66th Belarusian Mathematical Olympiad

Let $\mathcal{A}$ be a nonempty set of positive integers. We say that a positive integer $n$ is special if there exists a unique subset $\mathcal{B}$ of the set $\mathcal{A}$ such that (i) the number of the elements in $\mathcal{B}$ is odd; (ii) the sum of all elements of $\mathcal{B}$ is equal to $n$.

Prove that there exist infinitely many positive integers that are not special.

(IMO-2015 Shortlist, Problem C6)