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.HashSet;
import java.util.Scanner;
import java.util.Set;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			int m = scanner.nextInt();
			String[] a = new String[n];
			String[] b = new String[m];
			IntStream.range(0, n).forEach(i -> a[i] = scanner.next());
			IntStream.range(0, m).forEach(i -> b[i] = scanner.next());
			int line = 0;
			Set<Integer> preIndexSet = new HashSet<>();
			boolean found = false;
			for (int i = 0; i < n; i++) {
				Set<Integer> indexSet = getIndexSet(a[i], b[line]);
				if (indexSet.size() > 0) {
					if (line == 0) {
						line++;
						preIndexSet.addAll(indexSet);
					} else {
						preIndexSet.retainAll(indexSet);
						if (preIndexSet.size() > 0) {
							line++;
						}
					}
					if (line >= m) {
						found = true;
						break;
					}
				} else {
					line = 0;
					preIndexSet.clear();
				}
			}
			System.out.println(found ? "Yes" : "No");
		}
	}

	/**
	 * @param a
	 * @param b
	 * @return bがaの中で出現するindexのセット
	 */
	private static Set<Integer> getIndexSet(String a, String b) {
		Set<Integer> set = new HashSet<>();
		int from = 0;
		int index;
		while ((index = a.indexOf(b, from)) > 0) {
			set.add(index);
			from = index + 1;
		}
		return set;
	}
}