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.Text;

struct coord
{
    public int row;
    public int col;
}

class Program
{
    public static int Main()
    {
        do
        {
            new Program().solve();
        } while (false);
        return 0;
    }
    public void solve()
    {
        string[] str = Console.ReadLine().Split(' ');
        int N = int.Parse(str[0]);
        int M = int.Parse(str[1]);

        string[] A = new string[N];
        string[] B = new string[M];

        for (int i = 0; i < N; ++i)
        {
            A[i] = Console.ReadLine();
        }
        for (int i = 0; i < M; ++i)
        {
            B[i] = Console.ReadLine();
        }

        System.Collections.Generic.Queue<coord> queue = new Queue<coord>();
        for (int row = 0; row < N - M + 1; ++row)
        {
            int offset = 0;
            while (offset < N - M + 1)
            {
                int col = A[row].IndexOf(B[0], offset);
                if (col != -1)
                {
                    coord v;
                    v.row = row;
                    v.col = col;
                    queue.Enqueue(v);
                    offset = col + 1;
                }
                else
                {
                    break;
                }
            }
        }

        bool exist = false;
        while (queue.Count > 0)
        {
            bool match = true;
            coord v = queue.Dequeue();
            for (int i = 0; i < M; ++i)
            {
                if (A[v.row + i].IndexOf(B[i], v.col) != v.col)
                {
                    match = false;
                    break;
                }
            }
            if (match)
            {
                exist = true;
                break;
            }
        }

        if (exist)
        {
            Console.WriteLine("Yes");
        }
        else
        {
            Console.WriteLine("No");
        }
    }
}