Parents

You are given a rooted tree whose nodes each carry an integer value. The value of a set of nodes is the sum of the values of the nodes it contains.

For a positive integer $K$, a $K$-anti-parental subset is a set of nodes that satisfies both of the following:

1. it contains between $1$ and $K$ nodes, inclusive;
2. no node in the set is the parent of another node in the set (equivalently, the set contains no parent-child pair).

Given a node-valued tree and $K$, compute the maximum possible value of a $K$-anti-parental subset.

The first line contains the number of test cases $T$. Each test case is given as follows.

The first line of a test case contains two integers $N$ and $K$: the number of nodes and the parameter $K$, with $N \le 100000$ and $1 \le K \le 100$. Nodes are indexed from $0$ to $N-1$, and node $0$ is always the root.

The second line contains $N$ integers, the values of nodes $0$ through $N-1$ in order, each in the range $[-1000, 1000]$.

The third line contains $N-1$ integers: the parent index of each node from $1$ to $N-1$, in increasing order of index. The first of these integers is the parent of node $1$. The root (node $0$) has no parent entry. When $N = 1$ this line is empty.

For each test case, print a single line containing the maximum possible value of a $K$-anti-parental subset of that tree.