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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <string>
#include <cmath>
#include <ctype.h>
#include <map>
#include <vector>
#include <stdlib.h>
#include <stdio.h>
#include <cctype>
#include <queue>
#include <set>
#include <list>
#define PI 3.14159265359
#define rep(i,a,n) for(int i=a;i<(int)n;++i)
#define SZ(x) ((int)(x).size())	//size() unsigned -> int
#define DescSort(a) sort(a.begin(),a.end(),std::greater<int>())

using namespace std;
typedef long long ll;
const ll INF=1e9+7;

int n, m;
bool tmp_match(int i, int j, vector<string> a, vector<string> b) {
	rep(k, 0, m) {
		rep(l, 0, m) {
			if (a[i + k][j + l] != b[k][l]) {
				return false;
			}
			if (k == m - 1 && l == m - 1) {
				return true;
			}
		}
	}
}
int main(void) {
	cin >> n >> m;
	vector<string> a(n), b(m);
	rep(i, 0, n)cin >> a[i];
	rep(i, 0, m)cin >> b[i];
	if (m == 1) {
		char eval = b[0][0];
		rep(i, 0, n) {
			rep(j, 0, n) {
				if (a[i][j] == eval) {
					cout << "Yes" << endl;
					return 0;
				}
			}
		}
	}
	else {
		rep(i, 0, m) {
			rep(j, 0, m) {
				bool can = tmp_match(i, j, a, b);
				if (can) {
					cout << "Yes" << endl;
					return 0;
				}
			}
		}
	}
	cout << "No" << endl;
	return 0;
}