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 MOD = 998244353;
const int G = 15;
int fastpow(int x, int y) {
  if (y == 0) return 1;
  if (y & 1) return 1LL * x * fastpow(x, y - 1) % MOD;
  long long h = fastpow(x, y >> 1);
  return h * h % MOD;
}
const long long inv2 = fastpow(2, MOD - 2);
const long long inv3 = fastpow(3, MOD - 2);
const long long invn = fastpow(1 << (G + 1), MOD - 2);
int Rev(int x, int SZ) {
  int i, r = 0;
  for (i = 0; i < SZ; i++) {
    r = r << 1 | x & 1;
    x >>= 1;
  }
  return r;
}
void fft(vector<int>& a, bool f = false) {
  int i, j, k, x, y, z;
  const int N = a.size();
  for (i = 0; i < N; i++) {
    j = Rev(i, G + 1);
    if (i < j) {
      k = a[i];
      a[i] = a[j];
      a[j] = k;
    }
  }
  int t = 0;
  for (i = 1; i < N; i <<= 1, t++) {
    x = fastpow(f ? inv3 : 3, MOD / i >> 1);
    for (j = 0; j < N; j += i << 1) {
      y = 1;
      for (k = 0; k < i; k++) {
        z = (long long)a[i + j + k] * y % MOD;
        a[i + j + k] = a[j + k] - z;
        if (a[i + j + k] < 0) a[i + j + k] += MOD;
        a[j + k] += z;
        if (a[j + k] >= MOD) a[j + k] -= MOD;
        y = (long long)y * x % MOD;
      }
    }
  }
  if (f) {
    j = invn;
    for (i = 0; i < N; i++) a[i] = (long long)a[i] * j % MOD;
  }
}
vector<int> mult(const vector<int>& A, const vector<int>& B) {
  const int N = A.size();
  vector<int> a(A), b(B);
  a.resize(2 * N), b.resize(2 * N);
  fft(a);
  fft(b);
  vector<int> ab(2 * N);
  for (int i = 0; i < 2 * N; i++) ab[i] = (long long)a[i] * b[i] % MOD;
  fft(ab, true);
  ab.resize(N);
  return ab;
}
vector<int> square(const vector<int>& A) {
  const int N = A.size();
  vector<int> a(A);
  a.resize(2 * N);
  fft(a);
  for (int i = 0; i < 2 * N; i++) a[i] = (long long)a[i] * a[i] % MOD;
  fft(a, true);
  a.resize(N);
  return a;
}
const int K = 1 << G;
vector<int> get_next(const vector<int>& A, const vector<int>& B) {
  vector<int> ret(K);
  ret[0] = 1;
  for (int i = 1; i < K; i++)
    ret[i] = ((A[i - 1] + B[i - 1]) % MOD + B[i]) % MOD;
  return ret;
}
struct data {
  vector<int> A, B, C;
};
void step(data& d) {
  vector<int> D = get_next(d.B, d.C);
  swap(d.A, d.B);
  swap(d.B, d.C);
  swap(d.C, D);
}
void warp(data& d) {
  vector<int> AA = square(d.A), BB = square(d.B), CC = square(d.C);
  vector<int> AB = mult(d.A, d.B), BC = mult(d.B, d.C);
  vector<int> a(BB);
  for (int i = 1; i < K; i++) a[i] = (a[i] + AA[i - 1]) % MOD;
  vector<int> b(BC);
  for (int i = 1; i < K; i++) b[i] = (b[i] + AB[i - 1]) % MOD;
  vector<int> c(CC);
  for (int i = 1; i < K; i++) c[i] = (c[i] + BB[i - 1]) % MOD;
  swap(d.A, a);
  swap(d.B, b);
  swap(d.C, c);
}
void go(data& d, int n) {
  if (n == 1) return;
  if (n % 2) {
    go(d, n - 1);
    step(d);
  } else {
    go(d, n / 2);
    warp(d);
  }
}
int main() {
  data d;
  d.A = d.B = d.C = vector<int>(K);
  d.B[0] = d.C[0] = d.C[1] = 1;
  int n, k;
  scanf("%d%d", &n, &k);
  go(d, n);
  for (int i = 1; i <= k; i++) printf("%d ", d.C[i]);
}