TopCoder Statistics - Problem Statement

Problem Statement

Anu loves binary sequences of length n. A binary sequence of length n has n elements (indexed from 1 to n) and each of those elements is either a zero (0) or a one (1).

You are given the int n. You are also given an int k and two equally long int[]s L and R. For each valid i, the values L[i] and R[i] are the left and right endpoints of a range of indices. Both endpoints are included in the range. For example, L[0]=3 and R[0]=7 represents the indices from 3 to 7, inclusive. We will denote this range [3,7].

The ranges defined by L and R satisfy one additional restriction: Given any two ranges, either one is contained in the other, or they are disjoint. For example, it cannot be the case that L = {1, 4, 10} and R = {5, 7, 20} because none of the ranges [1,5] and [4,7] contains the other, and they are also not disjoint.

Anu wants to count the number of binary sequences of length n that satisfy the following properties:

There are never more than k consecutive ones in the sequence.
Each of the ranges defined by L and R has an even sum.

Return the number of such sequences, modulo 10^9 + 7.

Definition

Class:: CountBinarySequences
Method:: countSequences
Parameters:: int, int, int[], int[]
Returns:: int
Method signature:: int countSequences(int n, int k, int[] L, int[] R)
(be sure your method is public)

Constraints

n will be between 1 and 1,000,000,000 (10^9), inclusive.
k will be between 1 and 5, inclusive.
L will contain between 1 and 50 elements, inclusive.
R will contain the same number of elements as L.
For each valid i, L[i] will be less than or equal to R[i].
All elements of L and R will be between 1 and n, inclusive.
All ranges defined by L and R will be distinct.
For any two ranges defined by L and R, either one will be contained in the other, or they will be disjoint.

Examples

4

2

{2}

{3}

Returns: 5

The five valid sequences are 0000, 0001, 0110, 1000, and 1001.
4

1

{2}

{2}

Returns: 6

We cannot have two consecutive ones. The range [2,2] contains only the index 2. As the sum of this range must be even, the element at index 2 must be a zero. Hence, the six valid sequences are 0000, 0001, 0010, 1000, 1001, and 1010.
6

3

{1, 2, 3}

{6, 5, 4}

Returns: 6
1000

4

{10, 101, 201, 110, 121}

{100, 200, 300, 120, 130}

Returns: 444743885
1

5

{1}

{1}

Returns: 1
998

2

{313,365,189,913,334,360,160,931,313,402,389,328,376,47,906,383,381,927,338,178,934,933,162,332,191,188,380,912,970,360,161,179,966,405,971,381}

{313,365,189,913,334,362,160,931,340,405,389,329,398,425,907,383,382,927,338,178,934,933,162,332,191,188,384,912,970,365,161,179,966,405,971,381}

Returns: 420889003
294

1

{164,294,218,274,277,171,292,293,276,205,173}

{164,294,218,277,277,171,292,293,276,205,173}

Returns: 438033567
137

2

{54,60,40}

{54,60,42}

Returns: 742320169
439

3

{407,25,133,138,21,344,49,400,401,40,396,341,39,135,35,413,129,25,106,129,106,120,418,137,408,407,48,338,48,123,393,121,335,343,417,412}

{408,26,134,138,55,344,49,400,401,40,396,341,40,135,35,413,131,25,145,129,115,125,418,137,408,407,48,338,49,123,415,121,344,343,418,412}

Returns: 401041360
954

2

{182,871,215,868,270,184,933,877,885,172,274,190,213,870,578,581,581,270,213,495,886,595,592,583,867,189,271,876}

{182,871,215,868,272,184,933,877,885,224,274,190,213,872,578,583,581,270,215,495,886,595,592,583,867,189,271,876}

Returns: 524794569
985

2

{788,757,772,756,110,172,123,749,889,801,121,771,108,803,122,825,896,774,885,762,763,771,873,872,800,885,777,956,796,171,779,128,774,171}

{788,757,772,765,110,172,123,795,889,801,121,773,117,803,122,825,896,777,889,762,763,771,873,872,800,886,777,960,797,172,779,128,774,171}

Returns: 139653569
572

2

{131,518,245,143,171,167,129,261,164,183,515,358,138,376,134,342,410,412,265,428,180,162,431,245}

{142,518,245,143,171,168,150,261,164,183,518,358,138,377,134,342,410,412,265,428,181,171,431,246}

Returns: 555583625
329

3

{141,186,66,217,213,193,171,180,212,268,202,225,187,143,220,125,106,188,64,281}

{141,186,66,218,213,193,174,181,212,268,225,225,187,143,220,146,199,188,64,281}

Returns: 727556192
561

1

{380,382,97,461,533,532,384,534,462,383,96,92,535,96,100,520,516,98}

{382,382,97,462,533,535,384,534,462,383,96,107,535,98,101,520,516,98}

Returns: 757466398
962

3

{951,510,504,929,570,580,828,627,637,949,928,825}

{951,510,504,929,570,580,828,627,637,953,928,825}

Returns: 925499097
894

1

{515,531,688,711,720,656,710,811,689,881}

{515,531,698,711,722,733,710,811,689,881}

Returns: 568617336
258

4

{83,75,30,27,218,67,210,64,72,215,23,221,108,211,215,211,27,109,75,35,31,108,76,217,32,34,77,26,84,240,216}

{83,75,30,28,218,67,221,85,72,217,36,221,108,213,215,214,31,109,77,35,31,109,76,217,32,34,77,26,84,240,216}

Returns: 224518905
328

4

{264,93,95,94,99,101,57,89,327}

{264,93,95,94,99,101,57,96,327}

Returns: 256650238
593

1

{305,453,331,548,474,327,330,439,174,286,505,551,455,304,284,550,140,549,306,164,456,475}

{305,453,331,551,474,337,330,444,174,286,505,551,455,304,284,550,185,549,306,175,456,475}

Returns: 859057804
730

4

{180,720,173,661,161,157,663,170,692,722,662,677,182,712,155,715,691,669,698,670,674,171,160,712,721,159,693,685,140,671,165,714}

{180,720,173,673,161,157,663,173,692,722,662,677,182,722,161,715,691,669,698,670,694,171,160,713,721,159,693,685,185,671,165,714}

Returns: 722924145
517

3

{492,98,496,491,401,420,496,463,106,393,497,499,102,103,427,423,463,466,467,393,500,424,458,491,96,94,464,399,108,110,428,106,465,96,103,107,112,461,104,395,99,109,400}

{492,98,497,491,401,428,496,463,111,401,497,499,102,105,427,423,464,466,467,393,500,424,470,492,97,115,464,399,108,110,428,106,465,99,103,107,112,461,104,395,99,109,400}

Returns: 420908537
453

3

{96,188,237,306,45,236,70,385,380,382,69,207,318,233,221,384,93,387,73,77,231,93,240,55,234,212,223,60,231,393,207,320,386,75,209}

{96,242,237,321,45,236,70,385,387,382,78,209,318,233,223,384,94,387,73,77,231,93,240,55,234,212,223,96,236,393,207,320,386,75,209}

