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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
    // $list = explode(" ", trim(fgets(STDIN)));
fscanf(STDIN,"%d%d",$n ,$m);
for($i=0;$i<$n+$m;$i++){
  if($i<$n){
    $a_li[] = trim(fgets(STDIN));
  }else{
    $b_li[] = trim(fgets(STDIN));
  }
}
$true_count = 0;
//for($i=0;$i<$n;$i++){
  for($j=0;$j<$n-$m;$j++){
    $start_i = $i;
    $start_j = $j;
    $end = $i+$m;
    //echo "end ".$end."\n";
    for($k=0;$k<$m;$k++){
      for($s=$j;$s<$j+$m;$s++){
        //echo $k." ".$s."\n";
        //echo "k s j".$k." ".$s." ".$j."\n";
        //echo $a_li[$k][$s]." ".$b_li[$k][$s-$j]."\n";
        if($a_li[$k][$s]!=$b_li[$k][$s-$j]){
          break;
        }
        $true_count++;
        if($true_count==$m*$m){
          echo "Yes";
          exit;
        }
      }
    }
    $true_count = 0;
  }
//}
    

echo "No";