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
2016-11-27 19:00:14 Aditya
finally did it. Totally worth it. Now I really understand binary search.
2016-11-05 17:39:14
Guys, take a hint : complexity is N*log(max(X))
2016-11-02 02:33:02 ferol
I do not understand what for is t?
2016-10-06 07:32:19 Shreyans
No need for long int. 32-bit int good enough for AC.
2016-09-22 21:13:17
time limit exceeded :( . complexity : O(2nlogn)+O(n). would appreciate suggestions for optimisation
2016-08-30 14:47:22
Thanks all.. got more testcases from @manas0008 comment
2016-08-30 14:45:25
Hey guys.. this is my first submission to spoj and i keep getting wrong answer on my submission both on binary search & brute force option. What could i be messing up ? Do we need to print new lines with answer or anything like that. does any one have any bigger testcases ? any tips would be appreciated
2016-08-23 17:34:40
@mkfeuhrer @usumeet link pls link pls link pls
2016-08-19 18:56:13
My 50th :-) :-) :-)
2016-08-10 18:32:04


Last edit: 2016-08-10 18:32:25
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