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
rv6023: 2020-08-30 19:00:10

use this testcase:
1
4 3
1 5 4 8

ans : 3

hafiz_: 2020-08-25 19:03:19

@kishor_e it is also true choosing 1,4,9 but the answer will remain same.

dharan1011: 2020-08-22 22:30:11

AC 0.04 in on go!!

nakli_c0der: 2020-08-11 05:31:14

Those who got AC, kindly check this test case...
1
2 2
9 12


: answer should be 3

mr_cchef: 2020-08-04 14:51:00

AC in 0.03 seconds.

karlo_2107: 2020-08-01 15:47:56

AC 0.08!!! You need to binary search minimal distance between cows and after that check it out! Easy :)

gnomegeek: 2020-07-28 15:39:51

Great Question to feel and fell for BS (Binary Search) xD

kishor_e: 2020-07-28 12:09:05

why not choose 1,4,9?

danny_132: 2020-07-26 10:49:44

Really good problem on Binary search . This basically involves the concept of binary search on answer where we decide which side will give better answer(left or right if some condition satisfies) after finding the mid. Watch video on Binary search by ERRICHTO he has explained the concept really well using the largest >=x problem in his video.

adarshraj365_: 2020-07-26 06:06:37

AC in 0.07 sec !!
Great question to feel binary_search


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