TopCoder Statistics - Problem Statement

Problem Statement

This problem is about sets of non-negative integers.

A set S is called perfect if it has the following properties:

it is non-empty
whenever a and b are two (not necessarily distinct) elements of S, the number (a xor b) is also an element of S

It can be shown that the size of any perfect set must be a power of two.

You are given an int k, and two equally-long int[]s rank and value. We are interested in perfect sets that have the following properties:

The size of the set is 2^k.
For each i, the rank[i]-th smallest number in the set (0-based index) must be value[i].

If there are infinitely many such perfect sets, return -1. Otherwise, return the number of such perfect sets, modulo (10^9 + 7).

Definition

Class:: XorRank
Method:: count
Parameters:: int, int[], int[]
Returns:: int
Method signature:: int count(int k, int[] rank, int[] value)
(be sure your method is public)

Constraints

k will be between 1 and 30, inclusive.
rank will contain between 1 and 50 elements, inclusive.
rank and value will contain the same number of elements.
Each element in rank will be between 0 and (2^k-1), inclusive.
Each element in value will be between 0 and 1,000,000,000, inclusive.

Examples

2

{3}

{13}

Returns: 5

We want perfect sets that have 2^2 = 4 elements. The largest of those elements should be the number 13. We have 5 solutions: {0, 1, 12, 13} {0, 4, 9, 13} {0, 5, 8, 13} {0, 6, 11, 13} {0, 7, 10, 13}
2

{3, 1}

{13, 5}

Returns: 1

This time the only one is: {0, 5, 8, 13}.
6

{58}

{57}

Returns: 0

Since all numbers in the set are nonnegative (and distinct), the number with rank 58 must be at least 58. Thus, there is no solution.
10

{588, 588}

{1748912, 1748913}

Returns: 0

The 588-th number can't be both 1748912 and 1748913 at the same time.
1

{0}

{0}

Returns: -1

There are infinite number of them, like: {0,1}, {0,2}, {0,3}, ...
20

{1000000, 1000000, 0, 10, 1}

{449989776, 449989776, 0, 100, 1}

Returns: 863762835
10

{1000, 999}

{999, 10000000}

Returns: 0
10

{0}

{0}

Returns: -1
10

{0}

{1}

Returns: 0
10

{1}

{0}

Returns: 0
10

{67}

{456}

Returns: 0
23

{7522938,6550834,6689420,7989090,167847,4472784,7594339,516907,458625,6784552,6408614,1704285,4984319,6579159,4317896,2965333,546929,2617998,2371906,8331816,6353767,7452182,3537855,2064606,631380,6387834,3517958,5981782,583754,2854678,6409435,6091558,4961618,1348313,3751732,3646043,5630466,3514814,3793943}

{15045754,13101874,13379212,15978338,335783,8945616,15188835,1034027,916865,13569576,12817318,3408733,9968639,13157847,8636104,5930325,1094257,5236366,4743490,16664104,12707175,14904342,7075263,4128990,1262676,12776058,7036422,11963478,1167946,5709078,12819163,12183334,9922898,2696921,7503668,7291995,11260930,7029182,7587863}

Returns: 1
21

{1957169,1696310,1350567,1631371,1383455,995453,1748852,296045,1489562,1294371,818005,394856,11353,744571,160984,1717384,1882443,468905,1821524,1744303,1433690,1767499,1800361,1572002,1112126,667226,2054282,1001508,1195933,571261,1708968,272900,1462124,1335234,1092063,75524,1382043}

{3914289,3392566,2701223,3262603,2766879,1991037,3497844,592237,2979226,2588963,1635925,789864,22617,1489275,321752,3434632,3764811,937897,3643220,3488431,2867290,3534923,3600809,3143842,2224190,1334618,4108426,2003236,2391709,1142653,3417768,546052,2924140,2670274,2184159,151044,2763931}

Returns: 1
21

{83218,291290,1388078,2012388,1814233,192467,1360383,945357,514029,590090,194002,314742,917809,2029158,1023907,1842357,198140,1604543,861909,758146,5621,754685,1162992,1957002,1564898,1191857,453539,815657,255566,86248,1897309,2011693,1002047,85576,1304412,1420840,1166910,1635122,351315,2077756,508471,1538831}

