Problem Description

Mirko has found a matrix with N rows and M columns at the back seat of his car. The first row of the matrix consists of numbers 1, 2, … M, the second row of numbers M+1, M+2, … 2⋅M, and so on until the N-th row which consists of numbers (N-1)⋅M + 1, (N-1)⋅M + 2, … N⋅M, respectively.

For example, for N = 3 and M = 4:

Such a matrix wasn’t interesting enough to him, so he chose a row or a column K times and multiplied its values with a non-negative integer.

Naturally, now he wants to know the sum of all the values from the matrix. Since this sum can be very large, Mirko will be satisfied with the value modulo $10^9$ + 7. Help Mirko answer this question.

Input Format

The first line of input contains the numbers N (1 ≤ N ≤ 1,000,000), M (1 ≤ M ≤ 1,000,000), and K (1 ≤ K ≤ 1,000) from the task.

• Either the multiplication of the X-th row with Y, in the form of "R X Y", where “R” represents row multiplication, X is a positive integer (1 ≤ X ≤ N), and Y is a non-negative integer (0 ≤ Y ≤ $10^9$).

• Or the multiplication of the X-th column with Y, in the form of “S X Y”, where “S” represents column multiplication, X is a positive integer (1 ≤ X ≤ M), and Y is a non-negative integer (0 ≤ Y ≤ $10^9$).

Output Format

You must output the sum of the final values from the matrix modulo $10^9$ + 7.

Sample Input and Output

Sample Input #1

3 4 4
R 2 4
S 4 1
R 3 2
R 2 0

Sample Output #1

94

Sample Input #2

3 1 1
S 1 4

Sample Output #2

24

Sample Input #3

2 4 4
S 2 0
S 2 3
R 1 5
S 1 3

Sample Output #3

80

Notes

In test cases worth a total of 50 points, it will hold 1 ≤ N, M ≤ 1,000.

Clarification of the first test case:
After multiplying the second row with 4, the fourth column with 1, the third row with 2, and again the second row with 0, the final matrix looks like this:

The sum of the elements from the final matrix is 1 + 2 + 3 + 4 + 0 + 0 + 0 + 0 + 18 + 20 + 22 + 24 = 94.

见题面 Input 部分

见题面 Output 部分