#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T1,typename T2,typename T3>istream &operator>>(istream &is,tuple<T1,T2,T3>&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;}
template<typename T,size_t n>istream &operator>>(istream &is,array<T,n>&a){for(auto&i:a)is>>i;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define overload3(_1,_2,_3,name,...) name
#define rep1(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)
#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)
#define reps(i,l,r) rep2(i,l,r)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)
#define yn(x) cout<<((x)?"Yes\n":"No\n")
#define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end())
template<typename T>
inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();}
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
  if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
  else return init;
}
#ifdef LOCAL
#include<debug.h>
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
struct Timer{
  clock_t start;
  Timer(){
    start=clock();
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout<<fixed<<setprecision(16);
  }
  inline double now(){return (double)(clock()-start)/1000;}
  #ifdef LOCAL
  ~Timer(){
    cerr<<"time:";
    cerr<<now();
    cerr<<"ms\n";
  }
  #endif
}timer;
void SOLVE();
int main(){
  int testcase=1;
  //cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
}
template<typename T>
vector<vector<T>>matrix_mul(const vector<vector<T>>&a,const vector<vector<T>>&b){
  assert(a[0].size()==b.size());
  vector<vector<T>>ret(a.size(),vector<T>(b[0].size(),0));
  rep(i,a.size())rep(j,b.size())rep(k,b[0].size())ret[i][k]+=a[i][j]*b[j][k];
  return ret;
}
template<typename T>
vector<vector<T>>matrix_pow(vector<vector<T>>a,ll k){
  assert(a.size()==a[0].size());
  vector<vector<T>>ret(a.size(),vector<T>(a.size(),0));
  rep(i,a.size())ret[i][i]=1;
  while(k){
    if(k&1)ret=matrix_mul(ret,a);
    a=matrix_mul(a,a);
    k>>=1;
  }
  return ret;
}
template<typename T>
T matrix_det(vector<vector<T>>a){
  if(a.empty())return 1;
  assert(a.size()==a[0].size());
  int n=a.size();
  T ret=1;
  rep(i,n){
    int id=-1;
    reps(j,i,n){
      if(a[j][i]!=0){
        id=j;
        break;
      }
    }
    if(id==-1)return 0;
    if(i!=id){
      ret*=-1;
      swap(a[i],a[id]);
    }
    ret*=a[i][i];
    T inv=a[i][i].inv();
    rep(j,n)a[i][j]*=inv;
    reps(j,i+1,n){
      T x=a[j][i];
      rep(k,n)a[j][k]-=a[i][k]*x;
    }
  }
  return ret;
}
template<typename T>
vector<vector<T>>matrix_inv(vector<vector<T>>a){
  assert(a.size()==a[0].size());
  int n=a.size();
  vector<vector<T>>ret(n,vector<T>(n,0));
  rep(i,n)ret[i][i]=1;
  rep(i,n){
    int id=-1;
    reps(j,i,n){
      if(a[j][i]!=0){
        id=j;
        break;
      }
    }
    if(id==-1)return vector<vector<T>>(n,vector<T>(n,0));
    if(i!=id){
      swap(a[i],a[id]);
      swap(ret[i],ret[id]);
    }
    T inv=a[i][i].inv();
    rep(j,n){
      a[i][j]*=inv;
      ret[i][j]*=inv;
    }
    rep(j,n)if(i!=j){
      T x=a[j][i];
      rep(k,n){
        a[j][k]-=a[i][k]*x;
        ret[j][k]-=ret[i][k]*x;
      }
    }
  }
  return ret;
}
template<typename T>
std::pair<std::vector<T>,std::vector<std::vector<T>>>matrix_linear_equation(std::vector<std::vector<T>>mat,std::vector<T>c){
