結果

問題 No.1145 Sums of Powers
ユーザー beetbeet
提出日時 2020-07-31 22:38:12
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 901 ms / 2,000 ms
コード長 9,321 bytes
コンパイル時間 3,207 ms
コンパイル使用メモリ 223,556 KB
最終ジャッジ日時 2025-01-12 10:54:35
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
other AC * 6
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
using Int = long long;
const char newl = '\n';


template<typename T,T MOD = 1000000007>
struct Mint{
  static constexpr T mod = MOD;
  T v;
  Mint():v(0){}
  Mint(signed v):v(v){}
  Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}

  Mint pow(long long k){
    Mint res(1),tmp(v);
    while(k){
      if(k&1) res*=tmp;
      tmp*=tmp;
      k>>=1;
    }
    return res;
  }

  static Mint add_identity(){return Mint(0);}
  static Mint mul_identity(){return Mint(1);}

  Mint inv(){return pow(MOD-2);}

  Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
  Mint& operator/=(Mint a){return (*this)*=a.inv();}

  Mint operator+(Mint a) const{return Mint(v)+=a;}
  Mint operator-(Mint a) const{return Mint(v)-=a;}
  Mint operator*(Mint a) const{return Mint(v)*=a;}
  Mint operator/(Mint a) const{return Mint(v)/=a;}

  Mint operator-() const{return v?Mint(MOD-v):Mint(v);}

  bool operator==(const Mint a)const{return v==a.v;}
  bool operator!=(const Mint a)const{return v!=a.v;}
  bool operator <(const Mint a)const{return v <a.v;}

  static Mint comb(long long n,int k){
    Mint num(1),dom(1);
    for(int i=0;i<k;i++){
      num*=Mint(n-i);
      dom*=Mint(i+1);
    }
    return num/dom;
  }
};
template<typename T,T MOD> constexpr T Mint<T, MOD>::mod;
template<typename T,T MOD>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}



template<typename M_>
class Enumeration{
  using M = M_;
protected:
  static vector<M> fact,finv,invs;
public:
  static void init(int n){
    n=min<decltype(M::mod)>(n,M::mod-1);

    int m=fact.size();
    if(n<m) return;

    fact.resize(n+1,1);
    finv.resize(n+1,1);
    invs.resize(n+1,1);

    if(m==0) m=1;
    for(int i=m;i<=n;i++) fact[i]=fact[i-1]*M(i);
    finv[n]=M(1)/fact[n];
    for(int i=n;i>=m;i--) finv[i-1]=finv[i]*M(i);
    for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1];
  }

  static M Fact(int n){
    init(n);
    return fact[n];
  }
  static M Finv(int n){
    init(n);
    return finv[n];
  }
  static M Invs(int n){
    init(n);
    return invs[n];
  }

  static M C(int n,int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k]*finv[k];
  }

  static M P(int n,int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k];
  }

  // put n identical balls into k distinct boxes
  static M H(int n,int k){
    if(n<0||k<0) return M(0);
    if(!n&&!k) return M(1);
    init(n+k);
    return C(n+k-1,n);
  }
};
template<typename M>
vector<M> Enumeration<M>::fact=vector<M>();
template<typename M>
vector<M> Enumeration<M>::finv=vector<M>();
template<typename M>
vector<M> Enumeration<M>::invs=vector<M>();


constexpr int bmds(int x){
  const int v[] = {1012924417, 924844033, 998244353,
                   897581057, 645922817};
  return v[x];
}
constexpr int brts(int x){
  const int v[] = {5, 5, 3, 3, 3};
  return v[x];
}

template<int X>
struct NTT{
  static constexpr int md = bmds(X);
  static constexpr int rt = brts(X);
  using M = Mint<int, md>;
  vector< vector<M> > rts,rrts;

