Statistics

Problem Statement for "LCMSetEasy"

Problem Statement

For any non-empty sequence of positive integers s1, s2, ..., sK their least common multiple is the smallest positive integer that is divisible by each of the given numbers. We will use "lcm" to denote the least common multiple. For example, lcm(3) = 3, lcm(4,6) = 12, and lcm(2,5,7) = 70.


You are given a int[] S and an int x. Find out whether we can select some elements from S in such a way that their least common multiple will be precisely x. Formally, we are looking for some s1, s2, ..., sK, K >= 1, such that each si belongs to S, and x=lcm(s1, s2, ..., sK). Return "Possible" if such elements of S exist, and "Impossible" if they don't.

Definition

Class:
LCMSetEasy
Method:
include
Parameters:
int[], int
Returns:
String
Method signature:
String include(int[] S, int x)
(be sure your method is public)

Constraints

  • S will contain between 1 and 50 elements, inclusive.
  • Each element in S will be between 1 and 1,000,000,000, inclusive.
  • Elements in S will be distinct.
  • x will be between 2 and 1,000,000,000, inclusive.

Examples

  1. {2,3,4,5}

    20

    Returns: "Possible"

    We can obtain 20 in multiple ways. One of them: 20 = lcm(4, 5).

  2. {2,3,4}

    611

    Returns: "Impossible"

    If S={2,3,4}, the only values we can obtain are 2, 3, 4, 6, and 12.

  3. {2,3,4}

    12

    Returns: "Possible"

  4. {1,2,3,4,5,6,7,8,9,10}

    24

    Returns: "Possible"

  5. {100,200,300,400,500,600}

    2000

    Returns: "Possible"

  6. {100,200,300,400,500,600}

    8000

    Returns: "Impossible"

  7. {1000000000,999999999,999999998}

    999999999

    Returns: "Possible"

  8. {8648,653,1058,134,827,170,42,3,82150,5,74242,2}

    775726

    Returns: "Impossible"

  9. {4166867,22524}

    22524

    Returns: "Possible"

  10. {2,13,761,52,70,64,66,410,566,918,6566,67,1,542,6865,4558}

    64957438

    Returns: "Possible"

  11. {104,917,541,5,45965,248,4604088,76015397,14088,8,986265,72603,3299,5980263,686,16,88742,5027112,52,2403479,36124,3929,38,489653,2369,867513,55545860,81590,15,10,3}

    882002973

    Returns: "Impossible"

  12. {5,8200,1866,120,8,7588,5793,49,32,555,891,746,621,5690,7,56,8982,34,1,5717}

    190010400

    Returns: "Possible"

  13. {862,6048,478,156,78,2321,23,113,697,5,7232,10,6,1,9,2427,104,460,196,6599,4,3,129,9129,6840,992,32,474,13,8642,8,6082,517,3130,3416,368,5583,401,555,2,540,577,674,91,5673}

    779399712

    Returns: "Possible"

  14. {4063,3487464,6536,63,5242268,6,34983,7825,9893654,7,984,3685980}

    45752

    Returns: "Possible"

  15. {360,9,8522,996,688,2053636,77640,75760,435,66763,503,680,9150,550260,8831,43,6142,3436,4,7889,64810,2821,290250,59402,208288,9994,613,19737,7483,64,896545,463,5333061,5,447308}

    3075910

    Returns: "Impossible"

  16. {94,37,66,1,7,31,58,69,36,5,10,3,56,39,92,4,49,6,78,99,97,25,79,63,61,91,27,59,96,67,9}

    722272782

    Returns: "Possible"

  17. {41,2826746,9054871,76487,15723,5945,25,60,85,38376,6,1131351,149,5940,7,45,63775,54,79572,7442,306227,42135}

    371249711

    Returns: "Possible"

  18. {9788,8418,10,35,55,7250}

    37683800

    Returns: "Impossible"

  19. {20,79,10,43,11}

    373670

    Returns: "Possible"

  20. {860608562,806,10,669455,261105394,740266775,5418973,939845,899,508564,7997168,4092,96663580}

    770928

    Returns: "Impossible"

