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 int MAX = 5e5 + 10, mod = 1e9 + 9, base = 41, INF = 1e9 + 10, sq = 502;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL);
  double a, b, c, d;
  cin >> a >> b >> c >> d;
  double p = a / b;
  double q = (c / d);
  double r = (1 - p) * (1 - q);
  double ans = p / (1 - r);
  cout << fixed << setprecision(12) << ans << endl;
  return 0;
}