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;
const int M = 1000000007;
const int MM = 998244353;
const long double PI = acos(-1);
template <typename T, typename U>
static inline void amin(T &x, U y) {
  if (y < x) x = y;
}
template <typename T, typename U>
static inline void amax(T &x, U y) {
  if (x < y) x = y;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  return os << '(' << p.first << "," << p.second << ')';
}
const int MOD = 998244353;
struct Mint {
  int val;
  Mint(long long v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = v;
  }
  static int mod_inv(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  Mint &operator+=(const Mint &other) {
    val += other.val;
    if (val >= MOD) val -= MOD;
    return *this;
  }
  Mint &operator-=(const Mint &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return x % m;
    unsigned x_high = x >> 32, x_low = (unsigned)x;
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  Mint &operator*=(const Mint &other) {
    val = fast_mod((uint64_t)val * other.val);
    return *this;
  }
  Mint &operator/=(const Mint &other) { return *this *= other.inv(); }
  friend Mint operator+(const Mint &a, const Mint &b) { return Mint(a) += b; }
  friend Mint operator-(const Mint &a, const Mint &b) { return Mint(a) -= b; }
  friend Mint operator*(const Mint &a, const Mint &b) { return Mint(a) *= b; }
  friend Mint operator/(const Mint &a, const Mint &b) { return Mint(a) /= b; }
  Mint &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  Mint &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  Mint operator++(int32_t) {
    Mint before = *this;
    ++*this;
    return before;
  }
  Mint operator--(int32_t) {
    Mint before = *this;
    --*this;
    return before;
  }
  Mint operator-() const { return val == 0 ? 0 : MOD - val; }
  bool operator==(const Mint &other) const { return val == other.val; }
  bool operator!=(const Mint &other) const { return val != other.val; }
  Mint inv() const { return mod_inv(val); }
  Mint power(long long p) const {
    assert(p >= 0);
    Mint a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      a *= a;
      p >>= 1;
    }
    return result;
  }
  friend ostream &operator<<(ostream &stream, const Mint &m) {
    return stream << m.val;
  }
  friend istream &operator>>(istream &stream, Mint &m) {
    return stream >> m.val;
  }
};
namespace algebra {
const int inf = 1e9;
const int magic = 200;
namespace NTT {
vector<Mint> roots = {0, 1};
vector<int> bit_reverse;
int max_size = -1;
Mint root;
bool is_power_of_two(int n) { return (n & (n - 1)) == 0; }
int round_up_power_two(int n) {
  while (n & (n - 1)) n = (n | (n - 1)) + 1;
  return max(n, 1);
}
int get_length(int n) {
  assert(is_power_of_two(n));
  return __builtin_ctz(n);
}
void bit_reorder(int n, vector<Mint> &values) {
  if ((int)bit_reverse.size() != n) {
    bit_reverse.assign(n, 0);
    int length = get_length(n);
    for (int i = 0; i < n; i++)
      bit_reverse[i] = (bit_reverse[i >> 1] >> 1) + ((i & 1) << (length - 1));
  }
  for (int i = 0; i < n; i++)
    if (i < bit_reverse[i]) swap(values[i], values[bit_reverse[i]]);
}
void find_root() {
  max_size = 1 << __builtin_ctz(MOD - 1);
  root = 2;
  while (!(root.power(max_size) == 1 && root.power(max_size / 2) != 1)) root++;
