Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

I. Photo Processing

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEvlampiy has found one more cool application to process photos. However the application has certain limitations.

Each photo *i* has a contrast *v*_{i}. In order for the processing to be truly of high quality, the application must receive at least *k* photos with contrasts which differ as little as possible.

Evlampiy already knows the contrast *v*_{i} for each of his *n* photos. Now he wants to split the photos into groups, so that each group contains at least *k* photos. As a result, each photo must belong to exactly one group.

He considers a processing time of the *j*-th group to be the difference between the maximum and minimum values of *v*_{i} in the group. Because of multithreading the processing time of a division into groups is the maximum processing time among all groups.

Split *n* photos into groups in a such way that the processing time of the division is the minimum possible, i.e. that the the maximum processing time over all groups as least as possible.

Input

The first line contains two integers *n* and *k* (1 ≤ *k* ≤ *n* ≤ 3·10^{5}) — number of photos and minimum size of a group.

The second line contains *n* integers *v*_{1}, *v*_{2}, ..., *v*_{n} (1 ≤ *v*_{i} ≤ 10^{9}), where *v*_{i} is the contrast of the *i*-th photo.

Output

Print the minimal processing time of the division into groups.

Examples

Input

5 2

50 110 130 40 120

Output

20

Input

4 1

2 3 4 1

Output

0

Note

In the first example the photos should be split into 2 groups: [40, 50] and [110, 120, 130]. The processing time of the first group is 10, and the processing time of the second group is 20. Maximum among 10 and 20 is 20. It is impossible to split the photos into groups in a such way that the processing time of division is less than 20.

In the second example the photos should be split into four groups, each containing one photo. So the minimal possible processing time of a division is 0.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/15/2019 15:36:24 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|