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 double pi = acos(-1);
void gn(int &x) {
  int sg = 1;
  char c;
  while (((c = getchar()) < '0' || c > '9') && c != '-')
    ;
  if (c == '-')
    sg = -1, x = 0;
  else
    x = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') x = x * 10 + c - '0';
  x *= sg;
}
void gn(long long &x) {
  int sg = 1;
  char c;
  while (((c = getchar()) < '0' || c > '9') && c != '-')
    ;
  if (c == '-')
    sg = -1, x = 0;
  else
    x = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') x = x * 10 + c - '0';
  x *= sg;
}
const int mo = 1000000007;
int qp(int a, long long b) {
  int ans = 1;
  do {
    if (b & 1) ans = 1ll * ans * a % mo;
    a = 1ll * a * a % mo;
  } while (b >>= 1);
  return ans;
}
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
int a, b;
double work1() {
  int t = (a - b) / b;
  t /= 2;
  return 1.0 * (a - b) / 2 / t;
}
double work2() {
  int t = (a + b) / b;
  t /= 2;
  return 1.0 * (a + b) / 2 / t;
}
int main() {
  scanf("%d%d", &a, &b);
  if (b > a) {
    printf("-1\n");
    return 0;
  }
  if (a == b) {
    printf("%.10lf\n", 1.0 * b);
    return 0;
  }
  double ans = 1e18;
  ans = min(ans, work1());
  ans = min(ans, work2());
  printf("%.10lf\n", ans);
  return 0;
}