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;

namespace ABC054B
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] bufs = Console.ReadLine().Split(' ');
            int N = Int32.Parse(bufs[0]);
            int M = Int32.Parse(bufs[1]);
            string[] A = new string[N];
            string[] B = new string[M];

            bool res = false;

            for (int i = 0; i < N; i++)
            {
                A[i] = Console.ReadLine();
            }
            for (int i = 0; i < M; i++)
            {
                B[i] = Console.ReadLine();
            }

            int cur = -1;
            int seek = 0;

            while (seek < (N - M + 1))
            {
                cur = A[seek].IndexOf(B[0], cur + 1);
                seek++;
                if (cur != -1)
                {
                    int j = 1;
                    while (j < M)
                    {
                        if (A[seek].IndexOf(B[j], cur, M) != cur) { break; }
                        seek++;
                        j++;
                    }
                    if (j >= M)
                    {
                        res = true;
                    }
                }
            }

            Console.WriteLine(res ? "Yes" : "No");
            return;
        }

    }
}