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 main():
    a, b = [int(i) for i in input().split(" ")]
    eps = 0.0000000001
    if (b > a):
        print (-1)
    elif b == a:
        print(b)
    elif b == 0:
        print(0)
    else:
        x1, x2 = float('inf'), float('inf')
        z1, z2 = (a-b)/2, (a+b)/2
        k, kk = 1, 1
        while kk:
            while (z1/k) + eps >= b:
                x1 = (z1/k)
                k += kk
                kk *= 2
            k -= kk/2
            kk //= 4
        k, kk = 1, 1
        while kk:
            while (z2/k) + eps >= b:
                x2 = (z2/k)
                k += kk
                kk *= 2
            k -= kk/2
            kk //= 4
        if (min(x1, x2) != float('inf')):
            print(min(x1, x2))
        else:
            print(-1)
if __name__ == "__main__":
    main()