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 PYTHON):

Solution:
from decimal import *
getcontext().prec = 30

a, b = map(int, raw_input().split())

if b > a:
    print -1

else:
    d = int(a/b)
    if d % 2 == 0:
        d -= 1

    L = Decimal(b)
    R = Decimal(1e9)


    while R-L > 1e-9:
        M = (L+R)/2

        p = int(a/M)
        if p < d:
            R = M
        elif p > d:
            L = M
        else:
            if M - (a-M*p) > b:
                R = M
            else:
                L = M

    print L