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):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
import numpy as np

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



MOD = 10 ** 9 + 7

dp = np.zeros((N+1,N*N+1), dtype = np.int64) 
dp[0,0] = 1
for n in range(1,N+1):
    prev = dp
    dp = np.zeros_like(prev)
    for m in range(N):
        dp[m,m:] += prev[m,:N*N+1-m] 
        dp[m,m:] += prev[m,:N*N+1-m] * m 
        dp[m+1,m+1:] += (m+1) * prev[m,:N*N-m] 
        dp[m,m:] += prev[m,:N*N+1-m] * m 
        dp[m,m:] += (m+1) * prev[m+1,:N*N+1-m] 
    dp %= MOD

if K&1:
    answer = 0
else:
    answer = dp[0,K//2]

print(answer)