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;
long long sum(long long a[], long long n, long long s) {
  for (long long i = 0; i < n; i++) s += a[i];
  return s;
}
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void solve() {
  long double a, b, x, y, z;
  cin >> a >> b;
  x = int((a + b) / (2 * b));
  y = 2.0 * x;
  z = (1.0 * a + 1.0 * b) / y;
  if (a < b) {
    cout << -1 << endl;
    return;
  }
  cout << setprecision(12) << z << endl;
  return;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  long long t, T;
  T = 1;
  for (t = 1; t <= T; t++) {
    solve();
  }
  return 0;
}