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 long long int K = 998244353;
long long int mu(long long int a, long long int n) {
  if (n == 0) return 1;
  long long int q = mu(a, n / 2);
  if (n % 2 == 0) return q * q % K;
  return q * q % K * a % K;
}
long long int inv[100005];
namespace Poly {
inline void fft(vector<complex<double> > &a, bool inv) {
  int n = a.size(), j = 0;
  vector<complex<double> > roots(n / 2);
  for (int i = 1; i < n; i++) {
    int bit = (n >> 1);
    while (j >= bit) {
      j -= bit;
      bit >>= 1;
    }
    j += bit;
    if (i < j) swap(a[i], a[j]);
  }
  double ang = 2 * acos(-1) / n * (inv ? -1 : 1);
  for (int i = 0; i < n / 2; i++) {
    roots[i] = complex<double>(cos(ang * i), sin(ang * i));
  }
  for (int i = 2; i <= n; i <<= 1) {
    int step = n / i;
    for (int j = 0; j < n; j += i) {
      for (int k = 0; k < i / 2; k++) {
        complex<double> u = a[j + k], v = a[j + k + i / 2] * roots[step * k];
        a[j + k] = u + v;
        a[j + k + i / 2] = u - v;
      }
    }
  }
  if (inv)
    for (int i = 0; i < n; i++) a[i] /= n;
}
inline vector<long long int> multiply(vector<long long int> &v,
                                      vector<long long int> &w) {
  vector<complex<double> > fv(v.begin(), v.end()), fw(w.begin(), w.end());
  int n = 2;
  while (n < v.size() + w.size()) n <<= 1;
  fv.resize(n);
  fw.resize(n);
  fft(fv, 0);
  fft(fw, 0);
  for (int i = 0; i < n; i++) fv[i] *= fw[i];
  fft(fv, 1);
  n = v.size() + w.size() - 1;
  vector<long long int> ret(n);
  for (int i = 0; i < n; i++) ret[i] = (long long int)round(fv[i].real());
  return ret;
}
inline vector<long long int> multiply(vector<long long int> &v,
                                      vector<long long int> &w,
                                      long long int mod) {
  int n = 2;
  while (n < v.size() + w.size()) n <<= 1;
  vector<complex<double> > v1(n), v2(n), r1(n), r2(n);
  for (int i = 0; i < v.size(); i++) {
    v1[i] = complex<double>(v[i] >> 15, v[i] & 32767);
  }
  for (int i = 0; i < w.size(); i++) {
    v2[i] = complex<double>(w[i] >> 15, w[i] & 32767);
  }
  fft(v1, 0);
  fft(v2, 0);
  for (int i = 0; i < n; i++) {
    int j = (i ? (n - i) : i);
    complex<double> ans1 = (v1[i] + conj(v1[j])) * complex<double>(0.5, 0);
    complex<double> ans2 = (v1[i] - conj(v1[j])) * complex<double>(0, -0.5);
    complex<double> ans3 = (v2[i] + conj(v2[j])) * complex<double>(0.5, 0);
    complex<double> ans4 = (v2[i] - conj(v2[j])) * complex<double>(0, -0.5);
    r1[i] = (ans1 * ans3) + (ans1 * ans4) * complex<double>(0, 1);
    r2[i] = (ans2 * ans3) + (ans2 * ans4) * complex<double>(0, 1);
  }
  fft(r1, 1);
  fft(r2, 1);
  n = v.size() + w.size() - 1;
  vector<long long int> ret(n);
  for (int i = 0; i < n; i++) {
    long long int av = (long long int)round(r1[i].real());
    long long int bv =
        (long long int)round(r1[i].imag()) + (long long int)round(r2[i].real());
    long long int cv = (long long int)round(r2[i].imag());
    av %= mod, bv %= mod, cv %= mod;
    ret[i] = (av << 30) + (bv << 15) + cv;
    ret[i] %= mod;
    ret[i] += mod;
    ret[i] %= mod;
  }
  return ret;
}
inline vector<long long int> multiply_modx(vector<long long int> &v,
                                           vector<long long int> &w,
                                           long long int mod, int k) {
  int n = 2;
  while (n < v.size() + w.size()) n <<= 1;
  vector<complex<double> > v1(n), v2(n), r1(n), r2(n);
  for (int i = 0; i < v.size(); i++) {
    v1[i] = complex<double>(v[i] >> 15, v[i] & 32767);
  }
  for (int i = 0; i < w.size(); i++) {
    v2[i] = complex<double>(w[i] >> 15, w[i] & 32767);
  }
  fft(v1, 0);
  fft(v2, 0);
  for (int i = 0; i < n; i++) {
    int j = (i ? (n - i) : i);
    complex<double> ans1 = (v1[i] + conj(v1[j])) * complex<double>(0.5, 0);
    complex<double> ans2 = (v1[i] - conj(v1[j])) * complex<double>(0, -0.5);
    complex<double> ans3 = (v2[i] + conj(v2[j])) * complex<double>(0.5, 0);
    complex<double> ans4 = (v2[i] - conj(v2[j])) * complex<double>(0, -0.5);
