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 Control.Applicative ((<$>), (<*>))
import qualified Control.Monad as Monad (replicateM)
import qualified Data.List as List (transpose)
import qualified Data.List.Split as Split (chunksOf)

type Row = [Int]
type Matrix = [Row]

main = do
    [n,m,l] <- getLine'
    a <- Monad.replicateM n getLine'
    b <- Monad.replicateM m getLine'
    let result = toMatrix l $ dotProduct <$> a <*> List.transpose b
    mapM_ (putStrLn . printFormat) result

getLine' :: IO [Int]
getLine' = map (read :: String -> Int) . words <$> getLine

printFormat :: Row -> String
printFormat xs = unwords $ show <$> xs

toMatrix :: Int -> [Int] -> Matrix
toMatrix n xs = Split.chunksOf n xs

dotProduct :: Row -> Row -> Int
dotProduct xs ys = sum $ zipWith (*) xs ys