Statistics

Problem Statement for "ANDEquation"

Problem Statement

An AND-equation is an equation that looks like this: 
X[0] AND X[1] AND ... AND X[N-1] = Y
Here X[i] and Y are non-negative integers and the bitwise AND operation is defined in the Notes.

In C++, C#, and Java the operator AND is denoted "&". So for example (P & Q & R) is the bitwise AND of numbers P, Q, and R. In VB the same operator is denoted "And".

You are given a int[] A that contains exactly N+1 elements. Your task is to construct an AND-equation using each element of A exactly once. (That is, N of them will be on the left hand side of the AND-equation and the remaining one will be on the right hand side.) If this is possible, return the value of Y in this AND-equation. If no AND-equation can be constructed, return -1. (It can be shown that for each A there is at most one possible value Y, so the return value is always defined correctly.)

Definition

Class:
ANDEquation
Method:
restoreY
Parameters:
int[]
Returns:
int
Method signature:
int restoreY(int[] A)
(be sure your method is public)

Notes

  • AND 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 position where both numbers have 1 in their binary representations, the result also has 1. It has 0 in all other positions.
  • For example 42 AND 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 AND 000111 = 000010 (the result has ones only in the positions where both numbers have ones). Then the result can be converted back to decimal notation. In this case 000010 = 2, so 42 AND 7 = 2.
  • One of the ways to calculate the AND of more than two numbers X[0], X[1], ..., X[N-1] is "X[0] AND (X[1] AND (... AND X[N-1]))..))". Since the function is commutative and associative, you can also express it as "X[0] AND X[1] AND ... AND X[N-1]" and group the operands in any way you like.

Constraints

  • A will contain between 2 and 50 elements, inclusive.
  • Each element of A will be between 0 and 1048575, inclusive.

Examples

  1. {1, 3, 5}

    Returns: 1

    5 AND 3 = 1

  2. {31, 7}

    Returns: -1

    Clearly, no AND-equation is possible in this case.

  3. {31, 7, 7}

    Returns: 7

    7 AND 31 = 7 Note that duplicate elements are possible in the input. If an element appears several times in A, it must be used the same number of times in the equation.

  4. {32763,32751,32751,32763,24575,32751,32767,32767,32751,32767,24575,32767,32767,32767,24559,32767,32763,32763,32767,32751,32763,32767,32767,24555,32767,32767,32751,32751,32767,24575,32751,32767,32751,32767,32767,24575,32751,32767,32767,32767,32767,32767,32767,32767,32767,32767,32767}

    Returns: 24555

  5. {13,13,13,15,15}

    Returns: 13

  6. {15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15}

    Returns: 15

  7. {915198,915199,915198,917247,915198,917246,915454,1046526,917246,1046526,917246,1046271,1046270,915198,915454,915454,915454,1048318,915199,1046526,1048318,915198,915198,915455,915454,915199,915198,1046270,915198}

    Returns: 915198

  8. {65324,14980,14788,63622,14420,65093,14493,14340,47700,48260,15428,47110,14341,14885,14404,14406,64516,15013,14638,65029,14476,15886,14484,14476,47949,14340,32446,14598,48404,32292,48590,31748,14484,63566,14854,14342}

    Returns: 14340

  9. {37,21,13,14,54,36,36,15,4,108,6,52,5,21,85,22,70,13,68,102,36,36,84,31,47,68,20,5}

    Returns: 4

  10. {255,223,255,255,255,255,255,255,255,255,255,255,215,223,255,247,255}

    Returns: 215

  11. {88,88,88,90,88,89,94,121,125,88,88,124,88,120,88,90,120,88,92,92,88,88,88,90,88,93,88,92,89,90,88,88,90,89,120,89,88,88}

    Returns: 88

  12. {1,0,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,1,0,1,0,1,1,0,0,0,1}

    Returns: 0

    Zeros are possible in the input.

