Problem Statement
You are given N "512-Modulo counters". Each 512-Modulo counter contains a value that is between 0 and 511, inclusive. Each counter allows an incrementation operation. Let's say the value of counter is x, then after the incrementation the value of counter will be (x + 1) % 512.
You are given an array S of length N with the initial value of each counter. Now, you are planning to perform K steps. In each step, you select a counter uniformly at random from the given N counters and increment it. You need to find the expected sum of the array after K steps. (Note that the sum is computed exactly, not modulo 512.)
Let your answer be R/Q, then you need to return (R*Q-1) modulo (109+7). See Notes for the explanation of Q-1.
You are given integers A0, X, Y, N and an integer array P. Use the pseudocode below to generate the array S.
A[0] = A0
for i = 1 to N-1:
A[i] = (A[i-1] * X + Y) modulo 1812447359
S = P
for i = size(P) to N-1:
S[i] = A[i] modulo 512
Definition
- Class:
- ModCounters
- Method:
- findExpectedSum
- Parameters:
- int[], int, int, int, int, int
- Returns:
- int
- Method signature:
- int findExpectedSum(int[] P, int A0, int X, int Y, int N, int K)
- (be sure your method is public)
Notes
- It can be shown that the expected value of the sum of all counters is always a rational number R/Q such that Q and 1000000007 are relatively prime.
- Q-1 denotes the inverse element to Q when computing modulo 1000000007. That is, (Q * Q-1) mod 1000000007 = 1.
Constraints
- The length of P will be between 0 and min(N, 100) (inclusive)
- Integers in P will be between 0 and 511 (inclusive)
- A0 will be between 0 and 1812447358 (inclusive)
- X will be between 0 and 1812447358 (inclusive)
- Y will be between 0 and 1812447358 (inclusive)
- N will be between 1 and 2000000 (inclusive)
- K will be between 1 and 500000000 (inclusive)
Examples
{478, 135, 287, 286, 238}
361711600
88187871
415501685
5
1398216
Returns: 907283075
{}
340768325
829723516
96319779
5
981603
Returns: 935400859
{388, 302, 153, 212, 38}
585703634
230851803
445950441
5
5
Returns: 1098
{147, 83, 374, 337, 500}
528048293
842093637
941135252
5
10
Returns: 1451
{}
510069165
284814936
867995759
5
20
Returns: 1621
{}
867722159
971491214
789756720
5
100
Returns: 300626929
{}
191418696
541688893
575011826
5
500
Returns: 385920551
{73, 220, 504, 132, 41}
785258720
304759391
303405480
5
5000
Returns: 664425251
{503, 404, 283, 354, 95}
557180898
793300431
26862206
5
100000
Returns: 363194575
{259, 435, 36, 414, 443}
258065923
962694509
249766898
5
2000000
Returns: 459982260
{130, 255, 293, 74, 347, 299, 490, 501, 151, 248}
687998607
821317582
776072966
10
1995819
Returns: 436379211
{}
462562218
503193390
249996483
10
576822
Returns: 418998486
{41, 252, 38, 478, 418, 271, 149, 428, 12, 312}
703218014
809305343
992716445
10
5
Returns: 2404
{64, 308, 381, 240, 466, 497, 217, 6, 133, 371}
892187258
686925287
310362800
10
10
Returns: 2693
{}
103791881
503444732
872919914
10
20
Returns: 2453
{97, 336, 223, 478, 293, 381, 367, 397, 37, 444}
654578998
163843483
782823898
10
100
Returns: 321634610
{210, 13, 182, 314, 290, 233, 277, 371, 281, 353}
272564847
866573466
81792576
10
500
Returns: 715176689
{427, 128, 99, 485, 397, 510, 138, 422, 293, 158}
184475781
134167991
454035678
10
5000
Returns: 930855509
{172, 332, 290, 376, 473, 396, 101, 126, 168, 26}
155342101
955721166
346744465
10
100000
Returns: 386234582
{423, 272, 227, 399, 234, 125, 233, 386, 150, 140}
248460615
531744911
977845683
10
2000000
Returns: 665677518
{143, 508, 509, 511, 392, 425, 137, 51, 282, 394, 181, 347, 507, 302, 190, 123, 368, 169, 444, 497}
94437721
902823493
49038095
20
836657
Returns: 1733957
{}
808377601
551401290
548677191
20
508489
Returns: 111713120
{30, 384, 261, 21, 279, 91, 290, 58, 105, 129, 38, 56, 76, 17, 254, 417, 295, 63, 296, 476}
435063901
307269301
628550761
20
5
Returns: 3641
{206, 114, 309, 195, 111, 461, 278, 317, 504, 259, 175, 446, 88, 59, 171, 450, 490, 196, 105, 13}
747150930
552025770
723077268
20
10
Returns: 800005080
{105, 107, 256, 273, 175, 501, 6, 370, 414, 491, 470, 101, 5, 219, 28, 282, 185, 327, 75, 65}
452158441
253734997
57308770
20
20
Returns: 480587404
{}
956484277
594627749
709137596
20
100
Returns: 324626042
{363, 222, 152, 44, 348, 456, 23, 497, 377, 79, 352, 414, 143, 313, 310, 429, 141, 385, 124, 444}
158988129
233098782
449972012
20
500
Returns: 612394405
{}
84717651
819875277
893959406
20
5000
Returns: 846650071
{240, 147, 487, 119, 238, 415, 291, 270, 261, 456, 30, 334, 76, 17, 260, 143, 145, 143, 448, 30}
131770516
697631591
430904674
20
100000
Returns: 428209129
{}
268278313
610651059
107628005
20
2000000
Returns: 645151701
