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;
double ar[500009], vis[100004], cr[500009], dr[500009];
map<double, double> mp, mp1;
vector<double> v[500009];
string s, d, q;
int main() {
  double a, b, c, i, j, k, x, y, z, f, g, h;
  cin >> a >> b >> c >> g;
  cout << fixed << setprecision(10);
  a = (a / b);
  c = (c / g);
  i = (1.0 - a);
  j = (1.0 - c);
  x = (1 - (i * j));
  cout << (a / x) << endl;
}