Statistics

Problem Statement for "QuadraticIdentity"

Problem Statement

Bob likes playing with numbers. Recently he found out that (252 mod 100) = (625 mod 100) = 25, and that 162 mod 20 = 16. Mathematically speaking, 25 is a fixed point of squaring modulo 100 and 16 is a fixed point of squaring modulo 20. Bob now wonders whether he just got incredibly lucky, or whether there are many numbers like that.

For a given modulus m, find all fixed points of the function f(x) = x2 mod m.

Let A be an array that contains all the distinct values x such that 0 <= x < m and x = (x2 mod m), sorted in increasing order. Compute the array A. If A has at most 500 elements, return it.

Otherwise, to keep the output reasonably small, we will compress A as follows: While A has strictly more than 500 elements, repeatedly discard all elements whose indices are odd. (Each iteration of this cycle reduces A to approximately half of its previous length.) Once A has 500 or fewer elements, return it. For example, if the actual array A has 1011 elements, you would return an array with 253 elements. These would be the elements that had indices 0, 4, 8, 12, ... in the original array A.

Definition

Class:
QuadraticIdentity
Method:
getFixedPoints
Parameters:
long
Returns:
long[]
Method signature:
long[] getFixedPoints(long m)
(be sure your method is public)

Notes

  • It can be shown that under the constraints of the problem there are never more than 105 fixed points.

Constraints

  • m will be between 1 and 1015, inclusive.

Examples

  1. 20

    Returns: {0, 1, 5, 16 }

    The values 0 and 1 are fixed points for squaring modulo any m >= 2. We can easily verify that (52 mod 20) = (25 mod 20) = 5, hence 5 is also a fixed point of squaring modulo 20. The fourth one is mentioned in the problem statement. We can also verify that no other numbers between 0 and 19, inclusive, have this property. For example, (72 mod 20) = (49 mod 20) = 9, and 7 is not 9, hence 7 is not a fixed point in this case.

  2. 4262046602

    Returns: {0, 1, 27391046, 152613648, 180004693, 333799345, 361190390, 513804038, 541195083, 621181264, 648572309, 801185957, 828577002, 941255910, 968646955, 982371654, 1009762699, 1121260603, 1148651648, 1162376347, 1189767392, 1302446300, 1329837345, 1482450993, 1509842038, 1589828219, 1617219264, 1769832912, 1797223957, 1951018609, 1978409654, 2103632256, 2131023301, 2131023302, 2158414347, 2283636949, 2311027994, 2464822646, 2492213691, 2644827339, 2672218384, 2752204565, 2779595610, 2932209258, 2959600303, 3072279211, 3099670256, 3113394955, 3140786000, 3252283904, 3279674949, 3293399648, 3320790693, 3433469601, 3460860646, 3613474294, 3640865339, 3720851520, 3748242565, 3900856213, 3928247258, 4082041910, 4109432955, 4234655557 }

  3. 7

    Returns: {0, 1 }

  4. 14953739357693

    Returns: {0, 1, 7073918284439, 7879821073255 }

  5. 999998727899999

    Returns: {0, 1 }

  6. 990377764891511

    Returns: {0, 1 }

  7. 304250263527210

    Returns: {0, 782262849291, 1827176006656, 3935456304781, 5535931629306, 6352288815796, 7153987312836, 7885834795476, 8755441855161, 10723099809136, 12645090428971, 13501113059721, 14255082277150, 15113506738330, 16007843840626, 17350176111346, 19639349360631, 20664616896210, 21617261812510, 22363222636756, 23383368766681, 25012252654390, 26581483894680, 27754768300260, 28647771200686, 29560540698690, 30325503300730, 31740145459660, 33721886778580, 34994728636791, 35850252331531, 36565294078951, 37531783321956, 38530689730456, 40792307322130, 42174712050835, 43129793198206, 43920477407521, 44680108629871, 45838050620076, 47613522458580, 49265228480755, 50124052129866, 50882953539055, 51770590659151, 52673349121471, 54938706300556, 56355379884805, 57374191812861, 58020595184475, 58748777362276, 59922989868456, 61904656904805, 63679510226410, 64441711589970, 65291714691126, 66098744567856, 67043331266626, 68603213046291, 70613362928395, 71672675566570, 72434876930130, 73386459835690, 74324630119740, 76023235860286, 77764449474790, 78691512311776, 79673410230051, 80444886873715, 81509007596731, 83398760786341, 85027644674050, 86003730241716, 86827565853666, 87654937327881, 88443219706765, 90157897675846, 92139564712195, 93358250747476, 94069992540525, 94737355521810, 95756406488106, 97136084378971, 99404623025995, 100320446767255, 101210395424425, 101972596787985, 102812743666711, 104475557135950, 106260556129651, 107393628549285, 108189475827511, 108951677191071, 109903260096631, 111138186671226, 113469056790090, 114579764012715, 115506826849701, 116203151075935, 117103878112936, 118341166738081, 120350817684175, 121767845662750, 122561291110545, 123462018147546, 124368936426736, 125494823425686, 127084372494366, 128707948771480, 129745668587536, 130505468120665, 131455183487706, 132459257389096, 134724614568181, 136045559566840, 137008863786796, 137833997317380, 138609339111321, 139453516320756, 141339454771515, 143319769053825, 144222527516145, 144954338715550, 145721259149466, 146573857718926, 148174753272910, 150270865547166, 151329284485380, 152125131763605, 152907394612896, 153952307770261, 156060588068386, 157661063392911, 158477420579401, 159279119076441, 160010966559081, 160880573618766, 162848231572741, 164770222192576, 165626244823326, 166380214040755, 167238638501935, 168132975604231, 169475307874951, 171764481124236, 172789748659815, 173742393576115, 174488354400361, 175508500530286, 177137384417995, 178706615658285, 179879900063865, 180772902964291, 181685672462295, 182450635064335, 183865277223265, 185847018542185, 187119860400396, 187975384095136, 188690425842556, 189656915085561, 190655821494061, 192917439085735, 194299843814440, 195254924961811, 196045609171126, 196805240393476, 197963182383681, 199738654222185, 201390360244360, 202249183893471, 203008085302660, 203895722422756, 204798480885076, 207063838064161, 208480511648410, 209499323576466, 210145726948080, 210873909125881, 212048121632061, 214029788668410, 215804641990015, 216566843353575, 217416846454731, 218223876331461, 219168463030231, 220728344809896, 222738494692000, 223797807330175, 224560008693735, 225511591599295, 226449761883345, 228148367623891, 229889581238395, 230816644075381, 231798541993656, 232570018637320, 233634139360336, 235523892549946, 237152776437655, 238128862005321, 238952697617271, 239780069091486, 240568351470370, 242283029439451, 244264696475800, 245483382511081, 246195124304130, 246862487285415, 247881538251711, 249261216142576, 251529754789600, 252445578530860, 253335527188030, 254097728551590, 254937875430316, 256600688899555, 258385687893256, 259518760312890, 260314607591116, 261076808954676, 262028391860236, 263263318434831, 265594188553695, 266704895776320, 267631958613306, 268328282839540, 269229009876541, 270466298501686, 272475949447780, 273892977426355, 274686422874150, 275587149911151, 276494068190341, 277619955189291, 279209504257971, 280833080535085, 281870800351141, 282630599884270, 283580315251311, 284584389152701, 286849746331786, 288170691330445, 289133995550401, 289959129080985, 290734470874926, 291578648084361, 293464586535120, 295444900817430, 296347659279750, 297079470479155, 297846390913071, 298698989482531, 300299885036515, 302395997310771, 303454416248985 }

