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;
int main() {
  scanf("%d %d", &A, &B);
  if (B > A)
    puts("-1");
  else if (A == B)
    printf("%.12lf\n", (double)A);
  else {
    int C1 = A - B;
    int C2 = A + B;
    int step1 = C1 / (2 * B);
    int step2 = C2 / (2 * B);
    printf("%.12lf\n",
           min((((double)C1) / (2 * step1)), ((double)C2 / (2 * step2))));
  }
}