LIS to Original Sequence

AtCoder

IDarc125_c

Time2000ms

Memory256MB

Difficulty—

Given are an integer $N$ and a monotonically increasing sequence of $K$ integers $A=(A_1,A_2,\cdots,A_K)$. Find the **lexicographically smallest** permutation $P$ of $(1,2,\cdots,N)$ that satisfies the following condition. * $A$ is a longest increasing subsequence of $P$ (a monotonically increasing subsequence of $P$ with the maximum possible length). It is fine if $P$ has multiple longest increasing subsequences, one of which is $A$. From the Constraints of this problem, we can prove that there always exists a $P$ that satisfies the condition. ## Constraints * $1 \leq K \leq N \leq 2 \times 10^5$ * $1 \leq A_1 < A_2 < \cdots < A_K \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\cdots$ $A_K$ [samples]

Samples

Input #1

3 2
2 3

Output #1

2 1 3

$A$ is a longest increasing subsequence of $P$ when $P=(2,1,3),(2,3,1)$. The answer is the lexicographically smallest of the two, or $(2,1,3)$.

Input #2

5 1
4

Output #2

5 4 3 2 1

API Response (JSON)

{
  "problem": {
    "name": "LIS to Original Sequence",
    "description": {
      "content": "Given are an integer $N$ and a monotonically increasing sequence of $K$ integers $A=(A_1,A_2,\\cdots,A_K)$. Find the **lexicographically smallest** permutation $P$ of $(1,2,\\cdots,N)$ that satisfies th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc125_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are an integer $N$ and a monotonically increasing sequence of $K$ integers $A=(A_1,A_2,\\cdots,A_K)$. Find the **lexicographically smallest** permutation $P$ of $(1,2,\\cdots,N)$ that satisfies th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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