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:
def solve(a, b):

    if b > a:
        return -1

    if a == b:
        return a

    sol1 = (a + b) / (2 * int((a + b) / (2 * b)))
    u = (2 * int((a - b) / (2 * b)))
    sol2 = (a - b) / u if u != 0 else sol1 + 1
    return min(sol1, sol2)


if __name__ == '__main__':
    a, b = map(int, input().split())
    
    result = solve(a, b)
    
    print(result)