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:
x=raw_input().split(' ')
a=int(x[0])
b=int(x[1])

val1=(a-b)/(2*b)
if val1<=0:
    ans1=-1
else:
    ans1=float(a-b)/(2*val1)
    
    
val2=(a+b)/(2*b)
if val2<=0:
    ans2=-1
else:
    ans2=float(a+b)/(2*val2)
if ans1==-1 and ans2==-1:
    print "-1"
elif ans1!=-1 and ans2!=-1:
    print "%.12f"%min(ans1,ans2)
else:
    if ans1==-1:
        print "%.12f"%ans2
    else:
        print "%.12f"%ans1