Ex - Rearranging Problem

AtCoder

IDabc247_h

Time4000ms

Memory256MB

Difficulty—

There are $N$ people called Person $1$, Person $2$, $\dots$, Person $N$, lined up in a row in the order of $(1,2,\dots,N)$ from the front. Person $i$ is wearing Color $c_i$. Takahashi repeated the following operation $K$ times: choose two People $i$ and $j$ arbitrarily and swap the positions of Person $i$ and Person $j$. After the $K$ operations have ended, the color that the $i$\-th person from the front is wearing coincided with $c_i$, for every integer $i$ such that $1 \leq i \leq N$. How many possible permutations of people after the $K$ operations are there? Find the count modulo $998244353$. ## Constraints * $2 \leq N \leq 200000$ * $1 \leq K \leq 10^9$ * $1 \leq c_i \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $c_1$ $c_2$ $\dots$ $c_N$ [samples]

Samples

Input #1

4 1
1 1 2 1

Output #1

3

Here is a comprehensive list of possible Takahashi's operations and permutations of people after each operation.

*   Swap the positions of Person $1$ and Person $2$, resulting in a permutation $(2, 1, 3, 4)$.
*   Swap the positions of Person $1$ and Person $4$, resulting in a permutation $(4, 2, 3, 1)$.
*   Swap the positions of Person $2$ and Person $4$, resulting in a permutation $(1, 4, 3, 2)$.

Input #2

3 3
1 1 2

Output #2

1

Here is an example of a possible sequence of Takahashi's operations.

*   In the $1$\-st operation, he swaps the positions of Person $1$ and Person $3$, resulting in a permutation $(3, 2, 1)$.  
    In the $2$\-nd operation, he swaps the positions of Person $2$ and Person $3$, resulting in a permutation $(2, 3, 1)$.  
    In the $3$\-rd operation, he swaps the positions of Person $1$ and Person $3$, resulting in a permutation $(2, 1, 3)$.

Note that, during the sequence of operations, the color that the $i$\-th person from the front is wearing does not necessarily coincide with $c_i$.

Input #3

10 4
2 7 1 8 2 8 1 8 2 8

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Ex - Rearranging Problem",
    "description": {
      "content": "There are $N$ people called Person $1$, Person $2$, $\\dots$, Person $N$, lined up in a row in the order of $(1,2,\\dots,N)$ from the front. Person $i$ is wearing Color $c_i$.   Takahashi repeated the f",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc247_h"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people called Person $1$, Person $2$, $\\dots$, Person $N$, lined up in a row in the order of $(1,2,\\dots,N)$ from the front. Person $i$ is wearing Color $c_i$.  \nTakahashi repeated the f...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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