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 void Main(string[] args) {
		new Calc().calc();
    }
	public class Calc {
		public Calc() { }
		public void calc() {
			int[] NM = ReadLine<int>(' ');
			List<string> A = new List<string>(), B = new List<string>();
			for (int i = 0; i < NM[0]; i++) {
				A.Add(Console.ReadLine());
			}
			for (int i = 0; i < NM[1]; i++) {
				B.Add(Console.ReadLine());
			}
			var B_docked = B.Docking();
			for (int i = 0; i < NM[0] - NM[1] + 1; i++) {
				for (int n = 0; n < NM[0] - NM[1] + 1; n++) {
					var STR = A.RangeDocking(n,n+NM[1], _ => _.Substring(i, NM[1]));
					if (B_docked == STR) {
						Console.WriteLine("Yes");
						return;
					}
				}
			}
			Console.WriteLine("No");
			return;
		}
	}

	public static T ReadLine<T>() =>
		(T)Convert.ChangeType(Console.ReadLine(), typeof(T));
	
	public static T[] ReadLine<T>(params char[] separators) =>
		Console.ReadLine()
		.Split(separators)
		.Select(_ => (T)Convert.ChangeType(_, typeof(T)))
		.ToArray();
	
	public static List<T> ReadLines<T>(int readCount) {
		List<T> rt = new List<T>();
		for (int i = 0; i < readCount; i++) {
			rt.Add(ReadLine<T>());
		}
		return rt;
	}
}
public static class Utils {
	public static string Docking<T>(this IEnumerable<T> s, int sequenceRange, Func<T, string> filter = null) {
		string str = "";
		int c = 0;
		foreach (var item in s) {
			str += filter == null ? item.ToString() : filter(item);
			c++;
			if (c == sequenceRange) break;
		}
		return str;
	}

	public static string Docking<T>(this IEnumerable<T> s, Func<T, string> filter = null) {
		return s.Docking(s.Count(), filter);
	}

	public static string RangeDocking<T>(this IEnumerable<T> s,int start,int end,Func<T,string> filter = null) {
		string str = "";
		end = end < s.Count() ? end : s.Count();
		var items = s.ToArray();
		for (int i = start; i < end; i++) {
			str+= filter == null ? items[i].ToString() : filter(items[i]);
		}
		return str;
	}
}