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
2016-05-18 17:29:16
can anybody tell output for case
1
2 1
1
5
if this testcase is possible


Last edit: 2016-05-18 18:05:48
2016-05-16 23:06:42
ac .....was stuck b4, but topcoder tutorial really roks!!!! :)
2016-05-13 21:25:22 Dushyant Singh
int is sufficient in c++
2016-05-04 22:20:58 dinkar
Nice problem to learn how binary search can be applied.
2016-05-04 20:56:25
Great problem.....AC in first pass
2016-05-04 18:23:24
If you have no idea how to use binary search for this problem don’t waste your time trying to figure it out on your own.
As the guys and gals said in the comments before this - go to the Topcoder binary search tutorial
https://www.topcoder.com/community/data-science/data-science-tutorials/binary-search/

Then when you are done try out the test cases that
@manas0008 posted on 2016-01-25 11:23:11

If you still have problems look carefully at the parts of the program that you tied to optimize. The bug is probably there.
2016-04-17 12:22:14
Do we must sort those stalls? I used bubble sort and got WA, then qsort and got AC..
2016-04-01 21:23:29
finally finally Done !!!! Great ques on Binary search .Topcoder tutorials rocks :P
2016-04-01 15:24:45
1. Use Long int
2. If you are still stuck , Just see Top Coder Tutorial . It gives you a brief idea on how to actually use Binary Search here .
Ac in one go :) 0.0s
2016-04-01 10:53:50
Please give the link to the Topcoder tutorial
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