Median Pairs

You are given two numbers $N$ and $M$. A pair of arrays $(A, B)$ is called *beautiful* if and only if: - $|A| = |B| = N$ (i.e. both their lengths are equal to $N$); - For all $1 \le i \le N$, $1 \le A_i \le M$ and $1 \le B_i \le M$; - $median(A) \leq median(B)$; - $A$ is lexicographically smaller than $B$. Find the number of **beautiful** pairs of arrays. Since this number can be huge, print it m