Roughly Sorted

AtCoder

IDagc054_c

Time2000ms

Memory256MB

Difficulty—

Snuke received a permutation $P=(P_1,P_2,\cdots,P_N)$ of $(1,\ 2,\ ...\ N)$ and an integer $K$. He did some number of swaps of two adjacent elements in $P$ so that the following condition would be satisfied. * For each $1 \leq i \leq N$, there are at most $K$ indices $j$ such that $1 \leq j< i$ and $P_j>P_i$. Here, he did the **minimum** number of swaps needed to achieve this condition. Afterward, he has forgotten the original permutation he received. Given the permutation $P'$ after the swaps, find the number, modulo $998244353$, of permutations that the original permutation $P$ could be. ## Constraints * $2 \leq N \leq 5000$ * $1 \leq K \leq N-1$ * $1 \leq P'_i \leq N$ * $P'_i \neq P'_j$ ($i \neq j$) * For each $1 \leq i \leq N$, there is at most $K$ indices $j$ such that $1 \leq j< i$ and $P'_j>P'_i$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $P'_1$ $P'_2$ $\cdots$ $P'_N$ [samples]

Samples

Input #1

3 1
3 1 2

Output #1

2

$P$ could be one of the following two permutations.

*   $P=(3,1,2)$: The minimum number of swaps needed is $0$. After zero swaps, the permutation is equal to $P'$.
*   $P=(3,2,1)$: The minimum number of swaps needed is $1$: swapping $P_2$ and $P_3$ results in $P=(3,1,2)$, which satisfies the condition and is equal to $P'$.

Input #2

4 3
4 3 2 1

Output #2

Input #3

5 2
4 2 1 5 3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Roughly Sorted",
    "description": {
      "content": "Snuke received a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,\\ 2,\\ ...\\ N)$ and an integer $K$. He did some number of swaps of two adjacent elements in $P$ so that the following condition would be sat",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc054_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke received a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,\\ 2,\\ ...\\ N)$ and an integer $K$. He did some number of swaps of two adjacent elements in $P$ so that the following condition would be sat...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments