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 <bits/stdc++.h>
using namespace std;
int main(){
  int n, m;
  cin >> n >> m;
  vector<vector<char>> a(n+1, vector<char>(n+1,'z'));
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) cin >> a[i][j];
  }
  vector<vector<char>> b(m+1, vector<char>(m+1,'z'));
  for (int i = 1; i <= m; i++) {
    for (int j = 1; j <= m; j++) cin >> b[i][j];
  }
  
  for (int i = 0; i <= n-m; i++) {
    for (int j = 0; j <= n-m; j++) {
      for (int h = 1; h <= m; h++) {
        for (int w = 1; w <= m; w++) {
          if (a[i+h][j+w] != b[h][w]) break;
          if (h == m && w == m) {
            cout << "Yes" << endl;
            return 0;
          }
        }
      }
    }
  }
  
  cout << "No" << endl;
}