  21. {3,737,77,28,718,74,83,5,1,82,344,9,426,13,7,400,991,810,826}

    5449

    Returns: "Impossible"

  22. {2892,76,4,98753485,461,1,5330,5175407,97538281,615,567684,5,10455969,3,89428,74267101,99732,9895975,7,65639,955,663724,20284354,49030240,7528,82,613,2,280,36651,814,120,92345545,44,6339105,931021}

    4034

    Returns: "Impossible"

  23. {81780,2,172,9434,43082,80,655,187,624,606373,4,768414,58,70242,302713,98,95,42030,2107,734159,20,51,33,3,36468,10,953,69136,591516,83,94,7,8,858,776071,52811,5,56153,704,63769,50842,6,369,841439,885,937,75}

    118

    Returns: "Impossible"

  24. {5027,6,45,8540,40230,36194,831,3,9,61869,556,8942,15,10,56}

    11143710

    Returns: "Possible"

  25. {710740,5,726104752,9513818,14075381,67,250765018,7500801,8418,948,2095487,55506}

    66596726

    Returns: "Impossible"

  26. {402,217,917962,18,69570,6,10,837,792,7444,4720,5694169,118,8140,7}

    13085100

    Returns: "Impossible"

  27. {843798298,2163,17402471,1,498797355,3,395799679,313380,360513,4,765382,5240475,181723,7,75,2424,26,6311520,934453}

    498797355

    Returns: "Possible"

  28. {3362,5558,523,33,3,382,6,9,70,2212,3196,893,7,49,1,733,3326,41,2662,332,314,58,10,373,380,15,43,4141,2686,227,7190,93,5,54,335,398,90}

    924956802

    Returns: "Possible"

  29. {799}

    7990

    Returns: "Impossible"

  30. {293,5,40,740,10,13,609,3,1,9,965,23,86,945,978,17,6,43,19,8,7,182,70,4,807}

    35936140

    Returns: "Impossible"

  31. {5036,544,7,87}

    35252

    Returns: "Possible"

  32. {368660,66,77,30931,129804,7,10904,565,987,5,30,97007,846437,251077,15,607,93365,11639,11,99,1789,307035,853,63851,4,747542,832}

    425802300

    Returns: "Impossible"

  33. {86,6,53,10,60,74,1920,1,76,3818,7,151,8143,54,9,748,634,50,556,4,90,6632,45,13,398,9883,17,717,2917,11,48,5658,85,5760,7694,322,39,144,909,8,2}

    226867268

    Returns: "Impossible"

  34. {14323,87093007,63089,61211,23503991,5095247,493,5362641,37,18529426,3863020,225737,36098103,71,407,73147,6349}

    23503991

    Returns: "Possible"

  35. {704,161,5}

    10

    Returns: "Impossible"

  36. {7,472714,5805,4356,6,553,65,361,527,75949,891,1,4,209,8,886,755,9,26316,895,87028,7711,376,2,218,8468,8039,29,319,788,25869,55196,6043,1942,545,17,27,423734,30245,35,89123,9076,390,5601}

    87233256

    Returns: "Possible"

  37. {78,7,9,829,958,511}

    377285546

    Returns: "Impossible"

  38. {5,6,29,3,466,9,462,98,205,172,77,765,55,897,49,41,869,8,247,48,4,431,89,36,351,27,68,645}

    91631243

    Returns: "Impossible"

  39. {43,29,5,8,1,91,58,39,7,79,97,30,98,4,28,3,90,49,93,42,87,18,6,47,54,89,73,12,21,64,60}

    135577260

    Returns: "Possible"

  40. {7427411,96,2676,9327732,502,874624,7483996,2957,49,8234,49339367,20125225,657,51,69098690,6283,50,86671101,44142,59531102,733}

    63303456

    Returns: "Possible"

  41. {892,688,99,1000,48,2326,5,2,3144,116,6,7,3,67,7555,89,10,8965,1,2357,77,9062,9,244,8,6046,35}

    531614160

    Returns: "Possible"

