Statistics

Problem Statement for "TreeMovingDiv2"

Problem Statement

You are given m trees. The trees are labeled T(0) through T(m-1). Each tree contains n vertices labeled 0 through n-1. A cyclic rotation of edges is the following procedure:
  1. In each tree you choose one of its edges. Let e(i) be the edge chosen in the tree T(i).
  2. You remove the chosen edge from the tree, producing a graph with n vertices and only n-2 edges.
  3. For each valid i, you add the edge e(i) to the tree T(i+1). Also, you add the edge e(m-1) to the tree T(0). For example, if e(0) was an edge that connected vertices 4 and 7 in T(0), the graph T(1) will now get a new edge that connects its vertices 4 and 7.
  4. The procedure was successful if and only if each T(i) is a tree again.
Count all possible ways in which we can successfully perform a cyclic rotation of edges. Return that count modulo (10^9 + 7). You are given the int n. You are also given the int[]s roots, a, b, and c, each with m elements. These are inputs to a pseudorandom generator that will produce the trees. In order to generate the tree T(i), we will first generate a temporary sequence X: 
X[0] = c[i]
for k = 1 to n-2:
    X[k] = (a[i] * X[k - 1] + b[i]) modulo 1,000,000,007
and then we use that sequence to generate the edges of the tree: 
for j = 0 to n-2:
    u[j] = (roots[i] + j + 1) modulo n
    v[j] = (roots[i] + (X[j] modulo (j + 1))) modulo n
    add the edge between u[j] and v[j] to the tree T(i)

Definition

Class:
TreeMovingDiv2
Method:
count
Parameters:
int, int[], int[], int[], int[]
Returns:
int
Method signature:
int count(int n, int[] roots, int[] a, int[] b, int[] c)
(be sure your method is public)

Notes

  • The author's solution does not depend on any properties of the pseudorandom generator. It would solve any input of the allowed size within the given limits.

Constraints

  • n will be between 2 and 50, inclusive.
  • roots will contain between 2 and 50 elements, inclusive.
  • a and roots will contain the same number of elements.
  • b and roots will contain the same number of elements.
  • c and roots will contain the same number of elements.
  • Each element of roots will be between 0 and n - 1, inclusive.
  • Each element of a will be between 1 and 1,000,000,006, inclusive.
  • Each element of b will be between 0 and 1,000,000,006, inclusive.
  • Each element of c will be between 0 and 1,000,000,006, inclusive.

Examples

  1. 3

    {0, 2}

    {1, 2}

    {1, 0}

    {3, 5}

    Returns: 2

    There are two trees, each of them contains 3 vertices. The tree T(0) is generated as follows: X[0] = c[0] = 3 X[1] = (a[0] * X[0] + b[0]) modulo 1,000,000,007 = 4 u[0] = (roots[0] + 1) modulo n = 1 v[0] = (roots[0] + (X[0] modulo 1)) modulo n = 0 u[1] = (roots[0] + 2) modulo n = 2 v[1] = (roots[0] + (X[1] modulo 2)) modulo n = 0 Hence, the tree T(0) contains the edges 1-0 and 2-0. The tree T(1) contains the edges 0-2 and 1-2. There are two ways to do a successful cyclic rotation of edges: we can either choose the edge 0-2 in each tree, or we can choose the edge 0-1 in T(0) and the edge 1-2 in T(1).

  2. 3

    {0, 0, 1}

    {6, 1, 3}

    {6, 5, 5}

    {2, 5, 9}

    Returns: 2

    T(0) contains edges 1-0 and 2-0. T(1) contains edges 1-0 and 2-0. T(2) contains edges 2-1 and 0-1.

  3. 5

    {0, 1, 1, 1, 2}

    {7, 4, 7, 9, 2}

    {8, 3, 9, 5, 3}

    {6, 0, 1, 5, 9}

    Returns: 22

  4. 2

    {1, 0, 0}

    {122064284, 9662111, 120616497}

    {20137061, 408976122, 494878172}

    {242061783, 603049107, 805670429}

    Returns: 1

    Watch out for integer overflow when generating the temporary sequence X.

  5. 10

    {0, 1, 0, 4, 0, 2, 1, 8, 5, 5}

    {508821715, 481198414, 163209181, 56649169, 276327522, 13486359, 845629232, 482370937, 373100199, 297431939}

    {256979012, 884002808, 393825387, 609998779, 816536931, 123064634, 673095376, 18224901, 510687925, 466437174}

    {368733721, 596826005, 853637399, 436680590, 369153650, 853574577, 609377415, 903050702, 259325966, 105275092}

    Returns: 17765

  6. 2

    {1, 0, 0}

    {122064284, 9662111, 120616497}

    {20137061, 408976122, 494878172}

    {242061783, 603049107, 805670429}

    Returns: 1

  7. 3

    {0, 0, 1}

    {373206610, 937739946, 172315864}

    {870770575, 635025870, 765158489}

    {915938656, 747443899, 387215442}

    Returns: 2

  8. 2

    {1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0}

    {738597751, 196389825, 80842696, 566712262, 143001477, 553078467, 282407074, 181043763, 658220131, 331583655, 991836664, 464907072, 313767267, 996813840, 959717858, 135553865, 126055597, 426863114, 187764456, 750495445, 142104461, 427111521, 703748525, 442084515, 751924666, 585377714, 68106084, 630473341, 722056891, 729645821, 110996767, 475517731, 889384810, 13698574, 332242858, 766196983, 553609135, 535476714, 267096001, 477412916, 512781442, 298796425, 940910608, 200887455, 780283978, 666767987, 319985852, 93975602, 864200934, 648117425}

    {603728676, 349759805, 462160334, 955358162, 415196208, 216618046, 36532219, 661718203, 628013663, 749259798, 831644625, 16078161, 79988409, 665390721, 710233679, 975450517, 260088448, 416388040, 688424524, 155584701, 688098259, 83226551, 123144610, 718007698, 341760710, 888994051, 997687389, 184625334, 887187640, 69335235, 540326640, 397048921, 745787697, 745790087, 52384191, 586660809, 647210226, 847649836, 674463852, 455816851, 500495730, 193067383, 120556443, 316402794, 663699895, 17113689, 289335594, 836566418, 56887897, 794151916}

