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(int argc, char *argv[]) {
  int a, b, c, d;
  scanf("%d%d%d%d", &a, &b, &c, &d);
  int numerator = a, denominator = b;
  numerator *= b * d;
  denominator *= (b * d - (b - a) * (d - c));
  printf("%.12lf\n", (double)(numerator) / (double)(denominator));
  return 0;
}