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>
#include <vector>
#include <algorithm>
#include <chrono>

using namespace std;
using namespace std::chrono;

vector<string> a, b;
int n, m;

bool check(int s_i, int s_j) {
  for (int i = 0; i < m; ++i)
    for (int j = 0; j < m; ++j)
      if (a[s_i + i][s_j +j] != b[i][j])
        return false;
  return true;
}

int main() {
  auto start = high_resolution_clock::now();

  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);

  cin >> n >> m;
  a.resize(n);
  for (int i = 0; i < n; ++i)
    cin >> a[i];
  b.resize(m);
  for (int i = 0; i < m; ++i)
    cin >> b[i];

  for (int i = 0; i + m < n; ++i)
    for (int j = 0; j + m < n; ++j)
      if (check(i, j)) {
        cout << "Yes\n";
        return 0;
      }

  cout << "No\n";

  cerr << "Total execution time : " << duration_cast<milliseconds>(high_resolution_clock::now() - start).count() << " ms" << endl;

  return 0;
}