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() {
  double n1, m1, n2, m2, s = 1, ans = 0;
  int i;
  cin >> n1 >> m1 >> n2 >> m2;
  for (i = 0; i < 100000; i++) {
    ans += s * n1 / m1;
    s *= (1 - n1 / m1) * (1 - n2 / m2);
  }
  printf("%.12f", ans);
  return 0;
}