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:
def main():
    a, b = map(int, raw_input().split())
    if a == b:
        print "%.12f" % b
        return
    ans = -1
    x = a - b
    if x >= 2 * b:
        y = x / (2 * b)
        ans = x / 2.0 / y
    x = a + b
    if x >= 2 * b:
        y = x / (2 * b)
        tmp = x / 2.0 / y
        if ans != -1:
            ans = min(ans, tmp)
        else:
            ans = tmp
    if ans < -0.5:
        print -1
    else:
        print "%.12f" % ans
main()