Problem:
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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 PHP (judge verdict: Accepted)

<?php

fscanf(STDIN, '%d %d %d', $n, $m, $l);

for ($i = 0; $i < ($n + $m); $i++) {
    if ($i < $n) {
        $A[] = explode(' ', trim(fgets(STDIN)));
    } else {
        $B[] = explode(' ', trim(fgets(STDIN)));
    }
}

for ($i = 0; $i < $n; $i++) {
    for ($j = 0; $j < $l; $j++) {
        $C[$i][$j] = 0;
        for ($k = 0; $k < $m; $k++) {
            $C[$i][$j] += memoizeProduct($A, $B, $i, $j, $k);
        }
    }
    $result[] = implode(' ', $C[$i]);
}

echo implode(PHP_EOL, $result), PHP_EOL;

function memoizeProduct($A, $B, $i, $j, $k)
{
    static $memo;

    if (isset($memo[$i][$j][$k])) {
        return $memo[$i][$j][$k];
    }

    $memo[$i][$j][$k] = $A[$i][$k] * $B[$k][$j];

    return $memo[$i][$j][$k];
}