Minimum Modular

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 0 0 2 3 6 7 12 18

Output

13

Input

7 1 0 2 3 6 7 12 18

Output

7

inputFormat

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).

outputFormat

Output

Print a single positive integer — the minimum m.

Examples

Input

7 0 0 2 3 6 7 12 18

Output

13

Input

7 1 0 2 3 6 7 12 18

Output

7

样例

7 0
0 2 3 6 7 12 18

13

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