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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const int INF = 100000000;
const int mod = 1000 * 1000 * 1000 + 7;
const double PI = 3.1415926535897932;
double sqr(double first) { return first * first; };
long double sqr(long double first) { return first * first; };
long long sqr(long long first) { return first * first; };
long long sqr(int first) { return first * 1LL * first; };
long long bpm(long long a, long long n = -2, long long m = mod) {
  n = n >= 0 ? n : m + n;
  long long r = 1;
  while (n) {
    if (n & 1) r = (r * a) % m;
    a = (a * a) % m;
    n >>= 1;
  }
  return r;
}
const int N = 2000002;
int main(int argc, char *argv[]) {
  long double first, second;
  cin >> first >> second;
  cout.precision(10);
  cout.setf(cout.fixed);
  if (second > first) {
    cout << -1 << endl;
  } else if (second == first) {
    cout << second << endl;
  } else {
    long long c = second + first;
    if (c < second) {
      cout << -1 << endl;
      return 0;
    }
    if (c < second * 2) {
      cout << c << endl;
      return 0;
    }
    long long l = 2, r = c;
    while (l != r) {
      long long m = (l + r) >> 1;
      if (c >= second * 2 * m)
        l = m + 1;
      else
        r = m;
    }
    long double cc = c;
    cc = c / 2.0 / (l - 1);
    cout << cc << endl;
  }
  return 0;
}