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 N = 1 << 15, M = N << 1, P = 998244353;
int n, k, w[M], inv[M];
inline int Pow(long long x, int y = P - 2) {
  int ans = 1;
  for (; y; y >>= 1, x = x * x % P)
    if (y & 1) ans = ans * x % P;
  return ans;
}
inline void DFT(vector<int> &f, int n) {
  static unsigned long long F[M];
  for (int i = 0, j = 0; i < n; ++i) {
    F[i] = f[j];
    for (int k = n >> 1; (j ^= k) < k; k >>= 1)
      ;
  }
  for (int i = 1; i < n; i <<= 1)
    for (int j = 0; j < n; j += i << 1)
      for (int k = j; k < j + i; ++k) {
        int t = F[k + i] * w[i + k - j] % P;
        F[k + i] = F[k] + P - t, F[k] += t;
      }
  for (int i = 0; i < n; ++i) f[i] = F[i] % P;
}
inline void IDFT(vector<int> &f, int n) {
  reverse(f.begin() + 1, f.end()), DFT(f, n);
  for (int i = 0, I = Pow(n); i < n; ++i) f[i] = (long long)f[i] * I % P;
}
inline int Calc(int x) {
  int ans = 1;
  while (ans <= x) ans <<= 1;
  return ans;
}
inline vector<int> operator*(const vector<int> &x, const vector<int> &y) {
  if (!x.size() || !y.size()) return {0};
  if ((unsigned long long)x.size() * y.size() <= 1 << 8) {
    vector<int> ans;
    ans.resize(x.size() + y.size() - 1);
    for (unsigned i = 0; i < x.size(); ++i)
      for (unsigned j = 0; j < y.size(); ++j)
        ans[i + j] = (ans[i + j] + (long long)x[i] * y[j]) % P;
    return ans;
  }
  vector<int> a = x, b = y;
  int n = Calc(x.size() + y.size() - 2);
  a.resize(n), b.resize(n), DFT(a, n), DFT(b, n);
  for (int i = 0; i < n; ++i) a[i] = (long long)a[i] * b[i] % P;
  IDFT(a, n);
  return a.resize(min((int)x.size() + (int)y.size() - 1, k + 1)), a;
}
inline void operator*=(vector<int> &x, const vector<int> &y) { x = x * y; }
inline vector<int> operator+(const vector<int> &x, const vector<int> &y) {
  vector<int> ans = x;
  if (y.size() > x.size()) ans.resize(y.size());
  for (unsigned i = 0; i < y.size(); ++i) (ans[i] += y[i]) %= P;
  return ans;
}
inline void operator+=(vector<int> &x, const vector<int> &y) { x = x + y; }
inline vector<int> operator-(const vector<int> &x, const vector<int> &y) {
  vector<int> ans = x;
  if (y.size() > x.size()) ans.resize(y.size());
  for (unsigned i = 0; i < y.size(); ++i) (ans[i] += P - y[i]) %= P;
  return ans;
}
inline vector<int> PolyDiv2(const vector<int> &x) {
  vector<int> ans(x.size());
  for (unsigned i = 0; i < x.size(); ++i)
    ans[i] = (x[i] & 1 ? x[i] + P : x[i]) >> 1;
  return ans;
}
inline vector<int> Ext(const vector<int> &a, int n) {
  if (n <= (int)a.size()) return vector<int>(a.begin(), a.begin() + n);
  vector<int> ans = a;
  return ans.resize(n), ans;
}
vector<int> PolyInv(const vector<int> &a, int n = -1) {
  if (n == -1) n = a.size();
  if (n == 1) return {Pow(a[0])};
  vector<int> ans = PolyInv(a, (n + 1) / 2), tmp = Ext(a, n);
  int m = Calc(n * 2 - 1);
  ans.resize(m), tmp.resize(m), DFT(ans, m), DFT(tmp, m);
  for (int i = 0; i < m; ++i)
    ans[i] = (2 + (long long)(P - tmp[i]) * ans[i]) % P * ans[i] % P;
  IDFT(ans, m);
  return ans.resize(n), ans;
}
vector<int> PolySqrt(const vector<int> &a, int n = -1) {
  if (n == -1) n = a.size();
  if (n == 1) return {1};
  vector<int> ans = PolySqrt(a, (n + 1) / 2);
  return PolyDiv2(ans + Ext(a, n) * PolyInv(Ext(ans, n)));
}
inline vector<int> D(const vector<int> &a) {
  vector<int> ans(a.size() - 1);
  for (unsigned i = 1; i < a.size(); ++i) ans[i - 1] = (long long)a[i] * i % P;
  return ans;
}
inline vector<int> Int(const vector<int> &a) {
  vector<int> ans(a.size() + 1);
  for (unsigned i = 0; i < a.size(); ++i)
    ans[i + 1] = (long long)a[i] * inv[i + 1] % P;
  return ans;
}
inline vector<int> PolyLn(const vector<int> &a) {
  return Int(Ext(D(a) * PolyInv(a), a.size() - 1));
}
vector<int> PolyExp(const vector<int> &a, int n = -1) {
  if (n == -1) n = a.size();
  if (n == 1) return {1};
  vector<int> ans = PolyExp(a, (n + 1) / 2);
  return Ext(ans * (Ext(a, n) - PolyLn(Ext(ans, n)) + vector<int>{1}), n);
}
int main() {
  for (int i = 1; i < M; i <<= 1) {
    w[i] = 1, w[i + 1] = Pow(3, (P - 1) / i / 2);
    for (int j = 2; j < i; ++j)
      w[i + j] = (long long)w[i + j - 1] * w[i + 1] % P;
  }
  inv[1] = 1;
  for (int i = 2; i < M; ++i) inv[i] = (long long)(P - P / i) * inv[P % i] % P;
  scanf("%d%d", &n, &k);
  vector<int> s = {1, 6, 1}, c;
  s.resize(k + 1), s = PolySqrt(s);
  c = PolyLn(PolyDiv2(vector<int>{1, 1} + s));
  for (int &i : c) i = (long long)i * (n + 1) % P;
  c = PolyExp(c) * PolyInv(s);
  for (int i = 1; i <= k; ++i) printf("%d ", i > n ? 0 : c[i]);
  return 0;
}