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: f = [0 for _ in range(100001)]
  mo = 1000000007
  
  
  def ksm(a, b):
      ans = 1
      while b:
          if b & 1:
              ans = ans * a % mo
          b >>= 1
          a = a * a % mo
  
      return ans
  
  
  def main():
      n = int(input())
      l = list(map(int, input().split()))
      for i in range(1, n + 2):
          x = l[i - 1]
          if f[x]:
              l = f[x] - 1
              r = n - i + 1
              break
          else:
              f[x] = i
  
      print(n)
      t = l + r
      sum1 = 1
      sum = n + 1
      for i in range(2, n + 2):
          if t >= i - 1:
              sum1 = (sum1 * (t - i + 2) % mo * ksm(i - 1, mo - 2)) % mo
          else:
              sum1 = 0
          sum = (sum * (n - i + 2) % mo * ksm(i, mo - 2)) % mo
          print((sum - sum1 + mo) % mo)
  
  
  main()
  
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."}]