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: import sys
  import math
  
  N = int(input())
  a = list(map(int, input().split()))
  
  """
  def combination(n,k):
  	if k == 0:
  		return 1
  	elif k == n:
  		return 1
  	else:
  		return math.factorial(n)/math.factorial(n-k)/math.factorial(k)
  
  #hoge = "1 2 1 3"
  #a_array = list(map(int,hoge.split(" ")))
  #a_array = [2,3,1,4,5,1,6,7]
  #a_array = [1,2,1,3]
  #N = len(a_array)-1
  
  #print(N)
  #print(a_array)
  
  indexes = [i for i, x in enumerate(a_array) if x == 1]
  #print(indexes)
  r = indexes[0] + N-indexes[1]
  #print(r)
  
  for i in range(1,N+2):
  	if r >= i-1:
  		print(int(combination(N+1,i)-combination(r,i-1)))
  	else:
  		print(int(combination(N+1,i)))
  """
  
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."}]