output_description: Print the expected number of games that will be played, in the manner
  specified in the statement.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N A B C
attempt: import sys
  
  
  def main():
      input = sys.stdin.readline
      MOD = 10**9 + 7
      N, A, B, C = map(int, input().split())
  
      factrial = [1] * (2 * N)
      # pa[i] / pab[i] is the probobility that A wins i times when there is no draw.
      pa = [1] * (2 * N)
      pb = [1] * (2 * N)
      pab = [1] * (2 * N)
      for k in range(1, 2 * N):
          factrial[k] = (factrial[k - 1] * k) % MOD
          pa[k] = (pa[k - 1] * A) % MOD
          pb[k] = (pb[k - 1] * B) % MOD
          pab[k] = (pab[k - 1] * (A + B)) % MOD
  
      fact_inv = [1] * (2 * N)
      fact_inv[2 * N - 1] = pow(factrial[2 * N - 1], MOD - 2, MOD)
      pab_inv = [1] * (2 * N)
      pab_inv[2 * N - 1] = pow(pab[2 * N - 1], MOD - 2, MOD)
      for k in range(2 * N - 2, -1, -1):
          fact_inv[k] = (fact_inv[k + 1] * (k + 1)) % MOD
          pab_inv[k] = (pab_inv[k + 1] * (A + B)) % MOD
  
      def comb_mod(n, r, MOD=10**9 + 7):
          return (factrial[n] * fact_inv[r] * fact_inv[n - r]) % MOD
  
      ans = 0
      for m in range(N):
          E = (
              comb_mod(N + m - 1, N - 1)
              * (pa[N] * pb[m] + pa[m] * pb[N])
              * pab_inv[N + m]
              * (N + m)
              * 100
              * pow(100 - C, MOD - 2, MOD)
          ) % MOD
  
          ans = (ans + E) % MOD
  
      return ans
  
  
  if __name__ == "__main__":
      print(main())
  
problem_description: Statement
  
  Takahashi and Aoki will play a game. They will repeatedly play it until one of
  them have N wins in total.
  
  When they play the game once, Takahashi wins with probability A %, Aoki wins
  with probability B %, and the game ends in a draw (that is, nobody wins) with
  probability C %. Find the expected number of games that will be played, and
  print it as follows.
  
  We can represent the expected value as P/Q with coprime integers P and Q.
  Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q
  \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the
  constraints of this problem.)
samples: [{"input": "1 25 25 50", "output": "2\n    \n\nSince N=1, they will repeat the game until one of them wins. The expected\nnumber of games played is 2.\n\n* * *"}, {"input": "4 50 50 0", "output": "312500008\n    \n\nC may be 0.\n\n* * *"}, {"input": "1 100 0 0", "output": "1\n    \n\nB may also be 0.\n\n* * *"}, {"input": "100000 31 41 28", "output": "104136146"}]