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;
double qmin = 0x7fffffff;
int main(void) {
  long long a, b;
  cin >> a >> b;
  if (a < b) {
    puts("-1");
    return 0;
  }
  {
    int x = a + b;
    int now = ceil(x / b / 2);
    while (x / double(now) / 2.0 < b) now--;
    qmin = min(qmin, x / double(now) / 2.0);
  }
  {
    int x = a - b;
    int now = ceil(x / b / 2);
    while (x / double(now) / 2.0 < b) now--;
    qmin = min(qmin, x / double(now) / 2.0);
  }
  printf("%.12lf\n", qmin);
  return 0;
}