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>
namespace fei_standard_library {
const int maxn = 1 << 21, mod = 998244353;
class poly {
 private:
  std::vector<int> data;

 public:
  poly(std::size_t len = std::size_t(0)) { data = std::vector<int>(len); }
  poly(const std::vector<int> &b) { data = b; }
  poly(const std::vector<int> &b, int len) {
    data = b;
    data.resize(len);
  }
  poly(const poly &b, int len) {
    data = b.data;
    data.resize(len);
  }
  poly(const int &h) { data.push_back(h); }
  void resize(std::size_t len, int val = 0) { data.resize(len, val); }
  std::size_t size(void) const { return data.size(); }
  void clear(void) { data.clear(); }
  int &operator[](std::size_t b) { return data[b]; }
  const int &operator[](std::size_t b) const { return data[b]; }
  poly operator*(const poly &h) const;
  poly operator*=(const poly &h);
  poly operator*(const int &h) const;
  poly operator*=(const int &h);
  poly operator+(const poly &h) const;
  poly operator+=(const poly &h);
  poly operator-(const poly &h) const;
  poly operator-=(const poly &h);
  poly operator<<(const std::size_t &b) const;
  poly operator<<=(const std::size_t &b);
  poly operator>>(const std::size_t &b) const;
  poly operator>>=(const std::size_t &b);
  poly operator/(const int &h) const;
  poly operator/=(const int &h);
  poly inv(void) const;
  poly inv(const int &h) const;
  friend poly sqrt(const poly &h);
};
int qpow(int a, int b) {
  int res = 1;
  while (b) {
    if (b & 1) res = (long long)res * a % mod;
    a = (long long)a * a % mod, b >>= 1;
  }
  return res;
}
int rev[maxn];
void dft(std::vector<int> &f, int n, int b) {
  static int w[maxn];
  for (int i = 0; i < n; ++i)
    if (i < rev[i]) std::swap(f[i], f[rev[i]]);
  for (int i = 2; i <= n; i <<= 1) {
    w[0] = 1, w[1] = qpow(3, (mod - 1) / i);
    if (b == -1) w[1] = qpow(w[1], mod - 2);
    for (int j = 2; j < i / 2; ++j) w[j] = (long long)w[j - 1] * w[1] % mod;
    for (int j = 0; j < n; j += i)
      for (int k = 0; k < i / 2; ++k) {
        int p = f[j + k], q = (long long)f[j + i / 2 + k] * w[k] % mod;
        f[j + k] = (p + q) % mod, f[j + i / 2 + k] = (p - q + mod) % mod;
      }
  }
}
poly poly::operator*(const poly &h) const {
  int N = 1;
  while (N < (int)(size() + h.size() - 1)) N <<= 1;
  std::vector<int> f(this->data), g(h.data);
  f.resize(N), g.resize(N);
  for (int i = 0; i < N; ++i)
    rev[i] = (rev[i >> 1] >> 1) | (i & 1 ? N >> 1 : 0);
  dft(f, N, 1), dft(g, N, 1);
  for (int i = 0; i < N; ++i) f[i] = (long long)f[i] * g[i] % mod;
  dft(f, N, -1), f.resize(size() + h.size() - 1);
  for (int i = 0, inv = qpow(N, mod - 2); i < (int)f.size(); ++i)
    f[i] = (long long)f[i] * inv % mod;
  return f;
}
poly poly::operator*=(const poly &h) { return *this = *this * h; }
poly poly::operator*(const int &h) const {
  std::vector<int> f(size());
  for (int i = 0; i < (int)f.size(); ++i) f[i] = (long long)f[i] * h % mod;
  return f;
}
poly poly::operator*=(const int &h) {
  for (int i = 0; i < (int)size(); ++i) data[i] = (long long)data[i] * h % mod;
  return *this;
}
poly poly::operator+(const poly &h) const {
  std::vector<int> f(this->data);
  if (f.size() < h.size()) f.resize(h.size());
  for (int i = 0; i < (int)h.size(); ++i) f[i] = (f[i] + h[i]) % mod;
  return f;
}
poly poly::operator+=(const poly &h) {
  std::vector<int> &f = this->data;
