Plot

We call any sequence of points in the plane a plot. We want to replace a given plot $(P_1, \dots, P_n)$ with another one that has at most $m$ points ($m \le n$) and resembles the original as closely as possible.

The new plot is built as follows. The sequence $(P_1, \dots, P_n)$ is split into $s$ ($s \le m$) contiguous subsequences

$(P_{k_0+1}, \dots, P_{k_1}),\ (P_{k_1+1}, \dots, P_{k_2}),\ \dots,\ (P_{k_{s-1}+1}, \dots, P_{k_s})$

where $0 = k_0 < k_1 < k_2 < \dots < k_s = n$. Then each subsequence $(P_{k_{i-1}+1}, \dots, P_{k_i})$ (for $i = 1, \dots, s$) is replaced by a single new point $Q_i$. We say that each of the points $P_{k_{i-1}+1}, \dots, P_{k_i}$ has been contracted to the point $Q_i$. The result is a new plot consisting of the points $Q_1, \dots, Q_s$.

The resemblance of such a plot to the original is measured by the maximum distance from any point $P_1, \dots, P_n$ to the point it was contracted to:

$\max_{i=1,\dots,s} \left( \max_{j=k_{i-1}+1,\dots,k_i} d(P_j, Q_i) \right)$

where $d(P_j, Q_i)$ is the distance between the two points, given by the well-known formula

$d((x_1, y_1), (x_2, y_2)) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

The figure above shows an example plot $(P_1, \dots, P_7)$ and the new plot $(Q_1, Q_2)$, where $(P_1, \dots, P_4)$ are contracted to $Q_1$ and $(P_5, P_6, P_7)$ to $Q_2$.

Given a plot of $n$ points, among all plots with at most $m$ points obtainable this way (the split into contiguous subsequences is arbitrary), the resemblance to the original can be made as small as possible. Find that smallest possible resemblance value $d$.

The first line contains two integers $n$ and $m$ separated by a single space ($1 \le m \le n \le 100000$). Each of the next $n$ lines contains two integers separated by a single space; the $i$-th of them gives $x_i$ and $y_i$ ($-1000000 \le x_i, y_i \le 1000000$), the coordinates $(x_i, y_i)$ of the point $P_i$.

Print a single real number $d$: the minimum possible resemblance (the smallest achievable value of the maximum contraction distance) over all plots with at most $m$ points. Print it rounded to exactly $6$ digits after the decimal point.