976286, 170036753, 135530946, 334257343, 747255121, 276084101, 41631791, 233980651, 318090143, 876861055, 210502472, 494495119, 43412198, 652828310, 189627933, 566300102, 352921704, 956595521, 928318820, 527662514, 103887279, 445544491, 143550181, 900909695, 40593816, 814158372, 314833692, 265197532, 494477473, 350004980, 932849198, 415014832, 456327630, 26048036, 72468986, 502916999, 958755467, 632551260, 799640385, 689909906, 533600380, 940271224, 95377519, 73795973, 124050712, 935479842, 807639213, 377715252, 219973846, 127424757, 252416003, 11496774, 226775424, 913053896, 990803381, 175101755, 845924366, 193256220, 604913142, 29846859, 328021945, 69438636, 331932697, 5264991, 826334924, 928697800, 901437179, 241630969, 321245011, 193580426, 741342019, 870105129, 76438527, 490702275, 891841824, 663469171, 205551859, 459437786, 551583203, 777509742, 551425434, 364029319, 446326065, 170210306, 893716217, 423957829, 720957147, 932926486, 447615658, 257004971, 334351237, 317495180, 664781859, 146492454, 36195916, 295716303, 295519445, 740256704, 975072692, 123133368, 232534174, 744294957, 510882336, 400504162, 428074402, 268498237, 984263498, 894523373, 116358850, 644523089, 988595926, 13462237, 790418450, 425288406, 351960858, 912041763, 917879027, 795030677, 566238012, 900332288, 348377753, 607432848, 986712214, 848222906, 575281318, 940899439, 583142204, 363552357, 506687185, 693889104, 431099748, 265367404, 748369742, 739291001, 588232251, 663263042, 308260599, 595215119, 49604626, 467181767, 771078233, 540018380, 826008056, 967147030, 793465729, 494879431, 603911270, 320736607, 193487996, 863734772, 455921531, 14797073, 13602303, 963753922, 381230349, 387131544, 647625122, 234133487, 136666653, 115121476, 958850690, 281809940, 792082636, 808715058, 354059284, 487191869, 866202504, 34223432, 338493274, 400371637, 848353782, 2070974, 961698607, 67972833, 786397207, 105774277, 34387279, 669260444, 191696185, 895437889, 266229221, 80272310, 196308976, 956451601, 84304808, 364655284, 82654347, 783853895, 384321281, 600533960, 433742197, 262887887, 556026685, 647808552, 422207151, 655815953, 358974231, 486018864, 27703329, 708498946, 229787115, 7184445, 563924486, 619051319, 711199451, 333929043, 349128945, 210503688, 235083810, 126570980, 86237074, 442863448, 113060788, 620676697, 996912133, 678435652, 397554395, 338990080, 399689861, 365639276, 410983693, 908497976, 50377408, 18219232, 43943992, 171788038, 688292796, 880080405, 953544782, 345304283, 48615051, 139763751, 665805708, 902955319, 252970275, 734341266, 552637768, 306258052, 438627126, 125121520, 541878063, 408555137, 282278630, 337057770, 842921594, 144557033, 569946945, 911307087, 663510007, 143000559, 512877699, 714077556, 786864237, 812393771, 590273255, 456850418, 606378090, 973057536, 164841315, 781969594, 880366598, 743697208, 730985905, 369289755, 718464504, 661668946, 524759069, 55439492, 378293262, 341867736, 319550358, 31118182, 124869206, 629030560, 785966764, 429433187, 300806230, 787278987, 421172471, 914177787, 598426834, 596928468, 368343825, 921497650, 644489833, 272229846, 938870941, 272327929, 384330240, 136723941, 949165317, 200344516, 725385885, 536020691, 878100269, 747930003, 352352405, 670508783, 455051656, 906219082, 624703195, 639559611, 8501254, 515056910, 508845802, 737080751, 929023940, 351764415, 538130224, 702125205, 46687052, 256013318, 431156102, 553037725, 248280171, 892958546, 45010592, 903401503, 658981063, 120347756, 368660107, 709240647, 279490292, 84877022, 943601194, 674759969, 63747688, 727450943, 640449699, 67263484, 820556657, 22775233, 704946878, 982243061, 106679891, 621770040, 868714404, 185848511, 216174252, 405948555, 49244494, 650550269, 917218184, 48562307, 504423794, 156125928, 977207450, 556537580, 704958577, 674692275, 510250269, 498707180, 762080022, 339887212, 321611637, 228780097, 547175454, 791492927, 771515838, 743642904, 615189570, 346909833, 742109957, 728081838, 404984268, 931324620, 294367062, 973701510, 660813618, 978244723, 76796007, 495574402, 247155534, 731070430, 349229633, 918704316, 137974985, 865905133, 454850336, 145683525, 574078012, 422236817, 112436592, 890573851, 296821699, 650085333, 999767656, 357563139, 119348760, 957597794, 343388649, 442498138, 413540898, 943446072, 284572259, 899431394, 851365855, 150550553, 242269535, 618480803, 597282930, 485666074, 380780558, 992121639, 167774547, 902466434, 344612967, 874682347, 960584654, 304751897, 94819975, 584444608, 745218668, 217625830, 370285235, 790733892, 81381816, 618576489, 874770672, 827290544, 751477026, 776271154, 127101757, 660076447, 239346339, 806072432, 583000499, 240950177, 302771713, 507918900, 63811922, 460893622, 296871164, 658004738, 631721989, 517009845, 773896372, 719030023, 740290942, 203308741, 645119092, 782475843, 767963171, 389990680, 9969147, 794563482, 944146588, 349221114, 707755898, 378607775, 477344124, 596763205, 714820127, 917577960, 549595151, 853390623, 883678919, 337593328, 457755052, 971914470, 965693465, 7930495, 842856252, 159979536, 81307058, 305926094, 764446563, 189187853, 449317598, 509933071, 765197410, 953667606, 642425324, 779910326, 472508207, 44227914, 184478509, 787122805, 500304187, 783953806, 643880098, 322316231, 825029201, 42248906, 877415194, 944543314, 673940130, 197433793, 160793971, 596823119, 962676193, 314925033, 55242542, 578648374, 960792017, 209651055, 481146158, 285537480, 321076465, 75713509, 269091811, 904215230, 984848477, 858124436, 799609609, 925404732, 781556252, 604641360, 122122606, 473735091, 733059264, 814950920, 477729459, 840065599, 332930983, 329638880, 238936457, 578069266, 859423748, 815886280, 617725548, 94740638, 890038413, 520448143, 346941236, 826964887, 974531641, 251143163, 260074112, 80717764, 438505000, 307343588, 136235298, 32161007, 302521709, 204935313, 120140643, 839754639, 862966191, 538435227, 954032206, 197598706, 702373022, 212749984, 78210426, 613502702, 23650074, 148434111, 377681468, 849210302, 271331700, 654140784, 971850581, 280933617, 337308024, 457683746, 371778394, 885251211, 460264459, 513316600, 759276704, 691578791, 562058688, 539743988, 32737880, 709345940, 291798791, 775513836, 570631613, 103984454, 203574603, 564459182, 937775994, 713335203, 767390652, 470182117, 607198947, 129230928, 61669368, 550956751, 801429789, 28912174, 406078008, 673747078, 449914872, 323203530, 355904579, 205670568, 628821667, 210859671, 9725469, 935817324, 928601345, 925696284, 377747746, 380271651, 339292870, 413137, 166926463, 495257825, 597254960, 647781511, 41755740, 30412719, 855575801, 201210941, 986001231, 289849470, 635929133, 764687757, 374638328, 269127187, 592865777, 342486272, 988571659, 232053968, 833295527, 947362702, 582244259, 927749461, 455255677, 437232326, 888290202, 954662068, 249129418, 504246398, 649455908, 998027801, 3857469, 684129820, 740783309, 365207636, 277667265, 918154401, 134067830, 186603240, 219532983, 634941587, 395586462, 565988331, 637571381, 980881420, 682393487, 125470074, 595387139, 952267874, 94958710, 629966863, 320257983, 950410967, 453087878, 346642767, 629702181, 201097268, 924972469, 329425156, 332034038, 43060384, 995799176, 648090848, 970581463, 130670858, 719963750, 260309704, 345414850, 180310018, 703661444, 191331380, 935470715, 351119111, 144145941, 651462852, 538239796, 931400154, 432385134, 53398854, 187006996, 89380743, 228227352, 899793985, 235795659, 791735382, 62997083, 787614922, 289294936, 567883687, 804713914, 74277736, 319491633, 284724440, 51366828, 403176062, 36810203, 55970687, 49504454, 246554663, 508567709, 241097984, 653840063, 615500543, 32808074, 71916109, 972653954, 987316826, 921195943, 940773742, 259365861, 840760072, 952642013, 613364396, 215199265, 57246732, 582612445, 868374505, 280365946, 312019574, 376632696, 220686824, 770346356, 758519536, 618972739, 347553291, 985242515, 210022654, 625240249, 643394124, 90031800, 394407442, 603980687, 44210148, 330738807, 4085084, 904813516, 71460195, 632781636, 151863557, 206713428, 495893874, 279677186, 868544513, 703294484, 652063915, 659580793, 356769360, 892929447, 53056356, 734480413, 633808262, 835667932, 877702235, 408716453, 775183560, 179403655, 69291805, 157968141, 207494707, 101046143, 873403513, 353580959, 914996912, 461391923, 456792239, 645136847, 190476000, 998859170, 819825363, 964112594, 178013862, 458637260, 647639550, 366930668, 931639374, 947577750, 169206698, 574979114, 276715641, 75839513, 685260830, 811984674, 893462638, 844092074, 788496132, 795404284, 461411334, 146110472, 789255016, 401014460, 423093999, 745771641, 395557341, 371744924, 104315682, 142012901, 256253283, 958074497, 795041261, 838737940, 304781045, 579409703, 157824479, 391474250, 673155586, 265280768, 209530064, 179952744, 51834559, 748585385, 804193382, 38875493, 607360563, 68422057, 800833092, 199249888, 477558971, 899773399, 937493094, 113810178, 515648249, 792800003, 719782952, 950059829, 230485476, 838773762, 876036619, 62561958, 350844917, 345870364, 716002597, 315327784, 378425137, 684763504, 481183797, 563410712, 593081388, 402851922, 436678407, 227497503, 257398952, 318586409, 526553681, 525981352, 535895802, 678266858, 984241436, 52606081, 626460936, 39525830, 47861406, 857727471, 253770367, 532646571, 900949475, 446369562, 782685645, 399663243, 625687600, 709458817, 974671550, 610848040, 237010365, 70929354, 559855889, 98257819, 790451163, 526283744, 734206302, 834115406, 670365653, 925073712, 889194039, 245288723, 345383285, 122824024, 263134378, 262132098, 571726883, 776043588, 929756689, 743365015, 550490437, 768878167, 467568576, 477240345, 104626489, 200920706, 88920718, 647559230, 70359127, 700255282, 328283831, 671529830, 585925074, 481681429, 313871815, 913529459, 624079285, 931851278, 971018647, 549495905, 963373249, 17687827, 672143279, 145334634, 56125941, 839379210, 191024751, 387792843, 532434928, 575398872, 964046089, 68956989, 970544570, 734923868, 738782748, 83421742, 318038190, 284381502, 246894024, 750880805, 947583087, 677637243, 676091546, 416249957, 442087143, 163816508, 91916039, 941839674, 268764049, 278357062, 318578139, 707063642, 123775746, 130863219, 727359282, 828154062, 410748969, 799568948, 582439291, 894876527, 167626607, 168189336, 402561431, 480291256, 355768261, 851926077, 406497911, 988744114, 924406454, 812105311, 310493559, 964452010, 921515274, 32049086, 471438039, 497415500, 281683792, 245495528, 498702708, 508302592, 480609424, 103996857, 160404003, 969137435, 104852059, 64925417, 323257156, 606612431, 429819479, 701501204, 994364117, 609239776, 72682712, 131972638, 98941590, 580006536, 737990722, 663807039, 844314788, 316791120, 195847683, 670238649, 170829550, 291172727, 483117438, 629135027, 924485254, 133535934, 701788556, 483577865, 288704836, 145917884, 379383303, 756255172, 876536136, 599633739, 196672800, 929702664, 567500397, 968495293, 850261435, 16672438, 549614485, 744189066, 632438972, 721892432, 283470422, 499593655, 143942562, 734071411, 553397195, 546780635, 542909877, 205479752, 394800227, 738674657, 874432187, 51374445, 343448538, 280952449, 97670180, 444569648, 966728220, 345010286, 23618805, 371130895, 732393208, 817140606, 604736278, 832252493, 621415210, 261278365, 51422957, 949312303, 155176450, 924324944, 354877697, 243133606, 267324781, 728221028, 6591538, 698413221, 597570440, 536450181, 479321520, 540825012, 419417779, 840155795, 741536592, 846173366, 548122003, 706392986, 61629268, 631967848, 675987537, 956138172, 684902646, 983277020, 791549863, 574343222, 986240065, 412034857, 839980604, 617071014, 80786162, 623925628, 622678848, 241060342, 31014778, 373757953, 158031344, 266554593, 169832651, 794453727, 63037352, 698760170, 443927361, 375540128, 432121063, 505505754, 580175481, 38292591, 658830821, 136666680, 86220271, 74620159, 122200483, 512211247, 140041285, 717505288, 190392801, 82053139, 464412460, 150091925, 598126750, 138195637, 985614393, 49299551, 686370978, 281856851, 88158854, 2252721, 249977654, 556187515, 36416337, 112447060, 262686626, 838096879, 725968959, 176710183, 226163187, 426164697, 28184618, 366174065, 313362781, 60127211, 659975899, 477935688, 660700310, 950627899, 725442987, 388072967, 748025360, 806280357, 467769221, 31537869, 875803751, 280956705, 31460064, 866931474, 742166340, 338335536, 796604810, 985647880, 613743862, 683006562, 650756149, 157239140, 705422871, 979303747, 171136274, 268719243, 341540308, 810095177, 397293314, 279404569, 952602092, 748981602, 227759910, 624079151, 194477351, 805453582, 822333787, 306872024, 981388524, 748007443, 777697210, 560335743, 779114278, 730653929, 894757934, 147124165, 175733406, 163106971, 101270181, 932958450, 277266264, 674525028, 645815985, 300968022, 761152566, 869819600, 39892622, 382515242, 905544425, 738013487, 780792986, 33822824, 98854451, 178336707, 714382731, 970623250, 940276494, 117786023, 517917430, 208357526, 534016583, 363507793, 289704828, 774026446, 549108055, 812993734, 129187308, 246735166, 151468644, 917653528, 371184435, 769726866, 621433729, 724560950, 955782127, 469883229, 683794263, 206723734, 799019290, 415705929, 561879934, 654210487, 420476077, 789853976, 683998927, 965389104, 931492221, 956993263, 126590016, 430213021, 154011598, 260362066, 865031424, 290039132, 868575416, 448551819, 721620152, 769625126, 806385153, 59962872, 573208090, 373974090, 597148136, 246023682, 702729103, 642685855, 388534303, 745231132, 718816220, 838160993, 644877831, 513672258, 133446269, 961114076, 622800698, 764828437, 325896672, 716263038, 827395983, 533989073, 678484511, 746289309, 155338429, 458013016, 955431771, 852959055, 730812807, 609489323, 317078877, 918802986, 80763076, 566414502, 556246926, 812292365, 248105353, 256662765, 563738000, 534773043, 316129988, 431459486, 428079562, 354556417, 145391045, 482451650, 718529534, 936787877, 928782963, 774710547, 669777175, 594005482, 390668743, 474263788, 98519862, 235250697, 380920644, 934055991, 73639175, 741956263, 740787997, 341459734, 321939556, 160149139, 548501828, 947056706, 557918817, 276935953, 290135829, 189070756, 493086070, 366333227, 45859974, 857466632, 715361549, 241633592, 948859257, 878375833, 185413319, 555094239, 249002923, 331296754, 469262698, 804501537, 376573179, 21881137, 754911609, 972490691, 617653544, 201800216, 977524927, 965774734, 53224775, 172121243, 572479186, 618371198, 48809262, 384385816, 96812185, 87408160, 265179715, 515673267, 205523459, 852578708, 25621337, 558422967, 146488904, 945467836, 886411065, 124853351, 840568667, 946906286, 633412455, 253367943, 118694691, 345424901, 58178920, 65478757, 482508610, 747161757, 967017343, 919190794, 744678275, 927553361, 608433038, 920178477, 994491305, 952794535, 730946603, 671097322, 923677370, 464359791, 273480558, 908334451, 751271072, 476265470, 747733185, 462713377, 267618092, 536380332, 578062333, 116763605, 567191803, 822201580, 573137228, 923308731, 570367227, 999872174, 726194179, 752958590, 236462682, 257529155, 370275790, 665401655, 858376865, 595725602, 435704845, 790552537, 114660784, 20079972, 511679224, 9026411, 352589830, 336233774, 536920939, 207847979, 71280163, 328897730, 635168029, 31027885, 968884934, 7539957, 247978377, 763173136, 100025163, 357036715, 66334877, 308678587, 436977357, 87103202, 619991186, 932691001, 984902214, 556366913, 509853728, 580989252, 90167578, 2574241, 600135710, 378647869, 181625547, 664259652, 469991340, 983692224, 314134620, 247404477, 721419981, 226362074, 588234892, 660414675, 187612047, 839590283, 514856853, 207896106, 89868940, 156875319, 578528179, 112474668, 613894966, 540732889, 6797088, 535474935, 737336662, 858515544, 106482164, 182091754, 587509630, 106497918, 374834585, 764145686, 575299567, 531890565, 652885019, 556388534, 913071111, 287208453, 403237688, 122969075, 229433122, 672325511, 958848048, 757437716, 463351669, 778347943, 222451014, 362581096, 279004635, 654356814, 874344556, 49250804, 179895472, 283079398, 101692526, 209065383, 307010105, 793767949, 718466930, 200455343, 750651054, 335132570, 729565314, 978653130, 592850811, 637744179, 754434516, 226840934, 287819181, 460401466, 799965313, 488947184, 9881040, 510965329, 282620345, 24799359, 430789940, 637654327, 465581254, 146777871, 533535467, 30732897, 803924534, 231740514, 608498876, 228657765, 856791176, 278864311, 112584120, 748965916, 21311369, 111972219, 842584845, 622270407, 275728496, 86079552, 672152080, 594281594, 77197862, 987689068, 488476194, 563744821, 285614044, 983844293, 128248916, 508650973, 340549431, 339872697, 133419485, 975027701, 586022999, 808140740, 4778823, 333508218, 95076117, 134690114, 971077908, 437072410, 639490058, 638528300, 332584353, 641086571, 985101487, 919746996, 546756733, 259574049, 819163829, 438934807, 844638417, 452277250, 719097785, 471198267, 821868559, 277742779, 291577716, 241434695, 292064143, 288774435, 338281978, 817432354, 84855259, 612941264, 199725210, 667148628, 203500344, 77751487, 945649733, 301362360, 998458123, 768395404, 302614937, 38344527, 457708518, 182312703, 472080930, 553525600, 222595232, 368820958, 360565219, 746011791, 396006312, 528060690, 274088185, 57037271, 258829014, 55428460, 992913557, 272615574, 774449305, 972882871, 868230454, 678772421, 925233772, 769017505, 615553762, 55932698, 410661241, 217043489, 128026721, 376681879, 804434967, 859585352, 538664272, 205177210, 46270046, 538709279, 942178295, 364791507, 434943497, 917091406, 550939820, 806627078, 734131400, 493698025, 365846868, 336688418, 498015085, 9246360, 251706332, 204296723, 396856354, 241843849, 764683703, 516286213, 299792055, 957010432, 888513938, 244639460, 510359668, 570857928, 518665617, 918258861, 526049301, 928044211, 959681951, 112933908, 503963663, 176078054, 630529880, 760109910, 434033220, 19363455, 960194562, 239652151, 591021489, 551970423, 1424034, 873883553, 563942407, 915698117, 422991958, 176500127, 300452443, 911699742, 799624947, 138346723, 266738749, 896762749, 986407456, 662091077, 554353103, 570771230, 299517636, 253251878, 143142300, 398521717, 624790000, 750111553, 346544499, 996184792, 137459530, 422452363, 879200687, 297000511, 850669866, 50222474, 379502172, 557238185, 65043915, 70199011, 39373235, 2398212, 687424702, 688001490, 451850193, 550907719, 808954701, 455396427, 960573404, 174504357, 164331963, 476846800, 757292510, 756260206, 127473420, 687355017, 3811991, 301389459, 962708733, 89799187, 532730258, 612783777, 376901077, 985479119, 296893200, 749245728, 820788581, 699363272, 659006450, 515408567, 880269341, 591008462, 948300870, 925101615, 162714471, 17318827, 356760970, 940401671, 894848768, 266386430, 513833792, 400341981, 624812802, 851595012, 641042927, 861041008, 91910775, 839483024, 609588593, 762718828, 194512782, 499754612, 304829657, 11671373, 48013919, 70460897, 575171930, 461439960, 959416402, 839426734, 677175575, 846334071, 98720319, 418593601, 766027230, 403942760, 285327486, 179555240, 490582051, 160479473, 667684854, 563718909, 275878782, 125767915, 896793346, 977390146, 885289974, 703504479, 153313005, 249243132, 632606779, 532179489, 215154774, 538153065, 477519775, 168845153, 222857551, 792028484, 613639547, 157447244, 607303535, 877226123, 857348581, 360274572, 254504380, 467636405, 995311956, 115245007, 961546206, 572493152, 582260834, 252459945, 369656644, 515113059, 399332583, 544118418, 199537260, 452590772, 725307206, 112257355, 662397093, 526336374, 346570754, 846138599, 350874162, 298841300, 287757436, 259565123, 323463716, 54233331, 296983394, 305892937, 36852648, 671605992, 515420038, 818633980, 281335453, 777500611, 63322573, 589513277, 242195393, 442305403, 343461696, 458837579, 632947694, 467828658, 87458234, 795798213, 464217494, 724677978, 795325970, 264936608, 692409610, 541364613, 400803668, 201690511, 366330305, 704083564, 913056463, 672890394, 675377306, 657441681, 961506541, 753642618, 683059624, 203014408, 158990622, 905390377, 575435184, 892945838, 690542047, 768246148, 214077392, 249349965, 153927760, 594221414, 496735970, 521005266, 988163392, 135120786, 110653766, 32733652, 573489169, 550434494, 40532485, 132920969, 176509284, 852459679, 694321428, 596029790, 196646038, 590381423, 692880684, 394891853, 687751387, 584979002, 516916757, 211906325, 620730653, 277091772, 23233484, 491859248, 658763267, 970828953, 462386667, 449844650, 791392573, 460881357, 626294108, 603343921, 107791183, 146806407, 991532783, 117496504, 91876249, 211216717, 512865184, 803192343, 58794185, 939885977, 679174938, 891827438, 248804402, 691759784, 343927678, 495956468, 422156765, 972148245, 764070091, 416109030, 63983546, 175761446, 460857380, 974509081, 644795900, 140672228, 6222342, 441345955, 171852203, 217953816, 496746986, 833699327, 909633009, 506134290, 512952276, 357129174, 900460257, 371237434, 620232090, 308587171, 243558764, 18622568, 376228395, 328648180, 228183328, 606728781, 133114492, 891837261, 342863030, 478468775, 683393127, 306470232, 5671969, 955450176, 924595129, 3312772, 695124763, 946161015, 377374021, 264020996, 324155424, 230960074, 839500893, 127701639, 784862979, 91321615, 87278077, 458866723, 658179752, 233503820, 927032461, 256375607, 197637784, 168722468, 515684426, 438168136, 763782885, 295461940, 416253451, 516343457, 207095315, 983768859, 757121856, 989106375, 9015115, 522779505, 731537437, 188695925, 126037873, 167152238, 529963871, 271827706, 272919225, 769526498, 237609518, 106783936, 126726532, 552371061, 165641615, 513885372, 277557564, 199871937, 620292967, 319963681, 254762370, 362528473, 778584151, 518272324, 735292421, 660239413, 282669802, 740369752, 53782021, 686971635, 429904845, 241953793, 751715192, 934870295, 307379222, 164833209, 697244574, 484901948, 790030716, 842310543, 873524736, 417445795, 76079975, 279961671, 79572094, 339551646, 603126567, 948581461, 989429951, 161774255, 471334766, 687643941, 731624071, 258815796, 352481410, 831868018, 713942120, 688810713, 858189722, 707844764, 763217539, 384652040, 221157162, 545238780, 571977157, 855987490, 547145201, 738568148, 62785139, 765537883, 414395222, 376766113, 2884182, 801217057, 985695781, 524401023, 668801228, 544029854, 750050149, 550273726, 715056840, 843370345, 375204279, 974577097, 731978083, 330843425, 970222019, 560847293, 55024581, 7296591, 773425795, 161288447, 613747924, 674717474, 353804841, 17370001, 914635799, 415359503, 219088606, 704884448, 908741873, 146216729, 630186858, 282282606, 801027348, 345010009, 51439279, 827889685, 970227078, 389494851, 798969631, 997140659, 915099531, 297631661, 15464376, 522809009, 811169573, 509009002, 858408884, 289242715, 343915557, 723418320, 342078214, 794205669, 117323913, 584161748, 880345009, 358499482, 625702237, 272261185, 252609741, 857528689, 350876970, 40434638, 450285981, 50227427, 527303927, 384254184, 419411046, 307131858, 126994819, 327528330, 801476526, 924338911, 751403585, 822343768, 853512761, 506303040, 549876726, 448640722, 999894367, 337027673, 596635083, 242657971, 329501328, 662033796, 591629507, 618821766, 682906491, 116788574, 274725266, 20373286, 811706246, 463002430, 340678560, 297763254, 982687939, 266133278, 503833295, 506922329, 940293720, 833524277, 369172748, 415334667, 961706651, 688664475, 388822162, 207347110, 864786307, 78582798, 100969508, 850144493, 838944993, 69031170, 573790061, 686093460, 824628494, 551118521, 844554975, 832775685, 977849734, 710090692, 840904134, 936651806, 795166304, 513835839, 813383037, 679472991, 767436712, 75126700, 313735597, 438477255, 399497144, 207067539, 272318365, 308821490, 703597631, 874765020, 832607712, 652196252, 277099684, 112321620, 865363115, 644456649, 37883132, 215278802, 149682852, 123670911, 985044468, 314525364, 998753274, 946041640, 375764496, 171356482, 947651888, 949418313, 889322499, 34411888, 443661187, 113221310, 407321793, 933734485, 430490233, 454575200, 603895801, 353211409, 66913353, 981370658, 279035575, 672598783, 429696718, 194484233, 17553490, 209779644, 519849630, 850566988, 806120579, 821819367, 271772919, 799482952, 695556464, 583382412, 830721616, 307716714, 718744217, 777909689, 907380311, 712749546, 983141722, 733713092, 560623822, 506271621, 770456408, 826915705, 929913619, 322213713, 661790875, 761881225, 85678127, 788895163, 630155092, 463950962, 670967921, 891217610, 884688472, 906404395, 313797084, 16490470, 25066772, 168569988, 709450065, 805747037, 824259183, 285991276, 403878847, 109904766, 498203619, 133060065, 897859085, 772387467, 422981617, 562400659, 976828385, 771078385, 305680525, 338453814, 43595328, 18659436, 820374231, 23356855, 337957225, 472584049, 726991089, 715858743, 883152921, 607772689, 558839599, 599106372, 464522417, 204593788, 753358131, 446776353, 27124562, 632436332, 874333466, 400836811, 994542579, 92593269, 894039244, 19856168, 687067213, 846489024, 860548906, 210993934, 587406379, 327035671, 662892666, 141641533, 555625914, 989713888, 641638096, 651173216, 590659514, 94031984, 307881744, 566942939, 303966531, 20034392, 585832686, 516511482, 178430823, 776211637, 323158202, 492444477, 591449501, 812554524, 834086174, 456309598, 409493000, 330836988, 322932913, 839472232, 632178460, 648850544, 733339887, 852628297, 528925694, 421985072, 114190404, 151411494, 541905051, 281419489, 122222863, 349029309, 642246462, 470195957, 36097792, 893961941, 112166362, 557589129, 383483118, 321026232, 448036125, 702045696, 900909509, 612722503, 883884509, 95023947, 770784602, 474639451, 538508625, 497087458, 364610626, 94936519, 70178208, 238300304, 384492560, 508317435, 755111994, 396408868, 122195253, 613879591, 706510161, 332213016, 182922518, 334640025, 358766378, 823482025, 909369303, 619907327, 671724514, 472867425, 88398890, 150095646, 32181161, 496134728, 369319571, 508444804, 68022349, 323265694, 674712527, 222729017, 896712440, 334304886, 671257010, 45798684, 60864783, 26519121, 170201583, 568865774, 328324630, 198178670, 409802412, 625046188, 158519776, 694709972, 18349429, 703991954, 909149212, 467672407, 751639773, 740085518, 204325453, 609378977, 620711035, 208939751, 483879248, 244928693, 560944201, 558775345, 405422510, 236630312, 609286339, 508730750, 892442583, 347459184, 753170439, 778182730, 367060865, 562598076, 761275643, 272268518, 127396100, 208122106, 182806762, 747857047, 581019568, 123978271, 457032881, 303587827, 276674396, 225846408, 151862105, 713288277, 922064964, 54870523, 561260713, 177668395, 340126258, 185972012, 816554510, 117485811, 469033474, 789580011, 306285677, 726326328, 782522262, 530524085, 958723788, 716986823, 599301430, 168358760, 985728999, 598559052, 139155472, 761502142, 847781533, 227727889, 871172966, 448207094, 207499832, 41440142, 617436221, 51460097, 704285272, 912620044, 764263647, 284264533, 899182158, 376594988, 459306479, 45678640, 887548146, 316278066, 895619453, 218510661, 941786868, 396369012, 964233732, 18050300, 947266157, 979921606, 197593177, 964743582, 834143366, 571760388, 765237274, 668584881, 205498393, 665263630, 326062685, 200948470, 799913716, 925158413, 572138776, 674850569, 752651666, 839989503, 874429763, 989404770, 83120242, 147223068, 830626048, 822940985, 572531537, 496153776, 523843825, 691131323, 148201320, 826770411, 799099425, 597325801, 455483700, 664067946, 424196398, 199244526, 469365576, 502143896, 723957372, 319564629, 311708157, 537257036, 778947628, 401505076, 796795000, 162609291, 63377347, 656792435, 736819868, 907187604, 538175735, 653014944, 330489743, 37098013, 893717270, 293083311, 678275942, 267114787, 380617934, 190574238, 290509139, 828951853, 540024819, 329613263, 491958407, 453784893, 177729561, 948949775, 787774489, 662482956, 34734041, 308082651, 7653978, 554401712, 833592679, 637915842, 801766962, 79820315, 627483993, 810185370, 255080075, 435055587, 299767493, 994392741, 289039774, 126673790, 827383363, 685972245, 771347349, 539116915, 666030742, 625072804, 292040064, 100474115, 900541127, 177609936, 552222097, 465017604, 178585849, 444284033, 254608330, 173043225, 666957692, 566250475, 69757296, 84067654, 317768028, 83217548, 14164730, 478775379, 24352624, 106170540, 254817980, 464923921, 64265179, 228953609, 328892371, 598485390, 403097362, 746002760, 38573897, 978875983, 712863021, 209902441, 964598491, 849933272, 285736834, 314347533, 483718110, 560731007, 783064203, 352491179, 83067154, 324316097, 741141457, 915580282, 178196008, 664722948, 929331862, 539358042, 416444470, 201208523, 309852063, 678019160, 552226971, 582833692, 710322749, 160437281, 628210867, 335159312, 94371347, 580880692, 907367649, 854068505, 92082629, 780867125, 275939784, 303587848, 83134895, 849337847, 531986968, 235004847, 669128511, 773815901, 428840185, 815535237, 135172232, 494162953, 915211086, 863024516, 298031138, 243890306, 145703193, 929816968, 352245006, 660245867, 53837811, 277749125, 200410021, 538193975, 160025833, 699071218, 467683067, 216426894, 75025377, 395205363, 277787793, 568912040, 809234783, 818877654, 626868254, 746048244, 507322087, 817552855, 111080325, 787009682, 541863518, 291213084, 316824645, 746138861, 506486158, 179861435, 900870750, 92365539, 506096663, 547694871, 172126294, 571590192, 292674925, 12885552, 261312315, 755040665, 518428657, 767284908, 812319603, 963752138, 686257941, 656781050, 854983595, 143129878, 821274313, 306594235, 908955903, 234320269, 199408174, 421184292, 379417580, 615291705, 678242989, 252743901, 722905514, 778628966, 898416968, 978553253, 796814326, 553250904, 254777499, 50455911, 772347360, 364770135, 739151135, 675116492, 438449310, 28661062, 893030955, 938918197, 2814246, 961412594, 598342782, 119365504, 861195191, 213902782, 187749591, 766815079, 206663476, 855469061, 122073058, 649351993, 659758164, 541608885, 179704011, 704921624, 34801911, 21515548, 140806623, 97103450, 997210157, 804798551, 157286837, 172796519, 961663723, 154914637, 348191941, 413592511, 667782101, 595310194, 544738275, 788476442, 44418220, 251930933, 930798812, 456978489, 364913932, 63647638, 391455430, 640219121, 798054177, 90958289, 360649555, 957108127, 921540957, 821567320, 902791271, 575348397, 932998474, 863984265, 340368231, 534741062, 16516305, 713275087, 975725369, 710501696, 653047944, 157256581, 339261929, 836302097, 218715466, 157443893, 773297438, 657129870, 760135149, 124469002, 297116046, 71915663, 179724082, 958388778, 422947144, 439413273, 674605612, 55197703, 255375248, 283480030, 168942418, 932711501, 283949915, 420171894, 323175300, 365311423, 250427171, 710020706, 561518804, 554956022, 478968727, 544805070, 938901837, 307367846, 500936214, 572020854, 810846826, 627933831, 802275139, 493887877, 506828891, 553768122, 295401737, 138304524, 311786521, 772130249, 213930475, 408723254, 503823636, 768751280, 145024826, 985499973, 973144830, 874360975, 656759864, 840076272, 245102052, 629891625, 828926453, 573654935, 920738849, 647131463, 359230554, 725854550, 83071541, 565859553, 476298744, 901760397, 219277081, 28597421, 384376581, 347902013, 899161649, 144699844, 204437239, 917724986, 264137452, 459594356, 35999470, 103218242, 427039122, 160404667, 263492039, 475861680, 786411096, 396815814, 921730667, 91697075, 151141457, 669019444, 496780519, 747933240, 444203549, 773483154, 245332297, 743190071, 194096629, 232328118, 995406778, 755592030, 995108869, 715296073, 19471891, 252235846, 837006821, 800934717, 842872108, 774828175, 202018761, 794300622, 772073090, 726368408, 897356093, 51426066, 847379407, 707599572, 596210119, 908573339, 936750587, 168076312, 581577881, 454551251, 953006700, 66410680, 389987751, 279193694, 905990214, 162109689, 928371707, 656317886, 902001394, 165922376, 1148156, 518550067, 760390193, 73732694, 681097322, 964330451, 163138487, 145724922, 246303076, 606045613, 388651744, 322874807, 31224172, 747712877, 993109076, 737741687, 375268728, 628726997, 729238721, 638524855, 415231563, 969274509, 858122666, 724373983, 958714101, 55575186, 511091786, 800451415, 333893716, 190769848, 922040852, 373019206, 740856406, 460245968, 58859383, 431698096, 641016572, 885323860, 812132603, 19557026, 242295771, 455219012, 41340520, 917874644, 370800728, 989359852, 510725907, 301989667, 996163852, 114050697, 882819667, 261785321, 257083866, 643254110, 290576616, 636271143, 205827294, 241997643, 96994943, 702939490, 464169722, 639285311, 216625386, 435334990, 346408844, 70720863, 462722592, 689104461, 993267550, 569268148, 689359609, 592451675, 114546374, 366244368, 4436974, 97358283, 381466212, 572219004, 776605272, 223934078, 990707311, 857803740, 331613634, 337653185, 990575674, 476482858, 58033258, 967730336, 168940047, 825631376, 255256574, 673675918, 499083579, 361837244, 742531500, 232118703, 188517716, 761986639, 638269487, 450324508, 292812053, 367916839, 212160442, 812052992, 681681733, 247806835, 857377165, 518836244, 67609632, 429164277, 958500125, 812061192, 795031582, 940032671, 22396590, 303285197, 367651557, 468363584, 102217898, 10560060, 661477095, 362011964, 166495332, 3277000, 342295307, 601761610, 638943366, 466276792, 282901280, 616923289, 989092297, 404898756, 123187656, 14149045, 924544092, 583685068, 984121163, 235650079, 522344945, 60884355, 520683884, 276604872, 97168355, 84965995, 988027604, 423212379, 402589739, 770792339, 250521812, 993927155, 99304914, 899887769, 851983402, 673412270, 776695429, 38321592, 225047824, 577928994, 524053606, 195441634, 209143370, 356503880, 166941205, 620127739, 56121607, 14237478, 765152039, 809507035, 590111583, 134932224, 815734355, 308043697, 996212816, 511895280, 908696935, 769015394, 92347541, 786206378, 130591163, 917311498, 345802720, 449841082, 508075317, 634277187, 394464509, 975057542, 943355175, 420862917, 268791231, 674702260, 463833655, 336323650, 541406416, 464863474, 300966572, 375000770, 45936538, 336226310, 145997481, 647774190, 877195164, 795043314, 806532286, 435614275, 717638185, 893519014, 317758237, 541925470, 428735869, 105743211, 851582295, 814440136, 949793483, 382430284, 228425849, 995018692, 714684686, 594775645, 662367286, 956336813, 992931774, 776285628, 624437231, 760682491, 172037823, 942113360, 423619495, 312368712, 310891336, 423956858, 867174531, 654057829, 536662579, 898280892, 852928081, 289634043, 395358474, 877396213, 85451581, 668892711, 259751373, 233459280, 271001290, 761161847, 664818520, 906404689, 750716071, 490931317, 439823542, 511762372, 90412132, 457334236, 204303512, 738461745, 136756912, 242912996, 766792409, 318912869, 306564928, 703995966, 472827030, 878433941, 659781895, 470493435, 322204745, 928670366, 619315473, 437193295, 824301601, 828341654, 624728527, 154530190, 663533455, 874878742, 782130223, 221105738, 619245483, 347348638, 460956350, 71660012, 144436272, 167113597, 446254635, 821497787, 396179940, 323604368, 658778207, 953409072, 946530429, 699381890, 307601496, 592227286, 691006978, 26135280, 22144156, 718933397, 535413370, 381669640, 307723394, 615512298, 363413071, 140215241, 633669919, 169179828, 277177951, 687249301, 44210898, 667542097, 431075460, 476008315, 152310363, 433488568, 728219911, 459627867, 60876660, 489025997, 49050461, 51277579, 507251163, 880846215, 818413496, 971984063, 5267308, 800344023, 860743047, 370232035, 996512396, 959575603, 91996767, 708311050, 7858022, 916519035, 930113093, 698499151, 39189579, 725842095, 707824430, 177099911, 410938282, 285700891, 36987035, 972391735, 502704356, 158690304, 60629768, 742616188, 990912139, 575906902, 173642888, 860337307, 680402641, 33075275, 667615210, 912524259, 50995879, 15521737, 833909325, 350012156, 669855372, 563297531, 126878916, 549969588, 374297695, 12526580, 475184661, 530359240, 299127617, 563837329, 186533360, 506368705, 893310506, 796800848, 314674342, 855436627, 624563997, 668479471, 431436022, 400630037, 347134584, 35556445, 69203206, 376995447, 233163426, 286139952, 262200392, 364142270, 355236510, 457539101, 501711985, 1683233, 688219138, 798222417, 807941628, 103836229, 261480600, 482698823, 291486839, 411453069, 98034185, 44710169, 162838731, 916808251, 775828402, 797430335, 880709224, 339905455, 483380641, 593733218, 54254242, 57079109, 356550350, 602197511, 350972558, 626279782, 712568394, 149074361, 65612538, 129498568, 852267248, 270206221, 799466707, 510382708, 503011771, 696466750, 313444144, 783939240, 766025445, 974400259, 688913693, 686225855, 817854146, 478213615, 457436935, 381065561, 822060467, 994724801, 522536015, 443274133, 103356693, 854549450, 947088895, 42333643, 676913190, 440009875, 564123962, 943300575, 939501231, 159308630, 802712080, 816312261, 614349963, 491487570, 956542181, 150906194, 197494766, 798685422, 999759503, 457544123, 89247609, 542976287, 717844601, 43863724, 987394910, 970782748, 580424739, 709324616, 851103333, 476856761, 494210259, 43282308, 500621159, 259651658, 376565087, 363160117, 992252241, 885724393, 566926607, 218437502, 150378090, 174383244, 150032191, 997361297, 479705441, 768426884, 683778096, 918732157, 813258091, 756171671, 248637220, 544585318, 560415446, 393207556, 943588237, 297222371, 24599509, 650106819, 734365251, 341495964, 174396667, 575979509, 703779950, 391591064, 479344221, 532269341, 229553611, 266209601, 809561140, 749732257, 518522283, 780077098, 267416620, 798461006, 919763884, 865151213, 683333986, 213740057, 269017445, 671210215, 360160121, 842936539, 556659145, 318490525, 157791594, 930338150, 806120606, 502585568, 359614151, 565835663, 975498670, 972210564, 206310437, 721854814, 195587841, 721880976, 660015030, 768562400, 747435261, 604038609, 776190384, 996682230, 141990942, 649385438, 753540738, 753228872, 333806479, 380838315, 985487416, 65798227, 220298396, 375084959, 511779914, 165973325, 111169799, 237680787, 315077018, 356559667, 841655587, 759401003, 855749005, 224982584, 865600146, 453783417, 615712944, 342524816, 477616457, 57009507, 89435406, 580867288, 187960078, 901336784, 372933739, 289848465, 592121378, 774372406, 119811679, 520719198, 786414387, 228026795, 307621797, 158127862, 185347040, 383495055, 967320612, 253040179, 443859096, 558030539, 377950982, 843333593, 611436882, 95623751, 921054996, 413094891, 571912741, 467069613, 538447364, 775518537, 781658772, 634084128, 440730447, 779154468, 853867095, 789374998, 513780183, 866339182, 423003884, 170544838, 165768257, 991445096, 910675143, 665069040, 254714883, 352180628, 310113344, 390204373, 244027553, 536055436, 150002047, 464327168, 158346926, 709092940, 550853003, 191377959, 709658824, 765034425, 467556483, 266711607, 320706597, 999336154, 397594204, 552961388, 844171744, 976203690, 628259758, 898795057, 527794306, 889531860, 195749996, 450995590, 447807439, 281692063, 26095787, 945295871, 126392337, 813569395, 20144076, 442737439, 416529543, 419501466, 196085429, 411798820, 471004157, 125307674, 582285643, 394200789, 309838465, 132782625, 84450456, 901939616, 504226763, 666311301, 734623394, 174735850, 339646349, 966066921, 991239835, 349700640, 20729969, 993129690, 603467071, 290137534, 953939551, 908754613, 799092375, 130160201, 580927876, 789094223, 439117242, 784183378, 696040449, 286902331, 32799074, 223628525, 333094289, 783160330, 243282095, 208090719, 831227363, 87022339, 484714520, 632036957, 893109366, 636680257, 740545336, 667290576, 527532845, 371799743, 754192737, 883344373, 524344973, 165540309, 312102648, 592727687, 961062408, 223086749, 781833689, 187552263, 908178915, 552425293, 613448074, 71891770, 225014270, 371184057, 791373041, 885372652, 374680059, 620930935, 365894910, 419935826, 160817265, 7896330, 526821121, 162495601, 995020464, 479502160, 458105624, 974493550, 868450818, 686182598, 98353859, 771855409, 930087337, 462424650, 277718634, 686977327, 849370816, 144301928, 725110623, 605517712, 879582984, 492614285, 765381509, 875226322, 422321895, 532667023, 3536430, 840766547, 678278279, 187885095, 451250886, 436715648, 965675721, 675550256, 228326191, 749098232, 582814502, 958209024, 305930251, 889268140, 142523135, 544158447, 558999613, 516635922, 661279272, 773407432, 432010574, 889726181, 141319517, 274140584, 613880266, 342189892, 28432970, 142219778, 35509372, 544775001, 144411190, 436835812, 461481056, 898165562, 20806570, 214284156, 56360111, 67820873, 24271131, 44177063, 195541734, 187687816, 580434610, 635302647, 420620291, 235709786, 222449106, 485486128, 344688939, 34231409, 845679704, 576525516, 313937992, 717022853, 100248783, 561607014, 829454308, 169423546, 410991812, 290966521, 373161415, 54887624, 210571163, 895225938, 897922537, 982900555, 340160904, 410719153, 953349190, 83351835, 161479040, 209239804, 481573372, 581790109, 344077995, 933152360, 114486977, 206851932, 259993601, 972671869, 255310451, 351959051, 255095054, 122309737, 755482771, 699766139, 722659059, 187584620, 133425989, 864914079, 302190896, 585419802, 726896246, 484463532, 921898937, 672020062, 56333428, 147687836, 993785441, 103951864, 22062407, 699494054, 475176626, 447021126, 247277263, 502953819, 943346030, 570977279, 34219479, 457258560, 188834574, 613406410, 363750915, 266939031, 750231905, 210536586, 335749396, 643463852, 236035008, 412676104, 423225316, 120718693, 118834889, 313309338, 219754286, 710402136, 563353557, 444247203, 100680765, 638406075, 873369057, 34717716, 514799418, 938412850, 171717189, 36525899, 880795910, 198525714, 129843516, 369821248, 129253325, 806385283, 315959667, 185213210, 816926298, 573650665, 355849481, 116510789, 38130915, 687582226, 227976653, 501605422, 492251915, 559822654, 389604539, 587853712, 984250333, 803051828, 758384778, 455459550, 451495989, 26767124, 14023767, 143504598, 48092661, 716790210, 961795802, 670622104, 415372542, 65695663, 611176280, 337922745, 621619918, 825107496, 838200598, 73076616, 304125431, 805286486, 979046941, 305068061, 371895931, 118660309, 592067950, 969125996, 706476730, 335150290, 1623565, 482013708, 991683813, 128155796, 577946981, 300323756, 480100926, 969498726, 194153170, 429106997, 670851993, 533217041, 645273186, 721247916, 192674931, 615684026, 414406107, 225063857, 305049090, 496302246, 177571406, 695523790, 663331184, 443544109, 772772457, 230909949, 745656810, 786697074, 189288031, 24884787, 190218504, 524634906, 771009346, 986229061, 79144701, 509327183, 745014085, 728910312, 489819386, 16342592, 158265875, 229613147, 593113174, 277554729, 109458255, 667100056, 301453746, 171495076, 973196773, 91786776, 659096098, 565193980, 822182257, 423479773, 44228970, 250198470, 590177415, 735730355, 46031581, 224357299, 846709325, 761797962, 151572738, 439416405, 745271888, 382461834, 242541216, 925132305, 256701788, 303449985, 47836657, 192355740, 896707344, 644524345, 152648396, 229107639, 344892224, 144784044, 50128103, 596064240, 627298574, 571511753, 905484075, 754657308, 530317848, 138142490, 503357631, 507319906, 356911657, 217575828, 812464805, 275651924, 603025911, 803812200, 61182794, 46009698, 758840052, 204328637, 839056041, 609274697, 878840475, 954880781, 231284487, 237846540, 757379381, 141202678, 974452291, 377849075, 35374712, 810963427, 578966768, 768359766, 638914519, 803607116, 516722632, 744474331, 45517351, 651075727, 660542594, 592988418, 187677440, 956786871, 679973028, 232169103, 868266714, 91986855, 301628536, 541174033, 132614512, 341545543, 642624879, 463203376, 65143318, 910549988, 863077361, 761120418, 16108637, 401393267, 785917789, 280177232, 357026593, 365566268, 114869989, 837831007, 481818059, 381588947, 466462427, 949282115, 744640235, 727121678, 976001254, 79988505, 544149004, 583907634, 934554674, 864936504, 355385796, 608538447, 731137146, 671656353, 532298830, 970847168, 175945844, 718642572, 407254960, 650481177, 793888318, 98577585, 392249019, 604120555, 422396103, 726216752, 350938325, 726540905, 820128620, 262204657, 552660977, 463617155, 174372470, 59018915, 78836812, 30405509, 975931258, 79697799, 144282899, 373640121, 569043955, 785161403, 297468927, 410447199, 354830414, 308417234, 381964281, 778653323, 811600963, 280437605, 964793336, 928067086, 124063305, 898965552, 331957378, 836236312, 629910031, 400349812, 158920858, 617913244, 413094170, 580700925, 289614716, 450353571, 797265494, 955058680, 224378889, 875342833, 616066646, 75773065, 494739474, 861910137, 545014262, 953900749, 722303829, 122628089, 514682413, 234110672, 460179469, 534440297, 983955687, 553156399, 413056844, 395761437, 91196740, 446283869, 344235239, 489574154, 473939449, 51690471, 911916490, 617660916, 897080293, 301806120, 163850305, 843096378, 433825798, 814517636, 873365374, 581506017, 777888741, 734148213, 83148050, 86403414, 455568815, 115225859, 507146701, 595695729, 130150072, 457840285, 857118273, 942985535, 682720575, 215759361, 317994683, 50405383, 697224314, 650021498, 803728177, 239561122, 378307258, 211421351, 255053126, 800752374, 146022172, 610867226, 22795361, 681858092, 472462459, 136114125, 607424631, 671655830, 633072327, 157871920, 548746518, 633354901, 78186415, 35961287, 419717281, 222398984, 189477104, 747244332, 609675780, 641386695, 279237898, 17229924, 338684592, 628655526, 713688456, 403556027, 34970791, 723565676, 47836557, 65827220, 804150380, 903894371, 226666047, 844577629, 997076665, 38441714, 695829955, 206373678, 496079526, 823268817, 535292, 711469431, 907920205, 577244997, 351003234, 935313637, 484436188, 205422502, 820413035, 72231080, 965713723, 441837549, 221365468, 662735472, 529284509, 784832304, 11234486, 508172305, 296575441, 845400244, 188099933, 60106751, 139339846, 767637783, 874016449, 134266831, 543282494, 782755435, 755950940, 433225259, 922565108, 584179557, 24462696, 883448908, 825755349, 335450346, 461397397, 951875170, 173653217, 235236502, 489677604, 920035696, 310914092, 171694000, 424336854, 940498118, 392055856, 735966469, 140991112, 360547843, 167897735, 508362657, 625030988, 553474806, 572215592, 486166248, 962669913, 930383807, 260105152, 536551470, 950912611, 28855129, 976554842, 860654967, 139437496, 677550606, 40621331, 62044386, 512108133, 133279535, 786640632, 55940821, 576140541, 542680304, 525698103, 94720511, 849070456, 404431068, 146624641, 262532257, 934847212, 177967969, 828201264, 190902002, 828693204, 166459688, 117102990, 66701210, 632831865, 925272285, 459963358, 850473108, 476239635, 583870640, 749961282, 657949432, 457268767, 937931993, 435404293, 232090126, 903510690, 50725049, 305108920, 834020083, 755789889, 102418509, 687123952, 150386463, 30054298, 261630057, 967020137, 880321530, 181158402, 630458908, 158058090, 739566486, 562335787, 257914227, 287572167, 121802876, 733892802, 105415139, 88872354, 248176903, 370223350, 646434307, 565782067, 117869808, 214088062, 331919341, 388619260, 595180961, 795020842, 184563012, 711077543, 386757124, 177043608, 719560062, 553398790, 701867617, 475077458, 138500278, 486043786, 265935201, 111129843, 504635810, 111193705, 667741044, 75959963, 164123942, 481300703, 149054088, 80293730, 376499873, 275714445, 61630381, 728799473, 662521146, 992960892, 910480941, 436930963, 242314742, 12856475, 975561603, 532294144, 773862843, 507534598, 586103459, 462340770, 895812156, 217694073, 917663716, 429077359, 833264624, 150033165, 500785326, 304287417, 952196808, 769778144, 490629385, 250398505, 796149029, 359850667, 8425174, 626230706, 713433291, 748764340, 805905221, 893072328, 355145601, 438617312, 717301486, 714301938, 748063896, 894484965, 772387328, 466255749, 932053029, 84689382, 961835759, 262887549, 253764812, 877427961, 395681297, 779150535, 995010951, 538661299, 628263148, 874310743, 968925318, 519111103, 54602360, 170190901, 738914495, 976037816, 514479922, 279579441, 511013332, 668624083, 708303853, 35348224, 597578793, 920517769, 687472595, 251506175, 326638636, 22352374, 646997387, 806910304, 288697441, 790194045, 645687430, 316916684, 199795097, 274139978, 850234948, 411618060, 250170952, 379502771, 941410741, 378086847, 480682888, 425568705, 186220529, 654580948, 757479695, 844208553, 153796894, 741800649, 146270877, 752268586, 809464772, 33783580, 583641892, 410108417, 59805372, 933696944, 126119074, 678148113, 232865360, 410825143, 797123879, 358433404, 395562403, 593052777, 800162909, 20125687, 903726477, 477281005, 370991631, 853959000, 36696156, 779483101, 253355800, 435122515, 472118189, 470208571, 299555631, 514932801, 362987840, 521782673, 616731723, 712122916, 460823030, 422394374, 424042836, 221358060, 651693219, 62967888, 671128351, 46871109, 842200357, 893135934, 707296564, 410584224, 102054279, 732617062, 18237621, 132638184, 15062043, 513065804, 812461891, 979410574, 166727923, 558402049, 491266108, 690600375, 673651840, 95654063, 374649672, 924370699, 14642737, 526005575, 782382818, 593664377, 913650354, 556411464, 288283427, 85764689, 940982848, 355088253, 700390328, 972831694, 760291089, 31433727, 305166250, 746933221, 522215295, 937018105, 793637652, 710988302, 636989843, 805490679, 274192686, 220086070, 739386015, 402576179, 480156931, 720253237, 736674128, 960982221, 203381420, 105590214, 820806252, 990876106, 757618423, 110036223, 384738150, 849780553, 462738697, 998369885, 360549379, 362591363, 373490684, 364912493, 72198684, 40875193, 792828444, 227172098, 317063685, 961825338, 633370700, 48999387, 944344633, 441770523, 183416655, 372055115, 273049659, 5708233, 735538617, 975505234, 274003577, 727284475, 309328582, 372706358, 367296986, 76486715, 274080712, 715872227, 166030353, 217840088, 563550284, 268098568, 635985325, 695265183, 545699774, 921041402, 206075034, 220301974, 823424444, 512568470, 667784897, 611211485, 556033194, 281565768, 154317441, 70027659, 560249581, 743308852, 940960411, 421597936, 563848041, 722783755, 237125132, 790461763, 659259908, 371685839, 413496757, 1825299, 640704778, 498232458, 649052282, 147554771, 204817424, 925175715, 189904311, 936220320, 399397085, 979561840, 641065796, 290864582, 44457153, 817470741, 113620529, 759169233, 582004285, 329472842, 675069505, 357710187, 754070014, 646940203, 93016145, 89609913, 745356935, 712266391, 698090380, 876149896, 855427785, 104995919, 285477769, 920412541, 550662677, 869749461, 29399287, 779103242, 41139141, 929754370, 949165501, 75458682, 427994783, 410339318, 173773155, 255539031, 724954641, 236804708, 404617958, 392882787, 245732400, 887243461, 36828032, 317896680, 352205624, 627868974, 965921586, 552591379, 228936673, 686501051, 268047028, 118225279, 880336588, 987688032, 108468351, 821861087, 317059181, 497548443, 549902965, 481245819, 452302031, 909137385, 140844969, 96528688, 471966702, 522883022, 71011267, 920970328, 112801875, 115042296, 492203469, 689711642, 140349383, 233702703, 14038611, 402084118, 700633682, 802396546, 236408315, 839180274, 506398740, 622101889, 562640020, 299678382, 167839787, 817605101, 729734672, 36210731, 441929671, 571855243, 813952245, 550290093, 827220590, 899571498, 510516917, 316421228, 925054542, 497820607, 286521628, 952372803, 756619213, 805924336, 393979794, 399972759, 274849589, 965481410, 248616818, 934154320, 203583737, 217804875, 806207867, 770189588, 349290536, 700735654, 386832054, 45086319, 766275211, 478762346, 651871492, 992287249, 156835246, 162692585, 886251286, 131257168, 543076140, 282594420, 656801331, 258885093, 639120676, 934443300, 839697637, 248284409, 933872127, 280793805, 840117133, 710183305, 257921002, 903967583, 789898999, 918084259, 307139744, 242357366, 777156301, 283151638, 178564223, 186620993, 867072678, 284146284, 804995901, 421593670, 760683962, 946080061, 209483041, 215435897, 73281161, 509928719, 690264419, 269134601, 475570009, 91333104, 833069953, 484087595, 998785910, 618302295, 502684447, 318225796, 225964234, 112047148, 833585528, 396567625, 423566282, 918458391, 959189639, 414400066, 931197008, 284246940, 567779876, 113017399, 620537258, 163793477, 784274472, 613869526, 981406130, 156576886, 968669349, 141415429, 446849794, 603939729, 54462333, 408861209, 586867901, 86801396, 78985809, 21802134, 144309950, 91320232, 111055823, 323995441, 767935045, 204041804, 375294823, 2588822, 15072730, 416992088, 574704498, 594207597, 113520213, 135239597, 706637196, 416255740, 169816825, 590363422, 297370051, 434201038, 926548811, 870614692, 349312328, 250955780, 692739102, 769364180, 340130475, 983173665, 525919226, 278844711, 425912536, 178786487, 521423718, 923098544, 243109822, 221157695, 565455982, 930751096, 895010275, 679977265, 267559166, 892643258, 20866274, 160678046, 345598235, 401342670, 217324309, 565798892, 375002509, 606878960, 341571258, 962086509, 58027897, 625748372, 474191787, 341920972, 184494096, 915808145, 522969498, 890151547, 330172231, 508955794, 82797983, 676100829, 663135908, 985386643, 72725906, 482957392, 311279376, 308872607, 778925024, 614982120, 570940004, 45745001, 938853215, 594745755, 157850089, 384738345, 11435462, 961080761, 129248585, 807081934, 661848886, 589831282, 708069242, 465946859, 187316175, 811217576, 560346703, 424507385, 814956012, 133766153, 353479905, 704176960, 141519770, 395905165, 522196459, 739073429, 45012148, 74224868, 220149832, 919739930, 90385972, 107876295, 627951384, 124104533, 153588445, 579154565, 678078862, 495429024, 513668051, 815082691, 901970672, 720634138, 397502261, 800809036, 984818713, 203576266, 919872320, 951599090, 669655869, 970184865, 254616984, 661248181, 568881335, 848583163, 986216671, 71994759, 592556361, 694596637, 97689838, 688463235, 121942346, 714932482, 754449796, 354060841, 93781076, 332602684, 91715282, 210450590, 272444320, 527242432, 893436719, 928595262, 42346260, 446687315, 367767406, 361450845, 671248108, 491151972, 185628905, 569029545, 160996622, 753235015, 488429145, 689217888, 46862424, 133760713, 804578089, 597988498, 989025113, 353567059, 871583355, 967685384, 825907932, 383868954, 329833456, 240394003, 409993405, 150210591, 523144725, 109652774, 62044505, 517994899, 5281244, 758998568, 661519043, 32714598, 874486486, 417348224, 729418158, 593087709, 227300455, 841978393, 94893542, 239432716, 837800351, 92275722, 895444555, 252904151, 258644228, 202067670, 316817768, 950940626, 315078564, 724341307, 419228023, 503269146, 38524162, 848139463, 306749771, 978668106, 273232709, 299035349, 363660466, 682354187, 828525898, 294662283, 188381995, 892150419, 392361775, 397207361, 18171853, 886509205, 804002791, 787472648, 757485515, 57128461, 440354147, 488861000, 380584002, 549488044, 50326831, 609763510, 162388268, 371615424, 706047982, 170946751, 735718209, 211372910, 150741897, 333351459, 151576798, 312525821, 915790773, 554312482, 220030326, 264684202, 481343848, 848312047, 128888007, 184547787, 49859005, 779802875, 256924605, 871348954, 15053913, 352388197, 195896001, 852638472, 891351373, 902768330, 995423026, 99686237, 339942605, 459758786, 722458340, 525832865, 828687999, 35049692, 425536083, 210811323, 163321299, 377544886, 98606846, 67013160, 719457663, 434267288, 140554970, 958559022, 218087826, 283374705, 870419323, 108408708, 23279960, 554867368, 6028281, 489148781, 256499797, 687383069, 525595855, 626956473, 201960986, 328369524, 305774035, 909633009, 673077143, 648285004, 347432542, 141382315, 541106648, 988181655, 117321797, 432271868, 407361713, 259166289, 755677806, 117845831, 793035183, 319627408, 761229349, 534644605, 768479594, 692273791, 252559929, 302311226, 916438643, 476074164, 699015547, 618953706, 199651707, 245712309, 337348192, 759557717, 728036340, 498632393, 324149110, 470372086, 799078726, 311595966, 376820845, 639384549, 579119334, 310263182, 270457017, 772853390, 960809576, 568837841, 180516858, 130274267, 119908426, 232123797, 759408986, 865402608, 972732071, 270774811, 340544706, 226985260, 805816284, 695845469, 9305268, 631323359, 736199883, 117824257, 182384147, 524360430, 206472390, 296642230, 533696355, 425047078, 119032994, 560162526, 654033072, 531090884, 613593557, 99486341, 167588539, 614076564, 237236011, 495191700, 447748644, 702145304, 723303356, 978452070, 445028628, 297124703, 601130343, 783204968, 171555237, 947008469, 676069258, 894986130, 771233265, 192546121, 658162565, 12200821, 875258167, 970312836, 864333390, 612127234, 9158962, 828567805, 112835391, 782089189, 379233394, 897903994, 456031638, 7479982, 157225449, 446557997, 46771016, 520493579, 463886659, 470727388, 272464550, 295835331, 406780266, 798518402, 853450641, 351034687, 805571659, 863530979, 87001283, 901070540, 741156762, 863983816, 261873895, 996863637, 132505311, 842191904, 369853868, 451546048, 765064510, 312234938, 637409866, 355048186, 547737074, 703220074, 724481341, 474960360, 365159882, 97886696, 21877898, 502963574, 460189471, 418192749, 573967864, 602518438, 617500784, 8505110, 779206899, 669405703, 596563467, 474989398, 712019439, 382156367, 949193680, 914815841, 456531129, 878618655, 451371908, 879700380, 523081406, 165284372, 941350222, 418329391, 812577112, 786314513, 990979764, 845453341, 372373483, 452023373, 618981619, 662981789, 213205336, 4504346, 547330410, 514247919, 895702216, 552604039, 506458658, 516336234, 2439970, 421282634, 170179032, 325739013, 943590685, 27066614, 740422065, 59957611, 104590795, 635853470, 151075857, 704030819, 547621732, 796469656, 311238422, 481179280, 3255956, 965668558, 651899333, 298216420, 605182400, 988883247, 586749983, 880349721, 457538763, 929155175, 646148455, 130238505, 307438282, 340557637, 709773964, 199659231, 951847621, 913698988, 719418059, 616337203, 944818247, 191395186, 596794919, 113565957, 429935756, 536285305, 901492780, 357475375, 639164416, 132693499, 841694908, 868537924, 153375613, 624616634, 3255819, 552768798, 844558916, 491520639, 875599133, 5501175, 983967881, 429907508, 852821939, 474748976, 822812101, 8684175, 516127845, 747714585, 571326650, 269938165, 148282705, 847988421, 351589932, 851128896, 179333426, 972815738, 507050014, 608641593, 59787780, 154063997, 460439205, 173887923, 817635079, 175342455, 368868909, 4159561, 228854951, 334458582, 851852224, 552310283, 333441852, 996060747, 615525290, 880085503, 882477770, 875142096, 245650044, 970645292, 814439362, 772591158, 223459579, 406214161, 543577868, 940924920, 924068576, 879137165, 341157186, 941272407, 298589187, 417910492, 419384293, 56636252, 895550272, 880627799, 121920926, 401595239, 687927996, 289441796, 800640974, 490387651, 425527906, 740732246, 245463677, 156350906, 677821871, 149612879, 761890112, 75476835, 79608491, 454502093, 389372961, 599423549, 770542671, 82949674, 632882005, 228390945, 237829552, 369182013, 63853257, 310394731, 470139955, 732473612, 14262034, 700093415, 514622479, 49680893, 63203244, 73966966, 81689735, 439951705, 427045488, 382236131, 672054656, 351704144, 358644861, 39121888, 164509776, 63928858, 401999829, 242610743, 664380934, 33849114, 340652673, 174191513, 55580090, 54368436, 433009968, 719033301, 671343041, 418846319, 888415939, 697119752, 245560357, 965344628, 762180492, 378765987, 729710439, 426185970, 936187812, 355984300, 138108181, 344299800, 533534903, 641149054, 794043571, 518207240, 282304619, 37614742, 317768218, 35342898, 289008528, 145025335, 352394191, 343804213, 284755288, 244579110, 593459590, 198162350, 856335946, 734904654, 762202496, 293896601, 58492227, 805877942, 966221324, 428155620, 48912797, 25307206, 860475282, 561522765, 11054269, 671389919, 803710535, 809550413, 485463002, 862191362, 53106046, 859488927, 860915826, 512547436, 180773334, 280989801, 524983178, 659371030, 527996056, 176067390, 519589768, 921779617, 581773160, 677021606, 113119386, 476925726, 434100252, 283337066, 965361704, 445989376, 700261996, 287612211, 887726146, 856297869, 685185426, 464434949, 956671194, 809126141, 751990220, 190920381, 956141978, 166547149, 883428656, 350267304, 823021913, 528495451, 649893315, 901027933, 502544561, 492178716, 375488046, 111825294, 48075413, 895326270, 761356216, 466326796, 521543883, 264831600, 748573914, 440346479, 694776807, 530797087, 176647772, 294092513, 130609001, 782229381, 190233918, 430345650, 479932854, 870238090, 728946678, 928940969, 610970016, 895184602, 896489479, 687199558, 616224016, 964286974, 725989689, 838330482, 445824693, 834741878, 262011616, 833745726, 192679989, 624793033, 394080957, 938835644, 390680654, 809198543, 709657409, 513464596, 952977136, 235793102, 186060233, 943488723, 514127599, 493362110, 498864700, 156313904, 987041452, 950239421, 757095959, 328364916, 57044639, 34424298, 759188435, 895508404, 503915677, 336374860, 392108546, 381744677, 541827056, 105167020, 763963592, 591738300, 374570589, 241019730, 393146701, 441958433, 94740757, 664943785, 639278703, 780347759, 746914406, 447789029, 669446278, 932307489, 745683886, 858226304, 869025650, 499594390, 803458050, 458011032, 1177801, 270982697, 524786491, 695591325, 560595159, 171763644, 201044978, 261916186, 567315781, 417548506, 370230678, 510247509, 959607389, 476555452, 57466406, 995607212, 856936235, 358484430, 884828515, 783230380, 483842686, 294014208, 248351167, 748995135, 614120867, 755545433, 459518478, 682177292, 744075403, 35343006, 537656782, 846568124, 196996261, 566163997, 769798415, 198526122, 67825245, 646232960, 339653451, 376189395, 626681384, 538903760, 930955731, 536425115, 133665022, 556324968, 607642304, 410053539, 448930329, 849307921, 579678436, 770820760, 725129595, 861887050, 173841217, 337185529, 219237299, 513137966, 118382368, 898632765, 977623701, 982159252, 671906504, 480970290, 313961649, 323787000, 113631008, 45506830, 52748831, 727081116, 183512455, 352739572, 997462249, 241436326, 805833585, 820991610, 807023080, 680189562, 311270940, 707706229, 470244628, 261225277, 667961707, 63805328, 538268654, 584875285, 367435791, 46868794, 717711523, 73061506, 55466566, 85157588, 607786543, 180813632, 351523667, 363510706, 223360795, 591540224, 17610631, 421578653, 316861906, 731299468, 755413751, 218673521, 903774187, 239336984, 500383372, 126641205, 525423376, 164078564, 705321145, 862491283, 805179049, 950833297, 107018539, 69562224, 951510581, 181515719, 858138486, 66399725, 757055773, 204914786, 258663297, 608653119, 706056313, 750806309, 915443064, 903256262, 7728925, 196392148, 429723478, 131561647, 386852893, 467131926, 329520887, 10801125, 205678659, 398457590, 186766636, 816241112, 397990239, 938866158, 887397778, 379946001, 334222344, 697574865, 573547830, 602137813, 471079743, 93883267, 903928659, 667194184, 359806818, 409129398, 641202377, 977137517, 3868293, 705494099, 346006851, 386667726, 106225998, 940116672, 82104096, 88574317, 157293269, 964170069, 931821262, 525729211, 201231639, 319996332, 682174257, 188571227, 353167798, 534287276, 506922300, 250083339, 593107351, 335338995, 834380645, 703552729, 75637442, 23133637, 93250793, 364461685, 232363568, 995752501, 13402360, 553916308, 329229991, 378610415, 832521009, 916275221, 759123542, 773842877, 424257420, 346311080, 127493587, 875824966, 973194594, 115856350, 45016584, 627824162, 937787930, 430487760, 183202234, 962956215, 836550279, 845675628, 31457894, 423280609, 803431122, 413887668, 216412659, 53102679, 834053243, 71449327, 137768737, 414637338, 953966791, 253803835, 631323011, 954697033, 125016213, 454097193, 893365591, 817507917, 765688961, 641638079, 809128465, 640161744, 179196772, 198095390, 275681927, 342080301, 547473950, 527336586, 776626305, 367020472, 30117060, 348231840, 910481068, 700931088, 348290439, 85858282, 685131241, 526395931, 865887021, 596826184, 462284065, 805470927, 236275448, 485766374, 671910102, 536632013, 347506302, 998403616, 742253446, 993162526, 303479705, 146482398, 77710578, 201467500, 24805000, 81451438, 631443623, 843531733, 693249216, 338151497, 227221645, 860421708, 914581887, 989015674, 700007676, 438638489, 619935044, 834562733, 372686704, 452747785, 154499133, 520624989, 659496366, 449901086, 148356615, 711524116, 709108700, 307374573, 770843543, 522762204, 292938500, 896161473, 206903028, 454521025, 414829935, 431249494, 595983286, 362424894, 635468867, 566649155, 736595655, 25877168, 413399386, 64038443, 6235972, 991032573, 218909426, 515942749, 448841249, 441116605, 325658992, 911083256, 899181811, 646983378, 388857523, 933108972, 992055678, 664772287, 332490957, 662115271, 774702694, 943416390, 701540697, 910535797, 381785537, 950381484, 168873227, 394307130, 405850308, 783350315, 748552714, 238526672, 58794538, 554012035, 978432131, 981838082, 163740166, 972099118, 755203286, 811782071, 598053543, 381164351, 678577255, 318383093, 289768043, 833006224, 314991818, 500942869, 913695413, 810451334, 620028302, 682620869, 268418949, 575330169, 63117259, 812588163, 373426748, 793349186, 202375204, 975583460, 141186105, 753430981, 81063419, 990369300, 150943057, 179168347, 295889678, 665557500, 849825789, 582214799, 394813632, 685694661, 654893815, 942608332, 992840588, 321147494, 271089844, 257647096, 995411123, 501734458, 953937594, 421923357, 112804236, 121660737, 722830105, 351599305, 411675781, 475835149, 478544181, 542443206, 835918663, 46092617, 543905028, 954970973, 949025396, 599113146, 385782229, 707692185, 85327428, 178437490, 636922329, 612736866, 368619889, 447361865, 432267015, 695191301, 849509047, 471986537, 451628961, 986804927, 623672443, 459109359, 93551376, 906815612, 57263725, 93567935, 933660859, 734200363, 690819374, 425166307, 861386116, 409543414, 150601476, 507397813, 510715791, 714089902, 778491233, 43325424, 322553891, 629238046, 603175782, 725519681, 84514577, 394712753, 84345420, 322236844, 460541386, 585478304, 158117168, 242543965, 982257019, 704275596, 644075711, 722894403, 967342402, 711911550, 894036639, 681769835, 691065899, 781092765, 627682862, 110630556, 525344561, 826493120, 67713818, 58475312, 416087454, 840626378, 133964300, 221474918, 654238006, 997764667, 714384899, 239499067, 272079916, 815284624, 373423878, 262055793, 822618530, 956957557, 822372470, 60577970, 496024450, 381316818, 813427916, 943068316, 517647309, 227551610, 363805672, 594282253, 862487541, 950016699, 855278186, 138785352, 396126121, 238061846, 592491477, 467653544, 460498816, 38787310, 746390112, 47065519, 94159732, 723097459, 633350529, 658319868, 787793495, 844399965, 560330285, 374526867, 379048687, 521778048, 178061013, 302604627, 517111396, 114713733, 887421133, 222707155, 644818284, 715089005, 736342232, 598539842, 214702860, 318178745, 647304905, 731279339, 445518908, 134519233, 350175029, 163459590, 32168735, 783959971, 947857921, 825222768, 83147247, 171423715, 360008528, 220306160, 607434408, 816046722, 63313901, 674418257, 435113101, 487282177, 247128764, 793295849, 79182487, 291406122, 377421110, 199402809, 753855233, 689328478, 59528465, 23938181, 309863011, 268446956, 878570407, 441491357, 142822784, 878531849, 877215213, 326104278, 98772596, 433074166, 333972520, 48171281, 618129052, 938758537, 560719623, 808755799, 803227111, 45984865, 704952393, 662201643, 50767832, 759772819, 83632039, 720008308, 595338832, 129338510, 493995858, 691831353, 991319247, 358296450, 512781897, 101505341, 264496775, 324403037, 229011571, 308331099, 874877912, 67023258, 808054785, 228345664, 679600406, 611092668, 768655043, 966121163, 187030226, 984085326, 912276322, 22610660, 762739260, 68603404, 557047226, 92632520, 676012394, 718550906, 133384604, 709181919, 568422651, 878562173, 78366814, 527498099, 49885528, 604373538, 784369448, 344472441, 115217440, 355651587, 111710455, 664010600, 692371449, 338318376, 619027753, 472302379, 338243259, 32028762, 639499671, 629521199, 727637372, 756963838, 556490182, 84789250, 944617272, 62926512, 772253328, 786315779, 683290048, 613012244, 901762566, 298709777, 409435419, 936053772, 68558752, 729241886, 213482565, 563367979, 955226003, 332528575, 864325055, 770657202, 4574623, 684839397, 322092232, 674549727, 515364679, 927789100, 337835313, 449601612, 932878482, 264359498, 521581720, 696596870, 859790715, 983336308, 682067610, 3500650, 782120153, 887613838, 82959348, 810203562, 544355884, 248152092, 91585552, 411903169, 641097522, 437349565, 142516181, 665102021, 412999479, 377246142, 870785910, 113007415, 277257794, 174115858, 683485888, 723478445, 617973163, 92054028, 977561409, 71990150, 358945402, 53319768, 449892212, 152856836, 638348312, 972794413, 971580952, 679851619, 417537391, 725029136, 547475550, 932141648, 490878580, 365988245, 101538923, 689951737, 101566019, 807590278, 543029571, 943637802, 459907188, 796366748, 9784010, 582855797, 329054878, 10510696, 910982128, 574450096, 456087309, 571956248, 330494490, 28627927, 104707473, 653490192, 321248456, 308336718, 442791849, 235928924, 589115325, 692078488, 671673818, 165434672, 955563701, 120193419, 763081484, 656349433, 878515241, 882047162, 844246928, 319909646, 199784577, 62832328, 399879248, 142286542, 87791611, 999543630, 859971596, 390955533, 47307894, 995035207, 511972568, 269618340, 567300628, 947357132, 506220122, 89403197, 994049224, 988822482, 153447795, 125579972, 844362685, 462026634, 65406160, 208755045, 93082934, 230627616, 163949317, 90390121, 988264920, 861458626, 276705423, 847088806, 80908017, 112682632, 650973961, 165585078, 574825478, 951533326, 914447352, 191003493, 704174777, 275806952, 958386295, 868635621, 270165688, 866475292, 246528051, 539371752, 341812691, 564739770, 364014646, 668027655, 662655090, 739904764, 188647436, 56185241, 759716265, 817827300, 607115637, 516659280, 260266847, 236492446, 80036730, 724866490, 340293361, 92597559, 980930201, 453946952, 951929520, 882220782, 358701439, 798251354, 479967604, 678799075, 850360861, 553822355, 555417289, 506813460, 268247277, 892683501, 163713016, 584368947, 819184547, 369484265, 919215211, 548285115, 217338878, 958303877, 310025979, 86177056, 848464871, 857105918, 576624085, 680116579, 356871990, 158412760, 810815070, 794229088, 548570570, 47069114, 376256828, 392591833, 849581112, 890743453, 506559592, 226245266, 79789679, 629736251, 764559854, 101850177, 425490288, 783465326, 689223791, 18799218, 657523340, 707532540, 346387960, 806114262, 478974083, 478903024, 115131074, 182710550, 210300787, 859632603, 647938672, 636638999, 497103643, 468402335, 873990366, 710285498, 542226476, 195906942, 697079547, 74879143, 623615786, 524369321, 517963735, 318439331, 995298527, 403857805, 339938113, 456023297, 707312010, 333330249, 97445273, 298216412, 568542249, 981920653, 611020207, 157823788, 509986696, 121292349, 134286485, 242374384, 581344812, 322125913, 925374157, 195530059, 159454475, 995237506, 240671273, 738703574, 428538187, 442156502, 846814313, 676475630, 860189678, 836304233, 295984161, 953000938, 51654244, 445886875, 673134766, 186224469, 670093192, 253718302, 782508768, 155685876, 680076347, 70596562, 656229193, 335420905, 109913883, 666965488, 296788095, 262123435, 309510408, 201923853, 862828414, 265506759, 941075069, 392133140, 447883425, 220802536, 53141497, 743128724, 340213071, 275900166, 839614635, 472347099, 721066522, 142809165, 559067265, 552497083, 149441115, 241087159, 712946032, 570438107, 220056853, 493891999, 901633259, 342841473, 121269011, 923598733, 373035004, 742149104, 999706362, 311551346, 838492242, 25694251, 915542943, 558139146, 248255621, 661046898, 643313556, 378692919, 77151980, 917641833, 66634613, 460642547, 311178591, 10251914, 708444332, 588340923, 76824759, 217041036, 25609573, 262038599, 964222804, 12682518, 500720822, 190425475, 46041382, 850946407, 236409270, 356977898, 196293160, 375084795, 624918059, 897760277, 408010896, 869184624, 932909475, 151162701, 855919611, 234084302, 567984490, 339631108, 512363913, 464933874, 419235954, 992754105, 738036858, 258805827, 968631618, 496035639, 451391653, 64945262, 370134993, 202277715, 27141405, 484391000, 32962542, 642801720, 28512318, 38614280, 208428695, 804941210, 533600530, 35081458, 218713751, 8517377, 701089557, 92549280, 241796313, 135285414, 498230359, 914898590, 625661027, 820543038, 150357320, 636532631, 434314894, 701484466, 513337764, 819575587, 490513280, 827860339, 511865400, 260110988, 33022462, 797998245, 109694867, 730497452, 346677325, 941292824, 676981446, 853433777, 463584100, 123945711, 489291405, 857733168, 414038742, 821622932, 646328884, 558464454, 592904727, 765199782, 878084517, 104901761, 669313686, 638630709, 580619929, 900442152, 174989426, 312048551, 400113064, 4880073, 617185658, 105594145, 844108931, 110209259, 549685025, 446725385, 541556459, 560849599, 208481426, 812452357, 962173975, 632015387, 279383247, 64267592, 54057486, 879536710, 54423524, 207893990, 829424890, 310069791, 945079293, 398631794, 286523328, 739123960, 838556806, 967425748, 882343008, 279526085, 204121727, 590669323, 771403015, 221647836, 185769503, 511501400, 857253928, 131505291, 725409198, 584555734, 953037137, 385407871, 608338237, 201779634, 674320002, 520264978, 79008972, 116078074, 567175400, 616919049, 774516861, 533021903, 869475354, 619738151, 226802918, 975789308, 965685381, 364644457, 15246732, 47192867, 361954335, 479231425, 494051130, 148641571, 54488377, 889659155, 993013720, 195696391, 821729634, 480970463, 697763455, 291084541, 33634341, 407070755, 33622107, 126036721, 669862758, 563668207, 51543080, 649995348, 772668032, 52971129, 918183725, 451710197, 19559712, 167922040, 811459185, 308099350, 175177845, 817778355, 541425027, 576093428, 667390680, 706856576, 93016154, 783653926, 126422923, 791912395, 300729369, 549785616, 623040514, 538448710, 883337040, 918461475, 618103302, 259957943, 788658130, 974082009, 994824988, 264153689, 942121956, 497762707, 876592400, 100672517, 777862931, 155409085, 665743885, 475541826, 946066552, 604397717, 250115143, 149759817, 192606288, 496587394, 477150173, 59291046, 147424789, 577479485, 146251690, 372836543, 264724421, 901613551, 82109933, 928096883, 957254447, 650143446, 904815927, 280587216, 58111341, 682070229, 161023963, 998285198, 206638870, 485174431, 555231648, 364770095, 436790544, 388945448, 574748573, 801462481, 771968388, 447478285, 401816839, 233094364, 101755420, 51490035, 256112659, 435084367, 309913353, 514496896, 527082154, 561954656, 268384517, 864054251, 435575933, 96242685, 299435734, 320052009, 33469206, 916754732, 620520677, 893065250, 926178845, 342412182, 982267434, 274179801, 416252674, 281568185, 488122943, 200199954, 932699624, 883514322, 696415260, 574859777, 454241449, 807616785, 721599053, 481017349, 858775087, 72851178, 775917438, 875978437, 836839610, 470156871, 809940507, 151546618, 20311664, 295214267, 329638295, 795885086, 767376201, 850155410, 969176768, 727020310, 689256107, 564321562, 418275748, 176476823, 900167872, 410455619, 303561458, 409541784, 192987274, 813870048, 606577224, 68103372, 119497510, 957949582, 543858835, 806374453, 891364108, 284751643, 709804400, 601236636, 319463621, 880328466, 72343770, 48902283, 93340963, 311729624, 730196046, 739205327, 818831829, 686772727, 985404097, 955471531, 590961367, 18213340, 129691251, 23908651, 320132385, 794509122, 821671954, 480506532, 227572739, 266665771, 139217162, 65048853, 252991681, 273359910, 97086832, 362205583, 464452391, 618003186, 705391551, 778237215, 504255859, 809055368, 486739336, 69418830, 175974935, 603058722, 792627847, 569129521, 736208310, 898827113, 765779912, 616047872, 90272600, 331453414, 71189741, 101716059, 805431400, 878930669, 319619972, 135278725, 5762922, 909813304, 926408152, 44668077, 682183498, 535418329, 350171880, 949221534, 459817801, 9475063, 297750409, 828840811, 386241622, 672233021, 101911325, 570460208, 654616191, 296386755, 410883049, 89422955, 578006728, 58508844, 48604637, 48086064, 430311307, 317311656, 16970171, 328334683, 833616552, 490912021, 34222773, 366822708, 693205409, 39342776, 521777212, 100882671, 223954157, 11243496, 187261942, 652488483, 154788549, 777193557, 961672148, 755362346, 840376096, 133467757, 130148917, 264079721, 533241114, 774502647, 273577375, 796281304, 854040814, 259862020, 301692584, 917504529, 359489346, 251586096, 705144724, 409833646, 453113000, 892334629, 273394023, 464929813, 314442258, 466074625, 708578058, 799180079, 610313023, 755649221, 224612746, 72713544, 104962100, 705907949, 484328501, 795347348, 881520190, 349120657, 116248996, 526118406, 542410608, 609340300, 338712035, 530936779, 894936763, 643625671, 519445323, 33742373, 825544722, 225270782, 781760460, 379347536, 520290641, 644068779, 141292774, 146026252, 305263901, 771008118, 625111582, 89748501, 758050770, 956086681, 746288423, 680578223, 114404591, 235066083, 821352248, 660631174, 156150298, 41082181, 621870586, 24615177, 27469956, 544728851, 132056235, 143197570, 705613670, 761602181, 16234742, 603868736, 203435689, 700990576, 761460563, 530490834, 834283839, 182120954, 804564163, 613451659, 184831181, 958825861, 503109775, 261464336, 748254422, 741979916, 140918132, 815688506, 934894767, 817168923, 419064042, 319075108, 839898692, 74741521, 741248583, 677486932, 702849302, 596935350, 638062852, 122138741, 245423994, 323704671, 502421554, 70468295, 636944409, 773833008, 688760392, 53164457, 447225715, 379305614, 559770615, 384095551, 118844707, 577312861, 657809371, 742133427, 695677810, 752885980, 228248561, 158130891, 679575571, 712577767, 866517165, 728698809, 132670521, 423311987, 98416963, 839352691, 565598324, 517613726, 362630189, 264582541, 420639801, 218630390, 288542512, 760948242, 455005407, 258160472, 286098291, 925335912, 918108865, 868373677, 978650486, 171279148, 487365813, 998192058, 33990001, 964767103, 495474786, 584118335, 574008124, 162486001, 911853346, 352649986, 168119337, 809733897, 324008154, 125056985, 780228019, 498084895, 277977479, 635680514, 734532488, 994809838, 411305779, 593321373, 927328144, 192031336, 243921475, 216087051, 353292333, 258065801, 482838561, 414715236, 391011350, 39303670, 696671090, 955811435, 240768914, 346079010, 129841649, 541901074, 36155476, 403578963, 350127686, 236941074, 578030561, 130520727, 808069728, 335657291, 517657555, 529340217, 666581212, 483261205, 54424934, 899753706, 391571291, 380747442, 505331752, 351298828, 284973038, 719944870, 796096212, 387802739, 915953549, 747750069, 406493701, 390162580, 845746098, 267468219, 857412647, 520574784, 838459133, 806167811, 561542609, 714181803, 670254106, 741735657, 946425847, 596848851, 267901599, 132526444, 302190916, 172353357, 704818226, 83289841, 932349011, 471354892, 705362301, 664540455, 696717678, 593087885, 638199490, 178746528, 81133010, 88200845, 590507806, 954891700, 262280412, 440523043, 612669390, 276089754, 99008794, 473025027, 448407091, 495565071, 596138885, 60534660, 491143594, 188546050, 674384266, 761002528, 208555333, 358220867, 508238652, 87091043, 103976042, 628015775, 700088184, 719678829, 291950203, 320373747, 675066107, 494512253, 156106087, 59522427, 913535383, 348861672, 436572629, 743032878, 446049814, 713686812, 118270856, 198125192, 622575561, 553528240, 622049472, 735671402, 860356720, 424705899, 339600249, 370239722, 429250382, 10372422, 752981085, 180684315, 748607331, 309244031, 202460334, 92460208, 472426065, 545242636, 254427104, 247311222, 481989729, 448445545, 718543502, 116105590, 926000077, 730644145, 482559226, 941984201, 784650282, 225315401, 884755490, 516994964, 610575837, 322211831, 803746572, 816335213, 194631609, 157128771, 119493933, 90117321, 560666821, 333795772, 464091687, 431271545, 639890605, 44772507, 768955736, 244405013, 733856118, 480282963, 897484093, 322746884, 483819356, 147546395, 45662535, 83974221, 438627122, 915025919, 301889188, 987536702, 450506930, 469076879, 363226684, 587438495, 988356619, 761586040, 929944588, 924105215, 784086140, 964109456, 678533239, 896773585, 364012629, 758586295, 700231377, 482930499, 482569925, 304440764, 799592873, 164639172, 895377840, 293728286, 955095909, 612988080, 169952393, 386286552, 928601844, 441607203, 476456093, 522041416, 396915541, 24584016, 253054662, 635963177, 894318160, 840889821, 448026022, 249893172, 245373918, 821947756, 180826163, 185707600, 714403224, 653903470, 164512411, 12541946, 247971723, 26781343, 63417600, 399058571, 828752889, 196306702, 866524789, 615728613, 893949004, 708412322, 68395137, 990810250, 251590927, 408199080, 577516111, 97311805, 198221866, 184296149, 633122606, 173525945, 75283881, 2332861, 706090251, 165010319, 770308910, 115079689, 841866371, 217178386, 528727842, 345400753, 896078722, 98707673, 58684840, 268158973, 252734019, 547405775, 651151567, 620190044, 657068309, 337656742, 380392969, 830777994, 703565977, 941835690, 402781434, 357068858, 91512171, 951361733, 683237903, 158195282, 123358302, 350551008, 51748798, 291399951, 234634116, 392589486, 394334726, 532404697, 846730203, 847176687, 228589077, 108112001, 704941155, 453525655, 625199629, 534349882, 731457463, 959917327, 83879634, 500601503, 503430697, 56958198, 124996920, 928233063, 728832864, 213862089, 68784697, 188770866, 992580005, 544709217, 83168389, 260537986, 581364386, 557265845, 119143162, 134688995, 315094803, 614198590, 783636529, 786811984, 833687726, 280254840, 773733655, 717555133, 839204076, 541471680, 456912301, 246003658, 630200504, 274359745, 324655068, 876839035, 591258666, 878277885, 470010924, 564892169, 69701942, 9810675, 830872382, 636469016, 452191386, 271311390, 514499343, 121250754, 601812106, 735966358, 551506430, 446374818, 964967001, 45520416, 8576133, 347570630, 645093929, 272640739, 159583777, 366797950, 288294608, 948569318, 907091221, 555671866, 478174869, 982232570, 138581361, 783322677, 446491781, 129587614, 240337632, 414478003, 232904843, 493448315, 180901156, 956981715, 869824090, 53492764, 915743141, 608802549, 286593382, 416175139, 253521098, 646181764, 695664927, 746295109, 119662429, 133018764, 617428896, 173882570, 765844397, 584600903, 537873252, 991118523, 881493422, 123143149, 331991763, 6265206, 894486054, 843386471, 577244902, 540531839, 958269641, 890162511, 314533010, 503581206, 798107252, 189886534, 974165777, 353576677, 953630783, 649340467, 330719438, 150197957, 923800189, 414577172, 605800745, 103024273, 351617612, 696975304, 911930742, 403420688, 47233314, 794452602, 95008391, 626925742, 66110812, 541073721, 549623792, 405501828, 986579042, 522518585, 2691519, 833799648, 889616275, 475710895, 293334934, 73233206, 768248985, 970897937, 656013611, 79550550, 496648556, 630119365, 170712468, 296983371, 258614969, 116293437, 119904649, 76157796, 543273193, 322974363, 543524700, 584672900, 803142646, 267476483, 627336099, 43656261, 752045750, 991553715, 323899847, 660501812, 27387986, 363868080, 382139801, 3186745, 923341308, 123848951, 223818883, 827042303, 543874924, 164038966, 605103421, 13976246, 886860550, 679838010, 783453125, 796840191, 329309147, 774443827, 455663886, 506512296, 407505651, 732765550, 411443176, 643400521, 646689018, 864903929, 910616519, 735634332, 281882284, 807085149, 919656428, 991926531, 684950354, 657137022, 654754186, 791157386, 460879225, 20108915, 718716888, 990203023, 156291989, 703193228, 812725221, 318152798, 342985613, 914166624, 538396819, 440571088, 933624062, 996288039, 609850310, 628598123, 174721201, 765402964, 268712750, 441068502, 17192838, 590274235, 131225278, 328663656, 19006910, 830738097, 993651032, 774057307, 684214906, 127286991, 385516541, 834786723, 966446059, 539100110, 464384791, 802728701, 753454432, 975412581, 219486655, 829731379, 605156801, 524516661, 865549735, 897387470, 169212873, 524289596, 491523100, 382836442, 229620161, 832389701, 302745296, 979975752, 741836083, 70310188, 817979082, 502303680, 159225353, 345132657, 626055427, 987871716, 673825277, 433812532, 825879191, 161134102, 408832942, 201976787, 307807628, 355612268, 234394674, 627888351, 522577237, 586003204, 717532761, 622383438, 606497587, 306141233, 78813004, 878706960, 989741273, 774470825, 925246126, 288380089, 707096781, 270894101, 653649631, 610468970, 840016211, 860381531, 357911676, 274631799, 748781141, 952370791, 799743669, 175587316, 288179941, 318966513, 343000956, 337192341, 143262725, 606283084, 536453310, 986188245, 375576736, 879526282, 513554552, 429235348, 789360012, 846852326, 369249112, 914346141, 785785958, 398856779, 975086957, 471096003, 670384343, 739246604, 785786479, 979769964, 410270049, 660202868, 752340820, 403417286, 37272174, 143041520, 116851179, 76353965, 530482837, 872739754, 576960818, 617782230, 62928101, 640277503, 350142994, 3607559, 977373178, 271562122, 830054099, 712686875, 34982036, 836231657, 214042755, 875527787, 611164278, 925206788, 656711131, 6271440, 361926324, 945640342, 219296703, 363094395, 729988422, 565056570, 593539036, 867448352, 591652468, 938839401, 926970393, 547509161, 555501369, 963115546, 547158556, 781383773, 38012985, 187530471, 176160125, 958911841, 720629896, 624641772, 467138559, 457793359, 24155268, 355909643, 745516562, 874127328, 566799010, 430532995, 190671860, 697143600, 445254845, 305012895, 482264478, 860435038, 921213485, 133367366, 663309711, 979052981, 446282837, 890084869, 25738134, 796860678, 280558547, 626818657, 702505454, 802477100, 282572909, 310448515, 410177726, 17187823, 729019964, 539712566, 809158401, 281856405, 592704824, 961104245, 512677159, 915886678, 39184401, 533186713, 79857422, 797485921, 322830606, 581497426, 723736466, 754320084, 975471314, 85030274, 16745029, 863717594, 947269553, 575227052, 188767551, 434926932, 187676384, 912790905, 38849247, 48848315, 646778469, 437308556, 774357734, 838580704, 221438625, 114276142, 864290064, 281629963, 886571286, 141938371, 410592271, 669304684, 645535066, 996038241, 979100832, 304072840, 815657426, 717632946, 900322905, 685051248, 10018103, 243735118, 140532083, 245591632, 334623571, 901895829, 487599677, 816364185, 980111995, 168169041, 783421429, 698716803, 613823523, 487069835, 625013470, 351562653, 333176286, 157466640, 871472067, 666437656, 574512326, 356640452, 915593452, 127328227, 604687433, 970165551, 949522395, 443083374, 496889852, 829835037, 380399192, 816732874, 747511237, 992725630, 912906115, 335223164, 605016528, 653373445, 588944747, 840668916, 591068059, 767461642, 958514344, 616778957, 213468443, 603282999, 179108082, 587724156, 955574680, 633238741, 231881318, 762685464, 759887373, 299563103, 885919029, 236999548, 814950073, 9550893, 239344999, 725326129, 368845228, 64905532, 464853814, 908360670, 993659838, 720273331, 130659914, 96512582, 76597511, 741838197, 800193272, 931434851, 705663960, 857569823, 186054532, 732179110, 124372116, 109134076, 33987417, 903546188, 303040328, 910578400, 312554699, 977396985, 712221268, 882346395, 457545039, 523862219, 498523632, 172837042, 894051231, 692724952, 843702530, 418849230, 997133067, 281582010, 403606950, 648227494, 662080026, 289675998, 429732284, 887198740, 900002869, 850240390, 425026152, 999909178, 508969389, 733620532, 295500271, 895705251, 294555128, 928963741, 362784756, 361925093, 191987586, 559307331, 974356031, 325071620, 23788183, 381215295, 328116122, 819796057, 479547444, 125133225, 217627168, 313607657, 699836221, 498354958, 160982752, 358934805, 780903731, 203194630, 148770266, 740900788, 996099706, 937176905, 331434016, 254287259, 488043785, 939493677, 449494649, 642020332, 78259305, 333553572, 16406642, 501460254, 125960361, 855115390, 794473879, 485943641, 982221740, 471828783, 586845381, 791081572, 952185516, 254038717, 765749477, 416224509, 194379684, 427786418, 533615340, 750609395, 712754917, 910875279, 695201777, 522042287, 484286758, 192893192, 774252847, 249538066, 549256741, 630498856, 343882271, 620752786, 299405435, 630714993, 725819624, 966107568, 879649327, 971583830, 997495694, 508769977, 746192442, 558546831, 436852668, 343774080, 871252042, 115400675, 271445265, 245323327, 710549421, 247343431, 296526148, 805139402, 329854920, 515262172, 12480354, 772254096, 810171973, 363916531, 277704335, 343897548, 170996413, 34708059, 941168210, 551803064, 984552330, 950379377, 338880763, 881792852, 914474552, 104430086, 90066863, 169307124, 935305335, 943386287, 43123635, 169353047, 363668345, 201853580, 849438998, 790954372, 954723961, 371842043, 295955938, 245871447, 916806994, 274502036, 939871802, 814184093, 710832643, 323312027, 210580285, 706887091, 671454984, 957589379, 206228903, 875143974, 173234986, 685420650, 664862269, 848124369, 318217709, 701081622, 933837424, 853811274, 397004305, 180287186, 700277370, 62393784, 898210768, 931301518, 868301419, 424705685, 254705764, 372805949, 594339329, 54372331, 660045453, 208153081, 382140385, 308138878, 228094938, 914841801, 834678618, 721382500, 959969406, 819334682, 134514341, 203451833, 689045638, 805183783, 48781581, 697453620, 164119807, 993364836, 76951554, 908567704, 200887180, 51315009, 885023083, 234824074, 763774826, 746612079, 635347218, 980231664, 332623889, 875371639, 203929259, 155419182, 982131736, 150500967, 266862768, 641775005, 149820931, 6583369, 941484426, 790584428, 768378777, 557917968, 912355688, 717551239, 751523055, 381315970, 56166402, 269217005, 774441753, 31196508, 523964770, 287249575, 777471583, 547506460, 842916660, 289872742, 212783116, 542225344, 591475887, 944189871, 194634877, 892220040, 247627272, 512695, 825068513, 49421902, 340661468, 885786300, 44165986, 888431125, 310939862, 934441867, 818599675, 488103053, 379461981, 974889328, 639483279, 28510122, 825197056, 894627099, 415136846, 204837439, 722344305, 364819588, 616490715, 510817925, 738325522, 236526402, 912668299, 462235169, 628517926, 765748797, 998921662, 799021907, 571828358, 275979180, 269114247, 384873145, 666773536, 161175425, 279312978, 866148560, 756055572, 220992303, 580193007, 312695653, 492668304, 268620012, 454420947, 650926643, 94961186, 769807890, 326081218, 166929656, 426080588, 29096995, 128276599, 113825372, 850671038, 411026399, 801403544, 742012978, 857055568, 980275905, 902292028, 685475979, 275802099, 868056509, 298029279, 455064294, 957768751, 197318616, 444565324, 793559116, 686334514, 96429275, 914864523, 454684733, 242293550, 519453344, 864142412, 634158129, 607192144, 621928538, 271612758, 274116089, 707113386, 308748916, 447037217, 83417754, 930570624, 618449295, 216822638, 464705343, 318665769, 287874560, 541459195, 883261384, 324335072, 895792924, 969762043, 733126960, 25506383, 773156965, 134185964, 194154785, 65541850, 258055473, 264609272, 205377864, 202026184, 475593716, 499412586, 343719586, 490314863, 328650882, 75911363, 909832557, 646676350, 162224777, 364904449, 354257595, 713915800, 889529708, 56809747, 953035163, 944201205, 974343518, 552396854, 673816607, 964759875, 900615135, 78943007, 961455908, 331280439, 602187821, 625434901, 789063174, 841519243, 536164872, 222985848, 335265625, 330879593, 242603828, 572255385, 970164223, 342362744, 301244187, 589526515, 915416461, 90022916, 186843672, 476275458, 984413085, 779686579, 386725172, 723519068, 713087424, 842032149, 72620769, 622749139, 558365241, 604058618, 217467349, 148512823, 592669481, 716223725, 64354592, 186127266, 336776250, 966595492, 874033497, 27585080, 688202061, 103363430, 294926620, 349715333, 417195896, 671583524, 973596538, 629512129, 333786306, 989631928, 328684477, 455211813, 480770820, 573352715, 218277372, 518184540, 687632445, 910918220, 481804682, 33311808, 894717927, 447787445, 753259069, 731519098, 335074575, 496142261, 332602017, 26813798, 415477263, 97277784, 756974709, 901205161, 575209593, 289021331, 233276594, 753884234, 33116943, 509753980, 560724665, 999677707, 528565671, 786240291, 791945646, 886731561, 773003165, 992978992, 154953872, 772796695, 630022258, 849890049, 835906892, 923319387, 98240965, 831550813, 129852525, 864973244, 795149714, 272567285, 810189780, 48197344, 157011859, 196878872, 607663423, 561314910, 753474596, 609612621, 520493638, 77247664, 543083463, 510752170, 909380933, 467596834, 490525625, 602298777, 230915741, 942364718, 153408701, 255588489, 85285101, 965460995, 562666248, 729223261, 27880948, 574538232, 920790622, 126468847, 11354513, 282977414, 865384404, 936789397, 271282538, 247369590, 505603268, 874330958, 376393559, 218417682, 832414440, 601074829, 172856091, 483677843, 349531868, 218565513, 97844015, 557391699, 973113358, 438650207, 942526774, 162468100, 282686018, 169718984, 989845689, 40689555, 648005947, 561437567, 294566443, 98455897, 793006682, 280181232, 841315792, 524331359, 471979256, 192565943, 594420030, 750500035, 540544929, 644224376, 926000866, 378377926, 205027862, 160542864, 281854647, 875984378, 228816965, 470956417, 553434897, 138370230, 903560526, 408390590, 902704806, 224461199, 753891801, 542265182, 566236959, 15250196, 716393454, 941217135, 151965449, 132113979, 966430240, 598335246, 810701333, 98988100, 507314101, 400684888, 231449379, 554820999, 460752439, 637177998, 875199679, 721018326, 818684004, 550341920, 677710278, 677101155, 945650122, 12485694, 923655041, 87468620, 408454049, 689818723, 176289165, 818740348, 135993070, 986272898, 629135727, 292997509, 127203186, 436087452, 411316309, 530060318, 148468431, 939783238, 167747953, 278761230, 843516461, 740067670, 75915708, 697054716, 88881529, 120031661, 197889628, 722186442, 52580215, 537598911, 784728524, 751292715, 439559285, 424672736, 528404730, 946062618, 288152483, 728806484, 178734223, 480330752, 522653224, 717804687, 46932021, 634560970, 968962357, 590438717, 292116597, 130387835, 820584688, 601967535, 637168644, 458806728, 842587580, 812808626, 834983375, 972722793, 956362003, 751282032, 680830012, 681643558, 921942080, 988329114, 988627735, 217705413, 403759478, 709254065, 984017243, 278265721, 911255340, 450796364, 869433782, 724753561, 21206535, 476482570, 482623172, 975361854, 595749171, 909540740, 676100117, 313118672, 398925233, 404739916, 782780623, 660148930, 624269957, 43021917, 144554644, 959870335, 219286758, 994092851, 194095758, 452968310, 717446678, 212705180, 211836795, 909756476, 16522554, 22624548, 75011931, 717422770, 193678184, 641603810, 121757704, 165696889, 865514260, 599925706, 669375986, 272249483, 784310887, 429938392, 620740118, 159251432, 250107023, 589030662, 174107671, 168709536, 642263396, 20052514, 562812092, 163521068, 193536099, 994046535, 880831259, 125416452, 25527379, 875994127, 633376546, 335000515, 74971905, 292343548, 479938481, 126216260, 589973296, 967007132, 134178698, 759571345, 950187222, 387673996, 34792387, 509672539, 607647834, 594377994, 962712649, 578394027, 845629231, 469391699, 533531153, 359533679, 544023021, 107104798, 133727659, 717004926, 290502796, 538515447, 928420974, 623925257, 766858180, 43779230, 714277545, 585145678, 146045705, 16666623, 720459208, 681293289, 345344582, 645150923, 238045788, 456328679, 787165728, 127618554, 579781340, 24721886, 572527775, 722408839, 420069590, 798920915, 586621717, 62934322, 156713584, 241932449, 624051000, 812957188, 214493724, 914436825, 641196432, 523550209, 880268996, 106335862, 147471435, 490399608, 743156160, 640700091, 592317403, 990881805, 930874133, 201270232, 87017164, 501761050, 377251556, 834193480, 288256748, 477594544, 159375746, 664024072, 711285787, 340066072, 944667335, 174413131, 45317560, 955844880, 299027698, 639580795, 18524539, 523556138, 278886192, 562152766, 64812447, 352637550, 418220223, 817271272, 411673438, 393045704, 995710697, 26209796, 277934037, 479507078, 170479498, 941832268, 199461296, 387858693, 237689718, 788220575, 954692233, 262683175, 257714637, 445494697, 959677564, 416842177, 100522463, 36650658, 105603004, 889427679, 43690531, 532561335, 45138019, 249258843, 459998401, 233004225, 25547794, 373721927, 893537294, 248663623, 899938926, 437885587, 233946460, 220913281, 425533589, 956272560, 449893047, 38153031, 828132663, 220734534, 51111894, 531427563, 182144198, 501690335, 781803554, 560771779, 760028283, 679115748, 938905323, 517457727, 381367079, 32335247, 699903856, 801151042, 422956639, 427255777, 781662978, 930307151, 707707620, 499617910, 223608569, 387383275, 614276348, 748853520, 174016916, 241034766, 246683526, 404215926, 578245854, 631676450, 986902168, 357237382, 558319342, 997455420, 585864011, 411083829, 757618960, 527310729, 457526553, 324525976, 25522577, 649270007, 257606150, 21594443, 467009607, 756500267, 67180289, 978912868, 425395853, 412562736, 843943299, 336551345, 410909576, 437056020, 701180489, 404994437, 264475405, 485896870, 967190861, 975124232, 414825669, 546502966, 203654155, 116290021, 524926020, 656828779, 923714815, 581827921, 421163598, 222833252, 515114732, 290433308, 60696015, 918263408, 111105534, 803534996, 737642605, 91008368, 991366647, 792927814, 289119182, 813066825, 672365971, 159045084, 496952465, 768045544, 816634743, 315960019, 800993356, 549309951, 163554928, 207605173, 114008231, 261165667, 845701152, 706845387, 299291482, 846050637, 604853191, 473176139, 152121836, 280689139, 448983691, 74680331, 954981176, 378748840, 577777400, 730235468, 52482417, 141105696, 874446541, 775997973, 240780504, 662942112, 640456116, 33733791, 43233869, 316970001, 248248561, 951070602, 189139278, 596603386, 59881915, 923823665, 723825710, 283125965, 157116909, 24562308, 190009193, 864715310, 89144620, 85238516, 795748429, 861906427, 765818606, 772027227, 261284804, 984746528, 105934369, 797236837, 19241375, 42923000, 611533251, 372237146, 92890916, 886738128, 570683881, 281808253, 382442074, 383794247, 702358216, 892926125, 978241499, 49332711, 563791788, 438233457, 112320735, 103254683, 276958658, 531143101, 291373007, 379906614, 79971089, 745521396, 304944161, 656471180, 88992279, 882659765, 3382231, 63459993, 133865265, 315082892, 582378613, 791289126, 540968586, 748057106, 702165002, 128360872, 708237, 799322266, 181172541, 323928139, 134190759, 339634449, 592352994, 692845793, 603264654, 524351657, 674548340, 14744679, 730049078, 107270747, 727074809, 901649669, 972784568, 399933582, 956898975, 303474441, 730111006, 752175407, 701657782, 664867963, 710492927, 104201046, 738857515, 361249597, 398004261, 981434865, 372920614, 694689336, 280725654, 80468748, 428903491, 700792326, 767305981, 427227413, 652274720, 821359937, 885574384, 260643446, 25718724, 220942752, 603869807, 249728846, 848503290, 237137763, 787927672, 976533929, 441105080, 832179763, 385158678, 163773785, 538448252, 841191915, 604948353, 633829124, 3537835, 648081395, 360546881, 445503909, 90326931, 108830362, 982570527, 358042866, 722095438, 290427393, 398409032, 999262215, 251091619, 242966119, 711313407, 879975248, 211431254, 30304393, 337844610, 922478467, 809891685, 597790532, 747684050, 413412317, 373547699, 638194477, 403667843, 260996995, 360339180, 780179750, 444484966, 932631351, 826045668, 304802139, 343261539, 360204529, 797069203, 613999393, 88834124, 683584512, 513778065, 489995504, 133990491, 912364987, 217481447, 765166361, 276065618, 173195298, 756767412, 396089972, 731915461, 555336920, 9925926, 956178450, 210998127, 9430840, 722236121, 45724842, 220151278, 250499277, 523046920, 895772341, 382710536, 784655553, 648865675, 260815370, 82389744, 740052744, 813236329, 125404537, 68103359, 258379871, 979324244, 852319900, 379446344, 170452988, 659390322, 111370760, 601478404, 417530699, 100934296, 951766553, 315804012, 899515994, 600301881, 369482815, 655169009, 852907411, 68787880, 236792020, 834415368, 263221458, 877581683, 325241906, 871824066, 338072673, 538715893, 940623800, 342309766, 111551269, 549497358, 978748864, 76578305, 106085838, 294264059, 745144031, 155810607, 678571494, 507834571, 856109907, 762241582, 874486013, 290671486, 765329742, 535564928, 202096606, 208663626, 547313962, 635199518, 978894157, 859223656, 723911572, 299681598, 205459295, 723403095, 372519393, 621177871, 803313031, 694869031, 426963731, 327015712, 695235568, 107409222, 876526602, 782774561, 978280807, 493075734, 859422170, 547700180, 967424818, 890553694, 149097715, 787011066, 178166958, 207317657, 516059682, 724568765, 947401299, 364789254, 246178621, 175115256, 37567223, 66356952, 471802177, 720190697, 69984369, 49169552, 558607387, 153883667, 429813223, 786057323, 52870807, 15295950, 516982815, 860455671, 796059344, 217493646, 536762584, 333539994, 141770063, 890240208, 202147470, 773737909, 131695164, 340419592, 318773281, 328971246, 733296183, 389520198, 318499348, 862101940, 382226890, 296807365, 807132125, 779912381, 284535838, 149290398, 37827131, 833404259, 672133308, 467153425, 308512329, 413282207, 433743266, 494069973, 67605376, 612282607, 844679075, 13134595, 190323837, 882260005, 306705387, 974535421, 864743559, 718303505, 716320488, 889585922, 840180840, 266995989, 683079783, 600456646, 719449311, 657541907, 630475633, 938241147, 737733816, 266849676, 483517983, 805836329, 462890932, 22915814, 321580213, 494176356, 830520940, 932548916, 871159723, 331912768, 119734888, 889002323, 470328495, 650080202, 535673622, 682250027, 72180414, 217134168, 144401664, 211944297, 555763046, 943116243, 803975526, 788811234, 840435970, 282257577, 966989112, 891941199, 379468507, 742864522, 569557229, 261473347, 106117179, 751553100, 759626606, 329704444, 743683751, 994578364, 550758021, 46813710, 594661528, 486367216, 939943970, 287728788, 726297037, 508580095, 124616685, 903073673, 346286503, 799658742, 458322856, 282221721, 153066890, 29764085, 731872737, 466539813, 974002907, 800739513, 985446084, 482938749, 229527969, 86579190, 352569660, 977856456, 6079669, 842806393, 155195386, 276475588, 109596401, 300360180, 342605531, 983398902, 684725941, 657543852, 667864275, 438956844, 721545136, 49863417, 908418044, 120877377, 322407958, 983311148, 94859889, 127390234, 885678671, 603612489, 821662205, 560879189, 393571953, 38310886, 276892287, 584343355, 395077533, 617537621, 609360411, 214941993, 824204550, 419289537, 700845529, 21528536, 137345421, 597332531, 131097603, 328888784, 164762607, 324958262, 570096116, 744823218, 555385123, 76308188, 332000095, 727794820, 776671118, 959663256, 675046159, 866948281, 397548407, 121692414, 272663149, 879494262, 488920073, 601681407, 947097205, 942803262, 733417364, 502103427, 98727328, 447692066, 815598709, 177513153, 247433115, 700859215, 914228872, 826078702, 734567276, 650410071, 794340678, 859092851, 790846654, 367837979, 430344211, 545841518, 893076136, 183693624, 578796899, 159473576, 522978603, 658671011, 798874035, 23944436, 758028058, 536626206, 702269119, 487909725, 645325369, 224019096, 474091256, 407425060, 936839352, 731076648, 580760452, 47243740, 886901707, 662290096, 709693796, 621610003, 777948686, 851231539, 198446997, 971529220, 392471008, 389388953, 943691720, 586532681, 647408127, 454752151, 126128606, 574923467, 82469522, 183152952, 394143710, 447954853, 855704610, 287193872, 429869341, 843960916, 409054372, 549809191, 205869870, 501248453, 780528056, 17699128, 690542805, 191834065, 16247078, 596150893, 486489638, 457418530, 776752880, 390526995, 189548613, 432795644, 798999415, 865729161, 344630082, 995127689, 561802625, 696186251, 467500496, 996993401, 654669249, 304436958, 833208421, 579013184, 770763037, 739277177, 833560179, 307110760, 916294969, 701604696, 4432430, 396653595, 372519884, 171625497, 486234832, 546312330, 412484068, 941199639, 248571071, 664632998, 419861358, 991156960, 633587495, 43201175, 855913221, 145105936, 898617, 913738367, 67992649, 876976496, 669398720, 644611374, 580744200, 75454046, 522849234, 527916133, 339182590, 908878842, 272404010, 334078535, 666239614, 525942649, 873341455, 611333246, 996854795, 467734975, 134245304, 429203931, 170001927, 509809951, 91510446, 435715073, 623310876, 90111981, 286036476, 336944012, 510920914, 274108347, 7402078, 996491205, 313202777, 642952642, 36849494, 691429278, 343148755, 542345899, 7257556, 438125311, 185526069, 785849991, 351578985, 39857990, 612548765, 38987862, 533147062, 906810652, 677411744, 20359718, 115975780, 266287725, 806346653, 284034794, 97625059, 894070354, 42866308, 280720044, 41086295, 443719952, 226996291, 651593259, 843642949, 188205656, 391923167, 723288336, 458589320, 689539870, 822328115, 843259549, 943547460, 465037449, 566150538, 460470911, 756598156, 772505700, 113465533, 568822760, 316092708, 883200358, 262703929, 860561442, 946736453, 123451461, 477468528, 127518232, 373087520, 874182820, 305613891, 989367910, 555078310, 31591282, 429694384, 506147836, 574472674, 295105447, 667070678, 686194245, 867170356, 650141614, 130749767, 893635873, 865522071, 99933047, 193685634, 958382429, 265527785, 91168745, 344214569, 825066004, 359863080, 126064757, 865919612, 822696372, 376996861, 38007274, 895103476, 145274566, 636754103, 149883210, 63428559, 737210671, 8281280, 551988666, 994515535, 802613383, 787408103, 551297588, 159087455, 583521193, 869113842, 3021034, 365952844, 49245308, 561556188, 890687128, 156047607, 887853592, 240576100, 25999394, 341363207, 857232528, 551515294, 316157347, 708874082, 59420799, 697294946, 398300819, 367174691, 948622936, 180927650, 524598762, 148869280, 736734351, 821605798, 933378471, 381147280, 346210804, 60060987, 272968062, 501346124, 464672536, 491933804, 420749008, 903985146, 609770254, 880017967, 246830720, 539506425, 302270681, 139568043, 784777884, 785305265, 709475027, 734030644, 469269379, 207967220, 144654001, 521793772, 410615212, 594534083, 764876484, 812034419, 323561787, 833187315, 585891306, 30966077, 766823615, 609386515, 466009893, 94784963, 241312818, 571566201, 781744705, 784016825, 443242126, 615504288, 7772497, 624664688, 375296151, 528311694, 567320929, 94208474, 789972053, 403048005, 890586561, 198029917, 813704833, 384111108, 992328353, 293456872, 500929440, 985845005, 498933277, 567234706, 437057393, 536600004, 169445339, 403089746, 381139344, 601140998, 76091479, 919074327, 668594945, 978985866, 971249312, 55932080, 813699639, 867051165, 937493307, 731582145, 372507794, 698370297, 714974059, 159756132, 628817936, 833799776, 72706974, 630392271, 616883784, 172521949, 858413647, 769018227, 29980657, 705789939, 110725908, 387246022, 984384211, 941392882, 670561604, 298262992, 715407876, 1696044, 3592144, 11459367, 182142674, 380500055, 705727506, 695449812, 125036420, 272410674, 40751100, 707412671, 222601538, 6526357, 996454715, 378744074, 351885614, 105036337, 537627994, 364669808, 727010333, 456306906, 589236446, 427064003, 728916434, 90699647, 91076309, 119553180, 850905776, 974964420, 274902609, 533774736, 873121799, 315395808, 565200639, 275671154, 337798276, 511494708, 246542722, 70992011, 960157275, 445560899, 961671228, 77418111, 901776869, 171107190, 864824444, 910310085, 757369607, 20535010, 476734311, 752292297, 954026107, 493966833, 695876299, 857192903, 683049907, 751598720, 185577698, 53558717, 726496700, 428981839, 93996784, 109717109, 671111502, 608817227, 688668025, 554555028, 740642207, 472706141, 64873124, 263228685, 282060310, 257325804, 707046381, 825126835, 457834996, 453662784, 551075092, 412854500, 901052451, 314613837, 47665978, 621867814, 337424654, 691447705, 503183703, 390084354, 646720372, 735907279, 84975258, 140020055, 48628353, 218833615, 401796234, 378938214, 569393656, 253388692, 844062143, 219296405, 424602521, 863525570, 935026670, 120154335, 831186119, 925338338, 631027851, 675216634, 595610245, 968161045, 217674099, 679381347, 65782855, 617943998, 124211384, 581559489, 337289280, 917561452, 236335505, 777723281, 172739071, 521072494, 419342155, 762253000, 85476467, 618741451, 90038405, 44145231, 236865184, 450362121, 876573045, 855196210, 400720653, 404683820, 299690196, 662928347, 44310182, 584252170, 150395516, 381614059, 848615236, 486038525, 311276489, 137012108, 836548882, 358931186, 791572443, 61195926, 913350699, 798323191, 339215751, 691814457, 407605719, 942649984, 776622150, 617061215, 813099501, 174356519, 94378508, 5959629, 238487146, 451944767, 497657899, 370183810, 929036629, 719358845, 852125400, 750960814, 504990394, 889356102, 205318295, 14382076, 146064723, 459761488, 682327672, 816334121, 526949670, 424414030, 438619266, 59364698, 753945010, 180684289, 212331444, 92152585, 150250918, 217527463, 677640391, 246470744, 60023592, 710420102, 725544413, 842125505, 530131202, 82785152, 311777016, 550206980, 446480643, 924501122, 541377098, 623273900, 152042771, 699229411, 252524266, 763034959, 536909918, 814210504, 583050678, 161183699, 132128929, 895235695, 527765496, 818657251, 856479451, 858285943, 515795854, 714925451, 171957386, 439348721, 453127484, 479779833, 513795835, 942063463, 42319054, 978073836, 73194875, 60821036, 850713086, 898183061, 839416125, 865220253, 355265529, 800064073, 933585783, 373856171, 516881916, 275711171, 959965351, 728419768, 4950297, 848704076, 999897285, 783798023, 609038979, 428036446, 739081582, 477357913, 556268427, 460975154, 341439666, 681792682, 780587486, 54148273, 396182705, 844861341, 516897530, 962469978, 174542299, 6718446, 352924682, 635453920, 70279467, 176238202, 693882056, 183698416, 892848157, 194191953, 850746815, 200087142, 16290167, 142095730, 866081533, 556257591, 53231597, 997707406, 198413897, 269940429, 429101321, 132383590, 61117717, 726779254, 82870269, 90478378, 777779955, 380140386, 582443999, 85301954, 52018011, 345553840, 838402235, 424629535, 261778659, 594491265, 475202160, 312383250, 94594162, 316651584, 250584901, 266058925, 909121521, 539925211, 667548902, 266046233, 774309215, 686350518, 505731516, 197963731, 544802538, 318651946, 325682115, 951468808, 605852332, 141185259, 669850673, 883864351, 455427798, 656919612, 818815289, 687786, 578723908, 821460070, 738112555, 583065256, 982844069, 761304498, 124024334, 852612799, 207259282, 972084376, 161553271, 131236077, 245661157, 725159316, 768505748, 734005824, 706259769, 152498992, 294447954, 368650490, 829437379, 365942805, 618841728, 525145713, 786944034, 477408618, 749009653, 698700158, 136686565, 682077380, 936826741, 607534541, 506272228, 846467546, 357025882, 983317877, 348455418, 856162928, 247853863, 951760254, 4897441, 467757509, 37523350, 560928100, 924843896, 922202695, 918596781, 308484154, 590997557, 519808742, 82786113, 585166760, 992790171, 301414915, 752987857, 989303810, 257496672, 574191340, 44300346, 989010007, 479521154, 680197114, 955413470, 760501936, 476788607, 858448511, 230133850, 804089599, 906299279, 382454737, 661296785, 943362728, 244622183, 79159635, 89529780, 407326159, 589575952, 279566208, 283461106, 454551269, 997644838, 124453122, 385901747, 503496833, 216182128, 177783643, 882798853, 669611330, 650522971, 623780477, 355111559, 313331686, 652483903, 764962538, 964393032, 969597779, 415087776, 702084503, 391418814, 247242817, 441121406, 851911063, 577714028, 783524349, 598992861, 915790655, 493290650, 883531155, 553836747, 292446724, 746241130, 620990129, 900626550, 520349277, 560262719, 530508569, 348306541, 441714373, 561922639, 467268737, 710397982, 610114322, 557418863, 463944867, 714832283, 952032440, 769956162, 294429405, 165123810, 957528006, 50528324, 842845672, 681880085, 683938979, 334962908, 42632773, 438539014, 720195263, 293495323, 898732953, 648127588, 764115202, 214988790, 774553912, 386173130, 721216798, 279748089, 12954293, 732898687, 605385066, 265373270, 271848895, 291861811, 932233315, 399032712, 646528516, 434646700, 567913244, 754698517, 751154604, 550618946, 930312323, 709534201, 885128889, 854857451, 272391852, 984788211, 222575776, 222098696, 7775731, 363928032, 836837226, 485266580, 395042644, 601167526, 191727269, 636042200, 447827615, 706863747, 890627758, 84305187, 898880873, 408802641, 530997703, 572655374, 497280240, 955888594, 19505368, 922528746, 618082390, 435863518, 556322210, 333651554, 113776520, 306008270, 830493031, 175804704, 454206064, 197367105, 422850060, 859529240, 674987724, 485180900, 427033503, 563436773, 351216790, 596193923, 808059913, 856394670, 372896969, 537376551, 377783711, 694382704, 400221414, 235734038, 849731707, 594981574, 74482023, 390106849, 585524386, 821367180, 301995964, 789978885, 548100434, 493521518, 216343904, 634832540, 738845838, 275178453, 333097850, 972871214, 256855395, 67564171, 157183253, 588012836, 995437241, 484927120, 358125245, 961623751, 291945388, 590354747, 978535403, 835040142, 502719024, 179232444, 443132255, 443007307, 149894430, 29273349, 567198201, 568055901, 579335643, 495991624, 592309746, 731141778, 892013193, 261022117, 322290666, 145157150, 815696271, 494512150, 507194664, 31096526, 787954709, 929697676, 760772487, 117707264, 930884270, 984029741, 912373644, 306712999, 119020117, 594476607, 731896877, 429861571, 628132364, 874788842, 251082752, 278404749, 938921536, 807664499, 578803477, 533371005, 224245419, 153819527, 203049939, 857207640, 151591797, 968491889, 209708775, 784663832, 711597016, 706278762, 680983796, 438925239, 633024943, 303723478, 855441998, 137587555, 851188862, 37349980, 959674726, 865092435, 196444058, 890763024, 815248686, 232327978, 297126146, 808808727, 605634160, 798212938, 448111818, 785688735, 128974002, 118330398, 696183061, 437405013, 942039069, 644905654, 714658767, 744640918, 620804035, 131906036, 952961000, 31375410, 465347174, 467774780, 478707781, 625429393, 20062521, 904890718, 402354792, 624474782, 964917876, 67989822, 113966190, 24685962, 317050309, 153869474, 828372808, 732215287, 355409711, 754378875, 822411818, 845377774, 952039591, 405751625, 776223881, 216139785, 815752551, 614239416, 227229410, 131417204, 643201335, 382192869, 592629359, 593882853, 36838713, 738550496, 252140123, 508453570, 510079173, 732241253, 904853139, 68777010, 200105646, 699914495, 556455043, 444707692, 617025474, 171040720, 588436231, 593907073, 584206975, 972305637, 637730734, 628407780, 309801309, 337520915, 10275606, 542040224, 534715623, 984816896, 153803500, 19969772, 604523264, 806463411, 629645230, 667463282, 24652191, 905319396, 363299634, 612895502, 843410637, 883469211, 166947286, 586276259, 91159269, 486338040, 76197854, 409443489, 792610654, 325524216, 688887298, 313745951, 290821495, 759561358, 140346184, 410699390, 855396464, 392782716, 375639400, 718307121, 898254368, 598788001, 990107768, 15207804, 641358309, 470180366, 588103660, 647379572, 285284501, 62268761, 553540897, 649661114, 464767951, 428161096, 751613459, 221092875, 162836846, 462044106, 427882294, 22068789, 7367068, 222983403, 430431565, 147075471, 815895529, 168373844, 608533257, 489599214, 935156283, 713996974, 761951438, 556820229, 394886001, 271739738, 469943982, 280628690, 473498933, 158590992, 654419199, 384842742, 761983255, 984337667, 503255838, 17622808, 800941773, 573808756, 442484544, 451188382, 871643317, 804672921, 22880554, 143556530, 516770358, 602577038, 752044991, 113955415, 693668154, 932825858, 102311979, 58477297, 296314156, 142571474, 820047417, 326471307, 86806852, 624745194, 673719295, 650531969, 747383774, 613369215, 672048408, 11252199, 365892108, 307905066, 660522196, 214025966, 320647208, 586403608, 617806135, 554840404, 284453903, 771875070, 355055077, 972771681, 705921654, 902812300, 243504438, 995894483, 591897257, 188124063, 8878931, 228623910, 791741474, 47802722, 248097212, 501507693, 625660064, 517804493, 476524855, 774616679, 935012220, 919188632, 952524783, 552983081, 99216814, 81445622, 43494039, 81341795, 701769087, 118026334, 834126995, 599067933, 20994293, 411407139, 444306612, 475349025, 720206040, 858125217, 721733504, 212969127, 438949914, 24749803, 997370683, 623105503, 826388654, 232338463, 229099726, 635703671, 688043537, 383582425, 606997627, 442486332, 280668366, 370788849, 811685124, 278191847, 44829205, 236282267, 743425944, 752954410, 897285954, 127705130, 759683663, 839309230, 559332778, 405166386, 739388158, 170305265, 435156850, 885891955, 79189322, 166261056, 915996731, 638016710, 304126079, 276687242, 681395031, 808676774, 848633409, 329169612, 593999247, 429280690, 826004916, 110596667, 703781266, 192928736, 769496537, 458635410, 314064316, 381581282, 530017533, 930456144, 437839570, 246195942, 442633005, 925146023, 731131100, 54423037, 846947099, 523633791, 671404347, 455203018, 135432122, 935856300, 687475277, 412613080, 866525015, 453046087, 814321659, 994067332, 646592901, 44356543, 663166942, 198298862, 742075195, 536532454, 113591844, 730130274, 747071846, 101723986, 536384747, 393682626, 396961959, 333507768, 782371296, 458443064, 606325190, 594347411, 150072290, 555120567, 759086688, 445719484, 951878666, 447007068, 214038580, 755201448, 166692271, 507854888, 47192953, 501453574, 105097038, 828226646, 807093080, 975378554, 912897168, 654941875, 542774346, 116927431, 869628542, 785986310, 394746013, 861484233, 729388234, 502729349, 73710521, 134499277, 604401088, 75417215, 193591969, 860865676, 679232029, 877477026, 664845948, 276671100, 304313707, 612663022, 503877257, 481920315, 866422811, 796524457, 512040367, 570912843, 8178514, 22924707, 691640824, 124982634, 352799268, 225133362, 80817326, 419261301, 599023575, 609494266, 165952631, 300168885, 541816088, 604098665, 443470534, 798103935, 566717012, 575704448, 473220951, 61040941, 491418684, 182000360, 138815321, 886969890, 335714020, 622619353, 201732562, 522613227, 684508283, 380728091, 887020143, 339599206, 580055811, 997204240, 412196206, 991750002, 588745764, 624415545, 438399388, 963034443, 871417270, 424527199, 441454872, 428248806, 696395060, 590424171, 147213700, 955882368, 124463323, 374023976, 595238918, 172784823, 9170579, 230721697, 910575310, 721431538, 986051414, 796140463, 511516926, 634143390, 38236988, 567329678, 813366571, 761254577, 714408953, 431388743, 195574860, 258810701, 267795778, 398992612, 415663989, 211051998, 906510379, 963192869, 83265884, 211720220, 266666289, 396641560, 266259997, 141914592, 219486114, 727960502, 842816942, 455572648, 245081475, 646785589, 202112571, 653967966, 708839406, 80352208, 979876379, 472724605, 979562291, 548830017, 280098830, 806512650, 626310417, 143927557, 843193360, 579494304, 292709218, 561852852, 38674033, 399349436, 406542399, 821801030, 893132089, 602438235, 417002626, 499517537, 84415623, 233550665, 80443469, 807599967, 266163787, 569331490, 762589427, 742059563, 583439830, 933986669, 253040345, 866749400, 571695028, 717030600, 601505284, 137428165, 377804990, 885954760, 718037942, 536287492, 882614876, 201525010, 607372686, 527244627, 576769310, 766505033, 196768069, 834071590, 547266028, 555267868, 62377187, 546880960, 909170906, 788826152, 194062492, 248157618, 242546514, 382301547, 209732589, 407209800, 231244698, 192683379, 189579868, 592428759, 939640070, 362143043, 879937430, 816417229, 469526379, 782640048, 245141596, 340880626, 540277683, 273329687, 333588890, 896360703, 584843238, 18014478, 481141900, 176294933, 74068983, 916357021, 309758709, 614131361, 851071419, 565128174, 114009120, 512380700, 602838175, 359094791, 665469709, 617040860, 59885181, 232147701, 189825733, 940787271, 205753253, 657598283, 489032180, 258822694, 41276823, 276959676, 45963888, 436958120, 778086384, 543508180, 50458942, 557158892, 177024341, 818683863, 559376419, 816328809, 540587332, 314652607, 573572723, 510970630, 554408158, 319982431, 313320097, 36369311, 917717379, 530198830, 215607411, 423801442, 526109671, 828065340, 188997590, 150563236, 255522089, 735615532, 979266208, 931390241, 443037568, 374148131, 387429531, 539986681, 612093924, 133620720, 50948320, 22163991, 402749020, 250652756, 297076293, 627040085, 9194433, 110505940, 283327139, 903520628, 727848290, 255908148, 213318694, 50289212, 897812014, 521022268, 427958791, 178733011, 516327661, 245339999, 988787200, 561496807, 645934733, 410180831, 718031171, 745922105, 28299087, 63294270, 880278444, 48076918, 967970771, 83143185, 977975260, 350789876, 448945051, 62433502, 548137126, 217797183, 51522036, 913827927, 381873376, 738143848, 728126711, 417880604, 640310410, 570066778, 396342279, 867133657, 363026116, 840595509, 234388407, 943719343, 567757454, 688348856, 615094040, 591321319, 486254831, 991688191, 120506283, 28983423, 572802901, 223275921, 263130289, 306537659, 864371584, 168108646, 10626669, 625752822, 917965699, 389796226, 629220667, 38176364, 143781448, 865003692, 379290368, 547850999, 290785239, 29794669, 435705191, 680436843, 86439217, 346776082, 272861331, 482684882, 253604373, 568649957, 984042203, 190341261, 238363796, 242807248, 778068148, 411082470, 151467266, 189126672, 226112831, 323210914, 877776305, 969253139, 264548398, 571217176, 400471572, 53629664, 907169255, 513884930, 90109924, 409417511, 658548065, 793093562, 303842279, 694368758, 637433851, 297635532, 141751921, 288322231, 229746395, 436148823, 539090338, 545588947, 83458765, 94841021, 979412591, 779532964, 867123021, 377187421, 182739973, 306592483, 468586919, 622788768, 94894534, 829382387, 99975999, 502341463, 659274718, 648779466, 258327185, 719229313, 287983649, 534974711, 329649506, 966363026, 506245740, 582127408, 695121132, 316209178, 531136662, 342427766, 911725037, 262259806, 118741026, 590069742, 915795949, 161862453, 194590396, 403542829, 202665078, 555428987, 540535356, 313079019, 880405, 300202026, 466598012, 11883831, 543934699, 601379836, 601969238, 333777976, 78655320, 451982262, 942531828, 285494093, 702844642, 852031631, 255802322, 944131072, 608943332, 393068387, 201433910, 914429233, 457585609, 273839269, 775747148, 41988943, 116050508, 395649925, 892711631, 697626720, 741966068, 749332420, 21510667, 619486551, 256261028, 888989275, 652584185, 778734276, 564276759, 739686752, 929363079, 776047983, 447968549, 532180041, 599503838, 730041942, 376123224, 106323550, 24567379, 897260346, 183859197, 334569216, 939502294, 768157568, 364868344, 759946364, 714697722, 452483990, 370962545, 675850758, 729926341, 520795978, 781886826, 79975646, 386305336, 228305512, 245392155, 152788909, 962745443, 185284093, 354862495, 157052927, 721714817, 532511199, 104669545, 567200734, 985343226, 389496560, 17270905, 781535764, 323404992, 747540026, 235576875, 916250016, 720353748, 28820562, 454997128, 552884767, 42156877, 623027186, 81211245, 464850445, 773874394, 211555528, 558674658, 387496775, 896721579, 385735136, 478699260, 472711945, 948078374, 501482422, 117899499, 946480374, 85810244, 95236670, 207433158, 12325956, 282479307, 29501415, 458965357, 877293988, 518462968, 926470611, 877372900, 712776936, 446450353, 242711338, 105211784, 759164160, 865241339, 117892237, 62940384, 283415619, 322361553, 538956247, 360021452, 38037297, 812846538, 225105125, 55864381, 261014109, 317452587, 381067990, 246242283, 941653117, 309709453, 390898566, 69159366, 160957767, 372549512, 543063023, 861724035, 294210240, 332323667, 853412690, 302905785, 120860616, 964891371, 743577075, 567066932, 813682854, 820419078, 765691031, 798130554, 759369824, 694645007, 612547295, 56274736, 167402827, 70871869, 316520849, 760668043, 281405982, 22979460, 961751543, 924789630, 262855654, 592383332, 617237115, 415660368, 140078460, 477413783, 732803487, 708386008, 120192281, 727115437, 386141950, 816556216, 22288623, 895616985, 167054949, 51854910, 751113628, 161189366, 89585017, 388903530, 776836975, 908644377, 165087766, 275575903, 361371316, 684539050, 390067801, 230517450, 351635355, 214370618, 147375030, 435878368, 763686209, 348979318, 750657680, 732731411, 710211916, 796079949, 226871209, 902279532, 924605924, 424812777, 125493263, 820724086, 901967147, 459308764, 473586770, 22768401, 357735685, 178145053, 570408248, 248030563, 962276079, 417188963, 953451711, 862697681, 478280760, 965792816, 23365147, 51251159, 205405138, 81698980, 134358108, 587849598, 220924418, 968480156, 220629230, 580078031, 577341934, 84267406, 523680500, 216684500, 304482411, 440465101, 507089926, 516129640, 110639208, 323672466, 47239606, 191055601, 857181923, 281500472, 945276708, 848023215, 617331405, 495217719, 562372910, 79733724, 841781522, 226945561, 917926038, 349608875, 231751365, 748835144, 719319467, 830648052, 558152277, 538556814, 94710929, 357859751, 106115278, 647953020, 433546358, 918627089, 397633249, 739420770, 628981109, 598851973, 592677901, 963833371, 697662605, 513816612, 446639710, 424444111, 542859315, 678926462, 481691143, 237544106, 397878439, 883054134, 747203038, 660007928, 26934283, 646892046, 443396332, 240987219, 554127304, 927027699, 458411521, 610824555, 175566760, 59931672, 263934121, 4432073, 539307371, 140989585, 552391717, 101484986, 452063913, 61735043, 952828167, 186114686, 431450839, 130365601, 397990467, 275884068, 594149806, 666312612, 516235012, 387065329, 3657726, 91326669, 170824575, 822116225, 675509381, 585405900, 644610768, 46726314, 786268649, 901326505, 849163768, 666351619, 678341106, 680851837, 372980066, 965685312, 142496545, 864672036, 798197180, 22689370, 954661943, 533670230, 58376019, 145672922, 121923758, 932150604, 748525077, 783807577, 234437135, 17914581, 926885438, 351731495, 259964214, 982537181, 422423173, 170042421, 357497183, 495980659, 99713673, 316607470, 510680567, 539240747, 418564722, 803688526, 621634738, 283333369, 705699535, 821722286, 145223654, 502602108, 648945170, 464081062, 133548649, 434061655, 112282710, 714979045, 606136912, 705977283, 981871529, 865618412, 217603177, 331422518, 438034543, 481184401, 94720028, 72302420, 83722144, 449723201, 383792963, 871466747, 284525097, 938074178, 209386664, 383420168, 261990243, 90990034, 68176724, 232796490, 239581266, 470357035, 701105378, 771983923, 20974794, 186066897, 937165158, 204781252, 250053879, 475477694, 454264373, 10981319, 290521978, 904645068, 313806640, 179540325, 375249529, 161016478, 262181808, 663462759, 578333907, 774344306, 344580579, 565445485, 86441365, 312754990, 968415981, 145574856, 63547521, 272004265, 82994874, 918315753, 314655447, 407853436, 350375600, 921308751, 43196628, 822832063, 29542917, 153405648, 35522600, 560025710, 258087648, 39511588, 576571016, 404226518, 364427789, 436674743, 766124725, 526203700, 799885505, 169926739, 788459782, 50097481, 442491413, 490330018, 447724368, 782892210, 738186637, 830964428, 474224532, 977183564, 413020186, 753974780, 835310520, 933147690, 766027241, 248297871, 923306674, 892628946, 605545217, 974245223, 340921331, 594169415, 309660166, 180846890, 440598570, 318446226, 276145750, 603940074, 128572548, 142188899, 196446117, 476679623, 742868871, 672791028, 873758613, 183352951, 695550674, 183256503, 302251033, 164594750, 733277019, 982518559, 15493712, 178316467, 95452833, 914385264, 489159868, 560283747, 658584142, 843621353, 239583895, 111460228, 267300937, 948866946, 716089641, 783706718, 262164489, 137710840, 324705995, 583948972, 676949922, 797193542, 398384692, 653542865, 957398137, 664727511, 258279579, 707658627, 546356340, 415346509, 496073806, 937720787, 58182644, 818939359, 890278733, 301794995, 598465709, 155753454, 483322077, 253677540, 69999282, 413465043, 656774226, 753389502, 894145030, 194109169, 962694895, 102901211, 509711836, 558796887, 456282985, 19731100, 235899398, 296786760, 697143910, 743805976, 921060042, 675453987, 310117428, 809248209, 246566539, 474814625, 390032669, 266981947, 252969566, 727973994, 908383291, 549546704, 614499307, 31935849, 213496470, 390884199, 765403171, 237502295, 437199347, 42199675, 475277404, 289836248, 717472683, 216762580, 6182437, 984435952, 556696058, 500601797, 120922674, 134707922, 251039780, 689465994, 814817886, 287996912, 719164273, 375287508, 155619955, 535108543, 857435974, 998747422, 115295557, 153374957, 141064746, 642134772, 258939614, 275360898, 334220691, 926221245, 500803059, 969851781, 60932774, 892666571, 697448865, 204229907, 844615730, 211935495, 5436172, 41372809, 331468594, 452846557, 669806506, 469097424, 686554736, 187159068, 563656138, 496892836, 301903561, 215809244, 69790104, 91237473, 928097669, 348010018, 492006326, 220218270, 657868305, 148462453, 681464182, 699331903, 811208246, 824933130, 610750941, 966445058, 772330964, 259396766, 525857469, 223876523, 506923288, 963093114, 679744557, 934935146, 755266309, 495098827, 193501053, 429435478, 285372761, 479857813, 675272369, 261114344, 780761788, 833265851, 809465535, 641570319, 879328295, 824768359, 258146440, 842232544, 555114139, 381110568, 529542089, 851203446, 172248440, 538207671, 873358072, 300824026, 228712272, 702779707, 933269693, 95716570, 697841417, 372075660, 275297235, 378457921, 283470573, 331485445, 531802521, 949636829, 56492684, 372615018, 313793789, 265870407, 501749207, 156787804, 380706678, 269942844, 707841171, 326310015, 123399676, 949071975, 11025435, 754173894, 347439960, 740433144, 359848375, 252115822, 564792721, 224255352, 633256710, 450196436, 504697763, 320892307, 706969358, 655888743, 562751152, 597412194, 228862860, 136477898, 924692611, 412545139, 768553139, 584123505, 448354117, 19407927, 80550401, 111084691, 219700725, 568074595, 682081763, 439371846, 513547459, 410366203, 887857162, 690712238, 820461923, 613627130, 437608619, 420832952, 650117897, 364734718, 851531960, 743304453, 500868605, 948809155, 633238508, 651007901, 994664260, 74016691, 144707219, 391570874, 864430553, 108601042, 160492272, 595851050, 4314658, 734709511, 247383417, 493124345, 477784302, 676528826, 669778689, 869959719, 716919602, 256540872, 585007412, 309762002, 639084508, 728611967, 168315466, 658812120, 12015269, 497519790, 40845395, 264028987, 970981687, 445719100, 308199757, 223938033, 176580876, 11718382, 742711765, 830327784, 146830832, 860694078, 395204948, 537607301, 644549191, 287839689, 434677906, 831842357, 523162613, 38394849, 130682422, 396884621, 360960326, 127061675, 365047364, 136155323, 822425358, 937384704, 895752617, 428474231, 575345284, 139002724, 688635523, 387093468, 402307289, 535288098, 659009844, 560144114, 141363815, 624465870, 416280638, 447257551, 898864169, 91325988, 616832475, 17089340, 9213305, 524418087, 318231268, 252720932, 994535841, 944360812, 145939184, 979822090, 918225499, 754468511, 546742449, 551515543, 304227858, 122831683, 538599565, 837282880, 624896485, 162747823, 901269592, 551334845, 953441805, 547629049, 730178349, 926386783, 998778972, 59981728, 38373967, 354527787, 601462162, 929030703, 412976805, 901389185, 370774258, 907854170, 305837201, 270894414, 898716852, 832606270, 764693412, 957925141, 777898228, 304816294, 720242287, 561956951, 835486306, 424845329, 256308757, 500382486, 600786130, 129965533, 812098882, 424234230, 949354421, 428839453, 569334681, 657234662, 14234847, 827262719, 725514668, 439529160, 374958115, 283491429, 349423753, 498032763, 988681240, 367926228, 760987702, 382242899, 6697374, 830972085, 404912547, 839260777, 445893324, 970576048, 415304199, 422815282, 823689630, 415379016, 950483368, 289897877, 832889523, 600994771, 849640232, 702060505, 37993786, 767679518, 228613740, 186768113, 504733646, 554834552, 439264583, 140187906, 468653984, 652329553, 453915719, 642353848, 758982971, 676543001, 691574528, 566163621, 589050242, 140654942, 611438206, 753442341, 949458057, 99524826, 352939342, 528688694, 884239202, 548930615, 758795747, 580999905, 479327665, 116370140, 493254216, 980427172, 137096612, 460042758, 578930851, 767972830, 573195841, 763823627, 524002347, 294599204, 520945202, 863519453, 720089788, 901138669, 488972446, 193296323, 568373763, 399387695, 8010334, 252765243, 80784059, 886137596, 108818337, 596768616, 705344914, 650208616, 924129413, 568545289, 65794332, 226714655, 986635087, 380538986, 478501378, 462495464, 136520332, 67875789, 189343456, 575701666, 965640980, 138970621, 438329233, 105659373, 625767131, 489293984, 107530088, 987681051, 689246535, 928197866, 396158729, 642124171, 957015267, 373545143, 952340239, 634192142, 661620362, 52067456, 871737004, 191664730, 258375062, 556574305, 990344969, 332159098, 881833948, 593833759, 747601834, 389122521, 659879168, 134157857, 293851436, 677045458, 494125462, 537319016, 588869378, 930080650, 768501443, 223868523, 906830649, 844143108, 187812636, 456972010, 494430199, 653118006, 850193661, 487767142, 885540182, 240230139, 706708411, 543191295, 582510005, 981381073, 974797745, 404810138, 13433310, 290357943, 297576209, 853327485, 232987135, 710943066, 991427111, 672037767, 655945634, 680530494, 935957178, 511453366, 613556470, 453707577, 149732687, 501370899, 606262158, 210334552, 27760207, 805989175, 696695902, 415122419, 744573723, 767161415, 577437735, 526686211, 814224911, 212298864, 671793381, 525194346, 940644600, 980823005, 605856467, 702046011, 736260587, 780671328, 466232780, 859763796, 123387946, 792125833, 413668023, 592460000, 564939234, 508395838, 351308613, 850041249, 648796243, 367953495, 95302723, 777645141, 291092286, 718033765, 98441004, 462322928, 446942719, 449741634, 262949127, 766347935, 175258038, 536804641, 624003856, 467347371, 489748366, 136303639, 203396856, 157246271, 743709555, 45035531, 79219418, 677867923, 918608349, 276022083, 940054942, 645306875, 821392894, 209185071, 464212163, 836478187, 448072175, 375109713, 423772582, 274101789, 20919609, 443880553, 362085976, 425308151, 410463484, 263709622, 342190547, 647189501, 321868423, 646273774, 146346837, 531013209, 18735223, 899915816, 146288255, 515197357, 376539310, 624149060, 502370371, 241017514, 949986610, 441343172, 676115438, 389794864, 13676344, 57426460, 502038734, 701148507, 898296285, 491513722, 85571563, 463566675, 319152942, 315189778, 311490688, 127934135, 843338236, 603454169, 724168852, 847108278, 706301723, 375766576, 622622803, 258178562, 941432781, 435859645, 877020815, 307862487, 702648872, 803741390, 50481452, 333687947, 21059779, 965954663, 287848818, 668248810, 519832895, 919612804, 836957273, 305168297, 796593389, 59805343, 32503757, 694370340, 412824248, 150742409, 323475427, 550553853, 19577685, 285093778, 552616873, 987758681, 270390937, 36495984, 667461462, 655273005, 124070209, 445222754, 759008992, 678684124, 497763517, 41769604, 906389060, 802142404, 530640610, 341071463, 843953778, 392031099, 20232966, 957628601, 603954147, 798920876, 834853938, 955785300, 998808533, 586849030, 8269414, 335875025, 578727357, 910981213, 941194152, 17603041, 223536207, 26245843, 671757232, 996528913, 678551841, 108528061, 796716551, 399663773, 780739773, 320696267, 847977958, 431293717, 779656500, 692738430, 207544053, 673193946, 120586445, 509964972, 446802031, 315111219, 619913648, 179634902, 641983675, 663391354, 196807237, 23214201, 807990885, 278398567, 228960642, 983525135, 379357293, 162954345, 550153370, 595060339, 354302386, 774459338, 834610388, 409425621, 454187462, 799589054, 790986376, 596498515, 743540234, 763630685, 490241943, 100124939, 328591209, 777721282, 515844606, 645680139, 154878711, 188202738, 899264012, 343122466, 594276549, 729210866, 651486568, 639649661, 644843879, 931042719, 608629437, 879316733, 72349816, 519038209, 754918503, 795695296, 642429823, 862835, 505306139, 59910856, 562695351, 568075959, 910797336, 385606850, 741103864, 200381757, 474891549, 239700849, 805406989, 803200761, 443364976, 552170715, 178592049, 676667988, 222544219, 168092205, 349438085, 609205315, 640827632, 846780154, 106587634, 241717765, 574617557, 128475509, 850776991, 629508808, 92807179, 508813675, 692393934, 394328589, 150051072, 36169494, 235563351, 597896530, 865751711, 838286056, 880860044, 999710514, 29450030, 986052864, 161988750, 425443623, 83162048, 684400593, 703079660, 356845986, 323309935, 673754462, 244368318, 5705536, 298841787, 70177543, 325638709, 259442265, 909739962, 256221450, 167249719, 172355873, 212719312, 676260701, 951672839, 921140627, 495387466, 589541324, 206093132, 153820666, 864865147, 317607140, 458003529, 294111942, 590707873, 821028454, 476543462, 365896392, 706676178, 408233938, 813248478, 437429456, 343430514, 400538906, 871862934, 158668466, 651595713, 781852512, 439968395, 857837667, 259993186, 231866300, 241383973, 439647718, 588808282, 259837223, 402332437, 420839114, 886088952, 456708703, 528819737, 269578543, 343314238, 873039343, 875900509, 407835233, 547407124, 744058362, 546608508, 84796755, 963527421, 327488783, 45046394, 910456583, 514118845, 243625321, 725695355, 670181467, 617610262, 276168273, 928903897, 226190129, 922865750, 149745444, 757639476, 715115779, 622468780, 715458537, 202868181, 426743735, 501516683, 343369371, 334540159, 307730907, 126585798, 413232085, 109528407, 627604817, 139930442, 768188434, 478382331, 492179033, 640401881, 427051535, 763228188, 129138859, 672054030, 135283054, 692006222, 886837085, 736056677, 400969227, 235441355, 813705246, 904945766, 385065620, 444467352, 398361460, 793539062, 976171644, 325625014, 899830463, 699124964, 36645930, 946571970, 283115945, 934769261, 238969638, 812256990, 317050873, 385952457, 495364441, 632503029, 933073895, 147652015, 955003745, 593337810, 682721048, 437135057, 533064248, 814416791, 215390284, 837459908, 975600714, 675421076, 208263314, 499061019, 773840841, 95166947, 335416938, 865249090, 342756691, 282144457, 289528587, 752942839, 259665674, 202153671, 778657115, 719041, 307396675, 503301387, 602350827, 237519209, 484983566, 501039087, 808979839, 696193237, 506513041, 702695745, 380558026, 437571384, 656421344, 177702870, 137572021, 62009527, 360015816, 447136919, 794582561, 653729818, 971298057, 440853855, 320566960, 330016877, 860141861, 655052415, 713079763, 194229257, 171357543, 714616046, 482414417, 222378402, 961795262, 26092307, 544701728, 380252895, 230704060, 957757665, 528157154, 411893475, 552436630, 620450030, 217112462, 844960718, 588434477, 377854630, 501108757, 36987144, 120528232, 428087, 415129283, 980944958, 344525060, 613632043, 869252793, 369579268, 363055380, 910942859, 979410053, 408938965, 54913457, 434698742, 341627415, 662063608, 506390609, 286595899, 942709720, 913494860, 48707607, 199916440, 318271420, 702759999, 91197153, 638865083, 295295988, 225335030, 622149516, 670419008, 889267141, 665162200, 405162437, 511427224, 567857485, 121608115, 730067516, 764656452, 232493720, 38023826, 607118152, 82546758, 773319583, 726756336, 629641033, 84640891, 24711227, 430705543, 973944030, 265783917, 621371828, 288898291, 155985164, 655580396, 814803617, 25167882, 467164149, 123708613, 99065575, 932100846, 162561217, 62631093, 453217362, 719454365, 737799073, 197882398, 77115125, 943506111, 312480474, 360860347, 971360333, 352290522, 70711843, 194647962, 227422918, 591213269, 410008209, 739236268, 294850202, 179759398, 777481900, 901737012, 533634355, 730765311, 884110573, 750510182, 957360833, 942920679, 338052685, 795821255, 924869519, 876677465, 479345678, 425397887, 266676354, 617455340, 8963595, 517659648, 743839411, 686527323, 911395160, 485600781, 501402491, 452254639, 342077653, 920285986, 752490152, 511745596, 964916843, 193064794, 34813885, 76311802, 35118069, 388209949, 274510436, 572321969, 114360504, 240054580, 754917013, 881578403, 184447919, 739070564, 393743527, 57475989, 606859366, 527521093, 644505605, 48288805, 616022860, 907514852, 30635304, 503802215, 483740669, 393174342, 201476372, 830927661, 583024956, 594128985, 21021600, 540574500, 53720374, 571197411, 947410632, 764378175, 600446198, 14336928, 717093567, 351043624, 714870637, 151632000, 570020975, 863075487, 750757304, 951736474, 147115555, 287980015, 506216095, 950036866, 36298489, 598464053, 258551216, 869856307, 971898116, 855068040, 613267025, 63176595, 247576785, 528335369, 879622494, 235483901, 724313949, 973423798, 329665705, 973158196, 124919763, 935810645, 615227003, 670927611, 18296120, 523707506, 539800603, 255039386, 929257847, 985591463, 928999326, 254743805, 997527224, 963841566, 82114337, 760789725, 713180883, 898300265, 938734532, 847882207, 234185328, 221218427, 357097630, 418607927, 904894161, 373064320, 283094917, 831690356, 394617016, 690941625, 996225791, 520364861, 451922212, 967767186, 36902109, 206763797, 993765679, 869163582, 835510384, 100749826, 223664405, 393541726, 417079345, 382027021, 524339658, 219231448, 752628347, 409677404, 625342462, 756839819, 714170632, 741388750, 399391494, 51097911, 972581469, 908414571, 286198816, 239538886, 942523506, 389285621, 946293442, 856544355, 299117317, 79223106, 609289677, 237912886, 281455821, 792420312, 377223447, 818086064, 938307981, 169483343, 184097310, 387365271, 615358788, 661983521, 969096412, 700995598, 576016527, 180539470, 816013408, 668827921, 378708825, 33337552, 623649136, 832714882, 991397491, 142869558, 488610178, 396805379, 256623161, 931604189, 752557170, 8519109, 30407367, 639707796, 92800152, 839450083, 29991994, 392524777, 129383913, 150000472, 50444206, 935049114, 938525263, 208922217, 344307313, 210994662, 388042608, 47198313, 784317723, 78759257, 557478335, 552503175, 511883675, 392484670, 462523955, 91581861, 27927255, 309259667, 844658454, 145324321, 29157520, 635415913, 834223550, 104473329, 951784180, 747719522, 630280622, 320111262, 265261965, 611582583, 455695360, 682490150, 271237299, 73095784, 981950735, 744651642, 557474166, 267541091, 559214283, 578394393, 411536955, 102231569, 983294242, 80575630, 954432564, 408105428, 668491169, 409790789, 990588213, 505769023, 757353709, 907280971, 520293327, 382603457, 4176220, 632805720, 308857083, 587024020, 80456077, 851583329, 84425018, 914899192, 773344979, 891400600, 946804535, 858126888, 390739615, 450666061, 173681199, 53400379, 832932058, 634098171, 808282194, 625332739, 927486793, 690237379, 899168399, 71537118, 15255692, 908576802, 350003555, 115906312, 579527453, 13491212, 666782678, 759056158, 354381816, 188503391, 966034200, 737005321, 854171815, 860078955, 387104124, 246949791, 556805241, 339600187, 207713553, 990509555, 365522794, 435020787, 310728397, 893221264, 167693779, 442704785, 937770100, 473512889, 112693865, 336684070, 935351205, 822332505, 714027791, 861563628, 165690959, 581776818, 807531996, 129393355, 367111664, 625072428, 589915179, 108353659, 394287440, 424192319, 684799129, 648194981, 719919787, 275678294, 641593214, 551487777, 948304947, 341506759, 295411859, 691354429, 121557197, 311102403, 560229439, 712210479, 247551685, 388922873, 21194858, 557459984, 905369324, 672469333, 524914807, 277611057, 920684804, 798857750, 200557202, 984792285, 564080506, 919687806, 969377489, 335310324, 822440728, 628882647, 842837850, 9862929, 126998129, 212627539, 583979266, 903375041, 598560233, 691678267, 709003284, 201463763, 700056369, 533970368, 481204584, 804283304, 156090363, 692156003, 48863683, 906719168, 243853915, 282994208, 850038110, 397187430, 95102548, 58372593, 580600190, 278477100, 21519001, 917055254, 284661532, 740843928, 316709450, 80514240, 435669057, 926498978, 841636070, 193252232, 469202324, 751071976, 950072441, 580235901, 583276721, 938954697, 579309000, 276997772, 898149193, 665478918, 142296527, 145908813, 300216186, 567833524, 294542679, 298600416, 470748755, 945144782, 702488966, 672165264, 125018042, 246116673, 235075725, 427126551, 923182199, 934958855, 759575587, 367915974, 670410201, 12990761, 156534740, 785534635, 665915397, 968502971, 321148049, 987263407, 422311512, 147424894, 927205159, 930366874, 307923130, 355353578, 738853030, 630423782, 153405918, 255155875, 876636861, 316785079, 837118799, 600903305, 535474184, 239436248, 428541863, 832946181, 171097125, 340558546, 123621874, 521564715, 950336031, 393996859, 410591136, 999261, 781799511, 897882724, 167049789, 602262522, 809357529, 365272669, 119152525, 797926272, 656853438, 245392462, 951844753, 838900026, 67375735, 373931004, 654248249, 999523021, 311431757, 980014164, 834622901, 883858235, 220663775, 313937542, 413945542, 719876227, 994515097, 384990210, 935152378, 869569839, 19201971, 565957654, 713842576, 468570843, 953229865, 860463943, 773755993, 135050153, 187332155, 964123863, 804851352, 698712115, 645468261, 757590159, 584015393, 218369564, 11996385, 375360893, 839203083, 797919211, 917491452, 388862755, 220773589, 601859732, 496427121, 638637236, 179298101, 539427087, 172933322, 797204006, 822977720, 487388083, 531513950, 185630287, 159859251, 392596985, 763310939, 133450474, 801767802, 671626365, 8100927, 86012873, 444498051, 558623344, 667459858, 124252251, 100114539, 191360178, 718508684, 676678272, 566788886, 800099656, 220580065, 410934499, 574860957, 659581611, 616572110, 915009540, 753904799, 559715611, 579358075, 282632043, 903236902, 160210356, 621607989, 63642743, 683163128, 699019591, 394236700, 122104549, 545986329, 754459669, 764407960, 494053804, 136215010, 285331475, 291206541, 124343017, 88620735, 415120805, 463009450, 636908479, 498350086, 32140044, 682145629, 482505810, 808713193, 234337366, 447141894, 19989094, 403648559, 369718898, 854226707, 882377067, 108767528, 837180437, 309797818, 308548468, 11573498, 172807184, 209196587, 6461612, 866897664, 102337456, 968328418, 775784140, 26834518, 864169458, 588289557, 381456400, 805039970, 920423899, 26070221, 54814467, 899352766, 297034351, 732454530, 568611801, 420943996, 251345560, 472444139, 476404952, 26441879, 21909870, 971808442, 869154710, 499386202, 855391581, 236553921, 211377881, 850539845, 956467860, 507862523, 60407102, 441509690, 184928034, 19720691, 149987711, 950196951, 83031309, 524023159, 838490270, 758077720, 700952651, 107280008, 981641087, 344244117, 293775065, 118929082, 996427011, 423060900, 820389465, 871130794, 72166197, 480404061, 816701318, 331148252, 856038798, 380642268, 309621895, 168619855, 875434680, 842736122, 86331675, 102530508, 863382693, 562449290, 261939309, 323715197, 99957247, 405413361, 245976366, 287800669, 187113414, 231329163, 454327073, 918633938, 773675624, 63896938, 141031809, 279812966, 31949843, 47523840, 150331136, 437146173, 405480266, 741073727, 465332475, 71050218, 803795959, 23242673, 712261288, 571472613, 640812775, 126401020, 78251954, 700925968, 590058116, 476778862, 952870423, 180483491, 511082347, 513971498, 933442660, 393436937, 396306536, 61467396, 341525740, 72061732, 481601298, 269481953, 637227911, 116799825, 877459054, 7597738, 249122211, 639565962, 391192349, 385562103, 822579140, 716241724, 402222875, 623492096, 116574781, 453271429, 338050421, 509979050, 708860855, 574697281, 138026827, 767475747, 480815593, 749773221, 504580847, 324935939, 486267474, 477366221, 92942767, 399900610, 81499950, 263406090, 124870916, 109478677, 844211705, 310883866, 544386077, 653877157, 209255485, 55330172, 103139535, 992307919, 443894554, 194168049, 213814272, 474548677, 48257996, 57412555, 455742426, 155155961, 964763869, 523579779, 50730427, 775730310, 469327146, 734101680, 18345533, 778873472, 390344725, 60289958, 968864126, 824469026, 303240469, 628629397, 589705737, 841635287, 812338108, 493640228, 612787982, 968861742, 472313331, 664871183, 696351281, 739017711, 833738521, 724857248, 104534587, 865474389, 346617848, 146253064, 573444784, 481359648, 871563574, 35899847, 174937449, 905826334, 932437359, 808212321, 114761309, 806299849, 538023745, 193644750, 864331062, 640577648, 157246249, 556446767, 449543661, 763490822, 311997109, 42680856, 952029618, 113178632, 56371572, 530328424, 763494495, 670470967, 245817701, 748745950, 417702091, 208961036, 937376153, 85066219, 431892230, 622035340, 502985259, 90905925, 237382191, 612920114, 597732024, 968719745, 625838115, 686430645, 284230679, 743973456, 294643104, 810342792, 759896646, 225138813, 220035507, 886447914, 934920678, 219455305, 543313632, 822298460, 81882577, 938760817, 531016904, 582548054, 631719952, 724608374, 500454995, 120528746, 446701720, 746248955, 327200609, 150791886, 251802949, 213594874, 470544471, 105148519, 613059957, 364818751, 500487093, 330390856, 469193526, 56796145, 770268331, 778913057, 192123421, 237922539, 939839026, 936924225, 641275092, 116768739, 648265003, 877518357, 795052547, 349857495, 163280089, 880456100, 624572808, 979090159, 20812151, 720548030, 386986246, 18435308, 523773286, 921751725, 670740222, 964284508, 199437120, 189801509, 230223609, 589218257, 59654012, 640728940, 269752077, 295706667, 977005122, 253123199, 500675264, 2872725, 958437379, 630939528, 731673063, 365088912, 450140908, 209268602, 133463637, 388361071, 241834373, 512879577, 890278316, 898138620, 990349164, 603695609, 216796165, 893898771, 374571573, 206961798, 186463895, 269963691, 917728811, 934976417, 604712330, 669132977, 485660900, 279897179, 541104950, 808049466, 40040684, 591683772, 389662306, 580017115, 391419826, 790241973, 407290198, 130745575, 285289744, 688988859, 181150678, 376448571, 590703784, 305653950, 164862696, 571163110, 207911963, 447541856, 238077194, 966135492, 787486790, 542865314, 24375046, 4226660, 867716747, 348223346, 865079386, 888430747, 100425654, 698863580, 553390274, 209113887, 261027200, 190940223, 998782991, 503793829, 726294794, 88282138, 165063426, 771303708, 270433130, 787474601, 749051805, 421271495, 20289035, 80403701, 493302505, 38691334, 220635256, 171966136, 35284693, 7206021, 255417988, 179551539, 489005453, 997933612, 563316581, 90284603, 300011714, 937803514, 738235749, 642132983, 907907840, 391989808, 102671923, 719165452, 616273636, 523813089, 762545761, 81232813, 960638767, 459392902, 148650039, 294359919, 552706656, 534656568, 509198039, 520462695, 653885982, 127657716, 741486095, 530748492, 126801295, 479432070, 158691406, 460949877, 533244446, 793432009, 857749077, 624703073, 587650311, 577925261, 953303310, 821294907, 777065042, 741846319, 667437418, 623918841, 100292882, 349804397, 765276768, 891968504, 858938485, 723887672, 738227769, 607723006, 360684249, 608646297, 537718415, 868617184, 60432298, 57029871, 168152172, 325181220, 715915970, 527035686, 35102516, 803261585, 930676487, 209012227, 773183889, 678263916, 366926501, 431031471, 787333428, 387571909, 727899343, 421474828, 2442499, 926591767, 313715681, 322565675, 100164590, 963304415, 364206064, 46612122, 826178628, 250039336, 529081489, 934383355, 116469261, 146150905, 343276772, 577525506, 748868101, 206804583, 174686408, 484419500, 27550149, 180349765, 853686340, 72280143, 817224916, 41382947, 329715789, 448586175, 508646757, 6279278, 712683947, 108223373, 466495668, 879093794, 48049813, 441425127, 289717939, 941213152, 545802719, 912635785, 363965522, 435040704, 540330023, 541760301, 164658159, 771885966, 912604524, 29396382, 943402787, 806857348, 369134473, 877533672, 341344177, 521830990, 220439233, 50389355, 75983159, 7481372, 856729120, 784316609, 177854350, 303327431, 38099567, 592459038, 268104537, 457860329, 830080865, 306733425, 641768245, 986560926, 856825373, 375064482, 787210676, 713489629, 369286855, 940001504, 553658250, 680092562, 280028878, 652904805, 208663673, 758808541, 573155063, 372047650, 521409033, 525889763, 759879493, 102219357, 631932597, 477789827, 692901131, 149425816, 751011803, 265886063, 402908037, 978358175, 671832076, 293542434, 793801415, 28429361, 368859584, 916976276, 281999301, 487212488, 703631814, 822126101, 31431518, 419626061, 916270148, 301752294, 247561864, 249204916, 525413423, 224319087, 92662975, 307953184, 956184223, 868980707, 813241814, 47800649, 585905505, 245405705, 85781317, 737667649, 644873838, 574828513, 55564564, 238036376, 473586314, 728828030, 201779924, 85761213, 557479858, 481370325, 540109016, 721199470, 191326705, 108655918, 661486420, 908883077, 351731636, 430422907, 607768195, 562016897, 118197979, 163767416, 251419286, 203845323, 489341124, 94120222, 898131476, 798706713, 631247385, 216830703, 380946062, 981435764, 150247546, 836106906, 762406708, 993700323, 453502836, 261808566, 956471197, 486310289, 275920156, 627651760, 875743742, 683735442, 656551827, 104487770, 579380641, 930081789, 512763499, 970819592, 362435056, 889415254, 775667583, 837570451, 975284220, 954121265, 444954043, 676731007, 850958286, 396580192, 170305478, 821500616, 370628545, 699063051, 164232893, 821837476, 963143660, 110719195, 822688990, 684804441, 923423240, 942105042, 784514778, 193897903, 424544588, 839688362, 407213551, 466377244, 898798268, 804696582, 510582462, 679799837, 73797524, 432784339, 478437953, 716940223, 357103851, 754755436, 301825943, 76711600, 608297369, 409745802, 541789420, 138433192, 559890887, 675573577, 322754345, 177954183, 887074247, 90117806, 354913389, 454414512, 204299886, 759027484, 782056618, 730638608, 591172384, 872404775, 923401205, 484179078, 639877856, 715040909, 324759310, 814783158, 46902867, 641831866, 556858485, 995992026, 929762667, 360063664, 961047389, 250854813, 908200457, 442660414, 935984278, 354046079, 611485586, 994892803, 759427255, 369069511, 709159706, 125015907, 550321693, 280367740, 809708305, 244911815, 642792855, 746023376, 470264344, 151941467, 721204836, 792676424, 828320962, 839430122, 404699660, 310846520, 306717333, 409797395, 746937957, 343372582, 94132004, 202574456, 86621990, 614722812, 915334050, 891101379, 415908005, 862077914, 267832441, 539295181, 242229448, 199185503, 741062358, 291346488, 794026559, 880434030, 209718933, 273211010, 57326475, 290756775, 192958175, 388831138, 250383513, 537043887, 869019065, 612696, 53145178, 322330968, 141645010, 596136564, 467623602, 146899505, 853335976, 59620924, 559424956, 83241573, 116840185, 410887066, 615698358, 900979576, 48433428, 171381520, 557381155, 998138548, 234222766, 851984609, 451068689, 712662758, 944083838, 123570894, 172696568, 793503038, 129764320, 48070995, 26341185, 226577686, 161141130, 463045511, 478570776, 94700273, 854681108, 514995254, 214706154, 195769393, 254855216, 246862569, 816682346, 196816481, 43808307, 149709520, 359639475, 401831639, 313397344, 248108173, 843721554, 449636376, 174441453, 666498576, 111114212, 512360224, 764295313, 208790335, 396678961, 188282316, 76783433, 248485625, 230099825, 917411965, 457033272, 871019072, 414894396, 165585971, 556533472, 188330191, 133009589, 168215949, 739115212, 183801219, 51222208, 508461475, 285447201, 891695851, 406392042, 554164703, 782872655, 406847042, 614378349, 449016730, 534076958, 130359796, 248747538, 780571168, 648221823, 581449018, 960881958, 890642251, 393378888, 715269939, 6856555, 257918489, 324648607, 234400293, 958448019, 292464224, 906091456, 397768269, 906467717, 346748592, 717473814, 876918898, 124630969, 256302590, 606762240, 174489688, 779980978, 267729771, 556427762, 763726122, 666853300, 974596200, 104064425, 883777643, 459361827, 918249905, 153080978, 897319413, 927505448, 569701092, 501771968, 308810958, 474905203, 254542627, 229737574, 444346075, 674644640, 743335311, 751880483, 877994752, 423844766, 311855530, 952819194, 19962282, 18839814, 134553703, 520211783, 1349040, 874174155, 597679743, 613194285, 259505481, 292556673, 753074059, 461727230, 299297611, 620025479, 370586854, 693613710, 498700172, 230079428, 599491201, 421662274, 771828643, 679274684, 166286375, 631884046, 661647787, 315061688, 851677303, 226819693, 487551959, 521622830, 861864691, 720799928, 758613424, 84424191, 207305803, 940754911, 631985378, 489281157, 542188078, 207671785, 192794266, 720160255, 47301596, 294210464, 654731633, 595246036, 564020530, 544729379, 54252583, 730166965, 761957926, 178832512, 499736989, 168864857, 383903525, 58477039, 496036047, 557371461, 61039041, 103977436, 271931641, 810664341, 481276920, 552011968, 707832858, 841750142, 971768243, 470838963, 886325619, 869748885, 703790323, 402679378, 840893221, 735722026, 175976637, 105168650, 865424853, 238444657, 458195831, 203331293, 225805863, 6761454, 34359288, 488347327, 708616583, 673588088, 526140355, 394895330, 502958576, 530170963, 508395382, 138708031, 247189749, 975567505, 259118831, 734916269, 711484280, 924856753, 94061920, 9465146, 79075682, 16365069, 238015655, 620744864, 453938210, 264050570, 52052931, 555788274, 453410787, 844146512, 645929782, 140432413, 170493479, 512119318, 150669390, 793355550, 613457330, 849324187, 645414118, 730463603, 84691964, 290038121, 870738883, 96753953, 340124165, 186911092, 581146494, 119564284, 564991482, 711743348, 23213627, 682873529, 605724113, 186096491, 802431505, 959311280, 912518508, 55843527, 144738115, 540088829, 335503425, 633503919, 961984850, 441293362, 85674456, 889027180, 811710306, 44897989, 270707482, 462195036, 365172289, 259077173, 176931421, 961436861, 718202826, 748329564, 843361286, 256333729, 720137747, 220824872, 834335304, 690842472, 839415059, 738578328, 409035262, 467903010, 259087809, 251867686, 233491097, 393503034, 445339784, 252328232, 410021659, 319068245, 378620782, 420504669, 978442458, 437511052, 964486643, 669669387, 823930413, 938012636, 289833611, 888749579, 134809477, 91966815, 511792643, 180193473, 293833186, 936556431, 44249193, 92821553, 678705423, 909354611, 568495902, 19476275, 916105852, 723850213, 607387182, 581393687, 440360765, 792999858, 182777736, 457855776, 816819146, 729592583, 899269611, 685919012, 906378637, 192966846, 357435139, 232352108, 314371130, 606024219, 511859243, 341184529, 391502034, 677571813, 787235105, 267499340, 233362495, 93289953, 968887922, 935209478, 127062693, 9170768, 928140350, 426711460, 355326658, 870422440, 360875245, 564868985, 523568596, 111775101, 774154950, 68862260, 235850313, 479012750, 46186251, 615962998, 511426454, 96903554, 964515836, 285476037, 841663542, 204664507, 794417672, 732497168, 193908550, 348483307, 931704210, 571966984, 487702725, 443236689, 606139190, 17187751, 163184501, 600662807, 551629544, 972351687, 951183771, 338909479, 763856189, 184583251, 69082733, 111199978, 787539751, 219067888, 11181064, 835035748, 203813109, 415811814, 991483421, 529907731, 75041135, 671372048, 125999872, 732323495, 315367400, 418307232, 795867325, 486556073, 413822256, 670333234, 20322852, 796933844, 620483841, 280069664, 529783908, 195745551, 600982344, 290844266, 974293211, 143307584, 689429931, 904904003, 254335887, 818143241, 119796546, 972701162, 155417503, 396939973, 315181244, 762306991, 392874795, 911504164, 451003304, 25492649, 615261511, 207717726, 531281723, 374616228, 361809607, 105875278, 296610596, 899171583, 671481000, 379937487, 901004855, 725102042, 159466464, 951591341, 329345059, 188016334, 503875202, 23389410, 337127497, 237449921, 174282692, 704897983, 812567816, 592688945, 706355739, 55220162, 213951652, 852628843, 667429314, 691967483, 23979655, 925102386, 808970229, 303121355, 368412603, 254920474, 982987544, 597492974, 148861480, 416672581, 788761411, 511111911, 773420153, 499662215, 63603140, 826987668, 341303540, 955462734, 492930169, 936978312, 357477024, 339885032, 911191461, 166281134, 584514539, 196025053, 68694153, 638980908, 371591704, 449310498, 806538883, 487788440, 125245931, 486964401, 443018761, 250176889, 752929263, 21792640, 339139459, 485854616, 982962837, 527652782, 247096895, 938756644, 953156414, 184507352, 226301972, 492164241, 118048896, 270266209, 530937922, 953127479, 930389244, 606377021, 558986528, 589077621, 136855159, 417287202, 442149588, 678322856, 197908343, 935907272, 871504109, 854639033, 389761003, 827070831, 107126719, 100611211, 914254857, 856309833, 897235091, 209175068, 730410601, 543861370, 693891066, 828317871, 837201219, 146495234, 803919299, 291032001, 19148028, 748707736, 881233119, 219400332, 574228031, 784839619, 324974132, 181005908, 47538276, 677008880, 926300697, 968195379, 489091848, 21434667, 478111081, 736880434, 367792381, 360326004, 513167304, 777717519, 633260441, 436857829, 874204966, 718817590, 158342255, 934380715, 455760652, 223793713, 543062203, 783197417, 564860546, 164313998, 538216342, 584717510, 13384398, 243388291, 372700664, 29778050, 40350870, 501761668, 112228808, 587409051, 886531623, 488189491, 775381800, 56343299, 283206383, 395054001, 845817661, 482569709, 918906119, 236162857, 544380387, 646572889, 429857917, 782937789, 67787586, 492280478, 894807840, 490187347, 915968998, 814919606, 471571743, 399624451, 432677113, 368538112, 652296287, 680299337, 539076310, 488890994, 164038158, 982232708, 789444671, 724706419, 902719727, 633261723, 992889113, 745277047, 713106094, 156745882, 967222156, 983407716, 437945654, 6020921, 729431336, 533267831, 217314178, 471759209, 302776258, 576035035, 389551284, 942527637, 363957460, 339688665, 688310845, 245026414, 547848368, 359544435, 209283501, 534022572, 304272073, 648172356, 512983000, 714866394, 276205968, 247849239, 574988049, 833057938, 145422136, 610025129, 77598539, 690235033, 973033576, 967486160, 774832636, 433934205, 926497678, 897744057, 178762928, 462917825, 865842059, 606066114, 10055824, 309103268, 937428452, 1911813, 337753964, 339314403, 202269534, 604374392, 687250077, 235195695, 260059246, 116953541, 135245500, 774175494, 822243509, 737749566, 245803252, 833103702, 339552985, 532588229, 565407475, 543544240, 648855807, 79879879, 501580694, 334964140, 565941491, 724537703, 47932255, 163393332, 808699491, 202546651, 484258947, 854942543, 556726993, 672030567, 366419075, 676076741, 990535688, 275301210, 48235967, 846023167, 948000961, 227971173, 811745337, 161468853, 26717889, 714944573, 981324725, 724330743, 167768899, 933569070, 336421433, 725745071, 586363148, 163499195, 903537031, 386112592, 206969550, 829054555, 131445345, 389225255, 902953852, 992008742, 375316439, 465959605, 188107673, 584110087, 768238085, 721552440, 573408976, 940661599, 596714059, 877524035, 645244558, 487257090, 343665978, 541917281, 961583357, 93474413, 53317082, 564772648, 996218171, 512544416, 286449662, 281732546, 542695263, 84301095, 709239521, 390739834, 870508924, 600078521, 316679453, 624801467, 870933897, 841120126, 823763477, 611990147, 154876194, 411230791, 564858538, 751560272, 794569050, 861368787, 744090859, 637484388, 492152941, 176909835, 127894123, 350729072, 110586130, 277098819, 831763425, 839510743, 528236762, 845403666, 681034845, 978323989, 706480831, 231641895, 499495935, 642148795, 446158470, 496112682, 535565171, 259762421, 567966415, 963696025, 496045331, 68570085, 876815284, 974418880, 160214802, 144707026, 413696542, 1646010, 779145158, 177199130, 943659912, 473270757, 693500526, 609446288, 922031282, 248680277, 323919864, 291850613, 958461048, 210207959, 108234215, 124681921, 921711537, 358483525, 740269857, 589651364, 960407911, 264636861, 861962533, 738534192, 91247690, 936550851, 567738865, 1749991, 699542285, 988481635, 653378774, 75848275, 622196198, 924857050, 434187953, 741431889, 79033378, 592176331, 183426959, 277562449, 39990586, 261928442, 737379347, 958972054, 904930409, 266926972, 802480496, 350659733, 398412481, 171052881, 241805292, 614927307, 872688427, 405467042, 53784100, 707954727, 538334612, 581098805, 277803998, 76355520, 908835846, 925833280, 896263738, 961313780, 83522508, 556254513, 557686240, 750398320, 25732617, 711468386, 103338709, 595702804, 688670777, 653721043, 961509077, 909883901, 797334189, 873663730, 706989195, 227609295, 225004604, 948308586, 959209475, 309989870, 293041904, 413044418, 937813442, 284639782, 746300378, 428969087, 559910237, 538991065, 380671764, 280382962, 587720969, 414304008, 336646400, 199260854, 885028677, 831241007, 705882779, 152825792, 612414840, 903944038, 197352438, 518958614, 865625253, 790303974, 114079794, 888558902, 681844959, 921124939, 15416720, 986833323, 546079519, 848228182, 700649788, 218334615, 527267810, 360984803, 182526854, 237443138, 302947487, 711208504, 585113175, 782830047, 187559837, 844550557, 780715958, 309162202, 109419206, 865283281, 281320716, 937239929, 278954174, 452151725, 826729572, 157529890, 249782517, 89473706, 456380589, 513913410, 807808262, 789830057, 828497868, 631607301, 263712251, 127925239, 619785077, 727118510, 463943845, 6525885, 547072488, 242675088, 310744926, 857886018, 741883511, 421516239, 562294480, 85963332, 201875362, 722820444, 905178897, 755672462, 507731465, 730116961, 886210787, 865706283, 502071770, 835744904, 449421594, 981358039, 985471790, 433959125, 7214657, 545709948, 294435613, 227156800, 428495141, 898736342, 653541906, 412648577, 128457298, 569067505, 861413316, 504102249, 21112509, 908622895, 301067439, 437059686, 259432864, 561427370, 925960562, 204719289, 227775445, 756477691, 274774223, 505296297, 119898220, 857648874, 782814441, 599129801, 138308801, 652875789, 4433655, 195163, 755929077, 727012871, 867176026, 478025012, 875218382, 430651724, 967376590, 907059784, 49556412, 689449753, 697708473, 972164387, 514443043, 998613518, 91301162, 442900564, 455610951, 421942159, 740342326, 897178647, 872989181, 272350081, 777995281, 492554973, 39253882, 928912929, 446643330, 237870203, 561377880, 178181866, 648832522, 97051063, 788148791, 453776639, 857212960, 206929845, 585248301, 515694270, 557599868, 342230755, 199462768, 897263837, 700513815, 488367668, 518145395, 319099567, 402437125, 995643061, 225746900, 913729136, 79653140, 524869508, 163114895, 931614747, 471319717, 422262481, 433563319, 413851989, 684640722, 835624244, 800186666, 211444148, 315958465, 401210647, 74057530, 553479484, 307952106, 399538828, 581884116, 499316052, 245758962, 428448818, 199319951, 204051625, 635025271, 850342003, 544464029, 985267642, 944013383, 565651269, 845399721, 649269089, 318393347, 730252997, 642182171, 140485105, 41783786, 19942731, 245101939, 327886458, 816550202, 211876627, 279920114, 303914654, 469791083, 678541468, 288690665, 524032942, 691088776, 189155827, 979460717, 842132217, 793251991, 166034769, 27746655, 292269772, 995856833, 741453584, 329044179, 969884245, 37528377, 365974886, 19449896, 147044081, 489460780, 674198151, 258484355, 875888295, 914581410, 296810548, 321974413, 909974293, 449274149, 325057170, 510828317, 823991786, 733038263, 850807387, 660271663, 444278116, 710951997, 868570276, 644046454, 870970326, 220461954, 462832420, 933836741, 434426705, 888644230, 177601995, 606710616, 185950093, 158215840, 864107212, 356381642, 993763767, 231449518, 365919928, 661038682, 619633031, 621370441, 590828985, 984355059, 276668718, 11750019, 365395383, 11232727, 601703341, 611937982, 590398959, 174308987, 202402041, 940679266, 411264542, 552170147, 731266251, 766262812, 586897243, 145809538, 748748334, 143993276, 945408142, 948308261, 517671176, 898343238, 764145645, 14205569, 508113124, 448756712, 937750647, 44821899, 845070331, 366802204, 781693797, 312302667, 557189712, 590487365, 854431950, 425818177, 425096276, 158634524, 253259930, 425638724, 219468486, 165490450, 47578497, 584733802, 864440061, 983243830, 994478026, 619068552, 291302724, 545075811, 135186910, 351046902, 246556842, 358143619, 780536700, 595414680, 154568373, 609518995, 27899909, 648288238, 206544408, 530223360, 834610787, 650659704, 345000887, 248974814, 356702363, 448780989, 147944681, 726650712, 709980552, 481342369, 236432602, 458585519, 695350227, 407908183, 842954918, 410228061, 651170053, 384586870, 617897899, 908275448, 257877695, 691547661, 315326063, 814473462, 914449699, 436887180, 904594757, 936644744, 764159661, 216645870, 749059499, 768565278, 130036963, 308407817, 52920635, 485257467, 60093988, 765991268, 170011774, 108857869, 611256276, 244564658, 232117472, 573804698, 719430431, 652632022, 232421244, 840699313, 585170158, 508454857, 586139662, 588969820, 773143946, 253598438, 818759248, 54454185, 295515854, 628307780, 863850276, 82007080, 459507159, 847960891, 869825036, 383701938, 523987906, 765435309, 501348089, 896138115, 333598874, 364363661, 728347343, 957504261, 641691260, 902201447, 410651512, 99206546, 973867167, 54832968, 740468104, 63559590, 718729220, 945793131, 442526869, 163925513, 549176619, 784639840, 880745421, 120579670, 188177339, 868922603, 478375131, 463034791, 976092282, 62926669, 606257253, 429079936, 748916628, 65995304, 660311560, 986365261, 124367989, 734581803, 145743472, 65308484, 60642998, 127532324, 614614490, 902216504, 18796187, 58629725, 525637533, 360083386, 768669177, 409636969, 244392731, 847210471, 559943833, 412359221, 237225109, 298423711, 529467669, 422618526, 33035648, 989929882, 76865922, 743199014, 929906948, 542290244, 794441547, 694564297, 584194870, 525022984, 940170782, 414955741, 389743633, 373126497, 595755788, 400475254, 540562883, 94075246, 796547248, 882839728, 992948913, 581808210, 318486189, 932590622, 470676417, 48237284, 4907135, 922355567, 850677979, 119560217, 934434666, 738494183, 462781732, 224339550, 456921714, 542028699, 909531821, 555719295, 589297350, 473234754, 268819017, 809841216, 382510187, 294347098, 551920461, 771365169, 428071040, 876066904, 393680344, 867008916, 984882175, 964514000, 237257173, 942885840, 877687785, 344370631, 562222988, 927719083, 91800879, 288741066, 110317142, 848919765, 622057861, 89348241, 708395029, 732466463, 3436630, 118410857, 843366493, 114154242, 110624572, 636449323, 529788070, 2470819, 181723179, 289364960, 748189652, 873392978, 395221627, 13447651, 299316939, 438375455, 325519885, 35432492, 235085565, 180651567, 682994622, 752919986, 361438767, 18206286, 262926483, 572427654, 737462257, 898298740, 604452893, 685454043, 45584238, 725920177, 913284281, 631771346, 373318064, 479621116, 953969669, 733642479, 455928146, 374129804, 868030101, 89395769, 560815324, 406389767, 440918938, 581310353, 698289022, 550451551, 649193824, 476453901, 763482620, 3676213, 73125635, 905261189, 623862024, 869828413, 89967145, 432062799, 764069087, 170331754, 980928308, 137134459, 757061861, 166092770, 45297890, 573004200, 57109274, 698870111, 969865473, 938735875, 303567485, 27129400, 566516889, 330061209, 562483449, 691075883, 885548834, 975904837, 801534493, 722980647, 386734640, 379253732, 895016809, 922013087, 710939216, 625854275, 13164532, 44208672, 664433898, 824170884, 184314517, 824523496, 807383137, 188946887, 684455845, 302203271, 839241375, 328215688, 987347080, 723386639, 856142468, 333687461, 230728761, 755145498, 25205608, 549681577, 682285656, 488514332, 193337700, 104556354, 665522019, 834807517, 81244702, 776219741, 173058315, 151449312, 199918946, 221483803, 525461346, 955384699, 415286094, 338355086, 2442884, 928238328, 416858139, 182171988, 769635675, 718569520, 616829294, 338864769, 341156871, 907944717, 905976308, 783101615, 659680199, 20249801, 318642370, 848998400, 379933130, 892697310, 672100711, 422155037, 155673210, 191465314, 26609122, 669764705, 518475374, 307333299, 690743880, 153520552, 349657074, 930830167, 738780040, 743562613, 811799434, 598733845, 881396813, 837890569, 713100286, 478064726, 302629341, 742944455, 477785061, 309262715, 753180192, 325930125, 342609380, 438116886, 264438293, 760040353, 649392373, 218947805, 889504802, 692742792, 616026884, 216853965, 596400480, 607800821, 333149049, 183030673, 151811807, 703534650, 14589616, 514998014, 911241143, 544813206, 814691937, 389383523, 692567546, 875938303, 313202064, 65139533, 166028395, 620883836, 232290679, 331914638, 984517302, 88314595, 872001731, 868958586, 265041792, 73977727, 371903479, 622260828, 647485554, 250149017, 19109683, 704591541, 596022890, 78917601, 414506383, 906442253, 885711211, 647072199, 143664512, 129228899, 263085100, 42764539, 297413151, 408406961, 353535306, 125371331, 801776280, 965313300, 578042591, 648577839, 506304546, 815588687, 942982540, 150213285, 749254560, 134202173, 362045920, 328778912, 157621499, 1512144, 981573368, 753597292, 846763927, 305999988, 29992644, 851829997, 393098336, 799781939, 270093718, 654079995, 59888143, 970606424, 262244629, 567345785, 879711185, 859953799, 749403467, 704746095, 566282981, 964073068, 530379014, 855718823, 975047136, 739584248, 765104136, 641263605, 100185194, 569997940, 63556144, 107597757, 640803035, 121506996, 919640122, 65971145, 220207847, 729898743, 907123974, 954692979, 868677648, 442893142, 826740159, 375795160, 517232742, 88270513, 137603323, 539195609, 972582045, 388375765, 198007594, 373045581, 219041888, 999581171, 456084355, 827704825, 225177117, 475945967, 655612941, 824626447, 470284750, 338573871, 84447754, 183727913, 151494865, 596753197, 129507058, 670461015, 605036470, 57104469, 181402218, 409707583, 584095083, 3488703, 897223231, 446801432, 249294565, 654647221, 944317583, 413425606, 41052386, 225131584, 109912958, 102045546, 188403176, 930287119, 535736536, 495209834, 183219953, 925421256, 363157704, 551296872, 469471278, 565532263, 503072986, 780911642, 819156150, 76691364, 87832245, 179280537, 997200603, 203696167, 712960503, 777141015, 110822880, 403934604, 345282987, 974916987, 244766223, 457380010, 406765849, 208990481, 599774994, 939713054, 80244401, 176659101, 501261395, 168730694, 949211239, 145681810, 125367582, 177200689, 618854999, 980933486, 462759470, 28344385, 466840751, 34222417, 791842665, 28929276, 995504004, 466183425, 759268106, 375723867, 201924384, 496552550, 14159744, 397909817, 825875102, 542916218, 880016501, 210202996, 686763208, 172047353, 511516953, 976591445, 753120531, 63611053, 716540527, 807773657, 117821213, 408891686, 219162189, 441310518, 553644166, 25271707, 616760976, 812074961, 931743754, 140032077, 416202029, 442985046, 809187763, 109299428, 641283496, 227159790, 191609151, 510892972, 610342120, 677119379, 53513882, 76991648, 967165007, 294805396, 805823631, 454784301, 929658936, 925848335, 436354426, 150465365, 700202652, 111207703, 975622561, 616310664, 801493013, 706139130, 510447241, 436139143, 611311249, 269793743, 141273077, 825697626, 751078354, 133835872, 355046970, 280104385, 757991727, 402906619, 707531588, 555770754, 921580747, 904986352, 58046345, 18301937, 914045328, 118807565, 651166315, 754729303, 196369299, 6375339, 304437740, 684679369, 52745786, 90748873, 938978282, 238811239, 552968826, 329740795, 150335934, 391576774, 266334416, 456757832, 868186268, 467558346, 42322678, 341456534, 228678953, 428903566, 251269272, 827479838, 132100830, 759662450, 511480402, 792390931, 438759244, 95828094, 875356646, 554437873, 337086306, 324284338, 642307797, 91713170, 174330306, 602737056, 697745771, 261886878, 653281205, 298556658, 626279925, 722643824, 878443372, 407377679, 813008558, 823846346, 834917236, 865061838, 679646165, 306295809, 485433188, 383840, 294527741, 277938425, 615298134, 676610393, 988525984, 536945956, 240193513, 430282527, 746601064, 147336597, 279921389, 171126234, 789650002, 614093776, 160377875, 593407804, 288999182, 840386808, 269292459, 488581634, 136053081, 77585303, 512196813, 475887903, 415605969, 1951607, 797044437, 828077334, 838124258, 740184448, 598603022, 32833589, 422057858, 547426052, 698544973, 111701125, 579382742, 122196473, 111568959, 589267445, 757409624, 390030571, 525608267, 413697207, 31851449, 661203531, 58077284, 747175201, 475500759, 978273483, 489853796, 213781064, 644685182, 205863063, 210524559, 606841330, 587135132, 468502326, 285201459, 116842655, 453732173, 39095910, 601424878, 184162274, 421911695, 549611855, 8717597, 235729345, 378004380, 483402533, 954657708, 135095644, 636422978, 452032684, 621711963, 210477624, 45204217, 525555853, 689307869, 413469466, 711599580, 868972855, 456359554, 280550338, 59066000, 371261205, 697699987, 268785376, 690354237, 185544356, 330111771, 905028788, 491186464, 79703490, 473283525, 733187305, 853348352, 662673903, 537984892, 942781515, 438311425, 798965462, 668456546, 90739865, 429245730, 490878425, 421546250, 432275594, 305037229, 299607767, 218840237, 177050803, 693484018, 723283639, 48749238, 211463856, 769589920, 214847796, 979621834, 560264547, 616956302, 465388823, 288844681, 436882622, 683347099, 422542399, 356825658, 212176580, 298378487, 293583048, 359822383, 251683701, 28407227, 149426507, 306732176, 15173683, 175145276, 113517312, 509484463, 394178429, 668863267, 814895813, 12380733, 572823168, 589189751, 111889045, 444483268, 515280139, 214350566, 345391973, 393341703, 85643009, 543655826, 268795262, 842487111, 109173651, 429360775, 676751586, 42601946, 55863209, 245650157, 394614710, 497337180, 884005077, 896062815, 172430500, 141689731, 568334817, 782027809, 89326566, 420371763, 292610956, 283740748, 818774322, 350527930, 73722725, 902551068, 601671030, 521971114, 358149081, 148026110, 497173930, 355910973, 436938424, 155489836, 11557887, 413447083, 81211063, 354008792, 303518571, 525143068, 241822991, 510899796, 998982931, 608354683, 244884818, 635023158, 207335075, 470104364, 396705467, 168834080, 369574005, 86392469, 33992025, 409520139, 20692747, 806041443, 730487277, 460173579, 983154476, 549320904, 820180658, 333245032, 882339052, 30879197, 511678721, 634495552, 520244486, 513142198, 729199151, 25472512, 201065791, 532734493, 757921757, 628134019, 909860950, 749286469, 896216443, 850884079, 437353759, 504984830, 689809024, 575630004, 713067891, 618412983, 583034179, 717259718, 615330505, 229018949, 436637440, 161560527, 365069180, 715826588, 653417211, 217356668, 858293010, 887722095, 547910807, 782892317, 285618237, 527566901, 530017052, 658856533, 159619267, 637233813, 834495691, 680075443, 420772750, 319942851, 465014173, 418599869, 426511280, 415459195, 94122077, 324861439, 879212434, 441214941, 525927740, 337268422, 30581803, 730924599, 436133651, 187731175, 633100187, 86072684, 444143151, 622093648, 393906815, 852718040, 564573762, 772657369, 849562385, 572813969, 565833646, 179840076, 225646476, 419639368, 458140779, 645566402, 140630156, 295942282, 576914621, 192677309, 150194495, 205318684, 814688919, 798297996, 281853164, 48202839, 558442966, 550983169, 658387497, 679955119, 549044762, 476574912, 252753407, 403797507, 457611334, 472564289, 454397134, 287494217, 537300482, 935737914, 821153677, 308606385, 886289974, 200506127, 39678159, 391677812, 830859282, 987948065, 187821316, 343955961, 549003004, 933983632, 740680176, 715581983, 798981569, 248968501, 227569033, 523833979, 851897740, 612781754, 153437622, 506789545, 650885763, 798389540, 184417718, 356114699, 60646318, 196757871, 480765340, 569295451, 843125291, 537346363, 5214279, 609505472, 105198900, 918377065, 570184126, 719092933, 462758633, 558449109, 168279603, 835960673, 324988075, 540515715, 816920713, 201340343, 120212981, 667710326, 249778753, 286193764, 367712720, 23313134, 291401967, 63009369, 117816109, 297055052, 947700754, 494538460, 869134790, 233767029, 353732050, 463957737, 878609213, 755959513, 501897518, 908059986, 57144176, 817297153, 274232155, 146294697, 292427301, 649559062, 784107739, 386005827, 809494612, 695181097, 840547743, 194995043, 298999874, 371571118, 653979148, 933387335, 572391180, 925155393, 123476997, 452155446, 43132617, 241393774, 164553242, 897903469, 59332467, 531801601, 910609249, 611094918, 490249931, 409343131, 984721989, 866303406, 165927117, 913054422, 498541403, 978915376, 113004719, 463429222, 294952394, 634813642, 217847645, 697947697, 663178571, 629138889, 316651860, 398687937, 140322116, 108288656, 883186049, 517748867, 813620131, 799584522, 400615893, 486423792, 269355446, 183260952, 70739271, 895619162, 190938360, 176681460, 554712240, 520935414, 814847791, 628619071, 183078702, 329667756, 334627754, 758302817, 847462271, 411529428, 941133039, 951242503, 412040626, 9875056, 77815137, 698774134, 584076066, 228688060, 691952866, 97265782, 712258207, 562333966, 458343756, 809356215, 850607706, 22338003, 415495845, 150054917, 130619168, 378563332, 949994039, 220462274, 95113100, 5035141, 671791568, 880936077, 434468829, 311621397, 422683112, 832340248, 881753386, 236935891, 685468364, 280103294, 148366554, 539848934, 402968596, 392038102, 444341409, 642622946, 343032768, 437557180, 325609608, 251030849, 95391899, 826938474, 310296221, 209571617, 827076296, 908120898, 496186232, 564994543, 484491695, 446422127, 97228831, 358101174, 760009746, 154155688, 330946799, 428331713, 28344188, 288968611, 441180098, 91377547, 55561956, 613032116, 948498259, 770962831, 299354587, 241331845, 515417679, 500278855, 120134717, 60017847, 951036685, 719685712, 400441287, 886958866, 933003955, 751286636, 225999713, 709975068, 777504630, 681355758, 671787933, 160916858, 176004485, 862190316, 392931620, 363087931, 502038098, 144484042, 624239110, 738535168, 974553790, 845870906, 837568992, 693236019, 588977027, 796886384, 837096777, 324531231, 287591324, 310856227, 32838935, 588552283, 984418659, 946456083, 355309359, 554351835, 349501908, 361627442, 716390578, 721921169, 564946421, 894651533, 710714243, 568745732, 549082672, 82176432, 656495173, 41104907, 584874827, 505415459, 669789745, 420649209, 565810536, 988960696, 415629604, 148906476, 964221426, 759199200, 6776992, 860586535, 710915404, 655831603, 420772342, 308553697, 304330536, 658557129, 543036700, 950861877, 789021246, 441820983, 284857843, 748813540, 623181016, 542736146, 749060676, 775939356, 895776837, 944374791, 812548734, 485276027, 683938259, 65449626, 423311656, 672251975, 873880276, 390649747, 866361982, 427488421, 472200972, 498769569, 914847230, 133094131, 855933729, 828873647, 277540931, 824258239, 132336777, 991115143, 578693398, 675235898, 352432649, 985014635, 146137744, 129556322, 80406925, 786493602, 896711242, 974580259, 463204779, 230505617, 423626012, 686630101, 440145353, 415660717, 53449133, 368220985, 40523609, 105817449, 971740352, 870587062, 453441801, 694737120, 869460836, 535655027, 724172206, 30144438, 109466432, 22653391, 558718451, 52074342, 71691733, 787428602, 322213195, 517359385, 429546903, 215398782, 969107067, 512641695, 531903725, 57082260, 219938740, 157258241, 745134573, 980519766, 858949007, 355562791, 178149282, 325167500, 753099565, 539861263, 747345313, 625212590, 74824508, 610763401, 842361756, 711159237, 359574419, 946684942, 849928038, 397677441, 177890643, 522522715, 992070390, 523531424, 374721008, 276469989, 523461760, 155551215, 247956480, 907305559, 39628367, 522846145, 788034012, 406622892, 39444715, 994030287, 338473486, 974433363, 535484362, 145694676, 493833858, 986753915, 380718175, 718317991, 663946271, 853337645, 389352240, 853420700, 244152908, 734329515, 761518748, 998245694, 440397073, 767750245, 348453462, 491924808, 202494430, 12633442, 415145769, 931052132, 290058584, 617608817, 755561337, 715409331, 167258819, 308992128, 933752902, 600697901, 912125364, 342667115, 849669559, 829262652, 240877422, 270133694, 48808175, 789490837, 645242549, 474398628, 315515821, 423056777, 131124407, 621894890, 735735671, 511022114, 966899581, 301274533, 184255141, 924477491, 509737403, 234261102, 711534574, 361085514, 912065250, 981262809, 743576761, 660433461, 921735886, 409268980, 151387983, 616921678, 305883789, 469931231, 607900724, 202780124, 281868105, 476306322, 864351924, 31080580, 175935795, 933666201, 639655435, 812575661, 751871133, 13978774, 146831665, 86918610, 7962090, 928340971, 348257904, 503731263, 731999956, 719099599, 867005092, 170136737, 740402322, 244459857, 583719601, 402277275, 270068533, 968133275, 808871523, 558944985, 223617275, 706925060, 227157380, 801754494, 492163447, 436241849, 767675645, 498054195, 414701522, 450831190, 948459590, 211935464, 625380337, 638692830, 453701126, 665403135, 106331373, 925623916, 233787975, 995430654, 922919806, 136683948, 559612349, 308319076, 585920857, 355089854, 664334492, 775741232, 824344127, 445912245, 436152764, 187159917, 725144875, 470330985, 210968211, 611198689, 318745092, 931915033, 884526178, 573941818, 64191711, 549893715, 32427447, 410773120, 796626079, 758033922, 214824410, 914058863, 863143395, 875805478, 613375330, 442589943, 232081333, 848023908, 742370816, 76557803, 47113418, 368639918, 915874958, 2250878, 809563466, 255662035, 577093663, 733777739, 111150850, 120533557, 816313000, 715405848, 602490107, 233001468, 981329273, 334534545, 704853234, 258326540, 906181521, 974435952, 190186917, 402936403, 56283200, 435130597, 96820614, 869340225, 16817133, 192086598, 724599496, 541190419, 705846697, 650825779, 129095755, 149200357, 605190195, 485486621, 668268106, 570967754, 537191119, 671072559, 234067220, 221488448, 134607803, 259921800, 272688299, 285128699, 553909367, 251696393, 301495751, 919863894, 996523086, 231602559, 285462708, 300217253, 938373644, 802558858, 668638741, 303816814, 763214782, 780367390, 321289088, 198309308, 219119698, 914391377, 200334269, 983346256, 668241823, 748324735, 108984880, 26709413, 729067637, 822017731, 936888597, 796791360, 814163950, 785727512, 177829849, 161082234, 499196227, 136727290, 974428031, 430224433, 702923025, 134101779, 571594441, 531794543, 807881472, 218234293, 65719334, 53890669, 513060823, 410030629, 448750313, 626096808, 124747216, 219502688, 973473086, 324565260, 420942275, 822582658, 996474013, 16799560, 966743169, 239422391, 587636162, 699178385, 132548189, 365049310, 239709326, 990520927, 654526440, 410991604, 141510373, 123614413, 288351748, 797520642, 767147538, 106981212, 303599383, 811609654, 608947397, 634563036, 13548818, 731463745, 953102871, 221859612, 203644468, 355616521, 140088169, 912157033, 616617147, 665191147, 523447130, 794176938, 705632500, 645845628, 956066244, 356073517, 107755609, 779608107, 141728222, 770782034, 715702536, 339584868, 837228561, 534459549, 299988042, 226358612, 975247915, 398267820, 387586879, 57589112, 841370163, 585819210, 693519862, 258262329, 856141375, 800366631, 35695754, 535158674, 345184048, 208781353, 907277225, 63048446, 953766242, 829816594, 885961189, 703917397, 951187918, 326904946, 118826858, 751673883, 265467978, 857808819, 296358920, 487674908, 633304346, 358761917, 615830049, 623175347, 37995046, 269956802, 459966698, 33134951, 723085109, 933617976, 424445603, 12469108, 184112744, 235129184, 823300809, 383716068, 539372168, 644026013, 124407063, 463756919, 514868527, 93582752, 5055190, 975282380, 406338300, 204785959, 610013397, 298090202, 795296373, 965708483, 35541432, 919709956, 741241840, 356032796, 795998245, 372834727, 678894810, 646630969, 335142864, 24831215, 537735481, 102009105, 607090308, 809309388, 205958325, 191149058, 912649087, 776302450, 10796242, 493232130, 993533829, 303818098, 934965744, 788465667, 276358496, 454690296, 864888514, 366565454, 877062413, 324555628, 614070707, 826996180, 381066463, 505289096, 338998523, 220882409, 729616353, 578620586, 392065947, 716870409, 926579993, 427427742, 27184771, 592318033, 875414769, 783237232, 841143950, 633307635, 418722255, 660420019, 788703290, 604254800, 254654643, 967655006, 105272687, 474316616, 367763469, 475389071, 711054382, 401487063, 386937506, 774644592, 300983469, 325982667, 516505395, 786576346, 87311870, 962374289, 523291799, 828627393, 867160994, 178076700, 899657810, 569522423, 323723841, 749871647, 92846464, 523603948, 866694645, 600476795, 674837362, 266937566, 943039919, 864842264, 314000243, 350736533, 566896502, 360862583, 583094318, 677907402, 128186849, 956955337, 930246114, 629007570, 897978356, 361038954, 957595626, 447154295, 899551151, 291556551, 313439285, 900380549, 402592851, 13133932, 403087828, 570751758, 176197838, 105136790, 670207053, 86212026, 117879245, 946663081, 913769558, 469911332, 665832086, 343806, 865705189, 196982499, 536279927, 511363002, 508248577, 489027308, 816514805, 343929532, 673557572, 46657624, 406947039, 358368625, 201242781, 421156366, 497449579, 65077573, 33458691, 289055812, 195463593, 138066883, 921105425, 655210536, 891488193, 534530024, 631571786, 814173866, 49449383, 505542919, 293063396, 182841745, 432053269, 768862542, 646816772, 851229424, 680498346, 287856744, 311021364, 480990694, 133653683, 99206030, 188774369, 693672949, 861108677, 784510307, 208714950, 144753534, 304972822, 997671335, 322007412, 856225577, 25613822, 733130725, 746314466, 784329798, 765736637, 952832884, 426530839, 256672382, 188961067, 354213075, 619308722, 569347651, 849550206, 683325821, 731642920, 154726509, 551123810, 752291905, 681880137, 799529891, 242552831, 131340381, 133789077, 254926733, 380953829, 818316826, 12105051, 389556841, 462643473, 806447612, 823417742, 471263881, 573932443, 173314500, 506434806, 366509210, 498994611, 239068989, 314550168, 858121811, 179245867, 219884111, 537567536, 278480692, 643357774, 409065413, 579668647, 660218780, 719211554, 92874069, 464122220, 600454210, 113082407, 4805148, 518271264, 347408788, 422991245, 51871120, 921676160, 339928379, 988017048, 444769757, 202879565, 467739390, 564304958, 997853398, 344361395, 345713282, 99138151, 172803087, 855391522, 618312384, 819381252, 826644899, 31996773, 14090534, 634237325, 494297054, 604212526, 798275541, 178630148, 582781664, 970758127, 599221727, 942844073, 512527028, 590720034, 955021038, 964539553, 919175344, 435660301, 540138665, 395703965, 390354845, 412418116, 891204693, 143888605, 220709844, 730648985, 151668670, 919579167, 677118162, 256055746, 449403405, 936607295, 816833776, 443283414, 745169447, 614559934, 900859493, 290561000, 475741562, 475462725, 572037490, 354901097, 387655224, 605398084, 924578994, 808422995, 269086095, 871772501, 439348969, 289203779, 126259382, 425271436, 778470775, 585949633, 628923651, 944425527, 139732771, 399015015, 672457312, 691493920, 513807174, 81219734, 206660834, 81097583, 739578714, 497075205, 733911570, 789130360, 456190396, 900897085, 597297239, 55191381, 819842156, 814635345, 186544401, 826929067, 574910990, 900838169, 604058232, 155289259, 197527674, 587697887, 264074907, 543413682, 285433118, 810903335, 501905644, 545815814, 423359769, 782416982, 452495734, 92190067, 426219851, 92446683, 656048416, 655791127, 642454473, 116209358, 219106024, 426900383, 816076499, 663105437, 122016590, 590885893, 299355424, 488514854, 234427954, 286210564, 932569054, 103183662, 438371490, 304584672, 451636926, 902250845, 219070633, 991349593, 107540031, 985045145, 918107542, 204205485, 304987894, 865145298, 146024657, 486014896, 125966659, 156442938, 388389447, 841898798, 756448355, 245575033, 635776937, 605144630, 105434198, 382498802, 121824481, 268305965, 892846416, 482010046, 638849718, 881662827, 632649392, 178978969, 535652270, 291081673, 726460076, 337185926, 815618010, 106179472, 385508894, 964164520, 373275948, 746929516, 986427216, 531649378, 181219675, 405871256, 73484334, 503407293, 177368468, 713171863, 902478428, 988255851, 715212151, 609822308, 487161438, 28460442, 416119922, 792854725, 359826769, 697814324, 677302786, 51528803, 299838471, 293174663, 691164133, 274702588, 615118335, 551591635, 447276670, 28902284, 611151576, 219783885, 322720458, 729520320, 943123755, 912307943, 657826513, 377952667, 759840823, 58072984, 949974188, 242752068, 733918224, 215116497, 328382591, 912238129, 669289893, 145761910, 603384808, 727505080, 646194360, 16524114, 19099139, 785911189, 612351229, 737103117, 206566689, 575888852, 654393188, 383247536, 281582320, 293824323, 387535661, 16015739, 485401484, 584686425, 377314631, 555229638, 603819700, 2259554, 57951093, 690569314, 86753662, 839446234, 180438010, 511651659, 599259879, 279221155, 49059786, 716856186, 743295676, 683629444, 345381108, 530390205, 701368377, 776696342, 952287362, 348867064, 812346826, 165163229, 924177135, 112024498, 101735515, 578479508, 402875450, 938237979, 280953784, 17329016, 302121545, 774345878, 520791425, 382728689, 244120965, 288804644, 770726408, 277230450, 199355469, 586754339, 382375007, 617469777, 118130995, 481560789, 183357076, 992920745, 988092367, 270106016, 824338422, 198223559, 327450790, 8059015, 935131481, 685760260, 990859961, 653564020, 451276612, 798685563, 766682417, 639560165, 364556147, 706405726, 758813381, 867886487, 371508900, 597135413, 169817525, 852124001, 824379262, 911158080, 679431976, 738251795, 672262338, 907573043, 818162508, 440161735, 420880156, 294303227, 198342583, 947650990, 600425276, 69052031, 726149765, 959824919, 332184081, 830423291, 346229477, 923625842, 916016147, 549702526, 975400008, 43811044, 959086069, 931927007, 1103570, 73173850, 144883319, 91023573, 951163490, 447053392, 654288858, 235073767, 522973424, 274345957, 516841047, 746915894, 310286927, 567555611, 259457723, 807565701, 119200417, 415254700, 258748663, 97222799, 174584042, 376652580, 722141486, 973776794, 543060479, 794673602, 878799997, 997266796, 348237856, 599226424, 975724492, 154912390, 781964810, 990544063, 341568811, 44237627, 810952127, 582725696, 459304665, 419492848, 903422413, 180942241, 276482406, 724341474, 339874849, 891791463, 938386257, 938580435, 191185874, 948139787, 747349724, 22791483, 765256738, 280972704, 488943026, 553256341, 927550279, 243773642, 36373727, 766096306, 870299901, 831849439, 898202736, 803690064, 179539401, 987052605, 56721406, 171281331, 95766156, 603469651, 273740332, 609962361, 458147809, 268193681, 307448168, 68662315, 606061622, 807669117, 28733582, 972376295, 691575466, 985383946, 374219253, 401136128, 264873030, 857425655, 254928642, 691511837, 30502128, 443235156, 666000496, 970362694, 998753769, 299610648, 595216540, 252169460, 268854714, 984305050, 105978795, 119543423, 808010422, 798414781, 461460673, 139356154, 264155802, 713597028, 594925494, 275632420, 633255872, 685227632, 767159508, 73802220, 400042812, 64153625, 913637107, 347093451, 119306877, 568346109, 751019877, 559413099, 580705038, 527604955, 841245191, 817222687, 450874580, 574090017, 150004155, 570011997, 249997823, 835129135, 56646457, 67856558, 83202921, 757586051, 945697385, 301652108, 528783508, 922060145, 310092713, 684105875, 269724155, 996367667, 49705868, 655294557, 154345170, 821217577, 782001347, 161538258, 193662960, 68928598, 829048091, 986550159, 983559756, 198202532, 96780454, 45441486, 866421842, 146262334, 890149898, 884058923, 920835898, 749405158, 668835225, 736899974, 640747261, 242989105, 637697706, 430275172, 550004069, 277246982, 351341735, 367860916, 217851055, 356320966, 399348296, 730785027, 408662961, 186180618, 277095482, 51613420, 606447618, 535088035, 816848913, 55428221, 406312251, 173252508, 22503027, 150230107, 201646113, 100752159, 76012757, 654304308, 359266390, 968376697, 248657324, 613286305, 506644738, 159682642, 8510101, 349765461, 396214237, 388662229, 10005728, 428852454, 283663661, 127606926, 634674734, 824713766, 137765501, 884832395, 934366370, 509120199, 737491621, 651484440, 725613953, 719798305, 274221143, 598652927, 121788469, 643193460, 954508317, 883135142, 878551801, 673718681, 177871973, 18996494, 924636547, 831221627, 839777237, 409445380, 403116628, 648872107, 156392185, 435820946, 420349051, 558914759, 716281382, 281805537, 947767207, 692277576, 956568374, 227209994, 787804211, 175991607, 101445772, 256393418, 571436156, 999588372, 90098459, 481438732, 266304769, 435867529, 73248658, 286048211, 329564236, 147203674, 355351083, 334143359, 277070428, 160382652, 489036345, 254458691, 311613724, 28742581, 12143110, 473899517, 571183021, 592781562, 760468893, 406806514, 917143464, 129759954, 339078006, 454701243, 370858116, 501819180, 901793594, 616824572, 90527543, 903276074, 379121523, 803939266, 364974414, 405385898, 476697974, 857984449, 673634659, 590310820, 427138727, 140096934, 96614044, 214749221, 107496783, 670014282, 48227635, 220000045, 571978553, 211564881, 690642828, 910488385, 668839517, 356957905, 496388442, 856567496, 10831952, 972047210, 595271054, 161908793, 328459913, 551379864, 489368891, 524234963, 135230111, 511514954, 196711133, 852276424, 241996166, 760541374, 665549244, 675457765, 338958087, 793778960, 410161086, 405691110, 599280499, 761480500, 190052610, 735870266, 238377224, 875781772, 405046180, 548475587, 315987615, 887010334, 644507846, 888880131, 935212145, 482364843, 611446989, 470979687, 897994301, 980055765, 961402941, 772722617, 751374266, 937819141, 707510526, 558774510, 57505867, 453981893, 259242169, 925798598, 99415936, 502877412, 275201029, 360192767, 36561962, 137703873, 226877076, 856081835, 967867282, 981418147, 561775583, 