B - Archer - 爱码网

Problem description

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 $B - Archer$ for SmallR while $B - Archer$ 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 $B - Archer$ .

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
解题思路：等比数列极限求和。推导公式如下：

AC代码：

1 #include <bits/stdc++.h>
2 using namespace std;
3 int main(){
4     double a,b,c,d;
5     cin>>a>>b>>c>>d;
6     cout<<setiosflags(ios::fixed)<<setprecision(12)<<((a/b)*(1/(1-(1-a/b)*(1-c/d))))<<endl;
7     //printf("%.12f\n",(a/b)*(1/(1-(1-a/b)*(1-c/d))));
8     return 0;
9 }