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():
  
      U = 2 * 10**5
      MOD = 10**9 + 7
  
      fact = [1] * (U + 1)
      fact_inv = [1] * (U + 1)
      two = [1] * (U + 1)
      two_inv = [1] * (U + 1)
  
      for i in range(1, U + 1):
          fact[i] = (fact[i - 1] * i) % MOD
          two[i] = (two[i - 1] * 2) % MOD
      fact_inv[U] = pow(fact[U], MOD - 2, MOD)
      two_inv[U] = pow(two[U], MOD - 2, MOD)
  
      for i in range(U, 0, -1):
          fact_inv[i - 1] = (fact_inv[i] * i) % MOD
          two_inv[i - 1] = (two_inv[i] * 2) % MOD
  
      def comb(n, k):
          if k < 0 or k > n:
              return 0
          z = fact[n]
          z *= fact_inv[k]
          z %= MOD
          z *= fact_inv[n - k]
          z %= MOD
          return z
  
      B, W = map(int, input().split())
      p = 0
      q = 0
      for i in range(1, B + W + 1):
          ans = 1 - p + q
          ans %= MOD
          ans *= two_inv[1]
          ans %= MOD
          print(ans)
          p += comb(i - 1, B - 1) * two_inv[i] % MOD
          p %= MOD
          q += comb(i - 1, W - 1) * two_inv[i] % MOD
          q %= MOD
  
  
  if __name__ == "__main__":
      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"}]