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 Rust (1.15.1) (judge verdict: Accepted)

// https://atcoder.jp/contests/m-solutions2019/tasks/m_solutions2019_c
//
#![allow(unused_imports)]
use std::io::*;
use std::io::Write;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

// Input macros.
// Original by tanakh: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };

    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, [ next / $t:tt ]) => {
        {
            let len = read_value!($iter, usize);
            (0..len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
        }
    };

    ($iter:expr, switch) => {
        {
            let ty = read_value!($iter, i32);
            if ty == 1 {
                vec![ty, read_value!($iter, i32), read_value!($iter, i32)]
            } else if ty == 2 {
                vec![ty, read_value!($iter, i32)]
            } else {
                vec![ty, read_value!($iter, i32)]
            }
        }
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! read_line {
    ($t:tt) => {
        {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            s.trim_right().parse::<$t>().unwrap()
        }
    }
}

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! join {
    ($t:expr, $glue:expr) => {
        $t.into_iter().map(|w| w.to_string()).collect::<Vec<_>>().join($glue)
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

// ===

struct Combination {
    fact: Vec<i64>,
    invfact: Vec<i64>,
}

impl Combination {
    fn inv(a: i64) -> i64 {
        Combination::pow(a, MOD - 2)
    }

    fn pow(a: i64, p: i64) -> i64 {
        let mut p = p;
        let mut aa = a;
        let mut ret = 1;
        while p >= 1 {
            if p & 1 == 1 {
                ret *= aa;
                ret %= MOD;
            }
            p >>= 1;
            aa = aa * aa % MOD;
        }
        ret
    }

    fn new(upto: usize) -> Self {
        let mut fact = vec![0; upto];
        let mut invfact = vec![0; upto];

        fact[0] = 1;
        for i in 1..upto {
            fact[i] = fact[i - 1] * (i as i64) % MOD;
        }

        invfact[upto - 1] = Combination::inv(fact[upto - 1]);
        invfact[0] = 1;
        for i in (1..upto - 1).rev() {
            invfact[i] = invfact[i + 1] * ((i + 1) as i64) % MOD;
        }

        Combination {
            fact: fact,
            invfact: invfact,
        }
    }

    fn comb(&self, n: usize, r: usize) -> i64 {
        if r < 0 || r > n {
            return 0;
        }
        self.fact[n] * self.invfact[r] % MOD * self.invfact[n - r] % MOD
    }
}

//===

const MOD: i64 = 1e9 as i64 + 7;

fn main() {
    input! {
        n: usize,
        a: i64, b: i64, c: i64
    };

    let mut comb = Combination::new(n*2+100);
    let mut total = 0;

    let mut a_ab = a * Combination::inv(a + b) % MOD;
    let mut b_ab = b * Combination::inv(a + b) % MOD;
    let mut apow = vec![1; n+1];
    let mut bpow = vec![1; n+1];
    for i in 1..n+1 {
        apow[i] = apow[i-1] * a_ab % MOD;
        bpow[i] = bpow[i-1] * b_ab % MOD;
    }

    let mut draw_inv = 100 * Combination::inv(100 - c) % MOD;
    for i in 0..n {
        let game = n + i;
        let awin = comb.comb(game-1, n-1) * apow[n] % MOD * bpow[i] % MOD;
        let bwin = comb.comb(game-1, n-1) * apow[i] % MOD * bpow[n] % MOD;
        total += (game as i64) * (awin + bwin) % MOD;
        total %= MOD;
    }

    println!("{}", total * draw_inv % MOD);
}