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 a, b, c, d;
  scanf("%lf%lf%lf%lf", &a, &b, &c, &d);
  double p1 = a / b, p2 = c / d;
  double cur1 = 1, cur2 = 1;
  double ans = 0;
  for (int i = 0; i < 100000; i++) {
    ans += p1 * cur1 * cur2;
    cur1 *= (1 - p1);
    cur2 *= (1 - p2);
  }
  printf("%lf\n", ans);
  return 0;
}