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;
int mod = 998244353;
namespace fft {
int len, last = -1, step = 0, rev[1 << 16];
struct complx {
  double real, img;
  inline complx() { real = img = 0.0; }
  inline complx conjugate() { return complx(real, -img); }
  inline complx(double x) { real = x, img = 0.0; }
  inline complx(double x, double y) { real = x, img = y; }
  inline complx operator+(complx other) {
    return complx(real + other.real, img + other.img);
  }
  inline complx operator-(complx other) {
    return complx(real - other.real, img - other.img);
  }
  inline complx operator*(complx other) {
    return complx((real * other.real) - (img * other.img),
                  (real * other.img) + (img * other.real));
  }
} u[1 << 16], v[1 << 16], f[1 << 16], g[1 << 16], dp[1 << 16];
void build(int& a, int* A, int& b, int* B) {
  while (a > 1 && A[a - 1] == 0) a--;
  while (b > 1 && B[b - 1] == 0) b--;
  len = 1 << (32 - __builtin_clz(a + b) - (__builtin_popcount(a + b) == 1));
  for (int i = a; i < len; i++) A[i] = 0;
  for (int i = b; i < len; i++) B[i] = 0;
  if (!step++) {
    dp[1] = complx(1);
    for (int i = 1; (1 << i) < 1 << 16; i++) {
      double theta = (2.0 * acos(0.0)) / (1 << i);
      complx mul = complx(cos(theta), sin(theta));
      int lim = 1 << i;
      for (int j = lim >> 1; j < lim; j++) {
        dp[2 * j] = dp[j];
        dp[2 * j + 1] = dp[j] * mul;
      }
    }
  }
  if (last != len) {
    last = len;
    int bit = (32 - __builtin_clz(len) - (__builtin_popcount(len) == 1));
    for (int i = 0; i < len; i++)
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (bit - 1));
  }
}
void transform_unrolled(complx* in, complx* out, complx* ar) {
  for (int i = 0; i < len; i++) out[i] = in[rev[i]];
  for (int k = 1; k < len; k <<= 1) {
    for (int i = 0; i < len; i += (k << 1)) {
      complx z, *a = out + i, *b = out + i + k, *c = ar + k;
      if (k == 1) {
        z = (*b) * (*c);
        *b = *a - z, *a = *a + z;
      }
      for (int j = 0; j < k && k > 1; j += 2, a++, b++, c++) {
        z = (*b) * (*c);
        *b = *a - z, *a = *a + z;
        a++, b++, c++;
        z = (*b) * (*c);
        *b = *a - z, *a = *a + z;
      }
    }
  }
}
bool equals(int a, int* A, int b, int* B) {
  if (a != b) return false;
  for (a = 0; a < b && A[a] == B[a]; a++) {
  }
  return (a == b);
}
int mod_multiply(int a, int* A, int b, int* B, int mod, int* tp) {
  build(a, A, b, B);
  int flag = equals(a, A, b, B);
  for (int i = 0; i < len; i++) A[i] %= mod, B[i] %= mod;
  for (int i = 0; i < len; i++) u[i] = complx(A[i] & 32767, A[i] >> 15);
  for (int i = 0; i < len; i++) v[i] = complx(B[i] & 32767, B[i] >> 15);
  transform_unrolled(u, f, dp);
  for (int i = 0; i < len; i++) g[i] = f[i];
  if (!flag) transform_unrolled(v, g, dp);
  for (int i = 0; i < len; i++) {
    int j = (len - 1) & (len - i);
    complx c1 = f[j].conjugate(), c2 = g[j].conjugate();
    complx a1 = (f[i] + c1) * complx(0.5, 0);
    complx a2 = (f[i] - c1) * complx(0, -0.5);
    complx b1 = (g[i] + c2) * complx(0.5 / len, 0);
    complx b2 = (g[i] - c2) * complx(0, -0.5 / len);
    v[j] = a1 * b2 + a2 * b1;
    u[j] = a1 * b1 + a2 * b2 * complx(0, 1);
  }
  transform_unrolled(u, f, dp);
  transform_unrolled(v, g, dp);
  long long x, y, z;
  for (int i = 0; i < len; i++) {
    x = f[i].real + 0.5, y = g[i].real + 0.5, z = f[i].img + 0.5;
    tp[i] = (x + ((y % mod) << 15) + ((z % mod) << 30)) % mod;
  }
  return a + b - 1;
}
}  // namespace fft
map<int, vector<int>> name;
int A[1 << 16], B[1 << 16], tp[1 << 16], k;
vector<int> multi(vector<int>& a, vector<int> b, int g = 0) {
  for (int i = 0; i <= k; i++) {
    A[i] = a[i];
    B[i] = b[i];
    tp[i] = 0;
    if (g == 0) continue;
  }
  fft::mod_multiply(k + 1, A, k + 1, B, mod, tp);
  vector<int> ret;
  for (int i = 0; i <= k; i++) ret.push_back(tp[i]);
  return ret;
}
vector<int> dp_func(int n) {
  vector<int> bs(k + 1, 0);
  bs[0] = 1;
  if (n == 1) bs[1] = 1;
  if (n <= 1) {
    return bs;
  }
  if (name.count(n)) return name[n];
  int l = n / 2;
  int r = n - l;
  vector<int> a = dp_func(l);
  vector<int> b = dp_func(r);
  vector<int> ret = multi(a, b);
  a = dp_func(l - 1);
  b = dp_func(r - 1);
  vector<int> ret2 = multi(a, b, n == 2);
  for (int i = 0; i < k; i++) {
    ret[i + 1] += ret2[i];
    ret[i + 1] %= mod;
  }
  return name[n] = ret;
}
int main() {
  int i, j, l, m, n;
  cin >> n >> k;
  vector<int> ret = dp_func(n);
  for (int i = 1; i <= k; i++) {
    printf("%d ", ret[i]);
  }
}