600981805, 685980979, 155530095, 3150681, 986915617, 37137907, 825496818, 239856622, 831138663, 232755685, 426351716, 132660230, 537826865, 80249025, 370900887, 231633487, 297136325, 800396674, 263286647, 936148903, 743352892, 110889707, 829449113, 545974526, 118602438, 312611132, 87022530, 161275851, 681448316, 944211921, 870091514, 680480366, 610238170, 186385254, 950913333, 221422420, 361712178, 252108536, 949033565, 254074481, 185113171, 635951544, 116580466, 156482974, 462114850, 418213814, 645987297, 560844207, 283695379, 842266065, 949004047, 219522389, 288367018, 277287956, 370891690, 426761801, 264998913, 911181319, 179426237, 790234328, 565200946, 117851544, 598897487, 149428296, 192729059, 391194602, 48024410, 307636181, 67495444, 442406221, 280801923, 384660060, 843049901, 217111110, 176819660, 613923031, 678082357, 376018174, 323675171, 311356223, 501969378, 366839209, 466015296, 922114405, 572947484, 644046587, 262504779, 91527124, 713580148, 547925030, 609164093, 404329544, 910031762, 997446273, 425318611, 573059458, 868837503, 87503605, 472281054, 963933428, 531885653, 176027871, 352498651, 245468047, 29478418, 227251295, 326103028, 424678632, 182176080, 125578822, 258987792, 683779680, 390772662, 350346438, 432459518, 392171039, 727511963, 871979778, 969429828, 493513182, 279148693, 441996283, 408935911, 642761043, 579814841, 15604220, 840073097, 650603244, 579073510, 929317121, 610537970, 674987653, 910144727, 232369636, 866828388, 24882692, 748322055, 545636917, 617046799, 77103822, 467072794, 12341934, 967300508, 113626557, 891518271, 528808018, 336586100, 293594462, 61738626, 3669749, 424932038, 197377201, 445504294, 517183760, 993653398, 729576295, 249590652, 919444191, 872224318, 439183508, 486323228, 203256997, 774156838, 975617567, 256880739, 927787281, 727676552, 913049521, 794899667, 774052018, 211437596, 821998320, 637732103, 991519125, 216111207, 921628457, 373699181, 359365498, 341867021, 403488663, 304399777, 348900933, 628531804, 685646292, 45465952, 667488448, 347151922, 350871853, 672244779, 778920120, 878618456, 776700179, 204631356, 945362047, 481727801, 673222584, 4432643, 282932646, 956294849, 721001540, 537752855, 52204251, 693561426, 315414948, 81218379, 7327039, 782753908, 335999798, 244223817, 138546270, 319731027, 103479440, 363875841, 81985597, 731200424, 254810363, 118770146, 942547393, 736475817, 20368365, 913121630, 592840727, 979578498, 700800421, 506934419, 329432881, 605842681, 918766590, 949934589, 971938974, 768173547, 925992809, 627041587, 297909055, 207572444, 431318208, 784082939, 160375883, 351941007, 778682385, 737716660, 476046338, 33366079, 788996761, 929242776, 931179596, 795724784, 499979490, 393449570, 844529963, 120466407, 568014492, 620208404, 195351710, 895353698, 688241650, 603585731, 223950393, 891712439, 149717292, 647417334, 755917841, 31066113, 74006977, 860613498, 919235425, 645174984, 912059016, 155300632, 250228991, 416366849, 22414288, 212977655, 79789639, 532416084, 143223555, 398065358, 368061365, 139225062, 767394614, 143701616, 281973871, 840503049, 126815138, 113602774, 877740509, 498169302, 397073048, 908511913, 585941801, 663707880, 629765047, 985698277, 469849299, 954744533, 960781451, 919839701, 84730887, 182534658, 405590371, 360574177, 695370688, 94453001, 765917009, 276596558, 934814354, 841379541, 456854123, 471391733, 819779873, 525507964, 356640221, 475669035, 390553668, 100009502, 604687364, 769067667, 566692247, 332211286, 476742963, 482133722, 155473491, 471287437, 689531704, 730896820, 94517700, 408927946, 910526098, 823400869, 384394352, 638292111, 403135529, 854821164, 528324246, 319008872, 786666749, 690339140, 960958815, 836982967, 694135304, 956184280, 758468916, 703258162, 102610437, 856929513, 833159847, 441271163, 510682662, 855144256, 955837945, 641340033, 136258130, 809257012, 983258850, 758576374, 656374959, 687613463, 531858921, 873482224, 534276592, 269169445, 766168079, 482149861, 640346818, 706434308, 978608183, 683829258, 326579777, 290019066, 777561309, 779868319, 938977518, 317885813, 952385334, 574230698, 564422725, 782555569, 253640900, 450876807, 201305541, 471077483, 475138009, 870307518, 65947847, 858975905, 343067116, 830577577, 488790527, 510202829, 43825893, 588849953, 290514341, 102339290, 761973143, 756319946, 291962254, 266536622, 194143026, 66540550, 13299778, 699012986, 341476575, 660385749, 589448917, 367383485, 774265071, 976807279, 507343781, 191210198, 23189248, 849097363, 182493471, 528593111, 781009202, 563753299, 175387815, 787360904, 305641960, 960516825, 999609220, 294515957, 129186391, 782419357, 996587381, 891904351, 665884266, 277426834, 495613679, 110111624, 680070783, 679619356, 601603604, 321820659, 961406154, 459643178, 394464575, 429853513, 675143248, 228744022, 418902196, 767212934, 187525594, 849845205, 37295060, 708937656, 195580270, 301895268, 394687634, 292273426, 193510115, 904854796, 65540453, 396157923, 93786939, 636060655, 621493333, 711367874, 407192082, 562837899, 487921508, 580991280, 835446169, 503442540, 491532180, 907260061, 248454971, 668081161, 167596155, 17269610, 410954788, 619164991, 35607487, 640541250, 455910813, 120860142, 29391097, 815306675, 802314803, 641970011, 300015158, 810038586, 410480562, 383377829, 584439795, 102521554, 971303721, 216081040, 357851489, 375171962, 685431872, 842233505, 822837125, 223678311, 259027263, 325825015, 449202288, 36197287, 308434673, 270803335, 877209324, 182011070, 930223754, 637506969, 554424841, 739828104, 983695798, 140690184, 410321332, 523467683, 643336007, 188666293, 541570713, 363625587, 109558601, 573922025, 972924010, 585582857, 707418011, 413502821, 133277856, 497612088, 343062781, 608834452, 220360214, 17560425, 257544816, 197351574, 706888, 601096235, 569149810, 896936867, 873685085, 845674841, 403480942, 870215749, 263121914, 851672876, 882781561, 539159612, 238403854, 813312835, 835083311, 302791951, 947808448, 185469031, 543162329, 702674547, 477583543, 340980690, 823153508, 523777869, 50104172, 704321185, 116433931, 435853847, 262384141, 668415671, 259777422, 521802039, 475044427, 913176426, 325456338, 3327142, 465410596, 138310202, 518860767, 842316283, 63456631, 650101193, 423895028, 33962435, 213736298, 463143266, 793991464, 396727011, 850893084, 801294694, 959890743, 490356437, 635954698, 800788664, 992136587, 665731425, 95859235, 695347028, 243079274, 204051741, 542006295, 134029312, 646725201, 529159579, 43265303, 771021227, 934038118, 601731912, 994672277, 738118689, 818841533, 840128159, 856908235, 77962828, 911520917, 814265863, 163224544, 905302090, 130010179, 472811984, 945010108, 620039782, 283358563, 699128340, 670231327, 383175912, 427689271, 437439370, 326712559, 998603668, 817313097, 507578280, 286466307, 437811830, 347491990, 314923622, 945680745, 67581518, 263570065, 742095544, 316493383, 316712652, 595007802, 422985601, 480284696, 917757832, 569657180, 167216158, 509734091, 455471280, 251871912, 741575818, 281366398, 630259849, 600503067, 309324890, 586011230, 148589269, 450535947, 434841564, 29905058, 374461067, 672080091, 378898519, 206692095, 670310142, 739374841, 751013502, 427980164, 130946466, 284668659, 244365954, 689228545, 427382850, 310853258, 938380752, 933165540, 619821559, 335748597, 546999728, 462844129, 454259970, 407983802, 503099502, 536179891, 448412610, 667113745, 356804949, 791055758, 650389337, 879792412, 193840056, 28842253, 360094099, 704946152, 643252758, 151700516, 866443267, 737055737, 566914204, 696935309, 649366427, 450157780, 214431795, 215279310, 75839590, 351284487, 881079042, 57133089, 940979590, 250924737, 210283215, 498273879, 453343825, 595527736, 597056839, 306498671, 257750442, 812827705, 78055511, 557534672, 252924486, 904320893, 534166678, 758276614, 369238546, 10903530, 282468315, 982067187, 859624109, 471312057, 406989484, 619469757, 571287910, 136743768, 952618535, 489220410, 410707683, 804765457, 256721998, 599648877, 188062151, 842477697, 898296995, 695815515, 867369464, 407754319, 227869837, 339008176, 789196855, 218847241, 108192230, 189958076, 792319302, 856042407, 821664041, 159107932, 528668122, 12721276, 617120148, 934026704, 751635267, 278468088, 754936342, 563458131, 5957047, 259818451, 844661481, 438399087, 372999106, 358139503, 35525278, 197915643, 788775824, 838095055, 80187576, 153525385, 591816182, 104918731, 587857013, 764375978, 511418610, 506260079, 49256876, 298519624, 39266047, 892221729, 164409773, 271699943, 701288309, 316960629, 443114874, 847265564, 595196228, 117196650, 700530958, 591363252, 893980520, 950367221, 816531825, 943022573, 202264114, 903979, 319485784, 579023138, 935795519, 694001692, 229752298, 592595087, 180166705, 455820806, 321253607, 972082394, 316822878, 991781310, 577806178, 731280716, 687988710, 346164189, 471307243, 964049928, 708666612, 278088804, 176358342, 83150636, 882532126, 452537870, 798813651, 318787614, 438240123, 759609916, 8393787, 73853351, 564943900, 555605448, 187852177, 3227012, 759092817, 995848896, 738595173, 177044618, 578094674, 338707233, 431348403, 369939932, 260441032, 909420075, 885497438, 607160396, 893332633, 923260328, 630181560, 597231053, 834447059, 765007461, 275014831, 531389444, 91829161, 834926098, 301856913, 967762983, 268751069, 46288426, 294963747, 493842935, 194697491, 518269343, 966799262, 16651755, 71156904, 61041453, 672283129, 325903804, 806742416, 57073877, 942437062, 116293530, 950586170, 212665306, 271926952, 854735356, 927039129, 904850965, 678888906, 220879972, 494434256, 854649117, 326229768, 127291914, 9156731, 831532522, 113144235, 668991358, 101020560, 783131352, 346062456, 368721004, 463305645, 910865877, 878230795, 897915046, 138350015, 106282835, 767811961, 415689605, 326005145, 538189275, 965792488, 38087781, 47054307, 882051309, 365356631, 957299081, 64001795, 660888873, 333117895, 7862016, 737756561, 979025710, 688089064, 189878543, 30698856, 565012930, 107670690, 116673667, 266685971, 799273015, 383817591, 367396994, 51318879, 252320977, 408284767, 249842687, 540124309, 176313316, 714263809, 284019871, 908257755, 441043287, 6214358, 162636724, 755504164, 843050233, 885919129, 62549080, 74228922, 101198955, 240215356, 66927195, 805653558, 501395764, 946721877, 240537193, 506193720, 531644300, 636005121, 54516169, 803349885, 621246067, 192541018, 74163526, 846739453, 140278961, 432680543, 668094194, 965618607, 637073982, 163105159, 479936134, 465949859, 773868383, 894255431, 536527692, 288939324, 117788381, 325019344, 720082475, 940676752, 856283182, 395445226, 826177045, 594922358, 537848430, 327522858, 754835659, 996899231, 697119793, 726184244, 689477854, 669042219, 733007415, 21385665, 743216869, 420938407, 155494846, 274632668, 260489085, 36124455, 495565764, 422174808, 786725738, 764406548, 486712582, 588062309, 703484867, 407912894, 685383239, 576224069, 706817089, 24206696, 366893395, 490433685, 112922548, 977214701, 483176055, 207002439, 2728784, 514351025, 828949180, 205165086, 353883221, 413789016, 782312960, 550214604, 619414563, 8059716, 1922191, 266611324, 802492617, 689658177, 106796966, 212432132, 421163540, 743472969, 449383333, 980962379, 654888801, 162610031, 386834422, 902509410, 602526405, 780706488, 334823163, 51469143, 629834484, 743243108, 922513370, 180864880, 170049077, 166790849, 590180134, 233977485, 237074883, 388441852, 360943465, 88459345, 769019438, 438914361, 894142906, 800782980, 226627722, 309770206, 797811229, 612618437, 166874973, 612577699, 954574637, 665280265, 721285873, 713394050, 450938005, 763798726, 374273927, 840421701, 516219200, 175240714, 990318963, 81558327, 161341655, 892352619, 212529594, 420332743, 695098942, 605932708, 985837096, 569963622, 35476415, 838279477, 22820330, 696692280, 175581937, 64723607, 823612244, 448005873, 150612368, 914152352, 92540531, 587403197, 599042837, 920693432, 83415026, 702292856, 703116567, 470245103, 684446255, 667032258, 431334314, 377048919, 601686556, 878154335, 807914225, 735238951, 756720192, 79934057, 358424468, 907950705, 943991994, 986203515, 863648537, 218863225, 28234140, 838239489, 146503994, 959347131, 742942047, 147149675, 390126970, 245668980, 675368619, 486305280, 497011848, 315438854, 654982116, 681514976, 498948910, 418336567, 706078458, 547411409, 472113346, 513142747, 915763833, 358097671, 839052690, 982043020, 479293128, 206707787, 385449881, 446322219, 379029209, 548830809, 837652226, 834214400, 854841698, 793227058, 348874195, 543236652, 805680143, 338591648, 522376748, 497893540, 916626183, 489292487, 428103966, 410435090, 100229012, 310306594, 885355246, 790051418, 632088626, 733791497, 260805693, 136632833, 234738403, 435477024, 223957311, 656189300, 217722208, 39682638, 838581995, 210471055, 81170431, 848982352, 762801700, 603263606, 664089142, 138515649, 396085517, 416638710, 586251621, 131247585, 574786510, 69134232, 976209875, 726534293, 835497766, 391759456, 996846532, 968372548, 50336065, 580891097, 185684383, 2378142, 55371090, 293087850, 991603597, 883596386, 544756460, 466425084, 642358711, 436122462, 998758041, 956704696, 745571041, 474742789, 806561133, 103322543, 695460825, 365897798, 799333017, 205074225, 526909617, 679935145, 189958199, 255790090, 400381172, 575210902, 150221727, 708336415, 396518713, 934272633, 880616375, 198277802, 944636445, 550477726, 586487714, 624153813, 601775525, 260982540, 132705966, 666124228, 882682767, 381160915, 899618229, 409058673, 697094703, 280611612, 893272752, 216365298, 987472228, 381304322, 322679763, 602995453, 752963651, 6099384, 498447663, 387966084, 959440058, 101417335, 21286912, 322159142, 544339641, 420035335, 322405606, 60902265, 689380558, 442706216, 674694217, 549833209, 698380582, 870761731, 568560495, 668378970, 380462452, 410403798, 363123769, 170593663, 767526189, 212319605, 203794989, 295825844, 958812420, 421622602, 665681814, 242474813, 526374057, 144598797, 137063770, 778070917, 247237453, 351442642, 292635876, 650794744, 134910713, 226132253, 889530220, 638055153, 452906963, 359025314, 732360987, 26036251, 517128106, 755057360, 885831862, 22374411, 102398159, 467367032, 969074867, 580949038, 571079505, 73039926, 686889668, 498068066, 801770464, 256522466, 287870044, 110934648, 620127886, 720765365, 126489348, 569354735, 763102729, 604943279, 668751967, 834998753, 442802214, 780365199, 412188995, 939583032, 985143706, 697040581, 587830211, 280854229, 14396511, 914509323, 28595495, 270259574, 944548525, 472607913, 517053588, 259351952, 572338210, 171535456, 952353265, 697708754, 462540709, 198501379, 747033464, 722377808, 478686447, 319147622, 628571700, 734384558, 746963029, 648507368, 755942568, 868798112, 666545375, 360077376, 689078089, 835273207, 193879576, 942252526, 776742572, 914549658, 379815446, 294532689, 669264529, 33352107, 129819723, 138008522, 336549070, 492058110, 789098456, 334618736, 270618645, 667088592, 921231276, 978577015, 605751106, 755249011, 211830185, 436090330, 260627409, 913922154, 58018025, 271388309, 587427304, 14220695, 451478726, 227273681, 128765131, 856771938, 314644173, 995930631, 79442885, 701834397, 639283224, 864253829, 452492524, 749483642, 554000082, 877003141, 876935141, 458197738, 874279690, 329633530, 30790246, 431887880, 320307913, 870611227, 870066595, 291052424, 845458175, 929749931, 878544712, 541680993, 805002713, 948850480, 65665883, 216434605, 114652331, 204508556, 325770886, 121732337, 305074608, 536637114, 839231002, 267029286, 905289450, 761957863, 124024685, 38853066, 507590304, 59737203, 266969970, 410414652, 769293135, 454165584, 268864244, 54920061, 455970782, 983915516, 785290343, 37654900, 951351940, 627616424, 863079532, 530065657, 665500687, 641809629, 688026594, 608355095, 325880589, 338769590, 755421742, 957597725, 659831874, 939917913, 925430639, 972379394, 743912239, 591559124, 77832505, 90905778, 522531056, 736673289, 513817778, 95671091, 148907412, 161132305, 170018897, 52455859, 784744777, 215054744, 242869704, 120026262, 180062544, 749191268, 869184248, 643916302, 677644035, 611539750, 635881928, 287463846, 57810737, 804146474, 11407006, 14834292, 835088647, 11469799, 698194475, 406920396, 427569868, 75324951, 521533645, 163598950, 450948202, 450363334, 249866849, 188768717, 401760659, 772764914, 602697000, 602920871, 717207553, 111297150, 810352294, 550806408, 304453927, 41686723, 410942475, 48547424, 19143410, 399390837, 194137990, 288159873, 778804218, 105726580, 465139373, 56657401, 570857410, 274333096, 28856921, 803938218, 418409833, 218986606, 31542972, 295173529, 814120258, 419067815, 686432782, 690069752, 443409781, 208820046, 992816255, 222197035, 947481329, 863714746, 94691941, 421792850, 854744792, 484856726, 406801605, 191262575, 924122865, 392844962, 440878305, 317872033, 738698619, 167434643, 165330656, 928556809, 484768036, 714168527, 562288934, 445777293, 74342874, 170371330, 44580202, 750149392, 929312227, 843638638, 379142491, 873497018, 488390843, 380182932, 503208343, 560583688, 555983654, 366199071, 588218456, 456792163, 559823017, 468607243, 181714941, 248895007, 802210330, 287061417, 894451344, 297242567, 223459053, 840308961, 232291503, 912256034, 253366335, 517061048, 298097791, 795007700, 644312200, 112725273, 122310966, 498884388, 372767395, 412305679, 126894933, 190034909, 102460746, 313389624, 413008840, 929729734, 745313055, 429508764, 391910750, 978059439, 373905014, 9160733, 71938167, 682673829, 390385977, 377651613, 638700695, 717662547, 729487574, 950055036, 311091377, 178822082, 428580725, 522636468, 388671080, 609965791, 658153598, 841776004, 486994245, 678380475, 410933684, 734200604, 999576366, 712671108, 179503047, 77962483, 628862477, 366571057, 402872933, 207355366, 638889168, 686665531, 60231737, 347387822, 991976869, 360230752, 724973096, 603933485, 519183149, 792797814, 837601623, 609476957, 850965483, 518670014, 834917557, 182436010, 261725794, 858462222, 783861889, 537470783, 466689211, 141665388, 940536629, 176205394, 110824898, 270360611, 976955453, 857807004, 835381431, 956479440, 387551725, 219991969, 732620089, 537863775, 313877923, 526857945, 173810676, 146701605, 982312554, 976834426, 259934583, 193752078, 444118905, 606570312, 958227961, 777431619, 503255967, 15851264, 174753302, 758821941, 268395323, 859723353, 974846193, 827261456, 410655059, 400491057, 664396066, 635426188, 705389703, 445940254, 967129790, 812465481, 361219931, 713632802, 331593565, 96732398, 429973736, 300519118, 78165960, 849004256, 821564686, 386651376, 218333131, 165170379, 736188137, 714200766, 776241429, 184961694, 664462921, 688071888, 207305614, 105011746, 786313359, 944777301, 672855946, 838007134, 951804442, 775725404, 817838286, 629984829, 332853465, 739971826, 611326279, 786759224, 720663903, 912744110, 59937547, 36408515, 939092154, 709178809, 449353654, 310233112, 733100162, 408728069, 748042505, 764482160, 824053661, 424360525, 659833154, 328250636, 684711585, 740823308, 620740039, 783343290, 565435415, 627483297, 472642587, 887531442, 172054303, 546461412, 542405659, 427423085, 631163136, 367731750, 172463787, 170584789, 387529569, 651688837, 671129371, 604184749, 536455450, 418208534, 995481177, 823154709, 69049745, 496750152, 979342637, 970144235, 424688273, 518534199, 617775476, 438086079, 571693974, 34800954, 963139668, 645889136, 477650984, 258971420, 199301659, 232785008, 865452067, 513704624, 577538286, 741183878, 849523414, 37610341, 374185712, 436236386, 589418656, 849225667, 114426359, 872024546, 17664172, 259069706, 996567366, 960068724, 65417194, 652989413, 846073090, 828936456, 650462349, 125892197, 28818220, 394394655, 336739817, 682169746, 547122800, 509551994, 684155875, 252450338, 669665662, 124174354, 321939718, 182594714, 753102188, 212570, 227736185, 667310569, 182703375, 732623737, 181161, 501284141, 635454384, 899867658, 488820726, 382157835, 792867174, 18531748, 648844512, 26146949, 503306593, 49108499, 178748510, 443508068, 316040844, 983723810, 259240104, 211361933, 431226068, 592920460, 74560800, 73883799, 708038223, 481113331, 473493579, 712555404, 591181330, 762748146, 530622189, 87975818, 197064688, 633707397, 802163671, 801186862, 913968085, 947153096, 356199574, 783066663, 202291877, 28904128, 957827265, 913640485, 999041710, 112225695, 853779568, 176416753, 652283848, 518470505, 62558919, 143107425, 373533433, 974175137, 165463699, 427963340, 675519603, 923553152, 51034334, 179155979, 124287949, 160246052, 973096916, 481870381, 983714100, 319048897, 529780210, 23760146, 635470924, 642498007, 716991068, 156263806, 926149359, 659145947, 278479619, 652257320, 919589019, 315124154, 383826834, 142905610, 208926324, 700910366, 720136956, 103509315, 626842772, 992879482, 15502917, 602560438, 836060711, 768984259, 936081714, 18721106, 263263290, 858647025, 761036351, 773282260, 226215154, 243114078, 457961851, 130869602, 528216539, 892279249, 250467182, 285284738, 578115127, 533337406, 576527598, 731243706, 400199027, 107954188, 917804651, 685555048, 384233618, 914519902, 575036541, 731084134, 392573612, 800492455, 399003637, 844347034, 791728198, 460636902, 810800182, 51720055, 335829159, 503806338, 19909662, 973563225, 263394559, 458203459, 506258106, 385544484, 465632275, 615873958, 424573311, 167832436, 906989477, 389029173, 787740623, 98267326, 196605118, 422831319, 250773729, 388463332, 765212766, 193042938, 527476654, 563717578, 403124242, 852160802, 38975453, 57477144, 960438844, 815416224, 40698200, 879895941, 207752820, 158966052, 736847475, 107580503, 318588803, 882805210, 274057617, 339322518, 429420816, 745888018, 769895853, 534999300, 608455193, 892183014, 294443194, 677937724, 708366135, 710011710, 763930646, 315368876, 672363951, 996554985, 476630066, 684800214, 19145945, 979143862, 741114849, 134738786, 217752344, 3599794, 881896245, 177177001, 841730435, 782059280, 304270794, 256868420, 148625504, 827043850, 340308108, 809608457, 297094199, 330548520, 526289360, 598549527, 997884493, 890620019, 383157201, 496924421, 650517001, 906603577, 317109229, 733507414, 51260810, 427834474, 401727158, 179066991, 989074511, 805690956, 329423374, 367785870, 576411505, 702195917, 436857035, 187722859, 464975786, 179736471, 773525831, 755617659, 289937294, 663809479, 410880505, 825182120, 705144920, 946309965, 43581566, 94914150, 291360913, 139863459, 842243451, 835702689, 839167817, 671529156, 101508461, 606175302, 801958748, 237613701, 53748124, 375796053, 167575823, 920651803, 195609730, 112204525, 877290741, 324544210, 763513210, 169584385, 111676888, 710784952, 621759316, 954139727, 547562234, 268085073, 420719354, 435066693, 680128235, 471809904, 325733558, 719851557, 800935533, 334163071, 56511493, 318277138, 874803198, 195603914, 242992804, 857066774, 421085646, 587348122, 954428010, 936330041, 187007629, 913725636, 949609877, 231491044, 318476867, 480106312, 564919216, 920328203, 3419408, 843184757, 635289140, 799700078, 617391084, 17326434, 21370992, 383777280, 277871106, 752368598, 573014072, 424366244, 112317699, 882596795, 369965089, 169357376, 854196471, 682011778, 73281073, 145929986, 466426006, 694879263, 879018797, 585816051, 465889858, 223465258, 235995625, 298113263, 263554507, 533877740, 123041384, 869513131, 708642997, 523234711, 303250725, 932631148, 943694234, 912008286, 22565005, 664036414, 203926509, 425221741, 506085084, 738069748, 449811443, 999730561, 831049466, 702810474, 453166112, 482425181, 72517812, 879586868, 231848256, 863071772, 657410082, 567681985, 440493888, 996409854, 906327171, 250036825, 732714189, 478036633, 456117697, 504348375, 468159101, 782596044, 186918040, 116968859, 634542903, 461102842, 507742085, 214262351, 386107632, 821618852, 336254711, 745775127, 885138655, 176783212, 197850440, 49817035, 583015057, 208570773, 39781174, 841700199, 209876627, 528533739, 176551272, 167292002, 513563426, 201821337, 990283139, 163580768, 95104961, 519597448, 292672488, 901103459, 806165282, 677331579, 727153171, 36845399, 561403903, 576190110, 455287000, 60893419, 294035914, 12206689, 404564144, 540439219, 867798110, 64602344, 724770590, 27612367, 75601202, 850172255, 42743848, 484683054, 64697432, 554259113, 635925332, 618032821, 855076908, 879812879, 47255012, 80517451, 546377484, 894417984, 764329730, 5198953, 482515205, 870118825, 656909470, 424684888, 905266587, 599267695, 968802972, 609778817, 603336437, 408393506, 232621164, 154979066, 277798224, 907619783, 104636578, 700909385, 88775080, 622268858, 988705399, 66745231, 529733328, 443419520, 511382560, 446805733, 808559949, 743507792, 313397698, 753874906, 192248267, 677200253, 51001652, 804680468, 914156129, 4724265, 774071295, 807434121, 805234823, 428591115, 521309056, 344463539, 48320032, 848747686, 703987613, 52601520, 741855016, 264197831, 461614706, 71054907, 93182364, 242635667, 716866655, 666141495, 320885669, 767302108, 896420486, 973291949, 212345281, 625814988, 127394679, 191573599, 673878541, 844951281, 812731325, 728417132, 541798139, 487801363, 194322720, 155274476, 316794668, 492222696, 282889066, 276495318, 193486987, 864780066, 31063809, 788914753, 113809050, 900755664, 788570728, 904326272, 940312476, 814144865, 832148069, 155817479, 474940766, 411659971, 773652462, 561169169, 553262376, 31791039, 953990463, 87898876, 825252200, 184380536, 710868319, 566656356, 326924528, 629944124, 147243491, 768843209, 544659726, 96691843, 378001801, 395600225, 379303027, 357143681, 396021954, 6995089, 408936006, 716774932, 267533456, 223978919, 141578553, 594459012, 856905748, 699764225, 540017283, 899438216, 252192829, 718930719, 678443541, 331286895, 987396699, 537031230, 143276682, 600414485, 146612450, 253513990, 694948695, 411719127, 875910707, 235849661, 81807485, 632554971, 18174580, 227259254, 94945944, 165293663, 608119317, 898788199, 422748122, 719147251, 677626517, 229227499, 630929194, 33868029, 949359718, 153716531, 881289689, 126323047, 811592410, 82443338, 487770141, 627682785, 835163231, 399470232, 507574100, 937847057, 248819858, 891386083, 335465, 582457829, 868770722, 473213189, 511493397, 857240179, 797644385, 675167571, 799043930, 291259538, 496692576, 652851419, 993999212, 611513803, 367349869, 511799839, 122884815, 451854943, 581717224, 974446038, 587404654, 392792849, 345469133, 36082505, 282339152, 634193314, 319246723, 670089731, 691072143, 46748203, 320624540, 670789063, 570076335, 89600744, 13049160, 864459850, 465875465, 649342298, 749361152, 879348323, 717718093, 349973846, 66697636, 115524807, 266352770, 877608690, 476791467, 58968835, 395895116, 605259717, 251264181, 21329089, 356212964, 52886461, 413586774, 578842834, 623174434, 311258762, 566945340, 759188446, 207865984, 662165330, 116991447, 782314442, 749584429, 252056939, 983502359, 479987569, 127959097, 269098936, 745272270, 394222942, 238855569, 320494441, 336739901, 19706792, 637943367, 973149245, 635048578, 240476660, 151535324, 908273934, 674944820, 89270246, 120328832, 362398927, 550465109, 15695647, 637167889, 337781748, 706020746, 592753294, 391534590, 803002995, 288730621, 658933304, 203730220, 274657428, 749424658, 785394879, 419203163, 97517181, 27957362, 177246692, 658942047, 55756955, 553348436, 873083366, 118958913, 958272994, 374303516, 586423453, 639575774, 397701114, 601127152, 95030259, 744221602, 218490190, 721419167, 516522560, 364574363, 328437586, 206473855, 14471729, 993348540, 335386359, 559115888, 103684761, 414149379, 491059386, 644086078, 145983543, 939167550, 663030514, 429591373, 870689611, 925387318, 760025199, 825767554, 690821250, 81283911, 823689276, 901354928, 613742137, 720805892, 595519057, 428628542, 51538151, 620287095, 672861442, 557131372, 859603473, 875658004, 496787250, 585021333, 982631511, 258721639, 47089641, 825209611, 387673713, 600221936, 794684568, 715877941, 425997377, 119940538, 835474446, 935967966, 976302119, 618861591, 33351444, 249643076, 291170534, 870620433, 454825578, 433590944, 463544423, 646826752, 497067250, 777529852, 293254320, 308281377, 77750871, 222076942, 157416926, 588188926, 419152196, 371063322, 781569227, 327698019, 701153770, 333019265, 666834119, 147747357, 743491694, 340679992, 25924186, 503711359, 763714778, 483999817, 238883450, 715103885, 948386372, 119531739, 680213366, 436008298, 399482118, 918495900, 281624016, 888867207, 473191553, 353023861, 840055107, 893197021, 339875583, 165172633, 884843036, 546375722, 373191276, 594522578, 478866306, 835217552, 214641291, 556035685, 218454514, 206091462, 538393763, 630556997, 406028078, 683945719, 306357457, 766578308, 541028244, 529490665, 580731801, 413487100, 346303109, 535250704, 914191699, 690646613, 366791345, 360719226, 496378668, 6585136, 525378206, 828013287, 909820891, 950055613, 760164545, 845311210, 611267143, 461445780, 397401757, 745886150, 553670685, 972682848, 393106427, 323167200, 155162208, 473754311, 184541480, 665707126, 620590760, 16825787, 106752780, 776078872, 852124934, 930707969, 731260893, 878346501, 684808984, 13144819, 281405793, 160394766, 948298487, 503534359, 748061974, 782642780, 165592818, 321028516, 646841347, 733771628, 15569167, 807428102, 713882299, 624606596, 94001310, 341552549, 744714488, 254728604, 600059225, 245247836, 593791231, 637278227, 776133436, 622913166, 158741996, 151470003, 588096208, 187422445, 552136133, 329695649, 478498004, 143489138, 370584461, 921367630, 141760535, 475044219, 962164736, 782552059, 137052395, 131558756, 482292935, 597775199, 151946416, 871165631, 550583577, 620473941, 863957396, 597756143, 273634816, 390131441, 881230371, 396005875, 522253910, 576005592, 250706899, 844096675, 873695629, 890633604, 238020610, 713047229, 612789908, 638116753, 601219600, 800161013, 121327205, 446786845, 57324199, 93945280, 619640701, 311577064, 827886207, 437012966, 279481911, 893281778, 205350919, 398552367, 768843510, 942701810, 214565656, 567122297, 61019387, 409348861, 339770547, 591713539, 184347490, 592617431, 556633352, 678328292, 783677693, 70112616, 592261383, 662163081, 758561631, 560438900, 642607348, 310155336, 169506090, 881734340, 875050352, 283738334, 302456998, 660486340, 618086213, 130660449, 232345987, 791806602, 310457554, 55754952, 868064400, 300963575, 898592469, 711766739, 964119615, 709158133, 552989207, 958589590, 537113742, 771360511, 918613207, 488615328, 242219252, 942036356, 920809434, 282709741, 53178948, 464416978, 370385324, 578911005, 724983754, 371201102, 381817134, 387701703, 926728488, 352332820, 890399857, 435225392, 584210410, 655293936, 904880747, 665348178, 920960830, 754113504, 236413507, 619119236, 632103142, 564412790, 341649325, 926578329, 969261600, 105429660, 752215948, 634001421, 767005952, 606408034, 938858601, 628067511, 142744545, 779999639, 180136110, 51036982, 702949258, 651395466, 167479084, 770150398, 117634122, 19466892, 537965017, 790609987, 427254619, 784103081, 168408264, 257406565, 48823297, 631793115, 758781477, 854398981, 625732081, 746272709, 199911595, 523015181, 606831145, 578301976, 63710296, 376624211, 424898144, 401170136, 760404550, 514225752, 651968400, 370339431, 846341544, 236576993, 552319995, 996572128, 125491800, 835279291, 999703995, 269041513, 601600567, 707305659, 547515933, 173639648, 741981997, 131455026, 758999789, 83665723, 571618031, 832439785, 285093290, 577623855, 690786479, 269854645, 905253601, 659002538, 618079557, 24343200, 242633880, 234383459, 818503385, 673488073, 270306390, 804075121, 914931212, 876344086, 503501357, 825186205, 263397338, 712585074, 138780074, 148359792, 679617867, 177816278, 384372727, 885662786, 836884064, 443093671, 384776160, 814497543, 386085407, 965064839, 229353868, 122669735, 931695448, 64586671, 185344547, 7658898, 732432530, 895827656, 683502791, 456873662, 534651765, 275687534, 298971362, 544437719, 660404764, 720240632, 883754908, 113900621, 63579982, 452071996, 735022699, 79011845, 949814139, 803534104, 241911633, 981786110, 769419450, 324695746, 566985816, 572131946, 546784516, 185442037, 54707547, 808745388, 908121193, 330944355, 527532699, 781969228, 207178788, 729791173, 883963351, 643676183, 362609887, 789571365, 442657970, 652757863, 917057040, 754359464, 8668405, 472453089, 630834438, 656611062, 792557652, 613076933, 47405766, 175100551, 447415147, 708169051, 620085698, 718328274, 62344110, 519300933, 184080418, 11284588, 36808639, 618808891, 440907833, 17263894, 798926886, 385190427, 561912622, 645274106, 378200386, 523961867, 578386990, 533685463, 469604644, 664886148, 990393393, 563040325, 918315930, 243890652, 595334783, 513972685, 498886787, 10779730, 695797300, 787861563, 418244307, 48400191, 857055937, 529287887, 389016353, 56648801, 403386671, 301686591, 462246983, 537632686, 453077440, 15726478, 742799876, 510336652, 310794832, 423659300, 750532468, 125009031, 786627685, 552464712, 710313362, 891918374, 641465172, 679590986, 112018208, 786457664, 756035122, 109583544, 271760005, 973876313, 348463069, 240027896, 204978574, 295453035, 862671070, 905872565, 401108825, 115674636, 438059294, 990493175, 894737593, 114075416, 152850800, 742809156, 33782630, 771298923, 169425676, 843974252, 437505680, 235125595, 873895791, 717560280, 586162334, 172418324, 301936712, 816278159, 439891783, 179106829, 232147586, 659330450, 530336699, 444788127, 612143029, 346640411, 307713502, 924891530, 717404799, 889092563, 759719470, 453249632, 382424228, 353546680, 311363055, 161084300, 124308672, 225899443, 686561808, 697570840, 418157634, 423806368, 62491132, 319668722, 273570307, 206366950, 770942801, 63078564, 542991644, 881104468, 63320698, 479030289, 300962729, 455083191, 675267790, 85306734, 890253341, 895299245, 797985939, 903182710, 32121247, 559859981, 568230332, 983994522, 904997822, 619104977, 851547845, 965328534, 831498231, 99535738, 781830883, 428410338, 369741221, 243459286, 453537398, 967954640, 547314081, 585331361, 532926198, 773220822, 827053007, 922384374, 375618198, 266160963, 495068536, 742086919, 485413631, 451751209, 967637922, 988165466, 378127184, 531850666, 965515120, 113409624, 839029758, 205975033, 206434176, 256082279, 389908251, 714591943, 869953018, 347503381, 121979204, 801223288, 464663668, 44138865, 29646467, 929435979, 334915885, 990729492, 56547370, 37086904, 294114306, 937433258, 918223332, 653790691, 453414787, 103643291, 886257548, 624108208, 378756494, 742949184, 756076487, 82127547, 36456615, 136943371, 529441183, 174125870, 815689384, 167579784, 497883211, 684941083, 594719707, 80794188, 339788718, 940631772, 737909210, 94310471, 330177422, 242066068, 370852989, 635357234, 679618043, 689712586, 827941134, 926741638, 778706804, 833261488, 944014153, 309206024, 920399054, 898250021, 838737678, 394812732, 217694944, 913711247, 43185241, 554531586, 360530424, 31943877, 847801550, 274586828, 743629409, 792421234, 276098944, 450733600, 280795548, 755246679, 354141691, 483031142, 625082016, 866232745, 961797840, 499036668, 423184048, 187213381, 695397993, 83714781, 446702970, 526894697, 358545673, 691833372, 311114910, 591916937, 820696804, 104041443, 884663, 54172648, 821532214, 363328924, 258284963, 689212351, 871287133, 501158321, 959801353, 712115184, 755842521, 147838450, 308933842, 626445225, 689859263, 701515746, 510477305, 560196805, 447825810, 137780711, 92038591, 967842893, 403142144, 329417063, 704707550, 656755709, 739301913, 805675164, 650586776, 402311371, 161533860, 639934889, 815472398, 16276507, 699668637, 858505332, 301308015, 582399279, 80794797, 51734864, 215307516, 727694202, 663189894, 294567305, 426351882, 153574053, 748339558, 840650769, 950884155, 50584067, 408518074, 134833367, 267907121, 149984291, 642950281, 906245696, 804822540, 113110680, 120561069, 4694346, 965826092, 22787527, 775266255, 364916281, 812929891, 199601206, 834031340, 802137387, 500497475, 681742072, 657348152, 441253030, 85349420, 251548650, 804660362, 239911407, 731818479, 217489964, 93349823, 655711133, 458165516, 181010735, 167125641, 859159144, 381253455, 344478285, 53846748, 797632112, 915821932, 716133650, 835390849, 128087323, 640572157, 941787242, 140620891, 716433232, 841707583, 942767502, 848143298, 621389189, 457519092, 929518534, 360679041, 85067453, 503426252, 887433891, 351188268, 534191343, 896165794, 130442904, 212767040, 933948458, 640477778, 368296325, 256947912, 76903152, 486822579, 533919380, 175592937, 563535242, 281935784, 680016095, 55542431, 580010000, 176848400, 935678806, 365602520, 24307975, 221031158, 338901572, 837601500, 764696954, 326599245, 670958647, 264393750, 906890277, 732850185, 45709778, 167197117, 146957330, 863317071, 524340996, 826129138, 596900677, 593193661, 776995251, 801364503, 244923281, 999966462, 221112528, 522453337, 787347672, 663274245, 255304814, 453257698, 437357743, 261206987, 165820676, 876089130, 699200555, 367634829, 12220604, 634739492, 787437260, 567262715, 204776596, 126357195, 90920997, 924939964, 490639546, 839053033, 576426067, 856487234, 3883253, 639479584, 221303741, 515031933, 202819862, 160725359, 200603267, 965045510, 47732578, 860306735, 252382102, 736817180, 11883306, 472273200, 665257845, 711895371, 977307391, 62691670, 428534592, 182740684, 935737313, 201171043, 264242730, 660387918, 195088037, 903508321, 339738143, 108991491, 230768095, 318966918, 405669659, 940038702, 832074408, 66107865, 214704911, 990644625, 685821241, 689105762, 580518468, 889571919, 43807047, 552118927, 829928540, 962225495, 660775613, 133196726, 899776646, 485313819, 880861483, 431387418, 13155748, 594772122, 119244321, 671694735, 540064025, 164703110, 550692103, 848628755, 114840705, 101850939, 271416695, 786663733, 494698628, 391907547, 31382643, 927666304, 717455100, 196345733, 851464199, 589675245, 243259775, 538965609, 152853264, 810407813, 266249188, 398411554, 646779736, 767099327, 838169316, 410549696, 716105744, 155485767, 622571708, 949713374, 765966289, 866959589, 527622845, 451118148, 795207854, 888466640, 680742387, 60017598, 148376667, 247964500, 915488084, 963926375, 635981006, 58758348, 306986730, 860563059, 790584551, 309481462, 565862883, 410847860, 238625379, 368934199, 661183644, 842905870, 671200244, 262918432, 96820254, 579119998, 523009432, 52470745, 560954711, 117363437, 246946899, 164994454, 256805313, 570904073, 470529041, 512623578, 110173948, 840238924, 10412346, 591651531, 964741693, 209697998, 745181238, 863667984, 556536845, 429748167, 607832885, 187073678, 263500504, 626025620, 388635579, 632325330, 663704687, 249934304, 144278266, 255719181, 453737352, 651102951, 519874039, 656815889, 394741936, 982485242, 509425497, 645592503, 375907838, 434143114, 587199514, 536715175, 290192277, 970251531, 29080054, 644023030, 709239242, 376987875, 76777322, 608712001, 928488203, 770067794, 581499387, 213220148, 156946870, 208876059, 17852425, 174526654, 112923859, 460983314, 887302085, 661392523, 774866235, 625728564, 597423561, 11716062, 698162933, 662293024, 65454513, 969848526, 301218080, 424673439, 398725698, 742840608, 999224857, 924379709, 437867631, 444225872, 437108717, 804376397, 298188386, 744128141, 945080197, 709177328, 616897282, 249356670, 267748426, 530252870, 354734086, 703781416, 584487447, 773339552, 104451721, 556837066, 831050005, 18033764, 415688915, 244879889, 91868795, 845550254, 159005192, 169222138, 674799995, 617048332, 27833408, 370339675, 829867834, 318549645, 605693369, 456714130, 161672948, 680775023, 86135006, 419400074, 119732173, 451699185, 358369734, 117884062, 397553876, 352491300, 473281280, 88159161, 290926035, 593464667, 780314110, 814382708, 11708659, 500565404, 768203416, 51678757, 944726955, 395262602, 992404010, 980125383, 898992246, 747241047, 242532491, 384555538, 549994513, 145162642, 340965905, 567376880, 234045133, 677381637, 270405302, 21830931, 775814547, 7672190, 773832076, 645985313, 854491797, 918419478, 262416282, 707261830, 330420190, 680138585, 606529254, 799372449, 840214669, 835545207, 531275277, 484434626, 88211524, 207227635, 847460416, 953754344, 376162937, 59291605, 92622651, 883718144, 447996207, 600984925, 900979258, 928092943, 717155718, 41201827, 741655353, 593019240, 150543419, 933082926, 457302268, 900905392, 734524745, 319983166, 538591263, 305264191, 664662570, 631702923, 180753597, 376507301, 534136330, 753110593, 78947626, 922331786, 516724748, 355039105, 204130712, 748835431, 569315440, 66583883, 743941435, 883483626, 591962963, 713562027, 198101529, 462871948, 953633920, 793851365, 892324483, 802194679, 13045, 422220862, 745208971, 914708476, 781023925, 581859079, 649925343, 285379756, 592092864, 544852590, 910347269, 569917244, 473632696, 429914097, 66894551, 868982409, 340190464, 872757052, 793826169, 751999833, 907575326, 811271848, 223972162, 394329889, 128775693, 93874158, 242645257, 382136296, 943762871, 171075504, 3758482, 701788410, 882834018, 393999866, 894221658, 330696360, 884880143, 473868157, 208357313, 582857957, 622556712, 789985451, 23514085, 941143022, 790053216, 709955431, 198199094, 491768011, 539609056, 62873945, 420976295, 788618423, 921798236, 863131659, 463569707, 114759904, 101784134, 999342848, 293282722, 264005206, 963640007, 727410440, 55532135, 830165396, 37262970, 955630393, 708880888, 112068990, 576278702, 568255705, 413522373, 902714386, 594670782, 572045322, 955471241, 29025386, 820851884, 868474712, 880155367, 528997008, 297420570, 124871023, 175774186, 120992437, 316442674, 721832718, 677579251, 436195484, 720226782, 297580975, 241810971, 349050865, 837762373, 22577263, 134287133, 328644337, 567678059, 270581672, 951346026, 480416968, 51510456, 36973564, 407796278, 315112888, 244687291, 68492247, 883700490, 29301942, 580554254, 17124876, 474189113, 385270765, 527479324, 558966973, 289086591, 433333632, 877721116, 718588433, 526174624, 418746227, 79647509, 275690227, 297379501, 361846489, 780562068, 152505089, 506100600, 622755258, 708457882, 143095031, 602804501, 557331552, 945087821, 520491476, 75511352, 337245529, 335157045, 533519762, 18758935, 386553551, 909900344, 222528706, 157125749, 626293238, 266925136, 529179224, 381067013, 745022064, 185851484, 449398955, 476340203, 185006115, 734672936, 540057949, 735497190, 574661837, 278011753, 992323620, 994468165, 50309539, 821190829, 476655175, 87570567, 174653916, 937677580, 822999421, 868198324, 170316533, 961045235, 978932299, 198173996, 794041417, 670050407, 580627901, 736039078, 570772563, 504689885, 129631816, 70109625, 472737893, 722937401, 929473811, 374477489, 10216637, 16690937, 749530014, 38719015, 840254365, 948765576, 541699795, 698721633, 92415009, 35018998, 415239604, 729495824, 688550975, 292320998, 773626799, 263772601, 702847722, 275452733, 412332896, 272025092, 129636749, 69116735, 600397744, 4488739, 359986539, 150428548, 112173468, 49556767, 574060785, 681695961, 838678646, 561692018, 110876551, 169681133, 826182601, 470742219, 412800715, 355241836, 856768436, 260597391, 770314854, 302804269, 80027026, 140721491, 97706815, 738750579, 71943312, 327064531, 448729259, 561443567, 275310563, 76305883, 936297483, 257954947, 734148244, 189378732, 958796533, 183994159, 305528589, 262216048, 275595889, 339560119, 979140230, 360260655, 26634615, 546773922, 238907007, 45593558, 993558375, 646659450, 834136279, 779887250, 716938500, 999774389, 564832504, 690079475, 46733499, 968232410, 6163394, 504904303, 682808884, 633456307, 775611496, 823206228, 82712671, 812895693, 845315587, 358441764, 14714199, 926165282, 775796953, 865946023, 772303569, 113683291, 827038570, 164677630, 845576585, 215108824, 484166418, 803942535, 760519739, 421066940, 479671628, 940474706, 539639083, 185421531, 435788811, 138371200, 165501717, 731813088, 243009794, 25105963, 75166750, 739149652, 660406579, 633777609, 663951855, 20674936, 299667961, 673741032, 296319046, 458551226, 426636026, 565326684, 287100367, 478718896, 189262050, 601402922, 366785566, 829929679, 46223414, 189797723, 479483434, 796350311, 167739796, 990876109, 751643095, 129998184, 552620236, 683677689, 205884853, 278190052, 787587576, 404125718, 38717948, 897765953, 510741503, 561273477, 377004056, 738056958, 582942035, 774019778, 606032062, 204529697, 647288046, 418008031, 103474887, 694560094, 768803978, 473354616, 182440383, 238344536, 565616537, 502653361, 568044620, 563926309, 345587147, 967178065, 830063634, 622063266, 145095359, 611360745, 553174380, 104625900, 338946639, 294918443, 764385081, 837061792, 278865672, 657282461, 762097972, 536498312, 443871278, 650951173, 455559012, 467238255, 694352779, 907645415, 664554686, 734747698, 172408103, 471494986, 369323513, 141904425, 720474986, 44179960, 864331344, 347262751, 70170554, 901970548, 948534028, 37255498, 613884162, 699056021, 610030423, 936323934, 797026251, 350285140, 744333183, 784066470, 357492883, 933630086, 665726567, 628347824, 625866150, 665497560, 617329017, 243375193, 654690803, 79818133, 343257793, 528597367, 718119589, 699748163, 637708065, 27631604, 553030206, 836056911, 181091095, 440310352, 831751373, 377783149, 831161748, 876117316, 156409946, 539050332, 482955845, 579007210, 778107277, 723868804, 960469261, 80315641, 601286334, 917635008, 266635127, 569971161, 119372004, 906267832, 857051916, 701300606, 598210644, 9687365, 976962032, 334824814, 349216702, 125277147, 586456027, 600056962, 152736021, 927907645, 65278143, 292324810, 213214331, 6944091, 456831043, 549473889, 956197156, 203344035, 407370166, 899304802, 293903044, 18541980, 771373077, 216318153, 529065203, 698422714, 499278603, 913891607, 894092794, 995996744, 661263189, 382626160, 596256624, 715630672, 935836916, 318408265, 837622505, 432852275, 695822706, 331989995, 801521737, 711712640, 245090580, 495924443, 954561643, 445404866, 730294648, 619967043, 14219835, 224292797, 575168992, 518527252, 709252959, 879851109, 949155676, 625397491, 229887572, 679841292, 443737865, 696840829, 678988664, 939846705, 86490631, 232573670, 920835753, 266859255, 503973399, 983339838, 757178279, 638239012, 890725776, 301709453, 316342134, 33886571, 880737262, 150508803, 410855119, 863788624, 207604447, 924304527, 788709039, 192215143, 340165378, 701825033, 480580912, 905342988, 401728098, 634638158, 800080559, 947975557, 632502054, 167422785, 115761801, 885871543, 788152820, 402605643, 789975992, 635279210, 876695313, 46929197, 760550735, 35098346, 502767275, 75223684, 100949189, 798394747, 141181665, 545298470, 189128394, 476590600, 645370312, 283541081, 428129179, 971577845, 496636788, 2095084, 980659818, 636404686, 931674545, 418031164, 827928438, 199308214, 643827232, 835495321, 294730495, 387371668, 247066458, 136114452, 140522430, 977994711, 829723903, 409142637, 58429965, 539217591, 871945229, 789616714, 592363198, 808095386, 286287361, 727014692, 392422975, 17253283, 951277873, 757303372, 227539243, 44251297, 716018219, 549539307, 10842820, 728356585, 758891677, 341787669, 124679064, 965958429, 821069434, 814575530, 56023689, 453658414, 401824475, 691145377, 233506284, 797868228, 183842455, 567356442, 453782118, 772976530, 943754983, 356434115, 406805043, 329361701, 285737459, 555343822, 166155898, 113115616, 175879015, 88280879, 782259649, 228744881, 378629689, 187400733, 790993273, 733180818, 529616534, 763878807, 492913471, 939226073, 255553427, 361695507, 556988296, 467224429, 175665682, 144237207, 265687379, 491387183, 594047886, 900529401, 491305314, 370513900, 870363731, 291022555, 999343903, 943528669, 465995417, 545044218, 737723448, 257824210, 567178665, 465968740, 824842165, 811958843, 340086312, 239750329, 244517442, 649230956, 869918408, 798898985, 891154931, 768766084, 47070627, 607897750, 699495999, 86198184, 385225375, 891422291, 7696132, 106155135, 439453660, 281496841, 51015334, 314339410, 407294781, 993531369, 142899367, 925598538, 390626792, 734051436, 260228738, 837012683, 987450648, 275895065, 738892647, 518804315, 344926100, 410099888, 306971579, 550307885, 743258979, 89976655, 711002310, 633479336, 948766500, 959696356, 206253832, 975954265, 936793886, 333007657, 496156001, 488695165, 557654516, 73121656, 923238620, 980299987, 210055210, 494322403, 602285559, 344471462, 518935924, 321196749, 604280036, 311247039, 168579143, 381037688, 827888522, 734964304, 993849473, 460795162, 975410278, 548785087, 118214412, 947623986, 764863671, 185701808, 466405123, 763532805, 383508813, 323636667, 421383856, 912654341, 247950510, 969459716, 266350737, 387677595, 536038398, 652216299, 399700387, 215201218, 649873365, 909485222, 630245217, 186623554, 147731289, 664885118, 296616827, 980226656, 168357994, 585493073, 63383929, 163247565, 577432147, 250411834, 647335104, 987917947, 440048412, 989955673, 29737047, 937487709, 395849667, 95895102, 771133132, 367450099, 727192803, 687731713, 847783335, 287108793, 501970448, 58651855, 712622615, 758572425, 269115737, 992872064, 248906686, 523875705, 429785975, 917046313, 832164462, 700528086, 392276464, 504274496, 483810876, 558138072, 436000173, 556592010, 413177467, 51448609, 227415585, 825479754, 19524441, 356437186, 445469757, 704927822, 687426383, 776541234, 786041961, 260368078, 268817755, 342095768, 480653838, 792995344, 530873113, 640737510, 350835097, 407037121, 369454546, 151803410, 420879414, 608120983, 669778290, 289103925, 428292208, 455935804, 969178572, 822331362, 106969874, 295834054, 759339441, 786317125, 541580196, 166595790, 401521348, 511597252, 67563175, 858772526, 460606672, 923050057, 274388616, 757209001, 921186303, 175992268, 265720890, 580459982, 255009407, 900166473, 498924147, 434406142, 155829542, 83028344, 599301714, 777306184, 724682703, 795804590, 32437401, 373428121, 235447244, 893764058, 516114975, 327833637, 700739036, 623757450, 478629858, 170535742, 530423089, 205532478, 182765733, 728120705, 416941117, 143147639, 750766891, 665593673, 369681375, 461306549, 558144532, 588927141, 453804337, 545854395, 892680753, 424926793, 697512585, 190060185, 664537950, 115428789, 707048154, 83228124, 728956198, 389570571, 968852768, 98677824, 241544515, 651986877, 359063927, 665090445, 454346154, 576751343, 116167509, 392803556, 41358702, 99805582, 40241740, 544696294, 372708992, 512380976, 582507968, 684157098, 400773263, 701156053, 52583229, 97741260, 845941672, 142863035, 97860795, 959308883, 80171519, 113806494, 255820502, 130726879, 19790810, 405877118, 698315546, 239685908, 549773524, 410328477, 92118420, 555908317, 331376717, 727792260, 827449505, 97311253, 778272475, 752502128, 646217811, 637212870, 693756800, 886740841, 765417455, 544425867, 164236823, 191727585, 863695838, 49738007, 497853818, 251169960, 668620122, 820404839, 304330181, 914201600, 969787973, 884957450, 995732688, 532920979, 608268437, 158760421, 44151381, 978368966, 671032535, 743510694, 296645483, 82795088, 163292831, 756180434, 293149215, 500027718, 479003179, 368753917, 762528537, 166475034, 451256121, 831518399, 789583115, 613742809, 346819766, 529706978, 989882314, 309417911, 433694572, 807594826, 918889970, 520140811, 215760172, 664623728, 394184615, 184749597, 548009752, 930863579, 317874956, 698213348, 214144850, 366575666, 299939730, 33206530, 247213439, 92311869, 801768722, 397466400, 432336696, 67787477, 173663654, 664101306, 630029237, 399982024, 421763077, 507305174, 206992528, 892279244, 959943346, 537366749, 115374323, 987218950, 200264700, 507343551, 2731291, 403763765, 60109450, 364739289, 410406863, 612352150, 91799694, 645175397, 233219100, 417801837, 450872782, 666548914, 201366328, 865768500, 34211026, 760329154, 102740178, 528735644, 522745842, 880205046, 92175099, 408050468, 432868431, 602160438, 985777290, 941003019, 872288968, 122731044, 490349054, 713712022, 312985274, 416638085, 289568594, 38470830, 264415423, 630147597, 958354328, 183924595, 340628953, 637837776, 329155074, 352132282, 274528905, 972282951, 847316109, 77611406, 326148395, 253045180, 502206153, 175256505, 555294672, 580511090, 111252931, 368735774, 595778926, 460926243, 681516896, 169481904, 754280493, 32967371, 85647441, 559831404, 653302698, 686534856, 371239894, 476596335, 21827374, 323613203, 243306642, 146265493, 880194282, 865497150, 374488268, 344002952, 78934724, 605376620, 699877127, 600938103, 915073242, 623017235, 109821732, 142078407, 722027034, 656221229, 81258794, 109949152, 831529754, 706247039, 107743556, 594334213, 927115263, 282707002, 495985687, 266011332, 695040297, 982437040, 249915430, 931067751, 929114536, 514276386, 714065940, 299717748, 76813632, 744232866, 969529288, 991214654, 27070458, 265357903, 451403613, 997404555, 456516365, 833739461, 979675781, 261079945, 708169769, 215923074, 855207005, 775698427, 801696581, 208428725, 770753712, 869195153, 204197169, 615765245, 67828774, 609938050, 632706086, 873221645, 406798613, 105930828, 612925916, 250658843, 341439534, 517957639, 883577205, 82863519, 595656068, 899815985, 938406490, 560052779, 408104187, 150387617, 424438062, 156342221, 733323981, 165713874, 111570566, 575445024, 377934372, 337806848, 995782134, 972612076, 472833030, 862671243, 464426493, 126569367, 525128095, 402248200, 486498407, 987105524, 204760317, 328466013, 634331762, 360530816, 812165260, 941739762, 774892862, 239303112, 739960755, 812021516, 671209398, 888851031, 64602238, 631513467, 963400565, 664490530, 321164705, 29893913, 500164258, 417658035, 192536152, 679885931, 319765223, 54949917, 812037676, 372753856, 899119195, 938626430, 725753758, 263808225, 542053229, 661601075, 829335450, 424460480, 191734732, 525165770, 336253152, 931155350, 529960297, 292430550, 587523457, 811349453, 151464163, 205835154, 153859518, 768073663, 817850435, 781758898, 579096596, 686958103, 878169189, 613571447, 428906761, 981436072, 98084584, 190064073, 515379977, 179519764, 392373510, 14289689, 364194098, 655395227, 155177503, 168029493, 790849335, 718751532, 654387818, 788407256, 346349429, 818369682, 81624395, 678997002, 588692850, 514900412, 194872999, 317223743, 127223062, 215673663, 266041887, 736486556, 751960806, 233903923, 167820397, 450690654, 332320549, 372768127, 981814496, 619090598, 494096299, 616265157, 104789641, 696588951, 145617830, 256283826, 859279639, 257520052, 490292946, 784916125, 807035926, 40852286, 562215850, 896768652, 348221761, 898733165, 804788104, 648878203, 726412962, 215787091, 63061408, 978273712, 168585014, 788054327, 689141105, 725729878, 769608634, 855503941, 52272726, 396037057, 220304181, 59350196, 138864974, 631109610, 395935559, 300274044, 713711069, 686485580, 130130628, 688716713, 912822467, 793107302, 884496198, 40884067, 851421699, 815927266, 340675919, 631448671, 200836378, 760721997, 445402720, 990853690, 199557326, 428461611, 107184484, 909972832, 943943421, 506232939, 30526570, 17029708, 93682532, 55707545, 493229384, 446992648, 773501967, 265800019, 31467962, 775855721, 908003864, 621056161, 50923412, 786091235, 722809944, 478321486, 302399461, 465564703, 116767001, 24648158, 832486100, 841358107, 814803474, 742630141, 208020184, 161349930, 108523680, 546817414, 415308173, 558060597, 974756980, 989525225, 795041081, 269093111, 653192630, 380759674, 732055357, 355455824, 350639630, 349993487, 161387812, 266855778, 858862383, 119853880, 125645323, 282134431, 529107974, 591396747, 854307912, 222756291, 953218453, 649973808, 4541001, 876374626, 881006322, 222524609, 91180966, 411841678, 911865670, 791890908, 684770460, 133824697, 220482076, 33872841, 124763347, 847549623, 527886510, 751461280, 622100497, 568378357, 547508245, 12867459, 126077315, 752447830, 676442500, 407197408, 496836928, 501356967, 632117004, 707910041, 96734466, 487671957, 838339072, 805921784, 490944081, 331340851, 866621927, 964563975, 629247039, 277813560, 17575947, 822730511, 539185642, 712647768, 585093383, 79439345, 333963974, 23490268, 433502484, 658538343, 996158263, 684991256, 433699461, 999687167, 895967388, 70838841, 430921622, 258189777, 747598267, 583802092, 249698352, 793391115, 937240818, 203453623, 194499772, 453342323, 815116060, 341326658, 603014057, 327361396, 481744785, 477717167, 447912037, 68085061, 25365214, 372602076, 653335226, 397051159, 960933692, 42698736, 24783383, 703535299, 69831634, 354226013, 895433493, 580547700, 372825745, 429680900, 175425367, 122472101, 935684751, 712210905, 321796656, 552710467, 798881091, 458640818, 100548775, 739967322, 811409240, 317467362, 134898976, 434664811, 443199676, 23062718, 93899691, 205626828, 713047837, 243728220, 142260190, 401534696, 613443960, 169724481, 633306281, 504547257, 133139823, 604971392, 989783791, 491335329, 52894414, 937913813, 8661853, 900558234, 810153796, 632928598, 807440700, 32700684, 940025604, 18760794, 14873181, 983782861, 809104269, 544014927, 907457346, 199080640, 293963468, 525915073, 166645148, 302271759, 825897495, 600173437, 762619600, 225202437, 641001712, 829277099, 890365488, 48292904, 297077148, 917524246, 71835697, 9675322, 388869137, 543895613, 385708882, 107385949, 770549752, 270474568, 992730809, 194767022, 773560559, 749481116, 535273531, 833969371, 496281865, 359842334, 790479669, 192061098, 574750047, 499655081, 833037230, 428515199, 879133228, 821565126, 477913331, 892802526, 698086845, 62798361, 382572087, 474642929, 933316464, 801233696, 468197913, 486619486, 356142424, 672161006, 651628433, 189150190, 41703350, 610804178, 861249356, 328358296, 683458148, 84060963, 474572139, 758740555, 299876336, 344952066, 702884913, 793729144, 293001617, 654150485, 422639147, 647989679, 705687041, 966107758, 919782653, 173523512, 251389143, 124802347, 737721329, 907248537, 502206334, 86717779, 105206064, 84099482, 775868912, 127808160, 859434163, 927960417, 311622005, 439116906, 74098843, 719838928, 870329736, 811916149, 877379347, 19847044, 333549253, 509262209, 37641232, 958477979, 422481388, 181053454, 782344927, 428251529, 629470271, 422143615, 936455627, 542290908, 992247234, 162506983, 228849806, 879707964, 996485375, 50752989, 633073336, 375498946, 744786176, 659179459, 672689245, 390323514, 272514282, 997326174, 211491535, 73241187, 178130803, 827114690, 32035282, 923914974, 708897549, 391320319, 307127579, 633066805, 190259559, 549643428, 750294150, 369296292, 287587689, 588627410, 345019479, 697881897, 907754447, 794454794, 861172804, 162780862, 7075710, 24350563, 85947065, 375171597, 771634401, 542158404, 87597247, 517844317, 326373342, 223521870, 582313338, 640347332, 427247940, 841666388, 343523614, 135856761, 898949437, 188553504, 289498849, 450212560, 325480187, 400904386, 158097394, 331465730, 68949817, 829043537, 600106383, 962737818, 194168505, 719421389, 594561903, 925782691, 928195585, 806840245, 508835570, 417415700, 207916630, 730856323, 936324224, 492049540, 869319718, 962524940, 302987536, 291187667, 975609513, 645906917, 460237295, 775979552, 323811028, 318278001, 262668034, 432600604, 226727896, 990151290, 494257211, 894948649, 123987657, 272765421, 899437355, 607179069, 568972758, 226711749, 997865951, 302803957, 724742042, 199044482, 39310785, 709852123, 561308691, 737131462, 715400327, 455580794, 744228443, 465864313, 862775117, 448978205, 128912523, 923988193, 730783227, 148158515, 128005723, 98595528, 555886808, 785937865, 93632290, 211576330, 520848633, 467228207, 991273999, 365891502, 900434150, 222375400, 864039247, 986027358, 967480685, 356979863, 341384031, 474265552, 17486377, 589443547, 333785607, 71626539, 379085975, 350376774, 418601593, 926102185, 772737751, 286227285, 322243650, 390989738, 449150790, 868560507, 463223420, 224485420, 449985097, 147336067, 894290837, 402691311, 37797301, 283365689, 263728734, 149116903, 671058267, 430049195, 961423967, 968805031, 936760415, 105928722, 623688174, 794727529, 936733019, 688325325, 306260103, 826075988, 89719937, 32067572, 727104248, 240676165, 635964644, 703783494, 850112976, 70344930, 277832439, 837980107, 217196934, 124766865, 620936539, 243049578, 505728337, 262862623, 767546330, 42613568, 914771863, 7073915, 648163927, 917229477, 259415647, 775687438, 346904435, 474559098, 943111242, 719744435, 137507988, 572800590, 931467007, 537626629, 91288467, 864677257, 145325148, 990337415, 11994122, 367804203, 896407211, 213903328, 469253325, 934813916, 119626595, 890367644, 30187065, 327700806, 226139301, 877516137, 293718147, 25920419, 358602925, 279228180, 335074482, 450852215, 186422125, 994748754, 285467277, 271759827, 928115706, 125664085, 941645052, 351650958, 672470307, 751299165, 148351648, 899789225, 259778549, 41832045, 137679530, 172572785, 161566108, 203447555, 650348273, 728688297, 197350171, 480651776, 499649497, 468752075, 140246760, 81066047, 732232899, 126583289, 990404451, 472713178, 921104232, 616477480, 75486142, 149662305, 322371007, 54157776, 862173170, 624904837, 285945241, 384080969, 160142453, 284625173, 881479655, 922669361, 297403582, 962130633, 568375582, 324525232, 788283875, 494967697, 806316416, 419645398, 571514644, 237976154, 799098544, 823273127, 279124968, 206463151, 942924173, 620129221, 634382422, 709367167, 171046891, 896501801, 685649622, 910101380, 623071564, 770625988, 832857594, 626059261, 268646826, 445750026, 722527535, 116215285, 412358791, 282589260, 37248637, 715525319, 657632524, 859649310, 341473828, 622699626, 929202122, 695233532, 369490590, 411024187, 698564497, 16764793, 190679347, 231240444, 191653615, 620926603, 155546218, 273350998, 680012819, 594692094, 631367751, 373678636, 193338347, 223914556, 79513499, 302208950, 307597422, 417795460, 283280299, 37313753, 734158912, 649231594, 663391001, 640252661, 992786580, 38723022, 880598191, 41048136, 246968444, 796561553, 639994686, 306221930, 918860639, 70524170, 701775666, 758708455, 599581486, 112361635, 728350626, 612151866, 25363778, 128617155, 537170888, 38061559, 101665104, 289217598, 241182809, 475387906, 859235803, 459202196, 726650262, 360835210, 357272936, 545963110, 929581306, 712851368, 164949229, 681210606, 977313550, 833820462, 689346232, 162384329, 626549564, 155514952, 82577757, 480967462, 931679028, 538202263, 997511120, 43724190, 853030360, 123665298, 877456406, 774238865, 412083869, 906222609, 256579898, 218022587, 1907040, 695175690, 73512134, 652431294, 550108625, 151274283, 581405629, 271961884, 510461730, 618964590, 796143250, 887405612, 514177893, 871184289, 300099744, 516092275, 701008871, 422131012, 731374998, 840658071, 340642757, 624241585, 52635739, 242441263, 521446609, 526028433, 352013061, 450651168, 109269684, 346618725, 208577903, 42607175, 116152041, 298588646, 752009827, 662794063, 18948109, 560666269, 890924870, 391213186, 600995342, 688655125, 952612197, 970354038, 931006674, 322140695, 406145810, 719693105, 572122822, 324624869, 684329182, 431360186, 31150906, 838370613, 468940778, 638339683, 989780789, 627612060, 745006136, 664775532, 250728151, 710925691, 189248242, 925542783, 359013155, 510962624, 831897149, 537020873, 23949978, 354817650, 371928130, 930116671, 327486395, 431584563, 683568148, 956017286, 317245341, 298985474, 52438498, 91457790, 495921842, 368200035, 997414344, 951159225, 7127380, 951615375, 655384184, 378361218, 578335649, 937743717, 494216195, 894998337, 398101823, 5786712, 470094304, 736240894, 438556967, 948611403, 24462053, 355044531, 851771614, 128835350, 147283960, 185751169, 765288011, 59998761, 957744902, 570146786, 951289561, 600970868, 546757159, 494543700, 872248250, 152856306, 582769438, 203211239, 623401608, 124640140, 581585930, 480170826, 299559397, 693955440, 780995683, 109696153, 946566792, 49814326, 315284848, 834642195, 639845333, 359355781, 347763541, 530645943, 517273444, 685264430, 117064601, 298277929, 840531528, 301806734, 216849141, 59391510, 443124839, 628059774, 743071617, 926276785, 384290112, 14701508, 438962506, 407930017, 268245439, 467547473, 528374772, 242815049, 996579919, 484689696, 670058641, 788386642, 152346082, 302870057, 435557544, 159153727, 920355712, 888496577, 797234746, 625089484, 266631010, 351062331, 937426670, 191516406, 870998217, 470661363, 948840112, 631587610, 535383888, 109455068, 818476481, 308799160, 352480253, 772957950, 68806423, 660921384, 493177482, 449910144, 248929111, 748952580, 901761774, 505475360, 202844172, 998586761, 177252894, 61328136, 8938226, 309708563, 457972430, 763487571, 933874880, 713048482, 182909926, 454982039, 671204424, 944123532, 98601628, 691444083, 510187973, 278670074, 683216608, 808805919, 140958221, 969382749, 378745917, 684178307, 936854221, 84097337, 924712434, 979216310, 609510023, 536849296, 890737387, 823586937, 912632810, 950384953, 52854211, 538706675, 188291943, 796957419, 42637520, 383653263, 439849685, 983769665, 455737347, 85374801, 701973511, 237404354, 634156582, 425556144, 741948885, 616566810, 365820101, 247891357, 534539804, 239550831, 205397140, 363107848, 274340244, 627993730, 786087072, 648650183, 726213914, 881199094, 905159813, 285161159, 599769462, 858376866, 669107539, 711808799, 928698930, 297679100, 140291085, 348190325, 813416937, 652168935, 475491167, 748394778, 872769111, 77575185, 542435325, 281393734, 646554052, 911462528, 796467555, 714506772, 746410839, 591344822, 258079022, 327095371, 78558362, 243649277, 78372706, 155054171, 955417174, 680408798, 346778027, 463785871, 416972529, 900162059, 609299118, 63291262, 354040414, 944298638, 513613830, 799749522, 99927660, 872714539, 221349881, 729174335, 993304916, 993182551, 800784812, 735926514, 616626136, 919588539, 837482950, 946004925, 217897893, 58583363, 73627336, 987903813, 90297612, 628163706, 649407042, 379534703, 664752327, 230194825, 767648215, 210333394, 181790024, 438226806, 106398410, 472533715, 607282886, 394749860, 109000790, 705027668, 475748946, 622363480, 579283463, 342301116, 801251990, 538884990, 916390204, 445148082, 909189573, 398847478, 915685397, 579195674, 579343481, 462877122, 220698517, 969979383, 874121618, 11463713, 127778054, 602926651, 784928403, 513992599, 96109061, 477260304, 11352592, 750827978, 649630501, 937236385, 100409677, 827491582, 585174620, 508390260, 674089913, 37801171, 736460678, 466009019, 893278914, 315306294, 23794118, 10153674, 645244354, 321767474, 774916172, 818953195, 738561931, 747408722, 49195766, 149470624, 199160682, 701473844, 544093328, 548359104, 739714180, 954770477, 678587641, 109150516, 34613437, 729459961, 408714712, 739212007, 796512421, 923862888, 529742677, 759714947, 841465827, 368914804, 71204059, 846844466, 399253551, 255044869, 88166628, 892773075, 708210930, 829360335, 827533832, 142956655, 324026197, 600581891, 212568690, 19943430, 104191254, 410752195, 159354858, 736041676, 842121386, 648762233, 915552892, 192971931, 982080187, 743629960, 54572148, 597588384, 367333508, 432608704, 806612584, 139629503, 51446107, 15494939, 202623730, 787932106, 30396478, 728205537, 234286155, 545954159, 917775594, 589510303, 475289091, 208903047, 300889116, 64904044, 419987911, 929500829, 894611317, 752990985, 38039041, 388796549, 908733855, 807551852, 33169520, 292871220, 83171003, 917644165, 286271001, 381180097, 503667694, 320803537, 733170524, 408031256, 526555972, 15669051, 541447840, 285285898, 293288239, 510656649, 377671894, 358361445, 701311642, 946168166, 548454522, 386685784, 836533100, 35085822, 628935068, 680538609, 893882707, 788963208, 169756651, 267582268, 499208319, 478281581, 130643928, 684224050, 143410831, 970320029, 883062844, 332504577, 728902430, 399439084, 200005382, 195076345, 401352021, 191808551, 756768909, 63597262, 737609328, 286979734, 888268854, 259615433, 86265219, 185809227, 281674561, 479574288, 58007679, 664413006, 743171937, 672105653, 338946711, 68691256, 335439557, 171609220, 86057136, 288006965, 781689308, 467881219, 356078277, 496331314, 832709705, 654254568, 160938134, 221847997, 766109505, 610542622, 357390659, 857415354, 244391304, 27829517, 526081485, 105481466, 84190166, 258716500, 455221846, 283636618, 822198807, 214472139, 79155153, 64885295, 743732660, 554011714, 323565961, 250976486, 280059054, 24475132, 962598943, 86162161, 991491268, 89991510, 162461053, 703863617, 702802104, 986572898, 589373984, 863388740, 919214478, 42457928, 162767594, 307114037, 372117896, 636841447, 981913621, 516906448, 554960034, 815700138, 308385794, 656614083, 252304633, 408385064, 760442044, 270017481, 739187257, 61132013, 582932632, 644855168, 697031815, 108626111, 290117262, 702502852, 935211863, 339088494, 68081254, 452887545, 969415481, 219572653, 316263978, 824409551, 619017742, 129791343, 608403739, 127970861, 990726335, 559467348, 571360493, 957879080, 353195567, 640921384, 730172692, 413181953, 263885908, 281585179, 723307140, 772897476, 248115653, 422591876, 283310518, 679680506, 389709214, 41256783, 940405957, 733967747, 76244148, 812407810, 201953191, 203435274, 528530120, 650013961, 333319404, 950114531, 856430641, 992863487, 302525439, 154317014, 922679074, 687280273, 509647662, 674817709, 349155662, 267737408, 449503615, 456688100, 164488423, 981927858, 638025510, 882422650, 924801847, 147992404, 128937662, 635177125, 739959920, 634450230, 600280413, 973328246, 976885661, 645906177, 505318298, 843372301, 83626415, 501275634, 100340413, 811436908, 390484539, 157997145, 997622909, 368312195, 362475990, 318824405, 470952613, 186107930, 35139858, 719219086, 67019290, 618700886, 868824335, 413071927, 824462936, 725964453, 465744623, 249799697, 809338314, 872417761, 820153740, 279879182, 996260646, 818472551, 691843583, 625424693, 539779460, 242174846, 597788999, 881813510, 657890403, 646379844, 633805967, 751466055, 968620233, 104322397, 195625621, 24446642, 835057792, 744865661, 234086537, 425436216, 99898603, 472183908, 224433370, 384472378, 961532993, 914979127, 775437715, 461335631, 899824398, 404846969, 450559216, 657612881, 945205498, 113185584, 412132128, 541820060, 420711160, 797239640, 579837686, 578802294, 598633729, 358709491, 514267763, 820939572, 474947347, 967260284, 470368817, 28025323, 39759731, 943279654, 550708468, 514925660, 325864577, 93021959, 261889481, 130866344, 804464893, 264456795, 78234416, 144766657, 20605877, 277653990, 303492712, 679861291, 796472696, 714861202, 173855205, 986481836, 211720424, 846737577, 96687600, 417875520, 453137958, 22698637, 360095458, 327280938, 868937965, 424793331, 591996686, 109877361, 274503372, 406400834, 463499900, 746877580, 243669647, 436026610, 99282927, 230621230, 110056198, 284067571, 525145519, 410703404, 151662388, 386038082, 70352031, 281889668, 517045508, 7215005, 66597181, 931107907, 490303853, 422733848, 626552198, 351603024, 530458527, 230219336, 275860965, 788789139, 936896069, 575356448, 954683791, 436156982, 656058236, 709335584, 329799245, 69638761, 128953225, 222925891, 597005274, 597145705, 754283162, 803159106, 699506008, 999854377, 265091946, 444332732, 700175964, 283489935, 714892287, 443608973, 969340375, 75421167, 640369323, 344802922, 721001461, 337346338, 732767655, 490203906, 242692381, 459804106, 455028452, 679526942, 822714805, 927527792, 384822082, 885275226, 223006594, 202858469, 231763168, 983238867, 299544252, 642256234, 935142108, 446056954, 7260900, 185902438, 936958448, 378377420, 375713884, 800943190, 878197912, 484805375, 926641018, 353177587, 934978758, 721473725, 439771770, 270966658, 638135648, 684941199, 750933878, 330377935, 129985626, 320820744, 97718237, 715798852, 352067527, 121842319, 806883363, 521638057, 493151899, 562778802, 814240934, 252321458, 728550583, 75428438, 237786537, 184352843, 32344425, 708495613, 590854263, 4075275, 705908483, 333768806, 263896747, 347982966, 915903517, 670643575, 816201922, 634210932, 940599769, 710934623, 753565993, 176699013, 146178364, 572634604, 157500012, 156102362, 570864805, 305538367, 342354812, 742365385, 937804554, 459906069, 236152341, 472332267, 664838585, 977436585, 368413311, 386089316, 373705542, 286876036, 11974704, 805016514, 739855004, 418599788, 672553643, 492513127, 213248596, 271152023, 653864304, 716552320, 538958046, 135785024, 736947122, 952894174, 224744173, 587037901, 258147163, 958381027, 367841775, 172421772, 518042727, 140112006, 955473802, 280321406, 630542862, 184796180, 579892321, 426511368, 582318712, 975707088, 878778887, 148405646, 85989249, 519440844, 509644819, 55723953, 715212763, 348926826, 219623999, 730509255, 436064315, 373668681, 319384603, 400609734, 740368739, 463609294, 696909585, 209700886, 599277735, 687465179, 224166366, 62904184, 680697792, 24158159, 538895909, 383946235, 362534013, 783299782, 638303992, 877988199, 893697268, 254346891, 972900274, 471675432, 375596935, 970842605, 796000489, 784944245, 713287097, 918063562, 222634646, 128500613, 63760401, 887585511, 582341957, 910637787, 755299348, 828562746, 598574421, 892257333, 907096627, 389905080, 699362626, 431955002, 329648393, 713638519, 898122911, 650079379, 581289068, 141469958, 571529566, 95973547, 853812602, 710977729, 191760460, 400344262, 324003338, 583057003, 203373387, 330261876, 922231292, 179502261, 44285845, 908340028, 643084100, 560220811, 279519774, 40810187, 614339138, 929363825, 286992925, 175847794, 463195800, 965064468, 223520057, 951686203, 841855026, 743169438, 168036276, 139166515, 156096376, 246079675, 405767746, 154775450, 534258241, 902481749, 426614244, 888967354, 790163622, 245565372, 609108348, 779166123, 981435705, 956763361, 299774597, 758754427, 107033778, 600182348, 18588489, 162747759, 297270596, 10974150, 93957642, 255095337, 403585230, 300781400, 959500189, 818309376, 754256799, 412432316, 317104893, 978852477, 378442386, 397935571, 430685729, 22255245, 632772830, 254439920, 127686369, 801985276, 498230441, 879187269, 460210685, 568642730, 337216033, 815137555, 965458526, 519123130, 294968055, 55773773, 990967536, 618393920, 72888467, 783030443, 567705716, 525384073, 597413426, 653191059, 430384164, 139571530, 338230046, 57661305, 560916887, 78388240, 954045974, 640929634, 152263785, 316550944, 176594223, 481807027, 45859922, 934604328, 624166996, 129701620, 339999072, 357216685, 96592927, 284919962, 2412406, 405219901, 566709382, 420849464, 647803881, 574210807, 280837331, 637375344, 451764743, 815837558, 964311615, 377783182, 354957156, 52549125, 446745447, 849765889, 348352487, 707016852, 994588066, 931636447, 602652000, 197072143, 876004471, 149952308, 483299711, 527056538, 165368046, 667863481, 452739278, 739872726, 81686853, 844171520, 678278209, 183049346, 871813804, 753065996, 469943332, 302464253, 13608041, 200575969, 236614148, 640516964, 533500570, 829795900, 98498694, 299134457, 381975171, 49534226, 493645689, 382616944, 979976797, 272654058, 512774226, 122534466, 393620593, 556287380, 737574078, 194120403, 421603730, 885854900, 441930481, 205724727, 789337592, 785049187, 526074055, 861869436, 292492758, 147035697, 494946330, 19824185, 40692976, 958174090, 200305405, 728826651, 376699213, 386419459, 552584847, 862977909, 758396760, 851115714, 610938836, 69258656, 792651561, 11071573, 32042397, 625289958, 997042237, 3139859, 924877849, 435991067, 392373679, 912973580, 160278583, 637680464, 880057981, 865440083, 211518553, 5084024, 113465592, 55569948, 127217449, 121049298, 73466019, 556185387, 303901523, 511609893, 689298175, 8068099, 906354392, 554693122, 964726163, 20024579, 96972717, 618230002, 149613376, 81761310, 755069391, 587188972, 603878385, 846436205, 135644178, 879240231, 66973875, 530644601, 609903851, 147927065, 142693309, 885227752, 99208238, 300638795, 506719658, 483715545, 682172567, 284152519, 400209467, 196791534, 472961094, 158843968, 317851466, 441333848, 34871532, 820652419, 994773596, 618897319, 251592064, 796466759, 200141668, 243311656, 734784950, 449395600, 813592756, 584985175, 246258261, 954640736, 974736617, 448590236, 191949788, 590461933, 30854431, 156355665, 329698701, 920603726, 89167272, 224274482, 731777841, 321239134, 768900406, 164355608, 750046094, 415065228, 713017372, 863851792, 518297585, 834944451, 854546343, 301936156, 469133479, 296534397, 62931850, 728833602, 882211035, 878132340, 221467955, 432666394, 600393095, 639530379, 660492041, 292034115, 778098054, 531774392, 826234720, 971994128, 355021807, 243733790, 833778546, 5229, 339904889, 273757466, 794857567, 72315749, 108459266, 747245990, 471442338, 617004173, 217449190, 763016204, 633862972, 300615309, 130361534, 671757903, 137729575, 41347789, 541450231, 550599249, 861037843, 531960999, 948797235, 689835659, 571937823, 722369457, 540271319, 153705219, 89773221, 129697759, 12640494, 957024371, 640612134, 355215300, 161630543, 92008298, 887844364, 241321821, 703273435, 564505880, 534713129, 800065300, 330224568, 767037685, 586767903, 637802873, 72337710, 484465803, 131087526, 91102563, 172080348, 114100315, 833844674, 421813699, 123568374, 309888277, 308222558, 655993197, 420162323, 281325368, 841691849, 524271791, 268195471, 131805667, 879981184, 993959202, 568500669, 333443716, 201391661, 456501816, 243334030, 167343240, 116524072, 310435255, 47229567, 511973357, 599325139, 97028490, 799615080, 82722796, 195695672, 177545394, 897542429, 207757302, 654105302, 396209556, 522910341, 71956730, 38670652, 703383730, 53235863, 209331369, 743092899, 252737321, 182787556, 737482291, 631844253, 444981842, 259480432, 196642296, 791107695, 389023616, 105823873, 855327499, 117591268, 820761301, 391708411, 446817162, 58930559, 852021554, 334644395, 434373267, 993580485, 856690102, 810779198, 492204843, 964672217, 895089185, 648431193, 618280865, 42126949, 974362184, 689794451, 826277605, 680196519, 665491924, 494727039, 134263288, 550594335, 742084238, 290608387, 899947849, 360300598, 797655727, 615817877, 164542465, 552322930, 253263425, 243654922, 979299072, 56178899, 805016918, 973752466, 984696004, 720064134, 848649028, 675985047, 886060190, 47615545, 966104322, 407230309, 459701768, 307257311, 698107864, 2014388, 221250010, 252794874, 240374678, 562012509, 913189380, 332530674, 560139236, 353868428, 222665944, 858523253, 161938535, 327345652, 963346928, 677380286, 309261092, 781272040, 347339465, 211240289, 44640882, 43621536, 396077435, 856484782, 983535368, 112521593, 458813587, 947580464, 406954977, 326606216, 95727957, 49227329, 20297325, 439421995, 784330307, 733135496, 512062766, 601895890, 603333318, 641257074, 615713038, 380648924, 13651076, 463043366, 775609413, 902747664, 964802487, 640108761, 871610311, 205028299, 758194905, 553936231, 201227844, 965557620, 429419585, 871361225, 845781099, 59890279, 785960545, 6043410, 150074957, 294180159, 963087087, 733131781, 678604019, 228081064, 875411740, 921391298, 193519190, 850248278, 714215744, 205981179, 478912498, 999554412, 316702528, 196550191, 790074357, 389869558, 932437211, 918128911, 544874763, 912948036, 656397620, 589836772, 103826967, 707901697, 473281238, 317952883, 933025724, 506373500, 173995103, 601795397, 798259609, 962600613, 891910973, 113614063, 594334062, 44335334, 258092068, 266263737, 971429616, 637305183, 524170915, 85353812, 858990285, 123475548, 560309497, 314633111, 870870914, 903283710, 368934551, 851658393, 902755666, 300519805, 396583780, 355012976, 191285502, 413753944, 612073619, 743510361, 904134870, 8701917, 84845140, 774340373, 525885257, 8693076, 353660978, 772015192, 852246148, 820499674, 162622395, 361882019, 146457289, 156048982, 721841386, 668579737, 249131174, 668685630, 325135524, 663154111, 830105671, 767734949, 101886197, 197998085, 701087051, 18806946, 162946403, 215972262, 920294755, 598929277, 520096537, 428038020, 145964354, 584830397, 725145218, 812696393, 350450414, 856359009, 204321334, 516832066, 796665371, 384706316, 803669906, 921732050, 749390606, 675095657, 719049314, 480173608, 341635348, 346401849, 871015418, 962334138, 343771444, 623367624, 644524839, 681882748, 748412551, 271102559, 24289819, 294538961, 997795306, 634380042, 145936624, 567038076, 322796338, 103794029, 253002201, 719680962, 400829924, 376804096, 394268335, 724034476, 548865901, 280605518, 747754447, 506123433, 219627792, 840691427, 459396112, 443633580, 810040394, 527823476, 300747236, 888563027, 111681634, 295754166, 302132622, 592390057, 879245049, 646552032, 388344558, 554238595, 738696941, 164470594, 697013806, 938598702, 557565635, 351321044, 507211288, 484666131, 398992655, 999214199, 841828144, 502382782, 301522913, 900649677, 951403021, 561816391, 156632142, 885769261, 188062591, 574925715, 63220594, 19059182, 432490154, 538354849, 389743705, 595665444, 244998755, 745957455, 768056033, 109673243, 502365952, 389168381, 266011826, 286192213, 586075742, 401880729, 413849791, 136723077, 723436273, 769974363, 899719142, 420214454, 904481144, 41922053, 154646990, 715824835, 517527284, 429834075, 217072678, 805632645, 211736922, 838885288, 597002081, 15300224, 570478770, 381821800, 128259181, 932020831, 927291789, 358389087, 505279437, 557419909, 798815347, 959337103, 509444272, 511711842, 965633333, 811029744, 576769433, 763781449, 256812847, 722717331, 449492255, 38725296, 876768870, 368406166, 748535274, 526885543, 375371354, 374729798, 942765708, 683267379, 189110116, 566095106, 581290890, 522314867, 645371721, 229862895, 920576487, 380302484, 37507151, 617578688, 192157284, 964675273, 628099585, 757277069, 259515911, 56144051, 847368535, 792457740, 291687457, 699359222, 880270333, 421763167, 733153430, 699612723, 383740942, 404084453, 160913056, 122804626, 887648154, 885818608, 108031269, 199580019, 660958840, 678849811, 394414323, 682370752, 3674681, 635386767, 141664580, 149889713, 33628339, 963967796, 28239114, 574964578, 758596514, 357522271, 498275370, 649022145, 331825615, 404986673, 289729409, 907357081, 848404651, 300329694, 486888341, 354760132, 528165634, 688673709, 83761544, 93405626, 465129234, 992498311, 71091529, 602431975, 838650560, 654273414, 736596326, 488145466, 393076179, 550265560, 686310911, 68452569, 14624360, 148586914, 252481134, 370535936, 289333154, 489692824, 620683594, 866736802, 425833805, 630327627, 529142608, 985900678, 613074659, 308922711, 690699883, 773069706, 290109780, 588477077, 247627795, 485080166, 349401114, 352674526, 201727670, 429355314, 834193638, 558401651, 27255862, 691608742, 550033655, 180616795, 931771276, 169303299, 928859979, 339032555, 604359265, 74117050, 548113311, 603529624, 272426255, 60385135, 938298348, 242846965, 34046632, 100970385, 877501572, 472935711, 839058715, 881296420, 202310948, 450369512, 874699003, 90550162, 749604039, 584790543, 876211427, 17661910, 304735171, 215149704, 883936550, 558575690, 350088098, 836001195, 711026560, 180644664, 631023782, 233999047, 224325495, 190393642, 280763299, 338083072, 702766072, 111167760, 414545854, 351359606, 305953830, 341761233, 416194710, 782477115, 408786946, 360042924, 987034856, 696660033, 108830213, 341691793, 161564048, 756278125, 994268302, 899396774, 599389539, 54247713, 302968235, 380711989, 519547325, 792349823, 157114324, 441153248, 726367646, 369273548, 150438257, 284669961, 196791835, 977612343, 620924211, 772890509, 716872551, 203958679, 983120444, 20549684, 139042366, 502208396, 186735570, 654071607, 256799824, 211632126, 324155050, 437551158, 729812817, 475142355, 38909809, 907694702, 98039702, 82845166, 299849379, 468348818, 965127584, 571082206, 787603601, 932220470, 705859742, 587475810, 207313722, 682520297, 938586655, 90142832, 303635433, 536871458, 91134158, 532650608, 753091028, 779120917, 7145020, 87511057, 770482208, 424000422, 31859291, 871675623, 139903047, 110167280, 630810949, 165986123, 435748090, 139536487, 383414979, 308015382, 286232182, 769826364, 974249687, 470567988, 812729484, 320979897, 806180583, 507202783, 231650676, 606786758, 875288236, 570432660, 927052428, 32126026, 969685338, 430482654, 975863527, 873129747, 714514530, 342308182, 220482922, 623221519, 928426775, 682001977, 953295695, 243240213, 879862756, 66707606, 867003286, 918370078, 285045926, 612991978, 471670800, 57316294, 17896608, 843180241, 554447481, 947044304, 351802421, 846766017, 290327495, 561477842, 133485619, 733630005, 339326524, 545686611, 637138270, 718719632, 967589410, 990908350, 178879300, 369349263, 103258177, 404342077, 707591010, 284471516, 641991830, 116881924, 75528553, 850822246, 808609256, 513604399, 466593625, 509171145, 971739443, 952338630, 423690070, 371072818, 581400987, 969179646, 692029695, 780709109, 260892015, 560783592, 77354927, 33557227, 198743812, 60674344, 399128622, 575342906, 299898247, 664981161, 430151647, 281850027, 954993052, 358956826, 341621961, 2283369, 297497473, 638840826, 212715709, 226691751, 837485480, 576697040, 992948469, 85718321, 810566805, 277701102, 326026411, 813715886, 840502230, 121533479, 473978980, 630822641, 240631111, 381081552, 442913623, 289388995, 552808733, 67875550, 638821612, 377595466, 784946281, 569703858, 679926067, 560587415, 793399891, 640128367, 31475395, 504744143, 217925514, 401158777, 903993689, 801762098, 453037927, 176451714, 910985361, 456689559, 273677506, 13752221, 632047699, 179476781, 243730122, 297606864, 832060813, 347212805, 731147777, 231064678, 785081522, 577795782, 866926951, 972729902, 986416972, 802530001, 445710788, 361679778, 393613919, 780255533, 297981770, 700408820, 829207178, 467146107, 292679291, 329761372, 532577928, 811401915, 451399293, 377161995, 405662190, 594533589, 576335509, 284439158, 892376072, 103056320, 877427487, 804202836, 472794743, 673428102, 371851768, 537590691, 412313051, 897333601, 640230617, 258910778, 980505746, 191514789, 976761478, 537344395, 830701705, 451531835, 582775178, 598499854, 980848108, 465470525, 592919320, 887342572, 8069475, 877805046, 547464708, 534056703, 536813251, 399535170, 643988605, 695970044, 508444048, 26111655, 418388099, 956793309, 159615134, 488167471, 289003449, 244564709, 285081840, 304649057, 836066377, 34930658, 856648280, 211837356, 864366936, 89422282, 478676524, 933823346, 170895867, 664559643, 972272065, 622951657, 497991927, 907203281, 182101503, 78203044, 102234984, 319132354, 525247228, 195877153, 955115260, 628183270, 840410239, 49921477, 239499020, 591267577, 443751181, 655795940, 364689400, 175645447, 952013042, 683740389, 144446938, 171585956, 693614727, 688096210, 268890870, 971744558, 429182467, 363777526, 399767640, 568760513, 851121812, 309627697, 874958076, 79028474, 638428291, 599913865, 154550715, 690095832, 878026338, 325775453, 254388248, 433827627, 174234732, 906039705, 538989693, 137908277, 652543013, 939452907, 915104835, 488524595, 778104504, 721671539, 126618703, 83004657, 9329461, 151591260, 664972945, 847605881, 670063812, 811649708, 966211618, 526301191, 784110511, 267442877, 537674022, 481597440, 777567889, 487813366, 253134786, 385331419, 573829359, 516583748, 838144741, 334609561, 141513548, 971605331, 583867465, 697812149, 995600307, 347045355, 243778101, 734598909, 86114144, 338161334, 135162979, 358120443, 423698074, 550732072, 736723804, 720005738, 833431974, 660432265, 81062139, 145059663, 272361808, 281713898, 696101150, 71706286, 206625996, 527363026, 82148574, 277242573, 417901902, 622810770, 737738087, 782268623, 390732699, 87417481, 233177168, 7498934, 110514347, 985774106, 107566265, 449302664, 166468309, 565066999, 906014071, 269384991, 509504054, 527603732, 714027800, 668018130, 930094383, 933728271, 503956348, 536517435, 54220705, 454022403, 872740593, 363198896, 395423490, 409702665, 858345994, 906586087, 964307498, 363215019, 321555036, 906587702, 445685289, 341251242, 426447894, 433274804, 795951613, 784435476, 534663293, 497790070, 364487702, 523817737, 707506748, 858346166, 446532147, 877667440, 46582713, 755484735, 254551313, 299428744, 990875187, 178887713, 701250663, 905995260, 273477576, 325466850, 912184637, 932845768, 513324662, 794289660, 906340356, 526981096, 253302882, 512775323, 639645065, 906685224, 707435753, 579081112, 765126697, 699265543, 609641090, 579932068, 780346079, 794309084, 923245439, 115151701, 611885031, 278217151, 767156491, 438930284, 316770457, 564664167, 837884316, 835519488, 351335085, 230055625, 662039367, 285094318, 229650688, 765888526, 382246899, 587140799, 344420146, 904076941, 354453161, 801196716, 863579076, 940006854, 595896001, 297924515, 421444028, 644630302, 94829410, 416063914, 651877082, 215721180, 859654071, 178906769, 530025997, 313590053, 561941812, 880984748, 412066074, 473248824, 180258237, 512821375, 93966024, 668712825, 783329568, 73232268, 100654648, 144946608, 292429324, 216035197, 666564730, 135215608, 656763782, 896511605, 794391671, 147641513, 705997329, 695377420, 462856987, 145461658, 888355654, 270715131, 763823326, 798128341, 481579225, 418128894, 400820127, 161928669, 492644755, 850015591, 736800897, 904022519, 304626637, 410482399, 566415898, 385395437, 452162809, 554299648, 925536111, 166331756, 873221334, 246426967, 419490250, 85079873, 500863324, 204093575, 637042582, 434264805, 731292417, 841310561, 802903062, 329523428, 472304620, 762099710, 238382266, 183096788, 296490386, 498881534, 166291749, 382311337, 709991139, 712495681, 611462920, 171994361, 208155648, 633745163, 728304617, 855370568, 346370233, 549447381, 182961343, 250513401, 814601544, 586425454, 967441862, 691921836, 190187170, 495159352, 848578420, 191519258, 924876741, 349508393, 680146497, 9764402, 757239133, 749489068, 762641631, 26835731, 437125477, 145638321, 874889180, 184959400, 300218211, 197131961, 494307632, 823129344, 618462078, 177805644, 654822082, 288325734, 217429737, 95799167, 482954643, 119160204, 198137346, 450497746, 272845739, 319140117, 131397201, 985330025, 991397342, 672605278, 637027000, 48292716, 869711568, 381403899, 807216310, 496971570, 914446420, 31481985, 276425980, 105862772, 742621858, 322121585, 752118550, 283029390, 137123525, 600636696, 136411791, 857425872, 974137231, 694667050, 478668244, 466359353, 457857945, 473083661, 895512615, 958767746, 87228662, 28584449, 396445080, 667808697, 974722348, 843704187, 414145266, 577008856, 699686606, 348950542, 72811418, 992966949, 693494282, 839307345, 749394506, 920111651, 790317785, 94287427, 268960877, 370816064, 996677430, 899460007, 653078687, 190978353, 882326189, 801879377, 393105609, 287171392, 256932293, 975598100, 336197698, 511762350, 369311843, 515894424, 902376877, 5526244, 123292874, 597882445, 557623818, 592963667, 817778127, 890422207, 546246854, 811839584, 282010184, 47338417, 406780899, 29135338, 215828308, 256618040, 446857097, 946828720, 514264753, 778700299, 510147181, 766889100, 298395948, 229936807, 407000271, 705737477, 845553495, 877325244, 46739253, 794509573, 883828168, 431000238, 390412428, 1424577, 607435346, 61451462, 211998626, 72751478, 43303607, 785385944, 71212156, 944865798, 15325569, 149718294, 922948299, 385753228, 212011726, 223971877, 276221018, 851265029, 318144159, 972577126, 85738016, 451214995, 641793073, 881293738, 360505909, 98217199, 65623012, 949832032, 317293257, 545359694, 150561006, 253503404, 804679668, 324848465, 630469709, 124737130, 266266501, 848112952, 292019103, 866551932, 361509218, 259776653, 901403333, 244657158, 780208571, 790464048, 207447341, 34823695, 675913446, 270034344, 131878587, 237747502, 234475159, 899823465, 618812713, 382852638, 520918462, 150427347, 186440373, 97056201, 613840154, 847140206, 575052921, 539977192, 137298990, 531804588, 226982152, 160213603, 130493396, 711235848, 137882489, 138904921, 817261440, 535816980, 787086175, 193718520, 721712250, 855022484, 787226627, 848354140, 134188878, 426442861, 195525823, 556366953, 494583733, 334992443, 982980950, 674161645, 960719603, 565049916, 213325882, 800178193, 435309268, 678780634, 193607243, 302672064, 286281760, 479295623, 334298108, 493005468, 551781786, 745384278, 276635990, 9208959, 13118764, 466511715, 843208338, 888508237, 115895495, 595359173, 698717480, 690244627, 818153966, 311394811, 2043683, 572473070, 342512568, 762290310, 71291244, 435320761, 767866272, 195625403, 403783281, 746441939, 878280383, 389912584, 326502153, 294827225, 748912446, 71325256, 108763407, 151276226, 933328305, 687694202, 688095028, 833641208, 238342658, 464104360, 30938146, 612477145, 806938533, 283897885, 912635617, 219448727, 88980359, 509230170, 831775021, 400847638, 259762951, 61476021, 129054550, 740262376, 718896966, 989328731, 336145892, 758310888, 963704547, 852128423, 106350859, 781262892, 522774848, 432537954, 240615514, 658101236, 279020336, 329835068, 359776959, 447363201, 614382191, 993270829, 947341695, 246669628, 754620609, 443396120, 7879232, 498410509, 402450192, 511946486, 898120307, 305571908, 916837975, 170267778, 17673197, 691295912, 607720518, 402170763, 862229023, 544949158, 528357240, 813183298, 808739972, 780283942, 322845285, 13596828, 857448058, 546580616, 528287538, 315998506, 713254122, 976582366, 32086635, 187576844, 838942710, 449078450, 28159142, 106395526, 718684934, 664611940, 641283511, 795990563, 879424876, 665197116, 486911418, 70248888, 576972920, 186962287, 741174747, 312401896, 720891879, 846407047, 267550158, 558151472, 996559184, 492525513, 842467543, 894973884, 979163026, 915268259, 814086950, 771845825, 890882467, 28633323, 723663588, 976832329, 276943801, 923284654, 799462347, 23451617, 143776792, 44304157, 53960054, 599428607, 946701448, 469203167, 445155461, 504409469, 776034054, 105059280, 595826839, 84505175, 734052420, 483718687, 375055979, 996798916, 108753267, 988191128, 3976550, 839916359, 549333650, 449048977, 449257024, 789720603, 440435840, 499752223, 285416764, 636114048, 482760413, 18987487, 56113264, 829842489, 498154592, 842673260, 610481063, 458147121, 211289623, 157980544, 122048689, 478177980, 579015022, 570765477, 278671704, 983095864, 386818580, 50528460, 375034681, 205352815, 333742450, 537871139, 595121835, 35579849, 119180259, 789531153, 811222259, 533072262, 849463294, 447289437, 298284748, 284918139, 648929301, 656772546, 553165974, 750153478, 547125880, 83859687, 446075270, 7862313, 747104110, 547183774, 172747182, 588820638, 697308890, 512458428, 990606181, 620908639, 830430472, 640001911, 21685135, 454374774, 537802419, 920809124, 435478084, 715809443, 807373153, 980184311, 728483705, 212638248, 572190402, 936843659, 810459835, 755082467, 193807697, 975743418, 608431113, 764468599, 942020996, 482540028, 238775194, 252343679, 353831045, 235043335, 867788267, 523455943, 115547731, 362717278, 766334753, 479566286, 658110751, 454985935, 187827825, 534047225, 721758127, 198724279, 670448528, 322632552, 115544942, 755416385, 846801212, 107061965, 812329373, 114678027, 627289047, 306391122, 158436867, 955848607, 233862265, 75430499, 965804463, 772751509, 825124917, 459558692, 254192513, 158933496, 20654655, 307189144, 595659451, 414983837, 863382037, 37834661, 967263331, 987862510, 980952718, 248491138, 264671640, 703382267, 393251399, 543721946, 326486516, 661106706, 893362453, 826411410, 273710891, 988286003, 795494551, 226870413, 76261494, 593010246, 301768029, 744641836, 942272329, 355264171, 724578541, 435709465, 414541960, 156546120, 298811183, 669806228, 485884616, 966529452, 668006384, 128480101, 438145362, 370686884, 664921175, 980605948, 98414934, 910841979, 989531062, 206287147, 876139195, 751170888, 454613377, 398734355, 266278562, 831508496, 496756466, 520580019, 814924704, 320078143, 320377417, 22442484, 686980447, 187979415, 533785953, 390988584, 528419005, 771269267, 842070018, 197617845, 917305636, 106527016, 115496374, 452687186, 648069237, 927182110, 805939523, 501819569, 42974028, 840373295, 623954873, 981913994, 411087461, 314844212, 985466200, 551370215, 255970132, 532005670, 701382768, 375884205, 502196438, 367276358, 685601769, 948571001, 890012718, 980707936, 648316959, 558342576, 24856033, 193090055, 367781945, 718380339, 873446386, 177256227, 975035697, 852801009, 933922037, 885071071, 996984673, 813737383, 434141031, 755831513, 339649631, 14163425, 462079411, 227570450, 609230256, 303524394, 391473153, 884455999, 156773876, 994171649, 86155076, 324125221, 912275968, 192599539, 770059303, 304421477, 257870544, 325051284, 477567317, 306683092, 893580103, 241794652, 299990363, 367176812, 980545644, 719183864, 976740552, 596835975, 953743341, 828410263, 17551787, 530407797, 615867179, 970864943, 640663414, 2902996, 328717951, 587103193, 576159242, 668636602, 730674710, 41809587, 98882423, 529060593, 215338282, 665185727, 843061420, 141502390, 274068375, 890090289, 805524348, 646009486, 715850090, 149173442, 482953129, 222803474, 576690659, 965299890, 373406570, 430748900, 992072491, 197713458, 291032073, 931835562, 833686959, 904679957, 772286385, 350487922, 987198260, 764870168, 34405630, 416913140, 309675550, 112509985, 662858690, 389545599, 495207335, 428747543, 804272487, 902882260, 344075115, 79981698, 414622526, 510461074, 688663370, 4870799, 354849557, 580831046, 959643807, 702601794, 438415970, 953343876, 298180892, 241944465, 425914348, 91322734, 483482110, 412703697, 249260642, 521260497, 475336602, 851617014, 769182210, 720820389, 286058821, 660387521, 564818251, 294907757, 329715236, 484776856, 543934538, 187396979, 464774729, 884984690, 864394003, 805755707, 779637127, 787108545, 466242477, 754046450, 342993253, 532213731, 331167040, 719309625, 502621712, 236043914, 721689555, 135020191, 901237185, 30157280, 756370144, 341772132, 386234738, 740490698, 956189786, 499824731, 141673432, 580487156, 223758414, 681324168, 723605056, 774108407, 558497989, 90885661, 496685774, 991557356, 277015434, 125714841, 685246839, 421968011, 789108978, 732084200, 544062507, 602073449, 466104816, 247129008, 230623055, 385212463, 532819376, 666323293, 914845811, 262519185, 872929398, 159767188, 537280492, 714749213, 610646258, 494163479, 437217014, 778668052, 202124279, 79793229, 313826881, 467901833, 224858052, 533712016, 981462941, 498271938, 528277646, 602009763, 780329862, 918429866, 144406043, 594902614, 980171019, 703818790, 510519798, 981185497, 125511662, 124534600, 670480273, 980806531, 958625091, 577982923, 687083939, 557241770, 594390486, 723031403, 896006089, 678694814, 445072779, 663014666, 164996544, 368803513, 906333806, 813306606, 898456566, 480550428, 208882284, 536062258, 783639284, 467197333, 768765514, 85379379, 44153177, 417683879, 626806621, 954174726, 642278399, 960440458, 960000215, 889989982, 940837033, 241621252, 684776951, 600780127, 756726451, 203150585, 576392137, 536315255, 576813572, 640508129, 37889862, 594709203, 911142037, 690477193, 846224326, 246098272, 69178503, 697517337, 923866068, 163289767, 933649505, 853724673, 868107468, 621719956, 408306541, 16609477, 162438860, 950940283, 64044695, 457477872, 831225677, 453031928, 431813838, 902887740, 873676456, 559974943, 120872516, 508047297, 950291123, 832171236, 751443248, 263593112, 204430728, 228650016, 299929840, 295287870, 134836473, 429435205, 3055619, 35312972, 255644164, 546958686, 966330519, 33924073, 67871783, 858588469, 442844774, 534976248, 527160035, 241399329, 185118527, 962038161, 996627594, 308157848, 140319003, 200070965, 960864316, 710195729, 549493431, 408150748, 288897044, 403108762, 655696381, 646767171, 118401190, 393164861, 979184233, 644684276, 593065285, 468560667, 833440896, 844599319, 852329728, 922288890, 670871190, 348453443, 266370744, 582572258, 828209951, 598856922, 480135432, 768010680, 352256225, 313032153, 209681222, 936597122, 510754030, 851851147, 387721912, 44179604, 445345320, 799750983, 127601313, 875717745, 659657359, 178790102, 688444553, 828524245, 519909472, 486210435, 958412160, 54132051, 73692631, 800362015, 43052347, 949883509, 517732402, 453544387, 382371759, 844550394, 879380514, 369036648, 953430815, 319425339, 359745894, 719291691, 527203142, 456969484, 26649035, 405365323, 980674973, 854049439, 42322257, 511593281, 993300030, 202486164, 370793927, 214320750, 400673640, 148228911, 666212953, 857486854, 823561010, 140529712, 701089903, 85178780, 274284290, 194666837, 656991686, 34240303, 360578438, 244727954, 991221539, 977902513, 148644987, 511343715, 640292582, 304897418, 627395984, 1125567, 649083147, 75613724, 438366044, 517854689, 237704577, 414239449, 811153615, 441311402, 689715903, 729166114, 797647247, 914244721, 357113396, 626175443, 414350810, 566821461, 310397176, 402229051, 761785340, 24492359, 846485064, 259347525, 483945833, 219379342, 585006342, 369051540, 218898875, 677662313, 937289096, 311949251, 616697966, 335418103, 202889367, 707225682, 755897139, 250847168, 8402333, 956271497, 182641846, 731704140, 457613775, 442332194, 961923610, 71150931, 368287214, 388571137, 170425166, 57235040, 718123450, 677532485, 316493015, 992888211, 35636495, 458138252, 577954080, 773530884, 915389060, 456809206, 322915256, 110045241, 462095891, 986421578, 567691406, 552019646, 498593811, 150876657, 242357082, 772098468, 565403520, 61496806, 207384207, 539802361, 26669117, 8249700, 139777272, 630890890, 298519986, 692316521, 805254241, 894539281, 565768237, 593058264, 985659730, 480709821, 432382848, 167452311, 501260643, 956765195, 660366485, 66268875, 389355779, 773409148, 615516524, 322373209, 701703208, 460211605, 816785000, 661231289, 838400806, 841873180, 230688431, 917762383, 11800589, 662438248, 864872325, 544970962, 36187636, 490709363, 659223458, 276404796, 238179704, 352774352, 69072245, 916705824, 410155115, 603933877, 952175316, 799914327, 914470926, 477003875, 721252894, 113658943, 329023381, 539713698, 213117514, 945298794, 727738063, 439579927, 507924442, 726105590, 807321648, 892266246, 674736425, 823941487, 807872983, 390999934, 93210217, 766029242, 628522899, 340607702, 86232316, 394004395, 100843861, 287880781, 700243116, 264535580, 186022369, 405722399, 589519861, 47313146, 685604710, 219691788, 461646450, 548176261, 823062376, 855621013, 367203738, 661926924, 793547922, 362284702, 579018071, 122530361, 619129509, 749918228, 614922516, 240062213, 170456863, 960114064, 753221862, 65902904, 727751880, 395826050, 330252764, 600109633, 152175379, 444868123, 599698841, 948626854, 793846355, 133519747, 992384452, 86595986, 667895202, 769579575, 135466466, 267041207, 741746095, 453420697, 683528094, 404054342, 613378392, 703041372, 428214844, 342247071, 438934586, 512493417, 62476727, 823065645, 990279696, 558484149, 492493556, 891908705, 628458665, 477073204, 484901377, 881760293, 357009772, 36161976, 425956573, 982086439, 177411445, 769729715, 900823232, 968371485, 533912803, 884899026, 982203267, 598084797, 69955549, 86116268, 31375640, 624834316, 397412568, 303490181, 535977726, 781564079, 602839506, 171449939, 596834865, 692793563, 358084672, 87852659, 269290595, 753038096, 625720222, 582276192, 938648199, 986765579, 469638597, 120857392, 440696418, 945326788, 350367933, 916854670, 304440158, 744273491, 363084321, 747596621, 839202544, 619449190, 396957064, 472257838, 373233758, 768180828, 225677100, 507981202, 119149219, 994411458, 29181124, 422555462, 421598598, 727983138, 829749737, 956304188, 517635188, 292605013, 32191996, 703991119, 522827001, 182753866, 78527825, 157980010, 274622185, 318907705, 427880855, 797660434, 905196937, 847864310, 813700977, 458970706, 435554931, 390777988, 926521271, 524704554, 842682175, 908313273, 472930795, 226478343, 627628097, 573765236, 157998529, 486714510, 954465121, 656745933, 357153846, 410261842, 586075584, 726489676, 637306918, 701945836, 437747140, 65766342, 619873214, 142977340, 905298234, 405812551, 724079824, 11149733, 760612221, 145912018, 536352186, 219699834, 686640213, 693581921, 159983081, 571824399, 517414835, 97310809, 444564823, 771801937, 450690262, 837121058, 130791785, 221164743, 105569161, 425454380, 294119943, 530652041, 419846789, 371734716, 830920692, 582022401, 798598402, 654583486, 778898807, 446936700, 807110435, 666665343, 68192778, 949204982, 329248089, 497121723, 736356520, 798004112, 369601343, 588325646, 295885033, 435838240, 650797755, 943467204, 148456976, 743693760, 888272313, 128678301, 466326510, 654918422, 631268120, 282247403, 222516017, 748484995, 606176276, 171460213, 619594021, 349944640, 662083597, 837359707, 483582212, 484670437, 219046877, 8304445, 212141081, 600222466, 535342684, 848607501, 266877338, 941039113, 690933284, 564767164, 221139592, 669155413, 187342035, 302741719, 674899752, 625559809, 953246582, 850597607, 324138699, 21399275, 63808788, 62986259, 301967585, 329286166, 871279177, 151968802, 495546857, 478995931, 84629162, 117380764, 867094585, 692429745, 805873645, 90042938, 410732140, 588852855, 35972123, 10089713, 180777082, 436923602, 741919020, 101014681, 786386375, 851823088, 688492268, 902938790, 221247220, 491296624, 309732590, 221237491, 751975724, 974313487, 596830560, 148973709, 827538818, 347143215, 465724478, 857615409, 17473563, 926570994, 207271868, 474486249, 693177859, 207677362, 161931856, 629406681, 780602017, 686057992, 529742800, 292035000, 722593438, 480640531, 502561179, 932195304, 975583588, 586444176, 911530050, 862062621, 709419995, 706201041, 190552348, 977734235, 732388924, 468478220, 935061725, 726478639, 572870814, 563209556, 892430424, 625149264, 458859381, 170880655, 245612960, 858441722, 361841995, 463756686, 296541463, 478151763, 113063317, 947014530, 699930776, 856619734, 314027944, 328782921, 835438933, 933715825, 905638809, 198699685, 898045273, 322110677, 637087557, 81415778, 366107932, 363330533, 588328076, 850545202, 102560636, 736919722, 977206927, 224816569, 969203499, 169024220, 367346425, 974668104, 529924610, 490618446, 26696268, 284436599, 594281849, 605297193, 553558466, 803081701, 655559000, 339241878, 707791150, 990237917, 393845864, 134058463, 565696579, 49565936, 759079292, 956144925, 318419060, 663875592, 126340959, 155552935, 341623050, 274671160, 348225423, 728261774, 153133483, 441539039, 956561926, 34845739, 168581154, 753449889, 854896316, 710234834, 941454523, 391868854, 8801694, 459500330, 572219679, 198316741, 555451002, 428183113, 184501876, 382676747, 546341283, 690412501, 206462357, 871714492, 219665282, 13882341, 529117864, 746304578, 866813465, 721423761, 754860254, 975838554, 490051270, 827688960, 768981644, 356423126, 67036781, 463248633, 479111873, 409512368, 576263329, 251792486, 138791090, 243258958, 992583016, 578729675, 954368010, 229526489, 802377791, 153276677, 262234792, 582553294, 758760071, 66113323, 978082517, 884807141, 342178005, 172884901, 78034317, 159163210, 215468845, 310912306, 72793488, 210639428, 335720777, 984957878, 600453984, 694399627, 420176725, 588074409, 226309084, 587468161, 595372060, 670798199, 848821876, 671084282, 944312156, 322203609, 490065394, 8610680, 844327242, 49129334, 655545357, 851526107, 189393762, 995014610, 227104152, 16733902, 128954423, 597047361, 932413396, 913111136, 542292870, 31125188, 286614201, 889400741, 780899964, 291626998, 406642903, 976281945, 885637161, 539307746, 175953246, 32674109, 415749268, 878710398, 965692842, 110434804, 26938559, 314832253, 755560292, 947760728, 783374577, 414753009, 515224342, 1881642, 518450114, 845398302, 801174605, 385322463, 655748498, 16607410, 327097139, 428653132, 783782597, 89706144, 127690520, 128706581, 63758281, 282473784, 385033059, 597532911, 532172825, 68110538, 570929103, 241558358, 909300311, 515046425, 576822339, 421713443, 691020067, 49138343, 151471796, 509262617, 584822867, 330007859, 617929175, 134799259, 812531150, 132362433, 761437723, 777694837, 901341036, 669949521, 833945640, 522489816, 824626890, 378964215, 241367055, 765125449, 13039666, 200932966, 274233718, 840383417, 583842940, 816493213, 435676241, 111799934, 254100286, 960838694, 517990810, 878749304, 43253319, 719936275, 29171146, 229036815, 367122532, 643105218, 227458980, 580006564, 893179699, 668405512, 800484239, 687266519, 153178914, 231244492, 268185042, 569321566, 263820798, 686043160, 609206513, 856923394, 179404643, 505025734, 153241028, 73620751, 628030032, 317996360, 288171619, 675654684, 324763635, 255357107, 495066640, 896029599, 642042544, 844693266, 700346738, 799882245, 361463165, 575730857, 653744994, 3477144, 150321078, 987216297, 789860690, 145307130, 75718400, 319524377, 427990126, 723890326, 702020615, 761987795, 550609677, 629623517, 825161850, 294695461, 163985784, 110815936, 786938050, 956628313, 749394692, 456663628, 316218651, 304388152, 314392467, 995787159, 353101323, 641972533, 439852079, 572502075, 505949871, 479498723, 621923718, 472611687, 577404784, 488657381, 424987302, 864316913, 366852880, 703104624, 257800908, 293221433, 341391480, 150236620, 826108085, 795269070, 380697508, 799243110, 413824274, 371931555, 541297507, 983440832, 723841163, 295422876, 216194552, 357041757, 466956508, 199507586, 254586529, 13291329, 919395176, 78355850, 173117921, 454796725, 288362714, 893411202, 972165240, 718951016, 434497354, 515436271, 68878001, 116190937, 692188879, 685516046, 233928874, 554374425, 717715014, 40797153, 746373066, 512972002, 810459776, 754030543, 619017986, 846651863, 999146070, 130440628, 911543825, 945212439, 976015464, 402684401, 768096705, 75562029, 713343915, 892776274, 109057747, 188902661, 730904884, 276023640, 53706574, 826159459, 261594189, 405653286, 662519382, 78635544, 739402034, 942518942, 459018004, 724076958, 606152026, 378116881, 825124523, 757086820, 252970903, 113195334, 454173685, 351953257, 237134370, 834949086, 69515411, 476356283, 648576681, 877969212, 440214474, 73984140, 206192466, 425158240, 868566242, 444693278, 540600125, 619753894, 853564921, 380597652, 648989887, 933180503, 857127457, 263391090, 285250536, 400966524, 351047929, 575049666, 775710402, 105732936, 868437878, 196967629, 48769883, 762036511, 57978270, 50491239, 850002066, 321472656, 685552686, 670308422, 158433691, 280605792, 758776033, 637597819, 41350858, 383853938, 916289061, 95241932, 590011941, 200083072, 136208813, 634657612, 623489358, 164144609, 466425072, 822860630, 380649008, 978038998, 747634757, 676140707, 23134353, 189979124, 282662902, 265681010, 392610323, 206028886, 43884814, 984128538, 378446213, 867234328, 286226869, 179627399, 424481767, 89773983, 645320811, 912380984, 313678794, 90871997, 675386396, 267739948, 798472611, 134344224, 761802858, 738212667, 160274166, 66107390, 78321508, 861376458, 533351356, 175528312, 751907527, 532250053, 369799861, 525678496, 428193157, 555418348, 403279263, 147484178, 369275475, 877080686, 777564907, 366335813, 818332565, 458346548, 303476445, 700365090, 238175006, 945547171, 512153976, 110250367, 528075438, 578656336, 570733492, 561353696, 743529514, 600278659, 604827988, 17196607, 895040135, 35047547, 928081786, 979233583, 681723341, 991704048, 186355155, 418277292, 907473385, 859258629, 342639398, 909333968, 418587361, 206130764, 158101533, 322722833, 602467248, 845443360, 648834643, 391617372, 377153625, 508352794, 29064124, 720144783, 733658665, 348449802, 328915768, 372048123, 392010871, 88787285, 191195246, 254815970, 741434176, 665070330, 325780077, 911442080, 591934113, 850374435, 56015172, 262457612, 377304714, 478389844, 611836404, 218887324, 380996906, 435071923, 721334712, 745613170, 851695507, 768540527, 934536517, 575188879, 232616459, 698685868, 603745147, 987632042, 205588935, 256611479, 853888464, 268323530, 874999211, 230165934, 968493151, 839330495, 621451642, 42451914, 522078853, 717985036, 149916455, 695655197, 900773125, 162242175, 462021428, 387811613, 95442841, 301112973, 323336842, 464376549, 924205808, 600900849, 507224799, 676412698, 873752051, 571173246, 62281572, 5443456, 990553038, 564209844, 538240717, 101094507, 817810442, 506767508, 502996461, 129545310, 945860983, 689062577, 366204861, 350908825, 183055646, 569759095, 26639448, 424077446, 172114341, 406945130, 70631526, 957417884, 774574995, 367154467, 881940295, 142950770, 481442658, 807739971, 557756048, 793419099, 609756625, 25761781, 622916569, 931050146, 374823125, 31453257, 966268817, 581650612, 456239004, 305234581, 319659960, 979398468, 637269474, 466440226, 151743346, 945723215, 636401400, 985140053, 214741795, 194372877, 804894133, 785358923, 667246298, 776114244, 692440699, 99169963, 26759031, 869496530, 217547732, 275000457, 521322815, 62595282, 689293401, 358741296, 566482413, 314771872, 893516682, 954346066, 253364094, 349264378, 500005803, 539920821, 109765151, 994805855, 846884592, 822721024, 115034788, 200349692, 513798222, 152399535, 340944630, 311262855, 755433495, 441914420, 580204844, 973948884, 338728057, 190313346, 863726606, 832253736, 25844119, 368762146, 392884673, 278115705, 758595063, 259911826, 964085510, 977545993, 426418789, 447760471, 933690524, 84268639, 759822752, 533917343, 179430015, 178282755, 661767502, 188224710, 206946745, 3678138, 487288943, 117715303, 446898075, 623779188, 939058371, 317093745, 458838701, 108493193, 16031823, 346811367, 72261192, 39474076, 794391905, 214472531, 934659089, 669747739, 611782620, 855271143, 334849184, 150876864, 168366747, 206697246, 559946156, 873302912, 586467094, 518657599, 114583715, 287726940, 764729538, 534849854, 845819333, 300878642, 862337587, 627709694, 785412339, 747194401, 170905682, 608290158, 922755147, 50751644, 423182644, 750004427, 713608046, 738927253, 970100983, 313184871, 73939354, 142731752, 266363936, 833378707, 651888658, 141832336, 284088500, 707406735, 72941633, 690543627, 827310728, 512711548, 49711122, 396239778, 957380810, 979621927, 661132782, 970426319, 263146446, 353187372, 11842060, 480256819, 74189097, 724648819, 507397536, 417778520, 840979316, 266692110, 458898123, 68755285, 210239870, 355843335, 633939843, 69437896, 163822247, 976457490, 32509702, 717955615, 261899110, 37130712, 917327347, 298149608, 964953118, 458393373, 643265837, 854100691, 957877414, 917868533, 871458869, 675390124, 645340543, 879682665, 367974944, 960497614, 301584966, 138308660, 769569387, 647771046, 857608950, 722044553, 734627724, 416993242, 839329343, 161934133, 193661099, 937928950, 88767457, 251198446, 487929153, 330466850, 667341025, 591003066, 316840442, 734976997, 575284302, 397359960, 552581327, 633224558, 63564179, 879914862, 486684275, 409300831, 909001025, 535037027, 207166918, 594811118, 612168996, 765517140, 598983823, 619181648, 559446742, 562495900, 91802874, 861131354, 361121781, 12875038, 575627016, 251896233, 229861539, 340707103, 280027798, 732024563, 889656287, 275233477, 200663889, 50681569, 209919769, 100436306, 120478131, 721190361, 291704102, 375000750, 874099623, 338570488, 362933765, 593414501, 787463254, 544364638, 478391345, 509835032, 803901648, 881272532, 513220815, 330749659, 74640926, 47865922, 350139898, 545455843, 143653137, 981991948, 563718846, 373761406, 718506420, 948115584, 800814510, 21147094, 800877357, 957597089, 631501735, 508149410, 492904141, 337051638, 996738923, 565169101, 647012523, 180364287, 710659843, 72123367, 336267333, 161301038, 103513579, 127491652, 77765489, 54630123, 777454175, 84941, 387018891, 91143185, 526974239, 706298, 154534705, 214522957, 938755528, 941033910, 570390400, 21219697, 538253872, 719613411, 762298094, 724091369, 549591889, 203715399, 530279153, 424974466, 375406919, 607058640, 368225467, 472525584, 56922293, 600527011, 640491428, 287928079, 930110771, 574750840, 285335068, 1291557, 744216345, 673240379, 319956012, 762928278, 363517164, 486462969, 159329227, 923666643, 903534535, 666206326, 397051725, 889130400, 691098781, 130130194, 663523879, 383146487, 882497930, 196885043, 227248146, 737134257, 461844883, 502019606, 489875313, 647916265, 495137516, 816331911, 41584618, 530566886, 582104578, 64647486, 421448382, 762212539, 739595307, 397921558, 99606709, 437669803, 777260256, 456362589, 543136118, 388572597, 615615528, 76121113, 668077826, 990963596, 253019955, 269348340, 848756495, 423434518, 198232951, 848208114, 506331960, 739945337, 869127173, 76256404, 832940220, 78595291, 543699552, 298069694, 700572395, 546242360, 643785859, 456845695, 111774924, 126940803, 999193599, 735181743, 450168351, 866291200, 979356495, 171359554, 985892554, 934522922, 27244806, 820532666, 565473086, 345817173, 624384056, 336474436, 70610595, 506514906, 381262079, 106025110, 831517272, 575840603, 73397330, 216011066, 620569997, 554732940, 959811567, 65563946, 936758654, 963648722, 764273977, 368615184, 517327702, 182749712, 102584763, 821556020, 222215338, 788120538, 341240771, 320116223, 465860580, 687772193, 409306358, 233112342, 18861175, 651390468, 595973161, 599959050, 629660891, 366635414, 152438021, 422435252, 506529334, 12811513, 635766318, 321240751, 575259879, 796329348, 738777889, 797458634, 981817342, 242924064, 581751892, 912431261, 577148516, 393630575, 108427932, 168628261, 790627086, 230063837, 585547103, 433952160, 890468169, 91672627, 160218591, 305701983, 566308581, 328814656, 549628954, 829310634, 660198745, 534378621, 538313654, 786131235, 712406033, 957289928, 676438436, 537488299, 638262991, 465175952, 400449874, 804150546, 976931928, 481186533, 104021911, 806119469, 354925983, 120028364, 689593496, 291615865, 206139717, 51767710, 547036939, 812689751, 265355153, 623095993, 482318149, 289035084, 769355419, 312176601, 205363637, 434948576, 959657191, 996136419, 750818997, 220466483, 281266404, 336466746, 246313983, 351282672, 321172390, 77743587, 143124131, 239731730, 404514221, 279988678, 992022695, 138032537, 417878354, 707967903, 865789187, 489544062, 649927762, 284338471, 283731131, 363568427, 841016817, 208845580, 119278911, 643000700, 685376582, 440221530, 563735812, 619718721, 797057435, 140337207, 63724534, 685077563, 334047865, 273503, 646064026, 485207394, 615825807, 565351625, 182274455, 690732677, 224417843, 780914032, 330376678, 350180511, 368855356, 913115589, 518862106, 7603354, 321281877, 880674329, 664741681, 508528146, 944263259, 234638245, 763182582, 837276753, 646165945, 793680536, 51187841, 674718564, 288137635, 141448216, 321671854, 999360526, 4163356, 377517526, 321553799, 537968374, 360367760, 725644058, 567764758, 722427343, 800096608, 977390994, 307673579, 794216332, 697318017, 311090108, 724894646, 668786900, 836291466, 208288165, 552375412, 18688674, 767518056, 374165562, 53841300, 554812626, 931696754, 700904209, 204009265, 342418933, 872458173, 674572981, 23630226, 653996287, 435535967, 611386429, 688809195, 544400498, 203857977, 607805534, 978031316, 236068261, 467579946, 27938006, 192662213, 527725459, 944330897, 17995693, 896066518, 283383068, 288371831, 455445612, 337185657, 210183706, 234289851, 259711509, 865655553, 828704247, 508706654, 868695086, 769814240, 467456786, 513675910, 664724481, 679139386, 758653671, 506785752, 264293990, 68959739, 19278633, 631307175, 794723855, 368195244, 858513576, 688926002, 992148390, 741744977, 429355605, 739262568, 546120961, 778946643, 706995760, 595227979, 814427444, 374721888, 246218589, 575087924, 583450202, 518823948, 491104391, 465498686, 786496138, 975701607, 758662750, 749750166, 391660665, 667138154, 169358894, 850618034, 369776945, 289884708, 372826731, 395136086, 441740311, 863873247, 194332800, 143816459, 445303086, 250948549, 567812847, 132240382, 351879844, 476775576, 713742901, 442894377, 560754590, 90889144, 168907762, 391383542, 715692919, 784413241, 900506042, 441491816, 504182212, 246790759, 564958429, 66256961, 493212754, 66342779, 667737993, 544870691, 579611040, 631850814, 184793859, 90175417, 793823782, 520942979, 611733540, 844238888, 732139344, 589341555, 231733494, 995770568, 689956277, 586231791, 905282308, 3665317, 280357362, 147527619, 612235315, 552491094, 252575826, 91607116, 458033812, 988221590, 525283698, 475116418, 42260739, 390499639, 368438847, 454296984, 778166257, 39316940, 674908131, 997974522, 702870590, 981440539, 543698475, 643204439, 480779322, 222095731, 880226399, 2419398, 909021406, 78111904, 4137098, 186939882, 514085265, 110407863, 523300471, 858011566, 327515594, 261064347, 122029290, 638013340, 589075391, 583881847, 894006982, 951168140, 53130272, 28581330, 699222250, 660565703, 548907453, 54295347, 841395485, 649928203, 499394425, 366484376, 188738630, 914423402, 189753020, 639567876, 371808644, 408202992, 534352538, 845965582, 958630125, 962939639, 151139574, 114368654, 226419825, 967823940, 431108938, 558865579, 273282346, 156817972, 337030902, 346539014, 43998417, 252046675, 559044996, 330606735, 287762915, 404982475, 681406658, 383569452, 474007470, 679651074, 357843970, 454501393, 45991541, 897522734, 193591152, 644033413, 302823291, 842637850, 5672089, 78550650, 567291073, 919414193, 470480907, 409208442, 792889414, 631883320, 833732816, 788326760, 844267908, 744562912, 226310851, 458907544, 466895306, 608951613, 299918694, 607015424, 641060127, 895186746, 636290905, 488332339, 270579786, 16699424, 420858100, 419158428, 474039139, 936615023, 600079342, 628754101, 433897029, 893531254, 902485107, 875197608, 721329136, 534917188, 875702734, 362712279, 94095349, 130329079, 616102660, 125544962, 114201150, 157507311, 3406788, 848446401, 304183366, 601345031, 36090430, 800980793, 108512021, 894033305, 221989832, 958443564, 781832083, 374286257, 33677173, 362619512, 752129691, 46250674, 954816980, 256131415, 621616290, 761048264, 595806571, 536568241, 839619246, 528092795, 550791789, 482642015, 958110555, 811308941, 167135232, 250540277, 663571644, 422608742, 561137891, 869093977, 409367300, 828924055, 401633133, 169943509, 246727913, 104967069, 980509124, 298172321, 363968737, 94105317, 91074781, 852512072, 372687636, 167763412, 658432088, 938432095, 62382942, 155617518, 829896876, 674415760, 918417750, 408506821, 846477696, 288642631, 63415563, 718957666, 705616053, 141850727, 858891, 306878321, 494169580, 435393216, 403457455, 700236663, 216827360, 353081607, 187499531, 802469910, 443483127, 802309963, 490927945, 445575847, 138239705, 743391398, 150774965, 479299307, 229501200, 275877084, 142943569, 620534991, 345129809, 478415610, 428869816, 627088304, 617331729, 14817051, 593815187, 883789308, 64909111, 327178302, 771620319, 869336889, 627533822, 133288463, 334762711, 851691916, 734636192, 298909963, 91954914, 704133050, 712918284, 180036143, 504212529, 248294626, 725234917, 283037507, 970750118, 786688012, 901333151, 575843070, 802366502, 553746843, 566141201, 981056756, 585636749, 889313539, 414354335, 461363841, 746493536, 7575295, 464311533, 345343106, 933394868, 822514473, 667103656, 548652626, 415579913, 282670802, 476946743, 704890876, 14660571, 645445359, 983261848, 182943298, 12863279, 879551186, 635170082, 44840108, 114970292, 939607966, 67158685, 799601264, 497917115, 331185332, 151489505, 588547862, 396870407, 205050511, 417679202, 520853859, 697693795, 572945686, 41696732, 292607206, 773193048, 107903442, 699869875, 225049336, 570356346, 706355665, 577132660, 135494633, 978145799, 365111705, 500725483, 220574499, 614831955, 466249617, 359141141, 329454907, 119234973, 615167919, 311832496, 636229367, 31633047, 58872257, 549969869, 571767887, 108085052, 414771379, 246149311, 233859139, 135449049, 651767640, 203298466, 286389493, 594393731, 917926357, 183409280, 387409598, 249710698, 684808017, 415384273, 353066379, 988790303, 856207173, 120620483, 254247475, 97775738, 170276575, 523936510, 782366282, 386458067, 140950107, 610917219, 716864880, 868247857, 306541436, 462372335, 135085358, 868076151, 720527369, 148975543, 437464754, 598499411, 667595936, 332730210, 659729107, 865672048, 265663287, 845429770, 696635773, 494474378, 694517536, 480530052, 825690688, 421676000, 552863833, 914047771, 172306187, 72944453, 542240835, 897440477, 996708583, 556582609, 884802215, 486585167, 352974814, 905877606, 367559654, 765453918, 51396626, 343527117, 353393716, 168441919, 76287080, 581164005, 301995094, 748619468, 296237001, 456370951, 303392614, 843135020, 955950572, 338260101, 908226500, 941241711, 758283189, 564069989, 633422070, 975062014, 723316340, 94882456, 734974575, 866527426, 676355167, 377444805, 178194920, 460150857, 902508037, 416252139, 705291278, 493395561, 507730309, 713611565, 300984046, 507513232, 847291009, 23999649, 92976973, 398105081, 791278921, 902100556, 940050612, 992420184, 640699821, 130830617, 34963063, 427707344, 973924161, 942670705, 643127859, 904736160, 262806191, 888036510, 459887482, 880468101, 49822970, 869212741, 654555020, 106863038, 129979988, 471528277, 752058508, 69420315, 399478351, 630787560, 783641902, 27344126, 142217493, 156124462, 495525024, 321738237, 557671037, 613101844, 429606289, 365645317, 371551365, 649920733, 838019365, 31938562, 848109804, 210618956, 458321058, 316169338, 275560987, 545591380, 838671976, 464538222, 710493514, 888477955, 635691844, 267448056, 522325171, 623748666, 133115838, 152808629, 871075488, 855106232, 839621610, 13827634, 867657854, 522967331, 375021575, 915512338, 21484483, 587855456, 272243387, 850657897, 474673986, 238011769, 427903774, 815561524, 689663589, 194467083, 916902186, 386700488, 451041033, 625477179, 644483581, 273438564, 661526444, 104983918, 130341228, 506849022, 374385475, 923160100, 581106900, 44212600, 170801892, 253764517, 14112861, 341537753, 478776695, 351334179, 259573090, 312507004, 237521210, 794203363, 709438424, 617559021, 171102731, 271206091, 751059533, 69422204, 547892048, 761155486, 281690092, 422724848, 642165744, 760043035, 704034037, 431993550, 902468682, 635911191, 529501760, 106785665, 502912159, 21794726, 555342780, 791220477, 740103658, 128666286, 606813485, 749581214, 357302247, 719534776, 252473690, 582159936, 970676267, 817331058, 893834085, 718051353, 404385849, 369220217, 766506939, 625710742, 108810134, 972860956, 252439254, 714765480, 730450038, 791360378, 257436503, 110051332, 819964515, 696840842, 915740969, 250689304, 564828208, 171041684, 223373885, 183593347, 743158292, 276446316, 522701526, 935821119, 514268685, 331922965, 860228119, 341044400, 692115997, 890466176, 602873448, 171287143, 407243509, 541726176, 572082470, 67279627, 292168915, 122512419, 831351215, 282190761, 561952901, 912400047, 332599755, 588014234, 329483402, 76939607, 557468266, 110244123, 326014632, 788317923, 401025432, 727889275, 715274230, 846202784, 407138169, 643015805, 523901356, 646997045, 922778451, 528571476, 988579563, 564447590, 657901490, 117663310, 15224116, 367868319, 75118070, 393521326, 620703393, 368788248, 669296587, 545259492, 5147316, 248490576, 567930742, 141818752, 658539849, 129230905, 888179927, 728861232, 60065534, 193589813, 933913720, 493995459, 737704589, 877020333, 404787592, 308622788, 713793661, 303876639, 291673667, 416380258, 171586009, 899698330, 891619503, 7888529, 527407603, 364718458, 299237935, 143824464, 198184137, 547175002, 615718051, 56112709, 198273486, 953052427, 976825502, 390636079, 344809150, 265596775, 140242198, 875146067, 496140986, 910437303, 315107864, 298751639, 488964747, 259532856, 472305517, 889100625, 411545424, 257539771, 462067668, 958324364, 162507458, 954997422, 91555145, 683257410, 775421262, 442415381, 748732147, 333163894, 924503137, 591318525, 450433190, 945557102, 520657432, 99144988, 211656441, 523434982, 473348687, 203547308, 293191346, 625731897, 268850905, 67477269, 204350921, 868921426, 512300313, 759280744, 449093282, 201373431, 684176562, 127117775, 194222565, 459743122, 690515002, 190963304, 688784082, 398054912, 192873087, 919107817, 729632327, 754389182, 494312721, 559238727, 671605876, 531751108, 436948154, 50691571, 613743686, 719253161, 399959922, 384636140, 868584327, 964528209, 217739992, 48470427, 46296544, 905501082, 334552605, 698404708, 228816566, 359390411, 741661153, 794733254, 906995537, 963584134, 829132283, 827954650, 605539306, 438547644, 971262828, 305346641, 146375804, 793053661, 467028062, 774609971, 119094423, 491199379, 824970679, 625155826, 199552394, 755784104, 118864255, 608611764, 788698923, 774584894, 706793512, 387347608, 248695884, 43060034, 427572262, 935268033, 822803939, 290341468, 829782023, 337072317, 274124101, 141888376, 493897397, 510904315, 121098812, 18590828, 477733046, 411667894, 18325912, 238812239, 650413997, 297225071, 271767873, 352945821, 176898881, 417568810, 604565110, 479620172, 602427032, 517591030, 629054151, 197753402, 989646987, 701021681, 44664596, 385450977, 701610967, 363242832, 728377164, 984506844, 463173040, 784082219, 125957809, 261594454, 562219008, 214177689, 422521728, 721494938, 808211695, 332877158, 807839062, 688247259, 315692681, 693581149, 853462468, 180905569, 873656628, 629276917, 832694544, 523150176, 684537900, 674371981, 619793207, 70664902, 581784707, 640710427, 462134805, 154869069, 73924679, 685472072, 832495410, 252471253, 172521871, 215174787, 921676239, 596802468, 147427314, 207297906, 183806372, 986536995, 615785367, 801703268, 715065432, 749065932, 941703651, 556231057, 81001854, 42929015, 643000200, 573188709, 911727068, 53615328, 534168523, 532307549, 712736466, 228629192, 256831857, 428911600, 596621971, 706565834, 567707372, 106725305, 622728509, 127003735, 256582161, 634921307, 772657644, 350564477, 179823925, 658634764, 820286419, 919988969, 636789039, 46666170, 388842651, 224469742, 499650540, 43712585, 21769110, 87877050, 657077015, 535049152, 486151163, 300586834, 882055103, 475562064, 221206468, 473462921, 396044074, 314966395, 988010351, 671625307, 265306763, 851104423, 539038704, 124091913, 676944950, 967504526, 733752810, 112251925, 357608480, 34294165, 390150991, 377817543, 129194133, 530855135, 850419274, 928993411, 559556610, 804925135, 579058970, 664424029, 843953401, 219151120, 507174975, 580250440, 413758671, 446142848, 920691946, 805409690, 985621118, 243272515, 45331577, 242475116, 383651771, 103503202, 63052282, 158020194, 177908434, 10066281, 487716522, 192113192, 232039122, 561600171, 599262501, 673893763, 851815820, 193981746, 713074840, 163316139, 898655427, 806001894, 215742993, 724081039, 684831341, 60778867, 361299501, 385775260, 133237614, 19165502, 985544537, 898895128, 697094802, 38027807, 315813438, 521758041, 965258380, 206384839, 556297989, 354364620, 916161329, 797652328, 99910860, 428588773, 41077277, 854565606, 201760013, 902575837, 549664565, 958057416, 962525531, 718228971, 562183837, 910526170, 333006840, 916939120, 411155516, 515958580, 94043792, 773140984, 677777828, 495704161, 806255914, 45466961, 839862871, 155799130, 794810788, 895415997, 283368639, 492114269, 916512512, 502671180, 107633730, 742832840, 51856929, 885631732, 692499461, 82543598, 852136529, 584288292, 949626365, 1783818, 753107618, 853090962, 266337962, 718816832, 564673709, 776800606, 509831157, 161792667, 105416949, 42120325, 582965673, 115033102, 955124123, 655788444, 106956226, 211003352, 163580021, 840360556, 141620272, 156107837, 961731690, 694143616, 67618453, 174173823, 363390879, 558294713, 49172945, 602105909, 100876147, 580103383, 201276487, 896021220, 350818034, 580438787, 768745490, 890408857, 216447621, 984149969, 224063331, 101141762, 401476133, 933998615, 537845385, 315768180, 814909620, 450759993, 932714512, 205799236, 991109129, 368125198, 881685923, 716082837, 945975350, 164224636, 178403852, 593053447, 363922674, 819159285, 609920124, 634553282, 957458819, 989213508, 530672355, 843709014, 836276533, 544642297, 741227126, 498296923, 26749167, 59710066, 726613383, 697296537, 501102191, 982703096, 350130944, 293836115, 623837293, 228996211, 518706482, 31534359, 981757657, 315667509, 962689732, 695251494, 11030124, 15358883, 967440405, 673966724, 915698389, 149742149, 902216652, 146204173, 456866058, 434268430, 287977876, 320980186, 702210295, 812160008, 139644332, 180084174, 41723417, 405659011, 306300263, 836559014, 150294785, 620229288, 786429365, 963726438, 508778562, 62779827, 165895153, 713737174, 258400713, 579673736, 960579099, 531875255, 813866340, 605949345, 203968672, 894498693, 976712389, 577894232, 220366944, 795128251, 355425286, 882739609, 497581018, 880031637, 210566368, 637935882, 790332218, 140370298, 159130252, 694697623, 356074724, 571507101, 847386887, 32008336, 349857458, 177002858, 263458496, 979444647, 984567470, 869361166, 720733955, 376079208, 213512183, 733106399, 168705591, 806055716, 610609036, 952980094, 216697504, 788417895, 117750834, 485822251, 833009278, 934240772, 281636021, 122290485, 974203272, 741381122, 717435674, 706320195, 704605344, 445109024, 12175269, 69189659, 313150730, 925114665, 412247355, 680809254, 34751369, 943367790, 875304894, 976138428, 375942370, 595763268, 819701571, 904550147, 354034886, 985181851, 934513266, 39315829, 832675009, 902473098, 768916819, 540931997, 343377186, 273591164, 939772728, 259140492, 312368514, 971548070, 967320008, 96412438, 935497390, 203702826, 233101907, 921461692, 810130399, 592183720, 826037169, 7485374, 843049367, 717341120, 539919949, 31374381, 920559797, 921425055, 631873439, 511038706, 651480230, 503339777, 182732242, 394551617, 460111853, 968708209, 4781186, 875313059, 28632664, 195421823, 394249572, 792730119, 130249825, 129934791, 239720982, 236764237, 518826352, 720565446, 110184611, 774119149, 766958766, 793782045, 715384436, 213750100, 31379062, 379262599, 328415401, 912654817, 823984963, 81715508, 139259524, 283111507, 216687972, 904696378, 868314911, 498693700, 881164588, 189283400, 886733649, 417084357, 931366239, 699085045, 807465545, 377403901, 705097893, 702870257, 23188001, 23115684, 106237150, 704045683, 651708959, 580680938, 836802901, 52445906, 339941975, 496070319, 463518373, 773714300, 291436739, 97730214, 990537780, 770169440, 341100303, 496465717, 937022019, 347872712, 989138844, 518245535, 853685843, 574302733, 502716805, 13412705, 616750595, 986281002, 808530699, 189514307, 100566303, 713858157, 37405872, 403866615, 48801231, 875275310, 341132949, 820004985, 39228880, 256082961, 466795854, 546931521, 570394372, 898512144, 638190664, 859309161, 570475922, 996562258, 16124165, 109470874, 858759617, 695474592, 49102522, 96943560, 466433959, 265961480, 336063250, 186366850, 674370733, 856270669, 123205848, 350506064, 935658599, 442146419, 137193034, 917524672, 565029356, 809546359, 877426521, 498601182, 570275668, 537918237, 716634615, 241910436, 177577801, 958740243, 616635727, 582295056, 301029328, 872763820, 718251791, 192640532, 96119161, 18878034, 507871571, 575077042, 658148750, 93794528, 715275627, 419745183, 715352015, 658126158, 662212101, 703383664, 707477249, 437877115, 84664274, 725919647, 843089247, 462224598, 507606591, 793280638, 638802734, 714737545, 740952044, 401777425, 105134655, 532741060, 237570695, 402122451, 624374620, 899941927, 590668097, 483668761, 501389225, 207619008, 662931115, 830063993, 474130226, 63083316, 458705089, 780493022, 252215924, 507358602, 252286284, 279091134, 641044181, 333640033, 680756487, 299490689, 74325843, 563406664, 717888542, 449068473, 53515287, 953340973, 915700157, 705882431, 130131409, 647283946, 394973348, 752576059, 276051352, 688158422, 788940471, 610018911, 337533427, 607417103, 396434932, 715311458, 956918578, 479961203, 357480081, 633587670, 488047758, 61959084, 941657462, 395745696, 958042456, 303507274, 690808916, 378501680, 321799606, 163625708, 684691679, 235092199, 10702072, 344522184, 729304497, 862449606, 416773806, 249442018, 863604601, 103205400, 504944024, 639746113, 868815318, 752158423, 58620617, 369082446, 897300462, 785575222, 792344057, 211503910, 802337679, 692902870, 580723701, 724409268, 317158578, 64046209, 565629072, 23071129, 174760015, 861378118, 799146971, 210750302, 283641189, 402379777, 606757505, 850574025, 47133619, 870639303, 811843199, 848488668, 125875822, 355370743, 507850334, 955216783, 332549785, 172518748, 15191779, 44508152, 273761241, 550537930, 528987284, 540703545, 468724751, 944189165, 857914418, 17890826, 872439835, 975535663, 971047791, 786872577, 817539612, 831921646, 26798293, 594832200, 380038700, 648117402, 615851364, 996039493, 296740504, 262434051, 515985022, 457427797, 390410274, 270005062, 510928076, 751440873, 134333017, 394100065, 449788454, 76622887, 45105669, 372545423, 276775642, 950335984, 987247708, 686969778, 922271613, 893758691, 648401153, 585207996, 315843883, 732642662, 34859446, 937503006, 346458157, 761227672, 180487826, 897813932, 265867430, 328672229, 827845695, 571546051, 392033951, 709538010, 821691578, 729871976, 785011739, 649032430, 167397286, 466857690, 97422800, 711817289, 144518148, 13014544, 10300084, 9339054, 602285928, 803855102, 817095955, 257249182, 584901583, 258018047, 451354403, 794892631, 496695529, 615499900, 608556294, 183314915, 675726312, 525947887, 653106214, 475841815, 722674468, 265894758, 540688724, 252728041, 743547286, 858725584, 354068651, 576288573, 639156053, 319578649, 305814358, 561838040, 329751815, 875740767, 195086238, 49583626, 703733849, 583288917, 731613512, 707945970, 725469107, 109740012, 429452820, 723108827, 57260024, 635535835, 27278995, 880166623, 114149153, 487922496, 441981099, 861090804, 746736693, 508330222, 592066062, 810494947, 787116463, 121152650, 770487979, 236310673, 20743821, 515114142, 223527816, 693327383, 138294619, 814527683, 633848347, 365161890, 690051570, 952358718, 321625494, 787156189, 164764577, 55246534, 383879638, 160318386, 819225131, 906128533, 933879493, 848967746, 465426711, 109059343, 235576770, 356556188, 451656535, 774464817, 284759753, 384929419, 488175320, 402543998, 249876593, 605950734, 68589850, 102215567, 235920496, 595060791, 123475866, 448538630, 722004704, 190805191, 89281576, 941923104, 700009320, 146376612, 998837072, 485365947, 230651572, 479745422, 309559866, 306736453, 71645251, 800265749, 292803553, 115088874, 939214568, 364519959, 66960986, 675517478, 723443086, 123673460, 134713282, 808099056, 740451535, 433753617, 200272711, 928039662, 269559325, 123171878, 360517073, 768824991, 376741152, 69621638, 196783792, 362133056, 264684678, 832486849, 933364890, 632598002, 22501578, 612999666, 583263768, 469722851, 854666579, 459246959, 410194366, 726903631, 112392229, 131642322, 175314779, 55648299, 754073503, 273195784, 680992035, 44519457, 795526662, 639499234, 376831076, 359749632, 261920801, 70250873, 231758062, 598839245, 198311293, 7377242, 13423476, 352856762, 341325582, 414981569, 37022488, 359796341, 597837940, 513365151, 269620147, 286387897, 259995342, 586713980, 738022755, 872252505, 62128789, 497558287, 713520310, 181573024, 60348538, 434326366, 617848793, 79481666, 749033524, 753312579, 501626726, 468942679, 204997956, 101116289, 22042280, 405997410, 260635586, 635514197, 930007412, 686852784, 417226984, 741959035, 687480666, 127313674, 263757295, 236228056, 65217832, 24259694, 999561581, 729073587, 386158938, 303300457, 555943955, 492350242, 116455531, 311053471, 5257742, 120318288, 114970606, 899845876, 763962908, 973233373, 76938211, 386288671, 641462684, 23632315, 176070621, 311349747, 583949839, 132804339, 504133330, 84178723, 616481880, 439812936, 735824603, 661604126, 660566775, 391259795, 87268156, 160937355, 21830023, 65972129, 207798840, 672116847, 716657276, 561539369, 549433665, 260924215, 857372324, 376685535, 81738426, 936752576, 786715545, 980557920, 597366175, 524030598, 145434758, 97691290, 740218336, 76186195, 913390810, 11953620, 969505969, 63844528, 728599625, 851589541, 323349441, 439614265, 909770794, 37372693, 648034774, 13350762, 93036889, 195587864, 233070765, 774219035, 829571371, 33254181, 548509238, 182643337, 74149106, 349039457, 522495303, 270045770, 564170604, 367426344, 807928557, 725653011, 458249710, 159303889, 516833140, 358226178, 43827938, 504718189, 144499062, 528602766, 267443064, 787957701, 203017357, 676720993, 267539308, 551880849, 515413707, 937690972, 774705722, 375992768, 357755827, 927640523, 188523997, 833129816, 608706572, 649820547, 742274888, 755832759, 459439283, 871933447, 149760356, 123057181, 935688223, 721989991, 644812985, 251762496, 455572479, 644770504, 800241307, 856164073, 723437678, 511123722, 71315048, 253004314, 420046885, 551743256, 384668321, 371661620, 375747837, 3969380, 540998595, 822390318, 270544674, 92910342, 424476530, 174431064, 274988229, 614669537, 704293861, 456778699, 580289169, 550874281, 725965834, 416352523, 23681209, 326224020, 555667375, 327446484, 244235447, 576621524, 486519189, 152797620, 438162090, 384377077, 29698118, 956464548, 786851484, 286540486, 464649999, 372710234, 84697154, 390961322, 852453725, 355641450, 634358545, 522251661, 627691371, 225920469, 305879779, 62040419, 142809854, 191857390, 87545275, 35491551, 304752126, 54422411, 965064922, 530367541, 136100341, 18185016, 579460231, 451485991, 440111216, 446195827, 846725109, 323173094, 15537585, 757654227, 908947340, 35777071, 67551741, 647228230, 985051566, 208614278, 315416836, 219437559, 499186105, 473276902, 414532038, 10652639, 48648082, 813614337, 794697735, 173450244, 61425004, 326033748, 857498437, 495752009, 209618229, 24292764, 199615955, 607815980, 985875794, 429754924, 293662736, 135271516, 352446489, 24864385, 432891122, 553531055, 736082171, 337903468, 791992113, 389694079, 735743198, 624933217, 485507707, 198061971, 839017186, 392823932, 199478200, 126352935, 136708330, 625242136, 122422494, 37716226, 598611892, 739094127, 747492398, 328926057, 643693288, 113971294, 157400914, 599500034, 323622903, 977306106, 667509534, 602559169, 764804422, 607783128, 386025118, 775803154, 397557043, 73577118, 293825986, 945990842, 649112829, 331418042, 124056712, 110732462, 145417031, 697366302, 945218660, 978644367, 849255622, 469943286, 367357310, 897631733, 418812621, 406346191, 532677280, 106795437, 770926957, 927208506, 629992988, 256044323, 284245992, 360939707, 131891743, 991599473, 731775792, 962048798, 278441276, 602460289, 582552733, 188417680, 266480687, 344883892, 478353669, 510807904, 573491439, 300038239, 772370742, 180052112, 248544562, 58115415, 537205276, 995335651, 206914878, 473050717, 98532521, 227974356, 555153774, 791144733, 282038963, 221847590, 361660973, 587883053, 728058656, 810022936, 291501070, 249488335, 66164259, 119295743, 29237128, 379729983, 805950763, 813500988, 930659694, 824854190, 835625675, 502651083, 853021266, 869381541, 935816332, 282759869, 755351964, 555772840, 630584144, 309802237, 56004869, 333272386, 574044046, 362055262, 477598442, 217406243, 963317668, 154625311, 760635518, 785280212, 556987901, 660458899, 82089953, 547389542, 86090913, 879276305, 212912238, 347964241, 770293955, 771392611, 918125604, 691068915, 884204556, 676156859, 523704982, 97652282, 375339231, 161695803, 809896967, 29298959, 537754660, 809429349, 925227308, 596921721, 905511925, 197832116, 925381403, 602580890, 347727483, 113106143, 314547109, 363923035, 8510485, 637596725, 578663353, 17080892, 311093108, 562005895, 428446964, 733572425, 173807406, 333375831, 760272365, 196980474, 98154689, 13312819, 786209846, 288507485, 950068482, 977690596, 835743471, 62084796, 332215855, 394832554, 577635936, 386646097, 548575819, 723367476, 764545441, 432295855, 160059416, 214729175, 617477829, 267908627, 841896664, 565311011, 697882470, 842242736, 39743670, 397754450, 183444724, 747090749, 77125174, 387859360, 293274980, 267453217, 108349285, 583436871, 63597390, 723230243, 479501362, 523407147, 619745447, 883878969, 667977976, 684703694, 277301220, 576417682, 283295354, 180510032, 652048543, 400243881, 928051874, 718338853, 466562533, 220501330, 937695476, 110020935, 974031519, 986998920, 325146930, 604505220, 684523980, 440247299, 831362174, 57766588, 500739487, 145679625, 671485899, 524701189, 103977404, 162754023, 693685712, 456845135, 813270206, 738243751, 391416101, 801949610, 428517444, 168926872, 561780644, 806519488, 332274291, 531684924, 272632445, 757552753, 38765124, 327413575, 46695167, 885832564, 325760181, 708141686, 531410406, 215911461, 177232075, 716419378, 649456179, 289701421, 686584863, 159503415, 961917547, 407124365, 897107450, 143685236, 802557984, 848924699, 84136852, 88178559, 818194023, 394270856, 974593728, 312782433, 24967220, 335720040, 24173794, 907740663, 989536606, 264910119, 689054504, 185811444, 259324081, 150758327, 819059325, 760294010, 647639891, 981964351, 877128730, 547328580, 308111644, 301552582, 576345643, 579085719, 165920913, 545151594, 340486127, 659136833, 699935546, 99814853, 557620304, 574751479, 81574309, 46673430, 945133, 185200958, 67575946, 184783480, 173476800, 961833101, 746798396, 170170968, 893088547, 578638345, 687982574, 816410207, 89537768, 627034238, 205288650, 776340, 156729874, 209029704, 402004983, 868162134, 29375684, 712486836, 981303397, 519685750, 137638819, 331808016, 541394603, 354906875, 11606595, 660707086, 258606355, 178720104, 634553526, 49213137, 142764730, 785992836, 994566079, 711223503, 931668322, 894053930, 187548215, 63526194, 790141971, 516254003, 930112123, 760017866, 180036236, 953832405, 468828275, 543177525, 534599387, 152032568, 473517126, 280080229, 16339654, 512983222, 127760735, 834784763, 812806229, 230750256, 307753391, 959784094, 687401625, 545932808, 35482968, 453004538, 258607192, 149739752, 256751605, 56907307, 4171590, 689248681, 223922062, 915142246, 27480094, 164175679, 837817417, 149511971, 9666936, 373389641, 982385045, 901746135, 628192758, 115462674, 592618237, 971478160, 990789205, 99433991, 614065793, 229588765, 232252601, 292046115, 367759014, 377948826, 101178770, 550967889, 880354186, 163947976, 629445890, 256755725, 442318393, 767915354, 193756889, 829557719, 49582302, 834230787, 558158994, 937630628, 350382225, 825182920, 863156395, 788316155, 923369102, 2901903, 836283741, 878248181, 703499235, 304785552, 12502008, 258301961, 10767729, 469635025, 237698705, 448924773, 449445667, 23253893, 192593273, 913393700, 857561187, 444237398, 610854504, 681935870, 25296652, 745217145, 482223671, 777276554, 772640796, 195160095, 492075183, 890124685, 431213974, 115691041, 305627472, 457986370, 250761650, 705420852, 237311567, 433883742, 974624649, 823162494, 657347321, 393510472, 633073632, 849826648, 281793659, 877987597, 954351357, 225679890, 496462874, 151256434, 290695573, 549529742, 597085614, 101146588, 333672840, 409747087, 385210614, 391333344, 987377183, 43334703, 344993405, 572462323, 423214841, 871074336, 55214558, 733284356, 469692180, 243655956, 226754562, 867502782, 589469113, 197239107, 842497393, 756024457, 217992955, 424464688, 353579726, 356792467, 697689991, 422030017, 62412308, 874239642, 848818813, 953005112, 973759938, 402374346, 546459485, 791346383, 280755149, 243125677, 933846146, 41475689, 715278276, 38008581, 751786475, 558902156, 541334997, 298685601, 136820489, 864160283, 772723016, 383963001, 799569072, 488499406, 132686326, 8649952, 820320705, 382118060, 511340456, 952922685, 648506800, 86698249, 981233711, 64741365, 375536932, 495359157, 320432030, 616093038, 76236880, 937891623, 911773906, 436126430, 762586809, 241334237, 582084851, 285516517, 711603651, 698063266, 874268442, 791735449, 177477196, 97988319, 139606746, 251905090, 890797973, 47865432, 829314877, 24989840, 105113736, 242687779, 285471130, 553848844, 994538781, 768874172, 864322711, 542239217, 246674663, 203352273, 157351650, 902164987, 663501096, 833963398, 910545645, 26702070, 394692736, 928271643, 814187161, 492226016, 785648319, 450515415, 642342470, 732140886, 369818386, 274906174, 511600817, 250874414, 627151049, 792645329, 168727800, 29537366, 381468020, 817325246, 42756934, 574378756, 128317070, 678816456, 264451397, 191453362, 217212986, 320717866, 947483235, 258492903, 878162499, 413478344, 670239488, 548778454, 146252401, 297147862, 686195738, 704005888, 445160608, 496313996, 140175327, 913875388, 603543738, 505419378, 34620541, 717598297, 142008743, 624205008, 673818024, 648773566, 259500338, 498848147, 486466546, 926389380, 454997596, 973096358, 450129305, 484949010, 71981969, 917963618, 687988573, 856577021, 851997457, 761928523, 213313582, 201185483, 339230149, 644049832, 615953681, 61854702, 636518901, 531758171, 338437548, 71069586, 279202087, 949019695, 682251057, 778777609, 778972262, 598954616, 973368104, 9848330, 317325442, 572890809, 26218560, 985770990, 930683712, 969557557, 428542170, 539607752, 753854552, 781631044, 357641170, 8919868, 148009278, 926755973, 902953261, 286200505, 634039316, 423247378, 149586207, 765983457, 55286812, 929694115, 902178507, 529223090, 379073174, 118514450, 248362425, 148014129, 115332922, 545499419, 427078135, 95432161, 829238561, 81864014, 736246171, 420614245, 49411528, 44031083, 499784010, 707937549, 793307803, 516910124, 2785412, 279367928, 631176014, 333554244, 421487060, 271025882, 222468653, 492067889, 712631854, 691943931, 447809405, 811704635, 565150253, 581324507, 590294009, 494004948, 134958242, 660020489, 429818310, 703840377, 532744488, 271013663, 494050181, 589641638, 819486027, 839734045, 732074390, 969090789, 440224969, 88132448, 700073072, 233751129, 287854702, 176387067, 165691850, 302583447, 656010228, 478577190, 725780709, 351624502, 549029444, 421031302, 648336929, 356447423, 432748008, 924032572, 715453604, 385547656, 605211366, 944175512, 44108795, 295881388, 923155821, 941234465, 91367044, 329556078, 139375330, 757870341, 708805575, 136256927, 613025919, 556439773, 735632428, 838791825, 527399478, 410610678, 743604450, 333162836, 193816223, 853058341, 949499457, 923354521, 977316354, 52193695, 532447502, 640707828, 988270124, 205743339, 283897056, 685040903, 883369738, 90850757, 938572854, 186208515, 328667939, 173983181, 336151308, 456658434, 107570784, 416638043, 88593440, 342261358, 558478644, 102037852, 108784986, 304398074, 417422324, 475721813, 629254235, 116517220, 483390249, 102985244, 761498219, 919495574, 830699428, 683710444, 842103778, 46019574, 937378163, 917816099, 555907410, 152613440, 232480453, 839491433, 231141333, 702655491, 698014285, 753909301, 799037057, 282284508, 314983116, 816447654, 372578110, 504847842, 579014393, 866549973, 996870956, 159736586, 854855309, 40134571, 144605699, 586773031, 490223909, 260754252, 959472603, 212304098, 753704522, 824872614, 499681151, 739968178, 152897700, 700811210, 438768486, 302863913, 720976301, 133656407, 402403442, 657795167, 403963498, 296633416, 473416237, 149960063, 193484526, 679019432, 610502744, 171531584, 271910070, 127959530, 829232935, 186794806, 14519993, 319242084, 454085372, 889600786, 203396630, 682392150, 573513761, 98296505, 34357768, 708831960, 747181501, 828963814, 982225681, 452476522, 264475774, 730715803, 237450205, 812917426, 847188720, 505496880, 67791202, 903694870, 613451458, 644880185, 592413175, 282108840, 499435431, 238004604, 113214641, 391540958, 858487151, 734855596, 841499250, 207946724, 719317941, 201722860, 270246083, 964632532, 492463564, 790436188, 123323435, 724593125, 703952109, 928451267, 860842525, 184204124, 766997235, 479457834, 850055252, 891292832, 701334485, 405915581, 335450702, 460701803, 688083456, 295204065, 293767864, 830482398, 939803894, 610675067, 7262589, 943201399, 867735525, 389752957, 729932873, 762196447, 275769931, 766530025, 850545783, 602130710, 52458240, 746731334, 956290339, 400383234, 975662882, 690937088, 568602871, 59929137, 18013609, 766041015, 875078290, 815030867, 970199018, 235065477, 321825309, 355225593, 96405168, 21058854, 408881383, 700159831, 709784862, 34883339, 588948160, 331468269, 663658486, 705627993, 206588371, 999721333, 466698228, 759948103, 328872554, 739588795, 640177893, 713254900, 999962397, 228231586, 159867932, 171179151, 396621911, 504401606, 642446519, 806892573, 444903912, 646078212, 402934903, 694698584, 350421202, 412263160, 156583357, 755131230, 578889304, 113956184, 798227398, 382949059, 824568958, 711810030, 743965711, 638185230, 64143613, 118527096, 215248359, 143925704, 389936531, 499510131, 320904596, 734688837, 515122488, 596204084, 880019515, 778460121, 133957133, 861260814, 964533497, 102100617, 353528908, 711534797, 761794618, 951379361, 308176413, 311530055, 812107241, 249917495, 435521137, 404202656, 385707913, 643757992, 469650848, 67430499, 263435808, 758799713, 806437166, 90374211, 388829308, 698922502, 390823175, 274620659, 463700792, 799821238, 982980100, 804282016, 993043171, 680641882, 530322801, 719270608, 2870070, 936105267, 943771387, 830708546, 75038422, 956084005, 755598432, 295197596, 583285589, 976061125, 422757132, 202482047, 824360569, 661163697, 329467956, 113311605, 724495848, 585024152, 800365821, 525862685, 288400408, 31449848, 636071232, 694369899, 861577494, 613324041, 391723843, 445924766, 335550158, 143698461, 795357063, 571901520, 198108476, 428021209, 19470577, 916676115, 914746585, 62080056, 324937136, 721631289, 170536750, 636995177, 747666445, 988033968, 64219473, 915294906, 872854560, 887569979, 93433240, 30567384, 784470730, 353927867, 904199897, 824716488, 402804403, 968723434, 714806150, 257847450, 351808299, 458141919, 704326353, 404506040, 617667293, 368700628, 872636923, 734274614, 178260835, 635580868, 209974939, 388479678, 815491184, 275155074, 125418094, 610734154, 382468479, 9819626, 807640630, 712632899, 611911484, 781206975, 821471910, 334574269, 781968845, 546308067, 311186506, 595366630, 45447824, 671296395, 795790040, 613886337, 392861546, 466812082, 494987183, 461272056, 172300328, 607306080, 881607045, 865981509, 925759571, 713210930, 248081333, 219153577, 989141411, 755181917, 487733604, 368236529, 865082633, 406836813, 168563977, 790256491, 889181000, 780470281, 19090273, 379601543, 95256152, 245896871, 565555917, 381417137, 28865234, 382747444, 772429718, 298336850, 905461786, 186822447, 157272482, 385627257, 904475107, 536192153, 401330914, 70442480, 708623573, 768202889, 244146255, 970179848, 210468071, 312327114, 420373174, 702823260, 887992951, 881926537, 662419903, 979889146, 759183748, 361086438, 795005705, 248828463, 213621945, 178050273, 786868902, 436086698, 943108281, 164344073, 717050683, 461047860, 338736461, 34895557, 440086355, 522841058, 77564546, 900212274, 896299133, 487220521, 318841604, 617311999, 788722238, 858160601, 260007744, 939114724, 757197237, 27037021, 986600734, 22731741, 650810609, 170546764, 528552824, 897872937, 744894992, 130339254, 747523151, 371840227, 390357393, 977712649, 10996824, 546489175, 808978269, 414897013, 573598671, 238122615, 30166774, 233370781, 74623200, 29571886, 945348679, 493485174, 3437036, 470696882, 650684602, 263297323, 414181771, 279863303, 674618736, 789201110, 828164277, 755255912, 506377267, 946593464, 598803073, 545525534, 127228528, 820906614, 716909352, 788053500, 192449597, 231080008, 721918823, 325595621, 696012665, 940405279, 225899744, 103031888, 637175794, 47676400, 45782821, 596574328, 126412783, 707635999, 690302737, 59532277, 235148873, 710360057, 589032487, 591313346, 274015384, 139604853, 833819570, 450114260, 939947794, 651191947, 5579566, 574023969, 356815932, 315143752, 966217326, 378369216, 508699859, 405252822, 235037429, 72924873, 693640677, 162819566, 86275905, 187812986, 398013886, 960294868, 283078988, 671914937, 823612523, 68759615, 332461567, 970446946, 574394697, 681261828, 973032003, 657366601, 118358453, 29997383, 29025763, 119216183, 23678721, 419267266, 400771013, 102776453, 947683559, 193046033, 668859135, 310475533, 285031179, 936063949, 53674301, 334810541, 212648668, 124125294, 125687314, 765240467, 652342602, 976774622, 871443594, 698603969, 21213470, 341281192, 112388360, 187973269, 718407757, 131967231, 877977487, 476862017, 876240044, 54755630, 814572805, 69481780, 762592535, 375285115, 68509438, 264083333, 538800249, 310595309, 221946573, 319234189, 498851563, 466410239, 697650517, 311159064, 121922698, 318084331, 832914635, 879692845, 530625099, 443870204, 865881847, 66193468, 242942819, 739948976, 342039328, 932918253, 795946299, 434143676, 881895615, 369606430, 268941037, 456788355, 766218497, 482531323, 234434412, 93504119, 570378906, 378202240, 517069265, 842834951, 618621602, 77200519, 15219841, 266466549, 360257563, 682192474, 288896359, 594400550, 986784873, 981472470, 871195819, 316186673, 799816492, 683395473, 874767406, 929970549, 106961862, 780463385, 285777721, 792971482, 196524765, 457800066, 603132183, 292507570, 915885520, 525323858, 476059424, 700557885, 767066802, 420282713, 226196707, 400266157, 72795525, 731425573, 288984533, 712465882, 780290405, 831326184, 754274168, 739563704, 289749163, 244292368, 555669423, 730773251, 790355902, 796464692, 79190798, 301386161, 471779257, 744574627, 967577989, 307762861, 827625622, 474646333, 824929920, 585755199, 351169267, 244083150, 288356835, 263396799, 668301820, 211792036, 853955780, 835399518, 927740554, 303824648, 784278718, 727581004, 932213422, 147426359, 386380865, 151548487, 754306818, 573488770, 905478241, 398783433, 118684828, 233615445, 997366656, 200132094, 81555216, 738703074, 898670204, 953136826, 306781427, 169609607, 29483768, 436685632, 403515856, 219957842, 935703308, 38709419, 543705956, 86260884, 543783247, 394654825, 238187502, 88991062, 813448964, 914269659, 578330242, 404820421, 81703046, 465332364, 488918306, 325623983, 93298769, 624324833, 925828622, 639942992, 965387315, 799375417, 679690818, 370872656, 482105603, 434467963, 425611585, 633058806, 529753866, 795275415, 108960158, 7736728, 398152222, 526232791, 489669724, 911384944, 750908647, 329613229, 322637031, 927053084, 514820543, 245719954, 736929137, 828971378, 277336835, 606810423, 176747680, 533351357, 697958807, 427292906, 989719984, 105771196, 177577084, 57157146, 392943806, 596871620, 165889563, 670527728, 61369150, 238169978, 541192364, 410018088, 184240832, 501456160, 180540236, 835972714, 301814902, 30871024, 555249582, 468332608, 992237449, 266200853, 360328572, 300016773, 935117024, 844145233, 577187966, 288440988, 607891575, 574702476, 136264377, 767201901, 875122211, 47579507, 546115583, 440884929, 787296678, 258624721, 363677420, 604093803, 563767574, 658125677, 172891369, 319027995, 566007077, 628787199, 133079472, 649623317, 509691790, 510014621, 127412183, 216508998, 436283104, 766743269, 107600004, 693234421, 50133362, 15591641, 411674372, 178501710, 53434823, 250055545, 189413461, 986817796, 54367801, 539541837, 241491661, 252785478, 38609487, 508079185, 977101980, 287258943, 130396290, 397699260, 149576306, 766273323, 908971990, 622262296, 626300239, 534921071, 588665921, 288770842, 995312077, 634023556, 523593722, 950133784, 774610360, 683237486, 705616289, 587865949, 777717799, 922905628, 710882189, 660203978, 519273778, 302252297, 877502249, 489262586, 411770520, 470744185, 749930230, 254973511, 318083308, 247022036, 146374185, 818241210, 696415573, 908759882, 210336924, 301764833, 707191627, 558704536, 663179891, 21680638, 308216121, 937967976, 116180804, 12090507, 187228964, 16617659, 961177973, 285883578, 185323443, 268579286, 716920425, 201391016, 537445142, 181181290, 38057194, 603773641, 108263469, 223176616, 222561518, 16604538, 150406942, 396525760, 185588581, 5084025, 184994626, 138466757, 550161599, 89974691, 95759039, 947759608, 47024824, 781536556, 243131301, 171139589, 347848697, 153416540, 68009978, 803282199, 196368899, 857279270, 855100496, 855911064, 606465553, 144261795, 711143099, 44901671, 755631796, 518962983, 856585198, 407579242, 674788822, 278946477, 401128402, 992623738, 625927085, 670660502, 68254538, 788071932, 362467615, 260692870, 265492635, 175764097, 328575299, 583995754, 698513807, 448925166, 539383477, 149242201, 622167532, 794987304, 929861686, 701785864, 12154777, 948917200, 618438112, 276365243, 805643178, 684395890, 874860605, 550398239, 690550216, 222969935, 815242829, 907471934, 844447245, 504569133, 547057802, 774410311, 243718338, 220714614, 838490966, 615164881, 60179975, 936562584, 739349448, 59729822, 438321527, 755677705, 839155640, 338618579, 266434076, 790581926, 552006375, 359895173, 809982925, 740890849, 968955577, 939215698, 372194626, 16197292, 66933401, 574104790, 58014336, 843028439, 250053455, 808445567, 563039310, 696899997, 630097687, 944121541, 480643551, 167465800, 887678786, 922139609, 403425139, 119482117, 175406070, 571515200, 547878288, 505855660, 831375938, 106702542, 679787094, 640609210, 925549624, 942089836, 92928030, 927669668, 61202566, 329917866, 811540632, 731815779, 605339609, 277536139, 103826674, 696218084, 296857591, 237963312, 85858965, 119402780, 710639100, 598227133, 785300725, 390074576, 470833182, 751300950, 188284973, 471022212, 469274841, 984213648, 127262635, 521845203, 381649366, 110800344, 246680185, 943054184, 35532030, 156319295, 996079951, 709243099, 479336878, 700926480, 91548879, 729957113, 508626529, 560265828, 729652145, 180424978, 309002710, 138337515, 791990356, 559980361, 920164842, 108962049, 687157680, 88366838, 441868463, 937418860, 277511129, 727639014, 968845004, 470820152, 634782321, 647338905, 210302236, 159183949, 320482987, 714014158, 59485608, 647535474, 839524537, 65830108, 999166667, 965117881, 190327641, 264469467, 150033976, 975153138, 245670834, 872650956, 321699301, 112376803, 401369063, 229692283, 669559188, 159126627, 365348316, 794283454, 828778580, 94510833, 346296738, 802608509, 120913117, 417496008, 470407194, 169174518, 569202492, 59592655, 861093691, 526191618, 282875556, 230213331, 183418536, 694564937, 807111756, 91649783, 721536310, 369013791, 197136170, 48343187, 938765552, 581361906, 212021885, 74319049, 567877875, 630258893, 708819926, 883468257, 287476650, 392172300, 518047965, 206476329, 437780459, 174326995, 763200350, 440833354, 823738801, 962217910, 926467704, 230588439, 953107916, 194218264, 89523820, 322339359, 301394761, 461772355, 570161079, 535131765, 772568532, 530398826, 485413168, 288582373, 8051486, 993674759, 65152792, 70267543, 619943214, 876006725, 7990355, 905314079, 544532849, 646315684, 369335570, 794598671, 697983918, 953486506, 282934078, 373144577, 866860416, 169688019, 658902038, 18260015, 39323042, 821471988, 465877503, 22447654, 998580272, 58421872, 284190193, 588535491, 815828394, 618221308, 991228173, 567618699, 185247432, 713978073, 98125036, 944514249, 505555044, 731166019, 256996386, 594688123, 759801497, 107408901, 49943859, 999244278, 725537797, 732902286, 665727303, 160244894, 348198734, 910272776, 499900860, 217373873, 24439731, 989528739, 572564305, 927659160, 304516722, 932502077, 932064813, 408401765, 970875585, 341185890, 492974891, 817581059, 906412332, 884449059, 173385269, 809854830, 110540344, 644518909, 741558145, 922762320, 296740419, 221652177, 677069230, 118192677, 469574693, 256796136, 67160835, 406358537, 250739715, 469835151, 590916463, 666845071, 574803014, 613667323, 51359364, 455425225, 988691655, 122339349, 346163835, 701829058, 50817688, 114084308, 184238267, 226479503, 745981298, 163873236, 440497293, 174752213, 510263368, 589256435, 99259907, 790839861, 712356303, 585798436, 158117810, 836638347, 757380903, 599538689, 72340990, 793465931, 344449824, 482770635, 204414844, 375290925, 782112873, 959008827, 988583264, 428919492, 216792827, 874881991, 988173143, 798894942, 406976703, 229664733, 551904728, 688625353, 726814156, 510518072, 214075348, 432043377, 264457897, 788615011, 462627583, 792583868, 309517479, 304851066, 617799937, 114061065, 219080316, 349283472, 536672016, 993993121, 683004787, 177125005, 764278737, 145809257, 448845813, 183775140, 255473814, 475231739, 772502239, 943755347, 30771973, 833041234, 23360874, 595083644, 334348921, 774727162, 305302489, 633165639, 358267532, 293069121, 582601224, 621271722, 491249881, 638092001, 400984418, 838141024, 757345343, 838093111, 697454203, 568026997, 615171539, 403414334, 89507756, 755461734, 945942106, 767286552, 972891148, 767355034, 969963810, 476567984, 317151798, 123361958, 602572620, 558990484, 638912553, 818076798, 845960275, 783287516, 968674912, 517176845, 533541908, 774198697, 179191585, 697951547, 727796362, 851280596, 357814442, 307038199, 790368024, 682807970, 776583665, 937530980, 429086862, 923697069, 5511429, 950942212, 320435323, 99240989, 206160466, 471260481, 95058685, 61093065, 364090370, 5013787, 936356541, 933710432, 592163742, 284487106, 973205149, 935959964, 340343118, 712800948, 590068415, 914072861, 362116890, 152339469, 711083246, 978001435, 798799977, 802596922, 93913432, 950551769, 313981737, 915274704, 94088780, 204784281, 291664048, 509522798, 583174755, 234352499, 106134002, 509231202, 468183994, 595943717, 199148192, 671539599, 973670795, 699345984, 388084275, 925254120, 605581744, 733463035, 882113585, 51850420, 142418559, 344324063, 368860653, 721604693, 232636932, 645882524, 265172511, 990925510, 50746432, 73644502, 942981476, 235730672, 55640944, 515519394, 454385539, 84847356, 258536339, 773660077, 410930384, 362192910, 723856790, 68581367, 227527633, 465142183, 371883685, 249547988, 670599024, 963767926, 516618133, 198171545, 910509304, 797653507, 120584457, 675865832, 25270185, 775512913, 644671633, 678445341, 409597118, 553332051, 331445377, 329566380, 290290167, 40719949, 491226334, 746190552, 38646535, 257506970, 266580589, 619928451, 865535290, 358416914, 338042210, 530485049, 310226410, 909924, 847535334, 395626537, 614107350, 450162078, 699401314, 622134650, 991258581, 810619703, 23966302, 990319874, 655985736, 229607085, 372463503, 432276258, 619340763, 112971751, 152736935, 107769804, 421967910, 300239357, 40633086, 315834090, 588015880, 987099058, 714107867, 606160631, 629005037, 962472074, 381810567, 858941868, 403128030, 921399022, 181318834, 512170329, 752268271, 136095783, 816847335, 586906071, 749455547, 72169634, 853593578, 158662954, 777330362, 33213858, 429669832, 789157262, 593111469, 310914345, 956531802, 108707264, 955624231, 43613179, 189615509, 530265386, 909994581, 507866861, 629792995, 669747582, 839197729, 695034979, 581250581, 685826265, 587680483, 39105778, 68281119, 207211699, 437454725, 857563882, 51623706, 952334769, 361958194, 267589131, 67654338, 853001776, 330751834, 424866327, 781652773, 272785537, 890267397, 17623640, 618531225, 356965046, 132379331, 77701049, 269751759, 456436545, 465179071, 23324315, 23092547, 975916699, 993760263, 912137384, 582801943, 113781540, 410465879, 498363377, 299856873, 740710187, 286941927, 364861132, 278467647, 535278084, 106204310, 656270911, 881044943, 319422206, 956409470, 694908752, 567002033, 479174741, 171657179, 950186430, 258077399, 825551480, 783365910, 578345078, 891859754, 956274361, 272251717, 224887427, 552932071, 988957580, 270343820, 594507605, 965121683, 395126243, 525941715, 871608861, 254217806, 904405466, 510058027, 946689051, 410146318, 636855383, 239915823, 68901915, 208572197, 150092068, 472858371, 148037591, 101318689, 741262925, 175747041, 403351781, 671141853, 737730795, 475863890, 591269660, 305073812, 78185895, 6615213, 951657030, 897986942, 208221044, 796912284, 297759377, 938829500, 190470945, 298763581, 526298970, 743612838, 773316252, 563905488, 984476565, 289409025, 598092193, 373028793, 515996062, 652460221, 929120809, 789752384, 712425026, 767960176, 71994176, 840516205, 243355382, 243269845, 481055461, 788613668, 197952382, 717064466, 589248907, 460070991, 56820592, 826637928, 608284587, 232335262, 353109610, 290100520, 249825525, 309612090, 979048131, 231053093, 677904890, 475890311, 429456481, 495511402, 34093594, 411514135, 946855791, 693203580, 137242144, 919386823, 372265772, 888809007, 631778275, 102202935, 335107453, 151884743, 79231343, 927324632, 1436320, 937059892, 495265282, 559819006, 580585642, 439556227, 857625229, 679922056, 523306835, 897896189, 315632298, 175176852, 428287476, 566813720, 718758558, 907420713, 216252839, 926919892, 127123037, 754099009, 254241965, 239893975, 380127488, 983703475, 1679386, 881027018, 257882356, 580707412, 318103721, 935012618, 930737566, 696830532, 981207339, 310777383, 400857149, 768089839, 721981927, 836759066, 891846175, 781922080, 253319185, 865700336, 412509433, 712074087, 231464741, 662075935, 514530667, 888257360, 871285728, 554381490, 191231706, 690260628, 790633206, 770528002, 340547851, 387072390, 879932400, 442821337, 899289520, 697364721, 93940261, 726373697, 471493584, 739226062, 113876415, 641594455, 383469928, 603153114, 765891244, 265959145, 576932007, 9157954, 361445616, 282562651, 976966094, 766023326, 358009597, 649794742, 604729758, 36247491, 359384217, 955391379, 864366312, 112033654, 380441211, 669169080, 512099220, 452565240, 848580513, 503360015, 512972370, 158868410, 518043361, 550809965, 590140562, 578930594, 49913866, 203050814, 891625099, 821587176, 806755260, 48659621, 929477759, 877715008, 53344531, 931402962, 884286277, 490247450, 155988970, 560773564, 601574902, 775987265, 555393856, 330002183, 951622227, 237968216, 905502849, 774821005, 462146483, 749426223, 294275203, 694319726, 503349813, 535289556, 507295172, 758307553, 619176776, 630528597, 794958296, 804519693, 176169154, 420408477, 323153465, 427279624, 526588149, 472056285, 647708370, 335402488, 378234920, 560567352, 362446981, 852811105, 847869302, 661059827, 532082930, 590715257, 636672817, 697849268, 492706992, 833027164, 377589486, 884363068, 640854779, 340101886, 947022769, 126365269, 319525955, 851517339, 990268535, 857599020, 535890207, 314588962, 792672571, 897125332, 14210892, 793544569, 862225330, 363629267, 334539971, 336243088, 454351177, 444673059, 878539528, 998088663, 461558798, 966071543, 183346263, 862671339, 855580256, 682865135, 273813090, 359473311, 368554152, 752730953, 698714690, 584019593, 92083951, 776688437, 229683827, 76698666, 421091071, 134099713, 841376639, 952213352, 496278740, 613147274, 644149135, 880774398, 814250282, 788596104, 693742175, 52935097, 166491640, 47118089, 100330972, 306034686, 994918661, 196280259, 850500803, 479653802, 665055631, 824827310, 602323790, 320364590, 353489043, 132123474, 972767863, 153262817, 605722190, 664920537, 885124709, 166159627, 72612583, 623143172, 378183084, 877620294, 493081029, 937334948, 163344487, 470829871, 547839903, 586255388, 341141117, 750065191, 710333214, 215607914, 334465350, 388448569, 585884880, 284263460, 416170932, 888074119, 370728215, 231232657, 500051529, 314430639, 196496206, 547546664, 266866737, 195369463, 121404278, 168009668, 40889060, 200085617, 701576958, 537537012, 206480791, 38601013, 166412631, 103286068, 414425340, 267377128, 537818511, 465676051, 525687357, 776749533, 980206300, 53449637, 985263393, 724818415, 372683498, 314443093, 316500572, 57758437, 979991178, 296127037, 277643511, 827818107, 182580074, 749223674, 275344936, 871034595, 395980075, 727251503, 655974004, 785495060, 867840497, 89683602, 923706699, 838222198, 754081830, 992269534, 100487172, 712279817, 793241460, 890292690, 636990445, 704555237, 154614678, 485086551, 983335508, 844123830, 460762530, 328318041, 976851559, 754952876, 239357869, 455558998, 405413202, 229581264, 671043383, 969345626, 907354901, 652456883, 476782986, 642145916, 353465514, 823218830, 180964949, 508573825, 577299535, 229587441, 165593432, 826504905, 494833982, 174358146, 533992038, 797264800, 91070024, 491404731, 930177634, 206125727, 630040198, 216516544, 341207819, 368006606, 181504668, 829527700, 853169224, 315854032, 889108021, 643181794, 832361547, 586480694, 705889456, 955803111, 271995796, 901467161, 917364292, 704385474, 282865647, 107994512, 721040052, 945414070, 989910932, 411627788, 35635305, 769824678, 179455559, 284861006, 560757428, 74565677, 49067585, 639213623, 743269575, 573604571, 126249965, 915381982, 336220317, 942518353, 666280905, 342191942, 817573717, 339485389, 990109372, 42901287, 697727469, 674825748, 883174043, 707247286, 29267223, 524892128, 100591549, 480773160, 878217189, 845903483, 627095503, 452858352, 496427758, 835704109, 997091329, 704633455, 27165053, 183940802, 722047340, 363159881, 128353277, 900857400, 862254828, 675534551, 649249897, 315771917, 411811699, 216116039, 459672986, 683604025, 521633672, 644848817, 789051056, 561029071, 718070598, 166845432, 648599410, 730072310, 498734416, 773644977, 608571733, 821771888, 788939709, 888284179, 765599513, 458469991, 302312694, 342277552, 535820158, 424274135, 17216374, 774736307, 470254189, 580164740, 315643246, 524828875, 748912552, 280152048, 172427507, 691865961, 77565095, 700460437, 968014562, 575101430, 59065473, 442003740, 628620267, 311982108, 402075012, 55318089, 610556495, 613965380, 305519527, 878739174, 106855035, 621257172, 119267407, 323467561, 353117226, 979957333, 250934207, 646716376, 651303041, 514314213, 883826428, 382510527, 287981411, 529033124, 499666024, 512611441, 969000357, 470669040, 557188764, 106450508, 221666819, 117276812, 670742860, 54740658, 2900759, 864127691, 264940160, 224366211, 472613395, 82425706, 52791743, 236970000, 303308818, 213141229, 724978519, 597445768, 737379059, 669155102, 912028334, 405739593, 953823810, 886967841, 544216612, 261662561, 510029435, 320034128, 12056262, 423769605, 192247502, 128257309, 532010129, 187131810, 467789219, 777587361, 778067603, 469794284, 544844441, 429265443, 636342412, 79856110, 711487756, 889037347, 770095861, 885576622, 196085279, 889253436, 340955375, 746310, 371413850, 234800141, 380672404, 746478415, 753637738, 414705702, 233624560, 469825989, 331025035, 57750742, 640103697, 545983919, 554914525, 890345740, 965645841, 640961527, 809662075, 438669185, 918963263, 991696231, 524455587, 351473637, 955583363, 357490755, 900854712, 860542242, 285675084, 546122502, 104467514, 779748424, 369040824, 912605382, 937843489, 731001930, 648462403, 83356527, 275226594, 826104546, 827301643, 731696076, 852838707, 8912391, 742394575, 335815103, 281277895, 778722268, 131713700, 184440409, 497426494, 773235120, 854357274, 391808544, 886723724, 308638536, 32623258, 184401197, 430123977, 675331811, 702390160, 675786663, 552036300, 552960187, 732893155, 237094684, 724453884, 924888651, 157388608, 844683519, 395740236, 280645011, 147910804, 458243584, 418104272, 530487403, 46702437, 306730205, 603713102, 739803215, 542776635, 893021311, 555740546, 487619653, 314190881, 441996287, 545119175, 384788622, 912227514, 624014006, 422178196, 862826674, 813849277, 348876312, 689510167, 32266139, 580663069, 636050793, 690929310, 786520141, 891756229, 263530748, 3600455, 597234545, 292656141, 334601919, 269424608, 762565469, 138070805, 153252077, 210136919, 369013063, 185434179, 797931515, 139937296, 900762930, 373323772, 975846587, 616502508, 389092819, 166895436, 815481372, 377059917, 954923898, 661728270, 615343894, 19539410, 164553961, 128359868, 700158913, 781677126, 79159181, 550442214, 780882824, 638297765, 437580358, 811108523, 308508025, 918688754, 9276544, 521250142, 977469465, 877298521, 21889167, 544470770, 493580975, 514301027, 144460376, 451064536, 591741075, 919902255, 873940518, 120910643, 461270151, 798277197, 222422222, 685144509, 554680340, 693869966, 668596938, 601673486, 877812428, 364505939, 245540508, 723709882, 925409952, 579894363, 934344734, 197204487, 86157647, 660493352, 991150095, 664921729, 951478570, 751090324, 330681393, 74819229, 233485773, 645352198, 269407616, 874583811, 697975277, 80796635, 782022209, 15204939, 581105322, 239240528, 152170487, 699540248, 229295163, 379169198, 496319730, 466632855, 198431269, 115624637, 238872835, 956361008, 816594495, 689248553, 657398508, 904683831, 249106161, 483631365, 849607640, 651584461, 65441003, 783563255, 256370862, 654566118, 962865798, 972449578, 416882090, 848190775, 700371457, 76061398, 641637004, 817625332, 59937478, 590887887, 541741822, 934489128, 967678391, 495500144, 487168624, 855952890, 668125624, 946149544, 34632909, 696147473, 778699423, 773166574, 451845805, 92215744, 86203120, 355273655, 775541670, 893885631, 742174444, 996590125, 727801665, 11201076, 708645506, 81228597, 635652598, 807580913, 741219318, 245163124, 33902361, 355825186, 398859377, 950786714, 512075207, 568137957, 517385131, 362122738, 783058192, 922609020, 607428790, 833327393, 637867222, 193418572, 241718592, 178325459, 835276653, 527678788, 650989445, 703908494, 660310203, 299824655, 43346290, 353279399, 509960116, 946670112, 159885452, 621157385, 275722056, 383237713, 584623782, 581195988, 973178043, 950791033, 854667056, 999418733, 206067903, 525939244, 31460910, 114035967, 573885513, 951175835, 291943679, 572125323, 649163915, 827323819, 108121870, 2775233, 357895080, 33928571, 841666952, 752465523, 553814152, 358196707, 961398333, 100652001, 122065887, 228292200, 316644532, 414210512, 338960269, 741871736, 382596664, 502637270, 659682161, 614791119, 230893232, 387296597, 972404191, 403475469, 528654673, 36056707, 263209167, 804609395, 426040579, 341097031, 938799007, 273288192, 451474540, 451678890, 346101284, 29824549, 879287318, 354414441, 312162655, 145208124, 217209571, 842758057, 93339388, 8434527, 765628878, 246669335, 668123264, 345491359, 196881152, 489504865, 583666451, 435718275, 740550526, 714203301, 461556436, 100658199, 752653539, 183363782, 907463150, 28127057, 15432545, 427131087, 69861061, 88884165, 980005948, 972267831, 188914273, 650109227, 684314030, 663832674, 881519211, 409939724, 755195446, 728902334, 11015077, 989034972, 868137975, 989415277, 246904164, 641796562, 962056229, 448393813, 421699730, 533350450, 961280366, 861281683, 309974177, 87921444, 329461697, 84629432, 385544451, 925518044, 750998859, 587601828, 379765924, 967212528, 906702039, 373755770, 132989750, 658862245, 327805974, 305699219, 644497990, 532181808, 787003825, 598197011, 211490158, 37069385, 714777287, 879389390, 155680580, 392058182, 11214046, 661373167, 453896121, 111785164, 852816908, 163404256, 162998478, 814866684, 614532542, 388430046, 239354497, 572306415, 134239134, 996039135, 77534952, 58376640, 381574000, 985720736, 125741845, 282492589, 409776167, 420100283, 903607398, 931459207, 66189179, 251900837, 481936675, 952985006, 87374365, 40266621, 202972783, 351307312, 744818065, 964776874, 870504385, 63544993, 503798497, 555283589, 954851199, 421104212, 976260000, 113606452, 990026871, 341875319, 868104128, 966406969, 576497902, 600496120, 457557758, 128563413, 629123111, 462379302, 858446847, 24057608, 853646614, 951823358, 13753620, 77702738, 903970784, 258808327, 538026910, 586553160, 526397649, 76374884, 339316869, 751211484, 381287164, 886173401, 139138421, 80369633, 801075195, 199536927, 385379183, 980303001, 997730055, 736155849, 578602460, 429448173, 452987915, 769437218, 253650369, 467788896, 34719923, 761161452, 108777128, 911473128, 258510274, 964782115, 823262030, 319964451, 166295093, 996077832, 17944631, 470311426, 755827060, 304461894, 913860969, 89131721, 913492652, 519827077, 110032672, 352876391, 304085147, 756942016, 501690030, 411598510, 883129807, 2806943, 745255391, 259436256, 707470000, 942416123, 933547187, 466401784, 885751686, 597170255, 661486654, 170404259, 31562373, 909529342, 759348177, 710708864, 715701806, 567319622, 632205719, 395688173, 970031215, 141065327, 526874161, 576662917, 536763396, 294811583, 188432764, 192438168, 642081880, 615974321, 591901548, 554111061, 252014892, 408342931, 937603199, 310634244, 169408500, 132430836, 885731296, 168926249, 248924903, 822160560, 285864948, 542521476, 504211299, 465308592, 511832087, 650020783, 307601113, 79078580, 790978862, 189038888, 710103290, 621293673, 174583909, 302887949, 181465853, 986783548, 608157986, 892085875, 478008064, 286326305, 37726293, 314067765, 453988815, 69093546, 438748005, 145355991, 218065790, 484699939, 333293470, 526850088, 979423973, 308700808, 677365803, 715796019, 91546525, 884095006, 100194483, 21791717, 812466013, 376906893, 397670168, 804501496, 822380133, 368631575, 276858942, 989453968, 794335470, 357232663, 638687839, 251572503, 241708192, 373406634, 824567448, 457365624, 404062465, 12969051, 921638684, 672690892, 883559759, 720786099, 990681170, 319314286, 102127197, 129337546, 132296169, 426092353, 391448220, 234371023, 301914776, 324412300, 501949648, 538633834, 722298625, 886452347, 205568737, 250615242, 548503964, 141152229, 400701435, 637680724, 452503701, 320891317, 572666184, 97159247, 439361137, 55351156, 300092349, 218054421, 279039419, 246517368, 597615300, 704289189, 983816215, 607024031, 94866604, 151610952, 876033610, 374116238, 645613289, 914523948, 239537621, 105071823, 535989418, 36529073, 418727819, 842537736, 975171675, 477802541, 163426390, 815421539, 563570216, 332945987, 798808901, 72253934, 484358203, 49082123, 527303994, 670891529, 627238613, 437432237, 966856579, 586011619, 501297804, 728247994, 110421149, 53391927, 765288367, 112956279, 361117812, 412898967, 327878449, 893178076, 965441058, 184960317, 956368061, 698925309, 880065049, 575555776, 894922803, 197487999, 691073892, 287275861, 568869610, 941372714, 936298888, 462496547, 747475763, 30602366, 340820240, 960565123, 578136274, 886110043, 826521909, 149031123, 104787963, 442714900, 822661547, 996126687, 362790802, 863909491, 38569069, 368058369, 849894548, 558068588, 4210037, 427928886, 387147890, 215602178, 901400454, 228551370, 797652121, 585653320, 942528164, 71498219, 11038634, 704935732, 236517190, 390981690, 227728497, 606539051, 854552771, 664133388, 933006076, 13597636, 915084298, 156215019, 250500062, 377979015, 263685952, 444577338, 425560682, 259751091, 512331295, 513178870, 955088047, 232675484, 67633350, 62464733, 643823375, 836932664, 923126212, 128792847, 167787718, 781006911, 484668090, 109429226, 167159888, 291547775, 678740648, 813704028, 340705464, 941304831, 165559071, 126737406, 970880212, 767085267, 825296536, 572306893, 632194449, 199344013, 887499199, 341668538, 626344585, 467563674, 82028145, 478307286, 56076924, 475226466, 85952717, 333950471, 678917645, 239989389, 881387849, 294406125, 841695578, 115055063, 548001369, 996956396, 465857502, 598094892, 16500011, 468898616, 238858795, 298735174, 542166837, 476597320, 174636963, 342909848, 867247289, 650586175, 746835851, 328660983, 793075227, 963254043, 140047507, 441182069, 111499003, 112547793, 168261245, 763132681, 123378567, 933007762, 141035538, 386742600, 947091752, 960949088, 322532760, 90805296, 665731207, 842089516, 114729034, 27525874, 911045816, 375866323, 899296475, 265306421, 122503389, 967036240, 539667337, 981986866, 146665598, 635437670, 816251363, 88685448, 209317147, 576788510, 439023830, 950090008, 498522198, 877184977, 678272253, 222371790, 960897454, 272182710, 682161232, 39303265, 530208077, 51923477, 517552589, 274274001, 21074559, 594001708, 510798864, 960080672, 770219774, 614893428, 621645344, 491220983, 777019100, 325275018, 244647887, 264545632, 49351215, 167087295, 958010895, 37427886, 576051875, 463753622, 318418822, 114973944, 96107022, 133336032, 549298574, 569012295, 1521513, 755965635, 342149505, 782158435, 629992926, 239493297, 176388877, 721760732, 79574584, 186324750, 390359960, 406794332, 713934668, 169518240, 840345102, 435370382, 753892645, 742684690, 604107011, 478413601, 738276648, 19392437, 160198890, 801860373, 361786029, 431000663, 655054060, 112890850, 892343894, 264215385, 497961643, 211757260, 574912338, 932849853, 775673547, 24708363, 818087190, 828508044, 673426395, 131873064, 738348044, 947185043, 274847888, 660631464, 58062062, 329597432, 916975739, 662331963, 727320766, 182105438, 471630568, 774914357, 314062564, 518342566, 702871361, 345067245, 939493741, 208438716, 696482521, 689129391, 497953616, 17001994, 525107239, 792046830, 296180152, 24355547, 768596629, 349182910, 569286545, 19605602, 704136854, 38594611, 472463144, 354861516, 486316807, 775974429, 39938851, 762609770, 599473135, 671531059, 669183213, 962475286, 204287443, 422506075, 743820741, 113963211, 469395817, 8967297, 592455540, 621702076, 505702938, 821612599, 597634782, 821273199, 545975079, 801593829, 841616312, 209636548, 312656323, 92426655, 201878831, 416245381, 121485289, 386908022, 492508384, 323628190, 956134837, 728725306, 166622712, 69073833, 175414889, 452847133, 995013438, 623805837, 194872633, 908796621, 922013921, 181268640, 809380251, 744621905, 880535439, 475576347, 98196029, 287726804, 716347260, 93640850, 851285621, 234925455, 841211195, 918870162, 871490024, 897488333, 40287711, 90026279, 79505482, 19392415, 971413205, 644876241, 486979849, 46254052, 445369358, 609430188, 730659542, 804505660, 201314668, 25216236, 518687594, 6325399, 86717288, 580124973, 316318498, 928218672, 236753074, 969372146, 549562901, 404130580, 488203829, 113584614, 337774128, 858179219, 784340588, 586168133, 2437785, 352718296, 98941188, 981469165, 278953469, 915638273, 94906761, 319461829, 115579981, 14362056, 867226942, 256932820, 660490076, 565384957, 844323495, 815658580, 545375030, 438258622, 751120410, 996981382, 55920475, 168629884, 415700057, 543887393, 947553387, 528463324, 791622096, 360439619, 957583168, 128623128, 95973130, 357476713, 482833331, 953752701, 665221534, 619925040, 164716669, 859127725, 255711562, 769259735, 304617459, 405690480, 448044435, 288270097, 637815739, 501220280, 13750719, 251023523, 510490300, 172131792, 627813766, 360883544, 395819177, 738378083, 327348069, 766019937, 90925268, 676186779, 153573974, 649000017, 16784187, 748495976, 121678125, 845740443, 396256949, 237890081, 614279258, 34785855, 222804, 531564152, 406360498, 586969372, 180073261, 418568886, 417713100, 820416998, 493353181, 294209749, 144793246, 225981445, 187181986, 36790197, 902703123, 237310608, 4813802, 633193842, 781263317, 218014288, 770759755, 358850314, 235307098, 983234663, 546317390, 566407207, 381404460, 52837950, 206331728, 395046833, 430715265, 239507650, 302201028, 406081123, 860467179, 576804125, 211182784, 753947477, 410583995, 164850794, 662790709, 26589031, 231935786, 482241097, 771723915, 515131431, 545295417, 581958177, 751638214, 869693522, 829300807, 204290368, 738396844, 198287881, 180277190, 262695178, 638197496, 814573252, 193763625, 388255720, 501148560, 335520439, 275506293, 202265396, 904478834, 743209353, 991508139, 699960429, 440347440, 794250063, 618351042, 741320927, 532506482, 426022854, 184449744, 311274869, 407387777, 947303125, 595541133, 149956242, 169122372, 746696324, 213540984, 51031997, 828031552, 807430608, 690543484, 809609125, 626032873, 964616554, 219670540, 415166848, 892877396, 655112829, 184846829, 839147147, 340828044, 590188339, 294367116, 832925933, 277035639, 871479330, 366762574, 74408062, 982262065, 146385756, 81333713, 661152742, 307279401, 78672847, 324822913, 854651642, 299512834, 430669130, 60516853, 560088258, 43717460, 121456272, 945316902, 352040496, 707795775, 300400855, 89468521, 954039141, 784938062, 691518430, 434796287, 967868265, 600041900, 939591730, 75310060, 342833237, 898466775, 499163592, 683064305, 72277245, 17797462, 646423479, 503919065, 627245342, 374189210, 774266133, 726707352, 819571360, 525978993, 283757150, 882419271, 364851185, 658912066, 617922121, 267895833, 980936642, 159127912, 808510115, 824914865, 837275236, 478757865, 984084437, 200191213, 705460170, 555397654, 99810037, 264056807, 836588661, 958616257, 291597891, 969823086, 172446046, 106422265, 237637580, 126043113, 537513112, 487568656, 176756105, 895320178, 823802739, 106846629, 782415095, 572541676, 44338583, 351493065, 444274803, 468103021, 160796809, 484901231, 318125206, 440790612, 974889568, 863585856, 129826459, 30605110, 523346903, 881082005, 89622424, 798151190, 996688010, 750836785, 871142834, 165081855, 494194377, 109943311, 860196819, 837284820, 428258866, 949586843, 758109376, 896140227, 11180818, 530357130, 682905726, 29846042, 762508412, 364897253, 118011478, 76411516, 587553937, 197799837, 256839428, 299202370, 343946270, 22681497, 320188884, 662592664, 742276356, 939635482, 310120863, 611114608, 263707627, 824428437, 193079255, 216495307, 950732822, 986769202, 163510950, 464875182, 122265960, 899550888, 707963654, 199941329, 310554611, 335323529, 706659067, 398901254, 431661903, 90266127, 518295992, 966641565, 303653930, 399536895, 387595455, 206315860, 274191421, 128448391, 669508604, 335789559, 726696407, 251830073, 881434509, 984548489, 208828532, 55051710, 707837636, 469944375, 706539522, 528784898, 293665968, 173728373, 512208128, 455778325, 908215628, 102374167, 420351712, 182042297, 939002654, 858874878, 685822514, 626053176, 481264879, 689847144, 453426233, 903851108, 296603752, 639661371, 664474830, 969309839, 536702071, 532968558, 269832791, 679419421, 23379557, 628225488, 283582916, 612292360, 434908227, 630172269, 429920351, 128446753, 556071042, 935155650, 437850642, 143630577, 187830627, 370425617, 354870126, 788557432, 663832575, 582169102, 832360845, 989021818, 779878634, 771776810, 21581242, 289951655, 896504141, 650327089, 819573516, 135215754, 378333027, 180906644, 87435456, 504686057, 99140052, 283096666, 223594317, 938578911, 575808402, 939399871, 341992811, 821793044, 705542915, 487475472, 893968549, 839991689, 693582810, 465328166, 682397585, 815786894, 976611262, 195930681, 842629538, 164361257, 19787021, 202346997, 330831307, 203932769, 94319646, 338190645, 758227060, 743864291, 964156490, 744612276, 887230871, 55861675, 535919826, 461158711, 213773004, 190105238, 141973572, 685338111, 570137835, 54794982, 859890477, 224691674, 509144841, 938647919, 339242351, 121103145, 237142724, 817078776, 262864416, 749453273, 651041581, 824767033, 321452216, 544473944, 899083624, 175204857, 932982715, 449067201, 81572611, 610515395, 267353859, 950520225, 277380799, 212100498, 850311200, 128897966, 813212758, 960688557, 453215505, 173548651, 689263840, 69925770, 973773385, 937571936, 476176135, 903552360, 802007689, 778224638, 839913393, 535032292, 26194278, 55269179, 907244998, 888445204, 593154060, 813755306, 433741782, 417857133, 199110455, 462601700, 928068044, 620960689, 741708833, 926761138, 797906683, 799040921, 20401186, 125934727, 290070472, 444620667, 854360274, 250272642, 609656271, 446378569, 250652182, 233185539, 139788739, 469925458, 378290696, 738211751, 675734888, 823200289, 831096404, 724529479, 755658462, 252686758, 596252094, 685931825, 499957547, 602237683, 418994034, 292705171, 696650266, 620034150, 152137264, 175344333, 557458433, 223813491, 39000049, 657040597, 306457582, 59992106, 682629579, 907874711, 542564767, 388915922, 45469941, 331042276, 565894991, 262497499, 942960258, 939475175, 859509613, 373154111, 694910513, 790098642, 294700807, 395935279, 982223020, 788681036, 447986759, 138699090, 772352622, 360680996, 813166589, 92846552, 457118410, 830768676, 285870557, 333361520, 449091706, 816291485, 431361961, 785969282, 372811154, 23403426, 431249118, 686190007, 33200257, 854380677, 455598663, 882933043, 674343898, 9178914, 649381208, 754528962, 689452911, 829567431, 400569142, 969725660, 892238309, 520576547, 136014920, 574989187, 998466845, 666261989, 764519201, 738750983, 109823084, 313571394, 55419724, 785723221, 786750441, 284937201, 94809869, 614907409, 248928052, 276797201, 736375382, 274441030, 463192893, 721885234, 705781914, 118877743, 194062514, 166335019, 346993206, 562793110, 645885283, 617379516, 54854070, 825548558, 646669229, 920263098, 117897967, 701799527, 265582505, 18340811, 716954176, 382311321, 74274615, 413260428, 794841714, 219454972, 155830483, 235703675, 987600193, 934791427, 474246869, 703736674, 894075244, 485013648, 932439592, 656191720, 80138660, 638370849, 640479374, 364934138, 467961513, 627642441, 501388413, 991106090, 352366854, 67122885, 414379609, 579336887, 640178195, 44972038, 834483158, 910475883, 888769566, 77758473, 550216675, 226685011, 45435351, 613210055, 258895522, 295738157, 33551199, 610088696, 386547104, 539045734, 729602367, 770822934, 29293037, 795037559, 961002888, 403518287, 578929144, 415582352, 513471319, 459564702, 757400626, 47909007, 413228114, 785130758, 274957039, 249353462, 40589958, 547397016, 432206833, 274582420, 947231881, 121632360, 868845930, 817471979, 617175981, 102163821, 29047942, 912367553, 931415954, 45326663, 965105561, 805171799, 68853145, 886113222, 463806444, 672528931, 565507078, 309625921, 745512094, 868897393, 294083869, 272508395, 843843702, 458586362, 119623104, 942108740, 53251587, 420238428, 22583861, 37794908, 360948403, 102304176, 369532793, 923417974, 386063294, 768732069, 656974290, 588070459, 659973951, 338333705, 524727172, 987043499, 228952300, 953072685, 553903304, 797982450, 391770690, 186269942, 404149986, 934002448, 279248136, 525545686, 593346761, 142809298, 663633668, 18129478, 432223664, 619449008, 251933687, 344367228, 705815615, 109540336, 514617980, 718310415, 451580794, 539953557, 95716021, 769838159, 496043355, 796728729, 425029760, 55141939, 889900092, 882570225, 198758417, 288685926, 913927406, 710679920, 970673545, 601651701, 523778658, 718674786, 218821520, 285712598, 541373937, 957725635, 308820370, 681769116, 386547063, 509026261, 826556173, 404472066, 65276584, 541739144, 858198985, 449645127, 92064637, 924611521, 603613469, 475412291, 602520769, 450063250, 458731291, 579565155, 608580741, 740359112, 540721869, 909038270, 851818748, 907306128, 75926106, 773423449, 195394745, 498878325, 676676449, 613491202, 719235870, 454719803, 482516043, 567377595, 388938113, 868725428, 468097567, 448898902, 571607881, 466508657, 244935735, 811817866, 656350962, 914920149, 257788797, 238314768, 347418079, 142134811, 524309664, 74437323, 773018693, 63941559, 340184002, 534203097, 879538743, 929971007, 631392526, 966103328, 56347648, 336191289, 590878669, 389085199, 596131479, 600380623, 326018084, 656305109, 886317451, 105465956, 375160677, 980409343, 720664513, 81176424, 221081315, 915435212, 988960073, 147954826, 706296805, 885951018, 763980066, 809227352, 759408964, 623893116, 297521319, 969041454, 908200344, 229840079, 562236850, 851430754, 223021714, 518807539, 119321087, 477333965, 911536851, 74846119, 248712137, 817243169, 856971171, 269093140, 618136966, 514150295, 300147870, 694078531, 87482086, 171621958, 498246030, 543174772, 949348392, 447865230, 109306415, 855274165, 912890927, 571142155, 898187499, 624233134, 743175193, 291089757, 750937872, 854572097, 918742675, 254152597, 712352401, 124097037, 519421714, 67787693, 30146150, 642163688, 49192853, 669270313, 713518277, 361623154, 201917624, 635364566, 767728162, 860198176, 71221082, 330473000, 9849364, 417104483, 771052866, 324948550, 400536071, 301765559, 320837660, 632330141, 685196163, 442374952, 902066797, 142632563, 783132145, 286024357, 153032463, 573341823, 73505827, 640531769, 504212584, 113853701, 976473813, 280596725, 93149045, 369921688, 544861639, 15720539, 939308730, 754480269, 154447534, 182061626, 423890672, 72117911, 311688296, 702693079, 725498484, 32406528, 831737582, 516801267, 917290778, 703502454, 457981566, 645103218, 456097617, 951427899, 226276658, 792862258, 651432151, 818920000, 362346331, 390037810, 973492969, 832683684, 986216532, 358606610, 452517644, 342225260, 617157196, 619555656, 393796207, 635076365, 97271583, 723779739, 16815935, 830964033, 843379459, 914686648, 74523110, 223103645, 792391554, 885039834, 166361481, 191694944, 921413956, 259944918, 7461648, 614591069, 604358700, 31673234, 963727836, 681001264, 646785758, 593184548, 581337072, 875722663, 636806169, 564445465, 544270543, 274385125, 136764171, 943204225, 264638415, 623249214, 595076246, 357044746, 86943727, 593362853, 347807519, 246293981, 169980567, 582626853, 870294647, 409825255, 420751980, 677465567, 265979965, 147787502, 607253035, 715363599, 642494286, 622581212, 434376746, 304705340, 443150136, 16642519, 103526824, 404834349, 98937329, 791306136, 251766906, 4235359, 683348195, 763521829, 775611171, 546720191, 66880213, 721179595, 588750835, 223841818, 627339189, 207097600, 537037598, 