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:     # 拡張ユークリッド互除法
      # ax + by = gcd(a,b)の最小整数解を返す
      def egcd(a, b):
          if a == 0:
              return b, 0, 1
          else:
              g, y, x = egcd(b % a, a)
              return g, x - (b // a) * y, y
       
       
      # mを法とするaの乗法的逆元
      def modinv(a, m):
          g, x, y = egcd(a, m)
          if g != 1:
              raise Exception('modular inverse does not exist')
          else:
              return x % m
       
            
      n = int(input())
      A = list(map(int, input().split()))
      C = [-1] * (n+1)
      lr = 0
      for i, a in enumerate(A):
          if C[a] == -1:
              C[a] = i
          else:
              lr = C[a] + n - i
              break
       
       
      def combination(n):
          lst = [1]
          mod = 10**9+7
          for i in range(1, n+1):
              lst.append(lst[-1] * (n+1-i) % mod * modinv(i, mod) % mod)
          return lst
       
       
      NC = combination(n+1)
      LRC = combination(lr)
      for i in range(1, n+2):
          print(NC[i] - (LRC[i-1] if i-1 <= lr else 0))
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."}]