Statistics

Problem Statement for "CyclesNumber"

Problem Statement

The level-M weight of a permutation P, denoted W(P,M), is computed by finding the number of cycles of P and then taking that number to the M-th power. For example, the level-3 weight of a permutation with 5 cycles is 5^3.

The total level-M weight of all permutations on N elements, denoted T(N,M), is computed as the sum of W(P,M) over all N! possible permutations P on N elements.

You are given multiple queries. These are encoded as two int[]s n and m with the same number of elements. Return a int[] with the same number of elements as n. For each valid i, element i of the return value should be the value T( n[i], m[i] ) modulo 1,000,000,007.

Definition

Class:
CyclesNumber
Method:
getExpectation
Parameters:
int[], int[]
Returns:
int[]
Method signature:
int[] getExpectation(int[] n, int[] m)
(be sure your method is public)

Notes

  • Formally, a permutation on N elements is a bijective function P defined on an N-element set S.
  • A cycle of a permutation is a sequence c[0], c[1], ..., c[k-1] of distinct elements of S such that for each i, P(c[i]) = c[(i+1) mod k].

Constraints

  • n and m will contain the same number of elements.
  • n will contain between 1 and 300 elements, inclusive.
  • Each element of n will be between 1 and 100,000, inclusive.
  • Each element of m will be between 0 and 300, inclusive.

Examples

  1. {2}

    {2}

    Returns: {5 }

    Here are two permutations: (1, 2) and (2, 1). (1, 2) have 2 cycles. (2, 1) has one cycle. So answer is 1 * 1 + 2 * 2 = 5.

  2. {3}

    {0}

    Returns: {6 }

    Here answer is just number of permutations, 3! = 6.

  3. {1, 2, 3}

    {1, 3, 3}

    Returns: {1, 9, 53 }

    Could be more than one query.

  4. {10, 20, 30}

    {10, 20, 30}

    Returns: {586836447, 544389755, 327675273 }

    Do not forget take answers modulo 1,000,000,007.

  5. {1}

    {0}

    Returns: {1 }

  6. {1, 2}

    {2, 1}

    Returns: {1, 3 }

  7. {10, 100}

    {100, 10}

    Returns: {516142651, 63920840 }

  8. {12, 12}

    {12, 12}

    Returns: {541349597, 541349597 }

  9. {5}

    {6}

    Returns: {85324 }

  10. {35085, 11428, 53378, 34938, 14117, 5001, 49693, 70282, 73705, 43542, 44670, 6803, 20928, 17703, 44200}

    {287, 170, 125, 83, 0, 223, 44, 193, 35, 3, 161, 229, 52, 22, 47}

    Returns: {400257299, 827225276, 394141891, 127243563, 465859220, 909107521, 99863542, 115267255, 668620910, 497414290, 354831391, 221279653, 977399362, 364604020, 187529553 }

  11. {16548, 2784, 38248, 56445, 75158, 62512, 34777, 61512, 4817, 39990, 45019, 68377, 63303, 27114, 79811}

    {269, 289, 161, 6, 203, 262, 222, 275, 248, 266, 214, 191, 261, 16, 92}

    Returns: {183787596, 531635747, 319595800, 543241665, 118755107, 236490815, 72244927, 105368283, 990213033, 113808702, 584723803, 802304239, 819650758, 150915522, 774288068 }

  12. {63820, 86256, 34327, 22299, 43897, 44161, 72641, 51275, 9607, 94780, 59870, 50811, 75127, 44055, 2138}

    {96, 300, 45, 186, 6, 180, 117, 207, 272, 256, 30, 147, 253, 119, 278}

    Returns: {623157235, 302794910, 993101084, 482632585, 312181461, 330163362, 205855413, 286510677, 210394315, 40130116, 978912244, 370650159, 553397625, 874728874, 470493367 }

  13. {23278, 20154, 70305, 58262, 49623}

    {236, 22, 5, 68, 233}

    Returns: {930945806, 605649521, 156727694, 36228858, 166073401 }

  14. {2754, 33602, 46144, 89780, 35643, 56921, 83135, 55098, 47, 14238, 80949, 8207, 66889, 46539, 92675}

    {45, 42, 221, 4, 274, 193, 37, 279, 206, 14, 165, 134, 241, 16, 287}

    Returns: {348288520, 269844448, 564506583, 408102980, 849558966, 952608566, 430675777, 521681243, 968714508, 957076562, 867064906, 880967758, 180058742, 505303889, 877760057 }

  15. {43887, 54274, 45662, 3119, 83772, 83373, 21478, 54925, 8421, 94073, 89005, 18873, 48774, 87656, 30798, 97533, 10273, 82251, 7492, 99361, 67987, 50753, 70456, 40130, 19155, 85975, 38168, 51021, 48299, 16577, 70114, 44267, 67778, 15672, 82526, 21864, 77241, 50627, 56647, 8134, 97172, 17828, 59604, 87615, 2702, 45815, 58947, 96790, 97015, 94390, 93196, 87666, 59133, 39821, 56232, 3704, 20786, 68366, 42580, 67744, 67466, 72952, 18006, 45033, 65553, 13734, 71495, 95202, 48366, 29479, 74736, 44576, 12171, 35619, 66362, 31882, 26644, 42213, 34675, 52189, 5640, 65608, 10534, 25834, 66209, 26149, 99368, 2250, 25450, 35161, 74007, 30269, 11155, 78657, 41554, 10977, 44715, 72684, 70476, 17494, 70017, 17754, 63434, 64526, 95757, 52214, 3700, 33667, 93555, 75753, 63717, 44633, 51881, 29380, 65701, 16529, 79922, 83203, 782, 78801, 79844, 64812, 45010, 91198, 76628, 16033, 90607, 6873, 47271, 60393, 47428, 87681, 55151, 41355, 47012, 28390, 58858, 44963, 98791, 25228, 23682, 50119, 8185, 54360, 49196, 65599, 34797, 22922, 73274, 49337, 48303, 9065, 38785, 16034, 34789, 65907, 79358, 42236, 7198, 49885, 6764, 76805, 50911, 39127, 14086, 61021, 75174, 92582, 42559, 31808, 84783, 58383, 34854, 57570, 73763, 74911, 45096, 32561, 90502, 59702, 65667, 75361, 36048, 44195, 6393, 23883, 16167, 2610, 56115, 86535, 65072, 96176, 17288, 62564, 70138, 5605, 61645, 71030, 18554, 42709, 48468, 28949, 78341, 4215, 60740, 66076, 78826, 37842, 92504, 76036, 1827, 42025, 95663, 50660, 29829, 90177, 8210, 33209, 37368, 22023, 54534, 46875, 55703, 5690, 79569, 1701, 65118, 88313, 21597, 25984, 6111, 35318, 68783, 21749, 96551, 69630, 25436, 39683, 65515, 61262, 29379, 37021, 69182, 12080, 13531, 58028, 80329, 71430, 73060, 36609, 25599, 68251, 8884, 83295, 51431, 53270, 58794, 14543, 7885, 74713, 56710, 99838, 85733, 57149, 67803, 46723, 20166, 64648, 17638, 25489, 27739, 31630, 4923, 32045, 27286, 9626, 52908, 3390, 1437, 54031, 86012, 42195, 71687, 3926, 5485, 32314, 95784, 57104, 91597, 38193, 24370, 39871, 14775, 37035, 87943, 84284, 42575, 27789, 67567, 3404}

    {185, 78, 238, 115, 212, 113, 261, 222, 200, 286, 96, 199, 39, 254, 21, 146, 71, 243, 54, 64, 62, 235, 180, 282, 8, 227, 266, 180, 147, 185, 109, 199, 24, 54, 260, 48, 166, 42, 105, 196, 92, 214, 64, 243, 71, 2, 83, 44, 169, 16, 50, 74, 112, 234, 220, 102, 207, 30, 28, 77, 58, 236, 46, 68, 21, 183, 225, 105, 122, 120, 220, 174, 73, 45, 4, 149, 167, 205, 176, 117, 31, 29, 281, 33, 56, 127, 147, 120, 64, 285, 0, 278, 134, 215, 284, 188, 189, 66, 213, 17, 148, 179, 160, 1, 179, 259, 1, 150, 40, 193, 94, 166, 227, 53, 273, 101, 204, 36, 98, 105, 183, 218, 246, 145, 283, 278, 83, 198, 13, 133, 15, 82, 98, 187, 94, 51, 69, 51, 138, 62, 37, 184, 29, 130, 184, 66, 129, 210, 47, 133, 265, 283, 61, 273, 61, 168, 146, 157, 225, 120, 2, 47, 57, 51, 225, 198, 183, 92, 67, 198, 0, 212, 107, 122, 2, 213, 66, 42, 89, 274, 136, 215, 86, 199, 156, 33, 12, 62, 291, 201, 136, 291, 27, 278, 96, 158, 159, 280, 173, 11, 74, 157, 145, 102, 218, 108, 254, 23, 216, 33, 78, 87, 24, 281, 113, 32, 229, 296, 97, 205, 291, 222, 273, 186, 38, 110, 45, 224, 21, 273, 159, 15, 106, 18, 79, 268, 50, 25, 210, 241, 196, 170, 93, 207, 219, 53, 44, 22, 110, 77, 69, 298, 154, 186, 261, 215, 134, 145, 210, 94, 273, 270, 281, 46, 1, 297, 73, 266, 51, 232, 126, 282, 245, 15, 190, 151, 238, 191, 145, 275, 288, 300, 173, 101, 86, 20, 191, 26, 299, 49, 251, 190, 215, 90, 53, 37, 118, 293, 196, 69}

