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;
using System.Text;
using System.Threading.Tasks;

namespace ABC054B___Template_Matching
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int m = int.Parse(input[1]);
            List<string> nImage = new List<string>();
            List<string> mImage = new List<string>();
            for (int index = 1; index <= n; index++)
            {
                nImage.Add(Console.ReadLine());
            }
            for (int index = 1; index <= m; index++)
            {
                mImage.Add(Console.ReadLine());
            }

            string result = "No";

            if (ContainBInA(nImage, mImage))
            {
                result = "Yes";
            }

            Console.WriteLine(result);
        }


        public static bool ContainBInA(List<string> nImage, List<string> mImage)
        {
            bool res = false;
            int n = nImage.Count;
            int m = mImage.Count;


            //row pattern number
            int rowPattern = n - m + 1;

            //col pattern number
            int colPattern = n - m + 1;

            //search row
            for (int rowIndex = 0; rowIndex < rowPattern; rowIndex++)
            {
                //search col
                for (int colIndex = 0; colIndex < colPattern; colIndex++)
                {
                    //select target in nImage
                    int startCol = colIndex;
                    //int endCol = colIndex + m - 1;
                    int startRow = rowIndex;
                    int endRow = rowIndex + m - 1;

                    int mImageRow = 0;

                    bool result = true;
                    for (int index = startRow; index < endRow; index++)
                    {
                        if (nImage[index].Substring(startCol, m)!=mImage[mImageRow])
                        {
                            result = false;
                        }
                        mImageRow++;
                    }


                    if (result)
                    {
                        return true;


                    }



                }
            }


            return res;
        }
    }
}