  13. {1048519,1048519,1048519,1048519,1048519,1048519,1048519,1048519,1048519,1048519,1048519,1048551,1048519,1048519,1048551,1048519,1048551,1048519,1048527,1048527,1048519,1048535,1048551,1048519,1048519,1048519,1048519,1048551,1048519}

    Returns: 1048519

  14. {15,15,15,15,15,15,15,15,15,15,15,15,31,15,15,15,15,15,15,15,15,15,15,31,15,31,15,15,15,15,15,15,15,15,15,15,15,15,15}

    Returns: 15

  15. {982855,343399,343303,269623,269671,269575,401199,270303,286487,826831,417167,376167,367879,998791,335183}

    Returns: 269575

  16. {511,495,511,511,511,511,511,495,511,511,495,511,511,511,495,495,511,511,511,511,511,495,511,511,511,511,511,511,511,495}

    Returns: 495

  17. {511,495,495,511,255,495,239,495}

    Returns: 239

  18. {740,740,750,1012,996,740,740,740,740,756,756,998,748,740,740,748,740,756,740,740,749,742,740,740,740,740,742,740,740,740,740,1012}

    Returns: 740

  19. {1023,1023,1023,1023}

    Returns: 1023

  20. {7631,7631,7631,7631,7631,7631,8143,7631,7631}

    Returns: 7631

  21. {4095,4095,4030,3007,4095,3071,4095,4094,4095,4031,3071,4094,3006,4094,3071,4095,3071,4094,4094,3071,4031,4095,4095,4095,4095,4031,3070,3071,4094,4095,4094,3071,4095,4094,4094,4094,3071,4095,4095,3070,4094,4095,3071,4094,3071,3070,4095,4095,4094,4094}

    Returns: 3006

  22. {196541,262135,262069,262141,196605,262143,196607,262141,196533}

    Returns: 196533

  23. {16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383}

    Returns: 16383

  24. {63,59,59,63,27,31,31,63,63,63,31,59,59,63,63,63,27,59,63,63,31,27,31,27,59,63,59,63,31,63,31,59,59,59,59,59,27,27,27,59,59,63,63,63}

    Returns: 27

  25. {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}

    Returns: 3

  26. {935,2,692,304,826,658,10,576,225,360,37,625,320,370,734,112,621,388,779,582,341,456,976,30,920,49,841,616,1008,970,256,49,319,171,0,578,537,515,226,786,133,802,35,1,208,648,100,667,840,137}

    Returns: 0

  27. {33280,33284,33408,33284,37392,35328,33280,34304,33280,33280,33280,37384}

    Returns: 33280

  28. {2043,1915,1915,1915,2043,2043,1915,1915,1915,1915,1915,1915,1915,2043,1915,2043,2043,1915,2047,1915}

    Returns: 1915

  29. {1,1,1,1,1,1,9,5,1,1,1,1,3,1,1,1,1,1,1,3}

    Returns: 1

  30. {6,5,4,4,7,5,4,4,4,6,5,4,6,4,6,6,4}

    Returns: 4

  31. {517621,518133,521717,517621,517629,523767,517629,517623,517621,518141,520181,518141,521717,519671,521717,517623,519669,519671,521717,521725,517621,517623,517623,523765,517629,519679,522229,517621}

    Returns: 517621

  32. {127,127,127,127,127,255,127,127,127,127,255,127,127,127,127,127,127,127,127,127,127,127,127,127,127,127,127,127,127,127,127,127,255,127,127,127,127,127,127}

    Returns: 127

  33. {191411,256951,191411,191411,191411,256951,195507,191411,192435,191411, 191411,195511,191419,191411,256947,191415,191475,195579,191415,191411, 191483,191411,191419,191475,256947,191411,191411,191411,191419,256947, 191411,191411,191411}

    Returns: 191411

  34. {16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383,16383}

    Returns: 16383

  35. {11,11,14,10,11,11,10,10,10,15,15,15,15,14,14,10,10,10,15,15,10,10,14,15,14,14,10,10,11,10,11,11,10,15,10,15,15,10,11,15}

    Returns: 10

  36. {23,15,15,15,7,23,23,15,15}

    Returns: 7

  37. {131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071,131071}

    Returns: 131071

  38. {81911,81911,81919,81911,81911,98295,81911,81911,81911,81911,81911,81911,114679,81911,114679,131063,98295,81911,81911,81911,131071,81911,81919,81911,81911,81911,81911,81911,114687,81911,98295,81911,114679}

    Returns: 81911

  39. {59,59,63,63,59}

    Returns: 59

  40. {513,155,8,1220,32,1776,417,768,113,1088,105,12,113,1320,1046,112,100,137,9,0,169,270,1808,16,512,192,128,898,592,1024,4,296}

    Returns: 0

  41. {111,111,127,238,238,254,126,110,238,110,126,238,238,111,238,127,238,254,126,127,126,110,254}

    Returns: 110

  42. {23,31,9,25,29,15,11,27,27,29,31,23,27,31,27,19,29,31,27}

    Returns: -1

  43. {262143,262139,262139,262139,131071,262143,262143,262139,262139,262143,262143,262143,262139,262143,262127,262143,262143,262127,131067,262127,131055,262127,262143,262127,131071,262143,131071,262143,262143,131071,262143,262143,262143,262143,262143,131071,262143,262143,262143,262143,131067,262143,262143,262139,131071,262143}

