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 PYTHON):

Solution:
a,b=map(int,raw_input().split())
if a==b:
    print a
else:
    ans=1e999
    '''b/(a-kx)=1
    b=a-kx
    a-b=kx
    x=(a-b)/k'''
    if (a-b>=0):
        '''(a-b)/k>=b
        a-b>=b*k
        k<=(a-b)/b'''
        k=int(float(a-b)/b)
        if k%2:k-=1
        if k:
            ans=min(ans,(a-b)/float(k))
    '''(b-x)/(a-kx)=-1
    b-x=kx-a
    kx+x=a+b
    x(k+1)=a+b
    x=(a+b)/(k+1)
    (a+b)/(k+1)>=b
    a+b>=b(k+1)
    (a+b)/b>=k+1
    (a+b)/b-1>=k'''
    u=int(float(a+b)/b)
    u-=1
    if u%2==0:u-=1
    if u>0:
        ans=min(ans,(a+b)/float(u+1))
    if ans==1e999:ans=-1
    print '%.10f'%(ans)