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;
double p1, p2;
double fastPow(double b, int n) {
  if (n == 0) return 1.0;
  double po = fastPow(b, n / 2);
  po = po * po;
  if (n & 1) return po * b;
  return po;
}
double proba(int turno) {
  double ans = 1;
  ans = ans * fastPow(1 - p1, turno / 2);
  ans = ans * fastPow(1 - p2, turno / 2);
  return ans * p1;
  return ans * p1;
}
int main() {
  double a, b, c, d;
  while (cin >> a >> b >> c >> d) {
    double prob = 0;
    p1 = a / b;
    p2 = c / d;
    for (int i = 1; i < 100000; i += 2) prob = prob + proba(i);
    cout << prob << endl;
  }
}