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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using static System.Console;

class Program {
	static int n, m;
	static string[] a, b;

	static void Main() {
		n = NextInt();
		m = NextInt();
		Array.Resize(ref a, n);
		Array.Resize(ref b, n);

		for (var i = 0; i < n; i++) {
			a[i] = ReadLine();
		}
		for (var i = 0; i < m; i++) {
			b[i] = ReadLine();
		}
		for (var i = 0; i < n; i++) {
			for (var j = 0; j < n; j++) {
				if (Judge(i, j)) {
					WriteLine("Yes");
					return;
				}
			}
		}
		WriteLine("No");
	}

	static bool Judge(int ni, int nj) {
		for (var i = 0; i < m; i++) {
			for (var j = 0; j < m; j++) {
				if (ni + i >= n || nj + j >= n || b[i][j] != a[ni + i][nj + j]) {
					return false;
				}
			}
		}
		return true;
	}

	static int NextInt() {
		return int.Parse(NextString());
	}

	static string NextString() {
		var result = new List<char>();
		while (true) {
			int next = Read();
			if (next < 0)
				break;
			var nextChar = (char)next;
			if (!char.IsWhiteSpace(nextChar))
				result.Add(nextChar);
			else if (nextChar != '\r')
				break;
		}
		return string.Join("", result);
	}
}