Kは多角形のケイ

"1 ban ja nakya dame desu ka? K ban ja dame na n deshou ka?" This is Kei's motto. Lately Kei seems fixated on polygons, and looking at $N$ points spread across a wide two-dimensional plane, Kei keeps thinking about how to form a polygon from them.

Kei picks some of the $N$ points and connects them in any order, so that the chosen points are the vertices of a polygon. The polygon must satisfy these conditions:

• It is a simple polygon. That is, it has at least 3 vertices, and no two edges that are not consecutive share a point.
• All $N$ points, including the ones not chosen, lie inside or on the boundary of the polygon.

Kei wants the polygon whose perimeter, the sum of all edge lengths, is the $K$-th shortest among such polygons.

Your task is to help Kei. Among the polygons that satisfy the conditions, sort them by perimeter in ascending order and output the perimeter of the $K$-th one. If there are fewer than $K$ such polygons, output $-1$ instead.

The input consists of multiple datasets. Each dataset has the following format.

N K
x1 y1
...
xN yN

The first line of a dataset gives the number of points $N$ and the rank $K$ of the perimeter to find. Both $N$ and $K$ are integers, and $3 \le N \le 25$, $1 \le K \le 10$. The next $N$ lines give the coordinates of each point. On line $i$, the x coordinate $x_i$ and the y coordinate $y_i$ are integers. For all $1 \le i \le N$, $-100 \le x_i, y_i \le 100$.

You may assume that no line passes through any three distinct points. You may also assume that if the polygon with the $K$-th smallest perimeter exists, it is uniquely determined.

The input ends with a line containing two zeros. The total number of datasets does not exceed 50.

For each dataset, output on one line the perimeter of the $K$-th shortest simple polygon that can be formed from the given points. If no such polygon exists, output -1. The result must have an error of less than $10^{-4}$.