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 a, b, c;
  int k, q, f = 0;
  double p;
  scanf("%d", &a), scanf("%d", &b);
  if (b + a > 0) {
    c = b + a;
    q = c / (2 * (b));
    if (q >= 1) {
      f = 1;
      p = (double)c / (double)(2 * q);
    }
  }
  if (b - a <= 0) {
    c = a - b;
    q = c / (2 * b);
    if (q >= 1 && !f) {
      f = 1;
      p = (double)c / (double)(2 * q);
    }
  }
  if (f == 0)
    printf("-1\n");
  else
    cout << setprecision(10) << p << endl;
  return 0;
}