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;
double a, b, c, d;
signed main() {
  cin >> a >> b >> c >> d;
  a /= b;
  c /= d;
  double ans = a, que = 0, tmp = 1;
  while (abs(ans - que) > 1e-9) {
    que = ans;
    tmp *= (1 - a) * (1 - c);
    ans += tmp * a;
  }
  printf("%.12lf", ans);
  return 0;
}