  8. 608500527054420

    Returns: {0, 2092812319885, 5598269774020, 7265058313800, 9006390414736, 12767344028440, 14494193576500, 16271448728536, 19842408490905, 21780655498525, 23792786981601, 27157387659325, 28945825409865, 30565508300041, 34151646590985, 36214183678036, 37811733877281, 41521748550360, 43396159324596, 44919219929221, 47613522458580, 50379932881201, 51877426691805, 55452621422485, 57374191812861, 58832758153456, 62165171812381, 64633588121740, 66082398900441, 68933084456236, 71647093487256, 73277958975936, 75994729245436, 78691512311776, 80352898744405, 83398760786341, 85941153058761, 87548458819900, 89665087209985, 93036991794825, 94592638606180, 96672510341121, 100258812518865, 101831171906101, 104338565509816, 107390867310805, 108995338565400, 111612774996801, 114709146433596, 116187808660561, 118656224969920, 121960620318460, 123563333586616, 125669730335436, 129109444562385, 130557756405076, 133538165963125, 136325510122165, 137982048588021, 139705646853136, 143768000676301, 145445732776345, 147193170880756, 150775844036896, 152328190893880, 154583368726501, 158102005803820, 159511839288165, 161724360150640, 164892475792045, 166619325340105, 168460085775696, 172080038292085, 173840523992136, 175934264412621, 179074297223745, 180894988252980, 182662656153901, 186057612595141, 187975384095136, 189724844551320, 193347198898140, 195298586336140, 196755319538856, 199676575975240, 202152561607920, 203867239577001, 206523372601260, 209287302486900, 210719343813616, 212875661417056, 216377784516180, 218213381882860, 220728344809896, 223531277316985, 225403090739541, 228119861009041, 230816644075381, 232570018637320, 235761950348925, 238123036113600, 240041272148965, 242583664421385, 245629526463321, 246861153083545, 249591507781980, 252759623423385, 254337733550901, 256535425629561, 259883181703860, 261397330903996, 264438029877021, 267105077579341, 268608233394865, 270858248158576, 274239818458320, 275842531726476, 278379586411641, 280996030222545, 282870604883581, 285190117885596, 288546370471360, 290160191186580, 291830778616741, 295590550257640, 297129922129041, 298825037548401, 302604219509956, 304201769709201, 305879501809245, 309625568651400, 311357020496445, 312766594083021, 316576665144741, 318256355076661, 319934087176705, 323285642141385, 325595827833640, 327395749013256, 330024717545160, 332574014536765, 334224656427025, 337608464670400, 339845134043416, 341288282817196, 343791697795260, 347094774790401, 348600500747136, 351801707738845, 354102618150996, 355625188711156, 358795966670505, 361508657348125, 362844475577221, 365473518391696, 368420277611100, 370371665049100, 372675999522541, 375922939093780, 377636723362900, 380273499387496, 382862852988616, 384731202570001, 387442310834580, 390276650722960, 392040519733500, 395369682109480, 397753231190316, 399145484315656, 401829692147521, 404604804631665, 406319981536756, 408761872832236, 411695286660945, 413154781102141, 415114350861925, 418753050876160, 420453414603145, 422418386470081, 425794708462201, 427601576024260, 429412645401741, 432503685458845, 434643233610300, 436373787331405, 439956460487545, 441797220923136, 443407023557421, 446653963128660, 448952471710380, 450351361634461, 453854581144965, 456114880383240, 457533337281021, 461273541948220, 463007634661936, 464707998388921, 468682881099720, 470489995620645, 471903319426176, 474774655007940, 477794031228801, 479385919423125, 482624437634340, 484875115220860, 486526322307025, 489733596434005, 492113648520781, 493731373579081, 496660354152040, 499466211194665, 501106898505136, 504090233188465, 506642830134441, 508205662366480, 511715553076365, 513822847949125, 515427319203720, 518820517658521, 520913329978405, 522496796812705, 524927213752656, 528084123026461, 529761855126505, 532398631151101, 535050561935176, 536728294035220, 539392890082761, 542401782486565, 543847692498825, 546228188584156, 549448603141516, 551112750812625, 553034741432460, 556603853928760, 558077431734901, 560850952426765, 563497326334020, 565071690666561, 566942726334985, 570559493828325, 572259253166601, 574335296034501, 577900924417180, 579537895909336, 581271411038956, 584694155643885, 586693146696580, 588595541380561, 592217895727381, 593971345440760, 595699776149556, 599413455802876, 601220986187745, 602887338649596, 606235169875336 }

  9. 912750790581630

    Returns: {0, 3156933042901, 6727892805271, 9087071251545, 13941556534620, 15968866546270, 20870975980855, 23550989595211, 27630112870360, 30605453856055, 35051643814825, 38000709642610, 42852932623215, 45838050620076, 50293959857505, 53161451148520, 57817536054201, 60951557358406, 65320197536881, 68329113709780, 72454123363986, 75927343387896, 79308988839081, 82370193296391, 86382095469670, 88341904267695, 93059623421766, 95544385398540, 99639499357035, 102546876476331, 106260556129651, 109028489968035, 113594442033150, 115863788469430, 120782004533190, 123351975319860, 128253421931635, 131391147408885, 135531644444911, 138778584016150, 143432267091400, 146101098107251, 150995009796345, 153754370045640, 158438443285045, 160784845033176, 165500162356816, 167984924333590, 172142116539030, 175203396147781, 178643110374730, 181469028903085, 185594038557291, 188148427890346, 191031500634976, 195521291088201, 197759393440246, 202452243023745, 204961874571091, 209572584421915, 212319819138141, 216775065552760, 219883504777651, 224213167661770, 227859346101465, 232123250334690, 236317337997741, 239564277568980, 243674310158280, 246769164954235, 251174974616280, 253744945402950, 258141413524995, 260821427139351, 264976712026390, 268212048769665, 270721680317011, 274892781958795, 277619955189291, 281104778041165, 284147340128730, 288354418788150, 290813154687055, 295530873841126, 297908968096026, 302473008375175, 305141839391026, 310229539397856, 312867909522091, 317542655451736, 320730832578871, 324953857717776, 328110790760676, 332913377143270, 335231132158846, 340464447205246, 342589076725896, 347108359219336, 350060494124341, 353770344910620, 356587879063780, 360794957723200, 363237088056921, 367855284159000, 369957247652070, 373994019395920, 376893198769725, 380273499387496, 383861595510316, 387935575930540, 391044015155431, 395369682109480, 398532277157301, 403096317436450, 406045383264235, 410409504217791, 413284579386966, 418338633479130, 421206124770145, 425636843195565, 428711188083256, 432605239936156, 435465442015605, 440367551450190, 442397786587120, 447126688339695, 449636319887041, 452804435528446, 456375395290815, 459532328333716, 463103288096086, 465462466542360, 470316951825435, 472344261837085, 477246371271670, 479926384886026, 484005508161175, 486980849146870, 491427039105640, 494376104933425, 499228327914030, 502213445910891, 506669355148320, 509536846439335, 514192931345016, 517326952649221, 521695592827696, 524704509000595, 528829518654801, 532302738678711, 535684384129896, 538745588587206, 542757490760485, 544717299558510, 549435018712581, 551919780689355, 556014894647850, 558922271767146, 562635951420466, 565403885258850, 569969837323965, 572239183760245, 577157399824005, 579727370610675, 584628817222450, 587766542699700, 591907039735726, 595153979306965, 599807662382215, 602476493398066, 607370405087160, 610129765336455, 614813838575860, 617160240323991, 621875557647631, 624360319624405, 628517511829845, 631578791438596, 635018505665545, 637844424193900, 641969433848106, 644523823181161, 647406895925791, 651896686379016, 654134788731061, 658827638314560, 661337269861906, 665947979712730, 668695214428956, 673150460843575, 676258900068466, 680588562952585, 684234741392280, 688498645625505, 692692733288556, 695939672859795, 700049705449095, 703144560245050, 707550369907095, 710120340693765, 714516808815810, 717196822430166, 721352107317205, 724587444060480, 727097075607826, 731268177249610, 733995350480106, 737480173331980, 740522735419545, 744729814078965, 747188549977870, 751906269131941, 754284363386841, 758848403665990, 761517234681841, 766604934688671, 769243304812906, 773918050742551, 777106227869686, 781329253008591, 784486186051491, 789288772434085, 791606527449661, 796839842496061, 798964472016711, 803483754510151, 806435889415156, 810145740201435, 812963274354595, 817170353014015, 819612483347736, 824230679449815, 826332642942885, 830369414686735, 833268594060540, 836648894678311, 840236990801131, 844310971221355, 847419410446246, 851745077400295, 854907672448116, 859471712727265, 862420778555050, 866784899508606, 869659974677781, 874714028769945, 877581520060960, 882012238486380, 885086583374071, 888980635226971, 891840837306420, 896742946741005, 898773181877935, 903502083630510, 906011715177856, 909179830819261 }

