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:
x, y = [int(x) for x in input().split()]
n1 = x + y
ans1 = -1
ans2 = -1
if n1 // y  - (n1 // y % 2) != 0:
    ans1 = n1 / (n1 // y  - (n1 // y % 2))
n2 = x + y    
if n2 // y  - (n2 // y % 2) != 0:
    ans2 = n2 / (n2 // y  - (n2 // y % 2))
print(min(ans1, ans2))