Returns: 835465376
422

2

{56,61,57,75}

{56,61,57,76}

Returns: 227224498
201

3

{116,82,180,79,101,129,102,126,131,1}

{116,82,181,79,101,129,102,126,131,7}

Returns: 931462463
697

4

{523,533,181,269,488,397,142,281,451,531,278,268,390,241,536,525,517,138,522,143,271,523,403,526,463,199,453,452,200,402,581,175,391,593,520,199}

{526,538,181,269,488,397,142,281,470,531,283,269,391,241,536,525,517,138,522,143,273,523,403,526,463,201,453,453,200,402,583,177,391,593,531,199}

Returns: 239178008
226

4

{222,143,151,190,58,223,146,141,21,45,60,150,26,68,194,221,196,61,216,35,62,69,191,190,147,146,216,70,217,195,188,29,26,30,221,33}

{222,143,151,191,58,223,148,151,72,64,60,150,26,68,194,223,196,61,216,35,62,69,191,190,147,146,217,70,217,195,197,29,35,30,221,33}

Returns: 943497103
32

1

{24,23,3,27,7,6}

{24,23,8,27,7,6}

Returns: 382785
443

2

{326,321,38,146,327,259,39,56,271,41,270,112,144,145,261,126,131,216,121,39,135,134,50,113,323,221,263,262,318,220,119,46,51,54,47,260,136,54,321,259,57,217,224,267,115,325,214}

{326,322,60,146,327,264,41,56,271,41,270,122,144,145,261,148,133,230,121,39,135,134,50,113,323,221,263,262,328,220,119,51,51,54,47,260,136,57,321,259,57,217,224,267,115,325,272}

Returns: 935225043
302

3

{47,103,103,144}

{47,118,104,145}

Returns: 566143455
3

4

{2}

{2}

Returns: 4
888

4

{483,845,250,234,428,415,253,766,430,502,500,407,198,513,431,421,258,407}

{483,845,250,239,428,415,253,767,432,502,500,407,198,516,431,421,258,409}

Returns: 528764536
824

1

{221,583,271,101,184,228,613,193,613,379,383,194,309,191,64,615,384,584,644,546,643,377,310,614,322,189,660,316,100}

{221,585,274,101,222,228,615,193,613,379,383,194,310,191,266,615,384,584,644,546,643,379,310,614,322,194,660,316,100}

Returns: 591391491
921

2

{337,881,415,659,720,706,450,339,712,280,709,855,413,391,393,446,879,433,722,414,855,719,691}

{337,881,415,659,720,713,450,339,712,471,709,858,413,391,393,452,879,433,722,414,855,719,692}

Returns: 154705698
394

3

{384,136,391}

{384,136,391}

Returns: 436610431
281

2

{71,71,135,137,178,177,274,70,203,134,191,218,83,139,220,222,271,221,209,273,143,65,65,197,60,69,273,145,202,216,193,223,190,204,202,216,198}

{73,71,135,137,198,228,274,70,203,134,191,218,83,139,220,222,272,221,209,273,144,65,70,197,60,69,274,146,211,217,193,224,191,204,202,221,198}

Returns: 654126400
606

4

{283,492,579,142,25,137,11,572,121,468,479,141,571,26,2,143,118,66,302,467}

{288,492,579,142,25,137,160,572,121,468,479,141,571,26,314,143,118,74,302,467}

Returns: 630741763
123

2

{73,118,20}

{79,118,20}

Returns: 385240153
769

4

{277,345,714,273,236,656,284,560,224,682,666,740,559,547,655,224,741,237,568,550,654,348,233,278,715}

{278,345,719,285,236,656,284,560,224,682,667,741,559,547,655,226,741,237,568,550,654,348,233,278,716}

Returns: 298284402
397

2

{374,375,77,81,363,355,376,362,80,333,358,370,367,355,374,368,358,377,71,329,369,330,329,76,360,334,360,327,327}

{374,375,77,81,363,355,376,362,80,333,359,370,367,357,377,368,371,377,71,329,369,330,330,76,360,334,363,335,328}

Returns: 17771353
288

4

{266,26}

{266,26}

Returns: 910201367
929

3

{440,471,443,470,485,311,313,315,741,338,340,748,473,487,402,730,440,733,900,741,745,869,745,867,899,742,341,486,870,444,484,326,333,898,331,884,730}

{448,471,444,470,485,311,313,315,741,338,340,748,473,487,402,733,440,733,900,743,745,869,748,867,899,742,341,486,870,444,487,334,333,898,331,885,730}

Returns: 780788503
87

1

{43,79,75,22,78,23}

{43,80,75,22,78,23}

Returns: 324365249
156

1

{60,87,122,86,150,124,58,153,56,125,122,154,149,59,58,149,85}

{60,87,122,86,150,124,58,153,87,125,126,154,150,59,60,149,85}

Returns: 456988050
423

2

{188,267,83,370,197,227,87,57,342,278,23,34,239,236,103,66,63,372,322,228,237,54,36,220,94,240,271,272,277,204,225,265,164,98,194,98,37,56,37,230,102,197,40,96,35}

{191,267,90,370,198,227,87,57,343,278,144,46,239,236,103,66,63,372,322,238,237,70,36,227,94,240,272,272,277,204,225,268,337,98,207,99,39,56,37,230,102,197,40,104,35}

Returns: 340766497
602

3

{42,138,144,9,564,44,426}

{43,138,144,282,564,44,427}

Returns: 815120844
499

1

{405,410,405,256,177,165,176,257,236,236,399,471,150,173,397,261,166,169,165,219,239,233,260,409}

{407,410,405,256,177,166,176,257,236,237,399,471,150,173,411,261,166,169,165,262,239,245,260,409}

Returns: 641102605
560

1

{503,128,148,120,413,98,122,335,411,483,422,144,127,425,511,472,319}

{504,128,148,122,413,155,122,340,414,483,422,144,127,425,511,486,320}

Returns: 15694252
399

1

{378,385,68,8,4,66,73,37,88,32,32,377,77,63,382,67,263,373,366,387,78,75,256,87,7,373,257,256,364,36}

{378,385,68,8,95,66,73,37,88,33,37,377,77,68,390,67,263,373,366,387,78,75,257,87,47,378,257,256,364,36}

Returns: 626327670
523

4

{358,211,77,385,474,356,474,217,109,387,392,108,364,386,360,363,216,390,357,476,210,216,394,359,483,207,393,362,350,210,108,495,208,110,385,392,506,480,215,475}

{358,211,222,387,474,360,484,217,109,387,392,110,364,386,360,363,216,390,357,476,211,217,394,359,483,207,393,362,364,210,108,495,208,110,385,393,506,480,215,475}

Returns: 796442423
127

4

{43,114,28,95,38,25,119,103,36,41,101,25,99,36,40,21,104,98,83,102,120,42,115,42,44,39,27}

{43,114,28,95,38,28,119,103,37,41,101,25,99,41,40,87,104,104,83,102,120,42,115,44,44,39,27}

Returns: 629073675
476

2

{32,125,34,202,424,238,269,237,163,245,274,277,109,41,171,191,206,238,35,422,163,419,269,241,229,31,162,105,36,236,175,248,242,246,120,165,231}

