Statistics

Problem Statement for "RaceTrack"

Problem Statement

A race track is represented as a line segment. You are given its length, and a int[] pos containing the positions where judges may be located. Each element of pos is the distance from the starting point of the race track. The elements of pos are given in strictly increasing order (pos[i] < pos[i+1]).

You are given an int judges, the number of judges in the next competition. You must assign the judges to positions such that the distance between the two closest judges is as large as possible. Return a String containing exactly n characters, where n is the number of elements in pos. The i-th character should be '1' (one) if there is a judge assigned to the i-th position, and '0' (zero) if there is not. The judges are lazy and don't want to go far from the starting point, so if there are multiple optimal solutions, return the one that comes latest lexicographically.

Definition

Class:
RaceTrack
Method:
judgePositions
Parameters:
int, int, int[]
Returns:
String
Method signature:
String judgePositions(int length, int judges, int[] pos)
(be sure your method is public)

Constraints

  • length will be between 1 and 1000000, inclusive.
  • pos will contain between 2 and 50 elements, inclusive.
  • Each element of pos will be greater than the previous, if it exists.
  • Each element of pos will be between 0 and length, inclusive.
  • judges will be between 2 and number of elements in pos, inclusive.

Examples

  1. 11

    3

    {0, 5, 10, 11}

    Returns: "1110"

    Another solution that maximizes the distance between the two closest judges is "1101", but it is not the lexicographically latest.

  2. 11

    2

    {0, 5, 10, 11}

    Returns: "1001"

    The distance between the two judges should be as large as possible.

  3. 11

    4

    {0, 5, 10, 11}

    Returns: "1111"

    The judges do not have any choice.

  4. 1000

    5

    {6, 9, 33, 59, 100, 341, 431, 444, 565, 857}

    Returns: "1000010111"

  5. 1

    2

    {0, 1}

    Returns: "11"

  6. 2

    2

    {0, 1, 2}

    Returns: "101"

  7. 4

    2

    {0, 1}

    Returns: "11"

  8. 9

    3

    {2, 7, 8}

    Returns: "111"

  9. 16

    3

    {4, 5, 9, 14}

    Returns: "1011"

  10. 25

    2

    {9, 15, 16, 17, 22}

    Returns: "10001"

  11. 36

    2

    {1, 4, 9, 11, 19, 35}

    Returns: "100001"

  12. 49

    2

    {0, 19, 22, 24, 27, 32, 36}

    Returns: "1000001"

  13. 64

    8

    {3, 11, 16, 27, 33, 36, 51, 52}

    Returns: "11111111"

  14. 81

    3

    {14, 25, 36, 42, 43, 47, 66, 73, 80}

    Returns: "100001001"

  15. 100

    8

    {15, 18, 40, 43, 46, 47, 52, 62, 65, 88}

    Returns: "1111101110"

  16. 121

    2

    {8, 13, 42, 49, 53, 62, 74, 97, 99, 107, 115}

    Returns: "10000000001"

  17. 144

    10

    {8, 13, 32, 56, 57, 77, 97, 98, 117, 120, 133, 140}

    Returns: "111101101111"

  18. 169

    8

    {15, 24, 32, 47, 59, 65, 87, 97, 102, 151, 155, 157, 165}

    Returns: "1011011011001"

  19. 196

    2

    {23, 29, 30, 55, 57, 70, 95, 116, 118, 119, 127, 147, 150, 189}

    Returns: "10000000000001"

  20. 225

    9

    {6, 24, 35, 45, 101, 105, 110, 111, 143, 144, 159, 164, 169, 204, 205}

    Returns: "111110011010100"

  21. 256

    16

    {4, 7, 15, 30, 49, 62, 69, 73, 108, 109, 114, 135, 153, 158, 160, 202}

    Returns: "1111111111111111"

  22. 289

    11

    {14, 26, 29, 38, 55, 59, 66, 84, 107, 127, 169, 193, 253, 254, 256, 267, 277}

    Returns: "11011001111110010"

  23. 324

    6

    {16, 28, 31, 61, 62, 70, 78, 149, 160, 171, 201, 228, 238, 241, 271, 287, 295, 310}

    Returns: "100100010010010100"

  24. 361

    12

    {6, 44, 50, 52, 67, 89, 105, 113, 120, 139, 190, 200, 205, 206, 227, 236, 252, 266, 308}

    Returns: "1100111011101010101"

  25. 400

    6

    {6, 10, 16, 28, 74, 80, 103, 113, 143, 154, 169, 236, 245, 254, 296, 333, 334, 356, 385, 392}

    Returns: "10001000100100100100"

  26. 441

    10

    {38, 65, 76, 128, 141, 160, 210, 212, 245, 249, 258, 262, 272, 278, 288, 290, 360, 374, 381, 387, 411}

    Returns: "110101101000100010011"

  27. 484

    5

    {15, 41, 76, 80, 81, 96, 106, 113, 120, 121, 150, 169, 205, 306, 371, 392, 400, 418, 424, 425, 449, 462}

    Returns: "1000000100001100100000"

