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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int N, M;
char A[100][100];
char B[100][100];

int main(void) {
	int i, j, i2, j2;
	if (scanf("%d%d", &N, &M) != 2) return 1;
	for (i = 0; i < N; i++) {
		if (scanf("%s", A[i]) != 1) return 1;
	}
	for (i = 0; i < M; i++) {
		if (scanf("%s", B[i]) != 1) return 1;
	}
	for (i = 0; i < N; i++) {
		for (j = 0; j < N; j++) {
			int ok = 1;
			for (i2 = 0; i2 < M; i2++) {
				for (j2 = 0; j2 < M; j2++) {
					if (i + i2 >= N || j + j2 >= N || A[i + i2][j + j2] != B[i2][j2]) {
						ok = 0;
						i2 = M;
						break;
					}
				}
			}
			if (ok) {
				puts("Yes");
				return 0;
			}
		}
	}
	puts("No");
	return 0;
}