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, ans1, ans2;
  int i, j, cr, x, ar[14];
  scanf("%lf%lf%lf%lf", &a, &b, &c, &d);
  ans1 = (a * d);
  ans2 = (a * d + b * c - a * c);
  while (ans1 < ans2) ans1 *= 10;
  for (i = 0; i <= 12; i++) {
    ar[i] = (int)(ans1 / ans2);
    ans1 = (ans1 - ans2 * ar[i]) * 10;
  }
  if (ar[12] > 5 || (ar[12] == 5 && ar[11] % 2 != 0)) {
    cr = 1;
    for (j = 11; cr > 0 && j >= 0; j++) {
      x = ar[j] + cr;
      ar[j] = x % 10;
      cr = x / 10;
    }
  }
  printf("0.");
  for (i = 0; i < 12; i++) printf("%d", ar[i]);
  printf("\n");
  return (0);
}