Hollow Frame

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $r,c$, print a grid of $r$ rows and $c$ columns. A cell on the first or last row or first or last column is #; any other cell is .. Indices start at 1. If $r=1$ or $c=1$, every cell is on the border. Do not print spaces between characters.

Input

One line contains integers $r$ (rows) and $c$ (columns).

Output

Print exactly $r$ lines of $c$ characters.

Subtasks

• Subtask 1 (20%): $1\le r,c\le 2$.

• Subtask 2 (30%): $1\le r,c\le 8$.

• Subtask 3 (50%): $1\le r,c\le 30$.

Examples

Example 1

Input:

3 4

Output:

####
#..#
####

Explanation:

The first and last rows are entirely on the border; interior rows have # at each end. A one-row grid is all border. For this sample, the input is 3 4; the displayed rows follow these rules exactly.

Example 2

Input:

1 3

Output:

###

Explanation:

The first and last rows are entirely on the border; interior rows have # at each end. A one-row grid is all border. For this sample, the input is 1 3; the displayed rows follow these rules exactly.