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 setIO(string name = "") {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
}
using pi = pair<long long, long long>;
long long dx[] = {-1, 0, 1, 0};
long long dy[] = {0, 1, 0, -1};
const long long MAX = 200005;
const long long mod = 1e9 + 7;
const long long modulo = 998244353;
const long long inf = 1e9;
const long long infinity = 1e18;
vector<vector<long long> > g;
vector<bool> vis(MAX);
vector<long long> par;
vector<long long> dist;
void initgraph(long long n) {
  g.resize(n + 1);
  vis.resize(n + 1);
  par.resize(n + 1);
  dist.resize(n + 1);
}
void solve(long long tt = 0) {
  double a, b, c, d;
  cin >> a >> b >> c >> d;
  double ans = (a / b) * (1 / (1 - (1 - a / b) * (1 - c / d)));
  cout << fixed << setprecision(7) << ans;
}
int32_t main() {
  setIO();
  long long T = 1;
  for (long long i = 1; i <= T; i++) {
    solve(i);
  }
}