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;
int main() {
  cin.sync_with_stdio(false);
  scanf("%lf%lf%lf%lf", &a, &b, &c, &d);
  a /= b, c /= d, c = 1.0 - c, b = 1;
  double resp = 0;
  while (a * b > 1e-10) {
    resp += a * b;
    b *= (1.0 - a) * c;
  }
  printf("%.10lf\n", resp);
  return 0;
}