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:
# your code goes 
n,m = map(long,raw_input().split())
x1n = n-m
if x1n<0:
    x1=10**10
else:
    k=x1n/(2*m)
    if k==0:
        x1=10**10
    else:
        x1=x1n/(2.0*k)
x2n = n+m
k=x2n/(2*m)
if k==0:
    x2=10**10
else:
    x2=x2n/(2.0*k)
    
x=min(x1,x2)
if x==10**10:
    print -1
else:
    print x