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 = 1e6 + 10;
long long qpow(long long a, long long b, long long mod) {
  long long res = 1;
  while (b) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return res;
}
const long long mod = 998244353;
const long long G = 3;
const long long invG = qpow(G, mod - 2, mod);
const long long inv2 = qpow(2ll, mod - 2, mod);
int tr[N];
int getLen(int n) {
  int len = 1;
  while (len < (n << 1)) len <<= 1;
  for (int i = 0; i < len; i++)
    tr[i] = (tr[i >> 1] >> 1) | (i & 1 ? len >> 1 : 0);
  return len;
}
void NTT(long long *A, int len, int type) {
  for (int i = 0; i < len; i++)
    if (i < tr[i]) swap(A[i], A[tr[i]]);
  for (int i = 2; i <= len; i <<= 1) {
    int mid = i / 2;
    long long Wn = qpow(type == 1 ? G : invG, (mod - 1) / i, mod);
    for (int k = 0; k < len; k += i) {
      long long w = 1;
      for (int l = k; l < k + mid; l++) {
        long long t = w * A[l + mid] % mod;
        A[l + mid] = (A[l] - t + mod) % mod;
        A[l] = (A[l] + t) % mod;
        w = w * Wn % mod;
      }
    }
  }
  if (type == -1) {
    long long invn = qpow(len, mod - 2, mod);
    for (int i = 0; i < len; i++) A[i] = A[i] * invn % mod;
  }
}
void getDer(long long *f, long long *g, int len) {
  for (int i = 1; i < len; i++) g[i - 1] = f[i] * i % mod;
  g[len - 1] = 0;
}
void getInt(long long *f, long long *g, int len) {
  for (int i = 1; i < len; i++) g[i] = f[i - 1] * qpow(i, mod - 2, mod) % mod;
  g[0] = 0;
}
void getInv(long long *f, long long *g, int n) {
  if (n == 1) return (void)(g[0] = qpow(f[0], mod - 2, mod));
  getInv(f, g, (n + 1) >> 1);
  int len = getLen(n);
  static long long a[N];
  for (int i = 0; i < len; ++i) a[i] = i < n ? f[i] : 0;
  NTT(a, len, 1), NTT(g, len, 1);
  for (int i = 0; i < len; i++)
    g[i] = 1LL * (2 - 1LL * a[i] * g[i] % mod + mod) % mod * g[i] % mod;
  NTT(g, len, -1);
  for (int i = n; i < len; i++) g[i] = 0;
}
void getLn(long long *f, long long *g, int n) {
  static long long a[N], b[N];
  getDer(f, a, n);
  getInv(f, b, n);
  int len = getLen(n);
  NTT(a, len, 1), NTT(b, len, 1);
  for (int i = 0; i < len; i++) a[i] = a[i] * b[i] % mod;
  NTT(a, len, -1);
  getInt(a, g, len);
  for (int i = n; i < len; i++) g[i] = 0;
  for (int i = 0; i < len; i++) a[i] = b[i] = 0;
}
void getExp(long long *f, long long *g, int n) {
  if (n == 1) return (void)(g[0] = 1);
  getExp(f, g, (n + 1) >> 1);
  static long long a[N];
  getLn(g, a, n);
  a[0] = (f[0] + 1 - a[0] + mod) % mod;
  for (int i = 1; i < n; i++) a[i] = (f[i] - a[i] + mod) % mod;
  int len = getLen(n);
  NTT(a, len, 1), NTT(g, len, 1);
  for (int i = 0; i < len; i++) g[i] = g[i] * a[i] % mod;
  NTT(g, len, -1);
  for (int i = n; i < len; i++) g[i] = 0;
  for (int i = 0; i < len; i++) a[i] = 0;
}
void getPow(long long *f, long long *g, int n, long long k) {
  static long long a[N];
  getLn(f, a, n);
  for (int i = 0; i < n; i++) a[i] = a[i] * k % mod;
  getExp(a, g, n);
  for (int i = 0, len = getLen(n); i < len; i++) a[i] = 0;
}
struct Complex {
  long long x, y;
};
long long w;
Complex mul(Complex a, Complex b, long long mod) {
  Complex ans = {0, 0};
  ans.x = ((a.x * b.x % mod + a.y * b.y % mod * w % mod) % mod + mod) % mod;
  ans.y = ((a.x * b.y % mod + a.y * b.x % mod) % mod + mod) % mod;
  return ans;
}
long long binpow_imag(Complex a, long long b, long long mod) {
  Complex ans = {1, 0};
  while (b) {
    if (b & 1) ans = mul(ans, a, mod);
    a = mul(a, a, mod);
    b >>= 1;
  }
  return ans.x % mod;
}
long long cipolla(long long n, long long mod) {
  srand(time(0));
  n %= mod;
  if (mod == 2) return n;
  if (qpow(n, (mod - 1) / 2, mod) == mod - 1) return -1;
  long long a;
  while (1) {
    a = rand() % mod;
    w = ((a * a % mod - n) % mod + mod) % mod;
    if (qpow(w, (mod - 1) / 2, mod) == mod - 1) break;
  }
  Complex x = {a, 1};
  return binpow_imag(x, (mod + 1) / 2, mod);
}
void getSqrt(long long *f, long long *g, int n) {
  if (n == 1) {
    if (f[0] == 0)
      g[0] = f[0];
    else {
      long long t = cipolla(f[0], mod);
      g[0] = min(t, mod - t);
    }
    return;
  }
  getSqrt(f, g, (n + 1) >> 1);
  int len = getLen(n);
  static long long a[N], b[N];
  for (int i = 0; i < len; ++i) a[i] = i < n ? f[i] : 0;
  getInv(g, b, n);
  NTT(a, len, 1), NTT(b, len, 1);
  for (int i = 0; i < len; i++) a[i] = 1ll * a[i] * b[i] % mod;
  NTT(a, len, -1);
  for (int i = 0; i < n; i++) g[i] = (g[i] + a[i]) % mod * inv2 % mod;
  for (int i = n; i < len; i++) g[i] = 0;
  for (int i = 0; i < len; i++) a[i] = b[i] = 0;
}
long long a[N], b[N], f[N], g[N];
int main() {
  int k, n;
  scanf("%d%d", &k, &n);
  int m = n + 1;
  n = min(n, k) + 1;
  a[0] = 1, a[1] = 6, a[2] = 1;
  getSqrt(a, b, n);
  for (int i = 0; i < n; i++) a[i] = b[i];
  a[0] = (a[0] + 1) % mod, a[1] = (a[1] + 1) % mod;
  for (int i = 0; i < n; i++) a[i] = a[i] * inv2 % mod;
  getPow(a, f, n, k + 1);
  getInv(b, g, n);
  int len = getLen(n);
  NTT(f, len, 1), NTT(g, len, 1);
  for (int i = 0; i < len; i++) f[i] = f[i] * g[i] % mod;
  NTT(f, len, -1);
  for (int i = 1; i < n; i++) printf("%lld ", f[i]);
  for (int i = n; i < m; i++) printf("0 ");
  return 0;
}