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;
void panic() {
  cout << -1 << endl;
  exit(0);
}
const double EPS = 1e-9;
unsigned long long x, y;
double f(double l, double x) {
  while (x > l * 2 + EPS) {
    x -= l * 2;
  }
  return l - x;
}
int main() {
  ios::sync_with_stdio(false);
  cout.precision(10);
  cin >> x >> y;
  if (y > x) panic();
  double coef = double(x) / y;
  unsigned long long v = x - x % y;
  if (v % (2 * y) == 0) v -= y;
  double left = 0, right = y;
  double value;
  while (left < right + EPS) {
    double mid = (left + right) / 2;
    double curcoef = (v + mid) / (y - mid);
    if (abs(curcoef - coef) < EPS) {
      value = v + mid;
      break;
    } else if (curcoef > coef) {
      right = mid;
    } else {
      left = mid;
    }
  }
  cout << fixed << y * x / value << endl;
}