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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
int main(void){
  int m,n,i,j,Ai,Aj,a[51][51],b[51][51];
  scanf("%d %d",&n,&m);
  for(i=0;i<n;i++){
    for(j=0;j<n;j++){
      scanf("%d",&a[i][j]);
    }
  }
  for(i=0;i<m;i++){
    for(j=0;j<m;j++){
      scanf("%d",&b[i][j]);
    }
  }
  for(Ai=0;Ai<n-m+1;Ai++){
    for(Aj=0;Aj<n-m+1;Aj++){
  	  for(int i=0; i<m; i++){
        for(int j=0; j<m; j++){
          if(a[Ai+i][Aj+j]!=b[i][j]){
            break;
          }
          if((i==m-1)&&(j=m-1)){
            printf("Yes");
            return 0;
          }
        }
      }  
    }        
  }          
  printf("No");
}