    Returns: {939146903, 173706831, 486567832, 647867309, 639640373, 903023208, 180331702, 871767705, 753067265, 266831852, 894166986, 977304754, 506313686, 863470436, 798558585, 57134750, 14508881, 640597914, 647527736, 928089418, 486489118, 392998707, 293568889, 419631029, 377238103, 163133608, 557844797, 558590900, 267111649, 968215228, 880321558, 748374997, 308332545, 234063161, 115968337, 283318421, 448352762, 351088370, 646509515, 770663972, 84554958, 898883024, 513386775, 157445320, 485156285, 486608567, 823024885, 772734551, 499830444, 334065306, 463619304, 510492986, 63820039, 550754273, 947586389, 906974176, 316356916, 600645246, 882056585, 325921190, 137953864, 559803937, 684444796, 361671252, 194136372, 437025975, 236699065, 357027505, 703531307, 854488313, 187614464, 976421659, 65252887, 452424293, 200522617, 841007739, 766268520, 869842613, 626709035, 926210159, 519818943, 745487750, 671047345, 605529947, 934761032, 609429503, 425827094, 708251207, 215651720, 261600672, 251161076, 630271732, 338861479, 661951416, 977645092, 510591029, 866341151, 927032904, 54921968, 874187724, 413575939, 105756564, 574559310, 96189873, 505967604, 971111453, 933455012, 423880078, 639822039, 677741939, 435071663, 103901179, 815944603, 824350946, 186159889, 616404697, 158429045, 627600855, 491340793, 44561146, 62294036, 520284318, 596514021, 573031281, 142057366, 524077056, 222254229, 324482686, 808368130, 585321887, 895449089, 857813442, 338072696, 500177399, 940933850, 424098006, 235772088, 92748709, 203628243, 46852599, 442650663, 952981365, 612828862, 526863851, 522365469, 397274092, 778102383, 255058782, 292295021, 185601724, 997275999, 21779116, 211339697, 724778707, 969095331, 320984367, 12622970, 849079172, 301292426, 764412842, 498988660, 972911, 92916678, 706998115, 466573462, 77939354, 94347506, 272895967, 899105374, 792673032, 223762119, 479702388, 982134767, 291541195, 815376643, 643953489, 201635049, 805713931, 325417655, 898769348, 705847915, 743738889, 895406797, 866597898, 230577851, 910322023, 39876213, 403556185, 1790796, 89773684, 90414915, 918878230, 781697325, 198556558, 36881015, 62520956, 413377572, 158187580, 475054894, 504309846, 447982990, 789796475, 463695984, 706304105, 599141011, 833804490, 30272918, 68295529, 882355889, 21887323, 897858733, 525481320, 720465663, 348771906, 980598901, 209457316, 729108885, 486442570, 510187444, 724769658, 374306544, 489985754, 577762392, 130240853, 584990961, 920075004, 815244787, 79872038, 713032436, 821085558, 356497243, 560324453, 875067418, 212651398, 561826883, 370619232, 388232922, 489908067, 519544650, 654795205, 389043747, 716206935, 426155597, 223034002, 740685205, 545314518, 458395915, 800230582, 297693997, 28112008, 773881729, 93258666, 979138863, 200125949, 588871785, 536463529, 235511907, 572547798, 430395922, 481306241, 745003336, 355481081, 487908958, 209517785, 546944739, 707206543, 451665718, 798321651, 710110183, 683097397, 498145234, 107075900, 906422974, 461170015, 523084402, 42077432, 80846176, 283163971, 610794158, 245797085, 455278971, 100827164, 436062200, 450302013, 388697740, 586389617, 500895113, 256764245, 970377908, 978856586, 177944361, 769459599, 412859132, 368250500, 970902666, 659286852, 473682113, 701641940, 324938701, 778326773 }

  16. {66386, 89081, 93431, 13033, 63978, 68903, 99085, 30374, 82200, 68842, 65213, 43942, 41328, 79263, 82789, 54560, 85013, 35052, 44282, 88617, 63032, 23129, 30839, 13385, 95525, 93423, 6913, 90552, 67604, 93216, 18837, 48368, 5312, 18390, 19290, 85072, 21921, 89845, 89902, 52352, 97564, 23440, 73160, 32641, 66668, 85725, 23940, 63689, 65554, 87636, 687, 61683, 20417, 36267, 45900, 88697, 66183, 83685, 57510, 29466, 8768, 55952, 97850, 61916, 51946, 41757, 6198, 83607, 56280, 54584, 91386, 11568, 42902, 58119, 60797, 1897, 14635, 4982, 93546, 46227, 47860, 41985, 31237, 91800, 71860, 91088, 88260, 73673, 62404, 95616, 77149, 91120, 44716, 87239, 30614, 4281, 24203, 16603, 85639, 58824, 26521, 88759, 61460, 56174, 83802, 1868, 45638, 85070, 16389, 35281, 46722, 71355, 40732, 88362, 9371, 45351, 26979, 6149, 15480, 73192, 16848, 67777, 1318, 78637, 63710, 67557, 55108, 52389, 92311, 65478, 8404, 24699, 24046, 45756, 30001, 43135, 91486, 54356, 96615, 64003, 15331, 51894, 9601, 47065, 66804, 49227, 13437, 25685, 33707, 11750, 90757, 15867, 48260, 22927, 24907, 10801, 8572, 55346, 84582, 85806, 58786, 95734, 57249, 58639, 93669, 5293, 54345, 6757, 12311, 39207, 66520, 51457, 49339, 95891, 43560, 48206, 45768, 8272, 43662, 79390, 24305, 15872, 3535, 58248, 51359, 65548, 42121, 4322, 26820, 37619, 41429, 92135, 37626, 19885, 41916, 79295, 61826, 47278, 29674, 70044, 98842, 4517, 80693, 61723, 20411, 27262, 43277, 31553, 91783, 62373, 73154, 29051, 40915, 21321, 25807, 60759, 63218, 43362, 62395, 82110, 58580, 60719, 35347, 57195, 94330, 38461, 10398, 85368, 51597, 61078, 12917, 80036, 42219, 50171, 74217, 73899, 80307, 69520, 16950, 30560, 7519, 21105, 91248, 54558, 66747, 58216, 88747, 79891, 35745, 79613, 30811, 38086, 22934, 68194, 31123, 91426, 54689, 96534, 10866, 76447, 50539, 71790, 8281, 48268, 61052, 90993, 82926, 17678, 22052, 45127, 91699, 77059, 16824, 18316, 39887, 54520, 20249, 21013, 59531, 35158, 80852, 30410, 80381, 25715, 38890, 25071, 77081, 77868, 6447, 98325, 40514, 25141, 80100, 58635, 3375, 23712, 20770, 43653, 81612, 87270}

    {82, 166, 20, 51, 124, 21, 177, 110, 42, 89, 236, 222, 88, 48, 284, 268, 25, 121, 52, 212, 79, 121, 157, 87, 230, 65, 297, 188, 204, 11, 249, 159, 221, 221, 81, 291, 73, 98, 117, 153, 225, 258, 74, 300, 101, 81, 271, 86, 118, 255, 60, 48, 154, 90, 8, 255, 207, 118, 282, 118, 221, 39, 137, 128, 287, 152, 136, 120, 77, 104, 97, 4, 46, 209, 262, 154, 249, 36, 94, 238, 165, 258, 36, 223, 278, 158, 49, 230, 12, 72, 135, 171, 65, 225, 239, 154, 59, 253, 245, 179, 190, 63, 118, 183, 130, 136, 293, 269, 47, 52, 4, 177, 191, 230, 229, 198, 77, 91, 123, 91, 170, 105, 231, 73, 280, 124, 219, 190, 193, 82, 132, 293, 187, 202, 273, 221, 2, 118, 243, 115, 117, 79, 176, 227, 164, 1, 238, 172, 232, 27, 121, 11, 132, 68, 138, 93, 251, 93, 81, 123, 271, 64, 88, 141, 205, 280, 242, 28, 195, 288, 214, 132, 166, 69, 38, 118, 224, 154, 47, 187, 85, 213, 142, 234, 278, 246, 20, 28, 122, 75, 237, 219, 117, 52, 265, 253, 20, 191, 67, 98, 113, 10, 33, 37, 261, 275, 258, 245, 275, 254, 149, 98, 166, 200, 101, 264, 109, 98, 17, 264, 99, 153, 143, 240, 146, 70, 275, 200, 164, 64, 126, 78, 39, 190, 119, 186, 54, 224, 28, 10, 189, 289, 21, 200, 173, 54, 87, 100, 155, 210, 125, 226, 158, 103, 169, 144, 246, 298, 130, 248, 188, 260, 299, 187, 81, 234, 254, 268, 33, 68, 73, 222, 25, 184, 201, 252, 108, 107, 168, 12, 107, 116, 87, 65, 134, 126, 222, 70, 298, 263, 195, 193, 97, 2, 32, 116, 81, 126, 27, 255}

    Returns: {721352715, 285109605, 25713903, 845373607, 941085289, 224801870, 187654105, 431657494, 12838650, 551495318, 540757685, 42559633, 148413676, 773464217, 257462797, 152549834, 380667900, 217098622, 294699646, 806479360, 421879746, 756591261, 832093952, 822236330, 183393214, 441721024, 46788028, 778067120, 895729347, 294032491, 556752167, 660665897, 280246132, 85360987, 110726073, 335335097, 28909508, 124206143, 741675339, 290985648, 59277736, 256779178, 428114170, 474529729, 289514512, 819128924, 772472696, 350186722, 573261247, 964939795, 242429702, 538028878, 522472946, 886465932, 396648634, 534098501, 995751597, 554582837, 66622961, 818783675, 193628691, 821328511, 989801905, 291392112, 498263647, 31031921, 146308545, 486932521, 479226691, 647269542, 844839237, 906383785, 23352556, 359110338, 385900130, 222876150, 748125721, 257293394, 906476226, 326233131, 809553706, 707142448, 89951287, 915744754, 219418743, 680642070, 508938762, 140944083, 419399329, 247315, 430491949, 342518057, 272259475, 511618178, 281522835, 475520685, 77696746, 376971411, 138159190, 448293874, 987219333, 401014322, 516228412, 811164261, 617319632, 777527037, 522412362, 227301919, 583956717, 129057787, 232428688, 127756240, 208763076, 381839010, 487759300, 72080073, 134027441, 874056593, 71898216, 221455726, 939905888, 714181103, 254798717, 765198654, 953159698, 558560392, 165531005, 526747714, 679922763, 962203783, 832261740, 71925505, 898661375, 476162518, 838773515, 419836548, 9789567, 823913367, 326261725, 499554168, 135375016, 826373361, 436344072, 249240977, 174811187, 619742471, 696676294, 354820655, 570180305, 45575813, 975359290, 931420406, 531105896, 355631789, 134891284, 597192927, 505336071, 24588177, 647543273, 38579022, 267531509, 77053170, 820747317, 953604446, 108663611, 867022881, 823033788, 337296847, 382354891, 720398388, 389571157, 687158136, 900773347, 314961950, 630773671, 39465633, 646499962, 560129069, 320268783, 778832728, 93765480, 211277797, 889618179, 985452330, 446643079, 554669369, 629381477, 721496329, 266231138, 535133076, 345200741, 1290767, 533413409, 88481579, 942028525, 814519127, 106312985, 629129918, 489781700, 286568846, 15025457, 720714744, 629171947, 549242418, 284080811, 858866343, 204433006, 296258771, 109966266, 802575303, 597699689, 492042565, 338935229, 93471160, 917692960, 558318245, 344057179, 360474512, 426933521, 908356095, 765591320, 746266689, 405171925, 419315742, 486388197, 108238196, 146928721, 157857347, 729398118, 685813907, 100320724, 425346691, 389801809, 798834638, 110339412, 458993637, 857013916, 861668895, 209388495, 718474954, 64420981, 453321210, 794742024, 477267219, 900740033, 566527958, 330279915, 417381607, 454135098, 173284008, 785962596, 833026489, 656159983, 135802213, 971330372, 800025418, 93010553, 595033373, 556754420, 727709279, 620529101, 330113157, 934058393, 503693591, 929879574, 476490544, 312564065, 692281742, 449311901, 290994225, 524201962, 816818172, 133172130, 506420537, 373309525, 584495156, 236266475, 2544574, 832510461, 81802875, 430322101, 862990663, 454967225, 950450551, 179390398, 754272579, 829361622, 547163560, 435089537, 189897490, 186192292, 739071681, 463302538, 142216067, 969336618, 348229436, 842318176, 671082826, 983690638, 670908910 }

