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:
__author__ = 'trunghieu11'


def calc(x, b):
    two = 2
    answer = 10**20
    two = x / b
    two -= two % 2
    if two > 0:
        answer = 1.0 * x / two
    return answer


def solve(a, b):
    answer = min(calc(a + b, b), calc(a - b, b))
    return -1 if answer == 10**20 else answer


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