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_base::sync_with_stdio(false);
  cin.tie(0);
  long double a, b, res = -1;
  cin >> a >> b;
  long double k1 = (int)((a + b) / (2 * b));
  long double k2 = (int)((a - b) / (2 * b));
  k1 *= 2;
  if (k1 != 0) k1 = (a + b) / k1;
  k2 *= 2;
  if (k2 != 0) k2 = (a - b) / k2;
  if (k2 > 0 && k1 > 0)
    res = min(k1, k2);
  else if (k1 > 0)
    res = k1;
  else if (k2 > 0)
    res = k2;
  if (res == -1) cout << "-1" << '\n';
  ;
  if (res != -1) cout << fixed << setprecision(9) << res << '\n';
  ;
  return 0;
}