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 (Python):
anss = [1, 1, 1, 1, 2, 3, 1, 3, 7, 9, 4, 1, 4, 12, 24, 35, 24, 20, 1, 5, 18, 46, 93, 137, 148, 136, 100, 36, 1, 6, 25, 76, 187, 366, 591, 744, 884, 832, 716, 360, 252, 1, 7, 33, 115, 327, 765, 1523, 2553, 3696, 4852, 5708, 5892, 5452, 4212, 2844, 1764, 576, 1, 8, 42, 164, 524, 1400, 3226, 6436, 11323, 17640, 25472, 33280, 40520, 44240, 45512, 40608, 35496, 25632, 18108, 8064, 5184, 1, 9, 52, 224, 790, 2350, 6072, 13768, 27821, 50461, 83420, 127840, 182256, 242272, 301648, 350864, 382576, 389232, 373536, 332640, 273060, 208548, 136512, 81792, 46656, 14400, 1, 10, 63, 296, 1138, 3708, 10538, 26480, 59673, 121626, 226787, 390144, 628744, 949472, 1355952, 1826464, 2341600, 2833632, 3282464, 3584160, 3765600, 3719664, 3531924, 3093336, 2642364, 2010240, 1508544, 963072, 621504, 259200, 158400, 1, 11, 75, 381, 1582, 5582, 17222, 47194, 116457, 261163, 537459, 1022981, 1817652, 3040352, 4810720, 7230928, 10360160, 14178912, 18577792, 23327872, 28132048, 32571504, 36310464, 38903904, 40028724, 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import sys

N, K = map(int, input().split())

maxS = N*N//2
if K > maxS or K%2:
    print(0)
    sys.exit()

pos = 0
for i in range(1, 51):
    if i == N:
        pos += K//2
        break
    else:
        pos += i*i//2//2 + 1

print(anss[pos])