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;
int main() {
  double a, b;
  cin >> a >> b;
  int alpha = floor((1.0 * a) / (2 * b) - 0.5);
  if (alpha < 0) {
    cout << (-1) << endl;
    return 0;
  }
  cout << setprecision(11) << fixed;
  if (alpha == 0) {
    cout << (a + b) / 2.0;
  } else
    cout << min((a + b) / (2.0 * (alpha + 1)), (a - b) / (2.0 * alpha));
  return 0;
}