小朋友和二叉树

#include<bits/stdc++.h>
#define il inline
#define reg register int
#define numb (ch^‘0‘)
using namespace std;
typedef long long ll;
il void rd(int &x){
    char ch;bool fl=false;
    while(!isdigit(ch=getchar()))(ch==‘-‘)&&(fl=true);
    for(x=numb;isdigit(ch=getchar());x=x*10+numb);
    (fl==true)&&(x=-x);
}
namespace Miracle{
const int N=8*1e5+5;
const int mod=998244353;
const int G=3;
const int GI=332748118;
int n,m;
int c[N],d[N],e[N],t[N],co[N],p[N],ni[N],l[N];
int rev[N];
int inv2;
int qm(int x,int y){
    int ret=1;
    while(y){
        if(y&1) ret=(ll)ret*x%mod;
        x=(ll)x*x%mod;
        y>>=1;
    }
    return ret;
}
int mo(int x){
    return x>=mod?x-mod:x;
}
void NTT(int *f,int n,int c){
    for(reg i=0;i<n;++i){
        if(i>rev[i]){
            f[i]^=f[rev[i]]^=f[i]^=f[rev[i]];
        }
    }
    for(reg p=2;p<=n;p<<=1){
        int gen;
        if(c==1) gen=qm(G,(mod-1)/p);
        else gen=qm(GI,(mod-1)/p);
        for(reg l=0;l<n;l+=p){
            int buf=1;
            for(reg k=l;k<l+p/2;++k){
                int tmp=(ll)buf*f[k+p/2]%mod;
                f[k+p/2]=mo(f[k]-tmp+mod);
                f[k]=mo(f[k]+tmp);
                buf=(ll)buf*gen%mod;
            }
        }
    }
}
void calc(int *f,int *g,int n){
    for(reg i=0;i<n;++i){
        rev[i]=rev[i>>1]>>1|((i&1)?n>>1:0);
    }
    NTT(f,n,1);NTT(g,n,1);
    for(reg i=0;i<n;++i) f[i]=(ll)f[i]*g[i]%mod;
    NTT(f,n,-1);
    ll iv=qm(n,mod-2);
    for(reg i=0;i<n;++i) f[i]=(ll)f[i]*iv%mod;
}
void inv(int *f,int *g,int n){//mod n
    if(n==1){
        g[0]=qm(f[0],mod-2);return;
    }
    inv(f,g,n>>1);
    for(reg i=0;i<n/2;++i) d[i]=g[i],e[i]=f[i];
    for(reg i=n/2;i<=n;++i) d[i]=0,e[i]=f[i];
    for(reg i=n+1;i<=2*n;++i) d[i]=0,e[i]=0;
    
    for(reg i=0;i<2*n;++i){
        rev[i]=rev[i>>1]>>1|((i&1)?(2*n)>>1:0);
    }
    NTT(d,2*n,1);NTT(e,2*n,1);
    for(reg i=0;i<2*n;++i){
        g[i]=mo(mo(2*d[i])-(ll)e[i]*d[i]%mod*d[i]%mod+mod);
    }
    NTT(g,2*n,-1);
    ll iv=qm(2*n,mod-2);
    for(reg i=0;i<2*n;++i){
        if(i<n) g[i]=(ll)g[i]*iv%mod;
        else g[i]=0;
    }
}
void sqr(int *f,int *g,int n){
    if(n==1){
        g[0]=1;return;
    }
    sqr(f,g,n>>1);
    for(reg i=0;i<n/2;++i) co[i]=(ll)g[i]%mod,l[i]=g[i],p[i]=f[i],ni[i]=0;
    for(reg i=n/2;i<n;++i) co[i]=0,l[i]=0,p[i]=f[i],ni[i]=0;
    for(reg i=n;i<2*n;++i) co[i]=0,l[i]=0,p[i]=0,ni[i]=0;
    
    memset(ni,0,sizeof ni);
    inv(co,ni,n);
    
    calc(p,ni,2*n);
    
    for(reg i=0;i<2*n;++i){
        if(i<n) g[i]=((ll)g[i]+p[i])%mod*inv2%mod;
        else g[i]=0;    
    }
}
int main(){
    rd(n);rd(m);
    inv2=qm(2,mod-2);
    
    int lp=max(n,m);
    int x;
    for(reg i=1;i<=n;++i){
        rd(x);c[x]=1;
        lp=max(lp,x);
    }
    int len=1;
    for(;len<=lp;len<<=1);
    for(reg i=0;i<len;++i){
        c[i]=-4*c[i]+mod;
    }
    c[0]++;
    
//    cout<<" len len "<<len<<endl;
    sqr(c,t,len);
//    cout<<" sqrt "<<endl;
//    for(reg i=0;i<len;++i){
//        cout<<t[i]<<" ";
//    }cout<<endl;
    t[0]=(t[0]+1)%mod;
    
    
    memset(ni,0,sizeof ni);
    inv(t,ni,len);
    for(reg i=1;i<=m;++i){
        ll ans=2*ni[i]%mod;
        printf("%lld\n",ans);
    }
    return 0;
}    

}
signed main(){
    Miracle::main();
    return 0;
}

/*
   Author: *Miracle*
   Date: 2019/1/28 20:07:14
*/