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() {
  double a, b, c, d;
  cin >> a >> b >> c >> d;
  double p = a / b;
  double q = c / d;
  double s_k = (1 - p) * (1 - q);
  double prev = p, cur = p + p * s_k;
  while (abs(prev - cur) >= 0.00000000001) {
    prev = cur;
    s_k = s_k * (1 - p) * (1 - q);
    cur = cur + s_k * p;
  }
  printf("%8.7f\n", cur);
  return 0;
}