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;
const int N = 500050;
const int inf = 0x3f3f3f3f;
const long long mod = 998244353LL;
clock_t TIME_START, TIME_END;
void program_end() {}
int a, b;
void solve() {
  scanf("%d%d", &a, &b);
  if (a < b)
    puts("-1");
  else if (a == b)
    printf("%d\n", a);
  else {
    double down = floor((a + b) / 2.0 / b);
    double up = floor((a - b) / 2.0 / b);
    double ans = min((a + b) / down / 2.0, (a - b) / up / 2.0);
    printf("%.12lf\n", ans);
  }
}
int main() {
  TIME_START = clock();
  int Test = 1;
  while (Test--) solve();
  TIME_END = clock();
  program_end();
  return 0;
}