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.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const char White = '.';
    const char Black = '#';
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        var spl = input.ReadLine().Split(' ');
        var n = int.Parse(spl[0]);
        var m = int.Parse(spl[1]);

        var aa = new char[n][];
        for (int i = 0; i < aa.Length; i++) {
            aa[i] = input.ReadLine().ToCharArray();
        }
        var bb = new char[m][];
        for (int i = 0; i < bb.Length; i++) {
            bb[i] = input.ReadLine().ToCharArray();
        }

        for(int ai=0; ai<n; ai++) {
            for(int aj=0; aj<n; aj++) {
                var ok = true;
                for (int bi = 0; bi < m; bi++) {
                    for (int bj = 0; bj < m; bj++) {
                        if(ai+bi >= n || aj+bj >= n) {
                            ok = false;
                            break;
                        }
                        ok &= aa[ai+bi][aj+bj] == bb[bi][bj];
                    }
                }
                if(ok) return Yes;
            }
        }

        return No;
    }

    static int[] ToIntArray(string strs, int n) {
        var ret = new int[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = int.Parse(spl[i]);
        return ret;
    }
    static void SetArray<T>(T[] array, Func<T, int, T> f) {
        for (int i = 0; i < array.Length; i++)
            array[i] = f(array[i], i);
    }
    static void FillArray<T>(T[] array, T value) {
        for (int i = 0; i < array.Length; i++)
            array[i] = value;
    }
}