output_description: Print n+1 lines. The k-th line should contain the number of the different
  subsequences of the given sequence with length k, modulo 10^9+7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      n
      a_1 a_2 ... a_{n+1}
attempt: N=int(input())
  A=[int(x) for x in input().split()]
  #重複始点終点調査
  se=[]
  for i in range(len(A)):
    if A[i]==sum(A)-N*(N+1)/2:
      se.append(i)
  
  mod=10**9+7
   
  #階乗計算
  factorial=[1]
  for i in range(1,N+2):
      factorial.append(factorial[i-1]*i %mod)
  #逆元計算
  inverse=[0]*(N+2)
  inverse[N+2-1] = pow(factorial[N+2-1], mod-2,mod)
  for i in range(N+2-2, -1, -1):
      inverse[i] = inverse[i+1] * (i+1) % mod
  #combination計算
  def nCr(n,r):
    if n<r or n==0 or r==0:
      return 0
    return factorial[n] * inverse[r] * inverse[n-r] % mod
  
  print(N)
  if N==1:
    print(N)
  else:
    for i in range(1,N+1):
      ans = nCr(N+1, i+1)
      if if se[0] + N -se[1] >= i:
        ans-=nCr(se[0]+N-se[1],i)
        print(int(ans))
problem_description: Statement
  
  You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which
  consists of the n integers 1,...,n. It is known that each of the n integers
  1,...,n appears at least once in this sequence.
  
  For each integer k=1,...,n+1, find the number of the different subsequences
  (not necessarily contiguous) of the given sequence with length k, modulo
  10^9+7.
samples: [{"input": "3\n    1 2 1 3", "output": "3\n    5\n    4\n    1\n    \n\nThere are three subsequences with length 1: 1 and 2 and 3.\n\nThere are five subsequences with length 2: 1,1 and 1,2 and 1,3 and 2,1 and\n2,3.\n\nThere are four subsequences with length 3: 1,1,3 and 1,2,1 and 1,2,3 and\n2,1,3.\n\nThere is one subsequence with length 4: 1,2,1,3.\n\n* * *"}, {"input": "1\n    1 1", "output": "1\n    1\n    \n\nThere is one subsequence with length 1: 1.\n\nThere is one subsequence with length 2: 1,1.\n\n* * *"}, {"input": "32\n    29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9", "output": "32\n    525\n    5453\n    40919\n    237336\n    1107568\n    4272048\n    13884156\n    38567100\n    92561040\n    193536720\n    354817320\n    573166440\n    818809200\n    37158313\n    166803103\n    166803103\n    37158313\n    818809200\n    573166440\n    354817320\n    193536720\n    92561040\n    38567100\n    13884156\n    4272048\n    1107568\n    237336\n    40920\n    5456\n    528\n    33\n    1\n    \n\nBe sure to print the numbers modulo 10^9+7."}]