Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Matrix Multiplication

Write a program which reads a $n \times m$ matrix $A$ and a $m \times l$ matrix $B$, and prints their product, a $n \times l$ matrix $C$. An element of matrix $C$ is obtained by the following formula:

\[
c_{ij} = \sum_{k=1}^m a_{ik}b_{kj}
\]

where $a_{ij}$, $b_{ij}$ and $c_{ij}$ are elements of $A$, $B$ and $C$ respectively.

Input

In the first line, three integers $n$, $m$ and $l$ are given separated by space characters

In the following lines, the $n \times m$ matrix $A$ and the $m \times l$ matrix $B$ are given.

Output

Print elements of the $n \times l$ matrix $C$ ($c_{ij}$). Print a single space character between adjacent elements.

Constraints

$1 \leq n, m, l \leq 100$

$0 \leq a_{ij}, b_{ij} \leq 10000$

Sample Input

3 2 3
1 2
0 3
4 5
1 2 1
0 3 2

Sample Output

1 8 5
0 9 6
4 23 14

Note

      解説

Solution in JAVA (judge verdict: Accepted)

import java.io.*;

class Main {
	public static void main(String[] args) {
		BufferedReader kb = new BufferedReader( new InputStreamReader( System.in ) );
		try {

			String str = kb.readLine();
			String[] tmpArray = str.split( " " );
			int n=Integer.parseInt( tmpArray[0] );
			int m=Integer.parseInt( tmpArray[1] );
			int l=Integer.parseInt( tmpArray[2] );
						
			int[][] matrixA = new int[n][m];
			int[][] matrixB = new int[m][l];
			double[][] matrixC = new double[n][l];
			for( int i=0; i<n; i++ ) {
				str = kb.readLine();
				tmpArray = str.split( " " );
				for( int j=0; j<m; j++ ) {
					matrixA[i][j]=Integer.parseInt( tmpArray[j] );
				}
			}
			for( int i=0; i<m; i++ ) {
				str = kb.readLine();
				tmpArray = str.split( " " );
				for( int j=0; j<l; j++ ) {
					matrixB[i][j]=Integer.parseInt( tmpArray[j] );
				}
			}

			for( int i=0; i<n; i++ ) {
				for( int k=0; k<m; k++ ) {
					for( int j=0; j<l; j++ ) {
						matrixC[i][j]+=matrixA[i][k]*matrixB[k][j];
					}
				}
			}
			
			for( int i=0; i<n; i++ ) {
				for( int j=0; j<l; j++ ) {
					if( l-1 != j ) {
						System.out.printf( "%.0f ", matrixC[i][j] );
					} else {
						System.out.printf( "%.0f\n", matrixC[i][j] );
					}
				}
			}
			
		} catch( IOException e ) {
			System.err.println( e );
		}
	}
}