TopCoder Statistics - Problem Statement

Problem Statement

You have a set of cards. There is one non-negative integer on each card. Different cards may contain the same integer. For each i, the number written on the i-th card (0-based index) is number[i]. Your friend wants to select a subset of those cards such that the bitwise xor of the selected cards is less than or equal to limit.

You are given the long[] number and the long limit. Count the number of ways in which your friend can select the subset of cards. Two subsets count as different if they differ as sets of cards (even if the corresponding sets of numbers are the same, see Example 4).

Definition

Class:: XorCards
Method:: numberOfWays
Parameters:: long[], long
Returns:: long
Method signature:: long numberOfWays(long[] number, long limit)
(be sure your method is public)

Notes

XOR (exclusive or) is a binary operation, performed on two numbers in binary notation. First, the shorter number is prepended with leading zeroes until both numbers have the same number of digits (in binary). Then, the result is calculated as follows: for each bit where the numbers differ the result has 1 in its binary representation. It has 0 in all other positions.
For example 42 XOR 7 is performed as follows. First, the numbers are converted to binary: 42 is 101010 and 7 is 111. Then the shorter number is prepended with leading zeros until both numbers have the same number of digits. This means 7 becomes 000111. Then 101010 XOR 000111 = 101101 (the result has ones only in the positions where the two numbers differ). Then the result can be converted back to decimal notation. In this case 101101 = 45, so 42 XOR 7 = 45.
If your friend decides to select zero cards, the bitwise xor of numbers on selected cards is zero.
If your friend decides to select a single card, the bitwise xor of numbers on selected cards is the number on the selected card.

Constraints

number will contain between 1 and 50 elements, inclusive.
Each element in number will be between 0 and 1,000,000,000,000,000 (10^15), inclusive.
limit will be between 0 and 1,000,000,000,000,000 (10^15), inclusive.

Examples

{1,2}

2

Returns: 3

This set of cards has four possible subsets. Here they are, along with the corresponding bitwise xors: {} => 0, {1} => 1, {2} => 2, and {1,2} => 3. Note that limit=2. Out of these four subsets, for the first three the bitwise xor of selected numbers is at most equal to limit.
{5,5}

3

Returns: 2

The two good subsets are {} and {5,5}.
{1,2,3,4,5,6,7}

5

Returns: 96
{123, 456, 789, 147, 258, 369, 159, 357}

500

Returns: 125
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

1000000000000000

Returns: 4294967296
{1000000000000000, 999999999999999}

65535

Returns: 2
{94850781}

389830099

Returns: 2
{17472916,59510986,42560308,59510986,36092792,51911087,3367526,19911691,42560308,24093375,28876185,64709561,42729495,14795022,56312627,47134709,12604716,28575212,63746632,1868356,65500809,10726762}

127740247

Returns: 4194304
{1796897187,3110428520,495010234,3110428520,1250495315}

706385042245

Returns: 32
{1173388,13553697,13553697,1173388,8676532,13553697,2189810,13553697,1173388,8676532,10701832,8676532,11380449,14384703,1173388,2189810,13553697,14384703,13553697,13553697,1173388,8676532,1173388}

13082385

Returns: 6553600
{447092566,370130308,105957230,496765452,442320979,126628873,126628873,96898404,318562782,206582021,88186462,315930944,493274298,423802589,485833595,43630462,96711549,187307332,155214673,350418255,442320979,103009003,536779377,68321327,140335177,360577857,171187990,427497615}

847688216

Returns: 268435456
{347963,117851}

1045342

Returns: 4
{345891921,382252721,345891921,345891921,382252721,382252721,398067702,398067702,345891921,345891921,345891921,382252721,345891921,345891921,345891921,364380802,368124924,398067702}

948354736

Returns: 262144
{14,9,14,9,11,14,1,0,14,11,12,5,6,3,9,0,12,3,11,3,5,11}

13

Returns: 3670016
{13,11,11,4,11,11,4,11,13,11,8,4,11,9,11,6,4,11,11,4,15,11,11,8,9,0}

22

Returns: 67108864
{320235966202,320235966202,320235966202,320235966202,320235966202,614528978117,320235966202,320235966202,665872917799,614528978117,270795366515,320235966202,320235966202,320235966202,320235966202,320235966202,665872917799}

1828482228647

Returns: 131072
{118737329710}

49261899825

Returns: 1
{64802504,64802504,64802504,64802504,56889473,64802504,64802504,64802504,64802504,64802504,8204147,64802504,3635306,64802504,56889473,64802504,39061103,23898284,56889473,57781775,8204147,64802504,40101688,64802504,20473037,40101688,64802504,64802504,61158801,64949173}

24389516

Returns: 390070272
{3546270,3546270,3546270,1869121,3546270,1869121,1869121,1869121,3546270,1869121,1869121,1869121,3546270,3546270,3546270,1869121,3546270,1869121,1869121,1869121,1869121,3546270,1869121,3546270,1869121,1869121,1869121,3546270,3546270,3546270}

3856006

Returns: 1073741824
{172564452326,269421820672,207030719330,269421820672,237337281986,269421820672,172564452326,172564452326,172564452326}

367896085320

Returns: 512
{65069716763998,65069716763998,65069716763998,31449466968111,39589894299452,51986095960384,30701808095826,273928008525,64027590495288,54985882892490,44154616180100,41313531765162,43279255109598,30701808095826,50994534192686,39373064269149,3478382699652}

79591678423034

Returns: 131072
{4620229494258,4620229494258}

116371805856908

Returns: 4
{0,0}

1

Returns: 4
{2047,402,2047,350,3708,2396,321,402,402,849,350,3440,1395,839,3708,1698,1233,29,2907,3775,402,402}

6450

Returns: 4194304
{256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057,256015878057}

126004841217

Returns: 134217728
{8152,1182,5042,5042,2792,3227,7072,5775}

11821

Returns: 256
{18979775,18979775,18979775,129730384,99406593,18979775,303541169,124335603,124335603,416984272,187528979,395838648,148397171,153374719,191584869,408134687,129730384,416984272}

700821494

Returns: 262144
{115079435864185,115079435864185,115079435864185}

136313932599609

Returns: 8
{1556,773,1835,1997,715,1373,1835,1835,1746,1327,822,1796,48,1835,1643,1205,1913,944,1607,1556,263,46,115,1680}

3743

Returns: 16777216
{6981524016,6981524016,1032019805,5728047350,616002756}

13804162051

Returns: 32
{716825,716825,716825,817073,163249,604282,163249,225104,107346,306808,249881,676731,604282,28318,666491,22211,141866,78422,589851,847113,735608,87896,141866}

566879

Returns: 4535040
{841,841,841,841,841,841,841,841,20194,10235,20194,20194,841,841,841,841,841,22686,841,841,841,841,841,841}

18303

Returns: 8388608
{99368703,99368703,28931398,99368703,28931398,28931398,99368703,28931398,28931398,99368703,32157120,99368703,28931398,141122332,28931398,99368703,28931398,99368703,168273884,38746575,32157120,99368703}

