Planeetat

input/code.cpp: In constructor 'Garner::Garner(const std::vector<int>&)':
input/code.cpp:75:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    for (int i = 0; i < p.size(); ++i) {
                    ~~^~~~~~~~~~
input/code.cpp: In member function 'll Garner::eval(std::vector<int>, ll)':
input/code.cpp:81:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    for (int i = 0; i < p.size(); ++i) {
                    ~~^~~~~~~~~~

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using lll = __int128;
 
vector<ll> precalc = {0, 1, 3, 17, 142, 1569, 21576, 355081, 6805296, 148869153, 660215659, 920608908, 836504326, 639554500, 466620985, 872046927, 308717370, 502812808, 646301526, 985602096, 8033007, 199948617, 265123234, 963316760, 97012001, 520509077, 963089188, 609109590, 475681640, 268714573, 138142320, 659323185, 432287876, 833911481, 580044808, 724047794, 752488773, 369844336, 411404305, 966444867, 966304277, 670002988, 356672355, 499497440, 858083915, 849461059, 699627096, 696125320, 569657991, 589455080, 637699856, 159331976, 253230028, 126065421, 190780359, 657860743, 35914725, 627548423, 786042624, 88732365, 595484631, 907204844, 310896156, 654434332, 999859588, 891860619, 760802640, 321240817, 284705446, 581193655, 540500946, 828699763, 86377965, 299422367, 636989116, 804687707, 341628824, 969661800, 493359322, 269113227, 2788545, 136045625, 319856162, 734688215, 933443980, 548820306, 844116817, 949670148, 893770986, 562714601, 464787503, 785661356, 27520011, 33434941, 651969158, 596069751, 447474780, 454137267, 430168215, 427270537, 894456323, 432736565, 541462563, 580395437, 926815786, 263023838, 779713525, 129353767, 254646934, 327058306, 318061585, 873404148, 546897006, 256895690, 845805366, 521993981, 151412543, 452233370, 169107595, 352810726, 932989581, 82660203, 144142246, 7983114, 841762719, 398368184, 36362596, 5939420, 621718875, 180998347, 89322205, 709123956, 45239813, 623512817, 592243835, 375742205, 13182108, 741093354, 954650126, 632161601, 323889231, 855586538, 576541114, 402077493, 420399764, 23768284, 168259101, 986206037, 639024795, 827219225, 972138947, 118660280, 935496148, 260619316, 568756388, 474316106, 90646046, 327256160, 906940925, 61315684, 100123479, 904812330, 341615294, 269531078, 100088684, 608203198, 84183940, 718793427, 269849284, 338624606, 60645067, 579226929, 140045143, 723080187, 393278301, 585228375, 59206357, 101985982, 672040685, 139906388, 744500615, 662412691, 158778780, 73399837, 332041241, 281105866, 957970313, 29966196, 815538417, 292300246, 570909748, 771503216, 214191103, 101730853, 63227600, 308932805, 811045900, 464333632, 357992660, 77607798, 507287768, 341677483, 72934014, 46989119, 114936355, 602267494, 906589693, 582034332, 895922440, 156857108, 618036646, 157634170, 761405010, 817859847, 467337486, 632543264, 517776051, 994834897, 687965083, 457907638, 825497422, 243467865, 14399121, 407258784, 98570234, 748959757, 297443300, 406918679, 871245292, 252946284, 452320327, 942393032, 318555470, 766642481, 981668534, 724552884, 301298708, 142719827, 453758144, 985372383, 718141077, 18615310, 590242901, 715391284, 471018736, 571254190, 833968271, 832120869, 945980567, 722309937, 54672675, 115490430, 187087627, 626363638, 686555146, 318156532, 972513131, 167214298, 90260614, 306880672, 32986840, 478943540, 672206708, 393818545, 416131966, 388360852, 956022816, 146560536, 392214273, 327393841, 526526895, 175253967, 352945422, 306638803, 941328742, 230321990, 570405207, 35763767, 385325705, 457471115, 680333391, 913022330, 507476085, 625156383, 460862378, 719762476, 612136402, 543142329, 910689236, 864620931, 94770086, 124023110, 936801504, 312536722, 840866722, 550990595, 847033780, 9264261, 210329044, 369392790, 722084766, 940376498, 107971898, 858413915, 472976473, 311774094, 267458901, 145925718, 338817999, 630914080, 579431167, 386296719, 138838078, 585741448, 847119734, 643211690, 268683825, 351931792, 735656552, 8097207, 868683252, 134721277, 751435055, 835490594, 768101286, 361829871, 395204061, 571729313, 121053572, 334933401, 823546703, 791822392, 196085636, 914631844, 921218256, 269969740, 960245594, 308426560, 50228312, 203517952, 816105383, 292189633, 32732523, 666262122, 437188886, 72215308, 918176539, 415978508, 85324969, 769013382, 647852341, 689378978, 613167392, 340915335, 831071843, 565517411, 255908828, 91838622, 605127507, 57150948, 686992820, 685954022, 342552285, 849812665, 260415783, 694407779, 131097970, 232078836, 790843917, 602509046, 136064185, 155679521, 958411398, 943708467, 206313402, 358630277, 411970955, 489455840, 988325815, 978309818, 166561041, 394433021, 617840127, 693970966, 995469520, 143162639, 766345048, 552437316, 141371172, 32069679, 516006699, 884187788, 608358064, 219163692, 387670703, 175148085, 17199999, 