Minimum Telescope Radius for Observing Stars

EI is using his telescope to observe stars. There are \(n\) stars in the sky, each located at a 2D coordinate \((x,y)\). When the telescope is positioned at \((x_0,y_0)\), it can see all stars satisfying the inequality
\[ (x_0 - x)^2 + (y_0 - y)^2 \le r^2 \]
where \(r\) is an adjustable radius.

EI wants to know: if he wishes to see at least \(m\) stars, what is the minimum \(r\) he must set? You are allowed to choose the optimal telescope position.

Note: All formulas are in \(\LaTeX\) format. The answer should be printed as a floating point number with 6 decimal places.

inputFormat

The first line contains two integers \(n\) and \(m\) (\(1 \le m \le n\)). The next \(n\) lines each contain two real numbers \(x\) and \(y\) representing the coordinates of a star.

outputFormat

Output a single floating-point number: the minimum radius \(r\) required so that there is a circle of radius \(r\) (positioned arbitrarily) that covers at least \(m\) stars. The answer must be printed with 6 decimal places.

sample

3 2
0 0
1 0
0 1

0.500000