    Returns: -1

  44. {12,31,20,7,11,20,27,10,7,21,17,15,31,30,27}

    Returns: -1

  45. {901119,1032191,1044479,913343,917439,912319,917503,846847,1028095,1032191,982975,850943,835583,835583,847807,965631,1028095,977919,850943,1044479,847871,847807,917439,895999,834559,847871,1043455,1048511,965567,981951,1032127,962559,901119,1048575,851903,912383,851903,1047487,901119}

    Returns: -1

  46. {2047,2047,1535,2047,2047,1983,2047,1791,1535,2047,2047,1791,2047,2047,2047,2047,2047,1919,1535,1791,1919}

    Returns: -1

  47. {65535,52735,60414,65487,65487,52175,60831,61374,65023,56766}

    Returns: -1

  48. {15,15,11,15,5,7,15,13,15,15,15,15,7,5,15,15,15,11,15,15,15,7,11,15,15,7,15,15,15,15,13,15,15,15,15,13}

    Returns: -1

  49. {1362,1066,1659,2010,1912,1720,1851,1593,1799,1805,1139,1493,1141,1163,1211}

    Returns: -1

  50. {5757,8047,4093,3838,7671,7423,7135,7163,7676,2942,7663,7679,3518,7679,3541,8071,6135,7935,8127,7679,8187,4031,7161,8095,7907,7670,8186,6911,7903,8043,6140,3985,6133,8063,8191,4095,7679,7915,5118,7679,8175,8191,5887}

    Returns: -1

  51. {31,31,23,30,31}

    Returns: -1

  52. {1023,447,1023,1013,959,1023,959,1023,959,638,1023,767,990,959,1023,1023,1017,1019,767}

    Returns: -1

  53. {447,511,511}

    Returns: -1

  54. {98239,130815,128767,130719,130815,98303,131005,129023,130943,128991,130815,131039,130783,131071,122749,129021,131007,122879,131071,131037,122495,90031,131007,95791,122607,129007,131053,130815,131055,131039,98287,122877,131055,122847,90109,131071,130911,98175,131023,122879,122495,129007,98303,122879,131071,130815}

    Returns: -1

  55. {4095,4095,4095,4095,4095,4095,4087,4095,4095,4093,4095,3581,4093,3519,4031,4095,4095,4095,4095,4095,4095,4095,4095,4031}

    Returns: -1

  56. {511,511,511,511,507,511,511,479,511,511,511,511,511,511,507,511,511,511,511,479,495,511,511,511,511,511,511,511,507,511,511,511,511,511,507}

    Returns: -1

  57. {238,446,47,127,430,366,446,111,62,174,367,511,127,495,254,190,302,191,446}

    Returns: -1

  58. {6045,7839,6132,5854,7927,14300}

    Returns: -1

  59. {1446,1422,1398,1517,1350,1895,1372,1431,1870,1391,1422,1502,1391,1870,1957,1324,2031,1807,1919,1853,2012,1806,1845,1877,1485,1399,1980,1316,1999,1965,2013,1836,1478,1511,1294,1892,1887,1949,1933,1444,1303,1894}

    Returns: -1

  60. {795,957,989,1011,921,1009,921,923,823,1021,987,927,883,923,955,827,825,991,953,957,959,851,887,889,895,885,849,1023,895,989,857}

    Returns: -1

  61. {511,511,495,479,239,463,495,255,222,511,247,503}

    Returns: -1

  62. {246,247,255,251,255,255}

    Returns: -1

  63. {15345,31734,24575,30719,30591,20471,14704,26559,30591,26623,3966,32127,25584,31739,31728,31735,22335,25535,8189,29692,16371,30205,32703,32759,32703}

    Returns: -1

  64. {9,12,9,12,15,11,4,12,15,15,12,12,12,14,6,11,13,14,11,11,1,11,11,7}

    Returns: -1

  65. {94075,131037,94207,125755,126829,81851}

    Returns: -1

  66. {63076,112469,201830,151236,76916,9333,67092,7447,3540,155044,2020,95885,27941,228429,89669,156877,171415,83756,37895,3604,21812,83076,24108,1335,17678,72735,17862,55092,19468,1559,1510,1132,148660,126260,34526,5174,75014,230487,11364,11540,34100}

