409. Berland Flag
Time limit per test: 0.25
second(s)
Memory limit: 65536
kilobytes
input: standard
output: standard
The Berland is in trouble again. After the recent elections AllBerland Great Duma has divided into two coalitions:
Blueeyed coalition and Redeyed coalition. On the independence day the following question was raised: what will the national
flag look like?
Both coalitions agreed that the flag should be a square of
N^{2} x
N^{2} cells, each of
them painted blue of red. To make the flag acceptable for both coalitions, the following
requirements must be held:
every row of the flag must contain exactly K blue cells
every column of the flag must contain exactly K blue cells
if we split the flag into squares of N x N cells (there will be N x N such squares), then
every such square must contain exactly K blue cells.
You are the chief programmers in Berland. So, making the flag model is your duty.
Input
First line of the input contains two integer numbers N and K (1 ≤ N ≤ 20, 0 ≤ K ≤ N^{2}).
Output
Output description of the desired flag.
Print N^{2} lines which consist of N^{2} characters '*'
and '.'
,
where '*'
means blue cell and '.'
means red cell.
Output "NO SOLUTION"
(without quotes), if there is no flag which satisfies both coalitions.
If there are several solutions, output any of them.
Example(s)
sample input

sample output

2 2

*..*
.**.
.**.
*..*

sample input

sample output

3 1

*........
...*.....
......*..
.*.......
....*....
.......*.
..*......
.....*...
........*