    {195252894, 818702242, 507806502, 857876974, 630271747, 837983183, 173650496, 327044535, 513605100, 397430160, 578722555, 55251785, 272669579, 227581934, 488356968, 263019166, 32290174, 984348944, 821345813, 43550293, 749194118, 343803576, 781554885, 445335078, 879238813, 411503108, 297684663, 6754639, 783889995, 21521207, 666555110, 623372081, 145745331, 380625618, 616575890, 97421426, 723153493, 211812824, 661545405, 483432996, 27073730, 886308467, 246748062, 943778390, 432901505, 695186619, 32815658, 173950730, 60008654, 112512549}

    Returns: 1

  9. 50

    {1, 16}

    {294203649, 991997771}

    {947515001, 375811636}

    {56946626, 541338142}

    Returns: 61

  10. 20

    {9, 6, 9, 3, 8, 12, 11, 14, 1, 12, 5, 14, 19, 8, 1, 12, 15, 19, 14, 10}

    {306138313, 655317917, 257154092, 111731490, 702883715, 680021671, 97574306, 61628475, 735540955, 706561245, 79523164, 213341045, 476409021, 955623268, 180401172, 416699486, 968612697, 446573908, 564266775, 780013144}

    {770454918, 83533379, 741163848, 269373563, 666465245, 58543277, 11897281, 650608562, 206647555, 799146904, 838246930, 788571962, 101123151, 331197155, 598130935, 6712310, 842102144, 805266519, 452397949, 851031241}

    {146363219, 447877802, 319362635, 891077845, 793812278, 170912281, 7210147, 489743213, 80900234, 222801774, 529791655, 130251952, 615725919, 818019236, 419355177, 362557198, 341695159, 607946751, 717480312, 629958452}

    Returns: 836124395

  11. 10

    {7, 2, 3, 1, 1, 5, 4, 9, 8, 4, 0, 7, 4, 0, 5, 9, 1, 8, 8, 9, 0, 5, 7, 9, 7, 4, 6, 6, 3, 4, 4, 2, 4, 4, 7, 7, 6, 0, 9, 8, 6, 0, 3, 2, 2, 9, 1, 7, 8, 9}

    {393429754, 846922059, 175493561, 966743372, 345706685, 354197419, 306000254, 906503937, 97927548, 137541805, 629188079, 623576448, 179308858, 624528165, 802701783, 287092344, 124331450, 475651754, 279911221, 159551504, 390198326, 867226813, 373870640, 205734484, 994066533, 595054489, 227550337, 398220383, 740178148, 161648739, 264245408, 699391520, 488049103, 647232905, 258391149, 947747501, 710512783, 4765045, 335075381, 333442582, 320246465, 433701298, 337268449, 268866196, 286052277, 934401121, 526473545, 595757738, 848471925, 958485510}

    {634568948, 304326499, 154963013, 57036444, 825041151, 394838698, 116235376, 36095371, 877574864, 359497381, 345996692, 364194156, 914064043, 589972551, 162053972, 533943496, 951789929, 615282205, 737456110, 18467135, 976664995, 182559510, 780422690, 490734514, 993513994, 112430433, 56583486, 816258129, 92253490, 39882165, 212509941, 237720425, 260912120, 336749778, 135690349, 738498112, 524948965, 52293121, 90884805, 406861045, 772185725, 488931771, 17015759, 994249682, 333330190, 270906521, 290289971, 876702007, 492753405, 242411542}

    {273940321, 756783301, 962991260, 516059927, 526529735, 552388819, 872666560, 523122290, 301424835, 854600150, 725320763, 949156803, 375561504, 493095417, 692658739, 73886686, 21955958, 452697497, 951160470, 904056384, 113585128, 714884422, 977360720, 835144809, 399203306, 393545054, 305477477, 328126117, 966104984, 813506387, 819938348, 427587784, 832824690, 132730158, 999535516, 371052738, 410306645, 742593128, 812314440, 426215272, 143338736, 717035061, 704007571, 483151955, 303786401, 760255574, 642483017, 690044445, 726555298, 514164560}

    Returns: 530828860

  12. 15

    {11, 3, 13, 5, 0, 3, 0, 8, 9, 4, 9, 7, 5, 12, 12, 11, 12, 2, 6, 5, 13, 13, 11, 8, 14, 9, 2, 0, 3, 11, 10, 12, 10, 11, 11, 12, 13, 7, 12, 11, 2, 14, 8, 3, 6, 6, 4, 13, 5, 8}

    {983816220, 620877501, 728957664, 719453482, 891241034, 959047323, 459235325, 188837384, 749336264, 40650017, 404049008, 121578182, 640967952, 444329307, 181115164, 697849277, 12923013, 711014676, 308063158, 403714366, 341206103, 674610097, 743172147, 27978413, 95548595, 93823839, 844476902, 863583697, 568069127, 618319911, 659846531, 341309147, 735202433, 531047579, 967335611, 311192666, 753647731, 36420180, 609571991, 208600401, 915548304, 926479460, 672275772, 545217041, 864561330, 32472050, 852336473, 144521601, 383750815, 616511468}

    {715457951, 308091233, 686233659, 523365634, 260145657, 96581518, 754153775, 622990522, 78662953, 689973864, 609423534, 534351235, 56822117, 899080526, 236413795, 747521954, 249656307, 790813221, 238598034, 203856426, 170015231, 791645278, 991710627, 747864180, 331241135, 416320805, 820623220, 811261319, 154661650, 914880513, 270905767, 954448019, 261442212, 954262444, 293791600, 493225233, 67542211, 911866345, 567575019, 95716070, 410883122, 337767450, 375732581, 616839717, 416849487, 140196829, 200763187, 51759408, 992789421, 882490836}

    {650915191, 363659051, 226659197, 706291662, 748630395, 163284394, 663006670, 2890697, 639793395, 728890798, 570088430, 967259303, 101778889, 249725396, 968816738, 276471315, 905010209, 467925249, 798793109, 857289233, 494026470, 476417587, 98570430, 596160845, 211373787, 188742439, 364805067, 757845257, 317224756, 74104796, 455729968, 78933290, 769895010, 476555278, 45379277, 957039727, 395817921, 447349376, 629724490, 287334171, 227424105, 603337884, 467060652, 254067677, 237332026, 976429932, 93075762, 960441433, 132935737, 671265490}

    Returns: 755767349

    Watch out for integer overflow while calculating the answer.

