Inverse Problem

You are given an integer $N$ and an integer sequence $X$ of length $M$. Count, modulo $998244353$, the number of permutations $P = (P\_1,P\_2,\ldots,P\_N)$ of $(1,2,\ldots,N)$ that satisfy the following condition:

• The lexicographically smallest subsequence of $P$ of length $M$ coincides with $X$.

The first line contains integers $N$ ($1 \leq N \leq 250000$) and $M$ ($1 \leq M \leq N$).

The second line contains integers $X\_1,X\_2,\ldots,X\_M$ ($1 \leq X\_i \leq N$, $X\_i \neq X\_j$ for all $i \neq j$).

Print the answer.