#1100266 (C++17) No.3187 Mingle

• 問題: No.3187 Mingle
• ユーザー: GOTKAKO
• 提出日時: 2025-06-20 22:58:30
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 493 ms / 2,500 ms
• コード長: 6,070 bytes
• コンパイル時間: 2,291 ms
• コンパイル使用メモリ: 205,092 KB
• 実行使用メモリ: 47,588 KB
• 最終ジャッジ日時: 2025-06-20 22:58:54
• 合計ジャッジ時間: 11,693 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 30

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>
struct modint{ //mod変更が不可能.
    public:
    long long v = 0;
    static void setmod(int m){} //飾り.
    static constexpr long long getmod(){return mod;}
    modint(){v = 0;} modint(int a){v = a<0?a+mod:a;} modint(long long a){v = a<0?a+mod:a;}
    modint(unsigned int a){v = a;} modint(unsigned long long a){v = a;}
    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.
        if(b == 0) assert(false);
        int left = mod-2;
        while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
        return *this;
    }
    modint operator++(){*this += 1; return *this;}
    modint operator--(){*this -= 1; return *this;}
    modint operator++(int){*this += 1; return *this;}
    modint operator--(int){*this -= 1; return *this;}
    bool operator==(const modint b)const{return v == b.v;}
    bool operator!=(const modint b)const{return v != b.v;}
    bool operator>(const modint b)const{return v > b.v;}
    bool operator>=(const modint b)const{return v >= b.v;}
    bool operator<(const modint b)const{return v < b.v;}
    bool operator<=(const modint b)const{return v <= b.v;}
    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 modint(1)/v;} //素数mod必須.
};
 
template<int idx> //modが入力で与えられる場合. 
struct dynamic_modint{ //mod変更が可能 最初にsetmod必須 idxで複数個所持が可能.
    private:
    static int mod;
    public:
    long long v = 0;
    static constexpr long long getmod(){return mod;}
    static void setmod(int m){
        assert(m > 0);
        mod = m;
    }
    dynamic_modint(){v = 0;}
    dynamic_modint(int a){v = a<0?a+mod:a;} dynamic_modint(long long a){v = a<0?a+mod:a;}
    dynamic_modint(unsigned int a){v = a;}
    dynamic_modint(unsigned long long a){v = a;}
    long long val()const{return v;}
 
    dynamic_modint &operator=(const dynamic_modint &b) = default;
    dynamic_modint operator+()const{return (*this);}
    dynamic_modint operator-()const{return dynamic_modint(0)-(*this);}
    dynamic_modint operator+(const dynamic_modint b)const{return dynamic_modint(v)+=b;}
    dynamic_modint operator-(const dynamic_modint b)const{return dynamic_modint(v)-=b;}
    dynamic_modint operator*(const dynamic_modint b)const{return dynamic_modint(v)*=b;}
    dynamic_modint operator/(const dynamic_modint b)const{return dynamic_modint(v)/=b;}
    dynamic_modint operator+=(const dynamic_modint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    dynamic_modint operator-=(const dynamic_modint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    dynamic_modint operator*=(const dynamic_modint b){v = v*b.v%mod; return *this;}
    dynamic_modint operator/=(dynamic_modint b){ //b!=0 mod素数が必須.
        if(b == 0) assert(false);
        int left = mod-2;
        while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
        return *this;
    }
    dynamic_modint operator++(){*this += 1; return *this;}
    dynamic_modint operator--(){*this -= 1; return *this;}
    dynamic_modint operator++(int){*this += 1; return *this;}
    dynamic_modint operator--(int){*this -= 1; return *this;}
    bool operator==(const dynamic_modint b)const{return v == b.v;}
    bool operator!=(const dynamic_modint b)const{return v != b.v;}
    bool operator>(const dynamic_modint b)const{return v > b.v;}
    bool operator>=(const dynamic_modint b)const{return v >= b.v;}
    bool operator<(const dynamic_modint b)const{return v < b.v;}
    bool operator<=(const dynamic_modint b)const{return v <= b.v;}
    dynamic_modint pow(long long n)const{
        dynamic_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;
    }
    dynamic_modint inv()const{return dynamic_modint(1)/v;} //素数mod必須.
};
template<int idx> int dynamic_modint<idx>::mod=998244353;
using mint = dynamic_modint<0>;

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

    int N,mod; cin >> N >> mod;
    mint::setmod(mod);

    int Limit = N; //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.

    vector<vector<int>> D(N+1);
    for(int i=1; i<=N; i++) for(int k=i; k<=N; k+=i) D.at(k).push_back(i);

    mint all = 0;
    vector<mint> S(N+1);
    vector<mint> dp(N+1);
    for(int i=3; i<=N; i++){
        int ng = D.at(i).size();
        for(auto &d : D.at(i)) all -= S.at(d),S.at(d) = 0;
        dp.at(i) = all*inv.at(i-ng)+inv.at(i-ng)*i;
        for(auto &d : D.at(i)) S.at(d) = dp.at(i),all += S.at(d);
    }

    cout << dp.at(N).v << endl;
}