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sieve.hpp
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sieve.hpp
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#pragma once
template<int L=50101010>vector<int> sieve(int N){
bitset<L> isp;
int n,sq=ceil(sqrt(N));
for(int z=1;z<=5;z+=4){
for(int y=z;y<=sq;y+=6){
for(int x=1;x<=sq and (n=4*x*x+y*y)<=N;++x){
isp[n].flip();
}
for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){
isp[n].flip();
}
}
}
for(int z=2;z<=4;z+=2){
for(int y=z;y<=sq;y+=6){
for (int x=1;x<=sq and (n=3*x*x+y*y)<=N;x+=2){
isp[n].flip();
}
for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){
isp[n].flip();
}
}
}
for(int y=3;y<=sq;y+=6){
for(int z=1;z<=2;++z){
for(int x=z;x<=sq and (n=4*x*x+y*y)<=N;x+=3){
isp[n].flip();
}
}
}
for(int n=5;n<=sq;++n)if(isp[n]){
for(int k=n*n;k<=N;k+=n*n){
isp[k]=false;
}
}
isp[2]=isp[3]=true;
vector<int> ret;
for(int i=2;i<=N;i++)if(isp[i]){
ret.push_back(i);
}
return ret;
}
/**
* @brief Prime Sieve
*/