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 <bits/stdc++.h>

using namespace std ;

int main ( )

{
    int x, y ;
    bool flag = false ;
    scanf("%d%d",&x,&y) ;
    string arr1[x], arr2 [y];

    for (int i = 0 ; i<x; i++)
    {
        for (int j =0 ; j<x; j++)
            cin >> arr1[i][j] ;
    }
    for (int i = 0 ; i<y; i++)
    {
        for (int j =0 ; j<y; j++)
            cin >> arr2[i][j] ;

    }
    for (int i = 0 ; i<x; i++)
    {
        for (int j =0 ; j<x; j++)
            for (int m = 0 ; m<y; m++)
            {
                for (int n =0 ; n<y; n++)
                {
                    flag= false ;
                    if (arr2[m][n] ==arr1[i][j] )
                        flag = true ;
                }


            }
    }
    if (flag)
        cout << "Yes";
    else
        cout << "No" ;
    return 0 ;
}