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def inorder_traversal_iterating(root):
    result = []
    # using stack
    stack = []
    current = root
    while stack or current:
        if current:
            # traverse the left subtree
            stack.append(current)
            current = current.left

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# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None

# recursive version
def inorder_traversal_recursive(root):
    result = []

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def find_right_border(arr, target):
    left = 0
    right = len(arr) - 1

    right_border = -1       # keep track of the latest larger number
    while left <= right:
        mid = left + (right - left) // 2
        if arr[mid] <= target:
            left = mid + 1
        else:

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def find_left_border(arr, target):
    left = 0
    right = len(arr) - 1

    left_border = -1        # keep track of the latest smaller number
    while left <= right:
        mid = left + (right - left) // 2
        if arr[mid] < target:
            left_border = mid
            left = mid + 1

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def find_last_pos(arr, target):
    left = 0
    right = len(arr) - 1

    last_position = -1      # keep track of the latest valid mid position
    while left <= right:
        mid = left + (right - left) // 2
        if arr[mid] == target:
            last_position = mid
            left = mid + 1      # continue searching to the right

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def find_first_pos(arr, target):
    left = 0
    right = len(arr) - 1

    first_position = -1     # keep track of the latest valid mid position
    while left <= right:
        mid = left + (right - left) // 2
        if arr[mid] == target:
            first_position = mid
            right = mid - 1     # continue searching to the left

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def binary_search(arr, target):
    left = 0
    right = len(arr) - 1

    while left <= right:
        mid = left + (right - left) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1

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from collections import defaultdict

def longest_unique_substring(s):
    longest_length = float('-inf')
    n = len(s)

    # empty string has the longest length is 0
    if n == 0:
        return 0

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def longest_unique_substring(s):
    # function to check if the characters in the substring are all unique or not
    def is_all_unique(start_index, end_index):
        character_set = set()
        for z in range(start_index, end_index):
            if s[z] in character_set:
                return False
            character_set.add(s[z])
        return True

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def highestSum(arr, k):
    highest_sum = float('-inf')
    n = len(arr)

    # n must be not smaller than k
    if n < k:
        return -1

    left = 0
    right = 0