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;
double mind(double a, double b) { return a < b ? a : b; }
int main() {
  int a, b, k, dp = 0, cp = 0;
  double c, d;
  scanf("%d%d", &a, &b);
  if (a == b) {
    c = a, printf("%.12lf\n", c);
    return 0;
  }
  k = (a - b) / b;
  k -= k % 2;
  if (k == 0)
    cp = -1;
  else
    c = (double)(a - b) / k;
  k = (a + b) / b;
  k -= k % 2;
  if (k == 0)
    dp = -1;
  else
    d = (double)(a + b) / k;
  if (dp == -1 && cp == -1)
    printf("-1\n");
  else if (dp == -1)
    printf("%.12lf\n", c);
  else if (cp == -1)
    printf("%.12lf\n", d);
  else
    printf("%.12lf\n", mind(c, d));
  return 0;
}