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

        int[][] board = new int[N][N];
        int[][] temp = new int[M][M];

        for(int i = 0; i<N; i++) {
            String str = sc.next();
            for(int j = 0; j<N; j++) {
                board[i][j] = (str.charAt(j)=='#')?1:0;
            }
        }

        for(int i = 0; i<M; i++) {
            String str = sc.next();
            for(int j = 0; j<M; j++) {
                temp[i][j] = (str.charAt(j)=='#')?1:0;
            }
        }

        boolean f = false;
        for(int i = 0; i<=N-M; i++) {
            for(int j = 0; j<=N-M; j++) {
                f = true;
                for(int ii = 0; ii<M; ii++) {
                    for(int jj = 0; jj<M; jj++) {
                        if(board[i+ii][j+jj] != temp[ii][jj]) f=false;
                        //System.out.println(board[i+ii][j+jj] +" "+ temp[ii][jj]);
                    }

                }
                if(f)break;
            }
        }
        if(f) System.out.println("Yes");
        else System.out.println("No");

    }
}