For a given binary tree, convert it to its sum tree. That is, replace every node data with sum of its immediate children, keeping leaf nodes 0. Finally, return its preorder.

For example:

The input for the tree depicted in the below image would be :

1
2 3
4 -1 5 6
-1 7 -1 -1 -1 -1
-1 -1

Explanation :

Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.
The input ends when all nodes at the last level are null (-1).

Note :

The above format was just to provide clarity on how the input is formed for a given tree. 
 In the input, each value of the sequence will be present on a separate line.

Input format :

Elements are in the level order form. The input consists of values of nodes, each value is present on a separate line. In case a node is null, we take -1 in its place.

Output format :

Print the updated preorder form of the binary tree.

Note:

You are required to return the preorder form of the given tree and hence not required to print anything explicitly.

Constraints:

0 <= Number of nodes <= 10 ^ 7
0 <= Value of node <= 10 ^ 8