CF 312B(Archer-等比数列极限求和)

B. Archer

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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  for SmallR while  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 .

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.

Sample test(s)

input

1 2 1 2

output

0.666666666667

等比数列无限求和公式 a+ap+ap^2+...    0<p<1   -->     S=a/(1-p)

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
#include<cmath>
#include<cctype>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define RepD(i,n) for(int i=n;i>=0;i--)
int main()
{
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	double a,b,c,d;
	cin>>a>>b>>c>>d;
	printf("%.12lf\n",a/b/(1-(1-a/b)*(1-c/d)));
	
	return 0;
}