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;
using ll = long long;
using ldb = long double;
using pa = pair<ll, ll>;
using vec = vector<ll>;
const ll MOD = 1e9 + 7, N = 5e5 + 10;
const ll LINF = LLONG_MAX;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ldb a, b, c, d;
  cout << setprecision(10) << fixed;
  cin >> a >> b >> c >> d;
  ldb r1 = a / b;
  ldb r11 = r1;
  ldb r2 = c / d;
  r1 = 1 - r1;
  r2 = 1 - r2;
  r1 = r2 * r1;
  ldb ans = r11 / (1 - r1);
  cout << ans;
  return 0;
}