{168, 468, 439, 190, 333, 484, 23, 121, 50, 174, 158, 390, 95, 143, 491, 196, 208, 101, 480, 174, 304, 300, 7, 185, 61, 334, 146, 497, 145, 89, 355, 495, 260, 479, 10, 319, 157, 457, 94, 61, 47, 27, 200, 206, 257, 89, 170, 454, 402, 107, 251, 222, 496, 474, 163, 286, 447, 147, 372, 415, 364, 232, 319, 192, 63, 494, 507, 324, 85, 149, 5, 243, 336, 335, 268, 245, 65, 245, 273, 270, 373, 177, 432, 221, 184, 94, 72, 276, 391, 265, 493, 122, 382, 371, 509, 144, 155, 376, 402, 502}
919393310
57295953
888837582
100
716813
Returns: 977376231
{}
559255930
576136261
326722024
100
467040
Returns: 750123092
{}
911144361
265733122
411160696
100
5
Returns: 485741638
{}
445990285
28192113
810644519
100
10
Returns: 537434577
{}
471267547
896278899
342770313
100
20
Returns: 541586078
{}
28443618
32614323
786202403
100
100
Returns: 359611437
{}
648795388
438890790
746479708
100
500
Returns: 513488486
{129, 242, 155, 333, 503, 258, 9, 437, 62, 44, 117, 267, 169, 21, 192, 245, 444, 180, 31, 196, 498, 64, 282, 360, 11, 109, 72, 40, 376, 245, 195, 488, 507, 343, 220, 165, 256, 122, 429, 476, 78, 421, 373, 175, 182, 380, 217, 349, 66, 509, 359, 425, 56, 369, 180, 464, 294, 29, 307, 97, 86, 397, 78, 308, 86, 263, 448, 389, 140, 421, 194, 160, 135, 101, 499, 264, 454, 143, 271, 9, 7, 332, 241, 366, 345, 182, 427, 58, 310, 221, 176, 55, 442, 382, 297, 25, 358, 306, 361, 324}
885855019
683973038
988525672
100
5000
Returns: 623643692
{266, 204, 478, 379, 448, 282, 383, 478, 56, 505, 357, 61, 338, 95, 59, 147, 133, 197, 256, 62, 39, 101, 419, 248, 470, 485, 439, 413, 271, 341, 99, 420, 439, 103, 81, 381, 494, 19, 74, 468, 321, 258, 239, 161, 416, 162, 177, 290, 285, 433, 266, 478, 19, 404, 305, 252, 0, 341, 416, 4, 264, 442, 90, 256, 76, 34, 184, 167, 485, 191, 410, 197, 461, 18, 290, 202, 504, 342, 8, 43, 113, 149, 345, 61, 29, 75, 445, 192, 195, 135, 208, 93, 316, 219, 177, 373, 136, 106, 385, 178}
431242560
617600645
510460769
100
100000
Returns: 496407769
{}
393969509
963658386
734437754
100
2000000
Returns: 123322302
{497, 362, 269, 97, 17, 1, 302, 228, 488, 414, 239, 62, 61, 459, 228, 262, 225, 115, 198, 287, 364, 273, 103, 1, 325, 444, 130, 147, 127, 131, 159, 245, 94, 305, 172, 139, 212, 100, 450, 63, 384, 164, 447, 31, 120, 163, 197, 136, 278, 383, 381, 365, 458, 111, 85, 68, 385, 469, 134, 421, 297, 8, 91, 353, 51, 5, 270, 219, 98, 278, 30, 205, 480, 309, 287, 215, 499, 415, 302, 373, 341, 330, 123, 278, 398, 233, 380, 215, 251, 494, 238, 120, 439, 227, 73, 499, 491, 38, 173, 219}
888744273
775835081
838884437
500
1397190
Returns: 950109660
{}
191544767
652565874
175983241
500
1045639
Returns: 662585178
{47, 376, 483, 207, 133, 45, 189, 67, 193, 77, 203, 395, 293, 190, 111, 132, 149, 89, 426, 13, 397, 312, 72, 217, 11, 349, 320, 101, 221, 440, 127, 25, 324, 139, 229, 70, 257, 399, 75, 296, 440, 167, 271, 48, 50, 56, 503, 290, 108, 483, 82, 120, 396, 235, 398, 71, 49, 62, 117, 361, 172, 362, 90, 372, 135, 193, 78, 435, 436, 207, 66, 177, 423, 222, 469, 78, 97, 458, 317, 349, 424, 79, 16, 411, 93, 361, 204, 505, 161, 126, 79, 66, 137, 496, 481, 43, 324, 299, 403, 344}
452186619
523092180
426965216
500
5
Returns: 744250966
{400, 395, 59, 488, 210, 192, 47, 282, 347, 162, 265, 1, 248, 447, 142, 152, 323, 428, 354, 352, 401, 366, 98, 194, 56, 136, 58, 290, 463, 80, 207, 296, 161, 90, 472, 116, 190, 101, 454, 160, 101, 337, 145, 192, 219, 175, 240, 132, 231, 465, 129, 441, 205, 303, 301, 261, 66, 259, 430, 358, 188, 414, 117, 324, 427, 407, 257, 453, 459, 271, 119, 501, 128, 402, 278, 126, 326, 282, 421, 466, 226, 200, 119, 474, 452, 312, 154, 48, 232, 496, 293, 46, 308, 387, 164, 457, 376, 295, 375, 180}
35346765
265468649
134257466
500
10
Returns: 483042690
{493, 168, 255, 65, 501, 276, 51, 483, 291, 20, 105, 1, 206, 407, 63, 101, 410, 291, 30, 91, 368, 222, 313, 372, 438, 74, 384, 159, 424, 370, 452, 136, 361, 161, 347, 295, 320, 92, 135, 348, 50, 194, 102, 127, 97, 49, 488, 336, 272, 202, 0, 16, 119, 211, 332, 390, 12, 424, 300, 158, 67, 138, 185, 487, 375, 355, 141, 355, 406, 265, 187, 105, 139, 234, 464, 230, 123, 310, 345, 466, 182, 37, 465, 154, 108, 302, 16, 503, 364, 134, 152, 88, 174, 221, 492, 234, 306, 291, 305, 94}
977116857
719934168
87183797
500
20
Returns: 955993050
{69, 385, 373, 20, 156, 364, 449, 195, 294, 422, 209, 286, 321, 102, 86, 408, 46, 197, 313, 357, 388, 143, 201, 332, 106, 493, 181, 449, 93, 136, 303, 384, 448, 378, 12, 410, 123, 417, 468, 275, 215, 178, 135, 119, 3, 333, 320, 114, 4, 274, 259, 226, 357, 474, 417, 499, 5, 486, 16, 11, 175, 225, 438, 30, 353, 433, 308, 479, 199, 6, 306, 404, 455, 139, 291, 200, 395, 223, 85, 152, 20, 23, 304, 53, 292, 394, 119, 410, 300, 25, 1, 88, 374, 116, 265, 84, 83, 177, 67, 192}
120664948
116180317
837375195
500
100
Returns: 596680080
{453, 94, 78, 488, 173, 145, 183, 197, 314, 155, 13, 344, 188, 414, 367, 305, 260, 46, 231, 490, 79, 67, 310, 487, 242, 330, 329, 492, 395, 430, 167, 284, 168, 157, 273, 172, 296, 31, 334, 217, 268, 273, 425, 483, 349, 45, 464, 69, 441, 52, 275, 55, 312, 170, 332, 72, 9, 74, 267, 436, 363, 288, 309, 403, 168, 137, 276, 364, 295, 361, 235, 154, 243, 465, 343, 192, 265, 195, 208, 204, 77, 170, 95, 344, 322, 45, 310, 250, 407, 103, 406, 56, 318, 284, 169, 416, 384, 220, 280, 236}
