P7801 [COCI 2015/2016 #6] KRUMPIRKO

$\text{Mr. Potato}$ opened two new shops to sell potatoes. He bought $N$ bags of potatoes. The $i$-th bag costs $c_i$ and contains $a_i$ potatoes. He plans to distribute all $N$ bags between the two shops, bag by bag. In each shop, the average price of potatoes equals the **total cost of all bags in that shop divided by the total number of potatoes** in that shop. (Note that it is the number of potatoes, not the number of bags.) Let $P_1$ be the average potato price in the first shop, and $P_2$ be the average potato price in the second shop. $\text{Mr. Potato}$ wants to minimize $P_1 \times P_2$, under the condition that **in at least one shop, the number of bags is exactly $L$**.

The first line contains two integers $N$ and $L$. The second line contains $N$ integers $a_i$. The third line contains $N$ integers $c_i$.

Output one floating-point number on the first line: the minimum value of $P_1 \times P_2$, rounded to three digits after the decimal point.

**Constraints** For $30\%$ of the testdata, $2 \le N \le 20$. For $100\%$ of the testdata, $2 \le N \le 100$, $1 \le L < N$, $1 \le a_i \le 100$, $1 \le c_i \le 10^6$, $\sum\limits_{i=1}^{N} a_i \le 500$. **Source** **Translated from [COCI 2015-2016](https://hsin.hr/coci/archive/2015_2016/) [CONTEST #6](https://hsin.hr/coci/archive/2015_2016/contest6_tasks.pdf) T5 KRUMPIRKO**. **The score of this problem follows the original COCI setting, with a full score of $140$**. Translated by ChatGPT 5