#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
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 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 reps(i,a,n) for(int i=(a);i<int(n);i++)
#define rep(i,n) reps(i,0,n)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<x<<'\n',static_cast<void>(0)
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>
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
void SOLVE();
int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout<<fixed<<setprecision(16);
  #ifdef LOCAL
  clock_t start=clock();
  #endif
  int testcase=1;
  //cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
  #ifdef LOCAL
  cerr<<"time:";
  cerr<<(clock()-start)/1000;
  cerr<<"ms\n";
  #endif
}

constexpr int msb(unsigned int n){return n==0?-1:31-__builtin_clz(n);}
constexpr int msb(int n){return n==0?-1:31-__builtin_clz(n);}
constexpr int msb(unsigned long long n){return n==0?-1:63-__builtin_clzll(n);}
constexpr int msb(long long n){return n==0?-1:63-__builtin_clzll(n);}

constexpr int lsb(unsigned int n){return n==0?-1:__builtin_ctz(n);}
constexpr int lsb(int n){return n==0?-1:__builtin_ctz(n);}
constexpr int lsb(unsigned long long n){return n==0?-1:__builtin_ctzll(n);}
constexpr int lsb(long long n){return n==0?-1:__builtin_ctzll(n);}

constexpr unsigned int floor_pow2(unsigned int n){return n==0?0:1u<<msb(n);}
constexpr int floor_pow2(int n){return n<=0?0:1<<msb(n);}
constexpr unsigned long long floor_pow2(unsigned long long n){return n==0?0:1ull<<msb(n);}
constexpr long long floor_pow2(long long n){return n<=0?0:1ll<<msb(n);}

constexpr unsigned int ceil_pow2(unsigned int n){return n<=1?1:1u<<(msb(n-1)+1);}
constexpr int ceil_pow2(int n){return n<=1?1:1<<(msb(n-1)+1);}
constexpr unsigned long long ceil_pow2(unsigned long long n){return n<=1?1:1ull<<(msb(n-1)+1);}
constexpr long long ceil_pow2(long long n){return n<=1?1:1ll<<(msb(n-1)+1);}
constexpr int pow_mod(int a,int n,int mod){
  long long res=1;
  while(n){
    if(n&1)res=res*a%mod;
    a=(long long)a*a%mod;
    n>>=1;
  }
  return 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;
  static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
  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 T>
void transposed_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=h;
  while(len){
    if(len==1){
      int p=1<<(h-1);
      T rot=T::raw(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)*rot;
      }
      len--;
    }
    else{
      int p=1<<(h-len);
      T rot=T::raw(1),imag=T::raw(r.root[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;
        }
        if(s+1!=1<<(len-2))rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);
      }
      len-=2;
    }
  }
}
template<typename T>
void transposed_idft(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;
        if(s+1!=1<<len)rot*=T::raw(r.invrate2[lsb(~(unsigned int)s)]);
      }
      len++;
    }
    else{
      int p=1<<(h-len-2);
      T rot=T::raw(1),imag=T::raw(r.invroot[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);
        }
        if(s+1!=1<<len)rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);
      }
      len+=2;
    }
  }
}
template<typename T>
void ntt_doubling(std::vector<T>&a){