{32,125,34,207,424,238,270,237,163,245,274,277,109,41,172,298,206,239,35,422,165,424,269,242,229,31,162,178,36,250,175,248,242,246,120,165,231}

Returns: 967979453
586

3

{432,186,394,208,530,233,390,404,183,185,535,228,427,425,180,228}

{432,186,394,209,530,233,390,404,185,185,535,228,427,439,180,240}

Returns: 486415788
435

4

{398,391,92,414,400,387,95,306,420,412,421,391,305,94,399,420,302,90}

{398,394,92,414,400,400,95,306,420,412,421,392,305,94,399,422,302,90}

Returns: 795971034
681

4

{314,386,628,552,429,633,484,453,539,303,448,489,550,297,296,487,302,286,454,323,628,306,481,291,386,541,310,281,322,490,553,451,306,630,437,489,491,629,632}

{314,386,630,552,429,633,492,453,541,303,448,489,554,297,305,487,302,286,454,323,628,314,531,291,388,541,310,286,322,490,553,451,308,630,472,490,491,629,632}

Returns: 298810110
452

3

{404,56,408,44,56,304,98,392,393,360,281,368,310,390,371,42,277,67,95,60,272,389,409,312,94,41,378,42,306,280,376,380,404,369,390,377,268,241,305,278,405,304,43,94}

{404,56,408,44,60,304,98,392,393,382,281,368,310,391,371,42,278,67,95,60,272,394,409,312,96,105,378,44,306,280,377,380,409,369,390,377,268,315,305,278,405,306,43,94}

Returns: 253095194
859

4

{702,699,669,60,675,708,93,589,49,94,228,224}

{702,699,669,61,675,708,93,589,51,94,228,224}

Returns: 334167009
869

2

{108,650,91,649,97,648,60,98,643,643,111,331,323,65,304}

{108,650,102,649,97,648,65,98,644,651,111,331,333,65,304}

Returns: 487009417
993

2

{50,243,52,227,873,236,622,876,53,280}

{51,244,52,253,873,236,622,876,53,280}

Returns: 241763137
571

2

{130,396,188,188,482,152,336,153,204,331,250,136,198,380,96,149,204,381,379,269,132,159,395,137,467,483,453,332,389}

{139,396,220,188,482,152,336,155,205,331,250,136,199,380,282,149,204,381,379,269,133,159,395,137,474,483,453,332,389}

Returns: 244025193
161

4

{90,90,50,20,77,141,86,91,78,88,21}

{90,91,50,21,77,141,86,91,78,88,21}

Returns: 665795844
390

3

{357}

{357}

Returns: 968454763
777

3

{255,664}

{255,672}

Returns: 679196344
790

1

{360,358,335,506,507,734,701,703,239,746,247,705,361,254,504,500,339,373,707,706}

{360,358,340,506,507,734,744,704,239,746,247,705,361,254,504,507,339,373,707,706}

Returns: 355092027
449

2

{387,173,50,62,292,288,161,159,252,254,239,51,63,245,140,271,15,288,162,293,262,389,49,139,20,58,12,246,137,19,242,9,18,167}

{387,173,50,62,292,293,161,159,252,254,276,51,63,245,140,271,15,289,162,293,263,389,49,139,20,58,21,246,150,19,247,66,18,167}

Returns: 871050673
529

1

{482,261,446,242,452,510,248,243,508,225,492,444,332,404,436,508,451,492}

{499,261,446,242,452,510,252,243,510,226,493,444,332,404,436,508,451,492}

Returns: 231551553
427

4

{389,178}

{390,178}

Returns: 483825950
132

2

{93,116,48,107,119,62,92,120,115}

{93,116,48,110,120,97,92,120,115}

Returns: 709447174
310

2

{254,98,29,102,256,50,48,103,44,186,83,27,111,30,24,42,285,105,14,181,38,47,52,185,32,187,46,282,28,104,257,92,255}

{254,105,29,102,256,50,48,103,44,186,140,27,111,30,32,42,285,105,53,181,47,47,52,185,32,187,46,282,28,104,257,92,255}

Returns: 868729052
437

3

{388,89,88,63,360,393,39,389,394,102,361,136,101,60,391,388,86,385,64,429,431,385,134,60,55,65,338,430,83,430,135,342}

{388,89,88,63,360,393,137,389,394,102,361,136,101,65,391,389,86,385,64,429,431,394,134,60,92,65,362,431,83,430,135,342}

Returns: 562200257
500

3

{445,443,66}

{445,443,66}

Returns: 149835825
988

1

{685,233,660,795,423,742,671,806,225,676,564,562,225,676,405,801,683,763,545,762,617,800,409,799,226,661,673,557,672,557,684,616,227,678,422,762,610,228,660,421,227,409,420}

{685,233,660,800,423,809,671,806,225,678,564,562,226,677,424,801,683,763,618,763,617,800,409,799,226,661,673,558,672,564,684,616,228,678,422,762,610,228,661,421,227,410,420}

Returns: 390053813
158

4

{111,56,75,93,91,32}

{111,56,75,93,94,32}

Returns: 911163447
485

2

{461,165,162,449,459,460,88,213,223,93,224,125,169,219,179,180,162,31,116,225,28,451,212,34,217,44,92,227,211,45,88,164,217,20,43,115,90,452,448,182}

{461,165,166,449,461,460,89,213,224,93,224,125,169,219,180,180,162,31,116,225,45,451,212,34,217,44,92,227,211,45,94,164,220,132,43,117,90,452,453,182}

Returns: 982472319
492

3

{82,280,430,137,431,398,91,281,420,115,265,137,90,138,134,66,81,440,407,438,276,271,270,126}

{82,283,434,139,431,398,91,281,427,116,265,137,90,138,134,147,92,440,409,438,276,271,271,136}

Returns: 943649644
159

2

{83,73,59,118,37,90,116,112,82,37,119,147,146,138,74,146,84,82,74,75,47,46,112,138,42,59,34,48,139}

{83,73,69,118,37,90,116,119,84,38,119,147,146,138,75,147,84,82,74,75,47,46,112,139,42,93,48,48,139}

Returns: 111713773
787

3

{724,748,66,40,484,62,512,734,733,733,749,774,723,64,567,485,48,514,735,49,723,568,483,51,393,769,767,511,766,52,725,481,64,456,513}

{724,748,66,88,484,62,512,734,735,733,749,780,725,66,567,485,54,514,735,49,723,568,483,51,569,769,768,512,769,52,725,481,64,485,513}

Returns: 535358415
392

4

{366,23,321,381,386,52,56,46,19,46,366,19,326}

{375,23,326,381,386,52,56,47,20,46,366,29,326}

Returns: 695825880
215

4

{177,9,178,46,59,39,60,52,8}

{177,9,178,48,59,63,60,52,10}

Returns: 718989916
109

4

{55,88,103,48,106,49,52,51,102,107,101,56,53,87,106,85,85}

{55,88,103,57,107,49,52,52,102,107,101,56,53,87,106,86,88}

Returns: 744264248
212

4

{113,123,164,1,163,119,107,165,164,181,162,159,182,117,106,111,159,108}

{117,123,165,47,163,120,111,165,164,181,162,166,182,117,126,111,159,108}

Returns: 96291130
349

2

{303,203,316,130,156,199,267,155,184,302,307,265,311,150,151,195,133,307,133,149,145,148,134,152,266,318,190,198,263,259}

