Sliding Window Sort 2

AtCoder

IDarc165_b

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P=(P_1,P_2,\dots,P_N)$ of integers from $1$ to $N$ and an integer $K$. Consider the following operation on the permutation $P$. * Choose an integer $i$ such that $1 \leq i \leq N-K+1$, and sort $P_i,P_{i+1},\dots,P_{i+K-1}$ in ascending order. That is, let $(x_1,x_2,\dots,x_K)$ be the result of arranging $P_i,P_{i+1},\dots,P_{i+K-1}$ in order from smallest to largest, and replace $P_{i+j-1}$ with $x_j$ for each $1 \leq j \leq K$. Find the lexicographically largest permutation that can be obtained by performing the above operation on $P$ exactly once. What is lexicographical order on sequences?A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is **lexicographically smaller** than $T = (T_1,T_2,\ldots,T_{|T|})$ when 1. or 2. below holds. Here, $|S|$ and $|T|$ denotes the lengths of $S$ and $T$, respectively. 1. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$. 2. There is an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ that satisfy both of the following: * $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$. * $S_i$ is smaller than $T_i$ (as a number). ## Constraints * $1 \leq K \leq N \leq 2 \times 10^5$ * $1 \leq P_i \leq N$ * $(P_1,P_2,\dots,P_N)$ is a permutation of integers from $1$ to $N$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $P_1$ $P_2$ $\dots$ $P_N$ [samples]

Samples

Input #1

4 3
2 1 4 3

Output #1

2 1 3 4

If you perform the operation with $i=1$, we have $(P_1,P_2,P_3)=(2,1,4)$, and sorting it in ascending order yields $(1,2,4)$. Thus, the operation replaces $P_1,P_2,P_3$ with $1,2,4$, respectively, resulting in $P=(1,2,4,3)$. Similarly, if you perform the operation with $i=2$, $P$ becomes $(2,1,3,4)$.
The lexicographically greater between them is $(2,1,3,4)$, so the answer is $(2,1,3,4)$.

Input #2

5 1
3 1 4 2 5

Output #2

3 1 4 2 5

Input #3

20 7
9 4 3 1 11 12 13 15 17 7 2 5 6 20 19 18 8 16 14 10

Output #3

9 4 3 1 11 12 13 15 17 7 2 5 6 8 18 19 20 16 14 10

API Response (JSON)

{
  "problem": {
    "name": "Sliding Window Sort 2",
    "description": {
      "content": "You are given a permutation $P=(P_1,P_2,\\dots,P_N)$ of integers from $1$ to $N$ and an integer $K$. Consider the following operation on the permutation $P$. *   Choose an integer $i$ such that $1 \\le",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc165_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation $P=(P_1,P_2,\\dots,P_N)$ of integers from $1$ to $N$ and an integer $K$.\nConsider the following operation on the permutation $P$.\n\n*   Choose an integer $i$ such that $1 \\le...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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