    Returns: -1

  67. {60757,61169,65247,65403,65239,65535,63199,65271,63487,64725}

    Returns: -1

  68. {767,453,1019,999,239,479,471}

    Returns: -1

  69. {1027581,1045949,249338,1043448,524281,738815,1023993,1011135,1004415,1000959,1046396,509372,999281,1031613,1030654,728959,474998,1019773,256497,519674,1022399,198586,996341,260019,784883}

    Returns: -1

  70. {1048575,1047551,1048319,1048575,1047551,1047293,1047167,1048189,1048319,1048447,1048575,1048319,1048191,1047295}

    Returns: -1

  71. {191,255,255,255,255,255,254,255,255,255,255,254,191,255,255,251,255,255,255,255,255,255,127,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255}

    Returns: -1

  72. {255,255,255,255,255,255,255,255,255,191,255,255,191,251,255,223,255,255,255,251,255,191,255,251,255,255,251,255,255}

    Returns: -1

  73. {262142,261103,261886,261103,262143,262063,262143,261567,131070,196095,97279,196603,258047,131071,262135,126463,262127,216575,192511,229371,253951,262143,262143,253423,262142,262143,130039,262143,262143,122879,261631,247783,262143,262143}

    Returns: -1

  74. {90,723,255,71,1010,603,363,219,106,866,631,754,634,334,355,735,330,579,98,883,870,622,334,474,478,506,510,238,98,67,998,978,622,450,342,734,635,203,330,750,195,214,326,338,894}

    Returns: -1

  75. {32683,32750,28615,32683,32751}

    Returns: -1

  76. {511,1023,1023,1023,1023}

    Returns: -1

  77. {255,159,77,251,235,253,201,235,255,253,63,95,127,239,29,239,219,47,235,187,217,127,237,239,127,203,43,255,95,253,125,255,109,253,221,95,217,155,125,191,253,13,27,127,175,251,189,203}

    Returns: -1

  78. {32765,28671,32763,32767,32761,28671,28671,30717,30719,32767,30717,30719,32765,32767,32765,32767,32765,32765,32763,24575,24575,32767,32767,32765,30719,32763,24575,24575}

    Returns: -1

  79. {981368,753371,524143,896759,1040308,745397,655199,716669,1046959,386894,752639,116607,1048429,998895,1007015,407407,456703,523706,1044415}

    Returns: -1

  80. {393215,524223,521661,458367,522230,522941,489465,131059,392699,523772,524223,524023,522687,425983,393211,491263,261631,260991,491518,524287,392376,524287,62003,491517,524285,127871,524287,491002,457203,425726,424951,491451,520887,98301,393215,521213,260094,390846,524275}

    Returns: -1

  81. {8175,16367,14314,6139,6138,16379,6143,14334,6139,14334,8191,6123,8191,14314,16378,8186,8186,14335,14319,16367,6139,8175,14318,14314,8175,8191,14319,6126,8190,8175,8191,16363,8191,16363,6126,14334,16362,14319,8191,16363,16363,14318,16379,14330,16382,6127}

    Returns: -1

  82. {884709,1044461,880501,916855,884197,880501,1048037,1011573,880125,1048429,884725,880101,880119,884607,913383,880501,884085,912869,913405,880629,1043837,879981,1011061,1011173,912741,1015653,1044333,880631,884071,880119,1011053,1015141,1011559,1011071,1047911,1015661,1047925,1011685,916853,880485,912757,884095,879973,912871,1044327,1011175,916853,1015797,884725,884607}

    Returns: 879973

  83. {585935,585935,585935,585935,585935,586191,585935,585935,585935,585951,585935,585935,585935,585935,585935,585935,651471,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,717007,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935,585935}

    Returns: 585935

  84. {1040379,1040383,1048571,1048571,1048571,1048571,1040379,1040379,1040379,1040379,1040379,1040379,1048571,1048571,1048575,1048575,1048571,1048575,1048575,1048575,1048571,1048571,1040383,1048571,1040379,1040383,1040383,1048571,1048575,1048571,1048575,1040383,1040383,1040383,1040383,1040383,1048571,1040383,1040379,1040383,1048575,1048575,1040379,1048571,1040379,1048575,1040379,1040383,1040379,1048575}

    Returns: 1040379

  85. {2177,2177,526465,141457,2177,2177,2177,2177,2185,2177,34945,35201,2177,67713,26819,2209,2177,2185,2689,264321,2177,264897,788617,2177,2257,2177,2177,18595,39041,264385,264321,67713,2177,2179,10369,137345,133297,2177,2177,2437,534657,2177,2241,3205,2177,198785,2177,2177,2177,2193}

