#include <iostream>
#include <map>
#include <set>
#include <cmath>
#include <algorithm>
#include <vector>
#include <string>
#include <fstream>
#include <bitset>
#include <queue>
#include <stack>
#include <deque>
#include <complex>
#include <iomanip>
#include <stdio.h>
#include <string.h>
#include <random>
#include <functional>
#include <unordered_set>

using std::cin;
using std::cout;
using std::cerr;
using std::endl;

using std::map;
using std::set;
using std::bitset;
using std::vector;
using std::string;
using std::multimap;
using std::multiset;
using std::deque;
using std::queue;
using std::stack;
using std::pair;
using std::iterator;

using std::sort;
using std::stable_sort;
using std::reverse;
using std::max_element;
using std::min_element;
using std::unique;
using std::ios_base;
using std::swap;
using std::fill;

using std::setprecision;
using std::fixed;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef string S;

ll min(ll a, ll b) {return a < b ? a : b;}
//ll min(int a, ll b) {return a < b ? a : b;}
//ll min(ll a, int b) {return a < b ? a : b;}
//ll min(int a, int b) {return a < b ? a : b;}

ll max(ll a, ll b) {return a > b ? a : b;}
//ll max(int a, ll b) {return a > b ? a : b;}
//ll max(ll a, int b) {return a > b ? a : b;}
//ll max(int a, int b) {return a > b ? a : b;}

namespace MySpace{

};

#define F(i, n) for (int (i) = 0; (i) != (n); (i)++)
#define fi first
#define se second
#define re return
#define all(x) (x).begin(), (x).end()

const long long MOD = 998244353;
int n, k;
long long w[2010][2010];
long long dp[4010][4010][2];
long long cnk[4010][4010];

long long comp(long long n0, long long formed, long long oo)
{
    long long ans = 0;
    int free = k - formed * 2 - oo;
    if (free < 0) return 0;
    for (int len = 0 + (free == 0 ? n0 : 0); len <= n0; len++)
    {
        long long c = 0;
        if (formed) c = dp[len + formed - 1][formed - 1][0] + dp[len + formed - 1][formed - 1][1];
        else c = (len == 0);
        if (len == n0) {ans = (ans + c) % MOD; continue;}
        ans = (ans + c % MOD * cnk[n0 - len + free - 1][free - 1]) % MOD;
    }
    return ans;
}

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin >> k >> n;
    for (int i = 0; i <= 4000; i++) cnk[i][0] = 1, cnk[i][i] = 1;
    for (int i = 1; i <= 4000; i++)
    {
        for (int j = 1; j < i; j++)
        {
            cnk[i][j] = (cnk[i - 1][j - 1] + cnk[i - 1][j]) % MOD;
        }
    }
    dp[0][0][1] = 1;
    dp[1][0][1] = 2;
    dp[1][1][0] = 1;
    int colors = k / 2;
    for (int pos = 2; pos <= 400 + n + colors - 1; pos++)
    {
        for (int i = 0; i < 100 + colors; i++)
        {
            dp[pos][i][1] = (dp[pos - 1][i][0] * 2 + dp[pos - 1][i][1]) % MOD;
            dp[pos][i][0] = ((i ? dp[pos - 1][i - 1][0] : 0) + (i ? dp[pos - 1][i - 1][1] : 0)) % MOD;
        }
    }
    vector<int> res;
    for (int i = 2; i <= k + 1; i++)
    {
        long long ans = 0;
        if (i % 2 == 0)
        {
            res.push_back((comp(n - 1, i / 2 - 1, 1) + comp(n, i / 2 - 1, 1)) % MOD);
        }
        else
        {
            res.push_back(comp(n, i / 2, 0));
        }
    }
    for (int i = 0; i < res.size(); i++) cout << res[i] << " ";
    for (int i = res.size() - 2; i >= 0; i--) cout << res[i] << " ";
}


Measured memory_bytes: 338560