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;
long double a, b, ans, bcpy;
int line;
bool up;
void read() { cin >> a >> b; }
void build() {
  if (b > a) {
    ans = -1;
    printf("-1\n");
    return;
  }
  bcpy = b;
  bcpy = a - int(a / b) * b;
  if (int(a / b) % 2 == 0) {
    bcpy = abs(b - bcpy);
    up = true;
  } else
    up = false;
  if (int(a / b) != a / b)
    line = int(a / b) + 1;
  else {
    line = int(a / b);
    up = false;
  }
}
void sol() {
  if (ans == -1) return;
  if (up == false)
    ans = bcpy / (long double)(line) + b;
  else {
    line = int(a / b);
    bcpy = a - (line - 1) * b;
    ans = bcpy / (long double)(line) + b;
  }
  cout << setprecision(12) << ans << endl;
}
int main() {
  read();
  build();
  sol();
  return 0;
}