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;
long double a, b, c, d;
long double solve(int po) {
  long double ret = (a / b) * powl((1.0 - a / b), po) * powl((1.0 - c / d), po);
  if (ret < 1e-12) return ret;
  ret += solve(po + 1);
  return ret;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> a >> b >> c >> d;
  cout << fixed << setprecision(12) << solve(0);
  return 0;
}