ELMO 1999 Problem 2

Mr. Fat moves around on the lattice points according to the following rules: From point $(x,y)$ he may move to any of the points $(y,x)$ , $(3x,-2y)$ , $(-2x,3y)$ , $(x+1,y+4)$ and $(x-1,y-4)$ . Show that if he starts at $(0,1)$ he can never get to $(0,0)$ .