  static constexpr ntt_root<T::mod()>r;
  int n=a.size()/2;
  std::vector<T>b(a.begin(),a.begin()+n);
  idft(b);
  T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);
  for(int i=0;i<n;i++){
    b[i]*=now;
    now*=zeta;
  }
  dft(b);
  std::copy(b.begin(),b.end(),a.begin()+n);
}
template<typename T>
void transposed_ntt_doubling(std::vector<T>&a){
  static constexpr ntt_root<T::mod()>r;
  int n=a.size()/2;
  std::vector<T>b(a.begin(),a.begin()+n);
  a=std::vector<T>(a.begin()+n,a.end());
  transposed_dft(a);
  T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);
  for(int i=0;i<n;i++)a[i]*=now,now*=zeta;
  transposed_idft(a);
  for(int i=0;i<n;i++)a[i]+=b[i];
}
#include<type_traits>
template<int m>
struct mod_int{
private:
  static constexpr unsigned int umod=static_cast<unsigned int>(m);
  using uint=unsigned int;
  using mint=mod_int;
  uint v;
  static_assert(m<uint(1)<<31);
public:
  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+=1;
    return ret;
  }
  inline mint operator--(int){
    mint ret=*this;
    *this-=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(m-2);
  }
  mint sqrt()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);
    }
  }
  std::pair<bool,mint> safe_sqrt()const{
    if(this->pow((m-1)/2)==1)return std::make_pair(true,this->sqrt());
    else return std::make_pair(false,0);
  }
  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;
  }
};
using mint998=mod_int<998244353>;
using mint107=mod_int<1000000007>;
int sqrt_mod(int n,int mod){
  if(n<=1)return n;
  auto powmod=[&](int a,int b)->int {
    ll ret=1;
    while(b){
      if(b&1)ret=(ret*a)%mod;
      a=ll(a)*a%mod;
      b>>=1;
    }
    return ret;
  };
  if(powmod(n,(mod-1)/2)!=1)return -1;
  if(mod%8==1){
    int b=2;
    while(powmod(b,(mod-1)/2)==1)b++;
    int m2=mod-1,e=0;
    while(m2%2==0)m2>>=1,e++;
    int x=powmod(n,(m2-1)/2);
    int y=(ll(n)*x%mod)*x%mod;
    x=ll(x)*n%mod;
    int z=powmod(b,m2);
    while(y!=1){
      int j=0;
      int t=y;
      while(t!=1)t=ll(t)*t%mod,j++;
      z=powmod(z,1<<(e-j-1));
      x=ll(x)*z%mod;
      z=ll(z)*z%mod;
      y=ll(y)*z%mod;
      e=j;
    }
    return x;
  }
  else if(mod%8==5){
    int ret=powmod(n,(mod+3)/8);
    if(ll(ret)*ret%mod==n)return ret;
    else{
      ret=(ll(ret)*powmod(2,(mod-1)/4))%mod;
      return ret;
    }
  }
  else return powmod(n,(mod+1)/4);
}
template<typename T>
vector<vector<T>>convolution2d(const vector<vector<T>>&a,const vector<vector<T>>&b){
  int x=a.size()+b.size()-1,y=a[0].size()+b[0].size()-1;
  vector<T>f(a.size()*y),g(b.size()*y);
  rep(i,a.size())rep(j,a[i].size())f[i*y+j]=a[i][j];
  rep(i,b.size())rep(j,b[i].size())g[i*y+j]=b[i][j];
  auto c=ntt_convolution(f,g);
  vector<vector<T>>ret(x,vector<T>(y));
  rep(i,x)rep(j,y)ret[i][j]=c[i*y+j];
  return ret;
}
template<typename T>
vector<T> fps_inv(const vector<T> &a,int deg=-1){
  int n=a.size();
  if(deg==-1)deg=n;
  assert(a[0]!=T(0));
  vector<T> ret(deg);
  ret[0]=a[0].inv();
  for(int m=1;m<deg;m<<=1){
    vector<T> f(a.begin(),a.begin()+min(n,m*2));
    if(f.size()<m*2)f.resize(m*2,0);
    vector<T> g(ret);
    f.resize(m*2);
    dft(f);
    g.resize(m*2);
    dft(g);
    rep(i,m*2)f[i]*=g[i];
    idft(f);
    T inv=T::raw(m*2).inv();