56513486

Returns: 786432
{28483985028,28483985028,516109654,32927141191,27220652688,14693288914,21148344902,25547322620,22742420130,22742420130,516109654,516109654,23935211821,18125665211,31714208492,27220652688,31459057110,39500280,6419870405,14942096956,30550487795,23029646592,26700043829}

66826169339

Returns: 8388608
{3078272407771,3078272407771,3078272407771,6009914638346,6009914638346,6009914638346,6009914638346,8880678528176,6009914638346,6009914638346,6009914638346,3110039865811,6009914638346,8880678528176,6009914638346,3078272407771,3078272407771,6009914638346,6009914638346,31445627246199,16742162766107}

26304682655221

Returns: 1572864
{4,4,5,4,1,7,7,2,1,2,0,7,4,7,4,0,5,0,2,1,6,0,5,2,1}

2

Returns: 12582912
{2039473841,2131906455,330595239,2131906455,253523551,2131906455,316032261,653175048,316032261,1776547613,330595239,1004167570,330882000,330595239,339410124,311371558,1460438064,311371558,2039473841,653175048,2080638023,1042504380}

365896469

Returns: 714496
{8758257,27440243,35644303,32837531,20235702,15751314,29096303,3752070,52717063,48440448,48796810,32837531,13903564,49721868,42392662,16494759,12954034,64221666,7472047,17829311,13550433,13857781,40646500,39825235}

119847958

Returns: 16777216
{1732791681,477537135,1732791681,477537135,477537135,1888058626,1765525686,1888058626,1361798723,477537135,477537135,566273598,477537135,1995607703,477537135,1078552222}

3348512508

Returns: 65536
{5,14,13,13}

40

Returns: 16
{428,428,511,428,428,428,428,428,428,428,428,428,428,428,428,245,428,428,428,428,428,428}

347

Returns: 3145728
{10970663080321,10970663080321,10970663080321,10970663080321,1392251661411,10970663080321,10970663080321,10970663080321}

20328364895058

Returns: 256
{522787159046284,694218385472568,195620491063911,460704348246285,90215349322796,193461038067761,136566925388562}

1000000000000000

Returns: 114
{9569,9569,3645,31012,31012,3645,31012,31012,9569,31012,32244,23791,31012,9671,17201,31012,23791,31012,2175,3852,31012,30635,31012,31012,18442,31012,31012,31012}

5467

Returns: 44564480
{33260955583,33260955583,33260955583,33260955583,33260955583,59928439036,33260955583,49752786542,51034508179,33260955583,29600365158,33260955583,33260955583,33260955583,31537040477,67848946818,33260955583,33260955583}

106049320509

Returns: 262144
{344915374,344915374,344915374,534132489,344915374,203752373,209569048,150132827,365836533,344915374,344915374,70994636,344915374,344915374,344915374,534132489,93742832,455369578,242224191,344915374,180378809,374157181,534132489,186979854,180378809,374157181}

384265140

Returns: 48037888
{0,0,0,0,0,0,0,0,0}

0

Returns: 512
{483968784255,173628052070,463818289976,463818289976}

1026171429932

Returns: 16
{1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698,1052779378698}

5031696167716

Returns: 131072
{1139363827,1139363827,1811008518,1731291073,2052100896,1731291073,1731291073,1811008518,1729618451,345526101}

2756908370

Returns: 1024
{43485349,75414518,43485349,43485349,73028123,75414518,43485349,73028123,43485349,43485349,75414518,90054923,73028123,90054923,20039646,75414518,75414518,75414518,120761828,75414518,43485349,133614420,115777738,43485349,75414518,90054923,75414518,26797165,106109802}

146302294

Returns: 536870912
{62179993,62179993,62179993,26496582,20634057,15935322,20634057,14910222,104442753,20634057,84581617}

248536116

Returns: 2048
{7555,4637,4637,11822,4637,11822,4637,4637,4637,3051,4637}

13911

Returns: 1664
{205172527516,18388817974,519418237648}

497278825672

Returns: 6
{19957,19957,19957,2989,762,11526,2989,11526,15908,8148,2218,8593,21914,762,18439,18951,11466,2989,5855,2989,2218,11526,4792,18367,15750}

42390

Returns: 33554432
{64435684888,136541376414,12136964968,90007216858,89040941167,85567972624,72792275414,58881126113,60460309739,77244272239,120521174362,134628568018,126155138337,109495707779,37688069675,134822499097,73250352315,129290238776,121407872117}

85357874714

Returns: 325616
{70863218299}

1471275754512

Returns: 2
{9723,43753,9723,43753,43753}

100356

Returns: 32
{5880578,1556919,21650952}

17950363

Returns: 5
{62}

71

Returns: 2
{529788765350,529788765350,529788765350,85236229128,1777602481871,529788765350,43245876106,1439264389500,1777602481871,529788765350,1439264389500,529788765350,529788765350,529788765350,1777602481871,1046976785397,760450509750}

3492974172777

Returns: 131072
{7796351107294,7796351107294,7796351107294,7796351107294,15858951504206,7796351107294,7796351107294,7796351107294,15858951504206,7796351107294,7796351107294,7796351107294,6786161211696,7796351107294,7796351107294,7796351107294,6786161211696,7796351107294,7796351107294,7796351107294,7796351107294,7796351107294,7796351107294,7796351107294,7796351107294,7796351107294,7796351107294,7796351107294}

11163668209207

Returns: 201326592
{12857,7269,7269,1756,1863,2712,7217,8832,965,7934,965,13336,14880,2856,13475,6146,965,10594,7269,7233,10733,7167,12207,15987}

19912

Returns: 16777216
{28873,8337,25521,3307,21163,5254,8567,2461,12073,22225,23163,16171,14342,27300,22434,22225,30108,5766,11259,13785,11423,10018,24649,3389,5417,414,16391,5799}

47450

Returns: 268435456
{6331896147129,26118361816075,14192968382894,26118361816075,42086667543717,26118361816075,26118361816075,126904599236617,26118361816075,26118361816075,103218184509627,105942353680938,126904599236617}

166203791207409

Returns: 8192
{12,7,7,15,7,1}

21

Returns: 64
{10,10,23,20,30,23}

40

Returns: 64
{41472,102802,44894}

186685

Returns: 8
{219}

346

Returns: 2
{113182082}

2959462002

Returns: 2
{6593,505,4577,6108,7722,7655,8074,6479,7107,5360,4577,8074,274,3041,5360,7267,274,6191,2127,7107,3911,6368,2891,6085,5998,4879}

7010

Returns: 57434112
{457302828522959,534761657601376,226482104846092,480082361447470,480082361447470,480082361447470,226482104846092,330466099016213,462270969818082,90476800704392,226482104846092,330941893647857,90476800704392,453610200097811,545349468230510,90476800704392,226482104846092,531309405029496,330941893647857,536889149380384,333834914422158,90476800704392}

