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>
template <typename T>
inline void mn(T& x, const T& y) {
  if (y < x) x = y;
}
template <typename T>
inline void mx(T& x, const T& y) {
  if (x < y) x = y;
}
template <typename T>
inline int sz(const T& x) {
  return x.size();
}
using namespace std;
int main() {
  int x, y;
  cin >> x >> y;
  if (y > x) {
    cout << -1 << endl;
  } else if (y == x) {
    cout << x << endl;
  } else {
    double ans = numeric_limits<double>::max();
    int k1 = (x + y) / (2 * y);
    if (k1 >= 1) {
      ans = min(ans, 1.0 * (x + y) / (2 * k1));
    }
    int k2 = (x - y) / (2 * y);
    if (k2 >= 1) {
      ans = min(ans, 1.0 * (x - y) / (2 * k2));
    }
    cout << fixed << setprecision(9) << ans << endl;
  }
  return 0;
}