#1158634 (C++17) No.3505 Sum of Prod of Root

• 問題: No.3505 Sum of Prod of Root
• ユーザー: GOTKAKO
• 提出日時: 2026-04-18 00:35:49
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 293 ms / 2,000 ms
• コード長: 7,759 bytes
• コンパイル時間: 2,608 ms
• コンパイル使用メモリ: 230,772 KB
• 実行使用メモリ: 43,428 KB
• 最終ジャッジ日時: 2026-04-18 00:36:02
• 合計ジャッジ時間: 4,990 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge2_0

ファイルパターン	結果
sample	AC * 1
other	AC * 13

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;

template<typename T>
bool chmin(T &a,T b){ //a>bならa=bに更新してtrue.
    if(a > b){a = b; return true;}
    else return false;
}
template<typename T> 
bool chmax(T &a,T b){ //a<bならa=bに更新してtrue.
    if(a < b){a = b; return true;}
    else return false;
}
template<typename T> 
T safemod(T a,T m){a %= m,a += m;return a>=m?a-m:a;} //return x = a mod m. 
template<typename T> 
T floor(T a,T b){ //return a/b切り下げ.
    if(b < 0) a *= -1,b *= -1;
    return a<0?(a+1)/b-1:a/b; 
   
}
template<typename T> 
T ceil(T a,T b){ //return a/b切り上げ.
    if(b < 0) a *= -1,b *= -1;
    return a>0?(a-1)/b+1:a/b; 
}
template<typename T> 
pair<T,T> invgcd(T a,T b){
    //return {gcd(a,b),x} (xa≡g(mod b))
    a = safemod(a,b);
    if(a == 0) return {b,0};
    T x = 0,y = 1,memob = b;
    while(a){
        T q = b/a;
        b -= a*q;
        swap(x,y); y -= q*x;
        swap(a,b);
    }
    if(x < 0) x += memob/b;
    return {b,x};
}
template<typename T>
bool isABmoreC(T a,T b,T c){ //a*b=cはfalse
    if(c%b) return a>=ceil(c,b);
    else return a>ceil(c,b);
}
template<typename T>
bool isABmoreC2(T a,T b,T c){return a>=ceil(c,b);} //a*b=cはtrue.
template<typename T>
bool isABlessC(T a,T b,T c){ //a*b=cはfalse.
    if(c%b) return a<=floor(c,b);
    else return a<floor(c,b);
}
template<typename T>
bool isABlessC2(T a,T b,T c){return a<=floor(c,b);} //a*b=cはtrue.
template<typename T>
T Kthpower(T a,int k){ //return a^k オーバーフローは考慮しない.
    T ret = 1;
    while(k){
        if(k&1) ret *= a;
        a *= a; k >>= 1;
    }
    return ret;
}
template<typename T>
pair<T,bool> Kthpower2(T a,int k){ //return {a^k,オーバーした?} オーバーフローは考慮する.
    T ret = 1,maxv = numeric_limits<T>::max();
    while(k){
        if(k&1){
            if(isABmoreC(ret,a,maxv)) return {-1,true};
            ret *= a;
        }
        if(k == 1) break;
        if(isABmoreC(a,a,maxv)) return {-1,true};
        a *= a; k >>= 1;
    }
    return {ret,false};
}
template<typename T>
T Kthroot(T a,int k){ //return floor(a^(1/k));
    assert(k > 0 && a >= 0);
    if(k == 1 || a <= 1) return a;
    T ret = pow(a,1.0/k);
    while(true){
        auto [check,over] = Kthpower2(ret+1,k);
        if(over || check > a) break;
        ret++;
    }    
    while(true){
        auto [check,over] = Kthpower2(ret,k);
        if(!over && check <= a) break;
        ret--;
    }    
    return ret;
}
template<typename T>
T powmod(T a,T b,T m){//a^b(mod m)を返す.
    assert(b >= 0);
    __int128_t ret = 1,p = a;
    while(b){
        if(b&1) ret = ret*p%m;
        p = p*p%m; b >>= 1;
    }
    return T(ret);
}
template<typename T>
T divmod(T a,T b,T m){//a/b(mod m)を返す 素数mod必須.
    return (T)((__int128_t)a*powmod(b,m-2,m)%m); 
}

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

    int Limit = 1001001; //Limit->必要なサイズ fac->x! facinv->1/x! inv->1/x.
    vector<mint> fac(Limit+1,1),facinv(Limit+1);
    {
        int mod = mint::getmod(),invstart = min(mod-1,Limit); 
        for(int i=1; i<=Limit; i++) fac.at(i) = fac.at(i-1)*i;
        facinv.at(invstart) = fac.at(invstart).inv();
        for(int i=invstart-1; i>=0; i--) facinv.at(i) = facinv.at(i+1)*(i+1);
    }
    vector<mint> inv(Limit+1); for(int i=1; i<=Limit; i++) inv.at(i) = fac.at(i-1)*facinv.at(i); //必要なら解放.

    const mint div2 = mint(1)/2,div6 = mint(1)/6,div30 = mint(1)/30;
    auto range1 = [&](long long l,long long r) -> mint {
        if(l > r) return 0;
        mint b = r%mod,a = (l-1)%mod;
        return b*(b+1)*div2-a*(a+1)*div2;
    };
    auto f = [&](long long x,int k) -> mint {
        mint v = x%mod;
        if(k == 2) return v*(v+1)*(v*2+1)*div6;
        if(k == 3) return (v*(v+1)*div2).pow(2);
        if(k == 4) return div30*v*(v+1)*(v*2+1)*(v*v*3+v*3-1);
        cout << "AkaneKawaii" << endl;
        assert(false);
    };
    auto range2 = [&](long long l,long long r) -> mint {
        if(l > r) return 0;
        mint ret = f(r,4)*2+f(r,3)*3+f(r,2);
        ret -= f(l-1,4)*2+f(l-1,3)*3+f(l-1,2);
        return ret;
    };

    long long N; cin >> N;
    vector<pair<long long,long long>> sepa;
    for(int k=3; ; k++){
        long long v = 2;
        for(; ; v++){
            auto [l,over] = Kthpower2(v,k);
            if(over || l > N) break;
            if(l < 0){
                cout << "stop" << endl;
            }
            sepa.push_back({l,k});
        }
        if(v == 2) break;
    }
    sepa.push_back({1,-1}),sepa.push_back({N+1,-1});
    sort(sepa.begin(),sepa.end());
    sepa.erase(unique(sepa.begin(),sepa.end()),sepa.end());

    mint answer = 0,mul = 1;
    vector<int> P(64,1);
   
    for(int i=1; i<sepa.size(); i++){
        auto [l,p] = sepa.at(i-1);
        auto [r,ign] = sepa.at(i);
        if(p != -1) mul *= inv.at(P.at(p)++),mul *= P.at(p);
        if(l == r) continue;
        r--;
        long long l2 = Kthroot(l,2),r2 = Kthroot(r,2);
        answer += range2(l2+1,r2-1)*mul;
        if(l2 == r2) answer += mul*range1(l,r)*l2;
        else answer += mul*(range1(l,(l2+1)*(l2+1)-1)*l2+range1(r2*r2,r)*r2);
    }


    cout << answer << endl;
}