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.