Level Sum of Binary Tree

You are given a binary tree represented by its level-order traversal. Your task is to compute the sum of the nodes at each level of the tree. More formally, if the nodes at level ( i ) are denoted by ( n_1, n_2, \dots, n_k ), then the level sum ( S_i ) is given by

[ S_i = \sum_{j=1}^{k} n_j ]

Note that the binary tree may contain negative values and may be empty. The input is given as a single line of space-separated tokens. The token null represents a missing node in the tree.

For example, the input

1 2 3 4 5 6 7

represents the following binary tree:

         1
       /   \
      2     3
     / \   / \
    4   5 6   7

and the level sums are: (1) for level 0, (2+3=5) for level 1, and (4+5+6+7=22) for level 2.

inputFormat

Input is provided via standard input (stdin) as a single line containing space-separated tokens representing the level-order traversal of the binary tree. Each token is either an integer or the string null indicating that a node is missing. For example:

1 2 3 4 5 6 7

If the tree is empty, the input will be a single token null.

outputFormat

Output the level sums of the binary tree as a single line on standard output (stdout). The sums for each level should be printed in order and separated by a single space. If the tree is empty, output an empty line.## sample

null