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 <functional>
#include <string>
#include <vector>
using namespace std;
#define MAXSIZE 200
#define MAXL 100
typedef long long int lli;

int get_abs(int x);

int main(){
    int n, m;
    cin >> n >> m;
    vector<string> picA;
    for(int i = 0; i < n; i++){
        string a;
        cin >> a;
        picA.push_back(a);
    }

    vector<string> picB;
    for(int i = 0; i < m; i++){
        string b;
        cin >> b;
        picB.push_back(b);
    }

    bool exist_template = false;
    for(int upper_edge = 0; upper_edge < n - m + 1; upper_edge++){
        for(int i = upper_edge; i < upper_edge + m; i++){
            for(int left_edge = 0; left_edge < n - m + 1; left_edge++){
                if(picB[i - upper_edge] == picA[i].substr(left_edge, m)){
                    if(i == upper_edge + m - 1){
                        exist_template = true;
                        goto SEARCHFIN;
                    }
                }
            }
        }
    }

SEARCHFIN:
    string ans = (exist_template)? "Yes" : "No";
    cout << ans << endl;
    return 0;
}

int get_abs(int x){
    return (x > 0)? x : -x;
}