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: Wrong Answer)

import math

N, A, B, C = map(int,input().split())
mod = 10**9+7

def cmb(n, r, mod):
    if (r < 0 or r > n):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

g1 = [1, 1]
g2 = [1, 1]
inv = [0, 1] 
for i in range(2, 2*10**5+1):
    g1.append((g1[-1] * i) % mod)
    inv.append((-inv[mod % i] * (mod//i)) % mod)
    g2.append((g2[-1] * inv[-1]) % mod)

def g(a):
    b, u, v = mod, 1,0
    while b:
        t = a//b
        a -= t * b
        u -= t * v
        a,b,u,v = b,a,v,u
        u %= mod
    return u if u > 0 else u + mod

p1,p2 = A * g(A + B) % mod, B * g(A + B) % mod
p3 = (100 - C) * g(100) % mod

ans = 0
for i in range(N):
    ans += (N+i)*cmb(N+i-1,i,mod)% mod*(pow(p1,N,mod) * pow(p2,i,mod) % mod + pow(p2,i,mod) * pow(p2,N,mod) % mod)% mod
    ans %= mod
ans = ans * g(p3) % mod
print(ans)