Metro

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 Format

The first line contains three integers n, m, and k (1 ⩽ n, m, k ⩽ 1,000).

The second line contains three integers a, b, and c (1 ⩽ a, b, c ⩽ 1,000).

Output Format

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

Examples