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;

namespace AtConderBeginnerContest054
{
    class ProgramB
    {
        static void Main(string[] args)
        {
            string szTotal = Console.ReadLine();
            string[] szArr = szTotal.Split(' ');
            int n = int.Parse(szArr[0]);
            int m = int.Parse(szArr[1]);

            string[] a = new string[n];
            for( int i=0;i<a.Length;++i)
            {
                a[i] = Console.ReadLine();
            }
            string[] b = new string[m];
            for( int i=0;i<b.Length;++i)
            {
                b[i] = Console.ReadLine();
            }

            string result = Solve(a, b) ? "Yes" : "No";
            Console.WriteLine(result);
        }
        private static bool Solve(string[] a, string[] b)
        {
            // そもそもaが小さければ含まれない
            if( a.Length < b.Length) { return false; }

            int total = a.Length - b.Length;
            for( int i=0;i<= total;++i)
            {
                for(int j=0;j<=total;++j)
                {
                    // a[i][j] からマッチング判定



                    if(IsMatch(a, b, i, j))
                    {
                        return true;
                    }
                }
            }

            return false;
        }

        private static bool IsMatch(string[] a, string[] b, int startRow, int startCol)
        {
            for(int i=0;i<b.Length;++i)
            {
                for(int j=0;j<b.Length;++j)
                {
                    char ca = a[startRow + i][startCol + j];
                    char cb = b[i][j];
                    if( ca != cb) { return false; }
                }
            }
            return true;
        }
    }


}