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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

m = 10**9+7
def inv(x):
  m = 10**9+7
  t = x
  y = 1
  while True:
    if t == 1:
      break
    y *= m // t
    t = m % t
    y *= -1
    y %= m
  return y
import math
def cc(x,y):
  xx = math.factorial(x) % m
  yy = math.factorial(y) % m
  xy = math.factorial(x-y) % m
  return xx * inv(yy) * inv(xy) % m
n,a,b,c = map(int,input().split())
d = 100 - c
awin = a * inv(d)
bwin = b * inv(d)
asc = 0
bsc = 0
for i in range(n):
  p = cc(n-1+i,i) * awin**(n-1) * bwin**i * (n+i)
  asc += p
  asc %= m
for i in range(n):
  p = cc(n-1+i,i) * awin**i * bwin**(n-1) * (n+i)
  bsc += p
  bsc %= m
sc = asc * awin + bsc * bwin
sc %= m
scn = sc * 100 * inv(d)
scn %= m
print(scn)