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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
class Solve{
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        string[] str = Console.ReadLine().Split(' ');
        int N = int.Parse(str[0]);
        int M = int.Parse(str[1]);
        bool[,] A = new bool[N,N];
        bool[,] B = new bool[M,M];
        {
            string s;
            for(int i=0;i<N;i++){
                s = Console.ReadLine();
                for(int j=0;j<N;j++){
                    A[i,j] = s[j] == '.';
                }
            }
            for(int i=0;i<M;i++){
                s = Console.ReadLine();
                for(int j=0;j<M;j++){
                    B[i,j] = s[j] == '.';
                }
            }
        }
        bool ans = false;
        for(int i=0;i<N-M+1;i++){
            for(int j=0;j<N-M+1;j++){
                bool o = true;
                for(int k=0;k<M;k++){
                    for(int l=0;l<M;l++){
                        o &= A[i+k,j+l] == B[k,l];
                    }
                }
                ans |= o;
            }
        }
        sb.Append(ans ? "Yes\n" : "No\n");
    }
}