Minimum Permutation

AtCoder

IDabc299_g

Time2000ms

Memory256MB

Difficulty—

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: $N$ $M$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

4 3
2 3 1 3

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 $(2, 1, 3)$.

Input #2

4 4
2 3 1 4

Output #2

2 3 1 4

Input #3

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

Output #3

3 5 8 10 9 6 1 4 2 7

API Response (JSON)

{
  "problem": {
    "name": "Minimum Permutation",
    "description": {
      "content": "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 o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc299_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 $A$.\nAmong the length-$M$ subsequences of $A$ where each o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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