Minimum Modular

2000ms

262144K

Description:

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: $\text{[math]}$ .

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, ..., a_n (0 ≤ a_i ≤ 10⁶).

Output:

Print a single positive integer — the minimum m.

Sample Input:

7 0
0 2 3 6 7 12 18

Sample Output:

Sample Input:

7 1
0 2 3 6 7 12 18

Sample Output:

Informação

Provedor Codeforces

Código CF303C