K - Unique Subsequences Counting

An array $A$ of length $N$ is said to be *good* if and only if every subsequence of length $M$ appears at most once in the array. For example, $A = [1, 2, 2]$ is not *good* with length parameter $M = 2$, because the subsequence $[1, 2]$ appears twice. On the other hand, it would be *good* with length parameter $M = 3$. Given $N$ and $M$, count the number of arrays $A$ satisfying the following c