A9034. Minimum Modular

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: .

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 $a_{1},a_{2},...,a_{n}$ $(0<=a_{i}<=10^{6})$ .

Print a single positive integer — the minimum $m$ .