#1186874 (C++17) No.3688 LCM Sum

• 問題: No.3688 LCM Sum
• ユーザー: GOTKAKO
• 提出日時: 2026-09-15 05:10:14
• 言語: C++17 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 1,813 ms / 3,000 ms
• コード長: 3,774 bytes
• コンパイル時間: 1,304 ms
• コンパイル使用メモリ: 220,128 KB
• 実行使用メモリ: 248,700 KB
• 最終ジャッジ日時: 2026-09-15 05:10:37
• 合計ジャッジ時間: 13,418 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge1_0

ファイルパターン	結果
sample	AC * 3
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:
    int 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 = (long long)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 N,M; cin >> N >> M;
    if(N > M) swap(N,M);
    int Need = N;
    vector<bool> prime(Need+1);
    vector<int> allp,lpf(Need+1,1);
    allp.reserve(1857859);
    for(int i=2; i<=Need; i++){
        if(lpf.at(i) == 1) lpf.at(i) = i,allp.emplace_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<mint> F(N+1);
    F.at(1) = 1;
    for(int i=2; i<=N; i++){
        int k = i/lpf.at(i);
        if(lpf.at(i) != lpf.at(k)) F.at(i) = -F.at(k);
    }
    for(int i=1; i<=N; i++){
        F.at(i) *= i,F.at(i) *= i;
        F.at(i) += F.at(i-1);
    } 

    mint answer = 0;
    mint div4 = mint(1)/4;
    for(int d=1; d<=N; d++){
        int n = N/d,m = M/d;
        mint now = 0,mul = div4*d;
        int i = 1;
        while(i <= n){
            int m1 = n/i,r1 = n-m1*i;
            int m2 = m/i,r2 = m-m2*i;
            int k = min(r1/m1,r2/m2)+i;
            mint sum = F.at(k)-F.at(i-1);
            now += sum*m1*(m1+1)*m2*(m2+1);
            i = k+1;
        }
        answer += now*mul;
    }    
    cout << answer << endl;
}