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;
long double ans(int p, int q) {
  long double a = (long double)p;
  long double b = (long double)q;
  if (a < b) {
    return -1;
  }
  if (p == q) {
    return b;
  }
  long double x = 1e10;
  if (a > b) {
    long double j = floor(((a / (2 * b)) - 0.5));
    x = (a - b) / (2 * j);
  }
  long double i = floor(a / (2 * b) + 0.5);
  long double y = (a + b) / (2 * i);
  return min(x, y);
}
int main() {
  int a, b;
  cin >> a >> b;
  long double x = ans(a, b);
  if (a < b) {
    cout << -1 << endl;
  } else {
    cout << setprecision(15) << fixed << x << endl;
  }
}