CIIM 2018 Problem 3

Let $m$ be an integer and $\mathbb{Z}_m$ the set of integer modulo $m$ . An equivalence relation is defined in $\mathbb{Z}_m$ given by, $x \sim y$ if there exists a natural $t$ such that $y \equiv 2^tx (\bmod m)$ . Find al values of $m$ such that the number of equivalent classes is even.