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>
int a, b;
double calc(double x) {
  int l = 0, r = (int)1e9;
  while (l < r) {
    int t = (l + r + 1) / 2;
    int k = t * 2;
    double len = x / k;
    if (len >= (double)b)
      l = t;
    else
      r = t - 1;
  }
  return x / l / 2;
}
int main() {
  scanf("%d%d", &a, &b);
  if (a < b) {
    puts("-1");
    return 0;
  }
  double r1 = calc(a + b), r2 = calc(a - b);
  if (r2 < r1) r1 = r2;
  printf("%.12lf\n", r1);
  return 0;
}