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() {
  unsigned x, y, j, k;
  double a, b;
  a = b = 1e12;
  scanf("%u%u", &x, &y);
  if (x < y) {
    printf("-1\n");
    return 0;
  }
  j = x + y;
  k = j / (y << 1);
  a = ((double)j) / ((double)(k << 1));
  j = x - y;
  k = j / (y << 1);
  if (k) b = ((double)j) / ((double)(k << 1));
  printf("%.12lf\n", a > b ? b : a);
  return 0;
}