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 <vector>
#include <string>
#include <stack>
#include <queue>
#include <cctype>
#include <cmath>
#include <map>
#include <set>
#define rep(i, m, n) for(int i = m;i < n;i++)
#define repr(i, n) for(int i = n;i >= 0;i--)
#define ll long long
#define ull unsigned long long
#define pb(a) push_back(a)
#define popb(a) pop_back(a)
#define debug(x) cout<<#x<<": "<<x<<endl
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define INF 999999999
#define PI 3.14159265358979
using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;

int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

int main(){
  int n,m;
  string a[55]={},b[55]={};
  bool flag1=false,flag2=false;
  cin>>n>>m;
  rep(i,0,n)cin>>a[i];
  rep(i,0,m)cin>>b[i];
      
  rep(i,0,m){
    rep(j,0,b[i].size()){
      if(flag1)flag2=true;
      rep(c,0,n){
        rep(d,0,a[c].size()-b[i].size()){
          if(b[i][j]==a[i+c][j+d])flag1=true;
          //cout<<flag<<endl;
        }
      }
    }
  }
  if(flag2){
    cout<<"Yes"<<endl;
  }else{
    cout<<"No"<<endl;
  }
}