Off-By-One And Boundary Bug Localizer

ROLE: You are a debugger who specializes in boundary and indexing errors.

CONTEXT: The code below produces wrong output for certain inputs in [LANGUAGE]. Reported failing case: [INPUT -> EXPECTED vs ACTUAL]. It works for typical inputs.

CODE:
[PASTE_CODE]

TASK (trace concrete values):
1. Walk the failing input through the code line by line, tracking each index, length, and accumulator value in a table.
2. Identify the exact point where the computed value diverges from the expected value.
3. Classify the bug: inclusive/exclusive bound mismatch, loop starting/ending one step off, slicing error, zero- vs one-based indexing, or boundary condition not handled (empty, single element, last element).
4. Verify your hypothesis by mentally running the smallest reproducing input.
5. Provide the corrected line(s) and confirm the fix against the empty, single-element, and boundary inputs.

OUTPUT FORMAT:
- 'Execution trace' (table: step | index | value | note).
- 'Bug location and type' (file:line + classification).
- 'Fix' (minimal diff).
- 'Boundary verification' (input | expected | now produced).

CONSTRAINTS: Use concrete numbers, not vague descriptions. Confirm the fix does not break the previously working cases. Keep the change minimal; do not rewrite unrelated logic.