Problem: You are given a image with a height of H pixels and a width of W pixels. Each pixel is represented by a lowercase English letter. The pixel at the i-th row from the top and j-th column from the left is a_{ij}.

Put a box around this image and output the result. The box should consist of `#` and have a thickness of 1.

Constraints

* 1 ≤ H, W ≤ 100
* a_{ij} is a lowercase English letter.

Input

Input is given from Standard Input in the following format:


H W
a_{11} ... a_{1W}
:
a_{H1} ... a_{HW}


Output

Print the image surrounded by a box that consists of `#` and has a thickness of 1.

Examples

Input

2 3
abc
arc


Output

#####
#abc#
#arc#
#####


Input

1 1
z


Output

z#

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Main {
	public static String repeat(String piece, int times){
		String r = "";
		for(int i=0;i<times;i++) r = r+piece;
		return r;
	}
	
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int H = sc.nextInt();
        int W = sc.nextInt();
        sc.nextLine();
        
        System.out.println(repeat("#",W+2));
        for(int h=0;h<H;h++){
        	String pic = sc.nextLine();
        	System.out.println("#"+pic+"#");
        }
        System.out.println(repeat("#",W+2));
    }
}