#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
    return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
	template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
	template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
	template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	ModInt inv() const {		// should be prime
		return pow(mod-2);
	}
	// ll extgcd(ll a,ll b,ll &x,ll &y) const{
	// 	ll p[]={a,1,0},q[]={b,0,1};
	// 	while(*q){
	// 		ll t=*p/ *q;
	// 		rep(i,3) swap(p[i]-=t*q[i],q[i]);
	// 	}
	// 	if(p[0]<0) rep(i,3) p[i]=-p[i];
	// 	x=p[1],y=p[2];
	// 	return p[0];
	// }
	// ModInt inv() const {
	// 	ll x,y;
	// 	extgcd(v,mod,x,y);
	// 	return make(normS(x+mod));
	// }

	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	bool operator<(const ModInt& b) const { return v<b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
using mint = ModInt<998244353>;
//using mint = ModInt<1000000007>;

V<mint> fact,ifact,invs;
mint Choose(int a,int b){
	if(b<0 || a<b) return 0;
	return fact[a] * ifact[b] * ifact[a-b];
}
void InitFact(int N){	//[0,N]
	N++;
	fact.resize(N);
	ifact.resize(N);
	invs.resize(N);
	fact[0] = 1;
	rep1(i,N-1) fact[i] = fact[i-1] * i;
	ifact[N-1] = fact[N-1].inv();
	for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);
	rep1(i,N-1) invs[i] = fact[i-1] * ifact[i];
}
// inplace_fmt (without bit rearranging)
// fft:
// 		a[rev(i)] <- \sum_j \zeta^{ij} a[j]
// invfft:
//		a[i] <- (1/n) \sum_j \zeta^{-ij} a[rev(j)]
// These two are inversions.


// !!! CHANGE IF MOD is unusual !!!
const int ORDER_2_MOD_MINUS_1 = 23;	// ord_2 (mod-1)
const mint PRIMITIVE_ROOT = 3; // primitive root of (Z/pZ)*

void fft(V<mint>& a){
	static constexpr uint mod = mint::mod;
	static constexpr uint mod2 = mod + mod;
	static const int H = ORDER_2_MOD_MINUS_1;
	static const mint root = PRIMITIVE_ROOT;
	static mint magic[H-1];

	int n = si(a);
	assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H);	// n should be power of 2

	if(!magic[0]){		// precalc
		rep(i,H-1){
			mint w = -root.pow(((mod-1)>>(i+2))*3);
			magic[i] = w;
		}
	}
	int m = n;
	if(m >>= 1){
		rep(i,m){
			uint v = a[i+m].v;					// < M
			a[i+m].v = a[i].v + mod - v;		// < 2M
			a[i].v += v;						// < 2M
		}
	}
	if(m >>= 1){
		mint p = 1;
		for(int h=0,s=0; s<n; s += m*2){
			for(int i=s;i<s+m;i++){
				uint v = (a[i+m] * p).v;		// < M
				a[i+m].v = a[i].v + mod - v;	// < 3M
				a[i].v += v;					// < 3M
			}
			p *= magic[__builtin_ctz(++h)];
		}
	}
	while(m){
		if(m >>= 1){
			mint p = 1;
			for(int h=0,s=0; s<n; s += m*2){
				for(int i=s;i<s+m;i++){
					uint v = (a[i+m] * p).v;		// < M
					a[i+m].v = a[i].v + mod - v;	// < 4M
					a[i].v += v;					// < 4M
				}
				p *= magic[__builtin_ctz(++h)];
			}
		}
		if(m >>= 1){
			mint p = 1;
			for(int h=0,s=0; s<n; s += m*2){
				for(int i=s;i<s+m;i++){
					uint v = (a[i+m] * p).v;								// < M
					a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v;	// < 2M
					a[i+m].v = a[i].v + mod - v;							// < 3M
					a[i].v += v;											// < 3M
				}
				p *= magic[__builtin_ctz(++h)];
			}
		}
	}
	rep(i,n){
		a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v;		// < 2M
		a[i].v = (a[i].v >= mod) ? a[i].v - mod : a[i].v;		// < M
	}
	// finally < mod !!
}
void invfft(V<mint>& a){
	static constexpr uint mod = mint::mod;
	static constexpr uint mod2 = mod + mod;
	static const int H = ORDER_2_MOD_MINUS_1;
	static const mint root = PRIMITIVE_ROOT;
	static mint magic[H-1];

	int n = si(a);
	assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H);	// n should be power of 2

