Problem: PolandBall is standing in a row with Many Other Balls. More precisely, there are exactly n Balls. Balls are proud of their home land — and they want to prove that it's strong.

The Balls decided to start with selecting exactly m groups of Balls, each consisting either of single Ball or two neighboring Balls. Each Ball can join no more than one group.

The Balls really want to impress their Enemies. They kindly asked you to calculate number of such divisions for all m where 1 ≤ m ≤ k. Output all these values modulo 998244353, the Enemies will be impressed anyway.

Input

There are exactly two numbers n and k (1 ≤ n ≤ 109, 1 ≤ k < 215), denoting the number of Balls and the maximim number of groups, respectively.

Output

You should output a sequence of k values. The i-th of them should represent the sought number of divisions into exactly i groups, according to PolandBall's rules.

Examples

Input

3 3


Output

5 5 1 

Input

1 1


Output

1 

Input

5 10


Output

9 25 25 9 1 0 0 0 0 0 

Note

In the first sample case we can divide Balls into groups as follows: 

{1}, {2}, {3}, {12}, {23}.

{12}{3}, {1}{23}, {1}{2}, {1}{3}, {2}{3}.

{1}{2}{3}.

Therefore, output is: 5 5 1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <typename T>
void dout(string name, int idx, T arg) {
  cerr << name << " = " << to_string(arg);
}
template <typename T1, typename... T2>
void dout(string names, int idx, T1 arg, T2... args) {
  cerr << names.substr(0, names.find(',')) << " = " << to_string(arg) << ", ";
  dout(names.substr(names.find(',') + 2), idx + 1, args...);
}
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 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 enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<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 enable_if<!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>
string to_string(const Modular<T>& number) {
  return 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 common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
template <typename T>
class NTT {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  static Type md;
  static Modular<T> root;
  static int base;
  static int max_base;
  static vector<Modular<T>> roots;
  static vector<int> rev;
  static void clear() {
    root = 0;
    base = 0;
    max_base = 0;
    roots.clear();
    rev.clear();
  }
  static void init() {
    md = T::value;
    assert(md >= 3 && md % 2 == 1);
    auto tmp = md - 1;
    max_base = 0;
    while (tmp % 2 == 0) {
      tmp /= 2;
      max_base++;
    }
    root = 2;
    while (power(root, (md - 1) >> 1) == 1) {
      root++;
    }
    assert(power(root, md - 1) == 1);
    root = power(root, (md - 1) >> max_base);
    base = 1;
    rev = {0, 1};
    roots = {0, 1};
  }
  static void ensure_base(int nbase) {
    if (md != T::value) {
      clear();
    }
    if (roots.empty()) {
      init();
    }
    if (nbase <= base) {
      return;
    }
    assert(nbase <= max_base);
    rev.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    roots.resize(1 << nbase);
    while (base < nbase) {
      Modular<T> z = power(root, 1 << (max_base - 1 - base));
      for (int i = 1 << (base - 1); i < (1 << base); i++) {
        roots[i << 1] = roots[i];
        roots[(i << 1) + 1] = roots[i] * z;
      }
      base++;