879767330
46891487
333246252
500
500
Returns: 786703456
{170, 501, 57, 480, 378, 293, 159, 211, 280, 302, 365, 203, 80, 492, 255, 58, 496, 10, 147, 453, 323, 465, 282, 344, 234, 312, 243, 189, 366, 13, 411, 26, 76, 386, 93, 350, 407, 224, 172, 217, 169, 261, 196, 361, 462, 156, 185, 8, 72, 384, 103, 432, 192, 398, 213, 305, 355, 284, 259, 272, 121, 444, 430, 496, 416, 248, 297, 396, 78, 108, 126, 474, 162, 405, 12, 463, 229, 98, 479, 153, 253, 217, 493, 143, 368, 135, 509, 113, 85, 462, 398, 31, 180, 323, 307, 78, 274, 379, 21, 118}
592445117
249784398
12501659
500
5000
Returns: 877633416
{14, 428, 46, 52, 290, 70, 478, 343, 321, 336, 399, 370, 364, 126, 507, 6, 206, 345, 343, 281, 183, 210, 189, 56, 34, 250, 272, 339, 121, 78, 439, 364, 320, 72, 163, 240, 437, 286, 84, 185, 5, 477, 348, 84, 446, 219, 52, 286, 34, 68, 65, 291, 306, 138, 119, 263, 277, 106, 11, 383, 169, 69, 239, 193, 271, 149, 463, 440, 78, 116, 239, 130, 36, 365, 163, 469, 206, 377, 480, 316, 397, 266, 199, 356, 97, 175, 30, 432, 411, 55, 443, 465, 132, 218, 203, 186, 44, 138, 162, 384}
164479585
236847654
254958815
500
100000
Returns: 159653840
{223, 106, 173, 239, 257, 326, 454, 92, 14, 142, 255, 72, 402, 331, 418, 241, 429, 300, 364, 470, 11, 375, 54, 311, 407, 417, 181, 53, 377, 117, 334, 33, 374, 19, 164, 43, 506, 12, 495, 215, 410, 353, 284, 429, 178, 213, 185, 378, 330, 114, 169, 423, 299, 297, 196, 511, 203, 241, 369, 257, 349, 283, 87, 417, 351, 94, 101, 123, 144, 274, 303, 215, 431, 381, 175, 229, 384, 373, 17, 156, 429, 296, 464, 415, 393, 401, 342, 42, 498, 187, 178, 76, 410, 257, 433, 112, 448, 390, 18, 16}
786372172
673748359
148095897
500
2000000
Returns: 488357708
{511, 87, 492, 508, 247, 232, 350, 303, 343, 58, 52, 490, 154, 417, 297, 169, 44, 265, 111, 3, 124, 468, 378, 94, 126, 278, 82, 369, 59, 227, 323, 146, 31, 178, 346, 80, 40, 359, 311, 492, 196, 47, 314, 210, 432, 65, 470, 205, 392, 255, 27, 345, 127, 308, 25, 44, 353, 32, 14, 22, 327, 29, 499, 57, 27, 500, 171, 101, 445, 411, 403, 175, 237, 0, 465, 158, 118, 352, 217, 134, 286, 465, 80, 93, 274, 221, 21, 25, 445, 256, 306, 345, 351, 221, 511, 3, 491, 470, 112, 469}
107255749
999022891
557123865
5000
641194
Returns: 588198973
{}
56292813
602346958
479741229
5000
290220
Returns: 797231107
{334, 255, 409, 291, 162, 375, 319, 457, 506, 60, 221, 130, 403, 441, 270, 362, 140, 466, 167, 193, 399, 88, 137, 175, 510, 55, 59, 461, 422, 66, 33, 220, 316, 51, 256, 437, 195, 412, 18, 221, 104, 129, 171, 279, 10, 53, 19, 245, 137, 396, 439, 78, 62, 405, 325, 318, 34, 420, 363, 495, 315, 104, 49, 362, 33, 346, 11, 271, 195, 422, 439, 185, 244, 18, 267, 352, 185, 137, 412, 21, 285, 96, 17, 45, 461, 299, 44, 495, 421, 86, 112, 499, 273, 119, 445, 400, 246, 389, 363, 104}
464112495
90556613
374882203
5000
5
Returns: 196763910
{75, 58, 264, 491, 168, 30, 347, 82, 83, 67, 469, 190, 108, 340, 312, 90, 195, 300, 63, 90, 45, 270, 94, 173, 205, 335, 367, 289, 109, 202, 202, 277, 276, 282, 161, 210, 110, 40, 309, 53, 405, 336, 463, 318, 55, 498, 40, 388, 205, 196, 157, 460, 206, 241, 311, 211, 324, 333, 86, 98, 91, 270, 326, 44, 508, 459, 278, 324, 18, 431, 93, 81, 8, 111, 106, 55, 427, 286, 227, 159, 460, 288, 246, 470, 358, 458, 464, 92, 389, 486, 284, 90, 196, 405, 251, 358, 491, 128, 505, 327}
439119058
278779212
380720134
5000
10
Returns: 512104965
{304, 17, 250, 169, 403, 451, 379, 227, 152, 2, 242, 291, 370, 194, 299, 371, 400, 227, 143, 195, 222, 238, 452, 27, 253, 284, 175, 45, 286, 37, 447, 45, 293, 319, 428, 251, 263, 365, 282, 327, 14, 327, 345, 365, 172, 51, 284, 462, 217, 319, 315, 310, 12, 471, 501, 363, 436, 60, 496, 106, 288, 56, 299, 60, 339, 313, 432, 137, 5, 187, 62, 460, 285, 110, 110, 444, 118, 304, 447, 288, 24, 354, 434, 355, 459, 473, 80, 411, 128, 66, 370, 342, 197, 254, 110, 236, 137, 439, 388, 95}
84331288
339585103
718050631
5000
20
Returns: 812610555
{196, 46, 470, 233, 220, 39, 92, 436, 393, 61, 201, 325, 428, 63, 502, 426, 17, 450, 15, 274, 48, 472, 346, 323, 246, 225, 115, 189, 352, 148, 127, 256, 245, 213, 85, 479, 202, 414, 245, 53, 147, 51, 8, 478, 421, 31, 444, 335, 38, 261, 203, 256, 268, 208, 176, 4, 97, 302, 38, 416, 18, 242, 402, 410, 113, 436, 334, 412, 290, 281, 409, 494, 493, 13, 153, 359, 38, 509, 214, 218, 467, 75, 13, 269, 421, 345, 192, 189, 313, 302, 386, 406, 309, 60, 219, 142, 348, 109, 282, 151}
601608438
794414438
570595869
5000
100
Returns: 775293018