    rep(i,m)f[i]=0;
    reps(i,m,m*2)f[i]*=inv;
    dft(f);
    rep(i,m*2)f[i]*=g[i];
    idft(f);
    rep(i,m*2)f[i]*=inv;
    reps(i,m,min(deg,m*2))ret[i]-=f[i];
  }
  return ret;
}
template<typename T>
vector<T> fps_diff(const vector<T>&a){
  int n=a.size();
  vector<T>b(max(0,n-1));
  reps(i,1,n)b[i-1]=a[i]*i;
  return b;
}
template<typename T>
vector<T> fps_integral(const vector<T>&a){
  int n=a.size();
  vector<T>b(n+1);
  b[0]=0;
  if(n)b[1]=1;
  reps(i,2,n+1)b[i]=-b[T::mod()%i]*(T::mod()/i);
  rep(i,n)b[i+1]*=a[i];
  return b;
}
template<typename T>
vector<T> fps_log(const vector<T>&a,int deg=-1){
  int n=a.size();
  if(deg==-1)deg=n;
  vector<T>b=fps_integral(ntt_convolution(fps_diff(a),fps_inv(a,deg)));
  return {b.begin(),b.begin()+deg};
}
template<typename T>
vector<T> fps_exp(const vector<T>&a,int deg=-1){
  assert(a.empty()||a[0]==0);
  int n=a.size();
  if(deg==-1)deg=n;
  vector<T>b{1};
  for(int m=1;m<deg;m*=2){
    vector<T>nxt=fps_log(b,m*2);
    rep(i,m*2)nxt[i]*=-1;
    rep(i,min(n,m*2))nxt[i]+=a[i];
    nxt[0]++;
    b=ntt_convolution(b,nxt);
    b.resize(m*2);
  }
  return {b.begin(),b.begin()+deg};
}
template<typename T>
vector<T> fps_pow(vector<T> a,ll k,int deg=-1){
  int n=a.size();
  if(deg==-1)deg=n;
  if(k==0){
    vector<T>ret(deg,0);
    ret[0]=1;
    return ret;
  }
  int of=0;
  while(a[of]==0&&of!=n)of++;
  if(of==n)return vector<T>(deg,0);
  if(of!=0&&k>=deg)return vector<T>(deg,0);
  if(of*k>=deg)return vector<T>(deg,0);
  a.erase(a.begin(),a.begin()+of);
  n=a.size();
  T a0=a[0];
  T inv=a[0].inv();
  rep(i,n)a[i]*=inv;
  vector<T>lg=fps_log(a,deg);
  rep(i,deg)lg[i]*=k;
  vector<T>ep=fps_exp(lg,deg);
  T pw=a0.pow(k);
  rep(i,deg)ep[i]*=pw;
  vector<T>ret(deg,0);
  reps(i,of*k,deg)ret[i]=ep[i-of*k];
  return ret;
}
template<typename T>
vector<T>fps_pows(vector<T>f,vector<T>g,int n){
  int sz=f.size();
  vector<vector<T>>p(sz,vector<T>(2)),q(sz,vector<T>(2));
  q[0][0]=1;
  rep(i,min<int>(g.size(),sz))p[i][0]=g[i];
  rep(i,sz)q[i][1]=-f[i];
  int k=sz-1;
  while(k){
    int x=p.size(),y=p[0].size();
    vector<vector<T>>mq(q);
    for(int i=1;i<x;i+=2)rep(j,y)mq[i][j]=-mq[i][j];
    vector<vector<T>>f=convolution2d(p,mq);
    vector<vector<T>>g=convolution2d(q,mq);
    p.resize(k/2+1);
    q.resize(k/2+1);
    if(k&1)rep(i,p.size())p[i]=f[i*2+1];
    else rep(i,p.size())p[i]=f[i*2];
    rep(i,q.size())q[i]=g[i*2];
    rep(i,p.size())if(p[i].size()>n+1)p[i].resize(n+1);
    rep(i,q.size())if(q[i].size()>n+1)q[i].resize(n+1);
    k>>=1;
  }
  vector<T>f2(p[0]),g2(q[0]);
  vector<T>ret=ntt_convolution(f2,fps_inv(g2));
  ret.resize(n+1);
  return ret;
}
template<typename T>
vector<T>fps_divmod(vector<T>f,vector<T>g){
  if(f.empty())return f;
  int n=f.size(),m=g.size();
  vector<T>r(f);
  reverse(all(f)),reverse(all(g));
  vector<T>q=ntt_convolution(f,fps_inv(g,n));
  q.resize(max(0,n-m+1));
  auto p=ntt_convolution(g,q);
  reverse(all(p));
  rep(i,min<int>(p.size(),m))r[i]-=p[i];
  r.resize(m-1);
  while(!r.empty()&&r.back().val()==0)r.pop_back();
  return r;
}
template<typename T>
vector<T>fps_sqrt(vector<T>f,int deg=-1){
  if(deg==-1)deg=f.size();
  int prefix_zero=0;
  while(prefix_zero<f.size()&&f[prefix_zero].val()==0)prefix_zero++;
