Too Many LIS

You are given $2$ integers $N$ and $M$. You also have an empty set $S$. Consider an array $A$ of length $N$ such that $1 \leq A_i \leq M$ for each $1 \leq i \leq N$ (there are $M^N$ such arrays in total). For each of these $M^N$ arrays, insert **all** of its longest non-decreasing subsequences into $S$. Output the size of $S$. Since the size of $S$ might be large, output it modulo $10^9+7$. N