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;
inline long long int GCD(long long int x, long long int y) {
  if (x < y) swap(x, y);
  if (x == 0) return y;
  if (y == 0) return x;
  return GCD(x % y, y);
}
long long int phi(long long int n) {
  long long int result = n;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      result -= result / i;
    }
  }
  if (n > 1) result -= result / n;
  return result;
}
long long int power(long long int x, long long int n, long long int mod) {
  long long int res = 1;
  x %= mod;
  while (n) {
    if (n & 1) {
      res = ((res * x) % mod + mod) % mod;
    }
    x = ((x * x) % mod + mod) % mod;
    n >>= 1;
  }
  return res;
}
const long double eps = 1e-9;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int a, b;
  cin >> a >> b;
  if (a < b) {
    cout << -1 << endl;
    return 0;
  }
  long double x2 = a + b;
  long double x1 = a - b;
  long long int l = 1, h = 100000000000000;
  long double ans = 1e18 + 9;
  while (l < h) {
    long long int mid = (l + h) / 2;
    if (mid % 2) mid++;
    long double x = (long double)x2 / (long double)mid;
    if (x >= b) {
      ans = min(ans, x);
      l = mid + 1;
    } else {
      h = mid - 1;
    }
  }
  while (l < h) {
    long long int mid = (l + h) / 2;
    if (mid % 2) mid++;
    long double x = (long double)x1 / (long double)mid;
    if (x >= b) {
      ans = min(ans, x);
      l = mid + 1;
    } else {
      h = mid - 1;
    }
  }
  cout << setprecision(12) << fixed << ans << endl;
}