  10. 6746328388800

    Returns: {0, 4712508801, 37890064576, 98738301376, 105121727425, 115987773825, 122358723201, 153877838401, 213186484225, 239019127425, 261942595201, 272271901825, 284832209025, 298104545025, 392130337600, 396094997376, 409367333376, 486922758400, 500195094400, 504159754176, 514489060800, 546008176000, 563245171776, 620147528001, 630476834625, 649458986176, 655842412225, 669114748225, 681675055425, 763907169025, 776431656001, 780377536576, 792937843776, 883765604800, 907386026625, 934255374976, 946815682176, 991157731201, 1016990374401, 1037643443200, 1050915779200, 1054880438976, 1069922254401, 1135384437825, 1160750015425, 1168561993600, 1173274502401, 1181197519425, 1272012803776, 1289262276225, 1304228873025, 1327152340801, 1343658528576, 1388000577601, 1409120712000, 1434486289600, 1458106711425, 1518954948225, 1552132504000, 1562998550400, 1567711059201, 1578040365825, 1664909769601, 1675239076225, 1686105122625, 1710722851201, 1719282678400, 1776185034625, 1784095574976, 1797367910976, 1818787608001, 1829116914625, 1854949557825, 1938721262401, 1948975350400, 1959841396800, 2056367476801, 2069675633025, 2082200120001, 2107565697601, 2120090184576, 2173027881025, 2180938421376, 2187321847425, 2200594183425, 2215630454401, 2236077958401, 2295386604225, 2330851600000, 2334816259776, 2344142715201, 2354472021825, 2448497814400, 2465734810176, 2491100387776, 2516933030976, 2556562571200, 2569122878400, 2582395214400, 2607088161601, 2628208296000, 2692229450625, 2723748565825, 2727713225601, 2731659106176, 2738042532225, 2751314868225, 2841394780225, 2846107289025, 2858631776001, 2883997353601, 2940133081600, 2949459537025, 2957370077376, 2988889192576, 3003931008001, 3025051142400, 3098723428801, 3111995764801, 3122249852800, 3133115899200, 3229641979201, 3242202286401, 3246148166976, 3255474622401, 3280840200001, 3336975928000, 3350267043201, 3360596349825, 3392115465025, 3400026005376, 3413298341376, 3470200697601, 3495566275201, 3503378253376, 3508090762176, 3611443010176, 3621772316800, 3626484825601, 3639045132801, 3672970537600, 3729872893825, 3747109889601, 3780362664001, 3792922971201, 3801482798400, 3858385154625, 3883750732225, 3897023068225, 3900987728001, 3911317034625, 4005342827200, 4010055336001, 4016208873600, 4020921382401, 4031175470400, 4113407584000, 4138567596801, 4162163694976, 4172493001600, 4185053308800, 4198325644800, 4246632353601, 4271997931201, 4293118065600, 4308159881025, 4398239793025, 4409105839425, 4413051720000, 4419422669376, 4506304549825, 4520368627776, 4535410443201, 4556063512000, 4560776020801, 4569335848000, 4581896155200, 4630202864001, 4643475200001, 4668840777601, 4689288281601, 4780116042625, 4795082639425, 4805948685825, 4812319635201, 4903147396225, 4923594900225, 4942577051776, 4952906358400, 4966197473601, 5022333201600, 5031659657025, 5057025234625, 5060971115200, 5073495602176, 5086131128001, 5176958889025, 5180923548801, 5189483376000, 5204449972800, 5284275796801, 5294605103425, 5320437746625, 5345803324225, 5363040320001, 5415230167425, 5428502503425, 5453868081025, 5467932158976, 5478261465600, 5571514295425, 5575460176000, 5582380341825, 5586326222400, 5624216286976, 5681118643201, 5693643130176, 5703972436800, 5719008707776, 5734050523201, 5786240370625, 5803477366401, 5834996481601, 5845325788225, 5871158431425, 5956588576576, 5968357141825, 5979223188225, 6007786797376, 6073248980800, 6087542947200, 6092255456001, 6100815283200, 6122234980225, 6136299058176, 6195607704000, 6227126819200, 6233497768576, 6244363814976, 6254693121600, 6311595477825, 6349485542401, 6353431422976, 6362793698625, 6457550299201, 6467879605825, 6480439913025, 6493712249025, 6519077826625, 6588504669825, 6615374018176, 6627934325376, 6638263632000, 6642976140801, 6651535968000, 6733803901825 }

  11. 4497552259200

    Returns: {0, 4712508801, 75748248576, 95366585601, 105695892225, 122358723201, 141210432000, 166576009600, 191736022401, 213186484225, 227250562176, 242324258176, 261942595201, 268156901376, 278448782976, 284832209025, 288934732801, 299226614401, 308396426625, 312498950401, 320346748800, 333619084800, 358312032001, 379432166400, 384144675201, 396094997376, 409367333376, 426042641025, 434732910976, 451408218625, 464680554625, 476630876800, 486922758400, 500195094400, 546008176000, 562671006976, 586235224576, 596564531200, 673079408001, 691931116800, 708593947776, 763907169025, 777971246976, 814289840001, 839655417601, 858507126400, 863219635201, 871067433600, 875779942401, 886109249025, 905117601025, 911331907200, 921623788800, 934255374976, 946815682176, 960088018176, 976763325825, 980865849601, 993426156801, 1001985984000, 1012277865600, 1027319681025, 1032064070401, 1042355952001, 1052685258625, 1073962036225, 1084253917825, 1088199798400, 1113391691776, 1136955909376, 1147285216000, 1163948046976, 1173274502401, 1183566384001, 1254602123776, 1289262276225, 1365010524801, 1400525064576, 1451723285376, 1458106711425, 1468398593025, 1472501116801, 1493621251200, 1508663066625, 1531586534401, 1544146841601, 1552706668800, 1562998550400, 1567711059201, 1578040365825, 1589990688000, 1594703196801, 1603263024000, 1613554905600, 1624682721025, 1634974602625, 1638920483200, 1660197260800, 1675239076225, 1685530957825, 1710722851201, 1719282678400, 1729574560000, 1735945509376, 1746237390976, 1759509726976, 1765893153025, 1776185034625, 1782399340800, 1851933283201, 1856645792001, 1951245749376, 2023221801601, 2049054444801, 2069675633025, 2094898291200, 2120090184576, 2140711372800, 2145423881601, 2153983708800, 2164275590400, 2166700659201, 2176992540801, 2185552368000, 2190264876801, 2210886065025, 2215630454401, 2236077958401, 2240023838976, 2261300616576, 2271592498176, 2286634313601, 2296958075776, 2310230411776, 2316613837825, 2326905719425, 2333120025600, 2337222549376, 2347514430976, 2353897857025, 2367170193025, 2379730500225, 2406599848576, 2438168507776, 2453210323201, 2499696035200, 2548576908801, 2641673095425, 2692229450625, 2717421344001, 2727713225601, 2736273052800, 2740985561601, 2752935883776, 2763265190400, 2773557072000, 2782883527425, 2808249105025, 2812194985600, 2832642489600, 2849305320576, 2858805460225, 2868923657601, 2879252964225, 2887943234176, 2898235115776, 2904618541825, 2917890877825, 2928182759425, 2930451185025, 2940133081600, 2949459537025, 2955673843200, 2978597310976, 2999218499200, 3015881330176, 3025207785601, 3035499667201, 3041713973376, 3071661617025, 3122249852800, 3191627152000, 3238237626625, 3303656568576, 3318698384001, 3328990265601, 3337550092800, 3354212923776, 3370888231425, 3400026005376, 3409526145025, 3419644342401, 3429973649025, 3446636480001, 3459908816001, 3470200697601, 3480561884800, 3490853766400, 3500180221825, 3506394528000, 3516843052801, 3527172359425, 3541236437376, 3553005002625, 3566602014976, 3579874350976, 3590166232576, 3596549658625, 3613212489601, 3622382301825, 3632064198400, 3636776707201, 3647604960000, 3672970537600, 3707812446976, 3729872893825, 3759010667776, 3800908633600, 3814180969600, 3900221099776, 3904933608576, 3921608916225, 3946831574400, 3995587685376, 4005916992000, 4016208873600, 4022579822976, 4042198160001, 4052527466625, 4067563737601, 4077893044225, 4091957122176, 4103725687425, 4114017569025, 4138567596801, 4162163694976, 4172493001600, 4182784883200, 4187497392001, 4189765817601, 4199447714176, 4208774169601, 4214988475776, 4225280357376, 4231663783425, 4244936119425, 4258533131776, 4280593578625, 4305143606401, 4326263740800, 4351629318400, 4364901654400, 4381564485376, 4398239793025, 4411512129025, 4450941784576 }

