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;
bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second < b.second);
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
int main() {
  int t = 1;
  while (t--) {
    int a, b, c, d;
    cin >> a >> b >> c >> d;
    double p1 = (double)(a) / (double)(b);
    double p2 = (double)(c) / (double)(d);
    double p3 = 1 - p1;
    double p4 = 1 - p2;
    double p5 = p3 * p4 * p1;
    double p6 = p5 / p1;
    double p7 = 1 - p6;
    double p8 = p1 / p7;
    cout << fixed << setprecision(12) << p8 << endl;
  }
}