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>
const int G = 3;
const int MaxK = 40001;
const int inv2 = 499122177;
const int MaxN = 6e5 + 10;
const int mod = 998244353;
int n, k, lim, w[MaxN], rev[MaxN], _inv[MaxN];
void Mod(int &x) { x += x >> 31 & mod; }
void __init() {
  _inv[1] = 1;
  for (int i = 2; i < MaxN; i++)
    _inv[i] = (unsigned long long)(mod - mod / i) * _inv[mod % i] % mod;
}
int fast_pow(int a, int b) {
  int ret = 1;
  while (b) {
    if (b & 1) ret = (unsigned long long)ret * a % mod;
    a = (unsigned long long)a * a % mod, b >>= 1;
  }
  return ret;
}
void init(int n) {
  int l = 32 - __builtin_clz(n - 1);
  lim = (1 << l);
  for (int i = 0, ri = 0; i < lim; i++) {
    rev[i] = ri;
    for (int k = lim >> 1; (ri ^= k) < k;) k >>= 1;
  }
  int wn = fast_pow(G, (mod - 1) >> l);
  w[lim >> 1] = 1;
  for (int i = (lim >> 1) + 1; i < lim; i++)
    w[i] = (unsigned long long)w[i - 1] * wn % mod;
  for (int i = (lim >> 1) - 1; i; --i) w[i] = w[i << 1];
  lim = l;
}
struct poly {
  std::vector<int> v;
  inline poly() {}
  inline poly(int n) : v(n) {}
  inline poly(const poly &r) : v(r.v) {}
  inline poly(const std::vector<int> &r) : v(r) {}
  inline size_t size() { return v.size(); }
  inline bool empty() { return v.empty(); }
  inline void resize(int n) { v.resize(n); }
  inline void clear() { v.clear(); }
  inline void shl() { v.insert(v.begin(), 0); }
  void shrink() {
    while (!v.empty() && !v.back()) v.pop_back();
  }
  inline int &operator[](int i) { return v[i]; }
  inline static int len(int n) { return 1 << (32 - __builtin_clz(n - 1)); }
  void deriv() {
    for (int i = 1; i < v.size(); i++)
      v[i - 1] = (unsigned long long)i * v[i] % mod;
    v.pop_back();
  }
  void intg() {
    shl();
    for (int i = 1; i < v.size(); i++)
      v[i] = (unsigned long long)v[i] * _inv[i] % mod;
  }
  void dft(int n) {
    static unsigned long long tmp[MaxN];
    int ofs = lim - __builtin_ctz(n);
    resize(n);
    if (n <= 1) return;
    for (int i = 0; i < n; i++) tmp[rev[i] >> ofs] = v[i];
    for (int i = 0; i < n; i += 2) {
      int x = tmp[i], y = tmp[i + 1];
      tmp[i] = x + y, tmp[i + 1] = x + mod - y;
    }
    for (int i = 2; i < n; i <<= 1)
      for (int j = 0; j < n; j += (i << 1))
        for (int k = 0; k < i; ++k) {
          int y = (unsigned long long)tmp[i + j + k] * w[i + k] % mod;
          tmp[i + j + k] = tmp[j + k] + mod - y, tmp[j + k] += y;
        }
    for (int i = 0; i < n; i++) v[i] = tmp[i] % mod;
  }
  void idft(int n) {
    dft(n);
    if (n <= 1) return;
    std::reverse(v.begin() + 1, v.end());
    int tmp = mod - (mod - 1) / n;
    for (int i = 0; i < n; i++) v[i] = (unsigned long long)v[i] * tmp % mod;
  }
  void mul(int k) {
    int n = size();
    for (int i = 0; i < n; i++)
      v[i] = (unsigned long long)(v[i] * k % mod + mod) % mod;
  }
  void add(poly r) {
    int n = std::max(size(), r.size());
    resize(n);
    for (int i = 0; i < n; i++) v[i] = (unsigned long long)(v[i] + r[i]) % mod;
    shrink();
  }
  void mul(poly r) {
    int n = len(size() + r.size() - 1);
    dft(n), r.dft(n);
    for (int i = 0; i < n; i++) v[i] = (unsigned long long)v[i] * r[i] % mod;
    idft(n), shrink();
  }
  void inv() {
    std::vector<int> va(1);
    int n = size(), m = len(n);
    va[0] = fast_pow(v[0], mod - 2);
    poly a;
    v.resize(m), v.swap(va);
    for (int i = 1; i <= m; i <<= 1) {
      a.resize(i);
      for (int j = 0; j < i; j++) a[j] = va[j];
      a.dft(i << 1), dft(i << 1);
      for (int j = 0; j < (i << 1); j++)
        v[j] = v[j] * (2 + mod - (unsigned long long)v[j] * a[j] % mod) % mod;
      idft(i << 1), resize(i);
    }
    resize(n);
  }
  void ln() {
    poly f0 = *this;
    int n = size();
    deriv(), f0.inv(), mul(f0);
    resize(n), intg(), resize(n);
  }
  void exp() {
    std::vector<int> va(1);
    va[0] = 1;
    poly a;
    int n = size(), m = len(n);
    v.resize(m), v.swap(va);
    for (int i = 1; i <= m; i *= 2) {
      a = *this, a.resize(i), a.ln();
      for (int j = 0; j < i; j++) a[j] = (va[j] + !j + mod - a[j]) % mod;
      mul(a), resize(i);
    }
    resize(n);
  }
  void pw(int k) {
    ln();
    int n = size();
    for (int i = 0; i < n; i++) v[i] = (unsigned long long)v[i] * k % mod;
    exp();
  }
  void pw1(int k) {
    int n = size(), m = len(n);
    poly a;
    a.v.clear(), a.v.push_back(1), v.swap(a.v);
    while (k) {
      if (k & 1) mul(a);
      a.mul(a), k >>= 1;
      resize(n), a.resize(n);
    }
  }
  void sqrt() {
    std::vector<int> va(1);
    int n = size(), m = len(n);
    poly a, b;
    va[0] = ::sqrt(v[0]);
    v.resize(m), v.swap(va);
    for (int i = 1; i <= m; i <<= 1) {
      a.resize(i), b.resize(i);
      for (int j = 0; j < i; j++) a[j] = va[j], b[j] = v[j];
      b.inv(), a.mul(b);
      for (int j = 0; j < i; j++)
        v[j] = (unsigned long long)(v[j] + a[j]) % mod * inv2 % mod;
      resize(i << 1);
    }
    resize(n);
  }
} f, g, h;
inline int read() {
  unsigned long long x = 0;
  char ch = getchar();
  while (ch > '9' || ch < '0') ch = getchar();
  while (ch <= '9' && ch >= '0') x = ((x * 10) + (ch ^ 48)), ch = getchar();
  return x;
}
signed main() {
  int pw2 = 0;
  __init(), init(250000), n = read(), k = read();
  f.resize(MaxK), f[0] = 1, f[1] = 6, f[2] = 1;
  g = h = f, h.sqrt(), h[0]++, h[1]++, g.sqrt(), g.inv();
  h.pw1(n + 1), g.mul(h), pw2 = fast_pow(inv2, n + 1);
  for (int i = 1; i <= std::min(n, k); i++)
    printf("%d ", (unsigned long long)g[i] * pw2 % mod);
  for (int i = std::min(n, k) + 1; i <= k; i++) printf("%d ", 0);
  return 0;
}