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

..

....

....

....

.

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