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,area,counter=0;
    int flage=0;
    char cf,cs;
    cin>>n>>m;
    char af[n][n];
    char as[m][m];
    area=m*m;
    for(int i=0;i<n;i++)
        for(int j=0;j<n;j++)
            cin>>af[i][j];
    for(int k=0;k<m;k++)
        for(int l=0;l<m;l++)
            cin>>as[k][l];
        for(int z=0;z<n;z++)
            for(int x=0;x<n;x++){
                cf=af[z][x];
            	cs=as[0][0];
                     if(cf==cs){
                        int a=z;
                        int b=x;
                        for(int h=0;h<m;h++)
                            for(int g=0;g<m;g++){
                                cf=af[a][b];
                                cs=as[h][g];
                                if(cf==cs)
                                    counter+=1;
                                b++;
                            }
                        a++;
                    }
                    if(counter==area)
                        flage=1;
                    counter=0;
        }
        if(flage==1)
            printf("Yes");
        else
            printf("No");
    return 0;
}