OI-codes/S2OJ/946/946.cpp

#include <iostream>

using std::cin;
using std::cout;
const char endl = '\n';

const int N = 105;
const int mod = 1e9 + 7;

// clang-format off
int f[N][N]{
#ifdef ONLINE_JUDGE
{1},
{1, 1},
{2, 2, 2},
{8, 7, 6, 5},
{64, 51, 38, 25, 15},
{1024, 814, 584, 356, 155, 52},
{32768, 27562, 20950, 13674, 6794, 1731, 203},
{2097152, 1881132, 1559050, 1143026, 688940, 285399, 42597, 877},
{268435456, 252352192, 225134416, 183912440, 130448704, 73134373, 25675622, 2389418, 4140},
{719476260, 437453186, 285852834, 198930901, 417447372, 493700668, 936095345, 770727467, 287447420, 21147},
{371842544, 598590656, 444061297, 956708189, 127125386, 834823998, 128227000, 223478915, 929725695, 302765502, 115975},
{766762396, 413139421, 351102112, 112130130, 188617941, 339825372, 543187105, 114675694, 623357729, 261270827, 104995134, 678570},
{329376018, 705367106, 201640714, 352379330, 550132198, 846985547, 818860561, 624544091, 494980544, 959053918, 443889176, 751093169, 4213597},
{124160285, 828328425, 906083967, 147213859, 527558165, 193958029, 794519533, 742501375, 789123747, 444469745, 993581787, 979243161, 593627163, 27644437},
{121047601, 912065930, 1351624, 402906644, 713933492, 50841084, 863660427, 577705270, 887029586, 145474376, 588251882, 706568129, 777275244, 642664828, 190899322},
{243880903, 599607852, 442677191, 436289683, 281113930, 146582434, 584824855, 564630340, 394164220, 378918082, 150572902, 532909740, 763622255, 37460367, 184612284, 382958538},
{489373567, 413411086, 951426968, 887302037, 155903135, 283219023, 620782126, 905791112, 644465700, 989656495, 523232248, 664652865, 948982217, 20783496, 743914774, 684000569, 480142077},
{585862415, 487913812, 590859253, 163506170, 675080686, 265650536, 163485583, 426697524, 541587646, 670844388, 797779476, 563923072, 432598176, 907835837, 738939538, 774082037, 950670428, 864869230},
{157921350, 585213032, 124127002, 444551557, 903311742, 164413448, 386967031, 407995046, 262661729, 344515452, 135908010, 878209413, 368549114, 629205902, 255793356, 578014821, 143082468, 257436696, 76801385},
{134084614, 402761743, 842286714, 498687688, 314252511, 433353429, 874023832, 163451857, 900776051, 750447840, 374976568, 374596374, 409363634, 1428564, 912190395, 954400021, 334527550, 458752164, 941524580, 742164233},
{953612746, 62713484, 886653018, 688345870, 697128468, 646792556, 447421618, 157888096, 21488155, 259486619, 668079888, 781355645, 145564249, 348149153, 451544648, 902288907, 821364589, 27915451, 532351829, 752058720, 157873304},
{431750151, 79333107, 758273946, 860328871, 840463615, 976556515, 146605392, 618220382, 698863882, 145835594, 427902538, 38761432, 701961998, 464958606, 869153221, 553709997, 280018488, 290250685, 77551688, 344667085, 416460692, 812832668},
{686331837, 758771584, 485081276, 510183332, 730280308, 184674456, 873283293, 908734440, 930495524, 921797799, 212061161, 804809207, 51215048, 121939666, 630812700, 361452271, 26060826, 260673621, 368617358, 224024063, 925630581, 990272358, 706900318},
{349105660, 25145415, 494217168, 424339281, 884124084, 178064091, 100120309, 586769841, 537648583, 716807985, 873050578, 284978094, 16767349, 478326338, 360734130, 365771597, 696838864, 978081529, 737982499, 875617822, 24227796, 132241837, 339570145, 546020311},
{511821710, 985509751, 578878282, 683372471, 984664469, 445595417, 511225116, 297223834, 226459528, 50743021, 379480638, 49592809, 80759195, 105089674, 771654463, 22227793, 380679886, 708398028, 50944040, 764421492, 498261079, 315274861, 591041992, 688069697, 173093227},
{322050759, 980010103, 195981374, 266943379, 862920298, 642981702, 565788131, 461650931, 496112002, 294720715, 83658304, 655891864, 436544737, 505904269, 704369108, 690578043, 984206794, 499813591, 893187636, 280796490, 263963693, 225773893, 329099972, 884281955, 830106734, 759867260},