{166418,582618,2776238,4024804,3628505,384851,2720639,1890765,1028077,1180170,388050,629366,1835569,4058214,2047779,3684789,396284,3209151,1723733,1516418,11125,1509245,2325872,3914122,3129826,2383665,907043,1631401,511182,172392,3794525,4023341,2004031,171208,2608860,2841640,2333758,3270322,702675,4155452,1017015,3077647}

Returns: 1
29

{292620071,438027108,29363547,421771348,137253301,101350728,314562059,319447546,42084822,379182878,330051789,49403645,320332033,475911337,60419555,112414801,164406612,398043012,135974132,326041737,83415574,345264783,488943720,129266570,443905027,68456830,103800259,187738782,163083746,43206423,389223315,252203894,356823521,338820244,284706141,259776651,82996280,311223467,223434262,200880500}

{585240142,876054216,58727095,843542696,274506603,202701457,629124119,638895092,84169644,758365757,660103579,98807290,640664066,951822675,120839111,224829602,328813225,796086025,271948265,652083475,166831148,690529567,977887441,258533141,887810054,136913661,207600519,375477565,326167493,86412846,778446631,504407789,713647042,677640489,569412282,519553303,165992560,622446935,446868525,401761000}

Returns: 1
23

{2306560,2520064,5233836,7645536,2988166,2777157,6375460,4606344,3198505,2473335,7603420,3500801}

{36905030,40321025,83741349,122328647,47810615,44434476,102007397,73701571,51176142,39573370,121654688,56012875}

Returns: 23240159
23

{7729751,4035267,3337672,6033236,1391930,1187267,2381107,1118088,6567722,1846120}

{15459503,8070531,6675344,12066476,2783862,2374531,4762211,2236176,13135442,3692240}

Returns: 2048
22

{2057186,1686189,2835163,3174333}

{263313602,215829429,362903262,406318898}

Returns: 468085851
24

{4035255,7665322,14597154,16652520,7607945,16061307,2602349,824513,5926749,15159218,8175596,13419932,2297666,7732875,6688707,5931976,5686226,3845618,9978374,15183412,2435113,2075630,12997654,1804714,5766426,12321256,12207346,6241162,1968618,14318494,2243831,14579039,14252341,2713529,1895364,9754870}

{8070519,15330634,29194306,33305064,15215881,32122619,5204717,1649057,11853469,30318418,16351212,26839836,4595330,15465771,13377411,11863976,11372434,7691218,19956774,30366804,4870217,4151246,25995318,3609450,11532858,24642536,24414706,12482346,3937258,28636958,4487639,29158047,28504661,5427033,3790756,19509750}

Returns: 1
22

{599951,3392305,1025769,273576,3031165,1050078,3966702,428767,2631743,2407762,1581109,1500446,2009054,3362617,3770513}

{38396871,217107567,65649232,17508924,193994604,67205001,253868987,27441118,168431555,154096792,101191008,96028604,128579468,215207517,241312845}

Returns: 46480318
27

{43561456,100618593,112146999,14885444,38423300,61944464,3426410,15708696,3514962,73205159,46487492,86907022,33278258,33264033,73426299,82041297,55702924,58073225}

{174245827,402474374,448587996,59541777,153693200,247777857,13705640,62834787,14059851,292820639,185949970,347628089,133113034,133056134,293705197,328165191,222811699,232292900}

Returns: 262144
24

{9098631,7830461,13543365,6688662,9809167,8408428,808300,4102396,9702869,7720539,15380998,12068486,7772047,9255757,8853960,3213410,207198,14248799,8029109,11988950,14346708,7310751,1651476,9282907,10111972}

{582312441,501149385,866775242,428074229,627786492,538139622,51731172,262553415,620983784,494114716,984383699,772382802,497411066,592368585,566653601,205658517,13260663,911923065,513862893,767292916,918189158,467887710,105694306,594106297,647166308}

Returns: 1
21

{1081085,1331968,1143352,1928601,366632,72094,1879909}

{8647670,10656768,9148642,15429221,2932898,577144,15039894}

Returns: 589934536
23

{3384183,593763,4827216,567102,7378435,1699492}

{27073459,4750099,38617732,4536828,59027479,13595944}

Returns: 924221000
5

{19,0,6,25,7,20,23,10,15,17,2,1,16,7,3,24,15,13,4,15,10,14,27,9,15,13,6,22,20,25,23,22,29,22,0}

