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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp1
{
    public static class MyExtensions
    {
        public static string Slice(this string str, int start = 0, int stop = 0)
        {
            if (start > str.Length || stop > str.Length || start < 0 || stop < 0)
                return "";

            if (stop == 0) stop = str.Length;
            return str.Substring(start, stop - start);
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            B();
        }

        static void B()
        {
            var NM = ReadSplitInt();
            var A = new string[NM[0], NM[0]];
            var B = new string[NM[1], NM[1]];
            for (int i = 0; i < NM[0]; i++)
            {
                var input = Read().ToArray();
                for (int j = 0; j < NM[0]; j++)
                {
                    A[i, j] = input[j].ToString();
                }
            }

            for (int i = 0; i < NM[1]; i++)
            {
                var input = Read().ToArray();
                for (int j = 0; j < NM[1]; j++)
                {
                    B[i, j] = input[j].ToString();
                }
            }

            for (int i = 0; i < NM[0]; i++)
            {
                for (int j = 0; j < NM[0]; j++)
                {
                    var ok = true;
                    for (int ma = 0; ma < NM[1]; ma++)
                    {
                        for (int mb = 0; mb < NM[1]; mb++)
                        {
                            if (i + ma >= NM[0] || j + mb >= NM[0])
                                continue;

                            if (A[i + ma, j + mb] != B[ma, mb])
                                ok = false;
                        }
                    }
                    if (ok)
                    {
                        Console.WriteLine("Yes");
                        return;
                    }
                }
            }
            Console.WriteLine("No");
        }

        static IEnumerable<int> Range(int start, int stop)
        {
            if (start < 0 || stop < 0 || start > stop || (start <= 0 && stop <= 0))
                return new List<int>();

            return Enumerable.Range(start, stop - start);
        }

        static bool IsDigit(string str)
        {
            var i = 0;
            return int.TryParse(str, out i);
        }

        static int DigitsSum(long num)
        {
            return num.ToString().Select(x => x.ToString()).Sum(int.Parse);
        }

        static int[] ToIntArray(string str)
        {
            return str.Select(x => x.ToString()).Select(int.Parse).ToArray();
        }

        static string Read() => Console.ReadLine();
        static int ReadInt() => int.Parse(Read());
        static long ReadLong() => long.Parse(Read());

        static IList<string> ReadSplit() => Read().Split().ToList();
        static IList<int> ReadSplitInt() => Read().Split().Select(int.Parse).ToList();

        static void Print(object value = null) => Console.Write(value.ToString());
        static void Println(object value = null) => Console.WriteLine(value.ToString());
    }
}