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>
#pragma comment(linker, "/STACK:1000000000")
using namespace std;
double x, y;
int main() {
  scanf("%lf %lf", &x, &y);
  double h = x + y;
  if (h / 2 < y) {
    cout << "-1";
    return 0;
  }
  int l = 1;
  int r = 1000000000;
  while (r - l > 1) {
    int m = (r + l) / 2;
    if ((double)(h / 2 / m) >= y) {
      l = m;
    } else {
      r = m;
    }
  }
  int res = l;
  for (int i = r; i >= l; i--) {
    if ((double)(h / 2 / i) >= y) {
      res = i;
      break;
    }
  }
  printf("%.10lf", h / 2 / res);
  return 0;
}