Problem Statement

Given are integers $N$, $M$, $V$, and $A$. Consider the following procedure.

• Choose a sequence of $N$ integers between $1$ and $V$ (inclusive): $x=(x_1,x_2,\cdots,x_N)$.
• Choose a sequence of $M$ integers between $1$ and $V$ (inclusive): $y=(y_1,y_2,\cdots,y_M)$.
• Let $a$ be a variable and initialize it with $a=A$.
• For each $i=0,1,\cdots,N \times M-1$, do the following.
• Replace the value of $a$ with the median of $a,x_{(i \bmod N)+1},y_{(i \bmod M)+1}$.
• Print the final value of $a$.

Consider doing this procedure with every possible pair of sequences $x,y$. Find the sum of the values that will be printed, modulo $998244353$.

Constraints

• $1 \leq N,M \leq 200000$
• $1 \leq A \leq V \leq 200000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M V A

Output

Print the answer.