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;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var m = int.Parse(line[1]);
        var map = new char[n, n];
        var map2 = new char[m, m];
        for (int i = 0; i < n; i++)
        {
            var s = Console.ReadLine().Trim();
            for (int j = 0; j < n; j++) map[i, j] = s[j];
        }
        for (int i = 0; i < m; i++)
        {
            var s = Console.ReadLine().Trim();
            for (int j = 0; j < m; j++) map2[i, j] = s[j];
        }
        Console.WriteLine(checkMap(map, map2) ? "Yes" : "No");
    }
    public static bool checkMap(char[,] map, char[,] map2)
    {
        var n = map.GetLength(0); var m = map2.GetLength(0);
        for (int i = 0; i <= n - m; i++)
            for (int j = 0; j <= n - m; j++)
                if (checkMap2(map, map2, i, j)) return true;
        return false;
    }
    public static bool checkMap2(char[,] map, char[,] map2, int x, int y)
    {
        var m = map2.GetLength(0);
        for (int i = 0; i < m; i++)
            for (int j = 0; j < m; j++)
            {
                var nx = x + i;
                var ny = y + j;
                if (map[nx, ny] != map2[i, j]) return false;
            }
        return true;
    }
}