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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;
int main(){
  int N, M;
  cin >> N >> M;
  char mp[N][N];
  for(int i = 0; N > i; i++){
    for(int j = 0; N > j; j++){
      cin>>mp[i][j];
    }
  }
  char matching[M][M];
  for(int i = 0; M > i; i++){
    for(int j = 0; M > j; j++){
      cin>>matching[i][j];
    }
  }
  bool ok;
  for(int i = 0; M-N+1 >= i; i++){
    for(int j = 0; M-N+1 >= j; j++){
      ok = true;
      for(int k = 0; M > k; k++){
        for(int l = 0; M > l; l++){
          if(mp[k+i][l+j] != matching[k][l]){
            ok = false;
            break;
          }
        }
        if(!ok)break;
      }
    }
    if(ok)break;
  }
  if(ok)cout << "Yes" << endl;
  else cout << "No" << endl;
}