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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt(),M = sc.nextInt();
		char[][] arrayA = new char[N][N];
		char[][] arrayB = new char[N][N];
		int[] flg = new int[(N-M+1)*(N-M+1)];
		int sum=0;
		String buff;

		for(int i=0;i<N;i++) {
			buff = sc.next();
			for(int j=0;j<N;j++) {
				arrayA[i][j] = buff.charAt(j);
			}
		}
		for(int i=0;i<M;i++) {
			buff = sc.next();
			for(int j=0;j<M;j++) {
				arrayB[i][j] = buff.charAt(j);
			}
		}
		for(int i=0;i<N-M+1;i++) {
			flg[i] = sample(N,M,arrayA,arrayB);
			sum += flg[i];
			//System.out.println(flg[i]);
		}

		if(sum==0) {
			System.out.println("Yes");
		}else {
			System.out.println("No");
		}


	}
	public static int sample(int N,int M,char[][] arrayA,char[][] arrayB) {
		for(int i=0;i<N-M+1;i++) {
			for(int j=0;j<M;j++) {
				for(int l=0;l<M;l++) {
					if(arrayA[j][l+i]!=arrayB[j][l]) {
						return 1;
					}
				}
			}
			return 0;
		}
		return 0;
	}

}