#include<bits/stdc++.h>
#define LL long long
#define LLL __int128
#define uint unsigned
#define ldb long double
#define uLL unsigned long long
using namespace std;
const int N=55,M=16,Mod=998244353;
int n,m,c,L,sb,ans=1;
int b[N],frc[N],ivf[N],pw[N][N],pwb[N][N],F[N],f[N][N][1<<M];
inline int qpow(int x,int y,int z=1){
	for(;y;(y>>=1)&&(x=(LL)x*x%Mod))if(y&1)z=(LL)z*x%Mod;return z;
}
inline int Langrange(int* F,int n,int x){
    if(x<=n)return F[x];
    int z=0;
    for(int i=0;i<=n+1;++i){
        int v=1,w=F[i];
        for(int j=0;j<=n+1;++j)if(i!=j)v=(LL)v*(i-j)%Mod,w=(LL)w*(x-j)%Mod;
        z=(z+qpow(v,Mod-2,w))%Mod;
    }
    return z<0?z+Mod:z;
}
signed main(){
    cin.tie(0)->sync_with_stdio(0);
    cin>>n>>m>>c,L=n+1;
    for(int i=0;i<=n-m;++i)cin>>b[i],sb+=b[i];
    while(n<m+m)ans=1ll*ans*c%Mod,--n,--m;
    sb=qpow(sb,Mod-2);
    for(int i=0;i<=n-m;++i)b[i]=(LL)b[i]*sb%Mod;
    for(int i=0;i<=n-m;++i){
        pwb[i][0]=1;
        for(int j=1;j<=L;++j)pwb[i][j]=(LL)pwb[i][j-1]*b[i]%Mod;
    }
    for(int i=0;i<=L;++i){
        pw[i][0]=1;
        for(int j=1;j<=n;++j)pw[i][j]=(LL)pw[i][j-1]*i%Mod;
    }
    frc[0]=1,ivf[0]=1;
    for(int i=1;i<=L;++i)
        frc[i]=(LL)frc[i-1]*i%Mod,ivf[i]=qpow(frc[i],Mod-2);
    // if(m+m+m<=n){
    if(m<=16){
        f[0][0][1]=1;
        for(int i=0;i<=n-m;++i)
            for(int S=1;S<(1<<m);S+=2)
                for(int U=(1<<m)-1-(S>>1),T=U;;T=(T-1)&U){
                    for(int j=0;j<=L;++j)if(f[i][j][S])
                        for(int k=0;j+k<=L;++k)
                            f[i+1][j+k][S>>1|T]=(f[i+1][j+k][S>>1|T]+(LL)f[i][j][S]*pw[k][__builtin_popcount(T)]%Mod*ivf[k]%Mod*pwb[i][k])%Mod;
                    if(!T)break;
                }
        for(int i=0;i<=L;++i)F[i]=(LL)f[n-m+1][i][(1<<m)-1]*frc[i]%Mod,cout<<F[i]<<" \n"[i==L];
        cout<<(LL)Langrange(F,L,c)*ans%Mod<<'\n';
    }
    else{

    }
    return 0;
}
/*
1 1 1 1 1 1 1 1 1 1 1 1
                1 1 1 1 1 1 1 1 1 1 1 1
*/