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 Haskell (judge verdict: Accepted)

import Data.List (transpose)
import Control.Applicative
import Control.Monad
mult :: Num a => [[a]] -> [[a]] -> [[a]]
mult a b' = let b = transpose b' in
    map (\l ->  map (sum . zipWith (*) l) b ) a

readMatrix :: Int -> IO [[Int]]
readMatrix n = map (map read .words) <$> replicateM n getLine

main = do
    [n,m,l] <- map read . words <$> getLine
    a <- readMatrix n
    b <- readMatrix m
    mapM_ (putStrLn . unwords . map show) $ mult a b