#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<initializer_list>
constexpr bool isprime_constexpr(unsigned long long n){
  if(n==998244353)return true;
  if(n==1000000007)return true;
  if(n<64)return 2891462833508853932ll>>n&1;
  if(n%2==0)return false;
  unsigned long long d=n-1;
  int s=0;
  while(!(d&1))d>>=1,s++;
  int q=63;
  while(!(d>>q))q--;
  unsigned long long r=n;
  for(int i=0;i<5;i++)r*=2-r*n;
  auto redc=[&r,&n](__uint128_t x)->unsigned long long {
    x=(x+__uint128_t((unsigned long long)x*-r)*n)>>64;
    return x>=n?x-n:x;
  };
  __uint128_t r2=-__uint128_t(n)%n;
  unsigned long long one=redc(r2);
  for(unsigned long long base:{2,325,9375,28178,450775,9780504,1795265022}){
    if(base%n==0)continue;
    unsigned long long a=base=redc((base%n)*r2);
    for(int i=q-1;i>=0;i--){
      a=redc(__uint128_t(a)*a);
      if(d>>i&1)a=redc(__uint128_t(a)*base);
    }
    if(a==one)continue;
    for(int i=1;a!=n-one;i++){
      if(i>=s)return false;
      a=redc(__uint128_t(a)*a);
    }
  }
  return true;
}
constexpr int factorize_constexpr(unsigned long long n,unsigned long long*a){
  if(n<=1)return 0;
  int ptr=0;
  while(n%2==0){
    a[ptr++]=2;
    n/=2;
  }
  while(n>1){
    if(isprime_constexpr(n)){
      a[ptr++]=n;
      break;
    }
    unsigned long long pf=n;
    unsigned long long x=0,y=0;
    int c=1;
    do{
      x=((__uint128_t)x*x+c)%pf;
      y=((__uint128_t)y*y+c)%pf;
      y=((__uint128_t)y*y+c)%pf;
      unsigned long long g=std::gcd(x>y?x-y:y-x,pf);
      if(g==pf){
        c++;
        x=y=0;
        continue;
      }
      if(g>1)pf=g;
    }while(!isprime_constexpr(pf));
    while(n%pf==0){
      a[ptr++]=pf;
      n/=pf;
    }
  }
  return ptr;
}
#include<type_traits>
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);
}
namespace Random{
constexpr unsigned long long to_seed(const char*s){
  unsigned long long h=14695981039346656037ULL;
  while(*s){
    h^=static_cast<unsigned char>(*s++);
    h*=1099511628211ULL;
  }
  return h;
}
constexpr unsigned long long constexpr_random_seed=(to_seed(__TIME__)*0x9e3779b97f4a7c15ULL)^to_seed(__DATE__);
constexpr unsigned long long next_value(unsigned long long n){
  n^=n<<13;
  n^=n>>7;
  n^=n<<17;
  return n;
}
}
constexpr unsigned long long primitive_root_constexpr(unsigned long long x){
  if(!isprime_constexpr(x))throw "not prime";
  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;
  unsigned long long a[64]={};
  int ptr=factorize_constexpr(x-1,a);
  for(unsigned long long v=Random::constexpr_random_seed;;){
    unsigned long long g=v%(x-1)+1;
    bool ok=true;
    for(int i=0;i<ptr;i++){
      if(i>0&&a[i-1]==a[i])continue;
      if(pow_mod<unsigned long long>(g,(x-1)/a[i],x)==1){
        ok=false;
        break;
      }
    }
    if(ok)return g;
    v=Random::next_value(v);
  }
}
#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<auto m>
struct ntt_root{
  static_assert(1<=m&&m<(1ull<<63));
  static_assert(isprime_constexpr(m));
  using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>;
  using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>;
  static constexpr int rank2=lsb(m-1);
  static constexpr value_type g=primitive_root_constexpr(m);
  std::array<value_type,rank2+1>root,invroot;
  std::array<value_type,std::max(0,rank2-1)>rate2,invrate2;
  std::array<value_type,std::max(0,rank2-2)>rate3,invrate3;
  constexpr ntt_root(){
    root[rank2]=pow_mod<value_type>(g,m>>rank2,m);
    invroot[rank2]=pow_mod<value_type>(root[rank2],m-2,m);
    for(int i=rank2-1;i>=0;i--){
      root[i]=(mul_type)root[i+1]*root[i+1]%m;
      invroot[i]=(mul_type)invroot[i+1]*invroot[i+1]%m;
    }
    value_type prod=1,invprod=1;
    for(int i=0;i<rank2-1;i++){
      rate2[i]=(mul_type)root[i+2]*prod%m;
      invrate2[i]=(mul_type)invroot[i+2]*invprod%m;