  17. {44737, 44234, 26709, 88088, 51334, 52077, 73710, 8456, 70460, 40761, 85007, 49844, 90839, 23741, 75510, 55497, 22905, 42899, 29552, 46894, 70148, 94928, 76543, 76426, 89306, 4904, 24263, 99470, 57335, 83780, 44783, 60044, 93765, 14397, 2418, 65235, 2416, 81914, 91092, 7474, 52615, 8217, 21459, 93823, 12506, 17347, 44016, 84858, 24955, 33491, 31725, 24869, 98514, 32284, 57982, 3017, 4752, 9177, 66437, 28491, 62524, 43199, 72439, 18075, 90748, 21598, 96404, 65247, 97241, 62755, 76139, 87856, 81533, 31178, 15069, 55421, 14277, 60474, 8331, 86523, 97314, 46009, 86646, 9473, 18701, 59128, 76600, 69913, 30275, 72846, 18337, 32648, 29225, 32146, 21505, 11159, 34835, 81795, 40165, 12449, 31741, 30801, 544, 89309, 33701, 48846, 47556, 15140, 31335, 67384, 40869, 1850, 8319, 92056, 96786, 92862, 36653, 10337, 87881, 90665, 68172, 85396, 67691, 51960, 32144, 48201, 43831, 61086, 81030, 27440, 72838, 57261, 63636, 5075, 9679, 7229, 14151, 13216, 62079, 51217, 25814, 68598, 91671, 69386, 94025, 96343, 1375, 72013, 95035, 86958, 26695, 45479, 95380, 20010, 16944, 91557, 74325, 21477, 81664, 75906, 84022, 91240, 39664, 34046, 8254, 58574, 2390, 11791, 35978, 65718, 10123, 34320, 53870, 87259, 95548, 87358, 60704, 44383, 16099, 16558, 60895, 87687, 18072, 81453, 70400, 77966, 80862, 40549, 69891, 97057, 73580, 42629, 65277, 82931, 84253, 75397, 37860, 22183, 26012, 29390, 84934, 59605, 41236, 9431, 12264, 61761, 32516, 58393, 51790, 30755, 91667, 51023, 40564, 42251, 70310, 99365, 69931, 92416, 36844, 87670, 72127, 77524, 71959, 96101, 2551, 95087, 69167, 14095, 57575, 89521, 16699, 18193, 62975, 56185, 18188, 87967, 60434, 94727, 15912, 35936, 18362, 32491, 11160, 12995, 80254, 76560, 36904, 44286, 17944, 41403, 89993, 57282, 38753, 10354, 32372, 74306, 98273, 7077, 68740, 51556, 48622, 55748, 82703, 4574, 34332, 29281, 38530, 60519, 87835, 70969, 28223, 59901, 9344, 27517, 28559, 89013, 22081, 67141, 89720, 39400, 17228, 41101, 24183, 37130, 10607, 52916, 46727, 30854, 54790, 95645, 58837, 98600, 20816, 1021, 38006, 66029, 80903, 1011, 93872, 29089}

    {224, 223, 87, 151, 159, 153, 28, 120, 226, 115, 0, 20, 186, 150, 72, 216, 294, 32, 99, 235, 86, 11, 282, 75, 62, 74, 91, 283, 280, 273, 265, 3, 30, 46, 124, 238, 245, 269, 262, 183, 93, 215, 249, 48, 12, 131, 108, 196, 175, 258, 295, 9, 274, 93, 88, 102, 149, 91, 255, 9, 206, 71, 160, 254, 275, 235, 144, 72, 57, 115, 299, 241, 166, 38, 104, 190, 11, 104, 152, 255, 209, 18, 244, 232, 113, 105, 195, 61, 290, 282, 192, 177, 53, 97, 101, 22, 112, 268, 271, 103, 88, 132, 211, 146, 95, 299, 52, 2, 159, 286, 133, 222, 41, 7, 167, 200, 208, 294, 178, 291, 158, 239, 253, 198, 78, 92, 47, 221, 44, 185, 105, 27, 2, 208, 88, 51, 113, 158, 187, 136, 292, 83, 157, 274, 86, 266, 244, 281, 20, 154, 147, 145, 199, 15, 32, 276, 30, 183, 43, 132, 36, 277, 111, 22, 272, 260, 235, 265, 22, 65, 145, 135, 171, 279, 212, 139, 92, 285, 97, 110, 295, 234, 210, 125, 9, 86, 138, 212, 255, 26, 173, 145, 266, 16, 101, 246, 68, 187, 182, 189, 165, 281, 186, 23, 59, 299, 91, 167, 130, 97, 262, 171, 127, 241, 146, 276, 287, 292, 115, 165, 252, 178, 217, 182, 252, 250, 28, 300, 51, 194, 283, 71, 272, 149, 252, 35, 140, 146, 60, 63, 90, 252, 182, 73, 184, 35, 109, 182, 39, 223, 56, 221, 27, 225, 89, 263, 122, 30, 109, 267, 81, 91, 23, 2, 280, 80, 60, 125, 173, 18, 275, 120, 244, 195, 176, 94, 164, 24, 71, 219, 121, 265, 63, 139, 33, 274, 34, 9, 282, 45, 179, 79, 224, 268, 209, 232, 27, 26, 116, 33}

    Returns: {173739075, 557945385, 326144046, 835936724, 452430966, 400825828, 421291656, 291528448, 578760532, 866579771, 366590245, 348203584, 411849683, 226886761, 416836689, 994331732, 512552990, 762858225, 841075092, 555694316, 329481505, 162217797, 672377871, 953171804, 699473742, 247738187, 728715575, 402292917, 415295980, 942944153, 129239818, 274559202, 972227876, 885165983, 172896434, 470846120, 395503837, 453111214, 75968915, 879755098, 365121891, 283567201, 452558208, 89209054, 114264, 126924293, 469377789, 164897835, 509520514, 328213390, 745086217, 956627963, 38024140, 237010727, 659439383, 8121501, 110309462, 351163089, 816712652, 797132189, 131946110, 308834142, 210978337, 108045536, 751780805, 458538844, 161806602, 506433365, 471635103, 691791610, 759020876, 286232043, 975969102, 370479357, 156536202, 320934667, 644546673, 373737455, 733140344, 846251885, 697867144, 129628722, 162406837, 700226978, 106974982, 101349445, 286498652, 59735827, 144616668, 120687323, 100325792, 711305242, 501424629, 272593586, 904055947, 118708434, 999621191, 1099882, 164498484, 908498709, 789093834, 998225081, 488297386, 449059696, 88043151, 326892729, 672867435, 80375653, 214482732, 488465444, 292569970, 161097431, 729691517, 393230085, 164561884, 173477713, 817494813, 961276331, 465647258, 745512709, 219339793, 617317161, 744335713, 404303930, 907530671, 432320971, 280950996, 837595329, 967737392, 630723910, 686417813, 864670819, 646909577, 402436940, 443158107, 22783552, 444199879, 781552928, 77088165, 213347388, 799771813, 90413921, 214859543, 195369490, 18447680, 623508672, 424457335, 910312875, 662382403, 456536836, 314685519, 392336554, 178179540, 449381977, 822355329, 473738341, 672358081, 264385558, 40637265, 661951989, 804743497, 894456269, 874784966, 918756131, 974108039, 85114581, 836816030, 50015693, 794496792, 71505008, 198502850, 343595253, 99960447, 668567450, 539539158, 315769189, 157827735, 660803721, 774061860, 666772859, 293307559, 359456090, 480173308, 672946567, 146961639, 254863350, 776892188, 184690263, 951930000, 281491874, 969875025, 956252557, 512957310, 575534808, 694932336, 309804549, 575309564, 343264882, 505238390, 730009504, 773860663, 555444664, 969205713, 875244714, 913810964, 139976224, 907484091, 373769216, 467805256, 692975453, 449134597, 820983376, 773921663, 477275237, 701131975, 808215675, 367427120, 973757438, 110746881, 506824095, 35046920, 423247210, 810004601, 712032992, 939034392, 822585046, 997026023, 810442266, 705972855, 228925467, 722236713, 865395167, 4984187, 910010726, 351772541, 962591774, 4984624, 998817053, 27635291, 41944104, 388280238, 612326764, 418887744, 272790625, 417675531, 792686547, 764751496, 295498608, 420967262, 422583490, 160580018, 681240929, 877397358, 939348441, 199903532, 692040080, 504208481, 239444877, 657415626, 301919466, 48474721, 37099210, 753583333, 420113466, 226905147, 933820405, 814494926, 375265324, 848462080, 709005417, 404634715, 689388129, 991490490, 787038721, 728974569, 22200747, 593301699, 45177644, 63918780, 425989558, 987443057, 381071774, 123184938, 5271010, 983571654, 811562410, 882800207, 929764151, 954296087, 601719085, 91906353, 526560992, 66817564, 790457379, 461273122, 475883275, 475538317, 900464070, 758237478, 898179092 }

