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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
	public static void main(String[] args) throws Exception{
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
    	int m = scn.nextInt();
    	char[][] aa = new char[n][n];
    	char[][] bb = new char[m][m];
    	for(int i=0;i<n;i++){
      		String a = scn.next();
      		for(int j=0;j<n;j++){
        		aa[i][j]=a.charAt(j);
      		}
    	}
    	for(int i=0;i<m;i++){
      		String b = scn.next();
      		for(int j=0;j<m;j++){
        		bb[i][j]=b.charAt(j);
      		}
    	}
      	String ans = "No";
      	for(int i=0;i<n;i++){
      		for(int j=0;j<n;j++){
        		if(i+m>n || j+m>n){
          			break;
        		}
        		for(int k=0;k<m;k++){
          			for(int l=0;l<m;l++){
            			if(aa[i+k][j+l]==bb[k][l]){
              				ans = "Yes";
              				break;
            			}
          			}
        		}
            }
      	}
    	System.out.println(ans);
	}
}