Problem Description

This is a template problem.

You are given two matrices $A$ and $B$, where $A$ is of size $n \times p$ and $B$ is of size $p \times m$. Your task is to compute the matrix product $A \times B$.

Input Format

The first line contains three positive integers $n$, $p$, and $m$, representing the dimensions of the matrices.
The next $n$ lines each contain $p$ integers, representing matrix $A$.
The following $p$ lines each contain $m$ integers, representing matrix $B$.

Output Format

Output an $n$-row by $m$-column matrix, representing the result of the matrix multiplication $A \times B$. Each element of the result should be output modulo $10^9 + 7$.

Example Input 1

3 4 5
-2 -8 -9 8
-10 0 6 -8
-10 -6 6 9
4 -7 5 -5 9
10 -2 -10 5 5
-3 -7 -3 8 -2
-6 7 7 3 -2

Example Output 1

999999898 149 153 999999929 999999951
999999997 999999979 999999883 74 999999921
999999835 103 55 95 999999857

Constraints and Hints

• $1 \leq n, p, m \leq 500$
• $-10^9 \leq A_{i,j}, B_{i,j} \leq 10^9$

This problem involves performing matrix multiplication and ensuring that the result is output modulo $10^9 + 7$.