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;
long double ans = 1e10;
void check(int64_t x, int64_t y) {
  if (x < 0) return;
  long double k = 1. * x / 2;
  int64_t l = 1, r = 2e9 + 1;
  while (r - l > 1) {
    int64_t m = (l + r) / 2;
    if (k / m >= y)
      l = m;
    else
      r = m;
  }
  if (k / l >= y) ans = min(ans, k / l);
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int64_t a, b;
  cin >> a >> b;
  if (b > 0) {
    check(a + b, b);
    check(a - b, b);
    if (ans == 1e10)
      cout << fixed << setprecision(12) << -1 << "\n";
    else
      cout << fixed << setprecision(12) << ans << "\n";
  }
  return 0;
}