Monocarp wants to hang a garland on the Christmas tree.

The Christmas tree is a tree with $$$n$$$ vertices rooted at vertex $$$1$$$. The distance between two vertices of the tree is the number of edges on the shortest path between them, and the depth of a vertex is the distance from it to the root.

The garland consists of $$$n$$$ bulbs connected by wire and numbered from $$$1$$$ to $$$n$$$. The length of the wire between every two adjacent bulbs is $$$k$$$.

The garland must be hung on the tree according to the following rules:

every bulb must be placed on one of the vertices of the tree, and every vertex must have exactly one bulb on it;
bulb $$$1$$$ must be placed on the root of the tree;
each subsequent bulb has to be placed on such a vertex that its parent vertex has a bulb on it. If there are multiple such vertices, the vertex with the largest depth is chosen. If there are still multiple options, any of them can be chosen;
for each pair of subsequent bulbs, the distance between the vertices they are placed on must not exceed $$$k$$$.

Your task is to count the number of ways to hang the garland while following all the rules and output it modulo $$$998244353$$$. Two ways are considered different if there exists at least one integer $$$i \in [1, n]$$$ such that the $$$i$$$-th bulb is placed on different vertices in these two ways.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 3 \cdot 10^5$$$; $$$1 \le k \lt n$$$) — the number of vertices in the tree and the distance constraint between two consecutive bulbs.

The second line contains $$$n-1$$$ integers $$$p_2, p_3, \dots, p_n$$$ ($$$1 \le p_i \lt i$$$), where $$$p_i$$$ is the parent of the $$$i$$$-th vertex in the tree.

Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.

Output

For each test case, output one integer — the number of ways to hang the garland while following all the rules, modulo $$$998244353$$$.

Short Garland

Examples