Problem Description

Little S is playing a mini-game. The game features a $n \times m$ chessboard with $k$ stars placed on it. Initially, there is a catcher at position $(x, y)$. In each move, you can move the catcher to any position in the same row or column, ensuring that the new position $(x', y')$ is different from the original and satisfies $1 \leq x' \leq n$, $1 \leq y' \leq m$. The catcher will capture all stars on the path from $(x, y)$ to $(x', y')$. Once a star is captured, it disappears.

The goal of the game is to capture as many stars as possible in exactly two moves. However, Little S doesn't know how to play optimally, so he randomly chooses a new position to move to. For the $(n+m-2)^2$ different possible moves Little S can make, calculate the total number of stars captured, modulo $10^9+7$.

Input Format

The first line contains three positive integers $n, m, k$, representing the size of the chessboard and the number of stars.

The second line contains two positive integers $x, y$, indicating the initial position of the catcher.

The next $k$ lines each contain two positive integers, representing the positions $(p, q)$ of the stars. Multiple stars can be at the same position.

Output Format

A single line containing a non-negative integer, representing the total number of stars Little S can capture for the $(n+m-2)^2$ different move combinations, modulo $10^9+7$.

Sample Input and Output

Sample Input #1

3 3 4
2 2
1 1
1 2
1 3
3 1

Sample Output #1

11

Sample Input #2

5 8 9
2 7
1 7
2 2
4 7
4 5
4 7
2 8
5 2
1 7
1 7

Sample Output #2

153

Notes

【Sample Explanation #1】

In the grid, a valid sequence of moves for the catcher is:

$$(2,2) \to (1,2) \to (1,3)$$

In this sequence, the catcher captures one star at position $(1,2)$ and one star at position $(1,3)$.

【Data Range】

This problem is bundled with subtasks.

For $100\%$ of the data, $1 \leq k \leq 10^5$, $1 \leq n, m \leq 10^{18}$, $1 \leq x, p \leq n$, $1 \leq y, q \leq m$, $(x, y) \neq (p, q)$.

见题面 Input 部分

见题面 Output 部分