#include <iostream>
#include <algorithm>
#include <assert.h>
constexpr int p(998244353),N(2e6+10),_3((p+1)/3);
int inv[N],ifac[N],fac[N];
int fp(int a,int b){int ans(1),off(a);while(b){if(b&1) ans=1ll*ans*off%p;off=1ll*off*off%p;b>>=1;}return ans;}
void K(int a,int b,int c,int L,int deg,int coef,int res[])
{
	assert(a>=0);assert(b>=0);assert(c>=0);
	for(int i(0);i<=L && 3*i+a+b+c<=deg;++i) res[3*i+a+b+c]=(res[3*i+a+b+c]+1ll*coef*ifac[i+a]%p*ifac[i+b]%p*ifac[i+c])%p;
}
void J(int a,int b,int c,int L,int deg,int coef,int res[])
{
	assert(a>=0);assert(b>=0);assert(c>=0);
	for(int i(0);i<=L && 3*i+a+b+c<=deg;++i) res[3*i+a+b+c]=(res[3*i+a+b+c]+1ll*coef*ifac[i+a]%p*ifac[i+b]%p*ifac[i+c]%p*i)%p;
}
void F(int a,int b,int c,int deg,int coef,int res[])
{
	assert(a>=0);assert(b>=0);assert(c>=0);coef=1ll*coef*ifac[a]%p*ifac[b]%p;
	for(int i(0);i<=c && i+a+b<=deg;++i) res[i+a+b]=(res[i+a+b]+1ll*coef*ifac[i])%p;
}
void F(int a,int c,int deg,int coef,int res[])
{
	assert(a>=0);assert(c>=0);coef=1ll*coef*ifac[a]%p;
	for(int i(0);i<=c && i+a<=deg;++i) res[i+a]=(res[i+a]+1ll*coef*ifac[i])%p;
}
void FF(int a,int b,int c,int deg,int coef,int res[])
{
	assert(a>=0);assert(b>=0);assert(c>=0);
	int nd(deg-a);if(nd<0) return;static int T[N];
	std::fill(T,T+nd,0);F(b,c,nd-1,p-1,T);F(c,b,nd-1,p-1,T);coef=1ll*coef*ifac[a]%p;
	res[a]=(res[a]+coef)%p;
	for(int i(1),t(1);i<=nd;++i)
	{
		t=(2ll*t+T[i-1])*inv[i]%p;
		res[a+i]=(res[a+i]+1ll*t*coef)%p;
	}
}
void fg(int a,int b,int c,int L,int deg,int fx[],int gx[])
{
	assert(a>0);assert(b>0);assert(c>0);if(deg<0) return;
	int numf(0),numg(0);
	for(int i(0);i*2+a+b<=deg && i<=L;++i)
	{
		int j(deg-i*2-a-b);
		if(j<=i+c) numf=(numf+1ll*ifac[i+a]*ifac[i+b]%p*ifac[j])%p,
				   numg=(numg+1ll*ifac[i+a]*ifac[i+b]%p*ifac[j]%p*i)%p;
	}
	fx[deg]=numf,gx[deg]=numg;
	static int t1[N],t2[N];
	std::fill(t1,t1+deg,0);
	std::fill(t2,t2+deg,0);
	F(L+a,L+b,L+c,deg-2,p-2,t1+1);
	F(a-1,b-1,c-1,deg-2,2,t1+1);
	K(a-1,b-1,c,L,deg-2,2,t1+1);
	J(a,b,c,L,deg-1,p-1,t1);
	K(a,b,c,L,deg-1,1,t2);
	int x(1ll*(p-2)*a%p*b%p);
	for(int i(deg);i;--i)
	{
		fx[i-1]=(2*(p-gx[i])+1ll*(p+i-a-b)*fx[i]+t2[i-1])%p;
		gx[i-1]=(2ll*(p+i-1-a-b)*fx[i-1]+1ll*x*fx[i]+1ll*(p-i-a-b)*gx[i]+2*(i>1?t2[i-2]:0)+t1[i-1])%p*_3%p;
	}
}
void G(int a,int b,int c,int L,int deg,int coef,int res[],int fb[],int gb[],int fc[],int gc[])
{
	assert(a>0);assert(b>0);assert(c>0);if(deg<0) return;
	static int T[N];std::fill(T,T+deg,0);
	FF(a-1,b-1,c-1,deg-1,1,T);FF(a+L,b+L,c+L,deg-1,p-1,T);
	K(a-1,b,c,L,deg-1,p-1,T);
	for(int i(0);i<deg;++i)
	{
		T[i]=(T[i]+1ll*a*(fb[i+1]+fc[i+1])+p-fb[i]+p-fc[i]+gb[i+1]+gc[i+1])%p;
	}
	for(int i(1),t(0);i<=deg;++i)
	{
		t=(3ll*t+T[i-1])*inv[i]%p;
		res[i]=(res[i]+1ll*coef*t)%p;
	}
}
void H(int a,int b,int c,int L,int deg,int coef,int res[])
{
	assert(a>0);assert(b>0);assert(c>0);if(deg<0) return;
	static int fa[N],fb[N],fc[N],ga[N],gb[N],gc[N];
	fg(b,c,a,L,deg-1,fa,ga);
	fg(a,c,b,L,deg-1,fb,gb);
	fg(a,b,c,L,deg-1,fc,gc);
	static int T[N];std::fill(T,T+deg,0);
	G(a,b,c,L,deg-1,p-1,T,fb,gb,fc,gc);
	G(b,a,c,L,deg-1,p-1,T,fa,ga,fc,gc);
	G(c,a,b,L,deg-1,p-1,T,fa,ga,fb,gb);
	res[0]=(res[0]+1ll*(L+1)*coef)%p;
	for(int i(1),t(L+1);i<=deg;++i)
	{
		t=(3ll*t+T[i-1])*inv[i]%p;
		res[i]=(res[i]+1ll*coef*t)%p;
	}
}
int main()
{
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);int a,b,c,n;std::cin>>a>>b>>c>>n;
	fac[0]=1;for(int i(1);i<N;++i) fac[i]=1ll*fac[i-1]*i%p;ifac[N-1]=fp(fac[N-1],p-2);
	for(int i(N-1);i;--i) ifac[i-1]=1ll*ifac[i]*i%p,inv[i]=1ll*ifac[i]*fac[i-1]%p;
	static int fx[N];int x[3]={a,b,c};std::sort(x,x+3);int m(x[2]);
	FF(0,m-x[0],m-x[1],n,p-1,fx);
	H(m-a+1,m-b+1,m-c+1,n-1,n,p-1,fx);
	for(int i(1),j(_3);i<=n;++i,j=1ll*j*_3%p) std::cout<<(m+n+1+1ll*fac[i]*fx[i]%p*j)%p<<"\n";
	return 0;
}