  18. {82484, 21784, 2348, 51028, 24820, 27430, 67815, 99374, 10766, 38797, 78762, 7152, 52534, 61393, 70684, 60221, 63449, 40836, 12081, 17390, 55158, 63677, 97525, 30737, 14535, 78500, 55575, 45964, 65771, 26585, 49868, 42834, 46169, 17478, 46393, 13429, 83961, 8071, 98799, 50038, 97500, 10846, 61136, 68031, 35618, 70489, 48788, 41554, 94452, 64261, 74134, 9982, 72669, 45050, 4006, 24150, 54454, 53250, 96793, 94558, 49250, 95946, 59066, 68572, 37020, 40436, 48705, 66756, 63423, 29578, 75775, 61513, 44049, 86460, 49443, 10572, 36186, 41278, 31154, 26544, 9961, 27765, 92734, 72358, 44740, 75358, 91976, 55979, 94911, 4936, 62594, 99214, 24181, 58750, 43578, 8128, 385, 59375, 6105, 40337, 12235, 52155, 67708, 17831, 42760, 24139, 36687, 83237, 17661, 86338, 13646, 97962, 19950, 74375, 9297, 47163, 43356, 67588, 25156, 79899, 80522, 49666, 64655, 40508, 27863, 70350, 11239, 38294, 34038, 18394, 99778, 49201, 35645, 75785, 88164, 6377, 12657, 16070, 29259, 81317, 60810, 6935, 30235, 16854, 49734, 85370, 85108, 81069, 8512, 41981, 56087, 15424, 37994, 7084, 1530, 89678, 71760, 25441, 22683, 44925, 87157, 73454, 35631, 94735, 48905, 46675, 75782, 44421, 55187, 81837, 61065, 35060, 67914, 9031, 2327, 55499, 38855, 6524, 26333, 87651, 33182, 55190, 20902, 44519, 44900, 49410, 17294, 18304, 22375, 80883, 44546, 40536, 24904, 54187, 58944, 69238, 33398, 72862, 71202, 82450, 67651, 46818, 33350, 48082, 98496, 94231, 69554, 31673, 6912, 97184, 49049, 88602, 2323, 22911, 59785, 5746, 19543, 84297, 3994, 8837, 16411, 26977, 29283, 93811, 59616, 21015, 12446, 98146, 30450, 70228, 66168, 5348, 1989, 78927, 67734, 17028, 22476, 88059, 14607, 51648, 89536, 77574, 29101, 80286, 25913, 65069, 24313, 4701, 9725, 62311, 83561, 48479, 31589, 92415, 91181, 12262, 86759, 73863, 98945, 50000, 54597, 48056, 44047, 80250, 4914, 7790, 92068, 2320, 83847, 66553, 36466, 73778, 70389, 87862, 63180, 34995, 4573, 62546, 90446, 78526, 69718, 42935, 90000, 50068, 95966, 2376, 41425, 47648, 31528, 59208, 34121, 72274, 48135, 16542, 4055, 53690, 93079, 2726, 22838, 58194}

    {4, 243, 233, 262, 84, 215, 201, 187, 243, 273, 185, 171, 190, 150, 270, 165, 279, 163, 267, 140, 195, 100, 288, 81, 15, 94, 163, 49, 244, 140, 41, 152, 164, 293, 52, 134, 81, 274, 143, 183, 2, 243, 132, 32, 282, 181, 74, 209, 28, 20, 213, 44, 270, 139, 83, 68, 293, 104, 129, 243, 42, 183, 8, 1, 242, 166, 250, 56, 298, 228, 110, 166, 122, 168, 35, 149, 222, 209, 117, 135, 90, 51, 190, 257, 136, 140, 145, 115, 162, 43, 68, 247, 50, 153, 73, 28, 298, 205, 40, 250, 49, 126, 241, 192, 37, 37, 97, 290, 149, 177, 206, 36, 280, 103, 195, 235, 248, 297, 252, 112, 218, 186, 223, 244, 38, 201, 246, 149, 112, 64, 225, 257, 239, 265, 253, 153, 3, 234, 271, 263, 147, 249, 290, 56, 170, 193, 36, 133, 18, 26, 12, 56, 158, 125, 103, 272, 51, 74, 258, 27, 104, 237, 44, 235, 164, 56, 60, 189, 225, 88, 38, 38, 119, 17, 173, 87, 2, 137, 59, 98, 160, 36, 150, 254, 47, 55, 110, 171, 202, 237, 223, 101, 42, 151, 58, 121, 116, 145, 38, 71, 21, 216, 192, 217, 76, 222, 147, 190, 205, 173, 299, 105, 252, 94, 235, 132, 197, 160, 170, 29, 200, 190, 139, 132, 203, 260, 82, 125, 59, 198, 23, 70, 273, 127, 86, 244, 174, 116, 247, 174, 134, 254, 142, 115, 229, 172, 242, 299, 53, 136, 61, 293, 115, 269, 120, 25, 296, 92, 117, 117, 215, 38, 246, 6, 290, 276, 275, 230, 167, 71, 131, 278, 25, 168, 181, 125, 165, 0, 211, 131, 141, 191, 111, 254, 22, 295, 142, 73, 72, 130, 60, 56, 217, 247, 271, 281, 160, 84, 125, 288}

    Returns: {797884315, 843353014, 689429265, 763892037, 600545818, 795335068, 432164271, 950873983, 772356040, 20225024, 197459094, 305966, 306305923, 267804019, 960612969, 272951940, 443818823, 910038859, 61620662, 107705290, 488063396, 645096583, 504445576, 283091776, 964321336, 226812986, 538961596, 131568769, 770036973, 909730309, 172644817, 983887981, 467790047, 830419428, 88989501, 353242043, 51490592, 195536766, 71546336, 954972028, 338793066, 635771776, 76421726, 388420708, 818112361, 720547100, 457059177, 116923276, 397980309, 68952067, 142539395, 421600106, 601515794, 678226056, 482289444, 701763168, 901535954, 781078305, 419597995, 654984605, 401791737, 840560100, 645208348, 949450819, 117605319, 330477398, 414188390, 761363402, 615246861, 712266945, 114748493, 20750923, 351894119, 112433073, 848394887, 511663552, 420291705, 222264680, 692782141, 469941651, 714564254, 559508465, 963156267, 342312068, 445262271, 304997490, 361898398, 406486531, 193388246, 493830418, 73624682, 868514976, 132526292, 779020196, 632834836, 623608937, 175377753, 744076979, 250659516, 712333259, 303114089, 654008626, 779172265, 622396519, 186288615, 410519312, 297846182, 389851045, 514352775, 173961450, 719151191, 935709541, 430849166, 720198111, 937140501, 127985153, 290848747, 60784219, 947879042, 418620346, 617418545, 180090767, 625860266, 852682140, 407876880, 952513345, 897062827, 318736196, 310276847, 795618747, 172227580, 272565508, 451505469, 544981320, 286696439, 265679202, 969413102, 389912550, 972481156, 957721583, 395733945, 954798892, 905216900, 923654839, 194717343, 661043989, 681957117, 95876720, 351953038, 295294289, 209439530, 737436301, 398968601, 149389440, 191436546, 332457291, 586489176, 726789333, 735312890, 196580459, 407346144, 730740097, 592051378, 332830081, 781341040, 820851965, 193299203, 482299662, 141181057, 71508637, 745114062, 93091916, 461224741, 409934796, 378666964, 600309117, 595355805, 309458311, 750759993, 438954948, 112612816, 161101526, 334281541, 957075387, 750244747, 146828953, 791682256, 426024368, 589487915, 838060793, 695667602, 901629226, 282304466, 102907382, 349781989, 914645721, 337265503, 956861509, 668280448, 494874568, 219267829, 226173456, 721040987, 807268802, 943643797, 926013670, 14492372, 857650664, 396946077, 179418951, 357397506, 853762268, 658569758, 802395367, 938599230, 877305609, 102621060, 60849545, 244529997, 164189576, 204515758, 37131958, 895986580, 888440290, 172679752, 581252292, 37598570, 420114584, 512820276, 34667827, 554656137, 52048532, 186198304, 225680818, 889085647, 213479983, 639353647, 421697779, 167660847, 882027761, 982373583, 410664633, 464186123, 69615199, 909186051, 478827798, 954705553, 876408862, 33785901, 299682273, 460892713, 632609401, 565309652, 580124699, 617666595, 252661493, 88564366, 942392284, 295036219, 592529215, 184962338, 588110915, 351352125, 484310770, 535098818, 790665801, 361332188, 155227776, 190204224, 531632854, 138649086, 143407528, 567040411, 25883658, 136179362, 472880816, 886115424, 812042829, 328547403, 625741824, 361076339, 317772631, 784182749, 569281372, 394494718, 312353163, 595140331, 758342115, 917600995, 330957482, 385489665, 325709321, 632691058, 983737419, 411279315, 298521446, 374967200, 902688970, 27346559, 554920029 }

  19. {29873, 83912, 94106, 62179, 79735, 97454, 1797, 75852, 84641, 1652, 89197, 83011, 28528, 76224, 55835, 59443, 45367, 3823, 20210, 57965, 9895, 86221, 39164, 17218, 73528, 91036, 87853, 71696, 98896, 42512, 53896, 93219, 32245, 54703, 89163, 99543, 18732, 32237, 35480, 83225, 13573, 1257, 42075, 69536, 8869, 7969, 61983, 33190, 79581, 1815, 96084, 8280, 81672, 11324, 83994, 23003, 86687, 87065, 52207, 96521, 21148, 52472, 35254, 79950, 24325, 70011, 47452, 7867, 42178, 93904, 70598, 37253, 1515, 85720, 18238, 48682, 1554, 56172, 28797, 38007, 17131, 8237, 50288, 46517, 27888, 77815, 18090, 27111, 92789, 78505, 67752, 80615, 50266, 95478, 72579, 4371, 95099, 74312, 44050, 94055, 5726, 56262, 15374, 86834, 64134, 99681, 1268, 28977, 89181, 51089, 94455, 84568, 72657, 29526, 12449, 99071, 36829, 58246, 36740, 23877, 77521, 33231, 42685, 83555, 36029, 86737, 21229, 79394, 33998, 30450, 2836, 96548, 60762, 12366, 92683, 26866, 62089, 12443, 3609, 82897, 40306, 68821, 43660, 56515, 25199, 24404, 73369, 5998, 83710, 17633, 29017, 64310, 94669, 20710, 3041, 67435, 85206, 92168, 17042, 26781, 29616, 17066, 76587, 43048, 30807, 32381, 81387, 9984, 92685, 67015, 85109, 38044, 6631, 4568, 28314, 62836, 91460, 94918, 95820, 14805, 79511, 38375, 3597, 99211, 19523, 34801, 22080, 29470, 58780, 55224, 63023, 27935, 71259, 89845, 12743, 4092, 63180, 91297, 48541, 75840, 50366, 14206, 5833, 33103, 92342, 67132, 67548, 93464, 983, 53701, 98723, 23811, 30660, 32047, 76026, 20469, 15590, 65975, 19570, 53765, 77623, 92956, 38570, 45503, 10167, 15754, 75017, 44102, 59559, 12869, 27990, 37728, 41912, 21863, 17165, 77393, 15846, 74600, 87841, 37350, 58530, 96885, 27071, 56334, 69363, 2971, 11745, 58044, 17117, 94442, 18809, 71323, 52049, 63026, 8775, 60747, 2714, 58940, 7746, 28769, 16252, 52935, 7556, 73564, 94559, 34791, 8947, 31450, 66265, 22364, 19588, 93717, 77436, 94260, 62037, 17261, 73915, 93784, 68162, 80349, 85757, 53531, 27505, 17476, 29275, 41987, 88009, 31125, 54012, 66820, 38925, 76942, 74957, 95626, 18047, 2406, 23035, 12538, 26771, 27983}

