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:
def bs(R):
	l = 1
	r = R
	ans = R
	while(l <= r):
		mid = (l+r)//2
		if(R/mid > y):
			ans = mid
			l = mid + 1
		else:
			r = mid - 1
	if(ans&1): ans -= 1
	return R/ans
x,y = map(int,input().split())
if(x < y):
	print(-1)
elif(x == y):
	print(x)
elif(x%y == 0 and (x//y)%2 == 1):
	print(y)
else:
	print(bs(x+y))