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.

1 25 25 50

2

Since $N=1$, they will repeat the game until one of them wins. The expected number of games played is $2$.

4 50 50 0

312500008

$C$ may be $0$.

1 100 0 0

1

$B$ may also be $0$.

100000 31 41 28

104136146