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 as ma

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

if b>a:
    print(-1)
else:
    e=[]
    d=ma.ceil((a-b)/(2*b))
    if d>0:
        if (a-b)/(2*d)>=b:
            e.append((a-b)/(2*d))
    if d>1:
        d-=1
        if (a-b)/(2*d)>=b:
            e.append((a-b)/(2*d))
    d=ma.ceil((a+b)/(2*b))
    if d>0:
        if (a+b)/(2*d)>=b:
            e.append((a+b)/(2*d))
    if d>1:
        d-=1
        if (a+b)/(2*d)>=b:
            e.append((a+b)/(2*d))
    if len(e)==0:
        print(-1)
    else:
        print(min(e))