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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;



public class Main{

    public static void main(String[] args){

        Scanner in =new Scanner(System.in);
        int n=in.nextInt();
        int a=in.nextInt();
        int b=in.nextInt();
        int c=in.nextInt();

        double exvalue=0;
       
        int ncr;
        for(int x=0;x<30;x++){

            ncr = (factorial(n) / (factorial(n - x) * factorial(n)));
            exvalue=exvalue+( (n+x)*ncr*Math.pow(c, x)*(Math.pow(a, n)+Math.pow(b, n)) )/(Math.pow(100, n+x));
        }
        int sol=(int) Math.round(exvalue);
        System.out.print(sol/(Math.pow(10,9)+7));
        
    }


public static int factorial(int n){
    //1
    int fact = 1;
    //2
    for (int i = 1; i <= n; i++) {
        //3
        fact = fact * i;
    }
    //4
    return fact;
}
}