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, ans = 0, d, e, f, g, h;
  cin >> a >> b >> c >> d;
  int i = 0;
  e = a / b;
  f = c / d;
  g = (1 - f) * (1 - e);
  while (1) {
    h = pow(g, i);
    ans += e * h;
    if (h < 1e-8) break;
    i++;
  }
  printf("%0.12f\n", ans);
  return 0;
}