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<string>
#include<cstdio>
#include<algorithm>
#include<stack>
#include<queue>
#include<vector>
#include<cmath>
#include<utility>
#include<set>
#include<complex>
#include<map>
#define vi vector<int>
#define vvi vector<vector<int> >
#define ll long long int
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vb vector<bool>
#define vc vector<char>
#define vs vector<string>
#define ld long double
#define INF 1e9
#define EPS 0.0000000001
#define rep(i,n) for(int i=0;i<n;i++)
#define loop(i,s,n) for(int i=s;i<n;i++)
#define all(in) in.begin(), in.end()
#define MAX 9999999
using namespace std;
typedef pair<int, int> pii;
int main(){
    int n,m; cin>>n>>m;
    if(m>n)return puts("No")*0;
    vector<string>a(n); vector<string>b(m);
    rep(i,n)cin>>a[i]; rep(i,m)cin>>b[i];
    bool flag=true;;
    rep(i,n){
        rep(j,n){
            rep(k,m)rep(l,m){
                if((i+k)<n&&(j+l)<n&&b[k][l]!=a[i+k][j+l])flag=false;
            }
        if(flag)return puts("Yes") *0;
        }
    }
    puts("No");
}