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 long long oo = 1e9 + 7;
int main() {
  double a, x1, y1, b, c, d, x, y, k, f;
  int i;
  cin >> a >> b >> c >> d;
  x = a / b;
  y = c / d;
  x1 = x;
  y1 = (1 - x) * (1 - y);
  f = x1;
  for (i = 0; i < 10000; i++) {
    f = x1 + y1 * f;
  }
  cout << fixed << setprecision(12) << f;
  return 0;
}