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 gcd(int a, int b) { return (!b) ? a : gcd(b, a % b); }
void solve() {
  int a, b;
  cin >> a >> b;
  cout.precision(12);
  cout << fixed;
  if (a < b) {
    cout << -1;
    return;
  } else {
    double ans = 1e18;
    int k = (a + b) / (2 * b);
    if (k > 0) ans = min(ans, 1.0 * (a + b) / (2.0 * k));
    k = (a - b) / (2 * b);
    if (k > 0) ans = min(ans, 1.0 * (a - b) / (2.0 * k));
    cout << ans << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  if (fopen("input.txt", "r")) {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
  int t = 1;
  while (t--) {
    solve();
  }
}