}
void prepare_roots(int n) {
  if (max_size < 0) find_root();
  assert(n <= max_size);
  if ((int)roots.size() >= n) return;
  int length = get_length(roots.size());
  roots.resize(n);
  while (1 << length < n) {
    Mint z = root.power(max_size >> (length + 1));
    for (int i = 1 << (length - 1); i < 1 << length; i++) {
      roots[2 * i] = roots[i];
      roots[2 * i + 1] = roots[i] * z;
    }
    length++;
  }
}
void fft_iterative(int N, vector<Mint> &values) {
  assert(is_power_of_two(N));
  prepare_roots(N);
  bit_reorder(N, values);
  for (int n = 1; n < N; n *= 2)
    for (int start = 0; start < N; start += 2 * n)
      for (int i = 0; i < n; i++) {
        Mint even = values[start + i];
        Mint odd = values[start + n + i] * roots[n + i];
        values[start + n + i] = even - odd;
        values[start + i] = even + odd;
      }
}
const int FFT_CUTOFF = magic;
vector<Mint> mod_multiply(vector<Mint> left, vector<Mint> right) {
  int n = left.size();
  int m = right.size();
  if (min(n, m) < FFT_CUTOFF) {
    const uint64_t ULL_BOUND =
        numeric_limits<uint64_t>::max() - (uint64_t)MOD * MOD;
    vector<uint64_t> result(n + m - 1, 0);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) {
        result[i + j] += (uint64_t)((int)left[i]) * ((int)right[j]);
        if (result[i + j] > ULL_BOUND) result[i + j] %= MOD;
      }
    for (uint64_t &x : result)
      if (x >= MOD) x %= MOD;
    return vector<Mint>(result.begin(), result.end());
  }
  int N = round_up_power_two(n + m - 1);
  left.resize(N);
  right.resize(N);
  bool equal = left == right;
  fft_iterative(N, left);
  if (equal)
    right = left;
  else
    fft_iterative(N, right);
  Mint inv_N = Mint(N).inv();
  for (int i = 0; i < N; i++) left[i] *= right[i] * inv_N;
  reverse(left.begin() + 1, left.end());
  fft_iterative(N, left);
  left.resize(n + m - 1);
  return left;
}
template <typename T>
void mul(vector<T> &a, const vector<T> &b) {
  a = mod_multiply(a, b);
}
}  // namespace NTT
template <typename T>
struct poly {
  vector<T> a;
  void normalize() {
    while (!a.empty() && a.back() == T(0)) {
      a.pop_back();
    }
  }
  poly() {}
  poly(T a_0) : a{a_0} { normalize(); }
  poly(vector<T> t) : a(t) { normalize(); }
  poly operator+=(const poly &t) {
    a.resize(max(a.size(), t.a.size()));
    for (size_t i = 0; i < t.a.size(); i++) {
      a[i] += t.a[i];
    }
    normalize();
    return *this;
  }
  poly operator-=(const poly &t) {
    a.resize(max(a.size(), t.a.size()));
    for (size_t i = 0; i < t.a.size(); i++) {
      a[i] -= t.a[i];
    }
    normalize();
    return *this;
  }
  poly operator+(const poly &t) const { return poly(*this) += t; }
  poly operator-(const poly &t) const { return poly(*this) -= t; }
  poly mod_xk(size_t k) const {
    k = min(k, a.size());
    return vector<T>(begin(a), begin(a) + k);
  }
  poly mul_xk(size_t k) const {
    poly res(*this);
    res.a.insert(begin(res.a), k, 0);
    return res;
  }
  poly div_xk(size_t k) const {
    k = min(k, a.size());
    return vector<T>(begin(a) + k, end(a));
  }
  poly substr(size_t l, size_t r) const {
    l = min(l, a.size());
    r = min(r, a.size());
    return vector<T>(begin(a) + l, begin(a) + r);
  }
  poly inv(size_t n) const {
