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 mod = 998244353, N = 5e5;
int qmod1(const int &x) { return x >= mod ? x - mod : x; }
int qmod2(const int &x) { return x + (x >> 31 & mod); }
int qpower(int a, int b) {
  int ans = 1;
  for (; b; b >>= 1, a = 1ll * a * a % mod)
    if (b & 1) ans = 1ll * ans * a % mod;
  return ans;
}
struct Z {
  int x;
  Z(int v = 0) { x = qmod2(v % mod); }
  int qmod1(const int &x) const { return x >= mod ? x - mod : x; }
  int qmod2(const int &x) const { return x + (x >> 31 & mod); }
  int qpower(int a, int b) const {
    int ans = 1;
    for (; b; b >>= 1, a = 1ll * a * a % mod)
      if (b & 1) ans = 1ll * ans * a % mod;
    return ans;
  }
  Z operator+(const Z &b) const { return (Z){qmod1(x + b.x)}; }
  Z &operator+=(const Z &b) {
    x += b.x;
    if (x >= mod) x -= mod;
    return *this;
  }
  Z operator-(const Z &b) const { return (Z){qmod2(x - b.x)}; }
  Z &operator-=(const Z &b) {
    x -= b.x;
    x += x >> 31 & mod;
    return *this;
  }
  Z operator*(const Z &b) const { return (Z){(int)(1ll * x * b.x % mod)}; }
  Z &operator*=(const Z &b) {
    x = 1ll * x * b.x % mod;
    return *this;
  }
  int inv() const {
    assert(x != 0);
    return qpower(x, mod - 2);
  }
  Z operator/(const Z &b) const { return (Z){(int)(1ll * x * b.inv() % mod)}; }
  Z &operator/=(const Z &b) {
    x = 1ll * x * b.inv() % mod;
    return *this;
  }
  Z operator-() const { return (Z){qmod2(-x)}; }
};
bool zero(const Z &a) { return !a.x; }
void print(const Z &a) { printf("%d", a.x); }
Z inv[N], fac[N], ifac[N];
void prework(int n) {
  fac[0] = 1;
  for (int i = 1; i <= n; i++) fac[i] = fac[i - 1] * Z(i);
  inv[1] = 1;
  for (int i = 2; i <= n; i++) inv[i] = Z(mod - mod / i) * inv[mod % i];
  ifac[0] = 1;
  for (int i = 1; i <= n; i++) ifac[i] = ifac[i - 1] * inv[i];
}
template <typename T>
void simplify(T &a) {
  while (a.size() && zero(a[-1])) a.pop_back();
}
template <typename T>
bool zero(const T &a) {
  int n = a.size() - 1;
  while (n >= 0 && zero(a[n])) --n;
  return n < 0;
}
int limn = 0;
void setn(const int &n) { limn = n; }
template <class T>
struct Poly {
  vector<T> a;
  Poly() { a.resize(0); }
  Poly(const T &u, const T &v) {
    a.resize(2);
    a[0] = u, a[1] = v;
  }
  Poly(const int &u, const int &v) {
    a.resize(2);
    a[0] = u, a[1] = v;
  }
  Poly(const int &x) {
    a.resize(1);
    a[0] = T(x);
  }
  Poly(const T &x) {
    a.resize(1);
    a[0] = x;
  }
  int size() const { return a.size(); }
  void resize(const int &x) { a.resize(x); }
  void clear() { vector<T>().swap(a); }
  void pop_back() { a.pop_back(); }
  T operator[](const int &x) const {
    assert(x < (int)a.size());
    if (x >= 0) return a[x];
    assert(-x <= (int)a.size());
    return a[a.size() + x];
  }
  T &operator[](const int &x) {