  int n=mat.size(),m=mat[0].size();
  assert(n==c.size());
  int y=0;
  std::vector<std::pair<int,int>>detv;
  std::vector<int>rankv;
  for(int d=0;d<m;d++){
    int id=-1;
    for(int i=y;i<n;i++)if(mat[i][d].val()){
      id=i;
      break;
    }
    if(id==-1){
      rankv.push_back(d);
      continue;
    }
    for(int j=d;j<n;j++)std::swap(mat[y][j],mat[id][j]);
    std::swap(c[y],c[id]);
    T inv=mat[y][d].inv();
    for(int j=d;j<m;j++)mat[y][j]*=inv;
    c[y]*=inv;
    for(int i=0;i<n;i++)if(i!=y){
      c[i]-=mat[i][d]*c[y];
      for(int j=m-1;j>=d;j--)mat[i][j]-=mat[i][d]*mat[y][j];
    }
    detv.push_back({d,y++});
  }
  for(int i=y;i<n;i++)if(c[i].val())return std::make_pair(std::vector<T>{},std::vector<std::vector<T>>{});
  std::vector<T>ret1(m);
  std::vector<std::vector<T>>ret2(rankv.size(),std::vector<T>(m));
  for(auto [x,i]:detv)ret1[x]=c[i];
  for(int d=0;d<rankv.size();d++){
    ret2[d][rankv[d]]=-1;
    for(auto [x,i]:detv)ret2[d][x]=mat[i][rankv[d]];
  }
  return std::make_pair(ret1,ret2);
}
template<typename T>
std::vector<T>inverse_table(long long l,long long r){
  assert(l<=r);
  if(l==r)return std::vector<T>{};
  l=(l-1)%T::mod();
  r=(r-1)%T::mod();
  if(l<0)l+=T::mod();
  if(r<0)r+=T::mod();
  if(l>r){
    int n=std::max(r,T::mod()-l);
    std::vector<T>fact(n+1),factinv(n+1);
    fact[0]=1;
    for(int i=1;i<=n;i++)fact[i]=fact[i-1]*T::raw(i);
    factinv[n]=fact[n].inv();
    for(int i=n-1;i>=0;i--)factinv[i]=factinv[i+1]*T::raw(i+1);
    std::vector<T>ret;
    ret.reserve(r-l+T::mod());
    for(int i=l+1;i<T::mod();i++)ret.push_back(-fact[T::mod()-i-1]*factinv[T::mod()-i]);
    ret.push_back(0);
    for(int i=1;i<=r;i++)ret.push_back(fact[i-1]*factinv[i]);
    return ret;
  }
  else{
    int n=r-l;
    std::vector<T>ret(n);
    ret[0]=1;
    for(int i=1;i<n;i++)ret[i]=ret[i-1]*T::raw(l+i);
    T inv=(ret[n-1]*(n+l)).inv();
    for(int i=n-1;i>=0;i--){
      ret[i]*=inv;
      inv*=T::raw(i+1+l);
    }
    return ret;
  }
}
#include<initializer_list>
#include<type_traits>
struct is_modint_impl{
  template<typename T>
  static auto check(T&&x)->decltype(x.mod(),std::true_type{});
  template<typename T>
  static auto check(...)->std::false_type;
};
template<typename T>
struct is_modint:public decltype(is_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_modint_v=is_modint<T>::value;
struct is_dynamic_modint_impl{
  template<typename T>
  static auto check(T&&x)->decltype(x.set_mod((typename T::value_type)0),std::true_type{});
  template<typename T>
  static auto check(...)->std::false_type;
};
template<typename T>
struct is_dynamic_modint:public decltype(is_dynamic_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_dynamic_modint_v=is_dynamic_modint<T>::value;
template<typename T>
inline constexpr bool is_static_modint_v=is_modint_v<T>&&!is_dynamic_modint_v<T>;
struct is_uso_modint_impl{
  template<typename T>
  static auto check(T&&x)->decltype(x.uso(),std::true_type{});
  template<typename T>
  static auto check(...)->std::false_type;
};
template<typename T>
struct is_uso_modint:public decltype(is_uso_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_uso_modint_v=is_uso_modint<T>::value;
template<typename T>
struct F{
private:
  static int capacity;
