You have been given n distinct integers a1,a2,...,an. You can remove at most k of them. Find the minimum modular m (m \gt 0), so that for every pair of the remaining integers (ai,aj), the following unequality holds: .

The first line contains two integers n and k (1 \le n \le 5000,0 \le k \le 4), which we have mentioned above.

The second line contains n distinct integers a1,a2,...,an (0 \le ai \le 106).

Print a single positive integer - the minimum m.