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;
const int MAX_INT = std::numeric_limits<int>::max();
const int MIN_INT = std::numeric_limits<int>::min();
const int INF = MAX_INT;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
int lcm(int a, int b) { return a * (b / gcd(a, b)); }
int main() {
  double a, b, mn = INF, n;
  cin >> a >> b;
  n = floor((a - b) / (2 * b));
  if (n > 0) mn = (a - b) / n / 2;
  n = floor((a + b) / (2 * b));
  if (n > 0) mn = (mn < (a + b) / n / 2 ? mn : (a + b) / n / 2);
  if (mn == INF)
    printf("-1\n");
  else
    printf("%.12lf\n", mn);
  return 0;
}