    {77, 41, 39, 26, 229, 84, 257, 48, 209, 111, 252, 99, 275, 214, 31, 24, 15, 38, 189, 183, 254, 70, 81, 93, 197, 27, 279, 161, 97, 284, 78, 227, 207, 176, 191, 6, 50, 265, 257, 257, 281, 278, 122, 193, 152, 157, 75, 202, 174, 29, 108, 159, 153, 159, 166, 280, 247, 2, 17, 19, 291, 25, 55, 195, 268, 188, 42, 296, 70, 265, 38, 74, 170, 177, 25, 145, 110, 240, 114, 297, 151, 224, 4, 234, 244, 253, 108, 32, 72, 205, 51, 291, 79, 138, 180, 46, 270, 210, 142, 214, 62, 139, 258, 206, 94, 77, 242, 216, 262, 47, 20, 156, 214, 196, 250, 195, 162, 235, 163, 206, 85, 264, 119, 100, 12, 31, 31, 163, 102, 26, 205, 244, 183, 210, 186, 137, 204, 268, 272, 157, 2, 120, 76, 85, 64, 292, 229, 286, 2, 16, 77, 155, 275, 204, 159, 45, 7, 121, 283, 256, 190, 231, 60, 277, 211, 212, 138, 262, 264, 43, 23, 186, 100, 253, 24, 261, 190, 15, 142, 35, 209, 71, 47, 216, 174, 53, 64, 228, 140, 224, 7, 155, 235, 159, 253, 300, 38, 1, 264, 86, 54, 14, 112, 185, 44, 157, 205, 114, 110, 203, 49, 60, 226, 164, 56, 219, 100, 226, 103, 84, 259, 82, 79, 50, 195, 11, 285, 119, 40, 132, 19, 59, 64, 149, 111, 113, 156, 277, 153, 278, 150, 2, 82, 263, 284, 185, 115, 107, 143, 212, 19, 238, 275, 158, 285, 33, 10, 297, 170, 128, 198, 10, 34, 60, 144, 221, 41, 94, 195, 93, 14, 10, 26, 253, 61, 138, 137, 8, 234, 9, 242, 226, 207, 194, 7, 219, 99, 46, 217, 144, 78, 260, 163, 166, 121, 166, 171, 153, 74, 201}

    Returns: {954398016, 793455350, 532229800, 571381567, 901386989, 230738642, 288053972, 548949044, 237816907, 978526555, 227590470, 813535251, 485230758, 159302493, 345281129, 169018627, 465720680, 264879709, 488458657, 97590344, 330538768, 265118771, 476684466, 457451249, 403131451, 477892103, 491590675, 766892573, 116135172, 511132859, 483510724, 869289827, 227204180, 74825290, 891921147, 239625733, 310799915, 437332458, 764064615, 934912407, 6648373, 789233617, 227337460, 400629303, 570067883, 9809229, 234465760, 802207029, 165299652, 43393742, 131712329, 405517491, 429215763, 389555536, 237854463, 422152180, 912026301, 412521915, 266136365, 699204292, 967077858, 900446352, 559201823, 893301841, 262177561, 573358310, 359895870, 739709688, 182717219, 336783931, 369565732, 968791292, 617821869, 679247775, 45626708, 331798107, 22394385, 997906484, 476306530, 233598814, 950809104, 853804216, 359066637, 218650028, 732928411, 200015654, 486563851, 288641677, 440787059, 120854183, 978057433, 744505314, 433293816, 212584342, 83555276, 196484633, 674265620, 347979676, 925106093, 838263692, 656612544, 453927572, 168222817, 131688719, 477441357, 483933474, 549395719, 525291875, 568789156, 861037878, 415621647, 705362419, 93086183, 310967803, 988709220, 123581006, 891476943, 566787357, 985997958, 726043902, 939820994, 781802518, 658559883, 941918972, 849009019, 53934952, 682609931, 7584668, 779451208, 901755299, 238186653, 189488864, 537029129, 64173102, 134952994, 979173621, 796601682, 620024784, 642377251, 907185690, 509485581, 41775136, 705757781, 330290096, 439328215, 196657520, 648715586, 225598157, 335126417, 107613519, 479883086, 498142212, 52407026, 647857333, 353680804, 690962570, 344125182, 566383021, 704164509, 787903199, 761967544, 337620519, 537032981, 200879874, 794691598, 784396259, 570685129, 688952953, 593432859, 43117500, 120515079, 986650452, 482972695, 615749804, 429494207, 52816505, 870364502, 208856174, 9870362, 80613842, 776113633, 849768582, 259599793, 104046077, 448653356, 965919264, 821984509, 207695887, 599654759, 224083740, 26397393, 608396076, 94127307, 899574705, 688300242, 581545305, 458973369, 135067449, 152451595, 871038808, 160646904, 96387676, 679230901, 876749316, 281105045, 905748963, 159016354, 945524519, 83040946, 580747900, 513465183, 500238648, 809483469, 196944070, 287215208, 312457388, 876391715, 830626984, 50010762, 885361974, 480138001, 785798343, 26397298, 936334937, 603387356, 328540817, 730012522, 544463230, 6767566, 604221369, 454701899, 246726659, 800411257, 298723139, 433836377, 420389253, 108060416, 448899686, 750148168, 408068786, 485049239, 814448511, 818615613, 907563914, 323405891, 552396190, 718809914, 215675364, 260445957, 110566212, 217068741, 128007358, 813311073, 236077827, 48154879, 333924815, 376264272, 742971162, 793117524, 947502342, 6720392, 428699596, 908461213, 855207281, 993589983, 36888816, 733813558, 504366863, 196041905, 549640629, 875631411, 36788480, 221559329, 48633880, 844227236, 493738293, 558431400, 709460510, 62752457, 866494233, 700657652, 339244782, 165789180, 847685058, 795793411, 727067751, 110563791, 197849329, 758304782, 491585242, 495370405, 893989760, 465118125, 987578763, 378398984, 809541535, 349508653, 657365261, 522330649, 764864843 }

  20. {100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990, 99989, 99988, 99987, 99986, 99985, 99984, 99983, 99982, 99981, 99980, 99979, 99978, 99977, 99976, 99975, 99974, 99973, 99972, 99971, 99970, 99969, 99968, 99967, 99966, 99965, 99964, 99963, 99962, 99961, 99960, 99959, 99958, 99957, 99956, 99955, 99954, 99953, 99952, 99951, 99950, 99949, 99948, 99947, 99946, 99945, 99944, 99943, 99942, 99941, 99940, 99939, 99938, 99937, 99936, 99935, 99934, 99933, 99932, 99931, 99930, 99929, 99928, 99927, 99926, 99925, 99924, 99923, 99922, 99921, 99920, 99919, 99918, 99917, 99916, 99915, 99914, 99913, 99912, 99911, 99910, 99909, 99908, 99907, 99906, 99905, 99904, 99903, 99902, 99901, 99900, 99899, 99898, 99897, 99896, 99895, 99894, 99893, 99892, 99891, 99890, 99889, 99888, 99887, 99886, 99885, 99884, 99883, 99882, 99881, 99880, 99879, 99878, 99877, 99876, 99875, 99874, 99873, 99872, 99871, 99870, 99869, 99868, 99867, 99866, 99865, 99864, 99863, 99862, 99861, 99860, 99859, 99858, 99857, 99856, 99855, 99854, 99853, 99852, 99851, 99850, 99849, 99848, 99847, 99846, 99845, 99844, 99843, 99842, 99841, 99840, 99839, 99838, 99837, 99836, 99835, 99834, 99833, 99832, 99831, 99830, 99829, 99828, 99827, 99826, 99825, 99824, 99823, 99822, 99821, 99820, 99819, 99818, 99817, 99816, 99815, 99814, 99813, 99812, 99811, 99810, 99809, 99808, 99807, 99806, 99805, 99804, 99803, 99802, 99801, 99800, 99799, 99798, 99797, 99796, 99795, 99794, 99793, 99792, 99791, 99790, 99789, 99788, 99787, 99786, 99785, 99784, 99783, 99782, 99781, 99780, 99779, 99778, 99777, 99776, 99775, 99774, 99773, 99772, 99771, 99770, 99769, 99768, 99767, 99766, 99765, 99764, 99763, 99762, 99761, 99760, 99759, 99758, 99757, 99756, 99755, 99754, 99753, 99752, 99751, 99750, 99749, 99748, 99747, 99746, 99745, 99744, 99743, 99742, 99741, 99740, 99739, 99738, 99737, 99736, 99735, 99734, 99733, 99732, 99731, 99730, 99729, 99728, 99727, 99726, 99725, 99724, 99723, 99722, 99721, 99720, 99719, 99718, 99717, 99716, 99715, 99714, 99713, 99712, 99711, 99710, 99709, 99708, 99707, 99706, 99705, 99704, 99703, 99702, 99701}