{217770278, 196781219, 890030133, 37157328, 506726851, 398596965, 659090154, 164461980, 171196138, 432900123, 414177648, 969005208, 772702391, 49944042, 455929710, 137419373, 943545017, 914493864, 182760987, 365740932, 575380536, 268772977, 476434619, 384262114, 433073632, 612700665, 200033042},
{867243987, 419317505, 924705238, 470690638, 785733630, 636069944, 47184988, 429517972, 327113655, 171088007, 730658644, 759695884, 877945767, 126877050, 375168331, 29949383, 354344303, 715402345, 643780779, 235404899, 96456467, 947306130, 165323631, 839427048, 757122949, 315330535, 577080497, 40680577},
{742004924, 254372018, 291387829, 267349513, 54024762, 671245107, 613585423, 508809588, 231811039, 104767602, 167910887, 114090978, 909920550, 592620873, 356390422, 542638360, 87578277, 455438768, 894088070, 835976016, 969566965, 323042316, 212287755, 517833930, 442679595, 261582652, 823187406, 532793112, 159122123},
{733922348, 167366410, 876753742, 975422598, 799075476, 725829008, 872365212, 85018489, 340486853, 193566452, 599261528, 908283866, 800187671, 74553339, 199864122, 531353232, 700507329, 796422638, 830761055, 904523627, 962290437, 384793789, 30417305, 755042000, 79331844, 560314134, 348742603, 131981681, 16038223, 665114805},
{549790477, 671810211, 129382453, 966885251, 350592706, 596447982, 138443086, 691404995, 414285379, 196630498, 881923189, 163813881, 256102447, 71583160, 508771819, 681877733, 69375609, 207682964, 724982026, 837267786, 668534167, 138984993, 187812264, 924844266, 260256369, 841319659, 600930379, 54790790, 377702315, 626113287, 272358185},
{459478873, 948673060, 879976129, 77561086, 165638941, 509558379, 837667237, 103572912, 894613159, 206725937, 182772554, 998752430, 47107053, 551788393, 894748127, 994170493, 465274175, 508504228, 270177642, 700062682, 628387180, 156798153, 73871430, 830714579, 260430563, 237342573, 723016796, 489063843, 736112179, 110309822, 473238523, 365885605},
{461905191, 192165619, 747770106, 332106409, 398047884, 542104469, 197965617, 370342165, 11068589, 679254174, 758866370, 857614267, 645140882, 582386803, 555714996, 329617223, 461427609, 814724809, 139913691, 279486796, 254687615, 584423075, 179009767, 310504013, 840539020, 479836189, 75959175, 376095868, 716191358, 285404140, 70446126, 201071854, 744733441},
{310559811, 692706359, 114952121, 589789, 197188321, 269080294, 498208881, 629662567, 792354713, 176304605, 906976244, 468957371, 531603707, 897184676, 634643342, 637325685, 847138825, 474895813, 788073860, 313965361, 648791064, 944711077, 865937497, 622472778, 554274047, 626418740, 890567626, 794263440, 514221087, 940409196, 568590746, 975780789, 625062413, 692873095},
{720063004, 514071464, 720590190, 562298898, 707467805, 921118994, 71916204, 326117125, 12744339, 104010564, 446163721, 80786738, 594937065, 670679635, 989080689, 743456611, 91741554, 850963073, 209030382, 204167494, 514300043, 535977901, 567903595, 891459400, 1565124, 678215773, 565094050, 874198356, 542097582, 397868812, 971072020, 684763494, 952651896, 792935414, 463056339},
{363951854, 533712601, 613612726, 684833825, 885522596, 994755404, 453084167, 5686560, 592060426, 85188289, 163163883, 674500816, 814709411, 789909019, 747209202, 824975930, 473236787, 251853539, 248980472, 95331397, 320829588, 356098043, 499982795, 101569832, 562105659, 298126246, 59540251, 253450577, 570972450, 124186958, 108579178, 388935692, 360714078, 70717936, 995618862, 828412002},
{451501514, 455863211, 667442151, 284857856, 806818775, 62989212, 127942382, 918256345, 689813991, 817037279, 437212397, 820083716, 300971768, 334012433, 359525351, 414736829, 395405546, 291553822, 251302231, 81336112, 449119645, 251626769, 304104924, 522072698, 990312351, 425178419, 853656164, 166017455, 548825829, 503846746, 382171396, 902545004, 383608736, 961132395, 412843390, 201489221, 817756178},
