There are $10^{2015}$ planets in an Intergalactic empire. Every two planets are connected by a two-way space line served by one of $2015$ travel companies. The Emperor would like to close $k$ of these companies such that it is still possible to reach any planet from any other planet. Find the maximum value of $k$ for which this is always possible.

Let's think step by step and output the final answer within \boxed{}.
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