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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <vector>
#include <algorithm>
#include <string>
#include <random>
#include <map>
#include <math.h>
#pragma warning(disable : 4996)

#define MAX_N 50

char A[MAX_N][MAX_N+1];
char B[MAX_N][MAX_N+1];

int main(void) {
	int N, M;
	scanf("%d %d", &N, &M);
	for (int i = 0; i < N; ++i) {
		scanf("%s", &A[i]);
	}
	for (int i = 0; i < M; ++i) {
		scanf("%s", &B[i]);
	}
	for (int oy = 0; oy <= N - M; ++oy) {
		for (int ox = 0; ox <= N - M; ++ox) {
			bool match = true;
			for (int y = 0; y < M; ++y) {
				for (int x = 0; x < M; ++x) {
					if (A[oy + y][ox + x] != B[y][x]) {
						match = false;
						goto NOT_MATCH;
					}
				}
			}
		NOT_MATCH:
			if (match == true) {
				printf("Yes");
				return 0;
			}
		}
	}
	printf("No");
	return 0;
}