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>
typedef long long signed int* poly;
const long long signed int mod = 998244353, G = 3, Gi = (mod + 1) / 3;
long long signed int qpow(long long signed int a, long long signed int b) {
  long long signed int ret = 1;
  while (b) {
    if (b & 1) ret = ret * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return ret;
}
const int MAXN = 1000010;
int kaosu[MAXN], chaos[MAXN];
void kaosuSetup(int n) {
  int i;
  for (i = 0; (1 << i) < n; ++i) kaosu[1 << i] = 1 << i, chaos[1 << i] = i;
  kaosu[1 << i] = 1 << i, chaos[1 << i] = i;
  i = 1 << i;
  for (--i; ~i; --i)
    if (!kaosu[i]) kaosu[i] = kaosu[i + 1], chaos[i] = chaos[i + 1];
  return;
}
int rev[MAXN], rev_l;
void revCall(int n) {
  n = kaosu[n];
  rev[0] = 0;
  int l = chaos[n] - 1;
  for (int i = 1; i < n; ++i) rev[i] = (rev[i >> 1] >> 1) | ((1 & i) << l);
  rev_l = n;
  return;
}
void NTT(poly a, const int on) {
  for (int i = 0; i < rev_l; ++i)
    if (i < rev[i]) std::swap(a[i], a[rev[i]]);
  for (int s = 1; s < rev_l; s <<= 1) {
    long long signed int W = qpow(on > 0 ? G : Gi, (mod - 1) / (s << 1));
    for (int ue = 0; ue < rev_l; ue += (s << 1)) {
      long long signed int w = 1;
      for (int ksm = ue; ksm < ue + s; ++ksm, w = w * W % mod) {
        long long signed int x = a[ksm], y = w * a[ksm + s] % mod;
        a[ksm] = (x + y) % mod;
        a[ksm + s] = (mod + x - y) % mod;
      }
    }
  }
  if (on < 0) {
    long long signed int inv = qpow(rev_l, mod - 2);
    for (int i = 0; i < rev_l; ++i) a[i] = a[i] * inv % mod;
  }
  return;
}
int n, k;
long long signed int g[5][MAXN], f[3][MAXN];
void shift() {
  memcpy(g[0], f[0], sizeof(long long signed int) * k);
  memset(g[0] + k, 0, sizeof(long long signed int) * (rev_l - k));
  memcpy(g[1], f[1], sizeof(long long signed int) * k);
  memset(g[1] + k, 0, sizeof(long long signed int) * (rev_l - k));
  memcpy(g[2] + 1, f[1], sizeof(long long signed int) * (k - 1));
  g[2][0] = 0;
  memset(g[2] + k, 0, sizeof(long long signed int) * (rev_l - k));
  memcpy(g[3], f[2], sizeof(long long signed int) * k);
  memset(g[3] + k, 0, sizeof(long long signed int) * (rev_l - k));
  memcpy(g[4] + 1, f[2], sizeof(long long signed int) * (k - 1));
  g[4][0] = 0;
  memset(g[4] + k, 0, sizeof(long long signed int) * (rev_l - k));
  NTT(g[0], 1), NTT(g[1], 1), NTT(g[2], 1), NTT(g[3], 1), NTT(g[4], 1);
  for (int i = 0; i < rev_l; ++i)
    f[0][i] = (g[0][i] * g[0][i] % mod + g[1][i] * g[2][i] % mod) % mod,
    f[1][i] = (g[0][i] * g[1][i] % mod + g[2][i] * g[3][i] % mod) % mod,
    f[2][i] = (g[1][i] * g[1][i] % mod + g[3][i] * g[4][i] % mod) % mod;
  NTT(f[0], -1), NTT(f[1], -1), NTT(f[2], -1);
  return;
}
void setBit() {
  memcpy(f[2], f[1], sizeof(long long signed int) * k);
  memset(f[2] + k, 0, sizeof(long long signed int) * (rev_l - k));
  memcpy(f[1], f[0], sizeof(long long signed int) * k);
  memset(f[1] + k, 0, sizeof(long long signed int) * (rev_l - k));
  f[0][0] = 1;
  for (int i = 1; i < k; ++i)
    f[0][i] = (f[1][i] + f[1][i - 1] + f[2][i - 1]) % mod;
  return;
}
int main() {
  scanf("%d%d", &n, &k);
  ++k;
  static int sta[100], top = 0;
  while (n) sta[++top] = n & 1, n >>= 1;
  kaosuSetup(k * 2);
  revCall(k * 2);
  f[0][0] = 1;
  while (top) {
    shift();
    if (sta[top]) setBit();
    top--;
  }
  for (int i = 1; i < k; ++i) printf("%lld ", f[0][i]);
  return 0;
}