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.