Statistics

Problem Statement for "FoxIntegerLevelOne"

Problem Statement

Fox Jiro and Eel Saburo are good friends. One day Saburo found two interesting positive integers: A and B.


On the next day, Saburo met Jiro and wanted to tell him the two integers. However, he managed to forget their values. All Saburo could remember was their greatest common divisor G and their least common multiple L.


You are given two longs: G and L. Find the original integers A and B, and return the value of A+B. If there are multiple pairs of A and B that correspond to G and L, pick the one that minimizes A+B. If it is impossible to find such A and B (i.e., Saburo made a mistake somewhere), return -1.

Definition

Class:
FoxAndGCDLCM
Method:
get
Parameters:
long, long
Returns:
long
Method signature:
long get(long G, long L)
(be sure your method is public)

Notes

  • The greatest common divisor of two integers a and b is the largest positive integer that divides both a and b without any remainder.
  • The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.

Constraints

  • G will be between 1 and 1,000,000,000,000 (10^12), inclusive.
  • L will be between 1 and 1,000,000,000,000 (10^12), inclusive.

Examples

  1. 2

    20

    Returns: 14

    The possible pairs of A and B are {2, 20} and {4, 10}. We need to pick {4, 10} since 4+10 is the smallest sum of A and B.

  2. 5

    8

    Returns: -1

    There are no pairs of A and B such that their greatest common divisor is 5 and their least common multiple is 8.

