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 b>a:
    print -1
elif a==b:
    print float(b)
else:
    ans1 = float(a-b)/2
    ans2 = float(a+b)/2
    if ans1<b:
        ans1 = 1e10
    else:
        ans1 = ans1/int(ans1/b)
    if ans2<b:
        ans2 = 1e10
    else:
        ans2 = ans2/int(ans2/b)
    print min(ans1, ans2)