So, as you all know free WiFis are being
installed in our institute.
These are a special
type of WiFi and they start to interfere when
there is a signal coming from two different
WiFis at a single location. The WiFi
installation task is given to you.

There are N suitable locations for the
installation of WiFi.
These locations are
located along straight line positions
x1,x2,...,xN (0<=xi<=1000000000).
You have to install C WiFis.
You have to
install the WiFis at locations such that the
minimum distance between any two of them
is as large as possible.
What is the largest
minimum distance ?

Input
Line 1 of contains Two space-separated integers: N and C.

Each of the next N lines, contain an integer denoting the
location Xi.

Output
Print the largest minimum distance in a
single line.

Constraints

1 ≤ N ≤ 10^5
1 ≤ Xi ≤ 10^9

Example
Input:
5 3
1
2
8
4
9

Output:
3

Explanation
Example case 1. The WiFis can be installed at locations 1,4 and 8 or 1,4 and 9 resulting in a minimum distance of 3.

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见题面