F - Permutation Oddness

Score : $600$ points

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 $10^9+7$.

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 $10^9+7$.

3 2

2

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

39 14

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