      prod=(mul_type)prod*invroot[i+2]%m;
      invprod=(mul_type)invprod*root[i+2]%m;
    }
    prod=invprod=1;
    for(int i=0;i<rank2-2;i++){
      rate3[i]=(mul_type)root[i+3]*prod%m;
      invrate3[i]=(mul_type)invroot[i+3]*invprod%m;
      prod=(mul_type)prod*invroot[i+3]%m;
      invprod=(mul_type)invprod*root[i+3]%m;
    }
  }
};
template<typename T>
void dft(std::vector<T>&a){
  using value_type=typename T::value_type;
  using mul_type=typename T::mul_type;
  #ifdef NTT_SIMD
  if constexpr(std::numeric_limits<value_type>::digits<=32){
    if((int)a.size()>=32){
      dft_simd(a);
      return;
    }
  }
  #endif
  static constexpr ntt_root<T::mod()>r;
  static constexpr mul_type mod2=(mul_type)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 mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
        int of=s<<(h-len);
        for(int i=0;i<p;i++){
          const mul_type a0=a[i+of].val(),a1=(mul_type)a[i+of+p].val()*rot1,a2=(mul_type)a[i+of+p*2].val()*rot2,a3=(mul_type)a[i+of+p*3].val()*rot3;
          const mul_type m=(mul_type)T(a1+mod2-a3).val()*imag.val();
          const mul_type 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){
  using value_type=typename T::value_type;
  using mul_type=typename T::mul_type;
  #ifdef NTT_SIMD
  if constexpr(std::numeric_limits<value_type>::digits<=32){
    if((int)a.size()>=32){
      idft_simd(a);
      return;
    }
  }
  #endif
  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 mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
        int of=s<<(h-len+2);
        for(int i=0;i<p;i++){
          const mul_type 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 mul_type 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){
    if(n==0||m==0)return {};
    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>
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>power_projection(const std::vector<T>&f,const std::vector<T>&g,int m){
  assert(f.size()==g.size());
  const int n=ceil_pow2(f.size());
  std::vector<T>p(n*4),q(n*4);
  std::vector<T>prep(n*4),preq(n*4);
  T invn4=T(n*4).inv();
  for(int i=0;i<(int)f.size();i++)p[i+n-f.size()]=g[i],q[i]=-f[i];
  for(int x=n,y=1;x>1;x>>=1,y<<=1){
    std::copy(p.begin(),p.begin()+n*2,prep.begin());
    std::copy(q.begin(),q.begin()+n*2,preq.begin());
    dft(p),dft(q);
    for(int i=0;i<n*2;i++){
      T l=q[i*2],r=q[i*2+1];
      p[i*2]*=r,p[i*2+1]*=l;
      q[i*2]*=r,q[i*2+1]*=l;
    }
    idft(p),idft(q);
    for(int i=0;i<n*4;i++)p[i]*=invn4,q[i]*=invn4;
    for(int i=0;i<n*2;i++){
      p[n*2+i]+=prep[i];
      if(i%2==0)q[n*2+i]+=preq[i]+preq[i];
    }
    std::fill(prep.begin(),prep.end(),T()),std::fill(preq.begin(),preq.end(),T());
    for(int j=0;j<y*2;j++)for(int i=0;i<x/2;i++){
      prep[j*x+i]=p[j*x*2+i*2+1];
      preq[j*x+i]=q[j*x*2+i*2];
    }
    std::swap(p,prep);
    std::swap(q,preq);
  }
  for(int i=0;i<n;i++)p[i]=p[i*2],q[i]=q[i*2];
  p.resize(n),q.resize(n+1);
  q[n]=1;
  std::reverse(p.begin(),p.end()),std::reverse(q.begin(),q.end());
  p=ntt_convolution(p,fps_inv(q,m));
  p.resize(m);
  return p;
}
template<typename T>
void transposed_dft(std::vector<T>&a){
  using value_type=typename T::value_type;
  using mul_type=typename T::mul_type;
  #ifdef NTT_SIMD
  if constexpr(std::numeric_limits<value_type>::digits<=32){
    if((int)a.size()>=32){
      transposed_dft_simd(a);
      return;
    }
  }
  #endif
  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.root[2]);
      for(int s=0;s<(1<<(len-2));s++){
        const mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
        int of=s<<(h-len+2);
        for(int i=0;i<p;i++){
          const mul_type 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 mul_type 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){
