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 main() {
  int t, i, j, k, x, y, z, n, m, ln, sq, q, l, r, up, in, op = 1;
  int ct = 0, ok = 0, mx = -INT_MAX, mn = INT_MAX, hi = INT_MAX, lo = 0, mid;
  string s, st;
  double a, b, c, d, ans = 0.0, sum = 1.0, pre = 2.0;
  cin >> a >> b >> c >> d;
  while (1) {
    ans += (sum * (a / b));
    sum *= ((1.0 - (c / d)) * (1.0 - (a / b)));
    if (abs(pre - ans) < 0.000000001) break;
    pre = ans;
  }
  printf("%.10f\n", ans);
}