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Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

If $a$ , $b$ and $c$ are distinct positive integers such that $abc = 16$ , then the largest possible value of $a^b - b^c + c^a$ is

(A) $253$ (B) $63$ (C) $249$ (D) $263$ (E) $259$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.