Problem:
Score : 500 points

Problem 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.)

Constraints

1 \leq N \leq 100000

0 \leq A,B,C \leq 100

1 \leq A+B

A+B+C=100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B C

Output

Print the expected number of games that will be played, in the manner specified in the statement.

Sample Input 1

1 25 25 50

Sample Output 1

2

Since N=1, they will repeat the game until one of them wins.
The expected number of games played is 2.

Sample Input 2

4 50 50 0

Sample Output 2

312500008

C may be 0.

Sample Input 3

1 100 0 0

Sample Output 3

1

B may also be 0.

Sample Input 4

100000 31 41 28

Sample Output 4

104136146

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n, A, B, C = gets.split(" ").map(&:to_i)

dp = Array.new(n+1){Array.new(n+1)};

0.upto(n-1) do |j|
  dp[n][j] = 0
end

0.upto(n-1) do |i|
  dp[i][n] = 0
end

(n-1).downto(0) do |i|
  (n-1).downto(0) do |j|
    dp[i][j] = Rational(A,A+B)*dp[i+1][j] + Rational(B,A+B) \
      * dp[i][j+1] + Rational(100,A+B)
  end
end

p = dp[0][0].numerator
q = dp[0][0].denominator


#適切な値に設定する
MOD = 10**9 + 7
MAX = q

$fact = Array.new(MAX + 1) # i! mod p
$finv = Array.new(MAX + 1) # (i!)^(-1) mod p
$inv = Array.new(MAX + 1) # i^(-1) mod p

def com_init()
  $fact[0] = $fact[1] = 1
  $finv[0] = $finv[1] = 1
  $inv[1] = 1
  2.upto(MAX) do |i|
    $fact[i] = $fact[i-1] * i % MOD
    $inv[i] = MOD - $inv[MOD % i] * (MOD/i) % MOD
    $finv[i] = $finv[i-1] * $inv[i] % MOD
  end
end
com_init
puts p * $inv[q] % MOD