Chessboard

A chessboard has $N \times M$ cells. Rows are numbered $1, 2, \cdots, N$ from top to bottom, and columns are numbered $1, 2, \cdots, M$ from left to right. Cell $(i, j)$ is in row $i$ and column $j$. The board has $K$ forbidden cells. Neither $(1,1)$ nor $(N,M)$ is forbidden.

Pieces $A$ and $B$ start at $(1,1)$ and move together, one cell at a time, toward $(N,M)$ under these rules.

1. A piece at $(i,j)$ can move to $(i+1,j)$ or $(i,j+1)$. A move that leaves the board is not allowed.
2. At the start, piece $A$ moves from $(1,1)$ to $(1,2)$, and piece $B$ moves from $(1,1)$ to $(2,1)$.
3. While moving, the two pieces must not meet on any cell except $(1,1)$ and $(N,M)$.
4. Neither piece can move onto a forbidden cell.

Following these rules, count the pairs of paths $(a,b)$ that take pieces $A$ and $B$ from $(1,1)$ to $(N,M)$, where $a$ is the path of piece $A$ and $b$ is the path of piece $B$.

The first line contains $N$, $M$, and $K$, separated by spaces. ($2 \le N,M \le 1\,000\,000$, $0 \le K \le \min(N \times M-2,5\,000)$)

Each of the next $K$ lines contains the row number $x$ and column number $y$ of a forbidden cell, separated by a space. No cell is given twice. ($1 \le x \le N$, $1 \le y \le M$, $(x,y) \neq (1,1)$, $(x,y) \neq (N,M)$)

All numbers in the input are integers.

Print the number of path pairs that let pieces $A$ and $B$ start together at $(1,1)$ and reach $(N,M)$, modulo $10^9 + 7$.