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 a, b;
  cin >> a >> b;
  if (b > a) {
    cout << -1;
  } else {
    if (a == b) {
      printf("%.12lf", b);
      return 0;
    }
    double x = a + b;
    double k;
    for (int i = int(x) / (b + 1);; i--) {
      if (x / (2 * i) >= b) {
        k = double(x) / (2 * (i));
        break;
      }
    }
    x = a - b;
    for (int i = int(x) / (b + 1);; i--) {
      if (x / (2 * i) >= b) {
        k = min(x / (2 * (i)), k);
        break;
      }
    }
    printf("%.12lf", k);
  }
}