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 PYTHON3):

Solution:
from sys import stdin, stdout
input = stdin.readline


a, b = map(int, input().split())
z_plus, z_minus = float('inf'), float('inf')
steps_plus = int((a+b)/(2*b))
steps_minus = int((a-b)/(2*b))

if steps_plus > 0:
    z_plus = ((a+b)/(2*steps_plus))
if steps_minus > 0:
    z_minus = ((a-b)/(2*steps_minus))

ans = min(z_plus,z_minus)
if ans == float('inf'):
    stdout.write("-1")
else:
    stdout.write("{:.10f}".format(ans))