    assert(x < (int)a.size());
    if (x >= 0) return a[x];
    assert(-x <= (int)a.size());
    return a[a.size() + x];
  }
  Poly<T> operator*(const Poly<T> &b) const {
    Poly<T> c;
    if (!a.size() || !b.size()) return c;
    int n = a.size(), m = b.size();
    c.resize(n + m - 1);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) c[i + j] += a[i] * b[j];
    simplify(c);
    return c;
  }
  Poly<T> operator*(const T &b) const {
    Poly<T> c;
    int n = a.size();
    c.resize(n);
    for (int i = 0; i < (int)a.size(); i++) c[i] = a[i] * b;
    return c;
  }
  Poly<T> operator+(const Poly &b) const {
    Poly c;
    int n = a.size(), m = b.size();
    c.resize(max(n, m));
    for (int i = 0; i < n && i < m; i++) c[i] = a[i] + b[i];
    if (n < m)
      copy(b.a.begin() + n, b.a.end(), c.a.begin() + n);
    else
      copy(a.begin() + m, a.end(), c.a.begin() + m);
    simplify(c);
    return c;
  }
  Poly<T> operator-() const {
    Poly c;
    int n = a.size();
    c.resize(n);
    for (int i = 0; i < n; i++) c[i] = -a[i];
    return c;
  }
  Poly<T> operator-(const Poly<T> &b) const {
    Poly c;
    int n = a.size(), m = b.size();
    c.resize(max(n, m));
    for (int i = 0; i < n && i < m; i++) c[i] = a[i] - b[i];
    if (n < m)
      for (int i = n; i < m; i++) c[i] = -b[i];
    else
      copy(a.begin() + m, a.end(), c.a.begin() + m);
    simplify(c);
    return c;
  }
  Poly<T> operator/(const Poly<T> &b) const {
    assert(!zero(b));
    Poly c;
    int n = a.size(), m = b.size();
    if (n < m) return c;
    Poly<T> tmp = *this;
    c.resize(n - m + 1);
    for (int i = n - 1; i >= m - 1; i--) {
      T t = tmp[i] / b[m - 1];
      c[i - m + 1] = t;
      for (int j = 0; j < m; j++) tmp[i - j] -= b[m - 1 - j] * t;
    }
    return c;
  }
  Poly<T> operator%(const Poly<T> &b) const {
    assert(!zero(b));
    Poly<T> c;
    int n = a.size(), m = b.size();
    c = *this;
    for (int i = n - 1; i >= m - 1; i--) {
      T t = c[i] / b[m - 1];
      for (int j = 0; j < m; j++) c[i - j] -= b[m - 1 - j] * t;
    }
    simplify(c);
    return c;
  }
  Poly<T> &operator+=(const Poly<T> &b) {
    *this = *this + b;
    return *this;
  }
  Poly<T> &operator-=(const Poly<T> &b) {
    *this = *this - b;
    return *this;
  }
  Poly<T> &operator*=(const Poly<T> &b) {
    *this = *this * b;
    return *this;
  }
  Poly<T> &operator*=(const T &b) {
    *this = *this * b;
    return *this;
  }
  Poly<T> &operator/=(const Poly<T> &b) {
    *this = *this / b;
    return *this;
  }
  Poly<T> &operator%=(const Poly<T> &b) {
    *this = *this % b;
    return *this;
  }
  template <typename S>
  S operator()(const S &b) const {
    S ans;
    Poly<T> a = *this;
    int n = limn ? limn : a.size();
    a.resize(n);
    for (int i = n - 1; i >= 0; i--) {
      ans = ans * b + S(a[i]);