  static std::vector<T>fact,factinv,inv;
public:
  static void resize(int n){
    if(capacity>=n)return;
    fact.resize(n+1),factinv.resize(n+1),inv.resize(n+1);
    for(int i=capacity+1;i<=n;i++){
      fact[i]=fact[i-1]*T::raw(i);
      if constexpr(is_uso_modint_v<T>)inv[i]=T(1)/T(i);
      else inv[i]=-inv[T::mod()%i]*(T::mod()/i);
      factinv[i]=factinv[i-1]*inv[i];
    }
    capacity=n;
  }
  static T C(int n,int k){
    if(n<k)return 0;
    if(k<0)return 0;
    resize(n);
    return fact[n]*factinv[k]*factinv[n-k];
  }
  static T P(int n,int k){
    if(n<k)return 0;
    if(k<0)return 0;
    resize(n);
    return fact[n]*factinv[n-k];
  }
  static T H(int n,int k){
    if(n==0&&k==0)return 1;
    return C(n+k-1,k);
  }
  static T factorial(int n){
    resize(n);
    return fact[n];
  }
  static T factorial_inv(int n){
    resize(n);
    return factinv[n];
  }
  static T inverse(int n){
    resize(n);
    return inv[n];
  }
  static T S(long long n,int k){
    if(n<0)return 0;
    if(n<k)return 0;
    T ret=0;
    resize(k);
    for(int i=0;i<=k;i++){
      ret+=fact[k]*factinv[i]*factinv[k-i]*T::raw(i).pow(n)*((k-i)&1?-1:1);
    }
    return ret*factinv[k];
  }
  template<typename... INT>
  static T O(INT...k){
    int n=0;
    for(int i:std::initializer_list<int>{k...}){
      if(i<0)return 0;
      n+=i;
    }
    resize(n);
    T ret=fact[n];
    for(int i:std::initializer_list<int>{k...})ret*=factinv[i];
    return ret;
  }
};
template<typename T>int F<T>::capacity=1;
template<typename T>std::vector<T>F<T>::fact{1,1};
template<typename T>std::vector<T>F<T>::factinv{1,1};
template<typename T>std::vector<T>F<T>::inv{0,1};
#include<concepts>
template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>msb(T n){return n==0?-1:31-__builtin_clz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>msb(T n){return n==0?-1:63-__builtin_clzll(n);}

template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>lsb(T n){return n==0?-1:__builtin_ctz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>lsb(T n){return n==0?-1:__builtin_ctzll(n);}

template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>floor_pow2(T n){return n==0?0:T(1)<<msb(n);}

template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>ceil_pow2(T n){return n<=1?1:T(1)<<(msb(n-1)+1);}

template<std::integral T>
constexpr T safe_div(T a,T b){return a/b-(a%b&&(a^b)<0);}
template<std::integral T>
constexpr T safe_ceil(T a,T b){return a/b+(a%b&&(a^b)>0);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits<=32),T>pow_mod(T a,T n,T mod){
  using u64=unsigned long long;
  u64 res=1;
  while(n>0){
    if(n&1)res=((u64)res*a)%mod;
    a=((u64)a*a)%mod;
    n>>=1;
  }
  return T(res);
}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),T>pow_mod(T a,T n,T mod){
  using u128=__uint128_t;
  u128 res=1;
  while(n>0){
    if(n&1)res=((u128)res*a)%mod;
    a=((u128)a*a)%mod;
    n>>=1;
  }
  return T(res);
}
constexpr int primitive_root_constexpr(int x){
  if(x==167772161)return 3;
  if(x==469762049)return 3;
  if(x==754974721)return 11;
  if(x==880803841)return 26;
  if(x==998244353)return 3;
  if(x==2)return 1;
  int x2=x;
  int p[20]={};
  int c=0;
  x--;
  for(int i=2;i*i<=x;i++){
    if(x%i==0){
      p[c++]=i;
      while(x%i==0)x/=i;
