Two potato stores

A shopkeeper is opening two stores that sell potatoes. He buys potatoes from $N$ farmers. Farmer $i$ sells one bag holding $a_i$ potatoes for a total price of $c_i$. The shopkeeper buys every bag and puts each bag, whole, into one of the two stores.

Write $P_1$ for the average potato price in the first store and $P_2$ for the average potato price in the second store. The average potato price in a store is the sum of the bag prices in that store divided by the number of potatoes in that store. Because of shipping and stock limits, the shopkeeper wants the product of $P_1$ and $P_2$ to be as small as possible.

In the chosen division, at least one of the two stores must hold exactly $L$ bags.

The first line contains two integers $N$ and $L$ ($2 \le N \le 100$, $1 \le L < N$), the number of bags and the number of bags that at least one store must hold.

The second line contains $N$ integers $a_i$ ($1 \le a_i \le 100$), separated by spaces.

The third line contains $N$ integers $c_i$ ($1 \le c_i \le 1\,000\,000$), separated by spaces.

The sum of all $a_i$ is at most 500.

Print, on a single line, the smallest possible product of $P_1$ and $P_2$ with exactly three digits after the decimal point. Round the fourth decimal digit half up and pad with zeros so that three digits always appear.