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())

def f1(a,b,k):
    if k<=0:
        return 10000000000000000
    return 1.0*(a-b)/(2*k)

def f2(a,b,k):
    if k<0:
        return 10000000000000000
    return 1.0*(a+b)/(2*(k+1))

k1=(a-b)/(2*b)
k2=((a+b)/(2*b))-1

ans=min(f1(a,b,k1),f2(a,b,k2))
# print (ans,k1,k2)
if ans==10000000000000000:
    ans=-1

print(str.format('{0:.12f}', ans))