  if (f.size() < h.size()) f.resize(h.size());
  for (int i = 0; i < (int)h.size(); ++i) f[i] = (f[i] + h[i]) % mod;
  return f;
}
poly poly::operator-(const poly &h) const {
  std::vector<int> f(this->data);
  if (f.size() < h.size()) f.resize(h.size());
  for (int i = 0; i < (int)h.size(); ++i) f[i] = (f[i] - h[i] + mod) % mod;
  return f;
}
poly poly::operator-=(const poly &h) {
  std::vector<int> &f = this->data;
  if (f.size() < h.size()) f.resize(h.size());
  for (int i = 0; i < (int)h.size(); ++i) f[i] = (f[i] - h[i] + mod) % mod;
  return f;
}
poly poly::operator<<(const std::size_t &b) const {
  std::vector<int> f(size() + b);
  for (int i = 0; i < (int)size(); ++i) f[i + b] = data[i];
  return f;
}
poly poly::operator<<=(const std::size_t &b) { return *this = (*this) << b; }
poly poly::operator>>(const std::size_t &b) const {
  std::vector<int> f(size() - b);
  for (int i = 0; i < (int)f.size(); ++i) f[i] = data[i + b];
  return f;
}
poly poly::operator>>=(const std::size_t &b) { return *this = (*this) >> b; }
poly poly::operator/(const int &h) const {
  std::vector<int> f(this->data);
  int inv = qpow(h, mod - 2);
  for (int i = 0; i < (int)f.size(); ++i) f[i] = (long long)f[i] * inv % mod;
  return f;
}
poly poly::operator/=(const int &h) {
  int inv = qpow(h, mod - 2);
  for (int i = 0; i < (int)data.size(); ++i)
    data[i] = (long long)data[i] * inv % mod;
  return *this;
}
poly poly::inv(void) const {
  int N = 1;
  while (N < (int)(size() + size() - 1)) N <<= 1;
  std::vector<int> f(N), g(N), d(this->data);
  d.resize(N), f[0] = qpow(d[0], mod - 2);
  for (int w = 2; w < N; w <<= 1) {
    for (int i = 0; i < w; ++i) g[i] = d[i];
    for (int i = 0; i < w * 2; ++i)
      rev[i] = (rev[i >> 1] >> 1) | (i & 1 ? w : 0);
    dft(f, w << 1, 1), dft(g, w << 1, 1);
    for (int i = 0; i < w * 2; ++i)
      f[i] = (long long)f[i] * (2 - (long long)f[i] * g[i] % mod) % mod;
    dft(f, w << 1, -1);
    for (int i = 0, inv = qpow(w << 1, mod - 2); i < w; ++i)
      f[i] = (long long)f[i] * inv % mod;
    for (int i = w; i < w * 2; ++i) f[i] = 0;
  }
  f.resize(size());
  for (int i = 0; i < (int)f.size(); ++i) f[i] = (f[i] + mod) % mod;
  return f;
}
poly poly::inv(const int &h) const { return poly(*this, h).inv(); }
int modsqrt(int h) { return 1; }
poly sqrt(const poly &h) {
  int N = 1;
  while (N < (int)(h.size() + h.size() - 1)) N <<= 1;
  poly f(N), g(N), d(h);
  d.resize(N), f[0] = modsqrt(d[0]);
  for (int w = 2; w < N; w <<= 1) {
    g.resize(w);
    for (int i = 0; i < w; ++i) g[i] = d[i];
    f = (f + f.inv(w) * g) / 2;
    f.resize(w);
  }
  f.resize(h.size());
  return f;
}
}  // namespace fei_standard_library
int n, k;
struct Pair {
  fei_standard_library::poly f[3];
  Pair operator*(const Pair &b) const {
    Pair res;
    res.f[0] = f[0] * b.f[0] + ((f[1] * b.f[1]) << 1);
    res.f[1] = f[0] * b.f[1] + ((f[1] * b.f[2]) << 1);
    res.f[2] = f[1] * b.f[1] + ((f[2] * b.f[2]) << 1);
    for (int i = 0; i < 3; ++i)
      if ((int)res.f[i].size() > (k + 1)) res.f[i].resize(k + 1);
    return res;
  }
} ret, ans;
int main() {
  scanf("%d%d", &n, &k), --n;
  ret.f[0] = std::vector<int>{1, 1}, ret.f[1] = 1, ret.f[2] = 0, ans = ret;
  while (n) {
    if (n & 1) ans = ans * ret;
    ret = ret * ret, n >>= 1;
  }
  ans.f[0].resize(k + 1);
  for (int i = 1; i <= k; ++i) printf("%d ", ans.f[0][i]);
  return 0;
}