Split date ranges into details by months using pandas or numpy

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I have a list of events (A, B, C) in a dataframe and two dates for each event and I need to split those dates within their respective months.

Example:

data = {'Name': ['A', 'B', 'C'], 'Start_time': ['2017-12-15', '2017-12-15', '2017-12-15'], 'End_time': ['2018-01-17', '2017-12-22', '2018-05-22']}
df = pd.DataFrame(data)
Events Start_date End_date
A 2017-12-15 2018-01-17
B 2017-12-15 2017-12-22
C 2017-12-15 2018-05-22

Expected results:

Events Start_date End_date
A 2017-12-15 2017-12-31
A 2018-01-01 2018-01-17
B 2017-12-15 2017-12-22
C 2017-12-15 2017-12-31
C 2018-01-01 2018-01-31
C 2018-02-01 2018-02-28
C 2018-03-01 2018-03-31
C 2018-04-01 2018-04-30
C 2018-05-01 2018-05-22
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