{394, 84, 384, 318, 136, 177, 369, 308, 241, 209, 482, 183, 132, 437, 4, 101, 121, 242, 394, 300, 380, 52, 293, 235, 290, 421, 158, 175, 381, 87, 357, 216, 257, 437, 170, 476, 454, 293, 303, 225, 14, 301, 449, 418, 424, 498, 32, 55, 455, 384, 164, 444, 201, 98, 369, 382, 349, 178, 223, 382, 344, 249, 33, 29, 152, 377, 31, 473, 507, 202, 269, 111, 54, 72, 371, 260, 458, 139, 190, 8, 384, 286, 293, 188, 149, 12, 461, 413, 27, 509, 213, 167, 211, 215, 511, 3, 163, 9, 321, 1}
201753469
767060703
996687347
5000
500
Returns: 406824842
{271, 173, 342, 394, 409, 240, 65, 482, 77, 191, 459, 347, 429, 369, 90, 272, 489, 416, 421, 330, 89, 402, 503, 137, 98, 254, 128, 483, 230, 116, 299, 400, 323, 168, 59, 409, 143, 37, 271, 216, 98, 278, 373, 102, 10, 288, 263, 484, 505, 424, 491, 330, 137, 169, 469, 378, 65, 315, 402, 53, 200, 271, 315, 90, 312, 500, 495, 448, 309, 341, 359, 185, 180, 510, 472, 33, 331, 297, 230, 476, 490, 485, 169, 341, 473, 297, 71, 60, 79, 145, 165, 508, 506, 430, 109, 249, 448, 151, 324, 183}
521197098
942165944
57292216
5000
5000
Returns: 147112426
{18, 454, 131, 272, 230, 501, 316, 58, 241, 260, 6, 438, 402, 461, 459, 111, 262, 190, 131, 22, 17, 206, 244, 183, 505, 234, 113, 295, 367, 464, 83, 30, 194, 293, 36, 473, 12, 157, 125, 484, 110, 139, 45, 318, 15, 317, 181, 200, 168, 386, 320, 443, 300, 508, 248, 353, 321, 325, 464, 337, 305, 191, 459, 179, 243, 303, 497, 137, 60, 505, 159, 95, 63, 427, 228, 265, 10, 9, 80, 313, 511, 494, 187, 140, 248, 150, 307, 327, 383, 187, 1, 102, 339, 249, 399, 430, 73, 200, 227, 431}
563605483
985785567
665877606
5000
100000
Returns: 937982262
{432, 393, 393, 442, 328, 275, 72, 72, 21, 181, 387, 134, 112, 112, 453, 119, 372, 21, 219, 141, 363, 295, 74, 47, 53, 489, 107, 372, 329, 404, 211, 90, 147, 120, 58, 249, 111, 370, 405, 82, 493, 336, 77, 442, 141, 25, 274, 20, 51, 32, 69, 372, 279, 268, 124, 289, 112, 23, 68, 160, 478, 103, 280, 303, 466, 330, 51, 403, 371, 500, 173, 474, 239, 448, 322, 402, 49, 328, 192, 408, 324, 366, 180, 199, 72, 393, 396, 118, 169, 436, 111, 89, 13, 58, 476, 55, 101, 457, 427, 141}
89025347
965228710
821273871
5000
2000000
Returns: 484012083
{495, 269, 439, 508, 329, 105, 212, 263, 97, 441, 449, 418, 31, 278, 84, 126, 241, 82, 320, 122, 402, 84, 95, 314, 116, 446, 334, 41, 36, 7, 447, 300, 414, 391, 31, 324, 141, 497, 300, 351, 141, 290, 22, 260, 346, 38, 121, 320, 389, 414, 360, 245, 299, 494, 444, 374, 171, 147, 126, 88, 455, 39, 17, 466, 371, 346, 9, 394, 352, 261, 78, 394, 49, 371, 77, 182, 107, 146, 161, 396, 317, 169, 269, 39, 451, 426, 484, 274, 284, 278, 293, 72, 505, 88, 346, 461, 25, 95, 501, 276}
127248150
518440026
303272628
100000
510124
Returns: 607136486
{}
989251578
883982118
581583657
100000
1471775
Returns: 104508641
{409, 96, 16, 108, 196, 455, 26, 250, 63, 139, 310, 190, 276, 410, 309, 318, 303, 121, 31, 266, 250, 14, 135, 232, 189, 297, 301, 107, 356, 80, 462, 88, 307, 124, 364, 338, 115, 507, 72, 294, 510, 306, 249, 30, 324, 160, 485, 486, 150, 248, 230, 25, 2, 238, 402, 368, 60, 146, 410, 62, 33, 134, 309, 510, 434, 329, 73, 459, 504, 162, 192, 396, 454, 268, 126, 109, 505, 331, 504, 18, 469, 377, 383, 263, 362, 430, 144, 474, 329, 477, 185, 162, 343, 294, 382, 14, 340, 173, 110, 210}
572864917
318284577
735703218
100000
5
Returns: 773481178
{472, 90, 89, 65, 507, 30, 324, 29, 235, 188, 406, 135, 94, 149, 231, 374, 304, 269, 28, 190, 130, 4, 110, 310, 115, 29, 175, 482, 178, 174, 95, 86, 82, 457, 490, 13, 387, 14, 259, 120, 153, 482, 158, 63, 312, 261, 139, 232, 41, 311, 212, 242, 162, 262, 393, 30, 267, 343, 418, 188, 139, 162, 235, 2, 239, 109, 443, 294, 91, 317, 387, 74, 110, 315, 350, 405, 368, 94, 510, 215, 181, 52, 469, 56, 280, 131, 214, 69, 237, 381, 211, 435, 111, 51, 68, 132, 153, 155, 325, 365}
532278079
816158415
411355614
100000
10
Returns: 175948256
{187, 130, 411, 252, 117, 232, 122, 464, 120, 70, 152, 348, 279, 298, 430, 287, 196, 422, 409, 196, 106, 279, 331, 209, 408, 437, 6, 173, 141, 372, 75, 360, 458, 462, 47, 467, 96, 239, 145, 48, 164, 462, 182, 379, 68, 124, 475, 180, 285, 365, 273, 495, 142, 50, 508, 409, 192, 222, 469, 429, 38, 268, 232, 124, 85, 451, 232, 351, 59, 186, 115, 255, 407, 123, 372, 463, 178, 155, 487, 375, 55, 343, 241, 283, 161, 80, 291, 15, 274, 219, 103, 335, 509, 247, 334, 256, 82, 79, 209, 48}
448194932
11298459
891932935
100000
20
Returns: 730381458
{139, 268, 40, 327, 125, 31, 485, 237, 200, 4, 128, 405, 46, 410, 359, 158, 262, 497, 213, 463, 370, 298, 60, 491, 408, 26, 369, 354, 235, 42, 175, 424, 511, 458, 144, 100, 380, 296, 199, 335, 99, 191, 305, 474, 148, 60, 241, 15, 464, 409, 447, 508, 279, 333, 383, 362, 343, 484, 305, 443, 330, 293, 164, 404, 113, 384, 51, 297, 295, 472, 86, 278, 297, 218, 253, 175, 45, 304, 161, 314, 131, 155, 506, 407, 118, 192, 304, 25, 352, 85, 286, 217, 57, 89, 166, 367, 418, 15, 505, 428}
187151272
888422199
364940883
100000
100
Returns: 705581655