{630,0,210,804,237,667,758,338,493,548,82,63,539,237,109,795,493,447,128,493,338,466,886,319,493,447,210,713,667,804,758,713,932,713,0}

Returns: 1
5

{2,2,10,31,11,21,29,15,30,16,15,17,30,10,8,10,24,1,4,10}

{3477,3477,52877,126181,52899,74344,123248,64879,126155,70026,64879,70052,126155,52877,49944,52877,119442,46,13260,52877}

Returns: 1
20

{140976,838015,399840,750031,108125,659196}

{281904,1675967,799712,1500047,216221,1318396}

Returns: 256
4

{4,9,7,4,2,15,5,13,9,12,9,12,14,12,7,7,13,15,12,1,11,11,8,15,8,6,14,8,14,14,2,9,7,4,10,13,12,11,9,15,0,5}

{132,302,229,132,83,505,182,426,302,408,302,408,459,408,229,229,426,505,408,50,381,381,284,505,284,215,459,284,459,459,83,302,229,132,335,426,408,381,302,505,0,182}

Returns: 1
3

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

{0,41,67,106,129,168,194,235}

Returns: 1
16

{9104,57439,62597,40642,53304,41758,6044,16464,27997,47122,109,14470,22964,2133,48152,58116,41499,43482,6045,21933,63689,13894,8215,537,16803}

{18212,114875,125193,81286,106612,83518,12088,32932,55993,94242,221,28942,45932,4265,96308,116236,82999,86962,12089,43869,127377,27790,16431,1073,33603}

Returns: 1
3

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

{3676,4617,7253,3234,3676,0,4617,7851,7851,3234,0,766,3676,7851,4343,7253,0,0,7253,3676,7253,0,3676,3234,766,3234,4617,7253,7851,4617,0,3234,4343,3676,4617,766,4343,4343,3234,4617,7851,4343,3234,766,0,3676}

Returns: 1
4

{10,6,3,13,13,11,3,13,6,0,10,8,5,13,12,15,10,10,0,12,13,13,3}

{326,221,111,444,444,353,111,444,221,0,326,270,178,444,411,500,326,326,0,411,444,444,111}

Returns: 1
4

{6,14,5,9,9,4,1,13,2,15,4,5,3,2,8,15,9,7,8,0,3,14,14,10,7,4,0,2,9,14,13,15,13,14,7}

{21260,53776,17848,34746,34746,17182,1702,50340,4114,54454,17182,17848,5812,4114,33052,54454,34746,21930,33052,0,5812,53776,53776,37134,21930,17182,0,4114,34746,53776,50340,54454,50340,53776,21930}

Returns: 1
4

{13,8,0,7,12,7,12,7,11,3,7,15,2,0,9,9}

{28237,17001,0,15758,27474,15758,27474,15758,22236,5301,15758,32743,4522,0,18294,18294}

Returns: 1
2

{1,0,3,1,3,3,3,3,3,2,3}

{112638,0,630047,112638,630047,630047,630047,630047,630047,535265,630047}

Returns: 1
2

{0,0,2,2,3,1,0,2,0,0,0,2,3,2,1,3,1,0,0,2,1,2,0,0,3,0,3,0,3,0,2,3,2,3}

{0,0,216632,216632,231377,51689,0,216632,0,0,0,216632,231377,216632,51689,231377,51689,0,0,216632,51689,216632,0,0,231377,0,231377,0,231377,0,216632,231377,216632,231377}

Returns: 1
6

{23,14,20,22,23,23,42,10,25,50,7,35,16,26,27,24,27,18,50,41,16,44}

{1493,1001,1381,1480,1493,1493,2763,713,1596,3306,400,2226,1093,1676,1681,1569,1681,1256,3306,2683,1093,2886}

Returns: 1
3

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

{406891,279097,507826,0,406891,101081,0,0,406891,379104,406891,507826,261515,0,101081,279097,379104,161618,261515,0,161618,261515,379104,0,161618}

Returns: 1
2

{3,1,3,3,1,0,0,2,0,0,2,2,1,3,3,3,2,3,0,3,0,2,1,2,0,1,2,2,0,1,3}

{234802,7876,234802,234802,7876,0,0,232438,0,0,232438,232438,7876,234802,234802,234802,232438,234802,0,234802,0,232438,7876,232438,0,7876,232438,232438,0,7876,234802}

