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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define SZ(x) ((int)x.size())
#define FOR(i,a,b) for (int i=a;i<=b;++i)
#define FORD(i,a,b) for (int i=a;i>=b;--i)
using namespace std;
typedef long long LL;
typedef pair<int,int> pa;
typedef vector<int> vec;
void getint(int &v){
    char ch,fu=0;
    for(ch='*'; (ch<'0'||ch>'9')&&ch!='-'; ch=getchar());
    if(ch=='-') fu=1, ch=getchar();
    for(v=0; ch>='0'&&ch<='9'; ch=getchar()) v=v*10+ch-'0';
    if(fu) v=-v;
}
const int MO=1e9+7;
int n;
LL A,B,C,mul,t,ans,fac[500010],inv[500010];
LL pw(LL x,LL y){
	LL t=1;
	for (;y;y>>=1){
		if (y&1) t=t*x%MO;
		x=x*x%MO;
	}
	return t;
}
LL Co(int x,int y){
	return fac[x]*inv[y]%MO*inv[x-y]%MO;
}
int main(){
	fac[0]=1;
	FOR(i,1,500000) fac[i]=fac[i-1]*i%MO;
	inv[500000]=pw(fac[500000],MO-2);
	FORD(i,499999,0) inv[i]=inv[i+1]*(i+1)%MO;
	cin>>n>>A>>B>>C;
	mul=1ll*(A+B+C)*pw(A+B,MO-2)%MO;
	t=A+B;
	A=A*pw(t,MO-2)%MO;
	B=B*pw(t,MO-2)%MO;
	FOR(i,n,n+n-1) (ans+=Co(i-1,n-1)*pw(A,n)%MO*pw(B,i-n)%MO*i)%=MO;
	FOR(i,n,n+n-1) (ans+=Co(i-1,n-1)*pw(B,n)%MO*pw(A,i-n)%MO*i)%=MO;
	ans=ans*mul%MO;
	ans=(ans%MO+MO)%MO;
	cout<<ans<<endl;
	return 0;
}