D. Rectangle Restoration
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

In this problem, you have to restore some data about a rectangle. You know that the sum of lengths of some two sides of this rectangle is equal to $$$x$$$, and the sum of lengths of some three sides of this rectangle is equal to $$$y$$$. Note that each of the four sides of rectangle is included at most once into each of the two sums.

You have to calculate the minimum possible perimeter of a rectangle such that the sum of lengths of some two sides of this rectangle is equal to $$$x$$$, and the sum of lengths of some three sides of this rectangle is equal to $$$y$$$. Note that side lengths are not necessarily integers, but they are strictly positive.

Input

The only line contains two integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le 10^{9}$$$).

Output

If there is no rectangle meeting the constraints, print $$$-1$$$.

Otherwise, print one real number — the minimum possible perimeter of a rectangle meeting the constraints. The absolute or relative error of your answer must not exceed $$$10^{-4}$$$.

Examples
Input
10 15
Output
20.0000
Input
6 4
Output
7.0000
Input
10 2
Output
-1
Input
7 4
Output
7.5000
Input
500000000 1000000000
Output
1250000000.0
Note

In the first example, the rectangle in the answer is a square with side length equal $$$5$$$.

In the second example, the rectangle with minimum perimeter meeting the constraints has two sides with length $$$3$$$ each, and two sides with length $$$0.5$$$ each.

In the third example, there is no rectangle meeting the constraints.

In the fourth example, the rectangle with minimum perimeter meeting the constraints has two sides with length $$$3.5$$$, each, and two sides with length $$$0.25$$$ each.