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:
a, b = [int(i) for i in input().split()]

if a<b:
    print(-1)
else:
    opt1 = (a-b)//b
    if opt1&1:
        opt1 -= 1
    opt2 = (a+b)//b
    if opt2&1:
        opt2 -= 1
    if opt1 == 0:
        print((a+b)/opt2)
    elif opt2 == 0:
        print((a-b)/opt1)
    else:
        print(min((a-b)/opt1, (a+b)/opt2))