Count Set

Given a permutation $p$ of $\{1,2,\cdots, n\}$ and a non-negative integer $k$. Please calculate the number of subsets $T$ of $\{1,2,3,4,...n\}$ satisfying $|T|=k$ and $|P(T)\cap T|=0$.

Where $P(T)$ means $P(T)=\lbrace y|y=p_x,x\in T\rbrace$.

Each test contains multiple test cases. The first line contains the number of test cases $(1 \le T \le 15)$. Description of the test cases follows.

The first line contains two separated integers $n$, $k$.

The second line contains $n$ integers $P_1, P_2, \cdots, P_n\,(1\le P_i \le n)$, denoting the given permutation.

$1\leq n\leq 5 \times 10^5, 0\leq k\leq n$.

For all test cases,$\sum n\leq 5\times 10^6$

For each test case:

Print one integer in a line, denoting the answer number modulo $998\ 244\ 353$.

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

5
5
40

2022“杭电杯”中国大学生算法设计超级联赛（5）