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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader buff = null;
		buff = new BufferedReader(new InputStreamReader(System.in));

		String[] box = buff.readLine().split(" ");
		int N = Integer.parseInt(box[0]);
		int M = Integer.parseInt(box[1]);

		String[] img = new String[ N ];
		int img_h = N;
		int img_w = 0;
		for (int i = 0; i < N; ++i) {
			img[i] = buff.readLine();
		}
		img_w = img[0].length();

		int h = 0;
		int w = 0;
		String[] pre_img = new String[ N ];
		String line = null;
		while ((line = buff.readLine()) != null) {
			if(line.equals("")){ break; }
			pre_img[h] = line;
			++h;
		}
		w = pre_img[0].length();
		boolean flag = false;

		for (int i = 0; i <= img_h - h; ++i) {
			for (int j = 0; j <= img_w - w; ++j) {

				int k = 0;
				int l = 0;

				for (k = 0; k < h; ++k) {
					for (l = 0; l < w; ++l) {
						if (img[i + k].charAt(j + l) != pre_img[k].charAt(l)) {
							break;
						}
					}
					if (l != w) {
						break;
					}
				}

				if (k == h && l == w) {
					flag = true;
					break;
				}
			}
		}

		if (flag) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}

	}

}