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() {
  double x;
  double a, b;
  while (cin >> a >> b) {
    if (b > a) {
      x = -1;
    } else if (b == a) {
      x = a;
    } else {
      double r = (a + b) / 2;
      double d = (a - b) / 2;
      int rr = r / b, dd = d / b;
      while (r / rr < b) {
        rr--;
      }
      while (d / dd < b) {
        dd--;
      }
      if ((double)r / rr >= (double)d / dd) {
        x = (double)d / dd;
      } else {
        x = (double)r / rr;
      }
    }
    printf("%.12f\n", x);
  }
  return 0;
}