#725834 (C++17(gcc12)) No.1783 Remix Sum

• 問題: No.1783 Remix Sum
• ユーザー: tko919
• 提出日時: 2021-12-22 14:39:37
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 9,783 ms / 10,000 ms
• コード長: 12,928 bytes
• コンパイル時間: 9,047 ms
• コンパイル使用メモリ: 277,392 KB
• 最終ジャッジ日時: 2025-01-27 05:21:06
• ジャッジサーバーID （参考情報）: judge4 / judge1

ファイルパターン	結果
sample	AC * 4
other	AC * 76

ソースコード

#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; const double eps=1e-12;
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;}

template<int mod=120586241>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(int x){v=(x<mod?x:x-mod); return *this;}
    fp operator-()const{return fp()-*this;}
    fp pow(ll t){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;}
}; using Fp=fp<>;
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);}
};

template<typename T=Fp,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;
    }
};

NTT<Fp,6> ntt;
vector<Fp> mult(const vector<Fp>& a,const vector<Fp>& b,bool same=0){
    return ntt.mult(a,b,same);
}
factorial<Fp> fact(2010101);
template<typename T=Fp>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();}
    Poly inv()const{
        assert(this->front()!=0); const int n=this->size();
        Poly res(1); res.front()=T(1)/this->front();
        for(int k=1;k<n;k<<=1){
            Poly g=res,h=*this; h.resize(k*2); res.resize(k*2);
            g=(g.square()*h); g.resize(k*2);
            rep(i,k,min(k*2,n))res[i]-=g[i];
        }
        res.resize(n); return res;
    }
    Poly square()const{return Poly(mult(*this,*this,1));}
    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)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];} shrink(); 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];} shrink(); return *this;
    }
    Poly& operator*=(const Poly& g){
        *this=mult(*this,g,0);
        shrink(); 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_fast(); 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]*fact.inv(i);
        return res;
    }
    Poly log()const{
        assert(this->front()==1); const int n=this->size();
        Poly res=diff()*inv_fast(); res=res.inte(); //
        res.resize(n); return res;
    }
    Poly exp()const{
        assert(this->front()==0); const int n=this->size();
        Poly res(1),g(1); res.front()=g.front()=1;
        for(int k=1;k<n;k<<=1){
            g=(g+g-g.square()*res); g.resize(k);
            Poly q=*this; q.resize(k); q=q.diff();
            Poly w=(q+g*(res.diff()-res*q)),t=*this;
            w.resize(k*2-1); t.resize(k*2);
            res=(res+res*(t-w.inte())); res.resize(k*2);
        } 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*fact.inv(i);
        rep(i,0,n){res[i]*=fact.fact(i);} res=res.rev();
        res*=g; res.resize(n); res=res.rev();
        rep(i,0,n){res[i]*=fact.fact(i,1);} return res;
    }
    Poly inv_fast()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.ntt(f); ntt.ntt(g);
            rep(i,0,k*2)f[i]*=g[i];
            ntt.ntt(f,1);
            rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
            ntt.ntt(f); rep(i,0,k*2)f[i]*=g[i]; ntt.ntt(f,1);
            rep(i,0,k)f[i]=res[i];
            swap(res,f);
        } res.resize(n); return res;
    }
    Poly exp_fast()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.ntt(y); z1=z2;
            Poly z(k);
            rep(i,0,k)z[i]=y[i]*z1[i];
            ntt.ntt(z,1);
            rep(i,0,k>>1)z[i]=0;
            ntt.ntt(z);
            rep(i,0,k)z[i]*=-z1[i];
            ntt.ntt(z,1);
            c.insert(c.end(),z.begin()+(k>>1),z.end());
            z2=c; z2.resize(k*2);
            ntt.ntt(z2);
            Poly x=*this; x.resize(k); x=x.diff(); x.resize(k);
            ntt.ntt(x);
            rep(i,0,k)x[i]*=y[i];
            ntt.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.ntt(x);
            rep(i,0,k*2)x[i]*=z2[i];
            ntt.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.ntt(x);
            rep(i,0,k*2)x[i]*=y[i];
            ntt.ntt(x,1);
            b.insert(b.end(),x.begin()+k,x.end());
        } b.resize(n); return b;
    }
    Poly pow(ll t){
        int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
        Poly res(n); if(t*k>=n)return res;
        n-=t*k; Poly g(n); T c=(*this)[k],ic=T(1)/c;
        rep(i,0,n)g[i]=(*this)[i+k]*ic;
        g=g.log(); for(auto& x:g)x*=t; g=g.exp_fast(); //
        c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
    }
};
Fp nth(Poly<Fp> p,Poly<Fp> q,ll n){
    while(n){
        Poly<Fp> base(q),np,nq;
        for(int i=1;i<(int)q.size();i+=2)base[i]=-base[i];
        p*=base; q*=base;
        for(int i=n&1;i<(int)p.size();i+=2)np.emplace_back(p[i]);
        for(int i=0;i<(int)q.size();i+=2)nq.emplace_back(q[i]);
        swap(p,np); swap(q,nq);
        n>>=1;
    }
    return p[0]/q[0];
}

