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 "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef vector<vector<pair<int, int> > > vvp;
typedef vector<pair<int,int> > vp;
typedef vector<vector<int> > vvi;
typedef vector<int> vi;
typedef vector<vector<bool> > vvb;
typedef vector<bool> vb;
typedef vector<string> vs;
typedef pair<string, int> psi;
typedef pair<int, int> pii;
#define rep(i,s,n) for(int i = (s); i < (n); i++)
#define all(x) (x).begin(), (x).end()
#define yn(f) (f?"yes":"no")
#define YN(f) (f?"YES":"NO")
#define Yn(f) (f?"Yes":"No")
#define mod 1000000007
#define intmax 2147483647
#define intmin -2147483648
#define longmax 9223372036854775807
#define longmin -9223372036854775808
#define nil -1
int main() {
	int n, m;
	cin >> n >> m;
	vs A(n);
	vs B(m);
	rep(i, 0, n)cin >> A[i];
	rep(i, 0, m)cin >> B[i];
	int d = n - m;
	bool f;
	for (int i = 0; i < d+1; i++)
	{
		for (int j = 0; j < d+1; j++)
		{
			f = true;
			for (int k = 0; k < m; k++)
			{
				string w = A[k + j].substr(i,m);
				if (w != B[k])f = false;
			}
			if (f)break;
		}
		if (f)break;
	}
	cout << Yn(f) << endl;
}