  13. 20

    {2, 12, 16, 6, 7, 1, 4, 6, 11, 2, 15, 15, 19, 12, 13, 17, 17, 16, 14, 12, 11, 16, 14, 16, 15, 14, 9, 9, 7, 9, 15, 7, 10, 16, 4, 2, 7, 17, 16, 2, 16, 19, 4, 4, 16, 10, 10, 10, 3, 18}

    {79382666, 363140789, 728672069, 125315915, 835931865, 509296781, 509322436, 824834065, 43705383, 744054172, 930167280, 323163095, 561891015, 365973211, 325129022, 252293568, 332496525, 629705005, 972927701, 623386952, 48671224, 857906315, 764887944, 607269102, 142704853, 560072172, 380239293, 280649868, 169226975, 222225771, 479697937, 93625694, 251570889, 376201438, 331151105, 517407951, 683775081, 232535064, 305412396, 843121018, 807477446, 860080254, 495922041, 81410959, 651596570, 81531319, 642393707, 137588725, 9559902, 943241690}

    {744200635, 3190149, 944256804, 133426364, 964964230, 719304194, 461063737, 620941780, 361970476, 778388793, 850258184, 478963971, 495126146, 282980969, 515349798, 529380050, 707221673, 436076794, 40448198, 247150648, 111054422, 427663459, 659051643, 801544923, 901138829, 715184704, 508638476, 537926503, 815089594, 86393491, 337826551, 668247808, 218354370, 434128251, 439762950, 249044437, 112218377, 328657405, 176940330, 785793922, 102862488, 662423156, 30268648, 381537805, 68029725, 612984428, 871993430, 680351382, 204721401, 330006708}

    {972751809, 257450223, 226068662, 509110262, 527706974, 872229969, 161607371, 984520276, 685267390, 768418469, 827646937, 710530737, 800598016, 9531705, 135086846, 207213023, 349960292, 328369168, 106280972, 172784672, 123695566, 391916563, 6598626, 786785256, 534931114, 442337719, 366381641, 957813623, 990560097, 656949805, 499573072, 79616764, 558550734, 481812752, 384034326, 904756146, 992496697, 232488670, 950740122, 37190955, 508356648, 66843743, 37219615, 117929960, 991534005, 853158672, 960357994, 4519417, 844105340, 993363115}

    Returns: 348296097

  14. 25

    {21, 7, 23, 3, 11, 13, 17, 15, 15, 0, 0, 24, 24, 5, 16, 7, 9, 5, 17, 22, 1, 18, 7, 0, 2, 4, 16, 3, 12, 15, 17, 18, 6, 8, 9, 22, 19, 20, 5, 21, 2, 19, 20, 15, 20, 7, 4, 1, 4, 17}

    {669769131, 842128965, 767592250, 288091487, 866922292, 114146680, 662557507, 812200246, 695114099, 161706301, 705028208, 526197563, 98940725, 480741624, 293476947, 958017774, 411576899, 865067927, 1079632, 353005892, 999679007, 855778411, 134189446, 649089681, 834121465, 58841523, 702198586, 555524371, 702150688, 459320294, 580331788, 545054515, 498724218, 40439462, 335062832, 585885851, 726910029, 264190199, 684387466, 13246103, 402779279, 352858410, 830929364, 357761804, 715561701, 179602254, 482800550, 581874133, 544838798, 896234920}

    {825089639, 711987622, 766699447, 894722822, 400068736, 126079746, 509047600, 502804193, 271886568, 698799804, 109889754, 940293053, 342916960, 300916941, 593504885, 742958508, 296260054, 906575078, 127729395, 723711942, 304404665, 327921224, 870339580, 468740053, 238865970, 19075070, 567645471, 651823159, 291358482, 961391839, 105050373, 388770660, 927712465, 756673650, 892831468, 294943563, 949778899, 893263361, 944802549, 474648947, 745355157, 511258835, 94018203, 299095108, 155344286, 187307468, 77433907, 855408789, 999724684, 970086003}

    {935865944, 159293241, 489736606, 994309264, 458635630, 483125544, 951947489, 755460687, 23635942, 347741848, 377447336, 433665969, 645708868, 762366427, 411244845, 823658387, 819153808, 343596919, 953913617, 126017521, 209169641, 153449728, 832841081, 256629288, 347101596, 942567843, 134537227, 973672028, 46712601, 327613685, 135364692, 435995010, 790588322, 825637872, 724845362, 494538391, 391868701, 937244925, 59322169, 603342593, 293679485, 248113834, 800272703, 888845688, 925079630, 778161026, 119778735, 274916405, 955518519, 150464038}

    Returns: 704318263

  15. 30

    {17, 5, 27, 23, 5, 10, 1, 16, 28, 22, 22, 18, 18, 27, 6, 4, 10, 7, 9, 22, 20, 16, 4, 26, 24, 16, 22, 27, 24, 3, 27, 0, 11, 15, 7, 10, 21, 6, 14, 7, 6, 24, 21, 21, 0, 8, 8, 28, 14, 27}

    {355270121, 879359526, 767306655, 988921198, 811613122, 959363415, 712644617, 38131459, 474939302, 160077721, 231146475, 727782476, 724896522, 621962178, 437490804, 27005981, 731150412, 78725522, 76009631, 867645749, 707144128, 39074623, 155905243, 228380364, 395821639, 39633772, 237960977, 677623276, 303308536, 282802804, 695150466, 2403791, 15092675, 885593327, 479301682, 792101136, 657037378, 460305083, 865683955, 162310636, 589675692, 476948016, 654575632, 674379077, 92531479, 228661523, 272857785, 574941257, 170647885, 633030597}

    {853832323, 698258541, 24722585, 209816283, 518748037, 338736951, 219752827, 500755451, 965259562, 787214733, 645691672, 589938521, 490048985, 684817390, 868645624, 819783872, 167686148, 551838651, 929579566, 472038897, 540411124, 672767407, 537680596, 522420795, 808763663, 317938969, 956898202, 964627615, 951786426, 841732821, 171971157, 512635920, 179591883, 236539457, 38802811, 50762767, 289422326, 723915156, 554167860, 455898797, 847399994, 835914541, 43521538, 768825936, 511557263, 660095067, 39836147, 73935285, 211656665, 417601875}

    {962735293, 466945147, 197974068, 92095125, 528884213, 188275848, 741720193, 327024789, 777937940, 801130254, 929973111, 468109407, 639495256, 522172736, 581310223, 459432826, 264103891, 207836102, 265196744, 736480235, 838838744, 655087976, 32041274, 152286431, 961830927, 491130384, 136113801, 173640386, 720047942, 500393223, 470379799, 850539219, 579244046, 830895347, 63500405, 442254810, 988547477, 308523485, 384133065, 62027372, 283440024, 6586961, 370431666, 43879969, 679281602, 651094502, 692093699, 27822392, 256622644, 763733667}

