Tree

A binary tree is a very important fundamental data structure. Every node of a binary tree has at most two children, and the two children are ordered: the left child comes before the right child. Let $BT$ be a binary tree with $n$ nodes. The nodes of $BT$ are numbered from $1$ to $n$, each with a distinct number. A node that has no children is called a leaf node.

There are three ways to visit every node of a binary tree: preorder, inorder, and postorder traversal. For a node $v$, let $v.\text{left}$ denote its left child and $v.\text{right}$ its right child; if a child is absent, its value is empty ($\varnothing$). The three traversals are defined recursively as follows.

• Preorder: visit the current node first, then traverse the left subtree, then the right subtree.
• Inorder: traverse the left subtree, then visit the current node, then traverse the right subtree.
• Postorder: traverse the left subtree, then the right subtree, and finally visit the current node.

You are given the preorder and inorder traversals of some binary tree $BT$. From these two traversals the original binary tree can be reconstructed uniquely. Write a program that outputs the postorder traversal of the same tree.

The first line contains the number of test cases $T$. For each test case, the first line contains the number of nodes $n$ ($1 \le n \le 1{,}000$). The nodes of the binary tree are numbered from $1$ to $n$, each distinct. The next line contains the preorder traversal, and the line after that contains the inorder traversal, with the numbers separated by spaces. Every input is guaranteed to be a case in which the two traversals determine a unique binary tree.

For each test case, print the postorder traversal of the tree on one line, with the node numbers separated by spaces.