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>
const double INF = 1e30;
int a, b;
double calc(int x, int y) {
  if (x < 0 || x < 2 * y) {
    return INF;
  } else if (x == 0) {
    return 1.0 * y;
  }
  int k = x / (2 * y);
  return 1.0 * x / k / 2;
}
bool work() {
  double ret = std::min(calc(a - b, b), calc(a + b, b));
  if (ret > 1e20) {
    return false;
  }
  printf("%.12f\n", ret);
  return true;
}
int main() {
  scanf("%d%d", &a, &b);
  if (!work()) {
    puts("-1");
  }
  return 0;
}