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;
using System.Collections.Generic;
using System.Text;
using static MyIO;


public class B
{
	public static void Main()	
	{
		int N = GetInt();
		int M = GetInt();
		int[,] A = new int[N,N];
		int[,] B = new int[M,M];
		for(int i = 0; i < N; i++)
		{
			string str = GetString();
			for(int j = 0; j < N; j++)
				A[i,j] = (str[j] == '.') ? 0 : 1;
		}
		for(int i = 0; i < M; i++)
		{
			string str = GetString();
			for(int j = 0; j < M; j++)
				B[i,j] = (str[j] == '.') ? 0 : 1;
		}

		for(int left = 0; left < N - M + 1; left++)
		{
			for(int top = 0; top < N - M + 1; top++)
			{
				int sum = 0;
				for(int i = 0; i < M; i++)
				{
					for(int j = 0; j < M; j++)
					{
						sum += A[left + i, top + j]^B[i,j];
					}
				}
				if(sum == 0)
				{
					Console.WriteLine("Yes");
					return;
				}
			}
		}
		Console.WriteLine("No");
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}