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: Accepted)

def powmod(b,r,mod)
  a = 1
  while r > 0
    if r%2 == 1
      a = a * b % mod
    end
    b = b * b % mod
    r /= 2
  end
  a
end

def invmod(f, mod)
  powmod(f, mod-2, mod)
end

def factorial(n, mod)
  fs = [1]
  (1..n).each{ |k| fs << (fs[-1] * k) % mod }
  fs
end

def inv_factorial(n, mod)
  fs = [1]
  f = 1
  (1..n).each{ |k|
    f = f * k % mod
    fs << invmod(f, mod)
  }
  fs
end


N,A,B,C = gets.split.map &:to_i
Mod = 10**9 + 7

fs = factorial(2*N+2, Mod) 
is = inv_factorial(2*N+2, Mod)

Q = A+B
InvQ = invmod(Q, Mod)
Inv100 = invmod(100, Mod)
ans = 0
[[A,B],[B,A]].each{ |a,b|
  an = powmod(a, N, Mod)
  bn = 1
  inv100nm = powmod(InvQ, N, Mod)
  (0...N).each{ |m|
    v = fs[N+m-1] * is[N-1] % Mod * is[m] % Mod * an % Mod * bn % Mod * inv100nm % Mod
    ans = (ans + v*(N+m)) % Mod
    bn = bn * b % Mod
    inv100nm = inv100nm * InvQ % Mod
  }
}
p ans * 100 % Mod * invmod(100 - C, Mod) % Mod