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;
import java.util.StringTokenizer;

/**
 * Created by zzt on 17-2-11.
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        String[] a = new String[n];
        String[] b = new String[m];

        for (int i = 0; i < n; i++) {
            a[i] = scanner.next();
        }

        for (int i = 0; i < m; i++) {
            b[i] = scanner.next();
        }
        int[] next = new int[m + 1];
        next[0] = next[1] = 0;
        int j = 0;
        for (int i = 1; i < m; i++) {
            while (j>0&&b[i].equals(b[j]))
                j = next[j];
            if (b[i].equals(b[j]))
                j++;
            next[i+1] = j;
        }
        j=0;
        int off = -1;
        for (int i = 0; i < n; i++) {
            if (j==0)
                off = a[i].indexOf(b[j]);
            while (j>0&&off!=a[i].indexOf(b[j]))
                j = next[j];
            if (off==a[i].indexOf(b[j])&&off!=-1)
                j++;
            if (j == m) {
                System.out.println("Yes");
                return;
            }
        }
        System.out.println("No");
    }
}