K Swap

AtCoder

IDabc254_c

Time2000ms

Memory256MB

Difficulty—

We have a sequence of length $N$: $A=(a_1,\ldots,a_N)$. Additionally, you are given an integer $K$. You can perform the following operation zero or more times. * Choose an integer $i$ such that $1 \leq i \leq N-K$, then swap the values of $a_i$ and $a_{i+K}$. Determine whether it is possible to sort $A$ in ascending order. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq K \leq N-1$ * $1 \leq a_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $a_1$ $\ldots$ $a_N$ [samples]

Samples

Input #1

5 2
3 4 1 3 4

Output #1

Yes

The following sequence of operations sorts $A$ in ascending order.

*   Choose $i=1$ to swap the values of $a_1$ and $a_3$. $A$ is now $(1,4,3,3,4)$.
*   Choose $i=2$ to swap the values of $a_2$ and $a_4$. $A$ is now $(1,3,3,4,4)$.

Input #2

5 3
3 4 1 3 4

Output #2

No

Input #3

7 5
1 2 3 4 5 5 10

Output #3

Yes

No operations may be needed.

API Response (JSON)

{
  "problem": {
    "name": "K Swap",
    "description": {
      "content": "We have a sequence of length $N$: $A=(a_1,\\ldots,a_N)$. Additionally, you are given an integer $K$. You can perform the following operation zero or more times. *   Choose an integer $i$ such that $1 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc254_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence of length $N$: $A=(a_1,\\ldots,a_N)$. Additionally, you are given an integer $K$.\nYou can perform the following operation zero or more times.\n\n*   Choose an integer $i$ such that $1 ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments