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 = 0x3fffffff;
const int PRIME = 999983;
const int MOD = 1000000007;
const int MULTI = 1000000007;
const long double EPS = 1e-15;
inline bool isodd(int x) { return x & 1; }
inline bool isodd(long long x) { return x & 1; }
int main(void) {
  int a, b, c, d;
  scanf("%d%d%d%d", &a, &b, &c, &d);
  long double p = 1.0 * a / b, q = 1.0 * c / d, ans = 0, inc = 1;
  for (int i = 1; i <= 10000; i++) {
    ans += inc * p;
    inc *= (1 - p) * (1 - q);
    if (inc < EPS) break;
  }
  cout.precision(9);
  cout << ans << endl;
  return 0;
}