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 INF = 0x7f7f7f7f;
int main() {
  double a, b, ans = INF;
  scanf("%lf%lf", &a, &b);
  bool flag1 = 1, flag2 = 1;
  if (a >= b) {
    int n = (a - b) / 2.0 / b;
    if (a != b)
      ans = (a - b) / 2.0 / n;
    else
      ans = b;
  } else
    flag1 = 0;
  int n = (a + b) / 2.0 / b;
  if (n < 1)
    flag2 = 0;
  else
    ans = min(ans, (a + b) / 2.0 / n);
  if (flag1 || flag2)
    printf("%.12f\n", ans);
  else
    printf("-1\n");
  return 0;
}