259980983878512

Returns: 1936896
{3,3,1,3,1,1,1,1,3,1,3,0,0,3,0,1,0,1,0,0,3,3,1,1,3,1,1,0}

6

Returns: 268435456
{157184,157184,171177,171177,41361,205673,54878,41361,28349,125321,171177,171177,157184,193149,205673,171177,18362,157184,153865,62572,205673,157184,62572,54878,157184,215913}

273243

Returns: 67108864
{903647712057,874388212152,874388212152,748077558901,874388212152,483314850365,278209796736,874388212152,874388212152,475835289893,869115575054}

319749593310

Returns: 576
{16059226,7710083,5886530,7577608,13407029,13072478,5404377,5553512,1197417,14967738,4723973,2197385,14821432,14203900,2680950,3382555,4175202,1197417,16446246,10200229,4723973,14489858,3382555,2031167,8841113}

21675618

Returns: 33554432
{0,0,0,0,0,0,0,0,0,0,0,0}

0

Returns: 4096
{72833600599,72833600599,72833600599,72833600599}

483379988577

Returns: 16
{354647150813,354647150813,354647150813,354647150813,354647150813,354647150813}

4874760895126

Returns: 64
{34134114405,11305053171,30909598199}

66821343744

Returns: 8
{139063764810241,139063764810241,38524460352019,74019126155222,39769354041229,57650682144413,38588035851310,95759861055871,74019126155222,77580498923038,57650682144413,57650682144413,39769354041229,57650682144413,100826309894356,39769354041229,39769354041229,39769354041229,43264489488976,77580498923038,100826309894356,38669205823001,120602548087226,120602548087226,74019126155222}

279846098992243

Returns: 33554432
{133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567,133132668957567}

201934887016406

Returns: 16384
{169222847524489,287839693287286,145916941803024,439879253933962,353600076421171,104964790102694,60003823962152,14616351899160,534917365513185,346183707736579,104964790102694,51731955073824,137396483044195,119884362801217,439879253933962,128343311194657,475400643608551,91051747937442,436412903319693,14616351899160,338852843732326,452240687342811,165615165139075}

430430149258778

Returns: 6413912
{66876435558,25503880086,25503880086,66876435558,66876435558,25503880086,21533436954,25503880086,20267567844,25503880086,113122278968,134556924907,70712107616,25503880086,106760878309,42401887895,25503880086,28869800455,28869800455,115718147232,22358616852,56380482115,66876435558,59233853744,120764469982,25503880086,115322486720}

258928559645

Returns: 134217728
{1381247,1381247,1381247,1381247,1381247,1381247,967715,1381247,1381247,399415,967715,399415,399415,399415,1381247}

640873

Returns: 12288
{10,10,7,10,35,30,30,9}

99

Returns: 256
{21362885149,207251790997,88436218948,71069969483,21362885149,153345364194,181178680109,71069969483,222898522798}

282719845998

Returns: 512
{734,734,734,734,734,734,734,734,734,734,734,734,734,734,734,734,734,582,83,586,734,734,734,734,734,734,734,734,734,734}

2513

Returns: 1073741824
{109800603884,34005003189,101946809947,44737549732,130336832010,18864062197,36850128756,91503052667,21454988281,67806382384,79229095515,34005003189,83961475809,51627272691,18864062197,671983253,48129014272,114927845554,27563665139,33861484510,17505462450,90799181254,114927845554}

257932757353

Returns: 8388608
{4849,321,3354,15494,4849,12803,12803,5135,11756,12455,3776,3354,1577,9412,657,5210,10010,14629,8212,4849,10460,5919,3257,321,15023,11440,1629,427,10010,13075}

15414

Returns: 1010237440
{706,706}

191

Returns: 2
{3635062083,3635062083,3635062083,3635062083,3635062083}

188292872087

Returns: 32
{5875079711,1146123732,5473738542,5028941256,4682631110}

12794553166

Returns: 32
{53842506125,23323296681,20211988869,20211988869,20211988869}

113650575683

Returns: 32
{1525545551087,7348427149267,8458331654300,15397074313592,6475625092404,6961383161383,6282681199933,2484948381545,12119670282630,10561497368446,5019924786667,13336387896681,2932442473535,7348427149267,3111028619699,2060385927863,7207119817877,6133627086255,15208613190558,8631620578290,3285024805895}

30114806523361

Returns: 2097152
{3128210,17918258,17918258,3128210,3128210,17918258,17918258,17918258,13834901,17918258,17918258,27919405,17918258,13834901}

36841247

Returns: 16384
{1547059775,612539477,1682906686,1968035748,1052361257,1136423296,53072912,894174732,1550023366,369829201,1954135292,770906706,173379496,1517517185,1763440304,1039792322,313113194,1442435373}

2130269687

Returns: 260037
{684159671407,684159671407,21274342569526,21274342569526}

8413478663785

Returns: 8
{48910731,15514729,48910731,48910731,48910731,24900578,24900578,15514729,48910731,13103122,48910731,15514729,48910731,13103122,48910731,48910731,24900578,48910731,24900578,39189978,15514729}

35295715

Returns: 1114112
{7,7,7,7,7,4,7,7,7}

29

Returns: 512
{18439,29151,41041,29151,41041,46632,16130,41041,36107,41041,41041,40059,41041,23615}

65245

Returns: 16256
{6282633673628,2499206663952,2499206663952,274704682159,1163253302272,2331238896218,3942782676622,8479973022333,3667895657581,5479072663903,5216447954606,1714072335053,3709095404607,3942782676622,274704682159,1046923581336,8787837998934,1880117331344,5877017797582,2331238896218,6376787594529,3709095404607,274704682159,707455466992}

690040315430

Returns: 1316096
{1048154601,1048154601,1048154601,1048154601,1048154601,279437790,279437790,279437790,1048154601,1048154601,117059959}

1908503542

Returns: 2048
{31677193646842,31677193646842,31677193646842,31677193646842,31677193646842,31677193646842}

86254303955029

Returns: 64
{204426319801,82827975651,127237972044,192299158662,60840309061,127237972044,215195237423,192299158662,17427505878,215195237423,153106286567,192299158662,60840309061,215195237423,269830106703,109831116556,253930329711,92356227409,218396300339,153872705535,103536690729,139609168773,171899382526,139609168773,110131629136}

334685818315

Returns: 33554432
{58019000,824957543,201934017,860782168,860782168,15393029,97929195,649519066,445927454,942648855,186012396,420318112,649519066,560174308,706079901}

1812477345

Returns: 32768
{131235261,178867032,111012775,111012775,178867032,131235261,111012775,111012775}

41224451

Returns: 64
{7092,7092,7092,7092,22836,5684,29361,5410,7092,9796,22836,25359,5794,29361,7092}

50477

Returns: 32768
{1617005604108,702706157513,1617005604108}

753584783106

Returns: 4
{7649640,7649640,278760,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640,7649640}

466327

Returns: 4194304
{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0}

0

Returns: 134217728
{56}

85

Returns: 2
{13035164,2663773,13225905,1068206,11939484,12304973,4010856,14129569,803355,8527978,803355,2959584,15904593,15855855,15262504,16774360,3784331,13274705,16512319,2169505,6879034,8459343,2871037,5022840,7690625,14090464}

