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 x1, y1, x2, y2, p, result = 0;
  scanf("%lf %lf %lf %lf", &x1, &y1, &x2, &y2);
  x1 = x1 / y1;
  x2 = x2 / y2;
  p = x1;
  while (fabs(p) > 10e-10) {
    result = p + result;
    p = p * (1 - x1) * (1 - x2);
  }
  printf("%.12lf", result = 0 ? p : result);
}