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 MAXN = (int)1e6 + 7;
const int INF = (int)1e9 + 7;
map<long long, int> c[MAXN];
int n, k, x;
int a[MAXN];
long long pref[MAXN];
long long suff[MAXN];
int main() {
  int x, y;
  cin >> x >> y;
  if (y > x)
    cout << -1;
  else {
    double ans = INF;
    int fx = x - y;
    int lp = 0;
    int pieces = floor(double(fx) / double(y + y));
    if (pieces) ans = min(ans, double(fx) / double(pieces) / 2.0);
    fx = x + y;
    pieces = floor(double(fx) / double(y + y));
    if (pieces) ans = min(ans, double(fx) / double(pieces) / 2.0);
    cout << fixed << setprecision(10) << ans;
  }
  return 0;
}