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;
double x, y;
double f(int a, int b) {
  int n = (a + b) / 2;
  double k1 = (x + y) / n;
  double k2 = (x - y) / n;
  double k3 = (x + y) / (n + 1);
  if (k1 >= y * 2 && k2 < y * 2) {
    return k1;
  }
  if (k2 >= y * 2 && k3 < y * 2) {
    return k2;
  }
  if (k1 > y * 2) {
    return f(n + 1, b);
  } else {
    return f(a, n - 1);
  }
}
int main() {
  cin >> x >> y;
  if (x == y) {
    cout << x;
    return 0;
  }
  if (x < y) {
    cout << -1;
    return 0;
  }
  cout << fixed << setprecision(10) << f(1, 1000000000) / 2;
  return 0;
}