410256: GYM103993 K FTL

Monocarp is playing a video game. In the game, he controls a spaceship and has to destroy an enemy spaceship.

Monocarp has two lasers installed on his spaceship. Both lasers $$$1$$$ and $$$2$$$ have two values:

• $$$p_i$$$ — the power of the laser;
• $$$t_i$$$ — the reload time of the laser.

When a laser is fully charged, Monocarp can either shoot it or wait for the other laser to charge and shoot both of them at the same time.

An enemy spaceship has $$$h$$$ durability and $$$s$$$ shield capacity. When Monocarp shoots an enemy spaceship, it receives $$$(P - s)$$$ damage (i. e. $$$(P - s)$$$ gets subtracted from its durability), where $$$P$$$ is the total power of the lasers that Monocarp shoots (i. e. $$$p_i$$$ if he only shoots laser $$$i$$$ and $$$p_1 + p_2$$$ if he shoots both lasers at the same time). An enemy spaceship is considered destroyed when its durability becomes $$$0$$$ or lower.

Initially, both lasers are zero charged.

What's the lowest amount of time it can take Monocarp to destroy an enemy spaceship?

The first line contains two integers $$$p_1$$$ and $$$t_1$$$ ($$$2 \le p_1 \le 5000$$$; $$$1 \le t_1 \le 10^{12}$$$) — the power and the reload time of the first laser.

The second line contains two integers $$$p_2$$$ and $$$t_2$$$ ($$$2 \le p_2 \le 5000$$$; $$$1 \le t_2 \le 10^{12}$$$) — the power and the reload time of the second laser.

The third line contains two integers $$$h$$$ and $$$s$$$ ($$$1 \le h \le 5000$$$; $$$1 \le s < \min(p_1, p_2)$$$) — the durability and the shield capacity of an enemy spaceship. Note that the last constraint implies that Monocarp will always be able to destroy an enemy spaceship.

Print a single integer — the lowest amount of time it can take Monocarp to destroy an enemy spaceship.

5 10
4 9
16 1

20

10 1
5000 100000
25 9

25

In the first example, Monocarp waits for both lasers to charge, then shoots both lasers at $$$10$$$, they deal $$$(5 + 4 - 1) = 8$$$ damage. Then he waits again and shoots lasers at $$$20$$$, dealing $$$8$$$ more damage.

In the second example, Monocarp doesn't wait for the second laser to charge. He just shoots the first laser $$$25$$$ times, dealing $$$(10 - 9) = 1$$$ damage each time.