    }
  }
  if(x!=1)p[c++]=x;
  x=x2;
  for(int g=2;;g++){
    bool ok=true;
    for(int i=0;i<c;i++)if(pow_mod(g,(x-1)/p[i],x)==1){
      ok=false;
      break;
    }
    if(ok)return g;
  }
}
template<int m>
struct ntt_root{
  static constexpr int rank2=lsb(m-1);
  static constexpr int g=primitive_root_constexpr(m);
  std::array<int,rank2+1>root,invroot;
  std::array<int,std::max(0,rank2-1)>rate2,invrate2;
  std::array<int,std::max(0,rank2-2)>rate3,invrate3;
  constexpr ntt_root(){
    root[rank2]=pow_mod(g,m>>rank2,m);
    invroot[rank2]=pow_mod(root[rank2],m-2,m);
    for(int i=rank2-1;i>=0;i--){
      root[i]=(long long)root[i+1]*root[i+1]%m;
      invroot[i]=(long long)invroot[i+1]*invroot[i+1]%m;
    }
    int prod=1,invprod=1;
    for(int i=0;i<rank2-1;i++){
      rate2[i]=(long long)root[i+2]*prod%m;
      invrate2[i]=(long long)invroot[i+2]*invprod%m;
      prod=(long long)prod*invroot[i+2]%m;
      invprod=(long long)invprod*root[i+2]%m;
    }
    prod=invprod=1;
    for(int i=0;i<rank2-2;i++){
      rate3[i]=(long long)root[i+3]*prod%m;
      invrate3[i]=(long long)invroot[i+3]*invprod%m;
      prod=(long long)prod*invroot[i+3]%m;
      invprod=(long long)invprod*root[i+3]%m;
    }
  }
};
template<typename T>
void dft(std::vector<T>&a){
  static constexpr ntt_root<T::mod()>r;
  static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
  int n=a.size();
  int h=lsb(n);
  int len=0;
  while(len<h){
    if(h-len==1){
      T rot=T::raw(1);
      for(int s=0;s<(1<<len);s++){
        int of=s*2;
        T u=a[of],v=a[of+1]*rot;
        a[of]=u+v;
        a[of+1]=u-v;
        rot*=T::raw(r.rate2[lsb(~(unsigned int)s)]);
      }
      len++;
    }
    else{
      int p=1<<(h-len-2);
      T rot=T::raw(1),imag=T::raw(r.root[2]);
      for(int s=0;s<(1<<len);s++){
        const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
        int of=s<<(h-len);
        for(int i=0;i<p;i++){
          const unsigned long long a0=a[i+of].val(),a1=(unsigned long long)a[i+of+p].val()*rot1,a2=(unsigned long long)a[i+of+p*2].val()*rot2,a3=(unsigned long long)a[i+of+p*3].val()*rot3;
          const unsigned long long m=(unsigned long long)T(a1+mod2-a3).val()*imag.val();
          const unsigned long long k=mod2-a2;
          a[i+of]=a0+a2+a1+a3;
          a[i+of+p]=a0+a2+(mod2*2-a1-a3);
          a[i+of+p*2]=a0+k+m;
          a[i+of+p*3]=a0+k+(mod2-m);
        }
        rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);
      }
      len+=2;
    }
  }
}
template<typename T>
void idft(std::vector<T>&a){
  static constexpr ntt_root<T::mod()>r;
  int n=a.size();
  int h=lsb(n);
  int len=h;
  while(len){
    if(len==1){
      int p=1<<(h-1);
      for(int i=0;i<p;i++){
        T u=a[i],v=a[i+p];
        a[i]=u+v;
        a[i+p]=u-v;
      }
      len--;
    }
    else{
      int p=1<<(h-len);
      T rot=T::raw(1),imag=T::raw(r.invroot[2]);
      for(int s=0;s<(1<<(len-2));s++){
        const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
        int of=s<<(h-len+2);
        for(int i=0;i<p;i++){
          const unsigned long long a0=a[i+of].val(),a1=a[i+of+p].val(),a2=a[i+of+p*2].val(),a3=a[i+of+p*3].val();
          const unsigned long long k=T((T::mod()+a2-a3)*imag.val()).val();
