AtCoder Beginner Contest 247
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Problem Statement
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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 $998244353$.
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Constraints
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$2 \leq N \leq 200000$$1 \leq K \leq 10^9$$1 \leq c_i \leq N$- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N K
c_1 c_2 \dots c_N翻译中…
Output
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Print the answer.
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样例
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
132
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。