Hamilton cycles in circulant digraphs with prescribed number of distinct jumps

Let G be a digraph that consists of a finite set of vertices V(G). G is called a circulant digraph   if its automorphism group contains a |V(G)||V(G)|-cycle. A circulant digraph G   has arcs (i,i+a1),(i,i+a2),…,(i,i+aj)(mod|V(G)|) incident to each vertex ii, where integers aksaks satisfy 0