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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int an = in.nextInt();
		int bn = in.nextInt();
		int[][] a = new int[an][an];
		int[][] b = new int[bn][bn];
		for(int i=0;i<an;i++){
			String row = in.next();
			for(int j=0;j<an;j++){
				a[i][j] = row.charAt(j);
			}
		}
		for(int i=0;i<bn;i++){
			String row = in.next();
			for(int j=0;j<bn;j++){
				b[i][j] = row.charAt(j);
			}
		}
		boolean work = false;
		for(int i=0;i<an;i++){
			for(int j=0;j<an;j++){
				if(compare(a,b,i,j)){
					work = true;
					break;
				}
			}
		}
		System.out.println(work ? "YES" : "NO");
	}
	public static boolean compare(int[][] a, int[][] b, int ai, int aj){
		if(ai + b.length >= a.length || aj + b.length >= a.length) return false;
		for(int i=ai;i<ai+b.length;i++){
			for(int j=aj;j<aj+b.length;j++){
				if(a[i][j] != b[i-ai][j-aj]) return false;
			}
		}
		return true;
	}
}