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.</p>

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 

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 형식

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

예제 입력

EDBACFGIHKJ ABCDEFGHIJK
#

예제 출력

ACBDHJKIGFE