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>
const int oo = (1000000009 + 1);
using namespace std;
int x, y;
double res;
void impf() {
  freopen("in.txt", "r", stdin);
  freopen("out.txt", "w", stdout);
}
int main() {
  if (0) impf();
  ios_base::sync_with_stdio(false);
  cin >> x >> y;
  res = oo;
  if (x - y > 0) {
    if ((x - y) / (2 * y) > 0)
      if (res > double(x - y) / ((x - y) / (2 * y)) / 2)
        res = double(x - y) / ((x - y) / (2 * y)) / 2;
    if ((x + y) / (2 * y) > 0)
      if (res > double(x + y) / ((x + y) / (2 * y)) / 2)
        res = double(x + y) / ((x + y) / (2 * y)) / 2;
  } else if (x == y)
    res = y;
  cout << fixed;
  if (res != oo)
    cout << setprecision(10) << res;
  else
    cout << -1;
  return 0;
}