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(false);
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  double p = a / double(b);
  double q = c / double(d);
  q = 1 - q;
  double v = 1;
  double an = 0;
  while (v > 1e-7) {
    an = an + v * p;
    v *= (1 - p) * q;
  }
  cout << an;
  return 0;
}