{403145314, 302594789, 119692152, 801838972, 309188256, 640374867, 930604812, 463548456, 859729712, 616220450, 846353372, 790484235, 770481033, 897914912, 418395599, 934106855, 957114976, 213017240, 878174936, 526015728, 285827022, 851307532, 45488497, 506764881, 657262624, 482384244, 624191146, 41042634, 930861500, 523282256, 862176302, 591206152, 445143145, 98232994, 337753801, 580039286, 394539625, 366396447},
{445742553, 920930190, 618467072, 830108606, 410129292, 103013150, 526699502, 662467377, 289154902, 783869201, 833704838, 234742715, 121466416, 978991222, 675108227, 82848558, 396027899, 704774559, 233265149, 548109093, 761809919, 482936390, 702193112, 938839019, 52955263, 568236345, 660308411, 58801676, 358901394, 851410000, 924676245, 895214879, 7409527, 795655953, 362762125, 193892235, 408309456, 631325110, 683685664},
{841534010, 556349152, 636110463, 104393421, 316124540, 555447825, 808092758, 695139212, 32056979, 391521851, 915375601, 764002301, 453079523, 698106226, 292515850, 985598119, 335638237, 554668887, 459958304, 519173438, 345239465, 145649238, 742075755, 492752594, 475707840, 615454592, 892620658, 367245832, 392562692, 915668045, 572448455, 433406225, 758826887, 29418592, 885677275, 265999684, 23245001, 158111789, 83834338, 681586780},
{514851479, 790445500, 580811065, 226784910, 395103645, 70630538, 126702244, 988666831, 297547678, 755002235, 429217769, 337085154, 781063342, 975089165, 56075509, 201434726, 422033180, 342049785, 388335656, 433478739, 126972685, 984076482, 364134870, 216052286, 341802953, 462011635, 396243269, 523154481, 450523207, 199666167, 630116440, 369410996, 349080051, 866483443, 707394221, 225181557, 660624393, 828140730, 435450553, 864043371, 840750853},
{574794279, 780298930, 717498605, 457416440, 999243964, 81444157, 824289854, 340261948, 861008986, 289969281, 35405344, 915472694, 727987225, 505049953, 674922372, 589155591, 796938240, 849815851, 701763196, 814508375, 659421166, 330936448, 247521497, 772281187, 30213422, 682804165, 779868190, 269685870, 361955653, 110185220, 65747688, 890550949, 284167942, 302471994, 736103035, 810853021, 316189417, 666665569, 858354115, 172541785, 766342407, 683889724},
{342742191, 801813240, 451837162, 964284972, 666065915, 248317835, 35476411, 934310259, 789581466, 287955184, 661427574, 924788023, 756605552, 351632653, 50196887, 104853216, 627727442, 979789795, 270911774, 871335913, 647733415, 377034208, 148700028, 534632457, 788327101, 989648678, 898176729, 226474996, 960591003, 31201113, 708415457, 312120961, 417772228, 403066267, 876310201, 528791084, 201744011, 887306815, 225149667, 373766019, 626039819, 3425893, 216039853},
{918181383, 485535359, 303177672, 719707445, 591780285, 134245958, 218522202, 315813172, 700752839, 548272540, 437620754, 917968266, 979687501, 614976599, 959939269, 6631993, 20646513, 584270185, 815764999, 797243417, 554339252, 586373964, 593288105, 704544473, 563849774, 389637723, 36809926, 556999167, 715830709, 176283904, 85285627, 973763671, 42299689, 894144161, 331356191, 279329764, 807180946, 227890939, 581038881, 253992517, 912855384, 908072663, 733728244, 954226396},
{729556520, 649630450, 909829173, 156554452, 823452341, 129416469, 698721976, 540353255, 355902305, 332778653, 804768637, 146406952, 10106877, 835278272, 551614260, 601523379, 941589971, 943425007, 96461206, 969131497, 694931015, 305092242, 432193773, 449095750, 180776628, 923500261, 873161043, 57375992, 255281551, 174975664, 635375937, 426676640, 314553745, 994609240, 187767806, 65499253, 527395169, 655802119, 964339998, 873570362, 236228239, 607173609, 992410823, 254974603, 858087702},
{244812915, 938931203, 681133687, 901223827, 608571348, 787184552, 717686918, 377000300, 186799300, 681525108, 740598635, 37048369, 492943490, 334366799, 199143729, 474993845, 658001089, 556180984, 542902187, 452759254, 714035318, 498885606, 236848543, 435787456, 852612916, 857227247, 35555045, 698630692, 614405567, 221973246, 57495261, 545637525, 207436728, 940697619, 980600009, 236658538, 942457345, 473300474, 736140300, 910731313, 663507692, 611666819, 716777013, 231711677, 941017541, 540284076},
