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
list($n,$m)=explode(" ",trim(fgets(STDIN)));
$i=0;
while($i<$n){
  $a[]=trim(fgets(STDIN));
  ++$i;
}
$i=0;
while($i<$m){
  $b[]=trim(fgets(STDIN));
  ++$i;
}
$i=0;
while($i<$n-$m){
  $j=0;
  while($j<$n-$m){
    if(substr($a[$i],$j,$m)==substr($b[0],0,$m)){
      $flag=1;
      $k=$i+1;
      while($k<$i+$m){
        if(substr($a[$k],$j,$m)!=substr($b[$k-$i],0,$m)){
          $flag=0;
          break;
        }
        ++$k;
      }
      if($flag){
        echo "Yes";
        exit;
      }
    }
    ++$j;
  }
  ++$i;
}
echo "No";