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 maxx = 1000 * 1000 * 1000;
int bin(double x, int b) {
  int l = 1, r = maxx;
  while (r - l > 1) {
    int c = (l + r) / 2;
    if (x / c > b)
      l = c;
    else
      r = c;
  }
  if (x / r >= b) return r;
  return l;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  int a, b;
  cin >> a >> b;
  if (b > a) {
    cout << -1 << '\n';
    return 0;
  }
  double x1 = (a + b) / 2.0;
  double x2 = (b - a) / 2.0;
  int i = bin(x1, b);
  int j = bin(x2, b);
  cout.precision(10);
  if (x2 <= 0) {
    cout << fixed << x1 / (i) << '\n';
    return 0;
  }
  cout << fixed << min(x1 / (i), x2 / (j)) << '\n';
  return 0;
}