          a[i+of]=a0+a1+a2+a3;
          a[i+of+p]=(a0+T::mod()-a1+k)*rot1;
          a[i+of+p*2]=(a0+a1+T::mod()*2-a2-a3)*rot2;
          a[i+of+p*3]=(a0+T::mod()*2-a1-k)*rot3;
        }
        rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);
      }
      len-=2;
    }
  }
}
template<typename T>
std::vector<T>ntt_convolution(std::vector<T> a,std::vector<T> b){
  int n=a.size(),m=b.size(),s=n+m-1;
  if(std::min(n,m)<60){
    std::vector<T>ret(s,0);
    if(n<m)for(int i=0;i<m;i++)for(int j=0;j<n;j++)ret[i+j]+=a[j]*b[i];
    else for(int i=0;i<n;i++)for(int j=0;j<m;j++)ret[i+j]+=a[i]*b[j];
    return ret;
  }
  int z=ceil_pow2(s);
  a.resize(z,0);
  b.resize(z,0);
  dft(a),dft(b);
  std::vector<T>c(z);
  for(int i=0;i<z;i++)c[i]=a[i]*b[i];
  idft(c);
  T g=T::raw(z).inv();
  for(int i=0;i<s;i++)c[i]*=g;
  return {c.begin(),c.begin()+s};
}
template<typename M>
struct SWAG{
private:
  using S=typename M::S;
  std::vector<S>a,b;
  std::vector<S>proda,prodb;
  void eval(){
    proda.resize(a.size()+1,M::e());
    prodb.resize(b.size()+1,M::e());
    for(int i=1;i<(int)proda.size();i++)proda[i]=M::op(a[i-1],proda[i-1]);
    for(int i=1;i<(int)prodb.size();i++)prodb[i]=M::op(prodb[i-1],b[i-1]);
  }
public:
  SWAG():proda{M::e()},prodb{M::e()}{}
  void push_front(S v){
    a.emplace_back(move(v));
    proda.emplace_back(M::op(a.back(),proda.back()));
  }
  void push_back(S v){
    b.emplace_back(std::move(v));
    prodb.emplace_back(M::op(prodb.back(),b.back()));
  }
  inline S front()const{return a.empty()?b[0]:a.back();}
  inline S back()const{return b.empty()?a[0]:b.back();}
  void pop_front(){
    if(a.empty()){
      int mid=b.size()/2;
      a=std::vector<S>(b.rbegin()+mid,b.rend());
      b=std::vector<S>(b.end()-mid,b.end());
      eval();
    }
    a.pop_back();
    proda.pop_back();
  }
  void pop_back(){
    if(b.empty()){
      int mid=a.size()/2;
      b=vector<S>(a.rbegin()+mid,a.rend());
      a=vector<S>(a.end()-mid,a.end());
      eval();
    }
    b.pop_back();
    prodb.pop_back();
  }
  inline S all_prod()const{return M::op(proda.back(),prodb.back());}
  inline int size()const{return a.size()+b.size();}
  inline bool empty()const{return a.empty()&&b.empty();}
};
template<typename T>
std::vector<T>shift_sample_point(const std::vector<T>&f,T k,int m=-1){
  int n=f.size();
  if(m==-1)m=n;
  int c=k.val();
  std::vector<T>a=inverse_table<T>(c-n+1,c+m);
  std::vector<T>b(n);
  for(int i=0;i<n;i++){
    b[i]=F<T>::factorial_inv(i)*F<T>::factorial_inv(n-i-1)*f[i];
    if((n-i-1)&1)b[i]=-b[i];
  }
  int s=ceil_pow2(n+m-1);
  a.resize(s);
  b.resize(s);
  dft(a),dft(b);
  for(int i=0;i<s;i++)a[i]*=b[i];
  idft(a);
  a=std::vector<T>(a.begin()+n-1,a.begin()+n+m-1);
  T inv=T::raw(s).inv();
  struct M{
    using S=T;
    static inline S op(const S&x,const S&y){return x*y;}
    static inline S e(){return T::raw(1);}
  };
  SWAG<M>swag;
  for(int i=c-n+1;i<=c;i++)swag.push_back(i);
  for(int i=0;i<m;i++){
    T now=swag.all_prod();
    if(now.val())a[i]*=now*inv;
    else a[i]=f[(i+c)%T::mod()];
    swag.pop_front();
    swag.push_back(c+i+1);
  }
  return a;
}
template<typename T>
vector<vector<T>>poly_matrix_prod(const vector<vector<vector<T>>>&mat,ll k){
  int n=mat.size();
  auto shift=[](const vector<vector<vector<T>>>&m,T x){
