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문제 Consider a rooted tree, each of whose nodes is associated with an integer representing the node’s value. Naturally, the value of a subset of nodes of such a tree is regarded as the sum of the values of all the nodes contained in the subset. Given a positive integer K, let’s define the K-anti-parental subset to be a subset of nodes satisfying the following constraints: (1) the number of nodes in the subset is between 1 and K, inclusive, and (2) for any pair of nodes in the subset, one is not a parent of the other, and vice versa. Now, your task is to find the maximum of the values of the K-anti-parental subsets of an arbitrary node-valued tree.

입력

Your program is to read from standard input. The input consists of T test cases, where the positive integer T is given in the first line of the input, followed by the description of each test case. The first line of a test case contains two positive integers N and K, respectively indicating the number of nodes of the tree and the parameter K as explained above, in which we assume N ≤ 100,000 and 1 ≤ K ≤ 100. The tree’s nodes are indexed 0 to N-1, where the index 0 is always assigned to the root node. The following line contains N integers, separated by spaces, coming from the inclusive interval [-1,000, 1,000], which represent the values of the nodes enumerated in the increasing order of indices from 0 to N-1. The next following line contains N-1 integers, separated by spaces, each of which indicates the index of a corresponding node’s parent. Make sure that these numbers are for the N-1 nodes except the root, listed in the increasing order of indices from 1 (not 0) to N-1. Therefore, the first integer points to the parent of the node indexed 1. Note that the parent of the root node needs not be specified.

출력

Your program is to write to standard output. Print exactly one line per each test case. The line should contain the maximum possible value of the K-anti-parental subsets of the input tree.

예제 입력 1

3
7 3
6 2 -5 5 -3 4 1
0 0 2 2 0 5
3 2
4 -3 5
0 0
7 6
-1 -1 -1 -1 -1 -1 -1
0 1 2 3 4 5

12
5
-1