Today Jin has given a task to Shino, Shino has to travel from cell $(1,1)$ to cell $(N,M)$ in a grid of size $N * M$. But in order make this task interesting for Shino, Jin has decided to keep some special candies in some K special cells of the grid, where each candy has an amount of happiness associated with it.

Shino can travel only in right & down direction in the grid, as he is too careful & does not want to fall out of grid. Now, we call the value of a path the happiness of all cells lying on the path. All non-special cells have happiness equal to 0.

Now, you need to find and print the sum of the values of all paths from $(1,1)$ to $(N,M)$, traveling only right and down to an adjacent cell.

As Shino is not good at counting help him find the answer.

Input Format

The first Line contains a single integer T denoting number of test cases

The next line contains 3 space separated integers, N, M and K where N * M is the size of grid & K denoting number of special cells

The next K lines contains three integers $X_{i}, Y_i, H_i$ where $(Xi,Yi)$ is cell coordinate & $H_i$ is the amount of happiness Shino will get from a candy at cell $(X_i,Y_i)$

Constraints

$1 \le T \le 3$

$1 \le N,M,K \le 10^5$

$1 \le X_{i} \le N, 1 \le Y_{i} \le M$

$1 \le H_{i} \le 10^5$

Output Format

For each test case you will output a single integer denoting the total amount of happiness Shino will get. As the answer can be quiet large you can output answer modulo $10^9+7$