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 MN = 100005, dhihdwi = 1000000005, mod = 1000000007;
const double inf = 1000000000000000005LL;
double daj(double dif, int lb) {
  long long zd = 1LL, zg = inf;
  if (dif / 2.0 < (double)lb) return inf;
  while (zd != zg) {
    long long mid = (zd + zg + 1LL) >> 1;
    if (dif / (2.0 * mid) < (double)lb)
      zg = mid - 1;
    else
      zd = mid;
  }
  return dif / (2.0 * zd);
}
int main() {
  int a, b;
  scanf("%d%d", &a, &b);
  if (a == b) {
    printf("%d.0", b);
    return 0;
  }
  double ans = inf;
  if (a > b) ans = min(ans, daj(a - b, b));
  ans = min(ans, daj(a + b, b));
  if (ans >= inf - 0.000001)
    printf("-1");
  else
    printf("%.11lf", ans);
}