  42. {80,571549,6845319,21,428117,79197,5818273,549333907,1,7794038,34098,17416174,9238,35824,84,38804,9272153,638134,273309715,835,46418,66525142}

    1363920

    Returns: "Possible"

  43. {5526,10,3395,92,9,9814,2656,63,3364,593,14,8053,56,2734,6,921,1,781,8,8910,1205,740,8702,876,859,5161,8000,391,87,86,2218,9992,7852,293,48,754,563,862,11,622,33,3101,836,1522,4499}

    168786144

    Returns: "Possible"

  44. {8632,8,98867068,1}

    8632

    Returns: "Possible"

  45. {6,4,14364,2984,3120,1,9,74234,86,1601,7744,16063,167,92,46,4166,39,9997,9099,8,3,38992,10,555,174,278,48268,2834}

    73417426

    Returns: "Possible"

  46. {438,3593}

    1573734

    Returns: "Possible"

  47. {1579,6276,63,8242,4,43,63228,3,876944,539429,1662,622,994,10,7702,476521,20179,35,2,40337,82269,871,57032,230,878504,34431,9,6055,95,94,33699,1,7,470128,50,71785,14,323,7707,8}

    508

    Returns: "Impossible"

  48. {9,20,6,794,419,779,66,758,5,46,58,368,41,29,32,785,11,8,117,26,88,182,59,101,7,4,2,31,91,80,10,23,53,701,998,346,74,78,3,530,660,57,95,285,83,499,350,896,681,964}

    123626594

    Returns: "Possible"

  49. {258,50,373,1761,9,907,10,85,5791,4869,635,85887,16032,381,4844,827,981,97,30,5088,3,39,98084,462,73578,862,17,930,4,877,1,22,93230,8793,26,879,833,9669,77753,4288,44929,8,127,41,56,2987,71389}

    305542950

    Returns: "Possible"

  50. {7277,964,3844,6,2,4049,307,503,2039,187,3980,9908,4819}

    29464573

    Returns: "Possible"

  51. {8,93,371,2,8717,986,1,55,1661,218,5086,5,440,28,88,817,4070,321,654,510,11,10,95}

    3963

    Returns: "Impossible"

  52. {3171,29559,26506,4502,2149,68,49,54573,2304054,9,5398,4660,727,8965,4186,94195,4,6901096,666,10,7,830,78096,9399890,505734,6773,295,40651,9407186,7582514,61632,53,8372}

    937315890

    Returns: "Possible"

  53. {753,59,51,9425,568,64,848,41,7,2,6252,24,11,95,29,53,4617,85,1087,3,40,89,6,8888,79,8,87,4,4603,18,7135,44,8570,2888,32,7821,978,7158,5,5884,4805,34,6705,739,63,311,845,9,99}

    428987112

    Returns: "Possible"

  54. {357695,190314,4,28189,5,24,4599925,83055,1585,6,9,40012,92,785670,6606806,22,3819225,432,801226,256,16469,41982}

    4006130

    Returns: "Possible"

  55. {1254800,10,6250381,7,35444345,144380726,58927,1,4,87,180,745679,2098558,29906,573219,209,894,28112,849,4403,37}

    764173200

    Returns: "Possible"

  56. {476845,10238,74,6829,9503,85,640162,38571,193813,631622,2156,6,7848,24961,455,58,568,3,66,675,2,75793,923452,10,65,598029,78181,895,36,531447,10020,83,5,64758,56,2770,59,546132,802935,9813,1,2861,5571,54,9440,9775,8,163}

    599871010

    Returns: "Possible"

  57. {991,91,535,37,8,90,9,1,3,680,34,95,94,62,276,881,567}

    414447

    Returns: "Impossible"

  58. {96,72,51,9}

    1224

    Returns: "Possible"

  59. {98701,8800,6191,15,150,69319,9,182,691,601,91367,7,49639,2954,31,24,8,1699,893,2373,6953,11}

    288961408

    Returns: "Impossible"

  60. {82,62,82697,924193,6732275,413727,67107,52,1093,711291,9,3,82359,9914,48,758,58,895,8607,24,949,957535,9501}

    75783826

    Returns: "Possible"