  if(prefix_zero==f.size())return vector<T>(deg,0);
  if(prefix_zero&1)return vector<T>{};
  f.erase(f.begin(),f.begin()+prefix_zero);
  prefix_zero/=2;
  int sq=sqrt_mod(f[0].val(),T::mod());
  if(sq==-1)return vector<T>{};
  T inv0=f[0].inv();
  rep(i,f.size())f[i]*=inv0;
  vector<T>g{1};
  debug(f);
  T inv2=T::raw(2).inv();
  while(g.size()<deg-prefix_zero){
    vector<T>fp(f.begin(),f.begin()+min(f.size(),g.size()*2));
    fp=ntt_convolution(fp,fps_inv(g,g.size()*2));
    vector<T>nxtg(g);
    nxtg.resize(g.size()*2);
    rep(i,nxtg.size()){
      if(i<fp.size())nxtg[i]+=fp[i];
      nxtg[i]*=inv2;
    }
    swap(g,nxtg);
  }
  g.insert(g.begin(),prefix_zero,0);
  g.resize(deg);
  rep(i,g.size())g[i]*=sq;
  return g;
}
template<typename T>
std::vector<T>fps_middle_product(std::vector<T>a,std::vector<T>b){
  assert(a.size()>=b.size());
  std::reverse(b.begin(),b.end());
  int n=a.size(),m=b.size();
  int z=ceil_pow2(n);
  a.resize(z,0),b.resize(z,0);
  dft(a),dft(b);
  for(int i=0;i<z;i++)a[i]*=b[i];
  idft(a);
  T invz=T(z).inv();
  for(int i=m-1;i<n;i++)a[i]*=invz;
  return vector<T>(a.begin()+m-1,a.begin()+n);
}
template<typename T>
std::vector<T>multipoint_evaluation(std::vector<T>f,const std::vector<T>&x){
  int n=ceil_pow2((int)x.size()),log2n=msb(n);
  std::vector<std::vector<T>>f2(log2n+1,std::vector<T>(n*2));
  for(int i=0;i<x.size();i++)f2[0][i*2]=-x[i];
  for(int i=0;i<log2n;i++){
    int b=1<<i;
    for(int j=0;j<n*2;j+=b*4){
      std::vector<T>l(f2[i].begin()+j,f2[i].begin()+j+b);
      std::vector<T>r(f2[i].begin()+j+b*2,f2[i].begin()+j+b*3);
      l.resize(b*2,0),r.resize(b*2,0);
      ntt_doubling(l),ntt_doubling(r);
      for(int k=0;k<b;k++)l[k]++,r[k]++;
      for(int k=b;k<b*2;k++)l[k]--,r[k]--;
      std::copy(l.begin(),l.end(),f2[i].begin()+j);
      std::copy(r.begin(),r.end(),f2[i].begin()+j+b*2);
      for(int k=0;k<b*2;k++)f2[i+1][j+k]=l[k]*r[k]-T::raw(1);
    }
  }
  std::vector<T>g(f2[log2n].begin(),f2[log2n].begin()+n);
  idft(g);
  {
    T inv=T::raw(g.size()).inv();
    for(int i=0;i<n;i++)g[i]*=inv;
  }
  g.push_back(T::raw(1));
  std::reverse(g.begin(),g.end());
  g=fps_inv(g,f.size());
  f.resize(f.size()+n-1);
  f=fps_middle_product(f,g);
  std::reverse(f.begin(),f.end());
  transposed_idft(f);
  {
    T inv=T::raw(f.size()).inv();
    for(int i=0;i<f.size();i++)f[i]*=inv;
  }
  for(int i=log2n-1;i>=0;i--){
    std::vector<T>nxtf(n);
    int b=1<<i;
    for(int j=0;j<n;j+=b*2){
      std::vector<T>l(b*2),r(b*2);
      for(int k=0;k<b*2;k++)l[k]=f[j+k]*f2[i][j*2+b*2+k],r[k]=f[j+k]*f2[i][j*2+k];
      transposed_ntt_doubling(l),transposed_ntt_doubling(r);
      for(int k=0;k<b;k++)nxtf[j+k]=l[k],nxtf[j+b+k]=r[k];
    }
    std::swap(f,nxtf);
  }
  f.resize(x.size());
  return f;
}
using mint=mint998;
void SOLVE(){
  int n;
  cin>>n;
  vector<mint>a(n);
  cin>>a;
  mint ans=1;
  auto dfs=[&](auto self,int l,int r)->vector<mint> {
    if(l+1==r)return {a[l],-1};
    int mid=(l+r)/2;
    vector<mint>pl=self(self,l,mid);
    vector<mint>pr=self(self,mid,r);
    vector<mint>x(a.begin()+mid,a.begin()+r);
    vector<mint>b=multipoint_evaluation(pl,x);
    for(auto i:b)ans*=i;
    return ntt_convolution(pl,pr);
  };
  dfs(dfs,0,n);
  cout<<ans.val()<<endl;
}