Returns: 1
4

{10,8,7,2,5,8,6,2,11,4,9,10,2,5,8,1,11,6,9,2,10}

{606,535,227,73,170,535,218,73,615,147,558,606,73,170,535,57,615,218,558,73,606}

Returns: 1
3

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

{148751,257868,288747,493735,288747,380328,380328,288747,257868,402148,257868,380328,380328,109123,257868,257868,402148,109123,288747,109123,257868,493735,148751,0}

Returns: 1
2

{3,2,3,0,1,2,3,0,1,2,3,1,0,1,0,0,3,2,2,3,1,2,3}

{234150,133270,234150,0,105008,133270,234150,0,105008,133270,234150,105008,0,105008,0,0,234150,133270,133270,234150,105008,133270,234150}

Returns: 1
4

{9,13,6,4,5,10,0,5,15,8,9,14,10,15,5,10,8,8,4,9,10,4,9,13,2,6,10,15,1,13,0,12,9,10,3,0,6}

{2311,3354,1652,1053,1314,2641,0,1314,3955,2104,2311,3660,2641,3955,1314,2641,2104,2104,1053,2311,2641,1053,2311,3354,617,1652,2641,3955,319,3354,0,3109,2311,2641,854,0,1652}

Returns: 1
6

{7,2,4,7,20,42,8,15,51,56,63,2,39,55,20,62,1,24,56,62,0,24,55,26,62,31,18}

{1901,626,1077,1901,9312,23124,2231,4058,29596,30835,32542,626,22524,30633,9312,32308,298,10466,30835,32308,0,10466,30633,10896,32308,12175,8743}

Returns: 1
27

{70006548}

{560052389}

Returns: 45720391
28

{259909833,9293150,13798038}

{519819666,18586300,27596076}

Returns: 33554432
28

{28224712,234195265,225184868,19757932}

{112898850,936781063,900739475,79031728}

Returns: 974740338
29

{419374776,78116634,445897676,322470456}

{838749554,156233268,891795352,644940912}

Returns: 16777216
26

{58864597,17128923,35500794}

{117729194,34257846,71001589}

Returns: 8388608
28

{113576859,23130079,141142149,59101026}

{454307439,92520314,564568595,236404105}

Returns: 487370169
29

{210671882,315642884,304058678,373429771}

{421343764,631285770,608117358,746859543}

Returns: 16777216
29

{352230440,482178957,29383941}

{704460880,964357914,58767883}

Returns: 67108864
28

{259573908}

{519147817}

Returns: 134217728
27

{25401429,18465305,80880818}

{101605707,73861219,323523284}

Returns: 557763816
15

{2625,29466,26691,32007,13651,9037,19829,15448,12023,30185,30463,30046,3076,8136,29484,26351,31489,3954}

{680024,7540127,6840697,8192872,3500394,2319944,5077580,3959864,3078976,7722190,7798762,7696266,786991,2090020,7542433,6739797,8069313,1014019}

Returns: 1
3

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

{15719893,40943409,8734112,8734112,8734112,35268420,6985845,35268420,0,49674897,40943409,49674897,6985845,6985845,0,15719893,43999972,15719893,43999972,43999972,15719893,35268420,0,49674897,0,8734112,15719893,49674897,40943409,43999972,43999972,6985845,8734112,40943409,0,49674897,49674897,0,35268420}

Returns: 1
4

{0,2,11,7,13,6,7,0,3}

{0,1433332,6120918,4080934,7198762,3194364,4080934,0,1779246}

Returns: 1
12

{3898,2191,1758,3758,3245,1079,3135,1424,1896,3308,1253,1888,1931,3899,3781,560,108,1675,3235,787,530,786,2887,3092,648,831,4083,340,1958,1042}

{1996313,1122249,900614,1923961,1661135,552866,1604485,730395,971883,1695006,641511,967706,988886,1996487,1935828,287855,55586,857005,1655791,403143,271202,402969,1478628,1584167,331865,424682,2089944,174094,1002021,533280}

Returns: 1
5

{27,9,28,23,18,0,26,22,8,7,14,19,12,17,22,18,18,11,23}

{112304,39426,118379,97347,76978,0,109495,90436,34565,30939,58073,78261,51955,72095,90436,76978,76978,45608,97347}

Returns: 1
13

{1798,7659,4149,4662,7525,3520,2006,2657,5969,2844,1344,5979,1270,108,5920,1659,7935}

