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 Haskell (judge verdict: Accepted)

import Control.Applicative

import Control.Monad
    (replicateM)

import Data.List
    (transpose)

type Vector = [Int]

type Matrix = [Vector]

type Problem = (Matrix, Matrix)

type Result = Matrix

multiply :: Vector -> Vector -> Int

multiply matrix1 matrix2
    = sum $ zipWith (*) matrix1 matrix2

solve :: Problem -> Result

solve (matrix1, matrix2)
    = [[multiply vector1 vector2 | vector2 <- matrix2t] | vector1 <- matrix1] where
        matrix2t = transpose matrix2

output :: Result -> String

output matrix
    = init.concat $ [outputVector vector ++ "\n" | vector <- matrix]

outputVector :: Vector -> String

outputVector vector
    = init.concat $ [show x ++ " " | x <- vector]

input :: IO Problem

input
    = do
        [n, m, _] <- map read.words <$> getLine
        matrix1 <- inputMatrix n
        matrix2 <- inputMatrix m
        return (matrix1, matrix2)

inputMatrix :: Int -> IO Matrix

inputMatrix n
    = map (map read.words) <$> replicateM n getLine

main :: IO ()

main
    = putStrLn.output =<< solve <$> input