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 PyPy3 (2.4.0) (judge verdict: Accepted)

mod=10**9+7
n,a,b,c=map(int,input().split())
m=2*10**5
def modinv(n):
    return pow(n,mod-2,mod)
Fact=[1] #階乗
for i in range(1,m+1):
    Fact.append(Fact[i-1]*i%mod)
Finv=[0]*(m+1) #階乗の逆元
Finv[-1]=modinv(Fact[-1])
for i in range(m-1,-1,-1):
    Finv[i]=Finv[i+1]*(i+1)%mod
def comb(n,r):
    if n<r:
        return 0
    return Fact[n]*Finv[r]*Finv[n-r]%mod
p=a*modinv(100-c); q=b*modinv(100-c)
ans=0
for k in range(n,2*n):
    ans+=k*comb(k-1,n-1)*(pow(p,n,mod)*pow(q,k-n,mod)+pow(p,k-n,mod)*pow(q,n,mod))
    ans%=mod
ans*=100*modinv(100-c)
print(ans%mod)