output_description: Print the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo
  10^9+7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      n k
attempt: mod = 1000000007
  n, k = map(int, input().split())
  DP = [[[0] * (k + 1) for _ in range(n + 1)] for _ in range(n + 1)]
  DP[0][0][0] = 1
  for i in range(1, n + 1):
      for j in range(n + 1):
          for l in range(k + 1):
              if l - 2 * j >= 0:
                  DP[i][j][l] = (2 * j + 1) * DP[i - 1][j][l - 2 * j]
                  if j != n:
                      DP[i][j][l] += (j + 1) ** 2 * DP[i - 1][j + 1][l - 2 * j]
                  if j != 0:
                      DP[i][j][l] += DP[i - 1][j - 1][l - 2 * j]
              DP[i][j][l] %= mod
  print(DP[-1][0][-1])
  
problem_description: 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.
samples: [{"input": "3 2", "output": "2\n    \n\nThere are six permutations of {1,\\ 2,\\ 3}. Among them, two have oddness of 2:\n{2,\\ 1,\\ 3} and {1,\\ 3,\\ 2}.\n\n* * *"}, {"input": "39 14", "output": "74764168"}]