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;
const double inf = 2e9;
const double eps = 1e-9;
bool isEqual(double a, double b) {
  if (abs(a - b) < eps) return true;
  return false;
}
int main() {
  cout << fixed << setprecision(10);
  int a, b;
  cin >> a >> b;
  if (a == b)
    cout << a << endl;
  else {
    int k1 = (a + b) / (2 * b);
    double x1;
    if (k1 == 0)
      x1 = inf;
    else {
      x1 = (double)(a + b) / (2 * k1);
    }
    int k2 = (a - b) / (2 * b);
    double x2;
    if (k2 <= 0)
      x2 = inf;
    else {
      x2 = (double)(a - b) / (2 * k2);
    }
    double x = min(x1, x2);
    if (isEqual(x, inf))
      cout << -1 << endl;
    else
      cout << x << endl;
  }
}