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.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3 2");
            WillReturn.Add("#.#");
            WillReturn.Add(".#.");
            WillReturn.Add("#.#");
            WillReturn.Add("#.");
            WillReturn.Add(".#");
            //Yes
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("4 1");
            WillReturn.Add("....");
            WillReturn.Add("....");
            WillReturn.Add("....");
            WillReturn.Add("....");
            WillReturn.Add("#");
            //No
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] wkArr = InputList[0].Split(' ').Select(X => int.Parse(X)).ToArray();

        int N = wkArr[0];
        int M = wkArr[1];

        var AList = new List<string>();
        for (int I = 1; I <= N; I++) {
            AList.Add(InputList[I]);
        }
        int UB_A_X = AList[0].Length - 1;
        int UB_A_Y = AList.Count - 1;

        var BList = new List<string>();
        for (int I = 1; I <= M; I++) {
            BList.Add(InputList[N + I]);
        }
        int UB_B_X = BList[0].Length - 1;
        int UB_B_Y = BList.Count - 1;

        for (int X1 = 0; X1 <= UB_A_X - UB_B_X; X1++) {
            for (int Y1 = 0; Y1 <= UB_A_Y - UB_B_Y; Y1++) {

                bool IsOK = true;
                for (int X2 = 0; X2 <= UB_B_X; X2++) {
                    for (int Y2 = 0; Y2 <= UB_B_Y; Y2++) {
                        if (AList[Y1 + Y2][X1 + X2] != BList[Y2][X2]) {
                            IsOK = false;
                            break;
                        }
                    }
                    if (IsOK == false) break;
                }

                if (IsOK) {
                    Console.WriteLine("Yes");
                    return;
                }

            }
        }
        Console.WriteLine("No");
    }
}