On weighted bidegree of polynomial automorphisms of C^2

Let $F=(F_1,F_2):C^2 —> C^2 be a polynomial automorphism. It is well know that deg F_1 | deg F_2 or deg F_2 | deg F_1. On the other hand, if (d_1,d_2) \in (N{0})^2 is such that d_1 | d_2 or d_2 | d_1, then one can construct a polynomial automorphism F=(F_1,F_2) of C^2 with deg F_1=d_1 and deg F_2=d_2. Let us fix w=(w_1,w_2) \in (N{0})^2 and consider the weighted degree on C[x,y] with wdeg x=w_1$ and wdeg y=w_2. In this note we address the structure of the set {(\wdeg F_1,\wdeg F_2) : (F_1,F_2) is an automorphism of C^2}.