Problem Statement

You are given a multiset of integers with $N$ elements: $A=\lbrace A_1,A_2,...,A_N \rbrace$. It is guaranteed that every element of $A$ is between $1$ and $M$ (inclusive).

Let us repeat the following operation $K$ times.

• Choose an integer between $1$ and $M$ (inclusive) and add it to $A$. Then, delete the $X$-th smallest value in $A$.

Here, the $X$-th smallest value in $A$ is the $X$-th value from the front in the sequence of the elements of $A$ sorted in non-decreasing order.

There are $M^K$ ways to choose an integer $K$ times between $1$ and $M$. Assume that, for each of these ways, we have found the sum of the elements of $A$ after the operations with the corresponding choices. Find the sum, modulo $998244353$, of the $M^K$ values computed.

Constraints

• $1 \le N,M,K \le 2000$
• $1 \le X \le N+1$
• $1 \le A_i \le M$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M K X
A_1 A_2 \dots A_N

Output

Print the answer.