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 solution(int tc) {
  double a, b, c, d;
  cin >> a >> b >> c >> d;
  double ans = 1 / (1 - ((b - a) * (d - c) / (b * d)));
  ans *= (a / b);
  cout << ans << endl;
  return 1;
}
void testCase() {
  int tc = 1;
  for (int i = 0; i < tc; i++) {
    solution(i + 1);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  testCase();
}