Graham's rearrangement conjecture for subsets of prime cyclic groups

Let $p$) be prime and let $a_1,a_2,\dots,a_d$ be distinct nonzero elements of $\mathbb{Z}_p$. A set of elements is rearrangeable if its elements can be ordered so that all partial sums are distinct. Graham's rearrangement conjecture. There exists a rearrangement $a_{i_1},a_{i_2},\dots,a_{i_d}$ such that

$$\sum_{j=1}^t a_{i_j}$$

are distinct for $1\leq t\leq d$. This is the central rearrangement problem motivating the paper; the paper proves only an asymptotic version in general groups, while the full assertion remains open.