7811250

Returns: 31245004
{15498352253345}

109006698559224

Returns: 2
{42840,70792,42840}

181042

Returns: 8
{0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0}

0

Returns: 4194304
{118661,118661,118661,118661,118661,317712,317712,118661,118661,118661,118661,118661,317712,446157,446157}

981576

Returns: 32768
{3882}

1961

Returns: 1
{3,3,3,1,3,3,3,1,3,3,1,3,3,3,3,2,3}

0

Returns: 32768
{1713032,1480792,1713032,472481,1713032,472481,1867495,1713032,740310,1679189,472481,1480792,297916,1713032,618263,326872,1867495,1867495,1533784,854520,1938176,1679189,1480792}

3999564

Returns: 8388608
{20242,31006,28365,3277,22789,4713,4713,17831,2122,13694}

28180

Returns: 880
{21,15,21,1}

71

Returns: 16
{10849,30759,126,5587,20830,920,3026,23274,10274,15853,17148,25746,17738,27342,2492,15922,1811,17090,2123,8712,7998,21018,4810,17675,12409,3085,561,25851,24710}

14097

Returns: 230981632
{83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897,83029549897}

185758298032

Returns: 8388608
{11762,26729,23902,31280,16057,21246,28148,24580,9664,23902,25928,28148,17742,13997,6083,24404,24580,1787,10854,5789,19150,31617,24327,11762}

12179

Returns: 6236160
{141584158,141584158,141584158,141584158,141584158,141584158,141584158,141584158,141584158,141584158,141584158,141584158,141584158}

2364685566

Returns: 8192
{211,211,85,96,457,85,58}

1021

Returns: 128
{206759058,206759058,45484391,206759058,206759058,206759058,248490774,23953117,23953117,23953117,206759058,250929860,175911747,206759058,206759058,248490774,206759058,66393410,7715691}

367256975

Returns: 524288
{111238456556,111238456556,79351968680,79351968680,79351968680,79351968680,9571068590,111238456556}

110921384078

Returns: 192
{245167,434271,245167,443718,434271,443718,434271,443718,188676,338908,443718,272831,344993,245167,434271,272831}

725343

Returns: 65536
{20765493186907,20765493186907,20765493186907,91827524780244,20765493186907,20765493186907,31094053098708,20765493186907,20765493186907,20765493186907,134010586124881}

69065045183720

Returns: 1024
{215360895561,1047121902656,632316770510,215360895561,342820097740,3211976756,690006250954,420442028453,215360895561,544144785132,342820097740,838829220451,461704804655,101990664447,883601169673,273882604772,701276242225,911280574445,763656080747,1005131759611}

698458998492

Returns: 666096
{3,13,11,8,8,3}

2

Returns: 8
{877268611,6907003200,6907003200,6030708637,6030708637,6907003200,6907003200,877268611,6907003200,6907003200,8588706504,7358914638,5297158002,6907003200}

12761569097

Returns: 16384
{190416,90324,190416,59996,190416,190416}

154730

Returns: 40
{1,2,1,2,3,3,1,1,1,3,1,1,1,3,0,1,1,1,1,1,3,3,3,3,3,1,3,1,0}

1

Returns: 268435456
{160,160,160,160,160,160,662,160,36,160,160,160,884,160,160,160,160,160,160,160,160,54,390,160,61,160}

715

Returns: 46661632
{53239988240116,53239988240116}

143623100391642

Returns: 4
{5370248655,5370248655,5370248655,5370248655,4365241154,4365241154,3733635035,5370248655,5370248655,4175039085,5370248655,5370248655,5370248655,4365241154,5370248655,4365241154,5370248655}

15080724093

Returns: 131072
{62320,62320,62320,62320,62320,62320,62320,62320,62320,62320,62320,62320,62320,62320,62320,95834,62320,62320,62320,62320,62320,62320,62320,59291,95834}

17136

Returns: 8388608
{42437378,42437378,49985174,42437378,42437378,57458710,64157598,64157598,42437378,42437378,42437378,42437378,64157598,52785770,40081885,29425562,12188279,42437378}

62037206

Returns: 242688
{124,87,57,42,124,88,3,94,126,57,70,14,88,124,43,8,69,124,48,93,71,83,48,44}

205

Returns: 16777216
{3,3,4,7,1,5,5,0,0,2,6,6,2}

9

Returns: 8192
{142509562,235001688,235001688,241571060,74561847,235001688,142509562,74561847,177699993,235001688,147101900,134107409,130554171,130554171,134107409,202525236,134107409,134107409,130554171,141595836,130554171,96502608,74561847,120322369,108244410,147101900,92559749,74561847,130554171}

323082833

Returns: 536870912
{492973312,479209603,695623826,477446412,255922934,998012346,736191050,361908180,806029445,662854250,255046906,987673161,817568232}

1384254530

Returns: 8192
{6882145,6882145,6882145,312248,5661377,777506,6815570,7743629,6882145,6882145,4677420,7408931,5632655,6318646,6882145}

8598450

Returns: 32768
{8,8,8}

3

Returns: 4
{1726248,1726248,1726248,3162456,1726248}

2661521

Returns: 16
{21108186551,21108186551,21108186551,51561899622,119775238721,21108186551,21108186551,21108186551,21108186551,21108186551,21108186551,21108186551,2067819742,21108186551,106866543021,117558640854,21108186551,21108186551,17912485358,21108186551,21108186551,21108186551,119775238721,17912485358,69717326572,21108186551,107455128976}

234878839282

Returns: 134217728
{1628564880626,1458010402429,601516605998,796804476864,1861600717212,9730157828,9730157828,9730157828,601516605998,601516605998,171328093322,1040852624356,1506648853605,142024929718,171387370345,849880593051,601516605998,9730157828,881170289599,1196572349939,455809194003}

4040575329738

Returns: 2097152
{1139371649757,1031157217476,4275054062203,3819650582769,3482633924386,904041743856,3653906351365,451741927951,398904199121,451741927951,830629898338}

2280323610144

Returns: 1062
{230439168775302,871358722690135,933971064126848,279140017930193,66003370080178,669492557245193,696668845503284,389900693440761,780551931136717,529700159197054,317995492941156,969137414695412,680575544538582,907864928989350,737915241541389,265556158356642,654514048361953,911519171366054,938336501340216,675504637724932,202904209569917,901312711083496,506284871810745,908990636416485,371191254602724,252727349741571,754109438453009,693667102148943,860205030347996,137077747103272,105411037308476,349693310594251}

696730301101174

Returns: 2657815175
{19571795163729,997989487305292,279933343057784,970780237810874,988873834816340,322483033700563,100400033384935,447038313753582,811826497417852,960822465910847,585299493116234,612276636572131,415970085175186,180151507785600,398050933367353,739357370384083,578605271926230,573690761891892,254453605983753,208944616272249,465717572184712}

221993608953329

Returns: 413495
{252169030545198,213095283360849,807266218936090,517725625690398,200246041279414,603702635280711,55325270208297,330134420757446}

