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::sync_with_stdio(false);
  int a, b;
  cin >> a >> b;
  if (a < b) {
    cout << "-1\n";
    return 0;
  }
  if (a == b) {
    cout << b << "\n";
    return 0;
  }
  long long int k1 = -1, k2 = -1;
  k1 = (a - b) / (2 * b);
  k2 = (a + b) / (2 * b);
  double x;
  if (k1 == 0 and k2 == 0) {
    x = -1;
  } else if (k1 == 0) {
    x = (a + b) / (2.0 * k2);
  } else if (k2 == 0) {
    x = (a - b) / (2.0 * k1);
  } else {
    x = min((a + b) / (2.0 * k2), (a - b) / (2.0 * k1));
  }
  printf("%0.9lf\n", x);
  return 0;
}