    Returns: 126680391

  16. 35

    {6, 4, 25, 16, 15, 16, 14, 29, 7, 27, 10, 31, 30, 24, 24, 30, 5, 10, 2, 8, 2, 8, 7, 31, 5, 21, 21, 6, 1, 23, 4, 10, 24, 11, 32, 11, 11, 12, 4, 33, 13, 9, 1, 12, 18, 6, 1, 3, 26, 16}

    {650689315, 653314968, 320770753, 446664036, 357147465, 269246042, 865879689, 25497641, 831380746, 63185934, 6007403, 635849672, 481522882, 31697858, 815904191, 732730187, 105198052, 314088444, 694096112, 302297418, 953119177, 846457912, 10662828, 345591565, 982759791, 538403128, 369431459, 142986585, 131199516, 224930055, 90751583, 453832612, 747702088, 769408001, 188246138, 155546301, 700172327, 491960218, 654724480, 37468455, 184977526, 484270094, 989582955, 950729922, 376073260, 326732459, 598720712, 609161204, 894047, 366447177}

    {643549322, 702023276, 847165235, 679940737, 953852550, 745512510, 562703958, 87650595, 875175654, 408863213, 909118514, 55062861, 337839799, 993925366, 651833443, 33362323, 756724537, 727369667, 16860756, 657428187, 438794099, 573025172, 40140531, 779550461, 560351539, 621829341, 724733193, 78524265, 719227318, 302870427, 230366983, 524330776, 593982710, 559084855, 196904061, 805489895, 245876307, 288521104, 322030071, 144753821, 781064659, 684750220, 107271092, 686383238, 890043828, 238213370, 245276630, 248992693, 711692680, 57681162}

    {925849428, 368788165, 461642011, 282326860, 459812869, 799171430, 237093036, 216858667, 116306493, 675420901, 188601506, 900072642, 70745373, 275007451, 148640219, 956984723, 147158135, 928096593, 817862121, 689713084, 219280079, 416621140, 858283730, 913302474, 777796672, 577499773, 904269394, 308392258, 71167715, 171057103, 106171419, 793056729, 516314366, 469687727, 109344173, 28241792, 92952214, 13279733, 492715118, 628179010, 68762861, 187857052, 133484747, 109762958, 321655223, 576096856, 146481708, 294424116, 73068554, 920834597}

    Returns: 983249294

  17. 40

    {11, 18, 23, 16, 32, 20, 39, 23, 29, 9, 36, 13, 13, 26, 0, 27, 6, 39, 24, 24, 32, 7, 15, 13, 36, 11, 26, 9, 10, 2, 20, 5, 17, 37, 35, 25, 10, 27, 15, 12, 12, 29, 1, 23, 16, 35, 17, 17, 29, 20}

    {41223033, 395578257, 395875779, 337982553, 301838296, 114462772, 401422877, 661494322, 611205949, 766590089, 237158403, 837434585, 107478674, 658374496, 254885315, 506751128, 424771564, 232778773, 769026111, 521970003, 851073109, 29754124, 327345897, 144458899, 839427236, 814162650, 905193855, 74596678, 437390098, 48412565, 910602995, 396637971, 778614467, 909529132, 552061637, 66794315, 630299676, 688075102, 350564886, 481500260, 76906667, 608359699, 223294680, 486923840, 753043045, 185302915, 683745218, 307261056, 331735868, 398210127}

    {672292006, 688294195, 400155641, 290001467, 363703848, 958169715, 269613920, 794429856, 863515909, 792245409, 149953156, 704708336, 484971824, 377825808, 926974183, 815220426, 214289895, 372633240, 818710927, 286861674, 383628555, 209043352, 416309549, 833231203, 130249225, 920693241, 408953185, 805189455, 379655255, 183211408, 297287767, 357024032, 845862136, 42745926, 342875411, 852481103, 876691745, 705312171, 931395390, 834831674, 473044025, 714438658, 761807166, 864942062, 250052062, 2172967, 211474134, 172551928, 927419931, 505197042}

    {661546773, 967612076, 461051477, 380112728, 238889448, 213149729, 30661005, 788422775, 866813227, 419981304, 737332017, 934516080, 769564500, 34813760, 23738330, 301587158, 592108225, 83507772, 420317253, 9003787, 553981915, 627087384, 57483923, 103926878, 392525996, 244955781, 905845968, 803327891, 39470317, 343836642, 150014523, 502568200, 304970090, 179977934, 739171226, 975958218, 984598257, 384558299, 813730751, 378035793, 349695404, 651362919, 998610985, 264797245, 367029199, 452825596, 423829404, 342297371, 79205418, 947964954}

    Returns: 212992149

  18. 50

    {24, 27, 4, 45, 6, 3, 10, 9, 18, 29, 35, 30, 32, 15, 27, 34, 32, 40, 6, 24, 9, 22, 11, 14, 49, 13, 45, 12, 13, 31, 22, 13, 45, 35, 10, 41, 11, 38, 45, 11, 2, 28, 38, 45, 30, 13, 14, 25, 21, 9}

    {22143217, 616829721, 434510366, 496555102, 277519553, 269562134, 604745059, 579824450, 42439861, 668069722, 243170332, 242053960, 490060831, 694786813, 72279826, 766919625, 823425451, 386832024, 462042585, 280772717, 804513279, 505889710, 718363201, 765570167, 283032828, 293724249, 762915539, 957026170, 646862281, 889412954, 831088252, 305416068, 247168981, 828986478, 214756131, 636454772, 603561974, 915845121, 615869172, 800689884, 783714298, 739771383, 381948272, 784924687, 118587332, 332433119, 799665380, 39580854, 492823851, 382966306}

    {486956425, 387157845, 189449425, 366391387, 503626927, 991463207, 323270278, 674243527, 761772257, 801071350, 654214648, 110650147, 66033927, 74629491, 575237270, 396796245, 674754378, 488395097, 416670283, 511749923, 223050721, 159180032, 999971241, 554107076, 37874060, 523447506, 861008175, 231890561, 807524091, 524690003, 422604377, 492584148, 512132381, 845157138, 941915279, 363027428, 463961157, 391741919, 308622913, 504936548, 512548792, 596758039, 775060056, 547197453, 984751604, 53078870, 84349590, 271168570, 934355195, 178931474}

    {651530258, 468278997, 724128886, 668130331, 240066687, 824162883, 610773827, 249820755, 959483778, 747660358, 544690923, 400922746, 608461739, 256282787, 761133711, 434913495, 506251824, 254146710, 989298496, 572699350, 564092353, 185226058, 496787306, 764395328, 823221073, 588715715, 966750132, 138048121, 768958169, 597345531, 120821251, 154597181, 325663401, 237888524, 123670037, 218489614, 980649038, 460593114, 247123694, 694044215, 124778780, 1171601, 745683764, 899575257, 763604799, 250761426, 450532376, 66837814, 196755461, 427163503}

    Returns: 551191769

  19. 50

    {18, 19, 18, 49, 5, 14, 10, 23, 26, 16, 37, 22, 24, 9, 7, 42, 46, 0, 10, 43, 17, 48, 35, 24, 5, 31, 4, 47, 4, 15, 43, 2, 12, 13, 47, 4, 24, 23, 20, 41, 45, 5, 44, 6, 21, 4, 10, 21, 48, 28}

    {412553189, 864320332, 621503818, 612057373, 794004050, 241342136, 383456625, 208246869, 279922549, 628606020, 799690063, 466961383, 845498464, 773639133, 662285559, 108051187, 531239436, 691601057, 389055088, 329483317, 890036798, 972503387, 896561104, 136890749, 318742751, 578327842, 605293939, 526816921, 347211499, 493673122, 113774488, 359415037, 380747482, 364882398, 863199012, 79500638, 423827695, 545697860, 231646868, 154893655, 524363749, 278152661, 509074337, 701612395, 487610031, 961212470, 181431051, 117500436, 286865841, 97032993}

    {143964997, 374497798, 240370374, 710826613, 729182508, 862645761, 192087495, 428394047, 574672622, 230351023, 693290908, 504945096, 986167467, 123335812, 88330441, 848286034, 439002156, 46078835, 280811142, 812791739, 614494917, 525012376, 683892032, 331496920, 205129404, 545105500, 518272907, 69177251, 118089368, 103896082, 276839939, 138428005, 988191647, 61680548, 402924717, 473199222, 787099808, 940669117, 893639912, 328444682, 755893575, 479954049, 74829118, 172136111, 350657816, 358254072, 580879562, 187293102, 791213523, 177670181}

    {85049446, 862765356, 178433872, 882402758, 901279809, 101179077, 255000587, 970538333, 45547466, 171810590, 961265369, 444311840, 558620233, 286384536, 626647821, 123634269, 765816242, 129753870, 912898413, 699894097, 329871563, 687713314, 578379893, 145084215, 810991864, 438225601, 226918770, 715612678, 61566519, 422976418, 290084500, 203856215, 480952039, 145792660, 295858945, 548085749, 112508387, 691899795, 252577652, 873061477, 780573712, 578909581, 207958450, 295270100, 165813857, 192180294, 513336393, 703709262, 873978200, 530456063}

    Returns: 212736166

  20. 50

    {46, 31, 27, 35, 28, 13, 17, 39, 17, 42, 30, 11, 38, 6, 48, 45, 31, 41, 33, 3, 14, 37, 35, 28, 14, 4, 18, 13, 14, 14, 37, 28, 10, 22, 38, 16, 33, 8, 46, 39, 35, 5, 38, 43, 10, 22, 14, 4, 28, 29}

    {368728244, 87365427, 673203184, 674768737, 26915390, 459403334, 29181761, 843817872, 633223931, 348110261, 125825040, 823431240, 297608571, 990775249, 360987872, 776443497, 693879626, 700575879, 815581169, 393394014, 88179862, 882928103, 421473343, 4248318, 918143476, 666446578, 231588033, 632843763, 836594174, 179189787, 971999026, 279857049, 677536469, 358847403, 440961718, 443463323, 447532809, 687217867, 442630861, 127801273, 87339444, 965323794, 166815242, 30954138, 450670159, 302507183, 129935771, 621435644, 967208365, 828638189}

    {703426507, 891719550, 805617960, 534421982, 793183770, 85766466, 5479530, 262241876, 296144280, 555439774, 405728780, 525115779, 556484680, 8936099, 961436813, 208988627, 74037684, 46729331, 924323237, 425331848, 617950205, 272126326, 66397109, 465695000, 307130541, 323111426, 732351466, 443640146, 245521696, 336371100, 207265063, 374463632, 460392794, 102410935, 269000673, 529177381, 154611906, 948557573, 503928647, 348228781, 637593773, 684176893, 463041285, 522709973, 979556799, 132112132, 140713614, 79779930, 432986323, 258887706}

    {467754315, 302127409, 349913421, 142709687, 511244230, 58572952, 634570146, 291029757, 324657247, 980365380, 898040353, 670951982, 562098110, 591671253, 446664659, 469942984, 437394355, 247750117, 646451127, 773312814, 523187686, 440019946, 637836597, 204597316, 539729304, 303815917, 181308940, 496523770, 696575719, 958627303, 840262469, 121930196, 868366106, 391538044, 387040793, 686784682, 334148390, 916382246, 531769412, 927298351, 680162932, 463480037, 785106816, 24915497, 872027999, 518187314, 743702438, 873498408, 118521418, 349681128}

    Returns: 227689151

  21. 50

    {20, 35, 41, 29, 42, 3, 24, 6, 4, 26, 31, 0, 14, 37, 39, 7, 4, 44, 48, 5, 14, 22, 35, 35, 30, 31, 45, 38, 36, 6, 42, 4, 0, 26, 29, 36, 38, 35, 18, 33, 24, 14, 36, 33, 10, 44, 22, 33, 41, 31}

    {619870570, 529987177, 724902550, 957056750, 450315548, 486975720, 379939631, 479388868, 281492580, 772647236, 671536672, 589966554, 940207495, 207911360, 354657457, 369445178, 856519815, 414583429, 242107245, 162337439, 581290204, 868743441, 356451043, 576638621, 517544195, 269109230, 562914861, 148936060, 516465654, 159673723, 125190823, 419875711, 488869371, 647779680, 428789885, 321969924, 471237923, 123705139, 653614854, 805741624, 650315144, 842983733, 310012231, 874839809, 928274210, 539323442, 298017140, 125370847, 457062070, 560243380}

    {554060014, 408941294, 75898270, 239123884, 857185032, 600059182, 815076308, 96089705, 312583206, 880528526, 409338656, 664179930, 831834632, 894536393, 838338441, 569691227, 709073219, 633519099, 564040062, 746699960, 621405494, 310412279, 38836722, 599893080, 117959674, 101117352, 942634761, 526931036, 376749288, 863813385, 137690187, 319327255, 518733213, 143141321, 843904632, 175090069, 522124012, 661478762, 118012646, 662980148, 638187439, 597227734, 265114181, 164455831, 727349243, 905970199, 405580406, 267234026, 74759122, 45137963}

