Canyon Mapping

A canyon is a deep ravine between cliffs. Canyons are not limited to Earth. Valles Marineris runs along the equator of Mars and is roughly the size of the United States.

A mapping company draws maps of canyons like these. The outline of a canyon is given as a simple polygon in the plane. Every map is a square whose sides are parallel to the coordinate axes, because the company wants north at the top of every map. To show more detail, one canyon is sometimes drawn on several maps. Such a collection is called a mapping system.

A mapping system must cover the entire area of the canyon. All maps in the system have the same scale with respect to the canyon and the same printed size, so several of them can be laid out and compared.

Your mapping system holds exactly $k$ maps. A map that covers less area can be drawn in more detail, so you need the mapping system that covers the whole canyon while each map covers as little area as possible. All maps are squares and cover the same area of the canyon. Maps may overlap. Area is the square of the side length, so print the side length only.

The first line contains the number of vertices of the polygon $n$ and the number of square maps in the mapping system $k$, separated by a space. ($3 \le n \le 2000$, $1 \le k \le 3$)

Each of the next $n$ lines contains the coordinates $x$ and $y$ of one vertex of the polygon, in order. ($-20000 \le x, y \le 20000$) All coordinates are integers. No two edges of the polygon intersect and all vertices are distinct. The polygon is simple, it neither touches nor crosses itself, and its area is positive.

Print the smallest side length of one map, measured with respect to the canyon, over all mapping systems of $k$ equally sized square maps that cover the whole canyon. Round the value to exactly two decimal places.