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 $P(T)=\lbrace y|y=p_x,x\in T\rbrace$.
输入解释
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,$\sum n\leq 5\times 10^6$
输出解释
For each test case:
Print one integer in a line, denoting the answer number modulo $998\ 244\ 353$.