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 x, y;
  cin >> x >> y;
  if (x < y) {
    cout << -1 << endl;
    return 0;
  }
  if (x % y == 0 && ((x / y) & 1)) {
    cout << y << endl;
    return 0;
  }
  long long v = x / y;
  double d = x - y * v;
  if (v % 2 == 0)
    d += y;
  else
    ++v;
  double ans = y + d / v;
  printf("%.10lf\n", ans);
  return 0;
}