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;
void debug() { cout << endl; }
template <typename T, typename... E>
void debug(T t, E... e) {
  cout << t << (sizeof...(e) ? " " : "");
  debug(e...);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  double p1 = double(a) / b;
  double p2 = double(c) / d;
  double ans = p1 / (1 - (1 - p1) * (1 - p2));
  cout << ans << "\n";
}