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;
int main() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  long double answer = 0;
  long double misses = 1;
  while (true) {
    long double ll = misses * (long double)a / (long double)b;
    answer = answer + ll;
    if (ll < 1e-12) break;
    misses = misses * (1 - (long double)a / (long double)b) *
             (1 - (long double)c / (long double)d);
  }
  printf("%.12lf\n", (double)answer);
  return 0;
}