Given the postorder and inorder traversals of a binary tree, construct and return the binary tree.

Example

Testing

Input Format

The first line contains an integer T denoting the number of test cases.

For each test case, the input has 3 lines:

• The first line contains an integer n denoting the length of the arrays.
• The second line contains n space-separated integers denoting the postorder traversal of the binary tree.
• The third line contains n space-separated integers denoting the inorder traversal of the binary tree.

Output Format

For each test case, the output has a line containing the level order traversal of the tree.

Sample Input

5
8
4 7 5 2 8 6 3 1
4 2 7 5 1 8 6 3
5
5 6 4 2 1
5 4 6 2 1
5
11 12 10 9 8
8 9 11 10 12
4
48 14 11 28
14 48 28 11
1
6
6

Expected Output

1 2 3 4 5 6 7 8
1 2 4 5 6
8 9 10 11 12
28 14 11 48
6

Constraints

1 <= T <= 10
1 <= n <= 104
1 <= node value <= 104