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: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner stdIn = new Scanner(System.in);
        
        int count = 0;
        
        int n = stdIn.nextInt();
        double tw = stdIn.nextInt();
        double aw = stdIn.nextInt();
        
        double tc = 0;
        double ac = 0;
        
        if(tw != 0){
            tc = (100 / tw)* n;
        }
        
        if(aw != 0){
            ac = (100 / aw)* n;
        }
        
        System.out.println(tc);
        System.out.println(ac);
        
        if(tc != 0 && ac != 0){
            System.out.printf("%.0f", (tc + ac) / 4);
        }else if(tc == 0){
            System.out.printf("%.0f", ac);
        }else{
            System.out.printf("%.0f", tc);
        }
    }
}