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.

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.

Constraints

• All values in input are integers.
• $1 \leq n \leq 50$
• $0 \leq k \leq n^2$

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

见题面 Input 部分

见题面 Output 部分