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;
const int N = 1001100;
int arr[N];
const int mod = 100000000;
int main() {
  double a, b;
  while (cin >> a >> b) {
    if (a < b)
      cout << -1 << endl;
    else if (abs(a - b) < 0.001)
      cout << fixed << setprecision(10) << a << endl;
    else {
      int k1 = (a - b) / (2 * b);
      double x1 = (a - b) * 1.0 / (2 * k1);
      int k2 = ((a + b) / b - 2) / 2;
      double x2 = (a + b) * 1.0 / (2 * k2 + 2);
      cout << fixed << setprecision(10) << min(x1, x2) << endl;
    }
  }
  return 0;
}