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;
long long mul(long long a, long long b) { return (a * b) % (100000007); }
long long add(long long a, long long b) { return (a + b) % (100000007); }
long long sub(long long a, long long b) {
  return (a - b + llabs(a - b) / (100000007) * (100000007) + (100000007)) %
         (100000007);
}
void upd(long long &a, long long b) {
  a = (a % (100000007) + b % (100000007)) % (100000007);
}
double a, b;
int main() {
  cin >> a >> b;
  if (a < b) {
    cout << "-1\n";
    return 0;
  }
  double ans = 1e70;
  double m = floor((a + b) / b / 2) * 2;
  ans = min(ans, (a + b) / floor(m));
  m = floor((a - b) / b / 2) * 2;
  ans = min(ans, (a - b) / floor(m));
  printf("%.12lf\n", ans);
  return 0;
}