Mex Pairs

You are given two numbers $N$ and $M$. A pair of arrays $(A, B)$ is called $K$-beautiful if and only if: - $|A| = |B| = N$ (i.e. both their lengths are equal to $N$) - For all $i$ such that $1 \le i \le N$, $0 \le A_i \le M$ and $0 \le B_i \le M$. - $mex(A) \leq mex(B)$ - $A$ is lexicographically smaller than $B$ - The first index $i$ where $A_i \lt B_i$ is $K$ For each $K$ ($1 \le K \le N$), fi