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 int oo = (int)1e9;
const double PI = 2 * acos(0.0);
const double eps = 1e-9;
int main() {
  ios_base::sync_with_stdio(false);
  double a, b, c, d;
  cin >> a >> b >> c >> d;
  double ans = 0, p1 = 1, p2 = 1;
  for (int i = 1; i < (int)(1000001); i++) {
    ans += a / b * p1 * p2;
    p1 *= (b - a) / b;
    p2 *= (d - c) / d;
  }
  printf("%0.9f\n", ans);
  return 0;
}