Metro#8777

Metro

1 second

64 megabytes

Very easy

Semyon, Yura, and the other olympiad participants are traveling by metro. In total, there are $n$ people making the journey, and each person needs to take $m$ trips.

The metro offers three types of tickets:

A single-trip ticket, costing $a$ hryvnias.
An unlimited ticket for one person, costing $b$ hryvnias.
A group unlimited ticket for exactly $k$ people, costing $c$ hryvnias.

Note that the group ticket must be used by exactly $k$ people, no more, no less.

Your task is to calculate the minimum total cost for all the necessary tickets.

Input

The first line contains three integers $n$ , $m$ , and $k$ ( $1 ⩽ n, m, k ⩽ 1000$ 1 \leqslant n, m, k \leqslant 1000).

The second line contains three integers $a$ , $b$ , and $c$ ( $1 ⩽ a, b, c ⩽ 1000$ 1 \leqslant a, b, c \leqslant 1000).

Output

Output a single integer representing the minimum total cost of the tickets.

Examples

Example 1

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1 ⩽ n, m, k ⩽ 1000

1 ⩽ a, b, c ⩽ 1000