  3. 1000

    100

    Returns: -1

  4. 100

    1000

    Returns: 700

  5. 10

    950863963000

    Returns: 6298430

  6. 1

    1

    Returns: 2

  7. 1

    2

    Returns: 3

  8. 1

    3

    Returns: 4

  9. 1

    4

    Returns: 5

  10. 10

    100

    Returns: 70

  11. 100

    100

    Returns: 200

  12. 1000000000000

    1000000000000

    Returns: 2000000000000

  13. 1

    1000000000000

    Returns: 244144721

  14. 1

    999999999989

    Returns: 999999999990

  15. 999999999989

    999999999989

    Returns: 1999999999978

  16. 999999999999

    999999999999

    Returns: 1999999999998

  17. 2

    999999999999

    Returns: -1

  18. 3

    999999999999

    Returns: 3474462

  19. 4

    1000000000000

    Returns: 976566596

  20. 5

    999999999999

    Returns: -1

  21. 6

    999999999996

    Returns: 4999998

  22. 7

    1000000000000

    Returns: -1

  23. 100000

    100

    Returns: -1

  24. 2

    1

    Returns: -1

  25. 123456789

    1234567890

    Returns: 864197523

  26. 19690

    85411282000

    Returns: 103510330

  27. 91

    974879385662

    Returns: 19173063

  28. 369

    641851989165

    Returns: 248299362

  29. 3

    122110961292

    Returns: 41884935

  30. 182

    863259682740

    Returns: 25069954

  31. 3281

    717632203782

    Returns: 97193063

  32. 72350

    925524930800

    Returns: 652524650

  33. 2

    397120903970

    Returns: 23721028

  34. 27

    953698097898

    Returns: 10151703

  35. 31

    449521949054

    Returns: 19611561

  36. 69

    841048183521

    Returns: 15249414

  37. 32578

    622426993188

    Returns: 284959766

  38. 247531

    28163582118

    Returns: 311641529

  39. 1090

    698178988380

    Returns: 55680470

  40. 222

    871431576786

    Returns: 292015248

  41. 6

    762083046

    Returns: 152652

  42. 2125

    563403387750

    Returns: 79353875

  43. 4909

    385994876178

    Returns: 87738557

  44. 6

    102991956030

    Returns: 1864572

  45. 28

    511253791776

    Returns: 8518804

  46. 14

    646803209150

    Returns: 13589996

  47. 1

    108371180946

    Returns: 685553

  48. 170

    638273737150

    Returns: 20989560

  49. 1619

    942870265325

    Returns: 178323136

  50. 3

    736626285213

    Returns: 13372560

  51. 18780

    860762595120

    Returns: 623214300

  52. 2

    222499279704

    Returns: 1335994

  53. 17

    92945485908

    Returns: 78257137

  54. 1481

    7850792848

    Returns: 29266041

  55. 17

    69582930095

    Returns: 2176408

  56. 12764

    625037188820

    Returns: 178644944

  57. 3

    587347286976

    Returns: 4214901

  58. 186

    227988011070

    Returns: 13051992

  59. 5

    198567696250

    Returns: 1992885

  60. 19

    282175860786

    Returns: 4901905

  61. 2

    663725951812

    Returns: 87972414

  62. 10

    827402333520

    Returns: 6407830

  63. 1

    198856990744

    Returns: 4051801

  64. 15

    987671321910

    Returns: 7732875

  65. 83

    943705089305

    Returns: 17933644

  66. 2226

    749365445216

    Returns: -1

  67. 7751

    96333565096

    Returns: -1

  68. 4652

    288500735569

    Returns: -1

  69. 8227

    857477448634

    Returns: -1

  70. 255

    777831771063

    Returns: -1

  71. 9812

    432810069345

    Returns: -1

  72. 6562

    128303313570

    Returns: -1

  73. 8749

    161734062610

    Returns: -1

  74. 7403

    989921186969

    Returns: 171483092

  75. 7910

    954118069709

    Returns: -1

  76. 163751967973

    904315130722

    Returns: -1

  77. 735535648965

    772186675910

    Returns: -1

  78. 987509887063

    994467244792

    Returns: -1

  79. 710875448198

    774452058479

    Returns: -1

  80. 106095868877

    386899551256

    Returns: -1

  81. 463982085303

    618570719610

    Returns: -1

  82. 679081528294

    845480558019

    Returns: -1

  83. 235677577222

    478865972561

    Returns: -1

  84. 519414588838

    853840888864

    Returns: -1

  85. 127799255701

    568145978603

    Returns: -1

  86. 8271781382

    306055911134

    Returns: 314327692516

  87. 15424328614

    215940600596

    Returns: 138818957526

  88. 55899795662

    167699386986

    Returns: 223599182648

  89. 43733415291

    87466830582

    Returns: 131200245873

  90. 79278881041

    554952167287

    Returns: 634231048328

  91. 91687851397

    825190662573

    Returns: 916878513970

  92. 91686164344

    916861643440

    Returns: 641803150408

  93. 75299138487

    451794830922

    Returns: 376495692435

  94. 9546805544

    57280833264

    Returns: 47734027720

  95. 13218893807

    541974646087

    Returns: 555193539894

  96. 499999999979

    999999999958

    Returns: 1499999999937

  97. 499999999979

    499999999979

    Returns: 999999999958

  98. 772797527

    499999999969

    Returns: 500772797496

  99. 499999999943

    999999999886

    Returns: 1499999999829

  100. 499999999943

    499999999943

    Returns: 999999999886

  101. 999999999961

    999999999961

    Returns: 1999999999922

  102. 999999999959

    999999999959

    Returns: 1999999999918

  103. 499999999901

    999999999802

    Returns: 1499999999703

  104. 333333333323

    333333333323

    Returns: 666666666646

  105. 333333333323

    999999999969

    Returns: 1333333333292

  106. 10

    998862962000

    Returns: 4994316810

  107. 2

    1000000000000

    Returns: 488285346

  108. 2

    16

    Returns: 18

  109. 963761198400

    963761198400

    Returns: 1927522396800

  110. 68719476736

    412316860416

    Returns: 343597383680

  111. 1

    99999999977

    Returns: 99999999978

  112. 1

    187473

    Returns: 866

  113. 99999999977

    99999999977