    {436598448, 36456730, 226425701, 697983891, 416175920, 720999566, 312902231, 197660452, 722660494, 497748158, 831020073, 897592123, 565575988, 307023434, 561648765, 111218960, 105177203, 74574359, 969938376, 137903528, 421536541, 487293846, 107358764, 555282420, 854606016, 755545505, 426871114, 982467601, 626552180, 785450186, 685407699, 334971446, 255780166, 342316161, 773189909, 124246139, 260821125, 137069426, 519789168, 276502486, 284784883, 934189765, 948394448, 758356165, 574446870, 844194334, 977863747, 752115550, 658031911, 50012726}

    Returns: 700368026

  22. 50

    {44, 38, 46, 20, 15, 2, 31, 18, 42, 1, 23, 46, 28, 26, 26, 10, 36, 35, 13, 11, 23, 7, 30, 46, 38, 4, 9, 4, 9, 9, 47, 30, 49, 34, 23, 6, 46, 21, 45, 31, 13, 14, 30, 24, 6, 12, 34, 20, 21, 29}

    {576045624, 267576194, 776601917, 724800841, 683226894, 410069645, 540208690, 114959864, 634793962, 197184205, 702704383, 136925217, 97350330, 939591398, 348327042, 552381403, 504616082, 909014335, 859122139, 226248136, 369367812, 74135423, 586396016, 738963462, 706879459, 871771888, 484176227, 959995635, 710881057, 550223122, 983415360, 45350451, 300202273, 156288601, 6552590, 685932608, 494943038, 779769067, 569631575, 483681970, 993714194, 15610939, 262720409, 909214286, 405878255, 585650888, 171131238, 143849972, 137404587, 586815842}

    {818554255, 340023773, 936113124, 357686521, 331251758, 823179894, 624673080, 638765537, 34054864, 205617270, 826809267, 393178609, 697119112, 780136680, 711444805, 635426559, 757969481, 634169595, 498724154, 359240069, 211000047, 348698233, 421341806, 734091160, 924993550, 879123285, 861746051, 606426663, 213009612, 805116399, 773148049, 260395615, 285901628, 593937178, 415013320, 522240232, 594668849, 374399950, 437129383, 682764247, 519887637, 506483310, 653326348, 806201697, 61280951, 388656255, 965414465, 868548857, 11499189, 536420959}

    {110475314, 180851522, 689077254, 253258088, 317312346, 383426174, 987439059, 518151882, 1770267, 15130937, 58967055, 422994790, 277881862, 317342884, 676632871, 752494943, 186820787, 901398608, 703491089, 506289513, 323680659, 944633216, 166815468, 909762788, 583343457, 621135821, 381261284, 173444156, 261561373, 321101065, 235585661, 842979964, 643194232, 584266282, 864371756, 557912340, 68600393, 656519145, 93948189, 330739360, 770513374, 818760222, 525542808, 193034293, 280661005, 461373351, 208229786, 216871958, 197542397, 164205059}

    Returns: 975871833

  23. 50

    {18, 0, 6, 18, 37, 4, 42, 39, 45, 35, 20, 35, 46, 19, 16, 25, 21, 34, 28, 21, 16, 46, 30, 7, 0, 23, 28, 29, 31, 1, 3, 11, 35, 35, 2, 14, 1, 6, 25, 25, 11, 15, 28, 22, 45, 30, 42, 7, 46, 26}

    {46764595, 195654023, 828301283, 492544932, 106627046, 628130843, 890966560, 750530867, 283062611, 621721180, 28839359, 903460537, 739949255, 156727508, 47029355, 925806440, 962223544, 917989157, 285648215, 290158833, 52966961, 279527411, 330884905, 606321031, 306280178, 179467268, 815503055, 771055204, 200263725, 235739786, 356183808, 670825196, 302023987, 445220878, 584315301, 564439209, 223680880, 921289073, 590126756, 161622316, 556689888, 893270884, 405917398, 943588763, 883482305, 822467147, 634179880, 352817908, 627258298, 318421033}

    {669187762, 152212785, 792532706, 767421162, 395253020, 341267868, 729237119, 767580634, 759321793, 530706022, 539247139, 532242760, 267436325, 960704235, 289583901, 996129159, 393005009, 929787359, 433408246, 971780185, 509422603, 95812183, 512674886, 868289240, 440855415, 70989939, 72029339, 689717553, 49269936, 332558678, 699777909, 500226506, 344242048, 343495561, 281089276, 873185659, 962180955, 87321138, 756246121, 997515614, 811653306, 124566883, 750366512, 447947555, 690179934, 867547054, 226485986, 761035685, 649476732, 322671216}

    {79319448, 620213582, 270622266, 517360288, 222244036, 45852781, 367008612, 834848049, 399773514, 528718459, 286914043, 649634932, 281359740, 327662333, 492854446, 393770918, 858398907, 23190112, 732011070, 870880234, 222029514, 696939848, 226272171, 965480624, 603252901, 72865402, 40684186, 950559991, 482709838, 852956686, 80730890, 52225942, 30608292, 830011666, 955553604, 700406537, 290240396, 172173592, 787000685, 384976234, 670102594, 289469943, 393863171, 631507693, 396940611, 82347632, 442391095, 91693836, 445880885, 278397392}

    Returns: 786586009

  24. 50

    {46, 3, 11, 12, 10, 45, 3, 1, 32, 7, 17, 32, 14, 5, 7, 29, 2, 33, 43, 24, 20, 31, 30, 7, 17, 5, 0, 4, 41, 1, 46, 33, 33, 43, 47, 30, 10, 37, 1, 23, 46, 15, 34, 13, 45, 48, 46, 44, 25, 28}

    {2939649, 638275774, 880000649, 69800212, 339538393, 846192041, 536691696, 681069135, 636363993, 46258148, 574550992, 964963123, 897092096, 888407547, 40698940, 813775393, 124863727, 926963979, 712174296, 59102258, 546077303, 970375482, 265862605, 473678600, 905680903, 77097192, 222220499, 287147502, 175102478, 730767645, 214408339, 105811124, 113356890, 439185884, 572143468, 147978538, 247385994, 577352995, 801110750, 619986017, 119665582, 580442011, 358625576, 977963240, 551575162, 59283400, 802261250, 151720383, 822144738, 50026223}

