Parse this person name:

Luc Bègue (1309-1361, flourished 1324-1335)
user
first_name: Luc
last_name: Bègue
middle_names: []
temporal:
- start: 1309
  end: 1361
  type: life_span
- start: 1324
  end: 1335
  type: flourished
titles: []
extra_info: []
assistant