Contracting boundary of a cusped space

Let Formula: see text be a finitely generated group. Cashen and Mackay proved that if the contracting boundary of Formula: see text with the topology of fellow traveling quasi-geodesics is compact then Formula: see text is a hyperbolic group. Let Formula: see text be a finite collection of finitely generated infinite index subgroups of Formula: see text. Let Formula: see text be the cusped space obtained by attaching combinatorial horoballs to each left coset of elements of Formula: see text. In this article, we prove that if the combinatorial horoballs are contracting and Formula: see text has compact contracting boundary then Formula: see text is hyperbolic relative to Formula: see text.