    {228649265, 83295265, 62813017, 180951060, 164287014, 564388580, 538833890, 601428464, 775760718, 560827505, 247889747, 261241439, 833958281, 141271783, 166485529, 61864484, 28040537, 221609851, 76920335, 703213761, 512877892, 134098137, 895179970, 2487314, 542856552, 848995872, 286107898, 64180441, 885530267, 978894430, 335235765, 150122861, 402582467, 89258679, 855993235, 519098347, 34725786, 800242334, 661502124, 17299707, 693353504, 328789728, 138578672, 798521417, 437972377, 641405114, 786320045, 653522513, 586216799, 112716736}

    {462024316, 59575635, 442101815, 72634486, 123380461, 417107391, 45340697, 450306740, 383916026, 46101237, 219893764, 876275074, 284837618, 43014514, 607838552, 740079633, 235009752, 555047093, 760531052, 944298951, 415345637, 453041743, 404622342, 611132990, 918129613, 938455725, 290041624, 731471083, 117719031, 388607565, 925876127, 560234460, 418022359, 780789783, 341702713, 134072731, 216913131, 396656043, 361159706, 734180376, 569691813, 174040399, 971011538, 361153090, 394326750, 408354652, 672757140, 970310986, 690424110, 687556993}

    Returns: 646868846

  25. 50

    {44, 18, 26, 43, 47, 42, 21, 30, 18, 20, 15, 17, 4, 37, 27, 43, 10, 22, 36, 44, 17, 4, 29, 29, 41, 47, 29, 45, 35, 42, 7, 39, 18, 6, 20, 20, 23, 4, 0, 11, 25, 28, 26, 43, 33, 34, 9, 18, 22, 32}

    {210257030, 303942619, 983399382, 414799588, 290817163, 796858352, 47718619, 466755049, 932901296, 190299364, 931853685, 793001022, 696833855, 837223695, 28038110, 370136649, 230567456, 649946351, 50682532, 891956386, 532297981, 381159452, 725752551, 693849822, 913993536, 767878587, 179841421, 909266646, 563933283, 806833708, 520791946, 356760610, 221478778, 531594354, 727668885, 390447823, 999828956, 155360273, 442655380, 975866715, 245616977, 335761890, 159563470, 341679460, 506783257, 637394377, 623880068, 674134716, 992340966, 808203882}

    {634949017, 121534024, 898340920, 709248338, 292289538, 6834734, 452994700, 977952125, 222499298, 505972270, 672765498, 129304270, 974592713, 203644361, 621526260, 783269685, 711972335, 517878111, 356353990, 928293987, 109722998, 214465309, 660190131, 857022746, 455686823, 405007725, 706674487, 935794961, 439157448, 738811726, 901118752, 331022111, 228091301, 170719452, 707038615, 220989194, 769749997, 521051978, 299735592, 351835173, 571852104, 151096145, 328863735, 82013134, 105835801, 894153974, 611020890, 442291434, 574795137, 685217257}

    {399712583, 352160483, 781265648, 888215626, 638276580, 36927873, 99447078, 382461598, 61029047, 782104277, 675787741, 919489887, 621369, 354825417, 834011500, 313803589, 988231455, 503662846, 522603746, 677275649, 801977883, 957655013, 228568481, 21331187, 666776498, 255775622, 195026700, 408391470, 977671959, 751081333, 321199319, 982521695, 487817753, 272280545, 819033677, 419061124, 246332401, 136792942, 923338490, 842654124, 660042256, 529320584, 416480261, 234304618, 216820491, 60368685, 137284488, 313684536, 769445089, 207113656}

    Returns: 444941731

  26. 50

    {20, 15, 16, 2, 32, 44, 10, 13, 23, 37, 10, 24, 28, 48, 44, 40, 33, 23, 16, 34, 21, 15, 29, 18, 25, 24, 14, 20, 13, 46, 2, 13, 28, 43, 37, 0, 18, 18, 23, 13, 36, 20, 28, 3, 33, 12, 4, 31, 43, 26}

    {959114709, 375864791, 931700016, 837544309, 57905817, 578797155, 401993482, 316640131, 284632641, 765762395, 900685974, 26465702, 539691014, 810576391, 34368525, 187200424, 582471188, 640971529, 843733106, 828045689, 39187639, 470734736, 790774850, 826492253, 800048894, 165215928, 553547327, 393174343, 369517881, 121317037, 662567415, 436318598, 924689798, 242662077, 149906173, 511941222, 271091108, 13840267, 717127471, 297926363, 682641283, 458101950, 501822565, 307304983, 29179206, 400578119, 970342620, 655655591, 502487255, 781631419}

    {79282771, 600517016, 628060603, 295718433, 228288276, 783714028, 643397929, 144104289, 497232376, 180883518, 255294887, 400305590, 699242762, 23076806, 39591893, 422567085, 663076072, 517227615, 421669898, 315753871, 811300448, 467351359, 277685047, 427857398, 353685685, 627001799, 496391193, 852504070, 16757852, 211369441, 265660889, 91191220, 169750882, 129989065, 132134655, 575076506, 402237891, 513163522, 685651593, 37083806, 985119174, 238045304, 235618836, 440267275, 771904093, 415263175, 346154098, 254837338, 227989599, 898967000}

    {430868450, 207765691, 318614096, 627908690, 28312151, 374501266, 719877525, 61970168, 371853802, 268516755, 447840752, 397882477, 702176230, 344505968, 722822658, 676322877, 316653335, 676838603, 789051033, 17717661, 903629028, 910381114, 464079045, 965613358, 646867053, 95218038, 240636530, 217414907, 47695492, 924258451, 476054089, 773275710, 805436426, 26535161, 432884561, 571534195, 733520402, 912310498, 349179462, 788417250, 760453036, 644750128, 839331901, 504659221, 805573624, 734361672, 198090447, 435067393, 229934596, 801749326}

    Returns: 230968751

  27. 50

    {18, 18, 35, 37, 23, 45, 28, 46, 5, 0, 7, 14, 18, 18, 14, 8, 42, 13, 1, 42, 18, 39, 36, 40, 49, 20, 1, 15, 7, 41, 13, 15, 12, 6, 15, 36, 28, 35, 30, 2, 22, 29, 20, 34, 26, 2, 17, 5, 48, 29}

    {166432084, 451597098, 35098742, 182543679, 714217321, 719952278, 693443761, 102326046, 581169944, 909803611, 772532583, 149470873, 339432774, 759392540, 726740429, 448594414, 393207645, 144377251, 477208613, 660899811, 320375589, 366974790, 955697523, 561207391, 808361527, 370541239, 806135521, 720326216, 538772036, 787317644, 893560400, 496779272, 32811680, 820526631, 715497052, 268954423, 538077986, 106391467, 948606645, 653807060, 589016027, 727965751, 597727732, 185565125, 984387307, 683721824, 791961438, 883102652, 187227399, 539809072}

