Arctic Network

The Department of National Defence (DND) wants to connect several northern outposts with a wireless network. Two communication technologies are used to build the network: every outpost is equipped with a radio transceiver, and some outposts additionally have a satellite channel.

Any two outposts that both have a satellite channel can communicate through the satellite, no matter where they are located. Otherwise, two outposts can communicate by radio only if the distance between them is at most $D$, which depends on the transmitter power. Higher power gives a larger $D$ but costs more. For purchasing and maintenance reasons the transceivers at all outposts must be identical; that is, the value of $D$ is the same for every pair of outposts.

Determine the minimum $D$ such that every pair of outposts is connected by at least one communication path, whether direct or indirect.

The first line contains the number of test cases $N$. For each test case, the first line contains the number of satellite channels $S$ and the number of outposts $P$ ($1 \le S \le 100$, $S < P \le 500$). The next $P$ lines each contain the coordinates $(x, y)$ of an outpost in kilometres. Each coordinate is an integer between $0$ and $10\,000$ inclusive.

For each test case, output on a single line the minimum $D$ required to connect the network. Print the value to two decimal places.