Problem Statement

There is a grid with $H$ rows and $W$ columns, and the cell at row $i$ and column $j$ is denoted by cell $(i,j)$. Initially, you are at cell $(1,1)$.

You aim for cell $(H,W)$ by repeatedly moving from cell $(i,j)$ to cell $(i+1,j)$ or cell $(i,j+1)$. However, you cannot make a move that takes you outside the grid.

Good news is handed down at $N$ cells in this grid, and the $k$-th piece of good news is handed down at cell $(x_k, y_k)$.

Now, at every cell except cell $(1,1)$ and cell $(H,W)$, a white lotus flower blooms with a certain probability. The probability that a white lotus flower blooms at each cell is $\frac{2}{P}$ if good news is handed down at that cell, and $\frac{1}{P}$ otherwise (whether a white lotus flower blooms is determined independently for each cell). You can see a white lotus flower only when you are at the same cell as the one where it is blooming. Also, you cannot know whether a white lotus flower is blooming at any cell other than the one you are currently at.

You want to maximize the probability of seeing a white lotus flower at least once by the time you have moved from cell $(1,1)$ to cell $(H,W)$. Find the probability that you can see a white lotus flower when you use a way of moving that maximizes this probability, in $\bmod 998244353$ as described in the notes below.

Notes

It can be proved that the value to be found is a rational number. Also, under the constraints of this problem, it can be proved that when the value is expressed as $\frac{Y}{X}$ using $2$ coprime positive integers $X,Y$, there exists exactly one integer $Z$ in the range $0 \leq Z < 998244353$ such that $XZ \equiv Y \pmod{998244353}$. Output this $Z$.

Constraints

• All input values are integers.
• $2 \leq H,W \leq 2 \times 10^5$
• $0 \leq N \leq \min(HW - 2, 2 \times 10^5)$
• $2 \leq P < 998244353$
• $1 \leq x_k \leq H$
• $1 \leq y_k \leq W$
• $(x_k, y_k) \neq (1,1)$
• $(x_k, y_k) \neq (H,W)$
• $(x_k, y_k) \neq (x_l, y_l) (k \neq l)$

Input

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

$H$ $W$ $N$ $P$
$x_1$ $y_1$
$x_2$ $y_2$
$\vdots$
$x_N$ $y_N$

Output

Output the probability that you can see a white lotus flower at least once, in $\bmod 998244353$ as described in the notes.

Sample

3 4 3 3
1 2
2 1
3 3

690144245

2 2 1 2
1 2

1

12 15 8 2009
1 4
3 1
2 4
2 5
5 2
7 3
9 3
11 14

438033477