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-----
3 2

-----Sample Output-----
2

There are six permutations of {1,\ 2,\ 3}. Among them, two have oddness of 2: {2,\ 1,\ 3} and {1,\ 3,\ 2}.

见题面

见题面