#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=int>
struct Edge{
  int from,to;
  T weight;
  int index;
  Edge(int from_,int to_,T weight_=T(),int index_=-1):from(from_),to(to_),weight(weight_),index(index_){}
  Edge():from(-1),to(-1),weight(),index(-1){}
  friend std::ostream &operator<<(std::ostream &os,const Edge&e){
    os<<'[';
    os<<"from:"<<e.from;
    os<<"to:"<<e.to;
    os<<"weight:"<<e.weight;
    os<<"index:"<<e.index;
    os<<']';
    return os;
  }
};
template<typename T=int>
struct Tree{
  int n,r;
  std::vector<Edge<T>>edge;
  std::vector<Edge<T>>g;
  std::vector<int>ptr;
  struct tree_range{
    using iterator=typename std::vector<Edge<T>>::iterator;
    iterator l,r;
    iterator begin()const{return l;}
    iterator end()const{return r;}
    int size()const{return r-l;}
    bool empty()const{return !size();}
    Edge<T> &operator[](int i)const{return l[i];}
  };
  struct const_tree_range{
    using iterator=typename std::vector<Edge<T>>::const_iterator;
    iterator l,r;
    iterator begin()const{return l;}
    iterator end()const{return r;}
    int size()const{return r-l;}
    bool empty()const{return !size();}
    const Edge<T> &operator[](int i)const{return l[i];}
  };
  explicit Tree(int n_):n(n_){
    edge.reserve(n-1);
  }
  Tree():n(0){}
  Tree(int n_,const std::vector<Edge<T>>&e,bool dir=false):n(n_),r(-1),edge(e){
    if(!dir)build();
    else{
      std::vector<bool>seen(n,false);
      ptr.resize(n+1);
      for(const Edge<T>&i:edge)ptr[i.from]++,ptr[i.to]++,seen[i.to]=true;
      for(int i=1;i<=n;i++)ptr[i]+=ptr[i-1];
      r=std::find(seen.begin(),seen.end(),false)-seen.begin();
      assert(ptr[n]==n*2-2);
      g.resize(ptr[n]);
      for(const Edge<T>&i:edge)g[--ptr[i.to]]=Edge<T>(i.to,i.from,i.weight,i.index);
      for(const Edge<T>&i:edge)g[--ptr[i.from]]=i;
    }
  }
  template<bool weighted=false,bool index=1>
  void read(){
    for(int i=0;i<n-1;i++){
      int u,v;
      T w=T();
      std::cin>>u>>v;
      if constexpr(index)u--,v--;
      if constexpr(weighted)std::cin>>w;
      else w=1;
      edge.emplace_back(u,v,w,i);
    }
    build();
  }
  template<bool index=1>
  void readp(){
    ptr.resize(n+1);
    for(int i=1;i<n;i++){
      int p;
      std::cin>>p;
      if constexpr(index)p--;
      edge.emplace_back(p,i,1,i-1);
      ptr[p]++;
      ptr[i]++;
    }
    for(int i=1;i<=n;i++)ptr[i]+=ptr[i-1];
    g.resize(n*2-2);
    for(auto&&[u,v,w,i]:edge)g[--ptr[v]]=Edge<T>(v,u,w,i);
    for(int i=0;i<n-1;i++){
      g[--ptr[edge[i].from]]=edge[i];
    }
    r=0;
  }
  void add_edge(int u,int v){edge.emplace_back(u,v,1,edge.size());}
  void add_edge(int u,int v,T w){edge.emplace_back(u,v,w,edge.size());}
  void add_edge(int u,int v,T w,int idx){edge.emplace_back(u,v,w,idx);}
  inline bool is_directed()const{return r!=-1;}
  void build(){
    r=-1;
    ptr.assign(n+1,0);
    for(auto&&[u,v,w,i]:edge)ptr[u]++,ptr[v]++;
    for(int i=1;i<=n;i++)ptr[i]+=ptr[i-1];
    assert(ptr[n]==n*2-2);
    g.resize(n*2-2);
    for(auto&&[u,v,w,i]:edge){
      g[--ptr[u]]=Edge(u,v,w,i);
      g[--ptr[v]]=Edge(v,u,w,i);
    }
  }
  void remove_parent(int root=0){
    if(r!=-1){
      if(r!=root)build();
      else return;
    }
    edge.resize(n-1);
    std::vector<int>par(n,-1);
    par[root]=-1;
    std::queue<int>que;
    que.push(root);
    while(!que.empty()){
      int x=que.front();
      que.pop();
      for(int i=ptr[x];i<ptr[x+1];){
        const Edge<T>&e=g[i];