{159, 203, 123, 221, 32, 448, 232, 185, 233, 111, 304, 57, 148, 483, 209, 132, 31, 485, 319, 74, 436, 488, 301, 348, 212, 353, 310, 144, 389, 87, 150, 48, 152, 356, 432, 62, 213, 509, 56, 246, 367, 440, 377, 150, 364, 118, 245, 84, 386, 410, 377, 175, 90, 247, 473, 355, 202, 165, 410, 129, 204, 439, 60, 69, 84, 1, 52, 19, 255, 11, 191, 272, 433, 283, 407, 231, 24, 388, 7, 207, 264, 139, 217, 293, 243, 420, 6, 392, 378, 317, 52, 509, 319, 421, 365, 324, 370, 267, 479, 216}
843568016
650414522
22665371
100000
500
Returns: 654831575
{484, 458, 228, 171, 332, 433, 475, 130, 267, 224, 351, 345, 186, 444, 6, 177, 13, 506, 318, 287, 368, 163, 35, 465, 478, 461, 416, 180, 149, 467, 132, 100, 37, 61, 511, 436, 499, 456, 464, 194, 362, 33, 7, 80, 153, 238, 78, 87, 25, 295, 271, 205, 443, 338, 21, 161, 359, 201, 210, 406, 473, 296, 498, 175, 438, 185, 70, 341, 289, 109, 267, 63, 483, 29, 208, 218, 350, 420, 23, 90, 50, 146, 288, 148, 315, 511, 222, 198, 487, 233, 473, 153, 171, 320, 276, 414, 148, 365, 232, 372}
416761743
264655711
902374128
100000
5000
Returns: 668322801
{279, 130, 234, 93, 230, 159, 450, 171, 219, 129, 82, 426, 124, 423, 321, 380, 388, 192, 34, 502, 128, 133, 348, 501, 97, 502, 4, 452, 11, 316, 50, 266, 332, 337, 333, 43, 415, 17, 206, 187, 74, 0, 511, 374, 428, 186, 141, 121, 67, 43, 81, 167, 28, 215, 66, 120, 389, 213, 107, 45, 477, 23, 419, 74, 61, 418, 274, 334, 76, 331, 78, 167, 51, 6, 183, 78, 458, 111, 273, 147, 300, 226, 301, 415, 122, 157, 154, 150, 234, 125, 142, 21, 504, 463, 405, 56, 195, 66, 45, 371}
352972987
495323637
374147441
100000
100000
Returns: 598133637
{425, 184, 166, 154, 398, 138, 338, 225, 490, 440, 345, 370, 164, 423, 319, 364, 219, 339, 242, 398, 395, 250, 467, 105, 506, 349, 281, 411, 501, 39, 463, 396, 203, 356, 348, 107, 24, 502, 506, 477, 149, 173, 248, 397, 461, 154, 28, 345, 42, 331, 250, 390, 343, 90, 222, 95, 126, 138, 104, 496, 12, 291, 486, 406, 223, 336, 355, 63, 52, 201, 255, 10, 204, 320, 155, 69, 163, 259, 227, 394, 172, 173, 477, 491, 235, 6, 483, 497, 206, 6, 220, 345, 287, 141, 100, 453, 175, 338, 290, 223}
932415152
542780460
143431000
100000
2000000
Returns: 566765612
{296, 410, 417, 113, 336, 483, 22, 113, 300, 393, 206, 187, 296, 305, 47, 419, 496, 351, 472, 360, 509, 54, 21, 467, 173, 125, 340, 425, 211, 22, 48, 78, 163, 269, 473, 32, 200, 224, 338, 274, 109, 101, 53, 115, 88, 325, 85, 505, 122, 354, 69, 1, 465, 395, 99, 234, 457, 443, 448, 320, 15, 402, 259, 457, 195, 236, 3, 67, 151, 393, 62, 313, 13, 411, 247, 284, 47, 6, 142, 469, 426, 282, 398, 25, 209, 327, 54, 482, 49, 5, 510, 11, 343, 377, 389, 58, 36, 231, 222, 56}
814511997
70433021
143232927
2000000
287370
Returns: 705291073
{15, 400, 6, 236, 286, 49, 153, 0, 168, 87, 505, 434, 339, 103, 281, 441, 68, 384, 155, 231, 132, 340, 446, 323, 422, 312, 186, 38, 348, 189, 227, 382, 61, 408, 435, 27, 321, 275, 358, 3, 187, 103, 209, 76, 188, 470, 377, 334, 242, 259, 313, 450, 461, 359, 210, 507, 284, 57, 227, 339, 226, 419, 378, 177, 81, 421, 81, 372, 352, 69, 102, 112, 418, 509, 41, 192, 485, 505, 176, 505, 97, 152, 468, 429, 113, 490, 196, 273, 386, 340, 66, 357, 345, 156, 299, 436, 191, 48, 134, 266}
652739232
819930775
783731370
2000000
5
Returns: 274561818
{350, 269, 445, 180, 87, 271, 296, 108, 507, 115, 249, 142, 2, 19, 383, 184, 101, 439, 2, 229, 508, 121, 407, 0, 441, 146, 420, 80, 352, 312, 96, 229, 332, 273, 451, 491, 412, 39, 187, 382, 166, 164, 85, 278, 56, 367, 348, 413, 368, 254, 449, 476, 140, 298, 142, 69, 243, 84, 63, 165, 154, 454, 290, 349, 405, 474, 41, 264, 93, 178, 139, 504, 106, 90, 263, 328, 206, 150, 399, 482, 505, 452, 140, 464, 49, 215, 265, 270, 273, 281, 472, 76, 336, 423, 171, 153, 432, 209, 430, 116}
704078287
911963443
812174576
2000000
10
Returns: 778223464
{364, 499, 496, 167, 392, 88, 111, 447, 122, 40, 90, 497, 146, 510, 336, 114, 362, 323, 183, 132, 244, 33, 374, 150, 253, 69, 36, 375, 179, 85, 272, 226, 60, 347, 350, 133, 466, 456, 134, 371, 69, 223, 149, 453, 160, 173, 41, 24, 282, 219, 43, 287, 387, 237, 448, 226, 319, 281, 443, 253, 461, 140, 469, 284, 272, 110, 402, 125, 132, 230, 32, 218, 202, 364, 341, 384, 430, 213, 176, 11, 501, 369, 289, 178, 161, 200, 164, 347, 424, 192, 153, 274, 44, 217, 277, 221, 343, 256, 371, 314}
722878652
142958657
402580700
2000000
20
Returns: 998997755
{392, 251, 314, 285, 132, 359, 420, 220, 425, 431, 456, 119, 415, 56, 257, 68, 299, 416, 277, 499, 57, 418, 413, 498, 82, 392, 201, 378, 418, 281, 240, 329, 177, 453, 325, 374, 333, 8, 223, 328, 382, 306, 145, 179, 136, 183, 118, 213, 8, 199, 313, 471, 180, 334, 251, 235, 142, 338, 161, 462, 491, 377, 349, 302, 459, 278, 368, 473, 463, 279, 364, 119, 295, 344, 253, 439, 460, 377, 109, 437, 491, 440, 251, 106, 503, 32, 271, 335, 340, 327, 1, 93, 389, 141, 19, 148, 25, 171, 230, 103}
776094359
597167506
269370609
2000000
100
Returns: 378125657