180488480, 660440926, 864052274, 765128850, 483638267, 499688410, 640750115, 524434952, 827157815, 514841947, 891119953, 537621015, 892118064, 928120221, 364674640, 992761107, 724302220, 924628854, 760255237, 769488054, 235556227, 244177714, 854964962, 259182566, 77503409, 507837049, 779838104, 423943877, 886744385, 958705993, 455048970, 824356123, 713721861, 331904766, 623348072, 614726681, 902610163, 946917405, 630933809, 683877164, 640836005, 535209373, 166585714, 161480461, 455967117, 252642116, 897912756, 319743887, 916746661, 702589733, 778455519, 494137733, 289013415, 719760981, 955879877, 505371826, 707573819, 803154268, 969112213, 221690942, 226656978, 735346391, 982277351, 592777469, 447310232, 172403391, 748268363, 601914711, 314744304, 694374706, 788244971, 937988296, 79919141, 145294051, 52674283, 265392050, 996188166, 381465305, 372742716, 485059689, 315704434, 844900882, 764763714, 332232108, 961793773, 365663110, 538922989, 601146238, 25707931, 555697561, 878705277, 319447511, 428853013, 742394955, 53270809, 647847019, 542010010, 434050460, 846597947, 956068884, 662776175, 977629798, 900768919, 129073991, 76026409, 498192056, 215123369, 917836934, 826637623, 435940858, 632532526, 979699864, 273969950, 101600462, 797914606, 356500503, 216770185, 381331949, 326172660, 937009827, 853670387, 682492038, 972664354, 284139447, 315944240, 791739438, 46026170, 412249526, 789973123, 832181317, 394745079, 241250226, 163080658, 90324747, 780658649, 40050836, 753363258, 490090701, 507159728, 175535065, 880542882, 601405007, 875042173, 988657013, 624703488, 609933868, 870319039, 865917489, 237139139, 171461911, 722145611, 176534686, 748791413, 777888894, 189895535, 127548304, 62907885, 838377878, 35812203, 917533875, 810336630, 926341711, 888415765, 670767852, 513394863, 223454100, 439177115, 658683635, 622286412, 444809364, 970826379, 277126519, 793591686, 965618620, 524560088, 518622823, 740934331, 615919709, 579173509, 11324360, 445025848, 856961685, 923580922, 185212905, 392675418, 727388601, 865839801, 76975614, 882654461, 676444158, 68254115, 309825214, 324465365, 841768008, 273959910, 438044305, 547731766, 711485207, 611633037, 901608514, 588206840, 824678995, 715062417, 384420191, 339850593, 508303398, 393630144, 829399774, 404455930, 437595436, 84921880, 407863020, 683956864, 584483785, 227026419, 772984782, 401523829, 185477490, 738922901, 327552152, 770760761, 378607522, 394710363, 763322048, 572718610, 939574117, 900466080, 869504287, 674683595, 842164179, 895649271, 202668486, 109169255, 216662266, 371897295, 625604906, 869773593, 833554505, 306574822, 731350505, 654193167, 960565833, 804819530, 279245477, 885855615, 215870028, 964455102, 544427865, 470123903, 23511463, 264092633, 638794607, 79622179, 474381606, 554791439, 330903508, 511020268, 932195757, 352156109, 244536936, 294113392, 142386392, 964997788, 373655410, 830312898, 163010932, 863889744, 102244077, 676493916, 189730587, 400057013, 465021266, 603765333, 103120244, 784797374, 373899879, 595340442, 425658649, 294186115, 670989044, 79022991, 21873737, 425688347, 89846397, 488428951, 746805572, 248666732, 753576270, 684601776, 236729218, 422757346, 848575098, 293549644, 980667733, 772661211, 276677051, 501793049, 880460037, 883830717, 950820192, 307979260, 751943962, 510752702, 744824767, 442457467, 149970957, 528163627, 696218575, 25298630, 747095783, 884906140, 909133547, 733653555, 146854917, 937116871, 163855877, 659732814, 709087432, 19492549, 147701829, 364984477, 953983272, 567675621, 499525550, 157113580, 398331965, 653488931, 868545818, 937865416, 255354491, 424337212, 586865979, 617557895, 111291906, 81586380, 386029611, 722531365, 497424224, 534960648, 559936484, 225894714, 573885746, 447007271, 10245498, 561579300, 766053818, 530349910, 398231244, 729004111, 108441817, 872910612, 602083783, 995052453, 821631128, 269715702, 456899624, 348077669, 325709455, 866705688, 860556688, 386447238, 115474755, 884458677, 446486925, 965099577, 72891374, 77737598, 502245864, 129016649, 826847537, 819513705, 43884324, 555472343, 326476625, 762976966, 402514248, 839207200, 38977123, 705559546, 562644196, 350626583, 9509184, 130499500, 108601600, 132081101, 366869182, 458726032, 29886768, 148686953, 885348268, 801459787, 139572747, 673185038, 991695943, 862630555, 522110620, 80076634, 966502459, 477995047, 21572279, 721384935, 193349150, 242811185, 37255341, 604049970, 825401160, 507527461, 726484848, 396061745, 203154030, 58041031, 640367423, 318384869, 608357962, 824194966, 825656956, 77368019, 478243250, 106866672, 641605168, 666826892, 406075975, 779083698, 310454415, 342169482, 803327115, 807386468, 255782051, 744364732, 950122691, 232360024, 943838879, 865866499, 288404715, 96301762, 280687956, 545244197, 915823587, 417570436, 387247458, 160322947, 