        if(e.to!=par[x]){
          par[e.to]=x;
          assert(e.index<n-1);
          edge[e.index]=e;
          que.push(e.to);
          i++;
        }
        else{
          if(i+1==ptr[x+1])break;
          std::swap(g[i],g[ptr[x+1]-1]);
        }
      }
    }
    r=root;
  }
  void re_index(){
    assert((int)edge.size()==n-1);
    for(int i=0;i<n-1;i++)edge[i].index=i;
    build();
    if(r!=-1)remove_parent(r);
  }
  std::vector<int>bfs_order()const{
    assert(is_directed());
    std::vector<int>bfs(n);
    int p=0,q=0;
    bfs[q++]=root();
    while(p<q){
      int x=bfs[p++];
      for(const Edge<T>&e:(*this)[x])bfs[q++]=e.to;
    }
    return bfs;
  }
  std::vector<int>dfs_order()const{
    assert(is_directed());
    std::vector<int>res;
    res.reserve(n);
    std::vector<int>st(n);
    int p=0;
    st[p++]=root();
    while(p){
      int x=st[--p];
      res.push_back(x);
      p+=(*this)[x].size();
      for(const Edge<T>&e:(*this)[x])st[--p]=e.to;
      p+=(*this)[x].size();
    }
    return res;
  }
  std::vector<int>rbfs_order()const{
    std::vector<int>bfs=bfs_order();
    std::reverse(bfs.begin(),bfs.end());
    return bfs;
  }
  void hld(){
    assert(is_directed());
    std::vector<int>sub(n);
    for(int x:rbfs_order()){
      sub[x]=1;
      int mx=-1;
      for(Edge<T>&e:(*this)[x]){
        sub[x]+=sub[e.to];
        if(mx<sub[e.to]){
          mx=sub[e.to];
          std::swap((*this)[x][0],e);
        }
      }
    }
  }
  std::pair<std::vector<int>,std::vector<int>>in_out_order(){
    assert(is_directed());
    std::vector<int>in(n),out(n);
    int p=0;
    auto dfs=[&](auto self,int x)->void {
      in[x]=p++;
      for(const Edge<T>&e:(*this)[x]){
        self(self,e.to);
      }
      out[x]=p;
    };
    dfs(dfs,root());
    return std::make_pair(in,out);
  }
  std::pair<T,std::vector<int>>diameter()const{
    assert(!is_directed());
    static constexpr T inf=std::numeric_limits<T>::max();
    std::vector<T>dst(n,inf);
    dst[0]=0;
    std::vector<int>que(n);
    int p=0,q=1;
    que[0]=0;
    while(p<q){
      int x=que[p++];
      for(const Edge<T>&e:(*this)[x])if(dst[e.to]==inf){
        dst[e.to]=dst[x]+e.weight;
        que[q++]=e.to;
      }
    }
    int u=std::max_element(dst.begin(),dst.end())-dst.begin();
    std::fill(dst.begin(),dst.end(),inf);
    dst[u]=0;
    p=0,q=1;
    que[0]=u;
    while(p<q){
      int x=que[p++];
      for(const Edge<T>&e:(*this)[x])if(dst[e.to]==inf){
        dst[e.to]=dst[x]+e.weight;
        que[q++]=e.to;
      }
    }
    int v=std::max_element(dst.begin(),dst.end())-dst.begin();
    T weight=dst[v];
    std::vector<int>res;
    while(u!=v){
      res.push_back(v);
      for(const Edge<T>&e:(*this)[v])if(dst[e.to]<dst[v]){
        v=e.to;
        break;
      }
    }
    res.push_back(u);
    return std::make_pair(weight,res);
  }
  int size()const{return n;}
  tree_range operator[](int i){return tree_range{g.begin()+ptr[i],g.begin()+ptr[i+1]-(r!=-1&&r!=i)};}
  const_tree_range operator[](int i)const{return const_tree_range{g.begin()+ptr[i],g.begin()+ptr[i+1]-(r!=-1&&r!=i)};}
  const Edge<T>& get_edge(int i)const{return edge[i];}
  inline int parent(int i)const{return i==r?-1:g[ptr[i+1]-1].to;}
  const Edge<T>& parent_edge(int i)const{
    assert(r!=-1&&i!=r);
    return g[ptr[i+1]-1];
  }
  inline int root()const{return r;}
  typename std::vector<Edge<T>>::iterator begin(){return edge.begin();}
