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:
str_0=input()
list_0=str_0.split(' ')
a=int(list_0[0])
b=int(list_0[1])






if a<b:
    print(-1)
elif a==b:
    print('%.12f'% a)
else:
    n_1=((a+b)/2)//b
    t_1=(a+b)/(2*n_1)
    if b<=(a-b)/2:
        n_2=((a-b)/2)//b
        t_2=(a-b)/(2*n_2)
        if t_1<=t_2:
            t=t_1
        else:
            t=t_2
    else:
        t=t_1
    print('%.12f'% t)