526434891412352

Returns: 119
{821167815388766,98712232442651,609185211920646,189339228067980,88854487187522,700518066924948,747289204742049,356992913838953,884568608642725,977649414395449,641580982323430,471173577726554,725858570867334,844193471902038,491363443493240,10220906247883,530628573613618,566958528727709,94591882825619}

173138858829027

Returns: 80624
{769549131599036,296140427648457,712005875203067,687213030295779,556166418712103,628973858916448,446217495905508,429693010686287,490649367202934,199031751622903,535528567823253,683824710264509,603792771152607,886992755300511,513960892784026,353220937814135,809227479606200,793566996652558,963610920543839,152839105543873,767025873841433,777490279428503,302956570338434,767318758336666,833577457143899,550812142299732,960205808153201}

148678451971515

Returns: 17723853
{955573473073481,348804958727584,674244861680999,657929278131472,129711940895415,540159208827401,126120034818607,367350846778773,874145484124298,817682039927964,394042233777925,19890506905353,849478329066628,55605540799177,208077789371028,176226676397029,56876836601972,149776258106846,558889723709335,95037698172579,668438078220438,751600285698179,257413990913225,497432278591511,800989289404489,246509321388670,852146452256707,495937102019474,841839870009011,453067546063737,8864198408941,459533378854545,409081619886402,379245172054812,658330276563392,694366716117896,452276001095065,265865136686136,502557798388706,4029921809056}

203287628922503

Returns: 198523075120
{866065528549239,288935082565648,747600081871933,131633154716406,999916897376273,340593617871988,307090913629341,147208546283679,996966862156215,388843705805157,616695718849522,823405291398556,443753419854057,568218026589944,612113984494007,863629111221741,520556560796763}

590358256728170

Returns: 68727
{201447809454218,855043914760620,805898903824538,519624637451625,840342001147237,486953706419367,133849289096234,588810809574909,541383936760099,800528401402281,217863602894200,193076445449529,153109667438839,988523028111030,136836318724045,709631160551132,211119009542101,920433064009133,698259703482715,665382292800896,792218818879613,256427881750844,197637489421842,648615606946755,483340317461479}

893560024565498

Returns: 26630164
{441291490524789,564813072250978,578777984478449,839225959170888,70280167427816,996920989284517,915708477007234,270035155493368,31562853233400,717680210459449,469221767768055,65714426872351,561149020430454,75065099009807,433710049780387,691285879484166,6081032138960,188531484956919,416952345946867,747741561067313,763361264271485,347094291830924,551303318851400,360406621934083,360938565576029,418508877846590,401664137336607,73588715051856,500708279420336,867199990520464,817730736729920,602414854580051,419281863080941,26895740546741,247736239400019}

459843203970788

Returns: 14033300900
{560095709775491,198385067568751,901942361795998,667219141796720,378421309757054,855949831952437,985099186880696,727798777433352,864176350469617,447440488641850,625540307449764,945759571661541,894668704024559,233255165471886,248758538499165,266500049076607,924966879348140,236550461654308,20094018279637,697489602308995,901735709146363,458281718706390,325118724913077,240385545794193,471004281330780,851500219006562,598516028108251,6058595507116,885190594448212,547479505786357,668480072965614,187082100224937,712384501597660,952245481380527,761604165826809,367915600198821,419359088514942,485203001724917}

92086972355364

Returns: 22482170986
{52995711079076,429532512432578,959873705104803,335115110262925,950792081945764,545781861024821,145305791684053,73686307089267,512129252908002,412790809935712,719593177691003,804614228055545,730536963808429,597502661339614,339039120346878,161303786753067,450941153706258,158326432010454,239429525106303,24800252972436,730796338424809,320624190533799,744926116578723,900599256301401,791961445945591,765669110800166,226165631657876,884565634686410,551743365008006,452675006415769,449237814068055}

88166597949260

Returns: 168164440
{165362102787735,960281923469880,657439007104670,694274849798015,231975827704303,360156940286637,724411397815070,436195572383210,116003695953778,907989343066082,926684495384873,592766455515817,537608245976258,754156328429371,790830321236491,55516330015770,879146773358218,214868076171919,535884443661174,915463428892884,604959806212087,771012498578508,138425957988750,705325614342138,162494569616248,278853640937657,315449203755285,44642740920532,46533042546929,416817471554827,214704598930498,137640936538412,310143621953723,631477252863519,233791979608698,921206857508361,136742094860204,312547906940019,616346285072274,85676192562793}

557330734892846

Returns: 544268295794
{905053692443712,171672188017121,754214790989774,485203864187073,706779863985060,121938553587692,37491969830176,637390041048711,911392988822562,931371727324539,375440188968144,9937157067075,212736820743114,883718384110369,245110600353081,812461421733176,510671209149963,903696504773376,521351548404990,270014084741990,552328404374066,457545375685787,694641549829471,742768034991028,377174308813618,69541695260231,963507707470338,771335203801212,159083572837176,405824685260197,984612248096739,32373831171104,932905079367297,888106083523137,761034585233044,93699112181627,786722985243407,76099221181015,467610666453140,823142712004337,863933529855045,983844830220799}

650873309007933

Returns: 2542473863312
{691491060954999,889780741243807,123433782077675,770894712381087,41140825941466,794574136600024,83551201484025,881148149483910,782986296270978,278523263445093,597308530352583,201607810669478,826981269433968,926551581223099,880044654479777,123249745389920,960023301615520,618602434300415}

124341142503081

Returns: 28952
{819485716185608,100495773708784,347441513826594,423187403879067,446500172662624,59220245417969,342554093598823,516622044463204,943571105029639,722565634597084,207801055431506,482062091185320,144311848668567,446654362720542,185277217454714,606548959393131,101922166991450}

93041630382231

Returns: 10831
{449012858990188,256159674243939,355209093067393,80106605816712,498248987381795,41805214039649,787345897907817,92717237154652,480001680948905,694093962555294,628981884706720,133030576902044,480978063692704,773534282555159,967698603283894,14281312931611,286212804385179,957328443755659,59430362835483,954087969234713,35614586847072,330191754415463,481311776263579,332989998757729,12384217394099,148025309436582,389156928725931,659807676263203,252871064928380,817480008269026,28474405624260,636812615455669,29338319108191,888879826939080}

946898949606294

Returns: 14448531335
{71811878681775,718240364923350,813052789537887,348384316709848,657592876802695,125596479329683,401809027671683,421697766520333,441200100158541,163764802109150,283477731271297,10076072631768,236722557493088,694970614609461,612868876559371,657179941416316,910346790773885,70669591412028,983789371843848,512167276194349,198271483672226,808685445703106,254887700588372,686422916832121,682400819027347,247145186571799,100795776246133,367601154970191,772195305335115,953955169765959,705581625185150,217799037348623,168987328142899}