{14379,61260,33205,37305,60215,28160,16041,21254,47764,22755,10754,47822,10169,883,47377,13262,63484}

Returns: 1
2

{2,0,2,2,3,0,0,0,3,1,3,3}

{201466,0,201466,201466,212944,0,0,0,212944,11562,212944,212944}

Returns: 1
2

{0,2,0,2,0,2,2,0,2,2,2,0,2,0,0}

{0,897102736,0,897102736,0,897102736,897102736,0,897102736,897102736,897102736,0,897102736,0,0}

Returns: 176639087
16

{12753,59268,14090,31424,56246,14625,54437,18115,11098,25661,47540,16417,41098,22885,18577,21307,17989,16998,13768,52558,41556,18374,61911,13984,60796,48139,34534,12582,14606,258,59852,15245,57137,63593}

{3264585,15174160,3605784,8044602,14400400,3743861,13935354,4639101,2839960,6567518,12169756,4202620,10521870,5857900,4755537,5453303,4604660,4352913,3523647,13455276,10637831,4705036,15848268,3581999,15562274,12324332,8842011,3220246,3737511,65812,15322639,3901161,14628967,16278724}

Returns: 1
8

{100,110,141,21,239,150,61,102,42,224,220,254,226,188,45,32,81,175,192,36,181,240,176,95,133,128,218,181,99,252,12,42,65,136,8,206,105}

{3260767,3351678,4659227,645598,7809054,5105596,2039165,3273565,1504929,7602890,7017242,8336024,7614664,5968157,1510230,1315712,2886401,5454233,6295882,1429720,5884563,8131809,5768550,3091832,4575032,4456653,7004736,5884563,3161256,8323226,201851,1504929,2366762,4642798,186147,6502195,3332489}

Returns: 1
13

{528,4545,5667,6793,7318,7173,5693,6807,212,2707,1816,7713,7350,416,7430,6281,7994,7779,1290,1024,7078,2559,7896,3485,7080,160,5602,2605,6985,5667,851,7149,2577,1470,1832,3459,6035,5286,6757,4485,7584,6868,7377,1388,3089}

{528,4545,5667,6793,7318,7173,5693,6807,212,2707,1816,7713,7350,416,7430,6281,7994,7779,1290,1024,7078,2559,7896,3485,7080,160,5602,2605,6985,5667,851,7149,2577,1470,1832,3459,6035,5286,6757,4485,7584,6868,7377,1388,3089}

Returns: 1
16

{62253,60987,45706}

{62253,60987,45706}

Returns: 1
23

{1068774,8212454,6135952,6002020,3089109,6441932,2455684,8386640,7359563,3863587,292213,3332064,338784,2816700,7750876,4508287,3594580,2732816,2768869,2015130,2784479,6311886,7146395,7189316}

{1068774,8212454,6135952,6002020,3089109,6441932,2455684,8386640,7359563,3863587,292213,3332064,338784,2816700,7750876,4508287,3594580,2732816,2768869,2015130,2784479,6311886,7146395,7189316}

Returns: 1
30

{966367929,256106790}

{966367929,256106790}

Returns: 1
20

{47030,650028,66413,529822,735045,4268,692397,409467,165026,917197,259630,185842,437954,770584,683909,922142,111945,306786,919060,21915}

{47030,650028,66413,529822,735045,4268,692397,409467,165026,917197,259630,185842,437954,770584,683909,922142,111945,306786,919060,21915}

Returns: 1
13

{970,5376,6391,6494,3188,1886,974,7772,5646,7105,6732,7420,1375,8017,7827,7319}

{970,5376,6391,6494,3188,1886,974,7772,5646,7105,6732,7420,1375,8017,7827,7319}

Returns: 1
17

{64317,17498,17084,49124,97045,82305,89433,25366,3753,116895,71170,126091,27231,8519,100073,32829,118332,3543,70213,104892,21196,87943,125614,84668,37666,5697,74270,45516,160,37489,29589,20743,66066,23522,20193,126380,109702}

{64317,17498,17084,49124,97045,82305,89433,25366,3753,116895,71170,126091,27231,8519,100073,32829,118332,3543,70213,104892,21196,87943,125614,84668,37666,5697,74270,45516,160,37489,29589,20743,66066,23522,20193,126380,109702}

