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 $T$.

Sample Input 1

4 2
1 3

Sample Output 1

4

A tree satisfies the condition if the degree of one vertex is $3$ and the others' are $1$. Thus, the answer is $4$.

Sample Input 2

10 5
1 2 3 5 6

Sample Output 2

68521950

Sample Input 3

100 5
1 2 3 14 15

Sample Output 3

888770956

Print the count modulo $998244353$.