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>
double a, b;
int main() {
  double tmp;
  scanf("%lf%lf", &a, &b);
  if (b / a - 1 > 0.0000000000001) {
    printf("-1\n");
  } else {
    double tmp1;
    tmp = (a + b) / 2;
    tmp1 = tmp;
    long long l = 2, r = 1000000000;
    long long m;
    double m1;
    while (l <= r) {
      m = (l + r) / 2;
      m1 = (double)m;
      if (tmp / m1 - b >= 0) {
        tmp1 = tmp / m1;
        l = m + 1;
      } else {
        r = m - 1;
      }
    }
    printf("%.12f", tmp1);
  }
  return 0;
}