599651998, 491196367, 956570167, 44567239, 145858190, 299820758, 264547732, 578295099, 308266157, 93397131, 317274155, 294547686, 784285205, 889624969, 799635864, 142662329, 684903549, 33722344, 852785448, 226822970, 765070002, 897669730, 200957486, 104274420, 665876644, 698437441, 79635892, 967684655, 429564730, 196012369, 435694213, 982665600, 209136902, 584904247, 779357960, 330667392, 286627823, 722250955, 127733246, 593716772, 545294257, 944573968, 155923865, 505817284, 896160678, 494183203, 737451524, 339252397, 78213795, 519472767, 518455292, 541812982, 712941103, 140213475, 519108173, 153535542, 820607606, 46120887, 751434744, 27769599, 139423495, 83362775, 880337047, 52394077, 159654196, 69552785, 689976155, 512456141, 204378420, 382110260, 102858064, 111164182, 374306779, 221055440, 62425294, 968859653, 67151452, 111792224, 798928424, 925368471, 953742747, 903899155, 64242650, 129844414, 431847742, 231685280, 726571768, 550486299, 905100393, 982889221, 577273669, 667985476, 907748938, 52035954, 505855405, 711853817, 26343105, 959755045, 698344631, 919185306, 319349664, 607533165, 304503844, 356408373, 979476373, 207058640, 72506070, 326418262, 523980331, 735051059, 53408991, 335987384, 169081145, 730943905, 100424171, 732275010, 855834473, 814838909, 329305792, 699114390, 521931744, 932200058, 840227038, 856477360, 402997792, 520230480, 703152358, 393466244, 200485515, 582806867, 606105113, 132155035, 611878844, 780475213, 259195518, 598837556, 186379244, 205047785, 156103934, 521766369, 8847183, 606023252, 28426720, 53211429, 855005546, 374475974, 257942665, 629400369, 875692907, 683830685, 534812511, 335374563, 978991831, 479340948, 455047112, 505997465, 3185414, 776460657, 289486163, 137094827, 967066095, 752318019, 189944584, 261369694, 794838135, 842812749, 610731265, 50572868, 992674035, 762295691, 23671457, 293664342, 936023785, 542454949, 975619810, 1365831, 752988015, 716921296, 653171947, 81316752, 247145699, 948647509, 178708570, 5555699, 296997287, 662860900, 985772419, 750162768, 738552035, 174314700, 598780058, 188611582, 514786048, 288583979, 926577252, 173576432, 307975771, 573174489, 606723939, 219963008, 653593829, 73254955, 701196183, 236898454, 809253115, 633185861, 991448967, 414035306, 492921393, 427700195, 742128520, 220888697, 868753006, 203196093, 957939296, 840112068, 918138859, 391752727, 385021593, 427641817, 869026453, 982226498, 372503416, 771074571, 557907113, 428102172, 400205075, 933865028, 749606993, 596090568, 238293806, 282834962, 452502238, 451140030, 578142517, 733307489, 659018113, 825641807, 203946765, 430862499, 194952915, 517996787, 209015117, 363393010, 657152317, 782134088, 952470830, 904667627, 214673429, 592594541, 752651427, 659667796, 681309081, 387401067, 655606824, 453313240, 381672558, 588089468, 382166101, 683149870, 895660071, 140675035, 195961242, 934174832, 774747251, 73204757, 989775972, 695280411, 924547830, 962890310, 301560129, 902332105, 960437912, 126614461, 965774229, 297723018, 365751085, 306194375, 665393315, 891390008, 225596410, 170492875, 961351075, 947542514, 839106607, 482859064, 998804367, 39768311, 15275139, 288245353, 168637747, 645737172, 107548223, 489379776, 708594131, 928262341, 982709552, 147670054, 73465566, 413245494, 477478814, 44397970, 921194229, 494645630, 94474355, 850165230, 376039945, 605425853, 873082339, 753900667, 886688237, 853819447, 458926545, 647670785, 281927939, 982468468, 367551122, 358759088, 146522910, 458435915, 869881669, 459249039, 82374856, 671949296, 298105832, 261719335, 710666865, 572282356, 240094899, 709994305, 643655591, 531149756, 419283153, 585544471, 332726086, 686266396, 288072905, 289461393, 744906998, 125135409, 705380825, 421782586, 260700515, 224919083, 427037352, 582690992, 241133205, 442037460, 38634137, 192123071, 264653957, 731478322, 963298328, 993012474, 454626038, 584924214, 932026871, 849912332, 25822076, 567317883, 82627305, 344452781, 962978356, 373229593, 865529081, 894279133, 296022137, 525396108, 59874614, 22216077, 712221478, 533283517, 801024292, 480493031, 165272413, 338469969, 118307121, 166665503, 109785043, 7437743, 673497402, 744795261, 650319918, 760941934, 549335804, 966687940, 833136560, 785210964, 979072131, 72993549, 730245621, 490146833, 748193009, 220999623, 35319417, 793645813, 852549809, 289648639, 220173819, 432597513, 840091464, 530883880, 886390905, 490341024, 425325325, 850312869, 695392391, 390626624, 17002871, 362499765, 671788049, 645364128, 142193347, 940707657, 222671887, 305997583, 113031613, 901154546, 401892469, 638963537, 845028049, 973822787, 793074697, 883906887, 918184317, 498507014, 708479961, 290623775, 635284449, 124388407, 749754376, 72358889, 276209389, 216079947, 825514904, 127189608, 716213885, 803457203, 784813347, 488991460, 985695359, 144821584, 997816563, 397853642, 984838531, 600618712, 928876387, 999490554, 86774884, 726198017, 608890164, 663034863, 349410622, 393711377, 835456884, 704718563, 381249431, 944603284, 903346864, 853782212, 945838066, 237152652, 72310781, 339003741, 688138662, 648186010, 795519112, 192141377, 828594366, 38799115, 575389740, 92515713, 440852050, 340531105, 200747507, 1175950, 132467662, 497303449, 957929875, 201515256, 739022902, 712546781, 971387608, 111340629, 783919511, 811523667, 496448690, 301606576, 898498874, 225331340, 790683694, 318105436, 930846077, 976562192, 718184690, 444988475, 866519204, 913628906, 738066454, 937963515, 64624350, 143659875, 425597593, 650447545, 931070109, 956612761, 962110899, 272569919, 603377197, 177504388, 375286185, 470611196, 442693200, 684542954, 65839808, 417811670, 623864893, 806265176, 523881525, 730536836, 788510252, 893778684, 347438721, 460181448, 685175012, 735298003, 169151470, 393813389, 974863433, 768913156, 297839938, 871955253, 551293649, 741558982, 22074702, 636949114, 780327024, 784922412, 430754381, 670873151, 216518488, 447663112, 655283910, 186540876, 529357599, 229414702, 39721077, 792235402, 824528945, 481789411, 456571403, 951286542, 452439443, 625398260, 643048657, 823222393, 859347414, 716214557, 699833876, 639084445, 266267527, 968890569, 629273012, 639097031, 355051812, 540869129, 722702548, 459231004, 96177864, 80987479, 583222550, 14933826, 359327491, 871606675, 903046589, 294820341, 810225519, 587833933, 564397674, 947254716, 288738866, 389826746, 765069474, 586314581, 480223902, 378376157, 908744151, 396497276, 389399453, 990317938, 673366481, 572261000, 954701518, 905158707, 304297188, 300489090, 78508101, 379512112, 405991507, 921044373, 1640809, 648843936, 622213488, 648306948, 739386487, 690797497, 816016821, 788653714, 386164292, 346087870, 252716138, 993009443, 900287611, 943704248, 827195944, 839032301, 925326087, 806071208, 362605046, 235160622, 878656650, 987057783, 760022881, 373614482, 603494093, 785480978, 908697256, 953876221, 897636341, 558438414, 219185549, 817807949, 257010568, 481752811, 586577532, 965213262, 747492259, 887654508, 511749024, 40725362, 816849908, 459543387, 262804611, 566658046, 33181454, 554756594, 896996004, 742702451, 794886332, 172957299, 90683131, 798321183, 592345627, 254721044, 35508349, 548179688, 804504417, 299609085, 474379075, 58904603, 76396174, 922771084, 536556853, 80931504, 268052408, 801888922, 999412296, 349662664, 722304829, 735119110, 747356934, 627633098, 825484173, 179384918, 610137462, 10626182, 664584547, 456300681, 157530913, 380341931, 577286839, 368112641, 279870750, 303279283, 262029264, 341426280, 845022376, 683824150, 174215005, 67067902, 168559013, 772264792, 28447690, 810263455, 398130530, 945529051, 76396840, 553893084, 579883802, 279896677, 817701554, 118387239, 635583661, 871803788, 391231356, 583381467, 712291625, 453291483, 915458900, 384783912, 907201243, 404848226, 381759160, 779161046, 420925309, 660055091, 841370730, 785512902, 943268403, 685613147, 425004363, 365234504, 409381367, 116954347, 147360650, 72655832, 78150411, 292093051, 872228441, 195571717, 390870450, 447275750, 165758691, 643831570, 642009562, 233728864, 64998438, 329056590, 252442551, 382445473, 507094575, 169066251, 519526388, 860308774, 84901583, 521720986, 35791317, 784961538, 615440781, 214608300, 134559129, 470021988, 640291665, 16664060, 854051231, 506785434, 899032587, 770952034, 425087451, 307323227, 831263793, 982987777, 1378128, 361268355, 579938662, 267318899, 421059327, 426864144, 436889198, 565759145, 379039952, 836297202, 75235099, 264056692, 735028383, 922668892, 265124450, 673264765, 872794642, 475469955, 68480178, 323903148, 19805948, 659040929, 445078948, 582902832, 273283953, 190397369, 123622835, 654985380, 895748583, 803643947, 947350899, 169377996, 733613215, 472440356, 138809089, 548270525, 554600481, 567101570, 349080039, 628862396, 683954031, 230045699, 89319615, 768797370, 141407592, 34146749, 409078400, 791661779, 744768834, 561476826, 68727458, 289743080, 247859659, 282896743, 370902833, 461311091, 936857232, 386820422, 533855738, 520388945, 512041382, 223730824, 742985718, 800591291, 100617378, 817377387, 414962418, 563829887, 971905244, 752027653, 870090736, 649797472, 361127232, 150050108, 159392895, 974043111, 701596162, 79257995, 720323316, 260623422, 166420697, 807138510, 432272646, 775078740, 267868632, 877277232, 794750774, 616048764, 930067577, 89814731, 393064714, 517806091, 470818123, 348552490, 650958686, 558777641, 481698221, 642168203, 357911122, 12420244, 450630350, 31462213, 539694564, 744085434, 374209954, 846297706, 648664995, 251049084, 49174653, 889496638, 685441125, 758350296, 987706153, 104087630, 380252604, 370233249, 166931545, 800971444, 168507812, 786087413, 576632426, 389357857, 309994122, 736313566, 819565390, 63102128, 856599555, 490977347, 308147474, 23544302, 166555547, 987316036, 74518073, 262242872, 632403147, 798694487, 711385128, 506628934, 264289665, 775194197, 614619533, 161944960, 33614829, 508325781, 672034422, 605455043, 646075463, 263812752, 869478137, 357270635, 892625635, 96950431, 865732420, 470195204, 727698216, 721585139, 240347846, 730513448, 186842713, 180563321, 327061268, 607335556, 591603098, 682678045, 372660934, 589839146, 155501374, 467076386, 804215699, 730337766, 422264407, 457670631, 133734155, 591816231, 348918282, 856284526, 3585793, 140884413, 880886266, 235523647, 759443540, 152396164, 942145847, 231837144, 886495027, 357637188, 776505252, 300210576, 386009627, 78150784, 655897449, 530822604, 456048399, 785755353, 369636242, 467538154, 235251094, 117439123, 91461450, 468492821, 429979445, 435461903, 399185420, 489052077, 536027608, 672037433, 593575644, 625561776, 848120348, 810027253, 901706721, 110841123, 940278781, 386084222, 599051959, 539892823, 78685927, 666811141, 41241355, 681388883, 847072968, 142835745, 266833720, 423954828, 237320227, 144123180, 696580549, 964562980, 163252181, 32546619, 785108092, 672242837, 708715990, 59497837, 487000028, 383974570, 73866682, 363716918, 754118779, 744101922, 748710396, 780395170, 331605321, 876435750, 183746373, 947421686, 953051068, 175006696, 418203163, 940270809, 52642963, 115630108, 562112432, 183295468, 449935366, 946682541, 6653643, 88101977, 238709414, 647349035, 274411640, 621751417, 164335056, 601924175, 520991823, 392697329, 759957901, 534020468, 695756814, 25870500, 247821867, 584932812, 392394342, 708179808, 167308853, 225865374, 475819582, 414125827, 324220815, 604350485, 566732986, 909468622, 12295773, 394919769, 825750730, 755272381, 457791693, 501187398, 917336751, 440726181, 305421427, 433920249, 29982844, 920632693, 815529180, 698848112, 887713514, 132192263, 793448246, 896250020, 578938416, 335727327, 149477552, 280294157, 310324492, 106282905, 207194685, 718651928, 389843336, 269020333, 31045139, 239271404, 459217623, 745772762, 385040420, 764266327, 21600887, 5737227, 60883353, 686190958, 121230561, 502830979, 956019783, 62537086, 743191469, 323802943, 357392989, 118987021, 649466084, 954534735, 583817499, 794118975, 960140364, 85873822, 675898774, 687651837, 649288005, 507763192, 294017246, 503914064, 669461711, 411568182, 279626459, 912109771, 750937958, 91313472, 813221774, 825957445, 302731766, 814564276, 175620274, 945527773, 839400696, 454058505, 682977872, 582386318, 511940503, 942904671, 654538990, 695235412, 354364717, 663585832, 350786298, 164410586, 620365193, 669978807, 898273976, 297794622, 152992275, 557654875, 575163031, 619722010, 961152633, 949802036, 845638162, 602765671, 563114679, 154277479, 795089046, 81951633, 898731158, 229468047, 420507692, 338601827, 464913322, 613617758, 524223441, 747152392, 306276922, 77598909, 661983042, 119337864, 735338431, 662842189, 344218036, 516519297, 989453722, 579956655, 832179655, 764873230, 270445902, 89943089, 329564769, 956833507, 938136493, 743494706, 504799558, 341350111, 676996072, 213211098, 839600639, 323300961, 970310738, 84243874, 594180760, 471970211, 369980767, 837973586, 904856096, 598740677, 911761735, 445061389, 594514187, 604068303, 58223997, 508991675, 582242542, 805931520, 231351399, 217783077, 256627899, 798454793, 579152281, 396712095, 563343551, 735204039, 616308409, 925973465, 645269845, 209560403, 92618681, 48406628, 268642701, 960449751, 764876488, 944842827, 28062446, 667441902, 433555465, 728381535, 686111724, 854824844, 205698027, 441104659, 535909898, 127574489, 220047969, 320352060, 132304974, 615403622, 986102051, 617174283, 864959357, 821588380, 951392729, 201681698, 113198969, 869762795, 39581320, 827093870, 304022665, 197486131, 486013039, 499476791, 542680957, 930579949, 560634927, 679117873, 363215015, 45552247, 385701400, 170861582, 444984255, 460311884, 44643660, 214226691, 833462209, 432796437, 658027401, 455477862, 141617594, 524738092, 307481567, 98946357, 599666772, 941026730, 18660236, 338417919, 825814086, 653801175, 122070402, 265903451, 102698941, 959116944, 173627048, 988530088, 375352561, 618691603, 146216426, 814091102, 145876707, 819913142, 867352492, 678757322, 339718379, 233024154, 703803380, 92944304, 641439014, 208987226, 848526412, 294510624, 774530061, 204211269, 342631996, 576688108, 229621682, 74415756, 450106596, 738430795, 811447864, 32978359, 103877728, 393401641, 830975457, 313666630, 480518890, 687608318, 354670556, 500135505, 967435386, 950310530, 363818163, 140499073, 53344611, 203793020, 40129541, 560398742, 14243631, 887581739, 185267735, 398167442, 246048965, 855649557, 470426524, 117682610, 494111484, 299386778, 491196555, 246490482, 132153448, 808444212, 866987781, 236844957, 874224287, 26109899, 527033834, 370505843, 261872418, 877458640, 730168028, 690005310, 317298960, 572456289, 943431053, 901937432, 957405552, 265531102, 725316975, 142337298, 885864834, 413674379, 537374090, 724296973, 808210984, 904585722, 20353735, 704019825, 494834211, 481968210, 973123779, 722593238, 805086657, 161675087, 2990331, 120711150, 673750256, 231021470, 276566349, 125142802, 610697055, 495964307, 858036881, 626281577, 294265350, 314771580, 998003657, 765205646, 843232638, 472775561, 726088767, 848301800, 43166792, 721668551, 494429859, 101358191, 67492803, 178141309, 133160510, 589022520, 78256159, 247028286, 568371821, 754793933, 536502834, 496458750, 396583933, 937048406, 220279670, 307532627, 61893838, 59001391, 745614886, 420243497, 601284883, 743317688, 559177110, 721053118, 215922861, 218627116, 285714625, 973823791, 169522582, 407757500, 331676442, 229437031, 671106282, 624771434, 864356737, 517118264, 416573381, 440885288, 397576098, 436030095, 548190771, 276988121, 897150769, 682221963, 391466908, 676175523, 278326384, 381573318, 770020519, 275440213, 261866785, 100143577, 447729232, 223963432, 222945773, 508499540, 785064455, 860027906, 668881183, 916258982, 31060621, 252555300, 985495621, 284400159, 777225850, 714582336, 709532735, 635647471, 653594344, 670975860, 638779286, 529425003, 961936232, 618840517, 45666603, 86539808, 892408635, 382645957, 318565134, 886255320, 534436154, 641388502, 109723622, 439514278, 113785163, 307981550, 608138139, 636826633, 292818747, 81448316, 932751954, 975816646, 268322234, 362521961, 650618860, 946391731, 464991507, 993167252, 696121071, 146538678, 799172777, 737697974, 281532337, 621889858, 938507854, 381746403, 868778896, 591891603, 724469328, 41675675, 134110047, 3043175, 892398211, 509160445, 54998266, 213867271, 349513697, 886016590, 472858933, 903042077, 894474795, 719085043, 504020992, 864012404, 376996718, 141313111, 349772816, 913889901, 761369417, 609830804, 148782846, 962607632, 508060105, 655862789, 286279153, 147849819, 858681761, 458042441, 293808238, 848781502, 198671879, 353117219, 342297557, 973383347, 467701788, 148413456, 999784923, 884874414, 508754515, 932950614, 858470691, 436749876, 44731852, 470573462, 999192069, 37404632, 824307483, 899254824, 829635690, 631845991, 5419875, 536213766, 254375611, 941193441, 518857969, 584801358, 50482540, 163715479, 778754398, 787164622, 111016482, 254967978, 710950168, 415777042, 464384925, 166877628, 905889917, 973197823, 663773413, 555724277, 502677682, 486566289, 430883972, 498618519, 449215861, 422884352, 12569437, 267483656, 72450565, 642853700, 260495949, 109506761, 391670859, 454389044, 451282457, 354072204, 574860356, 575372229, 648240501, 789126189, 530441750, 785900131, 320726498, 318103560, 899952951, 602953461, 55494967, 126187503, 843001802, 404966570, 203107528, 88835891, 834094790, 523406563, 299554123, 737655813, 714722458, 373591810, 117945510, 718358909, 390686297, 313833045, 907030970, 936843474, 106461574, 433610867, 9726392, 649653973, 218854691, 605171074, 596714160, 20979021, 476324325, 979189489, 471748083, 394761887, 968002590, 693147664, 531925849, 715710896, 480153704, 355805701, 36803592, 398322563, 967014485, 892364478, 249465003, 36718086, 811408815, 591540602, 513260600, 2756956, 564314350, 431845292, 960817012, 607903981, 143372341, 625514940, 483390838, 194477893, 454487651, 666472901, 939588340, 835609504, 305606653, 801815049, 578132714, 681972382, 643386682, 397818739, 550234434, 895591319, 27935735, 996798997, 847848897, 258069035, 987469375, 127009019, 926687621, 736711561, 98634695, 533638970, 477418293, 28272600, 333684305, 835276574, 615381699, 769766244, 655558694, 429363457, 742047450, 121817257, 340857989, 433172438, 196442036, 404927123, 973492776, 217578106, 106086707, 12862561, 837124067, 981080152, 731814731, 164128776, 601871200, 95345571, 196036542, 988586829, 74537989, 758683590, 842681630, 200560185, 832478360, 734054730, 962863936, 261498026, 12846805, 792281767, 23210008, 782034472, 521427904, 211104522, 909004563, 127132858, 390333857, 58592924, 947111218, 454794436, 521854434, 874451738, 102114982, 632501761, 22802252, 729118304, 994463212, 292935098, 543443709, 7619741, 640409198, 941881805, 343473392, 297026815, 324786975, 651045058, 646584815, 642365410, 5383470, 668195687, 621233176, 887047197, 18263103, 235958942, 20391267, 112122222, 39186755, 912046568, 112442251, 327991521, 457231028, 34558622, 224988511, 904008361, 725862961, 790992990, 325677925, 863968581, 55582919, 6486293, 542759740, 842777048, 949909247, 152004184, 816850459, 974301023, 217344378, 694097826, 478246887, 230360801, 910929688, 944707282, 704825046, 819484168, 4051442, 561696686, 964844582, 399374776, 953664916, 837213018, 530904795, 502025644, 488312223, 701616313, 334181027, 885919558, 10348898, 778413963, 53844310, 688234443, 836395037, 646652314, 819736537, 833747305, 121282408, 440280142, 187639559, 330499573, 830996633, 439845086, 384545401, 118371684, 128750691, 21265040, 977444554, 851701165, 15421972, 906740619, 708197931, 494664460, 163883782, 955992062, 490796255, 346124303, 105036265, 433116539, 258579918, 629496625, 1334218, 596005178, 417242755, 71299974, 466287210, 96226087, 969962229, 282012261, 294617264, 98116137, 566376126, 307235670, 493162255, 606820448, 56529560, 429969985, 320136296, 386884144, 190791911, 60034525, 272028508, 283639588, 462748739, 271731966, 501136230, 379226791, 542897619, 454992071, 554622735, 485542048, 249013305, 30274017, 491316325, 426558819, 968667618, 731968846, 433485404, 387059690, 225395492, 872012473, 764956232, 260559216, 137742154, 694116283, 169975197, 131316632, 295234843, 121984687, 440271836, 613263757, 618587943, 425789513, 611530361, 30134106, 203482334, 132908742, 509123729, 16334164, 318502400, 88904426, 985412709, 539498055, 150091020, 407253710, 837998406, 403824590, 157202349, 240055054, 539703228, 904383104, 921395345, 207944312, 783626546, 713052318, 794137092, 289243869, 444322664, 625755783, 570319001, 233035277, 897588324, 345051448, 144843960, 145666927, 383582058, 640305891, 146789217, 493819854, 218432759, 914607734, 373300006, 270042378, 72312888, 447758710, 456403341, 2443497, 954191903, 590089132, 906720071, 374206950, 155586231, 64992196, 194321310, 676191950, 725733063, 438445569, 991257375, 83014565, 153222031, 465578602, 566714150, 416224829, 918441773, 533233552, 539304319, 526819820, 401136723, 257787949, 3395770, 455833957, 663487976, 650017358, 245595137, 439149354, 978648157, 386566645, 832792107, 353135616, 522041585, 67639956, 954956987, 51627764, 42938275, 654710426, 262140828, 229603756, 222131671, 961536428, 310231408, 815222871, 457841219, 946393439, 651371196, 778355790, 555297050, 288243286, 365504614, 39886002, 213876847, 736205210, 526622753, 790864653, 474922999, 195423959, 563824246, 817545920, 359662394, 919623157, 713281006, 917821471, 219205466, 738726691, 254785634, 7324251, 635869574, 116181781, 673153000, 720229013, 469725855, 596170873, 172278856, 390400008, 478724239, 632201952, 472374827, 468330772, 196600993, 453032433, 205640424, 430264638, 662638958, 326303597, 448649171, 279464504, 882946674, 403744381, 404139926, 917404421, 679652150, 235176592, 607610130, 154892837, 711395061, 592416693, 826605153, 14294192, 941754475, 679832806, 215798028, 668863077, 460133345, 690587038, 959252448, 417672947, 468337741, 682807634, 555372163, 368903452, 608938087, 373632283, 927129623, 74852496, 457717699, 410301443, 131324148, 295289631, 32451185, 695533768, 876102455, 878798277, 196806535, 345302036, 492667824, 460373797, 582332569, 424497303, 202421308, 460728109, 139880141, 124298941, 982384882, 156498217, 72792159, 207219958, 676477452, 216790807, 847971795, 672533041, 612683279, 321307165, 844190194, 878521685, 309910531, 767939831, 778451409, 836421346, 462882249, 810624274, 496455464, 487143438, 426825575, 400690366, 247011508, 992335599, 385361512, 396369760, 686625347, 164368801, 201198791, 624263873, 154230636, 209229265, 329978112, 939109847, 706128403, 15365031, 443248797, 532272726, 980148863, 356191953, 85598396, 634999601, 862924952, 961031752, 83396281, 810137989, 502203413, 676382877, 178199772, 644860222, 296935583, 106490691, 899947890, 700470618, 777039325, 975080096, 682432475, 23275920, 700470562, 575068561, 377445368, 296467813, 658875903, 219833020, 88743386, 467326010, 885491524, 116769870, 546486192, 281794717, 779462827, 512567257, 580816041, 290139641, 76896875, 478498576, 484648067, 921594153, 101816748, 163414976, 216635032, 524485129, 338430983, 675237999, 62016791, 165433159, 140312396, 201275598, 525200886, 623440042, 886884326, 130145621, 466866298, 473640090, 545000236, 685697009, 935255321, 917970834, 544911643, 277855039, 119475943, 267391477, 444937141, 62790136, 283715528, 508531027, 176506605, 469158262, 14427927, 635508772, 296448700, 97748270, 136190826, 817675486, 122102162, 616890745, 425768883, 111467431, 187622995, 152741792, 330631502, 35126317, 759941647, 898506527, 703621892, 503270054, 828463653, 294883368, 298178645, 870358895, 547916529, 354749195, 906517718, 101729597, 856249585, 763761973, 545721969, 107462432, 824445584, 602849514, 865504297, 406685837, 936633998, 809161386, 543937583, 93401932, 534577119, 38386699, 832249804, 766816683, 418573652, 394110006, 330973425, 679160978, 897607234, 267261132, 853086071, 362125638, 987071601, 111481241, 55185871, 489999778, 722606795, 157106435, 439964235, 9619543, 967427574, 408517540, 295363812, 378315344, 390798650, 195957665, 692475486, 77937019, 237279269, 225152744, 455280152, 586250636, 470401512, 75613219, 594117392, 875968867, 86779867, 668945533, 872019849, 562490661, 66925105, 642111063, 188428068, 272990885, 294371860, 202141981, 794194635, 45691350, 181510592, 719552257, 787965168, 758820924, 198299559, 172957157, 505973097, 646558222, 412687267, 124290114, 485328595, 666626388, 754169043, 528265657, 107345370, 531851592, 804280167, 424464353, 263517278, 846779233, 224953417, 759970304, 42646667, 526137642, 689716083, 437169362, 878139175, 574495524, 511641941, 138317269, 576697859, 497573168, 312541489, 822316301, 857146969, 29702757, 203446291, 362497244, 256316499, 527128899, 400386548, 494877607, 4274545, 825453294, 499078693, 627140341, 765367502, 126054944, 460013972, 406289379, 864282181, 731288872, 79119378, 898499259, 555845972, 116004851, 513198499, 448337939, 23914412, 822739215, 966977543, 494528217, 935563073, 65382007, 925652682, 557978661, 7540275, 44062629, 382337858, 636583931, 391700834, 112659182, 631809281, 972218821, 109204228, 38058171, 256122714, 64902513, 209466919, 890411623, 15775416, 381061101, 165607003, 418367506, 559916179, 466115604, 29908761, 35672733, 245841577, 719619642, 818441591, 839357797, 261672556, 89176865, 788099455, 485167096, 799994504, 986219172, 823857458, 163255876, 175439365, 185052530, 97262222, 511287378, 670789380, 165713017, 46400671, 957092089, 706312935, 666796011, 815505485, 811824001, 291498466, 85307102, 813537249, 595621145, 12300740, 195337914, 171536474, 155882174, 184632901, 181774072, 302969808, 225106782, 211812305, 857516017, 422248085, 467033655, 185059239, 104331192, 142051855, 371293485, 49777456, 323170494, 361731869, 668367385, 253421287, 921696583, 925118323, 22979004, 423646168, 692966254, 237330479, 410706901, 849157037, 583589166, 543869016, 600196882, 800191647, 198784130, 357824030, 490976815, 953184146, 637900125, 284870838, 867143774, 270270633, 645348255, 286445739, 47385494, 359875890, 147211723, 170900959, 119050006, 143902918, 619867449, 463803018, 56186444, 171204736, 670563453, 991411021, 767395876, 709004806, 35920131, 331778119, 669734285, 49112390, 467313076, 850620871, 287442950, 756882656, 892414703, 936903857, 36303423, 557133995, 181308326, 306281411, 682550415, 893795738, 809952503, 245780130, 640585742, 197477799, 620622603, 835241373, 353128477, 377402198, 95924358, 752644752, 104162972, 656616330, 183575527, 452148348, 192940625, 308345503, 338019731, 438220202, 846086363, 442293258, 87424236, 113502210, 299438554, 21217949, 113030647, 306339235, 584946105, 156084840, 990629782, 215059538, 10797747, 577469223, 690957356, 731834635, 236095793, 467661618, 466270550, 507451341, 422872926, 837297050, 414128039, 789796071, 612754643, 264759954, 103152697, 757791672, 281602229, 786760892, 234446109, 307316610, 537612209, 631954667, 674408729, 21491573, 433179947, 952832253, 18308495, 680948891, 230821716, 933808849, 731214378, 878147086, 627767363, 484675930, 224309855, 490311341, 706814396, 719714558, 522267890, 605066663, 336043953, 380268980, 216674965, 576956890, 871868855, 822195179, 273941040, 97080403, 503238898, 177173609, 587151030, 158964032, 25642321, 319679506, 742037586, 124583727, 555803714, 278329179, 574046740, 557983098, 540205555, 510025950, 514556818, 649692765, 774313515, 349239075, 671889416, 981959240, 656587229, 57032270, 321276649, 631207670, 487917329, 454884839, 976840660, 881920366, 660650130, 867820982, 390523727, 520294905, 365941947, 449394096, 986368587, 777214523, 467978626, 844466814, 580886354, 396872396, 109912749, 901034114, 627675542, 602267687, 162866186, 268486259, 107314351, 358085793, 191083454, 157062600, 281940720, 280752077, 482738152, 635387008, 981032713, 469617191, 443630285, 717767778, 742097374, 217950364, 88465608, 283311222, 391076383, 359652016, 904925863, 603666047, 331424803, 928285193, 204679654, 901928810, 235838055, 935410978, 976169639, 530645023, 346606883, 858027117, 701817321, 353088434, 60525601, 551812401, 635270490, 778291895, 610478154, 739698117, 275397100, 689720062, 750325701, 267373001, 388884353, 188898306, 27827497, 347652285, 497273479, 828701892, 112827404, 745290373, 632497623, 584703080, 896215106, 454557869, 942439165, 914006231, 894924402, 51294401, 966460341, 693581246, 842952630, 430336106, 530431653, 658559120, 344098674, 220632924, 330276625, 391179493, 12922700, 838437297, 990083470, 107080613, 468668782, 998094908, 670641055, 958998930, 238387891, 348653917, 54231269, 760664342, 297979694, 414122916, 506758289, 588131943, 724586957, 529812604, 133709674, 645554228, 673929316, 865043201, 19834363, 552553604, 796439080, 434498299, 613951973, 781918745, 472574091, 138066788, 649803667, 227369744, 13772995, 355897911, 939805072, 341327690, 901943478, 336001450, 985565274, 628013151, 422616792, 616930409, 48628764, 862539829, 830551659, 478817961, 494127296, 68479763, 327905784, 939217483, 442196139, 466503989, 150333576, 501984571, 530844185, 131224863, 83543848, 117225785, 61559730, 380608525, 909409640, 930647586, 374577324, 562439632, 955898907, 873154810, 966403526, 422454322, 833706789, 538052583, 671539312, 284961140, 248423532, 745139620, 526008797, 540652429, 704980097, 577277945, 719336381, 431856176, 28740907, 960965299, 230294579, 99460657, 518329477, 114385521, 371270319, 381154242, 195351059, 45471079, 689071526, 365124013, 488736581, 233724243, 618605556, 196870308, 379017361, 142176782, 681387424, 796099077, 444029110, 291445523, 719876983, 474553426, 386321247, 436786830, 425263058, 893939548, 799540105, 970424602, 895784485, 109393533, 510539955, 997635977, 52436581, 998922281, 303939183, 760276412, 113681974, 652842371, 402918552, 183192137, 105054418, 307806197, 893717999, 137073611, 555030145, 446151737, 417848478, 565042747, 823493665, 305201351, 130963098, 915258865, 530994689, 798918139, 898828288, 484047939, 668434148, 104523211, 805146028, 467260024, 185308211, 449114530, 831413346, 176951546, 570120286, 56176578, 95930658, 244439301, 75895384, 859577335, 778685529, 915452686, 695524756, 271160089, 553841352, 174609457, 192161445, 822584551, 668304392, 237407202, 199707981, 245099940, 298844639, 932553402, 481177222, 956437999, 780231157, 170066295, 469338833, 586506314, 849847004, 425270169, 172586649, 495190022, 434737790, 904143061, 425941452, 757380742, 381943607, 976997528, 776756777, 402171184, 147671036, 169645505, 633667106, 213781869, 239064145, 357202149, 110771012, 386723192, 985433570, 197452697, 174908428, 770387802, 256970870, 823016419, 493501148, 759188558, 667377533, 290330589, 459576633, 100462981, 551976439, 567058585, 684545256, 293778202, 279699982, 188648356, 457629981, 946932140, 953376961, 734702742, 359592399, 445628005, 977634903, 82533420, 686075820, 927912936, 229314802, 441665703, 993509921, 802118609, 28171381, 722831115, 104685486, 448790685, 168732236, 614876955, 759891743, 546305017, 987234556, 521534764, 53604488, 10473624, 43424675, 90666175, 389463551, 229308129, 915324415, 303579925, 575555100, 308908801, 892671005, 427828599, 506583673, 369966152, 950043252, 591797451, 223274283, 891943742, 157736846, 319460842, 427907798, 655008991, 510340559, 183538938, 47535908, 443313169, 174049558, 393113315, 486523146, 166548620, 10527183, 195701516, 537245143, 951690237, 924408333, 609426570, 696950750, 894293632, 567046917, 474469339, 64589607, 561156799, 631039462, 32841021, 761940403, 303411745, 733932560, 36162805, 598428726, 41817857, 778317345, 515249554, 614526121, 54271657, 854219197, 399660449, 614208536, 654811665, 884408836, 564324309, 137803051, 936161528, 15950171, 123262489, 969556780, 762252901, 955012243, 449079160, 766225988, 784760106, 250614101, 825906192, 526912392, 881537915, 311912877, 662691671, 483477298, 839350461, 776155932, 818402928, 524839294, 135800908, 873514485, 150163946, 134286588, 29762484, 287802812, 836955660, 638352139, 347590772, 528089718, 300551345, 610960545, 110097049, 699760105, 112613006, 248909671, 964587431, 213925876, 31084471, 135543049, 323739009, 413540241, 156454406, 94264908, 349211534, 107491332, 512834420, 136252849, 496128867, 360411244, 270926575, 703647093, 383781711, 49941331, 182558101, 886292358, 250061891, 929806569, 717724835, 824701233, 8370501, 260627992, 599120927, 481210675, 77535261, 675866300, 779663493, 193573976, 614717651, 986997819, 923732189, 836234376, 988365961, 558327957, 798113895, 94105197, 969813449, 293687053, 468072722, 148931667, 2220527, 960965281, 657131840, 562118502, 738379292, 470996727, 512802560, 685321051, 142233997, 455916022, 202406273, 259968676, 735322429, 748457627, 494158131, 903259301, 909675752, 971198888, 280658397, 581932166, 528276860, 902986174, 712457397, 370235647, 784004758, 448399437, 699736110, 268645244, 250461823, 835429452, 25847920, 91001914, 20639462, 565458078, 711683189, 457795083, 99623314, 995366860, 485958773, 121163233, 928120592, 162180830, 780370112, 746505940, 821967667, 369620143, 512095675, 896844119, 827484593, 669257017, 137937058, 540548937, 712563113, 594128143, 507844153, 529821127, 516690466, 974135134, 764927595, 220850626, 497022039, 538505867, 492028700, 346408236, 482890966, 124555489, 118040136, 379600119, 867733003, 148072097, 875025519, 46687131, 97268438, 359509432, 479897785, 572161590, 690146837, 85286078, 442465980, 710732838, 878923153, 456281694, 310672460, 717459766, 856017248, 181014472, 620103394, 456563991, 249528440, 931783815, 312451704, 892472049, 503330930, 327021488, 829834991, 239962523, 308794546, 666927777, 108917512, 389702115, 190144610, 374082203, 258082903, 679725679, 798683889, 392295809, 749696330, 509884597, 498096142, 191375973, 156899357, 186413341, 833423036, 912537177, 184205208, 397617181, 193007985, 202585561, 317107504, 297071610, 333749597, 697737275, 295057249, 923351785, 179105264, 687817672, 695527269, 737447060, 103212232, 238546843, 265837063, 847091568, 731127318, 105006345, 838024319, 374960626, 717542684, 836218624, 226827295, 954600891, 35484734, 953999847, 481057252, 67327398, 573765802, 825562381, 719707875, 27922839, 58346560, 776956834, 571942225, 350803055, 805163527, 758910073, 151583091, 162132909, 975308431, 603887735, 709794361, 435989003, 942775050, 307410489, 716563477, 45762114, 290553681, 837346065, 832179132, 935676945, 273414525, 166936137, 221447502, 757852760, 42796168, 100973867, 490425664, 236557600, 823363418, 257761854, 599835780, 645027281, 968908296, 777154178, 722165802, 463325756, 611439672, 740182126, 337913927, 291185758, 238522280, 938581257, 396226309, 969653389, 429220673, 805471900, 793245642, 679705713, 702128274, 91555307, 195556911, 278363070, 617029223, 885131174, 693877763, 561707826, 248958078, 63083723, 467244196, 731936887, 536979342, 137875006, 918839603, 349081052, 481131780, 962223952, 207792151, 288422237, 21835881, 850762468, 766824337, 296788975, 742032015, 37875533, 382328282, 228529201, 349154351, 25294506, 880716164, 309574630, 790942639, 760130387, 21221090, 498963217, 431376151, 386560922, 795526984, 827934979, 983346681, 472382963, 858998276, 321349160, 58559000, 881834681, 395242729, 311052172, 152242256, 309184309, 913307546, 541404432, 276884376, 357305209, 33043955, 475660796, 837832429, 402761792, 239099688, 843249011, 943667956, 379828001, 771574307, 40656203, 172490448, 365807068, 85958174, 119417626, 514680593, 614222259, 437419112, 291601981, 562488254, 939520201, 454864798, 797830840, 537497815, 206817698, 169570284, 959427024, 307677474, 29708582, 484075982, 490813295, 74021759, 540962338, 8627256, 631213332, 857277330, 502692775, 629143801, 485571455, 699617638, 549635360, 141564865, 83082038, 203494147, 343072164, 330828178, 99200620, 515302890, 875753037, 974163735, 893109054, 558620891, 450977892, 927079479, 61314673, 11476279, 962610215, 991224179, 787767150, 722300823, 237755507, 929204398, 16932118, 395001740, 476613838, 562844621, 35153077, 594486298, 987736816, 154107380, 579620539, 38015976, 576836161, 988958100, 372330952, 612301523, 702464584, 32333985, 784545155, 883428150, 423962918, 882986710, 35255548, 761406068, 944987501, 886756619, 339291335, 238733592, 576610705, 687381678, 275128213, 873421535, 455661499, 818217625, 122348486, 498627501, 483067785, 858408142, 382785266, 685500850, 320402981, 425396854, 423603677, 843485653, 414747421, 193351722, 53965144, 603643447, 574619286, 687201853, 985673926, 571118698, 636072048, 991490181, 382167418, 962447860, 490076925, 93311333, 906609238, 737665508, 639864296, 335515430, 850562678, 271670511, 630577790, 863467814, 897306587, 251971908, 740860867, 286284746, 84691621, 512913289, 404175749, 473537770, 938661443, 91907742, 757543057, 862238705, 534391838, 791511271, 294119455, 96531434, 633902376, 801432269, 296531697, 104982186, 58851918, 466926312, 399768315, 383801891, 793429415, 743174222, 774625635, 427853065, 608082406, 344937839, 83346014, 980487183, 492911784, 739707940, 650435032, 720527264, 226827684, 853583111, 772046721, 143214897, 220784143, 870341399, 82754891, 558232050, 855469728, 344249507, 33993635, 307631429, 559203309, 963097406, 949300030, 113655473, 691711559, 986938198, 344392856, 6116046, 785020066, 927038003, 747623631, 345231328, 635627831, 786314210, 340311050, 321734330, 126582335, 696165920, 622921719, 462472504, 543561703, 679281685, 326220795, 583765789, 16626218, 181686176, 986850709, 100604815, 659801920, 58779589, 464221259, 27241084, 781668200, 943804613, 130554307, 146925330, 306471092, 633600742, 216914890, 613381270, 570076125, 564106341, 410858590, 703702782, 812198733, 330535688, 937734245, 20674821, 691150526, 425663251, 887523347, 571179661, 928902216, 435359100, 627723369, 641921795, 792317626, 385514338, 898678275, 398095376, 104232675, 171156267, 804986705, 564103648, 168011484, 534947213, 207710091, 324931072, 762831570, 771781077, 395204439, 742575136, 630295142, 525402060, 351485402, 850809369, 8148980, 454737371, 842850904, 696852430, 515134141, 750075648, 904181791, 615266287, 654801478, 465121825, 529486581, 306616394, 309710443, 295638174, 740319558, 312750225, 585083836, 706402283, 47243460, 745471827, 439401981, 465283850, 255949491, 351691629, 186564021, 176631050, 702797863, 999441246, 857679183, 579066877, 487804937, 133461689, 771687924, 255916962, 438264273, 735542792, 206950591, 365454606, 14832815, 778415382, 424880271, 534606664, 603836423, 99576330, 621440155, 855459929, 127490334, 392343040, 39383041, 489349424, 794598871, 57693924, 39206391, 678642763, 650216422, 145260223, 903249232, 761652593, 156644176, 693111105, 598095357, 356232998, 786041974, 39837821, 365465335, 216797757, 640864674, 761810818, 568758535, 13210655, 267605984, 738589556, 96794388, 544361874, 193276613, 117308641, 248573753, 697161840, 880887217, 850569722, 99788734, 539110559, 42290871, 796979923, 19903381, 756917239, 16051102, 166065607, 711177630, 8430483, 124375538, 898099729, 227815363, 205540232, 81582375, 694032493, 896567039, 202059543, 360931372, 387080430, 837010468, 781814422, 702635068, 910767273, 284037000, 170218947, 230246578, 528668074, 136618890, 970731890, 60623828, 352643453, 40761342, 570138024, 772119393, 143313239, 496607978, 778119765, 84517315, 925559786, 76849525, 174548518, 52908137, 123589370, 459130576, 346286406, 620029383, 197604306, 622818232, 535170938, 163970340, 656649422, 637233920, 477733385, 369530916, 972768345, 651557981, 732167567, 108876134, 713569481, 407773906, 872762794, 646706477, 427779609, 3072507, 770642295, 538900397, 190535833, 947223029, 119257384, 630081275, 748647506, 663124740, 370769066, 27621461, 758986618, 443862004, 870020793, 895879554, 943458956, 979180795, 840473283, 525719941, 321439091, 516189505, 957238743, 908916954, 736528221, 893378688, 852044161, 653652411, 129965965, 332649107, 712949362, 707794305, 891436282, 719971067, 977973912, 586151210, 515155397, 998567470, 570505390, 625230698, 857697595, 896180621, 912361182, 602661665, 140628438, 736302233, 344499876, 780565481, 621674207, 902884003, 22581707, 663241715, 641750761, 290170857, 122363811, 420748846, 734253288, 676339468, 518773686, 327335824, 911059490, 999557279, 709330245, 389523462, 385040634, 882478903, 805134181, 932195808, 887599466, 696914688, 210779855, 587227786, 806427437, 289938359, 234242074, 548732275, 420871291, 346012146, 179936767, 190807103, 531034422, 123554898, 808741531, 469754696, 425324803, 804643242, 840331605, 816449496, 485741523, 504027926, 704960108, 26558336, 801969753, 429594920, 826461907, 443593357, 115313615, 891617107, 573530877, 310752890, 807868403, 527822, 128656596, 566242051, 791268630, 459387681, 63974218, 312461954, 156786464, 210535007, 775388082, 204332159, 118209941, 515719794, 142689890, 927630003, 595487883, 331829011, 929441228, 23384688, 675491992, 117392706, 264644573, 124976199, 536931500, 276044010, 174852815, 323830720, 31978166, 808906897, 466875479, 397837522, 409849440, 871585376, 228822489, 368110289, 769141667, 407492527, 556176956, 300399473, 683743315, 220566060, 168529148, 51967160, 896742438, 337636087, 967275017, 429163994, 499724824, 567454419, 75856363, 582699193, 252581882, 599372358, 48992852, 260680738, 608495450, 639906070, 944828610, 310453591, 123375766, 804088394, 30977743, 525051202, 380976306, 836836834, 825399067, 985950003, 526549120, 973850152, 553876160, 235926791, 330604227, 973092600, 343852201, 586593486, 805195229, 477489246, 522871916, 33805397, 102060646, 152367363, 7267172, 733721352, 978312153, 593400526, 697969206, 827601803, 850954739, 781454199, 813843036, 857315118, 693272644, 609511270, 125767055, 551624513, 744852960, 966341117, 991512548, 313658699, 141289834, 840662075, 128757198, 557428728, 944445244, 450279375, 404388289, 864034636, 123767613, 594872759, 404084079, 26309009, 517158123, 368708432, 921418634, 190937176, 99091806, 783103375, 638375427, 68400829, 217767784, 790988381, 313122220, 849923671, 813277170, 448716944, 934390946, 58880404, 121480873, 253274264, 789409659, 214147279, 676980482, 948617144, 337830264, 491553599, 652912650, 453739768, 176640378, 86816133, 522372161, 459596735, 805112159, 146774161, 698060226, 659299834, 230531746, 135787399, 205109784, 401551752, 521871281, 461508797, 514491661, 163348016, 768773476, 74719606, 40606742, 162830069, 941736405, 480821619, 585786151, 936887378, 110472137, 200742177, 889949039, 39284274, 39538257, 54622042, 170366176, 102840697, 442033117, 923010545, 401729912, 497890692, 553314377, 851799360, 558339205, 693976607, 999127852, 873716292, 679448411, 621077493, 891213589, 842634701, 401689473, 932031327, 862763264, 966365492, 707577575, 16109207, 48884666, 791297729, 486663353, 69415638, 237914381, 250122512, 424273577, 557549718, 788278792, 761944525, 498317181, 68215737, 484696294, 929939686, 478331945, 328502277, 514414334, 63009936, 606928512, 297686053, 923575759, 920477225, 160267569, 159981007, 233036108, 470769245, 263911885, 874549207, 239929965, 401332095, 622581750, 991315613, 505236701, 639370571, 197964722, 346975222, 803793768, 148172056, 619497331, 561108752, 658068426, 998234719, 767223407, 923853300, 656298427, 563136135, 148184111, 714845618, 345469800, 624187389, 90503865, 152836391, 620711120, 267904011, 934359491, 684203028, 140406753, 745838647, 986136178, 696944482, 730050053, 127670047, 236580481, 242784834, 467848959, 591449064, 858424472, 124287306, 773535639, 258309436, 750259444, 323595781, 146847688, 103143408, 272055900, 186400581, 739693101, 311568059, 28321421, 253224934, 619760961, 289328059, 570752181, 652806409, 317050098, 507246585, 666671517, 229877485, 894873242, 281038238, 18446753, 646899180, 345554381, 580863609, 48113826, 264940876, 404819283, 259432814, 231915072, 604907065, 283527015, 697340033, 803843336, 625849056, 156643731, 163970782, 613581549, 122082109, 347636757, 661658263, 44231959, 569856423, 970159371, 113008855, 733367497, 539112535, 689771034, 972016947, 771178332, 610993314, 374529139, 451955347, 233277620, 731146216, 433619594, 901398361, 769875769, 76261848, 204220219, 152127448, 270424370, 786648127, 580700385, 989303746, 490834525, 449481838, 531943992, 784445849, 667077797, 394979787, 930154041, 272874242, 884911891, 913831286, 215158775, 515632402, 312655740, 239902981, 252990349, 219196574, 843445935, 483703578, 671877542, 971336449, 315675124, 196977715, 683890314, 15841005, 436129342, 911196872, 571751853, 377169612, 142028911, 46877941, 209490651, 561405715, 230255455, 343716526, 772117802, 193220735, 322261194, 319728409, 785333150, 718044620, 246342074, 318097434, 550383358, 687347614, 192979961, 922190855, 622290983, 758532262, 373390485, 201766084, 231038097, 641729648, 40592210, 681362665, 850486227, 250887456, 706764823, 506993624, 893921223, 870375284, 147710594, 58872261, 180474759, 641302263, 953610692, 678975573, 558578531, 11160313, 313920283, 543270247, 283758638, 817822191, 783156182, 720568314, 927513222, 727849910, 253203990, 841236435, 942810339, 384822514, 516627656, 917530505, 122120707, 83754254, 155581228, 241246946, 1284495, 834580130, 608115556, 677309117, 801861255, 803954002, 407384396, 483390661, 511276856, 907710731, 254529171, 276621683, 715860861, 258277895, 477880507, 33220198, 245364750, 58655670, 689891452, 895194296, 754338927, 569514832, 502068717, 498386825, 712321779, 47052378, 403617593, 735137109, 368986676, 934778938, 945859841, 847173692, 387138870, 499547782, 411227820, 863303177, 532229073, 409252815, 597016103, 706662901, 823334524, 697435909, 506367612, 644245662, 371388544, 949561878, 639042362, 991903908, 443833343, 874648222, 736759900, 584625565, 792164915, 898481984, 629383377, 650220212, 575329608, 67441965, 947439283, 796587298, 709084160, 68803186, 542158835, 154462113, 329447875, 495617513, 36944318, 447104961, 317778778, 148375809, 942779611, 674021959, 798692036, 135902974, 232120452, 760146041, 538542831, 288691248, 915102965, 129407196, 960441913, 812789408, 509563489, 606039045, 907161570, 804296849, 800374286, 835130697, 643478547, 954569645, 980669405, 886123146, 682026846, 264969170, 336515149, 569413309, 103250217, 845239382, 57081063, 5365113, 209439134, 127310962, 654439871, 230957625, 166926984, 637420384, 814768858, 162987408, 210691122, 36199738, 800703312, 900891135, 535827869, 480970667, 750499101, 167208484, 248824069, 379775046, 768649229, 207875463, 643138861, 445069667, 961506598, 147365594, 277155011, 960033178, 243428244, 367554470, 984832658, 691051859, 663309320, 588266745, 980285868, 955231384, 391313727, 134977636, 603132266, 75623868, 100401880, 153857137, 353898309, 900268964, 570545634, 919732335, 754150125, 76833670, 769003071, 683091927, 786998359, 424558381, 599669881, 306872481, 452086029, 675237252, 28056529, 525579349, 692170438, 866509980, 100693626, 178781005, 131316703, 815068360, 794610808, 959936832, 713502277, 342602416, 937563537, 898313471, 491022982, 105667207, 800132237, 865745915, 832413680, 594408806, 855269798, 650850853, 90097294, 622501687, 787070613, 490234395, 903591387, 998006152, 61141107, 254430104, 967412560, 525979122, 723952730, 94035604, 177798386, 344642405, 274293248, 296789972, 736846449, 840058792, 388840535, 912239081, 947631293, 204931915, 130950856, 948917303, 163421724, 458701013, 913950911, 629328775, 797963992, 505003708, 151813221, 107352569, 116990054, 400047572, 562842356, 643131784, 950125199, 292202465, 921398706, 28441907, 993471188, 86287048, 439515689, 798061840, 415704384, 474277358, 48614492, 919202370, 932035856, 87524828, 984086628, 836419192, 66310875, 182714623, 16512804, 267198264, 543500517, 586407875, 596556968, 801791053, 654354283, 233646398, 946830218, 79314248, 768682634, 278294492, 300328906, 206839106, 744677218, 479199900, 834476466, 626070593, 752243307, 833835404, 648688294, 983316045, 417485522, 259675862, 815100976, 600374036, 208622331, 452909976, 802731884, 884971051, 848334485, 609185105, 467332826, 396380376, 291695927, 314100172, 681770645, 169332767, 387745527, 816072105, 5727036, 152449501, 294162467, 456123900, 636605662, 988295174, 549803754, 631543792, 747747609, 708997149, 576372684, 852489289, 472226774, 493905999, 823461536, 143701921, 430457554, 884398602, 788147073, 597761657, 682358685, 583913250, 642329298, 834271431, 575460696, 158031501, 356528505, 230806326, 653304601, 106497994, 597657817, 772928396, 668876589, 42075200, 717284236, 239984929, 271087280, 930309100, 755076365, 999311711, 476384332, 718678041, 824193965, 745889119, 329402376, 706918718, 675520454, 147530828, 302055012, 48117543, 208224091, 214115723, 446970239, 486800280, 751380505, 350289095, 672058576, 594963678, 510558197, 293992733, 723145371, 745491806, 224942225, 889173957, 359206139, 54849394, 574145119, 198410880, 114912151, 805839994, 674028770, 843359899, 495648774, 5442389, 777430148, 127612547, 56559493, 453090960, 2726481, 551409455, 528046689, 941542256, 933183042, 626572115, 519302910, 699327053, 996268870, 787175356, 667907031, 323195654, 875390543, 625719248, 147382714, 710596005, 329667330, 76566568, 58914499, 526997457, 980705905, 412179782, 34886264, 267573463, 325456225, 583429990, 689069017, 262430586, 805930646, 652466559, 784199441, 763839809, 793431938, 841020056, 923391922, 866017649, 433749599, 898423181, 49130168, 595227627, 631169009, 768008565, 447001489, 775522445, 702794038, 134874253, 646100558, 876139791, 495289381, 629590841, 259608918, 23776246, 861188748, 536757221, 542527941, 138341012, 154927691, 146698669, 398720702, 825997573, 76679582, 881127286, 168047594, 325484618, 986384236, 897957037, 995890760, 77130742, 528431485, 51641379, 840903872, 814462959, 658728041, 658997714, 569673086, 944756763, 124009313, 536934955, 868639554, 219731903, 687308074, 940694295, 514258301, 91269882, 584572867, 553757982, 162941455, 184524386, 465161599, 789352751, 944304439, 370196057, 561547168, 216775262, 601702347, 434236709, 217961361, 145742850, 548385299, 592283453, 980541149, 996548371, 78455533, 134117882, 224358399, 135944754, 934726352, 627659410, 226847819, 285051180, 628503447, 512109832, 957754075, 166468508, 243250464, 561158561, 135618535, 750485009, 753959462, 54294170, 477967634, 99342589, 652050019, 585552376, 436651263, 827313788, 848738616, 691143287, 150095515, 750492261, 682783025, 801012512, 998338368, 331225600, 598767062, 422671937, 353024195, 397758836, 305923785, 470971360, 898789169, 447257075, 718699583, 123022482, 866159850, 481513020, 289050370, 888232781, 699176430, 373035245, 710574037, 892474869, 762475907, 386947521, 437431430, 219693581, 890386029, 449613395, 698628275, 73721801, 910448153, 212443590, 860328155, 705553689, 772931367, 174736164, 380060093, 390082653, 927691906, 336586851, 43702976, 314729668, 514284697, 870674202, 313134262, 214483124, 674613420, 292490889, 601975101, 815163184, 466914835, 946737994, 865879990, 543873206, 736103979, 641250842, 1954186, 95591999, 639422387, 719547753, 207386852, 800649804, 857417049, 185527957, 310101795, 922723951, 251538461, 433149346, 582738049, 402784602, 524471682, 325214918, 738925951, 237041215, 163597308, 418966313, 338997077, 629761819, 481687245, 711734485, 327232018, 310529589, 286470583, 314696236, 187290139, 886193582, 210307168, 340367034, 309472339, 962376826, 706018729, 445632112, 205613627, 555893006, 10677655, 678817639, 730907382, 750785536, 730670607, 902806230, 172972298, 653454773, 524757749, 302737205, 361084046, 415944084, 193338285, 216272007, 423536365, 825555580, 908643694, 335589625, 882710590, 398871964, 79366778, 539966677, 945115534, 27150142, 703987190, 789800517, 615126604, 769716972, 494518861, 178790050, 787687958, 121664828, 621852309, 28079902, 283035338, 196048466, 42812597, 222782364, 257367855, 628363795, 519300780, 747137761, 232380766, 972246125, 532166710, 667442336, 423891344, 898431398, 665602787, 433237584, 97595021, 30004267, 927123690, 717384117, 170211619, 968432562, 754879357, 227363634, 499202317, 606268449, 294774558, 777748882, 581486229, 963948248, 334375522, 88603905, 47004640, 483723220, 661876499, 231481611, 266613894, 653680658, 133070507, 735777426, 170187634, 972451850, 788793288, 178629765, 239463353, 708924215, 49757163, 740834787, 48008887, 332360595, 569687098, 977169233, 614996278, 920457834, 189102254, 9785640, 572484316, 813087041, 569292244, 638409582, 547829243, 680684784, 637713454, 339097484, 748291292, 908717537, 697465130, 15438449, 931639444, 143378289, 838283797, 123946438, 623985905, 506897052, 749389093, 472767690, 590407886, 997639287, 238098920, 16578168, 303555985, 154925391, 468433104, 925249176, 792173332, 157687219, 214559169, 196474165, 464533041, 749308206, 815455895, 242535639, 783823327, 799430853, 351146674, 340576538, 310118349, 117051520, 844804021, 671446241, 801454034, 542780062, 933455162, 202553983, 204301702, 848674382, 839459477, 736692450, 669266555, 481606571, 35602268, 860571416, 755197974, 2960398, 379229372, 834755726, 400998722, 16946336, 283978059, 21833883, 431269679, 683116738, 790602506, 656842287, 718544638, 964276429, 248289034, 813453752, 828563989, 497950887, 319172930, 28641682, 602173423, 137419972, 37416799, 916670990, 772861824, 778588562, 237731751, 260398280, 769351421, 916437149, 998067020, 373222033, 743817678, 378444910, 902079586, 918175638, 110182898, 126519329, 560481480, 525546571, 757864165, 358511538, 669445757, 809183205, 583082543, 107335891, 294178226, 883263691, 103040486, 734872767, 853668249, 304522357, 895744895, 517433667, 173871456, 574663140, 927496042, 859098728, 574625308, 514982537, 899650509, 477930931, 903815669, 444941075, 422301508, 170824350, 707888331, 529563528, 859117511, 308757271, 810404431, 723731742, 63724962, 496988338, 375595949, 968111548, 946303337, 991325525, 850343413, 246458073, 127789340, 496827122, 447657, 762535708, 379970105, 206339084, 473260416, 321050563, 508413799, 405557937, 732929899, 368428242, 631133919, 873558801, 99705232, 167751503, 374194636, 282071292, 175340099, 652986, 497323670, 551691552, 657035401, 829317251, 466573700, 369666044, 502125745, 611972111, 469860325, 773223317, 406791032, 305465115, 619637900, 438011048, 392655494, 666223738, 191972384, 426406656, 263980963, 203178841, 552043912, 529288943, 229934829, 910827893, 338155306, 65737843, 873649720, 343174524, 587400428, 124764319, 975158009, 965030049, 79382285, 178924898, 824447534, 138262965, 231910981, 137620189, 472238568, 231670171, 963836666, 76959278, 719831245, 628818976, 481253717, 1168749, 850828760, 265153622, 497741859, 383433139, 379025802, 975443070, 520223569, 901712561, 329548976, 197547387, 170633156, 49732154, 175052723, 331801261, 739886722, 154199592, 293730245, 808704973, 126728029, 934427077, 986633460, 472573790, 850790057, 206996786, 384004969, 466782996, 155363863, 963858268, 856198967, 521250276, 357891278, 293593521, 323183884, 94344566, 260890431, 767911252, 576674082, 294425993, 64948795, 500832722, 428563121, 664920004, 537861258, 843701047, 449967056, 173561762, 287441866, 434250445, 587156345, 449115022, 990288833, 621696402, 360418008, 817448826, 780525897, 308620838, 61302110, 109979565, 277267743, 866080494, 562689280, 167966588, 672884301, 503522369, 787179356, 840134318, 120898376, 976201596, 135433179, 311594108, 476343074, 790941317, 827211400, 715688566, 276742807, 138467106, 263690172, 20265236, 252279162, 280843953, 963140450, 517415676, 41172453, 545461630, 127831088, 845871846, 654863625, 11541244, 911564814, 579708793, 952589172, 194926579, 616889793, 941708795, 483004528, 124147429, 865968175, 768998964, 156272096, 943747902, 563147990, 612818387, 428565322, 854914513, 186222327, 727720047, 707855322, 907104540, 898341387, 613068551, 930004973, 20376936, 752136012, 923385318, 841486364, 290543851, 310048144, 993551786, 462419436, 91635573, 692975036, 48522218, 77169561, 692713174, 53447476, 958534689, 608950179, 883577653, 524021632, 466828048, 413185150, 867861424, 765333128, 321813713, 475118903, 207565499, 414621554, 67742117, 641087394, 366004503, 246638647, 643173122, 238760560, 221297868, 788553090, 882615105, 624591013, 960567570, 207497839, 855245218, 4027312, 157256711, 315114818, 418191558, 473278583, 320017743, 835860744, 911216132, 195180023, 670669994, 458092392, 431221597, 2428053, 865247747, 519354830, 701400812, 704930052, 971929496, 531926318, 228774586, 13261273, 782674126, 643746454, 655112618, 689930435, 35631917, 832235036, 980652377, 545869264, 99721118, 829825090, 967283716, 793921253, 647312862, 207752586, 662161626, 751741994, 409856010, 657921980, 262916131, 504904825, 627225577, 697166229, 280425582, 363479804, 915782401, 578135568, 810037356, 248694825, 952790926, 322746634, 265805940, 385779087, 306410784, 968320138, 754702444, 993937694, 75987479, 38116152, 385391020, 625128246, 787521912, 665471456, 819976687, 140229743, 154261040, 488425412, 99641485, 266682036, 17392198, 509308563, 48564969, 235290290, 996607113, 686286452, 856575266, 211484594, 571390416, 762605047, 294726245, 350471871, 185666139, 131181842, 527587726, 199745685, 127527853, 830821685, 12719558, 384427566, 29558317, 585018800, 832545616, 877031930, 251028208, 888964005, 714462391, 508883024, 66549943, 830824008, 846380798, 727924923, 62565482, 435769853, 960987162, 475691512, 516021195, 821607720, 112187292, 676655487, 747632695, 976342180, 287538659, 218180481, 823913935, 288656121, 303343279, 480163552, 101864692, 438761723, 3055870, 107234283, 872186508, 866341094, 505203530, 65985260, 870183336, 401457473, 361292179, 312018548, 299848176, 275897311, 952884276, 421237898, 700629099, 465955363, 887408739, 947503796, 686844329, 731256372, 463909691, 537386600, 267420794, 267318438, 712054711, 114398045, 301218526, 79420914, 669625514, 480652155, 768396124, 947138903, 43190817, 131227933, 118362178, 379494495, 613863962, 391126566, 619451760, 324683835, 390866998, 556516503, 657325424, 168080165, 572083852, 679704524, 718155892, 769395572, 951009272, 639859333, 605231615, 567229233, 877706216, 772823446, 562033574, 267975974, 401267125, 488918924, 745060524, 443029619, 921444437, 452396025, 5462721, 557367335, 116854466, 632322714, 222383042, 128627713, 173811375, 149936384, 38318892, 312052362, 748916765, 386090449, 996006940, 974020895, 141022856, 415355432, 863675495, 562513610, 381218337, 520054887, 202249419, 164533382, 626601901, 564376866, 610753007, 74143190, 811848742, 433606903, 6976762, 938500214, 915367010, 736138121, 962848180, 37038473, 647019640, 248372752, 733519725, 10262294, 985674437, 966135366, 355408143, 280288675, 201106512, 251406831, 477734473, 843451988, 458357784, 511545726, 514005792, 918215461, 245119349, 594970719, 227388521, 642201864, 311681554, 947101630, 378337462, 970205730, 790998183, 699154759, 666398544, 268233470, 186511712, 856102007, 146117299, 117137332, 673610380, 105883963, 109787577, 572227755, 281022623, 97690514, 491485874, 595158487, 397745272, 543129686, 575760690, 961718604, 488940110, 442694747, 889265841, 687820181, 342444918, 62271787, 42917527, 710668553, 618768939, 782061045, 685012303, 168391853, 670272643, 937088718, 896813147, 801511060, 907425916, 952465619, 611027371, 538042086, 186066352, 562362043, 794287830, 472089071, 691337526, 267845586, 560973506, 375759246, 740555390, 868688364, 576634005, 747944774, 97147083, 125713375, 839771850, 89418972, 487764653, 767814727, 740005040, 725825645, 155304682, 255550437, 513364945, 796935154, 657589900, 714204783, 680557939, 540475929, 186377522, 151137850, 569861321, 459326606, 856524053, 363174747, 919201656, 527947464, 404603921, 128307681, 43365418, 183587794, 386801974, 799665682, 6310728, 658458344, 169065297, 792291060, 331630306, 57793990, 440125859, 73325610, 657357771, 959639929, 720088096, 960574168, 518590639, 695103045, 995243178, 724273534, 940905840, 44116653, 951465504, 417617893, 568322952, 237784287, 973945730, 394828300, 955264873, 180742884, 214173465, 737815724, 934031981, 219141018, 926334757, 915355652, 589103362, 291355660, 852130375, 699099188, 697465564, 273300238, 947578557, 135615058, 330422883, 540472702, 322557638, 138526429, 452929110, 850968580, 320115449, 501208092, 142263635, 534914944, 598270239, 939300817, 560228910, 816371371, 159874286, 843640880, 424386746, 6710189, 320203540, 433373676, 31292722, 639441078, 573278216, 332762283, 916118511, 787711872, 866284893, 111578751, 972776018, 806834742, 210086268, 191782528, 151120048, 981433416, 367583538, 159048373, 252121283, 964361064, 883568199, 848700084, 660749619, 973550864, 398375659, 236077391, 364129156, 839396279, 644196925, 206177322, 970162369, 939602336, 25936883, 296023316, 103702643, 540948495, 738934176, 492523639, 388192352, 271570875, 561971913, 523190054, 561865239, 686719259, 440004064, 866220655, 183918839, 131762357, 761109294, 283254648, 623543403, 888195439, 880543727, 272380554, 786136238, 258297550, 152843524, 260923081, 366587237, 327268984, 157520768, 932552880, 799614215, 490706937, 817605496, 210299838, 211362290, 982638474, 559691620, 229572680, 109069375, 274456459, 246504465, 567521840, 294124801, 800880618, 805386605, 253558976, 554474553, 699756348, 947630644, 136116335, 790758784, 999218807, 794425536, 465498669, 983056421, 45668304, 622670249, 443415551, 978193861, 345258148, 82014093, 805495209, 916231095, 735422418, 984497483, 973157800, 839802127, 144855445, 107431352, 965738491, 338517830, 858949575, 562188620, 332019875, 405664190, 786948780, 921232491, 9449113, 796783387, 837032561, 743082726, 70837451, 627436630, 498158895, 784891025, 259003838, 240809001, 535485655, 189049941, 894761940, 384049912, 501163705, 112120229, 636849891, 549111529, 690830098, 235147799, 655347345, 902187764, 714505640, 23710047, 569323411, 124047128, 687313255, 769378475, 447168190, 114913117, 395674565, 903350579, 388715893, 31583338, 772340688, 613630905, 764745793, 646906382, 281867615, 691257181, 636066127, 802075376, 266030791, 878934107, 380159746, 910635000, 877805194, 960432103, 196676563, 44918580, 559289977, 702997433, 203827399, 765699555, 517194993, 856579664, 56475111, 946870171, 172595340, 662795427, 886109970, 716664238, 877672124, 426565037, 246108343, 28988127, 798523413, 854931878, 307457208, 358893863, 219705741, 908814536, 340631574, 186446800, 158815982, 306744202, 747330916, 95205158, 483904129, 519816785, 101965706, 835749110, 356688942, 314347610, 630143464, 101222524, 412672501, 200289401, 510379202, 743861511, 296939785, 298583762, 336740788, 288305902, 593351369, 41494629, 966578577, 628250748, 606153521, 111568633, 460288788, 624482838, 418608568, 436985876, 636397930, 690040109, 838522660, 178091461, 167963347, 170935530, 918330998, 381055372, 696113247, 832469272, 719362672, 877623331, 135263813, 976260719, 181871440, 51537645, 243320629, 436428850, 272829721, 362385292, 956324482, 667494709, 513273331, 374332071, 932290711, 342412437, 822207449, 745161806, 441150153, 966819334, 719745782, 230182240, 114557398, 192977055, 675668785, 541262408, 489039420, 591718611, 250272064, 599017130, 466731011, 119280319, 19795056, 542407533, 244137180, 595403705, 559533576, 952568444, 437007637, 41417819, 363575628, 220116005, 653434097, 151834979, 678452641, 312121337, 22460764, 562335923, 787624867, 784837006, 994043940, 649079560, 578785065, 891174832, 849646124, 873767137, 870177745, 134747969, 295264336, 864530582, 428177883, 200081296, 675974355, 365043054, 652137584, 903844094, 515385523, 951826157, 944379660, 482709622, 674788933, 335485124, 965401989, 177549728, 322769534, 917530832, 169637265, 73717495, 220268033, 522841892, 328865795, 239933193, 30162017, 248457092, 358368356, 804513152, 148326615, 918752186, 881608567, 784021046, 476145709, 605472691, 766269868, 350807934, 253654421, 806848261, 587015404, 124089947, 737280759, 693107834, 50165613, 722048080, 724549751, 734640168, 798422516, 39729474, 263979431, 651515305, 624107814, 241312021, 214056187, 593114817, 222508614, 166306423, 499024859, 74425592, 604228721, 898521562, 360850682, 540386538, 109589400, 466180921, 301119621, 853346653, 685383473, 955185081, 379921923, 764014553, 531928184, 42021539, 44183409, 781074820, 665847544, 604564271, 76246251, 889644724, 676329043, 392213511, 652641168, 917078956, 938153908, 97683468, 636176411, 644028003, 424054268, 484355355, 355892086, 188659301, 242041422, 600969560, 547552145, 511052777, 808797808, 314928438, 165944824, 928304006, 355417979, 98007797, 312511991, 442598372, 753111497, 272207546, 177116012, 35789446, 8794053, 769364424, 746573760, 346861247, 910375867, 643650720, 701479024, 521770876, 432232995, 149693145, 402350772, 7620645, 127643494, 391800849, 44074381, 486825506, 181841148, 476624027, 304329360, 23724263, 818492668, 561938559, 576312854, 59782907, 515559155, 920173797, 130362602, 452412582, 505872326, 767354754, 714191174, 151056830, 317264935, 580625888, 178293694, 363794654, 388266509, 485217224, 931572149, 274856291, 858567024, 316386574, 589565147, 46510675, 803230246, 879583379, 371541727, 800163850, 602451931, 108089326, 351045718, 333742885, 642206205, 311501783, 446010179, 786171404, 514147475, 511544843, 733613254, 674243789, 335752193, 117611158, 62576623, 404591543, 526421796, 739902310, 805711469, 385404570, 789795168, 518881707, 378594001, 584463300, 842227504, 860125612, 810890224, 97994566, 259134151, 756258217, 488031134, 401656113, 132915401, 174940536, 561634685, 198417485, 311391860, 482395579, 64812333, 100550462, 972996911, 485522716, 393753158, 916859604, 283825466, 905885099, 751861929, 393628072, 280619434, 98484401, 672218007, 315529296, 63773822, 688911581, 78761101, 204099946, 121303458, 188252907, 331038038, 305989551, 39319980, 73169392, 940795456, 174569510, 333837063, 207452633, 806914986, 6391256, 959347981, 224481344, 743360987, 649339768, 406412687, 640188067, 61595846, 669308072, 784095785, 648626575, 14283284, 530396816, 782355960, 219895044, 33115827, 575375237, 284416884, 852052426, 756667150, 180465263, 332688917, 850136988, 426660585, 220099403, 611655392, 806820869, 323405405, 538087482, 913617977, 651652931, 986648323, 946842583, 511424451, 642748582, 356946107, 85060184, 550411018, 61938550, 174594884, 873518688, 305629222, 653453308, 33920119, 235930879, 230988309, 390906737, 185313830, 339420188, 899206985, 693140851, 940074260, 677958571, 750007845, 28237522, 895540758, 792084855, 219495364, 335379089, 323405567, 884825548, 433627701, 164152259, 843964436, 856622591, 637829881, 133217836, 623937444, 600409877, 401039754, 146874344, 506283340, 9127232, 808259151, 787923087, 382354162, 774342083, 145886557, 439473657, 539483950, 750745528, 742323727, 223912002, 388984463, 932380222, 319178854, 970670224, 177345959, 245487936, 554511402, 172216467, 33851460, 82894036, 508690556, 100316581, 927054633, 104204995, 470548737, 302028802, 824947427, 338820524, 147778897, 662276324, 705557281, 435139847, 293211950, 214623305, 478348238, 482618336, 68190692, 423301532, 980346295, 606454583, 731838731, 196434927, 837953499, 178081070, 227437644, 68133520, 247149520, 222551508, 586877438, 502545894, 48253735, 214138222, 510784498, 574523442, 128029949, 52421951, 7188534, 556049850, 278814794, 382132446, 988753551, 542531982, 967850617, 835455708, 867405109, 537012394, 981771901, 942025165, 551971324, 525562619, 529692077, 645997070, 137495659, 972432542, 22074736, 879089884, 905106447, 89601475, 617126769, 311133914, 359244883, 533855772, 430157891, 236212127, 613701167, 224432980, 150027408, 372245181, 105655281, 821194208, 348904487, 993263458, 557384888, 786172188, 238772241, 205989643, 925683706, 281128956, 736941649, 636178349, 356003045, 500069714, 924172883, 392692864, 605480632, 803169828, 342281073, 679399153, 279345938, 712835429, 504263729, 206420997, 651554187, 47221216, 198752063, 767574141, 383223397, 230844355, 869859190, 878423114, 453603254, 376468034, 276279869, 89904816, 847119148, 367845068, 442958044, 446454257, 656776990, 230320444, 265555428, 922591448, 33570800, 886875401, 553452081, 563112644, 737617646, 598580603, 919740, 174436867, 805400061, 915716056, 332677048, 471229981, 380509815, 45844875, 529456148, 524029586, 1442233, 221404260, 375749041, 698574027, 924949790, 687773956, 66002509, 707771982, 862528883, 315657056, 891201366, 860202163, 437649246, 687688795, 199582440, 393862870, 328814185, 197969758, 73903673, 951338727, 769765082, 399428010, 827441040, 255103379, 668770859, 926329489, 693375113, 162869327, 763456507, 216348293, 773674538, 697394946, 404890158, 760733963, 583884282, 350214310, 965294755, 33484647, 843166217, 497135186, 904962121, 991744461, 969171679, 728513758, 944330404, 626462275, 430672857, 308509374, 10765328, 147712193, 703280133, 744871889, 679213180, 66362246, 262206445, 397615665, 227739628, 335617168, 580121301, 697104118, 413370988, 957165250, 279571825, 649924287, 773234621, 827522916, 468109829, 15667236, 145560867, 655234112, 125093891, 311838148, 419317115, 598540226, 110181476, 239378292, 188767240, 957508339, 322607506, 552834403, 654265351, 248893100, 739751175, 215801428, 751462705, 483821118, 449023315, 167583181, 488029097, 87624525, 215014806, 694157470, 690371304, 927089341, 287713737, 563306692, 974842455, 86748869, 369200254, 460130530, 594849746, 745915299, 253802224, 283996531, 98808640, 284448188, 75484340, 407901502, 657426989, 606411667, 294448412, 69049058, 73024083, 790973825, 767586997, 181294804, 922347079, 318522320, 67831732, 706323129, 852417598, 285295638, 873452798, 606741792, 794547475, 655844514, 553010678, 606273180, 831497304, 923544137, 449559746, 912403426, 713633700, 291456530, 727967894, 314509052, 312518142, 4699314, 737891365, 546206006, 287079654, 560687768, 421269822, 154876666, 26109812, 208292976, 503685201, 62794722, 232692810, 391273589, 604565296, 100923491, 656343366, 627897530, 153123115, 222503441, 974599171, 498825739, 862499861, 52522910, 216248823, 680420670, 516601590, 571378181, 202072133, 782183192, 401740605, 92241063, 437630038, 912399265, 629617956, 199404775, 380077147, 794119676, 550300421, 472587802, 9565034, 222542677, 518187034, 234217050, 4674361, 65056298, 761892313, 163997170, 472144121, 143299376, 521559528, 82014402, 693666535, 660163185, 909606479, 408228445, 177644913, 453384976, 448798581, 315292148, 966942351, 921412020, 835136609, 449667087, 322056086, 467374781, 184736061, 913285405, 372772977, 922613270, 13550295, 318154229, 600525636, 321113140, 802917865, 323353352, 688727956, 904463610, 44781204, 127354496, 903029093, 34877096, 849332870, 781434066, 373419484, 619337542, 547001035, 12326309, 561039334, 350172508, 235070469, 441142121, 345202086, 403494839, 789255791, 273250689, 733109600, 53058501, 368463900, 490192206, 749429635, 87971406, 348686730, 962164764, 38767999, 559056899, 663612863, 621899424, 2589237, 11936306, 130489404, 113006795, 862073459, 358106742, 748107104, 547578005, 270058641, 707393223, 222830865, 213709696, 132093909, 968359217, 562102452, 909844443, 148563082, 439454924, 242949711, 461617678, 824096008, 226518401, 559921716, 620819167, 772051450, 570701949, 391173099, 560484984, 968766974, 225429161, 335370605, 441895175, 673454464, 514208767, 329671107, 489235999, 967007899, 839214856, 683366847, 169308824, 330045307, 496751685, 979820010, 392364561, 963679526, 367290372, 134026690, 530667734, 810215280, 692227328, 100344111, 395659063, 265496168, 134684291, 361054905, 261629870, 175472615, 557250562, 8514328, 309831923, 556521945, 661824566, 502224954, 723625721, 163102277, 313405060, 569570153, 313386608, 327585773, 786574733, 770031268, 296717586, 874431434, 59201669, 822580933, 617888427, 378607345, 176383027, 497577478, 782201732, 877558991, 485517008, 645465756, 935223815, 441010487, 204561889, 278178715, 821970660, 869480441, 807275923, 82727971, 142200132, 273943853, 315815955, 886044523, 927674070, 249037045, 752681192, 378441081, 601596609, 686384619, 706072709, 657527650, 890261659, 848742913, 436457039, 17689998, 478729376, 264353724, 235628723, 826630800, 970180380, 808316563, 547722722, 370271126, 949431287, 40025595, 978169167, 792281856, 68213850, 886937297, 863538394, 547480270, 483378849, 880691020, 335200943, 310121399, 852714745, 829805213, 104136007, 127473496, 692443814, 395387490, 125020091, 747743521, 351720161, 997656903, 611880841, 664819020, 32420744, 744111836, 696119127, 461260388, 771729522, 785671451, 208898373, 931630555, 421419233, 657139260, 721453201, 367351055, 30951032, 460462872, 863743991, 130622152, 582837829, 153065082, 555306110, 335970587, 953862940, 301288121, 674895415, 838065639, 638629412, 910463674, 17413361, 58993370, 716618599, 259192192, 271479399, 732916629, 93628761, 305297819, 278996913, 891756279, 72917419, 697412271, 702734338, 232043317, 617629585, 129932141, 949263885, 946189921, 450462435, 630997962, 416391838, 17361381, 602031804, 713226296, 585789334, 356999966, 581630160, 761468718, 957326255, 569444317, 120989127, 161788271, 925850970, 182432952, 178635250, 251856510, 921910227, 123019167, 154961973, 407636622, 657056757, 997071627, 898835474, 991747886, 858897329, 647180967, 825518894, 173918651, 126840502, 325437746, 299822947, 556696355, 988989906, 818496379, 599438658, 438182460, 773919049, 879694039, 711241983, 666305174, 365423060, 555828407, 319262948, 508743272, 934659841, 677751499, 108590014, 501247420, 889408331, 52247820, 389679106, 395572428, 478250461, 126394685, 598448805, 411515885, 640457261, 879078483, 722727194, 124663055, 880877339, 749647065, 827900707, 780161979, 931865776, 442373862, 78103908, 360216225, 265111159, 715962240, 476036208, 359375884, 171433473, 552316501, 14838942, 531829594, 999585249, 362122182, 219102361, 692718309, 574648905, 104300889, 110603107, 524725741, 204701267, 698431942, 328173261, 203881469, 906031238, 719773423, 491863516, 850853341, 34847050, 725878389, 63105974, 602614004, 1875350, 600279276, 98860099, 119544076, 983824059, 430917665, 708441316, 404713217, 345095437, 381633489, 470181930, 349879669, 498776405, 115716733, 104395333, 936463612, 387051731, 989389080, 302877227, 351367887, 481308519, 748420907, 152221925, 683046960, 895739895, 296174938, 32019695, 537323505, 115873013, 968575472, 722014396, 212859214, 225293797, 128811000, 413743658, 169878954, 986641955, 556747024, 155329159, 767340764, 386676277, 757742859, 735486205, 92589026, 828776132, 287534290, 776983967, 63882460, 935927376, 310251756, 909843401, 997060641, 966052733, 753028599, 529540970, 776711752, 485785301, 933417520, 453130265, 335449925, 880078374, 112026678, 317141114, 941076800, 720576877, 603458058, 232996966, 859451411, 447841359, 287821446, 635531172, 502318518, 241186889, 557256239, 461383283, 606712924, 689303577, 649156183, 600059358, 725903575, 943248555, 266080075, 28544114, 479251949, 333896681, 723480081, 881011949, 702864837, 695539707, 483116040, 35689686, 854502568, 374083804, 336330846, 272597514, 71203535, 904860824, 353845252, 551048017, 901575528, 990051725, 955010607, 106445388, 994206536, 686837622, 261580297, 225023215, 228229264, 248598185, 37031792, 515159405, 975419472, 721996698, 548042195, 928157294, 365325952, 418431092, 10719942, 92395875, 430807552, 750089198, 254336813, 587988220, 796860672, 493181617, 441488622, 937958562, 634053215, 123265793, 145918137, 682645279, 708398396, 223738589, 486313178, 680505001, 666041931, 699204479, 152629393, 516268344, 122559668, 978710615, 279639033, 500586931, 574921993, 158138260, 17050793, 985733668, 371683306, 956840906, 535543438, 569025092, 981729310, 941745448, 147905436, 863172211, 955220173, 339681022, 222291697, 895652097, 353385082, 566862737, 21156223, 915665676, 692869010, 248762469, 497188958, 54947934, 753348167, 207336615, 206859733, 275831332, 971251206, 596516540, 776726272, 619077117, 941109732, 698828317, 483819931, 403777353, 999984410, 540859548, 766168087, 42556950, 352681831, 642148258, 323523177, 892649254, 89591308, 924475705, 399992601, 553429048, 734298910, 732801840, 232287354, 702381152, 334175268, 74660040, 166313068, 419148475, 17579505, 309841520, 319575493, 93941810, 651463715, 965278000, 518492506, 914877500, 560993796, 199538365, 448156546, 444629797, 225019587, 30728198, 589441428, 979052894, 340870902, 477671532, 521291453, 474338986, 379303022, 959331654, 592203593, 536010405, 27711602, 641312694, 554612418, 8993140, 496328798, 679909068, 130111335, 269018970, 628292692, 368685292, 740328484, 567496849, 990823470, 907218535, 516458967, 556631151, 542833061, 17128619, 902232526, 495958555, 531289336, 815718025, 782394578, 906635411, 222942934, 328796455, 190401340, 527999374, 99168112, 96527507, 866090157, 508073209, 99924588, 823980014, 982999042, 79807757, 74234296, 568384826, 936592635, 146419388, 618698787, 30757234, 500033156, 598042313, 12629341, 744827742, 172572869, 35071897, 195248835, 595181126, 817424986, 140348269, 513278234, 656763431, 752772337, 854078414, 831379405, 318317934, 48799211, 383464841, 989799916, 78024677, 962211061, 826268389, 419031378, 640193490, 962568654, 786478963, 505452164, 64778264, 392248064, 647927846, 317087432, 698460391, 996198999, 499024878, 194334104, 292219618, 82356580, 240454414, 814359727, 584873449, 554242464, 336820078, 505229931, 614957277, 415913935, 661954218, 567066214, 220414901, 106538392, 392833371, 540112538, 586488205, 434615646, 576191612, 125851665, 211616903, 54245813, 977396150, 874431156, 620141514, 143290905, 722511905, 960375308, 307151723, 565589073, 764353115, 555181707, 235571039, 186821699, 708504335, 832414414, 243319378, 502834474, 970729754, 220339520, 135027779, 329423824, 189573529, 844877889, 149656899, 494773397, 657821263, 585376296, 195043987, 598552889, 755116060, 124068216, 22289761, 312343553, 974317525, 679531587, 998904984, 25830467, 156715733, 541955516, 560462618, 942167172, 120747512, 945172241, 472541333, 477690462, 171604485, 380742902, 700464483, 788373219, 244105693, 796501007, 540346253, 506608945, 679562057, 970908415, 328472950, 844810537, 945767655, 61969096, 130678473, 736915269, 660209997, 431439560, 427764247, 739102538, 587692041, 476096682, 907970827, 968531963, 511305870, 923800797, 605979784, 581098511, 545423752, 269044047, 922828524, 777529440, 522918237, 983469367, 106509169, 312832540, 375374917, 240239743, 232872499, 569771874, 612025364, 258966197, 415693584, 939356153, 574045914, 81359209, 70480906, 598463806, 522275204, 435183408, 194592642, 319922688, 752002064, 107549020, 203841461, 822962354, 343893035, 115051874, 222123944, 218318746, 625907715, 41364765, 914389704, 735842997, 123888790, 420845782, 700860145, 134045780, 134481818, 582122677, 772510295, 49354345, 983730948, 295129910, 932293635, 916508917, 923919239, 507169676, 376742454, 286279127, 371841454, 204135812, 783274501, 372355253, 573333464, 266440661, 986215333, 159406630, 428345646, 437037554, 974603776, 764142001, 848524003, 290117710, 782895802, 734235729, 880654733, 184598285, 242568810, 211428209, 99480656, 164084691, 492743022, 145882359, 955092069, 607670741, 621135502, 86790972, 265019839, 386781062, 883605169, 75998831, 756926299, 625587220, 384231116, 312943774, 729345771, 578593444, 232832069, 135185335, 867251618, 841958926, 199421686, 109963087, 519302387, 429550515, 8555341, 727635182, 993974600, 3448620, 41882395, 967304510, 934829663, 947354195, 253589777, 541478506, 995733651, 232275792, 129618409, 517194836, 394925326, 303477228, 828193624, 241356640, 532860612, 234582884, 507567906, 789258238, 643824002, 232322306, 229114039, 300939074, 631243442, 133288673, 713033880, 448230005, 989389572, 437093257, 410275647, 675329992, 248066522, 570704468, 776813015, 201262177, 440407039, 291774363, 944223584, 33826711, 890898823, 318671131, 25878772, 667033123, 667903231, 285634195, 566663795, 999043041, 417671294, 470556651, 889879346, 249820326, 833905396, 596816328, 858834747, 859242109, 45147698, 787097258, 569820741, 283078960, 644027507, 812055318, 171681636, 889680357, 590866541, 534867425, 369486708, 436666461, 724026750, 621040894, 880107277, 168174460, 91128459, 643787602, 77276388, 213695847, 557879440, 949165590, 224770600, 344506057, 878410657, 880758730, 602487099, 985998510, 17758461, 142284629, 784576978, 297062422, 386825951, 942570433, 758929440, 758690301, 740033941, 125373237, 405881318, 842686849, 477096740, 546127558, 861846823, 763699226, 838981590, 176462543, 166276198, 839089519, 742225651, 417105520, 959150513, 271423980, 313904061, 407565766, 750353153, 165820920, 64822114, 699408609, 943108903, 859128072, 649784877, 441171293, 210050228, 529865728, 623536137, 647055993, 714261187, 506307557, 358538722, 669560679, 374951313, 551081961, 854625813, 584941116, 840776737, 8571159, 678811494, 216084754, 717519654, 751206525, 903419766, 134778025, 129465052, 52276494, 694325007, 86803443, 881449319, 144864416, 442431099, 882347697, 687823456, 680006482, 263013765, 388157868, 893384486, 942411058, 407321355, 168826265, 550853046, 440451677, 637905178, 204567156, 87527770, 394699994, 897325556, 728287921, 859285841, 3526092, 684406243, 780891793, 284537341, 800679775, 52321716, 595323860, 114745582, 285335311, 716158614, 554189161, 160535322, 761506276, 100686192, 694307660, 328491503, 95789520, 96017333, 984102521, 812169112, 397430682, 869777484, 784289479, 162513366, 764980889, 628958214, 897107751, 79309293, 633753087, 594886386, 990593084, 103904810, 88986357, 825099627, 559529, 27980736, 720098533, 582699236, 164300905, 348252628, 895434048, 150317558, 907670751, 601846881, 399913218, 703434100, 750550410, 133994362, 447246671, 674371664, 979466913, 60296604, 477597125, 230252689, 545033774, 734762544, 628928143, 872114797, 706092450, 595036184, 450606202, 357102489, 826354941, 877814698, 412545430, 410318300, 478213240, 719122509, 120745717, 658179631, 169889142, 201662005, 27709965, 57617576, 367974630, 241792380, 940970586, 508181390, 322406350, 595189825, 291849169, 759015141, 411839920, 596619687, 184284383, 832188938, 946210277, 307906599, 422854283, 104681354, 274686046, 222472282, 677684486, 836747677, 769601591, 91391832, 438298089, 419736057, 861812250, 475945578, 730480812, 851556900, 768773938, 996508554, 483741053, 424424661, 298849144, 253782642, 637617557, 817327262, 181090617, 610048128, 509358860, 589888951, 762594042, 788025836, 33462286, 153722421, 445119745, 727834598, 456475003, 855422070, 532209847, 54743172, 41268819, 375435843, 164352092, 868180705, 811745654, 437361015, 343174001, 317257450, 123735912, 3749107, 505374893, 746146190, 853546316, 156691083, 769519713, 640847277, 611715872, 689874104, 280168185, 602586282, 171975159, 189684536, 155668075, 167283549, 172308160, 173152514, 849682326, 767436485, 160192998, 996417885, 452673684, 163186709, 221822185, 746004055, 365163923, 818516128, 928519434, 69377501, 988935724, 21640387, 413775846, 282944442, 714889681, 517361475, 890435715, 596017770, 36285311, 299655055, 357063310, 195035981, 676929778, 822948297, 450865897, 8957478, 724814255, 32047693, 308134308, 421638239, 547892465, 743955849, 291459322, 914415579, 925995539, 719988067, 74953426, 324547244, 96708981, 686996947, 586109435, 737138218, 94286185, 878071632, 174249733, 480126680, 182784726, 340355214, 691074477, 29176293, 671378043, 28297028, 627314188, 754905003, 684264730, 944853701, 586906951, 928341215, 205019184, 168525499, 808497110, 255692977, 647313651, 973189509, 324356118, 610205651, 30843818, 658266761, 448536554, 772861422, 359749936, 191041441, 158013395, 436366791, 466617273, 401317856, 375074665, 779552258, 35477899, 236904405, 64591172, 778635988, 865568355, 712020109, 951778815, 470214145, 431586199, 53415497, 437671868, 598102129, 908460071, 484240651, 216947369, 191285733, 864840832, 788957490, 583810172, 546765679, 962191989, 899637713, 899442382, 430573891, 983904993, 208030430, 752739573, 342440849, 53892927, 103978622, 818883919, 876857768, 644159395, 258234257, 374755086, 537503170, 949087814, 84711859, 48853804, 604302963, 162466407, 696964142, 504624122, 248964590, 847707453, 186631371, 746545796, 58928163, 416726215, 445981121, 50326172, 713815552, 404473113, 662911087, 220313966, 604861680, 439165155, 661585543, 367806806, 14418468, 435916037, 248192588, 446220382, 925012308, 258680357, 928149639, 576864430, 364908097, 65708660, 246939408, 950489607, 665096730, 117622551, 861941679, 82429845, 509300043, 418646236, 313128019, 567704944, 729245969, 225102226, 238176661, 22860167, 37536049, 772819040, 936199431, 225804075, 292452380, 151678585, 349502632, 340052759, 297364032, 81899533, 325059718, 692554223, 443670641, 247261753, 805229671, 546213487, 549981628, 557571135, 541668406, 294491001, 912699011, 705829749, 201116243, 705338979, 702211183, 980143725, 975708272, 504297935, 740166118, 54253568, 534617349, 104829723, 700736963, 935329577, 823270650, 877132039, 336321992, 493722300, 965664275, 471283058, 765281020, 873062226, 149658283, 176808437, 388797778, 204892456, 49034289, 641650929, 30988954, 887661694, 323994935, 852364357, 644099867, 716236588, 321079766, 749814558, 412985959, 69818617, 494483713, 168774514, 22646797, 707695206, 428856765, 110418497, 506746490, 670644605, 834986763, 903329580, 788189473, 114787775, 351251373, 679396860, 71177057, 501050413, 469573847, 658265854, 285658786, 962895772, 497960611, 824976631, 452920089, 313290465, 964921575, 675100452, 663605800, 551173537, 575666622, 135359172, 694448824, 798035818, 82307278, 196593622, 444133605, 126623894, 548327566, 742368550, 500443546, 575914310, 865377847, 175116007, 115053850, 152451942, 64481001, 583858967, 603031539, 255262588, 688647778, 372050141, 583997589, 488018843, 758479044, 243985851, 515847309, 524970893, 980809439, 236143878, 378662941, 266767467, 324843533, 915818998, 362592375, 584382846, 274656294, 490261450, 372641616, 741458687, 298296533, 549208711, 665430170, 185023287, 30702714, 291156366, 889618506, 442478830, 264451895, 459621691, 918579936, 958132564, 245920925, 744631212, 712410566, 349682135, 760321204, 18232780, 674095707, 73331907, 298013213, 556265955, 341363576, 492563854, 563162044, 692290695, 719557154, 931510224, 813265795, 54305809, 76365648, 719410189, 717281076, 763708365, 317884567, 117917751, 331162655, 669680363, 645268368, 234857897, 528030520, 782477871, 732059223, 18277241, 225059538, 191707764, 995233476, 206371733, 581263614, 682098438, 493361186, 437382120, 76314115, 332557112, 624592709, 647535906, 996528031, 652869029, 867275963, 351969542, 284069640, 857075155, 675882078, 569887081, 514956816, 515782820, 814784068, 823016468, 89884211, 158920350, 172937877, 599948406, 770599512, 83733178, 180132056, 299244299, 854224042, 891960691, 210776370, 728936562, 83882087, 140945211, 717547115, 925228910, 489142495, 223029411, 998886315, 149022510, 247961434, 705824991, 41176413, 805204838, 221227807, 557623378, 293883653, 735904992, 316403114, 309202803, 260374627, 110576759, 216173708, 590035105, 232898816, 562730071, 821996000, 700719266, 196518000, 16493125, 571356566, 955099992, 610834108, 846594953, 761977063, 575818529, 457650025, 106521088, 514756693, 120984157, 631592699, 795903920, 319284901, 606714197, 720104511, 315003115, 313502867, 538969228, 219609849, 237852145, 528912767, 254433101, 174864832, 325462329, 547837438, 191870065, 517738880, 78371401, 727813855, 656110511, 626895852, 310847026, 325982145, 576651014, 134412394, 220548979, 20070869, 165335528, 992376775, 461328009, 210487659, 544101483, 558049254, 389802546, 385768259, 392999838, 861604517, 860790653, 125219914, 436540525, 269859611, 171073635, 809451960, 848184602, 812903648, 581376991, 798816228, 902032814, 949129505, 605490968, 7665416, 229039527, 963414211, 812093126, 657449072, 33439016, 206952572, 241440753, 834540963, 642015923, 290025733, 324261738, 227716003, 728854590, 344660718, 534961071, 84585079, 513438636, 222739223, 804421065, 724027902, 851250176, 356774915, 776270187, 463486758, 635443055, 880853484, 449806895, 731797088, 410523377, 633883975, 146958114, 177293026, 551258029, 335705270, 919194832, 205953815, 737480372, 434204371, 437210562, 924041740, 651312584, 85251930, 369346408, 347058495, 143463696, 240645566, 600721821, 605198499, 401742659, 740691450, 489601862, 264268858, 360556398, 711320188, 967833191, 395627339, 967114571, 977801265, 824730488, 499240391, 34312618, 66312408, 466026486, 734057385, 430181027, 633600008, 387580183, 763215544, 828014812, 483981125, 11632475, 108901789, 837860586, 148125579, 152558085, 141844104, 553690170, 184687407, 381175373, 780685629, 860793614, 844843829, 790997861, 845633569, 651493734, 460689392, 903183703, 587431871, 693216434, 764670074, 65975716, 469779805, 868096817, 687206899, 262068910, 900355143, 694442893, 340151067, 760900325, 459439646, 290674265, 866776054, 875083076, 539664321, 162023608, 481288354, 805698802, 466853024, 123457223, 523247458, 104369880, 418855813, 128585376, 853188780, 679152963, 755205907, 232800459, 69344424, 43896137, 639219350, 413134774, 710516870, 168094684, 333187847, 927880433, 277908309, 422128660, 983412711, 543451510, 480768051, 369374702, 47085039, 576534744, 941579743, 907762984, 299847377, 337661732, 601931777, 495941816, 56451174, 626376774, 986418491, 400107365, 434443840, 430665365, 606432307, 635470007, 896567036, 190732137, 310703669, 17058250, 595322709, 748856742, 854382221, 69606003, 574769799, 60085046, 197954736, 891736282, 69238616, 986294351, 641413242, 634221744, 244436671, 31892134, 874300501, 397871802, 157761175, 933716914, 864059393, 312297870, 878974041, 716259742, 630137574, 111645765, 703868232, 472732206, 924835573, 260083217, 45008800, 752606077, 189621922, 429710357, 978384255, 60271442, 894357989, 250623875, 7832190, 726362732, 582042762, 527945691, 51434860, 498938479, 869068304, 639801455, 33239427, 679325656, 767183398, 970768353, 134720949, 171617763, 817094985, 788459607, 873608987, 416383502, 584495383, 611165899, 170128646, 873982115, 832293591, 534394539, 958080037, 979535601, 953650144, 657764253, 394841530, 42441204, 66253281, 149622561, 402611278, 133313045, 953260735, 329061212, 457502689, 528368, 516819786, 139502021, 893692228, 191040161, 623311814, 115076324, 468292997, 222934495, 235645708, 753188944, 989969679, 181050882, 762572871, 98504529, 442606148, 936566475, 730374611, 252821938, 111939794, 784862518, 472252884, 494818869, 757443772, 169476455, 133262898, 748117968, 374528265, 157290631, 613228202, 830573010, 967447586, 836438383, 962325558, 653490780, 782144788, 408850738, 497916592, 853851013, 10257066, 784693372, 54597194, 261650257, 706267628, 847935746, 580553208, 558041914, 899154858, 242246819, 251212641, 857654030, 90496880, 50002695, 947234285, 156261788, 859582963, 712998292, 413456173, 95528138, 883220181, 675406374, 336033645, 707287216, 993673108, 654496984, 698178102, 519970182, 753879397, 121257663, 435570205, 870253858, 161102711, 758822833, 617712713, 947549749, 803295191, 691863773, 229086328, 894277604, 287548032, 204989883, 142672471, 154989445, 369652910, 375657299, 661194201, 673896123, 507027884, 643538650, 531797743, 486803767, 648223296, 452811119, 136937664, 229995839, 477608353, 989534623, 357756738, 751853892, 259511790, 123260395, 919324843, 215433345, 458687138, 801902297, 823961159, 544508287, 844303800, 324512812, 531541475, 345808776, 273880783, 868487399, 995340749, 602110629, 694788109, 668040395, 950639093, 359602514, 268455866, 814595309, 502184639, 123907676, 199999859, 870315436, 317367551, 715044713, 638938187, 589980633, 628549449, 436201019, 170226016, 786804823, 785686044, 903950467, 321257348, 150330037, 917279624, 787475258, 864285306, 280395282, 62894638, 126881125, 231160098, 810119038, 73404046, 120567427, 366690913, 270324045, 382178657, 790848081, 217162860, 639937946, 843732676, 744403871, 903423733, 582771319, 829676640, 957353785, 164383846, 146300304, 324868928, 787024203, 694263249, 992223049, 343385430, 238500893, 34661584, 514291429, 38338311, 689895443, 953034541, 485327520, 307801835, 744455596, 37557998, 578110598, 361303616, 280750099, 115025520, 169640624, 517001542, 126989636, 505770001, 378547437, 922240241, 316362322, 462638678, 115091987, 328523113, 495962557, 687262173, 299943142, 914606, 816895485, 467503308, 48369097, 230293269, 376169319, 808137662, 866735375, 842920471, 827345381, 435888785, 811124847, 980867132, 671168301, 625536614, 335559220, 738636026, 704953607, 330147995, 430000225, 515669773, 952936861, 836999015, 92558639, 202764842, 804005456, 664971456, 426621861, 594650165, 992810806, 817834257, 187219438, 670278710, 818136049, 752187770, 845655626, 372638376, 175906106, 130608903, 495174200, 228766498, 198923946, 169659785, 130804572, 180567156, 795526462, 413379397, 15600987, 8208723, 119137725, 916216448, 722450198, 623308116, 980109092, 664316699, 968126951, 50448337, 662250276, 860151139, 197911928, 591297202, 420744285, 568491782, 711976559, 698834428, 824089993, 702173669, 286033369, 263247013, 509054747, 219568094, 899625629, 615859157, 984357454, 238286904, 652638987, 907483922, 588161303, 499483861, 517167598, 499854273, 971361694, 386563369, 262123593, 54262369, 792096889, 530490695, 58751798, 390004191, 865389467, 807840046, 677061202, 858241992, 647900710, 452114482, 511688874, 981796990, 185936326, 291980863, 931922695, 838467154, 93011909, 791161291, 483384104, 353817862, 54317795, 475410628, 26100505, 306647988, 405687265, 648714450, 982630509, 762720564, 799559178, 183207087, 157980851, 156180783, 137852061, 26745865, 49507511, 148083964, 963717938, 26775554, 635863554, 233945699, 455700918, 405463679, 5147995, 654932172, 104628380, 217022268, 109253714, 636636896, 543352399, 895109897, 850792298, 686583121, 686172240, 159084321, 41690286, 62175172, 130371153, 716726938, 632115032, 220943837, 117481460, 182784757, 222221068, 709046340, 2063150, 987919449, 696061412, 666986963, 808817101, 77965353, 646181053, 821260015, 456598210, 469561095, 947944996, 382232398, 736516432, 83426171, 211470458, 99988741, 416641757, 817680702, 299560426, 377477337, 933871551, 640534929, 18011583, 832356598, 322126381, 912181889, 260476161, 490303770, 52651516, 417698432, 94689466, 225837417, 235990172, 837802505, 733229790, 835981243, 547636231, 215080257, 52295316, 129640167, 428219902, 855249021, 184213919, 842572520, 685175841, 102566246, 780412052, 590699166, 454723084, 422494236, 946560842, 766160531, 37730725, 638690673, 609511872, 365645691, 805717650, 163419098, 636057972, 198494235, 21876866, 467941960, 826349706, 302152010, 267521891, 295704543, 670120664, 461093948, 57495268, 953042445, 821403841, 741599019, 705190614, 537205232, 18108147, 971869058, 631272700, 197721874, 289030005, 346609947, 82071673, 441408209, 561213032, 628482498, 786319655, 88260613, 764733640, 175833893, 865706485, 911517453, 838857593, 351671324, 783887692, 575816092, 717677266, 755504123, 313318555, 895921562, 472286283, 540091742, 690632966, 95341215, 212386352, 982158899, 645800133, 655414349, 440678357, 486625954, 904843818, 730347827, 363523891, 680221743, 110769706, 774243945, 754953274, 448358558, 640312936, 589393624, 665152272, 238898215, 484394086, 252597396, 901733873, 996865392, 675618858, 405243730, 78764769, 744588924, 979723996, 181647727, 757758083, 691148094, 908172759, 807998826, 437026758, 176547745, 643082097, 773977763, 545268115, 146350087, 643519142, 971971098, 160651687, 841927731, 447503009, 926721710, 132439736, 490394379, 439105091, 246163931, 285385042, 557070564, 523253464, 256822042, 260986615, 462238468, 424395233, 475058710, 410816494, 939194695, 302462268, 381267826, 466437059, 602673920, 458185781, 259818161, 148843247, 305561161, 708664322, 530732418, 519490362, 258685909, 311822793, 164501155, 13587366, 401103825, 678299482, 918867604, 894946041, 807742623, 863581305, 984445146, 863889389, 424891273, 488596440, 660569551, 947277919, 568543023, 168698720, 211604365, 900257501, 950997956, 683212399, 786355603, 153847028, 173272938, 560388919, 525126432, 696739913, 652965572, 844497619, 88842519, 441597546, 268812120, 108100642, 420114445, 863260081, 24697685, 693428181, 142726234, 243488984, 107599095, 519271555, 726257393, 446376026, 274778259, 903473204, 85995776, 996791218, 422997237, 146187381, 921259229, 844276759, 968860286, 88130584, 821924102, 171234312, 255928220, 309501707, 67053698, 592170872, 390976809, 760047, 809114859, 43720517, 65407313, 11450740, 24592550, 985001334, 803385288, 217884127, 762871790, 543485819, 302313446, 457494350, 652724189, 795843395, 779928967, 938394406, 112381445, 525447889, 316231373, 744996487, 798361753, 51942806, 768801550, 283022481, 389832087, 862718682, 648770812, 29501549, 776977831, 596469873, 976393747, 313164978, 882105034, 173728246, 620833741, 664606061, 648390625, 70098159, 820793820, 988843035, 353663354, 250780350, 175627753, 769012469, 806864511, 220195920, 199634430, 795636460, 555142542, 130456302, 209858789, 546032780, 449521754, 606050568, 569259488, 983480590, 724804001, 962349942, 635581683, 425266372, 251693989, 997794057, 510216058, 327102543, 505349663, 795013551, 492414985, 516637488, 130591407, 39015216, 567681526, 435155999, 291954029, 595195728, 363110658, 260602157, 177920888, 95067782, 86216246, 472422866, 189965481, 440678381, 2874961, 1621885, 720436423, 856382954, 854083818, 815845560, 140307404, 209387987, 525795155, 140686374, 407310645, 144280661, 706329438, 490357618, 789400542, 264308107, 457984940, 113369387, 505007631, 687088392, 6538539, 535252898, 719342847, 628688000, 758632079, 535452381, 801802924, 929106644, 31433604, 609972575, 570470242, 937030381, 956632182, 765167226, 865833229, 22445245, 528599902, 479181517, 29704642, 838678151, 788306014, 911355884, 42862524, 94607307, 826528645, 699064425, 344591023, 372048282, 560043048, 568619118, 45646691, 203631165, 754634765, 726249679, 253150382, 771866917, 794580452, 384752886, 732056018, 203331333, 703167326, 382526943, 482177615, 99356763, 406272243, 374102500, 898256917, 720235146, 587597082, 102602745, 390725521, 220988338, 585599642, 182571788, 444539246, 304341836, 85438090, 163519935, 722193723, 167362729, 383392211, 133997938, 225759204, 729605928, 703269295, 687382487, 591948544, 459386937, 744859460, 748976071, 79180666, 273380800, 187691140, 521858659, 957689979, 431603972, 47687145, 388177076, 75722508, 619576938, 635650853, 91723203, 901055283, 17191648, 77632928, 400968924, 576615861, 213566246, 60522522, 994214488, 956977482, 339699886, 708916123, 182286750, 315835419, 410697481, 531370361, 799602825, 116151730, 87262190, 111840788, 44276507, 98734566, 446555768, 788501121, 727493766, 565869619, 151243268, 390835754, 779302458, 661405391, 210785089, 890951371, 392290284, 451398645, 846671962, 36768056, 406142869, 399302828, 139155483, 10803701, 574452057, 30521027, 405005658, 432152475, 935287650, 183275227, 145208519, 864794387, 886095816, 667273380, 89706112, 662767453, 109587461, 147388677, 630726890, 780832531, 164386053, 218012442, 80492196, 11333212, 632388489, 386871662, 400847589, 728574058, 390512408, 30547405, 784145366, 639455685, 260245697, 647590103, 535438136, 323948654, 857521194, 131716196, 657557281, 323743161, 27952384, 841131769, 316154055, 150855697, 190841250, 365135253, 870621912, 190634894, 485224185, 117665848, 204577128, 758638503, 808962665, 921173641, 127665845, 778174515, 130283005, 935872083, 165007590, 331465639, 97886306, 929515759, 226992304, 706731283, 439598406, 681738400, 279442298, 534781837, 208610391, 223772946, 615989757, 385910744, 915688373, 106052135, 791362546, 532910494, 940413580, 953007851, 773728476, 908369273, 998227689, 784967460, 263432020, 435346051, 225328346, 946122360, 809402233, 34170331, 153142148, 148630640, 448383100, 263915276, 211071151, 985491411, 656234908, 493992881, 567848780, 410182780, 620442568, 311554491, 195352765, 145126519, 687810578, 778986168, 26655612, 326255182, 528829214, 545670130, 653774970, 812982517, 20970160, 735142650, 644399778, 914686135, 553580432, 658575588, 488601349, 545209658, 371242688, 772468897, 137442350, 690007132, 728034737, 717206294, 93984451, 696257974, 400293279, 52363469, 399688148, 120659427, 281001914, 956754991, 547745507, 219407630, 361392366, 235520677, 624328593, 589567019, 166075425, 576666848, 283222994, 887207394, 820625268, 45529351, 983035744, 843240803, 358778373, 219472812, 458876528, 132377557, 89156664, 392078895, 705756776, 399273728, 805482439, 87754901, 895838565, 796362890, 440108486, 275600989, 220402902, 725312189, 301734229, 488134341, 283760345, 972984295, 571230628, 669801202, 763535667, 633208715, 562992130, 686758478, 296965814, 772453204, 837336919, 850322545, 384691925, 6900995, 54668224, 688060453, 592536412, 296480121, 337248150, 527967596, 137606230, 838273890, 98128864, 579153279, 903768806, 37979849, 180302561, 877636939, 133772836, 126116710, 182559376, 353267632, 592641781, 614949017, 583844812, 934550654, 345649938, 928249765, 879943443, 404447251, 902494504, 824074180, 651706471, 482340424, 785628011, 758221004, 159597154, 525506966, 1943363, 218318693, 554762143, 99594478, 554374757, 167034206, 931486933, 97880420, 408011550, 894514365, 433458472, 130824468, 15512250, 378909402, 751235780, 846630254, 211624770, 61167834, 38979058, 783145367, 21231837, 74467081, 653339826, 933031397, 85630154, 977512708, 442796436, 686438635, 977549342, 159284237, 375133823, 359895919, 1589313, 431232271, 143335683, 44500654, 686329614, 767809752, 781329493, 831075235, 775660636, 248603716, 794711984, 882287824, 932664857, 391088414, 1552666, 182919026, 624244545, 893083612, 181672689, 330453669, 445371979, 852771631, 181489496, 77973106, 669790309, 333195658, 955257746, 314714255, 92723924, 480846116, 41502323, 287323273, 844292068, 113366576, 441391865, 304532597, 741157248, 382436409, 873523057, 985624073, 469834897, 782943290, 582214768, 725704336, 310194590, 783649317, 749445110, 216968000, 884055330, 49039078, 781316644, 857134054, 770318545, 431928431, 27006412, 580178025, 168150418, 875979728, 226346028, 83380205, 260626368, 535785340, 612981509, 365286907, 201377055, 579061828, 940384519, 358144432, 69470770, 719911539, 221686330, 993785820, 507822350, 997023441, 634504577, 937988661, 326960760, 99073407, 514402792, 937715794, 419071562, 954142076, 277323488, 186518, 234034686, 666514648, 358574773, 81586234, 217771763, 662137514, 84313889, 54403981, 861287632, 97511097, 951171772, 862024604, 427485252, 972411675, 201682169, 931771468, 53655584, 994509319, 122447332, 110388830, 45569183, 598685015, 561915531, 587963985, 836789556, 129498693, 339382739, 657085703, 850687666, 174940228, 882820911, 423120284, 173552820, 340331803, 84082634, 268585470, 518249098, 945366144, 854414418, 277336486, 833302394, 114611381, 184188479, 81102732, 429835160, 659734548, 607852664, 785611718, 196837364, 12804986, 332914189, 64914599, 12095560, 20766660, 612604219, 670129782, 486514273, 140310438, 817983514, 529390072, 805140125, 755204983, 341624309, 722817285, 998835186, 733414649, 847556809, 918499925, 492340754, 527433891, 10349807, 213308818, 444206843, 129828339, 805068604, 887296066, 652227242, 51837661, 225624838, 86647344, 934646613, 171504945, 428824058, 523936554, 948064755, 903239562, 870953479, 831161185, 210497760, 81755890, 308417577, 748687533, 801546979, 598546043, 713326084, 543949812, 372796566, 839502244, 897541075, 572701817, 355647213, 178125804, 663377529, 874036860, 82223488, 584151772, 591246088, 410181197, 161973837, 978525579, 759691536, 690498056, 301117393, 152230853, 895178767, 37676548, 88414566, 730819026, 217259228, 907975935, 129773248, 408763333, 900234325, 91334080, 63247823, 405931386, 616755790, 822794180, 283480208, 351953055, 701937001, 933944113, 767162122, 341381894, 368547624, 182532128, 533101118, 287616293, 870884104, 984352338, 417235392, 250638185, 610162353, 862601598, 823563070, 723016742, 575475377, 922556540, 447139901, 112988213, 380893896, 20382812, 31096487, 780899338, 791325989, 434054772, 376199159, 359598822, 743582157, 346712487, 160539127, 831825505, 963911490, 842405365, 88739141, 151541286, 269413181, 635114166, 135904290, 92706538, 575587716, 655492589, 742106372, 251201260, 356304733, 842810904, 547315889, 787396570, 674715625, 819344642, 828522859, 904782101, 727845906, 120248649, 33179928, 272004828, 436598079, 472967514, 58689028, 662790254, 958584745, 464530813, 778098453, 213993733, 201771414, 301680215, 766793517, 83514050, 172412982, 743797774, 740659853, 93092568, 290146361, 770040061, 932780157, 766755308, 638157819, 296945820, 986782558, 429843636, 684834879, 887304188, 702635914, 654510487, 645527097, 851367081, 543814937, 431947261, 80775035, 412152763, 611884618, 361731676, 139853154, 441807444, 800650503, 883806176, 385320999, 688341378, 739838442, 317748567, 633648291, 300488052, 815559266, 433038578, 27120884, 398298059, 419156389, 622422123, 958617716, 517795853, 273797874, 14804650, 739185742, 437996660, 485734566, 618676426, 555137729, 679732628, 871721557, 473389540, 717371688, 548972469, 406551515, 805802151, 108669201, 948957683, 235383260, 737026914, 213740376, 39117853, 827486294, 650747834, 15091608, 970611862, 824118147, 301136274, 514570326, 647791896, 957510338, 340640459, 476674261, 656639736, 897513723, 28720541, 143807555, 605029389, 979537734, 629828710, 854303304, 4057022, 259063123, 951455922, 410223342, 866614134, 242631121, 70482462, 799525680, 445963202, 579758236, 654379457, 751372563, 364878238, 653305099, 899963662, 740744222, 669555444, 355881548, 164867325, 164030385, 428942960, 494869467, 878440561, 198895725, 923624549, 21891527, 260786271, 814224043, 924637511, 436964624, 607635167, 886154626, 328302804, 871727400, 355389572, 764115595, 723746377, 771570314, 627407977, 998690572, 94967372, 139333510, 874453537, 296403258, 307723633, 766530292, 662306092, 41531416, 540146602, 409231188, 131050795, 608433847, 460150330, 768545263, 9101411, 456445654, 787525543, 288992062, 581680160, 950392659, 337212702, 471104247, 556191681, 617280958, 231147964, 579590115, 689037066, 59404473, 189103698, 168242879, 861546457, 170600105, 170888219, 878889643, 679455688, 934610943, 985134101, 291462778, 111558375, 167008640, 843855613, 202171257, 489987297, 860161144, 857596300, 262630681, 266477572, 276848827, 590601068, 917312190, 348875171, 336598103, 607862692, 83336866, 273032446, 478362900, 869428398, 896566724, 495687885, 566232192, 379096941, 324690266, 571233336, 523456242, 386467309, 255271572, 317835139, 304290662, 823298735, 757040819, 175563261, 179734902, 9114625, 160313519, 923713758, 7990122, 270233847, 72803336, 660458497, 927072317, 313847371, 315981653, 644377806, 660604505, 525467104, 881501617, 189854535, 860841611, 27800190, 57424085, 478647180, 855354750, 531889113, 374594210, 211041836, 998988779, 186557101, 440392959, 78819916, 291581870, 26484399, 595406048, 744295519, 410732205, 161175814, 370012025, 619666090, 478781742, 51322902, 822956145, 309520609, 73621370, 935619402, 370146530, 36306205, 218056415, 169037524, 222745299, 723771011, 229059272, 771483879, 552502789, 286736828, 804533915, 985989526, 926136430, 163277752, 256778135, 246401582, 368437509, 636079605, 231699640, 919871007, 888641650, 896499890, 807083, 368644468, 585913977, 249334195, 509207318, 690900723, 309444070, 495865467, 518525364, 93047751, 788475758, 76506578, 63090477, 416100951, 135402099, 230035977, 159853401, 415010328, 960006374, 208109019, 898840654, 905009758, 597916291, 484506509, 492689497, 648436637, 241351506, 643183236, 70539102, 456820739, 500081792, 791895765, 631701174, 896168964, 895343041, 851291961, 959806381, 930288937, 615034093, 521257135, 918794545, 753566836, 825971099, 613696196, 67650717, 40848778, 239044831, 713329758, 628603671, 823277432, 628706414, 925087951, 343038315, 775674706, 828424131, 439210566, 261991072, 499195258, 454671653, 972676998, 90616555, 748460820, 379304263, 756885551, 731717886, 294471310, 808798693, 710093066, 714703156, 821583600, 5806319, 486634508, 744006499, 882104834, 778291181, 951936934, 618566026, 850253455, 593752141, 750411169, 356246691, 637316352, 111777370, 291045884, 126715598, 46797598, 730683353, 752854551, 72587374, 187978587, 811246012, 373348724, 704280338, 550070379, 81471067, 986193407, 910822581, 799785894, 610102223, 234348924, 471292365, 524158965, 666776628, 607107540, 62099363, 816641978, 404238510, 578165229, 511154420, 699666045, 50475310, 287939463, 925402908, 930411224, 556872292, 154714314, 483158701, 809689799, 368277164, 892582417, 209879291, 445510144, 112288124, 967913344, 992731331, 719977257, 455698792, 527455107, 998260095, 434173579, 717408542, 3553366, 476415991, 866829227, 388087087, 606337510, 232304484, 41288804, 309605426, 259758858, 920829153, 583941759, 140061947, 830357886, 484741525, 726783028, 931432179, 504980288, 875503195, 706532816, 775250383, 542974801, 508217386, 315379500, 486561898, 986992870, 591345832, 204030418, 257246579, 260037767, 125426785, 535235329, 414517724, 632091922, 52736211, 922567887, 946616659, 985931713, 925767054, 509371013, 795773105, 103792450, 806744472, 167115485, 225868553, 852772742, 18176706, 643025727, 805365970, 514403166, 657021082, 323766526, 240504385, 852024678, 455363364, 533614315, 785726184, 450587115, 323186084, 934192486, 331336050, 195686346, 847836359, 433887708, 898870869, 682198871, 504819224, 438063632, 525341138, 319969397, 59278010, 663618993, 498934780, 250910775, 419504118, 429884369, 409732941, 728612206, 534970479, 928528740, 315822563, 343944225, 160454594, 985484216, 4957398, 105048403, 677999365, 924283282, 826458609, 946862428, 199687309, 499715638, 196748821, 601593515, 597168580, 199350049, 67952900, 80461352, 478900352, 764682579, 233795753, 219616446, 198866030, 604697917, 285910882, 196530291, 581238390, 382400823, 348705847, 687237492, 121159935, 988873940, 616934745, 394182060, 360292548, 499192546, 267525845, 730424624, 688405419, 81478263, 784170995, 657478738, 816615942, 277950279, 984492262, 622260693, 425197168, 753231425, 601266138, 809178637, 330895631, 342901031, 552449080, 239129720, 628606772, 574035888, 543821592, 710735023, 681217739, 237854902, 322906790, 893243884, 334426622, 204833898, 311361059, 475205058, 732704706, 819236925, 394964942, 588963582, 168284042, 625309286, 169737944, 710472905, 513747030, 723857031, 506470250, 132007263, 627273703, 438605545, 986600443, 188731166, 833352272, 976055566, 181351250, 129068228, 719954090, 995653522, 280007043, 673059458, 367457754, 965309499, 330721773, 519976409, 391501059, 283409717, 778064976, 87523282, 651589363, 162877232, 212403798, 471432235, 797941385, 509576886, 980134855, 449438299, 804203009, 400623873, 867719960, 644549007, 246828501, 553239327, 137228733, 714914537, 431556715, 397402717, 725098653, 703997259, 511581055, 25566127, 481302358, 547986320, 143148453, 775889472, 770447099, 870802989, 457298786, 456183616, 545749511, 604051305, 904258724, 401300497, 593196690, 361472588, 98580695, 44982397, 551973427, 173035553, 565594233, 497936321, 835248475, 267988046, 897745268, 5522516, 878568263, 645160046, 871055226, 483265849, 795155136, 187182188, 49499298, 94209540, 872470722, 765875885, 766341998, 754081973, 802314837, 441885373, 989642817, 794262890, 846342939, 118487754, 886773008, 893469070, 740899020, 568398618, 501329616, 909429047, 696821034, 737222709, 530953401, 93931739, 179970624, 210973390, 189144407, 657141682, 213568773, 645484612, 288098738, 501481638, 463574122, 950870922, 216270816, 748438347, 637168460, 179506064, 849591456, 865071841, 444544194, 233876178, 373393866, 451952288, 614848441, 569397219, 537537966, 10334084, 506043769, 62613502, 301966764, 499017348, 162947065, 287699775, 568039966, 604922095, 623219799, 108885356, 723352579, 489326321, 318097094, 612941240, 565777449, 767823211, 892272376, 827516949, 352082912, 390931169, 50315197, 993665717, 75342506, 672538065, 241834589, 220133742, 688793177, 578672458, 549469164, 457616160, 562116403, 98061720, 853690477, 683295810, 145294305, 702268756, 575339440, 339390135, 141945503, 282533207, 746103065, 477229643, 432043348, 932618034, 581014864, 910916356, 692467416, 488553471, 525607261, 146014379, 520586341, 979184414, 920560030, 50704646, 62970132, 14483452, 490414033, 390602982, 464087267, 463560487, 255623946, 89561864, 111684445, 636722512, 601976932, 852406472, 265914250, 854151810, 260333301, 152862176, 497825349, 587641229, 636345200, 673178927, 815333468, 692522670, 823057408, 536026404, 376720422, 486980778, 12765888, 624703671, 859814599, 962007755, 926563431, 883777908, 357369960, 111671243, 715112335, 478505186, 135135289, 222940670, 4377124, 711527916, 874523645, 873441167, 915692982, 383328348, 299870011, 78552449, 910990795, 887121282, 912488622, 92285225, 404355989, 11255535, 659225227, 617252824, 295694721, 682951044, 233203113, 147324642, 797370711, 739903604, 314528958, 111146210, 686723978, 175481913, 108253166, 348817432, 225951879, 532920139, 941772516, 656586962, 244082833, 745352817, 724514203, 984280569, 429540574, 948213483, 309501419, 776100564, 898523527, 175381961, 757443792, 340191979, 421593991, 950547724, 810513877, 308793068, 402049689, 722103241, 143867875, 898250350, 563264136, 287087697, 17995717, 353454648, 519345063, 17527446, 698196886, 216163593, 547804970, 306784824, 486667212, 687014226, 215538577, 866323652, 867040676, 636559264, 526987164, 868058854, 211849870, 600433605, 143998321, 306069697, 680822898, 484682658, 595812755, 411845773, 711204718, 858836724, 362022883, 48310969, 411338859, 854394918, 134301551, 813883406, 789728192, 802881701, 319826732, 71529230, 283079935, 852478052, 801991059, 187315340, 334250685, 955137791, 510923108, 528458461, 132884391, 427279928, 684516807, 589750407, 430111940, 17173246, 216757396, 616770348, 117082800, 862828128, 22185614, 476647369, 396687520, 847274919, 733781206, 140237489, 488287850, 355665962, 337078015, 402149994, 731767041, 437035999, 904589296, 672029077, 78373417, 570504372, 679948844, 112606309, 868057622, 27607822, 620692684, 865800881, 694579658, 325432721, 809991374, 719531470, 770974370, 420194844, 630792265, 153513850, 652864223, 32260842, 766955235, 974268092, 403778590, 920852774, 156758716, 860768952, 84076455, 470672322, 341680738, 390562623, 299398508, 234470479, 328209390, 315778501, 8284869, 818400248, 125311922, 857557178, 69291790, 893345498, 338711711, 845302750, 467437454, 370216649, 96343621, 689534384, 956479618, 257307530, 208385437, 701273021, 783427641, 361705330, 709815547, 676054625, 298176321, 379401208, 178382230, 302399559, 699390014, 304132822, 127376275, 428932655, 691530810, 572069597, 531034485, 943514738, 14506368, 504042963, 362505206, 986616579, 653658081, 516092491, 686962191, 212546635, 690967983, 603822983, 134730877, 258162253, 168714956, 352157330, 115887991, 851922581, 558057227, 160988271, 470910148, 826361136, 91756980, 794729498, 444679927, 659588227, 916353154, 433632756, 402887369, 442506721, 291073415, 471722130, 727118888, 122336204, 981994701, 521235209, 486912191, 456326070, 611898212, 911527390, 881548491, 320586492, 965902566, 312906114, 907725787, 255464130, 495417748, 687209764, 545805621, 280464575, 863123794, 118550253, 614402508, 973322736, 106529759, 790419119, 643103798, 373953222, 163193438, 526382510, 829592756, 403861206, 969504418, 709085221, 29610859, 814046943, 98252929, 397744083, 286918846, 305802809, 273252343, 559049211, 294611383, 538310418, 803575513, 768553024, 424785131, 487154716, 737446380, 686784806, 570258974, 960929871, 573229065, 875422190, 113859065, 589995042, 56187851, 494955530, 634363494, 454743078, 127422139, 457546695, 212138648, 57124387, 36638337, 915530917, 819941438, 538982770, 258230354, 811503710, 519101850, 431195848, 437411073, 702946888, 785760504, 662240458, 263022045, 393673486, 900924935, 222482011, 641455569, 66170907, 87457175, 705787735, 525358193, 895099618, 377159762, 559994580, 170665236, 404260182, 862847144, 689184494, 765446685, 347297166, 788328323, 478798341, 830412541, 939789903, 235871568, 474138325, 452106602, 619377584, 105734789, 955132303, 885268226, 863489609, 17679305, 990433948, 519793632, 567958288, 327840505, 165090896, 75395523, 572076116, 765701417, 363207573, 812915345, 964527429, 211522962, 630845288, 955698303, 369758503, 56487975, 179511963, 96427289, 944784602, 62866955, 751605809, 382964726, 727138686, 400542492, 148668631, 903026029, 254559576, 20988254, 543307355, 289671475, 986006108, 605164326, 728951318, 407475560, 338867590, 688178225, 536955746, 972492746, 530867659, 175044432, 971521414, 828223828, 772395949, 740097932, 653681431, 140871735, 889105862, 137593842, 495301590, 376785782, 249670867, 576878442, 347681384, 463255965, 996808968, 323449646, 903469097, 828862288, 979887646, 385346111, 152998318, 403978145, 887086944, 32134138, 655404847, 340411527, 206132327, 595500447, 133371962, 625722426, 959339813, 851808368, 724890538, 985324735, 110644048, 988045115, 743880778, 332769251, 948803772, 231499463, 415240178, 876872382, 673822092, 883664317, 286048049, 105004235, 191555513, 175933566, 884876900, 69236631, 868728223, 843412636, 20167985, 970311204, 822134375, 566899919, 616800210, 918519884, 343619732, 191277153, 870567842, 243849649, 859993663, 67785049, 598639212, 338266742, 968526549, 32286732, 611891169, 653154275, 705874265, 722061644, 937677432, 288804301, 717342363, 728049715, 343473517, 600801769, 821848501, 617288936, 656700787, 629720432, 146768180, 61227969, 508519312, 174138054, 195074984, 652254374, 751082854, 368806582, 14733081, 11376061, 106062279, 835564688, 571715772, 708740937, 598687094, 330435117, 116478412, 16870818, 420033529, 230248642, 339845466, 93610505, 633019972, 942031803, 834933012, 948058474, 504635763, 63823879, 42386296, 181541845, 516438228, 359445909, 482227217, 319861405, 116838340, 317505584, 880371112, 412077055, 135956303, 965535236, 448012325, 518814069, 539035765, 497693896, 817924649, 729610170, 575471110, 204354064, 95000865, 949380790, 908408077, 622296998, 359476817, 566400742, 155518186, 511779844, 88537503, 531022202, 341056995, 142570978, 795302968, 244192320, 289522781, 862636943, 968950927, 361411759, 557206956, 59623506, 688136757, 767178622, 790517827, 346485507, 688685156, 48326731, 176000149, 683619327, 378338430, 757076332, 338841571, 536772634, 256124899, 461931202, 116956627, 305888586, 168602525, 648731225, 688949906, 891414848, 486292160, 460330652, 672033388, 380190809, 5212010, 396072008, 624422055, 365996484, 611652094, 506873921, 243993924, 177653037, 386249628, 641177513, 497777055, 533619912, 175628284, 432130561, 529610359, 196337125, 614929424, 729745702, 873575104, 965802508, 50686493, 584143741, 296859373, 689810545, 519834154, 44048793, 384804807, 578907658, 253097668, 177423203, 720312567, 488435753, 472809253, 388427653, 721018002, 856418697, 657050789, 551212863, 756809582, 60363766, 494687132, 908774593, 23023072, 715178397, 521163589, 152693608, 592880012, 609302843, 843866109, 680498623, 885913155, 685255232, 33470829, 763713391, 404781916, 952233915, 734839416, 274075552, 135765931, 250595673, 56260886, 602887396, 955051684, 144155694, 510669753, 430165497, 15867679, 105242273, 512902082, 912400439, 746365510, 594339156, 931007273, 382645415, 596553012, 823865899, 680647654, 935542071, 782581906, 217038036, 208076423, 743723214, 81408054, 914777371, 914746710, 699402920, 360177412, 185199933, 921541999, 971925049, 643994194, 163273339, 55693563, 783013899, 205556682, 157594461, 22568344, 252620795, 399909357, 341996418, 729133825, 341380872, 324359611, 890579651, 436637730, 188055082, 472523572, 147882890, 607749577, 70360001, 356630443, 413219872, 693540009, 801781081, 688402909, 578276627, 749662349, 289468626, 991368111, 463139560, 67291639, 187466699, 718576309, 190016444, 249976366, 608072814, 128656484, 911723912, 62340238, 232719248, 299141515, 484198122, 103244194, 169534556, 646783856, 532455977, 514968246, 760982380, 362598310, 392580988, 520990434, 943039788, 186925998, 436709995, 161662698, 77601039, 12520443, 287456986, 99139220, 321908207, 293161929, 570729596, 845149288, 724216989, 323305259, 81778969, 754618499, 223026426, 592386543, 237641598, 59183885, 63057800, 70436997, 41998739, 713066124, 993899162, 993025832, 142821997, 78597955, 544524262, 984337859, 999312384, 201137530, 822648402, 243522321, 93395057, 469325970, 451121481, 295197662, 743048109, 682857763, 645534988, 489264762, 52012038, 349730365, 696838597, 814546239, 369407316, 949588760, 469659919, 456183405, 297851125, 746292543, 511198774, 486648895, 362201741, 935291618, 147659215, 797617219, 403640868, 689719974, 795433607, 601503003, 219726869, 46379817, 867469122, 820543534, 896932578, 684975592, 672655569, 415040938, 5634577, 237295759, 711415746, 390767176, 596327779, 198810965, 133533937, 240927166, 12691822, 832289067, 260364155, 590367924, 463437292, 210035861, 733876423, 4087228, 858672689, 41975622, 16241087, 217627447, 562674480, 858471283, 23519893, 216342938, 149149400, 326271196, 780941242, 123610810, 138661692, 798244656, 881707355, 620459588, 312273718, 725135331, 364957886, 611526140, 469880021, 732949285, 722575143, 260183540, 640611629, 748698185, 687618939, 958384584, 10721503, 127458593, 698378155, 65271164, 992318158, 373061043, 630174960, 230588317, 770511545, 917732004, 136553615, 206614917, 762586089, 626252755, 203416811, 672476834, 714290250, 716688860, 21528456, 551433909, 901967806, 878464671, 423643365, 380579615, 890294872, 418569069, 167541974, 953371882, 989123896, 937047718, 811947704, 162799928, 885833717, 523694305, 240134292, 937123236, 97345008, 153366253, 251054667, 43547875, 567352772, 214318168, 214344314, 338774374, 692726836, 415163727, 811885441, 881681686, 586356394, 253988992, 345480314, 578354316, 341009642, 157312428, 795862560, 949084001, 897431518, 206433358, 531577816, 460892076, 634561056, 251441784, 325512376, 363425570, 595793292, 738200620, 57616896, 347223207, 152007222, 276678533, 265811940, 768057011, 624574149, 123704128, 767711441, 955606020, 979909465, 706181602, 562547484, 998665682, 382882695, 962400543, 76799608, 243263036, 370847163, 389383807, 259989153, 361267025, 580099383, 412870862, 183884755, 391392544, 998560484, 179833358, 245822555, 655303516, 380808758, 853036220, 389099322, 582975316, 879384508, 702877981, 778508699, 748703480, 246462192, 971954762, 220157498, 273052480, 354622498, 768749990, 855915661, 323129850, 826110690, 219638450, 644226842, 92887257, 739935681, 136160120, 695758149, 172491520, 187506969, 51488652, 228773762, 366552032, 713958970, 630247144, 636937008, 620284215, 548781882, 889125101, 452705197, 303906138, 206327612, 393559126, 698486447, 651142238, 511515785, 580206870, 471214175, 810733672, 81475292, 349828852, 56137421, 137095032, 530821375, 792800903, 668885109, 206395950, 236451066, 337386317, 528092245, 576831540, 429845487, 781940837, 160752925, 403546836, 896349518, 144010761, 409852701, 372188498, 431418006, 57037901, 135682137, 132832935, 226324524, 854066227, 196965739, 620995587, 553782715, 931319523, 460574194, 138941785, 139787427, 352992927, 516805781, 415732107, 810192161, 346135673, 591073547, 865107033, 441940121, 371732568, 307193399, 402956734, 413006413, 238023474, 512855680, 423835787, 237273425, 261600122, 67717536, 337112868, 488708166, 335259710, 989853839, 316556454, 430394695, 823697937, 82722599, 666870210, 547047592, 387110726, 276882828, 514373656, 532754833, 762024526, 187163779, 931914996, 624745620, 769907171, 300349063, 918523306, 791724590, 16372814, 46553008, 992673908, 945716518, 364543968, 172141630, 281164996, 231507881, 665766090, 132645181, 495210176, 861463658, 744196856, 30447188, 754512506, 923351906, 610903491, 524895056, 83181664, 691423437, 302662157, 835063539, 681530151, 297905198, 983500928, 952558539, 473421748, 16623792, 326086370, 853132751, 503860761, 52661022, 136702494, 829697510, 444404580, 926631525, 787689964, 138193897, 352461586, 297151291, 45686118, 539970124, 435075224, 870385752, 822298761, 444791617, 777803929, 774330583, 485932035, 469013716, 819297436, 383530579, 184209506, 822779381, 402315987, 573232417, 852569600, 667279800, 102271379, 625463122, 552592771, 316148268, 866722913, 175520760, 989166980, 768114968, 302436637, 920130797, 568107821, 594924261, 84061404, 417852594, 912345459, 900202816, 616383566, 551109261, 118129305, 177444976, 668485058, 616844570, 807255864, 803862599, 505819033, 654764279, 682613676, 22388131, 849089025, 891645189, 350870383, 510537666, 817416267, 300323004, 580415585, 580693824, 427563279, 575630909, 452566390, 545541482, 733274241, 76946743, 130437522, 137609965, 483398787, 405621868, 892963915, 549078402, 446209830, 752805800, 407821467, 403991650, 531006513, 737531971, 733068415, 202071562, 904131646, 495776856, 479458180, 317028505, 949708666, 191223181, 620742628, 82416356, 985888000, 258370175, 808764909, 50037103, 975654447, 887360227, 589121866, 36121950, 332640906, 218801638, 202029859, 679471671, 675773387, 669153522, 382242437, 351433480, 249081381, 763746214, 827525417, 770433114, 451266748, 121842264, 19082587, 94964227, 311273051, 125803954, 235185790, 49340497, 430115685, 547785293, 572736071, 448352643, 981985209, 869402513, 183507989, 10849465, 931186049, 833864999, 301967638, 522328291, 506318562, 398796891, 115105830, 865862866, 419123268, 887355951, 284284590, 536220195, 455205834, 621696454, 186849798, 251762710, 239446578, 988093590, 418884317, 43604358, 385844617, 112449853, 361303332, 946509698, 919044453, 878953309, 250245201, 319040226, 155578585, 15866198, 233269510, 635818851, 830141245, 690645483, 312750318, 530822850, 17871006, 847297339, 238896295, 855817151, 465598465, 206308967, 878634554, 795352989, 464027631, 313398918, 953709164, 729179298, 760198737, 185651425, 718060649, 383364579, 183244042, 197028405, 610811487, 606683109, 186180402, 424897669, 910884752, 674143637, 104199005, 312095756, 531561965, 412255855, 770180362, 814799498, 136567258, 708259474, 395811933, 29435461, 815110563, 965221510, 63575061, 579873963, 491901057, 737405321, 489041499, 98085475, 578578337, 373107425, 841621660, 307426833, 843951463, 878290279, 159667530, 307552089, 542085922, 299717714, 362397877, 860503058, 905223826, 446223217, 804661270, 666133176, 323063974, 627146564, 719329574, 15824064, 362812055, 840290390, 431884996, 60757053, 52832681, 236386668, 372139863, 838258214, 733993774, 911422291, 420968787, 490817503, 510418180, 594386386, 506332172, 799743139, 728416900, 560256698, 740014949, 685668489, 527685926, 426229674, 369375028, 134234226, 909576483, 309610604, 149506966, 473610455, 429609691, 743449256, 428920186, 188266910, 677788176, 121260027, 415368125, 537919030, 829640329, 201432031, 782843364, 401072976, 222276325, 193356500, 536248710, 322342390, 516155195, 149316118, 224877225, 54244314, 614849325, 317293712, 61058739, 46459092, 754773871, 573229518, 506474133, 466648730, 563303256, 234944230, 387017572, 181831915, 518104459, 112950090, 425121264, 320574138, 130093652, 246360617, 252615559, 962305159, 378040787, 856650947, 782337727, 180330926, 419918827, 344839615, 939664368, 174751321, 990665727, 73895934, 866879449, 51572966, 316137394, 582959801, 985110755, 344536284, 841928643, 739941320, 963665656, 572685586, 205462291, 244020455, 593114696, 517769554, 575824462, 699587722, 37203946, 377670809, 689939758, 930911774, 297096810, 128566428, 895172349, 71061977, 412177644, 62807810, 843130035, 829342058, 28831243, 210261913, 156255478, 607023509, 703540489, 744569380, 291786642, 163645554, 803719700, 755558363, 690916324, 373495218, 818523049, 929544169, 910278440, 497902423, 150766200, 199946448, 717914135, 494060479, 564777290, 368492163, 908882470, 349779869, 480784570, 913630683, 117180994, 189675738, 401134267, 535744290, 349774838, 355390922, 968108736, 855082950, 863720895, 168465426, 772791451, 430724893, 530978639, 442084608, 417272869, 350303133, 650983802, 409864552, 513578062, 748478652, 86056825, 676537319, 770427607, 520735743, 411817472, 704317612, 753359796, 815182909, 288076616, 127278172, 498822637, 43519119, 200055446, 545605380, 627143315, 910741529, 887191360, 32318949, 644245479, 105121669, 38495891, 261663931, 922088126, 967271863, 880881784, 124222524, 928436044, 873044277, 449776860, 881779302, 215069323, 859273924, 820148838, 525055449, 649886347, 790776642, 224490123, 751323575, 515695090, 874556670, 709112548, 483465143, 596207480, 256868556, 350792315, 131294859, 221293965, 776766870, 687770349, 638347867, 175866728, 777879389, 3405367, 754466998, 729950046, 988818331, 128134441, 679019264, 265348316, 932555019, 299716276, 983908912, 483868449, 343421998, 265179310, 635251452, 583287301, 834125491, 176504873, 249006285, 825738190, 496802062, 132308885, 142668839, 552739636, 990220833, 961173017, 479039053, 95905645, 916763535, 57054960, 536416267, 644844531, 739054008, 248154246, 57190420, 408594416, 529788395, 326720016, 239287609, 830899739, 160952290, 526451521, 729945358, 429670127, 418129844, 937332824, 583181382, 535078787, 518095961, 944815385, 555720004, 265638303, 524235860, 777410382, 759768790, 963610496, 243255403, 836555278, 145305807, 43940110, 180874795, 575451331, 975054617, 738179547, 933090595, 397741026, 986263122, 701393483, 3763297, 10261463, 819407242, 541970735, 747178585, 473677033, 893383707, 96212417, 826004852, 640138567, 755917462, 861602341, 715568138, 106535222, 635879095, 593532131, 71043607, 798313182, 903231199, 206755064, 184200362, 59863850, 214808508, 919455991, 672875729, 494172693, 345239342, 816663091, 806677461, 509883150, 492022163, 258806206, 602402044, 164304608, 321426497, 882503359, 564370012, 921150344, 131034270, 942402348, 302236990, 333143328, 379160541, 945875229, 510861669, 551554190, 809343175, 816684067, 38094160, 102682534, 227973548, 776244029, 905776812, 749993363, 485362152, 229115425, 309431975, 431376216, 966093617, 59063489, 845734112, 24355725, 606285616, 937752424, 557414527, 241966512, 973605918, 836481160, 508328679, 261148443, 985355508, 963535340, 287574990, 551410315, 330541433, 916973400, 343854889, 811175524, 674821800, 484915273, 454338636, 902349231, 482824583, 492852753, 218861549, 974062051, 611255122, 790946259, 457077546, 812320436, 246102375, 217132331, 339370703, 417877848, 203120020, 657396260, 639301508, 467985171, 648313392, 533446998, 364932335, 770536038, 551648071, 445810402, 619286192, 797045796, 960531286, 404410044, 792781755, 438944387, 453340822, 894792431, 96299968, 666740027, 945993990, 273461802, 630453450, 514160401, 181059423, 867935576, 527603040, 157305088, 601267920, 179880007, 242196665, 990703817, 459251602, 637972184, 996446228, 560805799, 619197936, 297724100, 108812625, 976712024, 474357149, 491779479, 556272773, 109469696, 197193785, 230027184, 851046919, 180140355, 407727617, 893124688, 998882427, 226923725, 970290968, 86291886, 11831988, 699717384, 862388562, 316273567, 582518043, 670632983, 860289003, 428702756, 533495200, 656601297, 882992727, 663433053, 76692025, 487355887, 710900943, 11155034, 534635462, 901629098, 20675105, 473394872, 58131966, 107628632, 917558372, 679647388, 206310952, 643931277, 218019757, 843277931, 767388327, 778254437, 162190865, 319041342, 466167285, 242949261, 429813024, 391170192, 358176636, 770402848, 793788212, 896355203, 57524572, 405335498, 729463147, 958330724, 673877248, 37852572, 378063229, 840118433, 114116645, 539134658, 958443014, 264529392, 311827041, 544970811, 218927697, 867357856, 940528449, 295007410, 583189898, 230291018, 457451879, 581572128, 785666404, 437671675, 192347411, 297897570, 422869678, 716248517, 482937515, 480539262, 337602027, 261786649, 948779899, 291300904, 833216499, 728787361, 535243977, 773991569, 178813022, 21597388, 358728323, 26943955, 4965280, 516922019, 68501357, 132156001, 294690216, 17012482, 51720468, 527771280, 574048058, 128597743, 7916205, 721455242, 980134289, 709848801, 944913135, 843881092, 972211171, 353871165, 324586349, 730378566, 206587721, 956269168, 114101956, 75330456, 357914013, 999934256, 363635165, 666898211, 212095321, 512184807, 211456135, 993597531, 944668915, 902707160, 173441031, 876810326, 426260625, 844130711, 996705990, 313792965, 17147673, 217504017, 44365509, 993568615, 644231353, 274547594, 337035337, 799079311, 672947709, 668695006, 581506468, 287394315, 872396283, 532027053, 342612654, 418893796, 160779173, 858298591, 337073915, 11743219, 524102637, 599508311, 447437036, 196507541, 461111140, 462770830, 343929210, 138790217, 507793678, 853058922, 877839402, 487501050, 73414768, 949643282, 202130280, 291948430, 312531418, 187387815, 636521951, 49318853, 969223461, 167083689, 528504217, 891983533, 438687198, 786578439, 228560904, 70477992, 381284356, 675520833, 628437298, 268771147, 393198361, 95865439, 1057154, 782128273, 410919739, 574074405, 483099461, 729324767, 887982803, 248808203, 559112163, 493202679, 580155305, 91619197, 133364941, 444638650, 718719780, 97007969, 109281828, 507810890, 414358571, 65037218, 755920391, 67257541, 365961671, 2366275, 782995317, 422824875, 302021876, 280204950, 699635508, 700417420, 855461059, 886197706, 846920168, 931576520, 457788095, 591924491, 166090232, 120281579, 633329117, 893865479, 302583926, 814406385, 455134257, 212508309, 401967212, 75165658, 134729980, 583788686, 551698860, 589665167, 18095820, 527131437, 75761379, 498175469, 346278106, 61614382, 656551663, 754273456, 328138978, 887353434, 651104736, 68607246, 77806750, 834517407, 313213630, 260140872, 265491576, 835441268, 965107673, 512291340, 205866668, 369643030, 803680441, 21507215, 704502484, 131163931, 183910561, 708375741, 393130227, 738358246, 922751921, 393791608, 792555033, 359473012, 133114135, 922567568, 972136463, 47154257, 3251420, 862380984, 544894065, 776872840, 182001328, 492086616, 283704702, 298973167, 144243735, 470119952, 440690728, 353022805, 431571411, 742013977, 429262827, 639420928, 228648523, 844360954, 816775426, 148636937, 429471843, 273601308, 141602620, 672437068, 484209602, 127892344, 251040147, 177406806, 306588308, 125610039, 758611637, 323701202, 413902741, 671376557, 930099961, 5401259, 34401699, 357304725, 614311176, 584187859, 481310616, 993682879, 229009204, 576088784, 939695075, 246625860, 639570816, 913554150, 456077540, 39214490, 173528782, 304292385, 571861395, 925607337, 652702214, 545076588, 371408982, 570279131, 609393633, 765519127, 395919825, 537457060, 149843896, 41831191, 461246684, 882353130, 932343523, 292120205, 168932950, 784509633, 146022269, 386329528, 105616871, 990242213, 583497871, 437207239, 706768256, 462511660, 933794073, 494363935, 559964923, 65428555, 312275876, 873619094, 634699001, 120823637, 743521441, 417689693, 459712225, 182107553, 606714692, 296211183, 177617497, 866449253, 273993669, 70112705, 786419239, 885248801, 98366423, 536392160, 78538674, 863379799, 540477493, 977770015, 139704275, 216976224, 82126138, 509942948, 54614612, 627987791, 214004366, 993271677, 684561667, 365491497, 111541997, 531418074, 39724731, 39169842, 746510389, 84345680, 580807617, 367599750, 319035735, 633753965, 251702747, 239340343, 416603959, 989193706, 490828015, 145183851, 649339866, 996574198, 179640540, 965322344, 613554443, 666240881, 153142190, 796747372, 483695537, 887035137, 24116498, 662298495, 242956623, 584138299, 554696867, 795796236, 71512017, 511010421, 256712633, 730504081, 193359976, 232393466, 173158683, 498304049, 225514611, 233196391, 125739601, 220859050, 828288903, 858815245, 812489542, 102091805, 412254633, 540688430, 825160836, 826839116, 222369344, 100935737, 52749636, 47254658, 761579905, 551784865, 378619924, 674000867, 759138753, 56131620, 40644627, 416845334, 235088822, 913353638, 621232021, 376739569, 226665378, 660468345, 990847220, 552038730, 671585019, 191458206, 751700009, 883496552, 881252904, 649019471, 356348369, 495927593, 76248820, 738842884, 42208421, 668032417, 487475186, 555993391, 316365250, 192461456, 134326075, 751534583, 331481216, 771676560, 389584201, 479511498, 642417667, 79304700, 26483960, 59170511, 170534817, 616785971, 395745210, 873888843, 239457942, 978010683, 240642637, 978703233, 521958896, 403003937, 483677252, 738476121, 371795990, 449011198, 326580048, 763958513, 801321389, 177070792, 753927701, 700456958, 544421476, 4312729, 947797525, 216826065, 585082993, 399417192, 638124834, 343548888, 378330467, 327150943, 511935325, 731246250, 609077821, 947575044, 842648306, 952457501, 562352595, 308005208, 206121883, 366092434, 536023785, 274726165, 882335522, 280758726, 621169770, 11752707, 849509568, 213483700, 449667262, 73325708, 798426524, 276565918, 724302835, 115824360, 718114560, 158390574, 168940401, 272822518, 184602995, 54877843, 25686120, 939011248, 944605446, 798726889, 752899273, 353776395, 793019267, 94275670, 794706361, 311095379, 175675634, 329077959, 814186964, 481415979, 777022138, 545509927, 636367415, 495024486, 103661066, 488669867, 875994516, 529672610, 89858257, 854039423, 764901304, 502063923, 412258334, 82670317, 694062221, 960213641, 838529369, 681506019, 912126870, 496755841, 521927835, 839218222, 362888145, 794785419, 248375545, 466533919, 26355798, 377658009, 325034082, 590105091, 122023251, 874446667, 907625271, 26633538, 314318683, 965773211, 142035905, 985507628, 719298376, 545882775, 879418849, 833792117, 891491492, 743307570, 435657742, 278037278, 454274288, 521157073, 475361270, 43065087, 935270563, 126580430, 694062962, 146510504, 461570429, 68581528, 513680711, 168482906, 298683860, 364788323, 976792721, 291841178, 281545245, 716775932, 600492453, 600388829, 323728180, 81232686, 234229341, 859318664, 107044398, 102278609, 838761075, 533646085, 64578476, 567978627, 382691120, 369939335, 499765595, 329221502, 870964837, 753593289, 966734901, 904929647, 637315873, 693098821, 897971952, 337978640, 830225009, 591585372, 851764723, 937570741, 738683715, 834967185, 893039675, 342686592, 237519291, 683965484, 64242235, 355690827, 252688760, 418373630, 158654035, 896175380, 777199846, 138416530, 594442963, 75960729, 48661646, 666113620, 812716172, 466320162, 447673683, 316075267, 888360350, 86098211, 291065549, 208903086, 913032308, 82380889, 565456543, 448439948, 924341552, 3783694, 366451422, 240649069, 580640082, 795362686, 517523295, 968304623, 224111449, 717196993, 477437850, 545800583, 877672806, 151051688, 453014128, 996990775, 672825196, 326849710, 313311309, 961653888, 406180750, 443105475, 937392466, 934561735, 327999122, 732264422, 854651471, 52511365, 303334390, 874962458, 586916265, 754756450, 285093173, 100797476, 989944597, 545681869, 292495705, 839267763, 768589764, 703461326, 407158267, 644049620, 489545495, 300193298, 395383073, 343097956, 306917429, 577737441, 256181862, 232330266, 97052323, 910724228, 124463285, 76757493, 211454580, 738271875, 284355279, 762891019, 958701983, 436832809, 689127674, 733222304, 909304694, 884181147, 423819009, 419463339, 657433001, 245995486, 811201572, 452148253, 686753754, 699046591, 633824532, 489879671, 619476601, 574677550, 28023207, 335253071, 967618809, 609967326, 90562712, 37674522, 781476895, 209986008, 516746426, 910967209, 371664750, 290556536, 950820364, 951746187, 237308027, 29614686, 810243788, 955978009, 112952406, 361156729, 327815525, 876899748, 168541317, 405716106, 49275582, 3977623, 149336839, 146928152, 558011911, 126379667, 117201830, 784439228, 658566346, 755529989, 433513739, 430821914, 362337130, 605874289, 443005737, 718551810, 849731596, 252199690, 418333065, 500171676, 392619488, 902991135, 424449546, 355097840, 532210000, 140120340, 877245695, 130353559, 729717802, 325691206, 605199083, 379700980, 447028649, 442001441, 891860326, 115672579, 804493335, 136193132, 506765011, 405817376, 174807425, 563392417, 227832234, 569109134, 152286501, 843352333, 716316861, 412436129, 217754711, 327204182, 504968866, 415547101, 74321215, 219655360, 593697781, 256141683, 881804787, 721759943, 692407249, 327187892, 216362553, 506950007, 443297739, 276700591, 32682379, 726353180, 385529236, 558928031, 532053107, 33362290, 947629229, 669227120, 790004853, 500937981, 244581576, 598467183, 800724695, 468640246, 902416443, 163615999, 660131507, 370859619, 955330215, 918003585, 629812907, 336274652, 282605980, 980693615, 161538478, 517019223, 120741008, 2155947, 604531212, 220673231, 44357718, 900348585, 548779378, 251052947, 776279058, 598013317, 875363651, 301424480, 490556546, 563875445, 425885885, 593311574, 787515183, 883003008, 899990082, 162654291, 417453740, 78011706, 662034826, 794464594, 769292309, 907109406, 455042183, 955784055, 322871614, 970580692, 157865156, 942972597, 500788065, 849100938, 24164932, 672357794, 161244472, 302736730, 511042222, 834595518, 752436221, 170845888, 821573939, 124044016, 988048683, 237075368, 856435334, 690972617, 91988808, 489142439, 157197489, 855545483, 941993995, 701161598, 854073240, 261967644, 183027451, 15680614, 702666788, 965578221, 316752936, 891758886, 539919335, 64598349, 753271485, 28018153, 751541328, 203033986, 810824949, 7861442, 71486300, 203120977, 662674538, 516051304, 64131963, 415643581, 305187909, 767174642, 885805663, 945273946, 401886776, 762677353, 93340766, 34574003, 931346548, 822086315, 517955872, 479160442, 177436663, 262705427, 914973144, 696603633, 679379628, 567624160, 300996623, 448730106, 908022364, 150660198, 267491699, 22112522, 163086859, 300978555, 411016347, 508276033, 234653812, 997103463, 235601174, 616465143, 457941338, 929935948, 677870880, 825985699, 51254773, 983640749, 61725604, 641904773, 686394530, 844627829, 658297655, 374848963, 382144660, 94797583, 56282033, 514158506, 378310271, 878299401, 35729000, 671897872, 103049007, 977740107, 12090271, 523616887, 379801085, 769939843, 95518538, 955705110, 10597554, 755883736, 812932258, 425381601, 956532358, 980019378, 810672566, 225973597, 698126216, 82485749, 676734696, 866518367, 524356105, 176266590, 647469175, 933247782, 619199895, 907814843, 315077063, 661853405, 677563002, 206343326, 69262713, 132593623, 986157109, 497449108, 78306211, 631132748, 103324766, 668329655, 358382778, 823630127, 399573298, 890394498, 506229536, 207767788, 159248559, 44864407, 531210081, 238717823, 688100539, 61961808, 157089708, 849327143, 70053588, 207286459, 559462514, 456122195, 155386010, 744072595, 821260421, 961044703, 845142580, 830423159, 873604978, 46128058, 584991255, 204786374, 333023100, 654899213, 26582028, 847720596, 899716277, 475031541, 390056726, 639149332, 897422877, 182311091, 104277161, 256513005, 98658570, 615777575, 981839194, 368779137, 35553231, 938527662, 551268513, 292121004, 301849625, 738338411, 671468942, 338583186, 34969111, 58835094, 638751651, 605347779, 484379916, 816242549, 4681668, 149375076, 139439598, 666777115, 758628, 274386531, 67869381, 525068995, 996990448, 395599494, 196250339, 320556412, 596847936, 681893891, 617736091, 345573636, 843804812, 229821092, 701066034, 871464767, 630624231, 309512167, 752772320, 287693968, 558906117, 163052581, 811854958, 337280211, 877254270, 454481584, 962573776, 820142142, 932565919, 670000038, 65384320, 711845062, 544839951, 777732817, 573974762, 625869581, 936135612, 71656039, 976409758, 694405267, 24136567, 989902556, 455618568, 818642864, 576115098, 723647534, 906564052, 341405053, 144318003, 557084568, 468847063, 735212389, 123490918, 102168319, 788046874, 836644148, 63029311, 263565316, 630104425, 355188250, 797699018, 60138454, 402828309, 838705344, 600851180, 848889292, 950544997, 670108001, 330829853, 596523344, 967491387, 181226580, 993739933, 305935142, 516577536, 611412749, 337219887, 399113073, 799972482, 263503980, 182513162, 122918646, 563542572, 849397568, 659012143, 282305453, 910891451, 887833981, 774045448, 977164473, 348031559, 273239927, 688668595, 746642136, 120320496, 420069973, 967965059, 891503362, 481863805, 194370296, 927079235, 665816158, 439690874, 784472224, 89012472, 55099849, 536481419, 883003470, 717298223, 914312867, 990573170, 794525181, 580122670, 174923147, 119481907, 540912716, 873580131, 704842291, 498323872, 714008303, 364444509, 256084379, 476590845, 822137126, 69688683, 246895368, 449757010, 465286050, 296162018, 880329402, 978114368, 208775501, 353726938, 308174914, 977232878, 701126331, 939659250, 698447507, 983491002, 2978063, 52685793, 170672905, 183554048, 867823711, 563564876, 761269260, 997623095, 574103220, 583409091, 473909261, 947830876, 568505007, 501716958, 947139579, 197879379, 290072554, 281819993, 923369546, 73600496, 572205516, 385715795, 772833305, 915773505, 270952107, 652918209, 784277871, 360333921, 518518146, 360327076, 719554801, 116114921, 553045146, 636255975, 860517994, 176907883, 670435627, 327689483, 434777156, 805520939, 612228928, 324694521, 746512196, 888048108, 57434976, 792136763, 589855188, 473843001, 110993575, 36912439, 374946486, 185861314, 62587891, 892314872, 720361645, 621214196, 879567730, 547173014, 848442152, 599641235, 175829289, 496128927, 97141593, 272002147, 58529925, 43864872, 743780363, 787856053, 401756113, 548804945, 895820813, 242135714, 532858682, 922278399, 978550505, 285614453, 322828386, 612591435, 702939392, 391343097, 271004681, 150875091, 488050086, 687940841, 390206022, 271621142, 652451806, 769209410, 889685040, 646260751, 200047625, 152924460, 822376515, 337494597, 565493563, 647369914, 459089722, 143722520, 977294343, 808445205, 373235007, 766547785, 618259811, 43547801, 265416414, 562224371, 522298590, 202859748, 638630525, 704247193, 763810734, 643365034, 993624121, 836970594, 564071418, 239022053, 630900554, 692279201, 136892568, 413869248, 137182431, 440857704, 422935717, 706398500, 175105105, 869692520, 48134677, 24950454, 384850410, 823799778, 150546329, 90541576, 652381333, 725447829, 363944926, 170949597, 228622821, 221136553, 979929871, 552867767, 175734523, 672416253, 718778947, 346926847, 801454607, 505976620, 912098747, 998932730, 248924580, 169678209, 944640737, 171584081, 680617733, 600952973, 913133208, 175859428, 663598797, 11359155, 445441409, 415671368, 620875253, 887427348, 587715702, 604084247, 811010464, 774832099, 331475568, 542988401, 393875931, 251148967, 893024497, 992148840, 566384958, 920795715, 546297231, 416787314, 928446066, 248356412, 97971857, 715315094, 577044446, 607348937, 123833895, 620437714, 48384119, 698665277, 550383369, 857768415, 201293938, 106070997, 867662714, 252916728, 327559457, 74751242, 346977655, 556412886, 451691761, 196910516, 177534701, 721451961, 53089762, 153673317, 782172867, 573986017, 276621023, 981598428, 96235478, 510524782, 317756722, 372066387, 635888911, 767058363, 367211146, 953081702, 908951234, 860169764, 268485962, 743757486, 455682483, 47212712, 186569539, 214896351, 473992048, 366531878, 818145278, 363689916, 465524563, 119813883, 800172786, 677544661, 854224083, 670753652, 728535540, 896456264, 783144475, 876354666, 196006773, 272106858, 466035869, 827372079, 366469169, 124628748, 655131005, 273361254, 251028170, 955541808, 530717973, 365127600, 710694821, 190926311, 464477497, 884136952, 167671157, 324446201, 863075982, 133920055, 142453117, 227179477, 298345618, 840306778, 964142682, 566695688, 974057968, 116095622, 677610367, 694869085, 967391756, 698263917, 814627100, 601258338, 892747988, 947003186, 943819092, 119989922, 45969173, 602017507, 185144137, 690878319, 607852730, 179495131, 89164517, 279085628, 152928239, 425217198, 332092404, 502067071, 769484884, 464968273, 492333671, 564817241, 983050188, 579156183, 363572255, 318590667, 491504021, 289013306, 403945225, 851426985, 820410679, 206558349, 285721686, 173043853, 519834486, 533848836, 35540043, 605813369, 275356535, 607776831, 349179541, 121403700, 247183213, 200911145, 693589842, 649123772, 12228517, 433366393, 808307778, 784428604, 275440188, 780531955, 525152223, 615044243, 111118806, 731548545, 289994865, 538268178, 780244150, 849317443, 357606335, 751313775, 645776498, 530898317, 176863882, 614914788, 880915394, 678613604, 599706684, 529574067, 668780686, 2038532, 258946321, 202785523, 322774777, 240606855, 873238505, 160043500, 299769176, 719100711, 891521510, 921836984, 888399857, 612387272, 652407500, 49541996, 590852341, 301284191, 801038714, 665369413, 378802874, 927380471, 573319627, 962656003, 439751003, 304265160, 826460474, 87781173, 703040396, 410578319, 100340741, 603752197, 511108267, 445519034, 366914975, 484394474, 860009617, 553869939, 283113134, 106219325, 961218644, 346657413, 343314531, 964895036, 839720511, 803456867, 242297075, 340247985, 285450645, 746815050, 217170837, 242289322, 445341734, 92857177, 389104894, 215205667, 757864724, 867604162, 27000529, 306410242, 828530027, 714588258, 90948507, 998284154, 29614015, 64434165, 34137408, 424174077, 268369772, 778600105, 777760001, 501612432, 204867466, 311581866, 955688334, 862759113, 729057345, 701276410, 687074683, 942395183, 86030651, 436011956, 469162487, 243841682, 727271542, 901441651, 614804952, 22918218, 559123670, 756825901, 682545042, 675713904, 442162146, 952112516, 187529634, 330357595, 574123083, 603480065, 684659476, 813153120, 496672715, 266019474, 738355233, 720087822, 440427857, 248360261, 245786600, 549726063, 999809305, 227380888, 882567142, 206266839, 454336167, 330111527, 40895734, 229400017, 505927451, 195985564, 591756545, 968987240, 50522715, 567623662, 272093663, 330105329, 677733598, 736258013, 356753823, 906831023, 980728036, 71371235, 541137082, 757551697, 614290699, 543795501, 451396529, 656257790, 901638090, 614344970, 706501303, 463049987, 525550545, 580514543, 918300584, 459327622, 103793946, 613078519, 379342043, 432183220, 584275458, 359305590, 761054859, 277592189, 638404153, 270473493, 987987036, 778926136, 205979216, 863260090, 713155453, 841578419, 815056844, 39132983, 857072491, 906133406, 909036047, 908592756, 101331187, 554053196, 442017785, 866790569, 217139330, 585729767, 222526781, 576657696, 331930330, 688037751, 242238637, 563659961, 160948270, 520109181, 431429880, 703721198, 890385613, 253267385, 946646429, 34472911, 285564891, 426872200, 619768817, 386002605, 233834356, 88312497, 802938274, 650236708, 505694001, 334500219, 343749648, 70084423, 544578777, 269493061, 600222000, 164928972, 434317292, 642122122, 320016066, 328491088, 384688204, 76110218, 938522780, 593735588, 134003457, 299585518, 697646752, 593482905, 849870374, 741865711, 954788066, 668908909, 409690417, 54893977, 331325980, 723864624, 925877701, 356051434, 938929998, 810336263, 456802487, 471295762, 92008725, 271186502, 56792628, 453491091, 188318989, 432696749, 512207901, 191956206, 342262897, 229626989, 478231210, 912995671, 840555379, 970044133, 831248055, 907157053, 524807210, 58316676, 144384090, 109017709, 126833871, 190978953, 813392121, 484155797, 32126607, 258848292, 589890572, 948794452, 504753524, 209933463, 501400089, 61223244, 842919598, 707804062, 894597842, 344515613, 63633775, 818894066, 398092523, 276264928, 373482990, 861045521, 310157203, 651291442, 816780780, 529691634, 878764291, 47091325, 659097212, 65525168, 474219007, 654446225, 438380172, 173690312, 483356684, 241484586, 807494863, 377156126, 431297590, 504275472, 628727506, 374963859, 695835234, 189275672, 482623691, 346083749, 134275585, 878799399, 67252396, 699549087, 278179337, 833347865, 164346754, 757505827, 758395422, 532495546, 322524280, 870783333, 798355727, 14928710, 556635882, 610022967, 669665036, 846874202, 63637348, 170118101, 839360255, 468139035, 881260332, 572151274, 679297757, 741223544, 448207130, 527414633, 632610501, 800970727, 44085127, 431836565, 384291914, 769974323, 319194318, 144532869, 634991305, 388511992, 959780625, 475083231, 345364475, 386168482, 868064225, 557405953, 608510371, 266157695, 108061505, 859920700, 643585972, 48404890, 611193381, 30127933, 391482702, 261138645, 842744554, 949010350, 625195128, 756841966, 726307136, 358513980, 781686676, 582477106, 220668945, 78018916, 110610756, 115775739, 949428419, 517203953, 235933190, 413925922, 149757917, 884482915, 620135747, 603845824, 443645384, 598603555, 19819667, 731461067, 595190033, 47866575, 784579758, 359374886, 792741619, 149651119, 621667192, 696222826, 958722709, 324287860, 924223903, 191076609, 640339874, 214972979, 479277995, 490999297, 675078648, 658884735, 76573929, 392731770, 189908586, 849741894, 198052578, 691540520, 985827894, 532795307, 113834691, 578086152, 489952884, 648635917, 898964462, 360472527, 135604076, 370038495, 447750581, 8956901, 862580137, 530647245, 628780542, 466654588, 332211795, 251782183, 444522143, 91007839, 687810899, 161664945, 941406275, 81008205, 575507611, 183121889, 828676201, 350651063, 142222367, 249425797, 58471809, 419841288, 546803308, 600529056, 207626892, 894334555, 208010007, 159544651, 339920374, 303244701, 832186544, 110295461, 195780476, 28548969, 756208855, 941727477, 657354263, 418012399, 920406246, 544019970, 755523701, 114794573, 851291871, 662071351, 100558920, 476443891, 900529653, 106871609, 32173335, 201398389, 761921389, 579635895, 915288553, 523100715, 250644583, 260314057, 778742011, 534495625, 266060285, 458869592, 467418809, 186112899, 764872005, 649247432, 845821369, 944602366, 653667140, 755306585, 490309585, 71566332, 627168506, 508443116, 652101166, 931238551, 642612044, 115202270, 546699756, 264462074, 739128512, 135550901, 729950032, 657927017, 566973043, 355567789, 124824646, 976694431, 666277489, 369061037, 657219749, 879014530, 93625290, 325713722, 271090934, 719546074, 293706824, 532473061, 580041385, 536042196, 48868959, 50142107, 695307038, 523189119, 99505212, 715561047, 778811688, 621075162, 765628155, 802213727, 712571713, 187404004, 335067467, 669158929, 659805752, 369994105, 265144603, 574040474, 8427649, 243758000, 654343520, 463118494, 361177898, 462124186, 152946682, 286652257, 772223473, 827392154, 918028816, 431431977, 466916955, 80243838, 980284828, 456973986, 166364769, 622374883, 779293023, 934866224, 60750205, 805582045, 361062477, 615585641, 362617415, 802270630, 64542508, 535529341, 706962236, 452729681, 511785308, 165957870, 47468709, 786556942, 916770887, 619045212, 3471804, 523160004, 975577362, 922473813, 155354544, 441155921, 965721497, 13174856, 564829243, 162423819, 510007808, 503888149, 704392097, 117612405, 789102559, 526849534, 640463013, 955958775, 550801860, 614542332, 702739546, 828633645, 944639274, 797759514, 90287405, 577511036, 844563222, 823932426, 274365191, 96519297, 319890548, 901873580, 485383094, 564444133, 37069131, 235614917, 528381648, 423953447, 475309940, 669114808, 712751502, 931736379, 412577207, 443346822, 721175158, 361867194, 340413572, 113474984, 528147865, 540600086, 661630449, 105437490, 815255775, 830399967, 152366912, 951364249, 717243692, 136538288, 370498669, 42621483, 271148963, 750234701, 90108719, 638674381, 976741789, 389673284, 733760535, 242688289, 496202887, 268950886, 303301080, 620313052, 65683596, 790159698, 354988674, 580980300, 203593049, 739070984, 776098184, 104943657, 899861971, 151405405, 587674328, 711164027, 475603885, 337677850, 540788493, 91304384, 832684950, 765806005, 423683204, 21787378, 728994881, 798734217, 136795371, 174848745, 25890361, 215906497, 458627653, 367194602, 523722889, 418216611, 879134606, 58725491, 820544883, 642642319, 463716886, 619061082, 21664205, 733924863, 42636740, 280442661, 386369190, 406897777, 86071791, 334740115, 294994183, 474950626, 782070321, 227398293, 544932617, 846536590, 839885863, 326351935, 495122354, 891894647, 614514270, 142192856, 657097552, 994848063, 204546650, 917633804, 572942238, 204361624, 330879800, 928252304, 232135561, 159779711, 69887715, 262657383, 334443820, 848504803, 383717117, 549037461, 934261689, 66234789, 700093421, 967345944, 530611358, 180074065, 598755669, 641420366, 499402897, 615366957, 14404977, 481599152, 797640522, 754216747, 906697183, 141555648, 974100599, 221911217, 859985977, 101889637, 499243521, 185438234, 367400660, 282847004, 281924546, 582432572, 393624664, 643572581, 495174584, 735380798, 357530683, 851098862, 535980201, 763148777, 311735336, 213690241, 909167712, 877223629, 801620941, 606083110, 556866742, 682978406, 36577862, 269798307, 937698282, 572007951, 208896871, 693231997, 933590046, 700408799, 518010386, 636457583, 108305469, 422922103, 97295812, 983865622, 438372178, 557996945, 967381131, 978520220, 670113151, 48968240, 727141393, 899593562, 851799033, 281486583, 606455000, 860797616, 902708922, 686239050, 345475222, 650715359, 663947003, 285565396, 138012101, 147707232, 56969585, 239799861, 627819429, 897407157, 581241440, 408251316, 734642967, 240967204, 353100028, 780546809, 110882017, 670626938, 700119532, 22370689, 953074123, 907502203, 95644726, 191448912, 55948720, 732388441, 643642420, 469267991, 349463508, 873293881, 834920028, 803737878, 383127169, 894921138, 941931849, 781039917, 741215541, 7235228, 213088233, 495176234, 206972809, 880323643, 490085694, 755638505, 94304704, 700145504, 23508663, 47000444, 32897337, 897539811, 149710899, 984075498, 743628764, 110477779, 447088627, 960876792, 412817825, 208744510, 237519718, 563919747, 315233058, 632932982, 891860283, 740260305, 644645775, 432961393, 141974206, 437892664, 171940148, 619670563, 560143943, 808533726, 28184448, 65485650, 366863766, 970453557, 537258463, 407315164, 414441595, 495895830, 649490933, 807463901, 837641927, 139245284, 212908525, 449363689, 918621370, 459389400, 790734653, 941655118, 128778209, 655627454, 222450824, 755496712, 757242406, 22586750, 111070314, 814835255, 524802374, 810003202, 988581898, 694907444, 695392866, 698119479, 724640509, 862782189, 217883681, 75416894, 974221731, 466688521, 391773817, 281922520, 852980024, 311291076, 765799297, 410048052, 574575591, 869081242, 949911356, 333905218, 37614250, 545141734, 888851530, 24276806, 807269269, 707666263, 763952618, 303548059, 685772696, 975745712, 616732107, 332177230, 122060772, 135172359, 896322906, 175955885, 346087722, 504292389, 522364788, 563399642, 676462605, 155893070, 766452104, 892359825, 412870811, 320981275, 736642064, 201866765, 315794294, 56743500, 782192350, 598895844, 494573518, 69907768, 868452567, 428342738, 912252605, 785695509, 433402358, 65404401, 177559151, 412140735, 124911753, 981517559, 278144687, 626086243, 14989769, 429207003, 336166237, 725889961, 930617941, 519439987, 591579269, 368090898, 790653337, 726060600, 910171834, 921098332, 843413398, 3362282, 600273918, 61293853, 692522860, 80990327, 885355046, 434682053, 344111777, 39834551, 963104671, 915831108, 204183439, 846634809, 695117933, 917774901, 124826894, 773468123, 955795412, 659447068, 484519230, 993831111, 495337028, 495628239, 457358786, 970554532, 770792860, 95161160, 198274693, 640141524, 691169707, 14068046, 402666654, 146879278, 62185035, 578238287, 407392727, 832194418, 270935239, 470099754, 493609293, 593421474, 697208634, 433057629, 319110608, 109456988, 13333762, 722780978, 540846905, 592456160, 462735117, 276585559, 996516218, 891977060, 120173366, 35495608, 554604049, 852237594, 740979538, 298660171, 928892501, 741709169, 883526569, 588768735, 130790785, 553966865, 719253549, 257847966, 23906144, 439230476, 707391866, 33665113, 330519429, 681582396, 777588530, 464055137, 919128228, 521196583, 185241907, 931423425, 682428935, 970474687, 132143468, 446622245, 232006361, 976919891, 642485173, 904237108, 75783415, 834453521, 287566073, 848811331, 242824651, 159191631, 813369006, 987882404, 505314848, 196463591, 433697513, 740145838, 369036491, 634556322, 161042568, 407083954, 532185802, 78203046, 19981671, 616659647, 406913588, 14190192, 28039431, 546384191, 675997648, 88821882, 44525557, 515282293, 333337336, 436825655, 76694281, 259089728, 214548194, 994875613, 877323630, 670856419, 717737768, 630840920, 562570550, 124542711, 276967883, 919551121, 576950569, 604005030, 471697009, 624691888, 701007353, 892045194, 763239310, 722263994, 392445587, 733509562, 474070373, 186472077, 250743600, 833348324, 68106958, 896230119, 212044273, 949455128, 606935870, 376471395, 918606364, 991797010, 998759492, 81738875, 991563514, 995644137, 247163503, 251791457, 13846757, 949593091, 330671330, 107276822, 330798791, 107684962, 330949118, 288298650, 153870419, 980213068, 671741558, 488828496, 714123790, 667655822, 827033708, 590584939, 23869502, 321581515, 948893076, 424722815, 406918623, 472372940, 865056763, 288876819, 741656924, 543250405, 498050093, 52517454, 740673251, 596248162, 336723577, 409425081, 580798538, 293950247, 15169248, 732111451, 306919863, 524384872, 939049919, 878883465, 921683720, 4810156, 729234380, 591489936, 347683349, 538474902, 762613123, 503999659, 73083607, 110948475, 418712173, 815335729, 684376923, 692192331, 317480708, 532045421, 411172883, 516103591, 326381418, 216796452, 100039767, 207977247, 506922836, 557188769, 706887013, 609574691, 605372815, 298311539, 821594459, 490369974, 434490741, 752944926, 400848105, 34828308, 993733006, 25986363, 667026526, 508080553, 866767202, 758953271, 332149752, 867816695, 719696429, 989891005, 526002007, 871621434, 797395164, 556407805, 798900792, 62544088, 842153453, 479167414, 964180489, 847971974, 994036800, 714667808, 235089826, 944902560, 42397982, 518278387, 553506584, 16357564, 587903041, 304904836, 235622340, 585007138, 992481632, 353837128, 227579319, 554502724, 517933294, 879396737, 962820668, 611050710, 813430340, 696635100, 711475569, 836738294, 892582517, 839323387, 323933853, 495895965, 804316615, 784005455, 716209502, 147850238, 837560716, 281988972, 752258644, 222505967, 730803087, 733359364, 290371316, 996533210, 824750972, 226118012, 443187110, 633839360, 417846335, 73486899, 95643384, 957361305, 162396508, 308709424, 470708111, 385473779, 626471594, 968390208, 375573339, 755902037, 12626147, 62053850, 255738916, 337477761, 623985968, 147806452, 739024545, 327703653, 496800183, 305353650, 175716939, 795376483, 304285062, 281057384, 138006485, 506309971, 689675207, 773527323, 43372931, 718054964, 896858053, 75211126, 243379635, 553078226, 884629200, 618411537, 364195309, 143471047, 646706157, 283849506, 876905858, 591287643, 445968154, 424614443, 525140660, 298279044, 523966435, 333500717, 611391399, 533281620, 281816634, 671862466, 761303224, 63800060, 38593505, 425393675, 345257278, 848811971, 800599580, 122265327, 113743110, 708437388, 736178159, 141081817, 591251785, 490654971, 504560403, 527249724, 252058626, 692526506, 533219149, 379017637, 109740118, 736158860, 329594326, 367210513, 793057644, 366464812, 735229393, 152933783, 372017047, 185527268, 697105349, 959879158, 462600842, 597239104, 464134246, 682910759, 904406266, 229983257, 71737388, 179658664, 772112210, 14764861, 970896325, 730608154, 66179634, 273623120, 421972147, 61184812, 171975203, 407130893, 967963710, 269250661, 328859414, 215882302, 89775424, 127766918, 900489049, 367904971, 533674198, 592891446, 164897630, 194673911, 705963505, 377871141, 851859550, 18581471, 695437942, 55362259, 206702772, 83705698, 293147178, 701382654, 658664415, 213212600, 155069986, 815265247, 312519109, 822815014, 54447343, 132454374, 557011013, 613348857, 631625331, 314305318, 43341801, 439024922, 892133421, 875961239, 977771573, 30332970, 129182886, 178409646, 224563369, 219353098, 546741835, 599502779, 919162349, 463283789, 567403611, 543881924, 604912492, 365495889, 635398303, 583093146, 880786282, 674157720, 604330663, 292265568, 622083391, 848162842, 239224809, 631698751, 498424418, 479771278, 891405879, 316211315, 313825511, 693149542, 204382258, 393116836, 735196639, 135448450, 10229765, 558908749, 104601096, 410689240, 338989862, 788901170, 563560553, 896385254, 831549292, 43038638, 848067903, 725006504, 682894154, 592098692, 928026424, 168799838, 814677974, 725711827, 632792086, 469848156, 719482480, 628347562, 502057316, 984719535, 781072861, 589646299, 165431564, 32184632, 248306992, 665754157, 124895296, 369883479, 223256141, 275164370, 789907416, 617863353, 856678479, 535077153, 701119391, 353504893, 374663258, 90418876, 451345917, 58356770, 19073090, 835120121, 590090509, 223934509, 826507156, 244375119, 216960424, 668956224, 460254979, 548489762, 382398513, 503152739, 432496547, 128062245, 845703087, 753497210, 810287260, 79210387, 983625869, 753020142, 394828746, 403774913, 233648826, 276616798, 590796142, 162143901, 615916331, 898253774, 389481644, 574617051, 904810311, 148427678, 186442927, 942841213, 167976596, 65920338, 68676970, 346416901, 332038361, 628956171, 253756698, 860926838, 110048651, 49579355, 250949597, 114620219, 257115731, 209285931, 805413503, 675389925, 498162597, 389517120, 664101220, 71831703, 552829358, 373999334, 619121017, 247068145, 317016983, 885908035, 999512209, 11760169, 878803973, 510902288, 657951059, 484109392, 480763634, 103988787, 132374470, 431930705, 831485221, 852236551, 333213476, 649969741, 174602803, 308685233, 20958294, 875834479, 205670662, 292879167, 110048643, 113899507, 741694921, 168384932, 46798392, 25294672, 551290165, 404453660, 273908039, 224646955, 422525809, 388886164, 20878703, 896341627, 292715735, 623519523, 200740768, 387660876, 787017295, 772453052, 438977223, 601407655, 335036931, 15421970, 570527264, 828356018, 413818668, 858943708, 937745972, 517050574, 900794666, 180078225, 971132664, 408464178, 429647220, 104159168, 669924621, 205459184, 223076105, 666255790, 732652797, 638156127, 830810391, 520446210, 419929738, 691808742, 424390583, 254756162, 346000580, 880426927, 637007189, 656146483, 319356996, 133963673, 535129209, 360915037, 547035119, 366901674, 182208107, 977471138, 487825323, 836380724, 196218497, 830253798, 559917806, 579297338, 549938173, 655880246, 453950722, 273942144, 481098822, 154334120, 119934679, 154682359, 183755740, 438763308, 844150979, 90160114, 90625002, 260557748, 537916698, 346010766, 129224603, 818541463, 566115779, 782554005, 362831413, 912523293, 376619156, 228289222, 667299467, 449579331, 596933293, 957488568, 248669913, 779741612, 647697671, 879323810, 699565724, 334071539, 495030698, 549816994, 881727892, 71072845, 888593966, 430894577, 366845664, 100152050, 942092196, 480977141, 641326391, 246399015, 717458735, 160153357, 52509642, 836498067, 670556464, 740952592, 644780047, 640645468, 188638273, 511834087, 969671581, 954522412, 901055665, 191120216, 44527694, 118268806, 949898268, 447756275, 24222328, 409448493, 285142701, 432960429, 76132002, 284109378, 652089245, 980763464, 343050202, 253767125, 621933700, 495218658, 39466482, 879355966, 323359471, 904440018, 981309455, 714164042, 806684677, 439563161, 733660082, 961964942, 409515951, 109103342, 840175935, 513411884, 383605614, 119160793, 414783623, 617580992, 269896876, 350736859, 750704542, 766385368, 634120555, 871649392, 592591991, 182201083, 976509877, 996454506, 461577216, 149221738, 914713448, 618481604, 932962897, 545465120, 509572898, 49193230, 335186895, 149807768, 508716765, 474709616, 975104490, 653340165, 152210431, 112223230, 984022547, 157870284, 603224376, 2074716, 76219112, 300819705, 620083954, 20504176, 238186760, 407481746, 330515980, 3781564, 346425500, 308407375, 54719612, 493689503, 143345439, 637618915, 883109640, 361036978, 756095716, 261645787, 832205105, 939982849, 725057606, 255172628, 450764408, 87541600, 616830897, 900224957, 69618093, 197023150, 806541490, 378230941, 76590766, 547552271, 815988740, 637718048, 440624747, 232388351, 321872231, 694911972, 853668016, 344752106, 176274186, 132022993, 271836663, 717010443, 266411393, 354875039, 528643065, 704218400, 764394194, 67153157, 92574896, 742563732, 673467174, 530258697, 370417047, 903747587, 756287790, 25693038, 867867552, 641091806, 111641425, 470333604, 86036095, 431634508, 909525610, 735366419, 601956042, 123766532, 431149605, 305490241, 836846087, 376877656, 97776889, 603194009, 802309334, 735823110, 157083158, 887065174, 200007927, 677613927, 889542250, 492185388, 8891738, 347734208, 974697757, 148791624, 732356581, 416632236, 352313211, 790480265, 43484322, 675840197, 282558426, 797293246, 691866675, 129759614, 845140022, 358082082, 943566273, 748638095, 81103103, 94906062, 999883911, 709841841, 404802890, 440623493, 795381537, 407967965, 696386056, 515710786, 194790867, 622314390, 999522844, 362655720, 530579746, 966556848, 209622868, 48560022, 892105791, 315501299, 349412609, 630337690, 118900979, 41835090, 896490556, 601306232, 563494213, 449413241, 123450559, 669556923, 639758239, 904427254, 867084089, 79821059, 949438069, 871172224, 709408620, 581373376, 810435923, 565317648, 898798040, 734154788, 296850399, 925818699, 647768557, 10221782, 434117985, 786971319, 338665348, 649609454, 878280369, 522435725, 15021525, 748909352, 3827106, 288801679, 647482604, 963320572, 246160583, 944899842, 291766593, 215144771, 321118828, 428165873, 702872923, 620485918, 571049803, 781892997, 29726398, 614092670, 24729119, 526935729, 476917269, 651738224, 573847923, 826919733, 415492667, 347433171, 958968768, 615239253, 625913982, 686118335, 356022055, 244657955, 436924198, 487636463, 348678349, 293599945, 370176095, 318855970, 551023764, 29011585, 934283017, 608380662, 967954544, 470173258, 389330322, 345811604, 958752400, 316646002, 34185985, 557471490, 901852699, 510498958, 214368480, 684932216, 852094509, 733403183, 957762294, 938476595, 724415537, 356743661, 952187166, 224357144, 17853652, 201017400, 705507101, 728907414, 501597816, 437493446, 244648515, 318005309, 596581028, 925829452, 522293537, 205411494, 238642153, 894228107, 194654155, 232965540, 454665679, 200380036, 104675450, 653766237, 618273774, 998255388, 136533672, 278576218, 89955974, 360400735, 107226745, 925495522, 39711086, 374178959, 364103817, 714149599, 968385214, 304646416, 971154997, 206065003, 916919451, 695139829, 316247519, 733603237, 878734159, 809387528, 216082602, 95767359, 266452472, 710661664, 277270080, 782477961, 802278240, 248932475, 379782207, 395647199, 577743789, 127971554, 513496291, 906728407, 835272981, 733454718, 669075572, 513377096, 464138750, 526916356, 977527849, 457043627, 7441688, 715298107, 605051446, 182235897, 433833104, 180377387, 317277113, 678427144, 779082745, 120399289, 88245126, 968026059, 305299401, 812790143, 259079704, 294470658, 574858499, 990798941, 414160227, 879243776, 930559055, 441483424, 923469051, 607815711, 363266156, 77668545, 100272275, 346249546, 212056758, 136829564, 807409268, 493740820, 266297746, 29443687, 166412781, 813822558, 747748535, 625365606, 487095245, 942178799, 693234455, 358238089, 901032106, 317892591, 131067564, 907832512, 866810439, 593540505, 593818758, 926107458, 93411091, 860784678, 30100525, 163532572, 80559406, 409422899, 914744673, 778745428, 117664542, 461166439, 990252794, 91470593, 151403393, 112666149, 542735982, 617888623, 619466990, 892344733, 500512162, 470061153, 519167379, 565388240, 858901740, 764906566, 446099617, 220158630, 82537405, 974223455, 564176970, 481875325, 322107868, 389556002, 729025771, 928395739, 378472535, 462496499, 446107943, 344281347, 114588100, 141309583, 435454473, 152318835, 61359904, 30062680, 97205563, 856175151, 21670368, 383527769, 177514721, 473993581, 924646535, 324054893, 989861675, 341100385, 700001016, 879544115, 679078692, 386784290, 856130423, 800526238, 201997407, 43685044, 421258779, 867044698, 905065267, 5949220, 294564922, 806743320, 624257066, 336137244, 852181151, 761546077, 19958373, 208545090, 65346546, 218532106, 447683771, 344273553, 593024623, 575032829, 716487674, 524612391, 968693625, 361014184, 321947031, 827333005, 810344025, 362924426, 717385322, 341009954, 125514719, 651942081, 741484242, 831026139, 457760367, 599023571, 209911406, 518200532, 90283979, 43898689, 275890076, 969921307, 31553964, 724565173, 133476037, 595211366, 367675232, 167311782, 243049524, 562098639, 491959905, 285486391, 521141771, 109488022, 328180892, 415674268, 31426975, 869601572, 773779587, 386448705, 104454802, 371096243, 1634632, 784658992, 383218980, 565727688, 27145286, 270464178, 345324957, 216273258, 702334298, 181604283, 305770684, 961680296, 23082100, 385685416, 834938659, 951525895, 486999373, 985899425, 97885349, 710568499, 340412593, 380568375, 865010697, 717101581, 119611558, 994567673, 766035332, 627396162, 457850961, 731380220, 196393689, 709304354, 632186133, 369670210, 3322661, 263608693, 522228537, 391078000, 734176518, 174870835, 7444195, 597772349, 904171868, 825421978, 348396433, 878106821, 240545630, 628507075, 849346941, 395739469, 743445266, 675195765, 178228487, 382284039, 765838689, 365384346, 897992385, 885847016, 49475055, 35199166, 149250148, 646979185, 383027684, 13398197, 175638431, 48625927, 401243883, 595490297, 785696463, 394997634, 395181309, 427070253, 916086052, 594926256, 810578867, 454486905, 498068073, 553994615, 461169961, 160132930, 551724311, 445581663, 549800009, 244850473, 422623428, 235301043, 524867602, 934660023, 705866633, 748889239, 206226315, 350420156, 363078452, 691489702, 283495461, 476514747, 662555839, 100968140, 438001625, 594185433, 756387180, 432939488, 591852115, 725642248, 257564312, 257973988, 120361168, 502249240, 167279630, 445032304, 754393553, 852343215, 11657315, 672142514, 907508525, 87820954, 870921537, 446516958, 631979128, 985688646, 395336830, 779395720, 861025055, 655734208, 407223207, 291913930, 99336987, 639696179, 104720792, 337608701, 337037049, 104845319, 653318270, 503786755, 754981713, 877183371, 242376387, 159757067, 104905386, 857177099, 282370710, 636941173, 123462644, 150465050, 466184765, 659512188, 696531264, 436657384, 720994377, 702032487, 475770440, 463076968, 84146961, 116982760, 147951858, 966142892, 411665848, 82437734, 34027521, 397833182, 146755682, 799322238, 330465584, 666360489, 627433003, 184867234, 767633198, 806445088, 11602660, 601121227, 886821844, 424457614, 332352223, 339234531, 379884662, 981458354, 2312578, 617269161, 839598879, 584207253, 304102603, 15073665, 231474453, 36947414, 977916784, 819671319, 755782747, 664719718, 62524754, 471432666, 807196475, 404739227, 554372603, 936030439, 354727067, 339271084, 863810911, 471043863, 778979643, 409414113, 687947238, 356010026, 530361549, 999778685, 519216092, 673728308, 44897669, 475743395, 81014045, 147330670, 471360592, 977557230, 201088853, 392495088, 203962053, 783582972, 13126783, 465098553, 71338568, 212817257, 23898684, 182061407, 725732528, 304007648, 376409849, 21285325, 432050581, 438641218, 168989823, 666490142, 648869030, 306306491, 205910074, 777587036, 454768136, 365231664, 151245515, 340624327, 349187101, 427556647, 604826109, 660768751, 508625193, 496236878, 346217027, 303169133, 173377520, 210413140, 528254319, 995625117, 815617807, 725666135, 744830956, 779766357, 532808546, 879759236, 240228511, 504484857, 667900578, 8503438, 87925043, 154223365, 367843285, 118354429, 503196741, 693259045, 146841246, 696342500, 862536107, 127491548, 636341060, 293168081, 200341811, 83137104, 166603406, 859467038, 444733945, 84282013, 57345214, 75190352, 333906462, 808090466, 603572083, 816930920, 934973595, 349413745, 786817047, 440447186, 319950034, 528329085, 538620450, 606035307, 605564324, 528106733, 630550120, 327362305, 541041141, 415579823, 224040922, 90139349, 17758007, 346434295, 995295167, 144817231, 686921300, 706701391, 248555492, 946736643, 628496580, 580503733, 721207935, 551902663, 627215512, 681015775, 362641596, 860802371, 599042193, 36631376, 925663170, 196437694, 215064489, 14672990, 954154455, 8334243, 822158422, 896569060, 394336943, 608345611, 651322268, 799487124, 853393417, 633039664, 718104085, 933449542, 853371948, 818334732, 4557836, 647653376, 832288639, 913669002, 893945901, 499851387, 684491691, 25384244, 52258426, 738747787, 915047827, 993928682, 992351597, 12350319, 97273595, 990054793, 974365058, 958267608, 34267714, 117279643, 416205423, 602473068, 577273610, 19781068, 448660722, 524707326, 275929092, 514131770, 559656734, 611813506, 666415420, 718279524, 269521454, 448115866, 611342051, 191720765, 562925599, 453939797, 461644887, 582282067, 788130381, 695118938, 803549960, 3308944, 646167247, 882464702, 916071004, 678082829, 798693556, 778486074, 307317080, 139180497, 591501984, 628978786, 10866771, 457231970, 694600735, 994951898, 872292925, 476304196, 129287024, 673034715, 939871257, 374338882, 813603896, 307881731, 688508317, 665026386, 844389197, 80011061, 3626812, 957794480, 650553374, 606460989, 342583471, 593498911, 751318289, 77578256, 583221344, 405690450, 505098940, 15397504, 596383647, 935390235, 183907533, 529060076, 104873735, 291037869, 752049218, 50656497, 6776306, 315251041, 989689769, 971155506, 327717640, 524389067, 548400235, 431447497, 212028681, 981506646, 960906064, 359255844, 121592808, 472434661, 538967177, 850474959, 290266888, 633889930, 458371561, 360718843, 748160877, 800487303, 747524230, 643779430, 455834565, 708330954, 229959622, 648927780, 384899304, 114175473, 955327514, 761394914, 165588035, 753148863, 171036767, 591415219, 223421569, 803459436, 504560912, 79927559, 599042509, 852419177, 615769195, 927824164, 573764578, 680501808, 132284047, 435507193, 728647397, 486475898, 498747511, 442002384, 159148284, 729943377, 570770210, 745575543, 534299954, 628436707, 55323582, 493305867, 212575720, 113638692, 559547856, 446015953, 641489967, 83657750, 455279900, 687643333, 63533337, 597856337, 247574325, 206371602, 179681964, 858733729, 895454057, 25776251, 240078569, 363120203, 520780269, 285302564, 377024643, 415000118, 327515362, 46043818, 593069159, 702847682, 837880104, 987843875, 661393536, 779337786, 205097622, 324380252, 992993167, 920532798, 108625105, 608554564, 877558681, 737192979, 878914830, 498586475, 694273621, 735123755, 570500039, 261562131, 416391334, 452863859, 224738330, 222806884, 534424849, 782984823, 851510087, 401120147, 264299348, 646466343, 218788696, 135895389, 995521012, 57494342, 781606484, 149736755, 903946547, 511198308, 795232860, 868968744, 680084724, 778438733, 979974119, 950827674, 799457898, 845106662, 863341437, 882553154, 226960833, 778254445, 760885659, 454695160, 485885360, 607130479, 633051231, 684272078, 825384536, 915092062, 675620567, 928419186, 602257010, 264363493, 142756469, 565035288, 726532464, 154014842, 198325474, 751908382, 72886040, 595396222, 448722896, 314720898, 690299001, 248944325, 141911054, 412665238, 536278051, 975831731, 813187202, 143368498, 531511548, 576682132, 891989273, 992283081, 479991063, 827946590, 530945144, 690345600, 536386905, 238999054, 884338988, 10200494, 821826724, 997316104, 296593005, 530376030, 77796879, 84241624, 196151104, 757201375, 845648533, 88761643, 212260655, 311198379, 345189974, 378479832, 362164437, 121600835, 963820292, 660643000, 316644037, 563180271, 883384499, 14737180, 738145235, 349991420, 753168817, 646169698, 301080305, 469719135, 329382329, 474905219, 435977889, 433129440, 420985793, 507935177, 456117067, 532345822, 519634457, 267398909, 896824925, 467231899, 798458022, 968842122, 837274975, 109685047, 995910609, 415492387, 357289064, 198076547, 564964316, 388138062, 300439133, 132078710, 190060348, 372411900, 713337320, 654485077, 638208964, 837229982, 440151482, 718172502, 49042387, 205507323, 983908244, 578283733, 736928692, 785705676, 26920356, 594579838, 657693158, 368893177, 613445349, 175004586, 706433651, 183795646, 81425945, 56313019, 684468369, 258324528, 590673630, 886514323, 77501260, 231426942, 403967743, 1981066, 408101670, 992463724, 838264471, 135023352, 943027683, 24585210, 118019110, 178934752, 572561391, 180158845, 763266893, 969441054, 347096720, 173280325, 447441762, 494523918, 214712581, 749879476, 336476057, 82330351, 622199115, 348128381, 194866334, 814614038, 654950934, 388513949, 480431239, 431448466, 667948558, 183846080, 304951899, 367947369, 468565193, 406870542, 528639156, 132983342, 509288513, 643257922, 824516747, 678598285, 626430209, 777367306, 136721973, 991787486, 259205967, 973121850, 852496735, 100670918, 567332813, 750241333, 937646120, 512285330, 306827445, 797012687, 874520671, 934374281, 856977138, 834433441, 339604691, 159565550, 860014374, 45403174, 685797732, 157725574, 838681028, 309111990, 305876268, 859133177, 132532527, 827433176, 168654200, 223644038, 384146616, 988652653, 353076736, 771460132, 405965424, 148037074, 238270144, 566203328, 544085519, 269397562, 331667823, 636263862, 851716785, 494357114, 738093779, 898295014, 312836762, 761815611, 155649166, 438636171, 938121977, 953338691, 452498352, 939462423, 270205039, 776446093, 505970519, 329848295, 30941019, 864146124, 394799014, 47548739, 281636994, 582777311, 382886674, 680606138, 509698003, 396014170, 467712321, 927428437, 917564468, 831216950, 598517681, 332646283, 891352117, 486548149, 408716841, 827480228, 18504957, 662384330, 124128810, 622985774, 572565488, 243902839, 274413870, 86039648, 730264271, 625020776, 623147453, 197550128, 505277141, 168832331, 864192454, 370058548, 388127734, 864127528, 312657833, 600752245, 685847699, 417404039, 808565947, 459295404, 549215591, 842426220, 373100642, 336742721, 570346311, 473679242, 648742189, 744022171, 670062236, 843804431, 558580547, 218461273, 926239402, 353319861, 441138293, 578291677, 783778027, 951782261, 999381458, 386102041, 935238268, 554314775, 618342744, 390830564, 121669628, 248577548, 267737870, 151683557, 983673315, 556233717, 862616248, 189215520, 351553854, 338196580, 475131636, 364301046, 743865888, 882336070, 398007729, 301058139, 99116556, 614678184, 886625749, 215048629, 458412270, 772696494, 9401282, 537592905, 85710070, 690539515, 763141211, 600678147, 300787742, 225315237, 855924099, 708096693, 50899619, 872484877, 786153596, 358529240, 737544039, 48893607, 493119384, 979337008, 396938622, 660892325, 904671845, 155187712, 676017421, 222317418, 348894298, 337473855, 236751641, 165515888, 131326710, 500417809, 131910854, 777239430, 584736355, 68991797, 632605547, 461503388, 609209740, 101884911, 278786818, 983647866, 363131290, 82451531, 216873277, 276337163, 611071440, 410397022, 749534485, 153560970, 952858599, 538473894, 358654487, 360551777, 845849826, 246475793, 515170585, 226778609, 810914192, 363993814, 900885165, 950669783, 532397999, 934958541, 205943461, 502745718, 758195942, 11493844, 689790176, 598279779, 765915012, 501733137, 540182157, 95995533, 106465636, 999174258, 996119697, 360729980, 757205837, 142028431, 847226118, 409167127, 471280498, 653823078, 501707844, 425043023, 302299735, 337209828, 916782667, 140700017, 231788559, 94715664, 183757961, 775350807, 301577027, 775786462, 708824908, 786455848, 192385651, 727151418, 744374216, 352438515, 129890338, 173090570, 703870017, 505025488, 571038542, 592548537, 193965703, 400387957, 185500697, 909928439, 316072223, 475981792, 697797925, 174358439, 456626434, 576755423, 757903570, 333379452, 919165501, 563737076, 511521228, 642617231, 224005037, 332976281, 699163764, 624470054, 889213358, 567282741, 851243131, 344264521, 579855275, 674546881, 399352421, 263397284, 612685527, 600376356, 423521952, 271414308, 499101706, 946713548, 158201037, 986463884, 119802319, 247000599, 433073343, 463040448, 686422582, 361392129, 210219072, 67529986, 54069251, 292819697, 892592247, 245039253, 110944130, 949608363, 370445444, 240945291, 81150492, 305652985, 597450108, 199098663, 893824422, 568803480, 720602235, 414814597, 355411864, 829089865, 561241375, 581509536, 797841608, 414225940, 567606972, 643243460, 226705906, 632636636, 228209649, 530965056, 179937938, 742911695, 790812814, 716656901, 476570555, 631776162, 948528037, 48818892, 874714469, 681967344, 41680954, 196596638, 680011237, 517114367, 883152740, 912426537, 404313313, 669616143, 166773232, 831504902, 57814637, 407467057, 429510361, 615858194, 737671183, 500589065, 562869090, 937519496, 101718162, 198726305, 762656958, 46823037, 970809689, 364673704, 147774618, 308801029, 438436556, 346863031, 807813378, 342956173, 426249651, 707974118, 982694123, 279563309, 321869931, 238329623, 564144310, 930332662, 831161104, 37988541, 440170251, 601463054, 655669307, 24371396, 153010794, 331210487, 110159100, 741721539, 386047683, 378832264, 177866042, 327453227, 296129950, 597860850, 165494969, 927803439, 703721241, 886932680, 22701700, 664607623, 70172263, 685265283, 259226088, 423785384, 421512859, 200249165, 792599892, 70248112, 502762370, 369999662, 353433247, 929991977, 151446699, 926074549, 359210042, 666964488, 745511077, 963992632, 583287168, 848752331, 794240577, 160847032, 334127945, 951514349, 841755278, 188418420, 220574759, 494759991, 111633779, 108475698, 811257559, 765415921, 934216819, 43784464, 433170200, 208203465, 109601255, 897394165, 857596860, 413318694, 759826131, 797147989, 537325120, 121494752, 698007853, 91779689, 186594466, 675351231, 429468458, 494792233, 141802896, 235725527, 987059024, 80748295, 801458899, 502354678, 463014999, 923503616, 692251860, 576600673, 78656069, 230387198, 300823273, 73739675, 142424257, 338165333, 330047159, 618428804, 233717285, 386851521, 768725411, 317745125, 688619338, 611928319, 227537327, 709155939, 114450870, 255084768, 656674253, 51873096, 829063794, 107185336, 237668182, 956632385, 463604694, 283101673, 929467238, 136952165, 478315441, 11544206, 399724393, 426151970, 531665983, 803531571, 980591222, 439409629, 11123509, 396999886, 972296849, 801639266, 890349912, 141220154, 871276478, 41984451, 973028233, 986789280, 649158354, 586142204, 830921119, 178852819, 253654141, 886521856, 775493397, 385642919, 560493560, 969623019, 686357415, 162299867, 776884529, 8507569, 675979111, 432017916, 35332560, 86768003, 9138827, 760089619, 470210756, 704276228, 466802321, 629110407, 852124247, 931716929, 163222250, 99118140, 274543425, 384030077, 589066898, 409904759, 686277738, 150317004, 291705844, 864324147, 365329335, 905710178, 593134069, 983478553, 710484542, 922044882, 662866375, 967060480, 10816215, 711761181, 204162860, 630220432, 223021618, 279800607, 37100529, 161583750, 344578429, 479207040, 449942751, 738670197, 608907113, 136931900, 673090990, 917852268, 493621143, 141711306, 244891254, 682019505, 847044893, 626276516, 44471904, 395941398, 5110443, 73498506, 30151820, 540298538, 298995640, 803024014, 979551090, 546991734, 807054131, 265284586, 461210578, 55483582, 218302339, 880102719, 810789577, 211669769, 532529383, 16515280, 581279398, 949788434, 682529086, 679084419, 863669814, 256190242, 609996364, 148866481, 464913691, 669199973, 434883914, 114883607, 190466099, 62983634, 940916997, 782069734, 793204283, 897385223, 826097484, 410861305, 516400659, 221862580, 75288213, 284569248, 282426620, 233009033, 484570195, 462459978, 842593761, 446340808, 564407313, 899866736, 651019294, 969952485, 459453302, 733088375, 153079198, 725277987, 252222478, 774354103, 995904966, 638775100, 596580295, 889111860, 353513715, 814627794, 825873762, 125238547, 553330253, 700913054, 994724975, 574187823, 337587797, 470232014, 13095371, 379065950, 124123144, 6694867, 721110543, 648540900, 521235370, 546974714, 590725742, 321019049, 437128981, 470381758, 333953891, 904955424, 630174401, 771548643, 679561103, 400387836, 289070742, 288329009, 900499753, 702727232, 804383191, 217376509, 714955636, 873559533, 762333942, 922851649, 782283459, 853760233, 954018105, 147605194, 923900792, 784693326, 673876237, 923770810, 501002024, 470520584, 148042213, 524521415, 824131883, 144692090, 499912155, 405076215, 450550329, 951917320, 36356604, 664034903, 912850617, 475830103, 755181567, 231652114, 956865717, 471529067, 857938124, 170325837, 565274374, 806226033, 409931602, 369805461, 239357290, 974351749, 603460410, 181417782, 293328712, 519460332, 828747393, 689970035, 400819648, 519927042, 934357040, 766168895, 431511639, 167034968, 895420847, 633689952, 604325195, 833325784, 837839712, 507018404, 166157782, 480568892, 769156247, 137920332, 335354009, 67230346, 921533661, 51103870, 195858601, 175692109, 377704008, 206424280, 159299284, 439412500, 278040840, 622698625, 498208754, 208464734, 356547182, 801108361, 724850608, 359773423, 301593316, 644444726, 701835198, 691651521, 726864148, 922900347, 154243702, 461623586, 593754163, 183676317, 667991634, 306609163, 191034714, 709436955, 379973641, 727410492, 392658693, 159186786, 659105002, 505992748, 192123607, 427242602, 678642895, 678854301, 285337210, 235445561, 264462771, 47361772, 429275656, 39274774, 104835650, 789415055, 321263618, 591476708, 698245941, 363095451, 247520199, 375410292, 401838440, 529635772, 331724065, 393451638, 433508977, 253988705, 972036926, 73419743, 31913155, 858698700, 606917526, 692302781, 530669171, 854248283, 462106477, 128273567, 728812614, 990012556, 953421405, 714668440, 127234994, 289474080, 282557987, 214538114, 887656148, 12649404, 117039453, 177357527, 493522872, 357090066, 496519758, 358283769, 210299376, 64089242, 693729327, 545560147, 996663402, 978693978, 464603634, 596116597, 146683705, 855948143, 214170370, 309848142, 151835412, 19307673, 591534678, 646536511, 379949405, 847213354, 216008606, 327025987, 53460409, 570630818, 881278247, 190190653, 293897146, 722095484, 464171354, 309691773, 649629221, 425537330, 274336780, 417045919, 518220305, 990113094, 597880040, 405349828, 432265801, 242180370, 54914166, 277984877, 487299039, 610125180, 152068000, 609051093, 350079609, 246699829, 912951651, 331072632, 624794536, 863742145, 601597454, 980523334, 69019775, 519735978, 802573756, 66492191, 604284707, 743246485, 544690498, 116030367, 67132440, 552928648, 928034804, 485422184, 96366577, 430535499, 509326116, 861676117, 199700762, 158773908, 436093482, 597072333, 813647612, 874670005, 85998143, 903952749, 50864935, 712354918, 864138865, 401413540, 594750399, 163724994, 509809645, 144170278, 906195201, 11340870, 15527998, 26241181, 940165133, 497672680, 9365029, 995489006, 945049492, 22963699, 961192812, 484667910, 728851664, 831013005, 242727913, 333710357, 723500214, 19252759, 670338635, 235397539, 370397149, 354683056, 882035861, 710421784, 790374945, 235899198, 471015756, 406572945, 237783415, 622658573, 30514412, 540136774, 421353222, 379243789, 958708537, 431168764, 890592148, 985528625, 831685769, 930411747, 284219205, 742493009, 596933729, 2113915, 362764108, 417081335, 368903246, 444986401, 145898387, 61969102, 648495254, 364237688, 531770854, 350640158, 6009265, 761331686, 916917200, 54034415, 198656735, 186300803, 331950487, 484396267, 773347918, 183608197, 929911497, 381295063, 515186507, 759296095, 492308122, 801560293, 88247815, 918667385, 127782796, 906903933, 220709416, 391963323, 474473914, 318815156, 904993745, 988284476, 541867929, 77711459, 806599399, 124852871, 463145227, 375883788, 584307795, 717631044, 989511171, 830977940, 711092005, 9084353, 108595584, 728014048, 981439553, 68992278, 636191160, 219001686, 378907196, 347253909, 591338330, 336020243, 414748673, 298858246, 525713301, 494655372, 351449866, 602688111, 828453122, 685460164, 629301239, 933969446, 482952808, 580270624, 324257298, 66914393, 324664948, 557618604, 705188248, 188921109, 634907155, 94167273, 486349920, 423135095, 100501744, 389423383, 662025044, 264289944, 979571509, 631982984, 942589154, 523301622, 961115927, 449050993, 368520682, 857581247, 768960578, 801768160, 675913906, 428336729, 246027520, 258383672, 946245053, 431798746, 23286225, 366434334, 668213869, 154323914, 680001182, 656106837, 983058155, 216314493, 27230043, 7929688, 549756341, 233780612, 267256132, 987072123, 584795082, 493114881, 776541710, 470377825, 6753372, 973904345, 807113201, 447426723, 144074017, 166444653, 920705498, 639694073, 124066486, 960372961, 341121403, 242059311, 910627042, 455587333, 887530772, 416425750, 570241116, 476885922, 574238158, 711067904, 917163815, 466274691, 12615297, 293422426, 749365392, 760622741, 392485187, 273835646, 234409514, 684340922, 233246121, 914974841, 822346847, 582721329, 571324387, 1898523, 101560528, 584892960, 750532050, 965379897, 787947252, 231909502, 651167061, 403364947, 486468334, 682356104, 762472989, 678236401, 809155569, 741024458, 791565749, 72383693, 774339292, 308175909, 446887608, 389246569, 759222306, 789394576, 79187881, 906136705, 386501568, 406266398, 40150687, 781705602, 55981559, 864486760, 892299372, 840210849, 221348200, 827247304, 468664623, 745823178, 60267816, 388784903, 905729296, 871510586, 141856869, 338491270, 467355857, 66752750, 413175878, 119563353, 956857493, 925563600, 407766388, 885372286, 373559821, 833657728, 70770408, 833876460, 969995763, 137497115, 93387925, 475286818, 759779292, 258443151, 476986196, 735626651, 43809917, 352835888, 951393314, 903506679, 706299448, 412031456, 816413383, 394544747, 197706427, 601796309, 857349318, 524440297, 738915337, 504198387, 697343264, 359155946, 832770053, 499785211, 920572277, 983135300, 331934986, 757493648, 579883866, 925883646, 296000558, 123226891, 906601456, 712978136, 517324424, 778795735, 798577717, 213673548, 933322443, 175972757, 21667616, 856919979, 131037329, 288208345, 240940119, 803791981, 369614311, 762712454, 959943748, 232683400, 162221800, 405551976, 502552324, 241346352, 239152662, 507007837, 874032358, 862726637, 718135748, 43200355, 293175246, 981375080, 550304032, 277114693, 915089860, 823633002, 573878798, 245930795, 589209659, 960571754, 397667016, 763198552, 367836049, 102450726, 922961577, 85058127, 978170297, 882228704, 67075727, 31869255, 950503444, 100731637, 939412073, 419305358, 87759254, 75630408, 328716094, 415889250, 53017090, 440380562, 881494693, 843620623, 185577540, 601391238, 402318223, 72127147, 689033139, 250704586, 27047738, 185701047, 556557846, 360593595, 15280431, 557391887, 27682532, 398650240, 777151304, 814060868, 62504992, 81567727, 652961577, 929401198, 517067511, 45660128, 708056171, 214639969, 534591783, 396791219, 864439620, 357473055, 721073951, 935492677, 363964128, 737052135, 28297171, 808158750, 461056936, 438715479, 992198554, 541771526, 70365528, 108079825, 141713226, 88786993, 27473548, 62691507, 158206944, 293874992, 921700671, 824287742, 473033293, 782530771, 48001340, 428913806, 540575691, 987555932, 540024359, 473305711, 610954562, 305735235, 37170947, 111296614, 402979452, 602959391, 634697880, 407306443, 793142058, 810897239, 253978549, 495098149, 602067980, 379796184, 130117648, 713167586, 806165394, 146820302, 21853872, 265905726, 476143937, 35141321, 146766523, 935366556, 419442158, 417099338, 473996363, 99284553, 736951909, 914582206, 726389694, 163842181, 212664739, 446614849, 841681773, 180336277, 316340137, 312934939, 167829828, 187363344, 536806044, 692295327, 