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) {
		try (Scanner sc = new Scanner(System.in)) {
			int N = sc.nextInt();
			int M = sc.nextInt();
			char[][] nmap = new char[N][N];
			char[][] mmap = new char[M][M];
			int nwcnt = 0;
			int nbcnt = 0;
			int mwcnt = 0;
			int mbcnt = 0;
			for (int i = 0; i < N; i++) {
				nmap[i] = sc.next().toCharArray();
				for (char c : nmap[i]) {
					if (c == '.') {
						nwcnt++;
					} else {
						nbcnt++;
					}
				}
			}
			for (int i = 0; i < M; i++) {
				mmap[i] = sc.next().toCharArray();
				for (char c : mmap[i]) {
					if (c == '.') {
						mwcnt++;
					} else {
						mbcnt++;
					}
				}
			}

			if (nwcnt < mwcnt || nbcnt < mbcnt) {
				System.out.println("No");
			} else {

				boolean ngflg = false;
				boolean okflg = false;
				try {
					for (int r = 0; r < N - M + 1; r++) {
						for (int c = 0; c < N - M + 1; c++) {
							okflg = false;
							ngflg = false;
							for (int mr = 0; mr < M; mr++) {
								for (int mc = 0; mc < M; mc++) {
									if (r + mr >= N || c + mc >= N || nmap[r + mr][c + mc] != mmap[mr][mc]) {
										ngflg = true;
										break;
									}
								}
								if (ngflg) {
									break;
								}
								okflg = true;
							}
						}
					}

					if (okflg) {
						System.out.println("Yes");
					} else {
						System.out.println("No");
					}
				} catch (Exception e) {
					System.out.println("No");
				}

			}
		}
	}
}