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;
void parse() {
  cin >> a;
  cin >> b;
}
void solve() {
  if (a < b) {
    cout << -1 << endl;
    return;
  }
  if (a == b) {
    cout << b << endl;
    return;
  }
  float c1, c2;
  c1 = (float)(a - b);
  c2 = (float)(b + a);
  float p1, p2;
  p1 = (int)c1 / (2 * b);
  p2 = (int)c2 / (2 * b);
  cout << min(c1 / (2 * p1), c2 / (2 * p2)) << endl;
}
int main() {
  ios::sync_with_stdio(false);
  std::cout.precision(10);
  parse();
  solve();
  cout << endl;
  return 0;
}