    {300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300}

    Returns: {624541710, 113536636, 731805205, 565632055, 253937085, 503154962, 45402723, 140896964, 415455357, 326661501, 53366526, 839641795, 35252734, 839128579, 118967017, 125799191, 324683584, 614445000, 120797178, 128199821, 605953844, 748071947, 262671225, 396324041, 10630800, 795234806, 427098323, 880317915, 971577374, 74501654, 792334787, 522759635, 372592443, 338432576, 325184980, 151522369, 593969102, 27135009, 662306639, 732510540, 133750443, 592257572, 117360041, 403716075, 931977859, 679394379, 881425451, 382123397, 811181356, 813836758, 637988417, 311492911, 877529032, 142287873, 406966788, 252678590, 823933111, 165016653, 808059455, 788945529, 218886286, 509783897, 201568660, 659487634, 897097649, 275585773, 354797271, 745279506, 448968909, 288715625, 930875935, 730721752, 546218367, 798840772, 73037163, 834355636, 769814837, 995807971, 786732581, 732564942, 878598412, 883076283, 886935044, 359075227, 248456545, 150287987, 871740614, 144256774, 651899139, 940656962, 178727923, 838758561, 636009664, 596600057, 970361222, 289146155, 666357030, 600825990, 466441186, 368161980, 966344650, 622273074, 114418125, 427857829, 293769316, 328175537, 842048865, 389618518, 544850104, 918403300, 576035671, 765804572, 372371099, 250010166, 625140660, 573750374, 418090587, 810000567, 636362157, 586226600, 827633330, 375700599, 479918414, 27883571, 824835739, 307882280, 503092348, 993439872, 275909596, 820877212, 69329297, 480822445, 424435812, 324357505, 721154187, 496363092, 302127133, 654342297, 309817682, 607651535, 489882292, 105482129, 332526385, 504468990, 876372646, 116716702, 336986969, 913062132, 257976561, 953324031, 950919310, 35399109, 994790623, 967444317, 647903862, 900409876, 604005977, 160465747, 76624808, 497446396, 258427488, 209738334, 493302120, 358614645, 638482508, 257016962, 694604533, 828503879, 612082375, 386894062, 669774761, 91035938, 766327930, 695598029, 889440488, 548151164, 833888571, 479692357, 201946754, 522409714, 484998180, 223880774, 912888552, 524935868, 805097909, 244206821, 5868081, 177928523, 823781888, 16229083, 133517094, 955586883, 132618611, 24110003, 74997016, 157675844, 992583864, 208882783, 712069654, 353404527, 700205571, 601286900, 965050991, 689804910, 839359547, 760034991, 34853569, 565257570, 351002307, 752159853, 484536250, 108469153, 562169103, 50680224, 375329149, 964195018, 656754613, 632848049, 642996391, 835979389, 372807642, 116261394, 861030562, 694962773, 272093848, 905670992, 621960642, 641403734, 110413874, 419111460, 66325253, 345799152, 609533846, 748272594, 331446311, 7863348, 764867040, 616007404, 881213367, 878060535, 683916137, 293375582, 186829182, 869857271, 78027384, 799023526, 106162699, 968912540, 620571527, 261270125, 459811232, 862044337, 568257297, 696341038, 665293224, 59570580, 735119921, 163477150, 436672738, 6177461, 775490117, 20140865, 372047511, 626038832, 690911746, 442797998, 849610691, 202194829, 199607343, 394291757, 875000146, 665621599, 778364507, 320935753, 755287196, 417255807, 715521117, 734197069, 6338017, 377561969, 494263407, 491154025, 973417371, 410254022, 143508230, 246198954, 47671562, 878342823, 100476012, 365613099, 388096594, 480461954, 842093691, 855675915, 527608295, 83326704, 899110832, 459082761, 908726099, 989652301 }

  21. {34367, 64505, 62961, 84329, 66985, 16518, 3205, 71205, 67942, 95996, 89120, 97820, 11572, 33694, 6188, 26581, 76547, 90611, 74448, 88029, 83094, 40605, 25228, 95529, 85697, 30470, 10027, 90878, 58743, 8261, 21995, 90002, 4972, 72048, 32484, 70371, 22878, 3109, 99332, 42494, 80359, 20780, 26770, 46695, 24678, 88836, 46069, 58265, 89589, 78084, 73973, 34945, 97465, 95730, 9013, 93762, 39277, 67433, 98632, 36515, 6491, 12327, 12462, 59682, 74002, 99119, 92848, 39525, 1211, 35818, 3704, 73439, 91280, 31954, 7670, 62314, 13836, 78534, 70851, 96862, 84402, 51763, 1290, 80659, 34288, 87051, 92538, 9243, 63035, 38722, 31094, 55445, 4477, 62817, 36004, 68033, 8318, 67088, 72694, 25559, 95988, 6544, 57054, 53772, 74381, 535, 43666, 65511, 88060, 46700, 79926, 60744, 96582, 1771, 52114, 54728, 11038, 31804, 25394, 86952, 6582, 83606, 76491, 62489, 4725, 48259, 68962, 28463, 95951, 39638, 53996, 46748, 5841, 45293, 874, 77858, 94709, 47519, 6279, 33754, 43386, 27027, 21183, 16336, 58796, 70351, 58864, 2707, 10704, 81276, 56995, 76515, 41695, 85742, 18978, 12382, 30054, 94566, 49047, 26123, 31573, 15203, 69561, 48423, 92704, 33179, 54904, 51290, 897, 74256, 60020, 63520, 25525, 91640, 43567, 79555, 62423, 60155, 3693, 34374, 89396, 66256, 17760, 14675, 82643, 77481, 5054, 20099, 26315, 88493, 47805, 144, 98472, 80156, 2181, 28183, 57466, 72761, 23632, 25618, 15447, 7575, 1810, 36448, 21257, 93476, 50991, 50055, 42176, 39423, 49959, 69899, 90873, 14673, 36728, 65318, 97443, 54886, 65780, 15224, 28125, 34806, 24975, 12405, 26452, 59876, 65048, 45370, 89460, 15384, 22090, 89663, 36524, 78075, 18928, 81821, 64446, 81313, 93419, 89167, 26491, 54999, 77923, 86892, 38534, 77906, 9271, 83799, 43429, 36863, 30740, 2581, 6982, 8409, 97494, 80642, 82600, 89405, 9996, 61381, 28429, 5622, 60596, 26793, 17334, 60297, 33376, 12799, 95746, 54907, 872, 16131, 61468, 76613, 88733, 73127, 56883, 38083, 73872, 48547, 50606, 81250, 1941, 52597, 84644, 19509, 82682, 28116, 80582, 38286, 99222, 75042, 71318, 32038, 60739, 20870, 94403, 51130, 69559, 78237 }

    {270, 69, 288, 174, 198, 209, 267, 239, 239, 223, 14, 92, 287, 1, 63, 94, 90, 77, 295, 109, 38, 279, 155, 222, 178, 121, 121, 290, 162, 197, 258, 287, 120, 242, 126, 148, 129, 51, 115, 169, 246, 18, 73, 276, 45, 246, 162, 138, 185, 240, 202, 214, 235, 144, 115, 291, 215, 67, 296, 77, 88, 277, 77, 43, 265, 27, 272, 45, 175, 216, 266, 39, 263, 126, 163, 20, 207, 180, 178, 233, 259, 283, 106, 222, 295, 45, 52, 277, 127, 136, 234, 63, 55, 38, 82, 270, 242, 30, 12, 18, 274, 118, 263, 270, 275, 163, 252, 109, 282, 96, 85, 36, 189, 64, 119, 106, 172, 155, 48, 220, 276, 296, 218, 40, 282, 203, 284, 225, 45, 194, 78, 177, 168, 161, 260, 142, 20, 136, 248, 133, 94, 243, 295, 32, 51, 198, 175, 292, 220, 276, 98, 88, 282, 92, 43, 278, 201, 224, 288, 73, 179, 27, 65, 88, 19, 209, 168, 29, 104, 278, 86, 36, 208, 216, 127, 33, 1, 186, 289, 84, 29, 293, 6, 69, 96, 291, 195, 77, 119, 282, 242, 97, 149, 175, 254, 67, 179, 208, 14, 143, 31, 146, 189, 242, 191, 62, 181, 67, 266, 10, 277, 15, 235, 204, 44, 187, 22, 296, 293, 29, 15, 92, 210, 122, 37, 289, 188, 33, 263, 60, 154, 94, 173, 147, 54, 183, 104, 64, 179, 35, 110, 129, 112, 109, 6, 228, 163, 245, 132, 67, 46, 184, 216, 286, 129, 240, 236, 67, 206, 202, 174, 149, 104, 206, 157, 183, 142, 89, 151, 161, 83, 258, 118, 258, 219, 186, 280, 102, 117, 110, 127, 244, 202, 196, 15, 270, 179, 188, 18, 114, 248, 38, 158, 277, 161, 262, 25, 206, 252, 123 }

    Returns: {155553019, 314458191, 470288944, 170634447, 392737942, 512309382, 626818373, 291737631, 63056001, 188812178, 360849433, 842489316, 632445790, 880207826, 587582386, 598166741, 275245768, 652073016, 995338184, 135880977, 93180669, 449589106, 153185314, 181751711, 589054869, 17267978, 32155966, 198364116, 681952648, 845323939, 363417685, 186768054, 742152483, 368868540, 655291098, 580448553, 378767292, 441692412, 124306691, 383100234, 126601394, 849067450, 139417200, 357495300, 445439918, 211358617, 324672684, 945711002, 245210000, 550188760, 444260213, 517645060, 569327879, 302040302, 667672640, 251383533, 634144139, 873251243, 436734492, 673215660, 673864756, 686258888, 482249706, 343786166, 932766890, 603924520, 317143395, 894529028, 319058287, 851245558, 629775199, 788189964, 199935605, 460617222, 512202870, 18751459, 567592137, 105963738, 947325253, 33896262, 372816657, 840421911, 519300361, 318134556, 338873915, 369581553, 38870133, 309939172, 706340489, 570845531, 190745774, 423178947, 378697480, 323444698, 53456262, 84931292, 968904287, 432381407, 915410884, 847305347, 151177551, 186943689, 608183617, 9969446, 231525127, 244638843, 765398521, 721497132, 423971221, 296213134, 817646663, 297471830, 518868602, 125732456, 409541081, 74830966, 529123092, 830764660, 253018240, 159861396, 232632934, 121210423, 562582221, 437947772, 248796137, 927206518, 957793440, 120123650, 477879921, 440745169, 230874457, 918824878, 974683940, 916051461, 205097880, 486516691, 826605271, 8632040, 916408139, 973983877, 877729938, 404475358, 18792816, 408592359, 469974506, 869771378, 555470712, 590082721, 639486425, 613817992, 968531029, 287750452, 343299788, 360303163, 921363197, 957211635, 132022286, 619509715, 44933882, 987508007, 406018064, 862542763, 749798034, 42575588, 761605435, 166231961, 690612794, 403810360, 238260656, 730264872, 906680707, 267106386, 739821154, 728114603, 610249580, 448057547, 709174344, 299468293, 736127573, 705140983, 50652483, 583874092, 786365749, 381139443, 789382635, 348478470, 850963533, 52731211, 840273836, 710368710, 986271445, 768380610, 87544508, 516355763, 543973031, 925953352, 741550278, 587481637, 252217384, 895544190, 505512129, 672637793, 38247122, 778760177, 315560456, 753957788, 465863261, 38261975, 172778311, 249304376, 307211668, 454283345, 46369978, 369410182, 48347746, 811699480, 526862253, 160970218, 404517349, 413794589, 523192055, 140045510, 842469768, 776578744, 269906601, 141607974, 943463223, 661901543, 731745164, 769046450, 128068183, 365035496, 267314840, 580583840, 480063767, 746833391, 873518282, 658603742, 842761178, 157948301, 261767668, 516244214, 706503487, 388548977, 531991657, 330275425, 404360686, 250528343, 645618153, 56316589, 333835938, 469602483, 716905884, 737152456, 233367495, 787213140, 401475706, 763610849, 748362834, 415883183, 890162338, 407118412, 409608851, 96547136, 772517386, 842507414, 211809810, 442253482, 341833665, 966045072, 445107703, 999109292, 557095765, 443286490, 777901311, 48967155, 156241024, 920638176, 308300379, 566982705, 842696777, 375936043, 255752627, 207320293, 803623442, 425529123, 577074502, 454134069, 712347602, 896592035, 176272292, 904446393, 367167202, 307466964, 92314031, 288934521, 871187402, 415530406, 369241129, 693709704 }

