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 long long mod = 1000000007;
long long powmod(long long a, long long b) {
  long long res = 1;
  a %= mod;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod;
  }
  return res;
}
int a, b;
int main() {
  cin >> a >> b;
  if (a < b) {
    cout << "-1" << endl;
    return 0;
  }
  int k1 = (a - b) / (2 * b), k2 = (a + b) / (2 * b);
  double d1 = (a == b)    ? a
              : (k1 == 0) ? 9987654321
                          : (a - b) / double(2 * k1),
         d2 = (a + b) / double(2 * k2);
  double d3 = min(d1, d2);
  printf("%.12lf\n", d3);
  return 0;
}