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 PYTHON3):

Solution:
a,b=tuple(map(int,input().split()))
if (a-b<0):
    print(-1)
elif (a==b):
    print(a)
else:
    i1=(a+b)//(2*b)
    i2=(a-b)//(2*b)
    if i2==0:
        print((a+b)/(2*i1))
    else:
        x=(a+b)/2
        y=(a-b)/2
        print(min(x/i1,y/i2))