# hdu 4757 Tree

### Problem Description

Zero and One are good friends who always have fun with each other. This time, they decide to do something on a tree which is a kind of graph that there is only one path from node to node. First, Zero will give One an tree and every node in this tree has a value. Then, Zero will ask One a series of queries. Each query contains three parameters: x, y, z which mean that he want to know the maximum value produced by z xor each value on the path from node x to node y (include node x, node y). Unfortunately, One has no idea in this question. So he need you to solve it.

### Input

There are several test cases and the cases end with EOF. For each case:

The first line contains two integers n(1<=n<=10^5) and m(1<=m<=10^5), which are the amount of tree’s nodes and queries, respectively.

The second line contains n integers a[1..n] and ai is the value on the ith node.

The next n–1 lines contains two integers u v, which means there is an connection between u and v.

The next m lines contains three integers x y z, which are the parameters of Zero’s query.

### Output

For each query, output the answer.

3 2
1 2 2
1 2
2 3
1 3 1
2 3 2

3
0

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