Returns: 1
26

{20029278,38245787,20256146,29129935,10879517,40306742,31956304,48791971,16973048,1521158,46947710,36610434,54219818,46742885,50593238,27088968,23272967,22575468,53390305,8903433,57230199,9820644,44340286,48411600,38546370,26152049,12874704,20255852,2937866,22788337,59818384,27826418,7686063,35857464,65613533,60435311,56587265,63221032,28985630,31343465,60597889,17221943,35447932,59364534,1157642,23815802,33531018}

{20029278,38245787,20256146,29129935,10879517,40306742,31956304,48791971,16973048,1521158,46947710,36610434,54219818,46742885,50593238,27088968,23272967,22575468,53390305,8903433,57230199,9820644,44340286,48411600,38546370,26152049,12874704,20255852,2937866,22788337,59818384,27826418,7686063,35857464,65613533,60435311,56587265,63221032,28985630,31343465,60597889,17221943,35447932,59364534,1157642,23815802,33531018}

Returns: 1
10

{281,575,495,875,529,591,933,943,817,807,723,712,996,121,964,945,785,830,171,728,313,416,646,807,23,310,838,227,219,267}

{281,575,495,875,529,591,933,943,817,807,723,712,996,121,964,945,785,830,171,728,313,416,646,807,23,310,838,227,219,267}

Returns: 1
6

{58,37,21,53,15,10,35,38,50,5,15,55,39,45,57,19,48,16,26,3,55,1,34,57,49,27,33,34,13,55,6}

{58,37,21,53,15,10,35,38,50,5,15,55,39,45,57,19,48,16,26,3,55,1,34,57,49,27,33,34,13,55,6}

Returns: 1
3

{6,4,5,7,4,7,2,0,4,6,3,6,2,0,5,4,3,5,6,7,6,3,2,6,5,6,4,7,4,0,2,2,7}

{12,9,11,14,9,14,5,0,9,12,7,12,5,0,11,9,7,11,12,14,12,7,5,12,11,12,9,14,9,0,5,5,14}

Returns: 1
9

{99,214,429,162,214,187,15,490,85,262,213,263,113,339,54,388,327,350,361,219,77,352,173,233,425,104,172,280,422,366,451,427,111,108,467,121,441,36,78,232,451,462,478,503,371}

{195,422,853,330,422,371,23,986,165,526,421,527,233,683,102,780,647,702,729,435,157,712,349,465,849,208,348,560,838,734,899,851,215,212,939,249,889,76,158,464,899,918,958,999,739}

Returns: 1
3

{2,5,2,6,2,7,5,0,6,4,3,7,0}

{13,18,13,29,13,31,18,0,29,16,15,31,0}

Returns: 1
5

{10,28,6,23,16,15,0,17,6,26,15}

{697,1888,380,1499,1189,978,0,1191,380,1564,978}

Returns: 1
5

{10,22,6,29,19,18,26,27,20,19,13,5,22,2,6,24,17,8,18,19,18,5,18}

{22,46,12,57,39,38,52,53,42,39,27,9,46,4,12,48,35,18,38,39,38,9,38}

Returns: 1
5

{22,8,19,8,6,2,16,21,24,31,3,22,30,20,12,12,13,5,31}

{77,48,70,48,12,4,65,74,113,126,7,77,125,73,56,56,59,11,126}

Returns: 1
4

{11,2,7,8,9,4,2,14,15,9,13,13,15,13,11,7,13,1,6,15,1,3,6,8,10,9,4,3,14,0,0,3,11,3,4,7,9,2,9,3}

{23,5,14,17,18,8,5,28,31,18,26,26,31,26,23,14,26,3,13,31,3,6,13,17,20,18,8,6,28,0,0,6,23,6,8,14,18,5,18,6}

Returns: 1
6

{56,8,19,5,60,25,53,38,34,23,26,59,7,42,23,53,52,20,35,49,41,20,27,47,25,43,45,23,7,47,44,21,56,9,31,53,49,3,24,29,9,1,3,11,21,42,10,27}

{114,18,37,9,122,49,105,76,68,45,54,117,15,86,45,105,104,42,69,97,81,42,55,95,49,87,89,45,15,95,88,43,114,19,63,105,97,7,48,57,19,1,7,21,43,86,20,55}

