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.