Driver:
insert the value into the tree;

BTree:
insert the value from root(find the right place to put the value from root to leaf);
if the root splits
	create a new parent for the splitted old root;

InternalNode:
find the correct child for this value;
insert this value to that child
{
	if child is not full and hence, succesfully inserted
		return NULL;
	else child splitted(update internal node)
	{
		if internal node is not full
			insert the new child;
		else
			if left sibling is not full
				lookLeft(update parent if needed)
			else if right sibling is not full
				lookRight(update parent if needed)
			else
			{
				split
				maintain left right sibling, and parent-child relation
				return the new node after split
			}
	}
}

LeafNode:
if Leaf is not full
	put the value to the right slot;
	//NOTE: if it is the first child of parent, keys[0] of its parent need to be updated
else
{
	if left sibling is not full
		lookLeft(update parent if needed)
	else if right sibling is not full
		lookRight(update parent if needed)
	else
	{
		split;
		maintain left right sibling, and parent-child relation;
		return the new Leaf after split so their parent could update itself;
	}
}