There is a polyline going through points (0,0)—(x,x)—(2x,0)—(3x,x)—(4x,0)—...-(2kx,0)—(2kx+x,x)—.... We know that the polyline passes through the point (a,b). Find minimum positive value x such that it is true or determine that there is no such x.

Input Only one line containing two positive integers a and b (1 \le a,b \le 109).

Output Output the only line containing the answer. Your answer will be considered correct if its relative or absolute error doesn't exceed 10-9. If there is no such x then output -1 as the answer.

You can see following graphs for sample 1 and sample 3.