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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分