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

type Row = [Int]

type Rows = [Row]

type Matrix = (Int, Int, Rows)

type Problem = (Matrix, Matrix)

type Result = Rows

access :: Rows -> Int -> Int -> Int

access rows row col
    = rows !! row !! col
    
calcElement :: Matrix -> Matrix -> Int -> Int -> Int

calcElement (_, m, rows1) (_, _, rows2) row col
    = sum [access rows1 row x * access rows2 x col | x <- ms] where
        ms = [0..(m - 1)]

solve :: Problem -> Result

solve (mat1@(n, _, _), mat2@(_, l, _))
    = [[calcElement mat1 mat2 row col | col <- ls] | row <- ns] where
        ns = [0..(n - 1)]
        ls = [0..(l - 1)]

output :: Result -> String

output rows
    = init.concat $ [outputRow row ++ "\n" | row <- rows]
    
outputRow :: Row -> String

outputRow row
    = init.concat $ [show x ++ " " | x <- row]
    
input :: IO Problem

input
    = do
        [n, m, l] <- map read.words <$> getLine
        rows1 <- inputRows n []
        rows2 <- inputRows m []
        return ((n, m, rows1), (m, l, rows2))
        
inputRows :: Int -> Rows -> IO Rows

inputRows 0 rows
    = return rows
    
inputRows n rows
    = do
        row <- map read.words <$> getLine
        inputRows (n - 1) $ rows ++ [row]
    
main :: IO ()

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