#include #if __has_include() #endif using namespace std; #define eb emplace_back #define FO(n) for(ll IJK=n;IJK-->0;) #define fo(i,...) for(auto[i,i##stop,i##step]=for_range(0,__VA_ARGS__);ivoid 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{ 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);} auto encode_integer(char c){return c-'0';} constexpr auto abs(auto x){return x<0?-x:x;} constexpr auto pow(auto x,ll n,auto e){assert(n>=0);decltype(x)r=e;for(;n;x*=x,n>>=1)if(n&1)r*=x;return r;} constexpr auto pow(auto x,ll n){return pow(x,n,1);} bool amax(auto&a,const auto&b){return acommon_type_tgcd(T a,U b){return b?gcd(b,a%b):abs(a);} auto lcm(auto a,auto b){auto r=a/gcd(a,b);return!__builtin_mul_overflow(r,b,&r)?r:0;} auto mod(auto a,auto b){return(a%=b)<0?a+b:a;} auto inv_mod(auto x,auto m){assert(gcd(x,m)==1);decltype(x)a=mod(x,m),b=m,u=1,v=0;while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return mod(u,m);} i64 rand(){static i64 x=495;x^=x<<7;x^=x>>9;return x;} i64 rand(i64 l,i64 r=0){if(l>r)swap(l,r);return rand()%(r-l)+l;} templatestruct pair{ A a;B b; pair()=default; pair(A aa,B bb):a(aa),b(bb){} auto operator<=>(const pair&)const=default; }; 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 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;} template>auto sort(F f={})const{vec v=*this;ranges::sort(v,f);return v;} auto rle()const{vec>r;fe(*this,e)if(r.size()&&e==r.back().a)++r.back().b;else r.eb(e,1);return r;} auto rce()const{return sort().rle();} }; templaterequires(sizeof...(A)>=2)vec(const A&...a)->vec>>; auto sin(){string s;lin(s);return s;} templateauto sinen_integer(){vecr;fe(sin(),e)r.eb(encode_integer(e));return r;} } namespace my{ templatestruct montgomery64{ using modular=montgomery64; static inline ui64 N=998244353; static inline ui64 N_inv=996491785301655553ull; static inline ui64 R2=299560064; static int set_mod(ui64 N){ if(modular::N==N)return 0; assert(N<(1ull<<63)); assert(N&1); modular::N=N; R2=-ui128(N)%N; N_inv=N; FO(5)N_inv*=2-N*N_inv; assert(N*N_inv==1); return 0; } ui64 a; montgomery64(const i64&a=0):a(reduce((ui128)(a%(i64)N+N)*R2)){} static ui64 reduce(const ui128&T){ui128 r=(T+ui128(ui64(T)*-N_inv)*N)>>64;return r>=N?r-N:r;} auto&operator+=(const modular&b){if((a+=b.a)>=N)a-=N;return*this;} auto&operator-=(const modular&b){if(i64(a-=b.a)<0)a+=N;return*this;} auto&operator*=(const modular&b){a=reduce(ui128(a)*b.a);return*this;} friend auto operator+(const modular&a,const modular&b){return modular{a}+=b;} friend auto operator-(const modular&a,const modular&b){return modular{a}-=b;} friend auto operator*(const modular&a,const modular&b){return modular{a}*=b;} friend bool operator==(const modular&a,const modular&b){return a.a==b.a;} modular pow(ui128 n)const{return my::pow(*this,n);} ui64 val()const{return reduce(a);} }; } namespace my{ bool miller_rabin(ll n,vecas){ ll d=n-1; while(~d&1)d>>=1; using modular=montgomery64<__COUNTER__>; modular::set_mod(n); modular one=1,minus_one=n-1; fe(as,a){ if(a%n==0)continue; ll t=d; modular y=modular(a).pow(t); while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1; if(y!=minus_one&&~t&1)return 0; } return 1; } bool is_prime(ll n){ if(~n&1)return n==2; if(n<=1)return 0; if(n<4759123141LL)return miller_rabin(n,{2,7,61}); return miller_rabin(n,{2,325,9375,28178,450775,9780504,1795265022}); } ll pollard_rho(ll n){ if(~n&1)return 2; if(is_prime(n))return n; using modular=montgomery64<__COUNTER__>; modular::set_mod(n); modular R,one=1; auto f=[&](const modular&x){return x*x+R;}; while(1){ modular x,y,ys,q=one; R=rand(2,n),y=rand(2,n); ll g=1; constexpr ll m=128; for(ll r=1;g==1;r<<=1){ x=y; FO(r)y=f(y); for(ll k=0;g==1&&k0); vecres; auto f=[&](auto&f,ll m){ if(m==1)return; auto d=pollard_rho(m); if(d==m)res.eb(d); else f(f,d),f(f,m/d); }; f(f,n); return res.rce(); } } namespace my{ templateT lcm(const vec&a){T r=1;fe(a,e)r=lcm(r,e);return r;} templatepairinv_gcd(T a,T b){ a=mod(a,b); if(a==0)return{b,0}; T s=b,t=a; T m0=0,m1=1; while(t){ T u=s/t; s-=t*u; m0-=m1*u; swap(s,t); swap(m0,m1); } return{s,m0}; } templateauto canonicalize_congruence_system(const vec&R,const vec&M){ unordered_map>max_exponent_congruence; fo(i,R.size())fe(factorize(M[i]),p,q)amax(max_exponent_congruence[p],pair{(T)q,R[i]}); vecr,m; fe(max_exponent_congruence,p,v){ T pq=pow(p,v.a); r.eb(v.b%pq); m.eb(pq); } return tuple{r,m}; } templateT chinese_remainder_theorem_extended_euclidean(const vec&R,const vec&M){ T r0=0,m0=1; fo(i,R.size()){ T r1=mod(R[i],M[i]),m1=M[i]; if(m0T chinese_remainder_theorem_coprime_garner(const vec&r,const vec&m){ ll K=r.size(); vect(K),S(K+1),P(K+1,1); fo(i,K){ t[i]=mod((r[i]-S[i])*inv_mod(P[i],m[i]),m[i]); fo(j,i+1,K+1){ S[j]+=t[i]*P[j]; P[j]*=m[i]; if(jT chinese_remainder_theorem(const vec&R,const vec&M){ if(lcm(M))return chinese_remainder_theorem_extended_euclidean(R,M); fo(i,R.size())fo(j,i+1,R.size())if((R[i]-R[j])%gcd(M[i],M[j]))return-1; auto[r,m]=canonicalize_congruence_system(R,M); return chinese_remainder_theorem_coprime_garner(r,m); } } namespace my{entry void main(){ auto ns=sinen_integer(); auto ks=sinen_integer(); ll r2=ns.back()%2; ll r3=(ns.sum()%3==0?0:mod(pow(ns.sum()%3,ks.back()%2),3)); // ns.sum()%3!=0ならオイラーの定理 vecans{2,8,5,7,1,4}; pp(ans[mod(chinese_remainder_theorem({r2,r3},{2,3})-1,6)]); }}