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;
const int mod = 1e9 + 7;
const int N = 300010;
long long x, y, m, n, k;
pair<long long, long long> arr[N];
bool deleted[N];
string s;
int a, b, c, d;
int main() {
  while (cin >> a >> b >> c >> d) {
    double awin = a * 1.0 / b;
    double bwin = c * 1.0 / d;
    double ret = 0;
    double temp = 1;
    for (int i = 0; i < 10000; i++) {
      ret += temp * awin;
      temp *= (1 - awin) * (1 - bwin);
    }
    cout << fixed << setprecision(10) << ret << endl;
  }
  return 0;
}