Repair Depots

RoboCorp Oregon has already deployed several of its PoliceBots across the state, and now they want to be able to repair a bot whenever it breaks. They will build only a limited number of repair depots, and they want to position those depots so that every bot is close to one of them.

You are given the locations of the $n$ deployed PoliceBots ($1 \le n \le 16$) and the maximum number of repair depots $c$ ($1 \le c \le n$) that RoboCorp is willing to build. You may place each depot at any point in the plane (not only at a bot's location). Every bot is served by the depot nearest to it, and any bot can be repaired at any depot. Position at most $c$ depots so that the largest distance from any bot to its nearest depot is as small as possible, and report that minimum possible distance.

The first line contains an integer $t$ ($1 \le t \le 350$), the number of test cases.

Each test case begins with a line containing two integers $n$ and $c$. The next $n$ lines each contain two space-separated real numbers $x$ and $y$ ($0.0 \le x, y \le 10.0$), the Cartesian coordinates of one bot. Coordinates are real values; some may be written as integers.

For each test case, print on its own line the minimum achievable value of the maximum bot-to-nearest-depot distance. Print the value with at least one digit before the decimal point and exactly six digits after it. Your answer must be within $5\times10^{-7}$ of the true result; the true result will never have a $4$ or a $5$ as its seventh digit after the decimal point, so rounding to six places is unambiguous.