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 main():
      b, w = map(int, input().split())
      mod = 10**9 + 7
      fact = [1, 1]
      for i in range(2, 10**5):
          fact.append(fact[-1] * i % mod)
  
      half = pow(2, mod - 2, mod)
  
      def nCr(n, r, mod=10**9 + 7):
          return pow(fact[n - r] * fact[r] % mod, mod - 2, mod) * fact[n] % mod
  
      h = 1
  
      A, B, C = 0, 1, 0
      for i in range(1, b + w + 1):
          h = h * half % mod
          ans = B
          A = A * 2 % mod
          B = B * 2 % mod
          C = C * 2 % mod
          if i - 1 >= b:
              p = nCr(i - 1, b)
              ans = (ans - p) % mod
              C = (C + p) % mod
              B = (B - p) % mod
          if i - w - 1 >= 0:
              p = nCr(i - 1, i - w - 1)
              A = (A + p) % mod
              B = (B - p) % mod
          ans = (ans + A) % mod
          print(ans * h % mod)
  
  
  main()
  
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"}]