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.Scanner;




public class Main {

    public static void main(String[] args) {

    	Main main=new Main();

    	main.run();

    }

    void run() {
    	Scanner sc=new Scanner(System.in);

    	int H=sc.nextInt();
    	int W=sc.nextInt();

    	for(int i=0;i<W+2;i++) {
    		System.out.print("#");
    	}
    	System.out.println();

    	for(int i=0;i<H;i++) {

    		System.out.print("#");
    		System.out.print(sc.next());
    		System.out.println("#");

    	}

    	for(int i=0;i<W+2;i++) {
    		System.out.print("#");
    	}
    	System.out.println();

    }

}