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 a, b, c, d, ans, ans1, e, f;
long g, h;
int main() {
  scanf("%lf %lf", &a, &b);
  if (a < b)
    printf("-1");
  else if (a == b)
    printf("%.12lf", a);
  else {
    c = a + b;
    d = a - b;
    e = c / b;
    f = d / b;
    g = e;
    h = f;
    if (d < b) d = 1010101010;
    if (g % 2 != 0) g--;
    if (h % 2 != 0) h--;
    ans = c * 1.0 / (g * 1.0);
    ans1 = d * 1.0 / (h * 1.0);
    if (ans < ans1)
      printf("%.12lf", ans);
    else
      printf("%.12lf", ans1);
  }
}