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.IO;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtCodeeeer
{
    class AtCOOOOOOOOOOOder
    {
        static int[] hs;
        static long ans;
        static void Main(string[] args)
        {
            int[] nm = ReadLine().Split(' ').Select(int.Parse).ToArray();
            int n = nm[0];
            int m = nm[1];
            char[,] An = new char[n, n];
            for (int i = 0; i < n; i++)
            {
                var hoge = ReadLine();
                for (int j = 0; j < n; j++)
                {
                    An[i, j] = hoge[j];
                }
            }
            char[,] Bn = new char[m, m];
            for (int i = 0; i < m; i++)
            {
                var hoge = ReadLine();
                for (int j = 0; j < m; j++)
                {
                    Bn[i, j] = hoge[j];
                }
            }

            //探索
            //探索開始点 [i,j]
            for (int i = 0; i < n-m+1; i++)
            {
                for (int j = 0; j < n-m+1; j++)
                {
                    bool roop = true;
                    //照合処理
                    //見つかったら return;
                    //照合失敗時点で continue;
                    for (int k = 0; k < m; k++)
                    {
                        if (!roop) break;
                        for (int l = 0; l < m; l++)
                        {
                            if (An[i + k, j + l] != Bn[k, l]) { roop = false;  break; }
                            else
                            {
                                if (k == m - 1 && l == m - 1)
                                {
                                    Console.WriteLine("Yes");
                                    return;
                                }
                            }
                        }
                    }


                }
            }
            Console.WriteLine("No");

        }
    }
}