244425439, 789934672, 680056276, 214979299, 860921706, 107319155, 316165313, 965981656, 606430957, 841585452, 501119730, 668310812, 378443564, 371207456, 755942925, 528113576, 983914180, 986125547, 848006220, 419529610, 53751915, 659806304, 597702448, 208134673, 783769758, 974670184, 515677410, 141562686, 300791432, 937938694, 650736657, 422159400, 666732079, 947382007, 87673516, 55967662, 804678627, 661131710, 692785158, 841985974, 201632612, 945517170, 692816862, 817773860, 168951065, 445290969, 34875543, 652783472, 664136292, 389817602, 117154460, 622797299, 148415442, 5708337, 666556057, 755755784, 366882575, 914194185, 906339336, 741626213, 90170576, 471762897, 438418175, 550769962, 595559461, 905064324, 917231767, 964520213, 358490848, 81057698, 247832532, 341219882, 100102824, 341934238, 396889111, 209145178, 923964885, 559093402, 365469193, 120384141, 903956071, 152602509, 267601813, 978731849, 532938250, 594199322, 785028054, 456440644, 567440735, 988054619, 405996756, 699153707, 894273966, 877916508, 328571157, 127445368, 597814206, 421399429, 993196046, 417582204, 988281451, 517534077, 352254670, 336896544, 306733391, 963995186, 727299010, 750107064, 516100901, 451617315, 252736041, 547822253, 519556226, 161488653, 609702989, 962913750, 244708312, 871684984, 846374473, 601268294, 272544856, 214984956, 266321320, 450324802, 794618905, 329197003, 720425508, 718926483, 305295730, 175588666, 373544508, 720535299, 10433899, 109859248, 764634302, 147733353, 337233802, 560942707, 93268801, 831913393, 916124868, 415567211, 362520882, 687700843, 108480217, 487643969, 769614190, 164330043, 964265852, 326198123, 61287690, 497760458, 950598050, 461145285, 595217468, 597316323, 933967768, 13002237, 366847138, 513592965, 196084977, 337595660, 887375487, 394116005, 268719147, 459011241, 478586418, 428004344, 427585581, 398347825, 485529467, 974262726, 877043992, 865496933, 485169739, 204160831, 360850302, 826629207, 948631754, 572802768, 516487919, 507452190, 288860343, 55078051, 213000963, 750687739, 609530984, 502955628, 309477459, 723217487, 466348093, 987825043, 579172097, 899724792, 969650508, 53819821, 930938165, 806298514, 503183988, 215659602, 759949498, 275591144, 217965476, 112032447, 988483485, 689931614, 626024891, 585826791, 195944299, 406008749, 229336021, 971100806, 60752686, 672600506, 133860303, 975641493, 422579410, 522726497, 323293715, 589942941, 785922954, 511312487, 159512465, 831212924, 250550884, 82741720, 22404601, 650217395, 146107983, 551526542, 575599957, 162521050, 149485478, 152610625, 13547158, 605288134, 299255862, 647616848, 828357658, 519541900, 261610452, 808475240, 533655987, 830462483, 219754438, 998148668, 633792537, 339771115, 515071927, 732601227, 695109360, 138661897, 614396758, 953160893, 704575139, 483861263, 410546807, 751806895, 843172949, 945088802, 160043091, 275894659, 146367349, 827732507, 693846770, 740601331, 10258522, 879124922, 323026593, 107712067, 405595743, 949933359, 469293333, 89871061, 732935377, 637412130, 373131056, 701665527, 666687613, 101838884, 966450421, 697501479, 703016989, 537524642, 774468498, 460330472, 766502143, 391420755, 253300533, 915709450, 446285682, 564846955, 118204760, 337019520, 804948067, 456302554, 61797347, 51076318, 158135891, 663869420, 557790962, 404915771, 74671362, 20711704, 14956290, 535197310, 404342843, 489805444, 161980354, 790800991, 974413024, 243540404, 552360264, 310175781, 985139294, 939287185, 499443741, 88975671, 340441619, 881094737, 302635619, 130301897, 397900099, 229678788, 770583889, 479735507, 313647083, 264764513, 991014386, 57611778, 564681517, 451193458, 116090524, 847697460, 532190580, 173977459, 309076340, 604949964, 216552014, 145171809, 327972078, 263989410, 100043439, 736012429, 866499995, 884626657, 353718712, 217010272, 123616700, 87385887, 793180764, 730307885, 446934334, 304557638, 240613545, 103101145, 545905497, 958176451, 488859248, 736039744, 713924701, 528239124, 76186716, 674023710, 444760072, 207779409, 195285135, 22298341, 652813306, 460938297, 344108813, 504361467, 864850223, 836750902, 563978111, 415339206, 933932555, 740260623, 329318287, 618428005, 710468127, 599104505, 907596106, 380515644, 235540730, 7879934, 249935739, 72942155, 70396755, 166358717, 285269760, 265468928, 455214955, 452157803, 25983969, 709639725, 33830386, 157529403, 346365116, 656968732, 144719168, 278138424, 50820837, 946264276, 163727272, 258384742, 964406934, 799852861, 771053678, 169132451, 482537949, 64604156, 184280519, 171230101, 308345068, 341336338, 75168247, 536935039, 689188119, 67360753, 603173504, 670370518, 233307305, 689561519, 470268287, 476808633, 741232555, 163372059, 890258227, 243234423, 570016344, 291095796, 389144970, 604367506, 812364795, 639211190, 374673593, 643972257, 523643744, 581238074, 859458958, 417191144, 