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}.