#1174495 (C++23) No.3607 Sum of Powers of GCDs

• 問題: No.3607 Sum of Powers of GCDs
• ユーザー: Taiki0715
• 提出日時: 2026-07-31 21:54:04
• 言語: C++23 (gcc 15.2.0 + boost 1.90.0)
• 結果: AC
• 実行時間: 412 ms / 2,500 ms
• コード長: 13,080 bytes
• コンパイル時間: 2,631 ms
• コンパイル使用メモリ: 347,544 KB
• 実行使用メモリ: 43,124 KB
• 最終ジャッジ日時: 2026-07-31 21:54:12
• 合計ジャッジ時間: 6,543 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge1_1

ファイルパターン	結果
sample	AC * 1
other	AC * 11

ソースコード

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T1,typename T2,typename T3>istream &operator>>(istream &is,tuple<T1,T2,T3>&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;}
template<typename T,size_t n>istream &operator>>(istream &is,array<T,n>&a){for(auto&i:a)is>>i;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define overload3(_1,_2,_3,name,...) name
#define rep1(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)
#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)
#define reps(i,l,r) rep2(i,l,r)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)
#define yn(x) cout<<((x)?"Yes\n":"No\n")
#define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end())
template<typename T>
inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();}
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
  if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
  else return init;
}
#ifdef LOCAL
#include<debug.h>
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
struct Timer{
  clock_t start;
  Timer(){
    start=clock();
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout<<fixed<<setprecision(16);
  }
  inline double now(){return (double)(clock()-start)/1000;}
  #ifdef LOCAL
  ~Timer(){
    cerr<<"time:";
    cerr<<now();
    cerr<<"ms\n";
  }
  #endif
}timer;
void SOLVE();
int main(){
  int testcase=1;
  //cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
}
struct Quotients{
  std::vector<long long>dat;
  long long n,s;
  Quotients(){}
  explicit Quotients(long long n_):n(n_),s(std::sqrt(n_)){
    dat.resize(s*2-(s==n/s));
    std::iota(dat.begin(),dat.begin()+s,1);
    for(int i=s-(s==n/s);i>=1;i--)dat[dat.size()-i]=n/i;
  }
  const long long &operator[](int i)const{return dat[i];}
  int get_key(long long k)const{
    if(k<=s)return k-1;
    else return dat.size()-(int)((double)n/(double)k);
  }
  int size()const{return dat.size();}
};
#include<type_traits>
#include<optional>
#include<initializer_list>
constexpr bool isprime_constexpr(unsigned long long n){
  if(n==998244353)return true;
  if(n==1000000007)return true;
  if(n<64)return 2891462833508853932ll>>n&1;
  if(n%2==0)return false;
  unsigned long long d=n-1;
  int s=0;
  while(!(d&1))d>>=1,s++;
  int q=63;
  while(!(d>>q))q--;
  unsigned long long r=n;
  for(int i=0;i<5;i++)r*=2-r*n;
  auto redc=[&r,&n](__uint128_t x)->unsigned long long {
    x=(x+__uint128_t((unsigned long long)x*-r)*n)>>64;
    return x>=n?x-n:x;
  };
  __uint128_t r2=-__uint128_t(n)%n;
  unsigned long long one=redc(r2);
  for(unsigned long long base:{2,325,9375,28178,450775,9780504,1795265022}){
    if(base%n==0)continue;
    unsigned long long a=base=redc((base%n)*r2);
    for(int i=q-1;i>=0;i--){
      a=redc(__uint128_t(a)*a);
      if(d>>i&1)a=redc(__uint128_t(a)*base);
    }
    if(a==one)continue;
    for(int i=1;a!=n-one;i++){
      if(i>=s)return false;
      a=redc(__uint128_t(a)*a);
    }
  }
  return true;
}
constexpr std::pair<long long,long long>ext_gcd(long long a,long long b){
  if(b==0)return std::make_pair(1,0);
  auto [x,y]=ext_gcd(b,a%b);
  std::swap(x,y);
  return std::make_pair(x,y-a/b*x);
}
template<std::signed_integral T>
constexpr std::pair<T,T> inv_mod(T a,T b){
  a%=b;
  if(a<0)a+=b;
  if(a==0)return std::make_pair(b,0);
  T s=b,t=a;
  T m0=0,m1=1;
  while(t){
    T u=s/t;
    s-=t*u;
    m0-=m1*u;
    std::swap(s,t);
    std::swap(m0,m1);
  }
  if(m0<0)m0+=b/s;
  return std::make_pair(s,m0);
}
template<auto m>
struct modint{
  static_assert(1<=m&&m<(1ull<<63));
  using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>;
