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;

namespace AtCoder
{
    class Program
    {
        static char[,] a;
        static char[,] b;

        static void Main(string[] args)
        {
            //[summary]B - Template Matching
            var line = ReadLine();
            int n = line[0];
            int m = line[1];

            a = GetPicture(n);
            b = GetPicture(m);

            for(int i = 0; i <= n - m; i++)
            {
                for(int j = 0; j < n - m; j++)
                {
                    if (IsMatch(i, j))
                    {
                        Console.WriteLine("Yes");
                        return;
                    }
                }
            }

            Console.WriteLine("No");
        }

        static bool IsMatch(int y, int x)
        {
            int m = b.GetLength(0);

            for(int i = 0; i < m; i++)
            {
                for(int j = 0; j < m; j++)
                {
                    if (a[y + i, x + j] != b[i, j])
                    {
                        return false;
                    }
                }
            }

            return true;
        }

        static char[,] GetPicture(int n)
        {
            var picture = new char[n, n];

            for(int i = 0; i < n; i++)
            {
                var s = Console.ReadLine();

                for(int j = 0; j < n; j++)
                {
                    picture[i, j] = s[j];
                }
            }

            return picture;
        }

        static List<int> ReadLine()
        {
            var line = Console.ReadLine();
            var array = line.Split(' ');

            return array.Select(x => int.Parse(x)).ToList();
        }
    }
}