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;
long long x, y, ans1, ans2, x1, x2;
int main(int argc, char *argv[]) {
  cin >> x >> y;
  if (y > x)
    cout << "-1" << endl;
  else {
    x1 = x - y;
    ans1 = x1 / (y * 2);
    ans1 *= 2;
    x2 = x + y;
    ans2 = x2 / (y * 2);
    ans2 *= 2;
    if (x1 * ans2 < x2 * ans1) {
      printf("%.10f\n", x1 * 1.0 / ans1);
    } else {
      printf("%.10f\n", x2 * 1.0 / ans2);
    }
  }
  return 0;
}