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.


hide comments
zarif_2002: 2019-02-07 06:34:23

AC in one go.

deepakjain1998: 2019-01-30 14:15:46

first attempt AC !!! Thanks to Akash Yadav Sir and Sudama Sir

vickyand_27: 2019-01-02 16:54:56

my complexity is O(c*log(max(x[i]))*logn)

arpitkaushik18: 2018-12-18 08:14:40

Nice Problem on Binary Search : )

angrysum: 2018-11-26 10:35:15

@lapmid, you need to find that particular positions set for cows such that minimum distance of that particular set is largest among other sets.

vritta: 2018-11-20 02:31:24

For those who are not able to understand the approach to solve, this may help -
https://www.youtube.com/watch?v=TC6snf6KPdE

Last edit: 2018-11-20 02:33:32
suraj_13: 2018-11-02 11:02:34

Classic question, impressive way of using binary-search.

suraj_13: 2018-11-02 11:01:46

Those who are unable to solve refer to Topcoder tutorial: https://www.topcoder.com/community/competitive-programming/tutorials/binary-search and Commonlounge : https://www.commonlounge.com/discussion/a8cb881fae1946b5b689858a71e70558/37c42cbbcfa14644a94f08f69bd741d1

mayank_code: 2018-10-29 04:37:27

Finally AC :)

artistic_15: 2018-10-24 18:58:55

Very Good Problem. I didn't even knew we can implement binary search this way :)


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