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;
struct debugger {
  template <typename T>
  debugger& operator,(const T v) {
    cerr << v << " ";
    return *this;
  }
} dbg;
int main() {
  ios_base::sync_with_stdio(false);
  int i, j, k;
  double a, b, c, d;
  while (cin >> a >> b >> c >> d) {
    double p = a / b;
    double q = (1 - p) * (1 - (c / d));
    double ans = (p / (1 - q));
    printf("%.15lf\n", ans);
  }
}