Codeforces Round #320 (Div. 2) [Bayan Thanks-Round] C C Problem about Polyline 数学

                                                                       C. A Problem about Polyline

                                                                               time limit per test

1 second

                                                                               memory limit per test

256 megabytes

 

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 ≤ a, b ≤ 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.

Sample test(s)

Input

3 1

Output

1.000000000000

Input

1 3

Output

-1

Input

4 1

Output

1.250000000000

 

题解：对于a<b就是-1

       只有两种情况：

           上升段：a-2*ans*m=b;最小的ans是b所以m<=(a-b)/(2*b);可以得到ans的最小值