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;
inline int read() {
  int res = 0;
  char ch = getchar();
  bool fu = 0;
  while (!isdigit(ch)) {
    if (ch == '-') fu = 1;
    ch = getchar();
  }
  while (isdigit(ch)) res = (res << 3) + (res << 1) + (ch ^ 48), ch = getchar();
  return fu ? -res : res;
}
double ans;
double a, b;
double sum;
int main() {
  a = (double)read() / (double)read(), b = (double)read() / (double)read();
  ans = a;
  sum = (1 - a) * (1 - b);
  for (register int i = 1; i <= 100000; i++) {
    ans += sum * a;
    sum *= (1.0 - a) * (1 - b);
  }
  printf("%.12lf\n", ans);
  return 0;
}