  void ensure_base(int n){
    if((int)rts.size()>=n) return;
    rts.resize(n);rrts.resize(n);
    for(int i=1;i<n;i<<=1){
      if(!rts[i].empty()) continue;
      M w=M(rt).pow((md-1)/(i<<1));
      M rw=w.inv();
      rts[i].resize(i);rrts[i].resize(i);
      rts[i][0]=M(1);rrts[i][0]=M(1);
      for(int k=1;k<i;k++){
        rts[i][k]=rts[i][k-1]*w;
        rrts[i][k]=rrts[i][k-1]*rw;
      }
    }
  }

  void ntt(vector<M> &as,bool f){
    int n=as.size();
    assert((n&(n-1))==0);
    ensure_base(n);

    for(int i=0,j=1;j+1<n;j++){
      for(int k=n>>1;k>(i^=k);k>>=1);
      if(i>j) swap(as[i],as[j]);
    }

    for(int i=1;i<n;i<<=1){
      for(int j=0;j<n;j+=i*2){
        for(int k=0;k<i;k++){
          M z=as[i+j+k]*(f?rrts[i][k]:rts[i][k]);
          as[i+j+k]=as[j+k]-z;
          as[j+k]+=z;
        }
      }
    }

    if(f){
      M tmp=M(n).inv();
      for(int i=0;i<n;i++) as[i]*=tmp;
    }
  }

  vector<M> multiply(vector<M> as,vector<M> bs){
    int need=as.size()+bs.size()-1;
    int sz=1;
    while(sz<need) sz<<=1;
    as.resize(sz,M(0));
    bs.resize(sz,M(0));

    ntt(as,0);ntt(bs,0);
    for(int i=0;i<sz;i++) as[i]*=bs[i];
    ntt(as,1);

    as.resize(need);
    return as;
  }

  vector<int> multiply(vector<int> as,vector<int> bs){
    vector<M> am(as.size()),bm(bs.size());
    for(int i=0;i<(int)am.size();i++) am[i]=M(as[i]);
    for(int i=0;i<(int)bm.size();i++) bm[i]=M(bs[i]);
    vector<M> cm=multiply(am,bm);
    vector<int> cs(cm.size());
    for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v;
    return cs;
  }
};
template<int X> constexpr int NTT<X>::md;
template<int X> constexpr int NTT<X>::rt;


template<typename M_>
struct FormalPowerSeries : Enumeration<M_> {
  using M = M_;
  using super = Enumeration<M>;
  using super::fact;
  using super::finv;
  using super::invs;

  using Poly = vector<M>;
  using Conv = function<Poly(Poly, Poly)>;
  Conv conv;
  FormalPowerSeries(Conv conv):conv(conv){}

  Poly pre(const Poly &as,int deg){
    return Poly(as.begin(),as.begin()+min((int)as.size(),deg));
  }

  Poly add(Poly as,Poly bs){
    int sz=max(as.size(),bs.size());
    Poly cs(sz,M(0));
    for(int i=0;i<(int)as.size();i++) cs[i]+=as[i];
    for(int i=0;i<(int)bs.size();i++) cs[i]+=bs[i];
    return cs;
  }

  Poly sub(Poly as,Poly bs){
    int sz=max(as.size(),bs.size());
    Poly cs(sz,M(0));
    for(int i=0;i<(int)as.size();i++) cs[i]+=as[i];
    for(int i=0;i<(int)bs.size();i++) cs[i]-=bs[i];
    return cs;
  }

  Poly mul(Poly as,Poly bs){
    return conv(as,bs);
  }

  Poly mul(Poly as,M k){
    for(auto &a:as) a*=k;
    return as;
  }

  // F(0) must not be 0
  Poly inv(Poly as,int deg){
    assert(as[0]!=M(0));
    Poly rs({M(1)/as[0]});
    for(int i=1;i<deg;i<<=1)
      rs=pre(sub(add(rs,rs),mul(mul(rs,rs),pre(as,i<<1))),i<<1);
    return rs;
  }

  // not zero
  Poly div(Poly as,Poly bs){
    while(as.back()==M(0)) as.pop_back();
    while(bs.back()==M(0)) bs.pop_back();
    if(bs.size()>as.size()) return Poly();
    reverse(as.begin(),as.end());
    reverse(bs.begin(),bs.end());
    int need=as.size()-bs.size()+1;
    Poly ds=pre(mul(as,inv(bs,need)),need);
    reverse(ds.begin(),ds.end());
    return ds;
  }

