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)
    puts("-1");
  else if (b == a)
    printf("%.12lf\n", (double)a);
  else {
    double t = (a - b) / 2.0;
    t = a - t;
    long long l = 1;
    long long r = 1e18;
    while (r > l) {
      long long mid = (l + r + 1ll) >> 1ll;
      if (t / mid >= b)
        l = mid;
      else
        r = mid - 1;
    }
    t /= (1. * l);
    printf("%.12lf\n", (double)t);
  }
  return 0;
}