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 eps = 1e-9;
double s[10001];
double ans[10001];
int main() {
  int i;
  double a, b, c, d;
  double win1, lose1, win2, lose2;
  double t1, t2, t;
  while (scanf("%lf %lf %lf %lf", &a, &b, &c, &d) != EOF) {
    win1 = a / b;
    lose1 = 1 - win1;
    win2 = c / d;
    lose2 = 1 - win2;
    s[0] = win1;
    ans[0] = s[0];
    s[1] = win1 * lose1 * lose2;
    ans[1] += ans[0] + s[1];
    i = 1;
    while (ans[i] - ans[i - 1] > eps) {
      i++;
      s[i] = s[i - 1] * lose1 * lose2;
      ans[i] += ans[i - 1] + s[i];
    }
    printf("%.8lf\n", ans[i]);
  }
  return 0;
}