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())


pl = a - b
ad = a + b

if pl < 0:
    print -1
elif pl == 0:
    print a
else:
    x = 1e9
    k1 = ad / b
    k2 = pl / b
    k1 -= k1%2+1
    k2 -= k2%2
    while k1 > 2 and ad/(k1+1) < b :
        k1 -= 2
    x = min(x,float(ad)/(k1+1))
    while k2 > 3 and pl/k2 < b  :
        k2 -= 2
    if k2 > 0:
        x = min(x,float(pl)/k2)
    print x