    int d=m.size(),n=m[0].size();
    vector<vector<vector<T>>>ret(d,vector<vector<T>>(n,vector<T>(n)));
    rep(i,n)rep(j,n){
      vector<T>g(d);
      rep(l,d)g[l]=m[l][i][j];
      g=shift_sample_point(g,x);
      rep(l,d)ret[l][i][j]=g[l];
    }
    return ret;
  };
  auto fx=[](const vector<T>&f,T x)->T {
    T ret=0,power=1;
    rep(i,f.size()){
      ret+=f[i]*power;
      power*=x;
    }
    return ret;
  };
  int deg=1;
  rep(i,n)rep(j,n)chmax<int>(deg,mat[i][j].size()-1);
  ll v=1;
  while(deg*v*v<k)v*=2;
  vector<vector<vector<T>>>G(deg+1,vector<vector<T>>(n,vector<T>(n)));
  T inv=T(v).inv();
  rep(i,deg+1){
    T x=T(v)*i;
    rep(j,n)rep(l,n)G[i][j][l]=fx(mat[j][l],x);
  }
  for(ll w=1;w<v;w<<=1){
    T w2=w;
    auto g1=shift(G,w2*inv);
    auto g2=shift(G,(w2*deg*v+v)*inv);
    auto g3=shift(G,(w2*deg*v+v+w2)*inv);
    rep(i,w*deg+1){
      G[i]=matrix_mul(g1[i],G[i]),g2[i]=matrix_mul(g3[i],g2[i]);
    }
    copy(g2.begin(),g2.end()-1,back_inserter(G));
  }
  vector<vector<T>>ret(n,vector<T>(n,0));
  rep(i,n)ret[i][i]=1;
  ll i=0;
  while(i+v<=k)ret=matrix_mul(G[i/v],ret),i+=v;
  while(i<k){
    vector<vector<T>>mat2(n,vector<T>(n));
    rep(j,n)rep(l,n)mat2[j][l]=fx(mat[j][l],i);
    ret=matrix_mul(mat2,ret);
    i++;
  }
  return ret;
}
template<typename T>
vector<vector<T>>find_p_recursive(vector<T>a,int d){
  int n=a.size();
  int k=(n+2)/(d+2)-1;
  if(k<=0)return {};
  int m=(k+1)*(d+1);
  vector<vector<T>>mat(m-1,vector<T>(m));
  rep(i,m-1){
    rep(j,k+1){
      T p=1;
      rep(l,d+1){
        mat[i][(d+1)*j+l]=p*a[i+j];
        p*=i+j;
      }
    }
  }
  auto g=matrix_linear_equation(mat,vector<T>(m-1,0)).second;
  if(g.empty())return vector<vector<T>>{};
  vector<T>c=g[0];
  while(all_of(c.end()-d-1,c.end(),[](T x){return x==0;}))c.erase(c.end()-d-1,c.end());
  k=c.size()/(d+1);
  vector<vector<T>>ret(k);
  rep(j,k){
    int i=j*(d+1);
    vector<T>f(1+d,0),sum(1+d,0);
    f[0]=1;
    rep(l,d+1){
      rep(x,1+d)sum[x]+=f[x]*c[i+l];
      for(int x=d;x>=1;x--)f[x]=f[x-1]+f[x]*j;
      f[0]*=j;
    }
    ret[j]=sum;
  }
  return ret;
}
template<typename T>
T calc_p_recursive_naive(const vector<T>&a,const vector<vector<T>>&coef,ll n){
  if(a.size()>n)return a[n];
  int r=coef.size()-1;
  int d=coef[0].size()-1;
  assert(a.size()>=r);
  vector<pair<T,T>>que(r);
  rep(i,r)que[i]={a[i],1};
  int ptr=0;
  for(ll i=0;i<=n-r;i++){
    T num=0,den=1;
    rep(j,r){
      T c=0,power=1;
      rep(k,d+1){
        c+=coef[j][k]*power;
        power*=i;
      }
      int idx=ptr+j;
      if(idx>=r)idx-=r;
      num=num*que[idx].second+que[idx].first*den*c;
      den=den*que[idx].second;
    }
    T c=0,power=1;
    rep(k,d+1){
      c+=coef[r][k]*power;
      power*=i;
    }
    que[ptr++]=make_pair(num,-den*c);
    if(ptr==r)ptr=0;
  }
  if(--ptr==-1)ptr=r-1;
  return que[ptr].first/que[ptr].second;
}
template<typename T>
T calc_p_recursive_fast(const vector<T>&a,const vector<vector<T>>&coef,ll n){
  if(a.size()>n)return a[n];
  int deg=coef.size()-1;
  vector<vector<vector<T>>>num(deg,vector<vector<T>>(deg));
  rep(i,deg){
    num[0][i]=coef[deg-i-1];
    rep(j,num[0][i].size())num[0][i][j]=-num[0][i][j];
  }
  reps(i,1,deg)num[i][i-1]=coef[deg];
  vector<vector<vector<T>>>den={{coef[deg]}};
