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(void) {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  double ans = 0;
  double A = 1 - a * 1.0 / b;
  double B = 1 - c * 1.0 / d;
  double f = A * B;
  double pw = 1;
  for (int i = 0; i < 1000000; i++) {
    ans += (a * 1.0 / b) * pw;
    pw *= f;
  }
  printf("%.10f\n", ans);
  return 0;
}