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 main() {
  long long a, b, t;
  double ans, tt;
  scanf("%I64d%I64d", &a, &b);
  if (a < b) {
    printf("-1\n");
  } else if (a == b) {
    ans = (double)a;
    printf("%.12f\n", ans);
  } else {
    t = a / b;
    if (t % 2 == 0) {
      t--;
    }
    tt = ((double)a - t * b) / ((double)t + 1);
    ans = (double)b + tt;
    printf("%.12f\n", ans);
  }
}