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: Accepted)

import java.util.Scanner;

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

        int N = sc.nextInt();
        int M = sc.nextInt();

        if (M > N) {
            System.out.println("No");
            return;
        }

        char dataN[][] = new char[N][];
        for ( int i = 0; i < N; i++) {
            dataN[i] = sc.next().toCharArray();
        }

        char dataM[][] = new char[M][];
        for ( int i = 0; i < M; i++) {
            dataM[i] = sc.next().toCharArray();
        }

        int diff = N - M;
        for (int i = 0; i <= diff; i++ ) {
            for ( int j = 0; j <= diff; j++) {
                if (compareData(dataN,dataM,i,j,M)) {
                    System.out.println("Yes");
                    return ;
                }
            }
        }
        System.out.println("No");
    }

    private static boolean compareData(
        char dataN[][],
        char dataM[][],
        int startX,
        int startY,
        int len
    ) {
        for (int i = 0; i < len; i++ ) {
            for ( int j = 0; j < len; j++) {
                if (dataM[i][j] != dataN[i + startX][j + startY]) {
                    return false;
                }
            }
        }
        return true;
    }
}