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:
vals=list(map(int,input().split()))
x=vals[0]
y=vals[1]

if x-y>=0:
    k=(x-y)//(2*y)
    ans=[]
    if x-y==0:
        ans.append(x)
    elif k!=0:
        a=(x-y)/(2*k)
        if 2*k*a<=x<=(2*k+1)*a and 0<=y<=a:
            ans.append(a)
    
    k=((x+y)//(2*y))-1 
    # print(k)
    a=(x+y)/(2*(k+1))
    
    if (2*k+1)*a<=x<=2*(k+1)*a and 0<=y<=a:
        ans.append(a)
    else: None
    
    if len(ans)>0:
        print(min(ans))
    else:
        print("-1");
    
elif x+y>=0:
    ans=[]
    k=(x+3*y-1)//(2*y)-1
    a=(x+y)/(2*(k+1))
    
    if (2*k+1)*a<=x<=2*(k+1)*a and 0<=y<=a:
        ans.append(a)
    else: None
    
    if len(ans)>0:
        print(min(ans))
    else:
        print("-1");