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() {
  int a, b;
  scanf("%d%d", &a, &b);
  for (int i = a / b + 1; i >= 0; i--) {
    if ((i & 1) == 1 && a + b >= b * (i + 1)) {
      printf("%.10f\n", (a + b) / (i + 1.0));
      return 0;
    } else if ((i & 1) == 0 && a - b == i * b) {
      if (i == 0)
        printf("%d\n", b);
      else
        printf("%.10f\n", (a - b) / (double)i);
      return 0;
    }
  }
  printf("-1\n");
}