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

if a < b:
    print -1
elif a == b:
    print a
else:
    ans = (a + b) / 2.0
    lo = 1
    hi = 1000000000
    while lo + 1 < hi:
        mid = (lo + hi) / 2
        if ans / mid >= b:
            lo = mid
        else:
            hi = mid
    print '%0.15f' % (ans / lo)