125274475, 936568705, 478115692, 806750455, 437441034, 626321246, 643740495, 253021725, 801547424, 177447423, 305143220, 934652484, 238333991, 933637792, 891194985, 498352155, 886906044, 956221631, 431226278, 688179582, 666298415, 387141850, 528652910, 16947610, 745194856, 390349712, 412089100, 99670074, 333953632, 293470579, 385615842, 661594834, 788644851, 488573672, 70901694, 503979379, 126653809, 661878996, 295595747, 399857671, 318078524, 832154294, 23308093, 697341505, 390264236, 167129628, 757943221, 274292189, 875750479, 82776039, 881639730, 429000687, 329341976, 221098707, 623862541, 333124744, 97655005, 201719835, 810878834, 428659019, 134089708, 87599791, 312123340, 798290527, 860667760, 733830446, 976603370, 221998360, 876494167, 616291273, 596934125, 475628229, 511749200, 513127677, 895614902, 968327646, 625464263, 374604049, 150762124, 958238491, 511980105, 462129002, 224807278, 906475480, 207034463, 476364140, 90495163, 481007541, 30686239, 312833062, 450128000, 539174194, 686052181, 717115308, 741165271, 450048427, 538925871, 27187083, 789958899, 275245857, 965126183, 28309361, 513873065, 298405745, 324058167, 716152124, 960468664, 227174624, 207632129, 309075254, 586755224, 109997839, 507970668, 429729040, 914649498, 842923060, 772733489, 972224281, 979035251, 228207491, 300704510, 34674656, 71787856, 841520114, 299948583, 950554209, 398522722, 178840779, 141411300, 763916827, 153867862, 771680604, 609364525, 187328052, 38410180, 727243159, 916639976, 337980815, 395213814, 530471952, 383988607, 92649035, 811037152, 422967159, 473300710, 901630273, 304391445, 477902279, 609339943, 266199199, 322623682, 296853033, 661984235, 275821685, 300319636, 975797412, 748348710, 415680349, 578079520, 526172286, 825636767, 696413820, 791997054, 548480450, 666213265, 168051580, 255177131, 976832446, 842880007, 349599035, 880847312, 182230388, 512522048, 683119102, 599934613, 478303620, 704184745, 388146036, 450909770, 687837493, 520717678, 566127553, 820021103, 681010494, 343970017, 782295923, 846808921, 26169577, 950656603, 488051175, 79419575, 196069269, 513088121, 906255107, 387480999, 360719384, 978017263, 726524012, 192832504, 804105150, 920991987, 975153976, 799006460, 788527680, 149029691, 521136675, 603754126, 94194678, 661127899, 780497354, 198452061, 991995073, 594568081, 156746828, 179955330, 257705539, 82185409, 319134949, 32916646, 859100337, 596614086, 684320602, 709863301, 432992573, 656786109, 264650243, 647011979, 887846907, 871810846, 360471557, 416178213, 412964515, 289307317, 809352803, 379097745, 505400831, 794824825, 735266455, 645024869, 118799455, 580387599, 308435144, 357395211, 822961823, 864417642, 619262220, 356275831, 161466157, 244450993, 105841117, 70466661, 962396018, 865606636, 775901150, 316396101, 836034346, 841874191, 417339923, 210834760, 68453639, 276439653, 599337229, 552594124, 29264992, 353685596, 587648038, 660719081, 271738062, 845331529, 276273688, 172720913, 527004851, 540832601, 981448077, 667319091, 610994628, 436446428, 712444855, 622326763, 752932636, 185180385, 231791056, 14008042, 591840034, 52525471, 499646147, 444031955, 560955153, 822297385, 380383362, 790138811, 175191908, 720457970, 304652483, 266975830, 430906286, 871540075, 967987322, 587953949, 788539770, 386890440, 668044275, 664477844, 499899289, 540176961, 177012060, 858595877, 153792928, 254363920, 287006810, 456526798, 668976863, 282558037, 48388458, 971480361, 418534569, 629643276, 428682724, 547605031, 415978797, 42922438, 603027168, 218584632, 575515183, 376077771, 919131496, 183415145, 221560370, 998233958, 334620607, 751400883, 124478381, 569392816, 22904751, 840745346, 291589571, 22961742, 159707787, 119042078, 403701582, 129847336, 936742624, 342218385, 953018795, 632724972, 694697464, 64323389, 854085807, 271249057, 10991520, 542564870, 788412912, 549984635, 111496545, 757417873, 438232850, 4958056, 763940303, 648393233, 414255375, 899105184, 418013143, 282579348, 678686877, 245819290, 345089621, 585685666, 646246610, 421772410, 953338757, 730801049, 993067029, 852097145, 72571082, 352126407, 129385430, 220980900, 934324776, 207987118, 202340344, 164307678, 340533276, 439909328, 426473110, 675405137, 194557118, 113518042, 11413629, 819691594, 972790934, 587979037, 326235734, 549330624, 170931037, 189357608, 132804216, 102753078, 482182784, 411117467, 558004105, 721351356, 680876515, 250187302, 318717819, 787649146, 824971270, 771134133, 614712449, 623938604, 410262741, 145572633, 636561560, 132147109, 506066023, 603004731, 199522665, 910627227, 476025774, 667501652, 755187581, 782217218, 980179241, 261059759, 875207916, 725092134, 370075696, 3392915, 806086417, 360931630, 103044307, 843035930, 762278878, 565306015, 349366307, 964861730, 424379137, 91441052, 138468038, 268672649, 989445636, 842453063, 286624413, 597796325, 988108462, 534458087, 411033035, 403216376, 676218018, 840054539, 445657409, 284667192, 98268, 167040708, 262504341, 371823808, 561852099, 300850389, 487023038, 775812961, 336094925, 565054104, 775719213, 499910028, 718768283, 546523357, 727533351, 389104151, 148831174, 821951736, 530679603, 71567381, 332792359, 123192369, 512230859, 401155720, 803476501, 667510517, 249812978, 744220688, 526327241, 326547093, 394101582, 243905486, 459824330, 394669004, 930737816, 798273751, 996203986, 170572533, 595243813, 117945820, 131498517, 164731286, 734866724, 275641491, 291194633, 347927376, 80604053, 885610809, 221922112, 31227478, 588932022, 701096495, 533989424, 958209924, 4923423, 978891434, 740351428, 879779679, 643834715, 40286018, 274036749, 726094351, 949023286, 404488732, 2531455, 90555950, 2470612, 114814111, 723274545, 24890006, 324958482, 744249496, 68551135, 134528550, 408383619, 642509959, 295652718, 531554498, 474264682, 394952098, 236180021, 441043692, 660252942, 219850806, 287908599, 201187713, 325928925, 495616966, 670250385, 950207306, 555233885, 835906710, 701517701, 286034363, 121068187, 892924535, 418581613, 554073287, 744469099, 492327971, 591769150, 310046560, 1257394, 815095200, 388583377, 396130824, 622053618, 52782275, 774957928, 844562089, 429288404, 683669794, 178875148, 862935836, 388961822, 938552546, 593754454, 731515174, 634845449, 96789271, 547181238, 925339434, 612300669, 920649642, 620787980, 178870450, 683436678, 929794011, 906699373, 951644803, 816915360, 14861600, 778077496, 923447175, 736358125, 166661483, 471706388, 282812060, 324466669, 478125761, 730348887, 809038251, 957442022, 264135105, 555564632, 664452724, 562799342, 169882303, 749969258, 844744715, 554589798, 467465011, 759600533, 361249172, 495187561, 755947599, 777570602, 299748422, 248877873, 687806891, 390176859, 169227368, 682069268, 667143078, 990453002, 431174345, 514112204, 711143360, 392008394, 88713889, 154358084, 980161449, 188449393, 871415267, 512718844, 784371466, 241133357, 390187643, 713719546, 221943001, 426839386, 127011810, 281551764, 851756219, 279738210, 750256496, 735983388, 161177035, 417678332, 327208374, 322501381, 590641775, 288517056, 620926115, 380352337, 153881007, 278351119, 466746392, 37823667, 471568608, 232226911, 805138156, 153011598, 389978426, 361258003, 609734073, 254152001, 53545844, 690593762, 621251307, 893324081, 427938593, 493001348, 147806177, 983481223, 578425221, 485885153, 614435589, 453808826, 489537581, 285791028, 700520870, 155092116, 131757564, 845005119, 809516414, 25097596, 173043499, 564657567, 919985078, 585031163, 874549046, 796777420, 888919294, 480405450, 453500585, 401270680, 293862625, 696862446, 311969659, 257407399, 271097811, 200258562, 918349839, 196340952, 953086482, 513635362, 39201459, 379530984, 318132252, 707848759, 661581569, 176535316, 877604030, 377438840, 216291924, 334638660, 986387645, 46940507, 873536729, 721680669, 149693857, 122921484, 502315281, 798149851, 130152296, 474520366, 92612974, 923421118, 108225863, 972281031, 467305431, 682322975, 86753515, 548449645, 909050287, 555059704, 194374842, 8123375, 848827686, 366753355, 470571719, 677535785, 660350315, 578438802, 654731237, 659110673, 450310556, 15071734, 567675323, 604785397, 720375943, 108372654, 847789990, 529727470, 913096842, 345537989, 166256853, 301610610, 216490188, 559786951, 655994152, 154378079, 615723525, 861310950, 536478284, 720204844, 578168619, 841715727, 496723359, 973082575, 862025783, 938219182, 468008997, 286372471, 744046584, 393096745, 247035964, 996418099, 370917175, 772650924, 681371515, 506808893, 953147739, 251023528, 676375832, 508751751, 155476124, 442906940, 329792627, 447691285, 69451301, 278951481, 259915872, 372789553, 283467322, 311853718, 157216590, 874143057, 752255790, 130294346, 821131340, 590916039, 891865041, 134361757, 85505535, 328238744, 13423423, 430872834, 247784686, 437048463, 409574283, 791880250, 484662112, 161724290, 556679717, 827805746, 995183020, 750728638, 619105362, 282111363, 958276098, 906726825, 660784931, 601779513, 501858804, 413932831, 98467542, 874823902, 251445264, 823004121, 230973278, 776925449, 690393963, 734038609, 972499506, 260030835, 146551427, 773731914, 198791045, 116116812, 41610592, 838326329, 733446700, 157788744, 890137823, 88215623, 297787313, 464339143, 472969850, 906625515, 774897419, 41457172, 362060370, 578431091, 782866515, 961377361, 54634834, 977263055, 653380045, 931959505, 490829525, 501737619, 477266496, 884402125, 178984332, 535260308, 256609585, 494226580, 281459127, 203014711, 368800339, 866218460, 511523893, 981412971, 9075410, 955944000, 387477736, 435502841, 324599248, 982902252, 323894695, 925580937, 642048637, 999829548, 712274858, 913150984, 446986065, 8288143, 464555683, 896244230, 259402838, 392130508, 644793245, 241533118, 13253199, 537603738, 417882143, 748445963, 462160208, 385446319, 643905508, 738020166, 856486272, 854817954, 882298622, 502300252, 829204866, 548914666, 895467172, 691509404, 369378304, 92330050, 865621645, 357017046, 125888383, 791703404, 626750369, 993643623, 437509347, 458597573, 774079507, 650622610, 58548035, 936846032, 536757365, 150226671, 335948145, 315488569, 682048981, 26836323, 138369083, 299919937, 47118781, 593916424, 571204292, 971200262, 380343542, 826576204, 684928929, 409871288, 188877463, 179867949, 810762097, 499328905, 517145864, 847929490, 642766855, 990193720, 38119351, 172730388, 926979018, 872780453, 595677029, 987395636, 220152550, 526395859, 687128275, 131147580, 525368419, 586880885, 232748077, 329910361, 478563241, 42565558, 302327521, 583702658, 942946919, 222204202, 597050125, 517037921, 330782475, 467364709, 779091016, 15844829, 951285976, 411846237, 71926967, 301246393, 504058257, 745829323, 780097506, 28205773, 94105183, 178339193, 537824636, 793834200, 437259646, 524809922, 972687114, 377070861, 462748252, 191062318, 579023505, 863237741, 245555130, 751934328, 328570874, 850547449, 100312742, 938863462, 124415502, 607322095, 270968773, 645877140, 567473419, 986596884, 899994225, 974504867, 196296171, 45499291, 155728110, 857128700, 87148131, 471802039, 900310235, 716619075, 950737831, 628961864, 279784840, 228972879, 16337180, 125981727, 271388089, 842620461, 774486106, 819964779, 45528010, 669904881, 16239723, 191137816, 142227607, 118132678, 819456584, 274650199, 776339767, 251603610, 603550959, 758649821, 359103773, 482503393, 228293623, 96597009, 903013240, 756372491, 7134590, 790357300, 463219268, 919100998, 911303149, 14192530, 678494767, 695308453, 313539666, 488083581, 617863705, 485591236, 717496786, 771866713, 282349638, 41847827, 248484820, 478263224, 255993300, 200628052, 126734783, 432013102, 110849941, 703876814, 558268604, 297298796, 692519056, 928458188, 479526342, 520638979, 587269797, 201459897, 139294054, 45473272, 132927904, 243913094, 949358711, 256537744, 936594520, 634649786, 369169490, 347808550, 195482247, 853618990, 455934362, 299995164, 490386239, 153382828, 32143450, 216880981, 887236839, 67578928, 951110813, 963682685, 238807881, 914556731, 637350586, 428619533, 334816146, 773594258, 26109762, 837533713, 591658157, 729817446, 379217642, 822155480, 449166083, 104122697, 438159301, 535224381, 802761948, 708455954, 433691540, 90626591, 513334360, 830158353, 339076399, 744978330, 277590371, 594261577, 733669221, 904009882, 489173766, 633802509, 177938739, 707726145, 52742668, 68486491, 742063329, 80505044, 378012297, 25853234, 743071566, 516444937, 204801803, 407642343, 617942835, 694735975, 724494094, 220117889, 259076437, 729790589, 679150026, 141243801, 79124073, 751403367, 697860721, 360382496, 358005955, 20738088, 281878289, 366116899, 295476437, 543213432, 22119920, 64997926, 767546291, 474630423, 830116295, 361747894, 677346670, 620565138, 836807131, 514845467, 595555433, 115782134, 716786445, 375896230, 651689655, 417417387, 101205181, 187646827, 975183237, 72972586, 252266537, 546279930, 390754982, 284802677, 771938401, 813311340, 94074517, 762267662, 775752385, 419432974, 225714567, 263460328, 454864686, 874717929, 441569435, 716851698, 308650990, 390309595, 549925002, 849776401, 353430192, 943412014, 643134444, 659245429, 892069974, 2036719, 403721836, 12779992, 774327945, 26636396, 442836897, 61997318, 18997070, 116353290, 848753600, 529633824, 582870453, 111264346, 688830723, 435137697, 941996216, 522362322, 546175759, 59911241, 433972992, 362875888, 718437872, 723056836, 185028147, 989039335, 980175020, 216767761, 322611131, 737323459, 321868807, 11748773, 297832283, 19748376, 210643485, 899067492, 450269061, 357556500, 610198399, 651025971, 576375613, 926385159, 458116411, 279104241, 389272768, 121003084, 67202216, 84063888, 802918419, 183129665, 132978423, 534756686, 732486863, 707706036, 204640734, 145071999, 649985635, 482022432, 800103829, 305761168, 479694149, 773228862, 100605642, 401679917, 998700582, 981776891, 707830548, 692512784, 93211745, 756585053, 625060402, 373612307, 632330131, 93771928, 687089183, 838095256, 399191247, 449911124, 152428876, 385875921, 658975992, 955892088, 157279678, 600271353, 413457884, 859293642, 352030943, 537327693, 131280170, 111737265, 744006949, 720017971, 58336296, 15006432, 92951046, 926112419, 927555499, 935176184, 451887402, 489250407, 521696604, 215486494, 332580986, 41331742, 270523215, 204467465, 439538846, 530975376, 593308807, 691828287, 255613653, 497466052, 367579592, 64039546, 839625876, 297567726, 639170911, 690254049, 249672768, 627067476, 735335283, 511665495, 37774305, 497745485, 162621984, 864776468, 146124747, 851812520, 959792435, 383259023, 40846012, 618486467, 660011667, 679461091, 165849620, 262856359, 229421293, 449376220, 532670512, 467726748, 702782623, 876002162, 684144349, 446534283, 999999196, 393344042, 981455194, 375416658, 360962350, 367649789, 790532236, 565034678, 343470097, 679919368, 269138160, 849899874, 648344604, 287756300, 884853289, 865230095, 256537082, 19648508, 621635970, 510717093, 958053518, 545356713, 500704226, 595817079, 929888609, 59032031, 105366516, 691105089, 311720219, 550486451, 693023181, 939932563, 737640037, 339276303, 206739082, 306540353, 482415383, 3205268, 644969116, 787426353, 695636995, 201356901, 547102821, 633185388, 814121620, 358470807, 518626369, 549659249, 956624564, 48759688, 191781605, 300316051, 814569910, 522463746, 254421672, 20254736, 136265497, 467861549, 426634702, 777254667, 289853680, 576015960, 717274024, 951533610, 829410967, 362223130, 20608722, 136380333, 725392293, 682280584, 314585414, 199602692, 571494073, 798687630, 288663442, 980393201, 671033352, 883660769, 663641131, 481861494, 218971061, 130743392, 327601665, 305058655, 711263225, 136585461, 673418111, 942367240, 477209550, 678187975, 95848488, 522964944, 869697463, 560363942, 561708368, 72832409, 69815756, 742535227, 433462196, 709199387, 558529342, 241080095, 357416856, 326505829, 884650300, 203525555, 839272999, 768825430, 12176373, 908593599, 537656780, 540077701, 25566893, 196396175, 721605584, 486296580, 844785961, 643051267, 600657178, 385790286, 808336560, 64123935, 115106719, 489188881, 856182499, 42738444, 983368601, 284110374, 398362587, 974748281, 574972564, 793202443, 983079539, 138303208, 229650048, 871766526, 252986441, 729815916, 932047440, 56550270, 762273905, 905785993, 17393072, 78905349, 262443216, 440175144, 396808331, 677264433, 359293236, 730902148, 232268854, 108203963, 891299261, 818673541, 428848448, 957273323, 297111403, 84505173, 527537196, 148915880, 320532075, 678243586, 578307086, 379863737, 638780895, 321487799, 216845199, 280954129, 261997874, 658270901, 37226119, 665324711, 643476917, 834557259, 817254001, 600897164, 117981025, 1350695, 33478713, 899659392, 983436715, 857124377, 716963597, 165666902, 395737139, 942259926, 340438865, 313848845, 419383166, 637875235, 979508907, 641999762, 791805572, 391827635, 405513209, 590762639, 480457973, 524003632, 901830349, 224111220, 13138405, 720416077, 625748758, 150281364, 686458626, 709518159, 876184925, 708487444, 545520179, 194962862, 55527446, 164337522, 300702182, 776605732, 815660057, 138845289, 207734089, 388167871, 576807428, 436800567, 23898014, 964133436, 199335351, 988041888, 592517133, 223981643, 235638921, 105496187, 776089399, 90348009, 11000220, 977279367, 181353682, 12707504, 202969362, 429194225, 139024763, 75685565, 889531337, 841303289, 766028027, 202332008, 451942346, 397598904, 221905427, 579439399, 282294088, 399237747, 315000690, 648183515, 541613465, 908010934, 712880434, 851247718, 782855439, 189166428, 856756552, 949380887, 585744402, 90960815, 925496343, 508583654, 722439449, 768001407, 709009085, 707599250, 297526241, 377296753, 165948270, 875291044, 38808972, 574214609, 720691650, 37002769, 789066184, 546948755, 932798921, 245816887, 879422206, 617910129, 789189297, 690651620, 494094089, 711318338, 963947790, 381138687, 250274084, 115910365, 691579685, 447779778, 423830494, 98085887, 456193835, 990160472, 612865203, 257189395, 898084648, 550566612, 504000552, 713020849, 565982889, 1141883, 31528922, 267773647, 434410871, 889561841, 548160928, 916666102, 304969886, 676635724, 454117669, 212032787, 129107335, 919904966, 52817372, 785116510, 189694129, 885207068, 314009122, 93004001, 687789189, 589112768, 818363032, 69764706, 126229482, 545017197, 973899907, 600415423, 868737140, 642393628, 893762421, 945340593, 212989556, 407965179, 812149993, 708791353, 585801825, 968358359, 179318410, 813764409, 75268489, 590357938, 386965693, 615470896, 166865989, 832425379, 784674175, 564118511, 80231472, 398330097, 183136284, 507849251, 899704594, 103706921, 136743306, 645714830, 11222364, 302786200, 807291601, 642013870, 758049414, 63501258, 575387401, 90076122, 516480583, 33003591, 104181025, 574500023, 458376407, 243591678, 326146722, 454819804, 747753537, 365986764, 162846032, 80862701, 225974186, 978749604, 892464379, 346691821, 322921983, 431342184, 872330006, 170872311, 488237581, 7443976, 132049344, 203472284, 424125574, 237047856, 210186701, 982127071, 959348226, 534094831, 853101140, 856430611, 678896079, 643465539, 59236088, 204869285, 12050584, 499663092, 164785699, 430114618, 869187152, 645157038, 695394986, 85208978, 215060727, 700632722, 137025543, 681618868, 679176283, 999958276, 306072546, 981303669, 338335290, 395554243, 345701066, 171444627, 421317563, 19379110, 683424514, 94334206, 569433445, 929880443, 794136329, 188254630, 636467393, 888474575, 782842339, 649375519, 672678710, 944097282, 618909820, 288353478, 671397387, 65800656, 294920769, 467037655, 548186831, 343035422, 812094062, 794394144, 80028498, 948195673, 872499243, 205743384, 475870366, 416517908, 526167621, 741565698, 868467649, 661803806, 459476886, 506916442, 428978394, 743942428, 45046477, 390325110, 62405740, 230098036, 460242994, 78490425, 504460085, 667453170, 816373064, 482265350, 753482161, 600999055, 616309486, 613293271, 660705343, 349721626, 357330617, 989121731, 280166981, 402426814, 61065962, 884658146, 60764701, 247152646, 33742957, 888880363, 590361701, 16369248, 996437732, 97245003, 573850624, 618109544, 731590420, 778787670, 752398229, 741603582, 757709858, 747408926, 395822774, 987122179, 732274159, 169055944, 327320650, 372572089, 448460, 808127319, 61633986, 431201177, 957524910, 828667189, 56837675, 420866030, 26050966, 126803925, 458159369, 566356162, 808896600, 521672715, 778810756, 236333182, 848575073, 113351325, 76059024, 643936984, 308716528, 98610060, 176589179, 407811817, 548157618, 466788798, 717291467, 626820764, 158207612, 248938860, 299059301, 37092815, 72701451, 254982871, 169056800, 402739328, 59489355, 166840085, 455442069, 803560038, 201299294, 181774589, 931315071, 58584365, 449814323, 274741417, 716982440, 230012023, 946866003, 124097502, 622501088, 263534632, 556517506, 127548615, 16366954, 183610470, 316854343, 525781907, 289520937, 496101715, 309295980, 915307295, 451674681, 938534478, 767087375, 77641895, 861679043, 766335191, 337970583, 291616512, 208379468, 379793749, 696010849, 265331389, 948207864, 903565213, 913265978, 35933839, 231733031, 441950510, 951887674, 92384025, 659165375, 392372804, 582784917, 565445160, 172571296, 193255622, 476596774, 246546332, 722389431, 19476346, 899325699, 61674044, 677516724, 994332483, 163210242, 346792134, 528461965, 699040931, 278371069, 641319045, 592986923, 487963026, 951098798, 85469423, 8047577, 679875182, 893382019, 916525574, 225389879, 930540722, 323595398, 411927804, 376126672, 639404124, 768272460, 579235030, 419811825, 751629823, 465360898, 410740025, 978308781, 305122651, 987279604, 244935396, 487657072, 456082828, 853414225, 826571293, 429957323, 839119585, 741642167, 585951535, 700482806, 773601062, 737924222, 182975893, 968065920, 456717813, 644802349, 362963578, 101419941, 476656642, 858973609, 533141308, 577603644, 955410115, 734783472, 191065840, 587208526, 359726760, 565000893, 382426068, 24421279, 247294018, 974357826, 703190141, 655243251, 823003042, 47288820, 230583661, 841632891, 650580400, 450833480, 756808438, 97060861, 149283528, 351627525, 112858264, 669128205, 766519877, 711966535, 96329518, 811243328, 193911986, 188220869, 633280675, 457612410, 704983486, 848808634, 293232375, 803518461, 571537064, 238757713, 115447304, 16573583, 391165287, 28487875, 136151470, 902314358, 73975760, 225355377, 397146515, 675575836, 942901229, 671788458, 911593222, 203648090, 21300990, 941101506, 893362497, 599974571, 129334310, 313955346, 2656575, 286393241, 977596033, 465063655, 881038506, 574574217, 956070303, 209626034, 448993096, 51213232, 947156640, 421422693, 745336290, 812266437, 785929970, 965810876, 477673937, 699347361, 420027059, 92416359, 539506737, 512760917, 412499576, 430806047, 487980995, 861367356, 780982747, 946532647, 915835427, 747111395, 487410251, 464470371, 823708845, 774191040, 566777714, 276844998, 233568398, 263766479, 691165673, 220020219, 124384592, 432909711, 685411092, 252855646, 755045894, 841523006, 674108339, 473582140, 438277827, 171175329, 941054441, 828616330, 513084195, 521958848, 84896447, 335778611, 986496577, 907923831, 541052250, 904237992, 156082213, 666980668, 553612839, 504161420, 427112277, 884998687, 995448060, 869333817, 351255617, 736223932, 312835464, 479235068, 829942305, 513936194, 94077507, 964142972, 834252503, 364512573, 769628703, 368098647, 877113156, 23513630, 420789227, 496222644, 448476104, 995000223, 348752558, 849366947, 690864622, 338219813, 133546031, 381052893, 826924754, 976706406, 672211488, 250188387, 900462702, 101767912, 709835300, 845631066, 213481678, 761842281, 127261674, 592507598, 769683211, 718451061, 708268286, 544399769, 759001797, 40242327, 25842798, 269037047, 416683230, 134001186, 867811286, 197300315, 848925371, 33605972, 221641759, 374493900, 735201617, 572288890, 869039445, 795857881, 587929939, 322363467, 77230136, 162279779, 972743467, 935736750, 301533032, 525270478, 750002429, 95003315, 978308002, 689785451, 370947337, 550213713, 949411598, 845694673, 4568856, 106963359, 928303334, 765732904, 363179687, 84662144, 701818157, 594757362, 199964833, 479410117, 544590732, 845327842, 493614776, 136614545, 25562998, 672063432, 263122297, 431075316, 202697764, 543902974, 535756736, 463671837, 805022501, 764109803, 917490471, 922310654, 56554744, 644306556, 869706559, 363208328, 635368006, 816961375, 250080107, 127931943, 121567899, 141279433, 207006853, 948809070, 280614639, 836396795, 660992248, 955190490, 570819265, 639078831, 866217280, 588060351, 757611393, 927552310, 515378807, 327342330, 428736248, 554816954, 460267458, 803095932, 664871583, 217971877, 826933215, 958084659, 981503061, 735166220, 888398614, 715811523, 683976939, 945690350, 618577520, 371236200, 215348748, 493882664, 620373478, 589828470, 361219825, 957451814, 31530454, 173557197, 900121467, 265479510, 377281141, 647249855, 881773105, 313149068, 518745675, 55823166, 507561102, 231796583, 13412473, 854464632, 579087443, 868327998, 647303648, 404816546, 370890919, 417286602, 922108879, 783932186, 90937546, 767824838, 747712342, 160999003, 523503638, 338360005, 36619996, 551598471, 361738433, 234367079, 568677766, 498886406, 954331195, 246266993, 923767609, 601782538, 894351298, 644037305, 370849977, 208768776, 423946930, 66659839, 608102802, 934838715, 577236441, 980768480, 66560064, 764043763, 369378236, 210522590, 771069069, 230089261, 204528106, 47765016, 890175367, 280495079, 444771883, 892123537, 546911789, 648291137, 676124481, 778413206, 8810626, 289308721, 568354126, 566034911, 74231475, 696759296, 901032586, 376715049, 405710359, 388093148, 933649078, 152425548, 263583925, 62967777, 507080914, 311173397, 761366793, 917277278, 78771527, 734517636, 949373198, 49411113, 472208774, 919134752, 918796795, 555345911, 247955605, 380335181, 923428765, 911131046, 856362714, 128191760, 177168482, 963688145, 173227233, 415663013, 572629970, 315995745, 214210065, 261367349, 32394493, 961235016, 890234190, 168252459, 314441732, 59384254, 233885513, 677268198, 918135687, 232765821, 785017061, 589482804, 172969042, 208935626, 192471146, 455554525, 661621727, 63702323, 459729482, 71709297, 749199150, 5673033, 981364658, 871667195, 376568497, 794101951, 826131366, 644283307, 82521396, 344393368, 888711223, 884092631, 839702392, 237139968, 278869711, 698213100, 568068305, 588528923, 157525152, 372716565, 586421534, 175716550, 748172159, 782734743, 738689885, 52068108, 684939078, 517129612, 224360257, 538800521, 116637835, 215948733, 249792568, 833819771, 629783502, 526617734, 894307857, 865648418, 373590244, 768515949, 101876391, 575368908, 936661189, 160271357, 932448658, 16621158, 883951197, 940388498, 116059633, 694922592, 724092483, 239529513, 50687484, 666490954, 891310260, 988671540, 686257633, 45654965, 239236295, 42276507, 393561790, 428336367, 401176720, 158834707, 413730506, 512827838, 998444529, 996551402, 968766625, 688221194, 807303316, 710034741, 510400051, 678298490, 630674341, 761992844, 257970301, 98790585, 923125, 380683212, 661626775, 786908345, 717817386, 104808770, 371943829, 426489601, 860791515, 775038976, 68183316, 386685456, 481469038, 106550583, 501167425, 753351332, 342481166, 161032663, 197007120, 815289787, 490498964, 668195619, 110786341, 428705274, 298565555, 978453191, 462461626, 591271983, 643347368, 580940068, 317995902, 908576095, 186981526, 14324819, 841631637, 972334287, 926810607, 471828166, 577605658, 869849620, 643696228, 764724098, 21145578, 14284018, 238519025, 352375906, 704925961, 900193725, 354085121, 379381844, 201632445, 545431164, 247881718, 854121272, 174375609, 346114067, 721392267, 214691946, 628838978, 894116714, 406230582, 311769265, 970181411, 485181202, 163361424, 689952272, 354725703, 797294857, 208811764, 792624555, 381611574, 126206038, 569238566, 395424065, 651676111, 156627491, 671484996, 299332161, 737837718, 116255221, 565382248, 599882804, 460607653, 467279130, 731425715, 589789010, 959117144, 723501731, 516208247, 739133480, 229006803, 554550790, 821203046, 818978705, 937471500, 448143817, 787991688, 835188145, 117264602, 16467215, 21372341, 613134595, 786900329, 507450813, 385020662, 967223897, 674133840, 955838568, 307732414, 645272985, 423697433, 658770912, 878744167, 137766982, 526572938, 825554616, 292233647, 986261588, 718113442, 734407980, 430967212, 49135155, 623594924, 626710921, 54498358, 373306125, 240055112, 418468553, 813923262, 137148824, 386567948, 91167296, 109284395, 628642575, 493288121, 63259863, 455154325, 655278567, 256622600, 451764484, 78312997, 631401950, 120649925, 636756620, 470045664, 926837608, 210101796, 640523828, 330157772, 747336194, 544136645, 305631197, 709645549, 666972279, 61893872, 535096261, 439790260, 166635702, 911336972, 911975897, 739479142, 742675076, 133377622, 909508577, 507372402, 494230121, 335107243, 531080871, 377946524, 551506917, 151470505, 521347335, 808344387, 856758188, 220445958, 360080263, 277973885, 515573570, 60901503, 373019204, 206747034, 79186423, 38515524, 758268870, 819925477, 825858736, 490040971, 310775021, 223166012, 533979474, 658388335, 277691355, 72550272, 716709456, 688247388, 126746319, 802051689, 890580719, 936993434, 615500336, 460599330, 981552031, 630058075, 421915176, 248670865, 186596759, 461122723, 33040179, 262045131, 745513325, 250879029, 4246262, 700845043, 510691394, 953299045, 377216603, 882252120, 646042777, 639063217, 178386839, 850995512, 772291315, 329625950, 446669605, 648739340, 184677345, 104962248, 729775429, 882005312, 384903742, 746179138, 577022567, 970466923, 953311996, 854018173, 975112567, 59595162, 909744225, 10652801, 230736130, 742846581, 746692836, 77786025, 370425744, 591788982, 133833415, 89045920, 599047666, 246310847, 163902018, 465956269, 87231461, 837293016, 352954422, 468136717, 529945997, 141545117, 859226058, 623401520, 977536422, 233816195, 56598403, 576674687, 471884198, 257198054, 677224602, 470172574, 752799833, 534545563, 925355597, 165510643, 890243075, 273176991, 691265660, 950879502, 930047301, 377494854, 277104819, 731004131, 200262983, 805310158, 200694115, 403470485, 947846265, 857522827, 798243722, 835118498, 294151327, 513670409, 22066870, 263311427, 363111099, 391845318, 937385032, 233954675, 438844128, 179981597, 596649093, 138434257, 686925968, 148291101, 516182093, 848775931, 228618247, 673988658, 378399807, 520201838, 363942420, 321861351, 255719436, 251741825, 621016246, 592306806, 459150079, 646735536, 58458316, 301326441, 341742689, 458675226, 787656300, 837133771, 44480363, 781692411, 927558049, 436714692, 799984578, 176386648, 585101785, 713780568, 964904358, 330210038, 798202667, 514311795, 655929504, 917741077, 89312711, 617111860, 852818906, 698286242, 858275551, 911930997, 192537240, 952355310, 932109286, 62554160, 633573775, 335975534, 2146446, 211371943, 177952041, 263818091, 761784431, 452930492, 259700291, 38770320, 642575523, 493144463, 476875306, 399739150, 41494323, 196257994, 323192151, 867812147, 986699241, 584378389, 202726084, 688915918, 828936404, 532479608, 660678361, 973060123, 351016245, 218235592, 61197878, 228128364, 631426523, 762189262, 613362085, 547172186, 22943503, 870523017, 757902741, 326488152, 462370500, 651983682, 995307761, 476494826, 544508119, 727260994, 34049215, 31412499, 623411001, 954726765, 301570972, 337803533, 872981040, 365123577, 23151651, 976315832, 513514257, 831904126, 878026039, 618681663, 644496173, 474945727, 1220474, 179441874, 125098964, 173861717, 154309227, 976716964, 894501763, 805260242, 478639719, 967936993, 923220640, 243899591, 686795979, 206464236, 975848501, 713515927, 849680906, 541037196, 1359736, 533628860, 384320114, 960365888, 257686214, 279526551, 222101578, 79983407, 236124850, 953038993, 150204004, 218305728, 100793207, 839433571, 12633536, 915405262, 533124100, 283075627, 998639542, 433029297, 837818675, 921844962, 694137974, 573192157, 986715058, 494301126, 30451242, 434795363, 181929988, 688866769, 537127091, 266730150, 591983871, 498655996, 941777435, 568898965, 217894602, 466509053, 605651313, 804408842, 799200068, 492908933, 87754286, 545669225, 104356302, 673070185, 446348927, 677161019, 36305981, 87690377, 544887207, 634409177, 123403021, 145191438, 306309586, 628153241, 590344190, 671293740, 738536068, 859059279, 416365423, 979448976, 804472715, 9282398, 414004136, 362593106, 549113716, 805662169, 314361655, 561119147, 408627882, 338423292, 656173552, 35093442, 636716990, 419806107, 268047489, 800371193, 751821641, 833470176, 777819217, 44949503, 357893969, 951149745, 361788197, 169557118, 145397537, 160022882, 177800200, 392204646, 717203743, 928622621, 771993572, 50780033, 637712310, 686579130, 314977507, 123903505, 17676418, 709707074, 361017046, 672618416, 482878951, 444903489, 445992307, 215711705, 301661424, 66843468, 883932119, 750681819, 373142324, 175989734, 642049983, 633573300, 442417785, 978441943, 488447449, 342973703, 934581483, 412128754, 511611451, 216304344, 531617130, 419790832, 192706809, 597775817, 92704118, 544018642, 880797227, 657987442, 577285484, 960795701, 613180082, 251617745, 350150831, 558999632, 141666057, 443805922, 418481047, 683902023, 854942453, 272636184, 215324597, 64553525, 794653578, 140970565, 481158153, 423922005, 462408318, 702850541, 101088309, 87667354, 691970200, 565716070, 895709527, 275444149, 511822120, 327951884, 807093712, 420731819, 757994681, 229458096, 603151065, 367354262, 932156921, 840644859, 884542878, 690548184, 987163971, 186617969, 843356692, 934497685, 215763881, 518179766, 496720794, 701632213, 56442577, 728586945, 258940486, 66479849, 56854603, 772691752, 687315276, 171845400, 384498677, 687706217, 270874942, 662549991, 375250358, 524044593, 859443442, 393777032, 432042794, 263246582, 197980622, 55793149, 318769504, 571869907, 607082786, 407948316, 63993886, 12014105, 498421523, 868571512, 82315141, 916941164, 890334126, 119111371, 184818, 683388867, 385773359, 239304671, 545650805, 737862784, 772135369, 335887802, 578003389, 844647520, 974164428, 251921499, 121765557, 675647512, 701959646, 373638945, 797873087, 533131340, 575940255, 752242990, 89978760, 907663681, 189599055, 879268013, 69964568, 297314807, 285181750, 63680226, 589544253, 765391881, 584629208, 992025681, 322762584, 388041571, 318251606, 38776654, 733009735, 479456429, 65941852, 796591699, 483511241, 663648343, 394518486, 571669594, 309289280, 29290865, 561813076, 284164530, 283140272, 166222141, 52329764, 307999711, 480254952, 308852692, 912306496, 531852789, 474745939, 490648670, 439464315, 860373631, 292258337, 418935376, 487160509, 609563916, 661458904, 51664332, 585082002, 777512088, 231428688, 79481113, 398278375, 1673800, 582880816, 935779068, 429960320, 53925487, 90095740, 254509187, 646384259, 711688222, 903675311, 732521757, 733199787, 350142860, 709841894, 463498333, 762271045, 147841179, 858521177, 874046502, 282199391, 439963330, 233835455, 333465393, 905825268, 204285651, 223826534, 164896514, 524825540, 919021106, 139624847, 853850034, 757912031, 359438255, 91235454, 334022684, 276063142, 987297634, 59829320, 175405970, 850324118, 848092380, 489905184, 22097574, 337815514, 472228233, 598281711, 154451950, 75345294, 209673644, 807451038, 939632666, 845374572, 419592271, 906640291, 90082512, 356372387, 481207868, 759368282, 135220180, 411597741, 873734447, 923069349, 742800791, 647543833, 548174010, 541686413, 968835539, 480324536, 412642419, 805219251, 682085920, 717495393, 538301508, 332497073, 271920637, 617736765, 256611584, 195482705, 445945107, 321093199, 255265430, 898167660, 22440293, 65267428, 891786748, 804681979, 437000914, 340257653, 115671156, 299896209, 349291465, 152244331, 23398593, 740464200, 266701957, 371929125, 223924467, 257264739, 362903040, 411533770, 214441274, 829352748, 365181467, 908039065, 148982609, 819464284, 437531177, 856607224, 268468336, 829701692, 848119454, 720360274, 493093333, 694071440, 790820886, 384080048, 579373041, 553890274, 205171165, 522650359, 291544161, 514783669, 243380240, 353205020, 259107855, 834582425, 119016955, 69416506, 16725685, 784769339, 240179639, 808798025, 968794427, 483797326, 419075887, 575638983, 790781379, 915705897, 278912009, 659029441, 871651780, 295705346, 889870482, 943304895, 641474131, 667524344, 980539778, 538017413, 19332879, 794455634, 584198429, 640835988, 754441420, 803610802, 237271684, 238790639, 630141937, 749235724, 911178521, 30669002, 651460690, 762223502, 116506432, 526159164, 897672422, 91594808, 589894526, 356561724, 917520570, 618235429, 904649133, 279562694, 553998569, 824292198, 305210604, 329194773, 856338885, 560488545, 996568915, 769297601, 600562351, 716620817, 222314254, 649391516, 109653995, 590944536, 641554345, 945415053, 965217010, 59037209, 936899698, 149057588, 913293854, 549788579, 758378709, 857519367, 150595525, 46216824, 174918756, 32651953, 517046016, 849137156, 17901986, 35781859, 874752768, 859594845, 173583015, 97077628, 851811469, 100903859, 417976377, 829742250, 142371366, 17869789, 341208862, 679016079, 455480499, 904644094, 228786872, 700396135, 765488267, 978289965, 912450030, 31665606, 605078633, 940675761, 316851289, 976972816, 688584635, 838015901, 301321076, 309223032, 606838022, 14245863, 133720786, 191362118, 385338176, 491802591, 748300220, 794859781, 953617576, 732523109, 822288735, 416695915, 861262067, 937360942, 844772483, 425486201, 617791112, 525974311, 831955659, 266726216, 278177131, 604943459, 63852915, 431055152, 189272705, 450412372, 273924587, 912640039, 856046384, 709852554, 471570514, 328171075, 744743125, 552404876, 404111608, 100124971, 833435004, 276130059, 457645609, 739743212, 749899790, 360383565, 89656617, 486657748, 487097891, 385756507, 365334901, 885113456, 984983194, 302856249, 954668058, 611232712, 915716089, 355218757, 74489608, 981382834, 624146157, 128505580, 793242042, 990913681, 352654704, 705056546, 211966275, 895757967, 398367170, 145422575, 293286145, 445380280, 700357154, 859836871, 389504459, 453627057, 782595360, 289591245, 298018517, 335102177, 41165327, 356943471, 697271777, 684368090, 41179643, 89300969, 589908672, 486075406, 766368824, 591566083, 719449773, 293227479, 257224055, 822062855, 823647541, 54482688, 620895471, 678198233, 565218810, 301201956, 210835366, 833889317, 542919387, 450208978, 727987497, 170160429, 796910461, 969954800, 995946643, 313508475, 541640439, 668594573, 505562947, 96855614, 266362724, 351425901, 65132370, 130612430, 929064437, 372846201, 465755101, 516484687, 104131720, 478235664, 152713341, 506470125, 920763131, 471636812, 405316097, 590920254, 353749736, 474981367, 732195407, 631264860, 197576794, 183322029, 982879423, 619122125, 936442352, 794494327, 621641774, 177341186, 683058830, 810335491, 179277954, 869284783, 558013549, 414788811, 405448922, 534907728, 458081624, 299968641, 334238628, 515797301, 896493965, 470599946, 756575076, 342873061, 784326892, 655414706, 610590070, 382424760, 923638944, 174270194, 760860740, 879822039, 747072855, 349922797, 259685664, 410519179, 105992486, 886692946, 170377429, 427184623, 82602601, 360618647, 160660173, 311807440, 563562729, 355991249, 839173010, 237486138, 638523251, 505911652, 1735229, 396772821, 823610850, 979176240, 94026875, 333555100, 705693859, 383699670, 238595184, 838187960, 876684085, 543635397, 171427941, 985783136, 440600132, 423279286, 916030988, 765618609, 62064656, 604134288, 98274402, 322416380, 624450755, 256724010, 701758341, 297204679, 280435544, 674710723, 988661493, 430124178, 158046032, 354171600, 709677408, 641979505, 710176988, 348147860, 17549871, 845547145, 997059717, 472222169, 402315093, 995325901, 332949716, 928456422, 837283122, 803826395, 2979669, 818734935, 579551622, 844675284, 280659035, 167149675, 933694913, 625918782, 706945910, 31566627, 741451713, 589424869, 756170740, 3777370, 960596146, 529442385, 700228978, 249523680, 415992706, 555827334, 763238369, 85406491, 331823853, 12515703, 368920363, 299580553, 698365296, 505512054, 781456355, 124971180, 894721869, 466884554, 358167777, 824653643, 175776998, 839100890, 276333753, 1733641, 942882143, 967149343, 804436605, 268332551, 203676861, 358902077, 909645836, 480474735, 245136026, 317177830, 139464982, 384446190, 121471098, 176489162, 226461853, 481573924, 49283447, 731772601, 98389029, 372837794, 390039040, 872890564, 606447004, 928068607, 192561641, 13782711, 824108375, 438036575, 386358595, 696187388, 939174280, 235462671, 178192543, 75446242, 394689283, 644735935, 736686223, 733762278, 184179388, 591690815, 292176751, 470267659, 522659760, 750258012, 468975584, 675290144, 762981987, 260144459, 102382999, 191641427, 147085622, 844433621, 12520751, 664347338, 41482984, 483148075, 621877913, 307766417, 208997720, 960635810, 51932442, 689902498, 972224734, 432580337, 572439626, 142364130, 380135385, 635728913, 78091844, 550635360, 911373752, 600379995, 748696196, 457114149, 13632578, 819386527, 424832650, 689285563, 568154567, 625784098, 165248821, 194363373, 864608811, 28869533, 717236915, 682272269, 975278727, 272399241, 384125101, 596827373, 520634058, 567301305, 4338427, 855105459, 558420968, 946767605, 669167308, 476429424, 509870552, 145965995, 802596135, 980032988, 494590932, 273241894, 202749383, 738582832, 781777496, 68756005, 862665126, 133032235, 944963343, 697178053, 579570254, 723308443, 597002414, 599936159, 423701523, 69530019, 630475801, 28556647, 229448791, 434199235, 1290841, 190112926, 273958374, 400392263, 895073200, 415136726, 920821330, 451653156, 635750208, 237059309, 382118812, 498703690, 290557822, 356456644, 659629737, 731596047, 98500585, 280315004, 931035903, 891358406, 164413184, 135244603, 830115620, 459160979, 908677782, 357477512, 870708229, 660690685, 154730726, 52586766, 914590024, 733374194, 567073686, 555923257, 751219659, 380950444, 232889373, 362933119, 775051403, 231373259, 206048976, 877639351, 51364836, 295730348, 218821964, 887481039, 801982433, 177040136, 153548339, 628344391, 622590596, 954634977, 514614755, 188656462, 182950452, 84260233, 179660921, 275121852, 129027020, 629113909, 88325991, 46212458, 645412199, 891348474, 912507152, 528351035, 271972870, 283315707, 865168723, 102484749, 384855107, 958273032, 321730898, 379548125, 385902275, 671515632, 936595857, 216238048, 535008393, 307023969, 760574160, 734839629, 538353154, 606256839, 401908840, 619299744, 236190641, 306200941, 250427803, 494961138, 557447967, 681512930, 630976897, 514391167, 696656245, 897148708, 932141691, 42811741, 714987367, 205050585, 426476349, 214116198, 665246977, 125822776, 331673513, 827532728, 28052410, 193487823, 453012561, 740561871, 875645110, 614903210, 637811805, 640246579, 940937740, 651784113, 369572886, 816634463, 151498965, 677083856, 354533314, 849133947, 515551322, 487552835, 980306336, 110338830, 947109003, 387547001, 22998267, 213361183, 315376508, 739304033, 730307195, 25061780, 328913219, 987886179, 349911579, 728912727, 143639540, 42479750, 564153749, 164200249, 167360537, 383691296, 99720406, 574736331, 480485323, 795586248, 600109588, 774544427, 456947122, 225966821, 676576677, 568658839, 8199720, 334025101, 682996152, 459091858, 736526571, 86389560, 301436131, 592078528, 608848325, 461263817, 667406050, 612107453, 599523396, 983892534, 864323769, 529479095, 595795191, 728216066, 327653945, 356365151, 686456010, 697736589, 538374600, 652018775, 479844731, 547051753, 879550207, 928372148, 45116871, 432023672, 431073954, 377346795, 288807523, 958528951, 331726389, 321498800, 70316794, 413394269, 466256823, 628133995, 637418843, 134177023, 440815784, 113443688, 602548210, 552160247, 470733778, 207334779, 316606726, 407723490, 985257122, 341715139, 940190227, 716103549, 985498932, 975446027, 858425254, 544237688, 457774795, 720093667, 790026635, 593350500, 96621222, 661138159, 309057407, 168583835, 722332993, 477319712, 530156650, 489368043, 473400983, 842054217, 922748952, 975487579, 800320134, 820834818, 99165519, 265058232, 61062066, 422074635, 408564354, 709988489, 576447408, 81158628, 132918192, 360237988, 867590714, 365645122, 923148367, 658941615, 862655632, 680174135, 775949884, 612275460, 639609864, 22117823, 121318782, 380597202, 746575855, 793648487, 79729163, 985980459, 222387528, 928210772, 562042703, 668006147, 679843582, 789723880, 848404941, 297726170, 629694668, 959410998, 654869914, 216049658, 608696085, 899324923, 130520062, 335075842, 591595357, 626950166, 747505943, 635331475, 248455071, 529377632, 47468928, 120943145, 414702378, 774974842, 965490172, 482866887, 316124268, 820202309, 744418303, 656725412, 912500397, 546163590, 755609805, 197244453, 616918966, 344626604, 718486281, 865874358, 944506035, 913858093, 362780859, 249806799, 72593748, 557411967, 670915039, 534057255, 223919151, 112509429, 569748741, 644462582, 864979016, 520519963, 379158564, 444845913, 676311081, 440017254, 270008422, 996261877, 798295565, 622581844, 705270515, 219101737, 770642625, 842342619, 461894148, 281816738, 3194978, 832077709, 519003187, 743977626, 971330930, 886530034, 11979213, 435428605, 360240939, 527625944, 874022901, 318602533, 819315243, 484999859, 41697888, 340474483, 635172963, 794613274, 155737619, 685250782, 156338125, 24225983, 508085858, 522307967, 245375987, 370839615, 632993034, 735922628, 965181424, 239032084, 791177856, 906829252, 665444029, 310292741, 221781634, 962055512, 741373819, 61587989, 367534036, 25861223, 464332356, 150088255, 379838291, 946607393, 621596841, 730882313, 833388842, 910001441, 609292108, 241827908, 790327415, 799277550, 643822066, 230075025, 708759589, 864972540, 104106498, 821271892, 479809977, 722024106, 668193506, 841314822, 340327587, 402238508, 208155816, 208039592, 473215566, 758489152, 432050811, 373637170, 535821275, 364175119, 652060743, 853474529, 378947799, 811918301, 636162841, 393554188, 479518750, 351630745, 575781081, 151055347, 565864604, 721565279, 540791157, 865479701, 518855000, 598973636, 266269912, 109872548, 211891805, 673000774, 377319473, 44570242, 927947386, 318943370, 584674217, 311023413, 760641267, 943909996, 128726362, 171703075, 658428755, 325438478, 747274993, 618382201, 523209359, 399903988, 652791837, 633670841, 720002868, 574875296, 110227499, 612275788, 305605733, 468173586, 324478403, 130838068, 536300180, 886886063, 628467730, 464073830, 861396964, 566695830, 957999208, 471611698, 782493137, 977587672, 335796462, 354762939, 330780161, 244731666, 714576143, 606843774, 917842827, 399304121, 90532899, 6467626, 268453878, 688821290, 212552616, 437479948, 800820003, 429180379, 19328006, 484776746, 233017351, 870563425, 371506701, 279535038, 974608356, 554083693, 529811085, 292816906, 728928844, 777292830, 251540939, 277392557, 187033280, 263869507, 878936653, 635761044, 892299190, 220848912, 881865073, 255044066, 855403764, 298774934, 428860281, 663140980, 739101594, 621995943, 87741869, 584998023, 784726688, 337614892, 441919629, 380210952, 352909433, 362192934, 223527548, 755521490, 180739040, 912919023, 787763889, 883979805, 174302523, 834659305, 942285625, 335735086, 750114735, 192951654, 599748714, 210607300, 294994188, 857903637, 351565906, 354470796, 971756965, 579186288, 665839473, 304673335, 138706285, 549686242, 658183525, 590038680, 923239359, 775197195, 180166472, 403471704, 11425149, 369934924, 114228195, 233681499, 984945002, 151077241, 396730759, 1246838, 780543242, 758304670, 840310491, 951231129, 655050707, 824625649, 965124486, 402660193, 293747773, 376107806, 229294816, 490151094, 690231231, 325052821, 494208632, 646671861, 776716714, 57298798, 552026321, 180356096, 320802918, 213643058, 659460018, 740935843, 183805863, 259256863, 668259805, 165397444, 457538027, 701166056, 637203862, 459405571, 193006957, 119655963, 718720420, 42012465, 295900861, 173950460, 836228607, 360650967, 377027587, 464292974, 810613776, 527958320, 781107421, 863646244, 920274892, 386399014, 125135751, 114719515, 449963701, 145924836, 56374967, 773102496, 178165219, 393934970, 107166770, 829517069, 515031065, 177889930, 97875886, 53649812, 322795719, 433456085, 496455861, 934790483, 63120985, 96623013, 529663114, 275924758, 502204812, 754823996, 884570966, 675821435, 512621530, 834023975, 158301574, 949454682, 902777872, 451857848, 309758143, 139861602, 161094699, 776722307, 349012963, 714820655, 586640337, 19909290, 247414456, 756625786, 355186508, 831723080, 883113995, 322374066, 732171900, 372052573, 642031405, 56938844, 828130944, 577629278, 841499958, 869801264, 701708915, 279849428, 55317761, 557962232, 165641594, 388778686, 949551822, 85976308, 430245564, 186913738, 739831665, 804115657, 594624398, 282539612, 838830220, 592184122, 128071234, 420946209, 439520465, 308850046, 663457778, 772052079, 85607728, 731614994, 93939409, 812644313, 528596828, 441585736, 571764458, 689593570, 349617662, 221797624, 780906833, 175474632, 472918203, 859126220, 606390133, 68461124, 720117277, 203822897, 53780374, 532508662, 699627783, 294218911, 140455131, 771528942, 563861552, 229817591, 813509814, 569584666, 867826165, 247268134, 165659164, 15797792, 51580227, 367721988, 572023552, 414189532, 715494460, 638363695, 345515621, 536365386, 456181753, 677297448, 579908825, 875165371, 558932138, 948748767, 249647779, 717030238, 757890291, 627991736, 941334223, 414378975, 592053369, 492534517, 916598073, 267278825, 784284100, 646794792, 872072350, 831488782, 676957968, 815803207, 511917974, 706132870, 790239220, 518118492, 429963355, 840803139, 338090139, 182675229, 752488925, 797031605, 121115369, 115771275, 138821534, 477594399, 385675642, 912510965, 939186051, 274920671, 471601417, 118325829, 626803067, 633532814, 780479616, 223658988, 370286600, 963467486, 709722200, 299607740, 840083522, 536311218, 385648891, 605214357, 254056435, 278500447, 25253651, 980291954, 773265921, 269727888, 280007903, 380334953, 751842661, 406511864, 769913544, 570836827, 992756622, 848251392, 278676978, 492354232, 245268758, 578665852, 286568440, 50597360, 199077578, 298404128, 72750773, 796014320, 206418740, 118287459, 593341525, 712994683, 627075267, 414107578, 274242233, 944474164, 426967084, 178321661, 114198469, 722483109, 520540942, 342147074, 776560320, 295274846, 162619192, 386345190, 968372690, 393695375, 700382519, 437830107, 196281821, 544715899, 462551200, 892831573, 826580191, 144918182, 355773421, 592271135, 27750704, 671415859, 622870918, 222646892, 755408087, 840775429, 977607763, 374887293, 272970374, 112077652, 103814593, 157338053, 905415754, 576567740, 427040645, 650498715, 901751657, 569183321, 82595828, 349836870, 421607508, 909375687, 38217126, 808643300, 300569061, 161336824, 262424, 359815904, 238146393, 793818493, 625323130, 395787243, 653792366, 823774607, 188320838, 232300360, 745916750, 925970754, 244730766, 138816968, 730894134, 365427077, 924623858, 25042257, 170627936, 336392939, 704460251, 484816210, 185980196, 244612615, 136813315, 715458704, 901663640, 454889371, 566315418, 952901915, 680651178, 833203301, 623820670, 812686219, 341240115, 469804928, 186479256, 596512099, 97247528, 200310759, 13647406, 154041252, 719299883, 942335915, 377810059, 620517569, 80512706, 480217237, 233108987, 640168176, 208888150, 691703003, 672474147, 643610387, 847306527, 508698612, 460885906, 826234497, 462334508, 17496827, 924460313, 492257087, 897226245, 181884732, 755875596, 698450272, 313124709, 994671558, 359198348, 178729424, 895655034, 379207291, 859216391, 697721843, 108288909, 260628272, 448440447, 225955223, 348492399, 499448778, 115783180, 784751007, 420101158, 740283017, 507301152, 617391536, 403790423, 630928030, 750112333, 151382267, 188228724, 55254558, 59979228, 508271071, 84250504, 104041232, 545977063, 772347548, 582263867, 451401588, 660204866, 927035461, 990579577, 960181058, 723739162, 38048257, 222562772, 568128495, 302726602, 445961855, 797881206, 224756859, 80844636, 341184034, 776881974, 893180760, 717818965, 63825989, 308418858, 983424872, 248902789, 504022236, 725991129, 818798819, 644241603, 402628413, 948022319, 552821702, 957534794, 990176735, 614552249, 899461582, 849383817, 509123800, 111205783, 297847723, 313725149, 260612426, 924684539, 856003858, 849864323, 237201325, 19242713, 348409177, 620763670, 217708242, 887389335, 961881652, 272784554, 499239387, 673404633, 190305619, 523111464, 663362239, 862925695, 763502401, 550487192, 218329622, 744605549, 416372626, 49917591, 896857471, 661078683, 324875525, 921200817, 110429752, 615143442, 720568707, 382348911, 664552097, 979520919, 415944378, 264387391, 503933916, 212890514, 653544478, 889629670, 863379727, 692519738, 801204845, 62607718, 259049745, 434607797, 288101106, 893596185, 673661751, 503292828, 623562298, 277359527, 689032961, 371365871, 283909428, 733599553, 336172721, 830082525, 33868615, 274672131, 804414968, 947325516, 200358110, 214150384, 533911235, 276344273, 50980240, 953310706, 106872008, 554963917, 502171416, 859392375, 307223707, 695731011, 15239091, 61549265, 909622381, 170161240, 374193808, 824665275, 402823979, 10288882, 973663376, 870695973, 111268350, 702697814, 28917088, 104740576, 435032043, 371548598, 363086863, 794312699, 832574786, 850677879, 619344407, 404085975, 245094185, 457629097, 933954027, 138918418, 982573504, 928442544, 760959186, 778934610, 981733716, 553623406, 884561090, 679556899, 714669771, 907989669, 291635865, 376413249, 539240907, 739530277, 465987685, 597110362, 499667353, 753795243, 164363909, 42246593, 116216204, 512845824, 832401751, 337607659, 825991565, 195764959, 502002057, 639314235, 920509273, 788938641, 29956681, 712450961, 318273456, 232704756, 227439043, 455471084, 72816282, 43335259, 138557496, 372762489, 223965793, 263808500, 664433005, 928229262, 768069385, 826908701, 989585110, 831229972, 118002651, 871413886, 98001082, 893224820, 806898724, 201459896, 888768372, 112048042, 775381066, 92301707, 401303387, 32372226, 484569729, 100766652, 137390175, 357096387, 389564464, 301278326, 461072303, 636957886, 663426476, 844974658, 910851723, 43030990, 998510650, 857324220, 913534753, 760930940, 614187631, 144382724, 196106481, 824560707, 455777637, 23564765, 237227361, 803754681, 872383003, 61047639, 503645706, 386809483, 317832067, 212149401, 636810271, 998008321, 805616509, 542606787, 689306323, 131098680, 262617463, 172274398, 512716384, 64345566, 165516526, 636223728, 860901645, 79116737, 226458613, 290691376, 538474047, 852096474, 490038190, 948698857, 458586289, 101745762, 660508082, 956449125, 268623319, 943713212, 649296821, 2938279, 223348845, 285272481, 458942504, 319469032, 256295657, 555940880, 82318604, 695209087, 252089492, 373094716, 562497979, 508362098, 724207051, 766489877, 39522712, 325952663, 362262114, 707276455, 937836336, 8379229, 34919479, 711258773, 271519084, 883370195, 425385330, 350849189, 816563295, 277151208, 482525097, 253485247, 932815096, 278565763, 959878343, 279802323, 623258859, 94430741, 111800700, 591981417, 475935434, 782341317, 619923617, 129959407, 454553368, 959026, 352300573, 545454513, 391891466, 599211296, 391050927, 431034245, 829289823, 989901962, 434764404, 201112443, 676440968, 472961120, 734806346, 405162538, 257508574, 395470046, 314243364, 761878859, 363547169, 560162180, 989935648, 842323362, 183880897, 120996223, 585027126, 83668726, 512564389, 51818358, 862174141, 187485838, 676823170, 460875388, 461089972, 985151812, 565326316, 353765244, 668783392, 78197020, 300286522, 304138380, 402808807, 99392183, 722227928, 333173906, 161696661, 161551558, 935361043, 578820167, 972045336, 154438591, 173210280, 753602702, 938594622, 208817820, 988205763, 803408113, 894302339, 230737060, 18531041, 127696052, 256692751, 997278818, 926317538, 123191992, 706271276, 883141356, 120161810, 831660704, 150921324, 70647175, 642396226, 267587371, 118029922, 679950292, 385251615, 778280531, 605965033, 112538257, 171216023, 83812470, 507150671, 315383556, 919098430, 671814302, 830502036, 845256085, 279256190, 968274155, 398232510, 900504871, 429131518, 373105479, 841239312, 797652783, 895851846, 979200835, 849433676, 989647530, 311272670, 288352001, 658120115, 924640828, 317107590, 671823657, 334270827, 114306206, 581199037, 539909417, 335234827, 714332498, 56495806, 65427340, 987650678, 501221410, 828458015, 363658333, 318205290, 203491371, 879772557, 185521072, 125399433, 844817856, 818643884, 468594383, 856498998, 166767752, 876736334, 732808705, 788219089, 767183915, 575450018, 528574397, 476058298, 948984067, 672381601, 96270870, 763514440, 167585339, 381011998, 594667373, 508089486, 989651764, 349012578, 895594889, 270290293, 808767946, 191038507, 46172278, 679369411, 73516515, 307348684, 999299272, 973537680, 98471513, 136895427, 53480486, 328566126, 599942185, 501025219, 896105558, 903846322, 458043907, 159036713, 766748955, 415273813, 769634738, 836749320, 217158098, 124482612, 88078637, 290578887, 48244304, 249393406, 388633555, 196435018, 202164771, 285093149, 36226112, 837047869, 168507916, 500891371, 738915257, 83782231, 430949405, 784539911, 559562921, 423528810, 854069542, 398963115, 729456523, 420634590, 852908888, 109349401, 742544393, 124997929, 427817031, 797390565, 831733967, 203120705, 495119327, 212431824, 777671671, 566837759, 814460897, 278532621, 583871967, 946406631, 765033529, 949930308, 810646838, 109698256, 455556286, 524998706, 42023608, 980203260, 32948277, 890522922, 888105529, 824600859, 207351613, 430597218, 545740636, 153351817, 855776115, 135616073, 97373719, 153354503, 661101469, 979043623, 213948246, 680747906, 448280513, 33160870, 212348832, 91979566, 655303560, 398770651, 926157728, 42801976, 688631091, 821244311, 631284074, 661784466, 380072199, 230386024, 956051503, 519509833, 87277627, 76403450, 548081363, 910152449, 902433079, 227626590, 882578374, 888962993, 337852185, 294024365, 331106488, 589128496, 811552160, 333019623, 960530719, 459950119, 485382943, 647360122, 362701197, 353537321, 647635476, 624267470, 978465874, 145791755, 220076663, 515954669, 187085458, 486945557, 760892666, 439352500, 166217138, 8061694, 176643178, 643804430, 32640947, 855155810, 893843716, 386015318, 321324419, 781039915, 591879025, 113855067, 535945800, 282117735, 577789501, 973502610, 51537053, 61597338, 108428325, 296165099, 834406683, 881584531, 801498640, 78989653, 445137288, 375759903, 875594451, 930740635, 879907155, 919139458, 876244069, 362859412, 429801829, 323606577, 996853820, 934075265, 444572420, 114731922, 769867831, 247415525, 598636856, 160634359, 607253723, 366398387, 740118461, 168284869, 192559322, 597419629, 119527808, 19519195, 907648878, 146881911, 738069502, 223172580, 47201299, 184224262, 221521043, 103030222, 80457304, 189032628, 26621478, 809750770, 129743176, 524800864, 477064935, 258294158, 674661997, 288340905, 871503851, 775032818, 796288043, 872236605, 684924375, 137845351, 168868446, 156305667, 7614626, 990883301, 107234255, 781430821, 261266345, 653261122, 603365591, 352002572, 373009525, 247426834, 197082121, 922112642, 384159185, 846459796, 257006314, 337629541, 253229252, 573191651, 551148802, 938044258, 649639680, 790443691, 400463885, 720119941, 422408335, 150894321, 28649729, 554895494, 888624982, 279736795, 891278066, 410631779, 705585082, 330299773, 449759696, 633556310, 349046380, 569926239, 602579271, 376103278, 492195337, 905109630, 476819747, 349470005, 508730893, 575406150, 12031168, 401918651, 46337906, 39223833, 198502023, 457521223, 190524462, 89014418, 253740968, 996704378, 506119776, 589176950, 418173869, 467113832, 875568083, 921517910, 928601972, 847398257, 827708893, 399889303, 375202205, 48736583, 620354261, 494784712, 418095824, 906240842, 863599837, 476915191, 924807246, 44281186, 340392071, 219069780, 697599051, 947464027, 100173887, 771052744, 940136171, 601288987, 891005908, 31695624, 213702460, 324615414, 470592626, 270755246, 975903257, 324389261, 948099644, 87038642, 598019634, 484871230, 28289866, 99628342, 110010725, 340704788, 254041720, 479283496, 929069873, 246572856, 883358251, 750593788, 414364825, 85990081, 707674585, 667032760, 761473913, 514907320, 688587797, 446563358, 591626724, 154637402, 5056815, 525957254, 905868729, 892613047, 340567531, 556079195, 814493428, 402564503, 635279275, 592614169, 669283240, 487481539, 475508768, 317515066, 722748707, 595691453, 217469749, 853622186, 882376019, 529208278, 706200850, 517296644, 892859408, 173789133, 540420661, 954319611, 865960829, 454534604, 547585111, 941631818, 12962768, 703737349, 595909778, 357440813, 81120453, 325263143, 392569951, 566922514, 747136388, 34987620, 735803452, 597138568, 126365507, 482080049, 985777031, 909693040, 527874240, 425133240, 55056758, 572176746, 747206103, 878360254, 197194990, 975446005, 492923608, 929780204, 910371682, 184023803, 265232777, 829312252, 184150096, 607773557, 806476704, 243479830, 807955743, 147276298, 769283944, 247540443, 106736721, 115075637, 843019076, 887013894, 119512650, 975268213, 97636930, 788134497, 115102652, 16460891, 66436359, 289449427, 98835703, 341130406, 4749100, 837933198, 857823400, 822685715, 728182617, 968453218, 978897513, 949241804, 503205151, 719200820, 332892394, 305214998, 340091917, 779850805, 39498732, 932128483, 729560478, 351366921, 309840685, 384308528, 200705750, 462077687, 668846763, 406399286, 880739178, 32978922, 968231392, 598394210, 28539890, 160314166, 588242259, 701235007, 795113636, 22528973, 415304659, 966784900, 402988292, 621506754, 523890688, 420885035, 119036407, 499809702, 567153438, 68136608, 203101965, 772970170, 648210284, 245665266, 787638925, 212881391, 986305937, 552296368, 358658348, 606316993, 751229113, 663759338, 742314287, 294362883, 480749079, 611891322, 273433450, 400984077, 354771799, 493532564, 14550731, 214491432, 211332530, 701981042, 324774947, 407681206, 548334914, 880731599, 712577097, 360269440, 180795914, 31762421, 274102360, 968674554, 462947057, 616473855, 824909479, 343946937, 690348922, 459805405, 710054445, 841107906, 761567202, 568536325, 119791427, 522328375, 57163575, 57385865, 707827916, 687158809, 505161436, 435801398, 873474697, 253405880, 975753391, 301678892, 848114754, 30480159, 687959929, 578783022, 840140547, 556757159, 690521280, 196448720, 52263641, 413886720, 699948857, 993099685, 298504683, 81275851, 306003273, 197329109, 118147373, 454783553, 984861241, 223620664, 824093063, 960590254, 266926758, 799471738, 42224793, 739717203, 301931521, 614593494, 812535553, 645196012, 148907964, 967566509, 522031481, 636996808, 427642502, 18444734, 360718676, 450802789, 733363608, 493936360, 232470075, 790897326, 701259437, 4367251, 832447368, 375819097, 679067429, 441992385, 282865561, 734306044, 262065477, 105389114, 223371497, 79012643, 418217557, 635770688, 896230917, 191236063, 948122394, 581339997, 422418153, 909349268, 144242445, 844090925, 937403334, 896737427, 308359846, 987846759, 147661200, 686482480, 204766993, 227916769, 869785711, 363945023, 686234141, 783494875, 925194837, 215856475, 821775586, 169660482, 855460998, 224287147, 440386722, 805722355, 266687667, 700132518, 621429922, 120447667, 955831049, 924375985, 302388625, 712279191, 106016623, 89034059, 582719395, 596792059, 935049596, 334399937, 921412551, 125121548, 759872166, 997124717, 189405249, 910539086, 190711905, 357738620, 299987327, 695938859, 505387323, 317007321, 84120148, 479705499, 105869088, 662554537, 295398515, 587667008, 826120524, 820484479, 862598204, 49421640, 659899342, 342426299, 241397248, 638853281, 578334297, 485988033, 846952105, 19406732, 552791558, 485892495, 552522205, 920834869, 975306606, 453921980, 171774225, 625220954, 262248350, 900015701, 700434469, 214534240, 798390840, 933091405, 81082837, 609759424, 348952274, 275822749, 720581711, 425515017, 155041177, 590169974, 349256654, 132151929, 755362651, 574057423, 172294586, 344530919, 459872624, 309179442, 500580817, 764521143, 749831702, 992293836, 132623359, 718028822, 481529546, 2260458, 668516337, 169290197, 27411984, 414134302, 833469943, 877590676, 650046926, 634354445, 562065136, 891883507, 202217075, 955625508, 451761141, 620281926, 566496518, 312819006, 649002302, 868544861, 276305951, 478131595, 584388478, 238411070, 147260693, 397170910, 278392619, 377399700, 395345569, 129236411, 540747091, 474137759, 317583694, 929909026, 264952317, 891092650, 550170324, 127151673, 681593092, 614688345, 704089693, 966430327, 639483188, 683563606, 129886458, 425593826, 463378470, 572456384, 202403076, 939725562, 79306849, 549364264, 450141045, 462222450, 267863575, 343398230, 272718094, 177299461, 467599416, 36563832, 869892877, 709269460, 410033491, 784346617, 904705080, 868714833, 156298428, 373439820, 381606803, 541304636, 452797962, 117101047, 176885584, 922767449, 359537261, 422156506, 189094211, 737983741, 905780424, 988317078, 708870559, 897186754, 871517349, 523644463, 674915735, 536409530, 364874050, 641008105, 5954799, 134528670, 671858681, 25466246, 484526548, 175196284, 397572851, 652555622, 352957077, 184485410, 509206163, 918838319, 308007401, 801677227, 216982342, 422165870, 490646627, 154298591, 399389998, 111509125, 97259179, 716390553, 775827296, 702891745, 852448349, 173289322, 793990718, 91037916, 791676945, 632069995, 628467980, 442504825, 535297546, 882723349, 653312648, 991672909, 461380358, 86632947, 421863027, 77985869, 971499494, 84503523, 362604529, 184587311, 459842544, 590215002, 63676169, 752363463, 250384245, 447638152, 242744093, 521039088, 7676342, 306812983, 24290518, 37027220, 799420609, 579178113, 268610634, 328111516, 67964004, 261676218, 874283868, 705024782, 371635382, 468299274, 695886201, 384516625, 51435036, 402688462, 298168426, 538587142, 892969041, 468360594, 149495391, 597005137, 89387940, 574905293, 297900340, 86404819, 648975289, 680224958, 669683962, 764436224, 229495140, 208870105, 210329589, 694086106, 374163984, 7407525, 470554636, 811682225, 711338753, 450118467, 412015900, 201204105, 253669756, 117855128, 462943662, 450804274, 233442961, 481289848, 715695466, 993543706, 55538730, 494891984, 233834665, 65493507, 969258767, 600639501, 340578027, 412174350, 845386916, 795626003, 237155397, 590104774, 606259514, 687668963, 600460230, 414918578, 113009086, 303914480, 56923007, 296041985, 703498597, 283343968, 439481637, 320080448, 236190171, 834956763, 846800853, 570984688, 325954795, 267612289, 65949351, 56896399, 723912124, 333107294, 694339676, 362079228, 787040572, 341385579, 156516696, 725551009, 371937280, 32488187, 482887912, 566220697, 608651515, 19325145, 264480624, 57637494, 813702973, 81803738, 388242367, 264913628, 883893884, 91616217, 820475064, 721795374, 186793387, 300012563, 522273591, 156227135, 164947386, 498931935, 913735456, 776744544, 264579156, 394430803, 642908498, 200746145, 434399526, 67058151, 714409761, 31999092, 802414957, 649450541, 701428445, 255053377, 552717341, 855258027, 990564535, 170729919, 229474861, 286776414, 352775229, 929319621, 699339291, 426407100, 344640422, 431365635, 486651501, 688742719, 398925569, 98734489, 279454265, 572186668, 818703514, 128836521, 412379921, 78983057, 176148587, 168542368, 848836233, 345100940, 224003884, 158776508, 236386390, 545010027, 353381178, 275552578, 595198006, 186982498, 480787142, 213943463, 558509013, 569064230, 40265613, 382190554, 963864702, 54812965, 638417305, 647926416, 263728059, 482329783, 595385960, 583871357, 808494254, 638766398, 969647020, 641933936, 257449256, 773904163, 650231850, 803328044, 771578769, 556634708, 841233659, 927901983, 290556505, 922394674, 110480458, 895916504, 166849219, 973451028, 41196593, 883220667, 900371301, 666676720, 465423966, 471596056, 108089716, 275555480, 779925453, 142265782, 454575062, 384793873, 401275304, 979559134, 139297668, 408130662, 438928595, 433561215, 664715895, 374155261, 216465141, 225983047, 128476574, 360275287, 595439868, 568168268, 622047070, 744472072, 417464824, 949266170, 134569324, 681408744, 515524292, 332106103, 846567968, 278961048, 703932519, 190271475, 938832156, 354258554, 572232466, 206374970, 883607140, 731136786, 80015370, 338627406, 359590844, 379161424, 628297852, 581942811, 39921090, 560894499, 282171504, 846643979, 557724733, 293352076, 621126613, 378752824, 249976490, 140068723, 545051938, 129432360, 12296627, 856152291, 976148999, 832786913, 194824014, 459736346, 53458767, 221024980, 472309927, 881377372, 908991493, 199616023, 915767976, 162514422, 820589505, 737961171, 316410839, 955453283, 926995232, 586769696, 286368672, 93445838, 732383360, 701610823, 797338690, 795627850, 612294018, 754576638, 218944552, 555028833, 266784638, 964532222, 27053475, 221791433, 154599535, 794401559, 588470691, 473759319, 810093663, 415810080, 972681952, 644601762, 49438564, 564934745, 217940787, 198258227, 582866596, 450543217, 323984890, 71263475, 373127537, 983318190, 36295097, 457001374, 141282007, 900695689, 778438971, 97027023, 816042003, 882227322, 112865485, 5462956, 774364050, 84926657, 632503063, 842217037, 628316540, 806186095, 628205492, 142703325, 537017967, 886688672, 606781421, 436930278, 950351837, 45461354, 177170524, 61613116, 175101064, 728791799, 389422684, 864051831, 187828098, 652242318, 470754533, 66761150, 392251090, 455387177, 726071994, 252924870, 892042042, 520199721, 862380793, 616552548, 437873306, 553811134, 126081181, 299654614, 224701137, 789284850, 437612138, 4529486, 892311614, 776440626, 532468343, 156000044, 276848441, 737063650, 78367054, 858183910, 919120415, 504507025, 502009652, 58071235, 931379461, 400743980, 405808329, 49078536, 275875896, 141473448, 323340834, 338962983, 299350181, 722508813, 151016607, 411765283, 38885075, 347017239, 449848761, 287478834, 856972787, 78863554, 764670560, 498773839, 208482540, 819041234, 440669491, 172192276, 788981479, 445954936, 701649919, 480622938, 864564205, 845336245, 457964513, 11398892, 954639155, 659155645, 317441510, 429992377, 875037851, 83435037, 288470900, 549631322, 225144343, 852342028, 194582328, 922911798, 871430659, 788039284, 978808227, 705053049, 836943534, 897805289, 720454007, 350169051, 99573089, 857903598, 889323231, 164975787, 878133061, 948591746, 975956125, 975526953, 847111083, 703924894, 595280959, 609599497, 951802609, 603689743, 561299737, 428433417, 592091671, 461593788, 943186989, 759712395, 90877293, 354342387, 798547977, 672988945, 529323723, 312111974, 426461344, 368254750, 462722862, 902194196, 497214385, 877492361, 193928882, 799519269, 289030814, 812507199, 475448162, 479520177, 105187770, 574773965, 504115008, 215381025, 988520665, 332347526, 649032241, 482457449, 789727726, 878931462, 345607784, 70054471, 433366498, 322576330, 154817410, 561778810, 313526773, 130753345, 579906887, 446760017, 809265643, 168792944, 518584559, 612594075, 574148918, 601194138, 43544340, 110410591, 77950350, 890465668, 846547667, 973097228, 679457535, 580193676, 67880701, 986632461, 931516269, 328128529, 57933814, 650970631, 352992416, 344421492, 190898271, 868930972, 207071007, 946895067, 392817148, 232457259, 758576773, 701124841, 367705645, 248846656, 398815301, 551036972, 783785882, 982697093, 636587477, 735655022, 625103845, 526389266, 757178930, 85465473, 419894665, 771275352, 925391326, 285021342, 501448294, 511773676, 135785931, 58160365, 250933634, 336335374, 518153805, 593248568, 316671640, 183821616, 658887913, 771870690, 734161107, 830222178, 245216703, 187347009, 5239577, 454521487, 759854173, 528406567, 373459707, 165448716, 150685392, 762613449, 810006218, 973473561, 80133274, 643734077, 155331151, 126144556, 177385513, 402771134, 831945497, 253154216, 966896980, 563715610, 575181600, 249160778, 40884226, 702936743, 912921324, 665853648, 69593133, 275042106, 856313443, 402245336, 262539662, 748661284, 326749907, 909238941, 931311546, 424924757, 219535473, 215769920, 50400687, 14007180, 439059292, 931356023, 596979959, 420202095, 957767465, 543358761, 655247589, 232264627, 385612823, 403700847, 746763469, 937262193, 330879966, 879305502, 894374872, 516468526, 867744544, 704948645, 646851962, 34374948, 261939750, 885495263, 53900514, 287022726, 495551253, 197726258, 79698400, 123375664, 649307865, 608228548, 814074515, 975614111, 577795796, 96396143, 84007668, 64194344, 295151793, 18917768, 475229902, 606925405, 292925609, 159049171, 694964670, 411320029, 263336743, 887546414, 170879203, 471741747, 825467534, 426126392, 266544038, 12916982, 303008653, 552491294, 455453590, 883173418, 672349037, 971393952, 318554795, 432579492, 453683656, 49161398, 886324269, 861804713, 570065652, 67027930, 400396109, 928166477, 554834270, 779190542, 144330622, 798191015, 558016936, 490849852, 121170573, 548439776, 817737994, 626734391, 497477616, 689599915, 397607301, 570276749, 304996488, 931691765, 100934058, 600390017, 669161888, 300356228, 20275574, 792636713, 65729320, 792527815, 588730102, 841010827, 251463011, 697598844, 535331723, 198890961, 654662828, 194514746, 475707516, 547602773, 734476763, 202698746, 279392628, 377775415, 276831831, 606112866, 543332313, 884331757, 53626591, 572616087, 142118926, 130233248, 757425467, 696471593, 186526731, 663538037, 949423141, 277616245, 930847362, 37032278, 923141550, 993702198, 894876853, 764906565, 449854425, 924970892, 344774351, 489024690, 535330604, 746832779, 25793689, 519714068, 78572202, 512679745, 499104966, 313126062, 862370919, 931225234, 187824560, 867270090, 888848715, 21517676, 911849001, 954007468, 542869138, 300645362, 587772520, 924948668, 659325982, 486433748, 446173168, 72491704, 302421109, 37506367, 83743709, 847131728, 873814775, 21935115, 364919902, 576215555, 110726419, 282481507, 34739015, 555264407, 351150535, 220406767, 139644218, 422591173, 528257375, 289305356, 409581201, 193735011, 815552900, 834798103, 660246644, 569417369, 789152504, 456323580, 490500045, 353793572, 783382012, 49559864, 973195172, 777163712, 976071831, 529585566, 283737923, 432922905, 60553765, 943900073, 808656410, 529521776, 857865886, 879236491, 883612441, 555039690, 912422143, 760754766, 506248158, 384129276, 802586193, 956188306, 347970307, 902506835, 707896962, 388984564, 407004148, 145660563, 602754016, 506881546, 242686088, 127739444, 271079314, 21985277, 261446778, 426693536, 350832284, 100816483, 714795465, 44673435, 613478389, 740055542, 584912045, 958061872, 639468791, 762912377, 299261299, 289330851, 145230876, 798869818, 164705496, 561224213, 549043364, 572116551, 675273813, 622227207, 691632359, 767800887, 87345563, 966602101, 781480034, 268791127, 265692473, 863877459, 472575431, 645706964, 255841550, 651132079, 324577338, 401834874, 688488205, 619022967, 444028905, 755043090, 168605496, 740374115, 86907513, 25558823, 41271109, 74958323, 458813891, 430416798, 567023546, 538123728, 601496891, 668169020, 296083593, 300382352, 795394805, 898457338, 979379123, 683741612, 251884867, 396347108, 753107560, 196032771, 75159572, 558476979, 975935722, 580231789, 326554232, 791123169, 533660911, 358972014, 62796567, 318002745, 733768758, 371038475, 639668953, 724267838, 597109436, 278575906, 206257600, 695066212, 476906876, 874809731, 39483293, 838115664, 62614421, 805575695, 244214604, 326454895, 479006736, 712695369, 799041874, 126530043, 542624224, 83777492, 722261149, 231402201, 733900633, 269962911, 447732650, 480096959, 394673262, 416380680, 161947076, 800324173, 469485607, 434274348, 566416135, 901373273, 61794515, 916817281, 694389162, 15743644, 444155020, 238341598, 6951455, 763697163, 958553899, 657358755, 3807756, 436174859, 90302470, 359527963, 211452802, 318046494, 565001064, 179970332, 515067307, 181556519, 591013521, 387024361, 746099859, 231533765, 611048611, 267324699, 874978339, 633905347, 892347930, 876498939, 691900231, 698632767, 482193361, 522655466, 273359345, 352129241, 894586602, 189122117, 2270081, 856549001, 12820529, 343820723, 7259980, 899720047, 674012364, 84477396, 35547299, 796639912, 700045817, 91166200, 58228678, 758283931, 220736767, 511508872, 628305725, 40812216, 369817885, 255959320, 983041672, 970015586, 191830614, 719246604, 472194085, 682478890, 319980763, 798187642, 904502316, 588852480, 499199800, 637991759, 634946070, 531070786, 900302382, 544259275, 659845799, 302716471, 370222070, 611467191, 845034713, 868839490, 746880601, 572558737, 586900874, 318641703, 491151338, 449042149, 932446779, 519576412, 246097788, 541841428, 34900070, 279353493, 151886236, 971605377, 141321781, 269508008, 209092775, 67284138, 847010607, 251924898, 856641653, 51818394, 457003237, 621307653, 414342616, 832377525, 196314781, 663003679, 122740264, 373063346, 938076121, 186894394, 804060580, 499269274, 658181841, 627747132, 39558032, 819895571, 331029934, 788420230, 211425697, 892263728, 386179187, 55061908, 816732417, 516997622, 854774179, 121726326, 883413656, 373810269, 664277590, 944365559, 43646732, 119368020, 266144434, 960660273, 65890552, 960351565, 157138423, 860189887, 973747422, 946539723, 974509276, 168718704, 194017629, 467851479, 226518702, 99347422, 61464712, 30797075, 350999386, 917182292, 609027173, 116066576, 258814918, 482869710, 793764342, 472115331, 126922949, 422023471, 203897392, 484287730, 154259073, 302974706, 286094731, 224382508, 364041196, 641693274, 384554498, 576711522, 758142381, 780164739, 587530546, 458921206, 863296992, 783688141, 207407501, 815100100, 810422410, 803738356, 705487526, 287149227, 506608249, 827075240, 727765069, 612679313, 357082886, 96299230, 149763470, 64327037, 123592760, 721564021, 718399381, 455107641, 119310016, 803187207, 708053815, 77515367, 754626068, 644660211, 509136701, 303774599, 857887997, 600126461, 424280491, 467940912, 661065502, 832631509, 521923329, 811782933, 987139096, 448605619, 901478636, 705622440, 188262260, 464123105, 220775253, 209543561, 321753816, 254234682, 68141977, 358347167, 936757733, 888012065, 477222410, 120602454, 536232146, 276327415, 879274354, 618931311, 915208604, 831478580, 451180028, 665687662, 301740889, 818814654, 39884582, 385119681, 798111647, 851581481, 351383216, 542342849, 694032203, 293337327, 486706163, 538624840, 595536435, 383182289, 51274851, 812524392, 322659162, 167418716, 484455225, 325510177, 4444552, 645922723, 203673352, 845979267, 802868889, 582721, 281359490, 719229072, 3901614, 233226494, 576911445, 612282917, 348691817, 345620525, 507128451, 777916264, 151002591, 213235891, 94532863, 840956818, 453874279, 138960323, 356416639, 707601399, 257555031, 761548070, 652930442, 880665298, 973131149, 820731644, 331097084, 961537411, 627218934, 104901869, 685184750, 467541829, 340218440, 409769712, 464634582, 761426407, 935892082, 421307419, 414596326, 153726319, 406035956, 527422445, 511075184, 954216597, 579037635, 855758190, 231535947, 962104256, 467108431, 104079892, 793156367, 504395237, 426726972, 305037909, 396790220, 32982263, 474082275, 403441393, 936449424, 460906815, 483874270, 566691857, 235369584, 674856559, 511903707, 373231407, 604758053, 952786577, 437965937, 509311108, 624103291, 843196751, 970634831, 548233672, 234902853, 217663176, 651905157, 731845270, 4705258, 772652828, 602812525, 317860550, 422082451, 199688971, 265659112, 25184887, 1830288, 981543097, 158953819, 320899198, 323478953, 883934134, 499248512, 640904210, 129404283, 797661737, 948638582, 492532805, 83936370, 181153572, 732970594, 431826534, 306268875, 475043582, 363904010, 63649258, 541625765, 420902371, 220299249, 510818819, 222554154, 806236662, 219764861, 1644048, 985410632, 882656267, 944640705, 231102855, 953039734, 74992020, 868902488, 569025528, 411055127, 400044374, 167119856, 470405200, 159995889, 172488164, 907044692, 237700796, 511354586, 314411590, 471174902, 19006023, 507891353, 448222311, 709291271, 510199113, 253673120, 466937854, 686413532, 440745368, 277256898, 404012331, 356993340, 179103917, 267467973, 685535346, 215719313, 444762876, 346483125, 216078900, 20259432, 219401387, 231145854, 928970518, 505432312, 383775358, 155558700, 861122843, 860952739, 915115146, 589347349, 347783442, 430453397, 304475423, 577582086, 917472319, 847582123, 135189818, 528842313, 310602377, 955636411, 448258679, 36322063, 82128217, 343527712, 362995039, 40535407, 966496310, 574441739, 511651199, 408904359, 517287661, 283814361, 124147826, 708747628, 685994434, 571454895, 620547780, 798592368, 685846449, 764637917, 399955152, 335166678, 649249867, 684301634, 264687898, 187264630, 558046326, 418991407, 246466217, 41062152, 62278701, 150917055, 222342655, 699821883, 324067213, 343001549, 91288957, 838885496, 576551837, 197856313, 219328632, 193865636, 199049037, 353438157, 797998368, 600098683, 618209325, 66151606, 269834483, 587414910, 465879257, 519710173, 838795779, 73277463, 287696330, 777885901, 247542121, 460901296, 668251880, 232830867, 890675742, 855036031, 207034701, 115214632, 610968276, 29335507, 666381358, 251245191, 147913121, 434599783, 799077014, 965688149, 926508101, 283911533, 160906411, 149733073, 738286059, 444108887, 808966713, 417216033, 205969961, 759521380, 525447935, 875727692, 511279169, 351583344, 359573300, 183752215, 298944671, 368996280, 594142899, 237985565, 421221180, 735475011, 646247816, 695902663, 906785408, 954020681, 403094831, 578793795, 398922036, 289511398, 123449762, 362138518, 349839045, 567555217, 503874258, 647306165, 393815509, 991626595, 438066674, 546017643, 356952235, 581833143, 215180051, 563539816, 866079189, 216939908, 947978918, 623500746, 44947496, 311301183, 861686168, 609336902, 817518627, 329218151, 166010711, 892089641, 729129005, 715623162, 996196561, 481191742, 412377543, 38654505, 579117983, 396992764, 157964741, 751570629, 230376583, 914834237, 30661209, 362394097, 834445458, 908617883, 45726783, 507592506, 263588470, 620332318, 636511832, 837509480, 900911201, 469139941, 335907329, 803678076, 239810544, 971488286, 966487089, 59495665, 159611886, 881659517, 994623753, 880998434, 772675686, 780768007, 785648437, 991735321, 853915360, 65592929, 236473715, 156674190, 515826230, 614425463, 108282770, 265695391, 15462105, 128751603, 12228609, 404592331, 739585145, 849313277, 18729045, 749560093, 380916173, 30491890, 416407159, 642223294, 543615327, 87594737, 299253090, 898943489, 778148466, 667114463, 423363394, 770717782, 282163160, 855294835, 622183231, 265427605, 229066492, 275091985, 499827052, 125767673, 446987595, 25175925, 729750406, 758155592, 24405656, 735229829, 513166559, 385514801, 89570404, 589760913, 447293157, 772677314, 19899637, 749516705, 568934093, 242410073, 64271865, 132039731, 106037076, 619477552, 840740902, 691498048, 47765951, 734058794, 700918153, 920207561, 498012349, 200690934, 361876803, 112006018, 649622735, 691435629, 351278543, 322732591, 554237992, 880338799, 965239660, 590701594, 10985077, 676427363, 361942885, 297165072, 688576674, 984697862, 651399852, 206872701, 372660541, 877152440, 609529069, 439446482, 749973146, 575320036, 60690498, 303598593, 611492254, 314009991, 681729520, 338342447, 346312555, 594444478, 676945470, 450780135, 276978930, 715119143, 8418800, 707144805, 291108650, 625419197, 207741771, 866235905, 208933209, 791825151, 987706854, 814919272, 13283887, 970495062, 885948336, 609530598, 599867333, 166695847, 315906027, 617863412, 78226555, 775271228, 728304198, 29881475, 534325861, 656820336, 615357479, 350417848, 727614655, 131167743, 42088915, 133238487, 876885043, 153621336, 221571540, 462276107, 28402566, 241000623, 327650710, 20740887, 215327206, 408068816, 529876980, 268602237, 830760277, 998108744, 930950631, 906569580, 357628480, 255159843, 763273860, 465577454, 32176485, 126390127, 748858522, 440742400, 453382352, 370517836, 201941519, 473383917, 217860762, 589530206, 853735515, 586469734, 365396384, 22717745, 857229514, 366411574, 784252985, 149110874, 115122200, 788377960, 553917191, 633324118, 983803106, 555404243, 311751776, 899569108, 731042293, 65094033, 328922433, 997184629, 376868188, 49744583, 903029120, 826280504, 569148805, 734011541, 95139683, 17232490, 550330201, 883206452, 385491520, 448771538, 269989214, 452137401, 327900406, 321453436, 888535954, 326731202, 210012566, 335639552, 60379609, 485853408, 255953434, 40073996, 645907906, 124077714, 202561136, 159126563, 320825738, 440121274, 636364090, 136129930, 144595295, 866330664, 633211159, 8986497, 483393975, 922598989, 500962087, 695037616, 485205938, 386852479, 348163531, 45337040, 350874679, 213967555, 851772993, 371073736, 204404525, 506487138, 605557310, 672342478, 80239178, 344718989, 641623086, 836253247, 748240498, 452112619, 261495238, 178563128, 476177749, 349367636, 918934522, 155258001, 528913824, 800549044, 10210094, 183162956, 977470674, 482937384, 712865228, 981192550, 638895684, 384925601, 613084583, 115752319, 723231330, 914643789, 628789995, 200589911, 380453898, 641283869, 5857012, 866245754, 593877543, 71962210, 787893716, 966185262, 698595032, 538086558, 485831378, 512290100, 308539033, 578812529, 158338991, 877764420, 91009759, 268176921, 945762140, 745478266, 992307892, 126873417, 546883386, 436700484, 967075224, 893060332, 202090648, 218249030, 131185070, 306494084, 590810414, 195706034, 612554200, 780103194, 176369661, 841563040, 99930058, 733170665, 718996070, 824308206, 415613622, 943314993, 394245406, 796504997, 20535387, 267854353, 481525907, 384404338, 450325047, 134309189, 403726956, 52895363, 811293063, 43552085, 415050438, 815005252, 979775072, 479202551, 106165357, 826598057, 7344374, 60468110, 54273075, 504599735, 314784475, 880131822, 798062711, 472366880, 571508547, 708283924, 502916057, 922847726, 620021069, 326117989, 15198068, 2883644, 382480426, 12291772, 509511141, 138641800, 909236558, 76484196, 895033827, 129970428, 259248606, 82981860, 562736901, 262563180, 989236597, 715945111, 505406616, 968379322, 383136390, 249846644, 10156493, 502795452, 695785023, 413216685, 27056527, 658759211, 596853776, 814329622, 574624064, 119702760, 429510338, 842590154, 806764999, 135039676, 700857477, 37172145, 849984977, 33195117, 543238725, 319974142, 362301249, 909588945, 290081199, 115388062, 685381978, 166185520, 973867464, 901333514, 52655434, 612030420, 497268495, 577361881, 68838423, 689594270, 538060843, 676595691, 48950234, 400473002, 916449584, 941246833, 787575656, 395168618, 352051832, 775244421, 360465018, 812475502, 924640420, 609506317, 216516263, 763696724, 847952341, 788854766, 969370715, 410730925, 833076841, 738269063, 861348461, 572277052, 433086369, 292472171, 621969019, 617759436, 566734728, 688194307, 864447, 201222985, 530763228, 170482198, 756259836, 773559756, 65180756, 580529191, 102540662, 742642153, 324159312, 499546349, 662945180, 866232918, 537332671, 206393757, 207099398, 768201254, 158523871, 518810947, 742453276, 228584595, 468528151, 14863272, 682737213, 180160913, 778397573, 356470732, 828270056, 75056189, 257048643, 4926483, 279802008, 811165149, 398153941, 186131095, 288405256, 94440910, 758524869, 223968008, 120165047, 982452755, 340318653, 965255440, 613387518, 90453313, 455652954, 494190486, 467730627, 580389264, 703848386, 220023997, 889056804, 701889989, 357455044, 847351314, 743088628, 924760906, 73318835, 716261808, 17961828, 17605272, 671784379, 517678790, 853760090, 780733993, 678943618, 565285526, 97322278, 30615150, 214489749, 698489768, 190951471, 376228282, 496531085, 369835722, 909126262, 440075055, 761294587, 116068794, 935618209, 601038560, 339356195, 133036924, 700841365, 441351937, 19625927, 496435080, 164075161, 712027118, 673177250, 344219585, 150230736, 178995104, 363413623, 548845471, 522384874, 282451512, 654591734, 610661230, 972377109, 764616493, 787871156, 691933375, 854812047, 227203321, 359207266, 702913732, 718672762, 77173195, 330470668, 35421333, 871887843, 131323883, 699668828, 614486544, 172486028, 920509132, 209162165, 466965634, 997489200, 370155894, 945489387, 66582470, 372814073, 738229525, 454311448, 469521734, 25053622, 70549822, 542890725, 507917524, 21696533, 735054438, 466654851, 589385925, 472260162, 296663841, 884711602, 207910951, 419038959, 714493433, 755477243, 437949213, 564258386, 656955873, 82947536, 955863910, 862132311, 654749857, 955200883, 828375160, 469172629, 293649815, 126560954, 518096414, 182983902, 30817746, 796040601, 730152417, 36287763, 630635868, 952254731, 963204383, 960433523, 527696854, 52005868, 586313428, 382110422, 456297814, 511987490, 539941342, 26807622, 400859903, 515540407, 48593714, 549901377, 531248774, 145083319, 57829201, 933816472, 553168680, 928700874, 716226605, 65892971, 68815313, 900063733, 320018297, 203135468, 266588190, 123837801, 47130585, 328511503, 877631171, 401949509, 20662575, 655544559, 294148900, 495572668, 829268392, 270471613, 532341185, 430068532, 392892127, 843589656, 589908803, 974552992, 855210905, 710680748, 474545067, 271134559, 697189512, 655749289, 283866820, 833569354, 179681286, 641046968, 972094688, 597357880, 27664529, 772412044, 858683271, 699472718, 805294020, 207045752, 30428418, 900610352, 737995337, 53628038, 488441101, 951973252, 462012176, 996856526, 374346466, 280567000, 419096545, 221018758, 491839822, 41657865, 299238085, 266680831, 494866664, 852979633, 962842791, 464042465, 522049295, 51314073, 698004822, 572063536, 471623755, 73812220, 299746506, 770090404, 603882193, 824383394, 443435866, 694820111, 463251645, 46064084, 496803875, 914081552, 290604889, 313090159, 340437325, 168054823, 698183893, 18325159, 542481134, 991095049, 619653775, 195580859, 256762221, 549831764, 730254792, 352517462, 151061948, 891840387, 628495956, 438027795, 767125830, 944314436, 526573619, 563324540, 896776396, 227937986, 195715007, 576920375, 207515899, 735920892, 588778410, 927511890, 570692247, 932937611, 63879411, 572670486, 518941464, 971154919, 252184394, 534110815, 971520685, 182731607, 947320695, 731953150, 200837212, 974892038, 30821566, 390633798, 640326416, 17598360, 380382831, 852949568, 400171962, 27072757, 561454801, 855943689, 225959286, 173315105, 957129410, 597128401, 677727013, 214660145, 319660139, 874991169, 869503040, 654837376, 205059055, 625636692, 664357207, 266609683, 613408729, 634293618, 486202151, 206845651, 800744287, 554394075, 762407723, 585648684, 235222513, 260988418, 48481188, 284523783, 388643764, 856842083, 244195887, 169552046, 941358531, 738836681, 463212052, 194820512, 749360863, 878418849, 648827545, 193481617, 181481139, 504309312, 641647220, 726727144, 27486329, 579032373, 446764510, 4966301, 767667409, 468075403, 263901215, 658624322, 772428859, 355814327, 122790190, 795886185, 193571763, 901638525, 554643503, 466146212, 517970764, 311293381, 546009937, 394670002, 74706679, 819114662, 991721827, 598928985, 933591160, 340191027, 631933988, 122441311, 551815048, 633048805, 556279547, 357046414, 377822335, 732970929, 699538881, 204357751, 960822857, 678387901, 951661880, 219356303, 244945340, 241813563, 622620910, 313937522, 463708218, 155681170, 939917848, 624256620, 499336743, 980089116, 155052830, 58945305, 456258925, 915139711, 10495763, 952745480, 472917201, 481385877, 152205690, 881349902, 296339333, 955121098, 761653297, 969172003, 863762585, 351961899, 394383176, 565380516, 694094295, 464392320, 907169691, 151927070, 420425538, 509748852, 934572111, 209586626, 40633164, 775474693, 694945586, 161502919, 524673603, 840465991, 278832514, 411921193, 545007872, 695999388, 418012577, 678058826, 55276686, 159712263, 158762281, 334720184, 327299683, 245138924, 74561968, 939446478, 528148474, 499941453, 268367406, 887713589, 106728378, 769822986, 457807068, 236920255, 72501505, 623676236, 403059606, 475253092, 977833191, 308182405, 233091255, 949713433, 204223057, 233311105, 587631521, 191759544, 156434060, 544761141, 145305618, 516377767, 381771832, 100678712, 103449958, 925688406, 182804885, 348336848, 217564114, 553609239, 827695005, 912458168, 111847566, 440510952, 876870844, 277862496, 696985145, 117876343, 717090515, 712569967, 868087889, 953985799, 565284722, 408843531, 155079995, 962176781, 678036917, 563887417, 151350563, 814329245, 353200447, 540334940, 205351065, 536111997, 720559749, 37350572, 184138338, 872484465, 590074324, 444308077, 826790472, 743017556, 291245797, 635121229, 939056470, 11848457, 73473664, 197946279, 658296249, 470640546, 372799155, 309447920, 266720410, 213211317, 544049848, 677482841, 895119571, 102212864, 2367473, 387680944, 797918929, 27245256, 138225773, 502045647, 426113283, 518574817, 16253398, 269083314, 467897509, 557982732, 136314087, 973181949, 195231245, 516941297, 336089603, 479194763, 496477058, 760453625, 803997323, 240550651, 505377336, 753056420, 966770654, 862845527, 342286668, 941464077, 238791282, 179688552, 288474119, 538655520, 255930153, 960104632, 381312872, 652744910, 389801870, 788992465, 889978009, 336838862, 69269373, 174523905, 299565289, 894053422, 991059096, 376498831, 222921701, 547176296, 42857538, 258187620, 605739564, 120849659, 698844413, 74719500, 70220486, 997700068, 511840175, 664549721, 430257334, 252600072, 879535377, 711057492, 790319711, 106938332, 844425240, 714262458, 300414242, 381376072, 390313649, 213210735, 735426759, 443101092, 274093643, 168399627, 34096866, 592966027, 172814122, 261998372, 447029219, 82184022, 332761902, 647197462, 565092432, 676754674, 660494593, 410710647, 614452516, 4076968, 508726064, 43101001, 388859674, 375079688, 237262492, 534410159, 350006810, 866360877, 360782238, 511979790, 376066597, 374226799, 678595300, 744238484, 36318578, 344979592, 682349752, 495645952, 500637552, 657199295, 475133899, 714831058, 954215533, 353899265, 536099099, 914833469, 110304936, 120129162, 668737672, 840021768, 728906222, 497490695, 941791960, 29033380, 358010034, 244796594, 542083457, 688163013, 918560635, 772553507, 934463232, 314295868, 999558194, 180724729, 560227481, 149223444, 383876653, 491028084, 904042244, 454874086, 835755915, 327736847, 225029480, 345966153, 606812687, 669245577, 344645942, 35263651, 425608297, 474112669, 422577257, 573429744, 882902492, 353691398, 660821502, 813860389, 782019109, 149337289, 425528708, 783998208, 175705501, 959793276, 741093173, 607260857, 345303619, 866553075, 174877397, 916093419, 366983877, 670541945, 158424815, 56071799, 105713727, 298720534, 532392882, 669859572, 149613332, 258013581, 737540178, 361679638, 336993542, 349872834, 927700876, 397511018, 139844381, 443544410, 162979463, 619483509, 636663436, 863328616, 11435243, 434688622, 166023546, 280270145, 55618248, 13283151, 573654508, 620861056, 42566126, 523401281, 541403834, 894454048, 394585314, 653676945, 336190084, 564856073, 430220652, 769377546, 405207926, 521229190, 727593406, 839539887, 203482998, 819109465, 168005890, 678834962, 604308662, 834581691, 518588631, 92589482, 205051537, 171284886, 931516733, 582633573, 697146466, 687050947, 209477202, 267595335, 828647474, 432763358, 334420889, 106893385, 71925898, 356602595, 58135983, 679250290, 753240478, 290941087, 335312283, 62128250, 225049370, 232061218, 936749421, 47488609, 923046623, 187187160, 691000713, 112281689, 40614612, 617677326, 33351385, 101408078, 11504277, 518900462, 606467392, 629011055, 114525315, 723491386, 373665648, 72879038, 341008859, 905586062, 663217692, 540981826, 570881274, 197714810, 165770884, 737187222, 681531106, 110657237, 522995579, 969333126, 961378497, 7974125, 250337201, 212832571, 606946740, 901671848, 646999126, 384706554, 145831341, 535263725, 871000399, 147758188, 285923374, 894485852, 415403450, 301111570, 373866039, 697268188, 331948087, 460319634, 972304427, 444055413, 648986788, 667377785, 262113463, 378184366, 569360607, 483755997, 891070415, 648528536, 61059175, 469359455, 724735083, 846041929, 602663752, 706028194, 244289170, 952457377, 292629826, 444719109, 701161181, 741128424, 686404674, 217520428, 164891628, 179405853, 54935957, 661926409, 61887551, 459859040, 372212859, 225054754, 967133930, 144674806, 589511532, 625049895, 143444709, 463874502, 87712277, 651160443, 160197798, 964867807, 890094982, 645370007, 554762397, 478315441, 102394035, 16959063, 947161026, 24946177, 150897262, 498571515, 294969556, 566373255, 817247201, 800026379, 965719495, 783281602, 925211748, 462665667, 906997830, 40462560, 772546761, 512765794, 608228523, 650390572, 903095740, 777493414, 584974532, 126830840, 456581972, 332650539, 61084448, 315885666, 49423004, 404645722, 288147050, 298045862, 955373002, 793138366, 159556248, 335797354, 135326441, 244610198, 701924294, 395546968, 33363058, 597054807, 588767644, 264716129, 683997839, 204893033, 358177675, 729523217, 564169841, 377791239, 55400349, 684004742, 397242792, 658297453, 114264474, 195127885, 636896421, 633436315, 766749961, 787185717, 88466207, 112139092, 887909968, 242500791, 607818611, 67784378, 647714081, 807876906, 128828444, 808028200, 789448208, 84553302, 950983149, 686498125, 69151041, 875535043, 264742453, 837824793, 253680864, 880892376, 96808509, 881151299, 279981513, 868063239, 966751799, 425367869, 527490410, 207994218, 199243931, 508748388, 950630373, 399779240, 938252704, 483186006, 994106543, 648845756, 359242027, 312344703, 603622937, 697334797, 142858162, 125800643, 607434302, 531245547, 615058919, 151787043, 349113423, 210479695, 650829808, 169672155, 271965542, 44797159, 421954561, 314468812, 958906592, 676217386, 781933926, 560083488, 343237740, 719520007, 40802226, 449533027, 948317381, 468009830, 542247262, 22004002, 774773887, 827336301, 193134206, 560668490, 823597871, 267530682, 793651853, 297634265, 82758396, 346739129, 580938648, 215622394, 451258035, 345360236, 283516171, 621147049, 797242893, 824301689, 366781459, 222304975, 347785543, 478395360, 658739013, 288383412, 907485319, 409024492, 802582597, 939380411, 382694391, 264599448, 27868624, 265162183, 782252713, 419479374, 184704038, 563384540, 741016855, 217540768, 743198063, 990259131, 834518760, 653148158, 899309526, 503076066, 20557915, 119589598, 390607714, 776258069, 226590098, 675259756, 597170800, 522115733, 584574667, 681842542, 413618316, 493657297, 884183668, 723073222, 160150346, 381672541, 465112606, 820477475, 14423124, 476219576, 599782131, 166125411, 865706439, 334379700, 225759292, 710454413, 413891726, 474082848, 639151041, 27262359, 588934582, 58079654, 257306887, 714789496, 893330992, 383130497, 335116429, 641059382, 94044184, 402458719, 359935522, 537695687, 787742123, 678661413, 967528578, 842548816, 41012416, 614022603, 646536736, 634318132, 968593457, 323064046, 370517282, 578245485, 997968647, 872418193, 315899860, 999714203, 620505985, 413620197, 926344194, 199112611, 415236512, 432437056, 925813513, 554736793, 881072651, 573050014, 645747376, 332882035, 39689620, 178886833, 922445296, 749716104, 678417545, 815183306, 13102135, 425355494, 778667956, 875872673, 92206649, 642702978, 291460761, 371033886, 922290080, 260361041, 757454614, 448247143, 322130704, 869058051, 740431258, 534870901, 625956070, 531400550, 641675183, 692195176, 885723580, 290074071, 884552453, 854816918, 61828859, 897023535, 229374028, 444568763, 374109451, 475480528, 874285410, 461478990, 11194459, 952243202, 710588329, 658230399, 827932388, 13404570, 15327481, 940034488, 908142893, 400217114, 924410794, 756494928, 547841706, 636531721, 693689787, 467082308, 873468493, 385729971, 9186483, 77369532, 581357831, 116116339, 329084150, 444973328, 548114574, 477305007, 95433605, 354785140, 83187514, 575727017, 281116424, 873874179, 625192822, 557378956, 791923905, 200691808, 967986158, 756590521, 105556309, 152812121, 566690289, 79038436, 279203151, 774639419, 117570961, 30872538, 9603708, 529914674, 333977972, 596524296, 446337146, 773077011, 706452560, 756674171, 739726778, 412237645, 951155730, 995507250, 778723059, 3601436, 723815774, 84761851, 241046903, 869055650, 901269606, 772722556, 342898252, 420356068, 336431437, 350135236, 52923879, 272934161, 750766270, 925090500, 155222196, 385162799, 74701804, 665469594, 543925110, 450042853, 792167061, 383911452, 864245634, 724318767, 443279216, 298823600, 486919149, 131957416, 881208674, 756531385, 229288677, 343270880, 497554513, 160745147, 433617466, 748874366, 116357880, 346292381, 160806853, 572911390, 312877676, 729202272, 530723708, 631066767, 248677211, 718732546, 186800741, 143873107, 709143184, 676922125, 76368732, 800044776, 688048002, 214306279, 286928490, 864068627, 592999731, 463186048, 167464222, 738537979, 11897304, 65541196, 184212169, 552690273, 229408335, 569235858, 44481860, 247956018, 798547746, 630819160, 115200798, 977528422, 929237342, 993850708, 852947908, 538972263, 330283243, 180123381, 790708575, 188490135, 913016213, 285415542, 104012821, 441809771, 294483314, 280527984, 824334004, 223687294, 83287651, 931482462, 192213311, 453281562, 364333005, 757848593, 768051550, 462508159, 540204182, 37100124, 533547368, 453403377, 339302053, 118802702, 27759650, 447821415, 305823925, 436565100, 768317807, 645103722, 221037168, 794904816, 841087600, 614774838, 901005776, 53082378, 743029776, 947894466, 365927316, 159077980, 565190376, 192809323, 285000892, 924245185, 156794005, 923802484, 970280899, 393822496, 833227120, 637580071, 586711423, 632573332, 572277181, 479280910, 633304200, 606773983, 87969484, 568108895, 846391342, 334715727, 806047191, 421249030, 88075066, 772995188, 554923400, 365948873, 346723333, 414645759, 950355060, 400662295, 98572491, 847184893, 265391403, 213540163, 791436929, 133994329, 44131545, 173197334, 452391177, 355891107, 40632361, 305375496, 973548463, 779657127, 330653766, 984217324, 185864526, 996225461, 986380173, 890905127, 208491544, 742642770, 720280575, 153484999, 460272571, 728490931, 687582869, 43713878, 401899459, 890265145, 197112574, 140977449, 595186980, 941349969, 905769819, 469389003, 92300297, 807901333, 94409930, 390280641, 739782129, 446926803, 375675177, 140128024, 34620473, 828939445, 675060120, 190846056, 521298364, 760784245, 975400692, 879439686, 532870285, 462767868, 193054281, 368487186, 817818096, 775479822, 86650446, 140150203, 211928128, 558981436, 38757269, 142707188, 15458124, 855315353, 202852865, 589792621, 886816462, 370856, 206655626, 741961885, 672469263, 874495864, 759434449, 233392771, 890196865, 831275581, 78930146, 493555286, 439713781, 122573396, 379672507, 228100365, 993719915, 284129657, 317322666, 912058927, 111530473, 705368479, 260075057, 480156065, 303224478, 647663195, 298406145, 837047910, 715268173, 661967631, 581397940, 584569475, 546400936, 398047973, 388718664, 445548298, 504565923, 508734549, 786945787, 26070526, 726515131, 321790669, 557539940, 483215718, 142577815, 697192044, 695260556, 481805756, 695744844, 240244237, 836685850, 786179476, 931286687, 643606424, 885694355, 43041879, 860470805, 659699860, 938989580, 869839932, 599167188, 129451087, 269076005, 463914035, 957799481, 503752621, 461407357, 172193820, 703883985, 767755585, 168525007, 151119404, 271198577, 350555113, 147613031, 960793083, 697563695, 99906198, 917710060, 724762869, 665519014, 139761003, 166345819, 897887152, 985481741, 638119199, 13347742, 673588725, 131584546, 498315284, 560200622, 723387599, 522965009, 405483389, 161050110, 912597560, 28771221, 22095536, 10073134, 44777086, 605771223, 371965038, 609752670, 888750890, 595129801, 735116853, 231417241, 744648299, 322894049, 562274450, 631146436, 892396148, 877491186, 55545675, 459978254, 820166375, 886588476, 71983549, 105958781, 732713289, 472443633, 261626136, 232806491, 162608809, 286926791, 275748174, 392329536, 627562285, 592125099, 541640104, 236666103, 88511633, 868834948, 119045221, 81113655, 381519198, 683440453, 167626857, 73142907, 475214977, 292331093, 43468354, 588080128, 514722381, 449956584, 903337237, 527414578, 72573034, 626782868, 363411124, 762364681, 697871955, 495411849, 929787675, 916001318, 92759420, 663396299, 760342052, 101739264, 857952688, 616568534, 879883594, 646690114, 591993462, 205255828, 673376915, 438217187, 752455572, 831586165, 984084206, 435215346, 734072403, 609163336, 456535316, 849592944, 470035816, 348403257, 755350845, 955143475, 944733777, 771630218, 770778875, 251840998, 23483607, 861071735, 255455731, 640718975, 687725387, 50351388, 509550266, 246988232, 650823463, 101644007, 51684898, 582066092, 279124033, 179752954, 330630588, 546613029, 999364486, 799522461, 454565085, 79006339, 793136040, 563414052, 875137851, 924485670, 467861317, 652565510, 736153183, 315703875, 200024244, 474564303, 112316169, 545560996, 174817296, 945766927, 951744643, 682482689, 852411808, 110680680, 572836019, 364488835, 817843053, 695484292, 524517970, 872336069, 52577609, 699809955, 917548781, 282518911, 757188308, 857666833, 390731021, 138989658, 575482422, 887257531, 847975821, 767248518, 99613883, 303293314, 477425663, 543379681, 716502439, 34462815, 669693567, 303284781, 896847254, 827764824, 335039565, 354865727, 750264529, 967273255, 685479427, 479981080, 268798110, 306275036, 195619782, 757755182, 419299764, 621895895, 182398537, 998301481, 48584090, 923213728, 286103140, 800323873, 520711382, 944255672, 923738002, 801053342, 823186533, 141339234, 223942997, 333759238, 387490344, 327392612, 690090525, 327949045, 628486643, 304784540, 215617559, 340210894, 201996127, 527119751, 94321766, 176407437, 283877235, 448475853, 647558123, 163810822, 472645021, 479137012, 321345320, 681887205, 155201252, 202051293, 286348208, 476883373, 176033812, 233694652, 562042222, 87511887, 968204115, 291884399, 325518778, 109396016, 687916909, 467832303, 191975409, 567021427, 62983302, 64061660, 318463435, 113470713, 578475933, 959585534, 612648003, 707264035, 818339489, 675045053, 902632498, 669739141, 908652805, 280025448, 69232787, 760927207, 741247241, 524804904, 319273260, 65206632, 498142693, 601255442, 534524374, 225000109, 683838686, 786899042, 371160471, 511740669, 787462156, 732111598, 596187840, 256806679, 606927285, 593255714, 960160463, 50113322, 551180433, 848695192, 623824441, 603039204, 744263887, 849014546, 553222973, 471782762, 54156472, 890726155, 495333577, 955893856, 235550339, 881988648, 752367859, 262589385, 110118799, 858921560, 588689346, 225462771, 976311681, 996953986, 691888817, 221091617, 667745877, 356487282, 797042030, 73006242, 516811716, 827303774, 92683358, 912373217, 495524627, 134375174, 316636882, 440573223, 808648732, 857885625, 434324407, 387543032, 599435627, 909161491, 122607440, 572656036, 670759481, 524918399, 615688803, 167977847, 670030489, 381753178, 74822831, 40431478, 574326774, 548951909, 832606631, 464262274, 312631717, 844089882, 713966045, 120971662, 467549944, 161001045, 546983945, 438059941, 723855499, 481063299, 509514667, 898249928, 800552283, 978138065, 1745069, 989073027, 254290015, 340362057, 624887261, 930821699, 480631051, 456056862, 611763123, 422509392, 103531255, 22595958, 612509990, 753551728, 401767127, 134936791, 940203820, 973044063, 638582480, 634967324, 402141007, 541411225, 489825332, 964450468, 467883195, 205615986, 999165473, 828348704, 571304213, 748300067, 325565670, 495055533, 107142541, 2469948, 265696934, 171046977, 331394547, 581923641, 190102747, 75744699, 883187817, 106645962, 763624177, 893490921, 884911759, 7063445, 515346934, 114868751, 719779372, 24471501, 76093978, 172866498, 676028759, 720685629, 674280017, 877616993, 702351593, 610439765, 713809461, 895633146, 43450173, 335282237, 690745737, 167649651, 779922980, 866522040, 472176863, 425861230, 978050923, 58215631, 209156056, 769147736, 298905826, 963593218, 905539278, 859686572, 237226221, 332596568, 885990253, 845944402, 17273034, 85064675, 526410075, 274441650, 751237376, 28707384, 93072805, 731329371, 593968237, 147887246, 722072968, 590684562, 141748433, 934497206, 351730528, 374959455, 200754727, 508684702, 475443388, 318031946, 220020566, 131500455, 430276557, 267728179, 893729116, 879894563, 924522665, 653018663, 617571132, 629478429, 131403115, 997851164, 405033125, 219739762, 648850435, 707505822, 549233993, 157245627, 965154302, 724315058, 369103450, 476084033, 30840993, 377270335, 976351645, 383672329, 682831147, 38727765, 951069477, 431613046, 508322206, 723828985, 429740469, 86454873, 846244059, 808296224, 174480113, 546178712, 204506442, 116428906, 408107034, 401815809, 491320391, 537077325, 995520388, 621374354, 442849632, 681701523, 99966335, 29280527, 852631187, 285706385, 927569253, 943794198, 556860457, 480774272, 284067952, 451022432, 45443197, 966784780, 863949577, 481778060, 848349063, 501191394, 192917573, 113277440, 710220157, 600305916, 579619071, 780614174, 415355221, 758531198, 98000208, 129003953, 506629237, 724118456, 712258237, 127233834, 789458199, 661353282, 454762547, 149111286, 317989582, 428749922, 780705966, 423874729, 609607776, 934670706, 935909873, 745154778, 168853314, 354694058, 479621254, 158965026, 620594433, 751146379, 535366497, 789753317, 373138112, 631908098, 403752528, 785454363, 339664805, 640301250, 368998019, 834776980, 84551152, 195908176, 925070072, 112447404, 867691000, 972463875, 373993086, 583083559, 260260776, 916395900, 376142331, 989571, 414996653, 248901264, 829668977, 740039386, 121249438, 25729230, 931133272, 287666808, 64878411, 887933298, 343576323, 374853378, 500199990, 21805273, 729605561, 860711061, 682242873, 396603057, 50680168, 2810412, 786375633, 500271357, 927248683, 792090915, 941802922, 577410562, 687247779, 667768440, 462679751, 561759856, 602465857, 700789359, 647240355, 731424551, 113270451, 653248099, 486686836, 765720824, 214344586, 172313816, 770748036, 781664017, 741340757, 264355027, 385049434, 287094325, 799218716, 167595273, 370402754, 68537435, 367869321, 548926579, 28657137, 192958997, 438239619, 280172870, 662043044, 85515481, 604548438, 334065661, 237957076, 324110583, 263087481, 415333318, 493801538, 362351190, 180697959, 316206647, 468868484, 80538572, 383779878, 478368956, 232342220, 767102899, 142140661, 478306223, 62859758, 634122354, 412503128, 605023538, 649807645, 646580705, 173729670, 995018409, 679638005, 478416162, 955944785, 497064870, 448544432, 634143603, 821864877, 684318800, 601593320, 94299299, 258515613, 884429494, 75899707, 781289642, 358194341, 288501924, 812820345, 476270012, 444396974, 860339773, 126407303, 25850295, 45444807, 681428897, 515904675, 484292659, 174396353, 961620418, 253618058, 334674053, 898853370, 364251810, 554390268, 47677878, 731639450, 765723108, 97630168, 463472084, 548131021, 592216573, 223906348, 244522428, 262189021, 391902716, 692269216, 790949767, 702914721, 948951840, 421590537, 474403335, 539407756, 971419437, 889723201, 54170537, 909108216, 286635370, 638346943, 213298101, 93816961, 926169155, 797891819, 755423593, 269842697, 58469595, 321791953, 421836478, 703481033, 147287335, 897403453, 662471524, 941563150, 453680728, 577654848, 694644791, 538711706, 101516075, 87365364, 500906914, 479260624, 247866494, 680436266, 87555983, 89866772, 860657595, 29193850, 313376260, 743776840, 836835492, 296908811, 668691027, 747794270, 511095195, 471381502, 298992904, 31472130, 233898982, 376010436, 670653520, 654130755, 274410938, 497519039, 80136892, 754778533, 458213027, 189456530, 548840032, 472214535, 47426542, 470517555, 46711451, 673484002, 818297547, 461099580, 119220274, 941723364, 168889680, 714946585, 603100506, 614165180, 310954651, 310502192, 530909429, 840842568, 271384929, 631519593, 644731742, 135736070, 369740500, 548697619, 941927470, 123718622, 654646485, 218974962, 693672649, 680937998, 462991330, 618865207, 526326015, 651254173, 734304179, 997439602, 998940911, 187822092, 946117552, 989187233, 77062398, 805230405, 738941707, 152344162, 262653478, 902636940, 476240448, 400880529, 857401083, 654036036, 321135301, 466857149, 377885909, 569286379, 652431395, 905285261, 298002920, 990792368, 143177773, 448935855, 556758341, 800108661, 129498308, 576738381, 208785194, 260125700, 920859229, 712881229, 230975549, 389483084, 616302252, 468530008, 304424477, 357713623, 698179581, 691665447, 382751838, 523531459, 388597333, 74018859, 724982653, 699581714, 821991459, 13689010, 177821436, 46792027, 596645075, 1601716, 946895945, 659356052, 805360718, 391562161, 309290771, 155261413, 514234584, 660901546, 351471237, 534887955, 155925664, 54484293, 845451503, 116080693, 863756759, 22683467, 770614148, 845267340, 899388228, 438801726, 861193369, 371176211, 654568318, 15362921, 977088150, 91247833, 664538378, 725906585, 881027583, 369598495, 948001896, 628232565, 726155925, 457571357, 190443975, 712936462, 46316784, 423627799, 477833902, 100315468, 383105373, 112690210, 311398946, 320659203, 369483101, 809916460, 97486960, 355953930, 523180075, 867807418, 579842099, 907696564, 39775906, 922507651, 681990247, 130364805, 396576551, 140838327, 97605993, 842820577, 545671093, 382307614, 63916917, 879185383, 865531364, 585811099, 494515676, 646198390, 55349206, 118776376, 549151910, 136683679, 460736248, 455924797, 429770222, 200296171, 265238452, 406648521, 158669201, 979650728, 952994274, 763940696, 48810740, 851385121, 818649301, 716501514, 654506641, 16028109, 430577975, 51158281, 447480718, 349763601, 487008861, 165128172, 899786956, 713076398, 752008931, 384570637, 756892866, 697291762, 499144461, 520810808, 272487487, 925119874, 554440280, 556200105, 867780952, 227705689, 367952217, 327145501, 171980522, 251535995, 319223437, 150761101, 854695875, 614236821, 338378191, 43639390, 240686055, 436548727, 574314360, 38046159, 69504029, 774136416, 626958454, 632532688, 714142844, 396023740, 690769371, 44684481, 4031296, 764061115, 571699565, 72549450, 202368263, 722385729, 951168589, 103692788, 999498828, 913485076, 255286630, 882213258, 950974622, 951942620, 413276529, 171332775, 844584875, 246549554, 439991749, 366303061, 961853345, 23512736, 558453654, 491319306, 548008121, 635736145, 250831333, 620155763, 791735018, 746449258, 343346909, 218828382, 216333166, 197463398, 260959557, 191846168, 936201713, 292962417, 725587888, 515693395, 2262569, 716876570, 329130271, 986265107, 393759929, 29796075, 200464030, 308245131, 203685116, 212088222, 61417045, 299075886, 144750779, 647712158, 879569084, 838966545, 554715787, 366369629, 580526758, 619412933, 501850320, 320231367, 886373363, 143667961, 251084450, 814929211, 613048835, 620775269, 288984082, 950113230, 611314951, 203912963, 539877238, 503137159, 980332779, 658572970, 806195058, 922321560, 747995839, 229628886, 504171649, 710186988, 137305513, 652647531, 431566070, 111517944, 501150646, 211216058, 472502088, 836973152, 660648201, 195996551, 843833553, 223260677, 804255568, 86778367, 714314432, 137739479, 415330214, 638872368, 512939723, 647393691, 239495783, 647412830, 636062678, 601320665, 82303870, 613516069, 787511252, 912960774, 655350360, 799444612, 477977432, 319089557, 617196342, 292536785, 650534419, 920587222, 392072119, 284419425, 29673346, 763047972, 476829091, 659399215, 890925068, 901064533, 343546594, 709881694, 264859898, 715049504, 59272820, 177996985, 355985469, 780828465, 316496578, 298605892, 790959821, 432789751, 738320443, 443925765, 702784563, 699859478, 331382725, 119842542, 286132246, 867707295, 150632059, 89642976, 459907331, 741281629, 929249801, 853517931, 88520090, 194835327, 843487376, 673105828, 198141183, 128237349, 722202332, 816787343, 919928635, 759525406, 479231447, 343863675, 162601063, 488161018, 161876440, 214013778, 895108699, 893369671, 339849924, 787590792, 481818645, 298493516, 138049278, 617549920, 249494036, 588801784, 250100086, 212936416, 934635380, 578111791, 307332055, 358362928, 818333760, 508052226, 391134695, 772624765, 271099750, 491178247, 379179018, 377503842, 275213360, 371091010, 606465717, 558096696, 48586292, 745561162, 16151670, 7884774, 182243835, 969776242, 14725176, 752583609, 207388793, 630575029, 269988235, 331726409, 139201266, 302586782, 639977028, 236774838, 726255761, 131588385, 353671111, 388390286, 246937363, 523967964, 644173085, 282858495, 822177641, 922562478, 979729425, 478810819, 138729637, 839492779, 214727448, 8018871, 174036834, 160500263, 93065820, 985023477, 923706897, 719463832, 507780188, 492761888, 44413349, 605709221, 675749340, 493709524, 220262889, 223904960, 254616124, 342108103, 900200526, 253257904, 588989950, 623494583, 576827490, 996515108, 610400362, 946751210, 207350950, 815904694, 169164695, 49257431, 810828127, 627104982, 473543491, 499845759, 556743156, 394892831, 65376333, 445841724, 544775017, 137850233, 554440542, 509809788, 218503823, 944810347, 51663345, 699324589, 364716801, 672563000, 157126342, 798077651, 224037018, 119588890, 314782288, 853108586, 484751699, 785299749, 162882100, 466054354, 21354405, 130837911, 706985001, 134291575, 163644607, 336739290, 894683531, 190305676, 613253792, 81102774, 506548289, 890620829, 385326193, 479905374, 403130775, 759968491, 264650211, 560473778, 963584970, 862489213, 892649423, 446083097, 256056719, 234805803, 482194151, 930629204, 250889657, 336956367, 16843323, 108138083, 308727924, 851589586, 248309886, 617899826, 39378284, 401556298, 207841621, 896166980, 905836170, 180300948, 981197319, 981378720, 782185715, 465158815, 283527678, 312086060, 400855120, 870493325, 517828126, 961045222, 171961266, 253099827, 729637484, 291361581, 873261118, 283995680, 767242894, 952195625, 399575245, 552007575, 353016095, 77554556, 432993919, 918207041, 760374877, 358628277, 899681176, 607296295, 421056394, 742511283, 161760247, 705380856, 782572001, 828908382, 265119199, 871531328, 21552045, 262557384, 67279172, 160981156, 774023217, 645213915, 305557438, 42508182, 835123332, 766854518, 794463426, 778860186, 817101088, 456775008, 142623072, 789004062, 250962180, 514412584, 774109654, 827260011, 774916743, 772995789, 810864174, 685233296, 584200611, 335214654, 382004821, 317912043, 554079623, 443761463, 488236745, 642390830, 955323133, 329061900, 50227880, 861781350, 257076380, 521289918, 189568732, 510931574, 382549519, 87944157, 480246957, 692345649, 341079805, 107264382, 785356293, 910308253, 756258468, 429373582, 733705075, 802241141, 32805627, 899251046, 200233402, 698776722, 110892374, 472025582, 356494276, 145493020, 265885633, 876171601, 860154913, 878020965, 501439285, 51968475, 832330010, 972550390, 565859230, 926836915, 271016069, 226186846, 383250151, 385929488, 367423235, 653678986, 112901627, 266710288, 99716632, 864282727, 514648779, 618528220, 66198766, 428262803, 849827908, 987003916, 646887541, 178796475, 84830504, 398836951, 155663597, 847328424, 998951477, 434155002, 5871564, 65258862, 5207010, 450960553, 950431444, 978959166, 804355161, 709363274, 187988525, 253270225, 436483190, 946341160, 658023670, 412226367, 516194607, 158386606, 437416297, 191392507, 373448679, 596980206, 207864555, 461660839, 904695823, 772297721, 874974398, 483026779, 162493068, 8243330, 199789260, 78023929, 673467900, 786593374, 990384456, 820628681, 478792468, 816994467, 862451893, 379966548, 373041297, 70541982, 863190293, 307753572, 115478996, 466696350, 645671938, 884064788, 613953337, 147885090, 818236014, 335993672, 435472620, 467120152, 657801511, 148884198, 59011312, 917860798, 482208058, 411100236, 900871489, 788097281, 502530474, 919087187, 152788725, 337211455, 84733510, 64788083, 73615082, 754304899, 850785819, 763228826, 627780530, 614511443, 638879490, 381996566, 446301157, 40443628, 707609421, 154387449, 419776705, 255762406, 204160801, 843672029, 839878772, 835786394, 376709405, 428166166, 352188811, 908628223, 443636818, 874103243, 988818050, 526949821, 628732441, 966272636, 50783878, 105799338, 819596443, 690412871, 67686993, 202328031, 851450121, 687349008, 155094565, 756461144, 150334685, 972867569, 587852498, 502188967, 129058750, 380333719, 324934487, 621832235, 845927567, 829251775, 295069035, 396987913, 198980960, 235544149, 513028633, 904880941, 28105461, 290243744, 858019329, 748699114, 414856206, 351351663, 856521455, 789604424, 994417410, 295765475, 256251898, 810144080, 646415838, 257284517, 222171392, 945176884, 307614951, 253662668, 886974045, 715345690, 803274624, 711610027, 195880021, 111057610, 520516860, 353503171, 967646320, 693165451, 340643218, 975231736, 717455251, 204223790, 447288436, 378988845, 26344775, 176373171, 661392502, 377167445, 49152551, 752882056, 589470719, 827527801, 321778168, 992579255, 756407336, 880522324, 573952255, 350308567, 16789263, 877372907, 290405418, 531066223, 328435947, 224025835, 994947425, 400082735, 958185310, 438357627, 948378253, 82621623, 43165186, 63700880, 672468658, 57141603, 806156513, 965544306, 638914519, 326923476, 781106605, 96132700, 75213136, 602291537, 190140448, 11799583, 59654364, 913653800, 321521825, 956080, 267135848, 522495764, 150609738, 944076594, 283908370, 730728974, 112011827, 582733446, 17693610, 247619453, 23339695, 159891507, 217148302, 862818865, 150643801, 335198078, 625333950, 253857103, 373322845, 486576319, 161252343, 409380601, 804418495, 759875555, 181055031, 916268964, 97648763, 121635343, 565303343, 250166428, 367711808, 147302170, 235850244, 522310636, 519566622, 202528132, 864243892, 32444, 241309760, 760313092, 12214225, 333291067, 337349198, 498988850, 49093155, 475699233, 751062009, 830450044, 963800164, 153318188, 13166843, 187194792, 290277169, 338468260, 566033897, 816468005, 384487052, 734661363, 39788323, 744090786, 626909356, 758586953, 572601674, 116097562, 435410881, 587671097, 776834746, 90287077, 670262984, 558241214, 181878447, 962372221, 848169943, 444485016, 394518328, 248657753, 372005531, 657203423, 241767409, 56763228, 50819501, 60916089, 889690117, 119831868, 652431880, 601818850, 887432814, 496032211, 195230559, 410248851, 537663368, 633571046, 584467203, 215350332, 527508875, 708215317, 598617076, 578298742, 833827960, 907604685, 260948566, 748902499, 874357163, 277188686, 90747610, 745462888, 753831830, 969384782, 815104759, 430046243, 432014663, 137833929, 519131943, 414749557, 779773520, 796756812, 917750072, 212173989, 942260438, 896415632, 679450044, 875104329, 402286069, 227399851, 506318201, 516085042, 814852991, 429219643, 120567682, 466042744, 985462112, 961036539, 560299592, 821953482, 268189671, 248319152, 328518237, 509273638, 730123052, 295655443, 517051044, 99905028, 31391457, 513397441, 359685972, 291086307, 404037248, 580335919, 778759730, 269756071, 513506997, 581548382, 617276986, 732787348, 658398096, 433568301, 653655128, 460448812, 975788185, 807762037, 951757477, 130224198, 657132333, 27063450, 17719844, 868335731, 114745481, 780042094, 305413232, 546249252, 626559749, 331361812, 754641942, 52857390, 832350782, 953131211, 135857673, 33681282, 518252601, 765919756, 669238820, 394975176, 407574626, 264947530, 487274216, 232364598, 526430609, 974082248, 50188489, 81259202, 281328396, 190591227, 578628446, 278107570, 3138015, 624380706, 928718710, 467547534, 189117598, 270401036, 908130420, 362951809, 707735587, 242951397, 55844384, 928837861, 758875574, 319494451, 336307686, 103047282, 255602706, 966241646, 866175363, 303372817, 858873202, 356434041, 35010291, 729213163, 44391715, 331467094, 326781347, 180221934, 972423856, 407962834, 303608544, 473204053, 594630533, 359372533, 141066434, 678652403, 233164310, 523044845, 848066482, 662784916, 62823658, 310310120, 677979214, 201076504, 128801320, 972183991, 520436201, 246915996, 33305434, 615547168, 539340900, 613637370, 532713764, 16571839, 981320290, 685501825, 523576278, 55378418, 404164069, 949990691, 384907698, 968751101, 112040259, 630660822, 651183302, 371512467, 531433929, 878328716, 377366945, 118271307, 494697824, 856766818, 594029532, 553794948, 615590479, 779875467, 337767778, 517545689, 794320851, 952595357, 441819183, 951263653, 261686815, 377100272, 619507174, 432201014, 281731685, 58305525, 133563639, 295793256, 4461547, 148919477, 576556023, 565709538, 498732459, 860599268, 981216516, 121482744, 572477606, 347110167, 31202669, 390337733, 730533737, 288605079, 349938623, 183834888, 853956278, 32580642, 625310424, 911447749, 595183880, 534742250, 973262189, 129382585, 322969357, 330645009, 366605340, 164980035, 516992863, 856362033, 754465915, 690825436, 233870227, 138929962, 641019044, 467851926, 569785981, 994103074, 724082830, 152026462, 262022846, 101915293, 266270300, 342532342, 613882172, 82149313, 936703026, 320220148, 954294134, 440225207, 794839305, 443722833, 385345166, 824308525, 605242915, 399584653, 415274643, 433112005, 845394514, 668986501, 709352080, 754165440, 274572769, 75648567, 960076487, 9889879, 681942271, 804742647, 141744927, 820982579, 115767517, 557304989, 888276369, 120386176, 895879905, 91044724, 643304119, 992717561, 748689249, 82485953, 858304897, 142012264, 195560235, 616902288, 68134612, 290778153, 46040092, 851059082, 67833376, 85777378, 812950627, 421030380, 533969144, 457457787, 138968768, 99051782, 2531170, 174601572, 473597029, 259191313, 86454819, 295969987, 283190196, 996629863, 679328754, 643771320, 445273329, 187124074, 987959916, 591076913, 842297139, 801525338, 53458656, 409436569, 878500391, 592544055, 564679194, 71462075, 894051644, 124238102, 473427288, 162211479, 306037566, 126413962, 284841966, 282424432, 440107303, 551807366, 577001602, 160015353, 278033627, 227372982, 560859626, 11366090, 246255032, 470489704, 698199724, 936037252, 854102943, 853000730, 201930944, 231898575, 477542891, 111155568, 158561669, 54186810, 920253632, 404044548, 203357722, 987184422, 872564072, 326416952, 41185396, 586028472, 516911039, 105801861, 594933400, 329094538, 166535930, 731652312, 643262063, 512162070, 750126944, 197839530, 291516778, 466432054, 891251643, 872311117, 496604911, 205204632, 806308839, 401840321, 76841432, 935549025, 176633933, 800446764, 344212022, 250774233, 850652025, 26166418, 831615565, 588263933, 163268600, 352786605, 551438909, 205916117, 920860014, 294307810, 271644861, 249924093, 425860876, 116889278, 19782209, 404616988, 49677765, 695022355, 779688470, 575371015, 568681252, 459997849, 619764128, 131716327, 672080452, 151645626, 630129543, 93691233, 486218357, 626403099, 724103602, 320538427, 902213092, 895530720, 63124031, 757470602, 678963632, 309099836, 45353341, 745211520, 876442390, 88670689, 953250358, 582349393, 932818648, 900323453, 372410936, 43696982, 547841692, 34992234, 887124781, 455532735, 615206259, 899294727, 608547849, 887546701, 639231454, 338211178, 737774149, 793054282, 232826479, 425949580, 367337450, 301844568, 231250158, 736243736, 450104120, 549686119, 931947813, 661435305, 73160995, 736722807, 245649970, 412077559, 54403112, 613034581, 680029788, 550996087, 204923629, 511682620, 235494340, 969618433, 334927375, 748718446, 230664420, 237411527, 735935495, 828706758, 360565529, 43291976, 374631561, 52199155, 88899073, 194150161, 438663409, 603732365, 595576642, 397906136, 149481057, 403518598, 673664827, 463021713, 820885614, 962630676, 579326362, 788877260, 375444260, 217806508, 724313288, 103877418, 674197395, 18766138, 732267785, 196713729, 993277577, 733996165, 176109820, 801898741, 897033267, 381277633, 316992342, 12542461, 749338402, 294890972, 641170655, 872926756, 651386166, 900331146, 705873167, 829316785, 76262429, 321683337, 73488446, 772909494, 223661237, 541418253, 314324833, 209103352, 907977913, 604266746, 871991750, 632760278, 884646431, 146247935, 410810533, 887442598, 809535184, 867845608, 733104654, 509731749, 302505668, 396745692, 925689707, 633451615, 508343929, 938140182, 693855279, 25441245, 401225730, 422307711, 96507441, 8513396, 952683576, 37420854, 447300492, 136464462, 209707418, 185776306, 752674984, 959763566, 780636973, 546506330, 358870305, 817985896, 593339489, 593892913, 327325350, 683111576, 415560301, 475976762, 329816301, 341972286, 128240387, 33728018, 875955425, 110693841, 677481943, 431846384, 923165849, 811451153, 684353307, 924696759, 285700122, 511003923, 421027753, 607103103, 472177600, 200881781, 451659210, 781029969, 222898206, 679085710, 161829369, 775613028, 111609292, 130049641, 527736528, 224010525, 737847153, 843442279, 330531372, 294049572, 259548564, 905226947, 728233755, 476256678, 279988931, 229187485, 950857911, 6854623, 70775142, 28420013, 971293804, 288825033, 380998646, 652763775, 145442415, 544935600, 599972648, 614614066, 377202412, 185689538, 845470652, 48401221, 691337571, 979837762, 637643200, 745370184, 216710291, 408347408, 155564246, 846728942, 168271794, 919891225, 146697206, 52020302, 320040577, 638094109, 52492066, 672417976, 509239691, 402944285, 769213363, 154431370, 984900670, 514042447, 783827857, 233870857, 545258323, 844812607, 2216926, 842460601, 699462841, 118097232, 787263490, 367655722, 401464585, 484987973, 687189155, 915108837, 896101293, 932135071, 955131361, 746906605, 564486705, 528206640, 727411814, 27243750, 996274353, 644316362, 529818880, 245005483, 423403182, 386206765, 807415658, 971251902, 487801556, 685342801, 600476363, 515523954, 719859809, 406171129, 186517312, 847610314, 774765769, 348965842, 860977931, 567991422, 97840949, 154286496, 901696021, 700196516, 964563736, 236044068, 687934180, 46787048, 287327149, 653485536, 699624394, 238532445, 493276110, 444270422, 992095111, 194578035, 400618897, 510704195, 638357771, 429606476, 826419692, 515560652, 585869018, 405154677, 261087916, 384940891, 342299248, 939988842, 792004425, 986693105, 686897342, 572214428, 153338052, 198404597, 882404307, 929903067, 227314470, 379315543, 19518094, 61070075, 516301127, 516692249, 728241800, 752031240, 249601849, 182020147, 237786333, 633432524, 743880440, 324676653, 284966689, 842910828, 805528018, 230311270, 681954758, 494206996, 669972711, 855681813, 201960913, 731068549, 679163612, 594330936, 706009299, 679017959, 26994863, 247656229, 47736674, 622808017, 817851419, 898029932, 97314534, 334341287, 948750369, 152786407, 667736797, 370062452, 463594919, 568672758, 610244563, 27539596, 531699754, 313748400, 825909096, 27018308, 995269042, 616857815, 679988405, 619532988, 68616247, 448342695, 586395664, 781494349, 420955178, 467490462, 915266893, 454046827, 510120255, 242881051, 692320200, 609326927, 20197162, 954501428, 116744497, 56918311, 41856551, 472495979, 798008283, 757479074, 840848754, 904265297, 33614081, 19770507, 21095240, 82550654, 691568448, 116779804, 794749407, 492912486, 594791504, 3186784, 965529815, 801821214, 7172028, 801056421, 607033394, 19943605, 301111525, 742774913, 905441719, 183619396, 706225353, 765256036, 490887289, 279100475, 277113108, 289687682, 190666158, 866429256, 112900318, 515709567, 846604557, 514119557, 776636290, 626575322, 294709065, 364401304, 966717654, 705240485, 197051753, 201285143, 139202546, 181242385, 787857338, 356084929, 295715370, 755069775, 169133956, 98895098, 619833757, 504824215, 842806211, 261556814, 524405566, 591983935, 107326790, 827601904, 354951408, 810262442, 837144392, 882861833, 903372885, 699684826, 298727157, 24399130, 232288680, 507752797, 737003834, 268883384, 712792669, 97028677, 588582512, 25283358, 947179108, 858691594, 921220158, 613674852, 749925622, 224856056, 168869589, 381785388, 574229411, 50517909, 490789744, 419698092, 868246912, 113061198, 520573844, 629089158, 840984376, 500549075, 855490358, 546926051, 184511067, 902273823, 688469436, 711552525, 315521779, 719009681, 632313762, 557817083, 138911177, 147627765, 460269713, 799062397, 577296495, 177023057, 953712951, 195232757, 941214024, 213583937, 280153502, 145616568, 608670625, 735197660, 722640807, 990629454, 824480290, 140784810, 897818118, 189253412, 307955349, 355295652, 313121945, 317295745, 301930139, 805792657, 596387228, 498613176, 261045749, 777607483, 571687501, 123935785, 8408338, 828472240, 547897771, 302667363, 759526763, 154317275, 595226923, 388793747, 836661001, 222867375, 865804065, 524995064, 981160747, 893888151, 239269314, 343240184, 203350790, 14240394, 750715024, 886368395, 590802376, 689783809, 797129827, 214884972, 644620982, 853665186, 680107310, 56647886, 106445454, 61430883, 362163485, 558796130, 250215484, 528578110, 912655729, 805667016, 879468344, 56055957, 423225400, 607458187, 454300498, 233486486, 239602952, 912035203, 372517487, 675865201, 742493845, 547031714, 462529830, 453890560, 332605207, 131894706, 512362378, 671185485, 589510173, 650973039, 720579866, 170523778, 660095814, 862911173, 746996781, 492037287, 296196840, 556997175, 784206812, 972557863, 612267993, 429353848, 424484189, 982258938, 376831495, 178201854, 150935715, 943252999, 8361860, 246213973, 859262816, 876569743, 520604325, 147845998, 895520459, 955288120, 997445900, 951437523, 527783981, 213373095, 963327263, 837556227, 532670655, 86912371, 750863593, 54484984, 624780586, 896162180, 64278217, 169157030, 114611300, 11711110, 437997052, 39933482, 980457053, 686304790, 343792677, 954621134, 624551640, 7278257, 1421520, 299876154, 515956164, 169137726, 850871886, 901467141, 232308359, 714188467, 435022643, 611548790, 629530703, 55393210, 471983929, 444518288, 962443306, 11221136, 898734296, 198401958, 577497693, 473695144, 105989848, 915900913, 316842454, 710055783, 723927534, 160853476, 400926975, 194115825, 854823553, 518540127, 942863561, 652917726, 958140936, 557337752, 558244466, 177757206, 2243930, 738488956, 711356147, 561226677, 638233080, 264476649, 671625718, 319157579, 35014215, 618810902, 422453045, 112455869, 113923834, 149259846, 458267609, 179210388, 22807747, 110207675, 711347046, 876450843, 485202852, 390842894, 213755599, 882171760, 270534263, 867202201, 618110387, 685389978, 746374941, 846213940, 823756234, 583144165, 249931925, 270832377, 36193411, 217615843, 410683151, 355955036, 133589717, 110856993, 439279611, 23879242, 610029996, 227899680, 189723447, 879899478, 99244549, 701772235, 318199830, 465561497, 271792737, 435290491, 857694421, 30956146, 82482615, 496265435, 221332819, 261818624, 670659682, 249555775, 115643765, 587689893, 371149485, 108523412, 830097106, 561669247, 50918915, 921065273, 364829556, 631323571, 11702775, 273659340, 968901968, 552358462, 927356764, 158625226, 163716912, 939615930, 171272296, 394003380, 898327025, 906549358, 664819819, 849091757, 22108743, 797280884, 380240266, 15302973, 154867389, 864852201, 99694081, 912225967, 850256802, 496869488, 8754192, 446285275, 526396213, 885916911, 969840094, 436501693, 705358618, 539269529, 116719098, 914816450, 710996281, 861943228, 41523799, 35010083, 288574615, 742465398, 661641191, 240917873, 634726053, 495787964, 329148860, 396706490, 867582737, 701539257, 344459077, 221995806, 271110344, 153163281, 199870227, 849374123, 552413617, 34290711, 732742990, 267942180, 162492574, 403742904, 501969264, 935280839, 342820993, 319798054, 507979889, 238209955, 499160673, 931958175, 212847536, 832719770, 598897979, 267261714, 223295662, 325793636, 251303964, 611100403, 967572826, 239248258, 318036864, 168881679, 112182666, 406720715, 582960397, 278395518, 512535084, 499244266, 831929441, 520737194, 441551862, 884305871, 160169702, 133119678, 930002225, 35650331, 501731640, 748445830, 181859877, 239364787, 550686978, 679569447, 617751659, 818608798, 846726719, 566561010, 525449257, 519878989, 61405149, 475189892, 858548449, 653474882, 618738503, 670707499, 775696847, 934318310, 306731586, 592613478, 54076593, 235203996, 583209740, 575579167, 394602234, 93264678, 566306960, 457395883, 339544709, 314925171, 410720514, 697499840, 894267088, 210509902, 695407987, 574558428, 829136798, 225027327, 190568799, 271162348, 423846300, 104379168, 88536693, 127283833, 283460916, 431133959, 969233922, 129667452, 375551999, 831631823, 710150621, 943311456, 205764698, 726512686, 363573030, 361966188, 841355224, 112721411, 520530549, 338881487, 802907494, 657399782, 956318717, 383143225, 860437424, 732594526, 814860164, 370976617, 771887965, 58160279, 665666310, 999885276, 33816170, 167513686, 202724473, 839489711, 699444985, 39366211, 747112763, 305906964, 450971043, 52925568, 31643882, 280396349, 28067736, 802062683, 22381135, 554490106, 970027982, 218037700, 678219996, 991711852, 500080514, 666035215, 227362269, 404926644, 764284691, 468078998, 130927582, 431438652, 738202358, 258336150, 554798183, 305628487, 200882091, 256840452, 321330558, 711385609, 912395283, 898811138, 731336635, 33251634, 849855103, 330940135, 785323715, 596981146, 522533203, 880788040, 461518748, 677432197, 60705896, 674531064, 109250997, 72944075, 518471963, 257117391, 384421680, 244052741, 762360809, 940104741, 423483681, 540401707, 593350401, 237477358, 255041754, 930814203, 905576270, 311438085, 799892891, 841288785, 518594822, 621389855, 776898611, 440685794, 940763849, 594762303, 348885593, 777142387, 559471130, 481238841, 479755619, 711474020, 133491759, 963400161, 49475096, 879483418, 312789923, 820149309, 409635826, 791990737, 463317258, 787906585, 852299204, 919638565, 483476751, 201382919, 529206262, 131157212, 548604467, 660583721, 40845946, 663775673, 11321923, 746395710, 37424723, 6091325, 281952645, 137518200, 101741452, 4032871, 316419131, 929273590, 100670050, 671012025, 983579435, 339439480, 744649909, 983926755, 550301026, 965183364, 621939568, 295847638, 717952892, 578497741, 880302472, 394638488, 546062052, 795323290, 649060404, 878455383, 411646008, 517414716, 714561351, 442625280, 43196327, 97968055, 558600271, 413624660, 549502068, 52647129, 700968619, 318754953, 854675739, 586090359, 906866095, 127090673, 770615660, 555157921, 119029097, 417879568, 479084908, 132604139, 911849136, 887854261, 744178201, 700967101, 473608008, 656522852, 453927453, 453743401, 601430643, 141566570, 305057665, 609378638, 302820752, 812072555, 703595828, 169416747, 108584669, 179541642, 16581924, 818119640, 398825331, 884920532, 583713447, 975736393, 9164799, 968005062, 293499731, 539332560, 81296095, 823256515, 157903307, 608538803, 382168514, 22679348, 352402796, 242777689, 347139317, 505462432, 895001120, 417367074, 326220972, 243133778, 200504160, 904466103, 433195942, 222823834, 587572320, 584009376, 230476842, 614579308, 975899924, 333263423, 201531268, 152410063, 726562182, 935140205, 877535591, 107929381, 47992591, 29196379, 890272657, 805717174, 371673652, 824591443, 109920982, 44161527, 624814984, 481696432, 492331570, 163151272, 534631, 503105009, 10421508, 444083879, 543049778, 428572684, 45198384, 372684723, 505545877, 757106048, 733217757, 160937002, 246903447, 755744704, 761589842, 984839069, 259553282, 768484663, 273281203, 730539431, 822368970, 785826262, 177544040, 691589077, 621433011, 166265899, 557574662, 742585358, 145733453, 210910794, 122430105, 68874995, 734091139, 232047340, 270032420, 442667903, 447428145, 636065750, 142675142, 544944067, 194578569, 212490217, 78571625, 472874309, 251057476, 936748246, 596594886, 851790678, 271865120, 304816435, 215252266, 249165970, 42841452, 935762405, 243007219, 658558951, 449697892, 507646369, 978128453, 156114126, 743488134, 580616944, 648650547, 563677473, 177356613, 87676037, 897875825, 523635872, 827708810, 83613808, 366854266, 382064161, 2009046, 290580664, 133636534, 239872242, 316169620, 420384304, 801036302, 267724823, 398923010, 773863675, 886585592, 395230340, 438270047, 880355082, 129587105, 407443177, 324540844, 297455721, 162073838, 461658327, 982237740, 592229504, 663026992, 77842030, 633425440, 50213700, 964715574, 655772116, 363245184, 431846507, 153046898, 32669532, 16552114, 84970209, 574548317, 328707513, 713514594, 695373551, 756792100, 69327635, 573253255, 885799478, 144117247, 359874647, 766787302, 52841738, 593343403, 814695545, 542173858, 844251256, 825583194, 94177366, 726444077, 412089966, 936801509, 774068766, 977122990, 892580280, 252007100, 123851854, 527045495, 533586161, 559352284, 271797496, 226293586, 951515091, 495054561, 692249266, 15860533, 362082646, 868629358, 575699234, 521412498, 382387377, 437771480, 41951834, 825107968, 776293973, 952309962, 210908902, 431622251, 842196547, 309154125, 919668886, 754598311, 579710409, 374724541, 775371822, 501453987, 330508275, 542440174, 619692704, 595501749, 832074404, 173938368, 756675865, 138761437, 615723517, 30956832, 997970243, 921389512, 526737488, 160940533, 163864972, 723350423, 369771426, 978896403, 813738156, 644850608, 357110832, 412377177, 259379545, 128617154, 450356095, 459879708, 528817945, 285585582, 945281075, 117843594, 907559675, 286413089, 708120555, 386968061, 71648484, 79049716, 448645940, 816365093, 842870677, 654773626, 27910134, 727857285, 402213518, 932343186, 807074956, 567830853, 500989355, 571305727, 726389980, 644967909, 130937582, 890993355, 493167540, 761679737, 980575982, 80259313, 874910037, 948487625, 431523170, 559282041, 964328119, 500304725, 441433642, 590475288, 299160876, 223353424, 367573302, 133195911, 9949830, 688326012, 932476973, 295996802, 679971248, 307828209, 608989052, 399117935, 894262669, 893032195, 817780018, 712206359, 122069137, 706722909, 862516579, 492407480, 183094915, 163898310, 71154479, 509848649, 951288595, 394487888, 24719567, 891233139, 214080522, 194996543, 719511946, 308479667, 138615267, 970638342, 631308103, 174635397, 371180926, 727419731, 626628485, 239148433, 307777220, 511407697, 184699235, 709565690, 450430191, 656542621, 93036268, 362589078, 104944124, 367557972, 813458550, 653156544, 551027491, 742664275, 147339318, 582599030, 574574383, 383099323, 616523166, 203465322, 642061176, 484203619, 377809254, 32260942, 786345109, 873921143, 234477312, 514310183, 841839680, 502938463, 716043283, 645294949, 896782364, 733801615, 287556557, 47012275, 882099742, 253141648, 689749479, 522089996, 778894242, 537345150, 509722030, 643058229, 264016008, 120390241, 381205407, 15822246, 630935652, 236174221, 274146999, 140299287, 209059246, 519955982, 499121633, 642265953, 534021035, 177619676, 256128027, 252414591, 861230136, 345694256, 784194131, 309809536, 544667440, 56321318, 695066790, 500658451, 82598791, 857196227, 348399029, 201822041, 459620560, 580329271, 96794639, 168309919, 953879338, 336181135, 595922269, 905397848, 857286479, 452189497, 886366836, 873505471, 830109212, 712569687, 387853335, 235201795, 554129534, 968519189, 400914174, 523753343, 509103952, 108369413, 641069453, 977531334, 624990189, 404947398, 653308433, 968579861, 113020237, 75871713, 836107231, 328956093, 578400429, 164691967, 678764674, 813003949, 678001180, 694968123, 245200284, 995678152, 36477983, 602328708, 383105747, 181307655, 698221700, 94671303, 407649474, 78860676, 404032773, 540601387, 575798368, 895482293, 483739456, 105462723, 983818894, 411924308, 527783373, 792013053, 725104367, 298984706, 870803522, 260142092, 927775627, 987499407, 134672768, 986515306, 978760747, 165949518, 377227601, 616452796, 230825234, 111093072, 840153677, 268554231, 579756802, 392270394, 682444446, 6476843, 688013899, 719180513, 80284630, 739426364, 619714358, 170754766, 326879381, 578278621, 498251353, 245838791, 608714420, 917772070, 98972237, 780266445, 371542588, 537225071, 493014645, 472344934, 693002973, 681369695, 626446667, 524370546, 47448649, 972046031, 894922794, 760455554, 201233418, 859724444, 586325998, 363956034, 374239416, 182681038, 987416013, 285022473, 846959060, 198552119, 543091454, 561147434, 143310660, 522994981, 461789763, 412137425, 496482194, 770995163, 279097529, 657386190, 182297910, 149703898, 752766412, 60476384, 379384546, 955172807, 119199157, 390178190, 60932296, 848781707, 222191685, 612901883, 804051609, 519383662, 689857096, 11268737, 776773839, 102910876, 205956955, 131079898, 788203820, 211669468, 614281094, 658868442, 158056463, 420845123, 677890637, 28677063, 840358805, 475269762, 453306515, 781343147, 967190234, 453972120, 564579860, 608242931, 473339215, 624577634, 834578256, 537411562, 942657312, 672145133, 800451799, 782890641, 348432596, 406352476, 298995870, 7955073, 658642347, 232446240, 589612593, 261043858, 451178705, 519647956, 201138089, 710526981, 815707810, 997166080, 799462803, 513130736, 570263768, 364271482, 946927708, 303489004, 157436233, 15719835, 554238929, 251938506, 281129358, 629554229, 264042279, 938521940, 384482363, 652016917, 598321990, 241551362, 947910238, 576174190, 256723962, 148035699, 121109340, 614320966, 460766886, 316837677, 827617073, 252181843, 231112351, 107043620, 862033036, 267400125, 495151490, 257216833, 488474557, 983511928, 155155404, 596761292, 402704243, 999966299, 872515310, 867247217, 20980321, 32140345, 12051152, 384422279, 273026311, 294905749, 88159359, 794377973, 42880738, 216514311, 659306321, 956688385, 79902663, 399311746, 178564897, 352019809, 917988650, 504383334, 817738449, 156721626, 450877337, 916201190, 129702988, 155758420, 200354726, 168695405, 360295072, 260343113, 473240839, 648982425, 327937061, 501721161, 988509059, 968419801, 321620899, 139926173, 117244162, 309956823, 856231838, 333823937, 886178933, 326177434, 695503102, 755369319, 598138585, 267738163, 700603022, 359326118, 842435152, 985003337, 412972448, 731750958, 310724750, 561936662, 725559668, 453161095, 999475182, 211815498, 37846940, 139078296, 555665319, 970144709, 116813809, 681160150, 96604738, 816668897, 168017057, 591266566, 640340009, 870265645, 391566835, 967116212, 647891998, 482795404, 397504752, 161130788, 413064495, 702345607, 818436949, 992703229, 856116184, 274525508, 541739253, 227474851, 825397552, 50912465, 428802639, 234700379, 107771102, 524827823, 612667724, 950265989, 480999885, 659706660, 919224894, 643704242, 75317362, 702388978, 496828409, 223772084, 565467504, 225748531, 835391279, 224452757, 998043951, 15659831, 644343847, 138377151, 996075550, 724832962, 11763068, 207547047, 355838421, 326886951, 815372890, 145988622, 588839882, 691381961, 435890382, 688774997, 910904711, 425803915, 375958115, 627019470, 948690226, 939599192, 299512383, 280855500, 368142768, 883188568, 941217374, 821248350, 217277401, 81677749, 405062144, 126480188, 552770534, 640168217, 800447341, 92625257, 556673239, 201587930, 819679703, 318251001, 878880476, 370942938, 594953759, 274821768, 517765844, 570081484, 932603523, 251471005, 320016834, 792436540, 49152441, 902936744, 245500599, 880764495, 62194222, 258232400, 412084457, 652883552, 157345309, 757850059, 479476726, 300242481, 448966746, 110455531, 635526933, 144060540, 762617700, 713050393, 652192435, 268504151, 234163611, 674253299, 431029964, 995917256, 411235011, 719409468, 671750806, 406305967, 97944443, 520077335, 871512049, 363062844, 748938274, 683808801, 910778368, 403709388, 943733776, 709606158, 358477430, 475220667, 544449133, 766800292, 634929827, 677193668, 400325390, 839429247, 869214891, 651042219, 399198555, 911803894, 935996824, 70306486, 120290604, 484726797, 312811638, 546546881, 912805985, 159208085, 164981651, 361230640, 589256999, 528849136, 711264359, 973972744, 859688964, 901110846, 183242069, 132177157, 518101966, 481706113, 741526995, 247182183, 637107430, 886649000, 491738172, 873421119, 414428388, 815604709, 887207555, 756190006, 766678004, 741027402, 469248923, 961168716, 1081810, 64231064, 964874632, 275649672, 792932101, 438644684, 499681304, 387872464, 94977202, 454634388, 735864258, 277169763, 912299192, 548831991, 379691337, 833085699, 291363529, 110395041, 664305562, 828874633, 998208329, 725688297, 476563032, 632928712, 380105944, 936879701, 182265685, 72181727, 948716272, 19824975, 843011552, 777134915, 713958311, 272663546, 969445724, 829853795, 583791503, 353435506, 42333497, 228478291, 411506293, 584504602, 488130615, 978836515, 830988066, 570649071, 985986397, 136456304, 770125247, 953831334, 476121687, 406772247, 203622580, 384318571, 954140645, 423024523, 519574014, 487654527, 966709948, 360842044, 519060021, 105961404, 132194206, 658687262, 670124306, 920734798, 213249059, 964439177, 950438694, 214899137, 985273187, 234376210, 820829070, 211179065, 259287986, 592734827, 171954387, 654035838, 117110395, 426007288, 39111631, 598691409, 940698394, 617804006, 834533311, 394541794, 392314995, 839024223, 404908798, 104844275, 515957181, 571699709, 110081035, 692876371, 152519673, 446286230, 322898557, 554894278, 399087625, 843865048, 348350297, 217581082, 15366765, 303338894, 495978155, 387606703, 50843286, 193381417, 590303690, 499426761, 567638018, 887747649, 797486089, 28333604, 772768912, 892834400, 981975174, 190933533, 223660437, 795217860, 108055345, 911602379, 680465859, 244508024, 20665106, 865157788, 964286085, 783626317, 636997073, 236445758, 186713436, 138746641, 988639651, 80674553, 963532651, 527674113, 982868245, 813392515, 432899942, 96044822, 532072604, 390801795, 680015345, 61201862, 631870827, 344352347, 716482320, 704305792, 996538779, 822274775, 978520807, 732904143, 464846196, 582301026, 18232178, 99979549, 847723281, 757675333, 908618076, 493540446, 109378469, 610698991, 220271502, 924697318, 301287012, 989237320, 287592262, 487965007, 827139963, 80176555, 6419311, 141841660, 517921145, 612830189, 931167471, 391376280, 353620564, 608604537, 484675576, 92032729, 730111347, 279702440, 321349948, 547371036, 471147234, 431810363, 125144710, 802197558, 69351301, 369619960, 513562736, 129302498, 288748212, 563981314, 99138228, 89724125, 824990201, 152993971, 51187678, 81841392, 533204039, 254305350, 398125740, 633713071, 159313614, 83186467, 536479178, 300555677, 654795244, 977272025, 219172642, 924371844, 892734417, 406641796, 918230688, 558849522, 847691621, 761164174, 326314219, 512797631, 583361628, 824777470, 565260609, 865419056, 900117059, 310623879, 586038347, 571330282, 635902775, 357440813, 97903081, 487741263, 646978728, 200284981, 648103128, 498357410, 399888513, 482167493, 78522889, 221860893, 198183449, 192351180, 26494011, 587474051, 826112754, 943120284, 511127256, 746706459, 491925254, 215983782, 432263559, 80529577, 12680915, 870594753, 926667000, 540821977, 298671513, 790618215, 816179104, 684051917, 404053816, 314353847, 434936208, 21305637, 910889740, 333975333, 600702438, 967001010, 22523901, 314965202, 508675627, 682579856, 145458467, 27297931, 751250394, 765246187, 718140271, 863791948, 513824310, 806488180, 654431787, 101586543, 617838565, 678985254, 158754257, 122415764, 392592866, 807880484, 512090162, 775605411, 846904764, 30590691, 388349575, 903380355, 595391984, 490815942, 333626200, 887374291, 37921903, 29209416, 902804062, 197152935, 989972942, 82593412, 702811790, 981134902, 174329150, 934574951, 588606429, 681268117, 649460876, 598621354, 519439164, 446861404, 996682586, 444457320, 857372671, 83222270, 37753747, 430844632, 559280342, 433166650, 651447514, 928061021, 295498798, 612632368, 712731056, 484385183, 251675016, 88856265, 624954188, 772796284, 707268190, 751881724, 70873961, 990656696, 755338318, 41407080, 158276941, 334151552, 84100412, 746751774, 147175969, 180200571, 938115971, 889536287, 248537660, 862013976, 994718176, 411383750, 287854043, 701629866, 290744398, 483115171, 752722346, 612285673, 447130603, 972450881, 760017791, 547929153, 19627003, 525201322, 417007975, 553672272, 671644184, 50429453, 370028641, 825626048, 203501727, 819962376, 646712670, 781550807, 609095881, 360667936, 288121049, 147031640, 455550669, 111773522, 406860105, 573965904, 224120565, 164989355, 867085925, 246514376, 673746137, 471828280, 309651663, 297668579, 884899963, 605628487, 283760336, 115396571, 905635300, 360697854, 430785947, 270726110, 827062359, 325376609, 867610755, 22625938, 309652967, 554428635, 18309373, 871899493, 951658241, 670554191, 208081041, 709978535, 534807691, 689009243, 590660140, 397159482, 971592415, 816315492, 972058779, 977601186, 380422219, 7607248, 354095924, 303043887, 605312151, 76211408, 828529200, 608812317, 731747843, 233649906, 390288959, 328244552, 719260997, 368302231, 844506279, 963753112, 112527215, 967170457, 270461658, 861923805, 769838000, 899421191, 998916710, 378267036, 457436341, 714999916, 971911199, 654075301, 647287548, 316584733, 412653195, 871978726, 973486121, 57714658, 173506397, 413655982, 289818507, 316257874, 50580967, 403016428, 776455359, 704388014, 215268178, 365773293, 353837234, 199003338, 35971418, 533666571, 794653669, 435783091, 943612763, 83055123, 704693488, 738886661, 127347890, 600438282, 808158374, 725828271, 972507837, 301600665, 111011085, 75284648, 901375469, 486619179, 559049304, 146397087, 392181303, 260105572, 6609017, 625727511, 295576842, 630688062, 639360016, 390372162, 169846440, 655075746, 968658178, 239486580, 889946950, 816914029, 775028006, 534210301, 968542958, 461253489, 313208351, 907416082, 326326558, 182073621, 528211756, 805394896, 747092209, 949036269, 876494612, 914303285, 833318443, 97863800, 454883619, 349787005, 742325095, 894856889, 973549098, 202692308, 60976202, 407195296, 405448044, 685953473, 506774094, 311860313, 253874279, 396303676, 712705478, 957144568, 79582698, 752450691, 516834938, 218075149, 980973532, 889297129, 323237331, 710048284, 927111995, 760337456, 246117927, 741889871, 62434233, 663443255, 943933372, 125990402, 274146752, 898570789, 987875543, 523668442, 235868119, 932760820, 909922017, 733841940, 931354881, 909546277, 492446029, 741762929, 441582829, 698325556, 844607604, 410713436, 733854305, 896049200, 805519939, 814726149, 777659130, 542772260, 737118413, 515396419, 689014172, 818865536, 269149576, 594531636, 689869471, 273717616, 252872302, 546994757, 196497635, 18231180, 116894899, 679595040, 400390229, 682620973, 986729807, 391567318, 376671926, 392012441, 817041015, 433696765, 928269778, 204667746, 151274053, 910368149, 805570938, 6785325, 829824865, 711317993, 115322624, 626272492, 346650270, 961725308, 843665201, 577557656, 246397960, 484172143, 484483789, 692823597, 410641516, 855691064, 421515807, 137360585, 600891502, 795322012, 191064891, 95844662, 574899562, 399027448, 28775100, 623306120, 577831172, 294403476, 177329995, 722010937, 538496023, 692106481, 201698447, 254049866, 992895118, 400616109, 727766394, 533407164, 783315265, 403865452, 369657104, 383232966, 162111896, 78671292, 527936172, 169208943, 973298404, 969743309, 356065923, 924989877, 460487659, 254480946, 33837185, 260316277, 874046861, 692578227, 742653729, 111795425, 693762582, 646268388, 203422870, 21561470, 12706856, 497442003, 978406810, 356329503, 476352221, 907521065, 935870538, 467198043, 291237317, 474748872, 591548555, 445642577, 248719044, 63508596, 556588957, 828661055, 486136289, 39403749, 741678063, 377280933, 100763021, 734132733, 871319587, 414819485, 675559299, 723734986, 585640512, 579104924, 204572337, 275000069, 237988972, 809822494, 271622200, 56963742, 827791736, 755776618, 994404980, 589882621, 509290210, 358531675, 449041736, 38051497, 75270575, 817794159, 304258479, 397899690, 511458774, 702635950, 407274505, 8832219, 289922719, 900796177, 222682906, 240465465, 269842560, 910995250, 213212339, 32587837, 35671718, 221798745, 795742446, 835428217, 262994880, 133255863, 52358191, 483074422, 235961690, 383183607, 573297338, 860286138, 599277400, 378596006, 283876465, 651750241, 333986247, 570160581, 761199953, 389900888, 549528518, 497581418, 3382229, 863064787, 955930485, 879921419, 962723794, 182807499, 262413856, 307620283, 630821263, 345633173, 728803573, 175485723, 96094349, 791947447, 50940464, 230719166, 240288310, 468619470, 465444271, 408022056, 66910592, 936148960, 311811862, 125455724, 548812551, 53736590, 545432588, 194734162, 853309978, 649686088, 193585287, 859962045, 172066537, 371013601, 778521922, 998175445, 84121698, 338680318, 102469815, 25374775, 649281208, 689560250, 739129559, 359933618, 566146347, 782826083, 257904394, 991965085, 29067845, 904413941, 801595740, 959707387, 766757172, 333727004, 572548874, 546705774, 376702489, 980475106, 14518537, 991278921, 946335547, 67177267, 566457758, 670921023, 324603726, 150736414, 120481225, 67105129, 405203529, 669890446, 512741393, 658969137, 131492891, 619981178, 347514203, 387821476, 435026757, 681545141, 529348105, 155517541, 321099838, 793208911, 587341688, 635235112, 741021131, 130097143, 301866992, 652919478, 388007923, 768450230, 70249001, 713794158, 896527771, 56869814, 817253766, 221488289, 73872143, 431273999, 257348998, 993923183, 802586422, 932106657, 258828056] 136985716)," 0 (countGood [188749986, 43025141, 306806411, 885408463, 556260816, 483369158, 698256361, 814526941, 82297086, 399692927, 142440421, 4245511, 820838803, 309696682, 754534500, 554627895, 970778496, 686428872, 627071363, 351759234, 640474410, 29124833, 376472563, 122099150, 166904425, 188779876, 82771456, 921149156, 536810241, 404342138, 998779376, 874768811, 967529938, 841122969, 772449459, 119886029, 364198074, 408279935, 413267718, 685795278, 308407684, 753723671, 37725190, 161330137, 577209788, 525292491, 884135758, 456115239, 580118341, 442707785, 699046542, 813428173, 118134230, 60085235, 815838537, 360638699, 20099530, 323115449, 529231601, 665061552, 476011922, 230297999, 37184234, 712016941, 944573957, 973715861, 919854749, 732496221, 980887679, 407237583, 783332693, 597201608, 644080959, 588386248, 833580260, 347657083, 859957486, 711293338, 233028365, 828983473, 318065306, 281624978, 977991378, 497631478, 512133094, 476006560, 27935819, 932638161, 40970419, 887288597, 424914662, 91013203, 398934948, 233942963, 887011498, 549972358, 272178849, 318426727, 678641654, 401013937, 974293763, 728731321, 1573539, 976524852, 618943008, 449418051, 335159868, 510301350, 34468726, 906623001, 846907141, 372861192, 443103176, 692797275, 257905831, 145013620, 649563715, 909859837, 263337423, 486274036, 511631446, 687300339, 28385500, 404972471, 129566420, 539855715, 214982389, 821428158, 254158909, 464381983, 327543182, 655758792, 225215679, 660569487, 834459, 978177794, 62402508, 524411829, 189801436, 511659809, 993854145, 968482682, 954157984, 348334713, 161779150, 784770393, 786449594, 676556114, 584421615, 864319908, 415347006, 112073393, 823422770, 740198011, 363117025, 822686880, 49491132, 923669178, 849677668, 836484821, 232442420, 373326721, 234594638, 694976143, 948261060, 496495193, 281282633, 455703898, 167137622, 807095138, 863084498, 972072679, 646661778, 590674491, 506046888, 872936181, 886737330, 437195717, 160119874, 894881862, 239775484, 308705292, 245490091, 26834250, 8398195, 821484971, 743727362, 213365976, 241217052, 410252245, 889241902, 35658520, 175639084, 942326966, 853978024, 372030876, 336283719, 298745220, 763837975, 367161637, 397322919, 406621081, 141127532, 830321029, 838828761, 851923682, 611505957, 698939698, 959596109, 254761757, 858536339, 270168224, 947456212, 840174870, 273605789, 485409883, 244496304, 666750262, 709453149, 815497459, 562530642, 619962324, 508883188, 71210470, 53535972, 140832303, 695176857, 724249562, 880354188, 570710744, 241611876, 45738301, 420933432, 852723644, 581656721, 526005890, 888946534, 498606121, 437073042, 818692258, 135830747, 272781638, 547003819, 109986614, 771311331, 547573510, 732081486, 636399996, 866610586, 588751467, 946338988, 75022780, 532882083, 414869305, 193750052, 639763798, 77285136, 777016543, 341214107, 75153942, 839511394, 695589038, 467611420, 167330710, 608972063, 367905343, 575545709, 412231415, 241417964, 477425269, 558849472, 90775226, 141883975, 603506809, 140610226, 186260170, 598835769, 874972504, 771600898, 97669905, 712010511, 379497707, 983021074, 290327989, 419528891, 355421965, 571929045, 545295752, 238528092, 753807664, 731194233, 230917045, 623741812, 637020932, 119835360, 620168933, 227563298, 237390649, 755331705, 484075495, 813717546, 378470378, 732989366, 126699727, 33423146, 425458086, 7866727, 96589728, 549042574, 540550993, 384259117, 79333833, 415193520, 321821230, 38678313, 343430421, 710252378, 455488110, 204433088, 638041994, 255016033, 345096879, 290973109, 290367827, 871184255, 153423741, 62081036, 266461854, 199192490, 489528951, 153679814, 671068274, 8885007, 818145325, 904710031, 872346692, 640025865, 766145459, 888994217, 751845245, 186364794, 272667568, 818131505, 206824470, 838476591, 412116801, 987553422, 291585322, 450302893, 605906807, 689598994, 493583556, 451393072, 415422316, 970570407, 900754733, 611448635, 400438689, 336702964, 280744361, 796384448, 715358082, 575272003, 491671389, 379778145, 595812528, 558536691, 690107990, 790556773, 805351575, 174113266, 69386736, 926116746, 347978940, 66372807, 846108587, 318011546, 465151379, 823649570, 644556790, 541078342, 374245406, 570369339, 904449155, 462289756, 668560504, 782432886, 628460676, 61245663, 873457589, 471862855, 882946400, 805286733, 212330168, 315426610, 560245919, 941266279, 785619546, 478363150, 180006341, 607550439, 294860591, 697670189, 293191243, 207375105, 212856089, 490626593, 471335734, 919436938, 344157465, 387875568, 718897187, 300700694, 672489757, 374954741, 534090501, 203220197, 738594697, 448207740, 176826284, 535531868, 227949594, 140384735, 91433321, 339215321, 126542971, 844185331, 84989875, 65015795, 806744107, 76530884, 247814417, 872476406, 872285565, 858744552, 745926159, 70438638, 631117336, 556149783, 617039235, 370984641, 355820026, 140186574, 405159325, 780119558, 168935641, 587321291, 90452849, 999120110, 227960299, 51792250, 363736231, 617091235, 107636796, 143539708, 115063541, 561848909, 439088486, 55696864, 985072567, 27816428, 752517250, 124221394, 700590802, 821530475, 53467966, 717508198, 889635041, 742848050, 280074709, 293626124, 598607868, 729258688, 579562690, 462879738, 591686573, 520582070, 182059145, 540321587, 365393023, 639343076, 910374535, 37755537, 360848156, 368077304, 944366426, 167493318, 305819185, 796275659, 469086374, 157140010, 765436370, 483998534, 223904193, 213597563, 28769788, 338953315, 886341427, 221731666, 798010881, 557478641, 965851329, 129715853, 511009037, 382322539, 742966963, 330342448, 829104240, 582073383, 343825082, 998355181, 147813989, 647417248, 655239663, 628600267, 348428408, 204116440, 57600522, 937488871, 991357792, 781106359, 14423814, 808881397, 160826734, 975767325, 775377633, 171774629, 91649053, 493208618, 719883623, 102954455, 593679870, 417933198, 732625745, 44592295, 137978104, 898268144, 547942775, 517953029, 666220247, 732990442, 603861019, 677232286, 26363457, 587505941, 555195742, 563961887, 293456434, 505049440, 854745740, 60263395, 477282411, 315586306, 138603081, 294182943, 907787878, 905398850, 883949040, 116056431, 929254342, 971782094, 980525290, 321119150, 735608505, 959598332, 784020735, 365241711, 547441283, 589526597, 14589438, 904332668, 452378770, 47457268, 430989161, 143540890, 550953737, 802351133, 561727230, 544552861, 686051873, 596450333, 502686642, 816722654, 442121901, 861668165, 841528819, 118074227, 452783948, 875564922, 778757608, 468891727, 394383419, 259904679, 975027685, 938566635, 280101181, 549880144, 109975044, 790693347, 307270068, 178158165, 300695366, 690174296, 199408351, 697137014, 322897509, 450846425, 347710638, 31108697, 472504184, 672421292, 343391066, 351798544, 517262203, 791007743, 700363746, 846822829, 81579690, 198617402, 716345558, 354426048, 58378851, 758021632, 366664143, 40295936, 271276080, 859808757, 120218616, 367769325, 818567604, 525851326, 756076349, 832419826, 672213225, 92743779, 672876011, 699975068, 342091468, 610794078, 384986296, 33614820, 816523560, 56498407, 799252515, 842553621, 523360687, 702953835, 612780413, 768436163, 584845465, 982560604, 763736388, 423441666, 405843966, 591658376, 797900178, 722648557, 17451299, 505389771, 649875876, 999027995, 723787853, 70930611, 658526658, 387642165, 326569947, 438045367, 427223634, 295236877, 396780654, 383395126, 91729711, 470527593, 868880563, 188689712, 646698351, 101773026, 575682544, 418666131, 372623452, 348061654, 875860745, 97640648, 348347526, 821699237, 116076243, 117128762, 771122753, 568534822, 302500788, 653409643, 392486364, 689869540, 565640544, 830748308, 626264020, 632900066, 235905841, 820084972, 152978741, 908718995, 781521427, 984453578, 35855612, 938279138, 846840957, 566849592, 343938316, 8207952, 71019647, 149712078, 805125502, 78884648, 658039085, 633920567, 325821993, 890455682, 450254404, 813744187, 187082063, 815558106, 347041565, 929141270, 639582200, 258894364, 178862616, 587689799, 215456893, 259054239, 510097076, 531762567, 910088281, 396721605, 624468759, 869088219, 853478451, 606011603, 949643076, 683541074, 21593882, 29633373, 915948471, 665035028, 615418322, 350051138, 758545630, 546368706, 103862146, 292809778, 870310817, 215813834, 592157620, 104479398, 997059808, 926280919, 354273132, 774386362, 942438949, 585098340, 53764381, 809065591, 466928338, 935139635, 904384204, 537115802, 737499408, 808830688, 11187938, 26610539, 591474942, 456199610, 643948844, 269596648, 967385388, 802929928, 572718184, 654417040, 271189481, 539553739, 66439668, 23620387, 772522405, 145999334, 279646827, 40677164, 714543969, 290897818, 112934124, 450030507, 179556989, 128886341, 991532699, 224037406, 649992506, 174992060, 339409932, 836714578, 249230039, 771848186, 730871409, 344566800, 904354872, 387190893, 181087249, 342084958, 751530281, 680912857, 492845731, 83419657, 646864611, 777044142, 760418316, 790640068, 231940713, 119520490, 882822849, 743198902, 90750908, 577452772, 383468263, 992860554, 376186556, 177518995, 613284632, 978220082, 630474883, 19242432, 61836897, 575743151, 503189950, 845610688, 392918215, 357602489, 124128391, 182665371, 108235543, 694584882, 317471195, 375427241, 547416021, 646125273, 492300869, 83686464, 901885297, 975848741, 861712535, 179073314, 620692861, 170901800, 727999428, 15326635, 790158124, 191675946, 391476376, 717612319, 157916682, 923197076, 698439685, 819676880, 69474549, 558920686, 123078856, 286778962, 248315842, 772562668, 525241843, 756179415, 982694182, 672701907, 993082297, 633197676, 168100901, 806490757, 274622251, 71253831, 304980835, 996445433, 341603442, 696122556, 928464906, 462310917, 368555244, 614593302, 173634686, 340130875, 523878847, 313009819, 144658608, 879877437, 94428279, 591221285, 365709813, 654130784, 785479423, 973341199, 136509591, 184493659, 864234326, 955878678, 865853203, 165304166, 506836898, 771343773, 683686725, 533515338, 978504022, 283530784, 285857727, 13067368, 480371726, 251293913, 494943643, 658330913, 408033131, 211002390, 597152466, 618466221, 245988316, 935234172, 989246579, 192084157, 738154474, 876075146, 286665159, 222707556, 300763745, 328036058, 465078776, 518637895, 603412735, 25941082, 90259632, 689546239, 248817507, 282794583, 993073424, 186613538, 521868313, 607876533, 974409989, 340881849, 231284243, 457880675, 836247232, 282309706, 310432911, 99454925, 752922546, 937930959, 637673479, 349263362, 388381717, 531373510, 914301798, 222272678, 354779600, 851636465, 335909160, 182006697, 500036423, 575041659, 277206767, 345591072, 493575146, 593904927, 679275958, 269819791, 575674485, 227810028, 572883088, 34351407, 148146466, 320626677, 751619928, 995194739, 792510705, 125977067, 574380159, 783232977, 855450358, 622195928, 315105280, 550585808, 602591843, 607772757, 798870210, 267434347, 799516988, 99539582, 748257057, 258125542, 19416291, 743699325, 834243639, 201743073, 76425493, 231183251, 604890894, 19879958, 912558289, 374798770, 424089970, 963811141, 193125826, 14020884, 869876730, 597526897, 520827823, 347982684, 100032468, 560860621, 879619495, 152316379, 996122285, 44270128, 593029445, 308128806, 169598294, 485927339, 284299622, 545199516, 374164799, 912974636, 163234405, 475200246, 449401251, 563969496, 38691112, 252329215, 937255290, 443651705, 286011308, 831536818, 738359497, 641177931, 7496557, 868169197, 728910987, 395006297, 195597444, 957305260, 840412804, 785421058, 229565053, 271265165, 986522989, 809881074, 591483559, 592910651, 310358631, 796085982, 263183546, 90505475, 251945517, 631959543, 562366284, 214879891, 49622036, 443773876, 455114860, 624355544, 872331042, 943699529, 872173625, 375552299, 865429227, 266059996, 606636254, 44064586, 61736847, 533056490, 459008672, 924804739, 816492988, 179803594, 229039718, 213119614, 955036276, 244336967, 346494829, 128176524, 423276383, 497449484, 737231093, 194004067, 8450519, 869612638, 3060580, 681548430, 920978181, 146682402, 805662575, 377184806, 5447311, 556475093, 180283657, 333878681, 501441961, 904622141, 90094587, 766853862, 567027729, 435500292, 79388053, 822815265, 868174557, 377221132, 610408099, 982155190, 934357901, 915620943, 731470526, 55277755, 40216920, 642697458, 470047352, 313993206, 686406836, 328538470, 809920446, 443568126, 860775735, 787143423, 436912273, 8801233, 991390653, 334689247, 954713156, 741735422, 152141527, 495815455, 250638825, 644452855, 764949343, 746531449, 167119697, 176084944, 145828190, 345570817, 690643419, 708336107, 939417527, 900592515, 385194016, 963524539, 8761183, 136497928, 263143294, 226839250, 612781611, 44209766, 156341983, 271227338, 712259010, 288411254, 225404938, 349541637, 235388970, 468719882, 937840148, 530090493, 886054304, 298541382, 446978273, 85627746, 5227161, 218899412, 175864077, 980394999, 675210845, 593724875, 197490785, 222728226, 965717566, 894926909, 134540395, 1561832, 555631207, 245101843, 315760653, 170161965, 623955717, 892951478, 380295058, 387673753, 390856276, 183177551, 48770805, 633849989, 272712793, 721582885, 786003066, 723665979, 621388598, 787449366, 629273476, 34586127, 10581400, 379495101, 991205268, 119417158, 379815718, 594437074, 629665637, 706225250, 571904178, 348522377, 386590386, 271005147, 306233353, 389322291, 909265436, 317705000, 908426357, 72580175, 517455165, 449339567, 360248285, 802410037, 55618779, 799187541, 372852814, 358681446, 425775658, 787043870, 616131941, 285454567, 583529784, 462412064, 932109659, 215344886, 946661792, 461288201, 830522701, 738726519, 748078008, 218082424, 259052200, 872906456, 556905503, 244258468, 15132018, 54136765, 59748696, 898236789, 965192095, 413768332, 596936296, 178640919, 340256310, 674278649, 253331761, 422054626, 291606905, 673747784, 439622296, 663777844, 479206546, 487314339, 45387185, 332067262, 349290776, 181999041, 715631232, 145699883, 819106462, 301469902, 603060317, 962192767, 272061861, 360795262, 364420189, 699263424, 204701591, 69803661, 562766592, 177995700, 719773094, 664859684, 952864871, 184516294, 172629221, 899618970, 844813583, 214788894, 273694662, 467035843, 80653262, 967121196, 487307022, 373315634, 141864534, 68026757, 867625155, 499654026, 251329976, 355835437, 195562002, 767217782, 183550683, 425871286, 167557944, 230651935, 566098121, 64722137, 195370297, 215715162, 585753707, 202771836, 531576643, 323843120, 546863554, 272175728, 450806133, 507303782, 491354466, 402270106, 154275709, 531144975, 912033604, 272004719, 647026890, 37253863, 951818565, 945769859, 506508357, 987439523, 233657522, 610814810, 933239759, 238283261, 418381612, 284919857, 225871651, 653954689, 527012223, 524752391, 315386635, 505175794, 940218722, 915899303, 600141354, 821073887, 421441484, 237182799, 666770166, 40786045, 508630274, 665232550, 447247345, 99026989, 855010802, 310402921, 49656229, 246148623, 55452768, 972301402, 100358684, 927407109, 225117383, 875371086, 313884278, 350765826, 719133980, 888775071, 364766067, 618500125, 658812813, 296498627, 524245745, 271938095, 913770775, 972906139, 358782605, 830026376, 352158263, 882826455, 102670380, 123530628, 738926057, 935239977, 606485401, 13262110, 875693261, 61048173, 107669017, 789589207, 467516260, 29486557, 178000845, 169011360, 832315321, 150870310, 855996970, 525200318, 825611636, 312236377, 621063239, 88537582, 545178242, 730546503, 834478794, 434351456, 956499157, 747819223, 642443117, 29624069, 320105889, 81226588, 271635800, 924121738, 605352850, 955132937, 802118991, 637052142, 431716662, 803678144, 485328217, 501611031, 512378829, 749578967, 784980032, 215072718, 169269069, 686081443, 582488896, 656971594, 898872147, 227442103, 395361523, 752009470, 585763055, 758480415, 812440089, 404989963, 515648971, 457565311, 480285157, 499271225, 817086262, 117293099, 840216127, 475426236, 120282562, 162872721, 31771540, 858746394, 473305744, 203621869, 7634474, 483044162, 557373836, 671576182, 309942130, 582535706, 773339763, 390515644, 873957872, 264392179, 32001229, 133485276, 536352013, 447045308, 396254062, 302377415, 647092112, 713109140, 38765353, 727066725, 269112577, 26961998, 574309835, 489730796, 658697702, 841771859, 718609683, 916417075, 509450378, 71165455, 304915478, 359462341, 280901839, 385436662, 338002380, 659856448, 567691235, 699263778, 112705825, 907064617, 439456579, 702109120, 458688009, 141600188, 45495591, 706691211, 393626078, 674417730, 986946015, 153487601, 875015642, 517832485, 91051826, 709741474, 895645609, 804376091, 549844605, 259518026, 234997378, 110029818, 997183252, 191856366, 93909687, 424301454, 900831767, 907502519, 655870048, 559287543, 69564349, 572302285, 131135672, 800620961, 377997379, 281380095, 165518707, 57128766, 594702200, 89979640, 284225894, 324593824, 577652605, 440423360, 801708776, 446840643, 820279356, 567642605, 470003545, 473525594, 334866861, 914183849, 385117087, 669030798, 985273068, 441050785, 933482647, 306072970, 304245119, 827655811, 813880710, 55355010, 597794120, 717218416, 496297593, 120013475, 339555345, 333174124, 690430452, 874651079, 964884879, 709460227, 225505903, 738897750, 727728129, 89004676, 699813820, 855026300, 424508779, 643678523, 473858477, 363553586, 488688128, 582803674, 348587275, 910481196, 224850476, 361603464, 461963922, 641753789, 735158819, 195311177, 625382268, 377281274, 341095341, 758533591, 505913413, 230569969, 836546349, 580342930, 99486507, 161696841, 304941701, 654027334, 223998944, 731470940, 251485978, 161382766, 47645868, 68172679, 118104117, 849027198, 802862588, 320572430, 860390015, 941831247, 320860944, 541102282, 456490388, 990626378, 971372583, 465058749, 946591679, 873061380, 222586649, 234779281, 771087597, 756736654, 772755660, 462062687, 236069970, 887454582, 850817884, 590984306, 98137802, 894930846, 141217242, 282443794, 639001330, 345956760, 851153732, 888081677, 250475694, 237300932, 223247132, 593733736, 172398363, 340941548, 176073684, 108306293, 563169559, 706979553, 287640583, 748540508, 835209433, 435986002, 529816154, 537793492, 161428993, 962115465, 771226369, 574862655, 632040442, 323554743, 672953735, 224792457, 688044301, 503153007, 265520538, 29985815, 891688580, 804530177, 458122175, 793892813, 508825680, 614977208, 333913586, 775393675, 964888340, 988890282, 4670952, 55331441, 932472523, 67047902, 96300713, 268365102, 939016085, 139378602, 922592768, 670518693, 380224142, 183263565, 655298081, 509148151, 128567853, 69518274, 516943907, 34292530, 92693066, 110089822, 614083265, 288673936, 462237833, 676320675, 294701278, 161036105, 733679802, 845927863, 40708343, 388573119, 268528964, 615607193, 423059765, 463570647, 406912057, 27806094, 526308839, 814543732, 907271163, 138660918, 296254913, 753250839, 153179614, 128283075, 88385281, 581507562, 633165162, 767842375, 186602981, 125188798, 544202149, 124367639, 15184218, 857412987, 876657339, 412844150, 622430235, 934786625, 577626922, 22420771, 82825427, 743212636, 114980192, 862509262, 705872913, 160090291, 79857399, 613852652, 389906958, 834517680, 197439321, 536552508, 536981326, 76512868, 751243175, 200472110, 851468767, 457058292, 822201232, 836978263, 328196612, 746714791, 652432514, 695833385, 183701604, 466328571, 70695294, 283432166, 72892697, 326396710, 915875723, 448773429, 546201466, 468682347, 7294301, 606198598, 87251319, 264664582, 816674967, 886846893, 686303881, 207185822, 242062967, 620449631, 561080761, 110360682, 840184961, 47097631, 967486223, 399752541, 383756262, 567514594, 630527564, 889409508, 195109278, 799512173, 460015977, 86604447, 652616644, 776572123, 409288667, 935016360, 669575202, 960806458, 429944209, 18437295, 836611059, 778058337, 296768289, 701265651, 294473370, 377873320, 231950048, 856130657, 198990542, 404267203, 373933364, 803477711, 827150771, 593581459, 862237711, 35951903, 982826401, 409849959, 719574470, 853461495, 903872312, 124083677, 948986728, 948923449, 295734645, 836160715, 770087704, 561673296, 658237324, 763330355, 150071048, 490276168, 997744091, 862011424, 901905073, 301815065, 115463427, 28824870, 861123660, 345570703, 339801741, 862865414, 587012394, 773273632, 45790597, 502934042, 228575103, 586184226, 88106238, 553648522, 633612995, 888162312, 124610361, 631780052, 734386219, 737876170, 272420796, 912409413, 277505334, 66368860, 642514246, 248382514, 632856901, 715119231, 618961987, 41967494, 196878205, 687913706, 942436307, 822153534, 312492605, 678850778, 770837877, 800242365, 778725678, 655137135, 166441574, 324527929, 719742936, 599264102, 708459994, 196486543, 579264849, 223274538, 397208561, 533410883, 935204167, 320515635, 4586365, 86156236, 573504471, 555673158, 477081570, 452023939, 523707011, 726598730, 373105963, 229199941, 362238579, 504849264, 529548277, 511920156, 332187996, 393782934, 571004357, 657186911, 155777945, 280176229, 910090729, 206202000, 109809772, 814183133, 368115296, 993529862, 401449482, 642158363, 561351882, 261330946, 206379836, 178855647, 511375485, 534807337, 404164150, 760932730, 106369861, 141521679, 72850010, 204021139, 579555323, 540140397, 837845061, 672865986, 194153523, 937777429, 671892397, 168143422, 735507476, 112986156, 531681184, 394232765, 79181880, 508448828, 366285839, 190751732, 47614783, 91612852, 234519029, 868665761, 69950365, 879409929, 798469356, 20357246, 813209936, 802843449, 672118678, 253241542, 780279668, 937987392, 122402751, 939625539, 461517099, 27967626, 231718878, 552433507, 45750141, 944842601, 702735120, 656773500, 235152839, 140756167, 85208910, 832188590, 560482152, 773462927, 324991937, 966121530, 352538315, 986664385, 752304354, 999470659, 950437354, 376862926, 218874638, 871078903, 393898820, 453253250, 610889263, 354352533, 1320702, 435825935, 887113438, 191375013, 357399178, 436127938, 825075146, 2441104, 841193816, 507333815, 93876144, 68518560, 173717629, 675305022, 714016190, 40026078, 457343023, 353180883, 219452215, 586152480, 386616244, 365742876, 50902586, 218738750, 765188609, 497189880, 473356725, 80790917, 427310732, 264027099, 556336304, 940597609, 102588144, 718446227, 13826749, 132006886, 138931038, 170729657, 300982900, 527862920, 653340729, 872504596, 317234430, 267823596, 362629705, 104970793, 68166422, 399295846, 581193413, 305168519, 242498806, 454416193, 564962815, 35614774, 70561245, 512334719, 193656788, 886094660, 481026072, 698019517, 15303222, 420916369, 199312349, 401795424, 571547178, 642716553, 401012376, 717760041, 303228753, 972977967, 740017103, 322677445, 142699569, 556163384, 459453989, 409670947, 381539396, 730880516, 671577868, 356317618, 893038127, 445884295, 761011435, 221118019, 301974377, 671288312, 167948080, 963746138, 241770215, 687865321, 380581660, 667085229, 222724100, 601754222, 180163184, 89074914, 944364014, 787167789, 471120557, 302450320, 694741745, 550079930, 608915021, 627765222, 36657798, 626264189, 368974615, 753930997, 379638216, 78777247, 184012130, 444351021, 768432757, 797758713, 124016801, 348935343, 365231405, 906734335, 517205154, 422851497, 700283259, 864645611, 139714322, 797658955, 21091274, 288410405, 544347188, 535330913, 720830941, 233021712, 397054534, 392702321, 277698549, 208901381, 477536351, 629336345, 614546016, 392646297, 929204138, 591243532, 618816207, 35545709, 608696924, 384066883, 168946313, 27914900, 806410018, 973627019, 589935095, 723500089, 391693800, 115480268, 83638944, 878293846, 399992280, 270755503, 280072830, 205959301, 538547831, 614469970, 23597754, 368169147, 769407375, 718518871, 549508126, 747313813, 68254918, 273849068, 699907816, 424907367, 213505715, 821126809, 870163676, 557122947, 325068436, 207593239, 84787021, 946843032, 708927856, 728735599, 920113214, 851367531, 667973806, 45187344, 534897276, 713676870, 423048027, 652877162, 665579871, 144395181, 231804435, 631124547, 502584217, 369697865, 814122410, 971419934, 32349156, 278366398, 410295051, 72471204, 820915789, 728686363, 81491399, 374673698, 278781541, 388937801, 425577680, 589851604, 950986940, 516857693, 506228363, 980180649, 209172153, 522165993, 122200094, 501148128, 550782164, 271453248, 130320486, 978871994, 415236014, 346411006, 571684138, 990130923, 38621516, 870743488, 353543848, 372131359, 196317349, 995545718, 269081949, 605671372, 731888082, 942149538, 511620800, 952617814, 157607303, 641931848, 495573283, 171619400, 228012006, 865412287, 474773894, 967243478, 161364893, 319489296, 810500610, 423229851, 244041143, 111862321, 511851719, 300626019, 745249216, 68510537, 243745972, 167811758, 600843450, 683404978, 969495105, 92055311, 907940961, 346184234, 191979081, 217538085, 578697575, 556868444, 311550439, 850047353, 384428956, 262111036, 593301317, 664332037, 998975843, 867669867, 114080972, 164217859, 148961327, 388479266, 913873121, 65753268, 106292312, 252751952, 430590806, 725824546, 953566774, 549393121, 97064366, 363543174, 861709305, 202574899, 768052969, 693823212, 413573821, 803227423, 888564570, 677188017, 545713292, 350963950, 432550896, 202099554, 222015015, 302146942, 543580391, 522166299, 480258915, 61250715, 830168125, 125681891, 810122840, 382488252, 79483352, 403064238, 535273460, 493575974, 740241272, 974230199, 250677008, 436893375, 299970229, 956129276, 980505252, 358994994, 988174601, 262330544, 656872271, 692279723, 528839707, 475085772, 322315374, 908063364, 812430209, 722467100, 289181551, 945220058, 155554607, 782798811, 848759636, 219084767, 680294202, 273711165, 866124900, 557711331, 434402392, 975968947, 369816179, 698319222, 214595575, 858151032, 861439395, 958418702, 996076559, 699346099, 566456297, 701423118, 663591362, 888724403, 998748152, 718716428, 363681774, 259929412, 120779374, 818787894, 548842083, 565096353, 756711437, 37742864, 439282033, 208922978, 821663938, 685661536, 172255173, 734441345, 623448846, 118146407, 730353811, 547522760, 514698121, 668596007, 116951853, 735787407, 174337906, 63207511, 776354475, 787442091, 167726038, 536863988, 556078227, 58592262, 213401379, 734442891, 859644617, 487694311, 405517783, 131790021, 137635045, 648711838, 175362521, 867397296, 437908638, 421151195, 103423490, 548708602, 776132147, 697539224, 674115041, 392131454, 742284076, 792988014, 540925705, 119431659, 634096114, 825246178, 603715271, 700141547, 86813859, 968010633, 950094302, 892821945, 769243795, 466899212, 300590263, 407456130, 244930272, 900295658, 486724077, 272868160, 885053116, 217333757, 433037636, 418653010, 672157299, 568361049, 859097769, 172417488, 700765609, 499153169, 876515112, 386901442, 635668580, 507588556, 128740564, 237793396, 846524730, 44893187, 307828928, 747643908, 472781371, 31896267, 957226873, 70563517, 559578835, 386863251, 10454061, 87798253, 732210245, 261348105, 167795970, 954837070, 914859563, 782495411, 17662921, 736085985, 456127373, 121461285, 917733996, 186064870, 55879734, 873344082, 780497910, 545003510, 720277722, 839856741, 658303655, 602278772, 92510261, 812198770, 893422531, 643992143, 821916332, 761535201, 437032594, 169907011, 404317202, 345550129, 879256083, 250016516, 14419636, 638920687, 881743658, 543331995, 141838882, 205312943, 11688423, 304014243, 905772987, 478278764, 770600610, 525749599, 356959890, 796637996, 927895649, 210033346, 992782781, 532728854, 275618838, 120972505, 250696343, 369994121, 502998812, 952071945, 432573706, 659894301, 211750723, 327073727, 587112836, 228627350, 589728357, 781049823, 642953874, 244566149, 50958079, 606353343, 891252265, 973721562, 212882407, 428721918, 954827686, 838067377, 112775211, 331709154, 80739514, 990700483, 790757866, 499692618, 501021379, 535990276, 331237765, 412910766, 530467066, 491808925, 477482812, 351358312, 702983441, 248196320, 394269345, 381451422, 810972309, 724030870, 536759139, 652102231, 354822416, 832585775, 294801828, 614703017, 364992334, 229322089, 253418729, 15805468, 158926662, 93927926, 429912721, 833481278, 684982483, 568675517, 937722881, 545725932, 862704215, 813864998, 262076824, 310356815, 381754302, 164359696, 825774023, 104012238, 784291824, 755213969, 662472073, 291474393, 403215314, 319675222, 74935135, 403907936, 188468189, 940426081, 306535852, 865871341, 120235693, 35230197, 519412823, 135916786, 74311047, 509683143, 187498223, 95661248, 343255617, 227511519, 204935561, 112380940, 142257785, 403644876, 928153863, 813370820, 359377397, 186099205, 171757842, 634611945, 907789400, 336346283, 27390513, 47403167, 281650072, 396263592, 287089813, 842036912, 281498217, 821401028, 508492122, 615140282, 863782683, 812698257, 192388678, 468485971, 943850428, 237448424, 288123372, 24493201, 574103758, 230701879, 990996930, 515533298, 92367372, 976014291, 877270991, 347451058, 44331328, 11181192, 583089066, 632978635, 805166150, 320121323, 913628746, 450863358, 786026478, 790577697, 486446480, 176061666, 833022640, 586039237, 531900279, 978646031, 7704351, 515153925, 325094798, 461371808, 389284942, 494843990, 358979655, 835265048, 332359903, 971710194, 97378609, 144671637, 368825390, 216710765, 216515921, 499133780, 398945454, 971885268, 674371778, 421104858, 221823712, 663283337, 972863437, 427792511, 732399950, 653684377, 569945315, 236037829, 549785774, 692972180, 984768422, 271389385, 905742802, 862287825, 351317290, 578989390, 941648846, 676461893, 95989089, 283235279, 473785357, 369939902, 984024861, 144178197, 428688489, 704030684, 232437108, 419880288, 865816312, 845126321, 908434681, 112979952, 666667452, 9410045, 734474300, 432734440, 83695636, 464837662, 992208607, 157078969, 180768389, 734037330, 578212324, 698148671, 642345495, 141268308, 901670265, 357917857, 544058489, 838994585, 797754926, 1053705, 732702229, 199867029, 711876198, 864142730, 636054935, 71613242, 384389542, 557721665, 460188445, 572922087, 181068806, 586945841, 378006302, 572641271, 973366169, 365733172, 702267133, 953773838, 234226232, 17689306, 940202036, 78125228, 522779191, 84760009, 340637476, 8462272, 238706709, 88216611, 379843938, 721350904, 580484559, 455838950, 461481031, 837877999, 45670836, 193353592, 788918215, 351293726, 848725605, 554436178, 784177759, 847877311, 73977884, 100483312, 868645038, 407572186, 729789185, 132230175, 677954250, 709997454, 753620342, 434731549, 21277157, 90782639, 5664330, 342241196, 209982148, 540047478, 46593606, 974399544, 505374215, 610112992, 850044436, 121144533, 215393739, 838899901, 646328895, 171662537, 9306809, 987684889, 753294299, 446529223, 519722294, 467513773, 516857515, 836028062, 791990216, 788639786, 221277511, 98334970, 353738579, 78017696, 407467377, 955539851, 763830598, 18436607, 276987610, 162779865, 891239561, 362288521, 930501987, 924092581, 849245473, 53574101, 190842687, 902586402, 753028693, 866512028, 640004482, 150150399, 563084848, 818714519, 61742746, 355294744, 322876297, 500101348, 942396786, 997350853, 337687610, 224519203, 329477054, 615522247, 700383137, 148345327, 460448752, 900870134, 219399400, 195389496, 227862694, 577913985, 963676417, 440927992, 888838537, 778848882, 443646029, 45722369, 320137816, 348108348, 173917099, 242013966, 113953034, 821287706, 590384812, 684899768, 72816331, 82218520, 600737237, 832364465, 114785316, 862196499, 80763602, 118212969, 130695451, 515478796, 794953050, 46511360, 103072156, 705665766, 369638449, 894101406, 887683787, 270066547, 518522007, 923330492, 106460563, 889668721, 158958146, 8025417, 153700216, 587259573, 369404729, 835102004, 665769232, 178574446, 199895874, 56011613, 180242334, 508800600, 668570732, 381514979, 665654057, 64192372, 525948549, 727231362, 134539968, 641744618, 485265466, 582612599, 867455014, 887211214, 198163541, 529912311, 425557177, 261538448, 494635853, 661035858, 839424781, 882463499, 537093252, 650084869, 820554699, 769471059, 779397536, 517429987, 779668501, 501351941, 765809274, 962369896, 815694830, 471443532, 624384253, 341775738, 87651195, 706670902, 937644915, 651320083, 481961774, 508895302, 89562545, 519287732, 961079165, 200204760, 607103968, 619766058, 141287442, 792150639, 719721578, 317202792, 586911646, 713381689, 536401712, 719416419, 555146700, 203163134, 595126090, 940455494, 735808230, 757670799, 263510903, 250786249, 806653705, 426009943, 235175768, 770315082, 19573098, 446132289, 640744666, 231515638, 460772136, 305760021, 188881832, 743350600, 153253738, 488056998, 686427216, 16161784, 617348706, 33670852, 962753725, 247099432, 146070953, 188067281, 390637795, 259992338, 106411526, 18340737, 817079203, 64416729, 192579098, 23717114, 732794250, 317619225, 265014323, 752121160, 389512471, 51061728, 627357961, 284238119, 571173249, 210118348, 97742165, 143552910, 84476416, 788903243, 300593189, 29546423, 702943366, 777837646, 848042350, 657206139, 588920617, 759924318, 694430374, 225646528, 795007464, 3281251, 271123863, 805822639, 372103530, 427529946, 734837515, 780128898, 859386131, 517442603, 151837817, 418896443, 13031262, 480542174, 134393839, 709846168, 32039841, 816801072, 19764885, 585792871, 410450132, 337952452, 727105060, 420829470, 343335648, 105871770, 499327831, 100290901, 762287469, 435387077, 738072196, 676241119, 378963715, 503712908, 425183612, 218121480, 822276585, 521247657, 321712343, 602207482, 101999754, 439961703, 345541757, 522025915, 777348806, 149684856, 925430307, 713494126, 566544528, 973971489, 248255309, 131707363, 721145630, 888870314, 615344427, 8256160, 892490087, 926096834, 431961063, 439254982, 553980775, 746577668, 659004113, 491324901, 455892070, 103022620, 515503384, 318730058, 211792307, 198756289, 976816163, 445944792, 118771509, 211011049, 783406396, 655170301, 60264302, 342889892, 783956657, 760972930, 162965957, 944485650, 32700056, 891998851, 900915810, 963858203, 232148698, 844775744, 819435867, 284644666, 980190178, 907492113, 372909106, 907408858, 764087838, 864302483, 706559774, 859416105, 219492593, 216929442, 933025581, 950394400, 437185136, 803785635, 658116162, 549054718, 128142102, 671566060, 151122182, 220645360, 793245011, 357295918, 703519063, 476925401, 360856443, 164680929, 151318147, 695754341, 66859291, 117714114, 837610486, 997517354, 649877315, 197962020, 427678833, 908533643, 368273304, 401287364, 815996383, 357778186, 735851031, 709199762, 591240946, 37637617, 103921914, 931578159, 990065367, 778823634, 963597653, 909347738, 762071793, 505383911, 548322459, 989715943, 431217027, 657555567, 809675055, 446905680, 335645527, 607276024, 205770190, 533276301, 755017662, 170195334, 491076715, 308414801, 204988846, 495593065, 136358313, 67005643, 153210267, 471814181, 450101352, 807502968, 643708155, 919327024, 793457350, 504436440, 754647490, 776484878, 835699704, 520903642, 434072484, 800894215, 562429737, 144176502, 359832298, 417355758, 915950792, 943826818, 35832214, 643452628, 885386576, 422453696, 59430321, 170731114, 738579838, 579325325, 614662094, 757559933, 474468291, 331127886, 451307572, 827378870, 166216472, 810511780, 967751331, 252302171, 798355861, 667790540, 416999428, 466172239, 505173917, 198876342, 337569557, 682001786, 626908446, 850079474, 920275717, 910938832, 917486757, 571770326, 990987224, 902984088, 306541214, 9245553, 317387553, 660573143, 863723804, 483890023, 216714818, 494690217, 685021619, 521926507, 809405243, 963555890, 493124214, 93507108, 397520883, 858053709, 439528980, 53598975, 282190552, 687951970, 138475372, 880422731, 215155311, 706984194, 258573139, 1956568, 453433657, 708682004, 338823847, 787472134, 831785659, 453270270, 860053007, 789368390, 945186608, 313205531, 718874075, 451403773, 383021614, 660345384, 736670217, 736512023, 613009450, 894221786, 459488630, 253512392, 299813409, 846593778, 399950750, 358572598, 75663131, 632318117, 302817107, 550309584, 41217180, 201542645, 170964718, 579853026, 321493972, 563434911, 407128474, 876447043, 324769385, 883909708, 929053158, 322616006, 617415274, 733689550, 21083428, 149948694, 346304197, 347170355, 625057271, 276178428, 511505740, 719141170, 7075784, 59532135, 712190615, 413697858, 610078494, 852368703, 286737983, 503734685, 453439953, 217262566, 266038821, 620271259, 95075490, 533903338, 593916218, 970030031, 165512583, 855491032, 468199665, 328350201, 644636595, 282527907, 793684896, 952739749, 12119973, 571412086, 521010003, 268756647, 640652140, 841348031, 772808756, 708580713, 877794129, 956896043, 845432035, 102193862, 752833427, 909078120, 68476743, 977075671, 83886988, 642211165, 456621836, 800472419, 896520401, 973395853, 603144952, 37978450, 374159692, 500525648, 399031981, 395726599, 779726250, 654104093, 487176033, 818027111, 327670181, 825503778, 856375464, 141245743, 109994550, 48506703, 725523863, 791947286, 530436461, 569181122, 184684671, 901309646, 652981875, 18693758, 771477252, 731453061, 269687642, 14720667, 362382924, 552217140, 867833698, 195554693, 946526367, 186670605, 553651297, 872531303, 858657712, 616613208, 727616196, 920129329, 45088136, 305188625, 785712885, 179154601, 31993244, 862922278, 866872838, 776631570, 31245730, 755112892, 488667370, 606217250, 538659377, 436705324, 859411706, 979490511, 329555369, 626723596, 979612697, 648455468, 222513642, 149141799, 473256851, 631883486, 298697036, 762912934, 627170660, 191559622, 985271007, 564505776, 358376846, 776107406, 957609239, 216320114, 687536392, 320394473, 114822892, 474117717, 194197600, 349673098, 310907875, 244666978, 915716351, 607792604, 652137463, 896044778, 774512517, 184442378, 587900374, 7559917, 487662935, 336526300, 903234691, 439954446, 886297329, 368506117, 874918788, 523706438, 620358835, 510287534, 583565331, 838258358, 198151621, 228290589, 773473008, 179746990, 683154507, 947430252, 38817538, 211648760, 850841213, 425543779, 711921640, 468347536, 298846284, 459653297, 343947999, 552303486, 285601087, 898476657, 324025323, 508351251, 199806233, 641417862, 422858964, 699793121, 335738580, 75547771, 112990195, 929174834, 772231406, 913128516, 700480359, 887096324, 760306016, 12170504, 214282535, 864455667, 525141354, 311369768, 387512158, 926156806, 919262679, 838347802, 176969615, 737679146, 297317648, 426815315, 597156197, 245979309, 867031892, 812586557, 864534259, 319914560, 530232509, 970743094, 440969472, 626366103, 796707980, 6183838, 472793221, 814670786, 755999864, 989428358, 939131485, 679937210, 476328231, 292763114, 549858848, 310174074, 757316779, 271412416, 890204252, 221079355, 771267181, 31343877, 531089397, 668726507, 958717771, 753608874, 882902171, 991254288, 197570601, 339794189, 331751842, 132369076, 876284336, 92406772, 81129057, 760550456, 5915279, 734242351, 624546801, 398856343, 264027833, 801469244, 171713412, 416555224, 323326636, 393356724, 8018849, 21685248, 800812778, 778628957, 469776753, 915957627, 168459804, 446339121, 836750314, 186178756, 951052636, 606455685, 177954358, 847346815, 434368576, 254327757, 912615125, 135354273, 788685037, 610985443, 434305945, 338672482, 429538616, 183019196, 976218069, 206853161, 681199929, 98757258, 228302162, 458454318, 382111451, 142813186, 318557602, 90991524, 685740768, 700182257, 337351519, 594832476, 119074486, 539621487, 37446239, 19156983, 982360476, 548170989, 622062614, 98611338, 939786446, 384460899, 180201321, 54219525, 706681740, 635723471, 74470229, 423566515, 340151466, 968233895, 265261964, 75769447, 247525793, 446539444, 424839216, 947862861, 525777258, 469016223, 148933026, 138743624, 246868918, 631703704, 