How to get activity status that occurred within a interval during start and stop datetime, Sql Server

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create table [events](
  [EventName] varchar(100),
  [OccuredAtDatetime] datetime
);
insert into [events]
select 'EventA', '2019-07-03 00:14:01' union all
select 'EventA', '2019-07-03 01:14:01' union all
select 'EventA', '2019-07-03 01:34:01' union all
select 'EventB', '2019-07-03 01:13:03';

create table [interval](
  [IntervalName] varchar(100),
  [StartTime] datetime,
  [EndTime] datetime
);

insert into [interval]
select 'Interval1', '2019-07-03 00:00:00', '2019-07-03 00:30:00' union all
select 'Interval2', '2019-07-03 00:30:00', '2019-07-03 01:00:00' union all
select 'Interval3', '2019-07-03 01:00:00', '2019-07-03 01:30:00' union all
select 'Interval4', '2019-07-03 01:30:00', '2019-07-03 02:00:00';

declare @sql as varchar(max);
select @sql = 'select [t1].[EventName], ' + stuff((
		select ', max(case when [IntervalName] = ' + char(39) + [IntervalName] + char(39)
		+ ' and [t1].OccuredAtDatetime between [t2].[StartTime] and [t2].[EndTime] then '
		+ char(39) + 'Yes' + char(39) + ' else ' + char(39) + 'No' + char(39) 
		+ ' end) as [' + [IntervalName] + ']'
		from [dbo].[interval]
		for xml path('')
	),
	1, 1, ''
)
+ ' from [dbo].[events] as [t1], [dbo].[interval] as [t2]'
+ ' group by [t1].[EventName];';

exec(@sql);

View schema
Execution time: 0,03 sec, rows selected: 3, rows affected: 8, absolute service time: 0,19 sec, absolute service time: 0,19 sec

How to get activity status that occurred within a interval during star...