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() {
  cout << fixed << setprecision(12);
  int a, b, k;
  scanf("%d", &a);
  scanf("%d", &b);
  if (a < b) {
    printf("%d\n", -1);
    return 0;
  }
  if (a == b) {
    cout << (double)a << endl;
    return 0;
  }
  double x = 1.0;
  double m;
  double h = ((double)a / (double)b + 1.0) * 0.5;
  int mh = h + 1;
  for (k = mh; k > 0; k--) {
    m = (double)(a + b) / (double)(2 * k);
    if (m < b)
      continue;
    else {
      x = m;
      break;
    }
  }
  cout << x << endl;
  return 0;
}