  12. 3373164194400

    Returns: {0, 4712508801, 12567844576, 22897151200, 36188266401, 40134146976, 94792420801, 98738301376, 105121727425, 115987773825, 118394063425, 122402080801, 130214058976, 130961908000, 143522215200, 157823718976, 227250562176, 239019127425, 248608122400, 252616139776, 261168429600, 265880938401, 272271901825, 278448782976, 288778089600, 299806343200, 356708699425, 373945695201, 384275001825, 392896965825, 396842846400, 409367333376, 419758776801, 428318604000, 434732910976, 486922758400, 491635267201, 501964573825, 510586537825, 514489060800, 519201569601, 527056905376, 531769414176, 546008176000, 563245171776, 620147528001, 624093408576, 632178632800, 636891141601, 643044679200, 645513105601, 649415628576, 654072932800, 658011276000, 669114748225, 680934743776, 738541591425, 744955898401, 765403402401, 767105200576, 777971246976, 788999500576, 790768980001, 799328807200, 811889114400, 825161450400, 873468159201, 882063806625, 898833736801, 907386026625, 911331907200, 924666380001, 934995686625, 946815682176, 991157731201, 1016990374401, 1025075598625, 1029021479200, 1037643443200, 1039887525600, 1042355952001, 1050915779200, 1054880438976, 1069922254401, 1122112101825, 1135384437825, 1147204433376, 1160002166401, 1162246248801, 1168561993600, 1172570010976, 1174814093376, 1182899317600, 1187611826401, 1196171653600, 1208731960800, 1257038669601, 1268066923201, 1272012803776, 1289262276225, 1292460307776, 1303488561376, 1316124087201, 1317825885376, 1331098221376, 1383288068800, 1400525064576, 1409120712000, 1421918445025, 1425890642176, 1434442932000, 1439155440801, 1458106711425, 1518214636576, 1529983201825, 1544047279776, 1552132504000, 1556845012801, 1565404840000, 1569369499776, 1575796283425, 1579742164000, 1593033279201, 1649169007200, 1658495462625, 1662441343200, 1672832786625, 1683861040225, 1686105122625, 1687806920800, 1697925118176, 1708254424800, 1712966933601, 1719282678400, 1776185034625, 1784095574976, 1795123828576, 1803751337025, 1805453135200, 1810165644001, 1818787608001, 1822733488576, 1831285778400, 1854209246176, 1911111602401, 1921440909025, 1938677904801, 1940379702976, 1948975350400, 1959841396800, 1966212346176, 1985163616800, 2029505665825, 2046011853600, 2056367476801, 2068935321376, 2077487611200, 2082200120001, 2094767964576, 2102853188800, 2107565697601, 2120090184576, 2173027881025, 2180938421376, 2187321847425, 2191966674976, 2199889692000, 2202295981600, 2209216147425, 2212414178976, 2215630454401, 2236077958401, 2240023838976, 2295386604225, 2307954448801, 2320478935776, 2326905719425, 2330851600000, 2334816259776, 2337222549376, 2345844513376, 2354472021825, 2360886328801, 2413076176225, 2430313172001, 2438908819425, 2453210323201, 2465734810176, 2472161593825, 2489398589601, 2497994237025, 2516933030976, 2556562571200, 2569122878400, 2580226350625, 2583424382176, 2592786657825, 2596732538400, 2607088161601, 2609257025376, 2632920804801, 2691489138976, 2700084786400, 2714378752800, 2717321782176, 2723705208225, 2725407006400, 2727713225601, 2731659106176, 2738042532225, 2742687359776, 2751314868225, 2763134863776, 2822443509600, 2835011354176, 2845340660800, 2849305320576, 2858631776001, 2860333574176, 2869004440225, 2872969100001, 2883997353601, 2887943234176, 2940133081600, 2949459537025, 2957370077376, 2965965724800, 2977069197025, 2981033856801, 2989629504225, 3003931008001, 3025051142400, 3075059649376, 3088331985376, 3098723428801, 3107275718625, 3111221599200, 3119843563200, 3122249852800, 3133115899200, 3134885378625, 3159977710176, 3219286356000, 3238237626625, 3242209823776, 3246148166976, 3250805471200, 3255474622401, 3265099437600, 3269811946401, 3276127691200, 3280840200001, 3335274129825, 3346302383425, 3354212923776, 3360639707425 }

  13. 3212537328000

    Returns: {0, 20910176001, 40863824001, 54136160001, 79836458625, 115510133376, 131861354625, 141210432000, 147232346625, 167535029376, 182074256001, 187488677376, 197147952001, 202859669376, 208606320000, 213188976000, 222848250625, 228559968000, 238219242625, 247371488001, 259799450625, 267325136001, 273071786625, 282696128001, 291747909376, 293857200000, 308251605376, 314767376001, 328205253376, 332819200000, 334721024001, 340467674625, 353729376001, 354399408000, 359143797376, 364058682625, 373683024001, 379429674625, 384844096000, 399383322625, 405754272001, 421795296000, 429320981376, 435067632000, 451408218625, 464680554625, 475931456001, 500354229376, 520307877376, 526054528000, 546008176000, 562511872000, 592618650625, 646754810625, 688450400001, 714150698625, 783050357376, 793379664000, 808750656000, 813795984001, 829660832001, 834243488001, 839496282625, 849614480001, 855361130625, 860775552000, 875314778625, 881685728001, 900870256000, 907386026625, 914911712001, 927339674625, 940612010625, 945347141376, 960420837376, 971047440000, 975791829376, 980706714625, 996239333376, 1000660362625, 1001985984000, 1007031312001, 1021939632000, 1023072336000, 1031598906625, 1036334037376, 1042355952001, 1048102602625, 1062034336000, 1068550106625, 1101631269376, 1114059232000, 1121584917376, 1129430224000, 1142702560000, 1162656208000, 1169027157376, 1188980805376, 1194727456000, 1214681104000, 1261291578625, 1315427738625, 1351101413376, 1371055061376, 1380714336001, 1396755360000, 1410027696000, 1430937872001, 1443365834625, 1451723285376, 1462052592000, 1476591818625, 1481830064001, 1498333760001, 1502916416001, 1508663066625, 1518287408001, 1524034058625, 1528616714625, 1541878416001, 1543987706625, 1553039488000, 1567578714625, 1573949664001, 1579661381376, 1589990688000, 1593903312001, 1599649962625, 1605361680000, 1609274304001, 1615020954625, 1619603610625, 1623216672000, 1634974602625, 1644126848001, 1648246938625, 1664912261376, 1669827146625, 1674571536001, 1685198138625, 1690612560000, 1700271834625, 1705006965376, 1711522736001, 1729574560000, 1735113744001, 1737223034625, 1755899157376, 1761645808000, 1776185034625, 1794871792000, 1806122693376, 1828209930625, 1835735616001, 1856645792001, 1882346090625, 1922809888000, 1976946048000, 2003270645376, 2018641637376, 2028970944000, 2044341936000, 2065252112001, 2075581418625, 2085205760001, 2095535066625, 2108807402625, 2124178394625, 2144481077376, 2159852069376, 2169687520000, 2174094000001, 2179805717376, 2185552368000, 2190135024000, 2199794298625, 2206638720000, 2211045200001, 2215165290625, 2226416192001, 2236251642625, 2237577264000, 2245102949376, 2257530912000, 2270803248000, 2278441088001, 2291713424001, 2304141386625, 2310897952000, 2317413722625, 2336089845376, 2337367370625, 2352593541376, 2361790144000, 2372547189376, 2377462074625, 2382700320001, 2398247488000, 2402653968001, 2408400618625, 2428354266625, 2444857962625, 2513757621376, 2539457920000, 2591482816000, 2645618976000, 2665396448001, 2675725754625, 2691096746625, 2710905573376, 2717421344001, 2743121642625, 2757516048001, 2773557072000, 2781082757376, 2786829408000, 2803169994625, 2812021301376, 2816442330625, 2828524997376, 2837721600000, 2842766928001, 2852116005376, 2854225296000, 2858631776001, 2868467226625, 2874178944000, 2878585424001, 2883838218625, 2895089120001, 2904140901376, 2905418426625, 2919511893376, 2924094549376, 2937366885376, 2944380426625, 2949794848000, 2963067184000, 2970705024001, 2978438176000, 2986076016001, 2996405322625, 3000018384000, 3004762773376, 3011776314625, 3019302000001, 3029631306625, 3041713973376, 3051373248001, 3067414272000, 3077073546625, 3091005280000, 3106376272000, 3145973205376, 3165926853376, 3186837029376 }