542143143160956

Returns: 4136223928
{754879502638522,523222565661172,44455361582318,369513451195810,122729540781409,519400641229076,580589123932285,304432859089580,448283023481026,501924307364345,729902537410766,97591055343982,842560223976225,781637731988142,846273403393554,104425321038630,454525987528573,718643454934004,775406781800192}

435580884034476

Returns: 202834
{731314473228804,315028955804777,984560790591316,658324776506442,888327720261255,254544840210869,853417413314741,179103889415749,948039130419395,30342666878324,82889096803742,41474580951674,950968604499676,841953414974673,362951409549441,345088962765421,563727104271780,151000819904462,569799025249707,999758725569697,190203371423385,653464331222246,748114390890544,382572396176891,689645073763015,251142035679090,479316397278699,411034295225608,860970658533319,294124615642180,695198793224454,876302394926535,408607078507672,224213243716758,799936657330818,748001047776859,394539650778831,492854009833932,494754707131584}

970591854587110

Returns: 473921803996
{595718337164216,248488069521564,733008902145826,819598486770774,472201159933378,210000273907830,191920713132976,283075130900738,607609467486718,621841769688634,587005982696374,524832391967247,834181361361226,472183136670842,459543651334505,756100523133692,231318711571454,195140755099547}

749147699929315

Returns: 174425
{455354282547774,139842177064905,244651057622763,595288309530047,240107843222994,451477965945939,281642794224215,17044431182894,101570218308345,467205837986848,384969484917905,437686306306997,296781500393795,799289818906809,67343690932990,421918040446018,475704167093236,868469284548031,218125500274859,590727763262754,781048718913279,542703836702980,641106652755277,410444377524603,405153497098655}

738102446202514

Returns: 21997167
{421905154400500}

508741773640204

Returns: 2
{591322429106307,202625762456095,167641891825707,791149378902745,285511575447681,269880016826747,892575955843897,483595527603130,923066641576422,885102463469708,653278100245500,331535416605463,634333496720722,55329882047250,960714834305011,433128845731477,460175172674224,883450017716365,14427008123899,738948758230697,907052435243110,601300604156766,165419784177291,523794104988124,999548911674817,304566456570341,749354514218462,828994956891116,330182776195102,303728240970604,404142002966795,996122547761229,161374694967812,237362764811955,258003959919042,785592456857910}

946710664049277

Returns: 57782633304
{312477703406027,873758626275343,544038949408952,606612998664994,4308842772814,479893192121659,386594208564714,683158997116543,620572343154030,961703055454120,269638771624587,287648938368744,887970416373385,264923165375339,295625585187892,305985997407268,759534992146001,944237589912388}

294691219295405

Returns: 68612
{556619589089797,581072291356849}

710410654713910

Returns: 3
{713614818370940,101734714270551,424123850959205,554486674859080,941911425458352,535650300983494,820906388816697,235283579657389,880101248812386,454953473995022,360671610833398,554810305187932,937699968985044,54729974228667,963140320187773,242773121020668,609554606389332,495418543668008,366986722489025,99411573817161,893574684363554,892414855026289,566052188420071,878615681563839,887300697540327,35514685148657,829567548585235,635214744559820,835388835854826,722098552742509}

978908651192849

Returns: 933560039
{607401766731779,815775422970156,206638435055190,792777178670202,375490649317946,276512286491742,924313225976802,988115676743738,274562659810194,433019685083746,563669885484052,303881458064081,983710585725453,780252598723351,338979109947008,407751623786823,583635125238662,785423867673148,465176828010206,528114078725285,948061471153607}

906706460189632

Returns: 1688872
{753074743448502,873525061122597,82174303640729,521613077615783,853043020463271,347269211439077,764089139458499,320797192566258,773152442770724,659030062087801,798307563018934,131380352314809,582929138645894,472920949597758,544732924659746,17248793102510,750535178324976,800277605609610,512195447930955,206559711163937,604982444054208,330401544377354,689758442314376,175928531568096,842336370226259,709855267493720,850851890015520,734791061169338,144751985196986,749836151721198,711644768153994}

711435132038234

Returns: 1356954828
{762440527257224,592123927427214,622336223118358,432754420397368,548540920760898,300627380713112,634273861741994,43024637726816,453460478512816,435560006387075,467434354766020,68701038413121,203030693275582,135650211414703,378736950144624,433703880742376,505574957913747,754891518042663,642414420537208,815716745745693,259039464699862,340715575871685,662380967651345,469815267486665,308324318791898,778452552753888,80812809224588,752664816779508,405646276299616,276689002558232,710753364782448}

142390178114801

Returns: 271587711
{404580707195411,209783951030575,834365917587838,782024823984989,189479537126845,324755148518306,395868034057847,587082872662828}

811548924061464

Returns: 184
{114511612627860, 198928487673182, 177806853512544, 539188399412935, 284882157847853, 238524412609344, 201099822762047, 24810400189885, 434787137518035, 229764348474160, 382836645320810, 13369570574403, 99373634370021, 266074425829416, 349279903620245, 439235907726090, 335881102184187, 375799432943929, 112836612487997, 506745939780414, 54310076967473, 467780339102421, 98957157884045, 552734832029423, 546366350568282, 541762091710023, 135570860973533, 471268360173921, 407601396120358, 232357437263238, 68714750276423, 225889693955345, 6952145181236, 498538929253483, 288634800926927, 508611671836828, 467407185281081, 367054732292409, 245183935327225, 455641214340508, 237439099798301, 363439543147620, 7887743974885, 127644208444864, 27992703465186, 85762056638891, 132429116841142, 531785267549347, 427355445605891, 3978435169730 }

263800288364694

Returns: 527600576729388
{612295680503947, 479427226544159, 301034347583491, 537260017553000, 589991511708395, 16942349857932, 394082218242055, 203843068284650, 340983873962869, 760424111529599, 760140276999198, 363713339017914, 537240581316449, 431451589449463, 614013736906439, 320718685734238, 648298499681151, 624081636752612, 431708101915477, 635576054108206, 232270122923766, 178530487778080, 248001588659503, 202760182577350, 681056949190393, 463337090535272, 218843685857283, 630286213275775, 128526136677248, 688698922013266, 688841757117695, 218254952387821, 263478081595646, 522468169280584, 891737597020425, 163052856706381, 341830467684121, 153149240762237, 44338087898104, 249781869448453, 474374930832486, 540851547258599, 162637295982795, 874904233778969, 788509242470174, 475329422701110, 826598354241249, 597794184880802, 384023818019540, 901265995266763 }

424242424242

Returns: 424242424244
{1, 2, 3, 4, 5, 6, 7 }

5

Returns: 96
{45505516239, 767316198929, 853546556426, 990045709274, 954979136081, 602949515176, 848790540894, 929079880931, 54975604822, 769399084937, 960830790953, 312090865931, 77506687906, 88957572486, 785107955643, 145545723679, 673472245957, 454055397527, 161579457244, 589280225592, 255517948858, 748984417313, 639997976756, 112018288251, 526597535745, 449883510737, 326528899914, 710739011421, 82694250606, 243107492436, 417956404567, 325846496922, 289070145066, 867417871114, 632339572983, 322229018517, 756948559211, 544267764505, 887087908241, 154534724200, 165114960870, 176317264253, 649459122513, 429905547982, 322066375795, 664250463159, 629122968871, 766082034803, 173207795097, 406310239265 }

