Score : $600$ points
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 $10^9+7$.
Input is given from Standard Input in the following format:
$n$ $k$
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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