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 i, j, x, y;
  double yog, pin, anj, sur, gh, it, ul;
  cin >> x >> y;
  sur = (x + y) / 2.0;
  gh = (x - y) / 2.0;
  it = sur / y * 1.0;
  ul = gh / y * 1.0;
  i = (int)it;
  j = (int)ul;
  if (sur < y && gh < y)
    anj = -1;
  else {
    yog = sur / i * 1.0;
    pin = gh / j * 1.0;
    anj = yog;
    if (yog < pin) anj = yog;
  }
  cout << setprecision(9) << fixed << anj << endl;
  return 0;
}