#include "bits/stdc++.h"

using namespace std;

#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl

typedef long long ll;
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); }
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define rep1(i,n) for(ll i=1;i<=(ll)(n);i++)
#define rrep(i,n) for(ll i=(ll)(n)-1;i>=0;i--)
#define rrep1(i,n) for(ll i=(ll)(n);i>0;i--)
#define REP(i,a,b) for(ll i=(ll)a;i<(ll)b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = 1e18;
//const ll MOD = 1000000007;
const double pi = 3.14159265358979323846;
#define Sp(p) cout<<setprecision(15)<< fixed<<p<<endl;
int dx[4] = { 1,0, -1,0 }, dy[4] = { 0,1,0,-1 };
int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
#define fio() cin.tie(0); ios::sync_with_stdio(false);
#define mp make_pair

const ll MOD = 998244353;


const int MAXN = 4010;
vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
	ll a = 1;
	while (p) {
		if (p % 2)
			a = a*x%M;
		x = x*x%M;
		p /= 2;
	}
	return a;
}

ll mod_inverse(ll a, ll M = MOD) {
	return mod_pow(a, M - 2, M);
}

void set_fact(ll n, ll M = MOD) {
	fact[0] = fact[1] = rfact[0] = rfact[1] = 1;
	for (ll i = 2; i <= n; i++) {
		fact[i] = i * fact[i - 1] % M;
		rfact[i] = mod_inverse(fact[i], M);
	}
}

ll nCr(ll n, ll r, ll M = MOD) {
	ll ret = fact[n];
	ret = (ret*rfact[r]) % M;
	ret = (ret*rfact[n - r]) % M;
	return ret;
}


int main() {
  ll k, n;
  cin >> k >> n;
  set_fact(4003);
  REP (s, 2, 2*k + 1) {
    if (s % 2) {
      ll p = 0;
      for (int i = 1; i <= s; i++) {
        int j = s - i;
        if (i <= j && in(i, 1, k + 1) && in(j, 1, k + 1)) {
          p++;
        }
      }
      ll r = k - 2 * p;
      ll ans = 0;
      rep (q, p + 1) {
        if (n + r - 1 >= r + q - 1 && r + q - 1 >= 0) {
          ans = (ans + nCr(p, q) * mod_pow(2, q) % MOD * nCr(n + r - 1, r + q - 1) % MOD) % MOD;
        }
      }
      cout << ans << endl;
    }
    else {
      ll p = 0;
      for (int i = 1; i <= s; i++) {
        int j = s - i;
        if (i < j && in(i, 1, k + 1) && in(j, 1, k + 1)) {
          p++;
        }
        if (i == j) {
          break;
        }
      }
      ll r = k - 2 * p - 1;
      ll ans = 0;
      rep (q, p + 1) {
        if (n + r - 1 >= r + q - 1 && r + q - 1 >= 0) {
          ans = (ans + nCr(p, q) * mod_pow(2, q) % MOD * nCr(n + r - 1, r + q - 1)) % MOD;
        }
        if (n + r - 2 >= r + q - 1 && r + q - 1 >= 0) {        
          ans = (ans + nCr(p, q) * mod_pow(2, q) % MOD * nCr(n + r - 2, r + q - 1)) % MOD;
        }
      }
      cout << ans << endl;
    }
  }
  return 0;
}


Measured memory_bytes: 384