Returns: 1
4

{7,1,14,6,0,4,3,6,4,11,4,1,12,2,7,1,1,2,1,10,5,1,10,9,6,1,8}

{13,1,28,12,0,8,5,12,8,21,8,1,24,4,13,1,1,4,1,20,9,1,20,17,12,1,16}

Returns: 1
3

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

{17,14,2,31,12,17,12,29,19,14,29,0,29,29,17,2,2,0,2,12,12,12,2,14,17,12,14,14,12,0,14,31,0,17,29,19,12,0,14}

Returns: 1
13

{2984,2013,3704,514}

{2984,2013,3704,514}

Returns: -1
9

{78,183}

{161097,375582}

Returns: -1
5

{9}

{21}

Returns: -1
15

{1387,7759,2532}

{2841580,15890958,5187140}

Returns: -1
10

{307}

{307}

Returns: -1
18

{8630}

{17674312}

Returns: -1
11

{93,10}

{93,10}

Returns: -1
1

{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}

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

Returns: -1
13

{3569}

{29243312}

Returns: -1
9

{187}

{374}

Returns: -1
20

{34}

{25}

Returns: 0
20

{456,7897,94897}

{45648,7897897,45648978}

Returns: 0
4

{9,13}

{37,52}

Returns: 16
2

{0,3,3,3,3}

{0,46,46,46,46}

Returns: 14
3

{7}

{58}

Returns: 88
3

{6}

{25}

Returns: 24
3

{4}

{16}

Returns: 35
3

{4}

{16}

Returns: 35
2

{3,0,0}

{61,0,0}

Returns: 29
2

{2,0}

{19,0}

Returns: 12
2

{2}

{19}

Returns: 12
3

{4}

{16}

Returns: 35
10

{236,495,645,719,901,236,359}

{1904,3966,5143,5756,7191,1904,2846}

Returns: 1536
6

{4,41,30}

{98,687,497}

Returns: 1536
6

{4,48,5,61,1,47}

{4357,50642,4413,61871,56,47853}

Returns: 1280
2

{3,3}

{3252,3252}

Returns: 1204
4

{5,14}

{188,704}

Returns: 1920
3

{2,7,5,5}

{6290,13993,11835,11835}

Returns: 1577
4

{7,10,7}

{721,1505,721}

Returns: 1536
11

{1955}

{3911}

Returns: 1792
6

{20,6,41}

{344,96,647}

Returns: 1792
7

{28,77}

{113,311}

Returns: 1536
15

{22584,10153,10823,23309}

{46254617,20794935,22165287,47737917}

Returns: 999596753
7

{70,22}

{36215,11561}

Returns: 999663422
7

{90}

{5786}

Returns: 999410192
14

{12254}

{392107}

Returns: 999499994
11

{231,1064,694}

{7571925,34878647,22750236}

Returns: 999347832
7

{87,43,105}

{360069,179699,433705}

Returns: 999013658
7

{42,88}

{11224891,23319872}

Returns: 999140669
13

{6844,5576}

{897095293,730945743}

Returns: 999169562
15

{24945}

{12771997}

Returns: 999627019
13

{5823,4307,418}

{95413912,70694859,6826821}

Returns: 999027117
26

{44892933,36769253,25966522,54667378,1847722,16011532,56542288,39608723,16261194,29929330,52488029,37298942,8308184,34410747,19055606,61895858,50322322,2567050,41676412,57359710,14710722,21779796,3122963,46048732}

{179571734,147077014,103866090,218669514,7390888,64046130,226169155,158434892,65044777,119717322,209952119,149195769,33232738,137642988,76222426,247583432,201289291,10268202,166705649,229438840,58842888,87119185,12491855,184194928}

Returns: 64
29

{197688230,83232087,317618282,354917982,120285042,97215277,470015770,373805001,127509706,497971815,119733191,389879191,102603756,87507422,257207474,398587998,13256852,43984957,22294045,437559566,208281596,117882603}

{395376460,166464173,635236564,709835964,240570084,194430555,940031542,747610003,255019412,995943629,239466381,779758383,205207514,175014844,514414948,797175996,26513704,87969913,44588091,875119134,416563194,235765207}

Returns: 64
29

{182251944,270969912,95337106,295678320,305673824,79058251,417530373,387862155,224568322,174673812,98752869,205055037,168903382,415676640,403282713,278402433,294512647,241540944,79524289,47688377,42814693,32099351}

