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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;

class C
{
	static void Main()
	{
		var M = 1000000007;
		var h = Console.ReadLine().Split().Select(int.Parse).ToArray();
		var n = h[0];
		long c_ = 100 * ModInv(100 - h[3], M) % M, a = h[1] * c_ % M * ModInv(100, M) % M, b = h[2] * c_ % M * ModInv(100, M) % M;

		long e = 0, ncr = 1, pa = ModPow(a, n, M), pb = ModPow(b, n, M);
		for (var i = n; i < 2 * n; i++, ncr = ncr * (i - 1) % M * ModInv(i - n, M) % M, pa = pa * b % M, pb = pb * a % M) e = (e + i * ncr % M * (pa + pb)) % M;
		Console.WriteLine(c_ * e % M);
	}

	static long ModPow(long b, int i, int mod)
	{
		for (var r = 1L; ; b = b * b % mod)
		{
			if (i % 2 > 0) r = r * b % mod;
			if ((i /= 2) < 1) return r;
		}
	}
	static long ModInv(int x, int p) => ModPow(x, p - 2, p);
}