  14. 866421317361600

    Returns: {0, 3038675076801, 4815132811776, 9750259396801, 13321033538176, 16066492164801, 18374221367425, 21728434291201, 24983908913601, 29201614041600, 31912054451200, 35049467829376, 37176986585025, 40505366865601, 43760841488001, 47053475366976, 52106663196225, 55485108993601, 58740583616001, 62692994563200, 67246484342401, 70755083509825, 72441714369025, 75481929036801, 79761213209601, 83269107043200, 86283489067776, 90258831625600, 94170148660225, 99117438220801, 103462116018625, 107352882915201, 110477673244225, 113429174961025, 116075583187201, 120354162026176, 123774473908800, 126813148985601, 128563774077376, 131092433158401, 133939083225025, 139131094600576, 141374791619776, 143033500209600, 145743940619200, 147476916308800, 152301665880001, 155428628241601, 157747948156800, 161593633238401, 165839498963776, 169509323505600, 174489293577600, 179042783356801, 182298257979201, 184074715714176, 186732762652800, 191557512224001, 194923363860225, 196859900613376, 199344690230400, 202055130640000, 207776323857025, 211171637353600, 214829823182976, 218515429246401, 222273972258625, 226822240008001, 229845890310400, 233101364932800, 237203648869825, 240243863537601, 243814637678976, 248990856861825, 251701297271425, 254741511939201, 257842641657601, 261628556904001, 264884031526401, 267767789436225, 270738301996800, 273204020591425, 276645406875201, 281305622520000, 284965395940225, 287144564882176, 289997328297600, 293134741675776, 296555053558401, 298905940230976, 302808345840000, 305112916570176, 307849189622976, 310352016060801, 313217676971200, 318697837769025, 321854261990976, 325496595449025, 327575455208001, 331550797765825, 334946111262400, 339034428532800, 342073103609601, 344871831304000, 348226044227776, 353748876480000, 357646523846976, 360761323233025, 365307472468225, 369855740217601, 373944057488001, 377339370984576, 381314713542400, 383393573301376, 387035906759425, 391925306670976, 395567640129025, 397891221702976, 400233969122625, 403371382500801, 408055831019200, 410516327584000, 413044986665025, 415071388244800, 417315085264000, 421083648107200, 425013975985600, 429293260158400, 433204577193025, 437102224560001, 441080468150400, 444273002286400, 447528476908800, 451047527092800, 452909587306176, 455719078116225, 458148686796801, 462808902441600, 466001436577600, 467883164672001, 470216726517825, 474367498429825, 478939426789825, 482194901412225, 484804201795200, 488865146831425, 492219359755201, 495732734496000, 500843321725825, 505354481632000, 508543752038400, 512370038857600, 517421369477376, 521332686512001, 524131414206400, 527170089283201, 531449373456001, 534185646508801, 538379118763200, 540707922366976, 544345033795200, 546848694490176, 552686097261376, 555914080800001, 558104888454400, 560902531112001, 563604060096000, 566741473474176, 569526493082625, 572135793465600, 576238077402625, 578719648368576, 581430088778176, 584113968360000, 589559110940800, 593031385108800, 595460993789376, 598270484599425, 601182187006401, 604273558888000, 608552843060800, 611591518137601, 614416078475200, 616406650949376, 622418910811776, 626061244269825, 629128955540800, 632169170208576, 636446914790401, 639184727434176, 643529405232000, 647808689404800, 651162902328576, 655223847364801, 658607051404225, 663698181333825, 666825143695425, 669535584105025, 671381743947201, 674449455218176, 678067317474625, 681879362363200, 683906259836800, 687260472760576, 691605150558400, 696680952379776, 700167468478401, 704341901001025, 708206129920576, 710864176859200, 713705301562176, 718407847080001, 720651544099201, 722712963896001, 725020693098625, 726983062494976, 731945680163776, 734215209826176, 737831710641025, 739454309316801, 742405811033601, 745902318075201, 749835718178625, 752806230739200, 755801633210625, 758713335617601, 762323909068800, 767020146379201, 771583163313600, 776136653092801, 779392127715201, 782381525313025, 786562905441600, 790851101040001, 793978063401601, 795537721590976, 798324280790400, 802553278816576, 807644408746176, 810743880024001, 814128742504000, 818442770745601, 822505255372801, 825890117852800, 828626390905600, 831253788288001, 834483430267201, 836816992113025, 841122108929025, 844388910164800, 848021263350976, 850290793013376, 853001233422976, 856478729620801, 860582374999425, 863165842739200 }

  15. 782574093100800

    Returns: {0, 2240023838976, 6708438324225, 10249706642176, 12441740998401, 13777488986625, 17894842451200, 19296134144001, 21622273235200, 25296010401025, 28563353921025, 33227482189825, 36982404057600, 38813060563200, 40766748422400, 41929693618176, 44207843226625, 46593821886976, 48776431225600, 52932983667201, 61398630554625, 63790313350401, 65126061338625, 68454441619201, 71581403980801, 75993707851776, 83166858611200, 85645228947201, 88478700710401, 90284664268800, 91326347590401, 94170148660225, 95608599609601, 97163750361601, 101300047559425, 103686026219776, 110803831877376, 116075583187201, 117411331175425, 122597859045376, 124161624224001, 127005425293825, 128836081799425, 130262439507201, 137116832652801, 140512146149376, 143611617427201, 146349548920576, 148303236779776, 149320227154176, 151150883659776, 153861324069376, 156988286430976, 163635876518401, 166835476231425, 170344314842625, 171782765792001, 174626566861825, 176446894060801, 178353997645825, 180307685505025, 182138342010625, 186706930009600, 192388048652800, 193824735667200, 198488863936000, 199890155628801, 201482465637376, 204554283897601, 207748179475200, 212412307744000, 219120746068225, 221506724728576, 224801864711425, 227187843371776, 229370452710400, 231708441888001, 233539098393601, 235051571353600, 238416880212225, 241992652039425, 246656780308225, 252242358681600, 254580347859201, 257923477324800, 260033449312000, 262425132107776, 265714567955200, 272053729735425, 276202621094401, 278442644933376, 281569607294976, 282672712921600, 284280047704576, 286233735563776, 288406015595776, 290702150049025, 297091065246976, 302935318509825, 304527628518400, 305544618892800, 307882608070401, 310208747161600, 312546736339201, 315138713011200, 317115324338176, 322796442981376, 326063786501376, 329504881305601, 330727914770176, 335605696588800, 337582307915776, 341708275806976, 342735595488000, 347784025075201, 351769164235776, 357040915545601, 358899063134976, 361970881395201, 363563191403776, 365470294988800, 367423982848000, 368440973222400, 370417584549376, 375320059315201, 378281312531200, 383773612961025, 388960140830976, 390903511860225, 393006329228800, 395567640129025, 401153218502400, 406465060601601, 411918162054400, 413319453747201, 414911763755776, 416086807737601, 418772555200000, 419947599181825, 422941200883201, 425522848248576, 430197305824000, 433454320037376, 439291722808576, 440855487987201, 444972841451776, 446546935937025, 450829187956225, 452659844461825, 454086202169601, 459767320812801, 464441778388225, 466827757048576, 470017027454976, 472126999442176, 473957655947776, 475854430226176, 477818447392000, 479382212570625, 483499566035200, 488476629555201, 493151087130625, 495732734496000, 497709345822976, 499663033682176, 500690353363200, 503400793772800, 505962104673025, 509081912416000, 516621178648576, 518813213004801, 522312626598400, 523876391777025, 527003354138625, 529713794548225, 534900322418176, 539493084619776, 543353876064000, 545184532569600, 548625627373825, 550232962156801, 552186650016001, 555375920422401, 556703053984000, 560829021875200, 563043979699201, 569554162315776, 571497533345025, 577230836019201, 580730249612800, 582365179858176, 583700927846400, 588202582629376, 589776677114625, 594850172716801, 597697819596801, 601980071616001, 603535222368001, 606116869733376, 607671519565825, 610057498226176, 611808317683200, 613784929010176, 617921226208000, 624851977587201, 628579408371201, 630543425537025, 633243536640001, 634032509824000, 635207553805825, 638934984589825, 640793132179200, 644643594316800, 646883618155776, 652959367424001, 654913055283201, 658402139570176, 659429459251200, 664753394592001, 666089142580225, 671223486419200, 677871076506625, 680864678208001, 684725469652225, 686556126157825, 688120783148800, 691114384850176, 692264735884800, 693306419206401, 696805832800000, 699143821977601, 706261627635201, 710925755904001, 713330678297601, 716830091891200, 718465022136576, 719800770124800, 728305361445376, 732780671500801, 735969941907201, 738079913894401, 740319937733376, 741661389857025, 743638001184001, 744788352218625, 748329620536576, 751177267416576, 755841395685376, 759702187129600, 762959201342976, 764294949331200, 766643267815425, 769353708225025, 771307396084225, 775034826868225, 776892974457600 }

