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;
string mirror = "AHIMOTUVWXY";
string letter = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const int mxn = 1e6 + 5;
const int mod = 1e9 + 7;
int main() {
  long long n, m, i, j, k, x, y, t;
  double a, b, c, d, r;
  cin >> a >> b >> c >> d;
  double ans = a / b;
  r = (b - a) * (d - c);
  r = r / (b * d);
  r = 1 / (1 - r);
  ans = ans * r;
  cout << fixed << setprecision(10) << ans << endl;
}