  Poly mod(Poly as,Poly bs){
    if(as==Poly(as.size(),0)) return Poly({0});
    as=sub(as,mul(div(as,bs),bs));
    if(as==Poly(as.size(),0)) return Poly({0});
    while(as.back()==M(0)) as.pop_back();
    return as;
  }

  // F(0) must be 1
  Poly sqrt(Poly as,int deg){
    assert(as[0]==M(1));
    M inv2=M(1)/M(2);
    Poly ss({M(1)});
    for(int i=1;i<deg;i<<=1){
      ss=pre(add(ss,mul(pre(as,i<<1),inv(ss,i<<1))),i<<1);
      for(M &x:ss) x*=inv2;
    }
    return ss;
  }

  Poly diff(Poly as){
    int n=as.size();
    Poly rs(n-1);
    for(int i=1;i<n;i++) rs[i-1]=as[i]*M(i);
    return rs;
  }

  Poly integral(Poly as){
    super::init(as.size()+1);
    int n=as.size();
    Poly rs(n+1);
    rs[0]=M(0);
    for(int i=0;i<n;i++) rs[i+1]=as[i]*invs[i+1];
    return rs;
  }

  // F(0) must be 1
  Poly log(Poly as,int deg){
    return pre(integral(mul(diff(as),inv(as,deg))),deg);
  }

  // F(0) must be 0
  Poly exp(Poly as,int deg){
    Poly fs({M(1)});
    as[0]+=M(1);
    for(int i=1;i<deg;i<<=1)
      fs=pre(mul(fs,sub(pre(as,i<<1),log(fs,i<<1))),i<<1);
    return fs;
  }

  // not zero
  Poly pow(Poly as,long long k,int deg){
    if(as==Poly(as.size(),M(0))) return Poly(deg,M(0));

    int cnt=0;
    while(as[cnt]==M(0)) cnt++;
    if(cnt*k>=deg) return Poly(deg,M(0));
    as.erase(as.begin(),as.begin()+cnt);
    deg-=cnt*k;

    M c=as[0];
    Poly zs(cnt*k,M(0));
    Poly rs=mul(exp(mul(log(mul(as,c.inv()),deg),M(k)),deg),c.pow(k));
    zs.insert(zs.end(),rs.begin(),rs.end());
    return pre(zs,deg+cnt*k);
  }

  // x -> x + c
  Poly shift(Poly as,M c){
    super::init(as.size()+1);
    int n=as.size();
    for(int i=0;i<n;i++) as[i]*=fact[i];
    reverse(as.begin(),as.end());
    Poly bs(n,M(1));
    for(int i=1;i<n;i++)
      bs[i]=bs[i-1]*c*invs[i];
    as=pre(mul(as,bs),n);
    reverse(as.begin(),as.end());
    for(int i=0;i<n;i++) as[i]*=finv[i];
    return as;
  }
};

//INSERT ABOVE HERE
signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  int n,m;
  cin>>n>>m;

  vector<int> as(n);
  for(int i=0;i<n;i++) cin>>as[i];

  NTT<2> ntt;
  using M = decltype(ntt)::M;
  using Poly = vector<M>;
  using P = pair<Poly, Poly>;
  auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  queue<P> que;
  for(int a:as)
    que.emplace(Poly({M(1)}),Poly({M(1),-M(a)}));

  while(que.size()>1){
    auto x=que.front();que.pop();
    auto y=que.front();que.pop();

    Poly num=FPS.add(FPS.mul(x.first,y.second),FPS.mul(y.first,x.second));
    Poly den=FPS.mul(x.second,y.second);
    que.emplace(num,den);
  }

  auto p=que.front();
  Poly rs=FPS.mul(p.first,FPS.inv(p.second,m));
  for(int i=1;i<=m;i++){
    if(i!=1) cout<<' ';
    cout<<rs[i];
  }
  cout<<newl;
  return 0;
}
0