  16. 577614211574400

    Returns: {0, 1592933717376, 3438998640000, 5450114592000, 8087718491776, 9942587740800, 12465671817600, 14585935686400, 16305810782976, 18315268294401, 20336590763776, 22032407196801, 23878472119425, 27178548883200, 29533890464001, 31853101378176, 33977306563201, 35636015153025, 37416305203200, 39354584645376, 42139604253825, 44804699237376, 46807010862976, 49641087521025, 52002240889600, 54284435466625, 56281525062400, 58832703216001, 61568976268801, 65244172716801, 67822268550400, 69731273959425, 72278416699776, 73730675180800, 76720998541825, 79169293979776, 82049219574400, 84421428854400, 86283489067776, 88691730551425, 91459708250625, 92971014724225, 95546282832001, 98475265476225, 100510440091776, 104511758212225, 106292048262400, 107987864695425, 109990176321025, 111426863335425, 113875158773376, 117246413606400, 119465524777600, 121895133458176, 123957997926400, 125593261516801, 127460079972225, 129613416270976, 132452572039425, 133828706211201, 136505439907200, 139778025587200, 141687030996225, 143063165168001, 144696041114625, 147062566389376, 148069264882176, 150078722393601, 153275088844801, 155557140502401, 157580205660801, 159610008370176, 161062266851200, 162953772119425, 165032631878401, 167314683536001, 169476047977600, 171753020524800, 174975219619200, 177040471731201, 179042783356801, 181039872952576, 183322067529601, 184758754544001, 187421880593025, 190132321002625, 193259283364225, 194923363860225, 197593862040576, 199226737987200, 200959713676800, 203412253968001, 206797116448000, 208911425609601, 211621866019201, 214298599715200, 216950087051776, 218305146822400, 221314156940800, 223379409052801, 226774722549376, 229845890310400, 231541706743425, 234276205816576, 235916227649025, 237474346247425, 240139441230976, 242888732172801, 245107843344001, 248330042438401, 250830194904576, 252005238886401, 254646275206401, 256492340129025, 258041588702976, 261141059980801, 263878991474176, 265239130355200, 267951313453825, 270011486455425, 271541479686400, 273020496573825, 275387021848576, 277463912673025, 279596908592001, 282307349001601, 284991228583425, 286988318179200, 288623581769601, 290469646692225, 292062580409601, 295118366544001, 297485203917825, 299564063676801, 302161414853376, 304224279321600, 305600413493376, 307584038361601, 309430103284225, 312095198267776, 313574215155201, 315765022809600, 319185334692225, 320965624742400, 322872699635200, 325331758188801, 326686817959425, 328649187355776, 332439435014401, 334127605464576, 336839788563201, 339577720056576, 341580031682176, 343312173114625, 346048446167425, 347712526663425, 350377621646976, 353748876480000, 356215024418176, 358878150467200, 360579338806401, 362784388391425, 365307472468225, 368444885846401, 370441975442176, 374117171890176, 376322221475200, 378269521344001, 379980407304576, 382666757760001, 384026896641025, 387035906759425, 389805042802176, 392269221805825, 394266311401600, 396294455670400, 398354628672000, 400419880784001, 402482745252225, 405807054889600, 407921364051201, 410140475222401, 412364780150401, 414604644854400, 416176825038976, 417396712507776, 419866263417601, 421675996680576, 424171380233601, 427049563139200, 429072628297600, 430271762233600, 432548734780800, 434093214441601, 435770933875200, 437709213317376, 441080468150400, 443299579321600, 444778596209025, 447631047525376, 449997884899200, 451936164341376, 453376330696576, 455653303243776, 457773567112576, 460339494451200, 463049934860800, 465817912560000, 467598202610176, 469256911200000, 471266368711425, 472616670240001, 475814636460801, 478823646579201, 481652039232001, 484315165281025, 485998256620800, 488594449453825, 491072518851201, 492524777332225, 495189872315776, 498228118049025, 500867380389376, 503603653442176, 505299469875201, 507419733744001, 509102825083776, 511982750678400, 515629345795201, 518292471844225, 520957566827776, 522597588660225, 525321636716800, 527386888828801, 530631170992000, 532422224157825, 535087319141376, 538132654259200, 540041659668225, 541886076821376, 543420105465601, 545702157123201, 547723479592576, 550066227012225, 553579492752000, 555526792620801, 556957938549376, 559239990206976, 561237222722176, 562653156203776, 564662613715201, 567515377130625, 569451913883776, 572135793465600, 574018966231425, 575833921524225 }

  17. 2

    Returns: {0, 1 }

  18. 4

    Returns: {0, 1 }

  19. 281474976710656

    Returns: {0, 1 }

  20. 562949953421312

    Returns: {0, 1 }

  21. 3

    Returns: {0, 1 }

  22. 9

    Returns: {0, 1 }

  23. 205891132094649

    Returns: {0, 1 }

  24. 617673396283947

    Returns: {0, 1 }

  25. 5

    Returns: {0, 1 }

  26. 25

    Returns: {0, 1 }

  27. 95367431640625

    Returns: {0, 1 }

  28. 476837158203125

    Returns: {0, 1 }

  29. 1

    Returns: {0 }

  30. 91

    Returns: {0, 1, 14, 78 }

  31. 98

    Returns: {0, 1, 49, 50 }

  32. 1000000007

    Returns: {0, 1 }

  33. 10000000070

    Returns: {0, 1, 2000000015, 3000000021, 5000000035, 5000000036, 7000000050, 8000000056 }

