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 MOD = 998244353;
const int N = 1000005;
const double PI = 4 * atan(1);
const double eps = 1e-7;
const long long oo = 1e18;
long double a, b, x;
int main() {
  cin >> a >> b;
  long double ans = 1e18;
  long long k = (long long)((a - b) / (2 * b));
  if (k != 0) ans = (ans < (a - b) / (2 * k) ? ans : (a - b) / (2 * k));
  k = -1 + (long long)((a + b) / (2 * b));
  if (k != -1)
    ans = (ans < (a + b) / (2 * k + 2) ? ans : (a + b) / (2 * k + 2));
  if (ans == 1e18)
    cout << -1;
  else
    printf("%.12Lf", ans);
  return 0;
}