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;
int main() {
  ios::sync_with_stdio(false);
  int x, y;
  cin >> x >> y;
  int tx = x - y;
  int ty = x + y;
  x = tx;
  y = ty;
  if (x < 0)
    cout << "-1\n";
  else {
    int l = 1, r = 1e9 + 5;
    while (r - l > 1) {
      int mid = (l + r) / 2;
      if ((1LL * y * (mid - 1) + mid - 1) / mid <= x)
        l = mid;
      else
        r = mid;
    }
    long double ans = y;
    ans /= l;
    ans /= 2.0;
    cout << setprecision(19) << fixed << ans << "\n";
  }
  return 0;
}