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:
from __future__ import division
a, b = map(int, raw_input().split())
s = (a+b)/2

def largest_k(l, r):
    #print l,r
    if(r-l < 2):
        #print 'if'
        x = s/l
        if(x >= b and s/r < b):
            return l
        else:
            return -1
    elif(r-l < 3):
        #print 'elif'
        x1 = s/l
        x2 = s/(l+1)
        if(x1 >= b and x2 < b):
            return l
        elif(x2 >= b and s/r < b):
            return l+1
        else:
            return -1
    else:
        #print 'else'
        mid = (l+r)//2
        if(s/mid >= b and s/(mid+1) < b):
            return mid
        elif(s/mid < b):
            return largest_k(l, mid)
        else:
            return largest_k(mid+1, r)

if(a < b):
    print -1
elif(a == b):
    print a
else:
    k = largest_k(1, 1000000002)
    print s/k