Statistics

Problem Statement for "AliceGame"

Problem Statement

Alice and Kirito just played a game. The game consisted of a finite (possibly empty) sequence of turns. You do not know the exact number of turns. The turns were numbered starting from 1. In each turn, exactly one of our two players won. The winner of turn i scored 2*i-1 points.

You are given two longs x and y. Find out whether it is possible that at the end of the game Alice had exactly x points and Kirito had exactly y points. If it is possible, return the smallest number of turns Alice could have won. If the given final result is not possible, return -1 instead.

Definition

Class:
AliceGame
Method:
findMinimumValue
Parameters:
long, long
Returns:
long
Method signature:
long findMinimumValue(long x, long y)
(be sure your method is public)

Constraints

  • x and y are between 0 and 1,000,000,000,000, inclusive.

Examples

  1. 8

    17

    Returns: 2

    This final result is possible. Alice must have won at least two turns. One possibility is that Alice won turns 2 and 3 (for 3+5 = 8 points) and Kirito won turns 1, 4, and 5 (for 1+7+9 = 17 points).

  2. 17

    8

    Returns: 3

  3. 0

    0

    Returns: 0

  4. 9

    9

    Returns: -1

  5. 500000

    500000

    Returns: 294

  6. 0

    1000000000000

    Returns: 0

  7. 1000000000000

    0

    Returns: 1000000

  8. 1

    999999999999

    Returns: 1

  9. 2000001

    999997999999

    Returns: 3

  10. 999999999999

    1

    Returns: 999999

  11. 999999999998

    2

    Returns: -1

  12. 2

    999999999998

    Returns: -1

  13. 932765767597

    67234232403

    Returns: 740705

  14. 758061436054

    241938563946

    Returns: 508128

  15. 330577220114

    669422779886

    Returns: 181818

  16. 411272539527

    588727460473

    Returns: 232715

  17. 750769056733

    249230943267

    Returns: 500771

  18. 1000000000000

    1000000000000

    Returns: -1

  19. 804127930553

    171444078586

    Returns: -1

  20. 773611447136

    593814262551

    Returns: -1

  21. 963128051536

    775328156192

    Returns: -1

  22. 123157670343

    262647845900

    Returns: -1

  23. 400344234076

    804890866061

    Returns: -1

  24. 5869662412

    68159224394

    Returns: -1

  25. 9056435877

    184342976107

    Returns: 10421

  26. 417712389332

    388360282708

    Returns: -1

  27. 68562845609

    9365226727

    Returns: 182383

  28. 29882296722

    217034766834

    Returns: -1

  29. 65403676999

    148726944307

    Returns: -1

  30. 130638593846

    743702349998

    Returns: 72682

  31. 2813830661

    22112579500

    Returns: 9179

  32. 52852730407

    192379223274

    Returns: 56599

  33. 4613447655

    325409074

    Returns: 52239

  34. 61513379284

    75799481522

    Returns: -1

  35. 1215509340

    482548716

    Returns: -1

  36. 59396268432

    30382168098

    Returns: -1

  37. 175808746853

    28221432956

    Returns: 283705

  38. 23749521867

    153591269175

    Returns: -1

  39. 7613832948

    6378809442

    Returns: -1

  40. 473951591379

    229560874913

    Returns: -1

  41. 414283888

    48525281

    Returns: 14548

  42. 9616130617

    7745752843

    Returns: -1

  43. 19901699909

    26410631300

    Returns: 52691

  44. 1000000000000

    999998409369

    Returns: 414214

  45. 999998409369

    1000000000000

    Returns: 414213

  46. 90

    10

    Returns: 8

  47. 99

    1

    Returns: 9

  48. 98

    2

    Returns: -1

  49. 9

    7

    Returns: 3

  50. 11

    14

    Returns: 3

  51. 15

    34

    Returns: 3

  52. 42

    7

    Returns: 6

  53. 2

    2

    Returns: -1

  54. 2

    7

    Returns: -1

  55. 13

    23

    Returns: 3

  56. 14

    2

    Returns: -1

  57. 18

    7

    Returns: 4

  58. 23

    2

    Returns: -1

  59. 21

    79

    Returns: 3

  60. 9999999998

    2

    Returns: -1

  61. 66

    34

    Returns: 6

  62. 7

    2

    Returns: -1

  63. 26

    23

    Returns: 4

  64. 999950882

    2

    Returns: -1

  65. 2

    23

    Returns: -1

  66. 2

    14

    Returns: -1

  67. 2

    98

    Returns: -1

  68. 2

    167

    Returns: -1

  69. 29

    7

    Returns: 5

  70. 0

    2

    Returns: -1

  71. 910147492006

    300123123123

    Returns: 552290

  72. 205

    119

    Returns: 9

  73. 1

    1

    Returns: -1

  74. 0

    9

    Returns: 0

  75. 1000000000000

    2000001

    Returns: 998588

  76. 0

    25

    Returns: 0

  77. 34

    30

    Returns: 4

  78. 58

    167

    Returns: 4

  79. 1000000000000

    6000009

    Returns: 997554

  80. 999997790472

    999997790472

    Returns: 414214

  81. 980000000000

    980000000000

    Returns: 410052

  82. 500392965696

    499605034305

    Returns: 293172

  83. 439

    2

    Returns: -1

  84. 0

    1

    Returns: 0

  85. 398

    9602

    Returns: 4

  86. 30

    34

    Returns: 4

  87. 3

    1

    Returns: 1

  88. 203

    9998

    Returns: 3

  89. 2001

    997999

    Returns: 3

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