C. Minimum Modular
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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: .

Input

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

Print a single positive integer — the minimum m.

Examples
Input
7 00 2 3 6 7 12 18
Output
13
Input
7 10 2 3 6 7 12 18
Output
7