      if (limn) ans.resize(limn);
    }
    return ans;
  }
};
void print(const Poly<Z> &a) {
  int n = a.size();
  if (!n) {
    printf("0");
    return;
  }
  for (int i = n - 1; i >= 1; i--) print(a[i]), printf("x^%d + ", i);
  print(a[0]);
}
template <typename T>
Poly<T> monic(const Poly<T> &a) {
  Poly<T> ans = a;
  simplify(ans);
  if (zero(ans)) return ans;
  T t = ans[-1].inv();
  for (int i = 0; i < ans.size(); i++) ans[i] = a[i] * t;
  return ans;
}
template <typename T>
Poly<T> gcd(const Poly<T> &a, const Poly<T> &b) {
  if (zero(b)) return monic(a);
  return gcd(b, a % b);
}
template <typename T>
Poly<T> lcm(const Poly<T> &a, const Poly<T> &b) {
  if (zero(a) || zero(b)) return Poly<T>();
  return a * b / gcd(a, b);
}
template <typename T>
pair<Poly<T>, Poly<T> > exgcd(const Poly<T> &a, const Poly<T> &b,
                              const Poly<T> &c = Poly<T>(1)) {
  if (zero(b)) {
    assert(zero(c % a));
    return make_pair(c / a, 0);
  }
  pair<Poly<T>, Poly<T> > t = exgcd(b, a % b, c);
  return make_pair(t.second, t.first - a / b * t.second);
}
Poly<Z> Der(const Poly<Z> &a) {
  Poly<Z> ans;
  int n = a.size();
  if (n <= 1) return ans;
  ans.resize(n - 1);
  for (int i = 0; i < n - 1; i++) ans[i] = a[i + 1] * (Z(i + 1));
  return ans;
}
Poly<Z> Ln(const Poly<Z> &A) {
  Poly<Z> a = A;
  int n = limn ? limn : a.size();
  a.resize(n);
  Poly<Z> ans;
  ans.resize(n);
  ans[0] = 0;
  assert(a[0].x == 1);
  for (int i = 1; i < n; i++) {
    ans[i] = Z(i) * a[i];
    for (int j = 0; j < i; j++) ans[i] -= ans[j] * a[i - j];
  }
  for (int i = 1; i < n; i++) ans[i] *= inv[i];
  return ans;
}
Poly<Z> Exp(const Poly<Z> &A) {
  Poly<Z> a = A;
  int n = limn ? limn : a.size();
  a.resize(n);
  Poly<Z> ans;
  ans.resize(n);
  ans[0] = 1;
  assert(a[0].x == 0);
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < i; j++) ans[i] += ans[j] * a[i - j] * Z(i - j);
    ans[i] *= inv[i];
  }
  return ans;
}
Poly<Z> Inv(const Poly<Z> &A) {
  Poly<Z> a = A;
  int n = limn ? limn : a.size();
  a.resize(n);
  Poly<Z> ans;
  ans.resize(n);
  Z iv = a[0].inv();
  ans[0] = iv;
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < i; j++) ans[i] -= ans[j] * a[i - j];
    ans[i] *= iv;
  }
  return ans;
}
Poly<Z> Pow(const Poly<Z> &A, const int &K) {
  Poly<Z> a = A;
  int n = limn ? limn : a.size();
  a.resize(n);
  Poly<Z> tmp = a;
  simplify(tmp);
  if (zero(tmp)) return tmp;
  int pos = 0;
  for (int i = 0; i < tmp.size(); i++)
    if (!zero(tmp[i])) {
      pos = i;
      break;
    }
  copy(tmp.a.begin() + pos, tmp.a.end(), tmp.a.begin());
  tmp.resize(tmp.size() - pos);
  Z iv = tmp[0].inv();
  for (int i = 0; i < tmp.size(); i++) tmp[i] * iv;
  Poly<Z> ans = tmp;
  ans.resize(n);
  ans = Ln(ans);
  for (int i = 1; i < n; i++) ans[i] *= K;
