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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long double x, y, z;
  long double a, b;
  cin >> a >> b;
  y = ((a * 1.0) + (b * 1.0)) / 2.0;
  z = ((a * 1.0) - (b * 1.0)) / 2.0;
  int n, m;
  n = y / b;
  m = z / b;
  if (n <= 0 || m < 0) {
    cout << "-1";
    return 0;
  }
  n;
  long double ans = (y / (long double)(n * 1.0));
  if (m == 0) {
    if (a == b) ans = min(ans, b);
    printf("%.12Lf", ans);
    return 0;
  }
  ans = min(ans, (z / (long double)(m * 1.0)));
  printf("%.12Lf", ans);
  return 0;
}