    Returns: 2177

  86. {786431,1015807,753663,1015807,786431,786431,753663,1048575,786431,1048575,1015807,786431,1015807,1015807,786431,786431,1048575,1015807,1015807,786431,753663,753663,1015807,753663,753663,753663,1048575,786431,786431,1015807,1048575,1048575,753663,753663,753663,753663,753663,786431,786431,753663,753663,1048575,786431,753663,753663,1048575,1048575,1015807,1048575,1048575}

    Returns: 753663

  87. {522199,786391,1030103,235487,499703,514015,505855,505847,759767,243711,505815,776151,497655,243679,245751,237567,235479,767999,235479,770039,235479,767959,235479,251903,1023991,1032151,767991,767959,260055,260087,761815,243711,243671,759799,243711,243671,1038295,235479,507863,499703,759767,243671,235511,245719,235479,1021951,262103,514007,759775,759767}

    Returns: 235479

  88. {516,0,329728,2048,2,0,4160,266240,32800,32768,4112,786432,0,0,8192,16,65536,8192,262148,128,262144,16,0,131072,16385,2048,1024,40992,24,0,4,4096,0,16,128,4097,4,256,8194,4,10784,1024,0,0,0,6144,18436,0,0,426000}

    Returns: 0

  89. {301333,121108,47572,318237,113940,39188,39317,104732,646933,39700,39292,47380,579988,309588,39292,638388,64276,39198,826132,40276,170260,121108,55637,572692,302357,48508,39220,47380,56118,47381,891221,703255,39188,563988,694612,39190,170292,55580,104798,825751,56598,572700,768276,171796,39317,432404,39286,40215,301364,39188}

    Returns: 39188

  90. {1048279,1048279,1048311,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279,1048279}

    Returns: 1048279

  91. {1048575,1048567,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1032183,1048575,1048575,1032191,1048575,1048575,1048575,1032191,1048567,1032191,1048575,1048567,1048575,1048575,1032191,1048575,1048575,1048575,1048575,1048575,1048575,1032183,1048575,1032191,1032191,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575}

    Returns: 1032183

  92. {1042191,493071,1033743,511919,524111,1041967,501391,493103,509487,521823,511567,503599,1021519,509599,1027711,497215,493103,509535,511855,522095,495407,1035791,517839,1027903,505551,515647,499295,1017391,1017455,499551,493327,1029759,1042223,515791,1019487,493119,1042159,507471,1019471,501455,509535,497183,517711,497167,1042207,493551,515999,501679,509535,1037983}

    Returns: 493071

  93. {1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575}

    Returns: 1048575

  94. {523967,523967,523967,1048255,523967,1048319,524223,523967,523967,523967,523967,523967,523967,524031,523967,524223,523967,523967,524031,523967,1048319,523967,523967,523967,524223,523967,523967,523967,1048255,523967,523967,1048255,524223,523967,523967,1048255,523967,524031,523967,524031,1048255,523967,523967,524031,1048255,523967,523967,523967,523967,1048255}

    Returns: 523967

  95. {261987,786173,524277,261985,261859,524009,524149,1048417,262115,1048417,524019,523893,786149,1048177,786291,261995,523883,261739,261883,786301,1048165,786037,261729,786029,523875,1048317,261757,524129,261859,786149,1048423,261993,1048297,786417,261857,261731,1048567,1048551,524263,261737,524259,524147,786161,261873,1048191,261757,261753,262133,261857,261731}

    Returns: 261729

  96. {1048575,1048575,1048575,1040383,1040383,1048575,1048575,1040383,1048575,1048575,1040383,1040383,1048575,1040383,1048575,1040383,1048575,1040383,1040383,1048575,1048575,1048575,1040383,1040383,1040383,1048575,1048575,1048575,1048575,1048575,1048575,1040383,1048575,1048575,1048575,1040383,1040383,1048575,1048575,1048575,1048575,1040383,1048575,1040383,1040383,1048575,1048575,1048575,1048575,1048575}

    Returns: 1040383

  97. {1048575,1046527,1013759,1015807,1013759,1013759,1013759,1048575,1013759,1015807,1013759,1015807,1013759,1015807,1015807,1046527,1013759,1048575,1013759,1013759,1013759,1046527,1015807,1013759,1013759,1046527,1013759,1013759,1046527,1013759,1046527,1046527,1013759,1013759,1046527,1013759,1015807,1015807,1046527,1015807,1013759,1015807,1015807,1046527,1013759,1013759,1046527,1046527,1015807,1015807}

