- Time limit: 1.00 s
- Memory limit: 512 MB
Your task is to move from the top-left square to the bottom-right square. On each step you may move one square right or down. In addition, there are $m$ traps in the grid. You cannot move to a square with a trap.
What is the total number of possible paths?
The first input line contains two integers $n$ and $m$: the size of the grid and the number of traps.
After this, there are $m$ lines describing the traps. Each such line contains two integers $y$ and $x$: the location of a trap.
You can assume that there are no traps in the top-left and bottom-right square.
Print the number of paths modulo $10^9+7$.
- $1 \le n \le 10^6$
- $1 \le m \le 1000$
- $1 \le y,x \le n$