{364503889,541939825,190674212,591356641,611347648,158116502,835060747,775724311,449136645,349347624,197505739,410110074,337806765,831353281,806565426,556804866,589025294,483081889,159048578,95376754,85629387,64198702}

Returns: 128
26

{61105265,58893772,7173797,29813404,4179798,31333484,48448372,51515882,44774950,18295019,63531473,26441785,31479893,5687658,28332685,39636100,56489766,416560}

{122210530,117787544,14347595,59626808,8359596,62666969,96896745,103031765,89549900,36590038,127062947,52883570,62959786,11375317,56665371,79272200,112979532,833120}

Returns: 256
28

{113873188,141167504,4258426,172014405,120310737,36059574,14339245,32838492,14412382,12117516,219551394,249130358,69761060,35365856,101391068,103476630,102645699,14549954,84116411,31287078,227992224,200247203}

{455492752,564670016,17033702,688057629,481242945,144238290,57356985,131353968,57649522,48470076,878205582,996521434,279044252,141463432,405564284,413906526,410582787,58199818,336465643,125148318,911968904,800988803}

Returns: 256
28

{87904250,190545459,121402104,201942918,198061367,25937319,50719653,89828,29630813,174493032,96680650,3295484,92376032,168066718,234543903,58558428,121071199,111640853,57249451,189720951,8557285,238555916,256787074,248253697}

{175808501,381090919,242804208,403885837,396122734,51874638,101439306,179656,59261627,348986065,193361300,6590969,184752064,336133437,469087806,117116857,242142398,223281707,114498903,379441902,17114570,477111832,513574148,496507395}

Returns: 16
26

{47649393,50451515,9126723,24940185,52059225,32636129,33518173,41580611,15486325,62120673,52913293,57715743,42682623,31086881,31712352,39597033,19659802,39958852,33362155,49810781,31779422,18923115,22702504}

{190597571,201806059,36506895,99760742,208236903,130544518,134072690,166322442,61945302,248482694,211653175,230862974,170730491,124347522,126849412,158388130,78639213,159835408,133448622,199243123,127117688,75692459,90810021}

Returns: 32
29

{378020932,440224480,6347764,27024064,463968335,134621946,231255213,292571651,26732235,199114585,211871009,14292004,114384117,92015968,183515013,347685219,317417159,240092711,498032878,118396335}

{756041864,880448962,12695528,54048130,927936669,269243892,462510427,585143301,53464471,398229169,423742017,28584010,228768233,184031936,367030025,695370437,634834317,480185421,996065756,236792669}

Returns: 256
28

{150148175,244572276,208621825,142250363,21348911,9828932,233811117,42167522,176933139,141983955,250149101,16645051,190516360,148657774,4516800,94151660,130277404,46439500,206363343,148391913}

{300296350,489144552,417243650,284500726,42697823,19657865,467622235,84335045,353866279,283967910,500298203,33290102,381032720,297315548,9033600,188303321,260554809,92879000,412726687,296783826}

Returns: 256
26

{62726940,37371702,4297634,28489808,43177950,63411281,64658379,50381929,14576816,58187294,25439866,57192664,60435465,61595098}

{125453884,74743398,8595274,56979624,86355894,126822569,129316763,100763857,29153632,116374582,50879730,114385336,120870937,123190194}

Returns: 512
29

{265662190,398192014,216631773,21680967,258402071,454022030}

{531324382,796384030,433263549,43361927,516804135,908044062}

Returns: 1572864
29

{429569689,362058255}

{859139379,724116511}

Returns: 201326592
29

{272931905,479818348}

{545863811,959636696}

Returns: 201326592
29

{480381820,132092805}

{960763644,264185605}

Returns: 32505856
29

{159870555,378522921}

{319741111,757045843}

Returns: 201326592
29

{402723957,134976519,131393471,203024203}

{805447915,269953039,262786943,406048407}

Returns: 50331648
29

{450066329,146122328,439726030,207135625,139889684,103959823}

{900132665,292244664,879452046,414271241,279779380,207919631}

Returns: 786432
29

{86943999,442057344}

{173887999,884114688}

Returns: 267386880
29

{48975312,396000714}

{97950624,792001430}

Returns: 100663296
29

{320497882,269769555,233494588,360960581}

{640995738,539539091,466989180,721921157}

Returns: 1572864

Statistics

Problem Statement for "XorRank"

Problem Statement

Definition

Constraints

Examples