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;
const double pi = 3.1415926536;
const long long INF = 1e18;
const int32_t M = 1e6 + 7;
const int32_t MM = 998244353;
long long a, b, c, d;
void solve() {
  cin >> a >> b >> c >> d;
  double p, q, x;
  p = (double)a / b;
  q = (double)c / d;
  x = (1 - p) * (1 - q);
  x = 1 - x;
  cout << fixed << setprecision(12);
  cout << p / x;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  while (t--) solve();
  return 0;
}