Minimum Radio Range with Satellite Constraints

There are n villages in the Arctic region. Each village's coordinates are given as a pair of integers (x, y).

To enhance communication, a network will be established so that every pair of villages can communicate directly or indirectly.

Communication tools can be either radio transceivers or satellite devices.

Radio transceivers come in different models, each with a parameter d. Two villages can communicate directly by radio if the distance between them is at most d. Models with larger d values are more expensive. We will choose one model of radio transceiver and equip all villages with it (unlimited number of devices, but all of the same model).

Villages equipped with satellite devices can communicate directly regardless of distance, but only a limited number of satellite devices are available, so they can be assigned to only some villages.

Given k satellite devices, write a program to determine how to assign them so that the required d value of the radio transceivers is minimized.

Input Format
The first line contains two integers n, k separated by a space.
The next n lines each contain two integers x_i, y_i, representing the coordinates of the i-th village.

Output Format
A real number, the smallest possible d value, rounded to two decimal places.

Constraints
1 ≤ n ≤ 500
0 ≤ x, y ≤ 10⁴
0 ≤ k ≤ 100

Sample Input

3 2
10 10
10 0
30 0

Sample Output

10.00