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() {
  ios_base::sync_with_stdio(false);
  long long int a, b;
  cin >> a >> b;
  cout << fixed << setprecision(10);
  long double ans, x, y;
  x = a;
  y = b;
  if (x < y) {
    cout << "-1";
    return 0;
  }
  if (x == y) {
    ans = x;
    cout << ans;
  } else {
    long double a1 = x + y, a2 = x - y;
    int k = a1 / y;
    if (k % 2 == 1) k--;
    long double kk = k;
    ans = a1 / kk;
    k = a2 / y;
    if (k % 2 == 1) k--;
    if (k != 0) {
      double kk = k;
      ans = min(ans, a2 / kk);
    }
    cout << ans;
  }
  return 0;
}