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;
template <typename T, typename U>
inline void smin(T &a, const U &b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, const U &b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T1, class T2>
inline void gn(T1 &x1, T2 &x2) {
  gn(x1), gn(x2);
}
template <class T1, class T2, class T3>
inline void gn(T1 &x1, T2 &x2, T3 &x3) {
  gn(x1, x2), gn(x3);
}
template <class T1, class T2, class T3, class T4>
inline void gn(T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  gn(x1, x2, x3), gn(x4);
}
template <class T1, class T2, class T3, class T4, class T5>
inline void gn(T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  gn(x1, x2, x3, x4), gn(x5);
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T>
inline void println(T first) {
  print(first);
  putchar('\n');
}
template <class T>
inline void printsp(T first) {
  print(first);
  putchar(' ');
}
template <class T1, class T2>
inline void print(T1 x1, T2 x2) {
  printsp(x1), println(x2);
}
template <class T1, class T2, class T3>
inline void print(T1 x1, T2 x2, T3 x3) {
  printsp(x1), printsp(x2), println(x3);
}
template <class T1, class T2, class T3, class T4>
inline void print(T1 x1, T2 x2, T3 x3, T4 x4) {
  printsp(x1), printsp(x2), printsp(x3), println(x4);
}
template <class T1, class T2, class T3, class T4, class T5>
inline void print(T1 x1, T2 x2, T3 x3, T4 x4, T5 x5) {
  printsp(x1), printsp(x2), printsp(x3), printsp(x4), println(x5);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
int main() {
  int a, b, c, d;
  gn(a, b, c, d);
  double p = (double)a / b;
  double q = (double)c / d;
  double ans = p / (p + q - p * q);
  printf("%.10lf\n", ans);
  return 0;
}