Problem Statement

Given two Binary Trees A and B, you need to merge them in a single binary tree.

The merge rule is that if two nodes overlap, then sum of node values is the new value of the merged node.

Otherwise, the non-null node will be used as the node of new tree.

Problem Constraints

1 <= Number of Nodes in A , B <= 105

Input Format

First argument is an pointer to the root of binary tree A.

Second argument is an pointer to the root of binary tree B.

Output Format

Return a pointer to the root of new binary tree.

Example Input

Input 1:

 A =   2

      / \\

     1   4

    /

   5B =   3
      / \\
      6  1
      \\   \\
       2   7

Input 2:

 A =   12

      / \\

     11  14B =   3
      / \\
      6  1

Example Output

Output 1:

     5
    / \\
   7   5
  / \\   \\
 5   2   7

Output 2: