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<string>
#include<cmath>
using namespace std;

int main(){
	int n,m;
	cin>>n>>m;
	int i,j,x=-1,k,h,d,t;
	char a[51][51],b[51][51];
	char c;
	for(i=0;i<n;i++){
		for(j=0;j<n;j++)
		cin>>a[i][j];
	}
	for(i=0;i<m;i++){
		for(j=0;j<m;j++)
		cin>>b[i][j];
	}
	for(i=0;i<n;i++){
		for(j=0;j<n;j++){
			x=-1;
			if(a[i][j]==b[0][0]&&k+m<=n&&h+m<=n){
				k=i;
				h=j;
				x=0;
			for(d=0;d<m;d++){
				for(t=0;t<m;t++){
					if(a[d+k][t+h]!=b[d][t]){
						x=1;
						break;
					}
				}
				if(x==1)
				break;
			}
			}
			if(x==1)
			continue;
			else if(x==0){
			cout<<"Yes"<<endl;	
			return 0;
			}
			
		}
	}
	
	cout<<"No"<<endl;
	return 0;
}