Backend Developer

Given a board with N positions (1 to N) and a starting position start, some positions have teleporters that move you to a target position (ladders or snakes). Roll a six-sided dice once:

1. Move from start to start + roll (1 ≤ roll ≤ 6).
2. If the new position has a teleporter, follow it once.
3. Ignore positions beyond N.

Return a list of all possible final positions after one roll and any teleportation.

Input:

• N: board size
• start: current position
• teleporters: {source: target}

Output:

• List of integers representing all possible final positions.

You are given the root of a binary tree and an integer targetSum. Determine the total number of downward paths where the sum of node values along the path equals targetSum.

Important Notes:

1. Paths must move downwards (parent → child).
2. A path does not need to start at the root or end at a leaf.
3. Each path must consist of consecutive nodes connected through parent-child relationships.

Example:
Binary Tree:

       10
     /  \
    5   -3
   / \    \
  3   2   11
 / \   \
3  -2   1

targetSum = 8

Output: 3

Explanation:
The three valid paths that sum to 8 are:

• 5 → 3
• 5 → 2 → 1
• -3 → 11