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 math import ceil
a,b = map(int, raw_input().split())

if a-b == 0:
    print float(b)
else:
    v = a-b
    k = 2
    mx = 2*(10**9) 
    if float(v)/k >= b:
        l = int(v/(2.0*b))
        if l != 0:
            mx = min(float(v)/(l*2),mx)
    v = a + b
    if float(v)/2 >= b:
        l = int(v/(2.0*b))
        if l != 0:
            mx = min(float(v)/(l*2),mx)
    if mx != 2*(10**9): 
        print mx
    else:
        print -1