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 n, m, a, b, h, x, y;
  double c, d;
  cin >> n >> m;
  if (n < m) {
    cout << -1;
    return 0;
  }
  if (n == m) {
    cout << n;
    return 0;
  }
  a = n - m;
  b = n + m;
  x = a / m;
  y = b / m;
  if (x % 2 == 1) x--;
  if (y % 2 == 1) y--;
  if ((double)a / x > (double)b / y) {
    h = b / y;
    d = ((double)b / y) - h;
  } else {
    h = a / x;
    d = ((double)a / x) - h;
  }
  cerr << y << endl << x << endl;
  printf("%.12lf\n", (double)h + d);
}