output_description: Print the answers in B+W lines. In the i-th line, print the probability that
  the color of the i-th piece to be eaten is black, modulo 10^{9}+7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      B W
attempt: b, w = map(int, input().split())
  MOD = 10**9 + 7
  list_size = 200001
  
  f_list = [1] * list_size
  f_r_list = [1] * list_size
  
  for i in range(list_size - 1):
      f_list[i + 1] = int((f_list[i] * (i + 2)) % MOD)
  
  f_r_list[-1] = pow(f_list[-1], MOD - 2, MOD)
  
  for i in range(2, list_size + 1):
      f_r_list[-i] = int((f_r_list[-i + 1] * (list_size + 2 - i)) % MOD)
  
  
  def comb(n, r):
      if n < r:
          return 0
      elif n == 0 or r == 0 or n == r:
          return 1
      else:
          return (((f_list[n - 1] * f_r_list[n - r - 1]) % MOD) * f_r_list[r - 1]) % MOD
  
  
  two_pow = [1]
  for i in range(b + w + 1):
      two_pow.append((two_pow[-1] * 500000004) % MOD)
  
  ans = 500000004
  print(ans)
  for i in range(1, b + w):
      if i - 1 >= b - 1:
          ans -= comb(i - 1, b - 1) * two_pow[i + 1]
      if i - w >= 0:
          ans += comb(i - 1, i - w) * two_pow[i + 1]
      ans %= MOD
      print(ans)
  
problem_description: Statement
  
  Today, Snuke will eat B pieces of black chocolate and W pieces of white
  chocolate for an afternoon snack.
  
  He will repeat the following procedure until there is no piece left:
  
    * Choose black or white with equal probability, and eat a piece of that color if it exists.
  
  For each integer i from 1 to B+W (inclusive), find the probability that the
  color of the i-th piece to be eaten is black. It can be shown that these
  probabilities are rational, and we ask you to print them modulo 10^9 + 7, as
  described in Notes.
samples: [{"input": "2 1", "output": "500000004\n    750000006\n    750000006\n    \n\n  * There are three possible orders in which Snuke eats the pieces:\n    * white, black, black\n    * black, white, black\n    * black, black, white\n  * with probabilities \\frac{1}{2}, \\frac{1}{4}, \\frac{1}{4}, respectively. Thus, the probabilities of eating a black piece first, second and third are \\frac{1}{2},\\frac{3}{4} and \\frac{3}{4}, respectively.\n\n* * *"}, {"input": "3 2", "output": "500000004\n    500000004\n    625000005\n    187500002\n    187500002\n    \n\n  * They are \\frac{1}{2},\\frac{1}{2},\\frac{5}{8},\\frac{11}{16} and \\frac{11}{16}, respectively.\n\n* * *"}, {"input": "6 9", "output": "500000004\n    500000004\n    500000004\n    500000004\n    500000004\n    500000004\n    929687507\n    218750002\n    224609377\n    303710940\n    633300786\n    694091802\n    172485353\n    411682132\n    411682132"}]