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 a, b;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  if (ifstream("test.inp")) cin.rdbuf((new ifstream("test.inp"))->rdbuf());
  cout.precision(9);
  cout << fixed;
  cin >> a >> b;
  if (a == b)
    cout << a;
  else {
    double v = (b - a) / 2.0;
    int k = floor(v / b);
    if (k > 0) {
      cout << v / k;
      return 0;
    }
    v = (a + b) / 2.0;
    k = floor(v / b);
    if (k > 0) {
      cout << v / k;
      return 0;
    }
    cout << "-1";
  }
}