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 a, b;
int l, m, h;
double x1, x2, ans = 2e9;
int main(int argc, char **argv) {
  cin >> a >> b;
  if (b > a) return puts("-1");
  l = 1, h = 1e9;
  while (l <= h) {
    m = (l + h) / 2;
    x1 = (double)(a - b) / (2 * m);
    x2 = (double)(a + b) / (2 * m);
    if (x1 < b && x2 < b)
      h = m - 1;
    else {
      l = m + 1;
      if (x1 >= b) ans = min(ans, x1);
      if (x2 >= b) ans = min(ans, x2);
    }
  }
  printf("%.10lf\n", ans);
  return 0;
}