Problem Description

Given the coordinates of $N$ points, find the minimum radius and the center position of a circle that can cover at least $K$ of these points.

Input Format

The first line contains two integers $N, K$.

The next $N$ lines each contain two integers, giving the coordinates of a point.

Output Format

The first line contains the radius of the circle.

The second line contains the coordinates of the circle center.

This problem uses SPJ. Your answer is considered correct only if it satisfies the following two conditions:

• The error of $R$ does not exceed $10^{-4}$.

• Although there may be multiple valid solutions and you may output any one of them, the circle centered at your output coordinates must cover at least $K$ points when its radius is $R+0.0002$.

10 5 
1 8 
2 6 
4 8 
2 2 
9 7 
8 5 
5 3 
3 3 
4 6 
4 1 

2.236068 
3 4 

Hint

Constraints: for $100\%$ of the testdata, $2 \le K \le N \le 500$, $0 \le X, Y \le 10^4$.

Translated by ChatGPT 5