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 left, right;
  double a, b;
  scanf("%lf%lf", &a, &b);
  left = a - b;
  right = a + b;
  if (left < 0) {
    cout << "-1\n";
    return 0;
  }
  if (left == 0) {
    printf("%lf\n", a);
    return 0;
  }
  if (left < 2 * b) {
    printf("%lf\n", right / 2);
    return 0;
  }
  int n1 = left / (2 * b), n2 = right / (2 * b);
  printf("%.14lf\n", (left / n1 / 2) < (right / n2 / 2) ? (left / n1 / 2)
                                                        : (right / n2 / 2));
  return 0;
}