• You are given a \(N \times M\) matrix which has K special cells in it. You have to reach \((N, M)\) from \((1, 1)\). From any cell, you can only move rightwards or downwards.
• The \(K-special\) cells are those cells in this grid which have special strength at them. \(i^{th}\) special cell has \(P[i]\) units of strength and if you travel through this cell, you store the strength.
• Find the total strength you can store after travelling through all the possible paths in the grid to reach cell \((N,M)\).


• Note:
  1. The strength of a path is the sum of strength \(P[i]\) of all the special cells that are visited in this path.
  2. The cells that are not special have power quotient equals to zero.

Input format

• The first line contains the total number of test cases denoted by T.
• The first line of each test case contains three space separated integers N, M and K where N x M is the size of grid and K is the total number of special cells in the grid.
• Each of next K lines contains X[i], Y[i], and P[i] where (X[i],Y[i]) is the location of special cell and P[i] is the cell strength.

Output format

• For each test case, print in a new line a single integer representing the total strength that you can store, as the total strength can be too large, print it modulo \(10^9+7\).

Constraints

• \(1 \le T \le 3\)
• \(1 \le N, M, P[i] \le 10^5\)
• \(1 \le X[i] \le N\)
• \(1 \le Y[i] \le M\)
• \(1 \le K \le 10^6\)