24675번 - Two Permutations 다국어

Find the number of pairs $(p, q)$ of permutations of length $n$ such that $\sum\limits_{i=1}^n \max(p_i, q_i) = k$.

As the answer may be large, find it modulo $10^9 + 7$.

The only line contains two integers, $n$ and $k$ ($1 \le n \le 100$, $1 \le k \le n^2$).

Print the answer modulo $10^9 + 7$.