There is a grid that consists of `W \times H` cells. The upper-left-most cell is `(1, 1)`.
You are standing on the cell of `(1,1)` and you are going to move to cell of `(W, H)`.
You can only move to adjacent lower-left, lower or lower-right cells.

There are obstructions on several cells. You can not move to it. You cannot move out the grid, either.
Write a program that outputs the number of ways to reach `(W,H)` modulo 1,000,000,009.
You can assume that there is no obstruction at `(1,1)`.

The first line contains three integers, the width `W`, the height `H`, and the number of obstructions `N`.
(`1 \leq W \leq 75`, `2 \leq H \leq 10^{18}`, `0 \leq N \leq 30`)
Each of following `N` lines contains 2 integers, denoting the position of an obstruction `(x_i, y_i)`.

The last test case is followed by a line containing three zeros.

For each test case, print its case number and the number of ways to reach `(W,H)` modulo 1,000,000,009.

2 4 1 2 1 2 2 1 2 2 0 0 0

Case 1: 4 Case 2: 0

Source: ACM-ICPC Japan Alumni Group Spring Contest 2012
, Tokyo, Japan, 2012-04-15

http://acm-icpc.aitea.net/

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