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G - Minimum Permutation

Score : $600$ points

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.

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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:

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

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4 3
2 3 1 3

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 $(2, 1, 3)$.

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4 4
2 3 1 4

2 3 1 4

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

3 5 8 10 9 6 1 4 2 7