You have been given n distinct integers a₁, a₂, ..., 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: .

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, ..., a_n (0 ≤ a_i ≤ 10⁶).

Print a single positive integer — the minimum m.