Problem:
Score : 200 points

Problem Statement

You are given an image A composed of N rows and N columns of pixels, and a template image B composed of M rows and M columns of pixels.

A pixel is the smallest element of an image, and in this problem it is a square of size 1×1.

Also, the given images are binary images, and the color of each pixel is either white or black.

In the input, every pixel is represented by a character: . corresponds to a white pixel, and # corresponds to a black pixel.

The image A is given as N strings A_1,...,A_N.

The j-th character in the string A_i corresponds to the pixel at the i-th row and j-th column of the image A (1≦i,j≦N).

Similarly, the template image B is given as M strings B_1,...,B_M.

The j-th character in the string B_i corresponds to the pixel at the i-th row and j-th column of the template image B (1≦i,j≦M).

Determine whether the template image B is contained in the image A when only parallel shifts can be applied to the images.

Constraints

1≦M≦N≦50

A_i is a string of length N consisting of # and ..

B_i is a string of length M consisting of # and ..

Input

The input is given from Standard Input in the following format:

N M
A_1
A_2
:
A_N
B_1
B_2
:
B_M

Output

Print Yes if the template image B is contained in the image A. Print No otherwise.

Sample Input 1

3 2
#.#
.#.
#.#
#.
.#

Sample Output 1

Yes

The template image B is identical to the upper-left 2 × 2 subimage and the lower-right 2 × 2 subimage of A. Thus, the output should be Yes.

Sample Input 2

4 1
....
....
....
....
#

Sample Output 2

No

The template image B, composed of a black pixel, is not contained in the image A composed of white pixels.

Solution in Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val inputs: Seq[String] = scala.io.Source.stdin.getLines().toList
  val nums = inputs.head.split(" ").map(_.toInt)
  val n = nums(0)
  val m = nums(1)
  val images = inputs.tail

  println(solve(n, m, images))

  private def solve(n: Int, m: Int, images: Seq[String]): String = {
    val loopEnd = n - m
    val imagesTup = images.splitAt(n)
    val nImage  = imagesTup._1
    val mImage  = imagesTup._2
    val checkStart = mImage(0)(0)

    (0 to loopEnd).foreach { i =>
      val line = nImage(i)

      (0 to loopEnd).foreach { j =>
        if(line(j) == checkStart) {
          var ok = true
          (0 until m).foreach { k =>
            val checkLine = images(i + k).splitAt(j)._2.splitAt(m)._1
            if( checkLine != mImage(k)) {
              ok = false
            }
          }

          if(ok) {
            return "Yes"
          }
        }
      }

    }
    return "No"
  }
}