Background

Translated from ROIR 2021 Day 1 T1 Два станка。

Problem Description

There are two machines. The first machine needs $a$ minutes to start up, and then it produces $x$ parts per minute. The second machine needs $b$ minutes to start up, and then it produces $y$ parts per minute. The two machines cannot be in the startup process at the same time.

You have a total of $k$ minutes. Find the maximum number of parts that can be produced.

Input Format

The first line contains an integer $k$.

The second line contains two integers $a, x$.

The third line contains two integers $b, y$.

Output Format

Output a single integer: the maximum number of parts that can be produced.

20
10 4
5 3

65

Hint

[Sample Explanation]:

If you start the second machine first and then start the first machine, you can produce $3\times 15+5\times 4=65$ parts.

[Constraints]:

For all subtasks, $0\le k,a,x,b,y\le 10^9$. The final answer can be stored in long long.

Translated by ChatGPT 5