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
  
  write = sys.stdout.write
  
  B, W = map(int, sys.stdin.readline().split())
  MOD = 10**9 + 7
  
  L = B + W
  fact = [1] * (L + 1)
  rfact = [1] * (L + 1)
  for i in range(L):
      fact[i + 1] = r = fact[i] * (i + 1) % MOD
  rfact[L] = pow(fact[L], MOD - 2, MOD)
  for i in range(L, 0, -1):
      rfact[i - 1] = rfact[i] * i % MOD
  
  rev2 = pow(2, MOD - 2, MOD)
  
  p = q = 0
  
  L = min(B, W)
  r2 = "%d\n" % rev2
  for i in range(L):
      write(r2)
  base = pow(rev2, L - 1, MOD)
  
  rB = rfact[B - 1]
  rW = rfact[W - 1]
  for i in range(L, B + W):
      base = rev2 * base % MOD
      if i >= B:
          p = (p + (fact[i - 1] * rfact[i - B] % MOD) * (rB * base % MOD) % MOD) % MOD
      if i >= W:
          q = (q + (fact[i - 1] * rfact[i - W] % MOD) * (rW * base % MOD) % MOD) % MOD
      write("%d\n" % ((1 - p + q) * rev2 % 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"}]