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() {
  ios_base::sync_with_stdio(false);
  long long a, b;
  cin >> a >> b;
  if (a < b)
    cout << "-1";
  else if (a == b)
    cout << a;
  else if (a > b) {
    if (a % b == 0) {
      int k = a / b;
      if (k % 2 == 1) {
        printf("%.12lf", (double)b);
        return 0;
      }
    }
    double t1 = (double)(a + b) / (2 * b);
    double t2 = (double)(a - b) / (2 * b);
    long long k1 = t1;
    long long k2 = t2;
    t1 = (double)(a + b) / (2 * k1);
    t2 = (double)(a - b) / (2 * k2);
    double x = min(t1, t2);
    printf("%.12lf", x);
  }
  return 0;
}