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;
long long a, b;
double x1, x2, k;
bool findfs = true, findSd = true;
int main() {
  cin >> b >> a;
  k = (b - a) / a;
  k = (int)k / (int)2;
  k += 2;
  k *= 2;
  x1 = 0;
  while (x1 < a) {
    if (!findfs) break;
    x1 = (b - a) / k;
    k -= 2;
    if (k <= 0) {
      findfs = false;
    }
  }
  k = (b + a) / a;
  k = (int)k / (int)2;
  k += 2;
  k *= 2;
  x2 = 0;
  while (x2 < a) {
    if (findSd == false) break;
    x2 = (b + a) / k;
    k = k - 2;
    if (k < 0) {
      findSd = false;
    }
  }
  if (findfs && findSd) {
    printf("%.11f", min(x1, x2));
    return 0;
  }
  if (findfs) {
    printf("%.11f", x1);
    return 0;
  }
  if (findSd) {
    printf("%.11f", x2);
    return 0;
  }
  cout << -1;
  return 0;
}