  61. {1129,196,61,77,2941,219,5341,65,4,22,660,60,960,619,983,647,3,71,7,934,671,11,1375,754,5,8586,872,473,55,941,37,615}

    523200

    Returns: "Impossible"

  62. {1,7177955,16,7,94,31,6456,2,87614,62954,10,33,6428038,38,8213045,783625,151973,182,977786,868,982,6320,6472099,7516,453,822,9048484,730931,90,400,210264,1996,89396,1285,29707,34497,819,282014,70555}

    574236400

    Returns: "Possible"

  63. {5553,4,97971,103621,9215,7289,30676,231108,8584,184,29,543906,65,84,8,7553}

    181344321

    Returns: "Possible"

  64. {67395,25134,98791,43058,657029,710481,8245,31949,10,531027,914890,97360,9331,36887,665,268,75,8,97675,4389,61,647311,8015,338,16,7,599,5095,75208,6924,3699,4,915,886}

    4303

    Returns: "Impossible"

  65. {10,6464,2034,742,8,5496,63,8907,2419}

    6406

    Returns: "Impossible"

  66. {77,34557,256,746,839031,9,4410,231,1,32553,9626,94,23023,532059,41,730050}

    25779522

    Returns: "Possible"

  67. {9975580,202,84329,55320895,5944636,3930,14,4037099,289585,641992,2517474,484,70152762,92009623,36401,321,90187747,2,564103,16139,306,6306212,1,6}

    719300956

    Returns: "Possible"

  68. {1404,51,698,34,4,13,30,81,23,1,734,585,48,54,96,565,52,617,980,70,1953,2472,2275,166,3,5634,8612,4789,45,5,881,10,348}

    9

    Returns: "Impossible"

  69. {5031,11,15395,24743893,9166,255,6155,5306,62820,5932,547,10424738,371703003,985023993,9599,124924976,79,4243,383,917486}

    66891275

    Returns: "Impossible"

  70. {92,40612554,586,96617863,186078,7355670,4604894,4524350,25403,72120615,4854,852,637820,718886960,56590004,62514336,725,447655,58749,311172,2,3535133,455481230,819145904,5188525,6,4566,5973,70,634636781,53280,63006,7,621,72505,26495,19,94358727,29,8,8095}

    6

    Returns: "Possible"

  71. {67,21,13,68,48,1,2,10,92,8,3,9,25,50,7,5,93,4,88,38,76,14,59,91,33,6,60,56,66,16,89,62,28,79}

    543008553

    Returns: "Impossible"

  72. {33964,900,3,55,65458,952,6,5067124,72078,25066,52960,5856,9041016,2599,751463,7700427,42199,7,5,179616,2463511}

    283600800

    Returns: "Possible"

  73. {3,61,56,9,2,10,27,58,68,1,96,6,8,25,40,37,7,87,99,5,12,78,80,84,76}

    267472800

    Returns: "Possible"

  74. {85,6,24,3,7,38,5,57,10,13,66,44,18,4,1,9,90,96,36,2,23,16,31,22,86,77,12,49,47,40,67,53,50,41,62,42}

    216384

    Returns: "Impossible"

  75. {2, 3, 4 }

    12

    Returns: "Possible"

  76. {1000000000, 999999999, 999999998 }

    999999999

    Returns: "Possible"

  77. {100, 200, 300, 400, 500, 600 }

    8000

    Returns: "Impossible"

  78. {6000000, 8000000 }

    24000000

    Returns: "Possible"

  79. {2, 8 }

    16

    Returns: "Impossible"

  80. {5000000, 6000000 }

    30000000

    Returns: "Possible"

  81. {1, 2 }

    20

    Returns: "Impossible"

  82. {1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999989, 999999988, 999999987, 999999986, 999999985, 999999984, 999999983, 999999982, 999999981, 999999980, 999999979, 999999978, 999999977, 999999976, 999999975, 999999974, 999999973, 999999972, 999999971, 999999970, 999999969, 999999968, 999999967, 999999966, 999999965, 999999964, 999999963, 999999962, 999999961, 999999960, 999999959, 999999958, 999999957, 999999956, 999999955, 999999954, 999999953, 999999952 }