  vector<vector<T>>a0(deg,vector<T>(deg,0));
  rep(i,deg)a0[i][0]=a[deg-i-1];
  T ret=matrix_mul(poly_matrix_prod(num,n-deg+1),a0)[0][0];
  ret/=poly_matrix_prod(den,n-deg+1)[0][0];
  return ret;
}
template<typename T>
T kth_term_p_recursive(vector<T>a,int K){
  if(K<a.size())return a[K];
  if(all_of(all(a),[](T x){return x.val()==0;}))return 0;
  assert(a.size()>=5);
  int n=a.size()-2;
  for(int d=0;;d++){
    int k=(n+2)/(d+2)-1;
    if(k<=0)break;
    int s=(n+2)/(d+2)*(d+2)-2;
    vector<T>prefix(a.begin(),a.begin()+s);
    vector<vector<T>>b=find_p_recursive(prefix,d);
    if(b.empty())continue;
    bool ok=true;
    reps(i,s,a.size()){
      if(calc_p_recursive_naive(prefix,b,i).val()!=a[i].val()){
        ok=false;
        break;
      }
    }
    if(ok){
      if constexpr(T::mod()==998244353)return calc_p_recursive_fast(prefix,b,K);
      else return calc_p_recursive_naive(prefix,b,K);
    }
  }
  cerr<<"not found\n";
  __builtin_unreachable();
}
template<typename T>
std::vector<T>enumerate_p_recursive(std::vector<T>a,int K){
  if(a.size()>K){
    a.resize(K);
    return a;
  }
  int n=(int)a.size()-2;
  for(int d=0;;d++){
    int k=(n+2)/(d+2)-1;
    if(k<=0)break;
    int s=(n+2)/(d+2)*(d+2)-2;
    std::vector<T>prefix(a.begin(),a.begin()+s);
    std::vector<std::vector<T>>b=find_p_recursive(prefix,d);
    if(b.empty())continue;
    int r=(int)b.size()-1;
    int deg=(int)b[0].size()-1;
    std::vector<T>res(K);
    for(int i=0;i<r;i++)res[i]=prefix[i];
    for(int i=0;i<K-r;i++){
      T &v=res[i+r];
      for(int j=0;j<r;j++){
        T c=T::raw(0),power=T::raw(1);
        for(int l=0;l<=deg;l++){
          c+=b[j][l]*power;
          power*=T::raw(i);
        }
        v+=c*res[i+j];
      }
      T c=T::raw(0),power=T::raw(1);
      for(int l=0;l<=deg;l++){
        c+=b[r][l]*power;
        power*=T::raw(i);
      }
      v/=-c;
      if(i+r<(int)a.size()&&v!=a[i+r]){
        res.clear();
        break;
      }
    }
    if(!res.empty())return res;
  }
  __builtin_unreachable();
}
#include<optional>
constexpr int carmichael_constexpr(int n){
  if(n==998244353)return 998244352;
  if(n==1000000007)return 1000000006;
  if(n<=1)return n;
  int res=1;
  int t=0;
  while(n%2==0){
    n/=2;
    t++;
  }
  if(t==2)res=2;
  else if(t>=3)res=1<<(t-2);
  for(int i=3;i*i<=n;i++)if(n%i==0){
    int c=0;
    while(n%i==0){
      n/=i;
      c++;
    }
    int prod=i-1;
    for(int j=0;j<c-1;j++)prod*=i;
    res=std::lcm(res,prod);
  }
  if(n!=1)res=std::lcm(res,n-1);
  return res;
}
template<int m>
struct mod_int{
private:
  static constexpr unsigned int umod=static_cast<unsigned int>(m);
  static constexpr unsigned int car=carmichael_constexpr(m);
  using uint=unsigned int;
  using mint=mod_int;
  uint v;
  static_assert(m<uint(1)<<31);
  mint sqrt_impl()const{
    if(this->val()<=1)return *this;
    if constexpr(m%8==1){
      mint b=2;
      while(b.pow((m-1)/2).val()==1)b++;
      int m2=m-1,e=0;
      while(m2%2==0)m2>>=1,e++;
      mint x=this->pow((m2-1)/2);
      mint y=(*this)*x*x;
      x*=*this;
      mint z=b.pow(m2);
      while(y.val()!=1){
        int j=0;
        mint t=y;
        while(t.val()!=1)t*=t,j++;
        z=z.pow(1<<(e-j-1));
        x*=z;
        z*=z;
        y*=z;e=j;
