Setting

The Department of Things of Remote Scientific Interest (DTRSI) wishes to connect several outposts in remote regions by a wireless network. Two different communication technologies are to be used in establishing the network: every outpost will have a radio transceiver and some outposts will in addition have a satellite channel.

Any two outposts with a satellite channel can communicate via the satellite, regardless of their location. Otherwise, two outposts can communicate by radio only if the distance between them does not exceed \(d\), which depends on the power of the transceivers. Higher power yields higher \(d\), but costs more. Due to purchasing and maintenance considerations, the transceivers at the outposts must be identical; that is, the value of \(d\) is the same for every pair of outposts.

Your job is to determine the minimum \(D\) required for the transceivers. There must be at least one communication path (direct or indirect) between every pair of outposts.

Input

The first input line contains the number of test cases \(c\). The first line of each test case contains the number of available satellite channels \(1 \leq s \leq 100\), and the number of outposts \(S < p \leq 500\). The following \(p\) lines specify \(0 \leq x, y \leq 10,000\), the x and y coordinates of each outpost.

Output

For each test case, print a separate line that contains the minimum \(d\) required to connect the network. Output should be specified to 2 decimal points.

Sample Input

1
2 4
0 100
0 300
0 600
150 750

Sample Output

212.13

This is challenge 10369 of the ACM International Collegiate Programming Contest. Test input is provided by uDebug.

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Difficulty (1 vote)
Average test runtime 3.65
Points (changes over time) 10
Tried by 4 users
Solved by 4 users

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