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.Linq;
using System.Collections.Generic;

class P
{
    static void Main()
    {
        int[] NM = Console.ReadLine().Split().Select(int.Parse).ToArray();
        string[] A = new string[NM[0]].Select(x => Console.ReadLine()).ToArray();
        string[] B = new string[NM[1]].Select(x => Console.ReadLine()).ToArray();

        for (int i = 0; i <= NM[0] - NM[1]; i++)
        {
            string[] atemp = A.Where((_,x) => i <= x && x < NM[1] + i).ToArray();
            for (int j = 0; j <= NM[0] - NM[1]; j++)
            {
                string[] a = atemp.Select(x => x.Substring(j, NM[1])).ToArray();
                bool b = true;
                for (int k = 0; k < a.Length; k++)
                {
                    if (a[k] != B[k])
                    {
                        b = false;
                        break;
                    }
                }
                if (b)
                {
                    Console.WriteLine("Yes");
                    return;
                }
            }
        }
        Console.WriteLine("No");
    }
}