#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();
  }
}
#include<type_traits>
#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>;
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;
  }
}
#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>=0?a/b:-((-a+b-1)/b);}
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 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>
T bostan_mori(std::vector<T> p,std::vector<T> q,long long k){
  assert(p.size()<q.size());
  static constexpr ntt_root<T::mod()>r;
  int n=ceil_pow2((int)q.size()*2-1);
  p.resize(n,T::raw(0));
  q.resize(n,T::raw(0));
  dft(p),dft(q);
  T inv2=T::raw(2).inv();
  int n2=n/2;
  while(k){
    for(int i=0;i<n;i++)p[i]*=q[i^1];
    if(k&1){
      T prod=T::raw(1);
      for(int i=0;i<n2;i++){
        p[i]=(p[i*2]-p[i*2+1])*inv2*prod;
        prod*=r.invrate2[lsb(~i)];
      }
    }
    else{
      for(int i=0;i<n2;i++){
        p[i]=(p[i*2]+p[i*2+1])*inv2;
      }
    }
    for(int i=0;i<n2;i++)q[i]=q[i*2]*q[i*2+1];
    ntt_doubling(p),ntt_doubling(q);
    k>>=1;
  }
  idft(p);
  return p[0]/T::raw(n);
}
template<typename T>
std::vector<std::vector<T>>convolution2d(const std::vector<std::vector<T>>&a,const std::vector<std::vector<T>>&b){
  int x=a.size()+b.size()-1,y=a[0].size()+b[0].size()-1;
  std::vector<T>f(a.size()*y),g(b.size()*y);
  for(int i=0;i<a.size();i++)for(int j=0;j<a[i].size();j++)f[i*y+j]=a[i][j];
  for(int i=0;i<b.size();i++)for(int j=0;j<b[i].size();j++)g[i*y+j]=b[i][j];
  auto c=ntt_convolution(f,g);
  std::vector<std::vector<T>>ret(x,std::vector<T>(y));
  for(int i=0;i<x;i++)for(int j=0;j<y;j++)ret[i][j]=c[i*y+j];
  return ret;
}
template<typename T>
std::vector<T> fps_inv(const std::vector<T> &a,int deg=-1){
  int n=a.size();
  if(deg==-1)deg=n;
  const T zero=T::raw(0);
  assert(a[0]!=zero);
  std::vector<T> ret(ceil_pow2(deg));
  ret[0]=a[0].inv();
  for(int m=1;m<deg;m<<=1){
    std::vector<T> f(a.begin(),a.begin()+std::min(n,m*2));
    if(f.size()<m*2)f.resize(m*2,0);
    std::vector<T> g(ret);
    f.resize(m*2);
    dft(f);
    g.resize(m*2);
    dft(g);
    for(int i=0;i<m*2;i++)f[i]*=g[i];
    idft(f);
    T inv=T::raw(m*2).inv();
    for(int i=0;i<m;i++)f[i]=zero;
    for(int i=m;i<m*2;i++)f[i]*=inv;
    dft(f);
    for(int i=0;i<m*2;i++)f[i]*=g[i];
    idft(f);
    for(int i=0;i<m*2;i++)f[i]*=inv;
    for(int i=m;i<m*2;i++)ret[i]-=f[i];
  }
  ret.resize(deg);
  return ret;
}
template<typename T>
std::vector<T> fps_diff(const std::vector<T>&a){
  int n=a.size();
  std::vector<T>b(std::max(0,n-1));
  for(int i=1;i<n;i++)b[i-1]=a[i]*T::raw(i);
  return b;
}
template<typename T>
std::vector<T> fps_integral(const std::vector<T>&a){
  int n=a.size();
  std::vector<T>b(n+1);
  b[0]=0;
  if(n)b[1]=1;
  for(int i=2;i<=n;i++)b[i]=-b[T::mod()%i]*(T::mod()/i);
  for(int i=0;i<n;i++)b[i+1]*=a[i];
  return b;
}
template<typename T>
std::vector<T> fps_log(const std::vector<T>&a,int deg=-1){
  int n=a.size();
  if(deg==-1)deg=n;
  std::vector<T>b=fps_integral(ntt_convolution(fps_diff(a),fps_inv(a,deg)));
  return {b.begin(),b.begin()+deg};
}
template<typename T>
std::vector<T> fps_exp(const std::vector<T>&a,int deg=-1){
  assert(a.empty()||a[0]==0);
  int n=a.size();
  if(deg==-1)deg=n;
  std::vector<T>inv(ceil_pow2(deg));
  inv[0]=0,inv[1]=1;
  for(int i=2;i<inv.size();i++)inv[i]=-inv[T::mod()%i]*(T::mod()/i);
  std::vector<T>b{1,1<n?a[1]:T()},c{T::raw(1)},f1,f2(2,T::raw(1));
  T sinv=T::raw(2).inv();
  for(int m=2;m<deg;m*=2){
    std::vector<T>y(b);
    y.resize(m*2);
    dft(y);
    f1=f2;
    std::vector<T>z(m);
    for(int i=0;i<m;i++)z[i]=y[i]*f1[i];
    idft(z);
    for(int i=m/2;i<m;i++)z[i]*=sinv;
    std::fill(z.begin(),z.begin()+m/2,T());
    dft(z);
    for(int i=0;i<m;i++)z[i]*=-f1[i];
