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 System.Linq;
using System.Text;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var firstLine = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToList();
			var n = firstLine[0];
			var m = firstLine[1];

			var pictureA = new List<string>();
			var pictureB = new List<string>();

			for(int i = 0; i < n; i++)
			{
				pictureA.Add(Console.ReadLine());
			}

			for(int i = 0; i < m; i++)
			{
				pictureB.Add(Console.ReadLine());
			}

			var isMatched = true;

			for(int i = 0; i <= n - m; i++)
			{
				for(int j = 0; j <= n - m; j++)
				{
					isMatched = true;

					for(int k = 0; k < m; k++)
					{
						for(int l = 0; l < m; l++)
						{
							if(pictureA[i + k][j + l] != pictureB[k][l])
							{
								isMatched = false;
								break;
							}
						}

						if(!isMatched)
						{
							break;
						}
					}

					if(isMatched)
					{
						Console.WriteLine("Yes");
						return;
					}
				}
			}

			Console.WriteLine("No");
        }
	}
}