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 a;
  int b;
  cin >> a >> b;
  cout.precision(13);
  if (b > a) {
    cout << -1;
  } else if ((a % b == 0) && ((a / b) % 2 == 1)) {
    cout << b;
  } else {
    int k = a / b;
    if (k % 2 == 0) {
      k--;
    }
    int dist = a - k * b;
    double x1 = b;
    double x2 = (double)dist / (double)k + (double)b;
    double x = x1;
    double ang;
    double x_old;
    for (int i = 0; i < 50; i++) {
      ang = (x - b) / (k * x - a);
      x_old = x;
      if (ang > -1) {
        x = (x + x2) / 2.0;
        x1 = x_old;
      } else if (ang < -1) {
        x = (x + x1) / 2.0;
        x2 = x_old;
      } else {
        cout << x;
        return 0;
      }
    }
    cout << x;
  }
  return 0;
}