    Returns: 1013759

  98. {1048575,1048575,1015807,1048575,1048575,1048575,1015807,1015807,1015807,1015807,1015807,1048575,1048575,1048575,1015807,1048575,1015807,1015807,1048575,1015807,1048575,1048575,1048575,1048575,1015807,1015807,1048575,1048575,1048575,1015807,1015807,1048575,1015807,1015807,1048575,1048575,1048575,1048575,1048575,1015807,1048575,1048575,1048575,1048575,1048575,1015807,1048575,1048575,1048575,1048575}

    Returns: 1015807

  99. {1047389,1047039,1048063,1048413,1047935,1048447,1046909,1047421,1047423,1046877,1046877,1047005,1048029,1047901,1047389,1047005,1047933,1047903,1047901,1047901,1047933,1047007,1047007,1046909,1046879,1048029,1048413,1047389,1046879,1048445,1046877,1046909,1047037,1048061,1046877,1047005,1047037,1048063,1047421,1047517,1047519,1047517,1048029,1046877,1047005,1047421,1046879,1046877,1047037,1047389}

    Returns: 1046877

  100. {19488,19488,19488,117792,19488,19552,543776,19488,19488,19488,19488,19488,19488,19488,19488,19488,23584,19488,19488,19488,19488,19488,27680,19488,19488,19488,19488,19488,150560,19488,19488,19488,19488,19488,19488,158752,19488,19488,19488,19488,19488,19488,19488,19488,19488,19488,19488,19488,19488,19552}

    Returns: 19488

  101. {1048535,1048535,524279,1048567,524255,524247,524279,524247,524247,1048535,1048535,524287,524247,1048535,524279,1048535,1048543,524247,524287,1048535,1048535,1048535,524255,1048535,1048543,1048567,1048567,524247,1048575,524279,524247,1048567,524247,524247,524247,524287,524287,524255,1048535,524247,1048535,524247,1048575,1048535,524247,524255,524255,1048567,524279,524279}

    Returns: 524247

  102. {797915,208725,582124,786428,878844,1036231,779603,961278,333301,457469,981203,880366,973949,683379,99160,1013489,972025,392019,1040238,1022419,503671,719615,1026428,621261,504666,211951,749527,580847,106487,900601,956143,993510,411518,1006293,892263,447734,914800,1028453,1042372,681451,1021765,507377,228063,929142,130663,159194,434672,748391,1017343,708600}

    Returns: -1

  103. {586202,932806,29406,179534,867531,422011,1013315,766787,406627,766919,735970,210758,621507,1013083,343890,1029215,130531,63938,1031747,146030,900295,127343,79958,883395,963523,47719,47698,425850,31318,980479,455754,325367,376534,391502,996082,982767,456191,130558,750418,128579,130023,999275,490483,783682,30418,949502,801106,143682,589419,292062}

    Returns: -1

  104. {1048575,1048571,1048575,1048574,1032191,1047423,1048511,915455,1048575,1048573,1048511,1048575,1048060,1048575,982907,524287,1046519,1046399,1048575,1048575,523775,1048575,1048575,786431,1048574,1047550,1048063,1048575,1048575,786427,1048575,983039,917503,917375,1048575,982527,786431,917503,1048575,1029119,1048063,1044477,1048575,1048575,1048574,1048575,1046515,1048571,786431,1048063}

    Returns: -1

  105. {253258,1040377,524206,982563,1047416,1007590,506621,458734,523183,1031505,785911,1031663,892911,1048007,784886,489854,1048565,1048575,524151,342843,523610,1015677,850399,851823,1032111,908623,883711,1014771,622543,818107,450502,1040243,572155,1032023,457919,228731,1048255,1048567,753151,875006,261366,900792,908731,1013948,835583,712461,612604,524270,720350,655089}

    Returns: -1

  106. {808925,476911,478917,876475,909297,190654,457341,849563,1015806,961908,724957,764843,750126,908781,233198,347882,930622,862694,91135,515724,810855,504118,1045074,809093,505456,360341,455773,785822,873330,699893,1043103,524265,454396,442207,744879,1013791,515034,1027103,455423,65317,973183,849739,1010305,834271,988246,1030266,980207,182894,876281,148859}

    Returns: -1

  107. {1048575,1048575,1048575,1048575,1015807,1048575,1048575,1048575,1048575,1048575,917503,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,524287,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575}

    Returns: -1

  108. {1048574,1048575,1048575,1048575,1048575,1048575,1048575,524287,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048319,1048575,1048575,1048575,1048575}

