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: def cmb(n, r, mod):  # コンビネーションの高速計算
      if r < 0 or r > n:
          return 0
      r = min(r, n - r)
      return g1[n] * g2[r] * g2[n - r] % mod
  
  
  mod = 10**9 + 7  # 出力の制限
  N = 2 * 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)
  
  import sys
  
  write = sys.stdout.write
  
  B, W = map(int, input().split())
  
  p = [1]
  for i in range(1, B + W + 1):
      p.append((p[-1] * inverse[2]) % mod)
  
  BD = [0]
  for i in range(1, B + W + 1):
      t = (BD[-1] + cmb(i - 1, B - 1, mod) * p[i]) % mod
      BD.append(t)
  
  WD = [0]
  for i in range(1, B + W + 1):
      t = (WD[-1] + cmb(i - 1, W - 1, mod) * p[i]) % mod
      WD.append(t)
  
  for i in range(1, B + W + 1):
      ans = (1 - BD[i - 1] - WD[i - 1]) * p[1] + WD[i - 1]
      ans %= mod
      write(str(ans) + "\n")
  
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"}]