Velma and Queries
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## Algorithms, Binary search algorithm, Depth-first search, Easy-Medium, Searching algorithm

Problem
Editorial
Analytics

The "Mystery Incorporated" once went for an investigation. Since Scooby and Shaggy always create havoc during investigation, Velma decided to give them a question so as to keep them busy.
Velma gave them a tree consisting of N nodes, rooted at node 1 with a number in each node, and asked them several queries. Each query was of the form u l and they had to find the sum of values of all nodes situated at a depth l and were in the subtree of u.
Since Scooby and Shaggy are dumb, they need your help in solving this problem.

### Input

The first line will contain the number of test cases T.
The first line of each test case will contain two integers N and Q (1 ≤ N, Q ≤ 100,000) - the number of nodes and the number of queries.
The second line of each test case will contain N integers a1, a2, ..., aN, where ai (1 ≤ ai ≤ 10,00,000) is the value stored at the ith node.
The next N-1 lines of each test case will contain two integers u and v, meaning that there is an edge connecting u and v.
The next Q lines contains the queries each of the form u and l.

### Output

For each query in every test case, print the answer to the query on a single line.

### Constraints

• $1 \leq T \leq 5, 1 \leq N, Q \leq 1000, \ 1 \leq a_i \leq 10^6$ in 35% of test cases.
• $1 \leq T \leq 10, 1 \leq N, Q \leq 10^5, \ 1 \leq a_i \leq 10^6$ in 65% of test cases.
SAMPLE INPUT
1
6 5
1 2 3 4 5 6
1 2
2 3
2 6
1 4
4 5
1 1
1 3
2 1
5 3
2 3
SAMPLE OUTPUT
1
14
0
5
9
Explanation

The tree in the test case looks like this.

The depths of nodes are:

• Nodes at depth 1: 1
• Nodes at depth 2: 2, 4
• Nodes at depth 3: 3, 5 and 6

For the 2nd query , there are 3 nodes (3, 5, 6) at level 3 which are also in subtree of 1. So the answer would be 3+5+6 = 14.
For the 3rd query, there is only 1 node (1) which is at level 1, but it is not in the subtree of 2. So the answer would be 0.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

## This Problem was Asked in

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