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>
using namespace std;
template <class T>
T sqr(const T &a) {
  return a * a;
}
const double eps = 1e-11;
int main() {
  int a, b;
  long double ans = 2e18;
  scanf("%d%d", &a, &b);
  int l = 0, r = 1e9 + 1;
  while (r - l > 1) {
    int m = (l + r) / 2;
    long double x = (a + b) / 2.0 / m;
    if (x + eps >= b)
      l = m;
    else
      r = m;
  }
  if (l) ans = (a + b) / 2.0 / l;
  l = 0, r = 1e9 + 1;
  while (r - l > 1) {
    int m = (l + r) / 2;
    long double x = (a - b) / 2.0 / m;
    if (x + eps >= b)
      l = m;
    else
      r = m;
  }
  if (l && (a - b) / 2.0 / l < ans) ans = (a - b) / 2.0 / l;
  if (ans < 1e18)
    printf("%.20f\n", (double)ans);
  else
    puts("-1");
}