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 x, y, t, i;
long double bas, son, ans;
int main() {
  cin >> x >> y;
  if (y > x) {
    cout << -1 << '\n';
    return 0;
  }
  long double a = sqrt(y * y * 2);
  int t = (x + y) / y;
  if (t % 2 == 0)
    ans = y + (x + y - t * y) / (t);
  else
    ans = y + (y + x + y - t * y) / ((t - 1));
  if (ans > 1000000007 or ans < 0)
    cout << -1 << '\n';
  else
    cout << setprecision(15) << fixed << ans << '\n';
}