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 main() {
  long long int i, j, k, l, ans = 0, m, n, cnt = 0, sum = 0;
  long double a, b, c, d;
  cin >> a >> b >> c >> d;
  cout << setprecision(20) << fixed;
  long double temp, temp1, temp2;
  temp = (d - c) / d;
  temp1 = (b - a) / b;
  temp = temp * temp1;
  temp = 1 - temp;
  temp = 1 / temp;
  temp *= a;
  temp /= b;
  cout << temp;
}