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 collections
  import sys
  
  input = sys.stdin.readline
  
  ri = lambda: int(input())
  rs = lambda: input().rstrip()
  ril = lambda: list(map(int, input().split()))
  rsl = lambda: input().rstrip().split()
  ris = lambda n: [ri() for _ in range(n)]
  rss = lambda n: [rs() for _ in range(n)]
  rils = lambda n: [ril() for _ in range(n)]
  rsls = lambda n: [rsl() for _ in range(n)]
  
  
  class Combinations:
      def __init__(self, max_num, mod):
          self.mod = mod
          self.factorials = [1]
          for i in range(1, max_num + 1):
              self.factorials.append((self.factorials[-1] * i) % mod)
          self.invs = [pow(self.factorials[-1], mod - 2, mod)]
          for i in reversed(range(1, max_num + 1)):
              self.invs.append(self.invs[-1] * i % mod)
          self.invs = self.invs[::-1]
  
      def __call__(self, n, k):
          if n < 0 or k < 0 or k > n:
              return 0
          return self.factorials[n] * self.invs[k] * self.invs[n - k] % self.mod
  
  
  MOD = 10**9 + 7
  
  n = ri()
  ls = ril()
  counter = collections.Counter(ls)
  d = counter.most_common()[0][0]
  l, r = [i for i in range(n + 1) if ls[i] == d]
  
  combinations = Combinations(n + 1, MOD)
  for k in range(1, n + 2):
      res = combinations(n + 1, k) - combinations(l + n - r, k - 1)
      res += MOD
      res %= MOD
      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."}]