Function result of pushing nodes elements into tree tree where parent is index and parent distance is distance
tree
Format:
result of pushing nodes elements into tree tree where parent is index and parent distance is distance
Input:
list tree - 
    
    number index - 
    
    number distance - 
    
    list elements - 
    
    Output:
list - None
    Properties that reference this function:
result of pushing nodes [  ] into tree tree where parent is index and parent distance is distance = tree   (push children nodes finished)
    
    Conditional properties that reference this function:
- if the following are true: - ((length of stack tree) - 1) - index = back_i
- the element at index back_i of stack tree = node (value, distance, previous)
- result of splitting pairs into nodes that exist in the tree tree and new nodes = pair (exists, new)
- result of updating nodes exists in tree tree with parent index index and parent distance distance = updated
 - then result of adding or updating children pairs of the node at backwards index index in tree tree = result of pushing nodes new into tree updated where parent is index and parent distance is distance (link)
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