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>
int main() {
  double a, b;
  scanf("%lf%lf", &a, &b);
  double res = 0.0;
  double tmp;
  bool find = false;
  int i = int(a / b - 1);
  if (i % 2 == 1) i--;
  if (i >= 2) {
    tmp = (a - b) / (double)i;
    if (tmp > 0) {
      res = tmp;
      find = true;
    }
  }
  i = int(a / b);
  if (i % 2 == 0) i--;
  if (i >= 1) {
    tmp = (a + b) / (double)(i + 1);
    if (tmp > 0) {
      if (find) {
        res = tmp < res ? tmp : res;
      } else {
        res = tmp;
        find = true;
      }
    }
  }
  if (find) {
    printf("%.12lf\n", res);
  } else {
    printf("-1\n");
  }
  return 0;
}