#1174626 (C++17) No.3607 Sum of Powers of GCDs

• 問題: No.3607 Sum of Powers of GCDs
• ユーザー: GOTKAKO
• 提出日時: 2026-08-01 00:18:20
• 言語: C++17 (gcc 15.2.0 + boost 1.90.0)
• 結果: AC
• 実行時間: 1,093 ms / 2,500 ms
• コード長: 4,243 bytes
• コンパイル時間: 1,347 ms
• コンパイル使用メモリ: 227,232 KB
• 実行使用メモリ: 171,568 KB
• 最終ジャッジ日時: 2026-08-01 00:18:36
• 合計ジャッジ時間: 14,282 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge3_0

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;

//入力が必ず-mod<=a<modの時.
template<const int mod> //mod<2^30.
struct modint{ //mod変更が不可能.
    public:
    long long v;
    static void setmod(int m){} //飾り.
    static constexpr long long getmod(){return mod;}
    modint():v(0){}
    template<typename T>
    modint(T a):v(a){if(v < 0) v += mod;}
    long long val()const{return v;}
 
    modint &operator=(const modint &b) = default;
    modint &operator+()const{return (*this);}
    modint operator-()const{return modint(0)-(*this);}
    modint operator+(const modint b)const{return modint(v)+=b;}
    modint operator-(const modint b)const{return modint(v)-=b;}
    modint operator*(const modint b)const{return modint(v)*=b;}
    modint operator/(const modint b)const{return modint(v)/=b;}
    modint &operator+=(const modint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    modint &operator-=(const modint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    modint &operator*=(const modint b){v = v*b.v%mod; return *this;}
    modint &operator/=(modint b){ //b!=0 mod素数が必須.
        assert(b.v != 0);
        (*this) *= b.pow(mod-2);
        return *this;
    }
    modint pow(long long n)const{
        modint ret = 1,p = v;
        if(n < 0) p = p.inv(),n = -n;
        while(n){
            if(n&1) ret *= p;
            p *= p; n >>= 1;
        }
        return ret;
    }
    modint inv()const{return pow(mod-2);} //素数mod必須.
 
    modint &operator++(){*this += 1; return *this;}
    modint &operator--(){*this -= 1; return *this;}
    modint operator++(int){modint ret = *this; *this += 1; return ret;}
    modint operator--(int){modint ret = *this; *this -= 1; return ret;}
    friend bool operator==(const modint a,const modint b){return a.v==b.v;}
    friend bool operator!=(const modint a,const modint b){return a.v!=b.v;}
    friend bool operator<(const modint a,const modint b){return a.v<b.v;}
    friend bool operator<=(const modint a,const modint b){return a.v<=b.v;}
    friend bool operator>=(const modint a,const modint b){return a.v>=b.v;}
    friend bool operator>(const modint a,const modint b){return a.v>b.v;}
    friend ostream &operator<<(ostream &os,const modint a){return os<<a.v;}
    friend istream &operator>>(istream &is,modint &a){ //入力はmodをとってくれる.
        long long x; is >> x; x %= mod;
        a = modint(x); return is;
    }
};
using mint = modint<998244353>; const long long mod = 998244353;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int Need = 1001001;
    vector<bool> prime(Need+1);
    vector<int> allp,lpf(Need+1,1);
    for(int i=2; i<=Need; i++){
        if(lpf.at(i) == 1) lpf.at(i) = i,allp.push_back(i),prime.at(i) = true;
        for(auto &p : allp){
            if(p*i > Need || p > lpf.at(i)) break;
            lpf.at(p*i) = p;
        }
    }
    vector<vector<pair<int,int>>> Pf(Need+1);
    for(int i=2; i<=Need; i++){
        int n = i;
        while(n > 1){
            int p = lpf.at(n),e = 0;
            while(n%p == 0) n /= p,e++;
            Pf.at(i).emplace_back(pair{p,e});
        }
    }

    vector<int> mu(1001001,1);
    for(int i=1; i<1001001; i++) for(auto [p,e] : Pf.at(i)){
        if(e > 1){mu.at(i) = 0; break;}
        else mu.at(i) = -mu.at(i);
    }

    vector<vector<mint>> C(11,vector<mint>(1001001));
    for(int K=1; K<=10; K++) for(int i=1; i<1001001; i++){
        mint v = mint(i).pow(K);
        for(int k=i,l=1; k<1001001; k+=i,l++) C.at(K).at(k) += v*mu.at(l);
    }
    for(int K=1; K<=10; K++) for(int i=1; i<1001001; i++) C.at(K).at(i) += C.at(K).at(i-1);

    int T; cin >> T;
    while(T--){
        int N,M,K; cin >> N >> M >> K;
        auto Cs = [&](int l,int r) -> mint {return C.at(K).at(r)-C.at(K).at(l-1);};

        int g = 1;
        mint answer = 0;
        for(; g*g<=M; g++){
            mint now = Cs(g,g);
            answer += now*mint(M/g).pow(N);
        }
        while(g <= M){
            int m = M/g,r = M%g;
            int len = 1+r/m;
            mint now = Cs(g,g+len-1);

            answer += now*mint(m).pow(N),g += len;
        }
        cout << answer << "\n";
    }
}