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)

transpose :: [[Int]] -> [[Int]]
transpose ([]:_) = []
transpose m = (map head m):(transpose (map tail m))

calcCi :: [Int] -> [[Int]] -> [Int]
calcCi _ [] = []
calcCi x (y:ys) = (sumProduct x y):(calcCi x ys)
  where
      sumProduct :: [Int] -> [Int] -> Int
      sumProduct x y = sum $ zipWith (*) x y

mulAB :: [[Int]] -> [[Int]] -> [[Int]]
mulAB [] _ = []
mulAB (x:xs) y = (calcCi x yt):(mulAB xs y)
  where
      yt = transpose y

readMatrix :: Int -> Int -> IO [[Int]]
readMatrix 0 c = return []
readMatrix r c = do
    rows  <- getLine >>= return.(map $ \n -> read n :: Int).words
    rests <- readMatrix (r-1) c
    return $ rows:rests

printMatrix :: [[Int]] -> IO ()
printMatrix = mapM_ (\nums -> putStrLn $ unwords [show n | n <- nums])

main :: IO ()
main = do
    [n,m,l] <- getLine >>= return.(map $ \n -> read n :: Int).words
    a <- readMatrix n m
    b <- readMatrix m l
    printMatrix $ mulAB a b