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 double eps = 1e-10;
int cmp(double x) {
  if (x > eps) return 1;
  return 0;
}
int main() {
  int x, y;
  while (~scanf("%d %d", &x, &y)) {
    if (x < y)
      puts("-1");
    else if (x == y) {
      printf("%d.000000000000\n", x);
    } else {
      int now = (x - y) / y;
      if (now % 2 == 1) now--;
      double res = ((double)(x - y)) / ((double)now);
      now = (x + y) / y;
      if (now % 2 == 1) now--;
      double res2 = ((double)(x + y)) / ((double)now);
      if (cmp(res - res2) == 1) res = res2;
      printf("%.12lf\n", res);
    }
  }
  return 0;
}