Background

Xiao A has recently become obsessed with the game "Jump Jump".

Problem Description

The rules of the "Jump Jump" game played by Xiao A are as follows:

1. Set a counter $\text{cnt}$, and initialize it to $2$.
2. If you jump to the next tile but do not land on its center, gain $1$ point and reset $\text{cnt}$ to $2$.
3. If you jump to the next tile and land on its center, gain $\text{cnt}$ points and double $\text{cnt}$.
4. If the next tile is a special tile $x_i$ and you land on its center, gain an extra $y_i$ points.
5. The game ends when you fail to jump to the next tile, or when you have finished jumping all tiles.

It is known that there are $n$ tiles in total, numbered from $1$ to $n$ (excluding the starting tile).

The probability that Xiao A jumps to the next tile but does not land on its center is $a\%$. The probability that he jumps to the next tile and does land on its center is $b\%$. The remaining $(100-a-b)\%$ is the probability that he fails to jump to the next tile.

Compute his expected score, modulo $10^9+7$.

Input Format

The first line contains three integers $n,a,b$.

The second line contains an integer $m$, indicating that there are $m$ special tiles.

The next $m$ lines each contain two integers $x,y$, indicating the index of a special tile and its extra bonus score. It is guaranteed that all $x$ are distinct.

Output Format

Output one integer, the expected score.

3 0 100
0

14

3 100 0
0

3

3 0 0
0

0

3 0 100
3
1 10
2 10
3 10

44

114 5 14
3
14 15
92 65
100 100

190259152

Hint

[Sample 1 Explanation]

Xiao A always jumps to the next tile and lands on its center, so the expected score is $2+4+8=14$ points.

[Sample 2 Explanation]

Xiao A always jumps to the next tile but does not land on its center, so the expected score is $1+1+1=3$ points.

[Sample 3 Explanation]

Xiao A can never jump to the next tile, so the expected score is $0$ points.

[Sample 4 Explanation]

Xiao A always jumps to the next tile and lands on its center, so the expected score is $2+10+4+10+8+10=44$ points.

[Constraints and Notes]

This problem uses bundled testdata.

In the table below, a slash means there is no special restriction.

For $100\%$ of the testdata, $1\le n\le 10^{18}$, $0\le a,b,a+b\le 100$, $0\le m\le \min(n,10^5)$, $1\le x\le n$, $1\le y\le 100$.

Translated by ChatGPT 5