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() {
  int x, y;
  cin >> x >> y;
  if (x < y) {
    cout << -1 << endl;
    return 0;
  }
  if (x == y) {
    cout << x << endl;
    return 0;
  }
  int cnt1 = 0, cnt2 = 0;
  double ans1, ans2;
  int b1 = x + y;
  int max1 = b1 / y;
  if (max1 < 2) cnt1 = 1;
  int fact1 = max1 / 2 * 2;
  if (!cnt1) {
    ans1 = (b1 + 0.0) / fact1;
  }
  int b2 = x - y;
  int max2 = b2 / y;
  if (max2 < 2) cnt2 = 1;
  int fact2 = max2 / 2 * 2;
  if (!cnt2) {
    ans2 = (b2 + 0.0) / fact2;
  }
  double answer = 1e9 + 255;
  if (!cnt1) {
    if (ans1 < answer) answer = ans1;
  }
  if (!cnt2) {
    if (ans2 < answer) answer = ans2;
  }
  if (answer > 1e9)
    cout << -1 << endl;
  else
    printf("%.12f", answer);
  return 0;
}