#include #if __has_include() #endif using namespace std; #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll IJK=n;IJK-->0;) #define fo(i,...) for(auto[i,i##stop,i##step]=for_range(0,__VA_ARGS__);i(1,__VA_ARGS__);i>=i##stop;i+=i##step) #define fe(a,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):a) #define defpp templatevoid pp(const auto&...a){[[maybe_unused]]const char*c="";((o<(a...);} #define entry defpp void main();void main2();}int main(){my::io();my::main();}namespace my{ #define multiple_testcases LL(T);FO(T)main2();}void main2(){ namespace my{ void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<constexpr auto for_range(T s,T b){T a=0;if(s)swap(a,b);return array{a-s,b,1-s*2};} templateconstexpr auto for_range(T s,T a,T b,T c=1){return array{a-s,b,(1-s*2)*c};} void lin(auto&...a){(cin>>...>>a);} constexpr auto abs(auto x){return x<0?-x:x;} constexpr ll size10(auto x){x|=1;ll r=0;while(x>0)x/=10,++r;return r;} templateconstexpr ll maxsize10(){return size10(numeric_limits::max());} auto binary_search(ll o,ll x,const auto&f){while(abs(o-x)>1)(f((o+x)/2)?o:x)=(o+x)/2;return o;} constexpr ui64 kth_root_floor(ui64 a,ll k){ if (k==1)return a; auto within=[&](ui32 x){ui64 t=1;FO(k)if(__builtin_mul_overflow(t,x,&t))return false;return t<=a;}; ui64 r=0; of(i,sizeof(ui32)*CHAR_BIT)if(within(r|(1u<struct pair{ A a;B b; pair()=default; pair(A aa,B bb):a(aa),b(bb){} auto operator<=>(const pair&)const=default; }; templatestruct infinity{ templatestatic constexpr T ones(size_t n){return n?ones(n-1)*10+1:0;} templateconstexpr operator T()const{static constexpr T v=ones(maxsize10())*(1-is_negative*2);return v;} }; constexpr infinity oo; templateusing pack_back_t=tuple_element_t>; } namespace my{ templateconcept vectorial=is_base_of_v::value_type>,remove_cvref_t>; templatestruct core_t_helper{using type=T;}; templateusing core_t=core_t_helper::type; templatestruct vec; templatestruct hvec_helper{using type=vec::type>;}; templatestruct hvec_helper<0,T>{using type=T;}; templateusing hvec=hvec_helper::type; templatestruct vec:vector{ using C=core_t; using vector::vector; ll size()const{return vector::size();} auto&emplace_back(auto&&...a){vector::emplace_back(std::forward(a)...);return*this;} auto pop_back(){auto r=this->back();vector::pop_back();return r;} auto fold(const auto&f)const{ pairr{}; fe(*this,e){ if constexpr(!vectorial){ if(r.b)f(r.a,e); else r={e,1}; }else { } } return r; } auto sum()const{return fold([](auto&a,const auto&b){a+=b;}).a;} }; templaterequires(sizeof...(A)>=2)vec(const A&...a)->vec>>; } namespace my{ auto prime_enumerate(ll n){ vecsieve(n/3+1,1); for(ll p=5,d=4,i=1,rn=sqrt_floor(n);p<=rn;p+=d=6-d,i++){ if(!sieve[i])continue; for(ll q=(p*p)/3,r=d*p/3+(d*p%3==2),s=p*2;qr{2,3}; for(ll p=5,d=4,i=1;p<=n;p+=d=6-d,i++)if(sieve[i])r.eb(p); while(r.size()&&r.back()>n)r.pop_back(); return r; } } namespace my{ templateauto&multiple_mobius(vec&a){ll n=a.size()-1;fe(prime_enumerate(n),p)fo(i,1,n/p+1)a[i]-=a[i*p];return a;} } namespace my{ templateauto kth_power_enumerate(ll n){ vecres(size10(T(oo))); fo(b,2,res.size())res[b]=kth_root_floor(n,b)-1; res[1]=n-1; return res; } templateauto exact_kth_power_enumerate(ll n){ auto res=kth_power_enumerate(n); multiple_mobius(res); return res; } } namespace my{entry void main(){ multiple_testcases LL(K); pp(binary_search(oo,0,[&](ll X){ // X以下がK個以上あるか auto v=exact_kth_power_enumerate(X); ll cnt=v.sum(); cnt-=v[1]; // 原始1乗数は累乗数でないので除外 cnt++; // 一方1は累乗数なので追加 return cnt>=K; })); }}