577066225, 538448905, 241997711, 918275880, 666246025, 131624812, 586080391, 926113190, 367261302, 406172656, 888822051, 791671956, 992691833, 896860338, 731476336, 340683838, 722018153, 603954875, 240415991, 914463313, 318635211, 462768445, 414769319, 215134114, 521981506, 109137710, 284869584, 190346789, 293587178, 297631576, 808988257, 759135362, 932671361, 651013182, 149916701, 691760897, 750845414, 773748256, 795192319, 677616235, 94707751, 399251900, 844271990, 671301281, 106302520, 979560697, 297771366, 996756387, 926745288, 201000826, 669551589, 129453456, 693720496, 195628289, 498319867, 26812051, 476790258, 829386451, 930112253, 648275620, 618703631, 290218657, 88607275, 1200672, 22405429, 674894420, 253505052, 653670382, 980980984, 930844464, 281769048, 90797988, 215696044, 374726585, 780747353, 306685454, 889272301, 765470161, 377559977, 705918916, 835109163, 577654011, 737910162, 373518888, 272501802, 179656415, 455661117, 699693335, 490520141, 177093291, 781087158, 355547351, 256376388, 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565937296, 481363273, 593064809, 205495142, 847612238, 118069865, 368966647, 135050788, 936878811, 777203487, 552106070, 399385712, 872399286, 569523066, 572810313, 868698883, 240077516, 516853872, 596756751, 686477689, 618306455, 827092735, 605567003, 247172478, 471161663, 838489907, 877726013, 999810004, 55507762, 696391118, 259746164, 159274586, 882145861, 871335356, 13460808, 765174111, 201156081, 844433634, 652401239, 716763709, 208108419, 785611171, 218444433, 239487099, 144270713, 423843273, 831427979, 204940121, 174266507, 798963000, 914606370, 507785004, 754179838, 188584209, 199556757, 273275195, 654178954, 753577356, 853665420, 457057586, 135249694, 484673486, 34219115, 459102938, 654469880, 713317532, 195282799, 964866526, 443123136, 477650972, 257236191, 561837223, 533938044, 979240576, 599031090, 574519166, 109763135, 137194798, 202119472, 209946540, 594393477, 162985221, 22778150, 876919655, 552959901, 734766362, 60277630, 611687537, 311075158, 372379981, 425852053, 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115117839, 144627034, 827787356, 284550462, 947333790, 761215267, 956647815, 640184110, 721289839, 475961977, 244661443, 565889765, 251504829, 721295575, 571023926, 912215345, 705653338, 666480301, 230675253, 448610678, 930744417, 585173274, 19484408, 462999342, 698171224, 321924621, 596881257, 718968783, 364262349, 280004798, 24354794, 332170311, 769464524, 393611071, 277026304, 800380413, 29925512, 271128735, 724037054, 171864835, 83702131, 521949518, 586704245, 401049819, 780452718, 276370823, 18705619, 297283637, 794379336, 513133494, 89940552, 979286876, 493922400, 86334712, 703393727, 434420505, 977801898, 817438522, 311680170, 302118571, 462980415, 822421123, 561700757, 307387378, 408244712, 318736439, 732339881, 826966587, 157932425, 217343726, 581199950, 138656797, 155116347, 196118696, 902385987, 942162339, 952142399, 343036324, 291191485, 554970157, 166313856, 266032609, 789396410, 561260169, 594604152, 476138850, 178566350, 178218079, 71699556, 596969452, 682963076, 103042181, 467922960, 480940308, 985548598, 573505052, 776423101, 132646387, 890436040, 342996351, 164838952, 166515409, 855209783, 831592500, 184205117, 140969643, 347015127, 882073371, 293186619, 674432978, 946551967, 502059696, 690918722, 652514415, 740849608, 771368248, 196114030, 501309355, 437873793, 600255027, 148958968, 51512733, 502494272, 370929558, 224214005, 453317181, 914669526, 384882184, 401538332, 476744503, 526910824, 865944446, 267190641, 874293576, 52195669, 780317516, 843660973, 518680445, 529167776, 12651346, 255553971, 787458963, 271981923, 986176009, 899722936, 22736604, 431178500, 533951403, 363226900, 576581492, 492917494, 840391888, 418961673, 916050757, 959976801, 124708454, 511154047, 575663375, 396718071, 261563031, 913717198, 487018340, 676934628, 831050016, 732886554, 396107950, 471255379, 733988147, 189755397, 244473965, 336965891, 710880207, 503933920, 370601590, 882523722, 423819973, 608157217, 970284822, 494545669, 552057139, 350675417, 459751068, 146395568, 606685894, 797808272, 325165451, 449455533, 724225374, 297460892, 582713769, 635452845, 970744366, 935835207, 864343095, 719896449, 260927052, 117049238, 386745234, 758957136, 614583337, 246657828, 200248459, 991872661, 183891809, 725561333, 981111812, 868203116, 268718303, 825664424, 743072234, 784756842, 444399373, 477148575, 668870759, 529443686, 39610443, 112404926, 686623618, 737070426, 491732569, 360576642, 907357688, 526753221, 532284615, 305149885, 327151227, 531525937, 198538517, 684207898, 669859464, 30440622, 544782893, 123465341, 171829834, 423574054, 296285364, 482116496, 141010647, 504034249, 266134603, 833898560, 721158645, 691405606, 829675470, 343936737, 364064601};
 
