/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author zjsdut
 */

#include <bitset>
#include <iostream>
using std::to_string;
std::string to_string(const std::string &s) { return '"' + s + '"'; }

std::string to_string(const char *s) { return to_string((std::string) s); }

std::string to_string(bool b) { return (b ? "true" : "false"); }


template<size_t N>
std::string to_string(const std::bitset<N> &bs) {
  return bs.to_string();
}
// the declaration must goes before the definition!
template<typename A>
std::string to_string(const A &v);

template<typename A, typename B>
std::string to_string(const std::pair<A, B> &p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template<typename A>
std::string to_string(const A &v) {
  bool first = true;
  std::string res = "{";
  for (const auto &x : v) {
    if (!first) { res += ", "; }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}



void debug_out() { std::cerr << std::endl; }

template<typename Head, typename... Tail>
void debug_out(const Head &H, const Tail &... T) {
  std::cerr << " " << to_string(H);
  debug_out(T...);
}

#if defined LOCAL
#define debug(...)                                                                                 \
  std::cerr << "\033[90m" << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__),              \
      std::cerr << "\033[0m"
#else
#define debug(...) 42
#endif

#ifndef JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_
#define JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_

#include <iomanip>
#include <vector>
struct fast_ios {
  fast_ios() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(10);
  };
} fast_ios_;

template<typename T>
std::istream &operator>>(std::istream &stream, std::vector<T> &vec) {
  for (auto &x : vec)
    stream >> x;
  return stream;
}

template<typename T, typename U>
std::istream &operator>>(std::istream &in, std::pair<T, U> &p) {
  in >> p.first >> p.second;
  return in;
}

void scan() {}

template<class T, class... Args>
void scan(T &a, Args &... rest) {
  std::cin >> a;
  scan(rest...);
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const std::vector<T> &vec) {
  bool first = true;
  for (const T &t : vec) {
    if (first) first = false;
    else std::cout << ' ';
    std::cout << t;
  }
  return stream;
}

template<typename T, typename U>
std::ostream &operator<<(std::ostream &out, const std::pair<T,U> &p) {
  out << p.first << ' ' << p.second;
  return out;
}

template<typename T>
void print(const std::vector<std::vector<T>> &t) {
  for (const auto &row : t) {
    std::cout << row << '\n';
  }
}

template<typename T>
void print(const T &t) { std::cout << t << ' '; }

template<typename T, typename... Args>
void print(const T &t, const Args &... rest) {
  print(t);
  print(rest...);
}

template<typename T>
void println(const T &t) { std::cout << t << '\n'; }

template<typename T, typename... Args>
void println(const T &t, const Args &... rest) {
  print(t);
  println(rest...);
}
#endif //JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_

#ifndef ALGO_MODULAR
#define ALGO_MODULAR

#include <cassert>
using std::swap;
// tourist's modular-arithmetic class
template<typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template<typename T>
class Modular {
 public:
  using Type = typename std::decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}

  template<typename U>
  Modular(const U &x) { value = normalize(x); }

  template<typename U>
  static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0)
      v += mod();
    return v;
  }

  const Type &operator()() const { return value; }

  template<typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }

  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod())
      value -= mod();
    return *this;
  }

  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0)
      value += mod();
    return *this;
  }

  template<typename U>
  Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }

  template<typename U>
  Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }

  Modular &operator++() { return *this += 1; }

  Modular &operator--() { return *this -= 1; }

  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }

  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }

  Modular operator-() const { return Modular(-value); }

  template<typename U = T>
  typename std::enable_if<std::is_same<typename Modular<U>::Type, int>::value, Modular>::type &
  operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x),
        d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod()));
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }

  template<typename U = T>
  typename std::enable_if<std::is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type &
  operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
        rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }

  template<typename U = T>
  typename std::enable_if<!std::is_integral<typename Modular<U>::Type>::value, Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }

  template<typename U>
  friend const Modular<U> &abs(const Modular<U> &v) {
    return v;
  }

  template<typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

 private:
  Type value;
};

template<typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}

template<typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}

template<typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}

template<typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template<typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}

template<typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template<typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}

template<typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template<typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}

template<typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template<typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template<typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}

template<typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template<typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template<typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}

template<typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template<typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template<typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}

template<typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template<typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1)
      res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template<typename T>
bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template<typename T>
std::string to_string(const Modular<T> &number) {
  return std::to_string(number());
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template<typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename std::common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

template<int md>
using Mint = Modular<std::integral_constant<typename std::decay<decltype(md)>::type, md>>;
constexpr int M7 = 1000000007;
constexpr int M3 = 998244353;
using ModType = int;
struct VarMod {
  static ModType value;
};
ModType VarMod::value;
ModType &md = VarMod::value;
using vmint = Modular<VarMod>;
#endif
#ifndef ALGO_UTILS
#define ALGO_UTILS
#include <algorithm>