    assert(!is_zero());
    poly ans = a[0].inv();
    size_t a = 1;
    while (a < n) {
      poly C = (ans * mod_xk(2 * a)).substr(a, 2 * a);
      ans -= (ans * C).mod_xk(a).mul_xk(a);
      a *= 2;
    }
    return ans.mod_xk(n);
  }
  poly operator*=(const poly &t) {
    NTT::mul(a, t.a);
    normalize();
    return *this;
  }
  poly operator*(const poly &t) const { return poly(*this) *= t; }
  poly reverse(size_t n, bool rev = 0) const {
    poly res(*this);
    if (rev) {
      res.a.resize(max(n, res.a.size()));
    }
    std::reverse(res.a.begin(), res.a.end());
    return res.mod_xk(n);
  }
  pair<poly, poly> divmod_slow(const poly &b) const {
    vector<T> A(a);
    vector<T> res;
    while (A.size() >= b.a.size()) {
      res.push_back(A.back() / b.a.back());
      if (res.back() != T(0)) {
        for (size_t i = 0; i < b.a.size(); i++) {
          A[A.size() - i - 1] -= res.back() * b.a[b.a.size() - i - 1];
        }
      }
      A.pop_back();
    }
    std::reverse(begin(res), end(res));
    return {res, A};
  }
  pair<poly, poly> divmod(const poly &b) const {
    if (deg() < b.deg()) {
      return {poly{0}, *this};
    }
    int d = deg() - b.deg();
    if (min(d, b.deg()) < magic) {
      return divmod_slow(b);
    }
    poly D = (reverse(d + 1) * b.reverse(d + 1).inv(d + 1))
                 .mod_xk(d + 1)
                 .reverse(d + 1, 1);
    return {D, *this - D * b};
  }
  poly operator/(const poly &t) const { return divmod(t).first; }
  poly operator%(const poly &t) const { return divmod(t).second; }
  poly operator/=(const poly &t) { return *this = divmod(t).first; }
  poly operator%=(const poly &t) { return *this = divmod(t).second; }
  poly operator*=(const T &x) {
    for (auto &it : a) {
      it *= x;
    }
    normalize();
    return *this;
  }
  poly operator/=(const T &x) {
    for (auto &it : a) {
      it /= x;
    }
    normalize();
    return *this;
  }
  poly operator*(const T &x) const { return poly(*this) *= x; }
  poly operator/(const T &x) const { return poly(*this) /= x; }
  void print() const {
    for (auto it : a) {
      cout << it << ' ';
    }
    cout << endl;
  }
  T eval(T x) const {
    T res(0);
    for (int i = int(a.size()) - 1; i >= 0; i--) {
      res *= x;
      res += a[i];
    }
    return res;
  }
  T &lead() { return a.back(); }
  int deg() const { return a.empty() ? -inf : a.size() - 1; }
  bool is_zero() const { return a.empty(); }
  T operator[](int idx) const {
    return idx >= (int)a.size() || idx < 0 ? T(0) : a[idx];
  }
  T &coef(size_t idx) { return a[idx]; }
  bool operator==(const poly &t) const { return a == t.a; }
  bool operator!=(const poly &t) const { return a != t.a; }
  poly deriv() {
    vector<T> res;
    for (int i = 1; i <= deg(); i++) {
      res.push_back(T(i) * a[i]);
    }
    return res;
  }
  poly integr() {
    vector<T> res = {0};
    for (int i = 0; i <= deg(); i++) {
      res.push_back(a[i] / T(i + 1));
    }
    return res;
  }
  size_t leading_xk() const {
    if (is_zero()) {
      return inf;
    }
    int res = 0;
    while (a[res] == T(0)) {
      res++;
    }
    return res;
  }
  poly log(size_t n) {
    assert(a[0] == T(1));
    return (deriv().mod_xk(n) * inv(n)).integr().mod_xk(n);
  }
  poly exp(size_t n) {
    if (is_zero()) {
