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>
#include <stdlib.h>
#include <string.h>
const char yes[] = "Yes\n";
const char no[] = "No\n"; 
char **toalloc(int n){
	char **aloc = malloc(sizeof(char*)*n);
	for(int i = 0; i < n; ++i){
		aloc[i] = malloc(sizeof(char)*n+5);
	}
	return aloc;
}
void read(char **vetor, int n){
	for(int i = 0; i < n; ++i){
		for(int j = 0; j < n; ++j){
			scanf(" %c", &vetor[i][j]);
		}
	}
	return;
}
int main(){
	int m, n, found = 0, sposi;
	char **a, **b, *start;
	scanf("%d%d", &n/*A*/, &m/*B*/);
	a = toalloc(n);
	b = toalloc(m);
	read(a, n);
	read(b, m);
	//search
	for(int lin = 0; lin < n; ++lin){
		for(int col = 0; col < n; ++col){
			if(lin + m -1> n || col + m -1> n) continue;
			found = 1;
			for(int lb = 0; lb < m; ++lb){
				for(int cb = 0; cb < m; ++cb){
					if(a[lin+lb][col+cb] != b[lb][cb]){
						found = 0;
						break;
					}
					if(!found) break;
				}
				if(!found) break;
			}
			if(found) break;
		}
		if(found) break;
	}
	printf("%s", found ? yes: no);
	return 0;
}