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;
template <class P, class Q>
inline void smin(P &a, Q b) {
  if (b < a) a = b;
}
template <class P, class Q>
inline void smax(P &a, Q b) {
  if (a < b) a = b;
}
const double inf = 1e18;
double a, b;
double solve(double p, int r) {
  if (p < 0) return inf;
  int v = p / b;
  if (v % 2) v--;
  if (v < r) v = r;
  if (p / v < b) return inf;
  return p / v;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> a >> b;
  double ans;
  if (a == b)
    ans = a;
  else
    ans = min(solve(a - b, 0), solve(a + b, 2));
  if (ans >= inf / 2)
    cout << -1 << '\n';
  else {
    cout.setf(ios::fixed);
    cout.precision(12);
    cout << ans << '\n';
  }
  return 0;
}