Poly<Fp> MultivariateConvolution(const Poly<Fp>& f,const Poly<Fp>& g,vector<int>& a){
    int n=f.size(),k=a.size(),m=1<<__lg(4*n-1);
    if(k==0)return Poly<Fp>({f[0]*g[0]});
    
    vector<int> chi(n);
    rep(x,0,n){
        int t=x;
        rep(i,0,k-1){
            t/=a[i];
            chi[x]+=t;
        }
        chi[x]%=k;
    }

    vector F(k,Poly<Fp>(m)),G(k,Poly<Fp>(m));
    rep(i,0,n){
        F[chi[i]][i]=f[i];
        G[chi[i]][i]=g[i];
    }

    for(auto& v:F)ntt.ntt(v);
    for(auto& v:G)ntt.ntt(v);
    rep(x,0,m){
        Poly<Fp> tmp(k);
        rep(i,0,k)rep(j,0,k){
            tmp[(i+j)%k]+=F[i][x]*G[j][x];
        }
        rep(i,0,k)F[i][x]=tmp[i];
    }
    for(auto& v:F)ntt.ntt(v,1);
    Poly<Fp> res(n);
    rep(i,0,n)res[i]=F[chi[i]][i];
    return res;
}

const int ten[]={1,10,100,1000,10000,100000};

const Fp g=Fp(6).pow((Fp::get_mod()-1)/10);
const Fp ig=g.inv();
const Fp inv10=Fp(10).inv();
void ntt10(vector<Fp>& a){
    Fp cur=1;
    vector<Fp> b(10);
    rep(i,0,10){
        for(int j=a.size()-1;j>=0;j--){
            b[i]*=cur;
            b[i]+=a[j];
        }
        cur*=g;
    }
    a=b;
}
void intt10(vector<Fp>& a){
    Fp cur=1;
    vector<Fp> b(10);
    rep(i,0,10){
        for(int j=a.size()-1;j>=0;j--){
            b[i]*=cur;
            b[i]+=a[j];
        }
        cur*=ig;
    }
    rep(i,0,10)b[i]*=inv10;
    a=b;
}

Fp nCr(ll n,int r){
    Fp ret=1;
    for(ll x=n-r+1;x<=n;x++)ret*=x;
    ret*=fact.fact(r,1);
    return ret;
}

void Pow(Poly<Fp>& f,ll t,int k){
    vector<int> a(k,10);
    Poly<Fp> ret(f.size()),add(f.size());
    // ret[0]=1;
    // while(t){
    //     if(t&1){
    //         ret=MultivariateConvolution(ret,f,a);
    //     }
    //     f=MultivariateConvolution(f,f,a);
    //     t>>=1;
    // }

    Fp f0=f[0];
    const Fp invf0=f0.inv();
    Fp coeff=f0.pow(t);
    f[0]-=f0;
    add[0]=1;
    rep(d,0,50){
        if(t<d)break;
        if(f0==0 and d==t)coeff=1;
        rep(i,0,f.size())ret[i]+=add[i]*coeff*nCr(t,d);
        add=MultivariateConvolution(add,f,a);
        coeff*=invf0;
    }
    f=ret;
}

int main(){
    int n,k,t;
    ll m;
    cin>>n>>k>>m>>t;
    Poly<Fp> a(ten[k]);
    rep(_,0,n){
        int x;
        cin>>x;
        a[x]+=1;
    }

    rep(d,t,k){
        rep(base,0,ten[k]){
            if((base/ten[d])%10)continue;
            vector<Fp> tmp(10);
            rep(x,0,10)tmp[x]=a[x*ten[d]+base];
            ntt10(tmp);
            rep(x,0,10)a[x*ten[d]+base]=tmp[x];
        }
    }

    rep(base,0,ten[k-t]){
        Poly<Fp> tmp(ten[t]);
        rep(i,0,ten[t])tmp[i]=a[i+base*ten[t]];
        Pow(tmp,m,t);
        rep(i,0,ten[t])a[i+base*ten[t]]=tmp[i];
    }

    rep(d,t,k){
        rep(base,0,ten[k]){
            if((base/ten[d])%10)continue;
            vector<Fp> tmp(10);
            rep(x,0,10)tmp[x]=a[x*ten[d]+base];
            intt10(tmp);
            rep(x,0,10)a[x*ten[d]+base]=tmp[x];
        }
    }

    rep(i,0,ten[k])cout<<a[i]<<'\n';
    return 0;
}