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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int M = sc.nextInt();


    String[] A = new String[ N ];
    for(int i = 0 ;i < N ; i ++){
      A[ i ] = sc.next();
    }

    String[] B = new String[ M ];
    for(int i = 0 ;i < M ; i ++){
      B[ i ] = sc.next();
    }

    boolean[][] matchFlg = new boolean [ N - M + 1 ][ N - M + 1 ];

    for(int i = 0 ;i < N - M + 1 ; i ++){
      for(int j = 0 ; j < N - M + 1 ; j ++){
        if(i == 0){

          matchFlg[i][j] = B[i].equals( A[i].substring( j , j + M ) );
        }else{
          if(matchFlg[ i - 1 ][ j ]){
          matchFlg[i][j] = B[i].equals( A[i].substring( j , j + M ) );
          }
        }
      }
    }

    boolean result = false ;
    for(int j = 0 ; j < N - M + 1 ;j ++){
      if(matchFlg[ N - M ][ j ]){
        result = true;
        break;
      }
    }

    System.out.println(result ? "Yes" : "No");
  }
}