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 Scala (judge verdict: Accepted)

/**
  * http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_7_D&lang=jp
  * Structured Program II - Matrix Multiplication
  */
object Main {
  type Matrix[T] = Seq[Seq[T]]

  def main(args: Array[String]): Unit = {
    val Array(n, m, l) = io.StdIn.readLine().split(" ").map(_.toInt)
    val matrixA = readMatrix(n)
    val matrixB = readMatrix(m)
    val result = multiplyMatrix(matrixA, matrixB)
    result.foreach(row => println(row.mkString(" ")))
  }

  def readMatrix(rows: Int): Matrix[Int] = {
    Iterator.continually(io.StdIn.readLine()).takeWhile(_ != null).take(rows).map(_.split(" ").map(_.toInt).toSeq).toList
  }

  def swapDim(matrix: Matrix[Int]): Matrix[Int] = {
    val width = matrix.head.length
    (0 until width).map(column => matrix.map(_ (column)))
  }

  // element type is Long
  def multiplyMatrix(matrixA: Matrix[Int], matrixB: Matrix[Int]): Matrix[Long] = {
    val swappedB = swapDim(matrixB)
    matrixA.map(elemA => swappedB.map(elemB => (elemA zip elemB).foldLeft(0L)((acc, x) => acc + x._1 * x._2)))
  }
}