  22. {100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000 }

    {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300 }

    Returns: {139880539, 32329537, 140001995, 671972940, 798149454, 905350221, 706925861, 645309389, 648176724, 691989817, 486213074, 651977153, 142593165, 604392660, 82258976, 391268268, 772746203, 453520411, 299853696, 847524767, 443071747, 429007870, 595747254, 266706643, 938681076, 119736775, 900905562, 758736986, 351337103, 566754712, 130992056, 704073661, 827032424, 803789486, 361765766, 85049519, 255230589, 220447151, 767530948, 38493688, 820501851, 480962217, 161308469, 998717096, 400293514, 601713211, 17903876, 770337124, 364556306, 179209412, 899992054, 297076846, 853478206, 694066477, 628496981, 651259478, 297374933, 853591669, 610339536, 671115183, 793560364, 889114848, 460994653, 178710936, 321375919, 220242228, 4448934, 465094660, 192705674, 18226562, 685174891, 758248991, 750880674, 685332086, 83569947, 170852436, 800213502, 267497915, 934126390, 496014840, 340369566, 148113579, 417361421, 78931325, 895294269, 355294487, 19830392, 802486068, 370724742, 879261996, 212734826, 715756882, 653611765, 146598915, 395765867, 460338210, 526610599, 429260914, 735737644, 341570876, 505240768, 658558017, 400485290, 600240531, 212261247, 50868650, 411599637, 753818442, 768460138, 194076571, 166678559, 421817010, 129164473, 115128933, 886019277, 710591841, 423144653, 743148219, 361084551, 38510201, 539296291, 989664127, 252174592, 282720825, 750471272, 983443233, 771383272, 100067823, 836501996, 870462159, 698585930, 112084050, 371603489, 263386419, 450943718, 341636274, 290565293, 596096494, 724626972, 636450802, 852809508, 835497860, 316960528, 571297803, 70854501, 614443135, 207161949, 905110968, 582518927, 918082914, 404330499, 591710509, 336337777, 866447075, 680416761, 582833043, 101173742, 896597927, 311208754, 948653944, 974985486, 341848776, 696041622, 454141250, 262378370, 731949227, 157377261, 276993539, 148792428, 764220451, 504196107, 481894766, 943185942, 954021874, 553536410, 320183771, 843143940, 342477167, 179656086, 341013254, 326498250, 18491251, 787390262, 290139965, 504281761, 311276252, 350334939, 880853430, 945713426, 540527078, 928841738, 525538358, 204625118, 298701748, 305421801, 130620316, 124877350, 127247914, 822683945, 226420460, 517335847, 343541049, 154836410, 169884350, 76725787, 251614233, 923268650, 672335585, 52172808, 529450130, 993676053, 677594022, 879732608, 477415059, 798346537, 183732268, 708833604, 634364253, 90173358, 969440336, 174560971, 649893790, 581149083, 377956051, 8782921, 161826987, 31943486, 812510815, 723877872, 425632792, 411842520, 321052000, 839437185, 614110214, 463808433, 415681507, 561975758, 832362784, 290190673, 58899282, 924513481, 51047412, 748140775, 800086510, 64250690, 460695358, 480871922, 501583964, 387359283, 874682712, 339123833, 164014781, 447353486, 850505225, 750356201, 676395474, 387595277, 461667169, 397646728, 559087921, 636465104, 60972641, 547618280, 36182108, 49928710, 252234169, 61264344, 297500272, 578606529, 260741613, 165701697, 749473452, 81245117, 953062000, 444815851, 69948586, 347292899, 190663096, 220553914, 376839847, 996815348, 107748074, 198641889, 78569005, 584392421, 863936262, 914947678, 519398313, 474896767, 219714112, 627122348, 616041457, 126343319, 125447206, 926542303, 837116874, 33908056, 708470253, 473016754, 624541710 }

  23. {100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990, 99989, 99988, 99987, 99986, 99985, 99984, 99983, 99982, 99981, 99980, 99979, 99978, 99977, 99976, 99975, 99974, 99973, 99972, 99971, 99970, 99969, 99968, 99967, 99966, 99965, 99964, 99963, 99962, 99961, 99960, 99959, 99958, 99957, 99956, 99955, 99954, 99953, 99952, 99951, 99950, 99949, 99948, 99947, 99946, 99945, 99944, 99943, 99942, 99941, 99940, 99939, 99938, 99937, 99936, 99935, 99934, 99933, 99932, 99931, 99930, 99929, 99928, 99927, 99926, 99925, 99924, 99923, 99922, 99921, 99920, 99919, 99918, 99917, 99916, 99915, 99914, 99913, 99912, 99911, 99910, 99909, 99908, 99907, 99906, 99905, 99904, 99903, 99902, 99901, 99900, 99899, 99898, 99897, 99896, 99895, 99894, 99893, 99892, 99891, 99890, 99889, 99888, 99887, 99886, 99885, 99884, 99883, 99882, 99881, 99880, 99879, 99878, 99877, 99876, 99875, 99874, 99873, 99872, 99871, 99870, 99869, 99868, 99867, 99866, 99865, 99864, 99863, 99862, 99861, 99860, 99859, 99858, 99857, 99856, 99855, 99854, 99853, 99852, 99851, 99850, 99849, 99848, 99847, 99846, 99845, 99844, 99843, 99842, 99841, 99840, 99839, 99838, 99837, 99836, 99835, 99834, 99833, 99832, 99831, 99830, 99829, 99828, 99827, 99826, 99825, 99824, 99823, 99822, 99821, 99820, 99819, 99818, 99817, 99816, 99815, 99814, 99813, 99812, 99811, 99810, 99809, 99808, 99807, 99806, 99805, 99804, 99803, 99802, 99801, 99800, 99799, 99798, 99797, 99796, 99795, 99794, 99793, 99792, 99791, 99790, 99789, 99788, 99787, 99786, 99785, 99784, 99783, 99782, 99781, 99780, 99779, 99778, 99777, 99776, 99775, 99774, 99773, 99772, 99771, 99770, 99769, 99768, 99767, 99766, 99765, 99764, 99763, 99762, 99761, 99760, 99759, 99758, 99757, 99756, 99755, 99754, 99753, 99752, 99751, 99750, 99749, 99748, 99747, 99746, 99745, 99744, 99743, 99742, 99741, 99740, 99739, 99738, 99737, 99736, 99735, 99734, 99733, 99732, 99731, 99730, 99729, 99728, 99727, 99726, 99725, 99724, 99723, 99722, 99721, 99720, 99719, 99718, 99717, 99716, 99715, 99714, 99713, 99712, 99711, 99710, 99709, 99708, 99707, 99706, 99705, 99704, 99703, 99702, 99701 }

    {217, 214, 223, 285, 207, 265, 214, 208, 251, 279, 238, 273, 210, 241, 237, 274, 260, 274, 228, 264, 289, 232, 233, 271, 218, 270, 238, 277, 233, 265, 271, 298, 278, 242, 231, 233, 207, 244, 289, 258, 271, 227, 279, 281, 216, 263, 202, 276, 285, 230, 287, 274, 209, 220, 244, 227, 238, 230, 204, 219, 295, 275, 216, 273, 264, 295, 254, 271, 287, 243, 276, 205, 218, 255, 286, 233, 266, 236, 257, 250, 213, 292, 224, 222, 212, 216, 297, 249, 246, 201, 268, 240, 224, 232, 261, 288, 274, 214, 206, 261, 205, 230, 266, 222, 233, 299, 203, 298, 283, 208, 248, 244, 299, 220, 214, 259, 235, 211, 256, 281, 260, 271, 269, 283, 203, 229, 219, 225, 291, 273, 233, 244, 203, 247, 214, 235, 294, 217, 281, 276, 272, 229, 268, 271, 297, 281, 230, 232, 292, 285, 260, 251, 204, 277, 282, 255, 254, 249, 279, 245, 221, 212, 236, 272, 259, 250, 207, 300, 266, 236, 276, 286, 213, 244, 257, 209, 273, 235, 241, 264, 268, 249, 263, 272, 225, 293, 226, 279, 242, 205, 271, 263, 265, 207, 282, 272, 257, 289, 272, 271, 224, 296, 257, 237, 287, 262, 294, 260, 296, 282, 272, 212, 231, 283, 283, 204, 276, 257, 230, 217, 210, 201, 228, 275, 256, 210, 295, 261, 246, 214, 231, 218, 258, 236, 203, 293, 245, 296, 252, 289, 278, 272, 201, 257, 254, 232, 260, 278, 289, 290, 295, 299, 239, 270, 222, 295, 280, 264, 256, 274, 278, 235, 292, 284, 218, 242, 276, 263, 238, 276, 300, 264, 248, 201, 221, 250, 232, 229, 227, 269, 219, 270, 267, 206, 240, 237, 201, 219, 201, 204, 241, 227, 287, 232, 210, 205, 274, 234, 216, 260 }

