You have been given n distinct integers a 1, a 2, ..., a n . You can remove at most k of them. Find the minimum modular m (m 0), so that for every pair of the remaining integers (a i , a j ), the following unequality holds: .

输入描述:

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).

输出描述:

Print a single positive integer — the minimum m.