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;
void yala_bena() {
  cin.tie(0);
  std::ios::sync_with_stdio(0);
}
const int m_r = 199999;
double pii = 3.1415926536;
int main() {
  yala_bena();
  double a, b, c, d, ans1, ans2;
  cin >> a >> b >> c >> d;
  ans1 = (double)a / b;
  ans2 = (double)(1 - c / d) * (1 - a / b);
  cout << fixed << setprecision(12) << (double)ans1 / (1 - ans2) << endl;
}