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;
int main() {
  int Num, N, i, j, k, a, b, l, r, mid;
  double Min, ans;
  while (scanf("%d%d", &a, &b) != EOF) {
    if (b > a)
      printf("-1\n");
    else {
      l = 1, r = a * 2;
      Min = a;
      while (l < r) {
        mid = (l + r) / 2;
        if (mid % 2)
          ans = 1.0 * (b + a) / (mid + 1);
        else
          ans = 1.0 * (a - b) / mid;
        if (ans >= b) {
          if (Min > ans) Min = ans;
          l = mid + 1;
        } else
          r = mid;
      }
      printf("%.12lf\n", Min);
    }
  }
  return 0;
}