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: print("reference: maspy")
  
  # 基本的に重複がない
  # n+1Ck − (n+1)-(r-l+1)Ck−1
   
  MOD = 10 ** 9 + 7
  U = 10 ** 5 + 1
  
  # (a ^ n % MOD) を2部探索的に求められる。
  def power_mod(a, n):
    if n == 0:
      return 1
    x = (power_mod(a, n // 2) ** 2) % MOD
    return x if n % 2 == 0 else (a * x) % MOD
  
  """
  # practice 1
  def power_mod(a, n):
    if n == 0:
      return 1
    x = (power_mod(a, n // 2) ** 2) % MOD
    return x if n % 2 == 0 else (a * x) % MOD
      
  # practice 2
  def power_mod(a, n):
    if n == 0:
      return 1
    x = (power_mod(a, n // 2) ** 2) % MOD
    return x if n % 2 == 0 else (a * x) % MOD
  """
  
  # 逆元を求めている。
  def make_fact(fact, fact_inv):
    for i in range(1, U + 1):
      fact[i] = (fact[i - 1] * i) % MOD
    fact_inv[U] = power_mod(fact[U], MOD - 2)
    for i in range(U, 0, -1):　# [U, 1]
      fact_inv[i - 1] = (fact_inv[i] * i) % MOD
  
  def comb(n, k):
    if k < 0 or k > n:
      return 0
    x = fact[n]
    x *= fact_inv[k]
    x %= MOD
    x *= fact_inv[n-k]
    x %= MOD
    return x
   
  fact = [1] * (U + 1)
  fact_inv = [1] * (U + 1)
  make_fact(fact, fact_inv)
   
  # ここまではcombのtableを作っている。
    
  # 重複の起きる場所の間隔だけが問題
  n = int(input())
  A = [int(x) for x in input().split()]
   
  memo = dict()
  for i, a in enumerate(A): # lenを使うならこちらを積極的に。
    if a in memo: # 離脱条件を先に。
      d = i - memo[a]
      break
    memo[a] = i # ある数字が何番目にいるか。
  
  rest = n - d
   
  for k in range(1, n + 2): # [1, n + 1]
    ans = comb(n + 1, k) - comb(rest, k - 1)
    ans %= MOD
    print(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."}]