	if(!magic[0]){		// precalc
		rep(i,H-1){
			mint w = -root.pow(((mod-1)>>(i+2))*3);
			magic[i] = w.inv();
		}
	}
	int m = 1;
	if(m < n>>1){
		mint p = 1;
		for(int h=0,s=0; s<n; s += m*2){
			for(int i=s;i<s+m;i++){
				ull x = a[i].v + mod - a[i+m].v;	// < 2M
				a[i].v += a[i+m].v;					// < 2M
				a[i+m].v = (p.v * x) % mod;			// < M
			}
			p *= magic[__builtin_ctz(++h)];
		}
		m <<= 1;
	}
	for(;m < n>>1; m <<= 1){
		mint p = 1;
		for(int h=0,s=0; s<n; s+= m*2){
			for(int i=s;i<s+(m>>1);i++){
				ull x = a[i].v + mod2 - a[i+m].v;	// < 4M
				a[i].v += a[i+m].v;					// < 4M
				a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v;	// < 2M
				a[i+m].v = (p.v * x) % mod;		// < M
			}
			for(int i=s+(m>>1); i<s+m; i++){
				ull x = a[i].v + mod - a[i+m].v;	// < 2M
				a[i].v += a[i+m].v;	// < 2M
				a[i+m].v = (p.v * x) % mod;	// < M
			}
			p *= magic[__builtin_ctz(++h)];
		}
	}
	if(m < n){
		rep(i,m){
			uint x = a[i].v + mod2 - a[i+m].v;	// < 4M
			a[i].v += a[i+m].v;	// < 4M
			a[i+m].v = x;	// < 4M
		}
	}
	const mint in = mint(n).inv();
	rep(i,n) a[i] *= in;	// < M
	// finally < mod !!
}

// A,B = 500000 -> 70ms
// verify https://judge.yosupo.jp/submission/44937
V<mint> multiply(V<mint> a, V<mint> b) {
	int A = si(a), B = si(b);
	if (!A || !B) return {};
	int n = A+B-1;
	int s = 1; while(s<n) s*=2;
	if(a == b){			// # of fft call : 3 -> 2
		a.resize(s); fft(a);
		rep(i,s) a[i] *= a[i];
	}else{
		a.resize(s); fft(a);
		b.resize(s); fft(b);
		rep(i,s) a[i] *= b[i];
	}
	invfft(a); a.resize(n);
	return a;
}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);
	InitFact(500010);

	int N; ll K; cin >> N >> K; N++;
	V<mint> A(N); rep(i,N) cin >> A[i];
	VV<int> G(N);
	rep1(i,N-1){
		int p; cin >> p;
		G[p].pb(i);
	}
	V<int> dep(N);
	per(i,N) for(int j: G[i]) chmax(dep[i],dep[j]+1);
	V<mint> ans(N);
	V<deque<mint>> s(N); // first
	VV<mint> t(N);		 // last

	auto dfs1 = [&](auto& self,int v) -> void{
		if(G[v].empty()){
			s[v].push_back(A[v]);
			return;
		}
		for(int u: G[v]) self(self,u);
		int heavy = G[v][0];
		for(int u: G[v]) if(dep[u] > dep[heavy]) heavy = u;
		swap(s[v],s[heavy]);
		for(int u: G[v]) if(u != heavy){
			rep(i,si(s[u])) s[v][i] += s[u][i];
		}
		s[v].push_front(A[v]);
	};
	dfs1(dfs1,0);

	auto dfs = [&](auto& self,int v,deque<mint>& deq) -> void{
		if(deq.empty()){
			int n = si(s[v]);
			V<mint> f(n); rep(i,n) f[i] = s[v][i];
			V<mint> g(n);
			{
				mint C = 1;
				rep(i,n){
					g[i] = C;
					assert(C == Choose(K,i));
					C *= K-i;
					C *= invs[i+1];
				}
				show(g);
				reverse(all(g));
			}
			auto h = multiply(f,g);
			t[v].resize(n);
			rep(i,n) t[v][i] = h[n-1+i];
			deq.resize(n);
			rep(i,n) deq[i] = t[v][i];
		}
		show(si(deq));
		show(v);
		show(deq[0]);
		show("--------");
		ans[v] = deq[0];
		deq.pop_front();
		if(G[v].empty()) return;

		int heavy = G[v][0];
		for(int u: G[v]) if(dep[u] > dep[heavy]) heavy = u;
		for(int u: G[v]) if(u != heavy){
			deque<mint> _;
			self(self,u,_);
			rep(i,dep[u]+1) deq[i] -= t[u][i];
		}
		self(self,heavy,deq);
	};
	deque<mint> _;
	dfs(dfs,0,_);
	rep(v,N) cout << ans[v] << endl;
}