{398, 87, 422, 18, 414, 443, 283, 130, 341, 211, 180, 226, 228, 139, 4, 30, 82, 125, 431, 484, 62, 425, 501, 179, 136, 178, 436, 169, 213, 138, 172, 279, 337, 327, 167, 294, 137, 41, 422, 433, 130, 417, 330, 94, 269, 447, 499, 343, 249, 256, 38, 144, 415, 372, 488, 62, 74, 464, 238, 236, 406, 365, 436, 187, 350, 431, 340, 18, 135, 54, 158, 493, 275, 431, 266, 157, 297, 245, 1, 30, 60, 458, 276, 227, 197, 1, 287, 408, 454, 21, 116, 414, 430, 411, 310, 275, 30, 308, 463, 461}
977596487
262581233
469437250
2000000
500
Returns: 41579063
{95, 127, 207, 161, 314, 372, 205, 445, 247, 355, 365, 330, 77, 106, 60, 506, 95, 214, 466, 352, 412, 37, 188, 324, 435, 47, 118, 388, 385, 119, 370, 222, 193, 99, 462, 308, 85, 263, 435, 449, 292, 243, 99, 2, 130, 27, 404, 92, 341, 344, 350, 15, 130, 116, 236, 275, 145, 436, 21, 389, 31, 347, 139, 126, 91, 406, 134, 157, 452, 287, 82, 147, 20, 163, 13, 146, 143, 423, 248, 134, 421, 278, 195, 206, 497, 35, 267, 98, 102, 311, 229, 456, 42, 81, 77, 305, 202, 283, 98, 206}
811838439
430519478
115804966
2000000
5000
Returns: 703704037
{206, 500, 357, 338, 371, 159, 445, 31, 372, 120, 504, 87, 44, 209, 483, 165, 156, 169, 280, 67, 70, 196, 406, 206, 165, 429, 479, 78, 332, 438, 456, 371, 389, 83, 134, 501, 442, 386, 183, 16, 449, 494, 399, 315, 490, 392, 263, 83, 194, 28, 148, 413, 255, 231, 32, 137, 466, 40, 72, 267, 468, 387, 62, 243, 494, 484, 214, 390, 488, 234, 163, 509, 3, 111, 235, 203, 400, 51, 134, 436, 279, 261, 349, 32, 476, 488, 411, 62, 128, 316, 154, 238, 288, 476, 306, 331, 333, 89, 236, 270}
201337312
506290444
540926237
2000000
100000
Returns: 853314799
{361, 431, 338, 461, 495, 415, 468, 91, 485, 390, 494, 189, 398, 377, 39, 273, 151, 459, 2, 300, 15, 206, 306, 466, 66, 30, 345, 371, 86, 437, 274, 86, 143, 386, 482, 32, 351, 109, 377, 98, 395, 469, 9, 343, 322, 456, 258, 333, 155, 164, 186, 366, 475, 359, 167, 503, 332, 393, 397, 145, 482, 56, 1, 371, 27, 102, 443, 203, 457, 415, 97, 420, 355, 148, 45, 111, 90, 414, 251, 490, 489, 355, 439, 193, 276, 394, 138, 264, 66, 14, 204, 350, 142, 446, 363, 141, 301, 474, 386, 210}
973808339
339338830
92382197
2000000
2000000
Returns: 857168305
{279, 93, 462, 366, 457, 18, 33, 286, 20, 444, 327, 288, 39, 312, 314, 339, 207, 32, 123, 92, 101, 479, 169, 131, 16, 156, 224, 245, 459, 125, 383, 390, 203, 65, 124, 70, 286, 318, 273, 157, 0, 446, 267, 146, 441, 84, 76, 22, 328, 209, 31, 78, 69, 497, 194, 28, 319, 149, 104, 346, 166, 63, 23, 22, 144, 478, 445, 361, 24, 506, 253, 425, 19, 414, 367, 408, 250, 67, 248, 373, 86, 259, 321, 250, 342, 29, 445, 500, 146, 367, 68, 321, 447, 417, 70, 422, 261, 450, 204, 288}
506672684
349015066
540527856
2000000
1530932
Returns: 829827304
{115, 203, 507, 251, 82, 393, 0, 118, 257, 220, 394, 364, 319, 283, 201, 324, 219, 403, 165, 335, 154, 119, 159, 38, 128, 188, 78, 376, 6, 83, 444, 486, 239, 160, 244, 325, 83, 53, 286, 345, 419, 149, 167, 163, 168, 111, 30, 286, 82, 439, 104, 290, 65, 132, 232, 59, 376, 241, 2, 268, 301, 233, 214, 366, 335, 45, 44, 169, 20, 18, 359, 376, 55, 508, 67, 67, 190, 260, 189, 357, 467, 207, 32, 171, 99, 418, 232, 76, 307, 353, 176, 161, 13, 97, 486, 215, 34, 260, 417, 206}
310827789
208645799
566143059
2000000
1342344
Returns: 718042988
{130, 8, 367, 175, 66, 491, 247, 9, 491, 165, 333, 94, 248, 229, 369, 244, 64, 402, 502, 451, 465, 3, 411, 8, 210, 167, 351, 414, 471, 468, 59, 319, 453, 474, 349, 370, 320, 351, 404, 505, 4, 305, 217, 358, 140, 371, 434, 183, 419, 348, 6, 507, 88, 142, 115, 409, 250, 29, 22, 386, 140, 206, 460, 280, 463, 447, 109, 78, 173, 151, 140, 435, 509, 397, 0, 168, 134, 328, 30, 188, 454, 109, 423, 206, 266, 410, 34, 471, 390, 144, 390, 365, 70, 258, 411, 80, 273, 372, 93, 109}
787661042
30654027
433878210
2000000
1446184
Returns: 683275358
{20, 119, 390, 25, 103, 432, 327, 261, 248, 401, 459, 82, 456, 210, 62, 380, 153, 492, 458, 444, 378, 2, 319, 480, 200, 175, 143, 151, 369, 405, 363, 222, 14, 336, 80, 358, 229, 81, 449, 269, 123, 180, 456, 338, 283, 28, 285, 280, 328, 129, 122, 229, 48, 465, 167, 203, 41, 229, 362, 386, 246, 66, 372, 176, 182, 152, 84, 236, 508, 482, 497, 486, 273, 181, 291, 4, 122, 408, 500, 43, 16, 163, 165, 253, 97, 458, 206, 76, 408, 345, 469, 307, 289, 200, 398, 388, 155, 251, 223, 8}
946813146
604220808
923182385
2000000
1757703
Returns: 343489075
{28, 489, 503, 82, 456, 139, 297, 240, 287, 333, 172, 269, 193, 166, 484, 247, 235, 101, 463, 107, 192, 432, 74, 160, 285, 462, 315, 435, 226, 417, 243, 197, 68, 110, 251, 180, 242, 35, 483, 480, 362, 204, 241, 308, 246, 164, 504, 463, 436, 266, 281, 304, 288, 343, 455, 54, 196, 24, 175, 113, 47, 444, 469, 461, 170, 314, 26, 157, 189, 291, 471, 479, 385, 100, 94, 167, 53, 210, 273, 71, 156, 450, 259, 350, 73, 102, 119, 337, 483, 288, 210, 148, 400, 371, 8, 498, 415, 234, 172, 376}
867426622
552070192
285428075
2000000
34890
Returns: 814272825
