Permutation Oddness

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

inputFormat

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

outputFormat

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

样例

39 14

74764168