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() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  double hit = a * 1.0 / b;
  double mis1 = (b - a) * 1.0 / b;
  double mis2 = (d - c) * 1.0 / d * mis1;
  double ans = 1 / (1 - mis2);
  printf("%.9lf\n", ans * hit);
  return 0;
}