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
arjun_agrawal: 2017-09-05 06:45:06

Thought this question in a backward manner. Try to search for the answer in a binary search fashion and check its feasibility

pkgleb: 2017-08-27 18:47:35

First, I found solution using Indexed priority queue, but after topcoder's article lecture the solution just show up :)

kspoj: 2017-08-24 20:29:26

Quora helped :)

iket0512: 2017-08-20 07:29:56

Last edit: 2017-08-20 07:30:22
suchith: 2017-08-05 20:00:23

nice problem
thanks to quora thread and top coder tutorial

omaragha: 2017-08-03 16:48:57

Nice BS Problem

kotal_kahn: 2017-07-25 14:56:37

At last after understanding from both Topcoder binary search and the Quora answer

grb_avatar: 2017-07-23 23:40:32

if u having any problem read this link

https://www.topcoder.com/community/data-science/data-science-tutorials/binary-search

Last edit: 2017-07-23 23:42:27
i_insist: 2017-07-17 07:46:17

don't forget to add new line (cout<<endl) at the end.

siddiboy: 2017-07-14 08:20:37

any way to do it in O(N)??


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