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;
double eps = 1e-9;
int main() {
  double ans = -1;
  scanf("%d%d", &A, &B);
  if (A < B) {
    printf("-1\n");
    return 0;
  }
  double k = 1.0 * (A - B) / (2.0 * B);
  if ((int)(k + eps) == 0)
    ans = 1e100;
  else
    ans = 1.0 * (A - B) / (2.0 * (int)(k + eps));
  k = 1.0 * (A + B) / (2.0 * B);
  ans = min(ans, 1.0 * (A + B) / (2.0 * (int)(k + eps)));
  printf("%.10f\n", ans);
}