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: Accepted)

import java.util.Scanner;

public class Main {
	static int n;
	static int m;
	static int c;
	static int d;
	static String A;
	static String B;
	static char[][] a;
	static char[][] b;
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		n = scan.nextInt();
		m = scan.nextInt();
		a = new char[n][n];
		b = new char[m][m];
		for (int i = 0; i < n; i++) {
			A = scan.next();
			for (int j = 0; j < n; j++) {
				a[i][j] = A.charAt(j);
			}
		}
		for (int i = 0; i < m; i++) {
			B = scan.next();
			for (int j = 0; j < m; j++) {
				b[i][j] = B.charAt(j);
			}
		}
		for (c = 0; c <= n-m; c++) {
			for (d = 0; d <= n-m; d++) {
				if (search()) {
					System.out.println("Yes");
					return;
				}
			}
		}
		System.out.println("No");
	}
	static boolean search() {
		for (int k = 0; k < m; k++) {
			for (int l = 0; l < m; l++) {
				if (a[c+k][d+l] != b[k][l]) {
					return false;
				}
			}
		}
		return true;
	}
}