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;
const double PI = 2.0 * acos(0.0);
const double EX = 2.7182818284;
const int MOD = 1e9 + 7;
const int oo = 2e9 + 1e8;
int main() {
  double a, b, c, d, ans = 0, p = 1;
  scanf("%lf%lf%lf%lf", &a, &b, &c, &d);
  a /= b, c /= d;
  while (p > 1e-9) {
    ans += p * a;
    p *= (1 - a) * (1 - c);
  }
  printf("%.12lf\n", ans);
  return 0;
}