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 main() {
  double a, b, x;
  cin >> a >> b;
  double m = (a - b) / 2;
  double n = (a + b) / 2;
  long long p = ((long long)m) / b;
  long long q = ((long long)n) / b;
  m = p == 0 ? -1 : m / (double)p;
  n = q == 0 ? -1 : n / (double)q;
  if (m >= 1 && n < 1)
    printf("%.12lf", m);
  else if (m < 1 && n >= 1)
    printf("%.12lf", n);
  else if (m >= 1 && n >= 1)
    printf("%.12lf", min(m, n));
  else
    printf("-1");
  return 0;
}