Check if Point Is Reachable

Given an infinite integer grid and allowed moves that either double one coordinate or replace a coordinate by its difference with the other ((x,y) -> (2x,y), (x,2y), (x,y-x), (x-y,y)), determine whether (targetX,targetY) can be reached from (1,1). Targets up to 1e9 force a mathematical/reverse-reduction approach rather than brute-force search.