412663411, 818518819, 345341632, 486963755, 413261177, 782417344, 936796755, 66855064, 243180236, 611906556, 246699216, 337987729, 561691273, 752501180, 202027293, 183905494, 274566637, 466343829, 797872716, 318904859, 433537503, 367880653, 279917027, 267833328, 60774465, 512006306, 902180733, 952437964, 866161030, 51539845, 331830234, 379749169, 919143114, 529060771, 608492581, 434285199, 502626864, 32011291, 362439075, 262605870, 682758371, 968725854, 322542216, 405364864, 521793476, 322255800, 461113213, 972937455, 980700519, 186824005, 566815314, 706352744, 204257127, 396825651, 65594775, 212935550, 450797132, 490783360, 350192163, 893256774, 22736888, 508628281, 107584034, 547937171, 394161735, 614371221, 212295345, 70459309, 380901190, 352304395, 537504598, 74319995, 800915842, 391797909, 763668153, 585854750, 902821937, 690407521, 946503132, 401177804, 264693307, 691845718, 65925913, 35582168, 47749101, 531342328, 253411143, 636448911, 817547586, 200447708, 245010393, 997448846, 494082562, 417827854, 826901903, 244983958, 862383217, 624901432, 663427336, 164758749, 754687380, 916893148, 665091243, 145655932, 664480502, 550970532, 129392595, 658902596, 297648071, 471081280, 409827851, 714850991, 468883226, 112254969, 562650837, 633949322, 93953563, 348005962, 636686292, 141366129, 412822214, 494346133, 602624430, 660679363, 321413267, 303850031, 899602991, 797264600, 549691379, 556083543, 751660310, 677430279, 98963861, 211186651, 838042501, 530782544, 596182573, 607637187, 338718199, 929305526, 822977313, 683167847, 367554940, 895814907, 940950067, 828007994, 140181227, 924822814, 546445542, 473124003, 596689972, 91451807, 865545237, 514383890, 471942224, 723507508, 447172225, 892098918, 29947483, 120500228, 607697894, 684755474, 860352230, 934637857, 208004324, 898501605, 716273895, 508388128, 243856696, 983727507, 983354949, 286178676, 694099909, 992307947, 159184037, 748230505, 995293118, 321773230, 615303048, 685851682, 812406269, 44597279, 421830648, 324922813, 416877797, 580662105, 229982564, 239890878, 38523955, 341063021, 330967043, 664128111, 96255389, 798998871, 762110003, 624781948, 887457779, 961151838, 476889003, 581570571, 32452595, 874455259, 527056666, 726390889, 914228142, 860667448, 313057739, 854724387, 311572034, 562619873, 490570467, 121172469, 579984667, 563368366, 350358448, 34543284, 456404857, 798008016, 65573022, 658941178, 746844365, 231210331, 447077123, 530151198, 531465319, 115066986, 448767457, 965575604, 82981594, 695273951, 197230167, 376435944, 539019588, 952452023, 548324030, 514160222, 702588814, 696409163, 810539873, 799686205, 791286734, 939643279, 899107811, 467972361, 946081963, 885875975, 781189932, 972608132, 971593656, 18507577, 308035334, 826637638, 570777409, 292924805, 396090462, 920927620, 214501785, 325286798, 737193682, 623692036, 131690853, 72996476, 939868198, 508243785, 539580709, 975845688, 386739404, 470224232, 3617585, 666347350, 332375690, 944047529, 148681614, 112313318, 513088662, 730000423, 338308619, 464007380, 945963328, 92634977, 494977229, 976158605, 778822934, 128716603, 332058825, 125897118, 357873892, 204020069, 645336734, 402304156, 106366258, 359059503, 308108215, 762581444, 730834616, 662351469, 838665001, 285693123, 466544414, 252151950, 771004698, 246743370, 404926007, 114176282, 355110711, 709083525, 668230584, 176011217, 255149665, 935351464, 625844305, 527872717, 705661901, 12928549, 547739695, 910627658, 902319212, 686520521, 540165527, 198440280, 953329966, 377054737, 806848155, 418578072, 28108678, 854067033, 795952425, 670160647, 92537158, 592860439, 995894739, 834411692, 572279600, 144182151, 714441816, 174856557, 264886461, 198667438, 649756094, 175608910, 32542706, 555351851, 667177569, 769046837, 743100146, 334402122, 866073482, 443220273, 520860755, 550544521, 983548914, 633262163, 712750549, 592269438, 712136844, 815676994, 853666938, 428772959, 48218890, 839233148, 998774371, 795858632, 809110265, 155763433, 870011143, 503007859, 62981542, 440165979, 574664808, 175305048, 518890633, 997945220, 922962714, 195153881, 68149036, 10807536, 589570241, 272111852, 580692521, 102398745, 171215309, 639143081, 487021305, 2827841, 84306594, 201469039, 147146046, 128745720, 264757138, 446644482, 334361423, 821554069, 807043453, 890141402, 509708849, 205648648, 466662347, 320002276, 740618286, 789701852, 848029892, 489277161, 694988810, 879653363, 757849658, 454396501, 401078622, 958676772, 40779376, 863582639, 433906027, 725118637, 904739133, 974085754, 737414724, 486190191, 240876395, 782650761, 261289763, 71722805, 160177121, 682360495, 717360571, 501767253, 936682520, 907380271, 697372104, 915235678, 287527521, 909216101, 323120392, 146268838, 837696039, 944705459, 894511132, 200527295, 677288216, 570583204, 43029617, 252136015, 584971944, 341070172, 773589800, 503736523, 953001338, 490918833, 562662166, 53646966, 294425606, 217382829, 984915169, 405077523, 533236492, 663682192, 214426357, 905136901, 313973828, 940207652, 742972339, 561631802, 643628574, 792390659, 937953801, 291785671, 259659901, 412018216, 273686089, 752256183, 724430684, 263849877, 707288802, 602764182, 527595029, 223227211, 948901003, 336746514, 728385229, 936171671, 614797555, 564793483, 311392480, 639057631, 687123898, 933259475, 419385310, 918303091, 997518187, 456794998, 210895330, 629107867, 156964262, 719423936, 986284968, 610835594, 702443591, 120321634, 940477719, 792492372, 39405912, 606664262, 345834655, 589847823, 459193225, 46455752, 745743686, 125014325, 109957757, 611947689, 799525212, 13395544, 909993765, 269341917, 114471925, 228672971, 316624565, 437780111, 764105286, 673602735, 177761807, 823703890, 985648275, 672265245, 999678376, 310437730, 968663550, 808180345, 935389580, 4106277, 716168761, 887477678, 789632853, 37823155, 86273968, 306159874, 432571161, 505152904, 809492327, 529211082, 681791858, 239839145, 870095420, 146022938, 951543937, 830981550, 691779760, 519212919, 559543389, 527638458, 60113237, 612511339, 961290224, 584401206, 244904460, 880616541, 645854449, 824301052, 991834080, 193288526, 852238013, 682620092, 700596012, 752725628, 836050435, 432542013, 125711139, 108683825, 316353602, 304077562, 815821899, 211822543, 425005047, 680301623, 962945248, 931170361, 748949152, 95632129, 409374609, 765711251, 497348707, 225597175, 971596559, 695427847, 215952940, 657298481, 971172291, 902355136, 812203854, 438359035, 929515416, 155536311, 89237641, 574724676, 448668040, 935969721, 912787133, 719198094, 257978454, 628973267, 700013388, 202646880, 282691451, 766511748, 217866928, 876944699, 331029035, 344091132, 759462369, 909452475, 82035367, 554561189, 843112638, 151678237, 245308210, 27113082, 736105680, 380710180, 699741307, 287713237, 991144305, 464379299, 608370168, 329270566, 259939301, 995509696, 215150441, 595295974, 555724930, 324553397, 61677535, 166244625, 356032440, 878374896, 217147013, 480718675, 676511427, 831022027, 90984554, 943859967, 428835350, 897188884, 841730311, 807644709, 318136025, 773129205, 788716147, 512466884, 765843022, 949824931, 160120568, 177284645, 8559368, 542023515, 193080518, 479981355, 900763686, 239809437, 593382766, 459311445, 556545873, 748274439, 895262647, 321354532, 420683901, 661870565, 489162528, 508672261, 587992555, 242103688, 192745101, 889506224, 861430311, 90323738, 458527850, 192079474, 192482741, 415031261, 266594230, 854907394, 327229819, 653467995, 578032877, 496718469, 613206812, 730068273, 180344641, 669920657, 820156685, 67065087, 960946927, 178955010, 832525410, 303064599, 219299740, 813072745, 945473582, 376822695, 661420354, 5327240, 878298238, 671879087, 383796743, 616032884, 706948196, 371520862, 409546477, 611625450, 647608986, 727682412, 256929526, 779524883, 209063287, 688213887, 230821502, 929031034, 217019840, 927413974, 850278952, 816203148, 730414075, 487358081, 718237857, 938781332, 761269401, 957011319, 717439972, 986476987, 226650021, 196215411, 227310540, 204993434, 723029231, 500656187, 996158278, 120116628, 654358291, 715352355, 737480443, 632272546, 514090564, 463262247, 816201439, 801045117, 2609392, 576298259, 235901314, 508599619, 767152891, 164192783, 538829778, 130695717, 349951535, 982811548, 297144626, 334701611, 385192501, 210197918, 369584520, 19368276, 653423384, 718494644, 581731802, 554594087, 133697180, 898667946, 930916394, 469671471, 664165670, 814855202, 152473001, 733691916, 403853188, 47718259, 76152535, 820475441, 93084721, 453493769, 190508722, 43000194, 399858880, 635470411, 132759954, 933982633, 647176902, 388195707, 819918980, 667446795, 255214555, 483955694, 80243751, 687088125, 655317384, 589758066, 210938784, 199005101, 464083602, 353845264, 826364042, 792025407, 319781841, 537302661, 810326489, 671255025, 853924903, 817947416, 25080996, 596647360, 275539684, 141820640, 491439894, 831224059, 484130853, 586782380, 785527830, 763878664, 467375791, 179556223, 10982036, 517413960, 69326936, 534705162, 410434201, 717533971, 218515747, 641092891, 897819511, 854834599, 135177078, 697651971, 671781870, 85470054, 452870190, 871726095, 426386809, 912016741, 457828609, 509739765, 533215745, 653892664, 683599547, 37714202, 368109777, 662238207, 750794457, 867064874, 196878180, 456728264, 694216979, 416163301, 78580237, 538047358, 852399567, 977064829, 964246423, 667861018, 313148125, 681139386, 46824751, 152753467, 465071413, 632324471, 661849646, 282536254, 575636614, 925170291, 210535791, 931458703, 533356168, 419822586, 578376055, 436275898, 402613792, 8119232, 493039521, 259334313, 767977299, 743343210, 878075198, 681350807, 60452692, 166475429, 267641386, 291743651, 648206342, 308021633, 138700519, 884079044, 221946442, 339491836, 698037270, 155271445, 281180618, 634739975, 462556770, 69193805, 67131386, 118679757, 163100965, 630801272, 353843507, 73155691, 781286582, 874482134, 909031475, 743642634, 794957541, 210699358, 356835467, 504320828, 379786263, 998669429, 310597767, 589519955, 648887885, 157563051, 744428554, 258584259, 853595629, 691286986, 705819895, 679723561, 77077555, 921852572, 667357768, 951337677, 600870309, 369762294, 466325338, 348487260, 425596469, 871035679, 218761960, 947126218, 219388241, 295747734, 457608102, 475256254, 908850075, 573245876, 14484896, 446955325, 232820763, 684386006, 336156927, 619737851, 17853278, 861747393, 655846091, 699451008, 975024632, 738012931, 11873342, 845128999, 833591562, 328529272, 481533567, 151851852, 307031052, 805172286, 907194708, 91408935, 967528397, 598595899, 106522818, 300686502, 754363061, 839727548, 238984468, 259198451, 11542016, 728847923, 117914853, 660514545, 104889169, 53065775, 579652639, 732647830, 883830822, 462153696, 392856666, 49468106, 163041712, 970169827, 104459001, 669566658, 97704254, 563300533, 128042405, 577947849, 917270956, 137283609, 650388018, 255056093, 592412981, 720592080, 517675735, 288938674, 115996754, 736907722, 349890144, 533166203, 200805562, 832774298, 345840067, 205517752, 130032567, 292358776, 367076785, 217621923, 805636843, 677479421, 428705991, 561753914, 552531734, 543778726, 346679416, 155638212, 357841771, 149562244, 168619385, 304042816, 138946003, 826868675, 813795176, 442133906, 100544106, 883714491, 92852332, 694413453, 827175905, 585229280, 737239877, 774598657, 856125498, 780478183, 52226855, 955679461, 209856292, 633812298, 772195000, 410492540, 364484647, 250530175, 557132869, 592306158, 984982000, 160443900, 184576660, 666830602, 209248148, 605165963, 572244613, 456106220, 597376023, 377898488, 659052513, 409700530, 935778046, 459028754, 305789861, 33559014, 169631213, 970242274, 315445037, 649912562, 289107990, 178943773, 63341695, 184239924, 388369512, 374443606, 295747505, 91332503, 283768485, 317128108, 840339171, 98685859, 164925046, 420158631, 342488468, 368131850, 704194372, 52746111, 369545669, 421341388, 585502594, 677132612, 176652542, 436752879, 975986600, 416505779, 926915392, 972156876, 310829423, 534895869, 384500749, 818089402, 802877337, 681724221, 877309890, 544274298, 488091321, 9938641, 777051050, 950165805, 69302740, 315063524, 449734081, 420931941, 17395231, 954061176, 160175190, 538220159, 304603684, 844668959, 721106114, 871874483, 885569613, 719331907, 596648639, 375372264, 683138060, 480604737, 478770845, 6433478, 338579423, 527429380, 954292067, 206338385, 195088218, 876796755, 436675090, 551838203, 922265622, 568966941, 359171920, 423867060, 99074972, 862268892, 301440234, 557106107, 19841211, 869567307, 307018124, 914382371, 872723630, 851452142, 220610936, 904970241, 772160113, 7371974, 843810738, 653498814, 913190382, 462234632, 346996221, 525583716, 575945578, 172584892, 957364658, 635587686, 822450282, 601097233, 855115398, 403192318, 10774534, 104905110, 653552915, 822073844, 78281418, 346198842, 776160558, 618005333, 952596793, 630401638, 607574320, 859807756, 736292669, 788065952, 29273619, 539252120, 774599877, 683834450, 442283169, 978842799, 952431279, 592548085, 180067151, 10672354, 107884607, 334958062, 824479438, 982229010, 970668059, 643317810, 281641883, 363747247, 331492830, 85781546, 21463636, 718116094, 160141541, 532090160, 971880431, 503876505, 635926975, 149507759, 685239144, 28680886, 316662944, 10052322, 336725113, 210157288, 194754201, 791911114, 895827254, 866683208, 201986168, 41480083, 691798223, 446604025, 554131524, 193473332, 928863987, 514334973, 178650270, 632696770, 554044095, 831620949, 72147975, 678212083, 650485724, 349754574, 265031054, 847600053, 759915042, 84294308, 430245054, 545534887, 897379779, 232217301, 426966090, 43126143, 852078512, 100792490, 145244644, 953230568, 420373125, 615227693, 697164879, 789373667, 996593052, 580192017, 183560444, 16735240, 572143456, 69362610, 924353312, 724857747, 46557177, 179809842, 431113403, 567046305, 807843960, 190993905, 250671710, 400352995, 582470029, 912864487, 329124399, 319744365, 860475895, 566424105, 650381901, 46069614, 965280133, 262984414, 979218223, 397197066, 258104563, 766187296, 651246721, 4192882, 918405337, 798081138, 183984140, 623393558, 283585184, 712299364, 508612443, 220686206, 45347635, 692249921, 71382145, 140864811, 275339611, 403705366, 286929197, 727175250, 646519689, 93549258, 673498538, 403387142, 342250319, 127236995, 510132944, 212981156, 694925376, 608960525, 293782349, 873315371, 800680476, 715259350, 685859554, 260324498, 829131242, 447850631, 991671621, 695973020, 881875015, 463098193, 43600928, 228847161, 181194911, 445796645, 973672812, 570910716, 934252520, 73951775, 662714004, 819782406, 161789755, 80964312, 716269656, 528443145, 997061183, 898487129, 593912403, 945073325, 693145988, 137594699, 275502395, 643788863, 955661630, 669010876, 387168090, 540209298, 261385355, 597331542, 16100080, 500370731, 297202974, 272713352, 633559377, 704451363, 690607529, 122345575, 900019055, 924317299, 259823675, 810941022, 1914670, 251519072, 549399845, 858861947, 20929016, 422614112, 776374133, 38958667, 945435554, 930064952, 16666944, 594194297, 167037721, 757774452, 711704602, 664239028, 533485738, 954891337, 176607811, 218512726, 826565229, 109523478, 958101503, 25562169, 30620625, 600569468, 884430363, 292987939, 975500330, 158666238, 149330021, 608634699, 863555949, 429912243, 706878522, 388827967, 847353806, 991946458, 656550954, 685266084, 649868959, 123515534, 50352695, 831345060, 643663812, 776941665, 613430256, 10251195, 148009592, 698615650, 945032098, 414462329, 566170482, 343057773, 21370505, 44770023, 841996218, 546298688, 761100254, 177167733, 288978228, 115304455, 188478711, 1545056, 349382553, 163667182, 975295112, 65360984, 366571251, 726802273, 414491772, 278257948, 663928800, 533577738, 793039348, 250699757, 918539427, 811485161, 650850000, 390156466, 684426402, 711541560, 646598762, 522087195, 356742437, 257702958, 602608318, 367121510, 544894224, 831859403, 341425098, 305364760, 132351515, 858605356, 937948873, 118836709, 474717613, 672936132, 33119469, 307313522, 415003605, 418803364, 720120851, 906293391, 776589531, 287325339, 682669700, 210825636, 695512571, 769522162, 467782879, 652195224, 247933454, 523355371, 782464152, 722400764, 8108543, 166432282, 656751136, 184075031, 665465453, 293080622, 873798459, 921754518, 864232087, 579189532, 708248202, 392672944, 549753161, 993572388, 169676522, 435930469, 979088085, 625108220, 577088686, 677724154, 110634625, 504748267, 808228263, 90541304, 119320656, 150870711, 739844051, 29981320, 947345022, 482290134, 90858303, 281654147, 574567209, 241170714, 649237092, 639156873, 83417396, 796609048, 553351390, 188535017, 863174364, 606547142, 347412545, 130418999, 149893744, 4389348, 913816905, 804673878, 616042991, 714179067, 844027149, 603600967, 711165840, 126403809, 234815786, 60227380, 359867675, 735306289, 445324181, 682308164, 694685344, 896545077, 709694989, 192009656, 253019265, 565415067, 579571620, 19882019, 48699117, 423073156, 31256664, 862134905, 141908122, 532987217, 93724927, 269312847, 592131228, 489590058, 311195212, 370133405, 85153398, 493243440, 748389272, 637331703, 839021943, 797172769, 889942656, 59111219, 265361482, 228444944, 364813117, 788317709, 238175766, 891050330, 167529666, 135264466, 465569823, 49387098, 970079720, 468259260, 35086794, 180485115, 953625249, 389318991, 868547327, 126654635, 631752917, 485162368, 895549485, 167839246, 133798846, 714977657, 763115226, 4553547, 851637343, 713274586, 187783844, 543446879, 901035908, 32146729, 407087645, 541568557, 164907143, 761215688, 852948053, 511589277, 756610067, 337301518, 602826851, 390073724, 677505953, 283368302, 895777008, 882428396, 499082513, 639933836, 652844744, 78022899, 123538404, 787723011, 809816101, 477668546, 155952241, 864989774, 400514147, 321611644, 493933057, 116063827, 608548423, 106306318, 601132737, 365639326, 275850536, 79871748, 423398980, 332594695, 87987922, 877759519, 92173115, 321618292, 567024623, 475823194, 46375881, 883298157, 358348816, 920912179, 814050559, 806873149, 671852782, 220610071, 458017106, 343566289, 566389083, 344027348, 516786915, 139206926, 341111568, 994826013, 355063455, 123271044, 871486324, 316629138, 8685024, 882269961, 241825340, 47432479, 412149420, 256682347, 977208811, 688914733, 57206855, 322588522, 706505985, 52641702, 910142010, 823595055, 553458039, 77130836, 64873723, 389901462, 132942668, 48391539, 533475523, 914028852, 695569061, 574702725, 627911025, 836270225, 403287106, 862286084, 649344599, 981264116, 198330488, 173629993, 780302442, 857592142, 123837055, 91652873, 812669990, 729515583, 69377614, 248685925, 332690951, 676200008, 25549910, 716115013, 682428677, 624576110, 343167545, 429742254, 748701872, 924330907, 579204152, 758828454, 692098795, 973240216, 938625810, 273083611, 740551833, 238806342, 230943821, 685462077, 167257502, 654732497, 421288599, 253499187, 589085437, 481949945, 128885848, 778235549, 664209777, 841165875, 59428045, 872499506, 42623427, 71990301, 58672006, 101349998, 363793373, 835452503, 408951085, 880663696, 666407809, 462902963, 241708926, 573093973, 203181689, 153652106, 575450165, 433734963, 629470061, 904414461, 337300135, 85357052, 887397425, 77588905, 526096672, 112558719, 8521738, 37830069, 304953957, 625560387, 716006235, 138820459, 710135157, 539888298, 525800731, 90126781, 324319667, 477112589, 405397729, 265594117, 20829736, 304329481, 801768751, 480575729, 792427315, 739454847, 573564948, 117614174, 740840115, 263462105, 842145896, 550224278, 392983226, 221282557, 176226242, 23685901, 484069003, 71071443, 360257330, 701155946, 295971543, 103982695, 940325654, 293458404, 444230881, 949223932, 10648871, 584442447, 138053914, 683393576, 836333677, 870648574, 239357004, 153408660, 99355442, 897467097, 108592114, 923701376, 829022132, 641537587, 45657367, 363428266, 562680923, 618715071, 20085152, 737568442, 677279409, 797150209, 47085358, 369079241, 609238572, 718142260, 7472330, 84459093, 219444666, 975869183, 36342501, 863514054, 134254206, 218014090, 156123109, 16793644, 296390655, 27662562, 365517462, 82701227, 581541371, 650715883, 726192114, 403349543, 549798494, 264873220, 441963054, 656273453, 713533311, 546952031, 943089540, 552187197, 656943220, 963842229, 63922644, 553388831, 524344283, 471859283, 54322939, 511008678, 696386178, 219292888, 116937960, 77716557, 281538055, 929172062, 695724207, 999146309, 565866663, 756897534, 572584858, 827041224, 354718563, 746868241, 641788786, 834796227, 539988548, 239408475, 197643955, 374567074, 179955233, 387437006, 757901253, 44666305, 122570876, 685887029, 934092207, 998477581, 314436026, 787055595, 563002030, 399085446, 962327877, 63628418, 96436712, 595849098, 68487828, 714657932, 151601182, 483170402, 755657614, 661736049, 864022187, 406827599, 618672328, 815247396, 671017679, 256413551, 929744161, 990739694, 448462535, 12695194, 368406956, 400141083, 468848062, 508513452, 379624429, 263202355, 307387990, 269067668, 998847723, 149243310, 222026395, 917117161, 265165699, 249512534, 467871306, 914987993, 792384762, 353533175, 521947256, 865483249, 46110819, 803731558, 609355630, 923144842, 525729383, 398183770, 710281190, 36855048, 114256734, 243503856, 845876187, 550395999, 789388373, 274108050, 128348287, 757064715, 308080224, 346380440, 961506203, 407846959, 251226008, 943156917, 938225335, 176466985, 158325954, 661724464, 21798717, 627873290, 611758291, 666343415, 80223427, 609330668, 181738428, 620616017, 491440927, 177491647, 878182155, 331893397, 53059671, 346170214, 504614865, 165251073, 126504036, 958217656, 427308078, 886729257, 973821383, 428978145, 43881066, 678857861, 778577489, 380951752, 687090206, 568818060, 72745619, 483165804, 963597387, 950114975, 463068995, 512938102, 44114390, 710398203, 888516371, 177460636, 53881710, 731503063, 700144191, 570876004, 509882611, 199762984, 942974516, 254537589, 909625131, 229077490, 436578500, 137654283, 659580568, 599234428, 352306341, 686829707, 488268374, 530679378, 369974048, 873855044, 306298262, 931784677, 316993410, 511358465, 488843889, 835862325, 760194722, 559106116, 183854588, 109113611, 23938278, 437249435, 268897589, 364868589, 56492102, 278688047, 399936000, 387121904, 602879129, 87984262, 920056281, 49467794, 232158545, 278986638, 893054973, 783174914, 628803401, 526518697, 190200569, 716452612, 510082659, 449584376, 647078288, 262300156, 779730176, 771493293, 343312097, 213840883, 480058786, 517309158, 454760120, 308788913, 32828973, 195573505, 125315763, 563335171, 107200962, 273170317, 594618942, 217448520, 445043223, 127856952, 779260420, 108377618, 624218884, 709623531, 770867340, 818772762, 743265504, 671659445, 724370749, 58964581, 201843991, 704670234, 228625707, 505688689, 124470974, 205788217, 592155886, 102047854, 429573619, 501088597, 323736782, 836492830, 654784469, 167946548, 105707117, 276613928, 630409304, 590243178, 204535101, 39287453, 225544326, 653493025, 873617888, 701654588, 521163743, 185449175, 727904961, 155818038, 456466387, 395905708, 451827438, 730135235, 305474537, 552745401, 602543409, 564767951, 976039510, 180450476, 75402012, 835045103, 955842874, 83312376, 339873770, 595794567, 575991729, 548230218, 44929469, 515700401, 31768758, 296794422, 109144657, 663358519, 512513542, 194197997, 152535890, 152898556, 292632272, 899609164, 795954455, 936239060, 574758145, 958544730, 300630590, 709367646, 509888737, 69545961, 159995246, 477766146, 140408596, 63052847, 185921144, 302553327, 111133749, 463024230, 146773015, 362967675, 686944525, 963594058, 967660551, 931330487, 599883347, 45247849, 376591585, 868896014, 797461181, 291978761, 251756901, 176198683, 872741740, 327908880, 739232821, 693202986, 596079216, 19378204, 701794428, 134113633, 368969180, 971997615, 654530850, 559212045, 987506700, 430244963, 822286067, 453845499, 349067020, 543728878, 242633835, 124326109, 615306509, 409706802, 760341812, 462897851, 145761080, 38124093, 516385981, 198661200, 745204717, 909088547, 510249487, 494323891, 851606857, 675227574, 979524041, 158916321, 668023602, 803142471, 875314017, 481450954, 285169293, 493895848, 202802935, 763306501, 702829094, 898180635, 713913657, 65243239, 290913366, 460668347, 187915303, 232513019, 203275601, 221317765, 976787260, 426729853, 423488929, 352476265, 568223564, 111506564, 520927907, 328422950, 200868349, 331853802, 614798693, 346357081, 746599564, 661952731, 392128451, 25669376, 494007027, 235573494, 400179496, 968102146, 563831496, 416588107, 262167021, 984921389, 280667344, 833187400, 806763184, 162634689, 627831661, 125702922, 241391190, 320061200, 744164958, 899018498, 892280155, 623774520, 537715466, 675262455, 48501124, 789593769, 920381114, 279393688, 950060711, 972124262, 451206606, 770822074, 814361352, 277946217, 633948012, 451974035, 25446646, 581694273, 883489237, 355431873, 691864508, 150121431, 806013891, 611076189, 831339361, 893720139, 444434072, 104657649, 972963964, 994599317, 36787500, 472901364, 610177428, 295544235, 969432029, 751489773, 85966696, 632872547, 595893249, 804399494, 508592373, 87032757, 257623206, 55747859, 501563271, 65648637, 406217534, 696754658, 632801119, 921337199, 177859740, 390544477, 776913785, 352233561, 61949100, 696120255, 511105596, 284431540, 4787827, 404407500, 833061602, 925488913, 261191372, 640405296, 703331123, 842698197, 367137056, 389772569, 810368246, 325837137, 964090223, 54635108, 960531985, 491301597, 666434928, 741504154, 389600972, 353943355, 135586761, 59309921, 877110583, 472756034, 778972679, 318274635, 612121181, 973086734, 24156110, 605618698, 555203381, 450125933, 71643358, 54969265, 850912632, 585683651, 493110100, 470212202, 642191882, 104064232, 971876533, 412920936, 296526844, 786761362, 511056374, 3575737, 422611355, 712281979, 295821935, 873948709, 319827848, 16907925, 55195158, 861741562, 896301687, 632507249, 669135434, 270064285, 273987710, 813510095, 781124159, 15524438, 348748999, 807593468, 433672492, 342931545, 40298304, 449436507, 446228477, 890679048, 379536271, 711894339, 843366905, 965086068, 395155033, 63299099, 644938689, 740792572, 58540275, 37262896, 557842538, 238395619, 253635778, 767477347, 334869452, 57663820, 215178205, 77786780, 541661910, 596132636, 830364484, 151702390, 101080416, 138016364, 167951326, 378198378, 673598542, 266391757, 594664260, 645457917, 746159941, 690128267, 326925431, 20279454, 277054937, 47317677, 139870665, 406623648, 410441830, 22450388, 754963266, 880933195, 253251331, 803482962, 294597785, 81559647, 177929083, 482441780, 896732077, 16481752, 467679785, 72837974, 702687485, 168448618, 256857113, 883497894, 929083955, 165420082, 939528132, 529491308, 989972958, 789739383, 971554084, 416507586, 327957671, 964511362, 123217655, 877397792, 839821232, 588217283, 671036315, 997508096, 213024582, 327484283, 335925238, 192147080, 668206897, 717143409, 946467167, 139598966, 405454285, 358688717, 310711581, 120280469, 457593589, 701885855, 635433565, 885324654, 317933857, 764989178, 873259978, 844629696, 671424448, 520698848, 926542789, 706966089, 350228037, 255785024, 474619419, 898252426, 500196786, 442265288, 585804419, 501311001, 986777848, 395927423, 938192585, 700489154, 977503677, 580315920, 245906944, 622561449, 175126397, 251465656, 877723421, 496441935, 809866948, 837908211, 985627262, 543952558, 322789142, 199328407, 692192593, 34350899, 24734144, 992822617, 464481278, 28702405, 341031508, 582613564, 119013914, 377839962, 923840684, 60216905, 568045970, 55071500, 235191701, 789411817, 903601161, 394792031, 59592730, 861129675, 753478446, 277254458, 394020098, 821412556, 410191068, 868515153, 624775602, 589757387, 338780520, 117834992, 770526581, 91837370, 683444530, 22059631, 775266139, 868544380, 96074033, 10933185, 369113077, 100205578, 969626235, 131445624, 457332529, 993004782, 882536561, 540520133, 134089918, 469906043, 662395412, 641319257, 257003711, 784408931, 71511611, 330678551, 836169982, 635755384, 874437667, 893052213, 67220354, 952089692, 771019272, 306307120, 560979061, 675539010, 261696046, 62001444, 198558311, 961751765, 534444886, 964956655, 971168911, 150834615, 804892934, 701991563, 16191665, 316691995, 860364756, 497638078, 283892406, 783170727, 473761849, 670242330, 945473918, 85415863, 134017091, 644929503, 599644624, 998131003, 223149679, 353771143, 675415146, 895439566, 894827000, 820234294, 110963813, 342110860, 949567507, 373098507, 729540038, 734581080, 586706827, 417998916, 718955377, 903957209, 776578346, 518996763, 900391140, 57324891, 301167425, 902853129, 584947432, 898826437, 811410891, 309895949, 340034563, 626709124, 879794079, 63499035, 830847433, 40843755, 397692601, 828873300, 950588291, 476277202, 871291236, 156995170, 545525258, 783813005, 649792742, 228848057, 875550663, 701376627, 118026492, 134789383, 228360978, 834173431, 313757201, 694743782, 5923763, 970601587, 569602205, 325946223, 457916499, 772540678, 810320568, 886135427, 640959659, 291472345, 575096798, 905220802, 271902148, 107227860, 251906774, 707078892, 778807179, 855341656, 621723283, 449493808, 320834100, 7912829, 510587497, 941736877, 186640150, 861615510, 32092452, 949955673, 38239225, 466745030, 662614393, 53649259, 138091214, 384336374, 176897307, 390768289, 726830374, 96836487, 375365516, 28756161, 910011265, 357710338, 100212119, 611285068, 6549436, 273394018, 552725735, 840991065, 458481937, 701420927, 616685408, 479089841, 63349187, 906646954, 370095636, 57039404, 104717717, 344620899, 623360865, 201490818, 11676409, 120919356, 474460582, 369003572, 634959877, 735796794, 797252454, 46310713, 141316919, 70043810, 690241567, 803515113, 412699445, 663941510, 266134105, 756935906, 117003215, 801685077, 983450217, 405929794, 29433219, 142678654, 226337752, 143120100, 423915820, 236159266, 532123808, 529468441, 280022623, 518439964, 228940503, 23725244, 686429239, 769776112, 796265273, 939843191, 953529705, 765647196, 285228463, 454966610, 923541979, 25083917, 543969892, 948881297, 921001247, 955252304, 647911014, 234564830, 993406857, 785180448, 287460612, 172835850, 322523541, 824026536, 407066688, 898898240, 42995803, 647367283, 150771682, 801350031, 290927109, 376986011, 778745780, 715234344, 572130328, 60918167, 491243786, 745774061, 440244811, 777760956, 334615866, 228635694, 412599344, 727267354, 28859540, 124165557, 579329867, 530016520, 228948972, 706385580, 420270091, 748676026, 308437606, 74755240, 323102912, 219028540, 496250710, 799416148, 537817429, 826686038, 679954834, 358063243, 380556974, 141767598, 557523401, 115517538, 612894608, 20092953, 553915600, 37455292, 971092522, 462921025, 396352040, 723597358, 485555073, 411918420, 455428917, 496108387, 952117237, 60157057, 208537136, 809767620, 683690473, 394718953, 220528412, 322185087, 19098634, 701451601, 504686836, 563240849, 880295337, 343286400, 262317380, 321796637, 691502754, 550074949, 590680011, 950626781, 376833945, 341117312, 800207135, 688211771, 689065872, 936929506, 43031219, 841594767, 946222815, 612600273, 716243818, 907108708, 55576923, 773367635, 884624759, 690619707, 568356535, 482253942, 641660839, 42887950, 430559266, 455261266, 813727488, 804264091, 124106676, 590168877, 234694735, 487574316, 130255572, 645063156, 70296969, 402073035, 834713686, 659792448, 534788168, 425148366, 812187130, 599670181, 68905586, 151833224, 369603506, 14765312, 208509481, 311963224, 266918600, 204404155, 908774965, 213818393, 195241185, 87451103, 503015469, 843513543, 816780465, 294467967, 77831020, 903633335, 162600317, 893037192, 971323345, 304610858, 847441027, 323969042, 434602870, 22575838, 65738468, 841367714, 934338772, 225748318, 686296862, 957052779, 779415817, 301604943, 703471205, 907334367, 808849299, 648990802, 187725157, 129361299, 458928080, 968689567, 179000012, 613334298, 807710797, 262805808, 955231713, 622925632, 105591825, 790180603, 280087464, 268904104, 696305417, 105401620, 16423805, 61359705, 480394655, 918972356, 91759498, 402185589, 295960566, 628178983, 666311455, 728522986, 726499785, 280270619, 665356642, 2523392, 946967756, 482637139, 617793094, 178349803, 380480164, 674824234, 932487733, 211130311, 306049421, 443327981, 381857018, 193191278, 198823267, 712559655, 651014145, 551718282, 524337847, 329487597, 5039727, 802465377, 276792287, 172711772, 243545847, 516699879, 528571582, 580902981, 727466858, 806403749, 767735606, 966880808, 734022855, 54854027, 951106390, 533030378, 933912441, 435095372, 704121124, 25852585, 24745447, 86485382, 126487426, 688852436, 105170734, 503378062, 962145191, 35132024, 478434269, 676743061, 417535675, 784858021, 747384244, 143007330, 126306176, 458243717, 58848665, 253290067, 392681732, 459646729, 90919604, 446970108, 184032814, 826124826, 580457540, 931665039, 243160663, 717783291, 589354730, 538866918, 920849716, 771696210, 600783940, 612719439, 912533437, 374586150, 171305109, 541891120, 405071405, 706294161, 792927395, 421042610, 983693721, 213556468, 214775267, 189630777, 599203894, 363389878, 295399392, 441642683, 908025368, 678163102, 904426996, 719750592, 500496977, 355342555, 194442471, 273843668, 945372599, 518945457, 601446383, 957808082, 512225109, 658895251, 852891762, 921905306, 255165732, 913719739, 42750260, 630023614, 36210663, 217087832, 532427784, 856726144, 669851916, 819377892, 472679202, 586760278, 765752291, 442956656, 358489639, 78260797, 626931953, 818954979, 604811272, 629954539, 853668288, 735513710, 842063497, 972593793, 503054243, 541090722, 377581920, 382596438, 297477139, 955881256, 290956952, 334210, 992155351, 485790386, 699765676, 259830845, 780352717, 729279634, 436459958, 623686821, 830465634, 216881564, 578867357, 271789749, 893474578, 94837811, 771420941, 981052361, 32267781, 690754655, 907690745, 373830607, 680394946, 715802486, 507625279, 197488399, 917883703, 293360682, 160023880, 963594903, 743083968, 363690838, 218780454, 906409743, 61712189, 919436997, 934384281, 915326933, 410089154, 75704465, 871678105, 815129824, 513166796, 240613386, 96542246, 295126403, 893354858, 571890250, 217650323, 661378314, 4874573, 501970307, 514793366, 471015267, 354867759, 70083505, 934752258, 199767677, 998557945, 950320753, 481049373, 585511999, 584303570, 777218446, 902384304, 597441289, 574914067, 728211757, 560925347, 183966168, 422842089, 303854049, 396753055, 2183056, 720379209, 371102786, 347614898, 668207404, 81823269, 882523490, 404784249, 292143337, 530381730, 896114540, 871602619, 305304625, 854252079, 428330098, 24169962, 640340549, 803001359, 160048803, 828401624, 794479037, 595167488, 546910287, 910102245, 974359063, 679627540, 436404332, 348505239, 344212367, 450553750, 855540110, 262967689, 983471869, 333073749, 728318976, 710257289, 311573152, 614543618, 632826485, 614581736, 945768460, 809281627, 704924427, 968802436, 494332979, 7134439, 95994050, 136704761, 82403684, 694850128, 649623682, 830425362, 923772671, 179853197, 844506634, 151098168, 481543928, 402175311, 655761713, 383044602, 761450320, 211458088, 303839102, 421045923, 552878030, 389444669, 472606848, 80814252, 574488197, 486212075, 520900734, 271162524, 677056815, 938795070, 78998959, 455738688, 175169815, 31579838, 101526676, 678824125, 385591356, 705188085, 785991159, 881956970, 419619306, 18592972, 636308156, 621038841, 979270362, 759652432, 516238924, 134781277, 61828858, 223671402, 850779908, 81165330, 577881862, 260021465, 304021435, 263378049, 7066170, 755438313, 853945543, 367921773, 568449134, 704356760, 393845016, 732370578, 693276358, 849892767, 722036980, 884164738, 505310415, 663132469, 197131455, 576910570, 485900247, 637469926, 283726437, 313368902, 23154556, 140613369, 682081777, 428118113, 595134465, 625714835, 731108044, 366332235, 726163340, 195032005, 36068005, 893956444, 675522687, 638064276, 289371433, 895032322, 135989203, 723413953, 542487753, 740718187, 608688273, 727351484, 939776177, 420574308, 534198626, 503300400, 720386521, 304052083, 663428794, 396865245, 83356727, 200638056, 152124962, 243606471, 82526027, 321390929, 702428029, 97664980, 53321471, 246236798, 463718852, 530082575, 240348926, 581934619, 313694997, 60987255, 193023017, 391009672, 126837774, 894824264, 299069146, 179038758, 831074180, 114054912, 404209764, 736346545, 72054364, 49770388, 85295934, 957595424, 936078522, 786358037, 970525255, 117070508, 832505716, 379038025, 314951701, 380174568, 600615920, 917283903, 43718430, 893038474, 59920678, 944382666, 696116395, 350682776, 965532369, 904474244, 964682128, 121365609, 112883591, 290682780, 71039101, 541610924, 541820106, 942967481, 554586126, 868426620, 413978763, 859405813, 683416653, 770694255, 162002429, 245276150, 751832757, 917859144, 244485925, 597880737, 56567657, 875312759, 135252593, 433468754, 741001638, 373942441, 42588149, 482214870, 56587570, 384163649, 80585417, 471357602, 172362182, 578271642, 219966213, 220873024, 416962992, 378763852, 605093243, 244666837, 743736001, 886259360, 973963809, 562182152, 181192383, 409623114, 942142054, 91657675, 392542731, 322024810, 31985462, 886862166, 964910657, 363233279, 813586364, 207908303, 182927501, 203463110, 420055847, 844583882, 937252206, 59428683, 595604654, 846282577, 208794298, 890144934, 190933755, 231819424, 860624110, 998818487, 537279847, 621191950, 372835274, 870292595, 289877810, 531095644, 490112890, 16374014, 835285621, 387463495, 719709577, 524018960, 298095042, 891457573, 846231086, 693385908, 831598996, 840916004, 767829064, 731658344, 758810299, 941345695, 224966346, 45368090, 810511232, 183556412, 137698726, 979210941, 581836690, 913599238, 763096719, 324755831, 390535329, 741770661, 321175401, 495403270, 133779268, 732439598, 313105045, 971619616, 457350770, 68053288, 889487030, 532550060, 379649126, 114381384, 776914196, 386826304, 639171435, 337947430, 368013434, 23148747, 156707171, 736799432, 816364814, 946150937, 475836497, 963372216, 145902718, 823953255, 275936527, 491363833, 426756680, 476730116, 729356079, 536374490, 771709699, 893687019, 950787017, 230210869, 100610140, 122414247, 681657031, 213819278, 567423955, 412032426, 550782746, 699163121, 31050170, 203612192, 417570671, 326090021, 305453186, 483992728, 208642055, 947861741, 25761255, 61558915, 744887695, 666116827, 105184163, 948863547, 484216659, 767547533, 641836463, 695239459, 954135661, 629514189, 884213401, 546538169, 42805168, 356796050, 34444077, 540618797, 660768611, 349207550, 907072657, 762947440, 871964579, 523955868, 553944321, 708784313, 574680775, 730773456, 157011568, 831176259, 887533237, 556557127, 50360610, 413224275, 141812348, 890009491, 466862552, 478872277, 290909674, 378269963, 147660375, 537208742, 182028392, 647429099, 325027518, 273954733, 869751827, 687359483, 463963178, 843920556, 690817148, 350285464, 162432236, 591422345, 52940484, 399911403, 395686615, 140650044, 677946170, 344221093, 63911089, 393663308, 842007374, 869292570, 767998772, 69371034, 733587705, 101365280, 78118210, 110434822, 102976286, 170036753, 135530946, 334257343, 747255121, 276084101, 41631791, 233980651, 318090143, 876861055, 210502472, 494495119, 43412198, 652828310, 189627933, 566300102, 352921704, 956595521, 928318820, 527662514, 103887279, 445544491, 143550181, 900909695, 40593816, 814158372, 314833692, 265197532, 494477473, 350004980, 932849198, 415014832, 456327630, 26048036, 72468986, 502916999, 958755467, 632551260, 799640385, 689909906, 533600380, 940271224, 95377519, 73795973, 124050712, 935479842, 807639213, 377715252, 219973846, 127424757, 252416003, 11496774, 226775424, 913053896, 990803381, 175101755, 845924366, 193256220, 604913142, 29846859, 328021945, 69438636, 331932697, 5264991, 826334924, 928697800, 901437179, 241630969, 321245011, 193580426, 741342019, 870105129, 76438527, 490702275, 891841824, 663469171, 205551859, 459437786, 551583203, 777509742, 551425434, 364029319, 446326065, 170210306, 893716217, 423957829, 720957147, 932926486, 447615658, 257004971, 334351237, 317495180, 664781859, 146492454, 36195916, 295716303, 295519445, 740256704, 975072692, 123133368, 232534174, 744294957, 510882336, 400504162, 428074402, 268498237, 984263498, 894523373, 116358850, 644523089, 988595926, 13462237, 790418450, 425288406, 351960858, 912041763, 917879027, 795030677, 566238012, 900332288, 348377753, 607432848, 986712214, 848222906, 575281318, 940899439, 583142204, 363552357, 506687185, 693889104, 431099748, 265367404, 748369742, 739291001, 588232251, 663263042, 308260599, 595215119, 49604626, 467181767, 771078233, 540018380, 826008056, 967147030, 793465729, 494879431, 603911270, 320736607, 193487996, 863734772, 455921531, 14797073, 13602303, 963753922, 381230349, 387131544, 647625122, 234133487, 136666653, 115121476, 958850690, 281809940, 792082636, 808715058, 354059284, 487191869, 866202504, 34223432, 338493274, 400371637, 848353782, 2070974, 961698607, 67972833, 786397207, 105774277, 34387279, 669260444, 191696185, 895437889, 266229221, 80272310, 196308976, 956451601, 84304808, 364655284, 82654347, 783853895, 384321281, 600533960, 433742197, 262887887, 556026685, 647808552, 422207151, 655815953, 358974231, 486018864, 27703329, 708498946, 229787115, 7184445, 563924486, 619051319, 711199451, 333929043, 349128945, 210503688, 235083810, 126570980, 86237074, 442863448, 113060788, 620676697, 996912133, 678435652, 397554395, 338990080, 399689861, 365639276, 410983693, 908497976, 50377408, 18219232, 43943992, 171788038, 688292796, 880080405, 953544782, 345304283, 48615051, 139763751, 665805708, 902955319, 252970275, 734341266, 552637768, 306258052, 438627126, 125121520, 541878063, 408555137, 282278630, 337057770, 842921594, 144557033, 569946945, 911307087, 663510007, 143000559, 512877699, 714077556, 786864237, 812393771, 590273255, 456850418, 606378090, 973057536, 164841315, 781969594, 880366598, 743697208, 730985905, 369289755, 718464504, 661668946, 524759069, 55439492, 378293262, 341867736, 319550358, 31118182, 124869206, 629030560, 785966764, 429433187, 300806230, 787278987, 421172471, 914177787, 598426834, 596928468, 368343825, 921497650, 644489833, 272229846, 938870941, 272327929, 384330240, 136723941, 949165317, 200344516, 725385885, 536020691, 878100269, 747930003, 352352405, 670508783, 455051656, 906219082, 624703195, 639559611, 8501254, 515056910, 508845802, 737080751, 929023940, 351764415, 538130224, 702125205, 46687052, 256013318, 431156102, 553037725, 248280171, 892958546, 45010592, 903401503, 658981063, 120347756, 368660107, 709240647, 279490292, 84877022, 943601194, 674759969, 63747688, 727450943, 640449699, 67263484, 820556657, 22775233, 704946878, 982243061, 106679891, 621770040, 868714404, 185848511, 216174252, 405948555, 49244494, 650550269, 917218184, 48562307, 504423794, 156125928, 977207450, 556537580, 704958577, 674692275, 510250269, 498707180, 762080022, 339887212, 321611637, 228780097, 547175454, 791492927, 771515838, 743642904, 615189570, 346909833, 742109957, 728081838, 404984268, 931324620, 294367062, 973701510, 660813618, 978244723, 76796007, 495574402, 247155534, 731070430, 349229633, 918704316, 137974985, 865905133, 454850336, 145683525, 574078012, 422236817, 112436592, 890573851, 296821699, 650085333, 999767656, 357563139, 119348760, 957597794, 343388649, 442498138, 413540898, 943446072, 284572259, 899431394, 851365855, 150550553, 242269535, 618480803, 597282930, 485666074, 380780558, 992121639, 167774547, 902466434, 344612967, 874682347, 960584654, 304751897, 94819975, 584444608, 745218668, 217625830, 370285235, 790733892, 81381816, 618576489, 874770672, 827290544, 751477026, 776271154, 127101757, 660076447, 239346339, 806072432, 583000499, 240950177, 302771713, 507918900, 63811922, 460893622, 296871164, 658004738, 631721989, 517009845, 773896372, 719030023, 740290942, 203308741, 645119092, 782475843, 767963171, 389990680, 9969147, 794563482, 944146588, 349221114, 707755898, 378607775, 477344124, 596763205, 714820127, 917577960, 549595151, 853390623, 883678919, 337593328, 457755052, 971914470, 965693465, 7930495, 842856252, 159979536, 81307058, 305926094, 764446563, 189187853, 449317598, 509933071, 765197410, 953667606, 642425324, 779910326, 472508207, 44227914, 184478509, 787122805, 500304187, 783953806, 643880098, 322316231, 825029201, 42248906, 877415194, 944543314, 673940130, 197433793, 160793971, 596823119, 962676193, 314925033, 55242542, 578648374, 960792017, 209651055, 481146158, 285537480, 321076465, 75713509, 269091811, 904215230, 984848477, 858124436, 799609609, 925404732, 781556252, 604641360, 122122606, 473735091, 733059264, 814950920, 477729459, 840065599, 332930983, 329638880, 238936457, 578069266, 859423748, 815886280, 617725548, 94740638, 890038413, 520448143, 346941236, 826964887, 974531641, 251143163, 260074112, 80717764, 438505000, 307343588, 136235298, 32161007, 302521709, 204935313, 120140643, 839754639, 862966191, 538435227, 954032206, 197598706, 702373022, 212749984, 78210426, 613502702, 23650074, 148434111, 377681468, 849210302, 271331700, 654140784, 971850581, 280933617, 337308024, 457683746, 371778394, 885251211, 460264459, 513316600, 759276704, 691578791, 562058688, 539743988, 32737880, 709345940, 291798791, 775513836, 570631613, 103984454, 203574603, 564459182, 937775994, 713335203, 767390652, 470182117, 607198947, 129230928, 61669368, 550956751, 801429789, 28912174, 406078008, 673747078, 449914872, 323203530, 355904579, 205670568, 628821667, 210859671, 9725469, 935817324, 928601345, 925696284, 377747746, 380271651, 339292870, 413137, 166926463, 495257825, 597254960, 647781511, 41755740, 30412719, 855575801, 201210941, 986001231, 289849470, 635929133, 764687757, 374638328, 269127187, 592865777, 342486272, 988571659, 232053968, 833295527, 947362702, 582244259, 927749461, 455255677, 437232326, 888290202, 954662068, 249129418, 504246398, 649455908, 998027801, 3857469, 684129820, 740783309, 365207636, 277667265, 918154401, 134067830, 186603240, 219532983, 634941587, 395586462, 565988331, 637571381, 980881420, 682393487, 125470074, 595387139, 952267874, 94958710, 629966863, 320257983, 950410967, 453087878, 346642767, 629702181, 201097268, 924972469, 329425156, 332034038, 43060384, 995799176, 648090848, 970581463, 130670858, 719963750, 260309704, 345414850, 180310018, 703661444, 191331380, 935470715, 351119111, 144145941, 651462852, 538239796, 931400154, 432385134, 53398854, 187006996, 89380743, 228227352, 899793985, 235795659, 791735382, 62997083, 787614922, 289294936, 567883687, 804713914, 74277736, 319491633, 284724440, 51366828, 403176062, 36810203, 55970687, 49504454, 246554663, 508567709, 241097984, 653840063, 615500543, 32808074, 71916109, 972653954, 987316826, 921195943, 940773742, 259365861, 840760072, 952642013, 613364396, 215199265, 57246732, 582612445, 868374505, 280365946, 312019574, 376632696, 220686824, 770346356, 758519536, 618972739, 347553291, 985242515, 210022654, 625240249, 643394124, 90031800, 394407442, 603980687, 44210148, 330738807, 4085084, 904813516, 71460195, 632781636, 151863557, 206713428, 495893874, 279677186, 868544513, 703294484, 652063915, 659580793, 356769360, 892929447, 53056356, 734480413, 633808262, 835667932, 877702235, 408716453, 775183560, 179403655, 69291805, 157968141, 207494707, 101046143, 873403513, 353580959, 914996912, 461391923, 456792239, 645136847, 190476000, 998859170, 819825363, 964112594, 178013862, 458637260, 647639550, 366930668, 931639374, 947577750, 169206698, 574979114, 276715641, 75839513, 685260830, 811984674, 893462638, 844092074, 788496132, 795404284, 461411334, 146110472, 789255016, 401014460, 423093999, 745771641, 395557341, 371744924, 104315682, 142012901, 256253283, 958074497, 795041261, 838737940, 304781045, 579409703, 157824479, 391474250, 673155586, 265280768, 209530064, 179952744, 51834559, 748585385, 804193382, 38875493, 607360563, 68422057, 800833092, 199249888, 477558971, 899773399, 937493094, 113810178, 515648249, 792800003, 719782952, 950059829, 230485476, 838773762, 876036619, 62561958, 350844917, 345870364, 716002597, 315327784, 378425137, 684763504, 481183797, 563410712, 593081388, 402851922, 436678407, 227497503, 257398952, 318586409, 526553681, 525981352, 535895802, 678266858, 984241436, 52606081, 626460936, 39525830, 47861406, 857727471, 253770367, 532646571, 900949475, 446369562, 782685645, 399663243, 625687600, 709458817, 974671550, 610848040, 237010365, 70929354, 559855889, 98257819, 790451163, 526283744, 734206302, 834115406, 670365653, 925073712, 889194039, 245288723, 345383285, 122824024, 263134378, 262132098, 571726883, 776043588, 929756689, 743365015, 550490437, 768878167, 467568576, 477240345, 104626489, 200920706, 88920718, 647559230, 70359127, 700255282, 328283831, 671529830, 585925074, 481681429, 313871815, 913529459, 624079285, 931851278, 971018647, 549495905, 963373249, 17687827, 672143279, 145334634, 56125941, 839379210, 191024751, 387792843, 532434928, 575398872, 964046089, 68956989, 970544570, 734923868, 738782748, 83421742, 318038190, 284381502, 246894024, 750880805, 947583087, 677637243, 676091546, 416249957, 442087143, 163816508, 91916039, 941839674, 268764049, 278357062, 318578139, 707063642, 123775746, 130863219, 727359282, 828154062, 410748969, 799568948, 582439291, 894876527, 167626607, 168189336, 402561431, 480291256, 355768261, 851926077, 406497911, 988744114, 924406454, 812105311, 310493559, 964452010, 921515274, 32049086, 471438039, 497415500, 281683792, 245495528, 498702708, 508302592, 480609424, 103996857, 160404003, 969137435, 104852059, 64925417, 323257156, 606612431, 429819479, 701501204, 994364117, 609239776, 72682712, 131972638, 98941590, 580006536, 737990722, 663807039, 844314788, 316791120, 195847683, 670238649, 170829550, 291172727, 483117438, 629135027, 924485254, 133535934, 701788556, 483577865, 288704836, 145917884, 379383303, 756255172, 876536136, 599633739, 196672800, 929702664, 567500397, 968495293, 850261435, 16672438, 549614485, 744189066, 632438972, 721892432, 283470422, 499593655, 143942562, 734071411, 553397195, 546780635, 542909877, 205479752, 394800227, 738674657, 874432187, 51374445, 343448538, 280952449, 97670180, 444569648, 966728220, 345010286, 23618805, 371130895, 732393208, 817140606, 604736278, 832252493, 621415210, 261278365, 51422957, 949312303, 155176450, 924324944, 354877697, 243133606, 267324781, 728221028, 6591538, 698413221, 597570440, 536450181, 479321520, 540825012, 419417779, 840155795, 741536592, 846173366, 548122003, 706392986, 61629268, 631967848, 675987537, 956138172, 684902646, 983277020, 791549863, 574343222, 986240065, 412034857, 839980604, 617071014, 80786162, 623925628, 622678848, 241060342, 31014778, 373757953, 158031344, 266554593, 169832651, 794453727, 63037352, 698760170, 443927361, 375540128, 432121063, 505505754, 580175481, 38292591, 658830821, 136666680, 86220271, 74620159, 122200483, 512211247, 140041285, 717505288, 190392801, 82053139, 464412460, 150091925, 598126750, 138195637, 985614393, 49299551, 686370978, 281856851, 88158854, 2252721, 249977654, 556187515, 36416337, 112447060, 262686626, 838096879, 725968959, 176710183, 226163187, 426164697, 28184618, 366174065, 313362781, 60127211, 659975899, 477935688, 660700310, 950627899, 725442987, 388072967, 748025360, 806280357, 467769221, 31537869, 875803751, 280956705, 31460064, 866931474, 742166340, 338335536, 796604810, 985647880, 613743862, 683006562, 650756149, 157239140, 705422871, 979303747, 171136274, 268719243, 341540308, 810095177, 397293314, 279404569, 952602092, 748981602, 227759910, 624079151, 194477351, 805453582, 822333787, 306872024, 981388524, 748007443, 777697210, 560335743, 779114278, 730653929, 894757934, 147124165, 175733406, 163106971, 101270181, 932958450, 277266264, 674525028, 645815985, 300968022, 761152566, 869819600, 39892622, 382515242, 905544425, 738013487, 780792986, 33822824, 98854451, 178336707, 714382731, 970623250, 940276494, 117786023, 517917430, 208357526, 534016583, 363507793, 289704828, 774026446, 549108055, 812993734, 129187308, 246735166, 151468644, 917653528, 371184435, 769726866, 621433729, 724560950, 955782127, 469883229, 683794263, 206723734, 799019290, 415705929, 561879934, 654210487, 420476077, 789853976, 683998927, 965389104, 931492221, 956993263, 126590016, 430213021, 154011598, 260362066, 865031424, 290039132, 868575416, 448551819, 721620152, 769625126, 806385153, 59962872, 573208090, 373974090, 597148136, 246023682, 702729103, 642685855, 388534303, 745231132, 718816220, 838160993, 644877831, 513672258, 133446269, 961114076, 622800698, 764828437, 325896672, 716263038, 827395983, 533989073, 678484511, 746289309, 155338429, 458013016, 955431771, 852959055, 730812807, 609489323, 317078877, 918802986, 80763076, 566414502, 556246926, 812292365, 248105353, 256662765, 563738000, 534773043, 316129988, 431459486, 428079562, 354556417, 145391045, 482451650, 718529534, 936787877, 928782963, 774710547, 669777175, 594005482, 390668743, 474263788, 98519862, 235250697, 380920644, 934055991, 73639175, 741956263, 740787997, 341459734, 321939556, 160149139, 548501828, 947056706, 557918817, 276935953, 290135829, 189070756, 493086070, 366333227, 45859974, 857466632, 715361549, 241633592, 948859257, 878375833, 185413319, 555094239, 249002923, 331296754, 469262698, 804501537, 376573179, 21881137, 754911609, 972490691, 617653544, 201800216, 977524927, 965774734, 53224775, 172121243, 572479186, 618371198, 48809262, 384385816, 96812185, 87408160, 265179715, 515673267, 205523459, 852578708, 25621337, 558422967, 146488904, 945467836, 886411065, 124853351, 840568667, 946906286, 633412455, 253367943, 118694691, 345424901, 58178920, 65478757, 482508610, 747161757, 967017343, 919190794, 744678275, 927553361, 608433038, 920178477, 994491305, 952794535, 730946603, 671097322, 923677370, 464359791, 273480558, 908334451, 751271072, 476265470, 747733185, 462713377, 267618092, 536380332, 578062333, 116763605, 567191803, 822201580, 573137228, 923308731, 570367227, 999872174, 726194179, 752958590, 236462682, 257529155, 370275790, 665401655, 858376865, 595725602, 435704845, 790552537, 114660784, 20079972, 511679224, 9026411, 352589830, 336233774, 536920939, 207847979, 71280163, 328897730, 635168029, 31027885, 968884934, 7539957, 247978377, 763173136, 100025163, 357036715, 66334877, 308678587, 436977357, 87103202, 619991186, 932691001, 984902214, 556366913, 509853728, 580989252, 90167578, 2574241, 600135710, 378647869, 181625547, 664259652, 469991340, 983692224, 314134620, 247404477, 721419981, 226362074, 588234892, 660414675, 187612047, 839590283, 514856853, 207896106, 89868940, 156875319, 578528179, 112474668, 613894966, 540732889, 6797088, 535474935, 737336662, 858515544, 106482164, 182091754, 587509630, 106497918, 374834585, 764145686, 575299567, 531890565, 652885019, 556388534, 913071111, 287208453, 403237688, 122969075, 229433122, 672325511, 958848048, 757437716, 463351669, 778347943, 222451014, 362581096, 279004635, 654356814, 874344556, 49250804, 179895472, 283079398, 101692526, 209065383, 307010105, 793767949, 718466930, 200455343, 750651054, 335132570, 729565314, 978653130, 592850811, 637744179, 754434516, 226840934, 287819181, 460401466, 799965313, 488947184, 9881040, 510965329, 282620345, 24799359, 430789940, 637654327, 465581254, 146777871, 533535467, 30732897, 803924534, 231740514, 608498876, 228657765, 856791176, 278864311, 112584120, 748965916, 21311369, 111972219, 842584845, 622270407, 275728496, 86079552, 672152080, 594281594, 77197862, 987689068, 488476194, 563744821, 285614044, 983844293, 128248916, 508650973, 340549431, 339872697, 133419485, 975027701, 586022999, 808140740, 4778823, 333508218, 95076117, 134690114, 971077908, 437072410, 639490058, 638528300, 332584353, 641086571, 985101487, 919746996, 546756733, 259574049, 819163829, 438934807, 844638417, 452277250, 719097785, 471198267, 821868559, 277742779, 291577716, 241434695, 292064143, 288774435, 338281978, 817432354, 84855259, 612941264, 199725210, 667148628, 203500344, 77751487, 945649733, 301362360, 998458123, 768395404, 302614937, 38344527, 457708518, 182312703, 472080930, 553525600, 222595232, 368820958, 360565219, 746011791, 396006312, 528060690, 274088185, 57037271, 258829014, 55428460, 992913557, 272615574, 774449305, 972882871, 868230454, 678772421, 925233772, 769017505, 615553762, 55932698, 410661241, 217043489, 128026721, 376681879, 804434967, 859585352, 538664272, 205177210, 46270046, 538709279, 942178295, 364791507, 434943497, 917091406, 550939820, 806627078, 734131400, 493698025, 365846868, 336688418, 498015085, 9246360, 251706332, 204296723, 396856354, 241843849, 764683703, 516286213, 299792055, 957010432, 888513938, 244639460, 510359668, 570857928, 518665617, 918258861, 526049301, 928044211, 959681951, 112933908, 503963663, 176078054, 630529880, 760109910, 434033220, 19363455, 960194562, 239652151, 591021489, 551970423, 1424034, 873883553, 563942407, 915698117, 422991958, 176500127, 300452443, 911699742, 799624947, 138346723, 266738749, 896762749, 986407456, 662091077, 554353103, 570771230, 299517636, 253251878, 143142300, 398521717, 624790000, 750111553, 346544499, 996184792, 137459530, 422452363, 879200687, 297000511, 850669866, 50222474, 379502172, 557238185, 65043915, 70199011, 39373235, 2398212, 687424702, 688001490, 451850193, 550907719, 808954701, 455396427, 960573404, 174504357, 164331963, 476846800, 757292510, 756260206, 127473420, 687355017, 3811991, 301389459, 962708733, 89799187, 532730258, 612783777, 376901077, 985479119, 296893200, 749245728, 820788581, 699363272, 659006450, 515408567, 880269341, 591008462, 948300870, 925101615, 162714471, 17318827, 356760970, 940401671, 894848768, 266386430, 513833792, 400341981, 624812802, 851595012, 641042927, 861041008, 91910775, 839483024, 609588593, 762718828, 194512782, 499754612, 304829657, 11671373, 48013919, 70460897, 575171930, 461439960, 959416402, 839426734, 677175575, 846334071, 98720319, 418593601, 766027230, 403942760, 285327486, 179555240, 490582051, 160479473, 667684854, 563718909, 275878782, 125767915, 896793346, 977390146, 885289974, 703504479, 153313005, 249243132, 632606779, 532179489, 215154774, 538153065, 477519775, 168845153, 222857551, 792028484, 613639547, 157447244, 607303535, 877226123, 857348581, 360274572, 254504380, 467636405, 995311956, 115245007, 961546206, 572493152, 582260834, 252459945, 369656644, 515113059, 399332583, 544118418, 199537260, 452590772, 725307206, 112257355, 662397093, 526336374, 346570754, 846138599, 350874162, 298841300, 287757436, 259565123, 323463716, 54233331, 296983394, 305892937, 36852648, 671605992, 515420038, 818633980, 281335453, 777500611, 63322573, 589513277, 242195393, 442305403, 343461696, 458837579, 632947694, 467828658, 87458234, 795798213, 464217494, 724677978, 795325970, 264936608, 692409610, 541364613, 400803668, 201690511, 366330305, 704083564, 913056463, 672890394, 675377306, 657441681, 961506541, 753642618, 683059624, 203014408, 158990622, 905390377, 575435184, 892945838, 690542047, 768246148, 214077392, 249349965, 153927760, 594221414, 496735970, 521005266, 988163392, 135120786, 110653766, 32733652, 573489169, 550434494, 40532485, 132920969, 176509284, 852459679, 694321428, 596029790, 196646038, 590381423, 692880684, 394891853, 687751387, 584979002, 516916757, 211906325, 620730653, 277091772, 23233484, 491859248, 658763267, 970828953, 462386667, 449844650, 791392573, 460881357, 626294108, 603343921, 107791183, 146806407, 991532783, 117496504, 91876249, 211216717, 512865184, 803192343, 58794185, 939885977, 679174938, 891827438, 248804402, 691759784, 343927678, 495956468, 422156765, 972148245, 764070091, 416109030, 63983546, 175761446, 460857380, 974509081, 644795900, 140672228, 6222342, 441345955, 171852203, 217953816, 496746986, 833699327, 909633009, 506134290, 512952276, 357129174, 900460257, 371237434, 620232090, 308587171, 243558764, 18622568, 376228395, 328648180, 228183328, 606728781, 133114492, 891837261, 342863030, 478468775, 683393127, 306470232, 5671969, 955450176, 924595129, 3312772, 695124763, 946161015, 377374021, 264020996, 324155424, 230960074, 839500893, 127701639, 784862979, 91321615, 87278077, 458866723, 658179752, 233503820, 927032461, 256375607, 197637784, 168722468, 515684426, 438168136, 763782885, 295461940, 416253451, 516343457, 207095315, 983768859, 757121856, 989106375, 9015115, 522779505, 731537437, 188695925, 126037873, 167152238, 529963871, 271827706, 272919225, 769526498, 237609518, 106783936, 126726532, 552371061, 165641615, 513885372, 277557564, 199871937, 620292967, 319963681, 254762370, 362528473, 778584151, 518272324, 735292421, 660239413, 282669802, 740369752, 53782021, 686971635, 429904845, 241953793, 751715192, 934870295, 307379222, 164833209, 697244574, 484901948, 790030716, 842310543, 873524736, 417445795, 76079975, 279961671, 79572094, 339551646, 603126567, 948581461, 989429951, 161774255, 471334766, 687643941, 731624071, 258815796, 352481410, 831868018, 713942120, 688810713, 858189722, 707844764, 763217539, 384652040, 221157162, 545238780, 571977157, 855987490, 547145201, 738568148, 62785139, 765537883, 414395222, 376766113, 2884182, 801217057, 985695781, 524401023, 668801228, 544029854, 750050149, 550273726, 715056840, 843370345, 375204279, 974577097, 731978083, 330843425, 970222019, 560847293, 55024581, 7296591, 773425795, 161288447, 613747924, 674717474, 353804841, 17370001, 914635799, 415359503, 219088606, 704884448, 908741873, 146216729, 630186858, 282282606, 801027348, 345010009, 51439279, 827889685, 970227078, 389494851, 798969631, 997140659, 915099531, 297631661, 15464376, 522809009, 811169573, 509009002, 858408884, 289242715, 343915557, 723418320, 342078214, 794205669, 117323913, 584161748, 880345009, 358499482, 625702237, 272261185, 252609741, 857528689, 350876970, 40434638, 450285981, 50227427, 527303927, 384254184, 419411046, 307131858, 126994819, 327528330, 801476526, 924338911, 751403585, 822343768, 853512761, 506303040, 549876726, 448640722, 999894367, 337027673, 596635083, 242657971, 329501328, 662033796, 591629507, 618821766, 682906491, 116788574, 274725266, 20373286, 811706246, 463002430, 340678560, 297763254, 982687939, 266133278, 503833295, 506922329, 940293720, 833524277, 369172748, 415334667, 961706651, 688664475, 388822162, 207347110, 864786307, 78582798, 100969508, 850144493, 838944993, 69031170, 573790061, 686093460, 824628494, 551118521, 844554975, 832775685, 977849734, 710090692, 840904134, 936651806, 795166304, 513835839, 813383037, 679472991, 767436712, 75126700, 313735597, 438477255, 399497144, 207067539, 272318365, 308821490, 703597631, 874765020, 832607712, 652196252, 277099684, 112321620, 865363115, 644456649, 37883132, 215278802, 149682852, 123670911, 985044468, 314525364, 998753274, 946041640, 375764496, 171356482, 947651888, 949418313, 889322499, 34411888, 443661187, 113221310, 407321793, 933734485, 430490233, 454575200, 603895801, 353211409, 66913353, 981370658, 279035575, 672598783, 429696718, 194484233, 17553490, 209779644, 519849630, 850566988, 806120579, 821819367, 271772919, 799482952, 695556464, 583382412, 830721616, 307716714, 718744217, 777909689, 907380311, 712749546, 983141722, 733713092, 560623822, 506271621, 770456408, 826915705, 929913619, 322213713, 661790875, 761881225, 85678127, 788895163, 630155092, 463950962, 670967921, 891217610, 884688472, 906404395, 313797084, 16490470, 25066772, 168569988, 709450065, 805747037, 824259183, 285991276, 403878847, 109904766, 498203619, 133060065, 897859085, 772387467, 422981617, 562400659, 976828385, 771078385, 305680525, 338453814, 43595328, 18659436, 820374231, 23356855, 337957225, 472584049, 726991089, 715858743, 883152921, 607772689, 558839599, 599106372, 464522417, 204593788, 753358131, 446776353, 27124562, 632436332, 874333466, 400836811, 994542579, 92593269, 894039244, 19856168, 687067213, 846489024, 860548906, 210993934, 587406379, 327035671, 662892666, 141641533, 555625914, 989713888, 641638096, 651173216, 590659514, 94031984, 307881744, 566942939, 303966531, 20034392, 585832686, 516511482, 178430823, 776211637, 323158202, 492444477, 591449501, 812554524, 834086174, 456309598, 409493000, 330836988, 322932913, 839472232, 632178460, 648850544, 733339887, 852628297, 528925694, 421985072, 114190404, 151411494, 541905051, 281419489, 122222863, 349029309, 642246462, 470195957, 36097792, 893961941, 112166362, 557589129, 383483118, 321026232, 448036125, 702045696, 900909509, 612722503, 883884509, 95023947, 770784602, 474639451, 538508625, 497087458, 364610626, 94936519, 70178208, 238300304, 384492560, 508317435, 755111994, 396408868, 122195253, 613879591, 706510161, 332213016, 182922518, 334640025, 358766378, 823482025, 909369303, 619907327, 671724514, 472867425, 88398890, 150095646, 32181161, 496134728, 369319571, 508444804, 68022349, 323265694, 674712527, 222729017, 896712440, 334304886, 671257010, 45798684, 60864783, 26519121, 170201583, 568865774, 328324630, 198178670, 409802412, 625046188, 158519776, 694709972, 18349429, 703991954, 909149212, 467672407, 751639773, 740085518, 204325453, 609378977, 620711035, 208939751, 483879248, 244928693, 560944201, 558775345, 405422510, 236630312, 609286339, 508730750, 892442583, 347459184, 753170439, 778182730, 367060865, 562598076, 761275643, 272268518, 127396100, 208122106, 182806762, 747857047, 581019568, 123978271, 457032881, 303587827, 276674396, 225846408, 151862105, 713288277, 922064964, 54870523, 561260713, 177668395, 340126258, 185972012, 816554510, 117485811, 469033474, 789580011, 306285677, 726326328, 782522262, 530524085, 958723788, 716986823, 599301430, 168358760, 985728999, 598559052, 139155472, 761502142, 847781533, 227727889, 871172966, 448207094, 207499832, 41440142, 617436221, 51460097, 704285272, 912620044, 764263647, 284264533, 899182158, 376594988, 459306479, 45678640, 887548146, 316278066, 895619453, 218510661, 941786868, 396369012, 964233732, 18050300, 947266157, 979921606, 197593177, 964743582, 834143366, 571760388, 765237274, 668584881, 205498393, 665263630, 326062685, 200948470, 799913716, 925158413, 572138776, 674850569, 752651666, 839989503, 874429763, 989404770, 83120242, 147223068, 830626048, 822940985, 572531537, 496153776, 523843825, 691131323, 148201320, 826770411, 799099425, 597325801, 455483700, 664067946, 424196398, 199244526, 469365576, 502143896, 723957372, 319564629, 311708157, 537257036, 778947628, 401505076, 796795000, 162609291, 63377347, 656792435, 736819868, 907187604, 538175735, 653014944, 330489743, 37098013, 893717270, 293083311, 678275942, 267114787, 380617934, 190574238, 290509139, 828951853, 540024819, 329613263, 491958407, 453784893, 177729561, 948949775, 787774489, 662482956, 34734041, 308082651, 7653978, 554401712, 833592679, 637915842, 801766962, 79820315, 627483993, 810185370, 255080075, 435055587, 299767493, 994392741, 289039774, 126673790, 827383363, 685972245, 771347349, 539116915, 666030742, 625072804, 292040064, 100474115, 900541127, 177609936, 552222097, 465017604, 178585849, 444284033, 254608330, 173043225, 666957692, 566250475, 69757296, 84067654, 317768028, 83217548, 14164730, 478775379, 24352624, 106170540, 254817980, 464923921, 64265179, 228953609, 328892371, 598485390, 403097362, 746002760, 38573897, 978875983, 712863021, 209902441, 964598491, 849933272, 285736834, 314347533, 483718110, 560731007, 783064203, 352491179, 83067154, 324316097, 741141457, 915580282, 178196008, 664722948, 929331862, 539358042, 416444470, 201208523, 309852063, 678019160, 552226971, 582833692, 710322749, 160437281, 628210867, 335159312, 94371347, 580880692, 907367649, 854068505, 92082629, 780867125, 275939784, 303587848, 83134895, 849337847, 531986968, 235004847, 669128511, 773815901, 428840185, 815535237, 135172232, 494162953, 915211086, 863024516, 298031138, 243890306, 145703193, 929816968, 352245006, 660245867, 53837811, 277749125, 200410021, 538193975, 160025833, 699071218, 467683067, 216426894, 75025377, 395205363, 277787793, 568912040, 809234783, 818877654, 626868254, 746048244, 507322087, 817552855, 111080325, 787009682, 541863518, 291213084, 316824645, 746138861, 506486158, 179861435, 900870750, 92365539, 506096663, 547694871, 172126294, 571590192, 292674925, 12885552, 261312315, 755040665, 518428657, 767284908, 812319603, 963752138, 686257941, 656781050, 854983595, 143129878, 821274313, 306594235, 908955903, 234320269, 199408174, 421184292, 379417580, 615291705, 678242989, 252743901, 722905514, 778628966, 898416968, 978553253, 796814326, 553250904, 254777499, 50455911, 772347360, 364770135, 739151135, 675116492, 438449310, 28661062, 893030955, 938918197, 2814246, 961412594, 598342782, 119365504, 861195191, 213902782, 187749591, 766815079, 206663476, 855469061, 122073058, 649351993, 659758164, 541608885, 179704011, 704921624, 34801911, 21515548, 140806623, 97103450, 997210157, 804798551, 157286837, 172796519, 961663723, 154914637, 348191941, 413592511, 667782101, 595310194, 544738275, 788476442, 44418220, 251930933, 930798812, 456978489, 364913932, 63647638, 391455430, 640219121, 798054177, 90958289, 360649555, 957108127, 921540957, 821567320, 902791271, 575348397, 932998474, 863984265, 340368231, 534741062, 16516305, 713275087, 975725369, 710501696, 653047944, 157256581, 339261929, 836302097, 218715466, 157443893, 773297438, 657129870, 760135149, 124469002, 297116046, 71915663, 179724082, 958388778, 422947144, 439413273, 674605612, 55197703, 255375248, 283480030, 168942418, 932711501, 283949915, 420171894, 323175300, 365311423, 250427171, 710020706, 561518804, 554956022, 478968727, 544805070, 938901837, 307367846, 500936214, 572020854, 810846826, 627933831, 802275139, 493887877, 506828891, 553768122, 295401737, 138304524, 311786521, 772130249, 213930475, 408723254, 503823636, 768751280, 145024826, 985499973, 973144830, 874360975, 656759864, 840076272, 245102052, 629891625, 828926453, 573654935, 920738849, 647131463, 359230554, 725854550, 83071541, 565859553, 476298744, 901760397, 219277081, 28597421, 384376581, 347902013, 899161649, 144699844, 204437239, 917724986, 264137452, 459594356, 35999470, 103218242, 427039122, 160404667, 263492039, 475861680, 786411096, 396815814, 921730667, 91697075, 151141457, 669019444, 496780519, 747933240, 444203549, 773483154, 245332297, 743190071, 194096629, 232328118, 995406778, 755592030, 995108869, 715296073, 19471891, 252235846, 837006821, 800934717, 842872108, 774828175, 202018761, 794300622, 772073090, 726368408, 897356093, 51426066, 847379407, 707599572, 596210119, 908573339, 936750587, 168076312, 581577881, 454551251, 953006700, 66410680, 389987751, 279193694, 905990214, 162109689, 928371707, 656317886, 902001394, 165922376, 1148156, 518550067, 760390193, 73732694, 681097322, 964330451, 163138487, 145724922, 246303076, 606045613, 388651744, 322874807, 31224172, 747712877, 993109076, 737741687, 375268728, 628726997, 729238721, 638524855, 415231563, 969274509, 858122666, 724373983, 958714101, 55575186, 511091786, 800451415, 333893716, 190769848, 922040852, 373019206, 740856406, 460245968, 58859383, 431698096, 641016572, 885323860, 812132603, 19557026, 242295771, 455219012, 41340520, 917874644, 370800728, 989359852, 510725907, 301989667, 996163852, 114050697, 882819667, 261785321, 257083866, 643254110, 290576616, 636271143, 205827294, 241997643, 96994943, 702939490, 464169722, 639285311, 216625386, 435334990, 346408844, 70720863, 462722592, 689104461, 993267550, 569268148, 689359609, 592451675, 114546374, 366244368, 4436974, 97358283, 381466212, 572219004, 776605272, 223934078, 990707311, 857803740, 331613634, 337653185, 990575674, 476482858, 58033258, 967730336, 168940047, 825631376, 255256574, 673675918, 499083579, 361837244, 742531500, 232118703, 188517716, 761986639, 638269487, 450324508, 292812053, 367916839, 212160442, 812052992, 681681733, 247806835, 857377165, 518836244, 67609632, 429164277, 958500125, 812061192, 795031582, 940032671, 22396590, 303285197, 367651557, 468363584, 102217898, 10560060, 661477095, 362011964, 166495332, 3277000, 342295307, 601761610, 638943366, 466276792, 282901280, 616923289, 989092297, 404898756, 123187656, 14149045, 924544092, 583685068, 984121163, 235650079, 522344945, 60884355, 520683884, 276604872, 97168355, 84965995, 988027604, 423212379, 402589739, 770792339, 250521812, 993927155, 99304914, 899887769, 851983402, 673412270, 776695429, 38321592, 225047824, 577928994, 524053606, 195441634, 209143370, 356503880, 166941205, 620127739, 56121607, 14237478, 765152039, 809507035, 590111583, 134932224, 815734355, 308043697, 996212816, 511895280, 908696935, 769015394, 92347541, 786206378, 130591163, 917311498, 345802720, 449841082, 508075317, 634277187, 394464509, 975057542, 943355175, 420862917, 268791231, 674702260, 463833655, 336323650, 541406416, 464863474, 300966572, 375000770, 45936538, 336226310, 145997481, 647774190, 877195164, 795043314, 806532286, 435614275, 717638185, 893519014, 317758237, 541925470, 428735869, 105743211, 851582295, 814440136, 949793483, 382430284, 228425849, 995018692, 714684686, 594775645, 662367286, 956336813, 992931774, 776285628, 624437231, 760682491, 172037823, 942113360, 423619495, 312368712, 310891336, 423956858, 867174531, 654057829, 536662579, 898280892, 852928081, 289634043, 395358474, 877396213, 85451581, 668892711, 259751373, 233459280, 271001290, 761161847, 664818520, 906404689, 750716071, 490931317, 439823542, 511762372, 90412132, 457334236, 204303512, 738461745, 136756912, 242912996, 766792409, 318912869, 306564928, 703995966, 472827030, 878433941, 659781895, 470493435, 322204745, 928670366, 619315473, 437193295, 824301601, 828341654, 624728527, 154530190, 663533455, 874878742, 782130223, 221105738, 619245483, 347348638, 460956350, 71660012, 144436272, 167113597, 446254635, 821497787, 396179940, 323604368, 658778207, 953409072, 946530429, 699381890, 307601496, 592227286, 691006978, 26135280, 22144156, 718933397, 535413370, 381669640, 307723394, 615512298, 363413071, 140215241, 633669919, 169179828, 277177951, 687249301, 44210898, 667542097, 431075460, 476008315, 152310363, 433488568, 728219911, 459627867, 60876660, 489025997, 49050461, 51277579, 507251163, 880846215, 818413496, 971984063, 5267308, 800344023, 860743047, 370232035, 996512396, 959575603, 91996767, 708311050, 7858022, 916519035, 930113093, 698499151, 39189579, 725842095, 707824430, 177099911, 410938282, 285700891, 36987035, 972391735, 502704356, 158690304, 60629768, 742616188, 990912139, 575906902, 173642888, 860337307, 680402641, 33075275, 667615210, 912524259, 50995879, 15521737, 833909325, 350012156, 669855372, 563297531, 126878916, 549969588, 374297695, 12526580, 475184661, 530359240, 299127617, 563837329, 186533360, 506368705, 893310506, 796800848, 314674342, 855436627, 624563997, 668479471, 431436022, 400630037, 347134584, 35556445, 69203206, 376995447, 233163426, 286139952, 262200392, 364142270, 355236510, 457539101, 501711985, 1683233, 688219138, 798222417, 807941628, 103836229, 261480600, 482698823, 291486839, 411453069, 98034185, 44710169, 162838731, 916808251, 775828402, 797430335, 880709224, 339905455, 483380641, 593733218, 54254242, 57079109, 356550350, 602197511, 350972558, 626279782, 712568394, 149074361, 65612538, 129498568, 852267248, 270206221, 799466707, 510382708, 503011771, 696466750, 313444144, 783939240, 766025445, 974400259, 688913693, 686225855, 817854146, 478213615, 457436935, 381065561, 822060467, 994724801, 522536015, 443274133, 103356693, 854549450, 947088895, 42333643, 676913190, 440009875, 564123962, 943300575, 939501231, 159308630, 802712080, 816312261, 614349963, 491487570, 956542181, 150906194, 197494766, 798685422, 999759503, 457544123, 89247609, 542976287, 717844601, 43863724, 987394910, 970782748, 580424739, 709324616, 851103333, 476856761, 494210259, 43282308, 500621159, 259651658, 376565087, 363160117, 992252241, 885724393, 566926607, 218437502, 150378090, 174383244, 150032191, 997361297, 479705441, 768426884, 683778096, 918732157, 813258091, 756171671, 248637220, 544585318, 560415446, 393207556, 943588237, 297222371, 24599509, 650106819, 734365251, 341495964, 174396667, 575979509, 703779950, 391591064, 479344221, 532269341, 229553611, 266209601, 809561140, 749732257, 518522283, 780077098, 267416620, 798461006, 919763884, 865151213, 683333986, 213740057, 269017445, 671210215, 360160121, 842936539, 556659145, 318490525, 157791594, 930338150, 806120606, 502585568, 359614151, 565835663, 975498670, 972210564, 206310437, 721854814, 195587841, 721880976, 660015030, 768562400, 747435261, 604038609, 776190384, 996682230, 141990942, 649385438, 753540738, 753228872, 333806479, 380838315, 985487416, 65798227, 220298396, 375084959, 511779914, 165973325, 111169799, 237680787, 315077018, 356559667, 841655587, 759401003, 855749005, 224982584, 865600146, 453783417, 615712944, 342524816, 477616457, 57009507, 89435406, 580867288, 187960078, 901336784, 372933739, 289848465, 592121378, 774372406, 119811679, 520719198, 786414387, 228026795, 307621797, 158127862, 185347040, 383495055, 967320612, 253040179, 443859096, 558030539, 377950982, 843333593, 611436882, 95623751, 921054996, 413094891, 571912741, 467069613, 538447364, 775518537, 781658772, 634084128, 440730447, 779154468, 853867095, 789374998, 513780183, 866339182, 423003884, 170544838, 165768257, 991445096, 910675143, 665069040, 254714883, 352180628, 310113344, 390204373, 244027553, 536055436, 150002047, 464327168, 158346926, 709092940, 550853003, 191377959, 709658824, 765034425, 467556483, 266711607, 320706597, 999336154, 397594204, 552961388, 844171744, 976203690, 628259758, 898795057, 527794306, 889531860, 195749996, 450995590, 447807439, 281692063, 26095787, 945295871, 126392337, 813569395, 20144076, 442737439, 416529543, 419501466, 196085429, 411798820, 471004157, 125307674, 582285643, 394200789, 309838465, 132782625, 84450456, 901939616, 504226763, 666311301, 734623394, 174735850, 339646349, 966066921, 991239835, 349700640, 20729969, 993129690, 603467071, 290137534, 953939551, 908754613, 799092375, 130160201, 580927876, 789094223, 439117242, 784183378, 696040449, 286902331, 32799074, 223628525, 333094289, 783160330, 243282095, 208090719, 831227363, 87022339, 484714520, 632036957, 893109366, 636680257, 740545336, 667290576, 527532845, 371799743, 754192737, 883344373, 524344973, 165540309, 312102648, 592727687, 961062408, 223086749, 781833689, 187552263, 908178915, 552425293, 613448074, 71891770, 225014270, 371184057, 791373041, 885372652, 374680059, 620930935, 365894910, 419935826, 160817265, 7896330, 526821121, 162495601, 995020464, 479502160, 458105624, 974493550, 868450818, 686182598, 98353859, 771855409, 930087337, 462424650, 277718634, 686977327, 849370816, 144301928, 725110623, 605517712, 879582984, 492614285, 765381509, 875226322, 422321895, 532667023, 3536430, 840766547, 678278279, 187885095, 451250886, 436715648, 965675721, 675550256, 228326191, 749098232, 582814502, 958209024, 305930251, 889268140, 142523135, 544158447, 558999613, 516635922, 661279272, 773407432, 432010574, 889726181, 141319517, 274140584, 613880266, 342189892, 28432970, 142219778, 35509372, 544775001, 144411190, 436835812, 461481056, 898165562, 20806570, 214284156, 56360111, 67820873, 24271131, 44177063, 195541734, 187687816, 580434610, 635302647, 420620291, 235709786, 222449106, 485486128, 344688939, 34231409, 845679704, 576525516, 313937992, 717022853, 100248783, 561607014, 829454308, 169423546, 410991812, 290966521, 373161415, 54887624, 210571163, 895225938, 897922537, 982900555, 340160904, 410719153, 953349190, 83351835, 161479040, 209239804, 481573372, 581790109, 344077995, 933152360, 114486977, 206851932, 259993601, 972671869, 255310451, 351959051, 255095054, 122309737, 755482771, 699766139, 722659059, 187584620, 133425989, 864914079, 302190896, 585419802, 726896246, 484463532, 921898937, 672020062, 56333428, 147687836, 993785441, 103951864, 22062407, 699494054, 475176626, 447021126, 247277263, 502953819, 943346030, 570977279, 34219479, 457258560, 188834574, 613406410, 363750915, 266939031, 750231905, 210536586, 335749396, 643463852, 236035008, 412676104, 423225316, 120718693, 118834889, 313309338, 219754286, 710402136, 563353557, 444247203, 100680765, 638406075, 873369057, 34717716, 514799418, 938412850, 171717189, 36525899, 880795910, 198525714, 129843516, 369821248, 129253325, 806385283, 315959667, 185213210, 816926298, 573650665, 355849481, 116510789, 38130915, 687582226, 227976653, 501605422, 492251915, 559822654, 389604539, 587853712, 984250333, 803051828, 758384778, 455459550, 451495989, 26767124, 14023767, 143504598, 48092661, 716790210, 961795802, 670622104, 415372542, 65695663, 611176280, 337922745, 621619918, 825107496, 838200598, 73076616, 304125431, 805286486, 979046941, 305068061, 371895931, 118660309, 592067950, 969125996, 706476730, 335150290, 1623565, 482013708, 991683813, 128155796, 577946981, 300323756, 480100926, 969498726, 194153170, 429106997, 670851993, 533217041, 645273186, 721247916, 192674931, 615684026, 414406107, 225063857, 305049090, 496302246, 177571406, 695523790, 663331184, 443544109, 772772457, 230909949, 745656810, 786697074, 189288031, 24884787, 190218504, 524634906, 771009346, 986229061, 79144701, 509327183, 745014085, 728910312, 489819386, 16342592, 158265875, 229613147, 593113174, 277554729, 109458255, 667100056, 301453746, 171495076, 973196773, 91786776, 659096098, 565193980, 822182257, 423479773, 44228970, 250198470, 590177415, 735730355, 46031581, 224357299, 846709325, 761797962, 151572738, 439416405, 745271888, 382461834, 242541216, 925132305, 256701788, 303449985, 47836657, 192355740, 896707344, 644524345, 152648396, 229107639, 344892224, 144784044, 50128103, 596064240, 627298574, 571511753, 905484075, 754657308, 530317848, 138142490, 503357631, 507319906, 356911657, 217575828, 812464805, 275651924, 603025911, 803812200, 61182794, 46009698, 758840052, 204328637, 839056041, 609274697, 878840475, 954880781, 231284487, 237846540, 757379381, 141202678, 974452291, 377849075, 35374712, 810963427, 578966768, 768359766, 638914519, 803607116, 516722632, 744474331, 45517351, 651075727, 660542594, 592988418, 187677440, 956786871, 679973028, 232169103, 868266714, 91986855, 301628536, 541174033, 132614512, 341545543, 642624879, 463203376, 65143318, 910549988, 863077361, 761120418, 16108637, 401393267, 785917789, 280177232, 357026593, 365566268, 114869989, 837831007, 481818059, 381588947, 466462427, 949282115, 744640235, 727121678, 976001254, 79988505, 544149004, 583907634, 934554674, 864936504, 355385796, 608538447, 731137146, 671656353, 532298830, 970847168, 175945844, 718642572, 407254960, 650481177, 793888318, 98577585, 392249019, 604120555, 422396103, 726216752, 350938325, 726540905, 820128620, 262204657, 552660977, 463617155, 174372470, 59018915, 78836812, 30405509, 975931258, 79697799, 144282899, 373640121, 569043955, 785161403, 297468927, 410447199, 354830414, 308417234, 381964281, 778653323, 811600963, 280437605, 964793336, 928067086, 124063305, 898965552, 331957378, 836236312, 629910031, 400349812, 158920858, 617913244, 413094170, 580700925, 289614716, 450353571, 797265494, 955058680, 224378889, 875342833, 616066646, 75773065, 494739474, 861910137, 545014262, 953900749, 722303829, 122628089, 514682413, 234110672, 460179469, 534440297, 983955687, 553156399, 413056844, 395761437, 91196740, 446283869, 344235239, 489574154, 473939449, 51690471, 911916490, 617660916, 897080293, 301806120, 163850305, 843096378, 433825798, 814517636, 873365374, 581506017, 777888741, 734148213, 83148050, 86403414, 455568815, 115225859, 507146701, 595695729, 130150072, 457840285, 857118273, 942985535, 682720575, 215759361, 317994683, 50405383, 697224314, 650021498, 803728177, 239561122, 378307258, 211421351, 255053126, 800752374, 146022172, 610867226, 22795361, 681858092, 472462459, 136114125, 607424631, 671655830, 633072327, 157871920, 548746518, 633354901, 78186415, 35961287, 419717281, 222398984, 189477104, 747244332, 609675780, 641386695, 279237898, 17229924, 338684592, 628655526, 713688456, 403556027, 34970791, 723565676, 47836557, 65827220, 804150380, 903894371, 226666047, 844577629, 997076665, 38441714, 695829955, 206373678, 496079526, 823268817, 535292, 711469431, 907920205, 577244997, 351003234, 935313637, 484436188, 205422502, 820413035, 72231080, 965713723, 441837549, 221365468, 662735472, 529284509, 784832304, 11234486, 508172305, 296575441, 845400244, 188099933, 60106751, 139339846, 767637783, 874016449, 134266831, 543282494, 782755435, 755950940, 433225259, 922565108, 584179557, 24462696, 883448908, 825755349, 335450346, 461397397, 951875170, 173653217, 235236502, 489677604, 920035696, 310914092, 171694000, 424336854, 940498118, 392055856, 735966469, 140991112, 360547843, 167897735, 508362657, 625030988, 553474806, 572215592, 486166248, 962669913, 930383807, 260105152, 536551470, 950912611, 28855129, 976554842, 860654967, 139437496, 677550606, 40621331, 62044386, 512108133, 133279535, 786640632, 55940821, 576140541, 542680304, 525698103, 94720511, 849070456, 404431068, 146624641, 262532257, 934847212, 177967969, 828201264, 190902002, 828693204, 166459688, 117102990, 66701210, 632831865, 925272285, 459963358, 850473108, 476239635, 583870640, 749961282, 657949432, 457268767, 937931993, 435404293, 232090126, 903510690, 50725049, 305108920, 834020083, 755789889, 102418509, 687123952, 150386463, 30054298, 261630057, 967020137, 880321530, 181158402, 630458908, 158058090, 739566486, 562335787, 257914227, 287572167, 121802876, 733892802, 105415139, 88872354, 248176903, 370223350, 646434307, 565782067, 117869808, 214088062, 331919341, 388619260, 595180961, 795020842, 184563012, 711077543, 386757124, 177043608, 719560062, 553398790, 701867617, 475077458, 138500278, 486043786, 265935201, 111129843, 504635810, 111193705, 667741044, 75959963, 164123942, 481300703, 149054088, 80293730, 376499873, 275714445, 61630381, 728799473, 662521146, 992960892, 910480941, 436930963, 242314742, 12856475, 975561603, 532294144, 773862843, 507534598, 586103459, 462340770, 895812156, 217694073, 917663716, 429077359, 833264624, 150033165, 500785326, 304287417, 952196808, 769778144, 490629385, 250398505, 796149029, 359850667, 8425174, 626230706, 713433291, 748764340, 805905221, 893072328, 355145601, 438617312, 717301486, 714301938, 748063896, 894484965, 772387328, 466255749, 932053029, 84689382, 961835759, 262887549, 253764812, 877427961, 395681297, 779150535, 995010951, 538661299, 628263148, 874310743, 968925318, 519111103, 54602360, 170190901, 738914495, 976037816, 514479922, 279579441, 511013332, 668624083, 708303853, 35348224, 597578793, 920517769, 687472595, 251506175, 326638636, 22352374, 646997387, 806910304, 288697441, 790194045, 645687430, 316916684, 199795097, 274139978, 850234948, 411618060, 250170952, 379502771, 941410741, 378086847, 480682888, 425568705, 186220529, 654580948, 757479695, 844208553, 153796894, 741800649, 146270877, 752268586, 809464772, 33783580, 583641892, 410108417, 59805372, 933696944, 126119074, 678148113, 232865360, 410825143, 797123879, 358433404, 395562403, 593052777, 800162909, 20125687, 903726477, 477281005, 370991631, 853959000, 36696156, 779483101, 253355800, 435122515, 472118189, 470208571, 299555631, 514932801, 362987840, 521782673, 616731723, 712122916, 460823030, 422394374, 424042836, 221358060, 651693219, 62967888, 671128351, 46871109, 842200357, 893135934, 707296564, 410584224, 102054279, 732617062, 18237621, 132638184, 15062043, 513065804, 812461891, 979410574, 166727923, 558402049, 491266108, 690600375, 673651840, 95654063, 374649672, 924370699, 14642737, 526005575, 782382818, 593664377, 913650354, 556411464, 288283427, 85764689, 940982848, 355088253, 700390328, 972831694, 760291089, 31433727, 305166250, 746933221, 522215295, 937018105, 793637652, 710988302, 636989843, 805490679, 274192686, 220086070, 739386015, 402576179, 480156931, 720253237, 736674128, 960982221, 203381420, 105590214, 820806252, 990876106, 757618423, 110036223, 384738150, 849780553, 462738697, 998369885, 360549379, 362591363, 373490684, 364912493, 72198684, 40875193, 792828444, 227172098, 317063685, 961825338, 633370700, 48999387, 944344633, 441770523, 183416655, 372055115, 273049659, 5708233, 735538617, 975505234, 274003577, 727284475, 309328582, 372706358, 367296986, 76486715, 274080712, 715872227, 166030353, 217840088, 563550284, 268098568, 635985325, 695265183, 545699774, 921041402, 206075034, 220301974, 823424444, 512568470, 667784897, 611211485, 556033194, 281565768, 154317441, 70027659, 560249581, 743308852, 940960411, 421597936, 563848041, 722783755, 237125132, 790461763, 659259908, 371685839, 413496757, 1825299, 640704778, 498232458, 649052282, 147554771, 204817424, 925175715, 189904311, 936220320, 399397085, 979561840, 641065796, 290864582, 44457153, 817470741, 113620529, 759169233, 582004285, 329472842, 675069505, 357710187, 754070014, 646940203, 93016145, 89609913, 745356935, 712266391, 698090380, 876149896, 855427785, 104995919, 285477769, 920412541, 550662677, 869749461, 29399287, 779103242, 41139141, 929754370, 949165501, 75458682, 427994783, 410339318, 173773155, 255539031, 724954641, 236804708, 404617958, 392882787, 245732400, 887243461, 36828032, 317896680, 352205624, 627868974, 965921586, 552591379, 228936673, 686501051, 268047028, 118225279, 880336588, 987688032, 108468351, 821861087, 317059181, 497548443, 549902965, 481245819, 452302031, 909137385, 140844969, 96528688, 471966702, 522883022, 71011267, 920970328, 112801875, 115042296, 492203469, 689711642, 140349383, 233702703, 14038611, 402084118, 700633682, 802396546, 236408315, 839180274, 506398740, 622101889, 562640020, 299678382, 167839787, 817605101, 729734672, 36210731, 441929671, 571855243, 813952245, 550290093, 827220590, 899571498, 510516917, 316421228, 925054542, 497820607, 286521628, 952372803, 756619213, 805924336, 393979794, 399972759, 274849589, 965481410, 248616818, 934154320, 203583737, 217804875, 806207867, 770189588, 349290536, 700735654, 386832054, 45086319, 766275211, 478762346, 651871492, 992287249, 156835246, 162692585, 886251286, 131257168, 543076140, 282594420, 656801331, 258885093, 639120676, 934443300, 839697637, 248284409, 933872127, 280793805, 840117133, 710183305, 257921002, 903967583, 789898999, 918084259, 307139744, 242357366, 777156301, 283151638, 178564223, 186620993, 867072678, 284146284, 804995901, 421593670, 760683962, 946080061, 209483041, 215435897, 73281161, 509928719, 690264419, 269134601, 475570009, 91333104, 833069953, 484087595, 998785910, 618302295, 502684447, 318225796, 225964234, 112047148, 833585528, 396567625, 423566282, 918458391, 959189639, 414400066, 931197008, 284246940, 567779876, 113017399, 620537258, 163793477, 784274472, 613869526, 981406130, 156576886, 968669349, 141415429, 446849794, 603939729, 54462333, 408861209, 586867901, 86801396, 78985809, 21802134, 144309950, 91320232, 111055823, 323995441, 767935045, 204041804, 375294823, 2588822, 15072730, 416992088, 574704498, 594207597, 113520213, 135239597, 706637196, 416255740, 169816825, 590363422, 297370051, 434201038, 926548811, 870614692, 349312328, 250955780, 692739102, 769364180, 340130475, 983173665, 525919226, 278844711, 425912536, 178786487, 521423718, 923098544, 243109822, 221157695, 565455982, 930751096, 895010275, 679977265, 267559166, 892643258, 20866274, 160678046, 345598235, 401342670, 217324309, 565798892, 375002509, 606878960, 341571258, 962086509, 58027897, 625748372, 474191787, 341920972, 184494096, 915808145, 522969498, 890151547, 330172231, 508955794, 82797983, 676100829, 663135908, 985386643, 72725906, 482957392, 311279376, 308872607, 778925024, 614982120, 570940004, 45745001, 938853215, 594745755, 157850089, 384738345, 11435462, 961080761, 129248585, 807081934, 661848886, 589831282, 708069242, 465946859, 187316175, 811217576, 560346703, 424507385, 814956012, 133766153, 353479905, 704176960, 141519770, 395905165, 522196459, 739073429, 45012148, 74224868, 220149832, 919739930, 90385972, 107876295, 627951384, 124104533, 153588445, 579154565, 678078862, 495429024, 513668051, 815082691, 901970672, 720634138, 397502261, 800809036, 984818713, 203576266, 919872320, 951599090, 669655869, 970184865, 254616984, 661248181, 568881335, 848583163, 986216671, 71994759, 592556361, 694596637, 97689838, 688463235, 121942346, 714932482, 754449796, 354060841, 93781076, 332602684, 91715282, 210450590, 272444320, 527242432, 893436719, 928595262, 42346260, 446687315, 367767406, 361450845, 671248108, 491151972, 185628905, 569029545, 160996622, 753235015, 488429145, 689217888, 46862424, 133760713, 804578089, 597988498, 989025113, 353567059, 871583355, 967685384, 825907932, 383868954, 329833456, 240394003, 409993405, 150210591, 523144725, 109652774, 62044505, 517994899, 5281244, 758998568, 661519043, 32714598, 874486486, 417348224, 729418158, 593087709, 227300455, 841978393, 94893542, 239432716, 837800351, 92275722, 895444555, 252904151, 258644228, 202067670, 316817768, 950940626, 315078564, 724341307, 419228023, 503269146, 38524162, 848139463, 306749771, 978668106, 273232709, 299035349, 363660466, 682354187, 828525898, 294662283, 188381995, 892150419, 392361775, 397207361, 18171853, 886509205, 804002791, 787472648, 757485515, 57128461, 440354147, 488861000, 380584002, 549488044, 50326831, 609763510, 162388268, 371615424, 706047982, 170946751, 735718209, 211372910, 150741897, 333351459, 151576798, 312525821, 915790773, 554312482, 220030326, 264684202, 481343848, 848312047, 128888007, 184547787, 49859005, 779802875, 256924605, 871348954, 15053913, 352388197, 195896001, 852638472, 891351373, 902768330, 995423026, 99686237, 339942605, 459758786, 722458340, 525832865, 828687999, 35049692, 425536083, 210811323, 163321299, 377544886, 98606846, 67013160, 719457663, 434267288, 140554970, 958559022, 218087826, 283374705, 870419323, 108408708, 23279960, 554867368, 6028281, 489148781, 256499797, 687383069, 525595855, 626956473, 201960986, 328369524, 305774035, 909633009, 673077143, 648285004, 347432542, 141382315, 541106648, 988181655, 117321797, 432271868, 407361713, 259166289, 755677806, 117845831, 793035183, 319627408, 761229349, 534644605, 768479594, 692273791, 252559929, 302311226, 916438643, 476074164, 699015547, 618953706, 199651707, 245712309, 337348192, 759557717, 728036340, 498632393, 324149110, 470372086, 799078726, 311595966, 376820845, 639384549, 579119334, 310263182, 270457017, 772853390, 960809576, 568837841, 180516858, 130274267, 119908426, 232123797, 759408986, 865402608, 972732071, 270774811, 340544706, 226985260, 805816284, 695845469, 9305268, 631323359, 736199883, 117824257, 182384147, 524360430, 206472390, 296642230, 533696355, 425047078, 119032994, 560162526, 654033072, 531090884, 613593557, 99486341, 167588539, 614076564, 237236011, 495191700, 447748644, 702145304, 723303356, 978452070, 445028628, 297124703, 601130343, 783204968, 171555237, 947008469, 676069258, 894986130, 771233265, 192546121, 658162565, 12200821, 875258167, 970312836, 864333390, 612127234, 9158962, 828567805, 112835391, 782089189, 379233394, 897903994, 456031638, 7479982, 157225449, 446557997, 46771016, 520493579, 463886659, 470727388, 272464550, 295835331, 406780266, 798518402, 853450641, 351034687, 805571659, 863530979, 87001283, 901070540, 741156762, 863983816, 261873895, 996863637, 132505311, 842191904, 369853868, 451546048, 765064510, 312234938, 637409866, 355048186, 547737074, 703220074, 724481341, 474960360, 365159882, 97886696, 21877898, 502963574, 460189471, 418192749, 573967864, 602518438, 617500784, 8505110, 779206899, 669405703, 596563467, 474989398, 712019439, 382156367, 949193680, 914815841, 456531129, 878618655, 451371908, 879700380, 523081406, 165284372, 941350222, 418329391, 812577112, 786314513, 990979764, 845453341, 372373483, 452023373, 618981619, 662981789, 213205336, 4504346, 547330410, 514247919, 895702216, 552604039, 506458658, 516336234, 2439970, 421282634, 170179032, 325739013, 943590685, 27066614, 740422065, 59957611, 104590795, 635853470, 151075857, 704030819, 547621732, 796469656, 311238422, 481179280, 3255956, 965668558, 651899333, 298216420, 605182400, 988883247, 586749983, 880349721, 457538763, 929155175, 646148455, 130238505, 307438282, 340557637, 709773964, 199659231, 951847621, 913698988, 719418059, 616337203, 944818247, 191395186, 596794919, 113565957, 429935756, 536285305, 901492780, 357475375, 639164416, 132693499, 841694908, 868537924, 153375613, 624616634, 3255819, 552768798, 844558916, 491520639, 875599133, 5501175, 983967881, 429907508, 852821939, 474748976, 822812101, 8684175, 516127845, 747714585, 571326650, 269938165, 148282705, 847988421, 351589932, 851128896, 179333426, 972815738, 507050014, 608641593, 59787780, 154063997, 460439205, 173887923, 817635079, 175342455, 368868909, 4159561, 228854951, 334458582, 851852224, 552310283, 333441852, 996060747, 615525290, 880085503, 882477770, 875142096, 245650044, 970645292, 814439362, 772591158, 223459579, 406214161, 543577868, 940924920, 924068576, 879137165, 341157186, 941272407, 298589187, 417910492, 419384293, 56636252, 895550272, 880627799, 121920926, 401595239, 687927996, 289441796, 800640974, 490387651, 425527906, 740732246, 245463677, 156350906, 677821871, 149612879, 761890112, 75476835, 79608491, 454502093, 389372961, 599423549, 770542671, 82949674, 632882005, 228390945, 237829552, 369182013, 63853257, 310394731, 470139955, 732473612, 14262034, 700093415, 514622479, 49680893, 63203244, 73966966, 81689735, 439951705, 427045488, 382236131, 672054656, 351704144, 358644861, 39121888, 164509776, 63928858, 401999829, 242610743, 664380934, 33849114, 340652673, 174191513, 55580090, 54368436, 433009968, 719033301, 671343041, 418846319, 888415939, 697119752, 245560357, 965344628, 762180492, 378765987, 729710439, 426185970, 936187812, 355984300, 138108181, 344299800, 533534903, 641149054, 794043571, 518207240, 282304619, 37614742, 317768218, 35342898, 289008528, 145025335, 352394191, 343804213, 284755288, 244579110, 593459590, 198162350, 856335946, 734904654, 762202496, 293896601, 58492227, 805877942, 966221324, 428155620, 48912797, 25307206, 860475282, 561522765, 11054269, 671389919, 803710535, 809550413, 485463002, 862191362, 53106046, 859488927, 860915826, 512547436, 180773334, 280989801, 524983178, 659371030, 527996056, 176067390, 519589768, 921779617, 581773160, 677021606, 113119386, 476925726, 434100252, 283337066, 965361704, 445989376, 700261996, 287612211, 887726146, 856297869, 685185426, 464434949, 956671194, 809126141, 751990220, 190920381, 956141978, 166547149, 883428656, 350267304, 823021913, 528495451, 649893315, 901027933, 502544561, 492178716, 375488046, 111825294, 48075413, 895326270, 761356216, 466326796, 521543883, 264831600, 748573914, 440346479, 694776807, 530797087, 176647772, 294092513, 130609001, 782229381, 190233918, 430345650, 479932854, 870238090, 728946678, 928940969, 610970016, 895184602, 896489479, 687199558, 616224016, 964286974, 725989689, 838330482, 445824693, 834741878, 262011616, 833745726, 192679989, 624793033, 394080957, 938835644, 390680654, 809198543, 709657409, 513464596, 952977136, 235793102, 186060233, 943488723, 514127599, 493362110, 498864700, 156313904, 987041452, 950239421, 757095959, 328364916, 57044639, 34424298, 759188435, 895508404, 503915677, 336374860, 392108546, 381744677, 541827056, 105167020, 763963592, 591738300, 374570589, 241019730, 393146701, 441958433, 94740757, 664943785, 639278703, 780347759, 746914406, 447789029, 669446278, 932307489, 745683886, 858226304, 869025650, 499594390, 803458050, 458011032, 1177801, 270982697, 524786491, 695591325, 560595159, 171763644, 201044978, 261916186, 567315781, 417548506, 370230678, 510247509, 959607389, 476555452, 57466406, 995607212, 856936235, 358484430, 884828515, 783230380, 483842686, 294014208, 248351167, 748995135, 614120867, 755545433, 459518478, 682177292, 744075403, 35343006, 537656782, 846568124, 196996261, 566163997, 769798415, 198526122, 67825245, 646232960, 339653451, 376189395, 626681384, 538903760, 930955731, 536425115, 133665022, 556324968, 607642304, 410053539, 448930329, 849307921, 579678436, 770820760, 725129595, 861887050, 173841217, 337185529, 219237299, 513137966, 118382368, 898632765, 977623701, 982159252, 671906504, 480970290, 313961649, 323787000, 113631008, 45506830, 52748831, 727081116, 183512455, 352739572, 997462249, 241436326, 805833585, 820991610, 807023080, 680189562, 311270940, 707706229, 470244628, 261225277, 667961707, 63805328, 538268654, 584875285, 367435791, 46868794, 717711523, 73061506, 55466566, 85157588, 607786543, 180813632, 351523667, 363510706, 223360795, 591540224, 17610631, 421578653, 316861906, 731299468, 755413751, 218673521, 903774187, 239336984, 500383372, 126641205, 525423376, 164078564, 705321145, 862491283, 805179049, 950833297, 107018539, 69562224, 951510581, 181515719, 858138486, 66399725, 757055773, 204914786, 258663297, 608653119, 706056313, 750806309, 915443064, 903256262, 7728925, 196392148, 429723478, 131561647, 386852893, 467131926, 329520887, 10801125, 205678659, 398457590, 186766636, 816241112, 397990239, 938866158, 887397778, 379946001, 334222344, 697574865, 573547830, 602137813, 471079743, 93883267, 903928659, 667194184, 359806818, 409129398, 641202377, 977137517, 3868293, 705494099, 346006851, 386667726, 106225998, 940116672, 82104096, 88574317, 157293269, 964170069, 931821262, 525729211, 201231639, 319996332, 682174257, 188571227, 353167798, 534287276, 506922300, 250083339, 593107351, 335338995, 834380645, 703552729, 75637442, 23133637, 93250793, 364461685, 232363568, 995752501, 13402360, 553916308, 329229991, 378610415, 832521009, 916275221, 759123542, 773842877, 424257420, 346311080, 127493587, 875824966, 973194594, 115856350, 45016584, 627824162, 937787930, 430487760, 183202234, 962956215, 836550279, 845675628, 31457894, 423280609, 803431122, 413887668, 216412659, 53102679, 834053243, 71449327, 137768737, 414637338, 953966791, 253803835, 631323011, 954697033, 125016213, 454097193, 893365591, 817507917, 765688961, 641638079, 809128465, 640161744, 179196772, 198095390, 275681927, 342080301, 547473950, 527336586, 776626305, 367020472, 30117060, 348231840, 910481068, 700931088, 348290439, 85858282, 685131241, 526395931, 865887021, 596826184, 462284065, 805470927, 236275448, 485766374, 671910102, 536632013, 347506302, 998403616, 742253446, 993162526, 303479705, 146482398, 77710578, 201467500, 24805000, 81451438, 631443623, 843531733, 693249216, 338151497, 227221645, 860421708, 914581887, 989015674, 700007676, 438638489, 619935044, 834562733, 372686704, 452747785, 154499133, 520624989, 659496366, 449901086, 148356615, 711524116, 709108700, 307374573, 770843543, 522762204, 292938500, 896161473, 206903028, 454521025, 414829935, 431249494, 595983286, 362424894, 635468867, 566649155, 736595655, 25877168, 413399386, 64038443, 6235972, 991032573, 218909426, 515942749, 448841249, 441116605, 325658992, 911083256, 899181811, 646983378, 388857523, 933108972, 992055678, 664772287, 332490957, 662115271, 774702694, 943416390, 701540697, 910535797, 381785537, 950381484, 168873227, 394307130, 405850308, 783350315, 748552714, 238526672, 58794538, 554012035, 978432131, 981838082, 163740166, 972099118, 755203286, 811782071, 598053543, 381164351, 678577255, 318383093, 289768043, 833006224, 314991818, 500942869, 913695413, 810451334, 620028302, 682620869, 268418949, 575330169, 63117259, 812588163, 373426748, 793349186, 202375204, 975583460, 141186105, 753430981, 81063419, 990369300, 150943057, 179168347, 295889678, 665557500, 849825789, 582214799, 394813632, 685694661, 654893815, 942608332, 992840588, 321147494, 271089844, 257647096, 995411123, 501734458, 953937594, 421923357, 112804236, 121660737, 722830105, 351599305, 411675781, 475835149, 478544181, 542443206, 835918663, 46092617, 543905028, 954970973, 949025396, 599113146, 385782229, 707692185, 85327428, 178437490, 636922329, 612736866, 368619889, 447361865, 432267015, 695191301, 849509047, 471986537, 451628961, 986804927, 623672443, 459109359, 93551376, 906815612, 57263725, 93567935, 933660859, 734200363, 690819374, 425166307, 861386116, 409543414, 150601476, 507397813, 510715791, 714089902, 778491233, 43325424, 322553891, 629238046, 603175782, 725519681, 84514577, 394712753, 84345420, 322236844, 460541386, 585478304, 158117168, 242543965, 982257019, 704275596, 644075711, 722894403, 967342402, 711911550, 894036639, 681769835, 691065899, 781092765, 627682862, 110630556, 525344561, 826493120, 67713818, 58475312, 416087454, 840626378, 133964300, 221474918, 654238006, 997764667, 714384899, 239499067, 272079916, 815284624, 373423878, 262055793, 822618530, 956957557, 822372470, 60577970, 496024450, 381316818, 813427916, 943068316, 517647309, 227551610, 363805672, 594282253, 862487541, 950016699, 855278186, 138785352, 396126121, 238061846, 592491477, 467653544, 460498816, 38787310, 746390112, 47065519, 94159732, 723097459, 633350529, 658319868, 787793495, 844399965, 560330285, 374526867, 379048687, 521778048, 178061013, 302604627, 517111396, 114713733, 887421133, 222707155, 644818284, 715089005, 736342232, 598539842, 214702860, 318178745, 647304905, 731279339, 445518908, 134519233, 350175029, 163459590, 32168735, 783959971, 947857921, 825222768, 83147247, 171423715, 360008528, 220306160, 607434408, 816046722, 63313901, 674418257, 435113101, 487282177, 247128764, 793295849, 79182487, 291406122, 377421110, 199402809, 753855233, 689328478, 59528465, 23938181, 309863011, 268446956, 878570407, 441491357, 142822784, 878531849, 877215213, 326104278, 98772596, 433074166, 333972520, 48171281, 618129052, 938758537, 560719623, 808755799, 803227111, 45984865, 704952393, 662201643, 50767832, 759772819, 83632039, 720008308, 595338832, 129338510, 493995858, 691831353, 991319247, 358296450, 512781897, 101505341, 264496775, 324403037, 229011571, 308331099, 874877912, 67023258, 808054785, 228345664, 679600406, 611092668, 768655043, 966121163, 187030226, 984085326, 912276322, 22610660, 762739260, 68603404, 557047226, 92632520, 676012394, 718550906, 133384604, 709181919, 568422651, 878562173, 78366814, 527498099, 49885528, 604373538, 784369448, 344472441, 115217440, 355651587, 111710455, 664010600, 692371449, 338318376, 619027753, 472302379, 338243259, 32028762, 639499671, 629521199, 727637372, 756963838, 556490182, 84789250, 944617272, 62926512, 772253328, 786315779, 683290048, 613012244, 901762566, 298709777, 409435419, 936053772, 68558752, 729241886, 213482565, 563367979, 955226003, 332528575, 864325055, 770657202, 4574623, 684839397, 322092232, 674549727, 515364679, 927789100, 337835313, 449601612, 932878482, 264359498, 521581720, 696596870, 859790715, 983336308, 682067610, 3500650, 782120153, 887613838, 82959348, 810203562, 544355884, 248152092, 91585552, 411903169, 641097522, 437349565, 142516181, 665102021, 412999479, 377246142, 870785910, 113007415, 277257794, 174115858, 683485888, 723478445, 617973163, 92054028, 977561409, 71990150, 358945402, 53319768, 449892212, 152856836, 638348312, 972794413, 971580952, 679851619, 417537391, 725029136, 547475550, 932141648, 490878580, 365988245, 101538923, 689951737, 101566019, 807590278, 543029571, 943637802, 459907188, 796366748, 9784010, 582855797, 329054878, 10510696, 910982128, 574450096, 456087309, 571956248, 330494490, 28627927, 104707473, 653490192, 321248456, 308336718, 442791849, 235928924, 589115325, 692078488, 671673818, 165434672, 955563701, 120193419, 763081484, 656349433, 878515241, 882047162, 844246928, 319909646, 199784577, 62832328, 399879248, 142286542, 87791611, 999543630, 859971596, 390955533, 47307894, 995035207, 511972568, 269618340, 567300628, 947357132, 506220122, 89403197, 994049224, 988822482, 153447795, 125579972, 844362685, 462026634, 65406160, 208755045, 93082934, 230627616, 163949317, 90390121, 988264920, 861458626, 276705423, 847088806, 80908017, 112682632, 650973961, 165585078, 574825478, 951533326, 914447352, 191003493, 704174777, 275806952, 958386295, 868635621, 270165688, 866475292, 246528051, 539371752, 341812691, 564739770, 364014646, 668027655, 662655090, 739904764, 188647436, 56185241, 759716265, 817827300, 607115637, 516659280, 260266847, 236492446, 80036730, 724866490, 340293361, 92597559, 980930201, 453946952, 951929520, 882220782, 358701439, 798251354, 479967604, 678799075, 850360861, 553822355, 555417289, 506813460, 268247277, 892683501, 163713016, 584368947, 819184547, 369484265, 919215211, 548285115, 217338878, 958303877, 310025979, 86177056, 848464871, 857105918, 576624085, 680116579, 356871990, 158412760, 810815070, 794229088, 548570570, 47069114, 376256828, 392591833, 849581112, 890743453, 506559592, 226245266, 79789679, 629736251, 764559854, 101850177, 425490288, 783465326, 689223791, 18799218, 657523340, 707532540, 346387960, 806114262, 478974083, 478903024, 115131074, 182710550, 210300787, 859632603, 647938672, 636638999, 497103643, 468402335, 873990366, 710285498, 542226476, 195906942, 697079547, 74879143, 623615786, 524369321, 517963735, 318439331, 995298527, 403857805, 339938113, 456023297, 707312010, 333330249, 97445273, 298216412, 568542249, 981920653, 611020207, 157823788, 509986696, 121292349, 134286485, 242374384, 581344812, 322125913, 925374157, 195530059, 159454475, 995237506, 240671273, 738703574, 428538187, 442156502, 846814313, 676475630, 860189678, 836304233, 295984161, 953000938, 51654244, 445886875, 673134766, 186224469, 670093192, 253718302, 782508768, 155685876, 680076347, 70596562, 656229193, 335420905, 109913883, 666965488, 296788095, 262123435, 309510408, 201923853, 862828414, 265506759, 941075069, 392133140, 447883425, 220802536, 53141497, 743128724, 340213071, 275900166, 839614635, 472347099, 721066522, 142809165, 559067265, 552497083, 149441115, 241087159, 712946032, 570438107, 220056853, 493891999, 901633259, 342841473, 121269011, 923598733, 373035004, 742149104, 999706362, 311551346, 838492242, 25694251, 915542943, 558139146, 248255621, 661046898, 643313556, 378692919, 77151980, 917641833, 66634613, 460642547, 311178591, 10251914, 708444332, 588340923, 76824759, 217041036, 25609573, 262038599, 964222804, 12682518, 500720822, 190425475, 46041382, 850946407, 236409270, 356977898, 196293160, 375084795, 624918059, 897760277, 408010896, 869184624, 932909475, 151162701, 855919611, 234084302, 567984490, 339631108, 512363913, 464933874, 419235954, 992754105, 738036858, 258805827, 968631618, 496035639, 451391653, 64945262, 370134993, 202277715, 27141405, 484391000, 32962542, 642801720, 28512318, 38614280, 208428695, 804941210, 533600530, 35081458, 218713751, 8517377, 701089557, 92549280, 241796313, 135285414, 498230359, 914898590, 625661027, 820543038, 150357320, 636532631, 434314894, 701484466, 513337764, 819575587, 490513280, 827860339, 511865400, 260110988, 33022462, 797998245, 109694867, 730497452, 346677325, 941292824, 676981446, 853433777, 463584100, 123945711, 489291405, 857733168, 414038742, 821622932, 646328884, 558464454, 592904727, 765199782, 878084517, 104901761, 669313686, 638630709, 580619929, 900442152, 174989426, 312048551, 400113064, 4880073, 617185658, 105594145, 844108931, 110209259, 549685025, 446725385, 541556459, 560849599, 208481426, 812452357, 962173975, 632015387, 279383247, 64267592, 54057486, 879536710, 54423524, 207893990, 829424890, 310069791, 945079293, 398631794, 286523328, 739123960, 838556806, 967425748, 882343008, 279526085, 204121727, 590669323, 771403015, 221647836, 185769503, 511501400, 857253928, 131505291, 725409198, 584555734, 953037137, 385407871, 608338237, 201779634, 674320002, 520264978, 79008972, 116078074, 567175400, 616919049, 774516861, 533021903, 869475354, 619738151, 226802918, 975789308, 965685381, 364644457, 15246732, 47192867, 361954335, 479231425, 494051130, 148641571, 54488377, 889659155, 993013720, 195696391, 821729634, 480970463, 697763455, 291084541, 33634341, 407070755, 33622107, 126036721, 669862758, 563668207, 51543080, 649995348, 772668032, 52971129, 918183725, 451710197, 19559712, 167922040, 811459185, 308099350, 175177845, 817778355, 541425027, 576093428, 667390680, 706856576, 93016154, 783653926, 126422923, 791912395, 300729369, 549785616, 623040514, 538448710, 883337040, 918461475, 618103302, 259957943, 788658130, 974082009, 994824988, 264153689, 942121956, 497762707, 876592400, 100672517, 777862931, 155409085, 665743885, 475541826, 946066552, 604397717, 250115143, 149759817, 192606288, 496587394, 477150173, 59291046, 147424789, 577479485, 146251690, 372836543, 264724421, 901613551, 82109933, 928096883, 957254447, 650143446, 904815927, 280587216, 58111341, 682070229, 161023963, 998285198, 206638870, 485174431, 555231648, 364770095, 436790544, 388945448, 574748573, 801462481, 771968388, 447478285, 401816839, 233094364, 101755420, 51490035, 256112659, 435084367, 309913353, 514496896, 527082154, 561954656, 268384517, 864054251, 435575933, 96242685, 299435734, 320052009, 33469206, 916754732, 620520677, 893065250, 926178845, 342412182, 982267434, 274179801, 416252674, 281568185, 488122943, 200199954, 932699624, 883514322, 696415260, 574859777, 454241449, 807616785, 721599053, 481017349, 858775087, 72851178, 775917438, 875978437, 836839610, 470156871, 809940507, 151546618, 20311664, 295214267, 329638295, 795885086, 767376201, 850155410, 969176768, 727020310, 689256107, 564321562, 418275748, 176476823, 900167872, 410455619, 303561458, 409541784, 192987274, 813870048, 606577224, 68103372, 119497510, 957949582, 543858835, 806374453, 891364108, 284751643, 709804400, 601236636, 319463621, 880328466, 72343770, 48902283, 93340963, 311729624, 730196046, 739205327, 818831829, 686772727, 985404097, 955471531, 590961367, 18213340, 129691251, 23908651, 320132385, 794509122, 821671954, 480506532, 227572739, 266665771, 139217162, 65048853, 252991681, 273359910, 97086832, 362205583, 464452391, 618003186, 705391551, 778237215, 504255859, 809055368, 486739336, 69418830, 175974935, 603058722, 792627847, 569129521, 736208310, 898827113, 765779912, 616047872, 90272600, 331453414, 71189741, 101716059, 805431400, 878930669, 319619972, 135278725, 5762922, 909813304, 926408152, 44668077, 682183498, 535418329, 350171880, 949221534, 459817801, 9475063, 297750409, 828840811, 386241622, 672233021, 101911325, 570460208, 654616191, 296386755, 410883049, 89422955, 578006728, 58508844, 48604637, 48086064, 430311307, 317311656, 16970171, 328334683, 833616552, 490912021, 34222773, 366822708, 693205409, 39342776, 521777212, 100882671, 223954157, 11243496, 187261942, 652488483, 154788549, 777193557, 961672148, 755362346, 840376096, 133467757, 130148917, 264079721, 533241114, 774502647, 273577375, 796281304, 854040814, 259862020, 301692584, 917504529, 359489346, 251586096, 705144724, 409833646, 453113000, 892334629, 273394023, 464929813, 314442258, 466074625, 708578058, 799180079, 610313023, 755649221, 224612746, 72713544, 104962100, 705907949, 484328501, 795347348, 881520190, 349120657, 116248996, 526118406, 542410608, 609340300, 338712035, 530936779, 894936763, 643625671, 519445323, 33742373, 825544722, 225270782, 781760460, 379347536, 520290641, 644068779, 141292774, 146026252, 305263901, 771008118, 625111582, 89748501, 758050770, 956086681, 746288423, 680578223, 114404591, 235066083, 821352248, 660631174, 156150298, 41082181, 621870586, 24615177, 27469956, 544728851, 132056235, 143197570, 705613670, 761602181, 16234742, 603868736, 203435689, 700990576, 761460563, 530490834, 834283839, 182120954, 804564163, 613451659, 184831181, 958825861, 503109775, 261464336, 748254422, 741979916, 140918132, 815688506, 934894767, 817168923, 419064042, 319075108, 839898692, 74741521, 741248583, 677486932, 702849302, 596935350, 638062852, 122138741, 245423994, 323704671, 502421554, 70468295, 636944409, 773833008, 688760392, 53164457, 447225715, 379305614, 559770615, 384095551, 118844707, 577312861, 657809371, 742133427, 695677810, 752885980, 228248561, 158130891, 679575571, 712577767, 866517165, 728698809, 132670521, 423311987, 98416963, 839352691, 565598324, 517613726, 362630189, 264582541, 420639801, 218630390, 288542512, 760948242, 455005407, 258160472, 286098291, 925335912, 918108865, 868373677, 978650486, 171279148, 487365813, 998192058, 33990001, 964767103, 495474786, 584118335, 574008124, 162486001, 911853346, 352649986, 168119337, 809733897, 324008154, 125056985, 780228019, 498084895, 277977479, 635680514, 734532488, 994809838, 411305779, 593321373, 927328144, 192031336, 243921475, 216087051, 353292333, 258065801, 482838561, 414715236, 391011350, 39303670, 696671090, 955811435, 240768914, 346079010, 129841649, 541901074, 36155476, 403578963, 350127686, 236941074, 578030561, 130520727, 808069728, 335657291, 517657555, 529340217, 666581212, 483261205, 54424934, 899753706, 391571291, 380747442, 505331752, 351298828, 284973038, 719944870, 796096212, 387802739, 915953549, 747750069, 406493701, 390162580, 845746098, 267468219, 857412647, 520574784, 838459133, 806167811, 561542609, 714181803, 670254106, 741735657, 946425847, 596848851, 267901599, 132526444, 302190916, 172353357, 704818226, 83289841, 932349011, 471354892, 705362301, 664540455, 696717678, 593087885, 638199490, 178746528, 81133010, 88200845, 590507806, 954891700, 262280412, 440523043, 612669390, 276089754, 99008794, 473025027, 448407091, 495565071, 596138885, 60534660, 491143594, 188546050, 674384266, 761002528, 208555333, 358220867, 508238652, 87091043, 103976042, 628015775, 700088184, 719678829, 291950203, 320373747, 675066107, 494512253, 156106087, 59522427, 913535383, 348861672, 436572629, 743032878, 446049814, 713686812, 118270856, 198125192, 622575561, 553528240, 622049472, 735671402, 860356720, 424705899, 339600249, 370239722, 429250382, 10372422, 752981085, 180684315, 748607331, 309244031, 202460334, 92460208, 472426065, 545242636, 254427104, 247311222, 481989729, 448445545, 718543502, 116105590, 926000077, 730644145, 482559226, 941984201, 784650282, 225315401, 884755490, 516994964, 610575837, 322211831, 803746572, 816335213, 194631609, 157128771, 119493933, 90117321, 560666821, 333795772, 464091687, 431271545, 639890605, 44772507, 768955736, 244405013, 733856118, 480282963, 897484093, 322746884, 483819356, 147546395, 45662535, 83974221, 438627122, 915025919, 301889188, 987536702, 450506930, 469076879, 363226684, 587438495, 988356619, 761586040, 929944588, 924105215, 784086140, 964109456, 678533239, 896773585, 364012629, 758586295, 700231377, 482930499, 482569925, 304440764, 799592873, 164639172, 895377840, 293728286, 955095909, 612988080, 169952393, 386286552, 928601844, 441607203, 476456093, 522041416, 396915541, 24584016, 253054662, 635963177, 894318160, 840889821, 448026022, 249893172, 245373918, 821947756, 180826163, 185707600, 714403224, 653903470, 164512411, 12541946, 247971723, 26781343, 63417600, 399058571, 828752889, 196306702, 866524789, 615728613, 893949004, 708412322, 68395137, 990810250, 251590927, 408199080, 577516111, 97311805, 198221866, 184296149, 633122606, 173525945, 75283881, 2332861, 706090251, 165010319, 770308910, 115079689, 841866371, 217178386, 528727842, 345400753, 896078722, 98707673, 58684840, 268158973, 252734019, 547405775, 651151567, 620190044, 657068309, 337656742, 380392969, 830777994, 703565977, 941835690, 402781434, 357068858, 91512171, 951361733, 683237903, 158195282, 123358302, 350551008, 51748798, 291399951, 234634116, 392589486, 394334726, 532404697, 846730203, 847176687, 228589077, 108112001, 704941155, 453525655, 625199629, 534349882, 731457463, 959917327, 83879634, 500601503, 503430697, 56958198, 124996920, 928233063, 728832864, 213862089, 68784697, 188770866, 992580005, 544709217, 83168389, 260537986, 581364386, 557265845, 119143162, 134688995, 315094803, 614198590, 783636529, 786811984, 833687726, 280254840, 773733655, 717555133, 839204076, 541471680, 456912301, 246003658, 630200504, 274359745, 324655068, 876839035, 591258666, 878277885, 470010924, 564892169, 69701942, 9810675, 830872382, 636469016, 452191386, 271311390, 514499343, 121250754, 601812106, 735966358, 551506430, 446374818, 964967001, 45520416, 8576133, 347570630, 645093929, 272640739, 159583777, 366797950, 288294608, 948569318, 907091221, 555671866, 478174869, 982232570, 138581361, 783322677, 446491781, 129587614, 240337632, 414478003, 232904843, 493448315, 180901156, 956981715, 869824090, 53492764, 915743141, 608802549, 286593382, 416175139, 253521098, 646181764, 695664927, 746295109, 119662429, 133018764, 617428896, 173882570, 765844397, 584600903, 537873252, 991118523, 881493422, 123143149, 331991763, 6265206, 894486054, 843386471, 577244902, 540531839, 958269641, 890162511, 314533010, 503581206, 798107252, 189886534, 974165777, 353576677, 953630783, 649340467, 330719438, 150197957, 923800189, 414577172, 605800745, 103024273, 351617612, 696975304, 911930742, 403420688, 47233314, 794452602, 95008391, 626925742, 66110812, 541073721, 549623792, 405501828, 986579042, 522518585, 2691519, 833799648, 889616275, 475710895, 293334934, 73233206, 768248985, 970897937, 656013611, 79550550, 496648556, 630119365, 170712468, 296983371, 258614969, 116293437, 119904649, 76157796, 543273193, 322974363, 543524700, 584672900, 803142646, 267476483, 627336099, 43656261, 752045750, 991553715, 323899847, 660501812, 27387986, 363868080, 382139801, 3186745, 923341308, 123848951, 223818883, 827042303, 543874924, 164038966, 605103421, 13976246, 886860550, 679838010, 783453125, 796840191, 329309147, 774443827, 455663886, 506512296, 407505651, 732765550, 411443176, 643400521, 646689018, 864903929, 910616519, 735634332, 281882284, 807085149, 919656428, 991926531, 684950354, 657137022, 654754186, 791157386, 460879225, 20108915, 718716888, 990203023, 156291989, 703193228, 812725221, 318152798, 342985613, 914166624, 538396819, 440571088, 933624062, 996288039, 609850310, 628598123, 174721201, 765402964, 268712750, 441068502, 17192838, 590274235, 131225278, 328663656, 19006910, 830738097, 993651032, 774057307, 684214906, 127286991, 385516541, 834786723, 966446059, 539100110, 464384791, 802728701, 753454432, 975412581, 219486655, 829731379, 605156801, 524516661, 865549735, 897387470, 169212873, 524289596, 491523100, 382836442, 229620161, 832389701, 302745296, 979975752, 741836083, 70310188, 817979082, 502303680, 159225353, 345132657, 626055427, 987871716, 673825277, 433812532, 825879191, 161134102, 408832942, 201976787, 307807628, 355612268, 234394674, 627888351, 522577237, 586003204, 717532761, 622383438, 606497587, 306141233, 78813004, 878706960, 989741273, 774470825, 925246126, 288380089, 707096781, 270894101, 653649631, 610468970, 840016211, 860381531, 357911676, 274631799, 748781141, 952370791, 799743669, 175587316, 288179941, 318966513, 343000956, 337192341, 143262725, 606283084, 536453310, 986188245, 375576736, 879526282, 513554552, 429235348, 789360012, 846852326, 369249112, 914346141, 785785958, 398856779, 975086957, 471096003, 670384343, 739246604, 785786479, 979769964, 410270049, 660202868, 752340820, 403417286, 37272174, 143041520, 116851179, 76353965, 530482837, 872739754, 576960818, 617782230, 62928101, 640277503, 350142994, 3607559, 977373178, 271562122, 830054099, 712686875, 34982036, 836231657, 214042755, 875527787, 611164278, 925206788, 656711131, 6271440, 361926324, 945640342, 219296703, 363094395, 729988422, 565056570, 593539036, 867448352, 591652468, 938839401, 926970393, 547509161, 555501369, 963115546, 547158556, 781383773, 38012985, 187530471, 176160125, 958911841, 720629896, 624641772, 467138559, 457793359, 24155268, 355909643, 745516562, 874127328, 566799010, 430532995, 190671860, 697143600, 445254845, 305012895, 482264478, 860435038, 921213485, 133367366, 663309711, 979052981, 446282837, 890084869, 25738134, 796860678, 280558547, 626818657, 702505454, 802477100, 282572909, 310448515, 410177726, 17187823, 729019964, 539712566, 809158401, 281856405, 592704824, 961104245, 512677159, 915886678, 39184401, 533186713, 79857422, 797485921, 322830606, 581497426, 723736466, 754320084, 975471314, 85030274, 16745029, 863717594, 947269553, 575227052, 188767551, 434926932, 187676384, 912790905, 38849247, 48848315, 646778469, 437308556, 774357734, 838580704, 221438625, 114276142, 864290064, 281629963, 886571286, 141938371, 410592271, 669304684, 645535066, 996038241, 979100832, 304072840, 815657426, 717632946, 900322905, 685051248, 10018103, 243735118, 140532083, 245591632, 334623571, 901895829, 487599677, 816364185, 980111995, 168169041, 783421429, 698716803, 613823523, 487069835, 625013470, 351562653, 333176286, 157466640, 871472067, 666437656, 574512326, 356640452, 915593452, 127328227, 604687433, 970165551, 949522395, 443083374, 496889852, 829835037, 380399192, 816732874, 747511237, 992725630, 912906115, 335223164, 605016528, 653373445, 588944747, 840668916, 591068059, 767461642, 958514344, 616778957, 213468443, 603282999, 179108082, 587724156, 955574680, 633238741, 231881318, 762685464, 759887373, 299563103, 885919029, 236999548, 814950073, 9550893, 239344999, 725326129, 368845228, 64905532, 464853814, 908360670, 993659838, 720273331, 130659914, 96512582, 76597511, 741838197, 800193272, 931434851, 705663960, 857569823, 186054532, 732179110, 124372116, 109134076, 33987417, 903546188, 303040328, 910578400, 312554699, 977396985, 712221268, 882346395, 457545039, 523862219, 498523632, 172837042, 894051231, 692724952, 843702530, 418849230, 997133067, 281582010, 403606950, 648227494, 662080026, 289675998, 429732284, 887198740, 900002869, 850240390, 425026152, 999909178, 508969389, 733620532, 295500271, 895705251, 294555128, 928963741, 362784756, 361925093, 191987586, 559307331, 974356031, 325071620, 23788183, 381215295, 328116122, 819796057, 479547444, 125133225, 217627168, 313607657, 699836221, 498354958, 160982752, 358934805, 780903731, 203194630, 148770266, 740900788, 996099706, 937176905, 331434016, 254287259, 488043785, 939493677, 449494649, 642020332, 78259305, 333553572, 16406642, 501460254, 125960361, 855115390, 794473879, 485943641, 982221740, 471828783, 586845381, 791081572, 952185516, 254038717, 765749477, 416224509, 194379684, 427786418, 533615340, 750609395, 712754917, 910875279, 695201777, 522042287, 484286758, 192893192, 774252847, 249538066, 549256741, 630498856, 343882271, 620752786, 299405435, 630714993, 725819624, 966107568, 879649327, 971583830, 997495694, 508769977, 746192442, 558546831, 436852668, 343774080, 871252042, 115400675, 271445265, 245323327, 710549421, 247343431, 296526148, 805139402, 329854920, 515262172, 12480354, 772254096, 810171973, 363916531, 277704335, 343897548, 170996413, 34708059, 941168210, 551803064, 984552330, 950379377, 338880763, 881792852, 914474552, 104430086, 90066863, 169307124, 935305335, 943386287, 43123635, 169353047, 363668345, 201853580, 849438998, 790954372, 954723961, 371842043, 295955938, 245871447, 916806994, 274502036, 939871802, 814184093, 710832643, 323312027, 210580285, 706887091, 671454984, 957589379, 206228903, 875143974, 173234986, 685420650, 664862269, 848124369, 318217709, 701081622, 933837424, 853811274, 397004305, 180287186, 700277370, 62393784, 898210768, 931301518, 868301419, 424705685, 254705764, 372805949, 594339329, 54372331, 660045453, 208153081, 382140385, 308138878, 228094938, 914841801, 834678618, 721382500, 959969406, 819334682, 134514341, 203451833, 689045638, 805183783, 48781581, 697453620, 164119807, 993364836, 76951554, 908567704, 200887180, 51315009, 885023083, 234824074, 763774826, 746612079, 635347218, 980231664, 332623889, 875371639, 203929259, 155419182, 982131736, 150500967, 266862768, 641775005, 149820931, 6583369, 941484426, 790584428, 768378777, 557917968, 912355688, 717551239, 751523055, 381315970, 56166402, 269217005, 774441753, 31196508, 523964770, 287249575, 777471583, 547506460, 842916660, 289872742, 212783116, 542225344, 591475887, 944189871, 194634877, 892220040, 247627272, 512695, 825068513, 49421902, 340661468, 885786300, 44165986, 888431125, 310939862, 934441867, 818599675, 488103053, 379461981, 974889328, 639483279, 28510122, 825197056, 894627099, 415136846, 204837439, 722344305, 364819588, 616490715, 510817925, 738325522, 236526402, 912668299, 462235169, 628517926, 765748797, 998921662, 799021907, 571828358, 275979180, 269114247, 384873145, 666773536, 161175425, 279312978, 866148560, 756055572, 220992303, 580193007, 312695653, 492668304, 268620012, 454420947, 650926643, 94961186, 769807890, 326081218, 166929656, 426080588, 29096995, 128276599, 113825372, 850671038, 411026399, 801403544, 742012978, 857055568, 980275905, 902292028, 685475979, 275802099, 868056509, 298029279, 455064294, 957768751, 197318616, 444565324, 793559116, 686334514, 96429275, 914864523, 454684733, 242293550, 519453344, 864142412, 634158129, 607192144, 621928538, 271612758, 274116089, 707113386, 308748916, 447037217, 83417754, 930570624, 618449295, 216822638, 464705343, 318665769, 287874560, 541459195, 883261384, 324335072, 895792924, 969762043, 733126960, 25506383, 773156965, 134185964, 194154785, 65541850, 258055473, 264609272, 205377864, 202026184, 475593716, 499412586, 343719586, 490314863, 328650882, 75911363, 909832557, 646676350, 162224777, 364904449, 354257595, 713915800, 889529708, 56809747, 953035163, 944201205, 974343518, 552396854, 673816607, 964759875, 900615135, 78943007, 961455908, 331280439, 602187821, 625434901, 789063174, 841519243, 536164872, 222985848, 335265625, 330879593, 242603828, 572255385, 970164223, 342362744, 301244187, 589526515, 915416461, 90022916, 186843672, 476275458, 984413085, 779686579, 386725172, 723519068, 713087424, 842032149, 72620769, 622749139, 558365241, 604058618, 217467349, 148512823, 592669481, 716223725, 64354592, 186127266, 336776250, 966595492, 874033497, 27585080, 688202061, 103363430, 294926620, 349715333, 417195896, 671583524, 973596538, 629512129, 333786306, 989631928, 328684477, 455211813, 480770820, 573352715, 218277372, 518184540, 687632445, 910918220, 481804682, 33311808, 894717927, 447787445, 753259069, 731519098, 335074575, 496142261, 332602017, 26813798, 415477263, 97277784, 756974709, 901205161, 575209593, 289021331, 233276594, 753884234, 33116943, 509753980, 560724665, 999677707, 528565671, 786240291, 791945646, 886731561, 773003165, 992978992, 154953872, 772796695, 630022258, 849890049, 835906892, 923319387, 98240965, 831550813, 129852525, 864973244, 795149714, 272567285, 810189780, 48197344, 157011859, 196878872, 607663423, 561314910, 753474596, 609612621, 520493638, 77247664, 543083463, 510752170, 909380933, 467596834, 490525625, 602298777, 230915741, 942364718, 153408701, 255588489, 85285101, 965460995, 562666248, 729223261, 27880948, 574538232, 920790622, 126468847, 11354513, 282977414, 865384404, 936789397, 271282538, 247369590, 505603268, 874330958, 376393559, 218417682, 832414440, 601074829, 172856091, 483677843, 349531868, 218565513, 97844015, 557391699, 973113358, 438650207, 942526774, 162468100, 282686018, 169718984, 989845689, 40689555, 648005947, 561437567, 294566443, 98455897, 793006682, 280181232, 841315792, 524331359, 471979256, 192565943, 594420030, 750500035, 540544929, 644224376, 926000866, 378377926, 205027862, 160542864, 281854647, 875984378, 228816965, 470956417, 553434897, 138370230, 903560526, 408390590, 902704806, 224461199, 753891801, 542265182, 566236959, 15250196, 716393454, 941217135, 151965449, 132113979, 966430240, 598335246, 810701333, 98988100, 507314101, 400684888, 231449379, 554820999, 460752439, 637177998, 875199679, 721018326, 818684004, 550341920, 677710278, 677101155, 945650122, 12485694, 923655041, 87468620, 408454049, 689818723, 176289165, 818740348, 135993070, 986272898, 629135727, 292997509, 127203186, 436087452, 411316309, 530060318, 148468431, 939783238, 167747953, 278761230, 843516461, 740067670, 75915708, 697054716, 88881529, 120031661, 197889628, 722186442, 52580215, 537598911, 784728524, 751292715, 439559285, 424672736, 528404730, 946062618, 288152483, 728806484, 178734223, 480330752, 522653224, 717804687, 46932021, 634560970, 968962357, 590438717, 292116597, 130387835, 820584688, 601967535, 637168644, 458806728, 842587580, 812808626, 834983375, 972722793, 956362003, 751282032, 680830012, 681643558, 921942080, 988329114, 988627735, 217705413, 403759478, 709254065, 984017243, 278265721, 911255340, 450796364, 869433782, 724753561, 21206535, 476482570, 482623172, 975361854, 595749171, 909540740, 676100117, 313118672, 398925233, 404739916, 782780623, 660148930, 624269957, 43021917, 144554644, 959870335, 219286758, 994092851, 194095758, 452968310, 717446678, 212705180, 211836795, 909756476, 16522554, 22624548, 75011931, 717422770, 193678184, 641603810, 121757704, 165696889, 865514260, 599925706, 669375986, 272249483, 784310887, 429938392, 620740118, 159251432, 250107023, 589030662, 174107671, 168709536, 642263396, 20052514, 562812092, 163521068, 193536099, 994046535, 880831259, 125416452, 25527379, 875994127, 633376546, 335000515, 74971905, 292343548, 479938481, 126216260, 589973296, 967007132, 134178698, 759571345, 950187222, 387673996, 34792387, 509672539, 607647834, 594377994, 962712649, 578394027, 845629231, 469391699, 533531153, 359533679, 544023021, 107104798, 133727659, 717004926, 290502796, 538515447, 928420974, 623925257, 766858180, 43779230, 714277545, 585145678, 146045705, 16666623, 720459208, 681293289, 345344582, 645150923, 238045788, 456328679, 787165728, 127618554, 579781340, 24721886, 572527775, 722408839, 420069590, 798920915, 586621717, 62934322, 156713584, 241932449, 624051000, 812957188, 214493724, 914436825, 641196432, 523550209, 880268996, 106335862, 147471435, 490399608, 743156160, 640700091, 592317403, 990881805, 930874133, 201270232, 87017164, 501761050, 377251556, 834193480, 288256748, 477594544, 159375746, 664024072, 711285787, 340066072, 944667335, 174413131, 45317560, 955844880, 299027698, 639580795, 18524539, 523556138, 278886192, 562152766, 64812447, 352637550, 418220223, 817271272, 411673438, 393045704, 995710697, 26209796, 277934037, 479507078, 170479498, 941832268, 199461296, 387858693, 237689718, 788220575, 954692233, 262683175, 257714637, 445494697, 959677564, 416842177, 100522463, 36650658, 105603004, 889427679, 43690531, 532561335, 45138019, 249258843, 459998401, 233004225, 25547794, 373721927, 893537294, 248663623, 899938926, 437885587, 233946460, 220913281, 425533589, 956272560, 449893047, 38153031, 828132663, 220734534, 51111894, 531427563, 182144198, 501690335, 781803554, 560771779, 760028283, 679115748, 938905323, 517457727, 381367079, 32335247, 699903856, 801151042, 422956639, 427255777, 781662978, 930307151, 707707620, 499617910, 223608569, 387383275, 614276348, 748853520, 174016916, 241034766, 246683526, 404215926, 578245854, 631676450, 986902168, 357237382, 558319342, 997455420, 585864011, 411083829, 757618960, 527310729, 457526553, 324525976, 25522577, 649270007, 257606150, 21594443, 467009607, 756500267, 67180289, 978912868, 425395853, 412562736, 843943299, 336551345, 410909576, 437056020, 701180489, 404994437, 264475405, 485896870, 967190861, 975124232, 414825669, 546502966, 203654155, 116290021, 524926020, 656828779, 923714815, 581827921, 421163598, 222833252, 515114732, 290433308, 60696015, 918263408, 111105534, 803534996, 737642605, 91008368, 991366647, 792927814, 289119182, 813066825, 672365971, 159045084, 496952465, 768045544, 816634743, 315960019, 800993356, 549309951, 163554928, 207605173, 114008231, 261165667, 845701152, 706845387, 299291482, 846050637, 604853191, 473176139, 152121836, 280689139, 448983691, 74680331, 954981176, 378748840, 577777400, 730235468, 52482417, 141105696, 874446541, 775997973, 240780504, 662942112, 640456116, 33733791, 43233869, 316970001, 248248561, 951070602, 189139278, 596603386, 59881915, 923823665, 723825710, 283125965, 157116909, 24562308, 190009193, 864715310, 89144620, 85238516, 795748429, 861906427, 765818606, 772027227, 261284804, 984746528, 105934369, 797236837, 19241375, 42923000, 611533251, 372237146, 92890916, 886738128, 570683881, 281808253, 382442074, 383794247, 702358216, 892926125, 978241499, 49332711, 563791788, 438233457, 112320735, 103254683, 276958658, 531143101, 291373007, 379906614, 79971089, 745521396, 304944161, 656471180, 88992279, 882659765, 3382231, 63459993, 133865265, 315082892, 582378613, 791289126, 540968586, 748057106, 702165002, 128360872, 708237, 799322266, 181172541, 323928139, 134190759, 339634449, 592352994, 692845793, 603264654, 524351657, 674548340, 14744679, 730049078, 107270747, 727074809, 901649669, 972784568, 399933582, 956898975, 303474441, 730111006, 752175407, 701657782, 664867963, 710492927, 104201046, 738857515, 361249597, 398004261, 981434865, 372920614, 694689336, 280725654, 80468748, 428903491, 700792326, 767305981, 427227413, 652274720, 821359937, 885574384, 260643446, 25718724, 220942752, 603869807, 249728846, 848503290, 237137763, 787927672, 976533929, 441105080, 832179763, 385158678, 163773785, 538448252, 841191915, 604948353, 633829124, 3537835, 648081395, 360546881, 445503909, 90326931, 108830362, 982570527, 358042866, 722095438, 290427393, 398409032, 999262215, 251091619, 242966119, 711313407, 879975248, 211431254, 30304393, 337844610, 922478467, 809891685, 597790532, 747684050, 413412317, 373547699, 638194477, 403667843, 260996995, 360339180, 780179750, 444484966, 932631351, 826045668, 304802139, 343261539, 360204529, 797069203, 613999393, 88834124, 683584512, 513778065, 489995504, 133990491, 912364987, 217481447, 765166361, 276065618, 173195298, 756767412, 396089972, 731915461, 555336920, 9925926, 956178450, 210998127, 9430840, 722236121, 45724842, 220151278, 250499277, 523046920, 895772341, 382710536, 784655553, 648865675, 260815370, 82389744, 740052744, 813236329, 125404537, 68103359, 258379871, 979324244, 852319900, 379446344, 170452988, 659390322, 111370760, 601478404, 417530699, 100934296, 951766553, 315804012, 899515994, 600301881, 369482815, 655169009, 852907411, 68787880, 236792020, 834415368, 263221458, 877581683, 325241906, 871824066, 338072673, 538715893, 940623800, 342309766, 111551269, 549497358, 978748864, 76578305, 106085838, 294264059, 745144031, 155810607, 678571494, 507834571, 856109907, 762241582, 874486013, 290671486, 765329742, 535564928, 202096606, 208663626, 547313962, 635199518, 978894157, 859223656, 723911572, 299681598, 205459295, 723403095, 372519393, 621177871, 803313031, 694869031, 426963731, 327015712, 695235568, 107409222, 876526602, 782774561, 978280807, 493075734, 859422170, 547700180, 967424818, 890553694, 149097715, 787011066, 178166958, 207317657, 516059682, 724568765, 947401299, 364789254, 246178621, 175115256, 37567223, 66356952, 471802177, 720190697, 69984369, 49169552, 558607387, 153883667, 429813223, 786057323, 52870807, 15295950, 516982815, 860455671, 796059344, 217493646, 536762584, 333539994, 141770063, 890240208, 202147470, 773737909, 131695164, 340419592, 318773281, 328971246, 733296183, 389520198, 318499348, 862101940, 382226890, 296807365, 807132125, 779912381, 284535838, 149290398, 37827131, 833404259, 672133308, 467153425, 308512329, 413282207, 433743266, 494069973, 67605376, 612282607, 844679075, 13134595, 190323837, 882260005, 306705387, 974535421, 864743559, 718303505, 716320488, 889585922, 840180840, 266995989, 683079783, 600456646, 719449311, 657541907, 630475633, 938241147, 737733816, 266849676, 483517983, 805836329, 462890932, 22915814, 321580213, 494176356, 830520940, 932548916, 871159723, 331912768, 119734888, 889002323, 470328495, 650080202, 535673622, 682250027, 72180414, 217134168, 144401664, 211944297, 555763046, 943116243, 803975526, 788811234, 840435970, 282257577, 966989112, 891941199, 379468507, 742864522, 569557229, 261473347, 106117179, 751553100, 759626606, 329704444, 743683751, 994578364, 550758021, 46813710, 594661528, 486367216, 939943970, 287728788, 726297037, 508580095, 124616685, 903073673, 346286503, 799658742, 458322856, 282221721, 153066890, 29764085, 731872737, 466539813, 974002907, 800739513, 985446084, 482938749, 229527969, 86579190, 352569660, 977856456, 6079669, 842806393, 155195386, 276475588, 109596401, 300360180, 342605531, 983398902, 684725941, 657543852, 667864275, 438956844, 721545136, 49863417, 908418044, 120877377, 322407958, 983311148, 94859889, 127390234, 885678671, 603612489, 821662205, 560879189, 393571953, 38310886, 276892287, 584343355, 395077533, 617537621, 609360411, 214941993, 824204550, 419289537, 700845529, 21528536, 137345421, 597332531, 131097603, 328888784, 164762607, 324958262, 570096116, 744823218, 555385123, 76308188, 332000095, 727794820, 776671118, 959663256, 675046159, 866948281, 397548407, 121692414, 272663149, 879494262, 488920073, 601681407, 947097205, 942803262, 733417364, 502103427, 98727328, 447692066, 815598709, 177513153, 247433115, 700859215, 914228872, 826078702, 734567276, 650410071, 794340678, 859092851, 790846654, 367837979, 430344211, 545841518, 893076136, 183693624, 578796899, 159473576, 522978603, 658671011, 798874035, 23944436, 758028058, 536626206, 702269119, 487909725, 645325369, 224019096, 474091256, 407425060, 936839352, 731076648, 580760452, 47243740, 886901707, 662290096, 709693796, 621610003, 777948686, 851231539, 198446997, 971529220, 392471008, 389388953, 943691720, 586532681, 647408127, 454752151, 126128606, 574923467, 82469522, 183152952, 394143710, 447954853, 855704610, 287193872, 429869341, 843960916, 409054372, 549809191, 205869870, 501248453, 780528056, 17699128, 690542805, 191834065, 16247078, 596150893, 486489638, 457418530, 776752880, 390526995, 189548613, 432795644, 798999415, 865729161, 344630082, 995127689, 561802625, 696186251, 467500496, 996993401, 654669249, 304436958, 833208421, 579013184, 770763037, 739277177, 833560179, 307110760, 916294969, 701604696, 4432430, 396653595, 372519884, 171625497, 486234832, 546312330, 412484068, 941199639, 248571071, 664632998, 419861358, 991156960, 633587495, 43201175, 855913221, 145105936, 898617, 913738367, 67992649, 876976496, 669398720, 644611374, 580744200, 75454046, 522849234, 527916133, 339182590, 908878842, 272404010, 334078535, 666239614, 525942649, 873341455, 611333246, 996854795, 467734975, 134245304, 429203931, 170001927, 509809951, 91510446, 435715073, 623310876, 90111981, 286036476, 336944012, 510920914, 274108347, 7402078, 996491205, 313202777, 642952642, 36849494, 691429278, 343148755, 542345899, 7257556, 438125311, 185526069, 785849991, 351578985, 39857990, 612548765, 38987862, 533147062, 906810652, 677411744, 20359718, 115975780, 266287725, 806346653, 284034794, 97625059, 894070354, 42866308, 280720044, 41086295, 443719952, 226996291, 651593259, 843642949, 188205656, 391923167, 723288336, 458589320, 689539870, 822328115, 843259549, 943547460, 465037449, 566150538, 460470911, 756598156, 772505700, 113465533, 568822760, 316092708, 883200358, 262703929, 860561442, 946736453, 123451461, 477468528, 127518232, 373087520, 874182820, 305613891, 989367910, 555078310, 31591282, 429694384, 506147836, 574472674, 295105447, 667070678, 686194245, 867170356, 650141614, 130749767, 893635873, 865522071, 99933047, 193685634, 958382429, 265527785, 91168745, 344214569, 825066004, 359863080, 126064757, 865919612, 822696372, 376996861, 38007274, 895103476, 145274566, 636754103, 149883210, 63428559, 737210671, 8281280, 551988666, 994515535, 802613383, 787408103, 551297588, 159087455, 583521193, 869113842, 3021034, 365952844, 49245308, 561556188, 890687128, 156047607, 887853592, 240576100, 25999394, 341363207, 857232528, 551515294, 316157347, 708874082, 59420799, 697294946, 398300819, 367174691, 948622936, 180927650, 524598762, 148869280, 736734351, 821605798, 933378471, 381147280, 346210804, 60060987, 272968062, 501346124, 464672536, 491933804, 420749008, 903985146, 609770254, 880017967, 246830720, 539506425, 302270681, 139568043, 784777884, 785305265, 709475027, 734030644, 469269379, 207967220, 144654001, 521793772, 410615212, 594534083, 764876484, 812034419, 323561787, 833187315, 585891306, 30966077, 766823615, 609386515, 466009893, 94784963, 241312818, 571566201, 781744705, 784016825, 443242126, 615504288, 7772497, 624664688, 375296151, 528311694, 567320929, 94208474, 789972053, 403048005, 890586561, 198029917, 813704833, 384111108, 992328353, 293456872, 500929440, 985845005, 498933277, 567234706, 437057393, 536600004, 169445339, 403089746, 381139344, 601140998, 76091479, 919074327, 668594945, 978985866, 971249312, 55932080, 813699639, 867051165, 937493307, 731582145, 372507794, 698370297, 714974059, 159756132, 628817936, 833799776, 72706974, 630392271, 616883784, 172521949, 858413647, 769018227, 29980657, 705789939, 110725908, 387246022, 984384211, 941392882, 670561604, 298262992, 715407876, 1696044, 3592144, 11459367, 182142674, 380500055, 705727506, 695449812, 125036420, 272410674, 40751100, 707412671, 222601538, 6526357, 996454715, 378744074, 351885614, 105036337, 537627994, 364669808, 727010333, 456306906, 589236446, 427064003, 728916434, 90699647, 91076309, 119553180, 850905776, 974964420, 274902609, 533774736, 873121799, 315395808, 565200639, 275671154, 337798276, 511494708, 246542722, 70992011, 960157275, 445560899, 961671228, 77418111, 901776869, 171107190, 864824444, 910310085, 757369607, 20535010, 476734311, 752292297, 954026107, 493966833, 695876299, 857192903, 683049907, 751598720, 185577698, 53558717, 726496700, 428981839, 93996784, 109717109, 671111502, 608817227, 688668025, 554555028, 740642207, 472706141, 64873124, 263228685, 282060310, 257325804, 707046381, 825126835, 457834996, 453662784, 551075092, 412854500, 901052451, 314613837, 47665978, 621867814, 337424654, 691447705, 503183703, 390084354, 646720372, 735907279, 84975258, 140020055, 48628353, 218833615, 401796234, 378938214, 569393656, 253388692, 844062143, 219296405, 424602521, 863525570, 935026670, 120154335, 831186119, 925338338, 631027851, 675216634, 595610245, 968161045, 217674099, 679381347, 65782855, 617943998, 124211384, 581559489, 337289280, 917561452, 236335505, 777723281, 172739071, 521072494, 419342155, 762253000, 85476467, 618741451, 90038405, 44145231, 236865184, 450362121, 876573045, 855196210, 400720653, 404683820, 299690196, 662928347, 44310182, 584252170, 150395516, 381614059, 848615236, 486038525, 311276489, 137012108, 836548882, 358931186, 791572443, 61195926, 913350699, 798323191, 339215751, 691814457, 407605719, 942649984, 776622150, 617061215, 813099501, 174356519, 94378508, 5959629, 238487146, 451944767, 497657899, 370183810, 929036629, 719358845, 852125400, 750960814, 504990394, 889356102, 205318295, 14382076, 146064723, 459761488, 682327672, 816334121, 526949670, 424414030, 438619266, 59364698, 753945010, 180684289, 212331444, 92152585, 150250918, 217527463, 677640391, 246470744, 60023592, 710420102, 725544413, 842125505, 530131202, 82785152, 311777016, 550206980, 446480643, 924501122, 541377098, 623273900, 152042771, 699229411, 252524266, 763034959, 536909918, 814210504, 583050678, 161183699, 132128929, 895235695, 527765496, 818657251, 856479451, 858285943, 515795854, 714925451, 171957386, 439348721, 453127484, 479779833, 513795835, 942063463, 42319054, 978073836, 73194875, 60821036, 850713086, 898183061, 839416125, 865220253, 355265529, 800064073, 933585783, 373856171, 516881916, 275711171, 959965351, 728419768, 4950297, 848704076, 999897285, 783798023, 609038979, 428036446, 739081582, 477357913, 556268427, 460975154, 341439666, 681792682, 780587486, 54148273, 396182705, 844861341, 516897530, 962469978, 174542299, 6718446, 352924682, 635453920, 70279467, 176238202, 693882056, 183698416, 892848157, 194191953, 850746815, 200087142, 16290167, 142095730, 866081533, 556257591, 53231597, 997707406, 198413897, 269940429, 429101321, 132383590, 61117717, 726779254, 82870269, 90478378, 777779955, 380140386, 582443999, 85301954, 52018011, 345553840, 838402235, 424629535, 261778659, 594491265, 475202160, 312383250, 94594162, 316651584, 250584901, 266058925, 909121521, 539925211, 667548902, 266046233, 774309215, 686350518, 505731516, 197963731, 544802538, 318651946, 325682115, 951468808, 605852332, 141185259, 669850673, 883864351, 455427798, 656919612, 818815289, 687786, 578723908, 821460070, 738112555, 583065256, 982844069, 761304498, 124024334, 852612799, 207259282, 972084376, 161553271, 131236077, 245661157, 725159316, 768505748, 734005824, 706259769, 152498992, 294447954, 368650490, 829437379, 365942805, 618841728, 525145713, 786944034, 477408618, 749009653, 698700158, 136686565, 682077380, 936826741, 607534541, 506272228, 846467546, 357025882, 983317877, 348455418, 856162928, 247853863, 951760254, 4897441, 467757509, 37523350, 560928100, 924843896, 922202695, 918596781, 308484154, 590997557, 519808742, 82786113, 585166760, 992790171, 301414915, 752987857, 989303810, 257496672, 574191340, 44300346, 989010007, 479521154, 680197114, 955413470, 760501936, 476788607, 858448511, 230133850, 804089599, 906299279, 382454737, 661296785, 943362728, 244622183, 79159635, 89529780, 407326159, 589575952, 279566208, 283461106, 454551269, 997644838, 124453122, 385901747, 503496833, 216182128, 177783643, 882798853, 669611330, 650522971, 623780477, 355111559, 313331686, 652483903, 764962538, 964393032, 969597779, 415087776, 702084503, 391418814, 247242817, 441121406, 851911063, 577714028, 783524349, 598992861, 915790655, 493290650, 883531155, 553836747, 292446724, 746241130, 620990129, 900626550, 520349277, 560262719, 530508569, 348306541, 441714373, 561922639, 467268737, 710397982, 610114322, 557418863, 463944867, 714832283, 952032440, 769956162, 294429405, 165123810, 957528006, 50528324, 842845672, 681880085, 683938979, 334962908, 42632773, 438539014, 720195263, 293495323, 898732953, 648127588, 764115202, 214988790, 774553912, 386173130, 721216798, 279748089, 12954293, 732898687, 605385066, 265373270, 271848895, 291861811, 932233315, 399032712, 646528516, 434646700, 567913244, 754698517, 751154604, 550618946, 930312323, 709534201, 885128889, 854857451, 272391852, 984788211, 222575776, 222098696, 7775731, 363928032, 836837226, 485266580, 395042644, 601167526, 191727269, 636042200, 447827615, 706863747, 890627758, 84305187, 898880873, 408802641, 530997703, 572655374, 497280240, 955888594, 19505368, 922528746, 618082390, 435863518, 556322210, 333651554, 113776520, 306008270, 830493031, 175804704, 454206064, 197367105, 422850060, 859529240, 674987724, 485180900, 427033503, 563436773, 351216790, 596193923, 808059913, 856394670, 372896969, 537376551, 377783711, 694382704, 400221414, 235734038, 849731707, 594981574, 74482023, 390106849, 585524386, 821367180, 301995964, 789978885, 548100434, 493521518, 216343904, 634832540, 738845838, 275178453, 333097850, 972871214, 256855395, 67564171, 157183253, 588012836, 995437241, 484927120, 358125245, 961623751, 291945388, 590354747, 978535403, 835040142, 502719024, 179232444, 443132255, 443007307, 149894430, 29273349, 567198201, 568055901, 579335643, 495991624, 592309746, 731141778, 892013193, 261022117, 322290666, 145157150, 815696271, 494512150, 507194664, 31096526, 787954709, 929697676, 760772487, 117707264, 930884270, 984029741, 912373644, 306712999, 119020117, 594476607, 731896877, 429861571, 628132364, 874788842, 251082752, 278404749, 938921536, 807664499, 578803477, 533371005, 224245419, 153819527, 203049939, 857207640, 151591797, 968491889, 209708775, 784663832, 711597016, 706278762, 680983796, 438925239, 633024943, 303723478, 855441998, 137587555, 851188862, 37349980, 959674726, 865092435, 196444058, 890763024, 815248686, 232327978, 297126146, 808808727, 605634160, 798212938, 448111818, 785688735, 128974002, 118330398, 696183061, 437405013, 942039069, 644905654, 714658767, 744640918, 620804035, 131906036, 952961000, 31375410, 465347174, 467774780, 478707781, 625429393, 20062521, 904890718, 402354792, 624474782, 964917876, 67989822, 113966190, 24685962, 317050309, 153869474, 828372808, 732215287, 355409711, 754378875, 822411818, 845377774, 952039591, 405751625, 776223881, 216139785, 815752551, 614239416, 227229410, 131417204, 643201335, 382192869, 592629359, 593882853, 36838713, 738550496, 252140123, 508453570, 510079173, 732241253, 904853139, 68777010, 200105646, 699914495, 556455043, 444707692, 617025474, 171040720, 588436231, 593907073, 584206975, 972305637, 637730734, 628407780, 309801309, 337520915, 10275606, 542040224, 534715623, 984816896, 153803500, 19969772, 604523264, 806463411, 629645230, 667463282, 24652191, 905319396, 363299634, 612895502, 843410637, 883469211, 166947286, 586276259, 91159269, 486338040, 76197854, 409443489, 792610654, 325524216, 688887298, 313745951, 290821495, 759561358, 140346184, 410699390, 855396464, 392782716, 375639400, 718307121, 898254368, 598788001, 990107768, 15207804, 641358309, 470180366, 588103660, 647379572, 285284501, 62268761, 553540897, 649661114, 464767951, 428161096, 751613459, 221092875, 162836846, 462044106, 427882294, 22068789, 7367068, 222983403, 430431565, 147075471, 815895529, 168373844, 608533257, 489599214, 935156283, 713996974, 761951438, 556820229, 394886001, 271739738, 469943982, 280628690, 473498933, 158590992, 654419199, 384842742, 761983255, 984337667, 503255838, 17622808, 800941773, 573808756, 442484544, 451188382, 871643317, 804672921, 22880554, 143556530, 516770358, 602577038, 752044991, 113955415, 693668154, 932825858, 102311979, 58477297, 296314156, 142571474, 820047417, 326471307, 86806852, 624745194, 673719295, 650531969, 747383774, 613369215, 672048408, 11252199, 365892108, 307905066, 660522196, 214025966, 320647208, 586403608, 617806135, 554840404, 284453903, 771875070, 355055077, 972771681, 705921654, 902812300, 243504438, 995894483, 591897257, 188124063, 8878931, 228623910, 791741474, 47802722, 248097212, 501507693, 625660064, 517804493, 476524855, 774616679, 935012220, 919188632, 952524783, 552983081, 99216814, 81445622, 43494039, 81341795, 701769087, 118026334, 834126995, 599067933, 20994293, 411407139, 444306612, 475349025, 720206040, 858125217, 721733504, 212969127, 438949914, 24749803, 997370683, 623105503, 826388654, 232338463, 229099726, 635703671, 688043537, 383582425, 606997627, 442486332, 280668366, 370788849, 811685124, 278191847, 44829205, 236282267, 743425944, 752954410, 897285954, 127705130, 759683663, 839309230, 559332778, 405166386, 739388158, 170305265, 435156850, 885891955, 79189322, 166261056, 915996731, 638016710, 304126079, 276687242, 681395031, 808676774, 848633409, 329169612, 593999247, 429280690, 826004916, 110596667, 703781266, 192928736, 769496537, 458635410, 314064316, 381581282, 530017533, 930456144, 437839570, 246195942, 442633005, 925146023, 731131100, 54423037, 846947099, 523633791, 671404347, 455203018, 135432122, 935856300, 687475277, 412613080, 866525015, 453046087, 814321659, 994067332, 646592901, 44356543, 663166942, 198298862, 742075195, 536532454, 113591844, 730130274, 747071846, 101723986, 536384747, 393682626, 396961959, 333507768, 782371296, 458443064, 606325190, 594347411, 150072290, 555120567, 759086688, 445719484, 951878666, 447007068, 214038580, 755201448, 166692271, 507854888, 47192953, 501453574, 105097038, 828226646, 807093080, 975378554, 912897168, 654941875, 542774346, 116927431, 869628542, 785986310, 394746013, 861484233, 729388234, 502729349, 73710521, 134499277, 604401088, 75417215, 193591969, 860865676, 679232029, 877477026, 664845948, 276671100, 304313707, 612663022, 503877257, 481920315, 866422811, 796524457, 512040367, 570912843, 8178514, 22924707, 691640824, 124982634, 352799268, 225133362, 80817326, 419261301, 599023575, 609494266, 165952631, 300168885, 541816088, 604098665, 443470534, 798103935, 566717012, 575704448, 473220951, 61040941, 491418684, 182000360, 138815321, 886969890, 335714020, 622619353, 201732562, 522613227, 684508283, 380728091, 887020143, 339599206, 580055811, 997204240, 412196206, 991750002, 588745764, 624415545, 438399388, 963034443, 871417270, 424527199, 441454872, 428248806, 696395060, 590424171, 147213700, 955882368, 124463323, 374023976, 595238918, 172784823, 9170579, 230721697, 910575310, 721431538, 986051414, 796140463, 511516926, 634143390, 38236988, 567329678, 813366571, 761254577, 714408953, 431388743, 195574860, 258810701, 267795778, 398992612, 415663989, 211051998, 906510379, 963192869, 83265884, 211720220, 266666289, 396641560, 266259997, 141914592, 219486114, 727960502, 842816942, 455572648, 245081475, 646785589, 202112571, 653967966, 708839406, 80352208, 979876379, 472724605, 979562291, 548830017, 280098830, 806512650, 626310417, 143927557, 843193360, 579494304, 292709218, 561852852, 38674033, 399349436, 406542399, 821801030, 893132089, 602438235, 417002626, 499517537, 84415623, 233550665, 80443469, 807599967, 266163787, 569331490, 762589427, 742059563, 583439830, 933986669, 253040345, 866749400, 571695028, 717030600, 601505284, 137428165, 377804990, 885954760, 718037942, 536287492, 882614876, 201525010, 607372686, 527244627, 576769310, 766505033, 196768069, 834071590, 547266028, 555267868, 62377187, 546880960, 909170906, 788826152, 194062492, 248157618, 242546514, 382301547, 209732589, 407209800, 231244698, 192683379, 189579868, 592428759, 939640070, 362143043, 879937430, 816417229, 469526379, 782640048, 245141596, 340880626, 540277683, 273329687, 333588890, 896360703, 584843238, 18014478, 481141900, 176294933, 74068983, 916357021, 309758709, 614131361, 851071419, 565128174, 114009120, 512380700, 602838175, 359094791, 665469709, 617040860, 59885181, 232147701, 189825733, 940787271, 205753253, 657598283, 489032180, 258822694, 41276823, 276959676, 45963888, 436958120, 778086384, 543508180, 50458942, 557158892, 177024341, 818683863, 559376419, 816328809, 540587332, 314652607, 573572723, 510970630, 554408158, 319982431, 313320097, 36369311, 917717379, 530198830, 215607411, 423801442, 526109671, 828065340, 188997590, 150563236, 255522089, 735615532, 979266208, 931390241, 443037568, 374148131, 387429531, 539986681, 612093924, 133620720, 50948320, 22163991, 402749020, 250652756, 297076293, 627040085, 9194433, 110505940, 283327139, 903520628, 727848290, 255908148, 213318694, 50289212, 897812014, 521022268, 427958791, 178733011, 516327661, 245339999, 988787200, 561496807, 645934733, 410180831, 718031171, 745922105, 28299087, 63294270, 880278444, 48076918, 967970771, 83143185, 977975260, 350789876, 448945051, 62433502, 548137126, 217797183, 51522036, 913827927, 381873376, 738143848, 728126711, 417880604, 640310410, 570066778, 396342279, 867133657, 363026116, 840595509, 234388407, 943719343, 567757454, 688348856, 615094040, 591321319, 486254831, 991688191, 120506283, 28983423, 572802901, 223275921, 263130289, 306537659, 864371584, 168108646, 10626669, 625752822, 917965699, 389796226, 629220667, 38176364, 143781448, 865003692, 379290368, 547850999, 290785239, 29794669, 435705191, 680436843, 86439217, 346776082, 272861331, 482684882, 253604373, 568649957, 984042203, 190341261, 238363796, 242807248, 778068148, 411082470, 151467266, 189126672, 226112831, 323210914, 877776305, 969253139, 264548398, 571217176, 400471572, 53629664, 907169255, 513884930, 90109924, 409417511, 658548065, 793093562, 303842279, 694368758, 637433851, 297635532, 141751921, 288322231, 229746395, 436148823, 539090338, 545588947, 83458765, 94841021, 979412591, 779532964, 867123021, 377187421, 182739973, 306592483, 468586919, 622788768, 94894534, 829382387, 99975999, 502341463, 659274718, 648779466, 258327185, 719229313, 287983649, 534974711, 329649506, 966363026, 506245740, 582127408, 695121132, 316209178, 531136662, 342427766, 911725037, 262259806, 118741026, 590069742, 915795949, 161862453, 194590396, 403542829, 202665078, 555428987, 540535356, 313079019, 880405, 300202026, 466598012, 11883831, 543934699, 601379836, 601969238, 333777976, 78655320, 451982262, 942531828, 285494093, 702844642, 852031631, 255802322, 944131072, 608943332, 393068387, 201433910, 914429233, 457585609, 273839269, 775747148, 41988943, 116050508, 395649925, 892711631, 697626720, 741966068, 749332420, 21510667, 619486551, 256261028, 888989275, 652584185, 778734276, 564276759, 739686752, 929363079, 776047983, 447968549, 532180041, 599503838, 730041942, 376123224, 106323550, 24567379, 897260346, 183859197, 334569216, 939502294, 768157568, 364868344, 759946364, 714697722, 452483990, 370962545, 675850758, 729926341, 520795978, 781886826, 79975646, 386305336, 228305512, 245392155, 152788909, 962745443, 185284093, 354862495, 157052927, 721714817, 532511199, 104669545, 567200734, 985343226, 389496560, 17270905, 781535764, 323404992, 747540026, 235576875, 916250016, 720353748, 28820562, 454997128, 552884767, 42156877, 623027186, 81211245, 464850445, 773874394, 211555528, 558674658, 387496775, 896721579, 385735136, 478699260, 472711945, 948078374, 501482422, 117899499, 946480374, 85810244, 95236670, 207433158, 12325956, 282479307, 29501415, 458965357, 877293988, 518462968, 926470611, 877372900, 712776936, 446450353, 242711338, 105211784, 759164160, 865241339, 117892237, 62940384, 283415619, 322361553, 538956247, 360021452, 38037297, 812846538, 225105125, 55864381, 261014109, 317452587, 381067990, 246242283, 941653117, 309709453, 390898566, 69159366, 160957767, 372549512, 543063023, 861724035, 294210240, 332323667, 853412690, 302905785, 120860616, 964891371, 743577075, 567066932, 813682854, 820419078, 765691031, 798130554, 759369824, 694645007, 612547295, 56274736, 167402827, 70871869, 316520849, 760668043, 281405982, 22979460, 961751543, 924789630, 262855654, 592383332, 617237115, 415660368, 140078460, 477413783, 732803487, 708386008, 120192281, 727115437, 386141950, 816556216, 22288623, 895616985, 167054949, 51854910, 751113628, 161189366, 89585017, 388903530, 776836975, 908644377, 165087766, 275575903, 361371316, 684539050, 390067801, 230517450, 351635355, 214370618, 147375030, 435878368, 763686209, 348979318, 750657680, 732731411, 710211916, 796079949, 226871209, 902279532, 924605924, 424812777, 125493263, 820724086, 901967147, 459308764, 473586770, 22768401, 357735685, 178145053, 570408248, 248030563, 962276079, 417188963, 953451711, 862697681, 478280760, 965792816, 23365147, 51251159, 205405138, 81698980, 134358108, 587849598, 220924418, 968480156, 220629230, 580078031, 577341934, 84267406, 523680500, 216684500, 304482411, 440465101, 507089926, 516129640, 110639208, 323672466, 47239606, 191055601, 857181923, 281500472, 945276708, 848023215, 617331405, 495217719, 562372910, 79733724, 841781522, 226945561, 917926038, 349608875, 231751365, 748835144, 719319467, 830648052, 558152277, 538556814, 94710929, 357859751, 106115278, 647953020, 433546358, 918627089, 397633249, 739420770, 628981109, 598851973, 592677901, 963833371, 697662605, 513816612, 446639710, 424444111, 542859315, 678926462, 481691143, 237544106, 397878439, 883054134, 747203038, 660007928, 26934283, 646892046, 443396332, 240987219, 554127304, 927027699, 458411521, 610824555, 175566760, 59931672, 263934121, 4432073, 539307371, 140989585, 552391717, 101484986, 452063913, 61735043, 952828167, 186114686, 431450839, 130365601, 397990467, 275884068, 594149806, 666312612, 516235012, 387065329, 3657726, 91326669, 170824575, 822116225, 675509381, 585405900, 644610768, 46726314, 786268649, 901326505, 849163768, 666351619, 678341106, 680851837, 372980066, 965685312, 142496545, 864672036, 798197180, 22689370, 954661943, 533670230, 58376019, 145672922, 121923758, 932150604, 748525077, 783807577, 234437135, 17914581, 926885438, 351731495, 259964214, 982537181, 422423173, 170042421, 357497183, 495980659, 99713673, 316607470, 510680567, 539240747, 418564722, 803688526, 621634738, 283333369, 705699535, 821722286, 145223654, 502602108, 648945170, 464081062, 133548649, 434061655, 112282710, 714979045, 606136912, 705977283, 981871529, 865618412, 217603177, 331422518, 438034543, 481184401, 94720028, 72302420, 83722144, 449723201, 383792963, 871466747, 284525097, 938074178, 209386664, 383420168, 261990243, 90990034, 68176724, 232796490, 239581266, 470357035, 701105378, 771983923, 20974794, 186066897, 937165158, 204781252, 250053879, 475477694, 454264373, 10981319, 290521978, 904645068, 313806640, 179540325, 375249529, 161016478, 262181808, 663462759, 578333907, 774344306, 344580579, 565445485, 86441365, 312754990, 968415981, 145574856, 63547521, 272004265, 82994874, 918315753, 314655447, 407853436, 350375600, 921308751, 43196628, 822832063, 29542917, 153405648, 35522600, 560025710, 258087648, 39511588, 576571016, 404226518, 364427789, 436674743, 766124725, 526203700, 799885505, 169926739, 788459782, 50097481, 442491413, 490330018, 447724368, 782892210, 738186637, 830964428, 474224532, 977183564, 413020186, 753974780, 835310520, 933147690, 766027241, 248297871, 923306674, 892628946, 605545217, 974245223, 340921331, 594169415, 309660166, 180846890, 440598570, 318446226, 276145750, 603940074, 128572548, 142188899, 196446117, 476679623, 742868871, 672791028, 873758613, 183352951, 695550674, 183256503, 302251033, 164594750, 733277019, 982518559, 15493712, 178316467, 95452833, 914385264, 489159868, 560283747, 658584142, 843621353, 239583895, 111460228, 267300937, 948866946, 716089641, 783706718, 262164489, 137710840, 324705995, 583948972, 676949922, 797193542, 398384692, 653542865, 957398137, 664727511, 258279579, 707658627, 546356340, 415346509, 496073806, 937720787, 58182644, 818939359, 890278733, 301794995, 598465709, 155753454, 483322077, 253677540, 69999282, 413465043, 656774226, 753389502, 894145030, 194109169, 962694895, 102901211, 509711836, 558796887, 456282985, 19731100, 235899398, 296786760, 697143910, 743805976, 921060042, 675453987, 310117428, 809248209, 246566539, 474814625, 390032669, 266981947, 252969566, 727973994, 908383291, 549546704, 614499307, 31935849, 213496470, 390884199, 765403171, 237502295, 437199347, 42199675, 475277404, 289836248, 717472683, 216762580, 6182437, 984435952, 556696058, 500601797, 120922674, 134707922, 251039780, 689465994, 814817886, 287996912, 719164273, 375287508, 155619955, 535108543, 857435974, 998747422, 115295557, 153374957, 141064746, 642134772, 258939614, 275360898, 334220691, 926221245, 500803059, 969851781, 60932774, 892666571, 697448865, 204229907, 844615730, 211935495, 5436172, 41372809, 331468594, 452846557, 669806506, 469097424, 686554736, 187159068, 563656138, 496892836, 301903561, 215809244, 69790104, 91237473, 928097669, 348010018, 492006326, 220218270, 657868305, 148462453, 681464182, 699331903, 811208246, 824933130, 610750941, 966445058, 772330964, 259396766, 525857469, 223876523, 506923288, 963093114, 679744557, 934935146, 755266309, 495098827, 193501053, 429435478, 285372761, 479857813, 675272369, 261114344, 780761788, 833265851, 809465535, 641570319, 879328295, 824768359, 258146440, 842232544, 555114139, 381110568, 529542089, 851203446, 172248440, 538207671, 873358072, 300824026, 228712272, 702779707, 933269693, 95716570, 697841417, 372075660, 275297235, 378457921, 283470573, 331485445, 531802521, 949636829, 56492684, 372615018, 313793789, 265870407, 501749207, 156787804, 380706678, 269942844, 707841171, 326310015, 123399676, 949071975, 11025435, 754173894, 347439960, 740433144, 359848375, 252115822, 564792721, 224255352, 633256710, 450196436, 504697763, 320892307, 706969358, 655888743, 562751152, 597412194, 228862860, 136477898, 924692611, 412545139, 768553139, 584123505, 448354117, 19407927, 80550401, 111084691, 219700725, 568074595, 682081763, 439371846, 513547459, 410366203, 887857162, 690712238, 820461923, 613627130, 437608619, 420832952, 650117897, 364734718, 851531960, 743304453, 500868605, 948809155, 633238508, 651007901, 994664260, 74016691, 144707219, 391570874, 864430553, 108601042, 160492272, 595851050, 4314658, 734709511, 247383417, 493124345, 477784302, 676528826, 669778689, 869959719, 716919602, 256540872, 585007412, 309762002, 639084508, 728611967, 168315466, 658812120, 12015269, 497519790, 40845395, 264028987, 970981687, 445719100, 308199757, 223938033, 176580876, 11718382, 742711765, 830327784, 146830832, 860694078, 395204948, 537607301, 644549191, 287839689, 434677906, 831842357, 523162613, 38394849, 130682422, 396884621, 360960326, 127061675, 365047364, 136155323, 822425358, 937384704, 895752617, 428474231, 575345284, 139002724, 688635523, 387093468, 402307289, 535288098, 659009844, 560144114, 141363815, 624465870, 416280638, 447257551, 898864169, 91325988, 616832475, 17089340, 9213305, 524418087, 318231268, 252720932, 994535841, 944360812, 145939184, 979822090, 918225499, 754468511, 546742449, 551515543, 304227858, 122831683, 538599565, 837282880, 624896485, 162747823, 901269592, 551334845, 953441805, 547629049, 730178349, 926386783, 998778972, 59981728, 38373967, 354527787, 601462162, 929030703, 412976805, 901389185, 370774258, 907854170, 305837201, 270894414, 898716852, 832606270, 764693412, 957925141, 777898228, 304816294, 720242287, 561956951, 835486306, 424845329, 256308757, 500382486, 600786130, 129965533, 812098882, 424234230, 949354421, 428839453, 569334681, 657234662, 14234847, 827262719, 725514668, 439529160, 374958115, 283491429, 349423753, 498032763, 988681240, 367926228, 760987702, 382242899, 6697374, 830972085, 404912547, 839260777, 445893324, 970576048, 415304199, 422815282, 823689630, 415379016, 950483368, 289897877, 832889523, 600994771, 849640232, 702060505, 37993786, 767679518, 228613740, 186768113, 504733646, 554834552, 439264583, 140187906, 468653984, 652329553, 453915719, 642353848, 758982971, 676543001, 691574528, 566163621, 589050242, 140654942, 611438206, 753442341, 949458057, 99524826, 352939342, 528688694, 884239202, 548930615, 758795747, 580999905, 479327665, 116370140, 493254216, 980427172, 137096612, 460042758, 578930851, 767972830, 573195841, 763823627, 524002347, 294599204, 520945202, 863519453, 720089788, 901138669, 488972446, 193296323, 568373763, 399387695, 8010334, 252765243, 80784059, 886137596, 108818337, 596768616, 705344914, 650208616, 924129413, 568545289, 65794332, 226714655, 986635087, 380538986, 478501378, 462495464, 136520332, 67875789, 189343456, 575701666, 965640980, 138970621, 438329233, 105659373, 625767131, 489293984, 107530088, 987681051, 689246535, 928197866, 396158729, 642124171, 957015267, 373545143, 952340239, 634192142, 661620362, 52067456, 871737004, 191664730, 258375062, 556574305, 990344969, 332159098, 881833948, 593833759, 747601834, 389122521, 659879168, 134157857, 293851436, 677045458, 494125462, 537319016, 588869378, 930080650, 768501443, 223868523, 906830649, 844143108, 187812636, 456972010, 494430199, 653118006, 850193661, 487767142, 885540182, 240230139, 706708411, 543191295, 582510005, 981381073, 974797745, 404810138, 13433310, 290357943, 297576209, 853327485, 232987135, 710943066, 991427111, 672037767, 655945634, 680530494, 935957178, 511453366, 613556470, 453707577, 149732687, 501370899, 606262158, 210334552, 27760207, 805989175, 696695902, 415122419, 744573723, 767161415, 577437735, 526686211, 814224911, 212298864, 671793381, 525194346, 940644600, 980823005, 605856467, 702046011, 736260587, 780671328, 466232780, 859763796, 123387946, 792125833, 413668023, 592460000, 564939234, 508395838, 351308613, 850041249, 648796243, 367953495, 95302723, 777645141, 291092286, 718033765, 98441004, 462322928, 446942719, 449741634, 262949127, 766347935, 175258038, 536804641, 624003856, 467347371, 489748366, 136303639, 203396856, 157246271, 743709555, 45035531, 79219418, 677867923, 918608349, 276022083, 940054942, 645306875, 821392894, 209185071, 464212163, 836478187, 448072175, 375109713, 423772582, 274101789, 20919609, 443880553, 362085976, 425308151, 410463484, 263709622, 342190547, 647189501, 321868423, 646273774, 146346837, 531013209, 18735223, 899915816, 146288255, 515197357, 376539310, 624149060, 502370371, 241017514, 949986610, 441343172, 676115438, 389794864, 13676344, 57426460, 502038734, 701148507, 898296285, 491513722, 85571563, 463566675, 319152942, 315189778, 311490688, 127934135, 843338236, 603454169, 724168852, 847108278, 706301723, 375766576, 622622803, 258178562, 941432781, 435859645, 877020815, 307862487, 702648872, 803741390, 50481452, 333687947, 21059779, 965954663, 287848818, 668248810, 519832895, 919612804, 836957273, 305168297, 796593389, 59805343, 32503757, 694370340, 412824248, 150742409, 323475427, 550553853, 19577685, 285093778, 552616873, 987758681, 270390937, 36495984, 667461462, 655273005, 124070209, 445222754, 759008992, 678684124, 497763517, 41769604, 906389060, 802142404, 530640610, 341071463, 843953778, 392031099, 20232966, 957628601, 603954147, 798920876, 834853938, 955785300, 998808533, 586849030, 8269414, 335875025, 578727357, 910981213, 941194152, 17603041, 223536207, 26245843, 671757232, 996528913, 678551841, 108528061, 796716551, 399663773, 780739773, 320696267, 847977958, 431293717, 779656500, 692738430, 207544053, 673193946, 120586445, 509964972, 446802031, 315111219, 619913648, 179634902, 641983675, 663391354, 196807237, 23214201, 807990885, 278398567, 228960642, 983525135, 379357293, 162954345, 550153370, 595060339, 354302386, 774459338, 834610388, 409425621, 454187462, 799589054, 790986376, 596498515, 743540234, 763630685, 490241943, 100124939, 328591209, 777721282, 515844606, 645680139, 154878711, 188202738, 899264012, 343122466, 594276549, 729210866, 651486568, 639649661, 644843879, 931042719, 608629437, 879316733, 72349816, 519038209, 754918503, 795695296, 642429823, 862835, 505306139, 59910856, 562695351, 568075959, 910797336, 385606850, 741103864, 200381757, 474891549, 239700849, 805406989, 803200761, 443364976, 552170715, 178592049, 676667988, 222544219, 168092205, 349438085, 609205315, 640827632, 846780154, 106587634, 241717765, 574617557, 128475509, 850776991, 629508808, 92807179, 508813675, 692393934, 394328589, 150051072, 36169494, 235563351, 597896530, 865751711, 838286056, 880860044, 999710514, 29450030, 986052864, 161988750, 425443623, 83162048, 684400593, 703079660, 356845986, 323309935, 673754462, 244368318, 5705536, 298841787, 70177543, 325638709, 259442265, 909739962, 256221450, 167249719, 172355873, 212719312, 676260701, 951672839, 921140627, 495387466, 589541324, 206093132, 153820666, 864865147, 317607140, 458003529, 294111942, 590707873, 821028454, 476543462, 365896392, 706676178, 408233938, 813248478, 437429456, 343430514, 400538906, 871862934, 158668466, 651595713, 781852512, 439968395, 857837667, 259993186, 231866300, 241383973, 439647718, 588808282, 259837223, 402332437, 420839114, 886088952, 456708703, 528819737, 269578543, 343314238, 873039343, 875900509, 407835233, 547407124, 744058362, 546608508, 84796755, 963527421, 327488783, 45046394, 910456583, 514118845, 243625321, 725695355, 670181467, 617610262, 276168273, 928903897, 226190129, 922865750, 149745444, 757639476, 715115779, 622468780, 715458537, 202868181, 426743735, 501516683, 343369371, 334540159, 307730907, 126585798, 413232085, 109528407, 627604817, 139930442, 768188434, 478382331, 492179033, 640401881, 427051535, 763228188, 129138859, 672054030, 135283054, 692006222, 886837085, 736056677, 400969227, 235441355, 813705246, 904945766, 385065620, 444467352, 398361460, 793539062, 976171644, 325625014, 899830463, 699124964, 36645930, 946571970, 283115945, 934769261, 238969638, 812256990, 317050873, 385952457, 495364441, 632503029, 933073895, 147652015, 955003745, 593337810, 682721048, 437135057, 533064248, 814416791, 215390284, 837459908, 975600714, 675421076, 208263314, 499061019, 773840841, 95166947, 335416938, 865249090, 342756691, 282144457, 289528587, 752942839, 259665674, 202153671, 778657115, 719041, 307396675, 503301387, 602350827, 237519209, 484983566, 501039087, 808979839, 696193237, 506513041, 702695745, 380558026, 437571384, 656421344, 177702870, 137572021, 62009527, 360015816, 447136919, 794582561, 653729818, 971298057, 440853855, 320566960, 330016877, 860141861, 655052415, 713079763, 194229257, 171357543, 714616046, 482414417, 222378402, 961795262, 26092307, 544701728, 380252895, 230704060, 957757665, 528157154, 411893475, 552436630, 620450030, 217112462, 844960718, 588434477, 377854630, 501108757, 36987144, 120528232, 428087, 415129283, 980944958, 344525060, 613632043, 869252793, 369579268, 363055380, 910942859, 979410053, 408938965, 54913457, 434698742, 341627415, 662063608, 506390609, 286595899, 942709720, 913494860, 48707607, 199916440, 318271420, 702759999, 91197153, 638865083, 295295988, 225335030, 622149516, 670419008, 889267141, 665162200, 405162437, 511427224, 567857485, 121608115, 730067516, 764656452, 232493720, 38023826, 607118152, 82546758, 773319583, 726756336, 629641033, 84640891, 24711227, 430705543, 973944030, 265783917, 621371828, 288898291, 155985164, 655580396, 814803617, 25167882, 467164149, 123708613, 99065575, 932100846, 162561217, 62631093, 453217362, 719454365, 737799073, 197882398, 77115125, 943506111, 312480474, 360860347, 971360333, 352290522, 70711843, 194647962, 227422918, 591213269, 410008209, 739236268, 294850202, 179759398, 777481900, 901737012, 533634355, 730765311, 884110573, 750510182, 957360833, 942920679, 338052685, 795821255, 924869519, 876677465, 479345678, 425397887, 266676354, 617455340, 8963595, 517659648, 743839411, 686527323, 911395160, 485600781, 501402491, 452254639, 342077653, 920285986, 752490152, 511745596, 964916843, 193064794, 34813885, 76311802, 35118069, 388209949, 274510436, 572321969, 114360504, 240054580, 754917013, 881578403, 184447919, 739070564, 393743527, 57475989, 606859366, 527521093, 644505605, 48288805, 616022860, 907514852, 30635304, 503802215, 483740669, 393174342, 201476372, 830927661, 583024956, 594128985, 21021600, 540574500, 53720374, 571197411, 947410632, 764378175, 600446198, 14336928, 717093567, 351043624, 714870637, 151632000, 570020975, 863075487, 750757304, 951736474, 147115555, 287980015, 506216095, 950036866, 36298489, 598464053, 258551216, 869856307, 971898116, 855068040, 613267025, 63176595, 247576785, 528335369, 879622494, 235483901, 724313949, 973423798, 329665705, 973158196, 124919763, 935810645, 615227003, 670927611, 18296120, 523707506, 539800603, 255039386, 929257847, 985591463, 928999326, 254743805, 997527224, 963841566, 82114337, 760789725, 713180883, 898300265, 938734532, 847882207, 234185328, 221218427, 357097630, 418607927, 904894161, 373064320, 283094917, 831690356, 394617016, 690941625, 996225791, 520364861, 451922212, 967767186, 36902109, 206763797, 993765679, 869163582, 835510384, 100749826, 223664405, 393541726, 417079345, 382027021, 524339658, 219231448, 752628347, 409677404, 625342462, 756839819, 714170632, 741388750, 399391494, 51097911, 972581469, 908414571, 286198816, 239538886, 942523506, 389285621, 946293442, 856544355, 299117317, 79223106, 609289677, 237912886, 281455821, 792420312, 377223447, 818086064, 938307981, 169483343, 184097310, 387365271, 615358788, 661983521, 969096412, 700995598, 576016527, 180539470, 816013408, 668827921, 378708825, 33337552, 623649136, 832714882, 991397491, 142869558, 488610178, 396805379, 256623161, 931604189, 752557170, 8519109, 30407367, 639707796, 92800152, 839450083, 29991994, 392524777, 129383913, 150000472, 50444206, 935049114, 938525263, 208922217, 344307313, 210994662, 388042608, 47198313, 784317723, 78759257, 557478335, 552503175, 511883675, 392484670, 462523955, 91581861, 27927255, 309259667, 844658454, 145324321, 29157520, 635415913, 834223550, 104473329, 951784180, 747719522, 630280622, 320111262, 265261965, 611582583, 455695360, 682490150, 271237299, 73095784, 981950735, 744651642, 557474166, 267541091, 559214283, 578394393, 411536955, 102231569, 983294242, 80575630, 954432564, 408105428, 668491169, 409790789, 990588213, 505769023, 757353709, 907280971, 520293327, 382603457, 4176220, 632805720, 308857083, 587024020, 80456077, 851583329, 84425018, 914899192, 773344979, 891400600, 946804535, 858126888, 390739615, 450666061, 173681199, 53400379, 832932058, 634098171, 808282194, 625332739, 927486793, 690237379, 899168399, 71537118, 15255692, 908576802, 350003555, 115906312, 579527453, 13491212, 666782678, 759056158, 354381816, 188503391, 966034200, 737005321, 854171815, 860078955, 387104124, 246949791, 556805241, 339600187, 207713553, 990509555, 365522794, 435020787, 310728397, 893221264, 167693779, 442704785, 937770100, 473512889, 112693865, 336684070, 935351205, 822332505, 714027791, 861563628, 165690959, 581776818, 807531996, 129393355, 367111664, 625072428, 589915179, 108353659, 394287440, 424192319, 684799129, 648194981, 719919787, 275678294, 641593214, 551487777, 948304947, 341506759, 295411859, 691354429, 121557197, 311102403, 560229439, 712210479, 247551685, 388922873, 21194858, 557459984, 905369324, 672469333, 524914807, 277611057, 920684804, 798857750, 200557202, 984792285, 564080506, 919687806, 969377489, 335310324, 822440728, 628882647, 842837850, 9862929, 126998129, 212627539, 583979266, 903375041, 598560233, 691678267, 709003284, 201463763, 700056369, 533970368, 481204584, 804283304, 156090363, 692156003, 48863683, 906719168, 243853915, 282994208, 850038110, 397187430, 95102548, 58372593, 580600190, 278477100, 21519001, 917055254, 284661532, 740843928, 316709450, 80514240, 435669057, 926498978, 841636070, 193252232, 469202324, 751071976, 950072441, 580235901, 583276721, 938954697, 579309000, 276997772, 898149193, 665478918, 142296527, 145908813, 300216186, 567833524, 294542679, 298600416, 470748755, 945144782, 702488966, 672165264, 125018042, 246116673, 235075725, 427126551, 923182199, 934958855, 759575587, 367915974, 670410201, 12990761, 156534740, 785534635, 665915397, 968502971, 321148049, 987263407, 422311512, 147424894, 927205159, 930366874, 307923130, 355353578, 738853030, 630423782, 153405918, 255155875, 876636861, 316785079, 837118799, 600903305, 535474184, 239436248, 428541863, 832946181, 171097125, 340558546, 123621874, 521564715, 950336031, 393996859, 410591136, 999261, 781799511, 897882724, 167049789, 602262522, 809357529, 365272669, 119152525, 797926272, 656853438, 245392462, 951844753, 838900026, 67375735, 373931004, 654248249, 999523021, 311431757, 980014164, 834622901, 883858235, 220663775, 313937542, 413945542, 719876227, 994515097, 384990210, 935152378, 869569839, 19201971, 565957654, 713842576, 468570843, 953229865, 860463943, 773755993, 135050153, 187332155, 964123863, 804851352, 698712115, 645468261, 757590159, 584015393, 218369564, 11996385, 375360893, 839203083, 797919211, 917491452, 388862755, 220773589, 601859732, 496427121, 638637236, 179298101, 539427087, 172933322, 797204006, 822977720, 487388083, 531513950, 185630287, 159859251, 392596985, 763310939, 133450474, 801767802, 671626365, 8100927, 86012873, 444498051, 558623344, 667459858, 124252251, 100114539, 191360178, 718508684, 676678272, 566788886, 800099656, 220580065, 410934499, 574860957, 659581611, 616572110, 915009540, 753904799, 559715611, 579358075, 282632043, 903236902, 160210356, 621607989, 63642743, 683163128, 699019591, 394236700, 122104549, 545986329, 754459669, 764407960, 494053804, 136215010, 285331475, 291206541, 124343017, 88620735, 415120805, 463009450, 636908479, 498350086, 32140044, 682145629, 482505810, 808713193, 234337366, 447141894, 19989094, 403648559, 369718898, 854226707, 882377067, 108767528, 837180437, 309797818, 308548468, 11573498, 172807184, 209196587, 6461612, 866897664, 102337456, 968328418, 775784140, 26834518, 864169458, 588289557, 381456400, 805039970, 920423899, 26070221, 54814467, 899352766, 297034351, 732454530, 568611801, 420943996, 251345560, 472444139, 476404952, 26441879, 21909870, 971808442, 869154710, 499386202, 855391581, 236553921, 211377881, 850539845, 956467860, 507862523, 60407102, 441509690, 184928034, 19720691, 149987711, 950196951, 83031309, 524023159, 838490270, 758077720, 700952651, 107280008, 981641087, 344244117, 293775065, 118929082, 996427011, 423060900, 820389465, 871130794, 72166197, 480404061, 816701318, 331148252, 856038798, 380642268, 309621895, 168619855, 875434680, 842736122, 86331675, 102530508, 863382693, 562449290, 261939309, 323715197, 99957247, 405413361, 245976366, 287800669, 187113414, 231329163, 454327073, 918633938, 773675624, 63896938, 141031809, 279812966, 31949843, 47523840, 150331136, 437146173, 405480266, 741073727, 465332475, 71050218, 803795959, 23242673, 712261288, 571472613, 640812775, 126401020, 78251954, 700925968, 590058116, 476778862, 952870423, 180483491, 511082347, 513971498, 933442660, 393436937, 396306536, 61467396, 341525740, 72061732, 481601298, 269481953, 637227911, 116799825, 877459054, 7597738, 249122211, 639565962, 391192349, 385562103, 822579140, 716241724, 402222875, 623492096, 116574781, 453271429, 338050421, 509979050, 708860855, 574697281, 138026827, 767475747, 480815593, 749773221, 504580847, 324935939, 486267474, 477366221, 92942767, 399900610, 81499950, 263406090, 124870916, 109478677, 844211705, 310883866, 544386077, 653877157, 209255485, 55330172, 103139535, 992307919, 443894554, 194168049, 213814272, 474548677, 48257996, 57412555, 455742426, 155155961, 964763869, 523579779, 50730427, 775730310, 469327146, 734101680, 18345533, 778873472, 390344725, 60289958, 968864126, 824469026, 303240469, 628629397, 589705737, 841635287, 812338108, 493640228, 612787982, 968861742, 472313331, 664871183, 696351281, 739017711, 833738521, 724857248, 104534587, 865474389, 346617848, 146253064, 573444784, 481359648, 871563574, 35899847, 174937449, 905826334, 932437359, 808212321, 114761309, 806299849, 538023745, 193644750, 864331062, 640577648, 157246249, 556446767, 449543661, 763490822, 311997109, 42680856, 952029618, 113178632, 56371572, 530328424, 763494495, 670470967, 245817701, 748745950, 417702091, 208961036, 937376153, 85066219, 431892230, 622035340, 502985259, 90905925, 237382191, 612920114, 597732024, 968719745, 625838115, 686430645, 284230679, 743973456, 294643104, 810342792, 759896646, 225138813, 220035507, 886447914, 934920678, 219455305, 543313632, 822298460, 81882577, 938760817, 531016904, 582548054, 631719952, 724608374, 500454995, 120528746, 446701720, 746248955, 327200609, 150791886, 251802949, 213594874, 470544471, 105148519, 613059957, 364818751, 500487093, 330390856, 469193526, 56796145, 770268331, 778913057, 192123421, 237922539, 939839026, 936924225, 641275092, 116768739, 648265003, 877518357, 795052547, 349857495, 163280089, 880456100, 624572808, 979090159, 20812151, 720548030, 386986246, 18435308, 523773286, 921751725, 670740222, 964284508, 199437120, 189801509, 230223609, 589218257, 59654012, 640728940, 269752077, 295706667, 977005122, 253123199, 500675264, 2872725, 958437379, 630939528, 731673063, 365088912, 450140908, 209268602, 133463637, 388361071, 241834373, 512879577, 890278316, 898138620, 990349164, 603695609, 216796165, 893898771, 374571573, 206961798, 186463895, 269963691, 917728811, 934976417, 604712330, 669132977, 485660900, 279897179, 541104950, 808049466, 40040684, 591683772, 389662306, 580017115, 391419826, 790241973, 407290198, 130745575, 285289744, 688988859, 181150678, 376448571, 590703784, 305653950, 164862696, 571163110, 207911963, 447541856, 238077194, 966135492, 787486790, 542865314, 24375046, 4226660, 867716747, 348223346, 865079386, 888430747, 100425654, 698863580, 553390274, 209113887, 261027200, 190940223, 998782991, 503793829, 726294794, 88282138, 165063426, 771303708, 270433130, 787474601, 749051805, 421271495, 20289035, 80403701, 493302505, 38691334, 220635256, 171966136, 35284693, 7206021, 255417988, 179551539, 489005453, 997933612, 563316581, 90284603, 300011714, 937803514, 738235749, 642132983, 907907840, 391989808, 102671923, 719165452, 616273636, 523813089, 762545761, 81232813, 960638767, 459392902, 148650039, 294359919, 552706656, 534656568, 509198039, 520462695, 653885982, 127657716, 741486095, 530748492, 126801295, 479432070, 158691406, 460949877, 533244446, 793432009, 857749077, 624703073, 587650311, 577925261, 953303310, 821294907, 777065042, 741846319, 667437418, 623918841, 100292882, 349804397, 765276768, 891968504, 858938485, 723887672, 738227769, 607723006, 360684249, 608646297, 537718415, 868617184, 60432298, 57029871, 168152172, 325181220, 715915970, 527035686, 35102516, 803261585, 930676487, 209012227, 773183889, 678263916, 366926501, 431031471, 787333428, 387571909, 727899343, 421474828, 2442499, 926591767, 313715681, 322565675, 100164590, 963304415, 364206064, 46612122, 826178628, 250039336, 529081489, 934383355, 116469261, 146150905, 343276772, 577525506, 748868101, 206804583, 174686408, 484419500, 27550149, 180349765, 853686340, 72280143, 817224916, 41382947, 329715789, 448586175, 508646757, 6279278, 712683947, 108223373, 466495668, 879093794, 48049813, 441425127, 289717939, 941213152, 545802719, 912635785, 363965522, 435040704, 540330023, 541760301, 164658159, 771885966, 912604524, 29396382, 943402787, 806857348, 369134473, 877533672, 341344177, 521830990, 220439233, 50389355, 75983159, 7481372, 856729120, 784316609, 177854350, 303327431, 38099567, 592459038, 268104537, 457860329, 830080865, 306733425, 641768245, 986560926, 856825373, 375064482, 787210676, 713489629, 369286855, 940001504, 553658250, 680092562, 280028878, 652904805, 208663673, 758808541, 573155063, 372047650, 521409033, 525889763, 759879493, 102219357, 631932597, 477789827, 692901131, 149425816, 751011803, 265886063, 402908037, 978358175, 671832076, 293542434, 793801415, 28429361, 368859584, 916976276, 281999301, 487212488, 703631814, 822126101, 31431518, 419626061, 916270148, 301752294, 247561864, 249204916, 525413423, 224319087, 92662975, 307953184, 956184223, 868980707, 813241814, 47800649, 585905505, 245405705, 85781317, 737667649, 644873838, 574828513, 55564564, 238036376, 473586314, 728828030, 201779924, 85761213, 557479858, 481370325, 540109016, 721199470, 191326705, 108655918, 661486420, 908883077, 351731636, 430422907, 607768195, 562016897, 118197979, 163767416, 251419286, 203845323, 489341124, 94120222, 898131476, 798706713, 631247385, 216830703, 380946062, 981435764, 150247546, 836106906, 762406708, 993700323, 453502836, 261808566, 956471197, 486310289, 275920156, 627651760, 875743742, 683735442, 656551827, 104487770, 579380641, 930081789, 512763499, 970819592, 362435056, 889415254, 775667583, 837570451, 975284220, 954121265, 444954043, 676731007, 850958286, 396580192, 170305478, 821500616, 370628545, 699063051, 164232893, 821837476, 963143660, 110719195, 822688990, 684804441, 923423240, 942105042, 784514778, 193897903, 424544588, 839688362, 407213551, 466377244, 898798268, 804696582, 510582462, 679799837, 73797524, 432784339, 478437953, 716940223, 357103851, 754755436, 301825943, 76711600, 608297369, 409745802, 541789420, 138433192, 559890887, 675573577, 322754345, 177954183, 887074247, 90117806, 354913389, 454414512, 204299886, 759027484, 782056618, 730638608, 591172384, 872404775, 923401205, 484179078, 639877856, 715040909, 324759310, 814783158, 46902867, 641831866, 556858485, 995992026, 929762667, 360063664, 961047389, 250854813, 908200457, 442660414, 935984278, 354046079, 611485586, 994892803, 759427255, 369069511, 709159706, 125015907, 550321693, 280367740, 809708305, 244911815, 642792855, 746023376, 470264344, 151941467, 721204836, 792676424, 828320962, 839430122, 404699660, 310846520, 306717333, 409797395, 746937957, 343372582, 94132004, 202574456, 86621990, 614722812, 915334050, 891101379, 415908005, 862077914, 267832441, 539295181, 242229448, 199185503, 741062358, 291346488, 794026559, 880434030, 209718933, 273211010, 57326475, 290756775, 192958175, 388831138, 250383513, 537043887, 869019065, 612696, 53145178, 322330968, 141645010, 596136564, 467623602, 146899505, 853335976, 59620924, 559424956, 83241573, 116840185, 410887066, 615698358, 900979576, 48433428, 171381520, 557381155, 998138548, 234222766, 851984609, 451068689, 712662758, 944083838, 123570894, 172696568, 793503038, 129764320, 48070995, 26341185, 226577686, 161141130, 463045511, 478570776, 94700273, 854681108, 514995254, 214706154, 195769393, 254855216, 246862569, 816682346, 196816481, 43808307, 149709520, 359639475, 401831639, 313397344, 248108173, 843721554, 449636376, 174441453, 666498576, 111114212, 512360224, 764295313, 208790335, 396678961, 188282316, 76783433, 248485625, 230099825, 917411965, 457033272, 871019072, 414894396, 165585971, 556533472, 188330191, 133009589, 168215949, 739115212, 183801219, 51222208, 508461475, 285447201, 891695851, 406392042, 554164703, 782872655, 406847042, 614378349, 449016730, 534076958, 130359796, 248747538, 780571168, 648221823, 581449018, 960881958, 890642251, 393378888, 715269939, 6856555, 257918489, 324648607, 234400293, 958448019, 292464224, 906091456, 397768269, 906467717, 346748592, 717473814, 876918898, 124630969, 256302590, 606762240, 174489688, 779980978, 267729771, 556427762, 763726122, 666853300, 974596200, 104064425, 883777643, 459361827, 918249905, 153080978, 897319413, 927505448, 569701092, 501771968, 308810958, 474905203, 254542627, 229737574, 444346075, 674644640, 743335311, 751880483, 877994752, 423844766, 311855530, 952819194, 19962282, 18839814, 134553703, 520211783, 1349040, 874174155, 597679743, 613194285, 259505481, 292556673, 753074059, 461727230, 299297611, 620025479, 370586854, 693613710, 498700172, 230079428, 599491201, 421662274, 771828643, 679274684, 166286375, 631884046, 661647787, 315061688, 851677303, 226819693, 487551959, 521622830, 861864691, 720799928, 758613424, 84424191, 207305803, 940754911, 631985378, 489281157, 542188078, 207671785, 192794266, 720160255, 47301596, 294210464, 654731633, 595246036, 564020530, 544729379, 54252583, 730166965, 761957926, 178832512, 499736989, 168864857, 383903525, 58477039, 496036047, 557371461, 61039041, 103977436, 271931641, 810664341, 481276920, 552011968, 707832858, 841750142, 971768243, 470838963, 886325619, 869748885, 703790323, 402679378, 840893221, 735722026, 175976637, 105168650, 865424853, 238444657, 458195831, 203331293, 225805863, 6761454, 34359288, 488347327, 708616583, 673588088, 526140355, 394895330, 502958576, 530170963, 508395382, 138708031, 247189749, 975567505, 259118831, 734916269, 711484280, 924856753, 94061920, 9465146, 79075682, 16365069, 238015655, 620744864, 453938210, 264050570, 52052931, 555788274, 453410787, 844146512, 645929782, 140432413, 170493479, 512119318, 150669390, 793355550, 613457330, 849324187, 645414118, 730463603, 84691964, 290038121, 870738883, 96753953, 340124165, 186911092, 581146494, 119564284, 564991482, 711743348, 23213627, 682873529, 605724113, 186096491, 802431505, 959311280, 912518508, 55843527, 144738115, 540088829, 335503425, 633503919, 961984850, 441293362, 85674456, 889027180, 811710306, 44897989, 270707482, 462195036, 365172289, 259077173, 176931421, 961436861, 718202826, 748329564, 843361286, 256333729, 720137747, 220824872, 834335304, 690842472, 839415059, 738578328, 409035262, 467903010, 259087809, 251867686, 233491097, 393503034, 445339784, 252328232, 410021659, 319068245, 378620782, 420504669, 978442458, 437511052, 964486643, 669669387, 823930413, 938012636, 289833611, 888749579, 134809477, 91966815, 511792643, 180193473, 293833186, 936556431, 44249193, 