Print a Frame

Draw a frame which has a height of H cm and a width of W cm. For example, the following figure shows a frame which has a height of 6 cm and a width of 10 cm.

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

Constraints

• 3 ≤ H ≤ 300
• 3 ≤ W ≤ 300

Input

The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.

The input ends with two 0 (when both H and W are zero).

Output

For each dataset, print the frame made of '#' and '.'.

Print a blank line after each dataset.

Example

Input

3 4 5 6 3 3 0 0

Output

#..#

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

#.#

inputFormat

Input

The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space.

The input ends with two 0 (when both H and W are zero).

outputFormat

Output

For each dataset, print the frame made of '#' and '.'.

Print a blank line after each dataset.

Example

Input

3 4 5 6 3 3 0 0

Output

#..#

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

#.#

样例

3 4
5 6
3 3
0 0

####
#..#


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


#.#
###

</p>