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() {
  int x, y, temp;
  double ans;
  scanf("%d%d", &x, &y);
  if (x == y) {
    printf("%d\n", x);
  } else if (y > x) {
    printf("%d\n", -1);
  } else {
    temp = x / y;
    if ((temp & 1) == 0) temp--;
    ans = y + (1.0 * x - temp * 1.0 * y) / (temp + 1);
    temp = x - y;
    if (temp >= y * 2) {
      temp = temp / (2 * y);
      ans = min(ans, ((x - y) * 1.0) / temp);
    }
    printf("%.15lf\n", ans);
  }
  return 0;
}