## Grid Paths

Points: 10 (partial)
Time limit: 2.0s
Memory limit: 64M

Author:
Problem type

In a grid of size $$W$$ by $$H$$ $$(1 \leq W,H \leq 10^6)$$, you are to determine the amount of paths from the square $$(1,1)$$ to the square $$(W,H)$$ that do not go through $$X$$ blocked off squares only moving to the right or up. $$(0 \leq X \leq 2)$$.

#### Input Specification

The first line will contain three integers, $$W$$, $$H$$, and $$X$$.

The next $$X$$ lines will contain two integers $$x$$ and $$y$$. $$(1 \leq x \leq W)$$ $$(1 \leq y \leq H)$$

#### Output Specification

On one line, you are to output the number of valid paths through the grid modulo $$10^9 + 7$$.

$$X = 0$$

$$X = 1$$

$$X = 2$$
4 4 0
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