CF1468L.Prime Divisors Selection

Suppose you have a sequence of $k$ integers $A = [a_1, a_2, \dots , a_k]$ where each $a_i \geq 2$. A sequence of prime integers $P = [p_1, p_2, \dots, p_k]$ is called suitable for the sequence $A$ if $a_1$ is divisible by $p_1$, $a_2$ is divisible by $p_2$ and so on.

A sequence of prime integers $P$ is called friendly if there are no unique integers in this sequence.

A sequence $A$ is called ideal, if each sequence $P$ that is suitable for $A$ is friendly as well (i. e. there is no sequence $P$ that is suitable for $A$, but not friendly). For example, the sequence $[2, 4, 16]$ is ideal, while the sequence $[2, 4, 6]$ is not ideal (there exists a sequence $P = [2, 2, 3]$ which is suitable for $A$, but not friendly).

You are given $n$ different integers $x_1$, $x_2$, ..., $x_n$. You have to choose exactly $k$ of them in such a way that they form an ideal sequence, or report that it is impossible. Note that no integer can be chosen more than once.

假设你有一个由 $k$ 个整数构成的序列 $A = [a_1, a_2, \dots , a_k]$，其中每个 $a_i \geq 2$。一个由素数组成的序列 $P = [p_1, p_2, \dots, p_k]$ 被称为适用于序列 $A$，当且仅当 $a_1$ 被 $p_1$ 整除、$a_2$ 被 $p_2$ 整除，依此类推。

一个由素数组成的序列 $P$ 被称为友好的，当且仅当该序列中不存在唯一的（即只出现一次的）整数。

若序列 $A$ 满足：每一个适用于 $A$ 的序列 $P$ 都是友好的（即：不存在某个适用于 $A$ 却不友好的序列 $P$），则称 $A$ 为理想的。例如，序列 $[2, 4, 16]$ 是理想的，而序列 $[2, 4, 6]$ 不是理想的（因为存在一个适用于 $A$ 却不友好的序列 $P = [2, 2, 3]$）。

现给你 $n$ 个互不相同的整数 $x_1$, $x_2$, ..., $x_n$。你需要从中恰好选出 $k$ 个数，使得它们构成一个理想的序列；若不可能，则报告无解。注意：每个整数至多只能被选一次。

The first line contains two integers $n$ and $k$ ($1 \leq k \leq n \leq 1000$).

The second line contains $n$ pairwise distinct integers $x_1$, $x_2$, ..., $x_n$ ($2 \leq x_i \leq 10^{18}$).

第一行包含两个整数 $n$ 和 $k$（$1 \leq k \leq n \leq 1000$）。

第二行包含 $n$ 个两两不同的整数 $x_1$, $x_2$, ..., $x_n$（$2 \leq x_i \leq 10^{18}$）。

If it is impossible to choose exactly $k$ integers from $x_1$, $x_2$, ..., $x_n$ in such a way that the chosen integers form an ideal sequence, print $0$.

Otherwise, print $k$ pairwise distinct integers — the elements of the chosen ideal sequence. If there are multiple answers, print any of them.

如果无法从 $x_1$, $x_2$, ..., $x_n$ 中恰好选出 $k$ 个整数，使得所选整数构成一个理想序列，则输出 $0$。

否则，输出 $k$ 个两两不同的整数——即所选理想序列的元素。若存在多个答案，输出任意一个即可。