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 mod = 1000000007, maxn = 1010;
double a, b;
double funcao(double p);
int main() {
  scanf("%lf %lf", &a, &b);
  if (a < b) {
    printf("-1\n");
    return 0;
  } else if (a == b) {
    printf("%lf\n", b);
    return 0;
  }
  printf("%.12lf\n", min(funcao(a - b), funcao(a + b)));
}
double funcao(double p) {
  int ans = 0;
  int ini = 1, mid, fim = ceil(p) + 1;
  while (ini < fim) {
    mid = (ini + fim) / 2;
    double aux = p / (mid * 2.0);
    if (aux >= b) {
      ini = mid + 1;
      ans = max(ans, mid);
    } else {
      fim = mid;
    }
  }
  return p / (ans * 2.0);
}