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 di[] = {1, 0, -1, 0};
int dj[] = {0, 1, 0, -1};
int Di[] = {1, 1, 0, -1, -1, -1, 0, 1};
int Dj[] = {0, 1, 1, 1, 0, -1, -1, -1};
int main() {
  long double a, b, c, d;
  cin >> a >> b >> c >> d;
  long double ans = a / b;
  long double q = (1 - (a / b)) * (1 - (c / d));
  ans /= (1 - q);
  cout << fixed << setprecision(8) << ans;
  return 0;
}