  28. 529

    11

    {20, 37, 40, 81, 119, 121, 166, 192, 196, 205, 207, 358, 369, 394, 406, 421, 475, 479, 506, 515, 517, 519, 525}

    Returns: "10111011000101011010000"

  29. 576

    3

    {3, 21, 58, 95, 138, 197, 234, 256, 261, 295, 298, 397, 412, 416, 437, 468, 526, 539, 542, 544, 547, 554, 570, 576}

    Returns: "100000000100000000000001"

  30. 625

    25

    {19, 41, 49, 90, 101, 145, 156, 169, 183, 184, 201, 242, 251, 271, 313, 314, 322, 328, 414, 433, 484, 503, 507, 590, 591}

    Returns: "1111111111111111111111111"

  31. 676

    17

    {5, 58, 68, 110, 112, 113, 140, 159, 206, 209, 294, 301, 344, 354, 396, 417, 496, 498, 522, 534, 581, 593, 608, 612, 617, 642}

    Returns: "11010011101010111011111001"

  32. 729

    19

    {15, 48, 71, 74, 97, 159, 161, 186, 199, 246, 264, 296, 328, 355, 379, 397, 424, 440, 452, 488, 493, 513, 580, 601, 606, 645, 677}

    Returns: "111011010101111010110110111"

  33. 784

    3

    {135, 138, 147, 155, 192, 308, 338, 340, 343, 368, 384, 408, 410, 440, 470, 494, 521, 529, 548, 555, 564, 565, 596, 668, 676, 729, 749, 755}

    Returns: "1000000000000100000000000010"

  34. 841

    11

    {10, 38, 44, 97, 212, 221, 238, 262, 273, 328, 329, 342, 384, 385, 410, 415, 425, 492, 499, 515, 568, 593, 594, 597, 620, 645, 720, 793, 836}

    Returns: "10011000100100100100100001110"

  35. 900

    21

    {5, 24, 34, 61, 66, 119, 174, 299, 323, 325, 329, 332, 383, 437, 463, 466, 503, 529, 559, 609, 695, 707, 747, 756, 758, 788, 849, 868, 875, 893}

    Returns: "110101111000111011111110011101"

  36. 961

    12

    {24, 60, 183, 209, 221, 243, 258, 278, 314, 343, 351, 374, 380, 413, 433, 474, 550, 576, 626, 686, 688, 713, 740, 742, 780, 834, 856, 901, 906, 914, 941}

    Returns: "1010001001000101101010001010001"

  37. 1024

    22

    {1, 23, 29, 64, 126, 163, 175, 236, 256, 319, 381, 465, 567, 583, 587, 596, 601, 726, 753, 765, 790, 807, 857, 872, 878, 892, 903, 937, 977, 978, 989, 1017}

    Returns: "11011101111110100110111010111001"

  38. 1089

    17

    {0, 19, 74, 118, 149, 152, 167, 172, 235, 327, 338, 353, 474, 521, 552, 578, 600, 627, 629, 641, 653, 655, 706, 709, 759, 760, 805, 810, 833, 891, 934, 1007, 1052}

    Returns: "101100101100110101000010101001111"

  39. 1156

    29

    {10, 19, 43, 86, 102, 136, 227, 265, 307, 316, 347, 360, 362, 420, 433, 484, 501, 562, 570, 579, 721, 729, 737, 738, 746, 758, 773, 799, 885, 897, 928, 935, 948, 1126}

    Returns: "1111111111110111110110101111111011"

  40. 1225

    24

    {63, 65, 91, 130, 131, 136, 156, 159, 177, 212, 319, 381, 422, 431, 452, 486, 557, 592, 672, 732, 753, 764, 825, 827, 828, 839, 902, 908, 942, 963, 1048, 1091, 1143, 1217, 1223}

    Returns: "10110010111110111111101000101111110"

  41. 1296

    2

    {9, 64, 69, 178, 247, 260, 262, 356, 360, 364, 371, 372, 419, 469, 508, 562, 599, 608, 628, 635, 643, 658, 744, 773, 791, 908, 972, 1014, 1021, 1033, 1084, 1085, 1144, 1205, 1273, 1284}

    Returns: "100000000000000000000000000000000001"

  42. 1369

    6

    {42, 46, 103, 114, 123, 232, 271, 327, 343, 355, 423, 445, 507, 549, 558, 568, 631, 693, 730, 734, 748, 749, 757, 760, 793, 833, 837, 855, 1004, 1049, 1094, 1153, 1199, 1205, 1229, 1301, 1366}

    Returns: "1000000100000001000000000100001000001"

  43. 1444

    25

    {79, 80, 109, 120, 217, 282, 284, 351, 372, 403, 548, 582, 625, 642, 650, 655, 698, 700, 795, 823, 824, 860, 914, 990, 998, 1062, 1077, 1159, 1172, 1200, 1239, 1330, 1337, 1363, 1388, 1406, 1428, 1431}

    Returns: "10101101111110101011011101010111011010"

  44. 1521

    12

    {11, 17, 44, 150, 162, 181, 192, 218, 239, 349, 499, 507, 526, 579, 607, 671, 723, 755, 809, 818, 846, 850, 886, 915, 959, 1008, 1044, 1047, 1061, 1204, 1213, 1216, 1346, 1360, 1378, 1399, 1441, 1505, 1513}

    Returns: "100100000110001010001000100011001000010"

  45. 1600

    39

    {14, 21, 96, 174, 235, 237, 296, 311, 363, 393, 400, 407, 505, 526, 561, 608, 645, 730, 752, 763, 772, 844, 858, 874, 879, 883, 893, 959, 1043, 1057, 1162, 1233, 1265, 1300, 1328, 1331, 1420, 1477, 1480, 1540}

    Returns: "1111101111111111111111111111111111111111"

  46. 1681

    37

    {6, 32, 41, 94, 164, 183, 210, 247, 343, 359, 429, 468, 481, 518, 520, 614, 685, 725, 743, 873, 889, 895, 945, 953, 1022, 1033, 1043, 1076, 1087, 1101, 1115, 1187, 1222, 1321, 1355, 1364, 1578, 1596, 1610, 1617, 1680}

    Returns: "11111111111111011111101011111111111111101"

  47. 1764

    36

    {1, 5, 15, 93, 99, 102, 142, 182, 209, 258, 284, 322, 351, 384, 417, 418, 486, 501, 534, 654, 865, 882, 951, 1075, 1097, 1099, 1151, 1175, 1219, 1248, 1257, 1262, 1317, 1340, 1385, 1431, 1466, 1490, 1544, 1612, 1657, 1763}

    Returns: "101100111111111011111111101111011111111111"

  48. 1849

    31

    {183, 196, 260, 261, 282, 298, 329, 339, 354, 398, 463, 514, 535, 559, 611, 616, 667, 681, 719, 805, 819, 840, 904, 932, 980, 989, 1024, 1068, 1078, 1125, 1212, 1217, 1289, 1325, 1352, 1416, 1504, 1551, 1561, 1660, 1675, 1782, 1786}

    Returns: "1010111011111110101101111011011011111101010"

  49. 1936

    31

    {27, 36, 99, 128, 149, 214, 240, 292, 318, 319, 424, 457, 555, 595, 604, 666, 673, 727, 801, 1025, 1027, 1043, 1135, 1157, 1209, 1257, 1279, 1298, 1312, 1329, 1396, 1438, 1528, 1533, 1571, 1583, 1595, 1619, 1711, 1716, 1725, 1858, 1877, 1879}

    Returns: "10111111101111010111001111101011101011100101"

  50. 2025

    42

    {19, 75, 84, 137, 171, 192, 201, 231, 260, 279, 406, 422, 436, 643, 648, 703, 711, 717, 730, 781, 810, 830, 861, 862, 947, 993, 997, 1071, 1120, 1150, 1247, 1250, 1252, 1402, 1493, 1598, 1622, 1646, 1674, 1731, 1770, 1802, 1863, 1888, 1912}

    Returns: "111111111111111111111110110111101111111111111"

  51. 2116

    12

    {50, 79, 103, 150, 186, 207, 210, 273, 309, 325, 350, 419, 422, 483, 534, 563, 650, 679, 681, 727, 740, 798, 1128, 1164, 1170, 1200, 1215, 1241, 1283, 1335, 1337, 1367, 1458, 1482, 1502, 1542, 1550, 1551, 1636, 1651, 1702, 1730, 1798, 1813, 1892, 2078}

    Returns: "1000100001000100100001100000100010000010001001"

  52. 2209

    11

    {8, 56, 68, 99, 150, 200, 202, 228, 340, 382, 574, 575, 591, 595, 631, 632, 655, 763, 821, 932, 933, 944, 981, 1019, 1033, 1052, 1079, 1151, 1165, 1210, 1229, 1299, 1369, 1476, 1543, 1642, 1649, 1726, 1733, 1781, 1869, 1880, 1979, 2036, 2119, 2146, 2192}

    Returns: "10000100011000000100001000001000100100001000100"

  53. 2304

    3

    {69, 101, 109, 185, 226, 248, 279, 407, 418, 450, 489, 511, 518, 538, 545, 595, 669, 693, 807, 827, 908, 919, 923, 927, 953, 1036, 1202, 1207, 1232, 1233, 1249, 1392, 1470, 1485, 1547, 1562, 1629, 1918, 1928, 1935, 1951, 2027, 2045, 2070, 2081, 2085, 2212, 2241}

    Returns: "100000000000000000000000001000000000000000000001"

  54. 2401

    10

    {104, 115, 122, 124, 137, 147, 155, 156, 191, 215, 391, 408, 484, 512, 650, 694, 728, 790, 802, 846, 854, 868, 987, 994, 1018, 1085, 1104, 1119, 1137, 1187, 1274, 1344, 1461, 1533, 1585, 1602, 1652, 1670, 1707, 1709, 1714, 1761, 1860, 1883, 1928, 1966, 2138, 2170, 2400}

    Returns: "1000000000100010000001000010000100100000001000101"

  55. 2500

    32

    {125, 240, 331, 357, 363, 393, 431, 460, 508, 626, 674, 787, 798, 909, 924, 969, 1097, 1279, 1280, 1310, 1362, 1402, 1483, 1522, 1559, 1578, 1632, 1693, 1744, 1789, 1855, 1890, 1960, 1989, 2027, 2100, 2148, 2187, 2201, 2206, 2234, 2241, 2263, 2272, 2295, 2326, 2341, 2411, 2454, 2495}

    Returns: "11100101111101011100111010111110101110100100101110"

  56. 49

    50

    {0, 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}

    Returns: "11111111111111111111111111111111111111111111111111"

  57. 64

    2

    {0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 31, 32, 33, 35, 36, 37, 38, 40, 43, 44, 45, 46, 47, 48, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63}

    Returns: "10000000000000000000000000000000000000000000000001"

  58. 729

    3

    {3, 25, 32, 65, 108, 116, 128, 144, 157, 163, 192, 199, 206, 212, 226, 247, 255, 292, 305, 319, 326, 329, 341, 361, 378, 381, 389, 397, 403, 413, 415, 417, 447, 498, 510, 518, 538, 606, 621, 625, 642, 644, 659, 661, 683, 685, 693, 695, 713, 721}

    Returns: "10000000000000000000000100000000000000000000000001"

  59. 4096

    50

    {2, 72, 166, 206, 292, 375, 445, 471, 536, 562, 617, 643, 693, 819, 844, 854, 916, 1002, 1020, 1171, 1201, 1252, 1267, 1535, 1556, 1596, 1674, 1787, 1829, 1835, 1893, 2033, 2231, 2379, 2458, 2872, 2904, 2953, 3122, 3189, 3199, 3357, 3555, 3656, 3672, 3698, 3834, 3943, 4034, 4082}

    Returns: "11111111111111111111111111111111111111111111111111"

  60. 15625

    5

    {273, 576, 837, 1025, 1433, 1449, 1535, 2446, 2844, 2945, 3428, 3726, 3832, 3843, 3949, 4122, 4341, 4578, 4594, 4640, 4685, 4720, 5621, 5651, 6039, 7328, 7497, 7999, 8783, 9053, 9232, 9646, 10702, 10817, 10921, 11682, 12032, 12288, 12302, 12559, 12805, 13306, 13322, 13338, 13493, 13522, 13943, 13944, 14672, 14704}

    Returns: "10000000000010000000000001000000001000000000000010"

  61. 46656

    2

    {308, 448, 513, 603, 1134, 2865, 3572, 3579, 5388, 6248, 7099, 7888, 9436, 10461, 11185, 14579, 14757, 18581, 18618, 20117, 20163, 20508, 20691, 22487, 22633, 23721, 26062, 26820, 27920, 28026, 29342, 29953, 30161, 31594, 31601, 31677, 32247, 33888, 34694, 34773, 35519, 36019, 37019, 38406, 40297, 42621, 43581, 44172, 44402, 44596}

    Returns: "10000000000000000000000000000000000000000000000001"

  62. 117649

    6

    {63, 1054, 6587, 8261, 9644, 15088, 15956, 16122, 16556, 17960, 22430, 23596, 24734, 28242, 28591, 31438, 33528, 35000, 36971, 40156, 40589, 42905, 45112, 48890, 49864, 52255, 57137, 59482, 60313, 66092, 74143, 77093, 81501, 83348, 83513, 85297, 86302, 88252, 89311, 91245, 95520, 95858, 96997, 99511, 100396, 103260, 107579, 110433, 113530, 114074}

    Returns: "10000000001000000000001000000100000001000000000100"

  63. 262144

    8

    {2434, 4736, 13253, 13301, 22213, 24658, 28307, 31323, 32126, 38823, 41013, 46291, 47623, 54585, 58605, 59784, 69826, 71527, 72330, 75752, 79910, 84302, 86355, 90533, 96473, 104708, 108010, 116010, 116362, 121122, 121265, 126384, 128619, 142959, 147437, 151598, 151811, 158181, 161241, 167915, 181684, 189901, 191015, 201030, 206734, 217169, 217736, 225100, 233121, 235312}

    Returns: "10000001000000010000000100000100000100001000010000"

  64. 531441

    5

    {10981, 33648, 38632, 40791, 50202, 56895, 57300, 67547, 75436, 76737, 107085, 124677, 135061, 151538, 152802, 153692, 155019, 155417, 156256, 164882, 171789, 185521, 191560, 199642, 201819, 203419, 213030, 218203, 228419, 237336, 253364, 279434, 282345, 294013, 340852, 341317, 370042, 379325, 385434, 388466, 400477, 405087, 418755, 426265, 437592, 444604, 447535, 474742, 494569, 516595}

    Returns: "10000000000010000000000000000010000001000000000001"

  65. 1000000

    7

    {2811, 2891, 36942, 86246, 111270, 111718, 119569, 133205, 135671, 139051, 162256, 165173, 190321, 194298, 219512, 230969, 238374, 290734, 307973, 325533, 338379, 348938, 350327, 353050, 379422, 388075, 388705, 392798, 400243, 429764, 450327, 456252, 480564, 500847, 596878, 604953, 674567, 706754, 761838, 779845, 787381, 804304, 826444, 829135, 854935, 862739, 912582, 953933, 986329, 987499}

    Returns: "10000000001000000001000000000000100010000001000010"

  66. 1000000

    49

    {4702, 30532, 53714, 82356, 115954, 164111, 171986, 173830, 192843, 204421, 226726, 240469, 290943, 346336, 361172, 383541, 388329, 406216, 416786, 418865, 436567, 455709, 496243, 520234, 524173, 551774, 562374, 564862, 588787, 633266, 638097, 665358, 685272, 689605, 720113, 734897, 759697, 778862, 801432, 807074, 815312, 820423, 856790, 887665, 901298, 930698, 948106, 967253, 978987, 998697}

    Returns: "11111110111111111111111111111111111111111111111111"

  67. 1000000

    48

    {1994, 20573, 34715, 36515, 67633, 87576, 89341, 118365, 123167, 130687, 135627, 150432, 173090, 189661, 211096, 213328, 214671, 280710, 327992, 331111, 335672, 362455, 390955, 415358, 520342, 584140, 586575, 602876, 631332, 637822, 673386, 707398, 732134, 772768, 780406, 783664, 815192, 830045, 836858, 845309, 863957, 864013, 877029, 898063, 900486, 940299, 946328, 949937, 950497, 984975}

    Returns: "11111111111111111111111111111111111111111011111101"

  68. 1000000

    47

    {12227, 13301, 16314, 46859, 131836, 145770, 158588, 167894, 179112, 186641, 201365, 209253, 246120, 247814, 266728, 272062, 318517, 319872, 322958, 326160, 390226, 399341, 427527, 493162, 499846, 504919, 518121, 522025, 539722, 550253, 605941, 647371, 658342, 663047, 706313, 710651, 722233, 740390, 804218, 813632, 817312, 828646, 833527, 837096, 885520, 934102, 942613, 969579, 972882, 990803}

    Returns: "10111111111110111011111111111111111111111111111111"

  69. 1000000

    46

    {25093, 41516, 57455, 91598, 95859, 119011, 119420, 132411, 152540, 162463, 172790, 195325, 200793, 223449, 226765, 245102, 259262, 261453, 266389, 267595, 285276, 291335, 299231, 313487, 352184, 370779, 392278, 394673, 402821, 408165, 423066, 454074, 455436, 464786, 483462, 561894, 569998, 615448, 618050, 622502, 656202, 657669, 671534, 689211, 697474, 774456, 796735, 878279, 934995, 964212}

    Returns: "11111101111111111110111111111111011111111011111111"

  70. 1000000

    45

    {30177, 57649, 59259, 106601, 116229, 161411, 174131, 180028, 182298, 192670, 198310, 210770, 223245, 224474, 237201, 243874, 266224, 288317, 298313, 312826, 334714, 338062, 364852, 365454, 369329, 398450, 402153, 409869, 412181, 415600, 424534, 427194, 462627, 463053, 502404, 598940, 619297, 628831, 707911, 749384, 776070, 795229, 800267, 830373, 870272, 891776, 897022, 932748, 941775, 971865}

    Returns: "11011111011110111111111011111111101111111111111111"

  71. 1000000

    44

    {6227, 9270, 18397, 32033, 33820, 39101, 50691, 62211, 64689, 84984, 92812, 96612, 108505, 140746, 148649, 157002, 158062, 158399, 162948, 164968, 174070, 176422, 187899, 188254, 198208, 213341, 235248, 270106, 336825, 512187, 549140, 570991, 573261, 601787, 620438, 645903, 660112, 735362, 762553, 798561, 815260, 894960, 900407, 906284, 908940, 912753, 922625, 924600, 924871, 952951}

    Returns: "11110111111111110010111011111111111111111111111011"

  72. 1000000

    43

    {7160, 16871, 28374, 39426, 135793, 143484, 167509, 184132, 232694, 234521, 238211, 288842, 289674, 312185, 321016, 324767, 373140, 385430, 391857, 398374, 404982, 440720, 481625, 485042, 497698, 510491, 525605, 567756, 587084, 589484, 621719, 693426, 724052, 735464, 742924, 744485, 823770, 842879, 847530, 847673, 871258, 877037, 914455, 923457, 937469, 959274, 965286, 966158, 982595, 992029}

    Returns: "11111111101101111111111011111011111011101111111011"

  73. 1000000

    42

    {35029, 53184, 72847, 100874, 120153, 133469, 149061, 163996, 184062, 213535, 250217, 268180, 287606, 299581, 308388, 324734, 333506, 364155, 385433, 394065, 394332, 424903, 434240, 453778, 465422, 469605, 471847, 517506, 541893, 549718, 551229, 560347, 574375, 581619, 622928, 630743, 655120, 674838, 697387, 729977, 743225, 777725, 796180, 812002, 875280, 878427, 916465, 925270, 931553, 979114}

    Returns: "11111111111111111110111110011011101011111111101101"

  74. 1000000

    41

    {23997, 53305, 71143, 72999, 74397, 96957, 100492, 122679, 173497, 178790, 181796, 207569, 217232, 236528, 260036, 348568, 396197, 412898, 417742, 453360, 471004, 494528, 497456, 516049, 568162, 573494, 574391, 575602, 576161, 593072, 613080, 677045, 699772, 702841, 706878, 745752, 758540, 762401, 763112, 765113, 777549, 857747, 862308, 899351, 942505, 950061, 954618, 964359, 973406, 981305}

    Returns: "11101111110111111111110111000111101111001111111111"

  75. 1000000

    40

    {14901, 22638, 22649, 32839, 33501, 41060, 74910, 99306, 116015, 124761, 130748, 137897, 173414, 220823, 221633, 222083, 255169, 263167, 281963, 282348, 377673, 377911, 389837, 439189, 454777, 459459, 469383, 481743, 481854, 552705, 553914, 555768, 558038, 580163, 581063, 609632, 623779, 625017, 646585, 710017, 714714, 725945, 736158, 754835, 804081, 900062, 901775, 911191, 947282, 980873}

    Returns: "11010111111111001110101111110101110110111111111111"

  76. 1000000

    50

    {3968, 39637, 82283, 82707, 85391, 90489, 127602, 130592, 149664, 157925, 161071, 174551, 182306, 182718, 221362, 237271, 238543, 268556, 274622, 315342, 357784, 361453, 371285, 383469, 392266, 395268, 400863, 439359, 447975, 462588, 462635, 501263, 508941, 529312, 536653, 545505, 618076, 635409, 675787, 680673, 705312, 712145, 714376, 777274, 837826, 862205, 874273, 949562, 955739, 972262}

    Returns: "11111111111111111111111111111111111111111111111111"

  77. 1000000

    2

    {16373, 23455, 26604, 31706, 35508, 77379, 86621, 93132, 113086, 132711, 137416, 149893, 171354, 172532, 215717, 232073, 236990, 263937, 283632, 335587, 343801, 378367, 413520, 454854, 457167, 515891, 539923, 545990, 554210, 572833, 575564, 576406, 594870, 614023, 644089, 645538, 659604, 672249, 699401, 704854, 729348, 755939, 798336, 836625, 853465, 884804, 890104, 921557, 956585, 981199}

    Returns: "10000000000000000000000000000000000000000000000001"

  78. 1000000

    3

    {599, 24060, 25542, 46528, 47067, 70040, 73596, 84909, 102088, 105159, 107626, 129767, 192747, 205552, 210672, 210676, 211209, 230860, 237223, 277587, 296745, 297810, 310532, 364152, 367073, 377142, 413656, 443846, 456046, 480716, 535003, 539766, 552802, 595717, 615284, 658738, 690193, 706121, 733677, 750577, 793196, 802492, 817542, 819847, 885305, 889616, 945167, 950059, 987653, 997317}

    Returns: "10000000000000000000000000000100000000000000000010"

  79. 1000000

    4

    {73749, 94289, 95429, 117362, 132549, 145905, 151776, 152474, 156927, 172707, 215031, 223381, 224233, 224774, 277856, 297976, 298570, 320749, 335711, 336548, 337720, 353573, 408972, 468222, 496415, 522324, 544675, 545257, 565766, 582778, 586246, 596185, 619931, 654607, 680031, 680808, 683013, 717921, 746631, 805951, 825052, 840842, 851284, 851987, 856190, 863249, 895704, 899863, 978620, 992258}

    Returns: "10000000000000000000010000000000010000000000000010"

  80. 1000000

    5

    {13910, 20168, 67567, 72721, 76176, 134783, 165681, 166035, 173162, 183469, 209710, 246310, 309682, 347869, 371836, 373210, 384513, 391458, 416731, 418816, 443064, 445248, 447927, 463517, 469202, 473797, 478449, 479664, 499471, 505022, 516336, 607169, 637011, 642570, 656527, 659930, 689075, 694514, 701838, 704226, 811073, 820632, 847931, 861447, 888196, 912186, 920874, 952996, 972492, 987505}

    Returns: "10000000000100000000000001000000000000100000000100"

  81. 1000000

    6

    {15018, 24957, 37932, 89985, 92286, 170186, 186352, 196212, 209924, 264256, 292397, 296767, 319731, 345792, 349977, 354783, 356165, 360028, 375620, 395021, 399425, 419231, 429499, 513618, 530021, 566459, 578026, 591115, 597004, 604796, 608483, 624618, 674597, 710766, 730150, 750367, 757230, 768908, 803476, 827482, 833036, 837574, 842049, 863957, 888786, 902491, 925117, 951239, 979457, 985895}

    Returns: "10000000100000000001000000100000000001000000000010"

  82. 1000000

    7

    {10104, 29834, 78309, 78798, 87711, 104423, 142799, 144142, 162069, 214228, 219694, 230252, 247682, 275350, 297018, 302949, 322986, 347205, 380533, 424421, 451740, 481873, 482191, 482527, 496495, 513904, 555934, 570217, 591503, 629550, 635487, 646052, 653799, 660094, 663042, 679343, 689686, 741286, 759964, 806282, 808633, 829587, 842476, 843182, 849389, 887059, 899186, 950107, 952940, 992214}

    Returns: "10000000100000001000010000000010000000010000000001"

  83. 1000000

    8

    {35534, 111901, 116972, 157796, 162957, 200853, 213779, 225373, 239160, 318041, 322608, 336388, 367467, 397812, 407243, 420356, 503546, 514946, 533551, 545753, 576331, 576390, 582063, 582517, 656128, 693712, 705109, 722076, 723145, 748381, 757474, 772024, 776181, 780054, 788508, 801594, 834657, 847064, 855433, 865146, 869958, 873967, 884887, 888445, 909798, 939922, 957159, 960148, 967737, 980158}

    Returns: "10010000010000010010000010000001000000000010000000"

  84. 1000000

    9

    {1506, 45609, 80098, 82781, 91996, 124885, 125824, 203085, 227176, 271578, 316874, 324858, 328119, 354446, 360701, 374895, 375335, 383237, 420527, 424232, 424466, 426134, 450982, 468878, 473024, 495678, 503321, 506311, 541462, 549336, 573621, 604800, 613938, 659113, 676625, 685858, 698414, 699019, 715697, 724454, 743064, 779189, 779648, 848031, 849020, 895684, 909818, 920625, 925377, 932566}

    Returns: "10000100100001000000000100000010001000000100010000"

  85. 1000000

    10

    {34856, 61320, 88663, 88960, 90518, 91376, 100704, 114612, 189288, 213272, 214917, 214984, 227782, 245425, 261225, 282466, 367400, 370834, 376753, 382090, 389328, 411405, 426198, 530427, 556129, 566438, 568719, 582708, 584773, 622393, 622519, 641565, 663821, 675338, 677093, 707351, 733756, 741342, 750994, 815238, 817541, 845079, 845677, 852359, 889391, 916501, 917722, 946528, 973126, 980629}

    Returns: "10000001100000011000000100000100000100010000010000"

  86. 10

    2

    {1, 2 }

    Returns: "11"

  87. 20

    3

    {0, 3, 6, 9 }

    Returns: "1110"

  88. 1000000

    25

    {900000, 900001, 900003, 900006, 900010, 900015, 900021, 900028, 900036, 900045, 900055, 900066, 900078, 900091, 900105, 900120, 900136, 900153, 900171, 900190, 900210, 900231, 900253, 900276, 900300, 900325, 900351, 900378, 900406, 900435, 900465, 900496, 900528, 900561, 900595, 900630, 900666, 900703, 900741, 900780, 900820, 900861, 900903, 900946, 900990, 901035, 901081, 901128, 901176, 901225 }

    Returns: "10000000010001001001010101010101010101011111111111"

  89. 100000

    30

    {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 154, 160, 180, 200, 210, 220, 230, 300, 400, 500, 550, 660, 770, 880, 900, 1000, 1100, 1200, 1233, 1400, 1466, 1600, 1800, 2000, 2100, 2200, 2300, 3400, 4400, 4500, 4600, 4700, 5600, 7000, 9000, 10000, 99999 }

    Returns: "10000001000001000001111011101110101111111111111111"

  90. 1000000

    33

    {0, 2, 12, 36, 80, 150, 252, 392, 576, 810, 1100, 1452, 1872, 2366, 2940, 3600, 4352, 5202, 6156, 7220, 8400, 9702, 11132, 12696, 14400, 16250, 18252, 20412, 22736, 25230, 27900, 30752, 33792, 37026, 40460, 44100, 47952, 52022, 56316, 60840, 65600, 70602, 75852, 81356, 87120, 93150, 99452, 106032, 112896, 120050 }

    Returns: "10000000000010010101010111111111111111111111111111"

  91. 3

    3

    {0, 1, 2, 3 }

    Returns: "1110"

  92. 1000000

    25

    {20, 40, 50, 60, 70, 80, 90, 100, 200, 204, 206, 207, 208, 209, 210, 300, 301, 302, 303, 304, 305, 306, 307, 308, 401, 402, 403, 404, 405, 406, 407, 408, 409, 501, 502, 503, 504, 505, 506, 507, 508, 509, 1001, 1003, 1005, 1007, 1008, 2001, 20056, 340000 }

    Returns: "11111111110010010001000110001000110001000110100111"

  93. 50

    25

    {0, 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 }

    Returns: "10101010101010101010101010101010101010101010101010"

  94. 1000

    25

    {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 }

    Returns: "10101010101010101010101010101010101010101010101010"

  95. 10

    6

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

    Returns: "1111110000"

  96. 1000000

    25

    {20000, 40000, 60000, 80000, 100000, 120000, 140000, 160000, 180000, 200000, 220000, 240000, 260000, 280000, 300000, 320000, 340000, 360000, 380000, 400000, 420000, 440000, 460000, 480000, 500000, 520000, 540000, 560000, 580000, 600000, 620000, 640000, 660000, 680000, 700000, 720000, 740000, 760000, 780000, 800000, 820000, 840000, 860000, 880000, 900000, 920000, 940000, 960000, 980000, 1000000 }

    Returns: "10101010101010101010101010101010101010101010101010"

  97. 1000000

    2

    {0, 500000, 1000000 }

    Returns: "101"

