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 Python (3.4.3) (judge verdict: Accepted)

N, A, B, C = map(int, input().split())

MOD = 10**9 + 7
M = 2*N

fact = [1]*(M+1)
rfact = [1]*(M+1)
r = 1
for i in range(1, M+1):
  fact[i] = r = r * i % MOD
rfact[M] = r = pow(fact[M], MOD-2, MOD)
for i in range(M, 0, -1):
  rfact[i-1] = r = r * i % MOD

rev = pow(A+B, MOD-2, MOD)

p = 0
b = B * rev % MOD
e = 1
for k in range(N):
    v = fact[N+k-1] * rfact[N-1] * rfact[k] % MOD
    v = v * e * (N + k) % MOD
    e = e * b % MOD
    p += v
p *= pow(A * rev % MOD, N, MOD) * 100 * rev % MOD

q = 0
b = A * rev % MOD
e = 1
for k in range(N):
    v = fact[N+k-1] * rfact[N-1] * rfact[k] % MOD
    v = v * e * (N + k) % MOD
    e = e * b % MOD
    q += v
q *= pow(B * rev % MOD, N, MOD) * 100 * rev % MOD

print((p + q) % MOD)