Statistics

Problem Statement

The Ninja Turtles often battle the Foot Clan ninjas. The Turtles celebrate each victory with a pizza party. The amount of pizza they eat depends on the number of opponents they have defeated. Denote the number of defeated opponents as N. Three of the four Turtles have a moderate appetite and only consume floor(N / K) pizzas each. The fourth Turtle is always hungry and eats floor(N / 3) pizzas.



You are given ints P and K, where P is the total number of pizzas the Turtles ate after a battle. If there exists at least one value of N such that after defeating N opponents the Turtles would eat exactly P pizzas at the party, return the smallest such N. Otherwise, return -1.

Definition

Class:

NinjaTurtles

Method:

countOpponents

Parameters:

int, int

Returns:

int

Method signature:

int countOpponents(int P, int K)

(be sure your method is public)

Notes

• floor(X) is equal to the largest integer which is less or equal to X.

Constraints

• P will be between 1 and 1,000,000, inclusive.
• K will be between 4 and 100, inclusive.

Examples

1. 5

   4

   Returns: 6

   If the Turtles defeated 6 opponents, three of the four Turtles would eat floor(6 / 4) = 1 pizza each and the fourth one would eat floor(6 / 3) = 2 pizzas, which makes 5 pizzas in total. Note that you always have to return the smallest possible N. For example, in this scenario for N = 7 the Turtles would also eat 5 pizzas, but 7 is not a correct return value, because 6 is less than 7.

2. 1

   4

   Returns: 3

   After a fight with three opponents, only the hungry Turtle would eat a pizza.

3. 13

   6

   Returns: -1

   There is no value of N such that if the Turtles battle N opponents, they eat exactly 13 pizzas for K = 6.

4. 13

   17

   Returns: 30

   For K = 17, after defeating 30 opponents the Turtles will eat 13 pizzas in total.

5. 122

   21

   Returns: 258

6. 1000000

   100

   Returns: -1

7. 1000000

   99

   Returns: 2750007

8. 1000000

   98

   Returns: 2747667

9. 999999

   100

   Returns: 2752299

10. 1000000

    4

    Returns: 923079

11. 112

    8

    Returns: -1

12. 113

    8

    Returns: 160

13. 114

    8

    Returns: 162

14. 1

    100

    Returns: 3

15. 666

    66

    Returns: 1764

16. 1234

    4

    Returns: -1

17. 12345

    4

    Returns: 11396

18. 8462

    26

    Returns: 18861

19. 983325

    59

    Returns: 2559538

20. 93135

    100

    Returns: 256338

21. 69993

    22

    Returns: 149022

22. 69994

    22

    Returns: 149025

23. 69994

    11

    Returns: 115491

24. 903

    8

    Returns: 1278

25. 903

    4

    Returns: -1

26. 905

    4

    Returns: 836

27. 20000

    6

    Returns: 24000

28. 20005

    6

    Returns: 24006

29. 555555

    55

    Returns: 1432296

30. 52951

    92

    Returns: 144705

31. 52951

    96

    Returns: 145245

32. 52952

    96

    Returns: -1

33. 909090

    90

    Returns: 2479338

34. 909090

    95

    Returns: 2491263

35. 909090

    100

    Returns: 2502090

36. 44

    11

    Returns: -1

37. 44

    21

    Returns: 96

38. 4400

    5

    Returns: 4715

39. 3912

    79

    Returns: 10539

40. 100000

    4

    Returns: 92308

41. 100000

    5

    Returns: -1

42. 1000000

    51

    Returns: 2550000

43. 1000000

    7

    Returns: 1312500

44. 602408

    7

    Returns: -1

45. 602408

    9

    Returns: 903615

46. 293852

    40

    Returns: -1

47. 293852

    41

    Returns: 722877

48. 512000

    32

    Returns: 1198833

49. 709222

    88

    Returns: 1930260

50. 512512

    64

    Returns: 1347978

51. 80000

    67

    Returns: -1

52. 82000

    67

    Returns: 216876

53. 82222

    83

    Returns: 222537

54. 400000

    6

    Returns: 480000

55. 400000

    5

    Returns: 428574

56. 400001

    4

    Returns: 369232

57. 659554

    100

    Returns: 1815294

58. 878342

    36

    Returns: 2108022

59. 65281

    59

    Returns: 169923

60. 2512

    4

    Returns: -1

61. 4

    4

    Returns: 4

62. 13

    4

    Returns: 12

63. 1355

    4

    Returns: -1

64. 2358

    4

    Returns: 2178

65. 999999

    4

    Returns: 923076

66. 999997

    41

    Returns: -1

67. 999997

    42

    Returns: 2470584

68. 605553

    100

    Returns: 1666665

69. 763000

    100

    Returns: 2100000

70. 726666

    100

    Returns: 2000000

71. 10000

    4

    Returns: -1

72. 999999

    99

    Returns: 2750004

73. 100

    50

    Returns: 255

74. 1000000

    25

    Returns: 2205885

75. 2

    8

    Returns: 6

76. 790000

    70

    Returns: 2100000

77. 1000000

    21

    Returns: 2100000

78. 1000000

    50

    Returns: 2542377

79. 399666

    100

    Returns: 1100000

80. 460000

    30

    Returns: 1061544

81. 999875

    35

    Returns: 2386068

82. 676666

    100

    Returns: 1862391

83. 1000000

    14

    Returns: -1

84. 1000000

    95

    Returns: 2740386

85. 1000000

    6

    Returns: 1200000

86. 1000000

    11

    Returns: 1650000

87. 999920

    100

    Returns: 2752080

88. 696666

    10

    Returns: 1100000

89. 2

    4

    Returns: -1

90. 1000000

    23

    Returns: 2156250

91. 1000000

    15

    Returns: 1875000

92. 1000000

    40

    Returns: 2448984

93. 437

    4

    Returns: 404

94. 1000000

    86

    Returns: -1

95. 833335

    6

    Returns: 1000002

96. 1000000

    12

    Returns: 1714287

97. 1000000

    91

    Returns: 2730000

98. 1000000

    20

    Returns: 2068968

99. 833355

    6

    Returns: 1000026

100. 119166

     4

     Returns: 110000

101. 14

     5

     Returns: 15

102. 686667

     100

     Returns: 1889910

103. 300000

     100

     Returns: 825696

104. 999990

     100

     Returns: 2752272