The Greatest Two

AtCoder

IDwtf22_day2_b

Time5000ms

Memory256MB

Difficulty—

You are given integers $N$ and $K$, and a permutation $P=(P_1,P_2,\cdots,P_N)$ of $(1,2,\cdots,N)$. You can perform the following operation any number of times, possibly zero. * Choose an integer $i$ ($1 \leq i \leq N-K+1$). Swap the values of the two greatest elements among $P_i,P_{i+1},\cdots,P_{i+K-1}$. Find the number, modulo $998244353$, of permutations that $P$ can be after your operations. ## Constraints * $2 \leq K \leq N \leq 250000$ * $(P_1,P_2,\cdots,P_N)$ is a permutation of $(1,2,\cdots,N)$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $P_1$ $P_2$ $\cdots$ $P_N$ [samples]

Samples

Input #1

3 3
2 3 1

Output #1

2

In this case, the operation can only be performed with $i=1$.
After one operation, the two greatest elements among $P_1,P_2,P_3$, which are $P_2=3$ and $P_1=2$, have their values swapped, and you have $P=(3,2,1)$. After one more operation, you have $P=(2,3,1)$.
Thus, there are two permutations, $P=(2,3,1),(3,2,1)$, that $P$ can be after your operations.

Input #2

3 2
1 3 2

Output #2

Input #3

10 5
1 2 3 4 5 6 7 8 9 10

Output #3

Input #4

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

Output #4

API Response (JSON)

{
  "problem": {
    "name": "The Greatest Two",
    "description": {
      "content": "You are given integers $N$ and $K$, and a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$. You can perform the following operation any number of times, possibly zero. *   Choose an integer $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "wtf22_day2_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given integers $N$ and $K$, and a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$.\nYou can perform the following operation any number of times, possibly zero.\n\n*   Choose an integer $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments