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>
long long x, y;
long double fun(long double as) {
  long double cache = as / y;
  long long i = (long long)cache;
  if (i == 1)
    return as;
  else {
    return fun(as / i);
  }
}
int main() {
  long double ans, buf;
  scanf("%I64d %I64d", &x, &y);
  ans = (long double)(x + y) / 2;
  if (y > x) {
    printf("-1");
    return 0;
  }
  ans = fun(ans);
  printf("%.12lf", ans);
  return 0;
}