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;
char str[10050];
int main() {
  int i, j, n, m, k;
  double a, b, c, d, t1, t2;
  scanf("%lf%lf%lf%lf", &a, &b, &c, &d);
  t1 = a / b;
  t2 = c / d;
  double t = (1 - t1) * (1 - t2), sum = t1;
  double ans = t;
  while (t1 * ans > 1e-9) {
    sum += t1 * ans;
    ans *= t;
  }
  printf("%.8lf", sum);
  return 0;
}