Problem:
Score : 600 points

Problem Statement

Let us define the oddness of a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n} as \sum_{i = 1}^n |i - p_i|.

Find the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Constraints

All values in input are integers.

1 \leq n \leq 50

0 \leq k \leq n^2

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

2

There are six permutations of {1,\ 2,\ 3}. Among them, two have oddness of 2: {2,\ 1,\ 3} and {1,\ 3,\ 2}.

Sample Input 2

39 14

Sample Output 2

74764168

Solution in C (Clang 3.8.0) (judge verdict: Accepted)

// https://atcoder.jp/contests/abc134/submissions/6635211

#include <stdio.h>

int main() {
  int t[] = {
    1,
    1,
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    3,
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    9,
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    459755659,
    92556107,
    42398758,
    782901298,
    483436309,
    73995240,
    784415989,
    602791285,
    655683750,
    744368335,
    684929720,
    939318197,
    1937536,
    94209990,
    544006669,
    195169186,
    297173575,
    151918090,
    559870646,
    425964491,
    818978660,
    571568643,
    60393204,
    415731654,
    547756555,
    991386612,
    383053326,
    997830526,
    963081859,
    107336308,
    898219937,
    906988404,
    550036125,
    981857264,
    691293427,
    481189647,
    501756531,
    316529056,
    476096058,
    168221459,
    165690115,
    553028411,
    960794528,
    453386272,
    963889156,
    71983103,
    494867184,
    462967097,
    635240847,
    989817132,
    23786457,
    968645733,
    163475174,
    884798755,
    971346358,
    8231228,
    947835970,
    751371876,
    21594745,
    702982989,
    997528759,
    30899466,
    874470660,
    839706683,
    64336797,
    183002010,
    415355406,
    851375333,
    802315034,
    662347966,
    459017349,
    83113197,
    807783874,
    686211775,
    665742332,
    548408223,
    38712773,
    947065654,
    224142524,
    544199777,
    554457822,
    161813447,
    59932464,
    324817969,
    826816639,
    159675767,
    610260222,
    802832692,
    962264291,
    230527850,
    654881259,
    493134625,
    56109407,
    491401533,
    163680598,
    892934948,
    889185132,
    78662275,
    741528574,
    616484511,
    204394884,
    120980232,
    4959172,
    884202370,
    468625389,
    987185268,
    797914336,
    292935354,
    542176515,
    965256954,
    25044127,
    701524209,
    669825969,
    264620823,
    983915826,
    463815578,
    325409981,
    142164710,
    946513145,
    626025918,
    890502327,
    456729879,
    921471703,
    889764153,
    10834930,
    550258959,
    888111963,
    456661896,
    560525119,
    254574198,
    379302005,
    359197537,
    748972811,
    432885247,
    174603143,
    495215302,
    304225805,
    499574,
    89067439,
    956588800,
    479903186,
    900293862,
    918419160,
    874312513,
    779518268,
    750190343,
    34999197,
    204187488,
    29703716,
    310295240,
    212734818,
    705461990,
    880565621,
    542764103,
    578132976,
    871657196,
    920555643,
    635330221,
    603836039,
    905337022,
    446003049,
    531829391,
    914627500,
    109964459,
    793773872,
    883594493,
    588890899,
    761763418,
    850946563,
    47045637,
    406265955,
    398330580,
    175033998,
    98562597,
    74022406,
    109783010,
    888406279,
    62923507,
    851720727,
    920064661,
    659715101,
    731241623,
    740764931,
    68490942,
    26861674,
    832409630,
    156628069,
    65837301,
    277330611,
    504531610,
    621094682,
    513712789,
    824543274,
    863846088,
    522929299,
    50674845,
    205053841,
    391074024,
    703020653,
    598865065,
    977680558,
    126857946,
    571772915,
    596794646,
    195429545,
    328266420,
    36051456,
    451216030,
    522276964,
    948367998,
    561406981,
    389510759,
    585943971,
    108053297,
    459413669,
    288907310,
    136029766,
    802792879,
    520247265,
    414339912,
    337619243,
    597859489,
    40005835,
    350918,
    321070418,
    199829979,
    141119131,
    515535428,
    350920730,
    314377413,
    808898947,
    900198037,
    799762368,
    570476717,
    244997759,
    402733111,
    626061442,
    103647198,
    938528989,
    898060580,
    652361018,
    641847472,
    149112119,
    134262079,
    887185896,
    606038263,
    859408453,
    950373236,
    692335861,
    405660442,
    565431386,
    959094106,
    393940636,
    423632434,
    612413824,
    143336067,
    663257107,
    9730523,
    471491852,
    112828340,
    936303905,
    998673093,
    55233966,
    416039620,
    144081002,
    565258672,
    539355694,
    202448366,
    14002378,
    539019751,
    307827209,
    288622328,
    788194350,
    570120788,
    965430343,
    472467292,
  };

  int ind[] = {
    0,
    1,
    3,
    6,
    11,
    18,
    28,
    41,
    58,
    79,
    105,
    136,
    173,
    216,
    266,
    323,
    388,
    461,
    543,
    634,
    735,
    846,
    968,
    1101,
    1246,
    1403,
    1573,
    1756,
    1953,
    2164,
    2390,
    2631,
    2888,
    3161,
    3451,
    3758,
    4083,
    4426,
    4788,
    5169,
    5570,
    5991,
    6433,
    6896,
    7381,
    7888,
    8418,
    8971,
    9548,
    10149,
    10775,
  };

  int n, k;
  scanf("%d %d", &n, &k);

  if (k%2 || k/2+1 > ind[n]-ind[n-1]) {
    printf("0\n");
  } else {
    printf("%d\n", t[ind[n-1]+k/2]);
  }
}