Counting Is Fun

You are given integers $N$ and $M$. Find the number of arrays $A$ such that: - $|A| = N$ - $1 \le A_i \le M$ for all $i$ $(1 \le i \le N)$ - There exists an index $i$ $(1 \le i \le N - 1)$ such that $F(A, 1, i) = F(A, i + 1, N)$. Here, $F(A, l, r)$ denotes the number of distinct elements in $[A_l, A_{l + 1}, \ldots A_r]$ Since the number might be too large, please find it modulo $998\,244\,353