    Returns: {708833604, 612094250, 221743597, 79781818, 594586800, 542755622, 301733242, 18563218, 484678571, 707992723, 25471123, 863975150, 650128401, 448566404, 290248926, 391322184, 534852168, 701045990, 876729313, 768076034, 389302592, 921384804, 34535055, 440981231, 437037185, 813321405, 422933577, 865141418, 714162520, 337707306, 685937461, 604342590, 643659896, 554011532, 936012214, 885936322, 706612344, 107688336, 4997689, 980401078, 147409878, 584280947, 239956388, 148333240, 980779096, 814387920, 654703579, 430223011, 619427059, 661193119, 629699151, 403315907, 126508372, 911773931, 131251891, 384081583, 939247244, 248854490, 18135854, 538529226, 220008934, 350129157, 567748517, 828252382, 424142784, 543965238, 237299094, 392279791, 954349451, 980532675, 184378930, 658212081, 54100542, 820296115, 22041588, 532153617, 184510412, 156999126, 543090108, 44230417, 347099507, 280887167, 321832849, 178052198, 625102864, 20288477, 491834167, 19315418, 406811260, 435869278, 108297578, 388364300, 49335797, 32402339, 210480700, 141024682, 545725564, 412846932, 435945240, 10696370, 402506238, 178027991, 449916688, 135903098, 243989120, 645259184, 793744255, 868974915, 161892441, 201501577, 595015898, 897592484, 710011785, 88684867, 419720456, 855963394, 529392734, 119545783, 605829270, 823186808, 146736596, 356284153, 87087438, 833117531, 460655472, 553483600, 604356319, 652622044, 50009643, 780646147, 35146507, 247605470, 605699494, 279300515, 815045061, 414274538, 431316460, 96325942, 953664824, 956510868, 984421975, 796353920, 950033899, 699748079, 186081773, 135334723, 544781559, 955245262, 284137537, 601837943, 828176342, 397502888, 885618610, 816375988, 881940656, 245370104, 629240351, 11392435, 421635535, 555870029, 843726683, 831745783, 539711714, 410554308, 687800163, 560647837, 470714018, 828503879, 532438369, 916797025, 49836376, 606848441, 712850423, 700834098, 470495677, 64881770, 691442196, 921319646, 957976598, 19957100, 836845080, 535134827, 571189403, 547535211, 389897486, 882938922, 192332624, 814510590, 252149570, 972256220, 668303099, 712800251, 503243380, 896186941, 4064953, 238700309, 688237489, 540537516, 588827504, 575613579, 344583870, 907809075, 607065993, 785922023, 393266739, 282942074, 98396150, 905469668, 611776785, 494499853, 237873859, 203720853, 379101206, 52805716, 46579333, 28138091, 197625363, 155251251, 154348639, 165162930, 599875496, 544102813, 27885405, 282059511, 913342832, 466450574, 494836071, 858108747, 543829733, 805350313, 534264511, 691955985, 499375488, 488565267, 843964636, 410521788, 770935903, 108600167, 380372108, 234445456, 439127872, 803578243, 27407880, 244547142, 520802082, 702033428, 179978127, 886322114, 972162744, 86821784, 637837226, 851508250, 431870239, 222322940, 718581065, 754456706, 178866904, 780714426, 171514000, 560656087, 738817780, 348678965, 804010824, 783830181, 70035522, 792263666, 204631598, 371738722, 519181016, 516593971, 875000146, 976061531, 547403607, 282314190, 776131624, 865862150, 735618659, 136133739, 509021046, 494755448, 106680768, 561649188, 149836585, 121305058, 970925881, 834339900, 598450010, 785587389, 183517302, 849005017, 906186226, 997078004, 300639712, 477025806, 347220409, 232039482, 648597644, 675171028, 267253970, 79042415 }

  24. {10000 }

    {200 }

    Returns: {260528730 }

  25. {100000 }

    {300 }

    Returns: {624541710 }

  26. {100000, 99999, 99998 }

    {300, 300, 300 }

    Returns: {624541710, 113536636, 731805205 }

  27. {99000, 99001, 99002, 99003, 99004, 99005, 99006, 99007, 99008, 99009, 99010, 99011, 99012, 99013, 99014, 99015, 99016, 99017, 99018, 99019, 99020, 99021, 99022, 99023, 99024, 99025, 99026, 99027, 99028, 99029, 99030, 99031, 99032, 99033, 99034, 99035, 99036, 99037, 99038, 99039, 99040, 99041, 99042, 99043, 99044, 99045, 99046, 99047, 99048, 99049, 99050, 99051, 99052, 99053, 99054, 99055, 99056, 99057, 99058, 99059, 99060, 99061, 99062, 99063, 99064, 99065, 99066, 99067, 99068, 99069, 99070, 99071, 99072, 99073, 99074, 99075, 99076, 99077, 99078, 99079, 99080, 99081, 99082, 99083, 99084, 99085, 99086, 99087, 99088, 99089, 99090, 99091, 99092, 99093, 99094, 99095, 99096, 99097, 99098, 99099, 99100, 99101, 99102, 99103, 99104, 99105, 99106, 99107, 99108, 99109, 99110, 99111, 99112, 99113, 99114, 99115, 99116, 99117, 99118, 99119, 99120, 99121, 99122, 99123, 99124, 99125, 99126, 99127, 99128, 99129, 99130, 99131, 99132, 99133, 99134, 99135, 99136, 99137, 99138, 99139, 99140, 99141, 99142, 99143, 99144, 99145, 99146, 99147, 99148, 99149, 99150, 99151, 99152, 99153, 99154, 99155, 99156, 99157, 99158, 99159, 99160, 99161, 99162, 99163, 99164, 99165, 99166, 99167, 99168, 99169, 99170, 99171, 99172, 99173, 99174, 99175, 99176, 99177, 99178, 99179, 99180, 99181, 99182, 99183, 99184, 99185, 99186, 99187, 99188, 99189, 99190, 99191, 99192, 99193, 99194, 99195, 99196, 99197, 99198, 99199, 99200, 99201, 99202, 99203, 99204, 99205, 99206, 99207, 99208, 99209, 99210, 99211, 99212, 99213, 99214, 99215, 99216, 99217, 99218, 99219, 99220, 99221, 99222, 99223, 99224, 99225, 99226, 99227, 99228, 99229, 99230, 99231, 99232, 99233, 99234, 99235, 99236, 99237, 99238, 99239, 99240, 99241, 99242, 99243, 99244, 99245, 99246, 99247, 99248, 99249, 99250, 99251, 99252, 99253, 99254, 99255, 99256, 99257, 99258, 99259, 99260, 99261, 99262, 99263, 99264, 99265, 99266, 99267, 99268, 99269, 99270, 99271, 99272, 99273, 99274, 99275, 99276, 99277, 99278, 99279, 99280, 99281, 99282, 99283, 99284, 99285, 99286, 99287, 99288, 99289, 99290, 99291, 99292, 99293, 99294, 99295, 99296, 99297, 99298, 99299 }

    {300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300 }

    Returns: {961513750, 509968855, 492625636, 459013461, 654262327, 433834743, 769402591, 668299171, 159981453, 704040935, 40864660, 91950448, 11710332, 327434417, 6839107, 165171955, 938157457, 8967643, 327248346, 856349719, 603969393, 492335754, 321986946, 524987575, 281449465, 240596523, 759435501, 62885414, 6777712, 223678223, 535131902, 203552444, 920486281, 239330677, 449703433, 846528594, 162034932, 801127224, 695862885, 971431523, 516513659, 787291424, 371943815, 214249086, 133721270, 319419274, 720964253, 737882012, 994486120, 132077027, 328989487, 88330213, 564676971, 656948652, 692525690, 894041531, 953991071, 483728561, 475183238, 532907022, 962731773, 664254219, 362376741, 163394102, 504402584, 486698581, 367824101, 436140330, 90633041, 289397402, 982054208, 951047773, 450002955, 943429897, 400310182, 137573283, 504193896, 495738485, 148317857, 859205306, 617775219, 671601088, 467155953, 573842621, 404450316, 398929894, 95267999, 249388322, 523215764, 446755046, 345222455, 874945280, 769123501, 685213630, 970599558, 529937191, 802882479, 150181768, 262730710, 411442607, 499553774, 13982312, 282121166, 816052965, 441243522, 520082413, 798041607, 354765645, 765707130, 85380244, 446330676, 510872630, 548451401, 209908744, 779033439, 245305883, 919275168, 959939835, 46689424, 48762245, 270906768, 718376241, 583507847, 488345983, 97170420, 337537071, 465735812, 331346769, 565177159, 327983536, 532336193, 1017226, 411431174, 22894870, 499520243, 297036327, 543095094, 554377679, 970798375, 590999476, 160535967, 325547878, 438158225, 597258852, 759541143, 289397584, 177426450, 126274384, 618091269, 824835432, 478403762, 653967275, 724507442, 766742184, 837455103, 668042375, 190622700, 344930128, 59923624, 45986528, 729515083, 796574953, 437402475, 542887908, 867203509, 343884676, 829219227, 623562155, 740282716, 795093948, 255534094, 602027430, 481758729, 447409795, 592002087, 509144613, 261646609, 483993595, 727787819, 957418692, 990875536, 731863783, 667878856, 305547391, 537138710, 719198792, 602590820, 195321844, 814276736, 802342347, 202019860, 311334897, 759930795, 699155381, 231835609, 823916118, 459432842, 155450821, 3984143, 654184608, 463757165, 704813299, 262904296, 336759433, 614364819, 642423481, 568725829, 484282284, 121166260, 606968104, 242303479, 341294321, 677130274, 802749933, 450545996, 421704816, 459556427, 61291804, 116098013, 115400461, 918053058, 673717054, 11692651, 660753362, 525979882, 778930780, 680202190, 828724411, 706141672, 135691879, 147254687, 642141037, 540907773, 200585215, 976585290, 979389375, 231795791, 205490557, 339583534, 523734102, 466415761, 200597071, 901506174, 623053115, 413997117, 883890907, 764976391, 938947487, 789544820, 944164430, 821137085, 92752522, 186637566, 360132120, 575612336, 120581229, 114188274, 425743922, 912816917, 526167258, 235109756, 519824507, 792940676, 554255777, 454417304, 440232888, 613458704, 919032418, 847636131, 92371162, 508083027, 697723175, 139066345, 350686438, 798580129, 897952097, 759189947, 642629217, 505276283, 707133872, 265187334, 62544680, 205819099, 724921070, 359319951, 247202028, 162978658, 934277755, 712186357, 5336252, 881572876, 715765182, 999968616, 168288223, 244251563, 446476175, 45230408, 945152241, 258066396, 147582905 }

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