Meadow

A wide meadow is dotted with many flowers. Countless industrious bees fly between them, landing and taking off again, gathering the raw material called pollen that is turned into honey back in the hive. Because the survival and prosperity of the bee community depend on it, every single flower must be visited so that as much pollen as possible is collected.

Maya the bee has to draw up a schedule that sends the bees to visit every flower on the meadow. A schedule is made up of several sets of flowers (more precisely, sets of flower positions). Each bee is assigned exactly one set and must visit all of the flowers in that set in an arbitrary order; a flower may be visited any number of times. There are $B$ bees and each bee takes one set, so a schedule has at most $B$ sets.

• The weight of a visiting order of flowers is the largest distance between two consecutive flowers in that order.
• The weight of a set of flowers is the smallest weight over all visiting orders of that set. Each bee always flies along an order of minimum weight for its set.
• The weight of a schedule is the largest weight among all of its sets.

The distance between two flowers $(x_1, y_1)$ and $(x_2, y_2)$ is the Euclidean distance $\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}$.

Write a program that helps Maya find a schedule of the lowest possible weight.

The first line contains two natural numbers $F$ and $B$ ($1 \le F \le 2000$, $1 \le B \le F$), where $F$ is the number of flowers on the meadow and $B$ is the number of bees available for collecting pollen.

Each of the next $F$ lines contains two natural numbers $X$ and $Y$ ($1 \le X, Y \le 10000$), the coordinates of one flower.

Print a single line containing the minimum possible weight of a schedule for the given input, rounded to two decimal places.