#828962 (C++17) No.2097 AND^k

提出ソース
結果

問題	No.2097 AND^k
ユーザー	tko919
提出日時	2022-12-29 03:00:53
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	226 ms / 5,000 ms
コード長	15,284 bytes
コンパイル時間	3,459 ms
コンパイル使用メモリ	223,868 KB
実行使用メモリ	10,564 KB
最終ジャッジ日時	2024-11-24 05:12:16
合計ジャッジ時間	7,431 ms
ジャッジサーバーID （参考情報）	judge2 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	6 ms 5,760 KB
testcase_01	AC	6 ms 5,504 KB
testcase_02	AC	6 ms 5,632 KB
testcase_03	AC	6 ms 5,632 KB
testcase_04	AC	6 ms 5,760 KB
testcase_05	AC	5 ms 5,504 KB
testcase_06	AC	6 ms 5,632 KB
testcase_07	AC	6 ms 5,632 KB
testcase_08	AC	112 ms 8,504 KB
testcase_09	AC	60 ms 6,880 KB
testcase_10	AC	108 ms 8,408 KB
testcase_11	AC	57 ms 6,960 KB
testcase_12	AC	55 ms 6,824 KB
testcase_13	AC	226 ms 10,560 KB
testcase_14	AC	225 ms 10,556 KB
testcase_15	AC	225 ms 10,432 KB
testcase_16	AC	226 ms 10,560 KB
testcase_17	AC	224 ms 10,560 KB
testcase_18	AC	225 ms 10,560 KB
testcase_19	AC	225 ms 10,560 KB
testcase_20	AC	225 ms 10,560 KB
testcase_21	AC	225 ms 10,556 KB
testcase_22	AC	225 ms 10,560 KB
testcase_23	AC	226 ms 10,564 KB
testcase_24	AC	6 ms 5,632 KB
testcase_25	AC	225 ms 10,348 KB
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ソースコード

raw source code
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
using ll=long long int;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO{
    static constexpr int L=1<<16;
    char rdbuf[L];
    int rdLeft=0,rdRight=0;
    inline void reload(){
        int len=rdRight-rdLeft;
        memmove(rdbuf,rdbuf+rdLeft,len);
        rdLeft=0,rdRight=len;
        rdRight+=fread(rdbuf+len,1,L-len,stdin);
    }
    inline bool skip(){
        for(;;){
            while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
            if(rdLeft==rdRight){
                reload();
                if(rdLeft==rdRight)return false;
            }
            else break;
        }
        return true;
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        if(rdbuf[rdLeft]!='.')return true;
        rdLeft++;
        T base=.1;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x+=base*(rdbuf[rdLeft++]^48);
            base*=.1;
        }
        if(neg)x=-x;
        return true;
    }
    inline bool _read(char& x){
        if(!skip())return false;
        if(rdLeft+1>=rdRight)reload();
        x=rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string& x){
        if(!skip())return false;
        for(;;){
            int pos=rdLeft;
            while(pos<rdRight and rdbuf[pos]>' ')pos++;
            x.append(rdbuf+rdLeft,pos-rdLeft);
            if(rdLeft==pos)break;
            rdLeft=pos;
            if(rdLeft==rdRight)reload();
            else break;
        }
        return true;
    }
    template<typename T>inline bool _read(vector<T>& v){
        for(auto& x:v){
            if(!_read(x))return false;
        }
        return true;
    }

    char wtbuf[L],tmp[50];
    int wtRight=0;
    inline void flush(){
        fwrite(wtbuf,1,wtRight,stdout);
        wtRight=0;
    }
    inline void _write(const char& x){
        if(wtRight>L-32)flush();
        wtbuf[wtRight++]=x;
    }
    inline void _write(const string& x){
        for(auto& c:x)_write(c);
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
        if(wtRight>L-32)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2: _write("32768"); return;
                case 4: _write("2147483648"); return;
                case 8: _write("9223372036854775808"); return;
                }
            }
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    template<typename T>inline void _write(const vector<T>& v){
        rep(i,0,v.size()){
            if(i)_write(' ');
            _write(v[i]);
        }
    }
public:
    FastIO(){}
    ~FastIO(){flush();}
    inline void read(){}
    template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
        assert(_read(head));
        read(tail...); 
    }
    template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
    template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
        if(space)_write(' ');
        _write(head);
        write<ln,true>(tail...); 
    }
};

