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;
int main() {
  int a1, b1, c1, d1;
  cin >> a1 >> b1 >> c1 >> d1;
  float a, b, c, d;
  a = (float)a1;
  b = (float)b1;
  c = (float)c1;
  d = (float)d1;
  float e;
  e = (a * d) / (b * d - (b - a) * (d - c));
  printf("%.7f", e);
  return 0;
}