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 MAXN = 262151, MOD = 998244353, G = 3, INVG = 332748118;
int cnt, kk, limit;
int f[3][MAXN], g[5][MAXN], rev[MAXN];
inline int read() {
  register int num = 0, neg = 1;
  register char ch = getchar();
  while (!isdigit(ch) && ch != '-') {
    ch = getchar();
  }
  if (ch == '-') {
    neg = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    num = (num << 3) + (num << 1) + (ch - '0');
    ch = getchar();
  }
  return num * neg;
}
inline int qpow(int base, int exponent) {
  long long int res = 1;
  while (exponent) {
    if (exponent & 1) {
      res = 1ll * res * base % MOD;
    }
    base = 1ll * base * base % MOD, exponent >>= 1;
  }
  return res;
}
inline void NTT(int *cp, int cnt, int inv) {
  int cur = 0, res = 0, omg = 0;
  for (register int i = 0; i < cnt; i++) {
    if (i < rev[i]) {
      swap(cp[i], cp[rev[i]]);
    }
  }
  for (register int i = 2; i <= cnt; i <<= 1) {
    cur = i >> 1, res = qpow(inv == 1 ? G : INVG, (MOD - 1) / i);
    for (register int *p = cp; p != cp + cnt; p += i) {
      omg = 1;
      for (register int j = 0; j < cur; j++) {
        int t = 1ll * omg * p[j + cur] % MOD, t2 = p[j];
        p[j + cur] = (t2 - t + MOD) % MOD, p[j] = (t2 + t) % MOD;
        omg = 1ll * omg * res % MOD;
      }
    }
  }
  if (inv == -1) {
    int invl = qpow(cnt, MOD - 2);
    for (register int i = 0; i < cnt; i++) {
      cp[i] = 1ll * cp[i] * invl % MOD;
    }
  }
}
inline void shift(int fd) {
  int cnt = 1, limit = -1;
  while (cnt <= (fd << 1)) {
    cnt <<= 1, limit++;
  }
  for (register int i = 0; i < cnt; i++) {
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << limit);
    g[0][i] = g[1][i] = g[2][i] = g[3][i] = g[4][i] = 0;
  }
  NTT(f[0], cnt, 1), NTT(f[1], cnt, 1), NTT(f[2], cnt, 1);
  for (register int i = 0; i < cnt; i++) {
    g[0][i] = (long long int)f[0][i] * f[0][i] % MOD,
    g[1][i] = (long long int)f[1][i] * f[1][i] % MOD;
    g[2][i] = (long long int)f[2][i] * f[2][i] % MOD,
    g[3][i] = (long long int)f[0][i] * f[1][i] % MOD;
    g[4][i] = (long long int)f[1][i] * f[2][i] % MOD,
    f[0][i] = f[1][i] = f[2][i] = 0;
  }
  NTT(g[0], cnt, -1), NTT(g[1], cnt, -1), NTT(g[2], cnt, -1);
  NTT(g[3], cnt, -1), NTT(g[4], cnt, -1);
  for (register int i = 0; i < cnt; i++) {
    f[0][i] = (g[0][i] + (i ? g[1][i - 1] : 0)) % MOD;
    f[1][i] = (g[3][i] + (i ? g[4][i - 1] : 0)) % MOD;
    f[2][i] = (g[1][i] + (i ? g[2][i - 1] : 0)) % MOD;
  }
  for (register int i = 0; i < cnt; i++) {
    g[0][i] = g[1][i] = g[2][i] = g[3][i] = g[4][i] = 0;
  }
  for (register int i = fd; i < cnt; i++) {
    f[0][i] = f[1][i] = f[2][i] = 0;
  }
}
inline void setBit(int fd) {
  for (register int i = 0; i < fd; i++) {
    f[2][i] = f[1][i], f[1][i] = f[0][i], f[0][i] = 0;
  }
  f[0][0] = 1;
  for (register int i = 1; i < fd; i++) {
    f[0][i] = ((f[1][i - 1] + f[2][i - 1]) % MOD + f[1][i]) % MOD;
  }
}
int main() {
  cnt = read(), kk = read(), f[0][0] = f[1][0] = f[0][1] = 1, limit = log2(cnt);
  for (register int i = limit - 1; i >= 0; i--) {
    shift(kk + 10);
    if (cnt & (1 << i)) {
      setBit(kk + 10);
    }
  }
  for (register int i = 1; i <= kk; i++) {
    printf("%d ", f[0][i]);
  }
}