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 a, b, k1, k2;
double x1, x2;
int main() {
  scanf("%d%d", &a, &b);
  if (a < b) {
    printf("-1\n");
    return 0;
  }
  k1 = (a - b) / (2 * b);
  x1 = k1 ? (1. * (a - b) / 2. / k1) : (a == b ? a : a * 2);
  k2 = (a + b) / (2 * b) - 1;
  x2 = 1. * (a + b) / (2 * k2 + 2);
  printf("%.10lf\n", min(x1, x2));
  return 0;
}