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>
#pragma GCC optimize("Ofast,unroll-loops")
using namespace std;
constexpr int inf = 0x3f3f3f3f;
constexpr long long lnf = 0x3f3f3f3f3f3f3f3f;
namespace polynomial {
constexpr int mod = 998244353;
inline int add(int x, int y) { return (x += y) >= mod ? x - mod : x; }
inline void inc(int &x, int y) { (x += y) >= mod && (x -= mod); }
inline int sub(int x, int y) { return add(x, mod - y); }
inline void dec(int &x, int y) { inc(x, mod - y); }
inline int mul(int x, int y) { return 1LL * x * y % mod; }
inline int modpower(int x, int y) {
  int res = 1;
  for (; y; y >>= 1, x = mul(x, x))
    if (y & 1) res = mul(res, x);
  return res;
}
inline int inv(int a) {
  if ((a %= mod) < 0) a += mod;
  int b = mod, u = 0, v = 1;
  while (a) {
    int t = b / a;
    b -= t * a;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  if (u < 0) u += mod;
  return u;
}
using poly = vector<int>;
namespace ntt {
int G = -1, base = 1, max_base = -1;
poly rev = {0, 1}, roots = {0, 1};
void initialize() {
  int tmp = mod - 1;
  max_base = 0;
  while (tmp % 2 == 0) {
    tmp >>= 1;
    ++max_base;
  }
  G = 2;
  for (;; ++G)
    if (modpower(G, 1 << max_base) == 1 &&
        modpower(G, 1 << (max_base - 1)) != 1)
      break;
}
void make_base(int nbase) {
  if (max_base == -1) initialize();
  if (nbase <= base) return;
  assert(nbase <= max_base);
  rev.resize(1 << nbase);
  roots.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); ++i)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (nbase - 1));
  for (; base < nbase; ++base) {
    int z = modpower(G, 1 << (max_base - 1 - base));
    for (int i = 1 << (base - 1); i < (1 << base); ++i) {
      roots[i << 1] = roots[i];
      roots[i << 1 | 1] = mul(roots[i], z);
    }
  }
}
void ntt_transform(poly &a) {
  int n = (int)a.size();
  int zero = __builtin_ctz(n);
  make_base(zero);
  int shift = base - zero;
  for (int i = 0; i < n; ++i)
    if (i < (rev[i] >> shift)) swap(a[i], a[rev[i] >> shift]);
  for (int i = 1; i < n; i <<= 1)
    for (int j = 0; j < n; j += (i << 1))
      for (int k = 0; k < i; ++k) {
        int x = a[j + k], y = mul(a[j + k + i], roots[i + k]);
        a[j + k] = add(x, y);
        a[j + k + i] = sub(x, y);
      }
}
poly multiply(poly a, poly b) {
  int all = (int)a.size() + (int)b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < all) ++nbase;
  make_base(nbase);
  int sz = 1 << nbase;
  a.resize(sz), b.resize(sz);
  bool eql = (a == b);
  ntt_transform(a);
  if (eql)
    b = a;
  else
    ntt_transform(b);
  int invsz = inv(sz);
  for (int i = 0; i < sz; ++i) a[i] = mul(mul(a[i], b[i]), invsz);
  reverse(a.begin() + 1, a.end());
  ntt_transform(a);
  a.resize(all);
  return a;
}
poly poly_inv(poly a) {
  int n = (int)a.size();
  int m = (n + 1) >> 1;
  if (n == 1) return poly(1, inv(a[0]));
  poly b = poly_inv(poly(a.begin(), a.begin() + m));
  int all = n << 1, nbase = 0;
  while ((1 << nbase) < all) ++nbase;
  make_base(nbase);
  int sz = 1 << nbase;
  a.resize(sz), b.resize(sz);
  ntt_transform(a);
  ntt_transform(b);
  int invsz = inv(sz);
  for (int i = 0; i < sz; ++i)
    a[i] = mul(mul(sub(2, mul(a[i], b[i])), b[i]), invsz);
  reverse(a.begin() + 1, a.end());
  ntt_transform(a);
  a.resize(n);
  return a;
}
poly power(poly a, int k) {
  int nbase = 0, org = (int)a.size();
  while ((1 << nbase) < org) ++nbase;
  ntt::make_base(nbase);
  int sz = 1 << nbase;
  a.resize(sz);
  ntt::ntt_transform(a);
  int invsz = inv(sz);
  for (int i = 0; i < sz; ++i) a[i] = mul(modpower(a[i], k), invsz);
  reverse(a.begin() + 1, a.end());
  ntt::ntt_transform(a);
  a.resize(org);
  return a;
}
}  // namespace ntt
using ntt::multiply;
using ntt::poly_inv;
using ntt::power;
poly &operator+=(poly &a, const poly &b) {
  if (a.size() < b.size()) a.resize((int)b.size());
  for (int i = 0; i < (int)b.size(); ++i) inc(a[i], b[i]);
