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:
import math

a, b = list(map(int, input().split()))

x1 = a - b
x2 = a + b

if x1 < 0:
    print(-1)
elif x1 == 0:
    print('%.12f' % (x2 / 2))
else:
    res2 = x2 / (2 * math.floor((a + b) / (2 * b)))
    print('%.12f' % res2)