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: class BigCombination(object):
      __slots__ = ["mod", "factorial", "inverse"]
  
      def __init__(self, mod: int  10**9+7, max_n: int  10**6):
          fac, inv = [1], []
          fac_append, inv_append = fac.append, inv.append
  
          for i in range(1, max_n+1):
              fac_append(fac[-1] * i % mod)
  
          inv_append(pow(fac[-1], mod-2, mod))
  
          for i in range(max_n, 0, -1):
              inv_append(inv[-1] * i % mod)
  
          self.mod, self.factorial, self.inverse = mod, fac, inv[::-1]
  
      def get_combination(self, n, r):
          return self.factorial[n] * self.inverse[r] * self.inverse[n-r] % self.mod
  
      def get_permutation(self, n, r):
          return self.factorial[n] * self.inverse[n-r] % self.mod
  
  N = int(input())
  A = [int(x) for x in input().split()]
  se = []
  c = sum(A) - N * (N + 1) / 2
  for i in range(len(A)):
      if A[i] == c:
          se.append(i)
  l = se[0]
  r = se[1]
  import math
  
  Big = BigCombination()
  print(N)
  for i in range(2,N+2):
      k = Big.get_combination(N+1, i) 
      t = Big.get_combination(l+N-r,i-1)
      print(l+N-r,i-1)
      if l+N-r == 0 :t = 0
      res  = k -t
      print(res)
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."}]