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 get(x, y):
    if x < 2 * y:
        return float('inf')
    p = int(x / y)
    p -= p % 2
    return x / p
    


x, y = map(int, input().split())
if y > x:
    print(-1)
else:
    x1 = x + y
    x2 = x - y
    ans1 = get(x1, y)
    ans2 = get(x2, y)
    ans = min(ans1, ans2)
    if ans == float('inf'):
        print(-1)
    else:
        print(ans)