 
constexpr ll mAdd(ll a, ll b, ll c) {
	return (a+b >= c ? a+b-c : a+b);
}
constexpr ll mSub(ll a, ll b, ll c) {
	return (a < b ? a-b+c : a-b);
}
constexpr ll modPow(ll a, ll b, ll c) {
	return ((b & 1) ? (a * modPow(a, b ^ 1, c) % c) : (b == 0) ? 1 : (modPow(a*a % c, b >> 1, c)));
}
 
// Iterative NTT in O(n log n)
// Preconditions: P is prime, n = 2^m, 2^m | P-1, 3 is a generator of P
template<int P>
void ntt(vector<int>& vec, bool inv) {
	// Apply the bit-reverse permutation
	int n = vec.size();
	for (int i = 0; i < n; ++i) {
		int t = 0;
		for (int j = 0; (1<<j) < n; ++j) {
			if (i & (1<<j)) t |= n >> (j+1);
		}
		if (i < t) swap(vec[i], vec[t]);
	}
	// Do Cooley-Tukey
	int root = modPow(3, (inv ? (n-1) : 1) * (ll)(P-1) / n, P);
	for (int h = 1; h < n; h <<= 1) {
		ll curr = 1, mult = modPow(root, n / (2*h), P);
		for (int j = 0; j < h; ++j) {
			for (int i = j; i < n; i += 2*h) {
				ll v = (curr * vec[i^h]) % P;
				vec[i^h] = mSub(vec[i], v, P);
				vec[i] = mAdd(vec[i], v, P);
			}
			curr = (curr * mult) % P;
		}
	}
}
 