    }
  }
  static void fft(vector<Modular<T>>& a) {
    int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for (int k = 1; k < n; k <<= 1) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          Modular<T> x = a[i + j];
          Modular<T> y = a[i + j + k] * roots[j + k];
          a[i + j] = x + y;
          a[i + j + k] = x - y;
        }
      }
    }
  }
  static vector<Modular<T>> multiply(vector<Modular<T>> a,
                                     vector<Modular<T>> b) {
    if (a.empty() || b.empty()) {
      return {};
    }
    int eq = (a == b);
    int need = (int)a.size() + (int)b.size() - 1;
    int nbase = 0;
    while ((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz);
    b.resize(sz);
    fft(a);
    if (eq)
      b = a;
    else
      fft(b);
    Modular<T> inv_sz = 1 / static_cast<Modular<T>>(sz);
    for (int i = 0; i < sz; i++) {
      a[i] *= b[i] * inv_sz;
    }
    reverse(a.begin() + 1, a.end());
    fft(a);
    a.resize(need);
    return a;
  }
};
template <typename T>
typename NTT<T>::Type NTT<T>::md;
template <typename T>
Modular<T> NTT<T>::root;
template <typename T>
int NTT<T>::base;
template <typename T>
int NTT<T>::max_base;
template <typename T>
vector<Modular<T>> NTT<T>::roots;
template <typename T>
vector<int> NTT<T>::rev;
template <typename T>
vector<Modular<T>> inverse(const vector<Modular<T>>& a) {
  assert(!a.empty());
  int n = (int)a.size();
  vector<Modular<T>> b = {1 / a[0]};
  while ((int)b.size() < n) {
    vector<Modular<T>> x(a.begin(), a.begin() + min(a.size(), b.size() << 1));
    x.resize(b.size() << 1);
    b.resize(b.size() << 1);
    vector<Modular<T>> c = b;
    NTT<T>::fft(c);
    NTT<T>::fft(x);
    Modular<T> inv = 1 / static_cast<Modular<T>>((int)x.size());
    for (int i = 0; i < (int)x.size(); i++) {
      x[i] *= c[i] * inv;
    }
    reverse(x.begin() + 1, x.end());
    NTT<T>::fft(x);
    rotate(x.begin(), x.begin() + (x.size() >> 1), x.end());
    fill(x.begin() + (x.size() >> 1), x.end(), 0);
    NTT<T>::fft(x);
    for (int i = 0; i < (int)x.size(); i++) {
      x[i] *= c[i] * inv;
    }
    reverse(x.begin() + 1, x.end());
    NTT<T>::fft(x);
    for (int i = 0; i < ((int)x.size() >> 1); i++) {
      b[i + ((int)x.size() >> 1)] = -x[i];
    }
  }
  b.resize(n);
  return b;
}
template <typename T>
vector<Modular<T>> inverse_old(vector<Modular<T>> a) {
  assert(!a.empty());
  int n = (int)a.size();
  if (n == 1) {
    return {1 / a[0]};
  }
  int m = (n + 1) >> 1;
  vector<Modular<T>> b = inverse(vector<Modular<T>>(a.begin(), a.begin() + m));
  int need = n << 1;
  int nbase = 0;
  while ((1 << nbase) < need) {
    ++nbase;
  }
  NTT<T>::ensure_base(nbase);
  int size = 1 << nbase;
  a.resize(size);
  b.resize(size);
  NTT<T>::fft(a);
  NTT<T>::fft(b);
  Modular<T> inv = 1 / static_cast<Modular<T>>(size);
  for (int i = 0; i < size; ++i) {
    a[i] = (2 - a[i] * b[i]) * b[i] * inv;
  }
  reverse(a.begin() + 1, a.end());
  NTT<T>::fft(a);
  a.resize(n);
  return a;
}
template <typename T>
vector<Modular<T>> operator*(const vector<Modular<T>>& a,
                             const vector<Modular<T>>& b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  if (min(a.size(), b.size()) < 150) {
    vector<Modular<T>> c(a.size() + b.size() - 1, 0);
    for (int i = 0; i < (int)a.size(); i++) {