{303,203,316,157,156,199,267,155,271,302,307,265,311,150,151,195,134,319,133,149,150,148,134,152,266,318,190,198,263,260}

Returns: 33871844
653

3

{367,356,567,57,42,82,35,573,566,69,527,53,577,382,39,580,55,71,525,581,573,384,566}

{367,386,567,57,42,82,88,581,567,69,527,53,577,382,42,580,55,71,525,581,574,385,566}

Returns: 441160418
467

3

{325,317,120,455,119,188,74,133,268,126,318,197}

{325,317,120,456,135,188,75,133,326,126,318,198}

Returns: 736569856
869

2

{79,673,110,72,89,689,104,652,548,671,530,550,279,676,69,223,202,743,223,102,696,79,285,813,100,89,683,826,679,283,278,809,82,725,723,217,280,548,674}

{79,673,110,72,91,689,104,754,548,698,530,550,279,676,82,223,202,743,224,102,696,80,285,814,100,89,683,832,680,283,278,820,82,725,723,217,280,549,683}

Returns: 526255332
929

3

{220,92,231,896,668,517,444,669,68,438,450,586,867,847,436,692,443,694,891,87,894,452,428,867,555,217,446,439,872,80,93,897,544,520,583,655,437,88,523,518,554,217,440}

{220,92,231,896,671,517,444,669,95,438,450,586,867,865,440,692,444,694,897,87,894,452,456,869,555,217,446,439,872,83,93,897,545,520,583,655,437,88,523,518,554,218,440}

Returns: 611973076
653

2

{247,539}

{259,539}

Returns: 67193615
669

1

{467,510,566,179,449,492,442,464,343,494,175,543,567,466,176}

{467,510,566,180,449,493,443,467,352,494,175,573,567,466,176}

Returns: 455145776
396

1

{23,66,83,277,230,77,70,227,231,226,225,228,79,74,211,185,72,247,198}

{23,70,83,277,230,83,70,227,231,230,225,228,79,74,212,198,75,247,198}

Returns: 168826735
766

4

{671,588,279,283,276,247,590,682,677,291}

{671,591,279,283,276,294,590,682,677,291}

Returns: 848482769
556

2

{440,102,510,510,512,511,382,100,103,105,92,363,379,343,344,92,102,364,444,87,519,519,520,442,97,441,367,365,511,104,384,368,440,342,101,445,366,93,345,342,383,100,522,443,513,434}

{440,104,510,524,512,512,382,101,103,105,93,368,379,343,344,92,102,364,444,107,519,520,520,442,97,441,367,365,511,104,384,368,441,342,101,445,366,93,345,345,383,100,522,443,513,445}

Returns: 865208021
873

4

{347,629,664,197,747,469,623,449,754,668,631,208,746,621,755,180,752}

{350,629,664,204,749,469,623,477,754,670,631,209,746,621,755,180,752}

Returns: 27381671
661

1

{238,589,566,451,20,205,11,567,56,455,552,549,564,563,213,20,237,21,224,550,212,563,262,546,44,231,209,546,44,55,216,226,227,51}

{238,589,566,451,20,265,58,567,56,455,592,549,564,567,224,21,237,21,224,550,212,563,262,546,45,239,227,551,44,55,218,226,227,51}

Returns: 225708198
793

3

{570,564,553,657,647,615,686,116,101,562,122,656,503,696,558,628,526,693,121,697,530,537,126,656,690,629,692,535,577,690,129}

{570,564,566,657,647,620,698,116,132,563,122,657,589,696,558,628,539,693,121,697,530,537,126,656,690,629,692,535,577,691,129}

Returns: 664133310
832

3

{515,348,780,455,786}

{515,348,789,455,786}

Returns: 348787885
478

4

{138,216,96,225,211,160,125,227,178,147,188,186,398,117,219,141,91,218,212,88,177,398,135,123,81,399,220,98,124,89,135,227,95,95,90,211,214,157,280,97,177,280,123}

{138,220,96,225,214,160,125,228,178,231,188,186,398,144,219,141,91,218,212,91,178,399,135,125,98,399,220,98,124,90,136,227,95,96,90,211,214,192,280,97,177,282,123}

Returns: 786215868
747

1

{32,84,587,81,688,79,68,81,79,577,708,709,33,690,693,692,148,694,33,44,686,686,707,42,68,692,155,685,704,719,719}

{86,84,587,83,688,80,69,81,79,590,708,709,44,690,693,692,148,694,35,44,686,688,707,42,68,693,155,694,704,719,720}

Returns: 973196527
478

1

{442,310,374,361,424,298,351,358,420,448,306,300,309,443,446,372,372,416,308,307}

{442,310,374,361,424,298,351,358,420,448,309,300,309,443,446,372,374,425,308,307}

Returns: 450596258
583

4

{71,461,229,451,74,457,67,155,241,472,229,462,115,308,9,437,452,575,576,52,456,454,116,113,160,462,65,463,309,449,308,73,118,341,578}

{71,461,231,451,74,457,67,161,241,472,242,463,115,308,353,473,452,575,576,130,456,454,118,113,160,462,74,463,309,449,309,73,118,341,578}

Returns: 613277561
193

2

{166,146}

{166,148}

Returns: 845334623
342

4

{54,58,15,52,274,53,57,333,30,271,309,316,29,309,20,334,61,325,324,55,314,335,273,59,271}

{54,58,64,52,274,53,57,333,30,274,311,316,29,316,30,334,61,325,324,55,314,335,273,59,271}

Returns: 623006403
803

2

{615,604,99,712,755,87,104,715,534,614,721,724,111,748,746,720,749,547,530,725,104,546,723,749,539,720,108,534,753,537,621,549,100,754,99,717,536,87}

{615,622,100,725,755,87,104,717,534,615,721,724,111,748,760,722,750,547,551,725,105,546,723,749,539,720,108,539,753,537,621,549,100,754,99,717,536,88}

Returns: 502853702
55

4

{17,19,49,40,51,16,39,47}

{17,19,49,40,51,16,41,47}

Returns: 628623982
719

4

{520,103,76,320,302,637,75,62,589,156,291,137,174,136,304,319,554,291,320,587,105,65,134,133,264,174,139,77,305,325,61,569,157,160,63,73,109}

{590,106,76,320,302,637,75,62,589,156,305,137,174,136,304,319,554,292,322,587,105,65,134,142,328,176,139,77,305,325,61,569,157,160,64,78,109}

Returns: 543541508
421

3

{127,331,362,368,345,248,128,129,134,358}

{128,331,362,368,345,248,128,129,134,358}

Returns: 679696227
686

3

{246,143,245,426,670,250,251,429,138,125,258,434,288,134,659,289,140,417,128,252,435,288,425}

