#include<cstdio>
#include<cmath>
long long int ncr[41][41];
int main(){
int a,b,n,t;
double lna,lnb,lnn;
long long int k,sum=0;
scanf("%d %d %d %lld",&a,&b,&n,&k);
//printf("%d %d %d %lld\n",a,b,n,k);
ncr[0][0]=1;
if(a>b){
t=a;a=b;b=t;
}
t=a*a+b*b;
lna=log((a*a)/(double)t);
lnb=log((b*b)/(double)t);
lnn=log(a*b/2.0);
for(int i=1;i<=n;i++){
ncr[i][0]=1;
for(int j=1;j<=i;j++){
ncr[i][j]=ncr[i-1][j-1]+ncr[i-1][j];
}
}
for(int i=0;i<=n;i++){
sum+=ncr[n][i];
//printf("%d %lld %lld\n",i,sum,k);
if(sum>=k){
printf("%.12f",i*lna+(n-i)*lnb+lnn);
return 0;
}
}
}
