A Problem about Polyline

1000ms

262144K

Description:

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 Input:

3 1

Sample Output:

1.000000000000

Sample Input:

1 3

Sample Output:

-1

Sample Input:

4 1

Sample Output:

1.250000000000

Note:

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

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Informação

Provedor Codeforces

Código CF578A