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;
  double t, x1, x2;
  cin >> a >> b;
  t = (double)(a / b - 1) / 2;
  if (t == 0) {
    x2 = (a + b) / (2 * t + 2);
    if (x2 > 0) printf("%.12f\n", x2);
  } else if (t > 0) {
    t = (int)t;
    x1 = (a - b) / (2 * t);
    x2 = (a + b) / (2 * t + 2);
    if (x1 > 0 && x1 <= x2)
      printf("%.12f\n", x1);
    else if (x2 > 0 && x2 < x1)
      printf("%.12f\n", x2);
  } else
    cout << "-1" << endl;
  return 0;
}