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1775. Space Bowling

Time limit: 1.0 second
Memory limit: 64 MB
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.

Input

The first line contains space-separated integers n and k (1 ≤ kn ≤ 200). The i-th of following n lines contains space-separated integers xi and yi (−105xi, yi ≤ 105), which are the coordinates of the centers of pins. All pins are situated at different points.

Output

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 “0.000000”.

Sample

inputoutput
5 4
0 4
0 6
6 4
6 6
3 0
1.0000000000
Problem Author: Alexander Mironenko
Problem Source: XV Open USU Championship