  34. 1000000000000000

    Returns: {0, 1, 259918212890625, 740081787109376 }

  35. 22222

    Returns: {0, 1, 4879, 6233, 11111, 11112, 15990, 17344 }

  36. 72345678901234

    Returns: {0, 1, 36172839450617, 36172839450618 }

  37. 304239080928706

    Returns: {0, 1, 90092063755, 553899552438, 3031929891551, 4263090334272, 4353182398026, 4816989886709, 4907081950464, 7848919778260, 7939011842014, 9170172284735, 12561190638745, 12756001728723, 14848702525427, 16914373036771, 17378180525454, 17468272589208, 19201884923453, 19665692412136, 19755784475890, 21731362923480, 21821454987234, 22285262475917, 24018874810162, 24108966873916, 24572774362599, 24763292815030, 26638444873943, 27050804701712, 28925956760625, 29580282701739, 29670374765493, 31867794588421, 31957886652175, 34487364652202, 36580065448906, 36774876538884, 40933247846932, 41397055335615, 41487147399369, 44519077290920, 45750237733641, 45840329797395, 46304137286078, 48782167625191, 49336067177629, 49426159241383, 50657319684104, 52126153602622, 53599157511900, 53689249575654, 54243149128092, 56943143489331, 57033235553085, 58506239462363, 61850225439794, 66250440214399, 68537952101081, 71067430101108, 71157522164862, 73354941987790, 73445034051544, 73857516526101, 75974512051571, 76145028412783, 78262023938253, 78674506412810, 78764598476564, 80962018299492, 81052110363246, 83581588363273, 85869100249955, 90269315024560, 93613301001991, 95086304911269, 95176396975023, 97876391336262, 98430290888700, 98520382952454, 99993386861732, 101462220780250, 102693381222971, 102783473286725, 103337372839163, 105815403178276, 106279210666959, 106369302730713, 107600463173434, 110632393064985, 110722485128739, 111186292617422, 115344663925470, 115539475015448, 117632175812152, 120161653812179, 120251745875933, 122449165698861, 122539257762615, 123193583703729, 125068735762642, 125481095590411, 127356247649324, 127546766101755, 128010573590438, 128100665654192, 129834277988437, 130298085477120, 130388177540874, 132363755988464, 132453848052218, 132917655540901, 134651267875146, 134741359938900, 135205167427583, 137270837938927, 139363538735631, 139558349825609, 142949368179619, 144180528622340, 144270620686094, 147212458513890, 147302550577645, 147766358066328, 147856450130082, 149087610572803, 151565640911916, 152029448400599, 152119540464353, 152119540464354, 152209632528108, 152673440016791, 155151470355904, 156382630798625, 156472722862379, 156936530351062, 157026622414817, 159968460242613, 160058552306367, 161289712749088, 164680731103098, 164875542193076, 166968242989780, 169033913501124, 169497720989807, 169587813053561, 171321425387806, 171785232876489, 171875324940243, 173850903387833, 173940995451587, 174404802940270, 176138415274515, 176228507338269, 176692314826952, 176882833279383, 178757985338296, 179170345166065, 181045497224978, 181699823166092, 181789915229846, 183987335052774, 184077427116528, 186606905116555, 188699605913259, 188894417003237, 193052788311285, 193516595799968, 193606687863722, 196638617755273, 197869778197994, 197959870261748, 198423677750431, 200901708089544, 201455607641982, 201545699705736, 202776860148457, 204245694066975, 205718697976253, 205808790040007, 206362689592445, 209062683953684, 209152776017438, 210625779926716, 213969765904147, 218369980678752, 220657492565434, 223186970565461, 223277062629215, 225474482452143, 225564574515897, 225977056990454, 228094052515924, 228264568877136, 230381564402606, 230794046877163, 230884138940917, 233081558763845, 233171650827599, 235701128827626, 237988640714308, 242388855488913, 245732841466344, 247205845375622, 247295937439376, 249995931800615, 250549831353053, 250639923416807, 252112927326085, 253581761244603, 254812921687324, 254903013751078, 255456913303516, 257934943642629, 258398751131312, 258488843195066, 259720003637787, 262751933529338, 262842025593092, 263305833081775, 267464204389823, 267659015479801, 269751716276505, 272281194276532, 272371286340286, 274568706163214, 274658798226968, 275313124168082, 277188276226995, 277600636054764, 279475788113677, 279666306566108, 280130114054791, 280220206118545, 281953818452790, 282417625941473, 282507718005227, 284483296452817, 284573388516571, 285037196005254, 286770808339499, 286860900403253, 287324707891936, 289390378403280, 291483079199984, 291677890289962, 295068908643972, 296300069086693, 296390161150447, 299331998978243, 299422091041998, 299885898530681, 299975990594435, 301207151037156, 303685181376269, 304148988864952 }

  38. 978217616376000

    Returns: {0, 1829116914625, 6519077826625, 12104656200000, 15930825285376, 19296134144001, 22846073328001, 23996424362625, 27723855146625, 39517882314625, 42535010440000, 46446327474625, 49439929176001, 52031905848000, 56698340336001, 60944206061376, 63551966853376, 65790451101376, 68638097981376, 72549415016001, 79158572754625, 86398040181376, 89221224002625, 91098330400000, 95187139034625, 100584896501376, 105308333416000, 109219650450625, 112476664664001, 116913542370625, 120640973154625, 124171953530625, 126400108472001, 130236606864001, 132589345226625, 134827829474625, 140512146149376, 146621856642625, 153861324069376, 156830462712001, 161916593840001, 164877847056000, 167116331304000, 171782765792001, 174755079122625, 178267115765376, 182138342010625, 184876273504000, 188133287717376, 190061142933376, 193788573717376, 197970428994625, 201482465637376, 205893229917376, 211710015440001, 217675930472001, 222065591658625, 227651170032000, 229889654280000, 233429264157376, 235725398610625, 238307045976000, 241409715285376, 245211964712001, 247673770682625, 250906610693376, 255596571605376, 257794965064000, 263760880096000, 267672197130625, 274483338416001, 278442644933376, 281411783576001, 285928187544000, 292833106280001, 296933241528001, 299171725776001, 302019372656001, 304257856904001, 305360962530625, 307599446778625, 310593048480001, 313464221784000, 320568288040000, 322806772288000, 327496733200000, 334755144360000, 343115932146625, 344963750429376, 348513689613376, 350520298128001, 353391471432000, 358068235226625, 362478999506625, 365185498600000, 367809823757376, 371151413632000, 374328901584001, 377675995709376, 379914479957376, 382756622586625, 388342200960000, 390270056176000, 397995484874625, 407327706072001, 410344834197376, 412027996290625, 415755427074625, 417983582016001, 419841729605376, 422683872234625, 425677473936001, 428269450608000, 432935885096001, 435174369344001, 437880868437376, 441618628528000, 445529945562625, 449839569816000, 455358214973376, 458908154157376, 465458768762625, 469135703960001, 474790989960001, 477563424962625, 479491280178625, 483218710962625, 485457195210625, 488450796912001, 491981777288001, 493494250248000, 496671738200001, 500409498290625, 503115997384000, 507526761664000, 512612892792000, 518948084368000, 522821498861376, 527003354138625, 531909026936001, 534926155061376, 540326418632001, 542564902880001, 545026708850625, 549009162064000, 552186650016001, 555147903232000, 557772228389376, 560223705053376, 562052821968001, 565780252752001, 566930603786625, 570480542970625, 578081388248001, 586411368256000, 589776677114625, 594466638026625, 597699478037376, 600161284008000, 603535222368001, 606127199040000, 608578675704000, 612226580226625, 615493923746625, 617921226208000, 624166337872000, 626338617904000, 629516105856001, 633243536640001, 634393887674625, 637943826858625, 646993452392001, 653738011301376, 657239961002625, 664093587520000, 667106132954625, 669443355504001, 671497953501376, 673590482928000, 675409270536001, 678256917416001, 681274045541376, 683456654880000, 690616596045376, 695306556957376, 699044317048000, 702564968117376, 709271866850625, 712783903493376, 718973140248000, 721211624496000, 725878058984001, 730288823264001, 732995322357376, 736733082448000, 738971566696000, 741423043360000, 744047368517376, 746655129309376, 750186109685376, 755841395685376, 758613830688000, 765805308632001, 768043792880001, 776373772888000, 779837820048001, 783974618165376, 786582378957376, 788674908384000, 791668510085376, 795768645333376, 798541080336000, 802188984858625, 805701021501376, 809428452285376, 812959432661376, 815801575290625, 821376824357376, 823615308605376, 830011578306625, 835507076768001, 842116234506625, 845373248720001, 847301103936001, 851028534720001, 853267018968001, 855728824938625, 860960910888001, 863542558253376, 868219322048001, 871236450173376, 876891736173376, 881592026392000, 886757908125376, 888850437552000, 891458198344000, 898649676288001, 905168754114625, 908925215573376, 911163699821376, 913091555037376, 916818985821376, 921000841098625, 924531821474625, 928424194776001, 931385447992000, 934740427544001, 938290366728001, 945803800317376, 952500369744001, 954962175714625, 957586500872001, 962276461784001, 966014221874625, 970704182786625, 975609855584001 }

