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

def fun(a, b) :
    y = (a+b)/2
    m = math.floor(y / b);
    if m == 0:
        return -1
    return y/m
    
a,b = map(int, input().split())
if b > a:
    print("-1")
elif b == a:
    print(b)
elif b == 0:
    print(fun(a-1,1)); 
else:
    x,y = fun(a,b), fun(a-2*b,b)
    mini = min(x,y)
    if mini == -1:
        print(max(x,y))
    else:
        print(mini);