    idft(z);
    for(int i=m/2;i<m;i++)z[i]*=sinv;
    c.insert(c.end(),z.begin()+m/2,z.end());
    f2=c;
    f2.resize(m*2);
    dft(f2);
    std::vector<T>x(m);
    std::copy(a.begin(),a.begin()+std::min(n,m),x.begin());
    for(int i=0;i<m-1;i++)x[i]=x[i+1]*T::raw(i+1);
    x.back()=T();
    dft(x);
    for(int i=0;i<m;i++)x[i]*=y[i];
    idft(x);
    for(int i=0;i<m;i++)x[i]*=sinv;
    x.resize(m*2);
    for(int i=0;i<m-1;i++)x[m+i]=x[i]-b[i+1]*T::raw(i+1),x[i]=T();
    dft(x);
    for(int i=0;i<m*2;i++)x[i]*=f2[i];
    idft(x);
    sinv/=2;
    for(int i=0;i<m*2;i++)x[i]*=sinv;
    for(int i=(int)x.size()-1;i>=1;i--)x[i]=x[i-1]*inv[i];
    x[0]=T();
    for(int i=m;i<std::min(n,m*2);i++)x[i]+=a[i];
    std::fill(x.begin(),x.begin()+m,T());
    dft(x);
    for(int i=0;i<m*2;i++)x[i]*=y[i];
    idft(x);
    for(int i=m;i<m*2;i++)x[i]*=sinv;
    b.insert(b.end(),x.begin()+m,x.end());
  }
  b.resize(deg);
  return b;
}
template<typename T>
std::vector<T> fps_pow(std::vector<T> a,unsigned long long k,int deg=-1){
  int n=a.size();
  if(deg==-1)deg=n;
  if(k==0){
    std::vector<T>ret(deg,0);
    ret[0]=1;
    return ret;
  }
  int of=0;
  while(a[of]==0&&of!=n)of++;
  if(of==n)return std::vector<T>(deg,0);
  if(of!=0&&k>=deg)return std::vector<T>(deg,0);
  if(of*k>=deg)return std::vector<T>(deg,0);
  a.erase(a.begin(),a.begin()+of);
  n=a.size();
  T a0=a[0];
  T inv=a[0].inv();
  for(int i=0;i<n;i++)a[i]*=inv;
  std::vector<T>lg=fps_log(a,deg);
  T tk=T(k);
  for(int i=0;i<deg;i++)lg[i]*=tk;
  std::vector<T>ep=fps_exp(lg,deg);
  T pw=a0.pow(k);
  for(int i=0;i<deg;i++)ep[i]*=pw;
  std::vector<T>ret(deg,0);
  for(int i=of*k;i<deg;i++)ret[i]=ep[i-of*k];
  return ret;
}
template<typename T>
std::vector<T>fps_divmod(std::vector<T>f,std::vector<T>g){
  if(f.empty())return f;
  int n=f.size(),m=g.size();
  std::vector<T>r(f);
  std::reverse(f.begin(),f.end()),std::reverse(g.begin(),g.end());
  std::vector<T>q=ntt_convolution(f,fps_inv(g,n));
  q.resize(std::max(0,n-m+1));
  auto p=ntt_convolution(g,q);
  std::reverse(p.begin(),p.end());
  for(int i=0;i<std::min<int>(p.size(),m);i++)r[i]-=p[i];
  r.resize(m-1);
  while(!r.empty()&&r.back().val()==0)r.pop_back();
  return r;
}
template<typename T>
std::optional<std::vector<T>>fps_sqrt(std::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 std::make_optional(std::vector<T>(deg,0));
  if(prefix_zero&1)return std::nullopt;
  f.erase(f.begin(),f.begin()+prefix_zero);
  prefix_zero/=2;
  auto opt_sq=f[0].sqrt();
  if(!opt_sq)return std::nullopt;
  T sq=*opt_sq;
  T inv0=f[0].inv();
  for(int i=0;i<f.size();i++)f[i]*=inv0;
  std::vector<T>g{1};
  T inv2=T::raw(2).inv();
  while(g.size()<deg-prefix_zero){
    std::vector<T>fp(f.begin(),f.begin()+std::min(f.size(),g.size()*2));
    fp=ntt_convolution(fp,fps_inv(g,g.size()*2));
    std::vector<T>nxtg(g);
    nxtg.resize(g.size()*2);
    for(int i=0;i<nxtg.size();i++){
      if(i<fp.size())nxtg[i]+=fp[i];
      nxtg[i]*=inv2;
    }
    std::swap(g,nxtg);
  }
  g.insert(g.begin(),prefix_zero,0);
  g.resize(deg);
  for(int i=0;i<g.size();i++)g[i]*=sq;
  return g;
}
using mint=mint998;
void SOLVE(){
  int n,m;
  cin>>n>>m;
  vector<mint>f{0},g{1};
  rep(i,2,m+1){
    vector<mint>f2(i+1),g2(i+2);
    f2[1]++;
    f2[i]--;
    g2[0]++;
    g2[i]-=2;
    g2[i+1]++;
    vector<mint>nf,ng;
    vector<mint>a=ntt_convolution(f,g2),a2=ntt_convolution(f2,g);
    nf.resize(max(a.size(),a2.size()));
    rep(i,a.size())nf[i]+=a[i];
    rep(i,a2.size())nf[i]+=a2[i];
    ng=ntt_convolution(g,g2);
    f=move(nf);
    g=move(ng);
  }
  vector<mint>d(max(f.size(),g.size()));
  rep(i,g.size())d[i]+=g[i];
  rep(i,f.size())d[i]-=f[i];
  if(g.size()>=d.size())d.resize(g.size()+1);
  cout<<bostan_mori(g,d,n)<<endl;
}