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;
template <class T>
inline void mint(T& a, T b) {
  if (a > b) a = b;
}
template <class T>
inline void maxt(T& a, T b) {
  if (a < b) a = b;
}
const int maxn = 23333;
int w, h, cnt, ans = 0x3f3f3f3f;
pair<int, int> dc[maxn];
int main() {
  scanf("%d%d", &w, &h);
  if (h == 0 || w < h)
    puts("-1");
  else if (w == h)
    printf("%d\n", w);
  else
    printf("%.12lf\n", double(w + h) / 2. / ((w + h) / 2 / h));
}