      for (int j = 0; j < (int)b.size(); j++) {
        c[i + j] += a[i] * b[j];
      }
    }
    return c;
  }
  return NTT<T>::multiply(a, b);
}
template <typename T>
vector<Modular<T>>& operator*=(vector<Modular<T>>& a,
                               const vector<Modular<T>>& b) {
  return a = a * b;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<vector<Mint>> dp(6, vector<Mint>(k + 1));
  dp[0][0] = 1;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j <= k; j++) {
      if (j > 0) {
        dp[i + 1][j] += dp[i][j - 1];
        dp[i + 2][j] += dp[i][j - 1];
      }
      dp[i + 1][j] += dp[i][j];
    }
  }
  vector<vector<Mint>> dp_2(3, vector<Mint>(k + 1));
  for (int i = 0; i <= 2; i++) {
    for (int j = 0; j <= k; j++) {
      dp_2[i][j] = (1 - i < 0 ? 0 : dp[1 - i][j]);
    }
  }
  auto MultiplySlow = [&](const vector<vector<Mint>>& dp_a,
                          const vector<vector<Mint>>& dp_b) {
    vector<vector<Mint>> ret(3, vector<Mint>(k + 1));
    for (int i = 0; i <= k; i++) {
      for (int j = 0; j <= k; j++) {
        if (i + j <= k) {
          ret[0][i + j] += dp_a[0][i] * dp_b[0][j];
        }
      }
    }
    for (int i = 0; i <= k; i++) {
      for (int j = 0; j <= k; j++) {
        if (i + j <= k) {
          ret[2][i + j] += dp_a[1][i] * dp_b[1][j];
        }
      }
    }
    for (int k = 1; k < (int)ret[0].size(); k++) {
      ret[0][k] += ret[2][k - 1];
    }
    for (int i = 0; i <= k; i++) {
      for (int j = 0; j <= k; j++) {
        if (i + j <= k) {
          ret[1][i + j] += dp_a[0][i] * dp_b[1][j];
        }
      }
    }
    vector<Mint> ab_2(k + 1);
    for (int i = 0; i <= k; i++) {
      for (int j = 0; j <= k; j++) {
        if (i + j <= k) {
          ab_2[i + j] += dp_a[1][i] * dp_b[2][j];
        }
      }
    }
    vector<Mint> ab_22(k + 1);
    for (int i = 0; i <= k; i++) {
      for (int j = 0; j <= k; j++) {
        if (i + j <= k) {
          ab_22[i + j] += dp_a[2][i] * dp_b[2][j];
        }
      }
    }
    for (int k = 1; k < (int)ret[1].size(); k++) {
      ret[1][k] += ab_2[k - 1];
    }
    for (int k = 1; k < (int)ret[2].size(); k++) {
      ret[2][k] += ab_22[k - 1];
    }
    return ret;
  };
  auto Multiply = [&](const vector<vector<Mint>>& dp_a,
                      const vector<vector<Mint>>& dp_b) {
    vector<vector<Mint>> ret(3, vector<Mint>(k + 1));
    ret[0] = dp_a[0] * dp_b[0];
    ret[2] = dp_a[1] * dp_b[1];
    ret[0].resize(k + 1);
    ret[2].resize(k + 1);
    for (int k = 1; k < (int)ret[0].size(); k++) {
      ret[0][k] += ret[2][k - 1];
    }
    ret[1] = dp_a[0] * dp_b[1];
    ret[1].resize(k + 1);
    vector<Mint> ab_2 = dp_a[1] * dp_b[2];
    ab_2.resize(k + 1);
    for (int k = 1; k < (int)ret[1].size(); k++) {
      ret[1][k] += ab_2[k - 1];
    }
    vector<Mint> ab_22 = dp_a[2] * dp_b[2];
    ab_22.resize(k + 1);
    for (int k = 1; k < (int)ret[2].size(); k++) {
      ret[2][k] += ab_22[k - 1];
    }
    return ret;
  };
  vector<vector<Mint>> dp_n(3, vector<Mint>(k + 1));
  dp_n[0][0] = 1;
  int pw = 1;
  int op = 0;
  while (n > 0) {
    if (n & 1) {
      dp_n = Multiply(dp_n, dp_2);
      op += 1;
    }
    dp_2 = Multiply(dp_2, dp_2);
    op += 1;
    pw *= 2;
    n >>= 1;
  }
  42;
  for (int j = 1; j <= k; j++) {
    cout << dp_n[0][j] << ' ';
  }
  cout << '\n';
  return 0;
}