      return T(1);
    }
    assert(a[0] == T(0));
    poly ans = T(1);
    size_t a = 1;
    while (a < n) {
      poly C = ans.log(2 * a).div_xk(a) - substr(a, 2 * a);
      ans -= (ans * C).mod_xk(a).mul_xk(a);
      a *= 2;
    }
    return ans.mod_xk(n);
  }
  poly pow_slow(size_t k, size_t n) {
    return k ? k % 2 ? (*this * pow_slow(k - 1, n)).mod_xk(n)
                     : (*this * *this).mod_xk(n).pow_slow(k / 2, n)
             : T(1);
  }
  poly pow(size_t k, size_t n) {
    if (is_zero()) {
      return *this;
    }
    if (k < magic) {
      return pow_slow(k, n);
    }
    int i = leading_xk();
    T j = a[i];
    poly t = div_xk(i) / j;
    return bpow(j, k) * (t.log(n) * T(k)).exp(n).mul_xk(i * k).mod_xk(n);
  }
  poly sqrt(size_t n) const {
    poly b = {1};
    int cur = 1;
    while (cur < n) {
      vector<T> x(a.begin(), a.begin() + min(a.size(), b.a.size() << 1));
      b.a.resize(b.a.size() << 1);
      poly c(x);
      c *= b.inv(b.a.size());
      T inv2 = 1 / static_cast<T>(2);
      for (int i = (int)b.a.size() >> 1; i < (int)min(c.a.size(), b.a.size());
           i++) {
        b.a[i] = c.a[i] * inv2;
      }
      cur *= 2;
    }
    b.a.resize(n);
    return b;
  }
  poly mulx(T x) {
    T cur = 1;
    poly res(*this);
    for (int i = 0; i <= deg(); i++) {
      res.coef(i) *= cur;
      cur *= x;
    }
    return res;
  }
  poly mulx_sq(T x) {
    T cur = x;
    T total = 1;
    T xx = x * x;
    poly res(*this);
    for (int i = 0; i <= deg(); i++) {
      res.coef(i) *= total;
      total *= cur;
      cur *= xx;
    }
    return res;
  }
  vector<T> chirpz_even(T z, int n) {
    int m = deg();
    if (is_zero()) {
      return vector<T>(n, 0);
    }
    vector<T> vv(m + n);
    T zi = z.inv();
    T zz = zi * zi;
    T cur = zi;
    T total = 1;
    for (int i = 0; i <= max(n - 1, m); i++) {
      if (i <= m) {
        vv[m - i] = total;
      }
      if (i < n) {
        vv[m + i] = total;
      }
      total *= cur;
      cur *= zz;
    }
    poly w = (mulx_sq(z) * vv).substr(m, m + n).mulx_sq(z);
    vector<T> res(n);
    for (int i = 0; i < n; i++) {
      res[i] = w[i];
    }
    return res;
  }
  vector<T> chirpz(T z, int n) {
    auto even = chirpz_even(z, (n + 1) / 2);
    auto odd = mulx(z).chirpz_even(z, n / 2);
    vector<T> ans(n);
    for (int i = 0; i < n / 2; i++) {
      ans[2 * i] = even[i];
      ans[2 * i + 1] = odd[i];
    }
    if (n % 2 == 1) {
      ans[n - 1] = even.back();
    }
    return ans;
  }
  template <typename iter>
  vector<T> eval(vector<poly> &tree, int v, iter l, iter r) {
    if (r - l == 1) {
      return {eval(*l)};
    } else {
      auto m = l + (r - l) / 2;
      auto A = (*this % tree[2 * v]).eval(tree, 2 * v, l, m);
      auto B = (*this % tree[2 * v + 1]).eval(tree, 2 * v + 1, m, r);
      A.insert(end(A), begin(B), end(B));
      return A;
    }
  }
  vector<T> eval(vector<T> x) {
    int n = x.size();
    if (is_zero()) {
      return vector<T>(n, T(0));
    }
    vector<poly> tree(4 * n);
    build(tree, 1, begin(x), end(x));
    return eval(tree, 1, begin(x), end(x));
  }
  template <typename iter>
  poly inter(vector<poly> &tree, int v, iter l, iter r, iter ly, iter ry) {
    if (r - l == 1) {
      return {*ly / a[0]};
