Problem Statement

You are given integers $N$, $M$, $X$, and $Y$.

Find the number, modulo $998244353$, of pairs $(A, B)$ of sequences $A=(a_1,\ldots,a_N)$ and $B=(b_1,\ldots,b_N)$ that satisfy all of the following conditions:

• $A = (a_1, \ldots, a_N)$ is a sequence of non-negative integers.
• $B = (b_1, \ldots, b_N)$ is a subsequence of $(0, 1, \ldots, M - 1)$.
• $\sum\limits_{i=1}^{N} a_i = X$.
• $\sum\limits_{i=1}^{N} a_i b_i = Y$.

Constraints

• $1 \leq N \leq M \leq 2 \times 10^5$
• $1 \leq X, Y \leq 2 \times 10^5$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M X Y

Output

Print the answer modulo $998244353$.