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 M = log2(2005);
int main() {
  double a, b, c, d;
  scanf("%lf%lf%lf%lf", &a, &b, &c, &d);
  double ans = 0., aux = 1.;
  while (aux > 1e-9)
    ans += (aux * (a / b)), aux *= ((b - a) / b), aux *= ((d - c) / d);
  printf("%.10lf\n", ans);
}