Note

This problem has been confirmed to be solvable (AC) in C++ and Python, but some optimization may be required depending on the language or runtime.

Problem Statement

A popularity vote was held among $N$ candidates, numbered candidate $1, 2, \cdots, N$.

A total of $M$ people voted in this vote, and each person chose exactly $K$ candidates out of the $N$ candidates and voted for them.

For each $i\ (1\leq i\leq N)$, let $V_i$ be the number of votes received by candidate $i$, and define the sequence $V=(V_1, V_2, \cdots, V_N)$. How many possible sequences $V$ satisfy the following condition?

• Letting $\displaystyle V_{max}=\max_{1\leq i\leq N} V_i$, we have $V_{max}>V_1\geq L$.

Since the answer can be very large, find it modulo $998244353$.

Input

$N\ M\ K\ L$

• $2\leq N\leq 3000$
• $1\leq M\leq 3000$
• $1\leq K\leq N$
• $1\leq L\leq M$
• All inputs are integers.

Output

Let $m$ be the number of possible sequences $V$ satisfying the condition, modulo $998244353$. Print this $m$ on one line.

Print a newline at the end.

Sample

5 3 1 1

4

3000 3000 1500 1500

743177420