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: Runtime Error)

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

namespace program
{
    class Program
    {
        static void Main()
        {
          int[] num = Input.ScanIntArray();
          string[] A = new string[num[0]];
          string[] B = new string[num[1]];
          for(int i=0;i<num[0];i++)
            A[i] = Input.ScanStr();
          for(int i=0;i<num[1];i++)
            B[i] = Input.ScanStr();
          
          for(int i=0;i<=num[0]-num[1];i++){
            bool isSub = true;
            for(int j=0;j<=num[0]-num[1];j++){
              for(int k=j;k<j+num[1];k++){
                isSub &= A[k].Substring(i,num[1]) == B[j-k];
              }
              if(isSub){ Console.WriteLine("Yes"); return; }
            }
          }
            
          Console.WriteLine("No");
        }
    }

    static class Input
    {
        static public int ScanInt() { return int.Parse(Console.ReadLine()); }
        static public uint ScanUint() { return uint.Parse(Console.ReadLine()); }
        static public long ScanLong() { return long.Parse(Console.ReadLine()); }
        static public ulong ScanUlong() { return ulong.Parse(Console.ReadLine()); }
        static public int[] ScanIntArray() { return Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray(); }
        static public uint[] ScanUintArray() { return Console.ReadLine().Split(' ').Select(x => uint.Parse(x)).ToArray(); }
        static public long[] ScanLongArray() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray(); }
        static public ulong[] ScanUlongArray() { return Console.ReadLine().Split(' ').Select(x => ulong.Parse(x)).ToArray(); }

        static public string ScanStr() { return Console.ReadLine(); }
        static public string[] ScanStrArray() { return ScanStr().Split(' '); }
    }

    static class MyMath
    {
        public static int GCD(int a, int b)
        {
            Func<int, int, int> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }
        public static ulong GCD(ulong a, ulong b)
        {
            Func<ulong, ulong, ulong> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }
        public static int LCM(int a, int b)
        {
            return a * b / GCD(a, b);
        }
        public static ulong LCM(ulong a, ulong b)
        {
            return a * b / GCD(a, b);
        }
    }
}