    1000

    Returns: "Impossible"

  83. {100, 200, 300, 400, 500, 600 }

    2000

    Returns: "Possible"

  84. {595619502, 3, 912561327, 777762567, 482138661, 825049976, 956266151, 248315773, 633219928, 161055223, 533955415, 701653328, 514356447, 776311486, 207167212, 906287099, 840398188, 508368568, 796223764, 397122898, 699444056, 206897334, 632551577, 491089685, 361694749, 795352934, 559167496, 875072845, 962610587, 617234394, 314322234, 243726905, 975320696, 678744365, 490678285, 970980437, 189245343, 193064210, 227551235, 452024742, 179187233, 990891321, 905697962, 967647230, 209268736, 949394055, 652017642, 477252109, 213814282, 7 }

    1067856

    Returns: "Impossible"

  85. {16, 81, 625, 425, 51, 848, 2134165, 17 }

    810000

    Returns: "Possible"

  86. {3, 5, 7 }

    105

    Returns: "Possible"

  87. {2000, 3000, 5000 }

    30000

    Returns: "Possible"

  88. {1000000000, 2, 5, 10 }

    1000000000

    Returns: "Possible"

  89. {16, 81, 625 }

    810000

    Returns: "Possible"

  90. {2, 3, 4, 5 }

    20

    Returns: "Possible"

  91. {3, 4, 5 }

    60

    Returns: "Possible"

  92. {2, 3, 5 }

    30

    Returns: "Possible"

  93. {4, 14, 10 }

    70

    Returns: "Possible"

  94. {2, 3, 5, 7, 9, 11, 13, 17, 21, 23, 27 }

    1155

    Returns: "Possible"

  95. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44 }

    5454512

    Returns: "Impossible"

  96. {12, 15 }

    60

    Returns: "Possible"

  97. {1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999989, 999999988, 999999987, 999999986, 999999985, 999999984, 999999983, 999999982, 999999981, 999999980, 999999979, 999999978, 999999977, 999999976, 999999975, 999999974, 999999973, 999999972, 999999971, 999999970, 999999969, 999999968, 999999967, 999999966, 999999965, 999999964, 999999963, 999999962, 999999961, 999999960, 999999959, 999999958, 999999957, 999999956, 999999955, 999999954, 999999953, 999999952, 999999951 }

    20

    Returns: "Impossible"

  98. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 }

    74

    Returns: "Impossible"

  99. {2, 5, 7 }

    70

    Returns: "Possible"

  100. {2 }

    2

    Returns: "Possible"

  101. {1000000000, 5 }

    1000000000

    Returns: "Possible"

  102. {100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 14 }

    1000000000

    Returns: "Impossible"

  103. {100003, 100019, 100043, 100049, 100057, 100069, 100103, 100109, 100129, 100151, 100153, 100169, 100183, 100189, 100193, 100207, 100213, 100237, 100267, 100271, 100279, 100291, 100297, 100313, 100333, 100343, 100357, 100361, 100363, 100379, 100391, 100393, 100403, 100411, 100417, 100447, 100459, 100469, 100483, 100493, 100501, 100511, 100517, 100519, 100523, 100537, 100547, 100549, 100559 }

    1000000000

    Returns: "Impossible"

  104. {2, 3 }

    12

    Returns: "Impossible"

  105. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 }

    232792560

    Returns: "Possible"

  106. {2, 3, 4, 5, 6, 7, 8, 9, 10 }

    210

    Returns: "Possible"

  107. {3, 4, 5, 8, 7 }

    24

    Returns: "Possible"

  108. {500000000, 200000000 }

    1000000000

    Returns: "Possible"

  109. {999999937 }

    10

    Returns: "Impossible"

  110. {3, 5, 7, 11, 13, 17, 19 }

    4849845

    Returns: "Possible"

  111. {13466917, 44353434, 3, 5, 65435345, 7543534, 78, 8999, 866, 977, 8888, 695, 73, 745, 82, 94, 59989888, 433, 4, 5234, 64234, 7234, 2234, 26170819, 7234999, 723488, 8234, 954, 77345, 884, 432432434 }

