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 M = 1e9 + 9;
int gcd(int a, int b) {
  if (a < b) swap(a, b);
  if (b == 0) return a;
  return gcd(b, a % b);
}
int pwr(int a, int b) {
  if (b == 0) return 1;
  int p = pwr(a, b / 2);
  if (b % 2)
    return ((a * p) % M * p) % M;
  else
    return (p * p) % M;
}
int divi(int a, int b) { return (a * pwr(b, M - 2)) % M; }
bool isVowel(char c) {
  string sx = "aeiouyAEIOUY";
  for (char ch : sx) {
    if (c == ch) return true;
  }
  return false;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cerr.tie(0);
  double a, b, c, d, lcm;
  cin >> a >> b >> c >> d;
  double p = a / b, q = (1.0 - c / d) * (1.0 - a / b);
  printf("%6f", p / (1.0 - q));
  return 0;
}