    } else {
      auto m = l + (r - l) / 2;
      auto my = ly + (ry - ly) / 2;
      auto A = (*this % tree[2 * v]).inter(tree, 2 * v, l, m, ly, my);
      auto B = (*this % tree[2 * v + 1]).inter(tree, 2 * v + 1, m, r, my, ry);
      return A * tree[2 * v + 1] + B * tree[2 * v];
    }
  }
  friend ostream &operator<<(ostream &stream, const poly &p) {
    stream << "Polynomial : ";
    for (auto &j : p.a) stream << j << " ";
    return stream;
  }
};
template <typename T>
poly<T> operator*(const T &a, const poly<T> &b) {
  return b * a;
}
template <typename T>
poly<T> xk(int k) {
  return poly<T>{1}.mul_xk(k);
}
template <typename T>
T resultant(poly<T> a, poly<T> b) {
  if (b.is_zero()) {
    return 0;
  } else if (b.deg() == 0) {
    return bpow(b.lead(), a.deg());
  } else {
    int pw = a.deg();
    a %= b;
    pw -= a.deg();
    T mul = bpow(b.lead(), pw) * T((b.deg() & a.deg() & 1) ? -1 : 1);
    T ans = resultant(b, a);
    return ans * mul;
  }
}
template <typename iter>
poly<typename iter::value_type> kmul(iter L, iter R) {
  if (R - L == 1) {
    return vector<typename iter::value_type>{-*L, 1};
  } else {
    iter M = L + (R - L) / 2;
    return kmul(L, M) * kmul(M, R);
  }
}
template <typename T, typename iter>
poly<T> build(vector<poly<T>> &res, int v, iter L, iter R) {
  if (R - L == 1) {
    return res[v] = vector<T>{-*L, 1};
  } else {
    iter M = L + (R - L) / 2;
    return res[v] = build(res, 2 * v, L, M) * build(res, 2 * v + 1, M, R);
  }
}
template <typename T>
poly<T> inter(vector<T> x, vector<T> y) {
  int n = x.size();
  vector<poly<T>> tree(4 * n);
  return build(tree, 1, begin(x), end(x))
      .deriv()
      .inter(tree, 1, begin(x), end(x), begin(y), end(y));
}
};  // namespace algebra
using namespace algebra;
poly<Mint> dp[30][3];
int _runtimeTerror_() {
  int n, k;
  cin >> n >> k;
  dp[1][0] = poly<Mint>(vector<Mint>{1});
  dp[1][1] = poly<Mint>(vector<Mint>{1, 1});
  dp[1][2] = poly<Mint>(vector<Mint>{1, 3, 1});
  for (int i = 2; i < 30; ++i) {
    poly<Mint> tmp = dp[i - 1][1] * dp[i - 1][1];
    dp[i][2] = dp[i - 1][2] * dp[i - 1][2] + tmp.mul_xk(1);
    tmp = dp[i - 1][0] * dp[i - 1][1];
    dp[i][1] = dp[i - 1][2] * dp[i - 1][1] + tmp.mul_xk(1);
    tmp = dp[i - 1][0] * dp[i - 1][0];
    dp[i][0] = dp[i - 1][1] * dp[i - 1][1] + tmp.mul_xk(1);
    for (int j = 0; j < 3; ++j) dp[i][j] = dp[i][j].mod_xk(k + 1);
  }
  auto merge = [&](poly<Mint> &x, poly<Mint> &y, poly<Mint> &z, poly<Mint> &a,
                   poly<Mint> &b, poly<Mint> &c) {
    poly<Mint> tmp = a * x;
    x = b * y + tmp.mul_xk(1);
    tmp = a * y;
    poly<Mint> xx = b * y;
    y = z * b + tmp.mul_xk(1);
    z = c * z + xx.mul_xk(1);
    x.mod_xk(k + 1);
    y.mod_xk(k + 1);
    z.mod_xk(k + 1);
  };
  poly<Mint> a, b, c;
  for (int j = 29; j >= 1; --j) {
    if (n & (1 << j)) {
      a = dp[j][0], b = dp[j][1], c = dp[j][2];
      for (--j; j >= 1; --j) {
        if (n & (1 << j)) merge(a, b, c, dp[j][0], dp[j][1], dp[j][2]);
      }
      break;
    }
  }
  if (n >= 2 && n % 2 == 1)
    c = c + c.mul_xk(1) + b.mul_xk(1);
  else if (n == 1)
    c = dp[1][1];
  for (int i = 1; i <= k; ++i) cout << c[i] << " ";
  cout << "\n";
  return 0;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) _runtimeTerror_();
  return 0;
}