#include <climits>
#include <map>
#include <numeric>
#include <queue>
#include <set>

template<typename A, typename B>
bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template<typename A, typename B>
bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

using ll = long long;
using ull = unsigned long long;
using vl = std::vector<ll>;
using vb = std::vector<bool>;
using vi = std::vector<int>;
using pii = std::pair<int, int>;
using pli = std::pair<ll, int>;
using pil = std::pair<int, ll>;
using pll = std::pair<ll, ll>;
using vpii = std::vector<pii>;
template<typename T>
class vv {
  std::vector<std::vector<T>> data;

 public:
  vv(int n, int m, T init = T{}) {
    assert(n > 0 && m > 0);
    data.assign(n, std::vector<T>(m, init));
  }
  std::vector<T> &operator[](size_t i) { return data[i]; }
};
#define rng3(i, a, b) for (std::common_type<decltype(a), decltype(b)>::type i = a; i < b; ++i)
#define rng2(i, n) rng3(i, 0, n)
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define rng(...) GET_MACRO(__VA_ARGS__, rng3, rng2)(__VA_ARGS__)
#define up(i, a, b) for (std::common_type<decltype(a), decltype(b)>::type i = a; i <= b; ++i)
#define down(i, b, a) for (std::common_type<decltype(a), decltype(b)>::type i = b; i >= a; i--)
#define TOKENPASTE(x, y) x##y
#define TOKENPASTE2(x, y) TOKENPASTE(x, y)
#define rep(n)                                                                                     \
  for (int TOKENPASTE2(_iter_, __LINE__) = 0, TOKENPASTE2(_num_, __LINE__) = n;                    \
       TOKENPASTE2(_iter_, __LINE__) < TOKENPASTE2(_num_, __LINE__);                               \
       ++TOKENPASTE2(_iter_, __LINE__))
#define FOR(x, cont) for (const auto &x : cont)
#define For(x, cont) for (auto &x : cont)
#define ALL(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int) (x).size()
#define UNIQ(vec) (vec).erase(std::unique(ALL(vec)), std::end(vec))
#define LB(cont, x) int(std::lower_bound(ALL(cont), x) - std::begin(cont))
#define UB(cont, x) int(std::upper_bound(ALL(cont), x) - std::begin(cont))
template<typename T, typename U = std::less<T>>
using pq = std::priority_queue<T, std::vector<T>, U>;
template<typename T>
struct reversion_wrapper {
  T &iterable;
};
template<typename T>
auto begin(reversion_wrapper<T> w) {
  return std::rbegin(w.iterable);
}
template<typename T>
auto end(reversion_wrapper<T> w) {
  return std::rend(w.iterable);
}
template<typename T>
reversion_wrapper<T> reverse(T &&iterable) {
  return {iterable};
}
template<typename T, typename U>
T ceil(T x, U y) {
  assert(y > 0);
  if (x > 0) x += y - 1;
  return x / y;
}

template<typename T, typename U>
T floor(T x, U y) {
  assert(y > 0);
  if (x < 0) x -= y - 1;
  return x / y;
}
#endif
using namespace std;
class EStopOtherwise {
public:
  static void solve(istream&, ostream&) {
    using mint = Mint<M3>;
    int n, k;
    scan(k, n);
    vv<mint> binom(n + k, k);
    rng (i, 0, n + k) binom[i][0] = 1;
    rng (i, 1, n + k) rng (j, 1, k) {
      binom[i][j] = binom[i - 1][j] + binom[i - 1][j - 1];
    }

    vector<mint> pow(k + 1);
    pow[0] = 1;
    up (i, 1, k) pow[i] = pow[i - 1] * 2;
    auto calc = [&](int n_var, int sum) -> mint {
      assert(n_var >= 0);
      if (n_var > sum) return 0;
      if (n_var == 0) return sum == 0;
      return binom[sum - 1][n_var - 1];
    };
    auto solve = [&](int e) {
      int p = (e + 1) / 2 - max(1, e - k);
      mint ans = 0;
      if (e & 1) {
        up(q, 0, p) {
          int n_var = q + k - 2 * p;
          int sum = n + k - 2 * p;
          ans += binom[p][q] * pow[q] * calc(n_var, sum);
        }
      } else {
        up (q, 0, p) {
          int n_var = q + k - 1 - 2 * p;
          int sum = n + k - 1 - 2 * p;

          ans += binom[p][q] * pow[q] * (calc(n_var, sum) + calc(n_var, sum - 1));
        }
      }
      println(ans);
    };
    up (i, 2, 2 * k) solve(i);
  }
};
/*
 * Make sure that your laptop is plugged in or the build may be slow.
 */

#define in std::cin
#define out std::cout
int main() {
  EStopOtherwise solver;
  solver.solve(in, out);
  return 0;
}


Measured memory_bytes: 31744