  return a;
}
poly &operator-=(poly &a, const poly &b) {
  if (a.size() < b.size()) a.resize((int)b.size());
  for (int i = 0; i < (int)b.size(); ++i) dec(a[i], b[i]);
  return a;
}
poly &operator*=(poly &a, const int &b) {
  for (int &i : a) i = mul(i, b);
  return a;
}
poly &operator*=(poly &a, const poly &b) {
  if (min<int>(a.size(), b.size()) < 128) {
    poly c = a;
    a.assign((int)c.size() + (int)b.size() - 1, 0);
    for (int i = 0; i < (int)c.size(); ++i)
      for (int j = 0; j < (int)b.size(); ++j) inc(a[i + j], mul(c[i], b[j]));
  } else
    a = multiply(a, b);
  return a;
}
poly &operator/=(poly &a, const poly &b) {
  int n = (int)a.size(), m = (int)b.size();
  if (n < m)
    a.clear();
  else {
    poly c = b;
    reverse(a.begin(), a.end());
    reverse(c.begin(), c.end());
    c.resize(n - m + 1);
    a *= poly_inv(c);
    a.erase(a.begin() + n - m + 1, a.end());
    reverse(a.begin(), a.end());
  }
  return a;
}
poly &operator%=(poly &a, const poly &b) {
  int n = a.size(), m = b.size();
  if (n >= m) {
    poly c = a;
    (c /= b) *= b;
    a.resize(m - 1);
    for (int i = 0; i < m - 1; ++i) dec(a[i], c[i]);
  }
  return a;
}
poly operator+(poly a, const poly &b) { return a += b; }
poly operator-(poly a, const poly &b) { return a -= b; }
poly operator*(poly a, const poly &b) { return a *= b; }
poly operator/(poly a, const poly &b) { return a /= b; }
poly operator%(poly a, const poly &b) { return a %= b; }
poly operator-(poly a) {
  for (int &i : a) i = mod - i;
  return a;
}
poly operator*(poly a, const int &b) { return a *= b; }
poly derivative(const poly &a) {
  int n = (int)a.size();
  poly b(n - 1);
  for (int i = 1; i < n; ++i) b[i - 1] = mul(a[i], i);
  return b;
}
poly integral(const poly &a) {
  int n = (int)a.size();
  poly b(n + 1), invs(n + 1);
  for (int i = 1; i <= n; ++i) {
    invs[i] = (i == 1) ? 1 : mul(mod - mod / i, invs[mod % i]);
    b[i] = mul(a[i - 1], invs[i]);
  }
  return b;
}
poly poly_log(const poly &a) {
  poly b = integral(derivative(a) * poly_inv(a));
  b.resize((int)a.size());
  return b;
}
poly poly_exp(const poly &a) {
  poly b(1, 1);
  while (b.size() < a.size()) {
    poly c(a.begin(), a.begin() + min<int>(a.size(), b.size() << 1));
    inc(c[0], 1);
    poly d = b;
    b.resize((int)b.size() << 1);
    c -= poly_log(b);
    c *= d;
    for (int i = (int)b.size() >> 1; i < (int)b.size(); ++i) b[i] = c[i];
  }
  b.resize((int)a.size());
  return b;
}
poly poly_pow(const poly &a, int k) {
  int n = (int)a.size(), p = -1;
  poly b(n);
  for (int i = 0; i < n; ++i)
    if (a[i]) {
      p = i;
      break;
    }
  if (p == -1) {
    b[0] = !k;
    return b;
  }
  if (1LL * k * p >= n) return b;
  int ku = modpower(a[p], k), di = inv(a[p]);
  int sz = n - k * p;
  poly c(sz);
  for (int i = 0; i < sz; ++i) c[i] = mul(a[i + p], di);
  c = poly_log(c);
  for (int i = 0; i < sz; ++i) c[i] = mul(c[i], k);
  c = poly_exp(c);
  for (int i = 0; i < sz; ++i) b[i + k * p] = mul(c[i], ku);
  return b;
}
poly poly_sqrt(const poly &a) {
  poly b(1, 1);
  while (b.size() < a.size()) {
    poly c(a.begin(), a.begin() + min<int>(a.size(), b.size() << 1));
    poly d = b;
    b.resize((int)b.size() << 1);
    c *= poly_inv(b);
    for (int i = (int)b.size() >> 1; i < b.size(); ++i)
      b[i] = mul(c[i], mod + 1 >> 1);
  }
  b.resize(a.size());
  return b;
}
}  // namespace polynomial
using namespace polynomial;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
  cout << fixed << setprecision(12);
  int n, k;
  cin >> n >> k;
  poly K{1, 6, 1};
  K.resize(k + 1);
  K = poly_sqrt(K);
  poly z1{1, 1}, z2{1, 1};
  (z1 += K) *= (mod + 1 >> 1);
  (z2 -= K) *= (mod + 1 >> 1);
  z1 = poly_pow(z1, n + 1);
  z2 = poly_pow(z2, n + 1);
  poly ans = z1 - z2;
  ans *= poly_inv(K);
  for (int i = 1; i <= k; ++i) cout << ans[i] << " \n"[i == k];
  return 0;
}