{318, 506, 463, 120, 332, 126, 466, 61, 189, 401, 77, 80, 494, 180, 420, 493, 125, 372, 318, 465, 1, 123, 440, 3, 494, 349, 71, 316, 115, 129, 311, 186, 297, 196, 334, 52, 274, 448, 386, 226, 14, 94, 36, 156, 510, 386, 169, 75, 127, 375, 414, 292, 314, 26, 349, 325, 420, 255, 290, 396, 411, 422, 1, 240, 189, 500, 42, 335, 71, 46, 165, 406, 472, 387, 317, 219, 486, 30, 484, 104, 314, 113, 272, 9, 32, 325, 366, 418, 370, 238, 291, 105, 410, 324, 485, 38, 97, 104, 237, 108}
992769203
727617219
57900584
2000000
1215111
Returns: 211038137
{54, 429, 511, 134, 381, 486, 101, 184, 302, 288, 488, 6, 34, 106, 5, 335, 391, 199, 119, 382, 36, 487, 8, 145, 63, 95, 38, 361, 153, 357, 9, 74, 405, 241, 214, 491, 141, 170, 344, 258, 285, 206, 198, 392, 126, 462, 377, 233, 259, 332, 201, 246, 252, 52, 401, 143, 211, 45, 273, 327, 328, 218, 269, 225, 337, 46, 401, 40, 30, 120, 38, 123, 357, 482, 12, 272, 113, 413, 253, 251, 237, 187, 26, 229, 238, 197, 269, 439, 82, 240, 278, 226, 47, 291, 380, 5, 71, 168, 229, 66}
344920033
882642823
345898354
2000000
1146374
Returns: 200935006
{168, 249, 173, 434, 337, 140, 45, 507, 433, 499, 39, 71, 486, 226, 7, 157, 469, 71, 293, 377, 255, 69, 235, 237, 129, 235, 263, 76, 506, 230, 15, 455, 190, 386, 336, 488, 399, 41, 160, 441, 46, 338, 370, 141, 310, 287, 474, 65, 330, 18, 491, 6, 49, 174, 382, 248, 227, 494, 91, 409, 213, 39, 144, 159, 234, 213, 214, 439, 424, 457, 106, 321, 328, 91, 226, 190, 267, 214, 191, 52, 314, 295, 479, 114, 198, 215, 458, 44, 489, 372, 324, 268, 367, 239, 274, 313, 101, 214, 306, 292}
162920465
680834728
172132993
2000000
473925
Returns: 985496925
{283, 254, 296, 1, 393, 23, 112, 333, 23, 43, 396, 372, 258, 303, 413, 100, 187, 13, 111, 435, 390, 420, 259, 41, 269, 418, 509, 126, 316, 216, 88, 84, 83, 445, 169, 495, 295, 230, 483, 161, 235, 368, 226, 61, 30, 440, 209, 334, 92, 484, 481, 293, 35, 157, 114, 267, 335, 317, 496, 397, 457, 142, 318, 507, 348, 505, 128, 203, 45, 405, 165, 228, 229, 352, 347, 368, 202, 100, 261, 418, 122, 506, 88, 454, 102, 480, 377, 282, 220, 219, 506, 88, 22, 419, 377, 156, 221, 373, 440, 203}
718984256
970989157
341990563
2000000
1549926
Returns: 828151805
{55, 438, 274, 383, 248, 378, 311, 50, 440, 49, 156, 41, 194, 300, 335, 261, 346, 38, 120, 103, 190, 495, 470, 301, 126, 293, 164, 305, 26, 403, 7, 30, 267, 455, 438, 212, 67, 413, 437, 323, 268, 211, 239, 188, 448, 409, 132, 89, 319, 153, 340, 415, 177, 349, 33, 396, 40, 235, 244, 147, 109, 410, 52, 507, 501, 410, 441, 236, 477, 53, 134, 260, 465, 100, 296, 387, 226, 211, 177, 325, 166, 247, 116, 159, 469, 340, 37, 274, 37, 161, 477, 412, 423, 251, 429, 463, 280, 341, 491, 258}
413311889
496602384
896818598
2000000
732122
Returns: 640838324
{344, 149, 93, 236, 471, 45, 378, 328, 155, 278, 450, 68, 97, 426, 160, 97, 309, 257, 449, 406, 6, 114, 339, 431, 381, 251, 163, 22, 292, 11, 156, 88, 254, 372, 386, 212, 216, 163, 255, 411, 192, 5, 174, 259, 186, 346, 471, 286, 301, 39, 46, 188, 330, 229, 476, 417, 207, 248, 59, 449, 91, 273, 436, 156, 231, 349, 336, 328, 308, 388, 511, 99, 86, 98, 319, 302, 194, 475, 396, 38, 416, 362, 498, 399, 275, 374, 117, 367, 233, 132, 500, 36, 204, 262, 500, 421, 462, 248, 454, 164}
693549002
240884114
270680073
2000000
1596906
Returns: 488287038
{412, 262, 19, 216, 277, 485, 130, 393, 25, 448, 346, 7, 97, 342, 51, 123, 71, 212, 77, 511, 490, 422, 349, 222, 241, 67, 99, 29, 82, 80, 62, 296, 137, 257, 67, 88, 336, 167, 140, 329, 245, 439, 407, 424, 353, 57, 326, 144, 74, 33, 439, 486, 372, 188, 325, 343, 276, 443, 511, 419, 152, 175, 297, 460, 475, 487, 47, 113, 68, 119, 34, 465, 468, 1, 85, 384, 104, 139, 254, 187, 89, 382, 191, 411, 392, 489, 408, 389, 419, 137, 338, 49, 128, 251, 47, 34, 396, 367, 62, 288}
267999095
541719471
329363872
2000000
1560716
Returns: 860572368
{398, 116, 250, 303, 78, 403, 287, 221, 128, 153, 138, 52, 341, 284, 69, 234, 203, 298, 367, 505, 52, 8, 116, 405, 359, 125, 511, 221, 95, 343, 83, 85, 58, 239, 159, 325, 431, 191, 215, 275, 443, 282, 96, 387, 88, 449, 24, 100, 234, 319, 458, 458, 384, 464, 445, 16, 249, 46, 350, 479, 266, 250, 81, 504, 275, 236, 434, 186, 72, 26, 202, 188, 270, 284, 208, 250, 276, 509, 433, 48, 262, 191, 472, 54, 40, 47, 102, 436, 61, 64, 230, 160, 347, 35, 106, 446, 291, 502, 434, 14}
102066521
283210942
611186985
2000000
849489
Returns: 110201765
{195, 72, 370, 412, 0, 45, 180, 146, 365, 377, 51, 359, 454, 456, 393, 426, 293, 434, 248, 131, 490, 59, 19, 86, 478, 354, 184, 71, 299, 470, 82, 271, 125, 335, 193, 350, 99, 260, 452, 149, 302, 183, 165, 137, 428, 492, 430, 447, 180, 219, 403, 249, 199, 298, 267, 3, 17, 478, 451, 87, 248, 297, 163, 224, 255, 393, 328, 285, 199, 3, 203, 201, 435, 194, 449, 162, 116, 160, 15, 490, 397, 163, 502, 398, 71, 439, 39, 65, 110, 38, 467, 172, 105, 465, 369, 196, 447, 260, 480, 4}
364984695
64578016
575904452
2000000
1898038
Returns: 931513916
