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
jokysatria: 2015-06-15 02:09:10

someone can help me? can you explain to me, what is the relation of binary search with this problem? give me the clue. thx

Last edit: 2015-06-15 02:51:38
Maverick: 2015-06-03 17:55:35

Great Problem.Now i Know where and why to use Binary Search.

sharif ullah: 2015-06-03 08:28:52

ohh! 1,4,8 ans will be 3

Last edit: 2015-06-03 08:31:13
[Mayank Pratap]: 2015-05-28 17:41:32

Phew.....ACed ....
If u read topcoder tutorials 10 times ......u definitely get something.... :)

shuvadip: 2015-03-21 18:04:38

Sorry silly mistake!!!!

Last edit: 2015-03-30 19:20:16
John Jost: 2015-03-16 14:07:30

I'm with chilaka... I believe the farmer would have put the cows in 1,4,9. However, I don't believe that would change the answer of 3 because there would still be the minimum distance between stall 1 and stall 4 of 3.

chilaka ramakrishna: 2015-02-24 14:44:58

but it is said that the largest distance between any two cows as maximum as possible!!

kepler: 2015-02-24 13:04:03

We have to find the largest minimum distance, not maximum distance!

chilaka ramakrishna: 2015-02-24 12:45:21

why cant he put his cows in 1,4,9
from the above case the largest minimum distance becomes 4

Last edit: 2015-02-24 16:24:51
Kunwar Sachin Singh: 2015-01-23 14:40:36

good concept


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