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;
const int MX = 1e9 + 111;
int main() {
  scanf("%d%d", &a, &b);
  if (b > a) {
    printf("-1\n");
    return 0;
  }
  if (a == b) {
    printf("%d\n", a);
    return 0;
  }
  double x = 1e50;
  int lo = 0, hi = MX, mid;
  while (lo < hi) {
    mid = (lo + hi + 1) >> 1;
    if (a - b < b * 2ll * mid) {
      hi = mid - 1;
    } else {
      lo = mid;
    }
  }
  if (lo > 0) {
    x = (a - b) / (2.0 * lo);
  }
  lo = 0, hi = MX;
  while (lo < hi) {
    mid = (lo + hi + 1) >> 1;
    if (a + b < b * 2ll * (mid + 1)) {
      hi = mid - 1;
    } else {
      lo = mid;
    }
  }
  x = min(x, (a + b) / (2.0 * (lo + 1)));
  printf("%.15f\n", x);
  return 0;
}