    Returns: -1

  109. {1046527,1048503,1048063,915453,785343,786431,982527,983039,883710,1048575,884669,1048573,1047541,753663,916479,983039,948125,1048575,1048535,1048541,950271,1013759,1048575,917463,1048573,1048574,655356,1046527,1048575,1015799,917502,1047549,1048511,1046463,786429,917439,983006,916477,1041855,983037,655359,1015711,913407,913343,1044479,1013663,1048052,913373,786431,916991}

    Returns: -1

  110. {1011710,1048575,1048575,1015807,1048573,1034239,1048575,1048575,1046527,1030143,1048575,1044479,1036223,1048575,1048543,786431,1048575,1048575,1048575,1048542,1048575,786431,1048559,1015807,1048511,1048575,1044479,1048575,1048575,1048031,1040381,1048495,1048559,1048575,1048574,785918,1040351,1048495,917471,1048575,1048575,1040381,1048575,1048575,1048575,1047998,1048575,1048063,1048575,1042431}

    Returns: -1

  111. {515997,514876,1026895,523096,364345,519053,1043404,514831,904984,364376,917320,1048408,387912,368541,887674,391982,387902,523050,1018829,523048,1018655,892889,376651,383816,523263,510859,1030921,387884,392042,383834,908093,371465,511759,1019661,892683,379851,383804,495450,892776,514825,498603,899960,900031,515981,367483,363337,523178,383902,523213,518990}

    Returns: -1

  112. {697819,926068,1009643,978257,783045,729596,980332,930500,945360,751810,995950,682074,769632,1042531,948708,965874,1029611,1029700,753244,734411,720849,931812,765791,991727,669948,960609,963043,750793,1012697,1046640,946164,716115,766150,720739,670281,998638,784105,961788,961370,943356,715843,729179,963439,947533,1031756,697333,998773,949877,746871,1046872}

    Returns: -1

  113. {982783,1048575,909308,1048575,1048575,1048543,1048495,1048571,1048575,1040383,1048575,1048315,1048575,1048569,982975,1048571,1048574,917503,1048543,917499,1048575,1048511,1048319,1015807,1048543,1048573,1048303,1048511,1007615,916975,1048575,393215,1015039,1048527,1048511,1040383,1048559,1048573,1048575,1048319,1048575,1048510,1048511,1048060,983037,1048063,1048251,1048575,1048575,524271}

    Returns: -1

  114. {523639,507383,499191,515959,1048447,507255,1031679,983039,458743,1032063,499199,974711,1031671,1040375,1048575,982391,1048447,499575,442231,507263,974847,1047935,974719,441719,1031671,958327,1032063,515967,441719,982391,434039,957951,974335,966527,507383,515575,1048575,450551,450431,1048447,499191,1023479,442231,499199,966519,449911,966655,442367,449911,499063}

    Returns: -1

  115. {764747,212509,736074,469549,229021,212603,207802,731784,491134,995289,519740,256925,994137,782185,1048168,474011,1044330,487048,1011258,207567,244250,785295,485900,768622,469769,1015662,245404,733177,781036,260828,522959,1043278,1014782,507516,507692,470698,261822,764877,749243,1043384,780904,1047117,240218,260953,994169,473816,737112,212650,240265,241646}

    Returns: -1

  116. {13280,862,901452,289242,954833,201034,399680,295904,437576,196053,281578,1042803,123225,546144,284096,329579,6468,756732,332798,458055,733550,886655,327506,14810,813385,446808,58346,414545,547795,17396,790348,289611,598389,586609,586060,262632,574796,766954,594368,211412,547657,138601,83805,448364,28482,728549,623050,430920,283978,65899}

    Returns: -1

  117. {1015791,1048575,1048567,1015805,1048571,1048415,1048063,983027,1032063,1015805,1048567,999415,999423,1048061,983031,835583,983039,999423,1032191,1047551,1048541,917503,917503,999419,1048575,1048061,983023,1048543,917501,1047551,1048047,917503,801791,1047551,1032175,1048527,1031679,917503,1048543,1032189,1015771,1015799,1048527,1048559,835583,999389,1048571,1048575,1048575,1048565}

    Returns: -1

  118. {1048575,983039,524287,1048575,1048575,1048575,983039,1048575,1048575,1048575,1048575,786431,458751,983039,983039,1048575,1048575,786431,1048575,983039,524287,1048575,1048575,524287,983039,983039,1048575,1048575,1048575,1048575,1048575,1048575,1048575,1048575,262143,1048575,524287,1048575,1048575,1048575,1048575,1048575,1048575,786431,786431,1048575,1048575,1048575,1048575,1048575}

