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;
double T(int a, int b);
int main() {
  int a, b;
  cin >> a >> b;
  printf("%.15lf\n", T(a, b));
  return 0;
}
double T(int a, int b) {
  double x;
  if (a == 0 and b == 0) return 0;
  if (b == 0 and a != 0) return (double)(2.0000000000) / a;
  if (a < b) return -1;
  int k1 = (a - b) / (2 * b);
  int k2 = (a + b) / (2 * b) - 1;
  double x1, x2;
  if (k1 != 0)
    x1 = (a - b) / (2.000000000 * k1);
  else
    x1 = 1000000000;
  x2 = (a + b) / (2.000000000 * (k2 + 1.0000000000));
  if (x1 < x2)
    return x1;
  else
    return x2;
}