  ans = Exp(ans);
  if (pos * K >= n) return Poly<Z>();
  ans.resize(ans.size() + pos * K);
  copy(ans.a.begin(), ans.a.end(), ans.a.begin() + pos * K);
  ans.resize(n);
  iv = iv.inv();
  iv = qpower(iv.x, K);
  for (int i = 0; i < n; i++) ans[i] *= iv;
  return ans;
}
Poly<Z> Sqrt(const Poly<Z> &a) { return Pow(a, (mod + 1) >> 1); }
Poly<Z> mul(const Poly<Z> &A, const Poly<Z> &B) {
  Poly<Z> a = A, b = B;
  int n;
  if (limn)
    n = limn, a.resize(n), b.resize(n);
  else
    n = a.size() + b.size() - 1, a.resize(n), b.resize(n);
  Poly<Z> ans;
  ans.resize(n);
  for (int i = 0; i < n; i++)
    for (int j = 0; j + i < n; j++) ans[i + j] += a[i] * b[j];
  return ans;
}
struct FRAC {
  Poly<Z> u, v;
  FRAC(const Z &x) {
    u = x;
    v = Z(1);
  }
  FRAC(const int &x) {
    u = Z(x);
    v = Z(1);
  }
  FRAC() { u = Z(0), v = Z(1); }
  FRAC(const Poly<Z> &_u) {
    u = _u;
    v = Z(1);
  }
  FRAC(const Poly<Z> &_u, const Poly<Z> &_v) {
    u = _u, v = _v;
    simplify(u), simplify(v);
    if (zero(u)) {
      v = 1;
      return;
    }
    Poly<Z> d = gcd(u, v);
    u /= d, v /= d;
    Poly<Z> c = v[-1];
    u /= c, v /= c;
  }
  FRAC operator+(const FRAC &a) const {
    return (FRAC){u * a.v + v * a.u, v * a.v};
  }
  FRAC operator-(const FRAC &a) const {
    return (FRAC){u * a.v - v * a.u, v * a.v};
  }
  FRAC operator*(const FRAC &a) const { return (FRAC){u * a.u, v * a.v}; }
  FRAC operator/(const FRAC &a) const { return (FRAC){u * a.v, v * a.u}; }
  FRAC operator-() const { return (FRAC){-u, v}; }
  FRAC operator()(const FRAC &a) const {
    FRAC fz, fm;
    for (int i = (int)u.size() - 1; i >= 0; i--) fz = fz * a + (FRAC){u[i]};
    for (int i = (int)v.size() - 1; i >= 0; i--) fm = fm * a + (FRAC){v[i]};
    return fz / fm;
  }
  FRAC inv() { return (FRAC){v, u}; }
};
bool zero(const FRAC &a) { return zero(a.u); }
FRAC &operator+=(FRAC &a, const FRAC &b) {
  a = a + b;
  return a;
}
FRAC &operator-=(FRAC &a, const FRAC &b) {
  a = a - b;
  return a;
}
FRAC &operator*=(FRAC &a, const FRAC &b) {
  a = a * b;
  return a;
}
FRAC &operator/=(FRAC &a, const FRAC &b) {
  a = a / b;
  return a;
}
FRAC Der(const FRAC &a) {
  return (FRAC){Der(a.u) * a.v - a.u * Der(a.v), a.v * a.v};
}
void print(const FRAC &a) {
  putchar('('), print(a.u), printf(") / (");
  print(a.v);
  putchar(')');
}
struct Basis {
  vector<Poly<FRAC> > a;
  vector<Poly<FRAC> > c;
  int n;
  Basis(int _n) {
    n = _n;
    a.resize(n);
    for (int i = 0; i < n; i++) a[i].resize(n);
    c.resize(n);
    for (int i = 0; i < n; i++) c[i].resize(n);
  }
  pair<bool, Poly<FRAC> > ins(Poly<FRAC> x) {
    Poly<FRAC> tc;
    tc.resize(n);
    for (int i = 0; i < n; i++) {
      if (zero(x[i])) continue;
      if (zero(a[i])) {
        a[i] = x;
        c[i] = tc;
        c[i][i] = 1;
