This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<cstdio>
#include<vector>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long ll;
void f(double a,double b,double c,ll N,ll K){
if(N<0){
printf("%.12f",a+b-(double)log(2.0));
return;
}
if(a>b+1e-9)swap(a,b);
if(K<=(1ll<<N)){
f(a+b-c,(double)2.0*b-c,b,N-1,K);
}
else{
f((double)2.0*a-c,a+b-c,a,N-1,K-(1ll<<N));
}
}
int main(){
ll N,K;
double a,b,c;
scanf("%lf%lf%lld%lld",&a,&b,&N,&K);
if(a>b)swap(a,b);
c=(double)sqrt(a*a+b*b);
f((double)log(a),(double)log(b),(double)log(c),N-1,K);
}
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