K Derangement

AtCoder

IDarc144_c

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $N$ and $K$. Find the lexicographically smallest permutation $A = (A_1, A_2, \ldots, A_N)$ of the integers from $1$ through $N$ that satisfies the following condition: * $\lvert A_i - i\rvert \geq K$ for all $i$ ($1\leq i\leq N$). If there is no such permutation, print `-1`. What is lexicographical order on sequences?The following is an algorithm to determine the lexicographical order between different sequences $S$ and $T$. Below, let $S_i$ denote the $i$\-th element of $S$. Also, if $S$ is lexicographically smaller than $T$, we will denote that fact as $S \lt T$; if $S$ is lexicographically larger than $T$, we will denote that fact as $S \gt T$. 1. Let $L$ be the smaller of the lengths of $S$ and $T$. For each $i=1,2,\dots,L$, we check whether $S_i$ and $T_i$ are the same. 2. If there is an $i$ such that $S_i \neq T_i$, let $j$ be the smallest such $i$. Then, we compare $S_j$ and $T_j$. If $S_j$ is less than $T_j$ (as a number), we determine that $S \lt T$ and quit; if $S_j$ is greater than $T_j$, we determine that $S \gt T$ and quit. 3. If there is no $i$ such that $S_i \neq T_i$, we compare the lengths of $S$ and $T$. If $S$ is shorter than $T$, we determine that $S \lt T$ and quit; if $S$ is longer than $T$, we determine that $S \gt T$ and quit. ## Constraints * $2\leq N\leq 3\times 10^5$ * $1\leq K\leq N - 1$ ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

3 1

Output #1

2 3 1

Two permutations satisfy the condition: $(2, 3, 1)$ and $(3, 1, 2)$. For instance, the following holds for $(2, 3, 1)$:

*   $\lvert A_1 - 1\rvert = 1 \geq K$
*   $\lvert A_2 - 2\rvert = 1 \geq K$
*   $\lvert A_3 - 3\rvert = 2 \geq K$

Input #2

8 3

Output #2

4 5 6 7 8 1 2 3

Input #3

8 6

Output #3

\-1

API Response (JSON)

{
  "problem": {
    "name": "K Derangement",
    "description": {
      "content": "You are given positive integers $N$ and $K$. Find the lexicographically smallest permutation $A = (A_1, A_2, \\ldots, A_N)$ of the integers from $1$ through $N$ that satisfies the following condition: ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc144_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given positive integers $N$ and $K$. Find the lexicographically smallest permutation $A = (A_1, A_2, \\ldots, A_N)$ of the integers from $1$ through $N$ that satisfies the following condition:\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments