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HMMT 2014 U8

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The numbers 20,21,⋯ ,215,216=655362^{0}, 2^{1}, \cdots, 2^{15}, 2^{16}=65536 are written on a blackboard. You repeatedly take two numbers on the blackboard, subtract one from the other, erase them both, and write the result of the subtraction on the blackboard. What is the largest possible number that can remain on the blackboard when there is only one number left?

Dataset text NuminaMath olympiads. Quoted with source.

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