8534: Count Set

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

Where P(T)means P(T)={y∣y=px,x∈T}.

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 P1,P2,⋯,Pn,(1≤Pi≤n), denoting the given permutation.

 n1≤n≤5×105,0≤k≤n.

For all test cases 6∑n≤5×106

For each test case:

Print one integer in a line, denoting the answer number modulo $998244353$.

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