// Calculates a * b = c (mod P) for two polynomials a and b. P must be valid for ntt. Assumes 0 <= a[i], b[i] < P.
template<int P>
vector<int> polyMult(vector<int> a, vector<int> b) {
	for (int& v : a) v = (v % P);
	for (int& v : b) v = (v % P);
 
	int n = 1, t = (int)a.size() + b.size() - 1;
	while(n < t) n <<= 1;
 
	a.resize(n, 0); b.resize(n, 0);
	ntt<P>(a, 0); ntt<P>(b, 0);
 
	vector<int> c(n);
	int n_inv = modPow(n, P-2, P);
	for (int i = 0; i < n; ++i) c[i] = (ll)a[i]*b[i] % P * n_inv % P;
 
	ntt<P>(c, 1);
	c.resize(t);
	return c;
}
 
// Garner's algorithm for chinese remainder theorem in O(|P|^2)
// https://cp-algorithms.com/algebra/chinese-remainder-theorem.html
class Garner {
		vector<int> p;
		vector<vector<int>> inv;
	public:
		Garner(const vector<int>& primes) : p(primes), inv(primes.size()) {
			for (int i = 0; i < p.size(); ++i) {
				for (int j = 0; j < i; ++j) inv[i].push_back(modPow(p[j] % p[i], p[i] - 2, p[i]));
			}
		}
		ll eval(vector<int> r, ll mod) {
			ll res = 0, mult = 1;
			for (int i = 0; i < p.size(); ++i) {
				for (int j = 0; j < i; ++j) {
					r[i] = ((ll)r[i] - r[j]) * inv[i][j] % p[i];
					if (r[i] < 0) r[i] += p[i];
				}
				res = (res + mult * r[i]) % mod;
				mult = (mult * p[i]) % mod;
			}
			return (res < 0 ? res + mod : res);
		}
};
 
const ll MOD = (ll)1e9 + 7;
constexpr int NTTP[3] = {998244353, 1004535809, 1092616193};
vector<int> ntt_primes = {NTTP[0], NTTP[1], NTTP[2]};
Garner crt(ntt_primes);
 
