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;
  bool flag1=true;
  vector<string>A(N);
  vector<string>B(M);
  for(int i=0;i<N;i++){
    cin>>A.at(i);
  }
  for(int i=0;i<M;i++){
    cin>>B.at(i);
  }
  for(int i=0;i<N-M;i++){
    bool flag=true;
    for(int j=0;j<N-M;j++){
      for(int k=0;k<M;k++){
        for(int l=0;l<M;l++){
          if(B.at(k).at(l)!=A.at(i+k).at(j+l)){
            flag=false;
          }
        }
      }
    }
    if(flag){
      cout<<"Yes"<<endl;
      flag1=false;
      break;
    }
  }
  if(flag1){
    cout<<"No"<<endl;
  }
}