    52341638

    Returns: "Impossible"

  112. {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 }

    412595806

    Returns: "Impossible"

  113. {2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 21, 22, 26, 30, 33, 35, 39, 42, 55, 65, 66, 70, 77, 78, 91, 105, 110, 130, 143, 154, 165, 182, 195, 210, 231, 273, 286, 330, 385, 390, 429, 455, 462, 546, 770, 910, 1155, 1365, 2310 }

    1021020

    Returns: "Impossible"

  114. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 }

    999999997

    Returns: "Impossible"

  115. {3, 4, 5, 10 }

    60

    Returns: "Possible"

  116. {13466917, 44353434, 3, 5, 65435345, 7543534, 78, 8999, 866, 977, 8888, 695, 73, 745, 82, 94, 59989888, 433, 4, 5234, 64234, 7234, 2234, 26170819, 7234999, 723488, 8234, 2, 77345, 884, 432432434 }

    52341638

    Returns: "Possible"

  117. {10000000, 100000000 }

    100000000

    Returns: "Possible"

  118. {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 100 }

    100

    Returns: "Possible"

  119. {1000000, 1000000000 }

    1000000000

    Returns: "Possible"

  120. {3, 4, 5 }

    15

    Returns: "Possible"

  121. {900000001, 900000002, 900000003, 900000004, 900000005 }

    900000005

    Returns: "Possible"

  122. {10, 23 }

    100

    Returns: "Impossible"

  123. {4, 6, 11, 7 }

    84

    Returns: "Possible"

  124. {2, 3, 4, 5, 7 }

    42

    Returns: "Possible"

  125. {2, 5, 40 }

    20

    Returns: "Impossible"

  126. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    1000000000

    Returns: "Impossible"

  127. {999221, 999233, 999239, 999269, 999287, 999307, 999329, 999331, 999359, 999371, 999377, 999389, 999431, 999433, 999437, 999451, 999491, 999499, 999521, 999529, 999541, 999553, 999563, 999599, 999611, 999613, 999623, 999631, 999653, 999667, 999671, 999683, 999721, 999727, 999749, 999763, 999769, 999773, 999809, 999853, 999863, 999883, 999907, 999917, 999931, 999953, 999959, 999961, 999979, 999983 }

    1000000

    Returns: "Impossible"

  128. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 500, 502, 503, 508, 620, 897, 497, 268, 24323324, 556457, 2342367, 2344211, 97533, 46789, 32468975, 346789, 45668, 2342311, 243578, 123912, 3567853, 123332, 864223, 579896, 228521468, 7632235, 2357322, 62234232, 7821122, 6723214 }

    12692568

    Returns: "Impossible"

  129. {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245 }

    3

    Returns: "Impossible"

  130. {10000000, 1000000 }

    10000000

    Returns: "Possible"

  131. {5, 900000001 }

    205032709

    Returns: "Impossible"

  132. {2, 3, 4, 5, 6, 7, 8, 9, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42 }

    1000000

    Returns: "Impossible"

  133. {500000000, 2, 4, 8, 16, 32, 5, 10, 20, 40, 100000000, 200000000, 250000000 }

    1000000000

    Returns: "Possible"

  134. {1, 2, 3, 4, 5 }

    60

    Returns: "Possible"

  135. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    101

    Returns: "Impossible"

  136. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 39 }

    78

    Returns: "Possible"

  137. {2, 3, 5, 7 }

    210

    Returns: "Possible"

  138. {999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999989, 999999988, 999999987, 999999986, 999999985, 999999984, 999999983, 999999982, 999999981, 999999980, 999999979, 999999978, 999999977, 999999976, 999999975, 999999974, 999999973, 999999972, 999999971, 999999970, 999999969, 999999968, 999999967, 999999966, 999999965, 999999964, 999999963, 999999962, 999999961, 999999960, 999999959, 999999958, 999999957, 999999956, 999999955 }

    1000000000

    Returns: "Impossible"

  139. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43 }

    101

    Returns: "Impossible"

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