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 $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-4}$.

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

3.1622776589

1 1
0 0

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.