AGGRCOW - Aggressive cows

Farmer John has built a new long barn, with N (2 <= N <= 100,000) stalls. The stalls are located along a straight line at positions x1 ... xN (0 <= xi <= 1,000,000,000).

His C (2 <= C <= N) cows don't like this barn layout and become aggressive towards each other once put into a stall. To prevent the cows from hurting each other, FJ wants to assign the cows to the stalls, such that the minimum distance between any two of them is as large as possible. What is the largest minimum distance?

Input

t – the number of test cases, then t test cases follows.
* Line 1: Two space-separated integers: N and C
* Lines 2..N+1: Line i+1 contains an integer stall location, xi

Output

For each test case output one integer: the largest minimum distance.

Example

Input:

1
5 3
1
2
8
4
9

Output:

3

Output details:

FJ can put his 3 cows in the stalls at positions 1, 4 and 8,
resulting in a minimum distance of 3.


Added by:Roman Sol
Date:2005-02-16
Time limit:2s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:USACO February 2005 Gold Division

hide comments
2015-10-23 19:49:50 Rahul sant
Nice question,,just think whether a particular distance can be used as a minimum largest distance or not..
2015-10-23 19:05:35
learned a lot from this ...!! a must do problem for beginners!!
2015-10-19 21:32:00


Last edit: 2015-10-21 17:52:43
2015-10-03 08:31:57 .::High::Voltage::.
Please someone explain me how to do this problem as topcoder website is not working .
2015-09-30 21:32:46 Mit
Superb concept!
Highly recommended problem.
2015-09-18 10:57:03 thirupathireddy
good one on binary search.............
2015-09-10 19:31:43 Sriharshaa Sammeta
Though it would be good if you figure out for yourself....still....
check for these corner cases:
1
3 3
0 1000000000 500000000
Ans: 500000000

Also check for repetitive values:
1
10 3
1 2 9 8 4 4 8 9 2 1
Ans: 3

If these too pass then most probably it's an AC :D
2015-09-04 11:54:46 Aayush
this question taught me a new lesson..
plz tell me where I can find some more questions like this
2015-09-01 22:12:04
i got wa for using int and ac ,just replaced all int with long but an awesome problem
2015-08-14 16:22:36 Vicky
@sanyam jain can u provide me a topcoder link whrere u found tutorials
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