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Math/modint.hpp"

template<int mod=1000000007>struct fp {
    int v; static int get_mod(){return mod;}
    int inv() const{
        int tmp,a=v,b=mod,x=1,y=0;
        while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
        if(x<0){x+=mod;} return x;
    }
    fp(ll x=0){init(x%mod+mod);}
    fp& init(ll x){v=(x<mod?x:x-mod); return *this;}
    fp operator-()const{return fp()-*this;}
    fp pow(ll t){assert(t>=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
    fp& operator+=(const fp& x){return init(v+x.v);}
    fp& operator-=(const fp& x){return init(v+mod-x.v);}
    fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
    fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
    fp operator+(const fp& x)const{return fp(*this)+=x;}
    fp operator-(const fp& x)const{return fp(*this)-=x;}
    fp operator*(const fp& x)const{return fp(*this)*=x;}
    fp operator/(const fp& x)const{return fp(*this)/=x;}
    bool operator==(const fp& x)const{return v==x.v;}
    bool operator!=(const fp& x)const{return v!=x.v;}
    friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
    friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};
template<typename T>struct factorial {
    vector<T> Fact,Finv,Inv;
    factorial(int maxx){
        Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
        Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;
        rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();
        for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}
    }
    T fact(int n,bool inv=0){if(n<0)return 0; return (inv?Finv[n]:Fact[n]);}
    T inv(int n){if(n<0)return 0; return Inv[n];}
    T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(n-r,inv^1);}
    T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(r,inv^1)*fact(n-r,inv^1);}
    T nHr(int n,int r,bool inv=0){return nCr(n+r-1,r,inv);}
};

/**
 * @brief Modint
 */
#line 2 "library/Convolution/ntt.hpp"

template<typename T,unsigned p=3>struct NTT{
    vector<T> rt,irt;
    NTT(int lg=21){
        unsigned m=T::get_mod()-1; T prt=p;
        rt.resize(lg); irt.resize(lg);
        rep(k,0,lg){
            rt[k]=-prt.pow(m>>(k+2));
            irt[k]=rt[k].inv();
        }
    }
    void ntt(vector<T>& f,bool inv=0){
        int n=f.size();
        if(inv){
            for(int m=1;m<n;m<<=1){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j];
                        f[i]=x+y; f[j]=(x-y)*w;
                    } w*=irt[__builtin_ctz(++t)];
                }
             } T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
        }else{
            for(int m=n;m>>=1;){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j]*w;
                        f[i]=x+y; f[j]=x-y;
                    } w*=rt[__builtin_ctz(++t)];
                }
            }
         }
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
            ntt(c); rep(i,0,m)res[i]*=c[i];
        } ntt(res,1); res.resize(n); return res;
    }
};

/**
 * @brief Number Theoretic Transform
 */
#line 2 "library/FPS/fps.hpp"

