# Reconstruction Trees

## 문제

It is very easy to produce the various traversals of a binary tree, however this problem requires you to produce the tree from the traversals. Specifically, given the pre-order and in-order traversals of a binary tree (not necessarily a binary search tree), reconstruct, if possible, the original tree.

For instance, the following tree will produce the traversals shown

          E
         / \
        D   F
       / \
      B   G
     / \   \
    A   C   I
           / \
          H   K
             /
            J

    Preorder : EDBACFGIHKJ
    Inorder : ABCDEFGHIJK

    Postorder: ACBDHJKIGFE

## 입력

Input will consist of representations of several trees, each on a single line, and terminated by a #. Each line will consist of two strings of up to 26 unique uppercase letters in the form

<pre-order> <space> <in-order>.

You can assume that the two strings will be permutations of each other.

## 출력

Output will consist of the post-order traversal of the reconstructed tree if possible, otherwise the words 'Invalid tree'.

## 예제 입력 1 복사

    EDBACFGIHKJ ABCDEFGHIJK
    #

## 예제 출력 1 복사

    ACBDHJKIGFE