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>
#include <stdlib.h>
#include <string.h>

#define MAX(a,b) (a > b) ? a : b
#define MIN(a,b) (a < b) ? a : b
const int inf = 1000000000; // 10^9

int main(){
   int n,m;scanf("%d %d",&n,&m);
   char a[51][51];for(int i = 0;i < n;i++)scanf("%s",a[i]);
   char b[51][51];for(int i = 0;i < m;i++)scanf("%s",b[i]);
   int match = 1;
   //int count = 0;
   //printf("n:%d m:%d\n",n,m);
   for(int i = 0;i < (n-m);i++){
      for(int j = 0;j < (n-m);j++){
         for(int k = 0;k < m;k++){
            for(int l = 0;l < m;l++){
               //printf("i:%dj:%dk:%dl:%d\n",i,j,k,l);
               if(a[k][l] != b[i+k][j+l])match--;
               if(match == 0)break;
               //count++;
            }
            if(match == 0)break;
         }
         if(match == 0)break;
      }
      if(match == 0)break;
   }
   //printf("%d\n",count);
   if(match == 1)printf("Yes\n");
   else printf("No\n");
}