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: mod = 10**9 + 7
  b, w = map(int, input().split())
  
  
  def comb(n, r):
      if n < r:
          return 0
      if n < 0 or r < 0:
          return 0
      return fa[n] * fi[r] % mod * fi[n - r] % mod
  
  
  n = b + w + 10
  inv = [1] * (n + 1)
  fa = [1] * (n + 1)
  fi = [1] * (n + 1)
  for i in range(1, n):
      inv[i] = ((inv[i - 1] % 2) * mod + inv[i - 1]) // 2
      fa[i] = fa[i - 1] * i % mod
      fi[i] = pow(fa[i], mod - 2, mod)
  p, q = 0, 0
  for i in range(b + w):
      if i >= b:
          p *= 2
          p += comb(i - 1, b - 1)
          p %= mod
      if i >= w:
          q *= 2
          q += comb(i - 1, w - 1)
          q %= mod
      print(((q - p) * inv[i + 1] + inv[1]) % mod)
  
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"}]