Given two binary trees and imagine that when you put one of them to cover the other, some nodes of the two trees are overlapped while the others are not. Write a program to merge them into a new binary tree.

Problem Note

  • The merge rule is that if two nodes overlap, then sum node values up as the new value of the merged node. Otherwise, the NOT null node will be used as the node of the new tree.
  • The merging process must start from the root nodes of both trees.

Example

Input: 
	Tree 1                     Tree 2                  
          1                         2                             
         / \                       / \                            
        3   2                     1   3                        
       /                           \   \                      
      5                             4   7                  
Output: Merged tree
	     3
	    / \
	   4   5
	  / \   \ 
	 5   4   7