There is a polyline going through points $(0, 0) – (*x*, *x*) – (2*x*, 0) – (3*x*, *x*) – (4*x*, 0) – ... - (2*kx*, 0) – (2*kx* + *x*, *x*) – ...$.

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 $*b*$ ($1 ≤ *a*, *b* ≤ 10^{9}$).

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.

Note

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