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;
stack<time_t> time_stack;
void startTimer() { time_stack.push(clock()); }
double stopTimer() {
  double time = clock() - time_stack.top();
  time_stack.pop();
  return time / double(CLOCKS_PER_SEC);
}
bool eq(double a, double b) { return abs(a - b) < double(1e-7); }
int main() {
  startTimer();
  ios::sync_with_stdio(false);
  long long u, v;
  cin >> u >> v;
  if (v > u)
    cout << -1;
  else {
    cout.precision(9);
    cout << fixed << double(u + v) / (2 * ((u + v) / (2 * v)));
  }
  cout << endl;
  return 0;
}