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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分