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 double eps = 1e-12;
int a, b, c, d;
double ans, g[2];
int main() {
  scanf("%d%d%d%d", &a, &b, &c, &d);
  g[0] = 1.0 * a / b, g[1] = 1.0 * (d - c) / d;
  double tmp = 1;
  while (tmp > eps) {
    ans += tmp * g[0];
    tmp *= (1 - g[0]) * g[1];
  }
  printf("%.12lf\n", ans);
  return 0;
}