Let's have a race in the cartesian plane. We define a point as a pair, (x,y), where x and y are both integers. We will start the race at the point (0,0). Then, we stop at the points (18,20), (14,12), (35,25), (30,8), then back to (0,0), in that order. In order to tell how we can move each time, we have a movement vector (a,b). if we are at point (x,y) and the movement vector is (a,b), the next point we will visit is (x+a,y+b). The movement vector starts at (0,0). Before each move, we ma