  typename std::vector<Edge<T>>::iterator end(){return edge.end();}
  typename std::vector<Edge<T>>::const_iterator begin()const{return edge.begin();}
  typename std::vector<Edge<T>>::const_iterator end()const{return edge.end();}
};
struct StaticTopTree{
private:
  template<typename T>
  void build(Tree<T>t){
    int n=t.size();
    left.reserve(n*2-1),right.reserve(n*2-1),par.reserve(n*2-1),A.reserve(n*2-1),B.reserve(n*2-1);
    left.resize(n,-1),right.resize(n,-1),par.resize(n,-1),A.resize(n),B.resize(n);
    for(int i=0;i<n;i++){
      A[i]=t.parent(i);
      B[i]=i;
    }
    auto dfs=[&](auto self,int x)->std::pair<int,int> {
      std::vector<std::pair<int,int>>vs{{0,x}};
      while(t[x].size()>=1){
        std::priority_queue<std::pair<int,int>,std::vector<std::pair<int,int>>,std::greater<std::pair<int,int>>>que;
        int heavy=t[x][0].to;
        que.emplace(0,heavy);
        for(int i=1;i<t[x].size();i++)que.push(self(self,t[x][i].to));
        while((int)que.size()>=2){
          auto [d1,v1]=que.top();que.pop();
          auto [d2,v2]=que.top();que.pop();
          if(B[v2]==heavy)std::swap(d1,d2),std::swap(v1,v2);
          int nv=left.size();
          left.push_back(v1),right.push_back(v2),par.push_back(-1),A.push_back(x),B.push_back(B[v1]);
          par[v1]=par[v2]=nv;
          que.emplace(std::max(d1,d2)+1,nv);
        }
        vs.push_back(que.top());
        while(true){
          int sz=vs.size();
          if(sz>=3&&(vs[sz-3].first==vs[sz-2].first||vs[sz-3].first<=vs[sz-1].first)){
            int nv=left.size();
            left.push_back(vs[sz-3].second),right.push_back(vs[sz-2].second),par.push_back(-1),A.push_back(A[vs[sz-3].second]),B.push_back(B[vs[sz-2].second]);
            par[vs[sz-3].second]=par[vs[sz-2].second]=nv;
            vs[sz-3].first=std::max(vs[sz-3].first,vs[sz-2].first)+1;
            vs[sz-3].second=nv;
            vs[sz-2]=vs[sz-1];
            vs.pop_back();
          }
          else if(sz>=2&&vs[sz-2].first<=vs[sz-1].first){
            int nv=left.size();
            left.push_back(vs[sz-2].second),right.push_back(vs[sz-1].second),par.push_back(-1),A.push_back(A[vs[sz-2].second]),B.push_back(B[vs[sz-1].second]);
            par[vs[sz-2].second]=par[vs[sz-1].second]=nv;
            vs[sz-2].first=std::max(vs[sz-2].first,vs[sz-1].first)+1;
            vs[sz-2].second=nv;
            vs.pop_back();
          }
          else break;
        }
        x=heavy;
      }
      while((int)vs.size()>=2){
        int sz=vs.size();
        int nv=left.size();
        left.push_back(vs[sz-2].second),right.push_back(vs[sz-1].second),par.push_back(-1),A.push_back(A[vs[sz-2].second]),B.push_back(B[vs[sz-1].second]);
        par[vs[sz-2].second]=par[vs[sz-1].second]=nv;
        vs[sz-2].first=std::max(vs[sz-2].first,vs[sz-1].first)+1;
        vs[sz-2].second=nv;
        vs.pop_back();
      }
      return vs[0];
    };
    dfs(dfs,t.root());
  }
public:
  std::vector<int>left,right,par,A,B;
  StaticTopTree(){}
  template<typename T>
  explicit StaticTopTree(Tree<T>t,int){
    build(std::move(t));
  }
  template<typename T>
  explicit StaticTopTree(Tree<T>t){
    assert(t.is_directed());
    t.hld();
    build(std::move(t));
  }
};
template<typename T=int>
struct CentroidDecomposition:public Tree<T>{
private:
  using Tree<T>::Tree;
  using Tree<T>::g;
  using Tree<T>::ptr;
  using Tree<T>::remove_parent;
  using Tree<T>::hld;
  int boundaryA1,boundaryB1,boundaryA2,boundaryB2;
  std::vector<Edge<T>>adj1,adj2;