  using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>;
private:
  value_type v;
  static constexpr value_type umod=m;
  constexpr modint sqrt_impl()const{
    if(this->val()<=1)return *this;
    if(umod%8==1){
      modint b=2;
      while(b.pow((umod-1)/2).val()==1)b++;
      value_type m2=umod-1;
      int e=0;
      while(m2%2==0)m2>>=1,e++;
      modint x=this->pow((m2-1)/2);
      modint y=(*this)*x*x;
      x*=*this;
      modint z=b.pow(m2);
      while(y.val()!=1){
        int j=0;
        modint t=y;
        while(t.val()!=1)t*=t,j++;
        z=z.pow((value_type(1))<<(e-j-1));
        x*=z;
        z*=z;
        y*=z;
        e=j;
      }
      return x;
    }
    else if(umod%8==5){
      modint res=this->pow((umod+3)/8);
      if((res*res).val()==this->val())return res;
      else return res*modint(2).pow((umod-1)/4);
    }
    else return this->pow((umod+1)/4);
  }
  template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
  static constexpr value_type take_mod(U x){
    if constexpr(std::numeric_limits<U>::max()<umod)return x;
    if constexpr(umod==(1ull<<61)-1){
      value_type res=(x>>61)+(x&umod);
      if(res>=umod)res-=umod;
      return res;
    }
    if constexpr(umod==(1ull<<61)-(1ull<<24)+1){
      static constexpr value_type mask=(1ull<<61)-1;
      value_type high=x>>61,low=x&mask;
      mul_type t=low+(mul_type(high)<<24)-high;
      high=t>>61,low=t&mask;
      low=low+(mul_type(high)<<24)-high;
      if(low>=umod)low-=umod;
      return low;
    }
    return x%umod;
  }
public:
  constexpr modint():v(0){}
  template<typename U,std::enable_if_t<std::signed_integral<U>||std::is_same_v<U,__int128_t>,std::nullptr_t> =nullptr>
  constexpr modint(U x){
    x%=std::make_signed_t<value_type>(umod);
    v=x>=0?x:x+umod;
  }
  template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
  constexpr modint(U x):v(take_mod<U>(x)){}
  static constexpr value_type mod(){return umod;}
  template<typename U>
  static constexpr modint raw(U x){
    modint res;
    res.v=x;
    return res;
  }
  constexpr std::make_signed_t<value_type> val()const{return v;}
  constexpr modint &operator+=(const modint&b){
    this->v+=b.v;
    if(this->v>=umod)this->v-=umod;
    return *this;
  }
  constexpr modint &operator-=(const modint&b){
    this->v-=b.v;
    if(this->v>=umod)this->v+=umod;
    return *this;
  }
  constexpr modint &operator*=(const modint&b){
    this->v=take_mod(mul_type(this->v)*mul_type(b.v));
    return *this;
  }
  constexpr modint &operator/=(const modint&b){return *this*=b.inv();}
  constexpr modint operator+()const{return *this;}
  constexpr modint operator-()const{return modint()-*this;}
  friend constexpr modint operator+(const modint&a,const modint&b){return modint(a)+=b;}
  friend constexpr modint operator-(const modint&a,const modint&b){return modint(a)-=b;}
  friend constexpr modint operator*(const modint&a,const modint&b){return modint(a)*=b;}
  friend constexpr modint operator/(const modint&a,const modint&b){return modint(a)/=b;}
  constexpr auto operator<=>(const modint&)const=default;
  constexpr modint operator++(int){
    modint res=*this;
    this->v++;
    if(this->v==umod)this->v=0;
    return res;
  }
  constexpr modint operator--(int){
    modint res=*this;
    if(this->v==0)this->v=umod;
    this->v--;
    return res;
  }
  template<std::integral U>
  constexpr modint pow(U k)const{
    if constexpr(std::is_signed_v<U>){
      assert(0<=k);
    }
    modint res=1,a(*this);
    while(k){
      if(k&1)res*=a;
      a*=a;
      k>>=1;
    }
    return res;
  }
  constexpr modint inv()const{
    if constexpr(isprime_constexpr(umod)){
      if(std::is_constant_evaluated()){
        if(v==0){
          throw "no inverse";
        }
      }
      else assert(v!=0);
      return pow(umod-2);
    }
    else{
      modint res;
      auto [g,x]=inv_mod<std::make_signed_t<value_type>>(this->v,umod);
      if(std::is_constant_evaluated()){
        if(g!=1){
          throw "no inverse";
        }
      }
      else assert(g==1);
      res.v=x;
