Problem Description
Claris loves painting very much, so he painted a tree with beautiful colors.
The tree is a rooted tree with n nodes which are conveniently labeled by 1,2,...,n. Its root is the 1-st node, and the i-th node is painted with color ci. If ci=cj, then we think these two nodes have the same color.
We define depthi as the distance between the i-th node and the root, and simply, the distance between two adjacent nodes is always 1.
Standing in front of this beautiful tree, Claris comes up with m questions.
In each question, there are two integers x and d, which means that Claris wants to know the number of different kinds of colors occur in S, where S={v|v in x′s subtree and depthv≤depthx+d}.
Input
The first line of the input contains an integer T(1≤T≤500), denoting the number of test cases.
In every test case, there are two integers n(1≤n≤100000) and m(1≤m≤100000) in the first line, denoting the number of nodes and queries.
The second line contains n integers, the i-th integer ci(1≤ci≤n) denotes the color of the i-th node.
The third line contains n−1 integers, the i-th integer fi+1(1≤fi<i) denotes the father of the i+1-th node.
In the following m lines, each line contains two integers x(1≤x≤n) and d(0≤d<n), denoting each query.
The input has been encoded, if you read x and d, the real x and d are x⊕last and d⊕last, where last is the answer of the previous query and ⊕ means bitwise exclusive-or.
Notice :
If it is the first query in this test case, then last=0.
It is guaranteed that ∑n≤500000 and ∑m≤500000.
Output
For each query output a single integer in a line, denoting the answer.
Sample Input
1
5 8
1 3 3 2 2
1 1 3 3
1 0
0 0
3 0
1 3
2 1
2 0
6 2
4 1
Sample Output
1
2
3
1
1
2
1
1
