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 prob = 0;
  double at = 1.0;
  double p1acertar = (a / b);
  double p2errar = (1 - c / d);
  for (int i = 0; i < 100000; i++) {
    prob += at * p1acertar;
    at *= (1 - p1acertar);
    at *= p2errar;
  }
  printf("%.8lf\n", prob);
  return 0;
}