tree dp with prefix and suffix dp

/* codeforces 543D tree dp with prefix and suffix dp */

ll res[MAX];
vi v[MAX];vl prefix[MAX],suffix[MAX];ll ans[MAX];
void dfs(int s,int p){

    for(auto it : v[s]){
        if(it==p)continue;
        dfs(it,s);
        res[s] = res[s] * (res[it] + 1);
        if(res[s]>=mod)res[s]%=mod;
    }
}

void dfs2(int s,int p){
    ans[s]= res[s];
    ll pref = 1,suff = 1;
    int len = v[s].size();
    int cnt = 0;
    for(auto it : v[s]){
        prefix[s].pb(pref);
        suffix[s].pb(suff);
        pref = pref * (res[it] + 1);
        pref%=mod;
        suff = suff * (res[v[s][len - cnt - 1]] + 1);
        suff%=mod;
        cnt++;
    }
    reverse(all(suffix[s]));

    for(int i = 0;i<len;i++){
        if(v[s][i]==p)continue;
        ll temp = res[s];
        res[s] = prefix[s][i] * suffix[s][i] ;
        res[s]%=mod;
        res[v[s][i]] = (res[s] + 1) * res[v[s][i]];
        res[v[s][i]]%=mod;
        dfs2(v[s][i],s);
        res[s] = temp;
    }
}


int main()
{
    booster()
    ///read("input.txt");

    int n;
    cin>>n;
    for(int i = 1;i<n;i++){
        int a;
        cin>>a;
        v[a].pb(i+1);
        v[i+1].pb(a);
    }

    for(int i = 1;i<=n;i++)res[i] = 1;

    dfs(1,0);

    dfs2(1,0);

    for(int i = 1;i<=n;i++)cout<<ans[i]<<" ";


    return 0;
}