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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for (int i=0; i < (n); i++)
using namespace std;
using ll = long long;

int main(){
    int M,N; cin >> N >> M;
    vector<vector<char>> A(N),B(M);
    rep(i,N){
        rep(j,N){
            char x; cin >> x;
            A[i].push_back(x);
        }
    }
    rep(i,M){
        rep(j,M){
           char x; cin>>x;
           B[i].push_back(x);
        }
    }

    bool ans=false;
    for(int i=0; i<=N-M; i++){
        for(int j=0; j<=N-M; j++){
            bool flg=true;
            // 一致チェックループ
            for(int k=0; k<M; k++){
                for(int l=0; l<M; l++){
                    if(A[i+k][j+l] != B[k][l]){
                        flg = false;
                    }

                }
            }
            if(flg) ans=true;
        }
    }

    // rep(i,N){
    //     rep(j,N){
    //         cerr << A[i][j];
    //     }
    //     cerr << endl;
    // }
    // cerr << "-------------" << endl;
    // rep(i,M){
    //     rep(j,M){
    //        cerr << B[i][j];
    //     }
    //     cerr << endl;
    // }


    if(ans){
        cout << "Yes" << endl;
    }else{
        cout << "No" << endl;
    }
}