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 fractions import Fraction


def solve(a, b):
    x = Fraction(b)
    n = a // (x*2)
    a_ = a % (x*2)
    if b > a:
        return -1
    if a_ == x:
        return float(x)
    if a_ < x:
        return float((a+b)/(2*n))
    if a_ > x:
        return float((a+b)/(2*n+2))


a, b = map(Fraction, input().split())
print(solve(a, b))