  98. 1000000

    3

    {10, 20, 30, 40 }

    Returns: "1110"

  99. 100

    4

    {1, 2, 3, 4, 5 }

    Returns: "11110"

  100. 1000000

    25

    {0, 20000, 40000, 60000, 80000, 100000, 120000, 140000, 160000, 180000, 200000, 220000, 240000, 260000, 280000, 300000, 320000, 340000, 360000, 380000, 400000, 420000, 440000, 460000, 480000, 500000, 520000, 540000, 560000, 580000, 600000, 620000, 640000, 660000, 680000, 700000, 720000, 740000, 760000, 780000, 800000, 820000, 840000, 860000, 880000, 900000, 920000, 940000, 960000, 980000 }

    Returns: "10101010101010101010101010101010101010101010101010"

  101. 50

    4

    {0, 10, 20, 30, 40, 50 }

    Returns: "111100"

  102. 1000000

    25

    {600, 900, 3300, 5900, 10000, 24100, 43100, 44400, 56500, 57700, 58000, 59900, 65700, 69000, 100000, 124100, 143100, 144400, 156500, 156700, 157000, 157900, 165700, 169000, 170000, 184100, 193100, 204400, 212500, 225700, 235600, 246900, 255700, 269000, 270000, 284100, 293100, 304400, 312500, 325700, 435600, 446900, 455700, 469000, 570000, 684100, 793100, 804400, 912500, 925700 }

    Returns: "10000110100000111010000011010101010101011011111011"

  103. 100532

    5

    {14260, 27847, 69213, 71772, 79477, 82187, 99317, 100530 }

    Returns: "11100110"

  104. 886263

    14

    {623, 19605, 25971, 83899, 101063, 170158, 191710, 200385, 207091, 246498, 247444, 287921, 302218, 350996, 352284, 366684, 376824, 388154, 446260, 483986, 484893, 501199, 561479, 579371, 592816, 593808, 638786, 642356, 646884, 691128, 693333, 731312, 859876, 880105, 884032 }

    Returns: "10010100010101000111001000100101100"

  105. 1000000

    17

    {0, 5211, 18456, 21530, 89172, 133069, 142857, 174067, 175011, 176229, 180540, 202362, 238335, 285714, 289383, 368690, 377373, 383426, 428571, 455736, 465782, 478042, 490027, 513926, 513929, 516649, 520059, 571428, 595368, 634022, 636915, 641421, 665123, 692777, 702567, 703135, 714285, 722862, 723058, 747793, 760492, 857142, 885386, 897763, 898167, 930886, 956429, 961393, 979802, 1000000 }

    Returns: "10001100010011010010010000110100010000010100010010"

  106. 1000000

    8

    {0, 5211, 18456, 21530, 89172, 133069, 142857, 174067, 175011, 176229, 180540, 202362, 238335, 285714, 289383, 368690, 377373, 383426, 428571, 455736, 465782, 478042, 490027, 513926, 513929, 516649, 520059, 571428, 595368, 634022, 636915, 641421, 665123, 692777, 702567, 703135, 714285, 722862, 723058, 747793, 760492, 857142, 885386, 897763, 898167, 930886, 956429, 961393, 979802, 1000000 }

    Returns: "10000010000001000010000000010000000010000100000001"

  107. 666

    13

    {0, 10, 19, 37, 49, 88, 99, 102, 133, 142, 222, 333, 444, 555, 565, 575, 585, 595, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630 }

    Returns: "1011010010111101010000000000001000000000000000010"

  108. 1000000

    40

    {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, 239 }

    Returns: "11111111111111111111111111111111111111110000000000"

  109. 1000000

    50

    {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 }

    Returns: "11111111111111111111111111111111111111111111111111"

  110. 100000

    4

    {0, 5, 10, 15, 20, 25 }

    Returns: "111100"

  111. 50

    25

    {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 }

    Returns: "10101010101010101010101010101010101010101010101010"

  112. 196

    4

    {1, 24, 25, 35, 38, 64, 85, 96, 99, 102, 123, 134, 156, 180 }

    Returns: "10000100001001"

  113. 11

    4

    {0, 5, 10, 11 }

    Returns: "1111"

  114. 2

    3

    {0, 1, 2 }

    Returns: "111"

  115. 52

    48

    {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, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 }

    Returns: "111111111111111111111111111111111111111111111111"

  116. 11

    3

    {1, 2, 3, 4, 5 }

    Returns: "10101"

  117. 100

    3

    {2, 4, 6, 8 }

    Returns: "1110"

  118. 1000000

    10

    {28184, 28962, 28973, 29136, 30036, 30959, 31558, 32552, 32850, 33419, 34117, 34777, 35708, 36528, 36783, 37705, 38554, 39446, 39745, 39824, 40256, 40554, 41050, 41464, 41910, 42542, 43156, 43425, 43500, 43510, 44403, 45047, 45686, 45979, 46437, 46833, 47204, 47748, 47752, 47785, 47879, 48070, 48460, 49042, 49445, 49470, 49509, 49891, 50647, 51101 }

    Returns: "10000100010010001000001000010000010000000010000001"

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