{480432768, 545206003, 274489230, 888008154, 40016066, 286928972, 238248176, 895449176, 412768093, 792910405, 874666753, 965359532, 967728067, 24886601, 940823039, 236054152, 500750413, 25397091, 461999638, 434555123, 287413486, 98386808, 623604775, 18033343, 846491635, 912669600, 787437173, 975508943, 426723587, 759444260, 796695213, 160749914, 11907755, 73188549, 567676337, 30884957, 499921643, 134258019, 631738486, 882693811, 778206365, 299760079, 594217913, 978568397, 440410986, 534649902, 514254014},
{847128810, 212389525, 701125998, 878805956, 115467622, 74755813, 100644985, 530421200, 182735886, 614925233, 67333991, 799685484, 567460175, 615115005, 139139456, 620109355, 403304959, 330113757, 626045136, 733425560, 50269669, 336179821, 647216785, 669852199, 334540102, 745975904, 714496935, 513825878, 626746162, 520059267, 521330495, 854923299, 222036870, 183204082, 543557199, 94720918, 960388135, 106094531, 746463768, 958544561, 282013067, 784592361, 461090063, 389098502, 617861627, 525489702, 703863826, 647209774},
{404411734, 728831000, 895960345, 171639292, 4098612, 164413669, 43613252, 641923519, 440294586, 620902939, 310001661, 201402176, 603515327, 906750839, 585087174, 246651304, 274236792, 388068862, 769008901, 113416358, 442080910, 941669620, 609332642, 774190365, 949899374, 546017909, 458137232, 883253904, 658406874, 805180048, 890491819, 63398634, 807608514, 222659727, 394529753, 255999445, 807370194, 942520995, 899082442, 584860525, 919337909, 152026270, 340145783, 919995375, 101170347, 670726107, 786221920, 663152489, 900185117},
{530951103, 320231646, 171461192, 366194650, 539280267, 504756026, 75657390, 807857553, 204518178, 130503978, 116515680, 747413429, 80971414, 384948985, 611517293, 200525391, 294768673, 1189058, 949466871, 907630916, 167410801, 272715777, 171390713, 224092672, 212315849, 509317518, 108431119, 829257018, 86840730, 678768073, 874259830, 502172134, 688129860, 214134655, 506914172, 171381415, 599297269, 566555238, 5146156, 711710883, 238462641, 478929291, 813577858, 290416284, 513228366, 357361210, 403220045, 263206858, 745787657, 348985796},
{953833279, 146403010, 968776570, 455031343, 220517136, 140249895, 346732359, 332889981, 89935741, 873633645, 15800166, 347202277, 914786180, 528825537, 966225620, 514843928, 780718526, 641940303, 395603325, 845486768, 429952850, 552487795, 221814204, 770616412, 178550683, 12780771, 262877139, 541795941, 259616376, 255569226, 6289163, 211253547, 255820472, 721689992, 378527996, 873568389, 548799467, 795754141, 170736523, 731303770, 703417691, 265584637, 843712157, 277961548, 633548726, 345496464, 274305959, 359680267, 317178762, 222355131, 609459762},
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{547851185, 770441641, 275870840, 525902814, 636078442, 789597827, 907397451, 823685641, 215792168, 362250943, 218589388, 750994190, 133561221, 927020335, 4813109, 951926403, 908556818, 168827029, 598783649, 32113990, 959735642, 773128448, 676194190, 135815973, 493803418, 505109528, 976760223, 223589907, 761669512, 559129228, 83700659, 907083508, 719458021, 304845221, 48668041, 523011959, 90699905, 527159135, 998606992, 996172513, 404523805, 139310018, 111259600, 761670572, 164355617, 906261838, 351221445, 311694888, 915843992, 852491527, 935991763, 296706692, 756600466},
{40192184, 377470164, 887789046, 207633902, 578113363, 910247976, 698410198, 262394399, 628599584, 772563211, 444995351, 671122724, 224063543, 96493319, 455305313, 403589973, 736773000, 660928961, 906997999, 942116239, 318896816, 644957472, 860494889, 797082447, 116597898, 722565332, 911067719, 892632157, 112564449, 326809748, 154128889, 604000554, 730199518, 957953788, 851516898, 668743340, 754546423, 58189080, 623619074, 382209352, 356189162, 387999517, 948187716, 274900110, 211945210, 792742775, 496428969, 604897775, 686331624, 214795137, 468832620, 907831347, 116487128, 654591160},
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#endif
};
// clang-format on

