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.Linq;
using System.Collections.Generic;
using System.IO;

namespace ABC
{
  public class Program
  {
    public static void Main(string[] args)
    {
      Console.SetOut(new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false});
      var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
      int n = nm[0];
      int m = nm[1];
      int dif = n-m+1;
      List<string>nlist = new List<string>();
      List<string>mlist = new List<string>();
      for(int i=0; i<n; i++)
      {
        nlist.Add(Console.ReadLine());
      }
      for(int i=0; i<m; i++)
      {
        mlist.Add(Console.ReadLine());
      }

      for(int i=0; i<dif; i++)
      {
        for(int j=0; j<dif; j++)
        {
          string target = nlist[i].Substring(j, m);
          if(target != mlist[0])
          {
            continue;
          }else
          {
            int cnt=0;
            for(int k=0; k<m; k++)
            {
              string target_h = nlist[k].Substring(j, m);
              if(target_h == mlist[k]){
                cnt++;
              }
            }
            if(cnt==m)
            {
              Console.WriteLine("Yes");
              Console.Out.Flush();
              return;
            }
          }
        }
      }
      Console.WriteLine("No");
      Console.Out.Flush();
    }
  }
}