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() {
  double a, b, ans0 = 0, ans1, ans2;
  cin >> a >> b;
  if (a == b)
    cout << a << endl;
  else if (a < b)
    cout << -1 << endl;
  else {
    ans0 = (a + b) / 2;
    int k = (a - b) / (2 * b);
    if (k == 0) {
      ans1 = 10000000000000;
    } else {
      ans1 = (a - b) / (2 * k);
    }
    k = (a / b - 1) / 2;
    ans2 = (a + b) / (2 * k + 2);
    if (ans1 < ans2)
      printf("%.10f", ans1);
    else {
      printf("%.10f", ans2);
    }
  }
  return 0;
}