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;
template <class t>
inline void rd(t &s) {
  s = 0;
  register char c = getchar();
  while (!isdigit(c)) c = getchar();
  while (isdigit(c)) s = (s << 3) + (s << 1) + (c ^ 48), c = getchar();
  return;
}
signed main(void) {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  double A = (double)a / (double)b, B = (double)c / (double)d;
  printf("%.9lf\n", A * (1.0 / (1.0 - (1.0 - A) * (1.0 - B))));
  return 0;
}