template<typename T>struct Poly:vector<T>{
    Poly(int n=0){this->assign(n,T());}
    Poly(const vector<T>& f){this->assign(ALL(f));}
    T eval(const T& x){
        T res;
        for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);
        return res;
    }
    Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
    void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0)const{
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m);
        rep(i,0,a.size())res[i]=a[i];
        NTT(res,0);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m);
            rep(i,0,b.size())c[i]=b[i];
            NTT(c,0);
            rep(i,0,m)res[i]*=c[i];
        }
        NTT(res,1);
        res.resize(n);
        return res;
    }
    Poly square()const{return Poly(mult(*this,*this,1));}
    Poly operator-()const{return Poly()-*this;}
    Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
    Poly operator+(const T& g)const{return Poly(*this)+=g;}
    Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
    Poly operator-(const T& g)const{return Poly(*this)-=g;}
    Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
    Poly operator*(const T& g)const{return Poly(*this)*=g;}
    Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
    Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
    Poly& operator+=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;
    }
    Poly& operator+=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]+=g; return *this;
    }
    Poly& operator-=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;
    }
    Poly& operator-=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]-=g; return *this;
    }
    Poly& operator*=(const Poly& g){
        *this=mult(*this,g,0);
        return *this;
    }
    Poly& operator*=(const T& g){
        rep(i,0,this->size())(*this)[i]*=g;
        return *this;
    }
    Poly& operator/=(const Poly& g){
        if(g.size()>this->size()){
            this->clear(); return *this;
        }
        Poly g2=g;
        reverse(ALL(*this));
        reverse(ALL(g2));
        int n=this->size()-g2.size()+1;
        this->resize(n); g2.resize(n);
        *this*=g2.inv(); this->resize(n); 
        reverse(ALL(*this));
        shrink();
        return *this;
    }
    Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}
    Poly diff()const{
        Poly res(this->size()-1);
        rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
        return res;
    }
    Poly inte()const{
        Poly res(this->size()+1);
        for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;
        return res;
    }
    Poly log()const{
        assert(this->front()==1); const int n=this->size();
        Poly res=diff()*inv(); res=res.inte(); 
        res.resize(n); return res;
    }
    Poly shift(const int& c)const{
        const int n=this->size();
        Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;
        vector<T> fact(n,1);
        rep(i,0,n){
            if(i)fact[i]=fact[i-1]*i;
            res[i]*=fact[i];
        }
        res=res.rev();
        res*=g;
        res.resize(n);
        res=res.rev();
        rep(i,0,n)res[i]/=fact[i];
        return res;
    }
    Poly inv()const{
        const int n=this->size();
        Poly res(1); res.front()=T(1)/this->front();
        for(int k=1;k<n;k<<=1){
            Poly f(k*2),g(k*2);
            rep(i,0,min(n,k*2))f[i]=(*this)[i];
            rep(i,0,k)g[i]=res[i];
            NTT(f,0);
            NTT(g,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
            NTT(f,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k)f[i]=res[i];
            swap(res,f);
        } res.resize(n); return res;
    }
    Poly exp()const{
        const int n=this->size();
        if(n==1)return Poly({T(1)});
        Poly b(2),c(1),z1,z2(2);
        b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
        for(int k=2;k<n;k<<=1){
            Poly y=b;
            y.resize(k*2);
            NTT(y,0);
            z1=z2;
            Poly z(k);
            rep(i,0,k)z[i]=y[i]*z1[i];
            NTT(z,1);
            rep(i,0,k>>1)z[i]=0;
            NTT(z,0);
            rep(i,0,k)z[i]*=-z1[i];
            NTT(z,1);
            c.insert(c.end(),z.begin()+(k>>1),z.end());
            z2=c;
            z2.resize(k*2);
            NTT(z2,0);
            Poly x=*this;
            x.resize(k);
            x=x.diff();x.resize(k);
            NTT(x,0);
            rep(i,0,k)x[i]*=y[i];
            NTT(x,1);
            Poly bb=b.diff();
            rep(i,0,k-1)x[i]-=bb[i];
            x.resize(k*2);
            rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
            NTT(x,0);
            rep(i,0,k*2)x[i]*=z2[i];
            NTT(x,1);
            x.pop_back();
            x=x.inte();
            rep(i,k,min(n,k*2))x[i]+=(*this)[i];
            rep(i,0,k)x[i]=0;
            NTT(x,0);
            rep(i,0,k*2)x[i]*=y[i];
            NTT(x,1);
            b.insert(b.end(),x.begin()+k,x.end());
        } b.resize(n); return b;
    }
    Poly pow(ll t){
        if(t==0){
            Poly res(this->size()); res[0]=1;
            return res;
        }
        int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
        Poly res(n); if(__int128_t(t)*k>=n)return res;
        n-=t*k; Poly g(n); T c=(*this)[k],ic=c.inv();
        rep(i,0,n)g[i]=(*this)[i+k]*ic;
        g=g.log(); for(auto& x:g)x*=t; g=g.exp();
        c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
    }
    void NTT(vector<T>& a,bool inv)const;
};

/**
 * @brief Formal Power Series (NTT-friendly mod)
 */
#line 7 "sol.cpp"
using Fp=fp<998244353>;
NTT<Fp,3> ntt;
template<>void Poly<Fp>::NTT(vector<Fp>& v,bool inv)const{return ntt.ntt(v,inv);}

template<typename T>Poly<T> ProdOf_f_rk_x(Poly<T>& f,T r,int m){ // f(x)f(rx)...f(r^{m-1}x)
    assert(f[0]==1);
    T pwr=1,rm=T(r).pow(m),pwrm=1;
    auto g=f.log();
    rep(i,1,g.size()){
        pwr*=r;
        pwrm*=rm;
        if(pwr==1)g[i]*=m;
        else g[i]*=(pwrm-1)/(pwr-1);
    }
    return g.exp();
}   

factorial<Fp> fact(201010);

FastIO io;
int main(){
    int n,m,L;
    io.read(n,m,L);

    Fp two=Fp(2).pow(n).inv();
    Poly<Fp> f(L+1);
    f[0]=1;
    rep(i,1,L+1)f[i]=fact.fact(i,1)*two;
    auto ret=ProdOf_f_rk_x(f,Fp(2),m);
    two=Fp(2).pow(ll(n)*m);
    rep(i,1,L+1){
        ret[i]*=fact.fact(i)*two;
        io.write(ret[i].v);
    }
    return 0;
}
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結果

テストケース

ソースコード
