Robots#363

Robots

1 second

64 megabytes

Hard

A colony of robots operates according to the following rules:

In one year, $M$ robots produce $A$ new robots, and $N$ robots produce $B$ new robots.
Robots always try to produce as many new robots as possible.

Initially, there are $K$ robots in the colony. How many robots will there be after $T$ years? (All input values do not exceed $100$ , and the result does not exceed $2000000000$ .)

Input

A single line contains the integers $M$ , $A$ , $N$ , $B$ , $K$ , $T$ separated by spaces.

Output

Output a single integer — the required number of robots.

Examples

Example 1

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