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;
signed main() {
  long long n, m, a, b;
  while (cin >> a >> b) {
    if (a == b) {
      cout << a << "\n";
      continue;
    }
    if (a < b) {
      cout << "-1\n";
      continue;
    }
    if ((a - b) % 2 == 0 && ((a - b) / 2) % b == 0) {
      cout << b << "\n";
      continue;
    }
    n = (a + b) / (2 * b) - 1;
    double x = double(a + b) / double(1 + 2 * n + 1);
    cout << fixed << setprecision(10) << x << "\n";
  }
  return 0;
}