3452: Minimum Modular
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Description
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputYou 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