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: Runtime Error)

import java.util.BitSet;
import java.util.Scanner;

public class Main {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String s1 = sc.nextLine();
        String s1arr[] = s1.split(" ");
        int n = Integer.parseInt(s1arr[0]);
        int m = Integer.parseInt(s1arr[1]);
        int a[][] = new int[n][n];
        int b[][] = new int[m][m];
        BitSet bs = new BitSet(n * n);
        
        for (int i = 0; i < n; i++) {
            String str = sc.nextLine();
            String strarr[] = str.split(" ");
            for (int j = 0; j < n; j++) {
                a[i][j] = Integer.parseInt(strarr[j]);
            }
        }
        
        for (int i = 0; i < m; i++) {
            String str = sc.nextLine();
            String strarr[] = str.split(" ");
            for (int j = 0; j < m; j++) {
                b[i][j] = Integer.parseInt(strarr[j]);
            }
        }
        
        for (int i = 0; i < m - n; i++) {
            for (int j = 0; j < m - n; j++) {
                for (int k = 0; k < n; k++) {
                    for (int l = 0; l < n; l++) {
                        if (a[i][j] == b[i + k][j + l]) {
                            bs.set(k + n * l);
                        }
                    }
                }
                if(bs.cardinality() == n*n){
                    System.out.println("Yes");
                    System.exit(0);
                }
                bs.clear();
            }
        }
        System.out.println("No");
    }
    
}