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 data[200610] = {0};
long long int gcd(long long int a, long long int b) {
  if (a > b) swap(a, b);
  while (b) {
    long long int temp = a % b;
    a = b;
    b = temp;
  }
  return a;
}
inline void read(void) {}
inline void solve() {
  double temp1, temp2;
  scanf("%lf%lf", &temp1, &temp2);
  double num = (temp1 - temp2) / (2 * temp2);
  if (num < 0) {
    printf("-1");
    return;
  }
  num = floor(num);
  double x;
  if (num == 0) {
    x = (temp1 + temp2) / 2;
  } else if (num > 0) {
    double k = (temp1 - temp2) / 2 * num;
    double z = (temp1 + temp2) / (2 * (num + 1));
    x = min(z, k);
  }
  cout << std::fixed << setprecision(9) << x << endl;
}
int main() {
  cin.tie(NULL);
  ios_base::sync_with_stdio(false);
  long long int test = 1;
  while (test--) {
    read();
    solve();
  }
  return 0;
}