        return make_pair(1, 0);
      }
      FRAC t = -x[i] / a[i][i];
      tc[i] = t;
      x += a[i] * t;
      x.resize(n);
    }
    for (int j = 0; j < n; j++) tc[j] = -tc[j];
    Poly<FRAC> ans;
    ans.resize(n);
    setn(n);
    for (int j = 0; j < n; j++) ans += c[j] * tc[j];
    setn(0);
    simplify(ans);
    return make_pair(0, ans);
  }
};
template <typename T>
int mindeg(const Poly<T> &a) {
  int n = a.size() - 1;
  for (int i = 0; i < n; i++)
    if (!zero(a[i])) return i;
  return -1;
}
struct ODE {
  Poly<FRAC> a;
  int size() const { return a.size(); }
  int length() const {
    Poly<Z> t = 1;
    for (int i = 0; i < (int)a.size(); i++) t = lcm(t, a[i].v);
    Poly<FRAC> tmpa = a;
    for (int i = 0; i < (int)tmpa.size(); i++) tmpa[i] *= (FRAC){t};
    int mxpos = tmpa.size() - mindeg(t), mipos = tmpa.size() - (t.size() - 1);
    for (int i = 0; i < (int)tmpa.size(); i++)
      if (!zero(tmpa[i]))
        mxpos = max(mxpos, i - mindeg(tmpa[i].u)),
        mipos = min(mipos, i - (int)(tmpa[i].u.size() - 1));
    return mxpos - mipos;
  }
  Poly<Z> geta(const Poly<Z> &a0, const int &n) const {
    int m = a0.size();
    Poly<Z> t = 1;
    for (int i = 0; i < (int)a.size(); i++) t = lcm(t, a[i].v);
    Poly<FRAC> tmpa = a;
    for (int i = 0; i < (int)tmpa.size(); i++) tmpa[i] *= (FRAC){t};
    int mxpos = tmpa.size() - mindeg(t), mipos = tmpa.size() - (t.size() - 1);
    for (int i = 0; i < (int)tmpa.size(); i++)
      if (!zero(a[i]))
        mxpos = max(mxpos, i - mindeg(tmpa[i].u)),
        mipos = min(mipos, i - (int)(tmpa[i].u.size() - 1));
    assert(m >= mxpos - mipos);
    vector<vector<Z> > pw;
    pw.resize(n + 1);
    for (int i = 0; i <= n; i++) {
      pw[i].resize(tmpa.size() + 1);
      pw[i][0] = 1;
      for (int j = 1; j < (int)pw[i].size(); j++)
        pw[i][j] = pw[i][j - 1] * (Z){i - j + 1};
    }
    Poly<Z> ans = a0;
    ans.resize(n + 1);
    for (int i = m; i <= n; i++) {
      Z u = 0, v = 0;
      for (int j = 0; j < t.size(); j++) {
        if (zero(t[j])) continue;
        int d = mxpos - (tmpa.size() - j);
        if (!d)
          u += t[j] * pw[i][tmpa.size()];
        else
          v -= pw[i - d][tmpa.size()] * t[j] * ans[i - d];
      }
      for (int j = 0; j < (int)tmpa.size(); j++)
        for (int k = 0; k < tmpa[j].u.size(); k++) {
          if (zero(tmpa[j].u[k])) continue;
          int d = mxpos - (j - k);
          if (!d)
            u -= tmpa[j].u[k] * pw[i][j];
          else
            v += ans[i - d] * pw[i - d][j] * tmpa[j].u[k];
        }
      assert(!zero(u) || zero(v));
      if (!zero(u))
        ans[i] = v / u;
      else
        ans[i] = 1;
    }
    return ans;
  }
};
bool zero(const ODE &a) { return zero(a.a); }
void print(const ODE &a) {
  if (!a.size()) {
    puts("F=0");
    return;
  }
