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>
from math import floor
def main():
    a, b = map(int, input().split())
    if (b > a):
        print(-1)
        return
    if (b == a):
        print(a)
        return
    if ((a-b) % b == 0 and ((a - b) // b) % 2 == 0):
        y = (a - b) // b
        
        print((a - b) / y)
        return
    
    y = (a + b) / 2
    k = y // b    
    print((a+b) / 2  / k)

main()