  using value_type=typename T::value_type;
  using mul_type=typename T::mul_type;
  #ifdef NTT_SIMD
  if constexpr(std::numeric_limits<value_type>::digits<=32){
    if((int)a.size()>=32){
      transposed_idft_simd(a);
      return;
    }
  }
  #endif
  static constexpr ntt_root<T::mod()>r;
  static constexpr mul_type mod2=(mul_type)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 mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
        int of=s<<(h-len);
        for(int i=0;i<p;i++){
          const mul_type a0=a[i+of].val(),a1=(mul_type)a[i+of+p].val()*rot1,a2=(mul_type)a[i+of+p*2].val()*rot2,a3=(mul_type)a[i+of+p*3].val()*rot3;
          const mul_type m=(mul_type)T(a1+mod2-a3).val()*imag.val();
          const mul_type 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>
std::vector<T>transposed_ntt_convolution(std::vector<T>a,std::vector<T>b){
  assert(a.size()>=b.size());
  int n=a.size(),m=b.size();
  int s=ceil_pow2(n);
  T inv=T(s).inv();
  for(int i=0;i<n;i++)a[i]*=inv;
  a.resize(s),b.resize(s);
  transposed_idft(a);
  dft(b);
  for(int i=0;i<s;i++)a[i]*=b[i];
  transposed_dft(a);
  a.resize(n-m+1);
  return a;
}
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<optional>
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_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_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;
}
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;
    std::vector<T>l(b*2),r(b*2);
    for(int j=0;j<n*2;j+=b*4){
      std::copy(f2[i].begin()+j,f2[i].begin()+j+b,l.begin());
      std::copy(f2[i].begin()+j+b*2,f2[i].begin()+j+b*3,r.begin());
      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=transposed_ntt_convolution(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;
}
constexpr std::pair<long long,long long>ext_gcd(long long a,long long b){
  if(b==0)return std::make_pair(1,0);
  auto [x,y]=ext_gcd(b,a%b);
  std::swap(x,y);
  return std::make_pair(x,y-a/b*x);
}
template<std::signed_integral T>
constexpr std::pair<T,T> inv_mod(T a,T b){
  a%=b;
  if(a<0)a+=b;
  if(a==0)return std::make_pair(b,0);
  T s=b,t=a;
  T m0=0,m1=1;
  while(t){
    T u=s/t;
    s-=t*u;
    m0-=m1*u;
    std::swap(s,t);
    std::swap(m0,m1);
  }
  if(m0<0)m0+=b/s;
  return std::make_pair(s,m0);
}
template<auto m>
struct modint{
  static_assert(1<=m&&m<(1ull<<63));
  using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>;
  using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>;
private:
  value_type v;
  static constexpr value_type umod=m;
  constexpr modint sqrt_impl()const{
    if(this->val()<=1)return *this;
    if(umod%8==1){
      modint b=2;
      while(b.pow((umod-1)/2).val()==1)b++;
      value_type m2=umod-1;
      int e=0;
      while(m2%2==0)m2>>=1,e++;
      modint x=this->pow((m2-1)/2);
      modint y=(*this)*x*x;
      x*=*this;
      modint z=b.pow(m2);
      while(y.val()!=1){
        int j=0;
        modint t=y;
        while(t.val()!=1)t*=t,j++;
        z=z.pow((value_type(1))<<(e-j-1));
        x*=z;
        z*=z;
        y*=z;
        e=j;
      }
      return x;
    }
    else if(umod%8==5){
      modint res=this->pow((umod+3)/8);
      if((res*res).val()==this->val())return res;
      else return res*modint(2).pow((umod-1)/4);
    }
    else return this->pow((umod+1)/4);
  }
  template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
  static constexpr value_type take_mod(U x){
    if constexpr(std::numeric_limits<U>::max()<umod)return x;
    if constexpr(umod==(1ull<<61)-1){
      value_type res=(x>>61)+(x&umod);
      if(res>=umod)res-=umod;
      return res;
    }
    if constexpr(umod==(1ull<<61)-(1ull<<24)+1){
      static constexpr value_type mask=(1ull<<61)-1;
      value_type high=x>>61,low=x&mask;
