Minimise the Size

Consider an array $A = \{a_1, a_2,...,a_n\}$ of size $n \geq 1$. If $a_k = 2^x -1$ for all $ 1\leq k \leq n$, for some integer $x$ $(1 \leq x \leq 60)$, then $A$ is called $interesting$ $array$. You are given a number $C$. Find any $interesting$ $array$ $A$ of minimum possible size such that $ a_1 \bigoplus a_2 \bigoplus...\bigoplus a_n = C$, where $\bigoplus$ represents bitwise XOR operation.