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: def check(Ncount, min, K, not_this, i):
      count = 0
      if Ncount == 0:
          return 1
  
      for x in range(min, K + 1):
          if x in not_this:
              continue
          elif K >= (i - x) >= 1:
              not_this.append(i - x)
              count += check(Ncount - 1, x, K, not_this, i)
              not_this.pop()
          else:
              count += check(Ncount - 1, x, K, not_this, i)
  
      return count
  
  
  K, N = [int(x) for x in input().split()]
  
  for i in range(2, 2 * K):
      not_this = []
      print(check(N, 1, K, not_this, i))
  
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"}]