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>
#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;
int main() {
  double a, b;
  cin >> a >> b;
  long long l = 0, r = 1e10;
  double ans = 1e20;
  while (l <= r) {
    long long mid = (l + r) / 2;
    double x = (a + b) / 2 / (mid + 1);
    if (x + 1e-10 >= b) {
      l = mid + 1;
      ans = min(ans, x);
    } else
      r = mid - 1;
  }
  l = 1, r = 1e10;
  while (l <= r) {
    long long mid = (l + r) / 2;
    double x = (a - b) / 2 / mid;
    if (x + 1e-10 >= b) {
      l = mid + 1;
      ans = min(ans, x);
    } else
      r = mid - 1;
  }
  if (ans == 1e20)
    cout << -1 << endl;
  else
    printf("%.10f\n", ans);
  return 0;
}