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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;
class Simple {
    int N, M;
    string[] A, B;
    void Solve() {
        //input
        N = io.Int;
        M = io.Int;
        A = new string[N];
        B = new string[M];
        for (int i = 0; i < N; ++i)
            A[i] = io.String;
        for (int j = 0; j < M; ++j)
            B[j] = io.String;
        //cal
        for (int shiftX = 0; shiftX < N - M + 1; ++shiftX) {
            for (int shiftY = 0; shiftY < N - M + 1; ++shiftY) {
                for (int i = 0; i < M; ++i) {
                    for (int j = 0; j < M; ++j) {
                        if (A[i + shiftY][j + shiftX] != B[i][j])
                            goto BR;
                    }
                }
                //res(Contain)
                Console.WriteLine("Yes");
                return;
            BR:;
            }
        }
        //res(!Contain)
        Console.WriteLine("No");
    }

    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) { new Simple().Stream(); }
    void Stream() {
        Solve();
        io.writeFlush();
    }
}

class SimpleIO {
    string[] nextBuffer;
    int BufferCnt;
    char[] cs = new char[] { ' ' };
    StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    public SimpleIO() {
        nextBuffer = new string[0];
        BufferCnt = 0;
        Console.SetOut(sw);
    }
    public string Next() {
        if (BufferCnt < nextBuffer.Length)
            return nextBuffer[BufferCnt++];
        string st = Console.ReadLine();
        while (st == "")
            st = Console.ReadLine();
        nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        BufferCnt = 0;
        return nextBuffer[BufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void writeFlush() { Console.Out.Flush(); }
}