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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php 
  fscanf(STDIN, "%d %d",$N, $M);
  $N_img = ""; $M_img = "";
  $ans = "No";

  for($i=0;$i<$N;$i++){
   $N_img[$i] = str_split(trim(fgets(STDIN)));
  }
  for($j=0;$j<$M;$j++){
    $M_img[$j] = str_split(trim(fgets(STDIN)));
  }

	for($i=0;$i<$N-$M;$i++){
       for($j=0;$j<$N-$M;$j++){	
		
         $count = 0;

         for($k=0;$k<$M;$k++){
           for($l=0;$l<$M;$l++){
			if($N_img[$i+$k][$j+$l] == $M_img[$k][$l]){
              $count++;
            }
          } 
        }
      }
    }

	if($count == $M*$M) $ans = "Yes";
	echo $count."\n";
	echo $ans;
  
  ?>