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() {
  long long a, b;
  cin >> a >> b;
  if (a < b) {
    cout << -1 << endl;
    return 0;
  }
  a *= 2;
  b *= 2;
  long long val = (a + b) / 2;
  long long div = 1;
  long long step = 1ll << 30ll;
  while (step) {
    while (val / (div + step) >= b) div += step;
    step /= 2;
  }
  cout.setf(ios::scientific);
  cout.precision(12);
  cout << val * .5 / div << endl;
}