Problem Statement

You are given an integer $N$ and a set $S=\lbrace S_1,S_2,\ldots,S_K\rbrace$ consisting of integers between $1$ and $N-1$.

Find the number, modulo $998244353$, of trees $T$ with $N$ vertices numbered $1$ through $N$ such that:

• $d_i\in S$ for all $i\ (1\leq i \leq N)$, where $d_i$ is the degree of vertex $i$ in $T$.

Constraints

• $2\leq N \leq 2\times 10^5$
• $1\leq K \leq N-1$
• $1\leq S_1 < S_2 < \ldots < S_K \leq N-1$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N K
S_1 \ldots S_K

Output

Print the number, modulo $998244353$, of the conforming trees $T$.