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;
const int mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long double a, b, ans = INT_MAX;
  int k1, k2, k;
  cin >> a >> b;
  k1 = floor((a - b) / (2 * b));
  if (k1 > 0) ans = min(ans, (a - b) / (2 * k1));
  k2 = floor((a + b) / (2 * b));
  if (k2 > 0) ans = min(ans, (a + b) / (2 * k2));
  if (ans == INT_MAX)
    std::cout << "-1" << '\n';
  else
    std::cout << fixed << setprecision(12) << ans << '\n';
}