Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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C. Minimum Modular

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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: .

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 *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} ≤ 10^{6}).

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

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