      }
      return x;
    }
    else if constexpr(m%8==5){
      mint ret=this->pow((m+3)/8);
      if((ret*ret).val()==this->val())return ret;
      else return ret*mint::raw(2).pow((m-1)/4);
    }
    else{
      return this->pow((m+1)/4);
    }
  }
public:
  using value_type=uint;
  mod_int():v(0){}
  template<typename T,std::enable_if_t<std::is_signed_v<T>,std::nullptr_t> =nullptr>
  mod_int(T a){
    a%=m;
    if(a<0)v=a+umod;
    else v=a;
  }
  template<typename T,std::enable_if_t<std::is_unsigned_v<T>,std::nullptr_t> =nullptr>
  mod_int(T a):v(a%umod){}
  static constexpr mint raw(int a){
    mint ret;
    ret.v=a;
    return ret;
  }
  inline uint val()const{return this->v;}
  static constexpr int mod(){return m;}
  inline mint &operator+=(const mint &b){
    this->v+=b.v;
    if(this->v>=umod)this->v-=umod;
    return *this;
  }
  inline mint &operator-=(const mint &b){
    this->v-=b.v;
    if(this->v>=umod)this->v+=umod;
    return *this;
  }
  inline mint &operator*=(const mint &b){
    this->v=((unsigned long long)this->v*b.v)%umod;
    return *this;
  }
  inline mint &operator/=(const mint &b){
    *this*=b.inv();
    return *this;
  }
  inline mint operator+()const{return *this;}
  inline mint operator-()const{return mint()-*this;}
  friend inline mint operator+(const mint &a,const mint &b){return mint(a)+=b;}
  friend inline mint operator-(const mint &a,const mint &b){return mint(a)-=b;}
  friend inline mint operator*(const mint &a,const mint &b){return mint(a)*=b;}
  friend inline mint operator/(const mint &a,const mint &b){return mint(a)/=b;}
  friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();}
  friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);}
  inline mint operator++(int){
    mint ret=*this;
    *this+=mint::raw(1);
    return ret;
  }
  inline mint operator--(int){
    mint ret=*this;
    *this-=mint::raw(1);
    return ret;
  }
  mint pow(long long n)const{
    mint ret=mint::raw(1),a(*this);
    while(n){
      if(n&1)ret*=a;
      a*=a;
      n>>=1;
    }
    return ret;
  }
  inline mint inv()const{
    assert(this->v!=0);
    return pow(car-1);
  }
  std::optional<mint>sqrt()const{
    if(this->val()<=1||this->pow((m-1)/2)==1)return std::make_optional(this->sqrt_impl());
    else return std::nullopt;
  }
  static constexpr unsigned int order(){return car;}
  friend std::istream &operator>>(std::istream &is,mint &b){
    long long a;
    is>>a;
    b=mint(a);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os,const mint &b){
    os<<b.val();
    return os;
  }
};
template<int m>
struct std::hash<mod_int<m>>{
  std::size_t operator()(mod_int<m>x)const{
    return std::hash<unsigned int>()(x.val());
  }
};
using mint998=mod_int<998244353>;
using mint107=mod_int<1000000007>;
using mint=mint998;
mint calc(int n,int i){
  int l=i,r=n-i-1;
  mint res=0;
  rep(j,l+1)rep(k,r+1){
    res+=F<mint>::C(l,j)*F<mint>::C(r,k)*(j+1)*(k+1);
  }
  return res;
}
void SOLVE(){
  int n;
  cin>>n;
  vector<mint>a(n);
  cin>>a;
  vector<mint>coef(20);
  rep(i,20){
    vector<mint>dp(20);
    rep(j,i,i+20)dp[j-i]=calc(j,i);
    debug(i,dp);
    coef[i]=kth_term_p_recursive(dp,n-i);
  }
  coef=enumerate_p_recursive(coef,n);
  mint ans=0;
  rep(i,n)ans+=a[i]*coef[i];
  cout<<ans<<endl;
}