The inhabitants of planets orbiting around the pulsar PSR 2010+15
enjoy playing space bowling. A few cylindrical pins of unit diameter
are set on a huge field. A player chooses a certain point of the field
and rolls a ball from this point, trying to destroy as many pins as
possible. After the ball is released, it rolls in a straight line,
touching the surface all the time before rolling away from the field.
If the ball touches a pin, this pin dematerializes, and the ball doesn't change
direction. To score a strike, the player has to destroy at least
k pins in one shot.
Unfortunately, aliens haven't yet invented a machine that would return the
balls that rolled away from the field. Instead, they use a machine that
materializes a new ball from vacuum before each shot. A player enters the
diameter and in a second he obtains a ball of exactly the same diameter.
It is time for an alien Vas-Vas to roll a ball. There are n pins
standing on the field at the moment. Help Vas-Vas to determine the minimal
diameter of a ball, he can score a strike with.
The first line contains space-separated integers n and k
(1 ≤ k ≤ n ≤ 200). The i-th of following
n lines contains space-separated integers xi and
yi (−105 ≤ xi,
yi ≤ 105), which are the coordinates of the
centers of pins. All pins are situated at different points.
Output the minimal possible diameter of a ball which can be used to score
a strike, with absolute or relative error not exceeding 10−6.
If a strike can be scored with a ball of arbitrarily small diameter, output
Problem Author: Alexander Mironenko
Problem Source: XV Open USU Championship