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() {
  long double e = 1, a, b, c, d, p, s;
  cin >> a >> b >> c >> d;
  s = (1 - a / b) * (1 - c / d);
  p = s;
  while (e > 0.000000000001) {
    long double h = p;
    p = p * s + s;
    e = p - h;
  }
  cout << (p + 1) * (a / b) << endl;
  return 0;
}