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;
  scanf("%d%d", &a, &b);
  if (b > a) {
    printf("-1\n");
  } else if (a == b) {
    printf("%d.000000000\n", a);
  } else {
    int k((a - b) / b);
    if (k & 1) {
      k--;
    }
    double ans1(1. * (a - b) / k);
    k = (a + b) / b;
    if (k & 1) {
      k--;
    }
    double ans2(1. * (a + b) / k);
    printf("%.9f\n", min(ans1, ans2));
  }
}