    r1[i] = (ans1 * ans3) + (ans1 * ans4) * complex<double>(0, 1);
    r2[i] = (ans2 * ans3) + (ans2 * ans4) * complex<double>(0, 1);
  }
  fft(r1, 1);
  fft(r2, 1);
  if (n > k + 1) n = k + 1;
  vector<long long int> ret(n);
  for (int i = 0; i < n; i++) {
    long long int av = (long long int)round(r1[i].real());
    long long int bv =
        (long long int)round(r1[i].imag()) + (long long int)round(r2[i].real());
    long long int cv = (long long int)round(r2[i].imag());
    av %= mod, bv %= mod, cv %= mod;
    ret[i] = (av << 30) + (bv << 15) + cv;
    ret[i] %= mod;
    ret[i] += mod;
    ret[i] %= mod;
  }
  return ret;
}
inline vector<long long int> inverse(vector<long long int> &v, int m) {
  int n = 1;
  vector<long long int> R, V, G;
  R.push_back(mu(v[0], K - 2));
  V.push_back(v[0]);
  while (n <= m) {
    n <<= 1;
    for (int i = n / 2; i < v.size() && i < n; i++) V.push_back(v[i]);
    G = multiply(R, R, K);
    G = multiply_modx(G, V, K, n - 1);
    for (int i = n / 2; i <= n - 1; i++) {
      R.push_back((-G[i] + K) % K);
    }
  }
  R.resize(m + 1);
  return R;
}
inline vector<long long int> sqrt(vector<long long int> &v, int m) {
  assert(v[0] == 1 || v[0] == 0);
  long long int rev2 = mu(2, K - 2);
  int n = 1;
  vector<long long int> V, R, G, P;
  R.push_back(v[0]);
  V.push_back(v[0]);
  n = 1;
  while (n <= m) {
    n <<= 1;
    for (int i = n / 2; i < v.size() && i < n; i++) V.push_back(v[i]);
    G = inverse(R, n - 1);
    G = multiply_modx(G, V, K, n - 1);
    for (int i = n / 2; i < n; i++) {
      R.push_back(G[i] * rev2 % K);
    }
  }
  R.resize(m + 1);
  return R;
}
inline vector<long long int> derivative(vector<long long int> &a, int m) {
  vector<long long int> b;
  for (long long int i = 0; i + 1 < a.size(); i++) {
    b.push_back(a[i + 1] * (i + 1) % K);
  }
  return b;
}
inline vector<long long int> integrate(vector<long long int> &a, int m) {
  vector<long long int> b;
  b.push_back(0);
  for (long long int i = 1; i - 1 < a.size() && i <= m; i++) {
    b.push_back(a[i - 1] * inv[i] % K);
  }
  return b;
}
vector<long long int> ln(vector<long long int> &a, int m) {
  vector<long long int> b = inverse(a, m);
  vector<long long int> c = derivative(a, m);
  b = multiply_modx(b, c, K, m);
  b = integrate(b, m);
  return b;
}
vector<long long int> exp(vector<long long int> &v, int m) {
  assert(v.size() > 1);
  int n = 1;
  vector<long long int> R, G;
  R.push_back(1);
  while (n <= m) {
    n <<= 1;
    G = ln(R, n - 1);
    for (int i = 0; i < n && i <= m; i++) G[i] = (v[i] - G[i] + K) % K;
    G[0]++;
    R = multiply_modx(R, G, K, n - 1);
  }
  R.resize(m + 1);
  return R;
}
vector<long long int> pw(vector<long long int> &a, int n, int m) {
  vector<long long int> res;
  if (n == 0) {
    res.push_back(1);
    return res;
  }
  long long int M = mu(a[0], n);
  res = ln(a, m);
  for (int i = 0; i <= m; i++) res[i] = res[i] * n % K;
  res = exp(res, m);
  for (int i = 0; i <= m; i++) res[i] = res[i] * M % K;
  return res;
}
};  // namespace Poly
vector<long long int> A1, A2, X1, X2, S, R;
using namespace Poly;
int n, k;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  inv[1] = 1;
  for (int i = 2; i <= 100000; i++) inv[i] = (K - K / i) * 1ll * inv[K % i] % K;
  int k1;
  cin >> n >> k1;
  k = min(n, k1);
  S.push_back(1);
  S.push_back(6);
  S.push_back(1);
  S = sqrt(S, k);
  long long int rev2 = mu(2, K - 2);
  X1.resize(k + 1);
  X2.resize(k + 1);
  A1.resize(k + 1);
  A2.resize(k + 1);
  R = inverse(S, k);
  X1[0] = 1;
  X1[1] = 1;
  X2[0] = 1;
  X2[1] = 1;
  for (int i = 0; i <= k; i++) X1[i] = (X1[i] + S[i]) * rev2 % K;
  for (int i = 0; i <= k; i++) X2[i] = (X2[i] - S[i] + K) * rev2 % K;
  A1 = multiply_modx(X1, R, K, k);
  A2 = multiply_modx(X2, R, K, k);
  X1 = pw(X1, n, k);
  X1 = multiply_modx(A1, X1, K, k);
  X2 = pw(X2, n, k);
  X2 = multiply_modx(A2, X2, K, k);
  for (int i = 1; i <= k; i++) {
    cout << (X1[i] - X2[i] + K) % K << " ";
  }
  for (int i = k + 1; i <= k1; i++) cout << 0 << " ";
  return 0;
}