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: Runtime Error)

using System;
using System.Collections.Generic;
public class Hello{
    public static void Main(){
        var array = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
        var n = array[0];
        var m = array[1];
        var A = new string[n];
        var B = new string[m];
        var Hash = new HashSet<string>();
        var target = "";
        for(var i = 0;i < n;i++){
            A[i] = Console.ReadLine();
        }
        
        for(var i = 0;i < m;i++){
            B[i] = Console.ReadLine();
            target += B[i];
        }
        
        for(var a = 0;a < n - m + 1;a++){
            for(var b = 0;b < n - m + 1;b++){
                var temp = "";
                for(var y = 0;y < m;y++){
                    for(var x = 0;x < m;x++){
                       temp += A[a + y].Substring(b + x,m); 
                    }
                }
                Hash.Add(temp);
            }
        }
        
        if(Hash.Contains(target)){
            Console.WriteLine("Yes");
        }else{
            Console.WriteLine("No");
        }
       
    }
}