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;
int main() {
  ios_base::sync_with_stdio(0);
  long long int i, j;
  cin >> i >> j;
  if (j > i) {
    cout << -1;
    return 0;
  }
  long long int k = j;
  long long int frag = i / k;
  long long int a, b;
  long long int licz, mian;
  if (frag & 1) {
    a = -1;
    b = -a * 2 * (frag / 2 + 1) * k;
    if (a * i + b > j) {
      --frag;
      a = 1;
      b = -a * 2 * (frag / 2) * k;
    }
  } else {
    a = 1;
    b = -a * 2 * (frag / 2) * k;
    if (a * i + b < j) {
      --frag;
      a = -1;
      b = -a * 2 * (frag / 2 + 1) * k;
    }
  }
  ++frag;
  licz = k * frag + i - (j - b) / a;
  mian = frag;
  cout << licz / mian;
  licz = licz % mian;
  cout << ".";
  for (int a = 0; a < 16; ++a) {
    licz *= 10;
    if (licz < mian) {
      cout << 0;
    } else {
      cout << licz / mian;
      licz = licz % mian;
    }
  }
  return 0;
}