## Graph Theory 6

You are given a directed acyclic graph of \(N + 1\) nodes numbered from \(0\) to \(N\) and you need to perform \(Q\) queries on it. Node \(0\) has a value of \(0\), and every other node has a value of \(v_i\). Every node only has 1 child. Find the sum of values of a node and all of its children.

#### Input Specification

The first line will contain the integer \(N, Q\ (1 \le N, Q \le 10^5)\), the number of nodes and the number of queries.

The next \(N\) lines describes which nodes are connected. The \(K^{th}\) line contains the integers \(v_i, i\ (1 \le v_i \le 10^5),\ (0 \le i \le N)\), where \(i\) is the \(K^{th}\) node's child.

The next \(Q\) lines contains an integer \(j\ (1 \le j \le N)\), the node to query.

#### Output Specification

For every query, print the sum of values of the node and all of its children.

#### Sample Input

```
5 5
1 0
2 0
4 1
8 2
16 3
1
2
3
4
5
```

#### Sample Output

```
1
2
5
10
21
```

#### Subtasks

##### Subtask 1 [30%]

\((1 \le N, Q \le 10^3)\)

##### Subtask 2 [70%]

No further constraints.

## Comments