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;
  cin >> a >> b;
  if (a < b) {
    cout << -1;
    return 0;
  } else if (a == b) {
    cout.precision(6);
    cout << b;
    return 0;
  } else {
    double k1 = a + b;
    double k2 = a - b;
    double x;
    double value1 = k1 / b;
    int val1 = value1;
    if (val1 % 2 == 0) {
      x = k1 / val1;
    } else
      x = k1 / (val1 - 1);
    double value2 = k2 / b;
    int val2 = value2;
    if (val2 % 2 == 0) {
      if (val2 != 0) x = min(x, k2 / val2);
    } else {
      if (val2 != 1) x = min(x, k2 / (val2 - 1));
    }
    cout.precision(10);
    cout << x;
  }
}