{121, 16, 471, 39, 196, 236, 354, 50, 207, 163, 463, 501, 318, 365, 480, 266, 164, 488, 252, 510, 413, 247, 229, 281, 332, 496, 31, 376, 51, 416, 97, 162, 459, 281, 83, 68, 77, 108, 280, 491, 69, 299, 281, 263, 423, 271, 420, 174, 17, 468, 73, 93, 88, 367, 333, 443, 394, 135, 479, 114, 440, 10, 363, 245, 416, 473, 112, 231, 491, 307, 49, 333, 232, 59, 404, 450, 200, 143, 230, 332, 248, 457, 396, 368, 38, 164, 260, 167, 186, 80, 237, 350, 180, 367, 455, 251, 381, 507, 92, 126}
35288995
41304731
524160467
2000000
263786
Returns: 602080727
{181, 90, 233, 319, 446, 404, 244, 228, 347, 65, 10, 246, 301, 319, 353, 124, 87, 468, 471, 364, 145, 444, 305, 343, 114, 176, 436, 112, 40, 133, 367, 106, 208, 101, 99, 163, 385, 395, 139, 251, 86, 463, 267, 121, 186, 169, 420, 464, 202, 442, 218, 93, 365, 335, 474, 178, 33, 301, 102, 340, 168, 123, 366, 76, 254, 316, 339, 11, 344, 64, 47, 230, 279, 478, 335, 323, 115, 71, 232, 104, 228, 79, 504, 461, 46, 435, 124, 301, 481, 210, 242, 479, 431, 87, 161, 459, 368, 95, 277, 367}
807964965
295439599
759356337
2000000
1220408
Returns: 899255434
{391, 95, 393, 325, 399, 19, 319, 54, 114, 300, 245, 121, 106, 187, 494, 234, 2, 276, 393, 84, 196, 71, 455, 475, 115, 436, 131, 451, 55, 500, 82, 435, 415, 196, 463, 257, 471, 205, 111, 306, 246, 448, 485, 428, 189, 190, 449, 150, 156, 453, 501, 242, 59, 394, 241, 233, 178, 51, 140, 195, 464, 440, 74, 213, 230, 31, 390, 428, 253, 117, 497, 39, 353, 453, 314, 441, 409, 273, 477, 441, 290, 425, 9, 432, 230, 214, 478, 252, 72, 373, 311, 182, 456, 203, 450, 306, 355, 38, 490, 378}
950170151
99172661
251829700
2000000
1363462
Returns: 565719394
{286, 175, 335, 256, 118, 448, 439, 0, 400, 217, 451, 60, 210, 181, 364, 312, 144, 201, 357, 212, 403, 69, 23, 410, 494, 379, 15, 136, 327, 108, 432, 1, 19, 17, 488, 22, 66, 448, 249, 111, 207, 269, 463, 438, 361, 297, 129, 493, 327, 282, 239, 185, 489, 253, 175, 417, 217, 366, 309, 317, 381, 210, 494, 239, 421, 380, 336, 125, 354, 403, 143, 484, 481, 304, 462, 460, 312, 134, 43, 335, 419, 443, 106, 499, 293, 308, 369, 405, 212, 412, 74, 95, 381, 76, 507, 409, 293, 127, 511, 336}
822713886
187231109
927434567
2000000
1275727
Returns: 747038586
{428, 334, 89, 14, 250, 218, 278, 373, 339, 475, 480, 13, 50, 245, 472, 0, 231, 112, 431, 481, 213, 384, 71, 189, 168, 458, 429, 223, 402, 281, 170, 109, 117, 488, 448, 106, 243, 195, 343, 189, 107, 408, 389, 510, 250, 72, 419, 451, 167, 395, 48, 346, 502, 191, 387, 508, 325, 113, 226, 66, 257, 239, 43, 101, 4, 425, 135, 485, 404, 222, 407, 370, 315, 437, 361, 24, 357, 23, 29, 441, 398, 260, 60, 304, 86, 258, 351, 136, 447, 88, 8, 468, 443, 245, 457, 191, 366, 126, 144, 128}
415067258
682186175
651292654
2000000
5735
Returns: 719615612
{270, 241, 283, 347, 476, 224, 254, 245, 121, 150, 83, 382, 357, 248, 22, 175, 159, 180, 235, 428, 364, 280, 261, 50, 400, 268, 15, 330, 52, 463, 26, 319, 211, 0, 80, 328, 97, 34, 489, 141, 87, 422, 432, 412, 329, 263, 473, 304, 172, 444, 443, 256, 220, 275, 18, 6, 302, 399, 299, 436, 428, 340, 509, 31, 179, 298, 383, 285, 293, 400, 382, 505, 255, 307, 45, 360, 98, 349, 276, 363, 218, 114, 137, 380, 311, 489, 152, 283, 447, 280, 354, 257, 262, 187, 234, 145, 394, 133, 375, 387}
794840661
106054143
137060687
2000000
1840438
Returns: 329057119
{0, 511}
0
0
0
2
1
Returns: 256
After one step, the array has two equiprobable states : {0, 0} and {1, 511}. Hence, the expected sum = (0 + 512) / 2 = 256.
{0}
1001
1001
1001
2
2
Returns: 508
Here, the array is {0, 506}. Note that in the final array, the sum will be 508, independent of which counters are chosen in each step. Hence, the expected sum is 508.
{}
3583
1000
1812447358
2
2
Returns: 152
The array is {511, 23}. After 2 steps : the possible outcomes are {1, 23}, {0, 24}, {0, 24}, {511, 25}. Hence, the expected sum = 608 / 4 = 152.
{100, 101}
5000
50000
100000
1000
1000
Returns: 856925612
{}
100000000
100000000
100000000
10
1000
Returns: 454731206
{}
501296088
234548363
703491623
2000000
1894643
Returns: 804222535
{}
31413
134313
7585
1
1
Returns: 182
{}
454151
98563
47314
2000000
1
Returns: 77785307
{}
63732
97462
264621
1
2000000
Returns: 372
{}
100000
763184
314001
2000000
500000000
Returns: 403117022
{}
425701
41705
83629
2000000
500000000
Returns: 118090423
{}
22
23
24
2000000
500000000
Returns: 84360335
{100, 101, 102, 103, 104, 105}
32541
4105710
4159018
2000000
500000000
Returns: 447459754
{}
1812447358
1812447358
1812447358
2000000
500000000
Returns: 319196962
{}
4521
13513
154151
1
500000000
Returns: 169
{511, 511, 511, 510}
0
0
0
4
500000000
Returns: 516076976
{ }
501296088
234548363
703491623
2000000
500000000
Returns: 925671284
{ }
228
235
327
2000000
500000000
Returns: 990593653
{ }
1234
1234
1234
2000000
500000000
Returns: 841974687
{100 }
0
0
0
1
10000
Returns: 372
{0, 511 }
623
54353
34435
2000000
500000000
Returns: 328772427
{ }
501296088
234548363
703491623
2000000
1894643
Returns: 804222535