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>
double calculate(int x, int y) {
  if (y > x) return -1;
  if (y == x) return x;
  int n;
  double r1, r2;
  n = (int)(x - y) / (2 * y);
  if (n == 0)
    r1 = 1000000001;
  else
    r1 = (x - y) / (2.0 * n);
  n = (int)(x + y) / (2 * y);
  r2 = (x + y) / (2.0 * n);
  if (r1 < r2)
    return r1;
  else
    return r2;
}
int main() {
  int x, y;
  scanf("%d %d", &x, &y);
  double ret = calculate(x, y);
  if (ret == -1)
    printf("-1");
  else
    printf("%.10lf", ret);
  return 0;
}