{249,143,295,426,670,250,251,430,138,146,258,434,288,140,659,289,140,418,128,252,435,289,427}

Returns: 396918950
999999999

1

{44986140,467984968,59800166,539307498,260432273,628056296,148857409,215298819,657499777,1,244860014,94260729,525078192,163365010,178249928,365072675,270675851,580505785,592933737,725156532,690775717,402753096,558229740,482223133,679312712,384035584,113015785,435193054,18574526,196560981,708400119,349576643,77543581,131540525,1,450879035,568268416,667677762,339435253,647467305,609587910,284254517,315198198,325264520,497712942,298931615,417296466,513875138,34481498,230635117}

{59800165,482223132,77543580,558229739,270675850,647467304,163365009,230635116,667677761,18574525,260432272,113015784,539307497,178249927,196560980,384035583,284254516,592933736,609587909,999999995,708400118,417296465,568268415,497712941,690775716,402753095,131540524,450879034,34481497,215298818,725156531,365072674,94260728,148857408,999999995,467984967,580505784,679312711,349576642,657499776,628056295,298931614,325264519,339435252,513875137,315198197,435193053,525078191,44986139,244860013}

Returns: 75827945
999999999

2

{59800166,215298819,435193054,113015785,482223133,230635117,467984968,725156532,647467305,163365010,539307498,708400119,284254517,628056296,580505785,270675851,558229740,148857409,525078192,609587910,667677762,497712942,18574526,402753096,34481498,657499777,568268416,77543581,131540525,679312712,44986140,244860014,298931615,94260729,417296466,384035584,178249928,365072675,325264520,513875138,349576643,690775717,592933737,1,450879035,196560981,260432273,339435253,315198198,1}

{77543580,230635116,450879034,131540524,497712941,244860013,482223132,999999995,657499776,178249927,558229739,725156531,298931614,647467304,592933736,284254516,568268415,163365009,539307497,628056295,679312711,513875137,34481497,417296465,44986139,667677761,580505784,94260728,148857408,690775716,59800165,260432272,315198197,113015784,435193053,402753095,196560980,384035583,339435252,525078191,365072674,708400118,609587909,999999995,467984967,215298818,270675850,349576642,325264519,18574525}

Returns: 375723305
999999998

3

{94260729,196560981,384035584,525078192,1,34481498,497712942,178249928,667677762,148857409,349576643,690775717,325264520,1,657499777,628056296,230635117,284254517,609587910,450879035,44986140,244860014,725156532,215298819,708400119,568268416,482223133,77543581,435193054,679312712,315198198,365072675,59800166,113015785,270675851,580505785,18574526,513875138,339435253,260432273,402753096,131540525,647467305,592933737,539307498,163365010,467984968,558229740,298931615,417296466}

{113015784,215298818,402753095,539307497,999999995,44986139,513875137,196560980,679312711,163365009,365072674,708400118,339435252,18574525,667677761,647467304,244860013,298931614,628056295,467984967,59800165,260432272,999999995,230635116,725156531,580505784,497712941,94260728,450879034,690775716,325264519,384035583,77543580,131540524,284254516,592933736,34481497,525078191,349576642,270675850,417296465,148857408,657499776,609587909,558229739,178249927,482223132,568268415,315198197,435193053}

Returns: 259929239
999999999

4

{647467305,417296466,679312712,384035584,163365010,44986140,298931615,18574526,435193054,568268416,365072675,131540525,260432273,592933737,558229740,94260729,667677762,59800166,497712942,580505785,230635117,482223133,628056296,178249928,77543581,196560981,349576643,270675851,513875138,325264520,113015785,539307498,708400119,215298819,1,148857409,450879035,467984968,315198198,34481498,1,284254517,609587910,244860014,402753096,339435253,525078192,725156532,690775717,657499777}

{657499776,435193053,690775716,402753095,178249927,59800165,315198197,34481497,450879034,580505784,384035583,148857408,270675850,609587909,568268415,113015784,679312711,77543580,513875137,592933736,244860013,497712941,647467304,196560980,94260728,215298818,365072674,284254516,525078191,339435252,131540524,558229739,725156531,230635116,18574525,163365009,467984967,482223132,325264519,44986139,999999995,298931614,628056295,260432272,417296465,349576642,539307497,999999995,708400118,667677761}

Returns: 472341341
999999999

5

{690775717,215298819,435193054,592933737,34481498,349576643,450879035,18574526,230635117,77543581,131540525,284254517,384035584,628056296,59800166,365072675,513875138,497712942,417296466,298931615,244860014,568268416,580505785,270675851,148857409,1,647467305,315198198,679312712,196560981,657499777,260432273,558229740,1,609587910,539307498,44986140,163365010,725156532,339435253,113015785,402753096,467984968,667677762,482223133,708400119,525078192,178249928,325264520,94260729}

{708400118,230635116,450879034,609587909,44986139,365072674,467984967,34481497,244860013,94260728,148857408,298931614,402753095,647467304,77543580,384035583,525078191,513875137,435193053,315198197,260432272,580505784,592933736,284254516,163365009,999999995,657499776,325264519,690775716,215298818,667677761,270675850,568268415,18574525,628056295,558229739,59800165,178249927,999999995,349576642,131540524,417296465,482223132,679312711,497712941,725156531,539307497,196560980,339435252,113015784}

Returns: 133102405
1000000000

1

{1,343750001,250000001,156250001,250000001,687500001,937500001,500000001,906250001,500000001,625000001,812500001,593750001,468750001,375000001,62500001,625000001,125000001,218750001,375000001,500000001,750000001,31250001,750000001,875000001,843750001,187500001,312500001,812500001,750000001,187500001,500000001,968750001,93750001,718750001,250000001,406250001,437500001,562500001,875000001,781250001,531250001,1,375000001,281250001,1,1,875000001,62500001,1}

{125000000,375000000,281250000,187500000,500000000,750000000,968750000,1000000000,937500000,562500000,656250000,843750000,625000000,500000000,437500000,93750000,687500000,187500000,250000000,500000000,531250000,875000000,62500000,812500000,937500000,875000000,218750000,375000000,875000000,1000000000,250000000,750000000,1000000000,125000000,750000000,375000000,437500000,500000000,593750000,906250000,812500000,562500000,250000000,406250000,312500000,62500000,31250000,1000000000,125000000,500000000}

Returns: 511323738
1000000000

2

{125000001,718750001,437500001,750000001,500000001,187500001,250000001,750000001,250000001,625000001,312500001,250000001,1,312500001,468750001,625000001,31250001,1,375000001,1,937500001,437500001,531250001,687500001,500000001,656250001,500000001,937500001,500000001,281250001,906250001,875000001,156250001,187500001,93750001,843750001,875000001,968750001,625000001,343750001,62500001,687500001,125000001,562500001,750000001,781250001,125000001,812500001,500000001,812500001}

