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 int min(long long int a, long long int b, long long int c,
                  long long int d) {
  long long int arr[4] = {a, b, c, d};
  sort(arr, arr + 4);
  return arr[0];
}
long long int max(long long int a, long long int b, long long int c,
                  long long int d) {
  long long int arr[4] = {a, b, c, d};
  sort(arr, arr + 4);
  return arr[3];
}
long long int gcd(long long int a, long long int b) {
  if (b < a) {
    int temp = a;
    a = b;
    b = temp;
  }
  if (a == 0) {
    return b;
  }
  return gcd(b % a, a);
}
long long int lcm(long long int a, long long int b) {
  return (a * b / gcd(a, b));
}
vector<long long int> getprimes() {
  vector<long long int> pl(101, 1);
  for (int i = 2; i <= 100; i++) {
    if (pl[i] == 1) {
      for (int j = 2 * i; j <= 100; j += i) {
        pl[j] = 0;
      }
    }
  }
  return pl;
}
double dist(double x1, double y1, double x2, double y2) {
  return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
}
long long int fact(long long int first) {
  long long int ans = 1;
  if (first == 0) {
    return 1;
  }
  while (first > 0) {
    ans = (ans * first) % 1000000007;
    first--;
  }
  return ans % 1000000007;
}
long long int power(long long int a, long long int b) {
  long long int ans = 1;
  while (b > 0) {
    if (b % 2 == 1) {
      ans *= a;
      ans = ans;
    }
    b /= 2;
    a *= a;
    a = a;
  }
  return ans;
}
long long int mod(long long int a, long long int b) {
  return (((a % b) + b) % b);
}
vector<int> getbinary(int first) {
  vector<int> bin(16, 0);
  int iter = 0;
  while (first > 0) {
    if (first % 2 == 1) {
      bin[iter] = 1;
    } else {
      bin[iter] = 0;
    }
    iter++;
    first /= 2;
  }
  return bin;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int a, b;
  cin >> a >> b;
  if (a < b) {
    cout << -1 << endl;
  } else {
    long long int c = (a + b) / (2.0 * b);
    cout << setprecision(20) << (a + b) / (2.0 * c) << endl;
  }
}