    {899443259, 343788508, 463588499, 824015711, 766356271, 229955446, 967624210, 516832686, 238938224, 536093753, 90236102, 563335688, 544909926, 89244648, 494632624, 143972278, 52040595, 104667872, 291038083, 249662092, 113178286, 957784001, 632629743, 991220826, 262720692, 183013651, 920753046, 15290580, 980450511, 680114740, 831543875, 980918473, 581398988, 916482577, 573114571, 571934621, 137262095, 939005906, 910024334, 371619272, 158585034, 355318989, 717075902, 723759000, 148595512, 668012034, 462026946, 334778262, 511535205, 176500246}

    {368556717, 86489804, 657777929, 443489823, 834380274, 994321756, 482811902, 994125032, 48966823, 594454323, 608767461, 146130022, 709131986, 70177599, 948995607, 955079572, 364842300, 621659092, 846090995, 750694366, 995294006, 709961645, 288025184, 375811555, 395513938, 707505210, 149416870, 189302561, 612681152, 991764951, 871377287, 490530206, 875231820, 928091401, 205182786, 147694586, 173005136, 361275393, 911358246, 896890998, 559631475, 708858308, 993628627, 963950021, 214206630, 386375705, 662617801, 483473682, 308955575, 616273257}

    Returns: 868724040

  28. 50

    {13, 1, 6, 14, 3, 16, 42, 28, 38, 12, 39, 37, 43, 28, 39, 47, 39, 1, 11, 41, 22, 16, 16, 4, 5, 26, 21, 33, 49, 1, 9, 47, 13, 26, 40, 41, 44, 9, 1, 44, 31, 40, 27, 10, 49, 3, 47, 14, 9, 20}

    {160221319, 905793266, 57698206, 591481555, 164253660, 320322322, 142381995, 238966666, 217199772, 785947523, 673694722, 138478488, 590606051, 83025032, 965521227, 917188221, 505847211, 450796131, 367079862, 981996445, 208474494, 919438308, 688642905, 374788812, 523836706, 300110256, 930012280, 958692536, 626773354, 552398934, 396375387, 825910697, 551864864, 984287462, 279570411, 188591840, 105673007, 886447621, 557936252, 69339023, 348835226, 358791403, 648690868, 824073181, 694383751, 859719172, 409235259, 191860677, 949047892, 726797036}

    {946069980, 193344786, 603307698, 338770545, 865802526, 139693808, 232177688, 863322158, 174617326, 659906038, 740151800, 278764166, 722090075, 782499786, 298304362, 47195, 219034630, 68670606, 871120070, 3491230, 993074497, 251677944, 684742892, 225160192, 15823674, 770896018, 335489096, 586574870, 415783767, 603175176, 898425978, 827804484, 128775920, 512556128, 335452790, 140175148, 999680256, 261065558, 911289408, 541586125, 692585526, 705110462, 23813924, 533132247, 158765004, 120616730, 252790580, 484628192, 936823137, 690243599}

    {685525724, 449494025, 137687772, 898246722, 539290097, 651871198, 998585933, 121538190, 723301589, 257541895, 91917905, 255993545, 709990630, 917036387, 295224407, 21182954, 360236889, 413470496, 655198422, 305095294, 875769701, 292629805, 609972339, 434588646, 616965386, 583311985, 910130766, 656067013, 400051575, 455299091, 758657335, 661380210, 418863740, 645316443, 63467965, 622712483, 867139487, 832744720, 498812657, 530446472, 603758648, 959392450, 330911351, 763287422, 353833120, 854964604, 101310656, 877364178, 573290497, 197680713}

    Returns: 268758831

  29. 5

    {0, 1, 1, 1, 2 }

    {7, 4, 7, 9, 2 }

    {8, 3, 9, 5, 3 }

    {6, 0, 1, 5, 9 }

    Returns: 22

  30. 2

    {1, 0, 0 }

    {122064284, 9662111, 120616497 }

    {20137061, 408976122, 494878172 }

    {242061783, 603049107, 805670429 }

    Returns: 1

  31. 15

    {11, 3, 13, 5, 0, 3, 0, 8, 9, 4, 9, 7, 5, 12, 12, 11, 12, 2, 6, 5, 13, 13, 11, 8, 14, 9, 2, 0, 3, 11, 10, 12, 10, 11, 11, 12, 13, 7, 12, 11, 2, 14, 8, 3, 6, 6, 4, 13, 5, 8 }

    {983816220, 620877501, 728957664, 719453482, 891241034, 959047323, 459235325, 188837384, 749336264, 40650017, 404049008, 121578182, 640967952, 444329307, 181115164, 697849277, 12923013, 711014676, 308063158, 403714366, 341206103, 674610097, 743172147, 27978413, 95548595, 93823839, 844476902, 863583697, 568069127, 618319911, 659846531, 341309147, 735202433, 531047579, 967335611, 311192666, 753647731, 36420180, 609571991, 208600401, 915548304, 926479460, 672275772, 545217041, 864561330, 32472050, 852336473, 144521601, 383750815, 616511468 }

    {715457951, 308091233, 686233659, 523365634, 260145657, 96581518, 754153775, 622990522, 78662953, 689973864, 609423534, 534351235, 56822117, 899080526, 236413795, 747521954, 249656307, 790813221, 238598034, 203856426, 170015231, 791645278, 991710627, 747864180, 331241135, 416320805, 820623220, 811261319, 154661650, 914880513, 270905767, 954448019, 261442212, 954262444, 293791600, 493225233, 67542211, 911866345, 567575019, 95716070, 410883122, 337767450, 375732581, 616839717, 416849487, 140196829, 200763187, 51759408, 992789421, 882490836 }

    {650915191, 363659051, 226659197, 706291662, 748630395, 163284394, 663006670, 2890697, 639793395, 728890798, 570088430, 967259303, 101778889, 249725396, 968816738, 276471315, 905010209, 467925249, 798793109, 857289233, 494026470, 476417587, 98570430, 596160845, 211373787, 188742439, 364805067, 757845257, 317224756, 74104796, 455729968, 78933290, 769895010, 476555278, 45379277, 957039727, 395817921, 447349376, 629724490, 287334171, 227424105, 603337884, 467060652, 254067677, 237332026, 976429932, 93075762, 960441433, 132935737, 671265490 }

    Returns: 755767349

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