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;
const int N = 1e5;
const double eps = 1e-12;
int main() {
  ios_base::sync_with_stdio(0);
  int a, b, c, d, n, T, cas = 0;
  cin >> a >> b >> c >> d;
  double p = a * 1.0 / b;
  double q = c * 1.0 / d;
  double now = 1.0, win = 0, los = 0;
  while (now > eps) {
    win += now * p;
    los += now * q;
    now *= (1 - p) * (1 - q);
  }
  cout << fixed << setprecision(8) << win;
  return 0;
}