Description:
You have been given n distinct integers a1, a2, ..., an. You can remove at most k of them. Find the minimum modular m (m > 0), so that for every pair of the remaining integers (ai, aj), the following unequality holds: $$a_{i} \not\equiv a_{j} \mod m$$.
Input Format:
The first line contains two integers n and k (1 ≤ n ≤ 5000, 0 ≤ k ≤ 4), which we have mentioned above.
The second line contains n distinct integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output Format:
Print a single positive integer — the minimum m.
Note:
None