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;
const int INF = 0x3f3f3f3f;
const int M = 1001;
const int mod = 7340033;
const double eps = 1e-6;
const double Pi = 2 * acos(0.0);
inline int max(int a, int b) { return a > b ? a : b; }
inline int min(int a, int b) { return a < b ? a : b; }
inline int bit(int x) { return 1 << x; }
inline double dabs(double x) { return x > 0 ? x : (-x); }
inline int abs(int x) { return x > 0 ? x : (-x); }
inline int lowbit(int x) { return x & (-x); }
int main() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  double p = 1.0 * a / b, q = 1.0 * c / d;
  cout << p / (1 - (1 - p) * (1 - q)) << endl;
  return 0;
}