CHEF AND INFINITE GRID

Chef is standing at a point (a,b) in an $infinite$ grid. The only operation he can do is to move to point (a+b,b) ,(a,a+b) ,(a-b,b) and (a,b-a). Now he asks you $Q$ queries. In each query he gives a coordinate (x,y) and asks you if he can reach that coordinate from his current coordinate. If yes, then he $move$ to (x,y) else he stays at his current coordinate. $Note:$ - Suppose Chef moves in some