Score : $600$ points

问题描述

我们有一个长度为 $N$ 的整数序列 $A$，其中的整数都在 $1$ 到 $M$ 之间。在此条件下，从 $1$ 到 $M$ 的每个整数至少在序列 $A$ 中出现一次。

在 $A$ 的所有长度为 $M$ 的子序列中，每个整数 $1, \ldots, M$ 各恰好出现一次，请找出字典序最小的那个子序列。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

We have a sequence $A$ of length $N$ consisting of integers between $1$ and $M$. Here, every integer from $1$ to $M$ appears at least once in $A$.

Among the length-$M$ subsequences of $A$ where each of $1, \ldots, M$ appears once, find the lexicographically smallest one.

Constraints

• $1 \leq M \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq M$
• Every integer between $1$ and $M$, inclusive, appears at least once in $A$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $A_2$ $\ldots$ $A_N$

Output

Let $B_1, \ldots, B_M$ be the sought subsequence, and print it in the following format:

$B_1$ $B_2$ $\ldots$ $B_M$

Sample Input 1

4 3
2 3 1 3

Sample Output 1

2 1 3

The length-$3$ subsequences of $A$ where each of $1, 2, 3$ appears once are $(2, 3, 1)$ and $(2, 1, 3)$. The lexicographically smaller among them is $(2, 1, 3)$.

Sample Input 2

4 4
2 3 1 4

Sample Output 2

2 3 1 4

Sample Input 3

20 10
6 3 8 5 8 10 9 3 6 1 8 3 3 7 4 7 2 7 8 5

Sample Output 3

3 5 8 10 9 6 1 4 2 7

update @ 2024/3/10 12:25:08