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.Scanner;

public class Main {
  
  public static void main(String[] args) {
    
    Scanner sc = new Scanner(System.in);
    
    int N = Integer.parseInt(sc.next());
    int M = Integer.parseInt(sc.next());
    
    byte A[][] = new byte[N][N];
    byte B[][] = new byte[M][M];
    
    String input;
    for (int i = 0; i < N; i++) {
      input = sc.next();
      for (int j = 0; j < N; j++) {
        if (input.charAt(j) == '#') {
          A[i][j] = 1;
        } else {
          A[i][j] = 0;
        }
      }
    }
    for (int i = 0; i < M; i++) {
      input = sc.next();
      for (int j = 0; j < M; j++) {
        if (input.charAt(j) == '#') {
          B[i][j] = 1;
        } else {
          B[i][j] = 0;
        }
      }
    }
    boolean flag = true;
    for (int i = 0; i < N - M; i++) {
      for (int j = 0; j < N - M; j++) {
        if (B[0][0] == A[i][j]) {
          flag = true;
          for (int k = 0; k < M; k++) {
            for (int l = 0; l < M; l++) {
              if (B[k][l] != A[i + k][j + l]) {
                flag = false;
                break;
              }
            }
            if (!flag) {
              break;
            }
          }
          if (flag) {
            System.out.println("Yes");
            return;
          }
        }
      }
    }
    
    System.out.println("No");
  }
}