  39. 11835308030

    Returns: {0, 43485065, 71695715, 97380115, 109920266, 138130916, 169075830, 216384806, 298193805, 329860181, 350691810, 385460635, 417198496, 456391300, 514578610, 558063675, 586274325, 617940701, 652709526, 758805880, 825312566, 844438791, 865270420, 970969910, 995504055, 1060823596, 1132519311, 1234542296, 1273384490, 1341006836, 1379083980, 1450779695, 1510082665, 1540633381, 1560699960, 1667164500, 1691698645, 1742562731, 1777331556, 1858893765, 1918196735, 1949863111, 1989892450, 2021558826, 2040509745, 2075278570, 2146974285, 2171508430, 2206277255, 2237943631, 2277207920, 2398006520, 2429672896, 2445315496, 2473526146, 2536137436, 2556204015, 2614391325, 2665255411, 2686087040, 2752522241, 2791786530, 2846871391, 2925125281, 2953335931, 2973402510, 3036013800, 3094201110, 3160636311, 3199900600, 3232332026, 3271596315, 3338031516, 3362565661, 3400642805, 3453212295, 3478896695, 3507107345, 3550592410, 3660512675, 3688723325, 3732208390, 3766977215, 3817841301, 3861326365, 3880452590, 3915221415, 3958706480, 3986917130, 4034226106, 4096837395, 4168533110, 4203301935, 4246787000, 4285258341, 4375904975, 4395031200, 4442340176, 4514035891, 4573338861, 4611416005, 4654901070, 4765068126, 4813345355, 4891599245, 4923265621, 4981452931, 5053148646, 5091225790, 5124079311, 5221459425, 5293155140, 5327923965, 5340464116, 5371409030, 5437844231, 5481329295, 5509539945, 5553025010, 5572151235, 5606920060, 5638657921, 5736038035, 5767704411, 5788536040, 5811189476, 5839400126, 5855042726, 5917654015, 5961139080, 5989349730, 6015034130, 6027574281, 6055784931, 6086729845, 6134038821, 6215847820, 6247514196, 6268345825, 6303114650, 6334852511, 6374045315, 6432232625, 6475717690, 6503928340, 6535594716, 6570363541, 6676459895, 6742966581, 6762092806, 6782924435, 6888623925, 6913158070, 6978477611, 7050173326, 7152196311, 7191038505, 7258660851, 7296737995, 7368433710, 7427736680, 7458287396, 7478353975, 7584818515, 7609352660, 7660216746, 7694985571, 7776547780, 7835850750, 7867517126, 7907546465, 7939212841, 7958163760, 7992932585, 8064628300, 8089162445, 8123931270, 8155597646, 8194861935, 8315660535, 8347326911, 8362969511, 8391180161, 8453791451, 8473858030, 8532045340, 8582909426, 8603741055, 8670176256, 8709440545, 8764525406, 8842779296, 8870989946, 8891056525, 8953667815, 9011855125, 9078290326, 9117554615, 9149986041, 9189250330, 9255685531, 9280219676, 9318296820, 9370866310, 9396550710, 9424761360, 9468246425, 9578166690, 9606377340, 9649862405, 9684631230, 9735495316, 9778980380, 9798106605, 9832875430, 9876360495, 9904571145, 9951880121, 10014491410, 10086187125, 10120955950, 10164441015, 10202912356, 10293558990, 10312685215, 10359994191, 10431689906, 10490992876, 10529070020, 10572555085, 10682722141, 10730999370, 10809253260, 10840919636, 10899106946, 10970802661, 11008879805, 11041733326, 11139113440, 11210809155, 11245577980, 11258118131, 11289063045, 11355498246, 11398983310, 11427193960, 11470679025, 11489805250, 11524574075, 11556311936, 11653692050, 11685358426, 11706190055, 11728843491, 11757054141, 11772696741 }

  40. 411782264189298

    Returns: {0, 1, 205891132094649, 205891132094650 }

  41. 223092870

    Returns: {0, 367081, 864501, 1322685, 2187186, 5616325, 6113745, 7039956, 7354711, 7715995, 7852131, 8219211, 8895250, 9541896, 11623326, 12946011, 14196820, 14612521, 15630616, 16302286, 16663570, 17475745, 19706401, 20518576, 21246940, 21551530, 22048950, 22705761, 23067045, 23738715, 27142830, 27955005, 28286896, 29099071, 29827435, 30421755, 30788836, 31286256, 32319210, 35362041, 35723325, 36139026, 36535500, 36902580, 37461711, 38046646, 38504830, 39002250, 42045081, 43295890, 43942536, 44618575, 45034276, 45483075, 46409286, 46805760, 47221461, 50128156, 50650600, 51297246, 51668695, 52315341, 52837785, 53981851, 55304536, 57385966, 57980286, 59075731, 59573151, 59887906, 60553780, 60920860, 62740965, 64461111, 64822395, 65783796, 66145080, 66560781, 67324335, 67656226, 68468401, 72177105, 72905470, 73321171, 73717645, 74364291, 74731371, 75092655, 75508356, 75904830, 76831041, 79980615, 80396316, 81072355, 81414411, 82080285, 82665220, 83311866, 83987905, 86663655, 88174801, 88561110, 88976811, 89652850, 90019930, 90666576, 91342615, 93424045, 94746730, 95162431, 95611230, 96755296, 97059886, 98077981, 99247071, 101643256, 102598860, 102965941, 103463361, 103742926, 104110006, 104496315, 105153126, 105514410, 109079685, 110005896, 110402370, 110818071, 111546435, 111913516, 112410936, 112869120, 113733621, 117162760, 117660180, 118586391, 118901146, 119262430, 119398566, 119765646, 120441685, 121088331, 123169761, 124492446, 125743255, 126158956, 127177051, 127848721, 128210005, 129022180, 131252836, 132065011, 132793375, 133097965, 133595385, 134252196, 134613480, 135285150, 138689265, 139501440, 139833331, 140645506, 141373870, 141968190, 142335271, 142832691, 143865645, 146908476, 147269760, 147685461, 148081935, 148449015, 149008146, 149593081, 150051265, 150548685, 153591516, 154842325, 155488971, 156165010, 156580711, 157029510, 157955721, 158352195, 158767896, 161674591, 162197035, 162843681, 163215130, 163861776, 164384220, 165528286, 166850971, 168932401, 169526721, 170622166, 171119586, 171434341, 172100215, 172467295, 174287400, 176007546, 176368830, 177330231, 177691515, 178107216, 178870770, 179202661, 180014836, 183723540, 184451905, 184867606, 185264080, 185910726, 186277806, 186639090, 187054791, 187451265, 188377476, 191527050, 191942751, 192618790, 192960846, 193626720, 194211655, 194858301, 195534340, 198210090, 199721236, 200107545, 200523246, 201199285, 201566365, 202213011, 202889050, 204970480, 206293165, 206708866, 207157665, 208301731, 208606321, 209624416, 210793506, 213189691, 214145295, 214512376, 215009796, 215289361, 215656441, 216042750, 216699561, 217060845, 220626120, 221552331, 221948805, 222364506 }

  42. 935948505420947

    Returns: {0, 1, 35286553987839, 900661951433109 }

  43. 587566476

    Returns: {0, 1, 20984517, 65285164, 81606456, 86269681, 146891620, 167876136, 233161300, 354405177, 419690341, 440674857, 501296796, 505960021, 522281313, 566581960 }

  44. 3925899847

    Returns: {0, 1 }

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