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 solve() {
  int a;
  int b;
  cin >> a >> b;
  double res;
  if (b > a) {
    cout << -1 << endl;
    return;
  }
  if (b == a) {
    res = b;
    cout << fixed << setprecision(12) << res << endl;
    return;
  }
  int diff1 = a - b;
  int diff2 = a + b;
  double res1 = 1.0 * diff1;
  double res2 = 1.0 * diff2;
  double res11 = res1;
  double head1 = res11 / 2;
  double res22 = res2;
  double head2 = res22 / 2;
  if (head1 < b && head2 < b) {
    cout << -1 << endl;
    return;
  }
  int c;
  if (head1 < b) {
    c = (res1 / 2) / b + 1;
    while ((res2 / (2 * c)) < b) c--;
    res22 = res2 / c;
    head2 = res22 / 2;
    cout << fixed << setprecision(12) << head2 << endl;
    return;
  }
  if (head2 < b) {
    c = (res2 / 2) / b + 1;
    while ((res1 / (2 * c)) < b) c--;
    res11 = res1 / c;
    head1 = res11 / 2;
    cout << fixed << setprecision(12) << head1 << endl;
    return;
  }
  c = (res1 / 2) / b + 1;
  while ((res1 / (2 * c)) < b) c--;
  res11 = res1 / c;
  head1 = res11 / 2;
  c = (res2 / 2) / b + 1;
  while ((res2 / (2 * c)) < b) c--;
  res22 = res2 / c;
  head2 = res22 / 2;
  res = min(head1, head2);
  cout << fixed << setprecision(12) << res << endl;
}
int main() {
  solve();
  return 0;
}