  int n = a.size();
  printf("F(%d) =", n);
  putchar('('), print(a.a[0]);
  printf(")F");
  for (int i = 1; i < n; i++)
    printf(" + "), printf("("), print(a.a[i]), printf(")F(%d)", i);
  puts("");
}
ODE operator+(const ODE &A, const ODE &B) {
  if (zero(A)) return B;
  if (zero(B)) return A;
  Poly<FRAC> a = A.a, b = B.a;
  int n = a.size(), m = b.size();
  ODE ans;
  Poly<FRAC> tmp;
  tmp.resize(n + m);
  tmp[0] = 1, tmp[n] = 1;
  Basis bs(n + m);
  for (;;) {
    pair<bool, Poly<FRAC> > t = bs.ins(tmp);
    if (!t.first) {
      ans.a = t.second;
      break;
    }
    FRAC u = tmp[n - 1];
    tmp[n - 1] = Der(tmp[n - 1]);
    for (int i = n - 2; i >= 0; i--) tmp[i + 1] += tmp[i], tmp[i] = Der(tmp[i]);
    for (int i = 0; i < n; i++) tmp[i] += u * a[i];
    u = tmp[n + m - 1];
    tmp[n + m - 1] = Der(tmp[n + m - 1]);
    for (int i = n + m - 2; i >= n; i--)
      tmp[i + 1] += tmp[i], tmp[i] = Der(tmp[i]);
    for (int i = n; i < n + m; i++) tmp[i] += u * b[i - n];
  }
  return ans;
}
ODE operator*(const ODE &A, const ODE &B) {
  if (zero(A)) return B;
  if (zero(B)) return A;
  Poly<FRAC> a = A.a, b = B.a;
  int n = a.size(), m = b.size();
  ODE ans;
  Poly<FRAC> tmp;
  tmp.resize(n * m);
  tmp[0] = 1;
  Basis bs(n * m);
  for (int T = 0;; ++T) {
    pair<bool, Poly<FRAC> > t = bs.ins(tmp);
    if (!t.first) {
      ans.a = t.second;
      break;
    }
    Poly<FRAC> ttmp = tmp;
    tmp.clear();
    tmp.resize(n * m);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) {
        tmp[i * m + j] += Der(ttmp[i * m + j]);
        if (i != n - 1)
          tmp[(i + 1) * m + j] += ttmp[i * m + j];
        else {
          for (int k = 0; k < n; k++) tmp[k * m + j] += ttmp[i * m + j] * a[k];
        }
        if (j != m - 1)
          tmp[i * m + j + 1] += ttmp[i * m + j];
        else {
          for (int k = 0; k < m; k++) tmp[i * m + k] += ttmp[i * m + j] * b[k];
        }
      }
  }
  return ans;
}
ODE composite(const ODE &A, const FRAC &b) {
  if (zero(A)) return A;
  ODE ans;
  Poly<FRAC> tmp;
  Poly<FRAC> a = A.a;
  int n = a.size();
  FRAC db = Der(b);
  tmp.resize(n);
  tmp[0] = 1;
  Basis bs(n);
  for (;;) {
    pair<bool, Poly<FRAC> > t = bs.ins(tmp);
    if (!t.first) {
      ans.a = t.second;
      break;
    }
    FRAC u = tmp[n - 1] * db;
    tmp[n - 1] = Der(tmp[n - 1]);
    for (int i = n - 2; i >= 0; i--)
      tmp[i + 1] += tmp[i] * db, tmp[i] = Der(tmp[i]);
    if (!zero(u))
      for (int i = 0; i < n; i++) tmp[i] += a[i](b) * u;
  }
  return ans;
}
Poly<FRAC> trans_vector(const vector<Poly<FRAC> > &a, const int &n,
                        const int &m) {
  Poly<FRAC> ans;
  ans.resize(n * m);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      ans[i * m + j] = a[i][j];
    }
  return ans;
}
Poly<FRAC> composite(const FRAC &a, const Poly<FRAC> &b) {
