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;
void solutionA();
int main() {
  solutionA();
  return EXIT_SUCCESS;
}
void solutionA() {
  int a, b;
  for (; cin >> a >> b;) {
    if (b > a)
      cout << -1;
    else {
      if (a % b == 0 && (a / b) % 2 == 1)
        cout << b;
      else {
        double k = int((a + b) / 2.0 / b);
        double x = (a + b) / 2.0 / k;
        cout.precision(9);
        cout << fixed << x;
      }
    }
    cout << endl;
  }
}