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>
int main() {
  double a, b, c, d;
  while (scanf("%lf%lf%lf%lf", &a, &b, &c, &d) != EOF) {
    double Win_SmallR = a / b, Win_Zanoes = c / d;
    double defeat_SmallR = (1 - Win_SmallR);
    double defeat_Zanoes = (1 - Win_Zanoes);
    printf("%.12lf\n", Win_SmallR *
                           (1 - pow(defeat_SmallR * defeat_Zanoes, 10000)) /
                           (1 - defeat_SmallR * defeat_Zanoes));
  }
}