Design a Banking Component with Transfers and Activity Rankings

Problem Statement

Design an in-memory banking engine that handles account lifecycle management, deposits, atomic peer-to-peer transfers, and activity rankings. You will implement a class BankSystem along with a command parser process_transactions(commands: list[str]) -> list[str] to execute queries sequentially.

Commands to Support

1. CREATE

   • Creates a new account with a balance of 0 and cumulative outgoing transfer volume of 0.
   • Returns "true" if successful, or "false" if account_id already exists.

2. DEPOSIT

   • Deposits positive integer amount into account_id.
   • Returns the updated balance as a string if successful.
   • Returns "" (empty string) if the account does not exist or amount
   • Transfers amount from source_id to target_id.
   • Must satisfy invariants: source_id and target_id both exist, source_id != target_id, amount > 0, and source_id has a balance >= amount.
   • If valid, deduct amount from source_id, add amount to target_id, and increment source_id's total outgoing transfer volume by amount.
   • Returns "true" if successful, or "false" if any validation fails (no state changes on failure).

3. TOP_ACTIVITY

   • Returns the top k account IDs ranked by cumulative outgoing transfer volume in descending order.
   • In case of a tie in volume, sort lexicographically (alphabetical order) by account_id ascending.
   • If fewer than k accounts exist, return all accounts in ranked order.
   • Format output as a comma-separated list of IDs, e.g. "ACC1,ACC2". If no accounts exist or `k list[str]: """ Executes a sequence of string commands and returns the result of each command. """ pass

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## Example

### Input
```python
commands = [
    "CREATE A",
    "CREATE B",
    "CREATE C",
    "DEPOSIT A 100",
    "DEPOSIT B 50",
    "TRANSFER A B 30",
    "TRANSFER B C 20",
    "TRANSFER A C 10",
    "TOP_ACTIVITY 2",
    "TRANSFER C A 100",  # C only has 30, should fail
    "TOP_ACTIVITY 3"
]

Output

[
    "true",
    "true",
    "true",
    "100",
    "50",
    "true",
    "true",
    "true",
    "A,B",
    "false",
    "A,B,C"
]

Explanation

• After transfers: A has transferred 30 + 10 = 40, B has transferred 20, and C has transferred 0.
• TOP_ACTIVITY 2 returns "A,B".
• TRANSFER C A 100 fails because C has a balance of 30 (from TRANSFER B C 20 and TRANSFER A C 10), so balance is insufficient.
• TOP_ACTIVITY 3 returns "A,B,C".

Constraints

• 1 <= len(commands) <= 20,000
• Account IDs consist of alphanumeric characters ([a-zA-Z0-9]), length 1 <= len(account_id) <= 32.
• 1 <= amount <= 1,000,000,000
• 1 <= k <= 1,000
• Balances and transfer amounts fit within standard 64-bit signed integers.

Edge Cases

• Attempting to transfer to oneself (source_id == target_id).
• Insufficient funds or zero/negative transaction amounts.
• Operations on non-existent accounts.
• k larger than the total number of created accounts.