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() {
  long double x, y;
  cin >> x >> y;
  cout.precision(10);
  cout.setf(cout.fixed);
  if (y > x) {
    cout << -1 << endl;
  } else if (y == x) {
    cout << y << endl;
  } else {
    long double ans = y + x;
    if (ans < y) {
      cout << -1 << endl;
      return 0;
    }
    if (ans / 2 < y) {
      cout << ans << endl;
      return 0;
    }
    long long l = 2, r = 1000000000;
    while (l != r) {
      long long m = (l + r) / 2;
      if (ans / 2.0 / m >= y)
        l = m + 1;
      else
        r = m;
    }
    cout << ans / 2.0 / (l - 1) << endl;
  }
  return 0;
}