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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n, score = gets.split.map(&:to_i)

# dp[i][j][k]
# 上からi段目
# j個保留
# スコアがk

dp = Array.new(n + 1) { Array.new(n + 1) { Array.new(score + 2 * n + 1) { 0 } } }

dp[0][0][0] = 1
(0 ... n).each do |i|
  (0 ... n).each do |j|
    (0 ...score).each do |k|
      nj                    = j
      dp[i + 1][nj][k + nj] += dp[i][j][k]

      nj                    = j + 1
      dp[i + 1][nj][k + nj] += dp[i][j][k]

      nj                    = j
      x                     = j * 2
      dp[i + 1][nj][k + nj] += dp[i][j][k] * x

      if j >= 1
        nj                    = j - 1
        x                     = j * j
        dp[i + 1][nj][k + nj] += dp[i][j][k] * x
      end
    end
  end
end
ans = dp[n][0][score / 2]
ans = 0 if score & 1 != 0
puts ans % 10**9+7