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 9.2.1) (judge verdict: Accepted)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;

int main() {
  int n, m;
  cin >> n >> m;

  string a[55][55], b[55][55];
  rep(i, n) {
    string s;
    cin >> s;
    rep(j, (int)s.size()) a[i][j] = s[j];
  }
  rep(i, m) {
    string s;
    cin >> s;
    rep(j, (int)s.size()) b[i][j] = s[j];
  }

  rep(i, n-m+1) rep(j, n-m+1) {
    bool match = true;
    rep(k, m) {
      rep(l, m) {
        if (a[i+k][j+l] != b[k][l]) {
          match = false;
          break;
        }
      }
      if (!match) break;
    }
    // remaining match == true at this point infers that some part of image a perfectly matched to image b
    if (match) {
      cout << "Yes" << endl;
      return 0;
    }
  }

  cout << "No" << endl;
}