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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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