Preparing NOJ # Beat the Monster

5000ms 131072K

## Description:

LYA is playing a RPG game and he needs to kill a monster. The monster's health is $h$, LYA's attack is $a$ and the monster's defence is $d$. So every time the monster's health will decrease $a - d$. And each time LYA has a $\frac{p}{q}$ probability to trigger a critical hit, which will double LYA's attack, and the monster's health will decrease $2a - d$.
Since the monster has a huge health, he wants you to help him find out the expectation of the time he need to kill the monster.

## Input:

One line with 5 space-separated integers $h, a, d, p, q (1 \le h \le 5 \cdot 10^7, 0 \le d \lt a \le 10^5, 1 \le p \le q \le 10^7)$.

## Output:

Output answer in the fraction modulo $10^7 + 19$, that is, if the answer is $\frac{P}{Q}$, you should output $P \cdot Q^{-1}$ modulo $10^7+19$, where $Q^{-1}$ denotes the multiplicative inverse of $Q$ modulo $10^7+19$.

## Sample Input:

15 5 0 1 2

## Sample Output:

2500007

Info Provider NOJ

Code NOJ2379

Tags

Submitted 122

Passed 40

AC Rate 32.79%

Date 08/13/2019 00:47:12

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