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 A, B;
int main() {
  cin >> A >> B;
  double X1, X2;
  if (A < B) {
    cout << "-1\n";
    return 0;
  }
  double aux = (double)(A + B) / (double)B;
  int x = (int)floor(aux);
  if (x % 2 == 1) --x;
  X1 = (double)(A + B) / (double)x;
  aux = (double)(A - B) / (double)B;
  x = (int)floor(aux);
  if (x % 2 == 1) --x;
  X2 = (double)(A - B) / (double)x;
  cout << fixed << setprecision(15) << min(X1, X2) << "\n";
  return 0;
}