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: import sys
  
  readline = sys.stdin.readline
  sys.setrecursionlimit(10**7)
  
  import numpy as np
  
  MOD = 10**9 + 7
  
  B, W = map(int, readline().split())
  
  
  def cumprod(arr):
      L = len(arr)
      Lsq = int(L**0.5 + 1)
      arr = np.resize(arr, Lsq**2).reshape(Lsq, Lsq)
      for n in range(1, Lsq):
          arr[:, n] *= arr[:, n - 1]
          arr[:, n] %= MOD
      for n in range(1, Lsq):
          arr[n] *= arr[n - 1, -1]
          arr[n] %= MOD
      return arr.ravel()[:L]
  
  
  U = 2 * 10**5 + 100
  x = np.arange(U, dtype=np.int64)
  x[0] = 1
  fact = cumprod(x)
  x = np.arange(U, 0, -1, dtype=np.int64)
  x[0] = pow(int(fact[-1]), MOD - 2, MOD)
  fact_inv = cumprod(x)[::-1]
  
  x = np.full(U, pow(2, MOD - 2, MOD), dtype=np.int64)
  x[0] = 1
  pow2_inv = cumprod(x)
  
  # 各時点で、単色になっている確率
  black_only = np.zeros(B + W, np.int64)
  x = fact[W - 1 : B + W - 1] % MOD * fact_inv[0:B] % MOD * fact_inv[W - 1] % MOD
  black_only[W : B + W] = pow2_inv[W : B + W] * x % MOD
  np.cumsum(black_only, out=black_only)
  black_only %= MOD
  
  white_only = np.zeros(W + B, np.int64)
  x = fact[B - 1 : W + B - 1] % MOD * fact_inv[0:W] % MOD * fact_inv[B - 1] % MOD
  white_only[B : W + B] = pow2_inv[B : W + B] * x % MOD
  np.cumsum(white_only, out=white_only)
  white_only %= MOD
  
  answer = (1 + black_only - white_only) * pow(2, MOD - 2, MOD) % MOD
  print("\n".join(answer.astype(str)))
  
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"}]