Automobile

Mirko found a matrix with $N$ rows and $M$ columns on the back seat of his car. The first row holds $1, 2, \dots, M$, the second row holds $M+1, M+2, \dots, 2M$, and the same rule continues, so the $N$-th row holds $(N-1)M+1, (N-1)M+2, \dots, NM$.

For $N = 3$ and $M = 4$ the matrix is this one.

The matrix was not interesting enough for Mirko, so $K$ times he picked a row or a column and multiplied every value in it by a non-negative integer. He wants the sum of all values in the final matrix. That sum can be very large, so print it modulo $10^9+7$.

The first line contains $N$ ($1 \le N \le 10^6$), $M$ ($1 \le M \le 10^6$) and $K$ ($1 \le K \le 1000$), separated by spaces. Each of the next $K$ lines describes one operation, given in the order the operations were performed.

• "R X Y" multiplies every value in row $X$ by $Y$. $X$ is an integer with $1 \le X \le N$, and $Y$ is an integer with $0 \le Y \le 10^9$.
• "S X Y" multiplies every value in column $X$ by $Y$. $X$ is an integer with $1 \le X \le M$, and $Y$ is an integer with $0 \le Y \le 10^9$.

Print the sum of all values in the final matrix modulo $10^9+7$ on the first line.

Look at the first example. After the second row is multiplied by 4, the fourth column by 1, the third row by 2, and the second row by 0 again, the matrix is this one.

The sum of all values is $1 + 2 + 3 + 4 + 0 + 0 + 0 + 0 + 18 + 20 + 22 + 24 = 94$.