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 (2.11.7) (judge verdict: Wrong Answer)

import scala.io.{ StdIn => in}
import scala.annotation.tailrec

object Main extends App {
  val Array(n, m) = in.readLine.split(" ").map(_.toInt)
  val a = Iterator.continually(in.readLine.toCharArray)
    .take(n)
    .toArray
  val b = Iterator.continually(in.readLine.toCharArray)
    .take(m)
    .toArray

  val res = for {
    i <- 0 until n-m
    j <- 0 until n-m
    } yield {
      val res0 = for {
        k <- 0 until m
        l <- 0 until m
      } yield {
        a(i+k)(j+l) == b(k)(l)
      }
      res0.forall(_ == true)
    }

  val ans = if(res.exists(_ == true)) "Yes" else "No"
  println(ans)
}