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: Runtime Error)

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];

      if(n<m){
        //そもそもテンプレ画像のほうが大きい
        Console.WriteLine("No");
        Console.Out.Flush();
        return;
      }else{
        //横dif 縦dif分のなかでテンプレ画像が一致する場所
        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());
        }
        foreach (var item in mlist.Select((v, i) => new{v, i}))
        {
          for(int j=0; j<dif; j++){
            string target = nlist[item.i].Substring(j, item.v.Length);
            if(target!=item.v){
              continue;
            }else{
              //縦方向
              int cnt=0;
              for(int k=0; k<dif; k++){
                string target_h = nlist[item.i+k].Substring(j, item.v.Length);
                if(target_h==mlist[k]){
                  cnt++;
                }
              }
              if(cnt==m){
                Console.WriteLine("Yes");
                Console.Out.Flush();
                return;
              }
            }
          }
        }
      }
      Console.WriteLine("No");
      Console.Out.Flush();
    }
  }
}