      return res;
    }
  }
  std::optional<modint>sqrt()const{
    if(this->val()<=1||this->pow((umod-1)/2)==1)return std::make_optional(this->sqrt_impl());
    else return std::nullopt;
  }
  friend std::istream &operator>>(std::istream&is,modint&b){
    long long a;
    is>>a;
    b=modint(a);
    return is;
  }
  friend std::ostream &operator<<(std::ostream&os,const modint&b){
    os<<b.val();
    return os;
  }
};
template<auto m>
struct std::hash<modint<m>>{
  std::size_t operator()(modint<m>x)const{
    return std::hash<typename modint<m>::value_type>(x.val());
  }
};
using mint998=modint<998244353>;
using mint107=modint<1000000007>;
using mint61=modint<2305843009213693951>;
using mint6124=modint<2305843009196916737>;
std::vector<int>prime_sieve(int n){
  if(n<=6){
    if(n<=1)return std::vector<int>{};
    else if(n==2)return std::vector<int>{2};
    else if(n<=4)return std::vector<int>{2,3};
    else return std::vector<int>{2,3,5};
  }
  static constexpr int mod30table[8]={1,7,11,13,17,19,23,29};
  static constexpr uint8_t k_mask[][8] = {
    {0xfe, 0xfd, 0xfb, 0xf7, 0xef, 0xdf, 0xbf, 0x7f},
    {0xfd, 0xdf, 0xef, 0xfe, 0x7f, 0xf7, 0xfb, 0xbf},
    {0xfb, 0xef, 0xfe, 0xbf, 0xfd, 0x7f, 0xf7, 0xdf},
    {0xf7, 0xfe, 0xbf, 0xdf, 0xfb, 0xfd, 0x7f, 0xef},
    {0xef, 0x7f, 0xfd, 0xfb, 0xdf, 0xbf, 0xfe, 0xf7},
    {0xdf, 0xf7, 0x7f, 0xfd, 0xbf, 0xfe, 0xef, 0xfb},
    {0xbf, 0xfb, 0xf7, 0x7f, 0xfe, 0xef, 0xdf, 0xfd},
    {0x7f, 0xbf, 0xdf, 0xef, 0xf7, 0xfb, 0xfd, 0xfe},
  };
  static constexpr int c0[][8] = {
    {0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 0, 1, 1, 1, 1},
    {2, 2, 0, 2, 0, 2, 2, 1}, {3, 1, 1, 2, 1, 1, 3, 1},
    {3, 3, 1, 2, 1, 3, 3, 1}, {4, 2, 2, 2, 2, 2, 4, 1},
    {5, 3, 1, 4, 1, 3, 5, 1}, {6, 4, 2, 4, 2, 4, 6, 1},
  };
  static constexpr int c1[8]={6,4,2,4,2,4,6,2};
  n++;
  int sz=(n+29)/30;
  std::vector<uint8_t>p(sz,0xff);
  {
    int r=n%30;
    if(r==0);
    else if(r==1)p.back()=0x00;
    else if(r<=7)p.back()=0x01;
    else if(r<=11)p.back()=0x03;
    else if(r<=13)p.back()=0x07;
    else if(r<=17)p.back()=0x0f;
    else if(r<=19)p.back()=0x1f;
    else if(r<=23)p.back()=0x3f;
    else if(r<=29)p.back()=0x7f;
  }
  p[0]=0xfe;
  int sq=std::min(sz-1,((int)std::sqrt(n)+29)/30);
  for(int i=0;i<=sq;i++){
    for(uint8_t f=p[i];f>0;f=f&(f-1)){
      uint8_t l=__builtin_ctz(f);
      int m=mod30table[l];
      int pm=i*30+m*2;
      for(int j=i*pm+m*m/30,k=l;j<(int)p.size();j+=i*c1[k]+c0[l][k],k=(k+1)&7){
        p[j]&=k_mask[l][k];
      }
    }
  }
  std::vector<int>res{2,3,5};
  for(int i=0;i<(int)p.size()-1;i++){
    for(int j=p[i];j>0;j=j&(j-1))res.push_back(i*30+mod30table[__builtin_ctz(j)]);
  }
  for(int j=p.back();j>0;j=j&(j-1)){
    int l=__builtin_ctz(j);
    int k=(p.size()-1)*30+mod30table[l];
    if(k<n)res.push_back(k);
    else break;
  }
  return res;
}
template<typename T>
void divisor_zeta(std::vector<T>&a){
  int n=a.size()-1;
  std::vector<int>p=prime_sieve(n);
  for(int i:p)for(int j=1;j<=n/i;j++)a[i*j]+=a[j];
}
template<typename T>
void divisor_mobius(std::vector<T>&a){
  int n=a.size()-1;
  std::vector<int>p=prime_sieve(n);
  for(int i:p)for(int j=n/i;j>=1;j--)a[i*j]-=a[j];
}
template<typename T>
void multiplier_zeta(std::vector<T>&a){
  int n=a.size()-1;
  std::vector<int>p=prime_sieve(n);
  for(int i:p)for(int j=n/i;j>=1;j--)a[j]+=a[i*j];
}
template<typename T>
void multiplier_mobius(std::vector<T>&a){
  int n=a.size()-1;
  std::vector<int>p=prime_sieve(n);
  for(int i:p)for(int j=1;j<=n/i;j++)a[j]-=a[i*j];
}
using mint=mint998;
constexpr int nmax=1e6;
void SOLVE(){
  vector<vector<mint>>dp(11);
  rep(i,1,11){
    vector<mint>f(nmax+1);
    rep(j,nmax+1)f[j]=mint(j).pow(i);
    divisor_mobius(f);
    rep(j,1,nmax+1)f[j]+=f[j-1];
    dp[i]=move(f);
  }
  int t;
  cin>>t;
  while(t--){
    int n,m,k;
    cin>>n>>m>>k;
    const vector<mint>&f=dp[k];
    Quotients quo(m);
    mint ans=0;
    for(int i=1;i<=m;){
      int j=m/(m/i);
      ans+=(f[j]-f[i-1])*mint(m/i).pow(n);
      i=j+1;
    }
    cout<<ans<<'\n';
  }
}