Statistics

Problem Statement for "MegaCoolNumbers"

Problem Statement

A positive integer is called a cool number of power A if it can be separated into exactly A groups of consecutive digits, where the digits in each group form an arithmetic progression. An arithmetic progression is a sequence of numbers in which the difference between any two consecutive numbers is the same. A positive integer is called a mega cool number of power A if it is a cool number of power A, not a cool number of power A-1, and all its digits are in non-decreasing order.
Determine the number of mega cool numbers of power A that contain exactly N digits (with no leading zeroes). Return this number modulo 1,000,000,007.

Definition

Class:
MegaCoolNumbers
Method:
count
Parameters:
int, int
Returns:
int
Method signature:
int count(int N, int A)
(be sure your method is public)

Constraints

  • A and N will be between 1 and 1,000, inclusive.

Examples

  1. 3

    1

    Returns: 25

  2. 3

    5

    Returns: 0

  3. 10

    6

    Returns: 0

  4. 10

    2

    Returns: 643

  5. 6

    10

    Returns: 0

  6. 9

    4

    Returns: 13946

  7. 8

    10

    Returns: 0

  8. 8

    5

    Returns: 0

  9. 8

    6

    Returns: 0

  10. 6

    10

    Returns: 0

  11. 7

    8

    Returns: 0

  12. 29

    9

    Returns: 1550927

  13. 17

    7

    Returns: 154272

  14. 29

    7

    Returns: 13904532

  15. 13

    2

    Returns: 744

  16. 4

    10

    Returns: 0

  17. 33

    10

    Returns: 0

  18. 10

    3

    Returns: 7502

  19. 8

    9

    Returns: 0

  20. 27

    9

    Returns: 679757

  21. 56

    4

    Returns: 4328198

  22. 28

    1

    Returns: 9

  23. 64

    2

    Returns: 2580

  24. 28

    6

    Returns: 8752247

  25. 51

    5

    Returns: 38201689

  26. 65

    10

    Returns: 0

  27. 8

    1

    Returns: 11

  28. 52

    10

    Returns: 0

  29. 22

    6

    Returns: 2125867

  30. 80

    1

    Returns: 9

  31. 302

    2

    Returns: 11148

  32. 282

    9

    Returns: 678308819

  33. 28

    10

    Returns: 0

  34. 35

    2

    Returns: 1536

  35. 369

    6

    Returns: 528884859

  36. 194

    7

    Returns: 927974911

  37. 140

    4

    Returns: 62139602

  38. 231

    7

    Returns: 603901423

  39. 258

    5

    Returns: 901374186

  40. 142

    7

    Returns: 24704033

  41. 197

    3

    Returns: 1726380

  42. 23

    7

    Returns: 2386305

  43. 238

    1

    Returns: 9

  44. 192

    5

    Returns: 387626608

  45. 53

    2

    Returns: 2184

  46. 505

    4

    Returns: 766538468

  47. 7

    7

    Returns: 0

  48. 443

    4

    Returns: 873279675

  49. 548

    8

    Returns: 484028533

  50. 65

    2

    Returns: 2616

  51. 649

    8

    Returns: 330601169

  52. 138

    4

    Returns: 59572172

  53. 832

    3

    Returns: 29486040

  54. 455

    6

    Returns: 239344926

  55. 495

    7

    Returns: 70673564

  56. 139

    9

    Returns: 589827333

  57. 350

    5

    Returns: 429601569

  58. 270

    10

    Returns: 0

  59. 452

    10

    Returns: 0

  60. 988

    1

    Returns: 9

  61. 836

    3

    Returns: 29768256

  62. 63

    9

    Returns: 992381041

  63. 308

    8

    Returns: 267850613

  64. 400

    7

    Returns: 53957028

  65. 43

    1

    Returns: 9

  66. 844

    1

    Returns: 9

  67. 977

    6

    Returns: 928100631

  68. 149

    10

    Returns: 0

  69. 252

    4

    Returns: 351189986

  70. 574

    2

    Returns: 20940

  71. 216

    9

    Returns: 190312172

  72. 723

    7

    Returns: 873242124

  73. 582

    1

    Returns: 9

  74. 176

    8

    Returns: 230110582

  75. 904

    4

    Returns: 714463437

  76. 993

    4

    Returns: 804165142

  77. 315

    10

    Returns: 0

  78. 706

    4

    Returns: 511679299

  79. 190

    1

    Returns: 9

  80. 664

    10

    Returns: 0

  81. 554

    4

    Returns: 645406871

  82. 96

    1

    Returns: 9

  83. 963

    7

    Returns: 350994727

  84. 918

    3

    Returns: 35849868

  85. 743

    7

    Returns: 512504519

  86. 440

    10

    Returns: 0

  87. 420

    2

    Returns: 15396

  88. 740

    5

    Returns: 553012949

  89. 46

    7

    Returns: 326423760

  90. 471

    9

    Returns: 844419866

  91. 729

    6

    Returns: 752357982

  92. 216

    1

    Returns: 9

  93. 604

    2

    Returns: 22020

  94. 733

    9

    Returns: 153995176

  95. 23

    2

    Returns: 1104

  96. 908

    1

    Returns: 9

  97. 726

    4

    Returns: 164721112

  98. 852

    9

    Returns: 400626524

  99. 22

    3

    Returns: 29580

  100. 1000

    9

    Returns: 528971249

  101. 1

    1

    Returns: 9

    There 9 such numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9.

  102. 2

    1

    Returns: 45

    Any two-digit number with non-decreasing digits will be a mega cool number of power 1.

  103. 2

    2

    Returns: 0

    There are no such numbers.

  104. 10

    3

    Returns: 7502

  105. 1000

    1000

    Returns: 0

  106. 1000

    980

    Returns: 0

  107. 999

    9

    Returns: 604032056

  108. 1000

    999

    Returns: 0

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: