output_description: Print 2K-1 integers. The t-th of them (1\leq t\leq 2K-1) should be the answer
  for i=t+1.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      K N
attempt: k, n = map(int, input().split())
  mod = 998244353
  
  max_n = 5000
  fac, finv, inv = [0] * max_n, [0] * max_n, [0] * max_n
  
  
  def comInit(max_n):
      fac[0] = fac[1] = 1
      finv[0] = finv[1] = 1
      inv[1] = 1
  
      for i in range(2, max_n):
          fac[i] = fac[i - 1] * i % mod
          inv[i] = mod - inv[mod % i] * (mod // i) % mod
          finv[i] = finv[i - 1] * inv[i] % mod
  
  
  comInit(max_n)
  
  
  # 二項係数の計算
  def com(n, k):
      if n < k:
          return 0
      if (n < 0) | (k < 0):
          return 0
      return fac[n] * (finv[k] * finv[n - k] % mod) % mod
  
  
  ex2 = [1] * 1010
  for i in range(1, 1010):
      ex2[i] = (ex2[i - 1] * 2) % mod
  
  ans = []
  for j in range(2, k + 2):
      tmp = 0
      x = (j - 1) // 2
      for i in range(j // 2 + 1):
          comb1 = com(n + k - j, n - i)
          comb2 = (com(x, i) * ex2[i]) % mod
          if j % 2 == 0:
              comb1 += com(n + k - j - 1, n - i - 1)
              comb1 %= mod
          tmp += comb1 * comb2
          tmp %= mod
  
      ans.append(tmp)
  
  ans2 = ans[:-1]
  ans += ans2[::-1]
  print("\n".join(map(str, ans)))
  
problem_description: Statement
  
  Takahashi throws N dice, each having K sides with all integers from 1 to K.
  The dice are NOT pairwise distinguishable. For each i=2,3,...,2K, find the
  following value modulo 998244353:
  
    * The number of combinations of N sides shown by the dice such that the sum of no two different sides is i.
  
  Note that the dice are NOT distinguishable, that is, two combinations are
  considered different when there exists an integer k such that the number of
  dice showing k is different in those two.
samples: [{"input": "3 3", "output": "7\n    7\n    4\n    7\n    7\n    \n\n  * For i=2, the combinations (1,2,2),(1,2,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3) satisfy the condition, so the answer is 7.\n  * For i=3, the combinations (1,1,1),(1,1,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3) satisfy the condition, so the answer is 7.\n  * For i=4, the combinations (1,1,1),(1,1,2),(2,3,3),(3,3,3) satisfy the condition, so the answer is 4.\n\n* * *"}, {"input": "4 5", "output": "36\n    36\n    20\n    20\n    20\n    36\n    36\n    \n\n* * *"}, {"input": "6 1000", "output": "149393349\n    149393349\n    668669001\n    668669001\n    4000002\n    4000002\n    4000002\n    668669001\n    668669001\n    149393349\n    149393349"}]