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 math import floor
a, b = map(int, input().split())
if a < 0:
    print(-1)
elif b < 0:
    print(-1)
elif a < b:
    print(-1)
elif a == 0 and b != 0:
    print(-1)
elif a == b:
    print(b)
elif b == 0:
    print(0)
else:
    n1 = floor((a - b) / (2 * b))
    n2 = floor((a + b) / (2 * b))
    if n1 == 0:
        print((a + b) / (2 * n2))
    else:
        x1 = (a - b) / (2 * n1)
        x2 = (a + b) / (2 * n2)
        print(min(x1, x2))