Description

Input

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.

Output

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

Note

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.