92821553, 678705423, 909354611, 568495902, 19476275, 916105852, 723850213, 607387182, 581393687, 440360765, 792999858, 182777736, 457855776, 816819146, 729592583, 899269611, 685919012, 906378637, 192966846, 357435139, 232352108, 314371130, 606024219, 511859243, 341184529, 391502034, 677571813, 787235105, 267499340, 233362495, 93289953, 968887922, 935209478, 127062693, 9170768, 928140350, 426711460, 355326658, 870422440, 360875245, 564868985, 523568596, 111775101, 774154950, 68862260, 235850313, 479012750, 46186251, 615962998, 511426454, 96903554, 964515836, 285476037, 841663542, 204664507, 794417672, 732497168, 193908550, 348483307, 931704210, 571966984, 487702725, 443236689, 606139190, 17187751, 163184501, 600662807, 551629544, 972351687, 951183771, 338909479, 763856189, 184583251, 69082733, 111199978, 787539751, 219067888, 11181064, 835035748, 203813109, 415811814, 991483421, 529907731, 75041135, 671372048, 125999872, 732323495, 315367400, 418307232, 795867325, 486556073, 413822256, 670333234, 20322852, 796933844, 620483841, 280069664, 529783908, 195745551, 600982344, 290844266, 974293211, 143307584, 689429931, 904904003, 254335887, 818143241, 119796546, 972701162, 155417503, 396939973, 315181244, 762306991, 392874795, 911504164, 451003304, 25492649, 615261511, 207717726, 531281723, 374616228, 361809607, 105875278, 296610596, 899171583, 671481000, 379937487, 901004855, 725102042, 159466464, 951591341, 329345059, 188016334, 503875202, 23389410, 337127497, 237449921, 174282692, 704897983, 812567816, 592688945, 706355739, 55220162, 213951652, 852628843, 667429314, 691967483, 23979655, 925102386, 808970229, 303121355, 368412603, 254920474, 982987544, 597492974, 148861480, 416672581, 788761411, 511111911, 773420153, 499662215, 63603140, 826987668, 341303540, 955462734, 492930169, 936978312, 357477024, 339885032, 911191461, 166281134, 584514539, 196025053, 68694153, 638980908, 371591704, 449310498, 806538883, 487788440, 125245931, 486964401, 443018761, 250176889, 752929263, 21792640, 339139459, 485854616, 982962837, 527652782, 247096895, 938756644, 953156414, 184507352, 226301972, 492164241, 118048896, 270266209, 530937922, 953127479, 930389244, 606377021, 558986528, 589077621, 136855159, 417287202, 442149588, 678322856, 197908343, 935907272, 871504109, 854639033, 389761003, 827070831, 107126719, 100611211, 914254857, 856309833, 897235091, 209175068, 730410601, 543861370, 693891066, 828317871, 837201219, 146495234, 803919299, 291032001, 19148028, 748707736, 881233119, 219400332, 574228031, 784839619, 324974132, 181005908, 47538276, 677008880, 926300697, 968195379, 489091848, 21434667, 478111081, 736880434, 367792381, 360326004, 513167304, 777717519, 633260441, 436857829, 874204966, 718817590, 158342255, 934380715, 455760652, 223793713, 543062203, 783197417, 564860546, 164313998, 538216342, 584717510, 13384398, 243388291, 372700664, 29778050, 40350870, 501761668, 112228808, 587409051, 886531623, 488189491, 775381800, 56343299, 283206383, 395054001, 845817661, 482569709, 918906119, 236162857, 544380387, 646572889, 429857917, 782937789, 67787586, 492280478, 894807840, 490187347, 915968998, 814919606, 471571743, 399624451, 432677113, 368538112, 652296287, 680299337, 539076310, 488890994, 164038158, 982232708, 789444671, 724706419, 902719727, 633261723, 992889113, 745277047, 713106094, 156745882, 967222156, 983407716, 437945654, 6020921, 729431336, 533267831, 217314178, 471759209, 302776258, 576035035, 389551284, 942527637, 363957460, 339688665, 688310845, 245026414, 547848368, 359544435, 209283501, 534022572, 304272073, 648172356, 512983000, 714866394, 276205968, 247849239, 574988049, 833057938, 145422136, 610025129, 77598539, 690235033, 973033576, 967486160, 774832636, 433934205, 926497678, 897744057, 178762928, 462917825, 865842059, 606066114, 10055824, 309103268, 937428452, 1911813, 337753964, 339314403, 202269534, 604374392, 687250077, 235195695, 260059246, 116953541, 135245500, 774175494, 822243509, 737749566, 245803252, 833103702, 339552985, 532588229, 565407475, 543544240, 648855807, 79879879, 501580694, 334964140, 565941491, 724537703, 47932255, 163393332, 808699491, 202546651, 484258947, 854942543, 556726993, 672030567, 366419075, 676076741, 990535688, 275301210, 48235967, 846023167, 948000961, 227971173, 811745337, 161468853, 26717889, 714944573, 981324725, 724330743, 167768899, 933569070, 336421433, 725745071, 586363148, 163499195, 903537031, 386112592, 206969550, 829054555, 131445345, 389225255, 902953852, 992008742, 375316439, 465959605, 188107673, 584110087, 768238085, 721552440, 573408976, 940661599, 596714059, 877524035, 645244558, 487257090, 343665978, 541917281, 961583357, 93474413, 53317082, 564772648, 996218171, 512544416, 286449662, 281732546, 542695263, 84301095, 709239521, 390739834, 870508924, 600078521, 316679453, 624801467, 870933897, 841120126, 823763477, 611990147, 154876194, 411230791, 564858538, 751560272, 794569050, 861368787, 744090859, 637484388, 492152941, 176909835, 127894123, 350729072, 110586130, 277098819, 831763425, 839510743, 528236762, 845403666, 681034845, 978323989, 706480831, 231641895, 499495935, 642148795, 446158470, 496112682, 535565171, 259762421, 567966415, 963696025, 496045331, 68570085, 876815284, 974418880, 160214802, 144707026, 413696542, 1646010, 779145158, 177199130, 943659912, 473270757, 693500526, 609446288, 922031282, 248680277, 323919864, 291850613, 958461048, 210207959, 108234215, 124681921, 921711537, 358483525, 740269857, 589651364, 960407911, 264636861, 861962533, 738534192, 91247690, 936550851, 567738865, 1749991, 699542285, 988481635, 653378774, 75848275, 622196198, 924857050, 434187953, 741431889, 79033378, 592176331, 183426959, 277562449, 39990586, 261928442, 737379347, 958972054, 904930409, 266926972, 802480496, 350659733, 398412481, 171052881, 241805292, 614927307, 872688427, 405467042, 53784100, 707954727, 538334612, 581098805, 277803998, 76355520, 908835846, 925833280, 896263738, 961313780, 83522508, 556254513, 557686240, 750398320, 25732617, 711468386, 103338709, 595702804, 688670777, 653721043, 961509077, 909883901, 797334189, 873663730, 706989195, 227609295, 225004604, 948308586, 959209475, 309989870, 293041904, 413044418, 937813442, 284639782, 746300378, 428969087, 559910237, 538991065, 380671764, 280382962, 587720969, 414304008, 336646400, 199260854, 885028677, 831241007, 705882779, 152825792, 612414840, 903944038, 197352438, 518958614, 865625253, 790303974, 114079794, 888558902, 681844959, 921124939, 15416720, 986833323, 546079519, 848228182, 700649788, 218334615, 527267810, 360984803, 182526854, 237443138, 302947487, 711208504, 585113175, 782830047, 187559837, 844550557, 780715958, 309162202, 109419206, 865283281, 281320716, 937239929, 278954174, 452151725, 826729572, 157529890, 249782517, 89473706, 456380589, 513913410, 807808262, 789830057, 828497868, 631607301, 263712251, 127925239, 619785077, 727118510, 463943845, 6525885, 547072488, 242675088, 310744926, 857886018, 741883511, 421516239, 562294480, 85963332, 201875362, 722820444, 905178897, 755672462, 507731465, 730116961, 886210787, 865706283, 502071770, 835744904, 449421594, 981358039, 985471790, 433959125, 7214657, 545709948, 294435613, 227156800, 428495141, 898736342, 653541906, 412648577, 128457298, 569067505, 861413316, 504102249, 21112509, 908622895, 301067439, 437059686, 259432864, 561427370, 925960562, 204719289, 227775445, 756477691, 274774223, 505296297, 119898220, 857648874, 782814441, 599129801, 138308801, 652875789, 4433655, 195163, 755929077, 727012871, 867176026, 478025012, 875218382, 430651724, 967376590, 907059784, 49556412, 689449753, 697708473, 972164387, 514443043, 998613518, 91301162, 442900564, 455610951, 421942159, 740342326, 897178647, 872989181, 272350081, 777995281, 492554973, 39253882, 928912929, 446643330, 237870203, 561377880, 178181866, 648832522, 97051063, 788148791, 453776639, 857212960, 206929845, 585248301, 515694270, 557599868, 342230755, 199462768, 897263837, 700513815, 488367668, 518145395, 319099567, 402437125, 995643061, 225746900, 913729136, 79653140, 524869508, 163114895, 931614747, 471319717, 422262481, 433563319, 413851989, 684640722, 835624244, 800186666, 211444148, 315958465, 401210647, 74057530, 553479484, 307952106, 399538828, 581884116, 499316052, 245758962, 428448818, 199319951, 204051625, 635025271, 850342003, 544464029, 985267642, 944013383, 565651269, 845399721, 649269089, 318393347, 730252997, 642182171, 140485105, 41783786, 19942731, 245101939, 327886458, 816550202, 211876627, 279920114, 303914654, 469791083, 678541468, 288690665, 524032942, 691088776, 189155827, 979460717, 842132217, 793251991, 166034769, 27746655, 292269772, 995856833, 741453584, 329044179, 969884245, 37528377, 365974886, 19449896, 147044081, 489460780, 674198151, 258484355, 875888295, 914581410, 296810548, 321974413, 909974293, 449274149, 325057170, 510828317, 823991786, 733038263, 850807387, 660271663, 444278116, 710951997, 868570276, 644046454, 870970326, 220461954, 462832420, 933836741, 434426705, 888644230, 177601995, 606710616, 185950093, 158215840, 864107212, 356381642, 993763767, 231449518, 365919928, 661038682, 619633031, 621370441, 590828985, 984355059, 276668718, 11750019, 365395383, 11232727, 601703341, 611937982, 590398959, 174308987, 202402041, 940679266, 411264542, 552170147, 731266251, 766262812, 586897243, 145809538, 748748334, 143993276, 945408142, 948308261, 517671176, 898343238, 764145645, 14205569, 508113124, 448756712, 937750647, 44821899, 845070331, 366802204, 781693797, 312302667, 557189712, 590487365, 854431950, 425818177, 425096276, 158634524, 253259930, 425638724, 219468486, 165490450, 47578497, 584733802, 864440061, 983243830, 994478026, 619068552, 291302724, 545075811, 135186910, 351046902, 246556842, 358143619, 780536700, 595414680, 154568373, 609518995, 27899909, 648288238, 206544408, 530223360, 834610787, 650659704, 345000887, 248974814, 356702363, 448780989, 147944681, 726650712, 709980552, 481342369, 236432602, 458585519, 695350227, 407908183, 842954918, 410228061, 651170053, 384586870, 617897899, 908275448, 257877695, 691547661, 315326063, 814473462, 914449699, 436887180, 904594757, 936644744, 764159661, 216645870, 749059499, 768565278, 130036963, 308407817, 52920635, 485257467, 60093988, 765991268, 170011774, 108857869, 611256276, 244564658, 232117472, 573804698, 719430431, 652632022, 232421244, 840699313, 585170158, 508454857, 586139662, 588969820, 773143946, 253598438, 818759248, 54454185, 295515854, 628307780, 863850276, 82007080, 459507159, 847960891, 869825036, 383701938, 523987906, 765435309, 501348089, 896138115, 333598874, 364363661, 728347343, 957504261, 641691260, 902201447, 410651512, 99206546, 973867167, 54832968, 740468104, 63559590, 718729220, 945793131, 442526869, 163925513, 549176619, 784639840, 880745421, 120579670, 188177339, 868922603, 478375131, 463034791, 976092282, 62926669, 606257253, 429079936, 748916628, 65995304, 660311560, 986365261, 124367989, 734581803, 145743472, 65308484, 60642998, 127532324, 614614490, 902216504, 18796187, 58629725, 525637533, 360083386, 768669177, 409636969, 244392731, 847210471, 559943833, 412359221, 237225109, 298423711, 529467669, 422618526, 33035648, 989929882, 76865922, 743199014, 929906948, 542290244, 794441547, 694564297, 584194870, 525022984, 940170782, 414955741, 389743633, 373126497, 595755788, 400475254, 540562883, 94075246, 796547248, 882839728, 992948913, 581808210, 318486189, 932590622, 470676417, 48237284, 4907135, 922355567, 850677979, 119560217, 934434666, 738494183, 462781732, 224339550, 456921714, 542028699, 909531821, 555719295, 589297350, 473234754, 268819017, 809841216, 382510187, 294347098, 551920461, 771365169, 428071040, 876066904, 393680344, 867008916, 984882175, 964514000, 237257173, 942885840, 877687785, 344370631, 562222988, 927719083, 91800879, 288741066, 110317142, 848919765, 622057861, 89348241, 708395029, 732466463, 3436630, 118410857, 843366493, 114154242, 110624572, 636449323, 529788070, 2470819, 181723179, 289364960, 748189652, 873392978, 395221627, 13447651, 299316939, 438375455, 325519885, 35432492, 235085565, 180651567, 682994622, 752919986, 361438767, 18206286, 262926483, 572427654, 737462257, 898298740, 604452893, 685454043, 45584238, 725920177, 913284281, 631771346, 373318064, 479621116, 953969669, 733642479, 455928146, 374129804, 868030101, 89395769, 560815324, 406389767, 440918938, 581310353, 698289022, 550451551, 649193824, 476453901, 763482620, 3676213, 73125635, 905261189, 623862024, 869828413, 89967145, 432062799, 764069087, 170331754, 980928308, 137134459, 757061861, 166092770, 45297890, 573004200, 57109274, 698870111, 969865473, 938735875, 303567485, 27129400, 566516889, 330061209, 562483449, 691075883, 885548834, 975904837, 801534493, 722980647, 386734640, 379253732, 895016809, 922013087, 710939216, 625854275, 13164532, 44208672, 664433898, 824170884, 184314517, 824523496, 807383137, 188946887, 684455845, 302203271, 839241375, 328215688, 987347080, 723386639, 856142468, 333687461, 230728761, 755145498, 25205608, 549681577, 682285656, 488514332, 193337700, 104556354, 665522019, 834807517, 81244702, 776219741, 173058315, 151449312, 199918946, 221483803, 525461346, 955384699, 415286094, 338355086, 2442884, 928238328, 416858139, 182171988, 769635675, 718569520, 616829294, 338864769, 341156871, 907944717, 905976308, 783101615, 659680199, 20249801, 318642370, 848998400, 379933130, 892697310, 672100711, 422155037, 155673210, 191465314, 26609122, 669764705, 518475374, 307333299, 690743880, 153520552, 349657074, 930830167, 738780040, 743562613, 811799434, 598733845, 881396813, 837890569, 713100286, 478064726, 302629341, 742944455, 477785061, 309262715, 753180192, 325930125, 342609380, 438116886, 264438293, 760040353, 649392373, 218947805, 889504802, 692742792, 616026884, 216853965, 596400480, 607800821, 333149049, 183030673, 151811807, 703534650, 14589616, 514998014, 911241143, 544813206, 814691937, 389383523, 692567546, 875938303, 313202064, 65139533, 166028395, 620883836, 232290679, 331914638, 984517302, 88314595, 872001731, 868958586, 265041792, 73977727, 371903479, 622260828, 647485554, 250149017, 19109683, 704591541, 596022890, 78917601, 414506383, 906442253, 885711211, 647072199, 143664512, 129228899, 263085100, 42764539, 297413151, 408406961, 353535306, 125371331, 801776280, 965313300, 578042591, 648577839, 506304546, 815588687, 942982540, 150213285, 749254560, 134202173, 362045920, 328778912, 157621499, 1512144, 981573368, 753597292, 846763927, 305999988, 29992644, 851829997, 393098336, 799781939, 270093718, 654079995, 59888143, 970606424, 262244629, 567345785, 879711185, 859953799, 749403467, 704746095, 566282981, 964073068, 530379014, 855718823, 975047136, 739584248, 765104136, 641263605, 100185194, 569997940, 63556144, 107597757, 640803035, 121506996, 919640122, 65971145, 220207847, 729898743, 907123974, 954692979, 868677648, 442893142, 826740159, 375795160, 517232742, 88270513, 137603323, 539195609, 972582045, 388375765, 198007594, 373045581, 219041888, 999581171, 456084355, 827704825, 225177117, 475945967, 655612941, 824626447, 470284750, 338573871, 84447754, 183727913, 151494865, 596753197, 129507058, 670461015, 605036470, 57104469, 181402218, 409707583, 584095083, 3488703, 897223231, 446801432, 249294565, 654647221, 944317583, 413425606, 41052386, 225131584, 109912958, 102045546, 188403176, 930287119, 535736536, 495209834, 183219953, 925421256, 363157704, 551296872, 469471278, 565532263, 503072986, 780911642, 819156150, 76691364, 87832245, 179280537, 997200603, 203696167, 712960503, 777141015, 110822880, 403934604, 345282987, 974916987, 244766223, 457380010, 406765849, 208990481, 599774994, 939713054, 80244401, 176659101, 501261395, 168730694, 949211239, 145681810, 125367582, 177200689, 618854999, 980933486, 462759470, 28344385, 466840751, 34222417, 791842665, 28929276, 995504004, 466183425, 759268106, 375723867, 201924384, 496552550, 14159744, 397909817, 825875102, 542916218, 880016501, 210202996, 686763208, 172047353, 511516953, 976591445, 753120531, 63611053, 716540527, 807773657, 117821213, 408891686, 219162189, 441310518, 553644166, 25271707, 616760976, 812074961, 931743754, 140032077, 416202029, 442985046, 809187763, 109299428, 641283496, 227159790, 191609151, 510892972, 610342120, 677119379, 53513882, 76991648, 967165007, 294805396, 805823631, 454784301, 929658936, 925848335, 436354426, 150465365, 700202652, 111207703, 975622561, 616310664, 801493013, 706139130, 510447241, 436139143, 611311249, 269793743, 141273077, 825697626, 751078354, 133835872, 355046970, 280104385, 757991727, 402906619, 707531588, 555770754, 921580747, 904986352, 58046345, 18301937, 914045328, 118807565, 651166315, 754729303, 196369299, 6375339, 304437740, 684679369, 52745786, 90748873, 938978282, 238811239, 552968826, 329740795, 150335934, 391576774, 266334416, 456757832, 868186268, 467558346, 42322678, 341456534, 228678953, 428903566, 251269272, 827479838, 132100830, 759662450, 511480402, 792390931, 438759244, 95828094, 875356646, 554437873, 337086306, 324284338, 642307797, 91713170, 174330306, 602737056, 697745771, 261886878, 653281205, 298556658, 626279925, 722643824, 878443372, 407377679, 813008558, 823846346, 834917236, 865061838, 679646165, 306295809, 485433188, 383840, 294527741, 277938425, 615298134, 676610393, 988525984, 536945956, 240193513, 430282527, 746601064, 147336597, 279921389, 171126234, 789650002, 614093776, 160377875, 593407804, 288999182, 840386808, 269292459, 488581634, 136053081, 77585303, 512196813, 475887903, 415605969, 1951607, 797044437, 828077334, 838124258, 740184448, 598603022, 32833589, 422057858, 547426052, 698544973, 111701125, 579382742, 122196473, 111568959, 589267445, 757409624, 390030571, 525608267, 413697207, 31851449, 661203531, 58077284, 747175201, 475500759, 978273483, 489853796, 213781064, 644685182, 205863063, 210524559, 606841330, 587135132, 468502326, 285201459, 116842655, 453732173, 39095910, 601424878, 184162274, 421911695, 549611855, 8717597, 235729345, 378004380, 483402533, 954657708, 135095644, 636422978, 452032684, 621711963, 210477624, 45204217, 525555853, 689307869, 413469466, 711599580, 868972855, 456359554, 280550338, 59066000, 371261205, 697699987, 268785376, 690354237, 185544356, 330111771, 905028788, 491186464, 79703490, 473283525, 733187305, 853348352, 662673903, 537984892, 942781515, 438311425, 798965462, 668456546, 90739865, 429245730, 490878425, 421546250, 432275594, 305037229, 299607767, 218840237, 177050803, 693484018, 723283639, 48749238, 211463856, 769589920, 214847796, 979621834, 560264547, 616956302, 465388823, 288844681, 436882622, 683347099, 422542399, 356825658, 212176580, 298378487, 293583048, 359822383, 251683701, 28407227, 149426507, 306732176, 15173683, 175145276, 113517312, 509484463, 394178429, 668863267, 814895813, 12380733, 572823168, 589189751, 111889045, 444483268, 515280139, 214350566, 345391973, 393341703, 85643009, 543655826, 268795262, 842487111, 109173651, 429360775, 676751586, 42601946, 55863209, 245650157, 394614710, 497337180, 884005077, 896062815, 172430500, 141689731, 568334817, 782027809, 89326566, 420371763, 292610956, 283740748, 818774322, 350527930, 73722725, 902551068, 601671030, 521971114, 358149081, 148026110, 497173930, 355910973, 436938424, 155489836, 11557887, 413447083, 81211063, 354008792, 303518571, 525143068, 241822991, 510899796, 998982931, 608354683, 244884818, 635023158, 207335075, 470104364, 396705467, 168834080, 369574005, 86392469, 33992025, 409520139, 20692747, 806041443, 730487277, 460173579, 983154476, 549320904, 820180658, 333245032, 882339052, 30879197, 511678721, 634495552, 520244486, 513142198, 729199151, 25472512, 201065791, 532734493, 757921757, 628134019, 909860950, 749286469, 896216443, 850884079, 437353759, 504984830, 689809024, 575630004, 713067891, 618412983, 583034179, 717259718, 615330505, 229018949, 436637440, 161560527, 365069180, 715826588, 653417211, 217356668, 858293010, 887722095, 547910807, 782892317, 285618237, 527566901, 530017052, 658856533, 159619267, 637233813, 834495691, 680075443, 420772750, 319942851, 465014173, 418599869, 426511280, 415459195, 94122077, 324861439, 879212434, 441214941, 525927740, 337268422, 30581803, 730924599, 436133651, 187731175, 633100187, 86072684, 444143151, 622093648, 393906815, 852718040, 564573762, 772657369, 849562385, 572813969, 565833646, 179840076, 225646476, 419639368, 458140779, 645566402, 140630156, 295942282, 576914621, 192677309, 150194495, 205318684, 814688919, 798297996, 281853164, 48202839, 558442966, 550983169, 658387497, 679955119, 549044762, 476574912, 252753407, 403797507, 457611334, 472564289, 454397134, 287494217, 537300482, 935737914, 821153677, 308606385, 886289974, 200506127, 39678159, 391677812, 830859282, 987948065, 187821316, 343955961, 549003004, 933983632, 740680176, 715581983, 798981569, 248968501, 227569033, 523833979, 851897740, 612781754, 153437622, 506789545, 650885763, 798389540, 184417718, 356114699, 60646318, 196757871, 480765340, 569295451, 843125291, 537346363, 5214279, 609505472, 105198900, 918377065, 570184126, 719092933, 462758633, 558449109, 168279603, 835960673, 324988075, 540515715, 816920713, 201340343, 120212981, 667710326, 249778753, 286193764, 367712720, 23313134, 291401967, 63009369, 117816109, 297055052, 947700754, 494538460, 869134790, 233767029, 353732050, 463957737, 878609213, 755959513, 501897518, 908059986, 57144176, 817297153, 274232155, 146294697, 292427301, 649559062, 784107739, 386005827, 809494612, 695181097, 840547743, 194995043, 298999874, 371571118, 653979148, 933387335, 572391180, 925155393, 123476997, 452155446, 43132617, 241393774, 164553242, 897903469, 59332467, 531801601, 910609249, 611094918, 490249931, 409343131, 984721989, 866303406, 165927117, 913054422, 498541403, 978915376, 113004719, 463429222, 294952394, 634813642, 217847645, 697947697, 663178571, 629138889, 316651860, 398687937, 140322116, 108288656, 883186049, 517748867, 813620131, 799584522, 400615893, 486423792, 269355446, 183260952, 70739271, 895619162, 190938360, 176681460, 554712240, 520935414, 814847791, 628619071, 183078702, 329667756, 334627754, 758302817, 847462271, 411529428, 941133039, 951242503, 412040626, 9875056, 77815137, 698774134, 584076066, 228688060, 691952866, 97265782, 712258207, 562333966, 458343756, 809356215, 850607706, 22338003, 415495845, 150054917, 130619168, 378563332, 949994039, 220462274, 95113100, 5035141, 671791568, 880936077, 434468829, 311621397, 422683112, 832340248, 881753386, 236935891, 685468364, 280103294, 148366554, 539848934, 402968596, 392038102, 444341409, 642622946, 343032768, 437557180, 325609608, 251030849, 95391899, 826938474, 310296221, 209571617, 827076296, 908120898, 496186232, 564994543, 484491695, 446422127, 97228831, 358101174, 760009746, 154155688, 330946799, 428331713, 28344188, 288968611, 441180098, 91377547, 55561956, 613032116, 948498259, 770962831, 299354587, 241331845, 515417679, 500278855, 120134717, 60017847, 951036685, 719685712, 400441287, 886958866, 933003955, 751286636, 225999713, 709975068, 777504630, 681355758, 671787933, 160916858, 176004485, 862190316, 392931620, 363087931, 502038098, 144484042, 624239110, 738535168, 974553790, 845870906, 837568992, 693236019, 588977027, 796886384, 837096777, 324531231, 287591324, 310856227, 32838935, 588552283, 984418659, 946456083, 355309359, 554351835, 349501908, 361627442, 716390578, 721921169, 564946421, 894651533, 710714243, 568745732, 549082672, 82176432, 656495173, 41104907, 584874827, 505415459, 669789745, 420649209, 565810536, 988960696, 415629604, 148906476, 964221426, 759199200, 6776992, 860586535, 710915404, 655831603, 420772342, 308553697, 304330536, 658557129, 543036700, 950861877, 789021246, 441820983, 284857843, 748813540, 623181016, 542736146, 749060676, 775939356, 895776837, 944374791, 812548734, 485276027, 683938259, 65449626, 423311656, 672251975, 873880276, 390649747, 866361982, 427488421, 472200972, 498769569, 914847230, 133094131, 855933729, 828873647, 277540931, 824258239, 132336777, 991115143, 578693398, 675235898, 352432649, 985014635, 146137744, 129556322, 80406925, 786493602, 896711242, 974580259, 463204779, 230505617, 423626012, 686630101, 440145353, 415660717, 53449133, 368220985, 40523609, 105817449, 971740352, 870587062, 453441801, 694737120, 869460836, 535655027, 724172206, 30144438, 109466432, 22653391, 558718451, 52074342, 71691733, 787428602, 322213195, 517359385, 429546903, 215398782, 969107067, 512641695, 531903725, 57082260, 219938740, 157258241, 745134573, 980519766, 858949007, 355562791, 178149282, 325167500, 753099565, 539861263, 747345313, 625212590, 74824508, 610763401, 842361756, 711159237, 359574419, 946684942, 849928038, 397677441, 177890643, 522522715, 992070390, 523531424, 374721008, 276469989, 523461760, 155551215, 247956480, 907305559, 39628367, 522846145, 788034012, 406622892, 39444715, 994030287, 338473486, 974433363, 535484362, 145694676, 493833858, 986753915, 380718175, 718317991, 663946271, 853337645, 389352240, 853420700, 244152908, 734329515, 761518748, 998245694, 440397073, 767750245, 348453462, 491924808, 202494430, 12633442, 415145769, 931052132, 290058584, 617608817, 755561337, 715409331, 167258819, 308992128, 933752902, 600697901, 912125364, 342667115, 849669559, 829262652, 240877422, 270133694, 48808175, 789490837, 645242549, 474398628, 315515821, 423056777, 131124407, 621894890, 735735671, 511022114, 966899581, 301274533, 184255141, 924477491, 509737403, 234261102, 711534574, 361085514, 912065250, 981262809, 743576761, 660433461, 921735886, 409268980, 151387983, 616921678, 305883789, 469931231, 607900724, 202780124, 281868105, 476306322, 864351924, 31080580, 175935795, 933666201, 639655435, 812575661, 751871133, 13978774, 146831665, 86918610, 7962090, 928340971, 348257904, 503731263, 731999956, 719099599, 867005092, 170136737, 740402322, 244459857, 583719601, 402277275, 270068533, 968133275, 808871523, 558944985, 223617275, 706925060, 227157380, 801754494, 492163447, 436241849, 767675645, 498054195, 414701522, 450831190, 948459590, 211935464, 625380337, 638692830, 453701126, 665403135, 106331373, 925623916, 233787975, 995430654, 922919806, 136683948, 559612349, 308319076, 585920857, 355089854, 664334492, 775741232, 824344127, 445912245, 436152764, 187159917, 725144875, 470330985, 210968211, 611198689, 318745092, 931915033, 884526178, 573941818, 64191711, 549893715, 32427447, 410773120, 796626079, 758033922, 214824410, 914058863, 863143395, 875805478, 613375330, 442589943, 232081333, 848023908, 742370816, 76557803, 47113418, 368639918, 915874958, 2250878, 809563466, 255662035, 577093663, 733777739, 111150850, 120533557, 816313000, 715405848, 602490107, 233001468, 981329273, 334534545, 704853234, 258326540, 906181521, 974435952, 190186917, 402936403, 56283200, 435130597, 96820614, 869340225, 16817133, 192086598, 724599496, 541190419, 705846697, 650825779, 129095755, 149200357, 605190195, 485486621, 668268106, 570967754, 537191119, 671072559, 234067220, 221488448, 134607803, 259921800, 272688299, 285128699, 553909367, 251696393, 301495751, 919863894, 996523086, 231602559, 285462708, 300217253, 938373644, 802558858, 668638741, 303816814, 763214782, 780367390, 321289088, 198309308, 219119698, 914391377, 200334269, 983346256, 668241823, 748324735, 108984880, 26709413, 729067637, 822017731, 936888597, 796791360, 814163950, 785727512, 177829849, 161082234, 499196227, 136727290, 974428031, 430224433, 702923025, 134101779, 571594441, 531794543, 807881472, 218234293, 65719334, 53890669, 513060823, 410030629, 448750313, 626096808, 124747216, 219502688, 973473086, 324565260, 420942275, 822582658, 996474013, 16799560, 966743169, 239422391, 587636162, 699178385, 132548189, 365049310, 239709326, 990520927, 654526440, 410991604, 141510373, 123614413, 288351748, 797520642, 767147538, 106981212, 303599383, 811609654, 608947397, 634563036, 13548818, 731463745, 953102871, 221859612, 203644468, 355616521, 140088169, 912157033, 616617147, 665191147, 523447130, 794176938, 705632500, 645845628, 956066244, 356073517, 107755609, 779608107, 141728222, 770782034, 715702536, 339584868, 837228561, 534459549, 299988042, 226358612, 975247915, 398267820, 387586879, 57589112, 841370163, 585819210, 693519862, 258262329, 856141375, 800366631, 35695754, 535158674, 345184048, 208781353, 907277225, 63048446, 953766242, 829816594, 885961189, 703917397, 951187918, 326904946, 118826858, 751673883, 265467978, 857808819, 296358920, 487674908, 633304346, 358761917, 615830049, 623175347, 37995046, 269956802, 459966698, 33134951, 723085109, 933617976, 424445603, 12469108, 184112744, 235129184, 823300809, 383716068, 539372168, 644026013, 124407063, 463756919, 514868527, 93582752, 5055190, 975282380, 406338300, 204785959, 610013397, 298090202, 795296373, 965708483, 35541432, 919709956, 741241840, 356032796, 795998245, 372834727, 678894810, 646630969, 335142864, 24831215, 537735481, 102009105, 607090308, 809309388, 205958325, 191149058, 912649087, 776302450, 10796242, 493232130, 993533829, 303818098, 934965744, 788465667, 276358496, 454690296, 864888514, 366565454, 877062413, 324555628, 614070707, 826996180, 381066463, 505289096, 338998523, 220882409, 729616353, 578620586, 392065947, 716870409, 926579993, 427427742, 27184771, 592318033, 875414769, 783237232, 841143950, 633307635, 418722255, 660420019, 788703290, 604254800, 254654643, 967655006, 105272687, 474316616, 367763469, 475389071, 711054382, 401487063, 386937506, 774644592, 300983469, 325982667, 516505395, 786576346, 87311870, 962374289, 523291799, 828627393, 867160994, 178076700, 899657810, 569522423, 323723841, 749871647, 92846464, 523603948, 866694645, 600476795, 674837362, 266937566, 943039919, 864842264, 314000243, 350736533, 566896502, 360862583, 583094318, 677907402, 128186849, 956955337, 930246114, 629007570, 897978356, 361038954, 957595626, 447154295, 899551151, 291556551, 313439285, 900380549, 402592851, 13133932, 403087828, 570751758, 176197838, 105136790, 670207053, 86212026, 117879245, 946663081, 913769558, 469911332, 665832086, 343806, 865705189, 196982499, 536279927, 511363002, 508248577, 489027308, 816514805, 343929532, 673557572, 46657624, 406947039, 358368625, 201242781, 421156366, 497449579, 65077573, 33458691, 289055812, 195463593, 138066883, 921105425, 655210536, 891488193, 534530024, 631571786, 814173866, 49449383, 505542919, 293063396, 182841745, 432053269, 768862542, 646816772, 851229424, 680498346, 287856744, 311021364, 480990694, 133653683, 99206030, 188774369, 693672949, 861108677, 784510307, 208714950, 144753534, 304972822, 997671335, 322007412, 856225577, 25613822, 733130725, 746314466, 784329798, 765736637, 952832884, 426530839, 256672382, 188961067, 354213075, 619308722, 569347651, 849550206, 683325821, 731642920, 154726509, 551123810, 752291905, 681880137, 799529891, 242552831, 131340381, 133789077, 254926733, 380953829, 818316826, 12105051, 389556841, 462643473, 806447612, 823417742, 471263881, 573932443, 173314500, 506434806, 366509210, 498994611, 239068989, 314550168, 858121811, 179245867, 219884111, 537567536, 278480692, 643357774, 409065413, 579668647, 660218780, 719211554, 92874069, 464122220, 600454210, 113082407, 4805148, 518271264, 347408788, 422991245, 51871120, 921676160, 339928379, 988017048, 444769757, 202879565, 467739390, 564304958, 997853398, 344361395, 345713282, 99138151, 172803087, 855391522, 618312384, 819381252, 826644899, 31996773, 14090534, 634237325, 494297054, 604212526, 798275541, 178630148, 582781664, 970758127, 599221727, 942844073, 512527028, 590720034, 955021038, 964539553, 919175344, 435660301, 540138665, 395703965, 390354845, 412418116, 891204693, 143888605, 220709844, 730648985, 151668670, 919579167, 677118162, 256055746, 449403405, 936607295, 816833776, 443283414, 745169447, 614559934, 900859493, 290561000, 475741562, 475462725, 572037490, 354901097, 387655224, 605398084, 924578994, 808422995, 269086095, 871772501, 439348969, 289203779, 126259382, 425271436, 778470775, 585949633, 628923651, 944425527, 139732771, 399015015, 672457312, 691493920, 513807174, 81219734, 206660834, 81097583, 739578714, 497075205, 733911570, 789130360, 456190396, 900897085, 597297239, 55191381, 819842156, 814635345, 186544401, 826929067, 574910990, 900838169, 604058232, 155289259, 197527674, 587697887, 264074907, 543413682, 285433118, 810903335, 501905644, 545815814, 423359769, 782416982, 452495734, 92190067, 426219851, 92446683, 656048416, 655791127, 642454473, 116209358, 219106024, 426900383, 816076499, 663105437, 122016590, 590885893, 299355424, 488514854, 234427954, 286210564, 932569054, 103183662, 438371490, 304584672, 451636926, 902250845, 219070633, 991349593, 107540031, 985045145, 918107542, 204205485, 304987894, 865145298, 146024657, 486014896, 125966659, 156442938, 388389447, 841898798, 756448355, 245575033, 635776937, 605144630, 105434198, 382498802, 121824481, 268305965, 892846416, 482010046, 638849718, 881662827, 632649392, 178978969, 535652270, 291081673, 726460076, 337185926, 815618010, 106179472, 385508894, 964164520, 373275948, 746929516, 986427216, 531649378, 181219675, 405871256, 73484334, 503407293, 177368468, 713171863, 902478428, 988255851, 715212151, 609822308, 487161438, 28460442, 416119922, 792854725, 359826769, 697814324, 677302786, 51528803, 299838471, 293174663, 691164133, 274702588, 615118335, 551591635, 447276670, 28902284, 611151576, 219783885, 322720458, 729520320, 943123755, 912307943, 657826513, 377952667, 759840823, 58072984, 949974188, 242752068, 733918224, 215116497, 328382591, 912238129, 669289893, 145761910, 603384808, 727505080, 646194360, 16524114, 19099139, 785911189, 612351229, 737103117, 206566689, 575888852, 654393188, 383247536, 281582320, 293824323, 387535661, 16015739, 485401484, 584686425, 377314631, 555229638, 603819700, 2259554, 57951093, 690569314, 86753662, 839446234, 180438010, 511651659, 599259879, 279221155, 49059786, 716856186, 743295676, 683629444, 345381108, 530390205, 701368377, 776696342, 952287362, 348867064, 812346826, 165163229, 924177135, 112024498, 101735515, 578479508, 402875450, 938237979, 280953784, 17329016, 302121545, 774345878, 520791425, 382728689, 244120965, 288804644, 770726408, 277230450, 199355469, 586754339, 382375007, 617469777, 118130995, 481560789, 183357076, 992920745, 988092367, 270106016, 824338422, 198223559, 327450790, 8059015, 935131481, 685760260, 990859961, 653564020, 451276612, 798685563, 766682417, 639560165, 364556147, 706405726, 758813381, 867886487, 371508900, 597135413, 169817525, 852124001, 824379262, 911158080, 679431976, 738251795, 672262338, 907573043, 818162508, 440161735, 420880156, 294303227, 198342583, 947650990, 600425276, 69052031, 726149765, 959824919, 332184081, 830423291, 346229477, 923625842, 916016147, 549702526, 975400008, 43811044, 959086069, 931927007, 1103570, 73173850, 144883319, 91023573, 951163490, 447053392, 654288858, 235073767, 522973424, 274345957, 516841047, 746915894, 310286927, 567555611, 259457723, 807565701, 119200417, 415254700, 258748663, 97222799, 174584042, 376652580, 722141486, 973776794, 543060479, 794673602, 878799997, 997266796, 348237856, 599226424, 975724492, 154912390, 781964810, 990544063, 341568811, 44237627, 810952127, 582725696, 459304665, 419492848, 903422413, 180942241, 276482406, 724341474, 339874849, 891791463, 938386257, 938580435, 191185874, 948139787, 747349724, 22791483, 765256738, 280972704, 488943026, 553256341, 927550279, 243773642, 36373727, 766096306, 870299901, 831849439, 898202736, 803690064, 179539401, 987052605, 56721406, 171281331, 95766156, 603469651, 273740332, 609962361, 458147809, 268193681, 307448168, 68662315, 606061622, 807669117, 28733582, 972376295, 691575466, 985383946, 374219253, 401136128, 264873030, 857425655, 254928642, 691511837, 30502128, 443235156, 666000496, 970362694, 998753769, 299610648, 595216540, 252169460, 268854714, 984305050, 105978795, 119543423, 808010422, 798414781, 461460673, 139356154, 264155802, 713597028, 594925494, 275632420, 633255872, 685227632, 767159508, 73802220, 400042812, 64153625, 913637107, 347093451, 119306877, 568346109, 751019877, 559413099, 580705038, 527604955, 841245191, 817222687, 450874580, 574090017, 150004155, 570011997, 249997823, 835129135, 56646457, 67856558, 83202921, 757586051, 945697385, 301652108, 528783508, 922060145, 310092713, 684105875, 269724155, 996367667, 49705868, 655294557, 154345170, 821217577, 782001347, 161538258, 193662960, 68928598, 829048091, 986550159, 983559756, 198202532, 96780454, 45441486, 866421842, 146262334, 890149898, 884058923, 920835898, 749405158, 668835225, 736899974, 640747261, 242989105, 637697706, 430275172, 550004069, 277246982, 351341735, 367860916, 217851055, 356320966, 399348296, 730785027, 408662961, 186180618, 277095482, 51613420, 606447618, 535088035, 816848913, 55428221, 406312251, 173252508, 22503027, 150230107, 201646113, 100752159, 76012757, 654304308, 359266390, 968376697, 248657324, 613286305, 506644738, 159682642, 8510101, 349765461, 396214237, 388662229, 10005728, 428852454, 283663661, 127606926, 634674734, 824713766, 137765501, 884832395, 934366370, 509120199, 737491621, 651484440, 725613953, 719798305, 274221143, 598652927, 121788469, 643193460, 954508317, 883135142, 878551801, 673718681, 177871973, 18996494, 924636547, 831221627, 839777237, 409445380, 403116628, 648872107, 156392185, 435820946, 420349051, 558914759, 716281382, 281805537, 947767207, 692277576, 956568374, 227209994, 787804211, 175991607, 101445772, 256393418, 571436156, 999588372, 90098459, 481438732, 266304769, 435867529, 73248658, 286048211, 329564236, 147203674, 355351083, 334143359, 277070428, 160382652, 489036345, 254458691, 311613724, 28742581, 12143110, 473899517, 571183021, 592781562, 760468893, 406806514, 917143464, 129759954, 339078006, 454701243, 370858116, 501819180, 901793594, 616824572, 90527543, 903276074, 379121523, 803939266, 364974414, 405385898, 476697974, 857984449, 673634659, 590310820, 427138727, 140096934, 96614044, 214749221, 107496783, 670014282, 48227635, 220000045, 571978553, 211564881, 690642828, 910488385, 668839517, 356957905, 496388442, 856567496, 10831952, 972047210, 595271054, 161908793, 328459913, 551379864, 489368891, 524234963, 135230111, 511514954, 196711133, 852276424, 241996166, 760541374, 665549244, 675457765, 338958087, 793778960, 410161086, 405691110, 599280499, 761480500, 190052610, 735870266, 238377224, 875781772, 405046180, 548475587, 315987615, 887010334, 644507846, 888880131, 935212145, 482364843, 611446989, 470979687, 897994301, 980055765, 961402941, 772722617, 751374266, 937819141, 707510526, 558774510, 57505867, 453981893, 259242169, 925798598, 99415936, 502877412, 275201029, 360192767, 36561962, 137703873, 226877076, 856081835, 967867282, 981418147, 561775583, 600981805, 685980979, 155530095, 3150681, 986915617, 37137907, 825496818, 239856622, 831138663, 232755685, 426351716, 132660230, 537826865, 80249025, 370900887, 231633487, 297136325, 800396674, 263286647, 936148903, 743352892, 110889707, 829449113, 545974526, 118602438, 312611132, 87022530, 161275851, 681448316, 944211921, 870091514, 680480366, 610238170, 186385254, 950913333, 221422420, 361712178, 252108536, 949033565, 254074481, 185113171, 635951544, 116580466, 156482974, 462114850, 418213814, 645987297, 560844207, 283695379, 842266065, 949004047, 219522389, 288367018, 277287956, 370891690, 426761801, 264998913, 911181319, 179426237, 790234328, 565200946, 117851544, 598897487, 149428296, 192729059, 391194602, 48024410, 307636181, 67495444, 442406221, 280801923, 384660060, 843049901, 217111110, 176819660, 613923031, 678082357, 376018174, 323675171, 311356223, 501969378, 366839209, 466015296, 922114405, 572947484, 644046587, 262504779, 91527124, 713580148, 547925030, 609164093, 404329544, 910031762, 997446273, 425318611, 573059458, 868837503, 87503605, 472281054, 963933428, 531885653, 176027871, 352498651, 245468047, 29478418, 227251295, 326103028, 424678632, 182176080, 125578822, 258987792, 683779680, 390772662, 350346438, 432459518, 392171039, 727511963, 871979778, 969429828, 493513182, 279148693, 441996283, 408935911, 642761043, 579814841, 15604220, 840073097, 650603244, 579073510, 929317121, 610537970, 674987653, 910144727, 232369636, 866828388, 24882692, 748322055, 545636917, 617046799, 77103822, 467072794, 12341934, 967300508, 113626557, 891518271, 528808018, 336586100, 293594462, 61738626, 3669749, 424932038, 197377201, 445504294, 517183760, 993653398, 729576295, 249590652, 919444191, 872224318, 439183508, 486323228, 203256997, 774156838, 975617567, 256880739, 927787281, 727676552, 913049521, 794899667, 774052018, 211437596, 821998320, 637732103, 991519125, 216111207, 921628457, 373699181, 359365498, 341867021, 403488663, 304399777, 348900933, 628531804, 685646292, 45465952, 667488448, 347151922, 350871853, 672244779, 778920120, 878618456, 776700179, 204631356, 945362047, 481727801, 673222584, 4432643, 282932646, 956294849, 721001540, 537752855, 52204251, 693561426, 315414948, 81218379, 7327039, 782753908, 335999798, 244223817, 138546270, 319731027, 103479440, 363875841, 81985597, 731200424, 254810363, 118770146, 942547393, 736475817, 20368365, 913121630, 592840727, 979578498, 700800421, 506934419, 329432881, 605842681, 918766590, 949934589, 971938974, 768173547, 925992809, 627041587, 297909055, 207572444, 431318208, 784082939, 160375883, 351941007, 778682385, 737716660, 476046338, 33366079, 788996761, 929242776, 931179596, 795724784, 499979490, 393449570, 844529963, 120466407, 568014492, 620208404, 195351710, 895353698, 688241650, 603585731, 223950393, 891712439, 149717292, 647417334, 755917841, 31066113, 74006977, 860613498, 919235425, 645174984, 912059016, 155300632, 250228991, 416366849, 22414288, 212977655, 79789639, 532416084, 143223555, 398065358, 368061365, 139225062, 767394614, 143701616, 281973871, 840503049, 126815138, 113602774, 877740509, 498169302, 397073048, 908511913, 585941801, 663707880, 629765047, 985698277, 469849299, 954744533, 960781451, 919839701, 84730887, 182534658, 405590371, 360574177, 695370688, 94453001, 765917009, 276596558, 934814354, 841379541, 456854123, 471391733, 819779873, 525507964, 356640221, 475669035, 390553668, 100009502, 604687364, 769067667, 566692247, 332211286, 476742963, 482133722, 155473491, 471287437, 689531704, 730896820, 94517700, 408927946, 910526098, 823400869, 384394352, 638292111, 403135529, 854821164, 528324246, 319008872, 786666749, 690339140, 960958815, 836982967, 694135304, 956184280, 758468916, 703258162, 102610437, 856929513, 833159847, 441271163, 510682662, 855144256, 955837945, 641340033, 136258130, 809257012, 983258850, 758576374, 656374959, 687613463, 531858921, 873482224, 534276592, 269169445, 766168079, 482149861, 640346818, 706434308, 978608183, 683829258, 326579777, 290019066, 777561309, 779868319, 938977518, 317885813, 952385334, 574230698, 564422725, 782555569, 253640900, 450876807, 201305541, 471077483, 475138009, 870307518, 65947847, 858975905, 343067116, 830577577, 488790527, 510202829, 43825893, 588849953, 290514341, 102339290, 761973143, 756319946, 291962254, 266536622, 194143026, 66540550, 13299778, 699012986, 341476575, 660385749, 589448917, 367383485, 774265071, 976807279, 507343781, 191210198, 23189248, 849097363, 182493471, 528593111, 781009202, 563753299, 175387815, 787360904, 305641960, 960516825, 999609220, 294515957, 129186391, 782419357, 996587381, 891904351, 665884266, 277426834, 495613679, 110111624, 680070783, 679619356, 601603604, 321820659, 961406154, 459643178, 394464575, 429853513, 675143248, 228744022, 418902196, 767212934, 187525594, 849845205, 37295060, 708937656, 195580270, 301895268, 394687634, 292273426, 193510115, 904854796, 65540453, 396157923, 93786939, 636060655, 621493333, 711367874, 407192082, 562837899, 487921508, 580991280, 835446169, 503442540, 491532180, 907260061, 248454971, 668081161, 167596155, 17269610, 410954788, 619164991, 35607487, 640541250, 455910813, 120860142, 29391097, 815306675, 802314803, 641970011, 300015158, 810038586, 410480562, 383377829, 584439795, 102521554, 971303721, 216081040, 357851489, 375171962, 685431872, 842233505, 822837125, 223678311, 259027263, 325825015, 449202288, 36197287, 308434673, 270803335, 877209324, 182011070, 930223754, 637506969, 554424841, 739828104, 983695798, 140690184, 410321332, 523467683, 643336007, 188666293, 541570713, 363625587, 109558601, 573922025, 972924010, 585582857, 707418011, 413502821, 133277856, 497612088, 343062781, 608834452, 220360214, 17560425, 257544816, 197351574, 706888, 601096235, 569149810, 896936867, 873685085, 845674841, 403480942, 870215749, 263121914, 851672876, 882781561, 539159612, 238403854, 813312835, 835083311, 302791951, 947808448, 185469031, 543162329, 702674547, 477583543, 340980690, 823153508, 523777869, 50104172, 704321185, 116433931, 435853847, 262384141, 668415671, 259777422, 521802039, 475044427, 913176426, 325456338, 3327142, 465410596, 138310202, 518860767, 842316283, 63456631, 650101193, 423895028, 33962435, 213736298, 463143266, 793991464, 396727011, 850893084, 801294694, 959890743, 490356437, 635954698, 800788664, 992136587, 665731425, 95859235, 695347028, 243079274, 204051741, 542006295, 134029312, 646725201, 529159579, 43265303, 771021227, 934038118, 601731912, 994672277, 738118689, 818841533, 840128159, 856908235, 77962828, 911520917, 814265863, 163224544, 905302090, 130010179, 472811984, 945010108, 620039782, 283358563, 699128340, 670231327, 383175912, 427689271, 437439370, 326712559, 998603668, 817313097, 507578280, 286466307, 437811830, 347491990, 314923622, 945680745, 67581518, 263570065, 742095544, 316493383, 316712652, 595007802, 422985601, 480284696, 917757832, 569657180, 167216158, 509734091, 455471280, 251871912, 741575818, 281366398, 630259849, 600503067, 309324890, 586011230, 148589269, 450535947, 434841564, 29905058, 374461067, 672080091, 378898519, 206692095, 670310142, 739374841, 751013502, 427980164, 130946466, 284668659, 244365954, 689228545, 427382850, 310853258, 938380752, 933165540, 619821559, 335748597, 546999728, 462844129, 454259970, 407983802, 503099502, 536179891, 448412610, 667113745, 356804949, 791055758, 650389337, 879792412, 193840056, 28842253, 360094099, 704946152, 643252758, 151700516, 866443267, 737055737, 566914204, 696935309, 649366427, 450157780, 214431795, 215279310, 75839590, 351284487, 881079042, 57133089, 940979590, 250924737, 210283215, 498273879, 453343825, 595527736, 597056839, 306498671, 257750442, 812827705, 78055511, 557534672, 252924486, 904320893, 534166678, 758276614, 369238546, 10903530, 282468315, 982067187, 859624109, 471312057, 406989484, 619469757, 571287910, 136743768, 952618535, 489220410, 410707683, 804765457, 256721998, 599648877, 188062151, 842477697, 898296995, 695815515, 867369464, 407754319, 227869837, 339008176, 789196855, 218847241, 108192230, 189958076, 792319302, 856042407, 821664041, 159107932, 528668122, 12721276, 617120148, 934026704, 751635267, 278468088, 754936342, 563458131, 5957047, 259818451, 844661481, 438399087, 372999106, 358139503, 35525278, 197915643, 788775824, 838095055, 80187576, 153525385, 591816182, 104918731, 587857013, 764375978, 511418610, 506260079, 49256876, 298519624, 39266047, 892221729, 164409773, 271699943, 701288309, 316960629, 443114874, 847265564, 595196228, 117196650, 700530958, 591363252, 893980520, 950367221, 816531825, 943022573, 202264114, 903979, 319485784, 579023138, 935795519, 694001692, 229752298, 592595087, 180166705, 455820806, 321253607, 972082394, 316822878, 991781310, 577806178, 731280716, 687988710, 346164189, 471307243, 964049928, 708666612, 278088804, 176358342, 83150636, 882532126, 452537870, 798813651, 318787614, 438240123, 759609916, 8393787, 73853351, 564943900, 555605448, 187852177, 3227012, 759092817, 995848896, 738595173, 177044618, 578094674, 338707233, 431348403, 369939932, 260441032, 909420075, 885497438, 607160396, 893332633, 923260328, 630181560, 597231053, 834447059, 765007461, 275014831, 531389444, 91829161, 834926098, 301856913, 967762983, 268751069, 46288426, 294963747, 493842935, 194697491, 518269343, 966799262, 16651755, 71156904, 61041453, 672283129, 325903804, 806742416, 57073877, 942437062, 116293530, 950586170, 212665306, 271926952, 854735356, 927039129, 904850965, 678888906, 220879972, 494434256, 854649117, 326229768, 127291914, 9156731, 831532522, 113144235, 668991358, 101020560, 783131352, 346062456, 368721004, 463305645, 910865877, 878230795, 897915046, 138350015, 106282835, 767811961, 415689605, 326005145, 538189275, 965792488, 38087781, 47054307, 882051309, 365356631, 957299081, 64001795, 660888873, 333117895, 7862016, 737756561, 979025710, 688089064, 189878543, 30698856, 565012930, 107670690, 116673667, 266685971, 799273015, 383817591, 367396994, 51318879, 252320977, 408284767, 249842687, 540124309, 176313316, 714263809, 284019871, 908257755, 441043287, 6214358, 162636724, 755504164, 843050233, 885919129, 62549080, 74228922, 101198955, 240215356, 66927195, 805653558, 501395764, 946721877, 240537193, 506193720, 531644300, 636005121, 54516169, 803349885, 621246067, 192541018, 74163526, 846739453, 140278961, 432680543, 668094194, 965618607, 637073982, 163105159, 479936134, 465949859, 773868383, 894255431, 536527692, 288939324, 117788381, 325019344, 720082475, 940676752, 856283182, 395445226, 826177045, 594922358, 537848430, 327522858, 754835659, 996899231, 697119793, 726184244, 689477854, 669042219, 733007415, 21385665, 743216869, 420938407, 155494846, 274632668, 260489085, 36124455, 495565764, 422174808, 786725738, 764406548, 486712582, 588062309, 703484867, 407912894, 685383239, 576224069, 706817089, 24206696, 366893395, 490433685, 112922548, 977214701, 483176055, 207002439, 2728784, 514351025, 828949180, 205165086, 353883221, 413789016, 782312960, 550214604, 619414563, 8059716, 1922191, 266611324, 802492617, 689658177, 106796966, 212432132, 421163540, 743472969, 449383333, 980962379, 654888801, 162610031, 386834422, 902509410, 602526405, 780706488, 334823163, 51469143, 629834484, 743243108, 922513370, 180864880, 170049077, 166790849, 590180134, 233977485, 237074883, 388441852, 360943465, 88459345, 769019438, 438914361, 894142906, 800782980, 226627722, 309770206, 797811229, 612618437, 166874973, 612577699, 954574637, 665280265, 721285873, 713394050, 450938005, 763798726, 374273927, 840421701, 516219200, 175240714, 990318963, 81558327, 161341655, 892352619, 212529594, 420332743, 695098942, 605932708, 985837096, 569963622, 35476415, 838279477, 22820330, 696692280, 175581937, 64723607, 823612244, 448005873, 150612368, 914152352, 92540531, 587403197, 599042837, 920693432, 83415026, 702292856, 703116567, 470245103, 684446255, 667032258, 431334314, 377048919, 601686556, 878154335, 807914225, 735238951, 756720192, 79934057, 358424468, 907950705, 943991994, 986203515, 863648537, 218863225, 28234140, 838239489, 146503994, 959347131, 742942047, 147149675, 390126970, 245668980, 675368619, 486305280, 497011848, 315438854, 654982116, 681514976, 498948910, 418336567, 706078458, 547411409, 472113346, 513142747, 915763833, 358097671, 839052690, 982043020, 479293128, 206707787, 385449881, 446322219, 379029209, 548830809, 837652226, 834214400, 854841698, 793227058, 348874195, 543236652, 805680143, 338591648, 522376748, 497893540, 916626183, 489292487, 428103966, 410435090, 100229012, 310306594, 885355246, 790051418, 632088626, 733791497, 260805693, 136632833, 234738403, 435477024, 223957311, 656189300, 217722208, 39682638, 838581995, 210471055, 81170431, 848982352, 762801700, 603263606, 664089142, 138515649, 396085517, 416638710, 586251621, 131247585, 574786510, 69134232, 976209875, 726534293, 835497766, 391759456, 996846532, 968372548, 50336065, 580891097, 185684383, 2378142, 55371090, 293087850, 991603597, 883596386, 544756460, 466425084, 642358711, 436122462, 998758041, 956704696, 745571041, 474742789, 806561133, 103322543, 695460825, 365897798, 799333017, 205074225, 526909617, 679935145, 189958199, 255790090, 400381172, 575210902, 150221727, 708336415, 396518713, 934272633, 880616375, 198277802, 944636445, 550477726, 586487714, 624153813, 601775525, 260982540, 132705966, 666124228, 882682767, 381160915, 899618229, 409058673, 697094703, 280611612, 893272752, 216365298, 987472228, 381304322, 322679763, 602995453, 752963651, 6099384, 498447663, 387966084, 959440058, 101417335, 21286912, 322159142, 544339641, 420035335, 322405606, 60902265, 689380558, 442706216, 674694217, 549833209, 698380582, 870761731, 568560495, 668378970, 380462452, 410403798, 363123769, 170593663, 767526189, 212319605, 203794989, 295825844, 958812420, 421622602, 665681814, 242474813, 526374057, 144598797, 137063770, 778070917, 247237453, 351442642, 292635876, 650794744, 134910713, 226132253, 889530220, 638055153, 452906963, 359025314, 732360987, 26036251, 517128106, 755057360, 885831862, 22374411, 102398159, 467367032, 969074867, 580949038, 571079505, 73039926, 686889668, 498068066, 801770464, 256522466, 287870044, 110934648, 620127886, 720765365, 126489348, 569354735, 763102729, 604943279, 668751967, 834998753, 442802214, 780365199, 412188995, 939583032, 985143706, 697040581, 587830211, 280854229, 14396511, 914509323, 28595495, 270259574, 944548525, 472607913, 517053588, 259351952, 572338210, 171535456, 952353265, 697708754, 462540709, 198501379, 747033464, 722377808, 478686447, 319147622, 628571700, 734384558, 746963029, 648507368, 755942568, 868798112, 666545375, 360077376, 689078089, 835273207, 193879576, 942252526, 776742572, 914549658, 379815446, 294532689, 669264529, 33352107, 129819723, 138008522, 336549070, 492058110, 789098456, 334618736, 270618645, 667088592, 921231276, 978577015, 605751106, 755249011, 211830185, 436090330, 260627409, 913922154, 58018025, 271388309, 587427304, 14220695, 451478726, 227273681, 128765131, 856771938, 314644173, 995930631, 79442885, 701834397, 639283224, 864253829, 452492524, 749483642, 554000082, 877003141, 876935141, 458197738, 874279690, 329633530, 30790246, 431887880, 320307913, 870611227, 870066595, 291052424, 845458175, 929749931, 878544712, 541680993, 805002713, 948850480, 65665883, 216434605, 114652331, 204508556, 325770886, 121732337, 305074608, 536637114, 839231002, 267029286, 905289450, 761957863, 124024685, 38853066, 507590304, 59737203, 266969970, 410414652, 769293135, 454165584, 268864244, 54920061, 455970782, 983915516, 785290343, 37654900, 951351940, 627616424, 863079532, 530065657, 665500687, 641809629, 688026594, 608355095, 325880589, 338769590, 755421742, 957597725, 659831874, 939917913, 925430639, 972379394, 743912239, 591559124, 77832505, 90905778, 522531056, 736673289, 513817778, 95671091, 148907412, 161132305, 170018897, 52455859, 784744777, 215054744, 242869704, 120026262, 180062544, 749191268, 869184248, 643916302, 677644035, 611539750, 635881928, 287463846, 57810737, 804146474, 11407006, 14834292, 835088647, 11469799, 698194475, 406920396, 427569868, 75324951, 521533645, 163598950, 450948202, 450363334, 249866849, 188768717, 401760659, 772764914, 602697000, 602920871, 717207553, 111297150, 810352294, 550806408, 304453927, 41686723, 410942475, 48547424, 19143410, 399390837, 194137990, 288159873, 778804218, 105726580, 465139373, 56657401, 570857410, 274333096, 28856921, 803938218, 418409833, 218986606, 31542972, 295173529, 814120258, 419067815, 686432782, 690069752, 443409781, 208820046, 992816255, 222197035, 947481329, 863714746, 94691941, 421792850, 854744792, 484856726, 406801605, 191262575, 924122865, 392844962, 440878305, 317872033, 738698619, 167434643, 165330656, 928556809, 484768036, 714168527, 562288934, 445777293, 74342874, 170371330, 44580202, 750149392, 929312227, 843638638, 379142491, 873497018, 488390843, 380182932, 503208343, 560583688, 555983654, 366199071, 588218456, 456792163, 559823017, 468607243, 181714941, 248895007, 802210330, 287061417, 894451344, 297242567, 223459053, 840308961, 232291503, 912256034, 253366335, 517061048, 298097791, 795007700, 644312200, 112725273, 122310966, 498884388, 372767395, 412305679, 126894933, 190034909, 102460746, 313389624, 413008840, 929729734, 745313055, 429508764, 391910750, 978059439, 373905014, 9160733, 71938167, 682673829, 390385977, 377651613, 638700695, 717662547, 729487574, 950055036, 311091377, 178822082, 428580725, 522636468, 388671080, 609965791, 658153598, 841776004, 486994245, 678380475, 410933684, 734200604, 999576366, 712671108, 179503047, 77962483, 628862477, 366571057, 402872933, 207355366, 638889168, 686665531, 60231737, 347387822, 991976869, 360230752, 724973096, 603933485, 519183149, 792797814, 837601623, 609476957, 850965483, 518670014, 834917557, 182436010, 261725794, 858462222, 783861889, 537470783, 466689211, 141665388, 940536629, 176205394, 110824898, 270360611, 976955453, 857807004, 835381431, 956479440, 387551725, 219991969, 732620089, 537863775, 313877923, 526857945, 173810676, 146701605, 982312554, 976834426, 259934583, 193752078, 444118905, 606570312, 958227961, 777431619, 503255967, 15851264, 174753302, 758821941, 268395323, 859723353, 974846193, 827261456, 410655059, 400491057, 664396066, 635426188, 705389703, 445940254, 967129790, 812465481, 361219931, 713632802, 331593565, 96732398, 429973736, 300519118, 78165960, 849004256, 821564686, 386651376, 218333131, 165170379, 736188137, 714200766, 776241429, 184961694, 664462921, 688071888, 207305614, 105011746, 786313359, 944777301, 672855946, 838007134, 951804442, 775725404, 817838286, 629984829, 332853465, 739971826, 611326279, 786759224, 720663903, 912744110, 59937547, 36408515, 939092154, 709178809, 449353654, 310233112, 733100162, 408728069, 748042505, 764482160, 824053661, 424360525, 659833154, 328250636, 684711585, 740823308, 620740039, 783343290, 565435415, 627483297, 472642587, 887531442, 172054303, 546461412, 542405659, 427423085, 631163136, 367731750, 172463787, 170584789, 387529569, 651688837, 671129371, 604184749, 536455450, 418208534, 995481177, 823154709, 69049745, 496750152, 979342637, 970144235, 424688273, 518534199, 617775476, 438086079, 571693974, 34800954, 963139668, 645889136, 477650984, 258971420, 199301659, 232785008, 865452067, 513704624, 577538286, 741183878, 849523414, 37610341, 374185712, 436236386, 589418656, 849225667, 114426359, 872024546, 17664172, 259069706, 996567366, 960068724, 65417194, 652989413, 846073090, 828936456, 650462349, 125892197, 28818220, 394394655, 336739817, 682169746, 547122800, 509551994, 684155875, 252450338, 669665662, 124174354, 321939718, 182594714, 753102188, 212570, 227736185, 667310569, 182703375, 732623737, 181161, 501284141, 635454384, 899867658, 488820726, 382157835, 792867174, 18531748, 648844512, 26146949, 503306593, 49108499, 178748510, 443508068, 316040844, 983723810, 259240104, 211361933, 431226068, 592920460, 74560800, 73883799, 708038223, 481113331, 473493579, 712555404, 591181330, 762748146, 530622189, 87975818, 197064688, 633707397, 802163671, 801186862, 913968085, 947153096, 356199574, 783066663, 202291877, 28904128, 957827265, 913640485, 999041710, 112225695, 853779568, 176416753, 652283848, 518470505, 62558919, 143107425, 373533433, 974175137, 165463699, 427963340, 675519603, 923553152, 51034334, 179155979, 124287949, 160246052, 973096916, 481870381, 983714100, 319048897, 529780210, 23760146, 635470924, 642498007, 716991068, 156263806, 926149359, 659145947, 278479619, 652257320, 919589019, 315124154, 383826834, 142905610, 208926324, 700910366, 720136956, 103509315, 626842772, 992879482, 15502917, 602560438, 836060711, 768984259, 936081714, 18721106, 263263290, 858647025, 761036351, 773282260, 226215154, 243114078, 457961851, 130869602, 528216539, 892279249, 250467182, 285284738, 578115127, 533337406, 576527598, 731243706, 400199027, 107954188, 917804651, 685555048, 384233618, 914519902, 575036541, 731084134, 392573612, 800492455, 399003637, 844347034, 791728198, 460636902, 810800182, 51720055, 335829159, 503806338, 19909662, 973563225, 263394559, 458203459, 506258106, 385544484, 465632275, 615873958, 424573311, 167832436, 906989477, 389029173, 787740623, 98267326, 196605118, 422831319, 250773729, 388463332, 765212766, 193042938, 527476654, 563717578, 403124242, 852160802, 38975453, 57477144, 960438844, 815416224, 40698200, 879895941, 207752820, 158966052, 736847475, 107580503, 318588803, 882805210, 274057617, 339322518, 429420816, 745888018, 769895853, 534999300, 608455193, 892183014, 294443194, 677937724, 708366135, 710011710, 763930646, 315368876, 672363951, 996554985, 476630066, 684800214, 19145945, 979143862, 741114849, 134738786, 217752344, 3599794, 881896245, 177177001, 841730435, 782059280, 304270794, 256868420, 148625504, 827043850, 340308108, 809608457, 297094199, 330548520, 526289360, 598549527, 997884493, 890620019, 383157201, 496924421, 650517001, 906603577, 317109229, 733507414, 51260810, 427834474, 401727158, 179066991, 989074511, 805690956, 329423374, 367785870, 576411505, 702195917, 436857035, 187722859, 464975786, 179736471, 773525831, 755617659, 289937294, 663809479, 410880505, 825182120, 705144920, 946309965, 43581566, 94914150, 291360913, 139863459, 842243451, 835702689, 839167817, 671529156, 101508461, 606175302, 801958748, 237613701, 53748124, 375796053, 167575823, 920651803, 195609730, 112204525, 877290741, 324544210, 763513210, 169584385, 111676888, 710784952, 621759316, 954139727, 547562234, 268085073, 420719354, 435066693, 680128235, 471809904, 325733558, 719851557, 800935533, 334163071, 56511493, 318277138, 874803198, 195603914, 242992804, 857066774, 421085646, 587348122, 954428010, 936330041, 187007629, 913725636, 949609877, 231491044, 318476867, 480106312, 564919216, 920328203, 3419408, 843184757, 635289140, 799700078, 617391084, 17326434, 21370992, 383777280, 277871106, 752368598, 573014072, 424366244, 112317699, 882596795, 369965089, 169357376, 854196471, 682011778, 73281073, 145929986, 466426006, 694879263, 879018797, 585816051, 465889858, 223465258, 235995625, 298113263, 263554507, 533877740, 123041384, 869513131, 708642997, 523234711, 303250725, 932631148, 943694234, 912008286, 22565005, 664036414, 203926509, 425221741, 506085084, 738069748, 449811443, 999730561, 831049466, 702810474, 453166112, 482425181, 72517812, 879586868, 231848256, 863071772, 657410082, 567681985, 440493888, 996409854, 906327171, 250036825, 732714189, 478036633, 456117697, 504348375, 468159101, 782596044, 186918040, 116968859, 634542903, 461102842, 507742085, 214262351, 386107632, 821618852, 336254711, 745775127, 885138655, 176783212, 197850440, 49817035, 583015057, 208570773, 39781174, 841700199, 209876627, 528533739, 176551272, 167292002, 513563426, 201821337, 990283139, 163580768, 95104961, 519597448, 292672488, 901103459, 806165282, 677331579, 727153171, 36845399, 561403903, 576190110, 455287000, 60893419, 294035914, 12206689, 404564144, 540439219, 867798110, 64602344, 724770590, 27612367, 75601202, 850172255, 42743848, 484683054, 64697432, 554259113, 635925332, 618032821, 855076908, 879812879, 47255012, 80517451, 546377484, 894417984, 764329730, 5198953, 482515205, 870118825, 656909470, 424684888, 905266587, 599267695, 968802972, 609778817, 603336437, 408393506, 232621164, 154979066, 277798224, 907619783, 104636578, 700909385, 88775080, 622268858, 988705399, 66745231, 529733328, 443419520, 511382560, 446805733, 808559949, 743507792, 313397698, 753874906, 192248267, 677200253, 51001652, 804680468, 914156129, 4724265, 774071295, 807434121, 805234823, 428591115, 521309056, 344463539, 48320032, 848747686, 703987613, 52601520, 741855016, 264197831, 461614706, 71054907, 93182364, 242635667, 716866655, 666141495, 320885669, 767302108, 896420486, 973291949, 212345281, 625814988, 127394679, 191573599, 673878541, 844951281, 812731325, 728417132, 541798139, 487801363, 194322720, 155274476, 316794668, 492222696, 282889066, 276495318, 193486987, 864780066, 31063809, 788914753, 113809050, 900755664, 788570728, 904326272, 940312476, 814144865, 832148069, 155817479, 474940766, 411659971, 773652462, 561169169, 553262376, 31791039, 953990463, 87898876, 825252200, 184380536, 710868319, 566656356, 326924528, 629944124, 147243491, 768843209, 544659726, 96691843, 378001801, 395600225, 379303027, 357143681, 396021954, 6995089, 408936006, 716774932, 267533456, 223978919, 141578553, 594459012, 856905748, 699764225, 540017283, 899438216, 252192829, 718930719, 678443541, 331286895, 987396699, 537031230, 143276682, 600414485, 146612450, 253513990, 694948695, 411719127, 875910707, 235849661, 81807485, 632554971, 18174580, 227259254, 94945944, 165293663, 608119317, 898788199, 422748122, 719147251, 677626517, 229227499, 630929194, 33868029, 949359718, 153716531, 881289689, 126323047, 811592410, 82443338, 487770141, 627682785, 835163231, 399470232, 507574100, 937847057, 248819858, 891386083, 335465, 582457829, 868770722, 473213189, 511493397, 857240179, 797644385, 675167571, 799043930, 291259538, 496692576, 652851419, 993999212, 611513803, 367349869, 511799839, 122884815, 451854943, 581717224, 974446038, 587404654, 392792849, 345469133, 36082505, 282339152, 634193314, 319246723, 670089731, 691072143, 46748203, 320624540, 670789063, 570076335, 89600744, 13049160, 864459850, 465875465, 649342298, 749361152, 879348323, 717718093, 349973846, 66697636, 115524807, 266352770, 877608690, 476791467, 58968835, 395895116, 605259717, 251264181, 21329089, 356212964, 52886461, 413586774, 578842834, 623174434, 311258762, 566945340, 759188446, 207865984, 662165330, 116991447, 782314442, 749584429, 252056939, 983502359, 479987569, 127959097, 269098936, 745272270, 394222942, 238855569, 320494441, 336739901, 19706792, 637943367, 973149245, 635048578, 240476660, 151535324, 908273934, 674944820, 89270246, 120328832, 362398927, 550465109, 15695647, 637167889, 337781748, 706020746, 592753294, 391534590, 803002995, 288730621, 658933304, 203730220, 274657428, 749424658, 785394879, 419203163, 97517181, 27957362, 177246692, 658942047, 55756955, 553348436, 873083366, 118958913, 958272994, 374303516, 586423453, 639575774, 397701114, 601127152, 95030259, 744221602, 218490190, 721419167, 516522560, 364574363, 328437586, 206473855, 14471729, 993348540, 335386359, 559115888, 103684761, 414149379, 491059386, 644086078, 145983543, 939167550, 663030514, 429591373, 870689611, 925387318, 760025199, 825767554, 690821250, 81283911, 823689276, 901354928, 613742137, 720805892, 595519057, 428628542, 51538151, 620287095, 672861442, 557131372, 859603473, 875658004, 496787250, 585021333, 982631511, 258721639, 47089641, 825209611, 387673713, 600221936, 794684568, 715877941, 425997377, 119940538, 835474446, 935967966, 976302119, 618861591, 33351444, 249643076, 291170534, 870620433, 454825578, 433590944, 463544423, 646826752, 497067250, 777529852, 293254320, 308281377, 77750871, 222076942, 157416926, 588188926, 419152196, 371063322, 781569227, 327698019, 701153770, 333019265, 666834119, 147747357, 743491694, 340679992, 25924186, 503711359, 763714778, 483999817, 238883450, 715103885, 948386372, 119531739, 680213366, 436008298, 399482118, 918495900, 281624016, 888867207, 473191553, 353023861, 840055107, 893197021, 339875583, 165172633, 884843036, 546375722, 373191276, 594522578, 478866306, 835217552, 214641291, 556035685, 218454514, 206091462, 538393763, 630556997, 406028078, 683945719, 306357457, 766578308, 541028244, 529490665, 580731801, 413487100, 346303109, 535250704, 914191699, 690646613, 366791345, 360719226, 496378668, 6585136, 525378206, 828013287, 909820891, 950055613, 760164545, 845311210, 611267143, 461445780, 397401757, 745886150, 553670685, 972682848, 393106427, 323167200, 155162208, 473754311, 184541480, 665707126, 620590760, 16825787, 106752780, 776078872, 852124934, 930707969, 731260893, 878346501, 684808984, 13144819, 281405793, 160394766, 948298487, 503534359, 748061974, 782642780, 165592818, 321028516, 646841347, 733771628, 15569167, 807428102, 713882299, 624606596, 94001310, 341552549, 744714488, 254728604, 600059225, 245247836, 593791231, 637278227, 776133436, 622913166, 158741996, 151470003, 588096208, 187422445, 552136133, 329695649, 478498004, 143489138, 370584461, 921367630, 141760535, 475044219, 962164736, 782552059, 137052395, 131558756, 482292935, 597775199, 151946416, 871165631, 550583577, 620473941, 863957396, 597756143, 273634816, 390131441, 881230371, 396005875, 522253910, 576005592, 250706899, 844096675, 873695629, 890633604, 238020610, 713047229, 612789908, 638116753, 601219600, 800161013, 121327205, 446786845, 57324199, 93945280, 619640701, 311577064, 827886207, 437012966, 279481911, 893281778, 205350919, 398552367, 768843510, 942701810, 214565656, 567122297, 61019387, 409348861, 339770547, 591713539, 184347490, 592617431, 556633352, 678328292, 783677693, 70112616, 592261383, 662163081, 758561631, 560438900, 642607348, 310155336, 169506090, 881734340, 875050352, 283738334, 302456998, 660486340, 618086213, 130660449, 232345987, 791806602, 310457554, 55754952, 868064400, 300963575, 898592469, 711766739, 964119615, 709158133, 552989207, 958589590, 537113742, 771360511, 918613207, 488615328, 242219252, 942036356, 920809434, 282709741, 53178948, 464416978, 370385324, 578911005, 724983754, 371201102, 381817134, 387701703, 926728488, 352332820, 890399857, 435225392, 584210410, 655293936, 904880747, 665348178, 920960830, 754113504, 236413507, 619119236, 632103142, 564412790, 341649325, 926578329, 969261600, 105429660, 752215948, 634001421, 767005952, 606408034, 938858601, 628067511, 142744545, 779999639, 180136110, 51036982, 702949258, 651395466, 167479084, 770150398, 117634122, 19466892, 537965017, 790609987, 427254619, 784103081, 168408264, 257406565, 48823297, 631793115, 758781477, 854398981, 625732081, 746272709, 199911595, 523015181, 606831145, 578301976, 63710296, 376624211, 424898144, 401170136, 760404550, 514225752, 651968400, 370339431, 846341544, 236576993, 552319995, 996572128, 125491800, 835279291, 999703995, 269041513, 601600567, 707305659, 547515933, 173639648, 741981997, 131455026, 758999789, 83665723, 571618031, 832439785, 285093290, 577623855, 690786479, 269854645, 905253601, 659002538, 618079557, 24343200, 242633880, 234383459, 818503385, 673488073, 270306390, 804075121, 914931212, 876344086, 503501357, 825186205, 263397338, 712585074, 138780074, 148359792, 679617867, 177816278, 384372727, 885662786, 836884064, 443093671, 384776160, 814497543, 386085407, 965064839, 229353868, 122669735, 931695448, 64586671, 185344547, 7658898, 732432530, 895827656, 683502791, 456873662, 534651765, 275687534, 298971362, 544437719, 660404764, 720240632, 883754908, 113900621, 63579982, 452071996, 735022699, 79011845, 949814139, 803534104, 241911633, 981786110, 769419450, 324695746, 566985816, 572131946, 546784516, 185442037, 54707547, 808745388, 908121193, 330944355, 527532699, 781969228, 207178788, 729791173, 883963351, 643676183, 362609887, 789571365, 442657970, 652757863, 917057040, 754359464, 8668405, 472453089, 630834438, 656611062, 792557652, 613076933, 47405766, 175100551, 447415147, 708169051, 620085698, 718328274, 62344110, 519300933, 184080418, 11284588, 36808639, 618808891, 440907833, 17263894, 798926886, 385190427, 561912622, 645274106, 378200386, 523961867, 578386990, 533685463, 469604644, 664886148, 990393393, 563040325, 918315930, 243890652, 595334783, 513972685, 498886787, 10779730, 695797300, 787861563, 418244307, 48400191, 857055937, 529287887, 389016353, 56648801, 403386671, 301686591, 462246983, 537632686, 453077440, 15726478, 742799876, 510336652, 310794832, 423659300, 750532468, 125009031, 786627685, 552464712, 710313362, 891918374, 641465172, 679590986, 112018208, 786457664, 756035122, 109583544, 271760005, 973876313, 348463069, 240027896, 204978574, 295453035, 862671070, 905872565, 401108825, 115674636, 438059294, 990493175, 894737593, 114075416, 152850800, 742809156, 33782630, 771298923, 169425676, 843974252, 437505680, 235125595, 873895791, 717560280, 586162334, 172418324, 301936712, 816278159, 439891783, 179106829, 232147586, 659330450, 530336699, 444788127, 612143029, 346640411, 307713502, 924891530, 717404799, 889092563, 759719470, 453249632, 382424228, 353546680, 311363055, 161084300, 124308672, 225899443, 686561808, 697570840, 418157634, 423806368, 62491132, 319668722, 273570307, 206366950, 770942801, 63078564, 542991644, 881104468, 63320698, 479030289, 300962729, 455083191, 675267790, 85306734, 890253341, 895299245, 797985939, 903182710, 32121247, 559859981, 568230332, 983994522, 904997822, 619104977, 851547845, 965328534, 831498231, 99535738, 781830883, 428410338, 369741221, 243459286, 453537398, 967954640, 547314081, 585331361, 532926198, 773220822, 827053007, 922384374, 375618198, 266160963, 495068536, 742086919, 485413631, 451751209, 967637922, 988165466, 378127184, 531850666, 965515120, 113409624, 839029758, 205975033, 206434176, 256082279, 389908251, 714591943, 869953018, 347503381, 121979204, 801223288, 464663668, 44138865, 29646467, 929435979, 334915885, 990729492, 56547370, 37086904, 294114306, 937433258, 918223332, 653790691, 453414787, 103643291, 886257548, 624108208, 378756494, 742949184, 756076487, 82127547, 36456615, 136943371, 529441183, 174125870, 815689384, 167579784, 497883211, 684941083, 594719707, 80794188, 339788718, 940631772, 737909210, 94310471, 330177422, 242066068, 370852989, 635357234, 679618043, 689712586, 827941134, 926741638, 778706804, 833261488, 944014153, 309206024, 920399054, 898250021, 838737678, 394812732, 217694944, 913711247, 43185241, 554531586, 360530424, 31943877, 847801550, 274586828, 743629409, 792421234, 276098944, 450733600, 280795548, 755246679, 354141691, 483031142, 625082016, 866232745, 961797840, 499036668, 423184048, 187213381, 695397993, 83714781, 446702970, 526894697, 358545673, 691833372, 311114910, 591916937, 820696804, 104041443, 884663, 54172648, 821532214, 363328924, 258284963, 689212351, 871287133, 501158321, 959801353, 712115184, 755842521, 147838450, 308933842, 626445225, 689859263, 701515746, 510477305, 560196805, 447825810, 137780711, 92038591, 967842893, 403142144, 329417063, 704707550, 656755709, 739301913, 805675164, 650586776, 402311371, 161533860, 639934889, 815472398, 16276507, 699668637, 858505332, 301308015, 582399279, 80794797, 51734864, 215307516, 727694202, 663189894, 294567305, 426351882, 153574053, 748339558, 840650769, 950884155, 50584067, 408518074, 134833367, 267907121, 149984291, 642950281, 906245696, 804822540, 113110680, 120561069, 4694346, 965826092, 22787527, 775266255, 364916281, 812929891, 199601206, 834031340, 802137387, 500497475, 681742072, 657348152, 441253030, 85349420, 251548650, 804660362, 239911407, 731818479, 217489964, 93349823, 655711133, 458165516, 181010735, 167125641, 859159144, 381253455, 344478285, 53846748, 797632112, 915821932, 716133650, 835390849, 128087323, 640572157, 941787242, 140620891, 716433232, 841707583, 942767502, 848143298, 621389189, 457519092, 929518534, 360679041, 85067453, 503426252, 887433891, 351188268, 534191343, 896165794, 130442904, 212767040, 933948458, 640477778, 368296325, 256947912, 76903152, 486822579, 533919380, 175592937, 563535242, 281935784, 680016095, 55542431, 580010000, 176848400, 935678806, 365602520, 24307975, 221031158, 338901572, 837601500, 764696954, 326599245, 670958647, 264393750, 906890277, 732850185, 45709778, 167197117, 146957330, 863317071, 524340996, 826129138, 596900677, 593193661, 776995251, 801364503, 244923281, 999966462, 221112528, 522453337, 787347672, 663274245, 255304814, 453257698, 437357743, 261206987, 165820676, 876089130, 699200555, 367634829, 12220604, 634739492, 787437260, 567262715, 204776596, 126357195, 90920997, 924939964, 490639546, 839053033, 576426067, 856487234, 3883253, 639479584, 221303741, 515031933, 202819862, 160725359, 200603267, 965045510, 47732578, 860306735, 252382102, 736817180, 11883306, 472273200, 665257845, 711895371, 977307391, 62691670, 428534592, 182740684, 935737313, 201171043, 264242730, 660387918, 195088037, 903508321, 339738143, 108991491, 230768095, 318966918, 405669659, 940038702, 832074408, 66107865, 214704911, 990644625, 685821241, 689105762, 580518468, 889571919, 43807047, 552118927, 829928540, 962225495, 660775613, 133196726, 899776646, 485313819, 880861483, 431387418, 13155748, 594772122, 119244321, 671694735, 540064025, 164703110, 550692103, 848628755, 114840705, 101850939, 271416695, 786663733, 494698628, 391907547, 31382643, 927666304, 717455100, 196345733, 851464199, 589675245, 243259775, 538965609, 152853264, 810407813, 266249188, 398411554, 646779736, 767099327, 838169316, 410549696, 716105744, 155485767, 622571708, 949713374, 765966289, 866959589, 527622845, 451118148, 795207854, 888466640, 680742387, 60017598, 148376667, 247964500, 915488084, 963926375, 635981006, 58758348, 306986730, 860563059, 790584551, 309481462, 565862883, 410847860, 238625379, 368934199, 661183644, 842905870, 671200244, 262918432, 96820254, 579119998, 523009432, 52470745, 560954711, 117363437, 246946899, 164994454, 256805313, 570904073, 470529041, 512623578, 110173948, 840238924, 10412346, 591651531, 964741693, 209697998, 745181238, 863667984, 556536845, 429748167, 607832885, 187073678, 263500504, 626025620, 388635579, 632325330, 663704687, 249934304, 144278266, 255719181, 453737352, 651102951, 519874039, 656815889, 394741936, 982485242, 509425497, 645592503, 375907838, 434143114, 587199514, 536715175, 290192277, 970251531, 29080054, 644023030, 709239242, 376987875, 76777322, 608712001, 928488203, 770067794, 581499387, 213220148, 156946870, 208876059, 17852425, 174526654, 112923859, 460983314, 887302085, 661392523, 774866235, 625728564, 597423561, 11716062, 698162933, 662293024, 65454513, 969848526, 301218080, 424673439, 398725698, 742840608, 999224857, 924379709, 437867631, 444225872, 437108717, 804376397, 298188386, 744128141, 945080197, 709177328, 616897282, 249356670, 267748426, 530252870, 354734086, 703781416, 584487447, 773339552, 104451721, 556837066, 831050005, 18033764, 415688915, 244879889, 91868795, 845550254, 159005192, 169222138, 674799995, 617048332, 27833408, 370339675, 829867834, 318549645, 605693369, 456714130, 161672948, 680775023, 86135006, 419400074, 119732173, 451699185, 358369734, 117884062, 397553876, 352491300, 473281280, 88159161, 290926035, 593464667, 780314110, 814382708, 11708659, 500565404, 768203416, 51678757, 944726955, 395262602, 992404010, 980125383, 898992246, 747241047, 242532491, 384555538, 549994513, 145162642, 340965905, 567376880, 234045133, 677381637, 270405302, 21830931, 775814547, 7672190, 773832076, 645985313, 854491797, 918419478, 262416282, 707261830, 330420190, 680138585, 606529254, 799372449, 840214669, 835545207, 531275277, 484434626, 88211524, 207227635, 847460416, 953754344, 376162937, 59291605, 92622651, 883718144, 447996207, 600984925, 900979258, 928092943, 717155718, 41201827, 741655353, 593019240, 150543419, 933082926, 457302268, 900905392, 734524745, 319983166, 538591263, 305264191, 664662570, 631702923, 180753597, 376507301, 534136330, 753110593, 78947626, 922331786, 516724748, 355039105, 204130712, 748835431, 569315440, 66583883, 743941435, 883483626, 591962963, 713562027, 198101529, 462871948, 953633920, 793851365, 892324483, 802194679, 13045, 422220862, 745208971, 914708476, 781023925, 581859079, 649925343, 285379756, 592092864, 544852590, 910347269, 569917244, 473632696, 429914097, 66894551, 868982409, 340190464, 872757052, 793826169, 751999833, 907575326, 811271848, 223972162, 394329889, 128775693, 93874158, 242645257, 382136296, 943762871, 171075504, 3758482, 701788410, 882834018, 393999866, 894221658, 330696360, 884880143, 473868157, 208357313, 582857957, 622556712, 789985451, 23514085, 941143022, 790053216, 709955431, 198199094, 491768011, 539609056, 62873945, 420976295, 788618423, 921798236, 863131659, 463569707, 114759904, 101784134, 999342848, 293282722, 264005206, 963640007, 727410440, 55532135, 830165396, 37262970, 955630393, 708880888, 112068990, 576278702, 568255705, 413522373, 902714386, 594670782, 572045322, 955471241, 29025386, 820851884, 868474712, 880155367, 528997008, 297420570, 124871023, 175774186, 120992437, 316442674, 721832718, 677579251, 436195484, 720226782, 297580975, 241810971, 349050865, 837762373, 22577263, 134287133, 328644337, 567678059, 270581672, 951346026, 480416968, 51510456, 36973564, 407796278, 315112888, 244687291, 68492247, 883700490, 29301942, 580554254, 17124876, 474189113, 385270765, 527479324, 558966973, 289086591, 433333632, 877721116, 718588433, 526174624, 418746227, 79647509, 275690227, 297379501, 361846489, 780562068, 152505089, 506100600, 622755258, 708457882, 143095031, 602804501, 557331552, 945087821, 520491476, 75511352, 337245529, 335157045, 533519762, 18758935, 386553551, 909900344, 222528706, 157125749, 626293238, 266925136, 529179224, 381067013, 745022064, 185851484, 449398955, 476340203, 185006115, 734672936, 540057949, 735497190, 574661837, 278011753, 992323620, 994468165, 50309539, 821190829, 476655175, 87570567, 174653916, 937677580, 822999421, 868198324, 170316533, 961045235, 978932299, 198173996, 794041417, 670050407, 580627901, 736039078, 570772563, 504689885, 129631816, 70109625, 472737893, 722937401, 929473811, 374477489, 10216637, 16690937, 749530014, 38719015, 840254365, 948765576, 541699795, 698721633, 92415009, 35018998, 415239604, 729495824, 688550975, 292320998, 773626799, 263772601, 702847722, 275452733, 412332896, 272025092, 129636749, 69116735, 600397744, 4488739, 359986539, 150428548, 112173468, 49556767, 574060785, 681695961, 838678646, 561692018, 110876551, 169681133, 826182601, 470742219, 412800715, 355241836, 856768436, 260597391, 770314854, 302804269, 80027026, 140721491, 97706815, 738750579, 71943312, 327064531, 448729259, 561443567, 275310563, 76305883, 936297483, 257954947, 734148244, 189378732, 958796533, 183994159, 305528589, 262216048, 275595889, 339560119, 979140230, 360260655, 26634615, 546773922, 238907007, 45593558, 993558375, 646659450, 834136279, 779887250, 716938500, 999774389, 564832504, 690079475, 46733499, 968232410, 6163394, 504904303, 682808884, 633456307, 775611496, 823206228, 82712671, 812895693, 845315587, 358441764, 14714199, 926165282, 775796953, 865946023, 772303569, 113683291, 827038570, 164677630, 845576585, 215108824, 484166418, 803942535, 760519739, 421066940, 479671628, 940474706, 539639083, 185421531, 435788811, 138371200, 165501717, 731813088, 243009794, 25105963, 75166750, 739149652, 660406579, 633777609, 663951855, 20674936, 299667961, 673741032, 296319046, 458551226, 426636026, 565326684, 287100367, 478718896, 189262050, 601402922, 366785566, 829929679, 46223414, 189797723, 479483434, 796350311, 167739796, 990876109, 751643095, 129998184, 552620236, 683677689, 205884853, 278190052, 787587576, 404125718, 38717948, 897765953, 510741503, 561273477, 377004056, 738056958, 582942035, 774019778, 606032062, 204529697, 647288046, 418008031, 103474887, 694560094, 768803978, 473354616, 182440383, 238344536, 565616537, 502653361, 568044620, 563926309, 345587147, 967178065, 830063634, 622063266, 145095359, 611360745, 553174380, 104625900, 338946639, 294918443, 764385081, 837061792, 278865672, 657282461, 762097972, 536498312, 443871278, 650951173, 455559012, 467238255, 694352779, 907645415, 664554686, 734747698, 172408103, 471494986, 369323513, 141904425, 720474986, 44179960, 864331344, 347262751, 70170554, 901970548, 948534028, 37255498, 613884162, 699056021, 610030423, 936323934, 797026251, 350285140, 744333183, 784066470, 357492883, 933630086, 665726567, 628347824, 625866150, 665497560, 617329017, 243375193, 654690803, 79818133, 343257793, 528597367, 718119589, 699748163, 637708065, 27631604, 553030206, 836056911, 181091095, 440310352, 831751373, 377783149, 831161748, 876117316, 156409946, 539050332, 482955845, 579007210, 778107277, 723868804, 960469261, 80315641, 601286334, 917635008, 266635127, 569971161, 119372004, 906267832, 857051916, 701300606, 598210644, 9687365, 976962032, 334824814, 349216702, 125277147, 586456027, 600056962, 152736021, 927907645, 65278143, 292324810, 213214331, 6944091, 456831043, 549473889, 956197156, 203344035, 407370166, 899304802, 293903044, 18541980, 771373077, 216318153, 529065203, 698422714, 499278603, 913891607, 894092794, 995996744, 661263189, 382626160, 596256624, 715630672, 935836916, 318408265, 837622505, 432852275, 695822706, 331989995, 801521737, 711712640, 245090580, 495924443, 954561643, 445404866, 730294648, 619967043, 14219835, 224292797, 575168992, 518527252, 709252959, 879851109, 949155676, 625397491, 229887572, 679841292, 443737865, 696840829, 678988664, 939846705, 86490631, 232573670, 920835753, 266859255, 503973399, 983339838, 757178279, 638239012, 890725776, 301709453, 316342134, 33886571, 880737262, 150508803, 410855119, 863788624, 207604447, 924304527, 788709039, 192215143, 340165378, 701825033, 480580912, 905342988, 401728098, 634638158, 800080559, 947975557, 632502054, 167422785, 115761801, 885871543, 788152820, 402605643, 789975992, 635279210, 876695313, 46929197, 760550735, 35098346, 502767275, 75223684, 100949189, 798394747, 141181665, 545298470, 189128394, 476590600, 645370312, 283541081, 428129179, 971577845, 496636788, 2095084, 980659818, 636404686, 931674545, 418031164, 827928438, 199308214, 643827232, 835495321, 294730495, 387371668, 247066458, 136114452, 140522430, 977994711, 829723903, 409142637, 58429965, 539217591, 871945229, 789616714, 592363198, 808095386, 286287361, 727014692, 392422975, 17253283, 951277873, 757303372, 227539243, 44251297, 716018219, 549539307, 10842820, 728356585, 758891677, 341787669, 124679064, 965958429, 821069434, 814575530, 56023689, 453658414, 401824475, 691145377, 233506284, 797868228, 183842455, 567356442, 453782118, 772976530, 943754983, 356434115, 406805043, 329361701, 285737459, 555343822, 166155898, 113115616, 175879015, 88280879, 782259649, 228744881, 378629689, 187400733, 790993273, 733180818, 529616534, 763878807, 492913471, 939226073, 255553427, 361695507, 556988296, 467224429, 175665682, 144237207, 265687379, 491387183, 594047886, 900529401, 491305314, 370513900, 870363731, 291022555, 999343903, 943528669, 465995417, 545044218, 737723448, 257824210, 567178665, 465968740, 824842165, 811958843, 340086312, 239750329, 244517442, 649230956, 869918408, 798898985, 891154931, 768766084, 47070627, 607897750, 699495999, 86198184, 385225375, 891422291, 7696132, 106155135, 439453660, 281496841, 51015334, 314339410, 407294781, 993531369, 142899367, 925598538, 390626792, 734051436, 260228738, 837012683, 987450648, 275895065, 738892647, 518804315, 344926100, 410099888, 306971579, 550307885, 743258979, 89976655, 711002310, 633479336, 948766500, 959696356, 206253832, 975954265, 936793886, 333007657, 496156001, 488695165, 557654516, 73121656, 923238620, 980299987, 210055210, 494322403, 602285559, 344471462, 518935924, 321196749, 604280036, 311247039, 168579143, 381037688, 827888522, 734964304, 993849473, 460795162, 975410278, 548785087, 118214412, 947623986, 764863671, 185701808, 466405123, 763532805, 383508813, 323636667, 421383856, 912654341, 247950510, 969459716, 266350737, 387677595, 536038398, 652216299, 399700387, 215201218, 649873365, 909485222, 630245217, 186623554, 147731289, 664885118, 296616827, 980226656, 168357994, 585493073, 63383929, 163247565, 577432147, 250411834, 647335104, 987917947, 440048412, 989955673, 29737047, 937487709, 395849667, 95895102, 771133132, 367450099, 727192803, 687731713, 847783335, 287108793, 501970448, 58651855, 712622615, 758572425, 269115737, 992872064, 248906686, 523875705, 429785975, 917046313, 832164462, 700528086, 392276464, 504274496, 483810876, 558138072, 436000173, 556592010, 413177467, 51448609, 227415585, 825479754, 19524441, 356437186, 445469757, 704927822, 687426383, 776541234, 786041961, 260368078, 268817755, 342095768, 480653838, 792995344, 530873113, 640737510, 350835097, 407037121, 369454546, 151803410, 420879414, 608120983, 669778290, 289103925, 428292208, 455935804, 969178572, 822331362, 106969874, 295834054, 759339441, 786317125, 541580196, 166595790, 401521348, 511597252, 67563175, 858772526, 460606672, 923050057, 274388616, 757209001, 921186303, 175992268, 265720890, 580459982, 255009407, 900166473, 498924147, 434406142, 155829542, 83028344, 599301714, 777306184, 724682703, 795804590, 32437401, 373428121, 235447244, 893764058, 516114975, 327833637, 700739036, 623757450, 478629858, 170535742, 530423089, 205532478, 182765733, 728120705, 416941117, 143147639, 750766891, 665593673, 369681375, 461306549, 558144532, 588927141, 453804337, 545854395, 892680753, 424926793, 697512585, 190060185, 664537950, 115428789, 707048154, 83228124, 728956198, 389570571, 968852768, 98677824, 241544515, 651986877, 359063927, 665090445, 454346154, 576751343, 116167509, 392803556, 41358702, 99805582, 40241740, 544696294, 372708992, 512380976, 582507968, 684157098, 400773263, 701156053, 52583229, 97741260, 845941672, 142863035, 97860795, 959308883, 80171519, 113806494, 255820502, 130726879, 19790810, 405877118, 698315546, 239685908, 549773524, 410328477, 92118420, 555908317, 331376717, 727792260, 827449505, 97311253, 778272475, 752502128, 646217811, 637212870, 693756800, 886740841, 765417455, 544425867, 164236823, 191727585, 863695838, 49738007, 497853818, 251169960, 668620122, 820404839, 304330181, 914201600, 969787973, 884957450, 995732688, 532920979, 608268437, 158760421, 44151381, 978368966, 671032535, 743510694, 296645483, 82795088, 163292831, 756180434, 293149215, 500027718, 479003179, 368753917, 762528537, 166475034, 451256121, 831518399, 789583115, 613742809, 346819766, 529706978, 989882314, 309417911, 433694572, 807594826, 918889970, 520140811, 215760172, 664623728, 394184615, 184749597, 548009752, 930863579, 317874956, 698213348, 214144850, 366575666, 299939730, 33206530, 247213439, 92311869, 801768722, 397466400, 432336696, 67787477, 173663654, 664101306, 630029237, 399982024, 421763077, 507305174, 206992528, 892279244, 959943346, 537366749, 115374323, 987218950, 200264700, 507343551, 2731291, 403763765, 60109450, 364739289, 410406863, 612352150, 91799694, 645175397, 233219100, 417801837, 450872782, 666548914, 201366328, 865768500, 34211026, 760329154, 102740178, 528735644, 522745842, 880205046, 92175099, 408050468, 432868431, 602160438, 985777290, 941003019, 872288968, 122731044, 490349054, 713712022, 312985274, 416638085, 289568594, 38470830, 264415423, 630147597, 958354328, 183924595, 340628953, 637837776, 329155074, 352132282, 274528905, 972282951, 847316109, 77611406, 326148395, 253045180, 502206153, 175256505, 555294672, 580511090, 111252931, 368735774, 595778926, 460926243, 681516896, 169481904, 754280493, 32967371, 85647441, 559831404, 653302698, 686534856, 371239894, 476596335, 21827374, 323613203, 243306642, 146265493, 880194282, 865497150, 374488268, 344002952, 78934724, 605376620, 699877127, 600938103, 915073242, 623017235, 109821732, 142078407, 722027034, 656221229, 81258794, 109949152, 831529754, 706247039, 107743556, 594334213, 927115263, 282707002, 495985687, 266011332, 695040297, 982437040, 249915430, 931067751, 929114536, 514276386, 714065940, 299717748, 76813632, 744232866, 969529288, 991214654, 27070458, 265357903, 451403613, 997404555, 456516365, 833739461, 979675781, 261079945, 708169769, 215923074, 855207005, 775698427, 801696581, 208428725, 770753712, 869195153, 204197169, 615765245, 67828774, 609938050, 632706086, 873221645, 406798613, 105930828, 612925916, 250658843, 341439534, 517957639, 883577205, 82863519, 595656068, 899815985, 938406490, 560052779, 408104187, 150387617, 424438062, 156342221, 733323981, 165713874, 111570566, 575445024, 377934372, 337806848, 995782134, 972612076, 472833030, 862671243, 464426493, 126569367, 525128095, 402248200, 486498407, 987105524, 204760317, 328466013, 634331762, 360530816, 812165260, 941739762, 774892862, 239303112, 739960755, 812021516, 671209398, 888851031, 64602238, 631513467, 963400565, 664490530, 321164705, 29893913, 500164258, 417658035, 192536152, 679885931, 319765223, 54949917, 812037676, 372753856, 899119195, 938626430, 725753758, 263808225, 542053229, 661601075, 829335450, 424460480, 191734732, 525165770, 336253152, 931155350, 529960297, 292430550, 587523457, 811349453, 151464163, 205835154, 153859518, 768073663, 817850435, 781758898, 579096596, 686958103, 878169189, 613571447, 428906761, 981436072, 98084584, 190064073, 515379977, 179519764, 392373510, 14289689, 364194098, 655395227, 155177503, 168029493, 790849335, 718751532, 654387818, 788407256, 346349429, 818369682, 81624395, 678997002, 588692850, 514900412, 194872999, 317223743, 127223062, 215673663, 266041887, 736486556, 751960806, 233903923, 167820397, 450690654, 332320549, 372768127, 981814496, 619090598, 494096299, 616265157, 104789641, 696588951, 145617830, 256283826, 859279639, 257520052, 490292946, 784916125, 807035926, 40852286, 562215850, 896768652, 348221761, 898733165, 804788104, 648878203, 726412962, 215787091, 63061408, 978273712, 168585014, 788054327, 689141105, 725729878, 769608634, 855503941, 52272726, 396037057, 220304181, 59350196, 138864974, 631109610, 395935559, 300274044, 713711069, 686485580, 130130628, 688716713, 912822467, 793107302, 884496198, 40884067, 851421699, 815927266, 340675919, 631448671, 200836378, 760721997, 445402720, 990853690, 199557326, 428461611, 107184484, 909972832, 943943421, 506232939, 30526570, 17029708, 93682532, 55707545, 493229384, 446992648, 773501967, 265800019, 31467962, 775855721, 908003864, 621056161, 50923412, 786091235, 722809944, 478321486, 302399461, 465564703, 116767001, 24648158, 832486100, 841358107, 814803474, 742630141, 208020184, 161349930, 108523680, 546817414, 415308173, 558060597, 974756980, 989525225, 795041081, 269093111, 653192630, 380759674, 732055357, 355455824, 350639630, 349993487, 161387812, 266855778, 858862383, 119853880, 125645323, 282134431, 529107974, 591396747, 854307912, 222756291, 953218453, 649973808, 4541001, 876374626, 881006322, 222524609, 91180966, 411841678, 911865670, 791890908, 684770460, 133824697, 220482076, 33872841, 124763347, 847549623, 527886510, 751461280, 622100497, 568378357, 547508245, 12867459, 126077315, 752447830, 676442500, 407197408, 496836928, 501356967, 632117004, 707910041, 96734466, 487671957, 838339072, 805921784, 490944081, 331340851, 866621927, 964563975, 629247039, 277813560, 17575947, 822730511, 539185642, 712647768, 585093383, 79439345, 333963974, 23490268, 433502484, 658538343, 996158263, 684991256, 433699461, 999687167, 895967388, 70838841, 430921622, 258189777, 747598267, 583802092, 249698352, 793391115, 937240818, 203453623, 194499772, 453342323, 815116060, 341326658, 603014057, 327361396, 481744785, 477717167, 447912037, 68085061, 25365214, 372602076, 653335226, 397051159, 960933692, 42698736, 24783383, 703535299, 69831634, 354226013, 895433493, 580547700, 372825745, 429680900, 175425367, 122472101, 935684751, 712210905, 321796656, 552710467, 798881091, 458640818, 100548775, 739967322, 811409240, 317467362, 134898976, 434664811, 443199676, 23062718, 93899691, 205626828, 713047837, 243728220, 142260190, 401534696, 613443960, 169724481, 633306281, 504547257, 133139823, 604971392, 989783791, 491335329, 52894414, 937913813, 8661853, 900558234, 810153796, 632928598, 807440700, 32700684, 940025604, 18760794, 14873181, 983782861, 809104269, 544014927, 907457346, 199080640, 293963468, 525915073, 166645148, 302271759, 825897495, 600173437, 762619600, 225202437, 641001712, 829277099, 890365488, 48292904, 297077148, 917524246, 71835697, 9675322, 388869137, 543895613, 385708882, 107385949, 770549752, 270474568, 992730809, 194767022, 773560559, 749481116, 535273531, 833969371, 496281865, 359842334, 790479669, 192061098, 574750047, 499655081, 833037230, 428515199, 879133228, 821565126, 477913331, 892802526, 698086845, 62798361, 382572087, 474642929, 933316464, 801233696, 468197913, 486619486, 356142424, 672161006, 651628433, 189150190, 41703350, 610804178, 861249356, 328358296, 683458148, 84060963, 474572139, 758740555, 299876336, 344952066, 702884913, 793729144, 293001617, 654150485, 422639147, 647989679, 705687041, 966107758, 919782653, 173523512, 251389143, 124802347, 737721329, 907248537, 502206334, 86717779, 105206064, 84099482, 775868912, 127808160, 859434163, 927960417, 311622005, 439116906, 74098843, 719838928, 870329736, 811916149, 877379347, 19847044, 333549253, 509262209, 37641232, 958477979, 422481388, 181053454, 782344927, 428251529, 629470271, 422143615, 936455627, 542290908, 992247234, 162506983, 228849806, 879707964, 996485375, 50752989, 633073336, 375498946, 744786176, 659179459, 672689245, 390323514, 272514282, 997326174, 211491535, 73241187, 178130803, 827114690, 32035282, 923914974, 708897549, 391320319, 307127579, 633066805, 190259559, 549643428, 750294150, 369296292, 287587689, 588627410, 345019479, 697881897, 907754447, 794454794, 861172804, 162780862, 7075710, 24350563, 85947065, 375171597, 771634401, 542158404, 87597247, 517844317, 326373342, 223521870, 582313338, 640347332, 427247940, 841666388, 343523614, 135856761, 898949437, 188553504, 289498849, 450212560, 325480187, 400904386, 158097394, 331465730, 68949817, 829043537, 600106383, 962737818, 194168505, 719421389, 594561903, 925782691, 928195585, 806840245, 508835570, 417415700, 207916630, 730856323, 936324224, 492049540, 869319718, 962524940, 302987536, 291187667, 975609513, 645906917, 460237295, 775979552, 323811028, 318278001, 262668034, 432600604, 226727896, 990151290, 494257211, 894948649, 123987657, 272765421, 899437355, 607179069, 568972758, 226711749, 997865951, 302803957, 724742042, 199044482, 39310785, 709852123, 561308691, 737131462, 715400327, 455580794, 744228443, 465864313, 862775117, 448978205, 128912523, 923988193, 730783227, 148158515, 128005723, 98595528, 555886808, 785937865, 93632290, 211576330, 520848633, 467228207, 991273999, 365891502, 900434150, 222375400, 864039247, 986027358, 967480685, 356979863, 341384031, 474265552, 17486377, 589443547, 333785607, 71626539, 379085975, 350376774, 418601593, 926102185, 772737751, 286227285, 322243650, 390989738, 449150790, 868560507, 463223420, 224485420, 449985097, 147336067, 894290837, 402691311, 37797301, 283365689, 263728734, 149116903, 671058267, 430049195, 961423967, 968805031, 936760415, 105928722, 623688174, 794727529, 936733019, 688325325, 306260103, 826075988, 89719937, 32067572, 727104248, 240676165, 635964644, 703783494, 850112976, 70344930, 277832439, 837980107, 217196934, 124766865, 620936539, 243049578, 505728337, 262862623, 767546330, 42613568, 914771863, 7073915, 648163927, 917229477, 259415647, 775687438, 346904435, 474559098, 943111242, 719744435, 137507988, 572800590, 931467007, 537626629, 91288467, 864677257, 145325148, 990337415, 11994122, 367804203, 896407211, 213903328, 469253325, 934813916, 119626595, 890367644, 30187065, 327700806, 226139301, 877516137, 293718147, 25920419, 358602925, 279228180, 335074482, 450852215, 186422125, 994748754, 285467277, 271759827, 928115706, 125664085, 941645052, 351650958, 672470307, 751299165, 148351648, 899789225, 259778549, 41832045, 137679530, 172572785, 161566108, 203447555, 650348273, 728688297, 197350171, 480651776, 499649497, 468752075, 140246760, 81066047, 732232899, 126583289, 990404451, 472713178, 921104232, 616477480, 75486142, 149662305, 322371007, 54157776, 862173170, 624904837, 285945241, 384080969, 160142453, 284625173, 881479655, 922669361, 297403582, 962130633, 568375582, 324525232, 788283875, 494967697, 806316416, 419645398, 571514644, 237976154, 799098544, 823273127, 279124968, 206463151, 942924173, 620129221, 634382422, 709367167, 171046891, 896501801, 685649622, 910101380, 623071564, 770625988, 832857594, 626059261, 268646826, 445750026, 722527535, 116215285, 412358791, 282589260, 37248637, 715525319, 657632524, 859649310, 341473828, 622699626, 929202122, 695233532, 369490590, 411024187, 698564497, 16764793, 190679347, 231240444, 191653615, 620926603, 155546218, 273350998, 680012819, 594692094, 631367751, 373678636, 193338347, 223914556, 79513499, 302208950, 307597422, 417795460, 283280299, 37313753, 734158912, 649231594, 663391001, 640252661, 992786580, 38723022, 880598191, 41048136, 246968444, 796561553, 639994686, 306221930, 918860639, 70524170, 701775666, 758708455, 599581486, 112361635, 728350626, 612151866, 25363778, 128617155, 537170888, 38061559, 101665104, 289217598, 241182809, 475387906, 859235803, 459202196, 726650262, 360835210, 357272936, 545963110, 929581306, 712851368, 164949229, 681210606, 977313550, 833820462, 689346232, 162384329, 626549564, 155514952, 82577757, 480967462, 931679028, 538202263, 997511120, 43724190, 853030360, 123665298, 877456406, 774238865, 412083869, 906222609, 256579898, 218022587, 1907040, 695175690, 73512134, 652431294, 550108625, 151274283, 581405629, 271961884, 510461730, 618964590, 796143250, 887405612, 514177893, 871184289, 300099744, 516092275, 701008871, 422131012, 731374998, 840658071, 340642757, 624241585, 52635739, 242441263, 521446609, 526028433, 352013061, 450651168, 109269684, 346618725, 208577903, 42607175, 116152041, 298588646, 752009827, 662794063, 18948109, 560666269, 890924870, 391213186, 600995342, 688655125, 952612197, 970354038, 931006674, 322140695, 406145810, 719693105, 572122822, 324624869, 684329182, 431360186, 31150906, 838370613, 468940778, 638339683, 989780789, 627612060, 745006136, 664775532, 250728151, 710925691, 189248242, 925542783, 359013155, 510962624, 831897149, 537020873, 23949978, 354817650, 371928130, 930116671, 327486395, 431584563, 683568148, 956017286, 317245341, 298985474, 52438498, 91457790, 495921842, 368200035, 997414344, 951159225, 7127380, 951615375, 655384184, 378361218, 578335649, 937743717, 494216195, 894998337, 398101823, 5786712, 470094304, 736240894, 438556967, 948611403, 24462053, 355044531, 851771614, 128835350, 147283960, 185751169, 765288011, 59998761, 957744902, 570146786, 951289561, 600970868, 546757159, 494543700, 872248250, 152856306, 582769438, 203211239, 623401608, 124640140, 581585930, 480170826, 299559397, 693955440, 780995683, 109696153, 946566792, 49814326, 315284848, 834642195, 639845333, 359355781, 347763541, 530645943, 517273444, 685264430, 117064601, 298277929, 840531528, 301806734, 216849141, 59391510, 443124839, 628059774, 743071617, 926276785, 384290112, 14701508, 438962506, 407930017, 268245439, 467547473, 528374772, 242815049, 996579919, 484689696, 670058641, 788386642, 152346082, 302870057, 435557544, 159153727, 920355712, 888496577, 797234746, 625089484, 266631010, 351062331, 937426670, 191516406, 870998217, 470661363, 948840112, 631587610, 535383888, 109455068, 818476481, 308799160, 352480253, 772957950, 68806423, 660921384, 493177482, 449910144, 248929111, 748952580, 901761774, 505475360, 202844172, 998586761, 177252894, 61328136, 8938226, 309708563, 457972430, 763487571, 933874880, 713048482, 182909926, 454982039, 671204424, 944123532, 98601628, 691444083, 510187973, 278670074, 683216608, 808805919, 140958221, 969382749, 378745917, 684178307, 936854221, 84097337, 924712434, 979216310, 609510023, 536849296, 890737387, 823586937, 912632810, 950384953, 52854211, 538706675, 188291943, 796957419, 42637520, 383653263, 439849685, 983769665, 455737347, 85374801, 701973511, 237404354, 634156582, 425556144, 741948885, 616566810, 365820101, 247891357, 534539804, 239550831, 205397140, 363107848, 274340244, 627993730, 786087072, 648650183, 726213914, 881199094, 905159813, 285161159, 599769462, 858376866, 669107539, 711808799, 928698930, 297679100, 140291085, 348190325, 813416937, 652168935, 475491167, 748394778, 872769111, 77575185, 542435325, 281393734, 646554052, 911462528, 796467555, 714506772, 746410839, 591344822, 258079022, 327095371, 78558362, 243649277, 78372706, 155054171, 955417174, 680408798, 346778027, 463785871, 416972529, 900162059, 609299118, 63291262, 354040414, 944298638, 513613830, 799749522, 99927660, 872714539, 221349881, 729174335, 993304916, 993182551, 800784812, 735926514, 616626136, 919588539, 837482950, 946004925, 217897893, 58583363, 73627336, 987903813, 90297612, 628163706, 649407042, 379534703, 664752327, 230194825, 767648215, 210333394, 181790024, 438226806, 106398410, 472533715, 607282886, 394749860, 109000790, 705027668, 475748946, 622363480, 579283463, 342301116, 801251990, 538884990, 916390204, 445148082, 909189573, 398847478, 915685397, 579195674, 579343481, 462877122, 220698517, 969979383, 874121618, 11463713, 127778054, 602926651, 784928403, 513992599, 96109061, 477260304, 11352592, 750827978, 649630501, 937236385, 100409677, 827491582, 585174620, 508390260, 674089913, 37801171, 736460678, 466009019, 893278914, 315306294, 23794118, 10153674, 645244354, 321767474, 774916172, 818953195, 738561931, 747408722, 49195766, 149470624, 199160682, 701473844, 544093328, 548359104, 739714180, 954770477, 678587641, 109150516, 34613437, 729459961, 408714712, 739212007, 796512421, 923862888, 529742677, 759714947, 841465827, 368914804, 71204059, 846844466, 399253551, 255044869, 88166628, 892773075, 708210930, 829360335, 827533832, 142956655, 324026197, 600581891, 212568690, 19943430, 104191254, 410752195, 159354858, 736041676, 842121386, 648762233, 915552892, 192971931, 982080187, 743629960, 54572148, 597588384, 367333508, 432608704, 806612584, 139629503, 51446107, 15494939, 202623730, 787932106, 30396478, 728205537, 234286155, 545954159, 917775594, 589510303, 475289091, 208903047, 300889116, 64904044, 419987911, 929500829, 894611317, 752990985, 38039041, 388796549, 908733855, 807551852, 33169520, 292871220, 83171003, 917644165, 286271001, 381180097, 503667694, 320803537, 733170524, 408031256, 526555972, 15669051, 541447840, 285285898, 293288239, 510656649, 377671894, 358361445, 701311642, 946168166, 548454522, 386685784, 836533100, 35085822, 628935068, 680538609, 893882707, 788963208, 169756651, 267582268, 499208319, 478281581, 130643928, 684224050, 143410831, 970320029, 883062844, 332504577, 728902430, 399439084, 200005382, 195076345, 401352021, 191808551, 756768909, 63597262, 737609328, 286979734, 888268854, 259615433, 86265219, 185809227, 281674561, 479574288, 58007679, 664413006, 743171937, 672105653, 338946711, 68691256, 335439557, 171609220, 86057136, 288006965, 781689308, 467881219, 356078277, 496331314, 832709705, 654254568, 160938134, 221847997, 766109505, 610542622, 357390659, 857415354, 244391304, 27829517, 526081485, 105481466, 84190166, 258716500, 455221846, 283636618, 822198807, 214472139, 79155153, 64885295, 743732660, 554011714, 323565961, 250976486, 280059054, 24475132, 962598943, 86162161, 991491268, 89991510, 162461053, 703863617, 702802104, 986572898, 589373984, 863388740, 919214478, 42457928, 162767594, 307114037, 372117896, 636841447, 981913621, 516906448, 554960034, 815700138, 308385794, 656614083, 252304633, 408385064, 760442044, 270017481, 739187257, 61132013, 582932632, 644855168, 697031815, 108626111, 290117262, 702502852, 935211863, 339088494, 68081254, 452887545, 969415481, 219572653, 316263978, 824409551, 619017742, 129791343, 608403739, 127970861, 990726335, 559467348, 571360493, 957879080, 353195567, 640921384, 730172692, 413181953, 263885908, 281585179, 723307140, 772897476, 248115653, 422591876, 283310518, 679680506, 389709214, 41256783, 940405957, 733967747, 76244148, 812407810, 201953191, 203435274, 528530120, 650013961, 333319404, 950114531, 856430641, 992863487, 302525439, 154317014, 922679074, 687280273, 509647662, 674817709, 349155662, 267737408, 449503615, 456688100, 164488423, 981927858, 638025510, 882422650, 924801847, 147992404, 128937662, 635177125, 739959920, 634450230, 600280413, 973328246, 976885661, 645906177, 505318298, 843372301, 83626415, 501275634, 100340413, 811436908, 390484539, 157997145, 997622909, 368312195, 362475990, 318824405, 470952613, 186107930, 35139858, 719219086, 67019290, 618700886, 868824335, 413071927, 824462936, 725964453, 465744623, 249799697, 809338314, 872417761, 820153740, 279879182, 996260646, 818472551, 691843583, 625424693, 539779460, 242174846, 597788999, 881813510, 657890403, 646379844, 633805967, 751466055, 968620233, 104322397, 195625621, 24446642, 835057792, 744865661, 234086537, 425436216, 99898603, 472183908, 224433370, 384472378, 961532993, 914979127, 775437715, 461335631, 899824398, 404846969, 450559216, 657612881, 945205498, 113185584, 412132128, 541820060, 420711160, 797239640, 579837686, 578802294, 598633729, 358709491, 514267763, 820939572, 474947347, 967260284, 470368817, 28025323, 39759731, 943279654, 550708468, 514925660, 325864577, 93021959, 261889481, 130866344, 804464893, 264456795, 78234416, 144766657, 20605877, 277653990, 303492712, 679861291, 796472696, 714861202, 173855205, 986481836, 211720424, 846737577, 96687600, 417875520, 453137958, 22698637, 360095458, 327280938, 868937965, 424793331, 591996686, 109877361, 274503372, 406400834, 463499900, 746877580, 243669647, 436026610, 99282927, 230621230, 110056198, 284067571, 525145519, 410703404, 151662388, 386038082, 70352031, 281889668, 517045508, 7215005, 66597181, 931107907, 490303853, 422733848, 626552198, 351603024, 530458527, 230219336, 275860965, 788789139, 936896069, 575356448, 954683791, 436156982, 656058236, 709335584, 329799245, 69638761, 128953225, 222925891, 597005274, 597145705, 754283162, 803159106, 699506008, 999854377, 265091946, 444332732, 700175964, 283489935, 714892287, 443608973, 969340375, 75421167, 640369323, 344802922, 721001461, 337346338, 732767655, 490203906, 242692381, 459804106, 455028452, 679526942, 822714805, 927527792, 384822082, 885275226, 223006594, 202858469, 231763168, 983238867, 299544252, 642256234, 935142108, 446056954, 7260900, 185902438, 936958448, 378377420, 375713884, 800943190, 878197912, 484805375, 926641018, 353177587, 934978758, 721473725, 439771770, 270966658, 638135648, 684941199, 750933878, 330377935, 129985626, 320820744, 97718237, 715798852, 352067527, 121842319, 806883363, 521638057, 493151899, 562778802, 814240934, 252321458, 728550583, 75428438, 237786537, 184352843, 32344425, 708495613, 590854263, 4075275, 705908483, 333768806, 263896747, 347982966, 915903517, 670643575, 816201922, 634210932, 940599769, 710934623, 753565993, 176699013, 146178364, 572634604, 157500012, 156102362, 570864805, 305538367, 342354812, 742365385, 937804554, 459906069, 236152341, 472332267, 664838585, 977436585, 368413311, 386089316, 373705542, 286876036, 11974704, 805016514, 739855004, 418599788, 672553643, 492513127, 213248596, 271152023, 653864304, 716552320, 538958046, 135785024, 736947122, 952894174, 224744173, 587037901, 258147163, 958381027, 367841775, 172421772, 518042727, 140112006, 955473802, 280321406, 630542862, 184796180, 579892321, 426511368, 582318712, 975707088, 878778887, 148405646, 85989249, 519440844, 509644819, 55723953, 715212763, 348926826, 219623999, 730509255, 436064315, 373668681, 319384603, 400609734, 740368739, 463609294, 696909585, 209700886, 599277735, 687465179, 224166366, 62904184, 680697792, 24158159, 538895909, 383946235, 362534013, 783299782, 638303992, 877988199, 893697268, 254346891, 972900274, 471675432, 375596935, 970842605, 796000489, 784944245, 713287097, 918063562, 222634646, 128500613, 63760401, 887585511, 582341957, 910637787, 755299348, 828562746, 598574421, 892257333, 907096627, 389905080, 699362626, 431955002, 329648393, 713638519, 898122911, 650079379, 581289068, 141469958, 571529566, 95973547, 853812602, 710977729, 191760460, 400344262, 324003338, 583057003, 203373387, 330261876, 922231292, 179502261, 44285845, 908340028, 643084100, 560220811, 279519774, 40810187, 614339138, 929363825, 286992925, 175847794, 463195800, 965064468, 223520057, 951686203, 841855026, 743169438, 168036276, 139166515, 156096376, 246079675, 405767746, 154775450, 534258241, 902481749, 426614244, 888967354, 790163622, 245565372, 609108348, 779166123, 981435705, 956763361, 299774597, 758754427, 107033778, 600182348, 18588489, 162747759, 297270596, 10974150, 93957642, 255095337, 403585230, 300781400, 959500189, 818309376, 754256799, 412432316, 317104893, 978852477, 378442386, 397935571, 430685729, 22255245, 632772830, 254439920, 127686369, 801985276, 498230441, 879187269, 460210685, 568642730, 337216033, 815137555, 965458526, 519123130, 294968055, 55773773, 990967536, 618393920, 72888467, 783030443, 567705716, 525384073, 597413426, 653191059, 430384164, 139571530, 338230046, 57661305, 560916887, 78388240, 954045974, 640929634, 152263785, 316550944, 176594223, 481807027, 45859922, 934604328, 624166996, 129701620, 339999072, 357216685, 96592927, 284919962, 2412406, 405219901, 566709382, 420849464, 647803881, 574210807, 280837331, 637375344, 451764743, 815837558, 964311615, 377783182, 354957156, 52549125, 446745447, 849765889, 348352487, 707016852, 994588066, 931636447, 602652000, 197072143, 876004471, 149952308, 483299711, 527056538, 165368046, 667863481, 452739278, 739872726, 81686853, 844171520, 678278209, 183049346, 871813804, 753065996, 469943332, 302464253, 13608041, 200575969, 236614148, 640516964, 533500570, 829795900, 98498694, 299134457, 381975171, 49534226, 493645689, 382616944, 979976797, 272654058, 512774226, 122534466, 393620593, 556287380, 737574078, 194120403, 421603730, 885854900, 441930481, 205724727, 789337592, 785049187, 526074055, 861869436, 292492758, 147035697, 494946330, 19824185, 40692976, 958174090, 200305405, 728826651, 376699213, 386419459, 552584847, 862977909, 758396760, 851115714, 610938836, 69258656, 792651561, 11071573, 32042397, 625289958, 997042237, 3139859, 924877849, 435991067, 392373679, 912973580, 160278583, 637680464, 880057981, 865440083, 211518553, 5084024, 113465592, 55569948, 127217449, 121049298, 73466019, 556185387, 303901523, 511609893, 689298175, 8068099, 906354392, 554693122, 964726163, 20024579, 96972717, 618230002, 149613376, 81761310, 755069391, 587188972, 603878385, 846436205, 135644178, 879240231, 66973875, 530644601, 609903851, 147927065, 142693309, 885227752, 99208238, 300638795, 506719658, 483715545, 682172567, 284152519, 400209467, 196791534, 472961094, 158843968, 317851466, 441333848, 34871532, 820652419, 994773596, 618897319, 251592064, 796466759, 200141668, 243311656, 734784950, 449395600, 813592756, 584985175, 246258261, 954640736, 974736617, 448590236, 191949788, 590461933, 30854431, 156355665, 329698701, 920603726, 89167272, 224274482, 731777841, 321239134, 768900406, 164355608, 750046094, 415065228, 713017372, 863851792, 518297585, 834944451, 854546343, 301936156, 469133479, 296534397, 62931850, 728833602, 882211035, 878132340, 221467955, 432666394, 600393095, 639530379, 660492041, 292034115, 778098054, 531774392, 826234720, 971994128, 355021807, 243733790, 833778546, 5229, 339904889, 273757466, 794857567, 72315749, 108459266, 747245990, 471442338, 617004173, 217449190, 763016204, 633862972, 300615309, 130361534, 671757903, 137729575, 41347789, 541450231, 550599249, 861037843, 531960999, 948797235, 689835659, 571937823, 722369457, 540271319, 153705219, 89773221, 129697759, 12640494, 957024371, 640612134, 355215300, 161630543, 92008298, 887844364, 241321821, 703273435, 564505880, 534713129, 800065300, 330224568, 767037685, 586767903, 637802873, 72337710, 484465803, 131087526, 91102563, 172080348, 114100315, 833844674, 421813699, 123568374, 309888277, 308222558, 655993197, 420162323, 281325368, 841691849, 524271791, 268195471, 131805667, 879981184, 993959202, 568500669, 333443716, 201391661, 456501816, 243334030, 167343240, 116524072, 310435255, 47229567, 511973357, 599325139, 97028490, 799615080, 82722796, 195695672, 177545394, 897542429, 207757302, 654105302, 396209556, 522910341, 71956730, 38670652, 703383730, 53235863, 209331369, 743092899, 252737321, 182787556, 737482291, 631844253, 444981842, 259480432, 196642296, 791107695, 389023616, 105823873, 855327499, 117591268, 820761301, 391708411, 446817162, 58930559, 852021554, 334644395, 434373267, 993580485, 856690102, 810779198, 492204843, 964672217, 895089185, 648431193, 618280865, 42126949, 974362184, 689794451, 826277605, 680196519, 665491924, 494727039, 134263288, 550594335, 742084238, 290608387, 899947849, 360300598, 797655727, 615817877, 164542465, 552322930, 253263425, 243654922, 979299072, 56178899, 805016918, 973752466, 984696004, 720064134, 848649028, 675985047, 886060190, 47615545, 966104322, 407230309, 459701768, 307257311, 698107864, 2014388, 221250010, 252794874, 240374678, 562012509, 913189380, 332530674, 560139236, 353868428, 222665944, 858523253, 161938535, 327345652, 963346928, 677380286, 309261092, 781272040, 347339465, 211240289, 44640882, 43621536, 396077435, 856484782, 983535368, 112521593, 458813587, 947580464, 406954977, 326606216, 95727957, 49227329, 20297325, 439421995, 784330307, 733135496, 512062766, 601895890, 603333318, 641257074, 615713038, 380648924, 13651076, 463043366, 775609413, 902747664, 964802487, 640108761, 871610311, 205028299, 758194905, 553936231, 201227844, 965557620, 429419585, 871361225, 845781099, 59890279, 785960545, 6043410, 150074957, 294180159, 963087087, 733131781, 678604019, 228081064, 875411740, 921391298, 193519190, 850248278, 714215744, 205981179, 478912498, 999554412, 316702528, 196550191, 790074357, 389869558, 932437211, 918128911, 544874763, 912948036, 656397620, 589836772, 103826967, 707901697, 473281238, 317952883, 933025724, 506373500, 173995103, 601795397, 798259609, 962600613, 891910973, 113614063, 594334062, 44335334, 258092068, 266263737, 971429616, 637305183, 524170915, 85353812, 858990285, 123475548, 560309497, 314633111, 870870914, 903283710, 368934551, 851658393, 902755666, 300519805, 396583780, 355012976, 191285502, 413753944, 612073619, 743510361, 904134870, 8701917, 84845140, 774340373, 525885257, 8693076, 353660978, 772015192, 852246148, 820499674, 162622395, 361882019, 146457289, 156048982, 721841386, 668579737, 249131174, 668685630, 325135524, 663154111, 830105671, 767734949, 101886197, 197998085, 701087051, 18806946, 162946403, 215972262, 920294755, 598929277, 520096537, 428038020, 145964354, 584830397, 725145218, 812696393, 350450414, 856359009, 204321334, 516832066, 796665371, 384706316, 803669906, 921732050, 749390606, 675095657, 719049314, 480173608, 341635348, 346401849, 871015418, 962334138, 343771444, 623367624, 644524839, 681882748, 748412551, 271102559, 24289819, 294538961, 997795306, 634380042, 145936624, 567038076, 322796338, 103794029, 253002201, 719680962, 400829924, 376804096, 394268335, 724034476, 548865901, 280605518, 747754447, 506123433, 219627792, 840691427, 459396112, 443633580, 810040394, 527823476, 300747236, 888563027, 111681634, 295754166, 302132622, 592390057, 879245049, 646552032, 388344558, 554238595, 738696941, 164470594, 697013806, 938598702, 557565635, 351321044, 507211288, 484666131, 398992655, 999214199, 841828144, 502382782, 301522913, 900649677, 951403021, 561816391, 156632142, 885769261, 188062591, 574925715, 63220594, 19059182, 432490154, 538354849, 389743705, 595665444, 244998755, 745957455, 768056033, 109673243, 502365952, 389168381, 266011826, 286192213, 586075742, 401880729, 413849791, 136723077, 723436273, 769974363, 899719142, 420214454, 904481144, 41922053, 154646990, 715824835, 517527284, 429834075, 217072678, 805632645, 211736922, 838885288, 597002081, 15300224, 570478770, 381821800, 128259181, 932020831, 927291789, 358389087, 505279437, 557419909, 798815347, 959337103, 509444272, 511711842, 965633333, 811029744, 576769433, 763781449, 256812847, 722717331, 449492255, 38725296, 876768870, 368406166, 748535274, 526885543, 375371354, 374729798, 942765708, 683267379, 189110116, 566095106, 581290890, 522314867, 645371721, 229862895, 920576487, 380302484, 37507151, 617578688, 192157284, 964675273, 628099585, 757277069, 259515911, 56144051, 847368535, 792457740, 291687457, 699359222, 880270333, 421763167, 733153430, 699612723, 383740942, 404084453, 160913056, 122804626, 887648154, 885818608, 108031269, 199580019, 660958840, 678849811, 394414323, 682370752, 3674681, 635386767, 141664580, 149889713, 33628339, 963967796, 28239114, 574964578, 758596514, 357522271, 498275370, 649022145, 331825615, 404986673, 289729409, 907357081, 848404651, 300329694, 486888341, 354760132, 528165634, 688673709, 83761544, 93405626, 465129234, 992498311, 71091529, 602431975, 838650560, 654273414, 736596326, 488145466, 393076179, 550265560, 686310911, 68452569, 14624360, 148586914, 252481134, 370535936, 289333154, 489692824, 620683594, 866736802, 425833805, 630327627, 529142608, 985900678, 613074659, 308922711, 690699883, 773069706, 290109780, 588477077, 247627795, 485080166, 349401114, 352674526, 201727670, 429355314, 834193638, 558401651, 27255862, 691608742, 550033655, 180616795, 931771276, 169303299, 928859979, 339032555, 604359265, 74117050, 548113311, 603529624, 272426255, 60385135, 938298348, 242846965, 34046632, 100970385, 877501572, 472935711, 839058715, 881296420, 202310948, 450369512, 874699003, 90550162, 749604039, 584790543, 876211427, 17661910, 304735171, 215149704, 883936550, 558575690, 350088098, 836001195, 711026560, 180644664, 631023782, 233999047, 224325495, 190393642, 280763299, 338083072, 702766072, 111167760, 414545854, 351359606, 305953830, 341761233, 416194710, 782477115, 408786946, 360042924, 987034856, 696660033, 108830213, 341691793, 161564048, 756278125, 994268302, 899396774, 599389539, 54247713, 302968235, 380711989, 519547325, 792349823, 157114324, 441153248, 726367646, 369273548, 150438257, 284669961, 196791835, 977612343, 620924211, 772890509, 716872551, 203958679, 983120444, 20549684, 139042366, 502208396, 186735570, 654071607, 256799824, 211632126, 324155050, 437551158, 729812817, 475142355, 38909809, 907694702, 98039702, 82845166, 299849379, 468348818, 965127584, 571082206, 787603601, 932220470, 705859742, 587475810, 207313722, 682520297, 938586655, 90142832, 303635433, 536871458, 91134158, 532650608, 753091028, 779120917, 7145020, 87511057, 770482208, 424000422, 31859291, 871675623, 139903047, 110167280, 630810949, 165986123, 435748090, 139536487, 383414979, 308015382, 286232182, 769826364, 974249687, 470567988, 812729484, 320979897, 806180583, 507202783, 231650676, 606786758, 875288236, 570432660, 927052428, 32126026, 969685338, 430482654, 975863527, 873129747, 714514530, 342308182, 220482922, 623221519, 928426775, 682001977, 953295695, 243240213, 879862756, 66707606, 867003286, 918370078, 285045926, 612991978, 471670800, 57316294, 17896608, 843180241, 554447481, 947044304, 351802421, 846766017, 290327495, 561477842, 133485619, 733630005, 339326524, 545686611, 637138270, 718719632, 967589410, 990908350, 178879300, 369349263, 103258177, 404342077, 707591010, 284471516, 641991830, 116881924, 75528553, 850822246, 808609256, 513604399, 466593625, 509171145, 971739443, 952338630, 423690070, 371072818, 581400987, 969179646, 692029695, 780709109, 260892015, 560783592, 77354927, 33557227, 198743812, 60674344, 399128622, 575342906, 299898247, 664981161, 430151647, 281850027, 954993052, 358956826, 341621961, 2283369, 297497473, 638840826, 212715709, 226691751, 837485480, 576697040, 992948469, 85718321, 810566805, 277701102, 326026411, 813715886, 840502230, 121533479, 473978980, 630822641, 240631111, 381081552, 442913623, 289388995, 552808733, 67875550, 638821612, 377595466, 784946281, 569703858, 679926067, 560587415, 793399891, 640128367, 31475395, 504744143, 217925514, 401158777, 903993689, 801762098, 453037927, 176451714, 910985361, 456689559, 273677506, 13752221, 632047699, 179476781, 243730122, 297606864, 832060813, 347212805, 731147777, 231064678, 785081522, 577795782, 866926951, 972729902, 986416972, 802530001, 445710788, 361679778, 393613919, 780255533, 297981770, 700408820, 829207178, 467146107, 292679291, 329761372, 532577928, 811401915, 451399293, 377161995, 405662190, 594533589, 576335509, 284439158, 892376072, 103056320, 877427487, 804202836, 472794743, 673428102, 371851768, 537590691, 412313051, 897333601, 640230617, 258910778, 980505746, 191514789, 976761478, 537344395, 830701705, 451531835, 582775178, 598499854, 980848108, 465470525, 592919320, 887342572, 8069475, 877805046, 547464708, 534056703, 536813251, 399535170, 643988605, 695970044, 508444048, 26111655, 418388099, 956793309, 159615134, 488167471, 289003449, 244564709, 285081840, 304649057, 836066377, 34930658, 856648280, 211837356, 864366936, 89422282, 478676524, 933823346, 170895867, 664559643, 972272065, 622951657, 497991927, 907203281, 182101503, 78203044, 102234984, 319132354, 525247228, 195877153, 955115260, 628183270, 840410239, 49921477, 239499020, 591267577, 443751181, 655795940, 364689400, 175645447, 952013042, 683740389, 144446938, 171585956, 693614727, 688096210, 268890870, 971744558, 429182467, 363777526, 399767640, 568760513, 851121812, 309627697, 874958076, 79028474, 638428291, 599913865, 154550715, 690095832, 878026338, 325775453, 254388248, 433827627, 174234732, 906039705, 538989693, 137908277, 652543013, 939452907, 915104835, 488524595, 778104504, 721671539, 126618703, 83004657, 9329461, 151591260, 664972945, 847605881, 670063812, 811649708, 966211618, 526301191, 784110511, 267442877, 537674022, 481597440, 777567889, 487813366, 253134786, 385331419, 573829359, 516583748, 838144741, 334609561, 141513548, 971605331, 583867465, 697812149, 995600307, 347045355, 243778101, 734598909, 86114144, 338161334, 135162979, 358120443, 423698074, 550732072, 736723804, 720005738, 833431974, 660432265, 81062139, 145059663, 272361808, 281713898, 696101150, 71706286, 206625996, 527363026, 82148574, 277242573, 417901902, 622810770, 737738087, 782268623, 390732699, 87417481, 233177168, 7498934, 110514347, 985774106, 107566265, 449302664, 166468309, 565066999, 906014071, 269384991, 509504054, 527603732, 714027800, 668018130, 930094383, 933728271, 503956348, 536517435, 54220705, 454022403, 872740593, 363198896, 395423490, 409702665, 858345994, 906586087, 964307498, 363215019, 321555036, 906587702, 445685289, 341251242, 426447894, 433274804, 795951613, 784435476, 534663293, 497790070, 364487702, 523817737, 707506748, 858346166, 446532147, 877667440, 46582713, 755484735, 254551313, 299428744, 990875187, 178887713, 701250663, 905995260, 273477576, 325466850, 912184637, 932845768, 513324662, 794289660, 906340356, 526981096, 253302882, 512775323, 639645065, 906685224, 707435753, 579081112, 765126697, 699265543, 609641090, 579932068, 780346079, 794309084, 923245439, 115151701, 611885031, 278217151, 767156491, 438930284, 316770457, 564664167, 837884316, 835519488, 351335085, 230055625, 662039367, 285094318, 229650688, 765888526, 382246899, 587140799, 344420146, 904076941, 354453161, 801196716, 863579076, 940006854, 595896001, 297924515, 421444028, 644630302, 94829410, 416063914, 651877082, 215721180, 859654071, 178906769, 530025997, 313590053, 561941812, 880984748, 412066074, 473248824, 180258237, 512821375, 93966024, 668712825, 783329568, 73232268, 100654648, 144946608, 292429324, 216035197, 666564730, 135215608, 656763782, 896511605, 794391671, 147641513, 705997329, 695377420, 462856987, 145461658, 888355654, 270715131, 763823326, 798128341, 481579225, 418128894, 400820127, 161928669, 492644755, 850015591, 736800897, 904022519, 304626637, 410482399, 566415898, 385395437, 452162809, 554299648, 925536111, 166331756, 873221334, 246426967, 419490250, 85079873, 500863324, 204093575, 637042582, 434264805, 731292417, 841310561, 802903062, 329523428, 472304620, 762099710, 238382266, 183096788, 296490386, 498881534, 166291749, 382311337, 709991139, 712495681, 611462920, 171994361, 208155648, 633745163, 728304617, 855370568, 346370233, 549447381, 182961343, 250513401, 814601544, 586425454, 967441862, 691921836, 190187170, 495159352, 848578420, 191519258, 924876741, 349508393, 680146497, 9764402, 757239133, 749489068, 762641631, 26835731, 437125477, 145638321, 874889180, 184959400, 300218211, 197131961, 494307632, 823129344, 618462078, 177805644, 654822082, 288325734, 217429737, 95799167, 482954643, 119160204, 198137346, 450497746, 272845739, 319140117, 131397201, 985330025, 991397342, 672605278, 637027000, 48292716, 869711568, 381403899, 807216310, 496971570, 914446420, 31481985, 276425980, 105862772, 742621858, 322121585, 752118550, 283029390, 137123525, 600636696, 136411791, 857425872, 974137231, 694667050, 478668244, 466359353, 457857945, 473083661, 895512615, 958767746, 87228662, 28584449, 396445080, 667808697, 974722348, 843704187, 414145266, 577008856, 699686606, 348950542, 72811418, 992966949, 693494282, 839307345, 749394506, 920111651, 790317785, 94287427, 268960877, 370816064, 996677430, 899460007, 653078687, 190978353, 882326189, 801879377, 393105609, 287171392, 256932293, 975598100, 336197698, 511762350, 369311843, 515894424, 902376877, 5526244, 123292874, 597882445, 557623818, 592963667, 817778127, 890422207, 546246854, 811839584, 282010184, 47338417, 406780899, 29135338, 215828308, 256618040, 446857097, 946828720, 514264753, 778700299, 510147181, 766889100, 298395948, 229936807, 407000271, 705737477, 845553495, 877325244, 46739253, 794509573, 883828168, 431000238, 390412428, 1424577, 607435346, 61451462, 211998626, 72751478, 43303607, 785385944, 71212156, 944865798, 15325569, 149718294, 922948299, 385753228, 212011726, 223971877, 276221018, 851265029, 318144159, 972577126, 85738016, 451214995, 641793073, 881293738, 360505909, 98217199, 65623012, 949832032, 317293257, 545359694, 150561006, 253503404, 804679668, 324848465, 630469709, 124737130, 266266501, 848112952, 292019103, 866551932, 361509218, 259776653, 901403333, 244657158, 780208571, 790464048, 207447341, 34823695, 675913446, 270034344, 131878587, 237747502, 234475159, 899823465, 618812713, 382852638, 520918462, 150427347, 186440373, 97056201, 613840154, 847140206, 575052921, 539977192, 137298990, 531804588, 226982152, 160213603, 130493396, 711235848, 137882489, 138904921, 817261440, 535816980, 787086175, 193718520, 721712250, 855022484, 787226627, 848354140, 134188878, 426442861, 195525823, 556366953, 494583733, 334992443, 982980950, 674161645, 960719603, 565049916, 213325882, 800178193, 435309268, 678780634, 193607243, 302672064, 286281760, 479295623, 334298108, 493005468, 551781786, 745384278, 276635990, 9208959, 13118764, 466511715, 843208338, 888508237, 115895495, 595359173, 698717480, 690244627, 818153966, 311394811, 2043683, 572473070, 342512568, 762290310, 71291244, 435320761, 767866272, 195625403, 403783281, 746441939, 878280383, 389912584, 326502153, 294827225, 748912446, 71325256, 108763407, 151276226, 933328305, 687694202, 688095028, 833641208, 238342658, 464104360, 30938146, 612477145, 806938533, 283897885, 912635617, 219448727, 88980359, 509230170, 831775021, 400847638, 259762951, 61476021, 129054550, 740262376, 718896966, 989328731, 336145892, 758310888, 963704547, 852128423, 106350859, 781262892, 522774848, 432537954, 240615514, 658101236, 279020336, 329835068, 359776959, 447363201, 614382191, 993270829, 947341695, 246669628, 754620609, 443396120, 7879232, 498410509, 402450192, 511946486, 898120307, 305571908, 916837975, 170267778, 17673197, 691295912, 607720518, 402170763, 862229023, 544949158, 528357240, 813183298, 808739972, 780283942, 322845285, 13596828, 857448058, 546580616, 528287538, 315998506, 713254122, 976582366, 32086635, 187576844, 838942710, 449078450, 28159142, 106395526, 718684934, 664611940, 641283511, 795990563, 879424876, 665197116, 486911418, 70248888, 576972920, 186962287, 741174747, 312401896, 720891879, 846407047, 267550158, 558151472, 996559184, 492525513, 842467543, 894973884, 979163026, 915268259, 814086950, 771845825, 890882467, 28633323, 723663588, 976832329, 276943801, 923284654, 799462347, 23451617, 143776792, 44304157, 53960054, 599428607, 946701448, 469203167, 445155461, 504409469, 776034054, 105059280, 595826839, 84505175, 734052420, 483718687, 375055979, 996798916, 108753267, 988191128, 3976550, 839916359, 549333650, 449048977, 449257024, 789720603, 440435840, 499752223, 285416764, 636114048, 482760413, 18987487, 56113264, 829842489, 498154592, 842673260, 610481063, 458147121, 211289623, 157980544, 122048689, 478177980, 579015022, 570765477, 278671704, 983095864, 386818580, 50528460, 375034681, 205352815, 333742450, 537871139, 595121835, 35579849, 119180259, 789531153, 811222259, 533072262, 849463294, 447289437, 298284748, 284918139, 648929301, 656772546, 553165974, 750153478, 547125880, 83859687, 446075270, 7862313, 747104110, 547183774, 172747182, 588820638, 697308890, 512458428, 990606181, 620908639, 830430472, 640001911, 21685135, 454374774, 537802419, 920809124, 435478084, 715809443, 807373153, 980184311, 728483705, 212638248, 572190402, 936843659, 810459835, 755082467, 193807697, 975743418, 608431113, 764468599, 942020996, 482540028, 238775194, 252343679, 353831045, 235043335, 867788267, 523455943, 115547731, 362717278, 766334753, 479566286, 658110751, 454985935, 187827825, 534047225, 721758127, 198724279, 670448528, 322632552, 115544942, 755416385, 846801212, 107061965, 812329373, 114678027, 627289047, 306391122, 158436867, 955848607, 233862265, 75430499, 965804463, 772751509, 825124917, 459558692, 254192513, 158933496, 20654655, 307189144, 595659451, 414983837, 863382037, 37834661, 967263331, 987862510, 980952718, 248491138, 264671640, 703382267, 393251399, 543721946, 326486516, 661106706, 893362453, 826411410, 273710891, 988286003, 795494551, 226870413, 76261494, 593010246, 301768029, 744641836, 942272329, 355264171, 724578541, 435709465, 414541960, 156546120, 298811183, 669806228, 485884616, 966529452, 668006384, 128480101, 438145362, 370686884, 664921175, 980605948, 98414934, 910841979, 989531062, 206287147, 876139195, 751170888, 454613377, 398734355, 266278562, 831508496, 496756466, 520580019, 814924704, 320078143, 320377417, 22442484, 686980447, 187979415, 533785953, 390988584, 528419005, 771269267, 842070018, 197617845, 917305636, 106527016, 115496374, 452687186, 648069237, 927182110, 805939523, 501819569, 42974028, 840373295, 623954873, 981913994, 411087461, 314844212, 985466200, 551370215, 255970132, 532005670, 701382768, 375884205, 502196438, 367276358, 685601769, 948571001, 890012718, 980707936, 648316959, 558342576, 24856033, 193090055, 367781945, 718380339, 873446386, 177256227, 975035697, 852801009, 933922037, 885071071, 996984673, 813737383, 434141031, 755831513, 339649631, 14163425, 462079411, 227570450, 609230256, 303524394, 391473153, 884455999, 156773876, 994171649, 86155076, 324125221, 912275968, 192599539, 770059303, 304421477, 257870544, 325051284, 477567317, 306683092, 893580103, 241794652, 299990363, 367176812, 980545644, 719183864, 976740552, 596835975, 953743341, 828410263, 17551787, 530407797, 615867179, 970864943, 640663414, 2902996, 328717951, 587103193, 576159242, 668636602, 730674710, 41809587, 98882423, 529060593, 215338282, 665185727, 843061420, 141502390, 274068375, 890090289, 805524348, 646009486, 715850090, 149173442, 482953129, 222803474, 576690659, 965299890, 373406570, 430748900, 992072491, 197713458, 291032073, 931835562, 833686959, 904679957, 772286385, 350487922, 987198260, 764870168, 34405630, 416913140, 309675550, 112509985, 662858690, 389545599, 495207335, 428747543, 804272487, 902882260, 344075115, 79981698, 414622526, 510461074, 688663370, 4870799, 354849557, 580831046, 959643807, 702601794, 438415970, 953343876, 298180892, 241944465, 425914348, 91322734, 483482110, 412703697, 249260642, 521260497, 475336602, 851617014, 769182210, 720820389, 286058821, 660387521, 564818251, 294907757, 329715236, 484776856, 543934538, 187396979, 464774729, 884984690, 864394003, 805755707, 779637127, 787108545, 466242477, 754046450, 342993253, 532213731, 331167040, 719309625, 502621712, 236043914, 721689555, 135020191, 901237185, 30157280, 756370144, 341772132, 386234738, 740490698, 956189786, 499824731, 141673432, 580487156, 223758414, 681324168, 723605056, 774108407, 558497989, 90885661, 496685774, 991557356, 277015434, 125714841, 685246839, 421968011, 789108978, 732084200, 544062507, 602073449, 466104816, 247129008, 230623055, 385212463, 532819376, 666323293, 914845811, 262519185, 872929398, 159767188, 537280492, 714749213, 610646258, 494163479, 437217014, 778668052, 202124279, 79793229, 313826881, 467901833, 224858052, 533712016, 981462941, 498271938, 528277646, 602009763, 780329862, 918429866, 144406043, 594902614, 980171019, 703818790, 510519798, 981185497, 125511662, 124534600, 670480273, 980806531, 958625091, 577982923, 687083939, 557241770, 594390486, 723031403, 896006089, 678694814, 445072779, 663014666, 164996544, 368803513, 906333806, 813306606, 898456566, 480550428, 208882284, 536062258, 783639284, 467197333, 768765514, 85379379, 44153177, 417683879, 626806621, 954174726, 642278399, 960440458, 960000215, 889989982, 940837033, 241621252, 684776951, 600780127, 756726451, 203150585, 576392137, 536315255, 576813572, 640508129, 37889862, 594709203, 911142037, 690477193, 846224326, 246098272, 69178503, 697517337, 923866068, 163289767, 933649505, 853724673, 868107468, 621719956, 408306541, 16609477, 162438860, 950940283, 64044695, 457477872, 831225677, 453031928, 431813838, 902887740, 873676456, 559974943, 120872516, 508047297, 950291123, 832171236, 751443248, 263593112, 204430728, 228650016, 299929840, 295287870, 134836473, 429435205, 3055619, 35312972, 255644164, 546958686, 966330519, 33924073, 67871783, 858588469, 442844774, 534976248, 527160035, 241399329, 185118527, 962038161, 996627594, 308157848, 140319003, 200070965, 960864316, 710195729, 549493431, 408150748, 288897044, 403108762, 655696381, 646767171, 118401190, 393164861, 979184233, 644684276, 593065285, 468560667, 833440896, 844599319, 852329728, 922288890, 670871190, 348453443, 266370744, 582572258, 828209951, 598856922, 480135432, 768010680, 352256225, 313032153, 209681222, 936597122, 510754030, 851851147, 387721912, 44179604, 445345320, 799750983, 127601313, 875717745, 659657359, 178790102, 688444553, 828524245, 519909472, 486210435, 958412160, 54132051, 73692631, 800362015, 43052347, 949883509, 517732402, 453544387, 382371759, 844550394, 879380514, 369036648, 953430815, 319425339, 359745894, 719291691, 527203142, 456969484, 26649035, 405365323, 980674973, 854049439, 42322257, 511593281, 993300030, 202486164, 370793927, 214320750, 400673640, 148228911, 666212953, 857486854, 823561010, 140529712, 701089903, 85178780, 274284290, 194666837, 656991686, 34240303, 360578438, 244727954, 991221539, 977902513, 148644987, 511343715, 640292582, 304897418, 627395984, 1125567, 649083147, 75613724, 438366044, 517854689, 237704577, 414239449, 811153615, 441311402, 689715903, 729166114, 797647247, 914244721, 357113396, 626175443, 414350810, 566821461, 310397176, 402229051, 761785340, 24492359, 846485064, 259347525, 483945833, 219379342, 585006342, 369051540, 218898875, 677662313, 937289096, 311949251, 616697966, 335418103, 202889367, 707225682, 755897139, 250847168, 8402333, 956271497, 182641846, 731704140, 457613775, 442332194, 961923610, 71150931, 368287214, 388571137, 170425166, 57235040, 718123450, 677532485, 316493015, 992888211, 35636495, 458138252, 577954080, 773530884, 915389060, 456809206, 322915256, 110045241, 462095891, 986421578, 567691406, 552019646, 498593811, 150876657, 242357082, 772098468, 565403520, 61496806, 207384207, 539802361, 26669117, 8249700, 139777272, 630890890, 298519986, 692316521, 805254241, 894539281, 565768237, 593058264, 985659730, 480709821, 432382848, 167452311, 501260643, 956765195, 660366485, 66268875, 389355779, 773409148, 615516524, 322373209, 701703208, 460211605, 816785000, 661231289, 838400806, 841873180, 230688431, 917762383, 11800589, 662438248, 864872325, 544970962, 36187636, 490709363, 659223458, 276404796, 238179704, 352774352, 69072245, 916705824, 410155115, 603933877, 952175316, 799914327, 914470926, 477003875, 721252894, 113658943, 329023381, 539713698, 213117514, 945298794, 727738063, 439579927, 507924442, 726105590, 807321648, 892266246, 674736425, 823941487, 807872983, 390999934, 93210217, 766029242, 628522899, 340607702, 86232316, 394004395, 100843861, 287880781, 700243116, 264535580, 186022369, 405722399, 589519861, 47313146, 685604710, 219691788, 461646450, 548176261, 823062376, 855621013, 367203738, 661926924, 793547922, 362284702, 579018071, 122530361, 619129509, 749918228, 614922516, 240062213, 170456863, 960114064, 753221862, 65902904, 727751880, 395826050, 330252764, 600109633, 152175379, 444868123, 599698841, 948626854, 793846355, 133519747, 992384452, 86595986, 667895202, 769579575, 135466466, 267041207, 741746095, 453420697, 683528094, 404054342, 613378392, 703041372, 428214844, 342247071, 438934586, 512493417, 62476727, 823065645, 990279696, 558484149, 492493556, 891908705, 628458665, 477073204, 484901377, 881760293, 357009772, 36161976, 425956573, 982086439, 177411445, 769729715, 900823232, 968371485, 533912803, 884899026, 982203267, 598084797, 69955549, 86116268, 31375640, 624834316, 397412568, 303490181, 535977726, 781564079, 602839506, 171449939, 596834865, 692793563, 358084672, 87852659, 269290595, 753038096, 625720222, 582276192, 938648199, 986765579, 469638597, 120857392, 440696418, 945326788, 350367933, 916854670, 304440158, 744273491, 363084321, 747596621, 839202544, 619449190, 396957064, 472257838, 373233758, 768180828, 225677100, 507981202, 119149219, 994411458, 29181124, 422555462, 421598598, 727983138, 829749737, 956304188, 517635188, 292605013, 32191996, 703991119, 522827001, 182753866, 78527825, 157980010, 274622185, 318907705, 427880855, 797660434, 905196937, 847864310, 813700977, 458970706, 435554931, 390777988, 926521271, 524704554, 842682175, 908313273, 472930795, 226478343, 627628097, 573765236, 157998529, 486714510, 954465121, 656745933, 357153846, 410261842, 586075584, 726489676, 637306918, 701945836, 437747140, 65766342, 619873214, 142977340, 905298234, 405812551, 724079824, 11149733, 760612221, 145912018, 536352186, 219699834, 686640213, 693581921, 159983081, 571824399, 517414835, 97310809, 444564823, 771801937, 450690262, 837121058, 130791785, 221164743, 105569161, 425454380, 294119943, 530652041, 419846789, 371734716, 830920692, 582022401, 798598402, 654583486, 778898807, 446936700, 807110435, 666665343, 68192778, 949204982, 329248089, 497121723, 736356520, 798004112, 369601343, 588325646, 295885033, 435838240, 650797755, 943467204, 148456976, 743693760, 888272313, 128678301, 466326510, 654918422, 631268120, 282247403, 222516017, 748484995, 606176276, 171460213, 619594021, 349944640, 662083597, 837359707, 483582212, 484670437, 219046877, 8304445, 212141081, 600222466, 535342684, 848607501, 266877338, 941039113, 690933284, 564767164, 221139592, 669155413, 187342035, 302741719, 674899752, 625559809, 953246582, 850597607, 324138699, 21399275, 63808788, 62986259, 301967585, 329286166, 871279177, 151968802, 495546857, 478995931, 84629162, 117380764, 867094585, 692429745, 805873645, 90042938, 410732140, 588852855, 35972123, 10089713, 180777082, 436923602, 741919020, 101014681, 786386375, 851823088, 688492268, 902938790, 221247220, 491296624, 309732590, 221237491, 751975724, 974313487, 596830560, 148973709, 827538818, 347143215, 465724478, 857615409, 17473563, 926570994, 207271868, 474486249, 693177859, 207677362, 161931856, 629406681, 780602017, 686057992, 529742800, 292035000, 722593438, 480640531, 502561179, 932195304, 975583588, 586444176, 911530050, 862062621, 709419995, 706201041, 190552348, 977734235, 732388924, 468478220, 935061725, 726478639, 572870814, 563209556, 892430424, 625149264, 458859381, 170880655, 245612960, 858441722, 361841995, 463756686, 296541463, 478151763, 113063317, 947014530, 699930776, 856619734, 314027944, 328782921, 835438933, 933715825, 905638809, 198699685, 898045273, 322110677, 637087557, 81415778, 366107932, 363330533, 588328076, 850545202, 102560636, 736919722, 977206927, 224816569, 969203499, 169024220, 367346425, 974668104, 529924610, 490618446, 26696268, 284436599, 594281849, 605297193, 553558466, 803081701, 655559000, 339241878, 707791150, 990237917, 393845864, 134058463, 565696579, 49565936, 759079292, 956144925, 318419060, 663875592, 126340959, 155552935, 341623050, 274671160, 348225423, 728261774, 153133483, 441539039, 956561926, 34845739, 168581154, 753449889, 854896316, 710234834, 941454523, 391868854, 8801694, 459500330, 572219679, 198316741, 555451002, 428183113, 184501876, 382676747, 546341283, 690412501, 206462357, 871714492, 219665282, 13882341, 529117864, 746304578, 866813465, 721423761, 754860254, 975838554, 490051270, 827688960, 768981644, 356423126, 67036781, 463248633, 479111873, 409512368, 576263329, 251792486, 138791090, 243258958, 992583016, 578729675, 954368010, 229526489, 802377791, 153276677, 262234792, 582553294, 758760071, 66113323, 978082517, 884807141, 342178005, 172884901, 78034317, 159163210, 215468845, 310912306, 72793488, 210639428, 335720777, 984957878, 600453984, 694399627, 420176725, 588074409, 226309084, 587468161, 595372060, 670798199, 848821876, 671084282, 944312156, 322203609, 490065394, 8610680, 844327242, 49129334, 655545357, 851526107, 189393762, 995014610, 227104152, 16733902, 128954423, 597047361, 932413396, 913111136, 542292870, 31125188, 286614201, 889400741, 780899964, 291626998, 406642903, 976281945, 885637161, 539307746, 175953246, 32674109, 415749268, 878710398, 965692842, 110434804, 26938559, 314832253, 755560292, 947760728, 783374577, 414753009, 515224342, 1881642, 518450114, 845398302, 801174605, 385322463, 655748498, 16607410, 327097139, 428653132, 783782597, 89706144, 127690520, 128706581, 63758281, 282473784, 385033059, 597532911, 532172825, 68110538, 570929103, 241558358, 909300311, 515046425, 576822339, 421713443, 691020067, 49138343, 151471796, 509262617, 584822867, 330007859, 617929175, 134799259, 812531150, 132362433, 761437723, 777694837, 901341036, 669949521, 833945640, 522489816, 824626890, 378964215, 241367055, 765125449, 13039666, 200932966, 274233718, 840383417, 583842940, 816493213, 435676241, 111799934, 254100286, 960838694, 517990810, 878749304, 43253319, 719936275, 29171146, 229036815, 367122532, 643105218, 227458980, 580006564, 893179699, 668405512, 800484239, 687266519, 153178914, 231244492, 268185042, 569321566, 263820798, 686043160, 609206513, 856923394, 179404643, 505025734, 153241028, 73620751, 628030032, 317996360, 288171619, 675654684, 324763635, 255357107, 495066640, 896029599, 642042544, 844693266, 700346738, 799882245, 361463165, 575730857, 653744994, 3477144, 150321078, 987216297, 789860690, 145307130, 75718400, 319524377, 427990126, 723890326, 702020615, 761987795, 550609677, 629623517, 825161850, 294695461, 163985784, 110815936, 786938050, 956628313, 749394692, 456663628, 316218651, 304388152, 314392467, 995787159, 353101323, 641972533, 439852079, 572502075, 505949871, 479498723, 621923718, 472611687, 577404784, 488657381, 424987302, 864316913, 366852880, 703104624, 257800908, 293221433, 341391480, 150236620, 826108085, 795269070, 380697508, 799243110, 413824274, 371931555, 541297507, 983440832, 723841163, 295422876, 216194552, 357041757, 466956508, 199507586, 254586529, 13291329, 919395176, 78355850, 173117921, 454796725, 288362714, 893411202, 972165240, 718951016, 434497354, 515436271, 68878001, 116190937, 692188879, 685516046, 233928874, 554374425, 717715014, 40797153, 746373066, 512972002, 810459776, 754030543, 619017986, 846651863, 999146070, 130440628, 911543825, 945212439, 976015464, 402684401, 768096705, 75562029, 713343915, 892776274, 109057747, 188902661, 730904884, 276023640, 53706574, 826159459, 261594189, 405653286, 662519382, 78635544, 739402034, 942518942, 459018004, 724076958, 606152026, 378116881, 825124523, 757086820, 252970903, 113195334, 454173685, 351953257, 237134370, 834949086, 69515411, 476356283, 648576681, 877969212, 440214474, 73984140, 206192466, 425158240, 868566242, 444693278, 540600125, 619753894, 853564921, 380597652, 648989887, 933180503, 857127457, 263391090, 285250536, 400966524, 351047929, 575049666, 775710402, 105732936, 868437878, 196967629, 48769883, 762036511, 57978270, 50491239, 850002066, 321472656, 685552686, 670308422, 158433691, 280605792, 758776033, 637597819, 41350858, 383853938, 916289061, 95241932, 590011941, 200083072, 136208813, 634657612, 623489358, 164144609, 466425072, 822860630, 380649008, 978038998, 747634757, 676140707, 23134353, 189979124, 282662902, 265681010, 392610323, 206028886, 43884814, 984128538, 378446213, 867234328, 286226869, 179627399, 424481767, 89773983, 645320811, 912380984, 313678794, 90871997, 675386396, 267739948, 798472611, 134344224, 761802858, 738212667, 160274166, 66107390, 78321508, 861376458, 533351356, 175528312, 751907527, 532250053, 369799861, 525678496, 428193157, 555418348, 403279263, 147484178, 369275475, 877080686, 777564907, 366335813, 818332565, 458346548, 303476445, 700365090, 238175006, 945547171, 512153976, 110250367, 528075438, 578656336, 570733492, 561353696, 743529514, 600278659, 604827988, 17196607, 895040135, 35047547, 928081786, 979233583, 681723341, 991704048, 186355155, 418277292, 907473385, 859258629, 342639398, 909333968, 418587361, 206130764, 158101533, 322722833, 602467248, 845443360, 648834643, 391617372, 377153625, 508352794, 29064124, 720144783, 733658665, 348449802, 328915768, 372048123, 392010871, 88787285, 191195246, 254815970, 741434176, 665070330, 325780077, 911442080, 591934113, 850374435, 56015172, 262457612, 377304714, 478389844, 611836404, 218887324, 380996906, 435071923, 721334712, 745613170, 851695507, 768540527, 934536517, 575188879, 232616459, 698685868, 603745147, 987632042, 205588935, 256611479, 853888464, 268323530, 874999211, 230165934, 968493151, 839330495, 621451642, 42451914, 522078853, 717985036, 149916455, 695655197, 900773125, 162242175, 462021428, 387811613, 95442841, 301112973, 323336842, 464376549, 924205808, 600900849, 507224799, 676412698, 873752051, 571173246, 62281572, 5443456, 990553038, 564209844, 538240717, 101094507, 817810442, 506767508, 502996461, 129545310, 945860983, 689062577, 366204861, 350908825, 183055646, 569759095, 26639448, 424077446, 172114341, 406945130, 70631526, 957417884, 774574995, 367154467, 881940295, 142950770, 481442658, 807739971, 557756048, 793419099, 609756625, 25761781, 622916569, 931050146, 374823125, 31453257, 966268817, 581650612, 456239004, 305234581, 319659960, 979398468, 637269474, 466440226, 151743346, 945723215, 636401400, 985140053, 214741795, 194372877, 804894133, 785358923, 667246298, 776114244, 692440699, 99169963, 26759031, 869496530, 217547732, 275000457, 521322815, 62595282, 689293401, 358741296, 566482413, 314771872, 893516682, 954346066, 253364094, 349264378, 500005803, 539920821, 109765151, 994805855, 846884592, 822721024, 115034788, 200349692, 513798222, 152399535, 340944630, 311262855, 755433495, 441914420, 580204844, 973948884, 338728057, 190313346, 863726606, 832253736, 25844119, 368762146, 392884673, 278115705, 758595063, 259911826, 964085510, 977545993, 426418789, 447760471, 933690524, 84268639, 759822752, 533917343, 179430015, 178282755, 661767502, 188224710, 206946745, 3678138, 487288943, 117715303, 446898075, 623779188, 939058371, 317093745, 458838701, 108493193, 16031823, 346811367, 72261192, 39474076, 794391905, 214472531, 934659089, 669747739, 611782620, 855271143, 334849184, 150876864, 168366747, 206697246, 559946156, 873302912, 586467094, 518657599, 114583715, 287726940, 764729538, 534849854, 845819333, 300878642, 862337587, 627709694, 785412339, 747194401, 170905682, 608290158, 922755147, 50751644, 423182644, 750004427, 713608046, 738927253, 970100983, 313184871, 73939354, 142731752, 266363936, 833378707, 651888658, 141832336, 284088500, 707406735, 72941633, 690543627, 827310728, 512711548, 49711122, 396239778, 957380810, 979621927, 661132782, 970426319, 263146446, 353187372, 11842060, 480256819, 74189097, 724648819, 507397536, 417778520, 840979316, 266692110, 458898123, 68755285, 210239870, 355843335, 633939843, 69437896, 163822247, 976457490, 32509702, 717955615, 261899110, 37130712, 917327347, 298149608, 964953118, 458393373, 643265837, 854100691, 957877414, 917868533, 871458869, 675390124, 645340543, 879682665, 367974944, 960497614, 301584966, 138308660, 769569387, 647771046, 857608950, 722044553, 734627724, 416993242, 839329343, 161934133, 193661099, 937928950, 88767457, 251198446, 487929153, 330466850, 667341025, 591003066, 316840442, 734976997, 575284302, 397359960, 552581327, 633224558, 63564179, 879914862, 486684275, 409300831, 909001025, 535037027, 207166918, 594811118, 612168996, 765517140, 598983823, 619181648, 559446742, 562495900, 91802874, 861131354, 361121781, 12875038, 575627016, 251896233, 229861539, 340707103, 280027798, 732024563, 889656287, 275233477, 200663889, 50681569, 209919769, 100436306, 120478131, 721190361, 291704102, 375000750, 874099623, 338570488, 362933765, 593414501, 787463254, 544364638, 478391345, 509835032, 803901648, 881272532, 513220815, 330749659, 74640926, 47865922, 350139898, 545455843, 143653137, 981991948, 563718846, 373761406, 718506420, 948115584, 800814510, 21147094, 800877357, 957597089, 631501735, 508149410, 492904141, 337051638, 996738923, 565169101, 647012523, 180364287, 710659843, 72123367, 336267333, 161301038, 103513579, 127491652, 77765489, 54630123, 777454175, 84941, 387018891, 91143185, 526974239, 706298, 154534705, 214522957, 938755528, 941033910, 570390400, 21219697, 538253872, 719613411, 762298094, 724091369, 549591889, 203715399, 530279153, 424974466, 375406919, 607058640, 368225467, 472525584, 56922293, 600527011, 640491428, 287928079, 930110771, 574750840, 285335068, 1291557, 744216345, 673240379, 319956012, 762928278, 363517164, 486462969, 159329227, 923666643, 903534535, 666206326, 397051725, 889130400, 691098781, 130130194, 663523879, 383146487, 882497930, 196885043, 227248146, 737134257, 461844883, 502019606, 489875313, 647916265, 495137516, 816331911, 41584618, 530566886, 582104578, 64647486, 421448382, 762212539, 739595307, 397921558, 99606709, 437669803, 777260256, 456362589, 543136118, 388572597, 615615528, 76121113, 668077826, 990963596, 253019955, 269348340, 848756495, 423434518, 198232951, 848208114, 506331960, 739945337, 869127173, 76256404, 832940220, 78595291, 543699552, 298069694, 700572395, 546242360, 643785859, 456845695, 111774924, 126940803, 999193599, 735181743, 450168351, 866291200, 979356495, 171359554, 985892554, 934522922, 27244806, 820532666, 565473086, 345817173, 624384056, 336474436, 70610595, 506514906, 381262079, 106025110, 831517272, 575840603, 73397330, 216011066, 620569997, 554732940, 959811567, 65563946, 936758654, 963648722, 764273977, 368615184, 517327702, 182749712, 102584763, 821556020, 222215338, 788120538, 341240771, 320116223, 465860580, 687772193, 409306358, 233112342, 18861175, 651390468, 595973161, 599959050, 629660891, 366635414, 152438021, 422435252, 506529334, 12811513, 635766318, 321240751, 575259879, 796329348, 738777889, 797458634, 981817342, 242924064, 581751892, 912431261, 577148516, 393630575, 108427932, 168628261, 790627086, 230063837, 585547103, 433952160, 890468169, 91672627, 160218591, 305701983, 566308581, 328814656, 549628954, 829310634, 660198745, 534378621, 538313654, 786131235, 712406033, 957289928, 676438436, 537488299, 638262991, 465175952, 400449874, 804150546, 976931928, 481186533, 104021911, 806119469, 354925983, 120028364, 689593496, 291615865, 206139717, 51767710, 547036939, 812689751, 265355153, 623095993, 482318149, 289035084, 769355419, 312176601, 205363637, 434948576, 959657191, 996136419, 750818997, 220466483, 281266404, 336466746, 246313983, 351282672, 321172390, 77743587, 143124131, 239731730, 404514221, 279988678, 992022695, 138032537, 417878354, 707967903, 865789187, 489544062, 649927762, 284338471, 283731131, 363568427, 841016817, 208845580, 119278911, 643000700, 685376582, 440221530, 563735812, 619718721, 797057435, 140337207, 63724534, 685077563, 334047865, 273503, 646064026, 485207394, 615825807, 565351625, 182274455, 690732677, 224417843, 780914032, 330376678, 350180511, 368855356, 913115589, 518862106, 7603354, 321281877, 880674329, 664741681, 508528146, 944263259, 234638245, 763182582, 837276753, 646165945, 793680536, 51187841, 674718564, 288137635, 141448216, 321671854, 999360526, 4163356, 377517526, 321553799, 537968374, 360367760, 725644058, 567764758, 722427343, 800096608, 977390994, 307673579, 794216332, 697318017, 311090108, 724894646, 668786900, 836291466, 208288165, 552375412, 18688674, 767518056, 374165562, 53841300, 554812626, 931696754, 700904209, 204009265, 342418933, 872458173, 674572981, 23630226, 653996287, 435535967, 611386429, 688809195, 544400498, 203857977, 607805534, 978031316, 236068261, 467579946, 27938006, 192662213, 527725459, 944330897, 17995693, 896066518, 283383068, 288371831, 455445612, 337185657, 210183706, 234289851, 259711509, 865655553, 828704247, 508706654, 868695086, 769814240, 467456786, 513675910, 664724481, 679139386, 758653671, 506785752, 264293990, 68959739, 19278633, 631307175, 794723855, 368195244, 858513576, 688926002, 992148390, 741744977, 429355605, 739262568, 546120961, 778946643, 706995760, 595227979, 814427444, 374721888, 246218589, 575087924, 583450202, 518823948, 491104391, 465498686, 786496138, 975701607, 758662750, 749750166, 391660665, 667138154, 169358894, 850618034, 369776945, 289884708, 372826731, 395136086, 441740311, 863873247, 194332800, 143816459, 445303086, 250948549, 567812847, 132240382, 351879844, 476775576, 713742901, 442894377, 560754590, 90889144, 168907762, 391383542, 715692919, 784413241, 900506042, 441491816, 504182212, 246790759, 564958429, 66256961, 493212754, 66342779, 667737993, 544870691, 579611040, 631850814, 184793859, 90175417, 793823782, 520942979, 611733540, 844238888, 732139344, 589341555, 231733494, 995770568, 689956277, 586231791, 905282308, 3665317, 280357362, 147527619, 612235315, 552491094, 252575826, 91607116, 458033812, 988221590, 525283698, 475116418, 42260739, 390499639, 368438847, 454296984, 778166257, 39316940, 674908131, 997974522, 702870590, 981440539, 543698475, 643204439, 480779322, 222095731, 880226399, 2419398, 909021406, 78111904, 4137098, 186939882, 514085265, 110407863, 523300471, 858011566, 327515594, 261064347, 122029290, 638013340, 589075391, 583881847, 894006982, 951168140, 53130272, 28581330, 699222250, 660565703, 548907453, 54295347, 841395485, 649928203, 499394425, 366484376, 188738630, 914423402, 189753020, 639567876, 371808644, 408202992, 534352538, 845965582, 958630125, 962939639, 151139574, 114368654, 226419825, 967823940, 431108938, 558865579, 273282346, 156817972, 337030902, 346539014, 43998417, 252046675, 559044996, 330606735, 287762915, 404982475, 681406658, 383569452, 474007470, 679651074, 357843970, 454501393, 45991541, 897522734, 193591152, 644033413, 302823291, 842637850, 5672089, 78550650, 567291073, 919414193, 470480907, 409208442, 792889414, 631883320, 833732816, 788326760, 844267908, 744562912, 226310851, 458907544, 466895306, 608951613, 299918694, 607015424, 641060127, 895186746, 636290905, 488332339, 270579786, 16699424, 420858100, 419158428, 474039139, 936615023, 600079342, 628754101, 433897029, 893531254, 902485107, 875197608, 721329136, 534917188, 875702734, 362712279, 94095349, 130329079, 616102660, 125544962, 114201150, 157507311, 3406788, 848446401, 304183366, 601345031, 36090430, 800980793, 108512021, 894033305, 221989832, 958443564, 781832083, 374286257, 33677173, 362619512, 752129691, 46250674, 954816980, 256131415, 621616290, 761048264, 595806571, 536568241, 839619246, 528092795, 550791789, 482642015, 958110555, 811308941, 167135232, 250540277, 663571644, 422608742, 561137891, 869093977, 409367300, 828924055, 401633133, 169943509, 246727913, 104967069, 980509124, 298172321, 363968737, 94105317, 91074781, 852512072, 372687636, 167763412, 658432088, 938432095, 62382942, 155617518, 829896876, 674415760, 918417750, 408506821, 846477696, 288642631, 63415563, 718957666, 705616053, 141850727, 858891, 306878321, 494169580, 435393216, 403457455, 700236663, 216827360, 353081607, 187499531, 802469910, 443483127, 802309963, 490927945, 445575847, 138239705, 743391398, 150774965, 479299307, 229501200, 275877084, 142943569, 620534991, 345129809, 478415610, 428869816, 627088304, 617331729, 14817051, 593815187, 883789308, 64909111, 327178302, 771620319, 869336889, 627533822, 133288463, 334762711, 851691916, 734636192, 298909963, 91954914, 704133050, 712918284, 180036143, 504212529, 248294626, 725234917, 283037507, 970750118, 786688012, 901333151, 575843070, 802366502, 553746843, 566141201, 981056756, 585636749, 889313539, 414354335, 461363841, 746493536, 7575295, 464311533, 345343106, 933394868, 822514473, 667103656, 548652626, 415579913, 282670802, 476946743, 704890876, 14660571, 645445359, 983261848, 182943298, 12863279, 879551186, 635170082, 44840108, 114970292, 939607966, 67158685, 799601264, 497917115, 331185332, 151489505, 588547862, 396870407, 205050511, 417679202, 520853859, 697693795, 572945686, 41696732, 292607206, 773193048, 107903442, 699869875, 225049336, 570356346, 706355665, 577132660, 135494633, 978145799, 365111705, 500725483, 220574499, 614831955, 466249617, 359141141, 329454907, 119234973, 615167919, 311832496, 636229367, 31633047, 58872257, 549969869, 571767887, 108085052, 414771379, 246149311, 233859139, 135449049, 651767640, 203298466, 286389493, 594393731, 917926357, 183409280, 387409598, 249710698, 684808017, 415384273, 353066379, 988790303, 856207173, 120620483, 254247475, 97775738, 170276575, 523936510, 782366282, 386458067, 140950107, 610917219, 716864880, 868247857, 306541436, 462372335, 135085358, 868076151, 720527369, 148975543, 437464754, 598499411, 667595936, 332730210, 659729107, 865672048, 265663287, 845429770, 696635773, 494474378, 694517536, 480530052, 825690688, 421676000, 552863833, 914047771, 172306187, 72944453, 542240835, 897440477, 996708583, 556582609, 884802215, 486585167, 352974814, 905877606, 367559654, 765453918, 51396626, 343527117, 353393716, 168441919, 76287080, 581164005, 301995094, 748619468, 296237001, 456370951, 303392614, 843135020, 955950572, 338260101, 908226500, 941241711, 758283189, 564069989, 633422070, 975062014, 723316340, 94882456, 734974575, 866527426, 676355167, 377444805, 178194920, 460150857, 902508037, 416252139, 705291278, 493395561, 507730309, 713611565, 300984046, 507513232, 847291009, 23999649, 92976973, 398105081, 791278921, 902100556, 940050612, 992420184, 640699821, 130830617, 34963063, 427707344, 973924161, 942670705, 643127859, 904736160, 262806191, 888036510, 459887482, 880468101, 49822970, 869212741, 654555020, 106863038, 129979988, 471528277, 752058508, 69420315, 399478351, 630787560, 783641902, 27344126, 142217493, 156124462, 495525024, 321738237, 557671037, 613101844, 429606289, 365645317, 371551365, 649920733, 838019365, 31938562, 848109804, 210618956, 458321058, 316169338, 275560987, 545591380, 838671976, 464538222, 710493514, 888477955, 635691844, 267448056, 522325171, 623748666, 133115838, 152808629, 871075488, 855106232, 839621610, 13827634, 867657854, 522967331, 375021575, 915512338, 21484483, 587855456, 272243387, 850657897, 474673986, 238011769, 427903774, 815561524, 689663589, 194467083, 916902186, 386700488, 451041033, 625477179, 644483581, 273438564, 661526444, 104983918, 130341228, 506849022, 374385475, 923160100, 581106900, 44212600, 170801892, 253764517, 14112861, 341537753, 478776695, 351334179, 259573090, 312507004, 237521210, 794203363, 709438424, 617559021, 171102731, 271206091, 751059533, 69422204, 547892048, 761155486, 281690092, 422724848, 642165744, 760043035, 704034037, 431993550, 902468682, 635911191, 529501760, 106785665, 502912159, 21794726, 555342780, 791220477, 740103658, 128666286, 606813485, 749581214, 357302247, 719534776, 252473690, 582159936, 970676267, 817331058, 893834085, 718051353, 404385849, 369220217, 766506939, 625710742, 108810134, 972860956, 252439254, 714765480, 730450038, 791360378, 257436503, 110051332, 819964515, 696840842, 915740969, 250689304, 564828208, 171041684, 223373885, 183593347, 743158292, 276446316, 522701526, 935821119, 514268685, 331922965, 860228119, 341044400, 692115997, 890466176, 602873448, 171287143, 407243509, 541726176, 572082470, 67279627, 292168915, 122512419, 831351215, 282190761, 561952901, 912400047, 332599755, 588014234, 329483402, 76939607, 557468266, 110244123, 326014632, 788317923, 401025432, 727889275, 715274230, 846202784, 407138169, 643015805, 523901356, 646997045, 922778451, 528571476, 988579563, 564447590, 657901490, 117663310, 15224116, 367868319, 75118070, 393521326, 620703393, 368788248, 669296587, 545259492, 5147316, 248490576, 567930742, 141818752, 658539849, 129230905, 888179927, 728861232, 60065534, 193589813, 933913720, 493995459, 737704589, 877020333, 404787592, 308622788, 713793661, 303876639, 291673667, 416380258, 171586009, 899698330, 891619503, 7888529, 527407603, 364718458, 299237935, 143824464, 198184137, 547175002, 615718051, 56112709, 198273486, 953052427, 976825502, 390636079, 344809150, 265596775, 140242198, 875146067, 496140986, 910437303, 315107864, 298751639, 488964747, 259532856, 472305517, 889100625, 411545424, 257539771, 462067668, 958324364, 162507458, 954997422, 91555145, 683257410, 775421262, 442415381, 748732147, 333163894, 924503137, 591318525, 450433190, 945557102, 520657432, 99144988, 211656441, 523434982, 473348687, 203547308, 293191346, 625731897, 268850905, 67477269, 204350921, 868921426, 512300313, 759280744, 449093282, 201373431, 684176562, 127117775, 194222565, 459743122, 690515002, 190963304, 688784082, 398054912, 192873087, 919107817, 729632327, 754389182, 494312721, 559238727, 671605876, 531751108, 436948154, 50691571, 613743686, 719253161, 399959922, 384636140, 868584327, 964528209, 217739992, 48470427, 46296544, 905501082, 334552605, 698404708, 228816566, 359390411, 741661153, 794733254, 906995537, 963584134, 829132283, 827954650, 605539306, 438547644, 971262828, 305346641, 146375804, 793053661, 467028062, 774609971, 119094423, 491199379, 824970679, 625155826, 199552394, 755784104, 118864255, 608611764, 788698923, 774584894, 706793512, 387347608, 248695884, 43060034, 427572262, 935268033, 822803939, 290341468, 829782023, 337072317, 274124101, 141888376, 493897397, 510904315, 121098812, 18590828, 477733046, 411667894, 18325912, 238812239, 650413997, 297225071, 271767873, 352945821, 176898881, 417568810, 604565110, 479620172, 602427032, 517591030, 629054151, 197753402, 989646987, 701021681, 44664596, 385450977, 701610967, 363242832, 728377164, 984506844, 463173040, 784082219, 125957809, 261594454, 562219008, 214177689, 422521728, 721494938, 808211695, 332877158, 807839062, 688247259, 315692681, 693581149, 853462468, 180905569, 873656628, 629276917, 832694544, 523150176, 684537900, 674371981, 619793207, 70664902, 581784707, 640710427, 462134805, 154869069, 73924679, 685472072, 832495410, 252471253, 172521871, 215174787, 921676239, 596802468, 147427314, 207297906, 183806372, 986536995, 615785367, 801703268, 715065432, 749065932, 941703651, 556231057, 81001854, 42929015, 643000200, 573188709, 911727068, 53615328, 534168523, 532307549, 712736466, 228629192, 256831857, 428911600, 596621971, 706565834, 567707372, 106725305, 622728509, 127003735, 256582161, 634921307, 772657644, 350564477, 179823925, 658634764, 820286419, 919988969, 636789039, 46666170, 388842651, 224469742, 499650540, 43712585, 21769110, 87877050, 657077015, 535049152, 486151163, 300586834, 882055103, 475562064, 221206468, 473462921, 396044074, 314966395, 988010351, 671625307, 265306763, 851104423, 539038704, 124091913, 676944950, 967504526, 733752810, 112251925, 357608480, 34294165, 390150991, 377817543, 129194133, 530855135, 850419274, 928993411, 559556610, 804925135, 579058970, 664424029, 843953401, 219151120, 507174975, 580250440, 413758671, 446142848, 920691946, 805409690, 985621118, 243272515, 45331577, 242475116, 383651771, 103503202, 63052282, 158020194, 177908434, 10066281, 487716522, 192113192, 232039122, 561600171, 599262501, 673893763, 851815820, 193981746, 713074840, 163316139, 898655427, 806001894, 215742993, 724081039, 684831341, 60778867, 361299501, 385775260, 133237614, 19165502, 985544537, 898895128, 697094802, 38027807, 315813438, 521758041, 965258380, 206384839, 556297989, 354364620, 916161329, 797652328, 99910860, 428588773, 41077277, 854565606, 201760013, 902575837, 549664565, 958057416, 962525531, 718228971, 562183837, 910526170, 333006840, 916939120, 411155516, 515958580, 94043792, 773140984, 677777828, 495704161, 806255914, 45466961, 839862871, 155799130, 794810788, 895415997, 283368639, 492114269, 916512512, 502671180, 107633730, 742832840, 51856929, 885631732, 692499461, 82543598, 852136529, 584288292, 949626365, 1783818, 753107618, 853090962, 266337962, 718816832, 564673709, 776800606, 509831157, 161792667, 105416949, 42120325, 582965673, 115033102, 955124123, 655788444, 106956226, 211003352, 163580021, 840360556, 141620272, 156107837, 961731690, 694143616, 67618453, 174173823, 363390879, 558294713, 49172945, 602105909, 100876147, 580103383, 201276487, 896021220, 350818034, 580438787, 768745490, 890408857, 216447621, 984149969, 224063331, 101141762, 401476133, 933998615, 537845385, 315768180, 814909620, 450759993, 932714512, 205799236, 991109129, 368125198, 881685923, 716082837, 945975350, 164224636, 178403852, 593053447, 363922674, 819159285, 609920124, 634553282, 957458819, 989213508, 530672355, 843709014, 836276533, 544642297, 741227126, 498296923, 26749167, 59710066, 726613383, 697296537, 501102191, 982703096, 350130944, 293836115, 623837293, 228996211, 518706482, 31534359, 981757657, 315667509, 962689732, 695251494, 11030124, 15358883, 967440405, 673966724, 915698389, 149742149, 902216652, 146204173, 456866058, 434268430, 287977876, 320980186, 702210295, 812160008, 139644332, 180084174, 41723417, 405659011, 306300263, 836559014, 150294785, 620229288, 786429365, 963726438, 508778562, 62779827, 165895153, 713737174, 258400713, 579673736, 960579099, 531875255, 813866340, 605949345, 203968672, 894498693, 976712389, 577894232, 220366944, 795128251, 355425286, 882739609, 497581018, 880031637, 210566368, 637935882, 790332218, 140370298, 159130252, 694697623, 356074724, 571507101, 847386887, 32008336, 349857458, 177002858, 263458496, 979444647, 984567470, 869361166, 720733955, 376079208, 213512183, 733106399, 168705591, 806055716, 610609036, 952980094, 216697504, 788417895, 117750834, 485822251, 833009278, 934240772, 281636021, 122290485, 974203272, 741381122, 717435674, 706320195, 704605344, 445109024, 12175269, 69189659, 313150730, 925114665, 412247355, 680809254, 34751369, 943367790, 875304894, 976138428, 375942370, 595763268, 819701571, 904550147, 354034886, 985181851, 934513266, 39315829, 832675009, 902473098, 768916819, 540931997, 343377186, 273591164, 939772728, 259140492, 312368514, 971548070, 967320008, 96412438, 935497390, 203702826, 233101907, 921461692, 810130399, 592183720, 826037169, 7485374, 843049367, 717341120, 539919949, 31374381, 920559797, 921425055, 631873439, 511038706, 651480230, 503339777, 182732242, 394551617, 460111853, 968708209, 4781186, 875313059, 28632664, 195421823, 394249572, 792730119, 130249825, 129934791, 239720982, 236764237, 518826352, 720565446, 110184611, 774119149, 766958766, 793782045, 715384436, 213750100, 31379062, 379262599, 328415401, 912654817, 823984963, 81715508, 139259524, 283111507, 216687972, 904696378, 868314911, 498693700, 881164588, 189283400, 886733649, 417084357, 931366239, 699085045, 807465545, 377403901, 705097893, 702870257, 23188001, 23115684, 106237150, 704045683, 651708959, 580680938, 836802901, 52445906, 339941975, 496070319, 463518373, 773714300, 291436739, 97730214, 990537780, 770169440, 341100303, 496465717, 937022019, 347872712, 989138844, 518245535, 853685843, 574302733, 502716805, 13412705, 616750595, 986281002, 808530699, 189514307, 100566303, 713858157, 37405872, 403866615, 48801231, 875275310, 341132949, 820004985, 39228880, 256082961, 466795854, 546931521, 570394372, 898512144, 638190664, 859309161, 570475922, 996562258, 16124165, 109470874, 858759617, 695474592, 49102522, 96943560, 466433959, 265961480, 336063250, 186366850, 674370733, 856270669, 123205848, 350506064, 935658599, 442146419, 137193034, 917524672, 565029356, 809546359, 877426521, 498601182, 570275668, 537918237, 716634615, 241910436, 177577801, 958740243, 616635727, 582295056, 301029328, 872763820, 718251791, 192640532, 96119161, 18878034, 507871571, 575077042, 658148750, 93794528, 715275627, 419745183, 715352015, 658126158, 662212101, 703383664, 707477249, 437877115, 84664274, 725919647, 843089247, 462224598, 507606591, 793280638, 638802734, 714737545, 740952044, 401777425, 105134655, 532741060, 237570695, 402122451, 624374620, 899941927, 590668097, 483668761, 501389225, 207619008, 662931115, 830063993, 474130226, 63083316, 458705089, 780493022, 252215924, 507358602, 252286284, 279091134, 641044181, 333640033, 680756487, 299490689, 74325843, 563406664, 717888542, 449068473, 53515287, 953340973, 915700157, 705882431, 130131409, 647283946, 394973348, 752576059, 276051352, 688158422, 788940471, 610018911, 337533427, 607417103, 396434932, 715311458, 956918578, 479961203, 357480081, 633587670, 488047758, 61959084, 941657462, 395745696, 958042456, 303507274, 690808916, 378501680, 321799606, 163625708, 684691679, 235092199, 10702072, 344522184, 729304497, 862449606, 416773806, 249442018, 863604601, 103205400, 504944024, 639746113, 868815318, 752158423, 58620617, 369082446, 897300462, 785575222, 792344057, 211503910, 802337679, 692902870, 580723701, 724409268, 317158578, 64046209, 565629072, 23071129, 174760015, 861378118, 799146971, 210750302, 283641189, 402379777, 606757505, 850574025, 47133619, 870639303, 811843199, 848488668, 125875822, 355370743, 507850334, 955216783, 332549785, 172518748, 15191779, 44508152, 273761241, 550537930, 528987284, 540703545, 468724751, 944189165, 857914418, 17890826, 872439835, 975535663, 971047791, 786872577, 817539612, 831921646, 26798293, 594832200, 380038700, 648117402, 615851364, 996039493, 296740504, 262434051, 515985022, 457427797, 390410274, 270005062, 510928076, 751440873, 134333017, 394100065, 449788454, 76622887, 45105669, 372545423, 276775642, 950335984, 987247708, 686969778, 922271613, 893758691, 648401153, 585207996, 315843883, 732642662, 34859446, 937503006, 346458157, 761227672, 180487826, 897813932, 265867430, 328672229, 827845695, 571546051, 392033951, 709538010, 821691578, 729871976, 785011739, 649032430, 167397286, 466857690, 97422800, 711817289, 144518148, 13014544, 10300084, 9339054, 602285928, 803855102, 817095955, 257249182, 584901583, 258018047, 451354403, 794892631, 496695529, 615499900, 608556294, 183314915, 675726312, 525947887, 653106214, 475841815, 722674468, 265894758, 540688724, 252728041, 743547286, 858725584, 354068651, 576288573, 639156053, 319578649, 305814358, 561838040, 329751815, 875740767, 195086238, 49583626, 703733849, 583288917, 731613512, 707945970, 725469107, 109740012, 429452820, 723108827, 57260024, 635535835, 27278995, 880166623, 114149153, 487922496, 441981099, 861090804, 746736693, 508330222, 592066062, 810494947, 787116463, 121152650, 770487979, 236310673, 20743821, 515114142, 223527816, 693327383, 138294619, 814527683, 633848347, 365161890, 690051570, 952358718, 321625494, 787156189, 164764577, 55246534, 383879638, 160318386, 819225131, 906128533, 933879493, 848967746, 465426711, 109059343, 235576770, 356556188, 451656535, 774464817, 284759753, 384929419, 488175320, 402543998, 249876593, 605950734, 68589850, 102215567, 235920496, 595060791, 123475866, 448538630, 722004704, 190805191, 89281576, 941923104, 700009320, 146376612, 998837072, 485365947, 230651572, 479745422, 309559866, 306736453, 71645251, 800265749, 292803553, 115088874, 939214568, 364519959, 66960986, 675517478, 723443086, 123673460, 134713282, 808099056, 740451535, 433753617, 200272711, 928039662, 269559325, 123171878, 360517073, 768824991, 376741152, 69621638, 196783792, 362133056, 264684678, 832486849, 933364890, 632598002, 22501578, 612999666, 583263768, 469722851, 854666579, 459246959, 410194366, 726903631, 112392229, 131642322, 175314779, 55648299, 754073503, 273195784, 680992035, 44519457, 795526662, 639499234, 376831076, 359749632, 261920801, 70250873, 231758062, 598839245, 198311293, 7377242, 13423476, 352856762, 341325582, 414981569, 37022488, 359796341, 597837940, 513365151, 269620147, 286387897, 259995342, 586713980, 738022755, 872252505, 62128789, 497558287, 713520310, 181573024, 60348538, 434326366, 617848793, 79481666, 749033524, 753312579, 501626726, 468942679, 204997956, 101116289, 22042280, 405997410, 260635586, 635514197, 930007412, 686852784, 417226984, 741959035, 687480666, 127313674, 263757295, 236228056, 65217832, 24259694, 999561581, 729073587, 386158938, 303300457, 555943955, 492350242, 116455531, 311053471, 5257742, 120318288, 114970606, 899845876, 763962908, 973233373, 76938211, 386288671, 641462684, 23632315, 176070621, 311349747, 583949839, 132804339, 504133330, 84178723, 616481880, 439812936, 735824603, 661604126, 660566775, 391259795, 87268156, 160937355, 21830023, 65972129, 207798840, 672116847, 716657276, 561539369, 549433665, 260924215, 857372324, 376685535, 81738426, 936752576, 786715545, 980557920, 597366175, 524030598, 145434758, 97691290, 740218336, 76186195, 913390810, 11953620, 969505969, 63844528, 728599625, 851589541, 323349441, 439614265, 909770794, 37372693, 648034774, 13350762, 93036889, 195587864, 233070765, 774219035, 829571371, 33254181, 548509238, 182643337, 74149106, 349039457, 522495303, 270045770, 564170604, 367426344, 807928557, 725653011, 458249710, 159303889, 516833140, 358226178, 43827938, 504718189, 144499062, 528602766, 267443064, 787957701, 203017357, 676720993, 267539308, 551880849, 515413707, 937690972, 774705722, 375992768, 357755827, 927640523, 188523997, 833129816, 608706572, 649820547, 742274888, 755832759, 459439283, 871933447, 149760356, 123057181, 935688223, 721989991, 644812985, 251762496, 455572479, 644770504, 800241307, 856164073, 723437678, 511123722, 71315048, 253004314, 420046885, 551743256, 384668321, 371661620, 375747837, 3969380, 540998595, 822390318, 270544674, 92910342, 424476530, 174431064, 274988229, 614669537, 704293861, 456778699, 580289169, 550874281, 725965834, 416352523, 23681209, 326224020, 555667375, 327446484, 244235447, 576621524, 486519189, 152797620, 438162090, 384377077, 29698118, 956464548, 786851484, 286540486, 464649999, 372710234, 84697154, 390961322, 852453725, 355641450, 634358545, 522251661, 627691371, 225920469, 305879779, 62040419, 142809854, 191857390, 87545275, 35491551, 304752126, 54422411, 965064922, 530367541, 136100341, 18185016, 579460231, 451485991, 440111216, 446195827, 846725109, 323173094, 15537585, 757654227, 908947340, 35777071, 67551741, 647228230, 985051566, 208614278, 315416836, 219437559, 499186105, 473276902, 414532038, 10652639, 48648082, 813614337, 794697735, 173450244, 61425004, 326033748, 857498437, 495752009, 209618229, 24292764, 199615955, 607815980, 985875794, 429754924, 293662736, 135271516, 352446489, 24864385, 432891122, 553531055, 736082171, 337903468, 791992113, 389694079, 735743198, 624933217, 485507707, 198061971, 839017186, 392823932, 199478200, 126352935, 136708330, 625242136, 122422494, 37716226, 598611892, 739094127, 747492398, 328926057, 643693288, 113971294, 157400914, 599500034, 323622903, 977306106, 667509534, 602559169, 764804422, 607783128, 386025118, 775803154, 397557043, 73577118, 293825986, 945990842, 649112829, 331418042, 124056712, 110732462, 145417031, 697366302, 945218660, 978644367, 849255622, 469943286, 367357310, 897631733, 418812621, 406346191, 532677280, 106795437, 770926957, 927208506, 629992988, 256044323, 284245992, 360939707, 131891743, 991599473, 731775792, 962048798, 278441276, 602460289, 582552733, 188417680, 266480687, 344883892, 478353669, 510807904, 573491439, 300038239, 772370742, 180052112, 248544562, 58115415, 537205276, 995335651, 206914878, 473050717, 98532521, 227974356, 555153774, 791144733, 282038963, 221847590, 361660973, 587883053, 728058656, 810022936, 291501070, 249488335, 66164259, 119295743, 29237128, 379729983, 805950763, 813500988, 930659694, 824854190, 835625675, 502651083, 853021266, 869381541, 935816332, 282759869, 755351964, 555772840, 630584144, 309802237, 56004869, 333272386, 574044046, 362055262, 477598442, 217406243, 963317668, 154625311, 760635518, 785280212, 556987901, 660458899, 82089953, 547389542, 86090913, 879276305, 212912238, 347964241, 770293955, 771392611, 918125604, 691068915, 884204556, 676156859, 523704982, 97652282, 375339231, 161695803, 809896967, 29298959, 537754660, 809429349, 925227308, 596921721, 905511925, 197832116, 925381403, 602580890, 347727483, 113106143, 314547109, 363923035, 8510485, 637596725, 578663353, 17080892, 311093108, 562005895, 428446964, 733572425, 173807406, 333375831, 760272365, 196980474, 98154689, 13312819, 786209846, 288507485, 950068482, 977690596, 835743471, 62084796, 332215855, 394832554, 577635936, 386646097, 548575819, 723367476, 764545441, 432295855, 160059416, 214729175, 617477829, 267908627, 841896664, 565311011, 697882470, 842242736, 39743670, 397754450, 183444724, 747090749, 77125174, 387859360, 293274980, 267453217, 108349285, 583436871, 63597390, 723230243, 479501362, 523407147, 619745447, 883878969, 667977976, 684703694, 277301220, 576417682, 283295354, 180510032, 652048543, 400243881, 928051874, 718338853, 466562533, 220501330, 937695476, 110020935, 974031519, 986998920, 325146930, 604505220, 684523980, 440247299, 831362174, 57766588, 500739487, 145679625, 671485899, 524701189, 103977404, 162754023, 693685712, 456845135, 813270206, 738243751, 391416101, 801949610, 428517444, 168926872, 561780644, 806519488, 332274291, 531684924, 272632445, 757552753, 38765124, 327413575, 46695167, 885832564, 325760181, 708141686, 531410406, 215911461, 177232075, 716419378, 649456179, 289701421, 686584863, 159503415, 961917547, 407124365, 897107450, 143685236, 802557984, 848924699, 84136852, 88178559, 818194023, 394270856, 974593728, 312782433, 24967220, 335720040, 24173794, 907740663, 989536606, 264910119, 689054504, 185811444, 259324081, 150758327, 819059325, 760294010, 647639891, 981964351, 877128730, 547328580, 308111644, 301552582, 576345643, 579085719, 165920913, 545151594, 340486127, 659136833, 699935546, 99814853, 557620304, 574751479, 81574309, 46673430, 945133, 185200958, 67575946, 184783480, 173476800, 961833101, 746798396, 170170968, 893088547, 578638345, 687982574, 816410207, 89537768, 627034238, 205288650, 776340, 156729874, 209029704, 402004983, 868162134, 29375684, 712486836, 981303397, 519685750, 137638819, 331808016, 541394603, 354906875, 11606595, 660707086, 258606355, 178720104, 634553526, 49213137, 142764730, 785992836, 994566079, 711223503, 931668322, 894053930, 187548215, 63526194, 790141971, 516254003, 930112123, 760017866, 180036236, 953832405, 468828275, 543177525, 534599387, 152032568, 473517126, 280080229, 16339654, 512983222, 127760735, 834784763, 812806229, 230750256, 307753391, 959784094, 687401625, 545932808, 35482968, 453004538, 258607192, 149739752, 256751605, 56907307, 4171590, 689248681, 223922062, 915142246, 27480094, 164175679, 837817417, 149511971, 9666936, 373389641, 982385045, 901746135, 628192758, 115462674, 592618237, 971478160, 990789205, 99433991, 614065793, 229588765, 232252601, 292046115, 367759014, 377948826, 101178770, 550967889, 880354186, 163947976, 629445890, 256755725, 442318393, 767915354, 193756889, 829557719, 49582302, 834230787, 558158994, 937630628, 350382225, 825182920, 863156395, 788316155, 923369102, 2901903, 836283741, 878248181, 703499235, 304785552, 12502008, 258301961, 10767729, 469635025, 237698705, 448924773, 449445667, 23253893, 192593273, 913393700, 857561187, 444237398, 610854504, 681935870, 25296652, 745217145, 482223671, 777276554, 772640796, 195160095, 492075183, 890124685, 431213974, 115691041, 305627472, 457986370, 250761650, 705420852, 237311567, 433883742, 974624649, 823162494, 657347321, 393510472, 633073632, 849826648, 281793659, 877987597, 954351357, 225679890, 496462874, 151256434, 290695573, 549529742, 597085614, 101146588, 333672840, 409747087, 385210614, 391333344, 987377183, 43334703, 344993405, 572462323, 423214841, 871074336, 55214558, 733284356, 469692180, 243655956, 226754562, 867502782, 589469113, 197239107, 842497393, 756024457, 217992955, 424464688, 353579726, 356792467, 697689991, 422030017, 62412308, 874239642, 848818813, 953005112, 973759938, 402374346, 546459485, 791346383, 280755149, 243125677, 933846146, 41475689, 715278276, 38008581, 751786475, 558902156, 541334997, 298685601, 136820489, 864160283, 772723016, 383963001, 799569072, 488499406, 132686326, 8649952, 820320705, 382118060, 511340456, 952922685, 648506800, 86698249, 981233711, 64741365, 375536932, 495359157, 320432030, 616093038, 76236880, 937891623, 911773906, 436126430, 762586809, 241334237, 582084851, 285516517, 711603651, 698063266, 874268442, 791735449, 177477196, 97988319, 139606746, 251905090, 890797973, 47865432, 829314877, 24989840, 105113736, 242687779, 285471130, 553848844, 994538781, 768874172, 864322711, 542239217, 246674663, 203352273, 157351650, 902164987, 663501096, 833963398, 910545645, 26702070, 394692736, 928271643, 814187161, 492226016, 785648319, 450515415, 642342470, 732140886, 369818386, 274906174, 511600817, 250874414, 627151049, 792645329, 168727800, 29537366, 381468020, 817325246, 42756934, 574378756, 128317070, 678816456, 264451397, 191453362, 217212986, 320717866, 947483235, 258492903, 878162499, 413478344, 670239488, 548778454, 146252401, 297147862, 686195738, 704005888, 445160608, 496313996, 140175327, 913875388, 603543738, 505419378, 34620541, 717598297, 142008743, 624205008, 673818024, 648773566, 259500338, 498848147, 486466546, 926389380, 454997596, 973096358, 450129305, 484949010, 71981969, 917963618, 687988573, 856577021, 851997457, 761928523, 213313582, 201185483, 339230149, 644049832, 615953681, 61854702, 636518901, 531758171, 338437548, 71069586, 279202087, 949019695, 682251057, 778777609, 778972262, 598954616, 973368104, 9848330, 317325442, 572890809, 26218560, 985770990, 930683712, 969557557, 428542170, 539607752, 753854552, 781631044, 357641170, 8919868, 148009278, 926755973, 902953261, 286200505, 634039316, 423247378, 149586207, 765983457, 55286812, 929694115, 902178507, 529223090, 379073174, 118514450, 248362425, 148014129, 115332922, 545499419, 427078135, 95432161, 829238561, 81864014, 736246171, 420614245, 49411528, 44031083, 499784010, 707937549, 793307803, 516910124, 2785412, 279367928, 631176014, 333554244, 421487060, 271025882, 222468653, 492067889, 712631854, 691943931, 447809405, 811704635, 565150253, 581324507, 590294009, 494004948, 134958242, 660020489, 429818310, 703840377, 532744488, 271013663, 494050181, 589641638, 819486027, 839734045, 732074390, 969090789, 440224969, 88132448, 700073072, 233751129, 287854702, 176387067, 165691850, 302583447, 656010228, 478577190, 725780709, 351624502, 549029444, 421031302, 648336929, 356447423, 432748008, 924032572, 715453604, 385547656, 605211366, 944175512, 44108795, 295881388, 923155821, 941234465, 91367044, 329556078, 139375330, 757870341, 708805575, 136256927, 613025919, 556439773, 735632428, 838791825, 527399478, 410610678, 743604450, 333162836, 193816223, 853058341, 949499457, 923354521, 977316354, 52193695, 532447502, 640707828, 988270124, 205743339, 283897056, 685040903, 883369738, 90850757, 938572854, 186208515, 328667939, 173983181, 336151308, 456658434, 107570784, 416638043, 88593440, 342261358, 558478644, 102037852, 108784986, 304398074, 417422324, 475721813, 629254235, 116517220, 483390249, 102985244, 761498219, 919495574, 830699428, 683710444, 842103778, 46019574, 937378163, 917816099, 555907410, 152613440, 232480453, 839491433, 231141333, 702655491, 698014285, 753909301, 799037057, 282284508, 314983116, 816447654, 372578110, 504847842, 579014393, 866549973, 996870956, 159736586, 854855309, 40134571, 144605699, 586773031, 490223909, 260754252, 959472603, 212304098, 753704522, 824872614, 499681151, 739968178, 152897700, 700811210, 438768486, 302863913, 720976301, 133656407, 402403442, 657795167, 403963498, 296633416, 473416237, 149960063, 193484526, 679019432, 610502744, 171531584, 271910070, 127959530, 829232935, 186794806, 14519993, 319242084, 454085372, 889600786, 203396630, 682392150, 573513761, 98296505, 34357768, 708831960, 747181501, 828963814, 982225681, 452476522, 264475774, 730715803, 237450205, 812917426, 847188720, 505496880, 67791202, 903694870, 613451458, 644880185, 592413175, 282108840, 499435431, 238004604, 113214641, 391540958, 858487151, 734855596, 841499250, 207946724, 719317941, 201722860, 270246083, 964632532, 492463564, 790436188, 123323435, 724593125, 703952109, 928451267, 860842525, 184204124, 766997235, 479457834, 850055252, 891292832, 701334485, 405915581, 335450702, 460701803, 688083456, 295204065, 293767864, 830482398, 939803894, 610675067, 7262589, 943201399, 867735525, 389752957, 729932873, 762196447, 275769931, 766530025, 850545783, 602130710, 52458240, 746731334, 956290339, 400383234, 975662882, 690937088, 568602871, 59929137, 18013609, 766041015, 875078290, 815030867, 970199018, 235065477, 321825309, 355225593, 96405168, 21058854, 408881383, 700159831, 709784862, 34883339, 588948160, 331468269, 663658486, 705627993, 206588371, 999721333, 466698228, 759948103, 328872554, 739588795, 640177893, 713254900, 999962397, 228231586, 159867932, 171179151, 396621911, 504401606, 642446519, 806892573, 444903912, 646078212, 402934903, 694698584, 350421202, 412263160, 156583357, 755131230, 578889304, 113956184, 798227398, 382949059, 824568958, 711810030, 743965711, 638185230, 64143613, 118527096, 215248359, 143925704, 389936531, 499510131, 320904596, 734688837, 515122488, 596204084, 880019515, 778460121, 133957133, 861260814, 964533497, 102100617, 353528908, 711534797, 761794618, 951379361, 308176413, 311530055, 812107241, 249917495, 435521137, 404202656, 385707913, 643757992, 469650848, 67430499, 263435808, 758799713, 806437166, 90374211, 388829308, 698922502, 390823175, 274620659, 463700792, 799821238, 982980100, 804282016, 993043171, 680641882, 530322801, 719270608, 2870070, 936105267, 943771387, 830708546, 75038422, 956084005, 755598432, 295197596, 583285589, 976061125, 422757132, 202482047, 824360569, 661163697, 329467956, 113311605, 724495848, 585024152, 800365821, 525862685, 288400408, 31449848, 636071232, 694369899, 861577494, 613324041, 391723843, 445924766, 335550158, 143698461, 795357063, 571901520, 198108476, 428021209, 19470577, 916676115, 914746585, 62080056, 324937136, 721631289, 170536750, 636995177, 747666445, 988033968, 64219473, 915294906, 872854560, 887569979, 93433240, 30567384, 784470730, 353927867, 904199897, 824716488, 402804403, 968723434, 714806150, 257847450, 351808299, 458141919, 704326353, 404506040, 617667293, 368700628, 872636923, 734274614, 178260835, 635580868, 209974939, 388479678, 815491184, 275155074, 125418094, 610734154, 382468479, 9819626, 807640630, 712632899, 611911484, 781206975, 821471910, 334574269, 781968845, 546308067, 311186506, 595366630, 45447824, 671296395, 795790040, 613886337, 392861546, 466812082, 494987183, 461272056, 172300328, 607306080, 881607045, 865981509, 925759571, 713210930, 248081333, 219153577, 989141411, 755181917, 487733604, 368236529, 865082633, 406836813, 168563977, 790256491, 889181000, 780470281, 19090273, 379601543, 95256152, 245896871, 565555917, 381417137, 28865234, 382747444, 772429718, 298336850, 905461786, 186822447, 157272482, 385627257, 904475107, 536192153, 401330914, 70442480, 708623573, 768202889, 244146255, 970179848, 210468071, 312327114, 420373174, 702823260, 887992951, 881926537, 662419903, 979889146, 759183748, 361086438, 795005705, 248828463, 213621945, 178050273, 786868902, 436086698, 943108281, 164344073, 717050683, 461047860, 338736461, 34895557, 440086355, 522841058, 77564546, 900212274, 896299133, 487220521, 318841604, 617311999, 788722238, 858160601, 260007744, 939114724, 757197237, 27037021, 986600734, 22731741, 650810609, 170546764, 528552824, 897872937, 744894992, 130339254, 747523151, 371840227, 390357393, 977712649, 10996824, 546489175, 808978269, 414897013, 573598671, 238122615, 30166774, 233370781, 74623200, 29571886, 945348679, 493485174, 3437036, 470696882, 650684602, 263297323, 414181771, 279863303, 674618736, 789201110, 828164277, 755255912, 506377267, 946593464, 598803073, 545525534, 127228528, 820906614, 716909352, 788053500, 192449597, 231080008, 721918823, 325595621, 696012665, 940405279, 225899744, 103031888, 637175794, 47676400, 45782821, 596574328, 126412783, 707635999, 690302737, 59532277, 235148873, 710360057, 589032487, 591313346, 274015384, 139604853, 833819570, 450114260, 939947794, 651191947, 5579566, 574023969, 356815932, 315143752, 966217326, 378369216, 508699859, 405252822, 235037429, 72924873, 693640677, 162819566, 86275905, 187812986, 398013886, 960294868, 283078988, 671914937, 823612523, 68759615, 332461567, 970446946, 574394697, 681261828, 973032003, 657366601, 118358453, 29997383, 29025763, 119216183, 23678721, 419267266, 400771013, 102776453, 947683559, 193046033, 668859135, 310475533, 285031179, 936063949, 53674301, 334810541, 212648668, 124125294, 125687314, 765240467, 652342602, 976774622, 871443594, 698603969, 21213470, 341281192, 112388360, 187973269, 718407757, 131967231, 877977487, 476862017, 876240044, 54755630, 814572805, 69481780, 762592535, 375285115, 68509438, 264083333, 538800249, 310595309, 221946573, 319234189, 498851563, 466410239, 697650517, 311159064, 121922698, 318084331, 832914635, 879692845, 530625099, 443870204, 865881847, 66193468, 242942819, 739948976, 342039328, 932918253, 795946299, 434143676, 881895615, 369606430, 268941037, 456788355, 766218497, 482531323, 234434412, 93504119, 570378906, 378202240, 517069265, 842834951, 618621602, 77200519, 15219841, 266466549, 360257563, 682192474, 288896359, 594400550, 986784873, 981472470, 871195819, 316186673, 799816492, 683395473, 874767406, 929970549, 106961862, 780463385, 285777721, 792971482, 196524765, 457800066, 603132183, 292507570, 915885520, 525323858, 476059424, 700557885, 767066802, 420282713, 226196707, 400266157, 72795525, 731425573, 288984533, 712465882, 780290405, 831326184, 754274168, 739563704, 289749163, 244292368, 555669423, 730773251, 790355902, 796464692, 79190798, 301386161, 471779257, 744574627, 967577989, 307762861, 827625622, 474646333, 824929920, 585755199, 351169267, 244083150, 288356835, 263396799, 668301820, 211792036, 853955780, 835399518, 927740554, 303824648, 784278718, 727581004, 932213422, 147426359, 