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(void) {
  double a, b, c, d;
  cin >> a >> b >> c >> d;
  double p1 = a / b, p11 = p1, p2 = c / d;
  double res = p1;
  for (int i = 0; i < 100000; i++) {
    res += (1 - p11) * (1 - p2) * p1;
    p11 = 1 - (1 - p11) * (1 - p2) * (1 - p1);
  }
  cout << setprecision(9) << res << endl;
  return 0;
}