661108738687

Returns: 676975348416512
{3759823479587, 7435723457573, 9832498945898, 2345345577688, 5687435234534, 2345345678845, 3532455675878, 3453452525756, 4563456456688, 3453542354553, 23452355, 34555555235, 245235525235, 2345352432525, 245252523545, 7685685678, 5687688567568, 6788568756, 678568678, 6785678, 678, 678, 56, 78, 6578, 8, 8886786, 678678867, 67865867856, 65785687658, 5678887768, 678, 6, 0, 0, 0, 677645, 657456, 5675467756, 567453245, 45235, 3453455, 3453253523, 234523452345, 3453542345, 3452352345, 3453545555, 2222, 22345354, 234533452 }

123123123

Returns: 7879879936
{115986754660103, 571695633556173, 145679872041646, 748896958622500, 584240156358162, 997042966707971, 243377172855541, 39120288443814, 296404361878866, 892909181017195, 437650892333383, 110853862826451, 748523910383903, 638105260855269, 822555163282288, 662008159746045, 846053870766642, 616428769671477, 108615259929497, 957582929870536, 947443410972238, 888310419673172, 5980200961132, 347571663350921, 895240533076162, 753405306767122, 283747506666297, 597994967001358, 112912375233980, 526239534667825, 243870161471382, 285118727725272, 151544221712966, 174854392150571, 147194133617051, 666910095207798, 499436186321703, 116353755673085, 768139842990542, 878203296977383, 851060613042823, 676079737903718, 334798486503277, 484997878554196, 537060362108413, 448233232937332, 751166036247123, 710932145222969, 869362445557190, 147181050258040 }

25681450236598

Returns: 25681450236599
{842133572, 518731871, 1056171465, 1595448794, 297843800, 2081023413, 1069327149, 337053417, 1298643236, 1309849749, 1874109067, 1984800351, 1545012587, 398817568, 203142545, 1547146615, 1635337291, 667077472, 553622816, 1940091980, 104301277, 1122395835, 334294509, 1896509381, 649557411, 71299488, 924372273, 1766587059, 1906079324, 1907674222, 1906897337, 600729248, 278922445, 815585154, 48694394, 576766245, 749124919, 1118021544, 913819662, 2047768156, 280387645, 640445081, 1885084859, 1825400232, 1039262649, 2088227404, 1225063199, 527116292, 607821228, 1778686016 }

5860981

Returns: 3072842530816
{2674480008996, 5722332771360, 4373238608640, 1135766803800, 7521329056761, 939886719330, 1093565998656, 1477478109744, 16938571249152, 8137679297253, 3753267639682, 657325884800, 2133493861988, 2468304180324, 7194530026020, 2869837152768, 3994222201200, 2964899525616, 653712625314, 567931974525, 4835139719760, 3740401499460, 7381462012692, 671826854336, 1479186786350, 71834902608, 1027483454336, 2370782471820, 17079622560, 5232018575520, 6848465698364, 2560548681504, 1011762428768, 5887452560961, 844909776984, 903490330488, 6267041305850, 66164164506, 963606457027, 2703759534600, 165424538880, 382367399400, 1042259762292, 9825694977296, 1544817364220, 2757564699648, 1360743444750, 4453808720760, 902883451200, 439315799040 }

6651256343243

Returns: 425680405967616
{1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472, 0, 12884901888, 25769803776, 33333333333, 103079215104, 206158430208, 412316860416, 824633720832, 1649267441664, 3298534883328, 6597069766656, 13194139533312, 26388279066624, 52776558133248, 105553116266496, 211106232532992, 422212465065984, 844424930131968 }

10000000000000

Returns: 9966956396546
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312 }

1000000000000000

Returns: 1000000000000001
{159730427, 603350954, 263135932, 771024120, 900727532, 995003849, 270844748, 231075642, 991283852, 82317569, 546430434, 658403933, 2845342, 565806892, 268579278, 955941963, 567098061, 552478973, 762030781, 222956871, 643046130, 589844156, 848366023, 138785820, 484658726, 283739882, 592170241, 718147169, 340535201, 640758498, 857162197, 691022714, 116408393, 966625573, 737991013, 291285735, 839522211, 542232863, 391763725, 631138928, 430558568, 26980991, 714080118, 358487783, 967405417, 42568414, 162904384, 363567646, 524804821, 329713841 }

123456789

Returns: 129453827031040
{1286141121, 1965694136, 1906413152, 1934965726, 1970482486, 1568331914, 1798244646, 1963016959, 1185342530, 1096253238, 1872534073, 1982423443, 1172913690, 1557326757, 1613564167, 1744278431, 1304475198, 1469264241, 1504837018, 1308886574, 1982640793, 1198136978, 1034943812, 1283086231, 1663423243, 1445959574, 1795332754, 1603873138, 1060435944, 1962330444, 1084015879, 1705731424, 1290171739, 1224674313, 1343928816, 1596138258, 1058814141, 1474542443, 1491168250, 1525080772, 1896019084, 1933053433, 1323756998, 1770277947, 1810734114, 1888139015, 1581956181, 1625540570, 1906721395, 100000000 }

10000000

Returns: 5242880524288
{1, 2, 4, 1024, 1025, 1026, 1027, 1028, 1029 }

1024

Returns: 288
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312 }

100000000000

Returns: 100000000001
{333549187132221, 36698974936138, 256933528225222, 137907004915028, 221847050715595, 262985952068840, 6287197820930, 342656330831365, 231436613124640, 348525518188612, 371636145218757, 474696496559175, 308408590002066, 152537658235969, 491538470186601, 328076548692716, 461880614738184, 307166491659873, 107342344723305, 359809150806453, 447231444052384, 433249542202542, 405820021795803, 471035208611450, 515735164983376, 210476767566909, 494025906300821, 129931599408762, 289457144617645, 419956478521582, 542631684997598, 454514441632970, 276021484586288, 553985519551081, 314965740871337, 427133099268651, 387275436908795, 167650501121794, 140951713354366, 481771323395872, 170094578384384, 322143154616113, 396666764844354, 554782245845312, 107391730474419, 120531867865927, 23432318433875, 90061181492417, 129993670602437 }

836688377566342

Returns: 562949953421312
{562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311, 562949953421311 }

0

Returns: 562949953421312
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312 }

12345678912345

Returns: 12345678912346
{4795769098, 7987453934000, 9085415445288, 3928116592400, 3902215643907, 17561248390, 849925976652, 8718675624, 62986392024, 7342092340760, 1748022621462, 429392762064, 11498904936155, 6762025933902, 16790944564098, 544532498664, 4957180857388, 29576568100296, 2247531395109, 208628471442, 829441341400, 15971112576, 1557218539520, 14797116775440, 2605733249700, 7163869652100, 1698818578956, 6066262072728, 1102804784640, 2703280013248, 13535592640416, 1350334623638, 769443953004, 2487415648095, 3123694921248, 320053452660, 3560048557338, 14760400207360, 978641243910, 1310649593472, 2920288064340, 10318124887260, 1485032372070, 379065530000, 5139855082344, 3221289428910, 3155474814063, 3540614535513, 4288467466045, 4393246252584 }