      mul_type t=low+(mul_type(high)<<24)-high;
      high=t>>61,low=t&mask;
      low=low+(mul_type(high)<<24)-high;
      if(low>=umod)low-=umod;
      return low;
    }
    return x%umod;
  }
public:
  constexpr modint():v(0){}
  template<typename U,std::enable_if_t<std::signed_integral<U>||std::is_same_v<U,__int128_t>,std::nullptr_t> =nullptr>
  constexpr modint(U x){
    x%=std::make_signed_t<value_type>(umod);
    v=x>=0?x:x+umod;
  }
  template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
  constexpr modint(U x):v(take_mod<U>(x)){}
  static constexpr value_type mod(){return umod;}
  template<typename U>
  static constexpr modint raw(U x){
    modint res;
    res.v=x;
    return res;
  }
  constexpr std::make_signed_t<value_type> val()const{return v;}
  constexpr modint &operator+=(const modint&b){
    this->v+=b.v;
    if(this->v>=umod)this->v-=umod;
    return *this;
  }
  constexpr modint &operator-=(const modint&b){
    this->v-=b.v;
    if(this->v>=umod)this->v+=umod;
    return *this;
  }
  constexpr modint &operator*=(const modint&b){
    this->v=take_mod(mul_type(this->v)*mul_type(b.v));
    return *this;
  }
  constexpr modint &operator/=(const modint&b){return *this*=b.inv();}
  constexpr modint operator+()const{return *this;}
  constexpr modint operator-()const{return modint()-*this;}
  friend constexpr modint operator+(const modint&a,const modint&b){return modint(a)+=b;}
  friend constexpr modint operator-(const modint&a,const modint&b){return modint(a)-=b;}
  friend constexpr modint operator*(const modint&a,const modint&b){return modint(a)*=b;}
  friend constexpr modint operator/(const modint&a,const modint&b){return modint(a)/=b;}
  constexpr auto operator<=>(const modint&)const=default;
  constexpr modint operator++(int){
    modint res=*this;
    this->v++;
    if(this->v==umod)this->v=0;
    return res;
  }
  constexpr modint operator--(int){
    modint res=*this;
    if(this->v==0)this->v=umod;
    this->v--;
    return res;
  }
  template<std::integral U>
  constexpr modint pow(U k)const{
    if constexpr(std::is_signed_v<U>){
      assert(0<=k);
    }
    modint res=1,a(*this);
    while(k){
      if(k&1)res*=a;
      a*=a;
      k>>=1;
    }
    return res;
  }
  constexpr modint inv()const{
    if constexpr(isprime_constexpr(umod)){
      if(std::is_constant_evaluated()){
        if(v==0){
          throw "no inverse";
        }
      }
      else assert(v!=0);
      return pow(umod-2);
    }
    else{
      modint res;
      auto [g,x]=inv_mod<std::make_signed_t<value_type>>(this->v,umod);
      if(std::is_constant_evaluated()){
        if(g!=1){
          throw "no inverse";
        }
      }
      else assert(g==1);
      res.v=x;
      return res;
    }
  }
  std::optional<modint>sqrt()const{
    if(this->val()<=1||this->pow((umod-1)/2)==1)return std::make_optional(this->sqrt_impl());
    else return std::nullopt;
  }
  friend std::istream &operator>>(std::istream&is,modint&b){
    long long a;
    is>>a;
    b=modint(a);
    return is;
  }
  friend std::ostream &operator<<(std::ostream&os,const modint&b){
    os<<b.val();
    return os;
  }
};
template<auto m>
struct std::hash<modint<m>>{
  std::size_t operator()(modint<m>x)const{
    return std::hash<typename modint<m>::value_type>(x.val());
  }
};
using mint998=modint<998244353>;
using mint107=modint<1000000007>;
using mint61=modint<2305843009213693951>;
using mint6124=modint<2305843009196916737>;
using mint=mint998;
void SOLVE(){
  int n,m;
  cin>>n>>m;
  vector<mint>f(n),g(n),h(n);
  cin>>f>>g>>h;
  vector<mint>one(n);
  one[0]=1;
  auto g2=power_projection(g,one,n);
  debug(g2);
  rep(i,n)g2[i]*=h[i];
  vector<mint>x(m);
  rep(i,m)x[i]=f[1].pow(i);
  auto ans=multipoint_evaluation(g2,x);
  rep(i,m)cout<<ans[i]<<" \n"[i+1==m];
}