Matrix Pain CodeChef Solution

Problem

Chef is here with another matrix $A$ having $N$ rows and $M$ columns,
such that �(�,�)=(�−1)⋅�+�A(i,j)​=(i−1)⋅M+j.

Chef decided to make this matrix interesting. He performed $K$ operations on the matrix. In each operation, he will choose either a row or column and multiply all values in that row/column with a non-negative integer $V$.

• An operation is of the form $Q,X,V$:
  • If $Q=0:$ Multiply each element of the ��ℎXth row with $V$.
  • If $Q=1:$ Multiply each element of the ��ℎXth column with $V$.

Find the sum of all values in the matrix after all $K$ operations are done. Since the value can be large, print it modulo 109+7109+7.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of multiple lines of input.
  • The first line of each test case contains three space-separated integers $N$, $M$, and $K$ — the number of rows, columns, and the operations to be done, respectively.
  • The next $K$ lines describe the operations. The ��ℎith of these $K$ lines contain three space-separated integers ��Qi​, ��Xi​, and ��Vi​, as mentioned in the statement.

Output Format

For each test case, output on a new line, the sum of all elements of the matrix after performing the operations, modulo 109+7109+7.

Constraints

Sample 1:

2
2 2 2
1 2 0
0 1 2
1 3 1
1 2 6

5
16

Explanation:

Test case $1$ : The initial matrix is $[[1,2],[3,4]]$.

• In the first operation, multiply all elements of the second column with $0$. Thus, the matrix becomes $[[1,0],[3,0]]$.
• In the second operation, multiply all elements of the first row with $2$. Thus, the matrix becomes $[[2,0],[3,0]]$.

The sum of the elements of the updated matrix is $2+3=5$.

Test case $2$: The initial matrix is $[[1,2,3]]$.

• In the first operation, multiply all elements of the second column with $6$. Thus, the matrix becomes $[[1,12,3]]$.

The sum of the elements of the updated matrix is $1+12+3=16$.