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Problem Statement for "SumOfPowers"

Problem Statement

NOTE: This problem statement contains superscripts that may not display properly if viewed outside of the applet.


You are given ints n and k. Return the value of the sum 1k + 2k + 3k + ... + nk modulo 1000000007.

Definition

Class:
SumOfPowers
Method:
value
Parameters:
int, int
Returns:
int
Method signature:
int value(int n, int k)
(be sure your method is public)

Constraints

  • n will be between 1 and 109, inclusive.
  • k will be between 1 and 50, inclusive.

Examples

  1. 5

    1

    Returns: 15

    Here, we have arithmethic progression: 1 + 2 + 3 + 4 + 5 = 15.

  2. 4

    2

    Returns: 30

    Just a little bit more complicated example here: 12 + 22 + 32 + 42 = 1 + 4 + 9 + 16 = 30.

  3. 13

    5

    Returns: 1002001

    This one would be harder to check by hand.

  4. 1000000000

    50

    Returns: 16605204

  5. 1000000000

    49

    Returns: 642472098

  6. 1000000000

    40

    Returns: 405332886

  7. 1000000000

    20

    Returns: 155104048

  8. 1000000000

    1

    Returns: 21

  9. 1000000000

    2

    Returns: 999999916

  10. 1000000000

    3

    Returns: 441

  11. 1000000000

    4

    Returns: 999997732

  12. 12345678

    5

    Returns: 706711176

  13. 987654321

    39

    Returns: 77272707

  14. 850631174

    25

    Returns: 535145455

  15. 821724346

    35

    Returns: 444575177

  16. 896737453

    20

    Returns: 941145240

  17. 690526406

    32

    Returns: 75646351

  18. 850139567

    20

    Returns: 88624246

  19. 123456789

    1

    Returns: 383478132

  20. 545023771

    42

    Returns: 504219406

  21. 856849676

    36

    Returns: 834404315

  22. 548664177

    6

    Returns: 783137008

  23. 701407449

    35

    Returns: 700164338

  24. 581795643

    11

    Returns: 318434886

  25. 736038809

    10

    Returns: 361657666

  26. 901047034

    34

    Returns: 333530840

  27. 702128132

    13

    Returns: 279021524

  28. 915161033

    42

    Returns: 184504886

  29. 860078464

    43

    Returns: 662131087

  30. 863368673

    11

    Returns: 238376463

  31. 902707330

    16

    Returns: 628896502

  32. 612766544

    35

    Returns: 525223086

  33. 602123753

    40

    Returns: 102814101

  34. 545304038

    20

    Returns: 573971886

  35. 936381859

    3

    Returns: 950945820

  36. 704027238

    21

    Returns: 951756408

  37. 683308427

    38

    Returns: 372992528

  38. 969888422

    19

    Returns: 552895307

  39. 563882675

    29

    Returns: 250724632

  40. 647032339

    23

    Returns: 162923389

  41. 602071701

    43

    Returns: 738791726

  42. 725331253

    27

    Returns: 554255975

  43. 841611116

    41

    Returns: 754756366

  44. 673725181

    43

    Returns: 244189145

  45. 611317204

    40

    Returns: 255781409

  46. 588525101

    11

    Returns: 267011050

  47. 502232691

    37

    Returns: 552280193

  48. 959774626

    4

    Returns: 757145452

  49. 869230470

    4

    Returns: 559524135

  50. 802681805

    23

    Returns: 555832486

  51. 652955543

    35

    Returns: 510981805

  52. 951360219

    48

    Returns: 6340981

  53. 611916815

    22

    Returns: 380122611

  54. 573496201

    49

    Returns: 598971277

  55. 530481772

    48

    Returns: 993856504

  56. 680753686

    42

    Returns: 32366462

  57. 999999999

    1

    Returns: 28

  58. 641786019

    47

    Returns: 980477989

  59. 751609937

    42

    Returns: 936764622

  60. 869457677

    4

    Returns: 25186837

  61. 705121410

    44

    Returns: 868713821

  62. 729468031

    37

    Returns: 553640748

  63. 864307136

    11

    Returns: 619970484

  64. 621124268

    29

    Returns: 614223061

  65. 500000003

    2

    Returns: 0

  66. 536870911

    50

    Returns: 356514781

  67. 536870912

    49

    Returns: 208977026

  68. 536870913

    48

    Returns: 311884985

  69. 1

    1

    Returns: 1

  70. 1

    50

    Returns: 1

  71. 2

    1

    Returns: 3

  72. 2

    2

    Returns: 5

  73. 2

    50

    Returns: 898961332

  74. 3

    1

    Returns: 6

  75. 3

    2

    Returns: 14

  76. 3

    3

    Returns: 36

  77. 3

    50

    Returns: 609065612

  78. 999999999

    47

    Returns: 361818878

  79. 999999999

    49

    Returns: 476716327

  80. 987654321

    50

    Returns: 463175553

  81. 978653456

    49

    Returns: 231751340

  82. 999999999

    50

    Returns: 176895594

  83. 987654321

    49

    Returns: 168309305

  84. 100000000

    50

    Returns: 291807007

  85. 9999999

    50

    Returns: 117128363

  86. 5

    50

    Returns: 461562836

  87. 979597

    49

    Returns: 913827245

  88. 1000000000

    47

    Returns: 773364917

  89. 987946789

    31

    Returns: 123351620

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