  bool prepared=false;
  StaticTopTree stt;
  void prepare(){
    if(prepared)return;
    remove_parent();
    hld();
    stt=StaticTopTree(*this,0);
    prepared=true;
  }
public:
  template<typename Func>
  void run(const Func&f){
    prepare();
    int n=this->size();
    auto dfs=[&](auto self,int nd)->std::vector<Edge<T>> {
      if(nd<n){
        std::vector<Edge<T>>res(1);
        if(nd==0)res[0]=Edge<T>(-1,0);
        else{
          res[0]=g[ptr[nd+1]-1];
          std::swap(res[0].from,res[0].to);
        }
        return res;
      }
      int lv=stt.left[nd],rv=stt.right[nd];
      std::vector<Edge<T>>lch=self(self,lv);
      std::vector<Edge<T>>rch=self(self,rv);
      boundaryA1=stt.A[lv];
      boundaryB1=stt.B[lv];
      boundaryA2=stt.A[rv];
      boundaryB2=stt.B[rv];
      std::swap(adj1,lch);
      std::swap(adj2,rch);
      f(boundaryA1,boundaryA2);
      std::swap(adj1,lch);
      std::swap(adj2,rch);
      if(boundaryA1==boundaryA2){
        if(std::ssize(lch)<std::ssize(rch))std::swap(lch,rch);
        lch.insert(lch.end(),rch.begin(),rch.end());
      }
      return lch;
    };
    dfs(dfs,n*2-2);
  }
  typename Tree<T>::tree_range get(int c,int x){
    if(c==0){
      if(x==boundaryA1)return typename Tree<T>::tree_range{adj1.begin(),adj1.end()};
      if(x==boundaryB1)return typename Tree<T>::tree_range{g.begin()+ptr[x+1]-(!!x),g.begin()+ptr[x+1]};
      return typename Tree<T>::tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else if(c==1){
      if(x==boundaryA2)return typename Tree<T>::tree_range{adj2.begin(),adj2.end()};
      if(x==boundaryB2)return typename Tree<T>::tree_range{g.begin()+ptr[x+1],g.begin()+ptr[x+1]};
      return typename Tree<T>::tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else std::abort();
  }
  typename Tree<T>::const_tree_range get(int c,int x)const{
    if(c==0){
      if(x==boundaryA1)return typename Tree<T>::const_tree_range{adj1.begin(),adj1.end()};
      if(x==boundaryB1)return typename Tree<T>::const_tree_range{g.begin()+ptr[x+1]-(!!x),g.begin()+ptr[x+1]};
      return typename Tree<T>::const_tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else if(c==1){
      if(x==boundaryA2)return typename Tree<T>::const_tree_range{adj2.begin(),adj2.end()};
      if(x==boundaryB2)return typename Tree<T>::const_tree_range{g.begin()+ptr[x+1],g.begin()+ptr[x+1]};
      return typename Tree<T>::const_tree_range{g.begin()+ptr[x],g.begin()+ptr[x+1]};
    }
    else std::abort();
  }
  CentroidDecomposition(const Tree<T>&t){Tree<T>::operator=(t);}
};
#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);}
  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.val()>b.val();}
  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.val()>=b.val();}
  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>;
#include<initializer_list>
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;
  }
  static T rising_factorial(int x,int n){
    assert(n>=0);
    if(x>0){
      resize(x+n-1);
      return fact[x+n-1]*factinv[x-1];
    }
    else if(x+n>0)return T();
    else{
      resize(-x);
      T res=fact[-x]*factinv[-x-n];
      if(n&1)res=-res;
      return res;
    }
  }
  static T falling_factorial(int x,int n){return rising_factorial(x-n+1,n);}
};
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};
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/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<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){