  Poly<FRAC> u, v;
  u.resize(a.u.size()), v.resize(a.v.size());
  for (int i = 0; i < a.u.size(); i++) u[i] = a.u[i];
  for (int i = 0; i < a.v.size(); i++) v[i] = a.v[i];
  return exgcd(v % b, b, u % b).first % b;
}
void print(const Poly<FRAC> &a) {
  int n = a.size();
  putchar('('), print(a[0]), putchar(')');
  for (int i = 1; i < n; i++) printf(" + ("), print(a[i]), printf(")u^%d", i);
  puts("");
}
ODE composite(const ODE &A, const Poly<FRAC> &B) {
  if (!A.size()) return A;
  Poly<FRAC> b = monic(B);
  assert(b.size() > 1);
  Poly<FRAC> a = A.a;
  ODE ans;
  vector<Poly<FRAC> > tmp;
  assert(b.size() > 1);
  int n = a.size(), m = b.size();
  Poly<FRAC> du;
  {
    Poly<FRAC> u = b;
    for (int i = 0; i < m; i++) u[i] = Der(u[i]);
    simplify(u);
    Poly<FRAC> v = b;
    for (int i = 0; i < m - 1; i++) v[i] = v[i + 1] * FRAC(Poly<Z>(i + 1));
    v.pop_back();
    du = exgcd(v, b, -u).first % b;
  }
  --m;
  tmp.resize(n);
  tmp[0] = Poly<FRAC>(1);
  for (int i = 0; i < n; i++) tmp[i].resize(m);
  Basis bs(n * m);
  int T = 0;
  for (;;) {
    pair<bool, Poly<FRAC> > t = bs.ins(trans_vector(tmp, n, m));
    if (!t.first) {
      ans.a = t.second;
      break;
    }
    vector<Poly<FRAC> > ttmp = tmp;
    tmp.clear();
    tmp.resize(n);
    for (int i = 0; i < n; i++) tmp[i].resize(m);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) tmp[i][j] += Der(ttmp[i][j]);
    for (int i = 0; i < n - 1; i++) {
      Poly<FRAC> t = du * ttmp[i] % b;
      tmp[i + 1] += t;
    }
    for (int i = 0; i < n; i++)
      tmp[i] += composite(a[i], b) * du * ttmp[n - 1] % b;
    for (int i = 0; i < n; i++) {
      Poly<FRAC> t = ttmp[i];
      for (int j = 0; j < t.size() - 1; j++) t[j] = FRAC(j + 1) * t[j + 1];
      t.pop_back();
      tmp[i] += t * du % b;
    }
    for (int i = 0; i < n; i++) tmp[i].resize(m);
  }
  return ans;
}
Poly<Z> calc0(const int &n, const int &len) {
  setn(len);
  Poly<Z> X(0, 1);
  Poly<Z> t;
  t.resize(3);
  t[0] = 1, t[1] = 6, t[2] = 1;
  t = Sqrt(t);
  Poly<Z> r = (Poly<Z>(1, 1) + t) * Z((mod + 1) >> 1);
  return mul(Pow(r, n), Inv(t));
}
ODE getODE(const int &n) {
  Poly<Z> X(0, 1);
  ODE ans;
  ODE t;
  t.a = Poly<FRAC>(FRAC(n, X));
  Poly<FRAC> tf;
  tf.resize(3);
  tf[0] = -X, tf[1] = Poly<Z>(-1, -1), tf[2] = 1;
  ans = ans * composite(t, tf);
  t.a = Poly<FRAC>(FRAC((mod - 1) >> 1, X));
  FRAC tx;
  tx.u.resize(3);
  tx.u[0] = 1, tx.u[1] = 6, tx.u[2] = 1;
  ans = ans * composite(t, tx);
  return ans;
}
int main() {
  int n, K;
  scanf("%d%d", &n, &K);
  int tK = K;
  K = min(K, n);
  prework(20);
  ODE h = getODE(n + 1);
  Poly<Z> ans = h.geta(calc0(n + 1, h.length()), K);
  for (int i = 1; i <= K; i++) print(ans[i]), putchar(' ');
  for (int i = K + 1; i <= tK; i++) putchar('0'), putchar(' ');
  puts("");
}