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:
import math
a,b = map(int,raw_input().split())
if b>a:
    print -1
elif b==a:
    print b
else:
    x=(a-b)*1.0/2
    k = math.floor(x/b)
    if(k==0):
        ans1 = -1
    else:
        ans1 = (x*1.0)/k

    x = (a+b)*1.0/2
    k = math.floor(x/b)-1
    # print k
    if k<0:
        k+=1
    ans2 = (x*1.0)/(k+1)
    # print ans1,ans2
    if ans1!=-1:
        print min(ans1,ans2)
    else:
        print ans2