Problem: SmallR is an archer. SmallR is taking a match of archer with Zanoes. They try to shoot in the target in turns, and SmallR shoots first. The probability of shooting the target each time is <image> for SmallR while <image> for Zanoes. The one who shoots in the target first should be the winner.

Output the probability that SmallR will win the match.

Input

A single line contains four integers <image>.

Output

Print a single real number, the probability that SmallR will win the match.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

1 2 1 2


Output

0.666666666667

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  double a, b, c, d, i, s = 0, t = 0;
  cin >> a >> b >> c >> d;
  double s1 = a / b;
  double s2 = (b - a) / b;
  double z1 = c / d;
  double z2 = (d - c) / d;
  for (i = 0;; i++) {
    s += pow(s2 * z2, i) * s1;
    if (i > 0) t += pow(s2 * z2, i - 1) * s1;
    if ((abs(s - t)) <= 0.00000000006) break;
  }
  cout << fixed << setprecision(9) << s;
  return 0;
}