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.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

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

    private static void solve(Scanner in) {
        int N = in.nextInt(), M = in.nextInt();
        char[][] A = new char[N][N], B = new char[M][M];
        for (int i = 0; i < N; i++) {
            A[i] = in.next().toCharArray();
        }
        for (int j = 0; j < M; j++) {
            B[j] = in.next().toCharArray();
        }
        for (int h = 0; h < N - M + 1; h++) {
            for (int w = 0; w < N - M + 1; w++) {
                boolean ok = true;
                for (int i = 0; i < M; i++) {
                    for (int j = 0; j < M; j++) {
                        ok &= A[h + i][w + j] == B[i][j];
                    }
                }
                if (ok) {
                    System.out.println("Yes");
                    return;
                }
            }
        }
        System.out.println("No");
    }
}

class Scanner implements Closeable {
    private final InputStream stream;
    private final byte[] buf = new byte[1024];
    private int cur;
    private int num;

    Scanner(InputStream stream) {
        this.stream = stream;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    int nextInt() {
        return (int) nextLong();
    }

    long nextLong() {
        int c = read();
        while (isdel(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long l = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            l *= 10;
            l += c - '0';
            c = read();
        } while (!isdel(c));
        return l * sgn;
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String next() {
        int c = read();
        while (isdel(c))
            c = read();
        StringBuilder s = new StringBuilder();
        do {
            s.appendCodePoint(c);
            c = read();
        } while (!isdel(c));
        return s.toString();
    }

    private int read() {
        if (num == -1)
            throw new InputMismatchException();
        if (cur >= num) {
            cur = 0;
            try {
                num = stream.read(buf);
            } catch (Exception e) {
                throw new InputMismatchException();
            }
            if (num <= 0)
                return -1;
        }
        return buf[cur++];
    }

    private boolean isdel(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    @Override
    public void close() {
        try {
            stream.close();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
}