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 sys
  from collections import *
  import heapq
  import math
  import bisect
  from itertools import permutations,accumulate,combinations,product
  from fractions import gcd
  def input():
      return sys.stdin.readline()[:-1]
  def ruiseki(lst):
      return [0]+list(accumulate(lst))
  mod=pow(10,9)+7
  al=[chr(ord('a') + i) for i in range(26)]
  
  n=int(input())
  m=n+1
  a=list(map(int,input().split()))
  
  # MOD combination
  def cmb(n, r, mod=10**9+7):
      if ( r<0 or r>n ):
          return 0
      r = min(r, n-r)
      return g1[n] * g2[r] * g2[n-r] % mod
  
  N = 10**5
  g1 = [1, 1] # 元テーブル
  g2 = [1, 1] #逆元テーブル
  inverse = [0, 1] #逆元テーブル計算用テーブル
  
  for i in range( 2, N + 1 ):
      g1.append( ( g1[-1] * i ) % mod )
      inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
      g2.append( (g2[-1] * inverse[-1]) % mod )
  
  ma=0
  dic={}
  for i in range(m):
      if not a[i] in dic:
          dic[a[i]]=i
      else:
          ma=i-dic[a[i]]-1
  
  for k in range(1,m+1):
      if k==1:
          print(n)
          continue
      tmp=(cmb(m,k)
      if m-2-ma>=k-1:
          tmp-=cmb(m-2-ma,k-1)
      print(tmp%mod)
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."}]