Problem D. Hall of water life ≡

Statement

The main hall of the Nearsea Institute of Unspecified Underwater Studies has a shape of a long corridor. Along the corridor, there are N aquariums exhibiting various sea creatures. Aquariums are located at distances x₁, …, x_N from the hall entrance (x_i < x_i + 1).

The institute has recently got a new director, who decided that the aquarium maintenance is too costly, and issued an order to remove M (0 ≤ M ≤ N − 2) aquariums.

To minimize the disruption to the looks of the hall, it was decided that:

1. the first and the last aquariums should be left in their places;
2. the maximum distance between the adjacent aquariums must be as small as possible.

Your program must select aquariums for removal in such a way that the above conditions are satisfied.

Input file format

Input file contains integers N M followed by N integers x_i.

Output file format

Output file should contain a single integer — the smallest possible maximum distance.

Constraints

Sample tests

5 2
1 2 3 4 5

2

4 1
10 21 30 40

19