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.

Examples

Input

3 2

Output

2

Input

39 14

Output

74764168

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