{156250000,750000000,468750000,781250000,750000000,218750000,500000000,1000000000,375000000,656250000,375000000,281250000,250000000,343750000,500000000,750000000,62500000,31250000,437500000,125000000,968750000,500000000,562500000,750000000,562500000,687500000,531250000,1000000000,625000000,312500000,937500000,937500000,187500000,250000000,125000000,875000000,1000000000,1000000000,687500000,375000000,93750000,718750000,250000000,625000000,875000000,812500000,187500000,843750000,1000000000,875000000}

Returns: 563749985
1000000000

3

{750000001,750000001,125000001,906250001,468750001,375000001,250000001,562500001,250000001,1,1,437500001,625000001,187500001,218750001,562500001,125000001,687500001,62500001,250000001,718750001,843750001,312500001,812500001,500000001,750000001,500000001,1,875000001,62500001,812500001,500000001,937500001,1,250000001,750000001,93750001,625000001,156250001,500000001,593750001,312500001,281250001,875000001,125000001,437500001,375000001,625000001,968750001,500000001}

{812500000,1000000000,187500000,937500000,500000000,406250000,500000000,593750000,281250000,500000000,125000000,500000000,656250000,218750000,250000000,625000000,250000000,750000000,125000000,312500000,750000000,875000000,375000000,843750000,625000000,781250000,750000000,62500000,906250000,93750000,875000000,531250000,968750000,250000000,375000000,875000000,125000000,687500000,187500000,562500000,625000000,343750000,312500000,937500000,156250000,468750000,500000000,750000000,1000000000,1000000000}

Returns: 473203235
1000000000

4

{625000001,1,375000001,375000001,687500001,156250001,812500001,312500001,687500001,875000001,187500001,750000001,62500001,531250001,718750001,250000001,781250001,625000001,500000001,250000001,343750001,812500001,187500001,562500001,1,125000001,281250001,125000001,625000001,500000001,937500001,125000001,1,406250001,250000001,218750001,1,437500001,593750001,875000001,875000001,375000001,750000001,62500001,93750001,31250001,656250001,468750001,500000001,906250001}

{687500000,500000000,500000000,406250000,750000000,187500000,843750000,343750000,718750000,906250000,218750000,875000000,125000000,562500000,750000000,281250000,812500000,656250000,562500000,375000000,375000000,875000000,250000000,593750000,31250000,156250000,312500000,250000000,750000000,1000000000,968750000,187500000,250000000,437500000,500000000,250000000,62500000,468750000,625000000,937500000,1000000000,437500000,781250000,93750000,125000000,62500000,687500000,500000000,625000000,937500000}

Returns: 746841523
1000000000

5

{937500001,156250001,1,656250001,250000001,687500001,312500001,250000001,562500001,500000001,593750001,781250001,343750001,500000001,625000001,500000001,250000001,375000001,500000001,531250001,875000001,562500001,31250001,406250001,375000001,812500001,93750001,687500001,500000001,62500001,1,187500001,937500001,1,468750001,750000001,312500001,812500001,437500001,625000001,1,750000001,843750001,625000001,375000001,875000001,1,750000001,250000001,968750001}

{968750000,187500000,250000000,687500000,281250000,750000000,343750000,312500000,625000000,1000000000,625000000,812500000,375000000,531250000,687500000,750000000,375000000,500000000,625000000,562500000,937500000,593750000,62500000,437500000,406250000,875000000,125000000,718750000,562500000,93750000,62500000,250000000,1000000000,125000000,500000000,781250000,375000000,843750000,468750000,750000000,31250000,812500000,875000000,656250000,437500000,1000000000,500000000,1000000000,500000000,1000000000}

Returns: 127222216
1000000000

1

{499931702,499644271,497169279,320749948,499805164,498484043,496540230,499954279,456004518,499975514,165289256,476962364,499840588,498759671,380006163,491924537,446227745,499944119,499869572,419673547,498985185,90909091,499963423,499456527,464003696,499761867,499708949,499916525,498147164,499970073,499979966,487382090,499565221,497683955,226145755,401823224,499895657,493539629,499335756,280916604,1,489905672,484578111,434278356,471202956,494831703,495771393,499169696,481151025,353340866}

{500068299,500355730,502830722,679250053,500194837,501515958,503459771,500045722,543995483,500024487,834710745,523037637,500159413,501240330,619993838,508075464,553772256,500055882,500130429,580326454,501014816,909090910,500036578,500543474,535996305,500238134,500291052,500083476,501852837,500029928,500020035,512617911,500434780,502316046,773854246,598176777,500104344,506460372,500664245,719083397,1000000000,510094329,515421890,565721645,528797045,505168298,504228608,500830305,518848976,646659135}

Returns: 57022508
1000000000

2

{497683955,498985185,499456527,401823224,499979966,498147164,491924537,90909091,165289256,489905672,499805164,493539629,499335756,380006163,226145755,499944119,499963423,1,499970073,487382090,446227745,498759671,434278356,456004518,494831703,499916525,499708949,499975514,320749948,498484043,499840588,499761867,496540230,499954279,499169696,499869572,499644271,497169279,280916604,499931702,464003696,476962364,353340866,495771393,484578111,499565221,471202956,499895657,419673547,481151025}

{502316046,501014816,500543474,598176777,500020035,501852837,508075464,909090910,834710745,510094329,500194837,506460372,500664245,619993838,773854246,500055882,500036578,1000000000,500029928,512617911,553772256,501240330,565721645,543995483,505168298,500083476,500291052,500024487,679250053,501515958,500159413,500238134,503459771,500045722,500830305,500130429,500355730,502830722,719083397,500068299,535996305,523037637,646659135,504228608,515421890,500434780,528797045,500104344,580326454,518848976}

Returns: 889810081
1000000000

3

{497683955,499916525,476962364,499840588,496540230,499644271,499954279,401823224,499931702,446227745,493539629,499805164,499761867,494831703,499979966,499970073,498484043,481151025,226145755,498759671,471202956,498985185,491924537,487382090,90909091,1,499708949,380006163,497169279,353340866,280916604,495771393,165289256,434278356,464003696,499335756,499565221,498147164,499869572,320749948,484578111,499456527,456004518,419673547,499975514,499963423,499944119,489905672,499895657,499169696}

{502316046,500083476,523037637,500159413,503459771,500355730,500045722,598176777,500068299,553772256,506460372,500194837,500238134,505168298,500020035,500029928,501515958,518848976,773854246,501240330,528797045,501014816,508075464,512617911,909090910,1000000000,500291052,619993838,502830722,646659135,719083397,504228608,834710745,565721645,535996305,500664245,500434780,501852837,500130429,679250053,515421890,500543474,543995483,580326454,500024487,500036578,500055882,510094329,500104344,500830305}

Returns: 552207022
1000000000

4

{481151025,489905672,493539629,380006163,353340866,494831703,498985185,498759671,499916525,165289256,280916604,497683955,499979966,434278356,499970073,499335756,471202956,1,498147164,498484043,496540230,499869572,476962364,499895657,495771393,491924537,499840588,499963423,499944119,90909091,499805164,484578111,499975514,487382090,401823224,499565221,499931702,499708949,499456527,464003696,499169696,226145755,499954279,446227745,499644271,419673547,320749948,499761867,456004518,497169279}

