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
2017-02-03 03:22:29
@shingotem: As I understood the question, 1-4-9 minimum distance is also 3. In both cases the minimum distance is 3 so the max is 3. There is another possible arrangement, 2-4-8 (and 2-4-9), minimum distance is 2 (in both cases), so between 2 and 3, 3 is the max minimum distance. 5 would be the maximum maximum distance.
2017-02-01 16:21:57
why answer is not 5?
we can place cows at 1-4-9
so max(min) = 9-4 = 5?
where i am wrong ?
2017-01-29 21:51:32 Parth
good 1 :P
2017-01-19 16:42:32
Do we need to compute the whole search space first? I am having a hard time figuring out a way without computing a search space and without storing all the computed search space beforehand.
2017-01-18 04:52:00
Binary search on answer
2017-01-11 21:58:34
I don't understand
2016-12-31 14:08:18
AWESOME !!!!!!!!
2016-12-28 16:30:12
good problem, after so many tle and wa finally ac


Last edit: 2016-12-28 16:32:03
2016-12-16 17:45:21
This was pure JOY ! :)
2016-12-10 16:43:30
wowwii..first time..ac in 1 go
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