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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val mod = 1000000007
    fun pow(x: Long, y: Long): Long {
        if (y == 0L) {
            return 1L
        } else if (y % 2 == 0L) {
            val a = pow(x, y / 2)
            return a * a % mod
        } else {
            val a = pow(x, y / 2)
            return a * a % mod * x % mod
        }
    }

    fun div(x: Long, y: Long): Long {
        return x * pow(y, (mod - 2).toLong()) % mod
    }

    val (n, a, b, c) = readLine()!!.split(' ').map(String::toLong)
    val aPct = div(a, a + b)
    val bPct = div(b, a + b)

    var comb = 1L
    var ans = 0L
    for (i in 0 until n) {
        ans += pow(aPct, n) * pow(bPct, i) % mod * comb % mod * (n + i) % mod
        ans %= mod.toLong()
        ans += pow(bPct, n) * pow(aPct, i) % mod * comb % mod * (n + i) % mod
        ans %= mod.toLong()
        comb = div(comb * (n + i) % mod, (i + 1))
    }
    val l = div(a + b, 100)
    println(div(ans, l))
}