constexpr int binpow(int a, int b, int mod = ::mod) {
    int res = 1;
    a %= mod;

    while (b) {
        if (b & 1) res = static_cast<long long>(res) * a % mod;
        a = static_cast<long long>(a) * a % mod;
        b >>= 1;
    }

    return res;
}

namespace gen {
    const int n = 100;

    int c[N][N];
    int g[N], h[N][N];

    void main() {
        // === Init ===

        for (int i = 0; i <= n; i++) {
            c[i][0] = 1;

            for (int j = 1; j <= i; j++) {
                c[i][j] = (static_cast<long long>(c[i - 1][j]) + c[i - 1][j - 1]) % mod;
            }
        }

        // === calc g[] ===

        g[0] = 1;

        for (int i = 1; i <= n; i++) {
            g[i] = binpow(2, c[i][2]);

            for (int j = 1; j < i; j++) {
                g[i] = ((static_cast<long long>(g[i]) - static_cast<long long>(g[j]) * binpow(2, c[i - j][2]) % mod * c[i - 1][j - 1] % mod) % mod + mod) % mod;
            }
        }

        // === calc h[][] ===

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                h[i][j] = static_cast<long long>(g[j]) * binpow(binpow(2, j) - 1, i) % mod * binpow(2, c[i][2]) % mod;
            }
        }

        // === calc f[][] ===

        f[0][0] = 1;

        for (int i = 1; i <= n; i++) {
            f[i][0] = binpow(2, c[i][2]);

            for (int j = 1; j <= i; j++) {
                for (int k = 1; k <= j; k++) {
                    f[i][j] = (static_cast<long long>(f[i][j]) + static_cast<long long>(f[i - k][j - k]) * c[j - 1][k - 1] % mod) % mod;
                }

                for (int k = 1; k <= j; k++) {
                    for (int l = 1; l <= i - j; l++) {
                        f[i][j] = (static_cast<long long>(f[i][j]) + static_cast<long long>(f[i - k - l][j - k]) * c[j - 1][k - 1] % mod * c[i - j][l] % mod * h[k][l] % mod) % mod;
                    }
                }
            }
        }
    }

    __attribute__((noreturn)) void print() {
        for (int i = 0; i <= n; i++) {
            cout << "{";

            for (int j = 0; j < i; j++) {
                cout << f[i][j] << ", ";
            }

            cout << f[i][i] << "}," << endl;
        }

        exit(EXIT_SUCCESS);
    }
}  // namespace gen

int main() {
    std::ios::sync_with_stdio(false);
    cin.tie(nullptr);

    // === Generator ===

#ifndef ONLINE_JUDGE
    gen::main();
    gen::print();
#endif

    // === Answer ===

    int t;

    cin >> t;

    while (t--) {
        int n, m;

        cin >> n >> m;

        cout << f[n][m] << endl;
    }

    return 0;
}