{518848976,510094329,506460372,619993838,646659135,505168298,501014816,501240330,500083476,834710745,719083397,502316046,500020035,565721645,500029928,500664245,528797045,1000000000,501852837,501515958,503459771,500130429,523037637,500104344,504228608,508075464,500159413,500036578,500055882,909090910,500194837,515421890,500024487,512617911,598176777,500434780,500068299,500291052,500543474,535996305,500830305,773854246,500045722,553772256,500355730,580326454,679250053,500238134,543995483,502830722}

Returns: 738402458
1000000000

5

{499761867,499869572,499335756,499565221,353340866,498985185,487382090,446227745,1,165289256,498759671,494831703,401823224,499975514,499805164,471202956,498484043,499169696,499944119,493539629,499644271,434278356,90909091,456004518,280916604,499708949,499931702,484578111,499840588,491924537,495771393,499456527,497683955,380006163,464003696,497169279,481151025,499979966,499895657,499954279,320749948,499970073,226145755,498147164,419673547,499916525,489905672,499963423,496540230,476962364}

{500238134,500130429,500664245,500434780,646659135,501014816,512617911,553772256,1000000000,834710745,501240330,505168298,598176777,500024487,500194837,528797045,501515958,500830305,500055882,506460372,500355730,565721645,909090910,543995483,719083397,500291052,500068299,515421890,500159413,508075464,504228608,500543474,502316046,619993838,535996305,502830722,518848976,500020035,500104344,500045722,679250053,500029928,773854246,501852837,580326454,500083476,510094329,500036578,503459771,523037637}

Returns: 379718018
788725501

1

{115831791,140009278,115825782,115825849,95913666,115825848,768638483,115827094,115826780,115825827,115831839,115825784,115825846,115825866,115825819,115831230,95753070,115873634,115827899,115825874,115825709,115825847,115825783,115922573,115825854,115824837,115825825}

{115831825,140058604,115825784,115825849,131987388,115825848,781366553,115827840,115826786,115825827,115831840,115825784,115825846,115825866,115825819,115831346,140294818,115875088,115827899,115825874,115825709,115825847,115825783,115927276,115825854,115829570,115825825}

Returns: 18617722
319322928

3

{45932836,45932839,45932691,45932683,45933310,317244228,45932698,45935049,45932836,45932631,45933325,45609311,45932681,45933341,45932809,45932733,45934097,45932727,45938798,45939863,46669165,45932837,45932666,45932731,45933340,45932691,45932838,45938953,45932841,45932331}

{45932838,45932841,45932695,45932687,45933343,318392890,45932699,45935832,45932836,45933539,45933325,47700181,45932701,45933341,45932822,45932733,45934104,45932731,45938837,45960823,46809738,45932837,45932850,45932731,45933340,45932692,45932838,45939014,45932841,45934125}

Returns: 747351171
603852730

2

{80356903,80375926}

{80356903,80376112}

Returns: 501393031
514516069

4

{252170168,252171276,252170160,252170161,513068777,252170316,252170152,251851816,252170344,252170153,252170157,252170241,252170325,252170343,252184792,253345536,253287266,253132546,252170168,252171226,252190425,252170154,252170326,252170638,252007508,298151178,252171059,252170306,435013836,252170151}

{252170168,252171303,252170160,252170161,513510680,252170327,252170152,253352305,252170344,252170153,252170157,252170241,252170325,252170343,252189911,253348165,253319497,253274158,252170169,252171274,252193764,252170154,252170326,252170666,252529718,298275855,252171193,252170306,480903508,252170151}

Returns: 617832997
814031100

2

{169188416,170449461,170449557,170450595,805255466,170449496,170544690,170378643,181448484,170519836,213411548,170449495,183794587,190829313,170449481,308737316,170449509,170449497,170449449}

{184052406,170449465,170449558,170450655,808648734,170449496,170545877,170663827,183396133,170526927,215895457,170449495,183919750,203224774,170449509,313376043,170449509,170449497,170449452}

Returns: 702632223
470354327

3

{152230771,152229472,152229988,152229999,271537105,152229997,152230032}

{152231174,152231329,152229991,152229999,272339211,152230003,152230032}

Returns: 166012417
112112035

1

{27613604,99330922,27613670,27613735,27613667,28111984,34728048,27613734,27613610,27613663,27613611,83984686,27613488,27611773,27611770,27613604}

{27613607,101613029,27613671,27613735,27613667,28118242,34916491,27613734,27613610,27613663,27613611,92687462,27613755,27611773,27611774,27613612}

Returns: 66615423
572656612

1

{72812899,72810946,77485452,72811054,72896128,72811050,72811227,106604568,102091999,72811153,72811229,72811141,72811050,72293769,72811266,72811098,72811145,72810888,72811092,72811096,72811064,72811062,72811158,72811090,72811093,72811221,72810920,396988559}

{72812901,72810946,78341716,72811054,72896824,72811055,72811228,107129789,104091430,72811158,72811229,72811142,72811051,75142351,72811267,72811098,72811145,72811317,72811092,72811096,72811064,72811062,72811158,72811091,72811093,72811221,72810940,401872639}

Returns: 294580360
839576741

2

{214438236,215465775,220007825,215257664}

{219064669,215477758,220914007,215257664}

Returns: 87035753
450094128

3

{36950652,36950394,36995885,36950492}

{36950652,36950395,36995916,36950492}

Returns: 506132142
171227049

3

{56739277,56739083,56739304,56739295,56739094,56739113,56739117,56735015,56739314,57001782,56750735,56739317,67881438,56739083,56739127,148258429,56739305,61415985,56739226,56744538,56746568,56739289,56739281,56739291,56739124,56739288,56739112,56739313,56980260,168454059,56739118,56904835,56739061,56739088,56739097,56739081,56739306,56739287,56739081,56739285,64359690,56739283}

{56739308,56739085,56739304,56739295,56739094,56739114,56739117,56750763,56739314,57001827,56750755,56739317,72350444,56739086,56739127,163899453,56739305,61684226,56739228,56746330,56746710,56739289,56739296,56739291,56739124,56739288,56739112,56739313,56982170,169384757,56739124,56931195,56739099,56739088,56739097,56739082,56739306,56739287,56739081,56739287,65325541,56739283}

Returns: 554497294
26485948

1

{2948685,2948809,8505290,2948274,2955687,2948768,2948690,2948291,2948769,3207695,2948197,2948284,2952610,2949586,2948316,2948320,2948318,2947717,2948328,2948686,2948695,2948209,2947306,2948210,2948751,2948756,2948284,2948173,2948749,2948767,2948708,2948751,2948695,2948702,2948326,2948301,2948709,2948762,2948286,8091806,6813197,2947610}

{2948712,2949489,8521867,2948335,2955713,2948768,2948691,2948291,2948769,3226986,2948198,2948289,2954534,2949592,2948317,2948320,2948318,2948789,2948328,2948687,2948696,2948209,2955744,2948210,2948752,2948756,2948284,2948211,2948749,2948767,2948708,2948751,2948695,2948702,2948326,2948301,2948709,2948769,2948288,8352826,7175715,2949628}

