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;
const int INF = 2000000009;
const int Max = 1000007;
const double PI = acos(-1.0);
double binSearch(double p, double b) {
  int low = 0, high = INF, k;
  double x;
  while (low <= high) {
    k = (low + high) / 2;
    x = p / (2.0 * k);
    if (x < b)
      high = k - 1;
    else if (x == b)
      return x;
    else
      low = k + 1;
  }
  x = p / (2 * high);
  if (x < b) x = p / (2 * low);
  return x;
}
int main() {
  int i, j, k, l, temp, t, n, m, caseno = 0, ans;
  string str;
  double a, b, x;
  while (cin >> a >> b) {
    if (b > a) {
      cout << -1 << endl;
      continue;
    }
    x = binSearch((a + b), b);
    printf("%.10lf\n", x);
  }
  return 0;
}