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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Main
{
    class Program
    {
        static void Main(string[] args)
        {
            bool flag = false;
            string[] str = Console.ReadLine().Split(' ');
            int N, M, buf;
            N = int.Parse(str[0]);
            M = int.Parse(str[1]);
            string[] map = new string[N];
            string[] check = new string[M];
            for (int a = 0; a < N; a++)
            {
                map[a] = Console.ReadLine();
            }
            for (int a = 0; a < M; a++)
            {
                check[a] = Console.ReadLine();
            }

            for (int a = 0; a < N - M; a++)
            {
                buf = map[a].IndexOf(check[0]);
                if (buf != -1)
                {
                    flag = true;
                    for(int b = 0; b < M; b++)
                    {
                        if (map[a + b].IndexOf(check[b], buf) != buf)
                        {
                            flag = false;
                            break;
                        }
                    }
                }
                if (flag == true) break;
            }

            if (flag == true) Console.WriteLine("Yes");
            else Console.WriteLine("No");

        }
    }
}