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.

Input

Input is given from Standard Input in the following format:
N M V A

Output

Print the answer.

Constraints

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

Sample Input 1

2 1 2 1

Sample Output 1

11

For example, when x=(1,2),y=(2), the procedure goes as follows.

• Initialize a with a=1.
• For i=1: replace the value of a with the median of a(=1),x_1(=1),y_1(=2), which is 1.
• For i=2: replace the value of a with the median of a(=1),x_2(=2),y_1(=2), which is 2.
• Print a(=2).

There are three cases where 2 will be printed: (x=(1,2),y=(2)), (x=(2,1),y=(2)), (x=(2,2),y=(2)). In the other five cases, 1 will be printed.
Therefore, the answer is $2 \times 3 + 1\times 5=11$.

Sample Input 2

2 2 5 4

Sample Output 2

2019

Sample Input 3

2100 2300 2201 2022

Sample Output 3

407723438

见题面 Input 部分

见题面 Output 部分