Returns: 887617630
310209597

4

{85523805}

{85523851}

Returns: 842530993
531528037

3

{90786570,96026194,92208239,90810726,90812283,90810782,90810764,90986093,90811161,91004001,90810909,90810772,90813110,107751720,90810781,90817540,307504639,90785780,90810763,90810777,90812838,90936077,453864806,96865707,90810778,90854550,90859656,90810803,90811401,90810729}

{90959856,96211599,92476803,90810726,90812625,90810782,90810766,90993675,90811202,91010118,90810913,90810772,90813143,107829974,90810781,90817570,378839993,91027212,90810772,90810777,90812951,90940059,466159484,101165264,90810778,90855091,90888345,90810803,90811437,90810729}

Returns: 292487415
7594579

1

{2412492,2412716,2412475,6705680,2412476,2412552,2418174,2412507,2412368,2412482,2411113,2412367,2926474,2456503,2412271,2412282,2412266,2412358,2412281,2412523,2412248,2412450,2412489,2424632,2412378,2412681,2412283,2326138,2411789,2412245,6033309,2412363,2417255,2412480,2413049,2412488,2412280,2412495,2412461,2462509,2412455,2412387,2412270,2412480}

{2412492,2412720,2412475,6706761,2412476,2412568,2418200,2412519,2412368,2412482,2414286,2412367,2932856,2462147,2412271,2412282,2412266,2412389,2412281,2412524,2412248,2412461,2412489,2425915,2412378,2412693,2412283,2942258,2412721,2412283,6200544,2412363,2417664,2412480,2413652,2412496,2412281,2412495,2412461,2462532,2412455,2412387,2412270,2412481}

Returns: 530052916
581022481

3

{96159945,95885298,95882013,95882014,95882438,453171971,95880401,95894201,110665612,95882011,95968724,95882362,96046732,95882100,95868328,95882002,95882070,95886973,95882080,95882076,95897846,95882006,95882003,95882129,95966096,95881681}

{96160628,95886506,95882013,95882014,95882438,537368954,95898719,95896041,112389030,95882011,95972979,95882366,96156168,95882120,95977523,95882002,95882084,95886975,95882080,95882076,95898017,95882006,95882003,95882129,95968464,95882889}

Returns: 84399564
740467330

4

{518859634,593681280,395795933,369951529,369951429,369951430,369951521,369951424,369951437,369951402,708220401,370021894,369951427,369951302,392950557,264974300,369951429,369951568,369951536,370131354,370124795,370517494,369951288,371205742,369960609,369958095,369951998,369951292,699213530,370014328,370068139,369951521,370159198,369951438,369951309,444720342,369951290,369951301,369781676,351618860,388380659,383955697,369960818,369951304}

{535218839,654223381,395885537,369951529,369951429,369951430,369951521,369951435,369951437,369951576,730405095,370022133,369951427,369951302,393145110,545909328,369951431,369951568,369951536,370138807,370130858,370521088,369951303,377916337,369960767,369960057,369952001,369951292,701261997,370019827,370091106,369951529,370180092,369951438,369951313,517469532,369951291,369951301,370153783,396415035,388717162,385277130,369960958,369951304}

Returns: 741087795
674908220

2

{99584698,206524648,99584890,99584992,142969163,99585255,99599322,114737069,99595597,186671221,99584932,99589155,99586518,210217234,99584881,118816926,99584843,99584995,99584948,83497208,99608644,99593408,118551949,198252876,99584951,99585006,99584946,99585046,99584865,115976874,102929901,149865348,99584934,99584931,99584937,99584950,99584884,555495503,140204847,99582234,99584883,99585093,99584939,99585024}

{99585344,210200181,99584891,99584997,145985812,99585279,99599373,115691593,99598085,195327221,99584935,99589159,99586585,210379090,99584881,118881422,99584956,99584995,99584948,155274580,99615514,99594634,118804411,202123978,99584951,99585020,99584950,99585049,99584898,116387918,102935923,150408241,99584934,99584931,99584938,99584950,99584884,646326923,142276113,99589161,99584884,99585098,99584939,99585028}

Returns: 519473437
967231704

2

{84716496,84716675,84716395,84716495,84716499,84716236,84716521,84717981,84716498,84716314,85346282,84716394,464223944,96998846,84716511,84716478,908847179,84716496,84716319,84716526,84716800,84716180,86529695,84716640,84716309,84716778,84716236,84724457,84716661,84715558,84716317,84716503,84716522,84716374,84632431,120395183,84716403,84716312,84716392,84716803,84716523,64078529,84716401,84716316,84798758,84716321}

{84716497,84716677,84716395,84716498,84716499,84716412,84716524,84718404,84716498,84716314,85359457,84716394,846135128,97404462,84716512,84716530,919600097,84716496,84716319,84716528,84716800,84716684,90458716,84716654,84716309,84716796,84716279,84724511,84716666,84724778,84716317,84716507,84716522,84716374,85474480,126160698,84716403,84716313,84716392,84716808,84716523,145162412,84716408,84716318,84799299,84716321}

Returns: 490661267
58703290

3

{10005817,10005577,10005798,10005831,10005614,56803240,10060122}

{10005821,10005577,10005800,10005840,10005614,57353087,10060682}

Returns: 634439498
1000000000

1

{1,343750001,250000001,156250001,250000001,687500001,937500001,500000001,906250001,500000001,625000001,812500001,593750001,468750001,375000001,62500001,625000001,125000001,218750001,375000001,500000001,750000001,31250001,750000001,875000001,843750001,187500001,312500001,812500001,750000001,187500001,500000001,968750001,93750001,718750001,250000001,406250001,437500001,562500001,875000001,781250001,531250001,1,375000001,281250001,1,1,875000001,62500001,1}

{125000000,375000000,281250000,187500000,500000000,750000000,968750000,1000000000,937500000,562500000,656250000,843750000,625000000,500000000,437500000,93750000,687500000,187500000,250000000,500000000,531250000,875000000,62500000,812500000,937500000,875000000,218750000,375000000,875000000,1000000000,250000000,750000000,1000000000,125000000,750000000,375000000,437500000,500000000,593750000,906250000,812500000,562500000,250000000,406250000,312500000,62500000,31250000,1000000000,125000000,500000000}

Returns: 511323738
6

1

{1, 5}

{6, 5}

Returns: 8
999

5

{2, 2, 4, 7, 1, 10, 13, 20, 30, 34, 36, 30, 40, 43, 45, 40, 10, 50, 52, 54, 55, 50, 57, 58, 50, 61, 49, 70, 71, 75, 80, 82, 85, 90, 90, 89, 95, 94, 93, 102 }

{3, 6, 5, 8, 9, 11, 18, 21, 32, 34, 38, 39, 41, 43, 45, 46, 21, 51, 53, 54, 55, 55, 57, 58, 59, 62, 64, 77, 73, 77, 87, 83, 86, 90, 91, 92, 95, 97, 99, 105 }

Returns: 834811227

Statistics

Problem Statement for "CountBinarySequences"

Problem Statement

Definition

Constraints

Examples