386380865, 151548487, 754306818, 573488770, 905478241, 398783433, 118684828, 233615445, 997366656, 200132094, 81555216, 738703074, 898670204, 953136826, 306781427, 169609607, 29483768, 436685632, 403515856, 219957842, 935703308, 38709419, 543705956, 86260884, 543783247, 394654825, 238187502, 88991062, 813448964, 914269659, 578330242, 404820421, 81703046, 465332364, 488918306, 325623983, 93298769, 624324833, 925828622, 639942992, 965387315, 799375417, 679690818, 370872656, 482105603, 434467963, 425611585, 633058806, 529753866, 795275415, 108960158, 7736728, 398152222, 526232791, 489669724, 911384944, 750908647, 329613229, 322637031, 927053084, 514820543, 245719954, 736929137, 828971378, 277336835, 606810423, 176747680, 533351357, 697958807, 427292906, 989719984, 105771196, 177577084, 57157146, 392943806, 596871620, 165889563, 670527728, 61369150, 238169978, 541192364, 410018088, 184240832, 501456160, 180540236, 835972714, 301814902, 30871024, 555249582, 468332608, 992237449, 266200853, 360328572, 300016773, 935117024, 844145233, 577187966, 288440988, 607891575, 574702476, 136264377, 767201901, 875122211, 47579507, 546115583, 440884929, 787296678, 258624721, 363677420, 604093803, 563767574, 658125677, 172891369, 319027995, 566007077, 628787199, 133079472, 649623317, 509691790, 510014621, 127412183, 216508998, 436283104, 766743269, 107600004, 693234421, 50133362, 15591641, 411674372, 178501710, 53434823, 250055545, 189413461, 986817796, 54367801, 539541837, 241491661, 252785478, 38609487, 508079185, 977101980, 287258943, 130396290, 397699260, 149576306, 766273323, 908971990, 622262296, 626300239, 534921071, 588665921, 288770842, 995312077, 634023556, 523593722, 950133784, 774610360, 683237486, 705616289, 587865949, 777717799, 922905628, 710882189, 660203978, 519273778, 302252297, 877502249, 489262586, 411770520, 470744185, 749930230, 254973511, 318083308, 247022036, 146374185, 818241210, 696415573, 908759882, 210336924, 301764833, 707191627, 558704536, 663179891, 21680638, 308216121, 937967976, 116180804, 12090507, 187228964, 16617659, 961177973, 285883578, 185323443, 268579286, 716920425, 201391016, 537445142, 181181290, 38057194, 603773641, 108263469, 223176616, 222561518, 16604538, 150406942, 396525760, 185588581, 5084025, 184994626, 138466757, 550161599, 89974691, 95759039, 947759608, 47024824, 781536556, 243131301, 171139589, 347848697, 153416540, 68009978, 803282199, 196368899, 857279270, 855100496, 855911064, 606465553, 144261795, 711143099, 44901671, 755631796, 518962983, 856585198, 407579242, 674788822, 278946477, 401128402, 992623738, 625927085, 670660502, 68254538, 788071932, 362467615, 260692870, 265492635, 175764097, 328575299, 583995754, 698513807, 448925166, 539383477, 149242201, 622167532, 794987304, 929861686, 701785864, 12154777, 948917200, 618438112, 276365243, 805643178, 684395890, 874860605, 550398239, 690550216, 222969935, 815242829, 907471934, 844447245, 504569133, 547057802, 774410311, 243718338, 220714614, 838490966, 615164881, 60179975, 936562584, 739349448, 59729822, 438321527, 755677705, 839155640, 338618579, 266434076, 790581926, 552006375, 359895173, 809982925, 740890849, 968955577, 939215698, 372194626, 16197292, 66933401, 574104790, 58014336, 843028439, 250053455, 808445567, 563039310, 696899997, 630097687, 944121541, 480643551, 167465800, 887678786, 922139609, 403425139, 119482117, 175406070, 571515200, 547878288, 505855660, 831375938, 106702542, 679787094, 640609210, 925549624, 942089836, 92928030, 927669668, 61202566, 329917866, 811540632, 731815779, 605339609, 277536139, 103826674, 696218084, 296857591, 237963312, 85858965, 119402780, 710639100, 598227133, 785300725, 390074576, 470833182, 751300950, 188284973, 471022212, 469274841, 984213648, 127262635, 521845203, 381649366, 110800344, 246680185, 943054184, 35532030, 156319295, 996079951, 709243099, 479336878, 700926480, 91548879, 729957113, 508626529, 560265828, 729652145, 180424978, 309002710, 138337515, 791990356, 559980361, 920164842, 108962049, 687157680, 88366838, 441868463, 937418860, 277511129, 727639014, 968845004, 470820152, 634782321, 647338905, 210302236, 159183949, 320482987, 714014158, 59485608, 647535474, 839524537, 65830108, 999166667, 965117881, 190327641, 264469467, 150033976, 975153138, 245670834, 872650956, 321699301, 112376803, 401369063, 229692283, 669559188, 159126627, 365348316, 794283454, 828778580, 94510833, 346296738, 802608509, 120913117, 417496008, 470407194, 169174518, 569202492, 59592655, 861093691, 526191618, 282875556, 230213331, 183418536, 694564937, 807111756, 91649783, 721536310, 369013791, 197136170, 48343187, 938765552, 581361906, 212021885, 74319049, 567877875, 630258893, 708819926, 883468257, 287476650, 392172300, 518047965, 206476329, 437780459, 174326995, 763200350, 440833354, 823738801, 962217910, 926467704, 230588439, 953107916, 194218264, 89523820, 322339359, 301394761, 461772355, 570161079, 535131765, 772568532, 530398826, 485413168, 288582373, 8051486, 993674759, 65152792, 70267543, 619943214, 876006725, 7990355, 905314079, 544532849, 646315684, 369335570, 794598671, 697983918, 953486506, 282934078, 373144577, 866860416, 169688019, 658902038, 18260015, 39323042, 821471988, 465877503, 22447654, 998580272, 58421872, 284190193, 588535491, 815828394, 618221308, 991228173, 567618699, 185247432, 713978073, 98125036, 944514249, 505555044, 731166019, 256996386, 594688123, 759801497, 107408901, 49943859, 999244278, 725537797, 732902286, 665727303, 160244894, 348198734, 910272776, 499900860, 217373873, 24439731, 989528739, 572564305, 927659160, 304516722, 932502077, 932064813, 408401765, 970875585, 341185890, 492974891, 817581059, 906412332, 884449059, 173385269, 809854830, 110540344, 644518909, 741558145, 922762320, 296740419, 221652177, 677069230, 118192677, 469574693, 256796136, 67160835, 406358537, 250739715, 469835151, 590916463, 666845071, 574803014, 613667323, 51359364, 455425225, 988691655, 122339349, 346163835, 701829058, 50817688, 114084308, 184238267, 226479503, 745981298, 163873236, 440497293, 174752213, 510263368, 589256435, 99259907, 790839861, 712356303, 585798436, 158117810, 836638347, 757380903, 599538689, 72340990, 793465931, 344449824, 482770635, 204414844, 375290925, 782112873, 959008827, 988583264, 428919492, 216792827, 874881991, 988173143, 798894942, 406976703, 229664733, 551904728, 688625353, 726814156, 510518072, 214075348, 432043377, 264457897, 788615011, 462627583, 792583868, 309517479, 304851066, 617799937, 114061065, 219080316, 349283472, 536672016, 993993121, 683004787, 177125005, 764278737, 145809257, 448845813, 183775140, 255473814, 475231739, 772502239, 943755347, 30771973, 833041234, 23360874, 595083644, 334348921, 774727162, 305302489, 633165639, 358267532, 293069121, 582601224, 621271722, 491249881, 638092001, 400984418, 838141024, 757345343, 838093111, 697454203, 568026997, 615171539, 403414334, 89507756, 755461734, 945942106, 767286552, 972891148, 767355034, 969963810, 476567984, 317151798, 123361958, 602572620, 558990484, 638912553, 818076798, 845960275, 783287516, 968674912, 517176845, 533541908, 774198697, 179191585, 697951547, 727796362, 851280596, 357814442, 307038199, 790368024, 682807970, 776583665, 937530980, 429086862, 923697069, 5511429, 950942212, 320435323, 99240989, 206160466, 471260481, 95058685, 61093065, 364090370, 5013787, 936356541, 933710432, 592163742, 284487106, 973205149, 935959964, 340343118, 712800948, 590068415, 914072861, 362116890, 152339469, 711083246, 978001435, 798799977, 802596922, 93913432, 950551769, 313981737, 915274704, 94088780, 204784281, 291664048, 509522798, 583174755, 234352499, 106134002, 509231202, 468183994, 595943717, 199148192, 671539599, 973670795, 699345984, 388084275, 925254120, 605581744, 733463035, 882113585, 51850420, 142418559, 344324063, 368860653, 721604693, 232636932, 645882524, 265172511, 990925510, 50746432, 73644502, 942981476, 235730672, 55640944, 515519394, 454385539, 84847356, 258536339, 773660077, 410930384, 362192910, 723856790, 68581367, 227527633, 465142183, 371883685, 249547988, 670599024, 963767926, 516618133, 198171545, 910509304, 797653507, 120584457, 675865832, 25270185, 775512913, 644671633, 678445341, 409597118, 553332051, 331445377, 329566380, 290290167, 40719949, 491226334, 746190552, 38646535, 257506970, 266580589, 619928451, 865535290, 358416914, 338042210, 530485049, 310226410, 909924, 847535334, 395626537, 614107350, 450162078, 699401314, 622134650, 991258581, 810619703, 23966302, 990319874, 655985736, 229607085, 372463503, 432276258, 619340763, 112971751, 152736935, 107769804, 421967910, 300239357, 40633086, 315834090, 588015880, 987099058, 714107867, 606160631, 629005037, 962472074, 381810567, 858941868, 403128030, 921399022, 181318834, 512170329, 752268271, 136095783, 816847335, 586906071, 749455547, 72169634, 853593578, 158662954, 777330362, 33213858, 429669832, 789157262, 593111469, 310914345, 956531802, 108707264, 955624231, 43613179, 189615509, 530265386, 909994581, 507866861, 629792995, 669747582, 839197729, 695034979, 581250581, 685826265, 587680483, 39105778, 68281119, 207211699, 437454725, 857563882, 51623706, 952334769, 361958194, 267589131, 67654338, 853001776, 330751834, 424866327, 781652773, 272785537, 890267397, 17623640, 618531225, 356965046, 132379331, 77701049, 269751759, 456436545, 465179071, 23324315, 23092547, 975916699, 993760263, 912137384, 582801943, 113781540, 410465879, 498363377, 299856873, 740710187, 286941927, 364861132, 278467647, 535278084, 106204310, 656270911, 881044943, 319422206, 956409470, 694908752, 567002033, 479174741, 171657179, 950186430, 258077399, 825551480, 783365910, 578345078, 891859754, 956274361, 272251717, 224887427, 552932071, 988957580, 270343820, 594507605, 965121683, 395126243, 525941715, 871608861, 254217806, 904405466, 510058027, 946689051, 410146318, 636855383, 239915823, 68901915, 208572197, 150092068, 472858371, 148037591, 101318689, 741262925, 175747041, 403351781, 671141853, 737730795, 475863890, 591269660, 305073812, 78185895, 6615213, 951657030, 897986942, 208221044, 796912284, 297759377, 938829500, 190470945, 298763581, 526298970, 743612838, 773316252, 563905488, 984476565, 289409025, 598092193, 373028793, 515996062, 652460221, 929120809, 789752384, 712425026, 767960176, 71994176, 840516205, 243355382, 243269845, 481055461, 788613668, 197952382, 717064466, 589248907, 460070991, 56820592, 826637928, 608284587, 232335262, 353109610, 290100520, 249825525, 309612090, 979048131, 231053093, 677904890, 475890311, 429456481, 495511402, 34093594, 411514135, 946855791, 693203580, 137242144, 919386823, 372265772, 888809007, 631778275, 102202935, 335107453, 151884743, 79231343, 927324632, 1436320, 937059892, 495265282, 559819006, 580585642, 439556227, 857625229, 679922056, 523306835, 897896189, 315632298, 175176852, 428287476, 566813720, 718758558, 907420713, 216252839, 926919892, 127123037, 754099009, 254241965, 239893975, 380127488, 983703475, 1679386, 881027018, 257882356, 580707412, 318103721, 935012618, 930737566, 696830532, 981207339, 310777383, 400857149, 768089839, 721981927, 836759066, 891846175, 781922080, 253319185, 865700336, 412509433, 712074087, 231464741, 662075935, 514530667, 888257360, 871285728, 554381490, 191231706, 690260628, 790633206, 770528002, 340547851, 387072390, 879932400, 442821337, 899289520, 697364721, 93940261, 726373697, 471493584, 739226062, 113876415, 641594455, 383469928, 603153114, 765891244, 265959145, 576932007, 9157954, 361445616, 282562651, 976966094, 766023326, 358009597, 649794742, 604729758, 36247491, 359384217, 955391379, 864366312, 112033654, 380441211, 669169080, 512099220, 452565240, 848580513, 503360015, 512972370, 158868410, 518043361, 550809965, 590140562, 578930594, 49913866, 203050814, 891625099, 821587176, 806755260, 48659621, 929477759, 877715008, 53344531, 931402962, 884286277, 490247450, 155988970, 560773564, 601574902, 775987265, 555393856, 330002183, 951622227, 237968216, 905502849, 774821005, 462146483, 749426223, 294275203, 694319726, 503349813, 535289556, 507295172, 758307553, 619176776, 630528597, 794958296, 804519693, 176169154, 420408477, 323153465, 427279624, 526588149, 472056285, 647708370, 335402488, 378234920, 560567352, 362446981, 852811105, 847869302, 661059827, 532082930, 590715257, 636672817, 697849268, 492706992, 833027164, 377589486, 884363068, 640854779, 340101886, 947022769, 126365269, 319525955, 851517339, 990268535, 857599020, 535890207, 314588962, 792672571, 897125332, 14210892, 793544569, 862225330, 363629267, 334539971, 336243088, 454351177, 444673059, 878539528, 998088663, 461558798, 966071543, 183346263, 862671339, 855580256, 682865135, 273813090, 359473311, 368554152, 752730953, 698714690, 584019593, 92083951, 776688437, 229683827, 76698666, 421091071, 134099713, 841376639, 952213352, 496278740, 613147274, 644149135, 880774398, 814250282, 788596104, 693742175, 52935097, 166491640, 47118089, 100330972, 306034686, 994918661, 196280259, 850500803, 479653802, 665055631, 824827310, 602323790, 320364590, 353489043, 132123474, 972767863, 153262817, 605722190, 664920537, 885124709, 166159627, 72612583, 623143172, 378183084, 877620294, 493081029, 937334948, 163344487, 470829871, 547839903, 586255388, 341141117, 750065191, 710333214, 215607914, 334465350, 388448569, 585884880, 284263460, 416170932, 888074119, 370728215, 231232657, 500051529, 314430639, 196496206, 547546664, 266866737, 195369463, 121404278, 168009668, 40889060, 200085617, 701576958, 537537012, 206480791, 38601013, 166412631, 103286068, 414425340, 267377128, 537818511, 465676051, 525687357, 776749533, 980206300, 53449637, 985263393, 724818415, 372683498, 314443093, 316500572, 57758437, 979991178, 296127037, 277643511, 827818107, 182580074, 749223674, 275344936, 871034595, 395980075, 727251503, 655974004, 785495060, 867840497, 89683602, 923706699, 838222198, 754081830, 992269534, 100487172, 712279817, 793241460, 890292690, 636990445, 704555237, 154614678, 485086551, 983335508, 844123830, 460762530, 328318041, 976851559, 754952876, 239357869, 455558998, 405413202, 229581264, 671043383, 969345626, 907354901, 652456883, 476782986, 642145916, 353465514, 823218830, 180964949, 508573825, 577299535, 229587441, 165593432, 826504905, 494833982, 174358146, 533992038, 797264800, 91070024, 491404731, 930177634, 206125727, 630040198, 216516544, 341207819, 368006606, 181504668, 829527700, 853169224, 315854032, 889108021, 643181794, 832361547, 586480694, 705889456, 955803111, 271995796, 901467161, 917364292, 704385474, 282865647, 107994512, 721040052, 945414070, 989910932, 411627788, 35635305, 769824678, 179455559, 284861006, 560757428, 74565677, 49067585, 639213623, 743269575, 573604571, 126249965, 915381982, 336220317, 942518353, 666280905, 342191942, 817573717, 339485389, 990109372, 42901287, 697727469, 674825748, 883174043, 707247286, 29267223, 524892128, 100591549, 480773160, 878217189, 845903483, 627095503, 452858352, 496427758, 835704109, 997091329, 704633455, 27165053, 183940802, 722047340, 363159881, 128353277, 900857400, 862254828, 675534551, 649249897, 315771917, 411811699, 216116039, 459672986, 683604025, 521633672, 644848817, 789051056, 561029071, 718070598, 166845432, 648599410, 730072310, 498734416, 773644977, 608571733, 821771888, 788939709, 888284179, 765599513, 458469991, 302312694, 342277552, 535820158, 424274135, 17216374, 774736307, 470254189, 580164740, 315643246, 524828875, 748912552, 280152048, 172427507, 691865961, 77565095, 700460437, 968014562, 575101430, 59065473, 442003740, 628620267, 311982108, 402075012, 55318089, 610556495, 613965380, 305519527, 878739174, 106855035, 621257172, 119267407, 323467561, 353117226, 979957333, 250934207, 646716376, 651303041, 514314213, 883826428, 382510527, 287981411, 529033124, 499666024, 512611441, 969000357, 470669040, 557188764, 106450508, 221666819, 117276812, 670742860, 54740658, 2900759, 864127691, 264940160, 224366211, 472613395, 82425706, 52791743, 236970000, 303308818, 213141229, 724978519, 597445768, 737379059, 669155102, 912028334, 405739593, 953823810, 886967841, 544216612, 261662561, 510029435, 320034128, 12056262, 423769605, 192247502, 128257309, 532010129, 187131810, 467789219, 777587361, 778067603, 469794284, 544844441, 429265443, 636342412, 79856110, 711487756, 889037347, 770095861, 885576622, 196085279, 889253436, 340955375, 746310, 371413850, 234800141, 380672404, 746478415, 753637738, 414705702, 233624560, 469825989, 331025035, 57750742, 640103697, 545983919, 554914525, 890345740, 965645841, 640961527, 809662075, 438669185, 918963263, 991696231, 524455587, 351473637, 955583363, 357490755, 900854712, 860542242, 285675084, 546122502, 104467514, 779748424, 369040824, 912605382, 937843489, 731001930, 648462403, 83356527, 275226594, 826104546, 827301643, 731696076, 852838707, 8912391, 742394575, 335815103, 281277895, 778722268, 131713700, 184440409, 497426494, 773235120, 854357274, 391808544, 886723724, 308638536, 32623258, 184401197, 430123977, 675331811, 702390160, 675786663, 552036300, 552960187, 732893155, 237094684, 724453884, 924888651, 157388608, 844683519, 395740236, 280645011, 147910804, 458243584, 418104272, 530487403, 46702437, 306730205, 603713102, 739803215, 542776635, 893021311, 555740546, 487619653, 314190881, 441996287, 545119175, 384788622, 912227514, 624014006, 422178196, 862826674, 813849277, 348876312, 689510167, 32266139, 580663069, 636050793, 690929310, 786520141, 891756229, 263530748, 3600455, 597234545, 292656141, 334601919, 269424608, 762565469, 138070805, 153252077, 210136919, 369013063, 185434179, 797931515, 139937296, 900762930, 373323772, 975846587, 616502508, 389092819, 166895436, 815481372, 377059917, 954923898, 661728270, 615343894, 19539410, 164553961, 128359868, 700158913, 781677126, 79159181, 550442214, 780882824, 638297765, 437580358, 811108523, 308508025, 918688754, 9276544, 521250142, 977469465, 877298521, 21889167, 544470770, 493580975, 514301027, 144460376, 451064536, 591741075, 919902255, 873940518, 120910643, 461270151, 798277197, 222422222, 685144509, 554680340, 693869966, 668596938, 601673486, 877812428, 364505939, 245540508, 723709882, 925409952, 579894363, 934344734, 197204487, 86157647, 660493352, 991150095, 664921729, 951478570, 751090324, 330681393, 74819229, 233485773, 645352198, 269407616, 874583811, 697975277, 80796635, 782022209, 15204939, 581105322, 239240528, 152170487, 699540248, 229295163, 379169198, 496319730, 466632855, 198431269, 115624637, 238872835, 956361008, 816594495, 689248553, 657398508, 904683831, 249106161, 483631365, 849607640, 651584461, 65441003, 783563255, 256370862, 654566118, 962865798, 972449578, 416882090, 848190775, 700371457, 76061398, 641637004, 817625332, 59937478, 590887887, 541741822, 934489128, 967678391, 495500144, 487168624, 855952890, 668125624, 946149544, 34632909, 696147473, 778699423, 773166574, 451845805, 92215744, 86203120, 355273655, 775541670, 893885631, 742174444, 996590125, 727801665, 11201076, 708645506, 81228597, 635652598, 807580913, 741219318, 245163124, 33902361, 355825186, 398859377, 950786714, 512075207, 568137957, 517385131, 362122738, 783058192, 922609020, 607428790, 833327393, 637867222, 193418572, 241718592, 178325459, 835276653, 527678788, 650989445, 703908494, 660310203, 299824655, 43346290, 353279399, 509960116, 946670112, 159885452, 621157385, 275722056, 383237713, 584623782, 581195988, 973178043, 950791033, 854667056, 999418733, 206067903, 525939244, 31460910, 114035967, 573885513, 951175835, 291943679, 572125323, 649163915, 827323819, 108121870, 2775233, 357895080, 33928571, 841666952, 752465523, 553814152, 358196707, 961398333, 100652001, 122065887, 228292200, 316644532, 414210512, 338960269, 741871736, 382596664, 502637270, 659682161, 614791119, 230893232, 387296597, 972404191, 403475469, 528654673, 36056707, 263209167, 804609395, 426040579, 341097031, 938799007, 273288192, 451474540, 451678890, 346101284, 29824549, 879287318, 354414441, 312162655, 145208124, 217209571, 842758057, 93339388, 8434527, 765628878, 246669335, 668123264, 345491359, 196881152, 489504865, 583666451, 435718275, 740550526, 714203301, 461556436, 100658199, 752653539, 183363782, 907463150, 28127057, 15432545, 427131087, 69861061, 88884165, 980005948, 972267831, 188914273, 650109227, 684314030, 663832674, 881519211, 409939724, 755195446, 728902334, 11015077, 989034972, 868137975, 989415277, 246904164, 641796562, 962056229, 448393813, 421699730, 533350450, 961280366, 861281683, 309974177, 87921444, 329461697, 84629432, 385544451, 925518044, 750998859, 587601828, 379765924, 967212528, 906702039, 373755770, 132989750, 658862245, 327805974, 305699219, 644497990, 532181808, 787003825, 598197011, 211490158, 37069385, 714777287, 879389390, 155680580, 392058182, 11214046, 661373167, 453896121, 111785164, 852816908, 163404256, 162998478, 814866684, 614532542, 388430046, 239354497, 572306415, 134239134, 996039135, 77534952, 58376640, 381574000, 985720736, 125741845, 282492589, 409776167, 420100283, 903607398, 931459207, 66189179, 251900837, 481936675, 952985006, 87374365, 40266621, 202972783, 351307312, 744818065, 964776874, 870504385, 63544993, 503798497, 555283589, 954851199, 421104212, 976260000, 113606452, 990026871, 341875319, 868104128, 966406969, 576497902, 600496120, 457557758, 128563413, 629123111, 462379302, 858446847, 24057608, 853646614, 951823358, 13753620, 77702738, 903970784, 258808327, 538026910, 586553160, 526397649, 76374884, 339316869, 751211484, 381287164, 886173401, 139138421, 80369633, 801075195, 199536927, 385379183, 980303001, 997730055, 736155849, 578602460, 429448173, 452987915, 769437218, 253650369, 467788896, 34719923, 761161452, 108777128, 911473128, 258510274, 964782115, 823262030, 319964451, 166295093, 996077832, 17944631, 470311426, 755827060, 304461894, 913860969, 89131721, 913492652, 519827077, 110032672, 352876391, 304085147, 756942016, 501690030, 411598510, 883129807, 2806943, 745255391, 259436256, 707470000, 942416123, 933547187, 466401784, 885751686, 597170255, 661486654, 170404259, 31562373, 909529342, 759348177, 710708864, 715701806, 567319622, 632205719, 395688173, 970031215, 141065327, 526874161, 576662917, 536763396, 294811583, 188432764, 192438168, 642081880, 615974321, 591901548, 554111061, 252014892, 408342931, 937603199, 310634244, 169408500, 132430836, 885731296, 168926249, 248924903, 822160560, 285864948, 542521476, 504211299, 465308592, 511832087, 650020783, 307601113, 79078580, 790978862, 189038888, 710103290, 621293673, 174583909, 302887949, 181465853, 986783548, 608157986, 892085875, 478008064, 286326305, 37726293, 314067765, 453988815, 69093546, 438748005, 145355991, 218065790, 484699939, 333293470, 526850088, 979423973, 308700808, 677365803, 715796019, 91546525, 884095006, 100194483, 21791717, 812466013, 376906893, 397670168, 804501496, 822380133, 368631575, 276858942, 989453968, 794335470, 357232663, 638687839, 251572503, 241708192, 373406634, 824567448, 457365624, 404062465, 12969051, 921638684, 672690892, 883559759, 720786099, 990681170, 319314286, 102127197, 129337546, 132296169, 426092353, 391448220, 234371023, 301914776, 324412300, 501949648, 538633834, 722298625, 886452347, 205568737, 250615242, 548503964, 141152229, 400701435, 637680724, 452503701, 320891317, 572666184, 97159247, 439361137, 55351156, 300092349, 218054421, 279039419, 246517368, 597615300, 704289189, 983816215, 607024031, 94866604, 151610952, 876033610, 374116238, 645613289, 914523948, 239537621, 105071823, 535989418, 36529073, 418727819, 842537736, 975171675, 477802541, 163426390, 815421539, 563570216, 332945987, 798808901, 72253934, 484358203, 49082123, 527303994, 670891529, 627238613, 437432237, 966856579, 586011619, 501297804, 728247994, 110421149, 53391927, 765288367, 112956279, 361117812, 412898967, 327878449, 893178076, 965441058, 184960317, 956368061, 698925309, 880065049, 575555776, 894922803, 197487999, 691073892, 287275861, 568869610, 941372714, 936298888, 462496547, 747475763, 30602366, 340820240, 960565123, 578136274, 886110043, 826521909, 149031123, 104787963, 442714900, 822661547, 996126687, 362790802, 863909491, 38569069, 368058369, 849894548, 558068588, 4210037, 427928886, 387147890, 215602178, 901400454, 228551370, 797652121, 585653320, 942528164, 71498219, 11038634, 704935732, 236517190, 390981690, 227728497, 606539051, 854552771, 664133388, 933006076, 13597636, 915084298, 156215019, 250500062, 377979015, 263685952, 444577338, 425560682, 259751091, 512331295, 513178870, 955088047, 232675484, 67633350, 62464733, 643823375, 836932664, 923126212, 128792847, 167787718, 781006911, 484668090, 109429226, 167159888, 291547775, 678740648, 813704028, 340705464, 941304831, 165559071, 126737406, 970880212, 767085267, 825296536, 572306893, 632194449, 199344013, 887499199, 341668538, 626344585, 467563674, 82028145, 478307286, 56076924, 475226466, 85952717, 333950471, 678917645, 239989389, 881387849, 294406125, 841695578, 115055063, 548001369, 996956396, 465857502, 598094892, 16500011, 468898616, 238858795, 298735174, 542166837, 476597320, 174636963, 342909848, 867247289, 650586175, 746835851, 328660983, 793075227, 963254043, 140047507, 441182069, 111499003, 112547793, 168261245, 763132681, 123378567, 933007762, 141035538, 386742600, 947091752, 960949088, 322532760, 90805296, 665731207, 842089516, 114729034, 27525874, 911045816, 375866323, 899296475, 265306421, 122503389, 967036240, 539667337, 981986866, 146665598, 635437670, 816251363, 88685448, 209317147, 576788510, 439023830, 950090008, 498522198, 877184977, 678272253, 222371790, 960897454, 272182710, 682161232, 39303265, 530208077, 51923477, 517552589, 274274001, 21074559, 594001708, 510798864, 960080672, 770219774, 614893428, 621645344, 491220983, 777019100, 325275018, 244647887, 264545632, 49351215, 167087295, 958010895, 37427886, 576051875, 463753622, 318418822, 114973944, 96107022, 133336032, 549298574, 569012295, 1521513, 755965635, 342149505, 782158435, 629992926, 239493297, 176388877, 721760732, 79574584, 186324750, 390359960, 406794332, 713934668, 169518240, 840345102, 435370382, 753892645, 742684690, 604107011, 478413601, 738276648, 19392437, 160198890, 801860373, 361786029, 431000663, 655054060, 112890850, 892343894, 264215385, 497961643, 211757260, 574912338, 932849853, 775673547, 24708363, 818087190, 828508044, 673426395, 131873064, 738348044, 947185043, 274847888, 660631464, 58062062, 329597432, 916975739, 662331963, 727320766, 182105438, 471630568, 774914357, 314062564, 518342566, 702871361, 345067245, 939493741, 208438716, 696482521, 689129391, 497953616, 17001994, 525107239, 792046830, 296180152, 24355547, 768596629, 349182910, 569286545, 19605602, 704136854, 38594611, 472463144, 354861516, 486316807, 775974429, 39938851, 762609770, 599473135, 671531059, 669183213, 962475286, 204287443, 422506075, 743820741, 113963211, 469395817, 8967297, 592455540, 621702076, 505702938, 821612599, 597634782, 821273199, 545975079, 801593829, 841616312, 209636548, 312656323, 92426655, 201878831, 416245381, 121485289, 386908022, 492508384, 323628190, 956134837, 728725306, 166622712, 69073833, 175414889, 452847133, 995013438, 623805837, 194872633, 908796621, 922013921, 181268640, 809380251, 744621905, 880535439, 475576347, 98196029, 287726804, 716347260, 93640850, 851285621, 234925455, 841211195, 918870162, 871490024, 897488333, 40287711, 90026279, 79505482, 19392415, 971413205, 644876241, 486979849, 46254052, 445369358, 609430188, 730659542, 804505660, 201314668, 25216236, 518687594, 6325399, 86717288, 580124973, 316318498, 928218672, 236753074, 969372146, 549562901, 404130580, 488203829, 113584614, 337774128, 858179219, 784340588, 586168133, 2437785, 352718296, 98941188, 981469165, 278953469, 915638273, 94906761, 319461829, 115579981, 14362056, 867226942, 256932820, 660490076, 565384957, 844323495, 815658580, 545375030, 438258622, 751120410, 996981382, 55920475, 168629884, 415700057, 543887393, 947553387, 528463324, 791622096, 360439619, 957583168, 128623128, 95973130, 357476713, 482833331, 953752701, 665221534, 619925040, 164716669, 859127725, 255711562, 769259735, 304617459, 405690480, 448044435, 288270097, 637815739, 501220280, 13750719, 251023523, 510490300, 172131792, 627813766, 360883544, 395819177, 738378083, 327348069, 766019937, 90925268, 676186779, 153573974, 649000017, 16784187, 748495976, 121678125, 845740443, 396256949, 237890081, 614279258, 34785855, 222804, 531564152, 406360498, 586969372, 180073261, 418568886, 417713100, 820416998, 493353181, 294209749, 144793246, 225981445, 187181986, 36790197, 902703123, 237310608, 4813802, 633193842, 781263317, 218014288, 770759755, 358850314, 235307098, 983234663, 546317390, 566407207, 381404460, 52837950, 206331728, 395046833, 430715265, 239507650, 302201028, 406081123, 860467179, 576804125, 211182784, 753947477, 410583995, 164850794, 662790709, 26589031, 231935786, 482241097, 771723915, 515131431, 545295417, 581958177, 751638214, 869693522, 829300807, 204290368, 738396844, 198287881, 180277190, 262695178, 638197496, 814573252, 193763625, 388255720, 501148560, 335520439, 275506293, 202265396, 904478834, 743209353, 991508139, 699960429, 440347440, 794250063, 618351042, 741320927, 532506482, 426022854, 184449744, 311274869, 407387777, 947303125, 595541133, 149956242, 169122372, 746696324, 213540984, 51031997, 828031552, 807430608, 690543484, 809609125, 626032873, 964616554, 219670540, 415166848, 892877396, 655112829, 184846829, 839147147, 340828044, 590188339, 294367116, 832925933, 277035639, 871479330, 366762574, 74408062, 982262065, 146385756, 81333713, 661152742, 307279401, 78672847, 324822913, 854651642, 299512834, 430669130, 60516853, 560088258, 43717460, 121456272, 945316902, 352040496, 707795775, 300400855, 89468521, 954039141, 784938062, 691518430, 434796287, 967868265, 600041900, 939591730, 75310060, 342833237, 898466775, 499163592, 683064305, 72277245, 17797462, 646423479, 503919065, 627245342, 374189210, 774266133, 726707352, 819571360, 525978993, 283757150, 882419271, 364851185, 658912066, 617922121, 267895833, 980936642, 159127912, 808510115, 824914865, 837275236, 478757865, 984084437, 200191213, 705460170, 555397654, 99810037, 264056807, 836588661, 958616257, 291597891, 969823086, 172446046, 106422265, 237637580, 126043113, 537513112, 487568656, 176756105, 895320178, 823802739, 106846629, 782415095, 572541676, 44338583, 351493065, 444274803, 468103021, 160796809, 484901231, 318125206, 440790612, 974889568, 863585856, 129826459, 30605110, 523346903, 881082005, 89622424, 798151190, 996688010, 750836785, 871142834, 165081855, 494194377, 109943311, 860196819, 837284820, 428258866, 949586843, 758109376, 896140227, 11180818, 530357130, 682905726, 29846042, 762508412, 364897253, 118011478, 76411516, 587553937, 197799837, 256839428, 299202370, 343946270, 22681497, 320188884, 662592664, 742276356, 939635482, 310120863, 611114608, 263707627, 824428437, 193079255, 216495307, 950732822, 986769202, 163510950, 464875182, 122265960, 899550888, 707963654, 199941329, 310554611, 335323529, 706659067, 398901254, 431661903, 90266127, 518295992, 966641565, 303653930, 399536895, 387595455, 206315860, 274191421, 128448391, 669508604, 335789559, 726696407, 251830073, 881434509, 984548489, 208828532, 55051710, 707837636, 469944375, 706539522, 528784898, 293665968, 173728373, 512208128, 455778325, 908215628, 102374167, 420351712, 182042297, 939002654, 858874878, 685822514, 626053176, 481264879, 689847144, 453426233, 903851108, 296603752, 639661371, 664474830, 969309839, 536702071, 532968558, 269832791, 679419421, 23379557, 628225488, 283582916, 612292360, 434908227, 630172269, 429920351, 128446753, 556071042, 935155650, 437850642, 143630577, 187830627, 370425617, 354870126, 788557432, 663832575, 582169102, 832360845, 989021818, 779878634, 771776810, 21581242, 289951655, 896504141, 650327089, 819573516, 135215754, 378333027, 180906644, 87435456, 504686057, 99140052, 283096666, 223594317, 938578911, 575808402, 939399871, 341992811, 821793044, 705542915, 487475472, 893968549, 839991689, 693582810, 465328166, 682397585, 815786894, 976611262, 195930681, 842629538, 164361257, 19787021, 202346997, 330831307, 203932769, 94319646, 338190645, 758227060, 743864291, 964156490, 744612276, 887230871, 55861675, 535919826, 461158711, 213773004, 190105238, 141973572, 685338111, 570137835, 54794982, 859890477, 224691674, 509144841, 938647919, 339242351, 121103145, 237142724, 817078776, 262864416, 749453273, 651041581, 824767033, 321452216, 544473944, 899083624, 175204857, 932982715, 449067201, 81572611, 610515395, 267353859, 950520225, 277380799, 212100498, 850311200, 128897966, 813212758, 960688557, 453215505, 173548651, 689263840, 69925770, 973773385, 937571936, 476176135, 903552360, 802007689, 778224638, 839913393, 535032292, 26194278, 55269179, 907244998, 888445204, 593154060, 813755306, 433741782, 417857133, 199110455, 462601700, 928068044, 620960689, 741708833, 926761138, 797906683, 799040921, 20401186, 125934727, 290070472, 444620667, 854360274, 250272642, 609656271, 446378569, 250652182, 233185539, 139788739, 469925458, 378290696, 738211751, 675734888, 823200289, 831096404, 724529479, 755658462, 252686758, 596252094, 685931825, 499957547, 602237683, 418994034, 292705171, 696650266, 620034150, 152137264, 175344333, 557458433, 223813491, 39000049, 657040597, 306457582, 59992106, 682629579, 907874711, 542564767, 388915922, 45469941, 331042276, 565894991, 262497499, 942960258, 939475175, 859509613, 373154111, 694910513, 790098642, 294700807, 395935279, 982223020, 788681036, 447986759, 138699090, 772352622, 360680996, 813166589, 92846552, 457118410, 830768676, 285870557, 333361520, 449091706, 816291485, 431361961, 785969282, 372811154, 23403426, 431249118, 686190007, 33200257, 854380677, 455598663, 882933043, 674343898, 9178914, 649381208, 754528962, 689452911, 829567431, 400569142, 969725660, 892238309, 520576547, 136014920, 574989187, 998466845, 666261989, 764519201, 738750983, 109823084, 313571394, 55419724, 785723221, 786750441, 284937201, 94809869, 614907409, 248928052, 276797201, 736375382, 274441030, 463192893, 721885234, 705781914, 118877743, 194062514, 166335019, 346993206, 562793110, 645885283, 617379516, 54854070, 825548558, 646669229, 920263098, 117897967, 701799527, 265582505, 18340811, 716954176, 382311321, 74274615, 413260428, 794841714, 219454972, 155830483, 235703675, 987600193, 934791427, 474246869, 703736674, 894075244, 485013648, 932439592, 656191720, 80138660, 638370849, 640479374, 364934138, 467961513, 627642441, 501388413, 991106090, 352366854, 67122885, 414379609, 579336887, 640178195, 44972038, 834483158, 910475883, 888769566, 77758473, 550216675, 226685011, 45435351, 613210055, 258895522, 295738157, 33551199, 610088696, 386547104, 539045734, 729602367, 770822934, 29293037, 795037559, 961002888, 403518287, 578929144, 415582352, 513471319, 459564702, 757400626, 47909007, 413228114, 785130758, 274957039, 249353462, 40589958, 547397016, 432206833, 274582420, 947231881, 121632360, 868845930, 817471979, 617175981, 102163821, 29047942, 912367553, 931415954, 45326663, 965105561, 805171799, 68853145, 886113222, 463806444, 672528931, 565507078, 309625921, 745512094, 868897393, 294083869, 272508395, 843843702, 458586362, 119623104, 942108740, 53251587, 420238428, 22583861, 37794908, 360948403, 102304176, 369532793, 923417974, 386063294, 768732069, 656974290, 588070459, 659973951, 338333705, 524727172, 987043499, 228952300, 953072685, 553903304, 797982450, 391770690, 186269942, 404149986, 934002448, 279248136, 525545686, 593346761, 142809298, 663633668, 18129478, 432223664, 619449008, 251933687, 344367228, 705815615, 109540336, 514617980, 718310415, 451580794, 539953557, 95716021, 769838159, 496043355, 796728729, 425029760, 55141939, 889900092, 882570225, 198758417, 288685926, 913927406, 710679920, 970673545, 601651701, 523778658, 718674786, 218821520, 285712598, 541373937, 957725635, 308820370, 681769116, 386547063, 509026261, 826556173, 404472066, 65276584, 541739144, 858198985, 449645127, 92064637, 924611521, 603613469, 475412291, 602520769, 450063250, 458731291, 579565155, 608580741, 740359112, 540721869, 909038270, 851818748, 907306128, 75926106, 773423449, 195394745, 498878325, 676676449, 613491202, 719235870, 454719803, 482516043, 567377595, 388938113, 868725428, 468097567, 448898902, 571607881, 466508657, 244935735, 811817866, 656350962, 914920149, 257788797, 238314768, 347418079, 142134811, 524309664, 74437323, 773018693, 63941559, 340184002, 534203097, 879538743, 929971007, 631392526, 966103328, 56347648, 336191289, 590878669, 389085199, 596131479, 600380623, 326018084, 656305109, 886317451, 105465956, 375160677, 980409343, 720664513, 81176424, 221081315, 915435212, 988960073, 147954826, 706296805, 885951018, 763980066, 809227352, 759408964, 623893116, 297521319, 969041454, 908200344, 229840079, 562236850, 851430754, 223021714, 518807539, 119321087, 477333965, 911536851, 74846119, 248712137, 817243169, 856971171, 269093140, 618136966, 514150295, 300147870, 694078531, 87482086, 171621958, 498246030, 543174772, 949348392, 447865230, 109306415, 855274165, 912890927, 571142155, 898187499, 624233134, 743175193, 291089757, 750937872, 854572097, 918742675, 254152597, 712352401, 124097037, 519421714, 67787693, 30146150, 642163688, 49192853, 669270313, 713518277, 361623154, 201917624, 635364566, 767728162, 860198176, 71221082, 330473000, 9849364, 417104483, 771052866, 324948550, 400536071, 301765559, 320837660, 632330141, 685196163, 442374952, 902066797, 142632563, 783132145, 286024357, 153032463, 573341823, 73505827, 640531769, 504212584, 113853701, 976473813, 280596725, 93149045, 369921688, 544861639, 15720539, 939308730, 754480269, 154447534, 182061626, 423890672, 72117911, 311688296, 702693079, 725498484, 32406528, 831737582, 516801267, 917290778, 703502454, 457981566, 645103218, 456097617, 951427899, 226276658, 792862258, 651432151, 818920000, 362346331, 390037810, 973492969, 832683684, 986216532, 358606610, 452517644, 342225260, 617157196, 619555656, 393796207, 635076365, 97271583, 723779739, 16815935, 830964033, 843379459, 914686648, 74523110, 223103645, 792391554, 885039834, 166361481, 191694944, 921413956, 259944918, 7461648, 614591069, 604358700, 31673234, 963727836, 681001264, 646785758, 593184548, 581337072, 875722663, 636806169, 564445465, 544270543, 274385125, 136764171, 943204225, 264638415, 623249214, 595076246, 357044746, 86943727, 593362853, 347807519, 246293981, 169980567, 582626853, 870294647, 409825255, 420751980, 677465567, 265979965, 147787502, 607253035, 715363599, 642494286, 622581212, 434376746, 304705340, 443150136, 16642519, 103526824, 404834349, 98937329, 791306136, 251766906, 4235359, 683348195, 763521829, 775611171, 546720191, 66880213, 721179595, 588750835, 223841818, 627339189, 207097600, 537037598, 599651998, 491196367, 956570167, 44567239, 145858190, 299820758, 264547732, 578295099, 308266157, 93397131, 317274155, 294547686, 784285205, 889624969, 799635864, 142662329, 684903549, 33722344, 852785448, 226822970, 765070002, 897669730, 200957486, 104274420, 665876644, 698437441, 79635892, 967684655, 429564730, 196012369, 435694213, 982665600, 209136902, 584904247, 779357960, 330667392, 286627823, 722250955, 127733246, 593716772, 545294257, 944573968, 155923865, 505817284, 896160678, 494183203, 737451524, 339252397, 78213795, 519472767, 518455292, 541812982, 712941103, 140213475, 519108173, 153535542, 820607606, 46120887, 751434744, 27769599, 139423495, 83362775, 880337047, 52394077, 159654196, 69552785, 689976155, 512456141, 204378420, 382110260, 102858064, 111164182, 374306779, 221055440, 62425294, 968859653, 67151452, 111792224, 798928424, 925368471, 953742747, 903899155, 64242650, 129844414, 431847742, 231685280, 726571768, 550486299, 905100393, 982889221, 577273669, 667985476, 907748938, 52035954, 505855405, 711853817, 26343105, 959755045, 698344631, 919185306, 319349664, 607533165, 304503844, 356408373, 979476373, 207058640, 72506070, 326418262, 523980331, 735051059, 53408991, 335987384, 169081145, 730943905, 100424171, 732275010, 855834473, 814838909, 329305792, 699114390, 521931744, 932200058, 840227038, 856477360, 402997792, 520230480, 703152358, 393466244, 200485515, 582806867, 606105113, 132155035, 611878844, 780475213, 259195518, 598837556, 186379244, 205047785, 156103934, 521766369, 8847183, 606023252, 28426720, 53211429, 855005546, 374475974, 257942665, 629400369, 875692907, 683830685, 534812511, 335374563, 978991831, 479340948, 455047112, 505997465, 3185414, 776460657, 289486163, 137094827, 967066095, 752318019, 189944584, 261369694, 794838135, 842812749, 610731265, 50572868, 992674035, 762295691, 23671457, 293664342, 936023785, 542454949, 975619810, 1365831, 752988015, 716921296, 653171947, 81316752, 247145699, 948647509, 178708570, 5555699, 296997287, 662860900, 985772419, 750162768, 738552035, 174314700, 598780058, 188611582, 514786048, 288583979, 926577252, 173576432, 307975771, 573174489, 606723939, 219963008, 653593829, 73254955, 701196183, 236898454, 809253115, 633185861, 991448967, 414035306, 492921393, 427700195, 742128520, 220888697, 868753006, 203196093, 957939296, 840112068, 918138859, 391752727, 385021593, 427641817, 869026453, 982226498, 372503416, 771074571, 557907113, 428102172, 400205075, 933865028, 749606993, 596090568, 238293806, 282834962, 452502238, 451140030, 578142517, 733307489, 659018113, 825641807, 203946765, 430862499, 194952915, 517996787, 209015117, 363393010, 657152317, 782134088, 952470830, 904667627, 214673429, 592594541, 752651427, 659667796, 681309081, 387401067, 655606824, 453313240, 381672558, 588089468, 382166101, 683149870, 895660071, 140675035, 195961242, 934174832, 774747251, 73204757, 989775972, 695280411, 924547830, 962890310, 301560129, 902332105, 960437912, 126614461, 965774229, 297723018, 365751085, 306194375, 665393315, 891390008, 225596410, 170492875, 961351075, 947542514, 839106607, 482859064, 998804367, 39768311, 15275139, 288245353, 168637747, 645737172, 107548223, 489379776, 708594131, 928262341, 982709552, 147670054, 73465566, 413245494, 477478814, 44397970, 921194229, 494645630, 94474355, 850165230, 376039945, 605425853, 873082339, 753900667, 886688237, 853819447, 458926545, 647670785, 281927939, 982468468, 367551122, 358759088, 146522910, 458435915, 869881669, 459249039, 82374856, 671949296, 298105832, 261719335, 710666865, 572282356, 240094899, 709994305, 643655591, 531149756, 419283153, 585544471, 332726086, 686266396, 288072905, 289461393, 744906998, 125135409, 705380825, 421782586, 260700515, 224919083, 427037352, 582690992, 241133205, 442037460, 38634137, 192123071, 264653957, 731478322, 963298328, 993012474, 454626038, 584924214, 932026871, 849912332, 25822076, 567317883, 82627305, 344452781, 962978356, 373229593, 865529081, 894279133, 296022137, 525396108, 59874614, 22216077, 712221478, 533283517, 801024292, 480493031, 165272413, 338469969, 118307121, 166665503, 109785043, 7437743, 673497402, 744795261, 650319918, 760941934, 549335804, 966687940, 833136560, 785210964, 979072131, 72993549, 730245621, 490146833, 748193009, 220999623, 35319417, 793645813, 852549809, 289648639, 220173819, 432597513, 840091464, 530883880, 886390905, 490341024, 425325325, 850312869, 695392391, 390626624, 17002871, 362499765, 671788049, 645364128, 142193347, 940707657, 222671887, 305997583, 113031613, 901154546, 401892469, 638963537, 845028049, 973822787, 793074697, 883906887, 918184317, 498507014, 708479961, 290623775, 635284449, 124388407, 749754376, 72358889, 276209389, 216079947, 825514904, 127189608, 716213885, 803457203, 784813347, 488991460, 985695359, 144821584, 997816563, 397853642, 984838531, 600618712, 928876387, 999490554, 86774884, 726198017, 608890164, 663034863, 349410622, 393711377, 835456884, 704718563, 381249431, 944603284, 903346864, 853782212, 945838066, 237152652, 72310781, 339003741, 688138662, 648186010, 795519112, 192141377, 828594366, 38799115, 575389740, 92515713, 440852050, 340531105, 200747507, 1175950, 132467662, 497303449, 957929875, 201515256, 739022902, 712546781, 971387608, 111340629, 783919511, 811523667, 496448690, 301606576, 898498874, 225331340, 790683694, 318105436, 930846077, 976562192, 718184690, 444988475, 866519204, 913628906, 738066454, 937963515, 64624350, 143659875, 425597593, 650447545, 931070109, 956612761, 962110899, 272569919, 603377197, 177504388, 375286185, 470611196, 442693200, 684542954, 65839808, 417811670, 623864893, 806265176, 523881525, 730536836, 788510252, 893778684, 347438721, 460181448, 685175012, 735298003, 169151470, 393813389, 974863433, 768913156, 297839938, 871955253, 551293649, 741558982, 22074702, 636949114, 780327024, 784922412, 430754381, 670873151, 216518488, 447663112, 655283910, 186540876, 529357599, 229414702, 39721077, 792235402, 824528945, 481789411, 456571403, 951286542, 452439443, 625398260, 643048657, 823222393, 859347414, 716214557, 699833876, 639084445, 266267527, 968890569, 629273012, 639097031, 355051812, 540869129, 722702548, 459231004, 96177864, 80987479, 583222550, 14933826, 359327491, 871606675, 903046589, 294820341, 810225519, 587833933, 564397674, 947254716, 288738866, 389826746, 765069474, 586314581, 480223902, 378376157, 908744151, 396497276, 389399453, 990317938, 673366481, 572261000, 954701518, 905158707, 304297188, 300489090, 78508101, 379512112, 405991507, 921044373, 1640809, 648843936, 622213488, 648306948, 739386487, 690797497, 816016821, 788653714, 386164292, 346087870, 252716138, 993009443, 900287611, 943704248, 827195944, 839032301, 925326087, 806071208, 362605046, 235160622, 878656650, 987057783, 760022881, 373614482, 603494093, 785480978, 908697256, 953876221, 897636341, 558438414, 219185549, 817807949, 257010568, 481752811, 586577532, 965213262, 747492259, 887654508, 511749024, 40725362, 816849908, 459543387, 262804611, 566658046, 33181454, 554756594, 896996004, 742702451, 794886332, 172957299, 90683131, 798321183, 592345627, 254721044, 35508349, 548179688, 804504417, 299609085, 474379075, 58904603, 76396174, 922771084, 536556853, 80931504, 268052408, 801888922, 999412296, 349662664, 722304829, 735119110, 747356934, 627633098, 825484173, 179384918, 610137462, 10626182, 664584547, 456300681, 157530913, 380341931, 577286839, 368112641, 279870750, 303279283, 262029264, 341426280, 845022376, 683824150, 174215005, 67067902, 168559013, 772264792, 28447690, 810263455, 398130530, 945529051, 76396840, 553893084, 579883802, 279896677, 817701554, 118387239, 635583661, 871803788, 391231356, 583381467, 712291625, 453291483, 915458900, 384783912, 907201243, 404848226, 381759160, 779161046, 420925309, 660055091, 841370730, 785512902, 943268403, 685613147, 425004363, 365234504, 409381367, 116954347, 147360650, 72655832, 78150411, 292093051, 872228441, 195571717, 390870450, 447275750, 165758691, 643831570, 642009562, 233728864, 64998438, 329056590, 252442551, 382445473, 507094575, 169066251, 519526388, 860308774, 84901583, 521720986, 35791317, 784961538, 615440781, 214608300, 134559129, 470021988, 640291665, 16664060, 854051231, 506785434, 899032587, 770952034, 425087451, 307323227, 831263793, 982987777, 1378128, 361268355, 579938662, 267318899, 421059327, 426864144, 436889198, 565759145, 379039952, 836297202, 75235099, 264056692, 735028383, 922668892, 265124450, 673264765, 872794642, 475469955, 68480178, 323903148, 19805948, 659040929, 445078948, 582902832, 273283953, 190397369, 123622835, 654985380, 895748583, 803643947, 947350899, 169377996, 733613215, 472440356, 138809089, 548270525, 554600481, 567101570, 349080039, 628862396, 683954031, 230045699, 89319615, 768797370, 141407592, 34146749, 409078400, 791661779, 744768834, 561476826, 68727458, 289743080, 247859659, 282896743, 370902833, 461311091, 936857232, 386820422, 533855738, 520388945, 512041382, 223730824, 742985718, 800591291, 100617378, 817377387, 414962418, 563829887, 971905244, 752027653, 870090736, 649797472, 361127232, 150050108, 159392895, 974043111, 701596162, 79257995, 720323316, 260623422, 166420697, 807138510, 432272646, 775078740, 267868632, 877277232, 794750774, 616048764, 930067577, 89814731, 393064714, 517806091, 470818123, 348552490, 650958686, 558777641, 481698221, 642168203, 357911122, 12420244, 450630350, 31462213, 539694564, 744085434, 374209954, 846297706, 648664995, 251049084, 49174653, 889496638, 685441125, 758350296, 987706153, 104087630, 380252604, 370233249, 166931545, 800971444, 168507812, 786087413, 576632426, 389357857, 309994122, 736313566, 819565390, 63102128, 856599555, 490977347, 308147474, 23544302, 166555547, 987316036, 74518073, 262242872, 632403147, 798694487, 711385128, 506628934, 264289665, 775194197, 614619533, 161944960, 33614829, 508325781, 672034422, 605455043, 646075463, 263812752, 869478137, 357270635, 892625635, 96950431, 865732420, 470195204, 727698216, 721585139, 240347846, 730513448, 186842713, 180563321, 327061268, 607335556, 591603098, 682678045, 372660934, 589839146, 155501374, 467076386, 804215699, 730337766, 422264407, 457670631, 133734155, 591816231, 348918282, 856284526, 3585793, 140884413, 880886266, 235523647, 759443540, 152396164, 942145847, 231837144, 886495027, 357637188, 776505252, 300210576, 386009627, 78150784, 655897449, 530822604, 456048399, 785755353, 369636242, 467538154, 235251094, 117439123, 91461450, 468492821, 429979445, 435461903, 399185420, 489052077, 536027608, 672037433, 593575644, 625561776, 848120348, 810027253, 901706721, 110841123, 940278781, 386084222, 599051959, 539892823, 78685927, 666811141, 41241355, 681388883, 847072968, 142835745, 266833720, 423954828, 237320227, 144123180, 696580549, 964562980, 163252181, 32546619, 785108092, 672242837, 708715990, 59497837, 487000028, 383974570, 73866682, 363716918, 754118779, 744101922, 748710396, 780395170, 331605321, 876435750, 183746373, 947421686, 953051068, 175006696, 418203163, 940270809, 52642963, 115630108, 562112432, 183295468, 449935366, 946682541, 6653643, 88101977, 238709414, 647349035, 274411640, 621751417, 164335056, 601924175, 520991823, 392697329, 759957901, 534020468, 695756814, 25870500, 247821867, 584932812, 392394342, 708179808, 167308853, 225865374, 475819582, 414125827, 324220815, 604350485, 566732986, 909468622, 12295773, 394919769, 825750730, 755272381, 457791693, 501187398, 917336751, 440726181, 305421427, 433920249, 29982844, 920632693, 815529180, 698848112, 887713514, 132192263, 793448246, 896250020, 578938416, 335727327, 149477552, 280294157, 310324492, 106282905, 207194685, 718651928, 389843336, 269020333, 31045139, 239271404, 459217623, 745772762, 385040420, 764266327, 21600887, 5737227, 60883353, 686190958, 121230561, 502830979, 956019783, 62537086, 743191469, 323802943, 357392989, 118987021, 649466084, 954534735, 583817499, 794118975, 960140364, 85873822, 675898774, 687651837, 649288005, 507763192, 294017246, 503914064, 669461711, 411568182, 279626459, 912109771, 750937958, 91313472, 813221774, 825957445, 302731766, 814564276, 175620274, 945527773, 839400696, 454058505, 682977872, 582386318, 511940503, 942904671, 654538990, 695235412, 354364717, 663585832, 350786298, 164410586, 620365193, 669978807, 898273976, 297794622, 152992275, 557654875, 575163031, 619722010, 961152633, 949802036, 845638162, 602765671, 563114679, 154277479, 795089046, 81951633, 898731158, 229468047, 420507692, 338601827, 464913322, 613617758, 524223441, 747152392, 306276922, 77598909, 661983042, 119337864, 735338431, 662842189, 344218036, 516519297, 989453722, 579956655, 832179655, 764873230, 270445902, 89943089, 329564769, 956833507, 938136493, 743494706, 504799558, 341350111, 676996072, 213211098, 839600639, 323300961, 970310738, 84243874, 594180760, 471970211, 369980767, 837973586, 904856096, 598740677, 911761735, 445061389, 594514187, 604068303, 58223997, 508991675, 582242542, 805931520, 231351399, 217783077, 256627899, 798454793, 579152281, 396712095, 563343551, 735204039, 616308409, 925973465, 645269845, 209560403, 92618681, 48406628, 268642701, 960449751, 764876488, 944842827, 28062446, 667441902, 433555465, 728381535, 686111724, 854824844, 205698027, 441104659, 535909898, 127574489, 220047969, 320352060, 132304974, 615403622, 986102051, 617174283, 864959357, 821588380, 951392729, 201681698, 113198969, 869762795, 39581320, 827093870, 304022665, 197486131, 486013039, 499476791, 542680957, 930579949, 560634927, 679117873, 363215015, 45552247, 385701400, 170861582, 444984255, 460311884, 44643660, 214226691, 833462209, 432796437, 658027401, 455477862, 141617594, 524738092, 307481567, 98946357, 599666772, 941026730, 18660236, 338417919, 825814086, 653801175, 122070402, 265903451, 102698941, 959116944, 173627048, 988530088, 375352561, 618691603, 146216426, 814091102, 145876707, 819913142, 867352492, 678757322, 339718379, 233024154, 703803380, 92944304, 641439014, 208987226, 848526412, 294510624, 774530061, 204211269, 342631996, 576688108, 229621682, 74415756, 450106596, 738430795, 811447864, 32978359, 103877728, 393401641, 830975457, 313666630, 480518890, 687608318, 354670556, 500135505, 967435386, 950310530, 363818163, 140499073, 53344611, 203793020, 40129541, 560398742, 14243631, 887581739, 185267735, 398167442, 246048965, 855649557, 470426524, 117682610, 494111484, 299386778, 491196555, 246490482, 132153448, 808444212, 866987781, 236844957, 874224287, 26109899, 527033834, 370505843, 261872418, 877458640, 730168028, 690005310, 317298960, 572456289, 943431053, 901937432, 957405552, 265531102, 725316975, 142337298, 885864834, 413674379, 537374090, 724296973, 808210984, 904585722, 20353735, 704019825, 494834211, 481968210, 973123779, 722593238, 805086657, 161675087, 2990331, 120711150, 673750256, 231021470, 276566349, 125142802, 610697055, 495964307, 858036881, 626281577, 294265350, 314771580, 998003657, 765205646, 843232638, 472775561, 726088767, 848301800, 43166792, 721668551, 494429859, 101358191, 67492803, 178141309, 133160510, 589022520, 78256159, 247028286, 568371821, 754793933, 536502834, 496458750, 396583933, 937048406, 220279670, 307532627, 61893838, 59001391, 745614886, 420243497, 601284883, 743317688, 559177110, 721053118, 215922861, 218627116, 285714625, 973823791, 169522582, 407757500, 331676442, 229437031, 671106282, 624771434, 864356737, 517118264, 416573381, 440885288, 397576098, 436030095, 548190771, 276988121, 897150769, 682221963, 391466908, 676175523, 278326384, 381573318, 770020519, 275440213, 261866785, 100143577, 447729232, 223963432, 222945773, 508499540, 785064455, 860027906, 668881183, 916258982, 31060621, 252555300, 985495621, 284400159, 777225850, 714582336, 709532735, 635647471, 653594344, 670975860, 638779286, 529425003, 961936232, 618840517, 45666603, 86539808, 892408635, 382645957, 318565134, 886255320, 534436154, 641388502, 109723622, 439514278, 113785163, 307981550, 608138139, 636826633, 292818747, 81448316, 932751954, 975816646, 268322234, 362521961, 650618860, 946391731, 464991507, 993167252, 696121071, 146538678, 799172777, 737697974, 281532337, 621889858, 938507854, 381746403, 868778896, 591891603, 724469328, 41675675, 134110047, 3043175, 892398211, 509160445, 54998266, 213867271, 349513697, 886016590, 472858933, 903042077, 894474795, 719085043, 504020992, 864012404, 376996718, 141313111, 349772816, 913889901, 761369417, 609830804, 148782846, 962607632, 508060105, 655862789, 286279153, 147849819, 858681761, 458042441, 293808238, 848781502, 198671879, 353117219, 342297557, 973383347, 467701788, 148413456, 999784923, 884874414, 508754515, 932950614, 858470691, 436749876, 44731852, 470573462, 999192069, 37404632, 824307483, 899254824, 829635690, 631845991, 5419875, 536213766, 254375611, 941193441, 518857969, 584801358, 50482540, 163715479, 778754398, 787164622, 111016482, 254967978, 710950168, 415777042, 464384925, 166877628, 905889917, 973197823, 663773413, 555724277, 502677682, 486566289, 430883972, 498618519, 449215861, 422884352, 12569437, 267483656, 72450565, 642853700, 260495949, 109506761, 391670859, 454389044, 451282457, 354072204, 574860356, 575372229, 648240501, 789126189, 530441750, 785900131, 320726498, 318103560, 899952951, 602953461, 55494967, 126187503, 843001802, 404966570, 203107528, 88835891, 834094790, 523406563, 299554123, 737655813, 714722458, 373591810, 117945510, 718358909, 390686297, 313833045, 907030970, 936843474, 106461574, 433610867, 9726392, 649653973, 218854691, 605171074, 596714160, 20979021, 476324325, 979189489, 471748083, 394761887, 968002590, 693147664, 531925849, 715710896, 480153704, 355805701, 36803592, 398322563, 967014485, 892364478, 249465003, 36718086, 811408815, 591540602, 513260600, 2756956, 564314350, 431845292, 960817012, 607903981, 143372341, 625514940, 483390838, 194477893, 454487651, 666472901, 939588340, 835609504, 305606653, 801815049, 578132714, 681972382, 643386682, 397818739, 550234434, 895591319, 27935735, 996798997, 847848897, 258069035, 987469375, 127009019, 926687621, 736711561, 98634695, 533638970, 477418293, 28272600, 333684305, 835276574, 615381699, 769766244, 655558694, 429363457, 742047450, 121817257, 340857989, 433172438, 196442036, 404927123, 973492776, 217578106, 106086707, 12862561, 837124067, 981080152, 731814731, 164128776, 601871200, 95345571, 196036542, 988586829, 74537989, 758683590, 842681630, 200560185, 832478360, 734054730, 962863936, 261498026, 12846805, 792281767, 23210008, 782034472, 521427904, 211104522, 909004563, 127132858, 390333857, 58592924, 947111218, 454794436, 521854434, 874451738, 102114982, 632501761, 22802252, 729118304, 994463212, 292935098, 543443709, 7619741, 640409198, 941881805, 343473392, 297026815, 324786975, 651045058, 646584815, 642365410, 5383470, 668195687, 621233176, 887047197, 18263103, 235958942, 20391267, 112122222, 39186755, 912046568, 112442251, 327991521, 457231028, 34558622, 224988511, 904008361, 725862961, 790992990, 325677925, 863968581, 55582919, 6486293, 542759740, 842777048, 949909247, 152004184, 816850459, 974301023, 217344378, 694097826, 478246887, 230360801, 910929688, 944707282, 704825046, 819484168, 4051442, 561696686, 964844582, 399374776, 953664916, 837213018, 530904795, 502025644, 488312223, 701616313, 334181027, 885919558, 10348898, 778413963, 53844310, 688234443, 836395037, 646652314, 819736537, 833747305, 121282408, 440280142, 187639559, 330499573, 830996633, 439845086, 384545401, 118371684, 128750691, 21265040, 977444554, 851701165, 15421972, 906740619, 708197931, 494664460, 163883782, 955992062, 490796255, 346124303, 105036265, 433116539, 258579918, 629496625, 1334218, 596005178, 417242755, 71299974, 466287210, 96226087, 969962229, 282012261, 294617264, 98116137, 566376126, 307235670, 493162255, 606820448, 56529560, 429969985, 320136296, 386884144, 190791911, 60034525, 272028508, 283639588, 462748739, 271731966, 501136230, 379226791, 542897619, 454992071, 554622735, 485542048, 249013305, 30274017, 491316325, 426558819, 968667618, 731968846, 433485404, 387059690, 225395492, 872012473, 764956232, 260559216, 137742154, 694116283, 169975197, 131316632, 295234843, 121984687, 440271836, 613263757, 618587943, 425789513, 611530361, 30134106, 203482334, 132908742, 509123729, 16334164, 318502400, 88904426, 985412709, 539498055, 150091020, 407253710, 837998406, 403824590, 157202349, 240055054, 539703228, 904383104, 921395345, 207944312, 783626546, 713052318, 794137092, 289243869, 444322664, 625755783, 570319001, 233035277, 897588324, 345051448, 144843960, 145666927, 383582058, 640305891, 146789217, 493819854, 218432759, 914607734, 373300006, 270042378, 72312888, 447758710, 456403341, 2443497, 954191903, 590089132, 906720071, 374206950, 155586231, 64992196, 194321310, 676191950, 725733063, 438445569, 991257375, 83014565, 153222031, 465578602, 566714150, 416224829, 918441773, 533233552, 539304319, 526819820, 401136723, 257787949, 3395770, 455833957, 663487976, 650017358, 245595137, 439149354, 978648157, 386566645, 832792107, 353135616, 522041585, 67639956, 954956987, 51627764, 42938275, 654710426, 262140828, 229603756, 222131671, 961536428, 310231408, 815222871, 457841219, 946393439, 651371196, 778355790, 555297050, 288243286, 365504614, 39886002, 213876847, 736205210, 526622753, 790864653, 474922999, 195423959, 563824246, 817545920, 359662394, 919623157, 713281006, 917821471, 219205466, 738726691, 254785634, 7324251, 635869574, 116181781, 673153000, 720229013, 469725855, 596170873, 172278856, 390400008, 478724239, 632201952, 472374827, 468330772, 196600993, 453032433, 205640424, 430264638, 662638958, 326303597, 448649171, 279464504, 882946674, 403744381, 404139926, 917404421, 679652150, 235176592, 607610130, 154892837, 711395061, 592416693, 826605153, 14294192, 941754475, 679832806, 215798028, 668863077, 460133345, 690587038, 959252448, 417672947, 468337741, 682807634, 555372163, 368903452, 608938087, 373632283, 927129623, 74852496, 457717699, 410301443, 131324148, 295289631, 32451185, 695533768, 876102455, 878798277, 196806535, 345302036, 492667824, 460373797, 582332569, 424497303, 202421308, 460728109, 139880141, 124298941, 982384882, 156498217, 72792159, 207219958, 676477452, 216790807, 847971795, 672533041, 612683279, 321307165, 844190194, 878521685, 309910531, 767939831, 778451409, 836421346, 462882249, 810624274, 496455464, 487143438, 426825575, 400690366, 247011508, 992335599, 385361512, 396369760, 686625347, 164368801, 201198791, 624263873, 154230636, 209229265, 329978112, 939109847, 706128403, 15365031, 443248797, 532272726, 980148863, 356191953, 85598396, 634999601, 862924952, 961031752, 83396281, 810137989, 502203413, 676382877, 178199772, 644860222, 296935583, 106490691, 899947890, 700470618, 777039325, 975080096, 682432475, 23275920, 700470562, 575068561, 377445368, 296467813, 658875903, 219833020, 88743386, 467326010, 885491524, 116769870, 546486192, 281794717, 779462827, 512567257, 580816041, 290139641, 76896875, 478498576, 484648067, 921594153, 101816748, 163414976, 216635032, 524485129, 338430983, 675237999, 62016791, 165433159, 140312396, 201275598, 525200886, 623440042, 886884326, 130145621, 466866298, 473640090, 545000236, 685697009, 935255321, 917970834, 544911643, 277855039, 119475943, 267391477, 444937141, 62790136, 283715528, 508531027, 176506605, 469158262, 14427927, 635508772, 296448700, 97748270, 136190826, 817675486, 122102162, 616890745, 425768883, 111467431, 187622995, 152741792, 330631502, 35126317, 759941647, 898506527, 703621892, 503270054, 828463653, 294883368, 298178645, 870358895, 547916529, 354749195, 906517718, 101729597, 856249585, 763761973, 545721969, 107462432, 824445584, 602849514, 865504297, 406685837, 936633998, 809161386, 543937583, 93401932, 534577119, 38386699, 832249804, 766816683, 418573652, 394110006, 330973425, 679160978, 897607234, 267261132, 853086071, 362125638, 987071601, 111481241, 55185871, 489999778, 722606795, 157106435, 439964235, 9619543, 967427574, 408517540, 295363812, 378315344, 390798650, 195957665, 692475486, 77937019, 237279269, 225152744, 455280152, 586250636, 470401512, 75613219, 594117392, 875968867, 86779867, 668945533, 872019849, 562490661, 66925105, 642111063, 188428068, 272990885, 294371860, 202141981, 794194635, 45691350, 181510592, 719552257, 787965168, 758820924, 198299559, 172957157, 505973097, 646558222, 412687267, 124290114, 485328595, 666626388, 754169043, 528265657, 107345370, 531851592, 804280167, 424464353, 263517278, 846779233, 224953417, 759970304, 42646667, 526137642, 689716083, 437169362, 878139175, 574495524, 511641941, 138317269, 576697859, 497573168, 312541489, 822316301, 857146969, 29702757, 203446291, 362497244, 256316499, 527128899, 400386548, 494877607, 4274545, 825453294, 499078693, 627140341, 765367502, 126054944, 460013972, 406289379, 864282181, 731288872, 79119378, 898499259, 555845972, 116004851, 513198499, 448337939, 23914412, 822739215, 966977543, 494528217, 935563073, 65382007, 925652682, 557978661, 7540275, 44062629, 382337858, 636583931, 391700834, 112659182, 631809281, 972218821, 109204228, 38058171, 256122714, 64902513, 209466919, 890411623, 15775416, 381061101, 165607003, 418367506, 559916179, 466115604, 29908761, 35672733, 245841577, 719619642, 818441591, 839357797, 261672556, 89176865, 788099455, 485167096, 799994504, 986219172, 823857458, 163255876, 175439365, 185052530, 97262222, 511287378, 670789380, 165713017, 46400671, 957092089, 706312935, 666796011, 815505485, 811824001, 291498466, 85307102, 813537249, 595621145, 12300740, 195337914, 171536474, 155882174, 184632901, 181774072, 302969808, 225106782, 211812305, 857516017, 422248085, 467033655, 185059239, 104331192, 142051855, 371293485, 49777456, 323170494, 361731869, 668367385, 253421287, 921696583, 925118323, 22979004, 423646168, 692966254, 237330479, 410706901, 849157037, 583589166, 543869016, 600196882, 800191647, 198784130, 357824030, 490976815, 953184146, 637900125, 284870838, 867143774, 270270633, 645348255, 286445739, 47385494, 359875890, 147211723, 170900959, 119050006, 143902918, 619867449, 463803018, 56186444, 171204736, 670563453, 991411021, 767395876, 709004806, 35920131, 331778119, 669734285, 49112390, 467313076, 850620871, 287442950, 756882656, 892414703, 936903857, 36303423, 557133995, 181308326, 306281411, 682550415, 893795738, 809952503, 245780130, 640585742, 197477799, 620622603, 835241373, 353128477, 377402198, 95924358, 752644752, 104162972, 656616330, 183575527, 452148348, 192940625, 308345503, 338019731, 438220202, 846086363, 442293258, 87424236, 113502210, 299438554, 21217949, 113030647, 306339235, 584946105, 156084840, 990629782, 215059538, 10797747, 577469223, 690957356, 731834635, 236095793, 467661618, 466270550, 507451341, 422872926, 837297050, 414128039, 789796071, 612754643, 264759954, 103152697, 757791672, 281602229, 786760892, 234446109, 307316610, 537612209, 631954667, 674408729, 21491573, 433179947, 952832253, 18308495, 680948891, 230821716, 933808849, 731214378, 878147086, 627767363, 484675930, 224309855, 490311341, 706814396, 719714558, 522267890, 605066663, 336043953, 380268980, 216674965, 576956890, 871868855, 822195179, 273941040, 97080403, 503238898, 177173609, 587151030, 158964032, 25642321, 319679506, 742037586, 124583727, 555803714, 278329179, 574046740, 557983098, 540205555, 510025950, 514556818, 649692765, 774313515, 349239075, 671889416, 981959240, 656587229, 57032270, 321276649, 631207670, 487917329, 454884839, 976840660, 881920366, 660650130, 867820982, 390523727, 520294905, 365941947, 449394096, 986368587, 777214523, 467978626, 844466814, 580886354, 396872396, 109912749, 901034114, 627675542, 602267687, 162866186, 268486259, 107314351, 358085793, 191083454, 157062600, 281940720, 280752077, 482738152, 635387008, 981032713, 469617191, 443630285, 717767778, 742097374, 217950364, 88465608, 283311222, 391076383, 359652016, 904925863, 603666047, 331424803, 928285193, 204679654, 901928810, 235838055, 935410978, 976169639, 530645023, 346606883, 858027117, 701817321, 353088434, 60525601, 551812401, 635270490, 778291895, 610478154, 739698117, 275397100, 689720062, 750325701, 267373001, 388884353, 188898306, 27827497, 347652285, 497273479, 828701892, 112827404, 745290373, 632497623, 584703080, 896215106, 454557869, 942439165, 914006231, 894924402, 51294401, 966460341, 693581246, 842952630, 430336106, 530431653, 658559120, 344098674, 220632924, 330276625, 391179493, 12922700, 838437297, 990083470, 107080613, 468668782, 998094908, 670641055, 958998930, 238387891, 348653917, 54231269, 760664342, 297979694, 414122916, 506758289, 588131943, 724586957, 529812604, 133709674, 645554228, 673929316, 865043201, 19834363, 552553604, 796439080, 434498299, 613951973, 781918745, 472574091, 138066788, 649803667, 227369744, 13772995, 355897911, 939805072, 341327690, 901943478, 336001450, 985565274, 628013151, 422616792, 616930409, 48628764, 862539829, 830551659, 478817961, 494127296, 68479763, 327905784, 939217483, 442196139, 466503989, 150333576, 501984571, 530844185, 131224863, 83543848, 117225785, 61559730, 380608525, 909409640, 930647586, 374577324, 562439632, 955898907, 873154810, 966403526, 422454322, 833706789, 538052583, 671539312, 284961140, 248423532, 745139620, 526008797, 540652429, 704980097, 577277945, 719336381, 431856176, 28740907, 960965299, 230294579, 99460657, 518329477, 114385521, 371270319, 381154242, 195351059, 45471079, 689071526, 365124013, 488736581, 233724243, 618605556, 196870308, 379017361, 142176782, 681387424, 796099077, 444029110, 291445523, 719876983, 474553426, 386321247, 436786830, 425263058, 893939548, 799540105, 970424602, 895784485, 109393533, 510539955, 997635977, 52436581, 998922281, 303939183, 760276412, 113681974, 652842371, 402918552, 183192137, 105054418, 307806197, 893717999, 137073611, 555030145, 446151737, 417848478, 565042747, 823493665, 305201351, 130963098, 915258865, 530994689, 798918139, 898828288, 484047939, 668434148, 104523211, 805146028, 467260024, 185308211, 449114530, 831413346, 176951546, 570120286, 56176578, 95930658, 244439301, 75895384, 859577335, 778685529, 915452686, 695524756, 271160089, 553841352, 174609457, 192161445, 822584551, 668304392, 237407202, 199707981, 245099940, 298844639, 932553402, 481177222, 956437999, 780231157, 170066295, 469338833, 586506314, 849847004, 425270169, 172586649, 495190022, 434737790, 904143061, 425941452, 757380742, 381943607, 976997528, 776756777, 402171184, 147671036, 169645505, 633667106, 213781869, 239064145, 357202149, 110771012, 386723192, 985433570, 197452697, 174908428, 770387802, 256970870, 823016419, 493501148, 759188558, 667377533, 290330589, 459576633, 100462981, 551976439, 567058585, 684545256, 293778202, 279699982, 188648356, 457629981, 946932140, 953376961, 734702742, 359592399, 445628005, 977634903, 82533420, 686075820, 927912936, 229314802, 441665703, 993509921, 802118609, 28171381, 722831115, 104685486, 448790685, 168732236, 614876955, 759891743, 546305017, 987234556, 521534764, 53604488, 10473624, 43424675, 90666175, 389463551, 229308129, 915324415, 303579925, 575555100, 308908801, 892671005, 427828599, 506583673, 369966152, 950043252, 591797451, 223274283, 891943742, 157736846, 319460842, 427907798, 655008991, 510340559, 183538938, 47535908, 443313169, 174049558, 393113315, 486523146, 166548620, 10527183, 195701516, 537245143, 951690237, 924408333, 609426570, 696950750, 894293632, 567046917, 474469339, 64589607, 561156799, 631039462, 32841021, 761940403, 303411745, 733932560, 36162805, 598428726, 41817857, 778317345, 515249554, 614526121, 54271657, 854219197, 399660449, 614208536, 654811665, 884408836, 564324309, 137803051, 936161528, 15950171, 123262489, 969556780, 762252901, 955012243, 449079160, 766225988, 784760106, 250614101, 825906192, 526912392, 881537915, 311912877, 662691671, 483477298, 839350461, 776155932, 818402928, 524839294, 135800908, 873514485, 150163946, 134286588, 29762484, 287802812, 836955660, 638352139, 347590772, 528089718, 300551345, 610960545, 110097049, 699760105, 112613006, 248909671, 964587431, 213925876, 31084471, 135543049, 323739009, 413540241, 156454406, 94264908, 349211534, 107491332, 512834420, 136252849, 496128867, 360411244, 270926575, 703647093, 383781711, 49941331, 182558101, 886292358, 250061891, 929806569, 717724835, 824701233, 8370501, 260627992, 599120927, 481210675, 77535261, 675866300, 779663493, 193573976, 614717651, 986997819, 923732189, 836234376, 988365961, 558327957, 798113895, 94105197, 969813449, 293687053, 468072722, 148931667, 2220527, 960965281, 657131840, 562118502, 738379292, 470996727, 512802560, 685321051, 142233997, 455916022, 202406273, 259968676, 735322429, 748457627, 494158131, 903259301, 909675752, 971198888, 280658397, 581932166, 528276860, 902986174, 712457397, 370235647, 784004758, 448399437, 699736110, 268645244, 250461823, 835429452, 25847920, 91001914, 20639462, 565458078, 711683189, 457795083, 99623314, 995366860, 485958773, 121163233, 928120592, 162180830, 780370112, 746505940, 821967667, 369620143, 512095675, 896844119, 827484593, 669257017, 137937058, 540548937, 712563113, 594128143, 507844153, 529821127, 516690466, 974135134, 764927595, 220850626, 497022039, 538505867, 492028700, 346408236, 482890966, 124555489, 118040136, 379600119, 867733003, 148072097, 875025519, 46687131, 97268438, 359509432, 479897785, 572161590, 690146837, 85286078, 442465980, 710732838, 878923153, 456281694, 310672460, 717459766, 856017248, 181014472, 620103394, 456563991, 249528440, 931783815, 312451704, 892472049, 503330930, 327021488, 829834991, 239962523, 308794546, 666927777, 108917512, 389702115, 190144610, 374082203, 258082903, 679725679, 798683889, 392295809, 749696330, 509884597, 498096142, 191375973, 156899357, 186413341, 833423036, 912537177, 184205208, 397617181, 193007985, 202585561, 317107504, 297071610, 333749597, 697737275, 295057249, 923351785, 179105264, 687817672, 695527269, 737447060, 103212232, 238546843, 265837063, 847091568, 731127318, 105006345, 838024319, 374960626, 717542684, 836218624, 226827295, 954600891, 35484734, 953999847, 481057252, 67327398, 573765802, 825562381, 719707875, 27922839, 58346560, 776956834, 571942225, 350803055, 805163527, 758910073, 151583091, 162132909, 975308431, 603887735, 709794361, 435989003, 942775050, 307410489, 716563477, 45762114, 290553681, 837346065, 832179132, 935676945, 273414525, 166936137, 221447502, 757852760, 42796168, 100973867, 490425664, 236557600, 823363418, 257761854, 599835780, 645027281, 968908296, 777154178, 722165802, 463325756, 611439672, 740182126, 337913927, 291185758, 238522280, 938581257, 396226309, 969653389, 429220673, 805471900, 793245642, 679705713, 702128274, 91555307, 195556911, 278363070, 617029223, 885131174, 693877763, 561707826, 248958078, 63083723, 467244196, 731936887, 536979342, 137875006, 918839603, 349081052, 481131780, 962223952, 207792151, 288422237, 21835881, 850762468, 766824337, 296788975, 742032015, 37875533, 382328282, 228529201, 349154351, 25294506, 880716164, 309574630, 790942639, 760130387, 21221090, 498963217, 431376151, 386560922, 795526984, 827934979, 983346681, 472382963, 858998276, 321349160, 58559000, 881834681, 395242729, 311052172, 152242256, 309184309, 913307546, 541404432, 276884376, 357305209, 33043955, 475660796, 837832429, 402761792, 239099688, 843249011, 943667956, 379828001, 771574307, 40656203, 172490448, 365807068, 85958174, 119417626, 514680593, 614222259, 437419112, 291601981, 562488254, 939520201, 454864798, 797830840, 537497815, 206817698, 169570284, 959427024, 307677474, 29708582, 484075982, 490813295, 74021759, 540962338, 8627256, 631213332, 857277330, 502692775, 629143801, 485571455, 699617638, 549635360, 141564865, 83082038, 203494147, 343072164, 330828178, 99200620, 515302890, 875753037, 974163735, 893109054, 558620891, 450977892, 927079479, 61314673, 11476279, 962610215, 991224179, 787767150, 722300823, 237755507, 929204398, 16932118, 395001740, 476613838, 562844621, 35153077, 594486298, 987736816, 154107380, 579620539, 38015976, 576836161, 988958100, 372330952, 612301523, 702464584, 32333985, 784545155, 883428150, 423962918, 882986710, 35255548, 761406068, 944987501, 886756619, 339291335, 238733592, 576610705, 687381678, 275128213, 873421535, 455661499, 818217625, 122348486, 498627501, 483067785, 858408142, 382785266, 685500850, 320402981, 425396854, 423603677, 843485653, 414747421, 193351722, 53965144, 603643447, 574619286, 687201853, 985673926, 571118698, 636072048, 991490181, 382167418, 962447860, 490076925, 93311333, 906609238, 737665508, 639864296, 335515430, 850562678, 271670511, 630577790, 863467814, 897306587, 251971908, 740860867, 286284746, 84691621, 512913289, 404175749, 473537770, 938661443, 91907742, 757543057, 862238705, 534391838, 791511271, 294119455, 96531434, 633902376, 801432269, 296531697, 104982186, 58851918, 466926312, 399768315, 383801891, 793429415, 743174222, 774625635, 427853065, 608082406, 344937839, 83346014, 980487183, 492911784, 739707940, 650435032, 720527264, 226827684, 853583111, 772046721, 143214897, 220784143, 870341399, 82754891, 558232050, 855469728, 344249507, 33993635, 307631429, 559203309, 963097406, 949300030, 113655473, 691711559, 986938198, 344392856, 6116046, 785020066, 927038003, 747623631, 345231328, 635627831, 786314210, 340311050, 321734330, 126582335, 696165920, 622921719, 462472504, 543561703, 679281685, 326220795, 583765789, 16626218, 181686176, 986850709, 100604815, 659801920, 58779589, 464221259, 27241084, 781668200, 943804613, 130554307, 146925330, 306471092, 633600742, 216914890, 613381270, 570076125, 564106341, 410858590, 703702782, 812198733, 330535688, 937734245, 20674821, 691150526, 425663251, 887523347, 571179661, 928902216, 435359100, 627723369, 641921795, 792317626, 385514338, 898678275, 398095376, 104232675, 171156267, 804986705, 564103648, 168011484, 534947213, 207710091, 324931072, 762831570, 771781077, 395204439, 742575136, 630295142, 525402060, 351485402, 850809369, 8148980, 454737371, 842850904, 696852430, 515134141, 750075648, 904181791, 615266287, 654801478, 465121825, 529486581, 306616394, 309710443, 295638174, 740319558, 312750225, 585083836, 706402283, 47243460, 745471827, 439401981, 465283850, 255949491, 351691629, 186564021, 176631050, 702797863, 999441246, 857679183, 579066877, 487804937, 133461689, 771687924, 255916962, 438264273, 735542792, 206950591, 365454606, 14832815, 778415382, 424880271, 534606664, 603836423, 99576330, 621440155, 855459929, 127490334, 392343040, 39383041, 489349424, 794598871, 57693924, 39206391, 678642763, 650216422, 145260223, 903249232, 761652593, 156644176, 693111105, 598095357, 356232998, 786041974, 39837821, 365465335, 216797757, 640864674, 761810818, 568758535, 13210655, 267605984, 738589556, 96794388, 544361874, 193276613, 117308641, 248573753, 697161840, 880887217, 850569722, 99788734, 539110559, 42290871, 796979923, 19903381, 756917239, 16051102, 166065607, 711177630, 8430483, 124375538, 898099729, 227815363, 205540232, 81582375, 694032493, 896567039, 202059543, 360931372, 387080430, 837010468, 781814422, 702635068, 910767273, 284037000, 170218947, 230246578, 528668074, 136618890, 970731890, 60623828, 352643453, 40761342, 570138024, 772119393, 143313239, 496607978, 778119765, 84517315, 925559786, 76849525, 174548518, 52908137, 123589370, 459130576, 346286406, 620029383, 197604306, 622818232, 535170938, 163970340, 656649422, 637233920, 477733385, 369530916, 972768345, 651557981, 732167567, 108876134, 713569481, 407773906, 872762794, 646706477, 427779609, 3072507, 770642295, 538900397, 190535833, 947223029, 119257384, 630081275, 748647506, 663124740, 370769066, 27621461, 758986618, 443862004, 870020793, 895879554, 943458956, 979180795, 840473283, 525719941, 321439091, 516189505, 957238743, 908916954, 736528221, 893378688, 852044161, 653652411, 129965965, 332649107, 712949362, 707794305, 891436282, 719971067, 977973912, 586151210, 515155397, 998567470, 570505390, 625230698, 857697595, 896180621, 912361182, 602661665, 140628438, 736302233, 344499876, 780565481, 621674207, 902884003, 22581707, 663241715, 641750761, 290170857, 122363811, 420748846, 734253288, 676339468, 518773686, 327335824, 911059490, 999557279, 709330245, 389523462, 385040634, 882478903, 805134181, 932195808, 887599466, 696914688, 210779855, 587227786, 806427437, 289938359, 234242074, 548732275, 420871291, 346012146, 179936767, 190807103, 531034422, 123554898, 808741531, 469754696, 425324803, 804643242, 840331605, 816449496, 485741523, 504027926, 704960108, 26558336, 801969753, 429594920, 826461907, 443593357, 115313615, 891617107, 573530877, 310752890, 807868403, 527822, 128656596, 566242051, 791268630, 459387681, 63974218, 312461954, 156786464, 210535007, 775388082, 204332159, 118209941, 515719794, 142689890, 927630003, 595487883, 331829011, 929441228, 23384688, 675491992, 117392706, 264644573, 124976199, 536931500, 276044010, 174852815, 323830720, 31978166, 808906897, 466875479, 397837522, 409849440, 871585376, 228822489, 368110289, 769141667, 407492527, 556176956, 300399473, 683743315, 220566060, 168529148, 51967160, 896742438, 337636087, 967275017, 429163994, 499724824, 567454419, 75856363, 582699193, 252581882, 599372358, 48992852, 260680738, 608495450, 639906070, 944828610, 310453591, 123375766, 804088394, 30977743, 525051202, 380976306, 836836834, 825399067, 985950003, 526549120, 973850152, 553876160, 235926791, 330604227, 973092600, 343852201, 586593486, 805195229, 477489246, 522871916, 33805397, 102060646, 152367363, 7267172, 733721352, 978312153, 593400526, 697969206, 827601803, 850954739, 781454199, 813843036, 857315118, 693272644, 609511270, 125767055, 551624513, 744852960, 966341117, 991512548, 313658699, 141289834, 840662075, 128757198, 557428728, 944445244, 450279375, 404388289, 864034636, 123767613, 594872759, 404084079, 26309009, 517158123, 368708432, 921418634, 190937176, 99091806, 783103375, 638375427, 68400829, 217767784, 790988381, 313122220, 849923671, 813277170, 448716944, 934390946, 58880404, 121480873, 253274264, 789409659, 214147279, 676980482, 948617144, 337830264, 491553599, 652912650, 453739768, 176640378, 86816133, 522372161, 459596735, 805112159, 146774161, 698060226, 659299834, 230531746, 135787399, 205109784, 401551752, 521871281, 461508797, 514491661, 163348016, 768773476, 74719606, 40606742, 162830069, 941736405, 480821619, 585786151, 936887378, 110472137, 200742177, 889949039, 39284274, 39538257, 54622042, 170366176, 102840697, 442033117, 923010545, 401729912, 497890692, 553314377, 851799360, 558339205, 693976607, 999127852, 873716292, 679448411, 621077493, 891213589, 842634701, 401689473, 932031327, 862763264, 966365492, 707577575, 16109207, 48884666, 791297729, 486663353, 69415638, 237914381, 250122512, 424273577, 557549718, 788278792, 761944525, 498317181, 68215737, 484696294, 929939686, 478331945, 328502277, 514414334, 63009936, 606928512, 297686053, 923575759, 920477225, 160267569, 159981007, 233036108, 470769245, 263911885, 874549207, 239929965, 401332095, 622581750, 991315613, 505236701, 639370571, 197964722, 346975222, 803793768, 148172056, 619497331, 561108752, 658068426, 998234719, 767223407, 923853300, 656298427, 563136135, 148184111, 714845618, 345469800, 624187389, 90503865, 152836391, 620711120, 267904011, 934359491, 684203028, 140406753, 745838647, 986136178, 696944482, 730050053, 127670047, 236580481, 242784834, 467848959, 591449064, 858424472, 124287306, 773535639, 258309436, 750259444, 323595781, 146847688, 103143408, 272055900, 186400581, 739693101, 311568059, 28321421, 253224934, 619760961, 289328059, 570752181, 652806409, 317050098, 507246585, 666671517, 229877485, 894873242, 281038238, 18446753, 646899180, 345554381, 580863609, 48113826, 264940876, 404819283, 259432814, 231915072, 604907065, 283527015, 697340033, 803843336, 625849056, 156643731, 163970782, 613581549, 122082109, 347636757, 661658263, 44231959, 569856423, 970159371, 113008855, 733367497, 539112535, 689771034, 972016947, 771178332, 610993314, 374529139, 451955347, 233277620, 731146216, 433619594, 901398361, 769875769, 76261848, 204220219, 152127448, 270424370, 786648127, 580700385, 989303746, 490834525, 449481838, 531943992, 784445849, 667077797, 394979787, 930154041, 272874242, 884911891, 913831286, 215158775, 515632402, 312655740, 239902981, 252990349, 219196574, 843445935, 483703578, 671877542, 971336449, 315675124, 196977715, 683890314, 15841005, 436129342, 911196872, 571751853, 377169612, 142028911, 46877941, 209490651, 561405715, 230255455, 343716526, 772117802, 193220735, 322261194, 319728409, 785333150, 718044620, 246342074, 318097434, 550383358, 687347614, 192979961, 922190855, 622290983, 758532262, 373390485, 201766084, 231038097, 641729648, 40592210, 681362665, 850486227, 250887456, 706764823, 506993624, 893921223, 870375284, 147710594, 58872261, 180474759, 641302263, 953610692, 678975573, 558578531, 11160313, 313920283, 543270247, 283758638, 817822191, 783156182, 720568314, 927513222, 727849910, 253203990, 841236435, 942810339, 384822514, 516627656, 917530505, 122120707, 83754254, 155581228, 241246946, 1284495, 834580130, 608115556, 677309117, 801861255, 803954002, 407384396, 483390661, 511276856, 907710731, 254529171, 276621683, 715860861, 258277895, 477880507, 33220198, 245364750, 58655670, 689891452, 895194296, 754338927, 569514832, 502068717, 498386825, 712321779, 47052378, 403617593, 735137109, 368986676, 934778938, 945859841, 847173692, 387138870, 499547782, 411227820, 863303177, 532229073, 409252815, 597016103, 706662901, 823334524, 697435909, 506367612, 644245662, 371388544, 949561878, 639042362, 991903908, 443833343, 874648222, 736759900, 584625565, 792164915, 898481984, 629383377, 650220212, 575329608, 67441965, 947439283, 796587298, 709084160, 68803186, 542158835, 154462113, 329447875, 495617513, 36944318, 447104961, 317778778, 148375809, 942779611, 674021959, 798692036, 135902974, 232120452, 760146041, 538542831, 288691248, 915102965, 129407196, 960441913, 812789408, 509563489, 606039045, 907161570, 804296849, 800374286, 835130697, 643478547, 954569645, 980669405, 886123146, 682026846, 264969170, 336515149, 569413309, 103250217, 845239382, 57081063, 5365113, 209439134, 127310962, 654439871, 230957625, 166926984, 637420384, 814768858, 162987408, 210691122, 36199738, 800703312, 900891135, 535827869, 480970667, 750499101, 167208484, 248824069, 379775046, 768649229, 207875463, 643138861, 445069667, 961506598, 147365594, 277155011, 960033178, 243428244, 367554470, 984832658, 691051859, 663309320, 588266745, 980285868, 955231384, 391313727, 134977636, 603132266, 75623868, 100401880, 153857137, 353898309, 900268964, 570545634, 919732335, 754150125, 76833670, 769003071, 683091927, 786998359, 424558381, 599669881, 306872481, 452086029, 675237252, 28056529, 525579349, 692170438, 866509980, 100693626, 178781005, 131316703, 815068360, 794610808, 959936832, 713502277, 342602416, 937563537, 898313471, 491022982, 105667207, 800132237, 865745915, 832413680, 594408806, 855269798, 650850853, 90097294, 622501687, 787070613, 490234395, 903591387, 998006152, 61141107, 254430104, 967412560, 525979122, 723952730, 94035604, 177798386, 344642405, 274293248, 296789972, 736846449, 840058792, 388840535, 912239081, 947631293, 204931915, 130950856, 948917303, 163421724, 458701013, 913950911, 629328775, 797963992, 505003708, 151813221, 107352569, 116990054, 400047572, 562842356, 643131784, 950125199, 292202465, 921398706, 28441907, 993471188, 86287048, 439515689, 798061840, 415704384, 474277358, 48614492, 919202370, 932035856, 87524828, 984086628, 836419192, 66310875, 182714623, 16512804, 267198264, 543500517, 586407875, 596556968, 801791053, 654354283, 233646398, 946830218, 79314248, 768682634, 278294492, 300328906, 206839106, 744677218, 479199900, 834476466, 626070593, 752243307, 833835404, 648688294, 983316045, 417485522, 259675862, 815100976, 600374036, 208622331, 452909976, 802731884, 884971051, 848334485, 609185105, 467332826, 396380376, 291695927, 314100172, 681770645, 169332767, 387745527, 816072105, 5727036, 152449501, 294162467, 456123900, 636605662, 988295174, 549803754, 631543792, 747747609, 708997149, 576372684, 852489289, 472226774, 493905999, 823461536, 143701921, 430457554, 884398602, 788147073, 597761657, 682358685, 583913250, 642329298, 834271431, 575460696, 158031501, 356528505, 230806326, 653304601, 106497994, 597657817, 772928396, 668876589, 42075200, 717284236, 239984929, 271087280, 930309100, 755076365, 999311711, 476384332, 718678041, 824193965, 745889119, 329402376, 706918718, 675520454, 147530828, 302055012, 48117543, 208224091, 214115723, 446970239, 486800280, 751380505, 350289095, 672058576, 594963678, 510558197, 293992733, 723145371, 745491806, 224942225, 889173957, 359206139, 54849394, 574145119, 198410880, 114912151, 805839994, 674028770, 843359899, 495648774, 5442389, 777430148, 127612547, 56559493, 453090960, 2726481, 551409455, 528046689, 941542256, 933183042, 626572115, 519302910, 699327053, 996268870, 787175356, 667907031, 323195654, 875390543, 625719248, 147382714, 710596005, 329667330, 76566568, 58914499, 526997457, 980705905, 412179782, 34886264, 267573463, 325456225, 583429990, 689069017, 262430586, 805930646, 652466559, 784199441, 763839809, 793431938, 841020056, 923391922, 866017649, 433749599, 898423181, 49130168, 595227627, 631169009, 768008565, 447001489, 775522445, 702794038, 134874253, 646100558, 876139791, 495289381, 629590841, 259608918, 23776246, 861188748, 536757221, 542527941, 138341012, 154927691, 146698669, 398720702, 825997573, 76679582, 881127286, 168047594, 325484618, 986384236, 897957037, 995890760, 77130742, 528431485, 51641379, 840903872, 814462959, 658728041, 658997714, 569673086, 944756763, 124009313, 536934955, 868639554, 219731903, 687308074, 940694295, 514258301, 91269882, 584572867, 553757982, 162941455, 184524386, 465161599, 789352751, 944304439, 370196057, 561547168, 216775262, 601702347, 434236709, 217961361, 145742850, 548385299, 592283453, 980541149, 996548371, 78455533, 134117882, 224358399, 135944754, 934726352, 627659410, 226847819, 285051180, 628503447, 512109832, 957754075, 166468508, 243250464, 561158561, 135618535, 750485009, 753959462, 54294170, 477967634, 99342589, 652050019, 585552376, 436651263, 827313788, 848738616, 691143287, 150095515, 750492261, 682783025, 801012512, 998338368, 331225600, 598767062, 422671937, 353024195, 397758836, 305923785, 470971360, 898789169, 447257075, 718699583, 123022482, 866159850, 481513020, 289050370, 888232781, 699176430, 373035245, 710574037, 892474869, 762475907, 386947521, 437431430, 219693581, 890386029, 449613395, 698628275, 73721801, 910448153, 212443590, 860328155, 705553689, 772931367, 174736164, 380060093, 390082653, 927691906, 336586851, 43702976, 314729668, 514284697, 870674202, 313134262, 214483124, 674613420, 292490889, 601975101, 815163184, 466914835, 946737994, 865879990, 543873206, 736103979, 641250842, 1954186, 95591999, 639422387, 719547753, 207386852, 800649804, 857417049, 185527957, 310101795, 922723951, 251538461, 433149346, 582738049, 402784602, 524471682, 325214918, 738925951, 237041215, 163597308, 418966313, 338997077, 629761819, 481687245, 711734485, 327232018, 310529589, 286470583, 314696236, 187290139, 886193582, 210307168, 340367034, 309472339, 962376826, 706018729, 445632112, 205613627, 555893006, 10677655, 678817639, 730907382, 750785536, 730670607, 902806230, 172972298, 653454773, 524757749, 302737205, 361084046, 415944084, 193338285, 216272007, 423536365, 825555580, 908643694, 335589625, 882710590, 398871964, 79366778, 539966677, 945115534, 27150142, 703987190, 789800517, 615126604, 769716972, 494518861, 178790050, 787687958, 121664828, 621852309, 28079902, 283035338, 196048466, 42812597, 222782364, 257367855, 628363795, 519300780, 747137761, 232380766, 972246125, 532166710, 667442336, 423891344, 898431398, 665602787, 433237584, 97595021, 30004267, 927123690, 717384117, 170211619, 968432562, 754879357, 227363634, 499202317, 606268449, 294774558, 777748882, 581486229, 963948248, 334375522, 88603905, 47004640, 483723220, 661876499, 231481611, 266613894, 653680658, 133070507, 735777426, 170187634, 972451850, 788793288, 178629765, 239463353, 708924215, 49757163, 740834787, 48008887, 332360595, 569687098, 977169233, 614996278, 920457834, 189102254, 9785640, 572484316, 813087041, 569292244, 638409582, 547829243, 680684784, 637713454, 339097484, 748291292, 908717537, 697465130, 15438449, 931639444, 143378289, 838283797, 123946438, 623985905, 506897052, 749389093, 472767690, 590407886, 997639287, 238098920, 16578168, 303555985, 154925391, 468433104, 925249176, 792173332, 157687219, 214559169, 196474165, 464533041, 749308206, 815455895, 242535639, 783823327, 799430853, 351146674, 340576538, 310118349, 117051520, 844804021, 671446241, 801454034, 542780062, 933455162, 202553983, 204301702, 848674382, 839459477, 736692450, 669266555, 481606571, 35602268, 860571416, 755197974, 2960398, 379229372, 834755726, 400998722, 16946336, 283978059, 21833883, 431269679, 683116738, 790602506, 656842287, 718544638, 964276429, 248289034, 813453752, 828563989, 497950887, 319172930, 28641682, 602173423, 137419972, 37416799, 916670990, 772861824, 778588562, 237731751, 260398280, 769351421, 916437149, 998067020, 373222033, 743817678, 378444910, 902079586, 918175638, 110182898, 126519329, 560481480, 525546571, 757864165, 358511538, 669445757, 809183205, 583082543, 107335891, 294178226, 883263691, 103040486, 734872767, 853668249, 304522357, 895744895, 517433667, 173871456, 574663140, 927496042, 859098728, 574625308, 514982537, 899650509, 477930931, 903815669, 444941075, 422301508, 170824350, 707888331, 529563528, 859117511, 308757271, 810404431, 723731742, 63724962, 496988338, 375595949, 968111548, 946303337, 991325525, 850343413, 246458073, 127789340, 496827122, 447657, 762535708, 379970105, 206339084, 473260416, 321050563, 508413799, 405557937, 732929899, 368428242, 631133919, 873558801, 99705232, 167751503, 374194636, 282071292, 175340099, 652986, 497323670, 551691552, 657035401, 829317251, 466573700, 369666044, 502125745, 611972111, 469860325, 773223317, 406791032, 305465115, 619637900, 438011048, 392655494, 666223738, 191972384, 426406656, 263980963, 203178841, 552043912, 529288943, 229934829, 910827893, 338155306, 65737843, 873649720, 343174524, 587400428, 124764319, 975158009, 965030049, 79382285, 178924898, 824447534, 138262965, 231910981, 137620189, 472238568, 231670171, 963836666, 76959278, 719831245, 628818976, 481253717, 1168749, 850828760, 265153622, 497741859, 383433139, 379025802, 975443070, 520223569, 901712561, 329548976, 197547387, 170633156, 49732154, 175052723, 331801261, 739886722, 154199592, 293730245, 808704973, 126728029, 934427077, 986633460, 472573790, 850790057, 206996786, 384004969, 466782996, 155363863, 963858268, 856198967, 521250276, 357891278, 293593521, 323183884, 94344566, 260890431, 767911252, 576674082, 294425993, 64948795, 500832722, 428563121, 664920004, 537861258, 843701047, 449967056, 173561762, 287441866, 434250445, 587156345, 449115022, 990288833, 621696402, 360418008, 817448826, 780525897, 308620838, 61302110, 109979565, 277267743, 866080494, 562689280, 167966588, 672884301, 503522369, 787179356, 840134318, 120898376, 976201596, 135433179, 311594108, 476343074, 790941317, 827211400, 715688566, 276742807, 138467106, 263690172, 20265236, 252279162, 280843953, 963140450, 517415676, 41172453, 545461630, 127831088, 845871846, 654863625, 11541244, 911564814, 579708793, 952589172, 194926579, 616889793, 941708795, 483004528, 124147429, 865968175, 768998964, 156272096, 943747902, 563147990, 612818387, 428565322, 854914513, 186222327, 727720047, 707855322, 907104540, 898341387, 613068551, 930004973, 20376936, 752136012, 923385318, 841486364, 290543851, 310048144, 993551786, 462419436, 91635573, 692975036, 48522218, 77169561, 692713174, 53447476, 958534689, 608950179, 883577653, 524021632, 466828048, 413185150, 867861424, 765333128, 321813713, 475118903, 207565499, 414621554, 67742117, 641087394, 366004503, 246638647, 643173122, 238760560, 221297868, 788553090, 882615105, 624591013, 960567570, 207497839, 855245218, 4027312, 157256711, 315114818, 418191558, 473278583, 320017743, 835860744, 911216132, 195180023, 670669994, 458092392, 431221597, 2428053, 865247747, 519354830, 701400812, 704930052, 971929496, 531926318, 228774586, 13261273, 782674126, 643746454, 655112618, 689930435, 35631917, 832235036, 980652377, 545869264, 99721118, 829825090, 967283716, 793921253, 647312862, 207752586, 662161626, 751741994, 409856010, 657921980, 262916131, 504904825, 627225577, 697166229, 280425582, 363479804, 915782401, 578135568, 810037356, 248694825, 952790926, 322746634, 265805940, 385779087, 306410784, 968320138, 754702444, 993937694, 75987479, 38116152, 385391020, 625128246, 787521912, 665471456, 819976687, 140229743, 154261040, 488425412, 99641485, 266682036, 17392198, 509308563, 48564969, 235290290, 996607113, 686286452, 856575266, 211484594, 571390416, 762605047, 294726245, 350471871, 185666139, 131181842, 527587726, 199745685, 127527853, 830821685, 12719558, 384427566, 29558317, 585018800, 832545616, 877031930, 251028208, 888964005, 714462391, 508883024, 66549943, 830824008, 846380798, 727924923, 62565482, 435769853, 960987162, 475691512, 516021195, 821607720, 112187292, 676655487, 747632695, 976342180, 287538659, 218180481, 823913935, 288656121, 303343279, 480163552, 101864692, 438761723, 3055870, 107234283, 872186508, 866341094, 505203530, 65985260, 870183336, 401457473, 361292179, 312018548, 299848176, 275897311, 952884276, 421237898, 700629099, 465955363, 887408739, 947503796, 686844329, 731256372, 463909691, 537386600, 267420794, 267318438, 712054711, 114398045, 301218526, 79420914, 669625514, 480652155, 768396124, 947138903, 43190817, 131227933, 118362178, 379494495, 613863962, 391126566, 619451760, 324683835, 390866998, 556516503, 657325424, 168080165, 572083852, 679704524, 718155892, 769395572, 951009272, 639859333, 605231615, 567229233, 877706216, 772823446, 562033574, 267975974, 401267125, 488918924, 745060524, 443029619, 921444437, 452396025, 5462721, 557367335, 116854466, 632322714, 222383042, 128627713, 173811375, 149936384, 38318892, 312052362, 748916765, 386090449, 996006940, 974020895, 141022856, 415355432, 863675495, 562513610, 381218337, 520054887, 202249419, 164533382, 626601901, 564376866, 610753007, 74143190, 811848742, 433606903, 6976762, 938500214, 915367010, 736138121, 962848180, 37038473, 647019640, 248372752, 733519725, 10262294, 985674437, 966135366, 355408143, 280288675, 201106512, 251406831, 477734473, 843451988, 458357784, 511545726, 514005792, 918215461, 245119349, 594970719, 227388521, 642201864, 311681554, 947101630, 378337462, 970205730, 790998183, 699154759, 666398544, 268233470, 186511712, 856102007, 146117299, 117137332, 673610380, 105883963, 109787577, 572227755, 281022623, 97690514, 491485874, 595158487, 397745272, 543129686, 575760690, 961718604, 488940110, 442694747, 889265841, 687820181, 342444918, 62271787, 42917527, 710668553, 618768939, 782061045, 685012303, 168391853, 670272643, 937088718, 896813147, 801511060, 907425916, 952465619, 611027371, 538042086, 186066352, 562362043, 794287830, 472089071, 691337526, 267845586, 560973506, 375759246, 740555390, 868688364, 576634005, 747944774, 97147083, 125713375, 839771850, 89418972, 487764653, 767814727, 740005040, 725825645, 155304682, 255550437, 513364945, 796935154, 657589900, 714204783, 680557939, 540475929, 186377522, 151137850, 569861321, 459326606, 856524053, 363174747, 919201656, 527947464, 404603921, 128307681, 43365418, 183587794, 386801974, 799665682, 6310728, 658458344, 169065297, 792291060, 331630306, 57793990, 440125859, 73325610, 657357771, 959639929, 720088096, 960574168, 518590639, 695103045, 995243178, 724273534, 940905840, 44116653, 951465504, 417617893, 568322952, 237784287, 973945730, 394828300, 955264873, 180742884, 214173465, 737815724, 934031981, 219141018, 926334757, 915355652, 589103362, 291355660, 852130375, 699099188, 697465564, 273300238, 947578557, 135615058, 330422883, 540472702, 322557638, 138526429, 452929110, 850968580, 320115449, 501208092, 142263635, 534914944, 598270239, 939300817, 560228910, 816371371, 159874286, 843640880, 424386746, 6710189, 320203540, 433373676, 31292722, 639441078, 573278216, 332762283, 916118511, 787711872, 866284893, 111578751, 972776018, 806834742, 210086268, 191782528, 151120048, 981433416, 367583538, 159048373, 252121283, 964361064, 883568199, 848700084, 660749619, 973550864, 398375659, 236077391, 364129156, 839396279, 644196925, 206177322, 970162369, 939602336, 25936883, 296023316, 103702643, 540948495, 738934176, 492523639, 388192352, 271570875, 561971913, 523190054, 561865239, 686719259, 440004064, 866220655, 183918839, 131762357, 761109294, 283254648, 623543403, 888195439, 880543727, 272380554, 786136238, 258297550, 152843524, 260923081, 366587237, 327268984, 157520768, 932552880, 799614215, 490706937, 817605496, 210299838, 211362290, 982638474, 559691620, 229572680, 109069375, 274456459, 246504465, 567521840, 294124801, 800880618, 805386605, 253558976, 554474553, 699756348, 947630644, 136116335, 790758784, 999218807, 794425536, 465498669, 983056421, 45668304, 622670249, 443415551, 978193861, 345258148, 82014093, 805495209, 916231095, 735422418, 984497483, 973157800, 839802127, 144855445, 107431352, 965738491, 338517830, 858949575, 562188620, 332019875, 405664190, 786948780, 921232491, 9449113, 796783387, 837032561, 743082726, 70837451, 627436630, 498158895, 784891025, 259003838, 240809001, 535485655, 189049941, 894761940, 384049912, 501163705, 112120229, 636849891, 549111529, 690830098, 235147799, 655347345, 902187764, 714505640, 23710047, 569323411, 124047128, 687313255, 769378475, 447168190, 114913117, 395674565, 903350579, 388715893, 31583338, 772340688, 613630905, 764745793, 646906382, 281867615, 691257181, 636066127, 802075376, 266030791, 878934107, 380159746, 910635000, 877805194, 960432103, 196676563, 44918580, 559289977, 702997433, 203827399, 765699555, 517194993, 856579664, 56475111, 946870171, 172595340, 662795427, 886109970, 716664238, 877672124, 426565037, 246108343, 28988127, 798523413, 854931878, 307457208, 358893863, 219705741, 908814536, 340631574, 186446800, 158815982, 306744202, 747330916, 95205158, 483904129, 519816785, 101965706, 835749110, 356688942, 314347610, 630143464, 101222524, 412672501, 200289401, 510379202, 743861511, 296939785, 298583762, 336740788, 288305902, 593351369, 41494629, 966578577, 628250748, 606153521, 111568633, 460288788, 624482838, 418608568, 436985876, 636397930, 690040109, 838522660, 178091461, 167963347, 170935530, 918330998, 381055372, 696113247, 832469272, 719362672, 877623331, 135263813, 976260719, 181871440, 51537645, 243320629, 436428850, 272829721, 362385292, 956324482, 667494709, 513273331, 374332071, 932290711, 342412437, 822207449, 745161806, 441150153, 966819334, 719745782, 230182240, 114557398, 192977055, 675668785, 541262408, 489039420, 591718611, 250272064, 599017130, 466731011, 119280319, 19795056, 542407533, 244137180, 595403705, 559533576, 952568444, 437007637, 41417819, 363575628, 220116005, 653434097, 151834979, 678452641, 312121337, 22460764, 562335923, 787624867, 784837006, 994043940, 649079560, 578785065, 891174832, 849646124, 873767137, 870177745, 134747969, 295264336, 864530582, 428177883, 200081296, 675974355, 365043054, 652137584, 903844094, 515385523, 951826157, 944379660, 482709622, 674788933, 335485124, 965401989, 177549728, 322769534, 917530832, 169637265, 73717495, 220268033, 522841892, 328865795, 239933193, 30162017, 248457092, 358368356, 804513152, 148326615, 918752186, 881608567, 784021046, 476145709, 605472691, 766269868, 350807934, 253654421, 806848261, 587015404, 124089947, 737280759, 693107834, 50165613, 722048080, 724549751, 734640168, 798422516, 39729474, 263979431, 651515305, 624107814, 241312021, 214056187, 593114817, 222508614, 166306423, 499024859, 74425592, 604228721, 898521562, 360850682, 540386538, 109589400, 466180921, 301119621, 853346653, 685383473, 955185081, 379921923, 764014553, 531928184, 42021539, 44183409, 781074820, 665847544, 604564271, 76246251, 889644724, 676329043, 392213511, 652641168, 917078956, 938153908, 97683468, 636176411, 644028003, 424054268, 484355355, 355892086, 188659301, 242041422, 600969560, 547552145, 511052777, 808797808, 314928438, 165944824, 928304006, 355417979, 98007797, 312511991, 442598372, 753111497, 272207546, 177116012, 35789446, 8794053, 769364424, 746573760, 346861247, 910375867, 643650720, 701479024, 521770876, 432232995, 149693145, 402350772, 7620645, 127643494, 391800849, 44074381, 486825506, 181841148, 476624027, 304329360, 23724263, 818492668, 561938559, 576312854, 59782907, 515559155, 920173797, 130362602, 452412582, 505872326, 767354754, 714191174, 151056830, 317264935, 580625888, 178293694, 363794654, 388266509, 485217224, 931572149, 274856291, 858567024, 316386574, 589565147, 46510675, 803230246, 879583379, 371541727, 800163850, 602451931, 108089326, 351045718, 333742885, 642206205, 311501783, 446010179, 786171404, 514147475, 511544843, 733613254, 674243789, 335752193, 117611158, 62576623, 404591543, 526421796, 739902310, 805711469, 385404570, 789795168, 518881707, 378594001, 584463300, 842227504, 860125612, 810890224, 97994566, 259134151, 756258217, 488031134, 401656113, 132915401, 174940536, 561634685, 198417485, 311391860, 482395579, 64812333, 100550462, 972996911, 485522716, 393753158, 916859604, 283825466, 905885099, 751861929, 393628072, 280619434, 98484401, 672218007, 315529296, 63773822, 688911581, 78761101, 204099946, 121303458, 188252907, 331038038, 305989551, 39319980, 73169392, 940795456, 174569510, 333837063, 207452633, 806914986, 6391256, 959347981, 224481344, 743360987, 649339768, 406412687, 640188067, 61595846, 669308072, 784095785, 648626575, 14283284, 530396816, 782355960, 219895044, 33115827, 575375237, 284416884, 852052426, 756667150, 180465263, 332688917, 850136988, 426660585, 220099403, 611655392, 806820869, 323405405, 538087482, 913617977, 651652931, 986648323, 946842583, 511424451, 642748582, 356946107, 85060184, 550411018, 61938550, 174594884, 873518688, 305629222, 653453308, 33920119, 235930879, 230988309, 390906737, 185313830, 339420188, 899206985, 693140851, 940074260, 677958571, 750007845, 28237522, 895540758, 792084855, 219495364, 335379089, 323405567, 884825548, 433627701, 164152259, 843964436, 856622591, 637829881, 133217836, 623937444, 600409877, 401039754, 146874344, 506283340, 9127232, 808259151, 787923087, 382354162, 774342083, 145886557, 439473657, 539483950, 750745528, 742323727, 223912002, 388984463, 932380222, 319178854, 970670224, 177345959, 245487936, 554511402, 172216467, 33851460, 82894036, 508690556, 100316581, 927054633, 104204995, 470548737, 302028802, 824947427, 338820524, 147778897, 662276324, 705557281, 435139847, 293211950, 214623305, 478348238, 482618336, 68190692, 423301532, 980346295, 606454583, 731838731, 196434927, 837953499, 178081070, 227437644, 68133520, 247149520, 222551508, 586877438, 502545894, 48253735, 214138222, 510784498, 574523442, 128029949, 52421951, 7188534, 556049850, 278814794, 382132446, 988753551, 542531982, 967850617, 835455708, 867405109, 537012394, 981771901, 942025165, 551971324, 525562619, 529692077, 645997070, 137495659, 972432542, 22074736, 879089884, 905106447, 89601475, 617126769, 311133914, 359244883, 533855772, 430157891, 236212127, 613701167, 224432980, 150027408, 372245181, 105655281, 821194208, 348904487, 993263458, 557384888, 786172188, 238772241, 205989643, 925683706, 281128956, 736941649, 636178349, 356003045, 500069714, 924172883, 392692864, 605480632, 803169828, 342281073, 679399153, 279345938, 712835429, 504263729, 206420997, 651554187, 47221216, 198752063, 767574141, 383223397, 230844355, 869859190, 878423114, 453603254, 376468034, 276279869, 89904816, 847119148, 367845068, 442958044, 446454257, 656776990, 230320444, 265555428, 922591448, 33570800, 886875401, 553452081, 563112644, 737617646, 598580603, 919740, 174436867, 805400061, 915716056, 332677048, 471229981, 380509815, 45844875, 529456148, 524029586, 1442233, 221404260, 375749041, 698574027, 924949790, 687773956, 66002509, 707771982, 862528883, 315657056, 891201366, 860202163, 437649246, 687688795, 199582440, 393862870, 328814185, 197969758, 73903673, 951338727, 769765082, 399428010, 827441040, 255103379, 668770859, 926329489, 693375113, 162869327, 763456507, 216348293, 773674538, 697394946, 404890158, 760733963, 583884282, 350214310, 965294755, 33484647, 843166217, 497135186, 904962121, 991744461, 969171679, 728513758, 944330404, 626462275, 430672857, 308509374, 10765328, 147712193, 703280133, 744871889, 679213180, 66362246, 262206445, 397615665, 227739628, 335617168, 580121301, 697104118, 413370988, 957165250, 279571825, 649924287, 773234621, 827522916, 468109829, 15667236, 145560867, 655234112, 125093891, 311838148, 419317115, 598540226, 110181476, 239378292, 188767240, 957508339, 322607506, 552834403, 654265351, 248893100, 739751175, 215801428, 751462705, 483821118, 449023315, 167583181, 488029097, 87624525, 215014806, 694157470, 690371304, 927089341, 287713737, 563306692, 974842455, 86748869, 369200254, 460130530, 594849746, 745915299, 253802224, 283996531, 98808640, 284448188, 75484340, 407901502, 657426989, 606411667, 294448412, 69049058, 73024083, 790973825, 767586997, 181294804, 922347079, 318522320, 67831732, 706323129, 852417598, 285295638, 873452798, 606741792, 794547475, 655844514, 553010678, 606273180, 831497304, 923544137, 449559746, 912403426, 713633700, 291456530, 727967894, 314509052, 312518142, 4699314, 737891365, 546206006, 287079654, 560687768, 421269822, 154876666, 26109812, 208292976, 503685201, 62794722, 232692810, 391273589, 604565296, 100923491, 656343366, 627897530, 153123115, 222503441, 974599171, 498825739, 862499861, 52522910, 216248823, 680420670, 516601590, 571378181, 202072133, 782183192, 401740605, 92241063, 437630038, 912399265, 629617956, 199404775, 380077147, 794119676, 550300421, 472587802, 9565034, 222542677, 518187034, 234217050, 4674361, 65056298, 761892313, 163997170, 472144121, 143299376, 521559528, 82014402, 693666535, 660163185, 909606479, 408228445, 177644913, 453384976, 448798581, 315292148, 966942351, 921412020, 835136609, 449667087, 322056086, 467374781, 184736061, 913285405, 372772977, 922613270, 13550295, 318154229, 600525636, 321113140, 802917865, 323353352, 688727956, 904463610, 44781204, 127354496, 903029093, 34877096, 849332870, 781434066, 373419484, 619337542, 547001035, 12326309, 561039334, 350172508, 235070469, 441142121, 345202086, 403494839, 789255791, 273250689, 733109600, 53058501, 368463900, 490192206, 749429635, 87971406, 348686730, 962164764, 38767999, 559056899, 663612863, 621899424, 2589237, 11936306, 130489404, 113006795, 862073459, 358106742, 748107104, 547578005, 270058641, 707393223, 222830865, 213709696, 132093909, 968359217, 562102452, 909844443, 148563082, 439454924, 242949711, 461617678, 824096008, 226518401, 559921716, 620819167, 772051450, 570701949, 391173099, 560484984, 968766974, 225429161, 335370605, 441895175, 673454464, 514208767, 329671107, 489235999, 967007899, 839214856, 683366847, 169308824, 330045307, 496751685, 979820010, 392364561, 963679526, 367290372, 134026690, 530667734, 810215280, 692227328, 100344111, 395659063, 265496168, 134684291, 361054905, 261629870, 175472615, 557250562, 8514328, 309831923, 556521945, 661824566, 502224954, 723625721, 163102277, 313405060, 569570153, 313386608, 327585773, 786574733, 770031268, 296717586, 874431434, 59201669, 822580933, 617888427, 378607345, 176383027, 497577478, 782201732, 877558991, 485517008, 645465756, 935223815, 441010487, 204561889, 278178715, 821970660, 869480441, 807275923, 82727971, 142200132, 273943853, 315815955, 886044523, 927674070, 249037045, 752681192, 378441081, 601596609, 686384619, 706072709, 657527650, 890261659, 848742913, 436457039, 17689998, 478729376, 264353724, 235628723, 826630800, 970180380, 808316563, 547722722, 370271126, 949431287, 40025595, 978169167, 792281856, 68213850, 886937297, 863538394, 547480270, 483378849, 880691020, 335200943, 310121399, 852714745, 829805213, 104136007, 127473496, 692443814, 395387490, 125020091, 747743521, 351720161, 997656903, 611880841, 664819020, 32420744, 744111836, 696119127, 461260388, 771729522, 785671451, 208898373, 931630555, 421419233, 657139260, 721453201, 367351055, 30951032, 460462872, 863743991, 130622152, 582837829, 153065082, 555306110, 335970587, 953862940, 301288121, 674895415, 838065639, 638629412, 910463674, 17413361, 58993370, 716618599, 259192192, 271479399, 732916629, 93628761, 305297819, 278996913, 891756279, 72917419, 697412271, 702734338, 232043317, 617629585, 129932141, 949263885, 946189921, 450462435, 630997962, 416391838, 17361381, 602031804, 713226296, 585789334, 356999966, 581630160, 761468718, 957326255, 569444317, 120989127, 161788271, 925850970, 182432952, 178635250, 251856510, 921910227, 123019167, 154961973, 407636622, 657056757, 997071627, 898835474, 991747886, 858897329, 647180967, 825518894, 173918651, 126840502, 325437746, 299822947, 556696355, 988989906, 818496379, 599438658, 438182460, 773919049, 879694039, 711241983, 666305174, 365423060, 555828407, 319262948, 508743272, 934659841, 677751499, 108590014, 501247420, 889408331, 52247820, 389679106, 395572428, 478250461, 126394685, 598448805, 411515885, 640457261, 879078483, 722727194, 124663055, 880877339, 749647065, 827900707, 780161979, 931865776, 442373862, 78103908, 360216225, 265111159, 715962240, 476036208, 359375884, 171433473, 552316501, 14838942, 531829594, 999585249, 362122182, 219102361, 692718309, 574648905, 104300889, 110603107, 524725741, 204701267, 698431942, 328173261, 203881469, 906031238, 719773423, 491863516, 850853341, 34847050, 725878389, 63105974, 602614004, 1875350, 600279276, 98860099, 119544076, 983824059, 430917665, 708441316, 404713217, 345095437, 381633489, 470181930, 349879669, 498776405, 115716733, 104395333, 936463612, 387051731, 989389080, 302877227, 351367887, 481308519, 748420907, 152221925, 683046960, 895739895, 296174938, 32019695, 537323505, 115873013, 968575472, 722014396, 212859214, 225293797, 128811000, 413743658, 169878954, 986641955, 556747024, 155329159, 767340764, 386676277, 757742859, 735486205, 92589026, 828776132, 287534290, 776983967, 63882460, 935927376, 310251756, 909843401, 997060641, 966052733, 753028599, 529540970, 776711752, 485785301, 933417520, 453130265, 335449925, 880078374, 112026678, 317141114, 941076800, 720576877, 603458058, 232996966, 859451411, 447841359, 287821446, 635531172, 502318518, 241186889, 557256239, 461383283, 606712924, 689303577, 649156183, 600059358, 725903575, 943248555, 266080075, 28544114, 479251949, 333896681, 723480081, 881011949, 702864837, 695539707, 483116040, 35689686, 854502568, 374083804, 336330846, 272597514, 71203535, 904860824, 353845252, 551048017, 901575528, 990051725, 955010607, 106445388, 994206536, 686837622, 261580297, 225023215, 228229264, 248598185, 37031792, 515159405, 975419472, 721996698, 548042195, 928157294, 365325952, 418431092, 10719942, 92395875, 430807552, 750089198, 254336813, 587988220, 796860672, 493181617, 441488622, 937958562, 634053215, 123265793, 145918137, 682645279, 708398396, 223738589, 486313178, 680505001, 666041931, 699204479, 152629393, 516268344, 122559668, 978710615, 279639033, 500586931, 574921993, 158138260, 17050793, 985733668, 371683306, 956840906, 535543438, 569025092, 981729310, 941745448, 147905436, 863172211, 955220173, 339681022, 222291697, 895652097, 353385082, 566862737, 21156223, 915665676, 692869010, 248762469, 497188958, 54947934, 753348167, 207336615, 206859733, 275831332, 971251206, 596516540, 776726272, 619077117, 941109732, 698828317, 483819931, 403777353, 999984410, 540859548, 766168087, 42556950, 352681831, 642148258, 323523177, 892649254, 89591308, 924475705, 399992601, 553429048, 734298910, 732801840, 232287354, 702381152, 334175268, 74660040, 166313068, 419148475, 17579505, 309841520, 319575493, 93941810, 651463715, 965278000, 518492506, 914877500, 560993796, 199538365, 448156546, 444629797, 225019587, 30728198, 589441428, 979052894, 340870902, 477671532, 521291453, 474338986, 379303022, 959331654, 592203593, 536010405, 27711602, 641312694, 554612418, 8993140, 496328798, 679909068, 130111335, 269018970, 628292692, 368685292, 740328484, 567496849, 990823470, 907218535, 516458967, 556631151, 542833061, 17128619, 902232526, 495958555, 531289336, 815718025, 782394578, 906635411, 222942934, 328796455, 190401340, 527999374, 99168112, 96527507, 866090157, 508073209, 99924588, 823980014, 982999042, 79807757, 74234296, 568384826, 936592635, 146419388, 618698787, 30757234, 500033156, 598042313, 12629341, 744827742, 172572869, 35071897, 195248835, 595181126, 817424986, 140348269, 513278234, 656763431, 752772337, 854078414, 831379405, 318317934, 48799211, 383464841, 989799916, 78024677, 962211061, 826268389, 419031378, 640193490, 962568654, 786478963, 505452164, 64778264, 392248064, 647927846, 317087432, 698460391, 996198999, 499024878, 194334104, 292219618, 82356580, 240454414, 814359727, 584873449, 554242464, 336820078, 505229931, 614957277, 415913935, 661954218, 567066214, 220414901, 106538392, 392833371, 540112538, 586488205, 434615646, 576191612, 125851665, 211616903, 54245813, 977396150, 874431156, 620141514, 143290905, 722511905, 960375308, 307151723, 565589073, 764353115, 555181707, 235571039, 186821699, 708504335, 832414414, 243319378, 502834474, 970729754, 220339520, 135027779, 329423824, 189573529, 844877889, 149656899, 494773397, 657821263, 585376296, 195043987, 598552889, 755116060, 124068216, 22289761, 312343553, 974317525, 679531587, 998904984, 25830467, 156715733, 541955516, 560462618, 942167172, 120747512, 945172241, 472541333, 477690462, 171604485, 380742902, 700464483, 788373219, 244105693, 796501007, 540346253, 506608945, 679562057, 970908415, 328472950, 844810537, 945767655, 61969096, 130678473, 736915269, 660209997, 431439560, 427764247, 739102538, 587692041, 476096682, 907970827, 968531963, 511305870, 923800797, 605979784, 581098511, 545423752, 269044047, 922828524, 777529440, 522918237, 983469367, 106509169, 312832540, 375374917, 240239743, 232872499, 569771874, 612025364, 258966197, 415693584, 939356153, 574045914, 81359209, 70480906, 598463806, 522275204, 435183408, 194592642, 319922688, 752002064, 107549020, 203841461, 822962354, 343893035, 115051874, 222123944, 218318746, 625907715, 41364765, 914389704, 735842997, 123888790, 420845782, 700860145, 134045780, 134481818, 582122677, 772510295, 49354345, 983730948, 295129910, 932293635, 916508917, 923919239, 507169676, 376742454, 286279127, 371841454, 204135812, 783274501, 372355253, 573333464, 266440661, 986215333, 159406630, 428345646, 437037554, 974603776, 764142001, 848524003, 290117710, 782895802, 734235729, 880654733, 184598285, 242568810, 211428209, 99480656, 164084691, 492743022, 145882359, 955092069, 607670741, 621135502, 86790972, 265019839, 386781062, 883605169, 75998831, 756926299, 625587220, 384231116, 312943774, 729345771, 578593444, 232832069, 135185335, 867251618, 841958926, 199421686, 109963087, 519302387, 429550515, 8555341, 727635182, 993974600, 3448620, 41882395, 967304510, 934829663, 947354195, 253589777, 541478506, 995733651, 232275792, 129618409, 517194836, 394925326, 303477228, 828193624, 241356640, 532860612, 234582884, 507567906, 789258238, 643824002, 232322306, 229114039, 300939074, 631243442, 133288673, 713033880, 448230005, 989389572, 437093257, 410275647, 675329992, 248066522, 570704468, 776813015, 201262177, 440407039, 291774363, 944223584, 33826711, 890898823, 318671131, 25878772, 667033123, 667903231, 285634195, 566663795, 999043041, 417671294, 470556651, 889879346, 249820326, 833905396, 596816328, 858834747, 859242109, 45147698, 787097258, 569820741, 283078960, 644027507, 812055318, 171681636, 889680357, 590866541, 534867425, 369486708, 436666461, 724026750, 621040894, 880107277, 168174460, 91128459, 643787602, 77276388, 213695847, 557879440, 949165590, 224770600, 344506057, 878410657, 880758730, 602487099, 985998510, 17758461, 142284629, 784576978, 297062422, 386825951, 942570433, 758929440, 758690301, 740033941, 125373237, 405881318, 842686849, 477096740, 546127558, 861846823, 763699226, 838981590, 176462543, 166276198, 839089519, 742225651, 417105520, 959150513, 271423980, 313904061, 407565766, 750353153, 165820920, 64822114, 699408609, 943108903, 859128072, 649784877, 441171293, 210050228, 529865728, 623536137, 647055993, 714261187, 506307557, 358538722, 669560679, 374951313, 551081961, 854625813, 584941116, 840776737, 8571159, 678811494, 216084754, 717519654, 751206525, 903419766, 134778025, 129465052, 52276494, 694325007, 86803443, 881449319, 144864416, 442431099, 882347697, 687823456, 680006482, 263013765, 388157868, 893384486, 942411058, 407321355, 168826265, 550853046, 440451677, 637905178, 204567156, 87527770, 394699994, 897325556, 728287921, 859285841, 3526092, 684406243, 780891793, 284537341, 800679775, 52321716, 595323860, 114745582, 285335311, 716158614, 554189161, 160535322, 761506276, 100686192, 694307660, 328491503, 95789520, 96017333, 984102521, 812169112, 397430682, 869777484, 784289479, 162513366, 764980889, 628958214, 897107751, 79309293, 633753087, 594886386, 990593084, 103904810, 88986357, 825099627, 559529, 27980736, 720098533, 582699236, 164300905, 348252628, 895434048, 150317558, 907670751, 601846881, 399913218, 703434100, 750550410, 133994362, 447246671, 674371664, 979466913, 60296604, 477597125, 230252689, 545033774, 734762544, 628928143, 872114797, 706092450, 595036184, 450606202, 357102489, 826354941, 877814698, 412545430, 410318300, 478213240, 719122509, 120745717, 658179631, 169889142, 201662005, 27709965, 57617576, 367974630, 241792380, 940970586, 508181390, 322406350, 595189825, 291849169, 759015141, 411839920, 596619687, 184284383, 832188938, 946210277, 307906599, 422854283, 104681354, 274686046, 222472282, 677684486, 836747677, 769601591, 91391832, 438298089, 419736057, 861812250, 475945578, 730480812, 851556900, 768773938, 996508554, 483741053, 424424661, 298849144, 253782642, 637617557, 817327262, 181090617, 610048128, 509358860, 589888951, 762594042, 788025836, 33462286, 153722421, 445119745, 727834598, 456475003, 855422070, 532209847, 54743172, 41268819, 375435843, 164352092, 868180705, 811745654, 437361015, 343174001, 317257450, 123735912, 3749107, 505374893, 746146190, 853546316, 156691083, 769519713, 640847277, 611715872, 689874104, 280168185, 602586282, 171975159, 189684536, 155668075, 167283549, 172308160, 173152514, 849682326, 767436485, 160192998, 996417885, 452673684, 163186709, 221822185, 746004055, 365163923, 818516128, 928519434, 69377501, 988935724, 21640387, 413775846, 282944442, 714889681, 517361475, 890435715, 596017770, 36285311, 299655055, 357063310, 195035981, 676929778, 822948297, 450865897, 8957478, 724814255, 32047693, 308134308, 421638239, 547892465, 743955849, 291459322, 914415579, 925995539, 719988067, 74953426, 324547244, 96708981, 686996947, 586109435, 737138218, 94286185, 878071632, 174249733, 480126680, 182784726, 340355214, 691074477, 29176293, 671378043, 28297028, 627314188, 754905003, 684264730, 944853701, 586906951, 928341215, 205019184, 168525499, 808497110, 255692977, 647313651, 973189509, 324356118, 610205651, 30843818, 658266761, 448536554, 772861422, 359749936, 191041441, 158013395, 436366791, 466617273, 401317856, 375074665, 779552258, 35477899, 236904405, 64591172, 778635988, 865568355, 712020109, 951778815, 470214145, 431586199, 53415497, 437671868, 598102129, 908460071, 484240651, 216947369, 191285733, 864840832, 788957490, 583810172, 546765679, 962191989, 899637713, 899442382, 430573891, 983904993, 208030430, 752739573, 342440849, 53892927, 103978622, 818883919, 876857768, 644159395, 258234257, 374755086, 537503170, 949087814, 84711859, 48853804, 604302963, 162466407, 696964142, 504624122, 248964590, 847707453, 186631371, 746545796, 58928163, 416726215, 445981121, 50326172, 713815552, 404473113, 662911087, 220313966, 604861680, 439165155, 661585543, 367806806, 14418468, 435916037, 248192588, 446220382, 925012308, 258680357, 928149639, 576864430, 364908097, 65708660, 246939408, 950489607, 665096730, 117622551, 861941679, 82429845, 509300043, 418646236, 313128019, 567704944, 729245969, 225102226, 238176661, 22860167, 37536049, 772819040, 936199431, 225804075, 292452380, 151678585, 349502632, 340052759, 297364032, 81899533, 325059718, 692554223, 443670641, 247261753, 805229671, 546213487, 549981628, 557571135, 541668406, 294491001, 912699011, 705829749, 201116243, 705338979, 702211183, 980143725, 975708272, 504297935, 740166118, 54253568, 534617349, 104829723, 700736963, 935329577, 823270650, 877132039, 336321992, 493722300, 965664275, 471283058, 765281020, 873062226, 149658283, 176808437, 388797778, 204892456, 49034289, 641650929, 30988954, 887661694, 323994935, 852364357, 644099867, 716236588, 321079766, 749814558, 412985959, 69818617, 494483713, 168774514, 22646797, 707695206, 428856765, 110418497, 506746490, 670644605, 834986763, 903329580, 788189473, 114787775, 351251373, 679396860, 71177057, 501050413, 469573847, 658265854, 285658786, 962895772, 497960611, 824976631, 452920089, 313290465, 964921575, 675100452, 663605800, 551173537, 575666622, 135359172, 694448824, 798035818, 82307278, 196593622, 444133605, 126623894, 548327566, 742368550, 500443546, 575914310, 865377847, 175116007, 115053850, 152451942, 64481001, 583858967, 603031539, 255262588, 688647778, 372050141, 583997589, 488018843, 758479044, 243985851, 515847309, 524970893, 980809439, 236143878, 378662941, 266767467, 324843533, 915818998, 362592375, 584382846, 274656294, 490261450, 372641616, 741458687, 298296533, 549208711, 665430170, 185023287, 30702714, 291156366, 889618506, 442478830, 264451895, 459621691, 918579936, 958132564, 245920925, 744631212, 712410566, 349682135, 760321204, 18232780, 674095707, 73331907, 298013213, 556265955, 341363576, 492563854, 563162044, 692290695, 719557154, 931510224, 813265795, 54305809, 76365648, 719410189, 717281076, 763708365, 317884567, 117917751, 331162655, 669680363, 645268368, 234857897, 528030520, 782477871, 732059223, 18277241, 225059538, 191707764, 995233476, 206371733, 581263614, 682098438, 493361186, 437382120, 76314115, 332557112, 624592709, 647535906, 996528031, 652869029, 867275963, 351969542, 284069640, 857075155, 675882078, 569887081, 514956816, 515782820, 814784068, 823016468, 89884211, 158920350, 172937877, 599948406, 770599512, 83733178, 180132056, 299244299, 854224042, 891960691, 210776370, 728936562, 83882087, 140945211, 717547115, 925228910, 489142495, 223029411, 998886315, 149022510, 247961434, 705824991, 41176413, 805204838, 221227807, 557623378, 293883653, 735904992, 316403114, 309202803, 260374627, 110576759, 216173708, 590035105, 232898816, 562730071, 821996000, 700719266, 196518000, 16493125, 571356566, 955099992, 610834108, 846594953, 761977063, 575818529, 457650025, 106521088, 514756693, 120984157, 631592699, 795903920, 319284901, 606714197, 720104511, 315003115, 313502867, 538969228, 219609849, 237852145, 528912767, 254433101, 174864832, 325462329, 547837438, 191870065, 517738880, 78371401, 727813855, 656110511, 626895852, 310847026, 325982145, 576651014, 134412394, 220548979, 20070869, 165335528, 992376775, 461328009, 210487659, 544101483, 558049254, 389802546, 385768259, 392999838, 861604517, 860790653, 125219914, 436540525, 269859611, 171073635, 809451960, 848184602, 812903648, 581376991, 798816228, 902032814, 949129505, 605490968, 7665416, 229039527, 963414211, 812093126, 657449072, 33439016, 206952572, 241440753, 834540963, 642015923, 290025733, 324261738, 227716003, 728854590, 344660718, 534961071, 84585079, 513438636, 222739223, 804421065, 724027902, 851250176, 356774915, 776270187, 463486758, 635443055, 880853484, 449806895, 731797088, 410523377, 633883975, 146958114, 177293026, 551258029, 335705270, 919194832, 205953815, 737480372, 434204371, 437210562, 924041740, 651312584, 85251930, 369346408, 347058495, 143463696, 240645566, 600721821, 605198499, 401742659, 740691450, 489601862, 264268858, 360556398, 711320188, 967833191, 395627339, 967114571, 977801265, 824730488, 499240391, 34312618, 66312408, 466026486, 734057385, 430181027, 633600008, 387580183, 763215544, 828014812, 483981125, 11632475, 108901789, 837860586, 148125579, 152558085, 141844104, 553690170, 184687407, 381175373, 780685629, 860793614, 844843829, 790997861, 845633569, 651493734, 460689392, 903183703, 587431871, 693216434, 764670074, 65975716, 469779805, 868096817, 687206899, 262068910, 900355143, 694442893, 340151067, 760900325, 459439646, 290674265, 866776054, 875083076, 539664321, 162023608, 481288354, 805698802, 466853024, 123457223, 523247458, 104369880, 418855813, 128585376, 853188780, 679152963, 755205907, 232800459, 69344424, 43896137, 639219350, 413134774, 710516870, 168094684, 333187847, 927880433, 277908309, 422128660, 983412711, 543451510, 480768051, 369374702, 47085039, 576534744, 941579743, 907762984, 299847377, 337661732, 601931777, 495941816, 56451174, 626376774, 986418491, 400107365, 434443840, 430665365, 606432307, 635470007, 896567036, 190732137, 310703669, 17058250, 595322709, 748856742, 854382221, 69606003, 574769799, 60085046, 197954736, 891736282, 69238616, 986294351, 641413242, 634221744, 244436671, 31892134, 874300501, 397871802, 157761175, 933716914, 864059393, 312297870, 878974041, 716259742, 630137574, 111645765, 703868232, 472732206, 924835573, 260083217, 45008800, 752606077, 189621922, 429710357, 978384255, 60271442, 894357989, 250623875, 7832190, 726362732, 582042762, 527945691, 51434860, 498938479, 869068304, 639801455, 33239427, 679325656, 767183398, 970768353, 134720949, 171617763, 817094985, 788459607, 873608987, 416383502, 584495383, 611165899, 170128646, 873982115, 832293591, 534394539, 958080037, 979535601, 953650144, 657764253, 394841530, 42441204, 66253281, 149622561, 402611278, 133313045, 953260735, 329061212, 457502689, 528368, 516819786, 139502021, 893692228, 191040161, 623311814, 115076324, 468292997, 222934495, 235645708, 753188944, 989969679, 181050882, 762572871, 98504529, 442606148, 936566475, 730374611, 252821938, 111939794, 784862518, 472252884, 494818869, 757443772, 169476455, 133262898, 748117968, 374528265, 157290631, 613228202, 830573010, 967447586, 836438383, 962325558, 653490780, 782144788, 408850738, 497916592, 853851013, 10257066, 784693372, 54597194, 261650257, 706267628, 847935746, 580553208, 558041914, 899154858, 242246819, 251212641, 857654030, 90496880, 50002695, 947234285, 156261788, 859582963, 712998292, 413456173, 95528138, 883220181, 675406374, 336033645, 707287216, 993673108, 654496984, 698178102, 519970182, 753879397, 121257663, 435570205, 870253858, 161102711, 758822833, 617712713, 947549749, 803295191, 691863773, 229086328, 894277604, 287548032, 204989883, 142672471, 154989445, 369652910, 375657299, 661194201, 673896123, 507027884, 643538650, 531797743, 486803767, 648223296, 452811119, 136937664, 229995839, 477608353, 989534623, 357756738, 751853892, 259511790, 123260395, 919324843, 215433345, 458687138, 801902297, 823961159, 544508287, 844303800, 324512812, 531541475, 345808776, 273880783, 868487399, 995340749, 602110629, 694788109, 668040395, 950639093, 359602514, 268455866, 814595309, 502184639, 123907676, 199999859, 870315436, 317367551, 715044713, 638938187, 589980633, 628549449, 436201019, 170226016, 786804823, 785686044, 903950467, 321257348, 150330037, 917279624, 787475258, 864285306, 280395282, 62894638, 126881125, 231160098, 810119038, 73404046, 120567427, 366690913, 270324045, 382178657, 790848081, 217162860, 639937946, 843732676, 744403871, 903423733, 582771319, 829676640, 957353785, 164383846, 146300304, 324868928, 787024203, 694263249, 992223049, 343385430, 238500893, 34661584, 514291429, 38338311, 689895443, 953034541, 485327520, 307801835, 744455596, 37557998, 578110598, 361303616, 280750099, 115025520, 169640624, 517001542, 126989636, 505770001, 378547437, 922240241, 316362322, 462638678, 115091987, 328523113, 495962557, 687262173, 299943142, 914606, 816895485, 467503308, 48369097, 230293269, 376169319, 808137662, 866735375, 842920471, 827345381, 435888785, 811124847, 980867132, 671168301, 625536614, 335559220, 738636026, 704953607, 330147995, 430000225, 515669773, 952936861, 836999015, 92558639, 202764842, 804005456, 664971456, 426621861, 594650165, 992810806, 817834257, 187219438, 670278710, 818136049, 752187770, 845655626, 372638376, 175906106, 130608903, 495174200, 228766498, 198923946, 169659785, 130804572, 180567156, 795526462, 413379397, 15600987, 8208723, 119137725, 916216448, 722450198, 623308116, 980109092, 664316699, 968126951, 50448337, 662250276, 860151139, 197911928, 591297202, 420744285, 568491782, 711976559, 698834428, 824089993, 702173669, 286033369, 263247013, 509054747, 219568094, 899625629, 615859157, 984357454, 238286904, 652638987, 907483922, 588161303, 499483861, 517167598, 499854273, 971361694, 386563369, 262123593, 54262369, 792096889, 530490695, 58751798, 390004191, 865389467, 807840046, 677061202, 858241992, 647900710, 452114482, 511688874, 981796990, 185936326, 291980863, 931922695, 838467154, 93011909, 791161291, 483384104, 353817862, 54317795, 475410628, 26100505, 306647988, 405687265, 648714450, 982630509, 762720564, 799559178, 183207087, 157980851, 156180783, 137852061, 26745865, 49507511, 148083964, 963717938, 26775554, 635863554, 233945699, 455700918, 405463679, 5147995, 654932172, 104628380, 217022268, 109253714, 636636896, 543352399, 895109897, 850792298, 686583121, 686172240, 159084321, 41690286, 62175172, 130371153, 716726938, 632115032, 220943837, 117481460, 182784757, 222221068, 709046340, 2063150, 987919449, 696061412, 666986963, 808817101, 77965353, 646181053, 821260015, 456598210, 469561095, 947944996, 382232398, 736516432, 83426171, 211470458, 99988741, 416641757, 817680702, 299560426, 377477337, 933871551, 640534929, 18011583, 832356598, 322126381, 912181889, 260476161, 490303770, 52651516, 417698432, 94689466, 225837417, 235990172, 837802505, 733229790, 835981243, 547636231, 215080257, 52295316, 129640167, 428219902, 855249021, 184213919, 842572520, 685175841, 102566246, 780412052, 590699166, 454723084, 422494236, 946560842, 766160531, 37730725, 638690673, 609511872, 365645691, 805717650, 163419098, 636057972, 198494235, 21876866, 467941960, 826349706, 302152010, 267521891, 295704543, 670120664, 461093948, 57495268, 953042445, 821403841, 741599019, 705190614, 537205232, 18108147, 971869058, 631272700, 197721874, 289030005, 346609947, 82071673, 441408209, 561213032, 628482498, 786319655, 88260613, 764733640, 175833893, 865706485, 911517453, 838857593, 351671324, 783887692, 575816092, 717677266, 755504123, 313318555, 895921562, 472286283, 540091742, 690632966, 95341215, 212386352, 982158899, 645800133, 655414349, 440678357, 486625954, 904843818, 730347827, 363523891, 680221743, 110769706, 774243945, 754953274, 448358558, 640312936, 589393624, 665152272, 238898215, 484394086, 252597396, 901733873, 996865392, 675618858, 405243730, 78764769, 744588924, 979723996, 181647727, 757758083, 691148094, 908172759, 807998826, 437026758, 176547745, 643082097, 773977763, 545268115, 146350087, 643519142, 971971098, 160651687, 841927731, 447503009, 926721710, 132439736, 490394379, 439105091, 246163931, 285385042, 557070564, 523253464, 256822042, 260986615, 462238468, 424395233, 475058710, 410816494, 939194695, 302462268, 381267826, 466437059, 602673920, 458185781, 259818161, 148843247, 305561161, 708664322, 530732418, 519490362, 258685909, 311822793, 164501155, 13587366, 401103825, 678299482, 918867604, 894946041, 807742623, 863581305, 984445146, 863889389, 424891273, 488596440, 660569551, 947277919, 568543023, 168698720, 211604365, 900257501, 950997956, 683212399, 786355603, 153847028, 173272938, 560388919, 525126432, 696739913, 652965572, 844497619, 88842519, 441597546, 268812120, 108100642, 420114445, 863260081, 24697685, 693428181, 142726234, 243488984, 107599095, 519271555, 726257393, 446376026, 274778259, 903473204, 85995776, 996791218, 422997237, 146187381, 921259229, 844276759, 968860286, 88130584, 821924102, 171234312, 255928220, 309501707, 67053698, 592170872, 390976809, 760047, 809114859, 43720517, 65407313, 11450740, 24592550, 985001334, 803385288, 217884127, 762871790, 543485819, 302313446, 457494350, 652724189, 795843395, 779928967, 938394406, 112381445, 525447889, 316231373, 744996487, 798361753, 51942806, 768801550, 283022481, 389832087, 862718682, 648770812, 29501549, 776977831, 596469873, 976393747, 313164978, 882105034, 173728246, 620833741, 664606061, 648390625, 70098159, 820793820, 988843035, 353663354, 250780350, 175627753, 769012469, 806864511, 220195920, 199634430, 795636460, 555142542, 130456302, 209858789, 546032780, 449521754, 606050568, 569259488, 983480590, 724804001, 962349942, 635581683, 425266372, 251693989, 997794057, 510216058, 327102543, 505349663, 795013551, 492414985, 516637488, 130591407, 39015216, 567681526, 435155999, 291954029, 595195728, 363110658, 260602157, 177920888, 95067782, 86216246, 472422866, 189965481, 440678381, 2874961, 1621885, 720436423, 856382954, 854083818, 815845560, 140307404, 209387987, 525795155, 140686374, 407310645, 144280661, 706329438, 490357618, 789400542, 264308107, 457984940, 113369387, 505007631, 687088392, 6538539, 535252898, 719342847, 628688000, 758632079, 535452381, 801802924, 929106644, 31433604, 609972575, 570470242, 937030381, 956632182, 765167226, 865833229, 22445245, 528599902, 479181517, 29704642, 838678151, 788306014, 911355884, 42862524, 94607307, 826528645, 699064425, 344591023, 372048282, 560043048, 568619118, 45646691, 203631165, 754634765, 726249679, 253150382, 771866917, 794580452, 384752886, 732056018, 203331333, 703167326, 382526943, 482177615, 99356763, 406272243, 374102500, 898256917, 720235146, 587597082, 102602745, 390725521, 220988338, 585599642, 182571788, 444539246, 304341836, 85438090, 163519935, 722193723, 167362729, 383392211, 133997938, 225759204, 729605928, 703269295, 687382487, 591948544, 459386937, 744859460, 748976071, 79180666, 273380800, 187691140, 521858659, 957689979, 431603972, 47687145, 388177076, 75722508, 619576938, 635650853, 91723203, 901055283, 17191648, 77632928, 400968924, 576615861, 213566246, 60522522, 994214488, 956977482, 339699886, 708916123, 182286750, 315835419, 410697481, 531370361, 799602825, 116151730, 87262190, 111840788, 44276507, 98734566, 446555768, 788501121, 727493766, 565869619, 151243268, 390835754, 779302458, 661405391, 210785089, 890951371, 392290284, 451398645, 846671962, 36768056, 406142869, 399302828, 139155483, 10803701, 574452057, 30521027, 405005658, 432152475, 935287650, 183275227, 145208519, 864794387, 886095816, 667273380, 89706112, 662767453, 109587461, 147388677, 630726890, 780832531, 164386053, 218012442, 80492196, 11333212, 632388489, 386871662, 400847589, 728574058, 390512408, 30547405, 784145366, 639455685, 260245697, 647590103, 535438136, 323948654, 857521194, 131716196, 657557281, 323743161, 27952384, 841131769, 316154055, 150855697, 190841250, 365135253, 870621912, 190634894, 485224185, 117665848, 204577128, 758638503, 808962665, 921173641, 127665845, 778174515, 130283005, 935872083, 165007590, 331465639, 97886306, 929515759, 226992304, 706731283, 439598406, 681738400, 279442298, 534781837, 208610391, 223772946, 615989757, 385910744, 915688373, 106052135, 791362546, 532910494, 940413580, 953007851, 773728476, 908369273, 998227689, 784967460, 263432020, 435346051, 225328346, 946122360, 809402233, 34170331, 153142148, 148630640, 448383100, 263915276, 211071151, 985491411, 656234908, 493992881, 567848780, 410182780, 620442568, 311554491, 195352765, 145126519, 687810578, 778986168, 26655612, 326255182, 528829214, 545670130, 653774970, 812982517, 20970160, 735142650, 644399778, 914686135, 553580432, 658575588, 488601349, 545209658, 371242688, 772468897, 137442350, 690007132, 728034737, 717206294, 93984451, 696257974, 400293279, 52363469, 399688148, 120659427, 281001914, 956754991, 547745507, 219407630, 361392366, 235520677, 624328593, 589567019, 166075425, 576666848, 283222994, 887207394, 820625268, 45529351, 983035744, 843240803, 358778373, 219472812, 458876528, 132377557, 89156664, 392078895, 705756776, 399273728, 805482439, 87754901, 895838565, 796362890, 440108486, 275600989, 220402902, 725312189, 301734229, 488134341, 283760345, 972984295, 571230628, 669801202, 763535667, 633208715, 562992130, 686758478, 296965814, 772453204, 837336919, 850322545, 384691925, 6900995, 54668224, 688060453, 592536412, 296480121, 337248150, 527967596, 137606230, 838273890, 98128864, 579153279, 903768806, 37979849, 180302561, 877636939, 133772836, 126116710, 182559376, 353267632, 592641781, 614949017, 583844812, 934550654, 345649938, 928249765, 879943443, 404447251, 902494504, 824074180, 651706471, 482340424, 785628011, 758221004, 159597154, 525506966, 1943363, 218318693, 554762143, 99594478, 554374757, 167034206, 931486933, 97880420, 408011550, 894514365, 433458472, 130824468, 15512250, 378909402, 751235780, 846630254, 211624770, 61167834, 38979058, 783145367, 21231837, 74467081, 653339826, 933031397, 85630154, 977512708, 442796436, 686438635, 977549342, 159284237, 375133823, 359895919, 1589313, 431232271, 143335683, 44500654, 686329614, 767809752, 781329493, 831075235, 775660636, 248603716, 794711984, 882287824, 932664857, 391088414, 1552666, 182919026, 624244545, 893083612, 181672689, 330453669, 445371979, 852771631, 181489496, 77973106, 669790309, 333195658, 955257746, 314714255, 92723924, 480846116, 41502323, 287323273, 844292068, 113366576, 441391865, 304532597, 741157248, 382436409, 873523057, 985624073, 469834897, 782943290, 582214768, 725704336, 310194590, 783649317, 749445110, 216968000, 884055330, 49039078, 781316644, 857134054, 770318545, 431928431, 27006412, 580178025, 168150418, 875979728, 226346028, 83380205, 260626368, 535785340, 612981509, 365286907, 201377055, 579061828, 940384519, 358144432, 69470770, 719911539, 221686330, 993785820, 507822350, 997023441, 634504577, 937988661, 326960760, 99073407, 514402792, 937715794, 419071562, 954142076, 277323488, 186518, 234034686, 666514648, 358574773, 81586234, 217771763, 662137514, 84313889, 54403981, 861287632, 97511097, 951171772, 862024604, 427485252, 972411675, 201682169, 931771468, 53655584, 994509319, 122447332, 110388830, 45569183, 598685015, 561915531, 587963985, 836789556, 129498693, 339382739, 657085703, 850687666, 174940228, 882820911, 423120284, 173552820, 340331803, 84082634, 268585470, 518249098, 945366144, 854414418, 277336486, 833302394, 114611381, 184188479, 81102732, 429835160, 659734548, 607852664, 785611718, 196837364, 12804986, 332914189, 64914599, 12095560, 20766660, 612604219, 670129782, 486514273, 140310438, 817983514, 529390072, 805140125, 755204983, 341624309, 722817285, 998835186, 733414649, 847556809, 918499925, 492340754, 527433891, 10349807, 213308818, 444206843, 129828339, 805068604, 887296066, 652227242, 51837661, 225624838, 86647344, 934646613, 171504945, 428824058, 523936554, 948064755, 903239562, 870953479, 831161185, 210497760, 81755890, 308417577, 748687533, 801546979, 598546043, 713326084, 543949812, 372796566, 839502244, 897541075, 572701817, 355647213, 178125804, 663377529, 874036860, 82223488, 584151772, 591246088, 410181197, 161973837, 978525579, 759691536, 690498056, 301117393, 152230853, 895178767, 37676548, 88414566, 730819026, 217259228, 907975935, 129773248, 408763333, 900234325, 91334080, 63247823, 405931386, 616755790, 822794180, 283480208, 351953055, 701937001, 933944113, 767162122, 341381894, 368547624, 182532128, 533101118, 287616293, 870884104, 984352338, 417235392, 250638185, 610162353, 862601598, 823563070, 723016742, 575475377, 922556540, 447139901, 112988213, 380893896, 20382812, 31096487, 780899338, 791325989, 434054772, 376199159, 359598822, 743582157, 346712487, 160539127, 831825505, 963911490, 842405365, 88739141, 151541286, 269413181, 635114166, 135904290, 92706538, 575587716, 655492589, 742106372, 251201260, 356304733, 842810904, 547315889, 787396570, 674715625, 819344642, 828522859, 904782101, 727845906, 120248649, 33179928, 272004828, 436598079, 472967514, 58689028, 662790254, 958584745, 464530813, 778098453, 213993733, 201771414, 301680215, 766793517, 83514050, 172412982, 743797774, 740659853, 93092568, 290146361, 770040061, 932780157, 766755308, 638157819, 296945820, 986782558, 429843636, 684834879, 887304188, 702635914, 654510487, 645527097, 851367081, 543814937, 431947261, 80775035, 412152763, 611884618, 361731676, 139853154, 441807444, 800650503, 883806176, 385320999, 688341378, 739838442, 317748567, 633648291, 300488052, 815559266, 433038578, 27120884, 398298059, 419156389, 622422123, 958617716, 517795853, 273797874, 14804650, 739185742, 437996660, 485734566, 618676426, 555137729, 679732628, 871721557, 473389540, 717371688, 548972469, 406551515, 805802151, 108669201, 948957683, 235383260, 737026914, 213740376, 39117853, 827486294, 650747834, 15091608, 970611862, 824118147, 301136274, 514570326, 647791896, 957510338, 340640459, 476674261, 656639736, 897513723, 28720541, 143807555, 605029389, 979537734, 629828710, 854303304, 4057022, 259063123, 951455922, 410223342, 866614134, 242631121, 70482462, 799525680, 445963202, 579758236, 654379457, 751372563, 364878238, 653305099, 899963662, 740744222, 669555444, 355881548, 164867325, 164030385, 428942960, 494869467, 878440561, 198895725, 923624549, 21891527, 260786271, 814224043, 924637511, 436964624, 607635167, 886154626, 328302804, 871727400, 355389572, 764115595, 723746377, 771570314, 627407977, 998690572, 94967372, 139333510, 874453537, 296403258, 307723633, 766530292, 662306092, 41531416, 540146602, 409231188, 131050795, 608433847, 460150330, 768545263, 9101411, 456445654, 787525543, 288992062, 581680160, 950392659, 337212702, 471104247, 556191681, 617280958, 231147964, 579590115, 689037066, 59404473, 189103698, 168242879, 861546457, 170600105, 170888219, 878889643, 679455688, 934610943, 985134101, 291462778, 111558375, 167008640, 843855613, 202171257, 489987297, 860161144, 857596300, 262630681, 266477572, 276848827, 590601068, 917312190, 348875171, 336598103, 607862692, 83336866, 273032446, 478362900, 869428398, 896566724, 495687885, 566232192, 379096941, 324690266, 571233336, 523456242, 386467309, 255271572, 317835139, 304290662, 823298735, 757040819, 175563261, 179734902, 9114625, 160313519, 923713758, 7990122, 270233847, 72803336, 660458497, 927072317, 313847371, 315981653, 644377806, 660604505, 525467104, 881501617, 189854535, 860841611, 27800190, 57424085, 478647180, 855354750, 531889113, 374594210, 211041836, 998988779, 186557101, 440392959, 78819916, 291581870, 26484399, 595406048, 744295519, 410732205, 161175814, 370012025, 619666090, 478781742, 51322902, 822956145, 309520609, 73621370, 935619402, 370146530, 36306205, 218056415, 169037524, 222745299, 723771011, 229059272, 771483879, 552502789, 286736828, 804533915, 985989526, 926136430, 163277752, 256778135, 246401582, 368437509, 636079605, 231699640, 919871007, 888641650, 896499890, 807083, 368644468, 585913977, 249334195, 509207318, 690900723, 309444070, 495865467, 518525364, 93047751, 788475758, 76506578, 63090477, 416100951, 135402099, 230035977, 159853401, 415010328, 960006374, 208109019, 898840654, 905009758, 597916291, 484506509, 492689497, 648436637, 241351506, 643183236, 70539102, 456820739, 500081792, 791895765, 631701174, 896168964, 895343041, 851291961, 959806381, 930288937, 615034093, 521257135, 918794545, 753566836, 825971099, 613696196, 67650717, 40848778, 239044831, 713329758, 628603671, 823277432, 628706414, 925087951, 343038315, 775674706, 828424131, 439210566, 261991072, 499195258, 454671653, 972676998, 90616555, 748460820, 379304263, 756885551, 731717886, 294471310, 808798693, 710093066, 714703156, 821583600, 5806319, 486634508, 744006499, 882104834, 778291181, 951936934, 618566026, 850253455, 593752141, 750411169, 356246691, 637316352, 111777370, 291045884, 126715598, 46797598, 730683353, 752854551, 72587374, 187978587, 811246012, 373348724, 704280338, 550070379, 81471067, 986193407, 910822581, 799785894, 610102223, 234348924, 471292365, 524158965, 666776628, 607107540, 62099363, 816641978, 404238510, 578165229, 511154420, 699666045, 50475310, 287939463, 925402908, 930411224, 556872292, 154714314, 483158701, 809689799, 368277164, 892582417, 209879291, 445510144, 112288124, 967913344, 992731331, 719977257, 455698792, 527455107, 998260095, 434173579, 717408542, 3553366, 476415991, 866829227, 388087087, 606337510, 232304484, 41288804, 309605426, 259758858, 920829153, 583941759, 140061947, 830357886, 484741525, 726783028, 931432179, 504980288, 875503195, 706532816, 775250383, 542974801, 508217386, 315379500, 486561898, 986992870, 591345832, 204030418, 257246579, 260037767, 125426785, 535235329, 414517724, 632091922, 52736211, 922567887, 946616659, 985931713, 925767054, 509371013, 795773105, 103792450, 806744472, 167115485, 225868553, 852772742, 18176706, 643025727, 805365970, 514403166, 657021082, 323766526, 240504385, 852024678, 455363364, 533614315, 785726184, 450587115, 323186084, 934192486, 331336050, 195686346, 847836359, 433887708, 898870869, 682198871, 504819224, 438063632, 525341138, 319969397, 59278010, 663618993, 498934780, 250910775, 419504118, 429884369, 409732941, 728612206, 534970479, 928528740, 315822563, 343944225, 160454594, 985484216, 4957398, 105048403, 677999365, 924283282, 826458609, 946862428, 199687309, 499715638, 196748821, 601593515, 597168580, 199350049, 67952900, 80461352, 478900352, 764682579, 233795753, 219616446, 198866030, 604697917, 285910882, 196530291, 581238390, 382400823, 348705847, 687237492, 121159935, 988873940, 616934745, 394182060, 360292548, 499192546, 267525845, 730424624, 688405419, 81478263, 784170995, 657478738, 816615942, 277950279, 984492262, 622260693, 425197168, 753231425, 601266138, 809178637, 330895631, 342901031, 552449080, 239129720, 628606772, 574035888, 543821592, 710735023, 681217739, 237854902, 322906790, 893243884, 334426622, 204833898, 311361059, 475205058, 732704706, 819236925, 394964942, 588963582, 168284042, 625309286, 169737944, 710472905, 513747030, 723857031, 506470250, 132007263, 627273703, 438605545, 986600443, 188731166, 833352272, 976055566, 181351250, 129068228, 719954090, 995653522, 280007043, 673059458, 367457754, 965309499, 330721773, 519976409, 391501059, 283409717, 778064976, 87523282, 651589363, 162877232, 212403798, 471432235, 797941385, 509576886, 980134855, 449438299, 804203009, 400623873, 867719960, 644549007, 246828501, 553239327, 137228733, 714914537, 431556715, 397402717, 725098653, 703997259, 511581055, 25566127, 481302358, 547986320, 143148453, 775889472, 770447099, 870802989, 457298786, 456183616, 545749511, 604051305, 904258724, 401300497, 593196690, 361472588, 98580695, 44982397, 551973427, 173035553, 565594233, 497936321, 835248475, 267988046, 897745268, 5522516, 878568263, 645160046, 871055226, 483265849, 795155136, 187182188, 49499298, 94209540, 872470722, 765875885, 766341998, 754081973, 802314837, 441885373, 989642817, 794262890, 846342939, 118487754, 886773008, 893469070, 740899020, 568398618, 501329616, 909429047, 696821034, 737222709, 530953401, 93931739, 179970624, 210973390, 189144407, 657141682, 213568773, 645484612, 288098738, 501481638, 463574122, 950870922, 216270816, 748438347, 637168460, 179506064, 849591456, 865071841, 444544194, 233876178, 373393866, 451952288, 614848441, 569397219, 537537966, 10334084, 506043769, 62613502, 301966764, 499017348, 162947065, 287699775, 568039966, 604922095, 623219799, 108885356, 723352579, 489326321, 318097094, 612941240, 565777449, 767823211, 892272376, 827516949, 352082912, 390931169, 50315197, 993665717, 75342506, 672538065, 241834589, 220133742, 688793177, 578672458, 549469164, 457616160, 562116403, 98061720, 853690477, 683295810, 145294305, 702268756, 575339440, 339390135, 141945503, 282533207, 746103065, 477229643, 432043348, 932618034, 581014864, 910916356, 692467416, 488553471, 525607261, 146014379, 520586341, 979184414, 920560030, 50704646, 62970132, 14483452, 490414033, 390602982, 464087267, 463560487, 255623946, 89561864, 111684445, 636722512, 601976932, 852406472, 265914250, 854151810, 260333301, 152862176, 497825349, 587641229, 636345200, 673178927, 815333468, 692522670, 823057408, 536026404, 376720422, 486980778, 12765888, 624703671, 859814599, 962007755, 926563431, 883777908, 357369960, 111671243, 715112335, 478505186, 135135289, 222940670, 4377124, 711527916, 874523645, 873441167, 915692982, 383328348, 299870011, 78552449, 910990795, 887121282, 912488622, 92285225, 404355989, 11255535, 659225227, 617252824, 295694721, 682951044, 233203113, 147324642, 797370711, 739903604, 314528958, 111146210, 686723978, 175481913, 108253166, 348817432, 225951879, 532920139, 941772516, 656586962, 244082833, 745352817, 724514203, 984280569, 429540574, 948213483, 309501419, 776100564, 898523527, 175381961, 757443792, 340191979, 421593991, 950547724, 810513877, 308793068, 402049689, 722103241, 143867875, 898250350, 563264136, 287087697, 17995717, 353454648, 519345063, 17527446, 698196886, 216163593, 547804970, 306784824, 486667212, 687014226, 215538577, 866323652, 867040676, 636559264, 526987164, 868058854, 211849870, 600433605, 143998321, 306069697, 680822898, 484682658, 595812755, 411845773, 711204718, 858836724, 362022883, 48310969, 411338859, 854394918, 134301551, 813883406, 789728192, 802881701, 319826732, 71529230, 283079935, 852478052, 801991059, 187315340, 334250685, 955137791, 510923108, 528458461, 132884391, 427279928, 684516807, 589750407, 430111940, 17173246, 216757396, 616770348, 117082800, 862828128, 22185614, 476647369, 396687520, 847274919, 733781206, 140237489, 488287850, 355665962, 337078015, 402149994, 731767041, 437035999, 904589296, 672029077, 78373417, 570504372, 679948844, 112606309, 868057622, 27607822, 620692684, 865800881, 694579658, 325432721, 809991374, 719531470, 770974370, 420194844, 630792265, 153513850, 652864223, 32260842, 766955235, 974268092, 403778590, 920852774, 156758716, 860768952, 84076455, 470672322, 341680738, 390562623, 299398508, 234470479, 328209390, 315778501, 8284869, 818400248, 125311922, 857557178, 69291790, 893345498, 338711711, 845302750, 467437454, 370216649, 96343621, 689534384, 956479618, 257307530, 208385437, 701273021, 783427641, 361705330, 709815547, 676054625, 298176321, 379401208, 178382230, 302399559, 699390014, 304132822, 127376275, 428932655, 691530810, 572069597, 531034485, 943514738, 14506368, 504042963, 362505206, 986616579, 653658081, 516092491, 686962191, 212546635, 690967983, 603822983, 134730877, 258162253, 168714956, 352157330, 115887991, 851922581, 558057227, 160988271, 470910148, 826361136, 91756980, 794729498, 444679927, 659588227, 916353154, 433632756, 402887369, 442506721, 291073415, 471722130, 727118888, 122336204, 981994701, 521235209, 486912191, 456326070, 611898212, 911527390, 881548491, 320586492, 965902566, 312906114, 907725787, 255464130, 495417748, 687209764, 545805621, 280464575, 863123794, 118550253, 614402508, 973322736, 106529759, 790419119, 643103798, 373953222, 163193438, 526382510, 829592756, 403861206, 969504418, 709085221, 29610859, 814046943, 98252929, 397744083, 286918846, 305802809, 273252343, 559049211, 294611383, 538310418, 803575513, 768553024, 424785131, 487154716, 737446380, 686784806, 570258974, 960929871, 573229065, 875422190, 113859065, 589995042, 56187851, 494955530, 634363494, 454743078, 127422139, 457546695, 212138648, 57124387, 36638337, 915530917, 819941438, 538982770, 258230354, 811503710, 519101850, 431195848, 437411073, 702946888, 785760504, 662240458, 263022045, 393673486, 900924935, 222482011, 641455569, 66170907, 87457175, 705787735, 525358193, 895099618, 377159762, 559994580, 170665236, 404260182, 862847144, 689184494, 765446685, 347297166, 788328323, 478798341, 830412541, 939789903, 235871568, 474138325, 452106602, 619377584, 105734789, 955132303, 885268226, 863489609, 17679305, 990433948, 519793632, 567958288, 327840505, 165090896, 75395523, 572076116, 765701417, 363207573, 812915345, 964527429, 211522962, 630845288, 955698303, 369758503, 56487975, 179511963, 96427289, 944784602, 62866955, 751605809, 382964726, 727138686, 400542492, 148668631, 903026029, 254559576, 20988254, 543307355, 289671475, 986006108, 605164326, 728951318, 407475560, 338867590, 688178225, 536955746, 972492746, 530867659, 175044432, 971521414, 828223828, 772395949, 740097932, 653681431, 140871735, 889105862, 137593842, 495301590, 376785782, 249670867, 576878442, 347681384, 463255965, 996808968, 323449646, 903469097, 828862288, 979887646, 385346111, 152998318, 403978145, 887086944, 32134138, 655404847, 340411527, 206132327, 595500447, 133371962, 625722426, 959339813, 851808368, 724890538, 985324735, 110644048, 988045115, 743880778, 332769251, 948803772, 231499463, 415240178, 876872382, 673822092, 883664317, 286048049, 105004235, 191555513, 175933566, 884876900, 69236631, 868728223, 843412636, 20167985, 970311204, 822134375, 566899919, 616800210, 918519884, 343619732, 191277153, 870567842, 243849649, 859993663, 67785049, 598639212, 338266742, 968526549, 32286732, 611891169, 653154275, 705874265, 722061644, 937677432, 288804301, 717342363, 728049715, 343473517, 600801769, 821848501, 617288936, 656700787, 629720432, 146768180, 61227969, 508519312, 174138054, 195074984, 652254374, 751082854, 368806582, 14733081, 11376061, 106062279, 835564688, 571715772, 708740937, 598687094, 330435117, 116478412, 16870818, 420033529, 230248642, 339845466, 93610505, 633019972, 942031803, 834933012, 948058474, 504635763, 63823879, 42386296, 181541845, 516438228, 359445909, 482227217, 319861405, 116838340, 317505584, 880371112, 412077055, 135956303, 965535236, 448012325, 518814069, 539035765, 497693896, 817924649, 729610170, 575471110, 204354064, 95000865, 949380790, 908408077, 622296998, 359476817, 566400742, 155518186, 511779844, 88537503, 531022202, 341056995, 142570978, 795302968, 244192320, 289522781, 862636943, 968950927, 361411759, 557206956, 59623506, 688136757, 767178622, 790517827, 346485507, 688685156, 48326731, 176000149, 683619327, 378338430, 757076332, 338841571, 536772634, 256124899, 461931202, 116956627, 305888586, 168602525, 648731225, 688949906, 891414848, 486292160, 460330652, 672033388, 380190809, 5212010, 396072008, 624422055, 365996484, 611652094, 506873921, 243993924, 177653037, 386249628, 641177513, 497777055, 533619912, 175628284, 432130561, 529610359, 196337125, 614929424, 729745702, 873575104, 965802508, 50686493, 584143741, 296859373, 689810545, 519834154, 44048793, 384804807, 578907658, 253097668, 177423203, 720312567, 488435753, 472809253, 388427653, 721018002, 856418697, 657050789, 551212863, 756809582, 60363766, 494687132, 908774593, 23023072, 715178397, 521163589, 152693608, 592880012, 609302843, 843866109, 680498623, 885913155, 685255232, 33470829, 763713391, 404781916, 952233915, 734839416, 274075552, 135765931, 250595673, 56260886, 602887396, 955051684, 144155694, 510669753, 430165497, 15867679, 105242273, 512902082, 912400439, 746365510, 594339156, 931007273, 382645415, 596553012, 823865899, 680647654, 935542071, 782581906, 217038036, 208076423, 743723214, 81408054, 914777371, 914746710, 699402920, 360177412, 185199933, 921541999, 971925049, 643994194, 163273339, 55693563, 783013899, 205556682, 157594461, 22568344, 252620795, 399909357, 341996418, 729133825, 341380872, 324359611, 890579651, 436637730, 188055082, 472523572, 147882890, 607749577, 70360001, 356630443, 413219872, 693540009, 801781081, 688402909, 578276627, 749662349, 289468626, 991368111, 463139560, 67291639, 187466699, 718576309, 190016444, 249976366, 608072814, 128656484, 911723912, 62340238, 232719248, 299141515, 484198122, 103244194, 169534556, 646783856, 532455977, 514968246, 760982380, 362598310, 392580988, 520990434, 943039788, 186925998, 436709995, 161662698, 77601039, 12520443, 287456986, 99139220, 321908207, 293161929, 570729596, 845149288, 724216989, 323305259, 81778969, 754618499, 223026426, 592386543, 237641598, 59183885, 63057800, 70436997, 41998739, 713066124, 993899162, 993025832, 142821997, 78597955, 544524262, 984337859, 999312384, 201137530, 822648402, 243522321, 93395057, 469325970, 451121481, 295197662, 743048109, 682857763, 645534988, 489264762, 52012038, 349730365, 696838597, 814546239, 369407316, 949588760, 469659919, 456183405, 297851125, 746292543, 511198774, 486648895, 362201741, 935291618, 147659215, 797617219, 403640868, 689719974, 795433607, 601503003, 219726869, 46379817, 867469122, 820543534, 896932578, 684975592, 672655569, 415040938, 5634577, 237295759, 711415746, 390767176, 596327779, 198810965, 133533937, 240927166, 12691822, 832289067, 260364155, 590367924, 463437292, 210035861, 733876423, 4087228, 858672689, 41975622, 16241087, 217627447, 562674480, 858471283, 23519893, 216342938, 149149400, 326271196, 780941242, 123610810, 138661692, 798244656, 881707355, 620459588, 312273718, 725135331, 364957886, 611526140, 469880021, 732949285, 722575143, 260183540, 640611629, 748698185, 687618939, 958384584, 10721503, 127458593, 698378155, 65271164, 992318158, 373061043, 630174960, 230588317, 770511545, 917732004, 136553615, 206614917, 762586089, 626252755, 203416811, 672476834, 714290250, 716688860, 21528456, 551433909, 901967806, 878464671, 423643365, 380579615, 890294872, 418569069, 167541974, 953371882, 989123896, 937047718, 811947704, 162799928, 885833717, 523694305, 240134292, 937123236, 97345008, 153366253, 251054667, 43547875, 567352772, 214318168, 214344314, 338774374, 692726836, 415163727, 811885441, 881681686, 586356394, 253988992, 345480314, 578354316, 341009642, 157312428, 795862560, 949084001, 897431518, 206433358, 531577816, 460892076, 634561056, 251441784, 325512376, 363425570, 595793292, 738200620, 57616896, 347223207, 152007222, 276678533, 265811940, 768057011, 624574149, 123704128, 767711441, 955606020, 979909465, 706181602, 562547484, 998665682, 382882695, 962400543, 76799608, 243263036, 370847163, 389383807, 259989153, 361267025, 580099383, 412870862, 183884755, 391392544, 998560484, 179833358, 245822555, 655303516, 380808758, 853036220, 389099322, 582975316, 879384508, 702877981, 778508699, 748703480, 246462192, 971954762, 220157498, 273052480, 354622498, 768749990, 855915661, 323129850, 826110690, 219638450, 644226842, 92887257, 739935681, 136160120, 695758149, 172491520, 187506969, 51488652, 228773762, 366552032, 713958970, 630247144, 636937008, 620284215, 548781882, 889125101, 452705197, 303906138, 206327612, 393559126, 698486447, 651142238, 511515785, 580206870, 471214175, 810733672, 81475292, 349828852, 56137421, 137095032, 530821375, 792800903, 668885109, 206395950, 236451066, 337386317, 528092245, 576831540, 429845487, 781940837, 160752925, 403546836, 896349518, 144010761, 409852701, 372188498, 431418006, 57037901, 135682137, 132832935, 226324524, 854066227, 196965739, 620995587, 553782715, 931319523, 460574194, 138941785, 139787427, 352992927, 516805781, 415732107, 810192161, 346135673, 591073547, 865107033, 441940121, 371732568, 307193399, 402956734, 413006413, 238023474, 512855680, 423835787, 237273425, 261600122, 67717536, 337112868, 488708166, 335259710, 989853839, 316556454, 430394695, 823697937, 82722599, 666870210, 547047592, 387110726, 276882828, 514373656, 532754833, 762024526, 187163779, 931914996, 624745620, 769907171, 300349063, 918523306, 791724590, 16372814, 46553008, 992673908, 945716518, 364543968, 172141630, 281164996, 231507881, 665766090, 132645181, 495210176, 861463658, 744196856, 30447188, 754512506, 923351906, 610903491, 524895056, 83181664, 691423437, 302662157, 835063539, 681530151, 297905198, 983500928, 952558539, 473421748, 16623792, 326086370, 853132751, 503860761, 52661022, 136702494, 829697510, 444404580, 926631525, 787689964, 138193897, 352461586, 297151291, 45686118, 539970124, 435075224, 870385752, 822298761, 444791617, 777803929, 774330583, 485932035, 469013716, 819297436, 383530579, 184209506, 822779381, 402315987, 573232417, 852569600, 667279800, 102271379, 625463122, 552592771, 316148268, 866722913, 175520760, 989166980, 768114968, 302436637, 920130797, 568107821, 594924261, 84061404, 417852594, 912345459, 900202816, 616383566, 551109261, 118129305, 177444976, 668485058, 616844570, 807255864, 803862599, 505819033, 654764279, 682613676, 22388131, 849089025, 891645189, 350870383, 510537666, 817416267, 300323004, 580415585, 580693824, 427563279, 575630909, 452566390, 545541482, 733274241, 76946743, 130437522, 137609965, 483398787, 405621868, 892963915, 549078402, 446209830, 752805800, 407821467, 403991650, 531006513, 737531971, 733068415, 202071562, 904131646, 495776856, 479458180, 317028505, 949708666, 191223181, 620742628, 82416356, 985888000, 258370175, 808764909, 50037103, 975654447, 887360227, 589121866, 36121950, 332640906, 218801638, 202029859, 679471671, 675773387, 669153522, 382242437, 351433480, 249081381, 763746214, 827525417, 770433114, 451266748, 121842264, 19082587, 94964227, 311273051, 125803954, 235185790, 49340497, 430115685, 547785293, 572736071, 448352643, 981985209, 869402513, 183507989, 10849465, 931186049, 833864999, 301967638, 522328291, 506318562, 398796891, 115105830, 865862866, 419123268, 887355951, 284284590, 536220195, 455205834, 621696454, 186849798, 251762710, 239446578, 988093590, 418884317, 43604358, 385844617, 112449853, 361303332, 946509698, 919044453, 878953309, 250245201, 319040226, 155578585, 15866198, 233269510, 635818851, 830141245, 690645483, 312750318, 530822850, 17871006, 847297339, 238896295, 855817151, 465598465, 206308967, 878634554, 795352989, 464027631, 313398918, 953709164, 729179298, 760198737, 185651425, 718060649, 383364579, 183244042, 197028405, 610811487, 606683109, 186180402, 424897669, 910884752, 674143637, 104199005, 312095756, 531561965, 412255855, 770180362, 814799498, 136567258, 708259474, 395811933, 29435461, 815110563, 965221510, 63575061, 579873963, 491901057, 737405321, 489041499, 98085475, 578578337, 373107425, 841621660, 307426833, 843951463, 878290279, 159667530, 307552089, 542085922, 299717714, 362397877, 860503058, 905223826, 446223217, 804661270, 666133176, 323063974, 627146564, 719329574, 15824064, 362812055, 840290390, 431884996, 60757053, 52832681, 236386668, 372139863, 838258214, 733993774, 911422291, 420968787, 490817503, 510418180, 594386386, 506332172, 799743139, 728416900, 560256698, 740014949, 685668489, 527685926, 426229674, 369375028, 134234226, 909576483, 309610604, 149506966, 473610455, 429609691, 743449256, 428920186, 188266910, 677788176, 121260027, 415368125, 537919030, 829640329, 201432031, 782843364, 401072976, 222276325, 193356500, 536248710, 322342390, 516155195, 149316118, 224877225, 54244314, 614849325, 317293712, 61058739, 46459092, 754773871, 573229518, 506474133, 466648730, 563303256, 234944230, 387017572, 181831915, 518104459, 112950090, 425121264, 320574138, 130093652, 246360617, 252615559, 962305159, 378040787, 856650947, 782337727, 180330926, 419918827, 344839615, 939664368, 174751321, 990665727, 73895934, 866879449, 51572966, 316137394, 582959801, 985110755, 344536284, 841928643, 739941320, 963665656, 572685586, 205462291, 244020455, 593114696, 517769554, 575824462, 699587722, 37203946, 377670809, 689939758, 930911774, 297096810, 128566428, 895172349, 71061977, 412177644, 62807810, 843130035, 829342058, 28831243, 210261913, 156255478, 607023509, 703540489, 744569380, 291786642, 163645554, 803719700, 755558363, 690916324, 373495218, 818523049, 929544169, 910278440, 497902423, 150766200, 199946448, 717914135, 494060479, 564777290, 368492163, 908882470, 349779869, 480784570, 913630683, 117180994, 189675738, 401134267, 535744290, 349774838, 355390922, 968108736, 855082950, 863720895, 168465426, 772791451, 430724893, 530978639, 442084608, 417272869, 350303133, 650983802, 409864552, 513578062, 748478652, 86056825, 676537319, 770427607, 520735743, 411817472, 704317612, 753359796, 815182909, 288076616, 127278172, 498822637, 43519119, 200055446, 545605380, 627143315, 910741529, 887191360, 32318949, 644245479, 105121669, 38495891, 261663931, 922088126, 967271863, 880881784, 124222524, 928436044, 873044277, 449776860, 881779302, 215069323, 859273924, 820148838, 525055449, 649886347, 790776642, 224490123, 751323575, 515695090, 874556670, 709112548, 483465143, 596207480, 256868556, 350792315, 131294859, 221293965, 776766870, 687770349, 638347867, 175866728, 777879389, 3405367, 754466998, 729950046, 988818331, 128134441, 679019264, 265348316, 932555019, 299716276, 983908912, 483868449, 343421998, 265179310, 635251452, 583287301, 834125491, 176504873, 249006285, 825738190, 496802062, 132308885, 142668839, 552739636, 990220833, 961173017, 479039053, 95905645, 916763535, 57054960, 536416267, 644844531, 739054008, 248154246, 57190420, 408594416, 529788395, 326720016, 239287609, 830899739, 160952290, 526451521, 729945358, 429670127, 418129844, 937332824, 583181382, 535078787, 518095961, 944815385, 555720004, 265638303, 524235860, 777410382, 759768790, 963610496, 243255403, 836555278, 145305807, 43940110, 180874795, 575451331, 975054617, 738179547, 933090595, 397741026, 986263122, 701393483, 3763297, 10261463, 819407242, 541970735, 747178585, 473677033, 893383707, 96212417, 826004852, 640138567, 755917462, 861602341, 715568138, 106535222, 635879095, 593532131, 71043607, 798313182, 903231199, 206755064, 184200362, 59863850, 214808508, 919455991, 672875729, 494172693, 345239342, 816663091, 806677461, 509883150, 492022163, 258806206, 602402044, 164304608, 321426497, 882503359, 564370012, 921150344, 131034270, 942402348, 302236990, 333143328, 379160541, 945875229, 510861669, 551554190, 809343175, 816684067, 38094160, 102682534, 227973548, 776244029, 905776812, 749993363, 485362152, 229115425, 309431975, 431376216, 966093617, 59063489, 845734112, 24355725, 606285616, 937752424, 557414527, 241966512, 973605918, 836481160, 508328679, 261148443, 985355508, 963535340, 287574990, 551410315, 330541433, 916973400, 343854889, 811175524, 674821800, 484915273, 454338636, 902349231, 482824583, 492852753, 218861549, 974062051, 611255122, 790946259, 457077546, 812320436, 246102375, 217132331, 339370703, 417877848, 203120020, 657396260, 639301508, 467985171, 648313392, 533446998, 364932335, 770536038, 551648071, 445810402, 619286192, 797045796, 960531286, 404410044, 792781755, 438944387, 453340822, 894792431, 96299968, 666740027, 945993990, 273461802, 630453450, 514160401, 181059423, 867935576, 527603040, 157305088, 601267920, 179880007, 242196665, 990703817, 459251602, 637972184, 996446228, 560805799, 619197936, 297724100, 108812625, 976712024, 474357149, 491779479, 556272773, 109469696, 197193785, 230027184, 851046919, 180140355, 407727617, 893124688, 998882427, 226923725, 970290968, 86291886, 11831988, 699717384, 862388562, 316273567, 582518043, 670632983, 860289003, 428702756, 533495200, 656601297, 882992727, 663433053, 76692025, 487355887, 710900943, 11155034, 534635462, 901629098, 20675105, 473394872, 58131966, 107628632, 917558372, 679647388, 206310952, 643931277, 218019757, 843277931, 767388327, 778254437, 162190865, 319041342, 466167285, 242949261, 429813024, 391170192, 358176636, 770402848, 793788212, 896355203, 57524572, 405335498, 729463147, 958330724, 673877248, 37852572, 378063229, 840118433, 114116645, 539134658, 958443014, 264529392, 311827041, 544970811, 218927697, 867357856, 940528449, 295007410, 583189898, 230291018, 457451879, 581572128, 785666404, 437671675, 192347411, 297897570, 422869678, 716248517, 482937515, 480539262, 337602027, 261786649, 948779899, 291300904, 833216499, 728787361, 535243977, 773991569, 178813022, 21597388, 358728323, 26943955, 4965280, 516922019, 68501357, 132156001, 294690216, 17012482, 51720468, 527771280, 574048058, 128597743, 7916205, 721455242, 980134289, 709848801, 944913135, 843881092, 972211171, 353871165, 324586349, 730378566, 206587721, 956269168, 114101956, 75330456, 357914013, 999934256, 363635165, 666898211, 212095321, 512184807, 211456135, 993597531, 944668915, 902707160, 173441031, 876810326, 426260625, 844130711, 996705990, 313792965, 17147673, 217504017, 44365509, 993568615, 644231353, 274547594, 337035337, 799079311, 672947709, 668695006, 581506468, 287394315, 872396283, 532027053, 342612654, 418893796, 160779173, 858298591, 337073915, 11743219, 524102637, 599508311, 447437036, 196507541, 461111140, 462770830, 343929210, 138790217, 507793678, 853058922, 877839402, 487501050, 73414768, 949643282, 202130280, 291948430, 312531418, 187387815, 636521951, 49318853, 969223461, 167083689, 528504217, 891983533, 438687198, 786578439, 228560904, 70477992, 381284356, 675520833, 628437298, 268771147, 393198361, 95865439, 1057154, 782128273, 410919739, 574074405, 483099461, 729324767, 887982803, 248808203, 559112163, 493202679, 580155305, 91619197, 133364941, 444638650, 718719780, 97007969, 109281828, 507810890, 414358571, 65037218, 755920391, 67257541, 365961671, 2366275, 782995317, 422824875, 302021876, 280204950, 699635508, 700417420, 855461059, 886197706, 846920168, 931576520, 457788095, 591924491, 166090232, 120281579, 633329117, 893865479, 302583926, 814406385, 455134257, 212508309, 401967212, 75165658, 134729980, 583788686, 551698860, 589665167, 18095820, 527131437, 75761379, 498175469, 346278106, 61614382, 656551663, 754273456, 328138978, 887353434, 651104736, 68607246, 77806750, 834517407, 313213630, 260140872, 265491576, 835441268, 965107673, 512291340, 205866668, 369643030, 803680441, 21507215, 704502484, 131163931, 183910561, 708375741, 393130227, 738358246, 922751921, 393791608, 792555033, 359473012, 133114135, 922567568, 972136463, 47154257, 3251420, 862380984, 544894065, 776872840, 182001328, 492086616, 283704702, 298973167, 144243735, 470119952, 440690728, 353022805, 431571411, 742013977, 429262827, 639420928, 228648523, 844360954, 816775426, 148636937, 429471843, 273601308, 141602620, 672437068, 484209602, 127892344, 251040147, 177406806, 306588308, 125610039, 758611637, 323701202, 413902741, 671376557, 930099961, 5401259, 34401699, 357304725, 614311176, 584187859, 481310616, 993682879, 229009204, 576088784, 939695075, 246625860, 639570816, 913554150, 456077540, 39214490, 173528782, 304292385, 571861395, 925607337, 652702214, 545076588, 371408982, 570279131, 609393633, 765519127, 395919825, 537457060, 149843896, 41831191, 461246684, 882353130, 932343523, 292120205, 168932950, 784509633, 146022269, 386329528, 105616871, 990242213, 583497871, 437207239, 706768256, 462511660, 933794073, 494363935, 559964923, 65428555, 312275876, 873619094, 634699001, 120823637, 743521441, 417689693, 459712225, 182107553, 606714692, 296211183, 177617497, 866449253, 273993669, 70112705, 786419239, 885248801, 98366423, 536392160, 78538674, 863379799, 540477493, 977770015, 139704275, 216976224, 82126138, 509942948, 54614612, 627987791, 214004366, 993271677, 684561667, 365491497, 111541997, 531418074, 39724731, 39169842, 746510389, 84345680, 580807617, 367599750, 319035735, 633753965, 251702747, 239340343, 416603959, 989193706, 490828015, 145183851, 649339866, 996574198, 179640540, 965322344, 613554443, 666240881, 153142190, 796747372, 483695537, 887035137, 24116498, 662298495, 242956623, 584138299, 554696867, 795796236, 71512017, 511010421, 256712633, 730504081, 193359976, 232393466, 173158683, 498304049, 225514611, 233196391, 125739601, 220859050, 828288903, 858815245, 812489542, 102091805, 412254633, 540688430, 825160836, 826839116, 222369344, 100935737, 52749636, 47254658, 761579905, 551784865, 378619924, 674000867, 759138753, 56131620, 40644627, 416845334, 235088822, 913353638, 621232021, 376739569, 226665378, 660468345, 990847220, 552038730, 671585019, 191458206, 751700009, 883496552, 881252904, 649019471, 356348369, 495927593, 76248820, 738842884, 42208421, 668032417, 487475186, 555993391, 316365250, 192461456, 134326075, 751534583, 331481216, 771676560, 389584201, 479511498, 642417667, 79304700, 26483960, 59170511, 170534817, 616785971, 395745210, 873888843, 239457942, 978010683, 240642637, 978703233, 521958896, 403003937, 483677252, 738476121, 371795990, 449011198, 326580048, 763958513, 801321389, 177070792, 753927701, 700456958, 544421476, 4312729, 947797525, 216826065, 585082993, 399417192, 638124834, 343548888, 378330467, 327150943, 511935325, 731246250, 609077821, 947575044, 842648306, 952457501, 562352595, 308005208, 206121883, 366092434, 536023785, 274726165, 882335522, 280758726, 621169770, 11752707, 849509568, 213483700, 449667262, 73325708, 798426524, 276565918, 724302835, 115824360, 718114560, 158390574, 168940401, 272822518, 184602995, 54877843, 25686120, 939011248, 944605446, 798726889, 752899273, 353776395, 793019267, 94275670, 794706361, 311095379, 175675634, 329077959, 814186964, 481415979, 777022138, 545509927, 636367415, 495024486, 103661066, 488669867, 875994516, 529672610, 89858257, 854039423, 764901304, 502063923, 412258334, 82670317, 694062221, 960213641, 838529369, 681506019, 912126870, 496755841, 521927835, 839218222, 362888145, 794785419, 248375545, 466533919, 26355798, 377658009, 325034082, 590105091, 122023251, 874446667, 907625271, 26633538, 314318683, 965773211, 142035905, 985507628, 719298376, 545882775, 879418849, 833792117, 891491492, 743307570, 435657742, 278037278, 454274288, 521157073, 475361270, 43065087, 935270563, 126580430, 694062962, 146510504, 461570429, 68581528, 513680711, 168482906, 298683860, 364788323, 976792721, 291841178, 281545245, 716775932, 600492453, 600388829, 323728180, 81232686, 234229341, 859318664, 107044398, 102278609, 838761075, 533646085, 64578476, 567978627, 382691120, 369939335, 499765595, 329221502, 870964837, 753593289, 966734901, 904929647, 637315873, 693098821, 897971952, 337978640, 830225009, 591585372, 851764723, 937570741, 738683715, 834967185, 893039675, 342686592, 237519291, 683965484, 64242235, 355690827, 252688760, 418373630, 158654035, 896175380, 777199846, 138416530, 594442963, 75960729, 48661646, 666113620, 812716172, 466320162, 447673683, 316075267, 888360350, 86098211, 291065549, 208903086, 913032308, 82380889, 565456543, 448439948, 924341552, 3783694, 366451422, 240649069, 580640082, 795362686, 517523295, 968304623, 224111449, 717196993, 477437850, 545800583, 877672806, 151051688, 453014128, 996990775, 672825196, 326849710, 313311309, 961653888, 406180750, 443105475, 937392466, 934561735, 327999122, 732264422, 854651471, 52511365, 303334390, 874962458, 586916265, 754756450, 285093173, 100797476, 989944597, 545681869, 292495705, 839267763, 768589764, 703461326, 407158267, 644049620, 489545495, 300193298, 395383073, 343097956, 306917429, 577737441, 256181862, 232330266, 97052323, 910724228, 124463285, 76757493, 211454580, 738271875, 284355279, 762891019, 958701983, 436832809, 689127674, 733222304, 909304694, 884181147, 423819009, 419463339, 657433001, 245995486, 811201572, 452148253, 686753754, 699046591, 633824532, 489879671, 619476601, 574677550, 28023207, 335253071, 967618809, 609967326, 90562712, 37674522, 781476895, 209986008, 516746426, 910967209, 371664750, 290556536, 950820364, 951746187, 237308027, 29614686, 810243788, 955978009, 112952406, 361156729, 327815525, 876899748, 168541317, 405716106, 49275582, 3977623, 149336839, 146928152, 558011911, 126379667, 117201830, 784439228, 658566346, 755529989, 433513739, 430821914, 362337130, 605874289, 443005737, 718551810, 849731596, 252199690, 418333065, 500171676, 392619488, 902991135, 424449546, 355097840, 532210000, 140120340, 877245695, 130353559, 729717802, 325691206, 605199083, 379700980, 447028649, 442001441, 891860326, 115672579, 804493335, 136193132, 506765011, 405817376, 174807425, 563392417, 227832234, 569109134, 152286501, 843352333, 716316861, 412436129, 217754711, 327204182, 504968866, 415547101, 74321215, 219655360, 593697781, 256141683, 881804787, 721759943, 692407249, 327187892, 216362553, 506950007, 443297739, 276700591, 32682379, 726353180, 385529236, 558928031, 532053107, 33362290, 947629229, 669227120, 790004853, 500937981, 244581576, 598467183, 800724695, 468640246, 902416443, 163615999, 660131507, 370859619, 955330215, 918003585, 629812907, 336274652, 282605980, 980693615, 161538478, 517019223, 120741008, 2155947, 604531212, 220673231, 44357718, 900348585, 548779378, 251052947, 776279058, 598013317, 875363651, 301424480, 490556546, 563875445, 425885885, 593311574, 787515183, 883003008, 899990082, 162654291, 417453740, 78011706, 662034826, 794464594, 769292309, 907109406, 455042183, 955784055, 322871614, 970580692, 157865156, 942972597, 500788065, 849100938, 24164932, 672357794, 161244472, 302736730, 511042222, 834595518, 752436221, 170845888, 821573939, 124044016, 988048683, 237075368, 856435334, 690972617, 91988808, 489142439, 157197489, 855545483, 941993995, 701161598, 854073240, 261967644, 183027451, 15680614, 702666788, 965578221, 316752936, 891758886, 539919335, 64598349, 753271485, 28018153, 751541328, 203033986, 810824949, 7861442, 71486300, 203120977, 662674538, 516051304, 64131963, 415643581, 305187909, 767174642, 885805663, 945273946, 401886776, 762677353, 93340766, 34574003, 931346548, 822086315, 517955872, 479160442, 177436663, 262705427, 914973144, 696603633, 679379628, 567624160, 300996623, 448730106, 908022364, 150660198, 267491699, 22112522, 163086859, 300978555, 411016347, 508276033, 234653812, 997103463, 235601174, 616465143, 457941338, 929935948, 677870880, 825985699, 51254773, 983640749, 61725604, 641904773, 686394530, 844627829, 658297655, 374848963, 382144660, 94797583, 56282033, 514158506, 378310271, 878299401, 35729000, 671897872, 103049007, 977740107, 12090271, 523616887, 379801085, 769939843, 95518538, 955705110, 10597554, 755883736, 812932258, 425381601, 956532358, 980019378, 810672566, 225973597, 698126216, 82485749, 676734696, 866518367, 524356105, 176266590, 647469175, 933247782, 619199895, 907814843, 315077063, 661853405, 677563002, 206343326, 69262713, 132593623, 986157109, 497449108, 78306211, 631132748, 103324766, 668329655, 358382778, 823630127, 399573298, 890394498, 506229536, 207767788, 159248559, 44864407, 531210081, 238717823, 688100539, 61961808, 157089708, 849327143, 70053588, 207286459, 559462514, 456122195, 155386010, 744072595, 821260421, 961044703, 845142580, 830423159, 873604978, 46128058, 584991255, 204786374, 333023100, 654899213, 26582028, 847720596, 899716277, 475031541, 390056726, 639149332, 897422877, 182311091, 104277161, 256513005, 98658570, 615777575, 981839194, 368779137, 35553231, 938527662, 551268513, 292121004, 301849625, 738338411, 671468942, 338583186, 34969111, 58835094, 638751651, 605347779, 484379916, 816242549, 4681668, 149375076, 139439598, 666777115, 758628, 274386531, 67869381, 525068995, 996990448, 395599494, 196250339, 320556412, 596847936, 681893891, 617736091, 345573636, 843804812, 229821092, 701066034, 871464767, 630624231, 309512167, 752772320, 287693968, 558906117, 163052581, 811854958, 337280211, 877254270, 454481584, 962573776, 820142142, 932565919, 670000038, 65384320, 711845062, 544839951, 777732817, 573974762, 625869581, 936135612, 71656039, 976409758, 694405267, 24136567, 989902556, 455618568, 818642864, 576115098, 723647534, 906564052, 341405053, 144318003, 557084568, 468847063, 735212389, 123490918, 102168319, 788046874, 836644148, 63029311, 263565316, 630104425, 355188250, 797699018, 60138454, 402828309, 838705344, 600851180, 848889292, 950544997, 670108001, 330829853, 596523344, 967491387, 181226580, 993739933, 305935142, 516577536, 611412749, 337219887, 399113073, 799972482, 263503980, 182513162, 122918646, 563542572, 849397568, 659012143, 282305453, 910891451, 887833981, 774045448, 977164473, 348031559, 273239927, 688668595, 746642136, 120320496, 420069973, 967965059, 891503362, 481863805, 194370296, 927079235, 665816158, 439690874, 784472224, 89012472, 55099849, 536481419, 883003470, 717298223, 914312867, 990573170, 794525181, 580122670, 174923147, 119481907, 540912716, 873580131, 704842291, 498323872, 714008303, 364444509, 256084379, 476590845, 822137126, 69688683, 246895368, 449757010, 465286050, 296162018, 880329402, 978114368, 208775501, 353726938, 308174914, 977232878, 701126331, 939659250, 698447507, 983491002, 2978063, 52685793, 170672905, 183554048, 867823711, 563564876, 761269260, 997623095, 574103220, 583409091, 473909261, 947830876, 568505007, 501716958, 947139579, 197879379, 290072554, 281819993, 923369546, 73600496, 572205516, 385715795, 772833305, 915773505, 270952107, 652918209, 784277871, 360333921, 518518146, 360327076, 719554801, 116114921, 553045146, 636255975, 860517994, 176907883, 670435627, 327689483, 434777156, 805520939, 612228928, 324694521, 746512196, 888048108, 57434976, 792136763, 589855188, 473843001, 110993575, 36912439, 374946486, 185861314, 62587891, 892314872, 720361645, 621214196, 879567730, 547173014, 848442152, 599641235, 175829289, 496128927, 97141593, 272002147, 58529925, 43864872, 743780363, 787856053, 401756113, 548804945, 895820813, 242135714, 532858682, 922278399, 978550505, 285614453, 322828386, 612591435, 702939392, 391343097, 271004681, 150875091, 488050086, 687940841, 390206022, 271621142, 652451806, 769209410, 889685040, 646260751, 200047625, 152924460, 822376515, 337494597, 565493563, 647369914, 459089722, 143722520, 977294343, 808445205, 373235007, 766547785, 618259811, 43547801, 265416414, 562224371, 522298590, 202859748, 638630525, 704247193, 763810734, 643365034, 993624121, 836970594, 564071418, 239022053, 630900554, 692279201, 136892568, 413869248, 137182431, 440857704, 422935717, 706398500, 175105105, 869692520, 48134677, 24950454, 384850410, 823799778, 150546329, 90541576, 652381333, 725447829, 363944926, 170949597, 228622821, 221136553, 979929871, 552867767, 175734523, 672416253, 718778947, 346926847, 801454607, 505976620, 912098747, 998932730, 248924580, 169678209, 944640737, 171584081, 680617733, 600952973, 913133208, 175859428, 663598797, 11359155, 445441409, 415671368, 620875253, 887427348, 587715702, 604084247, 811010464, 774832099, 331475568, 542988401, 393875931, 251148967, 893024497, 992148840, 566384958, 920795715, 546297231, 416787314, 928446066, 248356412, 97971857, 715315094, 577044446, 607348937, 123833895, 620437714, 48384119, 698665277, 550383369, 857768415, 201293938, 106070997, 867662714, 252916728, 327559457, 74751242, 346977655, 556412886, 451691761, 196910516, 177534701, 721451961, 53089762, 153673317, 782172867, 573986017, 276621023, 981598428, 96235478, 510524782, 317756722, 372066387, 635888911, 767058363, 367211146, 953081702, 908951234, 860169764, 268485962, 743757486, 455682483, 47212712, 186569539, 214896351, 473992048, 366531878, 818145278, 363689916, 465524563, 119813883, 800172786, 677544661, 854224083, 670753652, 728535540, 896456264, 783144475, 876354666, 196006773, 272106858, 466035869, 827372079, 366469169, 124628748, 655131005, 273361254, 251028170, 955541808, 530717973, 365127600, 710694821, 190926311, 464477497, 884136952, 167671157, 324446201, 863075982, 133920055, 142453117, 227179477, 298345618, 840306778, 964142682, 566695688, 974057968, 116095622, 677610367, 694869085, 967391756, 698263917, 814627100, 601258338, 892747988, 947003186, 943819092, 119989922, 45969173, 602017507, 185144137, 690878319, 607852730, 179495131, 89164517, 279085628, 152928239, 425217198, 332092404, 502067071, 769484884, 464968273, 492333671, 564817241, 983050188, 579156183, 363572255, 318590667, 491504021, 289013306, 403945225, 851426985, 820410679, 206558349, 285721686, 173043853, 519834486, 533848836, 35540043, 605813369, 275356535, 607776831, 349179541, 121403700, 247183213, 200911145, 693589842, 649123772, 12228517, 433366393, 808307778, 784428604, 275440188, 780531955, 525152223, 615044243, 111118806, 731548545, 289994865, 538268178, 780244150, 849317443, 357606335, 751313775, 645776498, 530898317, 176863882, 614914788, 880915394, 678613604, 599706684, 529574067, 668780686, 2038532, 258946321, 202785523, 322774777, 240606855, 873238505, 160043500, 299769176, 719100711, 891521510, 921836984, 888399857, 612387272, 652407500, 49541996, 590852341, 301284191, 801038714, 665369413, 378802874, 927380471, 573319627, 962656003, 439751003, 304265160, 826460474, 87781173, 703040396, 410578319, 100340741, 603752197, 511108267, 445519034, 366914975, 484394474, 860009617, 553869939, 283113134, 106219325, 961218644, 346657413, 343314531, 964895036, 839720511, 803456867, 242297075, 340247985, 285450645, 746815050, 217170837, 242289322, 445341734, 92857177, 389104894, 215205667, 757864724, 867604162, 27000529, 306410242, 828530027, 714588258, 90948507, 998284154, 29614015, 64434165, 34137408, 424174077, 268369772, 778600105, 777760001, 501612432, 204867466, 311581866, 955688334, 862759113, 729057345, 701276410, 687074683, 942395183, 86030651, 436011956, 469162487, 243841682, 727271542, 901441651, 614804952, 22918218, 559123670, 756825901, 682545042, 675713904, 442162146, 952112516, 187529634, 330357595, 574123083, 603480065, 684659476, 813153120, 496672715, 266019474, 738355233, 720087822, 440427857, 248360261, 245786600, 549726063, 999809305, 227380888, 882567142, 206266839, 454336167, 330111527, 40895734, 229400017, 505927451, 195985564, 591756545, 968987240, 50522715, 567623662, 272093663, 330105329, 677733598, 736258013, 356753823, 906831023, 980728036, 71371235, 541137082, 757551697, 614290699, 543795501, 451396529, 656257790, 901638090, 614344970, 706501303, 463049987, 525550545, 580514543, 918300584, 459327622, 103793946, 613078519, 379342043, 432183220, 584275458, 359305590, 761054859, 277592189, 638404153, 270473493, 987987036, 778926136, 205979216, 863260090, 713155453, 841578419, 815056844, 39132983, 857072491, 906133406, 909036047, 908592756, 101331187, 554053196, 442017785, 866790569, 217139330, 585729767, 222526781, 576657696, 331930330, 688037751, 242238637, 563659961, 160948270, 520109181, 431429880, 703721198, 890385613, 253267385, 946646429, 34472911, 285564891, 426872200, 619768817, 386002605, 233834356, 88312497, 802938274, 650236708, 505694001, 334500219, 343749648, 70084423, 544578777, 269493061, 600222000, 164928972, 434317292, 642122122, 320016066, 328491088, 384688204, 76110218, 938522780, 593735588, 134003457, 299585518, 697646752, 593482905, 849870374, 741865711, 954788066, 668908909, 409690417, 54893977, 331325980, 723864624, 925877701, 356051434, 938929998, 810336263, 456802487, 471295762, 92008725, 271186502, 56792628, 453491091, 188318989, 432696749, 512207901, 191956206, 342262897, 229626989, 478231210, 912995671, 840555379, 970044133, 831248055, 907157053, 524807210, 58316676, 144384090, 109017709, 126833871, 190978953, 813392121, 484155797, 32126607, 258848292, 589890572, 948794452, 504753524, 209933463, 501400089, 61223244, 842919598, 707804062, 894597842, 344515613, 63633775, 818894066, 398092523, 276264928, 373482990, 861045521, 310157203, 651291442, 816780780, 529691634, 878764291, 47091325, 659097212, 65525168, 474219007, 654446225, 438380172, 173690312, 483356684, 241484586, 807494863, 377156126, 431297590, 504275472, 628727506, 374963859, 695835234, 189275672, 482623691, 346083749, 134275585, 878799399, 67252396, 699549087, 278179337, 833347865, 164346754, 757505827, 758395422, 532495546, 322524280, 870783333, 798355727, 14928710, 556635882, 610022967, 669665036, 846874202, 63637348, 170118101, 839360255, 468139035, 881260332, 572151274, 679297757, 741223544, 448207130, 527414633, 632610501, 800970727, 44085127, 431836565, 384291914, 769974323, 319194318, 144532869, 634991305, 388511992, 959780625, 475083231, 345364475, 386168482, 868064225, 557405953, 608510371, 266157695, 108061505, 859920700, 643585972, 48404890, 611193381, 30127933, 391482702, 261138645, 842744554, 949010350, 625195128, 756841966, 726307136, 358513980, 781686676, 582477106, 220668945, 78018916, 110610756, 115775739, 949428419, 517203953, 235933190, 413925922, 149757917, 884482915, 620135747, 603845824, 443645384, 598603555, 19819667, 731461067, 595190033, 47866575, 784579758, 359374886, 792741619, 149651119, 621667192, 696222826, 958722709, 324287860, 924223903, 191076609, 640339874, 214972979, 479277995, 490999297, 675078648, 658884735, 76573929, 392731770, 189908586, 849741894, 198052578, 691540520, 985827894, 532795307, 113834691, 578086152, 489952884, 648635917, 898964462, 360472527, 135604076, 370038495, 447750581, 8956901, 862580137, 530647245, 628780542, 466654588, 332211795, 251782183, 444522143, 91007839, 687810899, 161664945, 941406275, 81008205, 575507611, 183121889, 828676201, 350651063, 142222367, 249425797, 58471809, 419841288, 546803308, 600529056, 207626892, 894334555, 208010007, 159544651, 339920374, 303244701, 832186544, 110295461, 195780476, 28548969, 756208855, 941727477, 657354263, 418012399, 920406246, 544019970, 755523701, 114794573, 851291871, 662071351, 100558920, 476443891, 900529653, 106871609, 32173335, 201398389, 761921389, 579635895, 915288553, 523100715, 250644583, 260314057, 778742011, 534495625, 266060285, 458869592, 467418809, 186112899, 764872005, 649247432, 845821369, 944602366, 653667140, 755306585, 490309585, 71566332, 627168506, 508443116, 652101166, 931238551, 642612044, 115202270, 546699756, 264462074, 739128512, 135550901, 729950032, 657927017, 566973043, 355567789, 124824646, 976694431, 666277489, 369061037, 657219749, 879014530, 93625290, 325713722, 271090934, 719546074, 293706824, 532473061, 580041385, 536042196, 48868959, 50142107, 695307038, 523189119, 99505212, 715561047, 778811688, 621075162, 765628155, 802213727, 712571713, 187404004, 335067467, 669158929, 659805752, 369994105, 265144603, 574040474, 8427649, 243758000, 654343520, 463118494, 361177898, 462124186, 152946682, 286652257, 772223473, 827392154, 918028816, 431431977, 466916955, 80243838, 980284828, 456973986, 166364769, 622374883, 779293023, 934866224, 60750205, 805582045, 361062477, 615585641, 362617415, 802270630, 64542508, 535529341, 706962236, 452729681, 511785308, 165957870, 47468709, 786556942, 916770887, 619045212, 3471804, 523160004, 975577362, 922473813, 155354544, 441155921, 965721497, 13174856, 564829243, 162423819, 510007808, 503888149, 704392097, 117612405, 789102559, 526849534, 640463013, 955958775, 550801860, 614542332, 702739546, 828633645, 944639274, 797759514, 90287405, 577511036, 844563222, 823932426, 274365191, 96519297, 319890548, 901873580, 485383094, 564444133, 37069131, 235614917, 528381648, 423953447, 475309940, 669114808, 712751502, 931736379, 412577207, 443346822, 721175158, 361867194, 340413572, 113474984, 528147865, 540600086, 661630449, 105437490, 815255775, 830399967, 152366912, 951364249, 717243692, 136538288, 370498669, 42621483, 271148963, 750234701, 90108719, 638674381, 976741789, 389673284, 733760535, 242688289, 496202887, 268950886, 303301080, 620313052, 65683596, 790159698, 354988674, 580980300, 203593049, 739070984, 776098184, 104943657, 899861971, 151405405, 587674328, 711164027, 475603885, 337677850, 540788493, 91304384, 832684950, 765806005, 423683204, 21787378, 728994881, 798734217, 136795371, 174848745, 25890361, 215906497, 458627653, 367194602, 523722889, 418216611, 879134606, 58725491, 820544883, 642642319, 463716886, 619061082, 21664205, 733924863, 42636740, 280442661, 386369190, 406897777, 86071791, 334740115, 294994183, 474950626, 782070321, 227398293, 544932617, 846536590, 839885863, 326351935, 495122354, 891894647, 614514270, 142192856, 657097552, 994848063, 204546650, 917633804, 572942238, 204361624, 330879800, 928252304, 232135561, 159779711, 