Problem: 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.

Examples

Input

3 1


Output

1.000000000000


Input

1 3


Output

-1


Input

4 1


Output

1.250000000000

Note

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

<image> <image>

Solution (in PYTHON):

Solution:
a,b = map(int, raw_input().strip().split())
x = -1
if a == b: x = b
if (a-b) > 0:
    ka, kb = (a-b+2.0*a-1) // (2.0*a), (a-b)//(2.0*b)
    if ka <= kb: x = (a-b)/2.0/kb
    ka, kb = (a+b+2.0*a-1) // (2.0*a), (a+b)//(2.0*b)
    if ka <= kb and kb > 0: x_ = (a+b)/2.0/kb
    x = x_ if x < 0 else min(x, x_)
print x