Merge two N-ary trees by key rules

You are given two **N-ary trees** `A` and `B`. Each node has: - `key` (string): unique among siblings (i.e., within a node’s children list, no two children share the same key) - `value` (any scalar, e.g., string/int) - `children` (list of nodes) You must produce a merged tree `M = merge(A, B)` using these rules: ## Merge rules 1. **If a node exists in both trees at the same position (matched by `key`)**: - The merged node’s `key` stays the same. - The merged node’s `value` is **taken from tree `B`** (i.e., `B` overwrites `A`). - The merged node’s `children` are formed by merging children lists by key, recursively. 2. **If a child key exists only in one tree**: - Include that subtree unchanged in the output. Assume the two input roots have the **same key**. ## Task Implement a function to merge the two trees and return the merged root. ## Constraints - Total nodes across both trees: up to `2 * 10^5` - Keys are non-empty strings ## Clarifications - Sibling order in the output does not matter unless you choose to preserve a stable order.