4406549549272

Returns: 141009585576736
{970934889944996, 908075859335833, 964560267914452, 776188478882136, 358066570410915, 485430819281006, 195269687498959, 295610247517444, 729845787391979, 568373097087966, 338261279339559, 837009363129385, 898624570681656, 7507439268498, 274648301773929, 166768838972202, 913034124162916, 435028514479605, 328147325635628, 568635683266825, 475182496233700, 837903853997806, 404442270145350, 22819067453952, 132741070349308, 813579656392117, 294878296411128, 551196248423463, 557248175329396, 523413274530430, 988151687705412, 883311819569268, 28707004841626, 336985907592931, 687167595943573, 279905122301068, 247629568866780, 907355612164228, 12087290264767, 411148070302912, 848962329461612, 535167147357845, 351942584044597, 116417458921661, 625413103944613, 850123529827304, 569823093211311, 30061043727946, 358292867488503, 319924842045257 }

57411339252111

Returns: 57411339252112
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312 }

2152126322512

Returns: 2152126322513
{123, 456, 789, 147, 258, 369, 159, 357 }

500

Returns: 125
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312 }

10000000000

Returns: 10000000001
{433469246190245, 521831032817650, 96989001262935, 766214252790190, 62458651860878, 322432511046291, 401014031013109, 107354328423475, 91439554052636, 80815984673492, 650074406844429, 902921440661105, 387351251865872, 549134928099499, 98891299559427, 159647085762033, 327019862047893, 692465241497786, 573221848031557, 357732246207716, 446772087637821, 280672497694454, 231172273916327, 312508143409258, 177746805040558, 648569156693212, 491028833070046, 612969360354016, 979816177185361, 387710350333066, 707785187328283, 811762701923889, 901815430666447, 321686996645604, 40513579798294, 489627943962863, 132577137544565, 991199476013587, 392646145374210, 917712134675616, 118789517906479, 308226786426690, 220220817624299, 137315477539418, 851262641706117, 138672030322238, 574029482436678, 609075240237925, 965746796891804, 672160462278538 }

944309589163921

Returns: 944309589163922
{757147, 167851000, 301413356, 336971124, 659598368, 160567225, 391749387, 4890851, 35766290, 26239572, 473038164, 597006, 3615544, 326051436, 392289610, 118341522, 170427798, 37215528, 675016433, 168544290, 683447133, 950090226, 82426872, 116752251, 194041604, 706221268, 1069909134, 257655783, 84970743, 21417562, 37379060, 40873980, 8670528, 80835680, 436291072, 653352030, 106923810, 374079500, 466701606, 86546364, 247776867, 480572136, 222071040, 36629216, 366496748, 549646416, 278840198 }

744774477

Returns: 97619080380416
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312 }

562949953421311

Returns: 562949953421312
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

1000

Returns: 1125899906842624
{12, 3 }

11

Returns: 2
{281474976710656, 281474976710657, 281474976710658, 281474976710659, 281474976710660, 281474976710661, 281474976710662, 281474976710663, 281474976710664, 281474976710665, 281474976710666, 281474976710667, 281474976710668, 281474976710669, 281474976710670, 281474976710671, 281474976710672, 281474976710673, 281474976710674, 281474976710675, 281474976710676, 281474976710677, 281474976710678, 281474976710679, 281474976710680, 281474976710681, 281474976710682, 281474976710683, 281474976710684, 281474976710685, 281474976710686, 281474976710687, 281474976710688, 281474976710689, 281474976710690, 281474976710691, 281474976710692, 281474976710693, 281474976710694, 281474976710695, 281474976710696, 281474976710697, 281474976710698, 281474976710699, 281474976710700, 281474976710701, 281474976710702, 281474976710703, 281474976710704, 281474976710705 }

281474976710670

Returns: 694891348754432
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416 }

100000000000

Returns: 100000000001
{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 }

5

Returns: 1125899906842624
{10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000, 10000000000000 }

5

Returns: 562949953421312
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 838608, 8388608, 16777216, 33554432, 67108864 }

1234567890

Returns: 268435456
{281474976710657, 281474976710658, 281474976710660, 281474976710664, 281474976710672, 281474976710688, 281474976710720, 281474976710784, 281474976710912, 281474976711168, 281474976711680, 281474976712704, 281474976714752, 281474976718848, 281474976727040, 281474976743424, 281474976776192, 281474976841728, 281474976972800, 281474977234944, 281474977759232, 281474978807808, 281474980904960, 281474985099264, 281474993487872, 281475010265088, 281475043819520, 281475110928384, 281475245146112, 281475513581568, 281476050452480, 281477124194304, 281479271677952, 281483566645248, 281492156579840, 281509336449024, 281543696187392, 281612415664128, 281749854617600, 282024732524544, 282574488338432, 283673999966208, 285873023221760, 290271069732864, 299067162755072, 316659348799488, 351843720888320, 422212465065984, 562949953421312, 844424930131968 }

1000000000000000

Returns: 1000000000000001
{1234567890123, 12512512621, 38519, 2, 681257129, 84715195252, 91257951278, 1247812, 35627386, 35723657823, 632623623, 124124142, 1000000000000000, 123, 52858, 84284, 385637, 232528, 47886484, 2848442, 6346464, 3838383883, 1818182824, 939535000, 12122, 252526226, 23412345235 }

12514512621

Returns: 3055104
{721626662916753, 737321569007260, 808438297512826, 933509031627694, 592428347181038, 326664770684120, 590550583222362, 293884890359956, 317687495530187, 367630904511386, 313698074913708, 79646901738098, 783236631786844, 384636147959874, 334052213735976 }

158541424416301

Returns: 4614
{548906496475456, 876085050326080, 756083043188272, 210570954232160, 268132518969888, 985852133792810, 383452657785960, 137008882588904, 483974620014764, 374916141656960, 192376202099104, 833939462570240, 97440209369920, 871247433584928, 67805158813856, 390705099927740, 188543693785912, 503895701436592, 47863591770296, 78526703817200, 790416899573364, 773850375888000, 805285013926912, 971076544515000, 445415839223168, 634108391716088, 925862921616000, 40420265681600, 645507612745200, 626804281272400, 120721114515952, 76595305548168, 22427698721875, 323056523713600, 851254915423280, 757268207777084, 280631094624500, 641938840876000, 217693421634328, 148999591961464, 395404688769900, 246233984936080, 933084682149440, 477258785755648, 594113594518912, 227796065592160, 211049756552177, 352184409954875, 148874197962000, 537389411547168 }

537389411547168

Returns: 537389411547169

Statistics

Problem Statement for "XorCards"

Problem Statement

Definition

Notes

Constraints

Examples