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: from sys import exit, setrecursionlimit, stderr
  from functools import reduce
  from itertools import *
  from collections import *
  from bisect import bisect
  from heapq import *
  
  
  def read():
      return int(input())
  
  
  def reads():
      return [int(x) for x in input().split()]
  
  
  MOD = 10**9 + 7
  
  N = read()
  A = reads()
  
  fact = [1] * N
  for i in range(1, N):
      fact[i] = (fact[i - 1] * i) % MOD
  invfact = [0] * N
  invfact[-1] = pow(fact[-1], MOD - 2, MOD)
  for i in range(N - 2, -1, -1):
      invfact[i] = invfact[i + 1] * (i + 1) % MOD
  
  
  def comb(n, k):
      return fact[n] * invfact[n - k] * invfact[k] % MOD
  
  
  cnt = Counter(A)
  q = next(i for i in range(1, N + 1) if cnt[i] == 2)
  i1 = A.index(q)
  i2 = A.index(q, i1 + 1)
  m = N - (i2 - i1)
  # print(m)
  
  print(N)
  for k in range(2, N + 1):
      ans = comb(N - 1, k - 1) * 2 + comb(N - 1, k - 2)
      if m >= k - 1:
          ans -= comb(m, k - 1)
      if k <= N - 1:
          ans += comb(N - 1, k)
      print(ans % MOD)
  print(1)
  
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."}]