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, C;
double ans = 1e18;
int main() {
  cin >> A >> B;
  if (A >= B) {
    C = (A - B) / B;
    if (C - (C & 1)) ans = double(A - B) / (C - (C & 1));
  }
  C = (A + B) / B;
  if (C - (C & 1)) ans = min(ans, double(A + B) / (C - (C & 1)));
  if (B > ans || ans == 1e18)
    cout << -1;
  else
    printf("%.9lf", ans);
}