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;
long long modInverse(long long a, long long m);
long long gcd(long long a, long long b);
long long power(long long x, unsigned long long y, unsigned long long m);
void pairsort(int a[], int b[], int n);
long long logint(long long x, long long y);
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long power(long long x, unsigned long long y, unsigned long long m) {
  if (y == 0) return 1;
  long long p = power(x, y / 2, m) % m;
  p = (p * p) % m;
  return (y % 2 == 0) ? p : (x * p) % m;
}
long long modInverse(long long a, long long m) {
  long long m0 = m;
  long long y = 0, x = 1;
  if (m == 1) return 0;
  while (a > 1) {
    long long q = a / m;
    long long t = m;
    m = a % m, a = t;
    t = y;
    y = x - q * y;
    x = t;
  }
  if (x < 0) x += m0;
  return x;
}
void pairsort(int a[], int b[], int n) {
  pair<int, int> pairt[n];
  for (int i = 0; i < n; i++) {
    pairt[i].first = a[i];
    pairt[i].second = b[i];
  }
  sort(pairt, pairt + n);
  for (int i = 0; i < n; i++) {
    a[i] = pairt[i].first;
    b[i] = pairt[i].second;
  }
}
long long logint(long long x, long long y) {
  long long ans = 0;
  long long a = 1;
  for (long long i = 0; i < x; i++) {
    if (x <= a) {
      return ans;
    }
    ans++;
    a *= y;
  }
  return -1;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  double a, b, c, d;
  cin >> a >> b >> c >> d;
  double t = a / b, s = c / d * (1 - t);
  printf("%.12f", t / (t + s));
  return 0;
}