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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long a, b, a1, a2, b1, b2;
double ans1, ans2;
int main() {
  cin >> a >> b;
  ans1 = ans2 = 1000000000;
  a1 = a - b;
  b1 = a1 / (2 * b);
  if (b1 > 0) ans1 = double(a1) / (2 * b1);
  a2 = a + b;
  b2 = a2 / (2 * b);
  if (b2 > 0) ans2 = double(a2) / (2 * b2);
  if ((b1 <= 0) && (b2 <= 0))
    cout << "-1";
  else if (ans1 < ans2)
    printf("%.10f\n", ans1);
  else
    printf("%.10f\n", ans2);
  return 0;
}