Problem Statement

There are $K$ boxes numbered $1$ to $K$. Initially, all boxes are empty.

Snuke has some balls with integers from $1$ to $N$ written on them. Among them, $a_i$ balls have the number $i$. Balls with the same integer written on them cannot be distinguished.

Snuke has decided to put all of his balls in the boxes. He wants the balls with the number $1$ to have a majority in every box. In other words, in every box, the number of balls with $1$ should be greater than that of the other balls.

Find the number of such ways to put the balls in the boxes, modulo $998244353$.

Two ways are distinguished when there is a pair of integers $(i,j)$ satisfying $1 \leq i \leq K, 1 \leq j \leq N$ such that the numbers of balls with $j$ in Box $i$ are different.

Constraints

• All values in input are integers.
• $1 \leq N \leq 10^5$
• $1 \leq K \leq 200$
• $1 \leq a_i < 998244353$

Input

Input is given from Standard Input in the following format:

N K
a_1 \cdots a_N

Output

Print the number of ways, modulo $998244353$, to put the balls in the boxes so that the balls with the number $1$ have a majority in every box.