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 x, y;
double ans;
int main() {
  scanf("%d %d", &a, &b);
  if (a < b) {
    printf("-1");
    return 0;
  }
  int k = a + b;
  double x = (double)(a + b) / 2.0;
  int s = 1;
  int e = 1e9;
  while (s <= e) {
    int m = (s + e) / 2;
    if ((x / (double)m) >= (double)b) {
      s = m + 1;
    } else {
      e = m - 1;
    }
  }
  printf("%.12lf", x / (double)e);
}