// NTT modulo 10^9 + 7
// Who chose this modulo for this problem >>::((
vector<int> polyMultMod(vector<int> a, vector<int> b) {
	vector<int> v1 = polyMult<NTTP[0]>(a, b);
	vector<int> v2 = polyMult<NTTP[1]>(a, b);
	vector<int> v3 = polyMult<NTTP[2]>(a, b);
 
 
	/*
	cerr << "res mod " << NTTP[0] << ": ";
	for (auto v : v1) cerr << v << ' '; cerr << '\n';
 
	cerr << "res mod " << NTTP[1] << ": ";
	for (auto v : v2) cerr << v << ' '; cerr << '\n';
 
	cerr << "res mod " << NTTP[2] << ": ";
	for (auto v : v3) cerr << v << ' '; cerr << '\n';
 	*/
 
 
	int n = v1.size();
	vector<int> res(n);
	for (int i = 0; i < n; ++i) {
		res[i] = crt.eval({v1[i], v2[i], v3[i]}, MOD);
	}
 
	/* 
	cerr << "res mod " << MOD << ": ";
	for (auto v : res) cerr << v << ' '; cerr << '\n';
	*/ 
 
	return res;
}
 
// Actual solution
const int N = 5000;
ll fact[N+1];
ll inv_fact[N+1];
 
ll binom(ll a, ll b) {
	if (a < b || b < 0) return 0;
	ll dv = (inv_fact[b] * inv_fact[a-b]) % MOD;
	return (fact[a] * dv) % MOD;
}
 
// dp[n][k]	= \sum_{t = 1}^{n} dp[n-t][k-1] * precalc[t] * binom(n-1, t-1)
//		= (n-1)! \sum_{t = 1}^{n} (dp[n-t][k-1] / (n-t)!) (precalc[t]/(t-1)!)
// NTT!
 
int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
 
	fact[0] = 1;
	for (int i = 1; i <= N; ++i) fact[i] = (fact[i-1] * i) % MOD;
	inv_fact[N] = modPow(fact[N], MOD - 2, MOD);
	for (int i = N-1; i >= 0; --i) inv_fact[i] = (inv_fact[i+1] * (i+1)) % MOD;
 
 
	int n;
	cin >> n;
 
	vector<int> oth(n+1, 0);
	for (int i = 1; i <= n; ++i) oth[i] = (precalc[i] * inv_fact[i-1]) % MOD;
 
	vector<int> dp(n+1, 0);
	dp[0] = 1;
 
	for (int k = 1; k <= n; ++k) {
		// cerr << "dp at " << k << ": ";
		// for (int m = 0; m <= n; ++m) cout << dp[m] << ' '; cout << '\n';
 
		for (int m = 1; m <= n; ++m) dp[m] = (dp[m] * inv_fact[m]) % MOD;
		
		/*
		cerr << "dp, oth: ";
		for (auto v : dp) cerr << v << ' '; cerr << " ;; ";
		for (auto v : oth) cerr << v << ' '; cerr << " ;; ";
		cerr << '\n';
		*/
 
		vector<int> nxt = polyMultMod(dp, oth);
		for (int m = 1; m <= n; ++m) nxt[m] = (nxt[m] * fact[m-1]) % MOD;
		nxt.resize(n+1);
		dp = nxt;
 
		cout << dp[n] << '\n';
	}
}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 1, 2, 3

Verdict: ACCEPTED

Test 7

Group: 1, 2, 3

Verdict: ACCEPTED

Test 8

Group: 1, 2, 3

Verdict: ACCEPTED

Test 9

Group: 1, 2, 3

Verdict: ACCEPTED

Test 10

Group: 1, 2, 3

Verdict: ACCEPTED

Test 11

Group: 2, 3

Verdict: ACCEPTED

Test 12

Group: 2, 3

Verdict: ACCEPTED

Test 13

Group: 2, 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 16

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 17

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 18

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 19

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 20

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 21

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 22

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 23

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 24

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 25

Group: 3

Verdict: TIME LIMIT EXCEEDED