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: Wrong Answer)

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

using ll = uint_fast64_t;
using ld = long double;
using vi = vector<int>;
using vll = vector<ll>;

constexpr int inf = ~(1 << 31);
constexpr ll llinf = ~(1LL << 63);
constexpr int mod = 1e9 + 7;
constexpr ld pi = 3.14159265358979323846L;

constexpr int dy[4] = {0, 1, 0, -1};
constexpr int dx[4] = {1, 0, -1, 0};
struct Pos { int x, y; };

#define rep(i,n) for(int i=0; i<(n); ++i)
#define all(n) n.begin(),n.end()
#define DEBUG cerr << "DEBUG: DONE" << endl;

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    //cout << fixed << setprecision(6);
    int n, m;
    cin >> n >> m;
    vector<string> a(n), b(m);
    rep (i, n) cin >> a[i];
    rep (i, m) cin >> b[i];

    // loop a //
    for (int ah = 0; ah < n-m; ah++) {
        for (int aw = 0; aw < n-m; aw++) {
            // loop b //
            bool match = true;
            for (int bh = 0; bh < m; bh++) {
                for (int bw = 0; bw < m; bw++) {
                    if (a[ah+bh][aw+bw] != b[bh][bw]) {
                        match = false;
                        bh = bw = m;
                    }
                }
            }
            if (match) {
                cout << "Yes" << endl;
                return 0;
            }
        }
    }

    cout << "No" << endl;
    return 0;
}