Building an Amusement Park

Description:

Input:

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 10^5$$$, $$$1 \leq k \leq n$$$) — the number of bird habitats in the city and the number of bird habitats required to be inside the park.

The $$$i$$$-th of the next $$$n$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$0 \leq |x_i|, |y_i| \leq 10^5$$$) — the position of the $$$i$$$-th bird habitat.

Output:

Output a single real number $$$r$$$ denoting the minimum radius of a park with at least $$$k$$$ bird habitats inside. It is guaranteed that the given input always has a solution with $$$r \leq 2 \cdot 10^5$$$.

Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-4}$$$.

Formally, let your answer be $$$a$$$, and the jury's answer be $$$b$$$. Your answer is accepted if and only if $$$\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-4}$$$.

Sample Input:

8 4
-3 1
-4 4
1 5
2 2
2 -2
-2 -4
-1 -1
-6 0

Sample Output:

3.1622776589

Sample Input:

1 1
0 0

Sample Output:

0.0000000000

Note:

In the first example, Mr. Chanek can put the center of the park at $$$(-3, -1)$$$ with radius $$$\sqrt{10} \approx 3.162$$$. It can be proven this is the minimum $$$r$$$.

The following illustrates the first example. The blue points represent bird habitats and the red circle represents the amusement park.