    Returns: -1

  119. {1011709,1048559,1048575,1048571,1044475,1048575,1048427,1007599,1015679,1040383,1048429,1044475,1048447,1048575,1048575,1015805,1044463,1044351,1007613,1040383,1003519,1011707,1015807,1048447,1015791,1040383,1048447,1048553,1048553,1044463,1007599,1048445,1048447,1040235,1048557,1048559,1015679,1048571,1040383,1048429,1044351,1036285,1015807,1048575,1007615,1048447,1048443,1040381,1048575,1044479}

    Returns: -1

  120. {1046527,1048575,1048575,1048575,1048575,524283,1048575,524223,1048571,1048575,524287,524287,1048575,1048511,1048511,1046463,1048575,1048575,524287,1048575,1048575,1048575,1046527,522239,1048575,1046527,1048575,1048507,1048575,1048511,1048575,1048575,1048575,524287,1048575,1048575,1048575,1048571,1048575,1046527,1048571,1048571,1048575,1048575,1048575,1048571,1048575,524287,1048575,1048511}

    Returns: -1

  121. {524017,998273,507547,1044376,1044371,491196,1043455,1001468,1009662,1047262,1045172,459761,475135,524285,1040318,1027791,523263,485293,995259,503747,1023935,1044395,1047529,1014447,1016792,1023968,984781,993957,511912,1046527,1045229,1044204,1018622,1044214,1048575,488427,483230,1031163,476100,507871,1040382,522175,467853,1017828,1028765,1004220,1039077,520947,1031934,1006525}

    Returns: -1

  122. {2, 3, 7, 19}

    Returns: -1

  123. {191411, 256951, 191411, 191411, 191411, 256951, 195507, 191411, 192435, 191411, 191411, 195511, 191419, 191411, 256947, 191415, 191475, 195579, 191415, 191411, 191483, 191411, 191419, 191475, 256947, 191411, 191411, 191411, 191419, 256947, 191411, 191411, 191411 }

    Returns: 191411

  124. {1, 1 }

    Returns: 1

  125. {7, 7 }

    Returns: 7

  126. {45, 45 }

    Returns: 45

  127. {2, 2 }

    Returns: 2

  128. {5, 5 }

    Returns: 5

  129. {35, 35 }

    Returns: 35

  130. {30, 30 }

    Returns: 30

  131. {6, 6 }

    Returns: 6

  132. {4, 4 }

    Returns: 4

  133. {31, 31 }

    Returns: 31

  134. {2, 3, 7, 19 }

    Returns: -1

  135. {1, 3, 0 }

    Returns: -1

  136. {1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1 }

    Returns: 0

  137. {3, 3 }

    Returns: 3

  138. {2, 3, 4, 0 }

    Returns: 0

  139. {457, 457 }

    Returns: 457

  140. {0, 5 }

    Returns: -1

  141. {0, 1 }

    Returns: -1

  142. {1, 3 }

    Returns: -1

  143. {12, 12, 4, 12, 4, 12 }

    Returns: 4

  144. {1, 0 }

    Returns: -1

  145. {26, 26 }

    Returns: 26

  146. {5, 7, 5, 3 }

    Returns: -1

  147. {23, 23 }

    Returns: 23

  148. {5, 5, 5, 4 }

    Returns: -1

  149. {1048575, 1048574, 1048565, 1048564 }

    Returns: 1048564

  150. {1, 0, 0 }

    Returns: 0

  151. {0, 0, 0, 0, 1, 1, 1 }

    Returns: 0

  152. {3, 3, 3 }

    Returns: 3

  153. {0, 0 }

    Returns: 0

  154. {5, 3, 1 }

    Returns: 1

  155. {0, 3, 4 }

    Returns: 0

  156. {1048575, 1048575, 1048575, 1048575, 1048575, 1048575, 2, 3 }

    Returns: -1

  157. {5, 14, 4, 14, 5 }

    Returns: 4

  158. {10, 10 }

    Returns: 10

  159. {31, 7, 7 }

    Returns: 7

  160. {2, 3, 6, 9 }

    Returns: -1

  161. {12, 12 }

    Returns: 12

  162. {1, 3, 5, 0 }

    Returns: -1

  163. {2, 3, 2, 1 }

    Returns: -1

  164. {3, 1, 5 }

    Returns: 1

  165. {1, 3, 5 }

    Returns: 1

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