Problem Statement

There are $N$ chairs arranged in a row, called Chair $1$, Chair $2$, $\\ldots$, Chair $N$.
A chair seats only one person.

$M$ people will sit on $M$ of these chairs. Here, let us define the score as follows:

$\\displaystyle \\prod_{i=1}^{M-1} (B_{i+1} - B_i)$, where $B=(B_1,B_2,\\ldots,B_M)$ is the sorted list of the indices of the chairs the people sit on.

Person $i$ $(1 \\leq i \\leq K)$ is already sitting on Chair $A_i$.
There are ${} _ {N-K} \\mathrm{P} _ {M-K}$ ways for the other $M-K$ people to take seats. Find the sum of the scores for all of these ways.

Since this sum may be enormous, compute it modulo $998244353$.

Constraints

• $2 \\leq N \\leq 2 \\times 10^5$
• $2 \\leq M \\leq N$
• $0 \\leq K \\leq M$
• $1 \\leq A_1 \\lt A_2 \\lt \\ldots \\lt A_K \\leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$ $A_1$ $A_2$ $\\ldots$ $A_K$

Output

Print the answer.

Sample Input 1

5 3 2
1 3

Sample Output 1

7

If Person $3$ sits on Chair $2$, the score will be $(2-1) \\times (3-2)=1 \\times 1 = 1$.
If Person $3$ sits on Chair $4$, the score will be $(3-1) \\times (4-3)=2 \\times 1 = 2$.
If Person $3$ sits on Chair $5$, the score will be $(3-1) \\times (5-3)=2 \\times 2 = 4$.
The answer is $1+2+4=7$.

Sample Input 2

6 6 1
4

Sample Output 2

120

The score for every way of sitting will be $1$.
There are ${} _ {5} \\mathrm{P} _ {5} = 120$ ways of sitting, so the answer is $120$.

Sample Input 3

99 10 3
10 50 90

Sample Output 3

761621047