Problem Description
Byteasar has a tree T with n vertices conveniently labeled with 1,2,...,n. Each vertex of the tree has an integer value vi.
The value of a non-empty tree T is equal to v1⊕v2⊕...⊕vn, where ⊕ denotes bitwise-xor.
Now for every integer k from [0,m), please calculate the number of non-empty subtree of T which value are equal to k.
A subtree of T is a subgraph of T that is also a tree.
Input
The first line of the input contains an integer T(1≤T≤10), denoting the number of test cases.
In each test case, the first line of the input contains two integers n(n≤1000) and m(1≤m≤210), denoting the size of the tree T and the upper-bound of v.
The second line of the input contains n integers v1,v2,v3,...,vn(0≤vi<m), denoting the value of each node.
Each of the following n−1 lines contains two integers ai,bi, denoting an edge between vertices ai and bi(1≤ai,bi≤n).
It is guaranteed that m can be represent as 2k, where k is a non-negative integer.
Output
For each test case, print a line with m integers, the i-th number denotes the number of non-empty subtree of T which value are equal to i.
The answer is huge, so please module 109+7.
Sample Input
2
4 4
2 0 1 3
1 2
1 3
1 4
4 4
0 1 3 1
1 2
1 3
1 4
Sample Output
3 3 2 3
2 4 2 3