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 MOD = 998244353, G = 3, INV2 = (MOD + 1) >> 1, MAXN = 500005;
long long q_pow(long long a, long long b, long long p = MOD) {
  long long ret = 1;
  for (; b; a = a * a % p, b >>= 1)
    if (b & 1) ret = ret * a % p;
  return ret;
}
long long inv(long long x, long long p = MOD) { return q_pow(x, p - 2, p); }
int rev[MAXN];
void NTT(int* A, int LIM, int op) {
  for (int i = 0; i < LIM; ++i)
    if (i < rev[i]) swap(A[i], A[rev[i]]);
  for (int l = 2; l <= LIM; l <<= 1) {
    int g = q_pow(G, (MOD - 1) / l);
    if (op == -1) g = inv(g);
    for (int i = 0; i < LIM; i += l) {
      int w = 1;
      for (int j = i; j < i + (l >> 1); ++j, w = 1ll * w * g % MOD) {
        int x = A[j], y = 1ll * w * A[j + (l >> 1)] % MOD;
        A[j] = (x + y) % MOD, A[j + (l >> 1)] = (x - y) % MOD;
      }
    }
  }
}
void Multiply(int* A, int* B, int LIM, int L) {
  for (int i = 0; i < LIM; ++i)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (L - 1));
  NTT(A, LIM, 1), NTT(B, LIM, 1);
  for (int i = 0; i < LIM; ++i) A[i] = 1ll * A[i] * B[i] % MOD;
  NTT(A, LIM, -1);
  int invLIM = inv(LIM);
  for (int i = 0; i < LIM; ++i) A[i] = 1ll * A[i] * invLIM % MOD;
}
int T[MAXN];
void Inverse(const int* F, int* G, int LIM, int L) {
  if (LIM == 1) {
    G[0] = inv(F[0]);
    return;
  }
  Inverse(F, G, LIM >> 1, L - 1);
  for (int i = 0; i < (LIM << 1); ++i)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << L);
  for (int i = 0; i < LIM; ++i) T[i] = F[i];
  for (int i = LIM; i < (LIM << 1); ++i) T[i] = 0;
  NTT(T, LIM << 1, 1), NTT(G, LIM << 1, 1);
  for (int i = 0; i < (LIM << 1); ++i)
    G[i] = (2 * G[i] - 1ll * T[i] * G[i] % MOD * G[i]) % MOD;
  NTT(G, LIM << 1, -1);
  int invLIM = inv(LIM << 1);
  for (int i = 0; i < LIM; ++i) G[i] = 1ll * G[i] * invLIM % MOD;
  for (int i = LIM; i < (LIM << 1); ++i) G[i] = 0;
}
void Derivative(int* A, int LIM) {
  for (int i = 0; i < LIM; ++i) A[i] = 1ll * A[i + 1] * (i + 1) % MOD;
}
void Inter(int* A, int LIM) {
  for (int i = LIM; i >= 1; --i) A[i] = 1ll * A[i - 1] * inv(i) % MOD;
  A[0] = 0;
}
int Ai[MAXN];
void Ln(int* A, int LIM, int L) {
  Inverse(A, Ai, LIM, L), Derivative(A, LIM), Multiply(A, Ai, LIM << 1, L + 1),
      Inter(A, LIM);
  for (int i = LIM; i < (LIM << 1); ++i) A[i] = 0;
  for (int i = 0; i < (LIM << 1); ++i) Ai[i] = 0;
}
int Texp[MAXN];
void Exp(const int* F, int* G, int LIM, int L) {
  if (LIM == 1) {
    G[0] = 1;
    return;
  }
  Exp(F, G, LIM >> 1, L - 1);
  for (int i = 0; i < LIM; ++i) Texp[i] = G[i];
  Ln(G, LIM, L);
  for (int i = 0; i < LIM; ++i) G[i] = (-G[i] + F[i]) % MOD;
  ++G[0];
  Multiply(G, Texp, LIM << 1, L + 1);
  for (int i = LIM; i < (LIM << 1); ++i) G[i] = 0;
}
int I[MAXN];
void Pow(int* F, int LIM, long long K) {
  if (K == INV2)
    F[0] = 1, F[1] = 3;
  else
    F[0] = 1, F[1] = -3;
  I[1] = 1;
  for (int i = 2; i < LIM; ++i) {
    F[i] = (K * (6ll * F[i - 1] + 2 * F[i - 2]) -
            (6ll * (i - 1) * F[i - 1] + (long long)(i - 2) * F[i - 2])) %
           MOD;
    I[i] = -1ll * (MOD / i) * I[MOD % i] % MOD, F[i] = 1ll * F[i] * I[i] % MOD;
  }
}
int N, K, LIM = 1, L, A[MAXN], B[MAXN];
int main() {
  scanf("%d%d", &N, &K);
  int i;
  while (LIM <= K) LIM <<= 1, ++L;
  Pow(A, LIM, INV2);
  ++A[0], ++A[1];
  for (i = 0; i < LIM; ++i) A[i] = 1ll * A[i] * INV2 % MOD;
  Ln(A, LIM, L);
  for (i = 0; i < LIM; ++i) A[i] = 1ll * A[i] * (N + 1) % MOD;
  Exp(A, B, LIM, L);
  Pow(A, LIM, -INV2 + MOD);
  Multiply(A, B, LIM << 1, L + 1);
  for (i = N + 1; i < (LIM << 1); ++i) A[i] = 0;
  for (i = 1; i <= K; ++i) printf("%d ", (A[i] + MOD) % MOD);
  return 0;
}