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 <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> P;
typedef pair<ll, ll> Pl;

const int INT_INF = 2147483646;
const ll LL_INF = 9223372036854775807;

bool SecondCompare(const pair<int,int> &a,const pair<int,int> &b)
{
       return a.second<b.second;
}
 
bool SecondCompareDes(const pair<int,int> &a,const pair<int,int> &b)
{
       return a.second>b.second;
}

ll minll(ll a, ll b){
    if(a >= b)  return b;
    else    return a;
}

ll maxll(ll a, ll b){
    if(a >= b)  return a;
    else    return b;
}

ll n,m;
string a[100],b[100];

int main(){
    cin >> n >> m;
    for(int i = 0; i < n; i++){
        cin >> a[i];
    }
    for(int i = 0; i < m; i++){
        cin >> b[i];
    }
    bool flag = false;
    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++){
            if(a[i][j] == b[i][0]){
                flag = true;
                for(int k = 0; k < m; k++){
                    for(int l = 0; l < m; l++){
                        ll a_i = i+k;
                        ll a_j = j+l;
                        if(a_i > n || a_j > n){
                            flag = false;
                            break;
                        }
                        if(a[a_i][a_j] != b[k][l]){
                            flag = false;
                            break;
                        }  
                    }
                }
                if(flag){
                    cout << "Yes\n";
                    return 0;
                }
            }
        }
    }
    cout << "No\n";
}