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 <sstream>
#include <fstream>
#include <string>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <utility>
#include <bitset>
#include <cmath>
#include <cstdlib>
#include <cstdio>

using namespace std;

const long long INF = 100000000;
const long long MOD = 1000000007;


long long gcd(long long a,long long b){
  if(a<b){
    swap(a, b);
  }
  if(a%b==0)
    return b;
  return gcd(a % b, b);
}

int main()
{
  int N, M;
  cin >> N >> M;
  string A[N];
  string B[M];
  for (int i = 0; i < N;i++){
    cin >> A[i];
  }
  for (int i = 0; i < M; i++)
  {
    cin >> B[i];
  }
  bool ans = false;
  for (int i = 0; i < N; i++)
  {
    for (int j = 0; j < A[i].length();j++){
      //一致しているか
      bool an = true;
      for (int a = 0; a < M;a++){
        for (int b = 0; b < B[a].length();b++){
          if (i + a < N && j + b < A[i].length()){
            if (A[i + a][j + b] != B[a][b])
              an = false;
          }

        }
      }
      if(an)
        ans = true;
    }
  }

  if(ans)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}