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:
s=input().split()
a=int(s[0])
b=int(s[1])
if b>a:
    print("-1")
elif b==a:
    print(a)
else:
    m=(a+b)/(2*b)
    m=int(m)
    m=2*m
    m=(a+b)/m
    if b>m:
        m=b

    n=(a-b)/(2*b)
    n=int(n)
    n=2*n
    if n==0:
        n=m+1
    else:
        n=(a-b)/n
    if b>n:
        n=b

    print(min(m,n))