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 double EPS = 1e-9;
int main() {
  double a, b, c, d, tmp, ans, tt;
  while (~scanf("%lf%lf%lf%lf", &a, &b, &c, &d)) {
    tmp = (1.0 - a / b) * (1.0 - c / d);
    tt = tmp * a / b;
    ans = a / b;
    while (tt > EPS) {
      ans += tt;
      tt *= tmp;
    }
    printf("%.7lf\n", ans);
  }
  return 0;
}