% Author: Sergey Kopeliovich
% Source: SPBU Championship, October 2013

\gdef\thisproblemauthor{Sergey Kopeliovich}
\gdef\thisproblemdeveloper{Sergey Kopeliovich}

\begin{problem}{Convex and Compact}
{convexset.in}{convexset.out}
{2 seconds (\textsl{3 seconds for Java})}{256 mebibytes}{}

You are given $n$ points on the plane.

It is guaranteed that the points were obtained in the following way:

\t{x[i] = random [0..1000]}

\t{y[i] = random [0..1000]}

Here, the function \t{random [L..R]} returns a random integer from $L$ to $R$
inclusive, and all integers from $L$ to $R$ have the same probability.

You have to choose a set of $k$ points in such a way that the perimeter
of the convex hull of the chosen set will be minimal possible.

\InputFile

The first line of input contains the number of points $n$ ($3 \le n \le 60$)
and the number $k$ ($1 \le k \le 15$).
The next $n$ lines contain coordinates of points $x_i$ $y_i$
(integers from $0$ to $1000$).
The points are numbered by integers from $1$ to $n$.
It is guaranteed that you are lucky, so the $n$ randomly generated points
satisfy the following property:
no two points coincide and no three points lie on the same line.

\OutputFile

On the first line, print a real number: the perimeter of the convex hull
of the chosen set.
On the second line, print $k$ different integers from $1$ to $n$:
the numbers of the chosen points.
If there are several optimal answers, print any one of them.
You may print points in any order.

Consider three real numbers: the right answer, the perimeter of the
convex hull of the chosen set and the real number which you printed
on the first line.
Your answer will be accepted only if the difference
between the greatest and the least of these three numbers
will not exceed $10^{-6}$.

\Example

\begin{example}
\exmp{
5 4
0 0
0 1
4 4
2 0
2 1
}{
6
4 5 1 2
}%
\end{example}

\Note

In the example, the points are not random for simplicity.
In the testing system, the first test coincides with this example,
and all other tests are truly random.

\end{problem}
