Generalized Erdős--Ginzburg--Ziv Constants for finite abelian groups of rank three

Let $G$ be a finite abelian group with exponent $\exp(G)$. For positive integer $k$, the generalized Erdős--Ginzburg--Ziv constant, denoted by $\mathsf s_{k\exp(G)}(G)$ is the least integer $\ell$ such that every sequence of length at least $\ell$ over $G$ has a zero-sum subsequence of length $k\exp