69887715, 262657383, 334443820, 848504803, 383717117, 549037461, 934261689, 66234789, 700093421, 967345944, 530611358, 180074065, 598755669, 641420366, 499402897, 615366957, 14404977, 481599152, 797640522, 754216747, 906697183, 141555648, 974100599, 221911217, 859985977, 101889637, 499243521, 185438234, 367400660, 282847004, 281924546, 582432572, 393624664, 643572581, 495174584, 735380798, 357530683, 851098862, 535980201, 763148777, 311735336, 213690241, 909167712, 877223629, 801620941, 606083110, 556866742, 682978406, 36577862, 269798307, 937698282, 572007951, 208896871, 693231997, 933590046, 700408799, 518010386, 636457583, 108305469, 422922103, 97295812, 983865622, 438372178, 557996945, 967381131, 978520220, 670113151, 48968240, 727141393, 899593562, 851799033, 281486583, 606455000, 860797616, 902708922, 686239050, 345475222, 650715359, 663947003, 285565396, 138012101, 147707232, 56969585, 239799861, 627819429, 897407157, 581241440, 408251316, 734642967, 240967204, 353100028, 780546809, 110882017, 670626938, 700119532, 22370689, 953074123, 907502203, 95644726, 191448912, 55948720, 732388441, 643642420, 469267991, 349463508, 873293881, 834920028, 803737878, 383127169, 894921138, 941931849, 781039917, 741215541, 7235228, 213088233, 495176234, 206972809, 880323643, 490085694, 755638505, 94304704, 700145504, 23508663, 47000444, 32897337, 897539811, 149710899, 984075498, 743628764, 110477779, 447088627, 960876792, 412817825, 208744510, 237519718, 563919747, 315233058, 632932982, 891860283, 740260305, 644645775, 432961393, 141974206, 437892664, 171940148, 619670563, 560143943, 808533726, 28184448, 65485650, 366863766, 970453557, 537258463, 407315164, 414441595, 495895830, 649490933, 807463901, 837641927, 139245284, 212908525, 449363689, 918621370, 459389400, 790734653, 941655118, 128778209, 655627454, 222450824, 755496712, 757242406, 22586750, 111070314, 814835255, 524802374, 810003202, 988581898, 694907444, 695392866, 698119479, 724640509, 862782189, 217883681, 75416894, 974221731, 466688521, 391773817, 281922520, 852980024, 311291076, 765799297, 410048052, 574575591, 869081242, 949911356, 333905218, 37614250, 545141734, 888851530, 24276806, 807269269, 707666263, 763952618, 303548059, 685772696, 975745712, 616732107, 332177230, 122060772, 135172359, 896322906, 175955885, 346087722, 504292389, 522364788, 563399642, 676462605, 155893070, 766452104, 892359825, 412870811, 320981275, 736642064, 201866765, 315794294, 56743500, 782192350, 598895844, 494573518, 69907768, 868452567, 428342738, 912252605, 785695509, 433402358, 65404401, 177559151, 412140735, 124911753, 981517559, 278144687, 626086243, 14989769, 429207003, 336166237, 725889961, 930617941, 519439987, 591579269, 368090898, 790653337, 726060600, 910171834, 921098332, 843413398, 3362282, 600273918, 61293853, 692522860, 80990327, 885355046, 434682053, 344111777, 39834551, 963104671, 915831108, 204183439, 846634809, 695117933, 917774901, 124826894, 773468123, 955795412, 659447068, 484519230, 993831111, 495337028, 495628239, 457358786, 970554532, 770792860, 95161160, 198274693, 640141524, 691169707, 14068046, 402666654, 146879278, 62185035, 578238287, 407392727, 832194418, 270935239, 470099754, 493609293, 593421474, 697208634, 433057629, 319110608, 109456988, 13333762, 722780978, 540846905, 592456160, 462735117, 276585559, 996516218, 891977060, 120173366, 35495608, 554604049, 852237594, 740979538, 298660171, 928892501, 741709169, 883526569, 588768735, 130790785, 553966865, 719253549, 257847966, 23906144, 439230476, 707391866, 33665113, 330519429, 681582396, 777588530, 464055137, 919128228, 521196583, 185241907, 931423425, 682428935, 970474687, 132143468, 446622245, 232006361, 976919891, 642485173, 904237108, 75783415, 834453521, 287566073, 848811331, 242824651, 159191631, 813369006, 987882404, 505314848, 196463591, 433697513, 740145838, 369036491, 634556322, 161042568, 407083954, 532185802, 78203046, 19981671, 616659647, 406913588, 14190192, 28039431, 546384191, 675997648, 88821882, 44525557, 515282293, 333337336, 436825655, 76694281, 259089728, 214548194, 994875613, 877323630, 670856419, 717737768, 630840920, 562570550, 124542711, 276967883, 919551121, 576950569, 604005030, 471697009, 624691888, 701007353, 892045194, 763239310, 722263994, 392445587, 733509562, 474070373, 186472077, 250743600, 833348324, 68106958, 896230119, 212044273, 949455128, 606935870, 376471395, 918606364, 991797010, 998759492, 81738875, 991563514, 995644137, 247163503, 251791457, 13846757, 949593091, 330671330, 107276822, 330798791, 107684962, 330949118, 288298650, 153870419, 980213068, 671741558, 488828496, 714123790, 667655822, 827033708, 590584939, 23869502, 321581515, 948893076, 424722815, 406918623, 472372940, 865056763, 288876819, 741656924, 543250405, 498050093, 52517454, 740673251, 596248162, 336723577, 409425081, 580798538, 293950247, 15169248, 732111451, 306919863, 524384872, 939049919, 878883465, 921683720, 4810156, 729234380, 591489936, 347683349, 538474902, 762613123, 503999659, 73083607, 110948475, 418712173, 815335729, 684376923, 692192331, 317480708, 532045421, 411172883, 516103591, 326381418, 216796452, 100039767, 207977247, 506922836, 557188769, 706887013, 609574691, 605372815, 298311539, 821594459, 490369974, 434490741, 752944926, 400848105, 34828308, 993733006, 25986363, 667026526, 508080553, 866767202, 758953271, 332149752, 867816695, 719696429, 989891005, 526002007, 871621434, 797395164, 556407805, 798900792, 62544088, 842153453, 479167414, 964180489, 847971974, 994036800, 714667808, 235089826, 944902560, 42397982, 518278387, 553506584, 16357564, 587903041, 304904836, 235622340, 585007138, 992481632, 353837128, 227579319, 554502724, 517933294, 879396737, 962820668, 611050710, 813430340, 696635100, 711475569, 836738294, 892582517, 839323387, 323933853, 495895965, 804316615, 784005455, 716209502, 147850238, 837560716, 281988972, 752258644, 222505967, 730803087, 733359364, 290371316, 996533210, 824750972, 226118012, 443187110, 633839360, 417846335, 73486899, 95643384, 957361305, 162396508, 308709424, 470708111, 385473779, 626471594, 968390208, 375573339, 755902037, 12626147, 62053850, 255738916, 337477761, 623985968, 147806452, 739024545, 327703653, 496800183, 305353650, 175716939, 795376483, 304285062, 281057384, 138006485, 506309971, 689675207, 773527323, 43372931, 718054964, 896858053, 75211126, 243379635, 553078226, 884629200, 618411537, 364195309, 143471047, 646706157, 283849506, 876905858, 591287643, 445968154, 424614443, 525140660, 298279044, 523966435, 333500717, 611391399, 533281620, 281816634, 671862466, 761303224, 63800060, 38593505, 425393675, 345257278, 848811971, 800599580, 122265327, 113743110, 708437388, 736178159, 141081817, 591251785, 490654971, 504560403, 527249724, 252058626, 692526506, 533219149, 379017637, 109740118, 736158860, 329594326, 367210513, 793057644, 366464812, 735229393, 152933783, 372017047, 185527268, 697105349, 959879158, 462600842, 597239104, 464134246, 682910759, 904406266, 229983257, 71737388, 179658664, 772112210, 14764861, 970896325, 730608154, 66179634, 273623120, 421972147, 61184812, 171975203, 407130893, 967963710, 269250661, 328859414, 215882302, 89775424, 127766918, 900489049, 367904971, 533674198, 592891446, 164897630, 194673911, 705963505, 377871141, 851859550, 18581471, 695437942, 55362259, 206702772, 83705698, 293147178, 701382654, 658664415, 213212600, 155069986, 815265247, 312519109, 822815014, 54447343, 132454374, 557011013, 613348857, 631625331, 314305318, 43341801, 439024922, 892133421, 875961239, 977771573, 30332970, 129182886, 178409646, 224563369, 219353098, 546741835, 599502779, 919162349, 463283789, 567403611, 543881924, 604912492, 365495889, 635398303, 583093146, 880786282, 674157720, 604330663, 292265568, 622083391, 848162842, 239224809, 631698751, 498424418, 479771278, 891405879, 316211315, 313825511, 693149542, 204382258, 393116836, 735196639, 135448450, 10229765, 558908749, 104601096, 410689240, 338989862, 788901170, 563560553, 896385254, 831549292, 43038638, 848067903, 725006504, 682894154, 592098692, 928026424, 168799838, 814677974, 725711827, 632792086, 469848156, 719482480, 628347562, 502057316, 984719535, 781072861, 589646299, 165431564, 32184632, 248306992, 665754157, 124895296, 369883479, 223256141, 275164370, 789907416, 617863353, 856678479, 535077153, 701119391, 353504893, 374663258, 90418876, 451345917, 58356770, 19073090, 835120121, 590090509, 223934509, 826507156, 244375119, 216960424, 668956224, 460254979, 548489762, 382398513, 503152739, 432496547, 128062245, 845703087, 753497210, 810287260, 79210387, 983625869, 753020142, 394828746, 403774913, 233648826, 276616798, 590796142, 162143901, 615916331, 898253774, 389481644, 574617051, 904810311, 148427678, 186442927, 942841213, 167976596, 65920338, 68676970, 346416901, 332038361, 628956171, 253756698, 860926838, 110048651, 49579355, 250949597, 114620219, 257115731, 209285931, 805413503, 675389925, 498162597, 389517120, 664101220, 71831703, 552829358, 373999334, 619121017, 247068145, 317016983, 885908035, 999512209, 11760169, 878803973, 510902288, 657951059, 484109392, 480763634, 103988787, 132374470, 431930705, 831485221, 852236551, 333213476, 649969741, 174602803, 308685233, 20958294, 875834479, 205670662, 292879167, 110048643, 113899507, 741694921, 168384932, 46798392, 25294672, 551290165, 404453660, 273908039, 224646955, 422525809, 388886164, 20878703, 896341627, 292715735, 623519523, 200740768, 387660876, 787017295, 772453052, 438977223, 601407655, 335036931, 15421970, 570527264, 828356018, 413818668, 858943708, 937745972, 517050574, 900794666, 180078225, 971132664, 408464178, 429647220, 104159168, 669924621, 205459184, 223076105, 666255790, 732652797, 638156127, 830810391, 520446210, 419929738, 691808742, 424390583, 254756162, 346000580, 880426927, 637007189, 656146483, 319356996, 133963673, 535129209, 360915037, 547035119, 366901674, 182208107, 977471138, 487825323, 836380724, 196218497, 830253798, 559917806, 579297338, 549938173, 655880246, 453950722, 273942144, 481098822, 154334120, 119934679, 154682359, 183755740, 438763308, 844150979, 90160114, 90625002, 260557748, 537916698, 346010766, 129224603, 818541463, 566115779, 782554005, 362831413, 912523293, 376619156, 228289222, 667299467, 449579331, 596933293, 957488568, 248669913, 779741612, 647697671, 879323810, 699565724, 334071539, 495030698, 549816994, 881727892, 71072845, 888593966, 430894577, 366845664, 100152050, 942092196, 480977141, 641326391, 246399015, 717458735, 160153357, 52509642, 836498067, 670556464, 740952592, 644780047, 640645468, 188638273, 511834087, 969671581, 954522412, 901055665, 191120216, 44527694, 118268806, 949898268, 447756275, 24222328, 409448493, 285142701, 432960429, 76132002, 284109378, 652089245, 980763464, 343050202, 253767125, 621933700, 495218658, 39466482, 879355966, 323359471, 904440018, 981309455, 714164042, 806684677, 439563161, 733660082, 961964942, 409515951, 109103342, 840175935, 513411884, 383605614, 119160793, 414783623, 617580992, 269896876, 350736859, 750704542, 766385368, 634120555, 871649392, 592591991, 182201083, 976509877, 996454506, 461577216, 149221738, 914713448, 618481604, 932962897, 545465120, 509572898, 49193230, 335186895, 149807768, 508716765, 474709616, 975104490, 653340165, 152210431, 112223230, 984022547, 157870284, 603224376, 2074716, 76219112, 300819705, 620083954, 20504176, 238186760, 407481746, 330515980, 3781564, 346425500, 308407375, 54719612, 493689503, 143345439, 637618915, 883109640, 361036978, 756095716, 261645787, 832205105, 939982849, 725057606, 255172628, 450764408, 87541600, 616830897, 900224957, 69618093, 197023150, 806541490, 378230941, 76590766, 547552271, 815988740, 637718048, 440624747, 232388351, 321872231, 694911972, 853668016, 344752106, 176274186, 132022993, 271836663, 717010443, 266411393, 354875039, 528643065, 704218400, 764394194, 67153157, 92574896, 742563732, 673467174, 530258697, 370417047, 903747587, 756287790, 25693038, 867867552, 641091806, 111641425, 470333604, 86036095, 431634508, 909525610, 735366419, 601956042, 123766532, 431149605, 305490241, 836846087, 376877656, 97776889, 603194009, 802309334, 735823110, 157083158, 887065174, 200007927, 677613927, 889542250, 492185388, 8891738, 347734208, 974697757, 148791624, 732356581, 416632236, 352313211, 790480265, 43484322, 675840197, 282558426, 797293246, 691866675, 129759614, 845140022, 358082082, 943566273, 748638095, 81103103, 94906062, 999883911, 709841841, 404802890, 440623493, 795381537, 407967965, 696386056, 515710786, 194790867, 622314390, 999522844, 362655720, 530579746, 966556848, 209622868, 48560022, 892105791, 315501299, 349412609, 630337690, 118900979, 41835090, 896490556, 601306232, 563494213, 449413241, 123450559, 669556923, 639758239, 904427254, 867084089, 79821059, 949438069, 871172224, 709408620, 581373376, 810435923, 565317648, 898798040, 734154788, 296850399, 925818699, 647768557, 10221782, 434117985, 786971319, 338665348, 649609454, 878280369, 522435725, 15021525, 748909352, 3827106, 288801679, 647482604, 963320572, 246160583, 944899842, 291766593, 215144771, 321118828, 428165873, 702872923, 620485918, 571049803, 781892997, 29726398, 614092670, 24729119, 526935729, 476917269, 651738224, 573847923, 826919733, 415492667, 347433171, 958968768, 615239253, 625913982, 686118335, 356022055, 244657955, 436924198, 487636463, 348678349, 293599945, 370176095, 318855970, 551023764, 29011585, 934283017, 608380662, 967954544, 470173258, 389330322, 345811604, 958752400, 316646002, 34185985, 557471490, 901852699, 510498958, 214368480, 684932216, 852094509, 733403183, 957762294, 938476595, 724415537, 356743661, 952187166, 224357144, 17853652, 201017400, 705507101, 728907414, 501597816, 437493446, 244648515, 318005309, 596581028, 925829452, 522293537, 205411494, 238642153, 894228107, 194654155, 232965540, 454665679, 200380036, 104675450, 653766237, 618273774, 998255388, 136533672, 278576218, 89955974, 360400735, 107226745, 925495522, 39711086, 374178959, 364103817, 714149599, 968385214, 304646416, 971154997, 206065003, 916919451, 695139829, 316247519, 733603237, 878734159, 809387528, 216082602, 95767359, 266452472, 710661664, 277270080, 782477961, 802278240, 248932475, 379782207, 395647199, 577743789, 127971554, 513496291, 906728407, 835272981, 733454718, 669075572, 513377096, 464138750, 526916356, 977527849, 457043627, 7441688, 715298107, 605051446, 182235897, 433833104, 180377387, 317277113, 678427144, 779082745, 120399289, 88245126, 968026059, 305299401, 812790143, 259079704, 294470658, 574858499, 990798941, 414160227, 879243776, 930559055, 441483424, 923469051, 607815711, 363266156, 77668545, 100272275, 346249546, 212056758, 136829564, 807409268, 493740820, 266297746, 29443687, 166412781, 813822558, 747748535, 625365606, 487095245, 942178799, 693234455, 358238089, 901032106, 317892591, 131067564, 907832512, 866810439, 593540505, 593818758, 926107458, 93411091, 860784678, 30100525, 163532572, 80559406, 409422899, 914744673, 778745428, 117664542, 461166439, 990252794, 91470593, 151403393, 112666149, 542735982, 617888623, 619466990, 892344733, 500512162, 470061153, 519167379, 565388240, 858901740, 764906566, 446099617, 220158630, 82537405, 974223455, 564176970, 481875325, 322107868, 389556002, 729025771, 928395739, 378472535, 462496499, 446107943, 344281347, 114588100, 141309583, 435454473, 152318835, 61359904, 30062680, 97205563, 856175151, 21670368, 383527769, 177514721, 473993581, 924646535, 324054893, 989861675, 341100385, 700001016, 879544115, 679078692, 386784290, 856130423, 800526238, 201997407, 43685044, 421258779, 867044698, 905065267, 5949220, 294564922, 806743320, 624257066, 336137244, 852181151, 761546077, 19958373, 208545090, 65346546, 218532106, 447683771, 344273553, 593024623, 575032829, 716487674, 524612391, 968693625, 361014184, 321947031, 827333005, 810344025, 362924426, 717385322, 341009954, 125514719, 651942081, 741484242, 831026139, 457760367, 599023571, 209911406, 518200532, 90283979, 43898689, 275890076, 969921307, 31553964, 724565173, 133476037, 595211366, 367675232, 167311782, 243049524, 562098639, 491959905, 285486391, 521141771, 109488022, 328180892, 415674268, 31426975, 869601572, 773779587, 386448705, 104454802, 371096243, 1634632, 784658992, 383218980, 565727688, 27145286, 270464178, 345324957, 216273258, 702334298, 181604283, 305770684, 961680296, 23082100, 385685416, 834938659, 951525895, 486999373, 985899425, 97885349, 710568499, 340412593, 380568375, 865010697, 717101581, 119611558, 994567673, 766035332, 627396162, 457850961, 731380220, 196393689, 709304354, 632186133, 369670210, 3322661, 263608693, 522228537, 391078000, 734176518, 174870835, 7444195, 597772349, 904171868, 825421978, 348396433, 878106821, 240545630, 628507075, 849346941, 395739469, 743445266, 675195765, 178228487, 382284039, 765838689, 365384346, 897992385, 885847016, 49475055, 35199166, 149250148, 646979185, 383027684, 13398197, 175638431, 48625927, 401243883, 595490297, 785696463, 394997634, 395181309, 427070253, 916086052, 594926256, 810578867, 454486905, 498068073, 553994615, 461169961, 160132930, 551724311, 445581663, 549800009, 244850473, 422623428, 235301043, 524867602, 934660023, 705866633, 748889239, 206226315, 350420156, 363078452, 691489702, 283495461, 476514747, 662555839, 100968140, 438001625, 594185433, 756387180, 432939488, 591852115, 725642248, 257564312, 257973988, 120361168, 502249240, 167279630, 445032304, 754393553, 852343215, 11657315, 672142514, 907508525, 87820954, 870921537, 446516958, 631979128, 985688646, 395336830, 779395720, 861025055, 655734208, 407223207, 291913930, 99336987, 639696179, 104720792, 337608701, 337037049, 104845319, 653318270, 503786755, 754981713, 877183371, 242376387, 159757067, 104905386, 857177099, 282370710, 636941173, 123462644, 150465050, 466184765, 659512188, 696531264, 436657384, 720994377, 702032487, 475770440, 463076968, 84146961, 116982760, 147951858, 966142892, 411665848, 82437734, 34027521, 397833182, 146755682, 799322238, 330465584, 666360489, 627433003, 184867234, 767633198, 806445088, 11602660, 601121227, 886821844, 424457614, 332352223, 339234531, 379884662, 981458354, 2312578, 617269161, 839598879, 584207253, 304102603, 15073665, 231474453, 36947414, 977916784, 819671319, 755782747, 664719718, 62524754, 471432666, 807196475, 404739227, 554372603, 936030439, 354727067, 339271084, 863810911, 471043863, 778979643, 409414113, 687947238, 356010026, 530361549, 999778685, 519216092, 673728308, 44897669, 475743395, 81014045, 147330670, 471360592, 977557230, 201088853, 392495088, 203962053, 783582972, 13126783, 465098553, 71338568, 212817257, 23898684, 182061407, 725732528, 304007648, 376409849, 21285325, 432050581, 438641218, 168989823, 666490142, 648869030, 306306491, 205910074, 777587036, 454768136, 365231664, 151245515, 340624327, 349187101, 427556647, 604826109, 660768751, 508625193, 496236878, 346217027, 303169133, 173377520, 210413140, 528254319, 995625117, 815617807, 725666135, 744830956, 779766357, 532808546, 879759236, 240228511, 504484857, 667900578, 8503438, 87925043, 154223365, 367843285, 118354429, 503196741, 693259045, 146841246, 696342500, 862536107, 127491548, 636341060, 293168081, 200341811, 83137104, 166603406, 859467038, 444733945, 84282013, 57345214, 75190352, 333906462, 808090466, 603572083, 816930920, 934973595, 349413745, 786817047, 440447186, 319950034, 528329085, 538620450, 606035307, 605564324, 528106733, 630550120, 327362305, 541041141, 415579823, 224040922, 90139349, 17758007, 346434295, 995295167, 144817231, 686921300, 706701391, 248555492, 946736643, 628496580, 580503733, 721207935, 551902663, 627215512, 681015775, 362641596, 860802371, 599042193, 36631376, 925663170, 196437694, 215064489, 14672990, 954154455, 8334243, 822158422, 896569060, 394336943, 608345611, 651322268, 799487124, 853393417, 633039664, 718104085, 933449542, 853371948, 818334732, 4557836, 647653376, 832288639, 913669002, 893945901, 499851387, 684491691, 25384244, 52258426, 738747787, 915047827, 993928682, 992351597, 12350319, 97273595, 990054793, 974365058, 958267608, 34267714, 117279643, 416205423, 602473068, 577273610, 19781068, 448660722, 524707326, 275929092, 514131770, 559656734, 611813506, 666415420, 718279524, 269521454, 448115866, 611342051, 191720765, 562925599, 453939797, 461644887, 582282067, 788130381, 695118938, 803549960, 3308944, 646167247, 882464702, 916071004, 678082829, 798693556, 778486074, 307317080, 139180497, 591501984, 628978786, 10866771, 457231970, 694600735, 994951898, 872292925, 476304196, 129287024, 673034715, 939871257, 374338882, 813603896, 307881731, 688508317, 665026386, 844389197, 80011061, 3626812, 957794480, 650553374, 606460989, 342583471, 593498911, 751318289, 77578256, 583221344, 405690450, 505098940, 15397504, 596383647, 935390235, 183907533, 529060076, 104873735, 291037869, 752049218, 50656497, 6776306, 315251041, 989689769, 971155506, 327717640, 524389067, 548400235, 431447497, 212028681, 981506646, 960906064, 359255844, 121592808, 472434661, 538967177, 850474959, 290266888, 633889930, 458371561, 360718843, 748160877, 800487303, 747524230, 643779430, 455834565, 708330954, 229959622, 648927780, 384899304, 114175473, 955327514, 761394914, 165588035, 753148863, 171036767, 591415219, 223421569, 803459436, 504560912, 79927559, 599042509, 852419177, 615769195, 927824164, 573764578, 680501808, 132284047, 435507193, 728647397, 486475898, 498747511, 442002384, 159148284, 729943377, 570770210, 745575543, 534299954, 628436707, 55323582, 493305867, 212575720, 113638692, 559547856, 446015953, 641489967, 83657750, 455279900, 687643333, 63533337, 597856337, 247574325, 206371602, 179681964, 858733729, 895454057, 25776251, 240078569, 363120203, 520780269, 285302564, 377024643, 415000118, 327515362, 46043818, 593069159, 702847682, 837880104, 987843875, 661393536, 779337786, 205097622, 324380252, 992993167, 920532798, 108625105, 608554564, 877558681, 737192979, 878914830, 498586475, 694273621, 735123755, 570500039, 261562131, 416391334, 452863859, 224738330, 222806884, 534424849, 782984823, 851510087, 401120147, 264299348, 646466343, 218788696, 135895389, 995521012, 57494342, 781606484, 149736755, 903946547, 511198308, 795232860, 868968744, 680084724, 778438733, 979974119, 950827674, 799457898, 845106662, 863341437, 882553154, 226960833, 778254445, 760885659, 454695160, 485885360, 607130479, 633051231, 684272078, 825384536, 915092062, 675620567, 928419186, 602257010, 264363493, 142756469, 565035288, 726532464, 154014842, 198325474, 751908382, 72886040, 595396222, 448722896, 314720898, 690299001, 248944325, 141911054, 412665238, 536278051, 975831731, 813187202, 143368498, 531511548, 576682132, 891989273, 992283081, 479991063, 827946590, 530945144, 690345600, 536386905, 238999054, 884338988, 10200494, 821826724, 997316104, 296593005, 530376030, 77796879, 84241624, 196151104, 757201375, 845648533, 88761643, 212260655, 311198379, 345189974, 378479832, 362164437, 121600835, 963820292, 660643000, 316644037, 563180271, 883384499, 14737180, 738145235, 349991420, 753168817, 646169698, 301080305, 469719135, 329382329, 474905219, 435977889, 433129440, 420985793, 507935177, 456117067, 532345822, 519634457, 267398909, 896824925, 467231899, 798458022, 968842122, 837274975, 109685047, 995910609, 415492387, 357289064, 198076547, 564964316, 388138062, 300439133, 132078710, 190060348, 372411900, 713337320, 654485077, 638208964, 837229982, 440151482, 718172502, 49042387, 205507323, 983908244, 578283733, 736928692, 785705676, 26920356, 594579838, 657693158, 368893177, 613445349, 175004586, 706433651, 183795646, 81425945, 56313019, 684468369, 258324528, 590673630, 886514323, 77501260, 231426942, 403967743, 1981066, 408101670, 992463724, 838264471, 135023352, 943027683, 24585210, 118019110, 178934752, 572561391, 180158845, 763266893, 969441054, 347096720, 173280325, 447441762, 494523918, 214712581, 749879476, 336476057, 82330351, 622199115, 348128381, 194866334, 814614038, 654950934, 388513949, 480431239, 431448466, 667948558, 183846080, 304951899, 367947369, 468565193, 406870542, 528639156, 132983342, 509288513, 643257922, 824516747, 678598285, 626430209, 777367306, 136721973, 991787486, 259205967, 973121850, 852496735, 100670918, 567332813, 750241333, 937646120, 512285330, 306827445, 797012687, 874520671, 934374281, 856977138, 834433441, 339604691, 159565550, 860014374, 45403174, 685797732, 157725574, 838681028, 309111990, 305876268, 859133177, 132532527, 827433176, 168654200, 223644038, 384146616, 988652653, 353076736, 771460132, 405965424, 148037074, 238270144, 566203328, 544085519, 269397562, 331667823, 636263862, 851716785, 494357114, 738093779, 898295014, 312836762, 761815611, 155649166, 438636171, 938121977, 953338691, 452498352, 939462423, 270205039, 776446093, 505970519, 329848295, 30941019, 864146124, 394799014, 47548739, 281636994, 582777311, 382886674, 680606138, 509698003, 396014170, 467712321, 927428437, 917564468, 831216950, 598517681, 332646283, 891352117, 486548149, 408716841, 827480228, 18504957, 662384330, 124128810, 622985774, 572565488, 243902839, 274413870, 86039648, 730264271, 625020776, 623147453, 197550128, 505277141, 168832331, 864192454, 370058548, 388127734, 864127528, 312657833, 600752245, 685847699, 417404039, 808565947, 459295404, 549215591, 842426220, 373100642, 336742721, 570346311, 473679242, 648742189, 744022171, 670062236, 843804431, 558580547, 218461273, 926239402, 353319861, 441138293, 578291677, 783778027, 951782261, 999381458, 386102041, 935238268, 554314775, 618342744, 390830564, 121669628, 248577548, 267737870, 151683557, 983673315, 556233717, 862616248, 189215520, 351553854, 338196580, 475131636, 364301046, 743865888, 882336070, 398007729, 301058139, 99116556, 614678184, 886625749, 215048629, 458412270, 772696494, 9401282, 537592905, 85710070, 690539515, 763141211, 600678147, 300787742, 225315237, 855924099, 708096693, 50899619, 872484877, 786153596, 358529240, 737544039, 48893607, 493119384, 979337008, 396938622, 660892325, 904671845, 155187712, 676017421, 222317418, 348894298, 337473855, 236751641, 165515888, 131326710, 500417809, 131910854, 777239430, 584736355, 68991797, 632605547, 461503388, 609209740, 101884911, 278786818, 983647866, 363131290, 82451531, 216873277, 276337163, 611071440, 410397022, 749534485, 153560970, 952858599, 538473894, 358654487, 360551777, 845849826, 246475793, 515170585, 226778609, 810914192, 363993814, 900885165, 950669783, 532397999, 934958541, 205943461, 502745718, 758195942, 11493844, 689790176, 598279779, 765915012, 501733137, 540182157, 95995533, 106465636, 999174258, 996119697, 360729980, 757205837, 142028431, 847226118, 409167127, 471280498, 653823078, 501707844, 425043023, 302299735, 337209828, 916782667, 140700017, 231788559, 94715664, 183757961, 775350807, 301577027, 775786462, 708824908, 786455848, 192385651, 727151418, 744374216, 352438515, 129890338, 173090570, 703870017, 505025488, 571038542, 592548537, 193965703, 400387957, 185500697, 909928439, 316072223, 475981792, 697797925, 174358439, 456626434, 576755423, 757903570, 333379452, 919165501, 563737076, 511521228, 642617231, 224005037, 332976281, 699163764, 624470054, 889213358, 567282741, 851243131, 344264521, 579855275, 674546881, 399352421, 263397284, 612685527, 600376356, 423521952, 271414308, 499101706, 946713548, 158201037, 986463884, 119802319, 247000599, 433073343, 463040448, 686422582, 361392129, 210219072, 67529986, 54069251, 292819697, 892592247, 245039253, 110944130, 949608363, 370445444, 240945291, 81150492, 305652985, 597450108, 199098663, 893824422, 568803480, 720602235, 414814597, 355411864, 829089865, 561241375, 581509536, 797841608, 414225940, 567606972, 643243460, 226705906, 632636636, 228209649, 530965056, 179937938, 742911695, 790812814, 716656901, 476570555, 631776162, 948528037, 48818892, 874714469, 681967344, 41680954, 196596638, 680011237, 517114367, 883152740, 912426537, 404313313, 669616143, 166773232, 831504902, 57814637, 407467057, 429510361, 615858194, 737671183, 500589065, 562869090, 937519496, 101718162, 198726305, 762656958, 46823037, 970809689, 364673704, 147774618, 308801029, 438436556, 346863031, 807813378, 342956173, 426249651, 707974118, 982694123, 279563309, 321869931, 238329623, 564144310, 930332662, 831161104, 37988541, 440170251, 601463054, 655669307, 24371396, 153010794, 331210487, 110159100, 741721539, 386047683, 378832264, 177866042, 327453227, 296129950, 597860850, 165494969, 927803439, 703721241, 886932680, 22701700, 664607623, 70172263, 685265283, 259226088, 423785384, 421512859, 200249165, 792599892, 70248112, 502762370, 369999662, 353433247, 929991977, 151446699, 926074549, 359210042, 666964488, 745511077, 963992632, 583287168, 848752331, 794240577, 160847032, 334127945, 951514349, 841755278, 188418420, 220574759, 494759991, 111633779, 108475698, 811257559, 765415921, 934216819, 43784464, 433170200, 208203465, 109601255, 897394165, 857596860, 413318694, 759826131, 797147989, 537325120, 121494752, 698007853, 91779689, 186594466, 675351231, 429468458, 494792233, 141802896, 235725527, 987059024, 80748295, 801458899, 502354678, 463014999, 923503616, 692251860, 576600673, 78656069, 230387198, 300823273, 73739675, 142424257, 338165333, 330047159, 618428804, 233717285, 386851521, 768725411, 317745125, 688619338, 611928319, 227537327, 709155939, 114450870, 255084768, 656674253, 51873096, 829063794, 107185336, 237668182, 956632385, 463604694, 283101673, 929467238, 136952165, 478315441, 11544206, 399724393, 426151970, 531665983, 803531571, 980591222, 439409629, 11123509, 396999886, 972296849, 801639266, 890349912, 141220154, 871276478, 41984451, 973028233, 986789280, 649158354, 586142204, 830921119, 178852819, 253654141, 886521856, 775493397, 385642919, 560493560, 969623019, 686357415, 162299867, 776884529, 8507569, 675979111, 432017916, 35332560, 86768003, 9138827, 760089619, 470210756, 704276228, 466802321, 629110407, 852124247, 931716929, 163222250, 99118140, 274543425, 384030077, 589066898, 409904759, 686277738, 150317004, 291705844, 864324147, 365329335, 905710178, 593134069, 983478553, 710484542, 922044882, 662866375, 967060480, 10816215, 711761181, 204162860, 630220432, 223021618, 279800607, 37100529, 161583750, 344578429, 479207040, 449942751, 738670197, 608907113, 136931900, 673090990, 917852268, 493621143, 141711306, 244891254, 682019505, 847044893, 626276516, 44471904, 395941398, 5110443, 73498506, 30151820, 540298538, 298995640, 803024014, 979551090, 546991734, 807054131, 265284586, 461210578, 55483582, 218302339, 880102719, 810789577, 211669769, 532529383, 16515280, 581279398, 949788434, 682529086, 679084419, 863669814, 256190242, 609996364, 148866481, 464913691, 669199973, 434883914, 114883607, 190466099, 62983634, 940916997, 782069734, 793204283, 897385223, 826097484, 410861305, 516400659, 221862580, 75288213, 284569248, 282426620, 233009033, 484570195, 462459978, 842593761, 446340808, 564407313, 899866736, 651019294, 969952485, 459453302, 733088375, 153079198, 725277987, 252222478, 774354103, 995904966, 638775100, 596580295, 889111860, 353513715, 814627794, 825873762, 125238547, 553330253, 700913054, 994724975, 574187823, 337587797, 470232014, 13095371, 379065950, 124123144, 6694867, 721110543, 648540900, 521235370, 546974714, 590725742, 321019049, 437128981, 470381758, 333953891, 904955424, 630174401, 771548643, 679561103, 400387836, 289070742, 288329009, 900499753, 702727232, 804383191, 217376509, 714955636, 873559533, 762333942, 922851649, 782283459, 853760233, 954018105, 147605194, 923900792, 784693326, 673876237, 923770810, 501002024, 470520584, 148042213, 524521415, 824131883, 144692090, 499912155, 405076215, 450550329, 951917320, 36356604, 664034903, 912850617, 475830103, 755181567, 231652114, 956865717, 471529067, 857938124, 170325837, 565274374, 806226033, 409931602, 369805461, 239357290, 974351749, 603460410, 181417782, 293328712, 519460332, 828747393, 689970035, 400819648, 519927042, 934357040, 766168895, 431511639, 167034968, 895420847, 633689952, 604325195, 833325784, 837839712, 507018404, 166157782, 480568892, 769156247, 137920332, 335354009, 67230346, 921533661, 51103870, 195858601, 175692109, 377704008, 206424280, 159299284, 439412500, 278040840, 622698625, 498208754, 208464734, 356547182, 801108361, 724850608, 359773423, 301593316, 644444726, 701835198, 691651521, 726864148, 922900347, 154243702, 461623586, 593754163, 183676317, 667991634, 306609163, 191034714, 709436955, 379973641, 727410492, 392658693, 159186786, 659105002, 505992748, 192123607, 427242602, 678642895, 678854301, 285337210, 235445561, 264462771, 47361772, 429275656, 39274774, 104835650, 789415055, 321263618, 591476708, 698245941, 363095451, 247520199, 375410292, 401838440, 529635772, 331724065, 393451638, 433508977, 253988705, 972036926, 73419743, 31913155, 858698700, 606917526, 692302781, 530669171, 854248283, 462106477, 128273567, 728812614, 990012556, 953421405, 714668440, 127234994, 289474080, 282557987, 214538114, 887656148, 12649404, 117039453, 177357527, 493522872, 357090066, 496519758, 358283769, 210299376, 64089242, 693729327, 545560147, 996663402, 978693978, 464603634, 596116597, 146683705, 855948143, 214170370, 309848142, 151835412, 19307673, 591534678, 646536511, 379949405, 847213354, 216008606, 327025987, 53460409, 570630818, 881278247, 190190653, 293897146, 722095484, 464171354, 309691773, 649629221, 425537330, 274336780, 417045919, 518220305, 990113094, 597880040, 405349828, 432265801, 242180370, 54914166, 277984877, 487299039, 610125180, 152068000, 609051093, 350079609, 246699829, 912951651, 331072632, 624794536, 863742145, 601597454, 980523334, 69019775, 519735978, 802573756, 66492191, 604284707, 743246485, 544690498, 116030367, 67132440, 552928648, 928034804, 485422184, 96366577, 430535499, 509326116, 861676117, 199700762, 158773908, 436093482, 597072333, 813647612, 874670005, 85998143, 903952749, 50864935, 712354918, 864138865, 401413540, 594750399, 163724994, 509809645, 144170278, 906195201, 11340870, 15527998, 26241181, 940165133, 497672680, 9365029, 995489006, 945049492, 22963699, 961192812, 484667910, 728851664, 831013005, 242727913, 333710357, 723500214, 19252759, 670338635, 235397539, 370397149, 354683056, 882035861, 710421784, 790374945, 235899198, 471015756, 406572945, 237783415, 622658573, 30514412, 540136774, 421353222, 379243789, 958708537, 431168764, 890592148, 985528625, 831685769, 930411747, 284219205, 742493009, 596933729, 2113915, 362764108, 417081335, 368903246, 444986401, 145898387, 61969102, 648495254, 364237688, 531770854, 350640158, 6009265, 761331686, 916917200, 54034415, 198656735, 186300803, 331950487, 484396267, 773347918, 183608197, 929911497, 381295063, 515186507, 759296095, 492308122, 801560293, 88247815, 918667385, 127782796, 906903933, 220709416, 391963323, 474473914, 318815156, 904993745, 988284476, 541867929, 77711459, 806599399, 124852871, 463145227, 375883788, 584307795, 717631044, 989511171, 830977940, 711092005, 9084353, 108595584, 728014048, 981439553, 68992278, 636191160, 219001686, 378907196, 347253909, 591338330, 336020243, 414748673, 298858246, 525713301, 494655372, 351449866, 602688111, 828453122, 685460164, 629301239, 933969446, 482952808, 580270624, 324257298, 66914393, 324664948, 557618604, 705188248, 188921109, 634907155, 94167273, 486349920, 423135095, 100501744, 389423383, 662025044, 264289944, 979571509, 631982984, 942589154, 523301622, 961115927, 449050993, 368520682, 857581247, 768960578, 801768160, 675913906, 428336729, 246027520, 258383672, 946245053, 431798746, 23286225, 366434334, 668213869, 154323914, 680001182, 656106837, 983058155, 216314493, 27230043, 7929688, 549756341, 233780612, 267256132, 987072123, 584795082, 493114881, 776541710, 470377825, 6753372, 973904345, 807113201, 447426723, 144074017, 166444653, 920705498, 639694073, 124066486, 960372961, 341121403, 242059311, 910627042, 455587333, 887530772, 416425750, 570241116, 476885922, 574238158, 711067904, 917163815, 466274691, 12615297, 293422426, 749365392, 760622741, 392485187, 273835646, 234409514, 684340922, 233246121, 914974841, 822346847, 582721329, 571324387, 1898523, 101560528, 584892960, 750532050, 965379897, 787947252, 231909502, 651167061, 403364947, 486468334, 682356104, 762472989, 678236401, 809155569, 741024458, 791565749, 72383693, 774339292, 308175909, 446887608, 389246569, 759222306, 789394576, 79187881, 906136705, 386501568, 406266398, 40150687, 781705602, 55981559, 864486760, 892299372, 840210849, 221348200, 827247304, 468664623, 745823178, 60267816, 388784903, 905729296, 871510586, 141856869, 338491270, 467355857, 66752750, 413175878, 119563353, 956857493, 925563600, 407766388, 885372286, 373559821, 833657728, 70770408, 833876460, 969995763, 137497115, 93387925, 475286818, 759779292, 258443151, 476986196, 735626651, 43809917, 352835888, 951393314, 903506679, 706299448, 412031456, 816413383, 394544747, 197706427, 601796309, 857349318, 524440297, 738915337, 504198387, 697343264, 359155946, 832770053, 499785211, 920572277, 983135300, 331934986, 757493648, 579883866, 925883646, 296000558, 123226891, 906601456, 712978136, 517324424, 778795735, 798577717, 213673548, 933322443, 175972757, 21667616, 856919979, 131037329, 288208345, 240940119, 803791981, 369614311, 762712454, 959943748, 232683400, 162221800, 405551976, 502552324, 241346352, 239152662, 507007837, 874032358, 862726637, 718135748, 43200355, 293175246, 981375080, 550304032, 277114693, 915089860, 823633002, 573878798, 245930795, 589209659, 960571754, 397667016, 763198552, 367836049, 102450726, 922961577, 85058127, 978170297, 882228704, 67075727, 31869255, 950503444, 100731637, 939412073, 419305358, 87759254, 75630408, 328716094, 415889250, 53017090, 440380562, 881494693, 843620623, 185577540, 601391238, 402318223, 72127147, 689033139, 250704586, 27047738, 185701047, 556557846, 360593595, 15280431, 557391887, 27682532, 398650240, 777151304, 814060868, 62504992, 81567727, 652961577, 929401198, 517067511, 45660128, 708056171, 214639969, 534591783, 396791219, 864439620, 357473055, 721073951, 935492677, 363964128, 737052135, 28297171, 808158750, 461056936, 438715479, 992198554, 541771526, 70365528, 108079825, 141713226, 88786993, 27473548, 62691507, 158206944, 293874992, 921700671, 824287742, 473033293, 782530771, 48001340, 428913806, 540575691, 987555932, 540024359, 473305711, 610954562, 305735235, 37170947, 111296614, 402979452, 602959391, 634697880, 407306443, 793142058, 810897239, 253978549, 495098149, 602067980, 379796184, 130117648, 713167586, 806165394, 146820302, 21853872, 265905726, 476143937, 35141321, 146766523, 935366556, 419442158, 417099338, 473996363, 99284553, 736951909, 914582206, 726389694, 163842181, 212664739, 446614849, 841681773, 180336277, 316340137, 312934939, 167829828, 187363344, 536806044, 692295327, 125274475, 936568705, 478115692, 806750455, 437441034, 626321246, 643740495, 253021725, 801547424, 177447423, 305143220, 934652484, 238333991, 933637792, 891194985, 498352155, 886906044, 956221631, 431226278, 688179582, 666298415, 387141850, 528652910, 16947610, 745194856, 390349712, 412089100, 99670074, 333953632, 293470579, 385615842, 661594834, 788644851, 488573672, 70901694, 503979379, 126653809, 661878996, 295595747, 399857671, 318078524, 832154294, 23308093, 697341505, 390264236, 167129628, 757943221, 274292189, 875750479, 82776039, 881639730, 429000687, 329341976, 221098707, 623862541, 333124744, 97655005, 201719835, 810878834, 428659019, 134089708, 87599791, 312123340, 798290527, 860667760, 733830446, 976603370, 221998360, 876494167, 616291273, 596934125, 475628229, 511749200, 513127677, 895614902, 968327646, 625464263, 374604049, 150762124, 958238491, 511980105, 462129002, 224807278, 906475480, 207034463, 476364140, 90495163, 481007541, 30686239, 312833062, 450128000, 539174194, 686052181, 717115308, 741165271, 450048427, 538925871, 27187083, 789958899, 275245857, 965126183, 28309361, 513873065, 298405745, 324058167, 716152124, 960468664, 227174624, 207632129, 309075254, 586755224, 109997839, 507970668, 429729040, 914649498, 842923060, 772733489, 972224281, 979035251, 228207491, 300704510, 34674656, 71787856, 841520114, 299948583, 950554209, 398522722, 178840779, 141411300, 763916827, 153867862, 771680604, 609364525, 187328052, 38410180, 727243159, 916639976, 337980815, 395213814, 530471952, 383988607, 92649035, 811037152, 422967159, 473300710, 901630273, 304391445, 477902279, 609339943, 266199199, 322623682, 296853033, 661984235, 275821685, 300319636, 975797412, 748348710, 415680349, 578079520, 526172286, 825636767, 696413820, 791997054, 548480450, 666213265, 168051580, 255177131, 976832446, 842880007, 349599035, 880847312, 182230388, 512522048, 683119102, 599934613, 478303620, 704184745, 388146036, 450909770, 687837493, 520717678, 566127553, 820021103, 681010494, 343970017, 782295923, 846808921, 26169577, 950656603, 488051175, 79419575, 196069269, 513088121, 906255107, 387480999, 360719384, 978017263, 726524012, 192832504, 804105150, 920991987, 975153976, 799006460, 788527680, 149029691, 521136675, 603754126, 94194678, 661127899, 780497354, 198452061, 991995073, 594568081, 156746828, 179955330, 257705539, 82185409, 319134949, 32916646, 859100337, 596614086, 684320602, 709863301, 432992573, 656786109, 264650243, 647011979, 887846907, 871810846, 360471557, 416178213, 412964515, 289307317, 809352803, 379097745, 505400831, 794824825, 735266455, 645024869, 118799455, 580387599, 308435144, 357395211, 822961823, 864417642, 619262220, 356275831, 161466157, 244450993, 105841117, 70466661, 962396018, 865606636, 775901150, 316396101, 836034346, 841874191, 417339923, 210834760, 68453639, 276439653, 599337229, 552594124, 29264992, 353685596, 587648038, 660719081, 271738062, 845331529, 276273688, 172720913, 527004851, 540832601, 981448077, 667319091, 610994628, 436446428, 712444855, 622326763, 752932636, 185180385, 231791056, 14008042, 591840034, 52525471, 499646147, 444031955, 560955153, 822297385, 380383362, 790138811, 175191908, 720457970, 304652483, 266975830, 430906286, 871540075, 967987322, 587953949, 788539770, 386890440, 668044275, 664477844, 499899289, 540176961, 177012060, 858595877, 153792928, 254363920, 287006810, 456526798, 668976863, 282558037, 48388458, 971480361, 418534569, 629643276, 428682724, 547605031, 415978797, 42922438, 603027168, 218584632, 575515183, 376077771, 919131496, 183415145, 221560370, 998233958, 334620607, 751400883, 124478381, 569392816, 22904751, 840745346, 291589571, 22961742, 159707787, 119042078, 403701582, 129847336, 936742624, 342218385, 953018795, 632724972, 694697464, 64323389, 854085807, 271249057, 10991520, 542564870, 788412912, 549984635, 111496545, 757417873, 438232850, 4958056, 763940303, 648393233, 414255375, 899105184, 418013143, 282579348, 678686877, 245819290, 345089621, 585685666, 646246610, 421772410, 953338757, 730801049, 993067029, 852097145, 72571082, 352126407, 129385430, 220980900, 934324776, 207987118, 202340344, 164307678, 340533276, 439909328, 426473110, 675405137, 194557118, 113518042, 11413629, 819691594, 972790934, 587979037, 326235734, 549330624, 170931037, 189357608, 132804216, 102753078, 482182784, 411117467, 558004105, 721351356, 680876515, 250187302, 318717819, 787649146, 824971270, 771134133, 614712449, 623938604, 410262741, 145572633, 636561560, 132147109, 506066023, 603004731, 199522665, 910627227, 476025774, 667501652, 755187581, 782217218, 980179241, 261059759, 875207916, 725092134, 370075696, 3392915, 806086417, 360931630, 103044307, 843035930, 762278878, 565306015, 349366307, 964861730, 424379137, 91441052, 138468038, 268672649, 989445636, 842453063, 286624413, 597796325, 988108462, 534458087, 411033035, 403216376, 676218018, 840054539, 445657409, 284667192, 98268, 167040708, 262504341, 371823808, 561852099, 300850389, 487023038, 775812961, 336094925, 565054104, 775719213, 499910028, 718768283, 546523357, 727533351, 389104151, 148831174, 821951736, 530679603, 71567381, 332792359, 123192369, 512230859, 401155720, 803476501, 667510517, 249812978, 744220688, 526327241, 326547093, 394101582, 243905486, 459824330, 394669004, 930737816, 798273751, 996203986, 170572533, 595243813, 117945820, 131498517, 164731286, 734866724, 275641491, 291194633, 347927376, 80604053, 885610809, 221922112, 31227478, 588932022, 701096495, 533989424, 958209924, 4923423, 978891434, 740351428, 879779679, 643834715, 40286018, 274036749, 726094351, 949023286, 404488732, 2531455, 90555950, 2470612, 114814111, 723274545, 24890006, 324958482, 744249496, 68551135, 134528550, 408383619, 642509959, 295652718, 531554498, 474264682, 394952098, 236180021, 441043692, 660252942, 219850806, 287908599, 201187713, 325928925, 495616966, 670250385, 950207306, 555233885, 835906710, 701517701, 286034363, 121068187, 892924535, 418581613, 554073287, 744469099, 492327971, 591769150, 310046560, 1257394, 815095200, 388583377, 396130824, 622053618, 52782275, 774957928, 844562089, 429288404, 683669794, 178875148, 862935836, 388961822, 938552546, 593754454, 731515174, 634845449, 96789271, 547181238, 925339434, 612300669, 920649642, 620787980, 178870450, 683436678, 929794011, 906699373, 951644803, 816915360, 14861600, 778077496, 923447175, 736358125, 166661483, 471706388, 282812060, 324466669, 478125761, 730348887, 809038251, 957442022, 264135105, 555564632, 664452724, 562799342, 169882303, 749969258, 844744715, 554589798, 467465011, 759600533, 361249172, 495187561, 755947599, 777570602, 299748422, 248877873, 687806891, 390176859, 169227368, 682069268, 667143078, 990453002, 431174345, 514112204, 711143360, 392008394, 88713889, 154358084, 980161449, 188449393, 871415267, 512718844, 784371466, 241133357, 390187643, 713719546, 221943001, 426839386, 127011810, 281551764, 851756219, 279738210, 750256496, 735983388, 161177035, 417678332, 327208374, 322501381, 590641775, 288517056, 620926115, 380352337, 153881007, 278351119, 466746392, 37823667, 471568608, 232226911, 805138156, 153011598, 389978426, 361258003, 609734073, 254152001, 53545844, 690593762, 621251307, 893324081, 427938593, 493001348, 147806177, 983481223, 578425221, 485885153, 614435589, 453808826, 489537581, 285791028, 700520870, 155092116, 131757564, 845005119, 809516414, 25097596, 173043499, 564657567, 919985078, 585031163, 874549046, 796777420, 888919294, 480405450, 453500585, 401270680, 293862625, 696862446, 311969659, 257407399, 271097811, 200258562, 918349839, 196340952, 953086482, 513635362, 39201459, 379530984, 318132252, 707848759, 661581569, 176535316, 877604030, 377438840, 216291924, 334638660, 986387645, 46940507, 873536729, 721680669, 149693857, 122921484, 502315281, 798149851, 130152296, 474520366, 92612974, 923421118, 108225863, 972281031, 467305431, 682322975, 86753515, 548449645, 909050287, 555059704, 194374842, 8123375, 848827686, 366753355, 470571719, 677535785, 660350315, 578438802, 654731237, 659110673, 450310556, 15071734, 567675323, 604785397, 720375943, 108372654, 847789990, 529727470, 913096842, 345537989, 166256853, 301610610, 216490188, 559786951, 655994152, 154378079, 615723525, 861310950, 536478284, 720204844, 578168619, 841715727, 496723359, 973082575, 862025783, 938219182, 468008997, 286372471, 744046584, 393096745, 247035964, 996418099, 370917175, 772650924, 681371515, 506808893, 953147739, 251023528, 676375832, 508751751, 155476124, 442906940, 329792627, 447691285, 69451301, 278951481, 259915872, 372789553, 283467322, 311853718, 157216590, 874143057, 752255790, 130294346, 821131340, 590916039, 891865041, 134361757, 85505535, 328238744, 13423423, 430872834, 247784686, 437048463, 409574283, 791880250, 484662112, 161724290, 556679717, 827805746, 995183020, 750728638, 619105362, 282111363, 958276098, 906726825, 660784931, 601779513, 501858804, 413932831, 98467542, 874823902, 251445264, 823004121, 230973278, 776925449, 690393963, 734038609, 972499506, 260030835, 146551427, 773731914, 198791045, 116116812, 41610592, 838326329, 733446700, 157788744, 890137823, 88215623, 297787313, 464339143, 472969850, 906625515, 774897419, 41457172, 362060370, 578431091, 782866515, 961377361, 54634834, 977263055, 653380045, 931959505, 490829525, 501737619, 477266496, 884402125, 178984332, 535260308, 256609585, 494226580, 281459127, 203014711, 368800339, 866218460, 511523893, 981412971, 9075410, 955944000, 387477736, 435502841, 324599248, 982902252, 323894695, 925580937, 642048637, 999829548, 712274858, 913150984, 446986065, 8288143, 464555683, 896244230, 259402838, 392130508, 644793245, 241533118, 13253199, 537603738, 417882143, 748445963, 462160208, 385446319, 643905508, 738020166, 856486272, 854817954, 882298622, 502300252, 829204866, 548914666, 895467172, 691509404, 369378304, 92330050, 865621645, 357017046, 125888383, 791703404, 626750369, 993643623, 437509347, 458597573, 774079507, 650622610, 58548035, 936846032, 536757365, 150226671, 335948145, 315488569, 682048981, 26836323, 138369083, 299919937, 47118781, 593916424, 571204292, 971200262, 380343542, 826576204, 684928929, 409871288, 188877463, 179867949, 810762097, 499328905, 517145864, 847929490, 642766855, 990193720, 38119351, 172730388, 926979018, 872780453, 595677029, 987395636, 220152550, 526395859, 687128275, 131147580, 525368419, 586880885, 232748077, 329910361, 478563241, 42565558, 302327521, 583702658, 942946919, 222204202, 597050125, 517037921, 330782475, 467364709, 779091016, 15844829, 951285976, 411846237, 71926967, 301246393, 504058257, 745829323, 780097506, 28205773, 94105183, 178339193, 537824636, 793834200, 437259646, 524809922, 972687114, 377070861, 462748252, 191062318, 579023505, 863237741, 245555130, 751934328, 328570874, 850547449, 100312742, 938863462, 124415502, 607322095, 270968773, 645877140, 567473419, 986596884, 899994225, 974504867, 196296171, 45499291, 155728110, 857128700, 87148131, 471802039, 900310235, 716619075, 950737831, 628961864, 279784840, 228972879, 16337180, 125981727, 271388089, 842620461, 774486106, 819964779, 45528010, 669904881, 16239723, 191137816, 142227607, 118132678, 819456584, 274650199, 776339767, 251603610, 603550959, 758649821, 359103773, 482503393, 228293623, 96597009, 903013240, 756372491, 7134590, 790357300, 463219268, 919100998, 911303149, 14192530, 678494767, 695308453, 313539666, 488083581, 617863705, 485591236, 717496786, 771866713, 282349638, 41847827, 248484820, 478263224, 255993300, 200628052, 126734783, 432013102, 110849941, 703876814, 558268604, 297298796, 692519056, 928458188, 479526342, 520638979, 587269797, 201459897, 139294054, 45473272, 132927904, 243913094, 949358711, 256537744, 936594520, 634649786, 369169490, 347808550, 195482247, 853618990, 455934362, 299995164, 490386239, 153382828, 32143450, 216880981, 887236839, 67578928, 951110813, 963682685, 238807881, 914556731, 637350586, 428619533, 334816146, 773594258, 26109762, 837533713, 591658157, 729817446, 379217642, 822155480, 449166083, 104122697, 438159301, 535224381, 802761948, 708455954, 433691540, 90626591, 513334360, 830158353, 339076399, 744978330, 277590371, 594261577, 733669221, 904009882, 489173766, 633802509, 177938739, 707726145, 52742668, 68486491, 742063329, 80505044, 378012297, 25853234, 743071566, 516444937, 204801803, 407642343, 617942835, 694735975, 724494094, 220117889, 259076437, 729790589, 679150026, 141243801, 79124073, 751403367, 697860721, 360382496, 358005955, 20738088, 281878289, 366116899, 295476437, 543213432, 22119920, 64997926, 767546291, 474630423, 830116295, 361747894, 677346670, 620565138, 836807131, 514845467, 595555433, 115782134, 716786445, 375896230, 651689655, 417417387, 101205181, 187646827, 975183237, 72972586, 252266537, 546279930, 390754982, 284802677, 771938401, 813311340, 94074517, 762267662, 775752385, 419432974, 225714567, 263460328, 454864686, 874717929, 441569435, 716851698, 308650990, 390309595, 549925002, 849776401, 353430192, 943412014, 643134444, 659245429, 892069974, 2036719, 403721836, 12779992, 774327945, 26636396, 442836897, 61997318, 18997070, 116353290, 848753600, 529633824, 582870453, 111264346, 688830723, 435137697, 941996216, 522362322, 546175759, 59911241, 433972992, 362875888, 718437872, 723056836, 185028147, 989039335, 980175020, 216767761, 322611131, 737323459, 321868807, 11748773, 297832283, 19748376, 210643485, 899067492, 450269061, 357556500, 610198399, 651025971, 576375613, 926385159, 458116411, 279104241, 389272768, 121003084, 67202216, 84063888, 802918419, 183129665, 132978423, 534756686, 732486863, 707706036, 204640734, 145071999, 649985635, 482022432, 800103829, 305761168, 479694149, 773228862, 100605642, 401679917, 998700582, 981776891, 707830548, 692512784, 93211745, 756585053, 625060402, 373612307, 632330131, 93771928, 687089183, 838095256, 399191247, 449911124, 152428876, 385875921, 658975992, 955892088, 157279678, 600271353, 413457884, 859293642, 352030943, 537327693, 131280170, 111737265, 744006949, 720017971, 58336296, 15006432, 92951046, 926112419, 927555499, 935176184, 451887402, 489250407, 521696604, 215486494, 332580986, 41331742, 270523215, 204467465, 439538846, 530975376, 593308807, 691828287, 255613653, 497466052, 367579592, 64039546, 839625876, 297567726, 639170911, 690254049, 249672768, 627067476, 735335283, 511665495, 37774305, 497745485, 162621984, 864776468, 146124747, 851812520, 959792435, 383259023, 40846012, 618486467, 660011667, 679461091, 165849620, 262856359, 229421293, 449376220, 532670512, 467726748, 702782623, 876002162, 684144349, 446534283, 999999196, 393344042, 981455194, 375416658, 360962350, 367649789, 790532236, 565034678, 343470097, 679919368, 269138160, 849899874, 648344604, 287756300, 884853289, 865230095, 256537082, 19648508, 621635970, 510717093, 958053518, 545356713, 500704226, 595817079, 929888609, 59032031, 105366516, 691105089, 311720219, 550486451, 693023181, 939932563, 737640037, 339276303, 206739082, 306540353, 482415383, 3205268, 644969116, 787426353, 695636995, 201356901, 547102821, 633185388, 814121620, 358470807, 518626369, 549659249, 956624564, 48759688, 191781605, 300316051, 814569910, 522463746, 254421672, 20254736, 136265497, 467861549, 426634702, 777254667, 289853680, 576015960, 717274024, 951533610, 829410967, 362223130, 20608722, 136380333, 725392293, 682280584, 314585414, 199602692, 571494073, 798687630, 288663442, 980393201, 671033352, 883660769, 663641131, 481861494, 218971061, 130743392, 327601665, 305058655, 711263225, 136585461, 673418111, 942367240, 477209550, 678187975, 95848488, 522964944, 869697463, 560363942, 561708368, 72832409, 69815756, 742535227, 433462196, 709199387, 558529342, 241080095, 357416856, 326505829, 884650300, 203525555, 839272999, 768825430, 12176373, 908593599, 537656780, 540077701, 25566893, 196396175, 721605584, 486296580, 844785961, 643051267, 600657178, 385790286, 808336560, 64123935, 115106719, 489188881, 856182499, 42738444, 983368601, 284110374, 398362587, 974748281, 574972564, 793202443, 983079539, 138303208, 229650048, 871766526, 252986441, 729815916, 932047440, 56550270, 762273905, 905785993, 17393072, 78905349, 262443216, 440175144, 396808331, 677264433, 359293236, 730902148, 232268854, 108203963, 891299261, 818673541, 428848448, 957273323, 297111403, 84505173, 527537196, 148915880, 320532075, 678243586, 578307086, 379863737, 638780895, 321487799, 216845199, 280954129, 261997874, 658270901, 37226119, 665324711, 643476917, 834557259, 817254001, 600897164, 117981025, 1350695, 33478713, 899659392, 983436715, 857124377, 716963597, 165666902, 395737139, 942259926, 340438865, 313848845, 419383166, 637875235, 979508907, 641999762, 791805572, 391827635, 405513209, 590762639, 480457973, 524003632, 901830349, 224111220, 13138405, 720416077, 625748758, 150281364, 686458626, 709518159, 876184925, 708487444, 545520179, 194962862, 55527446, 164337522, 300702182, 776605732, 815660057, 138845289, 207734089, 388167871, 576807428, 436800567, 23898014, 964133436, 199335351, 988041888, 592517133, 223981643, 235638921, 105496187, 776089399, 90348009, 11000220, 977279367, 181353682, 12707504, 202969362, 429194225, 139024763, 75685565, 889531337, 841303289, 766028027, 202332008, 451942346, 397598904, 221905427, 579439399, 282294088, 399237747, 315000690, 648183515, 541613465, 908010934, 712880434, 851247718, 782855439, 189166428, 856756552, 949380887, 585744402, 90960815, 925496343, 508583654, 722439449, 768001407, 709009085, 707599250, 297526241, 377296753, 165948270, 875291044, 38808972, 574214609, 720691650, 37002769, 789066184, 546948755, 932798921, 245816887, 879422206, 617910129, 789189297, 690651620, 494094089, 711318338, 963947790, 381138687, 250274084, 115910365, 691579685, 447779778, 423830494, 98085887, 456193835, 990160472, 612865203, 257189395, 898084648, 550566612, 504000552, 713020849, 565982889, 1141883, 31528922, 267773647, 434410871, 889561841, 548160928, 916666102, 304969886, 676635724, 454117669, 212032787, 129107335, 919904966, 52817372, 785116510, 189694129, 885207068, 314009122, 93004001, 687789189, 589112768, 818363032, 69764706, 126229482, 545017197, 973899907, 600415423, 868737140, 642393628, 893762421, 945340593, 212989556, 407965179, 812149993, 708791353, 585801825, 968358359, 179318410, 813764409, 75268489, 590357938, 386965693, 615470896, 166865989, 832425379, 784674175, 564118511, 80231472, 398330097, 183136284, 507849251, 899704594, 103706921, 136743306, 645714830, 11222364, 302786200, 807291601, 642013870, 758049414, 63501258, 575387401, 90076122, 516480583, 33003591, 104181025, 574500023, 458376407, 243591678, 326146722, 454819804, 747753537, 365986764, 162846032, 80862701, 225974186, 978749604, 892464379, 346691821, 322921983, 431342184, 872330006, 170872311, 488237581, 7443976, 132049344, 203472284, 424125574, 237047856, 210186701, 982127071, 959348226, 534094831, 853101140, 856430611, 678896079, 643465539, 59236088, 204869285, 12050584, 499663092, 164785699, 430114618, 869187152, 645157038, 695394986, 85208978, 215060727, 700632722, 137025543, 681618868, 679176283, 999958276, 306072546, 981303669, 338335290, 395554243, 345701066, 171444627, 421317563, 19379110, 683424514, 94334206, 569433445, 929880443, 794136329, 188254630, 636467393, 888474575, 782842339, 649375519, 672678710, 944097282, 618909820, 288353478, 671397387, 65800656, 294920769, 467037655, 548186831, 343035422, 812094062, 794394144, 80028498, 948195673, 872499243, 205743384, 475870366, 416517908, 526167621, 741565698, 868467649, 661803806, 459476886, 506916442, 428978394, 743942428, 45046477, 390325110, 62405740, 230098036, 460242994, 78490425, 504460085, 667453170, 816373064, 482265350, 753482161, 600999055, 616309486, 613293271, 660705343, 349721626, 357330617, 989121731, 280166981, 402426814, 61065962, 884658146, 60764701, 247152646, 33742957, 888880363, 590361701, 16369248, 996437732, 97245003, 573850624, 618109544, 731590420, 778787670, 752398229, 741603582, 757709858, 747408926, 395822774, 987122179, 732274159, 169055944, 327320650, 372572089, 448460, 808127319, 61633986, 431201177, 957524910, 828667189, 56837675, 420866030, 26050966, 126803925, 458159369, 566356162, 808896600, 521672715, 778810756, 236333182, 848575073, 113351325, 76059024, 643936984, 308716528, 98610060, 176589179, 407811817, 548157618, 466788798, 717291467, 626820764, 158207612, 248938860, 299059301, 37092815, 72701451, 254982871, 169056800, 402739328, 59489355, 166840085, 455442069, 803560038, 201299294, 181774589, 931315071, 58584365, 449814323, 274741417, 716982440, 230012023, 946866003, 124097502, 622501088, 263534632, 556517506, 127548615, 16366954, 183610470, 316854343, 525781907, 289520937, 496101715, 309295980, 915307295, 451674681, 938534478, 767087375, 77641895, 861679043, 766335191, 337970583, 291616512, 208379468, 379793749, 696010849, 265331389, 948207864, 903565213, 913265978, 35933839, 231733031, 441950510, 951887674, 92384025, 659165375, 392372804, 582784917, 565445160, 172571296, 193255622, 476596774, 246546332, 722389431, 19476346, 899325699, 61674044, 677516724, 994332483, 163210242, 346792134, 528461965, 699040931, 278371069, 641319045, 592986923, 487963026, 951098798, 85469423, 8047577, 679875182, 893382019, 916525574, 225389879, 930540722, 323595398, 411927804, 376126672, 639404124, 768272460, 579235030, 419811825, 751629823, 465360898, 410740025, 978308781, 305122651, 987279604, 244935396, 487657072, 456082828, 853414225, 826571293, 429957323, 839119585, 741642167, 585951535, 700482806, 773601062, 737924222, 182975893, 968065920, 456717813, 644802349, 362963578, 101419941, 476656642, 858973609, 533141308, 577603644, 955410115, 734783472, 191065840, 587208526, 359726760, 565000893, 382426068, 24421279, 247294018, 974357826, 703190141, 655243251, 823003042, 47288820, 230583661, 841632891, 650580400, 450833480, 756808438, 97060861, 149283528, 351627525, 112858264, 669128205, 766519877, 711966535, 96329518, 811243328, 193911986, 188220869, 633280675, 457612410, 704983486, 848808634, 293232375, 803518461, 571537064, 238757713, 115447304, 16573583, 391165287, 28487875, 136151470, 902314358, 73975760, 225355377, 397146515, 675575836, 942901229, 671788458, 911593222, 203648090, 21300990, 941101506, 893362497, 599974571, 129334310, 313955346, 2656575, 286393241, 977596033, 465063655, 881038506, 574574217, 956070303, 209626034, 448993096, 51213232, 947156640, 421422693, 745336290, 812266437, 785929970, 965810876, 477673937, 699347361, 420027059, 92416359, 539506737, 512760917, 412499576, 430806047, 487980995, 861367356, 780982747, 946532647, 915835427, 747111395, 487410251, 464470371, 823708845, 774191040, 566777714, 276844998, 233568398, 263766479, 691165673, 220020219, 124384592, 432909711, 685411092, 252855646, 755045894, 841523006, 674108339, 473582140, 438277827, 171175329, 941054441, 828616330, 513084195, 521958848, 84896447, 335778611, 986496577, 907923831, 541052250, 904237992, 156082213, 666980668, 553612839, 504161420, 427112277, 884998687, 995448060, 869333817, 351255617, 736223932, 312835464, 479235068, 829942305, 513936194, 94077507, 964142972, 834252503, 364512573, 769628703, 368098647, 877113156, 23513630, 420789227, 496222644, 448476104, 995000223, 348752558, 849366947, 690864622, 338219813, 133546031, 381052893, 826924754, 976706406, 672211488, 250188387, 900462702, 101767912, 709835300, 845631066, 213481678, 761842281, 127261674, 592507598, 769683211, 718451061, 708268286, 544399769, 759001797, 40242327, 25842798, 269037047, 416683230, 134001186, 867811286, 197300315, 848925371, 33605972, 221641759, 374493900, 735201617, 572288890, 869039445, 795857881, 587929939, 322363467, 77230136, 162279779, 972743467, 935736750, 301533032, 525270478, 750002429, 95003315, 978308002, 689785451, 370947337, 550213713, 949411598, 845694673, 4568856, 106963359, 928303334, 765732904, 363179687, 84662144, 701818157, 594757362, 199964833, 479410117, 544590732, 845327842, 493614776, 136614545, 25562998, 672063432, 263122297, 431075316, 202697764, 543902974, 535756736, 463671837, 805022501, 764109803, 917490471, 922310654, 56554744, 644306556, 869706559, 363208328, 635368006, 816961375, 250080107, 127931943, 121567899, 141279433, 207006853, 948809070, 280614639, 836396795, 660992248, 955190490, 570819265, 639078831, 866217280, 588060351, 757611393, 927552310, 515378807, 327342330, 428736248, 554816954, 460267458, 803095932, 664871583, 217971877, 826933215, 958084659, 981503061, 735166220, 888398614, 715811523, 683976939, 945690350, 618577520, 371236200, 215348748, 493882664, 620373478, 589828470, 361219825, 957451814, 31530454, 173557197, 900121467, 265479510, 377281141, 647249855, 881773105, 313149068, 518745675, 55823166, 507561102, 231796583, 13412473, 854464632, 579087443, 868327998, 647303648, 404816546, 370890919, 417286602, 922108879, 783932186, 90937546, 767824838, 747712342, 160999003, 523503638, 338360005, 36619996, 551598471, 361738433, 234367079, 568677766, 498886406, 954331195, 246266993, 923767609, 601782538, 894351298, 644037305, 370849977, 208768776, 423946930, 66659839, 608102802, 934838715, 577236441, 980768480, 66560064, 764043763, 369378236, 210522590, 771069069, 230089261, 204528106, 47765016, 890175367, 280495079, 444771883, 892123537, 546911789, 648291137, 676124481, 778413206, 8810626, 289308721, 568354126, 566034911, 74231475, 696759296, 901032586, 376715049, 405710359, 388093148, 933649078, 152425548, 263583925, 62967777, 507080914, 311173397, 761366793, 917277278, 78771527, 734517636, 949373198, 49411113, 472208774, 919134752, 918796795, 555345911, 247955605, 380335181, 923428765, 911131046, 856362714, 128191760, 177168482, 963688145, 173227233, 415663013, 572629970, 315995745, 214210065, 261367349, 32394493, 961235016, 890234190, 168252459, 314441732, 59384254, 233885513, 677268198, 918135687, 232765821, 785017061, 589482804, 172969042, 208935626, 192471146, 455554525, 661621727, 63702323, 459729482, 71709297, 749199150, 5673033, 981364658, 871667195, 376568497, 794101951, 826131366, 644283307, 82521396, 344393368, 888711223, 884092631, 839702392, 237139968, 278869711, 698213100, 568068305, 588528923, 157525152, 372716565, 586421534, 175716550, 748172159, 782734743, 738689885, 52068108, 684939078, 517129612, 224360257, 538800521, 116637835, 215948733, 249792568, 833819771, 629783502, 526617734, 894307857, 865648418, 373590244, 768515949, 101876391, 575368908, 936661189, 160271357, 932448658, 16621158, 883951197, 940388498, 116059633, 694922592, 724092483, 239529513, 50687484, 666490954, 891310260, 988671540, 686257633, 45654965, 239236295, 42276507, 393561790, 428336367, 401176720, 158834707, 413730506, 512827838, 998444529, 996551402, 968766625, 688221194, 807303316, 710034741, 510400051, 678298490, 630674341, 761992844, 257970301, 98790585, 923125, 380683212, 661626775, 786908345, 717817386, 104808770, 371943829, 426489601, 860791515, 775038976, 68183316, 386685456, 481469038, 106550583, 501167425, 753351332, 342481166, 161032663, 197007120, 815289787, 490498964, 668195619, 110786341, 428705274, 298565555, 978453191, 462461626, 591271983, 643347368, 580940068, 317995902, 908576095, 186981526, 14324819, 841631637, 972334287, 926810607, 471828166, 577605658, 869849620, 643696228, 764724098, 21145578, 14284018, 238519025, 352375906, 704925961, 900193725, 354085121, 379381844, 201632445, 545431164, 247881718, 854121272, 174375609, 346114067, 721392267, 214691946, 628838978, 894116714, 406230582, 311769265, 970181411, 485181202, 163361424, 689952272, 354725703, 797294857, 208811764, 792624555, 381611574, 126206038, 569238566, 395424065, 651676111, 156627491, 671484996, 299332161, 737837718, 116255221, 565382248, 599882804, 460607653, 467279130, 731425715, 589789010, 959117144, 723501731, 516208247, 739133480, 229006803, 554550790, 821203046, 818978705, 937471500, 448143817, 787991688, 835188145, 117264602, 16467215, 21372341, 613134595, 786900329, 507450813, 385020662, 967223897, 674133840, 955838568, 307732414, 645272985, 423697433, 658770912, 878744167, 137766982, 526572938, 825554616, 292233647, 986261588, 718113442, 734407980, 430967212, 49135155, 623594924, 626710921, 54498358, 373306125, 240055112, 418468553, 813923262, 137148824, 386567948, 91167296, 109284395, 628642575, 493288121, 63259863, 455154325, 655278567, 256622600, 451764484, 78312997, 631401950, 120649925, 636756620, 470045664, 926837608, 210101796, 640523828, 330157772, 747336194, 544136645, 305631197, 709645549, 666972279, 61893872, 535096261, 439790260, 166635702, 911336972, 911975897, 739479142, 742675076, 133377622, 909508577, 507372402, 494230121, 335107243, 531080871, 377946524, 551506917, 151470505, 521347335, 808344387, 856758188, 220445958, 360080263, 277973885, 515573570, 60901503, 373019204, 206747034, 79186423, 38515524, 758268870, 819925477, 825858736, 490040971, 310775021, 223166012, 533979474, 658388335, 277691355, 72550272, 716709456, 688247388, 126746319, 802051689, 890580719, 936993434, 615500336, 460599330, 981552031, 630058075, 421915176, 248670865, 186596759, 461122723, 33040179, 262045131, 745513325, 250879029, 4246262, 700845043, 510691394, 953299045, 377216603, 882252120, 646042777, 639063217, 178386839, 850995512, 772291315, 329625950, 446669605, 648739340, 184677345, 104962248, 729775429, 882005312, 384903742, 746179138, 577022567, 970466923, 953311996, 854018173, 975112567, 59595162, 909744225, 10652801, 230736130, 742846581, 746692836, 77786025, 370425744, 591788982, 133833415, 89045920, 599047666, 246310847, 163902018, 465956269, 87231461, 837293016, 352954422, 468136717, 529945997, 141545117, 859226058, 623401520, 977536422, 233816195, 56598403, 576674687, 471884198, 257198054, 677224602, 470172574, 752799833, 534545563, 925355597, 165510643, 890243075, 273176991, 691265660, 950879502, 930047301, 377494854, 277104819, 731004131, 200262983, 805310158, 200694115, 403470485, 947846265, 857522827, 798243722, 835118498, 294151327, 513670409, 22066870, 263311427, 363111099, 391845318, 937385032, 233954675, 438844128, 179981597, 596649093, 138434257, 686925968, 148291101, 516182093, 848775931, 228618247, 673988658, 378399807, 520201838, 363942420, 321861351, 255719436, 251741825, 621016246, 592306806, 459150079, 646735536, 58458316, 301326441, 341742689, 458675226, 787656300, 837133771, 44480363, 781692411, 927558049, 436714692, 799984578, 176386648, 585101785, 713780568, 964904358, 330210038, 798202667, 514311795, 655929504, 917741077, 89312711, 617111860, 852818906, 698286242, 858275551, 911930997, 192537240, 952355310, 932109286, 62554160, 633573775, 335975534, 2146446, 211371943, 177952041, 263818091, 761784431, 452930492, 259700291, 38770320, 642575523, 493144463, 476875306, 399739150, 41494323, 196257994, 323192151, 867812147, 986699241, 584378389, 202726084, 688915918, 828936404, 532479608, 660678361, 973060123, 351016245, 218235592, 61197878, 228128364, 631426523, 762189262, 613362085, 547172186, 22943503, 870523017, 757902741, 326488152, 462370500, 651983682, 995307761, 476494826, 544508119, 727260994, 34049215, 31412499, 623411001, 954726765, 301570972, 337803533, 872981040, 365123577, 23151651, 976315832, 513514257, 831904126, 878026039, 618681663, 644496173, 474945727, 1220474, 179441874, 125098964, 173861717, 154309227, 976716964, 894501763, 805260242, 478639719, 967936993, 923220640, 243899591, 686795979, 206464236, 975848501, 713515927, 849680906, 541037196, 1359736, 533628860, 384320114, 960365888, 257686214, 279526551, 222101578, 79983407, 236124850, 953038993, 150204004, 218305728, 100793207, 839433571, 12633536, 915405262, 533124100, 283075627, 998639542, 433029297, 837818675, 921844962, 694137974, 573192157, 986715058, 494301126, 30451242, 434795363, 181929988, 688866769, 537127091, 266730150, 591983871, 498655996, 941777435, 568898965, 217894602, 466509053, 605651313, 804408842, 799200068, 492908933, 87754286, 545669225, 104356302, 673070185, 446348927, 677161019, 36305981, 87690377, 544887207, 634409177, 123403021, 145191438, 306309586, 628153241, 590344190, 671293740, 738536068, 859059279, 416365423, 979448976, 804472715, 9282398, 414004136, 362593106, 549113716, 805662169, 314361655, 561119147, 408627882, 338423292, 656173552, 35093442, 636716990, 419806107, 268047489, 800371193, 751821641, 833470176, 777819217, 44949503, 357893969, 951149745, 361788197, 169557118, 145397537, 160022882, 177800200, 392204646, 717203743, 928622621, 771993572, 50780033, 637712310, 686579130, 314977507, 123903505, 17676418, 709707074, 361017046, 672618416, 482878951, 444903489, 445992307, 215711705, 301661424, 66843468, 883932119, 750681819, 373142324, 175989734, 642049983, 633573300, 442417785, 978441943, 488447449, 342973703, 934581483, 412128754, 511611451, 216304344, 531617130, 419790832, 192706809, 597775817, 92704118, 544018642, 880797227, 657987442, 577285484, 960795701, 613180082, 251617745, 350150831, 558999632, 141666057, 443805922, 418481047, 683902023, 854942453, 272636184, 215324597, 64553525, 794653578, 140970565, 481158153, 423922005, 462408318, 702850541, 101088309, 87667354, 691970200, 565716070, 895709527, 275444149, 511822120, 327951884, 807093712, 420731819, 757994681, 229458096, 603151065, 367354262, 932156921, 840644859, 884542878, 690548184, 987163971, 186617969, 843356692, 934497685, 215763881, 518179766, 496720794, 701632213, 56442577, 728586945, 258940486, 66479849, 56854603, 772691752, 687315276, 171845400, 384498677, 687706217, 270874942, 662549991, 375250358, 524044593, 859443442, 393777032, 432042794, 263246582, 197980622, 55793149, 318769504, 571869907, 607082786, 407948316, 63993886, 12014105, 498421523, 868571512, 82315141, 916941164, 890334126, 119111371, 184818, 683388867, 385773359, 239304671, 545650805, 737862784, 772135369, 335887802, 578003389, 844647520, 974164428, 251921499, 121765557, 675647512, 701959646, 373638945, 797873087, 533131340, 575940255, 752242990, 89978760, 907663681, 189599055, 879268013, 69964568, 297314807, 285181750, 63680226, 589544253, 765391881, 584629208, 992025681, 322762584, 388041571, 318251606, 38776654, 733009735, 479456429, 65941852, 796591699, 483511241, 663648343, 394518486, 571669594, 309289280, 29290865, 561813076, 284164530, 283140272, 166222141, 52329764, 307999711, 480254952, 308852692, 912306496, 531852789, 474745939, 490648670, 439464315, 860373631, 292258337, 418935376, 487160509, 609563916, 661458904, 51664332, 585082002, 777512088, 231428688, 79481113, 398278375, 1673800, 582880816, 935779068, 429960320, 53925487, 90095740, 254509187, 646384259, 711688222, 903675311, 732521757, 733199787, 350142860, 709841894, 463498333, 762271045, 147841179, 858521177, 874046502, 282199391, 439963330, 233835455, 333465393, 905825268, 204285651, 223826534, 164896514, 524825540, 919021106, 139624847, 853850034, 757912031, 359438255, 91235454, 334022684, 276063142, 987297634, 59829320, 175405970, 850324118, 848092380, 489905184, 22097574, 337815514, 472228233, 598281711, 154451950, 75345294, 209673644, 807451038, 939632666, 845374572, 419592271, 906640291, 90082512, 356372387, 481207868, 759368282, 135220180, 411597741, 873734447, 923069349, 742800791, 647543833, 548174010, 541686413, 968835539, 480324536, 412642419, 805219251, 682085920, 717495393, 538301508, 332497073, 271920637, 617736765, 256611584, 195482705, 445945107, 321093199, 255265430, 898167660, 22440293, 65267428, 891786748, 804681979, 437000914, 340257653, 115671156, 299896209, 349291465, 152244331, 23398593, 740464200, 266701957, 371929125, 223924467, 257264739, 362903040, 411533770, 214441274, 829352748, 365181467, 908039065, 148982609, 819464284, 437531177, 856607224, 268468336, 829701692, 848119454, 720360274, 493093333, 694071440, 790820886, 384080048, 579373041, 553890274, 205171165, 522650359, 291544161, 514783669, 243380240, 353205020, 259107855, 834582425, 119016955, 69416506, 16725685, 784769339, 240179639, 808798025, 968794427, 483797326, 419075887, 575638983, 790781379, 915705897, 278912009, 659029441, 871651780, 295705346, 889870482, 943304895, 641474131, 667524344, 980539778, 538017413, 19332879, 794455634, 584198429, 640835988, 754441420, 803610802, 237271684, 238790639, 630141937, 749235724, 911178521, 30669002, 651460690, 762223502, 116506432, 526159164, 897672422, 91594808, 589894526, 356561724, 917520570, 618235429, 904649133, 279562694, 553998569, 824292198, 305210604, 329194773, 856338885, 560488545, 996568915, 769297601, 600562351, 716620817, 222314254, 649391516, 109653995, 590944536, 641554345, 945415053, 965217010, 59037209, 936899698, 149057588, 913293854, 549788579, 758378709, 857519367, 150595525, 46216824, 174918756, 32651953, 517046016, 849137156, 17901986, 35781859, 874752768, 859594845, 173583015, 97077628, 851811469, 100903859, 417976377, 829742250, 142371366, 17869789, 341208862, 679016079, 455480499, 904644094, 228786872, 700396135, 765488267, 978289965, 912450030, 31665606, 605078633, 940675761, 316851289, 976972816, 688584635, 838015901, 301321076, 309223032, 606838022, 14245863, 133720786, 191362118, 385338176, 491802591, 748300220, 794859781, 953617576, 732523109, 822288735, 416695915, 861262067, 937360942, 844772483, 425486201, 617791112, 525974311, 831955659, 266726216, 278177131, 604943459, 63852915, 431055152, 189272705, 450412372, 273924587, 912640039, 856046384, 709852554, 471570514, 328171075, 744743125, 552404876, 404111608, 100124971, 833435004, 276130059, 457645609, 739743212, 749899790, 360383565, 89656617, 486657748, 487097891, 385756507, 365334901, 885113456, 984983194, 302856249, 954668058, 611232712, 915716089, 355218757, 74489608, 981382834, 624146157, 128505580, 793242042, 990913681, 352654704, 705056546, 211966275, 895757967, 398367170, 145422575, 293286145, 445380280, 700357154, 859836871, 389504459, 453627057, 782595360, 289591245, 298018517, 335102177, 41165327, 356943471, 697271777, 684368090, 41179643, 89300969, 589908672, 486075406, 766368824, 591566083, 719449773, 293227479, 257224055, 822062855, 823647541, 54482688, 620895471, 678198233, 565218810, 301201956, 210835366, 833889317, 542919387, 450208978, 727987497, 170160429, 796910461, 969954800, 995946643, 313508475, 541640439, 668594573, 505562947, 96855614, 266362724, 351425901, 65132370, 130612430, 929064437, 372846201, 465755101, 516484687, 104131720, 478235664, 152713341, 506470125, 920763131, 471636812, 405316097, 590920254, 353749736, 474981367, 732195407, 631264860, 197576794, 183322029, 982879423, 619122125, 936442352, 794494327, 621641774, 177341186, 683058830, 810335491, 179277954, 869284783, 558013549, 414788811, 405448922, 534907728, 458081624, 299968641, 334238628, 515797301, 896493965, 470599946, 756575076, 342873061, 784326892, 655414706, 610590070, 382424760, 923638944, 174270194, 760860740, 879822039, 747072855, 349922797, 259685664, 410519179, 105992486, 886692946, 170377429, 427184623, 82602601, 360618647, 160660173, 311807440, 563562729, 355991249, 839173010, 237486138, 638523251, 505911652, 1735229, 396772821, 823610850, 979176240, 94026875, 333555100, 705693859, 383699670, 238595184, 838187960, 876684085, 543635397, 171427941, 985783136, 440600132, 423279286, 916030988, 765618609, 62064656, 604134288, 98274402, 322416380, 624450755, 256724010, 701758341, 297204679, 280435544, 674710723, 988661493, 430124178, 158046032, 354171600, 709677408, 641979505, 710176988, 348147860, 17549871, 845547145, 997059717, 472222169, 402315093, 995325901, 332949716, 928456422, 837283122, 803826395, 2979669, 818734935, 579551622, 844675284, 280659035, 167149675, 933694913, 625918782, 706945910, 31566627, 741451713, 589424869, 756170740, 3777370, 960596146, 529442385, 700228978, 249523680, 415992706, 555827334, 763238369, 85406491, 331823853, 12515703, 368920363, 299580553, 698365296, 505512054, 781456355, 124971180, 894721869, 466884554, 358167777, 824653643, 175776998, 839100890, 276333753, 1733641, 942882143, 967149343, 804436605, 268332551, 203676861, 358902077, 909645836, 480474735, 245136026, 317177830, 139464982, 384446190, 121471098, 176489162, 226461853, 481573924, 49283447, 731772601, 98389029, 372837794, 390039040, 872890564, 606447004, 928068607, 192561641, 13782711, 824108375, 438036575, 386358595, 696187388, 939174280, 235462671, 178192543, 75446242, 394689283, 644735935, 736686223, 733762278, 184179388, 591690815, 292176751, 470267659, 522659760, 750258012, 468975584, 675290144, 762981987, 260144459, 102382999, 191641427, 147085622, 844433621, 12520751, 664347338, 41482984, 483148075, 621877913, 307766417, 208997720, 960635810, 51932442, 689902498, 972224734, 432580337, 572439626, 142364130, 380135385, 635728913, 78091844, 550635360, 911373752, 600379995, 748696196, 457114149, 13632578, 819386527, 424832650, 689285563, 568154567, 625784098, 165248821, 194363373, 864608811, 28869533, 717236915, 682272269, 975278727, 272399241, 384125101, 596827373, 520634058, 567301305, 4338427, 855105459, 558420968, 946767605, 669167308, 476429424, 509870552, 145965995, 802596135, 980032988, 494590932, 273241894, 202749383, 738582832, 781777496, 68756005, 862665126, 133032235, 944963343, 697178053, 579570254, 723308443, 597002414, 599936159, 423701523, 69530019, 630475801, 28556647, 229448791, 434199235, 1290841, 190112926, 273958374, 400392263, 895073200, 415136726, 920821330, 451653156, 635750208, 237059309, 382118812, 498703690, 290557822, 356456644, 659629737, 731596047, 98500585, 280315004, 931035903, 891358406, 164413184, 135244603, 830115620, 459160979, 908677782, 357477512, 870708229, 660690685, 154730726, 52586766, 914590024, 733374194, 567073686, 555923257, 751219659, 380950444, 232889373, 362933119, 775051403, 231373259, 206048976, 877639351, 51364836, 295730348, 218821964, 887481039, 801982433, 177040136, 153548339, 628344391, 622590596, 954634977, 514614755, 188656462, 182950452, 84260233, 179660921, 275121852, 129027020, 629113909, 88325991, 46212458, 645412199, 891348474, 912507152, 528351035, 271972870, 283315707, 865168723, 102484749, 384855107, 958273032, 321730898, 379548125, 385902275, 671515632, 936595857, 216238048, 535008393, 307023969, 760574160, 734839629, 538353154, 606256839, 401908840, 619299744, 236190641, 306200941, 250427803, 494961138, 557447967, 681512930, 630976897, 514391167, 696656245, 897148708, 932141691, 42811741, 714987367, 205050585, 426476349, 214116198, 665246977, 125822776, 331673513, 827532728, 28052410, 193487823, 453012561, 740561871, 875645110, 614903210, 637811805, 640246579, 940937740, 651784113, 369572886, 816634463, 151498965, 677083856, 354533314, 849133947, 515551322, 487552835, 980306336, 110338830, 947109003, 387547001, 22998267, 213361183, 315376508, 739304033, 730307195, 25061780, 328913219, 987886179, 349911579, 728912727, 143639540, 42479750, 564153749, 164200249, 167360537, 383691296, 99720406, 574736331, 480485323, 795586248, 600109588, 774544427, 456947122, 225966821, 676576677, 568658839, 8199720, 334025101, 682996152, 459091858, 736526571, 86389560, 301436131, 592078528, 608848325, 461263817, 667406050, 612107453, 599523396, 983892534, 864323769, 529479095, 595795191, 728216066, 327653945, 356365151, 686456010, 697736589, 538374600, 652018775, 479844731, 547051753, 879550207, 928372148, 45116871, 432023672, 431073954, 377346795, 288807523, 958528951, 331726389, 321498800, 70316794, 413394269, 466256823, 628133995, 637418843, 134177023, 440815784, 113443688, 602548210, 552160247, 470733778, 207334779, 316606726, 407723490, 985257122, 341715139, 940190227, 716103549, 985498932, 975446027, 858425254, 544237688, 457774795, 720093667, 790026635, 593350500, 96621222, 661138159, 309057407, 168583835, 722332993, 477319712, 530156650, 489368043, 473400983, 842054217, 922748952, 975487579, 800320134, 820834818, 99165519, 265058232, 61062066, 422074635, 408564354, 709988489, 576447408, 81158628, 132918192, 360237988, 867590714, 365645122, 923148367, 658941615, 862655632, 680174135, 775949884, 612275460, 639609864, 22117823, 121318782, 380597202, 746575855, 793648487, 79729163, 985980459, 222387528, 928210772, 562042703, 668006147, 679843582, 789723880, 848404941, 297726170, 629694668, 959410998, 654869914, 216049658, 608696085, 899324923, 130520062, 335075842, 591595357, 626950166, 747505943, 635331475, 248455071, 529377632, 47468928, 120943145, 414702378, 774974842, 965490172, 482866887, 316124268, 820202309, 744418303, 656725412, 912500397, 546163590, 755609805, 197244453, 616918966, 344626604, 718486281, 865874358, 944506035, 913858093, 362780859, 249806799, 72593748, 557411967, 670915039, 534057255, 223919151, 112509429, 569748741, 644462582, 864979016, 520519963, 379158564, 444845913, 676311081, 440017254, 270008422, 996261877, 798295565, 622581844, 705270515, 219101737, 770642625, 842342619, 461894148, 281816738, 3194978, 832077709, 519003187, 743977626, 971330930, 886530034, 11979213, 435428605, 360240939, 527625944, 874022901, 318602533, 819315243, 484999859, 41697888, 340474483, 635172963, 794613274, 155737619, 685250782, 156338125, 24225983, 508085858, 522307967, 245375987, 370839615, 632993034, 735922628, 965181424, 239032084, 791177856, 906829252, 665444029, 310292741, 221781634, 962055512, 741373819, 61587989, 367534036, 25861223, 464332356, 150088255, 379838291, 946607393, 621596841, 730882313, 833388842, 910001441, 609292108, 241827908, 790327415, 799277550, 643822066, 230075025, 708759589, 864972540, 104106498, 821271892, 479809977, 722024106, 668193506, 841314822, 340327587, 402238508, 208155816, 208039592, 473215566, 758489152, 432050811, 373637170, 535821275, 364175119, 652060743, 853474529, 378947799, 811918301, 636162841, 393554188, 479518750, 351630745, 575781081, 151055347, 565864604, 721565279, 540791157, 865479701, 518855000, 598973636, 266269912, 109872548, 211891805, 673000774, 377319473, 44570242, 927947386, 318943370, 584674217, 311023413, 760641267, 943909996, 128726362, 171703075, 658428755, 325438478, 747274993, 618382201, 523209359, 399903988, 652791837, 633670841, 720002868, 574875296, 110227499, 612275788, 305605733, 468173586, 324478403, 130838068, 536300180, 886886063, 628467730, 464073830, 861396964, 566695830, 957999208, 471611698, 782493137, 977587672, 335796462, 354762939, 330780161, 244731666, 714576143, 606843774, 917842827, 399304121, 90532899, 6467626, 268453878, 688821290, 212552616, 437479948, 800820003, 429180379, 19328006, 484776746, 233017351, 870563425, 371506701, 279535038, 974608356, 554083693, 529811085, 292816906, 728928844, 777292830, 251540939, 277392557, 187033280, 263869507, 878936653, 635761044, 892299190, 220848912, 881865073, 255044066, 855403764, 298774934, 428860281, 663140980, 739101594, 621995943, 87741869, 584998023, 784726688, 337614892, 441919629, 380210952, 352909433, 362192934, 223527548, 755521490, 180739040, 912919023, 787763889, 883979805, 174302523, 834659305, 942285625, 335735086, 750114735, 192951654, 599748714, 210607300, 294994188, 857903637, 351565906, 354470796, 971756965, 579186288, 665839473, 304673335, 138706285, 549686242, 658183525, 590038680, 923239359, 775197195, 180166472, 403471704, 11425149, 369934924, 114228195, 233681499, 984945002, 151077241, 396730759, 1246838, 780543242, 758304670, 840310491, 951231129, 655050707, 824625649, 965124486, 402660193, 293747773, 376107806, 229294816, 490151094, 690231231, 325052821, 494208632, 646671861, 776716714, 57298798, 552026321, 180356096, 320802918, 213643058, 659460018, 740935843, 183805863, 259256863, 668259805, 165397444, 457538027, 701166056, 637203862, 459405571, 193006957, 119655963, 718720420, 42012465, 295900861, 173950460, 836228607, 360650967, 377027587, 464292974, 810613776, 527958320, 781107421, 863646244, 920274892, 386399014, 125135751, 114719515, 449963701, 145924836, 56374967, 773102496, 178165219, 393934970, 107166770, 829517069, 515031065, 177889930, 97875886, 53649812, 322795719, 433456085, 496455861, 934790483, 63120985, 96623013, 529663114, 275924758, 502204812, 754823996, 884570966, 675821435, 512621530, 834023975, 158301574, 949454682, 902777872, 451857848, 309758143, 139861602, 161094699, 776722307, 349012963, 714820655, 586640337, 19909290, 247414456, 756625786, 355186508, 831723080, 883113995, 322374066, 732171900, 372052573, 642031405, 56938844, 828130944, 577629278, 841499958, 869801264, 701708915, 279849428, 55317761, 557962232, 165641594, 388778686, 949551822, 85976308, 430245564, 186913738, 739831665, 804115657, 594624398, 282539612, 838830220, 592184122, 128071234, 420946209, 439520465, 308850046, 663457778, 772052079, 85607728, 731614994, 93939409, 812644313, 528596828, 441585736, 571764458, 689593570, 349617662, 221797624, 780906833, 175474632, 472918203, 859126220, 606390133, 68461124, 720117277, 203822897, 53780374, 532508662, 699627783, 294218911, 140455131, 771528942, 563861552, 229817591, 813509814, 569584666, 867826165, 247268134, 165659164, 15797792, 51580227, 367721988, 572023552, 414189532, 715494460, 638363695, 345515621, 536365386, 456181753, 677297448, 579908825, 875165371, 558932138, 948748767, 249647779, 717030238, 757890291, 627991736, 941334223, 414378975, 592053369, 492534517, 916598073, 267278825, 784284100, 646794792, 872072350, 831488782, 676957968, 815803207, 511917974, 706132870, 790239220, 518118492, 429963355, 840803139, 338090139, 182675229, 752488925, 797031605, 121115369, 115771275, 138821534, 477594399, 385675642, 912510965, 939186051, 274920671, 471601417, 118325829, 626803067, 633532814, 780479616, 223658988, 370286600, 963467486, 709722200, 299607740, 840083522, 536311218, 385648891, 605214357, 254056435, 278500447, 25253651, 980291954, 773265921, 269727888, 280007903, 380334953, 751842661, 406511864, 769913544, 570836827, 992756622, 848251392, 278676978, 492354232, 245268758, 578665852, 286568440, 50597360, 199077578, 298404128, 72750773, 796014320, 206418740, 118287459, 593341525, 712994683, 627075267, 414107578, 274242233, 944474164, 426967084, 178321661, 114198469, 722483109, 520540942, 342147074, 776560320, 295274846, 162619192, 386345190, 968372690, 393695375, 700382519, 437830107, 196281821, 544715899, 462551200, 892831573, 826580191, 144918182, 355773421, 592271135, 27750704, 671415859, 622870918, 222646892, 755408087, 840775429, 977607763, 374887293, 272970374, 112077652, 103814593, 157338053, 905415754, 576567740, 427040645, 650498715, 901751657, 569183321, 82595828, 349836870, 421607508, 909375687, 38217126, 808643300, 300569061, 161336824, 262424, 359815904, 238146393, 793818493, 625323130, 395787243, 653792366, 823774607, 188320838, 232300360, 745916750, 925970754, 244730766, 138816968, 730894134, 365427077, 924623858, 25042257, 170627936, 336392939, 704460251, 484816210, 185980196, 244612615, 136813315, 715458704, 901663640, 454889371, 566315418, 952901915, 680651178, 833203301, 623820670, 812686219, 341240115, 469804928, 186479256, 596512099, 97247528, 200310759, 13647406, 154041252, 719299883, 942335915, 377810059, 620517569, 80512706, 480217237, 233108987, 640168176, 208888150, 691703003, 672474147, 643610387, 847306527, 508698612, 460885906, 826234497, 462334508, 17496827, 924460313, 492257087, 897226245, 181884732, 755875596, 698450272, 313124709, 994671558, 359198348, 178729424, 895655034, 379207291, 859216391, 697721843, 108288909, 260628272, 448440447, 225955223, 348492399, 499448778, 115783180, 784751007, 420101158, 740283017, 507301152, 617391536, 403790423, 630928030, 750112333, 151382267, 188228724, 55254558, 59979228, 508271071, 84250504, 104041232, 545977063, 772347548, 582263867, 451401588, 660204866, 927035461, 990579577, 960181058, 723739162, 38048257, 222562772, 568128495, 302726602, 445961855, 797881206, 224756859, 80844636, 341184034, 776881974, 893180760, 717818965, 63825989, 308418858, 983424872, 248902789, 504022236, 725991129, 818798819, 644241603, 402628413, 948022319, 552821702, 957534794, 990176735, 614552249, 899461582, 849383817, 509123800, 111205783, 297847723, 313725149, 260612426, 924684539, 856003858, 849864323, 237201325, 19242713, 348409177, 620763670, 217708242, 887389335, 961881652, 272784554, 499239387, 673404633, 190305619, 523111464, 663362239, 862925695, 763502401, 550487192, 218329622, 744605549, 416372626, 49917591, 896857471, 661078683, 324875525, 921200817, 110429752, 615143442, 720568707, 382348911, 664552097, 979520919, 415944378, 264387391, 503933916, 212890514, 653544478, 889629670, 863379727, 692519738, 801204845, 62607718, 259049745, 434607797, 288101106, 893596185, 673661751, 503292828, 623562298, 277359527, 689032961, 371365871, 283909428, 733599553, 336172721, 830082525, 33868615, 274672131, 804414968, 947325516, 200358110, 214150384, 533911235, 276344273, 50980240, 953310706, 106872008, 554963917, 502171416, 859392375, 307223707, 695731011, 15239091, 61549265, 909622381, 170161240, 374193808, 824665275, 402823979, 10288882, 973663376, 870695973, 111268350, 702697814, 28917088, 104740576, 435032043, 371548598, 363086863, 794312699, 832574786, 850677879, 619344407, 404085975, 245094185, 457629097, 933954027, 138918418, 982573504, 928442544, 760959186, 778934610, 981733716, 553623406, 884561090, 679556899, 714669771, 907989669, 291635865, 376413249, 539240907, 739530277, 465987685, 597110362, 499667353, 753795243, 164363909, 42246593, 116216204, 512845824, 832401751, 337607659, 825991565, 195764959, 502002057, 639314235, 920509273, 788938641, 29956681, 712450961, 318273456, 232704756, 227439043, 455471084, 72816282, 43335259, 138557496, 372762489, 223965793, 263808500, 664433005, 928229262, 768069385, 826908701, 989585110, 831229972, 118002651, 871413886, 98001082, 893224820, 806898724, 201459896, 888768372, 112048042, 775381066, 92301707, 401303387, 32372226, 484569729, 100766652, 137390175, 357096387, 389564464, 301278326, 461072303, 636957886, 663426476, 844974658, 910851723, 43030990, 998510650, 857324220, 913534753, 760930940, 614187631, 144382724, 196106481, 824560707, 455777637, 23564765, 237227361, 803754681, 872383003, 61047639, 503645706, 386809483, 317832067, 212149401, 636810271, 998008321, 805616509, 542606787, 689306323, 131098680, 262617463, 172274398, 512716384, 64345566, 165516526, 636223728, 860901645, 79116737, 226458613, 290691376, 538474047, 852096474, 490038190, 948698857, 458586289, 101745762, 660508082, 956449125, 268623319, 943713212, 649296821, 2938279, 223348845, 285272481, 458942504, 319469032, 256295657, 555940880, 82318604, 695209087, 252089492, 373094716, 562497979, 508362098, 724207051, 766489877, 39522712, 325952663, 362262114, 707276455, 937836336, 8379229, 34919479, 711258773, 271519084, 883370195, 425385330, 350849189, 816563295, 277151208, 482525097, 253485247, 932815096, 278565763, 959878343, 279802323, 623258859, 94430741, 111800700, 591981417, 475935434, 782341317, 619923617, 129959407, 454553368, 959026, 352300573, 545454513, 391891466, 599211296, 391050927, 431034245, 829289823, 989901962, 434764404, 201112443, 676440968, 472961120, 734806346, 405162538, 257508574, 395470046, 314243364, 761878859, 363547169, 560162180, 989935648, 842323362, 183880897, 120996223, 585027126, 83668726, 512564389, 51818358, 862174141, 187485838, 676823170, 460875388, 461089972, 985151812, 565326316, 353765244, 668783392, 78197020, 300286522, 304138380, 402808807, 99392183, 722227928, 333173906, 161696661, 161551558, 935361043, 578820167, 972045336, 154438591, 173210280, 753602702, 938594622, 208817820, 988205763, 803408113, 894302339, 230737060, 18531041, 127696052, 256692751, 997278818, 926317538, 123191992, 706271276, 883141356, 120161810, 831660704, 150921324, 70647175, 642396226, 267587371, 118029922, 679950292, 385251615, 778280531, 605965033, 112538257, 171216023, 83812470, 507150671, 315383556, 919098430, 671814302, 830502036, 845256085, 279256190, 968274155, 398232510, 900504871, 429131518, 373105479, 841239312, 797652783, 895851846, 979200835, 849433676, 989647530, 311272670, 288352001, 658120115, 924640828, 317107590, 671823657, 334270827, 114306206, 581199037, 539909417, 335234827, 714332498, 56495806, 65427340, 987650678, 501221410, 828458015, 363658333, 318205290, 203491371, 879772557, 185521072, 125399433, 844817856, 818643884, 468594383, 856498998, 166767752, 876736334, 732808705, 788219089, 767183915, 575450018, 528574397, 476058298, 948984067, 672381601, 96270870, 763514440, 167585339, 381011998, 594667373, 508089486, 989651764, 349012578, 895594889, 270290293, 808767946, 191038507, 46172278, 679369411, 73516515, 307348684, 999299272, 973537680, 98471513, 136895427, 53480486, 328566126, 599942185, 501025219, 896105558, 903846322, 458043907, 159036713, 766748955, 415273813, 769634738, 836749320, 217158098, 124482612, 88078637, 290578887, 48244304, 249393406, 388633555, 196435018, 202164771, 285093149, 36226112, 837047869, 168507916, 500891371, 738915257, 83782231, 430949405, 784539911, 559562921, 423528810, 854069542, 398963115, 729456523, 420634590, 852908888, 109349401, 742544393, 124997929, 427817031, 797390565, 831733967, 203120705, 495119327, 212431824, 777671671, 566837759, 814460897, 278532621, 583871967, 946406631, 765033529, 949930308, 810646838, 109698256, 455556286, 524998706, 42023608, 980203260, 32948277, 890522922, 888105529, 824600859, 207351613, 430597218, 545740636, 153351817, 855776115, 135616073, 97373719, 153354503, 661101469, 979043623, 213948246, 680747906, 448280513, 33160870, 212348832, 91979566, 655303560, 398770651, 926157728, 42801976, 688631091, 821244311, 631284074, 661784466, 380072199, 230386024, 956051503, 519509833, 87277627, 76403450, 548081363, 910152449, 902433079, 227626590, 882578374, 888962993, 337852185, 294024365, 331106488, 589128496, 811552160, 333019623, 960530719, 459950119, 485382943, 647360122, 362701197, 353537321, 647635476, 624267470, 978465874, 145791755, 220076663, 515954669, 187085458, 486945557, 760892666, 439352500, 166217138, 8061694, 176643178, 643804430, 32640947, 855155810, 893843716, 386015318, 321324419, 781039915, 591879025, 113855067, 535945800, 282117735, 577789501, 973502610, 51537053, 61597338, 108428325, 296165099, 834406683, 881584531, 801498640, 78989653, 445137288, 375759903, 875594451, 930740635, 879907155, 919139458, 876244069, 362859412, 429801829, 323606577, 996853820, 934075265, 444572420, 114731922, 769867831, 247415525, 598636856, 160634359, 607253723, 366398387, 740118461, 168284869, 192559322, 597419629, 119527808, 19519195, 907648878, 146881911, 738069502, 223172580, 47201299, 184224262, 221521043, 103030222, 80457304, 189032628, 26621478, 809750770, 129743176, 524800864, 477064935, 258294158, 674661997, 288340905, 871503851, 775032818, 796288043, 872236605, 684924375, 137845351, 168868446, 156305667, 7614626, 990883301, 107234255, 781430821, 261266345, 653261122, 603365591, 352002572, 373009525, 247426834, 197082121, 922112642, 384159185, 846459796, 257006314, 337629541, 253229252, 573191651, 551148802, 938044258, 649639680, 790443691, 400463885, 720119941, 422408335, 150894321, 28649729, 554895494, 888624982, 279736795, 891278066, 410631779, 705585082, 330299773, 449759696, 633556310, 349046380, 569926239, 602579271, 376103278, 492195337, 905109630, 476819747, 349470005, 508730893, 575406150, 12031168, 401918651, 46337906, 39223833, 198502023, 457521223, 190524462, 89014418, 253740968, 996704378, 506119776, 589176950, 418173869, 467113832, 875568083, 921517910, 928601972, 847398257, 827708893, 399889303, 375202205, 48736583, 620354261, 494784712, 418095824, 906240842, 863599837, 476915191, 924807246, 44281186, 340392071, 219069780, 697599051, 947464027, 100173887, 771052744, 940136171, 601288987, 891005908, 31695624, 213702460, 324615414, 470592626, 270755246, 975903257, 324389261, 948099644, 87038642, 598019634, 484871230, 28289866, 99628342, 110010725, 340704788, 254041720, 479283496, 929069873, 246572856, 883358251, 750593788, 414364825, 85990081, 707674585, 667032760, 761473913, 514907320, 688587797, 446563358, 591626724, 154637402, 5056815, 525957254, 905868729, 892613047, 340567531, 556079195, 814493428, 402564503, 635279275, 592614169, 669283240, 487481539, 475508768, 317515066, 722748707, 595691453, 217469749, 853622186, 882376019, 529208278, 706200850, 517296644, 892859408, 173789133, 540420661, 954319611, 865960829, 454534604, 547585111, 941631818, 12962768, 703737349, 595909778, 357440813, 81120453, 325263143, 392569951, 566922514, 747136388, 34987620, 735803452, 597138568, 126365507, 482080049, 985777031, 909693040, 527874240, 425133240, 55056758, 572176746, 747206103, 878360254, 197194990, 975446005, 492923608, 929780204, 910371682, 184023803, 265232777, 829312252, 184150096, 607773557, 806476704, 243479830, 807955743, 147276298, 769283944, 247540443, 106736721, 115075637, 843019076, 887013894, 119512650, 975268213, 97636930, 788134497, 115102652, 16460891, 66436359, 289449427, 98835703, 341130406, 4749100, 837933198, 857823400, 822685715, 728182617, 968453218, 978897513, 949241804, 503205151, 719200820, 332892394, 305214998, 340091917, 779850805, 39498732, 932128483, 729560478, 351366921, 309840685, 384308528, 200705750, 462077687, 668846763, 406399286, 880739178, 32978922, 968231392, 598394210, 28539890, 160314166, 588242259, 701235007, 795113636, 22528973, 415304659, 966784900, 402988292, 621506754, 523890688, 420885035, 119036407, 499809702, 567153438, 68136608, 203101965, 772970170, 648210284, 245665266, 787638925, 212881391, 986305937, 552296368, 358658348, 606316993, 751229113, 663759338, 742314287, 294362883, 480749079, 611891322, 273433450, 400984077, 354771799, 493532564, 14550731, 214491432, 211332530, 701981042, 324774947, 407681206, 548334914, 880731599, 712577097, 360269440, 180795914, 31762421, 274102360, 968674554, 462947057, 616473855, 824909479, 343946937, 690348922, 459805405, 710054445, 841107906, 761567202, 568536325, 119791427, 522328375, 57163575, 57385865, 707827916, 687158809, 505161436, 435801398, 873474697, 253405880, 975753391, 301678892, 848114754, 30480159, 687959929, 578783022, 840140547, 556757159, 690521280, 196448720, 52263641, 413886720, 699948857, 993099685, 298504683, 81275851, 306003273, 197329109, 118147373, 454783553, 984861241, 223620664, 824093063, 960590254, 266926758, 799471738, 42224793, 739717203, 301931521, 614593494, 812535553, 645196012, 148907964, 967566509, 522031481, 636996808, 427642502, 18444734, 360718676, 450802789, 733363608, 493936360, 232470075, 790897326, 701259437, 4367251, 832447368, 375819097, 679067429, 441992385, 282865561, 734306044, 262065477, 105389114, 223371497, 79012643, 418217557, 635770688, 896230917, 191236063, 948122394, 581339997, 422418153, 909349268, 144242445, 844090925, 937403334, 896737427, 308359846, 987846759, 147661200, 686482480, 204766993, 227916769, 869785711, 363945023, 686234141, 783494875, 925194837, 215856475, 821775586, 169660482, 855460998, 224287147, 440386722, 805722355, 266687667, 700132518, 621429922, 120447667, 955831049, 924375985, 302388625, 712279191, 106016623, 89034059, 582719395, 596792059, 935049596, 334399937, 921412551, 125121548, 759872166, 997124717, 189405249, 910539086, 190711905, 357738620, 299987327, 695938859, 505387323, 317007321, 84120148, 479705499, 105869088, 662554537, 295398515, 587667008, 826120524, 820484479, 862598204, 49421640, 659899342, 342426299, 241397248, 638853281, 578334297, 485988033, 846952105, 19406732, 552791558, 485892495, 552522205, 920834869, 975306606, 453921980, 171774225, 625220954, 262248350, 900015701, 700434469, 214534240, 798390840, 933091405, 81082837, 609759424, 348952274, 275822749, 720581711, 425515017, 155041177, 590169974, 349256654, 132151929, 755362651, 574057423, 172294586, 344530919, 459872624, 309179442, 500580817, 764521143, 749831702, 992293836, 132623359, 718028822, 481529546, 2260458, 668516337, 169290197, 27411984, 414134302, 833469943, 877590676, 650046926, 634354445, 562065136, 891883507, 202217075, 955625508, 451761141, 620281926, 566496518, 312819006, 649002302, 868544861, 276305951, 478131595, 584388478, 238411070, 147260693, 397170910, 278392619, 377399700, 395345569, 129236411, 540747091, 474137759, 317583694, 929909026, 264952317, 891092650, 550170324, 127151673, 681593092, 614688345, 704089693, 966430327, 639483188, 683563606, 129886458, 425593826, 463378470, 572456384, 202403076, 939725562, 79306849, 549364264, 450141045, 462222450, 267863575, 343398230, 272718094, 177299461, 467599416, 36563832, 869892877, 709269460, 410033491, 784346617, 904705080, 868714833, 156298428, 373439820, 381606803, 541304636, 452797962, 117101047, 176885584, 922767449, 359537261, 422156506, 189094211, 737983741, 905780424, 988317078, 708870559, 897186754, 871517349, 523644463, 674915735, 536409530, 364874050, 641008105, 5954799, 134528670, 671858681, 25466246, 484526548, 175196284, 397572851, 652555622, 352957077, 184485410, 509206163, 918838319, 308007401, 801677227, 216982342, 422165870, 490646627, 154298591, 399389998, 111509125, 97259179, 716390553, 775827296, 702891745, 852448349, 173289322, 793990718, 91037916, 791676945, 632069995, 628467980, 442504825, 535297546, 882723349, 653312648, 991672909, 461380358, 86632947, 421863027, 77985869, 971499494, 84503523, 362604529, 184587311, 459842544, 590215002, 63676169, 752363463, 250384245, 447638152, 242744093, 521039088, 7676342, 306812983, 24290518, 37027220, 799420609, 579178113, 268610634, 328111516, 67964004, 261676218, 874283868, 705024782, 371635382, 468299274, 695886201, 384516625, 51435036, 402688462, 298168426, 538587142, 892969041, 468360594, 149495391, 597005137, 89387940, 574905293, 297900340, 86404819, 648975289, 680224958, 669683962, 764436224, 229495140, 208870105, 210329589, 694086106, 374163984, 7407525, 470554636, 811682225, 711338753, 450118467, 412015900, 201204105, 253669756, 117855128, 462943662, 450804274, 233442961, 481289848, 715695466, 993543706, 55538730, 494891984, 233834665, 65493507, 969258767, 600639501, 340578027, 412174350, 845386916, 795626003, 237155397, 590104774, 606259514, 687668963, 600460230, 414918578, 113009086, 303914480, 56923007, 296041985, 703498597, 283343968, 439481637, 320080448, 236190171, 834956763, 846800853, 570984688, 325954795, 267612289, 65949351, 56896399, 723912124, 333107294, 694339676, 362079228, 787040572, 341385579, 156516696, 725551009, 371937280, 32488187, 482887912, 566220697, 608651515, 19325145, 264480624, 57637494, 813702973, 81803738, 388242367, 264913628, 883893884, 91616217, 820475064, 721795374, 186793387, 300012563, 522273591, 156227135, 164947386, 498931935, 913735456, 776744544, 264579156, 394430803, 642908498, 200746145, 434399526, 67058151, 714409761, 31999092, 802414957, 649450541, 701428445, 255053377, 552717341, 855258027, 990564535, 170729919, 229474861, 286776414, 352775229, 929319621, 699339291, 426407100, 344640422, 431365635, 486651501, 688742719, 398925569, 98734489, 279454265, 572186668, 818703514, 128836521, 412379921, 78983057, 176148587, 168542368, 848836233, 345100940, 224003884, 158776508, 236386390, 545010027, 353381178, 275552578, 595198006, 186982498, 480787142, 213943463, 558509013, 569064230, 40265613, 382190554, 963864702, 54812965, 638417305, 647926416, 263728059, 482329783, 595385960, 583871357, 808494254, 638766398, 969647020, 641933936, 257449256, 773904163, 650231850, 803328044, 771578769, 556634708, 841233659, 927901983, 290556505, 922394674, 110480458, 895916504, 166849219, 973451028, 41196593, 883220667, 900371301, 666676720, 465423966, 471596056, 108089716, 275555480, 779925453, 142265782, 454575062, 384793873, 401275304, 979559134, 139297668, 408130662, 438928595, 433561215, 664715895, 374155261, 216465141, 225983047, 128476574, 360275287, 595439868, 568168268, 622047070, 744472072, 417464824, 949266170, 134569324, 681408744, 515524292, 332106103, 846567968, 278961048, 703932519, 190271475, 938832156, 354258554, 572232466, 206374970, 883607140, 731136786, 80015370, 338627406, 359590844, 379161424, 628297852, 581942811, 39921090, 560894499, 282171504, 846643979, 557724733, 293352076, 621126613, 378752824, 249976490, 140068723, 545051938, 129432360, 12296627, 856152291, 976148999, 832786913, 194824014, 459736346, 53458767, 221024980, 472309927, 881377372, 908991493, 199616023, 915767976, 162514422, 820589505, 737961171, 316410839, 955453283, 926995232, 586769696, 286368672, 93445838, 732383360, 701610823, 797338690, 795627850, 612294018, 754576638, 218944552, 555028833, 266784638, 964532222, 27053475, 221791433, 154599535, 794401559, 588470691, 473759319, 810093663, 415810080, 972681952, 644601762, 49438564, 564934745, 217940787, 198258227, 582866596, 450543217, 323984890, 71263475, 373127537, 983318190, 36295097, 457001374, 141282007, 900695689, 778438971, 97027023, 816042003, 882227322, 112865485, 5462956, 774364050, 84926657, 632503063, 842217037, 628316540, 806186095, 628205492, 142703325, 537017967, 886688672, 606781421, 436930278, 950351837, 45461354, 177170524, 61613116, 175101064, 728791799, 389422684, 864051831, 187828098, 652242318, 470754533, 66761150, 392251090, 455387177, 726071994, 252924870, 892042042, 520199721, 862380793, 616552548, 437873306, 553811134, 126081181, 299654614, 224701137, 789284850, 437612138, 4529486, 892311614, 776440626, 532468343, 156000044, 276848441, 737063650, 78367054, 858183910, 919120415, 504507025, 502009652, 58071235, 931379461, 400743980, 405808329, 49078536, 275875896, 141473448, 323340834, 338962983, 299350181, 722508813, 151016607, 411765283, 38885075, 347017239, 449848761, 287478834, 856972787, 78863554, 764670560, 498773839, 208482540, 819041234, 440669491, 172192276, 788981479, 445954936, 701649919, 480622938, 864564205, 845336245, 457964513, 11398892, 954639155, 659155645, 317441510, 429992377, 875037851, 83435037, 288470900, 549631322, 225144343, 852342028, 194582328, 922911798, 871430659, 788039284, 978808227, 705053049, 836943534, 897805289, 720454007, 350169051, 99573089, 857903598, 889323231, 164975787, 878133061, 948591746, 975956125, 975526953, 847111083, 703924894, 595280959, 609599497, 951802609, 603689743, 561299737, 428433417, 592091671, 461593788, 943186989, 759712395, 90877293, 354342387, 798547977, 672988945, 529323723, 312111974, 426461344, 368254750, 462722862, 902194196, 497214385, 877492361, 193928882, 799519269, 289030814, 812507199, 475448162, 479520177, 105187770, 574773965, 504115008, 215381025, 988520665, 332347526, 649032241, 482457449, 789727726, 878931462, 345607784, 70054471, 433366498, 322576330, 154817410, 561778810, 313526773, 130753345, 579906887, 446760017, 809265643, 168792944, 518584559, 612594075, 574148918, 601194138, 43544340, 110410591, 77950350, 890465668, 846547667, 973097228, 679457535, 580193676, 67880701, 986632461, 931516269, 328128529, 57933814, 650970631, 352992416, 344421492, 190898271, 868930972, 207071007, 946895067, 392817148, 232457259, 758576773, 701124841, 367705645, 248846656, 398815301, 551036972, 783785882, 982697093, 636587477, 735655022, 625103845, 526389266, 757178930, 85465473, 419894665, 771275352, 925391326, 285021342, 501448294, 511773676, 135785931, 58160365, 250933634, 336335374, 518153805, 593248568, 316671640, 183821616, 658887913, 771870690, 734161107, 830222178, 245216703, 187347009, 5239577, 454521487, 759854173, 528406567, 373459707, 165448716, 150685392, 762613449, 810006218, 973473561, 80133274, 643734077, 155331151, 126144556, 177385513, 402771134, 831945497, 253154216, 966896980, 563715610, 575181600, 249160778, 40884226, 702936743, 912921324, 665853648, 69593133, 275042106, 856313443, 402245336, 262539662, 748661284, 326749907, 909238941, 931311546, 424924757, 219535473, 215769920, 50400687, 14007180, 439059292, 931356023, 596979959, 420202095, 957767465, 543358761, 655247589, 232264627, 385612823, 403700847, 746763469, 937262193, 330879966, 879305502, 894374872, 516468526, 867744544, 704948645, 646851962, 34374948, 261939750, 885495263, 53900514, 287022726, 495551253, 197726258, 79698400, 123375664, 649307865, 608228548, 814074515, 975614111, 577795796, 96396143, 84007668, 64194344, 295151793, 18917768, 475229902, 606925405, 292925609, 159049171, 694964670, 411320029, 263336743, 887546414, 170879203, 471741747, 825467534, 426126392, 266544038, 12916982, 303008653, 552491294, 455453590, 883173418, 672349037, 971393952, 318554795, 432579492, 453683656, 49161398, 886324269, 861804713, 570065652, 67027930, 400396109, 928166477, 554834270, 779190542, 144330622, 798191015, 558016936, 490849852, 121170573, 548439776, 817737994, 626734391, 497477616, 689599915, 397607301, 570276749, 304996488, 931691765, 100934058, 600390017, 669161888, 300356228, 20275574, 792636713, 65729320, 792527815, 588730102, 841010827, 251463011, 697598844, 535331723, 198890961, 654662828, 194514746, 475707516, 547602773, 734476763, 202698746, 279392628, 377775415, 276831831, 606112866, 543332313, 884331757, 53626591, 572616087, 142118926, 130233248, 757425467, 696471593, 186526731, 663538037, 949423141, 277616245, 930847362, 37032278, 923141550, 993702198, 894876853, 764906565, 449854425, 924970892, 344774351, 489024690, 535330604, 746832779, 25793689, 519714068, 78572202, 512679745, 499104966, 313126062, 862370919, 931225234, 187824560, 867270090, 888848715, 21517676, 911849001, 954007468, 542869138, 300645362, 587772520, 924948668, 659325982, 486433748, 446173168, 72491704, 302421109, 37506367, 83743709, 847131728, 873814775, 21935115, 364919902, 576215555, 110726419, 282481507, 34739015, 555264407, 351150535, 220406767, 139644218, 422591173, 528257375, 289305356, 409581201, 193735011, 815552900, 834798103, 660246644, 569417369, 789152504, 456323580, 490500045, 353793572, 783382012, 49559864, 973195172, 777163712, 976071831, 529585566, 283737923, 432922905, 60553765, 943900073, 808656410, 529521776, 857865886, 879236491, 883612441, 555039690, 912422143, 760754766, 506248158, 384129276, 802586193, 956188306, 347970307, 902506835, 707896962, 388984564, 407004148, 145660563, 602754016, 506881546, 242686088, 127739444, 271079314, 21985277, 261446778, 426693536, 350832284, 100816483, 714795465, 44673435, 613478389, 740055542, 584912045, 958061872, 639468791, 762912377, 299261299, 289330851, 145230876, 798869818, 164705496, 561224213, 549043364, 572116551, 675273813, 622227207, 691632359, 767800887, 87345563, 966602101, 781480034, 268791127, 265692473, 863877459, 472575431, 645706964, 255841550, 651132079, 324577338, 401834874, 688488205, 619022967, 444028905, 755043090, 168605496, 740374115, 86907513, 25558823, 41271109, 74958323, 458813891, 430416798, 567023546, 538123728, 601496891, 668169020, 296083593, 300382352, 795394805, 898457338, 979379123, 683741612, 251884867, 396347108, 753107560, 196032771, 75159572, 558476979, 975935722, 580231789, 326554232, 791123169, 533660911, 358972014, 62796567, 318002745, 733768758, 371038475, 639668953, 724267838, 597109436, 278575906, 206257600, 695066212, 476906876, 874809731, 39483293, 838115664, 62614421, 805575695, 244214604, 326454895, 479006736, 712695369, 799041874, 126530043, 542624224, 83777492, 722261149, 231402201, 733900633, 269962911, 447732650, 480096959, 394673262, 416380680, 161947076, 800324173, 469485607, 434274348, 566416135, 901373273, 61794515, 916817281, 694389162, 15743644, 444155020, 238341598, 6951455, 763697163, 958553899, 657358755, 3807756, 436174859, 90302470, 359527963, 211452802, 318046494, 565001064, 179970332, 515067307, 181556519, 591013521, 387024361, 746099859, 231533765, 611048611, 267324699, 874978339, 633905347, 892347930, 876498939, 691900231, 698632767, 482193361, 522655466, 273359345, 352129241, 894586602, 189122117, 2270081, 856549001, 12820529, 343820723, 7259980, 899720047, 674012364, 84477396, 35547299, 796639912, 700045817, 91166200, 58228678, 758283931, 220736767, 511508872, 628305725, 40812216, 369817885, 255959320, 983041672, 970015586, 191830614, 719246604, 472194085, 682478890, 319980763, 798187642, 904502316, 588852480, 499199800, 637991759, 634946070, 531070786, 900302382, 544259275, 659845799, 302716471, 370222070, 611467191, 845034713, 868839490, 746880601, 572558737, 586900874, 318641703, 491151338, 449042149, 932446779, 519576412, 246097788, 541841428, 34900070, 279353493, 151886236, 971605377, 141321781, 269508008, 209092775, 67284138, 847010607, 251924898, 856641653, 51818394, 457003237, 621307653, 414342616, 832377525, 196314781, 663003679, 122740264, 373063346, 938076121, 186894394, 804060580, 499269274, 658181841, 627747132, 39558032, 819895571, 331029934, 788420230, 211425697, 892263728, 386179187, 55061908, 816732417, 516997622, 854774179, 121726326, 883413656, 373810269, 664277590, 944365559, 43646732, 119368020, 266144434, 960660273, 65890552, 960351565, 157138423, 860189887, 973747422, 946539723, 974509276, 168718704, 194017629, 467851479, 226518702, 99347422, 61464712, 30797075, 350999386, 917182292, 609027173, 116066576, 258814918, 482869710, 793764342, 472115331, 126922949, 422023471, 203897392, 484287730, 154259073, 302974706, 286094731, 224382508, 364041196, 641693274, 384554498, 576711522, 758142381, 780164739, 587530546, 458921206, 863296992, 783688141, 207407501, 815100100, 810422410, 803738356, 705487526, 287149227, 506608249, 827075240, 727765069, 612679313, 357082886, 96299230, 149763470, 64327037, 123592760, 721564021, 718399381, 455107641, 119310016, 803187207, 708053815, 77515367, 754626068, 644660211, 509136701, 303774599, 857887997, 600126461, 424280491, 467940912, 661065502, 832631509, 521923329, 811782933, 987139096, 448605619, 901478636, 705622440, 188262260, 464123105, 220775253, 209543561, 321753816, 254234682, 68141977, 358347167, 936757733, 888012065, 477222410, 120602454, 536232146, 276327415, 879274354, 618931311, 915208604, 831478580, 451180028, 665687662, 301740889, 818814654, 39884582, 385119681, 798111647, 851581481, 351383216, 542342849, 694032203, 293337327, 486706163, 538624840, 595536435, 383182289, 51274851, 812524392, 322659162, 167418716, 484455225, 325510177, 4444552, 645922723, 203673352, 845979267, 802868889, 582721, 281359490, 719229072, 3901614, 233226494, 576911445, 612282917, 348691817, 345620525, 507128451, 777916264, 151002591, 213235891, 94532863, 840956818, 453874279, 138960323, 356416639, 707601399, 257555031, 761548070, 652930442, 880665298, 973131149, 820731644, 331097084, 961537411, 627218934, 104901869, 685184750, 467541829, 340218440, 409769712, 464634582, 761426407, 935892082, 421307419, 414596326, 153726319, 406035956, 527422445, 511075184, 954216597, 579037635, 855758190, 231535947, 962104256, 467108431, 104079892, 793156367, 504395237, 426726972, 305037909, 396790220, 32982263, 474082275, 403441393, 936449424, 460906815, 483874270, 566691857, 235369584, 674856559, 511903707, 373231407, 604758053, 952786577, 437965937, 509311108, 624103291, 843196751, 970634831, 548233672, 234902853, 217663176, 651905157, 731845270, 4705258, 772652828, 602812525, 317860550, 422082451, 199688971, 265659112, 25184887, 1830288, 981543097, 158953819, 320899198, 323478953, 883934134, 499248512, 640904210, 129404283, 797661737, 948638582, 492532805, 83936370, 181153572, 732970594, 431826534, 306268875, 475043582, 363904010, 63649258, 541625765, 420902371, 220299249, 510818819, 222554154, 806236662, 219764861, 1644048, 985410632, 882656267, 944640705, 231102855, 953039734, 74992020, 868902488, 569025528, 411055127, 400044374, 167119856, 470405200, 159995889, 172488164, 907044692, 237700796, 511354586, 314411590, 471174902, 19006023, 507891353, 448222311, 709291271, 510199113, 253673120, 466937854, 686413532, 440745368, 277256898, 404012331, 356993340, 179103917, 267467973, 685535346, 215719313, 444762876, 346483125, 216078900, 20259432, 219401387, 231145854, 928970518, 505432312, 383775358, 155558700, 861122843, 860952739, 915115146, 589347349, 347783442, 430453397, 304475423, 577582086, 917472319, 847582123, 135189818, 528842313, 310602377, 955636411, 448258679, 36322063, 82128217, 343527712, 362995039, 40535407, 966496310, 574441739, 511651199, 408904359, 517287661, 283814361, 124147826, 708747628, 685994434, 571454895, 620547780, 798592368, 685846449, 764637917, 399955152, 335166678, 649249867, 684301634, 264687898, 187264630, 558046326, 418991407, 246466217, 41062152, 62278701, 150917055, 222342655, 699821883, 324067213, 343001549, 91288957, 838885496, 576551837, 197856313, 219328632, 193865636, 199049037, 353438157, 797998368, 600098683, 618209325, 66151606, 269834483, 587414910, 465879257, 519710173, 838795779, 73277463, 287696330, 777885901, 247542121, 460901296, 668251880, 232830867, 890675742, 855036031, 207034701, 115214632, 610968276, 29335507, 666381358, 251245191, 147913121, 434599783, 799077014, 965688149, 926508101, 283911533, 160906411, 149733073, 738286059, 444108887, 808966713, 417216033, 205969961, 759521380, 525447935, 875727692, 511279169, 351583344, 359573300, 183752215, 298944671, 368996280, 594142899, 237985565, 421221180, 735475011, 646247816, 695902663, 906785408, 954020681, 403094831, 578793795, 398922036, 289511398, 123449762, 362138518, 349839045, 567555217, 503874258, 647306165, 393815509, 991626595, 438066674, 546017643, 356952235, 581833143, 215180051, 563539816, 866079189, 216939908, 947978918, 623500746, 44947496, 311301183, 861686168, 609336902, 817518627, 329218151, 166010711, 892089641, 729129005, 715623162, 996196561, 481191742, 412377543, 38654505, 579117983, 396992764, 157964741, 751570629, 230376583, 914834237, 30661209, 362394097, 834445458, 908617883, 45726783, 507592506, 263588470, 620332318, 636511832, 837509480, 900911201, 469139941, 335907329, 803678076, 239810544, 971488286, 966487089, 59495665, 159611886, 881659517, 994623753, 880998434, 772675686, 780768007, 785648437, 991735321, 853915360, 65592929, 236473715, 156674190, 515826230, 614425463, 108282770, 265695391, 15462105, 128751603, 12228609, 404592331, 739585145, 849313277, 18729045, 749560093, 380916173, 30491890, 416407159, 642223294, 543615327, 87594737, 299253090, 898943489, 778148466, 667114463, 423363394, 770717782, 282163160, 855294835, 622183231, 265427605, 229066492, 275091985, 499827052, 125767673, 446987595, 25175925, 729750406, 758155592, 24405656, 735229829, 513166559, 385514801, 89570404, 589760913, 447293157, 772677314, 19899637, 749516705, 568934093, 242410073, 64271865, 132039731, 106037076, 619477552, 840740902, 691498048, 47765951, 734058794, 700918153, 920207561, 498012349, 200690934, 361876803, 112006018, 649622735, 691435629, 351278543, 322732591, 554237992, 880338799, 965239660, 590701594, 10985077, 676427363, 361942885, 297165072, 688576674, 984697862, 651399852, 206872701, 372660541, 877152440, 609529069, 439446482, 749973146, 575320036, 60690498, 303598593, 611492254, 314009991, 681729520, 338342447, 346312555, 594444478, 676945470, 450780135, 276978930, 715119143, 8418800, 707144805, 291108650, 625419197, 207741771, 866235905, 208933209, 791825151, 987706854, 814919272, 13283887, 970495062, 885948336, 609530598, 599867333, 166695847, 315906027, 617863412, 78226555, 775271228, 728304198, 29881475, 534325861, 656820336, 615357479, 350417848, 727614655, 131167743, 42088915, 133238487, 876885043, 153621336, 221571540, 462276107, 28402566, 241000623, 327650710, 20740887, 215327206, 408068816, 529876980, 268602237, 830760277, 998108744, 930950631, 906569580, 357628480, 255159843, 763273860, 465577454, 32176485, 126390127, 748858522, 440742400, 453382352, 370517836, 201941519, 473383917, 217860762, 589530206, 853735515, 586469734, 365396384, 22717745, 857229514, 366411574, 784252985, 149110874, 115122200, 788377960, 553917191, 633324118, 983803106, 555404243, 311751776, 899569108, 731042293, 65094033, 328922433, 997184629, 376868188, 49744583, 903029120, 826280504, 569148805, 734011541, 95139683, 17232490, 550330201, 883206452, 385491520, 448771538, 269989214, 452137401, 327900406, 321453436, 888535954, 326731202, 210012566, 335639552, 60379609, 485853408, 255953434, 40073996, 645907906, 124077714, 202561136, 159126563, 320825738, 440121274, 636364090, 136129930, 144595295, 866330664, 633211159, 8986497, 483393975, 922598989, 500962087, 695037616, 485205938, 386852479, 348163531, 45337040, 350874679, 213967555, 851772993, 371073736, 204404525, 506487138, 605557310, 672342478, 80239178, 344718989, 641623086, 836253247, 748240498, 452112619, 261495238, 178563128, 476177749, 349367636, 918934522, 155258001, 528913824, 800549044, 10210094, 183162956, 977470674, 482937384, 712865228, 981192550, 638895684, 384925601, 613084583, 115752319, 723231330, 914643789, 628789995, 200589911, 380453898, 641283869, 5857012, 866245754, 593877543, 71962210, 787893716, 966185262, 698595032, 538086558, 485831378, 512290100, 308539033, 578812529, 158338991, 877764420, 91009759, 268176921, 945762140, 745478266, 992307892, 126873417, 546883386, 436700484, 967075224, 893060332, 202090648, 218249030, 131185070, 306494084, 590810414, 195706034, 612554200, 780103194, 176369661, 841563040, 99930058, 733170665, 718996070, 824308206, 415613622, 943314993, 394245406, 796504997, 20535387, 267854353, 481525907, 384404338, 450325047, 134309189, 403726956, 52895363, 811293063, 43552085, 415050438, 815005252, 979775072, 479202551, 106165357, 826598057, 7344374, 60468110, 54273075, 504599735, 314784475, 880131822, 798062711, 472366880, 571508547, 708283924, 502916057, 922847726, 620021069, 326117989, 15198068, 2883644, 382480426, 12291772, 509511141, 138641800, 909236558, 76484196, 895033827, 129970428, 259248606, 82981860, 562736901, 262563180, 989236597, 715945111, 505406616, 968379322, 383136390, 249846644, 10156493, 502795452, 695785023, 413216685, 27056527, 658759211, 596853776, 814329622, 574624064, 119702760, 429510338, 842590154, 806764999, 135039676, 700857477, 37172145, 849984977, 33195117, 543238725, 319974142, 362301249, 909588945, 290081199, 115388062, 685381978, 166185520, 973867464, 901333514, 52655434, 612030420, 497268495, 577361881, 68838423, 689594270, 538060843, 676595691, 48950234, 400473002, 916449584, 941246833, 787575656, 395168618, 352051832, 775244421, 360465018, 812475502, 924640420, 609506317, 216516263, 763696724, 847952341, 788854766, 969370715, 410730925, 833076841, 738269063, 861348461, 572277052, 433086369, 292472171, 621969019, 617759436, 566734728, 688194307, 864447, 201222985, 530763228, 170482198, 756259836, 773559756, 65180756, 580529191, 102540662, 742642153, 324159312, 499546349, 662945180, 866232918, 537332671, 206393757, 207099398, 768201254, 158523871, 518810947, 742453276, 228584595, 468528151, 14863272, 682737213, 180160913, 778397573, 356470732, 828270056, 75056189, 257048643, 4926483, 279802008, 811165149, 398153941, 186131095, 288405256, 94440910, 758524869, 223968008, 120165047, 982452755, 340318653, 965255440, 613387518, 90453313, 455652954, 494190486, 467730627, 580389264, 703848386, 220023997, 889056804, 701889989, 357455044, 847351314, 743088628, 924760906, 73318835, 716261808, 17961828, 17605272, 671784379, 517678790, 853760090, 780733993, 678943618, 565285526, 97322278, 30615150, 214489749, 698489768, 190951471, 376228282, 496531085, 369835722, 909126262, 440075055, 761294587, 116068794, 935618209, 601038560, 339356195, 133036924, 700841365, 441351937, 19625927, 496435080, 164075161, 712027118, 673177250, 344219585, 150230736, 178995104, 363413623, 548845471, 522384874, 282451512, 654591734, 610661230, 972377109, 764616493, 787871156, 691933375, 854812047, 227203321, 359207266, 702913732, 718672762, 77173195, 330470668, 35421333, 871887843, 131323883, 699668828, 614486544, 172486028, 920509132, 209162165, 466965634, 997489200, 370155894, 945489387, 66582470, 372814073, 738229525, 454311448, 469521734, 25053622, 70549822, 542890725, 507917524, 21696533, 735054438, 466654851, 589385925, 472260162, 296663841, 884711602, 207910951, 419038959, 714493433, 755477243, 437949213, 564258386, 656955873, 82947536, 955863910, 862132311, 654749857, 955200883, 828375160, 469172629, 293649815, 126560954, 518096414, 182983902, 30817746, 796040601, 730152417, 36287763, 630635868, 952254731, 963204383, 960433523, 527696854, 52005868, 586313428, 382110422, 456297814, 511987490, 539941342, 26807622, 400859903, 515540407, 48593714, 549901377, 531248774, 145083319, 57829201, 933816472, 553168680, 928700874, 716226605, 65892971, 68815313, 900063733, 320018297, 203135468, 266588190, 123837801, 47130585, 328511503, 877631171, 401949509, 20662575, 655544559, 294148900, 495572668, 829268392, 270471613, 532341185, 430068532, 392892127, 843589656, 589908803, 974552992, 855210905, 710680748, 474545067, 271134559, 697189512, 655749289, 283866820, 833569354, 179681286, 641046968, 972094688, 597357880, 27664529, 772412044, 858683271, 699472718, 805294020, 207045752, 30428418, 900610352, 737995337, 53628038, 488441101, 951973252, 462012176, 996856526, 374346466, 280567000, 419096545, 221018758, 491839822, 41657865, 299238085, 266680831, 494866664, 852979633, 962842791, 464042465, 522049295, 51314073, 698004822, 572063536, 471623755, 73812220, 299746506, 770090404, 603882193, 824383394, 443435866, 694820111, 463251645, 46064084, 496803875, 914081552, 290604889, 313090159, 340437325, 168054823, 698183893, 18325159, 542481134, 991095049, 619653775, 195580859, 256762221, 549831764, 730254792, 352517462, 151061948, 891840387, 628495956, 438027795, 767125830, 944314436, 526573619, 563324540, 896776396, 227937986, 195715007, 576920375, 207515899, 735920892, 588778410, 927511890, 570692247, 932937611, 63879411, 572670486, 518941464, 971154919, 252184394, 534110815, 971520685, 182731607, 947320695, 731953150, 200837212, 974892038, 30821566, 390633798, 640326416, 17598360, 380382831, 852949568, 400171962, 27072757, 561454801, 855943689, 225959286, 173315105, 957129410, 597128401, 677727013, 214660145, 319660139, 874991169, 869503040, 654837376, 205059055, 625636692, 664357207, 266609683, 613408729, 634293618, 486202151, 206845651, 800744287, 554394075, 762407723, 585648684, 235222513, 260988418, 48481188, 284523783, 388643764, 856842083, 244195887, 169552046, 941358531, 738836681, 463212052, 194820512, 749360863, 878418849, 648827545, 193481617, 181481139, 504309312, 641647220, 726727144, 27486329, 579032373, 446764510, 4966301, 767667409, 468075403, 263901215, 658624322, 772428859, 355814327, 122790190, 795886185, 193571763, 901638525, 554643503, 466146212, 517970764, 311293381, 546009937, 394670002, 74706679, 819114662, 991721827, 598928985, 933591160, 340191027, 631933988, 122441311, 551815048, 633048805, 556279547, 357046414, 377822335, 732970929, 699538881, 204357751, 960822857, 678387901, 951661880, 219356303, 244945340, 241813563, 622620910, 313937522, 463708218, 155681170, 939917848, 624256620, 499336743, 980089116, 155052830, 58945305, 456258925, 915139711, 10495763, 952745480, 472917201, 481385877, 152205690, 881349902, 296339333, 955121098, 761653297, 969172003, 863762585, 351961899, 394383176, 565380516, 694094295, 464392320, 907169691, 151927070, 420425538, 509748852, 934572111, 209586626, 40633164, 775474693, 694945586, 161502919, 524673603, 840465991, 278832514, 411921193, 545007872, 695999388, 418012577, 678058826, 55276686, 159712263, 158762281, 334720184, 327299683, 245138924, 74561968, 939446478, 528148474, 499941453, 268367406, 887713589, 106728378, 769822986, 457807068, 236920255, 72501505, 623676236, 403059606, 475253092, 977833191, 308182405, 233091255, 949713433, 204223057, 233311105, 587631521, 191759544, 156434060, 544761141, 145305618, 516377767, 381771832, 100678712, 103449958, 925688406, 182804885, 348336848, 217564114, 553609239, 827695005, 912458168, 111847566, 440510952, 876870844, 277862496, 696985145, 117876343, 717090515, 712569967, 868087889, 953985799, 565284722, 408843531, 155079995, 962176781, 678036917, 563887417, 151350563, 814329245, 353200447, 540334940, 205351065, 536111997, 720559749, 37350572, 184138338, 872484465, 590074324, 444308077, 826790472, 743017556, 291245797, 635121229, 939056470, 11848457, 73473664, 197946279, 658296249, 470640546, 372799155, 309447920, 266720410, 213211317, 544049848, 677482841, 895119571, 102212864, 2367473, 387680944, 797918929, 27245256, 138225773, 502045647, 426113283, 518574817, 16253398, 269083314, 467897509, 557982732, 136314087, 973181949, 195231245, 516941297, 336089603, 479194763, 496477058, 760453625, 803997323, 240550651, 505377336, 753056420, 966770654, 862845527, 342286668, 941464077, 238791282, 179688552, 288474119, 538655520, 255930153, 960104632, 381312872, 652744910, 389801870, 788992465, 889978009, 336838862, 69269373, 174523905, 299565289, 894053422, 991059096, 376498831, 222921701, 547176296, 42857538, 258187620, 605739564, 120849659, 698844413, 74719500, 70220486, 997700068, 511840175, 664549721, 430257334, 252600072, 879535377, 711057492, 790319711, 106938332, 844425240, 714262458, 300414242, 381376072, 390313649, 213210735, 735426759, 443101092, 274093643, 168399627, 34096866, 592966027, 172814122, 261998372, 447029219, 82184022, 332761902, 647197462, 565092432, 676754674, 660494593, 410710647, 614452516, 4076968, 508726064, 43101001, 388859674, 375079688, 237262492, 534410159, 350006810, 866360877, 360782238, 511979790, 376066597, 374226799, 678595300, 744238484, 36318578, 344979592, 682349752, 495645952, 500637552, 657199295, 475133899, 714831058, 954215533, 353899265, 536099099, 914833469, 110304936, 120129162, 668737672, 840021768, 728906222, 497490695, 941791960, 29033380, 358010034, 244796594, 542083457, 688163013, 918560635, 772553507, 934463232, 314295868, 999558194, 180724729, 560227481, 149223444, 383876653, 491028084, 904042244, 454874086, 835755915, 327736847, 225029480, 345966153, 606812687, 669245577, 344645942, 35263651, 425608297, 474112669, 422577257, 573429744, 882902492, 353691398, 660821502, 813860389, 782019109, 149337289, 425528708, 783998208, 175705501, 959793276, 741093173, 607260857, 345303619, 866553075, 174877397, 916093419, 366983877, 670541945, 158424815, 56071799, 105713727, 298720534, 532392882, 669859572, 149613332, 258013581, 737540178, 361679638, 336993542, 349872834, 927700876, 397511018, 139844381, 443544410, 162979463, 619483509, 636663436, 863328616, 11435243, 434688622, 166023546, 280270145, 55618248, 13283151, 573654508, 620861056, 42566126, 523401281, 541403834, 894454048, 394585314, 653676945, 336190084, 564856073, 430220652, 769377546, 405207926, 521229190, 727593406, 839539887, 203482998, 819109465, 168005890, 678834962, 604308662, 834581691, 518588631, 92589482, 205051537, 171284886, 931516733, 582633573, 697146466, 687050947, 209477202, 267595335, 828647474, 432763358, 334420889, 106893385, 71925898, 356602595, 58135983, 679250290, 753240478, 290941087, 335312283, 62128250, 225049370, 232061218, 936749421, 47488609, 923046623, 187187160, 691000713, 112281689, 40614612, 617677326, 33351385, 101408078, 11504277, 518900462, 606467392, 629011055, 114525315, 723491386, 373665648, 72879038, 341008859, 905586062, 663217692, 540981826, 570881274, 197714810, 165770884, 737187222, 681531106, 110657237, 522995579, 969333126, 961378497, 7974125, 250337201, 212832571, 606946740, 901671848, 646999126, 384706554, 145831341, 535263725, 871000399, 147758188, 285923374, 894485852, 415403450, 301111570, 373866039, 697268188, 331948087, 460319634, 972304427, 444055413, 648986788, 667377785, 262113463, 378184366, 569360607, 483755997, 891070415, 648528536, 61059175, 469359455, 724735083, 846041929, 602663752, 706028194, 244289170, 952457377, 292629826, 444719109, 701161181, 741128424, 686404674, 217520428, 164891628, 179405853, 54935957, 661926409, 61887551, 459859040, 372212859, 225054754, 967133930, 144674806, 589511532, 625049895, 143444709, 463874502, 87712277, 651160443, 160197798, 964867807, 890094982, 645370007, 554762397, 478315441, 102394035, 16959063, 947161026, 24946177, 150897262, 498571515, 294969556, 566373255, 817247201, 800026379, 965719495, 783281602, 925211748, 462665667, 906997830, 40462560, 772546761, 512765794, 608228523, 650390572, 903095740, 777493414, 584974532, 126830840, 456581972, 332650539, 61084448, 315885666, 49423004, 404645722, 288147050, 298045862, 955373002, 793138366, 159556248, 335797354, 135326441, 244610198, 701924294, 395546968, 33363058, 597054807, 588767644, 264716129, 683997839, 204893033, 358177675, 729523217, 564169841, 377791239, 55400349, 684004742, 397242792, 658297453, 114264474, 195127885, 636896421, 633436315, 766749961, 787185717, 88466207, 112139092, 887909968, 242500791, 607818611, 67784378, 647714081, 807876906, 128828444, 808028200, 789448208, 84553302, 950983149, 686498125, 69151041, 875535043, 264742453, 837824793, 253680864, 880892376, 96808509, 881151299, 279981513, 868063239, 966751799, 425367869, 527490410, 207994218, 199243931, 508748388, 950630373, 399779240, 938252704, 483186006, 994106543, 648845756, 359242027, 312344703, 603622937, 697334797, 142858162, 125800643, 607434302, 531245547, 615058919, 151787043, 349113423, 210479695, 650829808, 169672155, 271965542, 44797159, 421954561, 314468812, 958906592, 676217386, 781933926, 560083488, 343237740, 719520007, 40802226, 449533027, 948317381, 468009830, 542247262, 22004002, 774773887, 827336301, 193134206, 560668490, 823597871, 267530682, 793651853, 297634265, 82758396, 346739129, 580938648, 215622394, 451258035, 345360236, 283516171, 621147049, 797242893, 824301689, 366781459, 222304975, 347785543, 478395360, 658739013, 288383412, 907485319, 409024492, 802582597, 939380411, 382694391, 264599448, 27868624, 265162183, 782252713, 419479374, 184704038, 563384540, 741016855, 217540768, 743198063, 990259131, 834518760, 653148158, 899309526, 503076066, 20557915, 119589598, 390607714, 776258069, 226590098, 675259756, 597170800, 522115733, 584574667, 681842542, 413618316, 493657297, 884183668, 723073222, 160150346, 381672541, 465112606, 820477475, 14423124, 476219576, 599782131, 166125411, 865706439, 334379700, 225759292, 710454413, 413891726, 474082848, 639151041, 27262359, 588934582, 58079654, 257306887, 714789496, 893330992, 383130497, 335116429, 641059382, 94044184, 402458719, 359935522, 537695687, 787742123, 678661413, 967528578, 842548816, 41012416, 614022603, 646536736, 634318132, 968593457, 323064046, 370517282, 578245485, 997968647, 872418193, 315899860, 999714203, 620505985, 413620197, 926344194, 199112611, 415236512, 432437056, 925813513, 554736793, 881072651, 573050014, 645747376, 332882035, 39689620, 178886833, 922445296, 749716104, 678417545, 815183306, 13102135, 425355494, 778667956, 875872673, 92206649, 642702978, 291460761, 371033886, 922290080, 260361041, 757454614, 448247143, 322130704, 869058051, 740431258, 534870901, 625956070, 531400550, 641675183, 692195176, 885723580, 290074071, 884552453, 854816918, 61828859, 897023535, 229374028, 444568763, 374109451, 475480528, 874285410, 461478990, 11194459, 952243202, 710588329, 658230399, 827932388, 13404570, 15327481, 940034488, 908142893, 400217114, 924410794, 756494928, 547841706, 636531721, 693689787, 467082308, 873468493, 385729971, 9186483, 77369532, 581357831, 116116339, 329084150, 444973328, 548114574, 477305007, 95433605, 354785140, 83187514, 575727017, 281116424, 873874179, 625192822, 557378956, 791923905, 200691808, 967986158, 756590521, 105556309, 152812121, 566690289, 79038436, 279203151, 774639419, 117570961, 30872538, 9603708, 529914674, 333977972, 596524296, 446337146, 773077011, 706452560, 756674171, 739726778, 412237645, 951155730, 995507250, 778723059, 3601436, 723815774, 84761851, 241046903, 869055650, 901269606, 772722556, 342898252, 420356068, 336431437, 350135236, 52923879, 272934161, 750766270, 925090500, 155222196, 385162799, 74701804, 665469594, 543925110, 450042853, 792167061, 383911452, 864245634, 724318767, 443279216, 298823600, 486919149, 131957416, 881208674, 756531385, 229288677, 343270880, 497554513, 160745147, 433617466, 748874366, 116357880, 346292381, 160806853, 572911390, 312877676, 729202272, 530723708, 631066767, 248677211, 718732546, 186800741, 143873107, 709143184, 676922125, 76368732, 800044776, 688048002, 214306279, 286928490, 864068627, 592999731, 463186048, 167464222, 738537979, 11897304, 65541196, 184212169, 552690273, 229408335, 569235858, 44481860, 247956018, 798547746, 630819160, 115200798, 977528422, 929237342, 993850708, 852947908, 538972263, 330283243, 180123381, 790708575, 188490135, 913016213, 285415542, 104012821, 441809771, 294483314, 280527984, 824334004, 223687294, 83287651, 931482462, 192213311, 453281562, 364333005, 757848593, 768051550, 462508159, 540204182, 37100124, 533547368, 453403377, 339302053, 118802702, 27759650, 447821415, 305823925, 436565100, 768317807, 645103722, 221037168, 794904816, 841087600, 614774838, 901005776, 53082378, 743029776, 947894466, 365927316, 159077980, 565190376, 192809323, 285000892, 924245185, 156794005, 923802484, 970280899, 393822496, 833227120, 637580071, 586711423, 632573332, 572277181, 479280910, 633304200, 606773983, 87969484, 568108895, 846391342, 334715727, 806047191, 421249030, 88075066, 772995188, 554923400, 365948873, 346723333, 414645759, 950355060, 400662295, 98572491, 847184893, 265391403, 213540163, 791436929, 133994329, 44131545, 173197334, 452391177, 355891107, 40632361, 305375496, 973548463, 779657127, 330653766, 984217324, 185864526, 996225461, 986380173, 890905127, 208491544, 742642770, 720280575, 153484999, 460272571, 728490931, 687582869, 43713878, 401899459, 890265145, 197112574, 140977449, 595186980, 941349969, 905769819, 469389003, 92300297, 807901333, 94409930, 390280641, 739782129, 446926803, 375675177, 140128024, 34620473, 828939445, 675060120, 190846056, 521298364, 760784245, 975400692, 879439686, 532870285, 462767868, 193054281, 368487186, 817818096, 775479822, 86650446, 140150203, 211928128, 558981436, 38757269, 142707188, 15458124, 855315353, 202852865, 589792621, 886816462, 370856, 206655626, 741961885, 672469263, 874495864, 759434449, 233392771, 890196865, 831275581, 78930146, 493555286, 439713781, 122573396, 379672507, 228100365, 993719915, 284129657, 317322666, 912058927, 111530473, 705368479, 260075057, 480156065, 303224478, 647663195, 298406145, 837047910, 715268173, 661967631, 581397940, 584569475, 546400936, 398047973, 388718664, 445548298, 504565923, 508734549, 786945787, 26070526, 726515131, 321790669, 557539940, 483215718, 142577815, 697192044, 695260556, 481805756, 695744844, 240244237, 836685850, 786179476, 931286687, 643606424, 885694355, 43041879, 860470805, 659699860, 938989580, 869839932, 599167188, 129451087, 269076005, 463914035, 957799481, 503752621, 461407357, 172193820, 703883985, 767755585, 168525007, 151119404, 271198577, 350555113, 147613031, 960793083, 697563695, 99906198, 917710060, 724762869, 665519014, 139761003, 166345819, 897887152, 985481741, 638119199, 13347742, 673588725, 131584546, 498315284, 560200622, 723387599, 522965009, 405483389, 161050110, 912597560, 28771221, 22095536, 10073134, 44777086, 605771223, 371965038, 609752670, 888750890, 595129801, 735116853, 231417241, 744648299, 322894049, 562274450, 631146436, 892396148, 877491186, 55545675, 459978254, 820166375, 886588476, 71983549, 105958781, 732713289, 472443633, 261626136, 232806491, 162608809, 286926791, 275748174, 392329536, 627562285, 592125099, 541640104, 236666103, 88511633, 868834948, 119045221, 81113655, 381519198, 683440453, 167626857, 73142907, 475214977, 292331093, 43468354, 588080128, 514722381, 449956584, 903337237, 527414578, 72573034, 626782868, 363411124, 762364681, 697871955, 495411849, 929787675, 916001318, 92759420, 663396299, 760342052, 101739264, 857952688, 616568534, 879883594, 646690114, 591993462, 205255828, 673376915, 438217187, 752455572, 831586165, 984084206, 435215346, 734072403, 609163336, 456535316, 849592944, 470035816, 348403257, 755350845, 955143475, 944733777, 771630218, 770778875, 251840998, 23483607, 861071735, 255455731, 640718975, 687725387, 50351388, 509550266, 246988232, 650823463, 101644007, 51684898, 582066092, 279124033, 179752954, 330630588, 546613029, 999364486, 799522461, 454565085, 79006339, 793136040, 563414052, 875137851, 924485670, 467861317, 652565510, 736153183, 315703875, 200024244, 474564303, 112316169, 545560996, 174817296, 945766927, 951744643, 682482689, 852411808, 110680680, 572836019, 364488835, 817843053, 695484292, 524517970, 872336069, 52577609, 699809955, 917548781, 282518911, 757188308, 857666833, 390731021, 138989658, 575482422, 887257531, 847975821, 767248518, 99613883, 303293314, 477425663, 543379681, 716502439, 34462815, 669693567, 303284781, 896847254, 827764824, 335039565, 354865727, 750264529, 967273255, 685479427, 479981080, 268798110, 306275036, 195619782, 757755182, 419299764, 621895895, 182398537, 998301481, 48584090, 923213728, 286103140, 800323873, 520711382, 944255672, 923738002, 801053342, 823186533, 141339234, 223942997, 333759238, 387490344, 327392612, 690090525, 327949045, 628486643, 304784540, 215617559, 340210894, 201996127, 527119751, 94321766, 176407437, 283877235, 448475853, 647558123, 163810822, 472645021, 479137012, 321345320, 681887205, 155201252, 202051293, 286348208, 476883373, 176033812, 233694652, 562042222, 87511887, 968204115, 291884399, 325518778, 109396016, 687916909, 467832303, 191975409, 567021427, 62983302, 64061660, 318463435, 113470713, 578475933, 959585534, 612648003, 707264035, 818339489, 675045053, 902632498, 669739141, 908652805, 280025448, 69232787, 760927207, 741247241, 524804904, 319273260, 65206632, 498142693, 601255442, 534524374, 225000109, 683838686, 786899042, 371160471, 511740669, 787462156, 732111598, 596187840, 256806679, 606927285, 593255714, 960160463, 50113322, 551180433, 848695192, 623824441, 603039204, 744263887, 849014546, 553222973, 471782762, 54156472, 890726155, 495333577, 955893856, 235550339, 881988648, 752367859, 262589385, 110118799, 858921560, 588689346, 225462771, 976311681, 996953986, 691888817, 221091617, 667745877, 356487282, 797042030, 73006242, 516811716, 827303774, 92683358, 912373217, 495524627, 134375174, 316636882, 440573223, 808648732, 857885625, 434324407, 387543032, 599435627, 909161491, 122607440, 572656036, 670759481, 524918399, 615688803, 167977847, 670030489, 381753178, 74822831, 40431478, 574326774, 548951909, 832606631, 464262274, 312631717, 844089882, 713966045, 120971662, 467549944, 161001045, 546983945, 438059941, 723855499, 481063299, 509514667, 898249928, 800552283, 978138065, 1745069, 989073027, 254290015, 340362057, 624887261, 930821699, 480631051, 456056862, 611763123, 422509392, 103531255, 22595958, 612509990, 753551728, 401767127, 134936791, 940203820, 973044063, 638582480, 634967324, 402141007, 541411225, 489825332, 964450468, 467883195, 205615986, 999165473, 828348704, 571304213, 748300067, 325565670, 495055533, 107142541, 2469948, 265696934, 171046977, 331394547, 581923641, 190102747, 75744699, 883187817, 106645962, 763624177, 893490921, 884911759, 7063445, 515346934, 114868751, 719779372, 24471501, 76093978, 172866498, 676028759, 720685629, 674280017, 877616993, 702351593, 610439765, 713809461, 895633146, 43450173, 335282237, 690745737, 167649651, 779922980, 866522040, 472176863, 425861230, 978050923, 58215631, 209156056, 769147736, 298905826, 963593218, 905539278, 859686572, 237226221, 332596568, 885990253, 845944402, 17273034, 85064675, 526410075, 274441650, 751237376, 28707384, 93072805, 731329371, 593968237, 147887246, 722072968, 590684562, 141748433, 934497206, 351730528, 374959455, 200754727, 508684702, 475443388, 318031946, 220020566, 131500455, 430276557, 267728179, 893729116, 879894563, 924522665, 653018663, 617571132, 629478429, 131403115, 997851164, 405033125, 219739762, 648850435, 707505822, 549233993, 157245627, 965154302, 724315058, 369103450, 476084033, 30840993, 377270335, 976351645, 383672329, 682831147, 38727765, 951069477, 431613046, 508322206, 723828985, 429740469, 86454873, 846244059, 808296224, 174480113, 546178712, 204506442, 116428906, 408107034, 401815809, 491320391, 537077325, 995520388, 621374354, 442849632, 681701523, 99966335, 29280527, 852631187, 285706385, 927569253, 943794198, 556860457, 480774272, 284067952, 451022432, 45443197, 966784780, 863949577, 481778060, 848349063, 501191394, 192917573, 113277440, 710220157, 600305916, 579619071, 780614174, 415355221, 758531198, 98000208, 129003953, 506629237, 724118456, 712258237, 127233834, 789458199, 661353282, 454762547, 149111286, 317989582, 428749922, 780705966, 423874729, 609607776, 934670706, 935909873, 745154778, 168853314, 354694058, 479621254, 158965026, 620594433, 751146379, 535366497, 789753317, 373138112, 631908098, 403752528, 785454363, 339664805, 640301250, 368998019, 834776980, 84551152, 195908176, 925070072, 112447404, 867691000, 972463875, 373993086, 583083559, 260260776, 916395900, 376142331, 989571, 414996653, 248901264, 829668977, 740039386, 121249438, 25729230, 931133272, 287666808, 64878411, 887933298, 343576323, 374853378, 500199990, 21805273, 729605561, 860711061, 682242873, 396603057, 50680168, 2810412, 786375633, 500271357, 927248683, 792090915, 941802922, 577410562, 687247779, 667768440, 462679751, 561759856, 602465857, 700789359, 647240355, 731424551, 113270451, 653248099, 486686836, 765720824, 214344586, 172313816, 770748036, 781664017, 741340757, 264355027, 385049434, 287094325, 799218716, 167595273, 370402754, 68537435, 367869321, 548926579, 28657137, 192958997, 438239619, 280172870, 662043044, 85515481, 604548438, 334065661, 237957076, 324110583, 263087481, 415333318, 493801538, 362351190, 180697959, 316206647, 468868484, 80538572, 383779878, 478368956, 232342220, 767102899, 142140661, 478306223, 62859758, 634122354, 412503128, 605023538, 649807645, 646580705, 173729670, 995018409, 679638005, 478416162, 955944785, 497064870, 448544432, 634143603, 821864877, 684318800, 601593320, 94299299, 258515613, 884429494, 75899707, 781289642, 358194341, 288501924, 812820345, 476270012, 444396974, 860339773, 126407303, 25850295, 45444807, 681428897, 515904675, 484292659, 174396353, 961620418, 253618058, 334674053, 898853370, 364251810, 554390268, 47677878, 731639450, 765723108, 97630168, 463472084, 548131021, 592216573, 223906348, 244522428, 262189021, 391902716, 692269216, 790949767, 702914721, 948951840, 421590537, 474403335, 539407756, 971419437, 889723201, 54170537, 909108216, 286635370, 638346943, 213298101, 93816961, 926169155, 797891819, 755423593, 269842697, 58469595, 321791953, 421836478, 703481033, 147287335, 897403453, 662471524, 941563150, 453680728, 577654848, 694644791, 538711706, 101516075, 87365364, 500906914, 479260624, 247866494, 680436266, 87555983, 89866772, 860657595, 29193850, 313376260, 743776840, 836835492, 296908811, 668691027, 747794270, 511095195, 471381502, 298992904, 31472130, 233898982, 376010436, 670653520, 654130755, 274410938, 497519039, 80136892, 754778533, 458213027, 189456530, 548840032, 472214535, 47426542, 470517555, 46711451, 673484002, 818297547, 461099580, 119220274, 941723364, 168889680, 714946585, 603100506, 614165180, 310954651, 310502192, 530909429, 840842568, 271384929, 631519593, 644731742, 135736070, 369740500, 548697619, 941927470, 123718622, 654646485, 218974962, 693672649, 680937998, 462991330, 618865207, 526326015, 651254173, 734304179, 997439602, 998940911, 187822092, 946117552, 989187233, 77062398, 805230405, 738941707, 152344162, 262653478, 902636940, 476240448, 400880529, 857401083, 654036036, 321135301, 466857149, 377885909, 569286379, 652431395, 905285261, 298002920, 990792368, 143177773, 448935855, 556758341, 800108661, 129498308, 576738381, 208785194, 260125700, 920859229, 712881229, 230975549, 389483084, 616302252, 468530008, 304424477, 357713623, 698179581, 691665447, 382751838, 523531459, 388597333, 74018859, 724982653, 699581714, 821991459, 13689010, 177821436, 46792027, 596645075, 1601716, 946895945, 659356052, 805360718, 391562161, 309290771, 155261413, 514234584, 660901546, 351471237, 534887955, 155925664, 54484293, 845451503, 116080693, 863756759, 22683467, 770614148, 845267340, 899388228, 438801726, 861193369, 371176211, 654568318, 15362921, 977088150, 91247833, 664538378, 725906585, 881027583, 369598495, 948001896, 628232565, 726155925, 457571357, 190443975, 712936462, 46316784, 423627799, 477833902, 100315468, 383105373, 112690210, 311398946, 320659203, 369483101, 809916460, 97486960, 355953930, 523180075, 867807418, 579842099, 907696564, 39775906, 922507651, 681990247, 130364805, 396576551, 140838327, 97605993, 842820577, 545671093, 382307614, 63916917, 879185383, 865531364, 585811099, 494515676, 646198390, 55349206, 118776376, 549151910, 136683679, 460736248, 455924797, 429770222, 200296171, 265238452, 406648521, 158669201, 979650728, 952994274, 763940696, 48810740, 851385121, 818649301, 716501514, 654506641, 16028109, 430577975, 51158281, 447480718, 349763601, 487008861, 165128172, 899786956, 713076398, 752008931, 384570637, 756892866, 697291762, 499144461, 520810808, 272487487, 925119874, 554440280, 556200105, 867780952, 227705689, 367952217, 327145501, 171980522, 251535995, 319223437, 150761101, 854695875, 614236821, 338378191, 43639390, 240686055, 436548727, 574314360, 38046159, 69504029, 774136416, 626958454, 632532688, 714142844, 396023740, 690769371, 44684481, 4031296, 764061115, 571699565, 72549450, 202368263, 722385729, 951168589, 103692788, 999498828, 913485076, 255286630, 882213258, 950974622, 951942620, 413276529, 171332775, 844584875, 246549554, 439991749, 366303061, 961853345, 23512736, 558453654, 491319306, 548008121, 635736145, 250831333, 620155763, 791735018, 746449258, 343346909, 218828382, 216333166, 197463398, 260959557, 191846168, 936201713, 292962417, 725587888, 515693395, 2262569, 716876570, 329130271, 986265107, 393759929, 29796075, 200464030, 308245131, 203685116, 212088222, 61417045, 299075886, 144750779, 647712158, 879569084, 838966545, 554715787, 366369629, 580526758, 619412933, 501850320, 320231367, 886373363, 143667961, 251084450, 814929211, 613048835, 620775269, 288984082, 950113230, 611314951, 203912963, 539877238, 503137159, 980332779, 658572970, 806195058, 922321560, 747995839, 229628886, 504171649, 710186988, 137305513, 652647531, 431566070, 111517944, 501150646, 211216058, 472502088, 836973152, 660648201, 195996551, 843833553, 223260677, 804255568, 86778367, 714314432, 137739479, 415330214, 638872368, 512939723, 647393691, 239495783, 647412830, 636062678, 601320665, 82303870, 613516069, 787511252, 912960774, 655350360, 799444612, 477977432, 319089557, 617196342, 292536785, 650534419, 920587222, 392072119, 284419425, 29673346, 763047972, 476829091, 659399215, 890925068, 901064533, 343546594, 709881694, 264859898, 715049504, 59272820, 177996985, 355985469, 780828465, 316496578, 298605892, 790959821, 432789751, 738320443, 443925765, 702784563, 699859478, 331382725, 119842542, 286132246, 867707295, 150632059, 89642976, 459907331, 741281629, 929249801, 853517931, 88520090, 194835327, 843487376, 673105828, 198141183, 128237349, 722202332, 816787343, 919928635, 759525406, 479231447, 343863675, 162601063, 488161018, 161876440, 214013778, 895108699, 893369671, 339849924, 787590792, 481818645, 298493516, 138049278, 617549920, 249494036, 588801784, 250100086, 212936416, 934635380, 578111791, 307332055, 358362928, 818333760, 508052226, 391134695, 772624765, 271099750, 491178247, 379179018, 377503842, 275213360, 371091010, 606465717, 558096696, 48586292, 745561162, 16151670, 7884774, 182243835, 969776242, 14725176, 752583609, 207388793, 630575029, 269988235, 331726409, 139201266, 302586782, 639977028, 236774838, 726255761, 131588385, 353671111, 388390286, 246937363, 523967964, 644173085, 282858495, 822177641, 922562478, 979729425, 478810819, 138729637, 839492779, 214727448, 8018871, 174036834, 160500263, 93065820, 985023477, 923706897, 719463832, 507780188, 492761888, 44413349, 605709221, 675749340, 493709524, 220262889, 223904960, 254616124, 342108103, 900200526, 253257904, 588989950, 623494583, 576827490, 996515108, 610400362, 946751210, 207350950, 815904694, 169164695, 49257431, 810828127, 627104982, 473543491, 499845759, 556743156, 394892831, 65376333, 445841724, 544775017, 137850233, 554440542, 509809788, 218503823, 944810347, 51663345, 699324589, 364716801, 672563000, 157126342, 798077651, 224037018, 119588890, 314782288, 853108586, 484751699, 785299749, 162882100, 466054354, 21354405, 130837911, 706985001, 134291575, 163644607, 336739290, 894683531, 190305676, 613253792, 81102774, 506548289, 890620829, 385326193, 479905374, 403130775, 759968491, 264650211, 560473778, 963584970, 862489213, 892649423, 446083097, 256056719, 234805803, 482194151, 930629204, 250889657, 336956367, 16843323, 108138083, 308727924, 851589586, 248309886, 617899826, 39378284, 401556298, 207841621, 896166980, 905836170, 180300948, 981197319, 981378720, 782185715, 465158815, 283527678, 312086060, 400855120, 870493325, 517828126, 961045222, 171961266, 253099827, 729637484, 291361581, 873261118, 283995680, 767242894, 952195625, 399575245, 552007575, 353016095, 77554556, 432993919, 918207041, 760374877, 358628277, 899681176, 607296295, 421056394, 742511283, 161760247, 705380856, 782572001, 828908382, 265119199, 871531328, 21552045, 262557384, 67279172, 160981156, 774023217, 645213915, 305557438, 42508182, 835123332, 766854518, 794463426, 778860186, 817101088, 456775008, 142623072, 789004062, 250962180, 514412584, 774109654, 827260011, 774916743, 772995789, 810864174, 685233296, 584200611, 335214654, 382004821, 317912043, 554079623, 443761463, 488236745, 642390830, 955323133, 329061900, 50227880, 861781350, 257076380, 521289918, 189568732, 510931574, 382549519, 87944157, 480246957, 692345649, 341079805, 107264382, 785356293, 910308253, 756258468, 429373582, 733705075, 802241141, 32805627, 899251046, 200233402, 698776722, 110892374, 472025582, 356494276, 145493020, 265885633, 876171601, 860154913, 878020965, 501439285, 51968475, 832330010, 972550390, 565859230, 926836915, 271016069, 226186846, 383250151, 385929488, 367423235, 653678986, 112901627, 266710288, 99716632, 864282727, 514648779, 618528220, 66198766, 428262803, 849827908, 987003916, 646887541, 178796475, 84830504, 398836951, 155663597, 847328424, 998951477, 434155002, 5871564, 65258862, 5207010, 450960553, 950431444, 978959166, 804355161, 709363274, 187988525, 253270225, 436483190, 946341160, 658023670, 412226367, 516194607, 158386606, 437416297, 191392507, 373448679, 596980206, 207864555, 461660839, 904695823, 772297721, 874974398, 483026779, 162493068, 8243330, 199789260, 78023929, 673467900, 786593374, 990384456, 820628681, 478792468, 816994467, 862451893, 379966548, 373041297, 70541982, 863190293, 307753572, 115478996, 466696350, 645671938, 884064788, 613953337, 147885090, 818236014, 335993672, 435472620, 467120152, 657801511, 148884198, 59011312, 917860798, 482208058, 411100236, 900871489, 788097281, 502530474, 919087187, 152788725, 337211455, 84733510, 64788083, 73615082, 754304899, 850785819, 763228826, 627780530, 614511443, 638879490, 381996566, 446301157, 40443628, 707609421, 154387449, 419776705, 255762406, 204160801, 843672029, 839878772, 835786394, 376709405, 428166166, 352188811, 908628223, 443636818, 874103243, 988818050, 526949821, 628732441, 966272636, 50783878, 105799338, 819596443, 690412871, 67686993, 202328031, 851450121, 687349008, 155094565, 756461144, 150334685, 972867569, 587852498, 502188967, 129058750, 380333719, 324934487, 621832235, 845927567, 829251775, 295069035, 396987913, 198980960, 235544149, 513028633, 904880941, 28105461, 290243744, 858019329, 748699114, 414856206, 351351663, 856521455, 789604424, 994417410, 295765475, 256251898, 810144080, 646415838, 257284517, 222171392, 945176884, 307614951, 253662668, 886974045, 715345690, 803274624, 711610027, 195880021, 111057610, 520516860, 353503171, 967646320, 693165451, 340643218, 975231736, 717455251, 204223790, 447288436, 378988845, 26344775, 176373171, 661392502, 377167445, 49152551, 752882056, 589470719, 827527801, 321778168, 992579255, 756407336, 880522324, 573952255, 350308567, 16789263, 877372907, 290405418, 531066223, 328435947, 224025835, 994947425, 400082735, 958185310, 438357627, 948378253, 82621623, 43165186, 63700880, 672468658, 57141603, 806156513, 965544306, 638914519, 326923476, 781106605, 96132700, 75213136, 602291537, 190140448, 11799583, 59654364, 913653800, 321521825, 956080, 267135848, 522495764, 150609738, 944076594, 283908370, 730728974, 112011827, 582733446, 17693610, 247619453, 23339695, 159891507, 217148302, 862818865, 150643801, 335198078, 625333950, 253857103, 373322845, 486576319, 161252343, 409380601, 804418495, 759875555, 181055031, 916268964, 97648763, 121635343, 565303343, 250166428, 367711808, 147302170, 235850244, 522310636, 519566622, 202528132, 864243892, 32444, 241309760, 760313092, 12214225, 333291067, 337349198, 498988850, 49093155, 475699233, 751062009, 830450044, 963800164, 153318188, 13166843, 187194792, 290277169, 338468260, 566033897, 816468005, 384487052, 734661363, 39788323, 744090786, 626909356, 758586953, 572601674, 116097562, 435410881, 587671097, 776834746, 90287077, 670262984, 558241214, 181878447, 962372221, 848169943, 444485016, 394518328, 248657753, 372005531, 657203423, 241767409, 56763228, 50819501, 60916089, 889690117, 119831868, 652431880, 601818850, 887432814, 496032211, 195230559, 410248851, 537663368, 633571046, 584467203, 215350332, 527508875, 708215317, 598617076, 578298742, 833827960, 907604685, 260948566, 748902499, 874357163, 277188686, 90747610, 745462888, 753831830, 969384782, 815104759, 430046243, 432014663, 137833929, 519131943, 414749557, 779773520, 796756812, 917750072, 212173989, 942260438, 896415632, 679450044, 875104329, 402286069, 227399851, 506318201, 516085042, 814852991, 429219643, 120567682, 466042744, 985462112, 961036539, 560299592, 821953482, 268189671, 248319152, 328518237, 509273638, 730123052, 295655443, 517051044, 99905028, 31391457, 513397441, 359685972, 291086307, 404037248, 580335919, 778759730, 269756071, 513506997, 581548382, 617276986, 732787348, 658398096, 433568301, 653655128, 460448812, 975788185, 807762037, 951757477, 130224198, 657132333, 27063450, 17719844, 868335731, 114745481, 780042094, 305413232, 546249252, 626559749, 331361812, 754641942, 52857390, 832350782, 953131211, 135857673, 33681282, 518252601, 765919756, 669238820, 394975176, 407574626, 264947530, 487274216, 232364598, 526430609, 974082248, 50188489, 81259202, 281328396, 190591227, 578628446, 278107570, 3138015, 624380706, 928718710, 467547534, 189117598, 270401036, 908130420, 362951809, 707735587, 242951397, 55844384, 928837861, 758875574, 319494451, 336307686, 103047282, 255602706, 966241646, 866175363, 303372817, 858873202, 356434041, 35010291, 729213163, 44391715, 331467094, 326781347, 180221934, 972423856, 407962834, 303608544, 473204053, 594630533, 359372533, 141066434, 678652403, 233164310, 523044845, 848066482, 662784916, 62823658, 310310120, 677979214, 201076504, 128801320, 972183991, 520436201, 246915996, 33305434, 615547168, 539340900, 613637370, 532713764, 16571839, 981320290, 685501825, 523576278, 55378418, 404164069, 949990691, 384907698, 968751101, 112040259, 630660822, 651183302, 371512467, 531433929, 878328716, 377366945, 118271307, 494697824, 856766818, 594029532, 553794948, 615590479, 779875467, 337767778, 517545689, 794320851, 952595357, 441819183, 951263653, 261686815, 377100272, 619507174, 432201014, 281731685, 58305525, 133563639, 295793256, 4461547, 148919477, 576556023, 565709538, 498732459, 860599268, 981216516, 121482744, 572477606, 347110167, 31202669, 390337733, 730533737, 288605079, 349938623, 183834888, 853956278, 32580642, 625310424, 911447749, 595183880, 534742250, 973262189, 129382585, 322969357, 330645009, 366605340, 164980035, 516992863, 856362033, 754465915, 690825436, 233870227, 138929962, 641019044, 467851926, 569785981, 994103074, 724082830, 152026462, 262022846, 101915293, 266270300, 342532342, 613882172, 82149313, 936703026, 320220148, 954294134, 440225207, 794839305, 443722833, 385345166, 824308525, 605242915, 399584653, 415274643, 433112005, 845394514, 668986501, 709352080, 754165440, 274572769, 75648567, 960076487, 9889879, 681942271, 804742647, 141744927, 820982579, 115767517, 557304989, 888276369, 120386176, 895879905, 91044724, 643304119, 992717561, 748689249, 82485953, 858304897, 142012264, 195560235, 616902288, 68134612, 290778153, 46040092, 851059082, 67833376, 85777378, 812950627, 421030380, 533969144, 457457787, 138968768, 99051782, 2531170, 174601572, 473597029, 259191313, 86454819, 295969987, 283190196, 996629863, 679328754, 643771320, 445273329, 187124074, 987959916, 591076913, 842297139, 801525338, 53458656, 409436569, 878500391, 592544055, 564679194, 71462075, 894051644, 124238102, 473427288, 162211479, 306037566, 126413962, 284841966, 282424432, 440107303, 551807366, 577001602, 160015353, 278033627, 227372982, 560859626, 11366090, 246255032, 470489704, 698199724, 936037252, 854102943, 853000730, 201930944, 231898575, 477542891, 111155568, 158561669, 54186810, 920253632, 404044548, 203357722, 987184422, 872564072, 326416952, 41185396, 586028472, 516911039, 105801861, 594933400, 329094538, 166535930, 731652312, 643262063, 512162070, 750126944, 197839530, 291516778, 466432054, 891251643, 872311117, 496604911, 205204632, 806308839, 401840321, 76841432, 935549025, 176633933, 800446764, 344212022, 250774233, 850652025, 26166418, 831615565, 588263933, 163268600, 352786605, 551438909, 205916117, 920860014, 294307810, 271644861, 249924093, 425860876, 116889278, 19782209, 404616988, 49677765, 695022355, 779688470, 575371015, 568681252, 459997849, 619764128, 131716327, 672080452, 151645626, 630129543, 93691233, 486218357, 626403099, 724103602, 320538427, 902213092, 895530720, 63124031, 757470602, 678963632, 309099836, 45353341, 745211520, 876442390, 88670689, 953250358, 582349393, 932818648, 900323453, 372410936, 43696982, 547841692, 34992234, 887124781, 455532735, 615206259, 899294727, 608547849, 887546701, 639231454, 338211178, 737774149, 793054282, 232826479, 425949580, 367337450, 301844568, 231250158, 736243736, 450104120, 549686119, 931947813, 661435305, 73160995, 736722807, 245649970, 412077559, 54403112, 613034581, 680029788, 550996087, 204923629, 511682620, 235494340, 969618433, 334927375, 748718446, 230664420, 237411527, 735935495, 828706758, 360565529, 43291976, 374631561, 52199155, 88899073, 194150161, 438663409, 603732365, 595576642, 397906136, 149481057, 403518598, 673664827, 463021713, 820885614, 962630676, 579326362, 788877260, 375444260, 217806508, 724313288, 103877418, 674197395, 18766138, 732267785, 196713729, 993277577, 733996165, 176109820, 801898741, 897033267, 381277633, 316992342, 12542461, 749338402, 294890972, 641170655, 872926756, 651386166, 900331146, 705873167, 829316785, 76262429, 321683337, 73488446, 772909494, 223661237, 541418253, 314324833, 209103352, 907977913, 604266746, 871991750, 632760278, 884646431, 146247935, 410810533, 887442598, 809535184, 867845608, 733104654, 509731749, 302505668, 396745692, 925689707, 633451615, 508343929, 938140182, 693855279, 25441245, 401225730, 422307711, 96507441, 8513396, 952683576, 37420854, 447300492, 136464462, 209707418, 185776306, 752674984, 959763566, 780636973, 546506330, 358870305, 817985896, 593339489, 593892913, 327325350, 683111576, 415560301, 475976762, 329816301, 341972286, 128240387, 33728018, 875955425, 110693841, 677481943, 431846384, 923165849, 811451153, 684353307, 924696759, 285700122, 511003923, 421027753, 607103103, 472177600, 200881781, 451659210, 781029969, 222898206, 679085710, 161829369, 775613028, 111609292, 130049641, 527736528, 224010525, 737847153, 843442279, 330531372, 294049572, 259548564, 905226947, 728233755, 476256678, 279988931, 229187485, 950857911, 6854623, 70775142, 28420013, 971293804, 288825033, 380998646, 652763775, 145442415, 544935600, 599972648, 614614066, 377202412, 185689538, 845470652, 48401221, 691337571, 979837762, 637643200, 745370184, 216710291, 408347408, 155564246, 846728942, 168271794, 919891225, 146697206, 52020302, 320040577, 638094109, 52492066, 672417976, 509239691, 402944285, 769213363, 154431370, 984900670, 514042447, 783827857, 233870857, 545258323, 844812607, 2216926, 842460601, 699462841, 118097232, 787263490, 367655722, 401464585, 484987973, 687189155, 915108837, 896101293, 932135071, 955131361, 746906605, 564486705, 528206640, 727411814, 27243750, 996274353, 644316362, 529818880, 245005483, 423403182, 386206765, 807415658, 971251902, 487801556, 685342801, 600476363, 515523954, 719859809, 406171129, 186517312, 847610314, 774765769, 348965842, 860977931, 567991422, 97840949, 154286496, 901696021, 700196516, 964563736, 236044068, 687934180, 46787048, 287327149, 653485536, 699624394, 238532445, 493276110, 444270422, 992095111, 194578035, 400618897, 510704195, 638357771, 429606476, 826419692, 515560652, 585869018, 405154677, 261087916, 384940891, 342299248, 939988842, 792004425, 986693105, 686897342, 572214428, 153338052, 198404597, 882404307, 929903067, 227314470, 379315543, 19518094, 61070075, 516301127, 516692249, 728241800, 752031240, 249601849, 182020147, 237786333, 633432524, 743880440, 324676653, 284966689, 842910828, 805528018, 230311270, 681954758, 494206996, 669972711, 855681813, 201960913, 731068549, 679163612, 594330936, 706009299, 679017959, 26994863, 247656229, 47736674, 622808017, 817851419, 898029932, 97314534, 334341287, 948750369, 152786407, 667736797, 370062452, 463594919, 568672758, 610244563, 27539596, 531699754, 313748400, 825909096, 27018308, 995269042, 616857815, 679988405, 619532988, 68616247, 448342695, 586395664, 781494349, 420955178, 467490462, 915266893, 454046827, 510120255, 242881051, 692320200, 609326927, 20197162, 954501428, 116744497, 56918311, 41856551, 472495979, 798008283, 757479074, 840848754, 904265297, 33614081, 19770507, 21095240, 82550654, 691568448, 116779804, 794749407, 492912486, 594791504, 3186784, 965529815, 801821214, 7172028, 801056421, 607033394, 19943605, 301111525, 742774913, 905441719, 183619396, 706225353, 765256036, 490887289, 279100475, 277113108, 289687682, 190666158, 866429256, 112900318, 515709567, 846604557, 514119557, 776636290, 626575322, 294709065, 364401304, 966717654, 705240485, 197051753, 201285143, 139202546, 181242385, 787857338, 356084929, 295715370, 755069775, 169133956, 98895098, 619833757, 504824215, 842806211, 261556814, 524405566, 591983935, 107326790, 827601904, 354951408, 810262442, 837144392, 882861833, 903372885, 699684826, 298727157, 24399130, 232288680, 507752797, 737003834, 268883384, 712792669, 97028677, 588582512, 25283358, 947179108, 858691594, 921220158, 613674852, 749925622, 224856056, 168869589, 381785388, 574229411, 50517909, 490789744, 419698092, 868246912, 113061198, 520573844, 629089158, 840984376, 500549075, 855490358, 546926051, 184511067, 902273823, 688469436, 711552525, 315521779, 719009681, 632313762, 557817083, 138911177, 147627765, 460269713, 799062397, 577296495, 177023057, 953712951, 195232757, 941214024, 213583937, 280153502, 145616568, 608670625, 735197660, 722640807, 990629454, 824480290, 140784810, 897818118, 189253412, 307955349, 355295652, 313121945, 317295745, 301930139, 805792657, 596387228, 498613176, 261045749, 777607483, 571687501, 123935785, 8408338, 828472240, 547897771, 302667363, 759526763, 154317275, 595226923, 388793747, 836661001, 222867375, 865804065, 524995064, 981160747, 893888151, 239269314, 343240184, 203350790, 14240394, 750715024, 886368395, 590802376, 689783809, 797129827, 214884972, 644620982, 853665186, 680107310, 56647886, 106445454, 61430883, 362163485, 558796130, 250215484, 528578110, 912655729, 805667016, 879468344, 56055957, 423225400, 607458187, 454300498, 233486486, 239602952, 912035203, 372517487, 675865201, 742493845, 547031714, 462529830, 453890560, 332605207, 131894706, 512362378, 671185485, 589510173, 650973039, 720579866, 170523778, 660095814, 862911173, 746996781, 492037287, 296196840, 556997175, 784206812, 972557863, 612267993, 429353848, 424484189, 982258938, 376831495, 178201854, 150935715, 943252999, 8361860, 246213973, 859262816, 876569743, 520604325, 147845998, 895520459, 955288120, 997445900, 951437523, 527783981, 213373095, 963327263, 837556227, 532670655, 86912371, 750863593, 54484984, 624780586, 896162180, 64278217, 169157030, 114611300, 11711110, 437997052, 39933482, 980457053, 686304790, 343792677, 954621134, 624551640, 7278257, 1421520, 299876154, 515956164, 169137726, 850871886, 901467141, 232308359, 714188467, 435022643, 611548790, 629530703, 55393210, 471983929, 444518288, 962443306, 11221136, 898734296, 198401958, 577497693, 473695144, 105989848, 915900913, 316842454, 710055783, 723927534, 160853476, 400926975, 194115825, 854823553, 518540127, 942863561, 652917726, 958140936, 557337752, 558244466, 177757206, 2243930, 738488956, 711356147, 561226677, 638233080, 264476649, 671625718, 319157579, 35014215, 618810902, 422453045, 112455869, 113923834, 149259846, 458267609, 179210388, 22807747, 110207675, 711347046, 876450843, 485202852, 390842894, 213755599, 882171760, 270534263, 867202201, 618110387, 685389978, 746374941, 846213940, 823756234, 583144165, 249931925, 270832377, 36193411, 217615843, 410683151, 355955036, 133589717, 110856993, 439279611, 23879242, 610029996, 227899680, 189723447, 879899478, 99244549, 701772235, 318199830, 465561497, 271792737, 435290491, 857694421, 30956146, 82482615, 496265435, 221332819, 261818624, 670659682, 249555775, 115643765, 587689893, 371149485, 108523412, 830097106, 561669247, 50918915, 921065273, 364829556, 631323571, 11702775, 273659340, 968901968, 552358462, 927356764, 158625226, 163716912, 939615930, 171272296, 394003380, 898327025, 906549358, 664819819, 849091757, 22108743, 797280884, 380240266, 15302973, 154867389, 864852201, 99694081, 912225967, 850256802, 496869488, 8754192, 446285275, 526396213, 885916911, 969840094, 436501693, 705358618, 539269529, 116719098, 914816450, 710996281, 861943228, 41523799, 35010083, 288574615, 742465398, 661641191, 240917873, 634726053, 495787964, 329148860, 396706490, 867582737, 701539257, 344459077, 221995806, 271110344, 153163281, 199870227, 849374123, 552413617, 34290711, 732742990, 267942180, 162492574, 403742904, 501969264, 935280839, 342820993, 319798054, 507979889, 238209955, 499160673, 931958175, 212847536, 832719770, 598897979, 267261714, 223295662, 325793636, 251303964, 611100403, 967572826, 239248258, 318036864, 168881679, 112182666, 406720715, 582960397, 278395518, 512535084, 499244266, 831929441, 520737194, 441551862, 884305871, 160169702, 133119678, 930002225, 35650331, 501731640, 748445830, 181859877, 239364787, 550686978, 679569447, 617751659, 818608798, 846726719, 566561010, 525449257, 519878989, 61405149, 475189892, 858548449, 653474882, 618738503, 670707499, 775696847, 934318310, 306731586, 592613478, 54076593, 235203996, 583209740, 575579167, 394602234, 93264678, 566306960, 457395883, 339544709, 314925171, 410720514, 697499840, 894267088, 210509902, 695407987, 574558428, 829136798, 225027327, 190568799, 271162348, 423846300, 104379168, 88536693, 127283833, 283460916, 431133959, 969233922, 129667452, 375551999, 831631823, 710150621, 943311456, 205764698, 726512686, 363573030, 361966188, 841355224, 112721411, 520530549, 338881487, 802907494, 657399782, 956318717, 383143225, 860437424, 732594526, 814860164, 370976617, 771887965, 58160279, 665666310, 999885276, 33816170, 167513686, 202724473, 839489711, 699444985, 39366211, 747112763, 305906964, 450971043, 52925568, 31643882, 280396349, 28067736, 802062683, 22381135, 554490106, 970027982, 218037700, 678219996, 991711852, 500080514, 666035215, 227362269, 404926644, 764284691, 468078998, 130927582, 431438652, 738202358, 258336150, 554798183, 305628487, 200882091, 256840452, 321330558, 711385609, 912395283, 898811138, 731336635, 33251634, 849855103, 330940135, 785323715, 596981146, 522533203, 880788040, 461518748, 677432197, 60705896, 674531064, 109250997, 72944075, 518471963, 257117391, 384421680, 244052741, 762360809, 940104741, 423483681, 540401707, 593350401, 237477358, 255041754, 930814203, 905576270, 311438085, 799892891, 841288785, 518594822, 621389855, 776898611, 440685794, 940763849, 594762303, 348885593, 777142387, 559471130, 481238841, 479755619, 711474020, 133491759, 963400161, 49475096, 879483418, 312789923, 820149309, 409635826, 791990737, 463317258, 787906585, 852299204, 919638565, 483476751, 201382919, 529206262, 131157212, 548604467, 660583721, 40845946, 663775673, 11321923, 746395710, 37424723, 6091325, 281952645, 137518200, 101741452, 4032871, 316419131, 929273590, 100670050, 671012025, 983579435, 339439480, 744649909, 983926755, 550301026, 965183364, 621939568, 295847638, 717952892, 578497741, 880302472, 394638488, 546062052, 795323290, 649060404, 878455383, 411646008, 517414716, 714561351, 442625280, 43196327, 97968055, 558600271, 413624660, 549502068, 52647129, 700968619, 318754953, 854675739, 586090359, 906866095, 127090673, 770615660, 555157921, 119029097, 417879568, 479084908, 132604139, 911849136, 887854261, 744178201, 700967101, 473608008, 656522852, 453927453, 453743401, 601430643, 141566570, 305057665, 609378638, 302820752, 812072555, 703595828, 169416747, 108584669, 179541642, 16581924, 818119640, 398825331, 884920532, 583713447, 975736393, 9164799, 968005062, 293499731, 539332560, 81296095, 823256515, 157903307, 608538803, 382168514, 22679348, 352402796, 242777689, 347139317, 505462432, 895001120, 417367074, 326220972, 243133778, 200504160, 904466103, 433195942, 222823834, 587572320, 584009376, 230476842, 614579308, 975899924, 333263423, 201531268, 152410063, 726562182, 935140205, 877535591, 107929381, 47992591, 29196379, 890272657, 805717174, 371673652, 824591443, 109920982, 44161527, 624814984, 481696432, 492331570, 163151272, 534631, 503105009, 10421508, 444083879, 543049778, 428572684, 45198384, 372684723, 505545877, 757106048, 733217757, 160937002, 246903447, 755744704, 761589842, 984839069, 259553282, 768484663, 273281203, 730539431, 822368970, 785826262, 177544040, 691589077, 621433011, 166265899, 557574662, 742585358, 145733453, 210910794, 122430105, 68874995, 734091139, 232047340, 270032420, 442667903, 447428145, 636065750, 142675142, 544944067, 194578569, 212490217, 78571625, 472874309, 251057476, 936748246, 596594886, 851790678, 271865120, 304816435, 215252266, 249165970, 42841452, 935762405, 243007219, 658558951, 449697892, 507646369, 978128453, 156114126, 743488134, 580616944, 648650547, 563677473, 177356613, 87676037, 897875825, 523635872, 827708810, 83613808, 366854266, 382064161, 2009046, 290580664, 133636534, 239872242, 316169620, 420384304, 801036302, 267724823, 398923010, 773863675, 886585592, 395230340, 438270047, 880355082, 129587105, 407443177, 324540844, 297455721, 162073838, 461658327, 982237740, 592229504, 663026992, 77842030, 633425440, 50213700, 964715574, 655772116, 363245184, 431846507, 153046898, 32669532, 16552114, 84970209, 574548317, 328707513, 713514594, 695373551, 756792100, 69327635, 573253255, 885799478, 144117247, 359874647, 766787302, 52841738, 593343403, 814695545, 542173858, 844251256, 825583194, 94177366, 726444077, 412089966, 936801509, 774068766, 977122990, 892580280, 252007100, 123851854, 527045495, 533586161, 559352284, 271797496, 226293586, 951515091, 495054561, 692249266, 15860533, 362082646, 868629358, 575699234, 521412498, 382387377, 437771480, 41951834, 825107968, 776293973, 952309962, 210908902, 431622251, 842196547, 309154125, 919668886, 754598311, 579710409, 374724541, 775371822, 501453987, 330508275, 542440174, 619692704, 595501749, 832074404, 173938368, 756675865, 138761437, 615723517, 30956832, 997970243, 921389512, 526737488, 160940533, 163864972, 723350423, 369771426, 978896403, 813738156, 644850608, 357110832, 412377177, 259379545, 128617154, 450356095, 459879708, 528817945, 285585582, 945281075, 117843594, 907559675, 286413089, 708120555, 386968061, 71648484, 79049716, 448645940, 816365093, 842870677, 654773626, 27910134, 727857285, 402213518, 932343186, 807074956, 567830853, 500989355, 571305727, 726389980, 644967909, 130937582, 890993355, 493167540, 761679737, 980575982, 80259313, 874910037, 948487625, 431523170, 559282041, 964328119, 500304725, 441433642, 590475288, 299160876, 223353424, 367573302, 133195911, 9949830, 688326012, 932476973, 295996802, 679971248, 307828209, 608989052, 399117935, 894262669, 893032195, 817780018, 712206359, 122069137, 706722909, 862516579, 492407480, 183094915, 163898310, 71154479, 509848649, 951288595, 394487888, 24719567, 891233139, 214080522, 194996543, 719511946, 308479667, 138615267, 970638342, 631308103, 174635397, 371180926, 727419731, 626628485, 239148433, 307777220, 511407697, 184699235, 709565690, 450430191, 656542621, 93036268, 362589078, 104944124, 367557972, 813458550, 653156544, 551027491, 742664275, 147339318, 582599030, 574574383, 383099323, 616523166, 203465322, 642061176, 484203619, 377809254, 32260942, 786345109, 873921143, 234477312, 514310183, 841839680, 502938463, 716043283, 645294949, 896782364, 733801615, 287556557, 47012275, 882099742, 253141648, 689749479, 522089996, 778894242, 537345150, 509722030, 643058229, 264016008, 120390241, 381205407, 15822246, 630935652, 236174221, 274146999, 140299287, 209059246, 519955982, 499121633, 642265953, 534021035, 177619676, 256128027, 252414591, 861230136, 345694256, 784194131, 309809536, 544667440, 56321318, 695066790, 500658451, 82598791, 857196227, 348399029, 201822041, 459620560, 580329271, 96794639, 168309919, 953879338, 336181135, 595922269, 905397848, 857286479, 452189497, 886366836, 873505471, 830109212, 712569687, 387853335, 235201795, 554129534, 968519189, 400914174, 523753343, 509103952, 108369413, 641069453, 977531334, 624990189, 404947398, 653308433, 968579861, 113020237, 75871713, 836107231, 328956093, 578400429, 164691967, 678764674, 813003949, 678001180, 694968123, 245200284, 995678152, 36477983, 602328708, 383105747, 181307655, 698221700, 94671303, 407649474, 78860676, 404032773, 540601387, 575798368, 895482293, 483739456, 105462723, 983818894, 411924308, 527783373, 792013053, 725104367, 298984706, 870803522, 260142092, 927775627, 987499407, 134672768, 986515306, 978760747, 165949518, 377227601, 616452796, 230825234, 111093072, 840153677, 268554231, 579756802, 392270394, 682444446, 6476843, 688013899, 719180513, 80284630, 739426364, 619714358, 170754766, 326879381, 578278621, 498251353, 245838791, 608714420, 917772070, 98972237, 780266445, 371542588, 537225071, 493014645, 472344934, 693002973, 681369695, 626446667, 524370546, 47448649, 972046031, 894922794, 760455554, 201233418, 859724444, 586325998, 363956034, 374239416, 182681038, 987416013, 285022473, 846959060, 198552119, 543091454, 561147434, 143310660, 522994981, 461789763, 412137425, 496482194, 770995163, 279097529, 657386190, 182297910, 149703898, 752766412, 60476384, 379384546, 955172807, 119199157, 390178190, 60932296, 848781707, 222191685, 612901883, 804051609, 519383662, 689857096, 11268737, 776773839, 102910876, 205956955, 131079898, 788203820, 211669468, 614281094, 658868442, 158056463, 420845123, 677890637, 28677063, 840358805, 475269762, 453306515, 781343147, 967190234, 453972120, 564579860, 608242931, 473339215, 624577634, 834578256, 537411562, 942657312, 672145133, 800451799, 782890641, 348432596, 406352476, 298995870, 7955073, 658642347, 232446240, 589612593, 261043858, 451178705, 519647956, 201138089, 710526981, 815707810, 997166080, 799462803, 513130736, 570263768, 364271482, 946927708, 303489004, 157436233, 15719835, 554238929, 251938506, 281129358, 629554229, 264042279, 938521940, 384482363, 652016917, 598321990, 241551362, 947910238, 576174190, 256723962, 148035699, 121109340, 614320966, 460766886, 316837677, 827617073, 252181843, 231112351, 107043620, 862033036, 267400125, 495151490, 257216833, 488474557, 983511928, 155155404, 596761292, 402704243, 999966299, 872515310, 867247217, 20980321, 32140345, 12051152, 384422279, 273026311, 294905749, 88159359, 794377973, 42880738, 216514311, 659306321, 956688385, 79902663, 399311746, 178564897, 352019809, 917988650, 504383334, 817738449, 156721626, 450877337, 916201190, 129702988, 155758420, 200354726, 168695405, 360295072, 260343113, 473240839, 648982425, 327937061, 501721161, 988509059, 968419801, 321620899, 139926173, 117244162, 309956823, 856231838, 333823937, 886178933, 326177434, 695503102, 755369319, 598138585, 267738163, 700603022, 359326118, 842435152, 985003337, 412972448, 731750958, 310724750, 561936662, 725559668, 453161095, 999475182, 211815498, 37846940, 139078296, 555665319, 970144709, 116813809, 681160150, 96604738, 816668897, 168017057, 591266566, 640340009, 870265645, 391566835, 967116212, 647891998, 482795404, 397504752, 161130788, 413064495, 702345607, 818436949, 992703229, 856116184, 274525508, 541739253, 227474851, 825397552, 50912465, 428802639, 234700379, 107771102, 524827823, 612667724, 950265989, 480999885, 659706660, 919224894, 643704242, 75317362, 702388978, 496828409, 223772084, 565467504, 225748531, 835391279, 224452757, 998043951, 15659831, 644343847, 138377151, 996075550, 724832962, 11763068, 207547047, 355838421, 326886951, 815372890, 145988622, 588839882, 691381961, 435890382, 688774997, 910904711, 425803915, 375958115, 627019470, 948690226, 939599192, 299512383, 280855500, 368142768, 883188568, 941217374, 821248350, 217277401, 81677749, 405062144, 126480188, 552770534, 640168217, 800447341, 92625257, 556673239, 201587930, 819679703, 318251001, 878880476, 370942938, 594953759, 274821768, 517765844, 570081484, 932603523, 251471005, 320016834, 792436540, 49152441, 902936744, 245500599, 880764495, 62194222, 258232400, 412084457, 652883552, 157345309, 757850059, 479476726, 300242481, 448966746, 110455531, 635526933, 144060540, 762617700, 713050393, 652192435, 268504151, 234163611, 674253299, 431029964, 995917256, 411235011, 719409468, 671750806, 406305967, 97944443, 520077335, 871512049, 363062844, 748938274, 683808801, 910778368, 403709388, 943733776, 709606158, 358477430, 475220667, 544449133, 766800292, 634929827, 677193668, 400325390, 839429247, 869214891, 651042219, 399198555, 911803894, 935996824, 70306486, 120290604, 484726797, 312811638, 546546881, 912805985, 159208085, 164981651, 361230640, 589256999, 528849136, 711264359, 973972744, 859688964, 901110846, 183242069, 132177157, 518101966, 481706113, 741526995, 247182183, 637107430, 886649000, 491738172, 873421119, 414428388, 815604709, 887207555, 756190006, 766678004, 741027402, 469248923, 961168716, 1081810, 64231064, 964874632, 275649672, 792932101, 438644684, 499681304, 387872464, 94977202, 454634388, 735864258, 277169763, 912299192, 548831991, 379691337, 833085699, 291363529, 110395041, 664305562, 828874633, 998208329, 725688297, 476563032, 632928712, 380105944, 936879701, 182265685, 72181727, 948716272, 19824975, 843011552, 777134915, 713958311, 272663546, 969445724, 829853795, 583791503, 353435506, 42333497, 228478291, 411506293, 584504602, 488130615, 978836515, 830988066, 570649071, 985986397, 136456304, 770125247, 953831334, 476121687, 406772247, 203622580, 384318571, 954140645, 423024523, 519574014, 487654527, 966709948, 360842044, 519060021, 105961404, 132194206, 658687262, 670124306, 920734798, 213249059, 964439177, 950438694, 214899137, 985273187, 234376210, 820829070, 211179065, 259287986, 592734827, 171954387, 654035838, 117110395, 426007288, 39111631, 598691409, 940698394, 617804006, 834533311, 394541794, 392314995, 839024223, 404908798, 104844275, 515957181, 571699709, 110081035, 692876371, 152519673, 446286230, 322898557, 554894278, 399087625, 843865048, 348350297, 217581082, 15366765, 303338894, 495978155, 387606703, 50843286, 193381417, 590303690, 499426761, 567638018, 887747649, 797486089, 28333604, 772768912, 892834400, 981975174, 190933533, 223660437, 795217860, 108055345, 911602379, 680465859, 244508024, 20665106, 865157788, 964286085, 783626317, 636997073, 236445758, 186713436, 138746641, 988639651, 80674553, 963532651, 527674113, 982868245, 813392515, 432899942, 96044822, 532072604, 390801795, 680015345, 61201862, 631870827, 344352347, 716482320, 704305792, 996538779, 822274775, 978520807, 732904143, 464846196, 582301026, 18232178, 99979549, 847723281, 757675333, 908618076, 493540446, 109378469, 610698991, 220271502, 924697318, 301287012, 989237320, 287592262, 487965007, 827139963, 80176555, 6419311, 141841660, 517921145, 612830189, 931167471, 391376280, 353620564, 608604537, 484675576, 92032729, 730111347, 279702440, 321349948, 547371036, 471147234, 431810363, 125144710, 802197558, 69351301, 369619960, 513562736, 129302498, 288748212, 563981314, 99138228, 89724125, 824990201, 152993971, 51187678, 81841392, 533204039, 254305350, 398125740, 633713071, 159313614, 83186467, 536479178, 300555677, 654795244, 977272025, 219172642, 924371844, 892734417, 406641796, 918230688, 558849522, 847691621, 761164174, 326314219, 512797631, 583361628, 824777470, 565260609, 865419056, 900117059, 310623879, 586038347, 571330282, 635902775, 357440813, 97903081, 487741263, 646978728, 200284981, 648103128, 498357410, 399888513, 482167493, 78522889, 221860893, 198183449, 192351180, 26494011, 587474051, 826112754, 943120284, 511127256, 746706459, 491925254, 215983782, 432263559, 80529577, 12680915, 870594753, 926667000, 540821977, 298671513, 790618215, 816179104, 684051917, 404053816, 314353847, 434936208, 21305637, 910889740, 333975333, 600702438, 967001010, 22523901, 314965202, 508675627, 682579856, 145458467, 27297931, 751250394, 765246187, 718140271, 863791948, 513824310, 806488180, 654431787, 101586543, 617838565, 678985254, 158754257, 122415764, 392592866, 807880484, 512090162, 775605411, 846904764, 30590691, 388349575, 903380355, 595391984, 490815942, 333626200, 887374291, 37921903, 29209416, 902804062, 197152935, 989972942, 82593412, 702811790, 981134902, 174329150, 934574951, 588606429, 681268117, 649460876, 598621354, 519439164, 446861404, 996682586, 444457320, 857372671, 83222270, 37753747, 430844632, 559280342, 433166650, 651447514, 928061021, 295498798, 612632368, 712731056, 484385183, 251675016, 88856265, 624954188, 772796284, 707268190, 751881724, 70873961, 990656696, 755338318, 41407080, 158276941, 334151552, 84100412, 746751774, 147175969, 180200571, 938115971, 889536287, 248537660, 862013976, 994718176, 411383750, 287854043, 701629866, 290744398, 483115171, 752722346, 612285673, 447130603, 972450881, 760017791, 547929153, 19627003, 525201322, 417007975, 553672272, 671644184, 50429453, 370028641, 825626048, 203501727, 819962376, 646712670, 781550807, 609095881, 360667936, 288121049, 147031640, 455550669, 111773522, 406860105, 573965904, 224120565, 164989355, 867085925, 246514376, 673746137, 471828280, 309651663, 297668579, 884899963, 605628487, 283760336, 115396571, 905635300, 360697854, 430785947, 270726110, 827062359, 325376609, 867610755, 22625938, 309652967, 554428635, 18309373, 871899493, 951658241, 670554191, 208081041, 709978535, 534807691, 689009243, 590660140, 397159482, 971592415, 816315492, 972058779, 977601186, 380422219, 7607248, 354095924, 303043887, 605312151, 76211408, 828529200, 608812317, 731747843, 233649906, 390288959, 328244552, 719260997, 368302231, 844506279, 963753112, 112527215, 967170457, 270461658, 861923805, 769838000, 899421191, 998916710, 378267036, 457436341, 714999916, 971911199, 654075301, 647287548, 316584733, 412653195, 871978726, 973486121, 57714658, 173506397, 413655982, 289818507, 316257874, 50580967, 403016428, 776455359, 704388014, 215268178, 365773293, 353837234, 199003338, 35971418, 533666571, 794653669, 435783091, 943612763, 83055123, 704693488, 738886661, 127347890, 600438282, 808158374, 725828271, 972507837, 301600665, 111011085, 75284648, 901375469, 486619179, 559049304, 146397087, 392181303, 260105572, 6609017, 625727511, 295576842, 630688062, 639360016, 390372162, 169846440, 655075746, 968658178, 239486580, 889946950, 816914029, 775028006, 534210301, 968542958, 461253489, 313208351, 907416082, 326326558, 182073621, 528211756, 805394896, 747092209, 949036269, 876494612, 914303285, 833318443, 97863800, 454883619, 349787005, 742325095, 894856889, 973549098, 202692308, 60976202, 407195296, 405448044, 685953473, 506774094, 311860313, 253874279, 396303676, 712705478, 957144568, 79582698, 752450691, 516834938, 218075149, 980973532, 889297129, 323237331, 710048284, 927111995, 760337456, 246117927, 741889871, 62434233, 663443255, 943933372, 125990402, 274146752, 898570789, 987875543, 523668442, 235868119, 932760820, 909922017, 733841940, 931354881, 909546277, 492446029, 741762929, 441582829, 698325556, 844607604, 410713436, 733854305, 896049200, 805519939, 814726149, 777659130, 542772260, 737118413, 515396419, 689014172, 818865536, 269149576, 594531636, 689869471, 273717616, 252872302, 546994757, 196497635, 18231180, 116894899, 679595040, 400390229, 682620973, 986729807, 391567318, 376671926, 392012441, 817041015, 433696765, 928269778, 204667746, 151274053, 910368149, 805570938, 6785325, 829824865, 711317993, 115322624, 626272492, 346650270, 961725308, 843665201, 577557656, 246397960, 484172143, 484483789, 692823597, 410641516, 855691064, 421515807, 137360585, 600891502, 795322012, 191064891, 95844662, 574899562, 399027448, 28775100, 623306120, 577831172, 294403476, 177329995, 722010937, 538496023, 692106481, 201698447, 254049866, 992895118, 400616109, 727766394, 533407164, 783315265, 403865452, 369657104, 383232966, 162111896, 78671292, 527936172, 169208943, 973298404, 969743309, 356065923, 924989877, 460487659, 254480946, 33837185, 260316277, 874046861, 692578227, 742653729, 111795425, 693762582, 646268388, 203422870, 21561470, 12706856, 497442003, 978406810, 356329503, 476352221, 907521065, 935870538, 467198043, 291237317, 474748872, 591548555, 445642577, 248719044, 63508596, 556588957, 828661055, 486136289, 39403749, 741678063, 377280933, 100763021, 734132733, 871319587, 414819485, 675559299, 723734986, 585640512, 579104924, 204572337, 275000069, 237988972, 809822494, 271622200, 56963742, 827791736, 755776618, 994404980, 589882621, 509290210, 358531675, 449041736, 38051497, 75270575, 817794159, 304258479, 397899690, 511458774, 702635950, 407274505, 8832219, 289922719, 900796177, 222682906, 240465465, 269842560, 910995250, 213212339, 32587837, 35671718, 221798745, 795742446, 835428217, 262994880, 133255863, 52358191, 483074422, 235961690, 383183607, 573297338, 860286138, 599277400, 378596006, 283876465, 651750241, 333986247, 570160581, 761199953, 389900888, 549528518, 497581418, 3382229, 863064787, 955930485, 879921419, 962723794, 182807499, 262413856, 307620283, 630821263, 345633173, 728803573, 175485723, 96094349, 791947447, 50940464, 230719166, 240288310, 468619470, 465444271, 408022056, 66910592, 936148960, 311811862, 125455724, 548812551, 53736590, 545432588, 194734162, 853309978, 649686088, 193585287, 859962045, 172066537, 371013601, 778521922, 998175445, 84121698, 338680318, 102469815, 25374775, 649281208, 689560250, 739129559, 359933618, 566146347, 782826083, 257904394, 991965085, 29067845, 904413941, 801595740, 959707387, 766757172, 333727004, 572548874, 546705774, 376702489, 980475106, 14518537, 991278921, 946335547, 67177267, 566457758, 670921023, 324603726, 150736414, 120481225, 67105129, 405203529, 669890446, 512741393, 658969137, 131492891, 619981178, 347514203, 387821476, 435026757, 681545141, 529348105, 155517541, 321099838, 793208911, 587341688, 635235112, 741021131, 130097143, 301866992, 652919478, 388007923, 768450230, 70249001, 713794158, 896527771, 56869814, 817253766, 221488289, 73872143, 431273999, 257348998, 993923183, 802586422, 932106657, 258828056] 136985716))
+
+
+-- Grouping test cases
+tests :: Test
+tests = TestList [TestLabel "Test1" test1, TestLabel "Test2" test2, TestLabel "Test3" test3, TestLabel "Test4" test4, TestLabel "Test5" test5, TestLabel "Test6" test6, TestLabel "Test7" test7, TestLabel "Test8" test8, TestLabel "Test9" test9]
+
+-- Running the tests
+main :: IO Counts
+main = runTestTT tests