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;
bool debug = 0;
int n, m, k;
int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
long long ln, lk, lm;
void fmain() {
  int a, b;
  cin >> a >> b;
  if (a < b)
    puts("-1");
  else if (a == b)
    printf("%d\n", a);
  else {
    int c = (a + b) / b;
    if (c & 1) c--;
    double ans = (double)(a + b) / c;
    c = (a - b) / b;
    if (c & 1) c--;
    if (c > 0) ans = min(ans, (double)(a - b) / c);
    printf("%.10lf\n", ans);
  }
}
int main() {
  fmain();
  return 0;
}