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
from decimal import *
import sys

inp=input().split()
a=int(inp[0])
b=int(inp[1])
getcontext().prec = 12
if b>a:
    print(-1)
else:
        s=a+b
        d=a-b
        c1=int((a+b)/b)
        if (a+b)%b==0:
            c1=round((a+b)/b)
        if c1%2==1:
            c1-=1
        c2=int((a-b)/b)

        if (a-b)%b==0:
            c2=round((a-b)/b)
        
        if c2%2==1:
            c2-=1
        if c1==0:
            c1=2
        if c2==0:
            if a==b:
                a2=b
            else:
                a2=437289472397
        else:
            a2=Decimal(d)/Decimal(c2)
        

        a1=Decimal(s)/Decimal(c1)
        ans=min(a1,a2)
        print(ans)