    Returns: 199999999954

  114. 1

    10000000000

    Returns: 9766649

  115. 1

    100

    Returns: 29

  116. 1000000000

    1000000000000

    Returns: 133000000000

  117. 500000000000

    1000000000000

    Returns: 1500000000000

  118. 10000000000

    100000000000

    Returns: 70000000000

  119. 999999999989

    1000000000000

    Returns: -1

  120. 100000000000

    1000000000000

    Returns: 700000000000

  121. 10000000000

    1000000000000

    Returns: 290000000000

  122. 89876476576

    84787483738

    Returns: -1

  123. 1

    5

    Returns: 6

  124. 5

    5

    Returns: 10

  125. 2

    549753716734

    Returns: 549753716736

  126. 2000000000

    2000000000

    Returns: 4000000000

  127. 2

    2

    Returns: 4

  128. 1

    29

    Returns: 30

  129. 4

    4

    Returns: 8

  130. 35309

    10723661081

    Returns: 46254790

  131. 6

    216

    Returns: 78

  132. 1

    12

    Returns: 7

  133. 10

    950863664450

    Returns: 6167220

  134. 2

    4

    Returns: 6

  135. 2

    100000000000

    Returns: 97658298

  136. 1000000000

    1000000000

    Returns: 2000000000

  137. 2

    19153781534

    Returns: 19153781536

  138. 107913405600

    971220650400

    Returns: 1079134056000

  139. 250000000000

    1000000000000

    Returns: 1250000000000

  140. 8

    16

    Returns: 24

  141. 999999999997

    1000000000000

    Returns: -1

  142. 2

    18

    Returns: 20

  143. 1000000000000

    99999999999

    Returns: -1

  144. 200000

    100000000000

    Returns: 3131400000

  145. 2

    200000014

    Returns: 200000016

  146. 1

    549755813888

    Returns: 549755813889

  147. 100000000000

    500000000000

    Returns: 600000000000

  148. 10000000000

    50000000000

    Returns: 60000000000

  149. 1

    100233665123

    Returns: 100233665124

  150. 1

    20

    Returns: 9

  151. 200560490130

    200560490130

    Returns: 401120980260

  152. 10

    240

    Returns: 110

  153. 2

    14

    Returns: 16

  154. 1

    521240920200

    Returns: 1470457

  155. 87178291199

    87178291199

    Returns: 174356582398

  156. 10

    10

    Returns: 20

  157. 100000000

    1000000000

    Returns: 700000000

  158. 30

    30000000210

    Returns: 30000000240

  159. 5

    5040

    Returns: 395

  160. 2

    549755813888

    Returns: 549755813890

  161. 1

    14100827177

    Returns: 14100827178

  162. 10000000000

    90000000000

    Returns: 100000000000

  163. 2

    94385732726

    Returns: 71561192

  164. 1000000000

    10000000000

    Returns: 7000000000

  165. 10

    9003500059

    Returns: -1

  166. 1

    95

    Returns: 24

  167. 5

    210

    Returns: 65

  168. 1000000007

    34000000238

    Returns: 19000000133

  169. 1

    2310

    Returns: 97

  170. 17179869184

    34359738368

    Returns: 51539607552

  171. 999999999961

    999999999989

    Returns: -1

  172. 2

    5

    Returns: -1

  173. 900000000025

    999999999999

    Returns: -1

  174. 123211123

    150863961

    Returns: -1

  175. 2

    6

    Returns: 8

  176. 11111111111

    22222222222

    Returns: 33333333333

  177. 10000000

    1000000000

    Returns: 290000000

  178. 1

    16

    Returns: 17

  179. 1000000

    950863963000

    Returns: -1

  180. 999999999999

    1000000000000

    Returns: -1

  181. 1

    87178291200

    Returns: 590539

  182. 100000000

    1000000000000

    Returns: 64100000000

  183. 1

    1000000007

    Returns: 1000000008

  184. 1

    1000000

    Returns: 15689

  185. 1

    100000000003

    Returns: 100000000004

  186. 1

    999999999091

    Returns: 999999999092

  187. 1

    963761198400

    Returns: 1963583

  188. 1

    455

    Returns: 48

  189. 44628547775

    454786481517

    Returns: -1

  190. 500000000000

    500000000000

    Returns: 1000000000000

  191. 1

    999962000357

    Returns: 1999962

  192. 1

    21

    Returns: 10

  193. 601681470393

    601681470393

    Returns: 1203362940786

  194. 999999999999

    888888888888

    Returns: -1

  195. 1000000000

    2000000000

    Returns: 3000000000

  196. 1000000

    1000000000000

    Returns: 15689000000

  197. 2

    99999999999

    Returns: -1

  198. 145

    145

    Returns: 290

  199. 1

    15

    Returns: 8

  200. 871782912000

    871782912000

    Returns: 1743565824000

  201. 1

    900000000013

    Returns: 900000000014

  202. 34359738368

    68719476736

    Returns: 103079215104

  203. 1000000007

    221000001547

    Returns: 30000000210

  204. 500

    100000000000

    Returns: 195568500

  205. 4

    100

    Returns: 104

  206. 185285839890

    185285839890

    Returns: 370571679780

  207. 10

    6061000

    Returns: 15610

  208. 5456

    654

    Returns: -1

  209. 5

    125

    Returns: 130

  210. 1

    30030

    Returns: 347

  211. 4294967296

    4294967296

    Returns: 8589934592

  212. 1

    999999999958

    Returns: 499999999981

  213. 1

    7

    Returns: 8

  214. 1

    32416190071

    Returns: 32416190072

  215. 3763

    94997732756

    Returns: 23749448241

  216. 1

    100000000000

    Returns: 48830173

  217. 1

    30

    Returns: 11

  218. 2

    318821883888

    Returns: 1623130

  219. 1

    4032

    Returns: 127

  220. 2

    13

    Returns: -1

  221. 1

    180

    Returns: 29

  222. 9326317000

    699473775000

    Returns: 261136876000

  223. 9999999999

    9999999999

    Returns: 19999999998

  224. 2

    21

    Returns: -1

  225. 2

    999999999958

    Returns: 999999999960

  226. 87178291199

    174356582398

    Returns: 261534873597

  227. 1

    87178291199

    Returns: 87178291200

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