#include <cstdio>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
ll combi[50][50];
void bc(){
combi[0][0]=1;
int i,j;
for(i=1;i<=40;++i){
combi[i][0]=combi[i][i]=1;
for(j=1;j<i;++j) combi[i][j]=combi[i-1][j-1]+combi[i-1][j];
}
}
typedef pair<double,ll> pd;
pd asdf[50];
int main()
{
bc();
int a,b,n;
ll k;
scanf("%d%d%d%I64d",&a,&b,&n,&k);
double r1=2*log(a)-log(a*a+b*b);
double r2=2*log(b)-log(a*a+b*b);
double s0=log(a)+log(b)-log(2);
int i;
for(i=0; i<=n; ++i){
asdf[i]={r1*i + r2*(n-i), combi[n][i]};
}
sort(asdf,asdf+n+1,greater<pd>());
int ind=0;
for(i=0; i<=n; ++i){
ind += asdf[i].second;
if(k<=ind){
printf("%.12f\n",asdf[i].first + s0);
break;
}
}
return 0;
}
