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;

#define ll long long
#define INF_LL 1LL << 60
#define INF 99999999
#define MOD (ll)1000000007
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define REP(i, a, n) for(int i = a; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()

void put_double(double obj){printf("%.12f\n",obj);};

template < typename T > std::string to_string( const T& n )
{
    std::ostringstream stm ;
    stm << n ;
    return stm.str() ;
}

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }


int main()
{
    int N,M;
    cin >> N >> M;

    vector<string> a(N);
    rep(i,N) cin >> a[i];
    vector<string> b(M);
    rep(i,M) cin >> b[i];

    rep(i, N-M+1)
    {
        rep(j, N-M+1)
        {
            vector<string> templete;

            // ここからテンプレ切り出し
            rep(I, M)
            {
                string tmp;
                rep(J, M)
                {
                    tmp += a[I][J];
                }
                templete.push_back(tmp);
            }
            //rep(I,M) cout << templete[I] << endl;
            if( b == templete )
            {
                cout << "Yes" << endl;
                return 0;
            }
        } 
    }
    cout << "No" << endl;
}