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;
int main() {
  int a, b;
  cin >> a >> b;
  double answ = numeric_limits<double>::max();
  double answer = numeric_limits<double>::max();
  if (a < b) {
    answer = -1;
  } else if (a == b) {
    answer = a;
  } else {
    int k = max(1, a / b - 3);
    do {
      answer = answ;
      if (k % 2 == 1) {
        answ = double(a + b) / double((k + 1));
      } else {
        answ = double(a - b) / double(k);
      }
      ++k;
    } while (answ >= b);
  }
  cout << std::setprecision(10) << std::fixed << answer << "\n";
  return 0;
}