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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

long mod = 1000000007;

int inv_mod(int a, int m)
{
    int b, x, u, q, abs_m, tmp;

    abs_m = (m < 0) ? -m : m;
    b = m;
    x = 1;
    u = 0;
    while (b > 0)
    {
        q = a / b;
        tmp = u;
        u = x - q * u;
        x = tmp;
        tmp = b;
        b = a - q * b;
        a = tmp;
    }

    return (x < 0) ? abs_m + x : x;
}

int main() {
    int N, A, B, C;
    double ans = 0;

    scanf("%d%d%d%d", &N, &A, &B, &C);
    // printf("%d %d %d %d\n", N, A, B, C);

    int kati = A + B;
    // printf("%d", kati);
    long kitai = (100 / kati) * N;

    // printf("%ld\n", kitai);
    ans = (long)inv_mod(kitai, mod);
    printf("%ld", (long)ans);

    return 0;
}