  #ifdef NTT_SIMD
  if((int)a.size()>=32){
    dft_simd(a);
    return;
  }
  #endif
  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){
  #ifdef NTT_SIMD
  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 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){
    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::enable_if_t<is_static_modint_v<T>,T>fast_factorial(int n){
  if(n>=T::mod())return T();
  static bool prepared=false;
  static std::vector<T>f;
  static constexpr int b=9;
  static constexpr int sz=T::mod()/(1<<b);
  if(!prepared){
    F<T>::resize(sz);
    f={1};
    for(int i=0;i<b;i++){
      std::vector<T>x(4<<i),y(4<<i);
      for(int j=0;j<(4<<i);j++)x[j]=F<T>::inverse(j+1);
      for(int j=0;j<(1<<i);j++){
        y[j]=f[j]*F<T>::factorial_inv(j)*F<T>::factorial_inv((1<<i)-j-1);
        if(((1<<i)-j-1)&1)y[j]=-y[j];
      }
      dft(x),dft(y);
      for(int j=0;j<(4<<i);j++)x[j]*=y[j];
      idft(x);
      f.resize(4<<i);
      T inv=T::raw(4<<i).inv();
      for(int j=0;j<(3<<i);j++)f[j+(1<<i)]=x[j+(1<<i)-1]*inv*F<T>::P((1<<i)+j,1<<i);
      std::vector<T>nf(2<<i);
      for(int j=0;j<(2<<i);j++)nf[j]=f[j*2]*f[j*2+1]*T::raw((2*j+1)<<i);
      std::swap(f,nf);
    }
    constexpr int s=ceil_pow2(sz-1);
    std::vector<T>x(s),y(s);
    for(int i=0;i<sz;i++)x[i]=F<T>::inverse(i+1);
    for(int i=0;i<(1<<b);i++){
      y[i]=f[i]*F<T>::factorial_inv(i)*F<T>::factorial_inv((1<<b)-i-1);
      if(!(i&1))y[i]=-y[i];
    }
    dft(x),dft(y);
    for(int i=0;i<s;i++)x[i]*=y[i];
    idft(x);
    T inv=T::raw(s).inv();
    f.resize(sz);
    for(int i=0;i<(1<<b);i++){
      f[i]*=T::raw((i+1)<<b);
      if(i)f[i]*=f[i-1];
    }
    for(int i=(1<<b);i<sz;i++){
      f[i]=f[i-1]*x[i-1]*inv*F<T>::P(i,1<<b)*T::raw((i+1)<<b);
    }
    prepared=true;
  }
  if((n&((1<<b)-1))<=1<<(b-1)||n/(1<<b)>=sz){
    T res=n>=(1<<b)?f[n/(1<<b)-1]:T::raw(1);
    for(int i=(n&~((1<<b)-1))+1;i<=n;i++)res*=T::raw(i);
    return res;
  }
  else{
    T c=T::raw(1);
    for(int i=(n+(1<<b)-1)&~((1<<b)-1);i>n;i--)c*=T::raw(i);
    return f[((n+(1<<b)-1)>>b)-1]/c;
  }
}
template<typename T>
T fast_comb(long long n,long long k){
  if(n<0||k<0)return T();
  T res=1;
  while(k){
    long long n2=n%T::mod(),k2=k%T::mod();
    n/=T::mod(),k/=T::mod();
    if(n2<k2)return T();
    res*=fast_factorial<T>(n2);
    res/=fast_factorial<T>(k2);
    res/=fast_factorial<T>(n2-k2);
  }
  return res;
}
using mint=mint998;
void SOLVE(){
  int n;
  ll k;
  cin>>n>>k;
  n++;
  vector<mint>a(n);
  cin>>a;
  CentroidDecomposition<> cd(n);
  cd.readp<0>();
  vector<int>dep(n);
  for(int x:cd.bfs_order()){
    for(auto e:cd[x])dep[e.to]=dep[x]+1;
  }
  vector<mint>ans(a);
  vector<mint>coefs(n+10);
  rep(i,coefs.size())coefs[i]=fast_comb<mint>(k,i);
  cd.run([&](int a1,int a2){
    if(a1==a2)return;
    vector<mint>vals;
    auto dfs=[&](auto self,int x,int p,int dep)->void {
      if(x!=a2){
        if(vals.size()<=dep)vals.resize(dep+1);
        vals[dep]+=a[x];
      }
      for(auto e:cd.get(1,x))if(e.to!=p)self(self,e.to,x,dep+1);
    };
    dfs(dfs,a2,-1,0);
    reverse(all(vals));
    vals.pop_back();
    vector<mint>coef(coefs.begin(),coefs.begin()+min(vals.size()+dep[a2]-dep[a1]+2,coefs.size()));
    vector<mint>f=ntt_convolution(coef,vals);
    int v=a2;
    rep(i,vals.size(),f.size()){
      ans[v]+=f[i];
      v=cd.parent(v);
      if(v==a1)break;
    }
  });
  rep(i,n)cout<<ans[i]<<'\n';
}