AMR10G - Christmas Play

My kid's kindergarten class is putting up a Christmas play.  (I hope he gets the lead role.)  The kids are all excited, but the teacher has a lot of work.  She has to produce costumes for a scene with K soldiers.  She wants to buy all the costumes in the same size, allowing for some small amount of length alteration to be done by the kids' parents later.  So she has taken all the kids' height measurements.  Can you help her select K kids from her class of N to play the soldier role, such that the height difference between the tallest and shortest in the group is minimized, and alternations will be easiest?  Tell her what this minimum difference is.
The first line contains the number of test cases T. T test cases follow each containing 2 lines.
The first line of each test case contains 2 integers N and K.
The second line contains N integers denoting the height of the N kids.
Output T lines, each line containing the required answer for the corresponding test case.
T <= 30
1 <= K <= N <= 20000
1 <= height <= 1000000000

3 1
2 5 4
3 2
5 2 4
3 3
2 5 4
In the first test case, the teacher needs to only select 1 kid and hence she can choose any kid since the height difference is going to be 0.
In the second test case, the teacher can choose kids with height 4 and 5.
In the third test case, the teacher is forced to choose all 3 kids and hence the answer = 5-2 = 3

hide comments
Stefan: 2012-06-02 17:28:29

What's the answer of:
6 2
32 21 15 3 4 5

Santiago Palacio: 2012-01-12 19:36:30

If you are getting TLE with T(nlog(n)+n) look for I/O optimizations.

Hazem: 2011-10-08 15:08:36

am getting WA
please more test cases

sri: 2011-10-05 19:35:51

am getting tle
my solution is o(nlogn +n)
please guide me

sri: 2011-02-23 14:41:45

superb question....

Manpreet Singh: 2011-01-14 10:11:14

nice one for python

numerix: 2011-01-12 21:56:28

Impossible with Python 3 because of too much i/o.
Edit: Okay, it IS posssible, but must be well optimized ...

Last edit: 2011-01-13 17:56:47

Added by:Varun Jalan
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ICPC Asia regionals, Amritapuri 2010