Population of Robots

Population refers to a group of individuals of the same species living in a specific area, capable of interbreeding, sharing a common origin and genetic makeup, and somewhat isolated from other populations of the same species (definition sourced from Wikipedia, not directly related to the task).

Consider a scenario where A robots produce C robots each year, and B robots produce D robots each year. Initially, there are N robots. Your task is to determine the maximum number of robots that can exist after K years.

Input

The input consists of six integers: A, B, C, D, N, K, where each value satisfies 1 ≤ A, B, C, D, N, K ≤ 10.

Output

The output should be a single integer representing the maximum number of robots possible after K years.

Examples