Remove Path: Delete All Nodes Along a Path in a Tree

Question

## Problem

Given a binary tree and a root-to-leaf path specified as a list of node values, remove all nodes on that path from the tree. If removing a node would leave its parent with no children and that parent is not on another path, remove it too (cascading deletion upward stops when a node has a surviving child).

Return the root of the modified tree.

```python
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def remove_path(root: TreeNode, path: list) -> TreeNode:
    pass
```

**Example:**
```
Tree:       1
           / \
          2   3
         / \
        4   5

path = [1, 2, 4]
After removal:
           1
          / \
         2   3
          \
           5
# Node 4 removed; node 2 kept because it still has child 5.
```

## Follow-ups

1. What if the path does not reach a leaf — should removal still happen?
2. How do you handle a path that doesn't exist in the tree?
3. What if you need to remove multiple paths simultaneously — does order of removal matter?
4. How does this problem change for an N-ary tree instead of a binary tree?

Remove Path: Delete All Nodes Along a Path in a Tree

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