You 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 $*m*$.