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:
#578A
from math import floor
[a,b] = list(map(float,input().split()))
if a < b:
    print(-1)
elif a == b:
    print(a)
else:
    a1 = (a + b)/2
    k1 = floor(a1/b)
    x1 = a1/k1
    a2 = (a - b)/2
    k2 = floor(a2/b)
    if k2 == 0:
        x2 = a
    else:
        x2 = a2/k2
    print(min(x1,x2))