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;
long long Ipow(long long base, long long exp) {
  long long result = 1;
  while (exp) {
    if (exp & 1) {
      result *= base % 100003;
      result %= 100003;
    }
    exp >>= 1;
    base *= base % 100003;
    base %= 100003;
  }
  return result % 100003;
}
int main() {
  long double p, q, a, b, c, d, sum = 0;
  cin >> a >> b >> c >> d;
  p = a / b;
  q = (1 - a / b) * (1 - c / d);
  for (int i = 0; i < 100003; i++) sum += p * pow(q, i);
  cout << fixed << setprecision(10) << sum;
  return 0;
}